LMFDB - Embedded newform 656.2.o.a.573.7

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			573.7
Character	$\chi$	$=$	656.573
Dual form			656.2.o.a.245.7

$q$-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 $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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	−0.998818	−	0.0486078i	$-0.984522\pi$
$3$	−1.64581	+	1.64581i	−0.950210	+	0.950210i	0.0486078	+	0.998818i	$0.484522\pi$
$4$	1.79770	+	0.876504i	0.898852	+	0.438252i
$5$	1.05875	−	1.05875i	0.473487	−	0.473487i	−0.429554	−	0.903041i	$-0.641329\pi$
$5$	1.05875	−	1.05875i	0.473487	−	0.473487i	0.903041	+	0.429554i	$0.141329\pi$
$6$	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	−0.990262	−	0.139216i	$-0.955542\pi$
$11$	−3.74605	−	3.74605i	−1.12948	−	1.12948i	−0.139216	−	0.990262i	$-0.544458\pi$
$12$	−4.40124	+	1.51612i	−1.27053	+	0.437667i
$13$	0.659366	−	0.659366i	0.182875	−	0.182875i	−0.609732	−	0.792607i	$-0.708723\pi$
$13$	0.659366	−	0.659366i	0.182875	−	0.182875i	0.792607	+	0.609732i	$0.208723\pi$
$14$	−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	$0.235727\pi$
$17$			5.56372i			1.34940i	−0.738092	+	0.674700i	$0.764273\pi$
$18$	−0.768823	+	3.33114i	−0.181213	+	0.785158i
$19$	−4.91609	+	4.91609i	−1.12783	+	1.12783i	−0.137298	+	0.990530i	$0.543842\pi$
$19$	−4.91609	+	4.91609i	−1.12783	+	1.12783i	−0.990530	+	0.137298i	$0.956158\pi$
$20$	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	$-0.690369\pi$
$23$		−	7.92682i		−	1.65286i	0.563042	−	0.826428i	$-0.309631\pi$
$24$	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	−0.685904	−	0.727692i	$-0.740593\pi$
$29$	0.225032	−	0.225032i	0.0417873	−	0.0417873i	0.727692	+	0.685904i	$0.240593\pi$
$30$	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	−0.00892271	−	0.999960i	$-0.502840\pi$
$37$	6.02825	−	6.02825i	0.991037	−	0.991037i	0.999960	+	0.00892271i	$0.00284022\pi$
$38$	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	−0.00744625	+	0.999972i	$0.502370\pi$
$43$	−6.60609	+	6.60609i	−1.00742	+	1.00742i	−0.999972	+	0.00744625i	$0.997630\pi$
$44$	−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	$0.0475221\pi$
$47$			2.03944i			0.297482i	−0.988876	+	0.148741i	$0.952478\pi$
$48$	−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	−0.989236	−	0.146326i	$-0.953255\pi$
$53$	−8.26702	−	8.26702i	−1.13556	−	1.13556i	−0.146326	−	0.989236i	$-0.546745\pi$
$54$	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	−0.823310	−	0.567592i	$-0.807875\pi$
$59$	−1.96420	+	1.96420i	−0.255717	+	0.255717i	0.567592	+	0.823310i	$0.307875\pi$
$60$	−3.05462	+	6.26501i	−0.394350	+	0.808809i
$61$	−7.57484	−	7.57484i	−0.969859	−	0.969859i	0.0297000	−	0.999559i	$-0.490545\pi$
$61$	−7.57484	−	7.57484i	−0.969859	−	0.969859i	−0.999559	+	0.0297000i	$0.990545\pi$
$62$	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	−0.205861	−	0.978581i	$-0.565999\pi$
$67$	6.32499	−	6.32499i	0.772721	−	0.772721i	0.978581	+	0.205861i	$0.0659994\pi$
$68$	−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	$-0.920619\pi$
$73$		−	4.21740i		−	0.493610i	0.969065	−	0.246805i	$-0.0793807\pi$
$74$	−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	$-0.925229\pi$
