LMFDB - Embedded newform 14.14.c.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,14,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, 14, names="a")

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

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
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:	$15.0123300533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2 x^{7} + 692094 x^{6} + 445371928 x^{5} + 480078817147 x^{4} + 153633603309480 x^{3} + \cdots + 23\!\cdots\!25 $ x^8 - 2x^7 + 692094x^6 + 445371928x^5 + 480078817147x^4 + 153633603309480x^3 + 48219450150076326x^2 + 340591169755393830*x + 2353882543131872025
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$-258.759 - 448.183i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.14.c.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-32.0000 - 55.4256i) q^{2} +(-679.656 + 1177.20i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-29011.3 - 50249.0i) q^{5} +86996.0 q^{6} +(-173759. - 258257. i) q^{7} +262144. q^{8} +(-126703. - 219456. i) q^{9} +O(q^{10})$	\(q+(-32.0000 - 55.4256i) q^{2} +(-679.656 + 1177.20i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-29011.3 - 50249.0i) q^{5} +86996.0 q^{6} +(-173759. - 258257. i) q^{7} +262144. q^{8} +(-126703. - 219456. i) q^{9} +(-1.85672e6 + 3.21593e6i) q^{10} +(-3.81607e6 + 6.60963e6i) q^{11} +(-2.78387e6 - 4.82181e6i) q^{12} +1.50447e7 q^{13} +(-8.75377e6 + 1.78949e7i) q^{14} +7.88707e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(1.56282e7 - 2.70688e7i) q^{17} +(-8.10899e6 + 1.40452e7i) q^{18} +(7.42832e7 + 1.28662e8i) q^{19} +2.37660e8 q^{20} +(4.22116e8 - 2.90230e7i) q^{21} +4.88457e8 q^{22} +(2.72315e8 + 4.71664e8i) q^{23} +(-1.78168e8 + 3.08596e8i) q^{24} +(-1.07296e9 + 1.85841e9i) q^{25} +(-4.81431e8 - 8.33863e8i) q^{26} -1.82272e9 q^{27} +(1.27196e9 - 8.74548e7i) q^{28} +5.67745e9 q^{29} +(-2.52386e9 - 4.37146e9i) q^{30} +(4.40028e8 - 7.62152e8i) q^{31} +(-5.36871e8 + 9.29888e8i) q^{32} +(-5.18723e9 - 8.98454e9i) q^{33} -2.00041e9 q^{34} +(-7.93619e9 + 1.62236e10i) q^{35} +1.03795e9 q^{36} +(-6.35555e9 - 1.10081e10i) q^{37} +(4.75412e9 - 8.23438e9i) q^{38} +(-1.02252e10 + 1.77106e10i) q^{39} +(-7.60513e9 - 1.31725e10i) q^{40} +4.58753e10 q^{41} +(-1.51163e10 - 2.24673e10i) q^{42} -6.31799e10 q^{43} +(-1.56306e10 - 2.70730e10i) q^{44} +(-7.35163e9 + 1.27334e10i) q^{45} +(1.74282e10 - 3.01865e10i) q^{46} +(5.60221e10 + 9.70331e10i) q^{47} +2.28055e10 q^{48} +(-3.65045e10 + 8.97491e10i) q^{49} +1.37338e11 q^{50} +(2.12436e10 + 3.67949e10i) q^{51} +(-3.08116e10 + 5.33672e10i) q^{52} +(6.36685e10 - 1.10277e11i) q^{53} +(5.83272e10 + 1.01026e11i) q^{54} +4.42836e11 q^{55} +(-4.55499e10 - 6.77006e10i) q^{56} -2.01948e11 q^{57} +(-1.81678e11 - 3.14676e11i) q^{58} +(2.26225e10 - 3.91833e10i) q^{59} +(-1.61527e11 + 2.79773e11i) q^{60} +(-1.50805e10 - 2.61202e10i) q^{61} -5.63236e10 q^{62} +(-3.46603e10 + 7.08544e10i) q^{63} +6.87195e10 q^{64} +(-4.36466e11 - 7.55982e11i) q^{65} +(-3.31983e11 + 5.75011e11i) q^{66} +(-9.77666e10 + 1.69337e11i) q^{67} +(6.40130e10 + 1.10874e11i) q^{68} -7.40323e11 q^{69} +(1.15316e12 - 7.92866e10i) q^{70} -1.17405e12 q^{71} +(-3.32144e10 - 5.75291e10i) q^{72} +(2.29968e11 - 3.98315e11i) q^{73} +(-4.06755e11 + 7.04520e11i) q^{74} +(-1.45848e12 - 2.52616e12i) q^{75} -6.08528e11 q^{76} +(2.37006e12 - 1.62956e11i) q^{77} +1.30883e12 q^{78} +(9.86612e11 + 1.70886e12i) q^{79} +(-4.86728e11 + 8.43038e11i) q^{80} +(1.44083e12 - 2.49559e12i) q^{81} +(-1.46801e12 - 2.54267e12i) q^{82} +4.81548e12 q^{83} +(-7.61543e11 + 1.55679e12i) q^{84} -1.81357e12 q^{85} +(2.02176e12 + 3.50179e12i) q^{86} +(-3.85871e12 + 6.68348e12i) q^{87} +(-1.00036e12 + 1.73267e12i) q^{88} +(3.46688e12 + 6.00481e12i) q^{89} +9.41008e11 q^{90} +(-2.61416e12 - 3.88541e12i) q^{91} -2.23081e12 q^{92} +(5.98136e11 + 1.03600e12i) q^{93} +(3.58541e12 - 6.21012e12i) q^{94} +(4.31010e12 - 7.46531e12i) q^{95} +(-7.29775e11 - 1.26401e12i) q^{96} -5.74063e11 q^{97} +(6.14254e12 - 8.48685e11i) q^{98} +1.93403e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9}+O(q^{10}) $ 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9	\( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9} - 4121600 q^{10} - 1008790 q^{11} - 745472 q^{12} + 53807264 q^{13} + 23506560 q^{14} - 88888916 q^{15} - 67108864 q^{16} - 165333028 q^{17} - 254960128 q^{18} - 423405794 q^{19} + 527564800 q^{20} + 231089600 q^{21} + 129125120 q^{22} + 286233866 q^{23} - 47710208 q^{24} - 472017432 q^{25} - 1721832448 q^{26} - 10405941644 q^{27} - 1038557184 q^{28} + 18200674816 q^{29} + 2844445312 q^{30} + 1507094246 q^{31} - 4294967296 q^{32} - 16888935028 q^{33} + 21162627584 q^{34} - 4300332526 q^{35} + 32634896384 q^{36} - 18959705336 q^{37} - 27097970816 q^{38} + 35759388756 q^{39} - 16882073600 q^{40} + 113651910624 q^{41} + 25531294208 q^{42} - 91557619424 q^{43} - 4132003840 q^{44} - 119804452768 q^{45} + 18318967424 q^{46} - 81351201078 q^{47} + 6106906624 q^{48} - 60954502168 q^{49} + 60418231296 q^{50} + 14996824142 q^{51} - 110197276672 q^{52} + 87497947440 q^{53} + 332990132608 q^{54} + 701637410348 q^{55} - 29815209984 q^{56} - 1807326928264 q^{57} - 582421594112 q^{58} - 194140265102 q^{59} + 182044499968 q^{60} + 175816313120 q^{61} - 192908063488 q^{62} + 3245184239332 q^{63} + 549755813888 q^{64} - 1689866774568 q^{65} - 1080891841792 q^{66} - 243815218758 q^{67} - 677204082688 q^{68} + 6044157952784 q^{69} + 3010938632576 q^{70} - 3275394679072 q^{71} - 1044316684288 q^{72} - 3492491920596 q^{73} - 1213421141504 q^{74} - 2370218127424 q^{75} + 3468540264448 q^{76} + 6381735922240 q^{77} - 4577201760768 q^{78} - 1016380081246 q^{79} - 1080452710400 q^{80} + 17492694092 q^{81} - 3636861139968 q^{82} + 7027495743296 q^{83} - 2580545830912 q^{84} + 569114840528 q^{85} + 2929843821568 q^{86} - 9706955821052 q^{87} - 264448245760 q^{88} - 8034124428036 q^{89} + 15334969954304 q^{90} - 11436513503632 q^{91} - 2344827830272 q^{92} - 3388371390552 q^{93} - 5206476868992 q^{94} + 1429435505438 q^{95} - 195421011968 q^{96} + 54351131725632 q^{97} - 461748942592 q^{98} - 25837834576328 q^{99}+O(q^{100}) \) 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9 - 4121600 * q^10 - 1008790 * q^11 - 745472 * q^12 + 53807264 * q^13 + 23506560 * q^14 - 88888916 * q^15 - 67108864 * q^16 - 165333028 * q^17 - 254960128 * q^18 - 423405794 * q^19 + 527564800 * q^20 + 231089600 * q^21 + 129125120 * q^22 + 286233866 * q^23 - 47710208 * q^24 - 472017432 * q^25 - 1721832448 * q^26 - 10405941644 * q^27 - 1038557184 * q^28 + 18200674816 * q^29 + 2844445312 * q^30 + 1507094246 * q^31 - 4294967296 * q^32 - 16888935028 * q^33 + 21162627584 * q^34 - 4300332526 * q^35 + 32634896384 * q^36 - 18959705336 * q^37 - 27097970816 * q^38 + 35759388756 * q^39 - 16882073600 * q^40 + 113651910624 * q^41 + 25531294208 * q^42 - 91557619424 * q^43 - 4132003840 * q^44 - 119804452768 * q^45 + 18318967424 * q^46 - 81351201078 * q^47 + 6106906624 * q^48 - 60954502168 * q^49 + 60418231296 * q^50 + 14996824142 * q^51 - 110197276672 * q^52 + 87497947440 * q^53 + 332990132608 * q^54 + 701637410348 * q^55 - 29815209984 * q^56 - 1807326928264 * q^57 - 582421594112 * q^58 - 194140265102 * q^59 + 182044499968 * q^60 + 175816313120 * q^61 - 192908063488 * q^62 + 3245184239332 * q^63 + 549755813888 * q^64 - 1689866774568 * q^65 - 1080891841792 * q^66 - 243815218758 * q^67 - 677204082688 * q^68 + 6044157952784 * q^69 + 3010938632576 * q^70 - 3275394679072 * q^71 - 1044316684288 * q^72 - 3492491920596 * q^73 - 1213421141504 * q^74 - 2370218127424 * q^75 + 3468540264448 * q^76 + 6381735922240 * q^77 - 4577201760768 * q^78 - 1016380081246 * q^79 - 1080452710400 * q^80 + 17492694092 * q^81 - 3636861139968 * q^82 + 7027495743296 * q^83 - 2580545830912 * q^84 + 569114840528 * q^85 + 2929843821568 * q^86 - 9706955821052 * q^87 - 264448245760 * q^88 - 8034124428036 * q^89 + 15334969954304 * q^90 - 11436513503632 * q^91 - 2344827830272 * q^92 - 3388371390552 * q^93 - 5206476868992 * q^94 + 1429435505438 * q^95 - 195421011968 * q^96 + 54351131725632 * q^97 - 461748942592 * q^98 - 25837834576328 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−32.0000	−	55.4256i	−0.353553	−	0.612372i
$2$	−32.0000	−	55.4256i	−0.353553	−	0.612372i
$3$	−679.656	+	1177.20i	−0.538271	+	0.932313i	0.460726	+	0.887542i	$0.347589\pi$
$3$	−679.656	+	1177.20i	−0.538271	+	0.932313i	−0.998997	+	0.0447704i	$0.985744\pi$
$4$	−2048.00	+	3547.24i	−0.250000	+	0.433013i
$5$	−29011.3	−	50249.0i	−0.830351	−	1.43821i	−0.897760	−	0.440484i	$-0.854807\pi$
$5$	−29011.3	−	50249.0i	−0.830351	−	1.43821i	0.0674096	−	0.997725i	$-0.478527\pi$
$6$	86996.0			0.761230
$7$	−173759.	−	258257.i	−0.558226	−	0.829689i
$7$	−173759.	−	258257.i	−0.558226	−	0.829689i
$8$	262144.			0.353553
$9$	−126703.	−	219456.i	−0.0794713	−	0.137648i
$10$	−1.85672e6	+	3.21593e6i	−0.587147	+	1.01697i
$11$	−3.81607e6	+	6.60963e6i	−0.649477	+	1.12493i	0.333771	+	0.942654i	$0.391679\pi$
$11$	−3.81607e6	+	6.60963e6i	−0.649477	+	1.12493i	−0.983248	+	0.182273i	$0.941655\pi$
$12$	−2.78387e6	−	4.82181e6i	−0.269135	−	0.466156i
$13$	1.50447e7			0.864475			0.432238	−	0.901760i	$-0.357724\pi$
$13$	1.50447e7			0.864475			0.432238	+	0.901760i	$0.357724\pi$
$14$	−8.75377e6	+	1.78949e7i	−0.310716	+	0.635182i
$15$	7.88707e7			1.78781
$16$	−8.38861e6	−	1.45295e7i	−0.125000	−	0.216506i
$17$	1.56282e7	−	2.70688e7i	0.157033	−	0.271989i	−0.776765	−	0.629791i	$-0.783141\pi$
$17$	1.56282e7	−	2.70688e7i	0.157033	−	0.271989i	0.933797	+	0.357802i	$0.116474\pi$
$18$	−8.10899e6	+	1.40452e7i	−0.0561947	+	0.0973321i
$19$	7.42832e7	+	1.28662e8i	0.362236	+	0.627412i	0.988329	−	0.152337i	$-0.0486800\pi$
$19$	7.42832e7	+	1.28662e8i	0.362236	+	0.627412i	−0.626092	+	0.779749i	$0.715347\pi$
$20$	2.37660e8			0.830351
$21$	4.22116e8	−	2.90230e7i	1.07401	−	0.0738443i
$22$	4.88457e8			0.918499
$23$	2.72315e8	+	4.71664e8i	0.383567	+	0.664358i	0.991569	−	0.129578i	$-0.0413622\pi$
$23$	2.72315e8	+	4.71664e8i	0.383567	+	0.664358i	−0.608002	+	0.793935i	$0.708029\pi$
$24$	−1.78168e8	+	3.08596e8i	−0.190308	+	0.329622i
$25$	−1.07296e9	+	1.85841e9i	−0.878965	+	1.52241i
$26$	−4.81431e8	−	8.33863e8i	−0.305638	−	0.529381i
$27$	−1.82272e9			−0.905434
$28$	1.27196e9	−	8.74548e7i	0.498822	−	0.0342970i
