LMFDB - Embedded newform 21.9.f.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,9,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, 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:	$8.55495081128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 1331 x^{10} + 1482 x^{9} + 1359381 x^{8} + 1222227 x^{7} + 474169529 x^{6} + \cdots + 556282980265104 $ x^12 - 3x^11 + 1331x^10 + 1482x^9 + 1359381x^8 + 1222227x^7 + 474169529x^6 + 1911324162x^5 + 121870629463x^4 + 259296590901x^3 + 9508380016437x^2 - 12075311354004*x + 556282980265104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$15.7115 + 27.2131i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.9.f.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.2115 + 26.3471i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-334.779 - 579.854i) q^{4} +(890.914 + 514.369i) q^{5} +1422.74i q^{6} +(2247.80 - 843.914i) q^{7} +12581.7 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})$	\(q+(-15.2115 + 26.3471i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-334.779 - 579.854i) q^{4} +(890.914 + 514.369i) q^{5} +1422.74i q^{6} +(2247.80 - 843.914i) q^{7} +12581.7 q^{8} +(1093.50 - 1894.00i) q^{9} +(-27104.3 + 15648.6i) q^{10} +(300.839 + 521.068i) q^{11} +(-27117.1 - 15656.1i) q^{12} -7312.22i q^{13} +(-11957.7 + 72060.2i) q^{14} +48109.3 q^{15} +(-105683. + 183048. i) q^{16} +(-17721.2 + 10231.3i) q^{17} +(33267.5 + 57621.1i) q^{18} +(109744. + 63360.6i) q^{19} -688800. i q^{20} +(71303.0 - 86738.2i) q^{21} -18304.8 q^{22} +(-134743. + 233381. i) q^{23} +(509558. - 294193. i) q^{24} +(333839. + 578226. i) q^{25} +(192656. + 111230. i) q^{26} -102276. i q^{27} +(-1.24186e6 - 1.02087e6i) q^{28} +912923. q^{29} +(-731815. + 1.26754e6i) q^{30} +(-606988. + 350445. i) q^{31} +(-1.60473e6 - 2.77947e6i) q^{32} +(24367.9 + 14068.8i) q^{33} -622534. i q^{34} +(2.43668e6 + 404345. i) q^{35} -1.46432e6 q^{36} +(463956. - 803595. i) q^{37} +(-3.33873e6 + 1.92762e6i) q^{38} +(-170979. - 296145. i) q^{39} +(1.12092e7 + 6.47163e6i) q^{40} -1.59919e6i q^{41} +(1.20067e6 + 3.19804e6i) q^{42} -2.68752e6 q^{43} +(201429. - 348885. i) q^{44} +(1.94843e6 - 1.12493e6i) q^{45} +(-4.09928e6 - 7.10016e6i) q^{46} +(-3.52985e6 - 2.03796e6i) q^{47} +9.88457e6i q^{48} +(4.34042e6 - 3.79390e6i) q^{49} -2.03128e7 q^{50} +(-478471. + 828737. i) q^{51} +(-4.24003e6 + 2.44798e6i) q^{52} +(3.54546e6 + 6.14091e6i) q^{53} +(2.69467e6 + 1.55577e6i) q^{54} +618969. i q^{55} +(2.82811e7 - 1.06179e7i) q^{56} +5.92616e6 q^{57} +(-1.38869e7 + 2.40529e7i) q^{58} +(980259. - 565953. i) q^{59} +(-1.61060e7 - 2.78964e7i) q^{60} +(-1.12167e7 - 6.47594e6i) q^{61} -2.13232e7i q^{62} +(859599. - 5.18015e6i) q^{63} +4.35317e7 q^{64} +(3.76118e6 - 6.51456e6i) q^{65} +(-741346. + 428016. i) q^{66} +(-1.72242e7 - 2.98332e7i) q^{67} +(1.18653e7 + 6.85046e6i) q^{68} +1.26026e7i q^{69} +(-4.77189e7 + 5.80487e7i) q^{70} +3.76248e7 q^{71} +(1.37581e7 - 2.38297e7i) q^{72} +(1.69906e7 - 9.80954e6i) q^{73} +(1.41149e7 + 2.44478e7i) q^{74} +(2.70410e7 + 1.56121e7i) q^{75} -8.48472e7i q^{76} +(1.11596e6 + 917375. i) q^{77} +1.04034e7 q^{78} +(-2.52578e7 + 4.37477e7i) q^{79} +(-1.88308e8 + 1.08720e8i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(4.21341e7 + 2.43261e7i) q^{82} +4.65723e7i q^{83} +(-7.41662e7 - 1.23072e7i) q^{84} -2.10507e7 q^{85} +(4.08812e7 - 7.08082e7i) q^{86} +(3.69734e7 - 2.13466e7i) q^{87} +(3.78506e6 + 6.55591e6i) q^{88} +(-6.94636e7 - 4.01048e7i) q^{89} +6.84472e7i q^{90} +(-6.17089e6 - 1.64364e7i) q^{91} +1.80436e8 q^{92} +(-1.63887e7 + 2.83860e7i) q^{93} +(1.07389e8 - 6.20008e7i) q^{94} +(6.51815e7 + 1.12898e8i) q^{95} +(-1.29983e8 - 7.50456e7i) q^{96} +5.45695e7i q^{97} +(3.39340e7 + 1.72068e8i) q^{98} +1.31587e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−15.2115	+	26.3471i	−0.950718	+	1.64669i	−0.206843	+	0.978374i	$0.566319\pi$
$2$	−15.2115	+	26.3471i	−0.950718	+	1.64669i	−0.743875	+	0.668318i	$0.767014\pi$
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$4$	−334.779	−	579.854i	−1.30773	−	2.26506i
$5$	890.914	+	514.369i	1.42546	+	0.822991i	0.996758	−	0.0804544i	$-0.0256371\pi$
$5$	890.914	+	514.369i	1.42546	+	0.822991i	0.428704	+	0.903445i	$0.358970\pi$
$6$			1422.74i			1.09780i
$7$	2247.80	−	843.914i	0.936194	−	0.351484i
$7$	2247.80	−	843.914i	0.936194	−	0.351484i
$8$	12581.7			3.07170
$9$	1093.50	−	1894.00i	0.166667	−	0.288675i
$10$	−27104.3	+	15648.6i	−2.71043	+	1.56486i
$11$	300.839	+	521.068i	0.0205477	+	0.0355897i	0.876116	−	0.482100i	$-0.160126\pi$
$11$	300.839	+	521.068i	0.0205477	+	0.0355897i	−0.855569	+	0.517689i	$0.826792\pi$
$12$	−27117.1	−	15656.1i	−1.30773	−	0.755019i
$13$		−	7312.22i		−	0.256021i	−0.991773	−	0.128011i	$-0.959141\pi$
$13$		−	7312.22i		−	0.256021i	0.991773	−	0.128011i	$-0.0408592\pi$
$14$	−11957.7	+	72060.2i	−0.311270	+	1.87579i
$15$	48109.3			0.950308
$16$	−105683.	+	183048.i	−1.61259	+	2.79309i
$17$	−17721.2	+	10231.3i	−0.212176	+	0.122500i	−0.602322	−	0.798253i	$-0.705758\pi$
$17$	−17721.2	+	10231.3i	−0.212176	+	0.122500i	0.390146	+	0.920753i	$0.372424\pi$
$18$	33267.5	+	57621.1i	0.316906	+	0.548898i
$19$	109744.	+	63360.6i	0.842103	+	0.486189i	0.857979	−	0.513685i	$-0.171720\pi$
$19$	109744.	+	63360.6i	0.842103	+	0.486189i	−0.0158752	+	0.999874i	$0.505053\pi$
$20$		−	688800.i		−	4.30500i
$21$	71303.0	−	86738.2i	0.366632	−	0.445998i
$22$	−18304.8			−0.0781403
$23$	−134743.	+	233381.i	−0.481498	+	0.833979i	−0.999775	−	0.0212343i	$-0.993240\pi$
$23$	−134743.	+	233381.i	−0.481498	+	0.833979i	0.518277	+	0.855213i	$0.326574\pi$
$24$	509558.	−	294193.i	1.53585	−	0.886723i
$25$	333839.	+	578226.i	0.854628	+	1.48026i
$26$	192656.	+	111230.i	0.421588	+	0.243404i
$27$		−	102276.i		−	0.192450i
$28$	−1.24186e6	−	1.02087e6i	−2.02042	−	1.66088i
$29$	912923.			1.29075			0.645375	−	0.763866i	$-0.276701\pi$
$29$	912923.			1.29075			0.645375	+	0.763866i	$0.276701\pi$
$30$	−731815.	+	1.26754e6i	−0.903475	+	1.56486i
$31$	−606988.	+	350445.i	−0.657254	+	0.379466i	−0.791230	−	0.611519i	$-0.790559\pi$
$31$	−606988.	+	350445.i	−0.657254	+	0.379466i	0.133976	+	0.990985i	$0.457226\pi$
$32$	−1.60473e6	−	2.77947e6i	−1.53039	−	2.65071i
$33$	24367.9	+	14068.8i	0.0205477	+	0.0118632i
$34$		−	622534.i		−	0.465852i
$35$	2.43668e6	+	404345.i	1.62378	+	0.269451i
$36$	−1.46432e6			−0.871821
$37$	463956.	−	803595.i	0.247554	−	0.428776i	−0.715293	−	0.698825i	$-0.753707\pi$
$37$	463956.	−	803595.i	0.247554	−	0.428776i	0.962847	+	0.270049i	$0.0870400\pi$
$38$	−3.33873e6	+	1.92762e6i	−1.60121	+	0.924457i
$39$	−170979.	−	296145.i	−0.0739070	−	0.128011i
$40$	1.12092e7	+	6.47163e6i	4.37859	+	2.52798i
$41$		−	1.59919e6i		−	0.565934i	−0.959130	−	0.282967i	$-0.908681\pi$
$41$		−	1.59919e6i		−	0.565934i	0.959130	−	0.282967i	$-0.0913187\pi$
$42$	1.20067e6	+	3.19804e6i	0.385858	+	1.02775i
$43$	−2.68752e6			−0.786099			−0.393050	−	0.919517i	$-0.628580\pi$
$43$	−2.68752e6			−0.786099			−0.393050	+	0.919517i	$0.628580\pi$
$44$	201429.	−	348885.i	0.0537417	−	0.0930834i
$45$	1.94843e6	−	1.12493e6i	0.475154	−	0.274330i
$46$	−4.09928e6	−	7.10016e6i	−0.915538	−	1.58576i
$47$	−3.52985e6	−	2.03796e6i	−0.723377	−	0.417642i	0.0926171	−	0.995702i	$-0.470477\pi$
$47$	−3.52985e6	−	2.03796e6i	−0.723377	−	0.417642i	−0.815995	+	0.578060i	$0.803810\pi$
$48$			9.88457e6i			1.86206i
$49$	4.34042e6	−	3.79390e6i	0.752917	−	0.658115i
$50$	−2.03128e7			−3.25004
$51$	−478471.	+	828737.i	−0.0707254	+	0.122500i
$52$	−4.24003e6	+	2.44798e6i	−0.579903	+	0.334807i
$53$	3.54546e6	+	6.14091e6i	0.449334	+	0.778269i	0.998343	−	0.0575477i	$-0.0183281\pi$
$53$	3.54546e6	+	6.14091e6i	0.449334	+	0.778269i	−0.549009	+	0.835816i	$0.684995\pi$
$54$	2.69467e6	+	1.55577e6i	0.316906	+	0.182966i
$55$			618969.i			0.0676423i
$56$	2.82811e7	−	1.06179e7i	2.87570	−	1.07965i
$57$	5.92616e6			0.561402
$58$	−1.38869e7	+	2.40529e7i	−1.22714	+	2.12547i
$59$	980259.	−	565953.i	0.0808970	−	0.0467059i	−0.459006	−	0.888433i	$-0.651794\pi$
$59$	980259.	−	565953.i	0.0808970	−	0.0467059i	0.539903	+	0.841727i	$0.318461\pi$
$60$	−1.61060e7	−	2.78964e7i	−1.24275	−	2.15250i
$61$	−1.12167e7	−	6.47594e6i	−0.810110	−	0.467717i	0.0368842	−	0.999320i	$-0.488257\pi$
$61$	−1.12167e7	−	6.47594e6i	−0.810110	−	0.467717i	−0.846994	+	0.531602i	$0.821590\pi$
$62$		−	2.13232e7i		−	1.44306i
$63$	859599.	−	5.18015e6i	0.0545675	−	0.328837i
$64$	4.35317e7			2.59469
$65$	3.76118e6	−	6.51456e6i	0.210703	−	0.364949i
$66$	−741346.	+	428016.i	−0.0390701	+	0.0225572i
$67$	−1.72242e7	−	2.98332e7i	−0.854752	−	1.48047i	−0.876875	−	0.480719i	$-0.840376\pi$
$67$	−1.72242e7	−	2.98332e7i	−0.854752	−	1.48047i	0.0221230	−	0.999755i	$-0.492957\pi$
$68$	1.18653e7	+	6.85046e6i	0.554938	+	0.320394i
$69$			1.26026e7i			0.555986i
$70$	−4.77189e7	+	5.80487e7i	−1.98746	+	2.41769i
$71$	3.76248e7			1.48061			0.740306	−	0.672270i	$-0.234681\pi$
$71$	3.76248e7			1.48061			0.740306	+	0.672270i	$0.234681\pi$
$72$	1.37581e7	−	2.38297e7i	0.511950	−	0.886723i
$73$	1.69906e7	−	9.80954e6i	0.598298	−	0.345428i	−0.170073	−	0.985431i	$-0.554400\pi$
$73$	1.69906e7	−	9.80954e6i	0.598298	−	0.345428i	0.768372	+	0.640004i	$0.221067\pi$
