LMFDB - Embedded newform 260.2.o.a.27.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.18
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0447185 + 1.41351i) q^{2} +(1.60820 + 1.60820i) q^{3} +(-1.99600 - 0.126420i) q^{4} +(1.86263 + 1.23718i) q^{5} +(-2.34511 + 2.20128i) q^{6} +(-0.275770 + 0.275770i) q^{7} +(0.267954 - 2.81571i) q^{8} +2.17259i q^{9} +O(q^{10})$	\(q+(-0.0447185 + 1.41351i) q^{2} +(1.60820 + 1.60820i) q^{3} +(-1.99600 - 0.126420i) q^{4} +(1.86263 + 1.23718i) q^{5} +(-2.34511 + 2.20128i) q^{6} +(-0.275770 + 0.275770i) q^{7} +(0.267954 - 2.81571i) q^{8} +2.17259i q^{9} +(-1.83206 + 2.57751i) q^{10} +0.822170i q^{11} +(-3.00665 - 3.41327i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-0.377470 - 0.402134i) q^{14} +(1.00584 + 4.98510i) q^{15} +(3.96804 + 0.504668i) q^{16} +(-4.59726 - 4.59726i) q^{17} +(-3.07097 - 0.0971552i) q^{18} +2.21590 q^{19} +(-3.56140 - 2.70489i) q^{20} -0.886983 q^{21} +(-1.16214 - 0.0367662i) q^{22} +(-2.72038 - 2.72038i) q^{23} +(4.95913 - 4.09729i) q^{24} +(1.93876 + 4.60882i) q^{25} +(0.967879 + 1.03112i) q^{26} +(1.33063 - 1.33063i) q^{27} +(0.585299 - 0.515573i) q^{28} +7.29375i q^{29} +(-7.09145 + 1.19883i) q^{30} -9.35295i q^{31} +(-0.890797 + 5.58628i) q^{32} +(-1.32221 + 1.32221i) q^{33} +(6.70384 - 6.29268i) q^{34} +(-0.854833 + 0.172479i) q^{35} +(0.274659 - 4.33650i) q^{36} +(-4.29663 - 4.29663i) q^{37} +(-0.0990918 + 3.13219i) q^{38} +2.27433 q^{39} +(3.98264 - 4.91310i) q^{40} +1.02689 q^{41} +(0.0396646 - 1.25376i) q^{42} +(4.26400 + 4.26400i) q^{43} +(0.103939 - 1.64105i) q^{44} +(-2.68789 + 4.04673i) q^{45} +(3.96693 - 3.72363i) q^{46} +(-3.16032 + 3.16032i) q^{47} +(5.56978 + 7.19299i) q^{48} +6.84790i q^{49} +(-6.60129 + 2.53435i) q^{50} -14.7866i q^{51} +(-1.50078 + 1.32199i) q^{52} +(0.615128 - 0.615128i) q^{53} +(1.82135 + 1.94036i) q^{54} +(-1.01717 + 1.53140i) q^{55} +(0.702593 + 0.850379i) q^{56} +(3.56360 + 3.56360i) q^{57} +(-10.3098 - 0.326166i) q^{58} +12.3097 q^{59} +(-1.37744 - 10.0774i) q^{60} +1.78854 q^{61} +(13.2205 + 0.418250i) q^{62} +(-0.599135 - 0.599135i) q^{63} +(-7.85640 - 1.50896i) q^{64} +(2.19190 - 0.442257i) q^{65} +(-1.80983 - 1.92808i) q^{66} +(7.04616 - 7.04616i) q^{67} +(8.59495 + 9.75732i) q^{68} -8.74982i q^{69} +(-0.205573 - 1.21602i) q^{70} +3.71294i q^{71} +(6.11738 + 0.582154i) q^{72} +(0.126153 - 0.126153i) q^{73} +(6.26545 - 5.88117i) q^{74} +(-4.29398 + 10.5298i) q^{75} +(-4.42294 - 0.280134i) q^{76} +(-0.226729 - 0.226729i) q^{77} +(-0.101705 + 3.21479i) q^{78} -8.97712 q^{79} +(6.76661 + 5.84919i) q^{80} +10.7976 q^{81} +(-0.0459209 + 1.45151i) q^{82} +(3.04802 + 3.04802i) q^{83} +(1.77042 + 0.112132i) q^{84} +(-2.87534 - 14.2506i) q^{85} +(-6.21787 + 5.83651i) q^{86} +(-11.7298 + 11.7298i) q^{87} +(2.31499 + 0.220303i) q^{88} -12.5718i q^{89} +(-5.59988 - 3.98032i) q^{90} +0.389997i q^{91} +(5.08598 + 5.77380i) q^{92} +(15.0414 - 15.0414i) q^{93} +(-4.32581 - 4.60846i) q^{94} +(4.12740 + 2.74147i) q^{95} +(-10.4164 + 7.55125i) q^{96} +(-3.35467 - 3.35467i) q^{97} +(-9.67955 - 0.306228i) q^{98} -1.78624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0447185	+	1.41351i	−0.0316208	+	0.999500i
$2$	−0.0447185	+	1.41351i	−0.0316208	+	0.999500i
$3$	1.60820	+	1.60820i	0.928493	+	0.928493i	0.997609	−	0.0691158i	$-0.0220178\pi$
$3$	1.60820	+	1.60820i	0.928493	+	0.928493i	−0.0691158	+	0.997609i	$0.522018\pi$
$4$	−1.99600	−	0.126420i	−0.998000	−	0.0632099i
$5$	1.86263	+	1.23718i	0.832992	+	0.553285i
$5$	1.86263	+	1.23718i	0.832992	+	0.553285i
$6$	−2.34511	+	2.20128i	−0.957388	+	0.898669i
$7$	−0.275770	+	0.275770i	−0.104231	+	0.104231i	−0.757299	−	0.653068i	$-0.773482\pi$
$7$	−0.275770	+	0.275770i	−0.104231	+	0.104231i	0.653068	+	0.757299i	$0.273482\pi$
$8$	0.267954	−	2.81571i	0.0947359	−	0.995502i
$9$			2.17259i			0.724198i
$10$	−1.83206	+	2.57751i	−0.579348	+	0.815080i
$11$			0.822170i			0.247894i	0.992289	+	0.123947i	$0.0395552\pi$
$11$			0.822170i			0.247894i	−0.992289	+	0.123947i	$0.960445\pi$
$12$	−3.00665	−	3.41327i	−0.867946	−	0.985326i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	−0.377470	−	0.402134i	−0.100883	−	0.107475i
$15$	1.00584	+	4.98510i	0.259707	+	1.28715i
$16$	3.96804	+	0.504668i	0.992009	+	0.126167i
$17$	−4.59726	−	4.59726i	−1.11500	−	1.11500i	−0.992464	−	0.122536i	$-0.960897\pi$
$17$	−4.59726	−	4.59726i	−1.11500	−	1.11500i	−0.122536	−	0.992464i	$-0.539103\pi$
$18$	−3.07097	−	0.0971552i	−0.723836	−	0.0228997i
$19$	2.21590			0.508362			0.254181	−	0.967157i	$-0.418194\pi$
$19$	2.21590			0.508362			0.254181	+	0.967157i	$0.418194\pi$
$20$	−3.56140	−	2.70489i	−0.796353	−	0.604832i
$21$	−0.886983			−0.193556
$22$	−1.16214	−	0.0367662i	−0.247770	−	0.00783859i
$23$	−2.72038	−	2.72038i	−0.567239	−	0.567239i	0.364115	−	0.931354i	$-0.381372\pi$
$23$	−2.72038	−	2.72038i	−0.567239	−	0.567239i	−0.931354	+	0.364115i	$0.881372\pi$
$24$	4.95913	−	4.09729i	1.01228	−	0.836355i
$25$	1.93876	+	4.60882i	0.387752	+	0.921764i
$26$	0.967879	+	1.03112i	0.189817	+	0.202219i
$27$	1.33063	−	1.33063i	0.256080	−	0.256080i
$28$	0.585299	−	0.515573i	0.110611	−	0.0974342i
$29$			7.29375i			1.35442i	0.735792	+	0.677208i	$0.236810\pi$
$29$			7.29375i			1.35442i	−0.735792	+	0.677208i	$0.763190\pi$
$30$	−7.09145	+	1.19883i	−1.29472	+	0.218876i
$31$		−	9.35295i		−	1.67984i	−0.542711	−	0.839920i	$-0.682602\pi$
$31$		−	9.35295i		−	1.67984i	0.542711	−	0.839920i	$-0.317398\pi$
$32$	−0.890797	+	5.58628i	−0.157472	+	0.987523i
$33$	−1.32221	+	1.32221i	−0.230167	+	0.230167i
$34$	6.70384	−	6.29268i	1.14970	−	1.07919i
$35$	−0.854833	+	0.172479i	−0.144493	+	0.0291542i
$36$	0.274659	−	4.33650i	0.0457765	−	0.722750i
$37$	−4.29663	−	4.29663i	−0.706361	−	0.706361i	0.259407	−	0.965768i	$-0.416473\pi$
$37$	−4.29663	−	4.29663i	−0.706361	−	0.706361i	−0.965768	+	0.259407i	$0.916473\pi$
$38$	−0.0990918	+	3.13219i	−0.0160748	+	0.508108i
$39$	2.27433			0.364185
$40$	3.98264	−	4.91310i	0.629710	−	0.776830i
$41$	1.02689			0.160373			0.0801865	−	0.996780i	$-0.474448\pi$
$41$	1.02689			0.160373			0.0801865	+	0.996780i	$0.474448\pi$
$42$	0.0396646	−	1.25376i	0.00612038	−	0.193459i
$43$	4.26400	+	4.26400i	0.650253	+	0.650253i	0.953054	−	0.302801i	$-0.0979216\pi$
$43$	4.26400	+	4.26400i	0.650253	+	0.650253i	−0.302801	+	0.953054i	$0.597922\pi$
$44$	0.103939	−	1.64105i	0.0156693	−	0.247398i
$45$	−2.68789	+	4.04673i	−0.400687	+	0.603251i
$46$	3.96693	−	3.72363i	0.584892	−	0.549019i
$47$	−3.16032	+	3.16032i	−0.460981	+	0.460981i	−0.898977	−	0.437996i	$-0.855688\pi$
$47$	−3.16032	+	3.16032i	−0.460981	+	0.460981i	0.437996	+	0.898977i	$0.355688\pi$
$48$	5.56978	+	7.19299i	0.803928	+	1.03822i
$49$			6.84790i			0.978272i
$50$	−6.60129	+	2.53435i	−0.933564	+	0.358411i
$51$		−	14.7866i		−	2.07054i
$52$	−1.50078	+	1.32199i	−0.208120	+	0.183327i
$53$	0.615128	−	0.615128i	0.0844943	−	0.0844943i	−0.663596	−	0.748091i	$-0.730971\pi$
