LMFDB - Embedded newform 930.2.be.a.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, 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:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.14
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.01126 - 1.99433i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.754227 + 2.81481i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.01126 - 1.99433i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.754227 + 2.81481i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.12527 - 0.695132i) q^{10} +(4.15635 + 2.39967i) q^{11} +(0.965926 + 0.258819i) q^{12} +(1.05350 - 0.282285i) q^{13} +(-2.52369 + 1.45705i) q^{14} +(-1.66464 - 1.49298i) q^{15} -1.00000 q^{16} +(-0.576133 - 0.154374i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(3.40703 - 1.96705i) q^{19} +(1.99433 + 1.01126i) q^{20} +(2.52369 + 1.45705i) q^{21} +(1.24216 + 4.63580i) q^{22} +(5.30027 + 5.30027i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.95469 - 4.03358i) q^{25} +(0.944543 + 0.545332i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.81481 - 0.754227i) q^{28} +0.421207 q^{29} +(-0.121385 - 2.23277i) q^{30} +(-3.08404 - 4.63559i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.39364 - 3.39364i) q^{33} +(-0.298228 - 0.516547i) q^{34} +(4.85094 + 4.35069i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.39539 + 1.71364i) q^{37} +(3.80005 + 1.01822i) q^{38} -1.09066i q^{39} +(0.695132 + 2.12527i) q^{40} +(2.22452 - 3.85297i) q^{41} +(0.754227 + 2.81481i) q^{42} +(-0.521872 + 1.94765i) q^{43} +(-2.39967 + 4.15635i) q^{44} +(-1.87294 + 1.22151i) q^{45} +7.49571i q^{46} +(-2.37586 - 2.37586i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-1.29214 - 0.746015i) q^{49} +(0.762889 - 4.94146i) q^{50} +(-0.298228 + 0.516547i) q^{51} +(0.282285 + 1.05350i) q^{52} +(-4.36059 + 1.16842i) q^{53} -1.00000 q^{54} +(8.98889 - 5.86243i) q^{55} +(-1.45705 - 2.52369i) q^{56} +(-1.01822 - 3.80005i) q^{57} +(0.297838 + 0.297838i) q^{58} +(6.78734 - 3.91867i) q^{59} +(1.49298 - 1.66464i) q^{60} -2.87286i q^{61} +(1.09711 - 5.45860i) q^{62} +(2.06059 - 2.06059i) q^{63} -1.00000i q^{64} +(0.502398 - 2.38649i) q^{65} +4.79934 q^{66} +(4.28109 - 1.14712i) q^{67} +(0.154374 - 0.576133i) q^{68} +(6.49147 - 3.74785i) q^{69} +(0.353728 + 6.50654i) q^{70} +(-4.67349 + 8.09471i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-1.33005 + 0.356385i) q^{73} +(3.31050 + 5.73395i) q^{74} +(-4.66087 + 1.81005i) q^{75} +(1.96705 + 3.40703i) q^{76} +(-9.88945 + 9.88945i) q^{77} +(0.771216 - 0.771216i) q^{78} +(-2.87242 - 4.97517i) q^{79} +(-1.01126 + 1.99433i) q^{80} +(0.500000 + 0.866025i) q^{81} +(4.29743 - 1.15149i) q^{82} +(-4.34972 + 1.16550i) q^{83} +(-1.45705 + 2.52369i) q^{84} +(-0.890496 + 0.992886i) q^{85} +(-1.74622 + 1.00818i) q^{86} +(0.109016 - 0.406854i) q^{87} +(-4.63580 + 1.24216i) q^{88} -13.0859 q^{89} +(-2.18811 - 0.460635i) q^{90} +3.17831i q^{91} +(-5.30027 + 5.30027i) q^{92} +(-5.27584 + 1.77918i) q^{93} -3.35997i q^{94} +(-0.477540 - 8.78394i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-4.86196 - 4.86196i) q^{97} +(-0.386166 - 1.44119i) q^{98} +(-2.39967 - 4.15635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	1.01126	−	1.99433i	0.452251	−	0.891891i
$5$	1.01126	−	1.99433i	0.452251	−	0.891891i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−0.754227	+	2.81481i	−0.285071	+	1.06390i	0.663717	+	0.747984i	$0.268978\pi$
$7$	−0.754227	+	2.81481i	−0.285071	+	1.06390i	−0.948787	+	0.315915i	$0.897689\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	2.12527	−	0.695132i	0.672071	−	0.219820i
$11$	4.15635	+	2.39967i	1.25319	+	0.723527i	0.971741	−	0.236050i	$-0.0758529\pi$
$11$	4.15635	+	2.39967i	1.25319	+	0.723527i	0.281445	+	0.959577i	$0.409186\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	1.05350	−	0.282285i	0.292189	−	0.0782917i	−0.109747	−	0.993960i	$-0.535004\pi$
$13$	1.05350	−	0.282285i	0.292189	−	0.0782917i	0.401936	+	0.915668i	$0.368337\pi$
$14$	−2.52369	+	1.45705i	−0.674485	+	0.389414i
$15$	−1.66464	−	1.49298i	−0.429808	−	0.385485i
$16$	−1.00000			−0.250000
$17$	−0.576133	−	0.154374i	−0.139733	−	0.0374413i	0.188275	−	0.982116i	$-0.439710\pi$
$17$	−0.576133	−	0.154374i	−0.139733	−	0.0374413i	−0.328008	+	0.944675i	$0.606377\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	3.40703	−	1.96705i	0.781626	−	0.451272i	−0.0553802	−	0.998465i	$-0.517637\pi$
$19$	3.40703	−	1.96705i	0.781626	−	0.451272i	0.837006	+	0.547193i	$0.184304\pi$
$20$	1.99433	+	1.01126i	0.445945	+	0.226125i
$21$	2.52369	+	1.45705i	0.550715	+	0.317955i
$22$	1.24216	+	4.63580i	0.264829	+	0.988357i
$23$	5.30027	+	5.30027i	1.10518	+	1.10518i	0.993775	+	0.111407i	$0.0355358\pi$
$23$	5.30027	+	5.30027i	1.10518	+	1.10518i	0.111407	+	0.993775i	$0.464464\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−2.95469	−	4.03358i	−0.590939	−	0.806716i
$26$	0.944543	+	0.545332i	0.185240	+	0.106948i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.81481	−	0.754227i	−0.531950	−	0.142535i
$29$	0.421207			0.0782161			0.0391081	−	0.999235i	$-0.487548\pi$
$29$	0.421207			0.0782161			0.0391081	+	0.999235i	$0.487548\pi$
$30$	−0.121385	−	2.23277i	−0.0221617	−	0.407646i
$31$	−3.08404	−	4.63559i	−0.553910	−	0.832576i
$31$	−3.08404	−	4.63559i	−0.553910	−	0.832576i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	3.39364	−	3.39364i	0.590758	−	0.590758i
$34$	−0.298228	−	0.516547i	−0.0511458	−	0.0885871i
$35$	4.85094	+	4.35069i	0.819959	+	0.735401i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	6.39539	+	1.71364i	1.05140	+	0.281721i	0.742829	−	0.669482i	$-0.233484\pi$
$37$	6.39539	+	1.71364i	1.05140	+	0.281721i	0.308568	+	0.951202i	$0.400150\pi$
$38$	3.80005	+	1.01822i	0.616449	+	0.165177i
$39$		−	1.09066i		−	0.174646i
$40$	0.695132	+	2.12527i	0.109910	+	0.336035i
$41$	2.22452	−	3.85297i	0.347411	−	0.601734i	−0.638378	−	0.769723i	$-0.720394\pi$
$41$	2.22452	−	3.85297i	0.347411	−	0.601734i	0.985789	+	0.167990i	$0.0537275\pi$
$42$	0.754227	+	2.81481i	0.116380	+	0.434335i
$43$	−0.521872	+	1.94765i	−0.0795847	+	0.297014i	−0.994234	−	0.107235i	$-0.965800\pi$
$43$	−0.521872	+	1.94765i	−0.0795847	+	0.297014i	0.914649	+	0.404249i	$0.132467\pi$
$44$	−2.39967	+	4.15635i	−0.361764	+	0.626593i
$45$	−1.87294	+	1.22151i	−0.279202	+	0.182092i
$46$			7.49571i			1.10518i
$47$	−2.37586	−	2.37586i	−0.346554	−	0.346554i	0.512270	−	0.858824i	$-0.328805\pi$
$47$	−2.37586	−	2.37586i	−0.346554	−	0.346554i	−0.858824	+	0.512270i	$0.828805\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	−1.29214	−	0.746015i	−0.184591	−	0.106574i
$50$	0.762889	−	4.94146i	0.107889	−	0.698828i
$51$	−0.298228	+	0.516547i	−0.0417603	+	0.0723310i
$52$	0.282285	+	1.05350i	0.0391458	+	0.146094i
$53$	−4.36059	+	1.16842i	−0.598974	+	0.160494i	−0.545551	−	0.838078i	$-0.683680\pi$
$53$	−4.36059	+	1.16842i	−0.598974	+	0.160494i	−0.0534224	+	0.998572i	$0.517013\pi$
$54$	−1.00000			−0.136083
$55$	8.98889	−	5.86243i	1.21206	−	0.790490i
$56$	−1.45705	−	2.52369i	−0.194707	−	0.337243i
$57$	−1.01822	−	3.80005i	−0.134866	−	0.503329i
$58$	0.297838	+	0.297838i	0.0391081	+	0.0391081i
$59$	6.78734	−	3.91867i	0.883637	−	0.510168i	0.0117809	−	0.999931i	$-0.496250\pi$
$59$	6.78734	−	3.91867i	0.883637	−	0.510168i	0.871856	+	0.489763i	$0.162917\pi$
$60$	1.49298	−	1.66464i	0.192742	−	0.214904i
$61$		−	2.87286i		−	0.367832i	−0.982942	−	0.183916i	$-0.941123\pi$
$61$		−	2.87286i		−	0.367832i	0.982942	−	0.183916i	$-0.0588774\pi$
$62$	1.09711	−	5.45860i	0.139333	−	0.693243i
$63$	2.06059	−	2.06059i	0.259609	−	0.259609i
$64$		−	1.00000i		−	0.125000i
$65$	0.502398	−	2.38649i	0.0623148	−	0.296008i
$66$	4.79934			0.590758
$67$	4.28109	−	1.14712i	0.523019	−	0.140142i	0.0123562	−	0.999924i	$-0.496067\pi$
$67$	4.28109	−	1.14712i	0.523019	−	0.140142i	0.510663	+	0.859781i	$0.329400\pi$
$68$	0.154374	−	0.576133i	0.0187206	−	0.0698664i
$69$	6.49147	−	3.74785i	0.781482	−	0.451189i
$70$	0.353728	+	6.50654i	0.0422786	+	0.777680i
$71$	−4.67349	+	8.09471i	−0.554641	+	0.960666i	0.443291	+	0.896378i	$0.353811\pi$
$71$	−4.67349	+	8.09471i	−0.554641	+	0.960666i	−0.997931	+	0.0642879i	$0.979522\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−1.33005	+	0.356385i	−0.155670	+	0.0417118i	−0.335813	−	0.941929i	$-0.609011\pi$
$73$	−1.33005	+	0.356385i	−0.155670	+	0.0417118i	0.180142	+	0.983641i	$0.442344\pi$
$74$	3.31050	+	5.73395i	0.384838	+	0.666559i
$75$	−4.66087	+	1.81005i	−0.538191	+	0.209006i
$76$	1.96705	+	3.40703i	0.225636	+	0.390813i
$77$	−9.88945	+	9.88945i	−1.12701	+	1.12701i
$78$	0.771216	−	0.771216i	0.0873230	−	0.0873230i
$79$	−2.87242	−	4.97517i	−0.323172	−	0.559751i	0.657968	−	0.753046i	$-0.271416\pi$
$79$	−2.87242	−	4.97517i	−0.323172	−	0.559751i	−0.981141	+	0.193295i	$0.938083\pi$
$80$	−1.01126	+	1.99433i	−0.113063	+	0.222973i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	4.29743	−	1.15149i	0.474572	−	0.127161i
