LMFDB - Embedded newform 1110.2.u.e.401.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.7
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.e.191.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.54744 - 0.778090i) q^{6} -1.56844 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.40810 + 1.78915i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.54744 - 0.778090i) q^{6} -1.56844 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.40810 + 1.78915i) q^{9} +1.00000 q^{10} +1.64384 q^{11} +(1.64440 - 0.544013i) q^{12} +(-0.629176 + 0.629176i) q^{13} +(1.10905 - 1.10905i) q^{14} +(0.778090 - 1.54744i) q^{15} -1.00000 q^{16} +(4.46856 + 4.46856i) q^{17} +(0.437662 - 2.96790i) q^{18} +(-4.49720 + 4.49720i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(-0.853250 - 2.57914i) q^{21} +(-1.16237 + 1.16237i) q^{22} +(-1.08064 - 1.08064i) q^{23} +(-0.778090 + 1.54744i) q^{24} +1.00000i q^{25} -0.889790i q^{26} +(-4.25212 - 2.98655i) q^{27} +1.56844i q^{28} +(0.289296 - 0.289296i) q^{29} +(0.544013 + 1.64440i) q^{30} +(-5.62866 - 5.62866i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.894273 + 2.70314i) q^{33} -6.31950 q^{34} +(1.10905 + 1.10905i) q^{35} +(1.78915 + 2.40810i) q^{36} +(-5.36910 - 2.85880i) q^{37} -6.36001i q^{38} +(-1.37690 - 0.692337i) q^{39} -1.00000i q^{40} -10.6225 q^{41} +(2.42706 + 1.22039i) q^{42} +(-0.834374 + 0.834374i) q^{43} -1.64384i q^{44} +(2.96790 + 0.437662i) q^{45} +1.52825 q^{46} -13.1074i q^{47} +(-0.544013 - 1.64440i) q^{48} -4.54001 q^{49} +(-0.707107 - 0.707107i) q^{50} +(-4.91714 + 9.77905i) q^{51} +(0.629176 + 0.629176i) q^{52} +4.14299i q^{53} +(5.11851 - 0.894888i) q^{54} +(-1.16237 - 1.16237i) q^{55} +(-1.10905 - 1.10905i) q^{56} +(-9.84174 - 4.94866i) q^{57} +0.409126i q^{58} +(8.55319 + 8.55319i) q^{59} +(-1.54744 - 0.778090i) q^{60} +(-9.70779 - 9.70779i) q^{61} +7.96013 q^{62} +(3.77695 - 2.80617i) q^{63} +1.00000i q^{64} +0.889790 q^{65} +(-2.54375 - 1.27906i) q^{66} +4.75260i q^{67} +(4.46856 - 4.46856i) q^{68} +(1.18912 - 2.36488i) q^{69} -1.56844 q^{70} +3.82480i q^{71} +(-2.96790 - 0.437662i) q^{72} +12.7222i q^{73} +(5.81801 - 1.77505i) q^{74} +(-1.64440 + 0.544013i) q^{75} +(4.49720 + 4.49720i) q^{76} -2.57826 q^{77} +(1.46317 - 0.484058i) q^{78} +(-0.689395 + 0.689395i) q^{79} +(0.707107 + 0.707107i) q^{80} +(2.59788 - 8.61690i) q^{81} +(7.51125 - 7.51125i) q^{82} +2.00378i q^{83} +(-2.57914 + 0.853250i) q^{84} -6.31950i q^{85} -1.17998i q^{86} +(0.633098 + 0.318337i) q^{87} +(1.16237 + 1.16237i) q^{88} +(-7.48295 + 7.48295i) q^{89} +(-2.40810 + 1.78915i) q^{90} +(0.986823 - 0.986823i) q^{91} +(-1.08064 + 1.08064i) q^{92} +(6.19370 - 12.3178i) q^{93} +(9.26833 + 9.26833i) q^{94} +6.36001 q^{95} +(1.54744 + 0.778090i) q^{96} +(3.88735 - 3.88735i) q^{97} +(3.21027 - 3.21027i) q^{98} +(-3.95854 + 2.94108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.544013	+	1.64440i	0.314086	+	0.949394i
$3$	0.544013	+	1.64440i	0.314086	+	0.949394i
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−1.54744	−	0.778090i	−0.631740	−	0.317654i
$7$	−1.56844			−0.592813			−0.296407	−	0.955062i	$-0.595788\pi$
$7$	−1.56844			−0.592813			−0.296407	+	0.955062i	$0.595788\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.40810	+	1.78915i	−0.802700	+	0.596384i
$10$	1.00000			0.316228
$11$	1.64384			0.495638			0.247819	−	0.968806i	$-0.420286\pi$
$11$	1.64384			0.495638			0.247819	+	0.968806i	$0.420286\pi$
$12$	1.64440	−	0.544013i	0.474697	−	0.157043i
$13$	−0.629176	+	0.629176i	−0.174502	+	0.174502i	−0.788954	−	0.614452i	$-0.789377\pi$
$13$	−0.629176	+	0.629176i	−0.174502	+	0.174502i	0.614452	+	0.788954i	$0.289377\pi$
$14$	1.10905	−	1.10905i	0.296407	−	0.296407i
$15$	0.778090	−	1.54744i	0.200902	−	0.399548i
$16$	−1.00000			−0.250000
$17$	4.46856	+	4.46856i	1.08378	+	1.08378i	0.996153	+	0.0876320i	$0.0279300\pi$
$17$	4.46856	+	4.46856i	1.08378	+	1.08378i	0.0876320	+	0.996153i	$0.472070\pi$
$18$	0.437662	−	2.96790i	0.103158	−	0.699542i
$19$	−4.49720	+	4.49720i	−1.03173	+	1.03173i	−0.0322497	+	0.999480i	$0.510267\pi$
$19$	−4.49720	+	4.49720i	−1.03173	+	1.03173i	−0.999480	+	0.0322497i	$0.989733\pi$
$20$	−0.707107	+	0.707107i	−0.158114	+	0.158114i
$21$	−0.853250	−	2.57914i	−0.186195	−	0.562814i
$22$	−1.16237	+	1.16237i	−0.247819	+	0.247819i
$23$	−1.08064	−	1.08064i	−0.225328	−	0.225328i	0.585410	−	0.810738i	$-0.300934\pi$
$23$	−1.08064	−	1.08064i	−0.225328	−	0.225328i	−0.810738	+	0.585410i	$0.800934\pi$
$24$	−0.778090	+	1.54744i	−0.158827	+	0.315870i
$25$			1.00000i			0.200000i
$26$		−	0.889790i		−	0.174502i
$27$	−4.25212	−	2.98655i	−0.818320	−	0.574763i
$28$			1.56844i			0.296407i
$29$	0.289296	−	0.289296i	0.0537209	−	0.0537209i	−0.679736	−	0.733457i	$-0.737906\pi$
$29$	0.289296	−	0.289296i	0.0537209	−	0.0537209i	0.733457	+	0.679736i	$0.237906\pi$
$30$	0.544013	+	1.64440i	0.0993228	+	0.300225i
$31$	−5.62866	−	5.62866i	−1.01094	−	1.01094i	−0.999940	−	0.0109977i	$-0.996499\pi$
$31$	−5.62866	−	5.62866i	−1.01094	−	1.01094i	−0.0109977	−	0.999940i	$-0.503501\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.894273	+	2.70314i	0.155673	+	0.470556i
$34$	−6.31950			−1.08378
$35$	1.10905	+	1.10905i	0.187464	+	0.187464i
$36$	1.78915	+	2.40810i	0.298192	+	0.401350i
$37$	−5.36910	−	2.85880i	−0.882675	−	0.469983i
$37$	−5.36910	−	2.85880i	−0.882675	−	0.469983i
$38$		−	6.36001i		−	1.03173i
$39$	−1.37690	−	0.692337i	−0.220480	−	0.110863i
$40$		−	1.00000i		−	0.158114i
$41$	−10.6225			−1.65896			−0.829479	−	0.558537i	$-0.811363\pi$
$41$	−10.6225			−1.65896			−0.829479	+	0.558537i	$0.811363\pi$
$42$	2.42706	+	1.22039i	0.374504	+	0.188310i
$43$	−0.834374	+	0.834374i	−0.127241	+	0.127241i	−0.767859	−	0.640618i	$-0.778678\pi$
$43$	−0.834374	+	0.834374i	−0.127241	+	0.127241i	0.640618	+	0.767859i	$0.278678\pi$
$44$		−	1.64384i		−	0.247819i
$45$	2.96790	+	0.437662i	0.442429	+	0.0652429i
$46$	1.52825			0.225328
$47$		−	13.1074i		−	1.91191i	−0.293511	−	0.955956i	$-0.594824\pi$
$47$		−	13.1074i		−	1.91191i	0.293511	−	0.955956i	$-0.405176\pi$
$48$	−0.544013	−	1.64440i	−0.0785216	−	0.237349i
$49$	−4.54001			−0.648572
$50$	−0.707107	−	0.707107i	−0.100000	−	0.100000i
$51$	−4.91714	+	9.77905i	−0.688537	+	1.36934i
$52$	0.629176	+	0.629176i	0.0872511	+	0.0872511i
$53$			4.14299i			0.569084i	0.958664	+	0.284542i	$0.0918415\pi$
$53$			4.14299i			0.569084i	−0.958664	+	0.284542i	$0.908159\pi$
$54$	5.11851	−	0.894888i	0.696541	−	0.121779i
$55$	−1.16237	−	1.16237i	−0.156734	−	0.156734i
$56$	−1.10905	−	1.10905i	−0.148203	−	0.148203i
$57$	−9.84174	−	4.94866i	−1.30357	−	0.655466i
$58$			0.409126i			0.0537209i
$59$	8.55319	+	8.55319i	1.11353	+	1.11353i	0.992669	+	0.120861i	$0.0385655\pi$
$59$	8.55319	+	8.55319i	1.11353	+	1.11353i	0.120861	+	0.992669i	$0.461435\pi$
$60$	−1.54744	−	0.778090i	−0.199774	−	0.100451i
$61$	−9.70779	−	9.70779i	−1.24296	−	1.24296i	−0.958769	−	0.284186i	$-0.908277\pi$
$61$	−9.70779	−	9.70779i	−1.24296	−	1.24296i	−0.284186	−	0.958769i	$-0.591723\pi$
$62$	7.96013			1.01094
$63$	3.77695	−	2.80617i	0.475851	−	0.353544i
$64$			1.00000i			0.125000i
$65$	0.889790			0.110365
$66$	−2.54375	−	1.27906i	−0.313114	−	0.157441i
$67$			4.75260i			0.580622i	0.956932	+	0.290311i	$0.0937588\pi$
$67$			4.75260i			0.580622i	−0.956932	+	0.290311i	$0.906241\pi$
$68$	4.46856	−	4.46856i	0.541892	−	0.541892i
$69$	1.18912	−	2.36488i	0.143153	−	0.284698i
$70$	−1.56844			−0.187464
$71$			3.82480i			0.453920i	0.973904	+	0.226960i	$0.0728786\pi$
$71$			3.82480i			0.453920i	−0.973904	+	0.226960i	$0.927121\pi$
$72$	−2.96790	−	0.437662i	−0.349771	−	0.0515790i
$73$			12.7222i			1.48902i	0.667611	+	0.744510i	$0.267317\pi$
$73$			12.7222i			1.48902i	−0.667611	+	0.744510i	$0.732683\pi$
$74$	5.81801	−	1.77505i	0.676329	−	0.206346i
$75$	−1.64440	+	0.544013i	−0.189879	+	0.0628173i
$76$	4.49720	+	4.49720i	0.515865	+	0.515865i
$77$	−2.57826			−0.293821
$78$	1.46317	−	0.484058i	0.165671	−	0.0548087i
$79$	−0.689395	+	0.689395i	−0.0775630	+	0.0775630i	−0.744824	−	0.667261i	$-0.767467\pi$
$79$	−0.689395	+	0.689395i	−0.0775630	+	0.0775630i	0.667261	+	0.744824i	$0.267467\pi$
$80$	0.707107	+	0.707107i	0.0790569	+	0.0790569i
$81$	2.59788	−	8.61690i	0.288653	−	0.957434i
$82$	7.51125	−	7.51125i	0.829479	−	0.829479i