$79$		−	4.13739i		−	0.465493i	0.972537	−	0.232746i	$-0.0747712\pi$
$80$	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	0.0286550	−	0.999589i	$-0.490878\pi$
$83$	−8.84563	−	8.84563i	−0.970934	−	0.970934i	−0.999589	+	0.0286550i	$0.990878\pi$
$84$	−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	$-0.946445\pi$
$97$		−	3.29849i		−	0.334911i	0.985880	−	0.167455i	$-0.0535550\pi$
$98$	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	0.383336	−	0.923609i	$-0.374775\pi$
$101$	−5.42968	−	5.42968i	−0.540274	−	0.540274i	−0.923609	+	0.383336i	$0.874775\pi$
$102$	9.70580	+	15.5302i	0.961018	+	1.53772i
$103$			14.8634i			1.46453i	0.681020	+	0.732265i	$0.261537\pi$
$103$			14.8634i			1.46453i	−0.681020	+	0.732265i	$0.738463\pi$
$104$	−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	−0.353359	−	0.935488i	$-0.614960\pi$
$107$	6.02159	−	6.02159i	0.582129	−	0.582129i	0.935488	+	0.353359i	$0.114960\pi$
$108$	−0.883299	−	2.56419i	−0.0849955	−	0.246739i
$109$	0.319278	−	0.319278i	0.0305813	−	0.0305813i	−0.691651	−	0.722232i	$-0.743116\pi$
$109$	0.319278	−	0.319278i	0.0305813	−	0.0305813i	0.722232	+	0.691651i	$0.243116\pi$
$110$	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	0.937947	−	0.346780i	$-0.112725\pi$
$131$	6.76621	+	6.76621i	0.591167	+	0.591167i	−0.346780	+	0.937947i	$0.612725\pi$
$132$	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	−0.984043	−	0.177933i	$-0.943059\pi$
$139$	−9.50390	+	9.50390i	−0.806110	+	0.806110i	0.177933	+	0.984043i	$0.443059\pi$
$140$	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	0.560770	−	0.827971i	$-0.310505\pi$
$149$	−3.26161	−	3.26161i	−0.267201	−	0.267201i	−0.827971	+	0.560770i	$0.810505\pi$
$150$	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	−0.868585	−	0.495540i	$-0.834970\pi$
$157$	−4.67424	+	4.67424i	−0.373045	+	0.373045i	0.495540	+	0.868585i	$0.334970\pi$
$158$	−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	0.773386	−	0.633935i	$-0.218561\pi$
$163$	1.78040	+	1.78040i	0.139451	+	0.139451i	−0.633935	+	0.773386i	$0.718561\pi$
$164$	−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	0.569446	−	0.822029i	$-0.307158\pi$
$173$	−3.32221	−	3.32221i	−0.252583	−	0.252583i	−0.822029	+	0.569446i	$0.807158\pi$
$174$	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	−0.983403	−	0.181435i	$-0.941926\pi$
$179$	−10.7296	+	10.7296i	−0.801968	+	0.801968i	0.181435	+	0.983403i	$0.441926\pi$
$180$	−2.35773	−	6.84441i	−0.175735	−	0.510152i
$181$	3.45819	+	3.45819i	0.257045	+	0.257045i	0.823851	−	0.566806i	$-0.191821\pi$
$181$	3.45819	+	3.45819i	0.257045	+	0.257045i	−0.566806	+	0.823851i	$0.691821\pi$
$182$	−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	$-0.807428\pi$
$191$		−	15.7205i		−	1.13750i	0.822512	−	0.568748i	$-0.192572\pi$
$192$	−15.6203	−	10.1351i	−1.12730	−	0.731438i
$193$		−	0.977304i		−	0.0703479i	−0.999381	−	0.0351739i	$-0.988801\pi$
$193$		−	0.977304i		−	0.0703479i	0.999381	−	0.0351739i	$-0.0111985\pi$
$194$	−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	−0.282271	+	0.959335i	$0.591088\pi$
$197$	−17.4268	+	17.4268i	−1.24161	+	1.24161i	−0.959335	+	0.282271i	$0.908912\pi$
