LMFDB - Embedded newform 930.2.o.e.491.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.13
Character	$\chi$	$=$	930.491
Dual form			930.2.o.e.161.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.556373 - 1.64026i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(1.64026 - 0.556373i) q^{6} +(-1.24695 + 2.15979i) q^{7} -1.00000i q^{8} +(-2.38090 + 1.82519i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.556373 - 1.64026i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(1.64026 - 0.556373i) q^{6} +(-1.24695 + 2.15979i) q^{7} -1.00000i q^{8} +(-2.38090 + 1.82519i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.404589 - 0.700769i) q^{11} +(0.556373 + 1.64026i) q^{12} +(3.21968 - 1.85888i) q^{13} +(-2.15979 - 1.24695i) q^{14} +(-1.30196 - 1.14232i) q^{15} +1.00000 q^{16} +(-3.37588 + 5.84719i) q^{17} +(-1.82519 - 2.38090i) q^{18} +(-3.45706 + 5.98781i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(4.23638 + 0.843679i) q^{21} +(0.700769 - 0.404589i) q^{22} +2.81543 q^{23} +(-1.64026 + 0.556373i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.85888 + 3.21968i) q^{26} +(4.31845 + 2.88980i) q^{27} +(1.24695 - 2.15979i) q^{28} +9.79927 q^{29} +(1.14232 - 1.30196i) q^{30} +(-5.56019 - 0.290293i) q^{31} +1.00000i q^{32} +(-0.924340 + 1.05352i) q^{33} +(-5.84719 - 3.37588i) q^{34} +2.49391i q^{35} +(2.38090 - 1.82519i) q^{36} +(-3.94549 - 2.27793i) q^{37} +(-5.98781 - 3.45706i) q^{38} +(-4.84039 - 4.24687i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(2.77433 - 1.60176i) q^{41} +(-0.843679 + 4.23638i) q^{42} +(5.26630 + 3.04050i) q^{43} +(0.404589 + 0.700769i) q^{44} +(-1.14932 + 2.77111i) q^{45} +2.81543i q^{46} +12.3679i q^{47} +(-0.556373 - 1.64026i) q^{48} +(0.390213 + 0.675869i) q^{49} +(0.866025 + 0.500000i) q^{50} +(11.4691 + 2.28409i) q^{51} +(-3.21968 + 1.85888i) q^{52} +(4.33368 + 7.50615i) q^{53} +(-2.88980 + 4.31845i) q^{54} +(-0.700769 - 0.404589i) q^{55} +(2.15979 + 1.24695i) q^{56} +(11.7450 + 2.33902i) q^{57} +9.79927i q^{58} +(1.80978 + 1.04488i) q^{59} +(1.30196 + 1.14232i) q^{60} -1.93145i q^{61} +(0.290293 - 5.56019i) q^{62} +(-0.973156 - 7.41816i) q^{63} -1.00000 q^{64} +(1.85888 - 3.21968i) q^{65} +(-1.05352 - 0.924340i) q^{66} +(1.82612 + 3.16294i) q^{67} +(3.37588 - 5.84719i) q^{68} +(-1.56643 - 4.61804i) q^{69} -2.49391 q^{70} +(-5.69119 + 3.28581i) q^{71} +(1.82519 + 2.38090i) q^{72} +(-11.0817 + 6.39801i) q^{73} +(2.27793 - 3.94549i) q^{74} +(-1.69869 - 0.338296i) q^{75} +(3.45706 - 5.98781i) q^{76} +2.01801 q^{77} +(4.24687 - 4.84039i) q^{78} +(-4.86732 - 2.81015i) q^{79} +(0.866025 - 0.500000i) q^{80} +(2.33735 - 8.69119i) q^{81} +(1.60176 + 2.77433i) q^{82} +(6.60136 + 11.4339i) q^{83} +(-4.23638 - 0.843679i) q^{84} +6.75175i q^{85} +(-3.04050 + 5.26630i) q^{86} +(-5.45205 - 16.0733i) q^{87} +(-0.700769 + 0.404589i) q^{88} +7.63447 q^{89} +(-2.77111 - 1.14932i) q^{90} +9.27175i q^{91} -2.81543 q^{92} +(2.61739 + 9.28166i) q^{93} -12.3679 q^{94} +6.91413i q^{95} +(1.64026 - 0.556373i) q^{96} +3.29345 q^{97} +(-0.675869 + 0.390213i) q^{98} +(2.24232 + 0.930006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.556373	−	1.64026i	−0.321222	−	0.947004i
$3$	−0.556373	−	1.64026i	−0.321222	−	0.947004i
$4$	−1.00000			−0.500000
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.64026	−	0.556373i	0.669633	−	0.227138i
$7$	−1.24695	+	2.15979i	−0.471304	+	0.816323i	−0.999461	−	0.0328240i	$-0.989550\pi$
$7$	−1.24695	+	2.15979i	−0.471304	+	0.816323i	0.528157	+	0.849147i	$0.322883\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.38090	+	1.82519i	−0.793633	+	0.608397i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.404589	−	0.700769i	−0.121988	−	0.211290i	0.798563	−	0.601911i	$-0.205594\pi$
$11$	−0.404589	−	0.700769i	−0.121988	−	0.211290i	−0.920552	+	0.390621i	$0.872260\pi$
$12$	0.556373	+	1.64026i	0.160611	+	0.473502i
$13$	3.21968	−	1.85888i	0.892978	−	0.515561i	0.0180623	−	0.999837i	$-0.494250\pi$
$13$	3.21968	−	1.85888i	0.892978	−	0.515561i	0.874915	+	0.484276i	$0.160917\pi$
$14$	−2.15979	−	1.24695i	−0.577227	−	0.333262i
$15$	−1.30196	−	1.14232i	−0.336165	−	0.294946i
$16$	1.00000			0.250000
$17$	−3.37588	+	5.84719i	−0.818770	+	1.41815i	0.0878187	+	0.996136i	$0.472010\pi$
$17$	−3.37588	+	5.84719i	−0.818770	+	1.41815i	−0.906589	+	0.422015i	$0.861323\pi$
$18$	−1.82519	−	2.38090i	−0.430202	−	0.561183i
$19$	−3.45706	+	5.98781i	−0.793105	+	1.37370i	0.130931	+	0.991392i	$0.458203\pi$
$19$	−3.45706	+	5.98781i	−0.793105	+	1.37370i	−0.924036	+	0.382307i	$0.875130\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	4.23638	+	0.843679i	0.924454	+	0.184106i
$22$	0.700769	−	0.404589i	0.149404	−	0.0862587i
$23$	2.81543			0.587059			0.293529	−	0.955950i	$-0.405170\pi$
$23$	2.81543			0.587059			0.293529	+	0.955950i	$0.405170\pi$
$24$	−1.64026	+	0.556373i	−0.334816	+	0.113569i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.85888	+	3.21968i	0.364557	+	0.631431i
$27$	4.31845	+	2.88980i	0.831087	+	0.556143i
$28$	1.24695	−	2.15979i	0.235652	−	0.408161i
$29$	9.79927			1.81968			0.909840	−	0.414960i	$-0.136204\pi$
$29$	9.79927			1.81968			0.909840	+	0.414960i	$0.136204\pi$
$30$	1.14232	−	1.30196i	0.208558	−	0.237705i
$31$	−5.56019	−	0.290293i	−0.998640	−	0.0521381i
$31$	−5.56019	−	0.290293i	−0.998640	−	0.0521381i
$32$			1.00000i			0.176777i
$33$	−0.924340	+	1.05352i	−0.160907	+	0.183394i
$34$	−5.84719	−	3.37588i	−1.00278	−	0.578958i
$35$			2.49391i			0.421547i
$36$	2.38090	−	1.82519i	0.396816	−	0.304199i
$37$	−3.94549	−	2.27793i	−0.648634	−	0.374489i	0.139299	−	0.990250i	$-0.455515\pi$
$37$	−3.94549	−	2.27793i	−0.648634	−	0.374489i	−0.787933	+	0.615761i	$0.788849\pi$
$38$	−5.98781	−	3.45706i	−0.971351	−	0.560810i
$39$	−4.84039	−	4.24687i	−0.775082	−	0.680044i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	2.77433	−	1.60176i	0.433277	−	0.250153i	−0.267465	−	0.963568i	$-0.586186\pi$
$41$	2.77433	−	1.60176i	0.433277	−	0.250153i	0.700742	+	0.713415i	$0.252853\pi$
$42$	−0.843679	+	4.23638i	−0.130183	+	0.653688i
$43$	5.26630	+	3.04050i	0.803103	+	0.463672i	0.844555	−	0.535469i	$-0.179865\pi$
$43$	5.26630	+	3.04050i	0.803103	+	0.463672i	−0.0414520	+	0.999140i	$0.513198\pi$
$44$	0.404589	+	0.700769i	0.0609941	+	0.105645i
$45$	−1.14932	+	2.77111i	−0.171331	+	0.413093i
$46$			2.81543i			0.415113i
$47$			12.3679i			1.80405i	0.431684	+	0.902025i	$0.357920\pi$
$47$			12.3679i			1.80405i	−0.431684	+	0.902025i	$0.642080\pi$
$48$	−0.556373	−	1.64026i	−0.0803055	−	0.236751i
$49$	0.390213	+	0.675869i	0.0557448	+	0.0965528i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	11.4691	+	2.28409i	1.60600	+	0.319837i
$52$	−3.21968	+	1.85888i	−0.446489	+	0.257780i
$53$	4.33368	+	7.50615i	0.595276	+	1.03105i	0.993508	+	0.113764i	$0.0362907\pi$
$53$	4.33368	+	7.50615i	0.595276	+	1.03105i	−0.398232	+	0.917285i	$0.630376\pi$
$54$	−2.88980	+	4.31845i	−0.393252	+	0.587667i
$55$	−0.700769	−	0.404589i	−0.0944916	−	0.0545548i
$56$	2.15979	+	1.24695i	0.288614	+	0.166631i
$57$	11.7450	+	2.33902i	1.55566	+	0.309811i
$58$			9.79927i			1.28671i
$59$	1.80978	+	1.04488i	0.235613	+	0.136031i	0.613159	−	0.789960i	$-0.289899\pi$
$59$	1.80978	+	1.04488i	0.235613	+	0.136031i	−0.377546	+	0.925991i	$0.623232\pi$
$60$	1.30196	+	1.14232i	0.168083	+	0.147473i
$61$		−	1.93145i		−	0.247297i	−0.992326	−	0.123649i	$-0.960540\pi$
$61$		−	1.93145i		−	0.247297i	0.992326	−	0.123649i	$-0.0394595\pi$
$62$	0.290293	−	5.56019i	0.0368672	−	0.706145i
$63$	−0.973156	−	7.41816i	−0.122606	−	0.934601i
$64$	−1.00000			−0.125000
$65$	1.85888	−	3.21968i	0.230566	−	0.399352i
$66$	−1.05352	−	0.924340i	−0.129679	−	0.113778i
$67$	1.82612	+	3.16294i	0.223097	+	0.386415i	0.955747	−	0.294191i	$-0.0950501\pi$
$67$	1.82612	+	3.16294i	0.223097	+	0.386415i	−0.732650	+	0.680605i	$0.761717\pi$
$68$	3.37588	−	5.84719i	0.409385	−	0.709076i
$69$	−1.56643	−	4.61804i	−0.188576	−	0.555947i
$70$	−2.49391			−0.298079
$71$	−5.69119	+	3.28581i	−0.675420	+	0.389954i	−0.798127	−	0.602489i	$-0.794176\pi$
$71$	−5.69119	+	3.28581i	−0.675420	+	0.389954i	0.122707	+	0.992443i	$0.460842\pi$
$72$	1.82519	+	2.38090i	0.215101	+	0.280592i
$73$	−11.0817	+	6.39801i	−1.29701	+	0.748831i	−0.979887	−	0.199553i	$-0.936051\pi$
$73$	−11.0817	+	6.39801i	−1.29701	+	0.748831i	−0.317126	+	0.948384i	$0.602718\pi$
$74$	2.27793	−	3.94549i	0.264804	−	0.458654i
$75$	−1.69869	−	0.338296i	−0.196148	−	0.0390631i
$76$	3.45706	−	5.98781i	0.396552	−	0.686849i
$77$	2.01801			0.229974
$78$	4.24687	−	4.84039i	0.480864	−	0.548066i
$79$	−4.86732	−	2.81015i	−0.547616	−	0.316167i	0.200544	−	0.979685i	$-0.435729\pi$