$53$	0.615128	−	0.615128i	0.0844943	−	0.0844943i	0.748091	+	0.663596i	$0.230971\pi$
$54$	1.82135	+	1.94036i	0.247855	+	0.264050i
$55$	−1.01717	+	1.53140i	−0.137156	+	0.206493i
$56$	0.702593	+	0.850379i	0.0938879	+	0.113637i
$57$	3.56360	+	3.56360i	0.472011	+	0.472011i
$58$	−10.3098	−	0.326166i	−1.35374	−	0.0428277i
$59$	12.3097			1.60258			0.801291	−	0.598275i	$-0.204147\pi$
$59$	12.3097			1.60258			0.801291	+	0.598275i	$0.204147\pi$
$60$	−1.37744	−	10.0774i	−0.177827	−	1.30099i
$61$	1.78854			0.229000			0.114500	−	0.993423i	$-0.463473\pi$
$61$	1.78854			0.229000			0.114500	+	0.993423i	$0.463473\pi$
$62$	13.2205	+	0.418250i	1.67900	+	0.0531178i
$63$	−0.599135	−	0.599135i	−0.0754839	−	0.0754839i
$64$	−7.85640	−	1.50896i	−0.982050	−	0.188620i
$65$	2.19190	−	0.442257i	0.271871	−	0.0548552i
$66$	−1.80983	−	1.92808i	−0.222774	−	0.237330i
$67$	7.04616	−	7.04616i	0.860825	−	0.860825i	−0.130609	−	0.991434i	$-0.541693\pi$
$67$	7.04616	−	7.04616i	0.860825	−	0.860825i	0.991434	+	0.130609i	$0.0416933\pi$
$68$	8.59495	+	9.75732i	1.04229	+	1.18325i
$69$		−	8.74982i		−	1.05335i
$70$	−0.205573	−	1.21602i	−0.0245707	−	0.145343i
$71$			3.71294i			0.440645i	0.975427	+	0.220322i	$0.0707110\pi$
$71$			3.71294i			0.440645i	−0.975427	+	0.220322i	$0.929289\pi$
$72$	6.11738	+	0.582154i	0.720941	+	0.0686075i
$73$	0.126153	−	0.126153i	0.0147650	−	0.0147650i	−0.699686	−	0.714451i	$-0.746677\pi$
$73$	0.126153	−	0.126153i	0.0147650	−	0.0147650i	0.714451	+	0.699686i	$0.246677\pi$
$74$	6.26545	−	5.88117i	0.728344	−	0.683672i
$75$	−4.29398	+	10.5298i	−0.495826	+	1.21588i
$76$	−4.42294	−	0.280134i	−0.507346	−	0.0321335i
$77$	−0.226729	−	0.226729i	−0.0258382	−	0.0258382i
$78$	−0.101705	+	3.21479i	−0.0115158	+	0.364003i
$79$	−8.97712			−1.01000			−0.505002	−	0.863118i	$-0.668508\pi$
$79$	−8.97712			−1.01000			−0.505002	+	0.863118i	$0.668508\pi$
$80$	6.76661	+	5.84919i	0.756530	+	0.653960i
$81$	10.7976			1.19974
$82$	−0.0459209	+	1.45151i	−0.00507112	+	0.160293i
$83$	3.04802	+	3.04802i	0.334563	+	0.334563i	0.854316	−	0.519753i	$-0.173976\pi$
$83$	3.04802	+	3.04802i	0.334563	+	0.334563i	−0.519753	+	0.854316i	$0.673976\pi$
$84$	1.77042	+	0.112132i	0.193169	+	0.0122346i
$85$	−2.87534	−	14.2506i	−0.311874	−	1.54570i
$86$	−6.21787	+	5.83651i	−0.670490	+	0.629367i
$87$	−11.7298	+	11.7298i	−1.25757	+	1.25757i
$88$	2.31499	+	0.220303i	0.246779	+	0.0234844i
$89$		−	12.5718i		−	1.33261i	−0.745681	−	0.666303i	$-0.767876\pi$
$89$		−	12.5718i		−	1.33261i	0.745681	−	0.666303i	$-0.232124\pi$
$90$	−5.59988	−	3.98032i	−0.590279	−	0.419562i
$91$			0.389997i			0.0408828i
$92$	5.08598	+	5.77380i	0.530250	+	0.601960i
$93$	15.0414	−	15.0414i	1.55972	−	1.55972i
$94$	−4.32581	−	4.60846i	−0.446173	−	0.475327i
$95$	4.12740	+	2.74147i	0.423462	+	0.281269i
$96$	−10.4164	+	7.55125i	−1.06312	+	0.770697i
$97$	−3.35467	−	3.35467i	−0.340616	−	0.340616i	0.515983	−	0.856599i	$-0.327427\pi$
$97$	−3.35467	−	3.35467i	−0.340616	−	0.340616i	−0.856599	+	0.515983i	$0.827427\pi$
$98$	−9.67955	−	0.306228i	−0.977783	−	0.0309337i
$99$	−1.78624			−0.179524
$100$	−3.28712	−	9.44430i	−0.328712	−	0.944430i
$101$	−18.1244			−1.80345			−0.901724	−	0.432312i	$-0.857698\pi$
$101$	−18.1244			−1.80345			−0.901724	+	0.432312i	$0.857698\pi$
$102$	20.9010	+	0.661235i	2.06950	+	0.0654721i
$103$	−8.43451	−	8.43451i	−0.831077	−	0.831077i	0.156587	−	0.987664i	$-0.449951\pi$
$103$	−8.43451	−	8.43451i	−0.831077	−	0.831077i	−0.987664	+	0.156587i	$0.949951\pi$
$104$	−1.80153	−	2.18048i	−0.176655	−	0.213813i
$105$	−1.65212	−	1.09736i	−0.161230	−	0.107091i
$106$	0.841980	+	0.896995i	0.0817803	+	0.0871239i
$107$	−10.1220	+	10.1220i	−0.978534	+	0.978534i	−0.999774	−	0.0212405i	$-0.993238\pi$
$107$	−10.1220	+	10.1220i	−0.978534	+	0.978534i	0.0212405	+	0.999774i	$0.493238\pi$
$108$	−2.82416	+	2.48772i	−0.271755	+	0.239381i
$109$		−	6.02509i		−	0.577099i	−0.957465	−	0.288549i	$-0.906827\pi$
$109$		−	6.02509i		−	0.577099i	0.957465	−	0.288549i	$-0.0931729\pi$
$110$	−2.11915	−	1.50626i	−0.202053	−	0.143617i
$111$		−	13.8196i		−	1.31170i
$112$	−1.23344	+	0.955091i	−0.116549	+	0.0902476i
$113$	−7.28057	+	7.28057i	−0.684898	+	0.684898i	−0.961100	−	0.276202i	$-0.910924\pi$
$113$	−7.28057	+	7.28057i	−0.684898	+	0.684898i	0.276202	+	0.961100i	$0.410924\pi$
$114$	−5.19653	+	4.87782i	−0.486700	+	0.456849i
$115$	−1.70145	−	8.43267i	−0.158661	−	0.786351i
$116$	0.922075	−	14.5583i	0.0856125	−	1.35171i
$117$	1.53626	+	1.53626i	0.142027	+	0.142027i
$118$	−0.550470	+	17.3998i	−0.0506749	+	1.60178i
$119$	2.53557			0.232435
$120$	14.3061	−	1.49637i	1.30596	−	0.136599i
$121$	10.3240			0.938549
$122$	−0.0799810	+	2.52812i	−0.00724114	+	0.228885i
$123$	1.65144	+	1.65144i	0.148905	+	0.148905i
$124$	−1.18240	+	18.6685i	−0.106183	+	1.67648i
$125$	−2.09076	+	10.9831i	−0.187003	+	0.982359i
$126$	0.873674	−	0.820089i	0.0778330	−	0.0730593i
$127$	−2.64277	+	2.64277i	−0.234508	+	0.234508i	−0.814571	−	0.580064i	$-0.803028\pi$
$127$	−2.64277	+	2.64277i	−0.234508	+	0.234508i	0.580064	+	0.814571i	$0.303028\pi$
$128$	2.48425	−	11.0376i	0.219578	−	0.975595i
$129$			13.7147i			1.20751i
$130$	0.527114	+	3.11804i	0.0462310	+	0.273470i
$131$			14.9688i			1.30783i	0.756567	+	0.653916i	$0.226875\pi$
$131$			14.9688i			1.30783i	−0.756567	+	0.653916i	$0.773125\pi$
$132$	2.80629	−	2.47198i	0.244256	−	0.215158i
$133$	−0.611078	+	0.611078i	−0.0529871	+	0.0529871i
$134$	9.64469	+	10.2749i	0.833174	+	0.887614i
$135$	4.12471	−	0.832238i	0.354998	−	0.0716276i
$136$	−14.1764	+	11.7127i	−1.21562	+	1.00435i
$137$	0.764404	+	0.764404i	0.0653075	+	0.0653075i	0.739006	−	0.673699i	$-0.235295\pi$
$137$	0.764404	+	0.764404i	0.0653075	+	0.0653075i	−0.673699	+	0.739006i	$0.735295\pi$
$138$	12.3679	+	0.391279i	1.05283	+	0.0333079i
$139$	−18.3089			−1.55294			−0.776469	−	0.630156i	$-0.782991\pi$
$139$	−18.3089			−1.55294			−0.776469	+	0.630156i	$0.782991\pi$
$140$	1.72805	−	0.236200i	0.146047	−	0.0199625i
$141$	−10.1648			−0.856034
$142$	−5.24826	−	0.166037i	−0.440425	−	0.0139335i
$143$	0.581362	+	0.581362i	0.0486159	+	0.0486159i
$144$	−1.09644	+	8.62093i	−0.0913699	+	0.718411i
$145$	−9.02370	+	13.5855i	−0.749377	+	1.12822i
$146$	0.172676	+	0.183959i	0.0142908	+	0.0152245i
$147$	−11.0128	+	11.0128i	−0.908318	+	0.908318i
$148$	8.03289	+	9.11925i	0.660300	+	0.749598i
$149$			1.16451i			0.0954004i	0.998862	+	0.0477002i	$0.0151892\pi$
$149$			1.16451i			0.0954004i	−0.998862	+	0.0477002i	$0.984811\pi$
$150$	−14.6919	−	6.54044i	−1.19959	−	0.534025i
$151$		−	1.00865i		−	0.0820831i	−0.999157	−	0.0410416i	$-0.986932\pi$
$151$		−	1.00865i		−	0.0820831i	0.999157	−	0.0410416i	$-0.0130676\pi$
$152$	0.593758	−	6.23932i	0.0481601	−	0.506076i
$153$	9.98798	−	9.98798i	0.807481	−	0.807481i
$154$	0.330622	−	0.310344i	0.0266423	−	0.0250083i
$155$	11.5713	−	17.4211i	0.929429	−	1.39929i
$156$	−4.53957	−	0.287521i	−0.363457	−	0.0230201i
$157$	−13.9094	−	13.9094i	−1.11009	−	1.11009i	−0.993138	−	0.116953i	$-0.962687\pi$
