LMFDB - Embedded newform 81.10.e.a.64.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not 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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			64.26
Character	$\chi$	$=$	81.64
Dual form			81.10.e.a.19.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(40.0613 + 14.5811i) q^{2} +(1000.08 + 839.170i) q^{4} +(306.059 - 1735.74i) q^{5} +(764.835 - 641.773i) q^{7} +(16914.7 + 29297.2i) q^{8} +O(q^{10})$	\(q+(40.0613 + 14.5811i) q^{2} +(1000.08 + 839.170i) q^{4} +(306.059 - 1735.74i) q^{5} +(764.835 - 641.773i) q^{7} +(16914.7 + 29297.2i) q^{8} +(37570.2 - 65073.5i) q^{10} +(-14169.6 - 80359.9i) q^{11} +(142043. - 51699.4i) q^{13} +(39998.1 - 14558.1i) q^{14} +(134370. + 762050. i) q^{16} +(1161.53 - 2011.82i) q^{17} +(423226. + 733050. i) q^{19} +(1.76267e6 - 1.47905e6i) q^{20} +(604084. - 3.42593e6i) q^{22} +(-512754. - 430252. i) q^{23} +(-1.08380e6 - 394471. i) q^{25} +6.44426e6 q^{26} +1.30346e6 q^{28} +(-564405. - 205427. i) q^{29} +(-1.38890e6 - 1.16542e6i) q^{31} +(-2.72080e6 + 1.54304e7i) q^{32} +(75866.9 - 63659.9i) q^{34} +(-879869. - 1.52398e6i) q^{35} +(-900563. + 1.55982e6i) q^{37} +(6.26631e6 + 3.55380e7i) q^{38} +(5.60293e7 - 2.03930e7i) q^{40} +(1.19014e7 - 4.33175e6i) q^{41} +(1.34805e6 + 7.64517e6i) q^{43} +(5.32648e7 - 9.22574e7i) q^{44} +(-1.42680e7 - 2.47130e7i) q^{46} +(6.26487e6 - 5.25685e6i) q^{47} +(-6.83423e6 + 3.87588e7i) q^{49} +(-3.76666e7 - 3.16060e7i) q^{50} +(1.85439e8 + 6.74944e7i) q^{52} +1.05094e7 q^{53} -1.43821e8 q^{55} +(3.17391e7 + 1.15521e7i) q^{56} +(-1.96155e7 - 1.64593e7i) q^{58} +(-2.49733e7 + 1.41631e8i) q^{59} +(-1.32541e8 + 1.11215e8i) q^{61} +(-3.86478e7 - 6.69400e7i) q^{62} +(-1.35897e8 + 2.35381e8i) q^{64} +(-4.62635e7 - 2.62373e8i) q^{65} +(2.06709e8 - 7.52358e7i) q^{67} +(2.84989e6 - 1.03727e6i) q^{68} +(-1.30274e7 - 7.38820e7i) q^{70} +(-6.86282e7 + 1.18868e8i) q^{71} +(-6.59416e7 - 1.14214e8i) q^{73} +(-5.88216e7 + 4.93572e7i) q^{74} +(-1.91891e8 + 1.08827e9i) q^{76} +(-6.24102e7 - 5.23684e7i) q^{77} +(-1.41188e8 - 5.13881e7i) q^{79} +1.36385e9 q^{80} +5.39946e8 q^{82} +(-4.18517e8 - 1.52328e8i) q^{83} +(-3.13652e6 - 2.63185e6i) q^{85} +(-5.74705e7 + 3.25932e8i) q^{86} +(2.11464e9 - 1.77440e9i) q^{88} +(-1.97851e8 - 3.42687e8i) q^{89} +(7.54601e7 - 1.30701e8i) q^{91} +(-1.51743e8 - 8.60576e8i) q^{92} +(3.27630e8 - 1.19247e8i) q^{94} +(1.40192e9 - 5.10257e8i) q^{95} +(-2.41831e8 - 1.37149e9i) q^{97} +(-8.38935e8 + 1.45308e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8}+O(q^{10}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23} + 2192178 q^{25} + 33129678 q^{26} - 12 q^{28} - 19657236 q^{29} - 4633692 q^{31} + 37550952 q^{32} + 14341770 q^{34} - 34449663 q^{35} - 3 q^{37} + 92022060 q^{38} + 6645801 q^{40} + 33127221 q^{41} + 2356203 q^{43} - 1001541 q^{44} - 3 q^{46} + 33488952 q^{47} - 93214644 q^{49} + 72027753 q^{50} + 160531713 q^{52} - 4841352 q^{53} - 12 q^{55} + 91770981 q^{56} - 320682489 q^{58} - 538090854 q^{59} + 36683436 q^{61} + 55862958 q^{62} - 956301315 q^{64} + 852347310 q^{65} - 109026897 q^{67} + 508886217 q^{68} - 815297649 q^{70} - 940878639 q^{71} - 221849931 q^{73} - 838884579 q^{74} + 908401146 q^{76} + 967811358 q^{77} - 1228059150 q^{79} + 2497115154 q^{80} - 12 q^{82} + 297703284 q^{83} + 1535949369 q^{85} - 2930201574 q^{86} + 2837227002 q^{88} - 1774997208 q^{89} + 551343507 q^{91} + 6896645517 q^{92} + 414852915 q^{94} + 9000269169 q^{95} + 3371772333 q^{97} - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	40.0613	+	14.5811i	1.77048	+	0.644401i	0.999976	+	0.00696084i	$0.00221572\pi$
$2$	40.0613	+	14.5811i	1.77048	+	0.644401i	0.770500	+	0.637440i	$0.220006\pi$
$3$		0			0
$3$		0			0
$4$	1000.08	+	839.170i	1.95329	+	1.63900i
$5$	306.059	−	1735.74i	0.218998	−	1.24200i	−0.654835	−	0.755772i	$-0.727262\pi$
$5$	306.059	−	1735.74i	0.218998	−	1.24200i	0.873833	−	0.486226i	$-0.161627\pi$
$6$		0			0
$7$	764.835	−	641.773i	0.120400	−	0.101028i	−0.580600	−	0.814189i	$-0.697182\pi$
$7$	764.835	−	641.773i	0.120400	−	0.101028i	0.701000	+	0.713162i	$0.252737\pi$
$8$	16914.7	+	29297.2i	1.46003	+	2.52884i
$9$		0			0
$10$	37570.2	−	65073.5i	1.18807	−	2.05780i
$11$	−14169.6	−	80359.9i	−0.291804	−	1.65490i	−0.679916	−	0.733290i	$-0.737984\pi$
$11$	−14169.6	−	80359.9i	−0.291804	−	1.65490i	0.388112	−	0.921612i	$-0.373127\pi$
$12$		0			0
$13$	142043.	−	51699.4i	1.37935	−	0.502042i	0.457368	−	0.889277i	$-0.348792\pi$
$13$	142043.	−	51699.4i	1.37935	−	0.502042i	0.921981	+	0.387235i	$0.126570\pi$
$14$	39998.1	−	14558.1i	0.278268	−	0.101281i
$15$		0			0
$16$	134370.	+	762050.i	0.512580	+	2.90699i
$17$	1161.53	−	2011.82i	0.00337295	−	0.00584211i	−0.864334	−	0.502918i	$-0.832260\pi$
$17$	1161.53	−	2011.82i	0.00337295	−	0.00584211i	0.867707	+	0.497076i	$0.165593\pi$
$18$		0			0
$19$	423226.	+	733050.i	0.745043	+	1.29045i	0.950175	+	0.311718i	$0.100905\pi$
$19$	423226.	+	733050.i	0.745043	+	1.29045i	−0.205131	+	0.978734i	$0.565762\pi$
$20$	1.76267e6	−	1.47905e6i	2.46340	−	2.06704i
$21$		0			0
$22$	604084.	−	3.42593e6i	0.549788	−	3.11800i
$23$	−512754.	−	430252.i	−0.382062	−	0.320588i	0.431449	−	0.902137i	$-0.358002\pi$
$23$	−512754.	−	430252.i	−0.382062	−	0.320588i	−0.813511	+	0.581549i	$0.802447\pi$
$24$		0			0
$25$	−1.08380e6	−	394471.i	−0.554906	−	0.201969i
$26$	6.44426e6			2.76562
$27$		0			0
$28$	1.30346e6			0.400761
$29$	−564405.	−	205427.i	−0.148184	−	0.0539344i	0.266864	−	0.963734i	$-0.414013\pi$
$29$	−564405.	−	205427.i	−0.148184	−	0.0539344i	−0.415047	+	0.909800i	$0.636235\pi$
$30$		0			0
$31$	−1.38890e6	−	1.16542e6i	−0.270111	−	0.226650i	0.497663	−	0.867370i	$-0.334191\pi$
$31$	−1.38890e6	−	1.16542e6i	−0.270111	−	0.226650i	−0.767775	+	0.640720i	$0.778636\pi$
$32$	−2.72080e6	+	1.54304e7i	−0.458692	+	2.60137i
$33$		0			0
$34$	75866.9	−	63659.9i	0.00973638	−	0.00816979i
$35$	−879869.	−	1.52398e6i	−0.0991088	−	0.171661i
$36$		0			0
$37$	−900563.	+	1.55982e6i	−0.0789962	+	0.136825i	−0.902817	−	0.430025i	$-0.858505\pi$
$37$	−900563.	+	1.55982e6i	−0.0789962	+	0.136825i	0.823821	+	0.566850i	$0.191838\pi$
$38$	6.26631e6	+	3.55380e7i	0.487513	+	2.76482i
$39$		0			0
$40$	5.60293e7	−	2.03930e7i	3.46055	−	1.25954i
$41$	1.19014e7	−	4.33175e6i	0.657763	−	0.239406i	0.00849298	−	0.999964i	$-0.497297\pi$
$41$	1.19014e7	−	4.33175e6i	0.657763	−	0.239406i	0.649270	+	0.760558i	$0.275074\pi$
$42$		0			0
$43$	1.34805e6	+	7.64517e6i	0.0601310	+	0.341020i	1.00000		0.000515817i	$-0.000164190\pi$
$43$	1.34805e6	+	7.64517e6i	0.0601310	+	0.341020i	−0.939869	+	0.341535i	$0.889053\pi$
$44$	5.32648e7	−	9.22574e7i	2.14241	−	3.71077i
$45$		0			0
$46$	−1.42680e7	−	2.47130e7i	−0.469845	−	0.813795i
$47$	6.26487e6	−	5.25685e6i	0.187271	−	0.157139i	−0.544332	−	0.838870i	$-0.683217\pi$
$47$	6.26487e6	−	5.25685e6i	0.187271	−	0.157139i	0.731603	+	0.681731i	$0.238772\pi$
$48$		0			0
$49$	−6.83423e6	+	3.87588e7i	−0.169359	+	0.960480i
$50$	−3.76666e7	−	3.16060e7i	−0.852298	−	0.715163i
$51$		0			0
$52$	1.85439e8	+	6.74944e7i	3.51712	+	1.28013i
$53$	1.05094e7			0.182952			0.0914760	−	0.995807i	$-0.470842\pi$
$53$	1.05094e7			0.182952			0.0914760	+	0.995807i	$0.470842\pi$
$54$		0			0
$55$	−1.43821e8			−2.11929
$56$	3.17391e7	+	1.15521e7i	0.431270	+	0.156969i
$57$		0			0
$58$	−1.96155e7	−	1.64593e7i	−0.227600	−	0.190979i
$59$	−2.49733e7	+	1.41631e8i	−0.268313	+	1.52168i	0.491118	+	0.871093i	$0.336588\pi$
$59$	−2.49733e7	+	1.41631e8i	−0.268313	+	1.52168i	−0.759431	+	0.650587i	$0.774523\pi$
$60$		0			0
$61$	−1.32541e8	+	1.11215e8i	−1.22565	+	1.02844i	−0.227137	+	0.973863i	$0.572937\pi$
$61$	−1.32541e8	+	1.11215e8i	−1.22565	+	1.02844i	−0.998510	+	0.0545769i	$0.982619\pi$
$62$	−3.86478e7	−	6.69400e7i	−0.332172	−	0.575338i
$63$		0			0
$64$	−1.35897e8	+	2.35381e8i	−1.01251	+	1.75372i
$65$	−4.62635e7	−	2.62373e8i	−0.321461	−	1.82309i
$66$		0			0
$67$	2.06709e8	−	7.52358e7i	1.25320	−	0.456129i	0.371721	−	0.928344i	$-0.378768\pi$
$67$	2.06709e8	−	7.52358e7i	1.25320	−	0.456129i	0.881483	+	0.472215i	$0.156546\pi$
$68$	2.84989e6	−	1.03727e6i	0.0161636	−	0.00588306i
$69$		0			0
$70$	−1.30274e7	−	7.38820e7i	−0.0648510	−	0.367788i
$71$	−6.86282e7	+	1.18868e8i	−0.320509	+	0.555138i	−0.980593	−	0.196054i	$-0.937187\pi$
