LMFDB - Embedded newform 544.2.x.a.77.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(77,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.1
Character	$\chi$	$=$	544.77
Dual form			544.2.x.a.325.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40969 - 0.112967i) q^{2} +(0.238533 - 0.238533i) q^{3} +(1.97448 + 0.318497i) q^{4} -3.01165i q^{5} +(-0.363205 + 0.309313i) q^{6} +(0.302065 + 0.125119i) q^{7} +(-2.74743 - 0.672035i) q^{8} +2.88620i q^{9} +(-0.340217 + 4.24551i) q^{10} +(2.95104 + 2.95104i) q^{11} +(0.546950 - 0.395006i) q^{12} +(2.52096 - 6.08613i) q^{13} +(-0.411685 - 0.210503i) q^{14} +(-0.718379 - 0.718379i) q^{15} +(3.79712 + 1.25773i) q^{16} +(3.50552 + 2.17057i) q^{17} +(0.326045 - 4.06867i) q^{18} +(2.28261 - 0.945488i) q^{19} +(0.959204 - 5.94644i) q^{20} +(0.101898 - 0.0422074i) q^{21} +(-3.82670 - 4.49344i) q^{22} +(-7.38275 - 3.05803i) q^{23} +(-0.815656 + 0.495051i) q^{24} -4.07006 q^{25} +(-4.24131 + 8.29480i) q^{26} +(1.40405 + 1.40405i) q^{27} +(0.556570 + 0.343252i) q^{28} +(-5.01678 - 5.01678i) q^{29} +(0.931542 + 1.09385i) q^{30} +(6.39232 + 2.64779i) q^{31} +(-5.21070 - 2.20197i) q^{32} +1.40784 q^{33} +(-4.69650 - 3.45584i) q^{34} +(0.376816 - 0.909715i) q^{35} +(-0.919249 + 5.69874i) q^{36} +0.671208 q^{37} +(-3.32459 + 1.07499i) q^{38} +(-0.850412 - 2.05308i) q^{39} +(-2.02394 + 8.27431i) q^{40} +(2.13265 - 5.14867i) q^{41} +(-0.148413 + 0.0479884i) q^{42} +(3.17554 - 7.66643i) q^{43} +(4.88686 + 6.76666i) q^{44} +8.69225 q^{45} +(10.0620 + 5.14490i) q^{46} -3.28912 q^{47} +(1.20575 - 0.605728i) q^{48} +(-4.87416 - 4.87416i) q^{49} +(5.73754 + 0.459781i) q^{50} +(1.35393 - 0.318429i) q^{51} +(6.91599 - 11.2140i) q^{52} +(-3.49515 - 1.44774i) q^{53} +(-1.82068 - 2.13790i) q^{54} +(8.88751 - 8.88751i) q^{55} +(-0.745817 - 0.546755i) q^{56} +(0.318948 - 0.770008i) q^{57} +(6.50540 + 7.63886i) q^{58} +(7.79973 + 3.23076i) q^{59} +(-1.18962 - 1.64723i) q^{60} +1.84912 q^{61} +(-8.71211 - 4.45469i) q^{62} +(-0.361120 + 0.871821i) q^{63} +(7.09674 + 3.69274i) q^{64} +(-18.3293 - 7.59225i) q^{65} +(-1.98463 - 0.159040i) q^{66} +(-1.28394 + 3.09971i) q^{67} +(6.23024 + 5.40223i) q^{68} +(-2.49047 + 1.03159i) q^{69} +(-0.633963 + 1.23985i) q^{70} +(4.62080 - 1.91400i) q^{71} +(1.93963 - 7.92964i) q^{72} +(-0.947663 + 0.392535i) q^{73} +(-0.946198 - 0.0758243i) q^{74} +(-0.970844 + 0.970844i) q^{75} +(4.80809 - 1.13984i) q^{76} +(0.522173 + 1.26064i) q^{77} +(0.966892 + 2.99028i) q^{78} +(3.41347 + 8.24084i) q^{79} +(3.78785 - 11.4356i) q^{80} -7.98878 q^{81} +(-3.58801 + 7.01713i) q^{82} +(2.36616 - 0.980097i) q^{83} +(0.214637 - 0.0508833i) q^{84} +(6.53700 - 10.5574i) q^{85} +(-5.34259 + 10.4486i) q^{86} -2.39334 q^{87} +(-6.12458 - 10.0910i) q^{88} +(-1.27793 - 1.27793i) q^{89} +(-12.2534 - 0.981936i) q^{90} +(1.52299 - 1.52299i) q^{91} +(-13.6031 - 8.38941i) q^{92} +(2.15637 - 0.893196i) q^{93} +(4.63666 + 0.371562i) q^{94} +(-2.84748 - 6.87443i) q^{95} +(-1.76817 + 0.717682i) q^{96} +(3.00634 - 7.25795i) q^{97} +(6.32046 + 7.42169i) q^{98} +(-8.51731 + 8.51731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	−1.40969	−	0.112967i	−0.996805	−	0.0798796i
$2$	−1.40969	−	0.112967i	−0.996805	−	0.0798796i
$3$	0.238533	−	0.238533i	0.137717	−	0.137717i	−0.634887	−	0.772605i	$-0.718954\pi$
$3$	0.238533	−	0.238533i	0.137717	−	0.137717i	0.772605	+	0.634887i	$0.218954\pi$
$4$	1.97448	+	0.318497i	0.987238	+	0.159249i
$5$		−	3.01165i		−	1.34685i	−0.739254	−	0.673426i	$-0.764822\pi$
$5$		−	3.01165i		−	1.34685i	0.739254	−	0.673426i	$-0.235178\pi$
$6$	−0.363205	+	0.309313i	−0.148278	+	0.126276i
$7$	0.302065	+	0.125119i	0.114170	+	0.0472907i	0.439037	−	0.898469i	$-0.355320\pi$
$7$	0.302065	+	0.125119i	0.114170	+	0.0472907i	−0.324867	+	0.945760i	$0.605320\pi$
$8$	−2.74743	−	0.672035i	−0.971363	−	0.237600i
$9$			2.88620i			0.962068i
$10$	−0.340217	+	4.24551i	−0.107586	+	1.34255i
$11$	2.95104	+	2.95104i	0.889773	+	0.889773i	0.994501	−	0.104728i	$-0.0333973\pi$
$11$	2.95104	+	2.95104i	0.889773	+	0.889773i	−0.104728	+	0.994501i	$0.533397\pi$
$12$	0.546950	−	0.395006i	0.157891	−	0.114028i
$13$	2.52096	−	6.08613i	0.699188	−	1.68799i	−0.0262067	−	0.999657i	$-0.508343\pi$
$13$	2.52096	−	6.08613i	0.699188	−	1.68799i	0.725395	−	0.688333i	$-0.241657\pi$
$14$	−0.411685	−	0.210503i	−0.110027	−	0.0562594i
$15$	−0.718379	−	0.718379i	−0.185485	−	0.185485i
$16$	3.79712	+	1.25773i	0.949280	+	0.314433i
$17$	3.50552	+	2.17057i	0.850212	+	0.526440i
$17$	3.50552	+	2.17057i	0.850212	+	0.526440i
$18$	0.326045	−	4.06867i	0.0768496	−	0.958994i
$19$	2.28261	−	0.945488i	0.523666	−	0.216910i	−0.105160	−	0.994455i	$-0.533536\pi$
$19$	2.28261	−	0.945488i	0.523666	−	0.216910i	0.628827	+	0.777546i	$0.283536\pi$
$20$	0.959204	−	5.94644i	0.214485	−	1.32966i
$21$	0.101898	−	0.0422074i	0.0222359	−	0.00921040i
$22$	−3.82670	−	4.49344i	−0.815855	−	0.958004i
$23$	−7.38275	−	3.05803i	−1.53941	−	0.637644i	−0.558047	−	0.829809i	$-0.688449\pi$
$23$	−7.38275	−	3.05803i	−1.53941	−	0.637644i	−0.981363	+	0.192165i	$0.938449\pi$
$24$	−0.815656	+	0.495051i	−0.166495	+	0.101052i
$25$	−4.07006			−0.814011
$26$	−4.24131	+	8.29480i	−0.831790	+	1.62674i
$27$	1.40405	+	1.40405i	0.270210	+	0.270210i
$28$	0.556570	+	0.343252i	0.105182	+	0.0648686i
$29$	−5.01678	−	5.01678i	−0.931592	−	0.931592i	0.0662130	−	0.997806i	$-0.478908\pi$
$29$	−5.01678	−	5.01678i	−0.931592	−	0.931592i	−0.997806	+	0.0662130i	$0.978908\pi$
$30$	0.931542	+	1.09385i	0.170076	+	0.199708i
$31$	6.39232	+	2.64779i	1.14810	+	0.475557i	0.873894	−	0.486116i	$-0.161587\pi$
$31$	6.39232	+	2.64779i	1.14810	+	0.475557i	0.274201	+	0.961672i	$0.411587\pi$
$32$	−5.21070	−	2.20197i	−0.921129	−	0.389256i
$33$	1.40784			0.245074
$34$	−4.69650	−	3.45584i	−0.805444	−	0.592672i
$35$	0.376816	−	0.909715i	0.0636935	−	0.153770i
$36$	−0.919249	+	5.69874i	−0.153208	+	0.949791i
$37$	0.671208			0.110346			0.0551730	−	0.998477i	$-0.482429\pi$
$37$	0.671208			0.110346			0.0551730	+	0.998477i	$0.482429\pi$
$38$	−3.32459	+	1.07499i	−0.539320	+	0.174386i
$39$	−0.850412	−	2.05308i	−0.136175	−	0.328755i
$40$	−2.02394	+	8.27431i	−0.320012	+	1.30828i
$41$	2.13265	−	5.14867i	0.333064	−	0.804087i	−0.665282	−	0.746592i	$-0.731689\pi$
$41$	2.13265	−	5.14867i	0.333064	−	0.804087i	0.998346	−	0.0574946i	$-0.0183112\pi$
$42$	−0.148413	+	0.0479884i	−0.0229005	+	0.00740478i
$43$	3.17554	−	7.66643i	0.484265	−	1.16912i	−0.473300	−	0.880901i	$-0.656937\pi$
$43$	3.17554	−	7.66643i	0.484265	−	1.16912i	0.957565	−	0.288218i	$-0.0930627\pi$
$44$	4.88686	+	6.76666i	0.736723	+	1.02011i
$45$	8.69225			1.29576
$46$	10.0620	+	5.14490i	1.48356	+	0.758574i
$47$	−3.28912			−0.479768			−0.239884	−	0.970802i	$-0.577109\pi$
$47$	−3.28912			−0.479768			−0.239884	+	0.970802i	$0.577109\pi$
$48$	1.20575	−	0.605728i	0.174035	−	0.0874293i
$49$	−4.87416	−	4.87416i	−0.696308	−	0.696308i
$50$	5.73754	+	0.459781i	0.811410	+	0.0650229i
$51$	1.35393	−	0.318429i	0.189589	−	0.0445890i
$52$	6.91599	−	11.2140i	0.959076	−	1.55510i
$53$	−3.49515	−	1.44774i	−0.480095	−	0.198862i	0.129493	−	0.991580i	$-0.458665\pi$
$53$	−3.49515	−	1.44774i	−0.480095	−	0.198862i	−0.609588	+	0.792718i	$0.708665\pi$
$54$	−1.82068	−	2.13790i	−0.247763	−	0.290931i
$55$	8.88751	−	8.88751i	1.19839	−	1.19839i
$56$	−0.745817	−	0.546755i	−0.0996640	−	0.0730632i
$57$	0.318948	−	0.770008i	0.0422457	−	0.101990i
$58$	6.50540	+	7.63886i	0.854200	+	1.00303i
$59$	7.79973	+	3.23076i	1.01544	+	0.420608i	0.827436	−	0.561560i	$-0.189799\pi$
$59$	7.79973	+	3.23076i	1.01544	+	0.420608i	0.188003	+	0.982169i	$0.439799\pi$
$60$	−1.18962	−	1.64723i	−0.153579	−	0.212656i
$61$	1.84912			0.236755			0.118378	−	0.992969i	$-0.462231\pi$
$61$	1.84912			0.236755			0.118378	+	0.992969i	$0.462231\pi$
$62$	−8.71211	−	4.45469i	−1.10644	−	0.565746i
$63$	−0.361120	+	0.871821i	−0.0454968	+	0.109839i
$64$	7.09674	+	3.69274i	0.887092	+	0.461592i
$65$	−18.3293	−	7.59225i	−2.27347	−	0.941703i
$66$	−1.98463	−	0.159040i	−0.244291	−	0.0195764i
$67$	−1.28394	+	3.09971i	−0.156858	+	0.378689i	−0.982698	−	0.185216i	$-0.940702\pi$
$67$	−1.28394	+	3.09971i	−0.156858	+	0.378689i	0.825840	+	0.563905i	$0.190702\pi$
$68$	6.23024	+	5.40223i	0.755528	+	0.655117i
$69$	−2.49047	+	1.03159i	−0.299818	+	0.124189i
$70$	−0.633963	+	1.23985i	−0.0757731	+	0.148191i
$71$	4.62080	−	1.91400i	0.548388	−	0.227150i	−0.0912473	−	0.995828i	$-0.529085\pi$
$71$	4.62080	−	1.91400i	0.548388	−	0.227150i	0.639635	+	0.768679i	$0.279085\pi$
$72$	1.93963	−	7.92964i	0.228587	−	0.934517i
$73$	−0.947663	+	0.392535i	−0.110916	+	0.0459427i	−0.437451	−	0.899242i	$-0.644119\pi$
$73$	−0.947663	+	0.392535i	−0.110916	+	0.0459427i	0.326536	+	0.945185i	$0.394119\pi$
$74$	−0.946198	−	0.0758243i	−0.109993	−	0.00881439i
$75$	−0.970844	+	0.970844i	−0.112103	+	0.112103i
$76$	4.80809	−	1.13984i	0.551526	−	0.130748i
$77$	0.522173	+	1.26064i	0.0595072	+	0.143663i
$78$	0.966892	+	2.99028i	0.109479	+	0.338582i