$74$	1.41149e7	+	2.44478e7i	0.470708	+	0.815290i
$75$	2.70410e7	+	1.56121e7i	0.854628	+	0.493420i
$76$		−	8.48472e7i		−	2.54322i
$77$	1.11596e6	+	917375.i	0.0317458	+	0.0260966i
$78$	1.04034e7			0.281059
$79$	−2.52578e7	+	4.37477e7i	−0.648465	+	1.12317i	0.335024	+	0.942210i	$0.391255\pi$
$79$	−2.52578e7	+	4.37477e7i	−0.648465	+	1.12317i	−0.983489	+	0.180965i	$0.942078\pi$
$80$	−1.88308e8	+	1.08720e8i	−4.59737	+	2.65429i
$81$	−2.39148e6	−	4.14217e6i	−0.0555556	−	0.0962250i
$82$	4.21341e7	+	2.43261e7i	0.931919	+	0.538044i
$83$			4.65723e7i			0.981330i	0.871348	+	0.490665i	$0.163246\pi$
$83$			4.65723e7i			0.981330i	−0.871348	+	0.490665i	$0.836754\pi$
$84$	−7.41662e7	−	1.23072e7i	−1.48967	−	0.247197i
$85$	−2.10507e7			−0.403265
$86$	4.08812e7	−	7.08082e7i	0.747359	−	1.29446i
$87$	3.69734e7	−	2.13466e7i	0.645375	−	0.372607i
$88$	3.78506e6	+	6.55591e6i	0.0631163	+	0.109321i
$89$	−6.94636e7	−	4.01048e7i	−1.10713	−	0.639199i	−0.169042	−	0.985609i	$-0.554067\pi$
$89$	−6.94636e7	−	4.01048e7i	−1.10713	−	0.639199i	−0.938083	+	0.346409i	$0.887401\pi$
$90$			6.84472e7i			1.04324i
$91$	−6.17089e6	−	1.64364e7i	−0.0899875	−	0.239686i
$92$	1.80436e8			2.51868
$93$	−1.63887e7	+	2.83860e7i	−0.219085	+	0.379466i
$94$	1.07389e8	−	6.20008e7i	1.37546	−	0.794120i
$95$	6.51815e7	+	1.12898e8i	0.800258	+	1.38609i
$96$	−1.29983e8	−	7.50456e7i	−1.53039	−	0.883569i
$97$			5.45695e7i			0.616401i	0.951321	+	0.308200i	$0.0997267\pi$
$97$			5.45695e7i			0.616401i	−0.951321	+	0.308200i	$0.900273\pi$
$98$	3.39340e7	+	1.72068e8i	0.367901	+	1.86551i
$99$	1.31587e6			0.0136985
$100$	2.23525e8	−	3.87156e8i	2.23525	−	3.87156i
$101$	−2.45903e7	+	1.41972e7i	−0.236308	+	0.136433i	−0.613479	−	0.789711i	$-0.710230\pi$
$101$	−2.45903e7	+	1.41972e7i	−0.236308	+	0.136433i	0.377171	+	0.926144i	$0.376897\pi$
$102$	−1.45565e7	−	2.52126e7i	−0.134480	−	0.232926i
$103$	−3.58972e7	−	2.07253e7i	−0.318942	−	0.184141i	0.331979	−	0.943287i	$-0.392284\pi$
$103$	−3.58972e7	−	2.07253e7i	−0.318942	−	0.184141i	−0.650921	+	0.759145i	$0.725617\pi$
$104$		−	9.20000e7i		−	0.786420i
$105$	1.08140e8	−	4.06002e7i	0.889672	−	0.334018i
$106$	−2.15727e8			−1.70876
$107$	7.87224e7	−	1.36351e8i	0.600570	−	1.04022i	−0.392165	−	0.919895i	$-0.628274\pi$
$107$	7.87224e7	−	1.36351e8i	0.600570	−	1.04022i	0.992735	−	0.120323i	$-0.0383929\pi$
$108$	−5.93051e7	+	3.42398e7i	−0.435910	+	0.251673i
$109$	−2.40101e7	−	4.15866e7i	−0.170093	−	0.294610i	0.768359	−	0.640019i	$-0.221074\pi$
$109$	−2.40101e7	−	4.15866e7i	−0.170093	−	0.294610i	−0.938452	+	0.345409i	$0.887740\pi$
$110$	−1.63080e7	−	9.41544e6i	−0.111386	−	0.0643087i
$111$		−	4.33941e7i		−	0.285851i
$112$	−8.30770e7	+	5.00642e8i	−0.527969	+	3.18167i
$113$	−1.81439e8			−1.11280			−0.556399	−	0.830915i	$-0.687817\pi$
$113$	−1.81439e8			−1.11280			−0.556399	+	0.830915i	$0.687817\pi$
$114$	−9.01458e7	+	1.56137e8i	−0.533735	+	0.924457i
$115$	−2.40088e8	+	1.38615e8i	−1.37271	+	0.792537i
$116$	−3.05628e8	−	5.29362e8i	−1.68795	−	2.92362i
$117$	−1.38493e7	−	7.99592e6i	−0.0739070	−	0.0426702i
$118$			3.44359e7i			0.177617i
$119$	−3.11993e7	+	3.79531e7i	−0.155581	+	0.189260i
$120$	6.05296e8			2.91906
$121$	1.06998e8	−	1.85327e8i	0.499156	−	0.864563i
$122$	3.41244e8	−	1.97017e8i	1.54037	−	0.889335i
$123$	−3.73935e7	−	6.47674e7i	−0.163371	−	0.282967i
$124$	4.06414e8	+	2.34643e8i	1.71902	+	0.992478i
$125$			2.85015e8i			1.16742i
$126$	1.23406e8	+	1.01446e8i	0.489614	+	0.402487i
$127$	−4.30455e8			−1.65468			−0.827338	−	0.561704i	$-0.810146\pi$
$127$	−4.30455e8			−1.65468			−0.827338	+	0.561704i	$0.810146\pi$
$128$	−2.51372e8	+	4.35388e8i	−0.936432	+	1.62195i
$129$	−1.08844e8	+	6.28414e7i	−0.393050	+	0.226927i
$130$	1.14426e8	+	1.98192e8i	0.400639	+	0.693927i
$131$	−4.01594e8	−	2.31860e8i	−1.36365	−	0.787302i	−0.373540	−	0.927614i	$-0.621856\pi$
$131$	−4.01594e8	−	2.31860e8i	−1.36365	−	0.787302i	−0.990107	+	0.140312i	$0.955190\pi$
$132$		−	1.88398e7i		−	0.0620556i
$133$	3.00153e8	+	4.98077e7i	0.959260	+	0.159180i
$134$	1.04802e9			3.25051
$135$	5.26076e7	−	9.11190e7i	0.158385	−	0.274330i
$136$	−2.22962e8	+	1.28727e8i	−0.651741	+	0.376283i
$137$	1.12140e8	+	1.94232e8i	0.318331	+	0.551365i	0.980140	−	0.198307i	$-0.0635444\pi$
$137$	1.12140e8	+	1.94232e8i	0.318331	+	0.551365i	−0.661809	+	0.749672i	$0.730211\pi$
$138$	−3.32042e8	−	1.91704e8i	−0.915538	−	0.528586i
$139$		−	5.87934e8i		−	1.57496i	−0.616340	−	0.787480i	$-0.711385\pi$
$139$		−	5.87934e8i		−	1.57496i	0.616340	−	0.787480i	$-0.288615\pi$
$140$	−5.81288e8	−	1.54829e9i	−1.51314	−	4.03032i
$141$	−1.90612e8			−0.482252
$142$	−5.72330e8	+	9.91304e8i	−1.40764	+	2.43811i
$143$	3.81017e6	−	2.19980e6i	0.00911171	−	0.00526065i
$144$	2.31128e8	+	4.00325e8i	0.537530	+	0.931029i
$145$	8.13336e8	+	4.69580e8i	1.83992	+	1.06228i
$146$			5.96871e8i			1.31362i
$147$	8.70753e7	−	2.55144e8i	0.186477	−	0.546406i
$148$	−6.21291e8			−1.29494
$149$	−1.19818e8	+	2.07531e8i	−0.243096	+	0.421054i	−0.961594	−	0.274474i	$-0.911496\pi$
$149$	−1.19818e8	+	2.07531e8i	−0.243096	+	0.421054i	0.718499	+	0.695528i	$0.244830\pi$
$150$	−8.22667e8	+	4.74967e8i	−1.62502	+	0.938206i
$151$	−4.44408e7	−	7.69737e7i	−0.0854818	−	0.148059i	0.820115	−	0.572199i	$-0.193910\pi$
$151$	−4.44408e7	−	7.69737e7i	−0.0854818	−	0.148059i	−0.905596	+	0.424140i	$0.860576\pi$
$152$	1.38076e9	+	7.97182e8i	2.58669	+	1.49342i
$153$			4.47518e7i			0.0816666i
$154$	−4.11456e7	+	1.54477e7i	−0.0731545	+	0.0274651i
$155$	−7.21032e8			−1.24919
$156$	−1.14481e8	+	1.98286e8i	−0.193301	+	0.334807i
$157$	7.53328e8	−	4.34934e8i	1.23990	−	0.715855i	0.270824	−	0.962629i	$-0.412704\pi$
$157$	7.53328e8	−	4.34934e8i	1.23990	−	0.715855i	0.969073	+	0.246774i	$0.0793705\pi$
$158$	−7.68417e8	−	1.33094e9i	−1.23302	−	2.13565i
$159$	2.87182e8	+	1.65805e8i	0.449334	+	0.259423i
$160$		−	3.30169e9i		−	5.03798i
$161$	−1.05921e8	+	6.38306e8i	−0.157645	+	0.950005i
$162$	1.45512e8			0.211271
$163$	3.96097e8	−	6.86060e8i	0.561114	−	0.971878i	−0.436285	−	0.899808i	$-0.643706\pi$
$163$	3.96097e8	−	6.86060e8i	0.561114	−	0.971878i	0.997400	−	0.0720698i	$-0.0229604\pi$
$164$	−9.27300e8	+	5.35377e8i	−1.28187	+	0.740089i
$165$	1.44732e7	+	2.50682e7i	0.0195266	+	0.0338211i
$166$	−1.22704e9	−	7.08434e8i	−1.61595	−	0.932969i
$167$			7.55525e8i			0.971366i	0.874135	+	0.485683i	$0.161429\pi$
$167$			7.55525e8i			0.971366i	−0.874135	+	0.485683i	$0.838571\pi$
$168$	8.97111e8	−	1.09131e9i	1.12618	−	1.36997i
$169$	7.62262e8			0.934453
$170$	3.20213e8	−	5.54624e8i	0.383392	−	0.664054i
$171$	2.40010e8	−	1.38570e8i	0.280701	−	0.162063i
$172$	8.99725e8	+	1.55837e9i	1.02801	+	1.78056i
$173$	7.72758e8	+	4.46152e8i	0.862699	+	0.498080i	0.864915	−	0.501918i	$-0.167372\pi$
$173$	7.72758e8	+	4.46152e8i	0.862699	+	0.498080i	−0.00221612	+	0.999998i	$0.500705\pi$
$174$			1.29885e9i			1.41698i
$175$	1.23838e9	+	1.01801e9i	1.32039	+	1.08542i
$176$	−1.27174e8			−0.132540
$177$	2.64670e7	−	4.58422e7i	0.0269657	−	0.0467059i
$178$	2.11329e9	−	1.22011e9i	2.10513	−	1.21540i
$179$	−7.04634e8	−	1.22046e9i	−0.686359	−	1.18881i	−0.973008	−	0.230773i	$-0.925874\pi$
$179$	−7.04634e8	−	1.22046e9i	−0.686359	−	1.18881i	0.286648	−	0.958036i	$-0.407459\pi$
$180$	−1.30459e9	−	7.53203e8i	−1.24275	−	0.717500i
$181$			1.87025e9i			1.74255i	0.490792	+	0.871277i	$0.336708\pi$
$181$			1.87025e9i			1.74255i	−0.490792	+	0.871277i	$0.663292\pi$
$182$	5.26920e8	+	8.74376e7i	0.480241	+	0.0796917i
$183$	−6.05699e8			−0.540073
$184$	−1.69529e9	+	2.93633e9i	−1.47902	+	2.56173i
$185$	8.26689e8	−	4.77289e8i	0.705757	−	0.407469i
$186$	−4.98593e8	−	8.63588e8i	−0.416576	−	0.721530i
$187$	−1.06624e7	−	6.15595e6i	−0.00871946	−	0.00503418i
$188$			2.72907e9i			2.18465i
$189$	−8.63121e7	−	2.29896e8i	−0.0676432	−	0.180171i
$190$	−3.96603e9			−3.04328
$191$	1.83331e8	−	3.17539e8i	0.137754	−	0.238596i	−0.788892	−	0.614531i	$-0.789345\pi$
$191$	1.83331e8	−	3.17539e8i	0.137754	−	0.238596i	0.926646	+	0.375935i	$0.122678\pi$
$192$	1.76303e9	−	1.01789e9i	1.29734	−	0.749022i
$193$	−7.46161e8	−	1.29239e9i	−0.537779	−	0.931460i	−0.999023	−	0.0441868i	$-0.985930\pi$
$193$	−7.46161e8	−	1.29239e9i	−0.537779	−	0.931460i	0.461245	−	0.887273i	$-0.347403\pi$
$194$	−1.43775e9	−	8.30084e8i	−1.01502	−	0.586023i
$195$		−	3.51786e8i		−	0.243299i
$196$	−3.65299e9	−	1.24669e9i	−2.47528	−	0.844763i
$197$	−1.60272e9			−1.06412			−0.532061	−	0.846706i	$-0.678582\pi$
$197$	−1.60272e9			−1.06412			−0.532061	+	0.846706i	$0.678582\pi$
$198$	−2.00163e7	+	3.46693e7i	−0.0130234	+	0.0225572i
$199$	−4.06947e8	+	2.34951e8i	−0.259493	+	0.149818i	−0.624103	−	0.781342i	$-0.714536\pi$
$199$	−4.06947e8	+	2.34951e8i	−0.259493	+	0.149818i	0.364610	+	0.931160i	$0.381202\pi$
$200$	4.20025e9	+	7.27505e9i	2.62516	+	4.54691i
$201$	−1.39516e9	−	8.05497e8i	−0.854752	−	0.493491i
$202$		−	8.63844e8i		−	0.518836i
$203$	2.05207e9	−	7.70429e8i	1.20839	−	0.453679i
$204$	6.40729e8			0.369959
$205$	8.22576e8	−	1.42474e9i	0.465758	−	0.806717i
$206$	1.09210e9	−	6.30525e8i	0.606449	−	0.350133i
$207$	2.94683e8	+	5.10405e8i	0.160499	+	0.277993i
$208$	1.33849e9	+	7.72775e8i	0.715089	+	0.412857i
$209$			7.62453e7i			0.0399602i
$210$	−5.75279e8	+	3.46677e9i	−0.295802	+	1.78257i
$211$	−6.28091e8			−0.316879			−0.158439	−	0.987369i	$-0.550646\pi$
