LMFDB - Embedded newform 656.2.o.a.245.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(245,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("656.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.o (of order $4$, 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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$164$
Relative dimension:	$82$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			245.7
Character	$\chi$	$=$	656.245
Dual form			656.2.o.a.573.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37799 + 0.318038i) q^{2} +(-1.64581 - 1.64581i) q^{3} +(1.79770 - 0.876504i) q^{4} +(1.05875 + 1.05875i) q^{5} +(2.79134 + 1.74448i) q^{6} +0.937357 q^{7} +(-2.19845 + 1.77955i) q^{8} +2.41740i q^{9} +O(q^{10})$	\(q+(-1.37799 + 0.318038i) q^{2} +(-1.64581 - 1.64581i) q^{3} +(1.79770 - 0.876504i) q^{4} +(1.05875 + 1.05875i) q^{5} +(2.79134 + 1.74448i) q^{6} +0.937357 q^{7} +(-2.19845 + 1.77955i) q^{8} +2.41740i q^{9} +(-1.79567 - 1.12222i) q^{10} +(-3.74605 + 3.74605i) q^{11} +(-4.40124 - 1.51612i) q^{12} +(0.659366 + 0.659366i) q^{13} +(-1.29167 + 0.298115i) q^{14} -3.48501i q^{15} +(2.46348 - 3.15139i) q^{16} -5.56372i q^{17} +(-0.768823 - 3.33114i) q^{18} +(-4.91609 - 4.91609i) q^{19} +(2.83132 + 0.975320i) q^{20} +(-1.54271 - 1.54271i) q^{21} +(3.97063 - 6.35341i) q^{22} +7.92682i q^{23} +(6.54705 + 0.689437i) q^{24} -2.75810i q^{25} +(-1.11830 - 0.698895i) q^{26} +(-0.958858 + 0.958858i) q^{27} +(1.68509 - 0.821597i) q^{28} +(0.225032 + 0.225032i) q^{29} +(1.10836 + 4.80230i) q^{30} -6.94370 q^{31} +(-2.39239 + 5.12606i) q^{32} +12.3306 q^{33} +(1.76947 + 7.66674i) q^{34} +(0.992426 + 0.992426i) q^{35} +(2.11886 + 4.34576i) q^{36} +(6.02825 + 6.02825i) q^{37} +(8.33781 + 5.21081i) q^{38} -2.17038i q^{39} +(-4.21171 - 0.443514i) q^{40} +(-3.49691 - 5.36392i) q^{41} +(2.61648 + 1.63520i) q^{42} +(-6.60609 - 6.60609i) q^{43} +(-3.45086 + 10.0177i) q^{44} +(-2.55942 + 2.55942i) q^{45} +(-2.52103 - 10.9231i) q^{46} -2.03944i q^{47} +(-9.24102 + 1.13217i) q^{48} -6.12136 q^{49} +(0.877179 + 3.80063i) q^{50} +(-9.15684 + 9.15684i) q^{51} +(1.76328 + 0.607408i) q^{52} +(-8.26702 + 8.26702i) q^{53} +(1.01634 - 1.62625i) q^{54} -7.93227 q^{55} +(-2.06074 + 1.66807i) q^{56} +16.1819i q^{57} +(-0.381659 - 0.238522i) q^{58} +(-1.96420 - 1.96420i) q^{59} +(-3.05462 - 6.26501i) q^{60} +(-7.57484 + 7.57484i) q^{61} +(9.56834 - 2.20836i) q^{62} +2.26596i q^{63} +(1.66640 - 7.82452i) q^{64} +1.39621i q^{65} +(-16.9914 + 3.92160i) q^{66} +(6.32499 + 6.32499i) q^{67} +(-4.87663 - 10.0019i) q^{68} +(13.0461 - 13.0461i) q^{69} +(-1.68318 - 1.05192i) q^{70} +7.58361 q^{71} +(-4.30188 - 5.31453i) q^{72} +4.21740i q^{73} +(-10.2241 - 6.38964i) q^{74} +(-4.53931 + 4.53931i) q^{75} +(-13.1466 - 4.52870i) q^{76} +(-3.51139 + 3.51139i) q^{77} +(0.690264 + 2.99076i) q^{78} +4.13739i q^{79} +(5.94474 - 0.728325i) q^{80} +10.4084 q^{81} +(6.52462 + 6.27927i) q^{82} +(-8.84563 + 8.84563i) q^{83} +(-4.12554 - 1.42115i) q^{84} +(5.89059 - 5.89059i) q^{85} +(11.2041 + 7.00213i) q^{86} -0.740719i q^{87} +(1.56924 - 14.9018i) q^{88} -17.2781 q^{89} +(2.71286 - 4.34084i) q^{90} +(0.618061 + 0.618061i) q^{91} +(6.94789 + 14.2501i) q^{92} +(11.4280 + 11.4280i) q^{93} +(0.648617 + 2.81032i) q^{94} -10.4098i q^{95} +(12.3740 - 4.49911i) q^{96} +3.29849i q^{97} +(8.43517 - 1.94682i) q^{98} +(-9.05570 - 9.05570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 164 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 16 q^{8}+O(q^{10}) $ 164 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 16 * q^8	$ 164 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 16 q^{8} - 16 q^{10} - 4 q^{16} + 4 q^{18} - 4 q^{20} - 16 q^{21} - 32 q^{31} + 16 q^{32} - 8 q^{33} + 40 q^{36} - 4 q^{37} - 44 q^{40} + 52 q^{42} - 36 q^{43} + 28 q^{45} - 16 q^{46} + 132 q^{49} + 16 q^{50} + 8 q^{51} + 20 q^{59} - 4 q^{61} - 48 q^{62} + 68 q^{64} + 76 q^{66} + 20 q^{72} - 56 q^{74} - 32 q^{77} - 8 q^{78} - 100 q^{80} - 140 q^{81} + 44 q^{82} - 4 q^{83} - 40 q^{84} - 12 q^{86} - 8 q^{90} - 80 q^{91} + 112 q^{92} - 136 q^{98}+O(q^{100}) $ 164 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 16 * q^8 - 16 * q^10 - 4 * q^16 + 4 * q^18 - 4 * q^20 - 16 * q^21 - 32 * q^31 + 16 * q^32 - 8 * q^33 + 40 * q^36 - 4 * q^37 - 44 * q^40 + 52 * q^42 - 36 * q^43 + 28 * q^45 - 16 * q^46 + 132 * q^49 + 16 * q^50 + 8 * q^51 + 20 * q^59 - 4 * q^61 - 48 * q^62 + 68 * q^64 + 76 * q^66 + 20 * q^72 - 56 * q^74 - 32 * q^77 - 8 * q^78 - 100 * q^80 - 140 * q^81 + 44 * q^82 - 4 * q^83 - 40 * q^84 - 12 * q^86 - 8 * q^90 - 80 * q^91 + 112 * q^92 - 136 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.37799	+	0.318038i	−0.974385	+	0.224887i
$2$	−1.37799	+	0.318038i	−0.974385	+	0.224887i
$3$	−1.64581	−	1.64581i	−0.950210	−	0.950210i	0.0486078	−	0.998818i	$-0.484522\pi$
$3$	−1.64581	−	1.64581i	−0.950210	−	0.950210i	−0.998818	+	0.0486078i	$0.984522\pi$
$4$	1.79770	−	0.876504i	0.898852	−	0.438252i
$5$	1.05875	+	1.05875i	0.473487	+	0.473487i	0.903041	−	0.429554i	$-0.141329\pi$
$5$	1.05875	+	1.05875i	0.473487	+	0.473487i	−0.429554	+	0.903041i	$0.641329\pi$
$6$	2.79134	+	1.74448i	1.13956	+	0.712181i
$7$	0.937357			0.354288			0.177144	−	0.984185i	$-0.443314\pi$
$7$	0.937357			0.354288			0.177144	+	0.984185i	$0.443314\pi$
$8$	−2.19845	+	1.77955i	−0.777271	+	0.629166i
$9$			2.41740i			0.805799i
$10$	−1.79567	−	1.12222i	−0.567840	−	0.354878i
$11$	−3.74605	+	3.74605i	−1.12948	+	1.12948i	−0.139216	+	0.990262i	$0.544458\pi$
$11$	−3.74605	+	3.74605i	−1.12948	+	1.12948i	−0.990262	+	0.139216i	$0.955542\pi$
$12$	−4.40124	−	1.51612i	−1.27053	−	0.437667i
$13$	0.659366	+	0.659366i	0.182875	+	0.182875i	0.792607	−	0.609732i	$-0.208723\pi$
$13$	0.659366	+	0.659366i	0.182875	+	0.182875i	−0.609732	+	0.792607i	$0.708723\pi$
$14$	−1.29167	+	0.298115i	−0.345213	+	0.0796745i
$15$		−	3.48501i		−	0.899825i
$16$	2.46348	−	3.15139i	0.615870	−	0.787848i
$17$		−	5.56372i		−	1.34940i	−0.738092	−	0.674700i	$-0.764273\pi$
$17$		−	5.56372i		−	1.34940i	0.738092	−	0.674700i	$-0.235727\pi$
$18$	−0.768823	−	3.33114i	−0.181213	−	0.785158i
$19$	−4.91609	−	4.91609i	−1.12783	−	1.12783i	−0.990530	−	0.137298i	$-0.956158\pi$
$19$	−4.91609	−	4.91609i	−1.12783	−	1.12783i	−0.137298	−	0.990530i	$-0.543842\pi$
$20$	2.83132	+	0.975320i	0.633102	+	0.218088i
$21$	−1.54271	−	1.54271i	−0.336648	−	0.336648i
$22$	3.97063	−	6.35341i	0.846542	−	1.35455i
$23$			7.92682i			1.65286i	0.563042	+	0.826428i	$0.309631\pi$
$23$			7.92682i			1.65286i	−0.563042	+	0.826428i	$0.690369\pi$
$24$	6.54705	+	0.689437i	1.33641	+	0.140731i
$25$		−	2.75810i		−	0.551620i
$26$	−1.11830	−	0.698895i	−0.219317	−	0.137065i
$27$	−0.958858	+	0.958858i	−0.184532	+	0.184532i
$28$	1.68509	−	0.821597i	0.318452	−	0.155267i
$29$	0.225032	+	0.225032i	0.0417873	+	0.0417873i	0.727692	−	0.685904i	$-0.240593\pi$
$29$	0.225032	+	0.225032i	0.0417873	+	0.0417873i	−0.685904	+	0.727692i	$0.740593\pi$
$30$	1.10836	+	4.80230i	0.202358	+	0.876776i
$31$	−6.94370			−1.24713			−0.623563	−	0.781773i	$-0.714316\pi$
$31$	−6.94370			−1.24713			−0.623563	+	0.781773i	$0.714316\pi$
$32$	−2.39239	+	5.12606i	−0.422918	+	0.906168i
$33$	12.3306			2.14648
$34$	1.76947	+	7.66674i	0.303462	+	1.31484i
$35$	0.992426	+	0.992426i	0.167751	+	0.167751i
$36$	2.11886	+	4.34576i	0.353143	+	0.724294i
$37$	6.02825	+	6.02825i	0.991037	+	0.991037i	0.999960	−	0.00892271i	$-0.00284022\pi$
$37$	6.02825	+	6.02825i	0.991037	+	0.991037i	−0.00892271	+	0.999960i	$0.502840\pi$
$38$	8.33781	+	5.21081i	1.35257	+	0.845305i
$39$		−	2.17038i		−	0.347540i
$40$	−4.21171	−	0.443514i	−0.665930	−	0.0701258i
$41$	−3.49691	−	5.36392i	−0.546125	−	0.837704i
$41$	−3.49691	−	5.36392i	−0.546125	−	0.837704i
$42$	2.61648	+	1.63520i	0.403732	+	0.252317i
$43$	−6.60609	−	6.60609i	−1.00742	−	1.00742i	−0.999972	−	0.00744625i	$-0.997630\pi$
$43$	−6.60609	−	6.60609i	−1.00742	−	1.00742i	−0.00744625	−	0.999972i	$-0.502370\pi$
$44$	−3.45086	+	10.0177i	−0.520237	+	1.51023i
$45$	−2.55942	+	2.55942i	−0.381535	+	0.381535i
$46$	−2.52103	−	10.9231i	−0.371705	−	1.61052i
$47$		−	2.03944i		−	0.297482i	−0.988876	−	0.148741i	$-0.952478\pi$
$47$		−	2.03944i		−	0.297482i	0.988876	−	0.148741i	$-0.0475221\pi$
$48$	−9.24102	+	1.13217i	−1.33383	+	0.163415i
$49$	−6.12136			−0.874480
$50$	0.877179	+	3.80063i	0.124052	+	0.537490i
$51$	−9.15684	+	9.15684i	−1.28221	+	1.28221i
$52$	1.76328	+	0.607408i	0.244523	+	0.0842323i
$53$	−8.26702	+	8.26702i	−1.13556	+	1.13556i	−0.146326	+	0.989236i	$0.546745\pi$
$53$	−8.26702	+	8.26702i	−1.13556	+	1.13556i	−0.989236	+	0.146326i	$0.953255\pi$
$54$	1.01634	−	1.62625i	0.138307	−	0.221304i
$55$	−7.93227			−1.06959
$56$	−2.06074	+	1.66807i	−0.275377	+	0.222906i
$57$			16.1819i			2.14335i
$58$	−0.381659	−	0.238522i	−0.0501143	−	0.0313195i
$59$	−1.96420	−	1.96420i	−0.255717	−	0.255717i	0.567592	−	0.823310i	$-0.307875\pi$