$157$	−13.9094	−	13.9094i	−1.11009	−	1.11009i	−0.116953	−	0.993138i	$-0.537313\pi$
$158$	0.401443	−	12.6892i	0.0319371	−	1.00950i
$159$	1.97849			0.156905
$160$	−8.57046	+	9.30307i	−0.677555	+	0.735473i
$161$	1.50040			0.118248
$162$	−0.482854	+	15.2625i	−0.0379366	+	1.19914i
$163$	−15.4779	−	15.4779i	−1.21232	−	1.21232i	−0.970260	−	0.242065i	$-0.922175\pi$
$163$	−15.4779	−	15.4779i	−1.21232	−	1.21232i	−0.242065	−	0.970260i	$-0.577825\pi$
$164$	−2.04967	−	0.129819i	−0.160052	−	0.0101372i
$165$	−4.09860	+	0.826971i	−0.319076	+	0.0643796i
$166$	−4.44469	+	4.17209i	−0.344975	+	0.323817i
$167$	−13.0603	+	13.0603i	−1.01064	+	1.01064i	−0.0106938	+	0.999943i	$0.503404\pi$
$167$	−13.0603	+	13.0603i	−1.01064	+	1.01064i	−0.999943	+	0.0106938i	$0.996596\pi$
$168$	−0.237670	+	2.49748i	−0.0183367	+	0.192685i
$169$		−	1.00000i		−	0.0769231i
$170$	20.2719	−	3.42704i	1.55479	−	0.262842i
$171$			4.81425i			0.368155i
$172$	−7.97189	−	9.04999i	−0.607851	−	0.690055i
$173$	−1.88337	+	1.88337i	−0.143190	+	0.143190i	−0.775068	−	0.631878i	$-0.782284\pi$
$173$	−1.88337	+	1.88337i	−0.143190	+	0.143190i	0.631878	+	0.775068i	$0.282284\pi$
$174$	−16.0556	−	17.1047i	−1.21717	−	1.29670i
$175$	−1.80562	−	0.736320i	−0.136492	−	0.0556606i
$176$	−0.414923	+	3.26240i	−0.0312760	+	0.245913i
$177$	19.7964	+	19.7964i	1.48799	+	1.48799i
$178$	17.7703	+	0.562192i	1.33194	+	0.0421380i
$179$	3.78420			0.282845			0.141422	−	0.989949i	$-0.454832\pi$
$179$	3.78420			0.282845			0.141422	+	0.989949i	$0.454832\pi$
$180$	5.87662	−	7.73748i	0.438018	−	0.576717i
$181$	14.3395			1.06585			0.532923	−	0.846164i	$-0.321094\pi$
$181$	14.3395			1.06585			0.532923	+	0.846164i	$0.321094\pi$
$182$	−0.551263	−	0.0174401i	−0.0408624	−	0.00129275i
$183$	2.87633	+	2.87633i	0.212624	+	0.212624i
$184$	−8.38874	+	6.93086i	−0.618426	+	0.510950i
$185$	−2.68731	−	13.3187i	−0.197575	−	0.979212i
$186$	20.5885	+	21.9337i	1.50962	+	1.60826i
$187$	3.77973	−	3.77973i	0.276401	−	0.276401i
$188$	6.70753	−	5.90848i	0.489197	−	0.430920i
$189$			0.733896i			0.0533831i
$190$	−4.05966	+	5.71150i	−0.294519	+	0.414356i
$191$		−	3.78197i		−	0.273654i	−0.990595	−	0.136827i	$-0.956310\pi$
$191$		−	3.78197i		−	0.273654i	0.990595	−	0.136827i	$-0.0436904\pi$
$192$	−10.2079	−	15.0613i	−0.736695	−	1.08696i
$193$	3.49821	−	3.49821i	0.251807	−	0.251807i	−0.569904	−	0.821711i	$-0.693020\pi$
$193$	3.49821	−	3.49821i	0.251807	−	0.251807i	0.821711	+	0.569904i	$0.193020\pi$
$194$	4.89187	−	4.59184i	0.351216	−	0.329675i
$195$	4.23624	+	2.81376i	0.303363	+	0.201498i
$196$	0.865711	−	13.6684i	0.0618365	−	0.976315i
$197$	−16.9407	−	16.9407i	−1.20698	−	1.20698i	−0.972001	−	0.234977i	$-0.924499\pi$
$197$	−16.9407	−	16.9407i	−1.20698	−	1.20698i	−0.234977	−	0.972001i	$-0.575501\pi$
$198$	0.0798781	−	2.52486i	0.00567669	−	0.179434i
$199$	25.9852			1.84204			0.921020	−	0.389515i	$-0.127357\pi$
$199$	25.9852			1.84204			0.921020	+	0.389515i	$0.127357\pi$
$200$	13.4966	−	4.22403i	0.954352	−	0.298684i
$201$	22.6632			1.59854
$202$	0.810498	−	25.6190i	0.0570264	−	1.80255i
$203$	−2.01139	−	2.01139i	−0.141172	−	0.141172i
$204$	−1.86932	+	29.5141i	−0.130879	+	2.06640i
$205$	1.91271	+	1.27045i	0.133589	+	0.0887319i
$206$	12.2994	−	11.5451i	0.856941	−	0.804382i
$207$	5.91029	−	5.91029i	0.410793	−	0.410793i
$208$	3.16268	−	2.44897i	0.219292	−	0.169806i
$209$			1.82185i			0.126020i
$210$	1.62501	−	2.28621i	0.112136	−	0.157763i
$211$		−	5.58430i		−	0.384439i	−0.981352	−	0.192219i	$-0.938431\pi$
$211$		−	5.58430i		−	0.384439i	0.981352	−	0.192219i	$-0.0615685\pi$
$212$	−1.30556	+	1.15003i	−0.0896662	+	0.0789845i
$213$	−5.97114	+	5.97114i	−0.409136	+	0.409136i
$214$	−13.8549	−	14.7602i	−0.947103	−	1.00899i
$215$	2.66690	+	13.2176i	0.181881	+	0.901431i
$216$	−3.39012	−	4.10322i	−0.230669	−	0.279189i
$217$	2.57926	+	2.57926i	0.175091	+	0.175091i
$218$	8.51650	+	0.269433i	0.576810	+	0.0182483i
$219$	0.405756			0.0274185
$220$	2.22388	−	2.92808i	0.149934	−	0.197411i
$221$	−6.50151			−0.437339
$222$	19.5342	+	0.617994i	1.31105	+	0.0414771i
$223$	−3.41426	−	3.41426i	−0.228636	−	0.228636i	0.583487	−	0.812122i	$-0.301688\pi$
$223$	−3.41426	−	3.41426i	−0.228636	−	0.228636i	−0.812122	+	0.583487i	$0.801688\pi$
$224$	−1.29487	−	1.78618i	−0.0865172	−	0.119344i
$225$	−10.0131	+	4.21214i	−0.667539	+	0.280809i
$226$	−9.96555	−	10.6167i	−0.662899	−	0.706213i
$227$	9.31565	−	9.31565i	0.618301	−	0.618301i	−0.326794	−	0.945096i	$-0.605968\pi$
$227$	9.31565	−	9.31565i	0.618301	−	0.618301i	0.945096	+	0.326794i	$0.105968\pi$
$228$	−6.66244	−	7.56346i	−0.441231	−	0.500903i
$229$			14.3456i			0.947986i	0.880529	+	0.473993i	$0.157188\pi$
$229$			14.3456i			0.947986i	−0.880529	+	0.473993i	$0.842812\pi$
$230$	11.9957	−	2.02792i	0.790974	−	0.133717i
$231$		−	0.729251i		−	0.0479812i
$232$	20.5371	+	1.95439i	1.34832	+	0.128312i
$233$	−1.74686	+	1.74686i	−0.114440	+	0.114440i	−0.762008	−	0.647568i	$-0.775786\pi$
$233$	−1.74686	+	1.74686i	−0.114440	+	0.114440i	0.647568	+	0.762008i	$0.275786\pi$
$234$	−2.24021	+	2.10281i	−0.146447	+	0.137465i
$235$	−9.79640	+	1.97661i	−0.639047	+	0.128940i
$236$	−24.5701	−	1.55619i	−1.59938	−	0.101299i
$237$	−14.4370	−	14.4370i	−0.937782	−	0.937782i
$238$	−0.113387	+	3.58404i	−0.00734979	+	0.232319i
$239$	4.56207			0.295096			0.147548	−	0.989055i	$-0.452862\pi$
$239$	4.56207			0.295096			0.147548	+	0.989055i	$0.452862\pi$
$240$	1.47538	+	20.2887i	0.0952355	+	1.30963i
$241$	21.2829			1.37095			0.685475	−	0.728096i	$-0.259595\pi$
$241$	21.2829			1.37095			0.685475	+	0.728096i	$0.259595\pi$
$242$	−0.461676	+	14.5931i	−0.0296776	+	0.938079i
$243$	13.3728	+	13.3728i	0.857865	+	0.857865i
$244$	−3.56993	−	0.226107i	−0.228542	−	0.0144750i
$245$	−8.47210	+	12.7551i	−0.541263	+	0.814893i
$246$	−2.40817	+	2.26047i	−0.153539	+	0.144122i
$247$	1.56688	−	1.56688i	0.0996980	−	0.0996980i
$248$	−26.3352	−	2.50616i	−1.67228	−	0.159141i
$249$			9.80362i			0.621279i
$250$	−15.4312	−	3.44645i	−0.975955	−	0.217972i
$251$			25.3663i			1.60111i	0.599263	+	0.800553i	$0.295461\pi$
$251$			25.3663i			1.60111i	−0.599263	+	0.800553i	$0.704539\pi$
$252$	1.12013	+	1.27162i	0.0705616	+	0.0801043i
$253$	2.23662	−	2.23662i	0.140615	−	0.140615i
$254$	−3.61739	−	3.85375i	−0.226975	−	0.241806i
$255$	18.2937	−	27.5419i	1.14560	−	1.72474i
$256$	15.4906	+	4.00508i	0.968164	+	0.250318i
$257$	2.82314	+	2.82314i	0.176103	+	0.176103i	0.789655	−	0.613552i	$-0.210260\pi$
$257$	2.82314	+	2.82314i	0.176103	+	0.176103i	−0.613552	+	0.789655i	$0.710260\pi$
$258$	−19.3858	−	0.613301i	−1.20691	−	0.0381824i
$259$	2.36976			0.147250
$260$	−4.43094	+	0.605645i	−0.274795	+	0.0375605i
$261$	−15.8464			−0.980865
$262$	−21.1585	−	0.669383i	−1.30718	−	0.0413546i
$263$	9.48595	+	9.48595i	0.584929	+	0.584929i	0.936254	−	0.351325i	$-0.114269\pi$
$263$	9.48595	+	9.48595i	0.584929	+	0.584929i	−0.351325	+	0.936254i	$0.614269\pi$
$264$	3.36867	+	4.07725i	0.207327	+	0.250937i