$211$	−6.28091e8			−0.316879			−0.158439	+	0.987369i	$0.550646\pi$
$212$	2.37389e9	−	4.11170e9i	1.17521	−	2.03553i
$213$	1.52381e9	−	8.79770e8i	0.740306	−	0.427416i
$214$	2.39497e9	+	4.14821e9i	1.14195	+	1.97791i
$215$	−2.39435e9	−	1.38238e9i	−1.12055	−	0.646953i
$216$		−	1.28680e9i		−	0.591149i
$217$	−1.06864e9	+	1.29998e9i	−0.481941	+	0.586268i
$218$	1.46092e9			0.646843
$219$	4.58747e8	−	7.94573e8i	0.199433	−	0.345428i
$220$	3.58912e8	−	2.07218e8i	0.153214	−	0.0884579i
$221$	7.48137e7	+	1.29581e8i	0.0313626	+	0.0543216i
$222$	1.14331e9	+	6.60089e8i	0.470708	+	0.271763i
$223$		−	5.07728e8i		−	0.205311i	−0.994717	−	0.102655i	$-0.967266\pi$
$223$		−	5.07728e8i		−	0.205311i	0.994717	−	0.102655i	$-0.0327339\pi$
$224$	−5.95274e9	−	4.89344e9i	−2.36442	−	1.94367i
$225$	1.46021e9			0.569752
$226$	2.75996e9	−	4.78038e9i	1.05796	−	1.83244i
$227$	−3.86619e9	+	2.23215e9i	−1.45606	+	0.840658i	−0.998814	−	0.0486813i	$-0.984498\pi$
$227$	−3.86619e9	+	2.23215e9i	−1.45606	+	0.840658i	−0.457248	+	0.889339i	$0.651165\pi$
$228$	−1.98396e9	−	3.43631e9i	−0.734163	−	1.27161i
$229$	−2.49386e8	−	1.43983e8i	−0.0906840	−	0.0523564i	0.453972	−	0.891016i	$-0.350007\pi$
$229$	−2.49386e8	−	1.43983e8i	−0.0906840	−	0.0523564i	−0.544656	+	0.838659i	$0.683340\pi$
$230$		−	8.43417e9i		−	3.01392i
$231$	6.66472e7	+	1.10595e7i	0.0234064	+	0.00388407i
$232$	1.14861e10			3.96479
$233$	−2.66936e9	+	4.62346e9i	−0.905697	+	1.56871i	−0.0857180	+	0.996319i	$0.527318\pi$
$233$	−2.66936e9	+	4.62346e9i	−0.905697	+	1.56871i	−0.819979	+	0.572394i	$0.806015\pi$
$234$	4.21338e8	−	2.43260e8i	0.140529	−	0.0811347i
$235$	−2.09653e9	−	3.63129e9i	−0.687431	−	1.19067i
$236$	−6.56340e8	−	3.78938e8i	−0.211583	−	0.122158i
$237$			2.36238e9i			0.748783i
$238$	−5.25366e8	−	1.39933e9i	−0.163740	−	0.436127i
$239$	−3.04700e9			−0.933858			−0.466929	−	0.884295i	$-0.654640\pi$
$239$	−3.04700e9			−0.933858			−0.466929	+	0.884295i	$0.654640\pi$
$240$	−5.08432e9	+	8.80630e9i	−1.53246	+	2.65429i
$241$	−2.17673e9	+	1.25674e9i	−0.645263	+	0.372543i	−0.786639	−	0.617413i	$-0.788181\pi$
$241$	−2.17673e9	+	1.25674e9i	−0.645263	+	0.372543i	0.141376	+	0.989956i	$0.454847\pi$
$242$	3.25521e9	+	5.63819e9i	0.949113	+	1.64391i
$243$	−1.93710e8	−	1.11839e8i	−0.0555556	−	0.0320750i
$244$			8.67203e9i			2.44659i
$245$	5.81841e9	−	1.14746e9i	1.61488	−	0.318474i
$246$	2.27524e9			0.621279
$247$	4.63307e8	−	8.02471e8i	0.124475	−	0.215596i
$248$	−7.63693e9	+	4.40918e9i	−2.01889	+	1.16560i
$249$	1.08899e9	+	1.88618e9i	0.283286	+	0.490665i
$250$	−7.50931e9	−	4.33550e9i	−1.92238	−	1.10989i
$251$			5.64539e8i			0.142232i	0.997468	+	0.0711162i	$0.0226561\pi$
$251$			5.64539e8i			0.142232i	−0.997468	+	0.0711162i	$0.977344\pi$
$252$	−3.29151e9	+	1.23576e9i	−0.816193	+	0.306431i
$253$	−1.62143e8			−0.0395747
$254$	6.54787e9	−	1.13412e10i	1.57313	−	2.72474i
$255$	−8.52553e8	+	4.92222e8i	−0.201633	+	0.116413i
$256$	−2.07542e9	−	3.59473e9i	−0.483222	−	0.836964i
$257$	5.88633e9	+	3.39847e9i	1.34931	+	0.779025i	0.988152	−	0.153480i	$-0.0490480\pi$
$257$	5.88633e9	+	3.39847e9i	1.34931	+	0.779025i	0.361159	+	0.932504i	$0.382381\pi$
$258$		−	3.82364e9i		−	0.862976i
$259$	3.64715e8	−	2.19786e9i	0.0810503	−	0.488429i
$260$	−5.03666e9			−1.10217
$261$	9.98281e8	−	1.72907e9i	0.215125	−	0.372607i
$262$	1.22177e10	−	7.05389e9i	2.59289	−	1.49701i
$263$	7.27257e8	+	1.25965e9i	0.152007	+	0.263285i	0.931965	−	0.362547i	$-0.118093\pi$
$263$	7.27257e8	+	1.25965e9i	0.152007	+	0.263285i	−0.779958	+	0.625832i	$0.784760\pi$
$264$	3.06590e8	+	1.77010e8i	0.0631163	+	0.0364402i
$265$			7.29470e9i			1.47919i
$266$	−5.87806e9	+	7.15051e9i	−1.17411	+	1.42827i
$267$	−3.75103e9			−0.738084
$268$	−1.15326e10	+	1.99751e10i	−2.23557	+	3.87212i
$269$	8.60630e9	−	4.96885e9i	1.64364	−	0.948957i	0.664119	−	0.747627i	$-0.268807\pi$
$269$	8.60630e9	−	4.96885e9i	1.64364	−	0.948957i	0.979523	−	0.201331i	$-0.0645266\pi$
$270$	1.60048e9	+	2.77211e9i	0.301158	+	0.521622i
$271$	−2.05721e9	−	1.18773e9i	−0.381419	−	0.220212i	0.297017	−	0.954872i	$-0.404008\pi$
$271$	−2.05721e9	−	1.18773e9i	−0.381419	−	0.220212i	−0.678435	+	0.734660i	$0.737342\pi$
$272$		−	4.32509e9i		−	0.790168i
$273$	−6.34249e8	−	5.21383e8i	−0.114185	−	0.0938656i
$274$	−6.82327e9			−1.21057
$275$	−2.00863e8	+	3.47906e8i	−0.0351213	+	0.0608318i
$276$	7.30767e9	−	4.21909e9i	1.25934	−	0.727080i
$277$	−4.32730e9	−	7.49510e9i	−0.735017	−	1.27309i	−0.954716	−	0.297520i	$-0.903841\pi$
$277$	−4.32730e9	−	7.49510e9i	−0.735017	−	1.27309i	0.219698	−	0.975568i	$-0.429493\pi$
$278$	1.54904e10	+	8.94336e9i	2.59348	+	1.49734i
$279$			1.53285e9i			0.252977i
$280$	3.06575e10	+	5.08734e9i	4.98775	+	0.827672i
$281$	1.93333e9			0.310084			0.155042	−	0.987908i	$-0.450449\pi$
$281$	1.93333e9			0.310084			0.155042	+	0.987908i	$0.450449\pi$
$282$	2.89949e9	−	5.02207e9i	0.458485	−	0.794120i
$283$	−3.70251e9	+	2.13765e9i	−0.577232	+	0.333265i	−0.760033	−	0.649885i	$-0.774817\pi$
$283$	−3.70251e9	+	2.13765e9i	−0.577232	+	0.333265i	0.182801	+	0.983150i	$0.441484\pi$
$284$	−1.25960e10	−	2.18169e10i	−1.93624	−	3.35367i
$285$	5.27970e9	+	3.04824e9i	0.800258	+	0.462029i
$286$			1.33849e8i			0.0200056i
$287$	−1.34958e9	−	3.59467e9i	−0.198917	−	0.529824i
$288$	−7.01907e9			−1.02026
$289$	−3.27852e9	+	5.67856e9i	−0.469988	+	0.814042i
$290$	−2.47441e10	+	1.42860e10i	−3.49848	+	2.01985i
$291$	1.27598e9	+	2.21007e9i	0.177940	+	0.308200i
$292$	−1.13762e10	−	6.56806e9i	−1.56483	−	0.903453i
$293$			3.87374e9i			0.525605i	0.964850	+	0.262803i	$0.0846468\pi$
$293$			3.87374e9i			0.525605i	−0.964850	+	0.262803i	$0.915353\pi$
$294$	5.39775e9	+	6.17530e9i	0.722475	+	0.826549i
$295$	1.16443e9			0.153754
$296$	5.83734e9	−	1.01106e10i	0.760411	−	1.31707i
$297$	5.32927e7	−	3.07686e7i	0.00684923	−	0.00395441i
$298$	−3.64522e9	−	6.31371e9i	−0.462231	−	0.800607i
$299$	1.70654e9	+	9.85270e8i	0.213516	+	0.123274i
$300$		−	2.09064e10i		−	2.58104i
$301$	−6.04100e9	+	2.26803e9i	−0.735941	+	0.276302i
$302$	2.70404e9			0.325077
$303$	−6.63939e8	+	1.14998e9i	−0.0787694	+	0.136433i
$304$	−2.31960e10	+	1.33922e10i	−2.71593	+	1.56804i
$305$	−6.66205e9	−	1.15390e10i	−0.769854	−	1.33343i
$306$	−1.17908e9	−	6.80741e8i	−0.134480	−	0.0776420i
$307$		−	1.39067e9i		−	0.156556i	−0.996932	−	0.0782782i	$-0.975058\pi$
$307$		−	1.39067e9i		−	0.156556i	0.996932	−	0.0782782i	$-0.0249423\pi$
$308$	1.58343e8	−	9.54214e8i	0.0175953	−	0.106033i
$309$	−1.93845e9			−0.212628
$310$	1.09680e10	−	1.89971e10i	1.18763	−	2.05703i
$311$	4.70138e9	−	2.71434e9i	0.502555	−	0.290150i	−0.227213	−	0.973845i	$-0.572961\pi$
$311$	4.70138e9	−	2.71434e9i	0.502555	−	0.290150i	0.729768	+	0.683695i	$0.239628\pi$
$312$	−2.15121e9	−	3.72600e9i	−0.227020	−	0.393210i
$313$	8.14891e9	+	4.70478e9i	0.849028	+	0.490187i	0.860323	−	0.509749i	$-0.170262\pi$
$313$	8.14891e9	+	4.70478e9i	0.849028	+	0.490187i	−0.0112944	+	0.999936i	$0.503595\pi$
$314$			2.64640e10i			2.72231i
$315$	3.43034e9	−	4.17292e9i	0.348413	−	0.423836i
$316$	3.38231e10			3.39207
$317$	−1.22828e9	+	2.12744e9i	−0.121635	+	0.210678i	−0.920413	−	0.390948i	$-0.872147\pi$
$317$	−1.22828e9	+	2.12744e9i	−0.121635	+	0.210678i	0.798777	+	0.601627i	$0.205480\pi$
$318$	−8.73694e9	+	5.04427e9i	−0.854379	+	0.493276i
$319$	2.74643e8	+	4.75695e8i	0.0265219	+	0.0459374i
$320$	3.87830e10	+	2.23913e10i	3.69863	+	2.13541i
$321$		−	7.36297e9i		−	0.693478i
$322$	−1.52063e10	−	1.25003e10i	−1.41449	−	1.16278i
$323$	−2.59305e9			−0.238232
$324$	−1.60124e9	+	2.77343e9i	−0.145303	+	0.251673i
$325$	4.22812e9	−	2.44111e9i	0.378978	−	0.218803i
$326$	1.20505e10	+	2.08720e10i	1.06692	+	1.84796i
$327$	−1.94481e9	−	1.12284e9i	−0.170093	−	0.0982034i
$328$		−	2.01205e10i		−	1.73838i
$329$	−9.65427e9	−	1.60204e9i	−0.824016	−	0.136738i
$330$	−8.80633e8			−0.0742573
$331$	−2.81839e9	+	4.88160e9i	−0.234795	+	0.406678i	−0.959213	−	0.282684i	$-0.908775\pi$
$331$	−2.81839e9	+	4.88160e9i	−0.234795	+	0.406678i	0.724418	+	0.689361i	$0.242109\pi$
$332$	2.70052e10	−	1.55914e10i	2.22277	−	1.28332i
$333$	−1.01467e9	−	1.75746e9i	−0.0825179	−	0.142925i
$334$	−1.99059e10	−	1.14927e10i	−1.59954	−	0.923495i
$335$		−	3.54384e10i		−	2.81381i
$336$	8.34173e9	+	2.22186e10i	0.654484	+	1.74325i
$337$	1.10404e9			0.0855985			0.0427993	−	0.999084i	$-0.486372\pi$
$337$	1.10404e9			0.0855985			0.0427993	+	0.999084i	$0.486372\pi$
$338$	−1.15951e10	+	2.00834e10i	−0.888402	+	1.53876i
$339$	−7.34827e9	+	4.24253e9i	−0.556399	+	0.321237i
$340$	7.04733e9	+	1.22063e10i	0.527362	+	0.913418i
$341$	−3.65211e8	−	2.10855e8i	−0.0270101	−	0.0155943i
$342$			8.43140e9i			0.616305i
$343$	6.55467e9	−	1.21909e10i	0.473559	−	0.880762i
$344$	−3.38135e10			−2.41466
$345$	−6.48239e9	+	1.12278e10i	−0.457571	+	0.792537i
$346$	−2.35096e10	+	1.35733e10i	−1.64037	+	0.947067i
$347$	1.19744e10	+	2.07402e10i	0.825913	+	1.43052i	0.901219	+	0.433363i	$0.142673\pi$
$347$	1.19744e10	+	2.07402e10i	0.825913	+	1.43052i	−0.0753060	+	0.997160i	$0.523993\pi$
$348$	−2.47558e10	−	1.42928e10i	−1.68795	−	0.974540i
$349$		−	1.00616e10i		−	0.678210i	−0.940749	−	0.339105i	$-0.889876\pi$
$349$		−	1.00616e10i		−	0.678210i	0.940749	−	0.339105i	$-0.110124\pi$