$29$	5.67745e9			1.77242			0.886209	−	0.463286i	$-0.153330\pi$
$29$	5.67745e9			1.77242			0.886209	+	0.463286i	$0.153330\pi$
$30$	−2.52386e9	−	4.37146e9i	−0.632088	−	1.09481i
$31$	4.40028e8	−	7.62152e8i	0.0890492	−	0.154238i	−0.818060	−	0.575132i	$-0.804951\pi$
$31$	4.40028e8	−	7.62152e8i	0.0890492	−	0.154238i	0.907109	+	0.420895i	$0.138284\pi$
$32$	−5.36871e8	+	9.29888e8i	−0.0883883	+	0.153093i
$33$	−5.18723e9	−	8.98454e9i	−0.699189	−	1.21103i
$34$	−2.00041e9			−0.222078
$35$	−7.93619e9	+	1.62236e10i	−0.729742	+	1.49178i
$36$	1.03795e9			0.0794713
$37$	−6.35555e9	−	1.10081e10i	−0.407232	−	0.705346i	0.587347	−	0.809336i	$-0.300173\pi$
$37$	−6.35555e9	−	1.10081e10i	−0.407232	−	0.705346i	−0.994578	+	0.103989i	$0.966839\pi$
$38$	4.75412e9	−	8.23438e9i	0.256140	−	0.443647i
$39$	−1.02252e10	+	1.77106e10i	−0.465322	+	0.805961i
$40$	−7.60513e9	−	1.31725e10i	−0.293573	−	0.508484i
$41$	4.58753e10			1.50829			0.754144	−	0.656710i	$-0.228052\pi$
$41$	4.58753e10			1.50829			0.754144	+	0.656710i	$0.228052\pi$
$42$	−1.51163e10	−	2.24673e10i	−0.424939	−	0.631584i
$43$	−6.31799e10			−1.52417			−0.762086	−	0.647476i	$-0.775825\pi$
$43$	−6.31799e10			−1.52417			−0.762086	+	0.647476i	$0.775825\pi$
$44$	−1.56306e10	−	2.70730e10i	−0.324739	−	0.562464i
$45$	−7.35163e9	+	1.27334e10i	−0.131978	+	0.228593i
$46$	1.74282e10	−	3.01865e10i	0.271223	−	0.469772i
$47$	5.60221e10	+	9.70331e10i	0.758094	+	1.31306i	0.943821	+	0.330456i	$0.107203\pi$
$47$	5.60221e10	+	9.70331e10i	0.758094	+	1.31306i	−0.185727	+	0.982601i	$0.559464\pi$
$48$	2.28055e10			0.269135
$49$	−3.65045e10	+	8.97491e10i	−0.376766	+	0.926308i
$50$	1.37338e11			1.24304
$51$	2.12436e10	+	3.67949e10i	0.169052	+	0.292807i
$52$	−3.08116e10	+	5.33672e10i	−0.216119	+	0.374329i
$53$	6.36685e10	−	1.10277e11i	0.394577	−	0.683427i	−0.598470	−	0.801145i	$-0.704225\pi$
$53$	6.36685e10	−	1.10277e11i	0.394577	−	0.683427i	0.993047	+	0.117718i	$0.0375579\pi$
$54$	5.83272e10	+	1.01026e11i	0.320119	+	0.554463i
$55$	4.42836e11			2.15718
$56$	−4.55499e10	−	6.77006e10i	−0.197363	−	0.293339i
$57$	−2.01948e11			−0.779925
$58$	−1.81678e11	−	3.14676e11i	−0.626644	−	1.08538i
$59$	2.26225e10	−	3.91833e10i	0.0698237	−	0.120938i	−0.829000	−	0.559249i	$-0.811090\pi$
$59$	2.26225e10	−	3.91833e10i	0.0698237	−	0.120938i	0.898824	+	0.438311i	$0.144423\pi$
$60$	−1.61527e11	+	2.79773e11i	−0.446954	+	0.774147i
$61$	−1.50805e10	−	2.61202e10i	−0.0374777	−	0.0649132i	0.846678	−	0.532105i	$-0.178599\pi$
$61$	−1.50805e10	−	2.61202e10i	−0.0374777	−	0.0649132i	−0.884156	+	0.467192i	$0.845266\pi$
$62$	−5.63236e10			−0.125935
$63$	−3.46603e10	+	7.08544e10i	−0.0698423	+	0.142775i
$64$	6.87195e10			0.125000
$65$	−4.36466e11	−	7.55982e11i	−0.717817	−	1.24330i
$66$	−3.31983e11	+	5.75011e11i	−0.494401	+	0.856329i
$67$	−9.77666e10	+	1.69337e11i	−0.132040	+	0.228699i	−0.924463	−	0.381273i	$-0.875486\pi$
$67$	−9.77666e10	+	1.69337e11i	−0.132040	+	0.228699i	0.792423	+	0.609972i	$0.208819\pi$
$68$	6.40130e10	+	1.10874e11i	0.0785164	+	0.135994i
$69$	−7.40323e11			−0.825852
$70$	1.15316e12	−	7.92866e10i	1.17153	−	0.0805495i
$71$	−1.17405e12			−1.08770			−0.543848	−	0.839184i	$-0.683033\pi$
$71$	−1.17405e12			−1.08770			−0.543848	+	0.839184i	$0.683033\pi$
$72$	−3.32144e10	−	5.75291e10i	−0.0280974	−	0.0486660i
$73$	2.29968e11	−	3.98315e11i	0.177856	−	0.308055i	−0.763290	−	0.646056i	$-0.776417\pi$
$73$	2.29968e11	−	3.98315e11i	0.177856	−	0.308055i	0.941146	+	0.338001i	$0.109751\pi$
$74$	−4.06755e11	+	7.04520e11i	−0.287956	+	0.498755i
$75$	−1.45848e12	−	2.52616e12i	−0.946242	−	1.63894i
$76$	−6.08528e11			−0.362236
$77$	2.37006e12	−	1.62956e11i	1.29589	−	0.0891005i
$78$	1.30883e12			0.658064
$79$	9.86612e11	+	1.70886e12i	0.456636	+	0.790917i	0.998781	−	0.0493681i	$-0.0157207\pi$
$79$	9.86612e11	+	1.70886e12i	0.456636	+	0.790917i	−0.542144	+	0.840285i	$0.682387\pi$
$80$	−4.86728e11	+	8.43038e11i	−0.207588	+	0.359552i
$81$	1.44083e12	−	2.49559e12i	0.566840	−	0.981796i
$82$	−1.46801e12	−	2.54267e12i	−0.533260	−	0.923633i
$83$	4.81548e12			1.61671			0.808356	−	0.588695i	$-0.200358\pi$
$83$	4.81548e12			1.61671			0.808356	+	0.588695i	$0.200358\pi$
$84$	−7.61543e11	+	1.55679e12i	−0.236526	+	0.483519i
$85$	−1.81357e12			−0.521569
$86$	2.02176e12	+	3.50179e12i	0.538876	+	0.933361i
$87$	−3.85871e12	+	6.68348e12i	−0.954041	+	1.65245i
$88$	−1.00036e12	+	1.73267e12i	−0.229625	+	0.397722i
$89$	3.46688e12	+	6.00481e12i	0.739442	+	1.28075i	0.952747	+	0.303765i	$0.0982438\pi$
$89$	3.46688e12	+	6.00481e12i	0.739442	+	1.28075i	−0.213305	+	0.976986i	$0.568423\pi$
$90$	9.41008e11			0.186645
$91$	−2.61416e12	−	3.88541e12i	−0.482573	−	0.717245i
$92$	−2.23081e12			−0.383567
$93$	5.98136e11	+	1.03600e12i	0.0958652	+	0.166043i
$94$	3.58541e12	−	6.21012e12i	0.536053	−	0.928472i
$95$	4.31010e12	−	7.46531e12i	0.601567	−	1.04194i
$96$	−7.29775e11	−	1.26401e12i	−0.0951538	−	0.164811i
$97$	−5.74063e11			−0.0699750			−0.0349875	−	0.999388i	$-0.511139\pi$
$97$	−5.74063e11			−0.0699750			−0.0349875	+	0.999388i	$0.511139\pi$
$98$	6.14254e12	−	8.48685e11i	0.700453	−	0.0967781i
$99$	1.93403e12			0.206459
$100$	−4.39482e12	−	7.61206e12i	−0.439482	−	0.761206i
$101$	−8.69619e12	+	1.50622e13i	−0.815155	+	1.41189i	0.0940617	+	0.995566i	$0.470015\pi$
$101$	−8.69619e12	+	1.50622e13i	−0.815155	+	1.41189i	−0.909217	+	0.416323i	$0.863318\pi$
$102$	1.35959e12	−	2.35488e12i	0.119538	−	0.207046i
$103$	1.18968e11	+	2.06059e11i	0.00981722	+	0.0170039i	0.870892	−	0.491474i	$-0.163542\pi$
$103$	1.18968e11	+	2.06059e11i	0.00981722	+	0.0170039i	−0.861075	+	0.508478i	$0.830208\pi$
$104$	3.94388e12			0.305638
$105$	−1.37045e13	−	2.03689e13i	−0.998006	−	1.48333i
$106$	−8.14957e12			−0.558016
$107$	4.58562e12	+	7.94252e12i	0.295395	+	0.511639i	0.975077	−	0.221868i	$-0.0712154\pi$
$107$	4.58562e12	+	7.94252e12i	0.295395	+	0.511639i	−0.679682	+	0.733507i	$0.737882\pi$
$108$	3.73294e12	−	6.46564e12i	0.226358	−	0.392064i
$109$	−1.60392e13	+	2.77807e13i	−0.916032	+	1.58661i	−0.110649	+	0.993860i	$0.535293\pi$
$109$	−1.60392e13	+	2.77807e13i	−0.916032	+	1.58661i	−0.805383	+	0.592755i	$0.798040\pi$
$110$	−1.41708e13	−	2.45445e13i	−0.762677	−	1.32099i
$111$	1.72783e13			0.876804
$112$	−2.29475e12	+	4.69105e12i	−0.109855	+	0.224571i
$113$	−1.20644e13			−0.545127			−0.272563	−	0.962138i	$-0.587871\pi$
$113$	−1.20644e13			−0.545127			−0.272563	+	0.962138i	$0.587871\pi$
$114$	6.46234e12	+	1.11931e13i	0.275745	+	0.477605i
$115$	1.58004e13	−	2.73671e13i	0.636990	−	1.10330i
$116$	−1.16274e13	+	2.01393e13i	−0.443104	+	0.767479i
$117$	−1.90621e12	−	3.30165e12i	−0.0687010	−	0.118994i
$118$	−2.89568e12			−0.0987456
$119$	−9.70625e12	+	6.67362e11i	−0.313326	+	0.0215430i
$120$	2.06755e13			0.632088
$121$	−1.18634e13	−	2.05480e13i	−0.343641	−	0.595203i
$122$	−9.65154e11	+	1.67170e12i	−0.0265007	+	0.0459006i
$123$	−3.11794e13	+	5.40044e13i	−0.811867	+	1.40620i
$124$	1.80236e12	+	3.12177e12i	0.0445246	+	0.0771188i
$125$	5.36828e13			1.25869
$126$	5.03628e12	−	3.46274e11i	0.112125	−	0.00770924i
$127$	2.67166e13			0.565012			0.282506	−	0.959266i	$-0.408834\pi$
$127$	2.67166e13			0.565012			0.282506	+	0.959266i	$0.408834\pi$
$128$	−2.19902e12	−	3.80882e12i	−0.0441942	−	0.0765466i
$129$	4.29406e13	−	7.43753e13i	0.820418	−	1.42101i
$130$	−2.79339e13	+	4.83829e13i	−0.507574	+	0.879143i
$131$	6.50876e12	+	1.12735e13i	0.112521	+	0.194893i	0.916786	−	0.399378i	$-0.130774\pi$
$131$	6.50876e12	+	1.12735e13i	0.112521	+	0.194893i	−0.804265	+	0.594271i	$0.797441\pi$
$132$	4.24938e13			0.699189
$133$	2.03206e13	−	4.15404e13i	0.318347	−	0.650781i
$134$	1.25141e13			0.186732
$135$	5.28795e13	+	9.15900e13i	0.751827	+	1.30220i
$136$	4.09683e12	−	7.09592e12i	0.0555195	−	0.0961625i
$137$	−1.61090e13	+	2.79017e13i	−0.208155	+	0.360534i	−0.951133	−	0.308781i	$-0.900079\pi$
$137$	−1.61090e13	+	2.79017e13i	−0.208155	+	0.360534i	0.742979	+	0.669315i	$0.233412\pi$
$138$	2.36903e13	+	4.10329e13i	0.291983	+	0.505729i
$139$	9.22280e13			1.08459			0.542296	−	0.840187i	$-0.317555\pi$
$139$	9.22280e13			1.08459			0.542296	+	0.840187i	$0.317555\pi$
$140$	−4.12956e13	−	6.13775e13i	−0.463524	−	0.688933i
$141$	−1.52303e14			−1.63224
$142$	3.75696e13	+	6.50725e13i	0.384559	+	0.666075i
$143$	−5.74117e13	+	9.94400e13i	−0.561457	+	0.972472i
$144$	−2.12572e12	+	3.68186e12i	−0.0198678	+	0.0344121i
$145$	−1.64710e14	−	2.85286e14i	−1.47173	−	2.54911i
$146$	−2.94358e13			−0.251526
$147$	−8.08420e13	−	1.03972e14i	−0.660807	−	0.849869i
$148$	5.20646e13			0.407232
$149$	3.34474e13	+	5.79326e13i	0.250410	+	0.433723i	0.963639	−	0.267208i	$-0.0861012\pi$
$149$	3.34474e13	+	5.79326e13i	0.250410	+	0.433723i	−0.713229	+	0.700931i	$0.752768\pi$
$150$	−9.33428e13	+	1.61674e14i	−0.669094	+	1.15891i
$151$	6.93982e13	−	1.20201e14i	0.476429	−	0.825198i	−0.523207	−	0.852206i	$-0.675264\pi$
$151$	6.93982e13	−	1.20201e14i	0.476429	−	0.825198i	0.999635	+	0.0270074i	$0.00859777\pi$
$152$	1.94729e13	+	3.37280e13i	0.128070	+	0.221824i
$153$	−7.92054e12			−0.0499184
$154$	−8.48739e13	−	1.26147e14i	−0.512731	−	0.762068i
$155$	−5.10631e13			−0.295768
$156$	−4.18826e13	−	7.25427e13i	−0.232661	−	0.402981i
$157$	1.13251e13	−	1.96157e13i	0.0603526	−	0.104534i	−0.834270	−	0.551355i	$-0.814111\pi$
$157$	1.13251e13	−	1.96157e13i	0.0603526	−	0.104534i	0.894623	+	0.446822i	$0.147444\pi$
$158$	6.31432e13	−	1.09367e14i	0.322891	−	0.559263i
$159$	8.65454e13	+	1.49901e14i	0.424778	+	0.735738i
$160$	6.23012e13			0.293573
$161$	7.44934e13	−	1.52283e14i	0.337093	−	0.689103i
$162$	−1.84426e14			−0.801633
$163$	9.11583e13	+	1.57891e14i	0.380695	+	0.659383i	0.991162	−	0.132659i	$-0.0423515\pi$
$163$	9.11583e13	+	1.57891e14i	0.380695	+	0.659383i	−0.610467	+	0.792042i	$0.709018\pi$
$164$	−9.39526e13	+	1.62731e14i	−0.377072	+	0.653107i
$165$	−3.00976e14	+	5.21306e14i	−1.16114	+	2.01116i
$166$	−1.54096e14	−	2.66901e14i	−0.571594	−	0.990029i
$167$	3.75120e14			1.33817			0.669087	−	0.743184i	$-0.266685\pi$
$167$	3.75120e14			1.33817			0.669087	+	0.743184i	$0.266685\pi$
$168$	1.10655e14	−	7.60821e12i	0.379719	−	0.0261079i
$169$	−7.65314e13			−0.252683
$170$	5.80343e13	+	1.00518e14i	0.184402	+	0.319394i
$171$	1.88238e13	−	3.26038e13i	0.0575748	−	0.0997225i
$172$	1.29392e14	−	2.24114e14i	0.381043	−	0.659986i
$173$	−2.06112e14	−	3.56997e14i	−0.584526	−	1.01243i	−0.994934	−	0.100527i	$-0.967947\pi$
$173$	−2.06112e14	−	3.56997e14i	−0.584526	−	1.01243i	0.410408	−	0.911902i	$-0.365386\pi$