$71$	−6.86282e7	+	1.18868e8i	−0.320509	+	0.555138i	0.660084	+	0.751192i	$0.270521\pi$
$72$		0			0
$73$	−6.59416e7	−	1.14214e8i	−0.271773	−	0.470725i	0.697543	−	0.716543i	$-0.254277\pi$
$73$	−6.59416e7	−	1.14214e8i	−0.271773	−	0.470725i	−0.969316	+	0.245818i	$0.920943\pi$
$74$	−5.88216e7	+	4.93572e7i	−0.228031	+	0.191341i
$75$		0			0
$76$	−1.91891e8	+	1.08827e9i	−0.659772	+	3.74176i
$77$	−6.24102e7	−	5.23684e7i	−0.202324	−	0.169770i
$78$		0			0
$79$	−1.41188e8	−	5.13881e7i	−0.407826	−	0.148437i	0.129957	−	0.991520i	$-0.458516\pi$
$79$	−1.41188e8	−	5.13881e7i	−0.407826	−	0.148437i	−0.537783	+	0.843083i	$0.680738\pi$
$80$	1.36385e9			3.72273
$81$		0			0
$82$	5.39946e8			1.31883
$83$	−4.18517e8	−	1.52328e8i	−0.967970	−	0.352312i	−0.190818	−	0.981625i	$-0.561114\pi$
$83$	−4.18517e8	−	1.52328e8i	−0.967970	−	0.352312i	−0.777152	+	0.629313i	$0.783336\pi$
$84$		0			0
$85$	−3.13652e6	−	2.63185e6i	−0.00651722	−	0.00546860i
$86$	−5.74705e7	+	3.25932e8i	−0.113293	+	0.642515i
$87$		0			0
$88$	2.11464e9	−	1.77440e9i	3.75894	−	3.15412i
$89$	−1.97851e8	−	3.42687e8i	−0.334258	−	0.578952i	0.649084	−	0.760717i	$-0.275152\pi$
$89$	−1.97851e8	−	3.42687e8i	−0.334258	−	0.578952i	−0.983342	+	0.181765i	$0.941819\pi$
$90$		0			0
$91$	7.54601e7	−	1.30701e8i	0.115354	−	0.199798i
$92$	−1.51743e8	−	8.60576e8i	−0.220832	−	1.25240i
$93$		0			0
$94$	3.27630e8	−	1.19247e8i	0.432820	−	0.157534i
$95$	1.40192e9	−	5.10257e8i	1.76590	−	0.642736i
$96$		0			0
$97$	−2.41831e8	−	1.37149e9i	−0.277357	−	1.57297i	−0.731372	−	0.681978i	$-0.761120\pi$
$97$	−2.41831e8	−	1.37149e9i	−0.277357	−	1.57297i	0.454015	−	0.890994i	$-0.349991\pi$
$98$	−8.38935e8	+	1.45308e9i	−0.918779	+	1.59137i
$99$		0			0
$100$	−7.52863e8	−	1.30400e9i	−0.752863	−	1.30400i
$101$	−1.38550e6	+	1.16257e6i	−0.00132483	+	0.00111166i	−0.643450	−	0.765488i	$-0.722497\pi$
$101$	−1.38550e6	+	1.16257e6i	−0.00132483	+	0.00111166i	0.642125	+	0.766600i	$0.278053\pi$
$102$		0			0
$103$	−3.01900e8	+	1.71216e9i	−0.264299	+	1.49891i	0.506726	+	0.862107i	$0.330856\pi$
$103$	−3.01900e8	+	1.71216e9i	−0.264299	+	1.49891i	−0.771024	+	0.636806i	$0.780255\pi$
$104$	3.91726e9	+	3.28697e9i	3.28347	+	2.75516i
$105$		0			0
$106$	4.21021e8	+	1.53239e8i	0.323912	+	0.117894i
$107$	9.60585e8			0.708449			0.354225	−	0.935160i	$-0.384745\pi$
$107$	9.60585e8			0.708449			0.354225	+	0.935160i	$0.384745\pi$
$108$		0			0
$109$	−1.53798e9			−1.04360			−0.521798	−	0.853069i	$-0.674738\pi$
$109$	−1.53798e9			−1.04360			−0.521798	+	0.853069i	$0.674738\pi$
$110$	−5.76166e9	−	2.09707e9i	−3.75215	−	1.36567i
$111$		0			0
$112$	5.91834e8	+	4.96607e8i	0.355401	+	0.298217i
$113$	−4.90269e7	+	2.78045e8i	−0.0282866	+	0.160421i	−0.995679	−	0.0928605i	$-0.970399\pi$
$113$	−4.90269e7	+	2.78045e8i	−0.0282866	+	0.160421i	0.967392	+	0.253282i	$0.0815100\pi$
$114$		0			0
$115$	−9.03740e8	+	7.58328e8i	−0.481841	+	0.404312i
$116$	−3.92065e8	−	6.79076e8i	−0.201047	−	0.348223i
$117$		0			0
$118$	−3.06560e9	+	5.30977e9i	−1.45561	+	2.52120i
$119$	−402757.	−	2.28415e6i	−0.000184112	−	0.00104415i
$120$		0			0
$121$	−4.04119e9	+	1.47087e9i	−1.71386	+	0.623794i
$122$	−6.93139e9	+	2.52282e9i	−2.83271	+	1.03102i
$123$		0			0
$124$	−4.11025e8	−	2.33104e9i	−0.156125	−	0.885426i
$125$	7.04805e8	−	1.22076e9i	0.258210	−	0.447234i
$126$		0			0
$127$	−7.69286e8	−	1.33244e9i	−0.262404	−	0.454498i	0.704476	−	0.709728i	$-0.251182\pi$
$127$	−7.69286e8	−	1.33244e9i	−0.262404	−	0.454498i	−0.966880	+	0.255230i	$0.917849\pi$
$128$	−2.73093e9	+	2.29152e9i	−0.899220	+	0.754535i
$129$		0			0
$130$	1.97232e9	−	1.11856e10i	0.605665	−	3.43490i
$131$	−4.39027e9	−	3.68387e9i	−1.30248	−	1.09291i	−0.989711	−	0.143077i	$-0.954300\pi$
$131$	−4.39027e9	−	3.68387e9i	−1.30248	−	1.09291i	−0.312765	−	0.949830i	$-0.601255\pi$
$132$		0			0
$133$	7.94150e8	+	2.89047e8i	0.220075	+	0.0801006i
$134$	9.37804e9			2.51270
$135$		0			0
$136$	7.85877e7			0.0196983
$137$	3.08044e9	+	1.12119e9i	0.747084	+	0.271916i	0.687378	−	0.726300i	$-0.258761\pi$
$137$	3.08044e9	+	1.12119e9i	0.747084	+	0.271916i	0.0597061	+	0.998216i	$0.480984\pi$
$138$		0			0
$139$	2.24656e9	+	1.88509e9i	0.510448	+	0.428316i	0.861287	−	0.508119i	$-0.169659\pi$
$139$	2.24656e9	+	1.88509e9i	0.510448	+	0.428316i	−0.350839	+	0.936436i	$0.614104\pi$
$140$	3.98934e8	−	2.26247e9i	0.0877657	−	0.497744i
$141$		0			0
$142$	−4.48256e9	+	3.76131e9i	−0.925184	+	0.776322i
$143$	−6.16725e9	−	1.06820e10i	−1.23333	−	2.13619i
$144$		0			0
$145$	−5.29309e8	+	9.16791e8i	−0.0994383	+	0.172232i
$146$	−9.76336e8	−	5.53707e9i	−0.177833	−	1.00854i
$147$		0			0
$148$	−2.20959e9	+	8.04226e8i	−0.378560	+	0.137784i
$149$	5.34439e8	−	1.94520e8i	0.0888301	−	0.0323315i	−0.297223	−	0.954808i	$-0.596060\pi$
$149$	5.34439e8	−	1.94520e8i	0.0888301	−	0.0323315i	0.386053	+	0.922477i	$0.373838\pi$
$150$		0			0
$151$	1.15596e9	+	6.55579e9i	0.180945	+	1.02619i	0.931055	+	0.364879i	$0.118890\pi$
$151$	1.15596e9	+	6.55579e9i	0.180945	+	1.02619i	−0.750110	+	0.661314i	$0.769999\pi$
$152$	−1.43175e10	+	2.47987e10i	−2.17556	+	3.76819i
$153$		0			0
$154$	−1.73665e9	−	3.00796e9i	−0.248810	−	0.430952i
$155$	−2.44796e9	+	2.05408e9i	−0.340653	+	0.285842i
$156$		0			0
$157$	5.55288e8	−	3.14919e9i	0.0729406	−	0.413667i	−0.926372	−	0.376609i	$-0.877090\pi$
$157$	5.55288e8	−	3.14919e9i	0.0729406	−	0.413667i	0.999313	−	0.0370583i	$-0.0117987\pi$
$158$	−4.90687e9	−	4.11735e9i	−0.626394	−	0.525607i
$159$		0			0
$160$	2.59505e10	+	9.44522e9i	3.13045	+	1.13939i
$161$	−6.68297e8			−0.0783886
$162$		0			0
$163$	−1.21348e10			−1.34644			−0.673222	−	0.739440i	$-0.735090\pi$
$163$	−1.21348e10			−1.34644			−0.673222	+	0.739440i	$0.735090\pi$
$164$	1.55374e10	+	5.65517e9i	1.67719	+	0.610447i
$165$		0			0
$166$	−1.45452e10	−	1.22049e10i	−1.48674	−	1.24752i
$167$	−3.99194e8	+	2.26394e9i	−0.0397155	+	0.225238i	−0.998205	−	0.0598901i	$-0.980925\pi$
$167$	−3.99194e8	+	2.26394e9i	−0.0397155	+	0.225238i	0.958489	+	0.285128i	$0.0920361\pi$
$168$		0			0
$169$	9.37983e9	−	7.87061e9i	0.884514	−	0.742196i
$170$	−8.72776e7	−	1.51169e8i	−0.00801462	−	0.0138817i
$171$		0			0
$172$	−5.06744e9	+	8.77706e9i	−0.441479	+	0.764665i
$173$	3.14934e9	+	1.78608e10i	0.267308	+	1.51598i	0.762381	+	0.647128i	$0.224030\pi$
$173$	3.14934e9	+	1.78608e10i	0.267308	+	1.51598i	−0.495073	+	0.868851i	$0.664859\pi$
$174$		0			0
$175$	−1.08209e9	+	3.93848e8i	−0.0872151	+	0.0317437i
$176$	5.93343e10	−	2.15959e10i	4.66121	−	1.69654i
$177$		0			0
$178$	−2.92939e9	−	1.66134e10i	−0.218719	−	1.24042i
$179$	−4.27926e9	+	7.41190e9i	−0.311552	+	0.539624i	−0.978699	−	0.205303i	$-0.934182\pi$
$179$	−4.27926e9	+	7.41190e9i	−0.311552	+	0.539624i	0.667147	+	0.744926i	$0.267515\pi$
$180$		0			0
$181$	9.02073e9	+	1.56244e10i	0.624724	+	1.08205i	0.988594	+	0.150604i	$0.0481219\pi$
$181$	9.02073e9	+	1.56244e10i	0.624724	+	1.08205i	−0.363870	+	0.931450i	$0.618545\pi$
$182$	4.92879e9	−	4.13575e9i	0.332981	−	0.279404i
$183$		0			0
$184$	3.93207e9	−	2.22999e10i	0.252895	−	1.43424i
$185$	2.43182e9	+	2.04054e9i	0.152637	+	0.128078i
$186$		0			0
$187$	−1.78128e8	−	6.48334e7i	−0.0106524	−	0.00387714i
$188$	1.06768e10			0.623347
$189$		0			0
$190$	6.36028e10			3.54067
$191$	−2.22149e10	−	8.08556e9i	−1.20780	−	0.439602i	−0.341858	−	0.939752i	$-0.611056\pi$
$191$	−2.22149e10	−	8.08556e9i	−1.20780	−	0.439602i	−0.865939	+	0.500150i	$0.833278\pi$
$192$		0			0
$193$	6.55309e9	+	5.49869e9i	0.339968	+	0.285267i	0.796747	−	0.604313i	$-0.206552\pi$
$193$	6.55309e9	+	5.49869e9i	0.339968	+	0.285267i	−0.456779	+	0.889580i	$0.650997\pi$
$194$	1.03098e10	−	5.84700e10i	0.522570	−	2.96364i
$195$		0			0
$196$	−3.93601e10	+	3.30270e10i	−1.90504	+	1.59852i
$197$	1.23748e10	+	2.14337e10i	0.585382	+	1.01391i	0.994828	+	0.101577i	$0.0323888\pi$
$197$	1.23748e10	+	2.14337e10i	0.585382	+	1.01391i	−0.409446	+	0.912334i	$0.634278\pi$
$198$		0			0
$199$	1.06946e10	−	1.85236e10i	0.483421	−	0.837310i	−0.516398	−	0.856349i	$-0.672727\pi$
$199$	1.06946e10	−	1.85236e10i	0.483421	−	0.837310i	0.999819	+	0.0190389i	$0.00606063\pi$
$200$	−6.77531e9	−	3.84247e10i	−0.299429	−	1.69815i
$201$		0			0
$202$	−7.24563e7	+	2.63719e7i	−0.00306193	+	0.00111445i
$203$	−5.63514e8	+	2.05102e8i	−0.0232902	+	0.00847693i
