LMFDB - Embedded newform 690.2.r.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.r (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	690.169
Dual form			690.2.r.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 - 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-2.05037 + 0.892171i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.0262635 + 0.0408667i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.989821 - 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-2.05037 + 0.892171i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.0262635 + 0.0408667i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(2.15647 - 0.591291i) q^{10} +(0.313282 + 2.17892i) q^{11} +(-0.989821 + 0.142315i) q^{12} +(-3.68532 - 5.73447i) q^{13} +(0.0318121 - 0.0367131i) q^{14} +(1.49446 - 1.66330i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.931584 + 3.17268i) q^{17} +(-0.755750 + 0.654861i) q^{18} +(-3.44362 - 1.01114i) q^{19} +(-2.21867 + 0.278374i) q^{20} +(0.00691343 - 0.0480839i) q^{21} -2.20133i q^{22} +(3.25539 + 3.52171i) q^{23} +1.00000 q^{24} +(3.40806 - 3.65857i) q^{25} +(2.83171 + 6.20057i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(-0.0367131 + 0.0318121i) q^{28} +(5.25274 - 1.54234i) q^{29} +(-1.71597 + 1.43369i) q^{30} +(3.13261 - 6.85945i) q^{31} +(-0.755750 - 0.654861i) q^{32} +(-1.19013 - 1.85187i) q^{33} +(-0.470582 - 3.27297i) q^{34} +(0.0173898 - 0.107224i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-0.676708 - 0.586371i) q^{37} +(3.26467 + 1.49092i) q^{38} +(5.73447 + 3.68532i) q^{39} +(2.23571 + 0.0402090i) q^{40} +(-4.50226 - 5.19589i) q^{41} +(-0.0136861 + 0.0466106i) q^{42} +(9.16661 - 4.18625i) q^{43} +(-0.313282 + 2.17892i) q^{44} +(-0.668452 + 2.13382i) q^{45} +(-2.72106 - 3.94915i) q^{46} -7.57126i q^{47} +(-0.989821 - 0.142315i) q^{48} +(2.90692 + 6.36528i) q^{49} +(-3.89404 + 3.13631i) q^{50} +(-2.16538 - 2.49898i) q^{51} +(-1.92045 - 6.54045i) q^{52} +(5.37936 - 8.37045i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-2.58631 - 4.18810i) q^{55} +(0.0408667 - 0.0262635i) q^{56} +(3.55247 - 0.510768i) q^{57} +(-5.41878 + 0.779102i) q^{58} +(-3.45967 + 2.22339i) q^{59} +(1.90253 - 1.17489i) q^{60} +(-3.90774 + 8.55676i) q^{61} +(-4.07692 + 6.34382i) q^{62} +(0.0136861 + 0.0466106i) q^{63} +(0.654861 + 0.755750i) q^{64} +(12.6724 + 8.46987i) q^{65} +(0.914465 + 2.00240i) q^{66} +(7.30008 + 1.04959i) q^{67} +3.30662i q^{68} +(-4.42418 - 1.85112i) q^{69} +(-0.0324723 + 0.103657i) q^{70} +(1.46948 - 10.2205i) q^{71} +(-0.909632 + 0.415415i) q^{72} +(4.30464 - 14.6602i) q^{73} +(0.586371 + 0.676708i) q^{74} +(-1.58026 + 4.74371i) q^{75} +(-3.01926 - 1.94036i) q^{76} +(-0.0972733 - 0.0444232i) q^{77} +(-5.15162 - 4.46391i) q^{78} +(6.51463 - 4.18670i) q^{79} +(-2.20723 - 0.357974i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.71698 + 5.78374i) q^{82} +(-2.79071 - 2.41816i) q^{83} +(0.0201802 - 0.0441885i) q^{84} +(-4.74067 - 5.67405i) q^{85} +(-9.66907 + 2.83910i) q^{86} +(-4.13735 + 3.58503i) q^{87} +(0.620186 - 2.11216i) q^{88} +(-0.627619 - 1.37429i) q^{89} +(0.965321 - 2.01697i) q^{90} +0.331138 q^{91} +(2.13134 + 4.29620i) q^{92} +7.54091i q^{93} +(-1.07750 + 7.49419i) q^{94} +(7.96281 - 0.999086i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-5.67682 + 4.91899i) q^{97} +(-1.97146 - 6.71419i) q^{98} +(1.85187 + 1.19013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.989821	−	0.142315i	−0.699909	−	0.100632i
$2$	−0.989821	−	0.142315i	−0.699909	−	0.100632i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$3$	−0.909632	+	0.415415i	−0.525176	+	0.239840i
$4$	0.959493	+	0.281733i	0.479746	+	0.140866i
$5$	−2.05037	+	0.892171i	−0.916955	+	0.398991i
$5$	−2.05037	+	0.892171i	−0.916955	+	0.398991i
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	−0.0262635	+	0.0408667i	−0.00992666	+	0.0154462i	−0.846181	−	0.532895i	$-0.821104\pi$
$7$	−0.0262635	+	0.0408667i	−0.00992666	+	0.0154462i	0.836255	+	0.548341i	$0.184740\pi$
$8$	−0.909632	−	0.415415i	−0.321603	−	0.146871i
$9$	0.654861	−	0.755750i	0.218287	−	0.251917i
$10$	2.15647	−	0.591291i	0.681937	−	0.186983i
$11$	0.313282	+	2.17892i	0.0944580	+	0.656970i	0.980955	+	0.194235i	$0.0622225\pi$
$11$	0.313282	+	2.17892i	0.0944580	+	0.656970i	−0.886497	+	0.462734i	$0.846868\pi$
$12$	−0.989821	+	0.142315i	−0.285737	+	0.0410828i
$13$	−3.68532	−	5.73447i	−1.02212	−	1.59045i	−0.785508	−	0.618851i	$-0.787598\pi$
$13$	−3.68532	−	5.73447i	−1.02212	−	1.59045i	−0.236615	−	0.971603i	$-0.576038\pi$
$14$	0.0318121	−	0.0367131i	0.00850214	−	0.00981199i
$15$	1.49446	−	1.66330i	0.385869	−	0.429463i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	0.931584	+	3.17268i	0.225942	+	0.769488i	0.991947	+	0.126654i	$0.0404237\pi$
$17$	0.931584	+	3.17268i	0.225942	+	0.769488i	−0.766005	+	0.642835i	$0.777758\pi$
$18$	−0.755750	+	0.654861i	−0.178132	+	0.154352i
$19$	−3.44362	−	1.01114i	−0.790020	−	0.231971i	−0.138260	−	0.990396i	$-0.544151\pi$
$19$	−3.44362	−	1.01114i	−0.790020	−	0.231971i	−0.651760	+	0.758425i	$0.725969\pi$
$20$	−2.21867	+	0.278374i	−0.496110	+	0.0622464i
$21$	0.00691343	−	0.0480839i	0.00150863	−	0.0104928i
$22$		−	2.20133i		−	0.469325i
$23$	3.25539	+	3.52171i	0.678796	+	0.734327i
$23$	3.25539	+	3.52171i	0.678796	+	0.734327i
$24$	1.00000			0.204124
$25$	3.40806	−	3.65857i	0.681613	−	0.731713i
$26$	2.83171	+	6.20057i	0.555343	+	1.21603i
$27$	−0.281733	+	0.959493i	−0.0542195	+	0.184655i
$28$	−0.0367131	+	0.0318121i	−0.00693812	+	0.00601192i
$29$	5.25274	−	1.54234i	0.975410	−	0.286406i	0.245082	−	0.969502i	$-0.421185\pi$
$29$	5.25274	−	1.54234i	0.975410	−	0.286406i	0.730328	+	0.683096i	$0.239367\pi$
$30$	−1.71597	+	1.43369i	−0.313291	+	0.261754i
$31$	3.13261	−	6.85945i	0.562633	−	1.23199i	−0.387995	−	0.921662i	$-0.626832\pi$
$31$	3.13261	−	6.85945i	0.562633	−	1.23199i	0.950628	−	0.310333i	$-0.100441\pi$
$32$	−0.755750	−	0.654861i	−0.133599	−	0.115764i
$33$	−1.19013	−	1.85187i	−0.207175	−	0.322370i
