LMFDB - Embedded newform 14.16.c.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,16,Mod(9,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 16, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.9770907140$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7979102 x^{8} - 3342530557 x^{7} + 48610066963550 x^{6} + \cdots + 51\!\cdots\!56 $ x^10 - x^9 + 7979102x^8 - 3342530557x^7 + 48610066963550x^6 - 20531463882664153x^5 + 122945882607722292337x^4 - 89586690298994071428648x^3 + 238785864099387585455090736x^2 - 108333121326673799746890760320x + 51761574501460447109413728819456
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{3}\cdot 5^{4}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.1
Root			$-1143.06 + 1979.84i$ of defining polynomial
Character	$\chi$	$=$	14.9
Dual form			14.16.c.b.11.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(64.0000 - 110.851i) q^{2} +(-3401.15 - 5890.97i) q^{3} +(-8192.00 - 14189.0i) q^{4} +(-55365.7 + 95896.2i) q^{5} -870695. q^{6} +(550858. + 2.10811e6i) q^{7} -2.09715e6 q^{8} +(-1.59612e7 + 2.76456e7i) q^{9} +O(q^{10})$	\(q+(64.0000 - 110.851i) q^{2} +(-3401.15 - 5890.97i) q^{3} +(-8192.00 - 14189.0i) q^{4} +(-55365.7 + 95896.2i) q^{5} -870695. q^{6} +(550858. + 2.10811e6i) q^{7} -2.09715e6 q^{8} +(-1.59612e7 + 2.76456e7i) q^{9} +(7.08681e6 + 1.22747e7i) q^{10} +(-2.69616e7 - 4.66989e7i) q^{11} +(-5.57245e7 + 9.65176e7i) q^{12} +2.39628e8 q^{13} +(2.68941e8 + 7.38556e7i) q^{14} +7.53228e8 q^{15} +(-1.34218e8 + 2.32472e8i) q^{16} +(-1.29246e9 - 2.23861e9i) q^{17} +(2.04303e9 + 3.53864e9i) q^{18} +(-2.01327e9 + 3.48709e9i) q^{19} +1.81422e9 q^{20} +(1.05452e10 - 1.04151e10i) q^{21} -6.90217e9 q^{22} +(-3.30987e9 + 5.73286e9i) q^{23} +(7.13273e9 + 1.23543e10i) q^{24} +(9.12807e9 + 1.58103e10i) q^{25} +(1.53362e10 - 2.65630e10i) q^{26} +1.19540e11 q^{27} +(2.53992e10 - 2.50857e10i) q^{28} +5.84976e9 q^{29} +(4.82066e10 - 8.34963e10i) q^{30} +(1.50673e11 + 2.60973e11i) q^{31} +(1.71799e10 + 2.97564e10i) q^{32} +(-1.83401e11 + 3.17660e11i) q^{33} -3.30870e11 q^{34} +(-2.32658e11 - 6.38917e10i) q^{35} +5.23017e11 q^{36} +(7.37480e10 - 1.27735e11i) q^{37} +(2.57699e11 + 4.46348e11i) q^{38} +(-8.15011e11 - 1.41164e12i) q^{39} +(1.16110e11 - 2.01109e11i) q^{40} +7.07723e11 q^{41} +(-4.79629e11 - 1.83552e12i) q^{42} -1.37858e12 q^{43} +(-4.41739e11 + 7.65115e11i) q^{44} +(-1.76741e12 - 3.06124e12i) q^{45} +(4.23663e11 + 7.33806e11i) q^{46} +(-1.97502e12 + 3.42084e12i) q^{47} +1.82598e12 q^{48} +(-4.14067e12 + 2.32254e12i) q^{49} +2.33679e12 q^{50} +(-8.79171e12 + 1.52277e13i) q^{51} +(-1.96303e12 - 3.40007e12i) q^{52} +(-3.72252e12 - 6.44759e12i) q^{53} +(7.65058e12 - 1.32512e13i) q^{54} +5.97100e12 q^{55} +(-1.15523e12 - 4.42102e12i) q^{56} +2.73898e13 q^{57} +(3.74384e11 - 6.48453e11i) q^{58} +(1.81514e13 + 3.14391e13i) q^{59} +(-6.17045e12 - 1.06875e13i) q^{60} +(1.22609e13 - 2.12365e13i) q^{61} +3.85723e13 q^{62} +(-6.70723e13 - 1.84191e13i) q^{63} +4.39805e12 q^{64} +(-1.32672e13 + 2.29794e13i) q^{65} +(2.34753e13 + 4.06605e13i) q^{66} +(-6.14489e12 - 1.06433e13i) q^{67} +(-2.11757e13 + 3.66773e13i) q^{68} +4.50295e13 q^{69} +(-2.19726e13 + 2.17014e13i) q^{70} -3.63576e13 q^{71} +(3.34731e13 - 5.79771e13i) q^{72} +(4.65083e13 + 8.05548e13i) q^{73} +(-9.43974e12 - 1.63501e13i) q^{74} +(6.20919e13 - 1.07546e14i) q^{75} +6.59710e13 q^{76} +(8.35943e13 - 8.25624e13i) q^{77} -2.08643e14 q^{78} +(-1.41191e14 + 2.44549e14i) q^{79} +(-1.48621e13 - 2.57419e13i) q^{80} +(-1.77549e14 - 3.07523e14i) q^{81} +(4.52943e13 - 7.84520e13i) q^{82} -2.65136e14 q^{83} +(-2.34166e14 - 6.43057e13i) q^{84} +2.86232e14 q^{85} +(-8.82289e13 + 1.52817e14i) q^{86} +(-1.98959e13 - 3.44607e13i) q^{87} +(5.65426e13 + 9.79347e13i) q^{88} +(-2.36137e14 + 4.09001e14i) q^{89} -4.52456e14 q^{90} +(1.32001e14 + 5.05161e14i) q^{91} +1.08458e14 q^{92} +(1.02492e15 - 1.77522e15i) q^{93} +(2.52803e14 + 4.37867e14i) q^{94} +(-2.22933e14 - 3.86131e14i) q^{95} +(1.16863e14 - 2.02412e14i) q^{96} -4.86827e14 q^{97} +(-7.54711e12 + 6.07641e14i) q^{98} +1.72136e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9}+O(q^{10}) $ 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9	\( 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9} - 1404032 q^{10} - 3405409 q^{11} + 39239680 q^{12} + 369408276 q^{13} + 411547520 q^{14} + 453669790 q^{15} - 1342177280 q^{16} - 3201713287 q^{17} + 5824692992 q^{18} - 1063446451 q^{19} - 359432192 q^{20} + 21058786691 q^{21} - 871784704 q^{22} - 31680429991 q^{23} - 5022679040 q^{24} + 39012502244 q^{25} + 23642129664 q^{26} + 66427564750 q^{27} + 13761560576 q^{28} + 294935242276 q^{29} + 29034866560 q^{30} + 30201804075 q^{31} + 171798691840 q^{32} - 482562276049 q^{33} - 819638601472 q^{34} - 1540311474205 q^{35} + 1491121405952 q^{36} + 1369689837461 q^{37} + 136121145728 q^{38} - 1048775641458 q^{39} - 23003660288 q^{40} + 3634838274156 q^{41} - 871978643968 q^{42} + 415602663752 q^{43} - 55794221056 q^{44} - 7616412162898 q^{45} + 4055095038848 q^{46} - 12606978599835 q^{47} - 1285805834240 q^{48} - 8067928630838 q^{49} + 9987200574464 q^{50} + 6857137867217 q^{51} - 3026192596992 q^{52} + 10616682242361 q^{53} + 4251364144000 q^{54} - 40851384759514 q^{55} - 4981314813952 q^{56} + 44665526899814 q^{57} + 18875855505664 q^{58} + 39993786962755 q^{59} - 3716462919680 q^{60} + 5148862074165 q^{61} + 7731661843200 q^{62} - 97668254816810 q^{63} + 43980465111040 q^{64} + 91302240851010 q^{65} + 61767971334272 q^{66} - 29267240444285 q^{67} - 52456870494208 q^{68} - 279695242712578 q^{69} + 18327124839296 q^{70} - 37767657205600 q^{71} + 95431769980928 q^{72} + 243869659370917 q^{73} - 175320299195008 q^{74} + 295809815641460 q^{75} + 34847013306368 q^{76} + 35960055270559 q^{77} - 268486564213248 q^{78} + 137356615917609 q^{79} + 2944468516864 q^{80} - 352056899083285 q^{81} + 232629649545984 q^{82} - 914604166510648 q^{83} - 456640427573248 q^{84} + 264981492485402 q^{85} + 26598570480128 q^{86} + 13\!\cdots\!90 q^{87}+ \cdots + 39\!\cdots\!96 q^{99}+O(q^{100}) \) 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9 - 1404032 * q^10 - 3405409 * q^11 + 39239680 * q^12 + 369408276 * q^13 + 411547520 * q^14 + 453669790 * q^15 - 1342177280 * q^16 - 3201713287 * q^17 + 5824692992 * q^18 - 1063446451 * q^19 - 359432192 * q^20 + 21058786691 * q^21 - 871784704 * q^22 - 31680429991 * q^23 - 5022679040 * q^24 + 39012502244 * q^25 + 23642129664 * q^26 + 66427564750 * q^27 + 13761560576 * q^28 + 294935242276 * q^29 + 29034866560 * q^30 + 30201804075 * q^31 + 171798691840 * q^32 - 482562276049 * q^33 - 819638601472 * q^34 - 1540311474205 * q^35 + 1491121405952 * q^36 + 1369689837461 * q^37 + 136121145728 * q^38 - 1048775641458 * q^39 - 23003660288 * q^40 + 3634838274156 * q^41 - 871978643968 * q^42 + 415602663752 * q^43 - 55794221056 * q^44 - 7616412162898 * q^45 + 4055095038848 * q^46 - 12606978599835 * q^47 - 1285805834240 * q^48 - 8067928630838 * q^49 + 9987200574464 * q^50 + 6857137867217 * q^51 - 3026192596992 * q^52 + 10616682242361 * q^53 + 4251364144000 * q^54 - 40851384759514 * q^55 - 4981314813952 * q^56 + 44665526899814 * q^57 + 18875855505664 * q^58 + 39993786962755 * q^59 - 3716462919680 * q^60 + 5148862074165 * q^61 + 7731661843200 * q^62 - 97668254816810 * q^63 + 43980465111040 * q^64 + 91302240851010 * q^65 + 61767971334272 * q^66 - 29267240444285 * q^67 - 52456870494208 * q^68 - 279695242712578 * q^69 + 18327124839296 * q^70 - 37767657205600 * q^71 + 95431769980928 * q^72 + 243869659370917 * q^73 - 175320299195008 * q^74 + 295809815641460 * q^75 + 34847013306368 * q^76 + 35960055270559 * q^77 - 268486564213248 * q^78 + 137356615917609 * q^79 + 2944468516864 * q^80 - 352056899083285 * q^81 + 232629649545984 * q^82 - 914604166510648 * q^83 - 456640427573248 * q^84 + 264981492485402 * q^85 + 26598570480128 * q^86 + 1332529214868790 * q^87 + 7141660295168 * q^88 + 315332760149685 * q^89 - 1949801513701888 * q^90 - 2638730194011720 * q^91 + 1038104329945088 * q^92 + 2962720310885787 * q^93 + 1613693260778880 * q^94 - 1346257729549705 * q^95 - 82291573391360 * q^96 + 58320039716044 * q^97 - 1279096378461056 * q^98 + 3930453838067596 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	64.0000	−	110.851i	0.353553	−	0.612372i
$2$	64.0000	−	110.851i	0.353553	−	0.612372i
$3$	−3401.15	−	5890.97i	−0.897876	−	1.55517i	−0.830204	−	0.557460i	$-0.811776\pi$
$3$	−3401.15	−	5890.97i	−0.897876	−	1.55517i	−0.0676724	−	0.997708i	$-0.521557\pi$
$4$	−8192.00	−	14189.0i	−0.250000	−	0.433013i
$5$	−55365.7	+	95896.2i	−0.316932	+	0.548942i	−0.979846	−	0.199753i	$-0.935986\pi$
$5$	−55365.7	+	95896.2i	−0.316932	+	0.548942i	0.662914	+	0.748695i	$0.269319\pi$
$6$	−870695.			−1.26979
$7$	550858.	+	2.10811e6i	0.252816	+	0.967514i
$7$	550858.	+	2.10811e6i	0.252816	+	0.967514i
$8$	−2.09715e6			−0.353553
$9$	−1.59612e7	+	2.76456e7i	−1.11236	+	1.92667i
$10$	7.08681e6	+	1.22747e7i	0.224105	+	0.388161i
$11$	−2.69616e7	−	4.66989e7i	−0.417158	−	0.722539i	0.578494	−	0.815687i	$-0.303641\pi$
$11$	−2.69616e7	−	4.66989e7i	−0.417158	−	0.722539i	−0.995652	+	0.0931473i	$0.970307\pi$
$12$	−5.57245e7	+	9.65176e7i	−0.448938	+	0.777584i
$13$	2.39628e8			1.05916			0.529581	−	0.848260i	$-0.322349\pi$
$13$	2.39628e8			1.05916			0.529581	+	0.848260i	$0.322349\pi$
$14$	2.68941e8	+	7.38556e7i	0.681863	+	0.187251i
$15$	7.53228e8			1.13826
$16$	−1.34218e8	+	2.32472e8i	−0.125000	+	0.216506i
$17$	−1.29246e9	−	2.23861e9i	−0.763924	−	1.32316i	−0.940813	−	0.338925i	$-0.889937\pi$
$17$	−1.29246e9	−	2.23861e9i	−0.763924	−	1.32316i	0.176889	−	0.984231i	$-0.443397\pi$
$18$	2.04303e9	+	3.53864e9i	0.786560	+	1.36236i
$19$	−2.01327e9	+	3.48709e9i	−0.516715	+	0.894976i	0.483097	+	0.875567i	$0.339512\pi$
$19$	−2.01327e9	+	3.48709e9i	−0.516715	+	0.894976i	−0.999812	+	0.0194093i	$0.993821\pi$
$20$	1.81422e9			0.316932
$21$	1.05452e10	−	1.04151e10i	1.27765	−	1.26188i
$22$	−6.90217e9			−0.589951
$23$	−3.30987e9	+	5.73286e9i	−0.202699	+	0.351085i	−0.949397	−	0.314078i	$-0.898305\pi$
$23$	−3.30987e9	+	5.73286e9i	−0.202699	+	0.351085i	0.746698	+	0.665163i	$0.231638\pi$
$24$	7.13273e9	+	1.23543e10i	0.317447	+	0.549835i
$25$	9.12807e9	+	1.58103e10i	0.299108	+	0.518071i
$26$	1.53362e10	−	2.65630e10i	0.374470	−	0.648601i
$27$	1.19540e11			2.19931
