LMFDB - Embedded newform 930.2.be.a.37.13

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			37.13
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.795067 + 2.08994i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.0433914 + 0.161939i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.795067 + 2.08994i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.0433914 + 0.161939i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.915617 + 2.04001i) q^{10} +(3.10212 + 1.79101i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-5.07586 + 1.36007i) q^{13} +(-0.145190 + 0.0838257i) q^{14} +(2.22451 - 0.227058i) q^{15} -1.00000 q^{16} +(7.84096 + 2.10098i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-1.88392 + 1.08768i) q^{19} +(-2.08994 + 0.795067i) q^{20} +(0.145190 + 0.0838257i) q^{21} +(0.927095 + 3.45997i) q^{22} +(-1.44181 - 1.44181i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.73574 + 3.32329i) q^{25} +(-4.55089 - 2.62746i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.161939 - 0.0433914i) q^{28} -4.55001 q^{29} +(1.73352 + 1.41241i) q^{30} +(4.42824 + 3.37501i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.53287 - 2.53287i) q^{33} +(4.05878 + 7.03001i) q^{34} +(-0.372942 + 0.0380667i) q^{35} +(0.500000 - 0.866025i) q^{36} +(8.44619 + 2.26315i) q^{37} +(-2.10124 - 0.563026i) q^{38} +5.25492i q^{39} +(-2.04001 - 0.915617i) q^{40} +(-4.57295 + 7.92059i) q^{41} +(0.0433914 + 0.161939i) q^{42} +(0.935119 - 3.48991i) q^{43} +(-1.79101 + 3.10212i) q^{44} +(0.356424 - 2.20748i) q^{45} -2.03902i q^{46} +(-6.62673 - 6.62673i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(6.03784 + 3.48595i) q^{49} +(-4.99149 - 0.291642i) q^{50} +(4.05878 - 7.03001i) q^{51} +(-1.36007 - 5.07586i) q^{52} +(-1.03619 + 0.277645i) q^{53} -1.00000 q^{54} +(-1.27672 + 7.90723i) q^{55} +(-0.0838257 - 0.145190i) q^{56} +(0.563026 + 2.10124i) q^{57} +(-3.21734 - 3.21734i) q^{58} +(9.81288 - 5.66547i) q^{59} +(0.227058 + 2.22451i) q^{60} -7.57409i q^{61} +(0.744745 + 5.51773i) q^{62} +(0.118547 - 0.118547i) q^{63} -1.00000i q^{64} +(-6.87813 - 9.52692i) q^{65} +3.58202 q^{66} +(-1.98892 + 0.532931i) q^{67} +(-2.10098 + 7.84096i) q^{68} +(-1.76585 + 1.01951i) q^{69} +(-0.290627 - 0.236793i) q^{70} +(-0.481177 + 0.833424i) q^{71} +(0.965926 - 0.258819i) q^{72} +(1.70902 - 0.457932i) q^{73} +(4.37207 + 7.57265i) q^{74} +(2.24317 + 4.46858i) q^{75} +(-1.08768 - 1.88392i) q^{76} +(-0.424639 + 0.424639i) q^{77} +(-3.71579 + 3.71579i) q^{78} +(4.34044 + 7.51786i) q^{79} +(-0.795067 - 2.08994i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-8.83426 + 2.36713i) q^{82} +(14.5761 - 3.90566i) q^{83} +(-0.0838257 + 0.145190i) q^{84} +(1.84316 + 18.0576i) q^{85} +(3.12897 - 1.80651i) q^{86} +(-1.17763 + 4.39497i) q^{87} +(-3.45997 + 0.927095i) q^{88} -13.3205 q^{89} +(1.81295 - 1.30889i) q^{90} -0.880994i q^{91} +(1.44181 - 1.44181i) q^{92} +(4.40612 - 3.40383i) q^{93} -9.37161i q^{94} +(-3.77104 - 3.07251i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-6.21382 - 6.21382i) q^{97} +(1.80446 + 6.73433i) q^{98} +(-1.79101 - 3.10212i) 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
$5$	0.795067	+	2.08994i	0.355565	+	0.934652i
$5$	0.795067	+	2.08994i	0.355565	+	0.934652i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−0.0433914	+	0.161939i	−0.0164004	+	0.0612071i	−0.973641	−	0.228086i	$-0.926753\pi$
$7$	−0.0433914	+	0.161939i	−0.0164004	+	0.0612071i	0.957241	+	0.289293i	$0.0934201\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.915617	+	2.04001i	−0.289543	+	0.645108i
$11$	3.10212	+	1.79101i	0.935324	+	0.540010i	0.888492	−	0.458893i	$-0.151754\pi$
$11$	3.10212	+	1.79101i	0.935324	+	0.540010i	0.0468328	+	0.998903i	$0.485087\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−5.07586	+	1.36007i	−1.40779	+	0.377216i	−0.881136	−	0.472863i	$-0.843220\pi$
$13$	−5.07586	+	1.36007i	−1.40779	+	0.377216i	−0.526654	+	0.850079i	$0.676554\pi$
$14$	−0.145190	+	0.0838257i	−0.0388038	+	0.0224034i
$15$	2.22451	−	0.227058i	0.574366	−	0.0586262i
$16$	−1.00000			−0.250000
$17$	7.84096	+	2.10098i	1.90171	+	0.509562i	0.996396	+	0.0848223i	$0.0270323\pi$
$17$	7.84096	+	2.10098i	1.90171	+	0.509562i	0.905315	+	0.424740i	$0.139634\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−1.88392	+	1.08768i	−0.432201	+	0.249531i	−0.700284	−	0.713865i	$-0.746943\pi$
$19$	−1.88392	+	1.08768i	−0.432201	+	0.249531i	0.268083	+	0.963396i	$0.413610\pi$
$20$	−2.08994	+	0.795067i	−0.467326	+	0.177782i
$21$	0.145190	+	0.0838257i	0.0316831	+	0.0182923i
$22$	0.927095	+	3.45997i	0.197657	+	0.737667i
$23$	−1.44181	−	1.44181i	−0.300638	−	0.300638i	0.540626	−	0.841263i	$-0.318188\pi$
$23$	−1.44181	−	1.44181i	−0.300638	−	0.300638i	−0.841263	+	0.540626i	$0.818188\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.73574	+	3.32329i	−0.747147	+	0.664658i
$26$	−4.55089	−	2.62746i	−0.892503	−	0.515287i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.161939	−	0.0433914i	−0.0306036	−	0.00820020i
$29$	−4.55001			−0.844916			−0.422458	−	0.906382i	$-0.638833\pi$
$29$	−4.55001			−0.844916			−0.422458	+	0.906382i	$0.638833\pi$
$30$	1.73352	+	1.41241i	0.316496	+	0.257870i
$31$	4.42824	+	3.37501i	0.795335	+	0.606170i
$31$	4.42824	+	3.37501i	0.795335	+	0.606170i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.53287	−	2.53287i	0.440916	−	0.440916i
$34$	4.05878	+	7.03001i	0.696075	+	1.20564i
$35$	−0.372942	+	0.0380667i	−0.0630387	+	0.00643444i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	8.44619	+	2.26315i	1.38855	+	0.372060i	0.874218	−	0.485534i	$-0.161375\pi$
$37$	8.44619	+	2.26315i	1.38855	+	0.372060i	0.514328	+	0.857594i	$0.328042\pi$
$38$	−2.10124	−	0.563026i	−0.340866	−	0.0913348i
$39$			5.25492i			0.841460i
$40$	−2.04001	−	0.915617i	−0.322554	−	0.144772i
$41$	−4.57295	+	7.92059i	−0.714175	+	1.23699i	0.249102	+	0.968477i	$0.419865\pi$
$41$	−4.57295	+	7.92059i	−0.714175	+	1.23699i	−0.963277	+	0.268510i	$0.913469\pi$
$42$	0.0433914	+	0.161939i	0.00669544	+	0.0249877i
$43$	0.935119	−	3.48991i	0.142604	−	0.532206i	−0.857246	−	0.514907i	$-0.827826\pi$
$43$	0.935119	−	3.48991i	0.142604	−	0.532206i	0.999850	−	0.0172994i	$-0.00550685\pi$
$44$	−1.79101	+	3.10212i	−0.270005	+	0.467662i
$45$	0.356424	−	2.20748i	0.0531325	−	0.329071i
$46$		−	2.03902i		−	0.300638i
$47$	−6.62673	−	6.62673i	−0.966608	−	0.966608i	0.0328522	−	0.999460i	$-0.489541\pi$
$47$	−6.62673	−	6.62673i	−0.966608	−	0.966608i	−0.999460	+	0.0328522i	$0.989541\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	6.03784	+	3.48595i	0.862548	+	0.497992i
$50$	−4.99149	−	0.291642i	−0.705903	−	0.0412444i
$51$	4.05878	−	7.03001i	0.568343	−	0.984398i
$52$	−1.36007	−	5.07586i	−0.188608	−	0.703895i
$53$	−1.03619	+	0.277645i	−0.142331	+	0.0381375i	−0.329281	−	0.944232i	$-0.606806\pi$
$53$	−1.03619	+	0.277645i	−0.142331	+	0.0381375i	0.186950	+	0.982369i	$0.440140\pi$
$54$	−1.00000			−0.136083
$55$	−1.27672	+	7.90723i	−0.172153	+	1.06621i
$56$	−0.0838257	−	0.145190i	−0.0112017	−	0.0194019i
$57$	0.563026	+	2.10124i	0.0745746	+	0.278316i
$58$	−3.21734	−	3.21734i	−0.422458	−	0.422458i
$59$	9.81288	−	5.66547i	1.27753	−	0.737581i	0.301135	−	0.953581i	$-0.402634\pi$
$59$	9.81288	−	5.66547i	1.27753	−	0.737581i	0.976393	+	0.216000i	$0.0693011\pi$
$60$	0.227058	+	2.22451i	0.0293131	+	0.287183i
$61$		−	7.57409i		−	0.969763i	−0.874580	−	0.484881i	$-0.838863\pi$
$61$		−	7.57409i		−	0.969763i	0.874580	−	0.484881i	$-0.161137\pi$
$62$	0.744745	+	5.51773i	0.0945827	+	0.700753i
$63$	0.118547	−	0.118547i	0.0149356	−	0.0149356i
$64$		−	1.00000i		−	0.125000i
$65$	−6.87813	−	9.52692i	−0.853126	−	1.18167i
$66$	3.58202			0.440916
$67$	−1.98892	+	0.532931i	−0.242986	+	0.0651078i	−0.378256	−	0.925701i	$-0.623476\pi$
$67$	−1.98892	+	0.532931i	−0.242986	+	0.0651078i	0.135271	+	0.990809i	$0.456810\pi$
$68$	−2.10098	+	7.84096i	−0.254781	+	0.950856i
$69$	−1.76585	+	1.01951i	−0.212583	+	0.122735i
$70$	−0.290627	−	0.236793i	−0.0347366	−	0.0283022i
$71$	−0.481177	+	0.833424i	−0.0571052	+	0.0989092i	−0.893165	−	0.449729i	$-0.851520\pi$
$71$	−0.481177	+	0.833424i	−0.0571052	+	0.0989092i	0.836060	+	0.548639i	$0.184854\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	1.70902	−	0.457932i	0.200026	−	0.0535969i	−0.157415	−	0.987533i	$-0.550316\pi$
$73$	1.70902	−	0.457932i	0.200026	−	0.0535969i	0.357441	+	0.933936i	$0.383649\pi$
$74$	4.37207	+	7.57265i	0.508243	+	0.880302i
$75$	2.24317	+	4.46858i	0.259019	+	0.515987i
$76$	−1.08768	−	1.88392i	−0.124766	−	0.216100i
$77$	−0.424639	+	0.424639i	−0.0483921	+	0.0483921i
$78$	−3.71579	+	3.71579i	−0.420730	+	0.420730i
$79$	4.34044	+	7.51786i	0.488337	+	0.845825i	0.999910	−	0.0134150i	$-0.00427025\pi$
$79$	4.34044	+	7.51786i	0.488337	+	0.845825i	−0.511573	+	0.859240i	$0.670937\pi$
$80$	−0.795067	−	2.08994i	−0.0888912	−	0.233663i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−8.83426	+	2.36713i	−0.975581	+	0.261406i
$83$	14.5761	−	3.90566i	1.59994	−	0.428702i	0.654914	−	0.755704i	$-0.272705\pi$