$350$	−4.56590e10	+	1.71422e10i	−3.04267	+	1.14234i
$351$	−7.47864e8			−0.0492713
$352$	9.65528e8	−	1.67234e9i	0.0628918	−	0.108932i
$353$	6.90008e9	−	3.98376e9i	0.444381	−	0.256563i	−0.261073	−	0.965319i	$-0.584076\pi$
$353$	6.90008e9	−	3.98376e9i	0.444381	−	0.256563i	0.705454	+	0.708756i	$0.250743\pi$
$354$	8.05205e8	+	1.39466e9i	0.0512735	+	0.0888084i
$355$	3.35205e10	+	1.93531e10i	2.11056	+	1.21853i
$356$			5.37050e10i			3.34360i
$357$	−3.76126e8	+	2.26662e9i	−0.0231558	+	0.139543i
$358$	4.28741e10			2.61014
$359$	2.83202e9	−	4.90521e9i	0.170498	−	0.295311i	−0.768096	−	0.640335i	$-0.778796\pi$
$359$	2.83202e9	−	4.90521e9i	0.170498	−	0.295311i	0.938594	+	0.345024i	$0.112129\pi$
$360$	2.45145e10	−	1.41534e10i	1.45953	−	0.842660i
$361$	−4.62652e8	−	8.01337e8i	−0.0272412	−	0.0471831i
$362$	−4.92757e10	−	2.84494e10i	−2.86945	−	1.65668i
$363$		−	1.00076e10i		−	0.576375i
$364$	−7.46485e9	+	9.08079e9i	−0.425222	+	0.517271i
$365$	2.01829e10			1.13714
$366$	9.21359e9	−	1.59584e10i	0.513458	−	0.889335i
$367$	−2.56504e9	+	1.48093e9i	−0.141394	+	0.0816338i	−0.569028	−	0.822318i	$-0.692680\pi$
$367$	−2.56504e9	+	1.48093e9i	−0.141394	+	0.0816338i	0.427634	+	0.903952i	$0.359347\pi$
$368$	−2.84799e10	−	4.93287e10i	−1.55292	−	2.68973i
$369$	−3.02887e9	−	1.74872e9i	−0.163371	−	0.0943223i
$370$			2.90411e10i			1.54955i
$371$	1.31519e10	+	1.08115e10i	0.694213	+	0.570676i
$372$	2.19463e10			1.14602
$373$	−1.00039e10	+	1.73272e10i	−0.516812	+	0.895144i	0.482998	+	0.875622i	$0.339548\pi$
$373$	−1.00039e10	+	1.73272e10i	−0.516812	+	0.895144i	−0.999809	+	0.0195224i	$0.993785\pi$
$374$	3.24383e8	−	1.87283e8i	0.0165795	−	0.00957218i
$375$	6.66442e9	+	1.15431e10i	0.337006	+	0.583711i
$376$	−4.44114e10	−	2.56410e10i	−2.22200	−	1.28287i
$377$		−	6.67550e9i		−	0.330460i
$378$	7.37002e9	+	1.22299e9i	0.360995	+	0.0599039i
$379$	3.99866e9			0.193802			0.0969008	−	0.995294i	$-0.469107\pi$
$379$	3.99866e9			0.193802			0.0969008	+	0.995294i	$0.469107\pi$
$380$	4.36428e10	−	7.55915e10i	2.09304	−	3.62526i
$381$	−1.74334e10	+	1.00652e10i	−0.827338	+	0.477664i
$382$	5.57748e9	+	9.66049e9i	0.261930	+	0.453676i
$383$	−7.95156e9	−	4.59083e9i	−0.369536	−	0.213352i	0.303720	−	0.952761i	$-0.401771\pi$
$383$	−7.95156e9	−	4.59083e9i	−0.369536	−	0.213352i	−0.673256	+	0.739410i	$0.735105\pi$
$384$			2.35110e10i			1.08130i
$385$	5.22357e8	+	1.39132e9i	0.0237752	+	0.0633263i
$386$	4.54009e10			2.04510
$387$	−2.93880e9	+	5.09015e9i	−0.131017	+	0.226927i
$388$	3.16424e10	−	1.82687e10i	1.39618	−	0.806086i
$389$	5.02686e9	+	8.70678e9i	0.219532	+	0.380241i	0.954665	−	0.297682i	$-0.0962135\pi$
$389$	5.02686e9	+	8.70678e9i	0.219532	+	0.380241i	−0.735133	+	0.677923i	$0.762880\pi$
$390$	9.26854e9	+	5.35119e9i	0.400639	+	0.231309i
$391$		−	5.51439e9i		−	0.235934i
$392$	5.46097e10	−	4.77337e10i	2.31273	−	2.02153i
$393$	−2.16861e10			−0.909098
$394$	2.43797e10	−	4.22269e10i	1.01168	−	1.75228i
$395$	−4.50050e10	+	2.59836e10i	−1.84873	+	1.06736i
$396$	−4.40525e8	−	7.63012e8i	−0.0179139	−	0.0310278i
$397$	−6.73987e9	−	3.89127e9i	−0.271325	−	0.156650i	0.358165	−	0.933658i	$-0.383403\pi$
$397$	−6.73987e9	−	3.89127e9i	−0.271325	−	0.156650i	−0.629490	+	0.777009i	$0.716736\pi$
$398$		−	1.42958e10i		−	0.569740i
$399$	1.33208e10	−	5.00117e9i	0.525581	−	0.197324i
$400$	−1.41124e11			−5.51265
$401$	−3.41778e9	+	5.91977e9i	−0.132180	+	0.228943i	−0.924517	−	0.381141i	$-0.875531\pi$
$401$	−3.41778e9	+	5.91977e9i	−0.132180	+	0.228943i	0.792337	+	0.610084i	$0.208864\pi$
$402$	4.24450e10	−	2.45056e10i	1.62526	−	0.938342i
$403$	2.56253e9	+	4.43843e9i	0.0971514	+	0.168271i
$404$	1.64647e10	+	9.50587e9i	0.618055	+	0.356834i
$405$		−	4.92042e9i		−	0.182887i
$406$	−1.09165e10	+	6.57854e10i	−0.401771	+	2.42117i
$407$	5.58304e8			0.0203466
$408$	−6.01997e9	+	1.04269e10i	−0.217247	+	0.376283i
$409$	4.46184e10	−	2.57605e10i	1.59449	−	0.920578i	0.601965	−	0.798523i	$-0.294385\pi$
$409$	4.46184e10	−	2.57605e10i	1.59449	−	0.920578i	0.992523	−	0.122055i	$-0.0389485\pi$
$410$	2.50252e10	+	4.33450e10i	0.885610	+	1.53392i
$411$	9.08335e9	+	5.24427e9i	0.318331	+	0.183788i
$412$			2.77536e10i			0.963230i
$413$	1.72581e9	−	2.09940e9i	0.0593189	−	0.0721599i
$414$	−1.79302e10			−0.610358
$415$	−2.39554e10	+	4.14919e10i	−0.807626	+	1.39885i
$416$	−2.03241e10	+	1.17341e10i	−0.678638	+	0.391812i
$417$	−1.37475e10	−	2.38113e10i	−0.454652	−	0.787480i
$418$	−2.00884e9	−	1.15981e9i	−0.0658022	−	0.0379909i
$419$		−	1.19081e10i		−	0.386356i	−0.981164	−	0.193178i	$-0.938120\pi$
$419$		−	1.19081e10i		−	0.386356i	0.981164	−	0.193178i	$-0.0618795\pi$
$420$	−5.97453e10	−	4.91135e10i	−1.92002	−	1.57835i
$421$	1.29732e10			0.412971			0.206485	−	0.978450i	$-0.433797\pi$
$421$	1.29732e10			0.412971			0.206485	+	0.978450i	$0.433797\pi$
$422$	9.55420e9	−	1.65484e10i	0.301262	−	0.521801i
$423$	−7.71978e9	+	4.45702e9i	−0.241126	+	0.139214i
$424$	4.46078e10	+	7.72630e10i	1.38022	+	2.39061i
$425$	−1.18320e10	−	6.83122e9i	−0.362663	−	0.209384i
$426$			5.35304e10i			1.62541i
$427$	−3.06779e10	−	5.09073e9i	−0.922815	−	0.153133i
$428$	−1.05419e11			−3.14153
$429$	1.02875e8	−	1.78184e8i	0.00303724	−	0.00526065i
$430$	7.28432e10	−	4.20560e10i	2.13066	−	1.23014i
$431$	−7.98559e9	−	1.38315e10i	−0.231418	−	0.400829i	0.726807	−	0.686841i	$-0.241003\pi$
$431$	−7.98559e9	−	1.38315e10i	−0.231418	−	0.400829i	−0.958226	+	0.286013i	$0.907670\pi$
$432$	1.87214e10	+	1.08088e10i	0.537530	+	0.310343i
$433$		−	9.11541e9i		−	0.259313i	−0.991559	−	0.129657i	$-0.958613\pi$
$433$		−	9.11541e9i		−	0.259313i	0.991559	−	0.129657i	$-0.0413875\pi$
$434$	−1.79949e10	−	4.79302e10i	−0.507213	−	1.35098i
$435$	4.39201e10			1.22661
$436$	−1.60761e10	+	2.78447e10i	−0.444872	+	0.770542i
$437$	−2.95744e10	+	1.70748e10i	−0.810942	+	0.468198i
$438$	1.39564e10	+	2.41733e10i	0.379209	+	0.656809i
$439$	1.87361e10	+	1.08173e10i	0.504452	+	0.291246i	0.730550	−	0.682859i	$-0.239264\pi$
$439$	1.87361e10	+	1.08173e10i	0.504452	+	0.291246i	−0.226098	+	0.974105i	$0.572597\pi$
$440$			7.78767e9i			0.207777i
$441$	−2.43939e9	−	1.23694e10i	−0.0644953	−	0.327034i
$442$	−4.55211e9			−0.119268
$443$	−1.09384e10	+	1.89458e10i	−0.284013	+	0.491925i	−0.972369	−	0.233448i	$-0.924999\pi$
$443$	−1.09384e10	+	1.89458e10i	−0.284013	+	0.491925i	0.688356	+	0.725373i	$0.258333\pi$
$444$	−2.51623e10	+	1.45274e10i	−0.647468	+	0.373816i
$445$	−4.12574e10	−	7.14598e10i	−1.05211	−	1.82231i
$446$	1.33772e10	+	7.72330e9i	0.338084	+	0.195193i
$447$			1.12067e10i			0.280703i
$448$	9.78505e10	−	3.67370e10i	2.42913	−	0.911993i
$449$	6.37327e9			0.156811			0.0784056	−	0.996922i	$-0.475017\pi$
$449$	6.37327e9			0.156811			0.0784056	+	0.996922i	$0.475017\pi$
$450$	−2.22120e10	+	3.84723e10i	−0.541674	+	0.938206i
$451$	8.33289e8	−	4.81100e8i	0.0201414	−	0.0116286i
$452$	6.07419e10	+	1.05208e11i	1.45524	+	2.52055i
$453$	−3.59970e9	−	2.07829e9i	−0.0854818	−	0.0493530i
$454$		−	1.35817e11i		−	3.19692i
$455$	2.95666e9	−	1.78176e10i	0.0689852	−	0.415721i
$456$	7.45611e10			1.72446
$457$	−2.54222e10	+	4.40326e10i	−0.582839	+	1.00951i	0.412302	+	0.911047i	$0.364725\pi$
$457$	−2.54222e10	+	4.40326e10i	−0.582839	+	1.00951i	−0.995141	+	0.0984597i	$0.968608\pi$
$458$	7.58707e9	−	4.38040e9i	0.172430	−	0.0995524i
$459$	1.04642e9	+	1.81245e9i	0.0235751	+	0.0408333i
$460$	1.60753e11	+	9.28109e10i	3.59028	+	2.07285i
$461$		−	5.80610e10i		−	1.28553i	−0.766065	−	0.642763i	$-0.777788\pi$
$461$		−	5.80610e10i		−	1.28553i	0.766065	−	0.642763i	$-0.222212\pi$
$462$	−1.30519e9	+	1.58773e9i	−0.0286487	+	0.0348504i
$463$	−9.30304e9			−0.202442			−0.101221	−	0.994864i	$-0.532275\pi$
$463$	−9.30304e9			−0.202442			−0.101221	+	0.994864i	$0.532275\pi$
$464$	−9.64801e10	+	1.67108e11i	−2.08145	+	3.60518i
$465$	−2.92018e10	+	1.68597e10i	−0.624594	+	0.360609i
$466$	−8.12098e10	−	1.40660e11i	−1.72213	−	2.98281i
$467$	3.12766e10	+	1.80576e10i	0.657586	+	0.379657i	0.791357	−	0.611355i	$-0.209375\pi$
$467$	3.12766e10	+	1.80576e10i	0.657586	+	0.379657i	−0.133771	+	0.991012i	$0.542709\pi$
$468$			1.07075e10i			0.223205i
$469$	−6.38933e10	−	5.25234e10i	−1.32058	−	1.08558i
$470$	1.27565e11			2.61421
$471$	2.03399e10	−	3.52297e10i	0.413299	−	0.715855i
$472$	1.23333e10	−	7.12063e9i	0.248491	−	0.143467i
$473$	−8.08510e8	−	1.40038e9i	−0.0161525	−	0.0279770i
$474$	−6.22418e10	−	3.59353e10i	−1.23302	−	0.711882i
$475$			8.46089e10i			1.66204i
$476$	3.24521e10	+	5.38514e9i	0.632143	+	0.104898i
$477$	1.55078e10			0.299556
$478$	4.63494e10	−	8.02795e10i	0.887836	−	1.53778i
$479$	5.41914e9	−	3.12874e9i	0.102941	−	0.0594330i	−0.447646	−	0.894211i	$-0.647737\pi$
$479$	5.41914e9	−	3.12874e9i	0.102941	−	0.0594330i	0.550587	+	0.834778i	$0.314404\pi$
$480$	−7.72023e10	−	1.33718e11i	−1.45434	−	2.51899i
$481$	−5.87607e9	−	3.39255e9i	−0.109776	−	0.0633791i
$482$		−	7.64674e10i		−	1.41673i
$483$	1.06355e10	+	2.83281e10i	0.195420	+	0.520510i
$484$	−1.43283e11			−2.61104
$485$	−2.80689e10	+	4.86167e10i	−0.507292	+	0.878656i
$486$	5.89324e9	−	3.40247e9i	0.105635	−	0.0609886i
$487$	5.15175e9	+	8.92309e9i	0.0915880	+	0.158635i	0.908180	−	0.418581i	$-0.137472\pi$
$487$	5.15175e9	+	8.92309e9i	0.0915880	+	0.158635i	−0.816591	+	0.577216i	$0.804139\pi$