$34$	−0.470582	−	3.27297i	−0.0807041	−	0.561309i
$35$	0.0173898	−	0.107224i	0.00293941	−	0.0181241i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−0.676708	−	0.586371i	−0.111250	−	0.0963988i	0.597459	−	0.801899i	$-0.296177\pi$
$37$	−0.676708	−	0.586371i	−0.111250	−	0.0963988i	−0.708710	+	0.705500i	$0.750722\pi$
$38$	3.26467	+	1.49092i	0.529599	+	0.241860i
$39$	5.73447	+	3.68532i	0.918250	+	0.590123i
$40$	2.23571	+	0.0402090i	0.353496	+	0.00635760i
$41$	−4.50226	−	5.19589i	−0.703135	−	0.811461i	0.286037	−	0.958219i	$-0.407662\pi$
$41$	−4.50226	−	5.19589i	−0.703135	−	0.811461i	−0.989173	+	0.146757i	$0.953116\pi$
$42$	−0.0136861	+	0.0466106i	−0.00211181	+	0.00719218i
$43$	9.16661	−	4.18625i	1.39789	−	0.638397i	0.433087	−	0.901352i	$-0.357424\pi$
$43$	9.16661	−	4.18625i	1.39789	−	0.638397i	0.964808	+	0.262955i	$0.0846971\pi$
$44$	−0.313282	+	2.17892i	−0.0472290	+	0.328485i
$45$	−0.668452	+	2.13382i	−0.0996469	+	0.318091i
$46$	−2.72106	−	3.94915i	−0.401199	−	0.582271i
$47$		−	7.57126i		−	1.10438i	−0.833718	−	0.552191i	$-0.813792\pi$
$47$		−	7.57126i		−	1.10438i	0.833718	−	0.552191i	$-0.186208\pi$
$48$	−0.989821	−	0.142315i	−0.142868	−	0.0205414i
$49$	2.90692	+	6.36528i	0.415275	+	0.909325i
$50$	−3.89404	+	3.13631i	−0.550701	+	0.443541i
$51$	−2.16538	−	2.49898i	−0.303214	−	0.349927i
$52$	−1.92045	−	6.54045i	−0.266319	−	0.906998i
$53$	5.37936	−	8.37045i	0.738912	−	1.14977i	−0.244722	−	0.969593i	$-0.578697\pi$
$53$	5.37936	−	8.37045i	0.738912	−	1.14977i	0.983634	−	0.180177i	$-0.0576669\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	−2.58631	−	4.18810i	−0.348739	−	0.564724i
$56$	0.0408667	−	0.0262635i	0.00546105	−	0.00350960i
$57$	3.55247	−	0.510768i	0.470536	−	0.0676528i
$58$	−5.41878	+	0.779102i	−0.711520	+	0.102301i
$59$	−3.45967	+	2.22339i	−0.450410	+	0.289461i	−0.746114	−	0.665819i	$-0.768082\pi$
$59$	−3.45967	+	2.22339i	−0.450410	+	0.289461i	0.295703	+	0.955280i	$0.404446\pi$
$60$	1.90253	−	1.17489i	0.245616	−	0.151677i
$61$	−3.90774	+	8.55676i	−0.500335	+	1.09558i	0.476025	+	0.879432i	$0.342077\pi$
$61$	−3.90774	+	8.55676i	−0.500335	+	1.09558i	−0.976360	+	0.216149i	$0.930650\pi$
$62$	−4.07692	+	6.34382i	−0.517770	+	0.805666i
$63$	0.0136861	+	0.0466106i	0.00172429	+	0.00587239i
$64$	0.654861	+	0.755750i	0.0818576	+	0.0944687i
$65$	12.6724	+	8.46987i	1.57182	+	1.05056i
$66$	0.914465	+	2.00240i	0.112563	+	0.246478i
$67$	7.30008	+	1.04959i	0.891847	+	0.128228i	0.572978	−	0.819571i	$-0.305788\pi$
$67$	7.30008	+	1.04959i	0.891847	+	0.128228i	0.318869	+	0.947799i	$0.396697\pi$
$68$			3.30662i			0.400987i
$69$	−4.42418	−	1.85112i	−0.532608	−	0.222849i
$70$	−0.0324723	+	0.103657i	−0.00388118	+	0.0123894i
$71$	1.46948	−	10.2205i	0.174396	−	1.21295i	−0.695065	−	0.718947i	$-0.744624\pi$
$71$	1.46948	−	10.2205i	0.174396	−	1.21295i	0.869461	−	0.494002i	$-0.164466\pi$
$72$	−0.909632	+	0.415415i	−0.107201	+	0.0489571i
$73$	4.30464	−	14.6602i	0.503820	−	1.71585i	−0.177730	−	0.984079i	$-0.556875\pi$
$73$	4.30464	−	14.6602i	0.503820	−	1.71585i	0.681549	−	0.731772i	$-0.261307\pi$
$74$	0.586371	+	0.676708i	0.0681642	+	0.0786657i
$75$	−1.58026	+	4.74371i	−0.182473	+	0.547756i
$76$	−3.01926	−	1.94036i	−0.346333	−	0.222574i
$77$	−0.0972733	−	0.0444232i	−0.0110853	−	0.00506250i
$78$	−5.15162	−	4.46391i	−0.583306	−	0.505438i
$79$	6.51463	−	4.18670i	0.732953	−	0.471040i	−0.120168	−	0.992754i	$-0.538343\pi$
$79$	6.51463	−	4.18670i	0.732953	−	0.471040i	0.853121	+	0.521713i	$0.174707\pi$
$80$	−2.20723	−	0.357974i	−0.246776	−	0.0400227i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	3.71698	+	5.78374i	0.410472	+	0.638707i
$83$	−2.79071	−	2.41816i	−0.306320	−	0.265428i	0.488112	−	0.872781i	$-0.337686\pi$
$83$	−2.79071	−	2.41816i	−0.306320	−	0.265428i	−0.794432	+	0.607353i	$0.792231\pi$
$84$	0.0201802	−	0.0441885i	0.00220184	−	0.00482136i
$85$	−4.74067	−	5.67405i	−0.514198	−	0.615437i
$86$	−9.66907	+	2.83910i	−1.04264	+	0.306148i
$87$	−4.13735	+	3.58503i	−0.443571	+	0.384356i
$88$	0.620186	−	2.11216i	0.0661120	−	0.225157i
$89$	−0.627619	−	1.37429i	−0.0665275	−	0.145675i	0.873447	−	0.486919i	$-0.161879\pi$
$89$	−0.627619	−	1.37429i	−0.0665275	−	0.145675i	−0.939975	+	0.341244i	$0.889152\pi$
$90$	0.965321	−	2.01697i	0.101754	−	0.212607i
$91$	0.331138			0.0347127
$92$	2.13134	+	4.29620i	0.222208	+	0.447910i
$93$			7.54091i			0.781956i
$94$	−1.07750	+	7.49419i	−0.111136	+	0.772967i
$95$	7.96281	−	0.999086i	0.816967	−	0.102504i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−5.67682	+	4.91899i	−0.576394	+	0.499448i	−0.893573	−	0.448918i	$-0.851810\pi$
$97$	−5.67682	+	4.91899i	−0.576394	+	0.499448i	0.317180	+	0.948366i	$0.397264\pi$
$98$	−1.97146	−	6.71419i	−0.199148	−	0.678235i
$99$	1.85187	+	1.19013i	0.186120	+	0.119612i
$100$	4.30075	−	2.55021i	0.430075	−	0.255021i
$101$	2.05612	−	2.37289i	0.204592	−	0.236112i	−0.644176	−	0.764877i	$-0.722800\pi$
$101$	2.05612	−	2.37289i	0.204592	−	0.236112i	0.848768	+	0.528766i	$0.177345\pi$
$102$	1.78770	+	2.78171i	0.177008	+	0.275430i
$103$	11.8025	−	1.69694i	1.16293	−	0.167204i	0.466296	−	0.884629i	$-0.345588\pi$
$103$	11.8025	−	1.69694i	1.16293	−	0.167204i	0.696636	+	0.717424i	$0.254679\pi$
$104$	0.970100	+	6.74719i	0.0951261	+	0.661616i
$105$	0.0287240	+	0.104758i	0.00280317	+	0.0102233i
$106$	−6.51585	+	7.51969i	−0.632875	+	0.730377i
$107$	−12.8279	−	5.85830i	−1.24012	−	0.566343i	−0.316113	−	0.948722i	$-0.602378\pi$
$107$	−12.8279	−	5.85830i	−1.24012	−	0.566343i	−0.924006	+	0.382378i	$0.875105\pi$
$108$	−0.540641	+	0.841254i	−0.0520232	+	0.0809497i
$109$	−13.9937	+	4.10891i	−1.34035	+	0.393562i	−0.871794	−	0.489872i	$-0.837044\pi$
$109$	−13.9937	+	4.10891i	−1.34035	+	0.393562i	−0.468555	+	0.883434i	$0.655225\pi$
$110$	1.96396	+	4.51354i	0.187256	+	0.430350i
$111$	0.859143	+	0.252267i	0.0815462	+	0.0239441i
$112$	−0.0441885	+	0.0201802i	−0.00417542	+	0.00190685i
$113$	−11.7167	−	1.68461i	−1.10221	−	0.158474i	−0.432891	−	0.901446i	$-0.642507\pi$
$113$	−11.7167	−	1.68461i	−1.10221	−	0.158474i	−0.669323	+	0.742972i	$0.733416\pi$
