LMFDB - Embedded newform 930.2.y.a.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	930.29
Dual form			930.2.y.a.449.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.32727 + 1.11282i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.11788 - 0.717333i) q^{5} +(1.72788 - 0.120141i) q^{6} +(0.344014 - 0.111777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.523274 - 2.95401i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.32727 + 1.11282i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.11788 - 0.717333i) q^{5} +(1.72788 - 0.120141i) q^{6} +(0.344014 - 0.111777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.523274 - 2.95401i) q^{9} +(1.29177 + 1.82520i) q^{10} +(-0.958310 - 2.94937i) q^{11} +(-1.46850 - 0.918426i) q^{12} +(-0.514703 + 0.373954i) q^{13} +(-0.344014 - 0.111777i) q^{14} +(3.60926 - 1.40473i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.42872 + 1.11406i) q^{17} +(-2.15966 + 2.08227i) q^{18} +(6.21594 + 4.51615i) q^{19} +(0.0277621 - 2.23590i) q^{20} +(-0.332211 + 0.531182i) q^{21} +(-0.958310 + 2.94937i) q^{22} +(-3.39722 - 1.10382i) q^{23} +(0.648204 + 1.60619i) q^{24} +(3.97087 + 3.03846i) q^{25} +0.636208 q^{26} +(2.59275 + 4.50307i) q^{27} +(0.212612 + 0.292636i) q^{28} +(-2.09538 - 1.52238i) q^{29} +(-3.74563 - 0.985021i) q^{30} +(-5.14638 - 2.12480i) q^{31} +1.00000 q^{32} +(4.55405 + 2.84818i) q^{33} +(-2.11907 - 2.91664i) q^{34} +(-0.808763 - 0.0100420i) q^{35} +(2.97113 - 0.415177i) q^{36} -7.20923 q^{37} +(-2.37428 - 7.30728i) q^{38} +(0.267006 - 1.06911i) q^{39} +(-1.33669 + 1.79256i) q^{40} +(-6.67913 + 9.19304i) q^{41} +(0.580985 - 0.234467i) q^{42} +(-5.56022 - 4.03974i) q^{43} +(2.50889 - 1.82281i) q^{44} +(-3.22724 + 5.88089i) q^{45} +(2.09960 + 2.88985i) q^{46} +(7.06025 - 5.12957i) q^{47} +(0.419684 - 1.68044i) q^{48} +(-5.55727 + 4.03759i) q^{49} +(-1.42654 - 4.79218i) q^{50} +(-5.79057 + 2.33689i) q^{51} +(-0.514703 - 0.373954i) q^{52} +(-1.15194 - 0.374287i) q^{53} +(0.549258 - 5.16704i) q^{54} +(-0.0860946 + 6.93386i) q^{55} -0.361718i q^{56} +(-13.2759 + 0.923079i) q^{57} +(0.800365 + 2.46327i) q^{58} +(-2.31107 - 3.18092i) q^{59} +(2.45130 + 2.99852i) q^{60} +10.8583i q^{61} +(2.91458 + 4.74397i) q^{62} +(-0.150177 - 1.07471i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.35833 - 0.422777i) q^{65} +(-2.01018 - 4.98103i) q^{66} +15.1272i q^{67} +3.60517i q^{68} +(5.73738 - 2.31542i) q^{69} +(0.648400 + 0.483503i) q^{70} +(-7.08557 - 2.30224i) q^{71} +(-2.64773 - 1.41050i) q^{72} +(-1.81726 - 5.59295i) q^{73} +(5.83239 + 4.23748i) q^{74} +(-8.65165 + 0.386008i) q^{75} +(-2.37428 + 7.30728i) q^{76} +(-0.659344 - 0.907509i) q^{77} +(-0.844418 + 0.707983i) q^{78} +(5.41909 + 1.76077i) q^{79} +(2.13504 - 0.664526i) q^{80} +(-8.45237 - 3.09151i) q^{81} +(10.8071 - 3.51143i) q^{82} +(-7.61938 + 10.4872i) q^{83} +(-0.607843 - 0.151807i) q^{84} +(-6.46248 - 4.81898i) q^{85} +(2.12382 + 6.53644i) q^{86} +(4.47527 - 0.311168i) q^{87} -3.10116 q^{88} +(4.86494 + 14.9727i) q^{89} +(6.06760 - 2.86082i) q^{90} +(-0.135266 + 0.186177i) q^{91} -3.57205i q^{92} +(9.19513 - 2.90680i) q^{93} -8.72695 q^{94} +(-9.92507 - 14.0236i) q^{95} +(-1.32727 + 1.11282i) q^{96} +(0.210577 - 0.0684205i) q^{97} +6.86916 q^{98} +(-9.21395 + 1.28753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.32727	+	1.11282i	−0.766298	+	0.642486i
$3$	−1.32727	+	1.11282i	−0.766298	+	0.642486i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.11788	−	0.717333i	−0.947147	−	0.320801i
$5$	−2.11788	−	0.717333i	−0.947147	−	0.320801i
$6$	1.72788	−	0.120141i	0.705404	−	0.0490472i
$7$	0.344014	−	0.111777i	0.130025	−	0.0422477i	−0.243282	−	0.969956i	$-0.578224\pi$
$7$	0.344014	−	0.111777i	0.130025	−	0.0422477i	0.373307	+	0.927708i	$0.378224\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.523274	−	2.95401i	0.174425	−	0.984671i
$10$	1.29177	+	1.82520i	0.408492	+	0.577178i
$11$	−0.958310	−	2.94937i	−0.288941	−	0.889270i	−0.985190	−	0.171469i	$-0.945149\pi$
$11$	−0.958310	−	2.94937i	−0.288941	−	0.889270i	0.696248	−	0.717801i	$-0.254851\pi$
$12$	−1.46850	−	0.918426i	−0.423920	−	0.265127i
$13$	−0.514703	+	0.373954i	−0.142753	+	0.103716i	−0.656870	−	0.754004i	$-0.728120\pi$
$13$	−0.514703	+	0.373954i	−0.142753	+	0.103716i	0.514117	+	0.857720i	$0.328120\pi$
$14$	−0.344014	−	0.111777i	−0.0919416	−	0.0298736i
$15$	3.60926	−	1.40473i	0.931906	−	0.362699i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.42872	+	1.11406i	0.831587	+	0.270199i	0.693714	−	0.720251i	$-0.255973\pi$
$17$	3.42872	+	1.11406i	0.831587	+	0.270199i	0.137873	+	0.990450i	$0.455973\pi$
$18$	−2.15966	+	2.08227i	−0.509037	+	0.490796i
$19$	6.21594	+	4.51615i	1.42604	+	1.03608i	0.990738	+	0.135788i	$0.0433567\pi$
$19$	6.21594	+	4.51615i	1.42604	+	1.03608i	0.435297	+	0.900287i	$0.356643\pi$
$20$	0.0277621	−	2.23590i	0.00620779	−	0.499961i
$21$	−0.332211	+	0.531182i	−0.0724943	+	0.115913i
$22$	−0.958310	+	2.94937i	−0.204312	+	0.628809i
$23$	−3.39722	−	1.10382i	−0.708370	−	0.230163i	−0.0673964	−	0.997726i	$-0.521469\pi$
$23$	−3.39722	−	1.10382i	−0.708370	−	0.230163i	−0.640974	+	0.767563i	$0.721469\pi$
$24$	0.648204	+	1.60619i	0.132314	+	0.327861i
$25$	3.97087	+	3.03846i	0.794173	+	0.607691i
$26$	0.636208			0.124771
$27$	2.59275	+	4.50307i	0.498975	+	0.866616i
$28$	0.212612	+	0.292636i	0.0401799	+	0.0553029i
$29$	−2.09538	−	1.52238i	−0.389103	−	0.282700i	0.375985	−	0.926626i	$-0.377304\pi$
$29$	−2.09538	−	1.52238i	−0.389103	−	0.282700i	−0.765088	+	0.643926i	$0.777304\pi$
$30$	−3.74563	−	0.985021i	−0.683855	−	0.179839i
$31$	−5.14638	−	2.12480i	−0.924317	−	0.381625i
$31$	−5.14638	−	2.12480i	−0.924317	−	0.381625i
$32$	1.00000			0.176777
$33$	4.55405	+	2.84818i	0.792758	+	0.495805i
$34$	−2.11907	−	2.91664i	−0.363417	−	0.500200i
$35$	−0.808763	−	0.0100420i	−0.136706	−	0.00169741i
$36$	2.97113	−	0.415177i	0.495189	−	0.0691961i
$37$	−7.20923			−1.18519			−0.592595	−	0.805501i	$-0.701896\pi$
$37$	−7.20923			−1.18519			−0.592595	+	0.805501i	$0.701896\pi$
$38$	−2.37428	−	7.30728i	−0.385159	−	1.18540i
$39$	0.267006	−	1.06911i	0.0427552	−	0.171194i
$40$	−1.33669	+	1.79256i	−0.211349	+	0.283429i
$41$	−6.67913	+	9.19304i	−1.04311	+	1.43571i	−0.148469	+	0.988917i	$0.547435\pi$
$41$	−6.67913	+	9.19304i	−1.04311	+	1.43571i	−0.894637	+	0.446795i	$0.852565\pi$
$42$	0.580985	−	0.234467i	0.0896480	−	0.0361790i
$43$	−5.56022	−	4.03974i	−0.847926	−	0.616055i	0.0766472	−	0.997058i	$-0.475578\pi$
$43$	−5.56022	−	4.03974i	−0.847926	−	0.616055i	−0.924573	+	0.381004i	$0.875578\pi$
$44$	2.50889	−	1.82281i	0.378229	−	0.274800i
$45$	−3.22724	+	5.88089i	−0.481089	+	0.876672i
$46$	2.09960	+	2.88985i	0.309569	+	0.426085i
$47$	7.06025	−	5.12957i	1.02984	−	0.748225i	0.0615664	−	0.998103i	$-0.480390\pi$
$47$	7.06025	−	5.12957i	1.02984	−	0.748225i	0.968277	+	0.249878i	$0.0803904\pi$
$48$	0.419684	−	1.68044i	0.0605761	−	0.242550i
$49$	−5.55727	+	4.03759i	−0.793895	+	0.576799i
$50$	−1.42654	−	4.79218i	−0.201743	−	0.677717i
$51$	−5.79057	+	2.33689i	−0.810842	+	0.327230i
$52$	−0.514703	−	0.373954i	−0.0713765	−	0.0518580i
$53$	−1.15194	−	0.374287i	−0.158231	−	0.0514122i	0.228831	−	0.973466i	$-0.426510\pi$
$53$	−1.15194	−	0.374287i	−0.158231	−	0.0514122i	−0.387061	+	0.922054i	$0.626510\pi$
$54$	0.549258	−	5.16704i	0.0747445	−	0.703145i
$55$	−0.0860946	+	6.93386i	−0.0116090	+	0.934962i
$56$		−	0.361718i		−	0.0483365i
$57$	−13.2759	+	0.923079i	−1.75843	+	0.122265i
$58$	0.800365	+	2.46327i	0.105093	+	0.323443i
$59$	−2.31107	−	3.18092i	−0.300876	−	0.414120i	0.631633	−	0.775268i	$-0.282385\pi$
$59$	−2.31107	−	3.18092i	−0.300876	−	0.414120i	−0.932509	+	0.361147i	$0.882385\pi$
$60$	2.45130	+	2.99852i	0.316461	+	0.387108i
$61$			10.8583i			1.39026i	0.718885	+	0.695129i	$0.244653\pi$
$61$			10.8583i			1.39026i	−0.718885	+	0.695129i	$0.755347\pi$
$62$	2.91458	+	4.74397i	0.370152	+	0.602484i
$63$	−0.150177	−	1.07471i	−0.0189205	−	0.135401i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.35833	−	0.422777i	0.168480	−	0.0524390i
$66$	−2.01018	−	4.98103i	−0.247436	−	0.613123i
$67$			15.1272i			1.84809i	0.382287	+	0.924043i	$0.375136\pi$
$67$			15.1272i			1.84809i	−0.382287	+	0.924043i	$0.624864\pi$
$68$			3.60517i			0.437191i
$69$	5.73738	−	2.31542i	0.690699	−	0.278744i
$70$	0.648400	+	0.483503i	0.0774986	+	0.0577896i
$71$	−7.08557	−	2.30224i	−0.840903	−	0.273226i	−0.143272	−	0.989683i	$-0.545762\pi$
$71$	−7.08557	−	2.30224i	−0.840903	−	0.273226i	−0.697631	+	0.716458i	$0.745762\pi$
$72$	−2.64773	−	1.41050i	−0.312038	−	0.166229i
$73$	−1.81726	−	5.59295i	−0.212694	−	0.654605i	−0.999309	−	0.0371613i	$-0.988168\pi$
$73$	−1.81726	−	5.59295i	−0.212694	−	0.654605i	0.786615	−	0.617443i	$-0.211832\pi$
$74$	5.83239	+	4.23748i	0.678001	+	0.492597i
$75$	−8.65165	+	0.386008i	−0.999006	+	0.0445723i
$76$	−2.37428	+	7.30728i	−0.272348	+	0.838202i
$77$	−0.659344	−	0.907509i	−0.0751392	−	0.103420i
$78$	−0.844418	+	0.707983i	−0.0956115	+	0.0801633i
$79$	5.41909	+	1.76077i	0.609695	+	0.198102i	0.597560	−	0.801824i	$-0.296137\pi$
$79$	5.41909	+	1.76077i	0.609695	+	0.198102i	0.0121356	+	0.999926i	$0.496137\pi$