$83$	−4.34972	+	1.16550i	−0.477443	+	0.127931i	−0.489512	−	0.871997i	$-0.662825\pi$
$83$	−4.34972	+	1.16550i	−0.477443	+	0.127931i	0.0120685	+	0.999927i	$0.496158\pi$
$84$	−1.45705	+	2.52369i	−0.158978	+	0.275357i
$85$	−0.890496	+	0.992886i	−0.0965878	+	0.107694i
$86$	−1.74622	+	1.00818i	−0.188299	+	0.108715i
$87$	0.109016	−	0.406854i	0.0116878	−	0.0436194i
$88$	−4.63580	+	1.24216i	−0.494178	+	0.132415i
$89$	−13.0859			−1.38710			−0.693549	−	0.720410i	$-0.743954\pi$
$89$	−13.0859			−1.38710			−0.693549	+	0.720410i	$0.743954\pi$
$90$	−2.18811	−	0.460635i	−0.230647	−	0.0485552i
$91$			3.17831i			0.333178i
$92$	−5.30027	+	5.30027i	−0.552591	+	0.552591i
$93$	−5.27584	+	1.77918i	−0.547079	+	0.184492i
$94$		−	3.35997i		−	0.346554i
$95$	−0.477540	−	8.78394i	−0.0489945	−	0.901213i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−4.86196	−	4.86196i	−0.493658	−	0.493658i	0.415799	−	0.909457i	$-0.363502\pi$
$97$	−4.86196	−	4.86196i	−0.493658	−	0.493658i	−0.909457	+	0.415799i	$0.863502\pi$
$98$	−0.386166	−	1.44119i	−0.0390086	−	0.145582i
$99$	−2.39967	−	4.15635i	−0.241176	−	0.417729i
$100$	4.03358	−	2.95469i	0.403358	−	0.295469i
$101$	−15.5695			−1.54922			−0.774610	−	0.632440i	$-0.782054\pi$
$101$	−15.5695			−1.54922			−0.774610	+	0.632440i	$0.782054\pi$
$102$	−0.576133	+	0.154374i	−0.0570457	+	0.0152853i
$103$	1.23382	+	4.60468i	0.121572	+	0.453713i	0.999694	−	0.0247235i	$-0.00787052\pi$
$103$	1.23382	+	4.60468i	0.121572	+	0.453713i	−0.878122	+	0.478436i	$0.841204\pi$
$104$	−0.545332	+	0.944543i	−0.0534742	+	0.0926201i
$105$	5.45796	−	3.55961i	0.532643	−	0.347382i
$106$	−3.90960	−	2.25721i	−0.379734	−	0.219240i
$107$	−4.26563	+	15.9195i	−0.412374	+	1.53900i	0.377664	+	0.925943i	$0.376728\pi$
$107$	−4.26563	+	15.9195i	−0.412374	+	1.53900i	−0.790038	+	0.613058i	$0.789939\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			12.0683i			1.15593i	0.816061	+	0.577965i	$0.196153\pi$
$109$			12.0683i			1.15593i	−0.816061	+	0.577965i	$0.803847\pi$
$110$	10.5015	+	2.21074i	1.00128	+	0.210786i
$111$	3.31050	−	5.73395i	0.314219	−	0.544243i
$112$	0.754227	−	2.81481i	0.0712677	−	0.265975i
$113$	0.403395	+	1.50549i	0.0379482	+	0.141625i	0.982301	−	0.187310i	$-0.0599770\pi$
$113$	0.403395	+	1.50549i	0.0379482	+	0.141625i	−0.944353	+	0.328935i	$0.893310\pi$
$114$	1.96705	−	3.40703i	0.184231	−	0.319097i
$115$	15.9304	−	5.21051i	1.48552	−	0.485883i
$116$			0.421207i			0.0391081i
$117$	−1.05350	−	0.282285i	−0.0973962	−	0.0260972i
$118$	7.57030	+	2.02845i	0.696902	+	0.186734i
$119$	0.869070	−	1.50527i	0.0796675	−	0.137988i
$120$	2.23277	−	0.121385i	0.203823	−	0.0110809i
$121$	6.01682	+	10.4214i	0.546984	+	0.947404i
$122$	2.03142	−	2.03142i	0.183916	−	0.183916i
$123$	−3.14594	−	3.14594i	−0.283660	−	0.283660i
$124$	4.63559	−	3.08404i	0.416288	−	0.276955i
$125$	−11.0323	+	1.81362i	−0.986755	+	0.162215i
$126$	2.91411			0.259609
$127$	10.6767	+	2.86081i	0.947404	+	0.253856i	0.699260	−	0.714867i	$-0.253513\pi$
$127$	10.6767	+	2.86081i	0.947404	+	0.253856i	0.248144	+	0.968723i	$0.420179\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.74622	+	1.00818i	0.153746	+	0.0887652i
$130$	2.04275	−	1.33225i	0.179161	−	0.116846i
$131$	−3.25251	−	5.63351i	−0.284173	−	0.492202i	0.688235	−	0.725488i	$-0.258386\pi$
$131$	−3.25251	−	5.63351i	−0.284173	−	0.492202i	−0.972408	+	0.233285i	$0.925052\pi$
$132$	3.39364	+	3.39364i	0.295379	+	0.295379i
$133$	2.96720	+	11.0738i	0.257289	+	0.960216i
$134$	3.83832	+	2.21606i	0.331581	+	0.191438i
$135$	0.695132	+	2.12527i	0.0598275	+	0.182914i
$136$	0.516547	−	0.298228i	0.0442935	−	0.0255729i
$137$	−4.51958	−	16.8673i	−0.386134	−	1.44107i	−0.836372	−	0.548162i	$-0.815328\pi$
$137$	−4.51958	−	16.8673i	−0.386134	−	1.44107i	0.450238	−	0.892909i	$-0.351339\pi$
$138$	7.24030	+	1.94003i	0.616335	+	0.165147i
$139$	−7.50320			−0.636413			−0.318207	−	0.948021i	$-0.603081\pi$
$139$	−7.50320			−0.636413			−0.318207	+	0.948021i	$0.603081\pi$
$140$	−4.35069	+	4.85094i	−0.367701	+	0.409979i
$141$	−2.90982	+	1.67998i	−0.245051	+	0.141480i
$142$	−9.02848	+	2.41917i	−0.757653	+	0.203013i
$143$	5.05611	+	1.35478i	0.422813	+	0.113292i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.425951	−	0.840025i	0.0353733	−	0.0697602i
$146$	−1.19249	−	0.688484i	−0.0986911	−	0.0569793i
$147$	−1.05502	+	1.05502i	−0.0870170	+	0.0870170i
$148$	−1.71364	+	6.39539i	−0.140860	+	0.525698i
$149$	0.950761	−	0.548922i	0.0778894	−	0.0449695i	−0.460549	−	0.887634i	$-0.652348\pi$
$149$	0.950761	−	0.548922i	0.0778894	−	0.0449695i	0.538439	+	0.842665i	$0.319014\pi$
$150$	−4.57563	−	2.01584i	−0.373599	−	0.164592i
$151$		−	7.24265i		−	0.589399i	−0.955590	−	0.294699i	$-0.904781\pi$
$151$		−	7.24265i		−	0.589399i	0.955590	−	0.294699i	$-0.0952195\pi$
$152$	−1.01822	+	3.80005i	−0.0825885	+	0.308225i
$153$	0.421759	+	0.421759i	0.0340972	+	0.0340972i
$154$	−13.9858			−1.12701
$155$	−12.3637	+	1.46280i	−0.993074	+	0.117495i
$156$	1.09066			0.0873230
$157$	−9.88336	−	9.88336i	−0.788778	−	0.788778i	0.192516	−	0.981294i	$-0.438335\pi$
$157$	−9.88336	−	9.88336i	−0.788778	−	0.788778i	−0.981294	+	0.192516i	$0.938335\pi$
$158$	1.48687	−	5.54909i	0.118289	−	0.441462i
$159$			4.51442i			0.358017i
$160$	−2.12527	+	0.695132i	−0.168018	+	0.0549550i
$161$	−18.9169	+	10.9217i	−1.49086	+	0.860747i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	7.74129	−	7.74129i	0.606345	−	0.606345i	−0.335644	−	0.941989i	$-0.608954\pi$
$163$	7.74129	−	7.74129i	0.606345	−	0.606345i	0.941989	+	0.335644i	$0.108954\pi$
$164$	3.85297	+	2.22452i	0.300867	+	0.173706i
$165$	−3.33617	−	10.1999i	−0.259721	−	0.794062i
$166$	−3.89985	−	2.25158i	−0.302687	−	0.174756i
$167$	−23.8790	−	6.39836i	−1.84781	−	0.495120i	−0.848400	−	0.529355i	$-0.822434\pi$
$167$	−23.8790	−	6.39836i	−1.84781	−	0.495120i	−0.999414	+	0.0342349i	$0.989101\pi$
$168$	−2.81481	+	0.754227i	−0.217168	+	0.0581899i
$169$	−10.2282	+	5.90523i	−0.786781	+	0.454248i
$170$	−1.33175	+	0.0724008i	−0.102141	+	0.00555289i
$171$	−3.93410			−0.300848
$172$	−1.94765	−	0.521872i	−0.148507	−	0.0397923i
$173$	4.36415	+	16.2872i	0.331801	+	1.23830i	0.907296	+	0.420492i	$0.138142\pi$
$173$	4.36415	+	16.2872i	0.331801	+	1.23830i	−0.575496	+	0.817805i	$0.695191\pi$
$174$	0.364776	−	0.210603i	0.0276536	−	0.0159658i
$175$	13.5823	−	5.27467i	1.02672	−	0.398728i
$176$	−4.15635	−	2.39967i	−0.313297	−	0.180882i
$177$	−2.02845	−	7.57030i	−0.152468	−	0.569018i
$178$	−9.25309	−	9.25309i	−0.693549	−	0.693549i
$179$	−7.35324	−	12.7362i	−0.549607	−	0.951948i	−0.998301	−	0.0582623i	$-0.981444\pi$
$179$	−7.35324	−	12.7362i	−0.549607	−	0.951948i	0.448694	−	0.893685i	$-0.351889\pi$
$180$	−1.22151	−	1.87294i	−0.0910458	−	0.139601i
$181$	3.00817	+	1.73677i	0.223596	+	0.129093i	0.607614	−	0.794232i	$-0.292127\pi$
$181$	3.00817	+	1.73677i	0.223596	+	0.129093i	−0.384018	+	0.923325i	$0.625460\pi$
$182$	−2.24741	+	2.24741i	−0.166589	+	0.166589i
$183$	−2.77497	−	0.743551i	−0.205132	−	0.0549648i
$184$	−7.49571			−0.552591
$185$	9.88499	−	11.0216i	0.726759	−	0.810322i
$186$	−4.98865	−	2.47252i	−0.365786	−	0.181294i
$187$	−2.02416	−	2.02416i	−0.148021	−	0.148021i
$188$	2.37586	−	2.37586i	0.173277	−	0.173277i
$189$	−1.45705	−	2.52369i	−0.105985	−	0.183572i
$190$	5.87351	−	6.54885i	0.426109	−	0.475104i
$191$	5.83524	−	10.1069i	0.422223	−	0.731312i	−0.573933	−	0.818902i	$-0.694583\pi$
$191$	5.83524	−	10.1069i	0.422223	−	0.731312i	0.996157	+	0.0875896i	$0.0279164\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	5.04822	+	1.35267i	0.363379	+	0.0973671i	0.435889	−	0.900001i	$-0.356434\pi$
$193$	5.04822	+	1.35267i	0.363379	+	0.0973671i	−0.0725096	+	0.997368i	$0.523101\pi$
$194$		−	6.87585i		−	0.493658i
$195$	−2.17514	−	1.10295i	−0.155765	−	0.0789838i
$196$	0.746015	−	1.29214i	0.0532868	−	0.0922954i
$197$	5.13258	+	19.1551i	0.365682	+	1.36474i	0.866495	+	0.499186i	$0.166368\pi$
$197$	5.13258	+	19.1551i	0.365682	+	1.36474i	−0.500813	+	0.865555i	$0.666966\pi$
$198$	1.24216	−	4.63580i	0.0882765	−	0.329452i
$199$	−3.96111	+	6.86085i	−0.280796	+	0.486353i	−0.971581	−	0.236707i	$-0.923932\pi$
$199$	−3.96111	+	6.86085i	−0.280796	+	0.486353i	0.690785	+	0.723060i	$0.257265\pi$
$200$	4.94146	+	0.762889i	0.349414	+	0.0539444i
$201$		−	4.43211i		−	0.312617i
$202$	−11.0093	−	11.0093i	−0.774610	−	0.774610i
$203$	−0.317685	+	1.18562i	−0.0222971	+	0.0832141i
$204$	−0.516547	−	0.298228i	−0.0361655	−	0.0208802i
$205$	−5.43453	−	8.33279i	−0.379564	−	0.581987i
$206$	−2.38356	+	4.12844i	−0.166070	+	0.287642i
$207$	−1.94003	−	7.24030i	−0.134842	−	0.503236i
$208$	−1.05350	+	0.282285i	−0.0730471	+	0.0195729i
$209$	18.8811			1.30603
$210$	6.37638	+	1.34234i	0.440012	+	0.0926303i
$211$	−9.96915	−	17.2671i	−0.686305	−	1.18871i	−0.973025	−	0.230700i	$-0.925898\pi$
$211$	−9.96915	−	17.2671i	−0.686305	−	1.18871i	0.286720	−	0.958014i	$-0.407435\pi$
$212$	−1.16842	−	4.36059i	−0.0802472	−	0.299487i
$213$	6.60931	+	6.60931i	0.452862	+	0.452862i
$214$	−14.2731	+	8.24057i	−0.975688	+	0.563313i