$114$	−3.58900			−0.336141
$115$	−9.81673	−	4.31646i	−0.915415	−	0.402512i
$116$	5.47450			0.508294
$117$	−6.74719	−	0.970100i	−0.623778	−	0.0896857i
$118$	3.74088	−	1.70840i	0.344376	−	0.157271i
$119$	−0.154124	−	0.0452548i	−0.0141285	−	0.00414850i
$120$	−2.05037	+	0.892171i	−0.187173	+	0.0814437i
$121$	5.90487	−	1.73383i	0.536806	−	0.157621i
$122$	5.08572	−	7.91353i	0.460439	−	0.716458i
$123$	6.25385	+	2.85604i	0.563891	+	0.257520i
$124$	4.93825	−	5.69904i	0.443468	−	0.511789i
$125$	−3.72374	+	10.5420i	−0.333061	+	0.942905i
$126$	−0.00691343	−	0.0480839i	−0.000615897	−	0.00428366i
$127$	17.5580	−	2.52447i	1.55802	−	0.224010i	0.691215	−	0.722649i	$-0.257076\pi$
$127$	17.5580	−	2.52447i	1.55802	−	0.224010i	0.866810	+	0.498639i	$0.166167\pi$
$128$	−0.540641	−	0.841254i	−0.0477863	−	0.0743570i
$129$	−6.59921	+	7.61589i	−0.581028	+	0.670542i
$130$	−11.3380	−	10.1871i	−0.994411	−	0.893470i
$131$	5.28346	+	3.39547i	0.461618	+	0.296664i	0.750703	−	0.660639i	$-0.229715\pi$
$131$	5.28346	+	3.39547i	0.461618	+	0.296664i	−0.289085	+	0.957303i	$0.593351\pi$
$132$	−0.620186	−	2.11216i	−0.0539802	−	0.183840i
$133$	0.131763	−	0.114174i	0.0114253	−	0.00990010i
$134$	−7.07640	−	2.07782i	−0.611308	−	0.179496i
$135$	−0.278374	−	2.21867i	−0.0239587	−	0.190953i
$136$	0.470582	−	3.27297i	0.0403520	−	0.280655i
$137$			20.8140i			1.77826i	0.457653	+	0.889131i	$0.348690\pi$
$137$			20.8140i			1.77826i	−0.457653	+	0.889131i	$0.651310\pi$
$138$	4.11570	+	2.46191i	0.350352	+	0.209571i
$139$	−3.73860			−0.317104			−0.158552	−	0.987351i	$-0.550683\pi$
$139$	−3.73860			−0.317104			−0.158552	+	0.987351i	$0.550683\pi$
$140$	0.0468938	−	0.0979810i	0.00396325	−	0.00828091i
$141$	3.14521	+	6.88706i	0.264875	+	0.579995i
$142$	−2.90905	+	9.90733i	−0.244122	+	0.831405i
$143$	11.3404	−	9.82652i	0.948333	−	0.821735i
$144$	0.959493	−	0.281733i	0.0799577	−	0.0234777i
$145$	−9.39405	+	7.84873i	−0.780134	+	0.651801i
$146$	−6.34719	+	13.8984i	−0.525297	+	1.15024i
$147$	−5.28846	−	4.58248i	−0.436185	−	0.377957i
$148$	−0.484097	−	0.753270i	−0.0397925	−	0.0619184i
$149$	−0.670773	−	4.66533i	−0.0549519	−	0.382199i	−0.998675	−	0.0514619i	$-0.983612\pi$
$149$	−0.670773	−	4.66533i	−0.0549519	−	0.382199i	0.943723	−	0.330737i	$-0.107297\pi$
$150$	2.23928	−	4.47053i	0.182836	−	0.365017i
$151$	−2.92305	+	1.87853i	−0.237874	+	0.152873i	−0.654147	−	0.756367i	$-0.726972\pi$
$151$	−2.92305	+	1.87853i	−0.237874	+	0.152873i	0.416273	+	0.909240i	$0.363336\pi$
$152$	2.71238	+	2.35029i	0.220003	+	0.190634i
$153$	3.00781	+	1.37362i	0.243167	+	0.111051i
$154$	0.0899611	+	0.0578145i	0.00724927	+	0.00465882i
$155$	−0.303213	+	16.8593i	−0.0243546	+	1.35417i
$156$	4.46391	+	5.15162i	0.357399	+	0.412460i
$157$	−2.09356	+	7.13001i	−0.167084	+	0.569037i	0.832796	+	0.553580i	$0.186739\pi$
$157$	−2.09356	+	7.13001i	−0.167084	+	0.569037i	−0.999881	+	0.0154573i	$0.995080\pi$
$158$	−7.04415	+	3.21695i	−0.560402	+	0.255927i
$159$	−1.41603	+	9.84870i	−0.112298	+	0.781053i
$160$	2.13382	+	0.668452i	0.168693	+	0.0528457i
$161$	−0.229419	+	0.0405449i	−0.0180807	+	0.00319539i
$162$			1.00000i			0.0785674i
$163$	−9.00864	−	1.29525i	−0.705611	−	0.101452i	−0.219838	−	0.975536i	$-0.570553\pi$
$163$	−9.00864	−	1.29525i	−0.705611	−	0.101452i	−0.485773	+	0.874085i	$0.661462\pi$
$164$	−2.85604	−	6.25385i	−0.223019	−	0.488344i
$165$	4.09239	+	2.73524i	0.318592	+	0.212938i
$166$	2.41816	+	2.79071i	0.187686	+	0.216601i
$167$	5.43621	+	18.5140i	0.420666	+	1.43266i	0.848690	+	0.528891i	$0.177392\pi$
$167$	5.43621	+	18.5140i	0.420666	+	1.43266i	−0.428023	+	0.903768i	$0.640790\pi$
$168$	−0.0262635	+	0.0408667i	−0.00202627	+	0.00315294i
$169$	−13.9021	+	30.4414i	−1.06940	+	2.34165i
$170$	3.88491	+	6.29097i	0.297959	+	0.482495i
$171$	−3.01926	+	1.94036i	−0.230888	+	0.148383i
$172$	9.97470	−	1.43415i	0.760564	−	0.109353i
$173$	−14.7786	+	2.12485i	−1.12360	+	0.161549i	−0.678970	−	0.734166i	$-0.737574\pi$
$173$	−14.7786	+	2.12485i	−1.12360	+	0.161549i	−0.444629	+	0.895715i	$0.646664\pi$
$174$	4.60544	−	2.95974i	0.349138	−	0.224377i
$175$	0.0600062	+	0.235363i	0.00453604	+	0.0177918i
$176$	−0.914465	+	2.00240i	−0.0689304	+	0.150936i
$177$	2.22339	−	3.45967i	0.167121	−	0.260045i
$178$	0.425648	+	1.44963i	0.0319037	+	0.108654i
$179$	−2.51964	−	2.90782i	−0.188327	−	0.217341i	0.653732	−	0.756726i	$-0.273202\pi$
$179$	−2.51964	−	2.90782i	−0.188327	−	0.217341i	−0.842059	+	0.539385i	$0.818657\pi$
$180$	−1.24254	+	1.85906i	−0.0926135	+	0.138566i
$181$	−3.15896	−	6.91717i	−0.234804	−	0.514149i	0.755148	−	0.655555i	$-0.227565\pi$
$181$	−3.15896	−	6.91717i	−0.234804	−	0.514149i	−0.989952	+	0.141406i	$0.954838\pi$
$182$	−0.327768	−	0.0471259i	−0.0242958	−	0.00349320i
$183$		−	9.40684i		−	0.695373i
$184$	−1.49824	−	4.55580i	−0.110451	−	0.335858i
$185$	1.91065	+	0.598540i	0.140474	+	0.0440056i
$186$	1.07318	−	7.46416i	0.0786896	−	0.547298i
$187$	−6.62118	+	3.02379i	−0.484188	+	0.221121i
$188$	2.13307	−	7.26457i	0.155570	−	0.529823i
$189$	−0.0318121	−	0.0367131i	−0.00231399	−	0.00267049i
$190$	−8.02395	−	0.144310i	−0.582118	−	0.0104694i
$191$	−0.374682	−	0.240793i	−0.0271110	−	0.0174232i	0.527015	−	0.849856i	$-0.323311\pi$
$191$	−0.374682	−	0.240793i	−0.0271110	−	0.0174232i	−0.554126	+	0.832433i	$0.686947\pi$
$192$	−0.909632	−	0.415415i	−0.0656470	−	0.0299800i
$193$	−13.3481	−	11.5662i	−0.960816	−	0.832552i	0.0251185	−	0.999684i	$-0.492004\pi$
$193$	−13.3481	−	11.5662i	−0.960816	−	0.832552i	−0.985934	+	0.167133i	$0.946549\pi$
$194$	6.31908	−	4.06103i	0.453684	−	0.291565i
$195$	−15.0457	−	2.44016i	−1.07745	−	0.174743i
$196$	0.995868	+	6.92641i	0.0711334	+	0.494744i
$197$	−9.90293	−	15.4093i	−0.705555	−	1.09786i	−0.990257	−	0.139249i	$-0.955531\pi$
$197$	−9.90293	−	15.4093i	−0.705555	−	1.09786i	0.284703	−	0.958616i	$-0.408105\pi$
$198$	−1.66365	−	1.44156i	−0.118231	−	0.102447i
$199$	0.725825	−	1.58934i	0.0514524	−	0.112665i	−0.882160	−	0.470950i	$-0.843911\pi$
$199$	0.725825	−	1.58934i	0.0514524	−	0.112665i	0.933612	+	0.358285i	$0.116638\pi$