$80$	2.13504	−	0.664526i	0.238705	−	0.0742963i
$81$	−8.45237	−	3.09151i	−0.939152	−	0.343502i
$82$	10.8071	−	3.51143i	1.19344	−	0.387772i
$83$	−7.61938	+	10.4872i	−0.836336	+	1.15112i	0.150375	+	0.988629i	$0.451952\pi$
$83$	−7.61938	+	10.4872i	−0.836336	+	1.15112i	−0.986710	+	0.162488i	$0.948048\pi$
$84$	−0.607843	−	0.151807i	−0.0663211	−	0.0165635i
$85$	−6.46248	−	4.81898i	−0.700955	−	0.522692i
$86$	2.12382	+	6.53644i	0.229017	+	0.704842i
$87$	4.47527	−	0.311168i	0.479799	−	0.0333607i
$88$	−3.10116			−0.330584
$89$	4.86494	+	14.9727i	0.515682	+	1.58711i	0.782037	+	0.623232i	$0.214181\pi$
$89$	4.86494	+	14.9727i	0.515682	+	1.58711i	−0.266355	+	0.963875i	$0.585819\pi$
$90$	6.06760	−	2.86082i	0.639581	−	0.301556i
$91$	−0.135266	+	0.186177i	−0.0141797	+	0.0195167i
$92$		−	3.57205i		−	0.372412i
$93$	9.19513	−	2.90680i	0.953491	−	0.301422i
$94$	−8.72695			−0.900117
$95$	−9.92507	−	14.0236i	−1.01829	−	1.43879i
$96$	−1.32727	+	1.11282i	−0.135464	+	0.113576i
$97$	0.210577	−	0.0684205i	0.0213808	−	0.00694705i	−0.298307	−	0.954470i	$-0.596422\pi$
$97$	0.210577	−	0.0684205i	0.0213808	−	0.00694705i	0.319688	+	0.947523i	$0.396422\pi$
$98$	6.86916			0.693890
$99$	−9.21395	+	1.28753i	−0.926036	+	0.129401i
$100$	−1.66268	+	4.71545i	−0.166268	+	0.471545i
$101$	3.28726	+	1.06810i	0.327095	+	0.106280i	0.467961	−	0.883749i	$-0.344989\pi$
$101$	3.28726	+	1.06810i	0.327095	+	0.106280i	−0.140866	+	0.990029i	$0.544989\pi$
$102$	6.05826	+	1.51303i	0.599857	+	0.149812i
$103$	5.77241	−	7.94505i	0.568773	−	0.782849i	−0.423636	−	0.905833i	$-0.639246\pi$
$103$	5.77241	−	7.94505i	0.568773	−	0.782849i	0.992409	+	0.122984i	$0.0392464\pi$
$104$	0.196599	+	0.605070i	0.0192781	+	0.0593320i
$105$	1.08462	−	0.886677i	0.105848	−	0.0865308i
$106$	0.711936	+	0.979895i	0.0691493	+	0.0951759i
$107$	−1.77438	+	5.46097i	−0.171536	+	0.527932i	−0.999458	−	0.0329099i	$-0.989523\pi$
$107$	−1.77438	+	5.46097i	−0.171536	+	0.527932i	0.827923	+	0.560842i	$0.189523\pi$
$108$	−3.48147	+	3.85738i	−0.335005	+	0.371176i
$109$	−0.546140	+	0.396794i	−0.0523108	+	0.0380060i	−0.613633	−	0.789591i	$-0.710293\pi$
$109$	−0.546140	+	0.396794i	−0.0523108	+	0.0380060i	0.561323	+	0.827597i	$0.310293\pi$
$110$	4.14527	−	5.55901i	0.395236	−	0.530030i
$111$	9.56857	−	8.02255i	0.908208	−	0.761467i
$112$	−0.212612	+	0.292636i	−0.0200900	+	0.0276515i
$113$	2.84263	+	8.74872i	0.267412	+	0.823011i	0.991128	+	0.132912i	$0.0424328\pi$
$113$	2.84263	+	8.74872i	0.267412	+	0.823011i	−0.723716	+	0.690098i	$0.757567\pi$
$114$	11.2830	+	7.05657i	1.05675	+	0.660908i
$115$	6.40312	+	4.77471i	0.597094	+	0.445244i
$116$	0.800365	−	2.46327i	0.0743120	−	0.228709i
$117$	0.835333	+	1.71612i	0.0772265	+	0.158655i
$118$			3.93183i			0.361954i
$119$	1.30405			0.119542
$120$	−0.220652	−	3.86669i	−0.0201427	−	0.352979i
$121$	1.11873	−	0.812808i	0.101703	−	0.0738916i
$122$	6.38232	−	8.78452i	0.577828	−	0.795313i
$123$	−1.36518	−	19.6343i	−0.123094	−	1.77036i
$124$	0.430487	−	5.55110i	0.0386588	−	0.498503i
$125$	−6.23025	−	9.28353i	−0.557250	−	0.830344i
$126$	−0.510204	+	0.957731i	−0.0454525	+	0.0853214i
$127$	7.38582	−	5.36611i	0.655385	−	0.476165i	−0.209716	−	0.977762i	$-0.567254\pi$
$127$	7.38582	−	5.36611i	0.655385	−	0.476165i	0.865101	+	0.501597i	$0.167254\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	11.8754	−	0.825704i	1.04557	−	0.0726992i
$130$	−1.34741	−	0.456373i	−0.118176	−	0.0400266i
$131$	−20.5246	+	6.66883i	−1.79324	+	0.582659i	−0.999667	−	0.0258174i	$-0.991781\pi$
$131$	−20.5246	+	6.66883i	−1.79324	+	0.582659i	−0.793572	+	0.608476i	$0.791781\pi$
$132$	−1.30150	+	5.21129i	−0.113281	+	0.453585i
$133$	2.64317	+	0.858818i	0.229192	+	0.0744690i
$134$	8.89157	−	12.2382i	0.768115	−	1.05722i
$135$	−2.26095	−	11.3968i	−0.194591	−	0.980884i
$136$	2.11907	−	2.91664i	0.181708	−	0.250100i
$137$	0.531951	+	0.732168i	0.0454476	+	0.0625533i	0.831136	−	0.556069i	$-0.187691\pi$
$137$	0.531951	+	0.732168i	0.0454476	+	0.0625533i	−0.785688	+	0.618622i	$0.787691\pi$
$138$	−6.00260	−	1.49913i	−0.510976	−	0.127615i
$139$	−2.43192	−	3.34725i	−0.206273	−	0.283910i	0.693329	−	0.720621i	$-0.256143\pi$
$139$	−2.43192	−	3.34725i	−0.206273	−	0.283910i	−0.899602	+	0.436711i	$0.856143\pi$
$140$	−0.240371	−	0.772282i	−0.0203150	−	0.0652697i
$141$	−3.66256	+	14.6651i	−0.308443	+	1.23502i
$142$	4.37912	+	6.02735i	0.367488	+	0.505804i
$143$	1.59617	+	1.15969i	0.133479	+	0.0969780i
$144$	1.31299	+	2.69742i	0.109416	+	0.224785i
$145$	3.34572	+	4.72732i	0.277847	+	0.392583i
$146$	−1.81726	+	5.59295i	−0.150397	+	0.462875i
$147$	2.88287	−	11.5432i	0.237775	−	0.952066i
$148$	−2.22777	−	6.85638i	−0.183122	−	0.563591i
$149$			21.0917i			1.72790i	0.503581	+	0.863948i	$0.332015\pi$
$149$			21.0917i			1.72790i	−0.503581	+	0.863948i	$0.667985\pi$
$150$	7.22622	+	4.77302i	0.590018	+	0.389716i
$151$	−2.90825	+	0.944947i	−0.236670	+	0.0768987i	−0.424951	−	0.905217i	$-0.639709\pi$
$151$	−2.90825	+	0.944947i	−0.236670	+	0.0768987i	0.188281	+	0.982115i	$0.439709\pi$
$152$	6.21594	−	4.51615i	0.504180	−	0.366308i
$153$	5.08510	−	9.54552i	0.411106	−	0.771710i
$154$			1.12174i			0.0903926i
$155$	9.37525	+	8.19175i	0.753038	+	0.657977i
$156$	1.09929	−	0.0764344i	0.0880137	−	0.00611965i
$157$	−2.43102	+	3.34602i	−0.194017	+	0.267041i	−0.894931	−	0.446204i	$-0.852776\pi$
$157$	−2.43102	+	3.34602i	−0.194017	+	0.267041i	0.700914	+	0.713245i	$0.252776\pi$
$158$	−3.34918	−	4.60975i	−0.266447	−	0.366732i
$159$	1.94544	−	0.785116i	0.154283	−	0.0622638i
$160$	−2.11788	−	0.717333i	−0.167433	−	0.0567102i
$161$	−1.29207			−0.101830
$162$	5.02096	+	7.46927i	0.394484	+	0.586841i
$163$	7.42944	+	2.41397i	0.581919	+	0.189077i	0.585160	−	0.810918i	$-0.301032\pi$
$163$	7.42944	+	2.41397i	0.581919	+	0.189077i	−0.00324116	+	0.999995i	$0.501032\pi$
$164$	−10.8071	−	3.51143i	−0.843890	−	0.274197i
$165$	−7.60185	−	9.29889i	−0.591803	−	0.723918i
$166$	12.3284	−	4.00575i	0.956871	−	0.310906i
$167$	2.58853	−	3.56280i	0.200306	−	0.275698i	−0.697033	−	0.717039i	$-0.745497\pi$
$167$	2.58853	−	3.56280i	0.200306	−	0.275698i	0.897340	+	0.441341i	$0.145497\pi$
$168$	0.402526	+	0.480096i	0.0310555	+	0.0370402i
$169$	−3.89214	+	11.9788i	−0.299396	+	0.921445i
$170$	2.39573	+	7.69719i	0.183744	+	0.590347i
$171$	16.5934	−	15.9988i	1.26893	−	1.22346i
$172$	2.12382	−	6.53644i	0.161940	−	0.498399i
$173$	−12.3328	+	8.96029i	−0.937644	+	0.681239i	−0.947852	−	0.318709i	$-0.896751\pi$
$173$	−12.3328	+	8.96029i	−0.937644	+	0.681239i	0.0102081	+	0.999948i	$0.496751\pi$
$174$	−3.80347	−	2.37876i	−0.288340	−	0.180333i
$175$	1.70566	+	0.601420i	0.128936	+	0.0454631i
$176$	2.50889	+	1.82281i	0.189115	+	0.137400i
$177$	6.60719	+	1.65013i	0.496627	+	0.124031i
$178$	4.86494	−	14.9727i	0.364642	−	1.12225i
$179$	−6.36246	−	19.5817i	−0.475553	−	1.46360i	−0.845211	−	0.534433i	$-0.820525\pi$
$179$	−6.36246	−	19.5817i	−0.475553	−	1.46360i	0.369658	−	0.929168i	$-0.379475\pi$
$180$	−6.59033	−	1.25200i	−0.491215	−	0.0933182i
$181$			11.0418i			0.820730i	0.911921	+	0.410365i	$0.134599\pi$
$181$			11.0418i			0.820730i	−0.911921	+	0.410365i	$0.865401\pi$
$182$	0.218864	−	0.0711133i	0.0162233	−	0.00527127i
$183$	−12.0833	−	14.4118i	−0.893220	−	1.06535i
$184$	−2.09960	+	2.88985i	−0.154785	+	0.213043i
$185$	15.2683	+	5.17142i	1.12255	+	0.380210i
$186$	−9.14760	−	3.05311i	−0.670734	−	0.223865i
$187$		−	11.1802i		−	0.817577i
$188$	7.06025	+	5.12957i	0.514922	+	0.374113i
$189$	1.39528	+	1.25931i	0.101492	+	0.0916012i
$190$	−0.213305	+	17.1791i	−0.0154748	+	1.24630i
$191$			17.4375i			1.26174i	0.775890	+	0.630868i	$0.217301\pi$
$191$			17.4375i			1.26174i	−0.775890	+	0.630868i	$0.782699\pi$
$192$	1.72788	−	0.120141i	0.124699	−	0.00867040i
$193$	18.0688	−	5.87089i	1.30062	−	0.422596i	0.424821	−	0.905277i	$-0.360337\pi$
$193$	18.0688	−	5.87089i	1.30062	−	0.422596i	0.875796	+	0.482681i	$0.160337\pi$
$194$	−0.210577	−	0.0684205i	−0.0151185	−	0.00491231i
$195$	−1.33239	+	2.07271i	−0.0954147	+	0.148430i
$196$	−5.55727	−	4.03759i	−0.396948	−	0.288399i
$197$	−14.8730	+	4.83252i	−1.05966	+	0.344303i	−0.786451	−	0.617653i	$-0.788084\pi$
$197$	−14.8730	+	4.83252i	−1.05966	+	0.344303i	−0.273205	+	0.961956i	$0.588084\pi$
$198$	8.21103	+	4.37419i	0.583532	+	0.310860i
$199$	−7.50039	−	10.3234i	−0.531688	−	0.731806i	0.455698	−	0.890134i	$-0.349390\pi$
$199$	−7.50039	−	10.3234i	−0.531688	−	0.731806i	−0.987387	+	0.158328i	$0.949390\pi$
$200$	4.11681	−	2.83758i	0.291102	−	0.200647i
$201$	−16.8339	−	20.0779i	−1.18737	−	1.41618i
$202$	−2.03164	−	2.79631i	−0.142946	−	0.196748i
$203$	−0.891008	−	0.289506i	−0.0625365	−	0.0203193i
$204$	−4.01190	−	4.78502i	−0.280889	−	0.335019i
$205$	20.7401	−	14.6786i	1.44855	−	1.02520i
$206$	−9.33996	+	3.03474i	−0.650746	+	0.211440i
$207$	−5.03839	+	9.45783i	−0.350192	+	0.657365i
$208$	0.196599	−	0.605070i	0.0136317	−	0.0419540i
$209$	7.36301	−	22.6610i	0.509310	−	1.56749i
$210$	−1.39865	+	0.0798138i	−0.0965160	+	0.00550767i
$211$	−18.1664			−1.25063			−0.625313	−	0.780374i	$-0.715029\pi$
$211$	−18.1664			−1.25063			−0.625313	+	0.780374i	$0.715029\pi$
$212$		−	1.21122i		−	0.0831867i