$174$	4.93915e14			1.34922
$175$	6.66384e14	−	4.58179e13i	1.75379	−	0.120583i
$176$	1.28046e14			0.324739
$177$	3.07511e13	+	5.32624e13i	0.0751681	+	0.130195i
$178$	2.21880e14	−	3.84308e14i	0.522864	−	0.905627i
$179$	−2.93674e14	+	5.08658e14i	−0.667299	+	1.15580i	0.311358	+	0.950293i	$0.399216\pi$
$179$	−2.93674e14	+	5.08658e14i	−0.667299	+	1.15580i	−0.978657	+	0.205503i	$0.934117\pi$
$180$	−3.01123e13	−	5.21560e13i	−0.0659891	−	0.114296i
$181$	−3.78507e14			−0.800136			−0.400068	−	0.916486i	$-0.631013\pi$
$181$	−3.78507e14			−0.800136			−0.400068	+	0.916486i	$0.631013\pi$
$182$	−1.31698e14	+	2.69224e14i	−0.268606	+	0.549099i
$183$	4.09983e13			0.0806926
$184$	7.13859e13	+	1.23644e14i	0.135611	+	0.234886i
$185$	−3.68765e14	+	6.38720e14i	−0.676291	+	1.17137i
$186$	3.82807e13	−	6.63041e13i	0.0677869	−	0.117410i
$187$	1.19276e14	+	2.06593e14i	0.203978	+	0.353301i
$188$	−4.58933e14			−0.758094
$189$	3.16715e14	+	4.70732e14i	0.505437	+	0.751228i
$190$	−5.51693e14			−0.850744
$191$	−2.68659e14	−	4.65331e14i	−0.400391	−	0.693498i	0.593382	−	0.804921i	$-0.297792\pi$
$191$	−2.68659e14	−	4.65331e14i	−0.400391	−	0.693498i	−0.993773	+	0.111423i	$0.964459\pi$
$192$	−4.67056e13	+	8.08965e13i	−0.0672839	+	0.116539i
$193$	5.09990e13	−	8.83329e13i	0.0710296	−	0.123027i	−0.828323	−	0.560251i	$-0.810705\pi$
$193$	5.09990e13	−	8.83329e13i	0.0710296	−	0.123027i	0.899353	+	0.437224i	$0.144038\pi$
$194$	1.83700e13	+	3.18178e13i	0.0247399	+	0.0428508i
$195$	1.18659e15			1.54552
$196$	−2.43600e14	−	3.13296e14i	−0.306912	−	0.394722i
$197$	8.14755e14			0.993108			0.496554	−	0.868006i	$-0.334599\pi$
$197$	8.14755e14			0.993108			0.496554	+	0.868006i	$0.334599\pi$
$198$	−6.18889e13	−	1.07195e14i	−0.0729943	−	0.126430i
$199$	9.16291e13	−	1.58706e14i	0.104590	−	0.181154i	−0.808981	−	0.587835i	$-0.799980\pi$
$199$	9.16291e13	−	1.58706e14i	0.104590	−	0.181154i	0.913570	+	0.406680i	$0.133314\pi$
$200$	−2.81269e14	+	4.87172e14i	−0.310761	+	0.538254i
$201$	−1.32895e14	−	2.30181e14i	−0.142146	−	0.246204i
$202$	1.11311e15			1.15280
$203$	−9.86508e14	−	1.46624e15i	−0.989411	−	1.47055i
$204$	−1.74027e14			−0.169052
$205$	−1.33090e15	−	2.30519e15i	−1.25241	−	2.16923i
$206$	7.61396e12	−	1.31878e13i	0.00694182	−	0.0120236i
$207$	6.90063e13	−	1.19522e14i	0.0609652	−	0.105595i
$208$	−1.26204e14	−	2.18592e14i	−0.108059	−	0.187164i
$209$	−1.13388e15			−0.941057
$210$	−6.90416e14	+	1.41139e15i	−0.555502	+	1.13559i
$211$	−2.29290e15			−1.78875			−0.894375	−	0.447317i	$-0.852379\pi$
$211$	−2.29290e15			−1.78875			−0.894375	+	0.447317i	$0.852379\pi$
$212$	2.60786e14	+	4.51695e14i	0.197288	+	0.341713i
$213$	7.97951e14	−	1.38209e15i	0.585475	−	1.01407i
$214$	2.93479e14	−	5.08321e14i	0.208876	−	0.361784i
$215$	1.83293e15	+	3.17473e15i	1.26560	+	2.19208i
$216$	−4.77816e14			−0.320119
$217$	−2.73290e14	+	1.87903e13i	−0.177679	+	0.0122165i
$218$	2.05302e15			1.29547
$219$	3.12598e14	+	5.41435e14i	0.191469	+	0.331634i
$220$	−9.06928e14	+	1.57085e15i	−0.539294	+	0.934084i
$221$	2.35122e14	−	4.07242e14i	0.135751	−	0.235127i
$222$	−5.52907e14	−	9.57663e14i	−0.309997	−	0.536931i
$223$	−1.06434e14			−0.0579559			−0.0289780	−	0.999580i	$-0.509225\pi$
$223$	−1.06434e14			−0.0579559			−0.0289780	+	0.999580i	$0.509225\pi$
$224$	3.33436e14	−	2.29257e13i	0.176360	−	0.0121258i
$225$	5.43786e14			0.279410
$226$	3.86062e14	+	6.68679e14i	0.192731	+	0.333820i
$227$	2.81510e13	−	4.87590e13i	0.0136561	−	0.0236530i	−0.859117	−	0.511780i	$-0.828986\pi$
$227$	2.81510e13	−	4.87590e13i	0.0136561	−	0.0236530i	0.872773	+	0.488127i	$0.162320\pi$
$228$	4.13590e14	−	7.16358e14i	0.194981	−	0.337718i
$229$	−1.09047e13	−	1.88875e13i	−0.00499669	−	0.00865452i	0.863516	−	0.504321i	$-0.168257\pi$
$229$	−1.09047e13	−	1.88875e13i	−0.00499669	−	0.00865452i	−0.868513	+	0.495667i	$0.834924\pi$
$230$	−2.02245e15			−0.900841
$231$	−1.41899e15	+	2.90079e15i	−0.614473	+	1.25614i
$232$	1.48831e15			0.626644
$233$	1.84743e15	+	3.19983e15i	0.756403	+	1.31013i	0.944674	+	0.328012i	$0.106379\pi$
$233$	1.84743e15	+	3.19983e15i	0.756403	+	1.31013i	−0.188270	+	0.982117i	$0.560288\pi$
$234$	−1.21998e14	+	2.11306e14i	−0.0485789	+	0.0841412i
$235$	3.25054e15	−	5.63010e15i	1.25897	−	2.18060i
$236$	9.26618e13	+	1.60495e14i	0.0349118	+	0.0604691i
$237$	−2.68223e15			−0.983176
$238$	3.47589e14	+	5.16619e14i	0.123970	+	0.184255i
$239$	1.54185e15			0.535125			0.267563	−	0.963540i	$-0.413782\pi$
$239$	1.54185e15			0.535125			0.267563	+	0.963540i	$0.413782\pi$
$240$	−6.61615e14	−	1.14595e15i	−0.223477	−	0.387073i
$241$	2.34610e15	−	4.06356e15i	0.771322	−	1.33597i	−0.165517	−	0.986207i	$-0.552929\pi$
$241$	2.34610e15	−	4.06356e15i	0.771322	−	1.33597i	0.936839	−	0.349761i	$-0.113737\pi$
$242$	−7.59259e14	+	1.31507e15i	−0.242991	+	0.420872i
$243$	5.05533e14	+	8.75609e14i	0.157510	+	0.272816i
$244$	1.23540e14			0.0374777
$245$	5.56884e15	−	7.69420e14i	1.64507	−	0.227292i
$246$	3.99097e15			1.14815
$247$	1.11757e15	+	1.93569e15i	0.313144	+	0.542382i
$248$	1.15351e14	−	1.99793e14i	0.0314836	−	0.0545312i
$249$	−3.27287e15	+	5.66878e15i	−0.870229	+	1.50728i
$250$	−1.71785e15	−	2.97540e15i	−0.445016	−	0.770790i
$251$	−5.95442e15			−1.50300			−0.751502	−	0.659731i	$-0.770670\pi$
$251$	−5.95442e15			−1.50300			−0.751502	+	0.659731i	$0.770670\pi$
$252$	−1.80353e14	−	2.68058e14i	−0.0443630	−	0.0659365i
$253$	−4.15670e15			−0.996472
$254$	−8.54932e14	−	1.48079e15i	−0.199762	−	0.345998i
$255$	1.23260e15	−	2.13493e15i	0.280745	−	0.486265i
$256$	−1.40737e14	+	2.43764e14i	−0.0312500	+	0.0541266i
$257$	2.17236e15	+	3.76264e15i	0.470292	+	0.814569i	0.999423	−	0.0339711i	$-0.0108154\pi$
$257$	2.17236e15	+	3.76264e15i	0.470292	+	0.814569i	−0.529131	+	0.848540i	$0.677482\pi$
$258$	−5.49640e15			−1.16025
$259$	−1.73859e15	+	3.55413e15i	−0.357890	+	0.731619i
$260$	3.57553e15			0.717817
$261$	−7.19349e14	−	1.24595e15i	−0.140856	−	0.243970i
$262$	4.16561e14	−	7.21505e14i	0.0795646	−	0.137810i
$263$	2.36665e15	−	4.09916e15i	0.440983	−	0.763805i	−0.556780	−	0.830660i	$-0.687963\pi$
$263$	2.36665e15	−	4.09916e15i	0.440983	−	0.763805i	0.997763	+	0.0668551i	$0.0212965\pi$
$264$	−1.35980e15	−	2.35524e15i	−0.247201	−	0.428164i
$265$	−7.38841e15			−1.31055
$266$	−2.95266e15	+	2.03013e14i	−0.511073	+	0.0351393i
$267$	−9.42515e15			−1.59208
$268$	−4.00452e14	−	6.93603e14i	−0.0660198	−	0.114350i
$269$	−1.78373e15	+	3.08952e15i	−0.287038	+	0.497165i	−0.973101	−	0.230377i	$-0.926004\pi$
$269$	−1.78373e15	+	3.08952e15i	−0.287038	+	0.497165i	0.686063	+	0.727542i	$0.259337\pi$
$270$	3.38429e15	−	5.86176e15i	0.531622	−	0.920797i
$271$	5.12500e15	+	8.87676e15i	0.785947	+	1.36130i	0.928432	+	0.371503i	$0.121157\pi$
$271$	5.12500e15	+	8.87676e15i	0.785947	+	1.36130i	−0.142485	+	0.989797i	$0.545509\pi$
$272$	−5.24394e14			−0.0785164
$273$	6.35063e15	−	4.36643e14i	0.928452	−	0.0638366i
$274$	2.06196e15			0.294375
$275$	−8.18894e15	−	1.41837e16i	−1.14173	−	1.97754i
$276$	1.51618e15	−	2.62610e15i	0.206463	−	0.357604i
$277$	2.13736e15	−	3.70201e15i	0.284288	−	0.492401i	−0.688148	−	0.725570i	$-0.741576\pi$
$277$	2.13736e15	−	3.70201e15i	0.284288	−	0.492401i	0.972436	+	0.233169i	$0.0749095\pi$
$278$	−2.95130e15	−	5.11179e15i	−0.383461	−	0.664174i
$279$	−2.23012e14			−0.0283074
$280$	−2.08042e15	+	4.25292e15i	−0.258003	+	0.527424i
$281$	1.02189e16			1.23826			0.619130	−	0.785288i	$-0.287485\pi$
$281$	1.02189e16			1.23826			0.619130	+	0.785288i	$0.287485\pi$
$282$	4.87369e15	+	8.44148e15i	0.577084	+	0.999539i
$283$	−1.57219e15	+	2.72311e15i	−0.181925	+	0.315103i	−0.942536	−	0.334104i	$-0.891566\pi$
$283$	−1.57219e15	+	2.72311e15i	−0.181925	+	0.315103i	0.760611	+	0.649208i	$0.224900\pi$
$284$	2.40446e15	−	4.16464e15i	0.271924	−	0.470986i
$285$	5.85877e15	+	1.01477e16i	0.647612	+	1.12170i
$286$	7.34870e15			0.794020
$287$	−7.97126e15	−	1.18476e16i	−0.841966	−	1.25141i
$288$	2.72093e14			0.0280974
$289$	4.46381e15	+	7.73154e15i	0.450681	+	0.780603i
$290$	−1.05414e16	+	1.82583e16i	−1.04067	+	1.80249i
$291$	3.90165e14	−	6.75786e14i	0.0376655	−	0.0652386i
$292$	9.41947e14	+	1.63150e15i	0.0889279	+	0.154028i
$293$	9.35028e15			0.863347			0.431673	−	0.902030i	$-0.357923\pi$
$293$	9.35028e15			0.863347			0.431673	+	0.902030i	$0.357923\pi$
$294$	−3.17575e15	+	7.80781e15i	−0.286806	+	0.705134i
$295$	−2.62523e15			−0.231913
$296$	−1.66607e15	−	2.88572e15i	−0.143978	−	0.249378i
$297$	6.95564e15	−	1.20475e16i	0.588058	−	1.01855i
$298$	2.14063e15	−	3.70769e15i	0.177067	−	0.306688i
$299$	4.09691e15	+	7.09606e15i	0.331584	+	0.574321i
$300$	1.19479e16			0.946242
$301$	1.09781e16	+	1.63167e16i	0.850833	+	1.26459i
$302$	−8.88296e15			−0.673772
$303$	−1.18208e16	−	2.04743e16i	−0.877548	−	1.51996i
$304$	1.24627e15	−	2.15859e15i	0.0905591	−	0.156853i
$305$	−8.75010e14	+	1.51556e15i	−0.0622392	+	0.107802i
$306$	2.53457e14	+	4.39001e14i	0.0176488	+	0.0305686i
$307$	8.82705e15			0.601750			0.300875	−	0.953664i	$-0.402721\pi$
$307$	8.82705e15			0.601750			0.300875	+	0.953664i	$0.402721\pi$
$308$	−4.27584e15	+	8.74091e15i	−0.285392	+	0.583414i
$309$	−3.23429e14			−0.0211373
$310$	1.63402e15	+	2.83021e15i	0.104570	+	0.181120i
$311$	5.31752e15	−	9.21021e15i	0.333247	−	0.577201i	−0.649899	−	0.760020i	$-0.725189\pi$
$311$	5.31752e15	−	9.21021e15i	0.333247	−	0.577201i	0.983147	+	0.182819i	$0.0585223\pi$
$312$	−2.68048e15	+	4.64274e15i	−0.164516	+	0.284950i
$313$	−6.24084e15	−	1.08094e16i	−0.375150	−	0.649778i	0.615200	−	0.788371i	$-0.289075\pi$
$313$	−6.24084e15	−	1.08094e16i	−0.375150	−	0.649778i	−0.990349	+	0.138593i	$0.955742\pi$
$314$	−1.44962e15			−0.0853514
$315$	4.56590e15	−	3.13933e14i	0.263335	−	0.0181058i
$316$	−8.08233e15			−0.456636
$317$	−8.49006e15	−	1.47052e16i	−0.469922	−	0.813928i	0.529487	−	0.848318i	$-0.322384\pi$
$317$	−8.49006e15	−	1.47052e16i	−0.469922	−	0.813928i	−0.999408	+	0.0343900i	$0.989051\pi$
$318$	5.53890e15	−	9.59366e15i	0.300364	−	0.520245i
$319$	−2.16655e16	+	3.75258e16i	−1.15114	+	1.99384i
$320$	−1.99364e15	−	3.45308e15i	−0.103794	−	0.179776i
$321$	−1.24666e16			−0.636010
$322$	−1.08242e16	+	7.44228e14i	−0.541168	+	0.0372085i
$323$	4.64364e15			0.227532
$324$	5.90164e15	+	1.02219e16i	0.283420	+	0.490898i
$325$	−1.61423e16	+	2.79593e16i	−0.759843	+	1.31609i
$326$	5.83413e15	−	1.01050e16i	0.269192	−	0.466254i
$327$	−2.18023e16	−	3.77627e16i	−0.986147	−	1.70806i
$328$	1.20259e16			0.533260