$200$	−4.61991	+	1.91219i	−0.326677	+	0.135212i
$201$	−7.07640	+	2.07782i	−0.499131	+	0.146558i
$202$	−2.37289	+	2.05612i	−0.166956	+	0.144668i
$203$	−0.0749246	+	0.255170i	−0.00525868	+	0.0179094i
$204$	−1.37362	−	3.00781i	−0.0961727	−	0.210589i
$205$	13.8669	+	6.63673i	0.968509	+	0.463529i
$206$	−11.9238			−0.830773
$207$	4.79336	−	0.154031i	0.333161	−	0.0107059i
$208$		−	6.81657i		−	0.472644i
$209$	1.12437	−	7.82015i	0.0777741	−	0.540931i
$210$	−0.0135230	−	0.107780i	−0.000933175	−	0.00743750i
$211$	−6.26510	−	1.83960i	−0.431307	−	0.126643i	0.0588708	−	0.998266i	$-0.481250\pi$
$211$	−6.26510	−	1.83960i	−0.431307	−	0.126643i	−0.490178	+	0.871622i	$0.663068\pi$
$212$	7.51969	−	6.51585i	0.516454	−	0.447510i
$213$	2.90905	+	9.90733i	0.199325	+	0.678839i
$214$	11.8636	+	7.62427i	0.810979	+	0.521184i
$215$	−15.0601	+	16.7616i	−1.02709	+	1.14313i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	0.198050	+	0.308173i	0.0134445	+	0.0209201i
$218$	14.4360	−	2.07558i	0.977728	−	0.140576i
$219$	2.17445	+	15.1236i	0.146936	+	1.02196i
$220$	−1.30163	−	4.74710i	−0.0877556	−	0.320050i
$221$	14.7605	−	17.0345i	0.992896	−	1.14586i
$222$	−0.814496	−	0.371968i	−0.0546654	−	0.0249649i
$223$	13.7503	−	21.3959i	0.920788	−	1.43277i	0.0193756	−	0.999812i	$-0.493832\pi$
$223$	13.7503	−	21.3959i	0.920788	−	1.43277i	0.901412	−	0.432962i	$-0.142531\pi$
$224$	0.0466106	−	0.0136861i	0.00311430	−	0.000914442i
$225$	−0.533153	−	4.97149i	−0.0355435	−	0.331433i
$226$	11.3577	+	3.33492i	0.755502	+	0.221836i
$227$	3.98807	−	1.82129i	0.264697	−	0.120883i	−0.278646	−	0.960394i	$-0.589886\pi$
$227$	3.98807	−	1.82129i	0.264697	−	0.120883i	0.543343	+	0.839511i	$0.317158\pi$
$228$	3.55247	+	0.510768i	0.235268	+	0.0338264i
$229$	14.1390			0.934330			0.467165	−	0.884170i	$-0.345275\pi$
$229$	14.1390			0.934330			0.467165	+	0.884170i	$0.345275\pi$
$230$	9.10252	+	5.66959i	0.600202	+	0.373841i
$231$	0.106937			0.00703594
$232$	−5.41878	−	0.779102i	−0.355760	−	0.0511506i
$233$	−9.14523	+	4.17649i	−0.599124	+	0.273611i	−0.691804	−	0.722085i	$-0.743184\pi$
$233$	−9.14523	+	4.17649i	−0.599124	+	0.273611i	0.0926803	+	0.995696i	$0.470457\pi$
$234$	6.54045	+	1.92045i	0.427563	+	0.125544i
$235$	6.75485	+	15.5239i	0.440638	+	1.01267i
$236$	−3.94593	+	1.15863i	−0.256858	+	0.0754204i
$237$	−4.18670	+	6.51463i	−0.271955	+	0.423170i
$238$	0.146115	+	0.0667283i	0.00947120	+	0.00432535i
$239$	7.61330	−	8.78622i	0.492464	−	0.568333i	−0.454059	−	0.890972i	$-0.650024\pi$
$239$	7.61330	−	8.78622i	0.492464	−	0.568333i	0.946522	+	0.322639i	$0.104570\pi$
$240$	2.15647	−	0.591291i	0.139200	−	0.0381677i
$241$	−2.60573	−	18.1233i	−0.167850	−	1.16742i	−0.883317	−	0.468776i	$-0.844695\pi$
$241$	−2.60573	−	18.1233i	−0.167850	−	1.16742i	0.715467	−	0.698646i	$-0.246214\pi$
$242$	−6.09152	+	0.875828i	−0.391577	+	0.0563003i
$243$	0.540641	+	0.841254i	0.0346821	+	0.0539664i
$244$	−6.16017	+	7.10921i	−0.394364	+	0.455121i
$245$	−11.6392	−	10.4577i	−0.743601	−	0.668119i
$246$	−5.78374	−	3.71698i	−0.368758	−	0.236986i
$247$	6.89249	+	23.4737i	0.438559	+	1.49359i
$248$	−5.69904	+	4.93825i	−0.361889	+	0.313579i
$249$	3.54306	+	1.04034i	0.224532	+	0.0659286i
$250$	5.18612	−	9.90476i	0.327999	−	0.626432i
$251$	1.67021	−	11.6166i	0.105423	−	0.733232i	−0.866712	−	0.498809i	$-0.833771\pi$
$251$	1.67021	−	11.6166i	0.105423	−	0.733232i	0.972135	−	0.234423i	$-0.0753200\pi$
$252$			0.0485784i			0.00306015i
$253$	−6.65367	+	8.19653i	−0.418313	+	0.515311i
$254$	−17.7386			−1.11302
$255$	6.66935	+	3.19195i	0.417651	+	0.199888i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−1.40249	+	4.77644i	−0.0874849	+	0.297946i	−0.991600	−	0.129343i	$-0.958713\pi$
$257$	−1.40249	+	4.77644i	−0.0874849	+	0.297946i	0.904115	+	0.427289i	$0.140531\pi$
$258$	7.61589	−	6.59921i	0.474145	−	0.410849i
$259$	0.0417358	−	0.0122547i	0.00259333	−	0.000761472i
$260$	9.77284	+	11.6970i	0.606086	+	0.725417i
$261$	2.27419	−	4.97978i	0.140769	−	0.308241i
$262$	−4.74645	−	4.11283i	−0.293237	−	0.254091i
$263$	6.07395	+	9.45125i	0.374536	+	0.582789i	0.976443	−	0.215777i	$-0.0692285\pi$
$263$	6.07395	+	9.45125i	0.374536	+	0.582789i	−0.601907	+	0.798566i	$0.705592\pi$
$264$	0.313282	+	2.17892i	0.0192811	+	0.134103i
$265$	−3.56183	+	21.9619i	−0.218802	+	1.34911i
$266$	−0.146671	+	0.0942595i	−0.00899296	+	0.00577942i
$267$	1.14180	+	0.989379i	0.0698773	+	0.0605490i
$268$	6.70867	+	3.06375i	0.409797	+	0.187148i
$269$	−14.7104	−	9.45380i	−0.896909	−	0.576408i	0.00896308	−	0.999960i	$-0.497147\pi$
$269$	−14.7104	−	9.45380i	−0.896909	−	0.576408i	−0.905872	+	0.423551i	$0.860783\pi$
$270$	−0.0402090	+	2.23571i	−0.00244704	+	0.136061i
$271$	−0.484554	−	0.559205i	−0.0294346	−	0.0339693i	0.740841	−	0.671680i	$-0.234427\pi$
$271$	−0.484554	−	0.559205i	−0.0294346	−	0.0339693i	−0.770276	+	0.637711i	$0.779882\pi$
$272$	−0.931584	+	3.17268i	−0.0564855	+	0.192372i
$273$	−0.301214	+	0.137560i	−0.0182303	+	0.00832550i
$274$	2.96214	−	20.6022i	0.178950	−	1.24462i
$275$	9.03941	+	6.27974i	0.545097	+	0.378683i
$276$	−3.72345	−	3.02257i	−0.224125	−	0.181938i
$277$			26.4883i			1.59152i	0.605609	+	0.795762i	$0.292930\pi$
$277$			26.4883i			1.59152i	−0.605609	+	0.795762i	$0.707070\pi$
$278$	3.70055	+	0.532059i	0.221944	+	0.0319108i
$279$	−3.13261	−	6.85945i	−0.187544	−	0.410665i
$280$	−0.0603606	+	0.0903100i	−0.00360724	+	0.00539706i
$281$	−1.14389	−	1.32013i	−0.0682390	−	0.0787521i	0.720604	−	0.693347i	$-0.243865\pi$
$281$	−1.14389	−	1.32013i	−0.0682390	−	0.0787521i	−0.788843	+	0.614595i	$0.789319\pi$
$282$	−2.13307	−	7.26457i	−0.127022	−	0.432599i
$283$	16.4559	−	25.6059i	0.978204	−	1.52212i	0.130635	−	0.991430i	$-0.458298\pi$
$283$	16.4559	−	25.6059i	0.978204	−	1.52212i	0.847569	−	0.530685i	$-0.178065\pi$
$284$	4.28940	−	9.39249i	0.254529	−	0.557341i
$285$	−6.82819	+	4.21667i	−0.404467	+	0.249774i
$286$	−12.6234	+	8.11259i	−0.746440	+	0.479708i
$287$	0.330584	−	0.0475308i	0.0195138	−	0.00280566i
$288$	−0.989821	+	0.142315i	−0.0583258	+	0.00838598i