$83$	14.5761	−	3.90566i	1.59994	−	0.428702i	0.945024	+	0.327002i	$0.106038\pi$
$84$	−0.0838257	+	0.145190i	−0.00914613	+	0.0158416i
$85$	1.84316	+	18.0576i	0.199919	+	1.95862i
$86$	3.12897	−	1.80651i	0.337405	−	0.194801i
$87$	−1.17763	+	4.39497i	−0.126255	+	0.471191i
$88$	−3.45997	+	0.927095i	−0.368834	+	0.0988286i
$89$	−13.3205			−1.41197			−0.705987	−	0.708225i	$-0.749496\pi$
$89$	−13.3205			−1.41197			−0.705987	+	0.708225i	$0.749496\pi$
$90$	1.81295	−	1.30889i	0.191102	−	0.137969i
$91$		−	0.880994i		−	0.0923533i
$92$	1.44181	−	1.44181i	0.150319	−	0.150319i
$93$	4.40612	−	3.40383i	0.456894	−	0.352961i
$94$		−	9.37161i		−	0.966608i
$95$	−3.77104	−	3.07251i	−0.386900	−	0.315233i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−6.21382	−	6.21382i	−0.630918	−	0.630918i	0.317381	−	0.948298i	$-0.397197\pi$
$97$	−6.21382	−	6.21382i	−0.630918	−	0.630918i	−0.948298	+	0.317381i	$0.897197\pi$
$98$	1.80446	+	6.73433i	0.182278	+	0.680270i
$99$	−1.79101	−	3.10212i	−0.180003	−	0.311775i
$100$	−3.32329	−	3.73574i	−0.332329	−	0.373574i
$101$	0.233218			0.0232061			0.0116030	−	0.999933i	$-0.496307\pi$
$101$	0.233218			0.0232061			0.0116030	+	0.999933i	$0.496307\pi$
$102$	7.84096	−	2.10098i	0.776371	−	0.208028i
$103$	0.188569	+	0.703750i	0.0185803	+	0.0693426i	0.974594	−	0.223981i	$-0.0719053\pi$
$103$	0.188569	+	0.703750i	0.0185803	+	0.0693426i	−0.956013	+	0.293324i	$0.905239\pi$
$104$	2.62746	−	4.55089i	0.257643	−	0.446252i
$105$	−0.0597550	+	0.370087i	−0.00583149	+	0.0361168i
$106$	−0.929019	−	0.536369i	−0.0902343	−	0.0520968i
$107$	1.26157	−	4.70823i	0.121960	−	0.455162i	−0.877753	−	0.479114i	$-0.840958\pi$
$107$	1.26157	−	4.70823i	0.121960	−	0.455162i	0.999713	+	0.0239518i	$0.00762483\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	6.61537i		−	0.633637i	−0.948486	−	0.316819i	$-0.897385\pi$
$109$		−	6.61537i		−	0.633637i	0.948486	−	0.316819i	$-0.102615\pi$
$110$	−6.49403	+	4.68848i	−0.619182	+	0.447029i
$111$	4.37207	−	7.57265i	0.414979	−	0.718764i
$112$	0.0433914	−	0.161939i	0.00410010	−	0.0153018i
$113$	−2.69194	−	10.0465i	−0.253236	−	0.945091i	−0.969063	−	0.246813i	$-0.920617\pi$
$113$	−2.69194	−	10.0465i	−0.253236	−	0.945091i	0.715827	−	0.698278i	$-0.246050\pi$
$114$	−1.08768	+	1.88392i	−0.101871	+	0.176445i
$115$	1.86697	−	4.15963i	0.174095	−	0.387888i
$116$		−	4.55001i		−	0.422458i
$117$	5.07586	+	1.36007i	0.469263	+	0.125739i
$118$	10.9448	+	2.93266i	1.00755	+	0.269974i
$119$	−0.680460	+	1.17859i	−0.0623777	+	0.108041i
$120$	−1.41241	+	1.73352i	−0.128935	+	0.158248i
$121$	0.915431	+	1.58557i	0.0832210	+	0.144143i
$122$	5.35569	−	5.35569i	0.484881	−	0.484881i
$123$	6.46713	+	6.46713i	0.583122	+	0.583122i
$124$	−3.37501	+	4.42824i	−0.303085	+	0.397668i
$125$	−9.91566	−	5.16524i	−0.886883	−	0.461993i
$126$	0.167651			0.0149356
$127$	11.5851	+	3.10421i	1.02801	+	0.275454i	0.733135	−	0.680083i	$-0.238056\pi$
$127$	11.5851	+	3.10421i	1.02801	+	0.275454i	0.294873	+	0.955537i	$0.404723\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.12897	−	1.80651i	−0.275490	−	0.159054i
$130$	1.87298	−	11.6001i	0.164271	−	1.01740i
$131$	6.99634	+	12.1180i	0.611273	+	1.05876i	0.991026	+	0.133669i	$0.0426758\pi$
$131$	6.99634	+	12.1180i	0.611273	+	1.05876i	−0.379753	+	0.925088i	$0.623991\pi$
$132$	2.53287	+	2.53287i	0.220458	+	0.220458i
$133$	−0.0943920	−	0.352276i	−0.00818483	−	0.0305462i
$134$	−1.78322	−	1.02954i	−0.154047	−	0.0889390i
$135$	−2.04001	−	0.915617i	−0.175576	−	0.0788037i
$136$	−7.03001	+	4.05878i	−0.602818	+	0.348037i
$137$	−0.144066	−	0.537663i	−0.0123084	−	0.0459356i	0.959499	−	0.281714i	$-0.0909028\pi$
$137$	−0.144066	−	0.537663i	−0.0123084	−	0.0459356i	−0.971807	+	0.235778i	$0.924236\pi$
$138$	−1.96955	−	0.527738i	−0.167659	−	0.0449241i
$139$	6.11986			0.519079			0.259540	−	0.965732i	$-0.416429\pi$
$139$	6.11986			0.519079			0.259540	+	0.965732i	$0.416429\pi$
$140$	−0.0380667	−	0.372942i	−0.00321722	−	0.0315194i
$141$	−8.11605	+	4.68581i	−0.683495	+	0.394616i
$142$	−0.929563	+	0.249076i	−0.0780072	+	0.0209020i
$143$	−18.1818	−	4.87181i	−1.52044	−	0.407401i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−3.61757	−	9.50927i	−0.300422	−	0.789702i
$146$	1.53227	+	0.884656i	0.126812	+	0.0732147i
$147$	4.92987	−	4.92987i	0.406609	−	0.406609i
$148$	−2.26315	+	8.44619i	−0.186030	+	0.694273i
$149$	8.47711	−	4.89426i	0.694472	−	0.400954i	−0.110813	−	0.993841i	$-0.535346\pi$
$149$	8.47711	−	4.89426i	0.694472	−	0.400954i	0.805285	+	0.592888i	$0.202012\pi$
$150$	−1.57360	+	4.74592i	−0.128484	+	0.387503i
$151$		−	15.8599i		−	1.29066i	−0.763904	−	0.645330i	$-0.776720\pi$
$151$		−	15.8599i		−	1.29066i	0.763904	−	0.645330i	$-0.223280\pi$
$152$	0.563026	−	2.10124i	0.0456674	−	0.170433i
$153$	−5.73998	−	5.73998i	−0.464050	−	0.464050i
$154$	−0.600531			−0.0483921
$155$	−3.53284	+	11.9381i	−0.283764	+	0.958894i
$156$	−5.25492			−0.420730
$157$	−6.28454	−	6.28454i	−0.501561	−	0.501561i	0.410362	−	0.911923i	$-0.365402\pi$
$157$	−6.28454	−	6.28454i	−0.501561	−	0.501561i	−0.911923	+	0.410362i	$0.865402\pi$
$158$	−2.24678	+	8.38508i	−0.178744	+	0.667081i
$159$			1.07274i			0.0850737i
$160$	0.915617	−	2.04001i	0.0723858	−	0.161277i
$161$	0.296047	−	0.170923i	0.0233318	−	0.0134706i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	8.52918	−	8.52918i	0.668057	−	0.668057i	−0.289209	−	0.957266i	$-0.593392\pi$
$163$	8.52918	−	8.52918i	0.668057	−	0.668057i	0.957266	+	0.289209i	$0.0933923\pi$
$164$	−7.92059	−	4.57295i	−0.618494	−	0.357088i
$165$	7.30736	+	3.27976i	0.568877	+	0.255329i
$166$	13.0686	+	7.54516i	1.01432	+	0.585618i
$167$	−14.6822	−	3.93408i	−1.13614	−	0.304428i	−0.358743	−	0.933436i	$-0.616795\pi$
$167$	−14.6822	−	3.93408i	−1.13614	−	0.304428i	−0.777399	+	0.629008i	$0.783461\pi$
$168$	−0.161939	+	0.0433914i	−0.0124939	+	0.00334772i
$169$	12.6562	−	7.30708i	0.973556	−	0.562083i
$170$	−11.4653	+	14.0720i	−0.879351	+	1.07927i
$171$	2.17536			0.166354
$172$	3.48991	+	0.935119i	0.266103	+	0.0713021i
$173$	−5.12245	−	19.1172i	−0.389453	−	1.45346i	−0.831027	−	0.556232i	$-0.812247\pi$
$173$	−5.12245	−	19.1172i	−0.389453	−	1.45346i	0.441574	−	0.897225i	$-0.354420\pi$
$174$	−3.94043	+	2.27501i	−0.298723	+	0.172468i
$175$	−0.376071	−	0.749163i	−0.0284283	−	0.0566314i
$176$	−3.10212	−	1.79101i	−0.233831	−	0.135002i
$177$	−2.93266	−	10.9448i	−0.220432	−	0.822665i
$178$	−9.41905	−	9.41905i	−0.705987	−	0.705987i
$179$	−12.2026	−	21.1356i	−0.912067	−	1.57975i	−0.811140	−	0.584852i	$-0.801153\pi$
$179$	−12.2026	−	21.1356i	−0.912067	−	1.57975i	−0.100927	−	0.994894i	$-0.532181\pi$
$180$	2.20748	+	0.356424i	0.164536	+	0.0265663i
$181$	−3.52955	−	2.03778i	−0.262349	−	0.151467i	0.363057	−	0.931767i	$-0.381733\pi$
$181$	−3.52955	−	2.03778i	−0.262349	−	0.151467i	−0.625406	+	0.780300i	$0.715066\pi$
$182$	0.622957	−	0.622957i	0.0461766	−	0.0461766i
$183$	−7.31601	−	1.96032i	−0.540815	−	0.144911i
$184$	2.03902			0.150319
$185$	1.98543	+	19.4514i	0.145972	+	1.43010i
$186$	5.52247	+	0.708725i	0.404927	+	0.0519663i
$187$	20.5607	+	20.5607i	1.50355	+	1.50355i
$188$	6.62673	−	6.62673i	0.483304	−	0.483304i
$189$	−0.0838257	−	0.145190i	−0.00609742	−	0.0105610i
$190$	−0.493935	−	4.83912i	−0.0358338	−	0.351067i
$191$	1.95916	−	3.39337i	0.141760	−	0.245535i	−0.786400	−	0.617718i	$-0.788057\pi$
$191$	1.95916	−	3.39337i	0.141760	−	0.245535i	0.928159	+	0.372183i	$0.121391\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−15.3572	−	4.11495i	−1.10543	−	0.296200i	−0.340459	−	0.940259i	$-0.610582\pi$
$193$	−15.3572	−	4.11495i	−1.10543	−	0.296200i	−0.764976	+	0.644059i	$0.777249\pi$
$194$		−	8.78766i		−	0.630918i
$195$	−10.9825	+	4.17801i	−0.786472	+	0.299194i
$196$	−3.48595	+	6.03784i	−0.248996	+	0.431274i
$197$	−4.52997	−	16.9061i	−0.322747	−	1.20451i	−0.916557	−	0.399903i	$-0.869044\pi$
$197$	−4.52997	−	16.9061i	−0.322747	−	1.20451i	0.593810	−	0.804605i	$-0.297623\pi$
$198$	0.927095	−	3.45997i	0.0658858	−	0.245889i
$199$	−0.823050	+	1.42556i	−0.0583445	+	0.101056i	−0.893722	−	0.448620i	$-0.851916\pi$
$199$	−0.823050	+	1.42556i	−0.0583445	+	0.101056i	0.835378	+	0.549676i	$0.185249\pi$
$200$	0.291642	−	4.99149i	0.0206222	−	0.352951i
$201$			2.05909i			0.145237i
$202$	0.164910	+	0.164910i	0.0116030	+	0.0116030i
$203$	0.197431	−	0.736824i	0.0138570	−	0.0517149i
$204$	7.03001	+	4.05878i	0.492199	+	0.284171i
$205$	−20.1894	−	3.25982i	−1.41009	−	0.227676i
$206$	−0.364288	+	0.630965i	−0.0253811	+	0.0439614i
$207$	0.527738	+	1.96955i	0.0366804	+	0.136893i
$208$	5.07586	−	1.36007i	0.351948	−	0.0943041i
$209$	−7.79219			−0.538997
$210$	−0.303944	+	0.219438i	−0.0209741	+	0.0151426i
$211$	12.9170	+	22.3728i	0.889240	+	1.54021i	0.840775	+	0.541385i	$0.182100\pi$
$211$	12.9170	+	22.3728i	0.889240	+	1.54021i	0.0484655	+	0.998825i	$0.484567\pi$
$212$	−0.277645	−	1.03619i	−0.0190688	−	0.0711656i
$213$	0.680487	+	0.680487i	0.0466262	+	0.0466262i
$214$	4.22128	−	2.43716i	0.288561	−	0.166601i
$215$	8.03720	−	0.820367i	0.548133	−	0.0559486i
