LMFDB - Embedded newform 930.2.be.a.37.2

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			37.2
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.98218 + 1.03487i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.211801 - 0.790453i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.98218 + 1.03487i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.211801 - 0.790453i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.13338 + 0.669853i) q^{10} +(-0.702599 - 0.405646i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-4.35376 + 1.16659i) q^{13} +(-0.708701 + 0.409169i) q^{14} +(-0.486579 - 2.18249i) q^{15} -1.00000 q^{16} +(0.689013 + 0.184621i) q^{17} +(0.258819 + 0.965926i) q^{18} +(6.50506 - 3.75570i) q^{19} +(-1.03487 - 1.98218i) q^{20} +(0.708701 + 0.409169i) q^{21} +(0.209978 + 0.783648i) q^{22} +(-3.45927 - 3.45927i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.85810 - 4.10259i) q^{25} +(3.90348 + 2.25367i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.790453 + 0.211801i) q^{28} -2.47163 q^{29} +(-1.19919 + 1.88731i) q^{30} +(-2.60412 + 4.92124i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.573670 - 0.573670i) q^{33} +(-0.356660 - 0.617752i) q^{34} +(0.398186 + 1.78601i) q^{35} +(0.500000 - 0.866025i) q^{36} +(10.2806 + 2.75467i) q^{37} +(-7.25545 - 1.94409i) q^{38} -4.50735i q^{39} +(-0.669853 + 2.13338i) q^{40} +(3.26969 - 5.66327i) q^{41} +(-0.211801 - 0.790453i) q^{42} +(2.54828 - 9.51031i) q^{43} +(0.405646 - 0.702599i) q^{44} +(2.23405 + 0.0948696i) q^{45} +4.89214i q^{46} +(-1.76114 - 1.76114i) q^{47} +(0.258819 - 0.965926i) q^{48} +(5.48222 + 3.16516i) q^{49} +(-4.92195 + 0.879992i) q^{50} +(-0.356660 + 0.617752i) q^{51} +(-1.16659 - 4.35376i) q^{52} +(-9.01723 + 2.41616i) q^{53} -1.00000 q^{54} +(1.81247 + 0.0769669i) q^{55} +(-0.409169 - 0.708701i) q^{56} +(1.94409 + 7.25545i) q^{57} +(1.74771 + 1.74771i) q^{58} +(10.3394 - 5.96947i) q^{59} +(2.18249 - 0.486579i) q^{60} -13.7850i q^{61} +(5.32123 - 1.63845i) q^{62} +(-0.578652 + 0.578652i) q^{63} -1.00000i q^{64} +(7.42269 - 6.81796i) q^{65} -0.811292 q^{66} +(12.2166 - 3.27343i) q^{67} +(-0.184621 + 0.689013i) q^{68} +(4.23672 - 2.44607i) q^{69} +(0.981339 - 1.54446i) q^{70} +(4.94341 - 8.56223i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(1.17258 - 0.314192i) q^{73} +(-5.32161 - 9.21730i) q^{74} +(3.22307 + 3.82254i) q^{75} +(3.75570 + 6.50506i) q^{76} +(-0.469456 + 0.469456i) q^{77} +(-3.18718 + 3.18718i) q^{78} +(-0.836534 - 1.44892i) q^{79} +(1.98218 - 1.03487i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-6.31655 + 1.69252i) q^{82} +(-15.6229 + 4.18614i) q^{83} +(-0.409169 + 0.708701i) q^{84} +(-1.55681 + 0.347086i) q^{85} +(-8.52671 + 4.92290i) q^{86} +(0.639706 - 2.38742i) q^{87} +(-0.783648 + 0.209978i) q^{88} -4.90936 q^{89} +(-1.51263 - 1.64680i) q^{90} +3.68853i q^{91} +(3.45927 - 3.45927i) q^{92} +(-4.07956 - 3.78909i) q^{93} +2.49062i q^{94} +(-9.00757 + 14.1764i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-9.66051 - 9.66051i) q^{97} +(-1.63841 - 6.11462i) q^{98} +(0.405646 + 0.702599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	−1.98218	+	1.03487i	−0.886459	+	0.462807i
$5$	−1.98218	+	1.03487i	−0.886459	+	0.462807i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	0.211801	−	0.790453i	0.0800534	−	0.298763i	−0.914278	−	0.405087i	$-0.867241\pi$
$7$	0.211801	−	0.790453i	0.0800534	−	0.298763i	0.994332	+	0.106324i	$0.0339079\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	2.13338	+	0.669853i	0.674633	+	0.211826i
$11$	−0.702599	−	0.405646i	−0.211842	−	0.122307i	0.390325	−	0.920677i	$-0.372363\pi$
$11$	−0.702599	−	0.405646i	−0.211842	−	0.122307i	−0.602167	+	0.798370i	$0.705696\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−4.35376	+	1.16659i	−1.20752	+	0.323553i	−0.805787	−	0.592205i	$-0.798258\pi$
$13$	−4.35376	+	1.16659i	−1.20752	+	0.323553i	−0.401730	+	0.915758i	$0.631591\pi$
$14$	−0.708701	+	0.409169i	−0.189408	+	0.109355i
$15$	−0.486579	−	2.18249i	−0.125634	−	0.563515i
$16$	−1.00000			−0.250000
$17$	0.689013	+	0.184621i	0.167110	+	0.0447771i	0.341404	−	0.939917i	$-0.389098\pi$
$17$	0.689013	+	0.184621i	0.167110	+	0.0447771i	−0.174294	+	0.984694i	$0.555764\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	6.50506	−	3.75570i	1.49236	−	0.861617i	0.492402	−	0.870368i	$-0.336119\pi$
$19$	6.50506	−	3.75570i	1.49236	−	0.861617i	0.999962	+	0.00875128i	$0.00278566\pi$
$20$	−1.03487	−	1.98218i	−0.231403	−	0.443230i
$21$	0.708701	+	0.409169i	0.154651	+	0.0892879i
$22$	0.209978	+	0.783648i	0.0447674	+	0.167074i
$23$	−3.45927	−	3.45927i	−0.721307	−	0.721307i	0.247564	−	0.968871i	$-0.420370\pi$
$23$	−3.45927	−	3.45927i	−0.721307	−	0.721307i	−0.968871	+	0.247564i	$0.920370\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.85810	−	4.10259i	0.571619	−	0.820519i
$26$	3.90348	+	2.25367i	0.765535	+	0.441982i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	0.790453	+	0.211801i	0.149382	+	0.0400267i
$29$	−2.47163			−0.458971			−0.229485	−	0.973312i	$-0.573704\pi$
$29$	−2.47163			−0.458971			−0.229485	+	0.973312i	$0.573704\pi$
$30$	−1.19919	+	1.88731i	−0.218941	+	0.344575i
$31$	−2.60412	+	4.92124i	−0.467713	+	0.883880i
$31$	−2.60412	+	4.92124i	−0.467713	+	0.883880i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.573670	−	0.573670i	0.0998631	−	0.0998631i
$34$	−0.356660	−	0.617752i	−0.0611666	−	0.105944i
$35$	0.398186	+	1.78601i	0.0673057	+	0.301891i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	10.2806	+	2.75467i	1.69011	+	0.452865i	0.970419	−	0.241425i	$-0.0776148\pi$
$37$	10.2806	+	2.75467i	1.69011	+	0.452865i	0.719695	+	0.694290i	$0.244281\pi$
$38$	−7.25545	−	1.94409i	−1.17699	−	0.315374i
$39$		−	4.50735i		−	0.721753i
$40$	−0.669853	+	2.13338i	−0.105913	+	0.337317i
$41$	3.26969	−	5.66327i	0.510639	−	0.884454i	−0.489285	−	0.872124i	$-0.662742\pi$
$41$	3.26969	−	5.66327i	0.510639	−	0.884454i	0.999924	−	0.0123293i	$-0.00392463\pi$
$42$	−0.211801	−	0.790453i	−0.0326817	−	0.121970i
$43$	2.54828	−	9.51031i	0.388609	−	1.45031i	−0.443790	−	0.896131i	$-0.646366\pi$
$43$	2.54828	−	9.51031i	0.388609	−	1.45031i	0.832399	−	0.554177i	$-0.186967\pi$
$44$	0.405646	−	0.702599i	0.0611534	−	0.105921i
$45$	2.23405	+	0.0948696i	0.333033	+	0.0141423i
$46$			4.89214i			0.721307i
$47$	−1.76114	−	1.76114i	−0.256888	−	0.256888i	0.566899	−	0.823787i	$-0.308143\pi$
$47$	−1.76114	−	1.76114i	−0.256888	−	0.256888i	−0.823787	+	0.566899i	$0.808143\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	5.48222	+	3.16516i	0.783174	+	0.452166i
$50$	−4.92195	+	0.879992i	−0.696069	+	0.124450i
$51$	−0.356660	+	0.617752i	−0.0499423	+	0.0865026i
$52$	−1.16659	−	4.35376i	−0.161777	−	0.603759i
$53$	−9.01723	+	2.41616i	−1.23861	+	0.331885i	−0.817927	−	0.575322i	$-0.804877\pi$
$53$	−9.01723	+	2.41616i	−1.23861	+	0.331885i	−0.420684	+	0.907207i	$0.638210\pi$
$54$	−1.00000			−0.136083
$55$	1.81247	+	0.0769669i	0.244393	+	0.0103782i
$56$	−0.409169	−	0.708701i	−0.0546775	−	0.0947042i
$57$	1.94409	+	7.25545i	0.257501	+	0.961008i
$58$	1.74771	+	1.74771i	0.229485	+	0.229485i
$59$	10.3394	−	5.96947i	1.34608	−	0.777159i	0.358387	−	0.933573i	$-0.383327\pi$
$59$	10.3394	−	5.96947i	1.34608	−	0.777159i	0.987692	+	0.156414i	$0.0499935\pi$
$60$	2.18249	−	0.486579i	0.281758	−	0.0628171i
$61$		−	13.7850i		−	1.76499i	−0.470323	−	0.882494i	$-0.655863\pi$
$61$		−	13.7850i		−	1.76499i	0.470323	−	0.882494i	$-0.344137\pi$
$62$	5.32123	−	1.63845i	0.675797	−	0.208084i
$63$	−0.578652	+	0.578652i	−0.0729033	+	0.0729033i
$64$		−	1.00000i		−	0.125000i
$65$	7.42269	−	6.81796i	0.920672	−	0.845664i
$66$	−0.811292			−0.0998631
$67$	12.2166	−	3.27343i	1.49250	−	0.399913i	0.581918	−	0.813248i	$-0.302303\pi$
$67$	12.2166	−	3.27343i	1.49250	−	0.399913i	0.910579	+	0.413334i	$0.135636\pi$
$68$	−0.184621	+	0.689013i	−0.0223885	+	0.0835551i
$69$	4.23672	−	2.44607i	0.510041	−	0.294472i
$70$	0.981339	−	1.54446i	0.117292	−	0.184598i
$71$	4.94341	−	8.56223i	0.586675	−	1.01615i	−0.407990	−	0.912986i	$-0.633770\pi$
$71$	4.94341	−	8.56223i	0.586675	−	1.01615i	0.994664	−	0.103164i	$-0.0328965\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	1.17258	−	0.314192i	0.137240	−	0.0367734i	−0.189545	−	0.981872i	$-0.560701\pi$
$73$	1.17258	−	0.314192i	0.137240	−	0.0367734i	0.326785	+	0.945099i	$0.394035\pi$
$74$	−5.32161	−	9.21730i	−0.618625	−	1.07149i
$75$	3.22307	+	3.82254i	0.372168	+	0.441389i
$76$	3.75570	+	6.50506i	0.430808	+	0.746182i
$77$	−0.469456	+	0.469456i	−0.0534994	+	0.0534994i
$78$	−3.18718	+	3.18718i	−0.360877	+	0.360877i
$79$	−0.836534	−	1.44892i	−0.0941175	−	0.163016i	0.815122	−	0.579289i	$-0.196670\pi$
$79$	−0.836534	−	1.44892i	−0.0941175	−	0.163016i	−0.909240	+	0.416272i	$0.863336\pi$
$80$	1.98218	−	1.03487i	0.221615	−	0.115702i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−6.31655	+	1.69252i	−0.697546	+	0.186907i
$83$	−15.6229	+	4.18614i	−1.71483	+	0.459488i	−0.976601	−	0.215059i	$-0.931006\pi$