$488$	−1.41124e11	−	8.14781e10i	−2.48841	−	1.43669i
$489$		−	3.70473e10i		−	0.647919i
$490$	−5.82744e10	+	1.70753e11i	−1.01087	+	2.96199i
$491$	−2.04917e10			−0.352575			−0.176288	−	0.984339i	$-0.556409\pi$
$491$	−2.04917e10			−0.352575			−0.176288	+	0.984339i	$0.556409\pi$
$492$	−2.50371e10	+	4.33655e10i	−0.427291	+	0.740089i
$493$	−1.61781e10	+	9.34040e9i	−0.273866	+	0.158117i
$494$	1.40952e10	+	2.44136e10i	0.236681	+	0.409943i
$495$	1.17233e9	+	6.76843e8i	0.0195266	+	0.0112737i
$496$		−	1.48144e11i		−	2.44769i
$497$	8.45731e10	−	3.17521e10i	1.38614	−	0.520412i
$498$	−6.62604e10			−1.07730
$499$	2.82677e10	−	4.89610e10i	0.455919	−	0.789675i	−0.542821	−	0.839848i	$-0.682644\pi$
$499$	2.82677e10	−	4.89610e10i	0.455919	−	0.789675i	0.998741	+	0.0501730i	$0.0159773\pi$
$500$	1.65267e11	−	9.54171e10i	2.64428	−	1.52667i
$501$	1.76662e10	+	3.05987e10i	0.280409	+	0.485683i
$502$	−1.48739e10	−	8.58747e9i	−0.234213	−	0.135223i
$503$			8.00320e10i			1.25024i	0.780530	+	0.625118i	$0.214949\pi$
$503$			8.00320e10i			1.25024i	−0.780530	+	0.625118i	$0.785051\pi$
$504$	1.08152e10	−	6.51750e10i	0.167615	−	1.01009i
$505$	−2.92105e10			−0.449131
$506$	2.46644e9	−	4.27201e9i	0.0376244	−	0.0651673i
$507$	3.08716e10	−	1.78237e10i	0.467227	−	0.269753i
$508$	1.44107e11	+	2.49601e11i	2.16387	+	3.74794i
$509$	6.46122e10	+	3.73038e10i	0.962594	+	0.555754i	0.896970	−	0.442091i	$-0.145763\pi$
$509$	6.46122e10	+	3.73038e10i	0.962594	+	0.555754i	0.0656235	+	0.997844i	$0.479096\pi$
$510$		−	2.99497e10i		−	0.442703i
$511$	2.99131e10	−	3.63885e10i	0.438711	−	0.533680i
$512$	−2.42124e9			−0.0352337
$513$	6.48026e9	−	1.12241e10i	0.0935671	−	0.162063i
$514$	−1.79080e11	+	1.03392e11i	−2.56563	+	1.48127i
$515$	−2.13209e10	−	3.69289e10i	−0.303093	−	0.524973i
$516$	7.28777e10	+	4.20760e10i	1.02801	+	0.593520i
$517$		−	2.45239e9i		−	0.0343263i
$518$	5.23593e10	+	4.30419e10i	0.727236	+	0.597823i
$519$	4.17290e10			0.575133
$520$	4.73220e10	−	8.19641e10i	0.647217	−	1.12101i
$521$	−6.18827e10	+	3.57280e10i	−0.839882	+	0.484906i	−0.857224	−	0.514944i	$-0.827813\pi$
$521$	−6.18827e10	+	3.57280e10i	−0.839882	+	0.484906i	0.0173421	+	0.999850i	$0.494480\pi$
$522$	3.03707e10	+	5.26036e10i	0.409047	+	0.708489i
$523$	4.14767e10	+	2.39466e10i	0.554367	+	0.320064i	0.750881	−	0.660437i	$-0.229629\pi$
$523$	4.14767e10	+	2.39466e10i	0.554367	+	0.320064i	−0.196515	+	0.980501i	$0.562962\pi$
$524$			3.10488e11i			4.11832i
$525$	7.39580e10	+	1.22727e10i	0.973526	+	0.161548i
$526$	−4.42507e10			−0.578065
$527$	7.17102e9	−	1.24206e10i	0.0929691	−	0.161027i
$528$	−5.15054e9	+	2.97366e9i	−0.0662700	+	0.0382610i
$529$	2.84424e9	+	4.92636e9i	0.0363198	+	0.0629077i
$530$	−1.92194e11	−	1.10963e11i	−2.43577	−	1.40629i
$531$		−	2.47548e9i		−	0.0311373i
$532$	−7.16038e10	−	1.90720e11i	−0.893901	−	2.38094i
$533$	−1.16937e10			−0.144891
$534$	5.70588e10	−	9.88287e10i	0.701710	−	1.21540i
$535$	1.40270e11	−	8.09848e10i	1.71218	−	0.988527i
$536$	−2.16709e11	−	3.75352e11i	−2.62554	−	4.54757i
$537$	−5.70753e10	−	3.29525e10i	−0.686359	−	0.396270i
$538$			3.02334e11i			3.60877i
$539$	3.28265e9	+	1.12030e9i	0.0388928	+	0.0132733i
$540$	−7.04476e10			−0.828498
$541$	2.54500e10	−	4.40807e10i	0.297097	−	0.514588i	−0.678373	−	0.734717i	$-0.737315\pi$
$541$	2.54500e10	−	4.40807e10i	0.297097	−	0.514588i	0.975471	+	0.220130i	$0.0706481\pi$
$542$	6.25866e10	−	3.61344e10i	0.725244	−	0.418720i
$543$	4.37316e10	+	7.57453e10i	0.503032	+	0.871277i
$544$	5.68752e10	+	3.28369e10i	0.649423	+	0.374945i
$545$		−	4.94001e10i		−	0.559941i
$546$	2.33848e10	−	8.77959e9i	0.263126	−	0.0987878i
$547$	3.72423e9			0.0415994			0.0207997	−	0.999784i	$-0.493379\pi$
$547$	3.72423e9			0.0415994			0.0207997	+	0.999784i	$0.493379\pi$
$548$	7.50843e10	−	1.30050e11i	0.832582	−	1.44207i
$549$	−2.45308e10	+	1.41629e10i	−0.270037	+	0.155906i
$550$	−6.11087e9	−	1.05843e10i	−0.0667809	−	0.115668i
$551$	1.00188e11	+	5.78433e10i	1.08695	+	0.627548i
$552$			1.58562e11i			1.70782i
$553$	−1.98551e10	+	1.19652e11i	−0.212311	+	1.27943i
$554$	2.63299e11			2.79518
$555$	2.23206e10	−	3.86604e10i	0.235252	−	0.407469i
$556$	−3.40916e11	+	1.96828e11i	−3.56737	+	2.05962i
$557$	7.06165e10	+	1.22311e11i	0.733644	+	1.27071i	0.955316	+	0.295587i	$0.0955152\pi$
$557$	7.06165e10	+	1.22311e11i	0.733644	+	1.27071i	−0.221672	+	0.975121i	$0.571151\pi$
$558$	−4.03860e10	−	2.33169e10i	−0.416576	−	0.240510i
$559$			1.96517e10i			0.201258i
$560$	−3.31529e11	+	4.03296e11i	−3.37108	+	4.10083i
$561$	−5.75771e8			−0.00581297
$562$	−2.94088e10	+	5.09375e10i	−0.294803	+	0.510614i
$563$	−1.01877e11	+	5.88187e10i	−1.01401	+	0.585439i	−0.912364	−	0.409381i	$-0.865745\pi$
$563$	−1.01877e11	+	5.88187e10i	−1.01401	+	0.585439i	−0.101647	+	0.994820i	$0.532411\pi$
$564$	6.38129e10	+	1.10527e11i	0.630655	+	1.09233i
$565$	−1.61646e11	−	9.33266e10i	−1.58625	−	0.915823i
$566$		−	1.30067e11i		−	1.26737i
$567$	−8.87122e9	−	7.29257e9i	−0.0858324	−	0.0705584i
$568$	4.73383e11			4.54799
$569$	4.05750e10	−	7.02780e10i	0.387088	−	0.670456i	−0.604969	−	0.796249i	$-0.706814\pi$
$569$	4.05750e10	−	7.02780e10i	0.387088	−	0.670456i	0.992056	+	0.125794i	$0.0401477\pi$
$570$	−1.60624e11	+	9.27365e10i	−1.52164	+	0.878519i
$571$	−7.77546e10	−	1.34675e11i	−0.731445	−	1.26690i	−0.956266	−	0.292499i	$-0.905513\pi$
$571$	−7.77546e10	−	1.34675e11i	−0.731445	−	1.26690i	0.224821	−	0.974400i	$-0.427820\pi$
$572$	−2.55113e9	−	1.47289e9i	−0.0238313	−	0.0137590i
$573$		−	1.71471e10i		−	0.159064i
$574$	1.15238e11	+	1.91227e10i	1.06157	+	0.176158i
$575$	−1.79930e11			−1.64601
$576$	4.76019e10	−	8.24489e10i	0.432448	−	0.749022i
$577$	1.76201e11	−	1.01730e11i	1.58966	−	0.917793i	0.596303	−	0.802759i	$-0.296636\pi$
$577$	1.76201e11	−	1.01730e11i	1.58966	−	0.917793i	0.993362	−	0.115034i	$-0.0366977\pi$
$578$	−9.97423e10	−	1.72759e11i	−0.893652	−	1.54785i
$579$	−6.04391e10	−	3.48945e10i	−0.537779	−	0.310487i
$580$		−	6.28822e11i		−	5.55668i
$581$	3.93030e10	+	1.04685e11i	0.344922	+	0.918715i
$582$	−7.76384e10			−0.676682
$583$	−2.13322e9	+	3.69485e9i	−0.0184655	+	0.0319833i
$584$	2.13771e11	−	1.23420e11i	1.83779	−	1.06105i
$585$	−8.22571e9	−	1.42473e10i	−0.0702344	−	0.121650i
$586$	−1.02062e11	−	5.89254e10i	−0.865511	−	0.499703i
$587$			2.05657e10i			0.173217i	0.996242	+	0.0866086i	$0.0276030\pi$
$587$			2.05657e10i			0.173217i	−0.996242	+	0.0866086i	$0.972397\pi$
$588$	−1.77097e11	+	3.49258e10i	−1.48150	+	0.292171i
$589$	−8.88175e10			−0.737968
$590$	−1.77128e10	+	3.06794e10i	−0.146177	+	0.253186i
$591$	−6.49100e10	+	3.74758e10i	−0.532061	+	0.307186i
$592$	9.80641e10	+	1.69852e11i	0.798405	+	1.38288i
$593$	1.33725e10	+	7.72063e9i	0.108142	+	0.0624359i	0.553096	−	0.833118i	$-0.313446\pi$
$593$	1.33725e10	+	7.72063e9i	0.108142	+	0.0624359i	−0.444953	+	0.895554i	$0.646780\pi$
$594$			1.87214e9i			0.0150381i
$595$	−4.73178e10	+	1.77650e10i	−0.377534	+	0.141741i
$596$	1.60450e11			1.27161
$597$	−1.09876e10	+	1.90310e10i	−0.0864977	+	0.149818i
$598$	−5.19180e10	+	2.99748e10i	−0.405988	+	0.234397i
$599$	−7.92224e10	−	1.37217e11i	−0.615376	−	1.06586i	−0.990318	−	0.138815i	$-0.955671\pi$
$599$	−7.92224e10	−	1.37217e11i	−0.615376	−	1.06586i	0.374942	−	0.927048i	$-0.377663\pi$
$600$	3.40221e11	+	1.96426e11i	2.62516	+	1.51564i
$601$			2.05957e11i			1.57862i	0.613993	+	0.789311i	$0.289562\pi$
$601$			2.05957e11i			1.57862i	−0.613993	+	0.789311i	$0.710438\pi$
$602$	3.21366e10	−	1.93663e11i	0.244689	−	1.47455i
$603$	−7.53387e10			−0.569835
$604$	−2.97557e10	+	5.15383e10i	−0.223574	+	0.387242i
$605$	1.90653e11	−	1.10073e11i	1.42305	−	0.821601i
$606$	−2.01990e10	−	3.49857e10i	−0.149775	−	0.259418i
$607$	1.65918e11	+	9.57931e10i	1.22219	+	0.705634i	0.965385	−	0.260829i	$-0.0839957\pi$
$607$	1.65918e11	+	9.57931e10i	1.22219	+	0.705634i	0.256808	+	0.966462i	$0.417329\pi$
$608$		−	4.06706e11i		−	2.97623i
$609$	6.50941e10	−	7.91853e10i	0.473230	−	0.575672i
$610$	4.05359e11			2.92766
$611$	−1.49020e10	+	2.58111e10i	−0.106925	+	0.185200i
$612$	2.59495e10	−	1.49820e10i	0.184979	−	0.106798i
$613$	2.63817e10	+	4.56945e10i	0.186836	+	0.323610i	0.944194	−	0.329391i	$-0.106843\pi$
$613$	2.63817e10	+	4.56945e10i	0.186836	+	0.323610i	−0.757358	+	0.653000i	$0.773510\pi$
$614$	3.66401e10	+	2.11542e10i	0.257800	+	0.148841i
$615$		−	7.69362e10i		−	0.537812i
$616$	1.40407e10	+	1.15421e10i	0.0975136	+	0.0801609i
$617$	−1.32360e11			−0.913303			−0.456652	−	0.889646i	$-0.650951\pi$
$617$	−1.32360e11			−0.913303			−0.456652	+	0.889646i	$0.650951\pi$
$618$	2.94867e10	−	5.10725e10i	0.202150	−	0.350133i
$619$	1.86981e11	−	1.07954e11i	1.27361	−	0.735318i	0.297943	−	0.954584i	$-0.403700\pi$
$619$	1.86981e11	−	1.07954e11i	1.27361	−	0.735318i	0.975665	+	0.219266i	$0.0703662\pi$
$620$	2.41386e11	+	4.18094e11i	1.63360	+	2.82948i
$621$	2.38693e10	+	1.37809e10i	0.160499	+	0.0926643i
$622$			1.65157e11i			1.10340i
$623$	−1.89985e11	−	3.15263e10i	−1.26115	−	0.209277i
$624$	7.22782e10			0.476726
$625$	−1.61971e10	+	2.80543e10i	−0.106150	+	0.183856i
$626$	−2.47914e11	+	1.43133e11i	−1.61437	+	0.932059i
$627$	1.78282e9	+	3.08794e9i	0.0115355	+	0.0199801i
$628$	−5.04397e11	−	2.91214e11i	−3.24290	−	1.87229i
$629$			1.89875e10i			0.121301i