$204$		0			0
$205$	−3.87629e9	−	2.19835e10i	−0.153293	−	0.869370i
$206$	−3.70597e10	+	6.41893e10i	−1.43384	+	2.48348i
$207$		0			0
$208$	5.84838e10	+	1.01297e11i	2.16646	+	3.75242i
$209$	5.29108e10	−	4.43975e10i	1.91817	−	1.60953i
$210$		0			0
$211$	−7.27307e9	+	4.12476e10i	−0.252608	+	1.43261i	0.549532	+	0.835473i	$0.314806\pi$
$211$	−7.27307e9	+	4.12476e10i	−0.252608	+	1.43261i	−0.802139	+	0.597137i	$0.796305\pi$
$212$	1.05103e10	+	8.81918e9i	0.357358	+	0.299859i
$213$		0			0
$214$	3.84823e10	+	1.40064e10i	1.25429	+	0.456525i
$215$	1.36827e10			0.436714
$216$		0			0
$217$	−1.81021e9			−0.0554193
$218$	−6.16136e10	−	2.24255e10i	−1.84766	−	0.672493i
$219$		0			0
$220$	−1.43833e11	−	1.20690e11i	−4.13958	−	3.47352i
$221$	6.09766e7	−	3.45816e8i	0.00171948	−	0.00975168i
$222$		0			0
$223$	−2.62380e10	+	2.20163e10i	−0.710493	+	0.596174i	−0.924737	−	0.380606i	$-0.875715\pi$
$223$	−2.62380e10	+	2.20163e10i	−0.710493	+	0.596174i	0.214245	+	0.976780i	$0.431271\pi$
$224$	7.82185e9	+	1.35478e10i	0.207584	+	0.359546i
$225$		0			0
$226$	−6.01829e9	+	1.04240e10i	−0.153456	+	0.265794i
$227$	2.23809e9	+	1.26928e10i	0.0559449	+	0.317279i	0.999919	−	0.0127408i	$-0.00405562\pi$
$227$	2.23809e9	+	1.26928e10i	0.0559449	+	0.317279i	−0.943974	+	0.330020i	$0.892945\pi$
$228$		0			0
$229$	4.45170e10	−	1.62029e10i	1.06971	−	0.389343i	0.253642	−	0.967298i	$-0.418372\pi$
$229$	4.45170e10	−	1.62029e10i	1.06971	−	0.389343i	0.816068	+	0.577956i	$0.196149\pi$
$230$	−4.72623e10	+	1.72021e10i	−1.11363	+	0.405327i
$231$		0			0
$232$	−3.52834e9	−	2.00102e10i	−0.0799604	−	0.453478i
$233$	7.99493e8	−	1.38476e9i	0.0177710	−	0.0307803i	−0.857003	−	0.515311i	$-0.827676\pi$
$233$	7.99493e8	−	1.38476e9i	0.0177710	−	0.0307803i	0.874774	+	0.484531i	$0.161010\pi$
$234$		0			0
$235$	−7.20713e9	−	1.24831e10i	−0.154155	−	0.267004i
$236$	−1.43828e11	+	1.20686e11i	−3.01813	+	2.53251i
$237$		0			0
$238$	1.71705e7	−	9.73787e7i	0.000346886	−	0.00196729i
$239$	4.63942e10	+	3.89294e10i	0.919758	+	0.771769i	0.973950	−	0.226762i	$-0.0728139\pi$
$239$	4.63942e10	+	3.89294e10i	0.919758	+	0.771769i	−0.0541922	+	0.998531i	$0.517258\pi$
$240$		0			0
$241$	1.08729e10	+	3.95741e9i	0.207619	+	0.0755673i	0.443736	−	0.896157i	$-0.353653\pi$
$241$	1.08729e10	+	3.95741e9i	0.207619	+	0.0755673i	−0.236117	+	0.971725i	$0.575875\pi$
$242$	−1.83342e11			−3.43632
$243$		0			0
$244$	−2.25880e11			−4.07966
$245$	6.51838e10	+	2.37250e10i	1.15583	+	0.420686i
$246$		0			0
$247$	9.80145e10	+	8.22439e10i	1.67554	+	1.40594i
$248$	1.06508e10	−	6.04036e10i	0.178792	−	1.01398i
$249$		0			0
$250$	4.60354e10	−	3.86283e10i	0.745353	−	0.625425i
$251$	3.03010e10	+	5.24829e10i	0.481865	+	0.834615i	0.999783	−	0.0208153i	$-0.00662620\pi$
$251$	3.03010e10	+	5.24829e10i	0.481865	+	0.834615i	−0.517918	+	0.855430i	$0.673293\pi$
$252$		0			0
$253$	−2.73095e10	+	4.73014e10i	−0.419055	+	0.725824i
$254$	−1.13901e10	−	6.45964e10i	−0.171702	−	0.973771i
$255$		0			0
$256$	−1.20513e10	+	4.38632e9i	−0.175370	+	0.0638294i
$257$	−1.60778e9	+	5.85185e8i	−0.0229894	+	0.00836746i	−0.353489	−	0.935439i	$-0.615005\pi$
$257$	−1.60778e9	+	5.85185e8i	−0.0229894	+	0.00836746i	0.330500	+	0.943806i	$0.392783\pi$
$258$		0			0
$259$	3.12268e8	+	1.77096e9i	0.00431200	+	0.0244546i
$260$	1.73908e11	−	3.01218e11i	2.36015	−	4.08791i
$261$		0			0
$262$	−1.22165e11	−	2.11596e11i	−1.60173	−	2.77428i
$263$	6.87309e10	−	5.76721e10i	0.885832	−	0.743301i	−0.0815380	−	0.996670i	$-0.525983\pi$
$263$	6.87309e10	−	5.76721e10i	0.885832	−	0.743301i	0.967370	+	0.253369i	$0.0815387\pi$
$264$		0			0
$265$	3.21650e9	−	1.82417e10i	0.0400661	−	0.227226i
$266$	2.76000e10	+	2.31592e10i	0.338020	+	0.283632i
$267$		0			0
$268$	2.69862e11	+	9.82216e10i	3.19547	+	1.16306i
$269$	8.91050e10			1.03757			0.518785	−	0.854905i	$-0.326385\pi$
$269$	8.91050e10			1.03757			0.518785	+	0.854905i	$0.326385\pi$
$270$		0			0
$271$	6.02821e9			0.0678933			0.0339466	−	0.999424i	$-0.489192\pi$
$271$	6.02821e9			0.0678933			0.0339466	+	0.999424i	$0.489192\pi$
$272$	1.68918e9	+	6.14813e8i	0.0187119	+	0.00681056i
$273$		0			0
$274$	1.07058e11	+	8.98324e10i	1.14747	+	0.962843i
$275$	−1.63426e10	+	9.26836e10i	−0.172316	+	0.977250i
$276$		0			0
$277$	−1.80353e10	+	1.51334e10i	−0.184062	+	0.154446i	−0.730163	−	0.683273i	$-0.760556\pi$
$277$	−1.80353e10	+	1.51334e10i	−0.184062	+	0.154446i	0.546101	+	0.837719i	$0.316111\pi$
$278$	6.25134e10	+	1.08276e11i	0.627728	+	1.08726i
$279$		0			0
$280$	2.97655e10	−	5.15554e10i	0.289403	−	0.501260i
$281$	2.54330e10	+	1.44238e11i	0.243344	+	1.38007i	0.824308	+	0.566141i	$0.191564\pi$
$281$	2.54330e10	+	1.44238e11i	0.243344	+	1.38007i	−0.580964	+	0.813929i	$0.697324\pi$
$282$		0			0
$283$	−8.02665e10	+	2.92146e10i	−0.743867	+	0.270746i	−0.686023	−	0.727580i	$-0.740645\pi$
$283$	−8.02665e10	+	2.92146e10i	−0.743867	+	0.270746i	−0.0578445	+	0.998326i	$0.518423\pi$
$284$	−1.68384e11	+	6.12868e10i	−1.53592	+	0.559029i
$285$		0			0
$286$	−9.13127e10	−	5.17860e11i	−0.807019	−	4.57683i
$287$	6.32259e9	−	1.09511e10i	0.0550081	−	0.0952768i
$288$		0			0
$289$	5.92912e10	+	1.02695e11i	0.499977	+	0.865986i
$290$	−3.45727e10	+	2.90099e10i	−0.287040	+	0.240855i
$291$		0			0
$292$	2.98980e10	−	1.69560e11i	0.240669	−	1.36490i
$293$	−1.62983e11	−	1.36759e11i	−1.29193	−	1.08406i	−0.991480	−	0.130259i	$-0.958419\pi$
$293$	−1.62983e11	−	1.36759e11i	−1.29193	−	1.08406i	−0.300448	−	0.953798i	$-0.597136\pi$
$294$		0			0
$295$	2.38192e11	+	8.66946e10i	1.83116	+	0.666489i
$296$	−6.09311e10			−0.461346
$297$		0			0
$298$	2.42466e10			0.178106
$299$	−9.50768e10	−	3.46051e10i	−0.687946	−	0.250392i
$300$		0			0
$301$	5.93750e9	+	4.98216e9i	0.0416922	+	0.0349839i
$302$	−4.92814e10	+	2.79489e11i	−0.340920	+	1.93345i
$303$		0			0
$304$	−5.01751e11	+	4.21019e11i	−3.36944	+	2.82729i
$305$	1.52475e11	+	2.64095e11i	1.00891	+	1.74748i
$306$		0			0
$307$	−1.08380e10	+	1.87720e10i	−0.0696348	+	0.120611i	−0.898741	−	0.438481i	$-0.855517\pi$
$307$	−1.08380e10	+	1.87720e10i	−0.0696348	+	0.120611i	0.829106	+	0.559092i	$0.188850\pi$
$308$	−1.84695e10	−	1.04746e11i	−0.116944	−	0.663220i
$309$		0			0
$310$	−1.28019e11	+	4.65952e10i	−0.787314	+	0.286559i
$311$	−1.04569e11	+	3.80599e10i	−0.633841	+	0.230699i	−0.638902	−	0.769288i	$-0.720611\pi$
$311$	−1.04569e11	+	3.80599e10i	−0.633841	+	0.230699i	0.00506132	+	0.999987i	$0.498389\pi$
$312$		0			0
$313$	−2.97901e10	−	1.68948e11i	−0.175438	−	0.994956i	−0.937637	−	0.347615i	$-0.886992\pi$
$313$	−2.97901e10	−	1.68948e11i	−0.175438	−	0.994956i	0.762200	−	0.647342i	$-0.224119\pi$
$314$	6.81643e10	−	1.18064e11i	0.395707	−	0.685384i
$315$		0			0
$316$	−9.80762e10	−	1.69873e11i	−0.553314	−	0.958368i
$317$	1.57795e11	−	1.32406e11i	0.877663	−	0.736447i	−0.0880341	−	0.996117i	$-0.528058\pi$
$317$	1.57795e11	−	1.32406e11i	0.877663	−	0.736447i	0.965697	+	0.259671i	$0.0836140\pi$
$318$		0			0
$319$	−8.51066e9	+	4.82664e10i	−0.0460156	+	0.260968i
$320$	3.66968e11	+	3.07923e11i	1.95638	+	1.64160i
$321$		0			0
$322$	−2.67728e10	−	9.74451e9i	−0.138785	−	0.0505136i
$323$	1.96636e9			0.0100520
$324$		0			0
$325$	−1.74340e11			−0.866806
$326$	−4.86136e11	−	1.76939e11i	−2.38385	−	0.867650i
$327$		0			0
$328$	3.28217e11	+	2.75406e11i	1.56577	+	1.31384i
$329$	1.41789e9	−	8.04125e9i	0.00667207	−	0.0378392i
$330$		0			0
$331$	2.39457e11	−	2.00929e11i	1.09648	−	0.920060i	0.0993006	−	0.995057i	$-0.468339\pi$
$331$	2.39457e11	−	2.00929e11i	1.09648	−	0.920060i	0.997184	+	0.0749980i	$0.0238950\pi$
$332$	−2.90723e11	−	5.03548e11i	−1.31328	−	2.27467i
$333$		0			0
$334$	−4.90031e10	+	8.48758e10i	−0.215459	+	0.373185i
$335$	−6.73251e10	−	3.81820e11i	−0.292062	−	1.65637i
$336$		0			0
$337$	−5.06360e10	+	1.84300e10i	−0.213858	+	0.0778379i	−0.446728	−	0.894670i	$-0.647411\pi$
$337$	−5.06360e10	+	1.84300e10i	−0.213858	+	0.0778379i	0.232870	+	0.972508i	$0.425188\pi$
$338$	4.90531e11	−	1.78539e11i	2.04428	−	0.744058i
$339$		0			0
$340$	−9.28211e8	−	5.26414e9i	−0.00376696	−	0.0213635i
$341$	−7.39731e10	+	1.28125e11i	−0.296264	+	0.513145i
$342$		0			0
$343$	3.97923e10	+	6.89222e10i	0.155230	+	0.268866i
$344$	−2.01180e11	+	1.68810e11i	−0.774590	+	0.649959i
$345$		0			0
$346$	−1.34264e11	+	7.61448e11i	−0.503636	+	2.85626i