$28$	2.53992e10	−	2.50857e10i	0.355742	−	0.351351i
$29$	5.84976e9			0.0629728			0.0314864	−	0.999504i	$-0.489976\pi$
$29$	5.84976e9			0.0629728			0.0314864	+	0.999504i	$0.489976\pi$
$30$	4.82066e10	−	8.34963e10i	0.402436	−	0.697040i
$31$	1.50673e11	+	2.60973e11i	0.983609	+	1.70366i	0.647959	+	0.761675i	$0.275623\pi$
$31$	1.50673e11	+	2.60973e11i	0.983609	+	1.70366i	0.335650	+	0.941987i	$0.391044\pi$
$32$	1.71799e10	+	2.97564e10i	0.0883883	+	0.153093i
$33$	−1.83401e11	+	3.17660e11i	−0.749113	+	1.29750i
$34$	−3.30870e11			−1.08035
$35$	−2.32658e11	−	6.38917e10i	−0.611235	−	0.167855i
$36$	5.23017e11			1.11236
$37$	7.37480e10	−	1.27735e11i	0.127714	−	0.221207i	−0.795077	−	0.606509i	$-0.792569\pi$
$37$	7.37480e10	−	1.27735e11i	0.127714	−	0.221207i	0.922790	+	0.385302i	$0.125903\pi$
$38$	2.57699e11	+	4.46348e11i	0.365372	+	0.632844i
$39$	−8.15011e11	−	1.41164e12i	−0.950996	−	1.64717i
$40$	1.16110e11	−	2.01109e11i	0.112052	−	0.194080i
$41$	7.07723e11			0.567524			0.283762	−	0.958895i	$-0.408417\pi$
$41$	7.07723e11			0.567524			0.283762	+	0.958895i	$0.408417\pi$
$42$	−4.79629e11	−	1.83552e12i	−0.321023	−	1.22854i
$43$	−1.37858e12			−0.773424			−0.386712	−	0.922201i	$-0.626389\pi$
$43$	−1.37858e12			−0.773424			−0.386712	+	0.922201i	$0.626389\pi$
$44$	−4.41739e11	+	7.65115e11i	−0.208579	+	0.361270i
$45$	−1.76741e12	−	3.06124e12i	−0.705087	−	1.22125i
$46$	4.23663e11	+	7.33806e11i	0.143330	+	0.248255i
$47$	−1.97502e12	+	3.42084e12i	−0.568640	+	0.984914i	0.428060	+	0.903750i	$0.359197\pi$
$47$	−1.97502e12	+	3.42084e12i	−0.568640	+	0.984914i	−0.996701	+	0.0811640i	$0.974136\pi$
$48$	1.82598e12			0.448938
$49$	−4.14067e12	+	2.32254e12i	−0.872168	+	0.489206i
$50$	2.33679e12			0.423003
$51$	−8.79171e12	+	1.52277e13i	−1.37182	+	2.37606i
$52$	−1.96303e12	−	3.40007e12i	−0.264790	−	0.458630i
$53$	−3.72252e12	−	6.44759e12i	−0.435279	−	0.753926i	0.562039	−	0.827111i	$-0.310017\pi$
$53$	−3.72252e12	−	6.44759e12i	−0.435279	−	0.753926i	−0.997318	+	0.0731848i	$0.976684\pi$
$54$	7.65058e12	−	1.32512e13i	0.777573	−	1.34680i
$55$	5.97100e12			0.528843
$56$	−1.15523e12	−	4.42102e12i	−0.0893839	−	0.342068i
$57$	2.73898e13			1.85578
$58$	3.74384e11	−	6.48453e11i	0.0222642	−	0.0385628i
$59$	1.81514e13	+	3.14391e13i	0.949553	+	1.64467i	0.746368	+	0.665534i	$0.231796\pi$
$59$	1.81514e13	+	3.14391e13i	0.949553	+	1.64467i	0.203185	+	0.979140i	$0.434871\pi$
$60$	−6.17045e12	−	1.06875e13i	−0.284566	−	0.492882i
$61$	1.22609e13	−	2.12365e13i	0.499515	−	0.865186i	−0.500485	−	0.865745i	$-0.666845\pi$
$61$	1.22609e13	−	2.12365e13i	0.499515	−	0.865186i	1.00000		0.000559716i	$0.000178163\pi$
$62$	3.85723e13			1.39103
$63$	−6.70723e13	−	1.84191e13i	−2.14530	−	0.589135i
$64$	4.39805e12			0.125000
$65$	−1.32672e13	+	2.29794e13i	−0.335682	+	0.581418i
$66$	2.34753e13	+	4.06605e13i	0.529703	+	0.917472i
$67$	−6.14489e12	−	1.06433e13i	−0.123866	−	0.214543i	0.797423	−	0.603421i	$-0.206196\pi$
$67$	−6.14489e12	−	1.06433e13i	−0.123866	−	0.214543i	−0.921289	+	0.388878i	$0.872863\pi$
$68$	−2.11757e13	+	3.66773e13i	−0.381962	+	0.661578i
$69$	4.50295e13			0.727995
$70$	−2.19726e13	+	2.17014e13i	−0.318894	+	0.314958i
$71$	−3.63576e13			−0.474414			−0.237207	−	0.971459i	$-0.576232\pi$
$71$	−3.63576e13			−0.474414			−0.237207	+	0.971459i	$0.576232\pi$
$72$	3.34731e13	−	5.79771e13i	0.393280	−	0.681181i
$73$	4.65083e13	+	8.05548e13i	0.492731	+	0.853434i	0.999965	−	0.00837382i	$-0.00266550\pi$
$73$	4.65083e13	+	8.05548e13i	0.492731	+	0.853434i	−0.507234	+	0.861808i	$0.669332\pi$
$74$	−9.43974e12	−	1.63501e13i	−0.0903072	−	0.156417i
$75$	6.20919e13	−	1.07546e14i	0.537125	−	0.930328i
$76$	6.59710e13			0.516715
$77$	8.35943e13	−	8.25624e13i	0.593603	−	0.586276i
$78$	−2.08643e14			−1.34491
$79$	−1.41191e14	+	2.44549e14i	−0.827185	+	1.43273i	0.0730538	+	0.997328i	$0.476726\pi$
$79$	−1.41191e14	+	2.44549e14i	−0.827185	+	1.43273i	−0.900238	+	0.435398i	$0.856608\pi$
$80$	−1.48621e13	−	2.57419e13i	−0.0792329	−	0.137235i
$81$	−1.77549e14	−	3.07523e14i	−0.862343	−	1.49362i
$82$	4.52943e13	−	7.84520e13i	0.200650	−	0.347536i
$83$	−2.65136e14			−1.07246			−0.536231	−	0.844071i	$-0.680153\pi$
$83$	−2.65136e14			−1.07246			−0.536231	+	0.844071i	$0.680153\pi$
$84$	−2.34166e14	−	6.43057e13i	−0.865822	−	0.237769i
$85$	2.86232e14			0.968448
$86$	−8.82289e13	+	1.52817e14i	−0.273447	+	0.473624i
$87$	−1.98959e13	−	3.44607e13i	−0.0565417	−	0.0979332i
$88$	5.65426e13	+	9.79347e13i	0.147488	+	0.255456i
$89$	−2.36137e14	+	4.09001e14i	−0.565898	+	0.980165i	0.431067	+	0.902320i	$0.358137\pi$
$89$	−2.36137e14	+	4.09001e14i	−0.565898	+	0.980165i	−0.996965	+	0.0778448i	$0.975196\pi$
$90$	−4.52456e14			−0.997143
$91$	1.32001e14	+	5.05161e14i	0.267773	+	1.02475i
$92$	1.08458e14			0.202699
$93$	1.02492e15	−	1.77522e15i	1.76632	−	3.05935i
$94$	2.52803e14	+	4.37867e14i	0.402090	+	0.696439i
$95$	−2.22933e14	−	3.86131e14i	−0.327527	−	0.567293i
$96$	1.16863e14	−	2.02412e14i	0.158724	−	0.274917i
$97$	−4.86827e14			−0.611767			−0.305884	−	0.952069i	$-0.598952\pi$
$97$	−4.86827e14			−0.611767			−0.305884	+	0.952069i	$0.598952\pi$
$98$	−7.54711e12	+	6.07641e14i	−0.00878183	+	0.707052i
$99$	1.72136e15			1.85613
$100$	1.49554e14	−	2.59036e14i	0.149554	−	0.259036i
$101$	3.78629e14	+	6.55805e14i	0.351401	+	0.608645i	0.986495	−	0.163790i	$-0.0523719\pi$
$101$	3.78629e14	+	6.55805e14i	0.351401	+	0.608645i	−0.635094	+	0.772435i	$0.719039\pi$
$102$	1.12534e15	+	1.94914e15i	0.970023	+	1.68013i
$103$	−1.24605e14	+	2.15822e14i	−0.0998288	+	0.172909i	−0.911614	−	0.411048i	$-0.865163\pi$
$103$	−1.24605e14	+	2.15822e14i	−0.0998288	+	0.172909i	0.811785	+	0.583957i	$0.198496\pi$
$104$	−5.02536e14			−0.374470
$105$	4.14922e14	+	1.58789e15i	0.287771	+	1.10129i
$106$	−9.52965e14			−0.615578
$107$	4.85052e14	−	8.40134e14i	0.292018	−	0.505790i	−0.682269	−	0.731101i	$-0.739007\pi$
$107$	4.85052e14	−	8.40134e14i	0.292018	−	0.505790i	0.974287	+	0.225311i	$0.0723399\pi$
$108$	−9.79274e14	−	1.69615e15i	−0.549827	−	0.952328i
$109$	1.47208e14	+	2.54971e14i	0.0771316	+	0.133596i	0.902011	−	0.431713i	$-0.142091\pi$
$109$	1.47208e14	+	2.54971e14i	0.0771316	+	0.133596i	−0.824880	+	0.565308i	$0.808757\pi$
$110$	3.82144e14	−	6.61892e14i	0.186974	−	0.323849i
$111$	−1.00331e15			−0.458684
$112$	−5.64011e14	−	1.54886e14i	−0.241075	−	0.0662031i
$113$	−2.58642e15			−1.03421			−0.517107	−	0.855921i	$-0.672991\pi$
$113$	−2.58642e15			−1.03421			−0.517107	+	0.855921i	$0.672991\pi$
$114$	1.75295e15	−	3.03619e15i	0.656119	−	1.13643i
$115$	−3.66506e14	−	6.34808e14i	−0.128484	−	0.222540i
$116$	−4.79212e13	−	8.30019e13i	−0.0157432	−	0.0272680i
$117$	−3.82475e15	+	6.62466e15i	−1.17817	+	2.04066i
$118$	4.64675e15			1.34287
$119$	4.00726e15	−	3.95780e15i	1.08704	−	1.07362i
$120$	−1.57963e15			−0.402436
$121$	6.34766e14	−	1.09945e15i	0.151958	−	0.263199i
$122$	−1.56940e15	−	2.71827e15i	−0.353211	−	0.611779i
$123$	−2.40707e15	−	4.16917e15i	−0.509567	−	0.882595i
$124$	2.46863e15	−	4.27579e15i	0.491805	−	0.851831i
$125$	−5.40078e15			−1.01305
$126$	−6.33441e15	+	6.25622e15i	−1.11925	+	1.10543i
$127$	−4.01509e15			−0.668601			−0.334300	−	0.942467i	$-0.608500\pi$
$127$	−4.01509e15			−0.668601			−0.334300	+	0.942467i	$0.608500\pi$
$128$	2.81475e14	−	4.87529e14i	0.0441942	−	0.0765466i
$129$	4.68875e15	+	8.12115e15i	0.694439	+	1.20280i
$130$	1.69820e15	+	2.94136e15i	0.237363	+	0.411125i
$131$	−1.29724e15	+	2.24689e15i	−0.171193	+	0.296516i	−0.938837	−	0.344361i	$-0.888096\pi$
$131$	−1.29724e15	+	2.24689e15i	−0.171193	+	0.296516i	0.767644	+	0.640877i	$0.221429\pi$
$132$	6.00969e15			0.749113
$133$	−8.46019e15	−	2.32331e15i	−0.996536	−	0.273665i
$134$	−1.57309e15			−0.175173
$135$	−6.61843e15	+	1.14635e16i	−0.697031	+	1.20729i
$136$	2.71049e15	+	4.69470e15i	0.270088	+	0.467806i
$137$	−8.63303e15	−	1.49529e16i	−0.814253	−	1.41033i	−0.909863	−	0.414908i	$-0.863814\pi$
$137$	−8.63303e15	−	1.49529e16i	−0.814253	−	1.41033i	0.0956109	−	0.995419i	$-0.469520\pi$
$138$	2.88188e15	−	4.99157e15i	0.257385	−	0.445804i
$139$	1.13249e16			0.958124			0.479062	−	0.877781i	$-0.340977\pi$
$139$	1.13249e16			0.958124			0.479062	+	0.877781i	$0.340977\pi$
$140$	9.99379e14	+	3.82458e15i	0.0801254	+	0.306636i
$141$	2.68694e16			2.04228
$142$	−2.32689e15	+	4.03028e15i	−0.167731	+	0.290518i
$143$	−6.46076e15	−	1.11904e16i	−0.441838	−	0.765286i
$144$	−4.28455e15	−	7.42106e15i	−0.278091	−	0.481668i
$145$	−3.23876e14	+	5.60969e14i	−0.0199581	+	0.0345684i
$146$	1.19061e16			0.696826
$147$	2.77650e16	+	1.64933e16i	1.54390	+	0.917121i
$148$	−2.41657e15			−0.127714
$149$	−7.32511e15	+	1.26875e16i	−0.368059	+	0.637496i	−0.989262	−	0.146153i	$-0.953311\pi$
$149$	−7.32511e15	+	1.26875e16i	−0.368059	+	0.637496i	0.621203	+	0.783649i	$0.286644\pi$
$150$	−7.94776e15	−	1.37659e16i	−0.379805	−	0.657841i
$151$	−2.06045e16	−	3.56880e16i	−0.936772	−	1.62254i	−0.771443	−	0.636299i	$-0.780465\pi$
$151$	−2.06045e16	−	3.56880e16i	−0.936772	−	1.62254i	−0.165329	−	0.986238i	$-0.552869\pi$
$152$	4.22214e15	−	7.31296e15i	0.182686	−	0.316422i
$153$	8.25169e16			3.39905
$154$	−3.80212e15	−	1.45505e16i	−0.149149	−	0.570786i
$155$	−3.33685e16			−1.24695
$156$	−1.33531e16	+	2.31283e16i	−0.475498	+	0.823587i
$157$	1.11386e16	+	1.92926e16i	0.378080	+	0.654854i	0.990783	−	0.135460i	$-0.0432511\pi$
$157$	1.11386e16	+	1.92926e16i	0.378080	+	0.654854i	−0.612703	+	0.790313i	$0.709918\pi$
$158$	1.80724e16	+	3.13023e16i	0.584908	+	1.01309i
$159$	−2.53217e16	+	4.38585e16i	−0.781654	+	1.35386i
$160$	−3.80470e15			−0.112052
$161$	−1.39088e16	−	3.81957e15i	−0.390926	−	0.107354i
$162$	−4.54525e16			−1.21954
$163$	−1.20124e16	+	2.08061e16i	−0.307768	+	0.533070i	−0.977874	−	0.209196i	$-0.932915\pi$
$163$	−1.20124e16	+	2.08061e16i	−0.307768	+	0.533070i	0.670106	+	0.742266i	$0.266249\pi$
$164$	−5.79767e15	−	1.00419e16i	−0.141881	−	0.245745i
$165$	−2.03083e16	−	3.51749e16i	−0.474835	−	0.822439i
$166$	−1.69687e16	+	2.93906e16i	−0.379173	+	0.656747i
$167$	5.01680e16			1.07165			0.535825	−	0.844329i	$-0.320001\pi$
$167$	5.01680e16			1.07165			0.535825	+	0.844329i	$0.320001\pi$
$168$	−2.21150e16	+	2.18420e16i	−0.451717	+	0.446142i
$169$	6.23562e15			0.121823
$170$	1.83188e16	−	3.17292e16i	0.342398	−	0.593051i
$171$	−6.42686e16	−	1.11316e17i	−1.14955	−	1.99108i
$172$	1.12933e16	+	1.95606e16i	0.193356	+	0.334902i
$173$	1.05273e16	−	1.82339e16i	0.172573	−	0.298905i	−0.766746	−	0.641951i	$-0.778125\pi$