$198$	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	−0.669730	−	0.742604i	$-0.733590\pi$
$211$	1.05855	−	1.05855i	0.0728738	−	0.0728738i	0.742604	+	0.669730i	$0.233590\pi$
$212$	−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	−0.900807	−	0.434220i	$-0.857024\pi$
$227$	−7.02985	+	7.02985i	−0.466587	+	0.466587i	0.434220	+	0.900807i	$0.357024\pi$
$228$	14.1835	−	29.0903i	0.939326	−	1.92655i
$229$	−12.2934	−	12.2934i	−0.812373	−	0.812373i	0.172616	−	0.984989i	$-0.444778\pi$
$229$	−12.2934	−	12.2934i	−0.812373	−	0.812373i	−0.984989	+	0.172616i	$0.944778\pi$
$230$	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	$0.0989052\pi$
$239$			9.45338i			0.611488i	−0.952114	+	0.305744i	$0.901095\pi$
$240$	−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	−0.748487	−	0.663149i	$-0.769220\pi$
$251$	−1.35201	+	1.35201i	−0.0853383	+	0.0853383i	0.663149	+	0.748487i	$0.269220\pi$
$252$	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	$-0.815882\pi$
$257$		−	17.5287i		−	1.09341i	0.837325	−	0.546706i	$-0.184118\pi$
$258$	−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	0.650336	−	0.759646i	$-0.274628\pi$
$269$	−1.79282	−	1.79282i	−0.109310	−	0.109310i	−0.759646	+	0.650336i	$0.774628\pi$
$270$	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	−0.714441	−	0.699696i	$-0.753319\pi$
$277$	−0.245403	+	0.245403i	−0.0147448	+	0.0147448i	0.699696	+	0.714441i	$0.253319\pi$
$278$	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	−0.858935	−	0.512085i	$-0.828873\pi$
$283$	−5.83493	+	5.83493i	−0.346850	+	0.346850i	0.512085	+	0.858935i	$0.328873\pi$
$284$	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	0.975830	−	0.218532i	$-0.0701269\pi$
$293$	12.9628	+	12.9628i	0.757297	+	0.757297i	−0.218532	+	0.975830i	$0.570127\pi$
$294$	−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	0.991980	−	0.126398i	$-0.0403417\pi$
$307$	15.1662	+	15.1662i	0.865581	+	0.865581i	−0.126398	+	0.991980i	$0.540342\pi$
$308$	−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	−0.535544	−	0.844507i	$-0.679893\pi$
$317$	5.50093	−	5.50093i	0.308963	−	0.308963i	0.844507	+	0.535544i	$0.179893\pi$
$318$	−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	0.997633	+	0.0687577i	$0.0219035\pi$
$331$	19.4013	+	19.4013i	1.06639	+	1.06639i	0.0687577	+	0.997633i	$0.478096\pi$
$332$	−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	0.844897	−	0.534929i	$-0.179662\pi$
$347$	5.77407	+	5.77407i	0.309968	+	0.309968i	−0.534929	+	0.844897i	$0.679662\pi$
$348$	−0.649244	+	1.33159i	−0.0348031	+	0.0713810i
$349$	10.0447	+	10.0447i	0.537683	+	0.537683i	0.922848	−	0.385165i	$-0.125855\pi$
$349$	10.0447	+	10.0447i	0.537683	+	0.537683i	−0.385165	+	0.922848i	$0.625855\pi$
$350$	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	$0.221438\pi$
$359$			24.2866i			1.28180i	−0.767625	+	0.640899i	$0.778562\pi$
$360$	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	−0.281110	−	0.959676i	$-0.590702\pi$
$373$	13.1053	−	13.1053i	0.678566	−	0.678566i	0.959676	+	0.281110i	$0.0907024\pi$
$374$	−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	−0.354070	−	0.935219i	$-0.615203\pi$
$379$	11.3137	−	11.3137i	0.581148	−	0.581148i	0.935219	+	0.354070i	$0.115203\pi$