$79$	3.41347	+	8.24084i	0.384045	+	0.927167i	0.991174	+	0.132564i	$0.0423211\pi$
$79$	3.41347	+	8.24084i	0.384045	+	0.927167i	−0.607129	+	0.794603i	$0.707679\pi$
$80$	3.78785	−	11.4356i	0.423495	−	1.27854i
$81$	−7.98878			−0.887643
$82$	−3.58801	+	7.01713i	−0.396229	+	0.774912i
$83$	2.36616	−	0.980097i	0.259720	−	0.107580i	−0.249024	−	0.968497i	$-0.580110\pi$
$83$	2.36616	−	0.980097i	0.259720	−	0.107580i	0.508744	+	0.860918i	$0.330110\pi$
$84$	0.214637	−	0.0508833i	0.0234189	−	0.00555183i
$85$	6.53700	−	10.5574i	0.709037	−	1.14511i
$86$	−5.34259	+	10.4486i	−0.576106	+	1.12670i
$87$	−2.39334			−0.256593
$88$	−6.12458	−	10.0910i	−0.652882	−	1.07570i
$89$	−1.27793	−	1.27793i	−0.135460	−	0.135460i	0.636125	−	0.771586i	$-0.280536\pi$
$89$	−1.27793	−	1.27793i	−0.135460	−	0.135460i	−0.771586	+	0.636125i	$0.780536\pi$
$90$	−12.2534	−	0.981936i	−1.29162	−	0.103505i
$91$	1.52299	−	1.52299i	0.159652	−	0.159652i
$92$	−13.6031	−	8.38941i	−1.41822	−	0.874656i
$93$	2.15637	−	0.893196i	0.223605	−	0.0926201i
$94$	4.63666	+	0.371562i	0.478235	+	0.0383237i
$95$	−2.84748	−	6.87443i	−0.292145	−	0.705301i
$96$	−1.76817	+	0.717682i	−0.180463	+	0.0732481i
$97$	3.00634	−	7.25795i	0.305248	−	0.736933i	−0.694599	−	0.719397i	$-0.744418\pi$
$97$	3.00634	−	7.25795i	0.305248	−	0.736933i	0.999846	−	0.0175354i	$-0.00558199\pi$
$98$	6.32046	+	7.42169i	0.638463	+	0.749704i
$99$	−8.51731	+	8.51731i	−0.856022	+	0.856022i
$100$	−8.03623	−	1.29630i	−0.803623	−	0.129630i
$101$	−9.15461	+	3.79196i	−0.910917	+	0.377314i	−0.788408	−	0.615153i	$-0.789094\pi$
$101$	−9.15461	+	3.79196i	−0.910917	+	0.377314i	−0.122510	+	0.992467i	$0.539094\pi$
$102$	−1.94461	+	0.295939i	−0.192545	+	0.0293023i
$103$	2.71286	−	2.71286i	0.267306	−	0.267306i	−0.560708	−	0.828014i	$-0.689471\pi$
$103$	2.71286	−	2.71286i	0.267306	−	0.267306i	0.828014	+	0.560708i	$0.189471\pi$
$104$	−11.0162	+	15.0271i	−1.08023	+	1.47352i
$105$	−0.127114	−	0.306880i	−0.0124051	−	0.0299484i
$106$	4.76354	+	2.43570i	0.462676	+	0.236576i
$107$	1.85978			0.179792			0.0898959	−	0.995951i	$-0.471347\pi$
$107$	1.85978			0.179792			0.0898959	+	0.995951i	$0.471347\pi$
$108$	2.32509	+	3.21946i	0.223732	+	0.309793i
$109$			17.1790i			1.64545i	0.568437	+	0.822727i	$0.307548\pi$
$109$			17.1790i			1.64545i	−0.568437	+	0.822727i	$0.692452\pi$
$110$	−13.5327	+	11.5247i	−1.29029	+	1.09884i
$111$	0.160105	−	0.160105i	0.0151965	−	0.0151965i
$112$	0.989609	+	0.855010i	0.0935093	+	0.0807908i
$113$	7.86341	+	18.9839i	0.739727	+	1.78586i	0.606992	+	0.794708i	$0.292376\pi$
$113$	7.86341	+	18.9839i	0.739727	+	1.78586i	0.132735	+	0.991152i	$0.457624\pi$
$114$	−0.536604	+	1.04945i	−0.0502576	+	0.0982896i
$115$	−9.20974	+	22.2343i	−0.858813	+	2.07336i
$116$	−8.30768	−	11.5033i	−0.771349	−	1.06806i
$117$	17.5658	+	7.27600i	1.62396	+	0.672667i
$118$	−10.6303	−	5.43549i	−0.978596	−	0.500377i
$119$	0.787313	+	1.09426i	0.0721729	+	0.100311i
$120$	1.49092	+	2.45647i	0.136102	+	0.224244i
$121$			6.41729i			0.583390i
$122$	−2.60669	−	0.208889i	−0.235999	−	0.0189119i
$123$	−0.719421	−	1.73683i	−0.0648680	−	0.156605i
$124$	11.7782	+	7.26393i	1.05771	+	0.652321i
$125$		−	2.80067i		−	0.250499i
$126$	0.607556	−	1.18821i	0.0541254	−	0.105854i
$127$	14.7795	+	14.7795i	1.31147	+	1.31147i	0.920334	+	0.391133i	$0.127917\pi$
$127$	14.7795	+	14.7795i	1.31147	+	1.31147i	0.391133	+	0.920334i	$0.372083\pi$
$128$	−9.58708	−	6.00733i	−0.847386	−	0.530978i
$129$	−1.07123	−	2.58617i	−0.0943162	−	0.227699i
$130$	24.9811	+	12.7734i	2.19098	+	1.12030i
$131$	5.93872	+	5.93872i	0.518868	+	0.518868i	0.917229	−	0.398361i	$-0.130421\pi$
$131$	5.93872	+	5.93872i	0.518868	+	0.518868i	−0.398361	+	0.917229i	$0.630421\pi$
$132$	2.77975	+	0.448394i	0.241946	+	0.0390277i
$133$	0.807795			0.0700447
$134$	2.16013	−	4.22459i	0.186607	−	0.364949i
$135$	4.22853	−	4.22853i	0.363934	−	0.363934i
$136$	−8.17246	−	8.31931i	−0.700783	−	0.713375i
$137$	−7.12080	−	7.12080i	−0.608371	−	0.608371i	0.334149	−	0.942520i	$-0.391551\pi$
$137$	−7.12080	−	7.12080i	−0.608371	−	0.608371i	−0.942520	+	0.334149i	$0.891551\pi$
$138$	3.62734	−	1.17288i	0.308780	−	0.0998424i
$139$			9.19242i			0.779691i	0.920880	+	0.389845i	$0.127472\pi$
$139$			9.19242i			0.779691i	−0.920880	+	0.389845i	$0.872528\pi$
$140$	1.03376	−	1.67620i	0.0873684	−	0.141664i
$141$	−0.784565	+	0.784565i	−0.0660723	+	0.0660723i
$142$	−6.73013	+	2.17615i	−0.564780	+	0.182619i
$143$	25.3999	−	10.5210i	2.12405	−	0.879808i
$144$	−3.63007	+	10.9593i	−0.302506	+	0.913272i
$145$	−15.1088	+	15.1088i	−1.25472	+	1.25472i
$146$	1.38026	−	0.446300i	0.114231	−	0.0369360i
$147$	−2.32530			−0.191787
$148$	1.32529	+	0.213778i	0.108938	+	0.0175725i
$149$	−9.44737	+	3.91323i	−0.773958	+	0.320584i	−0.734475	−	0.678636i	$-0.762571\pi$
$149$	−9.44737	+	3.91323i	−0.773958	+	0.320584i	−0.0394838	+	0.999220i	$0.512571\pi$
$150$	1.47827	−	1.25892i	0.120700	−	0.102790i
$151$	−20.3552			−1.65649			−0.828243	−	0.560370i	$-0.810659\pi$
$151$	−20.3552			−1.65649			−0.828243	+	0.560370i	$0.810659\pi$
$152$	−6.90671	+	1.06367i	−0.560208	+	0.0862749i
$153$	−6.26470	+	10.1176i	−0.506471	+	0.817962i
$154$	−0.593695	−	1.83610i	−0.0478413	−	0.147957i
$155$	7.97422	−	19.2515i	0.640505	−	1.54631i
$156$	−1.02522	−	4.32461i	−0.0820833	−	0.346246i
$157$	−13.5051	−	5.59401i	−1.07783	−	0.446451i	−0.228081	−	0.973642i	$-0.573245\pi$
$157$	−13.5051	−	5.59401i	−1.07783	−	0.446451i	−0.849747	+	0.527191i	$0.823245\pi$
$158$	−3.88101	−	12.0027i	−0.308756	−	0.954882i
$159$	−1.17904	+	0.488375i	−0.0935041	+	0.0387307i
$160$	−6.63156	+	15.6928i	−0.524271	+	1.24063i
$161$	−1.84745	−	1.84745i	−0.145599	−	0.145599i
$162$	11.2617	+	0.902468i	0.884806	+	0.0709046i
$163$	−5.19284			−0.406734			−0.203367	−	0.979103i	$-0.565188\pi$
$163$	−5.19284			−0.406734			−0.203367	+	0.979103i	$0.565188\pi$
$164$	5.85070	−	9.48668i	0.456863	−	0.740785i
$165$		−	4.23993i		−	0.330078i
$166$	−3.44629	+	1.11434i	−0.267484	+	0.0864895i
$167$	−13.1726	+	5.45625i	−1.01932	+	0.422218i	−0.828848	−	0.559474i	$-0.811003\pi$
$167$	−13.1726	+	5.45625i	−1.01932	+	0.422218i	−0.190476	+	0.981692i	$0.561003\pi$
$168$	−0.308321	+	0.0474831i	−0.0237875	+	0.00366340i
$169$	−21.4934	−	21.4934i	−1.65334	−	1.65334i
$170$	−10.4078	+	14.1442i	−0.798242	+	1.08481i
$171$	2.72887	+	6.58807i	0.208682	+	0.503803i
$172$	8.71176	−	14.1258i	0.664266	−	1.07708i
$173$	6.54878	+	6.54878i	0.497894	+	0.497894i	0.910782	−	0.412888i	$-0.135480\pi$
$173$	6.54878	+	6.54878i	0.497894	+	0.497894i	−0.412888	+	0.910782i	$0.635480\pi$
$174$	3.37387	+	0.270368i	0.255773	+	0.0204965i
$175$	−1.22942	−	0.509243i	−0.0929355	−	0.0384951i
$176$	7.49384	+	14.9171i	0.564869	+	1.12442i
$177$	2.63114	−	1.08985i	0.197768	−	0.0819184i
$178$	1.65713	+	1.94586i	0.124207	+	0.145848i
$179$	−1.50573	−	3.63516i	−0.112544	−	0.271705i	0.857565	−	0.514376i	$-0.171976\pi$
$179$	−1.50573	−	3.63516i	−0.112544	−	0.271705i	−0.970109	+	0.242671i	$0.921976\pi$
$180$	17.1626	+	2.76846i	1.27923	+	0.206349i
$181$	−0.150754	−	0.150754i	−0.0112055	−	0.0112055i	0.701482	−	0.712687i	$-0.252522\pi$
$181$	−0.150754	−	0.150754i	−0.0112055	−	0.0112055i	−0.712687	+	0.701482i	$0.752522\pi$
$182$	−2.31899	+	1.97490i	−0.171895	+	0.146389i
$183$	0.441076	−	0.441076i	0.0326052	−	0.0326052i
$184$	18.2285	+	13.3632i	1.34382	+	0.985148i
$185$		−	2.02145i		−	0.148620i
$186$	−3.14072	+	1.01554i	−0.230289	+	0.0744627i
$187$	3.93949	+	16.7504i	0.288084	+	1.22491i
$188$	−6.49429	−	1.04758i	−0.473645	−	0.0764024i
$189$	0.248441	+	0.599790i	0.0180714	+	0.0436283i
$190$	3.23750	+	10.0125i	0.234873	+	0.726384i
$191$		−	10.0600i		−	0.727913i	−0.931416	−	0.363957i	$-0.881426\pi$
$191$		−	10.0600i		−	0.727913i	0.931416	−	0.363957i	$-0.118574\pi$
$192$	2.57365	−	0.811968i	0.185737	−	0.0585987i
$193$	2.53330	−	1.04933i	0.182351	−	0.0755321i	−0.289640	−	0.957136i	$-0.593536\pi$
$193$	2.53330	−	1.04933i	0.182351	−	0.0755321i	0.471991	+	0.881604i	$0.343536\pi$
$194$	−5.05793	+	9.89187i	−0.363138	+	0.710195i
$195$	−6.18316	+	2.56115i	−0.442785	+	0.183408i
$196$	−8.07151	−	11.1763i	−0.576536	−	0.798309i
$197$	7.29696	+	7.29696i	0.519887	+	0.519887i	0.917537	−	0.397650i	$-0.130174\pi$
$197$	7.29696	+	7.29696i	0.519887	+	0.519887i	−0.397650	+	0.917537i	$0.630174\pi$
$198$	12.9690	−	11.0446i	0.921665	−	0.784908i
$199$	4.28242	+	10.3387i	0.303573	+	0.732889i	0.999885	+	0.0151507i	$0.00482280\pi$
$199$	4.28242	+	10.3387i	0.303573	+	0.732889i	−0.696312	+	0.717739i	$0.745177\pi$
$200$	11.1822	+	2.73522i	0.790700	+	0.193409i
$201$	0.433120	+	1.04564i	0.0305499	+	0.0737541i
$202$	13.3336	−	4.31134i	0.938146	−	0.303345i
$203$	−0.887696	−	2.14309i	−0.0623041	−	0.150415i
$204$	2.77473	−	0.197507i	0.194270	−	0.0138283i
$205$	−15.5060	−	6.42279i	−1.08299	−	0.448587i
$206$	−4.13077	+	3.51784i	−0.287804	+	0.245100i
$207$	8.82611	−	21.3081i	0.613457	−	1.48102i
$208$	17.2271	−	19.9391i	1.19448	−	1.38253i
$209$	9.52625	+	3.94590i	0.658944	+	0.272944i
$210$	0.144525	+	0.446967i	0.00997314	+	0.0308437i