$347$	−5.54056e10	−	4.64908e10i	−0.205150	−	0.172141i	0.534424	−	0.845216i	$-0.320529\pi$
$347$	−5.54056e10	−	4.64908e10i	−0.205150	−	0.172141i	−0.739574	+	0.673075i	$0.764973\pi$
$348$		0			0
$349$	−3.57222e11	−	1.30018e11i	−1.28891	−	0.469126i	−0.395543	−	0.918447i	$-0.629444\pi$
$349$	−3.57222e11	−	1.30018e11i	−1.28891	−	0.469126i	−0.893370	+	0.449321i	$0.851666\pi$
$350$	−4.90927e10			−0.174868
$351$		0			0
$352$	1.27854e12			4.43886
$353$	3.20853e11	+	1.16781e11i	1.09982	+	0.400300i	0.827248	−	0.561836i	$-0.189905\pi$
$353$	3.20853e11	+	1.16781e11i	1.09982	+	0.400300i	0.272567	+	0.962137i	$0.412127\pi$
$354$		0			0
$355$	1.85319e11	+	1.55501e11i	0.619289	+	0.519645i
$356$	8.97057e10	−	5.08746e11i	0.296002	−	1.67871i
$357$		0			0
$358$	−2.79507e11	+	2.34534e11i	−0.899329	+	0.754626i
$359$	−6.98481e10	−	1.20980e11i	−0.221937	−	0.384406i	0.733459	−	0.679733i	$-0.237905\pi$
$359$	−6.98481e10	−	1.20980e11i	−0.221937	−	0.384406i	−0.955396	+	0.295328i	$0.904571\pi$
$360$		0			0
$361$	−1.96897e11	+	3.41036e11i	−0.610179	+	1.05686i
$362$	1.33561e11	+	7.57465e11i	0.408783	+	2.31832i
$363$		0			0
$364$	1.85147e11	−	6.73878e10i	0.552789	−	0.201199i
$365$	−2.18429e11	+	7.95016e10i	−0.644157	+	0.234454i
$366$		0			0
$367$	−3.15129e10	−	1.78719e11i	−0.0906758	−	0.514248i	−0.995987	−	0.0894991i	$-0.971473\pi$
$367$	−3.15129e10	−	1.78719e11i	−0.0906758	−	0.514248i	0.905311	−	0.424749i	$-0.139638\pi$
$368$	2.58975e11	−	4.48557e11i	0.736109	−	1.27498i
$369$		0			0
$370$	6.76687e10	+	1.17206e11i	0.187707	+	0.325118i
$371$	8.03797e9	−	6.74466e9i	0.0220274	−	0.0184832i
$372$		0			0
$373$	1.97145e9	−	1.11806e10i	0.00527346	−	0.0299073i	−0.982057	−	0.188582i	$-0.939611\pi$
$373$	1.97145e9	−	1.11806e10i	0.00527346	−	0.0299073i	0.987331	+	0.158675i	$0.0507220\pi$
$374$	−6.19071e9	−	5.19462e9i	−0.0163613	−	0.0137288i
$375$		0			0
$376$	2.59980e11	+	9.46248e10i	0.670801	+	0.244152i
$377$	−9.07902e10			−0.231474
$378$		0			0
$379$	−2.31369e11			−0.576009			−0.288005	−	0.957629i	$-0.592992\pi$
$379$	−2.31369e11			−0.576009			−0.288005	+	0.957629i	$0.592992\pi$
$380$	1.83023e12	+	6.66149e11i	4.50276	+	1.63887i
$381$		0			0
$382$	−7.72061e11	−	6.47836e11i	−1.85510	−	1.55661i
$383$	2.86847e10	−	1.62679e11i	0.0681170	−	0.386310i	−0.931621	−	0.363431i	$-0.881605\pi$
$383$	2.86847e10	−	1.62679e11i	0.0681170	−	0.386310i	0.999738	−	0.0228798i	$-0.00728351\pi$
$384$		0			0
$385$	−1.09999e11	+	9.23004e10i	−0.255163	+	0.214107i
$386$	1.82348e11	+	3.15836e11i	0.418079	+	0.724134i
$387$		0			0
$388$	9.09065e11	−	1.57455e12i	2.03635	−	3.52706i
$389$	−1.27432e11	−	7.22702e11i	−0.282166	−	1.60024i	−0.715236	−	0.698883i	$-0.753681\pi$
$389$	−1.27432e11	−	7.22702e11i	−0.282166	−	1.60024i	0.433069	−	0.901361i	$-0.357431\pi$
$390$		0			0
$391$	−1.46117e9	+	5.31822e8i	−0.00316159	+	0.00115072i
$392$	−1.25112e12	+	4.55372e11i	−2.67617	+	0.974045i
$393$		0			0
$394$	1.83222e11	+	1.03910e12i	0.383040	+	2.17233i
$395$	−1.32408e11	+	2.29338e11i	−0.273671	+	0.474012i
$396$		0			0
$397$	−3.38008e11	−	5.85447e11i	−0.682920	−	1.18285i	−0.974086	−	0.226179i	$-0.927377\pi$
$397$	−3.38008e11	−	5.85447e11i	−0.682920	−	1.18285i	0.291166	−	0.956673i	$-0.405957\pi$
$398$	6.98534e11	−	5.86140e11i	1.39545	−	1.17092i
$399$		0			0
$400$	1.54976e11	−	8.78915e11i	0.302688	−	1.71663i
$401$	−3.73280e11	−	3.13219e11i	−0.720917	−	0.604921i	0.206722	−	0.978400i	$-0.433720\pi$
$401$	−3.73280e11	−	3.13219e11i	−0.720917	−	0.604921i	−0.927639	+	0.373479i	$0.878165\pi$
$402$		0			0
$403$	−2.57535e11	−	9.37349e10i	−0.486366	−	0.177023i
$404$	−2.36120e9			−0.00440978
$405$		0			0
$406$	−2.55657e10			−0.0466972
$407$	1.38108e11	+	5.02671e10i	0.249484	+	0.0908048i
$408$		0			0
$409$	2.10060e11	+	1.76262e11i	0.371184	+	0.311461i	0.809230	−	0.587492i	$-0.199885\pi$
$409$	2.10060e11	+	1.76262e11i	0.371184	+	0.311461i	−0.438046	+	0.898953i	$0.644329\pi$
$410$	1.65255e11	−	9.37209e11i	0.288820	−	1.63798i
$411$		0			0
$412$	−1.73872e12	+	1.45896e12i	−2.97298	+	2.49462i
$413$	7.17943e10	+	1.24351e11i	0.121427	+	0.210317i
$414$		0			0
$415$	−3.92493e11	+	6.79818e11i	−0.649554	+	1.12506i
$416$	4.11272e11	+	2.33244e12i	0.673302	+	3.81848i
$417$		0			0
$418$	2.76704e12	−	1.00712e12i	4.43325	−	1.61357i
$419$	−8.32453e11	+	3.02988e11i	−1.31946	+	0.480244i	−0.903285	−	0.429040i	$-0.858852\pi$
$419$	−8.32453e11	+	3.02988e11i	−1.31946	+	0.480244i	−0.416175	+	0.909285i	$0.636630\pi$
$420$		0			0
$421$	−9.22583e10	−	5.23223e11i	−0.143132	−	0.811741i	−0.968848	−	0.247655i	$-0.920340\pi$
$421$	−9.22583e10	−	5.23223e11i	−0.143132	−	0.811741i	0.825716	−	0.564085i	$-0.190771\pi$
$422$	−8.92805e11	+	1.54638e12i	−1.37041	+	2.37362i
$423$		0			0
$424$	1.77764e11	+	3.07896e11i	0.267114	+	0.462656i
$425$	−2.05247e9	+	1.72223e9i	−0.00305159	+	0.00256059i
$426$		0			0
$427$	−2.99971e10	+	1.70122e11i	−0.0436671	+	0.247648i
$428$	9.60665e11	+	8.06094e11i	1.38381	+	1.16115i
$429$		0			0
$430$	5.48145e11	+	1.99508e11i	0.773192	+	0.281419i
$431$	8.61984e11			1.20324			0.601619	−	0.798783i	$-0.294523\pi$
$431$	8.61984e11			1.20324			0.601619	+	0.798783i	$0.294523\pi$
$432$		0			0
$433$	2.19871e11			0.300589			0.150294	−	0.988641i	$-0.451978\pi$
$433$	2.19871e11			0.300589			0.150294	+	0.988641i	$0.451978\pi$
$434$	−7.25195e10	−	2.63950e10i	−0.0981186	−	0.0357122i
$435$		0			0
$436$	−1.53811e12	−	1.29063e12i	−2.03844	−	1.71046i
$437$	9.83848e10	−	5.57968e11i	0.129051	−	0.731885i
$438$		0			0
$439$	8.51495e11	−	7.14489e11i	1.09419	−	0.918132i	0.0971668	−	0.995268i	$-0.469022\pi$
$439$	8.51495e11	−	7.14489e11i	1.09419	−	0.918132i	0.997021	+	0.0771358i	$0.0245775\pi$
$440$	−2.43269e12	−	4.21355e12i	−3.09422	−	5.35934i
$441$		0			0
$442$	7.48518e9	−	1.29647e10i	0.00932829	−	0.0161571i
$443$	−2.33387e10	−	1.32360e11i	−0.0287911	−	0.163283i	0.967022	−	0.254692i	$-0.0819740\pi$
$443$	−2.33387e10	−	1.32360e11i	−0.0287911	−	0.163283i	−0.995813	+	0.0914091i	$0.970863\pi$
$444$		0			0
$445$	−6.55371e11	+	2.38536e11i	−0.792259	+	0.288359i
$446$	−1.37215e12	+	4.99423e11i	−1.64208	+	0.597670i
$447$		0			0
$448$	4.71220e10	+	2.67242e11i	0.0552679	+	0.313440i
$449$	−3.17493e11	+	5.49914e11i	−0.368660	+	0.638537i	−0.989356	−	0.145514i	$-0.953517\pi$
$449$	−3.17493e11	+	5.49914e11i	−0.368660	+	0.638537i	0.620697	+	0.784051i	$0.286850\pi$
$450$		0			0
$451$	−5.16737e11	−	8.95014e11i	−0.588132	−	1.01867i
$452$	−2.82358e11	+	2.36927e11i	−0.318183	+	0.266988i
$453$		0			0
$454$	−9.54148e10	+	5.41124e11i	−0.105406	+	0.597786i
$455$	−2.03768e11	−	1.70982e11i	−0.222887	−	0.187024i
$456$		0			0
$457$	6.05693e11	+	2.20454e11i	0.649575	+	0.236426i	0.645729	−	0.763567i	$-0.276554\pi$
$457$	6.05693e11	+	2.20454e11i	0.649575	+	0.236426i	0.00384599	+	0.999993i	$0.498776\pi$
$458$	2.01966e12			2.14479
$459$		0			0
$460$	−1.54018e12			−1.60384
$461$	−1.04273e10	−	3.79522e9i	−0.0107527	−	0.00391366i	0.336638	−	0.941634i	$-0.390710\pi$
$461$	−1.04273e10	−	3.79522e9i	−0.0107527	−	0.00391366i	−0.347391	+	0.937720i	$0.612932\pi$
$462$		0			0
$463$	1.23850e12	+	1.03922e12i	1.25251	+	1.05098i	0.996439	+	0.0843199i	$0.0268718\pi$
$463$	1.23850e12	+	1.03922e12i	1.25251	+	1.05098i	0.256069	+	0.966659i	$0.417573\pi$
$464$	8.07063e10	−	4.57708e11i	0.0808307	−	0.458414i
$465$		0			0
$466$	5.22201e10	−	4.38179e10i	0.0512981	−	0.0430442i
$467$	−3.91652e11	−	6.78361e11i	−0.381044	−	0.659987i	0.610168	−	0.792272i	$-0.291102\pi$
$467$	−3.91652e11	−	6.78361e11i	−0.381044	−	0.659987i	−0.991212	+	0.132285i	$0.957769\pi$
$468$		0			0
$469$	1.09814e11	−	1.90203e11i	0.104804	−	0.181526i
$470$	−1.06709e11	−	6.05178e11i	−0.100870	−	0.572061i
$471$		0			0
$472$	−4.57180e12	+	1.66400e12i	−4.23983	+	1.54317i
$473$	5.95264e11	−	2.16658e11i	0.546808	−	0.199022i
$474$		0			0
$475$	−1.69526e11	−	9.61430e11i	−0.152797	−	0.866555i
$476$	1.51400e9	−	2.62232e9i	0.00135174	−	0.00234129i
$477$		0			0
$478$	1.29098e12	+	2.23604e12i	1.13108	+	1.95909i
$479$	−2.45539e11	+	2.06032e11i	−0.213114	+	0.178824i	−0.743095	−	0.669185i	$-0.766643\pi$
$479$	−2.45539e11	+	2.06032e11i	−0.213114	+	0.178824i	0.529982	+	0.848009i	$0.322199\pi$
$480$		0			0
$481$	−4.72768e10	+	2.68120e11i	−0.0402712	+	0.228390i
$482$	3.77878e11	+	3.17078e11i	0.318890	+	0.267580i
$483$		0			0