$59$	−1.96420	−	1.96420i	−0.255717	−	0.255717i	−0.823310	+	0.567592i	$0.807875\pi$
$60$	−3.05462	−	6.26501i	−0.394350	−	0.808809i
$61$	−7.57484	+	7.57484i	−0.969859	+	0.969859i	−0.999559	−	0.0297000i	$-0.990545\pi$
$61$	−7.57484	+	7.57484i	−0.969859	+	0.969859i	0.0297000	+	0.999559i	$0.490545\pi$
$62$	9.56834	−	2.20836i	1.21518	−	0.280462i
$63$			2.26596i			0.285484i
$64$	1.66640	−	7.82452i	0.208300	−	0.978065i
$65$			1.39621i			0.173178i
$66$	−16.9914	+	3.92160i	−2.09150	+	0.482715i
$67$	6.32499	+	6.32499i	0.772721	+	0.772721i	0.978581	−	0.205861i	$-0.0659994\pi$
$67$	6.32499	+	6.32499i	0.772721	+	0.772721i	−0.205861	+	0.978581i	$0.565999\pi$
$68$	−4.87663	−	10.0019i	−0.591378	−	1.21291i
$69$	13.0461	−	13.0461i	1.57056	−	1.57056i
$70$	−1.68318	−	1.05192i	−0.201179	−	0.125729i
$71$	7.58361			0.900009			0.450005	−	0.893026i	$-0.351422\pi$
$71$	7.58361			0.900009			0.450005	+	0.893026i	$0.351422\pi$
$72$	−4.30188	−	5.31453i	−0.506981	−	0.626324i
$73$			4.21740i			0.493610i	0.969065	+	0.246805i	$0.0793807\pi$
$73$			4.21740i			0.493610i	−0.969065	+	0.246805i	$0.920619\pi$
$74$	−10.2241	−	6.38964i	−1.18852	−	0.742781i
$75$	−4.53931	+	4.53931i	−0.524155	+	0.524155i
$76$	−13.1466	−	4.52870i	−1.50802	−	0.519477i
$77$	−3.51139	+	3.51139i	−0.400160	+	0.400160i
$78$	0.690264	+	2.99076i	0.0781570	+	0.338637i
$79$			4.13739i			0.465493i	0.972537	+	0.232746i	$0.0747712\pi$
$79$			4.13739i			0.465493i	−0.972537	+	0.232746i	$0.925229\pi$
$80$	5.94474	−	0.728325i	0.664642	−	0.0814292i
$81$	10.4084			1.15649
$82$	6.52462	+	6.27927i	0.720524	+	0.693430i
$83$	−8.84563	+	8.84563i	−0.970934	+	0.970934i	−0.999589	−	0.0286550i	$-0.990878\pi$
$83$	−8.84563	+	8.84563i	−0.970934	+	0.970934i	0.0286550	+	0.999589i	$0.490878\pi$
$84$	−4.12554	−	1.42115i	−0.450133	−	0.155060i
$85$	5.89059	−	5.89059i	0.638924	−	0.638924i
$86$	11.2041	+	7.00213i	1.20817	+	0.755059i
$87$		−	0.740719i		−	0.0794135i
$88$	1.56924	−	14.9018i	0.167281	−	1.58854i
$89$	−17.2781			−1.83147			−0.915736	−	0.401781i	$-0.868391\pi$
$89$	−17.2781			−1.83147			−0.915736	+	0.401781i	$0.868391\pi$
$90$	2.71286	−	4.34084i	0.285960	−	0.457564i
$91$	0.618061	+	0.618061i	0.0647904	+	0.0647904i
$92$	6.94789	+	14.2501i	0.724368	+	1.48567i
$93$	11.4280	+	11.4280i	1.18503	+	1.18503i
$94$	0.648617	+	2.81032i	0.0668998	+	0.289862i
$95$		−	10.4098i		−	1.06802i
$96$	12.3740	−	4.49911i	1.26291	−	0.459189i
$97$			3.29849i			0.334911i	0.985880	+	0.167455i	$0.0535550\pi$
$97$			3.29849i			0.334911i	−0.985880	+	0.167455i	$0.946445\pi$
$98$	8.43517	−	1.94682i	0.852080	−	0.196659i
$99$	−9.05570	−	9.05570i	−0.910132	−	0.910132i
$100$	−2.41749	−	4.95825i	−0.241749	−	0.495825i
$101$	−5.42968	+	5.42968i	−0.540274	+	0.540274i	−0.923609	−	0.383336i	$-0.874775\pi$
$101$	−5.42968	+	5.42968i	−0.540274	+	0.540274i	0.383336	+	0.923609i	$0.374775\pi$
$102$	9.70580	−	15.5302i	0.961018	−	1.53772i
$103$		−	14.8634i		−	1.46453i	−0.681020	−	0.732265i	$-0.738463\pi$
$103$		−	14.8634i		−	1.46453i	0.681020	−	0.732265i	$-0.261537\pi$
$104$	−2.62296	−	0.276211i	−0.257202	−	0.0270847i
$105$		−	3.26669i		−	0.318797i
$106$	8.76263	−	14.0211i	0.851102	−	1.36185i
$107$	6.02159	+	6.02159i	0.582129	+	0.582129i	0.935488	−	0.353359i	$-0.114960\pi$
$107$	6.02159	+	6.02159i	0.582129	+	0.582129i	−0.353359	+	0.935488i	$0.614960\pi$
$108$	−0.883299	+	2.56419i	−0.0849955	+	0.246739i
$109$	0.319278	+	0.319278i	0.0305813	+	0.0305813i	0.722232	−	0.691651i	$-0.243116\pi$
$109$	0.319278	+	0.319278i	0.0305813	+	0.0305813i	−0.691651	+	0.722232i	$0.743116\pi$
$110$	10.9306	−	2.52276i	1.04219	−	0.240536i
$111$		−	19.8427i		−	1.88339i
$112$	2.30916	−	2.95398i	0.218195	−	0.279125i
$113$	10.1953			0.959089			0.479544	−	0.877518i	$-0.340802\pi$
$113$	10.1953			0.959089			0.479544	+	0.877518i	$0.340802\pi$
$114$	−5.14646	−	22.2985i	−0.482010	−	2.08844i
$115$	−8.39252	+	8.39252i	−0.782607	+	0.782607i
$116$	0.601781	+	0.207299i	0.0558740	+	0.0192472i
$117$	−1.59395	+	1.59395i	−0.147361	+	0.147361i
$118$	3.33134	+	2.08196i	0.306674	+	0.191660i
$119$		−	5.21519i		−	0.478076i
$120$	6.20174	+	7.66163i	0.566139	+	0.699408i
$121$		−	17.0659i		−	1.55144i
$122$	8.02896	−	12.8471i	0.726908	−	1.16312i
$123$	−3.07276	+	14.5833i	−0.277061	+	1.31493i
$124$	−12.4827	+	6.08619i	−1.12098	+	0.546556i
$125$	8.21388	−	8.21388i	0.734672	−	0.734672i
$126$	−0.720661	−	3.12247i	−0.0642016	−	0.278172i
$127$	−1.86845			−0.165798			−0.0828992	−	0.996558i	$-0.526418\pi$
$127$	−1.86845			−0.165798			−0.0828992	+	0.996558i	$0.526418\pi$
$128$	0.192210	+	11.3121i	0.0169891	+	0.999856i
$129$			21.7448i			1.91452i
$130$	−0.444046	−	1.92396i	−0.0389454	−	0.168742i
$131$	6.76621	−	6.76621i	0.591167	−	0.591167i	−0.346780	−	0.937947i	$-0.612725\pi$
$131$	6.76621	−	6.76621i	0.591167	−	0.591167i	0.937947	+	0.346780i	$0.112725\pi$
$132$	22.1668	−	10.8078i	1.92937	−	0.940701i
$133$	−4.60813	−	4.60813i	−0.399575	−	0.399575i
$134$	−10.7273	−	6.70418i	−0.926702	−	0.579153i
$135$	−2.03038			−0.174747
$136$	9.90092	+	12.2316i	0.848997	+	1.04885i
$137$	−2.18124			−0.186356			−0.0931781	−	0.995649i	$-0.529703\pi$
$137$	−2.18124			−0.186356			−0.0931781	+	0.995649i	$0.529703\pi$
$138$	−13.8282	+	22.1265i	−1.17713	+	1.88353i
$139$	−9.50390	−	9.50390i	−0.806110	−	0.806110i	0.177933	−	0.984043i	$-0.443059\pi$
$139$	−9.50390	−	9.50390i	−0.806110	−	0.806110i	−0.984043	+	0.177933i	$0.943059\pi$
$140$	2.65396	+	0.914223i	0.224300	+	0.0772659i
$141$	−3.35653	+	3.35653i	−0.282671	+	0.282671i
$142$	−10.4501	+	2.41187i	−0.876956	+	0.202400i
$143$	−4.94004			−0.413107
$144$	7.61816	+	5.95521i	0.634847	+	0.496267i
$145$			0.476504i			0.0395715i
$146$	−1.34129	−	5.81153i	−0.111006	−	0.480966i
$147$	10.0746	+	10.0746i	0.830940	+	0.830940i
$148$	16.1208	+	5.55322i	1.32512	+	0.456472i
$149$	−3.26161	+	3.26161i	−0.267201	+	0.267201i	−0.827971	−	0.560770i	$-0.810505\pi$
$149$	−3.26161	+	3.26161i	−0.267201	+	0.267201i	0.560770	+	0.827971i	$0.310505\pi$
$150$	4.81145	−	7.69879i	0.392853	−	0.628604i
$151$	22.2846			1.81350			0.906748	−	0.421672i	$-0.138557\pi$
$151$	22.2846			1.81350			0.906748	+	0.421672i	$0.138557\pi$
$152$	19.5562	+	2.05937i	1.58622	+	0.167037i
$153$	13.4497			1.08735
$154$	3.72190	−	5.95541i	0.299919	−	0.479901i
$155$	−7.35164	−	7.35164i	−0.590498	−	0.590498i
$156$	−1.90235	−	3.90171i	−0.152310	−	0.312387i
$157$	−4.67424	−	4.67424i	−0.373045	−	0.373045i	0.495540	−	0.868585i	$-0.334970\pi$
$157$	−4.67424	−	4.67424i	−0.373045	−	0.373045i	−0.868585	+	0.495540i	$0.834970\pi$
$158$	−1.31585	−	5.70128i	−0.104683	−	0.453569i
$159$	27.2119			2.15805
$160$	−7.96015	+	2.89428i	−0.629305	+	0.228813i
$161$			7.43026i			0.585587i
$162$	−14.3426	+	3.31026i	−1.12686	+	0.260078i
$163$	1.78040	−	1.78040i	0.139451	−	0.139451i	−0.633935	−	0.773386i	$-0.718561\pi$
$163$	1.78040	−	1.78040i	0.139451	−	0.139451i	0.773386	+	0.633935i	$0.218561\pi$
$164$	−10.9879	−	6.57769i	−0.858011	−	0.513631i
$165$	13.0550	+	13.0550i	1.01633	+	1.01633i
$166$	9.37594	−	15.0024i	0.727714	−	1.16441i
$167$	14.7022			1.13769			0.568846	−	0.822444i	$-0.307390\pi$
$167$	14.7022			1.13769			0.568846	+	0.822444i	$0.307390\pi$
$168$	6.13692	+	0.646249i	0.473474	+	0.0498592i
$169$		−	12.1305i		−	0.933113i
$170$	−6.24373	+	9.99059i	−0.478873	+	0.766243i
$171$	11.8841	−	11.8841i	0.908802	−	0.908802i
$172$	−17.6660	−	6.08552i	−1.34702	−	0.464017i
$173$	−3.32221	+	3.32221i	−0.252583	+	0.252583i	−0.822029	−	0.569446i	$-0.807158\pi$
$173$	−3.32221	+	3.32221i	−0.252583	+	0.252583i	0.569446	+	0.822029i	$0.307158\pi$
$174$	0.235577	+	1.02070i	0.0178590	+	0.0773793i
$175$		−	2.58532i		−	0.195432i
$176$	2.57695	+	21.0336i	0.194245	+	1.58547i
$177$			6.46541i			0.485970i
$178$	23.8090	−	5.49508i	1.78456	−	0.411873i
$179$	−10.7296	−	10.7296i	−0.801968	−	0.801968i	0.181435	−	0.983403i	$-0.441926\pi$
$179$	−10.7296	−	10.7296i	−0.801968	−	0.801968i	−0.983403	+	0.181435i	$0.941926\pi$
$180$	−2.35773	+	6.84441i	−0.175735	+	0.510152i
$181$	3.45819	−	3.45819i	0.257045	−	0.257045i	−0.566806	−	0.823851i	$-0.691821\pi$
$181$	3.45819	−	3.45819i	0.257045	−	0.257045i	0.823851	+	0.566806i	$0.191821\pi$
$182$	−1.04825	−	0.655114i	−0.0777013	−	0.0485603i
$183$	24.9335			1.84314
$184$	−14.1062	−	17.4268i	−1.03992	−	1.28472i
$185$			12.7648i			0.938487i
$186$	−19.3822	−	12.1132i	−1.42117	−	0.888179i
$187$	20.8420	+	20.8420i	1.52412	+	1.52412i
$188$	−1.78757	−	3.66630i	−0.130372	−	0.267393i
$189$	−0.898792	+	0.898792i	−0.0653775	+	0.0653775i
$190$	3.31071	+	14.3446i	0.240184	+	1.04067i
$191$			15.7205i			1.13750i	0.822512	+	0.568748i	$0.192572\pi$
$191$			15.7205i			1.13750i	−0.822512	+	0.568748i	$0.807428\pi$
$192$	−15.6203	+	10.1351i	−1.12730	+	0.731438i
$193$			0.977304i			0.0703479i	0.999381	+	0.0351739i	$0.0111985\pi$
$193$			0.977304i			0.0703479i	−0.999381	+	0.0351739i	$0.988801\pi$
$194$	−1.04904	−	4.54528i	−0.0753169	−	0.326332i