$83$			2.00378i			0.219943i	0.993935	+	0.109972i	$0.0350760\pi$
$83$			2.00378i			0.219943i	−0.993935	+	0.109972i	$0.964924\pi$
$84$	−2.57914	+	0.853250i	−0.281407	+	0.0930973i
$85$		−	6.31950i		−	0.685446i
$86$		−	1.17998i		−	0.127241i
$87$	0.633098	+	0.318337i	0.0678753	+	0.0341293i
$88$	1.16237	+	1.16237i	0.123909	+	0.123909i
$89$	−7.48295	+	7.48295i	−0.793191	+	0.793191i	−0.982012	−	0.188820i	$-0.939534\pi$
$89$	−7.48295	+	7.48295i	−0.793191	+	0.793191i	0.188820	+	0.982012i	$0.439534\pi$
$90$	−2.40810	+	1.78915i	−0.253836	+	0.188593i
$91$	0.986823	−	0.986823i	0.103447	−	0.103447i
$92$	−1.08064	+	1.08064i	−0.112664	+	0.112664i
$93$	6.19370	−	12.3178i	0.642257	−	1.27730i
$94$	9.26833	+	9.26833i	0.955956	+	0.955956i
$95$	6.36001			0.652523
$96$	1.54744	+	0.778090i	0.157935	+	0.0794135i
$97$	3.88735	−	3.88735i	0.394701	−	0.394701i	−0.481658	−	0.876359i	$-0.659965\pi$
$97$	3.88735	−	3.88735i	0.394701	−	0.394701i	0.876359	+	0.481658i	$0.159965\pi$
$98$	3.21027	−	3.21027i	0.324286	−	0.324286i
$99$	−3.95854	+	2.94108i	−0.397848	+	0.295590i
$100$	1.00000			0.100000
$101$	−4.85174			−0.482767			−0.241383	−	0.970430i	$-0.577601\pi$
$101$	−4.85174			−0.482767			−0.241383	+	0.970430i	$0.577601\pi$
$102$	−3.43789	−	10.3918i	−0.340402	−	1.02894i
$103$	7.40422	+	7.40422i	0.729559	+	0.729559i	0.970532	−	0.240973i	$-0.0774664\pi$
$103$	7.40422	+	7.40422i	0.729559	+	0.729559i	−0.240973	+	0.970532i	$0.577466\pi$
$104$	−0.889790			−0.0872511
$105$	−1.22039	+	2.42706i	−0.119097	+	0.236857i
$106$	−2.92954	−	2.92954i	−0.284542	−	0.284542i
$107$		−	10.1894i		−	0.985049i	−0.870299	−	0.492524i	$-0.836074\pi$
$107$		−	10.1894i		−	0.985049i	0.870299	−	0.492524i	$-0.163926\pi$
$108$	−2.98655	+	4.25212i	−0.287381	+	0.409160i
$109$	−9.85790	+	9.85790i	−0.944216	+	0.944216i	−0.998524	−	0.0543083i	$-0.982705\pi$
$109$	−9.85790	+	9.85790i	−0.944216	+	0.944216i	0.0543083	+	0.998524i	$0.482705\pi$
$110$	1.64384			0.156734
$111$	1.78014	−	10.3842i	0.168964	−	0.985622i
$112$	1.56844			0.148203
$113$	13.0116	−	13.0116i	1.22403	−	1.22403i	0.257839	−	0.966188i	$-0.416990\pi$
$113$	13.0116	−	13.0116i	1.22403	−	1.22403i	0.966188	−	0.257839i	$-0.0830104\pi$
$114$	10.4584	−	3.45993i	0.979518	−	0.324052i
$115$			1.52825i			0.142510i
$116$	−0.289296	−	0.289296i	−0.0268604	−	0.0268604i
$117$	0.389427	−	2.64081i	0.0360026	−	0.244143i
$118$	−12.0960			−1.11353
$119$	−7.00865	−	7.00865i	−0.642482	−	0.642482i
$120$	1.64440	−	0.544013i	0.150112	−	0.0496614i
$121$	−8.29778			−0.754343
$122$	13.7289			1.24296
$123$	−5.77879	−	17.4677i	−0.521056	−	1.57501i
$124$	−5.62866	+	5.62866i	−0.505469	+	0.505469i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−0.686446	+	4.65497i	−0.0611534	+	0.414697i
$127$	11.4287			1.01414			0.507068	−	0.861906i	$-0.330729\pi$
$127$	11.4287			1.01414			0.507068	+	0.861906i	$0.330729\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.82596	−	0.918134i	−0.160766	−	0.0808372i
$130$	−0.629176	+	0.629176i	−0.0551824	+	0.0551824i
$131$	3.48311	−	3.48311i	0.304320	−	0.304320i	−0.538381	−	0.842702i	$-0.680964\pi$
$131$	3.48311	−	3.48311i	0.304320	−	0.304320i	0.842702	+	0.538381i	$0.180964\pi$
$132$	2.70314	−	0.894273i	0.235278	−	0.0778365i
$133$	7.05358	−	7.05358i	0.611623	−	0.611623i
$134$	−3.36059	−	3.36059i	−0.290311	−	0.290311i
$135$	0.894888	+	5.11851i	0.0770197	+	0.440531i
$136$			6.31950i			0.541892i
$137$			4.49515i			0.384047i	0.981390	+	0.192023i	$0.0615049\pi$
$137$			4.49515i			0.384047i	−0.981390	+	0.192023i	$0.938495\pi$
$138$	0.831388	+	2.51305i	0.0707725	+	0.213925i
$139$		−	21.9294i		−	1.86002i	−0.367529	−	0.930012i	$-0.619796\pi$
$139$		−	21.9294i		−	1.86002i	0.367529	−	0.930012i	$-0.380204\pi$
$140$	1.10905	−	1.10905i	0.0937320	−	0.0937320i
$141$	21.5538	−	7.13060i	1.81516	−	0.600505i
$142$	−2.70454	−	2.70454i	−0.226960	−	0.226960i
$143$	−1.03427	+	1.03427i	−0.0864898	+	0.0864898i
$144$	2.40810	−	1.78915i	0.200675	−	0.149096i
$145$	−0.409126			−0.0339761
$146$	−8.99595	−	8.99595i	−0.744510	−	0.744510i
$147$	−2.46983	−	7.46559i	−0.203708	−	0.615751i
$148$	−2.85880	+	5.36910i	−0.234992	+	0.441338i
$149$			22.3567i			1.83153i	0.401716	+	0.915764i	$0.368414\pi$
$149$			22.3567i			1.83153i	−0.401716	+	0.915764i	$0.631586\pi$
$150$	0.778090	−	1.54744i	0.0635308	−	0.126348i
$151$			22.5415i			1.83440i	0.398426	+	0.917201i	$0.369557\pi$
$151$			22.5415i			1.83440i	−0.398426	+	0.917201i	$0.630443\pi$
$152$	−6.36001			−0.515865
$153$	−18.7557	−	2.76581i	−1.51631	−	0.223602i
$154$	1.82311	−	1.82311i	0.146910	−	0.146910i
$155$			7.96013i			0.639373i
$156$	−0.692337	+	1.37690i	−0.0554313	+	0.110240i
$157$	−2.37029			−0.189170			−0.0945848	−	0.995517i	$-0.530152\pi$
$157$	−2.37029			−0.189170			−0.0945848	+	0.995517i	$0.530152\pi$
$158$		−	0.974951i		−	0.0775630i
$159$	−6.81273	+	2.25384i	−0.540285	+	0.178741i
$160$	−1.00000			−0.0790569
$161$	1.69491	+	1.69491i	0.133577	+	0.133577i
$162$	4.25609	+	7.93005i	0.334390	+	0.623043i
$163$	8.06627	+	8.06627i	0.631799	+	0.631799i	0.948519	−	0.316720i	$-0.102582\pi$
$163$	8.06627	+	8.06627i	0.631799	+	0.631799i	−0.316720	+	0.948519i	$0.602582\pi$
$164$			10.6225i			0.829479i
$165$	1.27906	−	2.54375i	0.0995746	−	0.198031i
$166$	−1.41689	−	1.41689i	−0.109972	−	0.109972i
$167$	−5.21464	−	5.21464i	−0.403521	−	0.403521i	0.475951	−	0.879472i	$-0.342104\pi$
$167$	−5.21464	−	5.21464i	−0.403521	−	0.403521i	−0.879472	+	0.475951i	$0.842104\pi$
$168$	1.22039	−	2.42706i	0.0941548	−	0.187252i
$169$			12.2083i			0.939098i
$170$	4.46856	+	4.46856i	0.342723	+	0.342723i
$171$	2.78354	−	18.8759i	0.212862	−	1.44348i
$172$	0.834374	+	0.834374i	0.0636204	+	0.0636204i
$173$	−18.5616			−1.41121			−0.705605	−	0.708606i	$-0.749324\pi$
$173$	−18.5616			−1.41121			−0.705605	+	0.708606i	$0.749324\pi$
$174$	−0.672766	+	0.222570i	−0.0510023	+	0.0168730i
$175$		−	1.56844i		−	0.118563i
$176$	−1.64384			−0.123909
$177$	−9.41181	+	18.7179i	−0.707435	+	1.40692i
$178$		−	10.5825i		−	0.793191i
$179$	4.75163	−	4.75163i	0.355153	−	0.355153i	−0.506869	−	0.862023i	$-0.669197\pi$
$179$	4.75163	−	4.75163i	0.355153	−	0.355153i	0.862023	+	0.506869i	$0.169197\pi$
$180$	0.437662	−	2.96790i	0.0326214	−	0.221214i
$181$	1.37431			0.102152			0.0510759	−	0.998695i	$-0.483735\pi$
$181$	1.37431			0.102152			0.0510759	+	0.998695i	$0.483735\pi$
$182$			1.39558i			0.103447i
$183$	10.6823	−	21.2447i	0.789660	−	1.57045i
$184$		−	1.52825i		−	0.112664i
$185$	1.77505	+	5.81801i	0.130505	+	0.427748i
$186$	4.33042	+	13.0896i	0.317522	+	0.959778i
$187$	7.34562	+	7.34562i	0.537165	+	0.537165i
$188$	−13.1074			−0.955956
$189$	6.66917	+	4.68422i	0.485111	+	0.340727i
$190$	−4.49720	+	4.49720i	−0.326262	+	0.326262i
$191$	−8.07560	−	8.07560i	−0.584330	−	0.584330i	0.351760	−	0.936090i	$-0.385583\pi$
$191$	−8.07560	−	8.07560i	−0.584330	−	0.584330i	−0.936090	+	0.351760i	$0.885583\pi$
$192$	−1.64440	+	0.544013i	−0.118674	+	0.0392608i
$193$	−10.3501	+	10.3501i	−0.745016	+	0.745016i	−0.973539	−	0.228523i	$-0.926611\pi$
$193$	−10.3501	+	10.3501i	−0.745016	+	0.745016i	0.228523	+	0.973539i	$0.426611\pi$
$194$			5.49755i			0.394701i
$195$	0.484058	+	1.46317i	0.0346641	+	0.104780i
$196$			4.54001i			0.324286i
$197$			9.80467i			0.698554i	0.937020	+	0.349277i	$0.113573\pi$
$197$			9.80467i			0.698554i	−0.937020	+	0.349277i	$0.886427\pi$
$198$	0.719449	−	4.87877i	0.0511290	−	0.346719i
$199$	5.14958	+	5.14958i	0.365044	+	0.365044i	0.865666	−	0.500622i	$-0.166895\pi$
$199$	5.14958	+	5.14958i	0.365044	+	0.365044i	−0.500622	+	0.865666i	$0.666895\pi$
$200$	−0.707107	+	0.707107i	−0.0500000	+	0.0500000i
$201$	−7.81517	+	2.58548i	−0.551240	+	0.182366i
$202$	3.43070	−	3.43070i	0.241383	−	0.241383i
$203$	−0.453742	+	0.453742i	−0.0318464	+	0.0318464i
$204$	9.77905	+	4.91714i	0.684671	+	0.344269i
$205$	7.51125	+	7.51125i	0.524609	+	0.524609i
$206$	−10.4711			−0.729559
$207$	4.53570	+	0.668857i	0.315253	+	0.0464888i
$208$	0.629176	−	0.629176i	0.0436255	−	0.0436255i
$209$	−7.39270	+	7.39270i	−0.511364	+	0.511364i
$210$	−0.853250	−	2.57914i	−0.0588799	−	0.177977i
$211$	−0.591484			−0.0407194			−0.0203597	−	0.999793i	$-0.506481\pi$
$211$	−0.591484			−0.0407194			−0.0203597	+	0.999793i	$0.506481\pi$
$212$	4.14299			0.284542
$213$	−6.28949	+	2.08074i	−0.430949	+	0.142570i
$214$	7.20501	+	7.20501i	0.492524	+	0.492524i
$215$	1.17998			0.0804742