$173$	1.05273e16	−	1.82339e16i	0.172573	−	0.298905i	0.939319	+	0.343046i	$0.111459\pi$
$174$	−5.09335e15			−0.0799621
$175$	−2.83015e16	+	2.79522e16i	−0.425622	+	0.420368i
$176$	1.44749e16			0.208579
$177$	1.23471e17	−	2.13858e17i	1.70516	−	2.95343i
$178$	3.02255e16	+	5.23521e16i	0.400151	+	0.693081i
$179$	1.73974e16	+	3.01332e16i	0.220844	+	0.382514i	0.955065	−	0.296398i	$-0.0957854\pi$
$179$	1.73974e16	+	3.01332e16i	0.220844	+	0.382514i	−0.734220	+	0.678911i	$0.762452\pi$
$180$	−2.89572e16	+	5.01553e16i	−0.352543	+	0.610623i
$181$	−1.05050e17			−1.22689			−0.613446	−	0.789737i	$-0.710217\pi$
$181$	−1.05050e17			−1.22689			−0.613446	+	0.789737i	$0.710217\pi$
$182$	6.44458e16	+	1.76979e16i	0.722203	+	0.198329i
$183$	−1.66805e17			−1.79401
$184$	6.94130e15	−	1.20227e16i	0.0716650	−	0.124127i
$185$	8.16622e15	+	1.41443e16i	0.0809530	+	0.140215i
$186$	−1.31190e17	−	2.27228e17i	−1.24898	−	2.16329i
$187$	−6.96937e16	+	1.20713e17i	−0.637355	+	1.10393i
$188$	6.47175e16			0.568640
$189$	6.58497e16	+	2.52004e17i	0.556020	+	2.12786i
$190$	−5.70708e16			−0.463193
$191$	−9.91179e15	+	1.71677e16i	−0.0773396	+	0.133956i	−0.902101	−	0.431524i	$-0.857976\pi$
$191$	−9.91179e15	+	1.71677e16i	−0.0773396	+	0.133956i	0.824762	+	0.565480i	$0.191309\pi$
$192$	−1.49584e16	−	2.59087e16i	−0.112235	−	0.194396i
$193$	1.21654e17	+	2.10710e17i	0.877900	+	1.52057i	0.853641	+	0.520863i	$0.174390\pi$
$193$	1.21654e17	+	2.10710e17i	0.877900	+	1.52057i	0.0242599	+	0.999706i	$0.492277\pi$
$194$	−3.11569e16	+	5.39653e16i	−0.216292	+	0.374630i
$195$	1.80495e17			1.20560
$196$	6.68748e16	+	3.97256e16i	0.429874	+	0.255358i
$197$	2.19226e17			1.35642			0.678212	−	0.734866i	$-0.262755\pi$
$197$	2.19226e17			1.35642			0.678212	+	0.734866i	$0.262755\pi$
$198$	1.10167e17	−	1.90815e17i	0.656240	−	1.13664i
$199$	−1.14325e17	−	1.98017e17i	−0.655759	−	1.13581i	−0.981703	−	0.190419i	$-0.939015\pi$
$199$	−1.14325e17	−	1.98017e17i	−0.655759	−	1.13581i	0.325944	−	0.945389i	$-0.394318\pi$
$200$	−1.91429e16	−	3.31566e16i	−0.105751	−	0.183166i
$201$	−4.17994e16	+	7.23986e16i	−0.222433	+	0.385265i
$202$	9.69290e16			0.496957
$203$	3.22238e15	+	1.23319e16i	0.0159205	+	0.0609270i
$204$	2.88087e17			1.37182
$205$	−3.91836e16	+	6.78680e16i	−0.179866	+	0.311538i
$206$	1.59494e16	+	2.76252e16i	0.0705896	+	0.122265i
$207$	−1.05659e17	−	1.83007e17i	−0.450950	−	0.781069i
$208$	−3.21623e16	+	5.57068e16i	−0.132395	+	0.229315i
$209$	2.17124e17			0.862207
$210$	2.02574e17	+	5.56301e16i	0.776139	+	0.213140i
$211$	−3.29648e17			−1.21880			−0.609400	−	0.792863i	$-0.708589\pi$
$211$	−3.29648e17			−1.21880			−0.609400	+	0.792863i	$0.708589\pi$
$212$	−6.09898e16	+	1.05637e17i	−0.217640	+	0.376963i
$213$	1.23658e17	+	2.14181e17i	0.425965	+	0.737793i
$214$	−6.20866e16	−	1.07537e17i	−0.206488	−	0.357648i
$215$	7.63259e16	−	1.32200e17i	0.245123	−	0.424565i
$216$	−2.50694e17			−0.777573
$217$	−4.67160e17	+	4.61394e17i	−1.39965	+	1.38237i
$218$	3.76852e16			0.109081
$219$	3.16364e17	−	5.47958e17i	0.884822	−	1.53256i
$220$	−4.89144e16	−	8.47222e16i	−0.132211	−	0.228996i
$221$	−3.09710e17	−	5.36433e17i	−0.809119	−	1.40144i
$222$	−6.42120e16	+	1.11218e17i	−0.162169	+	0.280886i
$223$	−1.19425e17			−0.291614			−0.145807	−	0.989313i	$-0.546578\pi$
$223$	−1.19425e17			−0.291614			−0.145807	+	0.989313i	$0.546578\pi$
$224$	−5.32660e16	+	5.26086e16i	−0.125774	+	0.124221i
$225$	−5.82780e17			−1.33087
$226$	−1.65531e17	+	2.86708e17i	−0.365650	+	0.633325i
$227$	2.98051e17	+	5.16239e17i	0.636936	+	1.10321i	0.986101	+	0.166145i	$0.0531320\pi$
$227$	2.98051e17	+	5.16239e17i	0.636936	+	1.10321i	−0.349165	+	0.937061i	$0.613535\pi$
$228$	−2.24377e17	−	3.88633e17i	−0.463946	−	0.803578i
$229$	1.94610e16	−	3.37074e16i	0.0389402	−	0.0674464i	−0.845898	−	0.533344i	$-0.820935\pi$
$229$	1.94610e16	−	3.37074e16i	0.0389402	−	0.0674464i	0.884839	+	0.465898i	$0.154268\pi$
$230$	−9.38256e16			−0.181703
$231$	−7.70689e17	−	2.11644e17i	−1.44474	−	0.396749i
$232$	−1.22678e16			−0.0222642
$233$	7.56199e16	−	1.30977e17i	0.132882	−	0.230159i	−0.791904	−	0.610645i	$-0.790910\pi$
$233$	7.56199e16	−	1.30977e17i	0.132882	−	0.230159i	0.924786	+	0.380487i	$0.124243\pi$
$234$	4.89568e17	+	8.47957e17i	0.833094	+	1.44296i
$235$	−2.18697e17	−	3.78794e17i	−0.360440	−	0.624301i
$236$	2.97392e17	−	5.15098e17i	0.474776	−	0.822337i
$237$	1.92084e18			2.97084
$238$	−1.82262e17	−	6.97509e17i	−0.273130	−	1.04526i
$239$	4.53893e17			0.659128			0.329564	−	0.944133i	$-0.393098\pi$
$239$	4.53893e17			0.659128			0.329564	+	0.944133i	$0.393098\pi$
$240$	−1.01097e17	+	1.75104e17i	−0.142283	+	0.246441i
$241$	1.92360e15	+	3.33177e15i	0.00262414	+	0.00454514i	0.867334	−	0.497726i	$-0.165831\pi$
$241$	1.92360e15	+	3.33177e15i	0.00262414	+	0.00454514i	−0.864710	+	0.502271i	$0.832498\pi$
$242$	−8.12501e16	−	1.40729e17i	−0.107451	−	0.186110i
$243$	−3.50104e17	+	6.06397e17i	−0.448900	+	0.777518i
$244$	−4.01765e17			−0.499515
$245$	6.52892e15	−	5.25664e17i	0.00787220	−	0.633815i
$246$	−6.16211e17			−0.720636
$247$	−4.82437e17	+	8.35605e17i	−0.547284	+	0.947924i
$248$	−3.15984e17	−	5.47301e17i	−0.347758	−	0.602335i
$249$	9.01766e17	+	1.56190e18i	0.962939	+	1.66786i
$250$	−3.45650e17	+	5.98683e17i	−0.358168	+	0.620365i
$251$	−6.57705e16			−0.0661421			−0.0330711	−	0.999453i	$-0.510529\pi$
$251$	−6.57705e16			−0.0661421			−0.0330711	+	0.999453i	$0.510529\pi$
$252$	2.88108e17	+	1.10258e18i	0.281223	+	1.07623i
$253$	3.56958e17			0.338231
$254$	−2.56966e17	+	4.45077e17i	−0.236386	+	0.409433i
$255$	−9.73518e17	−	1.68618e18i	−0.869546	−	1.50610i
$256$	−3.60288e16	−	6.24037e16i	−0.0312500	−	0.0541266i
$257$	6.80768e17	−	1.17913e18i	0.573457	−	0.993257i	−0.422750	−	0.906246i	$-0.638935\pi$
$257$	6.80768e17	−	1.17913e18i	0.573457	−	0.993257i	0.996207	−	0.0870105i	$-0.0277314\pi$
$258$	1.20032e18			0.982085
$259$	3.09904e17	+	8.51047e16i	0.246309	+	0.0676403i
$260$	4.34738e17			0.335682
$261$	−9.33691e16	+	1.61720e17i	−0.0700486	+	0.121328i
$262$	1.66047e17	+	2.87602e17i	0.121052	+	0.209668i
$263$	−5.48888e17	−	9.50701e17i	−0.388880	−	0.673559i	0.603419	−	0.797424i	$-0.293805\pi$
$263$	−5.48888e17	−	9.50701e17i	−0.388880	−	0.673559i	−0.992299	+	0.123865i	$0.960471\pi$
$264$	3.84620e17	−	6.66181e17i	0.264851	−	0.458736i
$265$	8.24400e17			0.551815
$266$	−7.98994e17	+	7.89132e17i	−0.519913	+	0.513496i
$267$	3.21255e18			2.03243
$268$	−1.00678e17	+	1.74379e17i	−0.0619331	+	0.107271i
$269$	−2.47091e17	−	4.27975e17i	−0.147814	−	0.256021i	0.782605	−	0.622518i	$-0.213890\pi$
$269$	−2.47091e17	−	4.27975e17i	−0.147814	−	0.256021i	−0.930419	+	0.366497i	$0.880557\pi$
$270$	8.47159e17	+	1.46732e18i	0.492875	+	0.853685i
$271$	−8.47548e17	+	1.46800e18i	−0.479617	+	0.830721i	−0.999727	−	0.0233786i	$-0.992558\pi$
$271$	−8.47548e17	+	1.46800e18i	−0.479617	+	0.830721i	0.520110	+	0.854099i	$0.325891\pi$
$272$	6.93884e17			0.381962
$273$	2.52693e18	−	2.49574e18i	1.35324	−	1.33653i
$274$	−2.21006e18			−1.15153
$275$	4.92215e17	−	8.52541e17i	0.249551	−	0.432235i
$276$	−3.68881e17	−	6.38921e17i	−0.181999	−	0.315231i
$277$	1.83709e17	+	3.18194e17i	0.0882130	+	0.152789i	0.906756	−	0.421656i	$-0.138551\pi$
$277$	1.83709e17	+	3.18194e17i	0.0882130	+	0.152789i	−0.818543	+	0.574446i	$0.805218\pi$
$278$	7.24791e17	−	1.25537e18i	0.338748	−	0.586729i
$279$	−9.61969e18			−4.37653
$280$	4.87920e17	+	1.33991e17i	0.216104	+	0.0593457i
$281$	1.26913e18			0.547280			0.273640	−	0.961832i	$-0.411772\pi$
$281$	1.26913e18			0.547280			0.273640	+	0.961832i	$0.411772\pi$
$282$	1.71964e18	−	2.97850e18i	0.722053	−	1.25063i
$283$	1.55369e18	+	2.69107e18i	0.635281	+	1.10034i	0.986455	+	0.164030i	$0.0524492\pi$
$283$	1.55369e18	+	2.69107e18i	0.635281	+	1.10034i	−0.351174	+	0.936310i	$0.614217\pi$
$284$	2.97841e17	+	5.15876e17i	0.118603	+	0.205427i
$285$	−1.51646e18	+	2.62658e18i	−0.588157	+	1.01872i
$286$	−1.65395e18			−0.624853
$287$	3.89855e17	+	1.49196e18i	0.143479	+	0.549088i
$288$	−1.09685e18			−0.393280
$289$	−1.90970e18	+	3.30769e18i	−0.667161	+	1.15556i
$290$	4.14561e16	+	7.18041e16i	0.0141125	+	0.0244435i
$291$	1.65577e18	+	2.86788e18i	0.549291	+	0.951401i
$292$	7.61993e17	−	1.31981e18i	0.246365	−	0.426717i
$293$	−2.71988e18			−0.857123			−0.428562	−	0.903513i	$-0.640979\pi$
$293$	−2.71988e18			−0.857123			−0.428562	+	0.903513i	$0.640979\pi$
$294$	3.60526e18	−	2.02222e18i	1.10747	−	0.621188i
$295$	−4.01985e18			−1.20377
$296$	−1.54661e17	+	2.67880e17i	−0.0451536	+	0.0782083i
$297$	−3.22300e18	−	5.58240e18i	−0.917459	−	1.58909i
$298$	9.37614e17	+	1.62399e18i	0.260257	+	0.450778i
$299$	−7.93137e17	+	1.37375e18i	−0.214691	+	0.371856i
$300$	−2.03463e18			−0.537125
$301$	−7.59400e17	−	2.90619e18i	−0.195534	−	0.748299i
$302$	−5.27474e18			−1.32480
$303$	2.57555e18	−	4.46098e18i	0.631030	−	1.09298i
$304$	−5.40434e17	−	9.36059e17i	−0.129179	−	0.223744i
$305$	1.35767e18	+	2.35155e18i	0.316624	+	0.548410i
$306$	5.28108e18	−	9.14710e18i	1.20174	−	2.08148i
$307$	6.52602e18			1.44914			0.724571	−	0.689201i	$-0.242038\pi$
$307$	6.52602e18			1.44914			0.724571	+	0.689201i	$0.242038\pi$
$308$	−1.85628e18	−	5.09764e17i	−0.402266	−	0.110469i
$309$	1.69520e18			0.358536
$310$	−2.13558e18	+	3.69894e18i	−0.440863	+	0.763597i
$311$	−1.22467e18	−	2.12120e18i	−0.246784	−	0.427443i	0.715848	−	0.698257i	$-0.246041\pi$
$311$	−1.22467e18	−	2.12120e18i	−0.246784	−	0.427443i	−0.962632	+	0.270814i	$0.912707\pi$
$312$	1.70920e18	+	2.96042e18i	0.336228	+	0.582364i
$313$	−1.67046e18	+	2.89333e18i	−0.320815	+	0.555668i	−0.980656	−	0.195737i	$-0.937290\pi$
$313$	−1.67046e18	+	2.89333e18i	−0.320815	+	0.555668i	0.659841	+	0.751405i	$0.270623\pi$
$314$	2.85148e18			0.534686
$315$	5.47983e18	−	5.41219e18i	1.00332	−	0.990932i
$316$	4.62653e18			0.827185
$317$	−2.37971e18	+	4.12178e18i	−0.415508	+	0.719681i	−0.995482	−	0.0949545i	$-0.969729\pi$
$317$	−2.37971e18	+	4.12178e18i	−0.415508	+	0.719681i	0.579974	+	0.814635i	$0.303063\pi$
$318$	3.24118e18	+	5.61389e18i	0.552713	+	0.957327i
$319$	−1.57719e17	−	2.73177e17i	−0.0262696	−	0.0455003i
$320$	−2.43501e17	+	4.21756e17i	−0.0396165	+	0.0686177i
$321$	−6.59894e18			−1.04878
$322$	−1.31356e18	+	1.29735e18i	−0.203954	+	0.201437i
$323$	1.04083e19			1.57892
$324$	−2.90896e18	+	5.03846e18i	−0.431171	+	0.746811i
$325$	2.18734e18	+	3.78858e18i	0.316804	+	0.548721i
$326$	1.53759e18	+	2.66318e18i	0.217625	+	0.376937i