$329$	1.53251e16	−	3.13285e16i	0.666241	−	1.36197i
$330$	3.85249e16			1.64211
$331$	4.94829e14	+	8.57069e14i	0.0206811	+	0.0358207i	0.876181	−	0.481983i	$-0.160083\pi$
$331$	4.94829e14	+	8.57069e14i	0.0206811	+	0.0358207i	−0.855500	+	0.517803i	$0.826750\pi$
$332$	−9.86211e15	+	1.70817e16i	−0.404178	+	0.700056i
$333$	−1.61053e15	+	2.78953e15i	−0.0647265	+	0.112110i
$334$	−1.20038e16	−	2.07912e16i	−0.473116	−	0.819461i
$335$	1.13453e16			0.438557
$336$	−3.96266e15	−	5.88968e15i	−0.150239	−	0.223299i
$337$	−2.79262e16			−1.03853			−0.519264	−	0.854614i	$-0.673794\pi$
$337$	−2.79262e16			−1.03853			−0.519264	+	0.854614i	$0.673794\pi$
$338$	2.44900e15	+	4.24180e15i	0.0893369	+	0.154736i
$339$	8.19967e15	−	1.42022e16i	0.293426	−	0.508228i
$340$	3.71420e15	−	6.43317e15i	0.130392	−	0.225846i
$341$	3.35836e15	+	5.81685e15i	0.115671	+	0.200348i
$342$	−2.40945e15			−0.0814231
$343$	2.95213e16	−	6.16717e15i	0.978868	−	0.204491i
$344$	−1.65622e16			−0.538876
$345$	2.14777e16	+	3.72005e16i	0.685747	+	1.18775i
$346$	−1.31912e16	+	2.28478e16i	−0.413322	+	0.715895i
$347$	−1.54287e16	+	2.67234e16i	−0.474448	+	0.821768i	−0.999572	−	0.0292574i	$-0.990686\pi$
$347$	−1.54287e16	+	2.67234e16i	−0.474448	+	0.821768i	0.525124	+	0.851026i	$0.324019\pi$
$348$	−1.58053e16	−	2.73755e16i	−0.477021	−	0.826224i
$349$	−1.28693e16			−0.381233			−0.190616	−	0.981665i	$-0.561049\pi$
$349$	−1.28693e16			−0.381233			−0.190616	+	0.981665i	$0.561049\pi$
$350$	−2.38638e16	−	3.54686e16i	−0.693900	−	1.03134i
$351$	−2.74224e16			−0.782725
$352$	−4.09747e15	−	7.09703e15i	−0.114812	−	0.198861i
$353$	1.52031e16	−	2.63325e16i	0.418212	−	0.724364i	−0.577548	−	0.816357i	$-0.695990\pi$
$353$	1.52031e16	−	2.63325e16i	0.418212	−	0.724364i	0.995760	+	0.0919925i	$0.0293236\pi$
$354$	1.96807e15	−	3.40879e15i	0.0531519	−	0.0920618i
$355$	3.40607e16	+	5.89949e16i	0.903170	+	1.56434i
$356$	−2.84007e16			−0.739442
$357$	5.81129e15	−	1.18798e16i	0.148569	−	0.303714i
$358$	3.75902e16			0.943703
$359$	1.71300e16	+	2.96701e16i	0.422323	+	0.731485i	0.996166	−	0.0874804i	$-0.0278815\pi$
$359$	1.71300e16	+	2.96701e16i	0.422323	+	0.731485i	−0.573843	+	0.818965i	$0.694548\pi$
$360$	−1.92718e15	+	3.33798e15i	−0.0466613	+	0.0808198i
$361$	9.99051e15	−	1.73041e16i	0.237570	−	0.411482i
$362$	1.21122e16	+	2.09790e16i	0.282891	+	0.489981i
$363$	3.22522e16			0.739888
$364$	1.91363e16	−	1.31573e15i	0.431219	−	0.0296489i
$365$	−2.66866e16			−0.590731
$366$	−1.31195e15	−	2.27236e15i	−0.0285291	−	0.0494139i
$367$	5.55925e15	−	9.62891e15i	0.118765	−	0.205706i	−0.800514	−	0.599314i	$-0.795440\pi$
$367$	5.55925e15	−	9.62891e15i	0.118765	−	0.205706i	0.919278	+	0.393608i	$0.128773\pi$
$368$	4.56870e15	−	7.91321e15i	0.0958918	−	0.166089i
$369$	−5.81254e15	−	1.00676e16i	−0.119866	−	0.207613i
$370$	4.72019e16			0.956419
$371$	−3.95428e16	+	2.71881e15i	−0.787295	+	0.0541312i
$372$	−4.89993e15			−0.0958652
$373$	4.48029e16	+	7.76009e16i	0.861388	+	1.49197i	0.870589	+	0.492011i	$0.163738\pi$
$373$	4.48029e16	+	7.76009e16i	0.861388	+	1.49197i	−0.00920088	+	0.999958i	$0.502929\pi$
$374$	7.63369e15	−	1.32219e16i	0.144234	−	0.249821i
$375$	−3.64859e16	+	6.31954e16i	−0.677519	+	1.17350i
$376$	1.46858e16	+	2.54366e16i	0.268027	+	0.464236i
$377$	8.54156e16			1.53221
$378$	1.59557e16	−	3.26175e16i	0.281332	−	0.575115i
$379$	−3.87781e16			−0.672097			−0.336048	−	0.941845i	$-0.609091\pi$
$379$	−3.87781e16			−0.672097			−0.336048	+	0.941845i	$0.609091\pi$
$380$	1.76542e16	+	3.05779e16i	0.300783	+	0.520972i
$381$	−1.81581e16	+	3.14508e16i	−0.304130	+	0.526768i
$382$	−1.71942e16	+	2.97812e16i	−0.283119	+	0.490377i
$383$	−8.43523e15	−	1.46103e16i	−0.136554	−	0.236519i	0.789636	−	0.613576i	$-0.210269\pi$
$383$	−8.43523e15	−	1.46103e16i	−0.136554	−	0.236519i	−0.926190	+	0.377057i	$0.876936\pi$
$384$	5.97832e15			0.0951538
$385$	−7.69468e16	−	1.14366e17i	−1.20419	−	1.78978i
$386$	−6.52788e15			−0.100451
$387$	8.00508e15	+	1.38652e16i	0.121128	+	0.209800i
$388$	1.17568e15	−	2.03634e15i	0.0174938	−	0.0303001i
$389$	3.91512e16	−	6.78119e16i	0.572892	−	0.992279i	−0.423375	−	0.905955i	$-0.639155\pi$
$389$	3.91512e16	−	6.78119e16i	0.572892	−	0.992279i	0.996267	−	0.0863240i	$-0.0275120\pi$
$390$	−3.79708e16	−	6.57674e16i	−0.546424	−	0.946435i
$391$	1.70232e16			0.240930
$392$	−9.56944e15	+	2.35272e16i	−0.133207	+	0.327499i
$393$	−1.76949e16			−0.242268
$394$	−2.60721e16	−	4.51583e16i	−0.351117	−	0.608152i
$395$	5.72457e16	−	9.91525e16i	0.758337	−	1.31348i
$396$	−3.96089e15	+	6.86047e15i	−0.0516148	+	0.0893995i
$397$	−3.21256e16	−	5.56432e16i	−0.411826	−	0.713303i	0.583264	−	0.812283i	$-0.301775\pi$
$397$	−3.21256e16	−	5.56432e16i	−0.411826	−	0.713303i	−0.995089	+	0.0989799i	$0.968442\pi$
$398$	−1.17285e16			−0.147912
$399$	3.50903e16	+	5.21545e16i	0.435375	+	0.647095i
$400$	3.60024e16			0.439482
$401$	2.06233e15	+	3.57206e15i	0.0247696	+	0.0429023i	0.878145	−	0.478395i	$-0.158781\pi$
$401$	2.06233e15	+	3.57206e15i	0.0247696	+	0.0429023i	−0.853375	+	0.521298i	$0.825448\pi$
$402$	−8.50530e15	+	1.47316e16i	−0.100513	+	0.174093i
$403$	6.62011e15	−	1.14664e16i	0.0769808	−	0.133335i
$404$	−3.56196e16	−	6.16950e16i	−0.407577	−	0.705945i
$405$	−1.67201e17			−1.88270
$406$	−4.96991e16	+	1.01598e17i	−0.550718	+	1.12581i
$407$	9.70128e16			1.05795
$408$	5.56887e15	+	9.64557e15i	0.0597690	+	0.103523i
$409$	−5.14981e16	+	8.91973e16i	−0.543988	+	0.942215i	0.454682	+	0.890654i	$0.349753\pi$
$409$	−5.14981e16	+	8.91973e16i	−0.543988	+	0.942215i	−0.998670	+	0.0515613i	$0.983580\pi$
$410$	−8.51777e16	+	1.47532e17i	−0.885586	+	1.53388i
$411$	−2.18972e16	−	3.79271e16i	−0.224087	−	0.388130i
$412$	−9.74586e14			−0.00981722
$413$	−1.40502e16	+	9.66038e14i	−0.139318	+	0.00957897i
$414$	−8.83281e15			−0.0862178
$415$	−1.39703e17	−	2.41973e17i	−1.34244	−	2.32517i
$416$	−8.07708e15	+	1.39899e16i	−0.0764095	+	0.132345i
$417$	−6.26833e16	+	1.08571e17i	−0.583805	+	1.01118i
$418$	3.62841e16	+	6.28460e16i	0.332714	+	0.576277i
$419$	1.67636e17			1.51348			0.756739	−	0.653717i	$-0.226791\pi$
$419$	1.67636e17			1.51348			0.756739	+	0.653717i	$0.226791\pi$
$420$	1.00320e17	−	6.89762e15i	0.891802	−	0.0613167i
$421$	−1.10662e17			−0.968649			−0.484325	−	0.874888i	$-0.660935\pi$
$421$	−1.10662e17			−0.968649			−0.484325	+	0.874888i	$0.660935\pi$
$422$	7.33729e16	+	1.27086e17i	0.632419	+	1.09538i
$423$	1.41963e16	−	2.45888e16i	0.120493	−	0.208701i
$424$	1.66903e16	−	2.89085e16i	0.139504	−	0.241628i
$425$	3.35366e16	+	5.80872e16i	0.276052	+	0.478137i
$426$	−1.02138e17			−0.827987
$427$	−4.12536e15	+	8.43329e15i	−0.0329367	+	0.0673311i
$428$	−3.75654e16			−0.295395
$429$	−7.80404e16	−	1.35170e17i	−0.604432	−	1.04691i
$430$	1.17307e17	−	2.03182e17i	0.894913	−	1.55003i
$431$	−2.56990e16	+	4.45119e16i	−0.193114	+	0.334483i	−0.946281	−	0.323347i	$-0.895192\pi$
$431$	−2.56990e16	+	4.45119e16i	−0.193114	+	0.334483i	0.753167	+	0.657830i	$0.228525\pi$
$432$	1.52901e16	+	2.64833e16i	0.113179	+	0.196032i
$433$	1.22629e17			0.894173			0.447086	−	0.894491i	$-0.352462\pi$
$433$	1.22629e17			0.894173			0.447086	+	0.894491i	$0.352462\pi$
$434$	9.78675e15	+	1.45460e16i	0.0703000	+	0.104486i
$435$	4.47784e17			3.16876
$436$	−6.56966e16	−	1.13790e17i	−0.458016	−	0.793307i
$437$	−4.04569e16	+	7.00734e16i	−0.277884	+	0.481309i
$438$	2.00062e16	−	3.46518e16i	0.135389	−	0.234501i
$439$	4.05751e16	+	7.02782e16i	0.270546	+	0.468599i	0.969002	−	0.247054i	$-0.0794625\pi$
$439$	4.05751e16	+	7.02782e16i	0.270546	+	0.468599i	−0.698456	+	0.715653i	$0.746129\pi$
$440$	1.16087e17			0.762677
$441$	2.43212e16	−	3.36034e15i	0.157447	−	0.0217537i
$442$	−3.00956e16			−0.191981
$443$	5.44457e16	+	9.43028e16i	0.342247	+	0.592789i	0.984850	−	0.173411i	$-0.0554787\pi$
$443$	5.44457e16	+	9.43028e16i	0.342247	+	0.592789i	−0.642603	+	0.766200i	$0.722145\pi$
$444$	−3.53860e16	+	6.12904e16i	−0.219201	+	0.379667i
$445$	2.01157e17	−	3.48414e17i	1.22799	−	2.12694i
$446$	3.40588e15	+	5.89916e15i	0.0204905	+	0.0354906i
$447$	−9.09309e16			−0.539154
$448$	−1.19406e16	−	1.77473e16i	−0.0697783	−	0.103711i
$449$	−2.13503e17			−1.22971			−0.614856	−	0.788639i	$-0.710786\pi$
$449$	−2.13503e17			−1.22971			−0.614856	+	0.788639i	$0.710786\pi$
$450$	−1.74012e16	−	3.01397e16i	−0.0987863	−	0.171103i
$451$	−1.75063e17	+	3.03219e17i	−0.979598	+	1.69671i
$452$	2.47080e16	−	4.27955e16i	0.136282	−	0.236047i
$453$	9.43337e16	+	1.63391e17i	0.512895	+	0.888361i
$454$	−3.60333e15			−0.0193126
$455$	−1.19398e17	+	2.44079e17i	−0.630844	+	1.28961i
$456$	−5.29395e16			−0.275745
$457$	1.23322e17	+	2.13600e17i	0.633263	+	1.09684i	0.986880	+	0.161454i	$0.0516184\pi$
$457$	1.23322e17	+	2.13600e17i	0.633263	+	1.09684i	−0.353617	+	0.935390i	$0.615048\pi$
$458$	−6.97899e14	+	1.20880e15i	−0.00353319	+	0.00611967i
$459$	−2.84859e16	+	4.93389e16i	−0.142183	+	0.246268i
$460$	6.47186e16	+	1.12096e17i	0.318495	+	0.551650i
$461$	−2.14001e17			−1.03839			−0.519194	−	0.854656i	$-0.673768\pi$
$461$	−2.14001e17			−1.03839			−0.519194	+	0.854656i	$0.673768\pi$
$462$	2.06186e17	−	1.41765e16i	0.986474	−	0.0678260i
$463$	2.10637e16			0.0993706			0.0496853	−	0.998765i	$-0.484178\pi$
$463$	2.10637e16			0.0993706			0.0496853	+	0.998765i	$0.484178\pi$
$464$	−4.76259e16	−	8.24904e16i	−0.221552	−	0.383740i
$465$	3.47054e16	−	6.01114e16i	0.159203	−	0.275748i
$466$	1.18235e17	−	2.04789e17i	0.534858	−	0.926401i
$467$	−6.07893e16	−	1.05290e17i	−0.271186	−	0.469708i	0.697980	−	0.716117i	$-0.254083\pi$
$467$	−6.07893e16	−	1.05290e17i	−0.271186	−	0.469708i	−0.969166	+	0.246410i	$0.920749\pi$
$468$	1.56157e16			0.0687010
$469$	6.07202e16	−	4.17488e15i	0.263457	−	0.0181143i
$470$	−4.16069e17			−1.78045
$471$	1.53944e16	+	2.66639e16i	0.0649721	+	0.112535i
$472$	5.93036e15	−	1.02717e16i	0.0246864	−	0.0427581i
$473$	2.41099e17	−	4.17596e17i	0.989915	−	1.71458i
$474$	8.58313e16	+	1.48664e17i	0.347605	+	0.602070i
$475$	−3.18810e17			−1.27357
$476$	1.75111e16	−	3.57971e16i	0.0690030	−	0.141060i
$477$	−3.22680e16			−0.125430
$478$	−4.93392e16	−	8.54580e16i	−0.189195	−	0.327696i
$479$	3.61417e16	−	6.25992e16i	0.136719	−	0.236803i	−0.789534	−	0.613707i	$-0.789678\pi$
$479$	3.61417e16	−	6.25992e16i	0.136719	−	0.236803i	0.926253	+	0.376903i	$0.123011\pi$
$480$	−4.23434e16	+	7.33409e16i	−0.158022	+	0.273702i
$481$	−9.56175e16	−	1.65614e17i	−0.352042	−	0.609754i
$482$	−3.00301e17			−1.09081
$483$	1.28638e17	+	1.91194e17i	0.461013	+	0.685200i