$630$	5.77636e10	+	1.53856e11i	0.366684	+	0.976678i
$631$	4.81022e10			0.303422			0.151711	−	0.988425i	$-0.451522\pi$
$631$	4.81022e10			0.303422			0.151711	+	0.988425i	$0.451522\pi$
$632$	−3.17785e11	+	5.50420e11i	−1.99189	+	3.45005i
$633$	−2.54377e10	+	1.46865e10i	−0.158439	+	0.0914749i
$634$	−3.73679e10	−	6.47231e10i	−0.231282	−	0.400592i
$635$	−3.83499e11	−	2.21413e11i	−2.35868	−	1.36178i
$636$		−	2.22032e11i		−	1.35702i
$637$	−2.77419e10	−	3.17381e10i	−0.168491	−	0.192763i
$638$	−1.67109e10			−0.100860
$639$	4.11428e10	−	7.12613e10i	0.246769	−	0.427416i
$640$	−4.47901e11	+	2.58596e11i	−2.66970	+	1.54135i
$641$	1.60247e10	+	2.77557e10i	0.0949203	+	0.164407i	0.909575	−	0.415539i	$-0.136407\pi$
$641$	1.60247e10	+	2.77557e10i	0.0949203	+	0.164407i	−0.814655	+	0.579946i	$0.803074\pi$
$642$	1.93993e11	+	1.12002e11i	1.14195	+	0.659303i
$643$			2.31892e11i			1.35657i	0.734799	+	0.678285i	$0.237277\pi$
$643$			2.31892e11i			1.35657i	−0.734799	+	0.678285i	$0.762723\pi$
$644$	4.05585e11	−	1.52273e11i	2.35797	−	0.885276i
$645$	−1.29295e11			−0.747037
$646$	3.94441e10	−	6.83193e10i	0.226492	−	0.392295i
$647$	−6.01769e10	+	3.47431e10i	−0.343410	+	0.198268i	−0.661779	−	0.749699i	$-0.730198\pi$
$647$	−6.01769e10	+	3.47431e10i	−0.343410	+	0.198268i	0.318369	+	0.947967i	$0.396865\pi$
$648$	−3.00889e10	−	5.21155e10i	−0.170650	−	0.295574i
$649$	5.89800e8	+	3.40521e8i	0.00332450	+	0.00191940i
$650$			1.48531e11i			0.832080i
$651$	−1.28831e10	+	7.76368e10i	−0.0717294	+	0.432258i
$652$	−5.30420e11			−2.93514
$653$	5.96669e10	−	1.03346e11i	0.328156	−	0.568383i	−0.653990	−	0.756503i	$-0.726906\pi$
$653$	5.96669e10	−	1.03346e11i	0.328156	−	0.568383i	0.982146	+	0.188120i	$0.0602395\pi$
$654$	5.91671e10	−	3.41601e10i	0.323422	−	0.186728i
$655$	−2.38524e11	−	4.13135e11i	−1.29589	−	2.24454i
$656$	2.92729e11	+	1.69007e11i	1.58070	+	0.912619i
$657$		−	4.29069e10i		−	0.230285i
$658$	1.89065e11	−	2.29992e11i	1.00857	−	1.22690i
$659$	−1.46887e11			−0.778827			−0.389413	−	0.921063i	$-0.627322\pi$
$659$	−1.46887e11			−0.778827			−0.389413	+	0.921063i	$0.627322\pi$
$660$	9.69062e9	−	1.67846e10i	0.0510712	−	0.0884579i
$661$	−2.50843e11	+	1.44824e11i	−1.31400	+	0.758639i	−0.982756	−	0.184906i	$-0.940802\pi$
$661$	−2.50843e11	+	1.44824e11i	−1.31400	+	0.758639i	−0.331245	+	0.943545i	$0.607469\pi$
$662$	−8.57439e10	−	1.48513e11i	−0.446449	−	0.773272i
$663$	6.05991e9	+	3.49869e9i	0.0313626	+	0.0181072i
$664$			5.85958e11i			3.01435i
$665$	2.41791e11	+	1.98764e11i	1.23638	+	1.01637i
$666$	6.17387e10			0.313805
$667$	−1.23010e11	+	2.13059e11i	−0.621493	+	1.07646i
$668$	4.38094e11	−	2.52934e11i	2.20020	−	1.27028i
$669$	−1.18720e10	−	2.05630e10i	−0.0592681	−	0.102655i
$670$	9.33699e11	+	5.39071e11i	4.63348	+	2.67514i
$671$		−	7.79285e9i		−	0.0384420i
$672$	−3.55508e11	−	5.89933e10i	−1.74330	−	0.289285i
$673$	3.22729e11			1.57318			0.786590	−	0.617476i	$-0.211845\pi$
$673$	3.22729e11			1.57318			0.786590	+	0.617476i	$0.211845\pi$
$674$	−1.67941e10	+	2.90883e10i	−0.0813801	+	0.140954i
$675$	5.91386e10	−	3.41437e10i	0.284876	−	0.164473i
$676$	−2.55189e11	−	4.42001e11i	−1.22201	−	2.11659i
$677$	1.60199e11	+	9.24908e10i	0.762614	+	0.440295i	0.830233	−	0.557416i	$-0.188207\pi$
$677$	1.60199e11	+	9.24908e10i	0.762614	+	0.440295i	−0.0676198	+	0.997711i	$0.521540\pi$
$678$		−	2.58141e11i		−	1.22162i
$679$	4.60520e10	+	1.22661e11i	0.216655	+	0.577070i
$680$	−2.64853e11			−1.23871
$681$	−1.04387e11	+	1.80804e11i	−0.485354	+	0.840658i
$682$	1.11108e10	−	6.41483e9i	0.0513580	−	0.0296516i
$683$	1.72207e11	+	2.98271e11i	0.791349	+	1.37066i	0.925132	+	0.379647i	$0.123954\pi$
$683$	1.72207e11	+	2.98271e11i	0.791349	+	1.37066i	−0.133782	+	0.991011i	$0.542712\pi$
$684$	−1.60700e11	−	9.27804e10i	−0.734163	−	0.423869i
$685$			2.30726e11i			1.04793i
$686$	2.21488e11	+	3.58138e11i	1.00012	+	1.61716i
$687$	−1.34669e10			−0.0604560
$688$	2.84024e11	−	4.91944e11i	1.26766	−	2.19564i
$689$	4.49037e10	−	2.59252e10i	0.199253	−	0.115039i
$690$	−1.97214e11	−	3.41584e11i	−0.870043	−	1.50696i
$691$	2.42776e11	+	1.40167e11i	1.06486	+	0.614798i	0.926773	−	0.375622i	$-0.122571\pi$
$691$	2.42776e11	+	1.40167e11i	1.06486	+	0.614798i	0.138088	+	0.990420i	$0.455904\pi$
$692$		−	5.97450e11i		−	2.60542i
$693$	2.95781e9	−	1.11048e9i	0.0128244	−	0.00481480i
$694$	−7.28592e11			−3.14084
$695$	3.02415e11	−	5.23799e11i	1.29618	−	2.24505i
$696$	4.65187e11	−	2.68576e11i	1.98240	−	1.14454i
$697$	1.63619e10	+	2.83396e10i	0.0693269	+	0.120078i
$698$	2.65093e11	+	1.53051e11i	1.11680	+	0.644786i
$699$			2.49667e11i			1.04581i
$700$	1.75712e11	−	1.05889e12i	0.731830	−	4.41018i
$701$	9.43259e10			0.390624			0.195312	−	0.980741i	$-0.437428\pi$
$701$	9.43259e10			0.390624			0.195312	+	0.980741i	$0.437428\pi$
$702$	1.13761e10	−	1.97040e10i	0.0468432	−	0.0811347i
$703$	1.01833e11	−	5.87930e10i	0.416932	−	0.240716i
$704$	1.30960e10	+	2.26830e10i	0.0533149	+	0.0923441i
$705$	−1.69819e11	−	9.80449e10i	−0.687431	−	0.396889i
$706$			2.42396e11i			0.975679i
$707$	−4.32929e10	+	5.26647e10i	−0.173276	+	0.210786i
$708$	−3.54424e10			−0.141055
$709$	1.53739e11	−	2.66284e11i	0.608414	−	1.05380i	−0.383087	−	0.923712i	$-0.625139\pi$
$709$	1.53739e11	−	2.66284e11i	0.608414	−	1.05380i	0.991502	−	0.130093i	$-0.0415275\pi$
$710$	−1.01979e12	+	5.88778e11i	−4.01309	+	2.31696i
$711$	5.52388e10	+	9.56763e10i	0.216155	+	0.374392i
$712$	−8.73968e11	−	5.04586e11i	−3.40076	−	1.96343i
$713$		−	1.88880e11i		−	0.730848i
$714$	−5.39975e10	−	4.43885e10i	−0.207769	−	0.170796i
$715$	4.52604e9			0.0173179
$716$	−4.71793e11	+	8.17170e11i	−1.79515	+	3.10928i
$717$	−1.23403e11	+	7.12470e10i	−0.466929	+	0.269582i
$718$	8.61586e10	+	1.49231e11i	0.324191	+	0.561515i
$719$	−3.40028e11	−	1.96315e11i	−1.27233	−	0.734579i	−0.296903	−	0.954908i	$-0.595954\pi$
$719$	−3.40028e11	−	1.96315e11i	−1.27233	−	0.734579i	−0.975426	+	0.220329i	$0.929287\pi$
$720$			4.75540e11i			1.76953i
$721$	−9.81802e10	−	1.62921e10i	−0.363315	−	0.0602888i
$722$	2.81505e10			0.103595
$723$	−5.87718e10	+	1.01796e11i	−0.215088	+	0.372543i
$724$	1.08447e12	−	6.26122e11i	3.94698	−	2.27879i
$725$	3.04769e11	+	5.27876e11i	1.10311	+	1.91064i
$726$	2.63672e11	+	1.52231e11i	0.949113	+	0.547971i
$727$			3.27509e10i			0.117243i	0.998280	+	0.0586214i	$0.0186705\pi$
$727$			3.27509e10i			0.117243i	−0.998280	+	0.0586214i	$0.981330\pi$
$728$	−7.76401e10	−	2.06798e11i	−0.276414	−	0.736242i
$729$	−1.04604e10			−0.0370370
$730$	−3.07012e11	+	5.31761e11i	−1.08110	+	1.87251i
$731$	4.76259e10	−	2.74968e10i	0.166792	−	0.0962971i
$732$	2.02775e11	+	3.51217e11i	0.706270	+	1.22330i
$733$	−2.32722e11	−	1.34362e11i	−0.806160	−	0.465436i	0.0394608	−	0.999221i	$-0.487436\pi$
$733$	−2.32722e11	−	1.34362e11i	−0.806160	−	0.465436i	−0.845620	+	0.533785i	$0.820769\pi$
$734$		−	9.01085e10i		−	0.310443i
$735$	2.08815e11	−	1.82522e11i	0.715503	−	0.625412i
$736$	8.64902e11			2.94751
$737$	1.03634e10	−	1.79500e10i	0.0351264	−	0.0608407i
$738$	9.21473e10	−	5.32012e10i	0.310640	−	0.179348i
$739$	−4.78306e10	−	8.28450e10i	−0.160372	−	0.277772i	0.774630	−	0.632414i	$-0.217936\pi$
$739$	−4.78306e10	−	8.28450e10i	−0.160372	−	0.277772i	−0.935002	+	0.354642i	$0.884603\pi$
$740$	−5.53516e11	−	3.19573e11i	−1.84588	−	1.06572i
$741$		−	4.33334e10i		−	0.143731i
$742$	−4.84911e11	+	1.82055e11i	−1.59973	+	0.600602i
$743$	−5.80345e10			−0.190428			−0.0952140	−	0.995457i	$-0.530354\pi$
$743$	−5.80345e10			−0.190428			−0.0952140	+	0.995457i	$0.530354\pi$
$744$	−2.06197e11	+	3.57144e11i	−0.672962	+	1.16560i
$745$	−2.13495e11	+	1.23261e11i	−0.693047	+	0.400131i
$746$	−3.04347e11	−	5.27145e11i	−0.982685	−	1.70206i
$747$	8.82078e10	+	5.09268e10i	0.283286	+	0.163555i
$748$			8.24354e9i			0.0263334i
$749$	6.18836e10	−	3.72926e11i	0.196629	−	1.18494i
$750$	−4.05503e11			−1.28159
$751$	1.36549e11	−	2.36509e11i	0.429267	−	0.743513i	−0.567541	−	0.823345i	$-0.692105\pi$
$751$	1.36549e11	−	2.36509e11i	0.429267	−	0.743513i	0.996808	+	0.0798321i	$0.0254384\pi$
$752$	7.46088e11	−	4.30754e11i	2.33302	−	1.34697i
$753$	1.32004e10	+	2.28638e10i	0.0410590	+	0.0711162i
$754$	1.75880e11	+	1.01544e11i	0.544165	+	0.314174i
$755$		−	9.14359e10i		−	0.281403i
$756$	−1.04411e11	+	1.27013e11i	−0.319637	+	0.388830i
$757$	2.27585e11			0.693042			0.346521	−	0.938042i	$-0.387363\pi$
$757$	2.27585e11			0.693042			0.346521	+	0.938042i	$0.387363\pi$
$758$	−6.08255e10	+	1.05353e11i	−0.184251	+	0.319132i
$759$	−6.56681e9	+	3.79135e9i	−0.0197873	+	0.0114242i
$760$	8.20092e11	+	1.42044e12i	2.45815	+	4.25764i
$761$	1.07837e11	+	6.22595e10i	0.321535	+	0.185638i	0.652076	−	0.758153i	$-0.273898\pi$
$761$	1.07837e11	+	6.22595e10i	0.321535	+	0.185638i	−0.330542	+	0.943791i	$0.607231\pi$
$762$		−	6.12427e11i		−	1.81650i
$763$	−8.90654e10	−	7.32161e10i	−0.262791	−	0.216027i
$764$	−2.45502e11			−0.720579
$765$	−2.30189e10	+	3.98700e10i	−0.0672109	+	0.116413i
$766$	2.41910e11	−	1.39667e11i	0.702650	−	0.405675i
$767$	−4.13837e9	−	7.16787e9i	−0.0119577	−	0.0207114i
$768$	−1.68109e11	−	9.70578e10i	−0.483222	−	0.278988i
$769$		−	6.29709e11i		−	1.80067i	−0.435197	−	0.900335i	$-0.643321\pi$
$769$		−	6.29709e11i		−	1.80067i	0.435197	−	0.900335i	$-0.356679\pi$