$216$	−0.894888	−	5.11851i	−0.0608894	−	0.348271i
$217$	8.82820	+	8.82820i	0.599297	+	0.599297i
$218$		−	13.9412i		−	0.944216i
$219$	−20.9204	+	6.92104i	−1.41367	+	0.467681i
$220$	−1.16237	+	1.16237i	−0.0783672	+	0.0783672i
$221$	−5.62302			−0.378246
$222$	6.08397	+	8.60147i	0.408329	+	0.577293i
$223$	−0.315113			−0.0211015			−0.0105508	−	0.999944i	$-0.503358\pi$
$223$	−0.315113			−0.0211015			−0.0105508	+	0.999944i	$0.503358\pi$
$224$	−1.10905	+	1.10905i	−0.0741017	+	0.0741017i
$225$	−1.78915	−	2.40810i	−0.119277	−	0.160540i
$226$			18.4012i			1.22403i
$227$	9.38302	+	9.38302i	0.622773	+	0.622773i	0.946240	−	0.323467i	$-0.104848\pi$
$227$	9.38302	+	9.38302i	0.622773	+	0.622773i	−0.323467	+	0.946240i	$0.604848\pi$
$228$	−4.94866	+	9.84174i	−0.327733	+	0.651785i
$229$	25.4498			1.68177			0.840884	−	0.541216i	$-0.182036\pi$
$229$	25.4498			1.68177			0.840884	+	0.541216i	$0.182036\pi$
$230$	−1.08064	−	1.08064i	−0.0712550	−	0.0712550i
$231$	−1.40261	−	4.23970i	−0.0922850	−	0.278952i
$232$	0.409126			0.0268604
$233$	−7.54603			−0.494357			−0.247178	−	0.968970i	$-0.579503\pi$
$233$	−7.54603			−0.494357			−0.247178	+	0.968970i	$0.579503\pi$
$234$	1.59197	+	2.14270i	0.104070	+	0.140073i
$235$	−9.26833	+	9.26833i	−0.604599	+	0.604599i
$236$	8.55319	−	8.55319i	0.556765	−	0.556765i
$237$	−1.50868	−	0.758600i	−0.0979993	−	0.0492764i
$238$	9.91173			0.642482
$239$	−2.13485	−	2.13485i	−0.138092	−	0.138092i	0.634682	−	0.772774i	$-0.281131\pi$
$239$	−2.13485	−	2.13485i	−0.138092	−	0.138092i	−0.772774	+	0.634682i	$0.781131\pi$
$240$	−0.778090	+	1.54744i	−0.0502255	+	0.0998869i
$241$	12.4422	−	12.4422i	0.801472	−	0.801472i	−0.181854	−	0.983326i	$-0.558210\pi$
$241$	12.4422	−	12.4422i	0.801472	−	0.801472i	0.983326	+	0.181854i	$0.0582097\pi$
$242$	5.86741	−	5.86741i	0.377172	−	0.377172i
$243$	15.5829	−	0.415759i	0.999644	−	0.0266710i
$244$	−9.70779	+	9.70779i	−0.621478	+	0.621478i
$245$	3.21027	+	3.21027i	0.205097	+	0.205097i
$246$	16.4377	+	8.26528i	1.04803	+	0.526975i
$247$		−	5.65907i		−	0.360078i
$248$		−	7.96013i		−	0.505469i
$249$	−3.29501	+	1.09008i	−0.208813	+	0.0690812i
$250$			1.00000i			0.0632456i
$251$	1.93314	−	1.93314i	0.122019	−	0.122019i	−0.643460	−	0.765479i	$-0.722502\pi$
$251$	1.93314	−	1.93314i	0.122019	−	0.122019i	0.765479	+	0.643460i	$0.222502\pi$
$252$	−2.80617	−	3.77695i	−0.176772	−	0.237925i
$253$	−1.77640	−	1.77640i	−0.111681	−	0.111681i
$254$	−8.08133	+	8.08133i	−0.507068	+	0.507068i
$255$	10.3918	−	3.43789i	0.650758	−	0.215289i
$256$	1.00000			0.0625000
$257$	−0.00157497	−	0.00157497i	−9.82441e−5	−	9.82441e-5i	0.707058	−	0.707156i	$-0.250022\pi$
$257$	−0.00157497	−	0.00157497i	−9.82441e−5	−	9.82441e-5i	−0.707156	+	0.707058i	$0.750022\pi$
$258$	1.94036	−	0.641927i	0.120802	−	0.0399646i
$259$	8.42110	+	4.48384i	0.523262	+	0.278612i
$260$		−	0.889790i		−	0.0551824i
$261$	−0.179059	+	1.21425i	−0.0110835	+	0.0751600i
$262$			4.92586i			0.304320i
$263$	10.5582			0.651043			0.325522	−	0.945535i	$-0.394460\pi$
$263$	10.5582			0.651043			0.325522	+	0.945535i	$0.394460\pi$
$264$	−1.27906	+	2.54375i	−0.0787207	+	0.156557i
$265$	2.92954	−	2.92954i	0.179960	−	0.179960i
$266$			9.97527i			0.611623i
$267$	−16.3758	−	8.23413i	−1.00218	−	0.503921i
$268$	4.75260			0.290311
$269$			9.40474i			0.573417i	0.958018	+	0.286708i	$0.0925611\pi$
$269$			9.40474i			0.573417i	−0.958018	+	0.286708i	$0.907439\pi$
$270$	−4.25212	−	2.98655i	−0.258776	−	0.181756i
$271$	−6.28538			−0.381810			−0.190905	−	0.981609i	$-0.561142\pi$
$271$	−6.28538			−0.381810			−0.190905	+	0.981609i	$0.561142\pi$
$272$	−4.46856	−	4.46856i	−0.270946	−	0.270946i
$273$	2.15958	+	1.08589i	0.130703	+	0.0657208i
$274$	−3.17855	−	3.17855i	−0.192023	−	0.192023i
$275$			1.64384i			0.0991275i
$276$	−2.36488	−	1.18912i	−0.142349	−	0.0715764i
$277$	−17.7788	−	17.7788i	−1.06822	−	1.06822i	−0.997496	−	0.0707289i	$-0.977467\pi$
$277$	−17.7788	−	17.7788i	−1.06822	−	1.06822i	−0.0707289	−	0.997496i	$-0.522533\pi$
$278$	15.5064	+	15.5064i	0.930012	+	0.930012i
$279$	23.6249	+	3.48385i	1.41439	+	0.208573i
$280$			1.56844i			0.0937320i
$281$	15.9903	+	15.9903i	0.953902	+	0.953902i	0.998983	−	0.0450817i	$-0.0143548\pi$
$281$	15.9903	+	15.9903i	0.953902	+	0.953902i	−0.0450817	+	0.998983i	$0.514355\pi$
$282$	−10.1987	+	20.2829i	−0.607326	+	1.20783i
$283$	5.52382	+	5.52382i	0.328357	+	0.328357i	0.851962	−	0.523604i	$-0.175413\pi$
$283$	5.52382	+	5.52382i	0.328357	+	0.328357i	−0.523604	+	0.851962i	$0.675413\pi$
$284$	3.82480			0.226960
$285$	3.45993	+	10.4584i	0.204949	+	0.619502i
$286$		−	1.46268i		−	0.0864898i
$287$	16.6607			0.983453
$288$	−0.437662	+	2.96790i	−0.0257895	+	0.174885i
$289$			22.9361i			1.34918i
$290$	0.289296	−	0.289296i	0.0169880	−	0.0169880i
$291$	8.50713	+	4.27759i	0.498697	+	0.250757i
$292$	12.7222			0.744510
$293$			13.9882i			0.817202i	0.912713	+	0.408601i	$0.133983\pi$
$293$			13.9882i			0.817202i	−0.912713	+	0.408601i	$0.866017\pi$
$294$	7.02540	+	3.53254i	0.409729	+	0.206022i
$295$		−	12.0960i		−	0.704258i
$296$	−1.77505	−	5.81801i	−0.103173	−	0.338165i
$297$	−6.98982	−	4.90943i	−0.405590	−	0.284874i
$298$	−15.8085	−	15.8085i	−0.915764	−	0.915764i
$299$	1.35982			0.0786405
$300$	0.544013	+	1.64440i	0.0314086	+	0.0949394i
$301$	1.30866	−	1.30866i	0.0754301	−	0.0754301i
$302$	−15.9392	−	15.9392i	−0.917201	−	0.917201i
$303$	−2.63941	−	7.97821i	−0.151630	−	0.458336i
$304$	4.49720	−	4.49720i	0.257932	−	0.257932i
$305$			13.7289i			0.786114i
$306$	15.2180	−	11.3065i	0.869954	−	0.646352i
$307$			10.1886i			0.581493i	0.956800	+	0.290746i	$0.0939036\pi$
$307$			10.1886i			0.581493i	−0.956800	+	0.290746i	$0.906096\pi$
$308$			2.57826i			0.146910i
$309$	−8.14750	+	16.2035i	−0.463495	+	0.921784i
$310$	−5.62866	−	5.62866i	−0.319686	−	0.319686i
$311$	10.4912	−	10.4912i	0.594899	−	0.594899i	−0.344052	−	0.938951i	$-0.611800\pi$
$311$	10.4912	−	10.4912i	0.594899	−	0.594899i	0.938951	+	0.344052i	$0.111800\pi$
$312$	−0.484058	−	1.46317i	−0.0274044	−	0.0828357i
$313$	24.4934	−	24.4934i	1.38445	−	1.38445i	0.547922	−	0.836529i	$-0.315419\pi$
$313$	24.4934	−	24.4934i	1.38445	−	1.38445i	0.836529	−	0.547922i	$-0.184581\pi$
$314$	1.67605	−	1.67605i	0.0945848	−	0.0945848i
$315$	−4.65497	−	0.686446i	−0.262278	−	0.0386768i
$316$	0.689395	+	0.689395i	0.0387815	+	0.0387815i
$317$	18.8817			1.06050			0.530250	−	0.847841i	$-0.322098\pi$
$317$	18.8817			1.06050			0.530250	+	0.847841i	$0.322098\pi$
$318$	3.22362	−	6.41104i	0.180772	−	0.359513i
$319$	0.475557	−	0.475557i	0.0266261	−	0.0266261i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$	16.7555	−	5.54318i	0.935200	−	0.309390i
$322$	−2.39696			−0.133577
$323$	−40.1921			−2.23635
$324$	−8.61690	−	2.59788i	−0.478717	−	0.144327i
$325$	−0.629176	−	0.629176i	−0.0349004	−	0.0349004i
$326$	−11.4074			−0.631799
$327$	−21.5732	−	10.8475i	−1.19300	−	0.599868i
$328$	−7.51125	−	7.51125i	−0.414740	−	0.414740i
$329$			20.5581i			1.13341i
$330$	0.894273	+	2.70314i	0.0492281	+	0.148803i
$331$	−16.7777	+	16.7777i	−0.922187	+	0.922187i	−0.997184	−	0.0749970i	$-0.976105\pi$
$331$	−16.7777	+	16.7777i	−0.922187	+	0.922187i	0.0749970	+	0.997184i	$0.476105\pi$
$332$	2.00378			0.109972
$333$	18.0442	−	2.72187i	0.988813	−	0.149157i
$334$	7.37462			0.403521
$335$	3.36059	−	3.36059i	0.183609	−	0.183609i
$336$	0.853250	+	2.57914i	0.0465486	+	0.140703i
$337$			18.2617i			0.994779i	0.867527	+	0.497390i	$0.165708\pi$
$337$			18.2617i			0.994779i	−0.867527	+	0.497390i	$0.834292\pi$
$338$	−8.63255	−	8.63255i	−0.469549	−	0.469549i
$339$	28.4747	+	14.3178i	1.54653	+	0.777634i
$340$	−6.31950			−0.342723
$341$	−9.25264	−	9.25264i	−0.501059	−	0.501059i
$342$	11.3790	+	15.3155i	0.615307	+	0.828169i
$343$	18.0998			0.977296
$344$	−1.17998			−0.0636204
$345$	−2.51305	+	0.831388i	−0.135298	+	0.0447604i
$346$	13.1250	−	13.1250i	0.705605	−	0.705605i
$347$	−8.03823	+	8.03823i	−0.431515	+	0.431515i	−0.889144	−	0.457628i	$-0.848699\pi$
$347$	−8.03823	+	8.03823i	−0.431515	+	0.431515i	0.457628	+	0.889144i	$0.348699\pi$
$348$	0.318337	−	0.633098i	0.0170647	−	0.0339376i
$349$	−8.68067			−0.464665			−0.232333	−	0.972636i	$-0.574636\pi$
$349$	−8.68067			−0.464665			−0.232333	+	0.972636i	$0.574636\pi$
$350$	1.10905	+	1.10905i	0.0592813	+	0.0592813i
$351$	4.55440	−	0.796262i	0.243096	−	0.0425013i