$265$	1.90678	−	0.384729i	0.117133	−	0.0236337i
$266$	−0.836436	−	0.891089i	−0.0512852	−	0.0546361i
$267$	20.2179	−	20.2179i	1.23732	−	1.23732i
$268$	−14.9549	+	13.1734i	−0.913516	+	0.804691i
$269$		−	28.8302i		−	1.75781i	−0.477000	−	0.878904i	$-0.658276\pi$
$269$		−	28.8302i		−	1.75781i	0.477000	−	0.878904i	$-0.341724\pi$
$270$	0.991923	+	5.86752i	0.0603665	+	0.357086i
$271$			9.17157i			0.557133i	0.960417	+	0.278567i	$0.0898593\pi$
$271$			9.17157i			0.557133i	−0.960417	+	0.278567i	$0.910141\pi$
$272$	−15.9220	−	20.5622i	−0.965414	−	1.24677i
$273$	−0.627192	+	0.627192i	−0.0379594	+	0.0379594i
$274$	−1.11467	+	1.04631i	−0.0673399	+	0.0632097i
$275$	−3.78923	+	1.59399i	−0.228499	+	0.0961213i
$276$	−1.10615	+	17.4647i	−0.0665825	+	1.05125i
$277$	18.5053	+	18.5053i	1.11188	+	1.11188i	0.992897	+	0.118979i	$0.0379622\pi$
$277$	18.5053	+	18.5053i	1.11188	+	1.11188i	0.118979	+	0.992897i	$0.462038\pi$
$278$	0.818746	−	25.8797i	0.0491051	−	1.55216i
$279$	20.3202			1.21654
$280$	0.256594	+	2.45317i	0.0153344	+	0.146605i
$281$	18.8811			1.12635			0.563176	−	0.826337i	$-0.309579\pi$
$281$	18.8811			1.12635			0.563176	+	0.826337i	$0.309579\pi$
$282$	0.454557	−	14.3681i	0.0270685	−	0.855606i
$283$	−4.66224	−	4.66224i	−0.277141	−	0.277141i	0.554826	−	0.831967i	$-0.312785\pi$
$283$	−4.66224	−	4.66224i	−0.277141	−	0.277141i	−0.831967	+	0.554826i	$0.812785\pi$
$284$	0.469389	−	7.41103i	0.0278531	−	0.439764i
$285$	2.22884	+	11.0465i	0.132025	+	0.654337i
$286$	−0.847756	+	0.795761i	−0.0501289	+	0.0470543i
$287$	−0.283184	+	0.283184i	−0.0167158	+	0.0167158i
$288$	−12.1367	−	1.93534i	−0.715162	−	0.114041i
$289$			25.2696i			1.48645i
$290$	−18.7997	−	13.3626i	−1.10396	−	0.784678i
$291$		−	10.7900i		−	0.632518i
$292$	−0.267749	+	0.235852i	−0.0156688	+	0.0138022i
$293$	−21.2736	+	21.2736i	−1.24282	+	1.24282i	−0.283992	+	0.958827i	$0.591659\pi$
$293$	−21.2736	+	21.2736i	−1.24282	+	1.24282i	−0.958827	+	0.283992i	$0.908341\pi$
$294$	−15.0742	−	16.0591i	−0.879142	−	0.936586i
$295$	22.9283	+	15.2293i	1.33494	+	0.886684i
$296$	−13.2493	+	10.9467i	−0.770102	+	0.636267i
$297$	1.09401	+	1.09401i	0.0634807	+	0.0634807i
$298$	−1.64604	−	0.0520752i	−0.0953527	−	0.00301664i
$299$	−3.84720			−0.222490
$300$	9.90195	−	20.4746i	0.571690	−	1.18210i
$301$	−2.35176			−0.135553
$302$	1.42574	+	0.0451056i	0.0820421	+	0.00259553i
$303$	−29.1476	−	29.1476i	−1.67449	−	1.67449i
$304$	8.79277	+	1.11829i	0.504300	+	0.0641386i
$305$	3.33139	+	2.21275i	0.190755	+	0.126702i
$306$	13.6714	+	14.5647i	0.781544	+	0.832610i
$307$	19.0807	−	19.0807i	1.08899	−	1.08899i	0.0933621	−	0.995632i	$-0.470239\pi$
$307$	19.0807	−	19.0807i	1.08899	−	1.08899i	0.995632	−	0.0933621i	$-0.0297614\pi$
$308$	0.423889	+	0.481215i	0.0241533	+	0.0274198i
$309$		−	27.1287i		−	1.54330i
$310$	24.1073	+	17.1352i	1.36920	+	0.973211i
$311$			10.3602i			0.587475i	0.955886	+	0.293738i	$0.0948992\pi$
$311$			10.3602i			0.587475i	−0.955886	+	0.293738i	$0.905101\pi$
$312$	0.609416	−	6.40386i	0.0345014	−	0.362547i
$313$	5.32726	−	5.32726i	0.301114	−	0.301114i	−0.540335	−	0.841450i	$-0.681703\pi$
$313$	5.32726	−	5.32726i	0.301114	−	0.301114i	0.841450	+	0.540335i	$0.181703\pi$
$314$	20.2830	−	19.0390i	1.14464	−	1.07443i
$315$	−0.374726	−	1.85720i	−0.0211134	−	0.104642i
$316$	17.9183	+	1.13489i	1.00798	+	0.0638423i
$317$	12.8622	+	12.8622i	0.722415	+	0.722415i	0.969097	−	0.246681i	$-0.0793401\pi$
$317$	12.8622	+	12.8622i	0.722415	+	0.722415i	−0.246681	+	0.969097i	$0.579340\pi$
$318$	−0.0884753	+	2.79661i	−0.00496145	+	0.156826i
$319$	−5.99670			−0.335751
$320$	−12.7667	−	12.5304i	−0.713680	−	0.700472i
$321$	−32.5564			−1.81712
$322$	−0.0670956	+	2.12082i	−0.00373909	+	0.118189i
$323$	−10.1871	−	10.1871i	−0.566824	−	0.566824i
$324$	−21.5521	−	1.36503i	−1.19734	−	0.0758352i
$325$	4.62984	+	1.88802i	0.256817	+	0.104728i
$326$	22.5703	−	21.1860i	1.25005	−	1.17338i
$327$	9.68953	−	9.68953i	0.535832	−	0.535832i
$328$	0.275158	−	2.89142i	0.0151931	−	0.159652i
$329$		−	1.74304i		−	0.0960970i
$330$	−0.985645	−	5.83038i	−0.0542580	−	0.320952i
$331$			20.1455i			1.10729i	0.832751	+	0.553647i	$0.186764\pi$
$331$			20.1455i			1.10729i	−0.832751	+	0.553647i	$0.813236\pi$
$332$	−5.69851	−	6.46917i	−0.312746	−	0.355042i
$333$	9.33483	−	9.33483i	0.511545	−	0.511545i
$334$	−17.8768	−	19.0449i	−0.978174	−	1.04209i
$335$	21.8417	−	4.40698i	1.19334	−	0.240779i
$336$	−3.51958	−	0.447632i	−0.192009	−	0.0244203i
$337$	−7.26448	−	7.26448i	−0.395721	−	0.395721i	0.480999	−	0.876721i	$-0.340274\pi$
$337$	−7.26448	−	7.26448i	−0.395721	−	0.395721i	−0.876721	+	0.480999i	$0.840274\pi$
$338$	1.41351	+	0.0447185i	0.0768846	+	0.00243237i
$339$	−23.4172			−1.27185
$340$	3.93761	+	28.8078i	0.213547	+	1.56232i
$341$	7.68971			0.416421
$342$	−6.80497	−	0.215286i	−0.367971	−	0.0116413i
$343$	−3.81883	−	3.81883i	−0.206197	−	0.206197i
$344$	13.1487	−	10.8636i	0.708931	−	0.585726i
$345$	10.8251	−	16.2977i	0.582805	−	0.877437i
$346$	−2.57793	−	2.74638i	−0.138591	−	0.147646i
$347$	−21.0494	+	21.0494i	−1.12999	+	1.12999i	−0.139816	+	0.990178i	$0.544651\pi$
$347$	−21.0494	+	21.0494i	−1.12999	+	1.12999i	−0.990178	+	0.139816i	$0.955349\pi$
$348$	24.8955	−	21.9298i	1.33454	−	1.17556i
$349$		−	11.8903i		−	0.636472i	−0.948011	−	0.318236i	$-0.896910\pi$
$349$		−	11.8903i		−	0.636472i	0.948011	−	0.318236i	$-0.103090\pi$
$350$	1.12154	−	2.51933i	0.0599487	−	0.134664i
$351$		−	1.88180i		−	0.100443i
$352$	−4.59287	−	0.732386i	−0.244801	−	0.0390363i
$353$	−8.06460	+	8.06460i	−0.429235	+	0.429235i	−0.888368	−	0.459132i	$-0.848160\pi$
$353$	−8.06460	+	8.06460i	−0.429235	+	0.429235i	0.459132	+	0.888368i	$0.348160\pi$
$354$	−28.8675	+	27.0970i	−1.53429	+	1.44019i
$355$	−4.59358	+	6.91582i	−0.243802	+	0.367054i
$356$	−1.58932	+	25.0933i	−0.0842340	+	1.32994i
$357$	4.07770	+	4.07770i	0.215815	+	0.215815i
$358$	−0.169224	+	5.34899i	−0.00894376	+	0.282703i
$359$	−5.29931			−0.279687			−0.139843	−	0.990174i	$-0.544660\pi$
$359$	−5.29931			−0.279687			−0.139843	+	0.990174i	$0.544660\pi$
$360$	10.6742	+	8.65265i	0.562579	+	0.456035i
$361$	−14.0898			−0.741568
$362$	−0.641241	+	20.2690i	−0.0337029	+	1.06531i
$363$	16.6031	+	16.6031i	0.871436	+	0.871436i
$364$	0.0493034	−	0.778434i	0.00258420	−	0.0408010i
$365$	0.391049	−	0.0789015i	0.0204684	−	0.00412989i
$366$	−4.19434	+	3.93709i	−0.219241	+	0.205795i
$367$	1.07021	−	1.07021i	0.0558647	−	0.0558647i	−0.678623	−	0.734487i	$-0.737423\pi$
$367$	1.07021	−	1.07021i	0.0558647	−	0.0558647i	0.734487	+	0.678623i	$0.237423\pi$
$368$	−9.42169	−	12.1675i	−0.491139	−	0.634273i
$369$			2.23101i			0.116142i
$370$	18.9463	−	3.20293i	0.984970	−	0.166512i
$371$			0.339267i			0.0176139i
$372$	−31.9241	+	28.1211i	−1.65519	+	1.45801i
$373$	4.61033	−	4.61033i	0.238714	−	0.238714i	−0.577603	−	0.816317i	$-0.696012\pi$
$373$	4.61033	−	4.61033i	0.238714	−	0.238714i	0.816317	+	0.577603i	$0.196012\pi$