$484$	−5.27584e12	−	1.92025e12i	−4.37006	−	1.59057i
$485$	−2.45458e12			−2.01437
$486$		0			0
$487$	−4.23287e11			−0.341000			−0.170500	−	0.985358i	$-0.554538\pi$
$487$	−4.23287e11			−0.341000			−0.170500	+	0.985358i	$0.554538\pi$
$488$	−5.50018e12	−	2.00190e12i	−4.39023	−	1.59791i
$489$		0			0
$490$	2.26541e12	+	1.90091e12i	1.77527	+	1.48963i
$491$	−2.31973e11	+	1.31559e12i	−0.180124	+	1.02153i	0.751938	+	0.659234i	$0.229119\pi$
$491$	−2.31973e11	+	1.31559e12i	−0.180124	+	1.02153i	−0.932062	+	0.362300i	$0.881992\pi$
$492$		0			0
$493$	−1.06885e9	+	8.96876e8i	−0.000814906	+	0.000683787i
$494$	2.72738e12	+	4.72396e12i	2.06051	+	3.56890i
$495$		0			0
$496$	7.01484e11	−	1.21501e12i	0.520416	−	0.901386i
$497$	2.37967e10	+	1.34958e11i	0.0174950	+	0.0992188i
$498$		0			0
$499$	−1.23408e12	+	4.49167e11i	−0.891024	+	0.324306i	−0.746650	−	0.665217i	$-0.768339\pi$
$499$	−1.23408e12	+	4.49167e11i	−0.891024	+	0.324306i	−0.144374	+	0.989523i	$0.546117\pi$
$500$	1.72929e12	−	6.29409e11i	1.23738	−	0.450368i
$501$		0			0
$502$	4.48639e11	+	2.54436e12i	0.315304	+	1.78818i
$503$	−2.42146e11	+	4.19410e11i	−0.168664	+	0.292134i	−0.937950	−	0.346770i	$-0.887279\pi$
$503$	−2.42146e11	+	4.19410e11i	−0.168664	+	0.292134i	0.769286	+	0.638904i	$0.220612\pi$
$504$		0			0
$505$	1.59388e9	+	2.76068e9i	0.00109055	+	0.00188888i
$506$	−1.78376e12	+	1.49675e12i	−1.20965	+	1.01502i
$507$		0			0
$508$	3.48795e11	−	1.97812e12i	0.232372	−	1.31785i
$509$	3.98331e11	+	3.34239e11i	0.263035	+	0.220713i	0.764761	−	0.644314i	$-0.222857\pi$
$509$	3.98331e11	+	3.34239e11i	0.263035	+	0.220713i	−0.501726	+	0.865027i	$0.667301\pi$
$510$		0			0
$511$	−1.23734e11	−	4.50355e10i	−0.0802778	−	0.0292187i
$512$	1.27852e12			0.822228
$513$		0			0
$514$	−7.29425e10			−0.0460942
$515$	2.87947e12	+	1.04804e12i	1.80377	+	0.656517i
$516$		0			0
$517$	−5.11211e11	−	4.28957e11i	−0.314697	−	0.264062i
$518$	−1.33127e10	+	7.55003e10i	−0.00812425	+	0.0460749i
$519$		0			0
$520$	6.90426e12	−	5.79336e12i	4.14097	−	3.47469i
$521$	−1.53654e11	−	2.66136e11i	−0.0913635	−	0.158246i	0.816722	−	0.577032i	$-0.195789\pi$
$521$	−1.53654e11	−	2.66136e11i	−0.0913635	−	0.158246i	−0.908085	+	0.418786i	$0.862456\pi$
$522$		0			0
$523$	−2.84528e11	+	4.92818e11i	−0.166291	+	0.288024i	−0.937113	−	0.349026i	$-0.886512\pi$
$523$	−2.84528e11	+	4.92818e11i	−0.166291	+	0.288024i	0.770822	+	0.637050i	$0.219846\pi$
$524$	−1.29924e12	−	7.36836e12i	−0.752833	−	4.26953i
$525$		0			0
$526$	3.59437e12	−	1.30824e12i	2.04733	−	0.745166i
$527$	−3.95787e9	+	1.44055e9i	−0.00223519	+	0.000813541i
$528$		0			0
$529$	−2.34967e11	−	1.33256e12i	−0.130453	−	0.739839i
$530$	3.94841e11	−	6.83884e11i	0.217360	−	0.376479i
$531$		0			0
$532$	5.51657e11	+	9.55498e11i	0.298584	+	0.517163i
$533$	1.46656e12	−	1.23059e12i	0.787094	−	0.660450i
$534$		0			0
$535$	2.93995e11	−	1.66733e12i	0.155149	−	0.879892i
$536$	5.70062e12	+	4.78339e12i	2.98319	+	2.50319i
$537$		0			0
$538$	3.56966e12	+	1.29925e12i	1.83699	+	0.668610i
$539$	3.21150e12			1.63892
$540$		0			0
$541$	1.15323e12			0.578798			0.289399	−	0.957209i	$-0.406545\pi$
$541$	1.15323e12			0.578798			0.289399	+	0.957209i	$0.406545\pi$
$542$	2.41498e11	+	8.78981e10i	0.120203	+	0.0437505i
$543$		0			0
$544$	2.78830e10	+	2.33966e10i	0.0136504	+	0.0114540i
$545$	−4.70713e11	+	2.66954e12i	−0.228545	+	1.29614i
$546$		0			0
$547$	2.48400e12	−	2.08432e12i	1.18634	−	0.995457i	0.186424	−	0.982469i	$-0.440310\pi$
$547$	2.48400e12	−	2.08432e12i	1.18634	−	0.995457i	0.999916	−	0.0129874i	$-0.00413413\pi$
$548$	2.13983e12	+	3.70629e12i	1.01360	+	1.75561i
$549$		0			0
$550$	−2.00614e12	+	3.47473e12i	−0.934821	+	1.61916i
$551$	−8.82832e10	−	5.00679e11i	−0.0408034	−	0.231407i
$552$		0			0
$553$	−1.40965e11	+	5.13070e10i	−0.0640985	+	0.0233299i
$554$	−9.43179e11	+	3.43289e11i	−0.425403	+	0.154834i
$555$		0			0
$556$	6.64839e11	+	3.77049e12i	0.295039	+	1.67325i
$557$	1.72217e12	−	2.98288e12i	0.758101	−	1.31307i	−0.185717	−	0.982603i	$-0.559461\pi$
$557$	1.72217e12	−	2.98288e12i	0.758101	−	1.31307i	0.943818	−	0.330466i	$-0.107206\pi$
$558$		0			0
$559$	5.86732e11	+	1.01625e12i	0.254148	+	0.440197i
$560$	1.04312e12	−	8.75281e11i	0.448216	−	0.376098i
$561$		0			0
$562$	−1.08427e12	+	6.14920e12i	−0.458484	+	2.60019i
$563$	−3.09504e12	−	2.59705e12i	−1.29831	−	1.08941i	−0.990434	−	0.137985i	$-0.955937\pi$
$563$	−3.09504e12	−	2.59705e12i	−1.29831	−	1.08941i	−0.307876	−	0.951426i	$-0.599618\pi$
$564$		0			0
$565$	4.67610e11	+	1.70196e11i	0.193048	+	0.0702639i
$566$	−3.64156e12			−1.49147
$567$		0			0
$568$	−4.64331e12			−1.87180
$569$	−2.19892e12	−	8.00340e11i	−0.879434	−	0.320088i	−0.137453	−	0.990508i	$-0.543892\pi$
$569$	−2.19892e12	−	8.00340e11i	−0.879434	−	0.320088i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	1.90431e12	+	1.59791e12i	0.749679	+	0.629055i	0.935418	−	0.353544i	$-0.115023\pi$
$571$	1.90431e12	+	1.59791e12i	0.749679	+	0.629055i	−0.185739	+	0.982599i	$0.559468\pi$
$572$	2.79624e12	−	1.58583e13i	1.09217	−	6.19403i
$573$		0			0
$574$	4.12970e11	−	3.46523e11i	0.158787	−	0.133238i
$575$	3.86001e11	+	6.68574e11i	0.147260	+	0.255061i
$576$		0			0
$577$	1.65924e12	−	2.87388e12i	0.623185	−	1.07939i	−0.365704	−	0.930731i	$-0.619172\pi$
$577$	1.65924e12	−	2.87388e12i	0.623185	−	1.07939i	0.988889	−	0.148657i	$-0.0474949\pi$
$578$	8.77870e11	+	4.97865e12i	0.327156	+	1.85539i
$579$		0			0
$580$	−1.29870e12	+	4.72687e11i	−0.476521	+	0.173439i
$581$	−4.17857e11	+	1.52087e11i	−0.152137	+	0.0553733i
$582$		0			0
$583$	−1.48914e11	−	8.44535e11i	−0.0533861	−	0.302768i
$584$	2.23077e12	−	3.86381e12i	0.793592	−	1.37454i
$585$		0			0
$586$	−4.53522e12	−	7.85522e12i	−1.58876	−	2.75182i
$587$	−2.03967e12	+	1.71149e12i	−0.709068	+	0.594979i	−0.924338	−	0.381576i	$-0.875382\pi$
$587$	−2.03967e12	+	1.71149e12i	−0.709068	+	0.594979i	0.215269	+	0.976555i	$0.430937\pi$
$588$		0			0
$589$	2.66495e11	−	1.51137e12i	0.0912368	−	0.517430i
$590$	8.27816e12	+	6.94620e12i	2.81255	+	2.36001i
$591$		0			0
$592$	−1.30967e12	−	4.76680e11i	−0.438242	−	0.159507i
$593$	−1.89596e12			−0.629627			−0.314813	−	0.949154i	$-0.601942\pi$
$593$	−1.89596e12			−0.629627			−0.314813	+	0.949154i	$0.601942\pi$
$594$		0			0
$595$	−4.08797e9			−0.00133715
$596$	6.97719e11	+	2.53949e11i	0.226502	+	0.0824401i
$597$		0			0
$598$	−3.30432e12	−	2.77265e12i	−1.05664	−	0.886626i
$599$	−9.71267e11	+	5.50833e12i	−0.308260	+	1.74823i	0.299486	+	0.954101i	$0.403185\pi$
$599$	−9.71267e11	+	5.50833e12i	−0.308260	+	1.74823i	−0.607746	+	0.794131i	$0.707926\pi$
$600$		0			0
$601$	2.05421e12	−	1.72368e12i	0.642258	−	0.538918i	−0.262453	−	0.964945i	$-0.584531\pi$
$601$	2.05421e12	−	1.72368e12i	0.642258	−	0.538918i	0.904711	+	0.426027i	$0.140087\pi$
$602$	1.65219e11	+	2.86167e11i	0.0512714	+	0.0888046i
$603$		0			0
$604$	−4.34536e12	+	7.52639e12i	−1.32849	+	2.30102i
$605$	1.31622e12	+	7.46465e12i	0.399419	+	2.26522i
$606$		0			0
$607$	−9.48426e11	+	3.45199e11i	−0.283566	+	0.103210i	−0.479888	−	0.877330i	$-0.659323\pi$
$607$	−9.48426e11	+	3.45199e11i	−0.283566	+	0.103210i	0.196321	+	0.980540i	$0.437100\pi$
$608$	−1.24628e13	+	4.53607e12i	−3.69869	+	1.34621i
$609$		0			0
$610$	2.25756e12	+	1.28033e13i	0.660169	+	3.74400i
$611$	6.18104e11	−	1.07059e12i	0.179422	−	0.310768i
$612$		0			0
$613$	1.49765e12	+	2.59401e12i	0.428389	+	0.741992i	0.996730	−	0.0808013i	$-0.0257479\pi$
$613$	1.49765e12	+	2.59401e12i	0.428389	+	0.741992i	−0.568341	+	0.822793i	$0.692415\pi$
$614$	−7.07900e11	+	5.93999e11i	−0.201008	+	0.168666i
$615$		0			0
$616$	4.78594e11	−	2.71424e12i	0.133923	−	0.759513i
$617$	−4.11582e12	−	3.45359e12i	−1.14334	−	0.959372i	−0.143792	−	0.989608i	$-0.545930\pi$
$617$	−4.11582e12	−	3.45359e12i	−1.14334	−	0.959372i	−0.999543	+	0.0302359i	$0.990374\pi$
$618$		0			0
$619$	−5.17915e12	−	1.88506e12i	−1.41792	−	0.516079i	−0.484474	−	0.874806i	$-0.660989\pi$
$619$	−5.17915e12	−	1.88506e12i	−1.41792	−	0.516079i	−0.933443	+	0.358727i	$0.883211\pi$
$620$	−4.17189e12			−1.13389
$621$		0			0
$622$	−4.74412e12			−1.27086
$623$	−3.71250e11	−	1.35124e11i	−0.0987349	−	0.0359366i
$624$		0			0
$625$	−3.62884e12	−	3.04496e12i	−0.951279	−	0.798218i
$626$	1.27002e12	−	7.20266e12i	0.330542	−	1.87460i
$627$		0			0