$215$	3.35651	+	3.01037i	0.228912	+	0.205306i
$216$		−	1.00000i		−	0.0680414i
$217$	15.3744	−	5.18472i	1.04368	−	0.351962i
$218$	−8.53355	+	8.53355i	−0.577965	+	0.577965i
$219$			1.37697i			0.0930468i
$220$	5.86243	+	8.98889i	0.395245	+	0.606031i
$221$	−0.650534			−0.0437597
$222$	6.39539	−	1.71364i	0.429231	−	0.115012i
$223$	6.01346	−	22.4425i	0.402691	−	1.50286i	−0.405584	−	0.914058i	$-0.632932\pi$
$223$	6.01346	−	22.4425i	0.402691	−	1.50286i	0.808275	−	0.588806i	$-0.200402\pi$
$224$	2.52369	−	1.45705i	0.168621	−	0.0973535i
$225$	0.542049	+	4.97053i	0.0361366	+	0.331369i
$226$	−0.779300	+	1.34979i	−0.0518382	+	0.0897865i
$227$	−7.36975	+	1.97472i	−0.489148	+	0.131067i	−0.494959	−	0.868916i	$-0.664817\pi$
$227$	−7.36975	+	1.97472i	−0.489148	+	0.131067i	0.00581127	+	0.999983i	$0.498150\pi$
$228$	3.80005	−	1.01822i	0.251664	−	0.0674332i
$229$	−8.32398	−	14.4176i	−0.550064	−	0.952739i	−0.998269	−	0.0588082i	$-0.981270\pi$
$229$	−8.32398	−	14.4176i	−0.550064	−	0.952739i	0.448205	−	0.893931i	$-0.352063\pi$
$230$	14.9489	+	7.58013i	0.985702	+	0.499819i
$231$	6.99290	+	12.1121i	0.460099	+	0.796915i
$232$	−0.297838	+	0.297838i	−0.0195540	+	0.0195540i
$233$	−8.06182	+	8.06182i	−0.528147	+	0.528147i	−0.920020	−	0.391872i	$-0.871827\pi$
$233$	−8.06182	+	8.06182i	−0.528147	+	0.528147i	0.391872	+	0.920020i	$0.371827\pi$
$234$	−0.545332	−	0.944543i	−0.0356495	−	0.0617467i
$235$	−7.14085	+	2.33562i	−0.465818	+	0.152359i
$236$	3.91867	+	6.78734i	0.255084	+	0.441818i
$237$	−5.54909	+	1.48687i	−0.360452	+	0.0965828i
$238$	1.67891	−	0.449864i	0.108828	−	0.0291603i
$239$	4.38455	−	7.59426i	0.283613	−	0.491232i	−0.688659	−	0.725085i	$-0.741800\pi$
$239$	4.38455	−	7.59426i	0.283613	−	0.491232i	0.972272	+	0.233854i	$0.0751337\pi$
$240$	1.66464	+	1.49298i	0.107452	+	0.0963711i
$241$	21.1543	−	12.2135i	1.36267	−	0.786738i	0.372692	−	0.927955i	$-0.378435\pi$
$241$	21.1543	−	12.2135i	1.36267	−	0.786738i	0.989979	+	0.141217i	$0.0451016\pi$
$242$	−3.11454	+	11.6236i	−0.200210	+	0.747194i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	2.87286			0.183916
$245$	−2.79449	+	1.82253i	−0.178533	+	0.116437i
$246$		−	4.44903i		−	0.283660i
$247$	3.03404	−	3.03404i	0.193051	−	0.193051i
$248$	5.45860	+	1.09711i	0.346622	+	0.0696665i
$249$			4.50316i			0.285376i
$250$	−9.08341	−	6.51857i	−0.574485	−	0.412270i
$251$	15.3812	−	8.88036i	0.970855	−	0.560523i	0.0713581	−	0.997451i	$-0.477267\pi$
$251$	15.3812	−	8.88036i	0.970855	−	0.560523i	0.899497	+	0.436927i	$0.143933\pi$
$252$	2.06059	+	2.06059i	0.129805	+	0.129805i
$253$	9.31087	+	34.7486i	0.585369	+	2.18463i
$254$	5.52667	+	9.57247i	0.346774	+	0.600630i
$255$	0.728577	+	1.11713i	0.0456252	+	0.0699574i
$256$	1.00000			0.0625000
$257$	−30.6931	+	8.22418i	−1.91458	+	0.513010i	−0.922759	+	0.385378i	$0.874071\pi$
$257$	−30.6931	+	8.22418i	−1.91458	+	0.513010i	−0.991822	+	0.127633i	$0.959262\pi$
$258$	0.521872	+	1.94765i	0.0324903	+	0.121255i
$259$	−9.64716	+	16.7094i	−0.599445	+	1.03827i
$260$	2.38649	+	0.502398i	0.148004	+	0.0311574i
$261$	−0.364776	−	0.210603i	−0.0225791	−	0.0130360i
$262$	1.68362	−	6.28337i	0.104015	−	0.388188i
$263$	15.6454	+	15.6454i	0.964739	+	0.964739i	0.999399	−	0.0346599i	$-0.0110348\pi$
$263$	15.6454	+	15.6454i	0.964739	+	0.964739i	−0.0346599	+	0.999399i	$0.511035\pi$
$264$			4.79934i			0.295379i
$265$	−2.07950	+	9.87803i	−0.127743	+	0.606803i
$266$	−5.73219	+	9.92845i	−0.351463	+	0.608752i
$267$	−3.38687	+	12.6400i	−0.207273	+	0.773553i
$268$	1.14712	+	4.28109i	0.0700712	+	0.261509i
$269$	6.52749	−	11.3059i	0.397988	−	0.689336i	−0.595490	−	0.803363i	$-0.703042\pi$
$269$	6.52749	−	11.3059i	0.397988	−	0.689336i	0.993478	+	0.114028i	$0.0363752\pi$
$270$	−1.01126	+	1.99433i	−0.0615435	+	0.121371i
$271$		−	31.7272i		−	1.92729i	−0.267181	−	0.963646i	$-0.586092\pi$
$271$		−	31.7272i		−	1.92729i	0.267181	−	0.963646i	$-0.413908\pi$
$272$	0.576133	+	0.154374i	0.0349332	+	0.00936032i
$273$	3.07002	+	0.822608i	0.185806	+	0.0497865i
$274$	8.73116	−	15.1228i	0.527469	−	0.913602i
$275$	−2.60148	−	23.8553i	−0.156875	−	1.43853i
$276$	3.74785	+	6.49147i	0.225594	+	0.390741i
$277$	−15.3274	+	15.3274i	−0.920932	+	0.920932i	−0.997095	−	0.0761632i	$-0.975733\pi$
$277$	−15.3274	+	15.3274i	−0.920932	+	0.920932i	0.0761632	+	0.997095i	$0.475733\pi$
$278$	−5.30557	−	5.30557i	−0.318207	−	0.318207i
$279$	0.353065	+	5.55656i	0.0211375	+	0.332662i
$280$	−6.50654	+	0.353728i	−0.388840	+	0.0211393i
$281$	13.0178			0.776578			0.388289	−	0.921538i	$-0.373066\pi$
$281$	13.0178			0.776578			0.388289	+	0.921538i	$0.373066\pi$
$282$	−3.24548	−	0.869624i	−0.193265	−	0.0517853i
$283$	18.0431	−	18.0431i	1.07255	−	1.07255i	0.0753959	−	0.997154i	$-0.475978\pi$
$283$	18.0431	−	18.0431i	1.07255	−	1.07255i	0.997154	−	0.0753959i	$-0.0240221\pi$
$284$	−8.09471	−	4.67349i	−0.480333	−	0.277320i
$285$	−8.60823	−	1.81218i	−0.509908	−	0.107344i
$286$	2.61723	+	4.53318i	0.154760	+	0.268053i
$287$	9.16761	+	9.16761i	0.541147	+	0.541147i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−14.4143	−	8.32212i	−0.847902	−	0.489536i
$290$	0.895180	−	0.292794i	0.0525668	−	0.0171935i
$291$	−5.95466	+	3.43793i	−0.349069	+	0.201535i
$292$	−0.356385	−	1.33005i	−0.0208559	−	0.0778352i
$293$	7.54807	+	2.02250i	0.440963	+	0.118156i	0.472468	−	0.881348i	$-0.343363\pi$
$293$	7.54807	+	2.02250i	0.440963	+	0.118156i	−0.0315049	+	0.999504i	$0.510030\pi$
$294$	−1.49203			−0.0870170
$295$	−0.951335	−	17.4990i	−0.0553888	−	1.01883i
$296$	−5.73395	+	3.31050i	−0.333279	+	0.192419i
$297$	−4.63580	+	1.24216i	−0.268997	+	0.0720774i
$298$	1.06044	+	0.284143i	0.0614294	+	0.0164600i
$299$	7.08002	+	4.08765i	0.409448	+	0.236395i
$300$	−1.81005	−	4.66087i	−0.104503	−	0.269096i
$301$	−5.08866	−	2.93794i	−0.293306	−	0.169340i
$302$	5.12133	−	5.12133i	0.294699	−	0.294699i
$303$	−4.02967	+	15.0389i	−0.231499	+	0.863965i
$304$	−3.40703	+	1.96705i	−0.195407	+	0.112818i
$305$	−5.72942	−	2.90522i	−0.328066	−	0.166352i
$306$			0.596457i			0.0340972i
$307$	−1.16031	+	4.33034i	−0.0662224	+	0.247145i	−0.991100	−	0.133120i	$-0.957501\pi$
$307$	−1.16031	+	4.33034i	−0.0662224	+	0.247145i	0.924878	+	0.380265i	$0.124167\pi$
$308$	−9.88945	−	9.88945i	−0.563504	−	0.563504i
$309$	4.76712			0.271192
$310$	−9.77678	−	7.70808i	−0.555284	−	0.437789i
$311$	10.8687			0.616305			0.308153	−	0.951337i	$-0.400289\pi$
$311$	10.8687			0.616305			0.308153	+	0.951337i	$0.400289\pi$
$312$	0.771216	+	0.771216i	0.0436615	+	0.0436615i
$313$	−5.69305	+	21.2467i	−0.321790	+	1.20094i	0.595709	+	0.803200i	$0.296871\pi$
$313$	−5.69305	+	21.2467i	−0.321790	+	1.20094i	−0.917500	+	0.397737i	$0.869796\pi$
$314$		−	13.9772i		−	0.788778i
$315$	−2.02569	−	6.19328i	−0.114135	−	0.348952i
$316$	4.97517	−	2.87242i	0.279875	−	0.161586i
$317$	−8.14816	+	30.4093i	−0.457646	+	1.70796i	0.222544	+	0.974923i	$0.428564\pi$
$317$	−8.14816	+	30.4093i	−0.457646	+	1.70796i	−0.680190	+	0.733036i	$0.738103\pi$
$318$	−3.19218	+	3.19218i	−0.179008	+	0.179008i
$319$	1.75068	+	1.01076i	0.0980194	+	0.0565915i
$320$	−1.99433	−	1.01126i	−0.111486	−	0.0565313i
$321$	14.2731	+	8.24057i	0.796646	+	0.459944i
$322$	−21.0990	−	5.65347i	−1.17580	−	0.315055i
$323$	−2.26656	+	0.607324i	−0.126115	+	0.0337924i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−4.25139	−	3.41532i	−0.235825	−	0.189448i
$326$	10.9478			0.606345
$327$	11.6571	+	3.12350i	0.644636	+	0.172730i
$328$	1.15149	+	4.29743i	0.0635806	+	0.237286i
$329$	8.47952	−	4.89566i	0.467491	−	0.269906i
$330$	4.85339	−	9.57146i	0.267171	−	0.526891i
$331$	1.94850	+	1.12496i	0.107099	+	0.0618337i	0.552593	−	0.833451i	$-0.313639\pi$
$331$	1.94850	+	1.12496i	0.107099	+	0.0618337i	−0.445494	+	0.895285i	$0.646972\pi$
$332$	−1.16550	−	4.34972i	−0.0639653	−	0.238722i
$333$	−4.68175	−	4.68175i	−0.256558	−	0.256558i
$334$	−12.3607	−	21.4093i	−0.676347	−	1.17147i
$335$	2.04159	−	9.69794i	0.111544	−	0.529855i
$336$	−2.52369	−	1.45705i	−0.137679	−	0.0794888i
$337$	5.69956	−	5.69956i	0.310475	−	0.310475i	−0.534619	−	0.845093i	$-0.679545\pi$
$337$	5.69956	−	5.69956i	0.310475	−	0.310475i	0.845093	+	0.534619i	$0.179545\pi$
$338$	−11.4080	−	3.05677i	−0.620514	−	0.166266i
$339$	1.55860			0.0846515
$340$	−0.992886	−	0.890496i	−0.0538468	−	0.0482939i
$341$	−1.69448	−	26.6678i	−0.0917612	−	1.44414i
$342$	−2.78183	−	2.78183i	−0.150424	−	0.150424i
$343$	−11.3496	+	11.3496i	−0.612823	+	0.612823i
$344$	−1.00818	−	1.74622i	−0.0543573	−	0.0941497i
$345$	−0.909865	−	16.7362i	−0.0489855	−	0.901047i
$346$	−8.43090	+	14.6027i	−0.453248	+	0.785049i
$347$	−14.8283	−	3.97324i	−0.796027	−	0.213295i	−0.162188	−	0.986760i	$-0.551855\pi$
$347$	−14.8283	−	3.97324i	−0.796027	−	0.213295i	−0.633839	+	0.773465i	$0.718522\pi$
$348$	0.406854	+	0.109016i	0.0218097	+	0.00584389i
$349$			7.14362i			0.382389i	0.981552	+	0.191195i	$0.0612362\pi$
$349$			7.14362i			0.382389i	−0.981552	+	0.191195i	$0.938764\pi$
$350$	13.3339	+	5.87437i	0.712726	+	0.313998i
$351$	−0.545332	+	0.944543i	−0.0291077	+	0.0504160i