$79$	−4.86732	−	2.81015i	−0.547616	−	0.316167i	−0.748160	+	0.663518i	$0.769063\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	2.33735	−	8.69119i	0.259706	−	0.965688i
$82$	1.60176	+	2.77433i	0.176885	+	0.306373i
$83$	6.60136	+	11.4339i	0.724594	+	1.25503i	0.959141	+	0.282929i	$0.0913059\pi$
$83$	6.60136	+	11.4339i	0.724594	+	1.25503i	−0.234547	+	0.972105i	$0.575361\pi$
$84$	−4.23638	−	0.843679i	−0.462227	−	0.0920530i
$85$			6.75175i			0.732330i
$86$	−3.04050	+	5.26630i	−0.327865	+	0.567880i
$87$	−5.45205	−	16.0733i	−0.584521	−	1.72324i
$88$	−0.700769	+	0.404589i	−0.0747022	+	0.0431293i
$89$	7.63447			0.809252			0.404626	−	0.914482i	$-0.367402\pi$
$89$	7.63447			0.809252			0.404626	+	0.914482i	$0.367402\pi$
$90$	−2.77111	−	1.14932i	−0.292101	−	0.121149i
$91$			9.27175i			0.971944i
$92$	−2.81543			−0.293529
$93$	2.61739	+	9.28166i	0.271410	+	0.962464i
$94$	−12.3679			−1.27566
$95$			6.91413i			0.709375i
$96$	1.64026	−	0.556373i	0.167408	−	0.0567846i
$97$	3.29345			0.334399			0.167199	−	0.985923i	$-0.446528\pi$
$97$	3.29345			0.334399			0.167199	+	0.985923i	$0.446528\pi$
$98$	−0.675869	+	0.390213i	−0.0682731	+	0.0394175i
$99$	2.24232	+	0.930006i	0.225362	+	0.0934692i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$		−	2.54099i		−	0.252838i	−0.991977	−	0.126419i	$-0.959652\pi$
$101$		−	2.54099i		−	0.252838i	0.991977	−	0.126419i	$-0.0403484\pi$
$102$	−2.28409	+	11.4691i	−0.226159	+	1.13561i
$103$	−3.25687	−	5.64107i	−0.320909	−	0.555831i	0.659767	−	0.751471i	$-0.270655\pi$
$103$	−3.25687	−	5.64107i	−0.320909	−	0.555831i	−0.980676	+	0.195639i	$0.937322\pi$
$104$	−1.85888	−	3.21968i	−0.182278	−	0.315715i
$105$	4.09065	−	1.38754i	0.399207	−	0.135410i
$106$	−7.50615	+	4.33368i	−0.729061	+	0.420924i
$107$	1.33464	+	0.770553i	0.129024	+	0.0744921i	0.563123	−	0.826373i	$-0.309600\pi$
$107$	1.33464	+	0.770553i	0.129024	+	0.0744921i	−0.434099	+	0.900865i	$0.642933\pi$
$108$	−4.31845	−	2.88980i	−0.415543	−	0.278071i
$109$	−19.5290			−1.87054			−0.935271	−	0.353932i	$-0.884844\pi$
$109$	−19.5290			−1.87054			−0.935271	+	0.353932i	$0.884844\pi$
$110$	0.404589	−	0.700769i	0.0385760	−	0.0668157i
$111$	−1.54123	+	7.73900i	−0.146287	+	0.734553i
$112$	−1.24695	+	2.15979i	−0.117826	+	0.204081i
$113$	6.23706	−	3.60097i	0.586733	−	0.338750i	−0.177072	−	0.984198i	$-0.556662\pi$
$113$	6.23706	−	3.60097i	0.586733	−	0.338750i	0.763805	+	0.645448i	$0.223329\pi$
$114$	−2.33902	+	11.7450i	−0.219070	+	1.10002i
$115$	2.43824	−	1.40772i	0.227367	−	0.131270i
$116$	−9.79927			−0.909840
$117$	−4.27291	+	10.3023i	−0.395030	+	0.952451i
$118$	−1.04488	+	1.80978i	−0.0961886	+	0.166604i
$119$	−8.41912	−	14.5823i	−0.771780	−	1.33676i
$120$	−1.14232	+	1.30196i	−0.104279	+	0.118852i
$121$	5.17262	−	8.95923i	0.470238	−	0.814476i
$122$	1.93145			0.174865
$123$	−4.17086	−	3.65944i	−0.376074	−	0.329960i
$124$	5.56019	+	0.290293i	0.499320	+	0.0260691i
$125$		−	1.00000i		−	0.0894427i
$126$	7.41816	−	0.973156i	0.660862	−	0.0866956i
$127$	−7.97677	−	4.60539i	−0.707823	−	0.408662i	0.102431	−	0.994740i	$-0.467338\pi$
$127$	−7.97677	−	4.60539i	−0.707823	−	0.408662i	−0.810255	+	0.586078i	$0.800671\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.05718	−	10.3297i	0.181124	−	0.909483i
$130$	3.21968	+	1.85888i	0.282384	+	0.163035i
$131$	−13.9591	−	8.05927i	−1.21961	−	0.704142i	−0.254775	−	0.967000i	$-0.582001\pi$
$131$	−13.9591	−	8.05927i	−1.21961	−	0.704142i	−0.964834	+	0.262859i	$0.915335\pi$
$132$	0.924340	−	1.05352i	0.0804534	−	0.0916971i
$133$	−8.62160	−	14.9330i	−0.747587	−	1.29486i
$134$	−3.16294	+	1.82612i	−0.273236	+	0.157753i
$135$	5.18479	+	0.343414i	0.446236	+	0.0295564i
$136$	5.84719	+	3.37588i	0.501392	+	0.289479i
$137$	3.38204	+	5.85786i	0.288947	+	0.500471i	0.973559	−	0.228437i	$-0.0733615\pi$
$137$	3.38204	+	5.85786i	0.288947	+	0.500471i	−0.684612	+	0.728908i	$0.740028\pi$
$138$	4.61804	−	1.56643i	0.393114	−	0.133344i
$139$		−	2.92120i		−	0.247773i	−0.992296	−	0.123887i	$-0.960464\pi$
$139$		−	2.92120i		−	0.247773i	0.992296	−	0.123887i	$-0.0395359\pi$
$140$		−	2.49391i		−	0.210774i
$141$	20.2866	−	6.88119i	1.70844	−	0.579501i
$142$	−3.28581	−	5.69119i	−0.275739	−	0.477594i
$143$	−2.60529	−	1.50417i	−0.217865	−	0.125785i
$144$	−2.38090	+	1.82519i	−0.198408	+	0.152099i
$145$	8.48642	−	4.89964i	0.704759	−	0.406893i
$146$	−6.39801	−	11.0817i	−0.529503	−	0.917126i
$147$	0.891496	−	1.01609i	0.0735294	−	0.0838054i
$148$	3.94549	+	2.27793i	0.324317	+	0.187245i
$149$	−9.25026	−	5.34064i	−0.757811	−	0.437522i	0.0706982	−	0.997498i	$-0.477477\pi$
$149$	−9.25026	−	5.34064i	−0.757811	−	0.437522i	−0.828509	+	0.559975i	$0.810811\pi$
$150$	0.338296	−	1.69869i	0.0276218	−	0.138698i
$151$		−	8.63402i		−	0.702626i	−0.936258	−	0.351313i	$-0.885735\pi$
$151$		−	8.63402i		−	0.702626i	0.936258	−	0.351313i	$-0.114265\pi$
$152$	5.98781	+	3.45706i	0.485676	+	0.280405i
$153$	−2.63462	−	20.0832i	−0.212997	−	1.62363i
$154$			2.01801i			0.162616i
$155$	−4.96041	+	2.52869i	−0.398430	+	0.203110i
$156$	4.84039	+	4.24687i	0.387541	+	0.340022i
$157$	14.3655			1.14649			0.573245	−	0.819384i	$-0.305684\pi$
$157$	14.3655			1.14649			0.573245	+	0.819384i	$0.305684\pi$
$158$	2.81015	−	4.86732i	0.223563	−	0.387223i
$159$	9.90088	−	11.2846i	0.785191	−	0.894924i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−3.51072	+	6.08074i	−0.276683	+	0.479229i
$162$	8.69119	+	2.33735i	0.682844	+	0.183640i
$163$	−12.7393			−0.997819			−0.498909	−	0.866654i	$-0.666266\pi$
$163$	−12.7393			−0.997819			−0.498909	+	0.866654i	$0.666266\pi$
$164$	−2.77433	+	1.60176i	−0.216638	+	0.125076i
$165$	−0.273742	+	1.37454i	−0.0213108	+	0.107008i
$166$	−11.4339	+	6.60136i	−0.887443	+	0.512365i
$167$	−8.45705	+	14.6480i	−0.654426	+	1.13350i	0.327612	+	0.944813i	$0.393756\pi$
$167$	−8.45705	+	14.6480i	−0.654426	+	1.13350i	−0.982037	+	0.188686i	$0.939577\pi$
$168$	0.843679	−	4.23638i	0.0650913	−	0.326844i
$169$	0.410878	−	0.711662i	0.0316060	−	0.0547433i
$170$	−6.75175			−0.517836
$171$	−2.69799	−	20.5662i	−0.206320	−	1.57273i
$172$	−5.26630	−	3.04050i	−0.401552	−	0.231836i
$173$	3.02710	−	1.74770i	0.230146	−	0.132875i	−0.380493	−	0.924784i	$-0.624246\pi$
$173$	3.02710	−	1.74770i	0.230146	−	0.132875i	0.610639	+	0.791909i	$0.290912\pi$
$174$	16.0733	−	5.45205i	1.21852	−	0.413319i
$175$	1.24695	+	2.15979i	0.0942608	+	0.163265i
$176$	−0.404589	−	0.700769i	−0.0304970	−	0.0528224i
$177$	0.706955	−	3.54984i	0.0531380	−	0.266823i
$178$			7.63447i			0.572228i
$179$	8.22638	−	14.2485i	0.614869	−	1.06498i	−0.375539	−	0.926807i	$-0.622542\pi$
$179$	8.22638	−	14.2485i	0.614869	−	1.06498i	0.990408	−	0.138177i	$-0.0441244\pi$
$180$	1.14932	−	2.77111i	0.0856654	−	0.206546i
$181$	21.2577	−	12.2731i	1.58007	−	0.912256i	0.585226	−	0.810870i	$-0.301006\pi$
$181$	21.2577	−	12.2731i	1.58007	−	0.912256i	0.994847	−	0.101386i	$-0.0323277\pi$
$182$	−9.27175			−0.687268
$183$	−3.16808	+	1.07461i	−0.234191	+	0.0794373i
$184$		−	2.81543i		−	0.207557i
$185$	−4.55586			−0.334953
$186$	−9.28166	+	2.61739i	−0.680565	+	0.191916i
$187$	5.46337			0.399521
$188$		−	12.3679i		−	0.902025i
$189$	−11.6263	+	5.72349i	−0.845687	+	0.416323i
$190$	−6.91413			−0.501604
$191$	14.7094	−	8.49247i	1.06433	−	0.614493i	0.137706	−	0.990473i	$-0.456027\pi$
$191$	14.7094	−	8.49247i	1.06433	−	0.614493i	0.926628	+	0.375980i	$0.122694\pi$
$192$	0.556373	+	1.64026i	0.0401528	+	0.118375i
$193$	−2.03343	+	3.52201i	−0.146370	+	0.253520i	−0.929883	−	0.367855i	$-0.880092\pi$
$193$	−2.03343	+	3.52201i	−0.146370	+	0.253520i	0.783513	+	0.621375i	$0.213426\pi$
$194$			3.29345i			0.236456i
$195$	−6.31533	−	1.25770i	−0.452250	−	0.0900661i
$196$	−0.390213	−	0.675869i	−0.0278724	−	0.0482764i
$197$	−9.54331	−	16.5295i	−0.679933	−	1.17768i	−0.975001	−	0.222202i	$-0.928676\pi$
$197$	−9.54331	−	16.5295i	−0.679933	−	1.17768i	0.295068	−	0.955476i	$-0.404658\pi$
$198$	−0.930006	+	2.24232i	−0.0660927	+	0.159355i
$199$	−8.46400	+	4.88669i	−0.599997	+	0.346409i	−0.769041	−	0.639200i	$-0.779266\pi$
$199$	−8.46400	+	4.88669i	−0.599997	+	0.346409i	0.169043	+	0.985609i	$0.445932\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	4.17203	−	4.75509i	0.294273	−	0.335398i
$202$	2.54099			0.178784
$203$	−12.2192	+	21.1643i	−0.857623	+	1.48545i
$204$	−11.4691	−	2.28409i	−0.803001	−	0.159918i
$205$	1.60176	−	2.77433i	0.111872	−	0.193767i
$206$	5.64107	−	3.25687i	0.393032	−	0.226917i
$207$	−6.70326	+	5.13871i	−0.465909	+	0.357165i
$208$	3.21968	−	1.85888i	0.223244	−	0.128890i
$209$	5.59476			0.386998
$210$	1.38754	+	4.09065i	0.0957496	+	0.282282i
$211$	−10.1995	+	17.6661i	−0.702163	+	1.21618i	0.265543	+	0.964099i	$0.414449\pi$
$211$	−10.1995	+	17.6661i	−0.702163	+	1.21618i	−0.967706	+	0.252083i	$0.918885\pi$