$216$		−	1.00000i		−	0.0680414i
$217$	−0.738693	+	0.570658i	−0.0501457	+	0.0387388i
$218$	4.67777	−	4.67777i	0.316819	−	0.316819i
$219$		−	1.76931i		−	0.119559i
$220$	−7.90723	−	1.27672i	−0.533105	−	0.0860763i
$221$	−42.6571			−2.86943
$222$	8.44619	−	2.26315i	0.566871	−	0.151893i
$223$	0.831017	−	3.10140i	0.0556490	−	0.207685i	−0.932503	−	0.361161i	$-0.882380\pi$
$223$	0.831017	−	3.10140i	0.0556490	−	0.207685i	0.988152	+	0.153477i	$0.0490470\pi$
$224$	0.145190	−	0.0838257i	0.00970094	−	0.00560084i
$225$	4.89689	−	1.01019i	0.326459	−	0.0673458i
$226$	5.20043	−	9.00741i	0.345927	−	0.599164i
$227$	20.0230	−	5.36515i	1.32897	−	0.356097i	0.476641	−	0.879098i	$-0.341854\pi$
$227$	20.0230	−	5.36515i	1.32897	−	0.356097i	0.852332	+	0.523001i	$0.175188\pi$
$228$	−2.10124	+	0.563026i	−0.139158	+	0.0372873i
$229$	8.68551	+	15.0437i	0.573954	+	0.994118i	0.996154	+	0.0876155i	$0.0279247\pi$
$229$	8.68551	+	15.0437i	0.573954	+	0.994118i	−0.422200	+	0.906503i	$0.638742\pi$
$230$	4.26145	−	1.62116i	0.280992	−	0.106896i
$231$	0.300265	+	0.520075i	0.0197560	+	0.0342184i
$232$	3.21734	−	3.21734i	0.211229	−	0.211229i
$233$	15.2535	−	15.2535i	0.999288	−	0.999288i	−0.000711673	−	1.00000i	$-0.500227\pi$
$233$	15.2535	−	15.2535i	0.999288	−	0.999288i	1.00000		0.000711673i	$0.000226532\pi$
$234$	2.62746	+	4.55089i	0.171762	+	0.297501i
$235$	8.58080	−	19.1182i	0.559750	−	1.24713i
$236$	5.66547	+	9.81288i	0.368791	+	0.638764i
$237$	8.38508	−	2.24678i	0.544669	−	0.145944i
$238$	−1.31455	+	0.352232i	−0.0852095	+	0.0228318i
$239$	−3.68195	+	6.37732i	−0.238165	+	0.412514i	−0.960188	−	0.279355i	$-0.909879\pi$
$239$	−3.68195	+	6.37732i	−0.238165	+	0.412514i	0.722023	+	0.691869i	$0.243213\pi$
$240$	−2.22451	+	0.227058i	−0.143591	+	0.0146566i
$241$	−14.1843	+	8.18934i	−0.913694	+	0.527522i	−0.881618	−	0.471964i	$-0.843545\pi$
$241$	−14.1843	+	8.18934i	−0.913694	+	0.527522i	−0.0320762	+	0.999485i	$0.510212\pi$
$242$	−0.473862	+	1.76848i	−0.0304610	+	0.113682i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	7.57409			0.484881
$245$	−2.48495	+	15.3903i	−0.158758	+	0.983251i
$246$			9.14590i			0.583122i
$247$	8.08319	−	8.08319i	0.514321	−	0.514321i
$248$	−5.51773	+	0.744745i	−0.350376	+	0.0472914i
$249$		−	15.0903i		−	0.956310i
$250$	−3.35905	−	10.6638i	−0.212445	−	0.674438i
$251$	−13.0594	+	7.53987i	−0.824305	+	0.475913i	−0.851899	−	0.523707i	$-0.824549\pi$
$251$	−13.0594	+	7.53987i	−0.824305	+	0.475913i	0.0275939	+	0.999619i	$0.491215\pi$
$252$	0.118547	+	0.118547i	0.00746779	+	0.00746779i
$253$	−1.89037	−	7.05495i	−0.118847	−	0.443541i
$254$	5.99687	+	10.3869i	0.376277	+	0.651731i
$255$	17.9193	+	2.89329i	1.12215	+	0.181185i
$256$	1.00000			0.0625000
$257$	17.9072	−	4.79822i	1.11702	−	0.299305i	0.347344	−	0.937738i	$-0.387084\pi$
$257$	17.9072	−	4.79822i	1.11702	−	0.299305i	0.769677	+	0.638433i	$0.220417\pi$
$258$	−0.935119	−	3.48991i	−0.0582179	−	0.217272i
$259$	−0.732984	+	1.26957i	−0.0455454	+	0.0788869i
$260$	9.52692	−	6.87813i	0.590834	−	0.426563i
$261$	3.94043	+	2.27501i	0.243906	+	0.140819i
$262$	−3.62157	+	13.5159i	−0.223742	+	0.835015i
$263$	9.13897	+	9.13897i	0.563533	+	0.563533i	0.930309	−	0.366776i	$-0.119538\pi$
$263$	9.13897	+	9.13897i	0.563533	+	0.563533i	−0.366776	+	0.930309i	$0.619538\pi$
$264$			3.58202i			0.220458i
$265$	−1.40410	−	1.94482i	−0.0862532	−	0.119470i
$266$	0.182351	−	0.315842i	0.0111807	−	0.0193655i
$267$	−3.44761	+	12.8667i	−0.210990	+	0.787426i
$268$	−0.532931	−	1.98892i	−0.0325539	−	0.121493i
$269$	−5.10313	+	8.83888i	−0.311143	+	0.538916i	−0.978610	−	0.205723i	$-0.934045\pi$
$269$	−5.10313	+	8.83888i	−0.311143	+	0.538916i	0.667467	+	0.744640i	$0.267379\pi$
$270$	−0.795067	−	2.08994i	−0.0483862	−	0.127190i
$271$			15.4527i			0.938686i	0.883016	+	0.469343i	$0.155509\pi$
$271$			15.4527i			0.938686i	−0.883016	+	0.469343i	$0.844491\pi$
$272$	−7.84096	−	2.10098i	−0.475428	−	0.127391i
$273$	−0.850975	−	0.228018i	−0.0515034	−	0.0138003i
$274$	0.278315	−	0.482055i	0.0168136	−	0.0291220i
$275$	−17.5408	+	3.61851i	−1.05775	+	0.218204i
$276$	−1.01951	−	1.76585i	−0.0613674	−	0.106292i
$277$	−16.5768	+	16.5768i	−0.996004	+	0.996004i	−0.999992	−	0.00398797i	$-0.998731\pi$
$277$	−16.5768	+	16.5768i	−0.996004	+	0.996004i	0.00398797	+	0.999992i	$0.498731\pi$
$278$	4.32739	+	4.32739i	0.259540	+	0.259540i
$279$	−2.14746	−	5.13696i	−0.128565	−	0.307542i
$280$	0.236793	−	0.290627i	0.0141511	−	0.0173683i
$281$	12.0880			0.721112			0.360556	−	0.932738i	$-0.382587\pi$
$281$	12.0880			0.721112			0.360556	+	0.932738i	$0.382587\pi$
$282$	−9.05228	−	2.42555i	−0.539056	−	0.144440i
$283$	15.5899	−	15.5899i	0.926723	−	0.926723i	−0.0707699	−	0.997493i	$-0.522546\pi$
$283$	15.5899	−	15.5899i	0.926723	−	0.926723i	0.997493	+	0.0707699i	$0.0225456\pi$
$284$	−0.833424	−	0.481177i	−0.0494546	−	0.0285526i
$285$	−3.94383	+	2.84732i	−0.233612	+	0.168661i
$286$	−9.41161	−	16.3014i	−0.556520	−	0.963921i
$287$	−1.08422	−	1.08422i	−0.0639997	−	0.0639997i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	42.3441	+	24.4474i	2.49083	+	1.43808i
$290$	4.16607	−	9.28208i	0.244640	−	0.545062i
$291$	−7.61034	+	4.39383i	−0.446126	+	0.257571i
$292$	0.457932	+	1.70902i	0.0267984	+	0.100013i
$293$	21.0059	+	5.62851i	1.22718	+	0.328821i	0.813479	−	0.581594i	$-0.197571\pi$
$293$	21.0059	+	5.62851i	1.22718	+	0.328821i	0.413697	+	0.910415i	$0.364237\pi$
$294$	6.97189			0.406609
$295$	19.6424	+	16.0040i	1.14363	+	0.931786i
$296$	−7.57265	+	4.37207i	−0.440151	+	0.254121i
$297$	−3.45997	+	0.927095i	−0.200768	+	0.0537955i
$298$	9.45499	+	2.53346i	0.547713	+	0.146759i
$299$	9.27938	+	5.35745i	0.536640	+	0.309830i
$300$	−4.46858	+	2.24317i	−0.257993	+	0.129510i
$301$	0.524576	+	0.302864i	0.0302361	+	0.0174568i
$302$	11.2146	−	11.2146i	0.645330	−	0.645330i
$303$	0.0603613	−	0.225271i	0.00346767	−	0.0129415i
$304$	1.88392	−	1.08768i	0.108050	−	0.0623828i
$305$	15.8294	−	6.02191i	0.906390	−	0.344814i
$306$		−	8.11756i		−	0.464050i
$307$	−3.21403	+	11.9949i	−0.183434	+	0.684586i	0.811526	+	0.584316i	$0.198637\pi$
$307$	−3.21403	+	11.9949i	−0.183434	+	0.684586i	−0.994960	+	0.100270i	$0.968029\pi$
$308$	−0.424639	−	0.424639i	−0.0241961	−	0.0241961i
$309$	0.728576			0.0414472
$310$	−10.9396	+	5.94344i	−0.621329	+	0.337565i
$311$	−15.3264			−0.869083			−0.434541	−	0.900652i	$-0.643090\pi$
$311$	−15.3264			−0.869083			−0.434541	+	0.900652i	$0.643090\pi$
$312$	−3.71579	−	3.71579i	−0.210365	−	0.210365i
$313$	5.27141	−	19.6732i	0.297958	−	1.11199i	−0.640882	−	0.767640i	$-0.721431\pi$
$313$	5.27141	−	19.6732i	0.297958	−	1.11199i	0.938840	−	0.344355i	$-0.111902\pi$
$314$		−	8.88768i		−	0.501561i
$315$	0.342011	+	0.153504i	0.0192701	+	0.00864899i
$316$	−7.51786	+	4.34044i	−0.422912	+	0.244169i
$317$	9.14833	−	34.1420i	0.513822	−	1.91761i	0.139833	−	0.990175i	$-0.455343\pi$
$317$	9.14833	−	34.1420i	0.513822	−	1.91761i	0.373989	−	0.927433i	$-0.377990\pi$
$318$	−0.758541	+	0.758541i	−0.0425369	+	0.0425369i
$319$	−14.1147	−	8.14912i	−0.790271	−	0.456263i
$320$	2.08994	−	0.795067i	0.116831	−	0.0444456i
$321$	−4.22128	−	2.43716i	−0.235609	−	0.136029i
$322$	0.330197	+	0.0884761i	0.0184012	+	0.00493058i
$323$	−17.0569	+	4.57039i	−0.949073	+	0.254303i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	14.4422	−	21.9494i	0.801107	−	1.21754i
$326$	12.0621			0.668057
$327$	−6.38996	−	1.71218i	−0.353365	−	0.0946840i
$328$	−2.36713	−	8.83426i	−0.130703	−	0.487791i
$329$	1.36067	−	0.785582i	0.0750161	−	0.0433105i
$330$	2.84795	+	7.48622i	0.156774	+	0.412103i
$331$	12.0174	+	6.93822i	0.660534	+	0.381359i	0.792480	−	0.609898i	$-0.208789\pi$
$331$	12.0174	+	6.93822i	0.660534	+	0.381359i	−0.131947	+	0.991257i	$0.542123\pi$
$332$	3.90566	+	14.5761i	0.214351	+	0.799969i
$333$	−6.18304	−	6.18304i	−0.338829	−	0.338829i
$334$	−7.60006	−	13.1637i	−0.415857	−	0.720285i
$335$	−2.69512	−	3.73303i	−0.147250	−	0.203957i
$336$	−0.145190	−	0.0838257i	−0.00792078	−	0.00457307i
$337$	−7.21407	+	7.21407i	−0.392975	+	0.392975i	−0.875747	−	0.482771i	$-0.839630\pi$
$337$	−7.21407	+	7.21407i	−0.392975	+	0.392975i	0.482771	+	0.875747i	$0.339630\pi$
$338$	14.1162	+	3.78242i	0.767819	+	0.205737i
$339$	−10.4009			−0.564897
$340$	−18.0576	+	1.84316i	−0.979310	+	0.0999594i
$341$	7.69225	+	18.4007i	0.416559	+	0.996454i
$342$	1.53821	+	1.53821i	0.0831771	+	0.0831771i
$343$	−1.65633	+	1.65633i	−0.0894335	+	0.0894335i
$344$	1.80651	+	3.12897i	0.0974005	+	0.168703i
$345$	−3.53469	−	2.87994i	−0.190301	−	0.155051i
$346$	9.89581	−	17.1400i	0.532002	−	0.921455i
$347$	9.40075	+	2.51892i	0.504659	+	0.135223i	0.502161	−	0.864774i	$-0.332538\pi$
$347$	9.40075	+	2.51892i	0.504659	+	0.135223i	0.00249754	+	0.999997i	$0.499205\pi$
$348$	−4.39497	−	1.17763i	−0.235595	−	0.0631276i
$349$		−	29.0261i		−	1.55373i	−0.629668	−	0.776865i	$-0.716809\pi$
$349$		−	29.0261i		−	1.55373i	0.629668	−	0.776865i	$-0.283191\pi$
$350$	0.263816	−	0.795661i	0.0141015	−	0.0425299i
$351$	2.62746	−	4.55089i	0.140243	−	0.242909i
$352$	−0.927095	−	3.45997i	−0.0494143	−	0.184417i