$195$	2.29789	−	2.29789i	0.164556	−	0.164556i
$196$	−11.0044	+	5.36540i	−0.786028	+	0.383243i
$197$	−17.4268	−	17.4268i	−1.24161	−	1.24161i	−0.959335	−	0.282271i	$-0.908912\pi$
$197$	−17.4268	−	17.4268i	−1.24161	−	1.24161i	−0.282271	−	0.959335i	$-0.591088\pi$
$198$	15.3587	+	9.59859i	1.09149	+	0.682142i
$199$	−23.6963			−1.67979			−0.839894	−	0.542751i	$-0.817383\pi$
$199$	−23.6963			−1.67979			−0.839894	+	0.542751i	$0.817383\pi$
$200$	4.90818	+	6.06355i	0.347060	+	0.428758i
$201$		−	20.8195i		−	1.46849i
$202$	5.75520	−	9.20888i	0.404934	−	0.647935i
$203$	0.210935	+	0.210935i	0.0148047	+	0.0148047i
$204$	−8.43528	+	24.4873i	−0.590588	+	1.71445i
$205$	1.97670	−	9.38140i	0.138059	−	0.655225i
$206$	4.72711	+	20.4815i	0.329353	+	1.42702i
$207$	−19.1623			−1.33187
$208$	3.70225	−	0.453585i	0.256705	−	0.0314504i
$209$	36.8319			2.54771
$210$	1.03893	+	4.50147i	0.0716931	+	0.310631i
$211$	1.05855	+	1.05855i	0.0728738	+	0.0728738i	0.742604	−	0.669730i	$-0.233590\pi$
$211$	1.05855	+	1.05855i	0.0728738	+	0.0728738i	−0.669730	+	0.742604i	$0.733590\pi$
$212$	−7.61558	+	22.1077i	−0.523040	+	1.51837i
$213$	−12.4812	−	12.4812i	−0.855198	−	0.855198i
$214$	−10.2128	−	6.38259i	−0.698131	−	0.436305i
$215$		−	13.9884i		−	0.954000i
$216$	0.401669	−	3.81434i	0.0273301	−	0.259533i
$217$	−6.50873			−0.441841
$218$	−0.541504	−	0.338419i	−0.0366753	−	0.0229206i
$219$	6.94105	−	6.94105i	0.469033	−	0.469033i
$220$	−14.2599	+	6.95267i	−0.961400	+	0.468749i
$221$	3.66853	−	3.66853i	0.246772	−	0.246772i
$222$	6.31073	+	27.3430i	0.423549	+	1.83514i
$223$	−7.80529			−0.522681			−0.261340	−	0.965247i	$-0.584165\pi$
$223$	−7.80529			−0.522681			−0.261340	+	0.965247i	$0.584165\pi$
$224$	−2.24252	+	4.80495i	−0.149835	+	0.321044i
$225$	6.66741			0.444494
$226$	−14.0489	+	3.24247i	−0.934522	+	0.215686i
$227$	−7.02985	−	7.02985i	−0.466587	−	0.466587i	0.434220	−	0.900807i	$-0.357024\pi$
$227$	−7.02985	−	7.02985i	−0.466587	−	0.466587i	−0.900807	+	0.434220i	$0.857024\pi$
$228$	14.1835	+	29.0903i	0.939326	+	1.92655i
$229$	−12.2934	+	12.2934i	−0.812373	+	0.812373i	−0.984989	−	0.172616i	$-0.944778\pi$
$229$	−12.2934	+	12.2934i	−0.812373	+	0.812373i	0.172616	+	0.984989i	$0.444778\pi$
$230$	8.89566	−	14.2339i	0.586562	−	0.938558i
$231$	11.5582			0.760472
$232$	−0.895177	−	0.0942666i	−0.0587712	−	0.00618890i
$233$	−2.38502			−0.156248			−0.0781239	−	0.996944i	$-0.524893\pi$
$233$	−2.38502			−0.156248			−0.0781239	+	0.996944i	$0.524893\pi$
$234$	1.68951	−	2.70338i	0.110446	−	0.176725i
$235$	2.15925	−	2.15925i	0.140854	−	0.140854i
$236$	−5.25269	−	1.80942i	−0.341921	−	0.117783i
$237$	6.80937	−	6.80937i	0.442316	−	0.442316i
$238$	1.65863	+	7.18648i	0.107513	+	0.465830i
$239$		−	9.45338i		−	0.611488i	−0.952114	−	0.305744i	$-0.901095\pi$
$239$		−	9.45338i		−	0.611488i	0.952114	−	0.305744i	$-0.0989052\pi$
$240$	−10.9826	−	8.58524i	−0.708925	−	0.554175i
$241$	14.8486			0.956484			0.478242	−	0.878228i	$-0.341274\pi$
$241$	14.8486			0.956484			0.478242	+	0.878228i	$0.341274\pi$
$242$	5.42758	+	23.5165i	0.348898	+	1.51170i
$243$	−14.2537	−	14.2537i	−0.914374	−	0.914374i
$244$	−6.97794	+	20.2567i	−0.446717	+	1.29680i
$245$	−6.48099	−	6.48099i	−0.414055	−	0.414055i
$246$	−0.403800	−	21.0728i	−0.0257453	−	1.34355i
$247$		−	6.48300i		−	0.412503i
$248$	15.2654	−	12.3567i	0.969355	−	0.784649i
$249$	29.1165			1.84518
$250$	−8.70631	+	13.9310i	−0.550636	+	0.881071i
$251$	−1.35201	−	1.35201i	−0.0853383	−	0.0853383i	0.663149	−	0.748487i	$-0.269220\pi$
$251$	−1.35201	−	1.35201i	−0.0853383	−	0.0853383i	−0.748487	+	0.663149i	$0.769220\pi$
$252$	1.98613	+	4.07353i	0.125114	+	0.256608i
$253$	−29.6943	−	29.6943i	−1.86687	−	1.86687i
$254$	2.57471	−	0.594238i	0.161551	−	0.0372858i
$255$	−19.3896			−1.21422
$256$	−3.86253	−	15.5268i	−0.241408	−	0.970424i
$257$			17.5287i			1.09341i	0.837325	+	0.546706i	$0.184118\pi$
$257$			17.5287i			1.09341i	−0.837325	+	0.546706i	$0.815882\pi$
$258$	−6.91565	−	29.9640i	−0.430549	−	1.86548i
$259$	5.65062	+	5.65062i	0.351112	+	0.351112i
$260$	1.22378	+	2.50997i	0.0758957	+	0.155662i
$261$	−0.543990	+	0.543990i	−0.0336722	+	0.0336722i
$262$	−7.17185	+	11.4757i	−0.443079	+	0.708970i
$263$	−9.33597			−0.575681			−0.287840	−	0.957678i	$-0.592937\pi$
$263$	−9.33597			−0.575681			−0.287840	+	0.957678i	$0.592937\pi$
$264$	−27.1083	+	21.9429i	−1.66840	+	1.35049i
$265$	−17.5054			−1.07535
$266$	7.81551	+	4.88439i	0.479200	+	0.299481i
$267$	28.4365	+	28.4365i	1.74028	+	1.74028i
$268$	16.9143	+	5.82658i	1.03321	+	0.355915i
$269$	−1.79282	+	1.79282i	−0.109310	+	0.109310i	−0.759646	−	0.650336i	$-0.774628\pi$
$269$	−1.79282	+	1.79282i	−0.109310	+	0.109310i	0.650336	+	0.759646i	$0.274628\pi$
$270$	2.79784	−	0.645737i	0.170271	−	0.0392983i
$271$	−25.0064			−1.51903			−0.759515	−	0.650490i	$-0.774563\pi$
$271$	−25.0064			−1.51903			−0.759515	+	0.650490i	$0.774563\pi$
$272$	−17.5335	−	13.7061i	−1.06312	−	0.831056i
$273$		−	2.03443i		−	0.123129i
$274$	3.00573	−	0.693717i	0.181583	−	0.0419090i
$275$	10.3320	+	10.3320i	0.623042	+	0.623042i
$276$	12.0180	−	34.8879i	0.723400	−	2.10000i
$277$	−0.245403	−	0.245403i	−0.0147448	−	0.0147448i	0.699696	−	0.714441i	$-0.253319\pi$
$277$	−0.245403	−	0.245403i	−0.0147448	−	0.0147448i	−0.714441	+	0.699696i	$0.753319\pi$
$278$	16.1189	+	10.0737i	0.966745	+	0.604178i
$279$		−	16.7857i		−	1.00493i
$280$	−3.94788	−	0.415731i	−0.235931	−	0.0248447i
$281$	18.0981			1.07964			0.539821	−	0.841780i	$-0.318492\pi$
$281$	18.0981			1.07964			0.539821	+	0.841780i	$0.318492\pi$
$282$	3.55776	−	5.69276i	0.211861	−	0.338999i
$283$	−5.83493	−	5.83493i	−0.346850	−	0.346850i	0.512085	−	0.858935i	$-0.328873\pi$
$283$	−5.83493	−	5.83493i	−0.346850	−	0.346850i	−0.858935	+	0.512085i	$0.828873\pi$
$284$	13.6331	−	6.64707i	0.808975	−	0.394431i
$285$	−17.1326	+	17.1326i	−1.01485	+	1.01485i
$286$	6.80732	−	1.57112i	0.402525	−	0.0929022i
$287$	−3.27785	−	5.02791i	−0.193485	−	0.296788i
$288$	−12.3917	−	5.78334i	−0.730189	−	0.340787i
$289$	−13.9550			−0.820883
$290$	−0.151546	−	0.656617i	−0.00889910	−	0.0385579i
$291$	5.42869	−	5.42869i	0.318235	−	0.318235i
$292$	3.69657	+	7.58164i	0.216325	+	0.443682i
$293$	12.9628	−	12.9628i	0.757297	−	0.757297i	−0.218532	−	0.975830i	$-0.570127\pi$
$293$	12.9628	−	12.9628i	0.757297	−	0.757297i	0.975830	+	0.218532i	$0.0701269\pi$
$294$	−17.0868	−	10.6786i	−0.996523	−	0.622788i
$295$		−	4.15920i		−	0.242158i
$296$	−23.9804	−	2.52526i	−1.39383	−	0.146777i
$297$		−	7.18387i		−	0.416850i
$298$	3.45714	−	5.53177i	0.200267	−	0.320447i
$299$	−5.22668	+	5.22668i	−0.302266	+	0.302266i
$300$	−4.18161	+	12.1391i	−0.241426	+	0.700849i
$301$	−6.19226	−	6.19226i	−0.356916	−	0.356916i
$302$	−30.7079	+	7.08735i	−1.76704	+	0.407831i
$303$	17.8725			1.02675
$304$	−27.6032	+	3.38183i	−1.58315	+	0.193961i
$305$	−16.0397			−0.918432
$306$	−18.5336	+	4.27752i	−1.05949	+	0.244529i
$307$	15.1662	−	15.1662i	0.865581	−	0.865581i	−0.126398	−	0.991980i	$-0.540342\pi$
$307$	15.1662	−	15.1662i	0.865581	−	0.865581i	0.991980	+	0.126398i	$0.0403417\pi$
$308$	−3.23469	+	9.39019i	−0.184314	+	0.535056i
$309$	−24.4623	+	24.4623i	−1.39161	+	1.39161i
$310$	12.4686	+	7.79238i	0.708168	+	0.442578i
$311$	10.1110			0.573341			0.286671	−	0.958029i	$-0.407451\pi$
$311$	10.1110			0.573341			0.286671	+	0.958029i	$0.407451\pi$
$312$	3.86231	+	4.77149i	0.218660	+	0.270132i
$313$	8.01296			0.452919			0.226460	−	0.974021i	$-0.427285\pi$
$313$	8.01296			0.452919			0.226460	+	0.974021i	$0.427285\pi$
$314$	7.92764	+	4.95447i	0.447383	+	0.279597i
$315$	−2.39909	+	2.39909i	−0.135173	+	0.135173i
$316$	3.62644	+	7.43781i	0.204003	+	0.418409i
$317$	5.50093	+	5.50093i	0.308963	+	0.308963i	0.844507	−	0.535544i	$-0.179893\pi$
$317$	5.50093	+	5.50093i	0.308963	+	0.308963i	−0.535544	+	0.844507i	$0.679893\pi$
$318$	−37.4977	+	8.65441i	−2.10277	+	0.485315i
$319$	−1.68596			−0.0943957
$320$	10.0485	−	6.51991i	0.561729	−	0.364474i
$321$		−	19.8208i		−	1.10629i
$322$	−2.36310	−	10.2388i	−0.131691	−	0.570587i
$323$	−27.3517	+	27.3517i	−1.52189	+	1.52189i
$324$	18.7112	−	9.12299i	1.03951	−	0.506833i
$325$	1.81860	−	1.81860i	0.100878	−	0.100878i
$326$	−1.88713	+	3.01960i	−0.104519	+	0.167240i
$327$		−	1.05094i		−	0.0581173i
$328$	17.2332	+	5.56942i	0.951542	+	0.307520i
$329$		−	1.91168i		−	0.105394i
$330$	−22.1417	−	13.8377i	−1.21886	−	0.761739i
$331$	19.4013	−	19.4013i	1.06639	−	1.06639i	0.0687577	−	0.997633i	$-0.478096\pi$
$331$	19.4013	−	19.4013i	1.06639	−	1.06639i	0.997633	−	0.0687577i	$-0.0219035\pi$
$332$	−8.14860	+	23.6551i	−0.447212	+	1.29824i
$333$	−14.5727	+	14.5727i	−0.798577	+	0.798577i
$334$	−20.2595	+	4.67586i	−1.10855	+	0.255852i
$335$			13.3932i			0.731747i
$336$	−8.66214	+	1.06125i	−0.472558	+	0.0578959i
$337$	6.67510			0.363616			0.181808	−	0.983334i	$-0.441805\pi$
$337$	6.67510			0.363616			0.181808	+	0.983334i	$0.441805\pi$
$338$	3.85795	+	16.7157i	0.209845	+	0.909212i