$83$	−15.6229	+	4.18614i	−1.71483	+	0.459488i	−0.738232	+	0.674547i	$0.764339\pi$
$84$	−0.409169	+	0.708701i	−0.0446440	+	0.0773256i
$85$	−1.55681	+	0.347086i	−0.168860	+	0.0376468i
$86$	−8.52671	+	4.92290i	−0.919459	+	0.530850i
$87$	0.639706	−	2.38742i	0.0685837	−	0.255958i
$88$	−0.783648	+	0.209978i	−0.0835371	+	0.0223837i
$89$	−4.90936			−0.520391			−0.260196	−	0.965556i	$-0.583787\pi$
$89$	−4.90936			−0.520391			−0.260196	+	0.965556i	$0.583787\pi$
$90$	−1.51263	−	1.64680i	−0.159445	−	0.173588i
$91$			3.68853i			0.386663i
$92$	3.45927	−	3.45927i	0.360654	−	0.360654i
$93$	−4.07956	−	3.78909i	−0.423030	−	0.392911i
$94$			2.49062i			0.256888i
$95$	−9.00757	+	14.1764i	−0.924157	+	1.45446i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−9.66051	−	9.66051i	−0.980876	−	0.980876i	0.0189447	−	0.999821i	$-0.493969\pi$
$97$	−9.66051	−	9.66051i	−0.980876	−	0.980876i	−0.999821	+	0.0189447i	$0.993969\pi$
$98$	−1.63841	−	6.11462i	−0.165504	−	0.617670i
$99$	0.405646	+	0.702599i	0.0407690	+	0.0706139i
$100$	4.10259	+	2.85810i	0.410259	+	0.285810i
$101$	8.04761			0.800767			0.400384	−	0.916348i	$-0.368877\pi$
$101$	8.04761			0.800767			0.400384	+	0.916348i	$0.368877\pi$
$102$	0.689013	−	0.184621i	0.0682225	−	0.0182802i
$103$	0.0432264	+	0.161323i	0.00425923	+	0.0158956i	0.968023	−	0.250862i	$-0.0807142\pi$
$103$	0.0432264	+	0.161323i	0.00425923	+	0.0158956i	−0.963764	+	0.266758i	$0.914048\pi$
$104$	−2.25367	+	3.90348i	−0.220991	+	0.382768i
$105$	−1.82821	−	0.0776353i	−0.178415	−	0.00757643i
$106$	8.08462	+	4.66766i	0.785248	+	0.453363i
$107$	−2.75415	+	10.2786i	−0.266253	+	0.993671i	0.695225	+	0.718792i	$0.255305\pi$
$107$	−2.75415	+	10.2786i	−0.266253	+	0.993671i	−0.961479	+	0.274879i	$0.911362\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			3.42421i			0.327980i	0.986462	+	0.163990i	$0.0524364\pi$
$109$			3.42421i			0.327980i	−0.986462	+	0.163990i	$0.947564\pi$
$110$	−1.22719	−	1.33603i	−0.117008	−	0.127386i
$111$	−5.32161	+	9.21730i	−0.505105	+	0.874868i
$112$	−0.211801	+	0.790453i	−0.0200133	+	0.0746908i
$113$	−3.52412	−	13.1522i	−0.331522	−	1.23726i	−0.907591	−	0.419855i	$-0.862081\pi$
$113$	−3.52412	−	13.1522i	−0.331522	−	1.23726i	0.576069	−	0.817401i	$-0.304586\pi$
$114$	3.75570	−	6.50506i	0.351754	−	0.609255i
$115$	10.4368	+	3.27702i	0.973235	+	0.305583i
$116$		−	2.47163i		−	0.229485i
$117$	4.35376	+	1.16659i	0.402506	+	0.107851i
$118$	−11.5321	−	3.09002i	−1.06162	−	0.284460i
$119$	0.291868	−	0.505530i	0.0267555	−	0.0463419i
$120$	−1.88731	−	1.19919i	−0.172287	−	0.109470i
$121$	−5.17090	−	8.95627i	−0.470082	−	0.814206i
$122$	−9.74747	+	9.74747i	−0.882494	+	0.882494i
$123$	4.62404	+	4.62404i	0.416935	+	0.416935i
$124$	−4.92124	−	2.60412i	−0.441940	−	0.233857i
$125$	−1.41963	+	11.0898i	−0.126975	+	0.991906i
$126$	0.818337			0.0729033
$127$	−15.3230	−	4.10578i	−1.35970	−	0.364329i	−0.495991	−	0.868328i	$-0.665195\pi$
$127$	−15.3230	−	4.10578i	−1.35970	−	0.364329i	−0.863705	+	0.503998i	$0.831862\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	8.52671	+	4.92290i	0.750735	+	0.433437i
$130$	−10.0697	−	0.427610i	−0.883168	−	0.0375039i
$131$	8.04012	+	13.9259i	0.702469	+	1.21671i	0.967597	+	0.252499i	$0.0812523\pi$
$131$	8.04012	+	13.9259i	0.702469	+	1.21671i	−0.265128	+	0.964213i	$0.585414\pi$
$132$	0.573670	+	0.573670i	0.0499316	+	0.0499316i
$133$	−1.59092	−	5.93741i	−0.137951	−	0.514839i
$134$	−10.9531	−	6.32378i	−0.946205	−	0.546292i
$135$	−0.669853	+	2.13338i	−0.0576518	+	0.183612i
$136$	0.617752	−	0.356660i	0.0529718	−	0.0305833i
$137$	−3.67776	−	13.7256i	−0.314213	−	1.17266i	−0.924720	−	0.380647i	$-0.875701\pi$
$137$	−3.67776	−	13.7256i	−0.314213	−	1.17266i	0.610508	−	0.792010i	$-0.290965\pi$
$138$	−4.72545	−	1.26618i	−0.402257	−	0.107784i
$139$	13.6701			1.15949			0.579743	−	0.814799i	$-0.303153\pi$
$139$	13.6701			1.15949			0.579743	+	0.814799i	$0.303153\pi$
$140$	−1.78601	+	0.398186i	−0.150945	+	0.0336528i
$141$	2.15694	−	1.24531i	0.181647	−	0.104874i
$142$	−9.54993	+	2.55890i	−0.801412	+	0.214738i
$143$	3.53217	+	0.946443i	0.295375	+	0.0791456i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	4.89923	−	2.55781i	0.406859	−	0.212415i
$146$	−1.05131	−	0.606973i	−0.0870069	−	0.0502334i
$147$	−4.47621	+	4.47621i	−0.369192	+	0.369192i
$148$	−2.75467	+	10.2806i	−0.226432	+	0.845057i
$149$	5.04879	−	2.91492i	0.413613	−	0.238799i	−0.278728	−	0.960370i	$-0.589913\pi$
$149$	5.04879	−	2.91492i	0.413613	−	0.238799i	0.692341	+	0.721571i	$0.256580\pi$
$150$	0.423888	−	4.98200i	0.0346103	−	0.406779i
$151$			5.95883i			0.484923i	0.970161	+	0.242461i	$0.0779548\pi$
$151$			5.95883i			0.484923i	−0.970161	+	0.242461i	$0.922045\pi$
$152$	1.94409	−	7.25545i	0.157687	−	0.588495i
$153$	−0.504393	−	0.504393i	−0.0407777	−	0.0407777i
$154$	0.663911			0.0534994
$155$	0.0690052	−	12.4497i	0.00554263	−	0.999985i
$156$	4.50735			0.360877
$157$	−4.12260	−	4.12260i	−0.329019	−	0.329019i	0.523194	−	0.852213i	$-0.324740\pi$
$157$	−4.12260	−	4.12260i	−0.329019	−	0.329019i	−0.852213	+	0.523194i	$0.824740\pi$
$158$	−0.433022	+	1.61606i	−0.0344494	+	0.128567i
$159$		−	9.33532i		−	0.740339i
$160$	−2.13338	−	0.669853i	−0.168658	−	0.0529565i
$161$	−3.46707	+	2.00171i	−0.273243	+	0.157757i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−6.93443	+	6.93443i	−0.543147	+	0.543147i	−0.924450	−	0.381303i	$-0.875475\pi$
$163$	−6.93443	+	6.93443i	−0.543147	+	0.543147i	0.381303	+	0.924450i	$0.375475\pi$
$164$	5.66327	+	3.26969i	0.442227	+	0.255320i
$165$	−0.543446	+	1.73079i	−0.0423072	+	0.134742i
$166$	14.0071	+	8.08699i	1.08716	+	0.627672i
$167$	−0.211285	−	0.0566135i	−0.0163497	−	0.00438089i	0.250635	−	0.968082i	$-0.419361\pi$
$167$	−0.211285	−	0.0566135i	−0.0163497	−	0.00438089i	−0.266985	+	0.963701i	$0.586027\pi$
$168$	0.790453	−	0.211801i	0.0609848	−	0.0163408i
$169$	6.33601	−	3.65810i	0.487385	−	0.281392i
$170$	1.34626	+	0.855403i	0.103253	+	0.0656064i
$171$	−7.51140			−0.574411
$172$	9.51031	+	2.54828i	0.725154	+	0.194304i
$173$	0.00330312	+	0.0123274i	0.000251132	+	0.000937237i	0.966051	−	0.258350i	$-0.0831789\pi$
$173$	0.00330312	+	0.0123274i	0.000251132	+	0.000937237i	−0.965800	+	0.259288i	$0.916512\pi$
$174$	−2.14050	+	1.23582i	−0.162271	+	0.0936871i
$175$	−2.63756	−	3.12813i	−0.199381	−	0.236464i
$176$	0.702599	+	0.405646i	0.0529604	+	0.0305767i
$177$	3.09002	+	11.5321i	0.232261	+	0.866808i
$178$	3.47144	+	3.47144i	0.260196	+	0.260196i
$179$	−4.03883	−	6.99547i	−0.301877	−	0.522866i	0.674684	−	0.738106i	$-0.264280\pi$
$179$	−4.03883	−	6.99547i	−0.301877	−	0.522866i	−0.976561	+	0.215241i	$0.930946\pi$
$180$	−0.0948696	+	2.23405i	−0.00707116	+	0.166517i
$181$	12.0816	+	6.97533i	0.898021	+	0.518473i	0.876558	−	0.481297i	$-0.159834\pi$
$181$	12.0816	+	6.97533i	0.898021	+	0.518473i	0.0214632	+	0.999770i	$0.493168\pi$
$182$	2.60819	−	2.60819i	0.193332	−	0.193332i
$183$	13.3153	+	3.56782i	0.984295	+	0.263741i
$184$	−4.89214			−0.360654
$185$	−23.2287	+	5.17877i	−1.70781	+	0.380751i
$186$	0.205387	+	5.56397i	0.0150597	+	0.407970i
$187$	−0.409210	−	0.409210i	−0.0299244	−	0.0299244i
$188$	1.76114	−	1.76114i	0.128444	−	0.128444i
$189$	−0.409169	−	0.708701i	−0.0297626	−	0.0515504i
$190$	16.3935	−	3.65489i	1.18931	−	0.265153i
$191$	−4.35883	+	7.54971i	−0.315394	+	0.546278i	−0.979521	−	0.201342i	$-0.935470\pi$
$191$	−4.35883	+	7.54971i	−0.315394	+	0.546278i	0.664128	+	0.747619i	$0.268803\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	−2.49435	−	0.668360i	−0.179547	−	0.0481096i	0.167925	−	0.985800i	$-0.446293\pi$
$193$	−2.49435	−	0.668360i	−0.179547	−	0.0481096i	−0.347472	+	0.937690i	$0.612960\pi$
$194$			13.6620i			0.980876i
$195$	4.66451	+	8.93439i	0.334033	+	0.639805i
$196$	−3.16516	+	5.48222i	−0.226083	+	0.391587i
$197$	−2.96209	−	11.0547i	−0.211040	−	0.787612i	−0.987523	−	0.157474i	$-0.949665\pi$
$197$	−2.96209	−	11.0547i	−0.211040	−	0.787612i	0.776483	−	0.630138i	$-0.217002\pi$
$198$	0.209978	−	0.783648i	0.0149225	−	0.0556914i
$199$	−7.95335	+	13.7756i	−0.563798	+	0.976526i	0.433363	+	0.901220i	$0.357327\pi$
$199$	−7.95335	+	13.7756i	−0.563798	+	0.976526i	−0.997160	+	0.0753067i	$0.976006\pi$
$200$	−0.879992	−	4.92195i	−0.0622249	−	0.348035i
$201$			12.6476i			0.892091i
$202$	−5.69052	−	5.69052i	−0.400384	−	0.400384i
$203$	−0.523495	+	1.95371i	−0.0367422	+	0.137124i
$204$	−0.617752	−	0.356660i	−0.0432513	−	0.0249712i
$205$	−0.620388	+	14.6093i	−0.0433298	+	1.02036i
$206$	0.0835070	−	0.144638i	0.00581821	−	0.0100774i
$207$	1.26618	+	4.72545i	0.0880056	+	0.328441i
$208$	4.35376	−	1.16659i	0.301879	−	0.0808883i
$209$	−6.09394			−0.421526
$210$	1.23784	+	1.34764i	0.0854193	+	0.0929958i
$211$	−4.90609	−	8.49759i	−0.337749	−	0.584998i	0.646260	−	0.763117i	$-0.276332\pi$
$211$	−4.90609	−	8.49759i	−0.337749	−	0.584998i	−0.984009	+	0.178119i	$0.942999\pi$
$212$	−2.41616	−	9.01723i	−0.165942	−	0.619306i
$213$	6.99103	+	6.99103i	0.479018	+	0.479018i
$214$	9.21555	−	5.32060i	0.629962	−	0.363709i