$211$			14.2335i			0.979876i	0.871757	+	0.489938i	$0.162981\pi$
$211$			14.2335i			0.979876i	−0.871757	+	0.489938i	$0.837019\pi$
$212$	−6.43998	−	3.97172i	−0.442300	−	0.272779i
$213$	0.645662	−	1.55877i	0.0442400	−	0.106805i
$214$	−2.62172	−	0.210094i	−0.179217	−	0.0143617i
$215$	−23.0886	−	9.56362i	−1.57463	−	0.652233i
$216$	−2.91397	−	4.80112i	−0.198270	−	0.326675i
$217$	1.59961	+	1.59961i	0.108588	+	0.108588i
$218$	1.94066	−	24.2172i	0.131438	−	1.64020i
$219$	−0.132416	+	0.319682i	−0.00894787	+	0.0216021i
$220$	20.3788	−	14.7175i	1.37394	−	0.992257i
$221$	22.0476	−	15.8631i	1.48308	−	1.06707i
$222$	−0.243786	+	0.207613i	−0.0163619	+	0.0139341i
$223$	−19.3162	+	19.3162i	−1.29351	+	1.29351i	−0.360910	+	0.932601i	$0.617534\pi$
$223$	−19.3162	+	19.3162i	−1.29351	+	1.29351i	−0.932601	+	0.360910i	$0.882466\pi$
$224$	−1.29846	−	1.31710i	−0.0867569	−	0.0880021i
$225$		−	11.7470i		−	0.783134i
$226$	−8.94045	−	27.6499i	−0.594710	−	1.83924i
$227$			24.0236i			1.59450i	0.603646	+	0.797252i	$0.293714\pi$
$227$			24.0236i			1.59450i	−0.603646	+	0.797252i	$0.706286\pi$
$228$	0.875001	−	1.41878i	0.0579483	−	0.0939609i
$229$	8.24182	+	3.41387i	0.544635	+	0.225595i	0.637999	−	0.770037i	$-0.279762\pi$
$229$	8.24182	+	3.41387i	0.544635	+	0.225595i	−0.0933645	+	0.995632i	$0.529762\pi$
$230$	15.4947	−	30.3031i	1.02169	−	1.99813i
$231$	0.425260	+	0.176148i	0.0279800	+	0.0115897i
$232$	10.4118	+	17.1547i	0.683568	+	1.12626i
$233$	0.101886	−	0.0422027i	0.00667479	−	0.00276479i	−0.379344	−	0.925256i	$-0.623850\pi$
$233$	0.101886	−	0.0422027i	0.00667479	−	0.00276479i	0.386018	+	0.922491i	$0.373850\pi$
$234$	−23.9405	−	12.2413i	−1.56504	−	0.800238i
$235$			9.90569i			0.646176i
$236$	14.3714	+	8.86325i	0.935499	+	0.576948i
$237$	2.77994	+	1.15149i	0.180577	+	0.0747972i
$238$	−0.986256	−	1.63151i	−0.0639295	−	0.105755i
$239$			10.1288i			0.655181i	0.944820	+	0.327590i	$0.106237\pi$
$239$			10.1288i			0.655181i	−0.944820	+	0.327590i	$0.893763\pi$
$240$	−1.82424	−	3.63130i	−0.117754	−	0.234399i
$241$	5.00564	−	12.0847i	0.322442	−	0.778443i	−0.676670	−	0.736287i	$-0.736577\pi$
$241$	5.00564	−	12.0847i	0.322442	−	0.778443i	0.999111	−	0.0421558i	$-0.0134226\pi$
$242$	0.724942	−	9.04642i	0.0466010	−	0.581526i
$243$	−6.11775	+	6.11775i	−0.392454	+	0.392454i
$244$	3.65104	+	0.588939i	0.233734	+	0.0377030i
$245$	−14.6793	+	14.6793i	−0.937825	+	0.937825i
$246$	0.817958	+	2.52968i	0.0521511	+	0.161286i
$247$		−	16.2758i		−	1.03560i
$248$	−15.7831	−	11.5705i	−1.00223	−	0.734726i
$249$	0.330623	−	0.798194i	0.0209524	−	0.0505835i
$250$	−0.316383	+	3.94809i	−0.0200098	+	0.249699i
$251$	−5.88083	−	14.1976i	−0.371195	−	0.896143i	−0.993549	−	0.113407i	$-0.963824\pi$
$251$	−5.88083	−	14.1976i	−0.371195	−	0.896143i	0.622354	−	0.782736i	$-0.286176\pi$
$252$	−0.990696	+	1.60637i	−0.0624080	+	0.101192i
$253$	−12.7624	−	30.8112i	−0.802366	−	1.93708i
$254$	−19.1650	−	22.5041i	−1.20252	−	1.41204i
$255$	−0.958999	−	4.07758i	−0.0600549	−	0.255348i
$256$	12.8362	+	9.55152i	0.802264	+	0.596970i
$257$	16.0697	−	16.0697i	1.00240	−	1.00240i	0.00240333	−	0.999997i	$-0.499235\pi$
$257$	16.0697	−	16.0697i	1.00240	−	1.00240i	0.999997	−	0.00240333i	$-0.000765005\pi$
$258$	1.21795	+	3.76672i	0.0758263	+	0.234506i
$259$	0.202748	+	0.0839811i	0.0125982	+	0.00521833i
$260$	−33.7727	−	20.8286i	−2.09449	−	1.29173i
$261$	14.4794	−	14.4794i	0.896255	−	0.896255i
$262$	−7.70090	−	9.04266i	−0.475763	−	0.558657i
$263$	26.9963			1.66466			0.832331	−	0.554279i	$-0.187006\pi$
$263$	26.9963			1.66466			0.832331	+	0.554279i	$0.187006\pi$
$264$	−3.86795	−	0.946119i	−0.238056	−	0.0582296i
$265$	−4.36008	+	10.5262i	−0.267838	+	0.646617i
$266$	−1.13874	−	0.0912540i	−0.0698208	−	0.00559514i
$267$	−0.609658			−0.0373105
$268$	−3.52236	+	5.71136i	−0.215162	+	0.348877i
$269$	−2.81048	−	2.81048i	−0.171358	−	0.171358i	0.616218	−	0.787576i	$-0.288664\pi$
$269$	−2.81048	−	2.81048i	−0.171358	−	0.171358i	−0.787576	+	0.616218i	$0.788664\pi$
$270$	−6.43861	+	5.48325i	−0.391842	+	0.333700i
$271$			9.81895i			0.596459i	0.954494	+	0.298229i	$0.0963960\pi$
$271$			9.81895i			0.596459i	−0.954494	+	0.298229i	$0.903604\pi$
$272$	10.5809	+	12.6509i	0.641559	+	0.767073i
$273$		−	0.726565i		−	0.0439737i
$274$	9.23374	+	10.8426i	0.557830	+	0.655023i
$275$	−12.0109	−	12.0109i	−0.724285	−	0.724285i
$276$	−5.24594	+	1.24364i	−0.315769	+	0.0748581i
$277$	22.1928			1.33344			0.666718	−	0.745310i	$-0.267699\pi$
$277$	22.1928			1.33344			0.666718	+	0.745310i	$0.267699\pi$
$278$	1.03844	−	12.9585i	0.0622814	−	0.777199i
$279$	−7.64205	+	18.4495i	−0.457518	+	1.10455i
$280$	−1.64664	+	2.24614i	−0.0984053	+	0.134233i
$281$	−7.99546			−0.476969			−0.238484	−	0.971146i	$-0.576651\pi$
$281$	−7.99546			−0.476969			−0.238484	+	0.971146i	$0.576651\pi$
$282$	1.19463	−	1.01737i	0.0711389	−	0.0605833i
$283$	21.8273	−	21.8273i	1.29750	−	1.29750i	0.367459	−	0.930040i	$-0.380228\pi$
$283$	21.8273	−	21.8273i	1.29750	−	1.29750i	0.930040	−	0.367459i	$-0.119772\pi$
$284$	9.73326	−	2.30743i	0.577563	−	0.136921i
$285$	−2.31900	−	0.960560i	−0.137366	−	0.0568987i
$286$	−36.9946	+	11.9620i	−2.18754	+	0.707329i
$287$	1.28840	−	1.28840i	0.0760516	−	0.0760516i
$288$	6.35532	−	15.0391i	0.374491	−	0.886189i
$289$	7.57728	+	15.2179i	0.445722	+	0.895171i
$290$	23.0056	−	19.5920i	1.35093	−	1.15048i
$291$	−1.01415	−	2.44837i	−0.0594505	−	0.143526i
$292$	−1.99616	+	0.473223i	−0.116816	+	0.0276933i
$293$	11.3349	+	27.3648i	0.662190	+	1.59867i	0.794364	+	0.607442i	$0.207804\pi$
$293$	11.3349	+	27.3648i	0.662190	+	1.59867i	−0.132173	+	0.991227i	$0.542196\pi$
$294$	3.27796	+	0.262682i	0.191174	+	0.0153199i
$295$	9.72991	−	23.4901i	0.566498	−	1.36765i
$296$	−1.84410	−	0.451075i	−0.107186	−	0.0262182i
$297$			8.28685i			0.480852i
$298$	13.7600	−	4.44922i	0.797093	−	0.257736i
$299$	−37.2232	+	37.2232i	−2.15267	+	2.15267i
$300$	−2.22612	+	1.60770i	−0.128525	+	0.0928204i
$301$	1.91844	−	1.91844i	0.110577	−	0.110577i
$302$	28.6947	+	2.29947i	1.65119	+	0.132319i
$303$	−1.27917	+	3.08819i	−0.0734863	+	0.177412i
$304$	9.85651	−	0.719218i	0.565309	−	0.0412500i
$305$		−	5.56890i		−	0.318874i
$306$	9.97427	−	13.5551i	0.570191	−	0.774892i
$307$	−4.64801	−	1.92527i	−0.265276	−	0.109881i	0.246081	−	0.969249i	$-0.420857\pi$
$307$	−4.64801	−	1.92527i	−0.265276	−	0.109881i	−0.511357	+	0.859368i	$0.670857\pi$
$308$	0.629509	+	2.65541i	0.0358696	+	0.151306i
$309$		−	1.29421i		−	0.0736253i
$310$	−13.4160	+	26.2379i	−0.761977	+	1.49021i
$311$	−3.43855	+	1.42429i	−0.194982	+	0.0807643i	−0.478038	−	0.878339i	$-0.658652\pi$
$311$	−3.43855	+	1.42429i	−0.194982	+	0.0807643i	0.283056	+	0.959103i	$0.408652\pi$
$312$	0.956709	+	6.21219i	0.0541630	+	0.351696i
$313$	−11.1778	−	4.62998i	−0.631805	−	0.261702i	0.0437150	−	0.999044i	$-0.486081\pi$
$313$	−11.1778	−	4.62998i	−0.631805	−	0.261702i	−0.675520	+	0.737342i	$0.736081\pi$
$314$	18.4062	+	9.41148i	1.03872	+	0.531121i
$315$	2.62562	+	1.08757i	0.147937	+	0.0612775i
$316$	4.11513	+	17.3585i	0.231494	+	0.976494i
$317$			2.95208i			0.165806i	0.996558	+	0.0829028i	$0.0264191\pi$
$317$			2.95208i			0.165806i	−0.996558	+	0.0829028i	$0.973581\pi$
$318$	1.71726	−	0.555267i	0.0962991	−	0.0311378i
$319$		−	29.6094i		−	1.65781i
$320$	11.1212	−	21.3729i	0.621696	−	1.19478i
$321$	0.443620	−	0.443620i	0.0247604	−	0.0247604i
$322$	2.39564	+	2.81304i	0.133504	+	0.156765i
$323$	10.0540	+	1.64013i	0.559418	+	0.0912595i
$324$	−15.7737	−	2.54441i	−0.876315	−	0.141356i
$325$	−10.2604	+	24.7709i	−0.569147	+	1.37404i
$326$	7.32031	+	0.586618i	0.405435	+	0.0324898i
$327$	4.09777	+	4.09777i	0.226607	+	0.226607i
$328$	−9.31938	+	12.7124i	−0.514577	+	0.701924i
$329$	−0.993528	−	0.411533i	−0.0547750	−	0.0226885i
$330$	−0.478972	+	5.97701i	−0.0263665	+	0.329024i
$331$	4.28720	−	10.3502i	0.235646	−	0.568899i	−0.761178	−	0.648543i	$-0.775379\pi$
$331$	4.28720	−	10.3502i	0.235646	−	0.568899i	0.996823	+	0.0796446i	$0.0253785\pi$
$332$	4.98409	−	1.18156i	0.273538	−	0.0648466i
$333$			1.93724i			0.106160i
$334$	19.1857	−	6.20359i	1.04979	−	0.339445i
$335$	9.33524	+	3.86678i	0.510039	+	0.211265i
$336$	0.440003	−	0.0321065i	0.0240041	−	0.00175155i
$337$	4.80695	−	11.6050i	0.261851	−	0.632165i	−0.737202	−	0.675673i	$-0.763853\pi$
$337$	4.80695	−	11.6050i	0.261851	−	0.632165i	0.999053	+	0.0435075i	$0.0138532\pi$
$338$	27.8711	+	32.7272i	1.51599	+	1.78012i
$339$	6.40399	+	2.65262i	0.347817	+	0.144070i
$340$	16.2697	−	18.7633i	0.882346	−	1.01758i
$341$	11.0503	+	26.6777i	0.598406	+	1.44468i
$342$	−3.10264	−	9.59544i	−0.167771	−	0.518862i
$343$	−1.73830	−	4.19662i	−0.0938591	−	0.226596i
$344$	−13.8767	+	18.9289i	−0.748180	+	1.02058i
$345$	3.10679	+	7.50044i	0.167264	+	0.403810i
$346$	−8.49198	−	9.97157i	−0.456532	−	0.536075i
$347$	−15.3379	−	15.3379i	−0.823384	−	0.823384i	0.163208	−	0.986592i	$-0.447816\pi$
$347$	−15.3379	−	15.3379i	−0.823384	−	0.823384i	−0.986592	+	0.163208i	$0.947816\pi$
$348$	−4.72559	−	0.762272i	−0.253318	−	0.0408621i