$352$	−1.24216	−	4.63580i	−0.0662074	−	0.247089i
$353$	−1.05304	+	3.93000i	−0.0560477	+	0.209173i	−0.988271	−	0.152711i	$-0.951200\pi$
$353$	−1.05304	+	3.93000i	−0.0560477	+	0.209173i	0.932223	+	0.361884i	$0.117866\pi$
$354$	3.91867	−	6.78734i	0.208275	−	0.360743i
$355$	11.4174	+	17.5064i	0.605973	+	0.929141i
$356$		−	13.0859i		−	0.693549i
$357$	−1.22905	−	1.22905i	−0.0650483	−	0.0650483i
$358$	3.80632	−	14.2054i	0.201170	−	0.750777i
$359$	25.9018	+	14.9544i	1.36704	+	0.789263i	0.990549	−	0.137156i	$-0.0437962\pi$
$359$	25.9018	+	14.9544i	1.36704	+	0.789263i	0.376494	+	0.926419i	$0.377130\pi$
$360$	0.460635	−	2.18811i	0.0242776	−	0.115323i
$361$	−1.76144	+	3.05090i	−0.0927072	+	0.160574i
$362$	0.899018	+	3.35518i	0.0472514	+	0.176344i
$363$	11.6236	−	3.11454i	0.610081	−	0.163471i
$364$	−3.17831			−0.166589
$365$	−0.634279	+	3.01295i	−0.0331997	+	0.157705i
$366$	−1.43643	−	2.48797i	−0.0750834	−	0.130048i
$367$	2.50489	+	9.34838i	0.130754	+	0.487981i	0.999979	−	0.00643517i	$-0.00204839\pi$
$367$	2.50489	+	9.34838i	0.130754	+	0.487981i	−0.869225	+	0.494417i	$0.835382\pi$
$368$	−5.30027	−	5.30027i	−0.276296	−	0.276296i
$369$	−3.85297	+	2.22452i	−0.200578	+	0.115804i
$370$	14.7832	−	0.803688i	0.768541	−	0.0417818i
$371$		−	13.1555i		−	0.683000i
$372$	−1.77918	−	5.27584i	−0.0922461	−	0.273540i
$373$	2.23696	−	2.23696i	0.115826	−	0.115826i	−0.646818	−	0.762644i	$-0.723901\pi$
$373$	2.23696	−	2.23696i	0.115826	−	0.115826i	0.762644	+	0.646818i	$0.223901\pi$
$374$		−	2.86260i		−	0.148021i
$375$	−1.10354	+	11.1257i	−0.0569865	+	0.574531i
$376$	3.35997			0.173277
$377$	0.443742	−	0.118900i	0.0228539	−	0.00612367i
$378$	0.754227	−	2.81481i	0.0387932	−	0.144778i
$379$	0.0649906	−	0.0375223i	0.00333834	−	0.00192739i	−0.498330	−	0.866987i	$-0.666053\pi$
$379$	0.0649906	−	0.0375223i	0.00333834	−	0.00192739i	0.501668	+	0.865060i	$0.332720\pi$
$380$	8.78394	−	0.477540i	0.450607	−	0.0244973i
$381$	5.52667	−	9.57247i	0.283140	−	0.490412i
$382$	11.2728	−	3.02054i	0.576768	−	0.154545i
$383$	−31.2050	+	8.36135i	−1.59450	+	0.427245i	−0.943376	−	0.331726i	$-0.892369\pi$
$383$	−31.2050	+	8.36135i	−1.59450	+	0.427245i	−0.651125	+	0.758971i	$0.725703\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	9.72198	+	29.7236i	0.495478	+	1.51486i
$386$	2.61315	+	4.52611i	0.133006	+	0.230373i
$387$	1.42578	−	1.42578i	0.0724765	−	0.0724765i
$388$	4.86196	−	4.86196i	0.246829	−	0.246829i
$389$	−2.28769	−	3.96240i	−0.115991	−	0.200902i	0.802185	−	0.597076i	$-0.203671\pi$
$389$	−2.28769	−	3.96240i	−0.115991	−	0.200902i	−0.918175	+	0.396174i	$0.870338\pi$
$390$	−0.758156	−	2.31796i	−0.0383907	−	0.117374i
$391$	−2.23543	−	3.87189i	−0.113051	−	0.195810i
$392$	1.44119	−	0.386166i	0.0727911	−	0.0195043i
$393$	−6.28337	+	1.68362i	−0.316954	+	0.0849275i
$394$	−9.91539	+	17.1740i	−0.499530	+	0.865212i
$395$	−12.8269	+	0.697336i	−0.645392	+	0.0350868i
$396$	4.15635	−	2.39967i	0.208864	−	0.120588i
$397$	8.81010	−	32.8798i	0.442166	−	1.65019i	−0.281145	−	0.959665i	$-0.590714\pi$
$397$	8.81010	−	32.8798i	0.442166	−	1.65019i	0.723311	−	0.690522i	$-0.242619\pi$
$398$	−7.65228	+	2.05042i	−0.383574	+	0.102778i
$399$	11.4644			0.573937
$400$	2.95469	+	4.03358i	0.147735	+	0.201679i
$401$		−	12.3982i		−	0.619138i	−0.950877	−	0.309569i	$-0.899815\pi$
$401$		−	12.3982i		−	0.619138i	0.950877	−	0.309569i	$-0.100185\pi$
$402$	3.13398	−	3.13398i	0.156309	−	0.156309i
$403$	−4.55760	−	4.01302i	−0.227030	−	0.199903i
$404$		−	15.5695i		−	0.774610i
$405$	2.23277	−	0.121385i	0.110947	−	0.00603166i
$406$	−1.06300	+	0.613721i	−0.0527556	+	0.0304585i
$407$	22.4693	+	22.4693i	1.11376	+	1.11376i
$408$	−0.154374	−	0.576133i	−0.00764267	−	0.0285228i
$409$	−3.86116	−	6.68772i	−0.190922	−	0.330686i	0.754634	−	0.656146i	$-0.227814\pi$
$409$	−3.86116	−	6.68772i	−0.190922	−	0.330686i	−0.945556	+	0.325459i	$0.894481\pi$
$410$	2.04938	−	9.73496i	0.101212	−	0.480775i
$411$	−17.4623			−0.861353
$412$	−4.60468	+	1.23382i	−0.226856	+	0.0607860i
$413$	5.91114	+	22.0607i	0.290868	+	1.08553i
$414$	3.74785	−	6.49147i	0.184197	−	0.319039i
$415$	−2.07431	+	9.85339i	−0.101824	+	0.483684i
$416$	−0.944543	−	0.545332i	−0.0463100	−	0.0267371i
$417$	−1.94197	+	7.24754i	−0.0950988	+	0.354913i
$418$	13.3509	+	13.3509i	0.653015	+	0.653015i
$419$			4.70800i			0.230001i	0.993365	+	0.115000i	$0.0366870\pi$
$419$			4.70800i			0.230001i	−0.993365	+	0.115000i	$0.963313\pi$
$420$	3.55961	+	5.45796i	0.173691	+	0.266321i
$421$	4.83198	−	8.36923i	0.235496	−	0.407891i	−0.723921	−	0.689883i	$-0.757662\pi$
$421$	4.83198	−	8.36923i	0.235496	−	0.407891i	0.959417	+	0.281992i	$0.0909952\pi$
$422$	5.16041	−	19.2589i	0.251205	−	0.937509i
$423$	0.869624	+	3.24548i	0.0422825	+	0.157801i
$424$	2.25721	−	3.90960i	0.109620	−	0.189867i
$425$	1.07962	+	2.78001i	0.0523690	+	0.134850i
$426$			9.34697i			0.452862i
$427$	8.08656	+	2.16679i	0.391336	+	0.104858i
$428$	−15.9195	−	4.26563i	−0.769500	−	0.206187i
$429$	2.61723	−	4.53318i	0.126361	−	0.218864i
$430$	0.244755	+	4.50206i	0.0118031	+	0.217109i
$431$	14.6909	+	25.4454i	0.707636	+	1.22566i	0.965732	+	0.259542i	$0.0835716\pi$
$431$	14.6909	+	25.4454i	0.707636	+	1.22566i	−0.258096	+	0.966119i	$0.583095\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	11.0756	+	11.0756i	0.532260	+	0.532260i	0.921244	−	0.388984i	$-0.127174\pi$
$433$	11.0756	+	11.0756i	0.532260	+	0.532260i	−0.388984	+	0.921244i	$0.627174\pi$
$434$	14.5375	+	7.20518i	0.697821	+	0.345860i
$435$	−0.701157	−	0.628851i	−0.0336179	−	0.0301511i
$436$	−12.0683			−0.577965
$437$	28.4840	+	7.63228i	1.36258	+	0.365101i
$438$	−0.973663	+	0.973663i	−0.0465234	+	0.0465234i
$439$	0.661020	+	0.381640i	0.0315488	+	0.0182147i	0.515691	−	0.856774i	$-0.327535\pi$
$439$	0.661020	+	0.381640i	0.0315488	+	0.0182147i	−0.484143	+	0.874989i	$0.660868\pi$
$440$	−2.21074	+	10.5015i	−0.105393	+	0.500638i
$441$	0.746015	+	1.29214i	0.0355245	+	0.0615303i
$442$	−0.459997	−	0.459997i	−0.0218798	−	0.0218798i
$443$	−8.39236	−	31.3207i	−0.398733	−	1.48809i	−0.815328	−	0.578999i	$-0.803443\pi$
$443$	−8.39236	−	31.3207i	−0.398733	−	1.48809i	0.416595	−	0.909092i	$-0.363223\pi$
$444$	5.73395	+	3.31050i	0.272121	+	0.157109i
$445$	−13.2332	+	26.0975i	−0.627316	+	1.23714i
$446$	20.1214	−	11.6171i	0.952777	−	0.550086i
$447$	−0.284143	−	1.06044i	−0.0134395	−	0.0501569i
$448$	2.81481	+	0.754227i	0.132987	+	0.0356339i
$449$	−11.5437			−0.544783			−0.272392	−	0.962186i	$-0.587815\pi$
$449$	−11.5437			−0.544783			−0.272392	+	0.962186i	$0.587815\pi$
$450$	−3.13141	+	3.89798i	−0.147616	+	0.183753i
$451$	18.4917	−	10.6762i	0.870741	−	0.502723i
$452$	−1.50549	+	0.403395i	−0.0708124	+	0.0189741i
$453$	−6.99586	−	1.87454i	−0.328694	−	0.0880734i
$454$	−6.60754	−	3.81486i	−0.310107	−	0.179040i
$455$	6.33860	+	3.21411i	0.297158	+	0.150680i
$456$	3.40703	+	1.96705i	0.159549	+	0.0921155i
$457$	27.0914	−	27.0914i	1.26728	−	1.26728i	0.319795	−	0.947487i	$-0.396386\pi$
$457$	27.0914	−	27.0914i	1.26728	−	1.26728i	0.947487	−	0.319795i	$-0.103614\pi$
$458$	4.30881	−	16.0807i	0.201337	−	0.751401i
$459$	0.516547	−	0.298228i	0.0241103	−	0.0139201i
$460$	5.21051	+	15.9304i	0.242941	+	0.742761i
$461$		−	24.8244i		−	1.15619i	−0.815970	−	0.578094i	$-0.803797\pi$
$461$		−	24.8244i		−	1.15619i	0.815970	−	0.578094i	$-0.196203\pi$
$462$	−3.61979	+	13.5092i	−0.168408	+	0.628507i
$463$	−2.19722	−	2.19722i	−0.102113	−	0.102113i	0.654204	−	0.756318i	$-0.273004\pi$
$463$	−2.19722	−	2.19722i	−0.102113	−	0.102113i	−0.756318	+	0.654204i	$0.773004\pi$
$464$	−0.421207			−0.0195540
$465$	−1.78700	+	12.3210i	−0.0828702	+	0.571372i
$466$	−11.4011			−0.528147
$467$	19.5331	+	19.5331i	0.903882	+	0.903882i	0.995769	−	0.0918871i	$-0.0292899\pi$
$467$	19.5331	+	19.5331i	0.903882	+	0.903882i	−0.0918871	+	0.995769i	$0.529290\pi$
$468$	0.282285	−	1.05350i	0.0130486	−	0.0486981i
$469$			12.9157i			0.596390i
$470$	−6.70088	−	3.39781i	−0.309089	−	0.156729i
$471$	−12.1046	+	6.98859i	−0.557750	+	0.322017i
$472$	−2.02845	+	7.57030i	−0.0933672	+	0.348451i
$473$	−6.84280	+	6.84280i	−0.314632	+	0.314632i
$474$	−4.97517	−	2.87242i	−0.228517	−	0.131935i
$475$	−18.0010	−	7.93050i	−0.825942	−	0.363876i
$476$	1.50527	+	0.869070i	0.0689941	+	0.0398338i
$477$	4.36059	+	1.16842i	0.199658	+	0.0534982i
$478$	8.47029	−	2.26961i	0.387422	−	0.103809i
$479$	−31.0679	+	17.9371i	−1.41953	+	0.819566i	−0.996257	−	0.0864356i	$-0.972452\pi$
$479$	−31.0679	+	17.9371i	−1.41953	+	0.819566i	−0.423273	+	0.906002i	$0.639119\pi$
$480$	0.121385	+	2.23277i	0.00554043	+	0.101912i
$481$	7.22129			0.329262
$482$	23.5946	+	6.32215i	1.07470	+	0.287966i
$483$	5.65347	+	21.0990i	0.257242	+	0.960039i
$484$	−10.4214	+	6.01682i	−0.473702	+	0.273492i
$485$	−14.6131	+	4.77963i	−0.663546	+	0.217032i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	1.74576	+	6.51525i	0.0791078	+	0.295234i	0.994133	−	0.108162i	$-0.0344964\pi$
$487$	1.74576	+	6.51525i	0.0791078	+	0.295234i	−0.915026	+	0.403396i	$0.867830\pi$