$380$	−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	$-0.968136\pi$
$383$		−	3.91158i		−	0.199873i	0.994994	−	0.0999363i	$-0.0318639\pi$
$384$	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	−0.607531	−	0.794296i	$-0.707840\pi$
$389$	3.68359	−	3.68359i	0.186765	−	0.186765i	0.794296	+	0.607531i	$0.207840\pi$
$390$	−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	−0.141025	−	0.990006i	$-0.545040\pi$
$397$	16.9158	−	16.9158i	0.848981	−	0.848981i	0.990006	+	0.141025i	$0.0450399\pi$
$398$	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	$-0.915780\pi$
$409$		−	10.5773i		−	0.523016i	0.965201	−	0.261508i	$-0.0842198\pi$
$410$	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	0.326307	−	0.945264i	$-0.394196\pi$
$419$	−12.6697	−	12.6697i	−0.618956	−	0.618956i	−0.945264	+	0.326307i	$0.894196\pi$
$420$	−2.86327	+	5.87255i	−0.139713	+	0.286551i
$421$	5.71221	+	5.71221i	0.278396	+	0.278396i	0.832468	−	0.554072i	$-0.186927\pi$
$421$	5.71221	+	5.71221i	0.278396	+	0.278396i	−0.554072	+	0.832468i	$0.686927\pi$
$422$	−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	−0.578076	−	0.815983i	$-0.696196\pi$
$443$	5.00736	−	5.00736i	0.237907	−	0.237907i	0.815983	+	0.578076i	$0.196196\pi$
$444$	−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	0.589537	−	0.807742i	$-0.299310\pi$
$461$	−4.68506	−	4.68506i	−0.218205	−	0.218205i	−0.807742	+	0.589537i	$0.799310\pi$
$462$	−15.9270	−	3.67594i	−0.740993	−	0.171020i
$463$		−	29.5820i		−	1.37479i	−0.726284	−	0.687395i	$-0.758754\pi$
$463$		−	29.5820i		−	1.37479i	0.726284	−	0.687395i	$-0.241246\pi$
$464$	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	−0.992469	−	0.122492i	$-0.960911\pi$
$467$	−24.0945	−	24.0945i	−1.11496	−	1.11496i	−0.122492	−	0.992469i	$-0.539089\pi$
$468$	−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	$-0.884460\pi$
$479$		−	15.5418i		−	0.710123i	0.934843	−	0.355062i	$-0.115540\pi$
$480$	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	$-0.999914\pi$
$487$		−	0.0119772i		−	0.000542737i	1.00000		0.000271369i	$-8.63793e-5\pi$
$488$	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	−0.0183528	+	0.999832i	$0.505842\pi$
$491$	−22.5615	+	22.5615i	−1.01818	+	1.01818i	−0.999832	+	0.0183528i	$0.994158\pi$
$492$	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	0.326401	−	0.945231i	$-0.394164\pi$
$499$	28.4061	−	28.4061i	1.27163	−	1.27163i	0.945231	−	0.326401i	$-0.105836\pi$
$500$	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	−0.163273	+	0.986581i	$0.552205\pi$
$509$	−25.9419	+	25.9419i	−1.14985	+	1.14985i	−0.986581	+	0.163273i	$0.947795\pi$
$510$	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	−0.775001	−	0.631960i	$-0.782251\pi$
$523$	−3.27122	+	3.27122i	−0.143041	+	0.143041i	0.631960	+	0.775001i	$0.282251\pi$
$524$	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	0.613258	−	0.789883i	$-0.289859\pi$
$541$	−4.10820	−	4.10820i	−0.176625	−	0.176625i	−0.789883	+	0.613258i	$0.789859\pi$
$542$	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	−0.721579	−	0.692333i	$-0.756583\pi$
$547$	−0.684008	+	0.684008i	−0.0292461	+	0.0292461i	0.692333	+	0.721579i	$0.256583\pi$