$349$	22.2688	−	9.22403i	1.19202	−	0.493751i	0.303608	−	0.952797i	$-0.401809\pi$
$349$	22.2688	−	9.22403i	1.19202	−	0.493751i	0.888413	+	0.459046i	$0.151809\pi$
$350$	1.67558	+	0.856761i	0.0895635	+	0.0457958i
$351$	12.0848	−	5.00570i	0.645040	−	0.267185i
$352$	−8.87888	−	21.8751i	−0.473246	−	1.16595i
$353$			22.8085i			1.21397i	0.794713	+	0.606986i	$0.207621\pi$
$353$			22.8085i			1.21397i	−0.794713	+	0.606986i	$0.792379\pi$
$354$	−3.83222	+	1.23913i	−0.203680	+	0.0658589i
$355$	−5.76430	−	13.9162i	−0.305937	−	0.738598i
$356$	−2.11623	−	2.93026i	−0.112160	−	0.155304i
$357$	0.448818	+	0.0732170i	0.0237539	+	0.00387505i
$358$	1.71197	+	5.29457i	0.0904805	+	0.279826i
$359$			1.74995i			0.0923589i	0.998933	+	0.0461795i	$0.0147046\pi$
$359$			1.74995i			0.0923589i	−0.998933	+	0.0461795i	$0.985295\pi$
$360$	−23.8813	−	5.84149i	−1.25866	−	0.307874i
$361$	−9.11867	+	9.11867i	−0.479930	+	0.479930i
$362$	0.195487	+	0.229548i	0.0102746	+	0.0120648i
$363$	1.53074	+	1.53074i	0.0803429	+	0.0803429i
$364$	3.49217	−	2.52203i	0.183039	−	0.132190i
$365$	1.18218	+	2.85403i	0.0618781	+	0.149387i
$366$	−0.671609	+	0.571955i	−0.0351056	+	0.0298966i
$367$	−33.4689	+	13.8633i	−1.74706	+	0.723657i	−0.748925	+	0.662655i	$0.769430\pi$
$367$	−33.4689	+	13.8633i	−1.74706	+	0.723657i	−0.998138	+	0.0610019i	$0.980570\pi$
$368$	−24.1870	−	20.8972i	−1.26083	−	1.08934i
$369$	14.8601	+	6.15525i	0.773586	+	0.320430i
$370$	−0.228356	+	2.84962i	−0.0118717	+	0.148145i
$371$	−0.874621	−	0.874621i	−0.0454080	−	0.0454080i
$372$	4.54218	−	1.07680i	0.235501	−	0.0558294i
$373$	−1.84136	−	4.44544i	−0.0953421	−	0.230176i	0.869012	−	0.494791i	$-0.164755\pi$
$373$	−1.84136	−	4.44544i	−0.0953421	−	0.230176i	−0.964354	+	0.264615i	$0.914755\pi$
$374$	−3.66124	−	24.0579i	−0.189318	−	1.24401i
$375$	−0.668052	−	0.668052i	−0.0344981	−	0.0344981i
$376$	9.03663	+	2.21040i	0.466029	+	0.113993i
$377$	−43.1799	+	17.8857i	−2.22388	+	0.921160i
$378$	−0.282470	−	0.873586i	−0.0145287	−	0.0449324i
$379$			19.9861i			1.02662i	0.858204	+	0.513309i	$0.171580\pi$
$379$			19.9861i			1.02662i	−0.858204	+	0.513309i	$0.828420\pi$
$380$	−3.43280	−	14.4803i	−0.176099	−	0.742824i
$381$	7.05079			0.361223
$382$	−1.13644	+	14.1815i	−0.0581454	+	0.725587i
$383$	−25.0480	−	25.0480i	−1.27989	−	1.27989i	−0.940727	−	0.339165i	$-0.889855\pi$
$383$	−25.0480	−	25.0480i	−1.27989	−	1.27989i	−0.339165	−	0.940727i	$-0.610145\pi$
$384$	−3.71978	+	0.853890i	−0.189824	+	0.0435749i
$385$	3.79661	−	1.57261i	0.193493	−	0.0801474i
$386$	−3.68971	+	1.19305i	−0.187801	+	0.0607246i
$387$	22.1269	+	9.16525i	1.12477	+	0.465896i
$388$	8.24759	−	13.3731i	0.418708	−	0.678918i
$389$	−5.79977	+	14.0019i	−0.294060	+	0.709924i	0.705938	+	0.708273i	$0.250526\pi$
$389$	−5.79977	+	14.0019i	−0.294060	+	0.709924i	−0.999999	+	0.00165094i	$0.999474\pi$
$390$	9.00569	−	2.91194i	0.456021	−	0.147452i
$391$	−19.2427	−	26.7447i	−0.973144	−	1.35254i
$392$	10.1158	+	16.6670i	0.510925	+	0.841811i
$393$	2.83316			0.142914
$394$	−9.46216	−	11.1108i	−0.476697	−	0.559754i
$395$	24.8186	−	10.2802i	1.24876	−	0.517252i
$396$	−19.5300	+	14.1045i	−0.981418	+	0.708777i
$397$	11.9948			0.602002			0.301001	−	0.953624i	$-0.402679\pi$
$397$	11.9948			0.602002			0.301001	+	0.953624i	$0.402679\pi$
$398$	−4.86898	−	15.0581i	−0.244060	−	0.754797i
$399$	0.192686	−	0.192686i	0.00964636	−	0.00964636i
$400$	−15.4545	−	5.11904i	−0.772724	−	0.255952i
$401$	−11.7809	+	4.87982i	−0.588311	+	0.243686i	−0.656924	−	0.753957i	$-0.728143\pi$
$401$	−11.7809	+	4.87982i	−0.588311	+	0.243686i	0.0686128	+	0.997643i	$0.478143\pi$
$402$	−0.492444	−	1.52297i	−0.0245609	−	0.0759587i
$403$	32.2296	−	32.2296i	1.60547	−	1.60547i
$404$	−19.2833	+	4.57142i	−0.959380	+	0.227437i
$405$			24.0594i			1.19552i
$406$	1.00928	+	3.12138i	0.0500899	+	0.154911i
$407$	1.98076	+	1.98076i	0.0981828	+	0.0981828i
$408$	−3.93383	−	0.0350279i	−0.194754	−	0.00173414i
$409$	−12.1682	+	12.1682i	−0.601676	+	0.601676i	−0.940757	−	0.339081i	$-0.889884\pi$
$409$	−12.1682	+	12.1682i	−0.601676	+	0.601676i	0.339081	+	0.940757i	$0.389884\pi$
$410$	21.1332	+	10.8058i	1.04369	+	0.533662i
$411$	−3.39709			−0.167566
$412$	6.22052	−	4.49244i	0.306463	−	0.221327i
$413$	1.95179	+	1.95179i	0.0960415	+	0.0960415i
$414$	−14.8492	+	29.0409i	−0.729800	+	1.42728i
$415$	−2.95171	−	7.12607i	−0.144894	−	0.349805i
$416$	−26.5374	+	26.1619i	−1.30110	+	1.28269i
$417$	2.19270	+	2.19270i	0.107377	+	0.107377i
$418$	−12.9833	−	6.63866i	−0.635036	−	0.324708i
$419$		−	3.29796i		−	0.161116i	−0.996750	−	0.0805579i	$-0.974330\pi$
$419$		−	3.29796i		−	0.161116i	0.996750	−	0.0805579i	$-0.0256702\pi$
$420$	−0.153243	−	0.646413i	−0.00747749	−	0.0315417i
$421$	−3.27737	−	7.91226i	−0.159729	−	0.385620i	0.823672	−	0.567067i	$-0.191922\pi$
$421$	−3.27737	−	7.91226i	−0.159729	−	0.385620i	−0.983401	+	0.181447i	$0.941922\pi$
$422$	1.60792	−	20.0649i	0.0782722	−	0.976745i
$423$		−	9.49307i		−	0.461569i
$424$	8.62974	+	6.32641i	0.419097	+	0.307238i
$425$	−14.2676	−	8.83433i	−0.692082	−	0.428528i
$426$	−1.08627	+	2.12445i	−0.0526302	+	0.102930i
$427$	0.558553	+	0.231360i	0.0270303	+	0.0111963i
$428$	3.67210	+	0.592336i	0.177497	+	0.0286316i
$429$	3.54911	−	8.56832i	0.171353	−	0.413682i
$430$	31.4675	+	16.0900i	1.51750	+	0.775930i
$431$	9.20493	+	22.2227i	0.443386	+	1.07043i	0.974753	+	0.223287i	$0.0716786\pi$
$431$	9.20493	+	22.2227i	0.443386	+	1.07043i	−0.531367	+	0.847142i	$0.678321\pi$
$432$	3.56544	+	7.09729i	0.171542	+	0.341468i
$433$	16.7774	−	16.7774i	0.806269	−	0.806269i	−0.177798	−	0.984067i	$-0.556897\pi$
$433$	16.7774	−	16.7774i	0.806269	−	0.806269i	0.984067	+	0.177798i	$0.0568975\pi$
$434$	−2.07425	−	2.43566i	−0.0995674	−	0.116915i
$435$			7.20790i			0.345592i
$436$	−5.47148	+	33.9196i	−0.262037	+	1.62446i
$437$	−19.7433			−0.944448
$438$	0.222780	−	0.435695i	0.0106448	−	0.0208183i
$439$	−5.57169	−	13.4513i	−0.265922	−	0.641994i	0.733361	−	0.679839i	$-0.237950\pi$
$439$	−5.57169	−	13.4513i	−0.265922	−	0.641994i	−0.999284	+	0.0378456i	$0.987950\pi$
$440$	−30.3905	+	18.4451i	−1.44881	+	0.879336i
$441$	14.0678	−	14.0678i	0.669896	−	0.669896i
$442$	−32.8724	+	19.8715i	−1.56358	+	0.945191i
$443$	−4.33415	+	1.79526i	−0.205922	+	0.0852955i	−0.483260	−	0.875477i	$-0.660548\pi$
$443$	−4.33415	+	1.79526i	−0.205922	+	0.0852955i	0.277339	+	0.960772i	$0.410548\pi$
$444$	0.367118	−	0.265131i	0.0174226	−	0.0125826i
$445$	−3.84869	+	3.84869i	−0.182445	+	0.182445i
$446$	29.4121	−	25.0479i	1.39270	−	1.18605i
$447$	−1.32008	+	3.18694i	−0.0624374	+	0.150737i
$448$	1.68164	+	2.00338i	0.0794501	+	0.0946510i
$449$	11.9472	+	28.8431i	0.563824	+	1.36119i	0.906686	+	0.421806i	$0.138604\pi$
$449$	11.9472	+	28.8431i	0.563824	+	1.36119i	−0.342862	+	0.939386i	$0.611396\pi$
$450$	−1.32702	+	16.5597i	−0.0625565	+	0.780632i
$451$	21.4875	−	8.90040i	1.01180	−	0.419103i
$452$	9.47978	+	39.9878i	0.445891	+	1.88087i
$453$	−4.85540	+	4.85540i	−0.228126	+	0.228126i
$454$	2.71388	−	33.8660i	0.127368	−	1.58941i
$455$	−4.58671	−	4.58671i	−0.215028	−	0.215028i
$456$	−1.39376	+	1.90120i	−0.0652687	+	0.0890318i
$457$	−39.4719			−1.84642			−0.923209	−	0.384297i	$-0.874444\pi$
$457$	−39.4719			−1.84642			−0.923209	+	0.384297i	$0.874444\pi$
$458$	−11.2328	−	5.74357i	−0.524874	−	0.268380i
$459$	1.87434	+	7.96953i	0.0874867	+	0.371986i
$460$	−25.2660	+	40.9678i	−1.17803	+	1.91013i
$461$	17.3982	−	7.20658i	0.810316	−	0.335644i	0.0612361	−	0.998123i	$-0.480496\pi$
$461$	17.3982	−	7.20658i	0.810316	−	0.335644i	0.749080	+	0.662479i	$0.230496\pi$
$462$	−0.579587	−	0.296356i	−0.0269648	−	0.0137877i
$463$	−14.3521			−0.666998			−0.333499	−	0.942750i	$-0.608229\pi$
$463$	−14.3521			−0.666998			−0.333499	+	0.942750i	$0.608229\pi$
$464$	−12.7395	−	25.3591i	−0.591418	−	1.17727i
$465$	−2.69000	−	6.49423i	−0.124746	−	0.301163i
$466$	−0.148396	+	0.0479831i	−0.00687431	+	0.00222277i
$467$	−13.6431	−	32.9373i	−0.631326	−	1.52416i	−0.837956	−	0.545737i	$-0.816250\pi$
$467$	−13.6431	−	32.9373i	−0.631326	−	1.52416i	0.206630	−	0.978419i	$-0.433750\pi$
$468$	32.3659	+	19.9610i	1.49612	+	0.922696i
$469$	−0.775666	+	0.775666i	−0.0358169	+	0.0358169i
$470$	1.11902	−	13.9640i	0.0516163	−	0.644111i
$471$	−4.55578	+	1.88707i	−0.209919	+	0.0869515i
$472$	−19.2580	−	14.1180i	−0.886423	−	0.649832i
$473$	31.9951	−	13.2528i	1.47114	−	0.609364i
$474$	−3.78879	−	1.93729i	−0.174025	−	0.0889826i
$475$	−9.29035	+	3.84819i	−0.426270	+	0.176567i
$476$	1.20601	+	2.41135i	0.0552775	+	0.110524i
$477$	4.17846	−	10.0877i	0.191319	−	0.461884i
$478$	1.14422	−	14.2786i	0.0523356	−	0.653087i
$479$	−12.0682	−	4.99882i	−0.551411	−	0.228402i	0.0895404	−	0.995983i	$-0.471460\pi$
$479$	−12.0682	−	4.99882i	−0.551411	−	0.228402i	−0.640952	+	0.767581i	$0.721460\pi$
$480$	2.16141	+	5.32510i	0.0986543	+	0.243057i
$481$	1.69209	−	4.08506i	0.0771526	−	0.186263i
$482$	−8.42159	+	16.4702i	−0.383593	+	0.750199i
$483$	−0.881356			−0.0401031
$484$	−2.04389	+	12.6708i	−0.0929042	+	0.575945i
$485$	−21.8584	−	9.05406i	−0.992540	−	0.411123i