$484$	9.71851e16			0.343641
$485$	1.66543e16	+	2.88461e16i	0.0581038	+	0.100639i
$486$	3.23541e16	−	5.60390e16i	0.111377	−	0.192910i
$487$	7.15485e16	−	1.23926e17i	0.243032	−	0.420943i	−0.718545	−	0.695481i	$-0.755191\pi$
$487$	7.15485e16	−	1.23926e17i	0.243032	−	0.420943i	0.961576	+	0.274538i	$0.0885248\pi$
$488$	−3.95327e15	−	6.84727e15i	−0.0132504	−	0.0229503i
$489$	−2.47825e17			−0.819668
$490$	−2.20849e17	−	2.84035e17i	−0.720809	−	0.927038i
$491$	−4.93727e17			−1.59022			−0.795110	−	0.606466i	$-0.792587\pi$
$491$	−4.93727e17			−1.59022			−0.795110	+	0.606466i	$0.792587\pi$
$492$	−1.27711e17	−	2.21202e17i	−0.405934	−	0.703098i
$493$	8.87281e16	−	1.53682e17i	0.278328	−	0.482078i
$494$	7.15245e16	−	1.23884e17i	0.221427	−	0.383522i
$495$	−5.61086e16	−	9.71830e16i	−0.171434	−	0.296932i
$496$	−1.47649e16			−0.0445246
$497$	2.04002e17	+	3.03207e17i	0.607181	+	0.902449i
$498$	4.18928e17			1.23069
$499$	−3.15037e16	−	5.45660e16i	−0.0913498	−	0.158223i	0.816730	−	0.577021i	$-0.195785\pi$
$499$	−3.15037e16	−	5.45660e16i	−0.0913498	−	0.158223i	−0.908079	+	0.418798i	$0.862451\pi$
$500$	−1.09942e17	+	1.90426e17i	−0.314674	+	0.545031i
$501$	−2.54952e17	+	4.41590e17i	−0.720300	+	1.24760i
$502$	1.90541e17	+	3.30027e17i	0.531392	+	0.920398i
$503$	3.56567e17			0.981633			0.490816	−	0.871263i	$-0.336699\pi$
$503$	3.56567e17			0.981633			0.490816	+	0.871263i	$0.336699\pi$
$504$	−9.08598e15	+	1.85741e16i	−0.0246930	+	0.0504787i
$505$	1.00915e18			2.70746
$506$	1.33014e17	+	2.30388e17i	0.352306	+	0.610212i
$507$	5.20150e16	−	9.00926e16i	0.136012	−	0.235579i
$508$	−5.47157e16	+	9.47703e16i	−0.141253	+	0.244657i
$509$	−1.18870e17	−	2.05890e17i	−0.302976	−	0.524770i	0.673832	−	0.738884i	$-0.264647\pi$
$509$	−1.18870e17	−	2.05890e17i	−0.302976	−	0.524770i	−0.976809	+	0.214114i	$0.931314\pi$
$510$	−1.57773e17			−0.397034
$511$	−1.42827e17	+	9.82019e15i	−0.354874	+	0.0243997i
$512$	1.80144e16			0.0441942
$513$	−1.35398e17	−	2.34516e17i	−0.327981	−	0.568080i
$514$	1.39031e17	−	2.40809e17i	0.332546	−	0.575987i
$515$	6.90283e15	−	1.19560e16i	0.0163035	−	0.0282384i
$516$	1.75885e17	+	3.04641e17i	0.410209	+	0.710503i
$517$	−8.55136e17			−1.96946
$518$	2.52625e17	−	1.73695e16i	0.574556	−	0.0395042i
$519$	5.60341e17			1.25853
$520$	−1.14417e17	−	1.98176e17i	−0.253787	−	0.439572i
$521$	−1.27042e17	+	2.20044e17i	−0.278294	+	0.482019i	−0.970961	−	0.239238i	$-0.923102\pi$
$521$	−1.27042e17	+	2.20044e17i	−0.278294	+	0.482019i	0.692667	+	0.721258i	$0.256436\pi$
$522$	−4.60384e16	+	7.97408e16i	−0.0996005	+	0.172513i
$523$	−1.72196e17	−	2.98253e17i	−0.367928	−	0.637270i	0.621314	−	0.783562i	$-0.286599\pi$
$523$	−1.72196e17	−	2.98253e17i	−0.367928	−	0.637270i	−0.989241	+	0.146292i	$0.953266\pi$
$524$	−5.33198e16			−0.112521
$525$	−3.98975e17	+	8.15607e17i	−0.831592	+	1.69999i
$526$	−3.02931e17			−0.623644
$527$	−1.37537e16	−	2.38221e16i	−0.0279673	−	0.0484407i
$528$	−8.70273e16	+	1.50736e17i	−0.174797	+	0.302758i
$529$	1.03707e17	−	1.79625e17i	0.205753	−	0.356374i
$530$	2.36429e17	+	4.09508e17i	0.463349	+	0.802544i
$531$	−1.14654e16			−0.0221959
$532$	1.05737e17	+	1.57157e17i	0.202210	+	0.300543i
$533$	6.90182e17			1.30388
$534$	3.01605e17	+	5.22395e17i	0.562885	+	0.974946i
$535$	2.66069e17	−	4.60845e17i	0.490563	−	0.849680i
$536$	−2.56289e16	+	4.43906e16i	−0.0466830	+	0.0808574i
$537$	−3.99194e17	−	6.91424e17i	−0.718375	−	1.24426i
$538$	2.28318e17			0.405934
$539$	−4.53904e17	−	5.83770e17i	−0.797328	−	1.02545i
$540$	−4.33189e17			−0.751827
$541$	5.24957e17	+	9.09253e17i	0.900206	+	1.55920i	0.827226	+	0.561869i	$0.189918\pi$
$541$	5.24957e17	+	9.09253e17i	0.900206	+	1.55920i	0.0729798	+	0.997333i	$0.476749\pi$
$542$	3.28000e17	−	5.68112e17i	0.555748	−	0.962584i
$543$	2.57255e17	−	4.45578e17i	0.430690	−	0.745977i
$544$	1.67806e16	+	2.90649e16i	0.0277597	+	0.0480813i
$545$	1.86127e18			3.04251
$546$	−2.27421e17	−	3.38015e17i	−0.367349	−	0.545989i
$547$	−3.72752e17			−0.594980			−0.297490	−	0.954725i	$-0.596150\pi$
$547$	−3.72752e17			−0.594980			−0.297490	+	0.954725i	$0.596150\pi$
$548$	−6.59826e16	−	1.14285e17i	−0.104077	−	0.180267i
$549$	−3.82150e15	+	6.61902e15i	−0.00595680	+	0.0103175i
$550$	−5.24092e17	+	9.07754e17i	−0.807328	+	1.39833i
$551$	4.21739e17	+	7.30473e17i	0.642034	+	1.11204i
$552$	−1.94071e17			−0.291983
$553$	2.69893e17	−	5.51730e17i	0.401309	−	0.820377i
$554$	−2.73582e17			−0.402044
$555$	−5.01267e17	−	8.68219e17i	−0.728055	−	1.26103i
$556$	−1.88883e17	+	3.27155e17i	−0.271148	+	0.469642i
$557$	−6.86194e17	+	1.18852e18i	−0.973617	+	1.68635i	−0.289192	+	0.957271i	$0.593387\pi$
$557$	−6.86194e17	+	1.18852e18i	−0.973617	+	1.68635i	−0.684425	+	0.729083i	$0.739947\pi$
$558$	7.13637e15	+	1.23606e16i	0.0100082	+	0.0173347i
$559$	−9.50525e17			−1.31761
$560$	3.02294e17	−	2.07845e16i	0.414197	−	0.0284785i
$561$	−3.24268e17			−0.439182
$562$	−3.27004e17	−	5.66388e17i	−0.437791	−	0.758277i
$563$	3.79008e14	−	6.56461e14i	0.000501584	−	0.000868770i	−0.865775	−	0.500434i	$-0.833174\pi$
$563$	3.79008e14	−	6.56461e14i	0.000501584	−	0.000868770i	0.866276	+	0.499566i	$0.166507\pi$
$564$	3.11916e17	−	5.40255e17i	0.408060	−	0.706781i
$565$	3.50005e17	+	6.06226e17i	0.452646	+	0.784006i
$566$	2.01240e17			0.257281
$567$	−8.94862e17	+	6.15271e16i	−1.13101	+	0.0777637i
$568$	−3.07770e17			−0.384559
$569$	−2.04436e17	−	3.54094e17i	−0.252539	−	0.437410i	0.711685	−	0.702498i	$-0.247932\pi$
$569$	−2.04436e17	−	3.54094e17i	−0.252539	−	0.437410i	−0.964224	+	0.265088i	$0.914599\pi$
$570$	3.74961e17	−	6.49452e17i	0.457931	−	0.793159i
$571$	5.58205e17	−	9.66840e17i	0.673999	−	1.16740i	−0.302761	−	0.953066i	$-0.597908\pi$
$571$	5.58205e17	−	9.66840e17i	0.673999	−	1.16740i	0.976760	−	0.214334i	$-0.0687582\pi$
$572$	−2.35158e17	−	4.07306e17i	−0.280728	−	0.486236i
$573$	7.30383e17			0.862076
$574$	−4.01582e17	+	8.20936e17i	−0.468648	+	0.958036i
$575$	−1.16873e18			−1.34857
$576$	−8.70696e15	−	1.50809e16i	−0.00993392	−	0.0172060i
$577$	−2.09150e17	+	3.62259e17i	−0.235948	+	0.408673i	−0.959548	−	0.281546i	$-0.909153\pi$
$577$	−2.09150e17	+	3.62259e17i	−0.235948	+	0.408673i	0.723600	+	0.690219i	$0.242486\pi$
$578$	2.85684e17	−	4.94819e17i	0.318680	−	0.551970i
$579$	6.93236e16	+	1.20072e17i	0.0764664	+	0.132444i
$580$	1.34930e18			1.47173
$581$	−8.36735e17	−	1.24363e18i	−0.902491	−	1.34137i
$582$	−4.99411e16			−0.0532671
$583$	4.85927e17	+	8.41650e17i	0.512537	+	0.887740i
$584$	6.02846e16	−	1.04416e17i	0.0628815	−	0.108914i
$585$	−1.10603e17	+	1.91570e17i	−0.114092	+	0.197613i
$586$	−2.99209e17	−	5.18245e17i	−0.305239	−	0.528690i
$587$	−9.03947e17			−0.912001			−0.456000	−	0.889980i	$-0.650718\pi$
$587$	−9.03947e17			−0.912001			−0.456000	+	0.889980i	$0.650718\pi$
$588$	5.34377e17	−	7.38322e16i	0.533206	−	0.0736704i
$589$	1.30747e17			0.129027
$590$	8.40074e16	+	1.45505e17i	0.0819935	+	0.142017i
$591$	−5.53753e17	+	9.59128e17i	−0.534561	+	0.925887i
$592$	−1.06628e17	+	1.84686e17i	−0.101808	+	0.176337i
$593$	−4.00898e17	−	6.94375e17i	−0.378598	−	0.655751i	0.612261	−	0.790656i	$-0.290260\pi$
$593$	−4.00898e17	−	6.94375e17i	−0.378598	−	0.655751i	−0.990859	+	0.134905i	$0.956927\pi$
$594$	−8.90322e17			−0.831640
$595$	3.15125e17	+	4.68368e17i	0.291154	+	0.432740i
$596$	−2.74001e17			−0.250410
$597$	1.24553e17	+	2.15731e17i	0.112595	+	0.195020i
$598$	2.62202e17	−	4.54148e17i	0.234465	−	0.406106i
$599$	−4.17003e17	+	7.22270e17i	−0.368863	+	0.638889i	−0.989388	−	0.145298i	$-0.953586\pi$
$599$	−4.17003e17	+	7.22270e17i	−0.368863	+	0.638889i	0.620525	+	0.784186i	$0.286919\pi$
$600$	−3.82332e17	−	6.62218e17i	−0.334547	−	0.579453i
$601$	6.92618e17			0.599528			0.299764	−	0.954013i	$-0.403092\pi$
$601$	6.92618e17			0.599528			0.299764	+	0.954013i	$0.403092\pi$
$602$	5.53063e17	−	1.13060e18i	0.473584	−	0.968127i
$603$	4.95493e16			0.0419734
$604$	2.84255e17	+	4.92344e17i	0.238214	+	0.412599i
$605$	−6.88345e17	+	1.19225e18i	−0.570685	+	0.988455i
$606$	−7.56534e17	+	1.31035e18i	−0.620520	+	1.07477i
$607$	−1.42849e17	−	2.47422e17i	−0.115918	−	0.200776i	0.802228	−	0.597017i	$-0.203648\pi$
$607$	−1.42849e17	−	2.47422e17i	−0.115918	−	0.200776i	−0.918146	+	0.396241i	$0.870314\pi$
$608$	−1.59522e17			−0.128070
$609$	2.39654e18	−	1.64777e17i	1.90359	−	0.130883i
$610$	1.12001e17			0.0880196
$611$	8.42837e17	+	1.45984e18i	0.655353	+	1.13511i
$612$	1.62213e16	−	2.80961e16i	0.0124796	−	0.0216153i
$613$	−6.16171e17	+	1.06724e18i	−0.469038	+	0.812398i	−0.999374	−	0.0353898i	$-0.988733\pi$
$613$	−6.16171e17	+	1.06724e18i	−0.469038	+	0.812398i	0.530335	+	0.847788i	$0.322066\pi$
$614$	−2.82466e17	−	4.89245e17i	−0.212751	−	0.368495i
$615$	3.61822e18			2.69654
$616$	6.21297e17	−	4.27179e16i	0.458168	−	0.0315018i
$617$	1.82630e18			1.33265			0.666327	−	0.745659i	$-0.267865\pi$
$617$	1.82630e18			1.33265			0.666327	+	0.745659i	$0.267865\pi$
$618$	1.03497e16	+	1.79263e16i	0.00747316	+	0.0129439i
$619$	−1.10179e18	+	1.90835e18i	−0.787243	+	1.36354i	0.140407	+	0.990094i	$0.455159\pi$
$619$	−1.10179e18	+	1.90835e18i	−0.787243	+	1.36354i	−0.927650	+	0.373451i	$0.878175\pi$
$620$	1.04577e17	−	1.81133e17i	0.0739420	−	0.128071i
$621$	−4.96356e17	−	8.59714e17i	−0.347295	−	0.601532i
$622$	−6.80642e17			−0.471283
$623$	9.48384e17	−	1.93874e18i	0.649848	−	1.32846i
$624$	3.43102e17			0.232661
$625$	−2.47647e17	−	4.28938e17i	−0.166193	−	0.287855i
$626$	−3.99414e17	+	6.91805e17i	−0.265271	+	0.459463i
$627$	7.70648e17	−	1.33480e18i	0.506544	−	0.877359i
$628$	4.63878e16	+	8.03460e16i	0.0301763	+	0.0522669i
$629$	−3.97302e17			−0.255795
$630$	−1.63509e17	−	2.43022e17i	−0.104190	−	0.154857i
$631$	−6.70102e17			−0.422620			−0.211310	−	0.977419i	$-0.567773\pi$
$631$	−6.70102e17			−0.422620			−0.211310	+	0.977419i	$0.567773\pi$
$632$	2.58635e17	+	4.47968e17i	0.161445	+	0.279632i
$633$	1.55839e18	−	2.69920e18i	0.962833	−	1.66767i
$634$	−5.43364e17	+	9.41133e17i	−0.332285	+	0.575534i
$635$	−7.75083e17	−	1.34248e18i	−0.469158	−	0.812606i
$636$	−7.08980e17			−0.424778
$637$	−5.49200e17	+	1.35025e18i	−0.325705	+	0.800770i
$638$	2.77319e18			1.62796
$639$	1.48756e17	+	2.57653e17i	0.0864407	+	0.149720i
$640$	−1.27593e17	+	2.20997e17i	−0.0733933	+	0.127121i
$641$	−4.63406e17	+	8.02642e17i	−0.263866	+	0.457030i	−0.967266	−	0.253765i	$-0.918331\pi$
$641$	−4.63406e17	+	8.02642e17i	−0.263866	+	0.457030i	0.703400	+	0.710795i	$0.251664\pi$