$327$	1.00135e18	−	1.73439e18i	0.138509	−	0.239905i
$328$	−1.48420e18			−0.200650
$329$	−8.29945e18	−	2.27916e18i	−1.09668	−	0.301166i
$330$	−5.19891e18			−0.671519
$331$	−3.21187e17	+	5.56312e17i	−0.0405553	+	0.0702439i	−0.885591	−	0.464467i	$-0.846246\pi$
$331$	−3.21187e17	+	5.56312e17i	−0.0405553	+	0.0702439i	0.845035	+	0.534711i	$0.179579\pi$
$332$	2.17199e18	+	3.76200e18i	0.268116	+	0.464390i
$333$	2.35421e18	+	4.07762e18i	0.284128	+	0.492124i
$334$	3.21075e18	−	5.56118e18i	0.378886	−	0.656249i
$335$	1.36086e18			0.157029
$336$	1.00585e18	+	3.84936e18i	0.113499	+	0.434354i
$337$	4.32492e18			0.477258			0.238629	−	0.971111i	$-0.423302\pi$
$337$	4.32492e18			0.477258			0.238629	+	0.971111i	$0.423302\pi$
$338$	3.99080e17	−	6.91226e17i	0.0430709	−	0.0746011i
$339$	8.79681e18	+	1.52365e19i	0.928597	+	1.60838i
$340$	−2.34481e18	−	4.06133e18i	−0.242112	−	0.419350i
$341$	8.12478e18	−	1.40725e19i	0.820642	−	1.42139i
$342$	−1.64527e19			−1.62571
$343$	−7.17708e18	−	7.44960e18i	−0.693812	−	0.720156i
$344$	2.89109e18			0.273447
$345$	−2.49309e18	+	4.31815e18i	−0.230725	+	0.399627i
$346$	−1.34750e18	−	2.33394e18i	−0.122028	−	0.211358i
$347$	1.10959e18	+	1.92186e18i	0.0983309	+	0.170314i	0.910994	−	0.412420i	$-0.135316\pi$
$347$	1.10959e18	+	1.92186e18i	0.0983309	+	0.170314i	−0.812663	+	0.582734i	$0.801983\pi$
$348$	−3.25974e17	+	5.64604e17i	−0.0282709	+	0.0489666i
$349$	3.25470e18			0.276262			0.138131	−	0.990414i	$-0.455891\pi$
$349$	3.25470e18			0.276262			0.138131	+	0.990414i	$0.455891\pi$
$350$	1.28724e18	+	4.92619e18i	0.106942	+	0.409262i
$351$	2.86452e19			2.32942
$352$	9.26394e17	−	1.60456e18i	0.0737439	−	0.127728i
$353$	−6.00727e18	−	1.04049e19i	−0.468130	−	0.810825i	0.531207	−	0.847242i	$-0.321739\pi$
$353$	−6.00727e18	−	1.04049e19i	−0.468130	−	0.810825i	−0.999337	+	0.0364172i	$0.988405\pi$
$354$	−1.58043e19	−	2.73738e19i	−1.20573	−	2.08839i
$355$	2.01296e18	−	3.48655e18i	0.150357	−	0.260426i
$356$	7.73773e18			0.565898
$357$	−3.69446e19	−	1.01456e19i	−2.64569	−	0.726549i
$358$	4.45373e18			0.312321
$359$	−3.75173e18	+	6.49818e18i	−0.257646	+	0.446255i	−0.965611	−	0.259992i	$-0.916280\pi$
$359$	−3.75173e18	+	6.49818e18i	−0.257646	+	0.446255i	0.707965	+	0.706247i	$0.249613\pi$
$360$	3.70652e18	+	6.41988e18i	0.249286	+	0.431776i
$361$	−5.15979e17	−	8.93703e17i	−0.0339882	−	0.0588693i
$362$	−6.72319e18	+	1.16449e19i	−0.433772	+	0.751315i
$363$	−8.63574e18			−0.545758
$364$	6.08636e18	−	6.01124e18i	0.376788	−	0.372138i
$365$	−1.02999e19			−0.624648
$366$	−1.06755e19	+	1.84905e19i	−0.634279	+	1.09860i
$367$	−1.24394e19	−	2.15457e19i	−0.724111	−	1.25420i	−0.959339	−	0.282256i	$-0.908917\pi$
$367$	−1.24394e19	−	2.15457e19i	−0.724111	−	1.25420i	0.235228	−	0.971940i	$-0.424416\pi$
$368$	−8.88486e17	−	1.53890e18i	−0.0506748	−	0.0877713i
$369$	−1.12961e19	+	1.95654e19i	−0.631294	+	1.09343i
$370$	2.09055e18			0.114485
$371$	1.15416e19	−	1.13992e19i	0.619389	−	0.611743i
$372$	−3.35847e19			−1.76632
$373$	1.19560e19	−	2.07085e19i	0.616270	−	1.06741i	−0.373891	−	0.927473i	$-0.621976\pi$
$373$	1.19560e19	−	2.07085e19i	0.616270	−	1.06741i	0.990160	−	0.139938i	$-0.0446902\pi$
$374$	8.92079e18	+	1.54513e19i	0.450678	+	0.780597i
$375$	1.83689e19	+	3.18158e19i	0.909595	+	1.57546i
$376$	4.14192e18	−	7.17401e18i	0.201045	−	0.348220i
$377$	1.40176e18			0.0666983
$378$	3.21493e19	+	8.82872e18i	1.49963	+	0.411822i
$379$	−3.91987e19			−1.79258			−0.896288	−	0.443473i	$-0.853746\pi$
$379$	−3.91987e19			−1.79258			−0.896288	+	0.443473i	$0.853746\pi$
$380$	−3.65253e18	+	6.32636e18i	−0.163763	+	0.283646i
$381$	1.36559e19	+	2.36527e19i	0.600321	+	1.03979i
$382$	1.26871e18	+	2.19747e18i	0.0546873	+	0.0947212i
$383$	−1.18029e19	+	2.04433e19i	−0.498884	+	0.864092i	−0.999999	−	0.00128859i	$-0.999590\pi$
$383$	−1.18029e19	+	2.04433e19i	−0.498884	+	0.864092i	0.501116	+	0.865380i	$0.332923\pi$
$384$	−3.82936e18			−0.158724
$385$	3.28917e18	+	1.25875e19i	0.133700	+	0.511663i
$386$	3.11433e19			1.24154
$387$	2.20038e19	−	3.81116e19i	0.860329	−	1.49013i
$388$	3.98808e18	+	6.90756e18i	0.152942	+	0.264903i
$389$	−9.85557e18	−	1.70703e19i	−0.370732	−	0.642126i	0.618947	−	0.785433i	$-0.287560\pi$
$389$	−9.85557e18	−	1.70703e19i	−0.370732	−	0.642126i	−0.989678	+	0.143307i	$0.954226\pi$
$390$	1.15517e19	−	2.00080e19i	0.426245	−	0.738278i
$391$	1.71115e19			0.619387
$392$	8.68362e18	−	4.87071e18i	0.308358	−	0.172960i
$393$	1.76485e19			0.614842
$394$	1.40305e19	−	2.43015e19i	0.479568	−	0.830637i
$395$	−1.56342e19	−	2.70793e19i	−0.524322	−	0.908153i
$396$	−1.41014e19	−	2.44243e19i	−0.464032	−	0.803727i
$397$	1.21990e19	−	2.11293e19i	0.393908	−	0.682269i	−0.599053	−	0.800709i	$-0.704456\pi$
$397$	1.21990e19	−	2.11293e19i	0.393908	−	0.682269i	0.992961	+	0.118440i	$0.0377895\pi$
$398$	−2.92673e19			−0.927384
$399$	1.50879e19	+	5.77406e19i	0.469172	+	1.79550i
$400$	−4.90059e18			−0.149554
$401$	5.62777e18	−	9.74758e18i	0.168560	−	0.291954i	−0.769354	−	0.638823i	$-0.779422\pi$
$401$	5.62777e18	−	9.74758e18i	0.168560	−	0.291954i	0.937914	+	0.346869i	$0.112755\pi$
$402$	5.35032e18	+	9.26702e18i	0.157284	+	0.272424i
$403$	3.61054e19	+	6.25365e19i	1.04180	+	1.80445i
$404$	6.20346e18	−	1.07447e19i	0.175701	−	0.304323i
$405$	3.93204e19			1.09322
$406$	1.57324e18	+	4.32037e17i	0.0429388	+	0.0117917i
$407$	−7.95346e18			−0.213107
$408$	1.84375e19	−	3.19348e19i	0.485011	−	0.840064i
$409$	−7.40448e18	−	1.28249e19i	−0.191236	−	0.331231i	0.754424	−	0.656387i	$-0.227916\pi$
$409$	−7.40448e18	−	1.28249e19i	−0.191236	−	0.331231i	−0.945660	+	0.325157i	$0.894583\pi$
$410$	5.01550e18	+	8.68710e18i	0.127185	+	0.220291i
$411$	−5.87245e19	+	1.01714e20i	−1.46220	+	2.53260i
$412$	4.08305e18			0.0998288
$413$	−5.62781e19	+	5.55835e19i	−1.35118	+	1.33451i
$414$	−2.70487e19			−0.637740
$415$	1.46794e19	−	2.54255e19i	0.339898	−	0.588720i
$416$	4.11678e18	+	7.13046e18i	0.0936175	+	0.162150i
$417$	−3.85175e19	−	6.67143e19i	−0.860277	−	1.49004i
$418$	1.38960e19	−	2.40685e19i	0.304836	−	0.527992i
$419$	−3.94881e19			−0.850866			−0.425433	−	0.904990i	$-0.639878\pi$
$419$	−3.94881e19			−0.850866			−0.425433	+	0.904990i	$0.639878\pi$
$420$	1.91314e19	−	1.88953e19i	0.404928	−	0.399930i
$421$	1.88866e19			0.392678			0.196339	−	0.980536i	$-0.437095\pi$
$421$	1.88866e19			0.392678			0.196339	+	0.980536i	$0.437095\pi$
$422$	−2.10975e19	+	3.65419e19i	−0.430911	+	0.746359i
$423$	−6.30474e19	−	1.09201e20i	−1.26507	−	2.19117i
$424$	7.80669e18	+	1.35216e19i	0.153894	+	0.266553i
$425$	2.35953e19	−	4.08683e19i	0.456993	−	0.791534i
$426$	3.16564e19			0.602406
$427$	5.15229e19	+	1.41490e19i	0.963365	+	0.264556i
$428$	−1.58942e19			−0.292018
$429$	−4.39480e19	+	7.61202e19i	−0.793432	+	1.37426i
$430$	−9.76971e18	−	1.69216e19i	−0.173328	−	0.300213i
$431$	2.26313e19	+	3.91985e19i	0.394575	+	0.683424i	0.993047	−	0.117720i	$-0.0375584\pi$
$431$	2.26313e19	+	3.91985e19i	0.394575	+	0.683424i	−0.598472	+	0.801144i	$0.704225\pi$
$432$	−1.60444e19	+	2.77898e19i	−0.274913	+	0.476164i
$433$	8.27306e19			1.39318			0.696590	−	0.717470i	$-0.254700\pi$
$433$	8.27306e19			1.39318			0.696590	+	0.717470i	$0.254700\pi$
$434$	2.12478e19	+	8.13145e19i	0.351675	+	1.34585i
$435$	4.40620e18			0.0716795
$436$	2.41185e18	−	4.17745e18i	0.0385658	−	0.0667979i
$437$	−1.33273e19	−	2.30836e19i	−0.209475	−	0.362822i
$438$	−4.04946e19	−	7.01387e19i	−0.625664	−	1.08368i
$439$	−5.12022e17	+	8.86848e17i	−0.00777687	+	0.0134699i	−0.869888	−	0.493250i	$-0.835809\pi$
$439$	−5.12022e17	+	8.86848e17i	−0.00777687	+	0.0134699i	0.862111	+	0.506720i	$0.169142\pi$
$440$	−1.25221e19			−0.186974
$441$	1.88220e18	−	1.51542e20i	0.0276298	−	2.22456i
$442$	−7.92856e19			−1.14427
$443$	3.01244e19	−	5.21771e19i	0.427456	−	0.740375i	−0.569191	−	0.822206i	$-0.692743\pi$
$443$	3.01244e19	−	5.21771e19i	0.427456	−	0.740375i	0.996646	+	0.0818307i	$0.0260767\pi$
$444$	8.21914e18	+	1.42360e19i	0.114671	+	0.198616i
$445$	−2.61477e19	−	4.52892e19i	−0.358702	−	0.621291i
$446$	−7.64319e18	+	1.32384e19i	−0.103101	+	0.178576i
$447$	9.96552e19			1.32188
$448$	2.42270e18	+	9.27155e18i	0.0316020	+	0.120939i
$449$	−4.35637e19			−0.558827			−0.279414	−	0.960171i	$-0.590140\pi$
$449$	−4.35637e19			−0.558827			−0.279414	+	0.960171i	$0.590140\pi$
$450$	−3.72979e19	+	6.46019e19i	−0.470534	+	0.814988i
$451$	−1.90814e19	−	3.30499e19i	−0.236747	−	0.410059i
$452$	2.11880e19	+	3.66986e19i	0.258554	+	0.447828i
$453$	−1.40158e20	+	2.42760e20i	−1.68221	+	2.91368i
$454$	7.63010e19			0.900764
$455$	−5.57514e19	−	1.53102e19i	−0.647396	−	0.177785i
$456$	−5.74406e19			−0.656119
$457$	−5.95635e19	+	1.03167e20i	−0.669282	+	1.15923i	0.308823	+	0.951119i	$0.400065\pi$
$457$	−5.95635e19	+	1.03167e20i	−0.669282	+	1.15923i	−0.978105	+	0.208111i	$0.933269\pi$
$458$	−2.49100e18	−	4.31454e18i	−0.0275349	−	0.0476918i
$459$	−1.54501e20	−	2.67604e20i	−1.68010	−	2.91003i
$460$	−6.00484e18	+	1.04007e19i	−0.0642418	+	0.111270i
$461$	8.38337e19			0.882392			0.441196	−	0.897411i	$-0.354554\pi$
$461$	8.38337e19			0.882392			0.441196	+	0.897411i	$0.354554\pi$
$462$	−7.27851e19	+	7.18867e19i	−0.753750	+	0.744447i
$463$	1.31703e20			1.34195			0.670976	−	0.741479i	$-0.265875\pi$
$463$	1.31703e20			1.34195			0.670976	+	0.741479i	$0.265875\pi$
$464$	−7.85141e17	+	1.35990e18i	−0.00787159	+	0.0136340i
$465$	1.13491e20	+	1.96573e20i	1.11961	+	1.93921i
$466$	−9.67934e18	−	1.67651e19i	−0.0939618	−	0.162747i
$467$	4.91242e19	−	8.50856e19i	0.469266	−	0.812792i	−0.530117	−	0.847925i	$-0.677852\pi$
$467$	4.91242e19	−	8.50856e19i	0.469266	−	0.812792i	0.999383	+	0.0351322i	$0.0111852\pi$
$468$	1.25329e20			1.17817
$469$	1.90522e19	−	1.88170e19i	0.176258	−	0.174082i
$470$	−5.59864e19			−0.509740
$471$	7.57682e19	−	1.31234e20i	0.678938	−	1.17596i
$472$	−3.80662e19	−	6.59325e19i	−0.335718	−	0.581480i
$473$	3.71687e19	+	6.43780e19i	0.322640	+	0.558829i
$474$	1.22934e20	−	2.12928e20i	1.05035	−	1.81926i
$475$	−7.35092e19			−0.618215
$476$	−8.89846e19	−	2.44366e19i	−0.736652	−	0.202297i
$477$	2.37664e20			1.93676
$478$	2.90492e19	−	5.03147e19i	0.233037	−	0.403632i
$479$	6.55003e19	+	1.13450e20i	0.517282	+	0.895958i	0.999799	+	0.0200715i	$0.00638937\pi$
$479$	6.55003e19	+	1.13450e20i	0.517282	+	0.895958i	−0.482517	+	0.875887i	$0.660277\pi$
$480$	1.29404e19	+	2.24134e19i	0.100609	+	0.174260i
$481$	1.76721e19	−	3.06089e19i	0.135269	−	0.234293i