$628$	3.19804e12	−	2.68348e12i	0.820476	−	0.688461i
$629$	2.09206e9	+	3.62355e9i	0.000532900	+	0.000923009i
$630$		0			0
$631$	−1.86766e12	+	3.23488e12i	−0.468992	+	0.812318i	−0.999372	−	0.0354419i	$-0.988716\pi$
$631$	−1.86766e12	+	3.23488e12i	−0.468992	+	0.812318i	0.530379	+	0.847760i	$0.322049\pi$
$632$	−8.82626e11	−	5.00562e12i	−0.220064	−	1.24805i
$633$		0			0
$634$	8.25212e12	−	3.00353e12i	2.02845	−	0.738295i
$635$	−2.54823e12	+	9.27479e11i	−0.621951	+	0.226372i
$636$		0			0
$637$	1.03305e12	+	5.85874e12i	0.248597	+	1.40986i
$638$	−1.04473e12	+	1.80952e12i	−0.249637	+	0.432384i
$639$		0			0
$640$	3.14167e12	+	5.44154e12i	0.740204	+	1.28207i
$641$	2.83409e12	−	2.37809e12i	0.663060	−	0.556374i	−0.247942	−	0.968775i	$-0.579754\pi$
$641$	2.83409e12	−	2.37809e12i	0.663060	−	0.556374i	0.911002	+	0.412401i	$0.135310\pi$
$642$		0			0
$643$	−7.86248e11	+	4.45903e12i	−0.181389	+	1.02871i	0.749119	+	0.662435i	$0.230477\pi$
$643$	−7.86248e11	+	4.45903e12i	−0.181389	+	1.02871i	−0.930508	+	0.366271i	$0.880634\pi$
$644$	−6.68353e11	−	5.60814e11i	−0.153116	−	0.128479i
$645$		0			0
$646$	7.87748e10	+	2.86717e10i	0.0177968	+	0.00647749i
$647$	−7.61507e12			−1.70846			−0.854230	−	0.519896i	$-0.825971\pi$
$647$	−7.61507e12			−1.70846			−0.854230	+	0.519896i	$0.825971\pi$
$648$		0			0
$649$	1.17353e13			2.59653
$650$	−6.98429e12	−	2.54207e12i	−1.53466	−	0.558570i
$651$		0			0
$652$	−1.21358e13	−	1.01832e13i	−2.62999	−	2.20683i
$653$	5.58299e11	−	3.16627e12i	0.120159	−	0.681457i	−0.863906	−	0.503652i	$-0.831989\pi$
$653$	5.58299e11	−	3.16627e12i	0.120159	−	0.681457i	0.984066	−	0.177805i	$-0.0568996\pi$
$654$		0			0
$655$	−7.73794e12	+	6.49290e12i	−1.64263	+	1.37833i
$656$	4.90019e12	+	8.48738e12i	1.03311	+	1.78940i
$657$		0			0
$658$	1.74053e11	−	3.01468e11i	0.0361963	−	0.0626939i
$659$	−1.38988e12	−	7.88243e12i	−0.287074	−	1.62808i	−0.697780	−	0.716312i	$-0.745829\pi$
$659$	−1.38988e12	−	7.88243e12i	−0.287074	−	1.62808i	0.410706	−	0.911768i	$-0.365282\pi$
$660$		0			0
$661$	5.79096e12	−	2.10774e12i	1.17990	−	0.429447i	0.323731	−	0.946149i	$-0.395063\pi$
$661$	5.79096e12	−	2.10774e12i	1.17990	−	0.429447i	0.856165	+	0.516702i	$0.172840\pi$
$662$	1.25227e13	−	4.55791e12i	2.53419	−	0.922368i
$663$		0			0
$664$	−2.61633e12	−	1.48380e13i	−0.522320	−	2.96222i
$665$	7.44768e11	−	1.28998e12i	0.147681	−	0.255790i
$666$		0			0
$667$	2.01016e11	+	3.48170e11i	0.0393246	+	0.0681122i
$668$	−2.29906e12	+	1.92914e12i	−0.446742	+	0.374861i
$669$		0			0
$670$	2.87023e12	−	1.62779e13i	0.550275	−	3.12077i
$671$	1.08153e13	+	9.07509e12i	2.05962	+	1.72822i
$672$		0			0
$673$	−6.23701e12	−	2.27009e12i	−1.17195	−	0.426555i	−0.318597	−	0.947890i	$-0.603212\pi$
$673$	−6.23701e12	−	2.27009e12i	−1.17195	−	0.426555i	−0.853352	+	0.521336i	$0.825434\pi$
$674$	−2.29728e12			−0.428789
$675$		0			0
$676$	1.59854e13			2.94417
$677$	1.99676e12	+	7.26760e11i	0.365322	+	0.132966i	0.518157	−	0.855285i	$-0.326618\pi$
$677$	1.99676e12	+	7.26760e11i	0.365322	+	0.132966i	−0.152835	+	0.988252i	$0.548840\pi$
$678$		0			0
$679$	−1.06515e12	−	8.93766e11i	−0.192308	−	0.161365i
$680$	2.40525e10	−	1.36408e11i	0.00431389	−	0.0244653i
$681$		0			0
$682$	−4.83167e12	+	4.05425e12i	−0.855200	+	0.717598i
$683$	−1.76336e12	−	3.05423e12i	−0.310062	−	0.537043i	0.668314	−	0.743880i	$-0.267016\pi$
$683$	−1.76336e12	−	3.05423e12i	−0.310062	−	0.537043i	−0.978375	+	0.206837i	$0.933683\pi$
$684$		0			0
$685$	2.88889e12	−	5.00370e12i	0.501329	−	0.868328i
$686$	5.89167e11	+	3.34133e12i	0.101573	+	0.576051i
$687$		0			0
$688$	−5.64486e12	+	2.05456e12i	−0.960518	+	0.349600i
$689$	1.49279e12	−	5.43330e11i	0.252355	−	0.0918496i
$690$		0			0
$691$	−1.33168e11	−	7.55235e11i	−0.0222203	−	0.126017i	0.971680	−	0.236301i	$-0.0759352\pi$
$691$	−1.33168e11	−	7.55235e11i	−0.0222203	−	0.126017i	−0.993900	+	0.110284i	$0.964824\pi$
$692$	−1.18386e13	+	2.05051e13i	−1.96257	+	3.39927i
$693$		0			0
$694$	−1.54173e12	−	2.67036e12i	−0.252285	−	0.436971i
$695$	3.95961e12	−	3.32250e12i	0.643755	−	0.540174i
$696$		0			0
$697$	5.10906e9	−	2.89749e10i	0.000819961	−	0.00465023i
$698$	−1.24150e13	−	1.04174e13i	−1.97968	−	1.66115i
$699$		0			0
$700$	−1.41269e12	−	5.14176e11i	−0.222384	−	0.0809413i
$701$	3.18769e11			0.0498592			0.0249296	−	0.999689i	$-0.492064\pi$
$701$	3.18769e11			0.0498592			0.0249296	+	0.999689i	$0.492064\pi$
$702$		0			0
$703$	−1.52457e12			−0.235422
$704$	2.08408e13	+	7.58542e12i	3.19769	+	1.16387i
$705$		0			0
$706$	1.11510e13	+	9.35679e12i	1.68924	+	1.41744i
$707$	−3.13570e8	+	1.77835e9i	−4.72006e−5	+	0.000267688i
$708$		0			0
$709$	−1.72238e12	+	1.44525e12i	−0.255989	+	0.214800i	−0.761746	−	0.647876i	$-0.775658\pi$
$709$	−1.72238e12	+	1.44525e12i	−0.255989	+	0.214800i	0.505757	+	0.862676i	$0.331213\pi$
$710$	5.15675e12	+	8.93175e12i	0.761576	+	1.31909i
$711$		0			0
$712$	6.69318e12	−	1.15929e13i	0.976051	−	1.69057i
$713$	2.10737e11	+	1.19515e12i	0.0305379	+	0.173189i
$714$		0			0
$715$	−2.04287e13	+	7.43546e12i	−2.92324	+	1.06397i
$716$	−1.04995e13	+	3.82149e12i	−1.49300	+	0.543406i
$717$		0			0
$718$	−1.03417e12	−	5.86510e12i	−0.145223	−	0.823598i
$719$	1.90680e12	−	3.30267e12i	0.266088	−	0.460878i	−0.701760	−	0.712413i	$-0.747602\pi$
$719$	1.90680e12	−	3.30267e12i	0.266088	−	0.460878i	0.967848	+	0.251536i	$0.0809355\pi$
$720$		0			0
$721$	8.67913e11	+	1.50327e12i	0.119610	+	0.207171i
$722$	−1.28606e13	+	1.07914e13i	−1.76135	+	1.47795i
$723$		0			0
$724$	−4.09001e12	+	2.31956e13i	−0.553224	+	3.13749i
$725$	5.30668e11	+	4.45283e11i	0.0713348	+	0.0598570i
$726$		0			0
$727$	6.62748e12	+	2.41221e12i	0.879921	+	0.320265i	0.742178	−	0.670203i	$-0.233793\pi$
$727$	6.62748e12	+	2.41221e12i	0.879921	+	0.320265i	0.137743	+	0.990468i	$0.456015\pi$
$728$	5.10555e12			0.673677
$729$		0			0
$730$	−9.90976e12			−1.29155
$731$	1.69465e10	+	6.16804e9i	0.00219509	+	0.000798949i
$732$		0			0
$733$	−9.21470e12	−	7.73205e12i	−1.17900	−	0.989298i	−0.999985	−	0.00545120i	$-0.998265\pi$
$733$	−9.21470e12	−	7.73205e12i	−1.17900	−	0.989298i	−0.179014	−	0.983847i	$-0.557291\pi$
$734$	1.34347e12	−	7.61920e12i	0.170842	−	0.968896i
$735$		0			0
$736$	8.03406e12	−	6.74138e12i	1.00922	−	0.846834i
$737$	−8.97492e12	−	1.55450e13i	−1.12054	−	1.94083i
$738$		0			0
$739$	−4.91227e11	+	8.50831e11i	−0.0605874	+	0.104941i	−0.894728	−	0.446611i	$-0.852631\pi$
$739$	−4.91227e11	+	8.50831e11i	−0.0605874	+	0.104941i	0.834141	+	0.551552i	$0.185964\pi$
$740$	7.19666e11	+	4.08143e12i	0.0882243	+	0.500345i
$741$		0			0
$742$	4.20356e11	−	1.52997e11i	0.0509096	−	0.0185296i
$743$	1.24981e13	−	4.54895e12i	1.50451	−	0.547598i	0.547288	−	0.836945i	$-0.315660\pi$
$743$	1.24981e13	−	4.54895e12i	1.50451	−	0.547598i	0.957224	+	0.289347i	$0.0934382\pi$
$744$		0			0
$745$	−1.74067e11	−	9.87184e11i	−0.0207021	−	0.117407i
$746$	2.42005e11	−	4.19165e11i	0.0286088	−	0.0495519i
$747$		0			0
$748$	−1.23737e11	−	2.14319e11i	−0.0144525	−	0.0250324i
$749$	7.34689e11	−	6.16477e11i	0.0852973	−	0.0715729i
$750$		0			0
$751$	7.31937e11	−	4.15102e12i	0.0839641	−	0.476184i	−0.913611	−	0.406589i	$-0.866718\pi$
$751$	7.31937e11	−	4.15102e12i	0.0839641	−	0.476184i	0.997575	−	0.0695953i	$-0.0221708\pi$
$752$	4.84779e12	+	4.06778e12i	0.552794	+	0.463849i
$753$		0			0
$754$	−3.63717e12	−	1.32382e12i	−0.409820	−	0.149162i
$755$	1.17330e13			1.31416
$756$		0			0
$757$	6.86528e12			0.759848			0.379924	−	0.925018i	$-0.375950\pi$
$757$	6.86528e12			0.759848			0.379924	+	0.925018i	$0.375950\pi$
$758$	−9.26896e12	−	3.37362e12i	−1.01981	−	0.371181i
$759$		0			0
$760$	3.86622e13	+	3.24414e13i	4.20364	+	3.52727i
$761$	2.54144e12	−	1.44132e13i	0.274694	−	1.55787i	−0.465238	−	0.885185i	$-0.654031\pi$
$761$	2.54144e12	−	1.44132e13i	0.274694	−	1.55787i	0.739932	−	0.672681i	$-0.234858\pi$
$762$		0			0
$763$	−1.17630e12	+	9.87035e11i	−0.125649	+	0.105432i
$764$	−1.54316e13	−	2.67283e13i	−1.63867	−	2.83825i
$765$		0			0
$766$	3.52118e12	−	6.09887e12i	0.369538	−	0.640059i
$767$	3.77494e12	+	2.14087e13i	0.393850	+	2.23363i
$768$		0			0
$769$	−8.13618e12	+	2.96133e12i	−0.838981	+	0.305364i	−0.725539	−	0.688181i	$-0.758410\pi$
$769$	−8.13618e12	+	2.96133e12i	−0.838981	+	0.305364i	−0.113442	+	0.993545i	$0.536187\pi$
$770$	−5.75256e12	+	2.09376e12i	−0.589730	+	0.214644i