$289$	5.10325	−	3.27966i	0.300191	−	0.192921i
$290$	10.4154	−	6.43192i	0.611615	−	0.377696i
$291$	3.12039	−	6.83271i	0.182921	−	0.400540i
$292$	8.26054	−	12.8536i	0.483411	−	0.752203i
$293$	−4.82347	−	16.4272i	−0.281790	−	0.959688i	−0.971784	−	0.235873i	$-0.924205\pi$
$293$	−4.82347	−	16.4272i	−0.281790	−	0.959688i	0.689994	−	0.723815i	$-0.257613\pi$
$294$	4.58248	+	5.28846i	0.267256	+	0.308429i
$295$	5.10997	−	7.64540i	0.297514	−	0.445133i
$296$	0.371968	+	0.814496i	0.0216202	+	0.0473416i
$297$	−2.17892	−	0.313282i	−0.126434	−	0.0181784i
$298$			4.71330i			0.273034i
$299$	8.19798	−	31.6465i	0.474101	−	1.83017i
$300$	−2.85271	+	4.10635i	−0.164701	+	0.237080i
$301$	−0.0696685	+	0.484555i	−0.00401563	+	0.0279293i
$302$	3.16064	−	1.44342i	0.181874	−	0.0830592i
$303$	−0.884580	+	3.01260i	−0.0508178	+	0.173070i
$304$	−2.35029	−	2.71238i	−0.134799	−	0.155566i
$305$	0.378240	−	21.0309i	0.0216579	−	1.20423i
$306$	−2.78171	−	1.78770i	−0.159020	−	0.102196i
$307$	−3.21744	−	1.46935i	−0.183629	−	0.0838605i	0.321479	−	0.946917i	$-0.395820\pi$
$307$	−3.21744	−	1.46935i	−0.183629	−	0.0838605i	−0.505108	+	0.863056i	$0.668547\pi$
$308$	−0.0808176	−	0.0700288i	−0.00460501	−	0.00399026i
$309$	−10.0310	+	6.44652i	−0.570642	+	0.366729i
$310$	2.69945	−	16.6445i	0.153318	−	0.945345i
$311$	3.25671	+	22.6509i	0.184671	+	1.28441i	0.845540	+	0.533913i	$0.179279\pi$
$311$	3.25671	+	22.6509i	0.184671	+	1.28441i	−0.660869	+	0.750502i	$0.729812\pi$
$312$	−3.68532	−	5.73447i	−0.208640	−	0.324650i
$313$	−4.33762	−	3.75857i	−0.245177	−	0.212447i	0.523600	−	0.851964i	$-0.324589\pi$
$313$	−4.33762	−	3.75857i	−0.245177	−	0.212447i	−0.768777	+	0.639517i	$0.779134\pi$
$314$	3.08696	−	6.75950i	0.174207	−	0.381460i
$315$	−0.0696463	−	0.0833589i	−0.00392412	−	0.00469674i
$316$	7.43027	−	2.18172i	0.417985	−	0.122732i
$317$	16.2089	−	14.0451i	0.910382	−	0.788851i	−0.0675625	−	0.997715i	$-0.521522\pi$
$317$	16.2089	−	14.0451i	0.910382	−	0.788851i	0.977945	+	0.208864i	$0.0669767\pi$
$318$	2.80323	−	9.54693i	0.157197	−	0.535365i
$319$	5.00624	+	10.9621i	0.280295	+	0.613761i
$320$	−2.01697	−	0.965321i	−0.112752	−	0.0539631i
$321$	14.1023			0.787113
$322$	0.232854	−	0.00748257i	0.0129764	−	0.000416987i
$323$		−	11.8675i		−	0.660324i
$324$	0.142315	−	0.989821i	0.00790638	−	0.0549901i
$325$	−33.5397	−	6.06045i	−1.86045	−	0.336173i
$326$	8.73261	+	2.56413i	0.483655	+	0.142014i
$327$	11.0222	−	9.55077i	0.609528	−	0.528159i
$328$	1.93695	+	6.59665i	0.106950	+	0.364239i
$329$	0.309413	+	0.198847i	0.0170585	+	0.0109628i
$330$	−3.66147	−	3.28981i	−0.201558	−	0.181098i
$331$	17.6200	−	20.3346i	0.968482	−	1.11769i	−0.0245325	−	0.999699i	$-0.507810\pi$
$331$	17.6200	−	20.3346i	0.968482	−	1.11769i	0.993015	−	0.117989i	$-0.0376448\pi$
$332$	−1.99639	−	3.10644i	−0.109566	−	0.170488i
$333$	−0.886299	+	0.127431i	−0.0485689	+	0.00698315i
$334$	−2.74606	−	19.0992i	−0.150257	−	1.04506i
$335$	−15.9043	+	4.36086i	−0.868945	+	0.238259i
$336$	0.0318121	−	0.0367131i	0.00173549	−	0.00200286i
$337$	−22.2771	−	10.1736i	−1.21351	−	0.554192i	−0.297260	−	0.954796i	$-0.596073\pi$
$337$	−22.2771	−	10.1736i	−1.21351	−	0.554192i	−0.916251	+	0.400604i	$0.868800\pi$
$338$	18.0929	−	28.1531i	0.984125	−	1.53133i
$339$	11.3577	−	3.33492i	0.616865	−	0.181128i
$340$	−2.95007	−	6.77981i	−0.159990	−	0.367687i
$341$	15.9276	+	4.67677i	0.862528	+	0.253261i
$342$	3.26467	−	1.49092i	0.176533	−	0.0806199i
$343$	−0.673062	−	0.0967717i	−0.0363419	−	0.00522518i
$344$	−10.0773			−0.543330
$345$	10.7227	−	0.151631i	0.577293	−	0.00816356i
$346$	14.9306			0.802675
$347$	−10.3561	−	1.48899i	−0.555947	−	0.0799331i	−0.141386	−	0.989955i	$-0.545156\pi$
$347$	−10.3561	−	1.48899i	−0.555947	−	0.0799331i	−0.414561	+	0.910021i	$0.636065\pi$
$348$	−4.97978	+	2.27419i	−0.266944	+	0.121909i
$349$	6.93815	+	2.03723i	0.371391	+	0.109050i	0.462101	−	0.886827i	$-0.347096\pi$
$349$	6.93815	+	2.03723i	0.371391	+	0.109050i	−0.0907106	+	0.995877i	$0.528914\pi$
$350$	−0.0258997	−	0.241507i	−0.00138440	−	0.0129091i
$351$	6.54045	−	1.92045i	0.349104	−	0.102506i
$352$	1.19013	−	1.85187i	0.0634340	−	0.0987053i
$353$	19.8385	+	9.05996i	1.05590	+	0.482213i	0.866235	−	0.499636i	$-0.166533\pi$
$353$	19.8385	+	9.05996i	1.05590	+	0.482213i	0.189664	+	0.981849i	$0.439260\pi$
$354$	−2.69313	+	3.10803i	−0.143138	+	0.165190i
$355$	6.10543	+	22.2668i	0.324042	+	1.18180i
$356$	−0.215013	−	1.49545i	−0.0113957	−	0.0792585i
$357$	0.158995	−	0.0228601i	0.00841493	−	0.00120988i
$358$	2.08017	+	3.23680i	0.109940	+	0.171070i
$359$	8.57689	−	9.89826i	0.452671	−	0.522410i	−0.482840	−	0.875709i	$-0.660395\pi$
$359$	8.57689	−	9.89826i	0.452671	−	0.522410i	0.935511	+	0.353299i	$0.114940\pi$
$360$	1.49446	−	1.66330i	0.0787652	−	0.0876638i
$361$	−5.14771	−	3.30823i	−0.270932	−	0.174117i
$362$	2.14240	+	7.29633i	0.112602	+	0.383487i
$363$	−4.65100	+	4.03012i	−0.244114	+	0.211526i
$364$	0.317725	+	0.0932924i	0.0166533	+	0.00488985i
$365$	4.25333	+	33.8994i	0.222629	+	1.77438i
$366$	−1.33873	+	9.31109i	−0.0699767	+	0.486698i
$367$			15.3187i			0.799631i	0.916596	+	0.399816i	$0.130926\pi$
$367$			15.3187i			0.799631i	−0.916596	+	0.399816i	$0.869074\pi$
$368$	0.834629	+	4.72265i	0.0435080	+	0.246185i
$369$	−6.87515			−0.357906
$370$	−1.80602	−	0.864362i	−0.0938904	−	0.0449360i
$371$	0.200792	+	0.439674i	0.0104246	+	0.0228267i
$372$	−2.12452	+	7.23545i	−0.110151	+	0.375141i
$373$	−5.52260	+	4.78536i	−0.285949	+	0.247777i	−0.786010	−	0.618214i	$-0.787857\pi$
$373$	−5.52260	+	4.78536i	−0.285949	+	0.247777i	0.500061	+	0.865990i	$0.333311\pi$
$374$	6.98411	−	2.05072i	0.361140	−	0.106040i
$375$	−0.992075	−	11.1362i	−0.0512305	−	0.575073i
$376$	−3.14521	+	6.88706i	−0.162202	+	0.355173i
$377$	−28.2026	−	24.4377i	−1.45251	−	1.25860i
$378$	0.0262635	+	0.0408667i	0.00135085	+	0.00210196i
$379$	−1.06311	−	7.39410i	−0.0546083	−	0.379809i	−0.998737	−	0.0502337i	$-0.984003\pi$
$379$	−1.06311	−	7.39410i	−0.0546083	−	0.379809i	0.944129	−	0.329576i	$-0.106906\pi$