$488$	2.03142	+	2.03142i	0.0919580	+	0.0919580i
$489$	−5.47392	−	9.48111i	−0.247539	−	0.428751i
$490$	−3.26472	−	0.687281i	−0.147485	−	0.0310482i
$491$	16.4870	+	9.51879i	0.744049	+	0.429577i	0.823540	−	0.567259i	$-0.191996\pi$
$491$	16.4870	+	9.51879i	0.744049	+	0.429577i	−0.0794906	+	0.996836i	$0.525329\pi$
$492$	3.14594	−	3.14594i	0.141830	−	0.141830i
$493$	−0.242671	−	0.0650235i	−0.0109294	−	0.00292851i
$494$	4.29078			0.193051
$495$	−10.7158	+	0.582567i	−0.481640	+	0.0261844i
$496$	3.08404	+	4.63559i	0.138478	+	0.208144i
$497$	−19.2602	−	19.2602i	−0.863940	−	0.863940i
$498$	−3.18421	+	3.18421i	−0.142688	+	0.142688i
$499$	8.77037	+	15.1907i	0.392616	+	0.680030i	0.992794	−	0.119836i	$-0.0382369\pi$
$499$	8.77037	+	15.1907i	0.392616	+	0.680030i	−0.600178	+	0.799866i	$0.704904\pi$
$500$	−1.81362	−	11.0323i	−0.0811074	−	0.493378i
$501$	−12.3607	+	21.4093i	−0.552235	+	0.956499i
$502$	17.1555	+	4.59681i	0.765689	+	0.205166i
$503$	19.2968	+	5.17056i	0.860401	+	0.230544i	0.661932	−	0.749564i	$-0.269737\pi$
$503$	19.2968	+	5.17056i	0.860401	+	0.230544i	0.198469	+	0.980107i	$0.436403\pi$
$504$			2.91411i			0.129805i
$505$	−15.7448	+	31.0506i	−0.700635	+	1.38173i
$506$	−17.9872	+	31.1548i	−0.799630	+	1.38500i
$507$	3.05677	+	11.4080i	0.135756	+	0.506648i
$508$	−2.86081	+	10.6767i	−0.126928	+	0.473702i
$509$	−16.7606	+	29.0302i	−0.742901	+	1.28674i	0.208268	+	0.978072i	$0.433217\pi$
$509$	−16.7606	+	29.0302i	−0.742901	+	1.28674i	−0.951169	+	0.308671i	$0.900116\pi$
$510$	−0.274749	+	1.30511i	−0.0121661	+	0.0577913i
$511$		−	4.01263i		−	0.177508i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.01822	+	3.80005i	−0.0449555	+	0.167776i
$514$	−27.5186	−	15.8879i	−1.21380	−	0.700785i
$515$	10.4310	+	2.19590i	0.459643	+	0.0967629i
$516$	−1.00818	+	1.74622i	−0.0443826	+	0.0768729i
$517$	−4.17362	−	15.5762i	−0.183555	−	0.685038i
$518$	−18.6369	+	4.99374i	−0.818857	+	0.219412i
$519$	16.8618			0.740151
$520$	1.33225	+	2.04275i	0.0584232	+	0.0895806i
$521$	−4.71597	−	8.16830i	−0.206611	−	0.357860i	0.744034	−	0.668142i	$-0.232910\pi$
$521$	−4.71597	−	8.16830i	−0.206611	−	0.357860i	−0.950645	+	0.310282i	$0.899577\pi$
$522$	−0.109016	−	0.406854i	−0.00477151	−	0.0178075i
$523$	27.8322	+	27.8322i	1.21702	+	1.21702i	0.968671	+	0.248346i	$0.0798870\pi$
$523$	27.8322	+	27.8322i	1.21702	+	1.21702i	0.248346	+	0.968671i	$0.420113\pi$
$524$	5.63351	−	3.25251i	0.246101	−	0.142087i
$525$	−1.57959	−	14.4847i	−0.0689389	−	0.632163i
$526$			22.1260i			0.964739i
$527$	1.06120	+	3.14681i	0.0462267	+	0.137077i
$528$	−3.39364	+	3.39364i	−0.147689	+	0.147689i
$529$			33.1857i			1.44285i
$530$	−8.45525	+	5.51440i	−0.367273	+	0.239530i
$531$	−7.83735			−0.340112
$532$	−11.0738	+	2.96720i	−0.480108	+	0.128645i
$533$	1.25589	−	4.68706i	0.0543988	−	0.203019i
$534$	−11.3327	+	6.54293i	−0.490413	+	0.283140i
$535$	27.4351	+	24.6059i	1.18612	+	1.06381i
$536$	−2.21606	+	3.83832i	−0.0957191	+	0.165790i
$537$	−14.2054	+	3.80632i	−0.613007	+	0.164255i
$538$	12.6101	−	3.37888i	0.543662	−	0.145674i
$539$	−3.58038	−	6.20140i	−0.154218	−	0.267113i
$540$	−2.12527	+	0.695132i	−0.0914572	+	0.0299137i
$541$	−18.4749	−	31.9995i	−0.794299	−	1.37577i	−0.923283	−	0.384120i	$-0.874505\pi$
$541$	−18.4749	−	31.9995i	−0.794299	−	1.37577i	0.128984	−	0.991647i	$-0.458829\pi$
$542$	22.4345	−	22.4345i	0.963646	−	0.963646i
$543$	2.45616	−	2.45616i	0.105404	−	0.105404i
$544$	0.298228	+	0.516547i	0.0127864	+	0.0221468i
$545$	24.0681	+	12.2042i	1.03096	+	0.522770i
$546$	1.58916	+	2.75250i	0.0680096	+	0.117796i
$547$	−32.4896	+	8.70555i	−1.38915	+	0.372222i	−0.874437	−	0.485138i	$-0.838769\pi$
$547$	−32.4896	+	8.70555i	−1.38915	+	0.372222i	−0.514716	+	0.857361i	$0.672103\pi$
$548$	16.8673	−	4.51958i	0.720535	−	0.193067i
$549$	−1.43643	+	2.48797i	−0.0613053	+	0.106184i
$550$	15.0287	−	18.7077i	0.640826	−	0.797701i
$551$	1.43506	−	0.828534i	0.0611358	−	0.0352967i
$552$	−1.94003	+	7.24030i	−0.0825733	+	0.308168i
$553$	16.1706	−	4.33291i	0.687646	−	0.184254i
$554$	−21.6762			−0.920932
$555$	−8.08760	−	12.4008i	−0.343300	−	0.526383i
$556$		−	7.50320i		−	0.318207i
$557$	−6.22123	+	6.22123i	−0.263602	+	0.263602i	−0.826516	−	0.562914i	$-0.809680\pi$
$557$	−6.22123	+	6.22123i	−0.263602	+	0.263602i	0.562914	+	0.826516i	$0.309680\pi$
$558$	−3.67943	+	4.17874i	−0.155763	+	0.176900i
$559$			2.19917i			0.0930149i
$560$	−4.85094	−	4.35069i	−0.204990	−	0.183850i
$561$	−2.47908	+	1.43130i	−0.104667	+	0.0604295i
$562$	9.20499	+	9.20499i	0.388289	+	0.388289i
$563$	7.34058	+	27.3954i	0.309369	+	1.15458i	0.929119	+	0.369781i	$0.120567\pi$
$563$	7.34058	+	27.3954i	0.309369	+	1.15458i	−0.619750	+	0.784799i	$0.712766\pi$
$564$	−1.67998	−	2.90982i	−0.0707401	−	0.122525i
$565$	3.41038	+	0.717945i	0.143476	+	0.0302042i
$566$	25.5168			1.07255
$567$	−2.81481	+	0.754227i	−0.118211	+	0.0316746i
$568$	−2.41917	−	9.02848i	−0.101506	−	0.378827i
$569$	3.02644	−	5.24195i	0.126875	−	0.219754i	−0.795589	−	0.605836i	$-0.792839\pi$
$569$	3.02644	−	5.24195i	0.126875	−	0.219754i	0.922464	+	0.386082i	$0.126172\pi$
$570$	−4.80553	−	7.36835i	−0.201282	−	0.308626i
$571$	36.4371	+	21.0370i	1.52485	+	0.880371i	0.999566	+	0.0294417i	$0.00937295\pi$
$571$	36.4371	+	21.0370i	1.52485	+	0.880371i	0.525281	+	0.850929i	$0.323960\pi$
$572$	−1.35478	+	5.05611i	−0.0566462	+	0.211406i
$573$	−8.25228	−	8.25228i	−0.344744	−	0.344744i
$574$			12.9650i			0.541147i
$575$	5.71840	−	37.0397i	0.238474	−	1.54466i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	10.6376	−	39.6999i	0.442847	−	1.65273i	−0.278711	−	0.960375i	$-0.589907\pi$
$577$	10.6376	−	39.6999i	0.442847	−	1.65273i	0.721559	−	0.692353i	$-0.243426\pi$
$578$	−4.30785	−	16.0771i	−0.179183	−	0.668719i
$579$	2.61315	−	4.52611i	0.108599	−	0.188099i
$580$	0.840025	+	0.425951i	0.0348801	+	0.0176866i
$581$		−	13.1227i		−	0.544421i
$582$	−6.64157	−	1.77960i	−0.275302	−	0.0737669i
$583$	−20.9280	−	5.60763i	−0.866748	−	0.232244i
$584$	0.688484	−	1.19249i	0.0284897	−	0.0493455i
$585$	−1.62833	+	1.81556i	−0.0673234	+	0.0750643i
$586$	3.90717	+	6.76741i	0.161404	+	0.279559i
$587$	25.3708	−	25.3708i	1.04717	−	1.04717i	0.0483345	−	0.998831i	$-0.484609\pi$
$587$	25.3708	−	25.3708i	1.04717	−	1.04717i	0.998831	−	0.0483345i	$-0.0153913\pi$
$588$	−1.05502	−	1.05502i	−0.0435085	−	0.0435085i
$589$	−19.6259	−	9.72712i	−0.808669	−	0.400799i
$590$	11.7010	−	13.0464i	0.481721	−	0.537110i
$591$	19.8308			0.815729
$592$	−6.39539	−	1.71364i	−0.262849	−	0.0704302i
$593$	8.51392	−	8.51392i	0.349625	−	0.349625i	−0.510345	−	0.859970i	$-0.670482\pi$
$593$	8.51392	−	8.51392i	0.349625	−	0.349625i	0.859970	+	0.510345i	$0.170482\pi$
$594$	−4.15635	−	2.39967i	−0.170537	−	0.0984596i
$595$	−2.12315	−	3.25544i	−0.0870407	−	0.133460i
$596$	0.548922	+	0.950761i	0.0224847	+	0.0389447i
$597$	5.60186	+	5.60186i	0.229269	+	0.229269i
$598$	2.11592	+	7.89674i	0.0865266	+	0.322922i
$599$	26.2661	+	15.1648i	1.07321	+	0.619615i	0.929055	−	0.369940i	$-0.120622\pi$
$599$	26.2661	+	15.1648i	1.07321	+	0.619615i	0.144150	+	0.989556i	$0.453955\pi$
$600$	2.01584	−	4.57563i	0.0822962	−	0.186799i
$601$	27.5058	−	15.8805i	1.12199	−	0.647779i	0.180079	−	0.983652i	$-0.442365\pi$
$601$	27.5058	−	15.8805i	1.12199	−	0.647779i	0.941907	+	0.335873i	$0.109031\pi$
$602$	−1.52079	−	5.67567i	−0.0619828	−	0.231323i
$603$	−4.28109	−	1.14712i	−0.174340	−	0.0467141i
$604$	7.24265			0.294699
$605$	26.8684	−	1.46070i	1.09235	−	0.0593860i
$606$	−13.4835	+	7.78473i	−0.547732	+	0.316233i
$607$	36.6032	−	9.80780i	1.48568	−	0.398086i	0.577403	−	0.816459i	$-0.304066\pi$
$607$	36.6032	−	9.80780i	1.48568	−	0.398086i	0.908275	+	0.418373i	$0.137400\pi$
$608$	−3.80005	−	1.01822i	−0.154112	−	0.0412943i
$609$	1.06300	+	0.613721i	0.0430748	+	0.0248692i
$610$	−1.99702	−	6.10561i	−0.0808569	−	0.247209i
$611$	−3.17363	−	1.83230i	−0.128391	−	0.0741268i
$612$	−0.421759	+	0.421759i	−0.0170486	+	0.0170486i
$613$	−8.35860	+	31.1947i	−0.337601	+	1.25994i	0.563422	+	0.826170i	$0.309485\pi$
$613$	−8.35860	+	31.1947i	−0.337601	+	1.25994i	−0.901022	+	0.433773i	$0.857182\pi$
$614$	−3.88247	+	2.24155i	−0.156684	+	0.0904615i
$615$	−9.45541	+	3.09267i	−0.381279	+	0.124708i
$616$		−	13.9858i		−	0.563504i
$617$	−1.09079	+	4.07090i	−0.0439137	+	0.163888i	−0.984401	−	0.175942i	$-0.943703\pi$
$617$	−1.09079	+	4.07090i	−0.0439137	+	0.163888i	0.940487	+	0.339830i	$0.110370\pi$
$618$	3.37086	+	3.37086i	0.135596	+	0.135596i
$619$	−16.3608			−0.657597			−0.328798	−	0.944400i	$-0.606644\pi$
$619$	−16.3608			−0.657597			−0.328798	+	0.944400i	$0.606644\pi$
$620$	−1.46280	−	12.3637i	−0.0587473	−	0.496537i
$621$	−7.49571			−0.300792
$622$	7.68531	+	7.68531i	0.308153	+	0.308153i
$623$	9.86970	−	36.8342i	0.395421	−	1.47573i
$624$			1.09066i			0.0436615i
$625$	−7.53957	+	23.8360i	−0.301583	+	0.953440i
$626$	−19.0493	+	10.9981i	−0.761363	+	0.439573i
$627$	4.88678	−	18.2377i	0.195159	−	0.728344i
$628$	9.88336	−	9.88336i	0.394389	−	0.394389i
$629$	−3.42006	−	1.97457i	−0.136367	−	0.0787313i