$352$	1.16237	−	1.16237i	0.0619547	−	0.0619547i
$353$	−4.36437	+	4.36437i	−0.232292	+	0.232292i	−0.813649	−	0.581357i	$-0.802522\pi$
$353$	−4.36437	+	4.36437i	−0.232292	+	0.232292i	0.581357	+	0.813649i	$0.302522\pi$
$354$	−6.58041	−	19.8907i	−0.349745	−	1.05718i
$355$	2.70454	−	2.70454i	0.143542	−	0.143542i
$356$	7.48295	+	7.48295i	0.396596	+	0.396596i
$357$	7.71222	−	15.3378i	0.408174	−	0.811764i
$358$			6.71982i			0.355153i
$359$			20.7643i			1.09590i	0.836511	+	0.547950i	$0.184591\pi$
$359$			20.7643i			1.09590i	−0.836511	+	0.547950i	$0.815409\pi$
$360$	1.78915	+	2.40810i	0.0942965	+	0.126918i
$361$		−	21.4497i		−	1.12893i
$362$	−0.971785	+	0.971785i	−0.0510759	+	0.0510759i
$363$	−4.51410	−	13.6449i	−0.236929	−	0.716169i
$364$	−0.986823	−	0.986823i	−0.0517236	−	0.0517236i
$365$	8.99595	−	8.99595i	0.470870	−	0.470870i
$366$	7.46870	+	22.5758i	0.390395	+	1.18005i
$367$	−22.0692			−1.15200			−0.576002	−	0.817448i	$-0.695388\pi$
$367$	−22.0692			−1.15200			−0.576002	+	0.817448i	$0.695388\pi$
$368$	1.08064	+	1.08064i	0.0563320	+	0.0563320i
$369$	25.5801	−	19.0053i	1.33165	−	0.989376i
$370$	−5.36910	−	2.85880i	−0.279126	−	0.148622i
$371$		−	6.49802i		−	0.337360i
$372$	−12.3178	−	6.19370i	−0.638650	−	0.321128i
$373$			12.9551i			0.670787i	0.942078	+	0.335394i	$0.108869\pi$
$373$			12.9551i			0.670787i	−0.942078	+	0.335394i	$0.891131\pi$
$374$	−10.3883			−0.537165
$375$	1.54744	+	0.778090i	0.0799095	+	0.0401804i
$376$	9.26833	−	9.26833i	0.477978	−	0.477978i
$377$			0.364036i			0.0187488i
$378$	−8.02806	+	1.40357i	−0.412919	+	0.0721921i
$379$	−9.36563			−0.481080			−0.240540	−	0.970639i	$-0.577325\pi$
$379$	−9.36563			−0.481080			−0.240540	+	0.970639i	$0.577325\pi$
$380$		−	6.36001i		−	0.326262i
$381$	6.21738	+	18.7934i	0.318526	+	0.962814i
$382$	11.4206			0.584330
$383$	1.18802	+	1.18802i	0.0607051	+	0.0607051i	0.736808	−	0.676103i	$-0.236332\pi$
$383$	1.18802	+	1.18802i	0.0607051	+	0.0607051i	−0.676103	+	0.736808i	$0.736332\pi$
$384$	0.778090	−	1.54744i	0.0397068	−	0.0789675i
$385$	1.82311	+	1.82311i	0.0929142	+	0.0929142i
$386$		−	14.6372i		−	0.745016i
$387$	0.516434	−	3.50208i	0.0262518	−	0.178021i
$388$	−3.88735	−	3.88735i	−0.197350	−	0.197350i
$389$	22.0352	+	22.0352i	1.11723	+	1.11723i	0.992146	+	0.125085i	$0.0399204\pi$
$389$	22.0352	+	22.0352i	1.11723	+	1.11723i	0.125085	+	0.992146i	$0.460080\pi$
$390$	−1.37690	−	0.692337i	−0.0697219	−	0.0350578i
$391$		−	9.65777i		−	0.488414i
$392$	−3.21027	−	3.21027i	−0.162143	−	0.162143i
$393$	7.62248	+	3.83276i	0.384503	+	0.193337i
$394$	−6.93295	−	6.93295i	−0.349277	−	0.349277i
$395$	0.974951			0.0490551
$396$	2.94108	+	3.95854i	0.147795	+	0.198924i
$397$			19.3715i			0.972229i	0.873895	+	0.486115i	$0.161586\pi$
$397$			19.3715i			0.972229i	−0.873895	+	0.486115i	$0.838414\pi$
$398$	−7.28261			−0.365044
$399$	15.4361	+	7.76166i	0.772774	+	0.388569i
$400$		−	1.00000i		−	0.0500000i
$401$	15.3652	−	15.3652i	0.767300	−	0.767300i	−0.210331	−	0.977630i	$-0.567454\pi$
$401$	15.3652	−	15.3652i	0.767300	−	0.767300i	0.977630	+	0.210331i	$0.0674540\pi$
$402$	3.69795	−	7.35437i	0.184437	−	0.366803i
$403$	7.08284			0.352821
$404$			4.85174i			0.241383i
$405$	−7.93005	+	4.25609i	−0.394047	+	0.211487i
$406$		−	0.641688i		−	0.0318464i
$407$	−8.82597	−	4.69942i	−0.437487	−	0.232942i
$408$	−10.3918	+	3.43789i	−0.514470	+	0.170201i
$409$	−14.2762	−	14.2762i	−0.705914	−	0.705914i	0.259759	−	0.965673i	$-0.416357\pi$
$409$	−14.2762	−	14.2762i	−0.705914	−	0.705914i	−0.965673	+	0.259759i	$0.916357\pi$
$410$	−10.6225			−0.524609
$411$	−7.39182	+	2.44542i	−0.364612	+	0.120624i
$412$	7.40422	−	7.40422i	0.364780	−	0.364780i
$413$	−13.4151	−	13.4151i	−0.660115	−	0.660115i
$414$	−3.68018	+	2.73427i	−0.180871	+	0.134382i
$415$	1.41689	−	1.41689i	0.0695522	−	0.0695522i
$416$			0.889790i			0.0436255i
$417$	36.0606	−	11.9299i	1.76590	−	0.584208i
$418$		−	10.4549i		−	0.511364i
$419$			0.599281i			0.0292768i	0.999893	+	0.0146384i	$0.00465972\pi$
$419$			0.599281i			0.0292768i	−0.999893	+	0.0146384i	$0.995340\pi$
$420$	2.42706	+	1.22039i	0.118429	+	0.0595487i
$421$	2.61990	+	2.61990i	0.127686	+	0.127686i	0.768062	−	0.640376i	$-0.221221\pi$
$421$	2.61990	+	2.61990i	0.127686	+	0.127686i	−0.640376	+	0.768062i	$0.721221\pi$
$422$	0.418242	−	0.418242i	0.0203597	−	0.0203597i
$423$	23.4511	+	31.5639i	1.14023	+	1.53469i
$424$	−2.92954	+	2.92954i	−0.142271	+	0.142271i
$425$	−4.46856	+	4.46856i	−0.216757	+	0.216757i
$426$	2.97604	−	5.91865i	0.144189	−	0.286759i
$427$	15.2261	+	15.2261i	0.736840	+	0.736840i
$428$	−10.1894			−0.492524
$429$	−2.26340	−	1.13809i	−0.109278	−	0.0549477i
$430$	−0.834374	+	0.834374i	−0.0402371	+	0.0402371i
$431$	26.5760	−	26.5760i	1.28012	−	1.28012i	0.339523	−	0.940598i	$-0.389734\pi$
$431$	26.5760	−	26.5760i	1.28012	−	1.28012i	0.940598	−	0.339523i	$-0.110266\pi$
$432$	4.25212	+	2.98655i	0.204580	+	0.143691i
$433$	−35.9427			−1.72730			−0.863649	−	0.504094i	$-0.831826\pi$
$433$	−35.9427			−1.72730			−0.863649	+	0.504094i	$0.831826\pi$
$434$	−12.4850			−0.599297
$435$	−0.222570	−	0.672766i	−0.0106714	−	0.0322567i
$436$	9.85790	+	9.85790i	0.472108	+	0.472108i
$437$	9.71968			0.464955
$438$	9.89902	−	19.6869i	0.472993	−	0.940674i
$439$	−18.6711	−	18.6711i	−0.891124	−	0.891124i	0.103505	−	0.994629i	$-0.466994\pi$
$439$	−18.6711	−	18.6711i	−0.891124	−	0.891124i	−0.994629	+	0.103505i	$0.966994\pi$
$440$		−	1.64384i		−	0.0783672i
$441$	10.9328	−	8.12276i	0.520609	−	0.386798i
$442$	3.97608	−	3.97608i	0.189123	−	0.189123i
$443$	−11.8103			−0.561123			−0.280562	−	0.959836i	$-0.590521\pi$
$443$	−11.8103			−0.561123			−0.280562	+	0.959836i	$0.590521\pi$
$444$	−10.3842	−	1.78014i	−0.492811	−	0.0844818i
$445$	10.5825			0.501658
$446$	0.222819	−	0.222819i	0.0105508	−	0.0105508i
$447$	−36.7633	+	12.1623i	−1.73884	+	0.575258i
$448$		−	1.56844i		−	0.0741017i
$449$	−23.8504	−	23.8504i	−1.12557	−	1.12557i	−0.990889	−	0.134681i	$-0.956999\pi$
$449$	−23.8504	−	23.8504i	−1.12557	−	1.12557i	−0.134681	−	0.990889i	$-0.543001\pi$
$450$	2.96790	+	0.437662i	0.139908	+	0.0206316i
$451$	−17.4618			−0.822242
$452$	−13.0116	−	13.0116i	−0.612013	−	0.612013i
$453$	−37.0672	+	12.2629i	−1.74157	+	0.576160i
$454$	−13.2696			−0.622773
$455$	−1.39558			−0.0654257
$456$	−3.45993	−	10.4584i	−0.162026	−	0.489759i
$457$	5.62384	−	5.62384i	0.263072	−	0.263072i	−0.563229	−	0.826301i	$-0.690441\pi$
$457$	5.62384	−	5.62384i	0.263072	−	0.263072i	0.826301	+	0.563229i	$0.190441\pi$
$458$	−17.9957	+	17.9957i	−0.840884	+	0.840884i
$459$	−5.65524	−	32.3464i	−0.263964	−	1.50980i
$460$	1.52825			0.0712550
$461$	16.5535	+	16.5535i	0.770972	+	0.770972i	0.978276	−	0.207305i	$-0.0664692\pi$
$461$	16.5535	+	16.5535i	0.770972	+	0.770972i	−0.207305	+	0.978276i	$0.566469\pi$
$462$	3.98971	+	2.00612i	0.185618	+	0.0933333i
$463$	1.55048	−	1.55048i	0.0720571	−	0.0720571i	−0.670160	−	0.742217i	$-0.733774\pi$
$463$	1.55048	−	1.55048i	0.0720571	−	0.0720571i	0.742217	+	0.670160i	$0.233774\pi$
$464$	−0.289296	+	0.289296i	−0.0134302	+	0.0134302i
$465$	−13.0896	+	4.33042i	−0.607017	+	0.200818i
$466$	5.33585	−	5.33585i	0.247178	−	0.247178i
$467$	14.2943	+	14.2943i	0.661461	+	0.661461i	0.955724	−	0.294263i	$-0.0950743\pi$
$467$	14.2943	+	14.2943i	0.661461	+	0.661461i	−0.294263	+	0.955724i	$0.595074\pi$
$468$	−2.64081	−	0.389427i	−0.122071	−	0.0180013i
$469$		−	7.45415i		−	0.344201i
$470$		−	13.1074i		−	0.604599i
$471$	−1.28947	−	3.89770i	−0.0594156	−	0.179597i
$472$			12.0960i			0.556765i
$473$	−1.37158	+	1.37158i	−0.0630654	+	0.0630654i
$474$	1.60321	−	0.530387i	0.0736379	−	0.0243615i
$475$	−4.49720	−	4.49720i	−0.206346	−	0.206346i
$476$	−7.00865	+	7.00865i	−0.321241	+	0.321241i
$477$	−7.41244	−	9.97673i	−0.339392	−	0.456803i
$478$	3.01914			0.138092
$479$	−2.65048	−	2.65048i	−0.121103	−	0.121103i	0.643958	−	0.765061i	$-0.277291\pi$
$479$	−2.65048	−	2.65048i	−0.121103	−	0.121103i	−0.765061	+	0.643958i	$0.777291\pi$
$480$	−0.544013	−	1.64440i	−0.0248307	−	0.0750562i
$481$	5.17680	−	1.57942i	0.236042	−	0.0720156i
$482$			17.5959i			0.801472i
$483$	−1.86505	+	3.70916i	−0.0848629	+	0.168773i
$484$			8.29778i			0.377172i
$485$	−5.49755			−0.249631
$486$	−10.7248	+	11.3128i	−0.486487	+	0.513158i
$487$	−5.77603	+	5.77603i	−0.261737	+	0.261737i	−0.825759	−	0.564023i	$-0.809253\pi$