$212$	−4.33368	−	7.50615i	−0.297638	−	0.515524i
$213$	8.55601	+	7.50689i	0.586248	+	0.514364i
$214$	−0.770553	+	1.33464i	−0.0526739	+	0.0912339i
$215$	6.08100			0.414721
$216$	2.88980	−	4.31845i	0.196626	−	0.293834i
$217$	7.56027	−	11.6468i	0.513225	−	0.790640i
$218$		−	19.5290i		−	1.32267i
$219$	16.6599	+	14.6171i	1.12577	+	0.987735i
$220$	0.700769	+	0.404589i	0.0472458	+	0.0272774i
$221$			25.1014i			1.68850i
$222$	−7.73900	−	1.54123i	−0.519408	−	0.103441i
$223$	17.4442	+	10.0714i	1.16815	+	0.674431i	0.953243	−	0.302204i	$-0.0977223\pi$
$223$	17.4442	+	10.0714i	1.16815	+	0.674431i	0.214905	+	0.976635i	$0.431056\pi$
$224$	−2.15979	−	1.24695i	−0.144307	−	0.0833156i
$225$	0.390213	+	2.97451i	0.0260142	+	0.198301i
$226$	3.60097	+	6.23706i	0.239533	+	0.414883i
$227$	18.9901	−	10.9640i	1.26042	−	0.727704i	0.287264	−	0.957851i	$-0.407254\pi$
$227$	18.9901	−	10.9640i	1.26042	−	0.727704i	0.973156	+	0.230148i	$0.0739209\pi$
$228$	−11.7450	−	2.33902i	−0.777830	−	0.154906i
$229$	19.5144	+	11.2666i	1.28955	+	0.744519i	0.978573	−	0.205900i	$-0.0660121\pi$
$229$	19.5144	+	11.2666i	1.28955	+	0.744519i	0.310972	+	0.950419i	$0.399345\pi$
$230$	1.40772	+	2.43824i	0.0928221	+	0.160773i
$231$	−1.12277	−	3.31007i	−0.0738728	−	0.217786i
$232$		−	9.79927i		−	0.643354i
$233$			12.3700i			0.810388i	0.914231	+	0.405194i	$0.132796\pi$
$233$			12.3700i			0.810388i	−0.914231	+	0.405194i	$0.867204\pi$
$234$	−10.3023	−	4.27291i	−0.673485	−	0.279329i
$235$	6.18397	+	10.7110i	0.403398	+	0.698706i
$236$	−1.80978	−	1.04488i	−0.117806	−	0.0680156i
$237$	−1.90133	+	9.54716i	−0.123504	+	0.620155i
$238$	14.5823	−	8.41912i	0.945233	−	0.545731i
$239$	−7.84359	−	13.5855i	−0.507360	−	0.878773i	−0.999964	−	0.00851907i	$-0.997288\pi$
$239$	−7.84359	−	13.5855i	−0.507360	−	0.878773i	0.492604	−	0.870254i	$-0.336045\pi$
$240$	−1.30196	−	1.14232i	−0.0840413	−	0.0737364i
$241$	−16.0118	−	9.24439i	−1.03141	−	0.595484i	−0.114020	−	0.993478i	$-0.536373\pi$
$241$	−16.0118	−	9.24439i	−1.03141	−	0.595484i	−0.917388	+	0.397995i	$0.869706\pi$
$242$	8.95923	+	5.17262i	0.575921	+	0.332508i
$243$	−15.5562	+	1.00168i	−0.997933	+	0.0642581i
$244$			1.93145i			0.123649i
$245$	0.675869	+	0.390213i	0.0431797	+	0.0249298i
$246$	3.65944	−	4.17086i	0.233317	−	0.265924i
$247$			25.7051i			1.63558i
$248$	−0.290293	+	5.56019i	−0.0184336	+	0.353073i
$249$	15.0817	−	17.1895i	0.955766	−	1.08934i
$250$	1.00000			0.0632456
$251$	−9.51130	+	16.4741i	−0.600348	+	1.03983i	0.392420	+	0.919786i	$0.371638\pi$
$251$	−9.51130	+	16.4741i	−0.600348	+	1.03983i	−0.992768	+	0.120047i	$0.961695\pi$
$252$	0.973156	+	7.41816i	0.0613031	+	0.467300i
$253$	−1.13909	−	1.97297i	−0.0716142	−	0.124039i
$254$	4.60539	−	7.97677i	0.288968	−	0.500507i
$255$	11.0746	−	3.75649i	0.693520	−	0.235241i
$256$	1.00000			0.0625000
$257$	5.42996	−	3.13499i	0.338712	−	0.195555i	−0.320991	−	0.947082i	$-0.604016\pi$
$257$	5.42996	−	3.13499i	0.338712	−	0.195555i	0.659702	+	0.751527i	$0.270682\pi$
$258$	10.3297	+	2.05718i	0.643102	+	0.128074i
$259$	9.83968	−	5.68094i	0.611408	−	0.352997i
$260$	−1.85888	+	3.21968i	−0.115283	+	0.199676i
$261$	−23.3311	+	17.8856i	−1.44416	+	1.10709i
$262$	8.05927	−	13.9591i	0.497903	−	0.862394i
$263$	−20.0171			−1.23431			−0.617154	−	0.786842i	$-0.711714\pi$
$263$	−20.0171			−1.23431			−0.617154	+	0.786842i	$0.711714\pi$
$264$	1.05352	+	0.924340i	0.0648396	+	0.0568892i
$265$	7.50615	+	4.33368i	0.461099	+	0.266216i
$266$	14.9330	−	8.62160i	0.915604	−	0.528624i
$267$	−4.24761	−	12.5225i	−0.259950	−	0.766365i
$268$	−1.82612	−	3.16294i	−0.111548	−	0.193207i
$269$	9.59437	+	16.6179i	0.584979	+	1.01321i	0.994878	+	0.101082i	$0.0322306\pi$
$269$	9.59437	+	16.6179i	0.584979	+	1.01321i	−0.409899	+	0.912131i	$0.634436\pi$
$270$	−0.343414	+	5.18479i	−0.0208995	+	0.315536i
$271$		−	28.6405i		−	1.73979i	−0.493238	−	0.869895i	$-0.664187\pi$
$271$		−	28.6405i		−	1.73979i	0.493238	−	0.869895i	$-0.335813\pi$
$272$	−3.37588	+	5.84719i	−0.204693	+	0.354538i
$273$	15.2081	−	5.15855i	0.920435	−	0.312210i
$274$	−5.85786	+	3.38204i	−0.353886	+	0.204316i
$275$	−0.809178			−0.0487953
$276$	1.56643	+	4.61804i	0.0942881	+	0.277973i
$277$		−	8.82263i		−	0.530101i	−0.964235	−	0.265050i	$-0.914611\pi$
$277$		−	8.82263i		−	0.530101i	0.964235	−	0.265050i	$-0.0853886\pi$
$278$	2.92120			0.175202
$279$	13.7681	−	9.45726i	0.824274	−	0.566191i
$280$	2.49391			0.149039
$281$		−	19.8789i		−	1.18587i	−0.805249	−	0.592937i	$-0.797968\pi$
$281$		−	19.8789i		−	1.18587i	0.805249	−	0.592937i	$-0.202032\pi$
$282$	6.88119	+	20.2866i	0.409769	+	1.20805i
$283$	−9.93823			−0.590766			−0.295383	−	0.955379i	$-0.595447\pi$
$283$	−9.93823			−0.590766			−0.295383	+	0.955379i	$0.595447\pi$
$284$	5.69119	−	3.28581i	0.337710	−	0.194977i
$285$	11.3410	−	3.84683i	0.671781	−	0.227867i
$286$	1.50417	−	2.60529i	0.0889432	−	0.154054i
$287$			7.98927i			0.471592i
$288$	−1.82519	−	2.38090i	−0.107550	−	0.140296i
$289$	−14.2931	−	24.7563i	−0.840769	−	1.45625i
$290$	4.89964	+	8.48642i	0.287717	+	0.498340i
$291$	−1.83239	−	5.40211i	−0.107416	−	0.316677i
$292$	11.0817	−	6.39801i	0.648506	−	0.374415i
$293$	9.24636	+	5.33839i	0.540178	+	0.311872i	0.745151	−	0.666896i	$-0.232377\pi$
$293$	9.24636	+	5.33839i	0.540178	+	0.311872i	−0.204973	+	0.978768i	$0.565711\pi$
$294$	1.01609	+	0.891496i	0.0592594	+	0.0519931i
$295$	2.08975			0.121670
$296$	−2.27793	+	3.94549i	−0.132402	+	0.229327i
$297$	0.277883	−	4.19542i	0.0161244	−	0.243443i
$298$	5.34064	−	9.25026i	0.309375	−	0.535853i
$299$	9.06479	−	5.23356i	0.524230	−	0.302664i
$300$	1.69869	+	0.338296i	0.0980740	+	0.0195315i
$301$	−13.1337	+	7.58272i	−0.757012	+	0.437061i
$302$	8.63402			0.496832
$303$	−4.16788	+	1.41374i	−0.239439	+	0.0812172i
$304$	−3.45706	+	5.98781i	−0.198276	+	0.343425i
$305$	−0.965726	−	1.67269i	−0.0552973	−	0.0957777i
$306$	20.0832	−	2.63462i	1.14808	−	0.150611i
$307$	−13.6740	+	23.6841i	−0.780417	+	1.35172i	0.151282	+	0.988491i	$0.451660\pi$
$307$	−13.6740	+	23.6841i	−0.780417	+	1.35172i	−0.931699	+	0.363231i	$0.881673\pi$
$308$	−2.01801			−0.114987
$309$	−7.44078	+	8.48065i	−0.423291	+	0.482448i
$310$	−2.52869	−	4.96041i	−0.143620	−	0.281733i
$311$			21.7180i			1.23151i	0.787936	+	0.615757i	$0.211150\pi$
$311$			21.7180i			1.23151i	−0.787936	+	0.615757i	$0.788850\pi$
$312$	−4.24687	+	4.84039i	−0.240432	+	0.274033i
$313$	−4.42410	−	2.55426i	−0.250065	−	0.144375i	0.369729	−	0.929140i	$-0.379451\pi$
$313$	−4.42410	−	2.55426i	−0.250065	−	0.144375i	−0.619794	+	0.784765i	$0.712784\pi$
$314$			14.3655i			0.810691i
$315$	−4.55186	−	5.93774i	−0.256468	−	0.334554i
$316$	4.86732	+	2.81015i	0.273808	+	0.158083i
$317$	−6.74277	−	3.89294i	−0.378711	−	0.218649i	0.298546	−	0.954395i	$-0.403498\pi$
$317$	−6.74277	−	3.89294i	−0.378711	−	0.218649i	−0.677257	+	0.735746i	$0.736832\pi$
$318$	11.2846	+	9.90088i	0.632807	+	0.555214i
$319$	−3.96468	−	6.86702i	−0.221979	−	0.384480i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	0.521350	−	2.61786i	0.0290989	−	0.146115i
$322$	−6.08074	−	3.51072i	−0.338866	−	0.195645i
$323$	−23.3412	−	40.4282i	−1.29874	−	2.24949i
$324$	−2.33735	+	8.69119i	−0.129853	+	0.482844i
$325$		−	3.71776i		−	0.206224i
$326$		−	12.7393i		−	0.705564i
$327$	10.8654	+	32.0327i	0.600860	+	1.77141i
$328$	−1.60176	−	2.77433i	−0.0884423	−	0.153187i
$329$	−26.7121	−	15.4223i	−1.47269	−	0.850256i
$330$	−1.37454	−	0.273742i	−0.0756662	−	0.0150690i
$331$	−23.6410	+	13.6491i	−1.29943	+	0.750224i	−0.980305	−	0.197490i	$-0.936721\pi$
$331$	−23.6410	+	13.6491i	−1.29943	+	0.750224i	−0.319121	+	0.947714i	$0.603388\pi$
$332$	−6.60136	−	11.4339i	−0.362297	−	0.627517i
$333$	13.5515	−	1.77776i	0.742615	−	0.0974204i
$334$	−14.6480	−	8.45705i	−0.801505	−	0.462749i
$335$	3.16294	+	1.82612i	0.172810	+	0.0997718i
$336$	4.23638	+	0.843679i	0.231114	+	0.0460265i
$337$			25.5446i			1.39150i	0.718282	+	0.695752i	$0.244929\pi$
$337$			25.5446i			1.39150i	−0.718282	+	0.695752i	$0.755071\pi$
$338$	0.711662	+	0.410878i	0.0387093	+	0.0223488i
$339$	−9.37665	−	8.22691i	−0.509270	−	0.446824i
$340$		−	6.75175i		−	0.366165i
$341$	2.04616	+	4.01386i	0.110806	+	0.217363i
$342$	20.5662	−	2.69799i	1.11209	−	0.145890i
$343$	−19.4037			−1.04770
$344$	3.04050	−	5.26630i	0.163933	−	0.283940i
$345$	−3.66559	−	3.21613i	−0.197349	−	0.173150i
$346$	1.74770	+	3.02710i	0.0939567	+	0.162738i
$347$	−2.48436	+	4.30303i	−0.133367	+	0.230999i	−0.924973	−	0.380034i	$-0.875912\pi$
$347$	−2.48436	+	4.30303i	−0.133367	+	0.230999i	0.791605	+	0.611033i	$0.209246\pi$
$348$	5.45205	+	16.0733i	0.292261	+	0.861622i
$349$	17.2065			0.921042			0.460521	−	0.887649i	$-0.347663\pi$
$349$	17.2065			0.921042			0.460521	+	0.887649i	$0.347663\pi$