$771$		0			0
$772$	1.93930e12	+	1.09983e13i	0.196502	+	1.11442i
$773$	8.24454e11	−	1.42800e12i	0.0830536	−	0.143853i	−0.821507	−	0.570199i	$-0.806866\pi$
$773$	8.24454e11	−	1.42800e12i	0.0830536	−	0.143853i	0.904560	+	0.426346i	$0.140199\pi$
$774$		0			0
$775$	1.04556e12	+	1.81097e12i	0.104110	+	0.180324i
$776$	3.60904e13	−	3.02834e13i	3.57284	−	2.99797i
$777$		0			0
$778$	5.43272e12	−	3.08105e13i	0.531630	−	3.01502i
$779$	8.21236e12	+	6.89099e12i	0.799005	+	0.670445i
$780$		0			0
$781$	1.05246e13	+	3.83065e12i	1.01222	+	0.368419i
$782$	−6.62909e10			−0.00633904
$783$		0			0
$784$	−3.04545e13			−2.87891
$785$	−5.29624e12	−	1.92767e12i	−0.497800	−	0.181184i
$786$		0			0
$787$	−8.82485e11	−	7.40493e11i	−0.0820013	−	0.0688073i	0.600866	−	0.799350i	$-0.294823\pi$
$787$	−8.82485e11	−	7.40493e11i	−0.0820013	−	0.0688073i	−0.682867	+	0.730543i	$0.739267\pi$
$788$	−5.61074e12	+	3.18201e13i	−0.518385	+	2.93990i
$789$		0			0
$790$	−8.64846e12	+	7.25692e12i	−0.789981	+	0.662873i
$791$	1.40944e11	+	2.44123e11i	0.0128013	+	0.0221725i
$792$		0			0
$793$	−1.30767e13	+	2.26496e13i	−1.17428	+	2.03390i
$794$	−5.00457e12	−	2.83823e13i	−0.446863	−	2.53428i
$795$		0			0
$796$	2.62399e13	−	9.55056e12i	2.31662	−	0.843179i
$797$	−2.00303e13	+	7.29044e12i	−1.75843	+	0.640017i	−0.999932	−	0.0116562i	$-0.996290\pi$
$797$	−2.00303e13	+	7.29044e12i	−1.75843	+	0.640017i	−0.758500	+	0.651673i	$0.774067\pi$
$798$		0			0
$799$	−3.29904e9	−	1.87098e10i	−0.000286370	−	0.00162408i
$800$	9.03565e12	−	1.56502e13i	0.779928	−	1.35087i
$801$		0			0
$802$	−1.03870e13	−	1.79908e13i	−0.886554	−	1.53556i
$803$	−8.24388e12	+	6.91744e12i	−0.699700	+	0.587118i
$804$		0			0
$805$	−2.04538e11	+	1.15999e12i	−0.0171669	+	0.0973584i
$806$	−8.95041e12	−	7.51028e12i	−0.747025	−	0.626828i
$807$		0			0
$808$	−5.74953e10	−	2.09266e10i	−0.00474549	−	0.00172722i
$809$	−1.03932e13			−0.853059			−0.426530	−	0.904474i	$-0.640264\pi$
$809$	−1.03932e13			−0.853059			−0.426530	+	0.904474i	$0.640264\pi$
$810$		0			0
$811$	1.57077e13			1.27503			0.637515	−	0.770438i	$-0.279963\pi$
$811$	1.57077e13			1.27503			0.637515	+	0.770438i	$0.279963\pi$
$812$	−7.35677e11	−	2.67765e11i	−0.0593862	−	0.0216148i
$813$		0			0
$814$	4.79982e12	+	4.02753e12i	0.383191	+	0.321535i
$815$	−3.71396e12	+	2.10629e13i	−0.294868	+	1.67228i
$816$		0			0
$817$	−5.03376e12	+	4.22383e12i	−0.395269	+	0.331670i
$818$	5.84520e12	+	1.01242e13i	0.456467	+	0.790625i
$819$		0			0
$820$	1.45713e13	−	2.52382e13i	1.12547	−	1.94938i
$821$	2.68395e12	+	1.52215e13i	0.206173	+	1.16926i	0.895584	+	0.444893i	$0.146758\pi$
$821$	2.68395e12	+	1.52215e13i	0.206173	+	1.16926i	−0.689411	+	0.724370i	$0.742131\pi$
$822$		0			0
$823$	7.70324e12	−	2.80375e12i	0.585294	−	0.213030i	−0.0323644	−	0.999476i	$-0.510304\pi$
$823$	7.70324e12	−	2.80375e12i	0.585294	−	0.213030i	0.617658	+	0.786447i	$0.288081\pi$
$824$	−5.52680e13	+	2.01159e13i	−4.17639	+	1.52008i
$825$		0			0
$826$	1.06299e12	+	6.02852e12i	0.0794546	+	0.450610i
$827$	9.10905e12	−	1.57773e13i	0.677171	−	1.17289i	−0.298658	−	0.954360i	$-0.596539\pi$
$827$	9.10905e12	−	1.57773e13i	0.677171	−	1.17289i	0.975829	−	0.218534i	$-0.0701275\pi$
$828$		0			0
$829$	2.04567e12	+	3.54320e12i	0.150432	+	0.260555i	0.931386	−	0.364033i	$-0.118600\pi$
$829$	2.04567e12	+	3.54320e12i	0.150432	+	0.260555i	−0.780955	+	0.624588i	$0.785267\pi$
$830$	−2.56363e13	+	2.15114e13i	−1.87501	+	1.57332i
$831$		0			0
$832$	−7.13418e12	+	4.04599e13i	−0.516165	+	2.92732i
$833$	7.00378e10	+	5.87687e10i	0.00504000	+	0.00422906i
$834$		0			0
$835$	3.80745e12	+	1.38580e12i	0.271047	+	0.0986531i
$836$	9.01723e13			6.38476
$837$		0			0
$838$	−3.77670e13			−2.64554
$839$	1.20843e13	+	4.39833e12i	0.841964	+	0.306450i	0.726760	−	0.686892i	$-0.241025\pi$
$839$	1.20843e13	+	4.39833e12i	0.841964	+	0.306450i	0.115205	+	0.993342i	$0.463248\pi$
$840$		0			0
$841$	−1.08368e13	−	9.09313e12i	−0.746995	−	0.626803i
$842$	3.93319e12	−	2.23062e13i	0.269675	−	1.52940i
$843$		0			0
$844$	−4.18874e13	+	3.51477e13i	−2.84147	+	2.38428i
$845$	−1.07906e13	−	1.86899e13i	−0.728099	−	1.26110i
$846$		0			0
$847$	−2.14688e12	+	3.71850e12i	−0.143328	+	0.248252i
$848$	1.41215e12	+	8.00869e12i	0.0937776	+	0.531839i
$849$		0			0
$850$	−1.07337e11	+	3.90673e10i	−0.00705282	+	0.00256702i
$851$	1.13288e12	−	4.12336e11i	0.0740461	−	0.0269506i
$852$		0			0
$853$	−3.58621e12	−	2.03384e13i	−0.231935	−	1.31537i	−0.848974	−	0.528434i	$-0.822779\pi$
$853$	−3.58621e12	−	2.03384e13i	−0.231935	−	1.31537i	0.617040	−	0.786932i	$-0.288332\pi$
$854$	−3.68230e12	+	6.37792e12i	−0.236896	+	0.410316i
$855$		0			0
$856$	1.62480e13	+	2.81424e13i	1.03435	+	1.79155i
$857$	7.69826e12	−	6.45960e12i	0.487505	−	0.409065i	−0.365626	−	0.930762i	$-0.619145\pi$
$857$	7.69826e12	−	6.45960e12i	0.487505	−	0.409065i	0.853131	+	0.521697i	$0.174701\pi$
$858$		0			0
$859$	−3.48683e12	+	1.97748e13i	−0.218505	+	1.23920i	0.656214	+	0.754575i	$0.272157\pi$
$859$	−3.48683e12	+	1.97748e13i	−0.218505	+	1.23920i	−0.874719	+	0.484630i	$0.838954\pi$
$860$	1.36838e13	+	1.14821e13i	0.853029	+	0.715776i
$861$		0			0
$862$	3.45322e13	+	1.25687e13i	2.13030	+	0.775367i
$863$	1.22213e13			0.750013			0.375006	−	0.927022i	$-0.377641\pi$
$863$	1.22213e13			0.750013			0.375006	+	0.927022i	$0.377641\pi$
$864$		0			0
$865$	3.19657e13			1.94138
$866$	8.80832e12	+	3.20597e12i	0.532185	+	0.193699i
$867$		0			0
$868$	−1.81037e12	−	1.51908e12i	−0.108250	−	0.0908325i
$869$	−2.12897e12	+	1.20740e13i	−0.126643	+	0.718227i
$870$		0			0
$871$	2.54718e13	−	2.13734e13i	1.49961	−	1.25832i
$872$	−2.60146e13	−	4.50586e13i	−1.52368	−	2.63908i
$873$		0			0
$874$	1.20772e13	−	2.09184e13i	0.700109	−	1.21262i
$875$	−2.44390e11	−	1.38600e12i	−0.0140944	−	0.0799333i
$876$		0			0
$877$	2.78801e13	−	1.01475e13i	1.59146	−	0.579244i	0.613804	−	0.789459i	$-0.289639\pi$
$877$	2.78801e13	−	1.01475e13i	1.59146	−	0.579244i	0.977655	+	0.210215i	$0.0674164\pi$
$878$	4.45300e13	−	1.62076e13i	2.52888	−	0.920436i
$879$		0			0
$880$	−1.93252e13	−	1.09599e14i	−1.08631	−	6.16075i
$881$	−7.06961e12	+	1.22449e13i	−0.395370	+	0.684801i	−0.993148	−	0.116860i	$-0.962717\pi$
$881$	−7.06961e12	+	1.22449e13i	−0.395370	+	0.684801i	0.597778	+	0.801662i	$0.296050\pi$
$882$		0			0
$883$	−1.68209e13	−	2.91347e13i	−0.931164	−	1.61282i	−0.781336	−	0.624111i	$-0.785461\pi$
$883$	−1.68209e13	−	2.91347e13i	−0.931164	−	1.61282i	−0.149828	−	0.988712i	$-0.547872\pi$
$884$	3.51180e11	−	2.94675e11i	0.0193417	−	0.0162296i
$885$		0			0
$886$	9.94981e11	−	5.64282e12i	0.0542454	−	0.307641i
$887$	9.46668e12	+	7.94348e12i	0.513501	+	0.430878i	0.862359	−	0.506297i	$-0.168986\pi$
$887$	9.46668e12	+	7.94348e12i	0.513501	+	0.430878i	−0.348858	+	0.937176i	$0.613431\pi$
$888$		0			0
$889$	−1.44350e12	−	5.25392e11i	−0.0775103	−	0.0282115i
$890$	−2.97331e13			−1.58849
$891$		0			0
$892$	−4.47157e13			−2.36493
$893$	6.50499e12	+	2.36762e12i	0.342306	+	0.124589i
$894$		0			0
$895$	1.15555e13	+	9.69618e12i	0.601982	+	0.505123i
$896$	−6.18075e11	+	3.50528e12i	−0.0320372	+	0.181692i
$897$		0			0
$898$	−2.07375e13	+	1.74009e13i	−1.06418	+	0.892951i
$899$	5.44492e11	+	9.43087e11i	0.0278018	+	0.0481541i
$900$		0			0
$901$	1.22070e10	−	2.11431e10i	0.000617087	−	0.00106883i
$902$	−7.65083e12	−	4.33900e13i	−0.384839	−	2.18253i
$903$		0			0
$904$	−8.97522e12	+	3.26671e12i	−0.446979	+	0.162687i
$905$	2.98808e13	−	1.08757e13i	1.48072	−	0.538939i
$906$		0			0
$907$	4.04140e12	+	2.29199e13i	0.198289	+	1.12455i	0.907656	+	0.419714i	$0.137870\pi$
$907$	4.04140e12	+	2.29199e13i	0.198289	+	1.12455i	−0.709367	+	0.704839i	$0.751019\pi$
$908$	−8.41316e12	+	1.45720e13i	−0.410745	+	0.711432i
$909$		0			0
$910$	−5.67010e12	−	9.82091e12i	−0.274097	−	0.474750i
$911$	−2.29368e13	+	1.92462e13i	−1.10332	+	0.925791i	−0.997644	−	0.0686098i	$-0.978144\pi$
$911$	−2.29368e13	+	1.92462e13i	−1.10332	+	0.925791i	−0.105672	+	0.994401i	$0.533699\pi$
$912$		0			0
$913$	−6.31082e12	+	3.57904e13i	−0.300585	+	1.70470i
$914$	2.10504e13	+	1.76634e13i	0.997704	+	0.837173i
$915$		0			0
$916$	5.81177e13	+	2.11531e13i	2.72759	+	0.992760i
$917$	−5.72204e12			−0.267232
$918$		0			0
$919$	4.28637e13			1.98230			0.991152	−	0.132734i	$-0.0423758\pi$