$353$	−5.66507	+	21.1423i	−0.301521	+	1.12529i	0.634378	+	0.773023i	$0.281256\pi$
$353$	−5.66507	+	21.1423i	−0.301521	+	1.12529i	−0.935899	+	0.352269i	$0.885410\pi$
$354$	5.66547	−	9.81288i	0.301116	−	0.521549i
$355$	−2.12438	−	0.343006i	−0.112750	−	0.0182049i
$356$		−	13.3205i		−	0.705987i
$357$	0.962316	+	0.962316i	0.0509311	+	0.0509311i
$358$	6.31654	−	23.5737i	0.333840	−	1.24591i
$359$	−25.4461	−	14.6913i	−1.34300	−	0.775379i	−0.355749	−	0.934581i	$-0.615774\pi$
$359$	−25.4461	−	14.6913i	−1.34300	−	0.775379i	−0.987246	+	0.159203i	$0.949108\pi$
$360$	1.30889	+	1.81295i	0.0689847	+	0.0955510i
$361$	−7.13390	+	12.3563i	−0.375468	+	0.650330i
$362$	−1.05483	−	3.93670i	−0.0554409	−	0.206908i
$363$	1.76848	−	0.473862i	0.0928210	−	0.0248713i
$364$	0.880994			0.0461766
$365$	2.31584	+	3.20768i	0.121217	+	0.167898i
$366$	−3.78704	−	6.55935i	−0.197952	−	0.342863i
$367$	−0.00911101	−	0.0340027i	−0.000475591	−	0.00177493i	0.965688	−	0.259706i	$-0.0836258\pi$
$367$	−0.00911101	−	0.0340027i	−0.000475591	−	0.00177493i	−0.966163	+	0.257931i	$0.916959\pi$
$368$	1.44181	+	1.44181i	0.0751595	+	0.0751595i
$369$	7.92059	−	4.57295i	0.412329	−	0.238058i
$370$	−12.3503	+	15.1581i	−0.642063	+	0.788035i
$371$		−	0.179846i		−	0.00933715i
$372$	3.40383	+	4.40612i	0.176481	+	0.228447i
$373$	−9.70317	+	9.70317i	−0.502411	+	0.502411i	−0.912186	−	0.409775i	$-0.865607\pi$
$373$	−9.70317	+	9.70317i	−0.502411	+	0.502411i	0.409775	+	0.912186i	$0.365607\pi$
$374$			29.0772i			1.50355i
$375$	−7.55560	+	8.24093i	−0.390170	+	0.425560i
$376$	9.37161			0.483304
$377$	23.0952	−	6.18835i	1.18946	−	0.318716i
$378$	0.0433914	−	0.161939i	0.00223181	−	0.00832923i
$379$	−21.0283	+	12.1407i	−1.08015	+	0.623626i	−0.930937	−	0.365179i	$-0.881008\pi$
$379$	−21.0283	+	12.1407i	−1.08015	+	0.623626i	−0.149215	+	0.988805i	$0.547675\pi$
$380$	3.07251	−	3.77104i	0.157616	−	0.193450i
$381$	5.99687	−	10.3869i	0.307229	−	0.532136i
$382$	3.78481	−	1.01414i	0.193648	−	0.0518877i
$383$	−22.2210	+	5.95411i	−1.13544	+	0.304241i	−0.777117	−	0.629356i	$-0.783319\pi$
$383$	−22.2210	+	5.95411i	−1.13544	+	0.304241i	−0.358325	+	0.933597i	$0.616652\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−1.22509	−	0.549856i	−0.0624363	−	0.0280232i
$386$	−7.94947	−	13.7689i	−0.404617	−	0.700818i
$387$	−2.55479	+	2.55479i	−0.129867	+	0.129867i
$388$	6.21382	−	6.21382i	0.315459	−	0.315459i
$389$	3.27396	+	5.67067i	0.165997	+	0.287515i	0.937009	−	0.349306i	$-0.113583\pi$
$389$	3.27396	+	5.67067i	0.165997	+	0.287515i	−0.771012	+	0.636820i	$0.780249\pi$
$390$	−10.7201	−	4.81149i	−0.542833	−	0.243639i
$391$	−8.27595	−	14.3344i	−0.418533	−	0.724920i
$392$	−6.73433	+	1.80446i	−0.340135	+	0.0911389i
$393$	13.5159	−	3.62157i	0.681787	−	0.182684i
$394$	8.75123	−	15.1576i	0.440881	−	0.763628i
$395$	−12.2610	+	15.0485i	−0.616916	+	0.757171i
$396$	3.10212	−	1.79101i	0.155887	−	0.0900016i
$397$	−6.55068	+	24.4475i	−0.328769	+	1.22698i	0.581699	+	0.813404i	$0.302388\pi$
$397$	−6.55068	+	24.4475i	−0.328769	+	1.22698i	−0.910468	+	0.413579i	$0.864279\pi$
$398$	−1.59001	+	0.426042i	−0.0797000	+	0.0213556i
$399$	−0.364703			−0.0182580
$400$	3.73574	−	3.32329i	0.186787	−	0.166165i
$401$			9.44619i			0.471720i	0.971787	+	0.235860i	$0.0757907\pi$
$401$			9.44619i			0.471720i	−0.971787	+	0.235860i	$0.924209\pi$
$402$	−1.45599	+	1.45599i	−0.0726184	+	0.0726184i
$403$	−27.0674	−	11.1084i	−1.34832	−	0.553347i
$404$			0.233218i			0.0116030i
$405$	−1.41241	+	1.73352i	−0.0701833	+	0.0861393i
$406$	0.660618	−	0.381408i	0.0327859	−	0.0189290i
$407$	22.1478	+	22.1478i	1.09782	+	1.09782i
$408$	2.10098	+	7.84096i	0.104014	+	0.388185i
$409$	17.7200	+	30.6920i	0.876199	+	1.51762i	0.855480	+	0.517836i	$0.173262\pi$
$409$	17.7200	+	30.6920i	0.876199	+	1.51762i	0.0207191	+	0.999785i	$0.493404\pi$
$410$	−11.9710	−	16.5811i	−0.591206	−	0.818882i
$411$	−0.556630			−0.0274565
$412$	−0.703750	+	0.188569i	−0.0346713	+	0.00929014i
$413$	0.491665	+	1.83492i	0.0241933	+	0.0902905i
$414$	−1.01951	+	1.76585i	−0.0501063	+	0.0867867i
$415$	19.7516	+	27.3580i	0.969568	+	1.34295i
$416$	4.55089	+	2.62746i	0.223126	+	0.128822i
$417$	1.58394	−	5.91133i	0.0775656	−	0.289479i
$418$	−5.50991	−	5.50991i	−0.269499	−	0.269499i
$419$			32.8774i			1.60617i	0.595867	+	0.803083i	$0.296808\pi$
$419$			32.8774i			1.60617i	−0.595867	+	0.803083i	$0.703192\pi$
$420$	−0.370087	−	0.0597550i	−0.0180584	−	0.00291574i
$421$	−9.62992	+	16.6795i	−0.469334	+	0.812910i	−0.999385	−	0.0350557i	$-0.988839\pi$
$421$	−9.62992	+	16.6795i	−0.469334	+	0.812910i	0.530052	+	0.847965i	$0.322172\pi$
$422$	−6.68631	+	24.9537i	−0.325485	+	1.21473i
$423$	2.42555	+	9.05228i	0.117934	+	0.440137i
$424$	0.536369	−	0.929019i	0.0260484	−	0.0451172i
$425$	−36.2739	+	18.2091i	−1.75954	+	0.883271i
$426$			0.962355i			0.0466262i
$427$	1.22654	+	0.328650i	0.0593564	+	0.0159045i
$428$	4.70823	+	1.26157i	0.227581	+	0.0609801i
$429$	−9.41161	+	16.3014i	−0.454397	+	0.787038i
$430$	6.26325	+	5.10307i	0.302041	+	0.246092i
$431$	−3.20116	−	5.54457i	−0.154194	−	0.267073i	0.778571	−	0.627557i	$-0.215945\pi$
$431$	−3.20116	−	5.54457i	−0.154194	−	0.267073i	−0.932765	+	0.360484i	$0.882612\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	17.3040	+	17.3040i	0.831577	+	0.831577i	0.987732	−	0.156156i	$-0.0499101\pi$
$433$	17.3040	+	17.3040i	0.831577	+	0.831577i	−0.156156	+	0.987732i	$0.549910\pi$
$434$	−0.925850	−	0.118819i	−0.0444422	−	0.00570349i
$435$	−10.1215	+	1.03312i	−0.485291	+	0.0495342i
$436$	6.61537			0.316819
$437$	4.28448	+	1.14802i	0.204954	+	0.0549174i
$438$	1.25109	−	1.25109i	0.0597795	−	0.0597795i
$439$	20.8766	+	12.0531i	0.996386	+	0.575264i	0.907177	−	0.420749i	$-0.138233\pi$
$439$	20.8766	+	12.0531i	0.996386	+	0.575264i	0.0892093	+	0.996013i	$0.471566\pi$
$440$	−4.68848	−	6.49403i	−0.223515	−	0.309591i
$441$	−3.48595	−	6.03784i	−0.165997	−	0.287516i
$442$	−30.1631	−	30.1631i	−1.43471	−	1.43471i
$443$	−1.30381	−	4.86588i	−0.0619459	−	0.231185i	0.928011	−	0.372552i	$-0.121517\pi$
$443$	−1.30381	−	4.86588i	−0.0619459	−	0.231185i	−0.989957	+	0.141367i	$0.954850\pi$
$444$	7.57265	+	4.37207i	0.359382	+	0.207489i
$445$	−10.5907	−	27.8392i	−0.502048	−	1.31970i
$446$	2.78064	−	1.60540i	0.131667	−	0.0760179i
$447$	−2.53346	−	9.45499i	−0.119828	−	0.447206i
$448$	0.161939	+	0.0433914i	0.00765089	+	0.00205005i
$449$	−38.2962			−1.80731			−0.903655	−	0.428261i	$-0.859126\pi$
$449$	−38.2962			−1.80731			−0.903655	+	0.428261i	$0.859126\pi$
$450$	4.17693	+	2.74831i	0.196903	+	0.129557i
$451$	−28.3717	+	16.3804i	−1.33597	+	0.771323i
$452$	10.0465	−	2.69194i	0.472546	−	0.126618i
$453$	−15.3195	−	4.10485i	−0.719773	−	0.192862i
$454$	17.9521	+	10.3647i	0.842535	+	0.486438i
$455$	1.84123	−	0.700450i	0.0863182	−	0.0328376i
$456$	−1.88392	−	1.08768i	−0.0882226	−	0.0509354i
$457$	−8.07911	+	8.07911i	−0.377925	+	0.377925i	−0.870353	−	0.492428i	$-0.836109\pi$
$457$	−8.07911	+	8.07911i	−0.377925	+	0.377925i	0.492428	+	0.870353i	$0.336109\pi$
$458$	−4.49595	+	16.7791i	−0.210082	+	0.784036i
$459$	−7.03001	+	4.05878i	−0.328133	+	0.189448i
$460$	4.15963	+	1.86697i	0.193944	+	0.0870477i
$461$			15.4551i			0.719814i	0.932988	+	0.359907i	$0.117192\pi$
$461$			15.4551i			0.719814i	−0.932988	+	0.359907i	$0.882808\pi$
$462$	−0.155429	+	0.580068i	−0.00723120	+	0.0269872i
$463$	−24.9724	−	24.9724i	−1.16057	−	1.16057i	−0.984351	−	0.176217i	$-0.943614\pi$
$463$	−24.9724	−	24.9724i	−1.16057	−	1.16057i	−0.176217	−	0.984351i	$-0.556386\pi$
$464$	4.55001			0.211229
$465$	10.6170	+	6.50228i	0.492351	+	0.301536i
$466$	21.5717			0.999288
$467$	6.65960	+	6.65960i	0.308170	+	0.308170i	0.844199	−	0.536030i	$-0.180076\pi$
$467$	6.65960	+	6.65960i	0.308170	+	0.308170i	−0.536030	+	0.844199i	$0.680076\pi$
$468$	−1.36007	+	5.07586i	−0.0628694	+	0.234632i
$469$		−	0.345209i		−	0.0159403i
$470$	19.5862	−	7.45106i	0.903442	−	0.343692i
$471$	−7.69696	+	4.44384i	−0.354657	+	0.204761i
$472$	−2.93266	+	10.9448i	−0.134987	+	0.503777i
$473$	9.15131	−	9.15131i	0.420778	−	0.420778i
$474$	7.51786	+	4.34044i	0.345307	+	0.199363i
$475$	3.42314	−	10.3241i	0.157065	−	0.473703i
$476$	−1.17859	−	0.680460i	−0.0540206	−	0.0311888i
$477$	1.03619	+	0.277645i	0.0474437	+	0.0127125i
$478$	−7.11297	+	1.90592i	−0.325340	+	0.0871745i
$479$	20.1537	−	11.6357i	0.920845	−	0.531650i	0.0369405	−	0.999317i	$-0.488239\pi$
$479$	20.1537	−	11.6357i	0.920845	−	0.531650i	0.883905	+	0.467667i	$0.154905\pi$
$480$	−1.73352	−	1.41241i	−0.0791240	−	0.0644675i
$481$	−45.9497			−2.09513
$482$	−15.8206	−	4.23911i	−0.720608	−	0.193086i
$483$	−0.0884761	−	0.330197i	−0.00402580	−	0.0150245i
$484$	−1.58557	+	0.915431i	−0.0720715	+	0.0416105i
$485$	8.04613	−	17.9269i	0.365356	−	0.814020i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−1.90506	−	7.10977i	−0.0863264	−	0.322175i	0.909236	−	0.416282i	$-0.136667\pi$
$487$	−1.90506	−	7.10977i	−0.0863264	−	0.322175i	−0.995562	+	0.0941072i	$0.970000\pi$
$488$	5.35569	+	5.35569i	0.242441	+	0.242441i