$486$	9.31527	−	7.93306i	0.422549	−	0.359851i
$487$	−3.38513	+	8.17242i	−0.153395	+	0.370328i	−0.981831	−	0.189755i	$-0.939231\pi$
$487$	−3.38513	+	8.17242i	−0.153395	+	0.370328i	0.828437	+	0.560083i	$0.189231\pi$
$488$	−5.08032	−	1.24267i	−0.229975	−	0.0562530i
$489$	−1.23866	+	1.23866i	−0.0560143	+	0.0560143i
$490$	22.3516	−	19.0350i	1.00974	−	0.859915i
$491$	13.5248	+	5.60214i	0.610364	+	0.252821i	0.666384	−	0.745609i	$-0.267841\pi$
$491$	13.5248	+	5.60214i	0.610364	+	0.252821i	−0.0560204	+	0.998430i	$0.517841\pi$
$492$	−0.867302	−	3.65847i	−0.0391010	−	0.164937i
$493$	−6.69714	−	28.4757i	−0.301624	−	1.28248i
$494$	−1.83863	+	22.9439i	−0.0827237	+	1.03229i
$495$	25.6512	+	25.6512i	1.15293	+	1.15293i
$496$	20.9422	+	18.0938i	0.940333	+	0.812435i
$497$	1.63526			0.0733514
$498$	−0.556247	+	1.08786i	−0.0249260	+	0.0487482i
$499$	−43.4258			−1.94401			−0.972003	−	0.234969i	$-0.924501\pi$
$499$	−43.4258			−1.94401			−0.972003	+	0.234969i	$0.924501\pi$
$500$	0.892006	−	5.52985i	0.0398917	−	0.247303i
$501$	−1.84060	+	4.44359i	−0.0822318	+	0.198525i
$502$	6.68632	+	20.6786i	0.298425	+	0.922931i
$503$	−11.8762	+	28.6716i	−0.529532	+	1.27840i	0.402298	+	0.915509i	$0.368212\pi$
$503$	−11.8762	+	28.6716i	−0.529532	+	1.27840i	−0.931830	+	0.362895i	$0.881788\pi$
$504$	1.57805	−	2.15258i	0.0702917	−	0.0958836i
$505$	11.4201	+	27.5705i	0.508187	+	1.22687i
$506$	14.5105	+	44.8761i	0.645069	+	1.99499i
$507$	−10.2538			−0.455386
$508$	24.4745	+	33.8890i	1.08588	+	1.50358i
$509$	4.45116	−	10.7460i	0.197294	−	0.476310i	−0.794009	−	0.607906i	$-0.792010\pi$
$509$	4.45116	−	10.7460i	0.197294	−	0.476310i	0.991304	+	0.131595i	$0.0420099\pi$
$510$	0.891265	+	5.85648i	0.0394659	+	0.259329i
$511$	−0.335369			−0.0148359
$512$	−17.0161	−	14.9148i	−0.752014	−	0.659147i
$513$	4.53242	+	1.87739i	0.200111	+	0.0828889i
$514$	−24.4687	+	20.8380i	−1.07927	+	0.919126i
$515$	−8.17019	−	8.17019i	−0.360022	−	0.360022i
$516$	−1.29142	−	5.44751i	−0.0568517	−	0.239813i
$517$	−9.70633	−	9.70633i	−0.426884	−	0.426884i
$518$	−0.276326	−	0.141292i	−0.0121411	−	0.00620800i
$519$	3.12420			0.137137
$520$	45.2563	+	33.1771i	1.98462	+	1.45491i
$521$	15.1133	+	6.26015i	0.662128	+	0.274262i	0.688334	−	0.725394i	$-0.258343\pi$
$521$	15.1133	+	6.26015i	0.662128	+	0.274262i	−0.0262059	+	0.999657i	$0.508343\pi$
$522$	−22.0473	+	18.7759i	−0.964984	+	0.821799i
$523$	25.1921	−	10.4349i	1.10158	−	0.456287i	0.243547	−	0.969889i	$-0.421689\pi$
$523$	25.1921	−	10.4349i	1.10158	−	0.456287i	0.858029	+	0.513602i	$0.171689\pi$
$524$	9.83440	+	13.6173i	0.429618	+	0.594876i
$525$	−0.414729	+	0.171786i	−0.0181003	+	0.00749737i
$526$	−38.0565	−	3.04969i	−1.65934	−	0.132973i
$527$	16.6612	+	23.1568i	0.725773	+	1.00873i
$528$	5.34575	+	1.77069i	0.232644	+	0.0770593i
$529$	28.8900	+	28.8900i	1.25608	+	1.25608i
$530$	7.33549	−	14.3461i	0.318633	−	0.623156i
$531$	−9.32462	+	22.5116i	−0.404654	+	0.976921i
$532$	1.59497	+	0.257281i	0.0691508	+	0.0111545i
$533$	−25.9592	−	25.9592i	−1.12442	−	1.12442i
$534$	0.859431	+	0.0688711i	0.0371912	+	0.00298035i
$535$		−	5.60102i		−	0.242153i
$536$	5.61064	−	7.65337i	0.242343	−	0.330575i
$537$	−1.22627	−	0.507939i	−0.0529176	−	0.0219192i
$538$	3.64443	+	4.27942i	0.157123	+	0.184499i
$539$		−	28.7677i		−	1.23911i
$540$	9.69590	−	7.00235i	0.417245	−	0.301333i
$541$	−3.27318	+	3.27318i	−0.140725	+	0.140725i	−0.773960	−	0.633235i	$-0.781727\pi$
$541$	−3.27318	+	3.27318i	−0.140725	+	0.140725i	0.633235	+	0.773960i	$0.281727\pi$
$542$	1.10922	−	13.8417i	0.0476449	−	0.594553i
$543$	−0.0719198			−0.00308638
$544$	−13.4867	−	19.0292i	−0.578236	−	0.815870i
$545$	51.7373			2.21618
$546$	−0.0820778	+	1.02424i	−0.00351261	+	0.0438332i
$547$	−17.3978	+	17.3978i	−0.743877	+	0.743877i	−0.973322	−	0.229445i	$-0.926309\pi$
$547$	−17.3978	+	17.3978i	−0.743877	+	0.743877i	0.229445	+	0.973322i	$0.426309\pi$
$548$	−11.7919	−	16.3278i	−0.503725	−	0.697489i
$549$			5.33693i			0.227774i
$550$	15.5749	+	18.2885i	0.664115	+	0.779826i
$551$	−16.1946	−	6.70804i	−0.689915	−	0.285772i
$552$	7.53566	−	1.16053i	0.320739	−	0.0493955i
$553$			2.91636i			0.124016i
$554$	−31.2850	−	2.50705i	−1.32917	−	0.106514i
$555$	−0.482182	−	0.482182i	−0.0204675	−	0.0204675i
$556$	−2.92776	+	18.1502i	−0.124165	+	0.769741i
$557$	−12.1474	+	29.3263i	−0.514700	+	1.24260i	0.426420	+	0.904525i	$0.359775\pi$
$557$	−12.1474	+	29.3263i	−0.514700	+	1.24260i	−0.941120	+	0.338071i	$0.890225\pi$
$558$	12.8571	−	25.1449i	0.544286	−	1.06447i
$559$	−38.6535	−	38.6535i	−1.63487	−	1.63487i
$560$	2.57499	−	2.98036i	0.108813	−	0.125943i
$561$	4.93521	+	3.05582i	0.208365	+	0.129017i
$562$	11.2711	+	0.903221i	0.475445	+	0.0381001i
$563$	−7.30182	+	3.02451i	−0.307735	+	0.127468i	−0.531206	−	0.847243i	$-0.678261\pi$
$563$	−7.30182	+	3.02451i	−0.307735	+	0.127468i	0.223471	+	0.974710i	$0.428261\pi$
$564$	−1.79899	+	1.29922i	−0.0757510	+	0.0547071i
$565$	57.1731	−	23.6819i	2.40529	−	0.996303i
$566$	−33.2356	+	28.3041i	−1.39700	+	1.18971i
$567$	−2.41313	−	0.999551i	−0.101342	−	0.0419772i
$568$	−13.9816	+	2.15324i	−0.586655	+	0.0903478i
$569$	24.2471			1.01649			0.508246	−	0.861212i	$-0.330294\pi$
$569$	24.2471			1.01649			0.508246	+	0.861212i	$0.330294\pi$
$570$	3.16057	+	1.61607i	0.132382	+	0.0676896i
$571$	−22.5580	−	22.5580i	−0.944023	−	0.944023i	0.0544908	−	0.998514i	$-0.482646\pi$
$571$	−22.5580	−	22.5580i	−0.944023	−	0.944023i	−0.998514	+	0.0544908i	$0.982646\pi$
$572$	53.5024	−	12.6836i	2.23705	−	0.530329i
$573$	−2.39963	−	2.39963i	−0.100246	−	0.100246i
$574$	−1.96179	+	1.67070i	−0.0818835	+	0.0697336i
$575$	30.0482	+	12.4464i	1.25310	+	0.519050i
$576$	−10.6580	+	20.4826i	−0.444083	+	0.853443i
$577$	−0.0537083			−0.00223591			−0.00111795	−	0.999999i	$-0.500356\pi$
$577$	−0.0537083			−0.00223591			−0.00111795	+	0.999999i	$0.500356\pi$
$578$	−8.96253	−	22.3086i	−0.372792	−	0.927915i
$579$	0.353976	−	0.854574i	0.0147107	−	0.0355149i
$580$	−34.6441	+	25.0199i	−1.43852	+	1.03889i
$581$	0.837364			0.0347397
$582$	1.15306	+	3.56602i	0.0477957	+	0.147816i
$583$	−6.04199	−	14.5867i	−0.250234	−	0.604117i
$584$	2.86743	−	0.441599i	0.118655	−	0.0182735i
$585$	21.9128	−	52.9022i	0.905983	−	2.18724i
$586$	−12.8874	−	39.8565i	−0.532373	−	1.64646i
$587$	−12.8400	+	30.9986i	−0.529965	+	1.27945i	0.401581	+	0.915824i	$0.368461\pi$
$587$	−12.8400	+	30.9986i	−0.529965	+	1.27945i	−0.931546	+	0.363625i	$0.881539\pi$
$588$	−4.59125	−	0.740601i	−0.189340	−	0.0305419i
$589$	17.0946			0.704372
$590$	−16.3698	+	32.0147i	−0.673934	+	1.31802i
$591$	3.48113			0.143195
$592$	2.54866	+	0.844200i	0.104749	+	0.0346964i
$593$	7.75464	+	7.75464i	0.318445	+	0.318445i	0.848170	−	0.529725i	$-0.177705\pi$
$593$	7.75464	+	7.75464i	0.318445	+	0.318445i	−0.529725	+	0.848170i	$0.677705\pi$
$594$	0.936139	−	11.6819i	0.0384103	−	0.479315i
$595$	3.29553	−	2.37111i	0.135104	−	0.0972062i
$596$	−19.9000	+	4.71761i	−0.815134	+	0.193241i
$597$	3.48762	+	1.44462i	0.142739	+	0.0591243i
$598$	56.6783	−	48.2684i	2.31775	−	1.97384i
$599$	28.4941	−	28.4941i	1.16424	−	1.16424i	0.180700	−	0.983538i	$-0.442164\pi$
$599$	28.4941	−	28.4941i	1.16424	−	1.16424i	0.983538	−	0.180700i	$-0.0578364\pi$
$600$	3.31976	−	2.01488i	0.135529	−	0.0822573i
$601$	2.81139	−	6.78729i	0.114679	−	0.276859i	−0.856110	−	0.516793i	$-0.827126\pi$
$601$	2.81139	−	6.78729i	0.114679	−	0.276859i	0.970789	+	0.239934i	$0.0771257\pi$
$602$	−2.92113	+	2.48769i	−0.119056	+	0.101391i
$603$	−8.94638	−	3.70571i	−0.364325	−	0.150908i
$604$	−40.1909	−	6.48309i	−1.63535	−	0.263793i
$605$	19.3267			0.785741
$606$	2.15210	−	4.20890i	0.0874231	−	0.170975i
$607$	−9.37231	+	22.6267i	−0.380410	+	0.918391i	0.611476	+	0.791263i	$0.290576\pi$
$607$	−9.37231	+	22.6267i	−0.380410	+	0.918391i	−0.991886	+	0.127128i	$0.959424\pi$
$608$	−13.9759	−	0.0995805i	−0.566798	−	0.00403852i
$609$	−0.722943	−	0.299453i	−0.0292951	−	0.0121344i
$610$	−0.629101	+	7.85044i	−0.0254715	+	0.317855i
$611$	−8.29174	+	20.0180i	−0.335448	+	0.809843i
$612$	−15.5919	+	17.9817i	−0.630267	+	0.726869i
$613$	27.4614	−	11.3749i	1.10916	−	0.459427i	0.248509	−	0.968630i	$-0.420060\pi$
$613$	27.4614	−	11.3749i	1.10916	−	0.459427i	0.860647	+	0.509202i	$0.170060\pi$
$614$	6.33479	+	3.23911i	0.255651	+	0.130720i
$615$	−5.23074	+	2.16665i	−0.210924	+	0.0873676i
$616$	−0.587442	−	3.81443i	−0.0236687	−	0.153688i
$617$	−4.61029	+	1.90965i	−0.185603	+	0.0768795i	−0.473550	−	0.880767i	$-0.657028\pi$
$617$	−4.61029	+	1.90965i	−0.185603	+	0.0768795i	0.287946	+	0.957647i	$0.407028\pi$
$618$	−0.146203	+	1.82445i	−0.00588116	+	0.0733900i
$619$	5.71036	−	5.71036i	0.229519	−	0.229519i	−0.582973	−	0.812492i	$-0.698111\pi$
$619$	5.71036	−	5.71036i	0.229519	−	0.229519i	0.812492	+	0.582973i	$0.198111\pi$
$620$	21.8765	−	35.4718i	0.878579	−	1.42458i
$621$	−6.07214	−	14.6594i	−0.243666	−	0.588263i
$622$	5.00820	−	1.61938i	0.200811	−	0.0649311i
$623$	−0.226124	−	0.545912i	−0.00905947	−	0.0218715i
$624$	−0.646896	−	8.86537i	−0.0258966	−	0.354899i