$215$	4.79076	+	21.4883i	0.326727	+	1.46549i
$216$		−	1.00000i		−	0.0680414i
$217$	3.33845	+	3.10076i	0.226629	+	0.210493i
$218$	2.42128	−	2.42128i	0.163990	−	0.163990i
$219$			1.21395i			0.0820309i
$220$	−0.0769669	+	1.81247i	−0.00518911	+	0.122197i
$221$	−3.21518			−0.216276
$222$	10.2806	−	2.75467i	0.689987	−	0.184881i
$223$	−6.19165	+	23.1076i	−0.414624	+	1.54740i	0.370964	+	0.928647i	$0.379027\pi$
$223$	−6.19165	+	23.1076i	−0.414624	+	1.54740i	−0.785588	+	0.618750i	$0.787639\pi$
$224$	0.708701	−	0.409169i	0.0473521	−	0.0273387i
$225$	−4.52648	+	2.12390i	−0.301765	+	0.141593i
$226$	−6.80808	+	11.7919i	−0.452867	+	0.784389i
$227$	26.0864	−	6.98984i	1.73142	−	0.463932i	0.750909	−	0.660406i	$-0.229616\pi$
$227$	26.0864	−	6.98984i	1.73142	−	0.463932i	0.980509	+	0.196474i	$0.0629490\pi$
$228$	−7.25545	+	1.94409i	−0.480504	+	0.128751i
$229$	2.29130	+	3.96864i	0.151413	+	0.262255i	0.931747	−	0.363108i	$-0.118284\pi$
$229$	2.29130	+	3.96864i	0.151413	+	0.262255i	−0.780334	+	0.625363i	$0.784951\pi$
$230$	−5.06272	−	9.69712i	−0.333826	−	0.639409i
$231$	−0.331955	−	0.574963i	−0.0218411	−	0.0378298i
$232$	−1.74771	+	1.74771i	−0.114743	+	0.114743i
$233$	−5.72287	+	5.72287i	−0.374918	+	0.374918i	−0.869265	−	0.494347i	$-0.835407\pi$
$233$	−5.72287	+	5.72287i	−0.374918	+	0.374918i	0.494347	+	0.869265i	$0.335407\pi$
$234$	−2.25367	−	3.90348i	−0.147327	−	0.255178i
$235$	5.31344	+	1.66835i	0.346610	+	0.108831i
$236$	5.96947	+	10.3394i	0.388579	+	0.673039i
$237$	1.61606	−	0.433022i	0.104974	−	0.0281278i
$238$	−0.563845	+	0.151082i	−0.0365487	+	0.00979319i
$239$	11.3452	−	19.6505i	0.733861	−	1.27108i	−0.221361	−	0.975192i	$-0.571050\pi$
$239$	11.3452	−	19.6505i	0.733861	−	1.27108i	0.955221	−	0.295892i	$-0.0956169\pi$
$240$	0.486579	+	2.18249i	0.0314085	+	0.140879i
$241$	−16.7882	+	9.69269i	−1.08142	+	0.624361i	−0.931280	−	0.364303i	$-0.881307\pi$
$241$	−16.7882	+	9.69269i	−1.08142	+	0.624361i	−0.150144	+	0.988664i	$0.547974\pi$
$242$	−2.67666	+	9.98942i	−0.172062	+	0.642144i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	13.7850			0.882494
$245$	−14.1423	−	0.600555i	−0.903518	−	0.0383681i
$246$		−	6.53938i		−	0.416935i
$247$	−23.9402	+	23.9402i	−1.52328	+	1.52328i
$248$	1.63845	+	5.32123i	0.104042	+	0.337898i
$249$		−	16.1740i		−	1.02498i
$250$	8.84553	−	6.83788i	0.559441	−	0.432465i
$251$	10.3113	−	5.95322i	0.650842	−	0.375764i	−0.137937	−	0.990441i	$-0.544047\pi$
$251$	10.3113	−	5.95322i	0.650842	−	0.375764i	0.788779	+	0.614677i	$0.210714\pi$
$252$	−0.578652	−	0.578652i	−0.0364516	−	0.0364516i
$253$	1.02724	+	3.83372i	0.0645821	+	0.241024i
$254$	7.93176	+	13.7382i	0.497683	+	0.862012i
$255$	0.0676723	−	1.59359i	0.00423780	−	0.0997947i
$256$	1.00000			0.0625000
$257$	−18.2658	+	4.89429i	−1.13939	+	0.305298i	−0.778704	−	0.627391i	$-0.784123\pi$
$257$	−18.2658	+	4.89429i	−1.13939	+	0.305298i	−0.360682	+	0.932689i	$0.617456\pi$
$258$	−2.54828	−	9.51031i	−0.158649	−	0.592086i
$259$	4.35488	−	7.54287i	0.270599	−	0.468691i
$260$	6.81796	+	7.42269i	0.422832	+	0.460336i
$261$	2.14050	+	1.23582i	0.132494	+	0.0764952i
$262$	4.16187	−	15.5323i	0.257121	−	0.959590i
$263$	10.1396	+	10.1396i	0.625238	+	0.625238i	0.946866	−	0.321628i	$-0.104230\pi$
$263$	10.1396	+	10.1396i	0.625238	+	0.625238i	−0.321628	+	0.946866i	$0.604230\pi$
$264$		−	0.811292i		−	0.0499316i
$265$	15.3734	−	14.1209i	0.944380	−	0.867440i
$266$	−3.07343	+	5.32334i	−0.188444	+	0.326395i
$267$	1.27064	−	4.74208i	0.0777617	−	0.290211i
$268$	3.27343	+	12.2166i	0.199957	+	0.746248i
$269$	8.69427	−	15.0589i	0.530099	−	0.918159i	−0.469284	−	0.883047i	$-0.655488\pi$
$269$	8.69427	−	15.0589i	0.530099	−	0.918159i	0.999383	−	0.0351115i	$-0.0111786\pi$
$270$	1.98218	−	1.03487i	0.120632	−	0.0629801i
$271$		−	0.146948i		−	0.00892645i	−0.999990	−	0.00446322i	$-0.998579\pi$
$271$		−	0.146948i		−	0.00892645i	0.999990	−	0.00446322i	$-0.00142069\pi$
$272$	−0.689013	−	0.184621i	−0.0417776	−	0.0111943i
$273$	−3.56285	−	0.954662i	−0.215633	−	0.0577788i
$274$	−7.10489	+	12.3060i	−0.429222	+	0.743435i
$275$	−3.67230	+	1.72310i	−0.221448	+	0.103907i
$276$	2.44607	+	4.23672i	0.147236	+	0.255021i
$277$	13.4983	−	13.4983i	0.811034	−	0.811034i	−0.173755	−	0.984789i	$-0.555590\pi$
$277$	13.4983	−	13.4983i	0.811034	−	0.811034i	0.984789	+	0.173755i	$0.0555900\pi$
$278$	−9.66625	−	9.66625i	−0.579743	−	0.579743i
$279$	4.71585	−	2.95986i	0.282331	−	0.177202i
$280$	1.54446	+	0.981339i	0.0922991	+	0.0586462i
$281$	−16.4983			−0.984208			−0.492104	−	0.870536i	$-0.663772\pi$
$281$	−16.4983			−0.984208			−0.492104	+	0.870536i	$0.663772\pi$
$282$	−2.40576	−	0.644621i	−0.143261	−	0.0383866i
$283$	−14.3231	+	14.3231i	−0.851420	+	0.851420i	−0.990308	−	0.138888i	$-0.955647\pi$
$283$	−14.3231	+	14.3231i	−0.851420	+	0.851420i	0.138888	+	0.990308i	$0.455647\pi$
$284$	8.56223	+	4.94341i	0.508075	+	0.293337i
$285$	−11.3620	−	12.3698i	−0.673026	−	0.732721i
$286$	−1.82839	−	3.16686i	−0.108115	−	0.187260i
$287$	−3.78402	−	3.78402i	−0.223364	−	0.223364i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−14.2818	−	8.24559i	−0.840105	−	0.485035i
$290$	−5.27293	−	1.65563i	−0.309637	−	0.0972220i
$291$	11.8317	−	6.83101i	0.693584	−	0.400441i
$292$	0.314192	+	1.17258i	0.0183867	+	0.0686202i
$293$	12.2198	+	3.27428i	0.713887	+	0.191285i	0.597443	−	0.801912i	$-0.296184\pi$
$293$	12.2198	+	3.27428i	0.713887	+	0.191285i	0.116445	+	0.993197i	$0.462850\pi$
$294$	6.33032			0.369192
$295$	−14.3170	+	22.5325i	−0.833569	+	1.31189i
$296$	9.21730	−	5.32161i	0.535745	−	0.309313i
$297$	−0.783648	+	0.209978i	−0.0454719	+	0.0121841i
$298$	−5.63119	−	1.50887i	−0.326206	−	0.0874066i
$299$	19.0964	+	11.0253i	1.10437	+	0.637609i
$300$	−3.82254	+	3.22307i	−0.220694	+	0.186084i
$301$	−6.97772	−	4.02859i	−0.402189	−	0.232204i
$302$	4.21353	−	4.21353i	0.242461	−	0.242461i
$303$	−2.08287	+	7.77339i	−0.119658	+	0.446570i
$304$	−6.50506	+	3.75570i	−0.373091	+	0.215404i
$305$	14.2657	+	27.3244i	0.816849	+	1.56459i
$306$			0.713319i			0.0407777i
$307$	−2.03058	+	7.57825i	−0.115892	+	0.432513i	−0.999352	−	0.0359924i	$-0.988541\pi$
$307$	−2.03058	+	7.57825i	−0.115892	+	0.432513i	0.883460	+	0.468506i	$0.155207\pi$
$308$	−0.469456	−	0.469456i	−0.0267497	−	0.0267497i
$309$	−0.167014			−0.00950110
$310$	−8.85207	+	8.75448i	−0.502764	+	0.497221i
$311$	12.0405			0.682753			0.341377	−	0.939927i	$-0.389107\pi$
$311$	12.0405			0.682753			0.341377	+	0.939927i	$0.389107\pi$
$312$	−3.18718	−	3.18718i	−0.180438	−	0.180438i
$313$	1.24822	−	4.65843i	0.0705537	−	0.263310i	−0.921635	−	0.388059i	$-0.873146\pi$
$313$	1.24822	−	4.65843i	0.0705537	−	0.263310i	0.992188	+	0.124749i	$0.0398124\pi$
$314$			5.83023i			0.329019i
$315$	0.548166	−	1.74582i	0.0308856	−	0.0983659i
$316$	1.44892	−	0.836534i	0.0815081	−	0.0470587i
$317$	−5.91013	+	22.0569i	−0.331946	+	1.23884i	0.575196	+	0.818016i	$0.304926\pi$
$317$	−5.91013	+	22.0569i	−0.331946	+	1.23884i	−0.907142	+	0.420824i	$0.861741\pi$
$318$	−6.60107	+	6.60107i	−0.370170	+	0.370170i
$319$	1.73657	+	1.00261i	0.0972292	+	0.0561353i
$320$	1.03487	+	1.98218i	0.0578509	+	0.110807i
$321$	−9.21555	−	5.32060i	−0.514362	−	0.296967i
$322$	3.86701	+	1.03616i	0.215500	+	0.0577431i
$323$	5.17545	−	1.38676i	0.287970	−	0.0771613i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−7.65745	+	21.1960i	−0.424759	+	1.17574i
$326$	9.80677			0.543147
$327$	−3.30753	−	0.886250i	−0.182907	−	0.0490097i
$328$	−1.69252	−	6.31655i	−0.0934535	−	0.348773i
$329$	−1.76511	+	1.01909i	−0.0973135	+	0.0561840i
$330$	1.60813	−	0.839580i	0.0885246	−	0.0462174i
$331$	−20.7181	−	11.9616i	−1.13877	−	0.657469i	−0.192644	−	0.981269i	$-0.561706\pi$
$331$	−20.7181	−	11.9616i	−1.13877	−	0.657469i	−0.946126	+	0.323800i	$0.895040\pi$
$332$	−4.18614	−	15.6229i	−0.229744	−	0.857416i
$333$	−7.52590	−	7.52590i	−0.412417	−	0.412417i
$334$	0.109369	+	0.189433i	0.00598440	+	0.0103653i
$335$	−20.8280	+	19.1311i	−1.13795	+	1.04524i
$336$	−0.708701	−	0.409169i	−0.0386628	−	0.0223220i
$337$	16.9912	−	16.9912i	0.925572	−	0.925572i	−0.0718439	−	0.997416i	$-0.522888\pi$
$337$	16.9912	−	16.9912i	0.925572	−	0.925572i	0.997416	+	0.0718439i	$0.0228884\pi$
$338$	−7.06690	−	1.89357i	−0.384389	−	0.102997i
$339$	13.6162			0.739529
$340$	−0.347086	−	1.55681i	−0.0188234	−	0.0844298i
$341$	3.82593	−	2.40131i	0.207186	−	0.130038i
$342$	5.31136	+	5.31136i	0.287206	+	0.287206i
$343$	7.71362	−	7.71362i	0.416496	−	0.416496i
$344$	−4.92290	−	8.52671i	−0.265425	−	0.459729i
$345$	−5.86659	+	9.23301i	−0.315847	+	0.497088i
$346$	0.00638115	−	0.0110525i	0.000343052	−	0.000594184i
$347$	1.84411	+	0.494128i	0.0989970	+	0.0265262i	0.307978	−	0.951394i	$-0.400348\pi$
$347$	1.84411	+	0.494128i	0.0989970	+	0.0265262i	−0.208980	+	0.977920i	$0.567015\pi$
$348$	2.38742	+	0.639706i	0.127979	+	0.0342918i
$349$		−	3.59668i		−	0.192526i	−0.995356	−	0.0962629i	$-0.969311\pi$
$349$		−	3.59668i		−	0.192526i	0.995356	−	0.0962629i	$-0.0306890\pi$
$350$	−0.346883	+	4.07696i	−0.0185417	+	0.217923i