$339$	−16.7795	−	16.7795i	−0.911336	−	0.911336i
$340$	5.42641	−	15.7527i	0.294288	−	0.854308i
$341$	26.0115	−	26.0115i	1.40860	−	1.40860i
$342$	−12.5966	+	20.1558i	−0.681146	+	1.08990i
$343$	−12.2994			−0.664105
$344$	26.2790	+	2.76731i	1.41687	+	0.149204i
$345$	27.6250			1.48728
$346$	3.52138	−	5.63456i	0.189311	−	0.302916i
$347$	5.77407	−	5.77407i	0.309968	−	0.309968i	−0.534929	−	0.844897i	$-0.679662\pi$
$347$	5.77407	−	5.77407i	0.309968	−	0.309968i	0.844897	+	0.534929i	$0.179662\pi$
$348$	−0.649244	−	1.33159i	−0.0348031	−	0.0713810i
$349$	10.0447	−	10.0447i	0.537683	−	0.537683i	−0.385165	−	0.922848i	$-0.625855\pi$
$349$	10.0447	−	10.0447i	0.537683	−	0.537683i	0.922848	+	0.385165i	$0.125855\pi$
$350$	0.822230	+	3.56255i	0.0439500	+	0.190426i
$351$	−1.26448			−0.0674927
$352$	−10.2405	−	28.1645i	−0.545820	−	1.50117i
$353$	−9.60947			−0.511460			−0.255730	−	0.966748i	$-0.582316\pi$
$353$	−9.60947			−0.511460			−0.255730	+	0.966748i	$0.582316\pi$
$354$	−2.05625	−	8.90927i	−0.109288	−	0.473522i
$355$	8.02915	+	8.02915i	0.426143	+	0.426143i
$356$	−31.0609	+	15.1443i	−1.64622	+	0.802646i
$357$	−8.58323	+	8.58323i	−0.454273	+	0.454273i
$358$	18.1977	+	11.3729i	0.961778	+	0.601074i
$359$		−	24.2866i		−	1.28180i	−0.767625	−	0.640899i	$-0.778562\pi$
$359$		−	24.2866i		−	1.28180i	0.767625	−	0.640899i	$-0.221438\pi$
$360$	1.07215	−	10.1814i	0.0565072	−	0.536605i
$361$			29.3358i			1.54399i
$362$	−3.66551	+	5.86517i	−0.192655	+	0.308267i
$363$	−28.0872	+	28.0872i	−1.47419	+	1.47419i
$364$	1.65282	+	0.569358i	0.0866315	+	0.0298425i
$365$	−4.46517	+	4.46517i	−0.233718	+	0.233718i
$366$	−34.3581	+	7.92980i	−1.79593	+	0.414497i
$367$	23.9412			1.24972			0.624860	−	0.780737i	$-0.285156\pi$
$367$	23.9412			1.24972			0.624860	+	0.780737i	$0.285156\pi$
$368$	24.9805	+	19.5276i	1.30220	+	1.01795i
$369$	12.9667	−	8.45340i	0.675020	−	0.440067i
$370$	−4.05969	−	17.5898i	−0.211053	−	0.914448i
$371$	−7.74915	+	7.74915i	−0.402316	+	0.402316i
$372$	30.5609	+	10.5275i	1.58451	+	0.545826i
$373$	13.1053	+	13.1053i	0.678566	+	0.678566i	0.959676	−	0.281110i	$-0.0907024\pi$
$373$	13.1053	+	13.1053i	0.678566	+	0.678566i	−0.281110	+	0.959676i	$0.590702\pi$
$374$	−35.3486	−	22.0915i	−1.82783	−	1.14232i
$375$	−27.0370			−1.39619
$376$	3.62928	+	4.48361i	0.187166	+	0.231224i
$377$			0.296756i			0.0152837i
$378$	0.952675	−	1.52437i	0.0490003	−	0.0784054i
$379$	11.3137	+	11.3137i	0.581148	+	0.581148i	0.935219	−	0.354070i	$-0.115203\pi$
$379$	11.3137	+	11.3137i	0.581148	+	0.581148i	−0.354070	+	0.935219i	$0.615203\pi$
$380$	−9.12425	−	18.7138i	−0.468064	−	0.959996i
$381$	3.07512	+	3.07512i	0.157543	+	0.157543i
$382$	−4.99971	−	21.6627i	−0.255808	−	1.10836i
$383$			3.91158i			0.199873i	0.994994	+	0.0999363i	$0.0318639\pi$
$383$			3.91158i			0.199873i	−0.994994	+	0.0999363i	$0.968136\pi$
$384$	18.3012	−	18.9339i	0.933930	−	0.966216i
$385$	−7.43537			−0.378941
$386$	−0.310819	−	1.34671i	−0.0158203	−	0.0685459i
$387$	15.9695	−	15.9695i	0.811776	−	0.811776i
$388$	2.89114	+	5.92970i	0.146775	+	0.301035i
$389$	3.68359	+	3.68359i	0.186765	+	0.186765i	0.794296	−	0.607531i	$-0.207840\pi$
$389$	3.68359	+	3.68359i	0.186765	+	0.186765i	−0.607531	+	0.794296i	$0.707840\pi$
$390$	−2.43565	+	3.89729i	−0.123334	+	0.197347i
$391$	44.1026			2.23037
$392$	13.4575	−	10.8933i	0.679708	−	0.550193i
$393$	−22.2718			−1.12347
$394$	29.5563	+	18.4715i	1.48902	+	0.930582i
$395$	−4.38046	+	4.38046i	−0.220405	+	0.220405i
$396$	−24.2168	−	8.34211i	−1.21694	−	0.419207i
$397$	16.9158	+	16.9158i	0.848981	+	0.848981i	0.990006	−	0.141025i	$-0.0450399\pi$
$397$	16.9158	+	16.9158i	0.848981	+	0.848981i	−0.141025	+	0.990006i	$0.545040\pi$
$398$	32.6532	−	7.53632i	1.63676	−	0.377762i
$399$			15.1682i			0.759361i
$400$	−8.69185	−	6.79452i	−0.434592	−	0.339726i
$401$	−6.68430			−0.333798			−0.166899	−	0.985974i	$-0.553375\pi$
$401$	−6.68430			−0.333798			−0.166899	+	0.985974i	$0.553375\pi$
$402$	6.62138	+	28.6890i	0.330245	+	1.43088i
$403$	−4.57844	−	4.57844i	−0.228068	−	0.228068i
$404$	−5.00182	+	14.5201i	−0.248850	+	0.722402i
$405$	11.0199	+	11.0199i	0.547582	+	0.547582i
$406$	−0.357751	−	0.223581i	−0.0177549	−	0.0110961i
$407$	−45.1643			−2.23871
$408$	3.83584	−	36.4260i	0.189902	−	1.80335i
$409$			10.5773i			0.523016i	0.965201	+	0.261508i	$0.0842198\pi$
$409$			10.5773i			0.523016i	−0.965201	+	0.261508i	$0.915780\pi$
$410$	0.259764	+	13.5561i	0.0128288	+	0.669489i
$411$	3.58992	+	3.58992i	0.177078	+	0.177078i
$412$	−13.0278	−	26.7199i	−0.641833	−	1.31640i
$413$	−1.84116	−	1.84116i	−0.0905975	−	0.0905975i
$414$	26.4054	−	6.09432i	1.29775	−	0.299520i
$415$	−18.7306			−0.919450
$416$	−4.95741	+	1.80249i	−0.243057	+	0.0883744i
$417$			31.2833i			1.53195i
$418$	−50.7539	+	11.7139i	−2.48245	+	0.572947i
$419$	−12.6697	+	12.6697i	−0.618956	+	0.618956i	−0.945264	−	0.326307i	$-0.894196\pi$
$419$	−12.6697	+	12.6697i	−0.618956	+	0.618956i	0.326307	+	0.945264i	$0.394196\pi$
$420$	−2.86327	−	5.87255i	−0.139713	−	0.286551i
$421$	5.71221	−	5.71221i	0.278396	−	0.278396i	−0.554072	−	0.832468i	$-0.686927\pi$
$421$	5.71221	−	5.71221i	0.278396	−	0.278396i	0.832468	+	0.554072i	$0.186927\pi$
$422$	−1.79533	−	1.12201i	−0.0873955	−	0.0546188i
$423$	4.93012			0.239711
$424$	3.46309	−	32.8862i	0.168182	−	1.59710i
$425$	−15.3453			−0.744356
$426$	21.1684	+	13.2295i	1.02561	+	0.640970i
$427$	−7.10033	+	7.10033i	−0.343609	+	0.343609i
$428$	16.1030	+	5.54709i	0.778367	+	0.268129i
$429$	8.13038	+	8.13038i	0.392538	+	0.392538i
$430$	4.44883	+	19.2758i	0.214542	+	0.929563i
$431$	15.7038			0.756424			0.378212	−	0.925719i	$-0.376539\pi$
$431$	15.7038			0.756424			0.378212	+	0.925719i	$0.376539\pi$
$432$	0.659608	+	5.38386i	0.0317354	+	0.259031i
$433$	0.791646			0.0380441			0.0190220	−	0.999819i	$-0.493945\pi$
$433$	0.791646			0.0380441			0.0190220	+	0.999819i	$0.493945\pi$
$434$	8.96895	−	2.07002i	0.430524	−	0.0993642i
$435$	0.784236	−	0.784236i	0.0376013	−	0.0376013i
$436$	0.853816	+	0.294119i	0.0408904	+	0.0140857i
$437$	38.9690	−	38.9690i	1.86414	−	1.86414i
$438$	−7.35717	+	11.7722i	−0.351539	+	0.562498i
$439$	−8.29052			−0.395685			−0.197842	−	0.980234i	$-0.563393\pi$
$439$	−8.29052			−0.395685			−0.197842	+	0.980234i	$0.563393\pi$
$440$	17.4387	−	14.1159i	0.831359	−	0.672948i
$441$		−	14.7978i		−	0.704655i
$442$	−3.88846	+	6.22192i	−0.184955	+	0.295947i
$443$	5.00736	+	5.00736i	0.237907	+	0.237907i	0.815983	−	0.578076i	$-0.196196\pi$
$443$	5.00736	+	5.00736i	0.237907	+	0.237907i	−0.578076	+	0.815983i	$0.696196\pi$
$444$	−17.3922	−	35.6713i	−0.825399	−	1.69289i
$445$	−18.2932	−	18.2932i	−0.867178	−	0.867178i
$446$	10.7556	−	2.48238i	0.509292	−	0.117544i
$447$	10.7360			0.507795
$448$	1.56201	−	7.33437i	0.0737982	−	0.346516i
$449$	−22.7225			−1.07234			−0.536171	−	0.844110i	$-0.680130\pi$
$449$	−22.7225			−1.07234			−0.536171	+	0.844110i	$0.680130\pi$
$450$	−9.18762	+	2.12049i	−0.433109	+	0.0999608i
$451$	33.1931	+	6.99394i	1.56300	+	0.329332i
$452$	18.3280	−	8.93618i	0.862079	−	0.420323i
$453$	−36.6763	−	36.6763i	−1.72320	−	1.72320i
$454$	11.9228	+	7.45129i	0.559565	+	0.349707i
$455$			1.30874i			0.0613549i
$456$	−28.7965	−	35.5752i	−1.34852	−	1.66596i
$457$	36.0943			1.68842			0.844209	−	0.536014i	$-0.180071\pi$
$457$	36.0943			1.68842			0.844209	+	0.536014i	$0.180071\pi$
$458$	13.0304	−	20.8500i	0.608872	−	0.974256i
$459$	5.33482	+	5.33482i	0.249008	+	0.249008i
$460$	−7.73119	+	22.4433i	−0.360469	+	1.04643i
$461$	−4.68506	+	4.68506i	−0.218205	+	0.218205i	−0.807742	−	0.589537i	$-0.799310\pi$
$461$	−4.68506	+	4.68506i	−0.218205	+	0.218205i	0.589537	+	0.807742i	$0.299310\pi$
$462$	−15.9270	+	3.67594i	−0.740993	+	0.171020i
$463$			29.5820i			1.37479i	0.726284	+	0.687395i	$0.241246\pi$
$463$			29.5820i			1.37479i	−0.726284	+	0.687395i	$0.758754\pi$
$464$	1.26352	−	0.154802i	0.0586576	−	0.00718648i
$465$			24.1989i			1.12219i
$466$	3.28653	−	0.758526i	0.152246	−	0.0351380i
$467$	−24.0945	+	24.0945i	−1.11496	+	1.11496i	−0.122492	+	0.992469i	$0.539089\pi$
$467$	−24.0945	+	24.0945i	−1.11496	+	1.11496i	−0.992469	+	0.122492i	$0.960911\pi$
$468$	−1.46834	+	4.26255i	−0.0678743	+	0.197036i
$469$	5.92877	+	5.92877i	0.273765	+	0.273765i
$470$	−2.28870	+	3.66215i	−0.105570	+	0.168922i
$471$			15.3859i			0.708943i
$472$	7.81360	+	0.822812i	0.359650	+	0.0378730i
$473$	49.4935			2.27571
$474$	−7.21760	+	11.5489i	−0.331515	+	0.530457i
$475$	−13.5591	+	13.5591i	−0.622132	+	0.622132i
$476$	−4.57114	−	9.37538i	−0.209518	−	0.429720i
$477$	−19.9847	−	19.9847i	−0.915034	−	0.915034i
$478$	3.00653	+	13.0266i	0.137515	+	0.595825i
$479$			15.5418i			0.710123i	0.934843	+	0.355062i	$0.115540\pi$
$479$			15.5418i			0.710123i	−0.934843	+	0.355062i	$0.884460\pi$
$480$	17.8643	+	8.33748i	0.815392	+	0.380552i
$481$			7.94964i			0.362472i
$482$	−20.4612	+	4.72242i	−0.931983	+	0.215100i
$483$	12.2288	−	12.2288i	0.556430	−	0.556430i