$625$	−28.7849			−1.15140
$626$	15.2342	+	7.78958i	0.608881	+	0.311334i
$627$	3.21355	−	1.33110i	0.128337	−	0.0531589i
$628$	−24.8839	−	15.3466i	−0.992976	−	0.612396i
$629$	2.35293	+	1.45690i	0.0938175	+	0.0580905i
$630$	−3.57847	−	1.82975i	−0.142569	−	0.0728989i
$631$	6.52980			0.259947			0.129974	−	0.991517i	$-0.458511\pi$
$631$	6.52980			0.259947			0.129974	+	0.991517i	$0.458511\pi$
$632$	−3.84013	−	24.9351i	−0.152752	−	0.991865i
$633$	3.39517	+	3.39517i	0.134946	+	0.134946i
$634$	0.333488	−	4.16154i	0.0132445	−	0.165276i
$635$	44.5107	−	44.5107i	1.76635	−	1.76635i
$636$	−2.48354	+	0.588763i	−0.0984786	+	0.0233460i
$637$	−41.9523	+	17.3772i	−1.66221	+	0.688511i
$638$	−3.34489	+	41.7403i	−0.132425	+	1.65251i
$639$	5.52419	+	13.3366i	0.218533	+	0.527586i
$640$	−18.0920	+	28.8730i	−0.715148	+	1.14130i
$641$	5.31742	−	12.8374i	0.210026	−	0.507047i	−0.783401	−	0.621516i	$-0.786517\pi$
$641$	5.31742	−	12.8374i	0.210026	−	0.507047i	0.993427	+	0.114470i	$0.0365169\pi$
$642$	−0.675482	+	0.575254i	−0.0266592	+	0.0227035i
$643$	−7.16274	+	7.16274i	−0.282471	+	0.282471i	−0.834094	−	0.551623i	$-0.814009\pi$
$643$	−7.16274	+	7.16274i	−0.282471	+	0.282471i	0.551623	+	0.834094i	$0.314009\pi$
$644$	−3.05934	−	4.23615i	−0.120555	−	0.166928i
$645$	−7.78864	+	3.22616i	−0.306678	+	0.127030i
$646$	−13.9877	−	3.44785i	−0.550340	−	0.135654i
$647$	−6.65497	+	6.65497i	−0.261634	+	0.261634i	−0.825718	−	0.564084i	$-0.809229\pi$
$647$	−6.65497	+	6.65497i	−0.261634	+	0.261634i	0.564084	+	0.825718i	$0.309229\pi$
$648$	21.9486	+	5.36874i	0.862223	+	0.210904i
$649$	13.4832	+	32.5514i	0.529264	+	1.27776i
$650$	17.2624	−	33.7603i	0.677086	−	1.32419i
$651$	0.763119			0.0299090
$652$	−10.2531	−	1.65391i	−0.401544	−	0.0647719i
$653$		−	12.1973i		−	0.477318i	−0.971103	−	0.238659i	$-0.923292\pi$
$653$		−	12.1973i		−	0.477318i	0.971103	−	0.238659i	$-0.0767079\pi$
$654$	−5.31369	−	6.23952i	−0.207782	−	0.243985i
$655$	17.8854	−	17.8854i	0.698839	−	0.698839i
$656$	14.5736	−	16.8678i	0.569002	−	0.658577i
$657$	−1.13294	−	2.73515i	−0.0442000	−	0.106708i
$658$	1.35408	+	0.692371i	0.0527876	+	0.0269914i
$659$	8.34541	−	20.1476i	0.325091	−	0.784839i	−0.673852	−	0.738867i	$-0.735361\pi$
$659$	8.34541	−	20.1476i	0.325091	−	0.784839i	0.998943	−	0.0459724i	$-0.0146386\pi$
$660$	1.35041	−	8.37165i	0.0525646	−	0.325866i
$661$	0.232076	+	0.0961288i	0.00902669	+	0.00373898i	0.387192	−	0.921999i	$-0.373445\pi$
$661$	0.232076	+	0.0961288i	0.00902669	+	0.00373898i	−0.378166	+	0.925738i	$0.623445\pi$
$662$	−7.21287	+	14.1063i	−0.280336	+	0.548258i
$663$	1.47521	−	9.04297i	0.0572923	−	0.351200i
$664$	−7.15953	+	1.10260i	−0.277844	+	0.0427893i
$665$		−	2.43280i		−	0.0943398i
$666$	0.218844	−	2.73092i	0.00848004	−	0.105821i
$667$	21.6961	+	52.3791i	0.840078	+	2.02813i
$668$	−27.7467	+	6.57782i	−1.07355	+	0.254504i
$669$			9.21513i			0.356277i
$670$	−12.7230	−	6.50555i	−0.491533	−	0.251331i
$671$	5.45682	+	5.45682i	0.210658	+	0.210658i
$672$	−0.623896	−	0.00444536i	−0.0240673	−	0.000171483i
$673$	−12.2248	−	29.5132i	−0.471230	−	1.13765i	−0.963620	−	0.267275i	$-0.913877\pi$
$673$	−12.2248	−	29.5132i	−0.471230	−	1.13765i	0.492391	−	0.870374i	$-0.336123\pi$
$674$	−8.08732	+	15.8165i	−0.311512	+	0.609229i
$675$	−5.71458	−	5.71458i	−0.219954	−	0.219954i
$676$	−35.5926	−	49.2838i	−1.36895	−	1.89553i
$677$	−23.1674			−0.890397			−0.445198	−	0.895432i	$-0.646867\pi$
$677$	−23.1674			−0.890397			−0.445198	+	0.895432i	$0.646867\pi$
$678$	−8.72800	−	4.46282i	−0.335197	−	0.171394i
$679$	1.81622	−	1.81622i	0.0697001	−	0.0697001i
$680$	−25.0549	+	24.6126i	−0.960810	+	0.943851i
$681$	5.73044	+	5.73044i	0.219591	+	0.219591i
$682$	−12.5638	−	38.8558i	−0.481094	−	1.48786i
$683$		−	34.3974i		−	1.31618i	−0.752940	−	0.658090i	$-0.771365\pi$
$683$		−	34.3974i		−	1.31618i	0.752940	−	0.658090i	$-0.228635\pi$
$684$	3.28981	+	13.8771i	0.125789	+	0.530606i
$685$	−21.4454	+	21.4454i	−0.819386	+	0.819386i
$686$	1.97639	+	6.11232i	0.0754588	+	0.233369i
$687$	2.78027	−	1.15163i	0.106074	−	0.0439373i
$688$	21.7002	−	25.1164i	0.827313	−	0.957552i
$689$	−17.6222	+	17.6222i	−0.671354	+	0.671354i
$690$	−3.53232	−	10.9243i	−0.134473	−	0.415881i
$691$	−8.49081			−0.323006			−0.161503	−	0.986872i	$-0.551634\pi$
$691$	−8.49081			−0.323006			−0.161503	+	0.986872i	$0.551634\pi$
$692$	10.8446	+	15.0162i	0.412251	+	0.570830i
$693$	−3.63846	+	1.50710i	−0.138214	+	0.0572500i
$694$	19.8891	+	23.3545i	0.754981	+	0.886524i
$695$	27.6844			1.05013
$696$	6.57552	+	1.60840i	0.249245	+	0.0609664i
$697$	18.6516	−	13.4197i	0.706478	−	0.508306i
$698$	−32.4342	+	10.4874i	−1.22765	+	0.396955i
$699$	0.0142365	−	0.0343700i	0.000538474	−	0.00129999i
$700$	−2.26527	−	1.39706i	−0.0856192	−	0.0528037i
$701$	14.5601	+	6.03100i	0.549928	+	0.227788i	0.640306	−	0.768120i	$-0.278807\pi$
$701$	14.5601	+	6.03100i	0.549928	+	0.227788i	−0.0903779	+	0.995908i	$0.528807\pi$
$702$	−17.6014	+	5.69132i	−0.664322	+	0.214805i
$703$	1.53211	−	0.634619i	0.0577845	−	0.0239351i
$704$	10.0454	+	31.8402i	0.378599	+	1.20002i
$705$	2.36284	+	2.36284i	0.0889896	+	0.0889896i
$706$	2.57660	−	32.1529i	0.0969716	−	1.21009i
$707$	−3.23973			−0.121843
$708$	5.54224	−	1.31388i	0.208290	−	0.0493786i
$709$		−	17.7713i		−	0.667415i	−0.942677	−	0.333708i	$-0.891700\pi$
$709$		−	17.7713i		−	0.667415i	0.942677	−	0.333708i	$-0.108300\pi$
$710$	6.55382	+	20.2688i	0.245961	+	0.760676i
$711$	−23.7848	+	9.85197i	−0.891998	+	0.369478i
$712$	2.65221	+	4.36984i	0.0993958	+	0.163767i
$713$	−39.0959	−	39.0959i	−1.46415	−	1.46415i
$714$	−0.624424	−	0.153915i	−0.0233685	−	0.00576013i
$715$	−31.6855	−	76.4957i	−1.18497	−	2.86078i
$716$	−1.81525	−	7.65712i	−0.0678389	−	0.286160i
$717$	2.41607	+	2.41607i	0.0902296	+	0.0902296i
$718$	0.197687	−	2.46690i	0.00737760	−	0.0920638i
$719$	29.1566	+	12.0771i	1.08736	+	0.450399i	0.853085	−	0.521772i	$-0.174729\pi$
$719$	29.1566	+	12.0771i	1.08736	+	0.450399i	0.234274	+	0.972171i	$0.424729\pi$
$720$	33.0055	+	10.9325i	1.23004	+	0.407431i
$721$	1.15889	−	0.480028i	0.0431593	−	0.0178772i
$722$	13.8846	−	11.8244i	0.516733	−	0.440060i
$723$	−1.68859	−	4.07661i	−0.0627992	−	0.151611i
$724$	−0.249646	−	0.345676i	−0.00927803	−	0.0128469i
$725$	20.4186	+	20.4186i	0.758327	+	0.758327i
$726$	−1.98495	−	2.33079i	−0.0736684	−	0.0865039i
$727$	−6.77704	+	6.77704i	−0.251346	+	0.251346i	−0.821523	−	0.570176i	$-0.806875\pi$
$727$	−6.77704	+	6.77704i	−0.251346	+	0.251346i	0.570176	+	0.821523i	$0.306875\pi$
$728$	−5.20780	+	3.16080i	−0.193014	+	0.117147i
$729$		−	21.0478i		−	0.779547i
$730$	−1.34410	−	4.15686i	−0.0497474	−	0.153852i
$731$	27.7724	−	19.9821i	1.02720	−	0.739063i
$732$	1.01138	−	0.730412i	0.0373815	−	0.0269968i
$733$	−11.8328	−	28.5669i	−0.437055	−	1.05514i	−0.976961	−	0.213418i	$-0.931540\pi$
$733$	−11.8328	−	28.5669i	−0.437055	−	1.05514i	0.539906	−	0.841725i	$-0.318460\pi$
$734$	48.7470	−	15.7621i	1.79929	−	0.581790i
$735$			7.00299i			0.258309i
$736$	31.7356	+	32.1911i	1.16979	+	1.18658i
$737$	−12.9363	+	5.35840i	−0.476515	+	0.197379i
$738$	−20.2529	−	10.3557i	−0.745518	−	0.381200i
$739$	−12.4515	+	5.15760i	−0.458038	+	0.189725i	−0.599758	−	0.800181i	$-0.704737\pi$
$739$	−12.4515	+	5.15760i	−0.458038	+	0.189725i	0.141721	+	0.989907i	$0.454737\pi$
$740$	0.643826	−	3.99130i	0.0236675	−	0.146723i
$741$	−3.88232	−	3.88232i	−0.142620	−	0.142620i
$742$	1.13414	+	1.33175i	0.0416358	+	0.0488901i
$743$	10.8053	+	26.0864i	0.396410	+	0.957017i	0.988510	+	0.151153i	$0.0482987\pi$
$743$	10.8053	+	26.0864i	0.396410	+	0.957017i	−0.592101	+	0.805864i	$0.701701\pi$
$744$	−6.52472	+	1.00484i	−0.239208	+	0.0368393i
$745$	11.7853	+	28.4522i	0.431779	+	1.04241i
$746$	2.09357	+	6.47472i	0.0766510	+	0.237057i
$747$	2.82876	+	6.82923i	0.103499	+	0.249868i
$748$	2.44348	+	34.3279i	0.0893426	+	1.25515i
$749$	0.561774	+	0.232695i	0.0205268	+	0.00850248i
$750$	0.866282	+	1.01722i	0.0316321	+	0.0371435i
$751$	−15.8113	+	38.1719i	−0.576964	+	1.39291i	0.318562	+	0.947902i	$0.396800\pi$
$751$	−15.8113	+	38.1719i	−0.576964	+	1.39291i	−0.895525	+	0.445011i	$0.853200\pi$
$752$	−12.4892	−	4.13683i	−0.455434	−	0.150855i
$753$	−4.78937	−	1.98382i	−0.174534	−	0.0722944i
$754$	62.8909	−	20.3355i	2.29035	−	0.740574i
$755$			61.3029i			2.23104i
$756$	0.299510	+	1.26340i	0.0108931	+	0.0459494i
$757$	−0.248136	+	0.599054i	−0.00901867	+	0.0217730i	−0.928325	−	0.371770i	$-0.878751\pi$
$757$	−0.248136	+	0.599054i	−0.00901867	+	0.0217730i	0.919306	+	0.393543i	$0.128751\pi$
$758$	2.25777	−	28.1743i	0.0820058	−	1.02334i
$759$	−10.3937	−	4.30523i	−0.377269	−	0.156270i
$760$	3.20340	+	20.8006i	0.116200	+	0.754517i
$761$	−12.1383	−	12.1383i	−0.440014	−	0.440014i	0.452002	−	0.892017i	$-0.350710\pi$
$761$	−12.1383	−	12.1383i	−0.440014	−	0.440014i	−0.892017	+	0.452002i	$0.850710\pi$
$762$	−9.93947	−	0.796506i	−0.360069	−	0.0288544i
$763$	−2.14943	+	5.18919i	−0.0778146	+	0.187861i
$764$	3.20407	−	19.8632i	0.115919	−	0.718624i
$765$	30.4708	+	18.8671i	1.10167	+	0.682142i