$350$	−2.15979	+	1.24695i	−0.115445	+	0.0666525i
$351$	19.2758	+	1.27673i	1.02887	+	0.0681470i
$352$	0.700769	−	0.404589i	0.0373511	−	0.0215647i
$353$	3.34940	−	5.80134i	0.178271	−	0.308774i	−0.763018	−	0.646378i	$-0.776283\pi$
$353$	3.34940	−	5.80134i	0.178271	−	0.308774i	0.941288	+	0.337604i	$0.109616\pi$
$354$	3.54984	+	0.706955i	0.188672	+	0.0375742i
$355$	−3.28581	+	5.69119i	−0.174393	+	0.302057i
$356$	−7.63447			−0.404626
$357$	−19.2346	+	21.9228i	−1.01801	+	1.16028i
$358$	14.2485	+	8.22638i	0.753057	+	0.434778i
$359$	29.2825	−	16.9062i	1.54547	−	0.892277i	0.546990	−	0.837139i	$-0.315774\pi$
$359$	29.2825	−	16.9062i	1.54547	−	0.892277i	0.998479	−	0.0551375i	$-0.0175597\pi$
$360$	2.77111	+	1.14932i	0.146050	+	0.0605746i
$361$	−14.4026	−	24.9460i	−0.758031	−	1.31295i
$362$	12.2731	+	21.2577i	0.645062	+	1.11728i
$363$	−17.5734	−	3.49975i	−0.922362	−	0.183689i
$364$		−	9.27175i		−	0.485972i
$365$	−6.39801	+	11.0817i	−0.334887	+	0.580042i
$366$	−1.07461	−	3.16808i	−0.0561706	−	0.165598i
$367$	20.9805	−	12.1131i	1.09517	−	0.632297i	0.160223	−	0.987081i	$-0.448779\pi$
$367$	20.9805	−	12.1131i	1.09517	−	0.632297i	0.934948	+	0.354784i	$0.115445\pi$
$368$	2.81543			0.146765
$369$	−3.68187	+	8.87730i	−0.191671	+	0.462134i
$370$		−	4.55586i		−	0.236848i
$371$	−21.6156			−1.12222
$372$	−2.61739	−	9.28166i	−0.135705	−	0.481232i
$373$	32.0372			1.65882			0.829410	−	0.558640i	$-0.188677\pi$
$373$	32.0372			1.65882			0.829410	+	0.558640i	$0.188677\pi$
$374$			5.46337i			0.282504i
$375$	−1.64026	+	0.556373i	−0.0847026	+	0.0287310i
$376$	12.3679			0.637828
$377$	31.5505	−	18.2157i	1.62493	−	0.938156i
$378$	−5.72349	−	11.6263i	−0.294385	−	0.597991i
$379$	7.80196	−	13.5134i	0.400760	−	0.694137i	−0.593058	−	0.805160i	$-0.702079\pi$
$379$	7.80196	−	13.5134i	0.400760	−	0.694137i	0.993818	+	0.111023i	$0.0354128\pi$
$380$		−	6.91413i		−	0.354687i
$381$	−3.11597	+	15.6463i	−0.159636	+	0.801583i
$382$	8.49247	+	14.7094i	0.434512	+	0.752598i
$383$	1.73505	+	3.00520i	0.0886570	+	0.153558i	0.906944	−	0.421252i	$-0.138409\pi$
$383$	1.73505	+	3.00520i	0.0886570	+	0.153558i	−0.818287	+	0.574810i	$0.805076\pi$
$384$	−1.64026	+	0.556373i	−0.0837041	+	0.0283923i
$385$	1.74765	−	1.00901i	0.0890686	−	0.0514238i
$386$	−3.52201	−	2.03343i	−0.179266	−	0.103499i
$387$	−18.0880	+	2.37289i	−0.919466	+	0.120621i
$388$	−3.29345			−0.167199
$389$	6.03620	−	10.4550i	0.306048	−	0.530090i	−0.671446	−	0.741053i	$-0.734327\pi$
$389$	6.03620	−	10.4550i	0.306048	−	0.530090i	0.977494	+	0.210963i	$0.0676600\pi$
$390$	1.25770	−	6.31533i	0.0636864	−	0.319789i
$391$	−9.50456	+	16.4624i	−0.480666	+	0.832538i
$392$	0.675869	−	0.390213i	0.0341366	−	0.0197088i
$393$	−5.45284	+	27.3804i	−0.275059	+	1.38116i
$394$	16.5295	−	9.54331i	0.832744	−	0.480785i
$395$	−5.62030			−0.282788
$396$	−2.24232	−	0.930006i	−0.112681	−	0.0467346i
$397$	−0.279618	+	0.484313i	−0.0140336	+	0.0243070i	−0.872957	−	0.487797i	$-0.837801\pi$
$397$	−0.279618	+	0.484313i	−0.0140336	+	0.0243070i	0.858923	+	0.512104i	$0.171134\pi$
$398$	−4.88669	−	8.46400i	−0.244948	−	0.424262i
$399$	−19.6972	+	22.4500i	−0.986095	+	1.12391i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−21.0608			−1.05172			−0.525862	−	0.850570i	$-0.676257\pi$
$401$	−21.0608			−1.05172			−0.525862	+	0.850570i	$0.676257\pi$
$402$	4.75509	+	4.17203i	0.237162	+	0.208082i
$403$	−18.4416	+	9.40109i	−0.918643	+	0.468301i
$404$			2.54099i			0.126419i
$405$	−2.32139	−	8.69547i	−0.115351	−	0.432081i
$406$	−21.1643	−	12.2192i	−1.05037	−	0.606431i
$407$			3.68650i			0.182733i
$408$	2.28409	−	11.4691i	0.113079	−	0.567807i
$409$	2.71573	+	1.56793i	0.134284	+	0.0775292i	0.565637	−	0.824654i	$-0.308630\pi$
$409$	2.71573	+	1.56793i	0.134284	+	0.0775292i	−0.431353	+	0.902183i	$0.641964\pi$
$410$	2.77433	+	1.60176i	0.137014	+	0.0791052i
$411$	7.72673	−	8.80657i	0.381132	−	0.434396i
$412$	3.25687	+	5.64107i	0.160455	+	0.277916i
$413$	−4.51342	+	2.60582i	−0.222091	+	0.128224i
$414$	−5.13871	−	6.70326i	−0.252554	−	0.329447i
$415$	11.4339	+	6.60136i	0.561268	+	0.324048i
$416$	1.85888	+	3.21968i	0.0911391	+	0.157858i
$417$	−4.79153	+	1.62528i	−0.234642	+	0.0795902i
$418$			5.59476i			0.273649i
$419$		−	23.5226i		−	1.14915i	−0.818451	−	0.574577i	$-0.805167\pi$
$419$		−	23.5226i		−	1.14915i	0.818451	−	0.574577i	$-0.194833\pi$
$420$	−4.09065	+	1.38754i	−0.199603	+	0.0677052i
$421$	1.03198	+	1.78744i	0.0502956	+	0.0871146i	0.890077	−	0.455810i	$-0.150650\pi$
$421$	1.03198	+	1.78744i	0.0502956	+	0.0871146i	−0.839782	+	0.542924i	$0.817317\pi$
$422$	−17.6661	−	10.1995i	−0.859970	−	0.496504i
$423$	−22.5739	−	29.4468i	−1.09758	−	1.43175i
$424$	7.50615	−	4.33368i	0.364531	−	0.210462i
$425$	3.37588	+	5.84719i	0.163754	+	0.283630i
$426$	−7.50689	+	8.55601i	−0.363710	+	0.414540i
$427$	4.17152	+	2.40843i	0.201874	+	0.116552i
$428$	−1.33464	−	0.770553i	−0.0645121	−	0.0372461i
$429$	−1.01771	+	5.11023i	−0.0491354	+	0.246724i
$430$			6.08100i			0.293252i
$431$	18.5818	+	10.7282i	0.895055	+	0.516760i	0.875592	−	0.483051i	$-0.160471\pi$
$431$	18.5818	+	10.7282i	0.895055	+	0.516760i	0.0194621	+	0.999811i	$0.493805\pi$
$432$	4.31845	+	2.88980i	0.207772	+	0.139036i
$433$			19.3965i			0.932135i	0.884749	+	0.466067i	$0.154330\pi$
$433$			19.3965i			0.932135i	−0.884749	+	0.466067i	$0.845670\pi$
$434$	11.6468	+	7.56027i	0.559067	+	0.362905i
$435$	−12.7583	−	11.1939i	−0.611713	−	0.536706i
$436$	19.5290			0.935271
$437$	−9.73314	+	16.8583i	−0.465599	+	0.806441i
$438$	−14.6171	+	16.6599i	−0.698434	+	0.796043i
$439$	6.34860	+	10.9961i	0.303002	+	0.524815i	0.976815	−	0.214087i	$-0.0686777\pi$
$439$	6.34860	+	10.9961i	0.303002	+	0.524815i	−0.673812	+	0.738903i	$0.735344\pi$
$440$	−0.404589	+	0.700769i	−0.0192880	+	0.0334078i
$441$	−2.16265	−	0.896962i	−0.102983	−	0.0427125i
$442$	−25.1014			−1.19395
$443$	13.0921	−	7.55872i	0.622024	−	0.359126i	−0.155633	−	0.987815i	$-0.549742\pi$
$443$	13.0921	−	7.55872i	0.622024	−	0.359126i	0.777657	+	0.628689i	$0.216408\pi$
$444$	1.54123	−	7.73900i	0.0731435	−	0.367277i
$445$	6.61164	−	3.81723i	0.313422	−	0.180954i
$446$	−10.0714	+	17.4442i	−0.476895	+	0.826006i
$447$	−3.61344	+	18.1442i	−0.170910	+	0.858192i
$448$	1.24695	−	2.15979i	0.0589130	−	0.102040i
$449$	−15.6070			−0.736538			−0.368269	−	0.929719i	$-0.620049\pi$
$449$	−15.6070			−0.736538			−0.368269	+	0.929719i	$0.620049\pi$
$450$	−2.97451	+	0.390213i	−0.140220	+	0.0183948i
$451$	−2.24492	−	1.29611i	−0.105709	−	0.0610313i
$452$	−6.23706	+	3.60097i	−0.293366	+	0.169375i
$453$	−14.1620	+	4.80373i	−0.665390	+	0.225699i
$454$	10.9640	+	18.9901i	0.514564	+	0.891251i
$455$	4.63588	+	8.02957i	0.217333	+	0.376432i
$456$	2.33902	−	11.7450i	0.109535	−	0.550009i
$457$			7.87077i			0.368179i	0.982909	+	0.184089i	$0.0589336\pi$
$457$			7.87077i			0.368179i	−0.982909	+	0.184089i	$0.941066\pi$
$458$	−11.2666	+	19.5144i	−0.526455	+	0.911846i
$459$	−31.4758	+	15.4952i	−1.46916	+	0.723254i
$460$	−2.43824	+	1.40772i	−0.113683	+	0.0656352i
$461$	5.49791			0.256063			0.128032	−	0.991770i	$-0.459134\pi$
$461$	5.49791			0.256063			0.128032	+	0.991770i	$0.459134\pi$
$462$	3.31007	−	1.12277i	0.153998	−	0.0522359i
$463$			25.9653i			1.20671i	0.797473	+	0.603354i	$0.206170\pi$
$463$			25.9653i			1.20671i	−0.797473	+	0.603354i	$0.793830\pi$
$464$	9.79927			0.454920
$465$	6.90755	+	6.72946i	0.320330	+	0.312071i
$466$	−12.3700			−0.573031
$467$			8.76334i			0.405519i	0.979229	+	0.202760i	$0.0649910\pi$
$467$			8.76334i			0.405519i	−0.979229	+	0.202760i	$0.935009\pi$
$468$	4.27291	−	10.3023i	0.197515	−	0.476226i
$469$	−9.10837			−0.420585
$470$	−10.7110	+	6.18397i	−0.494059	+	0.285245i
$471$	−7.99257	−	23.5631i	−0.368278	−	1.08573i
$472$	1.04488	−	1.80978i	0.0480943	−	0.0833018i
$473$		−	4.92061i		−	0.226250i
$474$	−9.54716	−	1.90133i	−0.438516	−	0.0873308i
$475$	3.45706	+	5.98781i	0.158621	+	0.274740i
$476$	8.41912	+	14.5823i	0.385890	+	0.668381i
$477$	−24.0182	−	9.96158i	−1.09972	−	0.456109i
$478$	13.5855	−	7.84359i	0.621386	−	0.358757i
$479$	2.30224	+	1.32920i	0.105192	+	0.0607327i	0.551673	−	0.834060i	$-0.313990\pi$
$479$	2.30224	+	1.32920i	0.105192	+	0.0607327i	−0.446481	+	0.894793i	$0.647323\pi$
$480$	1.14232	−	1.30196i	0.0521395	−	0.0594262i
$481$	−16.9376			−0.772288
$482$	9.24439	−	16.0118i	0.421071	−	0.729316i
$483$	11.9273	+	2.37532i	0.542709	+	0.108081i
$484$	−5.17262	+	8.95923i	−0.235119	+	0.407238i
$485$	2.85221	−	1.64672i	0.129512	−	0.0747739i
$486$	−1.00168	−	15.5562i	−0.0454373	−	0.705645i
$487$	13.2743	−	7.66391i	0.601515	−	0.347285i	−0.168122	−	0.985766i	$-0.553770\pi$
$487$	13.2743	−	7.66391i	0.601515	−	0.347285i	0.769637	+	0.638481i	$0.220437\pi$