$630$	2.94693	−	5.81169i	0.117409	−	0.231543i
$631$	9.46747	+	5.46605i	0.376894	+	0.217600i	0.676466	−	0.736474i	$-0.263511\pi$
$631$	9.46747	+	5.46605i	0.376894	+	0.217600i	−0.299572	+	0.954074i	$0.596844\pi$
$632$	5.54909	+	1.48687i	0.220731	+	0.0591446i
$633$	−19.2589	+	5.16041i	−0.765473	+	0.205108i
$634$	−27.2643	+	15.7410i	−1.08280	+	0.625156i
$635$	16.5024	−	18.3998i	0.654876	−	0.730174i
$636$	−4.51442			−0.179008
$637$	−1.57185	−	0.421177i	−0.0622791	−	0.0166876i
$638$	0.523206	+	1.95263i	0.0207139	+	0.0773054i
$639$	8.09471	−	4.67349i	0.320222	−	0.184880i
$640$	−0.695132	−	2.12527i	−0.0274775	−	0.0840088i
$641$	6.60861	+	3.81548i	0.261024	+	0.150702i	0.624802	−	0.780783i	$-0.285180\pi$
$641$	6.60861	+	3.81548i	0.261024	+	0.150702i	−0.363777	+	0.931486i	$0.618513\pi$
$642$	4.26563	+	15.9195i	0.168351	+	0.628295i
$643$	−27.1184	−	27.1184i	−1.06945	−	1.06945i	−0.997401	−	0.0720457i	$-0.977047\pi$
$643$	−27.1184	−	27.1184i	−1.06945	−	1.06945i	−0.0720457	−	0.997401i	$-0.522953\pi$
$644$	−10.9217	−	18.9169i	−0.430374	−	0.745429i
$645$	3.77652	−	2.46300i	0.148700	−	0.0969804i
$646$	−2.03215	−	1.17326i	−0.0799537	−	0.0461613i
$647$	−30.6863	+	30.6863i	−1.20640	+	1.20640i	−0.234219	+	0.972184i	$0.575253\pi$
$647$	−30.6863	+	30.6863i	−1.20640	+	1.20640i	−0.972184	+	0.234219i	$0.924747\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	37.6141			1.47648
$650$	−0.591193	−	5.42118i	−0.0231885	−	0.212636i
$651$	−1.02887	−	16.1924i	−0.0403246	−	0.634631i
$652$	7.74129	+	7.74129i	0.303172	+	0.303172i
$653$	28.0755	−	28.0755i	1.09868	−	1.09868i	0.104113	−	0.994565i	$-0.466800\pi$
$653$	28.0755	−	28.0755i	1.09868	−	1.09868i	0.994565	−	0.104113i	$-0.0332003\pi$
$654$	6.03413	+	10.4514i	0.235953	+	0.408683i
$655$	−14.5242	+	0.789610i	−0.567508	+	0.0308526i
$656$	−2.22452	+	3.85297i	−0.0868528	+	0.150433i
$657$	1.33005	+	0.356385i	0.0518901	+	0.0139039i
$658$	9.45768	+	2.53418i	0.368699	+	0.0987925i
$659$		−	4.23943i		−	0.165145i	−0.996585	−	0.0825724i	$-0.973686\pi$
$659$		−	4.23943i		−	0.165145i	0.996585	−	0.0825724i	$-0.0263136\pi$
$660$	10.1999	−	3.33617i	0.397031	−	0.129860i
$661$	−15.1600	+	26.2580i	−0.589657	+	1.02132i	0.404620	+	0.914485i	$0.367404\pi$
$661$	−15.1600	+	26.2580i	−0.589657	+	1.02132i	−0.994277	+	0.106831i	$0.965929\pi$
$662$	0.582325	+	2.17327i	0.0226327	+	0.0844663i
$663$	−0.168371	+	0.628368i	−0.00653897	+	0.0244038i
$664$	2.25158	−	3.89985i	0.0873782	−	0.151343i
$665$	25.0853	+	5.28090i	0.972767	+	0.204784i
$666$		−	6.62100i		−	0.256558i
$667$	2.23251	+	2.23251i	0.0864431	+	0.0864431i
$668$	6.39836	−	23.8790i	0.247560	−	0.923907i
$669$	−20.1214	−	11.6171i	−0.777939	−	0.449143i
$670$	8.30110	−	5.41386i	0.320699	−	0.209156i
$671$	6.89391	−	11.9406i	0.266136	−	0.460962i
$672$	−0.754227	−	2.81481i	−0.0290949	−	0.108584i
$673$	−14.1265	+	3.78519i	−0.544537	+	0.145908i	−0.520593	−	0.853805i	$-0.674289\pi$
$673$	−14.1265	+	3.78519i	−0.544537	+	0.145908i	−0.0239441	+	0.999713i	$0.507622\pi$
$674$	8.06039			0.310475
$675$	4.94146	+	0.762889i	0.190197	+	0.0293636i
$676$	−5.90523	−	10.2282i	−0.227124	−	0.393390i
$677$	1.66919	+	6.22952i	0.0641524	+	0.239420i	0.990555	−	0.137114i	$-0.0437826\pi$
$677$	1.66919	+	6.22952i	0.0641524	+	0.239420i	−0.926403	+	0.376534i	$0.877116\pi$
$678$	1.10210	+	1.10210i	0.0423258	+	0.0423258i
$679$	17.3525	−	10.0185i	0.665929	−	0.384475i
$680$	−0.0724008	−	1.33175i	−0.00277644	−	0.0510703i
$681$			7.62973i			0.292372i
$682$	17.6588	−	20.0552i	0.676191	−	0.767952i
$683$	20.8763	−	20.8763i	0.798810	−	0.798810i	−0.184098	−	0.982908i	$-0.558936\pi$
$683$	20.8763	−	20.8763i	0.798810	−	0.798810i	0.982908	+	0.184098i	$0.0589364\pi$
$684$		−	3.93410i		−	0.150424i
$685$	−38.2094	−	8.04375i	−1.45991	−	0.307336i
$686$	−16.0508			−0.612823
$687$	−16.0807	+	4.30881i	−0.613517	+	0.164391i
$688$	0.521872	−	1.94765i	0.0198962	−	0.0742535i
$689$	−4.26406	+	2.46186i	−0.162448	+	0.0937893i
$690$	11.1909	−	12.4777i	0.426031	−	0.475016i
$691$	−7.97235	+	13.8085i	−0.303282	+	0.525301i	−0.976877	−	0.213800i	$-0.931416\pi$
$691$	−7.97235	+	13.8085i	−0.303282	+	0.525301i	0.673595	+	0.739101i	$0.264749\pi$
$692$	−16.2872	+	4.36415i	−0.619148	+	0.165900i
$693$	13.5092	−	3.61979i	0.513174	−	0.137504i
$694$	−7.67571	−	13.2947i	−0.291366	−	0.504661i
$695$	−7.58771	+	14.9639i	−0.287818	+	0.567611i
$696$	0.210603	+	0.364776i	0.00798290	+	0.0138268i
$697$	−1.87642	+	1.87642i	−0.0710744	+	0.0710744i
$698$	−5.05130	+	5.05130i	−0.191195	+	0.191195i
$699$	5.70056	+	9.87367i	0.215615	+	0.373456i
$700$	5.27467	+	13.5823i	0.199364	+	0.513362i
$701$	−23.4994	−	40.7021i	−0.887558	−	1.53730i	−0.842753	−	0.538300i	$-0.819067\pi$
$701$	−23.4994	−	40.7021i	−0.887558	−	1.53730i	−0.0448054	−	0.998996i	$-0.514267\pi$
$702$	−1.05350	+	0.282285i	−0.0397618	+	0.0106541i
$703$	25.1601	−	6.74163i	0.948931	−	0.254265i
$704$	2.39967	−	4.15635i	0.0904409	−	0.156648i
$705$	0.407849	+	7.50204i	0.0153605	+	0.282543i
$706$	−3.52354	+	2.03432i	−0.132610	+	0.0765626i
$707$	11.7429	−	43.8251i	0.441637	−	1.64821i
$708$	7.57030	−	2.02845i	0.284509	−	0.0762340i
$709$	−32.8126			−1.23230			−0.616152	−	0.787627i	$-0.711309\pi$
$709$	−32.8126			−1.23230			−0.616152	+	0.787627i	$0.711309\pi$
$710$	−4.30554	+	20.4522i	−0.161584	+	0.767557i
$711$			5.74484i			0.215448i
$712$	9.25309	−	9.25309i	0.346774	−	0.346774i
$713$	8.22361	−	40.9161i	0.307976	−	1.53232i
$714$		−	1.73814i		−	0.0650483i
$715$	7.81493	−	8.71350i	0.292262	−	0.325866i
$716$	12.7362	−	7.35324i	0.475974	−	0.274804i
$717$	−6.20068	−	6.20068i	−0.231569	−	0.231569i
$718$	7.74097	+	28.8897i	0.288890	+	1.07815i
$719$	11.6736	+	20.2192i	0.435351	+	0.754050i	0.997324	−	0.0731057i	$-0.0232910\pi$
$719$	11.6736	+	20.2192i	0.435351	+	0.754050i	−0.561974	+	0.827155i	$0.689958\pi$
$720$	1.87294	−	1.22151i	0.0698005	−	0.0455229i
$721$	−13.8919			−0.517361
$722$	−3.40283	+	0.911786i	−0.126640	+	0.0339332i
$723$	−6.32215	−	23.5946i	−0.235123	−	0.877492i
$724$	−1.73677	+	3.00817i	−0.0645465	+	0.111798i
$725$	−1.24454	−	1.69897i	−0.0462209	−	0.0630982i
$726$	10.4214	+	6.01682i	0.386776	+	0.223305i
$727$	−3.20065	+	11.9450i	−0.118705	+	0.443015i	−0.999537	−	0.0304145i	$-0.990317\pi$
$727$	−3.20065	+	11.9450i	−0.118705	+	0.443015i	0.880832	+	0.473429i	$0.156984\pi$
$728$	−2.24741	−	2.24741i	−0.0832945	−	0.0832945i
$729$		−	1.00000i		−	0.0370370i
$730$	−2.57898	+	1.68198i	−0.0954524	+	0.0622527i
$731$	0.601335	−	1.04154i	0.0222412	−	0.0385229i
$732$	0.743551	−	2.77497i	0.0274824	−	0.102566i
$733$	12.1931	+	45.5053i	0.450363	+	1.68078i	0.701374	+	0.712793i	$0.252570\pi$
$733$	12.1931	+	45.5053i	0.450363	+	1.68078i	−0.251012	+	0.967984i	$0.580763\pi$
$734$	−4.83908	+	8.38153i	−0.178614	+	0.309368i
$735$	1.03716	+	3.17097i	0.0382562	+	0.116963i
$736$		−	7.49571i		−	0.276296i
$737$	20.5464	+	5.50539i	0.756837	+	0.202794i
$738$	−4.29743	−	1.15149i	−0.158191	−	0.0423871i
$739$	24.1933	−	41.9040i	0.889964	−	1.54146i	0.0500470	−	0.998747i	$-0.484063\pi$
$739$	24.1933	−	41.9040i	0.889964	−	1.54146i	0.839917	−	0.542715i	$-0.182604\pi$
$740$	11.0216	+	9.88499i	0.405161	+	0.363379i
$741$	−2.14539	−	3.71592i	−0.0788129	−	0.136508i
$742$	9.30235	−	9.30235i	0.341500	−	0.341500i
$743$	−13.8078	−	13.8078i	−0.506558	−	0.506558i	0.406910	−	0.913468i	$-0.366606\pi$
$743$	−13.8078	−	13.8078i	−0.506558	−	0.506558i	−0.913468	+	0.406910i	$0.866606\pi$
$744$	2.47252	−	4.98865i	0.0906468	−	0.182893i
$745$	−0.133262	−	2.45123i	−0.00488233	−	0.0898063i
$746$	3.16354			0.115826
$747$	4.34972	+	1.16550i	0.159148	+	0.0426435i
$748$	2.02416	−	2.02416i	0.0740107	−	0.0740107i
$749$	−41.5933	−	24.0139i	−1.51979	−	0.877449i
$750$	−8.64741	+	7.08677i	−0.315759	+	0.258772i
$751$	−10.1492	−	17.5790i	−0.370351	−	0.641467i	0.619268	−	0.785179i	$-0.287429\pi$
$751$	−10.1492	−	17.5790i	−0.370351	−	0.641467i	−0.989619	+	0.143712i	$0.954096\pi$
$752$	2.37586	+	2.37586i	0.0866385	+	0.0866385i
$753$	−4.59681	−	17.1555i	−0.167517	−	0.625183i
$754$	0.397848	+	0.229698i	0.0144888	+	0.00836509i
$755$	−14.4442	−	7.32422i	−0.525679	−	0.266556i
$756$	2.52369	−	1.45705i	0.0917858	−	0.0529926i
$757$	−3.02808	−	11.3009i	−0.110057	−	0.410740i	0.888812	−	0.458271i	$-0.151531\pi$
$757$	−3.02808	−	11.3009i	−0.110057	−	0.410740i	−0.998870	+	0.0475316i	$0.984865\pi$
$758$	0.0724876	+	0.0194230i	0.00263287	+	0.000705475i
$759$	35.9744			1.30579
$760$	6.54885	+	5.87351i	0.237552	+	0.213055i
$761$	−6.53948	+	3.77557i	−0.237056	+	0.136864i	−0.613823	−	0.789444i	$-0.710369\pi$
$761$	−6.53948	+	3.77557i	−0.237056	+	0.136864i	0.376767	+	0.926308i	$0.377036\pi$
$762$	10.6767	−	2.86081i	0.386776	−	0.103636i
$763$	−33.9699	−	9.10221i	−1.22979	−	0.329522i
$764$	10.1069	+	5.83524i	0.365656	+	0.211112i
$765$	1.26763	−	0.414616i	0.0458314	−	0.0149905i
$766$	−27.9776	−	16.1529i	−1.01087	−	0.583628i
$767$	6.04429	−	6.04429i	0.218247	−	0.218247i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−21.8674	+	12.6252i	−0.788560	+	0.455275i	−0.839455	−	0.543429i	$-0.817126\pi$