$380$	7.92174	+	1.28477i	0.406377	+	0.0659072i
$381$	−14.9227	+	9.59021i	−0.764511	+	0.491321i
$382$	0.336600	+	0.291665i	0.0172219	+	0.0149229i
$383$	7.73077	+	3.53052i	0.395024	+	0.180401i	0.603016	−	0.797729i	$-0.293966\pi$
$383$	7.73077	+	3.53052i	0.395024	+	0.180401i	−0.207992	+	0.978131i	$0.566693\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	0.239080	+	0.00429983i	0.0121846	+	0.000219140i
$386$	11.5662	+	13.3481i	0.588703	+	0.679399i
$387$	2.83910	−	9.66907i	0.144319	−	0.491507i
$388$	−6.83271	+	3.12039i	−0.346878	+	0.158414i
$389$	1.95745	−	13.6144i	0.0992468	−	0.690277i	−0.878076	−	0.478521i	$-0.841173\pi$
$389$	1.95745	−	13.6144i	0.0992468	−	0.690277i	0.977323	−	0.211755i	$-0.0679180\pi$
$390$	14.5453	+	4.55655i	0.736531	+	0.230730i
$391$	−8.14060	+	13.6091i	−0.411688	+	0.688241i
$392$		−	6.99764i		−	0.353434i
$393$	−6.21653	−	0.893803i	−0.313583	−	0.0450864i
$394$	7.60917	+	16.6618i	0.383344	+	0.839407i
$395$	−9.62217	+	14.3964i	−0.484144	+	0.724364i
$396$	1.44156	+	1.66365i	0.0724413	+	0.0836017i
$397$	−0.653922	−	2.22705i	−0.0328194	−	0.111773i	0.941454	−	0.337141i	$-0.109460\pi$
$397$	−0.653922	−	2.22705i	−0.0328194	−	0.111773i	−0.974274	+	0.225368i	$0.927642\pi$
$398$	−0.944623	+	1.46986i	−0.0473497	+	0.0736775i
$399$	−0.0724267	+	0.158592i	−0.00362587	+	0.00793955i
$400$	4.84502	−	1.23524i	0.242251	−	0.0617622i
$401$	32.1048	−	20.6325i	1.60324	−	1.03034i	0.637626	−	0.770346i	$-0.279917\pi$
$401$	32.1048	−	20.6325i	1.60324	−	1.03034i	0.965611	−	0.259991i	$-0.0837197\pi$
$402$	7.30008	−	1.04959i	0.364095	−	0.0523489i
$403$	−50.8800	+	7.31544i	−2.53451	+	0.364408i
$404$	2.64136	−	1.69750i	0.131412	−	0.0844536i
$405$	1.17489	+	1.90253i	0.0583807	+	0.0945377i
$406$	0.110476	−	0.241910i	0.00548286	−	0.0120058i
$407$	1.06566	−	1.65819i	0.0528226	−	0.0821936i
$408$	0.931584	+	3.17268i	0.0461203	+	0.157071i
$409$	22.2929	+	25.7273i	1.10231	+	1.27214i	0.959292	+	0.282416i	$0.0911357\pi$
$409$	22.2929	+	25.7273i	1.10231	+	1.27214i	0.143019	+	0.989720i	$0.454319\pi$
$410$	−12.7813	−	8.54264i	−0.631223	−	0.421891i
$411$	−8.64646	−	18.9331i	−0.426498	−	0.933901i
$412$	11.8025	+	1.69694i	0.581466	+	0.0836022i
$413$		−	0.199779i		−	0.00983050i
$414$	−4.76649	−	0.529703i	−0.234260	−	0.0260335i
$415$	7.87941	+	2.46835i	0.386785	+	0.121166i
$416$	−0.970100	+	6.74719i	−0.0475630	+	0.330808i
$417$	3.40075	−	1.55307i	0.166536	−	0.0760543i
$418$	−2.22585	+	7.58053i	−0.108870	+	0.370776i
$419$	−19.8690	−	22.9300i	−0.970663	−	1.12020i	−0.992720	−	0.120448i	$-0.961567\pi$
$419$	−19.8690	−	22.9300i	−0.970663	−	1.12020i	0.0220566	−	0.999757i	$-0.492979\pi$
$420$	−0.00195329	+	0.108607i	−9.53107e−5	+	0.00529948i
$421$	4.36572	+	2.80568i	0.212772	+	0.136740i	0.642686	−	0.766129i	$-0.277820\pi$
$421$	4.36572	+	2.80568i	0.212772	+	0.136740i	−0.429914	+	0.902870i	$0.641456\pi$
$422$	5.93953	+	2.71249i	0.289132	+	0.132042i
$423$	−5.72197	−	4.95812i	−0.278212	−	0.241072i
$424$	−8.37045	+	5.37936i	−0.406505	+	0.261245i
$425$	14.7824	+	7.40444i	0.717050	+	0.359168i
$426$	−1.46948	−	10.2205i	−0.0711968	−	0.495184i
$427$	−0.247056	−	0.384427i	−0.0119559	−	0.0186037i
$428$	−10.6578	−	9.23503i	−0.515164	−	0.446392i
$429$	−6.23352	+	13.6495i	−0.300957	+	0.659004i
$430$	17.2923	−	14.4477i	0.833906	−	0.696729i
$431$	−12.4920	+	3.66797i	−0.601717	+	0.176680i	−0.568383	−	0.822764i	$-0.692431\pi$
$431$	−12.4920	+	3.66797i	−0.601717	+	0.176680i	−0.0333342	+	0.999444i	$0.510613\pi$
$432$	−0.755750	+	0.654861i	−0.0363610	+	0.0315070i
$433$	−11.1511	+	37.9772i	−0.535889	+	1.82507i	0.0285470	+	0.999592i	$0.490912\pi$
$433$	−11.1511	+	37.9772i	−0.535889	+	1.82507i	−0.564436	+	0.825477i	$0.690906\pi$
$434$	−0.152177	−	0.333221i	−0.00730473	−	0.0159951i
$435$	5.28465	−	11.0419i	0.253380	−	0.529418i
$436$	−14.5844			−0.698468
$437$	−7.64939	−	15.4191i	−0.365920	−	0.737594i
$438$		−	15.2792i		−	0.730066i
$439$	3.31275	−	23.0407i	0.158109	−	1.09967i	−0.744005	−	0.668174i	$-0.767076\pi$
$439$	3.31275	−	23.0407i	0.158109	−	1.09967i	0.902114	−	0.431497i	$-0.142015\pi$
$440$	0.612793	+	4.88403i	0.0292138	+	0.232837i
$441$	6.71419	+	1.97146i	0.319723	+	0.0938792i
$442$	−17.0345	+	14.7605i	−0.810247	+	0.702083i
$443$	5.51143	+	18.7702i	0.261856	+	0.891800i	0.980516	+	0.196438i	$0.0629376\pi$
$443$	5.51143	+	18.7702i	0.261856	+	0.891800i	−0.718660	+	0.695362i	$0.755244\pi$
$444$	0.753270	+	0.484097i	0.0357486	+	0.0229742i
$445$	2.51296	+	2.25787i	0.119126	+	0.107033i
$446$	−16.6553	+	19.2212i	−0.788651	+	0.910152i
$447$	2.54820	+	3.96508i	0.120526	+	0.187542i
$448$	−0.0480839	+	0.00691343i	−0.00227175	+	0.000326629i
$449$	−0.744691	−	5.17944i	−0.0351442	−	0.244433i	0.964675	−	0.263442i	$-0.0848579\pi$
$449$	−0.744691	−	5.17944i	−0.0351442	−	0.244433i	−0.999819	+	0.0190093i	$0.993949\pi$
$450$	−0.179791	+	4.99677i	−0.00847543	+	0.235550i
$451$	9.91096	−	11.4379i	0.466689	−	0.538588i
$452$	−10.7675	−	4.91734i	−0.506460	−	0.231292i
$453$	1.87853	−	2.92305i	0.0882610	−	0.137337i
$454$	−4.20667	+	1.23519i	−0.197429	+	0.0579703i
$455$	−0.678957	+	0.295432i	−0.0318300	+	0.0138501i
$456$	−3.44362	−	1.01114i	−0.161262	−	0.0473509i
$457$	2.45719	−	1.12216i	0.114942	−	0.0524925i	−0.357114	−	0.934061i	$-0.616239\pi$
$457$	2.45719	−	1.12216i	0.114942	−	0.0524925i	0.472056	+	0.881568i	$0.343512\pi$
$458$	−13.9951	−	2.01219i	−0.653947	−	0.0940233i
$459$	−3.30662			−0.154340
$460$	−8.20300	−	6.90730i	−0.382467	−	0.322055i
$461$	0.431935			0.0201172			0.0100586	−	0.999949i	$-0.496798\pi$
$461$	0.431935			0.0201172			0.0100586	+	0.999949i	$0.496798\pi$
$462$	−0.105849	−	0.0152187i	−0.00492452	−	0.000708039i
$463$	−4.47584	+	2.04405i	−0.208010	+	0.0949949i	−0.516696	−	0.856169i	$-0.672838\pi$
$463$	−4.47584	+	2.04405i	−0.208010	+	0.0949949i	0.308686	+	0.951164i	$0.400111\pi$
$464$	5.25274	+	1.54234i	0.243852	+	0.0716016i
$465$	−6.72778	−	15.4617i	−0.311993	−	0.717019i
$466$	9.64652	−	2.83247i	0.446866	−	0.131212i
$467$	15.8104	−	24.6014i	0.731618	−	1.13842i	−0.253633	−	0.967301i	$-0.581626\pi$