$487$	−5.77603	+	5.77603i	−0.261737	+	0.261737i	0.564023	+	0.825759i	$0.309253\pi$
$488$		−	13.7289i		−	0.621478i
$489$	−8.87601	+	17.6523i	−0.401387	+	0.798266i
$490$	−4.54001			−0.205097
$491$			0.605121i			0.0273087i	0.999907	+	0.0136544i	$0.00434645\pi$
$491$			0.605121i			0.0273087i	−0.999907	+	0.0136544i	$0.995654\pi$
$492$	−17.4677	+	5.77879i	−0.787503	+	0.260528i
$493$	2.58547			0.116444
$494$	4.00157	+	4.00157i	0.180039	+	0.180039i
$495$	4.87877	+	0.719449i	0.219284	+	0.0323368i
$496$	5.62866	+	5.62866i	0.252734	+	0.252734i
$497$		−	5.99895i		−	0.269090i
$498$	1.55912	−	3.10073i	0.0698659	−	0.138947i
$499$	−11.7173	−	11.7173i	−0.524539	−	0.524539i	0.394400	−	0.918939i	$-0.370952\pi$
$499$	−11.7173	−	11.7173i	−0.524539	−	0.524539i	−0.918939	+	0.394400i	$0.870952\pi$
$500$	−0.707107	−	0.707107i	−0.0316228	−	0.0316228i
$501$	5.73812	−	11.4118i	0.256360	−	0.509841i
$502$			2.73388i			0.122019i
$503$	−15.1330	−	15.1330i	−0.674748	−	0.674748i	0.284059	−	0.958807i	$-0.408319\pi$
$503$	−15.1330	−	15.1330i	−0.674748	−	0.674748i	−0.958807	+	0.284059i	$0.908319\pi$
$504$	4.65497	+	0.686446i	0.207349	+	0.0305767i
$505$	3.43070	+	3.43070i	0.152664	+	0.152664i
$506$	2.51220			0.111681
$507$	−20.0753	+	6.64147i	−0.891574	+	0.294958i
$508$		−	11.4287i		−	0.507068i
$509$	20.4200			0.905101			0.452551	−	0.891739i	$-0.350514\pi$
$509$	20.4200			0.905101			0.452551	+	0.891739i	$0.350514\pi$
$510$	−4.91714	+	9.77905i	−0.217735	+	0.433024i
$511$		−	19.9540i		−	0.882711i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	32.5538	−	5.69149i	1.43728	−	0.251286i
$514$	0.00222735			9.82441e−5
$515$		−	10.4711i		−	0.461414i
$516$	−0.918134	+	1.82596i	−0.0404186	+	0.0803832i
$517$		−	21.5465i		−	0.947615i
$518$	−9.12517	+	2.78406i	−0.400937	+	0.122325i
$519$	−10.0977	−	30.5226i	−0.443241	−	1.33979i
$520$	0.629176	+	0.629176i	0.0275912	+	0.0275912i
$521$	−27.5843			−1.20849			−0.604246	−	0.796798i	$-0.706525\pi$
$521$	−27.5843			−1.20849			−0.604246	+	0.796798i	$0.706525\pi$
$522$	−0.731988	−	0.985216i	−0.0320382	−	0.0431217i
$523$	24.4745	−	24.4745i	1.07019	−	1.07019i	0.0728501	−	0.997343i	$-0.476791\pi$
$523$	24.4745	−	24.4745i	1.07019	−	1.07019i	0.997343	−	0.0728501i	$-0.0232095\pi$
$524$	−3.48311	−	3.48311i	−0.152160	−	0.152160i
$525$	2.57914	−	0.853250i	0.112563	−	0.0372389i
$526$	−7.46574	+	7.46574i	−0.325522	+	0.325522i
$527$		−	50.3040i		−	2.19128i
$528$	−0.894273	−	2.70314i	−0.0389182	−	0.117639i
$529$		−	20.6645i		−	0.898455i
$530$			4.14299i			0.179960i
$531$	−35.8999	−	5.29398i	−1.55792	−	0.229739i
$532$	−7.05358	−	7.05358i	−0.305811	−	0.305811i
$533$	6.68344	−	6.68344i	0.289492	−	0.289492i
$534$	17.4018	−	5.75702i	0.753051	−	0.249130i
$535$	−7.20501	+	7.20501i	−0.311500	+	0.311500i
$536$	−3.36059	+	3.36059i	−0.145156	+	0.145156i
$537$	10.3985	+	5.22862i	0.448729	+	0.225632i
$538$	−6.65015	−	6.65015i	−0.286708	−	0.286708i
$539$	−7.46306			−0.321457
$540$	5.11851	−	0.894888i	0.220266	−	0.0385098i
$541$	−25.8071	+	25.8071i	−1.10953	+	1.10953i	−0.116323	+	0.993211i	$0.537111\pi$
$541$	−25.8071	+	25.8071i	−1.10953	+	1.10953i	−0.993211	+	0.116323i	$0.962889\pi$
$542$	4.44443	−	4.44443i	0.190905	−	0.190905i
$543$	0.747644	+	2.25992i	0.0320845	+	0.0969823i
$544$	6.31950			0.270946
$545$	13.9412			0.597175
$546$	−2.29489	+	0.759213i	−0.0982122	+	0.0324913i
$547$	11.6788	+	11.6788i	0.499350	+	0.499350i	0.911236	−	0.411886i	$-0.135130\pi$
$547$	11.6788	+	11.6788i	0.499350	+	0.499350i	−0.411886	+	0.911236i	$0.635130\pi$
$548$	4.49515			0.192023
$549$	40.7460	+	6.00862i	1.73900	+	0.256442i
$550$	−1.16237	−	1.16237i	−0.0495638	−	0.0495638i
$551$			2.60204i			0.110851i
$552$	2.51305	−	0.831388i	0.106963	−	0.0353862i
$553$	1.08127	−	1.08127i	0.0459804	−	0.0459804i
$554$	25.1430			1.06822
$555$	−8.60147	+	6.08397i	−0.365112	+	0.258250i
$556$	−21.9294			−0.930012
$557$	14.2831	−	14.2831i	0.605195	−	0.605195i	−0.336491	−	0.941687i	$-0.609240\pi$
$557$	14.2831	−	14.2831i	0.605195	−	0.605195i	0.941687	+	0.336491i	$0.109240\pi$
$558$	−19.1688	+	14.2419i	−0.811479	+	0.602906i
$559$		−	1.04994i		−	0.0444076i
$560$	−1.10905	−	1.10905i	−0.0468660	−	0.0468660i
$561$	−8.08301	+	16.0752i	−0.341265	+	0.678697i
$562$	−22.6137			−0.953902
$563$	28.5674	+	28.5674i	1.20397	+	1.20397i	0.972947	+	0.231027i	$0.0742086\pi$
$563$	28.5674	+	28.5674i	1.20397	+	1.20397i	0.231027	+	0.972947i	$0.425791\pi$
$564$	−7.13060	−	21.5538i	−0.300253	−	0.907579i
$565$	−18.4012			−0.774143
$566$	−7.81186			−0.328357
$567$	−4.07461	+	13.5151i	−0.171117	+	0.567579i
$568$	−2.70454	+	2.70454i	−0.113480	+	0.113480i
$569$	−28.2760	+	28.2760i	−1.18539	+	1.18539i	−0.207065	+	0.978327i	$0.566391\pi$
$569$	−28.2760	+	28.2760i	−1.18539	+	1.18539i	−0.978327	+	0.207065i	$0.933609\pi$
$570$	−9.84174	−	4.94866i	−0.412225	−	0.207277i
$571$	4.49985			0.188313			0.0941563	−	0.995557i	$-0.469985\pi$
$571$	4.49985			0.188313			0.0941563	+	0.995557i	$0.469985\pi$
$572$	1.03427	+	1.03427i	0.0432449	+	0.0432449i
$573$	8.88627	−	17.6727i	0.371229	−	0.738289i
$574$	−11.7809	+	11.7809i	−0.491726	+	0.491726i
$575$	1.08064	−	1.08064i	0.0450656	−	0.0450656i
$576$	−1.78915	−	2.40810i	−0.0745479	−	0.100337i
$577$	−18.3521	+	18.3521i	−0.764009	+	0.764009i	−0.977044	−	0.213036i	$-0.931665\pi$
$577$	−18.3521	+	18.3521i	−0.764009	+	0.764009i	0.213036	+	0.977044i	$0.431665\pi$
$578$	−16.2182	−	16.2182i	−0.674590	−	0.674590i
$579$	−22.6503	−	11.3891i	−0.941313	−	0.473315i
$580$			0.409126i			0.0169880i
$581$		−	3.14280i		−	0.130385i
$582$	−9.04017	+	2.99074i	−0.374727	+	0.123970i
$583$			6.81043i			0.282059i
$584$	−8.99595	+	8.99595i	−0.372255	+	0.372255i
$585$	−2.14270	+	1.59197i	−0.0885898	+	0.0658198i
$586$	−9.89119	−	9.89119i	−0.408601	−	0.408601i
$587$	11.8937	−	11.8937i	0.490908	−	0.490908i	−0.417685	−	0.908592i	$-0.637158\pi$
$587$	11.8937	−	11.8937i	0.490908	−	0.490908i	0.908592	+	0.417685i	$0.137158\pi$
$588$	−7.46559	+	2.46983i	−0.307876	+	0.101854i
$589$	50.6265			2.08603
$590$	8.55319	+	8.55319i	0.352129	+	0.352129i
$591$	−16.1228	+	5.33387i	−0.663203	+	0.219406i
$592$	5.36910	+	2.85880i	0.220669	+	0.117496i
$593$			13.6712i			0.561409i	0.959794	+	0.280705i	$0.0905681\pi$
$593$			13.6712i			0.561409i	−0.959794	+	0.280705i	$0.909432\pi$
$594$	8.41404	−	1.47106i	0.345232	−	0.0603582i
$595$			9.91173i			0.406341i
$596$	22.3567			0.915764
$597$	−5.66653	+	11.2694i	−0.231915	+	0.461226i
$598$	−0.961538	+	0.961538i	−0.0393202	+	0.0393202i
$599$		−	16.0843i		−	0.657186i	−0.944472	−	0.328593i	$-0.893426\pi$
$599$		−	16.0843i		−	0.657186i	0.944472	−	0.328593i	$-0.106574\pi$
$600$	−1.54744	−	0.778090i	−0.0631740	−	0.0317654i
$601$	−24.8780			−1.01479			−0.507397	−	0.861713i	$-0.669392\pi$
$601$	−24.8780			−1.01479			−0.507397	+	0.861713i	$0.669392\pi$
$602$			1.85073i			0.0754301i
$603$	−8.50312	−	11.4447i	−0.346274	−	0.466065i
$604$	22.5415			0.917201
$605$	5.86741	+	5.86741i	0.238544	+	0.238544i
$606$	7.50779	+	3.77510i	0.304983	+	0.153353i
$607$	9.34830	+	9.34830i	0.379436	+	0.379436i	0.870899	−	0.491463i	$-0.163538\pi$
$607$	9.34830	+	9.34830i	0.379436	+	0.379436i	−0.491463	+	0.870899i	$0.663538\pi$
$608$			6.36001i			0.257932i
$609$	−0.992975	−	0.499291i	−0.0402374	−	0.0202323i
$610$	−9.70779	−	9.70779i	−0.393057	−	0.393057i
$611$	8.24687	+	8.24687i	0.333633	+	0.333633i
$612$	−2.76581	+	18.7557i	−0.111801	+	0.758153i
$613$			26.4265i			1.06736i	0.845688	+	0.533678i	$0.179190\pi$
$613$			26.4265i			1.06736i	−0.845688	+	0.533678i	$0.820810\pi$
$614$	−7.20441	−	7.20441i	−0.290746	−	0.290746i
$615$	−8.26528	+	16.4377i	−0.333288	+	0.662833i
$616$	−1.82311	−	1.82311i	−0.0734551	−	0.0734551i
$617$	14.1919			0.571346			0.285673	−	0.958327i	$-0.407783\pi$
$617$	14.1919			0.571346			0.285673	+	0.958327i	$0.407783\pi$
$618$	−5.69644	−	17.2187i	−0.229145	−	0.692639i
$619$		−	44.4517i		−	1.78666i	−0.449398	−	0.893332i	$-0.648362\pi$
$619$		−	44.4517i		−	1.78666i	0.449398	−	0.893332i	$-0.351638\pi$
$620$	7.96013			0.319686
$621$	1.36761	+	7.82236i	0.0548804	+	0.313901i
$622$			14.8367i			0.594899i
$623$	11.7365	−	11.7365i	0.470214	−	0.470214i
$624$	1.37690	+	0.692337i	0.0551200	+	0.0277157i
$625$	−1.00000			−0.0400000
$626$			34.6390i			1.38445i
$627$	−16.1783	−	8.13483i	−0.646099	−	0.324874i
$628$			2.37029i			0.0945848i