$766$	32.4804	+	38.1396i	1.17356	+	1.37804i
$767$	39.3256	−	39.3256i	1.41997	−	1.41997i
$768$	5.34022	−	0.783511i	0.192699	−	0.0282725i
$769$		−	27.4804i		−	0.990968i	−0.868617	−	0.495484i	$-0.834991\pi$
$769$		−	27.4804i		−	0.990968i	0.868617	−	0.495484i	$-0.165009\pi$
$770$	−5.52971	+	1.78800i	−0.199277	+	0.0644351i
$771$		−	7.66631i		−	0.276096i
$772$	5.33614	−	1.26502i	0.192052	−	0.0455291i
$773$	14.5662	+	6.03350i	0.523908	+	0.217010i	0.628933	−	0.777460i	$-0.283492\pi$
$773$	14.5662	+	6.03350i	0.523908	+	0.217010i	−0.105024	+	0.994470i	$0.533492\pi$
$774$	−30.1568	−	15.4198i	−1.08396	−	0.554253i
$775$	−26.0171	−	10.7766i	−0.934563	−	0.387108i
$776$	−13.1373	+	17.9203i	−0.471602	+	0.643303i
$777$	0.0683945	−	0.0283299i	0.00245364	−	0.00101633i
$778$	9.75766	−	19.0832i	0.349829	−	0.684166i
$779$		−	13.7688i		−	0.493318i
$780$	−13.0242	+	3.08761i	−0.466342	+	0.110554i
$781$	19.2845	+	7.98788i	0.690052	+	0.285829i
$782$	24.1050	+	39.8757i	0.861994	+	1.42595i
$783$		−	14.0877i		−	0.503452i
$784$	−12.3774	−	24.6381i	−0.442049	−	0.879934i
$785$	−16.8472	+	40.6728i	−0.601303	+	1.45167i
$786$	−3.99389	−	0.320054i	−0.142457	−	0.0114159i
$787$	−2.43132	+	2.43132i	−0.0866672	+	0.0866672i	−0.749111	−	0.662444i	$-0.769519\pi$
$787$	−2.43132	+	2.43132i	−0.0866672	+	0.0866672i	0.662444	+	0.749111i	$0.269519\pi$
$788$	12.0836	+	16.7317i	0.430461	+	0.596043i
$789$	6.43951	−	6.43951i	0.229253	−	0.229253i
$790$	−36.1479	+	11.6882i	−1.28609	+	0.415849i
$791$			6.71825i			0.238873i
$792$	29.1246	−	17.6768i	1.03490	−	0.628117i
$793$	4.66155	−	11.2540i	0.165536	−	0.399640i
$794$	−16.9090	−	1.35502i	−0.600078	−	0.0480877i
$795$	1.47082	+	3.55086i	0.0521645	+	0.125936i
$796$	5.16270	+	21.7774i	0.182987	+	0.771880i
$797$	−10.7591	−	25.9747i	−0.381106	−	0.920071i	−0.991752	−	0.128168i	$-0.959090\pi$
$797$	−10.7591	−	25.9747i	−0.381106	−	0.920071i	0.610646	−	0.791903i	$-0.290910\pi$
$798$	−0.293395	+	0.249861i	−0.0103861	+	0.00884498i
$799$	−11.5301	−	7.13926i	−0.407904	−	0.252569i
$800$	21.2078	+	8.96213i	0.749810	+	0.316859i
$801$	3.68837	−	3.68837i	0.130322	−	0.130322i
$802$	17.1588	−	5.54820i	0.605897	−	0.195914i
$803$	−3.95498	−	1.63821i	−0.139568	−	0.0578110i
$804$	0.522151	+	2.20255i	0.0184148	+	0.0776779i
$805$	−5.56388	+	5.56388i	−0.196101	+	0.196101i
$806$	−49.0747	+	41.7930i	−1.72858	+	1.47209i
$807$	−1.34079			−0.0471980
$808$	27.7000	−	4.26594i	0.974481	−	0.150075i
$809$	6.88336	−	16.6179i	0.242006	−	0.584254i	−0.755476	−	0.655177i	$-0.772594\pi$
$809$	6.88336	−	16.6179i	0.242006	−	0.584254i	0.997482	+	0.0709223i	$0.0225942\pi$
$810$	2.71792	−	33.9165i	0.0954980	−	1.19170i
$811$	−17.5365			−0.615791			−0.307896	−	0.951420i	$-0.599625\pi$
$811$	−17.5365			−0.615791			−0.307896	+	0.951420i	$0.599625\pi$
$812$	−1.07017	−	4.51421i	−0.0375555	−	0.158418i
$813$	2.34215	+	2.34215i	0.0821426	+	0.0821426i
$814$	−2.56851	−	3.01603i	−0.0900262	−	0.105712i
$815$			15.6390i			0.547811i
$816$	5.54155	+	0.493771i	0.193993	+	0.0172855i
$817$		−	20.5019i		−	0.717270i
$818$	18.5280	−	15.7788i	0.647816	−	0.551692i
$819$	4.39565	+	4.39565i	0.153596	+	0.153596i
$820$	−28.5706	−	17.6203i	−0.997728	−	0.615327i
$821$	−23.0738			−0.805281			−0.402640	−	0.915358i	$-0.631907\pi$
$821$	−23.0738			−0.805281			−0.402640	+	0.915358i	$0.631907\pi$
$822$	4.78886	+	0.383759i	0.167031	+	0.0133851i
$823$	−18.4884	+	44.6350i	−0.644467	+	1.55588i	0.176127	+	0.984367i	$0.443643\pi$
$823$	−18.4884	+	44.6350i	−0.644467	+	1.55588i	−0.820593	+	0.571512i	$0.806357\pi$
$824$	−9.27653	+	5.63026i	−0.323163	+	0.196139i
$825$	−5.73000			−0.199493
$826$	−2.53095	−	2.97192i	−0.0880629	−	0.103406i
$827$	−6.76808	+	6.76808i	−0.235349	+	0.235349i	−0.814921	−	0.579572i	$-0.803220\pi$
$827$	−6.76808	+	6.76808i	−0.235349	+	0.235349i	0.579572	+	0.814921i	$0.303220\pi$
$828$	24.2135	−	39.2613i	0.841479	−	1.36442i
$829$	−15.7928	−	6.54159i	−0.548506	−	0.227199i	0.0911807	−	0.995834i	$-0.470936\pi$
$829$	−15.7928	−	6.54159i	−0.548506	−	0.227199i	−0.639687	+	0.768636i	$0.720936\pi$
$830$	3.35600	+	10.3790i	0.116489	+	0.360261i
$831$	5.29372	−	5.29372i	0.183637	−	0.183637i
$832$	40.3651	−	33.8825i	1.39941	−	1.17466i
$833$	−6.50675	−	27.6661i	−0.225446	−	0.958575i
$834$	−2.84333	−	3.33873i	−0.0984565	−	0.115611i
$835$	16.4323	+	39.6712i	0.568665	+	1.37288i
$836$	17.5526	+	10.8252i	0.607069	+	0.374397i
$837$	5.25754	+	12.6928i	0.181727	+	0.438728i
$838$	−0.372560	+	4.64911i	−0.0128699	+	0.160601i
$839$	6.63148	−	16.0098i	0.228944	−	0.552720i	−0.767105	−	0.641521i	$-0.778304\pi$
$839$	6.63148	−	16.0098i	0.228944	−	0.552720i	0.996049	+	0.0888011i	$0.0283035\pi$
$840$	0.143003	+	0.928557i	0.00493406	+	0.0320383i
$841$			21.3361i			0.735729i
$842$	3.72626	+	11.5241i	0.128415	+	0.397147i
$843$	−1.90718	+	1.90718i	−0.0656868	+	0.0656868i
$844$	−4.53334	+	28.1038i	−0.156044	+	0.967372i
$845$	−64.7307	+	64.7307i	−2.22680	+	2.22680i
$846$	−1.07240	+	13.3823i	−0.0368700	+	0.460094i
$847$	−0.802928	+	1.93844i	−0.0275889	+	0.0666055i
$848$	−11.4506	−	9.89319i	−0.393216	−	0.339733i
$849$		−	10.4131i		−	0.357376i
$850$	19.1150	+	14.0655i	0.655640	+	0.482442i
$851$	−4.95536	−	2.05258i	−0.169868	−	0.0703615i
$852$	1.77131	−	2.87211i	0.0606840	−	0.0983967i
$853$			8.21837i			0.281391i	0.990053	+	0.140696i	$0.0449339\pi$
$853$			8.21837i			0.281391i	−0.990053	+	0.140696i	$0.955066\pi$
$854$	−0.761253	−	0.389245i	−0.0260495	−	0.0133197i
$855$	19.8410	−	8.21841i	0.678548	−	0.281064i
$856$	−5.10962	−	1.24984i	−0.174643	−	0.0427186i
$857$	27.9444	+	11.5750i	0.954563	+	0.395393i	0.804944	−	0.593351i	$-0.202195\pi$
$857$	27.9444	+	11.5750i	0.954563	+	0.395393i	0.149619	+	0.988744i	$0.452195\pi$
$858$	−5.97110	+	11.6778i	−0.203850	+	0.398673i
$859$	51.7391	+	21.4311i	1.76532	+	0.731218i	0.995692	+	0.0927220i	$0.0295568\pi$
$859$	51.7391	+	21.4311i	1.76532	+	0.731218i	0.769625	+	0.638496i	$0.220443\pi$
$860$	−42.5420	−	26.2368i	−1.45067	−	0.894668i
$861$		−	0.614650i		−	0.0209472i
$862$	−10.4657	−	32.3670i	−0.356464	−	1.10243i
$863$			29.6836i			1.01044i	0.862990	+	0.505222i	$0.168589\pi$
$863$			29.6836i			1.01044i	−0.862990	+	0.505222i	$0.831411\pi$
$864$	−4.22442	−	10.4078i	−0.143718	−	0.354080i
$865$	19.7227	−	19.7227i	0.670590	−	0.670590i
$866$	−25.5462	+	21.7557i	−0.868097	+	0.739288i
$867$	5.43741	+	1.82255i	0.184664	+	0.0618969i
$868$	2.64892	+	3.66786i	0.0899101	+	0.124495i
$869$	−14.2458	+	34.3924i	−0.483255	+	1.16668i
$870$	0.814254	−	10.1609i	0.0276058	−	0.344488i
$871$	15.6285	+	15.6285i	0.529550	+	0.529550i
$872$	11.5449	−	47.1982i	0.390960	−	1.59833i
$873$	20.9479	+	8.67691i	0.708980	+	0.293669i
$874$	27.8320	+	2.23033i	0.941430	+	0.0754422i
$875$	0.350418	−	0.845983i	0.0118463	−	0.0285995i
$876$	−0.363271	+	0.589030i	−0.0122738	+	0.0199015i
$877$		−	31.4166i		−	1.06086i	−0.847728	−	0.530431i	$-0.822030\pi$
$877$		−	31.4166i		−	1.06086i	0.847728	−	0.530431i	$-0.177970\pi$
$878$	6.33484	+	19.5916i	0.213791	+	0.661184i
$879$	9.23116	+	3.82367i	0.311359	+	0.128969i
$880$	44.9251	−	22.5688i	1.51442	−	0.760795i
$881$	3.07962	−	7.43485i	0.103755	−	0.250487i	−0.863474	−	0.504394i	$-0.831716\pi$
$881$	3.07962	−	7.43485i	0.103755	−	0.250487i	0.967229	+	0.253908i	$0.0817159\pi$
$882$	−21.4205	+	18.2421i	−0.721266	+	0.614244i
$883$	−30.2275	−	12.5206i	−1.01724	−	0.421353i	−0.189146	−	0.981949i	$-0.560572\pi$
$883$	−30.2275	−	12.5206i	−1.01724	−	0.421353i	−0.828089	+	0.560596i	$0.810572\pi$
$884$	48.5849	−	24.2993i	1.63409	−	0.817273i
$885$	−3.28226	−	7.92407i	−0.110332	−	0.266365i
$886$	6.31263	−	2.04116i	0.212077	−	0.0685740i
$887$	−5.29402	−	12.7809i	−0.177756	−	0.429140i	0.809739	−	0.586790i	$-0.199608\pi$
$887$	−5.29402	−	12.7809i	−0.177756	−	0.429140i	−0.987495	+	0.157649i	$0.949608\pi$
$888$	−0.547475	+	0.332282i	−0.0183720	+	0.0111507i
$889$	2.61516	+	6.31356i	0.0877097	+	0.211750i
$890$	5.86024	−	4.99070i	0.196436	−	0.167289i
$891$	−23.5752	−	23.5752i	−0.789800	−	0.789800i
$892$	−44.2916	+	31.9873i	−1.48299	+	1.07101i
$893$	−7.50778	+	3.10982i	−0.251238	+	0.104066i
$894$	2.22092	−	4.34349i	0.0742788	−	0.145268i
$895$	−10.9478	+	4.53475i	−0.365946	+	0.151580i
$896$	−2.14429	−	3.01413i	−0.0716356	−	0.100695i
$897$			17.7579i			0.592920i
$898$	−13.5836	−	42.0097i	−0.453291	−	1.40188i
$899$	−18.7855	−	45.3522i	−0.626532	−	1.51258i
$900$	3.74139	−	23.1942i	0.124713	−	0.773140i
$901$	−9.10988	−	12.6615i	−0.303494	−	0.421816i
$902$	−31.2962	+	10.1195i	−1.04205	+	0.336941i
$903$		−	0.915222i		−	0.0304567i
$904$	−8.84629	−	57.4415i	−0.294223	−	1.91048i
$905$	−0.454020	+	0.454020i	−0.0150921	+	0.0150921i
$906$	7.39313	−	6.29613i	0.245620	−	0.209175i
$907$	−18.8559	−	18.8559i	−0.626101	−	0.626101i	0.320983	−	0.947085i	$-0.395987\pi$
$907$	−18.8559	−	18.8559i	−0.626101	−	0.626101i	−0.947085	+	0.320983i	$0.895987\pi$
$908$	−7.65147	+	47.4341i	−0.253923	+	1.57416i
$909$	−10.9444	−	26.4221i	−0.363002	−	0.876364i
$910$	5.94771	+	6.98400i	0.197165	+	0.231517i