$489$	−6.03104	−	10.4461i	−0.272733	−	0.472388i
$490$	−12.6397	+	9.12546i	−0.571004	+	0.412246i
$491$	−5.19707	−	3.00053i	−0.234541	−	0.135412i	0.378124	−	0.925755i	$-0.376569\pi$
$491$	−5.19707	−	3.00053i	−0.234541	−	0.135412i	−0.612665	+	0.790343i	$0.709902\pi$
$492$	−6.46713	+	6.46713i	−0.291561	+	0.291561i
$493$	−35.6765	−	9.55948i	−1.60679	−	0.430537i
$494$	11.4314			0.514321
$495$	5.05929	−	6.20950i	0.227398	−	0.279096i
$496$	−4.42824	−	3.37501i	−0.198834	−	0.151542i
$497$	−0.114085	−	0.114085i	−0.00511740	−	0.00511740i
$498$	10.6705	−	10.6705i	0.478155	−	0.478155i
$499$	7.09023	+	12.2806i	0.317402	+	0.549757i	0.979945	−	0.199267i	$-0.0638562\pi$
$499$	7.09023	+	12.2806i	0.317402	+	0.549757i	−0.662543	+	0.749024i	$0.730523\pi$
$500$	5.16524	−	9.91566i	0.230997	−	0.443442i
$501$	−7.60006	+	13.1637i	−0.339546	+	0.588110i
$502$	−14.5659	−	3.90293i	−0.650109	−	0.174196i
$503$	−7.47182	−	2.00207i	−0.333152	−	0.0892678i	0.0883654	−	0.996088i	$-0.471836\pi$
$503$	−7.47182	−	2.00207i	−0.333152	−	0.0892678i	−0.421517	+	0.906820i	$0.638502\pi$
$504$			0.167651i			0.00746779i
$505$	0.185424	+	0.487413i	0.00825126	+	0.0216896i
$506$	3.65191	−	6.32530i	0.162347	−	0.281194i
$507$	−3.78242	−	14.1162i	−0.167983	−	0.626922i
$508$	−3.10421	+	11.5851i	−0.137727	+	0.514004i
$509$	16.6540	−	28.8457i	0.738178	−	1.27856i	−0.215137	−	0.976584i	$-0.569020\pi$
$509$	16.6540	−	28.8457i	0.738178	−	1.27856i	0.953315	−	0.301978i	$-0.0976468\pi$
$510$	10.6250	+	14.7167i	0.470484	+	0.651669i
$511$			0.296628i			0.0131220i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.563026	−	2.10124i	0.0248582	−	0.0927720i
$514$	16.0552	+	9.26945i	0.708163	+	0.408858i
$515$	−1.32087	+	0.953628i	−0.0582047	+	0.0420219i
$516$	1.80651	−	3.12897i	0.0795272	−	0.137745i
$517$	−8.68837	−	32.4255i	−0.382114	−	1.42607i
$518$	−1.41602	+	0.379420i	−0.0622162	+	0.0166708i
$519$	−19.7916			−0.868756
$520$	11.6001	+	1.87298i	0.508699	+	0.0821355i
$521$	−2.52181	−	4.36790i	−0.110483	−	0.191361i	0.805482	−	0.592620i	$-0.201906\pi$
$521$	−2.52181	−	4.36790i	−0.110483	−	0.191361i	−0.915965	+	0.401258i	$0.868573\pi$
$522$	1.17763	+	4.39497i	0.0515435	+	0.192363i
$523$	26.6554	+	26.6554i	1.16556	+	1.16556i	0.983239	+	0.182322i	$0.0583614\pi$
$523$	26.6554	+	26.6554i	1.16556	+	1.16556i	0.182322	+	0.983239i	$0.441639\pi$
$524$	−12.1180	+	6.99634i	−0.529378	+	0.305637i
$525$	−0.820970	+	0.169359i	−0.0358301	+	0.00739145i
$526$			12.9245i			0.563533i
$527$	27.6308	+	35.7670i	1.20362	+	1.55803i
$528$	−2.53287	+	2.53287i	−0.110229	+	0.110229i
$529$		−	18.8424i		−	0.819234i
$530$	0.382350	−	2.36805i	0.0166082	−	0.102861i
$531$	−11.3309			−0.491721
$532$	0.352276	−	0.0943920i	0.0152731	−	0.00409241i
$533$	12.4391	−	46.4233i	0.538797	−	2.01082i
$534$	−11.5359	+	6.66027i	−0.499208	+	0.288218i
$535$	10.8430	−	1.10676i	0.468783	−	0.0478492i
$536$	1.02954	−	1.78322i	0.0444695	−	0.0770234i
$537$	−23.5737	+	6.31654i	−1.01728	+	0.272579i
$538$	−9.85849	+	2.64157i	−0.425030	+	0.113886i
$539$	12.4867	+	21.6276i	0.537841	+	0.931569i
$540$	0.915617	−	2.04001i	0.0394019	−	0.0877881i
$541$	−2.66429	−	4.61469i	−0.114547	−	0.198401i	0.803052	−	0.595909i	$-0.203208\pi$
$541$	−2.66429	−	4.61469i	−0.114547	−	0.198401i	−0.917598	+	0.397509i	$0.869875\pi$
$542$	−10.9267	+	10.9267i	−0.469343	+	0.469343i
$543$	−2.88186	+	2.88186i	−0.123673	+	0.123673i
$544$	−4.05878	−	7.03001i	−0.174019	−	0.301409i
$545$	13.8258	−	5.25966i	0.592230	−	0.225299i
$546$	−0.440497	−	0.762963i	−0.0188515	−	0.0326518i
$547$	30.4925	−	8.17043i	1.30376	−	0.349342i	0.460891	−	0.887457i	$-0.347530\pi$
$547$	30.4925	−	8.17043i	1.30376	−	0.349342i	0.842872	+	0.538114i	$0.180863\pi$
$548$	0.537663	−	0.144066i	0.0229678	−	0.00615421i
$549$	−3.78704	+	6.55935i	−0.161627	+	0.279946i
$550$	−14.9619	−	9.84451i	−0.637976	−	0.419771i
$551$	8.57186	−	4.94897i	0.365173	−	0.210833i
$552$	0.527738	−	1.96955i	0.0224620	−	0.0838295i
$553$	−1.40577	+	0.376675i	−0.0597794	+	0.0160179i
$554$	−23.4432			−0.996004
$555$	19.3025	+	3.11662i	0.819346	+	0.132293i
$556$			6.11986i			0.259540i
$557$	−24.6212	+	24.6212i	−1.04323	+	1.04323i	−0.0442094	+	0.999022i	$0.514077\pi$
$557$	−24.6212	+	24.6212i	−1.04323	+	1.04323i	−0.999022	+	0.0442094i	$0.985923\pi$
$558$	2.11390	−	5.15087i	0.0894884	−	0.218054i
$559$			18.9861i			0.803028i
$560$	0.372942	−	0.0380667i	0.0157597	−	0.00160861i
$561$	25.1816	−	14.5386i	1.06317	−	0.613821i
$562$	8.54754	+	8.54754i	0.360556	+	0.360556i
$563$	0.369813	+	1.38016i	0.0155858	+	0.0581669i	0.973281	−	0.229618i	$-0.0737478\pi$
$563$	0.369813	+	1.38016i	0.0155858	+	0.0581669i	−0.957695	+	0.287785i	$0.907081\pi$
$564$	−4.68581	−	8.11605i	−0.197308	−	0.341748i
$565$	18.8563	−	13.6136i	0.793289	−	0.572729i
$566$	22.0474			0.926723
$567$	−0.161939	+	0.0433914i	−0.00680079	+	0.00182227i
$568$	−0.249076	−	0.929563i	−0.0104510	−	0.0390036i
$569$	−14.5622	+	25.2225i	−0.610480	+	1.05738i	0.380679	+	0.924707i	$0.375690\pi$
$569$	−14.5622	+	25.2225i	−0.610480	+	1.05738i	−0.991159	+	0.132676i	$0.957643\pi$
$570$	−4.80207	−	0.775352i	−0.201137	−	0.0324759i
$571$	22.5211	+	13.0026i	0.942480	+	0.544141i	0.890737	−	0.454519i	$-0.150189\pi$
$571$	22.5211	+	13.0026i	0.942480	+	0.544141i	0.0517435	+	0.998660i	$0.483522\pi$
$572$	4.87181	−	18.1818i	0.203700	−	0.760220i
$573$	−2.77067	−	2.77067i	−0.115746	−	0.115746i
$574$		−	1.53332i		−	0.0639997i
$575$	10.1778	+	0.594665i	0.424442	+	0.0247993i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−3.22836	+	12.0484i	−0.134398	+	0.501581i	0.865601	+	0.500734i	$0.166936\pi$
$577$	−3.22836	+	12.0484i	−0.134398	+	0.501581i	−1.00000		0.000847531i	$0.999730\pi$
$578$	12.6549	+	47.2287i	0.526374	+	1.96445i
$579$	−7.94947	+	13.7689i	−0.330369	+	0.572215i
$580$	9.50927	−	3.61757i	0.394851	−	0.150211i
$581$			2.52991i			0.104958i
$582$	−8.48823	−	2.27441i	−0.351849	−	0.0942775i
$583$	−3.71164	−	0.994531i	−0.153720	−	0.0411892i
$584$	−0.884656	+	1.53227i	−0.0366073	+	0.0634058i
$585$	1.19317	+	11.6896i	0.0493316	+	0.483306i
$586$	10.8734	+	18.8334i	0.449178	+	0.777999i
$587$	13.6041	−	13.6041i	0.561503	−	0.561503i	−0.368231	−	0.929734i	$-0.620036\pi$
$587$	13.6041	−	13.6041i	0.561503	−	0.561503i	0.929734	+	0.368231i	$0.120036\pi$
$588$	4.92987	+	4.92987i	0.203305	+	0.203305i
$589$	−12.0134	−	1.54174i	−0.495003	−	0.0635261i
$590$	2.57279	+	25.2058i	0.105920	+	1.03771i
$591$	−17.5025			−0.719955
$592$	−8.44619	−	2.26315i	−0.347136	−	0.0930149i
$593$	−22.4759	+	22.4759i	−0.922976	+	0.922976i	−0.997239	−	0.0742623i	$-0.976340\pi$
$593$	−22.4759	+	22.4759i	−0.922976	+	0.922976i	0.0742623	+	0.997239i	$0.476340\pi$
$594$	−3.10212	−	1.79101i	−0.127282	−	0.0734860i
$595$	−3.00420	−	0.485064i	−0.123160	−	0.0198857i
$596$	4.89426	+	8.47711i	0.200477	+	0.347236i
$597$	1.16397	+	1.16397i	0.0476381	+	0.0476381i
$598$	2.77322	+	10.3498i	0.113405	+	0.423235i
$599$	−3.01174	−	1.73883i	−0.123056	−	0.0710467i	0.437208	−	0.899360i	$-0.355967\pi$
$599$	−3.01174	−	1.73883i	−0.123056	−	0.0710467i	−0.560265	+	0.828314i	$0.689301\pi$
$600$	−4.74592	−	1.57360i	−0.193752	−	0.0642418i
$601$	−4.74284	+	2.73828i	−0.193465	+	0.111697i	−0.593603	−	0.804758i	$-0.702295\pi$
$601$	−4.74284	+	2.73828i	−0.193465	+	0.111697i	0.400139	+	0.916455i	$0.368962\pi$
$602$	0.156774	+	0.585088i	0.00638963	+	0.0238464i
$603$	1.98892	+	0.532931i	0.0809953	+	0.0217026i
$604$	15.8599			0.645330
$605$	−2.58593	+	3.17384i	−0.105133	+	0.129035i
$606$	0.201973	−	0.116609i	0.00820459	−	0.00473692i
$607$	−10.9674	+	2.93870i	−0.445153	+	0.119278i	−0.474430	−	0.880293i	$-0.657346\pi$
$607$	−10.9674	+	2.93870i	−0.445153	+	0.119278i	0.0292778	+	0.999571i	$0.490679\pi$
$608$	2.10124	+	0.563026i	0.0852165	+	0.0228337i
$609$	−0.660618	−	0.381408i	−0.0267696	−	0.0154554i
$610$	15.4512	+	6.93496i	0.625602	+	0.280788i
$611$	42.6492	+	24.6235i	1.72540	+	0.996161i
$612$	5.73998	−	5.73998i	0.232025	−	0.232025i
$613$	5.21354	−	19.4572i	0.210573	−	0.785869i	−0.777105	−	0.629370i	$-0.783313\pi$
$613$	5.21354	−	19.4572i	0.210573	−	0.785869i	0.987678	−	0.156498i	$-0.0500205\pi$
$614$	−10.7543	+	6.20903i	−0.434010	+	0.250576i
$615$	−8.37414	+	18.6577i	−0.337678	+	0.752353i
$616$		−	0.600531i		−	0.0241961i
$617$	10.1385	−	37.8375i	0.408162	−	1.52328i	−0.389986	−	0.920821i	$-0.627520\pi$
$617$	10.1385	−	37.8375i	0.408162	−	1.52328i	0.798148	−	0.602461i	$-0.205813\pi$
$618$	0.515181	+	0.515181i	0.0207236	+	0.0207236i
$619$	−10.9383			−0.439647			−0.219823	−	0.975540i	$-0.570548\pi$
$619$	−10.9383			−0.439647			−0.219823	+	0.975540i	$0.570548\pi$
$620$	−11.9381	−	3.53284i	−0.479447	−	0.141882i
$621$	2.03902			0.0818233
$622$	−10.8374	−	10.8374i	−0.434541	−	0.434541i
$623$	0.577997	−	2.15711i	0.0231569	−	0.0864229i
$624$		−	5.25492i		−	0.210365i
$625$	2.91146	−	24.8299i	0.116458	−	0.993196i
$626$	17.6385	−	10.1836i	0.704976	−	0.407018i
$627$	−2.01677	+	7.52668i	−0.0805420	+	0.300587i
$628$	6.28454	−	6.28454i	0.250781	−	0.250781i
$629$	61.4714	+	35.4905i	2.45103	+	1.41510i