$482$	4.92441e17			0.00371109
$483$	2.48048e19	+	9.49269e19i	0.184049	+	0.704346i
$484$	−2.08000e19			−0.151958
$485$	2.69535e19	−	4.66848e19i	0.193889	−	0.335825i
$486$	4.48133e19	+	7.76189e19i	0.317420	+	0.549788i
$487$	8.47960e19	+	1.46871e20i	0.591437	+	1.02440i	0.994039	+	0.109024i	$0.0347724\pi$
$487$	8.47960e19	+	1.46871e20i	0.591437	+	1.02440i	−0.402602	+	0.915375i	$0.631894\pi$
$488$	−2.57130e19	+	4.45362e19i	−0.176605	+	0.305889i
$489$	1.63424e20			1.10535
$490$	−5.78526e19	−	3.43662e19i	−0.385347	−	0.228908i
$491$	−2.15412e20			−1.41305			−0.706527	−	0.707686i	$-0.749739\pi$
$491$	−2.15412e20			−1.41305			−0.706527	+	0.707686i	$0.749739\pi$
$492$	−3.94375e19	+	6.83077e19i	−0.254783	+	0.441298i
$493$	−7.56058e18	−	1.30953e19i	−0.0481064	−	0.0833228i
$494$	6.17519e19	+	1.06957e20i	0.386988	+	0.670284i
$495$	−9.53043e19	+	1.65072e20i	−0.588266	+	1.01891i
$496$	−8.08919e19			−0.491805
$497$	−2.00279e19	−	7.66457e19i	−0.119939	−	0.459002i
$498$	2.30852e20			1.36180
$499$	−2.52135e19	+	4.36711e19i	−0.146514	+	0.253770i	−0.929937	−	0.367719i	$-0.880139\pi$
$499$	−2.52135e19	+	4.36711e19i	−0.146514	+	0.253770i	0.783423	+	0.621489i	$0.213472\pi$
$500$	4.42432e19	+	7.66315e19i	0.253263	+	0.438664i
$501$	−1.70629e20	−	2.95538e20i	−0.962209	−	1.66660i
$502$	−4.20931e18	+	7.29074e18i	−0.0233848	+	0.0405036i
$503$	−2.17637e20			−1.19117			−0.595584	−	0.803293i	$-0.703079\pi$
$503$	−2.17637e20			−1.19117			−0.595584	+	0.803293i	$0.703079\pi$
$504$	1.40661e20	+	3.86277e19i	0.758480	+	0.208291i
$505$	−8.38522e19			−0.445481
$506$	2.28453e19	−	3.95692e19i	0.119583	−	0.207123i
$507$	−2.12083e19	−	3.67338e19i	−0.109382	−	0.189455i
$508$	3.28916e19	+	5.69699e19i	0.167150	+	0.289513i
$509$	1.05689e20	−	1.83059e20i	0.529233	−	0.916659i	−0.470186	−	0.882568i	$-0.655813\pi$
$509$	1.05689e20	−	1.83059e20i	0.529233	−	0.916659i	0.999419	−	0.0340912i	$-0.0108537\pi$
$510$	−2.49221e20			−1.22972
$511$	−1.44199e20	+	1.42419e20i	−0.701140	+	0.692486i
$512$	−9.22337e18			−0.0441942
$513$	−2.40667e20	+	4.16848e20i	−1.13641	+	1.96833i
$514$	−8.71383e19	−	1.50928e20i	−0.405495	−	0.702338i
$515$	−1.37977e19	−	2.38983e19i	−0.0632778	−	0.109600i
$516$	7.68205e19	−	1.33057e20i	0.347220	−	0.601402i
$517$	2.12999e20			0.948852
$518$	2.92678e19	−	2.89066e19i	0.128504	−	0.126918i
$519$	−1.43220e20			−0.619797
$520$	2.78233e19	−	4.81913e19i	0.118681	−	0.205562i
$521$	−2.21749e20	−	3.84080e20i	−0.932348	−	1.61487i	−0.779297	−	0.626655i	$-0.784423\pi$
$521$	−2.21749e20	−	3.84080e20i	−0.932348	−	1.61487i	−0.153051	−	0.988218i	$-0.548910\pi$
$522$	1.19512e19	+	2.07002e19i	0.0495318	+	0.0857917i
$523$	−6.11763e19	+	1.05960e20i	−0.249931	+	0.432893i	−0.963506	−	0.267685i	$-0.913741\pi$
$523$	−6.11763e19	+	1.05960e20i	−0.249931	+	0.432893i	0.713575	+	0.700578i	$0.247075\pi$
$524$	4.25081e19			0.171193
$525$	2.60923e20	+	7.16536e19i	1.03590	+	0.284475i
$526$	−1.40515e20			−0.549959
$527$	3.89478e20	−	6.74595e20i	1.50281	−	2.60294i
$528$	−4.92314e19	−	8.52712e19i	−0.187278	−	0.324375i
$529$	1.11407e20	+	1.92963e20i	0.417826	+	0.723696i
$530$	5.27616e19	−	9.13857e19i	0.195096	−	0.337917i
$531$	−1.15887e21			−4.22499
$532$	3.63406e19	+	1.39074e20i	0.130634	+	0.499929i
$533$	1.69590e20			0.601100
$534$	2.05603e20	−	3.56115e20i	0.718571	−	1.24460i
$535$	5.37105e19	+	9.30292e19i	0.185100	+	0.320602i
$536$	1.28868e19	+	2.23205e19i	0.0437933	+	0.0758522i
$537$	1.18342e20	−	2.04975e20i	0.396582	−	0.686900i
$538$	−6.32554e19			−0.209040
$539$	2.20099e20	+	1.30746e20i	0.717303	+	0.426100i
$540$	2.16873e20			0.697031
$541$	−1.88669e19	+	3.26784e19i	−0.0598027	+	0.103581i	−0.894377	−	0.447314i	$-0.852380\pi$
$541$	−1.88669e19	+	3.26784e19i	−0.0598027	+	0.103581i	0.834574	+	0.550896i	$0.185714\pi$
$542$	1.08486e20	+	1.87903e20i	0.339140	+	0.587408i
$543$	3.57291e20	+	6.18846e20i	1.10160	+	1.90802i
$544$	4.44086e19	−	7.69180e19i	0.135044	−	0.233903i
$545$	−3.26011e19			−0.0977818
$546$	−1.14932e20	−	4.39841e20i	−0.340015	−	1.30122i
$547$	−3.70815e20			−1.08206			−0.541031	−	0.841003i	$-0.681966\pi$
$547$	−3.70815e20			−1.08206			−0.541031	+	0.841003i	$0.681966\pi$
$548$	−1.41444e20	+	2.44987e20i	−0.407126	+	0.705163i
$549$	3.91398e20	+	6.77920e20i	1.11129	+	1.92480i
$550$	−6.30035e19	−	1.09125e20i	−0.176459	−	0.305637i
$551$	−1.17772e19	+	2.03986e19i	−0.0325390	+	0.0563591i
$552$	−9.44336e19			−0.257385
$553$	−5.93312e20	−	1.62933e20i	−1.59531	−	0.438097i
$554$	4.70296e19			0.124752
$555$	5.55491e19	−	9.62139e19i	0.145372	−	0.251791i
$556$	−9.27732e19	−	1.60688e20i	−0.239531	−	0.414880i
$557$	1.44839e20	+	2.50868e20i	0.368953	+	0.639046i	0.989402	−	0.145201i	$-0.0463829\pi$
$557$	1.44839e20	+	2.50868e20i	0.368953	+	0.639046i	−0.620449	+	0.784247i	$0.713050\pi$
$558$	−6.15660e20	+	1.06635e21i	−1.54734	+	2.68006i
$559$	−3.30345e20			−0.819181
$560$	4.60799e19	−	4.55111e19i	0.112746	−	0.111354i
$561$	9.48155e20			2.28906
$562$	8.12245e19	−	1.40685e20i	0.193493	−	0.335139i
$563$	1.01470e20	+	1.75751e20i	0.238519	+	0.413128i	0.960290	−	0.279005i	$-0.0900046\pi$
$563$	1.01470e20	+	1.75751e20i	0.238519	+	0.413128i	−0.721770	+	0.692133i	$0.756671\pi$
$564$	−2.20114e20	−	3.81249e20i	−0.510569	−	0.884331i
$565$	1.43199e20	−	2.48028e20i	0.327776	−	0.567724i
$566$	3.97745e20			0.898424
$567$	5.50488e20	−	5.43693e20i	1.22709	−	1.21194i
$568$	7.62474e19			0.167731
$569$	−8.47647e19	+	1.46817e20i	−0.184023	+	0.318738i	−0.943247	−	0.332092i	$-0.892246\pi$
$569$	−8.47647e19	+	1.46817e20i	−0.184023	+	0.318738i	0.759224	+	0.650830i	$0.225579\pi$
$570$	1.94106e20	+	3.36202e20i	0.415890	+	0.720342i
$571$	2.59990e20	+	4.50315e20i	0.549776	+	0.952239i	0.998290	+	0.0584633i	$0.0186201\pi$
$571$	2.59990e20	+	4.50315e20i	0.549776	+	0.952239i	−0.448514	+	0.893776i	$0.648047\pi$
$572$	−1.05853e20	+	1.83343e20i	−0.220919	+	0.382643i
$573$	1.34846e20			0.277765
$574$	1.90336e20	+	5.22693e19i	0.386974	+	0.106269i
$575$	−1.20851e20			−0.242516
$576$	−7.01981e19	+	1.21587e20i	−0.139045	+	0.240834i
$577$	−2.09625e19	−	3.63081e19i	−0.0409850	−	0.0709880i	0.844805	−	0.535074i	$-0.179716\pi$
$577$	−2.09625e19	−	3.63081e19i	−0.0409850	−	0.0709880i	−0.885790	+	0.464086i	$0.846383\pi$
$578$	2.44441e20	+	4.23385e20i	0.471754	+	0.817102i
$579$	8.27525e20	−	1.43332e21i	1.57649	−	2.73056i
$580$	1.06128e19			0.0199581
$581$	−1.46052e20	−	5.58934e20i	−0.271136	−	1.03762i
$582$	4.23877e20			0.776815
$583$	−2.00730e20	+	3.47675e20i	−0.363161	+	0.629013i
$584$	−9.75351e19	−	1.68936e20i	−0.174207	−	0.301735i
$585$	−4.23520e20	−	7.33558e20i	−0.746801	−	1.29350i
$586$	−1.74073e20	+	3.01503e20i	−0.303039	+	0.524879i
$587$	8.79511e20			1.51167			0.755833	−	0.654765i	$-0.227232\pi$
$587$	8.79511e20			1.51167			0.755833	+	0.654765i	$0.227232\pi$
$588$	6.57123e18	−	5.29070e20i	0.0111511	−	0.897807i
$589$	−1.21338e21			−2.03298
$590$	−2.57271e20	+	4.45606e20i	−0.425598	+	0.737158i
$591$	−7.45621e20	−	1.29145e21i	−1.21790	−	2.10947i
$592$	1.97966e19	+	3.42887e19i	0.0319284	+	0.0553016i
$593$	4.85908e20	−	8.41618e20i	0.773828	−	1.34031i	−0.161623	−	0.986852i	$-0.551673\pi$
$593$	4.85908e20	−	8.41618e20i	0.773828	−	1.34031i	0.935451	−	0.353456i	$-0.114994\pi$
$594$	−8.25088e20			−1.29748
$595$	1.57673e20	+	6.03408e20i	0.244839	+	0.936987i
$596$	2.40029e20			0.368059
$597$	−7.77676e20	+	1.34697e21i	−1.17758	+	2.03963i
$598$	1.01521e20	+	1.75840e20i	0.151810	+	0.262942i
$599$	4.93536e20	+	8.54830e20i	0.728816	+	1.26235i	0.957384	+	0.288819i	$0.0932625\pi$
$599$	4.93536e20	+	8.54830e20i	0.728816	+	1.26235i	−0.228568	+	0.973528i	$0.573404\pi$
$600$	−1.30216e20	+	2.25541e20i	−0.189902	+	0.328920i
$601$	2.83823e19			0.0408780			0.0204390	−	0.999791i	$-0.493494\pi$
$601$	2.83823e19			0.0408780			0.0204390	+	0.999791i	$0.493494\pi$
$602$	−3.70756e20	−	1.01816e20i	−0.527369	−	0.144824i
$603$	3.92319e20			0.551137
$604$	−3.37583e20	+	5.84712e20i	−0.468386	+	0.811268i
$605$	7.02885e19	+	1.21743e20i	0.0963206	+	0.166832i
$606$	−3.29670e20	−	5.71006e20i	−0.446206	−	0.772851i
$607$	−1.30906e20	+	2.26735e20i	−0.175002	+	0.303113i	−0.940162	−	0.340728i	$-0.889327\pi$
$607$	−1.30906e20	+	2.26735e20i	−0.175002	+	0.303113i	0.765160	+	0.643840i	$0.222660\pi$
$608$	−1.38351e20			−0.182686
$609$	6.16871e19	−	6.09257e19i	0.0804571	−	0.0794640i
$610$	3.47563e20			0.447775
$611$	−4.73270e20	+	8.19728e20i	−0.602282	+	1.04318i
$612$	−6.75978e20	−	1.17083e21i	−0.849762	−	1.47183i
$613$	4.30621e19	+	7.45857e19i	0.0534738	+	0.0926194i	0.891523	−	0.452975i	$-0.149637\pi$
$613$	4.30621e19	+	7.45857e19i	0.0534738	+	0.0926194i	−0.838049	+	0.545594i	$0.816304\pi$
$614$	4.17665e20	−	7.23418e20i	0.512349	−	0.887414i
$615$	5.33077e20			0.645991
$616$	−1.75310e20	+	1.73146e20i	−0.209870	+	0.207280i
$617$	−1.10789e21			−1.31026			−0.655129	−	0.755517i	$-0.727386\pi$
$617$	−1.10789e21			−1.31026			−0.655129	+	0.755517i	$0.727386\pi$
$618$	1.08493e20	−	1.87915e20i	0.126762	−	0.219557i
$619$	1.75535e20	+	3.04035e20i	0.202621	+	0.350949i	0.949372	−	0.314154i	$-0.101721\pi$
$619$	1.75535e20	+	3.04035e20i	0.202621	+	0.350949i	−0.746751	+	0.665103i	$0.768388\pi$
$620$	2.73354e20	+	4.73464e20i	0.311737	+	0.539945i
$621$	−3.95663e20	+	6.85308e20i	−0.445798	+	0.772145i
$622$	−3.13516e20			−0.349006
$623$	−9.92295e20	−	2.72500e20i	−1.09139	−	0.299714i
$624$	4.37555e20			0.475498
$625$	2.04516e19	−	3.54232e19i	0.0219597	−	0.0380354i
$626$	2.13819e20	+	3.70346e20i	0.226850	+	0.392917i
$627$	−7.38473e20	−	1.27907e21i	−0.774155	−	1.34088i
$628$	1.82495e20	−	3.16091e20i	0.189040	−	0.327427i
$629$	−3.81266e20			−0.390254
$630$	−2.49239e20	−	9.53826e20i	−0.252094	−	0.964751i
$631$	5.91534e20			0.591234			0.295617	−	0.955307i	$-0.404475\pi$
$631$	5.91534e20			0.591234			0.295617	+	0.955307i	$0.404475\pi$
$632$	2.96098e20	−	5.12857e20i	0.292454	−	0.506545i
$633$	1.12118e21	+	1.94195e21i	1.09433	+	1.89544i
$634$	3.04603e20	+	5.27587e20i	0.293808	+	0.508891i
$635$	2.22298e20	−	3.85032e20i	0.211901	−	0.367023i
$636$	8.29742e20			0.781654
$637$	−9.92221e20	+	5.56544e20i	−0.923767	+	0.518148i
$638$	−4.03760e19			−0.0371508
$639$	5.80311e20	−	1.00513e21i	0.527721	−	0.914039i
$640$	3.11681e19	+	5.39848e19i	0.0280131	+	0.0485201i
$641$	−6.46374e20	−	1.11955e21i	−0.574181	−	0.994511i	−0.996130	−	0.0878914i	$-0.971987\pi$
$641$	−6.46374e20	−	1.11955e21i	−0.574181	−	0.994511i	0.421949	−	0.906620i	$-0.361346\pi$