$488$	−1.93145			−0.0874327
$489$	7.08780	+	20.8957i	0.320521	+	0.944938i
$490$	−0.390213	+	0.675869i	−0.0176280	+	0.0305327i
$491$	−4.78641	−	8.29031i	−0.216008	−	0.374136i	0.737576	−	0.675264i	$-0.235970\pi$
$491$	−4.78641	−	8.29031i	−0.216008	−	0.374136i	−0.953584	+	0.301128i	$0.902637\pi$
$492$	4.17086	+	3.65944i	0.188037	+	0.164980i
$493$	−33.0811	+	57.2982i	−1.48990	+	2.58058i
$494$	−25.7051			−1.15653
$495$	2.40691	−	0.315752i	0.108183	−	0.0141920i
$496$	−5.56019	−	0.290293i	−0.249660	−	0.0130345i
$497$		−	16.3890i		−	0.735148i
$498$	17.1895	+	15.0817i	0.770278	+	0.675829i
$499$	13.4829	+	7.78437i	0.603578	+	0.348476i	0.770448	−	0.637503i	$-0.220033\pi$
$499$	13.4829	+	7.78437i	0.603578	+	0.348476i	−0.166870	+	0.985979i	$0.553366\pi$
$500$			1.00000i			0.0447214i
$501$	28.7318	+	5.72197i	1.28364	+	0.255639i
$502$	−16.4741	−	9.51130i	−0.735273	−	0.424510i
$503$	−2.15434	−	1.24381i	−0.0960572	−	0.0554587i	0.451202	−	0.892422i	$-0.350995\pi$
$503$	−2.15434	−	1.24381i	−0.0960572	−	0.0554587i	−0.547259	+	0.836963i	$0.684329\pi$
$504$	−7.41816	+	0.973156i	−0.330431	+	0.0433478i
$505$	−1.27050	−	2.20056i	−0.0565363	−	0.0979238i
$506$	1.97297	−	1.13909i	0.0877091	−	0.0506389i
$507$	−1.39591	−	0.277997i	−0.0619946	−	0.0123463i
$508$	7.97677	+	4.60539i	0.353912	+	0.204331i
$509$	1.88074	+	3.25754i	0.0833624	+	0.144388i	0.904692	−	0.426066i	$-0.140101\pi$
$509$	1.88074	+	3.25754i	0.0833624	+	0.144388i	−0.821330	+	0.570454i	$0.806767\pi$
$510$	3.75649	+	11.0746i	0.166340	+	0.490392i
$511$		−	31.9121i		−	1.41171i
$512$			1.00000i			0.0441942i
$513$	−32.2328	+	15.8679i	−1.42311	+	0.700583i
$514$	3.13499	+	5.42996i	0.138278	+	0.239505i
$515$	−5.64107	−	3.25687i	−0.248575	−	0.143515i
$516$	−2.05718	+	10.3297i	−0.0905622	+	0.454742i
$517$	8.66707	−	5.00393i	0.381177	−	0.220073i
$518$	5.68094	+	9.83968i	0.249606	+	0.432331i
$519$	−4.55087	−	3.99285i	−0.199761	−	0.175267i
$520$	−3.21968	−	1.85888i	−0.141192	−	0.0815173i
$521$	22.4231	+	12.9460i	0.982373	+	0.567173i	0.902986	−	0.429671i	$-0.141370\pi$
$521$	22.4231	+	12.9460i	0.982373	+	0.567173i	0.0793869	+	0.996844i	$0.474704\pi$
$522$	−17.8856	−	23.3311i	−0.782829	−	1.02117i
$523$		−	36.8783i		−	1.61258i	−0.591524	−	0.806288i	$-0.701473\pi$
$523$		−	36.8783i		−	1.61258i	0.591524	−	0.806288i	$-0.298527\pi$
$524$	13.9591	+	8.05927i	0.609805	+	0.352071i
$525$	2.84884	−	3.24697i	0.124333	−	0.141710i
$526$		−	20.0171i		−	0.872788i
$527$	20.4679	−	31.5315i	0.891596	−	1.37353i
$528$	−0.924340	+	1.05352i	−0.0402267	+	0.0458486i
$529$	−15.0733			−0.655362
$530$	−4.33368	+	7.50615i	−0.188243	+	0.326046i
$531$	−6.21599	+	0.815449i	−0.269751	+	0.0353875i
$532$	8.62160	+	14.9330i	0.373794	+	0.647430i
$533$	5.95496	−	10.3143i	0.257938	−	0.446761i
$534$	12.5225	−	4.24761i	0.541902	−	0.183812i
$535$	1.54111			0.0666278
$536$	3.16294	−	1.82612i	0.136618	−	0.0788765i
$537$	−27.9482	−	5.56591i	−1.20605	−	0.240187i
$538$	−16.6179	+	9.59437i	−0.716450	+	0.413643i
$539$	0.315752	−	0.546899i	0.0136004	−	0.0235566i
$540$	−5.18479	−	0.343414i	−0.223118	−	0.0147782i
$541$	−12.5610	+	21.7562i	−0.540038	+	0.935374i	0.458863	+	0.888507i	$0.348257\pi$
$541$	−12.5610	+	21.7562i	−0.540038	+	0.935374i	−0.998901	+	0.0468666i	$0.985076\pi$
$542$	28.6405			1.23022
$543$	−31.9584	−	28.0397i	−1.37146	−	1.20330i
$544$	−5.84719	−	3.37588i	−0.250696	−	0.144739i
$545$	−16.9126	+	9.76452i	−0.724458	+	0.418266i
$546$	5.15855	+	15.2081i	0.220766	+	0.650846i
$547$	−5.35576	−	9.27645i	−0.228996	−	0.396633i	0.728515	−	0.685030i	$-0.240211\pi$
$547$	−5.35576	−	9.27645i	−0.228996	−	0.396633i	−0.957511	+	0.288397i	$0.906878\pi$
$548$	−3.38204	−	5.85786i	−0.144474	−	0.250235i
$549$	3.52527	+	4.59859i	0.150455	+	0.196263i
$550$		−	0.809178i		−	0.0345035i
$551$	−33.8767	+	58.6762i	−1.44320	+	2.49969i
$552$	−4.61804	+	1.56643i	−0.196557	+	0.0666718i
$553$	12.1386	−	7.00825i	0.516188	−	0.298021i
$554$	8.82263			0.374838
$555$	2.53476	+	7.47278i	0.107594	+	0.317202i
$556$			2.92120i			0.123887i
$557$	−13.7761			−0.583714			−0.291857	−	0.956462i	$-0.594273\pi$
$557$	−13.7761			−0.583714			−0.291857	+	0.956462i	$0.594273\pi$
$558$	9.45726	+	13.7681i	0.400358	+	0.582850i
$559$	22.6077			0.956204
$560$			2.49391i			0.105387i
$561$	−3.03967	−	8.96134i	−0.128335	−	0.378348i
$562$	19.8789			0.838540
$563$	13.3968	−	7.73462i	0.564606	−	0.325976i	−0.190386	−	0.981709i	$-0.560974\pi$
$563$	13.3968	−	7.73462i	0.564606	−	0.325976i	0.754992	+	0.655734i	$0.227641\pi$
$564$	−20.2866	+	6.88119i	−0.854221	+	0.289750i
$565$	3.60097	−	6.23706i	0.151494	−	0.262395i
$566$		−	9.93823i		−	0.417735i
$567$	15.8566	+	15.8857i	0.665913	+	0.667136i
$568$	3.28581	+	5.69119i	0.137870	+	0.238797i
$569$	20.6937	+	35.8426i	0.867526	+	1.50260i	0.864517	+	0.502604i	$0.167625\pi$
$569$	20.6937	+	35.8426i	0.867526	+	1.50260i	0.00300954	+	0.999995i	$0.499042\pi$
$570$	3.84683	+	11.3410i	0.161126	+	0.475021i
$571$	−12.9537	+	7.47880i	−0.542094	+	0.312978i	−0.745927	−	0.666027i	$-0.767993\pi$
$571$	−12.9537	+	7.47880i	−0.542094	+	0.312978i	0.203833	+	0.979006i	$0.434660\pi$
$572$	2.60529	+	1.50417i	0.108933	+	0.0628923i
$573$	−22.1137	−	19.4022i	−0.923815	−	0.810539i
$574$	−7.98927			−0.333466
$575$	1.40772	−	2.43824i	0.0587059	−	0.101682i
$576$	2.38090	−	1.82519i	0.0992041	−	0.0760497i
$577$	11.1680	−	19.3435i	0.464929	−	0.805281i	−0.534269	−	0.845314i	$-0.679413\pi$
$577$	11.1680	−	19.3435i	0.464929	−	0.805281i	0.999198	+	0.0400337i	$0.0127465\pi$
$578$	24.7563	−	14.2931i	1.02973	−	0.594514i
$579$	6.90835	+	1.37581i	0.287101	+	0.0571765i
$580$	−8.48642	+	4.89964i	−0.352379	+	0.203446i
$581$	−32.9264			−1.36602
$582$	5.40211	−	1.83239i	0.223925	−	0.0759548i
$583$	3.50672	−	6.07381i	0.145233	−	0.251551i
$584$	6.39801	+	11.0817i	0.264752	+	0.458563i
$585$	1.45072	+	11.0585i	0.0599799	+	0.457214i
$586$	−5.33839	+	9.24636i	−0.220527	+	0.381964i
$587$	27.0794			1.11769			0.558844	−	0.829273i	$-0.311245\pi$
$587$	27.0794			1.11769			0.558844	+	0.829273i	$0.311245\pi$
$588$	−0.891496	+	1.01609i	−0.0367647	+	0.0419027i
$589$	20.9602	−	32.2898i	0.863648	−	1.33048i
$590$			2.08975i			0.0860337i
$591$	−21.8030	+	24.8501i	−0.896857	+	1.02220i
$592$	−3.94549	−	2.27793i	−0.162159	−	0.0936223i
$593$			22.2163i			0.912314i	0.889899	+	0.456157i	$0.150774\pi$
$593$			22.2163i			0.912314i	−0.889899	+	0.456157i	$0.849226\pi$
$594$	4.19542	+	0.277883i	0.172140	+	0.0114017i
$595$	−14.5823	−	8.41912i	−0.597818	−	0.345150i
$596$	9.25026	+	5.34064i	0.378906	+	0.218761i
$597$	12.7246	+	11.1643i	0.520783	+	0.456926i
$598$	5.23356	+	9.06479i	0.214016	+	0.370687i
$599$	−5.90993	+	3.41210i	−0.241473	+	0.139415i	−0.615854	−	0.787861i	$-0.711189\pi$
$599$	−5.90993	+	3.41210i	−0.241473	+	0.139415i	0.374381	+	0.927275i	$0.377855\pi$
$600$	−0.338296	+	1.69869i	−0.0138109	+	0.0693488i
$601$	40.0780	+	23.1390i	1.63482	+	0.943861i	0.982579	+	0.185845i	$0.0595023\pi$
$601$	40.0780	+	23.1390i	1.63482	+	0.943861i	0.652236	+	0.758016i	$0.273831\pi$
$602$	−7.58272	−	13.1337i	−0.309049	−	0.535288i
$603$	−10.1208	−	4.19761i	−0.412150	−	0.170940i
$604$			8.63402i			0.351313i
$605$		−	10.3452i		−	0.420593i
$606$	−1.41374	−	4.16788i	−0.0574292	−	0.169309i
$607$	−3.26505	−	5.65523i	−0.132524	−	0.229539i	0.792125	−	0.610359i	$-0.208975\pi$
$607$	−3.26505	−	5.65523i	−0.132524	−	0.229539i	−0.924649	+	0.380821i	$0.875642\pi$
$608$	−5.98781	−	3.45706i	−0.242838	−	0.140202i
$609$	41.5135	+	8.26744i	1.68221	+	0.335014i
$610$	1.67269	−	0.965726i	0.0677251	−	0.0391011i
$611$	22.9905	+	39.8208i	0.930098	+	1.61098i
$612$	2.63462	+	20.0832i	0.106498	+	0.811814i
$613$	0.515169	+	0.297433i	0.0208075	+	0.0120132i	0.510368	−	0.859956i	$-0.329509\pi$
$613$	0.515169	+	0.297433i	0.0208075	+	0.0120132i	−0.489560	+	0.871970i	$0.662843\pi$
$614$	−23.6841	−	13.6740i	−0.955812	−	0.551838i
$615$	−5.44179	−	1.08374i	−0.219434	−	0.0437005i
$616$		−	2.01801i		−	0.0813081i
$617$	10.1336	+	5.85065i	0.407964	+	0.235538i	0.689915	−	0.723891i	$-0.257648\pi$
$617$	10.1336	+	5.85065i	0.407964	+	0.235538i	−0.281950	+	0.959429i	$0.590981\pi$
$618$	−8.48065	−	7.44078i	−0.341142	−	0.299312i
$619$			21.4392i			0.861712i	0.902421	+	0.430856i	$0.141788\pi$
$619$			21.4392i			0.861712i	−0.902421	+	0.430856i	$0.858212\pi$
$620$	4.96041	−	2.52869i	0.199215	−	0.101555i
$621$	12.1583	+	8.13605i	0.487897	+	0.326488i
$622$	−21.7180			−0.870811
$623$	−9.51983	+	16.4888i	−0.381404	+	0.660611i
$624$	−4.84039	−	4.24687i	−0.193771	−	0.170011i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.55426	−	4.42410i	0.102089	−	0.176823i
$627$	−3.11277	−	9.17686i	−0.124312	−	0.366488i
$628$	−14.3655			−0.573245
$629$	26.6390	−	15.3800i	1.06216	−	0.613241i