$467$	15.8104	−	24.6014i	0.731618	−	1.13842i	0.985250	−	0.171119i	$-0.0547381\pi$
$468$	−6.20057	−	2.83171i	−0.286622	−	0.130896i
$469$	−0.234619	+	0.270765i	−0.0108337	+	0.0125027i
$470$	−4.47682	−	16.3272i	−0.206500	−	0.753118i
$471$	−1.05754	−	7.35539i	−0.0487291	−	0.338918i
$472$	4.07066	−	0.585272i	0.187367	−	0.0269393i
$473$	11.9932	+	18.6618i	0.551450	+	0.858073i
$474$	5.07121	−	5.85249i	0.232928	−	0.268814i
$475$	−15.4354	+	9.15269i	−0.708224	+	0.419954i
$476$	−0.135131	−	0.0868434i	−0.00619372	−	0.00398046i
$477$	−2.80323	−	9.54693i	−0.128351	−	0.437124i
$478$	−8.78622	+	7.61330i	−0.401872	+	0.348224i
$479$	1.56580	+	0.459760i	0.0715432	+	0.0210070i	0.317308	−	0.948322i	$-0.397221\pi$
$479$	1.56580	+	0.459760i	0.0715432	+	0.0210070i	−0.245765	+	0.969329i	$0.579039\pi$
$480$	−2.21867	+	0.278374i	−0.101268	+	0.0127060i
$481$	−0.868640	+	6.04152i	−0.0396066	+	0.275470i
$482$			18.3096i			0.833981i
$483$	0.191844	−	0.132185i	0.00872918	−	0.00601462i
$484$	6.15416			0.279734
$485$	7.25102	−	15.1505i	0.329252	−	0.687947i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	−1.56060	+	5.31490i	−0.0707174	+	0.240841i	−0.987265	−	0.159084i	$-0.949146\pi$
$487$	−1.56060	+	5.31490i	−0.0707174	+	0.240841i	0.916548	+	0.399926i	$0.130964\pi$
$488$	7.10921	−	6.16017i	0.321819	−	0.278858i
$489$	8.73261	−	2.56413i	0.394902	−	0.115954i
$490$	10.0324	+	12.0077i	0.453219	+	0.542453i
$491$	−5.93915	+	13.0049i	−0.268030	+	0.586904i	−0.995012	−	0.0997522i	$-0.968195\pi$
$491$	−5.93915	+	13.0049i	−0.268030	+	0.586904i	0.726982	+	0.686656i	$0.240922\pi$
$492$	5.19589	+	4.50226i	0.234249	+	0.202978i
$493$	9.78674	+	15.2285i	0.440773	+	0.685855i
$494$	−3.48169	−	24.2157i	−0.156648	−	1.08951i
$495$	−4.85883	−	0.788018i	−0.218388	−	0.0354188i
$496$	6.34382	−	4.07692i	0.284846	−	0.183059i
$497$	0.379084	+	0.328478i	0.0170043	+	0.0147343i
$498$	−3.35894	−	1.53398i	−0.150518	−	0.0687391i
$499$	28.0615	+	18.0340i	1.25621	+	0.807314i	0.987760	−	0.155981i	$-0.0498538\pi$
$499$	28.0615	+	18.0340i	1.25621	+	0.807314i	0.268445	+	0.963295i	$0.413490\pi$
$500$	−6.54292	+	9.06588i	−0.292608	+	0.405438i
$501$	−12.6360	−	14.5827i	−0.564533	−	0.651506i
$502$	−3.30642	+	11.2606i	−0.147573	+	0.502587i
$503$	34.2470	−	15.6401i	1.52700	−	0.697357i	0.537683	−	0.843147i	$-0.319300\pi$
$503$	34.2470	−	15.6401i	1.52700	−	0.697357i	0.989316	+	0.145790i	$0.0465725\pi$
$504$	0.00691343	−	0.0480839i	0.000307949	−	0.00214183i
$505$	−2.09879	+	6.69973i	−0.0933951	+	0.298134i
$506$	7.75244	−	7.16618i	0.344638	−	0.318576i
$507$		−	33.4657i		−	1.48626i
$508$	17.5580	+	2.52447i	0.779012	+	0.112005i
$509$	3.86186	+	8.45629i	0.171174	+	0.374818i	0.975704	−	0.219094i	$-0.0703100\pi$
$509$	3.86186	+	8.45629i	0.171174	+	0.374818i	−0.804530	+	0.593912i	$0.797583\pi$
$510$	−6.14720	−	4.10861i	−0.272203	−	0.181932i
$511$	0.486062	+	0.560945i	0.0215021	+	0.0248148i
$512$	−0.281733	−	0.959493i	−0.0124509	−	0.0424040i
$513$	1.94036	−	3.01926i	0.0856689	−	0.133303i
$514$	2.06797	−	4.52823i	0.0912143	−	0.199732i
$515$	−22.6855	+	14.0092i	−0.999644	+	0.617318i
$516$	−8.47754	+	5.44819i	−0.373203	+	0.239843i
$517$	16.4972	−	2.37194i	0.725545	−	0.104318i
$518$	−0.0430550	+	0.00619037i	−0.00189173	+	0.000271989i
$519$	12.5604	−	8.07210i	0.551342	−	0.354326i
$520$	−8.00871	−	12.9688i	−0.351205	−	0.568718i
$521$	−8.92759	+	19.5487i	−0.391125	+	0.856444i	0.606969	+	0.794726i	$0.292385\pi$
$521$	−8.92759	+	19.5487i	−0.391125	+	0.856444i	−0.998094	+	0.0617184i	$0.980342\pi$
$522$	−2.95974	+	4.60544i	−0.129544	+	0.201575i
$523$	−4.97055	−	16.9281i	−0.217347	−	0.740216i	−0.993912	−	0.110178i	$-0.964858\pi$
$523$	−4.97055	−	16.9281i	−0.217347	−	0.740216i	0.776565	−	0.630037i	$-0.216960\pi$
$524$	4.11283	+	4.74645i	0.179670	+	0.207350i
$525$	−0.152357	−	0.189166i	−0.00664940	−	0.00825590i
$526$	−4.66707	−	10.2195i	−0.203494	−	0.445590i
$527$	24.6812	+	3.54861i	1.07513	+	0.154580i
$528$		−	2.20133i		−	0.0958005i
$529$	−1.80487	+	22.9291i	−0.0784726	+	0.996916i
$530$	6.65108	−	21.2314i	0.288904	−	0.922234i
$531$	−0.585272	+	4.07066i	−0.0253986	+	0.176651i
$532$	0.158592	−	0.0724267i	0.00687585	−	0.00314010i
$533$	−13.2034	+	44.9666i	−0.571902	+	1.94772i
$534$	−0.989379	−	1.14180i	−0.0428146	−	0.0494107i
$535$	31.5286	+	0.567039i	1.36310	+	0.0245152i
$536$	−6.20437	−	3.98731i	−0.267988	−	0.172225i
$537$	3.49990	+	1.59835i	0.151032	+	0.0689739i
$538$	13.2153	+	11.4511i	0.569750	+	0.493691i
$539$	−12.9588	+	8.32808i	−0.558173	+	0.358716i
$540$	0.357974	−	2.20723i	0.0154047	−	0.0949840i
$541$	0.846878	+	5.89016i	0.0364101	+	0.253238i	0.999894	−	0.0145267i	$-0.00462414\pi$
$541$	0.846878	+	5.89016i	0.0364101	+	0.253238i	−0.963484	+	0.267765i	$0.913715\pi$
$542$	0.400039	+	0.622473i	0.0171831	+	0.0267375i
$543$	5.74699	+	4.97980i	0.246627	+	0.213704i
$544$	1.37362	−	3.00781i	0.0588935	−	0.128959i
$545$	25.0264	−	20.9095i	1.07201	−	0.895666i
$546$	0.317725	−	0.0932924i	0.0135974	−	0.00399255i
$547$	−29.3074	+	25.3950i	−1.25310	+	1.08581i	−0.260358	+	0.965512i	$0.583841\pi$
$547$	−29.3074	+	25.3950i	−1.25310	+	1.08581i	−0.992737	+	0.120302i	$0.961614\pi$
$548$	−5.86399	+	19.9709i	−0.250497	+	0.853115i
$549$	3.90774	+	8.55676i	0.166778	+	0.365194i
$550$	−8.05370	−	7.50226i	−0.343411	−	0.319898i
$551$	−19.6480			−0.837032
$552$	3.25539	+	3.52171i	0.138559	+	0.149894i
$553$			0.376189i			0.0159972i
$554$	3.76967	−	26.2186i	0.160158	−	1.11392i
$555$	−1.98663	+	0.249260i	−0.0843277	+	0.0105805i
$556$	−3.58716	−	1.05329i	−0.152130	−	0.0446693i
$557$	2.23285	−	1.93477i	0.0946087	−	0.0819789i	−0.606272	−	0.795257i	$-0.707336\pi$
$557$	2.23285	−	1.93477i	0.0946087	−	0.0819789i	0.700881	+	0.713278i	$0.252790\pi$
$558$	2.12452	+	7.23545i	0.0899381	+	0.306301i
$559$	−57.7878	−	37.1380i	−2.44416	−	1.57077i
$560$	0.0725987	−	0.0808006i	0.00306785	−	0.00341445i
$561$	4.76671	−	5.50107i	0.201251	−	0.232255i
$562$	0.944378	+	1.46948i	0.0398362	+	0.0619863i
$563$	−20.1325	+	2.89462i	−0.848484	+	0.121994i	−0.552822	−	0.833299i	$-0.686449\pi$