$374$	5.17365	+	5.51170i	0.267523	+	0.285003i
$375$	−21.0254	+	14.3007i	−1.08574	+	0.738483i
$376$	8.05172	+	9.74536i	0.415236	+	0.502579i
$377$	5.15746	+	5.15746i	0.265623	+	0.265623i
$378$	−1.03737	−	0.0328187i	−0.0533564	−	0.00168801i
$379$	−25.6874			−1.31947			−0.659736	−	0.751497i	$-0.729332\pi$
$379$	−25.6874			−1.31947			−0.659736	+	0.751497i	$0.729332\pi$
$380$	−7.89171	−	5.99376i	−0.404836	−	0.307474i
$381$	−8.50018			−0.435477
$382$	5.34584	+	0.169124i	0.273517	+	0.00865315i
$383$	7.08294	+	7.08294i	0.361921	+	0.361921i	0.864520	−	0.502599i	$-0.167623\pi$
$383$	7.08294	+	7.08294i	0.361921	+	0.361921i	−0.502599	+	0.864520i	$0.667623\pi$
$384$	21.7458	−	13.7555i	1.10971	−	0.701956i
$385$	−0.141807	−	0.702818i	−0.00722715	−	0.0358189i
$386$	4.78831	+	5.10118i	0.243719	+	0.259643i
$387$	−9.26393	+	9.26393i	−0.470912	+	0.470912i
$388$	6.27183	+	7.12003i	0.318404	+	0.361465i
$389$		−	12.1615i		−	0.616610i	−0.951288	−	0.308305i	$-0.900238\pi$
$389$		−	12.1615i		−	0.616610i	0.951288	−	0.308305i	$-0.0997618\pi$
$390$	−4.16671	+	5.86212i	−0.210990	+	0.296840i
$391$			25.0126i			1.26494i
$392$	19.2817	+	1.83492i	0.973872	+	0.0926774i
$393$	−24.0728	+	24.0728i	−1.21431	+	1.21431i
$394$	24.7034	−	23.1883i	1.24454	−	1.16821i
$395$	−16.7210	−	11.1063i	−0.841326	−	0.558820i
$396$	3.56534	+	0.225816i	0.179165	+	0.0113477i
$397$	16.9963	+	16.9963i	0.853018	+	0.853018i	0.990504	−	0.137486i	$-0.0439022\pi$
$397$	16.9963	+	16.9963i	0.853018	+	0.853018i	−0.137486	+	0.990504i	$0.543902\pi$
$398$	−1.16202	+	36.7302i	−0.0582468	+	1.84112i
$399$	−1.96547			−0.0983964
$400$	5.36715	+	19.2664i	0.268358	+	0.963319i
$401$	−10.9375			−0.546191			−0.273095	−	0.961987i	$-0.588047\pi$
$401$	−10.9375			−0.546191			−0.273095	+	0.961987i	$0.588047\pi$
$402$	−1.01347	+	32.0346i	−0.0505471	+	1.59774i
$403$	−6.61353	−	6.61353i	−0.329444	−	0.329444i
$404$	36.1764	+	2.29129i	1.79984	+	0.113996i
$405$	20.1119	+	13.3586i	0.999370	+	0.663795i
$406$	2.93307	−	2.75317i	0.145566	−	0.136638i
$407$	3.53256	−	3.53256i	0.175102	−	0.175102i
$408$	−41.6347	−	3.96212i	−2.06123	−	0.196154i
$409$			27.4799i			1.35879i	0.733771	+	0.679397i	$0.237759\pi$
$409$			27.4799i			1.35879i	−0.733771	+	0.679397i	$0.762241\pi$
$410$	−1.88132	+	2.64681i	−0.0929117	+	0.130717i
$411$			2.45863i			0.121275i
$412$	15.7690	+	17.9016i	0.776883	+	0.881947i
$413$	−3.39463	+	3.39463i	−0.167039	+	0.167039i
$414$	8.08993	+	8.61853i	0.397598	+	0.423578i
$415$	1.90637	+	9.44827i	0.0935799	+	0.463797i
$416$	3.32021	+	4.57998i	0.162786	+	0.224552i
$417$	−29.4443	−	29.4443i	−1.44189	−	1.44189i
$418$	−2.57519	−	0.0814703i	−0.125957	−	0.00398484i
$419$	−12.6786			−0.619391			−0.309695	−	0.950836i	$-0.600227\pi$
$419$	−12.6786			−0.619391			−0.309695	+	0.950836i	$0.600227\pi$
$420$	3.15890	+	2.39919i	0.154139	+	0.117069i
$421$	−1.77678			−0.0865951			−0.0432975	−	0.999062i	$-0.513786\pi$
$421$	−1.77678			−0.0865951			−0.0432975	+	0.999062i	$0.513786\pi$
$422$	7.89344	+	0.249722i	0.384247	+	0.0121563i
$423$	−6.86610	−	6.86610i	−0.333841	−	0.333841i
$424$	−1.56719	−	1.89685i	−0.0761097	−	0.0921190i
$425$	12.2750	−	30.1009i	0.595423	−	1.46011i
$426$	−8.17322	−	8.70726i	−0.395994	−	0.421868i
$427$	−0.493226	+	0.493226i	−0.0238689	+	0.0238689i
$428$	21.4832	−	18.9240i	1.03843	−	0.914724i
$429$			1.86989i			0.0902791i
$430$	−18.8024	+	3.17860i	−0.906732	+	0.153286i
$431$		−	10.8688i		−	0.523529i	−0.965132	−	0.261765i	$-0.915696\pi$
$431$		−	10.8688i		−	0.523529i	0.965132	−	0.261765i	$-0.0843044\pi$
$432$	5.95153	−	4.60847i	0.286343	−	0.221725i
$433$	−8.66547	+	8.66547i	−0.416436	+	0.416436i	−0.883973	−	0.467537i	$-0.845141\pi$
$433$	−8.66547	+	8.66547i	−0.416436	+	0.416436i	0.467537	+	0.883973i	$0.345141\pi$
$434$	−3.76114	+	3.53046i	−0.180540	+	0.169467i
$435$	−36.3601	+	7.33634i	−1.74333	+	0.351751i
$436$	−0.761691	+	12.0261i	−0.0364784	+	0.575945i
$437$	−6.02810	−	6.02810i	−0.288363	−	0.288363i
$438$	−0.0181448	+	0.573539i	−0.000866993	+	0.0274047i
$439$	−25.8681			−1.23462			−0.617310	−	0.786720i	$-0.711777\pi$
$439$	−25.8681			−1.23462			−0.617310	+	0.786720i	$0.711777\pi$
$440$	4.03941	+	3.27441i	0.192571	+	0.156101i
$441$	−14.8777			−0.708462
$442$	0.290738	−	9.18993i	0.0138290	−	0.437120i
$443$	9.49162	+	9.49162i	0.450961	+	0.450961i	0.895673	−	0.444713i	$-0.146694\pi$
$443$	9.49162	+	9.49162i	0.450961	+	0.450961i	−0.444713	+	0.895673i	$0.646694\pi$
$444$	−1.74708	+	27.5840i	−0.0829127	+	1.30908i
$445$	15.5536	−	23.4165i	0.737311	−	1.11005i
$446$	4.97875	−	4.67339i	0.235751	−	0.221292i
$447$	−1.87276	+	1.87276i	−0.0885786	+	0.0885786i
$448$	2.58268	−	1.75043i	0.122020	−	0.0827001i
$449$			20.3525i			0.960494i	0.877133	+	0.480247i	$0.159453\pi$
$449$			20.3525i			0.960494i	−0.877133	+	0.480247i	$0.840547\pi$
$450$	−5.50612	−	14.3419i	−0.259561	−	0.676085i
$451$			0.844276i			0.0397554i
$452$	15.4524	−	13.6116i	0.726821	−	0.640236i
$453$	1.62212	−	1.62212i	0.0762136	−	0.0762136i
$454$	12.7511	+	13.5843i	0.598441	+	0.637543i
$455$	−0.482497	+	0.726419i	−0.0226198	+	0.0340551i
$456$	10.9889	−	9.07918i	0.514604	−	0.425171i
$457$	1.07145	+	1.07145i	0.0501205	+	0.0501205i	0.731723	−	0.681602i	$-0.238717\pi$
$457$	1.07145	+	1.07145i	0.0501205	+	0.0501205i	−0.681602	+	0.731723i	$0.738717\pi$
$458$	−20.2776	−	0.641516i	−0.947512	−	0.0299761i
$459$	−12.2345			−0.571059
$460$	2.33004	+	17.0467i	0.108639	+	0.794807i
$461$	24.1135			1.12308			0.561538	−	0.827451i	$-0.310210\pi$
$461$	24.1135			1.12308			0.561538	+	0.827451i	$0.310210\pi$
$462$	1.03080	+	0.0326110i	0.0479572	+	0.00151720i
$463$	23.5272	+	23.5272i	1.09340	+	1.09340i	0.995163	+	0.0982398i	$0.0313212\pi$
$463$	23.5272	+	23.5272i	1.09340	+	1.09340i	0.0982398	+	0.995163i	$0.468679\pi$
$464$	−3.68092	+	28.9419i	−0.170883	+	1.34359i
$465$	46.6254	−	9.40756i	2.16220	−	0.436265i
$466$	−2.39108	−	2.54731i	−0.110764	−	0.118002i
$467$	23.9597	−	23.9597i	1.10872	−	1.10872i	0.115404	−	0.993319i	$-0.463184\pi$
$467$	23.9597	−	23.9597i	1.10872	−	1.10872i	0.993319	−	0.115404i	$-0.0368162\pi$
$468$	−2.87215	−	3.26058i	−0.132765	−	0.150720i
$469$			3.88623i			0.179449i
$470$	−2.35587	−	13.9357i	−0.108668	−	0.642804i
$471$		−	44.7381i		−	2.06142i
$472$	3.29842	−	34.6604i	0.151822	−	1.59537i
$473$	−3.50573	+	3.50573i	−0.161194	+	0.161194i
$474$	21.0523	−	19.7611i	0.966966	−	0.907660i
$475$	4.29610	+	10.2127i	0.197119	+	0.468590i
$476$	−5.06100	−	0.320546i	−0.231971	−	0.0146922i
$477$	1.33642	+	1.33642i	0.0611906	+	0.0611906i
$478$	−0.204009	+	6.44851i	−0.00933116	+	0.294948i
$479$	−0.624652			−0.0285411			−0.0142705	−	0.999898i	$-0.504543\pi$
$479$	−0.624652			−0.0285411			−0.0142705	+	0.999898i	$0.504543\pi$
$480$	−28.7442	+	1.17818i	−1.31199	+	0.0537764i
$481$	−6.07635			−0.277058
$482$	−0.951739	+	30.0835i	−0.0433505	+	1.37026i
$483$	2.41293	+	2.41293i	0.109792	+	0.109792i
$484$	−20.6068	−	1.30516i	−0.936672	−	0.0593256i
$485$	−2.09817	−	10.3988i	−0.0952728	−	0.472187i