$484$	−14.9583	−	30.6794i	−0.679922	−	1.39452i
$485$	−3.49227	+	3.49227i	−0.158576	+	0.158576i
$486$	24.1746	+	15.1082i	1.09658	+	0.685322i
$487$			0.0119772i			0.000542737i	1.00000		0.000271369i	$8.63793e-5\pi$
$487$			0.0119772i			0.000542737i	−1.00000		0.000271369i	$0.999914\pi$
$488$	3.17313	−	30.1327i	0.143641	−	1.36405i
$489$	−5.86040			−0.265016
$490$	10.9919	+	6.86953i	0.496565	+	0.310334i
$491$	−22.5615	−	22.5615i	−1.01818	−	1.01818i	−0.999832	−	0.0183528i	$-0.994158\pi$
$491$	−22.5615	−	22.5615i	−1.01818	−	1.01818i	−0.0183528	−	0.999832i	$-0.505842\pi$
$492$	7.25838	+	28.9097i	0.327233	+	1.30335i
$493$	1.25201	−	1.25201i	0.0563878	−	0.0563878i
$494$	2.06184	+	8.93350i	0.0927665	+	0.401937i
$495$		−	19.1754i		−	0.861871i
$496$	−17.1057	+	21.8823i	−0.768068	+	0.982545i
$497$	7.10855			0.318862
$498$	−40.1222	+	9.26014i	−1.79792	+	0.414957i
$499$	28.4061	+	28.4061i	1.27163	+	1.27163i	0.945231	+	0.326401i	$0.105836\pi$
$499$	28.4061	+	28.4061i	1.27163	+	1.27163i	0.326401	+	0.945231i	$0.394164\pi$
$500$	7.56663	−	21.9656i	0.338390	−	0.982333i
$501$	−24.1971	−	24.1971i	−1.08105	−	1.08105i
$502$	2.29305	+	1.43307i	0.102344	+	0.0639609i
$503$	−3.23625			−0.144297			−0.0721486	−	0.997394i	$-0.522986\pi$
$503$	−3.23625			−0.144297			−0.0721486	+	0.997394i	$0.522986\pi$
$504$	−4.03239	−	4.98162i	−0.179617	−	0.221899i
$505$	−11.4973			−0.511625
$506$	50.3623	+	31.4745i	2.23888	+	1.39921i
$507$	−19.9645	+	19.9645i	−0.886654	+	0.886654i
$508$	−3.35893	+	1.63771i	−0.149028	+	0.0726615i
$509$	−25.9419	−	25.9419i	−1.14985	−	1.14985i	−0.986581	−	0.163273i	$-0.947795\pi$
$509$	−25.9419	−	25.9419i	−1.14985	−	1.14985i	−0.163273	−	0.986581i	$-0.552205\pi$
$510$	26.7187	−	6.16662i	1.18312	−	0.273063i
$511$			3.95321i			0.174880i
$512$	10.2606	+	20.1673i	0.453460	+	0.891277i
$513$	9.42766			0.416241
$514$	−5.57479	−	24.1544i	−0.245894	−	1.06540i
$515$	15.7366	−	15.7366i	0.693436	−	0.693436i
$516$	19.0594	+	39.0906i	0.839042	+	1.72087i
$517$	7.63984	+	7.63984i	0.336000	+	0.336000i
$518$	−9.58360	−	5.98938i	−0.421079	−	0.263158i
$519$	10.9355			0.480014
$520$	−2.48462	−	3.06950i	−0.108958	−	0.134606i
$521$	−39.7509			−1.74152			−0.870760	−	0.491709i	$-0.836372\pi$
$521$	−39.7509			−1.74152			−0.870760	+	0.491709i	$0.836372\pi$
$522$	0.576603	−	0.922622i	0.0252372	−	0.0403821i
$523$	−3.27122	−	3.27122i	−0.143041	−	0.143041i	0.631960	−	0.775001i	$-0.282251\pi$
$523$	−3.27122	−	3.27122i	−0.143041	−	0.143041i	−0.775001	+	0.631960i	$0.782251\pi$
$524$	6.23304	−	18.0943i	0.272291	−	0.790452i
$525$	−4.25496	+	4.25496i	−0.185702	+	0.185702i
$526$	12.8649	−	2.96919i	0.560935	−	0.129463i
$527$			38.6328i			1.68287i
$528$	30.3762	−	38.8586i	1.32195	−	1.69110i
$529$	−39.8345			−1.73194
$530$	24.1222	−	5.56738i	1.04780	−	0.241831i
$531$	4.74825	−	4.74825i	0.206057	−	0.206057i
$532$	−12.3231	−	4.24501i	−0.534274	−	0.184044i
$533$	1.23105	−	5.84253i	0.0533225	−	0.253068i
$534$	−48.2290	−	30.1412i	−2.08707	−	1.30434i
$535$			12.7507i			0.551261i
$536$	−25.1608	−	2.64956i	−1.08678	−	0.114444i
$537$			35.3178i			1.52408i
$538$	1.90030	−	3.04066i	0.0819276	−	0.131092i
$539$	22.9310	−	22.9310i	0.987706	−	0.987706i
$540$	−3.65002	+	1.77964i	−0.157072	+	0.0765834i
$541$	−4.10820	+	4.10820i	−0.176625	+	0.176625i	−0.789883	−	0.613258i	$-0.789859\pi$
$541$	−4.10820	+	4.10820i	−0.176625	+	0.176625i	0.613258	+	0.789883i	$0.289859\pi$
$542$	34.4585	−	7.95297i	1.48012	−	0.341609i
$543$	−11.3830			−0.488493
$544$	28.5200	+	13.3106i	1.22278	+	0.570686i
$545$			0.676071i			0.0289597i
$546$	0.647024	+	2.80341i	0.0276901	+	0.119975i
$547$	−0.684008	−	0.684008i	−0.0292461	−	0.0292461i	0.692333	−	0.721579i	$-0.256583\pi$
$547$	−0.684008	−	0.684008i	−0.0292461	−	0.0292461i	−0.721579	+	0.692333i	$0.756583\pi$
$548$	−3.92123	+	1.91187i	−0.167507	+	0.0816710i
$549$	−18.3114	−	18.3114i	−0.781511	−	0.781511i
$550$	−17.5233	−	10.9514i	−0.747197	−	0.466969i
$551$		−	2.21255i		−	0.0942578i
$552$	−5.46504	+	51.8973i	−0.232608	+	2.20890i
$553$			3.87821i			0.164918i
$554$	0.416210	+	0.260115i	0.0176831	+	0.0110512i
$555$	21.0085	−	21.0085i	0.891760	−	0.891760i
$556$	−25.4154	−	8.75499i	−1.07785	−	0.371294i
$557$	−8.89809	−	8.89809i	−0.377024	−	0.377024i	0.493003	−	0.870027i	$-0.335899\pi$
$557$	−8.89809	−	8.89809i	−0.377024	−	0.377024i	−0.870027	+	0.493003i	$0.835899\pi$
$558$	5.33848	+	23.1305i	0.225996	+	0.979191i
$559$		−	8.71165i		−	0.368464i
$560$	5.57235	−	0.682700i	0.235475	−	0.0288494i
$561$		−	68.6041i		−	2.89647i
$562$	−24.9390	+	5.75588i	−1.05199	+	0.242797i
$563$	−2.97907	−	2.97907i	−0.125553	−	0.125553i	0.641538	−	0.767091i	$-0.278297\pi$
$563$	−2.97907	−	2.97907i	−0.125553	−	0.125553i	−0.767091	+	0.641538i	$0.778297\pi$
$564$	−3.09203	+	8.97606i	−0.130198	+	0.377960i
$565$	10.7942	+	10.7942i	0.454116	+	0.454116i
$566$	9.89619	+	6.18473i	0.415968	+	0.259964i
$567$	9.75637			0.409729
$568$	−16.6722	+	13.4954i	−0.699551	+	0.566255i
$569$			14.8051i			0.620662i	0.950629	+	0.310331i	$0.100440\pi$
$569$			14.8051i			0.620662i	−0.950629	+	0.310331i	$0.899560\pi$
$570$	18.1597	−	29.0573i	0.760626	−	1.21708i
$571$	5.84075	−	5.84075i	0.244428	−	0.244428i	−0.574251	−	0.818679i	$-0.694707\pi$
$571$	5.84075	−	5.84075i	0.244428	−	0.244428i	0.818679	+	0.574251i	$0.194707\pi$
$572$	−8.88073	+	4.32997i	−0.371322	+	0.181045i
$573$	25.8730	−	25.8730i	1.08086	−	1.08086i
$574$	6.11590	+	5.88592i	0.255273	+	0.245674i
$575$	21.8630			0.911748
$576$	18.9150	+	4.02835i	0.788123	+	0.167848i
$577$			5.62772i			0.234285i	0.993115	+	0.117143i	$0.0373735\pi$
$577$			5.62772i			0.234285i	−0.993115	+	0.117143i	$0.962627\pi$
$578$	19.2298	−	4.43822i	0.799856	−	0.184605i
$579$	1.60846	−	1.60846i	0.0668452	−	0.0668452i
$580$	0.417658	+	0.856614i	0.0173423	+	0.0355689i
$581$	−8.29152	+	8.29152i	−0.343990	+	0.343990i
$582$	−5.75414	+	9.20720i	−0.238517	+	0.381651i
$583$		−	61.9374i		−	2.56519i
$584$	−7.50508	−	9.27177i	−0.310562	−	0.383668i
$585$	−3.37518			−0.139547
$586$	−13.7400	+	21.9853i	−0.567593	+	0.908205i
$587$	25.7631	−	25.7631i	1.06336	−	1.06336i	0.0655047	−	0.997852i	$-0.479134\pi$
$587$	25.7631	−	25.7631i	1.06336	−	1.06336i	0.997852	−	0.0655047i	$-0.0208657\pi$
$588$	26.9416	+	9.28073i	1.11105	+	0.382731i
$589$	34.1359	+	34.1359i	1.40654	+	1.40654i
$590$	1.32278	+	5.73132i	0.0544580	+	0.235955i
$591$			57.3624i			2.35957i
$592$	33.8478	−	4.14689i	1.39114	−	0.170436i
$593$		−	23.5534i		−	0.967223i	−0.875283	−	0.483611i	$-0.839325\pi$
$593$		−	23.5534i		−	0.967223i	0.875283	−	0.483611i	$-0.160675\pi$
$594$	2.28474	+	9.89928i	0.0937440	+	0.406173i
$595$	5.52158	−	5.52158i	0.226363	−	0.226363i
$596$	−3.00459	+	8.72222i	−0.123073	+	0.357276i
$597$	38.9997	+	38.9997i	1.59615	+	1.59615i
$598$	5.54002	−	8.86458i	0.226548	−	0.362500i
$599$			23.8080i			0.972770i	0.873745	+	0.486385i	$0.161685\pi$
$599$			23.8080i			0.972770i	−0.873745	+	0.486385i	$0.838315\pi$
$600$	1.90154	−	18.0574i	0.0776298	−	0.737190i
$601$	−16.1268			−0.657826			−0.328913	−	0.944360i	$-0.606682\pi$
$601$	−16.1268			−0.657826			−0.328913	+	0.944360i	$0.606682\pi$
$602$	10.5022	+	6.56349i	0.428039	+	0.267508i
$603$	−15.2900	+	15.2900i	−0.622657	+	0.622657i
$604$	40.0612	−	19.5326i	1.63007	−	0.794769i
$605$	18.0685	−	18.0685i	0.734587	−	0.734587i
$606$	−24.6281	+	5.68412i	−1.00045	+	0.230902i
$607$	43.9405			1.78349			0.891745	−	0.452539i	$-0.149482\pi$
$607$	43.9405			1.78349			0.891745	+	0.452539i	$0.149482\pi$
$608$	36.9613	−	13.4390i	1.49898	−	0.545022i
$609$		−	0.694319i		−	0.0281352i
$610$	22.1025	−	5.10123i	0.894906	−	0.206543i
$611$	1.34473	−	1.34473i	0.0544021	−	0.0544021i
$612$	24.1786	−	11.7887i	0.977362	−	0.476531i
$613$	−22.3145	−	22.3145i	−0.901273	−	0.901273i	0.0942730	−	0.995546i	$-0.469947\pi$
$613$	−22.3145	−	22.3145i	−0.901273	−	0.901273i	−0.995546	+	0.0942730i	$0.969947\pi$
$614$	−16.0754	+	25.7223i	−0.648752	+	1.03807i
$615$	−18.6933	+	12.1867i	−0.753787	+	0.491417i
$616$	1.47093	−	13.9683i	0.0592657	−	0.562800i
$617$		−	0.295335i		−	0.0118898i	−0.999982	−	0.00594488i	$-0.998108\pi$
$617$		−	0.295335i		−	0.0118898i	0.999982	−	0.00594488i	$-0.00189232\pi$
$618$	25.9288	−	41.4887i	1.04301	−	1.66892i
$619$	12.9261	+	12.9261i	0.519545	+	0.519545i	0.917434	−	0.397889i	$-0.130257\pi$
$619$	12.9261	+	12.9261i	0.519545	+	0.519545i	−0.397889	+	0.917434i	$0.630257\pi$
$620$	−19.6598	−	6.77233i	−0.789558	−	0.271983i
$621$	−7.60069	−	7.60069i	−0.305005	−	0.305005i
$622$	−13.9328	+	3.21567i	−0.558655	+	0.128937i
$623$	−16.1957			−0.648868
$624$	−6.83973	−	5.34670i	−0.273808	−	0.214039i
$625$	3.60240			0.144096
$626$	−11.0418	+	2.54842i	−0.441318	+	0.101855i
$627$	−60.6183	−	60.6183i	−2.42086	−	2.42086i
$628$	−12.4999	−	4.30591i	−0.498800	−	0.171825i
$629$	33.5395	−	33.5395i	1.33731	−	1.33731i
$630$	2.54291	−	4.06891i	0.101312	−	0.162109i