$213$	11.9664	−	4.82926i	0.819925	−	0.330895i
$214$	4.64538	−	3.37507i	0.317552	−	0.230715i
$215$	8.87807	+	12.5442i	0.605480	+	0.855510i
$216$	5.08388	−	1.07433i	0.345914	−	0.0730988i
$217$	−2.00793	−	0.155715i	−0.136307	−	0.0105706i
$218$	0.675067			0.0457213
$219$	8.63591	+	5.40105i	0.583561	+	0.364969i
$220$	−6.62110	+	2.06080i	−0.446394	+	0.138939i
$221$	−2.18138	+	0.708773i	−0.146735	+	0.0476772i
$222$	−12.4567	+	0.866120i	−0.836037	+	0.0581302i
$223$	21.1753			1.41801			0.709003	−	0.705205i	$-0.249145\pi$
$223$	21.1753			1.41801			0.709003	+	0.705205i	$0.249145\pi$
$224$	0.344014	−	0.111777i	0.0229854	−	0.00746841i
$225$	11.0535	−	10.1400i	0.736899	−	0.676003i
$226$	2.84263	−	8.74872i	0.189089	−	0.581956i
$227$	−2.16784	−	1.57502i	−0.143884	−	0.104538i	0.513514	−	0.858081i	$-0.328343\pi$
$227$	−2.16784	−	1.57502i	−0.143884	−	0.104538i	−0.657399	+	0.753543i	$0.728343\pi$
$228$	−4.98037	−	12.3408i	−0.329833	−	0.817293i
$229$	12.9786	−	17.8634i	0.857647	−	1.18045i	−0.124479	−	0.992222i	$-0.539726\pi$
$229$	12.9786	−	17.8634i	0.857647	−	1.18045i	0.982125	−	0.188227i	$-0.0602742\pi$
$230$	−2.37372	−	7.62648i	−0.156519	−	0.502875i
$231$	1.88502	+	0.470777i	0.124025	+	0.0309748i
$232$	−2.09538	+	1.52238i	−0.137569	+	0.0999494i
$233$	3.32074	−	2.41266i	0.217549	−	0.158058i	−0.473674	−	0.880700i	$-0.657072\pi$
$233$	3.32074	−	2.41266i	0.217549	−	0.158058i	0.691223	+	0.722642i	$0.257072\pi$
$234$	0.332911	−	1.87937i	0.0217631	−	0.122858i
$235$	−18.6324	+	5.79929i	−1.21544	+	0.378304i
$236$	2.31107	−	3.18092i	0.150438	−	0.207060i
$237$	−9.15200	+	3.69345i	−0.594486	+	0.239915i
$238$	−1.05500	−	0.766503i	−0.0683856	−	0.0496850i
$239$	7.79845	−	24.0012i	0.504440	−	1.55251i	−0.297271	−	0.954793i	$-0.596076\pi$
$239$	7.79845	−	24.0012i	0.504440	−	1.55251i	0.801710	−	0.597713i	$-0.203924\pi$
$240$	−2.09427	+	3.25792i	−0.135185	+	0.210298i
$241$	5.02958	−	1.63421i	0.323984	−	0.105269i	−0.142510	−	0.989793i	$-0.545517\pi$
$241$	5.02958	−	1.63421i	0.323984	−	0.105269i	0.466493	+	0.884525i	$0.345517\pi$
$242$	−1.38283			−0.0888918
$243$	14.6588	−	5.30268i	0.940365	−	0.340167i
$244$	−10.3268	+	3.35539i	−0.661107	+	0.214807i
$245$	14.6659	−	4.56474i	0.936973	−	0.291630i
$246$	−10.4363	+	16.6869i	−0.665393	+	1.06392i
$247$	−4.88819			−0.311028
$248$	−3.61112	+	4.23790i	−0.229307	+	0.269107i
$249$	−1.55737	−	22.3983i	−0.0986941	−	1.41943i
$250$	−0.416346	+	11.1726i	−0.0263320	+	0.706616i
$251$	7.29576	−	5.30068i	0.460504	−	0.334576i	−0.333225	−	0.942847i	$-0.608137\pi$
$251$	7.29576	−	5.30068i	0.460504	−	0.334576i	0.793729	+	0.608271i	$0.208137\pi$
$252$	0.975703	−	0.474930i	0.0614635	−	0.0299178i
$253$			11.0775i			0.696436i
$254$	−9.12937			−0.572828
$255$	13.9401	−	0.795489i	0.872962	−	0.0498154i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.57090	+	7.91241i	−0.160368	+	0.493562i	−0.998665	−	0.0516514i	$-0.983552\pi$
$257$	−2.57090	+	7.91241i	−0.160368	+	0.493562i	0.838297	+	0.545214i	$0.183552\pi$
$258$	−10.0927	−	6.31217i	−0.628346	−	0.392979i
$259$	−2.48007	+	0.805825i	−0.154104	+	0.0500715i
$260$	0.821832	+	1.16120i	0.0509679	+	0.0720148i
$261$	−5.59360	+	5.39316i	−0.346235	+	0.333828i
$262$	20.5246	+	6.66883i	1.26801	+	0.412002i
$263$	−2.49512	−	3.43424i	−0.153856	−	0.211764i	0.725130	−	0.688612i	$-0.241779\pi$
$263$	−2.49512	−	3.43424i	−0.153856	−	0.211764i	−0.878986	+	0.476847i	$0.841779\pi$
$264$	4.11606	−	3.45102i	0.253326	−	0.212396i
$265$	2.17118	+	1.61902i	0.133374	+	0.0994555i
$266$	−1.63357	−	2.24842i	−0.100161	−	0.137859i
$267$	−23.1190	−	14.4590i	−1.41486	−	0.884878i
$268$	−14.3869	+	4.67458i	−0.878818	+	0.285545i
$269$	11.3258	+	8.22869i	0.690548	+	0.501712i	0.876840	−	0.480782i	$-0.159647\pi$
$269$	11.3258	+	8.22869i	0.690548	+	0.501712i	−0.186292	+	0.982494i	$0.559647\pi$
$270$	−4.86975	+	10.5492i	−0.296364	+	0.642004i
$271$	−8.40376	−	2.73055i	−0.510492	−	0.165869i	0.0424338	−	0.999099i	$-0.486489\pi$
$271$	−8.40376	−	2.73055i	−0.510492	−	0.165869i	−0.552926	+	0.833230i	$0.686489\pi$
$272$	−3.42872	+	1.11406i	−0.207897	+	0.0675497i
$273$	−0.0276477	−	0.397633i	−0.00167331	−	0.0240658i
$274$		−	0.905009i		−	0.0546736i
$275$	5.15623	−	14.6234i	0.310932	−	0.881822i
$276$	3.97504	+	4.74107i	0.239269	+	0.285379i
$277$	−6.37976	−	4.63517i	−0.383323	−	0.278500i	0.379391	−	0.925236i	$-0.376133\pi$
$277$	−6.37976	−	4.63517i	−0.383323	−	0.278500i	−0.762714	+	0.646736i	$0.776133\pi$
$278$			4.13743i			0.248146i
$279$	−8.96965	+	14.0906i	−0.536999	+	0.843583i
$280$	−0.259472	+	0.766076i	−0.0155064	+	0.0457818i
$281$	−9.45812	+	13.0180i	−0.564224	+	0.776588i	−0.991856	−	0.127365i	$-0.959348\pi$
$281$	−9.45812	+	13.0180i	−0.564224	+	0.776588i	0.427632	+	0.903953i	$0.359348\pi$
$282$	11.5830	−	9.71151i	0.689757	−	0.578312i
$283$	−24.8950	+	8.08886i	−1.47985	+	0.480833i	−0.934069	−	0.357093i	$-0.883768\pi$
$283$	−24.8950	+	8.08886i	−1.47985	+	0.480833i	−0.545783	+	0.837926i	$0.683768\pi$
$284$		−	7.45021i		−	0.442089i
$285$	28.7789	+	7.56824i	1.70471	+	0.448304i
$286$	−0.609684	−	1.87642i	−0.0360514	−	0.110955i
$287$	−1.27015	+	3.90911i	−0.0749743	+	0.230747i
$288$	0.523274	−	2.95401i	0.0308342	−	0.174067i
$289$	−3.23829	−	2.35276i	−0.190488	−	0.138397i
$290$	0.0719048	−	5.79105i	0.00422239	−	0.340062i
$291$	−0.203352	+	0.325146i	−0.0119207	+	0.0190604i
$292$	4.75764	−	3.45663i	0.278420	−	0.202284i
$293$	−4.55629	+	14.0228i	−0.266181	+	0.819222i	0.725238	+	0.688499i	$0.241730\pi$
$293$	−4.55629	+	14.0228i	−0.266181	+	0.819222i	−0.991419	+	0.130723i	$0.958270\pi$
$294$	−9.11721	+	7.64412i	−0.531726	+	0.445814i
$295$	2.61281	+	8.39463i	0.152123	+	0.488754i
$296$	−2.22777	+	6.85638i	−0.129487	+	0.398519i
$297$	10.7966	−	11.9623i	0.626481	−	0.694125i
$298$	12.3974	−	17.0635i	0.718160	−	0.988462i
$299$	2.16134	−	0.702262i	0.124994	−	0.0406129i
$300$	−3.04062	−	8.10892i	−0.175550	−	0.468169i
$301$	−2.36434	−	0.768222i	−0.136278	−	0.0442796i
$302$	2.90825	+	0.944947i	0.167351	+	0.0543756i
$303$	−5.55167	+	2.24047i	−0.318935	+	0.128712i
$304$	−7.68333			−0.440669
$305$	7.78899	−	22.9965i	0.445996	−	1.31678i
$306$	−9.72465	+	4.73354i	−0.555921	+	0.270599i
$307$	−12.6533	−	17.4157i	−0.722161	−	0.993969i	−0.999449	−	0.0331821i	$-0.989436\pi$
$307$	−12.6533	−	17.4157i	−0.722161	−	0.993969i	0.277289	−	0.960787i	$-0.410564\pi$
$308$	0.659344	−	0.907509i	0.0375696	−	0.0517101i
$309$	1.17985	+	16.9688i	0.0671196	+	0.965324i
$310$	−2.76974	−	12.1379i	−0.157311	−	0.689386i
$311$		−	14.5275i		−	0.823781i	−0.911233	−	0.411891i	$-0.864869\pi$
$311$		−	14.5275i		−	0.823781i	0.911233	−	0.411891i	$-0.135131\pi$
$312$	−0.934272	−	0.584310i	−0.0528927	−	0.0330800i
$313$	5.94163	−	4.31685i	0.335841	−	0.244003i	−0.407064	−	0.913400i	$-0.633447\pi$
$313$	5.94163	−	4.31685i	0.335841	−	0.244003i	0.742905	+	0.669397i	$0.233447\pi$
$314$	3.93348	−	1.27806i	0.221979	−	0.0721254i
$315$	−0.452869	+	2.38384i	−0.0255163	+	0.134314i
$316$			5.69797i			0.320536i
$317$	−4.60497	−	14.1726i	−0.258641	−	0.796015i	−0.993090	−	0.117352i	$-0.962560\pi$
$317$	−4.60497	−	14.1726i	−0.258641	−	0.796015i	0.734449	−	0.678663i	$-0.237440\pi$
$318$	−2.03537	−	0.508328i	−0.114138	−	0.0285056i
$319$	−2.48206	+	7.63898i	−0.138968	+	0.427701i
$320$	1.29177	+	1.82520i	0.0722119	+	0.102032i
$321$	−3.72200	−	9.22273i	−0.207742	−	0.514763i
$322$	1.04531	+	0.759462i	0.0582528	+	0.0423232i
$323$	16.2815	+	22.4095i	0.905926	+	1.24690i
$324$	0.328279	−	8.99401i	0.0182377	−	0.499667i
$325$	−3.18006	−	0.0789828i	−0.176398	−	0.00438118i
$326$	−4.59165	−	6.31986i	−0.254308	−	0.350025i
$327$	0.283314	−	1.13441i	0.0156673	−	0.0627328i
$328$	6.67913	+	9.19304i	0.368794	+	0.507601i
$329$	1.85546	−	2.55382i	0.102295	−	0.140797i
$330$	0.684277	+	11.9912i	0.0376682	+	0.660095i
$331$	2.22699	−	3.06518i	0.122406	−	0.168478i	−0.743416	−	0.668829i	$-0.766796\pi$
$331$	2.22699	−	3.06518i	0.122406	−	0.168478i	0.865822	+	0.500351i	$0.166796\pi$
$332$	−12.3284	−	4.00575i	−0.676610	−	0.219844i
$333$	−3.77240	+	21.2961i	−0.206726	+	1.16702i
$334$	−4.18833	+	1.36087i	−0.229175	+	0.0744635i
$335$	10.8513	−	32.0377i	0.592868	−	1.75041i
$336$	−0.0434569	−	0.625004i	−0.00237077	−	0.0340968i
$337$	2.83289	+	8.71874i	0.154317	+	0.474940i	0.998091	−	0.0617591i	$-0.0196710\pi$
$337$	2.83289	+	8.71874i	0.154317	+	0.474940i	−0.843774	+	0.536699i	$0.819671\pi$
$338$	10.1898	−	7.40330i	0.554250	−	0.402686i
$339$	−13.5087	−	8.44856i	−0.733690	−	0.458863i
$340$	2.58611	−	7.63533i	0.140251	−	0.414084i
$341$	−1.33501	+	17.2148i	−0.0722946	+	0.932235i
$342$	−22.8282	+	3.18994i	−1.23441	+	0.172492i
$343$	−2.94875	+	4.05861i	−0.159218	+	0.219144i
$344$	−5.56022	+	4.03974i	−0.299787	+	0.217808i
$345$	−13.8120	+	0.788181i	−0.743615	+	0.0424342i
$346$	15.2442			0.819531
$347$			13.8084i			0.741276i	0.928777	+	0.370638i	$0.120861\pi$
$347$			13.8084i			0.741276i	−0.928777	+	0.370638i	$0.879139\pi$
$348$	1.67887	+	4.16008i	0.0899970	+	0.223003i
$349$	6.54481	−	20.1429i	0.350336	−	1.07822i	−0.608329	−	0.793685i	$-0.708160\pi$
$349$	6.54481	−	20.1429i	0.350336	−	1.07822i	0.958665	−	0.284538i	$-0.0918401\pi$
$350$	−1.02640	−	1.48912i	−0.0548636	−	0.0795969i