$548$	−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	−0.870027	−	0.493003i	$-0.835899\pi$
$557$	−8.89809	+	8.89809i	−0.377024	+	0.377024i	0.493003	+	0.870027i	$0.335899\pi$
$558$	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	−0.767091	−	0.641538i	$-0.778297\pi$
$563$	−2.97907	+	2.97907i	−0.125553	+	0.125553i	0.641538	+	0.767091i	$0.278297\pi$
$564$	−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	$-0.899560\pi$
$569$		−	14.8051i		−	0.620662i	0.950629	−	0.310331i	$-0.100440\pi$
$570$	18.1597	+	29.0573i	0.760626	+	1.21708i
$571$	5.84075	+	5.84075i	0.244428	+	0.244428i	0.818679	−	0.574251i	$-0.194707\pi$
$571$	5.84075	+	5.84075i	0.244428	+	0.244428i	−0.574251	+	0.818679i	$0.694707\pi$
$572$	−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	$-0.962627\pi$
$577$		−	5.62772i		−	0.234285i	0.993115	−	0.117143i	$-0.0373735\pi$
$578$	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	0.997852	+	0.0655047i	$0.0208657\pi$
$587$	25.7631	+	25.7631i	1.06336	+	1.06336i	0.0655047	+	0.997852i	$0.479134\pi$
$588$	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	$0.160675\pi$
$593$			23.5534i			0.967223i	−0.875283	+	0.483611i	$0.839325\pi$
$594$	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	$-0.838315\pi$
$599$		−	23.8080i		−	0.972770i	0.873745	−	0.486385i	$-0.161685\pi$
$600$	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	−0.995546	−	0.0942730i	$-0.969947\pi$
$613$	−22.3145	+	22.3145i	−0.901273	+	0.901273i	0.0942730	+	0.995546i	$0.469947\pi$
$614$	−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	$0.00189232\pi$
$617$			0.295335i			0.0118898i	−0.999982	+	0.00594488i	$0.998108\pi$
$618$	25.9288	+	41.4887i	1.04301	+	1.66892i
$619$	12.9261	−	12.9261i	0.519545	−	0.519545i	−0.397889	−	0.917434i	$-0.630257\pi$
$619$	12.9261	−	12.9261i	0.519545	−	0.519545i	0.917434	+	0.397889i	$0.130257\pi$
$620$	−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	$-0.782327\pi$
$631$		−	31.7399i		−	1.26355i	0.775153	−	0.631773i	$-0.217673\pi$
$632$	−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	$0.144026\pi$
$641$			22.1375i			0.874379i	−0.899369	+	0.437190i	$0.855974\pi$
$642$	6.30376	−	27.3129i	0.248790	−	1.07795i
$643$	11.9706	−	11.9706i	0.472076	−	0.472076i	−0.430510	−	0.902586i	$-0.641666\pi$
$643$	11.9706	−	11.9706i	0.472076	−	0.472076i	0.902586	+	0.430510i	$0.141666\pi$
$644$	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	$0.146505\pi$
$647$			22.5965i			0.888362i	−0.895937	+	0.444181i	$0.853495\pi$
$648$	−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	−0.857505	−	0.514475i	$-0.827987\pi$
$653$	−8.76576	+	8.76576i	−0.343031	+	0.343031i	0.514475	+	0.857505i	$0.327987\pi$
$654$	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	−0.433820	−	0.901000i	$-0.642835\pi$
$659$	11.9930	−	11.9930i	0.467180	−	0.467180i	0.901000	+	0.433820i	$0.142835\pi$
$660$	34.9119	−	12.0263i	1.35894	−	0.468123i
$661$	14.2297	−	14.2297i	0.553472	−	0.553472i	−0.373969	−	0.927441i	$-0.622003\pi$
$661$	14.2297	−	14.2297i	0.553472	−	0.553472i	0.927441	+	0.373969i	$0.122003\pi$
$662$	−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	$0.0893028\pi$
$673$			14.3662i			0.553774i	−0.960902	+	0.276887i	$0.910697\pi$