$631$			31.7399i			1.26355i	0.775153	+	0.631773i	$0.217673\pi$
$631$			31.7399i			1.26355i	−0.775153	+	0.631773i	$0.782327\pi$
$632$	−7.36270	−	9.09587i	−0.292872	−	0.361814i
$633$		−	3.48436i		−	0.138491i
$634$	−9.32972	−	5.83072i	−0.370531	−	0.231567i
$635$	−1.97822	−	1.97822i	−0.0785034	−	0.0785034i
$636$	48.9190	−	23.8514i	1.93976	−	0.945768i
$637$	−4.03622	−	4.03622i	−0.159921	−	0.159921i
$638$	2.32323	−	0.536199i	0.0919778	−	0.0212283i
$639$			18.3326i			0.725226i
$640$	−11.7732	+	12.1802i	−0.465375	+	0.481463i
$641$		−	22.1375i		−	0.874379i	−0.899369	−	0.437190i	$-0.855974\pi$
$641$		−	22.1375i		−	0.874379i	0.899369	−	0.437190i	$-0.144026\pi$
$642$	6.30376	+	27.3129i	0.248790	+	1.07795i
$643$	11.9706	+	11.9706i	0.472076	+	0.472076i	0.902586	−	0.430510i	$-0.141666\pi$
$643$	11.9706	+	11.9706i	0.472076	+	0.472076i	−0.430510	+	0.902586i	$0.641666\pi$
$644$	6.51266	+	13.3574i	0.256635	+	0.526356i
$645$	−23.0222	+	23.0222i	−0.906500	+	0.906500i
$646$	28.9915	−	46.3893i	1.14066	−	1.82516i
$647$		−	22.5965i		−	0.888362i	−0.895937	−	0.444181i	$-0.853495\pi$
$647$		−	22.5965i		−	0.888362i	0.895937	−	0.444181i	$-0.146505\pi$
$648$	−22.8824	+	18.5222i	−0.898904	+	0.727623i
$649$	14.7160			0.577654
$650$	−1.92762	+	3.08439i	−0.0756076	+	0.120980i
$651$	10.7121	+	10.7121i	0.419842	+	0.419842i
$652$	1.64010	−	4.76115i	0.0642313	−	0.186461i
$653$	−8.76576	−	8.76576i	−0.343031	−	0.343031i	0.514475	−	0.857505i	$-0.327987\pi$
$653$	−8.76576	−	8.76576i	−0.343031	−	0.343031i	−0.857505	+	0.514475i	$0.827987\pi$
$654$	0.334240	+	1.44819i	0.0130698	+	0.0566286i
$655$	14.3275			0.559820
$656$	−25.5184	−	2.19380i	−0.996325	−	0.0856535i
$657$	−10.1951			−0.397750
$658$	0.607986	+	2.63427i	0.0237018	+	0.102695i
$659$	11.9930	+	11.9930i	0.467180	+	0.467180i	0.901000	−	0.433820i	$-0.142835\pi$
$659$	11.9930	+	11.9930i	0.467180	+	0.467180i	−0.433820	+	0.901000i	$0.642835\pi$
$660$	34.9119	+	12.0263i	1.35894	+	0.468123i
$661$	14.2297	+	14.2297i	0.553472	+	0.553472i	0.927441	−	0.373969i	$-0.122003\pi$
$661$	14.2297	+	14.2297i	0.553472	+	0.553472i	−0.373969	+	0.927441i	$0.622003\pi$
$662$	−20.5644	+	32.9051i	−0.799258	+	1.27889i
$663$	−12.0754			−0.468970
$664$	3.70547	−	35.1880i	0.143800	−	1.36556i
$665$		−	9.75771i		−	0.378388i
$666$	15.4463	−	24.7156i	0.598532	−	0.957710i
$667$	−1.78379	+	1.78379i	−0.0690684	+	0.0690684i
$668$	26.4302	−	12.8866i	1.02262	−	0.498596i
$669$	12.8460	+	12.8460i	0.496657	+	0.496657i
$670$	−4.25953	−	18.4556i	−0.164560	−	0.713003i
$671$		−	56.7515i		−	2.19087i
$672$	11.5988	−	4.21727i	0.447434	−	0.162685i
$673$		−	14.3662i		−	0.553774i	−0.960902	−	0.276887i	$-0.910697\pi$
$673$		−	14.3662i		−	0.553774i	0.960902	−	0.276887i	$-0.0893028\pi$
$674$	−9.19821	+	2.12293i	−0.354302	+	0.0817723i
$675$	2.64462	+	2.64462i	0.101792	+	0.101792i
$676$	−10.6324	−	21.8070i	−0.408939	−	0.838731i
$677$	−6.95122	−	6.95122i	−0.267157	−	0.267157i	0.560796	−	0.827954i	$-0.310495\pi$
$677$	−6.95122	−	6.95122i	−0.267157	−	0.267157i	−0.827954	+	0.560796i	$0.810495\pi$
$678$	28.4584	+	17.7854i	1.09294	+	0.683045i
$679$			3.09186i			0.118655i
$680$	−2.46759	+	23.4328i	−0.0946278	+	0.898606i
$681$			23.1396i			0.886712i
$682$	−27.5709	+	44.1162i	−1.05574	+	1.68930i
$683$	12.6712	−	12.6712i	0.484849	−	0.484849i	−0.421827	−	0.906676i	$-0.638611\pi$
$683$	12.6712	−	12.6712i	0.484849	−	0.484849i	0.906676	+	0.421827i	$0.138611\pi$
$684$	10.9477	−	31.7806i	0.418594	−	1.21516i
$685$	−2.30939	−	2.30939i	−0.0882373	−	0.0882373i
$686$	16.9484	−	3.91167i	0.647094	−	0.149348i
$687$	40.4654			1.54385
$688$	−37.0923	+	4.54439i	−1.41413	+	0.173253i
$689$	−10.9020			−0.415332
$690$	−38.0670	+	8.78580i	−1.44918	+	0.334470i
$691$	−6.98178	−	6.98178i	−0.265599	−	0.265599i	0.561725	−	0.827324i	$-0.310138\pi$
$691$	−6.98178	−	6.98178i	−0.265599	−	0.265599i	−0.827324	+	0.561725i	$0.810138\pi$
$692$	−3.06042	+	8.88429i	−0.116340	+	0.337730i
$693$	−8.48842	−	8.48842i	−0.322448	−	0.322448i
$694$	−6.12023	+	9.79297i	−0.232321	+	0.371736i
$695$		−	20.1245i		−	0.763366i
$696$	1.31815	+	1.62844i	0.0499643	+	0.0617258i
$697$	−29.8434	+	19.4558i	−1.13040	+	0.736941i
$698$	−10.6469	+	17.0362i	−0.402993	+	0.644828i
$699$	3.92530	+	3.92530i	0.148468	+	0.148468i
$700$	−2.26605	−	4.64765i	−0.0856485	−	0.175665i
$701$	−10.4092	+	10.4092i	−0.393151	+	0.393151i	−0.875809	−	0.482658i	$-0.839672\pi$
$701$	−10.4092	+	10.4092i	−0.393151	+	0.393151i	0.482658	+	0.875809i	$0.339672\pi$
$702$	1.74243	−	0.402151i	0.0657639	−	0.0151782i
$703$		−	59.2708i		−	2.23544i
$704$	23.0686	+	35.5535i	0.869432	+	1.33997i
$705$	−7.10745			−0.267682
$706$	13.2417	−	3.05617i	0.498359	−	0.115021i
$707$	−5.08955	+	5.08955i	−0.191412	+	0.191412i
$708$	5.66696	+	11.6229i	0.212978	+	0.436815i
$709$	−31.3121	+	31.3121i	−1.17595	+	1.17595i	−0.195183	+	0.980767i	$0.562530\pi$
$709$	−31.3121	+	31.3121i	−1.17595	+	1.17595i	−0.980767	+	0.195183i	$0.937470\pi$
$710$	−13.6176	−	8.51050i	−0.511061	−	0.319393i
$711$	−10.0017			−0.375094
$712$	37.9850	−	30.7472i	1.42355	−	1.15230i
$713$		−	55.0415i		−	2.06132i
$714$	9.09780	−	14.5574i	0.340477	−	0.544796i
$715$	−5.23027	−	5.23027i	−0.195601	−	0.195601i
$716$	−28.6932	−	9.88411i	−1.07232	−	0.369387i
$717$	−15.5585	+	15.5585i	−0.581042	+	0.581042i
$718$	7.72406	+	33.4667i	0.288259	+	1.24897i
$719$		−	8.51497i		−	0.317555i	−0.987314	−	0.158777i	$-0.949245\pi$
$719$		−	8.51497i		−	0.317555i	0.987314	−	0.158777i	$-0.0507552\pi$
$720$	1.76065	+	14.3708i	0.0656155	+	0.535568i
$721$		−	13.9323i		−	0.518865i
$722$	−9.32990	−	40.4244i	−0.347223	−	1.50444i
$723$	−24.4380	−	24.4380i	−0.908860	−	0.908860i
$724$	3.18568	−	9.24791i	0.118395	−	0.343696i
$725$	0.620659	−	0.620659i	0.0230507	−	0.0230507i
$726$	29.7710	−	47.6366i	1.10491	−	1.76796i
$727$	−22.1331			−0.820870			−0.410435	−	0.911890i	$-0.634623\pi$
$727$	−22.1331			−0.820870			−0.410435	+	0.911890i	$0.634623\pi$
$728$	−2.45865	−	0.258908i	−0.0911236	−	0.00959578i
$729$			15.6926i			0.581207i
$730$	4.73286	−	7.57305i	0.175171	−	0.280291i
$731$	−36.7544	+	36.7544i	−1.35941	+	1.35941i
$732$	44.8231	−	21.8543i	1.65671	−	0.807760i
$733$	−10.6124	+	10.6124i	−0.391980	+	0.391980i	−0.875392	−	0.483413i	$-0.839397\pi$
$733$	−10.6124	+	10.6124i	−0.391980	+	0.391980i	0.483413	+	0.875392i	$0.339397\pi$
$734$	−32.9907	+	7.61420i	−1.21771	+	0.281045i
$735$			21.3330i			0.786879i
$736$	−40.6334	−	18.9640i	−1.49777	−	0.699023i
$737$	−47.3875			−1.74554
$738$	−15.1795	+	15.7726i	−0.558765	+	0.580597i
$739$	10.6853	−	10.6853i	0.393064	−	0.393064i	−0.482714	−	0.875778i	$-0.660349\pi$
$739$	10.6853	−	10.6853i	0.393064	−	0.393064i	0.875778	+	0.482714i	$0.160349\pi$
$740$	11.1884	+	22.9473i	0.411294	+	0.843561i
$741$	−10.6698	+	10.6698i	−0.391965	+	0.391965i
$742$	8.21371	−	13.1428i	0.301535	−	0.482486i
$743$			22.9489i			0.841915i	0.907080	+	0.420957i	$0.138306\pi$
$743$			22.9489i			0.841915i	−0.907080	+	0.420957i	$0.861694\pi$
$744$	−45.4608	−	4.78725i	−1.66667	−	0.175509i
$745$	−6.90645			−0.253033
$746$	−22.2269	−	13.8910i	−0.813785	−	0.508584i
$747$	−21.3834	−	21.3834i	−0.782377	−	0.782377i
$748$	55.7359	+	19.1997i	2.03791	+	0.702009i
$749$	5.64438	+	5.64438i	0.206241	+	0.206241i
$750$	37.2567	−	8.59879i	1.36042	−	0.313983i
$751$		−	41.2205i		−	1.50416i	−0.659073	−	0.752079i	$-0.729051\pi$
$751$		−	41.2205i		−	1.50416i	0.659073	−	0.752079i	$-0.270949\pi$
$752$	−6.42706	−	5.02411i	−0.234371	−	0.183210i
$753$			4.45032i			0.162179i
$754$	−0.0943797	−	0.408927i	−0.00343710	−	0.0148922i
$755$	23.5938	+	23.5938i	0.858668	+	0.858668i
$756$	−0.827967	+	2.40356i	−0.0301129	+	0.0874165i
$757$	−0.113162	+	0.113162i	−0.00411293	+	0.00411293i	−0.709160	−	0.705047i	$-0.750926\pi$
$757$	−0.113162	+	0.113162i	−0.00411293	+	0.00411293i	0.705047	+	0.709160i	$0.250926\pi$
$758$	−19.1884	−	11.9920i	−0.696955	−	0.435570i
$759$			97.7425i			3.54783i
$760$	18.5248	+	22.8855i	0.671965	+	0.830144i
$761$			7.99101i			0.289674i	0.989456	+	0.144837i	$0.0462658\pi$
$761$			7.99101i			0.289674i	−0.989456	+	0.144837i	$0.953734\pi$
$762$	−5.21549	−	3.25948i	−0.188937	−	0.118078i
$763$	0.299278	+	0.299278i	0.0108346	+	0.0108346i
$764$	13.7791	+	28.2608i	0.498510	+	1.02244i
$765$	14.2399	+	14.2399i	0.514844	+	0.514844i
$766$	−1.24403	−	5.39012i	−0.0449487	−	0.194753i
$767$		−	2.59026i		−	0.0935287i
$768$	−19.1972	+	31.9112i	−0.692718	+	1.15149i
$769$	39.4719			1.42339			0.711697	−	0.702487i	$-0.247927\pi$
$769$	39.4719			1.42339			0.711697	+	0.702487i	$0.247927\pi$
$770$	10.2458	−	2.36473i	0.369235	−	0.0852188i
$771$	28.8490	−	28.8490i	1.03897	−	1.03897i
$772$	0.856611	+	1.75690i	0.0308301	+	0.0632323i
$773$	−13.5577	+	13.5577i	−0.487638	+	0.487638i	−0.907560	−	0.419922i	$-0.862057\pi$
$773$	−13.5577	+	13.5577i	−0.487638	+	0.487638i	0.419922	+	0.907560i	$0.362057\pi$
$774$	−16.9269	+	27.0847i	−0.608425	+	0.973540i
$775$			19.1514i			0.687939i