$351$	−3.01844	−	1.34817i	−0.161112	−	0.0719602i
$352$	−0.958310	−	2.94937i	−0.0510781	−	0.157202i
$353$	6.12174	−	8.42585i	0.325827	−	0.448463i	−0.614408	−	0.788989i	$-0.710605\pi$
$353$	6.12174	−	8.42585i	0.325827	−	0.448463i	0.940235	+	0.340526i	$0.110605\pi$
$354$	−4.37541	−	5.21859i	−0.232550	−	0.277365i
$355$	13.3549	+	9.95860i	0.708807	+	0.528547i
$356$	−12.7366	+	9.25366i	−0.675037	+	0.490443i
$357$	−1.73083	+	1.45117i	−0.0916050	+	0.0768042i
$358$	−6.36246	+	19.5817i	−0.336267	+	1.03492i
$359$	−9.60275	−	13.2171i	−0.506814	−	0.697570i	0.476564	−	0.879140i	$-0.341882\pi$
$359$	−9.60275	−	13.2171i	−0.506814	−	0.697570i	−0.983378	+	0.181570i	$0.941882\pi$
$360$	4.59579	+	4.88659i	0.242219	+	0.257546i
$361$	12.3710	+	38.0741i	0.651107	+	2.00390i
$362$	6.49020	−	8.93300i	0.341118	−	0.469508i
$363$	−0.580352	+	2.32376i	−0.0304606	+	0.121966i
$364$	−0.218864	−	0.0711133i	−0.0114716	−	0.00372735i
$365$	−0.163262	+	13.1488i	−0.00854555	+	0.688239i
$366$	1.30452	+	18.7618i	0.0681882	+	0.980693i
$367$	−21.8615			−1.14116			−0.570580	−	0.821242i	$-0.693282\pi$
$367$	−21.8615			−1.14116			−0.570580	+	0.821242i	$0.693282\pi$
$368$	3.39722	−	1.10382i	0.177092	−	0.0575408i
$369$	23.6613	+	24.5407i	1.23176	+	1.27754i
$370$	−9.31264	−	13.1582i	−0.484141	−	0.684065i
$371$	−0.438118			−0.0227460
$372$	5.60599	+	7.84684i	0.290657	+	0.406840i
$373$			32.0823i			1.66116i	0.556901	+	0.830579i	$0.311990\pi$
$373$			32.0823i			1.66116i	−0.556901	+	0.830579i	$0.688010\pi$
$374$	−6.57155	+	9.04497i	−0.339807	+	0.467704i
$375$	18.6001	+	5.38859i	0.960504	+	0.278266i
$376$	−2.69678	−	8.29983i	−0.139076	−	0.428031i
$377$	1.64780			0.0848660
$378$	−0.388603	−	1.83893i	−0.0199876	−	0.0945842i
$379$	2.37894	+	7.32161i	0.122198	+	0.376086i	0.993380	−	0.114874i	$-0.0366463\pi$
$379$	2.37894	+	7.32161i	0.122198	+	0.376086i	−0.871182	+	0.490959i	$0.836646\pi$
$380$	10.2702	−	13.7728i	0.526850	−	0.706531i
$381$	−3.83145	+	15.3413i	−0.196291	+	0.785960i
$382$	10.2495	−	14.1073i	0.524412	−	0.721791i
$383$	−6.55617	+	2.13023i	−0.335005	+	0.108850i	−0.471689	−	0.881765i	$-0.656355\pi$
$383$	−6.55617	+	2.13023i	−0.335005	+	0.108850i	0.136684	+	0.990615i	$0.456355\pi$
$384$	−1.46850	−	0.918426i	−0.0749391	−	0.0468682i
$385$	0.745427	+	2.39497i	0.0379905	+	0.122059i
$386$	−18.0688	−	5.87089i	−0.919675	−	0.298821i
$387$	−14.8430	+	14.3111i	−0.754510	+	0.727473i
$388$	0.130144	+	0.179127i	0.00660704	+	0.00909381i
$389$	−7.79733	+	23.9977i	−0.395341	+	1.21673i	0.533355	+	0.845891i	$0.320931\pi$
$389$	−7.79733	+	23.9977i	−0.395341	+	1.21673i	−0.928696	+	0.370842i	$0.879069\pi$
$390$	2.29624	−	0.893698i	0.116275	−	0.0452542i
$391$	−10.4184	−	7.56941i	−0.526881	−	0.382802i
$392$	2.12269	+	6.53296i	0.107212	+	0.329964i
$393$	19.8204	−	31.6914i	0.999805	−	1.59862i
$394$	14.8730	+	4.83252i	0.749290	+	0.243459i
$395$	−10.2140	−	7.61640i	−0.513920	−	0.383223i
$396$	−4.07178	−	8.36511i	−0.204615	−	0.420363i
$397$		−	5.57161i		−	0.279631i	−0.990178	−	0.139815i	$-0.955349\pi$
$397$		−	5.57161i		−	0.279631i	0.990178	−	0.139815i	$-0.0446509\pi$
$398$			12.7604i			0.639622i
$399$	−4.46390	+	1.80149i	−0.223475	+	0.0901871i
$400$	−4.99846	−	0.124146i	−0.249923	−	0.00620731i
$401$	19.3888	+	14.0868i	0.968228	+	0.703459i	0.955047	−	0.296454i	$-0.0958043\pi$
$401$	19.3888	+	14.0868i	0.968228	+	0.703459i	0.0131809	+	0.999913i	$0.495804\pi$
$402$	1.81740	+	26.1380i	0.0906434	+	1.30365i
$403$	3.44343	−	0.830866i	0.171530	−	0.0413884i
$404$			3.45643i			0.171964i
$405$	15.6835	+	12.6106i	0.779319	+	0.626627i
$406$	0.550673	+	0.757936i	0.0273294	+	0.0376157i
$407$	6.90867	+	21.2627i	0.342450	+	1.05395i
$408$	0.433127	+	6.22930i	0.0214430	+	0.308396i
$409$		−	21.9207i		−	1.08391i	−0.840408	−	0.541955i	$-0.817684\pi$
$409$		−	21.9207i		−	1.08391i	0.840408	−	0.541955i	$-0.182316\pi$
$410$	−25.4070	−	0.315467i	−1.25476	−	0.0155798i
$411$	−1.52081	−	0.379817i	−0.0750160	−	0.0187350i
$412$	9.33996	+	3.03474i	0.460147	+	0.149511i
$413$	−1.15059	−	0.835955i	−0.0566170	−	0.0411347i
$414$	9.63532	−	4.69006i	0.473550	−	0.230504i
$415$	23.6598	−	16.7450i	1.16141	−	0.821980i
$416$	−0.514703	+	0.373954i	−0.0252354	+	0.0183346i
$417$	6.95268	+	1.73641i	0.340474	+	0.0850324i
$418$	−19.2766	+	14.0053i	−0.942850	+	0.685020i
$419$	12.3572	+	17.0082i	0.603687	+	0.830904i	0.996040	−	0.0889110i	$-0.0283387\pi$
$419$	12.3572	+	17.0082i	0.603687	+	0.830904i	−0.392353	+	0.919815i	$0.628339\pi$
$420$	1.17845	+	0.757535i	0.0575022	+	0.0369639i
$421$	−0.0928946	+	0.0674919i	−0.00452741	+	0.00328935i	−0.590047	−	0.807369i	$-0.700891\pi$
$421$	−0.0928946	+	0.0674919i	−0.00452741	+	0.00328935i	0.585519	+	0.810659i	$0.300891\pi$
$422$	14.6969	+	10.6779i	0.715434	+	0.519793i
$423$	−11.4584	−	23.5402i	−0.557125	−	1.14457i
$424$	−0.711936	+	0.979895i	−0.0345747	+	0.0475879i
$425$	10.2300	+	14.8418i	0.496227	+	0.719933i
$426$	−12.5196	−	3.12673i	−0.606577	−	0.151491i
$427$	1.21370	+	3.73539i	0.0587352	+	0.180768i
$428$	−5.74201			−0.277550
$429$	−3.40907	+	0.237035i	−0.164592	+	0.0114442i
$430$	0.190804	−	15.3669i	0.00920137	−	0.741058i
$431$	−0.731701	−	1.00710i	−0.0352448	−	0.0485103i	0.791031	−	0.611776i	$-0.209545\pi$
$431$	−0.731701	−	1.00710i	−0.0352448	−	0.0485103i	−0.826276	+	0.563266i	$0.809545\pi$
$432$	−4.74442	−	2.11908i	−0.228266	−	0.101954i
$433$	5.00247			0.240403			0.120202	−	0.992749i	$-0.461646\pi$
$433$	5.00247			0.240403			0.120202	+	0.992749i	$0.461646\pi$
$434$	1.53292	+	1.30621i	0.0735826	+	0.0626999i
$435$	−9.70131	−	2.55124i	−0.465142	−	0.122323i
$436$	−0.546140	−	0.396794i	−0.0261554	−	0.0190030i
$437$	−16.1319	−	22.2037i	−0.771694	−	1.06215i
$438$	−3.81194	−	9.44561i	−0.182142	−	0.451329i
$439$	6.48390			0.309460			0.154730	−	0.987957i	$-0.450549\pi$
$439$	6.48390			0.309460			0.154730	+	0.987957i	$0.450549\pi$
$440$	6.56789	+	2.22456i	0.313112	+	0.106052i
$441$	9.01912	+	18.5290i	0.429482	+	0.882333i
$442$	2.18138	+	0.708773i	0.103758	+	0.0337129i
$443$	−8.09711	+	24.9203i	−0.384705	+	1.18400i	0.551988	+	0.833852i	$0.313869\pi$
$443$	−8.09711	+	24.9203i	−0.384705	+	1.18400i	−0.936694	+	0.350150i	$0.886131\pi$
$444$	10.5868	+	6.62114i	0.502425	+	0.314225i
$445$	0.437066	−	35.2003i	0.0207189	−	1.66865i
$446$	−17.1312	−	12.4466i	−0.811187	−	0.589362i
$447$	−23.4712	−	27.9942i	−1.11015	−	1.32408i
$448$	−0.344014	−	0.111777i	−0.0162531	−	0.00528096i
$449$	−4.95015	+	3.59650i	−0.233612	+	0.169729i	−0.698433	−	0.715676i	$-0.746119\pi$
$449$	−4.95015	+	3.59650i	−0.233612	+	0.169729i	0.464821	+	0.885405i	$0.346119\pi$
$450$	−14.9026	+	1.70639i	−0.702516	+	0.0804399i
$451$	33.5144	+	10.8895i	1.57813	+	0.512766i
$452$	−7.44211	+	5.40701i	−0.350047	+	0.254324i
$453$	2.80847	−	4.49054i	0.131953	−	0.210984i
$454$	0.828040	+	2.54844i	0.0388618	+	0.119604i
$455$	0.420028	−	0.297271i	0.0196912	−	0.0139363i
$456$	−3.22457	+	12.9113i	−0.151004	+	0.604629i
$457$	−8.07408	+	24.8495i	−0.377690	+	1.16241i	0.563956	+	0.825805i	$0.309279\pi$
$457$	−8.07408	+	24.8495i	−0.377690	+	1.16241i	−0.941646	+	0.336605i	$0.890721\pi$
$458$	−20.9997	+	6.82323i	−0.981253	+	0.318829i
$459$	3.87314	+	18.3282i	0.180783	+	0.855489i
$460$	−2.56235	+	7.56519i	−0.119470	+	0.352729i
$461$	4.08805	+	12.5817i	0.190399	+	0.585989i	1.00000		0.000992651i	$-0.000315971\pi$
$461$	4.08805	+	12.5817i	0.190399	+	0.585989i	−0.809600	+	0.586982i	$0.800316\pi$
$462$	−1.24829	−	1.48885i	−0.0580759	−	0.0692676i
$463$	−23.8294	−	17.3131i	−1.10745	−	0.804608i	−0.125188	−	0.992133i	$-0.539953\pi$
$463$	−23.8294	−	17.3131i	−1.10745	−	0.804608i	−0.982260	+	0.187525i	$0.939953\pi$
$464$	2.59003			0.120239
$465$	−21.5594	−	0.439697i	−0.999792	−	0.0203905i
$466$	−4.10466			−0.190144
$467$	6.34691	+	4.61130i	0.293700	+	0.213386i	0.724871	−	0.688885i	$-0.241899\pi$
$467$	6.34691	+	4.61130i	0.293700	+	0.213386i	−0.431171	+	0.902270i	$0.641899\pi$
$468$	−1.37399	+	1.32476i	−0.0635129	+	0.0612370i
$469$	1.69088	+	5.20398i	0.0780774	+	0.240297i
$470$	18.4827	+	6.26013i	0.852542	+	0.288758i
$471$	−0.496890	−	7.14634i	−0.0228955	−	0.329286i
$472$	−3.73939	+	1.21500i	−0.172120	+	0.0559250i
$473$	−6.58629	+	20.2705i	−0.302838	+	0.932039i
$474$	9.57508	+	2.39134i	0.439798	+	0.109838i
$475$	10.9606	+	36.8199i	0.502905	+	1.68941i
$476$	0.402975	+	1.24023i	0.0184703	+	0.0568458i
$477$	−1.70843	+	3.20698i	−0.0782234	+	0.146837i
$478$	−20.4166	+	14.8335i	−0.933834	+	0.678470i
$479$	30.8161	+	10.0127i	1.40802	+	0.457494i	0.911776	−	0.410688i	$-0.134712\pi$
$479$	30.8161	+	10.0127i	1.40802	+	0.457494i	0.496246	+	0.868182i	$0.334712\pi$
$480$	3.60926	−	1.40473i	0.164739	−	0.0641167i
$481$	3.71061	−	2.69592i	0.169189	−	0.122923i
$482$	−5.02958	−	1.63421i	−0.229091	−	0.0744362i
$483$	1.71493	−	1.43784i	0.0780319	−	0.0654241i
$484$	1.11873	+	0.812808i	0.0508516	+	0.0369458i
$485$	−0.495058	−	0.00614690i	−0.0224794	−	0.000279116i
$486$	−14.9761	−	4.32629i	−0.679329	−	0.196245i
$487$	−7.57747	+	23.3210i	−0.343368	+	1.05678i	0.619084	+	0.785325i	$0.287504\pi$
$487$	−7.57747	+	23.3210i	−0.343368	+	1.05678i	−0.962452	+	0.271453i	$0.912496\pi$