$630$	5.93774	−	4.55186i	0.236565	−	0.181350i
$631$	−3.87266	+	2.23588i	−0.154168	+	0.0890091i	−0.575100	−	0.818083i	$-0.695037\pi$
$631$	−3.87266	+	2.23588i	−0.154168	+	0.0890091i	0.420931	+	0.907093i	$0.361703\pi$
$632$	−2.81015	+	4.86732i	−0.111782	+	0.193612i
$633$	34.6516	+	6.90091i	1.37728	+	0.274286i
$634$	3.89294	−	6.74277i	0.154608	−	0.267789i
$635$	−9.21078			−0.365518
$636$	−9.90088	+	11.2846i	−0.392596	+	0.447462i
$637$	2.51272	+	1.45072i	0.0995577	+	0.0574796i
$638$	6.86702	−	3.96468i	0.271868	−	0.156963i
$639$	7.55291	−	18.2107i	0.298789	−	0.720404i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	4.13241	+	7.15755i	0.163221	+	0.282706i	0.936022	−	0.351942i	$-0.114478\pi$
$641$	4.13241	+	7.15755i	0.163221	+	0.282706i	−0.772801	+	0.634648i	$0.781145\pi$
$642$	2.61786	+	0.521350i	0.103319	+	0.0205760i
$643$		−	28.5474i		−	1.12580i	−0.826525	−	0.562901i	$-0.809685\pi$
$643$		−	28.5474i		−	1.12580i	0.826525	−	0.562901i	$-0.190315\pi$
$644$	3.51072	−	6.08074i	0.138342	−	0.239615i
$645$	−3.38330	−	9.97441i	−0.133217	−	0.392742i
$646$	40.4282	−	23.3412i	1.59063	−	0.918349i
$647$	13.2500			0.520910			0.260455	−	0.965486i	$-0.416127\pi$
$647$	13.2500			0.520910			0.260455	+	0.965486i	$0.416127\pi$
$648$	−8.69119	−	2.33735i	−0.341422	−	0.0918198i
$649$		−	1.69098i		−	0.0663768i
$650$	3.71776			0.145823
$651$	−23.3102	−	5.92081i	−0.913598	−	0.232055i
$652$	12.7393			0.498909
$653$		−	12.9745i		−	0.507731i	−0.967239	−	0.253866i	$-0.918298\pi$
$653$		−	12.9745i		−	0.507731i	0.967239	−	0.253866i	$-0.0817021\pi$
$654$	−32.0327	+	10.8654i	−1.25258	+	0.424872i
$655$	−16.1185			−0.629803
$656$	2.77433	−	1.60176i	0.108319	−	0.0625381i
$657$	14.7068	−	35.4592i	0.573765	−	1.38340i
$658$	15.4223	−	26.7121i	0.601222	−	1.04135i
$659$		−	40.7903i		−	1.58896i	−0.607287	−	0.794482i	$-0.707742\pi$
$659$		−	40.7903i		−	1.58896i	0.607287	−	0.794482i	$-0.292258\pi$
$660$	0.273742	−	1.37454i	0.0106554	−	0.0535041i
$661$	17.1606	+	29.7231i	0.667471	+	1.15609i	0.978609	+	0.205730i	$0.0659567\pi$
$661$	17.1606	+	29.7231i	0.667471	+	1.15609i	−0.311137	+	0.950365i	$0.600710\pi$
$662$	−13.6491	−	23.6410i	−0.530488	−	0.918833i
$663$	41.1728	−	13.9657i	1.59902	−	0.542385i
$664$	11.4339	−	6.60136i	0.443721	−	0.256183i
$665$	−14.9330	−	8.62160i	−0.579079	−	0.334331i
$666$	1.77776	+	13.5515i	0.0688866	+	0.525108i
$667$	27.5892			1.06826
$668$	8.45705	−	14.6480i	0.327213	−	0.566749i
$669$	6.81423	−	34.2164i	0.263454	−	1.32288i
$670$	−1.82612	+	3.16294i	−0.0705493	+	0.122195i
$671$	−1.35350	+	0.781444i	−0.0522513	+	0.0301673i
$672$	−0.843679	+	4.23638i	−0.0325456	+	0.163422i
$673$	18.3493	−	10.5940i	0.707312	−	0.408367i	−0.102753	−	0.994707i	$-0.532765\pi$
$673$	18.3493	−	10.5940i	0.707312	−	0.408367i	0.810065	+	0.586340i	$0.199432\pi$
$674$	−25.5446			−0.983942
$675$	4.66187	−	2.29499i	0.179435	−	0.0883342i
$676$	−0.410878	+	0.711662i	−0.0158030	+	0.0273716i
$677$	−7.38824	−	12.7968i	−0.283953	−	0.491821i	0.688402	−	0.725330i	$-0.258313\pi$
$677$	−7.38824	−	12.7968i	−0.283953	−	0.491821i	−0.972355	+	0.233509i	$0.924979\pi$
$678$	8.22691	−	9.37665i	0.315952	−	0.360108i
$679$	−4.10678	+	7.11315i	−0.157604	+	0.272977i
$680$	6.75175			0.258918
$681$	−28.5493	−	25.0487i	−1.09401	−	0.959868i
$682$	−4.01386	+	2.04616i	−0.153699	+	0.0783517i
$683$			23.7982i			0.910615i	0.890334	+	0.455307i	$0.150471\pi$
$683$			23.7982i			0.910615i	−0.890334	+	0.455307i	$0.849529\pi$
$684$	2.69799	+	20.5662i	0.103160	+	0.786367i
$685$	5.85786	+	3.38204i	0.223817	+	0.129221i
$686$		−	19.4037i		−	0.740835i
$687$	7.62291	−	38.2770i	0.290832	−	1.46036i
$688$	5.26630	+	3.04050i	0.200776	+	0.115918i
$689$	27.9061	+	16.1116i	1.06314	+	0.613802i
$690$	3.21613	−	3.66559i	0.122436	−	0.139547i
$691$	−2.97015	−	5.14446i	−0.112990	−	0.195704i	0.803984	−	0.594650i	$-0.202709\pi$
$691$	−2.97015	−	5.14446i	−0.112990	−	0.195704i	−0.916974	+	0.398946i	$0.869376\pi$
$692$	−3.02710	+	1.74770i	−0.115073	+	0.0664374i
$693$	−4.80469	+	3.68326i	−0.182515	+	0.139916i
$694$	−4.30303	−	2.48436i	−0.163341	−	0.0943048i
$695$	−1.46060	−	2.52983i	−0.0554037	−	0.0959621i
$696$	−16.0733	+	5.45205i	−0.609259	+	0.206659i
$697$			21.6293i			0.819270i
$698$			17.2065i			0.651275i
$699$	20.2901	−	6.88236i	0.767441	−	0.260315i
$700$	−1.24695	−	2.15979i	−0.0471304	−	0.0816323i
$701$	−6.52698	−	3.76835i	−0.246521	−	0.142329i	0.371649	−	0.928373i	$-0.378792\pi$
$701$	−6.52698	−	3.76835i	−0.246521	−	0.142329i	−0.618170	+	0.786044i	$0.712126\pi$
$702$	−1.27673	+	19.2758i	−0.0481872	+	0.727519i
$703$	27.2796	−	15.7499i	1.02887	−	0.594018i
$704$	0.404589	+	0.700769i	0.0152485	+	0.0264112i
$705$	14.1281	−	16.1026i	0.532097	−	0.606459i
$706$	5.80134	+	3.34940i	0.218336	+	0.126056i
$707$	5.48800	+	3.16850i	0.206398	+	0.119164i
$708$	−0.706955	+	3.54984i	−0.0265690	+	0.133411i
$709$			33.4552i			1.25644i	0.778036	+	0.628219i	$0.216216\pi$
$709$			33.4552i			1.25644i	−0.778036	+	0.628219i	$0.783784\pi$
$710$	−5.69119	−	3.28581i	−0.213587	−	0.123314i
$711$	16.7177	−	2.19312i	0.626961	−	0.0822483i
$712$		−	7.63447i		−	0.286114i
$713$	−15.6544	−	0.817300i	−0.586260	−	0.0306081i
$714$	−21.9228	−	19.2346i	−0.820439	−	0.719839i
$715$	−3.00833			−0.112505
$716$	−8.22638	+	14.2485i	−0.307434	+	0.532492i
$717$	−17.9198	+	20.4241i	−0.669226	+	0.762753i
$718$	16.9062	+	29.2825i	0.630935	+	1.09281i
$719$	−14.7184	+	25.4930i	−0.548904	+	0.950729i	0.449446	+	0.893307i	$0.351621\pi$
$719$	−14.7184	+	25.4930i	−0.548904	+	0.950729i	−0.998350	+	0.0574219i	$0.981712\pi$
$720$	−1.14932	+	2.77111i	−0.0428327	+	0.103273i
$721$	16.2447			0.604984
$722$	24.9460	−	14.4026i	0.928394	−	0.536009i
$723$	−6.25469	+	31.4068i	−0.232614	+	1.16803i
$724$	−21.2577	+	12.2731i	−0.790037	+	0.456128i
$725$	4.89964	−	8.48642i	0.181968	−	0.315178i
$726$	3.49975	−	17.5734i	0.129888	−	0.652209i
$727$	17.5950	−	30.4754i	0.652562	−	1.13027i	−0.329938	−	0.944003i	$-0.607028\pi$
$727$	17.5950	−	30.4754i	0.652562	−	1.13027i	0.982499	−	0.186267i	$-0.0596390\pi$
$728$	9.27175			0.343634
$729$	10.2981	+	24.9590i	0.381411	+	0.924406i
$730$	−11.0817	−	6.39801i	−0.410151	−	0.236801i
$731$	−35.5567	+	20.5287i	−1.31511	+	0.759281i
$732$	3.16808	−	1.07461i	0.117096	−	0.0397186i
$733$	−18.3462	−	31.7765i	−0.677631	−	1.17369i	−0.975692	−	0.219145i	$-0.929673\pi$
$733$	−18.3462	−	31.7765i	−0.677631	−	1.17369i	0.298061	−	0.954547i	$-0.403660\pi$
$734$	12.1131	+	20.9805i	0.447102	+	0.774403i
$735$	0.264015	−	1.32570i	0.00973835	−	0.0488994i
$736$			2.81543i			0.103778i
$737$	1.47766	−	2.55938i	0.0544303	−	0.0942760i
$738$	−8.87730	−	3.68187i	−0.326778	−	0.135532i
$739$	−9.90837	+	5.72060i	−0.364485	+	0.210436i	−0.671047	−	0.741415i	$-0.734155\pi$
$739$	−9.90837	+	5.72060i	−0.364485	+	0.210436i	0.306561	+	0.951851i	$0.400822\pi$
$740$	4.55586			0.167477
$741$	42.1630	−	14.3016i	1.54890	−	0.525383i
$742$		−	21.6156i		−	0.793533i
$743$	36.0723			1.32337			0.661683	−	0.749784i	$-0.269843\pi$
$743$	36.0723			1.32337			0.661683	+	0.749784i	$0.269843\pi$
$744$	9.28166	−	2.61739i	0.340282	−	0.0959580i
$745$	−10.6813			−0.391332
$746$			32.0372i			1.17296i
$747$	−36.5862	−	15.1742i	−1.33862	−	0.555195i
$748$	−5.46337			−0.199761
$749$	−3.32846	+	1.92169i	−0.121619	+	0.0702169i
$750$	−0.556373	−	1.64026i	−0.0203159	−	0.0598938i
$751$	16.3290	−	28.2827i	0.595854	−	1.03205i	−0.397572	−	0.917571i	$-0.630147\pi$
$751$	16.3290	−	28.2827i	0.595854	−	1.03205i	0.993426	−	0.114478i	$-0.0365196\pi$
$752$			12.3679i			0.451013i
$753$	32.3135	+	6.43527i	1.17757	+	0.234514i
$754$	18.2157	+	31.5505i	0.663376	+	1.14900i
$755$	−4.31701	−	7.47728i	−0.157112	−	0.272126i
$756$	11.6263	−	5.72349i	0.422843	−	0.208161i
$757$	−32.7695	+	18.9195i	−1.19103	+	0.687639i	−0.958539	−	0.284960i	$-0.908020\pi$
$757$	−32.7695	+	18.9195i	−1.19103	+	0.687639i	−0.232487	+	0.972600i	$0.574686\pi$
$758$	13.5134	+	7.80196i	0.490829	+	0.283380i
$759$	−2.60242	+	2.96612i	−0.0944618	+	0.107663i
$760$	6.91413			0.250802
$761$	6.19120	−	10.7235i	0.224431	−	0.388726i	−0.731718	−	0.681608i	$-0.761281\pi$
$761$	6.19120	−	10.7235i	0.224431	−	0.388726i	0.956149	+	0.292882i	$0.0946144\pi$
$762$	−15.6463	−	3.11597i	−0.566805	−	0.112880i
$763$	24.3518	−	42.1785i	0.881594	−	1.52697i
$764$	−14.7094	+	8.49247i	−0.532167	+	0.307247i
$765$	−12.3232	−	16.0752i	−0.445548	−	0.581201i
$766$	−3.00520	+	1.73505i	−0.108582	+	0.0626900i
$767$	7.76920			0.280530
$768$	−0.556373	−	1.64026i	−0.0200764	−	0.0591877i
$769$	18.8200	−	32.5972i	0.678666	−	1.17548i	−0.296717	−	0.954965i	$-0.595892\pi$
$769$	18.8200	−	32.5972i	0.678666	−	1.17548i	0.975383	−	0.220518i	$-0.0707749\pi$
$770$	1.00901	+	1.74765i	0.0363621	+	0.0629810i