$629$	−11.2175	−	36.7669i	−0.447269	−	1.46599i
$630$	3.77695	−	2.80617i	0.150477	−	0.111800i
$631$	4.17746	+	4.17746i	0.166302	+	0.166302i	0.785352	−	0.619050i	$-0.212482\pi$
$631$	4.17746	+	4.17746i	0.166302	+	0.166302i	−0.619050	+	0.785352i	$0.712482\pi$
$632$	−0.974951			−0.0387815
$633$	−0.321775	−	0.972636i	−0.0127894	−	0.0386588i
$634$	−13.3514	+	13.3514i	−0.530250	+	0.530250i
$635$	−8.08133	−	8.08133i	−0.320698	−	0.320698i
$636$	2.25384	+	6.81273i	0.0893707	+	0.270142i
$637$	2.85647	−	2.85647i	0.113177	−	0.113177i
$638$			0.672539i			0.0266261i
$639$	−6.84314	−	9.21049i	−0.270710	−	0.364361i
$640$			1.00000i			0.0395285i
$641$			27.7886i			1.09758i	0.835960	+	0.548791i	$0.184912\pi$
$641$			27.7886i			1.09758i	−0.835960	+	0.548791i	$0.815088\pi$
$642$	−7.92829	+	15.7675i	−0.312905	+	0.622295i
$643$	−3.14293	−	3.14293i	−0.123945	−	0.123945i	0.642413	−	0.766358i	$-0.277933\pi$
$643$	−3.14293	−	3.14293i	−0.123945	−	0.123945i	−0.766358	+	0.642413i	$0.777933\pi$
$644$	1.69491	−	1.69491i	0.0667887	−	0.0667887i
$645$	0.641927	+	1.94036i	0.0252758	+	0.0764018i
$646$	28.4201	−	28.4201i	1.11817	−	1.11817i
$647$	10.4437	−	10.4437i	0.410582	−	0.410582i	−0.471359	−	0.881941i	$-0.656236\pi$
$647$	10.4437	−	10.4437i	0.410582	−	0.410582i	0.881941	+	0.471359i	$0.156236\pi$
$648$	7.93005	−	4.25609i	0.311522	−	0.167195i
$649$	14.0601	+	14.0601i	0.551908	+	0.551908i
$650$	0.889790			0.0349004
$651$	−9.71442	+	19.3197i	−0.380738	+	0.757200i
$652$	8.06627	−	8.06627i	0.315899	−	0.315899i
$653$	7.10309	−	7.10309i	0.277965	−	0.277965i	−0.554331	−	0.832296i	$-0.687026\pi$
$653$	7.10309	−	7.10309i	0.277965	−	0.277965i	0.832296	+	0.554331i	$0.187026\pi$
$654$	22.9249	−	7.58419i	0.896433	−	0.296565i
$655$	−4.92586			−0.192469
$656$	10.6225			0.414740
$657$	−22.7619	−	30.6363i	−0.888027	−	1.19524i
$658$	−14.5368	−	14.5368i	−0.566703	−	0.566703i
$659$	−9.05248			−0.352635			−0.176317	−	0.984333i	$-0.556418\pi$
$659$	−9.05248			−0.352635			−0.176317	+	0.984333i	$0.556418\pi$
$660$	−2.54375	−	1.27906i	−0.0990154	−	0.0497873i
$661$	−20.1666	−	20.1666i	−0.784391	−	0.784391i	0.196177	−	0.980568i	$-0.437147\pi$
$661$	−20.1666	−	20.1666i	−0.784391	−	0.784391i	−0.980568	+	0.196177i	$0.937147\pi$
$662$		−	23.7273i		−	0.922187i
$663$	−3.05900	−	9.24650i	−0.118802	−	0.359104i
$664$	−1.41689	+	1.41689i	−0.0549858	+	0.0549858i
$665$	−9.97527			−0.386824
$666$	−10.8345	+	14.6838i	−0.419828	+	0.568985i
$667$	−0.625246			−0.0242096
$668$	−5.21464	+	5.21464i	−0.201761	+	0.201761i
$669$	−0.171426	−	0.518172i	−0.00662770	−	0.0200337i
$670$			4.75260i			0.183609i
$671$	−15.9581	−	15.9581i	−0.616055	−	0.616055i
$672$	−2.42706	−	1.22039i	−0.0936260	−	0.0470774i
$673$	−7.56707			−0.291689			−0.145845	−	0.989308i	$-0.546590\pi$
$673$	−7.56707			−0.291689			−0.145845	+	0.989308i	$0.546590\pi$
$674$	−12.9130	−	12.9130i	−0.497390	−	0.497390i
$675$	2.98655	−	4.25212i	0.114953	−	0.163664i
$676$	12.2083			0.469549
$677$	−3.72965			−0.143342			−0.0716710	−	0.997428i	$-0.522833\pi$
$677$	−3.72965			−0.143342			−0.0716710	+	0.997428i	$0.522833\pi$
$678$	−30.2589	+	10.0105i	−1.16208	+	0.384450i
$679$	−6.09707	+	6.09707i	−0.233984	+	0.233984i
$680$	4.46856	−	4.46856i	0.171361	−	0.171361i
$681$	−10.3249	+	20.5339i	−0.395653	+	0.786861i
$682$	13.0852			0.501059
$683$	−9.79474	−	9.79474i	−0.374785	−	0.374785i	0.494431	−	0.869217i	$-0.335376\pi$
$683$	−9.79474	−	9.79474i	−0.374785	−	0.374785i	−0.869217	+	0.494431i	$0.835376\pi$
$684$	−18.8759	−	2.78354i	−0.721738	−	0.106431i
$685$	3.17855	−	3.17855i	0.121446	−	0.121446i
$686$	−12.7985	+	12.7985i	−0.488648	+	0.488648i
$687$	13.8450	+	41.8496i	0.528220	+	1.59666i
$688$	0.834374	−	0.834374i	0.0318102	−	0.0318102i
$689$	−2.60667	−	2.60667i	−0.0993063	−	0.0993063i
$690$	1.18912	−	2.36488i	0.0452689	−	0.0900293i
$691$		−	13.8014i		−	0.525029i	−0.964928	−	0.262515i	$-0.915448\pi$
$691$		−	13.8014i		−	0.525029i	0.964928	−	0.262515i	$-0.0845518\pi$
$692$			18.5616i			0.705605i
$693$	6.20872	−	4.61290i	0.235850	−	0.175230i
$694$		−	11.3678i		−	0.431515i
$695$	−15.5064	+	15.5064i	−0.588191	+	0.588191i
$696$	0.222570	+	0.672766i	0.00843649	+	0.0255011i
$697$	−47.4674	−	47.4674i	−1.79795	−	1.79795i
$698$	6.13816	−	6.13816i	0.232333	−	0.232333i
$699$	−4.10514	−	12.4087i	−0.155271	−	0.469340i
$700$	−1.56844			−0.0592813
$701$	5.58493	+	5.58493i	0.210940	+	0.210940i	0.804667	−	0.593727i	$-0.202344\pi$
$701$	5.58493	+	5.58493i	0.210940	+	0.210940i	−0.593727	+	0.804667i	$0.702344\pi$
$702$	−2.65741	+	3.78349i	−0.100297	+	0.142799i
$703$	37.0026	−	11.2894i	1.39558	−	0.425786i
$704$			1.64384i			0.0619547i
$705$	−20.2829	−	10.1987i	−0.763900	−	0.384107i
$706$		−	6.17215i		−	0.232292i
$707$	7.60965			0.286190
$708$	18.7179	+	9.41181i	0.703462	+	0.353717i
$709$	−13.9927	+	13.9927i	−0.525507	+	0.525507i	−0.919229	−	0.393722i	$-0.871187\pi$
$709$	−13.9927	+	13.9927i	−0.525507	+	0.525507i	0.393722	+	0.919229i	$0.371187\pi$
$710$			3.82480i			0.143542i
$711$	0.426700	−	2.89356i	0.0160025	−	0.108517i
$712$	−10.5825			−0.396596
$713$			12.1651i			0.455585i
$714$	5.39211	+	16.2988i	0.201795	+	0.609969i
$715$	1.46268			0.0547010
$716$	−4.75163	−	4.75163i	−0.177577	−	0.177577i
$717$	2.34916	−	4.67194i	0.0877311	−	0.174477i
$718$	−14.6826	−	14.6826i	−0.547950	−	0.547950i
$719$			26.6215i			0.992813i	0.868090	+	0.496407i	$0.165347\pi$
$719$			26.6215i			0.992813i	−0.868090	+	0.496407i	$0.834653\pi$
$720$	−2.96790	−	0.437662i	−0.110607	−	0.0163107i
$721$	−11.6130	−	11.6130i	−0.432492	−	0.432492i
$722$	15.1672	+	15.1672i	0.564466	+	0.564466i
$723$	27.2286	+	13.6912i	1.01264	+	0.509182i
$724$		−	1.37431i		−	0.0510759i
$725$	0.289296	+	0.289296i	0.0107442	+	0.0107442i
$726$	12.8403	+	6.45642i	0.476549	+	0.239620i
$727$	−10.4677	−	10.4677i	−0.388226	−	0.388226i	0.485828	−	0.874054i	$-0.338518\pi$
$727$	−10.4677	−	10.4677i	−0.388226	−	0.388226i	−0.874054	+	0.485828i	$0.838518\pi$
$728$	1.39558			0.0517236
$729$	9.16099	+	25.3984i	0.339296	+	0.940680i
$730$			12.7222i			0.470870i
$731$	−7.45690			−0.275804
$732$	−21.2447	−	10.6823i	−0.785225	−	0.394830i
$733$		−	14.9277i		−	0.551369i	−0.961248	−	0.275684i	$-0.911096\pi$
$733$		−	14.9277i		−	0.551369i	0.961248	−	0.275684i	$-0.0889044\pi$
$734$	15.6053	−	15.6053i	0.576002	−	0.576002i
$735$	−3.53254	+	7.02540i	−0.130300	+	0.259136i
$736$	−1.52825			−0.0563320
$737$			7.81253i			0.287778i
$738$	−4.64908	+	31.5266i	−0.171135	+	1.16051i
$739$		−	14.3573i		−	0.528141i	−0.964503	−	0.264071i	$-0.914935\pi$
$739$		−	14.3573i		−	0.528141i	0.964503	−	0.264071i	$-0.0850652\pi$
$740$	5.81801	−	1.77505i	0.213874	−	0.0652523i
$741$	9.30577	−	3.07861i	0.341856	−	0.113096i
$742$	4.59479	+	4.59479i	0.168680	+	0.168680i
$743$	34.5132			1.26617			0.633083	−	0.774084i	$-0.281789\pi$
$743$	34.5132			1.26617			0.633083	+	0.774084i	$0.281789\pi$
$744$	13.0896	−	4.33042i	0.479889	−	0.158761i
$745$	15.8085	−	15.8085i	0.579180	−	0.579180i
$746$	−9.16060	−	9.16060i	−0.335394	−	0.335394i
$747$	−3.58506	−	4.82530i	−0.131171	−	0.176548i
$748$	7.34562	−	7.34562i	0.268582	−	0.268582i
$749$			15.9815i			0.583950i
$750$	−1.64440	+	0.544013i	−0.0600450	+	0.0198646i
$751$		−	26.5644i		−	0.969350i	−0.874694	−	0.484675i	$-0.838938\pi$
$751$		−	26.5644i		−	0.969350i	0.874694	−	0.484675i	$-0.161062\pi$
$752$			13.1074i			0.477978i
$753$	4.23051	+	2.12720i	0.154168	+	0.0775196i
$754$	−0.257412	−	0.257412i	−0.00937440	−	0.00937440i
$755$	15.9392	−	15.9392i	0.580089	−	0.580089i
$756$	4.68422	−	6.66917i	0.170363	−	0.242556i
$757$	26.5621	−	26.5621i	0.965417	−	0.965417i	−0.0340046	−	0.999422i	$-0.510826\pi$
$757$	26.5621	−	26.5621i	0.965417	−	0.965417i	0.999422	+	0.0340046i	$0.0108261\pi$
$758$	6.62250	−	6.62250i	0.240540	−	0.240540i
$759$	1.95472	−	3.88749i	0.0709519	−	0.141107i
$760$	4.49720	+	4.49720i	0.163131	+	0.163131i
$761$	−3.25195			−0.117883			−0.0589415	−	0.998261i	$-0.518773\pi$
$761$	−3.25195			−0.117883			−0.0589415	+	0.998261i	$0.518773\pi$
$762$	−17.6853	−	8.89258i	−0.640670	−	0.322144i
$763$	15.4615	−	15.4615i	0.559744	−	0.559744i
$764$	−8.07560	+	8.07560i	−0.292165	+	0.292165i
$765$	11.3065	+	15.2180i	0.408789	+	0.550207i
$766$	−1.68012			−0.0607051
$767$	−10.7629			−0.388627
$768$	0.544013	+	1.64440i	0.0196304	+	0.0593372i