$630$	0.133294	+	0.350382i	0.00531057	+	0.0139596i
$631$	20.8270	+	12.0245i	0.829111	+	0.478687i	0.853548	−	0.521014i	$-0.174446\pi$
$631$	20.8270	+	12.0245i	0.829111	+	0.478687i	−0.0244372	+	0.999701i	$0.507779\pi$
$632$	−8.38508	−	2.24678i	−0.333541	−	0.0893719i
$633$	24.9537	−	6.68631i	0.991819	−	0.265757i
$634$	30.6109	−	17.6732i	1.21572	−	0.701893i
$635$	2.72328	+	26.6802i	0.108070	+	1.05877i
$636$	−1.07274			−0.0425369
$637$	−35.3884	−	9.48228i	−1.40214	−	0.375702i
$638$	−4.21829	−	15.7429i	−0.167004	−	0.623267i
$639$	0.833424	−	0.481177i	0.0329697	−	0.0190351i
$640$	2.04001	+	0.915617i	0.0806385	+	0.0361929i
$641$	−30.9911	−	17.8927i	−1.22407	−	0.706720i	−0.258290	−	0.966067i	$-0.583159\pi$
$641$	−30.9911	−	17.8927i	−1.22407	−	0.706720i	−0.965784	+	0.259348i	$0.916492\pi$
$642$	−1.26157	−	4.70823i	−0.0497901	−	0.185819i
$643$	−1.81904	−	1.81904i	−0.0717360	−	0.0717360i	0.670329	−	0.742064i	$-0.266153\pi$
$643$	−1.81904	−	1.81904i	−0.0717360	−	0.0717360i	−0.742064	+	0.670329i	$0.766153\pi$
$644$	0.170923	+	0.296047i	0.00673530	+	0.0116659i
$645$	1.28777	−	7.97567i	0.0507058	−	0.314042i
$646$	−15.2928	−	8.82932i	−0.601688	−	0.347385i
$647$	11.4810	−	11.4810i	0.451365	−	0.451365i	−0.444442	−	0.895808i	$-0.646598\pi$
$647$	11.4810	−	11.4810i	0.451365	−	0.451365i	0.895808	+	0.444442i	$0.146598\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	40.5876			1.59320
$650$	25.7327	−	5.30845i	1.00932	−	0.208215i
$651$	0.360025	+	0.861219i	0.0141105	+	0.0337538i
$652$	8.52918	+	8.52918i	0.334028	+	0.334028i
$653$	0.113362	−	0.113362i	0.00443619	−	0.00443619i	−0.704885	−	0.709321i	$-0.749002\pi$
$653$	0.113362	−	0.113362i	0.00443619	−	0.00443619i	0.709321	+	0.704885i	$0.249002\pi$
$654$	−3.30768	−	5.72908i	−0.129341	−	0.224025i
$655$	−19.7634	+	24.2566i	−0.772221	+	0.947784i
$656$	4.57295	−	7.92059i	0.178544	−	0.309247i
$657$	−1.70902	−	0.457932i	−0.0666754	−	0.0178656i
$658$	1.51763	+	0.406647i	0.0591633	+	0.0158528i
$659$		−	33.8326i		−	1.31793i	−0.752173	−	0.658966i	$-0.770994\pi$
$659$		−	33.8326i		−	1.31793i	0.752173	−	0.658966i	$-0.229006\pi$
$660$	−3.27976	+	7.30736i	−0.127664	+	0.284439i
$661$	−9.06747	+	15.7053i	−0.352684	+	0.610866i	−0.986719	−	0.162438i	$-0.948064\pi$
$661$	−9.06747	+	15.7053i	−0.352684	+	0.610866i	0.634035	+	0.773304i	$0.281397\pi$
$662$	3.59149	+	13.4036i	0.139587	+	0.520946i
$663$	−11.0405	+	41.2036i	−0.428776	+	1.60021i
$664$	−7.54516	+	13.0686i	−0.292809	+	0.507160i
$665$	0.661189	−	0.477357i	0.0256398	−	0.0185111i
$666$		−	8.74414i		−	0.338829i
$667$	6.56025	+	6.56025i	0.254014	+	0.254014i
$668$	3.93408	−	14.6822i	0.152214	−	0.568071i
$669$	−2.78064	−	1.60540i	−0.107506	−	0.0620684i
$670$	0.733908	−	4.54539i	0.0283533	−	0.175604i
$671$	13.5653	−	23.4957i	0.523681	−	0.907043i
$672$	−0.0433914	−	0.161939i	−0.00167386	−	0.00624693i
$673$	−19.0230	+	5.09721i	−0.733284	+	0.196483i	−0.606091	−	0.795395i	$-0.707263\pi$
$673$	−19.0230	+	5.09721i	−0.733284	+	0.196483i	−0.127193	+	0.991878i	$0.540597\pi$
$674$	−10.2022			−0.392975
$675$	0.291642	−	4.99149i	0.0112253	−	0.192122i
$676$	7.30708	+	12.6562i	0.281041	+	0.486778i
$677$	1.15532	+	4.31171i	0.0444026	+	0.165713i	0.984567	−	0.175009i	$-0.0559954\pi$
$677$	1.15532	+	4.31171i	0.0444026	+	0.165713i	−0.940164	+	0.340721i	$0.889329\pi$
$678$	−7.35452	−	7.35452i	−0.282449	−	0.282449i
$679$	1.27588	−	0.736632i	0.0489639	−	0.0282693i
$680$	−14.0720	−	11.4653i	−0.539635	−	0.439675i
$681$		−	20.7293i		−	0.794350i
$682$	−7.57202	+	18.4505i	−0.289948	+	0.706506i
$683$	16.0663	−	16.0663i	0.614761	−	0.614761i	−0.329422	−	0.944183i	$-0.606854\pi$
$683$	16.0663	−	16.0663i	0.614761	−	0.614761i	0.944183	+	0.329422i	$0.106854\pi$
$684$			2.17536i			0.0831771i
$685$	1.00914	−	0.728569i	0.0385574	−	0.0278372i
$686$	−2.34241			−0.0894335
$687$	16.7791	−	4.49595i	0.640163	−	0.171531i
$688$	−0.935119	+	3.48991i	−0.0356511	+	0.133052i
$689$	4.88192	−	2.81858i	0.185986	−	0.107379i
$690$	−0.462978	−	4.53583i	−0.0176253	−	0.172676i
$691$	10.6947	−	18.5238i	0.406847	−	0.704680i	−0.587687	−	0.809088i	$-0.699961\pi$
$691$	10.6947	−	18.5238i	0.406847	−	0.704680i	0.994535	+	0.104408i	$0.0332948\pi$
$692$	19.1172	−	5.12245i	0.726728	−	0.194726i
$693$	0.580068	−	0.155429i	0.0220350	−	0.00590425i
$694$	4.86619	+	8.42849i	0.184718	+	0.319941i
$695$	4.86570	+	12.7902i	0.184566	+	0.485158i
$696$	−2.27501	−	3.94043i	−0.0862339	−	0.149361i
$697$	−52.4973	+	52.4973i	−1.98848	+	1.98848i
$698$	20.5245	−	20.5245i	0.776865	−	0.776865i
$699$	−10.7858	−	18.6816i	−0.407958	−	0.706603i
$700$	0.749163	−	0.376071i	0.0283157	−	0.0142142i
$701$	11.9222	+	20.6499i	0.450296	+	0.779936i	0.998404	−	0.0564718i	$-0.0179851\pi$
$701$	11.9222	+	20.6499i	0.450296	+	0.779936i	−0.548108	+	0.836408i	$0.684652\pi$
$702$	5.07586	−	1.36007i	0.191576	−	0.0513326i
$703$	−18.3735	+	4.92317i	−0.692971	+	0.185681i
$704$	1.79101	−	3.10212i	0.0675012	−	0.116916i
$705$	−16.2459	−	13.2366i	−0.611855	−	0.498518i
$706$	−18.9557	+	10.9441i	−0.713407	+	0.411886i
$707$	−0.0101197	+	0.0377671i	−0.000380589	+	0.00142038i
$708$	10.9448	−	2.93266i	0.411333	−	0.110216i
$709$	−29.3437			−1.10202			−0.551012	−	0.834497i	$-0.685758\pi$
$709$	−29.3437			−1.10202			−0.551012	+	0.834497i	$0.685758\pi$
$710$	−1.25962	−	1.74470i	−0.0472727	−	0.0654776i
$711$		−	8.68087i		−	0.325558i
$712$	9.41905	−	9.41905i	0.352994	−	0.352994i
$713$	−1.51855	−	11.2508i	−0.0568703	−	0.421345i
$714$			1.36092i			0.0509311i
$715$	−4.27397	−	41.8724i	−0.159837	−	1.56594i
$716$	21.1356	−	12.2026i	0.789873	−	0.456033i
$717$	5.20706	+	5.20706i	0.194461	+	0.194461i
$718$	−7.60479	−	28.3815i	−0.283808	−	1.05919i
$719$	17.9327	+	31.0603i	0.668775	+	1.15835i	0.978247	+	0.207444i	$0.0665146\pi$
$719$	17.9327	+	31.0603i	0.668775	+	1.15835i	−0.309471	+	0.950909i	$0.600152\pi$
$720$	−0.356424	+	2.20748i	−0.0132831	+	0.0822679i
$721$	−0.122147			−0.00454898
$722$	−13.7816	+	3.69278i	−0.512899	+	0.137431i
$723$	4.23911	+	15.8206i	0.157654	+	0.588374i
$724$	2.03778	−	3.52955i	0.0757337	−	0.131175i
$725$	16.9976	−	15.1210i	0.631277	−	0.561581i
$726$	1.58557	+	0.915431i	0.0588462	+	0.0339748i
$727$	−0.544357	+	2.03157i	−0.0201891	+	0.0753467i	−0.975285	−	0.220949i	$-0.929085\pi$
$727$	−0.544357	+	2.03157i	−0.0201891	+	0.0753467i	0.955096	+	0.296295i	$0.0957513\pi$
$728$	0.622957	+	0.622957i	0.0230883	+	0.0230883i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.630625	+	3.90572i	−0.0233405	+	0.144557i
$731$	14.6645	−	25.3996i	0.542384	−	0.939437i
$732$	1.96032	−	7.31601i	0.0724555	−	0.270407i
$733$	−0.390471	−	1.45726i	−0.0144224	−	0.0538250i	0.958340	−	0.285631i	$-0.0922032\pi$
$733$	−0.390471	−	1.45726i	−0.0144224	−	0.0538250i	−0.972762	+	0.231806i	$0.925537\pi$
$734$	0.0176011	−	0.0304860i	0.000649669	−	0.00112526i
$735$	14.2227	+	6.38358i	0.524614	+	0.235462i
$736$			2.03902i			0.0751595i
$737$	−7.12437	−	1.90897i	−0.262429	−	0.0703177i
$738$	8.83426	+	2.36713i	0.325194	+	0.0871354i
$739$	20.4684	−	35.4524i	0.752944	−	1.30414i	−0.193446	−	0.981111i	$-0.561966\pi$
$739$	20.4684	−	35.4524i	0.752944	−	1.30414i	0.946390	−	0.323026i	$-0.104700\pi$
$740$	−19.4514	+	1.98543i	−0.715049	+	0.0729859i
$741$	−5.71568	−	9.89984i	−0.209971	−	0.363680i
$742$	0.127170	−	0.127170i	0.00466857	−	0.00466857i
$743$	9.13656	+	9.13656i	0.335188	+	0.335188i	0.854553	−	0.519365i	$-0.173831\pi$
$743$	9.13656	+	9.13656i	0.335188	+	0.335188i	−0.519365	+	0.854553i	$0.673831\pi$
$744$	−0.708725	+	5.52247i	−0.0259831	+	0.202464i
$745$	16.9686	+	13.8254i	0.621682	+	0.506524i
$746$	−13.7224			−0.502411
$747$	−14.5761	−	3.90566i	−0.533313	−	0.142901i
$748$	−20.5607	+	20.5607i	−0.751774	+	0.751774i
$749$	0.707704	+	0.408593i	0.0258590	+	0.0149297i
$750$	−11.1698	+	0.484598i	−0.407865	+	0.0176950i
$751$	11.5686	+	20.0375i	0.422145	+	0.731177i	0.996149	−	0.0876756i	$-0.0279439\pi$
$751$	11.5686	+	20.0375i	0.422145	+	0.731177i	−0.574004	+	0.818853i	$0.694611\pi$
$752$	6.62673	+	6.62673i	0.241652	+	0.241652i
$753$	3.90293	+	14.5659i	0.142231	+	0.530812i
$754$	20.7066	+	11.9550i	0.754090	+	0.435374i
$755$	33.1463	−	12.6097i	1.20632	−	0.458914i
$756$	0.145190	−	0.0838257i	0.00528052	−	0.00304871i
$757$	−7.96321	−	29.7191i	−0.289428	−	1.08016i	−0.945543	−	0.325498i	$-0.894468\pi$
$757$	−7.96321	−	29.7191i	−0.289428	−	1.08016i	0.656115	−	0.754661i	$-0.272199\pi$
$758$	−23.4540	−	6.28449i	−0.851889	−	0.228263i
$759$	−7.30383			−0.265112
$760$	4.83912	−	0.493935i	0.175533	−	0.0179169i
$761$	21.0392	−	12.1470i	0.762670	−	0.440328i	−0.0675836	−	0.997714i	$-0.521529\pi$
$761$	21.0392	−	12.1470i	0.762670	−	0.440328i	0.830254	+	0.557386i	$0.188196\pi$
$762$	11.5851	−	3.10421i	0.419683	−	0.112454i
$763$	1.07129	+	0.287050i	0.0387831	+	0.0103919i
$764$	3.39337	+	1.95916i	0.122768	+	0.0708800i
$765$	7.43257	−	16.5599i	0.268725	−	0.598725i
$766$	−19.9228	−	11.5025i	−0.719841	−	0.415601i
$767$	−42.1034	+	42.1034i	−1.52026	+	1.52026i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−15.3971	+	8.88949i	−0.555232	+	0.320563i	−0.751230	−	0.660041i	$-0.770539\pi$