$488$	10.3268	+	3.35539i	0.467473	+	0.151891i
$489$	−12.5472	+	5.06363i	−0.567402	+	0.228985i
$490$	−14.5481	−	4.92748i	−0.657216	−	0.222601i
$491$	14.4912			0.653981			0.326990	−	0.945028i	$-0.393966\pi$
$491$	14.4912			0.653981			0.326990	+	0.945028i	$0.393966\pi$
$492$	18.2514	−	7.36569i	0.822838	−	0.332071i
$493$	−5.48845	−	7.55421i	−0.247188	−	0.340224i
$494$	3.95463	+	2.87321i	0.177927	+	0.129272i
$495$	20.4377	+	3.88263i	0.918604	+	0.174511i
$496$	5.41243	−	1.30597i	0.243026	−	0.0586396i
$497$	−2.69487			−0.120882
$498$	−11.9054	+	19.0360i	−0.533495	+	0.853022i
$499$	1.35325	+	1.86259i	0.0605797	+	0.0833808i	0.838232	−	0.545314i	$-0.183590\pi$
$499$	1.35325	+	1.86259i	0.0605797	+	0.0833808i	−0.777652	+	0.628695i	$0.783590\pi$
$500$	6.90391	−	8.79409i	0.308752	−	0.393284i
$501$	0.529083	+	7.60935i	0.0236377	+	0.339961i
$502$	−9.01806			−0.402496
$503$	4.94721	+	15.2259i	0.220585	+	0.678891i	0.998710	+	0.0507812i	$0.0161711\pi$
$503$	4.94721	+	15.2259i	0.220585	+	0.678891i	−0.778125	+	0.628110i	$0.783829\pi$
$504$	−1.06852	−	0.189277i	−0.0475956	−	0.00843108i
$505$	−6.19586	−	4.62017i	−0.275712	−	0.205595i
$506$	6.51119	−	8.96188i	0.289457	−	0.398404i
$507$	−8.16429	−	20.2303i	−0.362589	−	0.898459i
$508$	7.38582	+	5.36611i	0.327693	+	0.238083i
$509$	8.77049	−	6.37214i	0.388745	−	0.282440i	−0.376196	−	0.926540i	$-0.622768\pi$
$509$	8.77049	−	6.37214i	0.388745	−	0.282440i	0.764941	+	0.644100i	$0.222768\pi$
$510$	−11.7453	−	7.55021i	−0.520092	−	0.334329i
$511$	−1.25032	−	1.72092i	−0.0553111	−	0.0761291i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.22013	+	39.7001i	−0.186323	+	1.75280i
$514$	6.73070	−	4.89014i	0.296878	−	0.215695i
$515$	−17.9245	+	12.6859i	−0.789850	+	0.559010i
$516$	4.45499	+	11.0390i	0.196120	+	0.485966i
$517$	−21.8949	−	15.9076i	−0.962939	−	0.699616i
$518$	2.48007	+	0.805825i	0.108968	+	0.0354059i
$519$	6.39772	−	25.6168i	0.280829	−	1.12445i
$520$	0.0176625	−	1.42249i	0.000774550	−	0.0623805i
$521$		−	16.9359i		−	0.741974i	−0.928638	−	0.370987i	$-0.879019\pi$
$521$		−	16.9359i		−	0.741974i	0.928638	−	0.370987i	$-0.120981\pi$
$522$	7.69534	−	1.07532i	0.336816	−	0.0470656i
$523$	−0.667440	−	2.05417i	−0.0291851	−	0.0898225i	0.935403	−	0.353584i	$-0.115037\pi$
$523$	−0.667440	−	2.05417i	−0.0291851	−	0.0898225i	−0.964588	+	0.263761i	$0.915037\pi$
$524$	−12.6849	−	17.4592i	−0.554141	−	0.762710i
$525$	−2.93314	+	1.09985i	−0.128013	+	0.0480012i
$526$			4.24495i			0.185089i
$527$	−15.2783	−	13.0187i	−0.665535	−	0.567104i
$528$	−5.35842	+	0.372575i	−0.233195	+	0.0162142i
$529$	−8.28469	−	6.01918i	−0.360204	−	0.261704i
$530$	−0.804886	−	2.58600i	−0.0349620	−	0.112329i
$531$	−10.6058	+	5.16244i	−0.460252	+	0.224031i
$532$			2.77919i			0.120493i
$533$		−	7.22937i		−	0.313139i
$534$	10.2049	+	25.2866i	0.441607	+	1.09426i
$535$	7.67526	−	10.2929i	0.331831	−	0.445000i
$536$	14.3869	+	4.67458i	0.621418	+	0.201911i
$537$	30.2355	+	18.9098i	1.30476	+	0.816019i
$538$	−4.32608	−	13.3143i	−0.186511	−	0.574020i
$539$	17.2340	+	12.5212i	0.742319	+	0.539326i
$540$	10.1404	−	5.67211i	0.436372	−	0.244089i
$541$	4.16415	−	12.8159i	0.179031	−	0.551000i	−0.820764	−	0.571268i	$-0.806452\pi$
$541$	4.16415	−	12.8159i	0.179031	−	0.551000i	0.999795	+	0.0202678i	$0.00645187\pi$
$542$	5.19381	+	7.14867i	0.223093	+	0.307062i
$543$	−12.2875	−	14.6554i	−0.527307	−	0.628924i
$544$	3.42872	+	1.11406i	0.147005	+	0.0477649i
$545$	1.44130	−	0.448600i	0.0617383	−	0.0192159i
$546$	−0.211355	+	0.337942i	−0.00904517	+	0.0144626i
$547$	−26.9319	+	8.75072i	−1.15153	+	0.374154i	−0.821718	−	0.569894i	$-0.806984\pi$
$547$	−26.9319	+	8.75072i	−1.15153	+	0.374154i	−0.329809	+	0.944048i	$0.606984\pi$
$548$	−0.531951	+	0.732168i	−0.0227238	+	0.0312767i
$549$	32.0754	+	5.68184i	1.36895	+	0.242495i
$550$	−12.7669	+	8.79979i	−0.544381	+	0.375224i
$551$	−6.14946	−	18.9261i	−0.261976	−	0.806279i
$552$	−0.429148	−	6.17207i	−0.0182658	−	0.262701i
$553$	2.06106			0.0876450
$554$	2.43685	+	7.49986i	0.103532	+	0.318638i
$555$	−26.0200	+	10.1270i	−1.10449	+	0.429867i
$556$	2.43192	−	3.34725i	0.103136	−	0.141955i
$557$		−	37.4093i		−	1.58509i	−0.609817	−	0.792543i	$-0.708757\pi$
$557$		−	37.4093i		−	1.58509i	0.609817	−	0.792543i	$-0.291243\pi$
$558$	15.5389	−	6.12732i	0.657812	−	0.259390i
$559$	4.37254			0.184939
$560$	0.660205	−	0.467255i	0.0278988	−	0.0197451i
$561$	12.4415	+	14.8391i	0.525281	+	0.626507i
$562$	15.3036	−	4.97243i	0.645542	−	0.209749i
$563$	4.10697			0.173088			0.0865442	−	0.996248i	$-0.472418\pi$
$563$	4.10697			0.173088			0.0865442	+	0.996248i	$0.472418\pi$
$564$	−15.0791	+	1.04846i	−0.634946	+	0.0441482i
$565$	0.255382	−	20.5679i	0.0107440	−	0.865298i
$566$	24.8950	+	8.08886i	1.04641	+	0.340000i
$567$	−3.25329	−	0.118744i	−0.136625	−	0.00498680i
$568$	−4.37912	+	6.02735i	−0.183744	+	0.252902i
$569$	−4.17820	−	12.8592i	−0.175159	−	0.539085i	0.824481	−	0.565889i	$-0.191467\pi$
$569$	−4.17820	−	12.8592i	−0.175159	−	0.539085i	−0.999641	+	0.0268042i	$0.991467\pi$
$570$	−18.8341	−	23.0386i	−0.788874	−	0.964983i
$571$	−28.0452	−	38.6009i	−1.17366	−	1.61540i	−0.632980	−	0.774168i	$-0.718169\pi$
$571$	−28.0452	−	38.6009i	−1.17366	−	1.61540i	−0.540676	−	0.841231i	$-0.681831\pi$
$572$	−0.609684	+	1.87642i	−0.0254922	+	0.0784569i
$573$	−19.4048	−	23.1443i	−0.810647	−	0.966866i
$574$	3.32528	−	2.41596i	0.138795	−	0.100840i
$575$	−10.1360	−	14.7055i	−0.422700	−	0.613260i
$576$	−2.15966	+	2.08227i	−0.0899859	+	0.0867614i
$577$	14.4128	−	19.8375i	0.600012	−	0.825845i	−0.395698	−	0.918381i	$-0.629497\pi$
$577$	14.4128	−	19.8375i	0.600012	−	0.825845i	0.995709	+	0.0925357i	$0.0294972\pi$
$578$	1.23692	+	3.80684i	0.0514490	+	0.158344i
$579$	−17.4488	+	27.8995i	−0.725148	+	1.15946i
$580$	−3.46206	+	4.64279i	−0.143754	+	0.192781i
$581$	−1.44895	+	4.45941i	−0.0601125	+	0.185007i
$582$	0.355631	−	0.143521i	0.0147414	−	0.00594915i
$583$			3.75617i			0.155565i
$584$	−5.88077			−0.243348
$585$	−0.538109	−	4.23375i	−0.0222481	−	0.175044i
$586$	11.9285	−	8.66658i	0.492763	−	0.358013i
$587$	14.3424	−	19.7406i	0.591972	−	0.814780i	−0.402972	−	0.915212i	$-0.632023\pi$
$587$	14.3424	−	19.7406i	0.591972	−	0.814780i	0.994944	+	0.100433i	$0.0320227\pi$
$588$	11.8691	−	0.825265i	0.489473	−	0.0340333i
$589$	−22.3937	−	36.4494i	−0.922716	−	1.50187i
$590$	2.82043	−	8.32716i	0.116115	−	0.342824i
$591$	14.3627	−	22.9650i	0.590802	−	0.944652i
$592$	5.83239	−	4.23748i	0.239710	−	0.174159i
$593$	−9.47367	−	29.1569i	−0.389037	−	1.19733i	−0.933509	−	0.358553i	$-0.883270\pi$
$593$	−9.47367	−	29.1569i	−0.389037	−	1.19733i	0.544472	−	0.838779i	$-0.316730\pi$
$594$	−15.7659	+	3.33166i	−0.646883	+	0.136700i
$595$	−2.76183	−	0.935440i	−0.113224	−	0.0383493i
$596$	−20.0594	+	6.51768i	−0.821663	+	0.266975i
$597$	21.4431	+	5.35534i	0.877606	+	0.219179i
$598$	−2.16134	−	0.702262i	−0.0883838	−	0.0287176i
$599$	11.2161	−	15.4376i	0.458277	−	0.630764i	−0.515874	−	0.856665i	$-0.672533\pi$
$599$	11.2161	−	15.4376i	0.458277	−	0.630764i	0.974150	+	0.225901i	$0.0725326\pi$
$600$	−2.30639	+	8.34749i	−0.0941580	+	0.340785i
$601$	−19.9772	+	27.4962i	−0.814885	+	1.12159i	0.175666	+	0.984450i	$0.443792\pi$
$601$	−19.9772	+	27.4962i	−0.814885	+	1.12159i	−0.990551	+	0.137144i	$0.956208\pi$
$602$	1.46124	+	2.01123i	0.0595559	+	0.0819716i
$603$	44.6861	+	7.91569i	1.81976	+	0.322352i
$604$	−1.79740	−	2.47390i	−0.0731350	−	0.100662i
$605$	−2.95240	+	0.918928i	−0.120032	+	0.0373597i
$606$	5.80831	+	1.45061i	0.235947	+	0.0589269i
$607$	−3.50284	−	4.82124i	−0.142176	−	0.195688i	0.731991	−	0.681315i	$-0.238592\pi$
$607$	−3.50284	−	4.82124i	−0.142176	−	0.195688i	−0.874166	+	0.485627i	$0.838592\pi$
$608$	6.21594	+	4.51615i	0.252090	+	0.183154i
$609$	1.50477	−	0.607277i	0.0609764	−	0.0246081i
$610$	−19.8184	+	14.0263i	−0.802425	+	0.567910i
$611$	−1.71571	+	5.28042i	−0.0694102	+	0.213623i
$612$	10.6497	+	1.88649i	0.430489	+	0.0762569i
$613$	9.61990	+	29.6070i	0.388544	+	1.19582i	0.933876	+	0.357596i	$0.116404\pi$
$613$	9.61990	+	29.6070i	0.388544	+	1.19582i	−0.545332	+	0.838220i	$0.683596\pi$
$614$			21.5270i			0.868760i
$615$	−11.1930	+	42.5624i	−0.451346	+	1.71628i
$616$	−1.06684	+	0.346637i	−0.0429842	+	0.0139664i
$617$	−10.2165	+	7.42269i	−0.411299	+	0.298826i	−0.774127	−	0.633030i	$-0.781811\pi$
$617$	−10.2165	+	7.42269i	−0.411299	+	0.298826i	0.362829	+	0.931856i	$0.381811\pi$
$618$	9.01951	−	14.4216i	0.362818	−	0.580121i
$619$		−	26.7399i		−	1.07477i	−0.843338	−	0.537383i	$-0.819413\pi$
$619$		−	26.7399i		−	1.07477i	0.843338	−	0.537383i	$-0.180587\pi$
$620$	−4.89371	+	11.4478i	−0.196536	+	0.459754i
$621$	−3.83756	−	18.1599i	−0.153996	−	0.728731i
$622$	−8.53908	+	11.7530i	−0.342386	+	0.471254i
$623$	3.34721	+	4.60704i	0.134103	+	0.184577i
$624$	0.412393	+	1.02187i	0.0165089	+	0.0409075i
$625$	6.53556	+	24.1306i	0.261422	+	0.965224i
$626$	−7.34426			−0.293536
$627$	15.4449	+	38.2709i	0.616810	+	1.52839i
$628$	−3.93348	−	1.27806i	−0.156963	−	0.0510003i
$629$	−24.7184	−	8.03150i	−0.985588	−	0.320237i
$630$	1.76756	−	1.66238i	0.0704214	−	0.0662307i
$631$	25.4685	−	8.27521i	1.01388	−	0.329431i	0.245484	−	0.969401i	$-0.421053\pi$