$674$	−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	−0.827954	−	0.560796i	$-0.810495\pi$
$677$	−6.95122	+	6.95122i	−0.267157	+	0.267157i	0.560796	+	0.827954i	$0.310495\pi$
$678$	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	0.906676	−	0.421827i	$-0.138611\pi$
$683$	12.6712	+	12.6712i	0.484849	+	0.484849i	−0.421827	+	0.906676i	$0.638611\pi$
$684$	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	−0.827324	−	0.561725i	$-0.810138\pi$
$691$	−6.98178	+	6.98178i	−0.265599	+	0.265599i	0.561725	+	0.827324i	$0.310138\pi$
$692$	−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	0.482658	−	0.875809i	$-0.339672\pi$
$701$	−10.4092	−	10.4092i	−0.393151	−	0.393151i	−0.875809	+	0.482658i	$0.839672\pi$
$702$	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	−0.980767	−	0.195183i	$-0.937470\pi$
$709$	−31.3121	−	31.3121i	−1.17595	−	1.17595i	−0.195183	−	0.980767i	$-0.562530\pi$
$710$	−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	$0.0507552\pi$
$719$			8.51497i			0.317555i	−0.987314	+	0.158777i	$0.949245\pi$
$720$	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	0.483413	−	0.875392i	$-0.339397\pi$
$733$	−10.6124	−	10.6124i	−0.391980	−	0.391980i	−0.875392	+	0.483413i	$0.839397\pi$
$734$	−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	0.875778	−	0.482714i	$-0.160349\pi$
$739$	10.6853	+	10.6853i	0.393064	+	0.393064i	−0.482714	+	0.875778i	$0.660349\pi$
$740$	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	$-0.861694\pi$
$743$		−	22.9489i		−	0.841915i	0.907080	−	0.420957i	$-0.138306\pi$
$744$	−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	$0.270949\pi$
$751$			41.2205i			1.50416i	−0.659073	+	0.752079i	$0.729051\pi$
$752$	−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	0.705047	−	0.709160i	$-0.250926\pi$
$757$	−0.113162	−	0.113162i	−0.00411293	−	0.00411293i	−0.709160	+	0.705047i	$0.750926\pi$
$758$	−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	$-0.953734\pi$
$761$		−	7.99101i		−	0.289674i	0.989456	−	0.144837i	$-0.0462658\pi$
$762$	−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	0.419922	−	0.907560i	$-0.362057\pi$
$773$	−13.5577	−	13.5577i	−0.487638	−	0.487638i	−0.907560	+	0.419922i	$0.862057\pi$
$774$	−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	0.465754	−	0.884914i	$-0.345783\pi$
$787$	−11.7589	−	11.7589i	−0.419161	−	0.419161i	−0.884914	+	0.465754i	$0.845783\pi$
$788$	−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	0.913560	−	0.406705i	$-0.133322\pi$
$797$	14.3091	+	14.3091i	0.506855	+	0.506855i	−0.406705	+	0.913560i	$0.633322\pi$
$798$	−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	−0.443862	−	0.896095i	$-0.646392\pi$
$811$	12.8787	−	12.8787i	0.452233	−	0.452233i	0.896095	+	0.443862i	$0.146392\pi$
$812$	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	−0.146131	+	0.989265i	$0.546682\pi$
$821$	−32.5326	+	32.5326i	−1.13540	+	1.13540i	−0.989265	+	0.146131i	$0.953318\pi$
$822$	−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	0.989159	+	0.146850i	$0.0469134\pi$
$827$	32.6689	+	32.6689i	1.13601	+	1.13601i	0.146850	+	0.989159i	$0.453087\pi$
$828$	−34.4481	−	16.7958i	−1.19715	−	0.583695i