$769$	28.6343	+	28.6343i	1.03258	+	1.03258i	0.999451	+	0.0331270i	$0.0105466\pi$
$769$	28.6343	+	28.6343i	1.03258	+	1.03258i	0.0331270	+	0.999451i	$0.489453\pi$
$770$	−2.57826			−0.0929142
$771$	0.00173308	−	0.00344669i	6.24153e−5	−	0.000124130i
$772$	10.3501	+	10.3501i	0.372508	+	0.372508i
$773$		−	14.0416i		−	0.505041i	−0.967591	−	0.252521i	$-0.918740\pi$
$773$		−	14.0416i		−	0.505041i	0.967591	−	0.252521i	$-0.0812596\pi$
$774$	2.11117	+	2.84152i	0.0758844	+	0.102136i
$775$	5.62866	−	5.62866i	0.202187	−	0.202187i
$776$	5.49755			0.197350
$777$	−2.79204	+	16.2869i	−0.100164	+	0.584290i
$778$	−31.1625			−1.11723
$779$	47.7716	−	47.7716i	1.71160	−	1.71160i
$780$	1.46317	−	0.484058i	0.0523899	−	0.0173320i
$781$			6.28737i			0.224980i
$782$	6.82907	+	6.82907i	0.244207	+	0.244207i
$783$	−2.09412	+	0.366122i	−0.0748376	+	0.0130841i
$784$	4.54001			0.162143
$785$	1.67605	+	1.67605i	0.0598207	+	0.0598207i
$786$	−8.10008	+	2.67973i	−0.288920	+	0.0955829i
$787$	−8.86917			−0.316152			−0.158076	−	0.987427i	$-0.550529\pi$
$787$	−8.86917			−0.316152			−0.158076	+	0.987427i	$0.550529\pi$
$788$	9.80467			0.349277
$789$	5.74378	+	17.3618i	0.204484	+	0.618097i
$790$	−0.689395	+	0.689395i	−0.0245276	+	0.0245276i
$791$	−20.4078	+	20.4078i	−0.725619	+	0.725619i
$792$	−4.87877	−	0.719449i	−0.173360	−	0.0255645i
$793$	12.2158			0.433797
$794$	−13.6977	−	13.6977i	−0.486115	−	0.486115i
$795$	6.41104	+	3.22362i	0.227376	+	0.114330i
$796$	5.14958	−	5.14958i	0.182522	−	0.182522i
$797$	15.5188	−	15.5188i	0.549703	−	0.549703i	−0.376652	−	0.926355i	$-0.622925\pi$
$797$	15.5188	−	15.5188i	0.549703	−	0.549703i	0.926355	+	0.376652i	$0.122925\pi$
$798$	−16.4033	+	5.42668i	−0.580671	+	0.192102i
$799$	58.5712	−	58.5712i	2.07210	−	2.07210i
$800$	0.707107	+	0.707107i	0.0250000	+	0.0250000i
$801$	4.63156	−	31.4078i	0.163648	−	1.10974i
$802$			21.7296i			0.767300i
$803$			20.9133i			0.738015i
$804$	2.58548	+	7.81517i	0.0911828	+	0.275620i
$805$		−	2.39696i		−	0.0844818i
$806$	−5.00832	+	5.00832i	−0.176411	+	0.176411i
$807$	−15.4651	+	5.11630i	−0.544399	+	0.180102i
$808$	−3.43070	−	3.43070i	−0.120692	−	0.120692i
$809$	−13.9615	+	13.9615i	−0.490861	+	0.490861i	−0.908577	−	0.417717i	$-0.862830\pi$
$809$	−13.9615	+	13.9615i	−0.490861	+	0.490861i	0.417717	+	0.908577i	$0.362830\pi$
$810$	2.59788	−	8.61690i	0.0912802	−	0.302767i
$811$	2.45176			0.0860930			0.0430465	−	0.999073i	$-0.486294\pi$
$811$	2.45176			0.0860930			0.0430465	+	0.999073i	$0.486294\pi$
$812$	0.453742	+	0.453742i	0.0159232	+	0.0159232i
$813$	−3.41933	−	10.3357i	−0.119921	−	0.362488i
$814$	9.56389	−	2.91791i	0.335214	−	0.102273i
$815$		−	11.4074i		−	0.399585i
$816$	4.91714	−	9.77905i	0.172134	−	0.342335i
$817$		−	7.50470i		−	0.262556i
$818$	20.1896			0.705914
$819$	−0.610792	+	4.14194i	−0.0213428	+	0.144731i
$820$	7.51125	−	7.51125i	0.262304	−	0.262304i
$821$		−	30.8973i		−	1.07832i	−0.842202	−	0.539162i	$-0.818741\pi$
$821$		−	30.8973i		−	1.07832i	0.842202	−	0.539162i	$-0.181259\pi$
$822$	3.49763	−	6.95598i	0.121994	−	0.242618i
$823$	−48.7342			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$823$	−48.7342			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$824$			10.4711i			0.364780i
$825$	−2.70314	+	0.894273i	−0.0941111	+	0.0311346i
$826$	18.9719			0.660115
$827$	36.1060	+	36.1060i	1.25553	+	1.25553i	0.953205	+	0.302324i	$0.0977626\pi$
$827$	36.1060	+	36.1060i	1.25553	+	1.25553i	0.302324	+	0.953205i	$0.402237\pi$
$828$	0.668857	−	4.53570i	0.0232444	−	0.157626i
$829$	6.67303	+	6.67303i	0.231764	+	0.231764i	0.813429	−	0.581665i	$-0.197598\pi$
$829$	6.67303	+	6.67303i	0.231764	+	0.231764i	−0.581665	+	0.813429i	$0.697598\pi$
$830$			2.00378i			0.0695522i
$831$	19.5635	−	38.9074i	0.678652	−	1.34968i
$832$	−0.629176	−	0.629176i	−0.0218128	−	0.0218128i
$833$	−20.2873	−	20.2873i	−0.702913	−	0.702913i
$834$	−17.0630	+	33.9344i	−0.590844	+	1.17505i
$835$			7.37462i			0.255209i
$836$	7.39270	+	7.39270i	0.255682	+	0.255682i
$837$	7.12342	+	40.7440i	0.246221	+	1.40832i
$838$	−0.423756	−	0.423756i	−0.0146384	−	0.0146384i
$839$	−20.2839			−0.700279			−0.350140	−	0.936697i	$-0.613866\pi$
$839$	−20.2839			−0.700279			−0.350140	+	0.936697i	$0.613866\pi$
$840$	−2.57914	+	0.853250i	−0.0889886	+	0.0294399i
$841$			28.8326i			0.994228i
$842$	−3.70510			−0.127686
$843$	−17.5955	+	34.9934i	−0.606021	+	1.20524i
$844$			0.591484i			0.0203597i
$845$	8.63255	−	8.63255i	0.296969	−	0.296969i
$846$	−38.9015	−	5.73662i	−1.33746	−	0.197229i
$847$	13.0145			0.447185
$848$		−	4.14299i		−	0.142271i
$849$	−6.07834	+	12.0884i	−0.208608	+	0.414873i
$850$		−	6.31950i		−	0.216757i
$851$	2.71273	+	8.89136i	0.0929910	+	0.304792i
$852$	2.08074	+	6.28949i	0.0712850	+	0.215474i
$853$	40.0727	+	40.0727i	1.37206	+	1.37206i	0.857382	+	0.514680i	$0.172089\pi$
$853$	40.0727	+	40.0727i	1.37206	+	1.37206i	0.514680	+	0.857382i	$0.327911\pi$
$854$	−21.5329			−0.736840
$855$	−15.3155	+	11.3790i	−0.523780	+	0.389154i
$856$	7.20501	−	7.20501i	0.246262	−	0.246262i
$857$	24.9268	+	24.9268i	0.851485	+	0.851485i	0.990316	−	0.138831i	$-0.0443346\pi$
$857$	24.9268	+	24.9268i	0.851485	+	0.851485i	−0.138831	+	0.990316i	$0.544335\pi$
$858$	2.40522	−	0.795715i	0.0821130	−	0.0271653i
$859$	17.6848	−	17.6848i	0.603399	−	0.603399i	−0.337814	−	0.941213i	$-0.609687\pi$
$859$	17.6848	−	17.6848i	0.603399	−	0.603399i	0.941213	+	0.337814i	$0.109687\pi$
$860$		−	1.17998i		−	0.0402371i
$861$	9.06367	+	27.3969i	0.308889	+	0.933684i
$862$			37.5841i			1.28012i
$863$			20.5644i			0.700021i	0.936746	+	0.350010i	$0.113822\pi$
$863$			20.5644i			0.700021i	−0.936746	+	0.350010i	$0.886178\pi$
$864$	−5.11851	+	0.894888i	−0.174135	+	0.0304447i
$865$	13.1250	+	13.1250i	0.446263	+	0.446263i
$866$	25.4153	−	25.4153i	0.863649	−	0.863649i
$867$	−37.7160	+	12.4775i	−1.28090	+	0.423759i
$868$	8.82820	−	8.82820i	0.299648	−	0.299648i
$869$	−1.13326	+	1.13326i	−0.0384431	+	0.0384431i
$870$	0.633098	+	0.318337i	0.0214640	+	0.0107926i
$871$	−2.99022	−	2.99022i	−0.101320	−	0.101320i
$872$	−13.9412			−0.472108
$873$	−2.40607	+	16.3162i	−0.0814331	+	0.552219i
$874$	−6.87285	+	6.87285i	−0.232478	+	0.232478i
$875$	−1.10905	+	1.10905i	−0.0374928	+	0.0374928i
$876$	6.92104	+	20.9204i	0.233840	+	0.706834i
$877$	25.7161			0.868372			0.434186	−	0.900823i	$-0.357036\pi$
$877$	25.7161			0.868372			0.434186	+	0.900823i	$0.357036\pi$
$878$	26.4049			0.891124
$879$	−23.0023	+	7.60980i	−0.775847	+	0.256672i
$880$	1.16237	+	1.16237i	0.0391836	+	0.0391836i
$881$	16.4414			0.553926			0.276963	−	0.960881i	$-0.410672\pi$
$881$	16.4414			0.553926			0.276963	+	0.960881i	$0.410672\pi$
$882$	−1.98699	+	13.4743i	−0.0669055	+	0.453703i
$883$	−21.5260	−	21.5260i	−0.724408	−	0.724408i	0.245092	−	0.969500i	$-0.421182\pi$
$883$	−21.5260	−	21.5260i	−0.724408	−	0.724408i	−0.969500	+	0.245092i	$0.921182\pi$
$884$			5.62302i			0.189123i
$885$	19.8907	−	6.58041i	0.668619	−	0.221198i
$886$	8.35113	−	8.35113i	0.280562	−	0.280562i
$887$	−8.59625			−0.288634			−0.144317	−	0.989532i	$-0.546098\pi$
$887$	−8.59625			−0.288634			−0.144317	+	0.989532i	$0.546098\pi$
$888$	8.60147	−	6.08397i	0.288646	−	0.204165i
$889$	−17.9252			−0.601193
$890$	−7.48295	+	7.48295i	−0.250829	+	0.250829i
$891$	4.27051	−	14.1648i	0.143067	−	0.474540i
$892$			0.315113i			0.0105508i
$893$	58.9467	+	58.9467i	1.97258	+	1.97258i
$894$	17.3955	−	34.5956i	0.581792	−	1.15705i
$895$	−6.71982			−0.224619
$896$	1.10905	+	1.10905i	0.0370508	+	0.0370508i
$897$	0.739761	+	2.23609i	0.0246999	+	0.0746608i
$898$	33.7296			1.12557
$899$	−3.25669			−0.108617
$900$	−2.40810	+	1.78915i	−0.0802700	+	0.0596384i
$901$	−18.5132	+	18.5132i	−0.616764	+	0.616764i
$902$	12.3473	−	12.3473i	0.411121	−	0.411121i
$903$	2.86389	+	1.44003i	0.0953045	+	0.0479213i
$904$	18.4012			0.612013
$905$	−0.971785	−	0.971785i	−0.0323032	−	0.0323032i
$906$	17.5393	−	34.8817i	0.582705	−	1.15887i
$907$	−6.42906	+	6.42906i	−0.213474	+	0.213474i	−0.805741	−	0.592268i	$-0.798233\pi$
$907$	−6.42906	+	6.42906i	−0.213474	+	0.213474i	0.592268	+	0.805741i	$0.298233\pi$
$908$	9.38302	−	9.38302i	0.311386	−	0.311386i
$909$	11.6835	−	8.68050i	0.387517	−	0.287914i
$910$	0.986823	−	0.986823i	0.0327129	−	0.0327129i
$911$	−35.5905	−	35.5905i	−1.17917	−	1.17917i	−0.979957	−	0.199209i	$-0.936163\pi$
$911$	−35.5905	−	35.5905i	−1.17917	−	1.17917i	−0.199209	−	0.979957i	$-0.563837\pi$