$642$	−4.22332e20	+	7.31500e20i	−0.370801	+	0.642247i
$643$	1.24553e21			1.08087			0.540435	−	0.841386i	$-0.318260\pi$
$643$	1.24553e21			1.08087			0.540435	+	0.841386i	$0.318260\pi$
$644$	5.97448e19	+	2.28641e20i	0.0512456	+	0.196114i
$645$	−1.03838e21			−0.880359
$646$	6.66132e20	−	1.15377e21i	0.558234	−	0.966889i
$647$	−1.91677e20	−	3.31994e20i	−0.158777	−	0.275010i	0.775651	−	0.631162i	$-0.217422\pi$
$647$	−1.91677e20	−	3.31994e20i	−0.158777	−	0.275010i	−0.934428	+	0.356152i	$0.884088\pi$
$648$	3.72347e20	+	6.44923e20i	0.304884	+	0.528075i
$649$	9.78780e20	−	1.69530e21i	0.792228	−	1.37218i
$650$	5.59959e20			0.448029
$651$	4.30694e21	+	1.18275e21i	3.40652	+	0.935486i
$652$	3.93623e20			0.307768
$653$	6.59318e19	−	1.14197e20i	0.0509619	−	0.0882687i	−0.839419	−	0.543485i	$-0.817105\pi$
$653$	6.59318e19	−	1.14197e20i	0.0509619	−	0.0882687i	0.890381	+	0.455216i	$0.150438\pi$
$654$	−1.28173e20	−	2.22002e20i	−0.0979408	−	0.169638i
$655$	−1.43646e20	−	2.48802e20i	−0.108513	−	0.187951i
$656$	−9.49890e19	+	1.64526e20i	−0.0709405	+	0.122873i
$657$	−2.96932e21			−2.19238
$658$	−7.83812e20	+	7.74138e20i	−0.572161	+	0.565098i
$659$	−9.87739e20			−0.712856			−0.356428	−	0.934323i	$-0.616005\pi$
$659$	−9.87739e20			−0.712856			−0.356428	+	0.934323i	$0.616005\pi$
$660$	−3.32731e20	+	5.76306e20i	−0.237418	+	0.411220i
$661$	−2.80847e19	−	4.86441e19i	−0.0198134	−	0.0343178i	0.855949	−	0.517061i	$-0.172974\pi$
$661$	−2.80847e19	−	4.86441e19i	−0.0198134	−	0.0343178i	−0.875762	+	0.482743i	$0.839641\pi$
$662$	4.11119e19	+	7.12080e19i	0.0286769	+	0.0496699i
$663$	−2.10674e21	+	3.64898e21i	−1.45298	+	2.51663i
$664$	5.56029e20			0.379173
$665$	6.91201e20	−	6.82669e20i	0.466060	−	0.460307i
$666$	6.02679e20			0.401818
$667$	−1.93619e19	+	3.35358e19i	−0.0127645	+	0.0221088i
$668$	−4.10976e20	−	7.11831e20i	−0.267913	−	0.464038i
$669$	4.06182e20	+	7.03527e20i	0.261833	+	0.453508i
$670$	8.70953e19	−	1.50853e20i	0.0555180	−	0.0961599i
$671$	−1.32230e21			−0.833508
$672$	4.91081e20	+	1.34859e20i	0.306114	+	0.0840639i
$673$	8.85823e19			0.0546052			0.0273026	−	0.999627i	$-0.491308\pi$
$673$	8.85823e19			0.0546052			0.0273026	+	0.999627i	$0.491308\pi$
$674$	2.76795e20	−	4.79423e20i	0.168736	−	0.292260i
$675$	1.09117e21	+	1.88996e21i	0.657832	+	1.13940i
$676$	−5.10822e19	−	8.84770e19i	−0.0304558	−	0.0527509i
$677$	1.15283e20	−	1.99676e20i	0.0679753	−	0.117737i	−0.830035	−	0.557712i	$-0.811679\pi$
$677$	1.15283e20	−	1.99676e20i	0.0679753	−	0.117737i	0.898010	+	0.439975i	$0.145013\pi$
$678$	2.25198e21			1.31323
$679$	−2.68172e20	−	1.02628e21i	−0.154664	−	0.591894i
$680$	−6.00272e20			−0.342398
$681$	2.02743e21	−	3.51161e21i	1.14378	−	1.98109i
$682$	−1.03997e21	−	1.80128e21i	−0.580281	−	1.00508i
$683$	1.08437e21	+	1.87818e21i	0.598442	+	1.03653i	0.993051	+	0.117683i	$0.0375467\pi$
$683$	1.08437e21	+	1.87818e21i	0.598442	+	1.03653i	−0.394609	+	0.918849i	$0.629120\pi$
$684$	−1.05298e21	+	1.82381e21i	−0.574775	+	0.995539i
$685$	1.91190e21			1.03225
$686$	−1.28513e21	+	3.18814e20i	−0.686303	+	0.170257i
$687$	−2.64759e20			−0.139854
$688$	1.85029e20	−	3.20480e20i	0.0966780	−	0.167451i
$689$	−8.92020e20	−	1.54502e21i	−0.461031	−	0.798529i
$690$	3.19115e20	+	5.52724e20i	0.163147	+	0.282579i
$691$	2.54582e20	−	4.40950e20i	0.128749	−	0.222999i	−0.794443	−	0.607338i	$-0.792237\pi$
$691$	2.54582e20	−	4.40950e20i	0.128749	−	0.222999i	0.923192	+	0.384339i	$0.125571\pi$
$692$	−3.44960e20			−0.172573
$693$	9.48225e20	+	3.62881e21i	0.469258	+	1.79583i
$694$	2.84054e20			0.139061
$695$	−6.27008e20	+	1.08601e21i	−0.303660	+	0.525954i
$696$	4.17247e19	+	7.22694e19i	0.0199905	+	0.0346246i
$697$	−9.14704e20	−	1.58431e21i	−0.433546	−	0.750923i
$698$	2.08301e20	−	3.60788e20i	0.0976732	−	0.169175i
$699$	−1.02878e21			−0.477247
$700$	6.28458e20	+	1.72585e20i	0.288430	+	0.0792076i
$701$	2.29854e21			1.04368			0.521840	−	0.853043i	$-0.325246\pi$
$701$	2.29854e21			1.04368			0.521840	+	0.853043i	$0.325246\pi$
$702$	1.83329e21	−	3.17535e21i	0.823575	−	1.42647i
$703$	2.96950e20	+	5.14332e20i	0.131983	+	0.228601i
$704$	−1.18578e20	−	2.05384e20i	−0.0521448	−	0.0903174i
$705$	−1.48764e21	+	2.57667e21i	−0.647262	+	1.12109i
$706$	−1.53786e21			−0.662036
$707$	−1.17394e21	+	1.15945e21i	−0.500033	+	0.493861i
$708$	−4.04590e21			−1.70516
$709$	6.98128e20	−	1.20919e21i	0.291131	−	0.504253i	−0.682947	−	0.730468i	$-0.739302\pi$
$709$	6.98128e20	−	1.20919e21i	0.291131	−	0.504253i	0.974077	+	0.226215i	$0.0726352\pi$
$710$	−2.57659e20	−	4.46279e20i	−0.106318	−	0.184149i
$711$	−4.50714e21	−	7.80660e21i	−1.84026	−	3.18742i
$712$	4.95215e20	−	8.57737e20i	0.200075	−	0.346541i
$713$	−1.99483e21			−0.797507
$714$	−3.48910e21	+	3.44604e21i	−1.38031	+	1.36327i
$715$	1.43082e21			0.560130
$716$	2.85039e20	−	4.93702e20i	0.110422	−	0.191257i
$717$	−1.54376e21	−	2.67387e21i	−0.591815	−	1.02505i
$718$	4.80221e20	+	8.31767e20i	0.182183	+	0.315550i
$719$	−5.56884e20	+	9.64551e20i	−0.209073	+	0.362125i	−0.951423	−	0.307888i	$-0.900378\pi$
$719$	−5.56884e20	+	9.64551e20i	−0.209073	+	0.362125i	0.742350	+	0.670013i	$0.233711\pi$
$720$	9.48869e20			0.352543
$721$	−5.23616e20	−	1.43793e20i	−0.192530	−	0.0528718i
$722$	−1.32091e20			−0.0480666
$723$	1.30849e19	−	2.26637e19i	0.00471230	−	0.00816194i
$724$	8.60569e20	+	1.49055e21i	0.306723	+	0.531260i
$725$	5.33970e19	+	9.24862e19i	0.0188357	+	0.0326244i
$726$	−5.52687e20	+	9.57283e20i	−0.192955	+	0.334207i
$727$	3.13110e21			1.08190			0.540951	−	0.841054i	$-0.318064\pi$
$727$	3.13110e21			1.08190			0.540951	+	0.841054i	$0.318064\pi$
$728$	−2.76826e20	−	1.05940e21i	−0.0946720	−	0.362305i
$729$	−3.32236e20			−0.112458
$730$	−6.59192e20	+	1.14175e21i	−0.220846	+	0.382517i
$731$	1.78176e21	+	3.08609e21i	0.590837	+	1.02336i
$732$	1.36646e21	+	2.36679e21i	0.448503	+	0.776830i
$733$	1.56079e20	−	2.70337e20i	0.0507067	−	0.0878266i	−0.839558	−	0.543270i	$-0.817186\pi$
$733$	1.56079e20	−	2.70337e20i	0.0507067	−	0.0878266i	0.890265	+	0.455444i	$0.150519\pi$
$734$	−3.18449e21			−1.02405
$735$	−3.11887e21	+	1.74940e21i	−0.992756	+	0.556845i
$736$	−2.27452e20			−0.0716650
$737$	−3.31352e20	+	5.73919e20i	−0.103344	+	0.178996i
$738$	1.44590e21	+	2.50438e21i	0.446392	+	0.773173i
$739$	−1.88749e21	−	3.26922e21i	−0.576833	−	0.999104i	−0.995840	−	0.0911212i	$-0.970955\pi$
$739$	−1.88749e21	−	3.26922e21i	−0.576833	−	0.999104i	0.419007	−	0.907983i	$-0.362378\pi$
$740$	1.33795e20	−	2.31740e20i	0.0404765	−	0.0701074i
$741$	6.56336e21			1.96557
$742$	−5.24948e20	−	2.00895e21i	−0.155628	−	0.595581i
$743$	2.71859e21			0.797862			0.398931	−	0.916981i	$-0.369381\pi$
$743$	2.71859e21			0.797862			0.398931	+	0.916981i	$0.369381\pi$
$744$	−2.14942e21	+	3.72290e21i	−0.624488	+	1.08165i
$745$	−8.11119e20	−	1.40490e21i	−0.233299	−	0.404086i
$746$	−1.53037e21	−	2.65068e21i	−0.435768	−	0.754773i
$747$	4.23188e21	−	7.32984e21i	1.19297	−	2.06628i
$748$	2.28372e21			0.637355
$749$	2.03829e21	+	5.59747e20i	0.563186	+	0.154660i
$750$	4.70243e21			1.28636
$751$	1.42878e21	−	2.47472e21i	0.386959	−	0.670233i	−0.605080	−	0.796165i	$-0.706859\pi$
$751$	1.42878e21	−	2.47472e21i	0.386959	−	0.670233i	0.992039	+	0.125932i	$0.0401920\pi$
$752$	−5.30166e20	−	9.18274e20i	−0.142160	−	0.246229i
$753$	2.23695e20	+	3.87452e20i	0.0593874	+	0.102862i
$754$	8.97129e19	−	1.55387e20i	0.0235814	−	0.0408442i
$755$	4.56312e21			1.18757
$756$	3.03623e21	−	2.99875e21i	0.782386	−	0.772729i
$757$	−4.49236e21			−1.14619			−0.573093	−	0.819490i	$-0.694257\pi$
$757$	−4.49236e21			−1.14619			−0.573093	+	0.819490i	$0.694257\pi$
$758$	−2.50872e21	+	4.34522e21i	−0.633771	+	1.09772i
$759$	−1.21407e21	−	2.10283e21i	−0.303689	−	0.526005i
$760$	4.67524e20	+	8.09775e20i	0.115798	+	0.200568i
$761$	−3.60948e20	+	6.25180e20i	−0.0885237	+	0.153328i	−0.906887	−	0.421373i	$-0.861548\pi$
$761$	−3.60948e20	+	6.25180e20i	−0.0885237	+	0.153328i	0.818364	+	0.574701i	$0.194882\pi$
$762$	3.49591e21			0.848982
$763$	−4.56417e20	+	4.50783e20i	−0.109756	+	0.108401i
$764$	3.24789e20			0.0773396
$765$	−4.56861e21	+	7.91306e21i	−1.07727	+	1.86588i
$766$	1.51078e21	+	2.61674e21i	0.352764	+	0.611005i
$767$	4.34957e21	+	7.53368e21i	1.00573	+	1.74198i
$768$	−2.45079e20	+	4.24489e20i	−0.0561173	+	0.0971980i
$769$	7.26296e21			1.64690			0.823448	−	0.567391i	$-0.192047\pi$
$769$	7.26296e21			1.64690			0.823448	+	0.567391i	$0.192047\pi$
$770$	1.60585e21	+	4.40991e20i	0.360598	+	0.0990261i
$771$	−9.26158e21			−2.05957
$772$	1.99317e21	−	3.45228e21i	0.438950	−	0.760284i
$773$	3.33809e21	+	5.78175e21i	0.728035	+	1.26099i	0.957712	+	0.287727i	$0.0928996\pi$
$773$	3.33809e21	+	5.78175e21i	0.728035	+	1.26099i	−0.229677	+	0.973267i	$0.573767\pi$
$774$	−2.81648e21	−	4.87829e21i	−0.608344	−	1.05368i
$775$	−2.75071e21	+	4.76436e21i	−0.588412	+	1.01916i
$776$	1.02095e21			0.216292
$777$	−5.52683e20	−	2.11509e21i	−0.115963	−	0.443784i
$778$	−2.52303e21			−0.524294
$779$	−1.42484e21	+	2.46790e21i	−0.293248	+	0.507921i
$780$	−1.47861e21	−	2.56103e21i	−0.301401	−	0.522042i
$781$	9.80259e20	+	1.69786e21i	0.197906	+	0.342783i
$782$	1.09514e21	−	1.89683e21i	0.218986	−	0.379296i
$783$	6.99281e20			0.138496
$784$	1.58274e19	−	1.27432e21i	0.00310485	−	0.249981i
$785$	−2.46679e21			−0.479302
$786$	1.12950e21	−	1.95636e21i	0.217380	−	0.376512i
$787$	2.52764e21	+	4.37801e21i	0.481843	+	0.834576i	0.999783	−	0.0208410i	$-0.00663438\pi$
$787$	2.52764e21	+	4.37801e21i	0.481843	+	0.834576i	−0.517940	+	0.855417i	$0.673301\pi$
$788$	−1.79590e21	−	3.11059e21i	−0.339106	−	0.587349i
$789$	−3.73370e21	+	6.46696e21i	−0.698332	+	1.20955i
$790$	−4.00236e21			−0.741503
$791$	−1.42475e21	−	5.45245e21i	−0.261466	−	1.00062i
$792$	−3.60995e21			−0.656240
$793$	2.93805e21	−	5.08886e21i	0.529067	−	0.916371i
$794$	−1.56147e21	−	2.70455e21i	−0.278535	−	0.482437i
$795$	−2.80391e21	−	4.85651e21i	−0.495462	−	0.858165i
$796$	−1.87311e21	+	3.24432e21i	−0.327880	+	0.567904i
$797$	−1.08398e22			−1.87967			−0.939836	−	0.341626i	$-0.889022\pi$
$797$	−1.08398e22			−1.87967			−0.939836	+	0.341626i	$0.889022\pi$
$798$	7.36625e21	+	2.02289e21i	1.26539	+	0.347497i
$799$	1.02105e22			1.73759
$800$	−3.13638e20	+	5.43237e20i	−0.0528754	+	0.0915829i
$801$	−7.53805e21	−	1.30563e22i	−1.25897	−	2.18060i
$802$	−7.20354e20	−	1.24769e21i	−0.119190	−	0.206442i
$803$	2.50788e21	−	4.34378e21i	0.411093	−	0.712034i
$804$	1.36968e21			0.222433