$771$	−8.16327	−	7.16231i	−0.293993	−	0.257944i
$772$	2.03343	−	3.52201i	0.0731848	−	0.126760i
$773$	40.3903			1.45274			0.726368	−	0.687306i	$-0.241207\pi$
$773$	40.3903			1.45274			0.726368	+	0.687306i	$0.241207\pi$
$774$	−2.37289	−	18.0880i	−0.0852917	−	0.650160i
$775$	−3.03150	+	4.67012i	−0.108895	+	0.167756i
$776$		−	3.29345i		−	0.118228i
$777$	−14.7927	−	12.9789i	−0.530687	−	0.465615i
$778$	10.4550	+	6.03620i	0.374830	+	0.216408i
$779$			22.1495i			0.793589i
$780$	6.31533	+	1.25770i	0.226125	+	0.0450331i
$781$	4.60519	+	2.65881i	0.164787	+	0.0951396i
$782$	−16.4624	−	9.50456i	−0.588693	−	0.339882i
$783$	42.3177	+	28.3180i	1.51231	+	1.01200i
$784$	0.390213	+	0.675869i	0.0139362	+	0.0241382i
$785$	12.4409	−	7.18274i	0.444034	−	0.256363i
$786$	−27.3804	−	5.45284i	−0.976628	−	0.194496i
$787$	0.0309626	+	0.0178763i	0.00110370	+	0.000637220i	0.500552	−	0.865707i	$-0.333130\pi$
$787$	0.0309626	+	0.0178763i	0.00110370	+	0.000637220i	−0.499448	+	0.866344i	$0.666464\pi$
$788$	9.54331	+	16.5295i	0.339966	+	0.588839i
$789$	11.1370	+	32.8332i	0.396487	+	1.16889i
$790$		−	5.62030i		−	0.199961i
$791$			17.9610i			0.638618i
$792$	0.930006	−	2.24232i	0.0330463	−	0.0796775i
$793$	−3.59034	−	6.21865i	−0.127497	−	0.220831i
$794$	−0.484313	−	0.279618i	−0.0171876	−	0.00992328i
$795$	2.93213	−	14.7232i	0.103992	−	0.522177i
$796$	8.46400	−	4.88669i	0.299999	−	0.173204i
$797$	−7.42556	−	12.8614i	−0.263027	−	0.455576i	0.704018	−	0.710182i	$-0.251387\pi$
$797$	−7.42556	−	12.8614i	−0.263027	−	0.455576i	−0.967045	+	0.254606i	$0.918054\pi$
$798$	−22.4500	−	19.6972i	−0.794721	−	0.697275i
$799$	−72.3177	−	41.7526i	−2.55842	−	1.47710i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−18.1769	+	13.9344i	−0.642249	+	0.492347i
$802$		−	21.0608i		−	0.743681i
$803$	8.96705	+	5.17713i	0.316440	+	0.182697i
$804$	−4.17203	+	4.75509i	−0.147136	+	0.167699i
$805$			7.02143i			0.247473i
$806$	−9.40109	−	18.4416i	−0.331139	−	0.649579i
$807$	21.9197	−	24.9830i	0.771609	−	0.879444i
$808$	−2.54099			−0.0893918
$809$	−13.0314	+	22.5710i	−0.458159	+	0.793555i	−0.998864	−	0.0476574i	$-0.984824\pi$
$809$	−13.0314	+	22.5710i	−0.458159	+	0.793555i	0.540704	+	0.841213i	$0.318158\pi$
$810$	8.69547	−	2.32139i	0.305528	−	0.0815653i
$811$	−6.69971	−	11.6042i	−0.235258	−	0.407480i	0.724089	−	0.689706i	$-0.242260\pi$
$811$	−6.69971	−	11.6042i	−0.235258	−	0.407480i	−0.959348	+	0.282227i	$0.908927\pi$
$812$	12.2192	−	21.1643i	0.428811	−	0.742723i
$813$	−46.9779	+	15.9348i	−1.64759	+	0.558859i
$814$	−3.68650			−0.129212
$815$	−11.0326	+	6.36965i	−0.386453	+	0.223119i
$816$	11.4691	+	2.28409i	0.401501	+	0.0799592i
$817$	−36.4119	+	21.0224i	−1.27389	+	0.735481i
$818$	−1.56793	+	2.71573i	−0.0548214	+	0.0949534i
$819$	−16.9227	−	22.0751i	−0.591328	−	0.771366i
$820$	−1.60176	+	2.77433i	−0.0559358	+	0.0968837i
$821$	36.2181			1.26402			0.632010	−	0.774960i	$-0.282230\pi$
$821$	36.2181			1.26402			0.632010	+	0.774960i	$0.282230\pi$
$822$	8.80657	+	7.72673i	0.307165	+	0.269501i
$823$	26.7549	+	15.4469i	0.932616	+	0.538446i	0.887638	−	0.460542i	$-0.152345\pi$
$823$	26.7549	+	15.4469i	0.932616	+	0.538446i	0.0449777	+	0.998988i	$0.485678\pi$
$824$	−5.64107	+	3.25687i	−0.196516	+	0.113459i
$825$	0.450205	+	1.32726i	0.0156741	+	0.0462093i
$826$	−2.60582	−	4.51342i	−0.0906682	−	0.157042i
$827$	−26.1931	−	45.3677i	−0.910822	−	1.57759i	−0.812906	−	0.582396i	$-0.802116\pi$
$827$	−26.1931	−	45.3677i	−0.910822	−	1.57759i	−0.0979165	−	0.995195i	$-0.531218\pi$
$828$	6.70326	−	5.13871i	0.232954	−	0.178582i
$829$			14.6902i			0.510212i	0.966913	+	0.255106i	$0.0821104\pi$
$829$			14.6902i			0.510212i	−0.966913	+	0.255106i	$0.917890\pi$
$830$	−6.60136	+	11.4339i	−0.229137	+	0.396876i
$831$	−14.4714	+	4.90867i	−0.502007	+	0.170280i
$832$	−3.21968	+	1.85888i	−0.111622	+	0.0644451i
$833$	−5.26925			−0.182569
$834$	−1.62528	−	4.79153i	−0.0562788	−	0.165917i
$835$			16.9141i			0.585336i
$836$	−5.59476			−0.193499
$837$	−23.1725	−	17.3215i	−0.800960	−	0.598717i
$838$	23.5226			0.812575
$839$			19.2472i			0.664489i	0.943193	+	0.332244i	$0.107806\pi$
$839$			19.2472i			0.664489i	−0.943193	+	0.332244i	$0.892194\pi$
$840$	−1.38754	−	4.09065i	−0.0478748	−	0.141141i
$841$	67.0258			2.31123
$842$	−1.78744	+	1.03198i	−0.0615993	+	0.0355644i
$843$	−32.6065	+	11.0601i	−1.12303	+	0.380929i
$844$	10.1995	−	17.6661i	0.351081	−	0.608091i
$845$		−	0.821757i		−	0.0282693i
$846$	29.4468	−	22.5739i	1.01240	−	0.776106i
$847$	12.9000	+	22.3435i	0.443250	+	0.767732i
$848$	4.33368	+	7.50615i	0.148819	+	0.257762i
$849$	5.52936	+	16.3013i	0.189767	+	0.559458i
$850$	−5.84719	+	3.37588i	−0.200557	+	0.115792i
$851$	−11.1083	−	6.41336i	−0.380786	−	0.219847i
$852$	−8.55601	−	7.50689i	−0.293124	−	0.257182i
$853$	8.59614			0.294326			0.147163	−	0.989112i	$-0.452986\pi$
$853$	8.59614			0.294326			0.147163	+	0.989112i	$0.452986\pi$
$854$	−2.40843	+	4.17152i	−0.0824148	+	0.142747i
$855$	−12.6196	−	16.4618i	−0.431582	−	0.562983i
$856$	0.770553	−	1.33464i	0.0263369	−	0.0456169i
$857$	−23.4587	+	13.5439i	−0.801334	+	0.462651i	−0.843938	−	0.536441i	$-0.819768\pi$
$857$	−23.4587	+	13.5439i	−0.801334	+	0.462651i	0.0426031	+	0.999092i	$0.486435\pi$
$858$	−5.11023	−	1.01771i	−0.174460	−	0.0347439i
$859$	35.3811	−	20.4273i	1.20719	−	0.696969i	0.245042	−	0.969512i	$-0.421198\pi$
$859$	35.3811	−	20.4273i	1.20719	−	0.696969i	0.962144	+	0.272543i	$0.0878648\pi$
$860$	−6.08100			−0.207360
$861$	13.1045	−	4.44502i	0.446599	−	0.151486i
$862$	−10.7282	+	18.5818i	−0.365404	+	0.632899i
$863$	−6.32948	−	10.9630i	−0.215458	−	0.373184i	0.737956	−	0.674849i	$-0.235791\pi$
$863$	−6.32948	−	10.9630i	−0.215458	−	0.373184i	−0.953414	+	0.301664i	$0.902458\pi$
$864$	−2.88980	+	4.31845i	−0.0983130	+	0.146917i
$865$	1.74770	−	3.02710i	0.0594235	−	0.102924i
$866$	−19.3965			−0.659119
$867$	−32.6545	+	37.2181i	−1.10901	+	1.26399i
$868$	−7.56027	+	11.6468i	−0.256612	+	0.395320i
$869$			4.54782i			0.154274i
$870$	11.1939	−	12.7583i	0.379509	−	0.432546i
$871$	11.7591	+	6.78909i	0.398440	+	0.230040i
$872$			19.5290i			0.661336i
$873$	−7.84136	+	6.01117i	−0.265390	+	0.203447i
$874$	−16.8583	−	9.73314i	−0.570240	−	0.329228i
$875$	2.15979	+	1.24695i	0.0730141	+	0.0421547i
$876$	−16.6599	−	14.6171i	−0.562887	−	0.493868i
$877$	−11.3521	−	19.6624i	−0.383333	−	0.663953i	0.608203	−	0.793781i	$-0.291891\pi$
$877$	−11.3521	−	19.6624i	−0.383333	−	0.663953i	−0.991536	+	0.129829i	$0.958557\pi$
$878$	−10.9961	+	6.34860i	−0.371101	+	0.214255i
$879$	3.61191	−	18.1366i	0.121827	−	0.611731i
$880$	−0.700769	−	0.404589i	−0.0236229	−	0.0136387i
$881$	−25.4712	−	44.1175i	−0.858148	−	1.48636i	−0.873694	−	0.486476i	$-0.838282\pi$
$881$	−25.4712	−	44.1175i	−0.858148	−	1.48636i	0.0155463	−	0.999879i	$-0.495051\pi$
$882$	0.896962	−	2.16265i	0.0302023	−	0.0728202i
$883$			3.76099i			0.126567i	0.997996	+	0.0632837i	$0.0201573\pi$
$883$			3.76099i			0.126567i	−0.997996	+	0.0632837i	$0.979843\pi$
$884$		−	25.1014i		−	0.844252i
$885$	−1.16268	−	3.42773i	−0.0390831	−	0.115222i
$886$	7.55872	+	13.0921i	0.253940	+	0.439837i
$887$	8.62979	+	4.98241i	0.289760	+	0.167293i	0.637834	−	0.770174i	$-0.279831\pi$
$887$	8.62979	+	4.98241i	0.289760	+	0.167293i	−0.348074	+	0.937467i	$0.613164\pi$
$888$	7.73900	+	1.54123i	0.259704	+	0.0517203i
$889$	19.8933	−	11.4854i	0.667200	−	0.385208i
$890$	3.81723	+	6.61164i	0.127954	+	0.221623i
$891$	−7.03618	+	1.87842i	−0.235721	+	0.0629294i
$892$	−17.4442	−	10.0714i	−0.584074	−	0.337216i
$893$	−74.0569	−	42.7568i	−2.47822	−	1.43080i
$894$	−18.1442	−	3.61344i	−0.606833	−	0.120851i
$895$		−	16.4528i		−	0.549955i
$896$	2.15979	+	1.24695i	0.0721534	+	0.0416578i
$897$	−13.6278	−	11.9568i	−0.455019	−	0.399226i
$898$		−	15.6070i		−	0.520811i
$899$	−54.4858	−	2.84466i	−1.81720	−	0.0948747i
$900$	−0.390213	−	2.97451i	−0.0130071	−	0.0991505i
$901$	−58.5198			−1.94958
$902$	1.29611	−	2.24492i	0.0431557	−	0.0747478i
$903$	19.7448	+	17.3238i	0.657067	+	0.576499i
$904$	−3.60097	−	6.23706i	−0.119766	−	0.207441i
$905$	12.2731	−	21.2577i	0.407973	−	0.706630i
$906$	−4.80373	−	14.1620i	−0.159593	−	0.470502i
$907$	8.43562			0.280100			0.140050	−	0.990144i	$-0.455274\pi$
$907$	8.43562			0.280100			0.140050	+	0.990144i	$0.455274\pi$
$908$	−18.9901	+	10.9640i	−0.630210	+	0.363852i
$909$	4.63780	+	6.04984i	0.153826	+	0.200661i
$910$	−8.02957	+	4.63588i	−0.266178	+	0.153678i
$911$	4.40644	−	7.63218i	0.145992	−	0.252866i	−0.783751	−	0.621076i	$-0.786696\pi$
$911$	4.40644	−	7.63218i	0.145992	−	0.252866i	0.929743	+	0.368210i	$0.120029\pi$
$912$	11.7450	+	2.33902i	0.388915	+	0.0774528i
$913$	5.34168	−	9.25206i	0.176784	−	0.306198i
$914$	−7.87077			−0.260342