$911$	6.87532	−	2.84785i	0.227789	−	0.0943534i	−0.265870	−	0.964009i	$-0.585659\pi$
$911$	6.87532	−	2.84785i	0.227789	−	0.0943534i	0.493659	+	0.869656i	$0.335659\pi$
$912$	2.17955	−	2.52266i	0.0721720	−	0.0835337i
$913$	9.87496	+	4.09034i	0.326813	+	0.135371i
$914$	55.6434	+	4.45902i	1.84052	+	0.147491i
$915$	−1.32837	−	1.32837i	−0.0439145	−	0.0439145i
$916$	15.1860	+	9.36562i	0.501759	+	0.309449i
$917$	1.05083	+	2.53693i	0.0347014	+	0.0837767i
$918$	−1.74196	−	11.4463i	−0.0574931	−	0.377786i
$919$	2.23644	+	2.23644i	0.0737734	+	0.0737734i	0.743031	−	0.669257i	$-0.233388\pi$
$919$	2.23644	+	2.23644i	0.0737734	+	0.0737734i	−0.669257	+	0.743031i	$0.733388\pi$
$920$	40.2453	−	54.8979i	1.32685	−	1.80993i
$921$	−1.56795	+	0.649465i	−0.0516656	+	0.0214006i
$922$	−25.3403	+	8.19366i	−0.834538	+	0.269844i
$923$		−	32.9479i		−	1.08449i
$924$	0.783563	+	0.483245i	0.0257773	+	0.0158976i
$925$	−2.73186			−0.0898228
$926$	20.2321	+	1.62131i	0.664867	+	0.0532796i
$927$	7.82987	+	7.82987i	0.257167	+	0.257167i
$928$	15.0941	+	37.1877i	0.495489	+	1.22075i
$929$	−26.9496	+	11.1629i	−0.884188	+	0.366243i	−0.778119	−	0.628116i	$-0.783826\pi$
$929$	−26.9496	+	11.1629i	−0.884188	+	0.366243i	−0.106068	+	0.994359i	$0.533826\pi$
$930$	3.05844	+	9.45876i	0.100290	+	0.310165i
$931$	−15.7343	−	6.51734i	−0.515669	−	0.213597i
$932$	0.214613	−	0.0508777i	0.00702990	−	0.00166655i
$933$	−0.480467	+	1.15995i	−0.0157298	+	0.0379751i
$934$	15.5117	+	47.9728i	0.507560	+	1.56972i
$935$	50.4463	−	11.8644i	1.64977	−	0.388007i
$936$	−43.3711	−	31.7951i	−1.41763	−	1.03926i
$937$	−53.9625			−1.76288			−0.881439	−	0.472298i	$-0.843425\pi$
$937$	−53.9625			−1.76288			−0.881439	+	0.472298i	$0.843425\pi$
$938$	1.18108	−	1.00583i	0.0385635	−	0.0328414i
$939$	−3.77067	+	1.56186i	−0.123051	+	0.0509695i
$940$	−3.15494	+	19.5586i	−0.102903	+	0.637930i
$941$	−13.8595			−0.451807			−0.225903	−	0.974150i	$-0.572533\pi$
$941$	−13.8595			−0.451807			−0.225903	+	0.974150i	$0.572533\pi$
$942$	6.63544	−	2.14554i	0.216194	−	0.0699053i
$943$	−31.4896	+	31.4896i	−1.02544	+	1.02544i
$944$	25.5531	+	22.0775i	0.831682	+	0.718563i
$945$	1.80636	−	0.748219i	0.0587609	−	0.0243396i
$946$	−46.6004	+	15.0680i	−1.51511	+	0.489903i
$947$	38.0733	−	38.0733i	1.23722	−	1.23722i	0.276083	−	0.961134i	$-0.410964\pi$
$947$	38.0733	−	38.0733i	1.23722	−	1.23722i	0.961134	−	0.276083i	$-0.0890363\pi$
$948$	5.12218	+	3.15899i	0.166361	+	0.102599i
$949$			6.75717i			0.219347i
$950$	13.5313	−	4.37527i	0.439012	−	0.141952i
$951$	0.704170	+	0.704170i	0.0228343	+	0.0228343i
$952$	−1.42771	−	3.53550i	−0.0462722	−	0.114586i
$953$	15.4891	−	15.4891i	0.501741	−	0.501741i	−0.410238	−	0.911979i	$-0.634554\pi$
$953$	15.4891	−	15.4891i	0.501741	−	0.501741i	0.911979	+	0.410238i	$0.134554\pi$
$954$	−7.02993	+	13.7486i	−0.227602	+	0.445126i
$955$	−30.2971			−0.980391
$956$	−3.22601	+	19.9992i	−0.104337	+	0.646819i
$957$	−7.06284	−	7.06284i	−0.228309	−	0.228309i
$958$	16.4478	+	8.41012i	0.531405	+	0.271719i
$959$	−1.25999	−	3.04189i	−0.0406873	−	0.0982278i
$960$	−2.44537	−	7.75093i	−0.0789238	−	0.250160i
$961$	11.9307	+	11.9307i	0.384862	+	0.384862i
$962$	−2.84680	+	5.56754i	−0.0917846	+	0.179505i
$963$			5.36771i			0.172972i
$964$	13.7325	−	22.2666i	0.442293	−	0.717160i
$965$	−3.16020	−	7.62941i	−0.101731	−	0.245599i
$966$	1.24244	+	0.0995640i	0.0399749	+	0.00320342i
$967$			49.1635i			1.58099i	0.612467	+	0.790496i	$0.290177\pi$
$967$			49.1635i			1.58099i	−0.612467	+	0.790496i	$0.709823\pi$
$968$	4.31264	−	17.6311i	0.138614	−	0.566684i
$969$	2.78943	−	2.00698i	0.0896094	−	0.0644734i
$970$	29.7909	+	15.2327i	0.956528	+	0.489093i
$971$	10.7671	+	4.45989i	0.345534	+	0.143125i	0.548700	−	0.836020i	$-0.315123\pi$
$971$	10.7671	+	4.45989i	0.345534	+	0.143125i	−0.203166	+	0.979144i	$0.565123\pi$
$972$	−14.0279	+	10.1309i	−0.449944	+	0.324948i
$973$	−1.15015	+	2.77671i	−0.0368721	+	0.0890171i
$974$	5.69521	−	11.1382i	0.182486	−	0.356891i
$975$	3.46123	+	8.35614i	0.110848	+	0.267611i
$976$	7.02131	+	2.32569i	0.224747	+	0.0744436i
$977$	36.5450	−	36.5450i	1.16918	−	1.16918i	0.186776	−	0.982402i	$-0.440196\pi$
$977$	36.5450	−	36.5450i	1.16918	−	1.16918i	0.982402	−	0.186776i	$-0.0598039\pi$
$978$	1.88607	−	1.60621i	0.0603097	−	0.0513609i
$979$		−	7.54246i		−	0.241058i
$980$	−33.6592	+	24.3086i	−1.07520	+	0.776509i
$981$	−49.5822			−1.58304
$982$	−18.4329	−	9.42515i	−0.588218	−	0.300769i
$983$	18.5621	+	44.8128i	0.592038	+	1.42931i	0.881531	+	0.472125i	$0.156513\pi$
$983$	18.5621	+	44.8128i	0.592038	+	1.42931i	−0.289494	+	0.957180i	$0.593487\pi$
$984$	0.809344	+	5.25531i	0.0258010	+	0.167533i
$985$	21.9759	−	21.9759i	0.700210	−	0.700210i
$986$	6.22412	+	40.8985i	0.198216	+	1.30247i
$987$	−0.335154	+	0.138825i	−0.0106681	+	0.00441885i
$988$	5.18380	−	32.1362i	0.164919	−	1.02239i
$989$	−46.8884	+	46.8884i	−1.49096	+	1.49096i
$990$	−33.2626	−	39.0581i	−1.05715	−	1.24135i
$991$	−14.6750	+	35.4286i	−0.466167	+	1.12543i	0.499656	+	0.866224i	$0.333460\pi$
$991$	−14.6750	+	35.4286i	−0.466167	+	1.12543i	−0.965823	+	0.259203i	$0.916540\pi$
$992$	−27.4781	−	27.8725i	−0.872431	−	0.884953i
$993$	−1.44623	−	3.49151i	−0.0458947	−	0.110800i
$994$	−2.30522	−	0.184730i	−0.0731170	−	0.00585928i
$995$	31.1365	−	12.8972i	0.987094	−	0.408868i
$996$	0.907030	−	1.47071i	0.0287403	−	0.0466013i
$997$	−15.1362	+	15.1362i	−0.479369	+	0.479369i	−0.904930	−	0.425561i	$-0.860077\pi$
$997$	−15.1362	+	15.1362i	−0.479369	+	0.479369i	0.425561	+	0.904930i	$0.360077\pi$
$998$	61.2171	+	4.90568i	1.93779	+	0.155286i
$999$	0.942413	+	0.942413i	0.0298166	+	0.0298166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.x.a.77.1	yes	280
17.2	even	8		544.2.v.a.461.37	✓	280
32.5	even	8		544.2.v.a.485.37	yes	280
544.325	even	8	inner	544.2.x.a.325.1	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.v.a.461.37	✓	280	17.2	even	8
544.2.v.a.485.37	yes	280	32.5	even	8
544.2.x.a.77.1	yes	280	1.1	even	1	trivial
544.2.x.a.325.1	yes	280	544.325	even	8	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40969 - 0.112967i) q^{2} +(0.238533 - 0.238533i) q^{3} +(1.97448 + 0.318497i) q^{4} -3.01165i q^{5} +(-0.363205 + 0.309313i) q^{6} +(0.302065 + 0.125119i) q^{7} +(-2.74743 - 0.672035i) q^{8} +2.88620i q^{9} +(-0.340217 + 4.24551i) q^{10} +(2.95104 + 2.95104i) q^{11} +(0.546950 - 0.395006i) q^{12} +(2.52096 - 6.08613i) q^{13} +(-0.411685 - 0.210503i) q^{14} +(-0.718379 - 0.718379i) q^{15} +(3.79712 + 1.25773i) q^{16} +(3.50552 + 2.17057i) q^{17} +(0.326045 - 4.06867i) q^{18} +(2.28261 - 0.945488i) q^{19} +(0.959204 - 5.94644i) q^{20} +(0.101898 - 0.0422074i) q^{21} +(-3.82670 - 4.49344i) q^{22} +(-7.38275 - 3.05803i) q^{23} +(-0.815656 + 0.495051i) q^{24} -4.07006 q^{25} +(-4.24131 + 8.29480i) q^{26} +(1.40405 + 1.40405i) q^{27} +(0.556570 + 0.343252i) q^{28} +(-5.01678 - 5.01678i) q^{29} +(0.931542 + 1.09385i) q^{30} +(6.39232 + 2.64779i) q^{31} +(-5.21070 - 2.20197i) q^{32} +1.40784 q^{33} +(-4.69650 - 3.45584i) q^{34} +(0.376816 - 0.909715i) q^{35} +(-0.919249 + 5.69874i) q^{36} +0.671208 q^{37} +(-3.32459 + 1.07499i) q^{38} +(-0.850412 - 2.05308i) q^{39} +(-2.02394 + 8.27431i) q^{40} +(2.13265 - 5.14867i) q^{41} +(-0.148413 + 0.0479884i) q^{42} +(3.17554 - 7.66643i) q^{43} +(4.88686 + 6.76666i) q^{44} +8.69225 q^{45} +(10.0620 + 5.14490i) q^{46} -3.28912 q^{47} +(1.20575 - 0.605728i) q^{48} +(-4.87416 - 4.87416i) q^{49} +(5.73754 + 0.459781i) q^{50} +(1.35393 - 0.318429i) q^{51} +(6.91599 - 11.2140i) q^{52} +(-3.49515 - 1.44774i) q^{53} +(-1.82068 - 2.13790i) q^{54} +(8.88751 - 8.88751i) q^{55} +(-0.745817 - 0.546755i) q^{56} +(0.318948 - 0.770008i) q^{57} +(6.50540 + 7.63886i) q^{58} +(7.79973 + 3.23076i) q^{59} +(-1.18962 - 1.64723i) q^{60} +1.84912 q^{61} +(-8.71211 - 4.45469i) q^{62} +(-0.361120 + 0.871821i) q^{63} +(7.09674 + 3.69274i) q^{64} +(-18.3293 - 7.59225i) q^{65} +(-1.98463 - 0.159040i) q^{66} +(-1.28394 + 3.09971i) q^{67} +(6.23024 + 5.40223i) q^{68} +(-2.49047 + 1.03159i) q^{69} +(-0.633963 + 1.23985i) q^{70} +(4.62080 - 1.91400i) q^{71} +(1.93963 - 7.92964i) q^{72} +(-0.947663 + 0.392535i) q^{73} +(-0.946198 - 0.0758243i) q^{74} +(-0.970844 + 0.970844i) q^{75} +(4.80809 - 1.13984i) q^{76} +(0.522173 + 1.26064i) q^{77} +(0.966892 + 2.99028i) q^{78} +(3.41347 + 8.24084i) q^{79} +(3.78785 - 11.4356i) q^{80} -7.98878 q^{81} +(-3.58801 + 7.01713i) q^{82} +(2.36616 - 0.980097i) q^{83} +(0.214637 - 0.0508833i) q^{84} +(6.53700 - 10.5574i) q^{85} +(-5.34259 + 10.4486i) q^{86} -2.39334 q^{87} +(-6.12458 - 10.0910i) q^{88} +(-1.27793 - 1.27793i) q^{89} +(-12.2534 - 0.981936i) q^{90} +(1.52299 - 1.52299i) q^{91} +(-13.6031 - 8.38941i) q^{92} +(2.15637 - 0.893196i) q^{93} +(4.63666 + 0.371562i) q^{94} +(-2.84748 - 6.87443i) q^{95} +(-1.76817 + 0.717682i) q^{96} +(3.00634 - 7.25795i) q^{97} +(6.32046 + 7.42169i) q^{98} +(-8.51731 + 8.51731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

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