$351$	−2.25367	+	3.90348i	−0.120292	+	0.208352i
$352$	−0.209978	−	0.783648i	−0.0111919	−	0.0417686i
$353$	8.11124	−	30.2716i	0.431718	−	1.61119i	−0.317084	−	0.948398i	$-0.602704\pi$
$353$	8.11124	−	30.2716i	0.431718	−	1.61119i	0.748801	−	0.662795i	$-0.230630\pi$
$354$	5.96947	−	10.3394i	0.317274	−	0.549534i
$355$	−0.937958	+	22.0877i	−0.0497816	+	1.17229i
$356$		−	4.90936i		−	0.260196i
$357$	0.412763	+	0.412763i	0.0218458	+	0.0218458i
$358$	−2.09065	+	7.80243i	−0.110495	+	0.412371i
$359$	−0.905566	−	0.522829i	−0.0477939	−	0.0275938i	0.475913	−	0.879493i	$-0.342118\pi$
$359$	−0.905566	−	0.522829i	−0.0477939	−	0.0275938i	−0.523707	+	0.851899i	$0.675451\pi$
$360$	1.64680	−	1.51263i	0.0867939	−	0.0797227i
$361$	18.7106	−	32.4076i	0.984766	−	1.70567i
$362$	−3.61070	−	13.4753i	−0.189774	−	0.708247i
$363$	9.98942	−	2.67666i	0.524308	−	0.140488i
$364$	−3.68853			−0.193332
$365$	−1.99912	+	1.83625i	−0.104639	+	0.0961139i
$366$	−6.89250	−	11.9382i	−0.360277	−	0.624018i
$367$	−8.36628	−	31.2234i	−0.436716	−	1.62985i	−0.736926	−	0.675974i	$-0.763723\pi$
$367$	−8.36628	−	31.2234i	−0.436716	−	1.62985i	0.300209	−	0.953873i	$-0.402943\pi$
$368$	3.45927	+	3.45927i	0.180327	+	0.180327i
$369$	−5.66327	+	3.26969i	−0.294818	+	0.170213i
$370$	20.0871	+	12.7632i	1.04428	+	0.663528i
$371$			7.63944i			0.396620i
$372$	3.78909	−	4.07956i	0.196455	−	0.211515i
$373$	23.2038	−	23.2038i	1.20145	−	1.20145i	0.227718	−	0.973727i	$-0.426873\pi$
$373$	23.2038	−	23.2038i	1.20145	−	1.20145i	0.973727	−	0.227718i	$-0.0731265\pi$
$374$			0.578710i			0.0299244i
$375$	−10.3445	−	4.24152i	−0.534190	−	0.219031i
$376$	−2.49062			−0.128444
$377$	10.7609	−	2.88338i	0.554215	−	0.148502i
$378$	−0.211801	+	0.790453i	−0.0108939	+	0.0406565i
$379$	−28.7330	+	16.5890i	−1.47592	+	0.852121i	−0.999631	−	0.0271696i	$-0.991351\pi$
$379$	−28.7330	+	16.5890i	−1.47592	+	0.852121i	−0.476286	+	0.879290i	$0.658017\pi$
$380$	−14.1764	−	9.00757i	−0.727232	−	0.462079i
$381$	7.93176	−	13.7382i	0.406357	−	0.703830i
$382$	8.42060	−	2.25629i	0.430836	−	0.115442i
$383$	−15.8470	+	4.24619i	−0.809743	+	0.216970i	−0.639857	−	0.768494i	$-0.721007\pi$
$383$	−15.8470	+	4.24619i	−0.809743	+	0.216970i	−0.169886	+	0.985464i	$0.554340\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	0.444722	−	1.41637i	0.0226652	−	0.0721850i
$386$	1.29117	+	2.23637i	0.0657189	+	0.113828i
$387$	−6.96203	+	6.96203i	−0.353900	+	0.353900i
$388$	9.66051	−	9.66051i	0.490438	−	0.490438i
$389$	−10.6861	−	18.5089i	−0.541808	−	0.938438i	−0.998800	−	0.0489679i	$-0.984407\pi$
$389$	−10.6861	−	18.5089i	−0.541808	−	0.938438i	0.456993	−	0.889470i	$-0.348927\pi$
$390$	3.01926	−	9.61587i	0.152886	−	0.486919i
$391$	−1.74483	−	3.02213i	−0.0882398	−	0.152836i
$392$	6.11462	−	1.63841i	0.308835	−	0.0827521i
$393$	−15.5323	+	4.16187i	−0.783502	+	0.209939i
$394$	−5.72231	+	9.91133i	−0.288286	+	0.499326i
$395$	3.15760	+	2.00632i	0.158876	+	0.100949i
$396$	−0.702599	+	0.405646i	−0.0353069	+	0.0203845i
$397$	−1.08651	+	4.05490i	−0.0545303	+	0.203510i	−0.987816	−	0.155624i	$-0.950261\pi$
$397$	−1.08651	+	4.05490i	−0.0545303	+	0.203510i	0.933286	+	0.359134i	$0.116928\pi$
$398$	15.3647	−	4.11695i	0.770162	−	0.206364i
$399$	6.14686			0.307728
$400$	−2.85810	+	4.10259i	−0.142905	+	0.205130i
$401$			10.2875i			0.513731i	0.966447	+	0.256865i	$0.0826897\pi$
$401$			10.2875i			0.513731i	−0.966447	+	0.256865i	$0.917310\pi$
$402$	8.94318	−	8.94318i	0.446045	−	0.446045i
$403$	5.59666	−	24.4638i	0.278789	−	1.21863i
$404$			8.04761i			0.400384i
$405$	−1.88731	−	1.19919i	−0.0937813	−	0.0595881i
$406$	1.75165	−	1.01132i	0.0869329	−	0.0501907i
$407$	−6.10570	−	6.10570i	−0.302648	−	0.302648i
$408$	0.184621	+	0.689013i	0.00914008	+	0.0341112i
$409$	6.43397	+	11.1440i	0.318139	+	0.551033i	0.980100	−	0.198505i	$-0.0636087\pi$
$409$	6.43397	+	11.1440i	0.318139	+	0.551033i	−0.661961	+	0.749539i	$0.730275\pi$
$410$	10.7690	−	9.89167i	0.531845	−	0.488515i
$411$	14.2098			0.700917
$412$	−0.161323	+	0.0432264i	−0.00794782	+	0.00212961i
$413$	−2.52868	−	9.43717i	−0.124428	−	0.464373i
$414$	2.44607	−	4.23672i	0.120218	−	0.208223i
$415$	26.6353	−	24.4653i	1.30747	−	1.20095i
$416$	−3.90348	−	2.25367i	−0.191384	−	0.110495i
$417$	−3.53809	+	13.2043i	−0.173261	+	0.646619i
$418$	4.30906	+	4.30906i	0.210763	+	0.210763i
$419$			5.40224i			0.263917i	0.991255	+	0.131958i	$0.0421265\pi$
$419$			5.40224i			0.263917i	−0.991255	+	0.131958i	$0.957873\pi$
$420$	0.0776353	−	1.82821i	0.00378822	−	0.0892075i
$421$	−6.76469	+	11.7168i	−0.329691	+	0.571042i	−0.982450	−	0.186524i	$-0.940278\pi$
$421$	−6.76469	+	11.7168i	−0.329691	+	0.571042i	0.652759	+	0.757565i	$0.273611\pi$
$422$	−2.53958	+	9.47783i	−0.123625	+	0.461373i
$423$	0.644621	+	2.40576i	0.0313425	+	0.116972i
$424$	−4.66766	+	8.08462i	−0.226682	+	0.392624i
$425$	2.72669	−	2.29908i	0.132264	−	0.111522i
$426$		−	9.88682i		−	0.479018i
$427$	−10.8964	−	2.91968i	−0.527314	−	0.141293i
$428$	−10.2786	−	2.75415i	−0.496835	−	0.133127i
$429$	−1.82839	+	3.16686i	−0.0882754	+	0.152897i
$430$	11.8069	−	18.5821i	0.569381	−	0.896108i
$431$	−2.66965	−	4.62397i	−0.128593	−	0.222729i	0.794539	−	0.607213i	$-0.207713\pi$
$431$	−2.66965	−	4.62397i	−0.128593	−	0.222729i	−0.923132	+	0.384484i	$0.874379\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−19.1933	−	19.1933i	−0.922372	−	0.922372i	0.0748248	−	0.997197i	$-0.476160\pi$
$433$	−19.1933	−	19.1933i	−0.922372	−	0.922372i	−0.997197	+	0.0748248i	$0.976160\pi$
$434$	−0.168076	−	4.55321i	−0.00806792	−	0.218561i
$435$	1.20265	+	5.39431i	0.0576624	+	0.258637i
$436$	−3.42421			−0.163990
$437$	−35.4947	−	9.51078i	−1.69794	−	0.454962i
$438$	0.858389	−	0.858389i	0.0410154	−	0.0410154i
$439$	−10.2564	−	5.92153i	−0.489511	−	0.282619i	0.234861	−	0.972029i	$-0.424537\pi$
$439$	−10.2564	−	5.92153i	−0.489511	−	0.282619i	−0.724372	+	0.689410i	$0.757870\pi$
$440$	1.33603	−	1.22719i	0.0636929	−	0.0585038i
$441$	−3.16516	−	5.48222i	−0.150722	−	0.261058i
$442$	2.27347	+	2.27347i	0.108138	+	0.108138i
$443$	6.16991	+	23.0264i	0.293141	+	1.09402i	0.942682	+	0.333692i	$0.108295\pi$
$443$	6.16991	+	23.0264i	0.293141	+	1.09402i	−0.649541	+	0.760327i	$0.725039\pi$
$444$	−9.21730	−	5.32161i	−0.437434	−	0.252553i
$445$	9.73125	−	5.08054i	0.461306	−	0.240841i
$446$	20.7177	−	11.9614i	0.981010	−	0.566387i
$447$	1.50887	+	5.63119i	0.0713672	+	0.266346i
$448$	−0.790453	−	0.211801i	−0.0373454	−	0.0100067i
$449$	−28.5681			−1.34821			−0.674107	−	0.738634i	$-0.735471\pi$
$449$	−28.5681			−1.34821			−0.674107	+	0.738634i	$0.735471\pi$
$450$	4.70253	+	1.69888i	0.221679	+	0.0800860i
$451$	−4.59456	+	2.65267i	−0.216349	+	0.124909i
$452$	13.1522	−	3.52412i	0.618628	−	0.165761i
$453$	−5.75579	−	1.54226i	−0.270431	−	0.0724617i
$454$	−23.3885	−	13.5033i	−1.09768	−	0.633743i
$455$	−3.81714	−	7.31135i	−0.178950	−	0.342761i
$456$	6.50506	+	3.75570i	0.304627	+	0.175877i
$457$	16.8559	−	16.8559i	0.788485	−	0.788485i	−0.192761	−	0.981246i	$-0.561744\pi$
$457$	16.8559	−	16.8559i	0.788485	−	0.788485i	0.981246	+	0.192761i	$0.0617442\pi$
$458$	1.18606	−	4.42644i	0.0554210	−	0.206834i
$459$	0.617752	−	0.356660i	0.0288342	−	0.0166474i
$460$	−3.27702	+	10.4368i	−0.152792	+	0.486618i
$461$		−	32.8701i		−	1.53092i	−0.643486	−	0.765458i	$-0.722513\pi$
$461$		−	32.8701i		−	1.53092i	0.643486	−	0.765458i	$-0.277487\pi$
$462$	−0.171833	+	0.641288i	−0.00799438	+	0.0298354i
$463$	−15.5745	−	15.5745i	−0.723810	−	0.723810i	0.245569	−	0.969379i	$-0.421025\pi$
$463$	−15.5745	−	15.5745i	−0.723810	−	0.723810i	−0.969379	+	0.245569i	$0.921025\pi$
$464$	2.47163			0.114743
$465$	12.0076	+	3.28888i	0.556841	+	0.152518i
$466$	8.09336			0.374918
$467$	16.6968	+	16.6968i	0.772637	+	0.772637i	0.978567	−	0.205930i	$-0.0660220\pi$
$467$	16.6968	+	16.6968i	0.772637	+	0.772637i	−0.205930	+	0.978567i	$0.566022\pi$
$468$	−1.16659	+	4.35376i	−0.0539255	+	0.201253i
$469$		−	10.3500i		−	0.477918i
$470$	−2.57747	−	4.93687i	−0.118890	−	0.227721i
$471$	5.04913	−	2.91512i	0.232652	−	0.134322i
$472$	3.09002	−	11.5321i	0.142230	−	0.530809i
$473$	−5.64824	+	5.64824i	−0.259706	+	0.259706i
$474$	−1.44892	−	0.836534i	−0.0665511	−	0.0384233i
$475$	3.18399	−	37.4218i	0.146091	−	1.71703i
$476$	0.505530	+	0.291868i	0.0231709	+	0.0133777i
$477$	9.01723	+	2.41616i	0.412870	+	0.110628i
$478$	−21.9173	+	5.87271i	−1.00247	+	0.268612i
$479$	29.7826	−	17.1950i	1.36080	−	0.785661i	0.371073	−	0.928604i	$-0.378990\pi$
$479$	29.7826	−	17.1950i	1.36080	−	0.785661i	0.989731	+	0.142943i	$0.0456566\pi$
$480$	1.19919	−	1.88731i	0.0547351	−	0.0861437i
$481$	−47.9727			−2.18737
$482$	18.7248	+	5.01730i	0.852893	+	0.228532i
$483$	−1.03616	−	3.86701i	−0.0471470	−	0.175955i
$484$	8.95627	−	5.17090i	0.407103	−	0.235041i
$485$	29.1462	+	9.15154i	1.32346	+	0.415550i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	4.43026	+	16.5340i	0.200754	+	0.749226i	0.990702	+	0.136051i	$0.0434411\pi$
$487$	4.43026	+	16.5340i	0.200754	+	0.749226i	−0.789947	+	0.613175i	$0.789892\pi$