$486$	−19.5005	+	18.3045i	−0.884563	+	0.830310i
$487$	25.7445	−	25.7445i	1.16659	−	1.16659i	0.183590	−	0.983003i	$-0.441228\pi$
$487$	25.7445	−	25.7445i	1.16659	−	1.16659i	0.983003	−	0.183590i	$-0.0587719\pi$
$488$	0.479246	−	5.03601i	0.0216945	−	0.227970i
$489$		−	49.7831i		−	2.25127i
$490$	−17.6505	−	12.5458i	−0.797370	−	0.566760i
$491$		−	9.90039i		−	0.446798i	−0.974727	−	0.223399i	$-0.928285\pi$
$491$		−	9.90039i		−	0.446798i	0.974727	−	0.223399i	$-0.0717153\pi$
$492$	−3.08750	−	3.50505i	−0.139195	−	0.158020i
$493$	33.5313	−	33.5313i	1.51017	−	1.51017i
$494$	2.14472	+	2.28486i	0.0964956	+	0.102801i
$495$	−3.32710	−	2.20990i	−0.149542	−	0.0993278i
$496$	4.72014	−	37.1128i	0.211940	−	1.66642i
$497$	−1.02392	−	1.02392i	−0.0459289	−	0.0459289i
$498$	−13.8575	−	0.438404i	−0.620968	−	0.0196453i
$499$	27.9236			1.25003			0.625017	−	0.780611i	$-0.285092\pi$
$499$	27.9236			1.25003			0.625017	+	0.780611i	$0.285092\pi$
$500$	5.56164	−	21.6580i	0.248724	−	0.968574i
$501$	−42.0071			−1.87674
$502$	−35.8554	−	1.13434i	−1.60030	−	0.0506282i
$503$	−8.69201	−	8.69201i	−0.387558	−	0.387558i	0.486258	−	0.873815i	$-0.338362\pi$
$503$	−8.69201	−	8.69201i	−0.387558	−	0.387558i	−0.873815	+	0.486258i	$0.838362\pi$
$504$	−1.84753	+	1.52645i	−0.0822955	+	0.0679934i
$505$	−33.7591	−	22.4232i	−1.50226	−	0.997820i
$506$	3.06145	+	3.26149i	0.136098	+	0.144991i
$507$	1.60820	−	1.60820i	0.0714225	−	0.0714225i
$508$	5.60906	−	4.94087i	0.248862	−	0.219216i
$509$			18.9225i			0.838726i	0.907819	+	0.419363i	$0.137747\pi$
$509$			18.9225i			0.838726i	−0.907819	+	0.419363i	$0.862253\pi$
$510$	38.1126	+	27.0899i	1.68766	+	1.19956i
$511$			0.0695780i			0.00307795i
$512$	−6.35393	+	21.7170i	−0.280807	+	0.959764i
$513$	2.94855	−	2.94855i	0.130182	−	0.130182i
$514$	−4.11678	+	3.86428i	−0.181583	+	0.170446i
$515$	−5.27533	−	26.1454i	−0.232459	−	1.15210i
$516$	1.73381	−	27.3745i	0.0763267	−	1.20510i
$517$	−2.59832	−	2.59832i	−0.114274	−	0.114274i
$518$	−0.105972	+	3.34967i	−0.00465615	+	0.147176i
$519$	−6.05766			−0.265902
$520$	−0.657938	−	6.29024i	−0.0288525	−	0.275845i
$521$	24.7708			1.08523			0.542614	−	0.839982i	$-0.317435\pi$
$521$	24.7708			1.08523			0.542614	+	0.839982i	$0.317435\pi$
$522$	0.708626	−	22.3989i	0.0310157	−	0.980374i
$523$	31.9322	+	31.9322i	1.39630	+	1.39630i	0.810344	+	0.585954i	$0.199280\pi$
$523$	31.9322	+	31.9322i	1.39630	+	1.39630i	0.585954	+	0.810344i	$0.300720\pi$
$524$	1.89236	−	29.8778i	0.0826679	−	1.30522i
$525$	−1.71965	−	4.08794i	−0.0750516	−	0.178413i
$526$	−13.8326	+	12.9842i	−0.603132	+	0.566140i
$527$	−42.9980	+	42.9980i	−1.87302	+	1.87302i
$528$	−5.91386	+	4.57930i	−0.257368	+	0.199289i
$529$		−	8.19903i		−	0.356479i
$530$	0.458548	+	2.71245i	0.0199181	+	0.117821i
$531$			26.7439i			1.16059i
$532$	1.29696	−	1.14246i	0.0562305	−	0.0495319i
$533$	0.726120	−	0.726120i	0.0314517	−	0.0314517i
$534$	27.6740	+	29.4822i	1.19757	+	1.27582i
$535$	−31.3764	+	6.33078i	−1.35652	+	0.273703i
$536$	−17.9519	−	21.7279i	−0.775402	−	0.938504i
$537$	6.08574	+	6.08574i	0.262619	+	0.262619i
$538$	40.7516	+	1.28924i	1.75693	+	0.0555832i
$539$	−5.63014			−0.242507
$540$	−8.33813	+	1.13970i	−0.358816	+	0.0490450i
$541$	−37.9058			−1.62970			−0.814849	−	0.579674i	$-0.803180\pi$
$541$	−37.9058			−1.62970			−0.814849	+	0.579674i	$0.803180\pi$
$542$	−12.9641	−	0.410139i	−0.556855	−	0.0176170i
$543$	23.0607	+	23.0607i	0.989630	+	0.989630i
$544$	29.7768	−	21.5864i	1.27667	−	0.925507i
$545$	7.45413	−	11.2225i	0.319300	−	0.480719i
$546$	−0.858493	−	0.914587i	−0.0367401	−	0.0391407i
$547$	12.9198	−	12.9198i	0.552411	−	0.552411i	−0.374725	−	0.927136i	$-0.622263\pi$
$547$	12.9198	−	12.9198i	0.552411	−	0.552411i	0.927136	+	0.374725i	$0.122263\pi$
$548$	−1.42912	−	1.62239i	−0.0610488	−	0.0693050i
$549$			3.88578i			0.165841i
$550$	−2.08367	−	5.42738i	−0.0888479	−	0.231424i
$551$			16.1622i			0.688534i
$552$	−24.6369	−	2.34455i	−1.04862	−	0.0997905i
$553$	2.47562	−	2.47562i	0.105274	−	0.105274i
$554$	−26.9849	+	25.3298i	−1.14648	+	1.07616i
$555$	17.0974	−	25.7409i	0.725745	−	1.09264i
$556$	36.5445	+	2.31460i	1.54983	+	0.0981611i
$557$	−4.01335	−	4.01335i	−0.170051	−	0.170051i	0.616951	−	0.787002i	$-0.288368\pi$
$557$	−4.01335	−	4.01335i	−0.170051	−	0.170051i	−0.787002	+	0.616951i	$0.788368\pi$
$558$	−0.908688	+	28.7227i	−0.0384678	+	1.21593i
$559$	6.03020			0.255050
$560$	−3.47905	+	0.252995i	−0.147017	+	0.0106910i
$561$	12.1571			0.513273
$562$	−0.844335	+	26.6885i	−0.0356161	+	1.12579i
$563$	−30.9791	−	30.9791i	−1.30562	−	1.30562i	−0.924547	−	0.381069i	$-0.875556\pi$
$563$	−30.9791	−	30.9791i	−1.30562	−	1.30562i	−0.381069	−	0.924547i	$-0.624444\pi$
$564$	20.2890	+	1.28504i	0.854322	+	0.0541099i
$565$	−22.5684	+	4.55360i	−0.949459	+	0.191571i
$566$	6.79859	−	6.38161i	0.285766	−	0.268239i
$567$	−2.97765	+	2.97765i	−0.125050	+	0.125050i
$568$	10.4545	+	0.994895i	0.438663	+	0.0417449i
$569$			7.46971i			0.313147i	0.987666	+	0.156573i	$0.0500448\pi$
$569$			7.46971i			0.313147i	−0.987666	+	0.156573i	$0.949955\pi$
$570$	−15.7140	+	2.65649i	−0.658185	+	0.111268i
$571$		−	9.11459i		−	0.381434i	−0.981645	−	0.190717i	$-0.938919\pi$
$571$		−	9.11459i		−	0.381434i	0.981645	−	0.190717i	$-0.0610812\pi$
$572$	−1.08690	−	1.23389i	−0.0454457	−	0.0515917i
$573$	6.08216	−	6.08216i	0.254086	−	0.254086i
$574$	−0.387619	−	0.412947i	−0.0161789	−	0.0172361i
$575$	7.26358	−	17.8119i	0.302912	−	0.742809i
$576$	3.27835	−	17.0688i	0.136598	−	0.711199i
$577$	−6.82293	−	6.82293i	−0.284042	−	0.284042i	0.550676	−	0.834719i	$-0.314370\pi$
$577$	−6.82293	−	6.82293i	−0.284042	−	0.284042i	−0.834719	+	0.550676i	$0.814370\pi$
$578$	−35.7188	−	1.13002i	−1.48571	−	0.0470027i
$579$	11.2516			0.467602
$580$	19.7288	−	25.9760i	0.819193	−	1.07859i
$581$	−1.68110			−0.0697438
$582$	15.2517	+	0.482511i	0.632202	+	0.0200007i
$583$	0.505740	+	0.505740i	0.0209456	+	0.0209456i
$584$	−0.321405	−	0.389011i	−0.0132999	−	0.0160974i
$585$	0.960844	+	4.76210i	0.0397260	+	0.196889i
$586$	−29.1191	−	31.0217i	−1.20290	−	1.28150i
$587$	16.5414	−	16.5414i	0.682735	−	0.682735i	−0.277881	−	0.960616i	$-0.589632\pi$
$587$	16.5414	−	16.5414i	0.682735	−	0.682735i	0.960616	+	0.277881i	$0.0896319\pi$
$588$	23.3737	−	20.5893i	0.963917	−	0.849087i
$589$		−	20.7252i		−	0.853967i
$590$	−22.5520	+	31.7283i	−0.928452	+	1.30623i
$591$		−	54.4881i		−	2.24134i
$592$	−14.8808	−	19.2175i	−0.611597	−	0.789836i
$593$	9.53305	−	9.53305i	0.391475	−	0.391475i	−0.483738	−	0.875213i	$-0.660721\pi$
$593$	9.53305	−	9.53305i	0.391475	−	0.391475i	0.875213	+	0.483738i	$0.160721\pi$
$594$	−1.59531	+	1.49746i	−0.0654562	+	0.0614416i
$595$	4.72282	+	3.13696i	0.193617	+	0.128603i
$596$	0.147217	−	2.32436i	0.00603025	−	0.0952097i
$597$	41.7893	+	41.7893i	1.71032	+	1.71032i
$598$	0.172041	−	5.43805i	0.00703529	−	0.222378i
$599$	−23.6663			−0.966979			−0.483489	−	0.875350i	$-0.660631\pi$