$915$	−2.20633	+	2.51468i	−0.0729392	+	0.0831327i
$916$	−19.5144	−	11.2666i	−0.644773	−	0.372260i
$917$	34.8126	−	20.0991i	1.14961	−	0.663730i
$918$	−15.4952	−	31.4758i	−0.511418	−	1.03886i
$919$	18.2801	+	31.6620i	0.603004	+	1.04443i	0.992363	+	0.123348i	$0.0393631\pi$
$919$	18.2801	+	31.6620i	0.603004	+	1.04443i	−0.389359	+	0.921086i	$0.627304\pi$
$920$	−1.40772	−	2.43824i	−0.0464111	−	0.0803863i
$921$	46.4559	+	9.25173i	1.53077	+	0.304855i
$922$			5.49791i			0.181064i
$923$	−12.2159	+	21.1585i	−0.402090	+	0.696441i
$924$	1.12277	+	3.31007i	0.0369364	+	0.108893i
$925$	−3.94549	+	2.27793i	−0.129727	+	0.0748978i
$926$	−25.9653			−0.853272
$927$	18.0503	+	7.48639i	0.592850	+	0.245885i
$928$			9.79927i			0.321677i
$929$	−38.2432			−1.25472			−0.627360	−	0.778729i	$-0.715865\pi$
$929$	−38.2432			−1.25472			−0.627360	+	0.778729i	$0.715865\pi$
$930$	−6.72946	+	6.90755i	−0.220668	+	0.226508i
$931$	−5.39597			−0.176846
$932$		−	12.3700i		−	0.405194i
$933$	35.6231	−	12.0833i	1.16625	−	0.395589i
$934$	−8.76334			−0.286745
$935$	4.73142	−	2.73168i	0.154734	−	0.0893356i
$936$	10.3023	+	4.27291i	0.336742	+	0.139664i
$937$	19.4594	−	33.7047i	0.635712	−	1.10108i	−0.350652	−	0.936506i	$-0.614040\pi$
$937$	19.4594	−	33.7047i	0.635712	−	1.10108i	0.986364	−	0.164579i	$-0.0526266\pi$
$938$		−	9.10837i		−	0.297399i
$939$	−1.72819	+	8.67779i	−0.0563974	+	0.283189i
$940$	−6.18397	−	10.7110i	−0.201699	−	0.349353i
$941$	4.49534	+	7.78615i	0.146544	+	0.253821i	0.929948	−	0.367691i	$-0.119852\pi$
$941$	4.49534	+	7.78615i	0.146544	+	0.253821i	−0.783404	+	0.621513i	$0.786518\pi$
$942$	23.5631	−	7.99257i	0.767728	−	0.260412i
$943$	7.81093	−	4.50964i	0.254359	−	0.146854i
$944$	1.80978	+	1.04488i	0.0589032	+	0.0340078i
$945$	−7.20690	+	10.7698i	−0.234440	+	0.350342i
$946$	4.92061			0.159983
$947$	15.1424	−	26.2273i	0.492061	−	0.852274i	−0.507897	−	0.861418i	$-0.669577\pi$
$947$	15.1424	−	26.2273i	0.492061	−	0.852274i	0.999958	+	0.00914336i	$0.00291046\pi$
$948$	1.90133	−	9.54716i	0.0617522	−	0.310077i
$949$	−23.7863	+	41.1991i	−0.772136	+	1.33738i
$950$	−5.98781	+	3.45706i	−0.194270	+	0.112162i
$951$	−2.63393	+	13.2258i	−0.0854111	+	0.428876i
$952$	−14.5823	+	8.41912i	−0.472617	+	0.272865i
$953$	−24.3532			−0.788876			−0.394438	−	0.918922i	$-0.629061\pi$
$953$	−24.3532			−0.788876			−0.394438	+	0.918922i	$0.629061\pi$
$954$	9.96158	−	24.0182i	0.322518	−	0.777618i
$955$	8.49247	−	14.7094i	0.274810	−	0.475985i
$956$	7.84359	+	13.5855i	0.253680	+	0.439386i
$957$	−9.05786	+	10.3237i	−0.292799	+	0.333719i
$958$	−1.32920	+	2.30224i	−0.0429445	+	0.0743821i
$959$	−16.8690			−0.544728
$960$	1.30196	+	1.14232i	0.0420207	+	0.0368682i
$961$	30.8315	+	3.22817i	0.994563	+	0.104134i
$962$		−	16.9376i		−	0.546090i
$963$	−4.58404	+	0.601360i	−0.147719	+	0.0193785i
$964$	16.0118	+	9.24439i	0.515704	+	0.297742i
$965$			4.06687i			0.130917i
$966$	−2.37532	+	11.9273i	−0.0764248	+	0.383753i
$967$	−0.774386	−	0.447092i	−0.0249026	−	0.0143775i	0.487497	−	0.873125i	$-0.337910\pi$
$967$	−0.774386	−	0.447092i	−0.0249026	−	0.0143775i	−0.512400	+	0.858747i	$0.671243\pi$
$968$	−8.95923	−	5.17262i	−0.287961	−	0.166254i
$969$	−53.3263	+	60.7788i	−1.71309	+	1.95250i
$970$	1.64672	+	2.85221i	0.0528731	+	0.0915789i
$971$	50.4102	−	29.1043i	1.61774	−	0.934002i	0.630236	−	0.776403i	$-0.282958\pi$
$971$	50.4102	−	29.1043i	1.61774	−	0.934002i	0.987503	−	0.157599i	$-0.0503754\pi$
$972$	15.5562	−	1.00168i	0.498967	−	0.0321290i
$973$	6.30917	+	3.64260i	0.202263	+	0.116776i
$974$	7.66391	+	13.2743i	0.245568	+	0.425336i
$975$	−6.09809	+	2.06846i	−0.195295	+	0.0662438i
$976$		−	1.93145i		−	0.0618243i
$977$		−	15.2487i		−	0.487850i	−0.969794	−	0.243925i	$-0.921565\pi$
$977$		−	15.2487i		−	0.487850i	0.969794	−	0.243925i	$-0.0784351\pi$
$978$	−20.8957	+	7.08780i	−0.668172	+	0.226643i
$979$	−3.08882	−	5.35000i	−0.0987192	−	0.170987i
$980$	−0.675869	−	0.390213i	−0.0215899	−	0.0124649i
$981$	46.4966	−	35.6442i	1.48452	−	1.13803i
$982$	8.29031	−	4.78641i	0.264554	−	0.152741i
$983$	−4.94134	−	8.55865i	−0.157604	−	0.272978i	0.776400	−	0.630240i	$-0.217044\pi$
$983$	−4.94134	−	8.55865i	−0.157604	−	0.272978i	−0.934004	+	0.357262i	$0.883710\pi$
$984$	−3.65944	+	4.17086i	−0.116659	+	0.132962i
$985$	−16.5295	−	9.54331i	−0.526674	−	0.304075i
$986$	−57.2982	−	33.0811i	−1.82475	−	1.05352i
$987$	−10.4346	+	52.3953i	−0.332136	+	1.66776i
$988$		−	25.7051i		−	0.817788i
$989$	14.8269	+	8.56033i	0.471469	+	0.272203i
$990$	0.315752	+	2.40691i	0.0100353	+	0.0764967i
$991$		−	36.2620i		−	1.15190i	−0.817485	−	0.575950i	$-0.804632\pi$
$991$		−	36.2620i		−	1.15190i	0.817485	−	0.575950i	$-0.195368\pi$
$992$	0.290293	−	5.56019i	0.00921681	−	0.176536i
$993$	35.5413	+	31.1833i	1.12787	+	0.989573i
$994$	16.3890			0.519828
$995$	−4.88669	+	8.46400i	−0.154919	+	0.268327i
$996$	−15.0817	+	17.1895i	−0.477883	+	0.544669i
$997$	−13.8522	−	23.9927i	−0.438704	−	0.759857i	0.558886	−	0.829244i	$-0.311229\pi$
$997$	−13.8522	−	23.9927i	−0.438704	−	0.759857i	−0.997590	+	0.0693875i	$0.977896\pi$
$998$	−7.78437	+	13.4829i	−0.246410	+	0.426794i
$999$	−10.4556	−	21.2388i	−0.330802	−	0.671966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.491.13	yes	40
3.2	odd	2	inner	930.2.o.e.491.1	yes	40
31.6	odd	6	inner	930.2.o.e.161.11	yes	40
93.68	even	6	inner	930.2.o.e.161.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.3	✓	40	93.68	even	6	inner
930.2.o.e.161.11	yes	40	31.6	odd	6	inner
930.2.o.e.491.1	yes	40	3.2	odd	2	inner
930.2.o.e.491.13	yes	40	1.1	even	1	trivial

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.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.556373 - 1.64026i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(1.64026 - 0.556373i) q^{6} +(-1.24695 + 2.15979i) q^{7} -1.00000i q^{8} +(-2.38090 + 1.82519i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.556373 - 1.64026i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(1.64026 - 0.556373i) q^{6} +(-1.24695 + 2.15979i) q^{7} -1.00000i q^{8} +(-2.38090 + 1.82519i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.404589 - 0.700769i) q^{11} +(0.556373 + 1.64026i) q^{12} +(3.21968 - 1.85888i) q^{13} +(-2.15979 - 1.24695i) q^{14} +(-1.30196 - 1.14232i) q^{15} +1.00000 q^{16} +(-3.37588 + 5.84719i) q^{17} +(-1.82519 - 2.38090i) q^{18} +(-3.45706 + 5.98781i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(4.23638 + 0.843679i) q^{21} +(0.700769 - 0.404589i) q^{22} +2.81543 q^{23} +(-1.64026 + 0.556373i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.85888 + 3.21968i) q^{26} +(4.31845 + 2.88980i) q^{27} +(1.24695 - 2.15979i) q^{28} +9.79927 q^{29} +(1.14232 - 1.30196i) q^{30} +(-5.56019 - 0.290293i) q^{31} +1.00000i q^{32} +(-0.924340 + 1.05352i) q^{33} +(-5.84719 - 3.37588i) q^{34} +2.49391i q^{35} +(2.38090 - 1.82519i) q^{36} +(-3.94549 - 2.27793i) q^{37} +(-5.98781 - 3.45706i) q^{38} +(-4.84039 - 4.24687i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(2.77433 - 1.60176i) q^{41} +(-0.843679 + 4.23638i) q^{42} +(5.26630 + 3.04050i) q^{43} +(0.404589 + 0.700769i) q^{44} +(-1.14932 + 2.77111i) q^{45} +2.81543i q^{46} +12.3679i q^{47} +(-0.556373 - 1.64026i) q^{48} +(0.390213 + 0.675869i) q^{49} +(0.866025 + 0.500000i) q^{50} +(11.4691 + 2.28409i) q^{51} +(-3.21968 + 1.85888i) q^{52} +(4.33368 + 7.50615i) q^{53} +(-2.88980 + 4.31845i) q^{54} +(-0.700769 - 0.404589i) q^{55} +(2.15979 + 1.24695i) q^{56} +(11.7450 + 2.33902i) q^{57} +9.79927i q^{58} +(1.80978 + 1.04488i) q^{59} +(1.30196 + 1.14232i) q^{60} -1.93145i q^{61} +(0.290293 - 5.56019i) q^{62} +(-0.973156 - 7.41816i) q^{63} -1.00000 q^{64} +(1.85888 - 3.21968i) q^{65} +(-1.05352 - 0.924340i) q^{66} +(1.82612 + 3.16294i) q^{67} +(3.37588 - 5.84719i) q^{68} +(-1.56643 - 4.61804i) q^{69} -2.49391 q^{70} +(-5.69119 + 3.28581i) q^{71} +(1.82519 + 2.38090i) q^{72} +(-11.0817 + 6.39801i) q^{73} +(2.27793 - 3.94549i) q^{74} +(-1.69869 - 0.338296i) q^{75} +(3.45706 - 5.98781i) q^{76} +2.01801 q^{77} +(4.24687 - 4.84039i) q^{78} +(-4.86732 - 2.81015i) q^{79} +(0.866025 - 0.500000i) q^{80} +(2.33735 - 8.69119i) q^{81} +(1.60176 + 2.77433i) q^{82} +(6.60136 + 11.4339i) q^{83} +(-4.23638 - 0.843679i) q^{84} +6.75175i q^{85} +(-3.04050 + 5.26630i) q^{86} +(-5.45205 - 16.0733i) q^{87} +(-0.700769 + 0.404589i) q^{88} +7.63447 q^{89} +(-2.77111 - 1.14932i) q^{90} +9.27175i q^{91} -2.81543 q^{92} +(2.61739 + 9.28166i) q^{93} -12.3679 q^{94} +6.91413i q^{95} +(1.64026 - 0.556373i) q^{96} +3.29345 q^{97} +(-0.675869 + 0.390213i) q^{98} +(2.24232 + 0.930006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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