$642$	3.98930e17	+	6.90967e17i	0.224864	+	0.389475i
$643$	−3.52164e17			−0.196505			−0.0982524	−	0.995162i	$-0.531325\pi$
$643$	−3.52164e17			−0.196505			−0.0982524	+	0.995162i	$0.531325\pi$
$644$	3.87623e17	+	5.76122e17i	0.214117	+	0.318241i
$645$	−4.98305e18			−2.72494
$646$	−1.48597e17	−	2.57377e17i	−0.0804447	−	0.139334i
$647$	−6.27425e17	+	1.08673e18i	−0.336267	+	0.582431i	−0.983727	−	0.179668i	$-0.942498\pi$
$647$	−6.27425e17	+	1.08673e18i	−0.336267	+	0.582431i	0.647461	+	0.762099i	$0.275831\pi$
$648$	3.77705e17	−	6.54205e17i	0.200408	−	0.347117i
$649$	1.72658e17	+	2.99053e17i	0.0906978	+	0.157093i
$650$	2.06622e18			1.07458
$651$	1.63623e17	−	3.34488e17i	0.0842498	−	0.172228i
$652$	−7.46769e17			−0.380695
$653$	−1.29155e18	−	2.23703e18i	−0.651891	−	1.12911i	−0.982664	−	0.185398i	$-0.940643\pi$
$653$	−1.29155e18	−	2.23703e18i	−0.651891	−	1.12911i	0.330772	−	0.943711i	$-0.392691\pi$
$654$	−1.39535e18	+	2.41681e18i	−0.697311	+	1.20778i
$655$	3.77655e17	−	6.54117e17i	0.186864	−	0.323659i
$656$	−3.84830e17	−	6.66545e17i	−0.188536	−	0.326554i
$657$	−1.16550e17			−0.0565377
$658$	−2.22681e18	+	1.53106e17i	−1.06958	+	0.0735401i
$659$	−3.21927e17			−0.153110			−0.0765548	−	0.997065i	$-0.524392\pi$
$659$	−3.21927e17			−0.153110			−0.0765548	+	0.997065i	$0.524392\pi$
$660$	−1.23280e18	−	2.13527e18i	−0.580572	−	1.00558i
$661$	7.59869e17	−	1.31613e18i	0.354347	−	0.613748i	−0.632659	−	0.774431i	$-0.718036\pi$
$661$	7.59869e17	−	1.31613e18i	0.354347	−	0.613748i	0.987006	+	0.160683i	$0.0513697\pi$
$662$	3.16690e16	−	5.48524e16i	0.0146237	−	0.0253290i
$663$	3.19603e17	+	5.53569e17i	0.146142	+	0.253125i
$664$	1.26235e18			0.571594
$665$	−2.67689e18	+	1.84052e17i	−1.20030	+	0.0825277i
$666$	2.06148e17			0.0915371
$667$	1.54606e18	+	2.67785e18i	0.679841	+	1.17752i
$668$	−7.68245e17	+	1.33064e18i	−0.334544	+	0.579446i
$669$	7.23384e16	−	1.25294e17i	0.0311960	−	0.0540331i
$670$	−3.63050e17	−	6.28822e17i	−0.155053	−	0.268560i
$671$	2.30193e17			0.0973636
$672$	−1.99634e17	+	4.08103e17i	−0.0836246	+	0.170950i
$673$	−1.02435e18			−0.424963			−0.212481	−	0.977165i	$-0.568154\pi$
$673$	−1.02435e18			−0.424963			−0.212481	+	0.977165i	$0.568154\pi$
$674$	8.93639e17	+	1.54783e18i	0.367175	+	0.635965i
$675$	1.95570e18	−	3.38737e18i	0.795844	−	1.37844i
$676$	1.56736e17	−	2.71475e17i	0.0631707	−	0.109415i
$677$	−7.58866e17	−	1.31439e18i	−0.302927	−	0.524686i	0.673870	−	0.738850i	$-0.264631\pi$
$677$	−7.58866e17	−	1.31439e18i	−0.302927	−	0.524686i	−0.976798	+	0.214164i	$0.931297\pi$
$678$	−1.04956e18			−0.414967
$679$	9.97486e16	+	1.48256e17i	0.0390619	+	0.0580575i
$680$	−4.75417e17			−0.184402
$681$	3.82660e16	+	6.62787e16i	0.0147014	+	0.0254635i
$682$	2.14935e17	−	3.72278e17i	0.0817916	−	0.141667i
$683$	−7.63115e17	+	1.32175e18i	−0.287644	+	0.498214i	−0.973247	−	0.229762i	$-0.926205\pi$
$683$	−7.63115e17	+	1.32175e18i	−0.287644	+	0.498214i	0.685603	+	0.727976i	$0.259539\pi$
$684$	7.71023e16	+	1.33545e17i	0.0287874	+	0.0498613i
$685$	1.86937e18			0.691365
$686$	−1.28650e18	−	1.43889e18i	−0.471307	−	0.527134i
$687$	2.96457e16			0.0107583
$688$	5.29992e17	+	9.17972e17i	0.190522	+	0.329993i
$689$	9.57875e17	−	1.65909e18i	0.341102	−	0.590806i
$690$	1.37457e18	−	2.38083e18i	0.484896	−	0.839865i
$691$	1.24722e18	+	2.16025e18i	0.435850	+	0.754914i	0.997365	−	0.0725526i	$-0.0231145\pi$
$691$	1.24722e18	+	2.16025e18i	0.435850	+	0.754914i	−0.561515	+	0.827467i	$0.689781\pi$
$692$	1.68847e18			0.584526
$693$	−3.36055e17	−	4.99477e17i	−0.115251	−	0.171297i
$694$	1.97488e18			0.670971
$695$	−2.67565e18	−	4.63436e18i	−0.900592	−	1.55987i
$696$	−1.01154e18	+	1.75204e18i	−0.337304	+	0.584228i
$697$	7.16947e17	−	1.24179e18i	0.236850	−	0.410237i
$698$	4.11818e17	+	7.13290e17i	0.134786	+	0.233456i
$699$	−5.02245e18			−1.62860
$700$	−1.20223e18	+	2.45766e18i	−0.386233	+	0.789559i
$701$	−2.18959e17			−0.0696939			−0.0348470	−	0.999393i	$-0.511094\pi$
$701$	−2.18959e17			−0.0696939			−0.0348470	+	0.999393i	$0.511094\pi$
$702$	8.77516e17	+	1.51990e18i	0.276735	+	0.479319i
$703$	9.44221e17	−	1.63544e18i	0.295028	−	0.511004i
$704$	−2.62238e17	+	4.54210e17i	−0.0811846	+	0.140616i
$705$	4.41850e18	+	7.65307e18i	1.35533	+	2.34750i
$706$	−1.94600e18			−0.591441
$707$	5.40098e18	−	3.71349e17i	1.62647	−	0.111829i
$708$	−2.51913e17			−0.0751681
$709$	−1.81269e18	−	3.13966e18i	−0.535947	−	0.928288i	−0.999117	−	0.0420182i	$-0.986621\pi$
$709$	−1.81269e18	−	3.13966e18i	−0.535947	−	0.928288i	0.463170	−	0.886270i	$-0.346712\pi$
$710$	2.17989e18	−	3.77567e18i	0.638637	−	1.10615i
$711$	2.50013e17	−	4.33036e17i	0.0725790	−	0.125710i
$712$	9.08822e17	+	1.57413e18i	0.261432	+	0.452814i
$713$	4.79306e17			0.136625
$714$	−8.44404e17	+	5.80578e16i	−0.238513	+	0.0163992i
$715$	6.66234e18			1.86482
$716$	−1.20289e18	−	2.08346e18i	−0.333649	−	0.577898i
$717$	−1.04793e18	+	1.81506e18i	−0.288042	+	0.498904i
$718$	1.09632e18	−	1.89889e18i	0.298627	−	0.517238i
$719$	1.70480e18	+	2.95280e18i	0.460188	+	0.797069i	0.998970	−	0.0453763i	$-0.0144487\pi$
$719$	1.70480e18	+	2.95280e18i	0.460188	+	0.797069i	−0.538782	+	0.842445i	$0.681115\pi$
$720$	2.46680e17			0.0659891
$721$	3.25444e16	−	6.65289e16i	0.00862773	−	0.0176373i
$722$	−1.27878e18			−0.335974
$723$	3.18908e18	+	5.52365e18i	0.830360	+	1.43823i
$724$	7.75183e17	−	1.34266e18i	0.200034	−	0.346469i
$725$	−6.09165e18	+	1.05510e19i	−1.55789	+	2.69835i
$726$	−1.03207e18	−	1.78760e18i	−0.261590	−	0.453087i
$727$	−3.42614e18			−0.860659			−0.430330	−	0.902672i	$-0.641603\pi$
$727$	−3.42614e18			−0.860659			−0.430330	+	0.902672i	$0.641603\pi$
$728$	−6.85286e17	−	1.01854e18i	−0.170615	−	0.253584i
$729$	3.21995e18			0.794547
$730$	8.53971e17	+	1.47912e18i	0.208855	+	0.361747i
$731$	−9.87387e17	+	1.71020e18i	−0.239345	+	0.414558i
$732$	−8.39645e16	+	1.45431e17i	−0.0201731	+	0.0349409i
$733$	−1.89221e18	−	3.27740e18i	−0.450602	−	0.780466i	0.547821	−	0.836596i	$-0.315457\pi$
$733$	−1.89221e18	−	3.27740e18i	−0.450602	−	0.780466i	−0.998424	+	0.0561292i	$0.982124\pi$
$734$	−7.11584e17			−0.167958
$735$	−2.87914e18	+	7.07857e18i	−0.673589	+	1.65607i
$736$	−5.84793e17			−0.135611
$737$	−7.46168e17	−	1.29240e18i	−0.171513	−	0.297070i
$738$	−3.72002e17	+	6.44327e17i	−0.0847578	+	0.146805i
$739$	−2.10926e17	+	3.65334e17i	−0.0476365	+	0.0825089i	−0.888861	−	0.458178i	$-0.848502\pi$
$739$	−2.10926e17	+	3.65334e17i	−0.0476365	+	0.0825089i	0.841224	+	0.540687i	$0.181836\pi$
$740$	−1.51046e18	−	2.61620e18i	−0.338145	−	0.585685i
$741$	−3.03825e18			−0.674226
$742$	1.41606e18	+	2.10468e18i	0.311499	+	0.462979i
$743$	2.61249e18			0.569676			0.284838	−	0.958576i	$-0.408060\pi$
$743$	2.61249e18			0.569676			0.284838	+	0.958576i	$0.408060\pi$
$744$	1.56798e17	+	2.71582e17i	0.0338934	+	0.0587052i
$745$	1.94070e18	−	3.36140e18i	0.415856	−	0.720284i
$746$	2.86739e18	−	4.96646e18i	0.609094	−	1.05498i
$747$	−6.10136e17	−	1.05679e18i	−0.128482	−	0.222538i
$748$	−9.77112e17			−0.203978
$749$	1.25442e18	−	2.56435e18i	0.259604	−	0.530696i
$750$	4.67019e18			0.958156
$751$	−3.56367e18	−	6.17247e18i	−0.724834	−	1.25545i	−0.959042	−	0.283263i	$-0.908583\pi$
$751$	−3.56367e18	−	6.17247e18i	−0.724834	−	1.25545i	0.234209	−	0.972186i	$-0.424750\pi$
$752$	9.39894e17	−	1.62794e18i	0.189523	−	0.328264i
$753$	4.04696e18	−	7.00953e18i	0.809024	−	1.40127i
$754$	−2.73330e18	−	4.73421e18i	−0.541718	−	0.938284i
$755$	−8.05331e18			−1.58241
$756$	−2.31843e18	+	1.59406e17i	−0.451650	+	0.0310537i
$757$	−3.59421e18			−0.694194			−0.347097	−	0.937829i	$-0.612832\pi$
$757$	−3.59421e18			−0.694194			−0.347097	+	0.937829i	$0.612832\pi$
$758$	1.24090e18	+	2.14930e18i	0.237622	+	0.411574i
$759$	2.82512e18	−	4.89326e18i	0.536372	−	0.929024i
$760$	1.12987e18	−	1.95699e18i	0.212686	−	0.368383i
$761$	1.41193e18	+	2.44554e18i	0.263520	+	0.456431i	0.967175	−	0.254111i	$-0.0817830\pi$
$761$	1.41193e18	+	2.44554e18i	0.263520	+	0.456431i	−0.703654	+	0.710542i	$0.748450\pi$
$762$	2.32424e18			0.430104
$763$	9.96153e18	−	6.84915e17i	1.82775	−	0.125669i
$764$	2.20085e18			0.400391
$765$	2.29785e17	+	3.97999e17i	0.0414498	+	0.0717931i
$766$	−5.39855e17	+	9.35056e17i	−0.0965584	+	0.167244i
$767$	3.40350e17	−	5.89503e17i	0.0603608	−	0.104548i
$768$	−1.91306e17	−	3.31352e17i	−0.0336419	−	0.0582695i
$769$	−6.54784e18			−1.14177			−0.570883	−	0.821031i	$-0.693399\pi$
$769$	−6.54784e18			−1.14177			−0.570883	+	0.821031i	$0.693399\pi$
$770$	−3.87648e18	+	7.92452e18i	−0.670268	+	1.37020i
$771$	−5.90584e18			−1.01258
$772$	2.08892e17	+	3.61812e17i	0.0355148	+	0.0615135i
$773$	−4.55938e18	+	7.89708e18i	−0.768669	+	1.33137i	0.169616	+	0.985510i	$0.445747\pi$
$773$	−4.55938e18	+	7.89708e18i	−0.768669	+	1.33137i	−0.938285	+	0.345863i	$0.887586\pi$
$774$	5.12325e17	−	8.87373e17i	0.0856504	−	0.148351i
$775$	9.44262e17	+	1.63551e18i	0.156542	+	0.271139i
$776$	−1.50487e17			−0.0247399
$777$	−3.00227e18	−	4.46226e18i	−0.489455	−	0.727475i
$778$	−5.01136e18			−0.810192
$779$	3.40776e18	+	5.90242e18i	0.546357	+	0.946317i
$780$	−2.43013e18	+	4.20911e18i	−0.386380	+	0.669230i
$781$	4.48026e18	−	7.76004e18i	0.706434	−	1.22358i
$782$	−5.44741e17	−	9.43520e17i	−0.0851817	−	0.147539i
$783$	−1.03484e19			−1.60481
$784$	1.61023e18	−	2.22478e17i	0.247647	−	0.0342162i
$785$	−1.31423e18			−0.200455
$786$	5.66236e17	+	9.80750e17i	0.0856547	+	0.148358i
$787$	−3.53303e16	+	6.11938e16i	−0.00530043	+	0.00918062i	−0.868663	−	0.495403i	$-0.835021\pi$
$787$	−3.53303e16	+	6.11938e16i	−0.00530043	+	0.00918062i	0.863363	+	0.504583i	$0.168354\pi$
$788$	−1.66862e18	+	2.89013e18i	−0.248277	+	0.430028i
$789$	3.21702e18	+	5.57204e18i	0.474737	+	0.822268i
$790$	−7.32745e18			−1.07245
$791$	2.09631e18	+	3.11573e18i	0.304304	+	0.452285i
$792$	5.06994e17			0.0729943
$793$	−2.26882e17	−	3.92972e17i	−0.0323985	−	0.0561159i
$794$	−2.05604e18	+	3.56117e18i	−0.291205	+	0.504381i
$795$	5.02158e18	−	8.69763e18i	0.705430	−	1.22184i
$796$	3.75313e17	+	6.50061e17i	0.0522948	+	0.0905772i
$797$	1.34020e19			1.85222			0.926108	−	0.377258i	$-0.123133\pi$
$797$	1.34020e19			1.85222			0.926108	+	0.377258i	$0.123133\pi$
$798$	1.76781e18	−	3.61385e18i	0.242335	−	0.495394i
$799$	3.50209e18			0.476182
$800$	−1.15208e18	−	1.99546e18i	−0.155380	−	0.269127i
$801$	8.78528e17	−	1.52166e18i	0.117529	−	0.203566i
$802$	1.31989e17	−	2.28612e17i	0.0175148	−	0.0303365i
$803$	1.75514e18	+	3.04000e18i	0.231026	+	0.400150i
$804$	1.08868e18			0.142146