$769$	−15.3971	+	8.88949i	−0.555232	+	0.320563i	0.195998	+	0.980604i	$0.437206\pi$
$770$	−0.477462	−	1.25508i	−0.0172065	−	0.0452298i
$771$		−	18.5389i		−	0.667663i
$772$	4.11495	−	15.3572i	0.148100	−	0.552717i
$773$	−11.7202	−	11.7202i	−0.421545	−	0.421545i	0.464191	−	0.885735i	$-0.346345\pi$
$773$	−11.7202	−	11.7202i	−0.421545	−	0.421545i	−0.885735	+	0.464191i	$0.846345\pi$
$774$	−3.61302			−0.129867
$775$	−27.7589	+	2.10818i	−0.997128	+	0.0757282i
$776$	8.78766			0.315459
$777$	1.03660	+	1.03660i	0.0371877	+	0.0371877i
$778$	−1.69473	+	6.32481i	−0.0607590	+	0.226756i
$779$		−	19.8957i		−	0.712836i
$780$	−4.17801	−	10.9825i	−0.149597	−	0.393236i
$781$	−2.98534	+	1.72359i	−0.106824	+	0.0616748i
$782$	4.28395	−	15.9879i	0.153194	−	0.571726i
$783$	3.21734	−	3.21734i	0.114979	−	0.114979i
$784$	−6.03784	−	3.48595i	−0.215637	−	0.124498i
$785$	8.13771	−	18.1310i	0.290447	−	0.647122i
$786$	12.1180	+	6.99634i	0.432236	+	0.249551i
$787$	−26.6818	−	7.14938i	−0.951105	−	0.254848i	−0.250274	−	0.968175i	$-0.580521\pi$
$787$	−26.6818	−	7.14938i	−0.951105	−	0.254848i	−0.700831	+	0.713327i	$0.747187\pi$
$788$	16.9061	−	4.52997i	0.602254	−	0.161374i
$789$	11.1929	−	6.46223i	0.398478	−	0.230061i
$790$	−19.3107	+	1.97107i	−0.687043	+	0.0701274i
$791$	1.74372			0.0619995
$792$	3.45997	+	0.927095i	0.122945	+	0.0329429i
$793$	10.3013	+	38.4450i	0.365810	+	1.36522i
$794$	−21.9190	+	12.6549i	−0.777876	+	0.449107i
$795$	−2.24196	+	0.852899i	−0.0795143	+	0.0302492i
$796$	−1.42556	−	0.823050i	−0.0505278	−	0.0291722i
$797$	10.2993	+	38.4377i	0.364821	+	1.36153i	0.867663	+	0.497153i	$0.165621\pi$
$797$	10.2993	+	38.4377i	0.364821	+	1.36153i	−0.502842	+	0.864379i	$0.667712\pi$
$798$	−0.257884	−	0.257884i	−0.00912899	−	0.00912899i
$799$	−38.0373	−	65.8825i	−1.34566	−	2.33076i
$800$	4.99149	+	0.291642i	0.176476	+	0.0103111i
$801$	11.5359	+	6.66027i	0.407602	+	0.235329i
$802$	−6.67946	+	6.67946i	−0.235860	+	0.235860i
$803$	6.12176	+	1.64032i	0.216032	+	0.0578857i
$804$	−2.05909			−0.0726184
$805$	0.592596	+	0.482826i	0.0208863	+	0.0170174i
$806$	−11.2847	−	26.9943i	−0.397488	−	0.950834i
$807$	7.21692	+	7.21692i	0.254047	+	0.254047i
$808$	−0.164910	+	0.164910i	−0.00580152	+	0.00580152i
$809$	−25.6091	−	44.3563i	−0.900369	−	1.55948i	−0.827016	−	0.562178i	$-0.809963\pi$
$809$	−25.6091	−	44.3563i	−0.900369	−	1.55948i	−0.0733529	−	0.997306i	$-0.523370\pi$
$810$	−2.22451	+	0.227058i	−0.0781613	+	0.00797802i
$811$	9.36541	−	16.2214i	0.328864	−	0.569609i	−0.653423	−	0.756993i	$-0.726668\pi$
$811$	9.36541	−	16.2214i	0.328864	−	0.569609i	0.982287	+	0.187384i	$0.0600009\pi$
$812$	0.736824	+	0.197431i	0.0258574	+	0.00692848i
$813$	14.9262	+	3.99946i	0.523484	+	0.140267i
$814$			31.3217i			1.09782i
$815$	24.6068	+	11.0442i	0.861938	+	0.386863i
$816$	−4.05878	+	7.03001i	−0.142086	+	0.246100i
$817$	2.03422	+	7.59182i	0.0711685	+	0.265604i
$818$	−9.17256	+	34.2325i	−0.320711	+	1.19691i
$819$	−0.440497	+	0.762963i	−0.0153922	+	0.0266601i
$820$	3.25982	−	20.1894i	0.113838	−	0.705044i
$821$		−	42.3942i		−	1.47957i	−0.672844	−	0.739784i	$-0.734928\pi$
$821$		−	42.3942i		−	1.47957i	0.672844	−	0.739784i	$-0.265072\pi$
$822$	−0.393597	−	0.393597i	−0.0137283	−	0.0137283i
$823$	−9.83913	+	36.7201i	−0.342971	+	1.27998i	0.551994	+	0.833848i	$0.313867\pi$
$823$	−9.83913	+	36.7201i	−0.342971	+	1.27998i	−0.894965	+	0.446136i	$0.852800\pi$
$824$	−0.630965	−	0.364288i	−0.0219807	−	0.0126906i
$825$	−1.04467	+	17.8796i	−0.0363707	+	0.622488i
$826$	−0.949824	+	1.64514i	−0.0330486	+	0.0572419i
$827$	−10.3998	−	38.8126i	−0.361637	−	1.34965i	−0.871924	−	0.489642i	$-0.837127\pi$
$827$	−10.3998	−	38.8126i	−0.361637	−	1.34965i	0.510287	−	0.860004i	$-0.329539\pi$
$828$	−1.96955	+	0.527738i	−0.0684465	+	0.0183402i
$829$	4.70847			0.163532			0.0817660	−	0.996652i	$-0.473944\pi$
$829$	4.70847			0.163532			0.0817660	+	0.996652i	$0.473944\pi$
$830$	−5.37855	+	33.3115i	−0.186692	+	1.15626i
$831$	11.7216	+	20.3024i	0.406617	+	0.704281i
$832$	1.36007	+	5.07586i	0.0471520	+	0.175974i
$833$	40.0185	+	40.0185i	1.38656	+	1.38656i
$834$	5.29995	−	3.05993i	0.183522	−	0.105957i
$835$	−3.45132	−	33.8128i	−0.119438	−	1.17014i
$836$		−	7.79219i		−	0.269499i
$837$	−5.51773	+	0.744745i	−0.190721	+	0.0257422i
$838$	−23.2478	+	23.2478i	−0.803083	+	0.803083i
$839$		−	47.3208i		−	1.63370i	−0.576853	−	0.816848i	$-0.695719\pi$
$839$		−	47.3208i		−	1.63370i	0.576853	−	0.816848i	$-0.304281\pi$
$840$	−0.219438	−	0.303944i	−0.00757132	−	0.0104871i
$841$	−8.29739			−0.286117
$842$	−18.6036	+	4.98481i	−0.641122	+	0.171788i
$843$	3.12862	−	11.6762i	0.107755	−	0.402148i
$844$	−22.3728	+	12.9170i	−0.770105	+	0.444620i
$845$	25.3339	+	20.6412i	0.871514	+	0.710079i
$846$	−4.68581	+	8.11605i	−0.161101	+	0.279036i
$847$	−0.296488	+	0.0794437i	−0.0101874	+	0.00272972i
$848$	1.03619	−	0.277645i	0.0355828	−	0.00953438i
$849$	−11.0237	−	19.0936i	−0.378333	−	0.655292i
$850$	−38.5253	−	12.7738i	−1.32141	−	0.438136i
$851$	−8.91476	−	15.4408i	−0.305594	−	0.529304i
$852$	−0.680487	+	0.680487i	−0.0233131	+	0.0233131i
$853$	−6.02519	+	6.02519i	−0.206299	+	0.206299i	−0.802692	−	0.596394i	$-0.796600\pi$
$853$	−6.02519	+	6.02519i	−0.206299	+	0.206299i	0.596394	+	0.802692i	$0.296600\pi$
$854$	0.634903	+	1.09968i	0.0217259	+	0.0376304i
$855$	1.72956	+	4.54639i	0.0591497	+	0.155483i
$856$	2.43716	+	4.22128i	0.0833004	+	0.144281i
$857$	−14.0657	+	3.76888i	−0.480474	+	0.128743i	−0.490923	−	0.871203i	$-0.663341\pi$
$857$	−14.0657	+	3.76888i	−0.480474	+	0.128743i	0.0104493	+	0.999945i	$0.496674\pi$
$858$	−18.1818	+	4.87181i	−0.620717	+	0.166321i
$859$	11.7117	−	20.2853i	0.399599	−	0.692126i	−0.594077	−	0.804408i	$-0.702483\pi$
$859$	11.7117	−	20.2853i	0.399599	−	0.692126i	0.993676	+	0.112282i	$0.0358159\pi$
$860$	0.820367	+	8.03720i	0.0279743	+	0.274066i
$861$	−1.32790	+	0.766662i	−0.0452546	+	0.0261278i
$862$	1.65704	−	6.18416i	0.0564391	−	0.210633i
$863$	−24.7093	+	6.62084i	−0.841114	+	0.225376i	−0.653557	−	0.756878i	$-0.726724\pi$
$863$	−24.7093	+	6.62084i	−0.841114	+	0.225376i	−0.187558	+	0.982254i	$0.560057\pi$
$864$	1.00000			0.0340207
$865$	35.8813	−	25.9051i	1.22000	−	0.880801i
$866$			24.4715i			0.831577i
$867$	34.5738	−	34.5738i	1.17419	−	1.17419i
$868$	−0.570658	−	0.738693i	−0.0193694	−	0.0250729i
$869$			31.0951i			1.05483i
$870$	−7.88754	−	6.42649i	−0.267413	−	0.217878i
$871$	9.37068	−	5.41016i	0.317513	−	0.183316i
$872$	4.67777	+	4.67777i	0.158409	+	0.158409i
$873$	2.27441	+	8.48823i	0.0769773	+	0.287283i
$874$	2.21781	+	3.84136i	0.0750186	+	0.129936i
$875$	1.26671	−	1.38160i	0.0428225	−	0.0467067i
$876$	1.76931			0.0597795
$877$	−18.9266	+	5.07137i	−0.639106	+	0.171248i	−0.563798	−	0.825912i	$-0.690661\pi$
$877$	−18.9266	+	5.07137i	−0.639106	+	0.171248i	−0.0753076	+	0.997160i	$0.523994\pi$
$878$	6.23915	+	23.2848i	0.210561	+	0.785825i
$879$	10.8734	−	18.8334i	0.366752	−	0.635233i
$880$	1.27672	−	7.90723i	0.0430381	−	0.266553i
$881$	3.00549	+	1.73522i	0.101258	+	0.0584611i	0.549774	−	0.835314i	$-0.314714\pi$
$881$	3.00549	+	1.73522i	0.101258	+	0.0584611i	−0.448516	+	0.893775i	$0.648047\pi$
$882$	1.80446	−	6.73433i	0.0607593	−	0.226757i
$883$	27.7648	+	27.7648i	0.934361	+	0.934361i	0.997975	−	0.0636132i	$-0.0202624\pi$
$883$	27.7648	+	27.7648i	0.934361	+	0.934361i	−0.0636132	+	0.997975i	$0.520262\pi$
$884$		−	42.6571i		−	1.43471i
$885$	20.5425	−	14.8310i	0.690527	−	0.498538i
$886$	2.51877	−	4.36263i	0.0846196	−	0.146565i
$887$	0.443926	−	1.65675i	0.0149056	−	0.0556284i	−0.958072	−	0.286526i	$-0.907500\pi$
$887$	0.443926	−	1.65675i	0.0149056	−	0.0556284i	0.972978	+	0.230898i	$0.0741662\pi$
$888$	2.26315	+	8.44619i	0.0759463	+	0.283436i
$889$	−1.00538	+	1.74138i	−0.0337195	+	0.0584039i
$890$	12.1965	−	27.1741i	0.408828	−	0.910876i
$891$			3.58202i			0.120002i
$892$	3.10140	+	0.831017i	0.103842	+	0.0278245i
$893$	19.6920	+	5.27646i	0.658968	+	0.176570i
$894$	4.89426	−	8.47711i	0.163689	−	0.283517i
$895$	34.4702	−	42.3070i	1.15221	−	1.41417i
$896$	0.0838257	+	0.145190i	0.00280042	+	0.00485047i
$897$	7.57658	−	7.57658i	0.252975	−	0.252975i
$898$	−27.0795	−	27.0795i	−0.903655	−	0.903655i
$899$	−20.1485	−	15.3563i	−0.671992	−	0.512163i
$900$	1.01019	+	4.89689i	0.0336729	+	0.163230i
$901$	−8.70802			−0.290106
$902$	−31.6445	−	8.47912i	−1.05365	−	0.282324i
$903$	0.428314	−	0.428314i	0.0142534	−	0.0142534i
$904$	9.00741	+	5.20043i	0.299582	+	0.172964i
$905$	1.45263	−	8.99673i	0.0482871	−	0.299061i
$906$	−7.92995	−	13.7351i	−0.263455	−	0.456318i
$907$	−28.5209	−	28.5209i	−0.947019	−	0.947019i	0.0516461	−	0.998665i	$-0.483553\pi$
$907$	−28.5209	−	28.5209i	−0.947019	−	0.947019i	−0.998665	+	0.0516461i	$0.983553\pi$
$908$	5.36515	+	20.0230i	0.178049	+	0.664487i
$909$	−0.201973	−	0.116609i	−0.00669902	−	0.00386768i
$910$	1.79724	+	0.806653i	0.0595779	+	0.0267403i
$911$	4.37116	−	2.52369i	0.144823	−	0.0836137i	−0.425838	−	0.904800i	$-0.640021\pi$
$911$	4.37116	−	2.52369i	0.144823	−	0.0836137i	0.570661	+	0.821186i	$0.306687\pi$