$488$	−9.74747	−	9.74747i	−0.441247	−	0.441247i
$489$	−4.90339	−	8.49291i	−0.221739	−	0.384063i
$490$	9.57545	+	10.4248i	0.432575	+	0.470943i
$491$	11.0041	+	6.35321i	0.496607	+	0.286716i	0.727311	−	0.686308i	$-0.240770\pi$
$491$	11.0041	+	6.35321i	0.496607	+	0.286716i	−0.230704	+	0.973024i	$0.574103\pi$
$492$	−4.62404	+	4.62404i	−0.208468	+	0.208468i
$493$	−1.70299	−	0.456315i	−0.0766988	−	0.0205514i
$494$	33.8565			1.52328
$495$	−1.53116	−	0.972891i	−0.0688206	−	0.0437282i
$496$	2.60412	−	4.92124i	0.116928	−	0.220970i
$497$	−5.72102	−	5.72102i	−0.256623	−	0.256623i
$498$	−11.4367	+	11.4367i	−0.512492	+	0.512492i
$499$	−2.43076	−	4.21020i	−0.108816	−	0.188475i	0.806475	−	0.591268i	$-0.201373\pi$
$499$	−2.43076	−	4.21020i	−0.108816	−	0.188475i	−0.915291	+	0.402794i	$0.868039\pi$
$500$	−11.0898	−	1.41963i	−0.495953	−	0.0634877i
$501$	0.109369	−	0.189433i	0.00488624	−	0.00846322i
$502$	−11.5007	−	3.08161i	−0.513303	−	0.137539i
$503$	35.8974	+	9.61867i	1.60059	+	0.428875i	0.945219	−	0.326436i	$-0.105848\pi$
$503$	35.8974	+	9.61867i	1.60059	+	0.428875i	0.655366	+	0.755312i	$0.272514\pi$
$504$			0.818337i			0.0364516i
$505$	−15.9518	+	8.32821i	−0.709847	+	0.370601i
$506$	1.98448	−	3.43722i	0.0882208	−	0.152803i
$507$	1.89357	+	7.06690i	0.0840964	+	0.313852i
$508$	4.10578	−	15.3230i	0.182165	−	0.679848i
$509$	4.44111	−	7.69223i	0.196849	−	0.340952i	−0.750656	−	0.660693i	$-0.770263\pi$
$509$	4.44111	−	7.69223i	0.196849	−	0.340952i	0.947505	+	0.319741i	$0.103596\pi$
$510$	−1.17469	+	1.07899i	−0.0520163	+	0.0477785i
$511$		−	0.993418i		−	0.0439462i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.94409	−	7.25545i	0.0858338	−	0.320336i
$514$	16.3766	+	9.45505i	0.722342	+	0.417044i
$515$	−0.252631	−	0.275038i	−0.0111322	−	0.0121196i
$516$	−4.92290	+	8.52671i	−0.216718	+	0.375367i
$517$	0.522976	+	1.95177i	0.0230004	+	0.0858388i
$518$	−8.41297	+	2.25425i	−0.369645	+	0.0990460i
$519$	−0.0127623			−0.000560202
$520$	0.427610	−	10.0697i	0.0187519	−	0.441584i
$521$	−0.216911	−	0.375700i	−0.00950303	−	0.0164597i	0.861235	−	0.508207i	$-0.169692\pi$
$521$	−0.216911	−	0.375700i	−0.00950303	−	0.0164597i	−0.870738	+	0.491748i	$0.836358\pi$
$522$	−0.639706	−	2.38742i	−0.0279992	−	0.104494i
$523$	−0.933792	−	0.933792i	−0.0408319	−	0.0408319i	0.686396	−	0.727228i	$-0.259192\pi$
$523$	−0.933792	−	0.933792i	−0.0408319	−	0.0408319i	−0.727228	+	0.686396i	$0.759192\pi$
$524$	−13.9259	+	8.04012i	−0.608356	+	0.351234i
$525$	3.70419	−	1.73807i	0.161664	−	0.0758555i
$526$		−	14.3396i		−	0.625238i
$527$	−2.70283	+	2.91002i	−0.117737	+	0.126763i
$528$	−0.573670	+	0.573670i	−0.0249658	+	0.0249658i
$529$			0.933058i			0.0405677i
$530$	−20.8556	−	0.885638i	−0.905910	−	0.0384696i
$531$	−11.9389			−0.518106
$532$	5.93741	−	1.59092i	0.257419	−	0.0689753i
$533$	−7.62876	+	28.4709i	−0.330438	+	1.23321i
$534$	−4.25163	+	2.45468i	−0.183986	+	0.106224i
$535$	−5.17778	−	23.2243i	−0.223855	−	1.00407i
$536$	6.32378	−	10.9531i	0.273146	−	0.473103i
$537$	7.80243	−	2.09065i	0.336700	−	0.0902184i
$538$	−16.7960	+	4.50049i	−0.724129	+	0.194030i
$539$	−2.56787	−	4.44768i	−0.110606	−	0.191575i
$540$	−2.13338	−	0.669853i	−0.0918059	−	0.0288259i
$541$	−18.6718	−	32.3406i	−0.802765	−	1.39043i	−0.917790	−	0.397067i	$-0.870028\pi$
$541$	−18.6718	−	32.3406i	−0.802765	−	1.39043i	0.115025	−	0.993363i	$-0.463305\pi$
$542$	−0.103908	+	0.103908i	−0.00446322	+	0.00446322i
$543$	−9.86461	+	9.86461i	−0.423331	+	0.423331i
$544$	0.356660	+	0.617752i	0.0152917	+	0.0264859i
$545$	−3.54360	−	6.78740i	−0.151791	−	0.290740i
$546$	1.84427	+	3.19436i	0.0789273	+	0.136706i
$547$	−1.57306	+	0.421501i	−0.0672593	+	0.0180221i	−0.292292	−	0.956329i	$-0.594418\pi$
$547$	−1.57306	+	0.421501i	−0.0672593	+	0.0180221i	0.225032	+	0.974351i	$0.427751\pi$
$548$	13.7256	−	3.67776i	0.586329	−	0.157106i
$549$	−6.89250	+	11.9382i	−0.294165	+	0.509508i
$550$	3.81513	+	1.37829i	0.162678	+	0.0587704i
$551$	−16.0781	+	9.28272i	−0.684952	+	0.395457i
$552$	1.26618	−	4.72545i	0.0538922	−	0.201128i
$553$	−1.32248	+	0.354358i	−0.0562377	+	0.0150688i
$554$	−19.0895			−0.811034
$555$	1.00972	−	23.7775i	0.0428602	−	1.00930i
$556$			13.6701i			0.579743i
$557$	10.2330	−	10.2330i	0.433586	−	0.433586i	−0.456260	−	0.889846i	$-0.650811\pi$
$557$	10.2330	−	10.2330i	0.433586	−	0.433586i	0.889846	+	0.456260i	$0.150811\pi$
$558$	−5.42755	−	1.24167i	−0.229766	−	0.0525642i
$559$			44.3784i			1.87701i
$560$	−0.398186	−	1.78601i	−0.0168264	−	0.0754727i
$561$	0.501178	−	0.289355i	0.0211597	−	0.0122166i
$562$	11.6661	+	11.6661i	0.492104	+	0.492104i
$563$	4.69523	+	17.5228i	0.197880	+	0.738499i	0.991502	+	0.130088i	$0.0415261\pi$
$563$	4.69523	+	17.5228i	0.197880	+	0.738499i	−0.793622	+	0.608411i	$0.791807\pi$
$564$	1.24531	+	2.15694i	0.0524371	+	0.0908237i
$565$	20.5963	+	22.4231i	0.866491	+	0.943346i
$566$	20.2559			0.851420
$567$	0.790453	−	0.211801i	0.0331959	−	0.00889482i
$568$	−2.55890	−	9.54993i	−0.107369	−	0.400706i
$569$	−20.0098	+	34.6581i	−0.838856	+	1.45294i	0.0519955	+	0.998647i	$0.483442\pi$
$569$	−20.0098	+	34.6581i	−0.838856	+	1.45294i	−0.890852	+	0.454294i	$0.849891\pi$
$570$	−0.712603	+	16.7809i	−0.0298477	+	0.702874i
$571$	−9.37488	−	5.41259i	−0.392326	−	0.226510i	0.290841	−	0.956771i	$-0.406065\pi$
$571$	−9.37488	−	5.41259i	−0.392326	−	0.226510i	−0.683168	+	0.730262i	$0.739398\pi$
$572$	−0.946443	+	3.53217i	−0.0395728	+	0.147688i
$573$	−6.16431	−	6.16431i	−0.257518	−	0.257518i
$574$			5.35142i			0.223364i
$575$	−24.0789	+	4.30505i	−1.00416	+	0.179533i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−4.10891	+	15.3346i	−0.171056	+	0.638390i	0.826134	+	0.563474i	$0.190535\pi$
$577$	−4.10891	+	15.3346i	−0.171056	+	0.638390i	−0.997190	+	0.0749157i	$0.976131\pi$
$578$	4.26823	+	15.9293i	0.177535	+	0.662570i
$579$	1.29117	−	2.23637i	0.0536593	−	0.0929406i
$580$	2.55781	+	4.89923i	0.106207	+	0.203430i
$581$			13.2358i			0.549113i
$582$	−13.1965	−	3.53599i	−0.547012	−	0.146572i
$583$	7.31560	+	1.96021i	0.302981	+	0.0811836i
$584$	0.606973	−	1.05131i	0.0251167	−	0.0435034i
$585$	−9.83722	+	2.19318i	−0.406719	+	0.0906769i
$586$	−6.32542	−	10.9560i	−0.261301	−	0.452586i
$587$	11.2659	−	11.2659i	0.464992	−	0.464992i	−0.435296	−	0.900288i	$-0.643356\pi$
$587$	11.2659	−	11.2659i	0.464992	−	0.464992i	0.900288	+	0.435296i	$0.143356\pi$
$588$	−4.47621	−	4.47621i	−0.184596	−	0.184596i
$589$	1.54275	+	41.7932i	0.0635678	+	1.72206i
$590$	26.0566	−	5.80924i	1.07273	−	0.239162i
$591$	11.4446			0.470769
$592$	−10.2806	−	2.75467i	−0.422529	−	0.113216i
$593$	10.7371	−	10.7371i	0.440921	−	0.440921i	−0.451400	−	0.892322i	$-0.649075\pi$
$593$	10.7371	−	10.7371i	0.440921	−	0.440921i	0.892322	+	0.451400i	$0.149075\pi$
$594$	0.702599	+	0.405646i	0.0288280	+	0.0166439i
$595$	−0.0553788	+	1.30410i	−0.00227031	+	0.0534628i
$596$	2.91492	+	5.04879i	0.119400	+	0.206806i
$597$	−11.2477	−	11.2477i	−0.460339	−	0.460339i
$598$	−5.70711	−	21.2992i	−0.233381	−	0.870991i
$599$	18.1424	+	10.4745i	0.741280	+	0.427978i	0.822534	−	0.568715i	$-0.192559\pi$
$599$	18.1424	+	10.4745i	0.741280	+	0.427978i	−0.0812547	+	0.996693i	$0.525893\pi$
$600$	4.98200	+	0.423888i	0.203389	+	0.0173051i
$601$	2.47052	−	1.42636i	0.100775	−	0.0581823i	−0.448766	−	0.893649i	$-0.648136\pi$
$601$	2.47052	−	1.42636i	0.100775	−	0.0581823i	0.549540	+	0.835467i	$0.314803\pi$
$602$	2.08535	+	7.78264i	0.0849926	+	0.317197i
$603$	−12.2166	−	3.27343i	−0.497499	−	0.133304i
$604$	−5.95883			−0.242461
$605$	19.5182	+	12.4018i	0.793529	+	0.504203i
$606$	6.96943	−	4.02380i	0.283114	−	0.163456i
$607$	14.8928	−	3.99050i	0.604478	−	0.161969i	0.0564166	−	0.998407i	$-0.482033\pi$
$607$	14.8928	−	3.99050i	0.604478	−	0.161969i	0.548062	+	0.836438i	$0.315366\pi$
$608$	7.25545	+	1.94409i	0.294248	+	0.0788434i
$609$	−1.75165	−	1.01132i	−0.0709804	−	0.0409806i
$610$	9.23392	−	29.4086i	0.373871	−	1.19072i
$611$	9.72209	+	5.61305i	0.393314	+	0.227080i
$612$	0.504393	−	0.504393i	0.0203889	−	0.0203889i
$613$	−2.65751	+	9.91797i	−0.107336	+	0.400583i	−0.998600	−	0.0529021i	$-0.983153\pi$
$613$	−2.65751	+	9.91797i	−0.107336	+	0.400583i	0.891264	+	0.453485i	$0.149820\pi$
$614$	6.79447	−	3.92279i	0.274202	−	0.158311i
$615$	−13.9510	−	4.38042i	−0.562557	−	0.176636i
$616$			0.663911i			0.0267497i
$617$	8.84298	−	33.0024i	0.356005	−	1.32863i	−0.523210	−	0.852204i	$-0.675266\pi$
$617$	8.84298	−	33.0024i	0.356005	−	1.32863i	0.879215	−	0.476425i	$-0.158068\pi$
$618$	0.118097	+	0.118097i	0.00475055	+	0.00475055i
$619$	19.5034			0.783908			0.391954	−	0.919985i	$-0.371799\pi$
$619$	19.5034			0.783908			0.391954	+	0.919985i	$0.371799\pi$
$620$	12.4497	+	0.0690052i	0.499992	+	0.00277131i
$621$	−4.89214			−0.196315
$622$	−8.51391	−	8.51391i	−0.341377	−	0.341377i
$623$	−1.03981	+	3.88062i	−0.0416591	+	0.155474i
$624$			4.50735i			0.180438i
$625$	−8.66256	−	23.4512i	−0.346502	−	0.938049i
$626$	−4.17664	+	2.41138i	−0.166932	+	0.0963782i
$627$	1.57723	−	5.88629i	0.0629884	−	0.235076i