$919$	4.28637e13			1.98230			0.991152	+	0.132734i	$0.0423758\pi$
$920$	−3.75034e13	−	1.36501e13i	−1.72594	−	0.628191i
$921$		0			0
$922$	−3.62392e11	−	3.04083e11i	−0.0165154	−	0.0138581i
$923$	−3.60277e12	+	2.04323e13i	−0.163391	+	0.926638i
$924$		0			0
$925$	1.59133e12	−	1.33529e12i	0.0714700	−	0.0599704i
$926$	3.44628e13	+	5.96912e13i	1.54028	+	2.66785i
$927$		0			0
$928$	4.70545e12	−	8.15008e12i	0.208274	−	0.360741i
$929$	−5.85871e12	−	3.32264e13i	−0.258066	−	1.46357i	−0.788078	−	0.615576i	$-0.788924\pi$
$929$	−5.85871e12	−	3.32264e13i	−0.258066	−	1.46357i	0.530012	−	0.847990i	$-0.322188\pi$
$930$		0			0
$931$	−3.13046e13	+	1.13939e13i	−1.36563	+	0.497050i
$932$	1.96161e12	−	7.13968e11i	0.0851611	−	0.0309961i
$933$		0			0
$934$	−5.79882e12	−	3.28868e13i	−0.249333	−	1.41404i
$935$	−1.67052e11	+	2.89343e11i	−0.00714825	+	0.0123811i
$936$		0			0
$937$	−6.14862e12	−	1.06497e13i	−0.260585	−	0.451346i	0.705813	−	0.708399i	$-0.250582\pi$
$937$	−6.14862e12	−	1.06497e13i	−0.260585	−	0.451346i	−0.966398	+	0.257052i	$0.917249\pi$
$938$	7.17265e12	−	6.01857e12i	0.302529	−	0.253852i
$939$		0			0
$940$	3.26772e12	−	1.85322e13i	0.136512	−	0.774196i
$941$	−5.56222e12	−	4.66725e12i	−0.231257	−	0.194048i	0.519794	−	0.854291i	$-0.326009\pi$
$941$	−5.56222e12	−	4.66725e12i	−0.231257	−	0.194048i	−0.751051	+	0.660244i	$0.770453\pi$
$942$		0			0
$943$	−7.96622e12	−	2.89947e12i	−0.328057	−	0.119403i
$944$	−1.11285e14			−4.56104
$945$		0			0
$946$	2.70062e13			1.09636
$947$	1.42198e13	+	5.17559e12i	0.574538	+	0.209115i	0.612915	−	0.790148i	$-0.289997\pi$
$947$	1.42198e13	+	5.17559e12i	0.574538	+	0.209115i	−0.0383772	+	0.999263i	$0.512219\pi$
$948$		0			0
$949$	−1.52713e13	−	1.28142e13i	−0.611194	−	0.512853i
$950$	7.22729e12	−	4.09880e13i	0.287885	−	1.63268i
$951$		0			0
$952$	6.01067e10	−	5.04355e10i	0.00237168	−	0.00199008i
$953$	1.45515e13	+	2.52039e13i	0.571463	+	0.989803i	0.996416	+	0.0845877i	$0.0269573\pi$
$953$	1.45515e13	+	2.52039e13i	0.571463	+	0.989803i	−0.424953	+	0.905215i	$0.639709\pi$
$954$		0			0
$955$	−2.08335e13	+	3.60847e13i	−0.810490	+	1.40381i
$956$	1.37298e13	+	7.78653e13i	0.531621	+	3.01497i
$957$		0			0
$958$	−1.28408e13	+	4.67367e12i	−0.492547	+	0.179272i
$959$	3.07557e12	−	1.11942e12i	0.117420	−	0.0427374i
$960$		0			0
$961$	−4.02037e12	−	2.28006e13i	−0.152058	−	0.862366i
$962$	−5.80346e12	+	1.00519e13i	−0.218474	+	0.378407i
$963$		0			0
$964$	7.55286e12	+	1.30819e13i	0.281686	+	0.487894i
$965$	1.15500e13	−	9.69156e12i	0.428753	−	0.359767i
$966$		0			0
$967$	2.21207e12	−	1.25453e13i	0.0813541	−	0.461382i	−0.916730	−	0.399508i	$-0.869181\pi$
$967$	2.21207e12	−	1.25453e13i	0.0813541	−	0.461382i	0.998084	−	0.0618744i	$-0.0197078\pi$
$968$	−1.11448e14	−	9.35161e13i	−4.07975	−	3.42332i
$969$		0			0
$970$	−9.83336e13	−	3.57905e13i	−3.56639	−	1.29806i
$971$	−2.01914e13			−0.728920			−0.364460	−	0.931219i	$-0.618746\pi$
$971$	−2.01914e13			−0.728920			−0.364460	+	0.931219i	$0.618746\pi$
$972$		0			0
$973$	2.92804e12			0.104730
$974$	−1.69574e13	−	6.17200e12i	−0.603733	−	0.219741i
$975$		0			0
$976$	−1.02561e14	−	8.60587e13i	−3.61790	−	3.03578i
$977$	−1.70449e12	+	9.66662e12i	−0.0598505	+	0.339429i	−0.999999	−	0.00133561i	$-0.999575\pi$
$977$	−1.70449e12	+	9.66662e12i	−0.0598505	+	0.339429i	0.940149	+	0.340765i	$0.110686\pi$
$978$		0			0
$979$	−2.47348e13	+	2.07550e13i	−0.860572	+	0.722106i
$980$	4.52800e13	+	7.84272e13i	1.56815	+	2.71612i
$981$		0			0
$982$	−2.84759e13	+	4.93217e13i	−0.977182	+	1.69253i
$983$	1.32916e12	+	7.53805e12i	0.0454032	+	0.257495i	0.999057	−	0.0434106i	$-0.0138224\pi$
$983$	1.32916e12	+	7.53805e12i	0.0454032	+	0.257495i	−0.953654	+	0.300905i	$0.902711\pi$
$984$		0			0
$985$	4.09909e13	−	1.49195e13i	1.38747	−	0.504999i
$986$	−5.58972e10	+	2.03449e10i	−0.00188340	+	0.000685503i
$987$		0			0
$988$	2.90061e13	+	1.64502e14i	0.968462	+	5.49242i
$989$	2.59813e12	−	4.50010e12i	0.0863531	−	0.149568i
$990$		0			0
$991$	2.11872e13	+	3.66972e13i	0.697816	+	1.20865i	0.969222	+	0.246188i	$0.0791782\pi$
$991$	2.11872e13	+	3.66972e13i	0.697816	+	1.20865i	−0.271405	+	0.962465i	$0.587488\pi$
$992$	2.17619e13	−	1.82604e13i	0.713499	−	0.598697i
$993$		0			0
$994$	−1.01451e12	+	5.75357e12i	−0.0329623	+	0.186938i
$995$	−2.88790e13	−	2.42324e13i	−0.934069	−	0.783777i
$996$		0			0
$997$	−2.09231e13	−	7.61537e12i	−0.670652	−	0.244097i	−0.0158234	−	0.999875i	$-0.505037\pi$
$997$	−2.09231e13	−	7.61537e12i	−0.670652	−	0.244097i	−0.654829	+	0.755777i	$0.727259\pi$
$998$	−5.59880e13			−1.78652
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.64.26		156
3.2	odd	2		27.10.e.a.4.1	✓	156
27.7	even	9	inner	81.10.e.a.19.26		156
27.20	odd	18		27.10.e.a.7.1	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.1	✓	156	3.2	odd	2
27.10.e.a.7.1	yes	156	27.20	odd	18
81.10.e.a.19.26		156	27.7	even	9	inner
81.10.e.a.64.26		156	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(40.0613 + 14.5811i) q^{2} +(1000.08 + 839.170i) q^{4} +(306.059 - 1735.74i) q^{5} +(764.835 - 641.773i) q^{7} +(16914.7 + 29297.2i) q^{8} +O(q^{10})\)	\(q+(40.0613 + 14.5811i) q^{2} +(1000.08 + 839.170i) q^{4} +(306.059 - 1735.74i) q^{5} +(764.835 - 641.773i) q^{7} +(16914.7 + 29297.2i) q^{8} +(37570.2 - 65073.5i) q^{10} +(-14169.6 - 80359.9i) q^{11} +(142043. - 51699.4i) q^{13} +(39998.1 - 14558.1i) q^{14} +(134370. + 762050. i) q^{16} +(1161.53 - 2011.82i) q^{17} +(423226. + 733050. i) q^{19} +(1.76267e6 - 1.47905e6i) q^{20} +(604084. - 3.42593e6i) q^{22} +(-512754. - 430252. i) q^{23} +(-1.08380e6 - 394471. i) q^{25} +6.44426e6 q^{26} +1.30346e6 q^{28} +(-564405. - 205427. i) q^{29} +(-1.38890e6 - 1.16542e6i) q^{31} +(-2.72080e6 + 1.54304e7i) q^{32} +(75866.9 - 63659.9i) q^{34} +(-879869. - 1.52398e6i) q^{35} +(-900563. + 1.55982e6i) q^{37} +(6.26631e6 + 3.55380e7i) q^{38} +(5.60293e7 - 2.03930e7i) q^{40} +(1.19014e7 - 4.33175e6i) q^{41} +(1.34805e6 + 7.64517e6i) q^{43} +(5.32648e7 - 9.22574e7i) q^{44} +(-1.42680e7 - 2.47130e7i) q^{46} +(6.26487e6 - 5.25685e6i) q^{47} +(-6.83423e6 + 3.87588e7i) q^{49} +(-3.76666e7 - 3.16060e7i) q^{50} +(1.85439e8 + 6.74944e7i) q^{52} +1.05094e7 q^{53} -1.43821e8 q^{55} +(3.17391e7 + 1.15521e7i) q^{56} +(-1.96155e7 - 1.64593e7i) q^{58} +(-2.49733e7 + 1.41631e8i) q^{59} +(-1.32541e8 + 1.11215e8i) q^{61} +(-3.86478e7 - 6.69400e7i) q^{62} +(-1.35897e8 + 2.35381e8i) q^{64} +(-4.62635e7 - 2.62373e8i) q^{65} +(2.06709e8 - 7.52358e7i) q^{67} +(2.84989e6 - 1.03727e6i) q^{68} +(-1.30274e7 - 7.38820e7i) q^{70} +(-6.86282e7 + 1.18868e8i) q^{71} +(-6.59416e7 - 1.14214e8i) q^{73} +(-5.88216e7 + 4.93572e7i) q^{74} +(-1.91891e8 + 1.08827e9i) q^{76} +(-6.24102e7 - 5.23684e7i) q^{77} +(-1.41188e8 - 5.13881e7i) q^{79} +1.36385e9 q^{80} +5.39946e8 q^{82} +(-4.18517e8 - 1.52328e8i) q^{83} +(-3.13652e6 - 2.63185e6i) q^{85} +(-5.74705e7 + 3.25932e8i) q^{86} +(2.11464e9 - 1.77440e9i) q^{88} +(-1.97851e8 - 3.42687e8i) q^{89} +(7.54601e7 - 1.30701e8i) q^{91} +(-1.51743e8 - 8.60576e8i) q^{92} +(3.27630e8 - 1.19247e8i) q^{94} +(1.40192e9 - 5.10257e8i) q^{95} +(-2.41831e8 - 1.37149e9i) q^{97} +(-8.38935e8 + 1.45308e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8}+O(q^{10}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23} + 2192178 q^{25} + 33129678 q^{26} - 12 q^{28} - 19657236 q^{29} - 4633692 q^{31} + 37550952 q^{32} + 14341770 q^{34} - 34449663 q^{35} - 3 q^{37} + 92022060 q^{38} + 6645801 q^{40} + 33127221 q^{41} + 2356203 q^{43} - 1001541 q^{44} - 3 q^{46} + 33488952 q^{47} - 93214644 q^{49} + 72027753 q^{50} + 160531713 q^{52} - 4841352 q^{53} - 12 q^{55} + 91770981 q^{56} - 320682489 q^{58} - 538090854 q^{59} + 36683436 q^{61} + 55862958 q^{62} - 956301315 q^{64} + 852347310 q^{65} - 109026897 q^{67} + 508886217 q^{68} - 815297649 q^{70} - 940878639 q^{71} - 221849931 q^{73} - 838884579 q^{74} + 908401146 q^{76} + 967811358 q^{77} - 1228059150 q^{79} + 2497115154 q^{80} - 12 q^{82} + 297703284 q^{83} + 1535949369 q^{85} - 2930201574 q^{86} + 2837227002 q^{88} - 1774997208 q^{89} + 551343507 q^{91} + 6896645517 q^{92} + 414852915 q^{94} + 9000269169 q^{95} + 3371772333 q^{97} - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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