$805$	−9.81323e18	+	6.74718e17i	−1.27098	+	0.0873875i
$806$	−8.47374e17			−0.108867
$807$	−2.42465e18	−	4.19962e18i	−0.309009	−	0.535219i
$808$	−2.27965e18	+	3.94848e18i	−0.288201	+	0.499178i
$809$	4.91594e18	−	8.51466e18i	0.616512	−	1.06783i	−0.373606	−	0.927588i	$-0.621879\pi$
$809$	4.91594e18	−	8.51466e18i	0.616512	−	1.06783i	0.990117	−	0.140242i	$-0.0447880\pi$
$810$	5.35044e18	+	9.26724e18i	0.665636	+	1.15292i
$811$	6.51385e18			0.803900			0.401950	−	0.915662i	$-0.368333\pi$
$811$	6.51385e18			0.803900			0.401950	+	0.915662i	$0.368333\pi$
$812$	7.22148e18	−	4.96520e17i	0.884122	−	0.0607886i
$813$	−1.39329e19			−1.69221
$814$	−3.10441e18	−	5.37700e18i	−0.374042	−	0.647860i
$815$	5.28924e18	−	9.16122e18i	0.632220	−	1.09504i
$816$	3.56408e17	−	6.17316e17i	0.0422631	−	0.0732018i
$817$	−4.69321e18	−	8.12887e18i	−0.552111	−	0.956284i
$818$	6.59175e18			0.769316
$819$	−5.21454e17	+	1.06599e18i	−0.0603769	+	0.123426i
$820$	1.09027e19			1.25241
$821$	5.95963e18	+	1.03224e19i	0.679186	+	1.17638i	0.975226	+	0.221209i	$0.0710002\pi$
$821$	5.95963e18	+	1.03224e19i	0.679186	+	1.17638i	−0.296041	+	0.955175i	$0.595666\pi$
$822$	−1.40142e18	+	2.42733e18i	−0.158453	+	0.274450i
$823$	−6.83851e18	+	1.18447e19i	−0.767119	+	1.32869i	0.172000	+	0.985097i	$0.444977\pi$
$823$	−6.83851e18	+	1.18447e19i	−0.767119	+	1.32869i	−0.939119	+	0.343592i	$0.888356\pi$
$824$	3.11868e16	+	5.40171e16i	0.00347091	+	0.00601179i
$825$	2.22627e19			2.45825
$826$	5.03151e17	+	7.47831e17i	0.0551224	+	0.0819281i
$827$	−1.06354e19			−1.15603			−0.578014	−	0.816027i	$-0.696172\pi$
$827$	−1.06354e19			−1.15603			−0.578014	+	0.816027i	$0.696172\pi$
$828$	2.82650e17	+	4.89564e17i	0.0304826	+	0.0527974i
$829$	−5.42054e18	+	9.38865e18i	−0.580013	+	1.00461i	0.415464	+	0.909610i	$0.363619\pi$
$829$	−5.42054e18	+	9.38865e18i	−0.580013	+	1.00461i	−0.995477	+	0.0950026i	$0.969714\pi$
$830$	−8.94101e18	+	1.54863e19i	−0.949247	+	1.64414i
$831$	2.90534e18	+	5.03219e18i	0.306048	+	0.530091i
$832$	1.03387e18			0.108059
$833$	1.85890e18	+	2.39075e18i	0.192781	+	0.247937i
$834$	8.02346e18			0.825624
$835$	−1.08827e19	−	1.88494e19i	−1.11115	−	1.92458i
$836$	2.32218e18	−	4.02214e18i	0.235264	−	0.407490i
$837$	−8.02051e17	+	1.38919e18i	−0.0806281	+	0.139652i
$838$	−5.36435e18	−	9.29133e18i	−0.535095	−	0.926812i
$839$	2.39827e17			0.0237380			0.0118690	−	0.999930i	$-0.496222\pi$
$839$	2.39827e17			0.0237380			0.0118690	+	0.999930i	$0.496222\pi$
$840$	−3.59255e18	−	5.33959e18i	−0.352848	−	0.524436i
$841$	2.19728e19			2.14147
$842$	3.54120e18	+	6.13353e18i	0.342469	+	0.593174i
$843$	−6.94532e18	+	1.20296e19i	−0.666520	+	1.15445i
$844$	4.69587e18	−	8.13348e18i	0.447188	−	0.774552i
$845$	2.22027e18	+	3.84562e18i	0.209815	+	0.363411i
$846$	−1.81713e18			−0.170403
$847$	−3.24530e18	+	6.63422e18i	−0.302004	+	0.617373i
$848$	−2.13636e18			−0.197288
$849$	−2.13709e18	−	3.70155e18i	−0.195850	−	0.339222i
$850$	2.14635e18	−	3.71758e18i	0.195199	−	0.338094i
$851$	3.46143e18	−	5.99537e18i	0.312402	−	0.541095i
$852$	3.26841e18	+	5.66105e18i	0.292738	+	0.507037i
$853$	−1.21442e18			−0.107944			−0.0539722	−	0.998542i	$-0.517188\pi$
$853$	−1.21442e18			−0.107944			−0.0539722	+	0.998542i	$0.517188\pi$
$854$	5.99432e17	−	4.12145e16i	0.0528766	−	0.00363558i
$855$	−2.18441e18			−0.191229
$856$	1.20209e18	+	2.08208e18i	0.104438	+	0.180892i
$857$	8.69060e18	−	1.50526e19i	0.749332	−	1.29788i	−0.198811	−	0.980038i	$-0.563708\pi$
$857$	8.69060e18	−	1.50526e19i	0.749332	−	1.29788i	0.948143	−	0.317843i	$-0.102959\pi$
$858$	−4.99459e18	+	8.65088e18i	−0.427398	+	0.740275i
$859$	−5.41238e18	−	9.37452e18i	−0.459656	−	0.796147i	0.539287	−	0.842122i	$-0.318694\pi$
$859$	−5.41238e18	−	9.37452e18i	−0.459656	−	0.796147i	−0.998943	+	0.0459751i	$0.985361\pi$
$860$	−1.50154e19			−1.26560
$861$	1.93647e19	−	1.33144e18i	1.61991	−	0.111378i
$862$	3.28947e18			0.273104
$863$	−2.77663e18	−	4.80926e18i	−0.228796	−	0.396286i	0.728656	−	0.684880i	$-0.240145\pi$
$863$	−2.77663e18	−	4.80926e18i	−0.228796	−	0.396286i	−0.957451	+	0.288594i	$0.906812\pi$
$864$	9.78568e17	−	1.69493e18i	0.0800298	−	0.138616i
$865$	−1.19591e19	+	2.07138e19i	−0.970723	+	1.68134i
$866$	−3.92412e18	−	6.79678e18i	−0.316138	−	0.547567i
$867$	−1.21354e19			−0.970355
$868$	4.93044e17	−	1.00791e18i	0.0391298	−	0.0799913i
$869$	−1.50599e19			−1.18630
$870$	−1.43291e19	−	2.48187e19i	−1.12032	−	1.94046i
$871$	−1.47087e18	+	2.54762e18i	−0.114145	+	0.197705i
$872$	−4.20458e18	+	7.28255e18i	−0.323866	+	0.560953i
$873$	7.27354e16	+	1.25981e17i	0.00556101	+	0.00963195i
$874$	5.17849e18			0.392987
$875$	−9.32788e18	−	1.38640e19i	−0.702637	−	1.04432i
$876$	−2.56080e18			−0.191469
$877$	6.14792e18	+	1.06485e19i	0.456279	+	0.790299i	0.998761	−	0.0497690i	$-0.0158485\pi$
$877$	6.14792e18	+	1.06485e19i	0.456279	+	0.790299i	−0.542482	+	0.840068i	$0.682515\pi$
$878$	2.59681e18	−	4.49781e18i	0.191305	−	0.331350i
$879$	−6.35498e18	+	1.10071e19i	−0.464715	+	0.804909i
$880$	−3.71478e18	−	6.43418e18i	−0.269647	−	0.467042i
$881$	1.11597e18			0.0804096			0.0402048	−	0.999191i	$-0.487199\pi$
$881$	1.11597e18			0.0804096			0.0402048	+	0.999191i	$0.487199\pi$
$882$	−9.64528e17	−	1.24049e18i	−0.0689873	−	0.0887251i
$883$	−3.31732e18			−0.235528			−0.117764	−	0.993042i	$-0.537573\pi$
$883$	−3.31732e18			−0.235528			−0.117764	+	0.993042i	$0.537573\pi$
$884$	9.63058e17	+	1.66806e18i	0.0678754	+	0.117564i
$885$	1.78425e18	−	3.09042e18i	0.124832	−	0.216215i
$886$	3.48453e18	−	6.03538e18i	0.242005	−	0.419165i
$887$	−1.09736e19	−	1.90068e19i	−0.756563	−	1.31041i	−0.944594	−	0.328242i	$-0.893544\pi$
$887$	−1.09736e19	−	1.90068e19i	−0.756563	−	1.31041i	0.188031	−	0.982163i	$-0.439790\pi$
$888$	4.52941e18			0.309997
$889$	−4.64226e18	−	6.89976e18i	−0.315405	−	0.468784i
$890$	−2.57481e19			−1.73664
$891$	1.09966e19	+	1.90467e19i	0.736299	+	1.27531i
$892$	2.17976e17	−	3.77546e17i	0.0144890	−	0.0250957i
$893$	−8.32300e18	+	1.44159e19i	−0.549219	+	0.951274i
$894$	2.90979e18	+	5.03990e18i	0.190620	+	0.330163i
$895$	3.40794e19			2.21637
$896$	−6.01555e17	+	1.22973e18i	−0.0388394	+	0.0793977i
$897$	−1.11380e19			−0.713929
$898$	6.83211e18	+	1.18336e19i	0.434769	+	0.753042i
$899$	2.49824e18	−	4.32708e18i	0.157832	−	0.273374i
$900$	−1.11367e18	+	1.92894e18i	−0.0698525	+	0.120988i
$901$	−1.99004e18	−	3.44686e18i	−0.123923	−	0.214641i
$902$	2.24081e19			1.38536
$903$	−2.66693e19	+	1.83367e18i	−1.63697	+	0.112552i
$904$	−3.16262e18			−0.192731
$905$	1.09810e19	+	1.90196e19i	0.664393	+	1.15076i
$906$	6.03736e18	−	1.04570e19i	0.362672	−	0.628166i
$907$	1.06858e19	−	1.85084e19i	0.637324	−	1.10388i	−0.348694	−	0.937237i	$-0.613375\pi$
$907$	1.06858e19	−	1.85084e19i	0.637324	−	1.10388i	0.986018	−	0.166640i	$-0.0532919\pi$
$908$	1.15307e17	+	1.99717e17i	0.00682804	+	0.0118265i
$909$	4.40733e18			0.259126
$910$	1.73490e19	−	1.19285e18i	1.01276	−	0.0696330i
$911$	3.42317e19			1.98408			0.992041	−	0.125916i	$-0.0401870\pi$
$911$	3.42317e19			1.98408			0.992041	+	0.125916i	$0.0401870\pi$
$912$	1.69406e18	+	2.93420e18i	0.0974907	+	0.168859i
$913$	−1.83762e19	+	3.18286e19i	−1.05002	+	1.81868i
$914$	7.89259e18	−	1.36704e19i	0.447785	−	0.775586i
$915$	−1.18941e18	−	2.06012e18i	−0.0670032	−	0.116053i
$916$	8.93311e16			0.00499669
$917$	1.78051e18	−	3.63981e18i	0.0988879	−	0.202152i
$918$	3.64619e18			0.201077
$919$	−3.73402e18	−	6.46751e18i	−0.204468	−	0.354149i	0.745495	−	0.666511i	$-0.232213\pi$
$919$	−3.73402e18	−	6.46751e18i	−0.204468	−	0.354149i	−0.949963	+	0.312362i	$0.898880\pi$
$920$	4.14199e18	−	7.17413e18i	0.225210	−	0.390075i
$921$	−5.99936e18	+	1.03912e19i	−0.323905	+	0.561019i
$922$	6.84803e18	+	1.18611e19i	0.367126	+	0.635880i
$923$	−1.76633e19			−0.940286
$924$	−7.38368e18	−	1.09743e19i	−0.390306	−	0.580109i
$925$	2.72769e19			1.43177
$926$	−6.74038e17	−	1.16747e18i	−0.0351328	−	0.0608518i
$927$	3.01472e16	−	5.22165e16i	0.00156037	−	0.00270265i
$928$	−3.04806e18	+	5.27939e18i	−0.156661	+	0.271345i
$929$	−6.36522e18	−	1.10249e19i	−0.324871	−	0.562694i	0.656615	−	0.754226i	$-0.271988\pi$
$929$	−6.36522e18	−	1.10249e19i	−0.324871	−	0.562694i	−0.981486	+	0.191532i	$0.938654\pi$
$930$	−4.44229e18			−0.225148
$931$	−1.42590e19	+	1.97009e18i	−0.717655	+	0.0991549i
$932$	−1.51341e19			−0.756403
$933$	7.22817e18	+	1.25196e19i	0.358755	+	0.621381i
$934$	−3.89051e18	+	6.73857e18i	−0.191757	+	0.332134i
$935$	6.92072e18	−	1.19870e19i	0.338747	−	0.586727i
$936$	−4.99702e17	−	8.65509e17i	−0.0242895	−	0.0420706i
$937$	−2.72689e18			−0.131632			−0.0658158	−	0.997832i	$-0.520965\pi$
$937$	−2.72689e18			−0.131632			−0.0658158	+	0.997832i	$0.520965\pi$
$938$	−2.17444e18	−	3.23186e18i	−0.104239	−	0.154930i
$939$	1.69665e19			0.807729
$940$	1.33142e19	+	2.30609e19i	0.629484	+	1.09030i
$941$	5.49855e18	−	9.52377e18i	0.258176	−	0.447174i	−0.707577	−	0.706636i	$-0.750212\pi$
$941$	5.49855e18	−	9.52377e18i	0.258176	−	0.447174i	0.965753	+	0.259462i	$0.0835453\pi$
$942$	9.85242e17	−	1.70649e18i	0.0459422	−	0.0795742i
$943$	1.24926e19	+	2.16377e19i	0.578529	+	1.00204i
$944$	−7.59086e17			−0.0349118
$945$	1.44655e19	−	2.95711e19i	0.660733	−	1.35071i
$946$	−3.08607e19			−1.39995
$947$	6.74952e18	+	1.16905e19i	0.304087	+	0.526694i	0.977058	−	0.212975i	$-0.0683153\pi$
$947$	6.74952e18	+	1.16905e19i	0.304087	+	0.526694i	−0.672971	+	0.739669i	$0.734982\pi$
$948$	5.49320e18	−	9.51451e18i	0.245794	−	0.425728i
$949$	3.45980e18	−	5.99255e18i	0.153752	−	0.266306i
$950$	1.02019e19	+	1.76702e19i	0.450276	+	0.779901i
$951$	2.30813e19			1.01178
$952$	−2.54443e18	+	1.74945e17i	−0.110777	+	0.00761660i
$953$	−3.83785e18			−0.165952			−0.0829762	−	0.996552i	$-0.526443\pi$
$953$	−3.83785e18			−0.165952			−0.0829762	+	0.996552i	$0.526443\pi$
$954$	1.03257e18	+	1.78847e18i	0.0443463	+	0.0768100i
$955$	−1.55883e19	+	2.69997e19i	−0.664930	+	1.15169i
$956$	−3.15771e18	+	5.46931e18i	−0.133781	+	0.231716i
$957$	−2.94502e19	−	5.10093e19i	−1.23926	−	2.14645i
$958$	−4.62613e18			−0.193349
$959$	1.00049e19	−	6.87896e17i	0.415329	−	0.0285563i
$960$	5.41995e18			0.223477
$961$	1.18215e19	+	2.04755e19i	0.484140	+	0.838556i
$962$	−6.11952e18	+	1.05993e19i	−0.248931	+	0.431161i
$963$	1.16202e18	−	2.01268e18i	0.0469509	−	0.0813213i
$964$	9.60962e18	+	1.66443e19i	0.385661	+	0.667984i
$965$	−5.91819e18			−0.235918
$966$	6.48062e18	−	1.32480e19i	0.256605	−	0.524566i
$967$	−1.52113e19			−0.598267			−0.299133	−	0.954211i	$-0.596698\pi$