$628$	4.12260	−	4.12260i	0.164510	−	0.164510i
$629$	6.57488	+	3.79601i	0.262158	+	0.151357i
$630$	−1.62209	+	0.846871i	−0.0646258	+	0.0337402i
$631$	−22.5592	−	13.0246i	−0.898068	−	0.518500i	−0.0214953	−	0.999769i	$-0.506843\pi$
$631$	−22.5592	−	13.0246i	−0.898068	−	0.518500i	−0.876573	+	0.481269i	$0.840176\pi$
$632$	−1.61606	−	0.433022i	−0.0642834	−	0.0172247i
$633$	9.47783	−	2.53958i	0.376710	−	0.100939i
$634$	19.7757	−	11.4175i	0.785393	−	0.453447i
$635$	34.6219	−	7.71886i	1.37393	−	0.306313i
$636$	9.33532			0.370170
$637$	−27.5607	−	7.38488i	−1.09200	−	0.292600i
$638$	−0.518988	−	1.93689i	−0.0205469	−	0.0766822i
$639$	−8.56223	+	4.94341i	−0.338717	+	0.195558i
$640$	0.669853	−	2.13338i	0.0264783	−	0.0843291i
$641$	29.3403	+	16.9396i	1.15887	+	0.669074i	0.951033	−	0.309089i	$-0.100024\pi$
$641$	29.3403	+	16.9396i	1.15887	+	0.669074i	0.207838	+	0.978163i	$0.433357\pi$
$642$	2.75415	+	10.2786i	0.108697	+	0.405664i
$643$	19.0216	+	19.0216i	0.750139	+	0.750139i	0.974505	−	0.224366i	$-0.0720312\pi$
$643$	19.0216	+	19.0216i	0.750139	+	0.750139i	−0.224366	+	0.974505i	$0.572031\pi$
$644$	−2.00171	−	3.46707i	−0.0788785	−	0.136622i
$645$	−21.9960	−	0.934066i	−0.866093	−	0.0367788i
$646$	−4.64019	−	2.67901i	−0.182566	−	0.105404i
$647$	−2.26428	+	2.26428i	−0.0890180	+	0.0890180i	−0.750214	−	0.661196i	$-0.770049\pi$
$647$	−2.26428	+	2.26428i	−0.0890180	+	0.0890180i	0.661196	+	0.750214i	$0.270049\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−9.68597			−0.380207
$650$	20.4024	−	9.57317i	0.800249	−	0.375491i
$651$	−3.85916	+	2.42216i	−0.151252	+	0.0949320i
$652$	−6.93443	−	6.93443i	−0.271573	−	0.271573i
$653$	−33.5912	+	33.5912i	−1.31452	+	1.31452i	−0.396481	+	0.918043i	$0.629769\pi$
$653$	−33.5912	+	33.5912i	−1.31452	+	1.31452i	−0.918043	+	0.396481i	$0.870231\pi$
$654$	1.71210	+	2.96545i	0.0669485	+	0.115958i
$655$	−30.3485	−	19.2832i	−1.18581	−	0.753458i
$656$	−3.26969	+	5.66327i	−0.127660	+	0.221113i
$657$	−1.17258	−	0.314192i	−0.0457468	−	0.0122578i
$658$	1.96872	+	0.527517i	0.0767487	+	0.0205648i
$659$		−	15.3921i		−	0.599590i	−0.954004	−	0.299795i	$-0.903082\pi$
$659$		−	15.3921i		−	0.599590i	0.954004	−	0.299795i	$-0.0969182\pi$
$660$	−1.73079	−	0.543446i	−0.0673710	−	0.0211536i
$661$	10.4255	−	18.0574i	0.405504	−	0.702353i	−0.588876	−	0.808223i	$-0.700430\pi$
$661$	10.4255	−	18.0574i	0.405504	−	0.702353i	0.994380	+	0.105870i	$0.0337628\pi$
$662$	6.19178	+	23.1080i	0.240650	+	0.898119i
$663$	0.832149	−	3.10562i	0.0323180	−	0.120612i
$664$	−8.08699	+	14.0071i	−0.313836	+	0.543580i
$665$	9.29794	+	10.1226i	0.360559	+	0.392539i
$666$			10.6432i			0.412417i
$667$	8.55004	+	8.55004i	0.331059	+	0.331059i
$668$	0.0566135	−	0.211285i	0.00219044	−	0.00817484i
$669$	−20.7177	−	11.9614i	−0.800992	−	0.462453i
$670$	28.2554	+	1.19987i	1.09160	+	0.0463550i
$671$	−5.59183	+	9.68534i	−0.215870	+	0.373898i
$672$	0.211801	+	0.790453i	0.00817041	+	0.0304924i
$673$	43.7259	−	11.7163i	1.68551	−	0.451631i	0.716285	−	0.697808i	$-0.245841\pi$
$673$	43.7259	−	11.7163i	1.68551	−	0.451631i	0.969225	+	0.246177i	$0.0791746\pi$
$674$	−24.0292			−0.925572
$675$	−0.879992	−	4.92195i	−0.0338709	−	0.189446i
$676$	3.65810	+	6.33601i	0.140696	+	0.243693i
$677$	4.43834	+	16.5641i	0.170579	+	0.636611i	0.997262	+	0.0739431i	$0.0235583\pi$
$677$	4.43834	+	16.5641i	0.170579	+	0.636611i	−0.826683	+	0.562668i	$0.809775\pi$
$678$	−9.62809	−	9.62809i	−0.369764	−	0.369764i
$679$	−9.68229	+	5.59007i	−0.371572	+	0.214527i
$680$	−0.855403	+	1.34626i	−0.0328032	+	0.0516266i
$681$			27.0067i			1.03490i
$682$	−4.40332	−	1.00736i	−0.168612	−	0.0385738i
$683$	29.2899	−	29.2899i	1.12075	−	1.12075i	0.129120	−	0.991629i	$-0.458785\pi$
$683$	29.2899	−	29.2899i	1.12075	−	1.12075i	0.991629	−	0.129120i	$-0.0412151\pi$
$684$		−	7.51140i		−	0.287206i
$685$	21.4942	+	23.4007i	0.821250	+	0.894093i
$686$	−10.9087			−0.416496
$687$	−4.42644	+	1.18606i	−0.168879	+	0.0452511i
$688$	−2.54828	+	9.51031i	−0.0971522	+	0.362577i
$689$	36.4402	−	21.0388i	1.38826	−	0.801513i
$690$	10.6770	−	2.38041i	0.406467	−	0.0906208i
$691$	20.6607	−	35.7855i	0.785972	−	1.36134i	−0.142445	−	0.989803i	$-0.545496\pi$
$691$	20.6607	−	35.7855i	0.785972	−	1.36134i	0.928417	−	0.371541i	$-0.121170\pi$
$692$	−0.0123274	+	0.00330312i	−0.000468618	+	0.000125566i
$693$	0.641288	−	0.171833i	0.0243605	−	0.00652738i
$694$	−0.954582	−	1.65338i	−0.0362354	−	0.0627616i
$695$	−27.0967	+	14.1468i	−1.02784	+	0.536618i
$696$	−1.23582	−	2.14050i	−0.0468435	−	0.0811354i
$697$	3.29841	−	3.29841i	0.124936	−	0.124936i
$698$	−2.54324	+	2.54324i	−0.0962629	+	0.0962629i
$699$	−4.04668	−	7.00906i	−0.153060	−	0.265107i
$700$	3.12813	−	2.63756i	0.118232	−	0.0996904i
$701$	6.57126	+	11.3818i	0.248193	+	0.429883i	0.963025	−	0.269414i	$-0.0868299\pi$
$701$	6.57126	+	11.3818i	0.248193	+	0.429883i	−0.714831	+	0.699297i	$0.753497\pi$
$702$	4.35376	−	1.16659i	0.164322	−	0.0440300i
$703$	77.2215	−	20.6914i	2.91246	−	0.780392i
$704$	−0.405646	+	0.702599i	−0.0152884	+	0.0264802i
$705$	−2.98672	+	4.70059i	−0.112486	+	0.177034i
$706$	−27.1407	+	15.6697i	−1.02145	+	0.589737i
$707$	1.70449	−	6.36126i	0.0641041	−	0.239240i
$708$	−11.5321	+	3.09002i	−0.433404	+	0.116130i
$709$	−18.4406			−0.692550			−0.346275	−	0.938133i	$-0.612554\pi$
$709$	−18.4406			−0.692550			−0.346275	+	0.938133i	$0.612554\pi$
$710$	16.2816	−	14.9551i	0.611037	−	0.561255i
$711$			1.67307i			0.0627450i
$712$	−3.47144	+	3.47144i	−0.130098	+	0.130098i
$713$	26.0322	−	8.01554i	0.974914	−	0.300184i
$714$		−	0.583736i		−	0.0218458i
$715$	−7.98086	+	1.77931i	−0.298467	+	0.0665424i
$716$	6.99547	−	4.03883i	0.261433	−	0.150938i
$717$	16.0446	+	16.0446i	0.599195	+	0.599195i
$718$	0.270636	+	1.01003i	0.0101000	+	0.0376939i
$719$	−9.34054	−	16.1783i	−0.348343	−	0.603348i	0.637612	−	0.770358i	$-0.279922\pi$
$719$	−9.34054	−	16.1783i	−0.348343	−	0.603348i	−0.985955	+	0.167009i	$0.946589\pi$
$720$	−2.23405	−	0.0948696i	−0.0832583	−	0.00353558i
$721$	0.136674			0.00509000
$722$	−36.1460	+	9.68530i	−1.34522	+	0.360449i
$723$	−5.01730	−	18.7248i	−0.186596	−	0.696384i
$724$	−6.97533	+	12.0816i	−0.259236	+	0.449010i
$725$	−7.06417	+	10.1401i	−0.262357	+	0.376594i
$726$	−8.95627	−	5.17090i	−0.332398	−	0.191910i
$727$	−8.38362	+	31.2881i	−0.310931	+	1.16041i	0.616787	+	0.787130i	$0.288434\pi$
$727$	−8.38362	+	31.2881i	−0.310931	+	1.16041i	−0.927718	+	0.373281i	$0.878233\pi$
$728$	2.60819	+	2.60819i	0.0966658	+	0.0966658i
$729$		−	1.00000i		−	0.0370370i
$730$	2.71202	+	0.115167i	0.100376	+	0.00426250i
$731$	3.51160	−	6.08226i	0.129881	−	0.224961i
$732$	−3.56782	+	13.3153i	−0.131870	+	0.492147i
$733$	3.83438	+	14.3101i	0.141626	+	0.528555i	0.999882	+	0.0153343i	$0.00488126\pi$
$733$	3.83438	+	14.3101i	0.141626	+	0.528555i	−0.858256	+	0.513221i	$0.828452\pi$
$734$	−16.1624	+	27.9941i	−0.596565	+	1.03328i
$735$	4.24039	−	13.5050i	0.156409	−	0.498138i
$736$		−	4.89214i		−	0.180327i
$737$	−9.91124	−	2.65571i	−0.365085	−	0.0978243i
$738$	6.31655	+	1.69252i	0.232515	+	0.0623023i
$739$	−21.2773	+	36.8534i	−0.782699	+	1.35568i	0.147665	+	0.989038i	$0.452824\pi$
$739$	−21.2773	+	36.8534i	−0.782699	+	1.35568i	−0.930364	+	0.366638i	$0.880509\pi$
$740$	−5.17877	−	23.2287i	−0.190375	−	0.853903i
$741$	−16.9282	−	29.3206i	−0.621875	−	1.07712i
$742$	5.40190	−	5.40190i	0.198310	−	0.198310i
$743$	−6.05986	−	6.05986i	−0.222315	−	0.222315i	0.587158	−	0.809473i	$-0.300247\pi$
$743$	−6.05986	−	6.05986i	−0.222315	−	0.222315i	−0.809473	+	0.587158i	$0.800247\pi$
$744$	−5.56397	+	0.205387i	−0.203985	+	0.00752987i
$745$	−6.99106	+	11.0027i	−0.256133	+	0.403109i
$746$	−32.8151			−1.20145
$747$	15.6229	+	4.18614i	0.571611	+	0.153163i
$748$	0.409210	−	0.409210i	0.0149622	−	0.0149622i
$749$	7.54143	+	4.35405i	0.275558	+	0.159093i
$750$	4.31549	+	10.3139i	0.157579	+	0.376610i
$751$	16.9980	+	29.4414i	0.620265	+	1.07433i	0.989436	+	0.144969i	$0.0463083\pi$
$751$	16.9980	+	29.4414i	0.620265	+	1.07433i	−0.369171	+	0.929361i	$0.620358\pi$
$752$	1.76114	+	1.76114i	0.0642220	+	0.0642220i
$753$	3.08161	+	11.5007i	0.112300	+	0.419110i
$754$	−9.64797	−	5.57026i	−0.351358	−	0.202857i
$755$	−6.16660	−	11.8115i	−0.224426	−	0.429864i
$756$	0.708701	−	0.409169i	0.0257752	−	0.0148813i
$757$	1.40674	+	5.25004i	0.0511290	+	0.190816i	0.986767	−	0.162145i	$-0.0518414\pi$
$757$	1.40674	+	5.25004i	0.0511290	+	0.190816i	−0.935638	+	0.352961i	$0.885175\pi$
$758$	32.0475	+	8.58711i	1.16402	+	0.311898i
$759$	−3.96896			−0.144064
$760$	3.65489	+	16.3935i	0.132577	+	0.594655i
$761$	−1.34596	+	0.777089i	−0.0487909	+	0.0281694i	−0.524197	−	0.851597i	$-0.675634\pi$
$761$	−1.34596	+	0.777089i	−0.0487909	+	0.0281694i	0.475406	+	0.879766i	$0.342301\pi$
$762$	−15.3230	+	4.10578i	−0.555093	+	0.148737i
$763$	2.70668	+	0.725252i	0.0979882	+	0.0262559i
$764$	−7.54971	−	4.35883i	−0.273139	−	0.157697i
$765$	1.52178	+	0.477819i	0.0550200	+	0.0172756i
$766$	14.2080	+	8.20301i	0.513357	+	0.296387i