$769$	−21.8674	+	12.6252i	−0.788560	+	0.455275i	0.0508952	+	0.998704i	$0.483793\pi$
$770$	−14.1433	+	27.8923i	−0.509690	+	1.00517i
$771$			31.7758i			1.14438i
$772$	−1.35267	+	5.04822i	−0.0486836	+	0.181690i
$773$	−0.384948	−	0.384948i	−0.0138456	−	0.0138456i	0.700150	−	0.713996i	$-0.253116\pi$
$773$	−0.384948	−	0.384948i	−0.0138456	−	0.0138456i	−0.713996	+	0.700150i	$0.753116\pi$
$774$	2.01636			0.0724765
$775$	−9.58562	+	26.1365i	−0.344326	+	0.938850i
$776$	6.87585			0.246829
$777$	13.6431	+	13.6431i	0.489445	+	0.489445i
$778$	1.18420	−	4.41948i	0.0424555	−	0.158446i
$779$		−	17.5029i		−	0.627107i
$780$	1.10295	−	2.17514i	0.0394919	−	0.0778826i
$781$	−38.8493	+	22.4296i	−1.39014	+	0.802595i
$782$	1.15715	−	4.31853i	0.0413794	−	0.154430i
$783$	−0.297838	+	0.297838i	−0.0106439	+	0.0106439i
$784$	1.29214	+	0.746015i	0.0461477	+	0.0266434i
$785$	−29.7053	+	9.71599i	−1.06023	+	0.346778i
$786$	−5.63351	−	3.25251i	−0.200941	−	0.116013i
$787$	−20.1209	−	5.39137i	−0.717232	−	0.192182i	−0.118296	−	0.992978i	$-0.537743\pi$
$787$	−20.1209	−	5.39137i	−0.717232	−	0.192182i	−0.598936	+	0.800797i	$0.704410\pi$
$788$	−19.1551	+	5.13258i	−0.682371	+	0.182841i
$789$	19.1617	−	11.0630i	0.682174	−	0.393853i
$790$	−9.56308	−	8.57690i	−0.340239	−	0.305152i
$791$	−4.54193			−0.161492
$792$	4.63580	+	1.24216i	0.164726	+	0.0441382i
$793$	−0.810964	−	3.02656i	−0.0287982	−	0.107476i
$794$	29.4792	−	17.0198i	1.04618	−	0.604011i
$795$	9.00323	+	4.56526i	0.319312	+	0.161913i
$796$	−6.86085	−	3.96111i	−0.243176	−	0.140398i
$797$	−2.84912	−	10.6330i	−0.100921	−	0.376642i	0.896930	−	0.442173i	$-0.145792\pi$
$797$	−2.84912	−	10.6330i	−0.100921	−	0.376642i	−0.997850	+	0.0655315i	$0.979126\pi$
$798$	8.10655	+	8.10655i	0.286969	+	0.286969i
$799$	1.00204	+	1.73558i	0.0354496	+	0.0614004i
$800$	−0.762889	+	4.94146i	−0.0269722	+	0.174707i
$801$	11.3327	+	6.54293i	0.400421	+	0.231183i
$802$	8.76688	−	8.76688i	0.309569	−	0.309569i
$803$	−6.38335	−	1.71041i	−0.225264	−	0.0603592i
$804$	4.43211			0.156309
$805$	2.65145	+	48.7711i	0.0934512	+	1.71896i
$806$	−0.385075	−	6.06034i	−0.0135637	−	0.213466i
$807$	−9.23126	−	9.23126i	−0.324956	−	0.324956i
$808$	11.0093	−	11.0093i	0.387305	−	0.387305i
$809$	−20.5018	−	35.5101i	−0.720804	−	1.24847i	−0.960678	−	0.277666i	$-0.910439\pi$
$809$	−20.5018	−	35.5101i	−0.720804	−	1.24847i	0.239873	−	0.970804i	$-0.422894\pi$
$810$	1.66464	+	1.49298i	0.0584895	+	0.0524578i
$811$	−21.5183	+	37.2708i	−0.755610	+	1.30875i	0.189461	+	0.981888i	$0.439326\pi$
$811$	−21.5183	+	37.2708i	−0.755610	+	1.30875i	−0.945071	+	0.326866i	$0.894007\pi$
$812$	−1.18562	−	0.317685i	−0.0416070	−	0.0111486i
$813$	−30.6462	−	8.21161i	−1.07481	−	0.287994i
$814$			31.7764i			1.11376i
$815$	−7.61020	−	23.2672i	−0.266574	−	0.815013i
$816$	0.298228	−	0.516547i	0.0104401	−	0.0180828i
$817$	2.05309	+	7.66225i	0.0718287	+	0.268068i
$818$	1.99868	−	7.45918i	0.0698823	−	0.260804i
$819$	1.58916	−	2.75250i	0.0555296	−	0.0961802i
$820$	8.33279	−	5.43453i	0.290994	−	0.189782i
$821$		−	43.4950i		−	1.51799i	−0.651099	−	0.758993i	$-0.725692\pi$
$821$		−	43.4950i		−	1.51799i	0.651099	−	0.758993i	$-0.274308\pi$
$822$	−12.3477	−	12.3477i	−0.430676	−	0.430676i
$823$	3.03629	−	11.3316i	0.105838	−	0.394994i	−0.892601	−	0.450848i	$-0.851122\pi$
$823$	3.03629	−	11.3316i	0.105838	−	0.394994i	0.998439	+	0.0558543i	$0.0177882\pi$
$824$	−4.12844	−	2.38356i	−0.143821	−	0.0830352i
$825$	−23.7157	−	3.66136i	−0.825676	−	0.127472i
$826$	−11.4194	+	19.7791i	−0.397333	+	0.688201i
$827$	1.95471	+	7.29507i	0.0679718	+	0.253674i	0.991548	−	0.129741i	$-0.0414145\pi$
$827$	1.95471	+	7.29507i	0.0679718	+	0.253674i	−0.923576	+	0.383415i	$0.874748\pi$
$828$	7.24030	−	1.94003i	0.251618	−	0.0674208i
$829$	37.4469			1.30058			0.650292	−	0.759684i	$-0.274647\pi$
$829$	37.4469			1.30058			0.650292	+	0.759684i	$0.274647\pi$
$830$	−8.43416	+	5.50064i	−0.292754	+	0.190930i
$831$	10.8381	+	18.7721i	0.375969	+	0.651197i
$832$	−0.282285	−	1.05350i	−0.00978646	−	0.0365236i
$833$	0.629277	+	0.629277i	0.0218031	+	0.0218031i
$834$	−6.49796	+	3.75160i	−0.225006	+	0.129907i
$835$	−36.9084	+	41.1522i	−1.27727	+	1.42413i
$836$			18.8811i			0.653015i
$837$	5.45860	+	1.09711i	0.188677	+	0.0379216i
$838$	−3.32906	+	3.32906i	−0.115000	+	0.115000i
$839$			52.1215i			1.79944i	0.436473	+	0.899718i	$0.356228\pi$
$839$			52.1215i			1.79944i	−0.436473	+	0.899718i	$0.643772\pi$
$840$	−1.34234	+	6.37638i	−0.0463151	+	0.220006i
$841$	−28.8226			−0.993882
$842$	9.33466	−	2.50122i	0.321694	−	0.0861976i
$843$	3.36926	−	12.5742i	0.116043	−	0.433080i
$844$	17.2671	−	9.96915i	0.594357	−	0.343152i
$845$	1.43361	+	26.3700i	0.0493177	+	0.907157i
$846$	−1.67998	+	2.90982i	−0.0577590	+	0.100042i
$847$	−33.8725	+	9.07610i	−1.16387	+	0.311858i
$848$	4.36059	−	1.16842i	0.149743	−	0.0401236i
$849$	−12.7584	−	22.0982i	−0.437867	−	0.758407i
$850$	−1.20236	+	2.72917i	−0.0412406	+	0.0936096i
$851$	24.8145	+	42.9800i	0.850632	+	1.47334i
$852$	−6.60931	+	6.60931i	−0.226431	+	0.226431i
$853$	−12.8648	+	12.8648i	−0.440483	+	0.440483i	−0.892174	−	0.451692i	$-0.850821\pi$
$853$	−12.8648	+	12.8648i	−0.440483	+	0.440483i	0.451692	+	0.892174i	$0.350821\pi$
$854$	4.18591	+	7.25021i	0.143239	+	0.248097i
$855$	−3.97841	+	7.84588i	−0.136059	+	0.268324i
$856$	−8.24057	−	14.2731i	−0.281657	−	0.487844i
$857$	−11.5981	+	3.10771i	−0.396184	+	0.106157i	−0.451410	−	0.892317i	$-0.649079\pi$
$857$	−11.5981	+	3.10771i	−0.396184	+	0.106157i	0.0552258	+	0.998474i	$0.482412\pi$
$858$	5.05611	−	1.35478i	0.172613	−	0.0462514i
$859$	27.9439	−	48.4002i	0.953432	−	1.65139i	0.215517	−	0.976500i	$-0.430856\pi$
$859$	27.9439	−	48.4002i	0.953432	−	1.65139i	0.737915	−	0.674893i	$-0.235810\pi$
$860$	−3.01037	+	3.35651i	−0.102653	+	0.114456i
$861$	11.2280	−	6.48248i	0.382649	−	0.220922i
$862$	−7.60457	+	28.3806i	−0.259013	+	0.966649i
$863$	−19.0136	+	5.09469i	−0.647231	+	0.173425i	−0.567477	−	0.823389i	$-0.692080\pi$
$863$	−19.0136	+	5.09469i	−0.647231	+	0.173425i	−0.0797546	+	0.996815i	$0.525414\pi$
$864$	1.00000			0.0340207
$865$	36.8954	+	7.76713i	1.25448	+	0.264090i
$866$			15.6633i			0.532260i
$867$	−11.7693	+	11.7693i	−0.399705	+	0.399705i
$868$	5.18472	+	15.3744i	0.175981	+	0.521841i
$869$		−	27.5714i		−	0.935296i
$870$	−0.0511281	−	0.940458i	−0.00173340	−	0.0318845i
$871$	4.18632	−	2.41697i	0.141848	−	0.0818960i
$872$	−8.53355	−	8.53355i	−0.288983	−	0.288983i
$873$	1.77960	+	6.64157i	0.0602304	+	0.224783i
$874$	14.7444	+	25.5381i	0.498738	+	0.863839i
$875$	3.21583	−	32.4216i	0.108715	−	1.09605i
$876$	−1.37697			−0.0465234
$877$	16.6340	−	4.45708i	0.561692	−	0.150505i	0.0332084	−	0.999448i	$-0.489428\pi$
$877$	16.6340	−	4.45708i	0.561692	−	0.150505i	0.528484	+	0.848944i	$0.322761\pi$
$878$	0.197551	+	0.737272i	0.00666704	+	0.0248817i
$879$	3.90717	−	6.76741i	0.131786	−	0.228259i
$880$	−8.98889	+	5.86243i	−0.303015	+	0.197622i
$881$	−10.7879	−	6.22839i	−0.363453	−	0.209840i	0.307141	−	0.951664i	$-0.400628\pi$
$881$	−10.7879	−	6.22839i	−0.363453	−	0.209840i	−0.670594	+	0.741824i	$0.733961\pi$
$882$	−0.386166	+	1.44119i	−0.0130029	+	0.0485274i
$883$	−30.0148	−	30.0148i	−1.01008	−	1.01008i	−0.999949	−	0.0101286i	$-0.996776\pi$
$883$	−30.0148	−	30.0148i	−1.01008	−	1.01008i	−0.0101286	−	0.999949i	$-0.503224\pi$
$884$		−	0.650534i		−	0.0218798i
$885$	−17.1490	−	3.61016i	−0.576456	−	0.121354i
$886$	16.2128	−	28.0814i	0.544679	−	0.943412i
$887$	1.07153	−	3.99901i	0.0359785	−	0.134274i	−0.945601	−	0.325330i	$-0.894525\pi$
$887$	1.07153	−	3.99901i	0.0359785	−	0.134274i	0.981579	+	0.191056i	$0.0611913\pi$
$888$	1.71364	+	6.39539i	0.0575060	+	0.214615i
$889$	−16.1053	+	27.8952i	−0.540155	+	0.935575i
$890$	−27.8110	+	9.09640i	−0.932228	+	0.304912i
$891$			4.79934i			0.160784i
$892$	22.4425	+	6.01346i	0.751432	+	0.201346i
$893$	−12.7680	−	3.42118i	−0.427266	−	0.114486i
$894$	0.548922	−	0.950761i	0.0183587	−	0.0317982i
$895$	−32.8362	+	1.78514i	−1.09759	+	0.0596708i
$896$	1.45705	+	2.52369i	0.0486768	+	0.0843106i
$897$	5.78081	−	5.78081i	0.193016	−	0.193016i
$898$	−8.16266	−	8.16266i	−0.272392	−	0.272392i
$899$	−1.29902	−	1.95254i	−0.0433247	−	0.0651209i
$900$	−4.97053	+	0.542049i	−0.165684	+	0.0180683i
$901$	2.69266			0.0897054
$902$	20.6248	+	5.52641i	0.686732	+	0.184009i
$903$	−4.15488	+	4.15488i	−0.138266	+	0.138266i
$904$	−1.34979	−	0.779300i	−0.0448932	−	0.0259191i
$905$	6.50575	−	4.24296i	0.216258	−	0.141041i
$906$	−3.62133	−	6.27232i	−0.120310	−	0.208384i
$907$	−10.7585	−	10.7585i	−0.357230	−	0.357230i	0.505561	−	0.862791i	$-0.331286\pi$
$907$	−10.7585	−	10.7585i	−0.357230	−	0.357230i	−0.862791	+	0.505561i	$0.831286\pi$
$908$	−1.97472	−	7.36975i	−0.0655334	−	0.244574i
$909$	13.4835	+	7.78473i	0.447221	+	0.258203i
$910$	2.20935	+	6.75479i	0.0732392	+	0.223919i
$911$	−46.4500	+	26.8179i	−1.53896	+	0.888518i	−0.540058	+	0.841628i	$0.681598\pi$
$911$	−46.4500	+	26.8179i	−1.53896	+	0.888518i	−0.998900	+	0.0468895i	$0.985069\pi$