$631$	25.4685	−	8.27521i	1.01388	−	0.329431i	0.768400	+	0.639970i	$0.221053\pi$
$632$	3.34918	−	4.60975i	0.133223	−	0.183366i
$633$	24.1116	−	20.2159i	0.958351	−	0.803509i
$634$	−4.60497	+	14.1726i	−0.182887	+	0.562868i
$635$	−19.4916	+	6.06671i	−0.773500	+	0.240750i
$636$	1.34786	+	1.60761i	0.0534463	+	0.0637458i
$637$	1.35047	−	4.15632i	0.0535076	−	0.164679i
$638$	6.49811	−	4.72115i	0.257262	−	0.186912i
$639$	−10.5085	+	19.7262i	−0.415712	+	0.780355i
$640$	0.0277621	−	2.23590i	0.00109739	−	0.0883815i
$641$	−8.13032	−	5.90702i	−0.321128	−	0.233313i	0.415528	−	0.909580i	$-0.363597\pi$
$641$	−8.13032	−	5.90702i	−0.321128	−	0.233313i	−0.736657	+	0.676267i	$0.763597\pi$
$642$	−2.40983	+	9.64908i	−0.0951083	+	0.380819i
$643$	3.37817	−	10.3969i	0.133222	−	0.410015i	−0.862087	−	0.506760i	$-0.830843\pi$
$643$	3.37817	−	10.3969i	0.133222	−	0.410015i	0.995309	+	0.0967449i	$0.0308431\pi$
$644$	−0.399273	−	1.22884i	−0.0157335	−	0.0484229i
$645$	−25.7430	−	6.76987i	−1.01363	−	0.266563i
$646$		−	27.6997i		−	1.08983i
$647$	−27.6916	+	8.99754i	−1.08867	+	0.353730i	−0.797732	−	0.603012i	$-0.793967\pi$
$647$	−27.6916	+	8.99754i	−1.08867	+	0.353730i	−0.290937	+	0.956742i	$0.593967\pi$
$648$	−5.55213	+	7.08335i	−0.218108	+	0.278260i
$649$	−7.16700	+	9.86452i	−0.281329	+	0.387216i
$650$	2.52630	+	1.93309i	0.0990895	+	0.0758220i
$651$	2.83834	−	2.02778i	0.111243	−	0.0794751i
$652$			7.81178i			0.305933i
$653$	−24.6766	−	17.9286i	−0.965668	−	0.701599i	−0.0112081	−	0.999937i	$-0.503568\pi$
$653$	−24.6766	−	17.9286i	−0.965668	−	0.701599i	−0.954460	+	0.298338i	$0.903568\pi$
$654$	−0.895994	+	0.751226i	−0.0350361	+	0.0293753i
$655$	48.2524	+	0.599128i	1.88538	+	0.0234099i
$656$		−	11.3632i		−	0.443659i
$657$	−17.4725	+	2.44156i	−0.681669	+	0.0952543i
$658$	−3.00219	+	0.975471i	−0.117038	+	0.0380278i
$659$	−7.04300	−	2.28841i	−0.274356	−	0.0891437i	0.168608	−	0.985683i	$-0.446073\pi$
$659$	−7.04300	−	2.28841i	−0.274356	−	0.0891437i	−0.442964	+	0.896540i	$0.646073\pi$
$660$	6.49467	−	10.1033i	0.252805	−	0.393271i
$661$	−28.4474	−	20.6682i	−1.10647	−	0.803900i	−0.124369	−	0.992236i	$-0.539691\pi$
$661$	−28.4474	−	20.6682i	−1.10647	−	0.803900i	−0.982105	+	0.188336i	$0.939691\pi$
$662$	−3.60334	+	1.17080i	−0.140048	+	0.0455043i
$663$	2.10654	−	3.36821i	0.0818111	−	0.130810i
$664$	7.61938	+	10.4872i	0.295689	+	0.406982i
$665$	−4.98187	−	3.71491i	−0.193189	−	0.144058i
$666$	15.5695	−	15.0116i	0.603306	−	0.581687i
$667$	5.43803	+	7.48481i	0.210562	+	0.289813i
$668$	4.18833	+	1.36087i	0.162051	+	0.0526537i
$669$	−28.1053	+	23.5643i	−1.08661	+	0.911048i
$670$	−27.6102	+	19.5409i	−1.06667	+	0.754930i
$671$	32.0251	−	10.4056i	1.23631	−	0.401703i
$672$	−0.332211	+	0.531182i	−0.0128153	+	0.0204908i
$673$	−10.5561	+	32.4882i	−0.406906	+	1.25233i	0.512387	+	0.858755i	$0.328761\pi$
$673$	−10.5561	+	32.4882i	−0.406906	+	1.25233i	−0.919293	+	0.393574i	$0.871239\pi$
$674$	2.83289	−	8.71874i	0.109119	−	0.335833i
$675$	−3.38691	+	25.7591i	−0.130362	+	0.991466i
$676$	−12.5952			−0.484432
$677$		−	25.3996i		−	0.976187i	−0.872791	−	0.488093i	$-0.837693\pi$
$677$		−	25.3996i		−	0.976187i	0.872791	−	0.488093i	$-0.162307\pi$
$678$	5.96280	+	14.7752i	0.229000	+	0.567439i
$679$	0.0647935	−	0.0470752i	0.00248655	−	0.00180658i
$680$	−6.58014	+	4.65704i	−0.252337	+	0.178589i
$681$	4.63001	−	0.321928i	0.177422	−	0.0123363i
$682$	11.1987	−	13.1424i	0.428819	−	0.503248i
$683$	6.14397			0.235092			0.117546	−	0.993067i	$-0.462497\pi$
$683$	6.14397			0.235092			0.117546	+	0.993067i	$0.462497\pi$
$684$	20.3434	+	10.8374i	0.777849	+	0.414377i
$685$	−0.601403	−	1.93223i	−0.0229784	−	0.0738268i
$686$	4.77118	−	1.55025i	0.182165	−	0.0591889i
$687$	2.65276	+	38.1523i	0.101209	+	1.45560i
$688$	6.87282			0.262024
$689$	0.732871	−	0.238124i	0.0279202	−	0.00907181i
$690$	11.6374	+	7.48085i	0.443030	+	0.284791i
$691$	1.72623	−	5.31278i	0.0656688	−	0.202108i	−0.912838	−	0.408322i	$-0.866114\pi$
$691$	1.72623	−	5.31278i	0.0656688	−	0.202108i	0.978507	+	0.206214i	$0.0661142\pi$
$692$	−12.3328	−	8.96029i	−0.468822	−	0.340619i
$693$	−3.02581	+	1.47283i	−0.114941	+	0.0559483i
$694$	8.11640	−	11.1713i	0.308094	−	0.424055i
$695$	2.74943	+	8.83358i	0.104292	+	0.335077i
$696$	1.08699	−	4.35239i	0.0412024	−	0.164977i
$697$	−33.1425	+	24.0794i	−1.25536	+	0.912073i
$698$	−17.1345	+	12.4490i	−0.648552	+	0.471201i
$699$	−1.72266	+	6.89761i	−0.0651568	+	0.260892i
$700$	−0.0449059	+	1.80803i	−0.00169728	+	0.0683371i
$701$	4.52818	−	6.23250i	0.171027	−	0.235398i	−0.714896	−	0.699231i	$-0.753526\pi$
$701$	4.52818	−	6.23250i	0.171027	−	0.235398i	0.885923	+	0.463832i	$0.153526\pi$
$702$	1.64953	+	2.86489i	0.0622575	+	0.108128i
$703$	−44.8121	−	32.5579i	−1.69012	−	1.22795i
$704$	−0.958310	+	2.94937i	−0.0361177	+	0.111159i
$705$	18.2766	−	28.4317i	0.688338	−	1.07080i
$706$	−9.90518	+	3.21839i	−0.372786	+	0.121126i
$707$	1.25025			0.0470206
$708$	0.472372	+	6.79373i	0.0177528	+	0.255324i
$709$	19.1764	−	6.23077i	0.720183	−	0.234002i	0.0740804	−	0.997252i	$-0.476398\pi$
$709$	19.1764	−	6.23077i	0.720183	−	0.234002i	0.646103	+	0.763251i	$0.276398\pi$
$710$	−4.95086	−	15.9065i	−0.185803	−	0.596961i
$711$	8.03700	−	15.0867i	0.301411	−	0.565795i
$712$	15.7433			0.590004
$713$	15.1380	+	12.8991i	0.566922	+	0.483076i
$714$	2.25325	−	0.156670i	0.0843256	−	0.00586321i
$715$	−2.54863	−	3.60107i	−0.0953133	−	0.134673i
$716$	16.6571	−	12.1021i	0.622507	−	0.452278i
$717$	16.3583	+	40.5342i	0.610912	+	1.51378i
$718$			16.3372i			0.609698i
$719$	−5.87557			−0.219122			−0.109561	−	0.993980i	$-0.534944\pi$
$719$	−5.87557			−0.219122			−0.109561	+	0.993980i	$0.534944\pi$
$720$	−0.845807	−	6.65467i	−0.0315214	−	0.248005i
$721$	1.09772	−	3.37843i	0.0408811	−	0.125819i
$722$	12.3710	−	38.0741i	0.460402	−	1.41697i
$723$	−4.85702	+	7.76604i	−0.180634	+	0.288822i
$724$	−10.5014	+	3.41210i	−0.390280	+	0.126810i
$725$	−3.69478	−	12.4119i	−0.137221	−	0.460967i
$726$	1.83539	−	1.53884i	0.0681176	−	0.0571117i
$727$	34.3125	+	11.1488i	1.27258	+	0.413486i	0.865961	−	0.500112i	$-0.166708\pi$
$727$	34.3125	+	11.1488i	1.27258	+	0.413486i	0.406618	+	0.913598i	$0.366708\pi$
$728$	0.135266	+	0.186177i	0.00501328	+	0.00690018i
$729$	−13.5553	+	23.3507i	−0.502047	+	0.864840i
$730$	7.86075	−	10.5416i	0.290939	−	0.390163i
$731$	−14.5639	−	20.0456i	−0.538667	−	0.741412i
$732$	9.97251	−	15.9454i	0.368595	−	0.589357i
$733$	−7.63726	+	2.48150i	−0.282089	+	0.0916562i	−0.446644	−	0.894712i	$-0.647381\pi$
$733$	−7.63726	+	2.48150i	−0.282089	+	0.0916562i	0.164556	+	0.986368i	$0.447381\pi$
$734$	17.6863	+	12.8499i	0.652814	+	0.474297i
$735$	−14.3859	+	22.3791i	−0.530632	+	0.825467i
$736$	−3.39722	−	1.10382i	−0.125223	−	0.0406875i
$737$	44.6159	−	14.4966i	1.64345	−	0.533989i
$738$	−4.71775	−	33.7616i	−0.173663	−	1.24278i
$739$		−	1.84481i		−	0.0678626i	−0.999424	−	0.0339313i	$-0.989197\pi$
$739$		−	1.84481i		−	0.0678626i	0.999424	−	0.0339313i	$-0.0108027\pi$
$740$	−0.200143	+	16.1191i	−0.00735741	+	0.592549i
$741$	6.48794	−	5.43967i	0.238340	−	0.199831i
$742$	0.354445	+	0.257520i	0.0130121	+	0.00945384i
$743$			32.1066i			1.17788i	0.808178	+	0.588938i	$0.200454\pi$
$743$			32.1066i			1.17788i	−0.808178	+	0.588938i	$0.799546\pi$
$744$	0.0769168	−	9.64334i	0.00281991	−	0.353542i
$745$	15.1297	−	44.6697i	0.554311	−	1.63657i
$746$	18.8575	−	25.9551i	0.690422	−	0.950284i
$747$	26.9922	+	27.9954i	0.987594	+	1.02430i
$748$	10.6330	−	3.45487i	0.388781	−	0.126323i
$749$			2.07698i			0.0758914i
$750$	−11.8804	−	15.2923i	−0.433813	−	0.558396i
$751$	6.65313	+	20.4762i	0.242776	+	0.747189i	0.995994	+	0.0894176i	$0.0285006\pi$
$751$	6.65313	+	20.4762i	0.242776	+	0.747189i	−0.753218	+	0.657771i	$0.771499\pi$
$752$	−2.69678	+	8.29983i	−0.0983413	+	0.302664i
$753$	−3.78473	+	15.1543i	−0.137923	+	0.552252i
$754$	−1.33310	−	0.968553i	−0.0485486	−	0.0352726i
$755$	6.83717	+	0.0848940i	0.248830	+	0.00308961i
$756$	−0.766508	+	1.71614i	−0.0278776	+	0.0624154i
$757$	31.7365	−	23.0579i	1.15348	−	0.838054i	0.164542	−	0.986370i	$-0.447385\pi$
$757$	31.7365	−	23.0579i	1.15348	−	0.838054i	0.988940	+	0.148316i	$0.0473854\pi$
$758$	2.37894	−	7.32161i	0.0864068	−	0.265933i
$759$	−12.3272	−	14.7028i	−0.447450	−	0.533677i
$760$	−16.4042	+	5.10577i	−0.595044	+	0.185206i
$761$	−5.87060	+	18.0678i	−0.212809	+	0.654959i	0.786493	+	0.617599i	$0.211895\pi$
$761$	−5.87060	+	18.0678i	−0.212809	+	0.654959i	−0.999302	+	0.0373594i	$0.988105\pi$
$762$	12.1171	−	10.1593i	0.438957	−	0.368034i
$763$	−0.143527	+	0.197549i	−0.00519604	+	0.00715174i
$764$	−16.5841	+	5.38850i	−0.599991	+	0.194949i
$765$	−17.6170	+	16.5686i	−0.636943	+	0.599039i
$766$	6.55617	+	2.13023i	0.236884	+	0.0769683i
$767$	2.37903	+	0.772994i	0.0859019	+	0.0279112i
$768$	0.648204	+	1.60619i	0.0233901	+	0.0579582i
$769$	−51.6413			−1.86223			−0.931116	−	0.364723i	$-0.881164\pi$
$769$	−51.6413			−1.86223			−0.931116	+	0.364723i	$0.881164\pi$
$770$	0.804663	−	2.37572i	0.0289980	−	0.0856150i
$771$	−5.39280	−	13.3628i	−0.194217	−	0.481250i
$772$	11.1671	+	15.3702i	0.401913	+	0.553186i
$773$	−26.0466	+	35.8501i	−0.936833	+	1.28944i	0.0203010	+	0.999794i	$0.493538\pi$