$829$	−31.8076	−	31.8076i	−1.10472	−	1.10472i	−0.993833	−	0.110890i	$-0.964630\pi$
$829$	−31.8076	−	31.8076i	−1.10472	−	1.10472i	−0.110890	−	0.993833i	$-0.535370\pi$
$830$	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	−0.140806	−	0.990037i	$-0.544969\pi$
$853$	24.8028	−	24.8028i	0.849231	−	0.849231i	0.990037	+	0.140806i	$0.0449694\pi$
$854$	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	$-0.849596\pi$
$857$		−	26.6469i		−	0.910240i	0.890430	−	0.455120i	$-0.150404\pi$
$858$	−13.7893	+	8.61780i	−0.470760	+	0.294207i
$859$	−22.9697	+	22.9697i	−0.783716	+	0.783716i	−0.980456	−	0.196740i	$-0.936965\pi$
$859$	−22.9697	+	22.9697i	−0.783716	+	0.783716i	0.196740	+	0.980456i	$0.436965\pi$
$860$	−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	0.576131	−	0.817358i	$-0.304562\pi$
$877$	−7.14373	−	7.14373i	−0.241227	−	0.241227i	−0.817358	+	0.576131i	$0.804562\pi$
$878$	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	−0.506633	−	0.862162i	$-0.669110\pi$
$883$	10.5647	−	10.5647i	0.355529	−	0.355529i	0.862162	+	0.506633i	$0.169110\pi$
$884$	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	−0.973904	−	0.226962i	$-0.927121\pi$
$907$	−22.4952	+	22.4952i	−0.746942	+	0.746942i	0.226962	+	0.973904i	$0.427121\pi$
$908$	−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	$0.202647\pi$
$929$			36.2397i			1.18899i	−0.804101	+	0.594493i	$0.797353\pi$
$930$	−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	0.579180	−	0.815200i	$-0.303373\pi$
$941$	−7.24009	−	7.24009i	−0.236020	−	0.236020i	−0.815200	+	0.579180i	$0.803373\pi$
$942$	−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	0.688067	−	0.725647i	$-0.258459\pi$
$947$	−1.15645	−	1.15645i	−0.0375797	−	0.0375797i	−0.725647	+	0.688067i	$0.758459\pi$
$948$	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	$0.198182\pi$
$953$			36.0048i			1.16631i	−0.812360	+	0.583156i	$0.801818\pi$
$954$	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	0.492270	−	0.870442i	$-0.336167\pi$
$971$	−11.7842	−	11.7842i	−0.378172	−	0.378172i	−0.870442	+	0.492270i	$0.836167\pi$
$972$	−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	$-0.805672\pi$
$977$		−	35.8378i		−	1.14655i	0.819362	−	0.573277i	$-0.194328\pi$
$978$	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	$-0.739987\pi$
$983$		−	45.7122i		−	1.45799i	0.684517	−	0.728997i	$-0.260013\pi$
$984$	−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	$-0.755546\pi$
$991$		−	43.7372i		−	1.38936i	0.719319	−	0.694679i	$-0.244454\pi$
$992$	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	0.791915	−	0.610631i	$-0.209084\pi$
$997$	5.72412	+	5.72412i	0.181285	+	0.181285i	−0.610631	+	0.791915i	$0.709084\pi$
$998$	−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.573.7	yes	164
16.5	even	4	inner	656.2.o.a.245.8	yes	164
41.40	even	2	inner	656.2.o.a.573.8	yes	164
656.245	even	4	inner	656.2.o.a.245.7	✓	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
656.2.o.a.245.7	✓	164	656.245	even	4	inner
656.2.o.a.245.8	yes	164	16.5	even	4	inner
656.2.o.a.573.7	yes	164	1.1	even	1	trivial
656.2.o.a.573.8	yes	164	41.40	even	2	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

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