$776$	−5.86982	−	7.25157i	−0.210714	−	0.260316i
$777$		−	18.5997i		−	0.667261i
$778$	−6.24746	−	3.90442i	−0.223982	−	0.139980i
$779$	−9.17841	+	43.5606i	−0.328851	+	1.56072i
$780$	2.11682	−	6.14505i	0.0757943	−	0.220028i
$781$	−28.4086	+	28.4086i	−1.01654	+	1.01654i
$782$	−60.7729	+	14.0263i	−2.17324	+	0.501579i
$783$	−0.431546			−0.0154222
$784$	−15.0799	+	19.2908i	−0.538566	+	0.688957i
$785$		−	9.89771i		−	0.353264i
$786$	30.6903	−	7.08328i	1.09469	−	0.252652i
$787$	−11.7589	+	11.7589i	−0.419161	+	0.419161i	−0.884914	−	0.465754i	$-0.845783\pi$
$787$	−11.7589	+	11.7589i	−0.419161	+	0.419161i	0.465754	+	0.884914i	$0.345783\pi$
$788$	−46.6028	−	16.0535i	−1.66016	−	0.571884i
$789$	15.3653	+	15.3653i	0.547018	+	0.547018i
$790$	4.64307	−	7.42938i	0.165193	−	0.264325i
$791$	9.55659			0.339793
$792$	36.0236	+	3.79347i	1.28004	+	0.134795i
$793$	−9.98918			−0.354726
$794$	−28.6897	−	17.9299i	−1.01816	−	0.636310i
$795$	28.8106	+	28.8106i	1.02181	+	1.02181i
$796$	−42.5990	+	20.7699i	−1.50988	+	0.736170i
$797$	14.3091	−	14.3091i	0.506855	−	0.506855i	−0.406705	−	0.913560i	$-0.633322\pi$
$797$	14.3091	−	14.3091i	0.506855	−	0.506855i	0.913560	+	0.406705i	$0.133322\pi$
$798$	−4.82407	−	20.9016i	−0.170770	−	0.739910i
$799$	−11.3469			−0.401423
$800$	14.1382	+	6.59844i	0.499860	+	0.233290i
$801$		−	41.7679i		−	1.47580i
$802$	9.21088	−	2.12586i	0.325248	−	0.0750667i
$803$	−15.7986	−	15.7986i	−0.557521	−	0.557521i
$804$	−18.2484	−	37.4273i	−0.643571	−	1.31996i
$805$	−7.86679	+	7.86679i	−0.277268	+	0.277268i
$806$	7.76516	+	4.85292i	0.273516	+	0.170937i
$807$	5.90128			0.207735
$808$	2.27451	−	21.5993i	0.0800171	−	0.759861i
$809$	−31.5131			−1.10794			−0.553971	−	0.832536i	$-0.686888\pi$
$809$	−31.5131			−1.10794			−0.553971	+	0.832536i	$0.686888\pi$
$810$	−18.6900	−	11.6805i	−0.656699	−	0.410412i
$811$	12.8787	+	12.8787i	0.452233	+	0.452233i	0.896095	−	0.443862i	$-0.146392\pi$
$811$	12.8787	+	12.8787i	0.452233	+	0.452233i	−0.443862	+	0.896095i	$0.646392\pi$
$812$	0.564084	+	0.194313i	0.0197955	+	0.00681906i
$813$	41.1558	+	41.1558i	1.44340	+	1.44340i
$814$	62.2358	−	14.3639i	2.18137	−	0.503456i
$815$	3.76999			0.132057
$816$	6.29909	+	51.4145i	0.220512	+	1.79987i
$817$			64.9522i			2.27239i
$818$	−3.36399	−	14.5755i	−0.117619	−	0.509619i
$819$	−1.49410	+	1.49410i	−0.0522080	+	0.0522080i
$820$	−4.66931	−	18.5976i	−0.163059	−	0.649455i
$821$	−32.5326	−	32.5326i	−1.13540	−	1.13540i	−0.989265	−	0.146131i	$-0.953318\pi$
$821$	−32.5326	−	32.5326i	−1.13540	−	1.13540i	−0.146131	−	0.989265i	$-0.546682\pi$
$822$	−6.08859	−	3.80514i	−0.212364	−	0.132719i
$823$	−8.75230			−0.305086			−0.152543	−	0.988297i	$-0.548746\pi$
$823$	−8.75230			−0.305086			−0.152543	+	0.988297i	$0.548746\pi$
$824$	26.4501	+	32.6764i	0.921432	+	1.13834i
$825$		−	34.0090i		−	1.18404i
$826$	3.12265	+	1.95154i	0.108651	+	0.0679027i
$827$	32.6689	−	32.6689i	1.13601	−	1.13601i	0.146850	−	0.989159i	$-0.453087\pi$
$827$	32.6689	−	32.6689i	1.13601	−	1.13601i	0.989159	−	0.146850i	$-0.0469134\pi$
$828$	−34.4481	+	16.7958i	−1.19715	+	0.583695i
$829$	−31.8076	+	31.8076i	−1.10472	+	1.10472i	−0.110890	+	0.993833i	$0.535370\pi$
$829$	−31.8076	+	31.8076i	−1.10472	+	1.10472i	−0.993833	+	0.110890i	$0.964630\pi$
$830$	25.8106	−	5.95704i	0.895898	−	0.206772i
$831$			0.807775i			0.0280214i
$832$	6.25799	−	4.06045i	0.216957	−	0.140771i
$833$			34.0576i			1.18002i
$834$	−9.94925	−	43.1080i	−0.344514	−	1.49271i
$835$	15.5660	+	15.5660i	0.538682	+	0.538682i
$836$	66.2128	−	32.2833i	2.29002	−	1.11654i
$837$	6.65802	−	6.65802i	0.230135	−	0.230135i
$838$	13.4293	−	21.4882i	0.463907	−	0.742297i
$839$	50.9883			1.76031			0.880155	−	0.474686i	$-0.157438\pi$
$839$	50.9883			1.76031			0.880155	+	0.474686i	$0.157438\pi$
$840$	5.81325	+	7.18168i	0.200576	+	0.247791i
$841$		−	28.8987i		−	0.996508i
$842$	−6.05466	+	9.68806i	−0.208657	+	0.333872i
$843$	−29.7861	−	29.7861i	−1.02589	−	1.02589i
$844$	2.83079	+	0.975139i	0.0974399	+	0.0335657i
$845$	12.8431	−	12.8431i	0.441817	−	0.441817i
$846$	−6.79365	+	1.56796i	−0.233571	+	0.0539077i
$847$		−	15.9968i		−	0.549656i
$848$	5.68697	+	46.4182i	0.195291	+	1.59401i
$849$			19.2064i			0.659161i
$850$	21.1456	−	4.88038i	0.725289	−	0.167396i
$851$	−47.7848	+	47.7848i	−1.63804	+	1.63804i
$852$	−33.3773	−	11.4977i	−1.14349	−	0.393904i
$853$	24.8028	+	24.8028i	0.849231	+	0.849231i	0.990037	−	0.140806i	$-0.0449694\pi$
$853$	24.8028	+	24.8028i	0.849231	+	0.849231i	−0.140806	+	0.990037i	$0.544969\pi$
$854$	7.52600	−	12.0423i	0.257534	−	0.412080i
$855$	25.1646			0.860612
$856$	−23.9539	−	2.52247i	−0.818728	−	0.0862162i
$857$			26.6469i			0.910240i	0.890430	+	0.455120i	$0.150404\pi$
$857$			26.6469i			0.910240i	−0.890430	+	0.455120i	$0.849596\pi$
$858$	−13.7893	−	8.61780i	−0.470760	−	0.294207i
$859$	−22.9697	−	22.9697i	−0.783716	−	0.783716i	0.196740	−	0.980456i	$-0.436965\pi$
$859$	−22.9697	−	22.9697i	−0.783716	−	0.783716i	−0.980456	+	0.196740i	$0.936965\pi$
$860$	−12.2609	−	25.1470i	−0.418092	−	0.857505i
$861$	−2.88027	+	13.6697i	−0.0981594	+	0.465863i
$862$	−21.6396	+	4.99439i	−0.737048	+	0.170110i
$863$	−41.4358			−1.41049			−0.705246	−	0.708962i	$-0.749164\pi$
$863$	−41.4358			−1.41049			−0.705246	+	0.708962i	$0.749164\pi$
$864$	−2.62120	−	7.20912i	−0.0891751	−	0.245259i
$865$	−7.03478			−0.239190
$866$	−1.09088	+	0.251773i	−0.0370696	+	0.00855560i
$867$	22.9673	+	22.9673i	0.780011	+	0.780011i
$868$	−11.7008	+	5.70493i	−0.397150	+	0.193638i
$869$	−15.4989	−	15.4989i	−0.525764	−	0.525764i
$870$	−0.831252	+	1.33009i	−0.0281821	+	0.0450941i
$871$			8.34097i			0.282623i
$872$	−1.27009	−	0.133747i	−0.0430107	−	0.00452924i
$873$	−7.97375			−0.269870
$874$	−41.3052	+	66.0924i	−1.39717	+	2.23561i
$875$	7.69934	−	7.69934i	0.260285	−	0.260285i
$876$	6.39410	−	18.5618i	0.216036	−	0.627146i
$877$	−7.14373	+	7.14373i	−0.241227	+	0.241227i	−0.817358	−	0.576131i	$-0.804562\pi$
$877$	−7.14373	+	7.14373i	−0.241227	+	0.241227i	0.576131	+	0.817358i	$0.304562\pi$
$878$	11.4242	−	2.63670i	0.385549	−	0.0889842i
$879$	−42.6688			−1.43918
$880$	−19.5410	+	24.9977i	−0.658727	+	0.842671i
$881$	−26.6637			−0.898324			−0.449162	−	0.893450i	$-0.648277\pi$
$881$	−26.6637			−0.898324			−0.449162	+	0.893450i	$0.648277\pi$
$882$	4.70624	+	20.3911i	0.158467	+	0.686605i
$883$	10.5647	+	10.5647i	0.355529	+	0.355529i	0.862162	−	0.506633i	$-0.169110\pi$
$883$	10.5647	+	10.5647i	0.355529	+	0.355529i	−0.506633	+	0.862162i	$0.669110\pi$
$884$	3.37945	−	9.81041i	0.113663	−	0.329960i
$885$	−6.84526	+	6.84526i	−0.230101	+	0.230101i
$886$	−8.49262	−	5.30756i	−0.285315	−	0.178311i
$887$	−15.9407			−0.535237			−0.267618	−	0.963525i	$-0.586237\pi$
$887$	−15.9407			−0.535237			−0.267618	+	0.963525i	$0.586237\pi$
$888$	35.3111	+	43.6233i	1.18496	+	1.46390i
$889$	−1.75141			−0.0587403
$890$	31.0257	+	19.3898i	1.03998	+	0.649949i
$891$	−38.9904	+	38.9904i	−1.30623	+	1.30623i
$892$	−14.0316	+	6.84137i	−0.469813	+	0.229066i
$893$	−10.0260	+	10.0260i	−0.335509	+	0.335509i
$894$	−14.7941	+	3.41445i	−0.494788	+	0.114196i
$895$		−	22.7199i		−	0.759444i
$896$	0.180169	+	10.6035i	0.00601903	+	0.354237i
$897$	17.2043			0.574433
$898$	31.3113	−	7.22661i	1.04487	−	0.241155i
$899$	−1.56255	−	1.56255i	−0.0521141	−	0.0521141i
$900$	11.9860	−	5.84402i	0.399535	−	0.194801i
$901$	45.9954	+	45.9954i	1.53233	+	1.53233i
$902$	−47.9641	+	0.919094i	−1.59703	+	0.0306025i
$903$			20.3826i			0.678290i
$904$	−22.4138	+	18.1430i	−0.745472	+	0.603426i
$905$	7.32270			0.243415
$906$	62.2040	+	38.8751i	2.06659	+	1.29154i
$907$	−22.4952	−	22.4952i	−0.746942	−	0.746942i	0.226962	−	0.973904i	$-0.427121\pi$
$907$	−22.4952	−	22.4952i	−0.746942	−	0.746942i	−0.973904	+	0.226962i	$0.927121\pi$
$908$	−18.7993	−	6.47590i	−0.623876	−	0.214910i
$909$	−13.1257	−	13.1257i	−0.435352	−	0.435352i
$910$	−0.416230	−	1.80343i	−0.0137979	−	0.0597833i
$911$	−14.8160			−0.490875			−0.245437	−	0.969412i	$-0.578932\pi$
$911$	−14.8160			−0.490875			−0.245437	+	0.969412i	$0.578932\pi$
$912$	50.9955	+	39.8638i	1.68863	+	1.32002i
$913$		−	66.2724i		−	2.19330i
$914$	−49.7375	+	11.4793i	−1.64517	+	0.379702i
$915$	26.3984	+	26.3984i	0.872703	+	0.872703i
$916$	−11.3247	+	32.8752i	−0.374179	+	1.08623i
$917$	6.34236	−	6.34236i	0.209443	−	0.209443i
$918$	−9.04799	−	5.65464i	−0.298628	−	0.186631i
$919$	28.0881			0.926541			0.463270	−	0.886217i	$-0.346676\pi$
$919$	28.0881			0.926541			0.463270	+	0.886217i	$0.346676\pi$
$920$	3.51566	−	33.3855i	0.115908	−	1.10069i
$921$	−49.9215			−1.64497
$922$	4.96593	−	7.94598i	0.163544	−	0.261687i
$923$	5.00038	+	5.00038i	0.164589	+	0.164589i
$924$	20.7782	−	10.1308i	0.683552	−	0.333279i
$925$	16.6265	−	16.6265i	0.546676	−	0.546676i
$926$	−9.40818	−	40.7636i	−0.309172	−	1.33958i
$927$	35.9306			1.18012
$928$	−1.69189	+	0.615163i	−0.0555389	+	0.0201937i
$929$		−	36.2397i		−	1.18899i	−0.804101	−	0.594493i	$-0.797353\pi$