$773$	−26.0466	+	35.8501i	−0.936833	+	1.28944i	−0.957134	+	0.289646i	$0.906462\pi$
$774$	20.4200	−	2.85343i	0.733983	−	0.102565i
$775$	−13.9795	−	24.0744i	−0.502157	−	0.864776i
$776$		−	0.221414i		−	0.00794828i
$777$	2.39498	−	3.82941i	0.0859195	−	0.137379i
$778$	20.4137	−	14.8314i	0.731866	−	0.531732i
$779$	−83.0342	+	26.9795i	−2.97501	+	0.966639i
$780$	−2.38300	−	0.626678i	−0.0853250	−	0.0224387i
$781$			23.1043i			0.826736i
$782$	3.97948	+	12.2476i	0.142306	+	0.437972i
$783$	1.42260	−	13.3828i	0.0508394	−	0.478263i
$784$	2.12269	−	6.53296i	0.0758103	−	0.233320i
$785$	7.54884	−	5.34262i	0.269429	−	0.190686i
$786$	−34.6628	+	13.9888i	−1.23638	+	0.498963i
$787$	−6.84969	−	4.97659i	−0.244165	−	0.177396i	0.458972	−	0.888451i	$-0.348218\pi$
$787$	−6.84969	−	4.97659i	−0.244165	−	0.177396i	−0.703137	+	0.711055i	$0.748218\pi$
$788$	−9.19201	−	12.6517i	−0.327452	−	0.450699i
$789$	7.13338	+	1.78154i	0.253955	+	0.0634244i
$790$	3.78645	+	12.1654i	0.134716	+	0.432826i
$791$	1.95581	+	2.69194i	0.0695406	+	0.0957144i
$792$	−1.62275	+	9.16085i	−0.0576621	+	0.325517i
$793$	−4.06049	−	5.58878i	−0.144192	−	0.198463i
$794$	−3.27491	+	4.50752i	−0.116222	+	0.159966i
$795$	−4.68341	+	0.267258i	−0.166103	+	0.00947866i
$796$	7.50039	−	10.3234i	0.265844	−	0.365903i
$797$	−4.29387	−	1.39516i	−0.152097	−	0.0494192i	0.231979	−	0.972721i	$-0.425480\pi$
$797$	−4.29387	−	1.39516i	−0.152097	−	0.0494192i	−0.384076	+	0.923302i	$0.625480\pi$
$798$	4.67026	+	1.16638i	0.165325	+	0.0412895i
$799$	29.9223	−	9.72234i	1.05857	−	0.343952i
$800$	3.97087	+	3.03846i	0.140391	+	0.107426i
$801$	46.7753	−	6.53624i	1.65273	−	0.230947i
$802$	−7.40584	−	22.7928i	−0.261509	−	0.804843i
$803$	−14.7542	+	10.7195i	−0.520664	+	0.378285i
$804$	13.8933	−	22.2144i	0.489977	−	0.783440i
$805$	2.73646	+	0.926847i	0.0964476	+	0.0326671i
$806$	−3.27417	−	1.35181i	−0.115328	−	0.0476157i
$807$	−24.1894	+	1.68191i	−0.851508	+	0.0592059i
$808$	2.03164	−	2.79631i	0.0714728	−	0.0983739i
$809$	−39.0917	+	28.4018i	−1.37439	+	0.998553i	−0.377011	+	0.926209i	$0.623048\pi$
$809$	−39.0917	+	28.4018i	−1.37439	+	0.998553i	−0.997380	+	0.0723446i	$0.976952\pi$
$810$	−5.27587	−	19.4207i	−0.185375	−	0.682375i
$811$	51.6702			1.81439			0.907194	−	0.420713i	$-0.138220\pi$
$811$	51.6702			1.81439			0.907194	+	0.420713i	$0.138220\pi$
$812$		−	0.936861i		−	0.0328774i
$813$	14.1926	−	5.72769i	0.497758	−	0.200879i
$814$	6.90867	−	21.2627i	0.242149	−	0.745258i
$815$	−14.0031	−	10.4419i	−0.490506	−	0.365764i
$816$	3.31108	−	5.29419i	0.115911	−	0.185334i
$817$	−16.3180	−	50.2216i	−0.570894	−	1.75703i
$818$	−12.8847	+	17.7342i	−0.450502	+	0.620063i
$819$	0.479188	+	0.496998i	0.0167442	+	0.0173665i
$820$	20.3693	+	15.1891i	0.711325	+	0.530425i
$821$	33.2598	−	24.1646i	1.16077	−	0.843352i	0.170899	−	0.985289i	$-0.445333\pi$
$821$	33.2598	−	24.1646i	1.16077	−	0.843352i	0.989876	+	0.141937i	$0.0453329\pi$
$822$	1.00711	+	1.20119i	0.0351270	+	0.0418963i
$823$	0.0882904	−	0.271730i	0.00307761	−	0.00947191i	−0.949506	−	0.313749i	$-0.898415\pi$
$823$	0.0882904	−	0.271730i	0.00307761	−	0.00947191i	0.952584	+	0.304277i	$0.0984149\pi$
$824$	−5.77241	−	7.94505i	−0.201092	−	0.276779i
$825$	9.42944	+	25.1470i	0.328291	+	0.875507i
$826$	0.439488	+	1.35260i	0.0152917	+	0.0470631i
$827$	26.0232	−	35.8178i	0.904915	−	1.24551i	−0.0639590	−	0.997953i	$-0.520373\pi$
$827$	26.0232	−	35.8178i	0.904915	−	1.24551i	0.968874	−	0.247556i	$-0.0796273\pi$
$828$	−10.5519	−	1.86916i	−0.366703	−	0.0649579i
$829$	−0.402874	−	0.130902i	−0.0139924	−	0.00454640i	0.302012	−	0.953304i	$-0.402342\pi$
$829$	−0.402874	−	0.130902i	−0.0139924	−	0.00454640i	−0.316005	+	0.948758i	$0.602342\pi$
$830$	−28.9836	−	0.359876i	−1.00604	−	0.0124915i
$831$	13.6257	−	0.947406i	0.472672	−	0.0328652i
$832$	0.636208			0.0220565
$833$	−23.5524	+	7.65265i	−0.816043	+	0.265149i
$834$	−4.60420	−	5.49147i	−0.159430	−	0.190154i
$835$	−8.03792	+	5.68877i	−0.278164	+	0.196868i
$836$	23.8272			0.824081
$837$	−3.77516	−	28.6836i	−0.130489	−	0.991450i
$838$		−	21.0233i		−	0.726237i
$839$	15.1401	−	20.8385i	0.522693	−	0.719425i	−0.463302	−	0.886201i	$-0.653335\pi$
$839$	15.1401	−	20.8385i	0.522693	−	0.719425i	0.985995	+	0.166775i	$0.0533354\pi$
$840$	−0.508114	−	1.30553i	−0.0175316	−	0.0450451i
$841$	−6.88852	−	21.2007i	−0.237535	−	0.731058i
$842$	0.114824			0.00395710
$843$	−1.93320	−	27.8035i	−0.0665828	−	0.957604i
$844$	−5.61372	−	17.2773i	−0.193232	−	0.594708i
$845$	16.8359	−	22.5777i	0.579172	−	0.776697i
$846$	−4.56659	+	25.7795i	−0.157003	+	0.886318i
$847$	0.294007	−	0.404666i	0.0101022	−	0.0139045i
$848$	1.15194	−	0.374287i	0.0395576	−	0.0128531i
$849$	24.0408	−	38.4396i	0.825079	−	1.31924i
$850$	0.447568	−	18.0203i	0.0153515	−	0.618091i
$851$	24.4914	+	7.95772i	0.839553	+	0.272787i
$852$	8.29073	+	9.88842i	0.284036	+	0.338772i
$853$	−1.96919	−	2.71035i	−0.0674237	−	0.0928007i	0.773973	−	0.633218i	$-0.218266\pi$
$853$	−1.96919	−	2.71035i	−0.0674237	−	0.0928007i	−0.841397	+	0.540417i	$0.818266\pi$
$854$	1.21370	−	3.73539i	0.0415320	−	0.127822i
$855$	−46.6193	+	21.9806i	−1.59435	+	0.751720i
$856$	4.64538	+	3.37507i	0.158776	+	0.115357i
$857$	−0.520665	−	1.60244i	−0.0177856	−	0.0547384i	0.941770	−	0.336258i	$-0.109161\pi$
$857$	−0.520665	−	1.60244i	−0.0177856	−	0.0547384i	−0.959555	+	0.281520i	$0.909161\pi$
$858$	2.89732	+	1.81204i	0.0989129	+	0.0618619i
$859$	−40.1067	−	13.0314i	−1.36842	−	0.444627i	−0.469576	−	0.882892i	$-0.655593\pi$
$859$	−40.1067	−	13.0314i	−1.36842	−	0.444627i	−0.898846	+	0.438265i	$0.855593\pi$
$860$	−9.18680	+	12.3199i	−0.313267	+	0.420106i
$861$	−2.66430	−	6.60187i	−0.0907991	−	0.224991i
$862$			1.24484i			0.0423995i
$863$		−	21.3726i		−	0.727531i	−0.931490	−	0.363766i	$-0.881491\pi$
$863$		−	21.3726i		−	0.727531i	0.931490	−	0.363766i	$-0.118509\pi$
$864$	2.59275	+	4.50307i	0.0882072	+	0.153198i
$865$	32.5469	−	10.1301i	1.10663	−	0.344435i
$866$	−4.04708	−	2.94038i	−0.137526	−	0.0999181i
$867$	6.91627	−	0.480893i	0.234889	−	0.0163320i
$868$	−0.472391	−	1.95777i	−0.0160340	−	0.0664511i
$869$		−	17.6703i		−	0.599424i
$870$	6.34894	+	7.76628i	0.215249	+	0.263302i
$871$	−5.65689	−	7.78604i	−0.191676	−	0.263820i
$872$	0.208607	+	0.642027i	0.00706433	+	0.0217418i
$873$	−0.0919257	−	0.657849i	−0.00311121	−	0.0222648i
$874$			27.4452i			0.928349i
$875$	−3.18098	−	2.49727i	−0.107537	−	0.0844230i
$876$	−2.46806	+	9.88226i	−0.0833881	+	0.333891i
$877$	−33.9303	−	11.0246i	−1.14574	−	0.372275i	−0.326206	−	0.945299i	$-0.605770\pi$
$877$	−33.9303	−	11.0246i	−1.14574	−	0.372275i	−0.819539	+	0.573024i	$0.805770\pi$
$878$	−5.24559	−	3.81114i	−0.177030	−	0.128620i
$879$	−9.55743	−	23.6823i	−0.322364	−	0.798786i
$880$	−4.00597	−	5.66022i	−0.135041	−	0.190806i
$881$	1.11668	−	0.811318i	0.0376220	−	0.0273340i	−0.568815	−	0.822465i	$-0.692598\pi$
$881$	1.11668	−	0.811318i	0.0376220	−	0.0273340i	0.606437	+	0.795131i	$0.292598\pi$
$882$	3.59445	−	20.2916i	0.121032	−	0.683253i
$883$	22.1457	−	16.0898i	0.745263	−	0.541465i	−0.149092	−	0.988823i	$-0.547635\pi$
$883$	22.1457	−	16.0898i	0.745263	−	0.541465i	0.894355	+	0.447358i	$0.147635\pi$
$884$	−1.34817	−	1.85559i	−0.0453437	−	0.0624103i
$885$	−12.8096	−	8.23433i	−0.430589	−	0.276794i
$886$	21.1985	−	15.4016i	0.712178	−	0.517428i
$887$	22.6633	+	16.4659i	0.760960	+	0.552870i	0.899205	−	0.437528i	$-0.144146\pi$
$887$	22.6633	+	16.4659i	0.760960	+	0.552870i	−0.138244	+	0.990398i	$0.544146\pi$
$888$	−4.67305	−	11.5794i	−0.156817	−	0.388578i
$889$	1.94102	−	2.67158i	0.0650996	−	0.0896019i
$890$	−21.0438	+	28.2207i	−0.705390	+	0.945962i
$891$	−1.01805	+	27.8918i	−0.0341058	+	0.934411i
$892$	6.54354	+	20.1390i	0.219094	+	0.674302i
$893$	67.0520			2.24381
$894$	2.53396	+	36.4438i	0.0847484	+	1.21886i
$895$	−0.571604	+	46.0357i	−0.0191066	+	1.53880i
$896$	0.212612	+	0.292636i	0.00710288	+	0.00977627i
$897$	−2.08719	+	3.33727i	−0.0696891	+	0.111428i
$898$	6.11873			0.204185
$899$	7.54887	+	12.2870i	0.251769	+	0.409796i
$900$	13.0595	+	7.37905i	0.435316	+	0.245968i
$901$	−3.53269	−	2.56665i	−0.117691	−	0.0855075i
$902$	−20.7130	−	28.5091i	−0.689669	−	0.949248i
$903$	3.99300	−	1.61145i	0.132879	−	0.0536256i
$904$	9.19895			0.305953
$905$	7.92064	−	23.3852i	0.263291	−	0.777352i
$906$	−4.91157	+	1.98215i	−0.163176	+	0.0658526i
$907$	41.4771	+	13.4767i	1.37722	+	0.447487i	0.901756	−	0.432246i	$-0.142279\pi$
$907$	41.4771	+	13.4767i	1.37722	+	0.447487i	0.475468	+	0.879733i	$0.342279\pi$
$908$	0.828040	−	2.54844i	0.0274795	−	0.0845731i
$909$	4.87531	−	9.15170i	0.161704	−	0.303543i
$910$	−0.514541	−	0.00638882i	−0.0170569	−	0.000211787i
$911$	−42.1916	−	30.6540i	−1.39787	−	1.01561i	−0.994949	−	0.100378i	$-0.967995\pi$
$911$	−42.1916	−	30.6540i	−1.39787	−	1.01561i	−0.402922	−	0.915234i	$-0.632005\pi$
$912$	10.1978	−	8.55014i	0.337684	−	0.283124i
$913$	38.2324	+	12.4224i	1.26531	+	0.411123i
$914$	21.1382	−	15.3578i	0.699190	−	0.507992i
$915$	15.2529	+	39.1903i	0.504245	+	1.29559i
$916$	20.9997	+	6.82323i	0.693851	+	0.225446i
$917$	−6.31531	+	4.58834i	−0.208550	+	0.151520i
$918$	7.63964	−	17.1044i	0.252146	−	0.564530i