$599$	−23.6663			−0.966979			−0.483489	+	0.875350i	$0.660631\pi$
$600$	28.4982	+	14.9121i	1.16344	+	0.608783i
$601$	13.4784			0.549795			0.274897	−	0.961474i	$-0.411356\pi$
$601$	13.4784			0.549795			0.274897	+	0.961474i	$0.411356\pi$
$602$	0.105167	−	3.32423i	0.00428630	−	0.135485i
$603$	15.3084	+	15.3084i	0.623407	+	0.623407i
$604$	−0.127514	+	2.01328i	−0.00518847	+	0.0819190i
$605$	19.2298	+	12.7727i	0.781804	+	0.519285i
$606$	42.5038	−	39.8969i	1.72660	−	1.62070i
$607$	16.2073	−	16.2073i	0.657834	−	0.657834i	−0.297033	−	0.954867i	$-0.595997\pi$
$607$	16.2073	−	16.2073i	0.657834	−	0.657834i	0.954867	+	0.297033i	$0.0959973\pi$
$608$	−1.97392	+	12.3786i	−0.0800528	+	0.502020i
$609$		−	6.46944i		−	0.262155i
$610$	−3.27672	+	4.60999i	−0.132670	+	0.186653i
$611$			4.46937i			0.180811i
$612$	−21.1987	+	18.6733i	−0.856907	+	0.754825i
$613$	−0.635203	+	0.635203i	−0.0256556	+	0.0256556i	−0.719818	−	0.694163i	$-0.755775\pi$
$613$	−0.635203	+	0.635203i	−0.0256556	+	0.0256556i	0.694163	+	0.719818i	$0.255775\pi$
$614$	26.1175	+	27.8240i	1.05401	+	1.12288i
$615$	1.03288	+	5.11914i	0.0416499	+	0.206424i
$616$	−0.699156	+	0.577650i	−0.0281698	+	0.0232742i
$617$	−16.8468	−	16.8468i	−0.678227	−	0.678227i	0.281372	−	0.959599i	$-0.409211\pi$
$617$	−16.8468	−	16.8468i	−0.678227	−	0.678227i	−0.959599	+	0.281372i	$0.909211\pi$
$618$	38.3466	+	1.21316i	1.54253	+	0.0488003i
$619$	5.11308			0.205512			0.102756	−	0.994707i	$-0.467234\pi$
$619$	5.11308			0.205512			0.102756	+	0.994707i	$0.467234\pi$
$620$	−25.2987	+	33.3096i	−1.01602	+	1.33775i
$621$	−7.23966			−0.290518
$622$	−14.6443	−	0.463295i	−0.587181	−	0.0185764i
$623$	3.46691	+	3.46691i	0.138899	+	0.138899i
$624$	9.02464	+	1.14778i	0.361275	+	0.0459481i
$625$	−17.4824	+	17.8708i	−0.699296	+	0.714832i
$626$	7.29188	+	7.76834i	0.291442	+	0.310485i
$627$	−2.92989	+	2.92989i	−0.117008	+	0.117008i
$628$	26.0047	+	29.5216i	1.03770	+	1.17804i
$629$			39.5055i			1.57519i
$630$	2.64193	−	0.446626i	0.105257	−	0.0177940i
$631$			25.4301i			1.01236i	0.862429	+	0.506178i	$0.168942\pi$
$631$			25.4301i			1.01236i	−0.862429	+	0.506178i	$0.831058\pi$
$632$	−2.40545	+	25.2769i	−0.0956837	+	1.00546i
$633$	8.98065	−	8.98065i	0.356949	−	0.356949i
$634$	−18.7560	+	17.6057i	−0.744897	+	0.699211i
$635$	−8.19208	+	1.65291i	−0.325093	+	0.0655936i
$636$	−3.94907	−	0.250121i	−0.156591	−	0.00991794i
$637$	4.84220	+	4.84220i	0.191855	+	0.191855i
$638$	0.268164	−	8.47638i	0.0106167	−	0.335583i
$639$	−8.06671			−0.319114
$640$	18.2827	−	17.4855i	0.722689	−	0.691174i
$641$	−33.6710			−1.32992			−0.664962	−	0.746877i	$-0.731552\pi$
$641$	−33.6710			−1.32992			−0.664962	+	0.746877i	$0.731552\pi$
$642$	1.45588	−	46.0187i	0.0574589	−	1.81621i
$643$	−6.67990	−	6.67990i	−0.263430	−	0.263430i	0.563016	−	0.826446i	$-0.309641\pi$
$643$	−6.67990	−	6.67990i	−0.263430	−	0.263430i	−0.826446	+	0.563016i	$0.809641\pi$
$644$	−2.99479	−	0.189680i	−0.118011	−	0.00747444i
$645$	−16.9676	+	25.5454i	−0.668097	+	1.00585i
$646$	14.8550	−	13.9439i	0.584464	−	0.548617i
$647$	−4.23583	+	4.23583i	−0.166528	+	0.166528i	−0.785451	−	0.618924i	$-0.787569\pi$
$647$	−4.23583	+	4.23583i	−0.166528	+	0.166528i	0.618924	+	0.785451i	$0.287569\pi$
$648$	2.89326	−	30.4029i	0.113658	−	1.19434i
$649$			10.1206i			0.397270i
$650$	−2.87576	+	6.45988i	−0.112797	+	0.253377i
$651$			8.29591i			0.325142i
$652$	28.9372	+	32.8507i	1.13327	+	1.28653i
$653$	15.8120	−	15.8120i	0.618772	−	0.618772i	−0.326444	−	0.945216i	$-0.605851\pi$
$653$	15.8120	−	15.8120i	0.618772	−	0.618772i	0.945216	+	0.326444i	$0.105851\pi$
$654$	13.2629	+	14.1295i	0.518621	+	0.552508i
$655$	−18.5191	+	27.8813i	−0.723603	+	1.08941i
$656$	4.07473	+	0.518238i	0.159091	+	0.0202338i
$657$	0.274078	+	0.274078i	0.0106928	+	0.0106928i
$658$	2.46380	+	0.0779463i	0.0960489	+	0.00303866i
$659$	12.6866			0.494198			0.247099	−	0.968990i	$-0.420523\pi$
$659$	12.6866			0.494198			0.247099	+	0.968990i	$0.420523\pi$
$660$	8.28536	−	1.13249i	0.322507	−	0.0440821i
$661$	6.64270			0.258371			0.129186	−	0.991620i	$-0.458764\pi$
$661$	6.64270			0.258371			0.129186	+	0.991620i	$0.458764\pi$
$662$	−28.4757	−	0.900875i	−1.10674	−	0.0350135i
$663$	−10.4557	−	10.4557i	−0.406066	−	0.406066i
$664$	9.39905	−	7.76559i	0.364754	−	0.301363i
$665$	−1.89422	+	0.382196i	−0.0734549	+	0.0148209i
$666$	12.7774	+	13.6123i	0.495114	+	0.527465i
$667$	19.8418	−	19.8418i	0.768278	−	0.768278i
$668$	27.7195	−	24.4173i	1.07250	−	0.944733i
$669$		−	10.9816i		−	0.424573i
$670$	5.25257	+	31.0705i	0.202925	+	1.20036i
$671$			1.47049i			0.0567675i
$672$	0.790122	−	4.95493i	0.0304796	−	0.191141i
$673$	−22.3465	+	22.3465i	−0.861393	+	0.861393i	−0.991500	−	0.130107i	$-0.958468\pi$
$673$	−22.3465	+	22.3465i	−0.861393	+	0.861393i	0.130107	+	0.991500i	$0.458468\pi$
$674$	10.5932	−	9.94353i	0.408037	−	0.383010i
$675$	8.71242	+	3.55286i	0.335341	+	0.136750i
$676$	−0.126420	+	1.99600i	−0.00486230	+	0.0767693i
$677$	19.4412	+	19.4412i	0.747188	+	0.747188i	0.973950	−	0.226762i	$-0.0728140\pi$
$677$	19.4412	+	19.4412i	0.747188	+	0.747188i	−0.226762	+	0.973950i	$0.572814\pi$
$678$	1.04718	−	33.1003i	0.0402168	−	1.27121i
$679$	1.85023			0.0710054
$680$	−40.8961	+	4.27759i	−1.56829	+	0.164038i
$681$	29.9628			1.14818
$682$	−0.343873	+	10.8695i	−0.0131676	+	0.416213i
$683$	−2.48920	−	2.48920i	−0.0952465	−	0.0952465i	0.657878	−	0.753124i	$-0.271454\pi$
$683$	−2.48920	−	2.48920i	−0.0952465	−	0.0952465i	−0.753124	+	0.657878i	$0.771454\pi$
$684$	0.608617	−	9.60924i	0.0232710	−	0.367419i
$685$	0.478093	+	2.36951i	0.0182670	+	0.0905342i
$686$	5.56871	−	5.22717i	0.212614	−	0.199574i
$687$	−23.0706	+	23.0706i	−0.880198	+	0.880198i
$688$	14.7678	+	19.0716i	0.563017	+	0.727098i
$689$		−	0.869922i		−	0.0331414i
$690$	22.5528	+	16.0302i	0.858569	+	0.610259i
$691$			31.7913i			1.20940i	0.796454	+	0.604699i	$0.206706\pi$
$691$			31.7913i			1.20940i	−0.796454	+	0.604699i	$0.793294\pi$
$692$	3.99730	−	3.52111i	0.151955	−	0.133853i
$693$	0.492591	−	0.492591i	0.0187120	−	0.0187120i
$694$	−28.8122	−	30.6948i	−1.09370	−	1.16516i
$695$	−34.1026	−	22.6514i	−1.29358	−	0.859216i
$696$	29.8846	+	36.1707i	1.13277	+	1.37105i
$697$	−4.72087	−	4.72087i	−0.178816	−	0.178816i
$698$	16.8070	+	0.531716i	0.636154	+	0.0201258i
$699$	−5.61858			−0.212514
$700$	3.51094	+	1.69796i	0.132701	+	0.0641769i
$701$	−4.81933			−0.182024			−0.0910118	−	0.995850i	$-0.529010\pi$
$701$	−4.81933			−0.182024			−0.0910118	+	0.995850i	$0.529010\pi$
$702$	2.65993	+	0.0841513i	0.100393	+	0.00317609i
$703$	−9.52090	−	9.52090i	−0.359087	−	0.359087i
$704$	1.24062	−	6.45930i	0.0467576	−	0.243444i
$705$	−18.9333	−	12.5758i	−0.713070	−	0.473631i
$706$	−11.0387	−	11.7600i	−0.415448	−	0.442593i
$707$	4.99817	−	4.99817i	0.187975	−	0.187975i
$708$	−37.0109	−	42.0162i	−1.39095	−	1.57907i
$709$		−	25.3141i		−	0.950691i	−0.879799	−	0.475346i	$-0.842323\pi$
$709$		−	25.3141i		−	0.950691i	0.879799	−	0.475346i	$-0.157677\pi$