$912$	1.01822	+	3.80005i	0.0337166	+	0.125832i
$913$	−20.8758	−	5.59364i	−0.690887	−	0.185123i
$914$	38.3130			1.26728
$915$	−4.28911	+	4.78227i	−0.141794	+	0.158097i
$916$	14.4176	−	8.32398i	0.476369	−	0.275032i
$917$	18.3104	−	4.90626i	0.604663	−	0.162019i
$918$	0.576133	+	0.154374i	0.0190152	+	0.00509511i
$919$	13.3876	+	7.72932i	0.441615	+	0.254967i	0.704282	−	0.709920i	$-0.251269\pi$
$919$	13.3876	+	7.72932i	0.441615	+	0.254967i	−0.262667	+	0.964886i	$0.584602\pi$
$920$	−7.58013	+	14.9489i	−0.249910	+	0.492851i
$921$	3.88247	+	2.24155i	0.127932	+	0.0738615i
$922$	17.5535	−	17.5535i	0.578094	−	0.578094i
$923$	−2.63851	+	9.84704i	−0.0868475	+	0.324119i
$924$	−12.1121	+	6.99290i	−0.398457	+	0.230049i
$925$	−11.9843	−	30.8596i	−0.394042	−	1.01466i
$926$		−	3.10733i		−	0.102113i
$927$	1.23382	−	4.60468i	0.0405240	−	0.151238i
$928$	−0.297838	−	0.297838i	−0.00977702	−	0.00977702i
$929$	−7.88388			−0.258662			−0.129331	−	0.991602i	$-0.541283\pi$
$929$	−7.88388			−0.258662			−0.129331	+	0.991602i	$0.541283\pi$
$930$	−9.97585	+	7.44865i	−0.327121	+	0.244251i
$931$	−5.86979			−0.192375
$932$	−8.06182	−	8.06182i	−0.264074	−	0.264074i
$933$	2.81302	−	10.4983i	0.0920941	−	0.343700i
$934$			27.6239i			0.903882i
$935$	−6.08381	+	1.98988i	−0.198962	+	0.0650762i
$936$	0.944543	−	0.545332i	0.0308734	−	0.0178247i
$937$	10.6302	−	39.6725i	0.347274	−	1.29604i	−0.542659	−	0.839953i	$-0.682582\pi$
$937$	10.6302	−	39.6725i	0.347274	−	1.29604i	0.889933	−	0.456091i	$-0.150751\pi$
$938$	−9.13275	+	9.13275i	−0.298195	+	0.298195i
$939$	19.0493	+	10.9981i	0.621651	+	0.358910i
$940$	−2.33562	−	7.14085i	−0.0761796	−	0.232909i
$941$	38.4133	+	22.1779i	1.25224	+	0.722980i	0.971553	−	0.236820i	$-0.0761052\pi$
$941$	38.4133	+	22.1779i	1.25224	+	0.722980i	0.280684	+	0.959800i	$0.409439\pi$
$942$	−13.5009	−	3.61756i	−0.439884	−	0.117866i
$943$	32.2123	−	8.63127i	1.04898	−	0.281073i
$944$	−6.78734	+	3.91867i	−0.220909	+	0.127542i
$945$	−6.50654	+	0.353728i	−0.211658	+	0.0115068i
$946$	−9.67718			−0.314632
$947$	−43.0884	−	11.5455i	−1.40018	−	0.375178i	−0.521773	−	0.853084i	$-0.674729\pi$
$947$	−43.0884	−	11.5455i	−1.40018	−	0.375178i	−0.878411	+	0.477906i	$0.841396\pi$
$948$	−1.48687	−	5.54909i	−0.0482914	−	0.180226i
$949$	−1.30060	+	0.750905i	−0.0422194	+	0.0243754i
$950$	−7.12090	−	18.3363i	−0.231033	−	0.594909i
$951$	27.2643	+	15.7410i	0.884104	+	0.510438i
$952$	0.449864	+	1.67891i	0.0145802	+	0.0544139i
$953$	−25.9032	−	25.9032i	−0.839085	−	0.839085i	0.149653	−	0.988739i	$-0.452184\pi$
$953$	−25.9032	−	25.9032i	−0.839085	−	0.839085i	−0.988739	+	0.149653i	$0.952184\pi$
$954$	2.25721	+	3.90960i	0.0730798	+	0.126578i
$955$	−14.2556	−	21.8582i	−0.461300	−	0.707314i
$956$	7.59426	+	4.38455i	0.245616	+	0.141806i
$957$	1.42943	−	1.42943i	0.0462068	−	0.0462068i
$958$	−34.6518	−	9.28492i	−1.11955	−	0.299982i
$959$	50.8871			1.64323
$960$	−1.49298	+	1.66464i	−0.0481856	+	0.0537260i
$961$	−11.9774	+	28.5927i	−0.386366	+	0.922345i
$962$	5.10622	+	5.10622i	0.164631	+	0.164631i
$963$	11.6539	−	11.6539i	0.375542	−	0.375542i
$964$	12.2135	+	21.1543i	0.393369	+	0.681335i
$965$	7.80275	−	8.69991i	0.251179	−	0.280060i
$966$	−10.9217	+	18.9169i	−0.351399	+	0.608640i
$967$	−19.5776	−	5.24580i	−0.629573	−	0.168694i	−0.0700971	−	0.997540i	$-0.522331\pi$
$967$	−19.5776	−	5.24580i	−0.629573	−	0.168694i	−0.559476	+	0.828847i	$0.688998\pi$
$968$	−11.6236	−	3.11454i	−0.373597	−	0.100105i
$969$			2.34652i			0.0753811i
$970$	−13.7127	−	6.95330i	−0.440289	−	0.223257i
$971$	−25.0176	+	43.3317i	−0.802852	+	1.39058i	0.114880	+	0.993379i	$0.463352\pi$
$971$	−25.0176	+	43.3317i	−0.802852	+	1.39058i	−0.917732	+	0.397200i	$0.869982\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	5.65912	−	21.1201i	0.181423	−	0.677080i
$974$	−3.37254	+	5.84142i	−0.108063	+	0.187171i
$975$	−4.39928	+	3.22258i	−0.140890	+	0.103205i
$976$			2.87286i			0.0919580i
$977$	−5.65200	−	5.65200i	−0.180824	−	0.180824i	0.610891	−	0.791715i	$-0.290811\pi$
$977$	−5.65200	−	5.65200i	−0.180824	−	0.180824i	−0.791715	+	0.610891i	$0.790811\pi$
$978$	2.83351	−	10.5748i	0.0906057	−	0.338145i
$979$	−54.3894	−	31.4017i	−1.73829	−	1.00360i
$980$	−1.82253	−	2.79449i	−0.0582185	−	0.0892667i
$981$	6.03413	−	10.4514i	0.192655	−	0.333688i
$982$	4.92729	+	18.3889i	0.157236	+	0.586813i
$983$	−48.4607	+	12.9850i	−1.54566	+	0.414158i	−0.928089	−	0.372359i	$-0.878549\pi$
$983$	−48.4607	+	12.9850i	−1.54566	+	0.414158i	−0.617569	+	0.786517i	$0.711882\pi$
$984$	4.44903			0.141830
$985$	43.3919	+	9.13475i	1.38258	+	0.291057i
$986$	−0.125616	−	0.217573i	−0.00400042	−	0.00692894i
$987$	−2.53418	−	9.45768i	−0.0806638	−	0.301041i
$988$	3.03404	+	3.03404i	0.0965257	+	0.0965257i
$989$	−13.0891	+	7.55701i	−0.416210	+	0.240299i
$990$	−7.98917	−	7.16529i	−0.253912	−	0.227728i
$991$			8.00797i			0.254381i	0.991878	+	0.127191i	$0.0405960\pi$
$991$			8.00797i			0.254381i	−0.991878	+	0.127191i	$0.959404\pi$
$992$	−1.09711	+	5.45860i	−0.0348332	+	0.173311i
$993$	1.59094	−	1.59094i	0.0504870	−	0.0504870i
$994$		−	27.2381i		−	0.863940i
$995$	9.67706	+	14.8379i	0.306783	+	0.470393i
$996$	−4.50316			−0.142688
$997$	−1.13028	+	0.302857i	−0.0357963	+	0.00959159i	−0.276673	−	0.960964i	$-0.589232\pi$
$997$	−1.13028	+	0.302857i	−0.0357963	+	0.00959159i	0.240876	+	0.970556i	$0.422565\pi$
$998$	−4.53988	+	16.9431i	−0.143707	+	0.536323i
$999$	−5.73395	+	3.31050i	−0.181414	+	0.104740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.14	✓	64
5.3	odd	4		930.2.be.b.223.15	yes	64
31.26	odd	6		930.2.be.b.367.15	yes	64
155.88	even	12	inner	930.2.be.a.553.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.14	✓	64	1.1	even	1	trivial
930.2.be.a.553.14	yes	64	155.88	even	12	inner
930.2.be.b.223.15	yes	64	5.3	odd	4
930.2.be.b.367.15	yes	64	31.26	odd	6

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.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.01126 - 1.99433i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.754227 + 2.81481i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(1.01126 - 1.99433i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.754227 + 2.81481i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.12527 - 0.695132i) q^{10} +(4.15635 + 2.39967i) q^{11} +(0.965926 + 0.258819i) q^{12} +(1.05350 - 0.282285i) q^{13} +(-2.52369 + 1.45705i) q^{14} +(-1.66464 - 1.49298i) q^{15} -1.00000 q^{16} +(-0.576133 - 0.154374i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(3.40703 - 1.96705i) q^{19} +(1.99433 + 1.01126i) q^{20} +(2.52369 + 1.45705i) q^{21} +(1.24216 + 4.63580i) q^{22} +(5.30027 + 5.30027i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.95469 - 4.03358i) q^{25} +(0.944543 + 0.545332i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.81481 - 0.754227i) q^{28} +0.421207 q^{29} +(-0.121385 - 2.23277i) q^{30} +(-3.08404 - 4.63559i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.39364 - 3.39364i) q^{33} +(-0.298228 - 0.516547i) q^{34} +(4.85094 + 4.35069i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.39539 + 1.71364i) q^{37} +(3.80005 + 1.01822i) q^{38} -1.09066i q^{39} +(0.695132 + 2.12527i) q^{40} +(2.22452 - 3.85297i) q^{41} +(0.754227 + 2.81481i) q^{42} +(-0.521872 + 1.94765i) q^{43} +(-2.39967 + 4.15635i) q^{44} +(-1.87294 + 1.22151i) q^{45} +7.49571i q^{46} +(-2.37586 - 2.37586i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-1.29214 - 0.746015i) q^{49} +(0.762889 - 4.94146i) q^{50} +(-0.298228 + 0.516547i) q^{51} +(0.282285 + 1.05350i) q^{52} +(-4.36059 + 1.16842i) q^{53} -1.00000 q^{54} +(8.98889 - 5.86243i) q^{55} +(-1.45705 - 2.52369i) q^{56} +(-1.01822 - 3.80005i) q^{57} +(0.297838 + 0.297838i) q^{58} +(6.78734 - 3.91867i) q^{59} +(1.49298 - 1.66464i) q^{60} -2.87286i q^{61} +(1.09711 - 5.45860i) q^{62} +(2.06059 - 2.06059i) q^{63} -1.00000i q^{64} +(0.502398 - 2.38649i) q^{65} +4.79934 q^{66} +(4.28109 - 1.14712i) q^{67} +(0.154374 - 0.576133i) q^{68} +(6.49147 - 3.74785i) q^{69} +(0.353728 + 6.50654i) q^{70} +(-4.67349 + 8.09471i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-1.33005 + 0.356385i) q^{73} +(3.31050 + 5.73395i) q^{74} +(-4.66087 + 1.81005i) q^{75} +(1.96705 + 3.40703i) q^{76} +(-9.88945 + 9.88945i) q^{77} +(0.771216 - 0.771216i) q^{78} +(-2.87242 - 4.97517i) q^{79} +(-1.01126 + 1.99433i) q^{80} +(0.500000 + 0.866025i) q^{81} +(4.29743 - 1.15149i) q^{82} +(-4.34972 + 1.16550i) q^{83} +(-1.45705 + 2.52369i) q^{84} +(-0.890496 + 0.992886i) q^{85} +(-1.74622 + 1.00818i) q^{86} +(0.109016 - 0.406854i) q^{87} +(-4.63580 + 1.24216i) q^{88} -13.0859 q^{89} +(-2.18811 - 0.460635i) q^{90} +3.17831i q^{91} +(-5.30027 + 5.30027i) q^{92} +(-5.27584 + 1.77918i) q^{93} -3.35997i q^{94} +(-0.477540 - 8.78394i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-4.86196 - 4.86196i) q^{97} +(-0.386166 - 1.44119i) q^{98} +(-2.39967 - 4.15635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

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