$767$	−38.0515	+	38.0515i	−1.37396	+	1.37396i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	7.21474	−	4.16543i	0.260170	−	0.150209i	−0.364242	−	0.931304i	$-0.618672\pi$
$769$	7.21474	−	4.16543i	0.260170	−	0.150209i	0.624412	+	0.781095i	$0.285339\pi$
$770$	−1.31599	+	0.687060i	−0.0474251	+	0.0247599i
$771$		−	18.9101i		−	0.681031i
$772$	0.668360	−	2.49435i	0.0240548	−	0.0897737i
$773$	−19.3834	−	19.3834i	−0.697172	−	0.697172i	0.266628	−	0.963800i	$-0.414091\pi$
$773$	−19.3834	−	19.3834i	−0.697172	−	0.697172i	−0.963800	+	0.266628i	$0.914091\pi$
$774$	9.84579			0.353900
$775$	12.7470	+	24.7490i	0.457887	+	0.889011i
$776$	−13.6620			−0.490438
$777$	6.15872	+	6.15872i	0.220943	+	0.220943i
$778$	−5.53154	+	20.6440i	−0.198315	+	0.740123i
$779$		−	49.1199i		−	1.75990i
$780$	−8.93439	+	4.66451i	−0.319902	+	0.167016i
$781$	−6.94647	+	4.01055i	−0.248564	+	0.143509i
$782$	−0.903190	+	3.37075i	−0.0322980	+	0.120538i
$783$	−1.74771	+	1.74771i	−0.0624580	+	0.0624580i
$784$	−5.48222	−	3.16516i	−0.195794	−	0.113041i
$785$	12.4381	+	3.90540i	0.443934	+	0.139390i
$786$	13.9259	+	8.04012i	0.496721	+	0.286782i
$787$	21.6885	+	5.81143i	0.773113	+	0.207155i	0.623746	−	0.781627i	$-0.285610\pi$
$787$	21.6885	+	5.81143i	0.773113	+	0.207155i	0.149367	+	0.988782i	$0.452276\pi$
$788$	11.0547	−	2.96209i	0.393806	−	0.105520i
$789$	−12.4185	+	7.16981i	−0.442110	+	0.255252i
$790$	−0.814080	−	3.65145i	−0.0289637	−	0.129913i
$791$	−11.1426			−0.396186
$792$	0.783648	+	0.209978i	0.0278457	+	0.00746124i
$793$	16.0814	+	60.0167i	0.571068	+	2.13125i
$794$	3.63553	−	2.09897i	0.129020	−	0.0744897i
$795$	9.66082	+	18.5043i	0.342634	+	0.656280i
$796$	−13.7756	−	7.95335i	−0.488263	−	0.281899i
$797$	2.95424	+	11.0254i	0.104645	+	0.390539i	0.998305	−	0.0582059i	$-0.0185380\pi$
$797$	2.95424	+	11.0254i	0.104645	+	0.390539i	−0.893660	+	0.448745i	$0.851871\pi$
$798$	−4.34649	−	4.34649i	−0.153864	−	0.153864i
$799$	−0.888305	−	1.53859i	−0.0314260	−	0.0544314i
$800$	4.92195	−	0.879992i	0.174017	−	0.0311124i
$801$	4.25163	+	2.45468i	0.150224	+	0.0867319i
$802$	7.27433	−	7.27433i	0.256865	−	0.256865i
$803$	−0.951306	−	0.254902i	−0.0335709	−	0.00899529i
$804$	−12.6476			−0.446045
$805$	4.80085	−	7.55571i	0.169208	−	0.266304i
$806$	−21.2560	+	13.3411i	−0.748710	+	0.469921i
$807$	12.2956	+	12.2956i	0.432824	+	0.432824i
$808$	5.69052	−	5.69052i	0.200192	−	0.200192i
$809$	10.2795	+	17.8047i	0.361409	+	0.625979i	0.988193	−	0.153214i	$-0.0489624\pi$
$809$	10.2795	+	17.8047i	0.361409	+	0.625979i	−0.626784	+	0.779193i	$0.715629\pi$
$810$	0.486579	+	2.18249i	0.0170966	+	0.0766847i
$811$	−16.5459	+	28.6583i	−0.581005	+	1.00633i	0.414356	+	0.910115i	$0.364007\pi$
$811$	−16.5459	+	28.6583i	−0.581005	+	1.00633i	−0.995361	+	0.0962145i	$0.969327\pi$
$812$	−1.95371	−	0.523495i	−0.0685618	−	0.0183711i
$813$	0.141941	+	0.0380329i	0.00497808	+	0.00133387i
$814$			8.63476i			0.302648i
$815$	6.56909	−	20.9215i	0.230105	−	0.732850i
$816$	0.356660	−	0.617752i	0.0124856	−	0.0216257i
$817$	−19.1411	−	71.4357i	−0.669664	−	2.49922i
$818$	3.33047	−	12.4295i	0.116447	−	0.434586i
$819$	1.84427	−	3.19436i	0.0644439	−	0.111620i
$820$	−14.6093	−	0.620388i	−0.510180	−	0.0216649i
$821$			42.8654i			1.49601i	0.663691	+	0.748007i	$0.268989\pi$
$821$			42.8654i			1.49601i	−0.663691	+	0.748007i	$0.731011\pi$
$822$	−10.0478	−	10.0478i	−0.350459	−	0.350459i
$823$	9.06377	−	33.8265i	0.315943	−	1.17912i	−0.607165	−	0.794576i	$-0.707693\pi$
$823$	9.06377	−	33.8265i	0.315943	−	1.17912i	0.923108	−	0.384541i	$-0.125640\pi$
$824$	0.144638	+	0.0835070i	0.00503872	+	0.00290910i
$825$	−0.713931	−	3.99314i	−0.0248559	−	0.139023i
$826$	−4.88504	+	8.46114i	−0.169972	+	0.294401i
$827$	6.37553	+	23.7938i	0.221699	+	0.827392i	0.983700	+	0.179816i	$0.0575504\pi$
$827$	6.37553	+	23.7938i	0.221699	+	0.827392i	−0.762001	+	0.647576i	$0.775783\pi$
$828$	−4.72545	+	1.26618i	−0.164221	+	0.0440028i
$829$	37.7487			1.31107			0.655533	−	0.755167i	$-0.272444\pi$
$829$	37.7487			1.31107			0.655533	+	0.755167i	$0.272444\pi$
$830$	−36.1336	−	1.53442i	−1.25421	−	0.0532605i
$831$	9.54474	+	16.5320i	0.331103	+	0.573488i
$832$	1.16659	+	4.35376i	0.0404442	+	0.150940i
$833$	3.19297	+	3.19297i	0.110630	+	0.110630i
$834$	11.8387	−	6.83507i	0.409940	−	0.236679i
$835$	0.477392	−	0.106433i	0.0165208	−	0.00368327i
$836$		−	6.09394i		−	0.210763i
$837$	1.63845	+	5.32123i	0.0566332	+	0.183929i
$838$	3.81996	−	3.81996i	0.131958	−	0.131958i
$839$			10.3460i			0.357183i	0.983923	+	0.178591i	$0.0571540\pi$
$839$			10.3460i			0.357183i	−0.983923	+	0.178591i	$0.942846\pi$
$840$	−1.34764	+	1.23784i	−0.0464979	+	0.0427097i
$841$	−22.8910			−0.789346
$842$	13.0684	−	3.50166i	0.450366	−	0.120675i
$843$	4.27008	−	15.9362i	0.147069	−	0.548871i
$844$	8.49759	−	4.90609i	0.292499	−	0.168874i
$845$	−8.77348	+	13.8079i	−0.301817	+	0.475008i
$846$	1.24531	−	2.15694i	0.0428147	−	0.0741572i
$847$	−8.17471	+	2.19041i	−0.280886	+	0.0752633i
$848$	9.01723	−	2.41616i	0.309653	−	0.0829712i
$849$	−10.1280	−	17.5422i	−0.347591	−	0.602045i
$850$	−3.55376	−	0.302367i	−0.121893	−	0.0103711i
$851$	−26.0341	−	45.0924i	−0.892437	−	1.54575i
$852$	−6.99103	+	6.99103i	−0.239509	+	0.239509i
$853$	2.79040	−	2.79040i	0.0955416	−	0.0955416i	−0.657720	−	0.753262i	$-0.728479\pi$
$853$	2.79040	−	2.79040i	0.0955416	−	0.0955416i	0.753262	+	0.657720i	$0.228479\pi$
$854$	5.64039	+	9.76945i	0.193010	+	0.334304i
$855$	14.8890	−	7.77331i	0.509192	−	0.265841i
$856$	5.32060	+	9.21555i	0.181854	+	0.314981i
$857$	31.6596	−	8.48317i	1.08147	−	0.289780i	0.326273	−	0.945275i	$-0.394207\pi$
$857$	31.6596	−	8.48317i	1.08147	−	0.289780i	0.755199	+	0.655496i	$0.227540\pi$
$858$	3.53217	−	0.946443i	0.120586	−	0.0323110i
$859$	−7.64856	+	13.2477i	−0.260966	+	0.452006i	−0.966499	−	0.256671i	$-0.917374\pi$
$859$	−7.64856	+	13.2477i	−0.260966	+	0.452006i	0.705533	+	0.708677i	$0.250708\pi$
$860$	−21.4883	+	4.79076i	−0.732745	+	0.163363i
$861$	4.63446	−	2.67571i	0.157942	−	0.0911879i
$862$	−1.38191	+	5.15737i	−0.0470682	+	0.175661i
$863$	1.32501	−	0.355036i	0.0451039	−	0.0120856i	−0.236197	−	0.971705i	$-0.575901\pi$
$863$	1.32501	−	0.355036i	0.0451039	−	0.0120856i	0.281300	+	0.959620i	$0.409234\pi$
$864$	1.00000			0.0340207
$865$	−0.0193047	−	0.0210169i	−0.000656378	−	0.000714597i
$866$			27.1434i			0.922372i
$867$	11.6610	−	11.6610i	0.396029	−	0.396029i
$868$	−3.10076	+	3.33845i	−0.105247	+	0.113314i
$869$			1.35735i			0.0460448i
$870$	2.96395	−	4.66475i	0.100487	−	0.158150i
$871$	−49.3695	+	28.5035i	−1.67282	+	0.965804i
$872$	2.42128	+	2.42128i	0.0819949	+	0.0819949i
$873$	3.53599	+	13.1965i	0.119675	+	0.446634i
$874$	18.3734	+	31.8237i	0.621490	+	1.07645i
$875$	8.46532	+	3.47099i	0.286180	+	0.117341i
$876$	−1.21395			−0.0410154
$877$	26.0430	−	6.97819i	0.879409	−	0.235637i	0.209257	−	0.977861i	$-0.432896\pi$
$877$	26.0430	−	6.97819i	0.879409	−	0.235637i	0.670152	+	0.742224i	$0.266229\pi$
$878$	3.06521	+	11.4395i	0.103446	+	0.386065i
$879$	−6.32542	+	10.9560i	−0.213351	+	0.369535i
$880$	−1.81247	−	0.0769669i	−0.0610984	−	0.00259455i
$881$	43.8280	+	25.3041i	1.47660	+	0.852518i	0.999651	−	0.0264114i	$-0.00840798\pi$
$881$	43.8280	+	25.3041i	1.47660	+	0.852518i	0.476953	+	0.878929i	$0.341741\pi$
$882$	−1.63841	+	6.11462i	−0.0551681	+	0.205890i
$883$	15.2803	+	15.2803i	0.514222	+	0.514222i	0.915817	−	0.401595i	$-0.131544\pi$
$883$	15.2803	+	15.2803i	0.514222	+	0.514222i	−0.401595	+	0.915817i	$0.631544\pi$
$884$		−	3.21518i		−	0.108138i
$885$	−18.0592	−	19.6610i	−0.607054	−	0.660898i
$886$	11.9194	−	20.6449i	0.400439	−	0.693580i
$887$	1.29328	−	4.82660i	0.0434242	−	0.162061i	−0.940809	−	0.338937i	$-0.889933\pi$
$887$	1.29328	−	4.82660i	0.0434242	−	0.162061i	0.984233	+	0.176876i	$0.0565992\pi$
$888$	2.75467	+	10.2806i	0.0924407	+	0.344993i
$889$	−6.49086	+	11.2425i	−0.217696	+	0.377061i
$890$	−10.4735	−	3.28855i	−0.351073	−	0.110232i
$891$		−	0.811292i		−	0.0271793i
$892$	−23.1076	−	6.19165i	−0.773699	−	0.207312i
$893$	−18.0706	−	4.84200i	−0.604710	−	0.162031i
$894$	2.91492	−	5.04879i	0.0974894	−	0.168857i
$895$	15.2451	+	9.68663i	0.509587	+	0.323788i
$896$	0.409169	+	0.708701i	0.0136694	+	0.0236760i
$897$	−15.5921	+	15.5921i	−0.520606	+	0.520606i
$898$	20.2007	+	20.2007i	0.674107	+	0.674107i
$899$	6.43642	−	12.1635i	0.214667	−	0.405675i
$900$	−2.12390	−	4.52648i	−0.0707967	−	0.150883i
$901$	−6.65906			−0.221846
$902$	5.12457	+	1.37312i	0.170629	+	0.0457200i
$903$	5.69729	−	5.69729i	0.189594	−	0.189594i
$904$	−11.7919	−	6.80808i	−0.392194	−	0.226434i
$905$	−31.1666	−	1.32349i	−1.03601	−	0.0439944i
$906$	2.97942	+	5.16050i	0.0989845	+	0.171446i
$907$	−15.4385	−	15.4385i	−0.512628	−	0.512628i	0.402703	−	0.915331i	$-0.368071\pi$
$907$	−15.4385	−	15.4385i	−0.512628	−	0.512628i	−0.915331	+	0.402703i	$0.868071\pi$
$908$	6.98984	+	26.0864i	0.231966	+	0.865709i
$909$	−6.96943	−	4.02380i	−0.231162	−	0.133461i
$910$	−2.47077	+	7.86903i	−0.0819054	+	0.260856i
$911$	17.1639	−	9.90959i	0.568666	−	0.328319i	−0.187950	−	0.982179i	$-0.560184\pi$