$805$	1.13635e21	−	1.12232e21i	0.182828	−	0.180571i
$806$	9.24299e21			1.47333
$807$	−1.68079e21	+	2.91121e21i	−0.265437	+	0.459751i
$808$	−7.94043e20	−	1.37532e21i	−0.124239	−	0.215189i
$809$	5.25457e21	+	9.10119e21i	0.814561	+	1.41086i	0.909643	+	0.415391i	$0.136355\pi$
$809$	5.25457e21	+	9.10119e21i	0.814561	+	1.41086i	−0.0950818	+	0.995469i	$0.530311\pi$
$810$	2.51651e21	−	4.35872e21i	0.386510	−	0.669455i
$811$	−8.89807e21			−1.35406			−0.677032	−	0.735953i	$-0.736734\pi$
$811$	−8.89807e21			−1.35406			−0.677032	+	0.735953i	$0.736734\pi$
$812$	1.48579e20	−	1.46745e20i	0.0224021	−	0.0221255i
$813$	1.15306e22			1.72255
$814$	−5.09022e20	+	8.81651e20i	−0.0753448	+	0.130501i
$815$	−1.33015e21	−	2.30389e21i	−0.195083	−	0.337894i
$816$	−2.36001e21	−	4.08765e21i	−0.342955	−	0.594015i
$817$	2.77545e21	−	4.80723e21i	0.399640	−	0.692196i
$818$	−1.89555e21			−0.270449
$819$	−1.60724e22	−	4.41374e21i	−2.27222	−	0.623989i
$820$	1.28397e21			0.179866
$821$	3.76617e19	−	6.52321e19i	0.00522789	−	0.00905498i	−0.863400	−	0.504521i	$-0.831669\pi$
$821$	3.76617e19	−	6.52321e19i	0.00522789	−	0.00905498i	0.868628	+	0.495466i	$0.165003\pi$
$822$	7.51674e21	+	1.30194e22i	1.03393	+	1.79082i
$823$	−2.83888e21	−	4.91708e21i	−0.386944	−	0.670206i	0.605093	−	0.796155i	$-0.293136\pi$
$823$	−2.83888e21	−	4.91708e21i	−0.386944	−	0.670206i	−0.992037	+	0.125948i	$0.959803\pi$
$824$	2.61315e20	−	4.52612e20i	0.0352948	−	0.0611324i
$825$	−6.69639e21			−0.896264
$826$	2.55970e21	+	9.79585e21i	0.339499	+	1.29925i
$827$	−1.32985e22			−1.74787			−0.873937	−	0.486040i	$-0.838441\pi$
$827$	−1.32985e22			−1.74787			−0.873937	+	0.486040i	$0.838441\pi$
$828$	−1.73112e21	+	2.99838e21i	−0.225475	+	0.390535i
$829$	−2.12490e21	−	3.68044e21i	−0.274271	−	0.475052i	0.695680	−	0.718352i	$-0.255103\pi$
$829$	−2.12490e21	−	3.68044e21i	−0.274271	−	0.475052i	−0.969951	+	0.243300i	$0.921770\pi$
$830$	−1.87897e21	−	3.25446e21i	−0.240344	−	0.416288i
$831$	1.24965e21	−	2.16445e21i	0.158409	−	0.274372i
$832$	1.05389e21			0.132395
$833$	1.05509e22	+	6.26755e21i	1.31357	+	0.780298i
$834$	−9.86049e21			−1.21661
$835$	−2.77758e21	+	4.81092e21i	−0.339640	+	0.588274i
$836$	−1.77868e21	−	3.08077e21i	−0.215552	−	0.373347i
$837$	1.80115e22	+	3.11968e22i	2.16326	+	3.74688i
$838$	−2.52724e21	+	4.37731e21i	−0.300827	+	0.521047i
$839$	3.87280e20			0.0456888			0.0228444	−	0.999739i	$-0.492728\pi$
$839$	3.87280e20			0.0456888			0.0228444	+	0.999739i	$0.492728\pi$
$840$	−8.70154e20	−	3.33004e21i	−0.101742	−	0.389363i
$841$	−8.59497e21			−0.996034
$842$	1.20874e21	−	2.09360e21i	0.138833	−	0.240465i
$843$	−4.31651e21	−	7.47642e21i	−0.491390	−	0.851113i
$844$	2.70048e21	+	4.67736e21i	0.304700	+	0.527756i
$845$	−3.45240e20	+	5.97972e20i	−0.0386096	+	0.0668738i
$846$	−1.61401e22			−1.78908
$847$	2.66742e21	+	7.32516e20i	0.293066	+	0.0804807i
$848$	1.99851e21			0.217640
$849$	1.05687e22	−	1.83055e22i	1.14081	−	1.97594i
$850$	−3.02020e21	−	5.23114e21i	−0.323143	−	0.559699i
$851$	4.88192e20	+	8.45574e20i	0.0517749	+	0.0896768i
$852$	2.02601e21	−	3.50915e21i	0.212983	−	0.368897i
$853$	−1.05026e22			−1.09441			−0.547203	−	0.837000i	$-0.684308\pi$
$853$	−1.05026e22			−1.09441			−0.547203	+	0.837000i	$0.684308\pi$
$854$	4.86590e21	−	4.80584e21i	0.502607	−	0.496404i
$855$	1.42331e22			1.45732
$856$	−1.01723e21	+	1.76189e21i	−0.103244	+	0.178824i
$857$	−2.05546e21	−	3.56016e21i	−0.206801	−	0.358190i	0.743904	−	0.668286i	$-0.232972\pi$
$857$	−2.05546e21	−	3.56016e21i	−0.206801	−	0.358190i	−0.950705	+	0.310097i	$0.899639\pi$
$858$	5.62535e21	+	9.74338e21i	0.561041	+	0.971751i
$859$	−8.25734e21	+	1.43021e22i	−0.816378	+	1.41401i	0.0919555	+	0.995763i	$0.470688\pi$
$859$	−8.25734e21	+	1.43021e22i	−0.816378	+	1.41401i	−0.908334	+	0.418246i	$0.862645\pi$
$860$	−2.50105e21			−0.245123
$861$	7.46311e21	−	7.37099e21i	0.725097	−	0.716147i
$862$	5.79361e21			0.558014
$863$	−2.20067e21	+	3.81167e21i	−0.210123	+	0.363944i	−0.951753	−	0.306866i	$-0.900720\pi$
$863$	−2.20067e21	+	3.81167e21i	−0.210123	+	0.363944i	0.741630	+	0.670809i	$0.234053\pi$
$864$	2.05369e21	+	3.55709e21i	0.194393	+	0.336699i
$865$	1.16571e21	+	2.01906e21i	0.109388	+	0.189465i
$866$	5.29476e21	−	9.17079e21i	0.492563	−	0.853145i
$867$	2.59807e22			2.39611
$868$	1.03737e22	+	2.84878e21i	0.948495	+	0.260472i
$869$	1.52269e22			1.38027
$870$	2.81997e20	−	4.88433e20i	0.0253425	−	0.0438946i
$871$	−1.47249e21	−	2.55042e21i	−0.131194	−	0.227235i
$872$	−3.08717e20	−	5.34714e20i	−0.0272701	−	0.0472332i
$873$	7.77034e21	−	1.34586e22i	0.680508	−	1.17867i
$874$	−3.41180e21			−0.296243
$875$	−2.97506e21	−	1.13854e22i	−0.256115	−	0.980142i
$876$	−1.03666e22			−0.884822
$877$	1.08511e22	−	1.87947e22i	0.918286	−	1.59052i	0.116269	−	0.993218i	$-0.462906\pi$
$877$	1.08511e22	−	1.87947e22i	0.918286	−	1.59052i	0.802017	−	0.597301i	$-0.203760\pi$
$878$	6.55388e19	+	1.13517e20i	0.00549908	+	0.00952468i
$879$	9.25074e21	+	1.60227e22i	0.769591	+	1.33297i
$880$	−8.01414e20	+	1.38809e21i	−0.0661054	+	0.114498i
$881$	−1.35213e22			−1.10585			−0.552927	−	0.833230i	$-0.686489\pi$
$881$	−1.35213e22			−1.10585			−0.552927	+	0.833230i	$0.686489\pi$
$882$	−1.66781e22	−	9.90733e21i	−1.35249	−	0.803419i
$883$	−3.50656e21			−0.281953			−0.140976	−	0.990013i	$-0.545024\pi$
$883$	−3.50656e21			−0.281953			−0.140976	+	0.990013i	$0.545024\pi$
$884$	−5.07428e21	+	8.78891e21i	−0.404560	+	0.700718i
$885$	1.36721e22	+	2.36808e22i	1.08084	+	1.87207i
$886$	−3.85593e21	−	6.67866e21i	−0.302257	−	0.523524i
$887$	2.26310e20	−	3.91981e20i	0.0175905	−	0.0304676i	−0.857096	−	0.515156i	$-0.827734\pi$
$887$	2.26310e20	−	3.91981e20i	0.0175905	−	0.0304676i	0.874687	+	0.484689i	$0.161067\pi$
$888$	2.10410e21			0.162169
$889$	−2.21174e21	−	8.46423e21i	−0.169033	−	0.646881i
$890$	−6.69382e21			−0.507282
$891$	−9.57400e21	+	1.65827e22i	−0.719467	+	1.24615i
$892$	9.78328e20	+	1.69451e21i	0.0729034	+	0.126272i
$893$	−7.95252e21	−	1.37742e22i	−0.587650	−	1.01784i
$894$	6.37793e21	−	1.10469e22i	0.467357	−	0.809486i
$895$	−3.85288e21			−0.279970
$896$	1.18282e21	+	3.24820e20i	0.0852329	+	0.0234063i
$897$	1.07903e22			0.771064
$898$	−2.78808e21	+	4.82909e21i	−0.197575	+	0.342210i
$899$	8.81400e20	+	1.52663e21i	0.0619406	+	0.107284i
$900$	4.77413e21	+	8.26904e21i	0.332717	+	0.576284i
$901$	−9.62242e21	+	1.66665e22i	−0.665041	+	1.15188i
$902$	−4.88483e21			−0.334811
$903$	−1.45374e22	+	1.43580e22i	−0.988165	+	0.975968i
$904$	5.42412e21			0.365650
$905$	5.81616e21	−	1.00739e22i	0.388841	−	0.673493i
$906$	1.79402e22	+	3.10733e22i	1.18950	+	2.06028i
$907$	−1.12461e22	−	1.94789e22i	−0.739518	−	1.28088i	−0.952712	−	0.303873i	$-0.901720\pi$
$907$	−1.12461e22	−	1.94789e22i	−0.739518	−	1.28088i	0.213194	−	0.977010i	$-0.431613\pi$
$908$	4.88326e21	−	8.45806e21i	0.318468	−	0.551603i
$909$	−2.41735e22			−1.56354
$910$	−5.26525e21	+	5.20026e21i	−0.337760	+	0.333591i
$911$	1.73489e22			1.10379			0.551893	−	0.833915i	$-0.313906\pi$
$911$	1.73489e22			1.10379			0.551893	+	0.833915i	$0.313906\pi$
$912$	−3.67620e21	+	6.36736e21i	−0.231973	+	0.401789i
$913$	7.14848e21	+	1.23815e22i	0.447387	+	0.774896i
$914$	7.62413e21	+	1.32054e22i	0.473254	+	0.819700i
$915$	9.23526e21	−	1.59959e22i	0.568579	−	0.984808i
$916$	−6.37696e20			−0.0389402
$917$	−5.45129e21	−	1.49701e21i	−0.330164	−	0.0906683i
$918$	−3.95523e22			−2.37603
$919$	−7.41318e21	+	1.28400e22i	−0.441711	+	0.765065i	−0.997817	−	0.0660460i	$-0.978962\pi$
$919$	−7.41318e21	+	1.28400e22i	−0.441711	+	0.765065i	0.556106	+	0.831111i	$0.312295\pi$
$920$	7.68620e20	+	1.33129e21i	0.0454258	+	0.0786798i
$921$	−2.21960e22	−	3.84446e22i	−1.30115	−	2.25366i
$922$	5.36536e21	−	9.29307e21i	0.311973	−	0.540353i
$923$	−8.71229e21			−0.502481
$924$	3.31048e21	+	1.26691e22i	0.189388	+	0.724778i
$925$	2.69271e21			0.152801
$926$	8.42896e21	−	1.45994e22i	0.474451	−	0.821774i
$927$	−3.97769e21	−	6.88956e21i	−0.222092	−	0.384674i
$928$	1.00498e20	+	1.74068e20i	0.00556606	+	0.00964069i
$929$	−6.40893e21	+	1.11006e22i	−0.352102	+	0.609858i	−0.986617	−	0.163052i	$-0.947866\pi$
$929$	−6.40893e21	+	1.11006e22i	−0.352102	+	0.609858i	0.634516	+	0.772910i	$0.281200\pi$
$930$	2.90537e22			1.58336
$931$	2.37412e20	−	1.91148e22i	0.0128346	−	1.03335i
$932$	−2.47791e21			−0.132882
$933$	−8.33060e21	+	1.44290e22i	−0.443163	+	0.767581i
$934$	−6.28790e21	−	1.08910e22i	−0.331821	−	0.574731i
$935$	−7.71728e21	−	1.33667e22i	−0.403996	−	0.699741i
$936$	8.02108e21	−	1.38929e22i	0.416547	−	0.721481i
$937$	4.63011e21			0.238531			0.119265	−	0.992862i	$-0.461946\pi$
$937$	4.63011e21			0.238531			0.119265	+	0.992862i	$0.461946\pi$
$938$	−8.66549e20	−	3.31624e21i	−0.0442866	−	0.169483i
$939$	2.27260e22			1.15221
$940$	−3.58313e21	+	6.20616e21i	−0.180220	+	0.312151i
$941$	9.33997e21	+	1.61773e22i	0.466040	+	0.807205i	0.999248	−	0.0387792i	$-0.0123469\pi$
$941$	9.33997e21	+	1.61773e22i	0.466040	+	0.807205i	−0.533208	+	0.845984i	$0.679014\pi$
$942$	−9.69833e21	−	1.67980e22i	−0.480082	−	0.831526i
$943$	−2.34247e21	+	4.05728e21i	−0.115037	+	0.199249i
$944$	−9.74494e21			−0.474776
$945$	−2.78120e22	−	7.63763e21i	−1.34429	−	0.369164i
$946$	9.51518e21			0.456282
$947$	−5.61848e21	+	9.73149e21i	−0.267297	+	0.462972i	−0.968163	−	0.250321i	$-0.919464\pi$
$947$	−5.61848e21	+	9.73149e21i	−0.267297	+	0.462972i	0.700866	+	0.713293i	$0.252797\pi$
$948$	−1.57355e22	−	2.72547e22i	−0.742709	−	1.28641i
$949$	1.11447e22	+	1.93032e22i	0.521881	+	0.903925i
$950$	−4.70459e21	+	8.14859e21i	−0.218572	+	0.378578i
$951$	3.23750e22			1.49230
$952$	−8.40384e21	+	8.30011e21i	−0.384327	+	0.379583i
$953$	1.02511e22			0.465131			0.232566	−	0.972581i	$-0.425288\pi$
$953$	1.02511e22			0.465131			0.232566	+	0.972581i	$0.425288\pi$
$954$	1.52105e22	−	2.63453e22i	0.684747	−	1.18602i
$955$	−1.09755e21	−	1.90101e21i	−0.0490227	−	0.0849099i
$956$	−3.71829e21	−	6.44028e21i	−0.164782	−	0.285411i
$957$	−1.07285e21	+	1.85823e21i	−0.0471737	+	0.0817073i
$958$	1.67681e22			0.731547
$959$	2.67666e22	−	2.64363e22i	1.15866	−	1.14435i
$960$	3.31273e21			0.142283
$961$	−3.36721e22	+	5.83217e22i	−1.43498	+	2.48545i
$962$	−2.26203e21	−	3.91794e21i	−0.0956499	−	0.165670i
$963$	1.54840e22	+	2.68191e22i	0.649661	+	1.12525i
$964$	3.15162e19	−	5.45877e19i	0.00131207	−	0.00227257i
$965$	−2.69418e22			−1.11294
$966$	1.21103e22	+	3.32568e21i	0.496393	+	0.136317i