$710$	−9.57014	−	6.80232i	−0.359161	−	0.255287i
$711$		−	19.5036i		−	0.731443i
$712$	−35.3984	−	3.36865i	−1.32661	−	0.126246i
$713$	−25.4436	+	25.4436i	−0.952871	+	0.952871i
$714$	−5.94620	+	5.58150i	−0.222531	+	0.208882i
$715$	0.363610	+	1.80211i	0.0135982	+	0.0673951i
$716$	−7.55327	−	0.478398i	−0.282279	−	0.0178786i
$717$	7.33670	+	7.33670i	0.273994	+	0.273994i
$718$	0.236977	−	7.49061i	0.00884391	−	0.279547i
$719$	17.8561			0.665921			0.332961	−	0.942941i	$-0.391952\pi$
$719$	17.8561			0.665921			0.332961	+	0.942941i	$0.391952\pi$
$720$	−12.7079	+	14.7011i	−0.473596	+	0.547877i
$721$	4.65196			0.173248
$722$	0.630075	−	19.9160i	0.0234490	−	0.741197i
$723$	34.2270	+	34.2270i	1.27292	+	1.27292i
$724$	−28.6216	−	1.81280i	−1.06371	−	0.0673720i
$725$	−33.6156	+	14.1408i	−1.24845	+	0.525178i
$726$	−24.2110	+	22.7261i	−0.898556	+	0.843445i
$727$	−35.3041	+	35.3041i	−1.30936	+	1.30936i	−0.387477	+	0.921880i	$0.626653\pi$
$727$	−35.3041	+	35.3041i	−1.30936	+	1.30936i	−0.921880	+	0.387477i	$0.873347\pi$
$728$	1.09812	+	0.104501i	0.0406989	+	0.00387307i
$729$			10.6193i			0.393308i
$730$	0.0940407	+	0.556278i	0.00348060	+	0.0205888i
$731$		−	39.2054i		−	1.45006i
$732$	−5.37753	−	6.10478i	−0.198759	−	0.225639i
$733$	14.6703	−	14.6703i	0.541859	−	0.541859i	−0.382214	−	0.924074i	$-0.624838\pi$
$733$	14.6703	−	14.6703i	0.541859	−	0.541859i	0.924074	+	0.382214i	$0.124838\pi$
$734$	1.46490	+	1.56061i	0.0540703	+	0.0576033i
$735$	−34.1375	+	6.88789i	−1.25918	+	0.254064i
$736$	17.6201	−	12.7735i	0.649486	−	0.470838i
$737$	5.79314	+	5.79314i	0.213393	+	0.213393i
$738$	−3.15355	−	0.0997675i	−0.116084	−	0.00367249i
$739$	29.6878			1.09208			0.546041	−	0.837758i	$-0.316134\pi$
$739$	29.6878			1.09208			0.546041	+	0.837758i	$0.316134\pi$
$740$	3.68011	+	26.9239i	0.135284	+	0.989743i
$741$	5.03969			0.185138
$742$	−0.479556	−	0.0151715i	−0.0176051	−	0.000556964i
$743$	21.9023	+	21.9023i	0.803518	+	0.803518i	0.983644	−	0.180126i	$-0.0576505\pi$
$743$	21.9023	+	21.9023i	0.803518	+	0.803518i	−0.180126	+	0.983644i	$0.557651\pi$
$744$	−38.3217	−	46.3825i	−1.40494	−	1.70047i
$745$	−1.44071	+	2.16905i	−0.0527836	+	0.0794678i
$746$	6.31057	+	6.72290i	0.231046	+	0.246143i
$747$	−6.62210	+	6.62210i	−0.242290	+	0.242290i
$748$	−8.02218	+	7.06651i	−0.293320	+	0.258377i
$749$		−	5.58270i		−	0.203987i
$750$	−19.2738	−	30.3590i	−0.703781	−	1.10855i
$751$		−	6.72720i		−	0.245479i	−0.992439	−	0.122740i	$-0.960832\pi$
$751$		−	6.72720i		−	0.245479i	0.992439	−	0.122740i	$-0.0391680\pi$
$752$	−14.1352	+	10.9454i	−0.515457	+	0.399136i
$753$	−40.7940	+	40.7940i	−1.48661	+	1.48661i
$754$	−7.52074	+	7.05947i	−0.273889	+	0.257091i
$755$	1.24789	−	1.87875i	0.0454153	−	0.0683746i
$756$	0.0927790	−	1.46486i	0.00337434	−	0.0532763i
$757$	14.5990	+	14.5990i	0.530609	+	0.530609i	0.920754	−	0.390145i	$-0.127575\pi$
$757$	14.5990	+	14.5990i	0.530609	+	0.530609i	−0.390145	+	0.920754i	$0.627575\pi$
$758$	1.14870	−	36.3093i	0.0417227	−	1.31881i
$759$	7.19384			0.261120
$760$	8.82513	−	10.8869i	0.320121	−	0.394911i
$761$	23.2357			0.842294			0.421147	−	0.906993i	$-0.361628\pi$
$761$	23.2357			0.842294			0.421147	+	0.906993i	$0.361628\pi$
$762$	0.380116	−	12.0151i	0.0137701	−	0.435260i
$763$	1.66154	+	1.66154i	0.0601516	+	0.0601516i
$764$	−0.478117	+	7.54882i	−0.0172977	+	0.273107i
$765$	30.9608	−	6.24694i	1.11939	−	0.225858i
$766$	−10.3285	+	9.69504i	−0.373185	+	0.350296i
$767$	8.70425	−	8.70425i	0.314292	−	0.314292i
$768$	18.4710	+	31.3529i	0.666515	+	1.13135i
$769$		−	7.52587i		−	0.271390i	−0.990751	−	0.135695i	$-0.956673\pi$
$769$		−	7.52587i		−	0.271390i	0.990751	−	0.135695i	$-0.0433267\pi$
$770$	0.999779	−	0.169016i	0.0360295	−	0.00609091i
$771$			9.08034i			0.327020i
$772$	−7.42468	+	6.54019i	−0.267220	+	0.235387i

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0447185 + 1.41351i) q^{2} +(1.60820 + 1.60820i) q^{3} +(-1.99600 - 0.126420i) q^{4} +(1.86263 + 1.23718i) q^{5} +(-2.34511 + 2.20128i) q^{6} +(-0.275770 + 0.275770i) q^{7} +(0.267954 - 2.81571i) q^{8} +2.17259i q^{9} +O(q^{10})\)	\(q+(-0.0447185 + 1.41351i) q^{2} +(1.60820 + 1.60820i) q^{3} +(-1.99600 - 0.126420i) q^{4} +(1.86263 + 1.23718i) q^{5} +(-2.34511 + 2.20128i) q^{6} +(-0.275770 + 0.275770i) q^{7} +(0.267954 - 2.81571i) q^{8} +2.17259i q^{9} +(-1.83206 + 2.57751i) q^{10} +0.822170i q^{11} +(-3.00665 - 3.41327i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-0.377470 - 0.402134i) q^{14} +(1.00584 + 4.98510i) q^{15} +(3.96804 + 0.504668i) q^{16} +(-4.59726 - 4.59726i) q^{17} +(-3.07097 - 0.0971552i) q^{18} +2.21590 q^{19} +(-3.56140 - 2.70489i) q^{20} -0.886983 q^{21} +(-1.16214 - 0.0367662i) q^{22} +(-2.72038 - 2.72038i) q^{23} +(4.95913 - 4.09729i) q^{24} +(1.93876 + 4.60882i) q^{25} +(0.967879 + 1.03112i) q^{26} +(1.33063 - 1.33063i) q^{27} +(0.585299 - 0.515573i) q^{28} +7.29375i q^{29} +(-7.09145 + 1.19883i) q^{30} -9.35295i q^{31} +(-0.890797 + 5.58628i) q^{32} +(-1.32221 + 1.32221i) q^{33} +(6.70384 - 6.29268i) q^{34} +(-0.854833 + 0.172479i) q^{35} +(0.274659 - 4.33650i) q^{36} +(-4.29663 - 4.29663i) q^{37} +(-0.0990918 + 3.13219i) q^{38} +2.27433 q^{39} +(3.98264 - 4.91310i) q^{40} +1.02689 q^{41} +(0.0396646 - 1.25376i) q^{42} +(4.26400 + 4.26400i) q^{43} +(0.103939 - 1.64105i) q^{44} +(-2.68789 + 4.04673i) q^{45} +(3.96693 - 3.72363i) q^{46} +(-3.16032 + 3.16032i) q^{47} +(5.56978 + 7.19299i) q^{48} +6.84790i q^{49} +(-6.60129 + 2.53435i) q^{50} -14.7866i q^{51} +(-1.50078 + 1.32199i) q^{52} +(0.615128 - 0.615128i) q^{53} +(1.82135 + 1.94036i) q^{54} +(-1.01717 + 1.53140i) q^{55} +(0.702593 + 0.850379i) q^{56} +(3.56360 + 3.56360i) q^{57} +(-10.3098 - 0.326166i) q^{58} +12.3097 q^{59} +(-1.37744 - 10.0774i) q^{60} +1.78854 q^{61} +(13.2205 + 0.418250i) q^{62} +(-0.599135 - 0.599135i) q^{63} +(-7.85640 - 1.50896i) q^{64} +(2.19190 - 0.442257i) q^{65} +(-1.80983 - 1.92808i) q^{66} +(7.04616 - 7.04616i) q^{67} +(8.59495 + 9.75732i) q^{68} -8.74982i q^{69} +(-0.205573 - 1.21602i) q^{70} +3.71294i q^{71} +(6.11738 + 0.582154i) q^{72} +(0.126153 - 0.126153i) q^{73} +(6.26545 - 5.88117i) q^{74} +(-4.29398 + 10.5298i) q^{75} +(-4.42294 - 0.280134i) q^{76} +(-0.226729 - 0.226729i) q^{77} +(-0.101705 + 3.21479i) q^{78} -8.97712 q^{79} +(6.76661 + 5.84919i) q^{80} +10.7976 q^{81} +(-0.0459209 + 1.45151i) q^{82} +(3.04802 + 3.04802i) q^{83} +(1.77042 + 0.112132i) q^{84} +(-2.87534 - 14.2506i) q^{85} +(-6.21787 + 5.83651i) q^{86} +(-11.7298 + 11.7298i) q^{87} +(2.31499 + 0.220303i) q^{88} -12.5718i q^{89} +(-5.59988 - 3.98032i) q^{90} +0.389997i q^{91} +(5.08598 + 5.77380i) q^{92} +(15.0414 - 15.0414i) q^{93} +(-4.32581 - 4.60846i) q^{94} +(4.12740 + 2.74147i) q^{95} +(-10.4164 + 7.55125i) q^{96} +(-3.35467 - 3.35467i) q^{97} +(-9.67955 - 0.306228i) q^{98} -1.78624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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