$929$		−	36.2397i		−	1.18899i	0.804101	−	0.594493i	$-0.202647\pi$
$930$	−7.69615	−	33.3457i	−0.252367	−	1.09345i
$931$	30.0932	+	30.0932i	0.986263	+	0.986263i
$932$	−4.28756	+	2.09048i	−0.140444	+	0.0684760i
$933$	−16.6408	−	16.6408i	−0.544795	−	0.544795i
$934$	25.5390	−	40.8649i	0.835662	−	1.33714i
$935$			44.1329i			1.44330i
$936$	0.667711	−	6.34073i	0.0218248	−	0.207253i
$937$	−21.9887			−0.718339			−0.359169	−	0.933272i	$-0.616940\pi$
$937$	−21.9887			−0.718339			−0.359169	+	0.933272i	$0.616940\pi$
$938$	−10.0554	−	6.28421i	−0.328319	−	0.205187i
$939$	−13.1878	−	13.1878i	−0.430368	−	0.430368i
$940$	1.98910	−	5.77429i	0.0648774	−	0.188337i
$941$	−7.24009	+	7.24009i	−0.236020	+	0.236020i	−0.815200	−	0.579180i	$-0.803373\pi$
$941$	−7.24009	+	7.24009i	−0.236020	+	0.236020i	0.579180	+	0.815200i	$0.303373\pi$
$942$	−4.89328	−	21.2015i	−0.159432	−	0.690783i
$943$	42.5189	−	27.7193i	1.38460	−	0.902666i
$944$	−11.0287	+	1.35120i	−0.358955	+	0.0439777i
$945$	−1.90319			−0.0619108
$946$	−68.2015	+	15.7408i	−2.21742	+	0.511777i
$947$	−1.15645	+	1.15645i	−0.0375797	+	0.0375797i	−0.725647	−	0.688067i	$-0.758459\pi$
$947$	−1.15645	+	1.15645i	−0.0375797	+	0.0375797i	0.688067	+	0.725647i	$0.258459\pi$
$948$	6.27279	−	18.2097i	0.203731	−	0.591423i
$949$	−2.78081	+	2.78081i	−0.0902690	+	0.0902690i
$950$	14.3719	−	22.9965i	0.466287	−	0.746105i
$951$		−	18.1070i		−	0.587160i
$952$	9.28070	+	11.4654i	0.300789	+	0.371595i
$953$		−	36.0048i		−	1.16631i	−0.812360	−	0.583156i	$-0.801818\pi$
$953$		−	36.0048i		−	1.16631i	0.812360	−	0.583156i	$-0.198182\pi$
$954$	33.8945	+	21.1827i	1.09737	+	0.685817i
$955$	−16.6441	+	16.6441i	−0.538590	+	0.538590i
$956$	−8.28592	−	16.9944i	−0.267986	−	0.549637i
$957$	2.77478	+	2.77478i	0.0896957	+	0.0896957i
$958$	−4.94288	−	21.4164i	−0.159697	−	0.691933i
$959$	−2.04460			−0.0660237
$960$	−27.2685	−	5.80742i	−0.880087	−	0.187434i
$961$	17.2150			0.555324
$962$	−2.52828	−	10.9545i	−0.0815152	−	0.353188i
$963$	−14.5566	+	14.5566i	−0.469079	+	0.469079i
$964$	26.6934	−	13.0149i	0.859737	−	0.419181i
$965$	−1.03472	+	1.03472i	−0.0333088	+	0.0333088i
$966$	−12.9619	+	20.7404i	−0.417044	+	0.667311i
$967$	−0.929058			−0.0298765			−0.0149382	−	0.999888i	$-0.504755\pi$
$967$	−0.929058			−0.0298765			−0.0149382	+	0.999888i	$0.504755\pi$
$968$	30.3695	+	37.5185i	0.976114	+	1.20589i
$969$	90.0317			2.89223
$970$	3.70164	−	5.92298i	0.118852	−	0.190176i
$971$	−11.7842	+	11.7842i	−0.378172	+	0.378172i	−0.870442	−	0.492270i	$-0.836167\pi$
$971$	−11.7842	+	11.7842i	−0.378172	+	0.378172i	0.492270	+	0.870442i	$0.336167\pi$
$972$	−38.1173	−	13.1305i	−1.22261	−	0.421160i
$973$	−8.90854	−	8.90854i	−0.285595	−	0.285595i
$974$	−0.00380919	−	0.0165044i	−0.000122054	−	0.000528835i
$975$	−5.98613			−0.191710
$976$	5.21081	+	42.5317i	0.166794	+	1.36141i
$977$			35.8378i			1.14655i	0.819362	+	0.573277i	$0.194328\pi$
$977$			35.8378i			1.14655i	−0.819362	+	0.573277i	$0.805672\pi$
$978$	8.07556	−	1.86383i	0.258228	−	0.0595986i
$979$	64.7246	−	64.7246i	2.06861	−	2.06861i
$980$	−17.3315	−	5.97029i	−0.553635	−	0.190714i
$981$	−0.771821	+	0.771821i	−0.0246424	+	0.0246424i
$982$	38.2648	+	23.9140i	1.22108	+	0.763128i
$983$			45.7122i			1.45799i	0.684517	+	0.728997i	$0.260013\pi$
$983$			45.7122i			1.45799i	−0.684517	+	0.728997i	$0.739987\pi$
$984$	−19.1963	−	37.5287i	−0.611956	−	1.19637i
$985$		−	36.9012i		−	1.17577i
$986$	−1.32707	+	2.12345i	−0.0422626	+	0.0676243i
$987$	−3.14627	+	3.14627i	−0.100147	+	0.100147i
$988$	−5.68238	−	11.6545i	−0.180781	−	0.370780i
$989$	52.3653	−	52.3653i	1.66512	−	1.66512i
$990$	6.09851	+	26.4235i	0.193823	+	0.839795i
$991$			43.7372i			1.38936i	0.719319	+	0.694679i	$0.244454\pi$
$991$			43.7372i			1.38936i	−0.719319	+	0.694679i	$0.755546\pi$
$992$	16.6120	−	35.5938i	0.527432	−	1.13011i
$993$	−63.8617			−2.02659
$994$	−9.79551	+	2.26079i	−0.310695	+	0.0717078i
$995$	−25.0885	−	25.0885i	−0.795358	−	0.795358i
$996$	52.3429	−	25.5207i	1.65855	−	0.808656i
$997$	5.72412	−	5.72412i	0.181285	−	0.181285i	−0.610631	−	0.791915i	$-0.709084\pi$
$997$	5.72412	−	5.72412i	0.181285	−	0.181285i	0.791915	+	0.610631i	$0.209084\pi$
$998$	−48.1775	−	30.1091i	−1.52503	−	0.953086i
$999$	−11.5605			−0.365757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.o.a.245.7	✓	164
16.13	even	4	inner	656.2.o.a.573.8	yes	164
41.40	even	2	inner	656.2.o.a.245.8	yes	164
656.573	even	4	inner	656.2.o.a.573.7	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
656.2.o.a.245.7	✓	164	1.1	even	1	trivial
656.2.o.a.245.8	yes	164	41.40	even	2	inner
656.2.o.a.573.7	yes	164	656.573	even	4	inner
656.2.o.a.573.8	yes	164	16.13	even	4	inner

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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37799 + 0.318038i) q^{2} +(-1.64581 - 1.64581i) q^{3} +(1.79770 - 0.876504i) q^{4} +(1.05875 + 1.05875i) q^{5} +(2.79134 + 1.74448i) q^{6} +0.937357 q^{7} +(-2.19845 + 1.77955i) q^{8} +2.41740i q^{9} +O(q^{10})\)	\(q+(-1.37799 + 0.318038i) q^{2} +(-1.64581 - 1.64581i) q^{3} +(1.79770 - 0.876504i) q^{4} +(1.05875 + 1.05875i) q^{5} +(2.79134 + 1.74448i) q^{6} +0.937357 q^{7} +(-2.19845 + 1.77955i) q^{8} +2.41740i q^{9} +(-1.79567 - 1.12222i) q^{10} +(-3.74605 + 3.74605i) q^{11} +(-4.40124 - 1.51612i) q^{12} +(0.659366 + 0.659366i) q^{13} +(-1.29167 + 0.298115i) q^{14} -3.48501i q^{15} +(2.46348 - 3.15139i) q^{16} -5.56372i q^{17} +(-0.768823 - 3.33114i) q^{18} +(-4.91609 - 4.91609i) q^{19} +(2.83132 + 0.975320i) q^{20} +(-1.54271 - 1.54271i) q^{21} +(3.97063 - 6.35341i) q^{22} +7.92682i q^{23} +(6.54705 + 0.689437i) q^{24} -2.75810i q^{25} +(-1.11830 - 0.698895i) q^{26} +(-0.958858 + 0.958858i) q^{27} +(1.68509 - 0.821597i) q^{28} +(0.225032 + 0.225032i) q^{29} +(1.10836 + 4.80230i) q^{30} -6.94370 q^{31} +(-2.39239 + 5.12606i) q^{32} +12.3306 q^{33} +(1.76947 + 7.66674i) q^{34} +(0.992426 + 0.992426i) q^{35} +(2.11886 + 4.34576i) q^{36} +(6.02825 + 6.02825i) q^{37} +(8.33781 + 5.21081i) q^{38} -2.17038i q^{39} +(-4.21171 - 0.443514i) q^{40} +(-3.49691 - 5.36392i) q^{41} +(2.61648 + 1.63520i) q^{42} +(-6.60609 - 6.60609i) q^{43} +(-3.45086 + 10.0177i) q^{44} +(-2.55942 + 2.55942i) q^{45} +(-2.52103 - 10.9231i) q^{46} -2.03944i q^{47} +(-9.24102 + 1.13217i) q^{48} -6.12136 q^{49} +(0.877179 + 3.80063i) q^{50} +(-9.15684 + 9.15684i) q^{51} +(1.76328 + 0.607408i) q^{52} +(-8.26702 + 8.26702i) q^{53} +(1.01634 - 1.62625i) q^{54} -7.93227 q^{55} +(-2.06074 + 1.66807i) q^{56} +16.1819i q^{57} +(-0.381659 - 0.238522i) q^{58} +(-1.96420 - 1.96420i) q^{59} +(-3.05462 - 6.26501i) q^{60} +(-7.57484 + 7.57484i) q^{61} +(9.56834 - 2.20836i) q^{62} +2.26596i q^{63} +(1.66640 - 7.82452i) q^{64} +1.39621i q^{65} +(-16.9914 + 3.92160i) q^{66} +(6.32499 + 6.32499i) q^{67} +(-4.87663 - 10.0019i) q^{68} +(13.0461 - 13.0461i) q^{69} +(-1.68318 - 1.05192i) q^{70} +7.58361 q^{71} +(-4.30188 - 5.31453i) q^{72} +4.21740i q^{73} +(-10.2241 - 6.38964i) q^{74} +(-4.53931 + 4.53931i) q^{75} +(-13.1466 - 4.52870i) q^{76} +(-3.51139 + 3.51139i) q^{77} +(0.690264 + 2.99076i) q^{78} +4.13739i q^{79} +(5.94474 - 0.728325i) q^{80} +10.4084 q^{81} +(6.52462 + 6.27927i) q^{82} +(-8.84563 + 8.84563i) q^{83} +(-4.12554 - 1.42115i) q^{84} +(5.89059 - 5.89059i) q^{85} +(11.2041 + 7.00213i) q^{86} -0.740719i q^{87} +(1.56924 - 14.9018i) q^{88} -17.2781 q^{89} +(2.71286 - 4.34084i) q^{90} +(0.618061 + 0.618061i) q^{91} +(6.94789 + 14.2501i) q^{92} +(11.4280 + 11.4280i) q^{93} +(0.648617 + 2.81032i) q^{94} -10.4098i q^{95} +(12.3740 - 4.49911i) q^{96} +3.29849i q^{97} +(8.43517 - 1.94682i) q^{98} +(-9.05570 - 9.05570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 164 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 16 q^{8}+O(q^{10}) \) 164 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 16 * q^8	\( 164 q - 4 q^{2} - 4 q^{4} - 4 q^{5} - 16 q^{8} - 16 q^{10} - 4 q^{16} + 4 q^{18} - 4 q^{20} - 16 q^{21} - 32 q^{31} + 16 q^{32} - 8 q^{33} + 40 q^{36} - 4 q^{37} - 44 q^{40} + 52 q^{42} - 36 q^{43} + 28 q^{45} - 16 q^{46} + 132 q^{49} + 16 q^{50} + 8 q^{51} + 20 q^{59} - 4 q^{61} - 48 q^{62} + 68 q^{64} + 76 q^{66} + 20 q^{72} - 56 q^{74} - 32 q^{77} - 8 q^{78} - 100 q^{80} - 140 q^{81} + 44 q^{82} - 4 q^{83} - 40 q^{84} - 12 q^{86} - 8 q^{90} - 80 q^{91} + 112 q^{92} - 136 q^{98}+O(q^{100}) \) 164 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 - 16 * q^8 - 16 * q^10 - 4 * q^16 + 4 * q^18 - 4 * q^20 - 16 * q^21 - 32 * q^31 + 16 * q^32 - 8 * q^33 + 40 * q^36 - 4 * q^37 - 44 * q^40 + 52 * q^42 - 36 * q^43 + 28 * q^45 - 16 * q^46 + 132 * q^49 + 16 * q^50 + 8 * q^51 + 20 * q^59 - 4 * q^61 - 48 * q^62 + 68 * q^64 + 76 * q^66 + 20 * q^72 - 56 * q^74 - 32 * q^77 - 8 * q^78 - 100 * q^80 - 140 * q^81 + 44 * q^82 - 4 * q^83 - 40 * q^84 - 12 * q^86 - 8 * q^90 - 80 * q^91 + 112 * q^92 - 136 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more