$912$	9.84174	+	4.94866i	0.325893	+	0.163867i
$913$			3.29390i			0.109012i
$914$			7.95330i			0.263072i
$915$	−22.5758	+	7.46870i	−0.746332	+	0.246908i
$916$		−	25.4498i		−	0.840884i
$917$	−5.46303	+	5.46303i	−0.180405	+	0.180405i
$918$	26.8712	+	18.8735i	0.886883	+	0.622919i
$919$	−34.3198	−	34.3198i	−1.13210	−	1.13210i	−0.989827	−	0.142278i	$-0.954557\pi$
$919$	−34.3198	−	34.3198i	−1.13210	−	1.13210i	−0.142278	−	0.989827i	$-0.545443\pi$
$920$	−1.08064	+	1.08064i	−0.0356275	+	0.0356275i
$921$	−16.7541	+	5.54272i	−0.552066	+	0.182639i
$922$	−23.4101			−0.770972
$923$	−2.40647	−	2.40647i	−0.0792100	−	0.0792100i
$924$	−4.23970	+	1.40261i	−0.139476	+	0.0461425i
$925$	2.85880	−	5.36910i	0.0939967	−	0.176535i
$926$			2.19272i			0.0720571i
$927$	−31.0773	−	4.58283i	−1.02071	−	0.150520i
$928$		−	0.409126i		−	0.0134302i
$929$	−39.9456			−1.31057			−0.655287	−	0.755380i	$-0.727452\pi$
$929$	−39.9456			−1.31057			−0.655287	+	0.755380i	$0.727452\pi$
$930$	6.19370	−	12.3178i	0.203099	−	0.403918i
$931$	20.4173	−	20.4173i	0.669151	−	0.669151i
$932$			7.54603i			0.247178i
$933$	22.9590	+	11.5443i	0.751643	+	0.377944i
$934$	−20.2152			−0.661461
$935$		−	10.3883i		−	0.339733i
$936$	2.14270	−	1.59197i	0.0700364	−	0.0520351i
$937$	30.0452			0.981534			0.490767	−	0.871291i	$-0.336717\pi$
$937$	30.0452			0.981534			0.490767	+	0.871291i	$0.336717\pi$
$938$	5.27088	+	5.27088i	0.172100	+	0.172100i
$939$	53.6018	+	26.9522i	1.74923	+	0.879553i
$940$	9.26833	+	9.26833i	0.302300	+	0.302300i
$941$			9.31327i			0.303604i	0.988411	+	0.151802i	$0.0485076\pi$
$941$			9.31327i			0.303604i	−0.988411	+	0.151802i	$0.951492\pi$
$942$	3.66788	+	1.84430i	0.119506	+	0.0600905i
$943$	11.4791	+	11.4791i	0.373810	+	0.373810i
$944$	−8.55319	−	8.55319i	−0.278383	−	0.278383i
$945$	−1.40357	−	8.02806i	−0.0456583	−	0.261153i
$946$		−	1.93971i		−	0.0630654i
$947$	28.7924	+	28.7924i	0.935628	+	0.935628i	0.998050	−	0.0624214i	$-0.0198823\pi$
$947$	28.7924	+	28.7924i	0.935628	+	0.935628i	−0.0624214	+	0.998050i	$0.519882\pi$
$948$	−0.758600	+	1.50868i	−0.0246382	+	0.0489997i
$949$	−8.00450	−	8.00450i	−0.259837	−	0.259837i
$950$	6.36001			0.206346
$951$	10.2719	+	31.0490i	0.333089	+	1.00683i
$952$		−	9.91173i		−	0.321241i
$953$	0.610654			0.0197810			0.00989052	−	0.999951i	$-0.496852\pi$
$953$	0.610654			0.0197810			0.00989052	+	0.999951i	$0.496852\pi$
$954$	12.2960	+	1.81323i	0.398098	+	0.0587055i
$955$			11.4206i			0.369562i
$956$	−2.13485	+	2.13485i	−0.0690461	+	0.0690461i
$957$	1.04072	+	0.523296i	0.0336415	+	0.0169158i
$958$	3.74834			0.121103
$959$		−	7.05036i		−	0.227668i
$960$	1.54744	+	0.778090i	0.0499435	+	0.0251128i
$961$			32.3636i			1.04399i
$962$	−2.54373	+	4.77737i	−0.0820131	+	0.154029i
$963$	18.2304	+	24.5371i	0.587467	+	0.790698i
$964$	−12.4422	−	12.4422i	−0.400736	−	0.400736i
$965$	14.6372			0.471190
$966$	−1.30398	−	3.94156i	−0.0419549	−	0.126818i
$967$	8.52355	−	8.52355i	0.274099	−	0.274099i	−0.556649	−	0.830748i	$-0.687913\pi$
$967$	8.52355	−	8.52355i	0.274099	−	0.274099i	0.830748	+	0.556649i	$0.187913\pi$
$968$	−5.86741	−	5.86741i	−0.188586	−	0.188586i
$969$	−21.8650	−	66.0918i	−0.702406	−	2.12317i
$970$	3.88735	−	3.88735i	0.124815	−	0.124815i
$971$			56.8693i			1.82502i	0.409053	+	0.912511i	$0.365859\pi$
$971$			56.8693i			1.82502i	−0.409053	+	0.912511i	$0.634141\pi$
$972$	−0.415759	−	15.5829i	−0.0133355	−	0.499822i
$973$			34.3948i			1.10265i
$974$		−	8.16853i		−	0.261737i
$975$	0.692337	−	1.37690i	0.0221725	−	0.0440960i
$976$	9.70779	+	9.70779i	0.310739	+	0.310739i
$977$	−37.9131	+	37.9131i	−1.21295	+	1.21295i	−0.242896	+	0.970052i	$0.578097\pi$
$977$	−37.9131	+	37.9131i	−1.21295	+	1.21295i	−0.970052	+	0.242896i	$0.921903\pi$
$978$	−6.20579	−	18.7584i	−0.198439	−	0.599826i
$979$	−12.3008	+	12.3008i	−0.393135	+	0.393135i
$980$	3.21027	−	3.21027i	0.102548	−	0.102548i
$981$	6.10153	−	41.3761i	0.194807	−	1.32104i
$982$	−0.427885	−	0.427885i	−0.0136544	−	0.0136544i
$983$	−31.8655			−1.01635			−0.508175	−	0.861254i	$-0.669680\pi$
$983$	−31.8655			−1.01635			−0.508175	+	0.861254i	$0.669680\pi$
$984$	8.26528	−	16.4377i	0.263487	−	0.524016i
$985$	6.93295	−	6.93295i	0.220902	−	0.220902i
$986$	−1.82820	+	1.82820i	−0.0582219	+	0.0582219i
$987$	−33.8058	+	11.1839i	−1.07605	+	0.355987i
$988$	−5.65907			−0.180039
$989$	1.80331			0.0573419
$990$	−3.95854	+	2.94108i	−0.125811	+	0.0934738i
$991$	17.0198	+	17.0198i	0.540652	+	0.540652i	0.923720	−	0.383068i	$-0.125133\pi$
$991$	17.0198	+	17.0198i	0.540652	+	0.540652i	−0.383068	+	0.923720i	$0.625133\pi$
$992$	−7.96013			−0.252734
$993$	−36.7166	−	18.4620i	−1.16517	−	0.585873i
$994$	4.24190	+	4.24190i	0.134545	+	0.134545i
$995$		−	7.28261i		−	0.230874i
$996$	1.09008	+	3.29501i	0.0345406	+	0.104407i
$997$	39.9508	−	39.9508i	1.26526	−	1.26526i	0.316745	−	0.948511i	$-0.397410\pi$
$997$	39.9508	−	39.9508i	1.26526	−	1.26526i	0.948511	−	0.316745i	$-0.102590\pi$
$998$	16.5708			0.524539
$999$	14.2921	+	28.1911i	0.452182	+	0.891926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.401.7	yes	40
3.2	odd	2	inner	1110.2.u.e.401.13	yes	40
37.6	odd	4	inner	1110.2.u.e.191.13	yes	40
111.80	even	4	inner	1110.2.u.e.191.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.7	✓	40	111.80	even	4	inner
1110.2.u.e.191.13	yes	40	37.6	odd	4	inner
1110.2.u.e.401.7	yes	40	1.1	even	1	trivial
1110.2.u.e.401.13	yes	40	3.2	odd	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.54744 - 0.778090i) q^{6} -1.56844 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.40810 + 1.78915i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.544013 + 1.64440i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.54744 - 0.778090i) q^{6} -1.56844 q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.40810 + 1.78915i) q^{9} +1.00000 q^{10} +1.64384 q^{11} +(1.64440 - 0.544013i) q^{12} +(-0.629176 + 0.629176i) q^{13} +(1.10905 - 1.10905i) q^{14} +(0.778090 - 1.54744i) q^{15} -1.00000 q^{16} +(4.46856 + 4.46856i) q^{17} +(0.437662 - 2.96790i) q^{18} +(-4.49720 + 4.49720i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(-0.853250 - 2.57914i) q^{21} +(-1.16237 + 1.16237i) q^{22} +(-1.08064 - 1.08064i) q^{23} +(-0.778090 + 1.54744i) q^{24} +1.00000i q^{25} -0.889790i q^{26} +(-4.25212 - 2.98655i) q^{27} +1.56844i q^{28} +(0.289296 - 0.289296i) q^{29} +(0.544013 + 1.64440i) q^{30} +(-5.62866 - 5.62866i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.894273 + 2.70314i) q^{33} -6.31950 q^{34} +(1.10905 + 1.10905i) q^{35} +(1.78915 + 2.40810i) q^{36} +(-5.36910 - 2.85880i) q^{37} -6.36001i q^{38} +(-1.37690 - 0.692337i) q^{39} -1.00000i q^{40} -10.6225 q^{41} +(2.42706 + 1.22039i) q^{42} +(-0.834374 + 0.834374i) q^{43} -1.64384i q^{44} +(2.96790 + 0.437662i) q^{45} +1.52825 q^{46} -13.1074i q^{47} +(-0.544013 - 1.64440i) q^{48} -4.54001 q^{49} +(-0.707107 - 0.707107i) q^{50} +(-4.91714 + 9.77905i) q^{51} +(0.629176 + 0.629176i) q^{52} +4.14299i q^{53} +(5.11851 - 0.894888i) q^{54} +(-1.16237 - 1.16237i) q^{55} +(-1.10905 - 1.10905i) q^{56} +(-9.84174 - 4.94866i) q^{57} +0.409126i q^{58} +(8.55319 + 8.55319i) q^{59} +(-1.54744 - 0.778090i) q^{60} +(-9.70779 - 9.70779i) q^{61} +7.96013 q^{62} +(3.77695 - 2.80617i) q^{63} +1.00000i q^{64} +0.889790 q^{65} +(-2.54375 - 1.27906i) q^{66} +4.75260i q^{67} +(4.46856 - 4.46856i) q^{68} +(1.18912 - 2.36488i) q^{69} -1.56844 q^{70} +3.82480i q^{71} +(-2.96790 - 0.437662i) q^{72} +12.7222i q^{73} +(5.81801 - 1.77505i) q^{74} +(-1.64440 + 0.544013i) q^{75} +(4.49720 + 4.49720i) q^{76} -2.57826 q^{77} +(1.46317 - 0.484058i) q^{78} +(-0.689395 + 0.689395i) q^{79} +(0.707107 + 0.707107i) q^{80} +(2.59788 - 8.61690i) q^{81} +(7.51125 - 7.51125i) q^{82} +2.00378i q^{83} +(-2.57914 + 0.853250i) q^{84} -6.31950i q^{85} -1.17998i q^{86} +(0.633098 + 0.318337i) q^{87} +(1.16237 + 1.16237i) q^{88} +(-7.48295 + 7.48295i) q^{89} +(-2.40810 + 1.78915i) q^{90} +(0.986823 - 0.986823i) q^{91} +(-1.08064 + 1.08064i) q^{92} +(6.19370 - 12.3178i) q^{93} +(9.26833 + 9.26833i) q^{94} +6.36001 q^{95} +(1.54744 + 0.778090i) q^{96} +(3.88735 - 3.88735i) q^{97} +(3.21027 - 3.21027i) q^{98} +(-3.95854 + 2.94108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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