$770$	−4.46030e10	−	7.40147e9i	−0.126882	−	0.0210550i
$771$	3.17862e11			0.899540
$772$	−4.99598e11	+	8.65330e11i	−1.40654	+	2.43620i
$773$	−3.84983e11	+	2.22270e11i	−1.07826	+	0.622533i	−0.930426	−	0.366479i	$-0.880563\pi$
$773$	−3.84983e11	+	2.22270e11i	−1.07826	+	0.622533i	−0.147833	+	0.989012i	$0.547230\pi$
$774$	−8.94071e10	−	1.54858e11i	−0.249120	−	0.431488i
$775$	−4.05273e11	−	2.33984e11i	−1.12342	−	0.648604i
$776$			6.86576e11i			1.89340i
$777$	−3.66209e10	−	9.75414e10i	−0.100472	−	0.267611i
$778$	−3.05864e11			−0.834854
$779$	1.01326e11	−	1.75502e11i	0.275151	−	0.476575i
$780$	−2.03985e11	+	1.17771e11i	−0.551086	+	0.318170i
$781$	1.13190e10	+	1.96051e10i	0.0304232	+	0.0526945i
$782$	1.45288e11	+	8.38820e10i	0.388510	+	0.224307i
$783$		−	9.33700e10i		−	0.248405i
$784$	2.35758e11	+	1.19545e12i	0.624026	+	3.16423i
$785$	8.94867e11			2.35657
$786$	3.29878e11	−	5.71365e11i	0.864297	−	1.49701i
$787$	−5.29049e11	+	3.05447e11i	−1.37910	+	0.796226i	−0.992052	−	0.125832i	$-0.959840\pi$
$787$	−5.29049e11	+	3.05447e11i	−1.37910	+	0.796226i	−0.387052	+	0.922058i	$0.626507\pi$
$788$	5.36556e11	+	9.29342e11i	1.39159	+	2.41030i
$789$	5.89078e10	+	3.40104e10i	0.152007	+	0.0877616i
$790$		−	1.58100e12i		−	4.05904i
$791$	−4.07838e11	+	1.53119e11i	−1.04179	+	0.391131i
$792$	1.65558e10			0.0420775
$793$	−4.73535e10	+	8.20187e10i	−0.119746	+	0.207405i
$794$	2.05047e11	−	1.18384e11i	0.515907	−	0.297859i
$795$	1.70570e11	+	2.95435e11i	0.427005	+	0.739595i
$796$	2.72475e11	+	1.57313e11i	0.678694	+	0.391844i
$797$		−	1.06199e11i		−	0.263201i	−0.991303	−	0.131601i	$-0.957988\pi$
$797$		−	1.06199e11i		−	0.263201i	0.991303	−	0.131601i	$-0.0420117\pi$
$798$	−7.08635e10	+	4.27040e11i	−0.174748	+	1.05307i
$799$	8.34041e10			0.204645
$800$	1.07144e12	−	1.85579e12i	2.61582	−	4.53074i
$801$	−1.51917e11	+	8.77092e10i	−0.369042	+	0.213066i
$802$	−1.03979e11	−	1.80097e11i	−0.251332	−	0.435320i
$803$	1.02229e10	+	5.90218e9i	0.0245873	+	0.0141955i
$804$			1.07865e12i			2.58141i
$805$	−4.22692e11	+	5.14193e11i	−1.00656	+	1.22446i
$806$	−1.55920e11			−0.369454
$807$	2.32370e11	−	4.02477e11i	0.547881	−	0.948957i
$808$	−3.09388e11	+	1.78625e11i	−0.725867	+	0.419080i
$809$	−6.13479e10	−	1.06258e11i	−0.143221	−	0.248066i	0.785487	−	0.618878i	$-0.212413\pi$
$809$	−6.13479e10	−	1.06258e11i	−0.143221	−	0.248066i	−0.928708	+	0.370813i	$0.879079\pi$
$810$	1.29639e11	+	7.48470e10i	0.301158	+	0.173874i
$811$			6.52192e11i			1.50762i	0.657092	+	0.753810i	$0.271786\pi$
$811$			6.52192e11i			1.50762i	−0.657092	+	0.753810i	$0.728214\pi$
$812$	−1.13373e12	−	9.31978e11i	−2.60786	−	2.14379i
$813$	−1.11089e11			−0.254279
$814$	−8.49263e9	+	1.47097e10i	−0.0193439	+	0.0335047i
$815$	7.05777e11	−	4.07480e11i	1.59969	−	0.923584i
$816$	−1.01132e11	−	1.75166e11i	−0.228102	−	0.395084i
$817$	−2.94938e11	−	1.70283e11i	−0.661977	−	0.382193i
$818$			1.56742e12i			3.50084i
$819$	−3.78784e10	−	6.28558e9i	−0.0841892	−	0.0139704i
$820$	−1.10153e12			−2.43635
$821$	−6.43359e9	+	1.11433e10i	−0.0141606	+	0.0245268i	−0.873019	−	0.487686i	$-0.837841\pi$
$821$	−6.43359e9	+	1.11433e10i	−0.0141606	+	0.0245268i	0.858858	+	0.512213i	$0.171174\pi$
$822$	−2.76343e11	+	1.59546e11i	−0.605286	+	0.349462i
$823$	−3.00730e11	−	5.20880e11i	−0.655508	−	1.13537i	−0.981766	−	0.190092i	$-0.939121\pi$
$823$	−3.00730e11	−	5.20880e11i	−0.655508	−	1.13537i	0.326258	−	0.945281i	$-0.394212\pi$
$824$	−4.51647e11	−	2.60759e11i	−0.979694	−	0.565627i
$825$			1.87869e10i			0.0405545i
$826$	2.90610e10	+	7.74051e10i	0.0624295	+	0.166284i
$827$	−4.78355e11			−1.02265			−0.511327	−	0.859386i	$-0.670846\pi$
$827$	−4.78355e11			−1.02265			−0.511327	+	0.859386i	$0.670846\pi$
$828$	1.97307e11	−	3.41746e11i	0.419780	−	0.727080i
$829$	5.38653e11	−	3.10991e11i	1.14049	−	0.658461i	0.193937	−	0.981014i	$-0.437874\pi$
$829$	5.38653e11	−	3.10991e11i	1.14049	−	0.658461i	0.946551	+	0.322553i	$0.104541\pi$
$830$	−7.28794e11	−	1.26231e12i	−1.53565	−	2.65982i
$831$	−3.50511e11	−	2.02368e11i	−0.735017	−	0.424363i
$832$		−	3.18313e11i		−	0.664296i
$833$	−3.81006e10	+	1.11641e11i	−0.0791320	+	0.231869i
$834$	8.36479e11			1.72898
$835$	−3.88619e11	+	6.73107e11i	−0.799425	+	1.38464i
$836$	4.42112e10	−	2.55253e10i	0.0905122	−	0.0522572i
$837$	3.58420e10	+	6.20802e10i	0.0730282	+	0.126489i
$838$	3.13745e11	+	1.81141e11i	0.636210	+	0.367316i
$839$		−	5.90368e11i		−	1.19145i	−0.803189	−	0.595724i	$-0.796865\pi$
$839$		−	5.90368e11i		−	1.19145i	0.803189	−	0.595724i	$-0.203135\pi$
$840$	1.36059e12	−	5.10818e11i	2.73280	−	1.02600i
$841$	3.33182e11			0.666036
$842$	−1.97342e11	+	3.41806e11i	−0.392619	+	0.680036i
$843$	7.82997e10	−	4.52064e10i	0.155042	−	0.0895137i
$844$	2.10272e11	+	3.64201e11i	0.414392	+	0.717748i
$845$	6.79110e11	+	3.92084e11i	1.33203	+	0.769046i
$846$		−	2.71192e11i		−	0.529413i
$847$	8.41113e10	−	5.06875e11i	0.163426	−	0.984844i
$848$	−1.49877e12			−2.89836
$849$	−9.99678e10	+	1.73149e11i	−0.192411	+	0.333265i
$850$	3.59966e11	−	2.07826e11i	0.689581	−	0.398130i
$851$	1.25029e11	+	2.16557e11i	0.238393	+	0.412909i
$852$	−1.02028e12	−	5.89057e11i	−1.93624	−	1.11789i
$853$			5.81608e11i			1.09859i	0.835630	+	0.549293i	$0.185103\pi$
$853$			5.81608e11i			1.09859i	−0.835630	+	0.549293i	$0.814897\pi$
$854$	6.00783e11	−	7.30837e11i	1.12950	−	1.37401i
$855$	2.85104e11			0.533505
$856$	9.90460e11	−	1.71553e12i	1.84477	−	3.19523i
$857$	6.13387e11	−	3.54139e11i	1.13713	−	0.656524i	0.191414	−	0.981509i	$-0.438693\pi$
$857$	6.13387e11	−	3.54139e11i	1.13713	−	0.656524i	0.945719	+	0.324985i	$0.105359\pi$
$858$	3.12975e9	+	5.42089e9i	0.00577511	+	0.0100028i
$859$	4.02486e11	+	2.32376e11i	0.739228	+	0.426794i	0.821789	−	0.569792i	$-0.192976\pi$
$859$	4.02486e11	+	2.32376e11i	0.739228	+	0.426794i	−0.0825604	+	0.996586i	$0.526310\pi$
$860$			1.85116e12i			3.38416i
$861$	−1.38711e11	−	1.14027e11i	−0.252405	−	0.207490i
$862$	4.85891e11			0.880055
$863$	−1.50445e11	+	2.60578e11i	−0.271227	+	0.469779i	−0.969176	−	0.246368i	$-0.920763\pi$
$863$	−1.50445e11	+	2.60578e11i	−0.271227	+	0.469779i	0.697949	+	0.716147i	$0.254096\pi$
$864$	−2.84273e11	+	1.64125e11i	−0.510129	+	0.294523i
$865$	4.58974e11	+	7.94966e11i	0.819830	+	1.41999i
$866$	2.40164e11	+	1.38659e11i	0.427009	+	0.246534i
$867$			3.06642e11i			0.542695i
$868$	1.11156e12	+	1.84453e11i	1.95818	+	0.324942i
$869$	−3.03941e10			−0.0532979
$870$	−6.68091e11	+	1.15717e12i	−1.16616	+	2.01985i
$871$	−2.18147e11	+	1.25947e11i	−0.379033	+	0.218835i
$872$	−3.02087e11	−	5.23230e11i	−0.522475	−	0.904954i
$873$	1.03355e11	+	5.96718e10i	0.177940	+	0.102733i
$874$		−	1.03893e12i		−	1.78050i
$875$	2.40528e11	+	6.40657e11i	0.410331	+	1.09293i
$876$	−6.14315e11			−1.04322
$877$	4.54432e11	−	7.87099e11i	0.768193	−	1.33055i	−0.170350	−	0.985384i	$-0.554490\pi$
$877$	4.54432e11	−	7.87099e11i	0.768193	−	1.33055i	0.938542	−	0.345165i	$-0.112177\pi$
$878$	−5.70007e11	+	3.29094e11i	−0.959184	+	0.553785i
$879$	9.05784e10	+	1.56886e11i	0.151729	+	0.262803i
$880$	−1.13301e11	−	6.54143e10i	−0.188931	−	0.109079i
$881$		−	2.51454e11i		−	0.417402i	−0.977979	−	0.208701i	$-0.933076\pi$
$881$		−	2.51454e11i		−	0.417402i	0.977979	−	0.208701i	$-0.0669236\pi$
$882$	3.63004e11	+	1.23886e11i	0.599842	+	0.204714i
$883$	−4.92813e11			−0.810661			−0.405330	−	0.914170i	$-0.632843\pi$
$883$	−4.92813e11			−0.810661			−0.405330	+	0.914170i	$0.632843\pi$
$884$	5.00921e10	−	8.67621e10i	0.0820277	−	0.142076i
$885$	4.71596e10	−	2.72276e10i	0.0768771	−	0.0443850i
$886$	−3.32778e11	−	5.76389e11i	−0.540033	−	0.935364i
$887$	−1.90407e10	−	1.09932e10i	−0.0307602	−	0.0177594i	0.484541	−	0.874769i	$-0.338987\pi$
$887$	−1.90407e10	−	1.09932e10i	−0.0307602	−	0.0177594i	−0.515301	+	0.857009i	$0.672320\pi$
$888$		−	5.45971e11i		−	0.878047i
$889$	−9.67578e11	+	3.63267e11i	−1.54910	+	0.581593i
$890$	2.51034e12			4.00104
$891$	1.43890e9	−	2.49225e9i	0.00228308	−	0.00395441i
$892$	−2.94408e11	+	1.69977e11i	−0.465040	+	0.268491i
$893$	−2.58253e11	−	4.47307e11i	−0.406106	−	0.703396i
$894$	−2.95263e11	−	1.70470e11i	−0.462231	−	0.266869i
$895$		−	1.44977e12i		−	2.25947i
$896$	−1.97603e11	+	1.19080e12i	−0.306592	+	1.84760i
$897$	9.21530e10			0.142344
$898$	−9.69470e10	+	1.67917e11i	−0.149083	+	0.258220i
$899$	−5.54133e11	+	3.19929e11i	−0.848351	+	0.489796i
$900$	−4.88848e11	−	8.46710e11i	−0.745082	−	1.29052i
$901$	−1.25659e11	−	7.25494e10i	−0.190676	−	0.110087i
$902$			2.92730e10i			0.0442222i
$903$	−1.91628e11	+	2.33110e11i	−0.288209	+	0.350599i
$904$	−2.28280e12			−3.41818
$905$	−9.62001e11	+	1.66623e12i	−1.43411	+	2.48394i
$906$	1.09514e11	−	6.32278e10i	0.162538	−	0.0938415i
$907$	5.94037e11	+	1.02890e12i	0.877777	+	1.52035i	0.853775	+	0.520643i	$0.174308\pi$
$907$	5.94037e11	+	1.02890e12i	0.877777	+	1.52035i	0.0240025	+	0.999712i	$0.492359\pi$
$908$	2.58864e12	+	1.49455e12i	3.80827	+	2.19871i
$909$			6.20987e10i			0.0909551i
$910$	4.24465e11	+	3.48931e11i	0.618980	+	0.508832i
$911$	2.55559e10			0.0371037			0.0185519	−	0.999828i	$-0.494094\pi$
$911$	2.55559e10			0.0371037			0.0185519	+	0.999828i	$0.494094\pi$
$912$	−6.26292e11	+	1.08477e12i	−0.905311	+	1.56804i
$913$	−2.42673e10	+	1.40108e10i	−0.0349252	+	0.0201641i