$911$	17.1639	−	9.90959i	0.568666	−	0.328319i	0.756616	+	0.653859i	$0.226851\pi$
$912$	−1.94409	−	7.25545i	−0.0643754	−	0.240252i
$913$	12.6747	+	3.39618i	0.419472	+	0.112397i
$914$	−23.8378			−0.788485
$915$	−30.0856	+	6.70749i	−0.994598	+	0.221743i
$916$	−3.96864	+	2.29130i	−0.131128	+	0.0757066i
$917$	12.7107	−	3.40582i	0.419744	−	0.112470i
$918$	−0.689013	−	0.184621i	−0.0227408	−	0.00609339i
$919$	−25.1130	−	14.4990i	−0.828401	−	0.478278i	0.0249036	−	0.999690i	$-0.492072\pi$
$919$	−25.1130	−	14.4990i	−0.828401	−	0.478278i	−0.853305	+	0.521412i	$0.825405\pi$
$920$	9.69712	−	5.06272i	0.319705	−	0.166913i
$921$	−6.79447	−	3.92279i	−0.223885	−	0.129260i
$922$	−23.2427	+	23.2427i	−0.765458	+	0.765458i
$923$	−11.5338	+	43.0449i	−0.379641	+	1.41684i
$924$	0.574963	−	0.331955i	0.0189149	−	0.0109205i
$925$	40.6842	−	34.3039i	1.33769	−	1.12790i
$926$			22.0257i			0.723810i
$927$	0.0432264	−	0.161323i	0.00141974	−	0.00529855i
$928$	−1.74771	−	1.74771i	−0.0573714	−	0.0573714i
$929$	−24.5675			−0.806034			−0.403017	−	0.915192i	$-0.632038\pi$
$929$	−24.5675			−0.806034			−0.403017	+	0.915192i	$0.632038\pi$
$930$	−6.16509	−	10.8163i	−0.202161	−	0.354679i
$931$	47.5496			1.55837
$932$	−5.72287	−	5.72287i	−0.187459	−	0.187459i
$933$	−3.11631	+	11.6302i	−0.102023	+	0.380756i
$934$		−	23.6129i		−	0.772637i
$935$	1.23461	+	0.387651i	0.0403760	+	0.0126775i
$936$	3.90348	−	2.25367i	0.127589	−	0.0736637i
$937$	−10.2387	+	38.2114i	−0.334484	+	1.24831i	0.569944	+	0.821684i	$0.306965\pi$
$937$	−10.2387	+	38.2114i	−0.334484	+	1.24831i	−0.904428	+	0.426627i	$0.859702\pi$
$938$	−7.31854	+	7.31854i	−0.238959	+	0.238959i
$939$	4.17664	+	2.41138i	0.136299	+	0.0786925i
$940$	−1.66835	+	5.31344i	−0.0544156	+	0.173305i
$941$	−42.8571	−	24.7436i	−1.39710	−	0.806618i	−0.403015	−	0.915194i	$-0.632038\pi$
$941$	−42.8571	−	24.7436i	−1.39710	−	0.806618i	−0.994088	+	0.108576i	$0.965371\pi$
$942$	−5.63157	−	1.50898i	−0.183487	−	0.0491651i
$943$	−30.9015	+	8.28002i	−1.00629	+	0.269635i
$944$	−10.3394	+	5.96947i	−0.336520	+	0.194290i
$945$	1.54446	+	0.981339i	0.0502413	+	0.0319230i
$946$	7.98781			0.259706
$947$	4.49926	+	1.20557i	0.146206	+	0.0391758i	0.331180	−	0.943568i	$-0.392553\pi$
$947$	4.49926	+	1.20557i	0.146206	+	0.0391758i	−0.184974	+	0.982743i	$0.559220\pi$
$948$	0.433022	+	1.61606i	0.0140639	+	0.0524872i
$949$	−4.73861	+	2.73584i	−0.153822	+	0.0888091i
$950$	−28.7126	+	24.2098i	−0.931560	+	0.785469i
$951$	−19.7757	−	11.4175i	−0.641271	−	0.370238i
$952$	−0.151082	−	0.563845i	−0.00489659	−	0.0182743i
$953$	13.8799	+	13.8799i	0.449615	+	0.449615i	0.895227	−	0.445611i	$-0.147014\pi$
$953$	13.8799	+	13.8799i	0.449615	+	0.449615i	−0.445611	+	0.895227i	$0.647014\pi$
$954$	−4.66766	−	8.08462i	−0.151121	−	0.261749i
$955$	0.827040	−	19.4757i	0.0267624	−	0.630219i
$956$	19.6505	+	11.3452i	0.635542	+	0.366930i
$957$	−1.41790	+	1.41790i	−0.0458343	+	0.0458343i
$958$	−33.2182	−	8.90080i	−1.07323	−	0.287572i
$959$	−11.6284			−0.375501
$960$	−2.18249	+	0.486579i	−0.0704394	+	0.0157043i
$961$	−17.4372	−	25.6310i	−0.562489	−	0.826805i
$962$	33.9218	+	33.9218i	1.09368	+	1.09368i
$963$	7.52447	−	7.52447i	0.242473	−	0.242473i
$964$	−9.69269	−	16.7882i	−0.312180	−	0.540712i
$965$	5.63593	−	1.25651i	0.181427	−	0.0404486i
$966$	−2.00171	+	3.46707i	−0.0644040	+	0.111551i
$967$	16.8305	+	4.50973i	0.541233	+	0.145023i	0.519071	−	0.854731i	$-0.326278\pi$
$967$	16.8305	+	4.50973i	0.541233	+	0.145023i	0.0221628	+	0.999754i	$0.492945\pi$
$968$	−9.98942	−	2.67666i	−0.321072	−	0.0860310i
$969$			5.35802i			0.172125i
$970$	−14.1384	−	27.0806i	−0.453956	−	0.869506i
$971$	2.68666	−	4.65343i	0.0862189	−	0.149336i	−0.819691	−	0.572806i	$-0.805855\pi$
$971$	2.68666	−	4.65343i	0.0862189	−	0.149336i	0.905910	+	0.423470i	$0.139188\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	2.89535	−	10.8056i	0.0928208	−	0.346412i
$974$	8.55861	−	14.8240i	0.274236	−	0.474990i
$975$	−18.4918	−	12.8824i	−0.592212	−	0.412568i
$976$			13.7850i			0.441247i
$977$	−27.5921	−	27.5921i	−0.882750	−	0.882750i	0.111063	−	0.993813i	$-0.464574\pi$
$977$	−27.5921	−	27.5921i	−0.882750	−	0.882750i	−0.993813	+	0.111063i	$0.964574\pi$
$978$	−2.53818	+	9.47261i	−0.0811620	+	0.302901i
$979$	3.44932	+	1.99146i	0.110241	+	0.0636474i
$980$	0.600555	−	14.1423i	0.0191840	−	0.451759i
$981$	1.71210	−	2.96545i	0.0546633	−	0.0946795i
$982$	−3.28866	−	12.2735i	−0.104945	−	0.391662i
$983$	−19.5945	+	5.25032i	−0.624966	+	0.167459i	−0.557384	−	0.830255i	$-0.688195\pi$
$983$	−19.5945	+	5.25032i	−0.624966	+	0.167459i	−0.0675817	+	0.997714i	$0.521528\pi$
$984$	6.53938			0.208468
$985$	17.3115	+	18.8470i	0.551590	+	0.600515i
$986$	0.881532	+	1.52686i	0.0280737	+	0.0486251i
$987$	−0.527517	−	1.96872i	−0.0167911	−	0.0626651i
$988$	−23.9402	−	23.9402i	−0.761638	−	0.761638i
$989$	−41.7139	+	24.0835i	−1.32642	+	0.765811i
$990$	0.394758	+	1.77063i	0.0125462	+	0.0562744i
$991$			34.3339i			1.09065i	0.838224	+	0.545326i	$0.183594\pi$
$991$			34.3339i			1.09065i	−0.838224	+	0.545326i	$0.816406\pi$
$992$	−5.32123	+	1.63845i	−0.168949	+	0.0520209i
$993$	16.9163	−	16.9163i	0.536821	−	0.536821i
$994$			8.09075i			0.256623i
$995$	1.50906	−	35.5364i	0.0478404	−	1.12658i
$996$	16.1740			0.512492
$997$	−15.5241	+	4.15968i	−0.491655	+	0.131738i	−0.496124	−	0.868252i	$-0.665244\pi$
$997$	−15.5241	+	4.15968i	−0.491655	+	0.131738i	0.00446966	+	0.999990i	$0.498577\pi$
$998$	−1.25826	+	4.69587i	−0.0398294	+	0.148645i
$999$	9.21730	−	5.32161i	0.291623	−	0.168368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.2	✓	64
5.3	odd	4		930.2.be.b.223.5	yes	64
31.26	odd	6		930.2.be.b.367.5	yes	64
155.88	even	12	inner	930.2.be.a.553.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.2	✓	64	1.1	even	1	trivial
930.2.be.a.553.2	yes	64	155.88	even	12	inner
930.2.be.b.223.5	yes	64	5.3	odd	4
930.2.be.b.367.5	yes	64	31.26	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.98218 + 1.03487i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.211801 - 0.790453i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(-1.98218 + 1.03487i) q^{5} +(0.866025 - 0.500000i) q^{6} +(0.211801 - 0.790453i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.13338 + 0.669853i) q^{10} +(-0.702599 - 0.405646i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-4.35376 + 1.16659i) q^{13} +(-0.708701 + 0.409169i) q^{14} +(-0.486579 - 2.18249i) q^{15} -1.00000 q^{16} +(0.689013 + 0.184621i) q^{17} +(0.258819 + 0.965926i) q^{18} +(6.50506 - 3.75570i) q^{19} +(-1.03487 - 1.98218i) q^{20} +(0.708701 + 0.409169i) q^{21} +(0.209978 + 0.783648i) q^{22} +(-3.45927 - 3.45927i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.85810 - 4.10259i) q^{25} +(3.90348 + 2.25367i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.790453 + 0.211801i) q^{28} -2.47163 q^{29} +(-1.19919 + 1.88731i) q^{30} +(-2.60412 + 4.92124i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.573670 - 0.573670i) q^{33} +(-0.356660 - 0.617752i) q^{34} +(0.398186 + 1.78601i) q^{35} +(0.500000 - 0.866025i) q^{36} +(10.2806 + 2.75467i) q^{37} +(-7.25545 - 1.94409i) q^{38} -4.50735i q^{39} +(-0.669853 + 2.13338i) q^{40} +(3.26969 - 5.66327i) q^{41} +(-0.211801 - 0.790453i) q^{42} +(2.54828 - 9.51031i) q^{43} +(0.405646 - 0.702599i) q^{44} +(2.23405 + 0.0948696i) q^{45} +4.89214i q^{46} +(-1.76114 - 1.76114i) q^{47} +(0.258819 - 0.965926i) q^{48} +(5.48222 + 3.16516i) q^{49} +(-4.92195 + 0.879992i) q^{50} +(-0.356660 + 0.617752i) q^{51} +(-1.16659 - 4.35376i) q^{52} +(-9.01723 + 2.41616i) q^{53} -1.00000 q^{54} +(1.81247 + 0.0769669i) q^{55} +(-0.409169 - 0.708701i) q^{56} +(1.94409 + 7.25545i) q^{57} +(1.74771 + 1.74771i) q^{58} +(10.3394 - 5.96947i) q^{59} +(2.18249 - 0.486579i) q^{60} -13.7850i q^{61} +(5.32123 - 1.63845i) q^{62} +(-0.578652 + 0.578652i) q^{63} -1.00000i q^{64} +(7.42269 - 6.81796i) q^{65} -0.811292 q^{66} +(12.2166 - 3.27343i) q^{67} +(-0.184621 + 0.689013i) q^{68} +(4.23672 - 2.44607i) q^{69} +(0.981339 - 1.54446i) q^{70} +(4.94341 - 8.56223i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(1.17258 - 0.314192i) q^{73} +(-5.32161 - 9.21730i) q^{74} +(3.22307 + 3.82254i) q^{75} +(3.75570 + 6.50506i) q^{76} +(-0.469456 + 0.469456i) q^{77} +(-3.18718 + 3.18718i) q^{78} +(-0.836534 - 1.44892i) q^{79} +(1.98218 - 1.03487i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-6.31655 + 1.69252i) q^{82} +(-15.6229 + 4.18614i) q^{83} +(-0.409169 + 0.708701i) q^{84} +(-1.55681 + 0.347086i) q^{85} +(-8.52671 + 4.92290i) q^{86} +(0.639706 - 2.38742i) q^{87} +(-0.783648 + 0.209978i) q^{88} -4.90936 q^{89} +(-1.51263 - 1.64680i) q^{90} +3.68853i q^{91} +(3.45927 - 3.45927i) q^{92} +(-4.07956 - 3.78909i) q^{93} +2.49062i q^{94} +(-9.00757 + 14.1764i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-9.66051 - 9.66051i) q^{97} +(-1.63841 - 6.11462i) q^{98} +(0.405646 + 0.702599i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more