$967$	−1.52113e19			−0.598267			−0.299133	+	0.954211i	$0.596698\pi$
$968$	−3.10992e18	−	5.38654e18i	−0.121495	−	0.210436i
$969$	−3.15608e18	+	5.46649e18i	−0.122474	+	0.212131i
$970$	1.06587e18	−	1.84615e18i	0.0410856	−	0.0711623i
$971$	6.61147e18	+	1.14514e19i	0.253147	+	0.438464i	0.964391	−	0.264482i	$-0.0852010\pi$
$971$	6.61147e18	+	1.14514e19i	0.253147	+	0.438464i	−0.711243	+	0.702946i	$0.751868\pi$
$972$	−4.14133e18			−0.157510
$973$	−1.60255e19	−	2.38185e19i	−0.605448	−	0.899874i
$974$	−9.15821e18			−0.343698
$975$	−2.19424e19	−	3.80054e19i	−0.818003	−	1.41682i
$976$	−2.53009e17	+	4.38225e17i	−0.00936942	+	0.0162283i
$977$	−5.13953e18	+	8.90193e18i	−0.189064	+	0.327469i	−0.944938	−	0.327248i	$-0.893879\pi$
$977$	−5.13953e18	+	8.90193e18i	−0.189064	+	0.327469i	0.755874	+	0.654717i	$0.227212\pi$
$978$	7.93041e18	+	1.37359e19i	0.289796	+	0.501942i
$979$	−5.29194e19			−1.92100
$980$	−8.67567e18	+	2.13298e19i	−0.312848	+	0.769161i
$981$	8.12886e18			0.291193
$982$	1.57993e19	+	2.73651e19i	0.562227	+	0.973806i
$983$	1.07731e19	−	1.86595e19i	0.380840	−	0.659633i	−0.610343	−	0.792137i	$-0.708968\pi$
$983$	1.07731e19	−	1.86595e19i	0.380840	−	0.659633i	0.991182	+	0.132504i	$0.0423017\pi$
$984$	−8.17350e18	+	1.41569e19i	−0.287038	+	0.497165i
$985$	−2.36371e19	−	4.09406e19i	−0.824628	−	1.42830i
$986$	−1.13572e19			−0.393615
$987$	2.64640e19	+	3.93333e19i	0.911160	+	1.35425i
$988$	−9.15513e18			−0.313144
$989$	−1.72049e19	−	2.97997e19i	−0.584622	−	1.01260i
$990$	−3.59095e18	+	6.21971e18i	−0.121222	+	0.209962i
$991$	−5.69307e18	+	9.86069e18i	−0.190927	+	0.330696i	−0.945558	−	0.325454i	$-0.894483\pi$
$991$	−5.69307e18	+	9.86069e18i	−0.190927	+	0.330696i	0.754630	+	0.656150i	$0.227816\pi$
$992$	4.72477e17	+	8.18354e17i	0.0157418	+	0.0272656i
$993$	−1.34525e18			−0.0445281
$994$	1.02774e19	−	2.10096e19i	0.337964	−	0.690885i
$995$	−1.06331e19			−0.347384
$996$	−1.34057e19	−	2.32193e19i	−0.435114	−	0.753640i
$997$	2.35204e19	−	4.07386e19i	0.758449	−	1.31367i	−0.185192	−	0.982702i	$-0.559291\pi$
$997$	2.35204e19	−	4.07386e19i	0.758449	−	1.31367i	0.943641	−	0.330970i	$-0.107376\pi$
$998$	−2.01623e18	+	3.49222e18i	−0.0645941	+	0.111880i
$999$	1.15844e19	+	2.00648e19i	0.368721	+	0.638644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.c.a.11.2	yes	8
3.2	odd	2		126.14.g.d.109.4		8
7.2	even	3	inner	14.14.c.a.9.2	✓	8
7.3	odd	6		98.14.a.k.1.2		4
7.4	even	3		98.14.a.l.1.3		4
7.5	odd	6		98.14.c.n.79.3		8
7.6	odd	2		98.14.c.n.67.3		8
21.2	odd	6		126.14.g.d.37.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.a.9.2	✓	8	7.2	even	3	inner
14.14.c.a.11.2	yes	8	1.1	even	1	trivial
98.14.a.k.1.2		4	7.3	odd	6
98.14.a.l.1.3		4	7.4	even	3
98.14.c.n.67.3		8	7.6	odd	2
98.14.c.n.79.3		8	7.5	odd	6
126.14.g.d.37.4		8	21.2	odd	6
126.14.g.d.109.4		8	3.2	odd	2

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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-32.0000 - 55.4256i) q^{2} +(-679.656 + 1177.20i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-29011.3 - 50249.0i) q^{5} +86996.0 q^{6} +(-173759. - 258257. i) q^{7} +262144. q^{8} +(-126703. - 219456. i) q^{9} +O(q^{10})\)	\(q+(-32.0000 - 55.4256i) q^{2} +(-679.656 + 1177.20i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-29011.3 - 50249.0i) q^{5} +86996.0 q^{6} +(-173759. - 258257. i) q^{7} +262144. q^{8} +(-126703. - 219456. i) q^{9} +(-1.85672e6 + 3.21593e6i) q^{10} +(-3.81607e6 + 6.60963e6i) q^{11} +(-2.78387e6 - 4.82181e6i) q^{12} +1.50447e7 q^{13} +(-8.75377e6 + 1.78949e7i) q^{14} +7.88707e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(1.56282e7 - 2.70688e7i) q^{17} +(-8.10899e6 + 1.40452e7i) q^{18} +(7.42832e7 + 1.28662e8i) q^{19} +2.37660e8 q^{20} +(4.22116e8 - 2.90230e7i) q^{21} +4.88457e8 q^{22} +(2.72315e8 + 4.71664e8i) q^{23} +(-1.78168e8 + 3.08596e8i) q^{24} +(-1.07296e9 + 1.85841e9i) q^{25} +(-4.81431e8 - 8.33863e8i) q^{26} -1.82272e9 q^{27} +(1.27196e9 - 8.74548e7i) q^{28} +5.67745e9 q^{29} +(-2.52386e9 - 4.37146e9i) q^{30} +(4.40028e8 - 7.62152e8i) q^{31} +(-5.36871e8 + 9.29888e8i) q^{32} +(-5.18723e9 - 8.98454e9i) q^{33} -2.00041e9 q^{34} +(-7.93619e9 + 1.62236e10i) q^{35} +1.03795e9 q^{36} +(-6.35555e9 - 1.10081e10i) q^{37} +(4.75412e9 - 8.23438e9i) q^{38} +(-1.02252e10 + 1.77106e10i) q^{39} +(-7.60513e9 - 1.31725e10i) q^{40} +4.58753e10 q^{41} +(-1.51163e10 - 2.24673e10i) q^{42} -6.31799e10 q^{43} +(-1.56306e10 - 2.70730e10i) q^{44} +(-7.35163e9 + 1.27334e10i) q^{45} +(1.74282e10 - 3.01865e10i) q^{46} +(5.60221e10 + 9.70331e10i) q^{47} +2.28055e10 q^{48} +(-3.65045e10 + 8.97491e10i) q^{49} +1.37338e11 q^{50} +(2.12436e10 + 3.67949e10i) q^{51} +(-3.08116e10 + 5.33672e10i) q^{52} +(6.36685e10 - 1.10277e11i) q^{53} +(5.83272e10 + 1.01026e11i) q^{54} +4.42836e11 q^{55} +(-4.55499e10 - 6.77006e10i) q^{56} -2.01948e11 q^{57} +(-1.81678e11 - 3.14676e11i) q^{58} +(2.26225e10 - 3.91833e10i) q^{59} +(-1.61527e11 + 2.79773e11i) q^{60} +(-1.50805e10 - 2.61202e10i) q^{61} -5.63236e10 q^{62} +(-3.46603e10 + 7.08544e10i) q^{63} +6.87195e10 q^{64} +(-4.36466e11 - 7.55982e11i) q^{65} +(-3.31983e11 + 5.75011e11i) q^{66} +(-9.77666e10 + 1.69337e11i) q^{67} +(6.40130e10 + 1.10874e11i) q^{68} -7.40323e11 q^{69} +(1.15316e12 - 7.92866e10i) q^{70} -1.17405e12 q^{71} +(-3.32144e10 - 5.75291e10i) q^{72} +(2.29968e11 - 3.98315e11i) q^{73} +(-4.06755e11 + 7.04520e11i) q^{74} +(-1.45848e12 - 2.52616e12i) q^{75} -6.08528e11 q^{76} +(2.37006e12 - 1.62956e11i) q^{77} +1.30883e12 q^{78} +(9.86612e11 + 1.70886e12i) q^{79} +(-4.86728e11 + 8.43038e11i) q^{80} +(1.44083e12 - 2.49559e12i) q^{81} +(-1.46801e12 - 2.54267e12i) q^{82} +4.81548e12 q^{83} +(-7.61543e11 + 1.55679e12i) q^{84} -1.81357e12 q^{85} +(2.02176e12 + 3.50179e12i) q^{86} +(-3.85871e12 + 6.68348e12i) q^{87} +(-1.00036e12 + 1.73267e12i) q^{88} +(3.46688e12 + 6.00481e12i) q^{89} +9.41008e11 q^{90} +(-2.61416e12 - 3.88541e12i) q^{91} -2.23081e12 q^{92} +(5.98136e11 + 1.03600e12i) q^{93} +(3.58541e12 - 6.21012e12i) q^{94} +(4.31010e12 - 7.46531e12i) q^{95} +(-7.29775e11 - 1.26401e12i) q^{96} -5.74063e11 q^{97} +(6.14254e12 - 8.48685e11i) q^{98} +1.93403e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9}+O(q^{10}) \) 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9	\( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9} - 4121600 q^{10} - 1008790 q^{11} - 745472 q^{12} + 53807264 q^{13} + 23506560 q^{14} - 88888916 q^{15} - 67108864 q^{16} - 165333028 q^{17} - 254960128 q^{18} - 423405794 q^{19} + 527564800 q^{20} + 231089600 q^{21} + 129125120 q^{22} + 286233866 q^{23} - 47710208 q^{24} - 472017432 q^{25} - 1721832448 q^{26} - 10405941644 q^{27} - 1038557184 q^{28} + 18200674816 q^{29} + 2844445312 q^{30} + 1507094246 q^{31} - 4294967296 q^{32} - 16888935028 q^{33} + 21162627584 q^{34} - 4300332526 q^{35} + 32634896384 q^{36} - 18959705336 q^{37} - 27097970816 q^{38} + 35759388756 q^{39} - 16882073600 q^{40} + 113651910624 q^{41} + 25531294208 q^{42} - 91557619424 q^{43} - 4132003840 q^{44} - 119804452768 q^{45} + 18318967424 q^{46} - 81351201078 q^{47} + 6106906624 q^{48} - 60954502168 q^{49} + 60418231296 q^{50} + 14996824142 q^{51} - 110197276672 q^{52} + 87497947440 q^{53} + 332990132608 q^{54} + 701637410348 q^{55} - 29815209984 q^{56} - 1807326928264 q^{57} - 582421594112 q^{58} - 194140265102 q^{59} + 182044499968 q^{60} + 175816313120 q^{61} - 192908063488 q^{62} + 3245184239332 q^{63} + 549755813888 q^{64} - 1689866774568 q^{65} - 1080891841792 q^{66} - 243815218758 q^{67} - 677204082688 q^{68} + 6044157952784 q^{69} + 3010938632576 q^{70} - 3275394679072 q^{71} - 1044316684288 q^{72} - 3492491920596 q^{73} - 1213421141504 q^{74} - 2370218127424 q^{75} + 3468540264448 q^{76} + 6381735922240 q^{77} - 4577201760768 q^{78} - 1016380081246 q^{79} - 1080452710400 q^{80} + 17492694092 q^{81} - 3636861139968 q^{82} + 7027495743296 q^{83} - 2580545830912 q^{84} + 569114840528 q^{85} + 2929843821568 q^{86} - 9706955821052 q^{87} - 264448245760 q^{88} - 8034124428036 q^{89} + 15334969954304 q^{90} - 11436513503632 q^{91} - 2344827830272 q^{92} - 3388371390552 q^{93} - 5206476868992 q^{94} + 1429435505438 q^{95} - 195421011968 q^{96} + 54351131725632 q^{97} - 461748942592 q^{98} - 25837834576328 q^{99}+O(q^{100}) \) 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9 - 4121600 * q^10 - 1008790 * q^11 - 745472 * q^12 + 53807264 * q^13 + 23506560 * q^14 - 88888916 * q^15 - 67108864 * q^16 - 165333028 * q^17 - 254960128 * q^18 - 423405794 * q^19 + 527564800 * q^20 + 231089600 * q^21 + 129125120 * q^22 + 286233866 * q^23 - 47710208 * q^24 - 472017432 * q^25 - 1721832448 * q^26 - 10405941644 * q^27 - 1038557184 * q^28 + 18200674816 * q^29 + 2844445312 * q^30 + 1507094246 * q^31 - 4294967296 * q^32 - 16888935028 * q^33 + 21162627584 * q^34 - 4300332526 * q^35 + 32634896384 * q^36 - 18959705336 * q^37 - 27097970816 * q^38 + 35759388756 * q^39 - 16882073600 * q^40 + 113651910624 * q^41 + 25531294208 * q^42 - 91557619424 * q^43 - 4132003840 * q^44 - 119804452768 * q^45 + 18318967424 * q^46 - 81351201078 * q^47 + 6106906624 * q^48 - 60954502168 * q^49 + 60418231296 * q^50 + 14996824142 * q^51 - 110197276672 * q^52 + 87497947440 * q^53 + 332990132608 * q^54 + 701637410348 * q^55 - 29815209984 * q^56 - 1807326928264 * q^57 - 582421594112 * q^58 - 194140265102 * q^59 + 182044499968 * q^60 + 175816313120 * q^61 - 192908063488 * q^62 + 3245184239332 * q^63 + 549755813888 * q^64 - 1689866774568 * q^65 - 1080891841792 * q^66 - 243815218758 * q^67 - 677204082688 * q^68 + 6044157952784 * q^69 + 3010938632576 * q^70 - 3275394679072 * q^71 - 1044316684288 * q^72 - 3492491920596 * q^73 - 1213421141504 * q^74 - 2370218127424 * q^75 + 3468540264448 * q^76 + 6381735922240 * q^77 - 4577201760768 * q^78 - 1016380081246 * q^79 - 1080452710400 * q^80 + 17492694092 * q^81 - 3636861139968 * q^82 + 7027495743296 * q^83 - 2580545830912 * q^84 + 569114840528 * q^85 + 2929843821568 * q^86 - 9706955821052 * q^87 - 264448245760 * q^88 - 8034124428036 * q^89 + 15334969954304 * q^90 - 11436513503632 * q^91 - 2344827830272 * q^92 - 3388371390552 * q^93 - 5206476868992 * q^94 + 1429435505438 * q^95 - 195421011968 * q^96 + 54351131725632 * q^97 - 461748942592 * q^98 - 25837834576328 * q^99

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