$914$	−7.73420e11	−	1.33960e12i	−1.10823	−	1.91951i
$915$	−5.39626e11	−	3.11553e11i	−0.769854	−	0.444475i
$916$			1.92810e11i			0.273872i
$917$	−1.09837e12	−	1.82265e11i	−1.55336	−	0.257767i
$918$	−6.36702e10			−0.0896532
$919$	1.22858e11	−	2.12796e11i	0.172243	−	0.298333i	−0.766961	−	0.641694i	$-0.778232\pi$
$919$	1.22858e11	−	2.12796e11i	0.172243	−	0.298333i	0.939204	+	0.343361i	$0.111565\pi$
$920$	−3.02071e12	+	1.74401e12i	−4.21656	+	2.43443i
$921$	−3.25176e10	−	5.63222e10i	−0.0451940	−	0.0782782i
$922$	1.52974e12	+	8.83195e11i	2.11687	+	1.22217i
$923$		−	2.75121e11i		−	0.379068i
$924$	−1.58992e10	−	4.23482e10i	−0.0218116	−	0.0580960i
$925$	6.19546e11			0.846266
$926$	1.41513e11	−	2.45108e11i	0.192465	−	0.333360i
$927$	−7.85073e10	+	4.53262e10i	−0.106314	+	0.0613805i
$928$	−1.46499e12	−	2.53744e12i	−1.97535	−	3.42140i
$929$	−3.29055e11	−	1.89980e11i	−0.441779	−	0.255061i	0.262573	−	0.964912i	$-0.415429\pi$
$929$	−3.29055e11	−	1.89980e11i	−0.441779	−	0.255061i	−0.704352	+	0.709851i	$0.748762\pi$
$930$		−	1.02584e12i		−	1.37135i
$931$	7.16718e11	−	1.41346e11i	0.954002	−	0.188141i
$932$	3.57458e12			4.73763
$933$	1.26937e11	−	2.19862e11i	0.167518	−	0.290150i
$934$	−9.51529e11	+	5.49365e11i	−1.25036	+	0.721894i
$935$	−6.33287e9	−	1.09688e10i	−0.00828617	−	0.0143521i
$936$	−1.74248e11	−	1.00602e11i	−0.227020	−	0.131070i
$937$		−	6.12774e11i		−	0.794954i	−0.917612	−	0.397477i	$-0.869886\pi$
$937$		−	6.12774e11i		−	0.794954i	0.917612	−	0.397477i	$-0.130114\pi$
$938$	2.35575e12	−	8.84442e11i	3.04311	−	1.14251i
$939$	4.40041e11			0.566019
$940$	−1.40375e12	+	2.43136e12i	−1.79795	+	3.11414i
$941$	−4.08180e11	+	2.35663e11i	−0.520587	+	0.300561i	−0.737175	−	0.675702i	$-0.763841\pi$
$941$	−4.08180e11	+	2.35663e11i	−0.520587	+	0.300561i	0.216588	+	0.976263i	$0.430507\pi$
$942$	6.18799e11	+	1.07179e12i	0.785862	+	1.36115i
$943$	3.73222e11	+	2.15480e11i	0.471977	+	0.272496i
$944$			2.39245e11i			0.301270i
$945$	4.13547e10	−	2.49214e11i	0.0518559	−	0.312496i
$946$	4.91946e10			0.0614260
$947$	−2.41447e11	+	4.18199e11i	−0.300208	+	0.519976i	−0.976183	−	0.216949i	$-0.930390\pi$
$947$	−2.41447e11	+	4.18199e11i	−0.300208	+	0.519976i	0.675975	+	0.736925i	$0.263723\pi$
$948$	1.36984e12	−	7.90875e11i	1.69604	−	0.979207i
$949$	−7.17296e10	−	1.24239e11i	−0.0884369	−	0.153177i
$950$	−2.22920e12	−	1.28703e12i	−2.73687	−	1.58013i
$951$			1.14882e11i			0.140452i
$952$	−3.92539e11	+	4.77514e11i	−0.477898	+	0.581350i
$953$	−1.49762e12			−1.81564			−0.907822	−	0.419357i	$-0.862256\pi$
$953$	−1.49762e12			−1.81564			−0.907822	+	0.419357i	$0.862256\pi$
$954$	−2.35897e11	+	4.08586e11i	−0.284793	+	0.493276i
$955$	3.26665e11	−	1.88600e11i	0.392725	−	0.226740i
$956$	1.02007e12	+	1.76682e12i	1.22123	+	2.11524i
$957$	2.22461e10	+	1.28438e10i	0.0265219	+	0.0153125i
$958$			1.90371e11i			0.226016i
$959$	4.15984e11	+	3.41959e11i	0.491816	+	0.404296i
$960$	2.09428e12			2.46575
$961$	−1.80823e11	+	3.13194e11i	−0.212011	+	0.367214i
$962$	1.78767e11	−	1.03211e11i	0.208732	−	0.120511i
$963$	−1.72166e11	−	2.98200e11i	−0.200190	−	0.346739i
$964$	1.45745e12	+	8.41459e11i	1.68766	+	0.974372i
$965$		−	1.53521e12i		−	1.77035i
$966$	−9.08145e11	−	1.50699e11i	−1.04291	−	0.173062i
$967$	1.00153e12			1.14540			0.572700	−	0.819765i	$-0.305896\pi$
$967$	1.00153e12			1.14540			0.572700	+	0.819765i	$0.305896\pi$
$968$	1.34622e12	−	2.33172e12i	1.53326	−	2.65568i
$969$	−1.05018e11	+	6.06325e10i	−0.119116	+	0.0687717i
$970$	−8.53939e11	−	1.47907e12i	−0.964584	−	1.67071i
$971$	−6.06577e10	−	3.50207e10i	−0.0682352	−	0.0393956i	0.465494	−	0.885051i	$-0.345877\pi$
$971$	−6.06577e10	−	3.50207e10i	−0.0682352	−	0.0393956i	−0.533729	+	0.845655i	$0.679210\pi$
$972$			1.49765e11i			0.167782i
$973$	−4.96166e11	−	1.32156e12i	−0.553574	−	1.47447i
$974$	−3.13463e11			−0.348298
$975$	1.14159e11	−	1.97730e11i	0.126326	−	0.218803i
$976$	2.37081e12	−	1.36879e12i	2.61275	−	1.50847i
$977$	−3.08389e11	−	5.34146e11i	−0.338471	−	0.586248i	0.645675	−	0.763613i	$-0.276576\pi$
$977$	−3.08389e11	−	5.34146e11i	−0.338471	−	0.586248i	−0.984145	+	0.177364i	$0.943243\pi$
$978$	9.76087e11	+	5.63544e11i	1.06692	+	0.615988i
$979$		−	4.82603e10i		−	0.0525363i
$980$	−2.61324e12	−	2.98968e12i	−2.83319	−	3.24131i
$981$	−1.05020e11			−0.113396
$982$	3.11709e11	−	5.39896e11i	0.335200	−	0.580583i
$983$	−2.73200e11	+	1.57732e11i	−0.292595	+	0.168930i	−0.639111	−	0.769114i	$-0.720698\pi$
$983$	−2.73200e11	+	1.57732e11i	−0.292595	+	0.168930i	0.346517	+	0.938044i	$0.387364\pi$
$984$	−4.70472e11	−	8.14882e11i	−0.501827	−	0.869189i
$985$	−1.42788e12	−	8.24388e11i	−1.51687	−	0.875763i
$986$		−	5.68326e11i		−	0.601298i
$987$	−4.28458e11	+	1.60860e11i	−0.451481	+	0.169504i
$988$	−6.20422e11			−0.651117
$989$	3.62124e11	−	6.27217e11i	0.378505	−	0.655590i
$990$	−3.56657e10	+	2.05916e10i	−0.0371287	+	0.0214362i
$991$	8.08096e11	+	1.39966e12i	0.837854	+	1.45121i	0.891686	+	0.452655i	$0.149523\pi$
$991$	8.08096e11	+	1.39966e12i	0.837854	+	1.45121i	−0.0538320	+	0.998550i	$0.517144\pi$
$992$	1.94810e12	+	1.12474e12i	2.01171	+	1.16146i
$993$			2.63606e11i			0.271118i
$994$	−4.49908e11	+	2.71125e12i	−0.460870	+	2.77731i
$995$	−4.83406e11			−0.493197
$996$	7.29139e11	−	1.26291e12i	0.740923	−	1.28332i
$997$	−1.27154e11	+	7.34121e10i	−0.128691	+	0.0742997i	−0.562963	−	0.826482i	$-0.690339\pi$
$997$	−1.27154e11	+	7.34121e10i	−0.128691	+	0.0742997i	0.434273	+	0.900782i	$0.357005\pi$
$998$	8.59987e11	+	1.48954e12i	0.866902	+	1.50152i
$999$	−8.21884e10	−	4.74515e10i	−0.0825179	−	0.0476418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.9.f.b.19.1	yes	12
3.2	odd	2		63.9.m.d.19.6		12
7.2	even	3		147.9.d.b.97.12		12
7.3	odd	6	inner	21.9.f.b.10.1	✓	12
7.5	odd	6		147.9.d.b.97.11		12
21.17	even	6		63.9.m.d.10.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.9.f.b.10.1	✓	12	7.3	odd	6	inner
21.9.f.b.19.1	yes	12	1.1	even	1	trivial
63.9.m.d.10.6		12	21.17	even	6
63.9.m.d.19.6		12	3.2	odd	2
147.9.d.b.97.11		12	7.5	odd	6
147.9.d.b.97.12		12	7.2	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.2115 + 26.3471i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-334.779 - 579.854i) q^{4} +(890.914 + 514.369i) q^{5} +1422.74i q^{6} +(2247.80 - 843.914i) q^{7} +12581.7 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\)	\(q+(-15.2115 + 26.3471i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-334.779 - 579.854i) q^{4} +(890.914 + 514.369i) q^{5} +1422.74i q^{6} +(2247.80 - 843.914i) q^{7} +12581.7 q^{8} +(1093.50 - 1894.00i) q^{9} +(-27104.3 + 15648.6i) q^{10} +(300.839 + 521.068i) q^{11} +(-27117.1 - 15656.1i) q^{12} -7312.22i q^{13} +(-11957.7 + 72060.2i) q^{14} +48109.3 q^{15} +(-105683. + 183048. i) q^{16} +(-17721.2 + 10231.3i) q^{17} +(33267.5 + 57621.1i) q^{18} +(109744. + 63360.6i) q^{19} -688800. i q^{20} +(71303.0 - 86738.2i) q^{21} -18304.8 q^{22} +(-134743. + 233381. i) q^{23} +(509558. - 294193. i) q^{24} +(333839. + 578226. i) q^{25} +(192656. + 111230. i) q^{26} -102276. i q^{27} +(-1.24186e6 - 1.02087e6i) q^{28} +912923. q^{29} +(-731815. + 1.26754e6i) q^{30} +(-606988. + 350445. i) q^{31} +(-1.60473e6 - 2.77947e6i) q^{32} +(24367.9 + 14068.8i) q^{33} -622534. i q^{34} +(2.43668e6 + 404345. i) q^{35} -1.46432e6 q^{36} +(463956. - 803595. i) q^{37} +(-3.33873e6 + 1.92762e6i) q^{38} +(-170979. - 296145. i) q^{39} +(1.12092e7 + 6.47163e6i) q^{40} -1.59919e6i q^{41} +(1.20067e6 + 3.19804e6i) q^{42} -2.68752e6 q^{43} +(201429. - 348885. i) q^{44} +(1.94843e6 - 1.12493e6i) q^{45} +(-4.09928e6 - 7.10016e6i) q^{46} +(-3.52985e6 - 2.03796e6i) q^{47} +9.88457e6i q^{48} +(4.34042e6 - 3.79390e6i) q^{49} -2.03128e7 q^{50} +(-478471. + 828737. i) q^{51} +(-4.24003e6 + 2.44798e6i) q^{52} +(3.54546e6 + 6.14091e6i) q^{53} +(2.69467e6 + 1.55577e6i) q^{54} +618969. i q^{55} +(2.82811e7 - 1.06179e7i) q^{56} +5.92616e6 q^{57} +(-1.38869e7 + 2.40529e7i) q^{58} +(980259. - 565953. i) q^{59} +(-1.61060e7 - 2.78964e7i) q^{60} +(-1.12167e7 - 6.47594e6i) q^{61} -2.13232e7i q^{62} +(859599. - 5.18015e6i) q^{63} +4.35317e7 q^{64} +(3.76118e6 - 6.51456e6i) q^{65} +(-741346. + 428016. i) q^{66} +(-1.72242e7 - 2.98332e7i) q^{67} +(1.18653e7 + 6.85046e6i) q^{68} +1.26026e7i q^{69} +(-4.77189e7 + 5.80487e7i) q^{70} +3.76248e7 q^{71} +(1.37581e7 - 2.38297e7i) q^{72} +(1.69906e7 - 9.80954e6i) q^{73} +(1.41149e7 + 2.44478e7i) q^{74} +(2.70410e7 + 1.56121e7i) q^{75} -8.48472e7i q^{76} +(1.11596e6 + 917375. i) q^{77} +1.04034e7 q^{78} +(-2.52578e7 + 4.37477e7i) q^{79} +(-1.88308e8 + 1.08720e8i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(4.21341e7 + 2.43261e7i) q^{82} +4.65723e7i q^{83} +(-7.41662e7 - 1.23072e7i) q^{84} -2.10507e7 q^{85} +(4.08812e7 - 7.08082e7i) q^{86} +(3.69734e7 - 2.13466e7i) q^{87} +(3.78506e6 + 6.55591e6i) q^{88} +(-6.94636e7 - 4.01048e7i) q^{89} +6.84472e7i q^{90} +(-6.17089e6 - 1.64364e7i) q^{91} +1.80436e8 q^{92} +(-1.63887e7 + 2.83860e7i) q^{93} +(1.07389e8 - 6.20008e7i) q^{94} +(6.51815e7 + 1.12898e8i) q^{95} +(-1.29983e8 - 7.50456e7i) q^{96} +5.45695e7i q^{97} +(3.39340e7 + 1.72068e8i) q^{98} +1.31587e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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