$967$	−3.34613e22			−1.36096			−0.680478	−	0.732769i	$-0.738228\pi$
$967$	−3.34613e22			−1.36096			−0.680478	+	0.732769i	$0.738228\pi$
$968$	−1.33120e21	+	2.30571e21i	−0.0537253	+	0.0930549i
$969$	−3.54002e22	−	6.13150e22i	−1.41768	−	2.45549i
$970$	−3.45005e21	−	5.97566e21i	−0.137100	−	0.237464i
$971$	−1.11584e22	+	1.93270e22i	−0.440006	+	0.762113i	−0.997689	−	0.0679409i	$-0.978357\pi$
$971$	−1.11584e22	+	1.93270e22i	−0.440006	+	0.762113i	0.557683	+	0.830054i	$0.311690\pi$
$972$	1.14722e22			0.448900
$973$	6.23838e21	+	2.38740e22i	0.242229	+	0.926998i
$974$	2.17078e22			0.836418
$975$	1.48789e22	−	2.57711e22i	0.568902	−	0.985367i
$976$	3.29126e21	+	5.70063e21i	0.124879	+	0.216296i
$977$	−1.17182e20	−	2.02965e20i	−0.00441216	−	0.00764208i	0.863811	−	0.503816i	$-0.168071\pi$
$977$	−1.17182e20	−	2.02965e20i	−0.00441216	−	0.00764208i	−0.868223	+	0.496174i	$0.834738\pi$
$978$	1.04592e22	−	1.81158e22i	0.390801	−	0.676886i
$979$	2.54665e22			0.944277
$980$	−7.51211e21	+	4.21360e21i	−0.276418	+	0.155045i
$981$	−9.39846e21			−0.343193
$982$	−1.37864e22	+	2.38787e22i	−0.499590	+	0.865315i
$983$	2.14541e22	+	3.71596e22i	0.771540	+	1.33635i	0.936719	+	0.350083i	$0.113847\pi$
$983$	2.14541e22	+	3.71596e22i	0.771540	+	1.33635i	−0.165178	+	0.986264i	$0.552820\pi$
$984$	5.04800e21	+	8.74339e21i	0.180159	+	0.312045i
$985$	−1.21376e22	+	2.10229e22i	−0.429894	+	0.744598i
$986$	−1.93551e21			−0.0680328
$987$	1.48012e22	+	5.66435e22i	0.516319	+	1.97593i
$988$	1.58085e22			0.547284
$989$	4.56291e21	−	7.90319e21i	0.156772	−	0.271538i
$990$	1.21989e22	+	2.11292e22i	0.415967	+	0.720475i
$991$	8.73975e21	+	1.51377e22i	0.295765	+	0.512280i	0.975163	−	0.221490i	$-0.0710922\pi$
$991$	8.73975e21	+	1.51377e22i	0.295765	+	0.512280i	−0.679398	+	0.733770i	$0.737759\pi$
$992$	−5.17708e21	+	8.96697e21i	−0.173879	+	0.301168i
$993$	4.36962e21			0.145655
$994$	−9.77806e21	−	2.68521e21i	−0.323485	−	0.0888343i
$995$	2.53188e22			0.831324
$996$	1.47745e22	−	2.55902e22i	0.481469	−	0.833930i
$997$	−1.03392e21	−	1.79080e21i	−0.0334405	−	0.0579207i	0.848821	−	0.528681i	$-0.177313\pi$
$997$	−1.03392e21	−	1.79080e21i	−0.0334405	−	0.0579207i	−0.882261	+	0.470760i	$0.843980\pi$
$998$	3.22733e21	+	5.58990e21i	0.103601	+	0.179442i
$999$	8.81586e21	−	1.52695e22i	0.280882	−	0.486501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.16.c.b.9.1	✓	10
3.2	odd	2		126.16.g.c.37.4		10
7.2	even	3		98.16.a.h.1.5		5
7.3	odd	6		98.16.c.n.67.5		10
7.4	even	3	inner	14.16.c.b.11.1	yes	10
7.5	odd	6		98.16.a.i.1.1		5
7.6	odd	2		98.16.c.n.79.5		10
21.11	odd	6		126.16.g.c.109.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.16.c.b.9.1	✓	10	1.1	even	1	trivial
14.16.c.b.11.1	yes	10	7.4	even	3	inner
98.16.a.h.1.5		5	7.2	even	3
98.16.a.i.1.1		5	7.5	odd	6
98.16.c.n.67.5		10	7.3	odd	6
98.16.c.n.79.5		10	7.6	odd	2
126.16.g.c.37.4		10	3.2	odd	2
126.16.g.c.109.4		10	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(64.0000 - 110.851i) q^{2} +(-3401.15 - 5890.97i) q^{3} +(-8192.00 - 14189.0i) q^{4} +(-55365.7 + 95896.2i) q^{5} -870695. q^{6} +(550858. + 2.10811e6i) q^{7} -2.09715e6 q^{8} +(-1.59612e7 + 2.76456e7i) q^{9} +O(q^{10})\)	\(q+(64.0000 - 110.851i) q^{2} +(-3401.15 - 5890.97i) q^{3} +(-8192.00 - 14189.0i) q^{4} +(-55365.7 + 95896.2i) q^{5} -870695. q^{6} +(550858. + 2.10811e6i) q^{7} -2.09715e6 q^{8} +(-1.59612e7 + 2.76456e7i) q^{9} +(7.08681e6 + 1.22747e7i) q^{10} +(-2.69616e7 - 4.66989e7i) q^{11} +(-5.57245e7 + 9.65176e7i) q^{12} +2.39628e8 q^{13} +(2.68941e8 + 7.38556e7i) q^{14} +7.53228e8 q^{15} +(-1.34218e8 + 2.32472e8i) q^{16} +(-1.29246e9 - 2.23861e9i) q^{17} +(2.04303e9 + 3.53864e9i) q^{18} +(-2.01327e9 + 3.48709e9i) q^{19} +1.81422e9 q^{20} +(1.05452e10 - 1.04151e10i) q^{21} -6.90217e9 q^{22} +(-3.30987e9 + 5.73286e9i) q^{23} +(7.13273e9 + 1.23543e10i) q^{24} +(9.12807e9 + 1.58103e10i) q^{25} +(1.53362e10 - 2.65630e10i) q^{26} +1.19540e11 q^{27} +(2.53992e10 - 2.50857e10i) q^{28} +5.84976e9 q^{29} +(4.82066e10 - 8.34963e10i) q^{30} +(1.50673e11 + 2.60973e11i) q^{31} +(1.71799e10 + 2.97564e10i) q^{32} +(-1.83401e11 + 3.17660e11i) q^{33} -3.30870e11 q^{34} +(-2.32658e11 - 6.38917e10i) q^{35} +5.23017e11 q^{36} +(7.37480e10 - 1.27735e11i) q^{37} +(2.57699e11 + 4.46348e11i) q^{38} +(-8.15011e11 - 1.41164e12i) q^{39} +(1.16110e11 - 2.01109e11i) q^{40} +7.07723e11 q^{41} +(-4.79629e11 - 1.83552e12i) q^{42} -1.37858e12 q^{43} +(-4.41739e11 + 7.65115e11i) q^{44} +(-1.76741e12 - 3.06124e12i) q^{45} +(4.23663e11 + 7.33806e11i) q^{46} +(-1.97502e12 + 3.42084e12i) q^{47} +1.82598e12 q^{48} +(-4.14067e12 + 2.32254e12i) q^{49} +2.33679e12 q^{50} +(-8.79171e12 + 1.52277e13i) q^{51} +(-1.96303e12 - 3.40007e12i) q^{52} +(-3.72252e12 - 6.44759e12i) q^{53} +(7.65058e12 - 1.32512e13i) q^{54} +5.97100e12 q^{55} +(-1.15523e12 - 4.42102e12i) q^{56} +2.73898e13 q^{57} +(3.74384e11 - 6.48453e11i) q^{58} +(1.81514e13 + 3.14391e13i) q^{59} +(-6.17045e12 - 1.06875e13i) q^{60} +(1.22609e13 - 2.12365e13i) q^{61} +3.85723e13 q^{62} +(-6.70723e13 - 1.84191e13i) q^{63} +4.39805e12 q^{64} +(-1.32672e13 + 2.29794e13i) q^{65} +(2.34753e13 + 4.06605e13i) q^{66} +(-6.14489e12 - 1.06433e13i) q^{67} +(-2.11757e13 + 3.66773e13i) q^{68} +4.50295e13 q^{69} +(-2.19726e13 + 2.17014e13i) q^{70} -3.63576e13 q^{71} +(3.34731e13 - 5.79771e13i) q^{72} +(4.65083e13 + 8.05548e13i) q^{73} +(-9.43974e12 - 1.63501e13i) q^{74} +(6.20919e13 - 1.07546e14i) q^{75} +6.59710e13 q^{76} +(8.35943e13 - 8.25624e13i) q^{77} -2.08643e14 q^{78} +(-1.41191e14 + 2.44549e14i) q^{79} +(-1.48621e13 - 2.57419e13i) q^{80} +(-1.77549e14 - 3.07523e14i) q^{81} +(4.52943e13 - 7.84520e13i) q^{82} -2.65136e14 q^{83} +(-2.34166e14 - 6.43057e13i) q^{84} +2.86232e14 q^{85} +(-8.82289e13 + 1.52817e14i) q^{86} +(-1.98959e13 - 3.44607e13i) q^{87} +(5.65426e13 + 9.79347e13i) q^{88} +(-2.36137e14 + 4.09001e14i) q^{89} -4.52456e14 q^{90} +(1.32001e14 + 5.05161e14i) q^{91} +1.08458e14 q^{92} +(1.02492e15 - 1.77522e15i) q^{93} +(2.52803e14 + 4.37867e14i) q^{94} +(-2.22933e14 - 3.86131e14i) q^{95} +(1.16863e14 - 2.02412e14i) q^{96} -4.86827e14 q^{97} +(-7.54711e12 + 6.07641e14i) q^{98} +1.72136e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9}+O(q^{10}) \) 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9	\( 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9} - 1404032 q^{10} - 3405409 q^{11} + 39239680 q^{12} + 369408276 q^{13} + 411547520 q^{14} + 453669790 q^{15} - 1342177280 q^{16} - 3201713287 q^{17} + 5824692992 q^{18} - 1063446451 q^{19} - 359432192 q^{20} + 21058786691 q^{21} - 871784704 q^{22} - 31680429991 q^{23} - 5022679040 q^{24} + 39012502244 q^{25} + 23642129664 q^{26} + 66427564750 q^{27} + 13761560576 q^{28} + 294935242276 q^{29} + 29034866560 q^{30} + 30201804075 q^{31} + 171798691840 q^{32} - 482562276049 q^{33} - 819638601472 q^{34} - 1540311474205 q^{35} + 1491121405952 q^{36} + 1369689837461 q^{37} + 136121145728 q^{38} - 1048775641458 q^{39} - 23003660288 q^{40} + 3634838274156 q^{41} - 871978643968 q^{42} + 415602663752 q^{43} - 55794221056 q^{44} - 7616412162898 q^{45} + 4055095038848 q^{46} - 12606978599835 q^{47} - 1285805834240 q^{48} - 8067928630838 q^{49} + 9987200574464 q^{50} + 6857137867217 q^{51} - 3026192596992 q^{52} + 10616682242361 q^{53} + 4251364144000 q^{54} - 40851384759514 q^{55} - 4981314813952 q^{56} + 44665526899814 q^{57} + 18875855505664 q^{58} + 39993786962755 q^{59} - 3716462919680 q^{60} + 5148862074165 q^{61} + 7731661843200 q^{62} - 97668254816810 q^{63} + 43980465111040 q^{64} + 91302240851010 q^{65} + 61767971334272 q^{66} - 29267240444285 q^{67} - 52456870494208 q^{68} - 279695242712578 q^{69} + 18327124839296 q^{70} - 37767657205600 q^{71} + 95431769980928 q^{72} + 243869659370917 q^{73} - 175320299195008 q^{74} + 295809815641460 q^{75} + 34847013306368 q^{76} + 35960055270559 q^{77} - 268486564213248 q^{78} + 137356615917609 q^{79} + 2944468516864 q^{80} - 352056899083285 q^{81} + 232629649545984 q^{82} - 914604166510648 q^{83} - 456640427573248 q^{84} + 264981492485402 q^{85} + 26598570480128 q^{86} + 13\!\cdots\!90 q^{87}+ \cdots + 39\!\cdots\!96 q^{99}+O(q^{100}) \) 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9 - 1404032 * q^10 - 3405409 * q^11 + 39239680 * q^12 + 369408276 * q^13 + 411547520 * q^14 + 453669790 * q^15 - 1342177280 * q^16 - 3201713287 * q^17 + 5824692992 * q^18 - 1063446451 * q^19 - 359432192 * q^20 + 21058786691 * q^21 - 871784704 * q^22 - 31680429991 * q^23 - 5022679040 * q^24 + 39012502244 * q^25 + 23642129664 * q^26 + 66427564750 * q^27 + 13761560576 * q^28 + 294935242276 * q^29 + 29034866560 * q^30 + 30201804075 * q^31 + 171798691840 * q^32 - 482562276049 * q^33 - 819638601472 * q^34 - 1540311474205 * q^35 + 1491121405952 * q^36 + 1369689837461 * q^37 + 136121145728 * q^38 - 1048775641458 * q^39 - 23003660288 * q^40 + 3634838274156 * q^41 - 871978643968 * q^42 + 415602663752 * q^43 - 55794221056 * q^44 - 7616412162898 * q^45 + 4055095038848 * q^46 - 12606978599835 * q^47 - 1285805834240 * q^48 - 8067928630838 * q^49 + 9987200574464 * q^50 + 6857137867217 * q^51 - 3026192596992 * q^52 + 10616682242361 * q^53 + 4251364144000 * q^54 - 40851384759514 * q^55 - 4981314813952 * q^56 + 44665526899814 * q^57 + 18875855505664 * q^58 + 39993786962755 * q^59 - 3716462919680 * q^60 + 5148862074165 * q^61 + 7731661843200 * q^62 - 97668254816810 * q^63 + 43980465111040 * q^64 + 91302240851010 * q^65 + 61767971334272 * q^66 - 29267240444285 * q^67 - 52456870494208 * q^68 - 279695242712578 * q^69 + 18327124839296 * q^70 - 37767657205600 * q^71 + 95431769980928 * q^72 + 243869659370917 * q^73 - 175320299195008 * q^74 + 295809815641460 * q^75 + 34847013306368 * q^76 + 35960055270559 * q^77 - 268486564213248 * q^78 + 137356615917609 * q^79 + 2944468516864 * q^80 - 352056899083285 * q^81 + 232629649545984 * q^82 - 914604166510648 * q^83 - 456640427573248 * q^84 + 264981492485402 * q^85 + 26598570480128 * q^86 + 1332529214868790 * q^87 + 7141660295168 * q^88 + 315332760149685 * q^89 - 1949801513701888 * q^90 - 2638730194011720 * q^91 + 1038104329945088 * q^92 + 2962720310885787 * q^93 + 1613693260778880 * q^94 - 1346257729549705 * q^95 - 82291573391360 * q^96 + 58320039716044 * q^97 - 1279096378461056 * q^98 + 3930453838067596 * q^99

Introduction

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