$919$	13.5111	+	41.5829i	0.445690	+	1.37169i	0.881726	+	0.471763i	$0.156382\pi$
$919$	13.5111	+	41.5829i	0.445690	+	1.37169i	−0.436036	+	0.899929i	$0.643618\pi$
$920$	6.51969	−	4.61426i	0.214948	−	0.152128i
$921$	36.1748	+	9.03454i	1.19200	+	0.297698i
$922$	4.08805	−	12.5817i	0.134633	−	0.414357i
$923$	4.50790	−	1.46470i	0.148379	−	0.0482113i
$924$	0.134767	+	1.93824i	0.00443350	+	0.0637633i
$925$	−28.6269	−	21.9049i	−0.941246	−	0.720229i
$926$	9.10203	+	28.0132i	0.299111	+	0.920570i
$927$	−20.4492	−	21.2092i	−0.671640	−	0.696602i
$928$	−2.09538	−	1.52238i	−0.0687843	−	0.0499747i
$929$	14.3951			0.472288			0.236144	−	0.971718i	$-0.424116\pi$
$929$	14.3951			0.472288			0.236144	+	0.971718i	$0.424116\pi$
$930$	17.1835	+	13.0280i	0.563468	+	0.427205i
$931$	−52.7780			−1.72973
$932$	3.32074	+	2.41266i	0.108774	+	0.0790292i
$933$	16.1665	+	19.2819i	0.529268	+	0.631262i
$934$	−2.42430	−	7.46124i	−0.0793256	−	0.244139i
$935$	−8.01992	+	23.6784i	−0.262280	+	0.774365i
$936$	1.89026	−	0.264139i	0.0617850	−	0.00863364i
$937$	16.7414	−	5.43962i	0.546918	−	0.177705i	−0.0225083	−	0.999747i	$-0.507165\pi$
$937$	16.7414	−	5.43962i	0.546918	−	0.177705i	0.569427	+	0.822042i	$0.307165\pi$
$938$	1.69088	−	5.20398i	0.0552090	−	0.169916i
$939$	−3.08227	+	12.3416i	−0.100586	+	0.402752i
$940$	−11.2732	−	15.9284i	−0.367691	−	0.519527i
$941$	−11.1242	−	34.2369i	−0.362640	−	1.11609i	−0.951446	−	0.307817i	$-0.900402\pi$
$941$	−11.1242	−	34.2369i	−0.362640	−	1.11609i	0.588806	−	0.808275i	$-0.299598\pi$
$942$	−3.79852	+	6.07358i	−0.123763	+	0.197888i
$943$	32.8380	−	23.8582i	1.06935	−	0.776930i
$944$	3.73939	+	1.21500i	0.121707	+	0.0395450i
$945$	−2.05170	−	3.66795i	−0.0667418	−	0.119318i
$946$	17.2431	−	12.5279i	0.560622	−	0.407316i
$947$	30.0936	+	9.77800i	0.977910	+	0.317742i	0.754005	−	0.656869i	$-0.228119\pi$
$947$	30.0936	+	9.77800i	0.977910	+	0.317742i	0.223905	+	0.974611i	$0.428119\pi$
$948$	−6.34080	−	7.56273i	−0.205940	−	0.245626i
$949$	3.02685	+	2.19914i	0.0982557	+	0.0713870i
$950$	12.7749	−	36.2304i	0.414473	−	1.17547i
$951$	21.8836	+	13.6864i	0.709624	+	0.443812i
$952$	0.402975	−	1.24023i	0.0130605	−	0.0401960i
$953$	−57.9263	−	18.8214i	−1.87642	−	0.609685i	−0.988830	−	0.149045i	$-0.952380\pi$
$953$	−57.9263	−	18.8214i	−1.87642	−	0.609685i	−0.887587	−	0.460640i	$-0.847620\pi$
$954$	3.26716	−	1.59031i	0.105778	−	0.0514883i
$955$	12.5085	−	36.9307i	0.404766	−	1.19505i
$956$	25.2363			0.816201
$957$	−5.20644	−	12.9010i	−0.168300	−	0.417031i
$958$	−19.0454	−	26.2137i	−0.615328	−	0.846926i
$959$	0.264838	+	0.192416i	0.00855206	+	0.00621344i
$960$	−3.74563	−	0.985021i	−0.120890	−	0.0317914i
$961$	21.9704	+	21.8701i	0.708724	+	0.705486i
$962$	−4.58657			−0.147877
$963$	15.2033	+	8.09912i	0.489919	+	0.260990i
$964$	3.10845	+	4.27842i	0.100116	+	0.137798i
$965$	−42.4789	−	0.527441i	−1.36744	−	0.0169789i
$966$	−2.23255	+	0.155230i	−0.0718310	+	0.00499446i
$967$	4.45597			0.143294			0.0716472	−	0.997430i	$-0.477174\pi$
$967$	4.45597			0.143294			0.0716472	+	0.997430i	$0.477174\pi$
$968$	−0.427319	−	1.31515i	−0.0137345	−	0.0422706i
$969$	−46.5476	−	11.6251i	−1.49532	−	0.373452i
$970$	0.396897	+	0.295960i	0.0127436	+	0.00950272i
$971$	−14.9237	+	20.5407i	−0.478925	+	0.659184i	−0.978298	−	0.207204i	$-0.933564\pi$
$971$	−14.9237	+	20.5407i	−0.478925	+	0.659184i	0.499373	+	0.866387i	$0.333564\pi$
$972$	9.57298	+	12.3028i	0.307053	+	0.394611i
$973$	−1.21076	−	0.879668i	−0.0388151	−	0.0282008i
$974$	19.8381	−	14.4132i	0.635653	−	0.461829i
$975$	4.30868	−	3.43399i	0.137988	−	0.109976i
$976$	−6.38232	−	8.78452i	−0.204293	−	0.281185i
$977$	37.4572	−	27.2143i	1.19836	−	0.870662i	0.204240	−	0.978921i	$-0.434528\pi$
$977$	37.4572	−	27.2143i	1.19836	−	0.870662i	0.994123	+	0.108259i	$0.0345277\pi$
$978$	13.1272	+	3.27847i	0.419761	+	0.104834i
$979$	39.4981	−	28.6970i	1.26236	−	0.917162i
$980$	8.87335	+	12.5376i	0.283449	+	0.400498i
$981$	0.886354	+	1.82094i	0.0282991	+	0.0581381i
$982$	−11.7237	−	8.51774i	−0.374117	−	0.271812i
$983$	53.8902	+	17.5100i	1.71883	+	0.558482i	0.991763	−	0.128085i	$-0.0408831\pi$
$983$	53.8902	+	17.5100i	1.71883	+	0.558482i	0.727067	+	0.686567i	$0.240883\pi$
$984$	−19.0952	−	4.76896i	−0.608732	−	0.152029i
$985$	34.9658	+	0.434154i	1.11410	+	0.0138333i
$986$			9.33751i			0.297367i
$987$	0.379247	+	5.45438i	0.0120716	+	0.173615i
$988$	−1.51054	−	4.64895i	−0.0480565	−	0.147903i
$989$	14.4302	+	19.8614i	0.458852	+	0.631556i
$990$	−14.2523	−	15.1541i	−0.452966	−	0.481628i
$991$		−	8.10705i		−	0.257529i	−0.991675	−	0.128764i	$-0.958899\pi$
$991$		−	8.10705i		−	0.257529i	0.991675	−	0.128764i	$-0.0411011\pi$
$992$	−5.14638	−	2.12480i	−0.163398	−	0.0674625i
$993$	0.455186	+	6.54655i	0.0144449	+	0.207748i
$994$	2.18020	+	1.58401i	0.0691516	+	0.0502416i
$995$	8.47963	+	27.2440i	0.268822	+	0.863694i
$996$	20.8208	−	8.40259i	0.659731	−	0.266246i
$997$		−	1.41851i		−	0.0449246i	−0.999748	−	0.0224623i	$-0.992849\pi$
$997$		−	1.41851i		−	0.0449246i	0.999748	−	0.0224623i	$-0.00715058\pi$
$998$		−	2.30228i		−	0.0728775i
$999$	−18.6917	−	32.4637i	−0.591380	−	1.02710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.a.29.7	✓	128
3.2	odd	2		930.2.y.b.29.7	yes	128
5.4	even	2		930.2.y.b.29.26	yes	128
15.14	odd	2	inner	930.2.y.a.29.26	yes	128
31.15	odd	10	inner	930.2.y.a.449.26	yes	128
93.77	even	10		930.2.y.b.449.26	yes	128
155.139	odd	10		930.2.y.b.449.7	yes	128
465.449	even	10	inner	930.2.y.a.449.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.7	✓	128	1.1	even	1	trivial
930.2.y.a.29.26	yes	128	15.14	odd	2	inner
930.2.y.a.449.7	yes	128	465.449	even	10	inner
930.2.y.a.449.26	yes	128	31.15	odd	10	inner
930.2.y.b.29.7	yes	128	3.2	odd	2
930.2.y.b.29.26	yes	128	5.4	even	2
930.2.y.b.449.7	yes	128	155.139	odd	10
930.2.y.b.449.26	yes	128	93.77	even	10

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.32727 + 1.11282i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.11788 - 0.717333i) q^{5} +(1.72788 - 0.120141i) q^{6} +(0.344014 - 0.111777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.523274 - 2.95401i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.32727 + 1.11282i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.11788 - 0.717333i) q^{5} +(1.72788 - 0.120141i) q^{6} +(0.344014 - 0.111777i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.523274 - 2.95401i) q^{9} +(1.29177 + 1.82520i) q^{10} +(-0.958310 - 2.94937i) q^{11} +(-1.46850 - 0.918426i) q^{12} +(-0.514703 + 0.373954i) q^{13} +(-0.344014 - 0.111777i) q^{14} +(3.60926 - 1.40473i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(3.42872 + 1.11406i) q^{17} +(-2.15966 + 2.08227i) q^{18} +(6.21594 + 4.51615i) q^{19} +(0.0277621 - 2.23590i) q^{20} +(-0.332211 + 0.531182i) q^{21} +(-0.958310 + 2.94937i) q^{22} +(-3.39722 - 1.10382i) q^{23} +(0.648204 + 1.60619i) q^{24} +(3.97087 + 3.03846i) q^{25} +0.636208 q^{26} +(2.59275 + 4.50307i) q^{27} +(0.212612 + 0.292636i) q^{28} +(-2.09538 - 1.52238i) q^{29} +(-3.74563 - 0.985021i) q^{30} +(-5.14638 - 2.12480i) q^{31} +1.00000 q^{32} +(4.55405 + 2.84818i) q^{33} +(-2.11907 - 2.91664i) q^{34} +(-0.808763 - 0.0100420i) q^{35} +(2.97113 - 0.415177i) q^{36} -7.20923 q^{37} +(-2.37428 - 7.30728i) q^{38} +(0.267006 - 1.06911i) q^{39} +(-1.33669 + 1.79256i) q^{40} +(-6.67913 + 9.19304i) q^{41} +(0.580985 - 0.234467i) q^{42} +(-5.56022 - 4.03974i) q^{43} +(2.50889 - 1.82281i) q^{44} +(-3.22724 + 5.88089i) q^{45} +(2.09960 + 2.88985i) q^{46} +(7.06025 - 5.12957i) q^{47} +(0.419684 - 1.68044i) q^{48} +(-5.55727 + 4.03759i) q^{49} +(-1.42654 - 4.79218i) q^{50} +(-5.79057 + 2.33689i) q^{51} +(-0.514703 - 0.373954i) q^{52} +(-1.15194 - 0.374287i) q^{53} +(0.549258 - 5.16704i) q^{54} +(-0.0860946 + 6.93386i) q^{55} -0.361718i q^{56} +(-13.2759 + 0.923079i) q^{57} +(0.800365 + 2.46327i) q^{58} +(-2.31107 - 3.18092i) q^{59} +(2.45130 + 2.99852i) q^{60} +10.8583i q^{61} +(2.91458 + 4.74397i) q^{62} +(-0.150177 - 1.07471i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.35833 - 0.422777i) q^{65} +(-2.01018 - 4.98103i) q^{66} +15.1272i q^{67} +3.60517i q^{68} +(5.73738 - 2.31542i) q^{69} +(0.648400 + 0.483503i) q^{70} +(-7.08557 - 2.30224i) q^{71} +(-2.64773 - 1.41050i) q^{72} +(-1.81726 - 5.59295i) q^{73} +(5.83239 + 4.23748i) q^{74} +(-8.65165 + 0.386008i) q^{75} +(-2.37428 + 7.30728i) q^{76} +(-0.659344 - 0.907509i) q^{77} +(-0.844418 + 0.707983i) q^{78} +(5.41909 + 1.76077i) q^{79} +(2.13504 - 0.664526i) q^{80} +(-8.45237 - 3.09151i) q^{81} +(10.8071 - 3.51143i) q^{82} +(-7.61938 + 10.4872i) q^{83} +(-0.607843 - 0.151807i) q^{84} +(-6.46248 - 4.81898i) q^{85} +(2.12382 + 6.53644i) q^{86} +(4.47527 - 0.311168i) q^{87} -3.10116 q^{88} +(4.86494 + 14.9727i) q^{89} +(6.06760 - 2.86082i) q^{90} +(-0.135266 + 0.186177i) q^{91} -3.57205i q^{92} +(9.19513 - 2.90680i) q^{93} -8.72695 q^{94} +(-9.92507 - 14.0236i) q^{95} +(-1.32727 + 1.11282i) q^{96} +(0.210577 - 0.0684205i) q^{97} +6.86916 q^{98} +(-9.21395 + 1.28753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Introduction

L-functions

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