$912$	−0.563026	−	2.10124i	−0.0186436	−	0.0695790i
$913$	52.2120	+	13.9902i	1.72796	+	0.463006i
$914$	−11.4256			−0.377925
$915$	−1.71976	−	16.8486i	−0.0568535	−	0.556999i
$916$	−15.0437	+	8.68551i	−0.497059	+	0.286977i
$917$	−2.26596	+	0.607162i	−0.0748286	+	0.0200503i
$918$	−7.84096	−	2.10098i	−0.258790	−	0.0693426i
$919$	−39.0565	−	22.5493i	−1.28835	−	0.743832i	−0.309994	−	0.950739i	$-0.600327\pi$
$919$	−39.0565	−	22.5493i	−1.28835	−	0.743832i	−0.978361	+	0.206907i	$0.933660\pi$
$920$	1.62116	+	4.26145i	0.0534481	+	0.140496i
$921$	10.7543	+	6.20903i	0.354368	+	0.204594i
$922$	−10.9284	+	10.9284i	−0.359907	+	0.359907i
$923$	1.30887	−	4.88478i	0.0430820	−	0.160784i
$924$	−0.520075	+	0.300265i	−0.0171092	+	0.00987800i
$925$	−39.0739	+	19.6146i	−1.28474	+	0.644925i
$926$		−	35.3164i		−	1.16057i
$927$	0.188569	−	0.703750i	0.00619343	−	0.0231142i
$928$	3.21734	+	3.21734i	0.105615	+	0.105615i
$929$	11.8011			0.387181			0.193590	−	0.981082i	$-0.437987\pi$
$929$	11.8011			0.387181			0.193590	+	0.981082i	$0.437987\pi$
$930$	2.90954	+	12.1051i	0.0954076	+	0.396943i
$931$	−15.1664			−0.497059
$932$	15.2535	+	15.2535i	0.499644	+	0.499644i
$933$	−3.96677	+	14.8042i	−0.129866	+	0.484668i
$934$			9.41810i			0.308170i
$935$	−26.6236	+	59.3179i	−0.870685	+	1.93990i
$936$	−4.55089	+	2.62746i	−0.148751	+	0.0858812i
$937$	−4.62640	+	17.2659i	−0.151138	+	0.564054i	0.848267	+	0.529568i	$0.177646\pi$
$937$	−4.62640	+	17.2659i	−0.151138	+	0.564054i	−0.999405	+	0.0344858i	$0.989021\pi$
$938$	0.244099	−	0.244099i	0.00797013	−	0.00797013i
$939$	−17.6385	−	10.1836i	−0.575611	−	0.332329i
$940$	19.1182	+	8.58080i	0.623567	+	0.279875i
$941$	38.5170	+	22.2378i	1.25562	+	0.724931i	0.972220	−	0.234071i	$-0.0752048\pi$
$941$	38.5170	+	22.2378i	1.25562	+	0.724931i	0.283398	+	0.959002i	$0.408538\pi$
$942$	−8.58484	−	2.30030i	−0.279709	−	0.0749479i
$943$	18.0133	−	4.82665i	0.586593	−	0.157177i
$944$	−9.81288	+	5.66547i	−0.319382	+	0.184395i
$945$	0.236793	−	0.290627i	0.00770287	−	0.00945410i
$946$	12.9419			0.420778
$947$	16.6193	+	4.45313i	0.540055	+	0.144707i	0.518527	−	0.855061i	$-0.326480\pi$
$947$	16.6193	+	4.45313i	0.540055	+	0.144707i	0.0215275	+	0.999768i	$0.493147\pi$
$948$	2.24678	+	8.38508i	0.0729719	+	0.272335i
$949$	−8.05195	+	4.64879i	−0.261377	+	0.150906i
$950$	9.72078	−	4.87972i	0.315384	−	0.158319i
$951$	−30.6109	−	17.6732i	−0.992627	−	0.573094i
$952$	−0.352232	−	1.31455i	−0.0114159	−	0.0426047i
$953$	−25.9528	−	25.9528i	−0.840694	−	0.840694i	0.148255	−	0.988949i	$-0.452634\pi$
$953$	−25.9528	−	25.9528i	−0.840694	−	0.840694i	−0.988949	+	0.148255i	$0.952634\pi$
$954$	0.536369	+	0.929019i	0.0173656	+	0.0300781i
$955$	8.64961	+	1.39658i	0.279895	+	0.0451924i
$956$	−6.37732	−	3.68195i	−0.206257	−	0.119083i
$957$	−11.5246	+	11.5246i	−0.372537	+	0.372537i
$958$	22.4785	+	6.02310i	0.726248	+	0.194597i
$959$	0.0933197			0.00301345
$960$	−0.227058	−	2.22451i	−0.00732828	−	0.0717957i
$961$	8.21861	+	29.8907i	0.265116	+	0.964216i
$962$	−32.4914	−	32.4914i	−1.04756	−	1.04756i
$963$	−3.44666	+	3.44666i	−0.111067	+	0.111067i
$964$	−8.18934	−	14.1843i	−0.263761	−	0.456847i
$965$	−3.60999	−	35.3673i	−0.116210	−	1.13851i
$966$	0.170923	−	0.296047i	0.00549935	−	0.00952515i
$967$	45.9167	+	12.3033i	1.47658	+	0.395649i	0.905183	−	0.425023i	$-0.139734\pi$
$967$	45.9167	+	12.3033i	1.47658	+	0.395649i	0.571400	+	0.820672i	$0.306401\pi$
$968$	−1.76848	−	0.473862i	−0.0568410	−	0.0152305i
$969$			17.6586i			0.567277i
$970$	18.3657	−	6.98678i	0.589688	−	0.224332i
$971$	2.20234	−	3.81457i	0.0706765	−	0.122415i	−0.828521	−	0.559957i	$-0.810818\pi$
$971$	2.20234	−	3.81457i	0.0706765	−	0.122415i	0.899198	+	0.437542i	$0.144151\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−0.265549	+	0.991042i	−0.00851311	+	0.0317714i
$974$	3.68029	−	6.37445i	0.117924	−	0.204251i
$975$	−17.4636	−	19.6310i	−0.559284	−	0.628695i
$976$			7.57409i			0.242441i
$977$	−25.7722	−	25.7722i	−0.824525	−	0.824525i	0.162228	−	0.986753i	$-0.448132\pi$
$977$	−25.7722	−	25.7722i	−0.824525	−	0.824525i	−0.986753	+	0.162228i	$0.948132\pi$
$978$	3.12190	−	11.6511i	0.0998272	−	0.372560i
$979$	−41.3219	−	23.8572i	−1.32065	−	0.762480i
$980$	−15.3903	−	2.48495i	−0.491625	−	0.0793788i
$981$	−3.30768	+	5.72908i	−0.105606	+	0.182915i
$982$	−1.55319	−	5.79658i	−0.0495643	−	0.184976i
$983$	−24.8768	+	6.66572i	−0.793447	+	0.212604i	−0.632705	−	0.774393i	$-0.718055\pi$
$983$	−24.8768	+	6.66572i	−0.793447	+	0.212604i	−0.160742	+	0.986996i	$0.551389\pi$
$984$	−9.14590			−0.291561
$985$	31.7311	−	22.9089i	1.01104	−	0.729937i
$986$	−18.4675	−	31.9866i	−0.588125	−	1.01866i
$987$	−0.406647	−	1.51763i	−0.0129437	−	0.0483066i
$988$	8.08319	+	8.08319i	0.257160	+	0.257160i
$989$	−6.38004	+	3.68352i	−0.202874	+	0.117129i
$990$	7.96824	−	0.813328i	0.253247	−	0.0258492i
$991$			20.3884i			0.647657i	0.946116	+	0.323829i	$0.104970\pi$
$991$			20.3884i			0.647657i	−0.946116	+	0.323829i	$0.895030\pi$
$992$	−0.744745	−	5.51773i	−0.0236457	−	0.175188i
$993$	9.81213	−	9.81213i	0.311378	−	0.311378i
$994$		−	0.161340i		−	0.00511740i
$995$	−3.63373	−	0.586709i	−0.115197	−	0.0185999i
$996$	15.0903			0.478155
$997$	29.4856	−	7.90064i	0.933818	−	0.250216i	0.240336	−	0.970690i	$-0.422742\pi$
$997$	29.4856	−	7.90064i	0.933818	−	0.250216i	0.693482	+	0.720474i	$0.256076\pi$
$998$	−3.67017	+	13.6973i	−0.116177	+	0.433579i
$999$	−7.57265	+	4.37207i	−0.239588	+	0.138326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.13	✓	64
5.3	odd	4		930.2.be.b.223.9	yes	64
31.26	odd	6		930.2.be.b.367.9	yes	64
155.88	even	12	inner	930.2.be.a.553.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.13	✓	64	1.1	even	1	trivial
930.2.be.a.553.13	yes	64	155.88	even	12	inner
930.2.be.b.223.9	yes	64	5.3	odd	4
930.2.be.b.367.9	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.795067 + 2.08994i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.0433914 + 0.161939i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.795067 + 2.08994i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.0433914 + 0.161939i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.915617 + 2.04001i) q^{10} +(3.10212 + 1.79101i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-5.07586 + 1.36007i) q^{13} +(-0.145190 + 0.0838257i) q^{14} +(2.22451 - 0.227058i) q^{15} -1.00000 q^{16} +(7.84096 + 2.10098i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-1.88392 + 1.08768i) q^{19} +(-2.08994 + 0.795067i) q^{20} +(0.145190 + 0.0838257i) q^{21} +(0.927095 + 3.45997i) q^{22} +(-1.44181 - 1.44181i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.73574 + 3.32329i) q^{25} +(-4.55089 - 2.62746i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.161939 - 0.0433914i) q^{28} -4.55001 q^{29} +(1.73352 + 1.41241i) q^{30} +(4.42824 + 3.37501i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.53287 - 2.53287i) q^{33} +(4.05878 + 7.03001i) q^{34} +(-0.372942 + 0.0380667i) q^{35} +(0.500000 - 0.866025i) q^{36} +(8.44619 + 2.26315i) q^{37} +(-2.10124 - 0.563026i) q^{38} +5.25492i q^{39} +(-2.04001 - 0.915617i) q^{40} +(-4.57295 + 7.92059i) q^{41} +(0.0433914 + 0.161939i) q^{42} +(0.935119 - 3.48991i) q^{43} +(-1.79101 + 3.10212i) q^{44} +(0.356424 - 2.20748i) q^{45} -2.03902i q^{46} +(-6.62673 - 6.62673i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(6.03784 + 3.48595i) q^{49} +(-4.99149 - 0.291642i) q^{50} +(4.05878 - 7.03001i) q^{51} +(-1.36007 - 5.07586i) q^{52} +(-1.03619 + 0.277645i) q^{53} -1.00000 q^{54} +(-1.27672 + 7.90723i) q^{55} +(-0.0838257 - 0.145190i) q^{56} +(0.563026 + 2.10124i) q^{57} +(-3.21734 - 3.21734i) q^{58} +(9.81288 - 5.66547i) q^{59} +(0.227058 + 2.22451i) q^{60} -7.57409i q^{61} +(0.744745 + 5.51773i) q^{62} +(0.118547 - 0.118547i) q^{63} -1.00000i q^{64} +(-6.87813 - 9.52692i) q^{65} +3.58202 q^{66} +(-1.98892 + 0.532931i) q^{67} +(-2.10098 + 7.84096i) q^{68} +(-1.76585 + 1.01951i) q^{69} +(-0.290627 - 0.236793i) q^{70} +(-0.481177 + 0.833424i) q^{71} +(0.965926 - 0.258819i) q^{72} +(1.70902 - 0.457932i) q^{73} +(4.37207 + 7.57265i) q^{74} +(2.24317 + 4.46858i) q^{75} +(-1.08768 - 1.88392i) q^{76} +(-0.424639 + 0.424639i) q^{77} +(-3.71579 + 3.71579i) q^{78} +(4.34044 + 7.51786i) q^{79} +(-0.795067 - 2.08994i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-8.83426 + 2.36713i) q^{82} +(14.5761 - 3.90566i) q^{83} +(-0.0838257 + 0.145190i) q^{84} +(1.84316 + 18.0576i) q^{85} +(3.12897 - 1.80651i) q^{86} +(-1.17763 + 4.39497i) q^{87} +(-3.45997 + 0.927095i) q^{88} -13.3205 q^{89} +(1.81295 - 1.30889i) q^{90} -0.880994i q^{91} +(1.44181 - 1.44181i) q^{92} +(4.40612 - 3.40383i) q^{93} -9.37161i q^{94} +(-3.77104 - 3.07251i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-6.21382 - 6.21382i) q^{97} +(1.80446 + 6.73433i) q^{98} +(-1.79101 - 3.10212i) 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

Introduction

L-functions

Modular forms

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