$563$	−20.1325	+	2.89462i	−0.848484	+	0.121994i	−0.295661	+	0.955293i	$0.595540\pi$
$564$	1.07750	+	7.49419i	0.0453710	+	0.315562i
$565$	25.5266	−	6.99922i	1.07391	−	0.294459i
$566$	−19.9326	+	23.0034i	−0.837828	+	0.966905i
$567$	0.0441885	+	0.0201802i	0.00185574	+	0.000847489i
$568$	−5.58243	+	8.68644i	−0.234234	+	0.364475i
$569$	33.4089	−	9.80972i	1.40057	−	0.411245i	0.507692	−	0.861539i	$-0.330499\pi$
$569$	33.4089	−	9.80972i	1.40057	−	0.411245i	0.892880	+	0.450294i	$0.148681\pi$
$570$	7.35879	−	3.20200i	0.308226	−	0.134117i
$571$	8.11064	+	2.38150i	0.339420	+	0.0996626i	0.447000	−	0.894534i	$-0.352492\pi$
$571$	8.11064	+	2.38150i	0.339420	+	0.0996626i	−0.107581	+	0.994196i	$0.534310\pi$
$572$	13.6495	−	6.23352i	0.570714	−	0.260636i
$573$	0.440852	+	0.0633849i	0.0184168	+	0.00264794i
$574$	−0.333984			−0.0139402
$575$	23.9790	+	0.0921470i	0.999993	+	0.00384280i
$576$	1.00000			0.0416667
$577$	11.0800	+	1.59306i	0.461265	+	0.0663198i	0.369030	−	0.929417i	$-0.379690\pi$
$577$	11.0800	+	1.59306i	0.461265	+	0.0663198i	0.0922345	+	0.995737i	$0.470599\pi$
$578$	−5.51805	+	2.52001i	−0.229520	+	0.104818i
$579$	16.9466	+	4.97597i	0.704277	+	0.206794i
$580$	−11.2248	+	4.88419i	−0.466083	+	0.202805i
$581$	0.172116	−	0.0505379i	0.00714058	−	0.00209666i
$582$	−4.06103	+	6.31908i	−0.168335	+	0.261934i
$583$	19.9238	+	9.09890i	0.825160	+	0.376838i
$584$	−10.0057	+	11.5472i	−0.414040	+	0.477827i
$585$	14.6998	−	4.03058i	0.607760	−	0.166644i
$586$	2.43653	+	16.9465i	0.100652	+	0.700052i
$587$	−8.19959	+	1.17892i	−0.338433	+	0.0486594i	−0.309436	−	0.950920i	$-0.600140\pi$
$587$	−8.19959	+	1.17892i	−0.338433	+	0.0486594i	−0.0289969	+	0.999580i	$0.509231\pi$
$588$	−3.78321	−	5.88679i	−0.156017	−	0.242767i
$589$	−17.7234	+	20.4538i	−0.730278	+	0.842786i
$590$	−6.14601	+	6.84036i	−0.253027	+	0.281613i
$591$	15.4093	+	9.90293i	0.633852	+	0.407352i
$592$	−0.252267	−	0.859143i	−0.0103681	−	0.0353105i
$593$	−14.9504	+	12.9546i	−0.613938	+	0.531980i	−0.905377	−	0.424609i	$-0.860412\pi$
$593$	−14.9504	+	12.9546i	−0.613938	+	0.531980i	0.291439	+	0.956590i	$0.405866\pi$
$594$	2.11216	+	0.620186i	0.0866629	+	0.0254465i
$595$	0.356386	−	0.0447154i	0.0146104	−	0.00183315i
$596$	0.670773	−	4.66533i	0.0274759	−	0.191099i
$597$			1.74723i			0.0715093i
$598$	−12.6183	+	30.1577i	−0.516001	+	1.23324i
$599$	−33.8462			−1.38292			−0.691460	−	0.722415i	$-0.743032\pi$
$599$	−33.8462			−1.38292			−0.691460	+	0.722415i	$0.743032\pi$
$600$	3.40806	−	3.65857i	0.139134	−	0.149360i
$601$	−15.5775	−	34.1101i	−0.635421	−	1.39138i	−0.903754	−	0.428052i	$-0.859200\pi$
$601$	−15.5775	−	34.1101i	−0.635421	−	1.39138i	0.268333	−	0.963326i	$-0.413527\pi$
$602$	0.137919	−	0.469708i	0.00562115	−	0.0191439i
$603$	5.57377	−	4.82970i	0.226981	−	0.196680i
$604$	−3.33389	+	0.978917i	−0.135654	+	0.0398316i
$605$	−10.5603	+	8.82314i	−0.429338	+	0.358712i
$606$	1.30431	−	2.85605i	0.0529841	−	0.116019i
$607$	−5.99277	−	5.19277i	−0.243239	−	0.210768i	0.524706	−	0.851283i	$-0.324175\pi$
$607$	−5.99277	−	5.19277i	−0.243239	−	0.210768i	−0.767945	+	0.640516i	$0.778721\pi$
$608$	1.94036	+	3.01926i	0.0786920	+	0.122447i
$609$	−0.0378476	−	0.263235i	−0.00153366	−	0.0106668i
$610$	−3.36740	+	20.7630i	−0.136342	+	0.840671i
$611$	−43.4171	+	27.9025i	−1.75647	+	1.12881i
$612$	2.49898	+	2.16538i	0.101015	+	0.0875302i
$613$	−12.1220	−	5.53591i	−0.489601	−	0.223593i	0.155288	−	0.987869i	$-0.450369\pi$
$613$	−12.1220	−	5.53591i	−0.489601	−	0.223593i	−0.644889	+	0.764276i	$0.723097\pi$
$614$	2.97558	+	1.91229i	0.120084	+	0.0771736i
$615$	−15.3708	−	0.276443i	−0.619811	−	0.0111472i
$616$	0.0700288	+	0.0808176i	0.00282154	+	0.00325623i
$617$	5.49708	−	18.7213i	0.221304	−	0.753692i	−0.771739	−	0.635939i	$-0.780613\pi$
$617$	5.49708	−	18.7213i	0.221304	−	0.753692i	0.993043	−	0.117753i	$-0.0375690\pi$
$618$	10.8463	−	4.95334i	0.436303	−	0.199253i
$619$	0.892654	−	6.20854i	0.0358788	−	0.249542i	−0.963987	−	0.265951i	$-0.914314\pi$
$619$	0.892654	−	6.20854i	0.0358788	−	0.249542i	0.999865	+	0.0164084i	$0.00522320\pi$
$620$	−5.04073	+	16.0909i	−0.202441	+	0.646227i
$621$	−4.29620	+	2.13134i	−0.172401	+	0.0855279i
$622$		−	22.8838i		−	0.917558i
$623$	0.0726464	+	0.0104450i	0.00291052	+	0.000418469i
$624$	2.83171	+	6.20057i	0.113359	+	0.248222i
$625$	−1.77021	−	24.9372i	−0.0708084	−	0.997490i
$626$	3.75857	+	4.33762i	0.150223	+	0.173366i
$627$	2.22585	+	7.58053i	0.0888917	+	0.302737i
$628$	−4.01751	+	6.25137i	−0.160316	+	0.249457i
$629$	1.22996	−	2.69323i	0.0490417	−	0.107386i
$630$	0.0570742	+	0.0924221i	0.00227389	+	0.00368218i
$631$	16.9549	−	10.8962i	0.674963	−	0.433772i	−0.157749	−	0.987479i	$-0.550424\pi$
$631$	16.9549	−	10.8962i	0.674963	−	0.433772i	0.832712	+	0.553707i	$0.186787\pi$
$632$	−7.66513	+	1.10208i	−0.304902	+	0.0438384i
$633$	6.46313	−	0.929258i	0.256886	−	0.0369347i
$634$	−18.0427	+	11.5954i	−0.716569	+	0.460511i
$635$	−33.7483	+	20.8409i	−1.33926	+	0.827044i
$636$	−4.13337	+	9.05082i	−0.163899	+	0.358888i
$637$	25.7885	−	40.1277i	1.02178	−	1.58992i
$638$	−3.39521	−	11.5630i	−0.134417	−	0.457784i
$639$	−6.76182	−	7.80356i	−0.267494	−	0.308704i
$640$	1.85906	+	1.24254i	0.0734857	+	0.0491157i
$641$	12.7239	+	27.8614i	0.502564	+	1.10046i	0.975628	+	0.219433i	$0.0704207\pi$
$641$	12.7239	+	27.8614i	0.502564	+	1.10046i	−0.473064	+	0.881028i	$0.656852\pi$
$642$	−13.9587	−	2.00696i	−0.550908	−	0.0792086i
$643$			39.6527i			1.56375i	0.623435	+	0.781875i	$0.285737\pi$
$643$			39.6527i			1.56375i	−0.623435	+	0.781875i	$0.714263\pi$
$644$	−0.231548	−	0.0257321i	−0.00912428	−	0.00101399i
$645$	6.73617	−	21.5031i	0.265236	−	0.846682i
$646$	−1.68892	+	11.7467i	−0.0664495	+	0.462167i
$647$	6.05486	−	2.76516i	0.238041	−	0.108710i	−0.292823	−	0.956167i	$-0.594595\pi$
$647$	6.05486	−	2.76516i	0.238041	−	0.108710i	0.530864	+	0.847457i	$0.321867\pi$
$648$	−0.281733	+	0.959493i	−0.0110675	+	0.0376924i
$649$	−5.92845	−	6.84180i	−0.232712	−	0.268564i
$650$	32.3358	+	10.7720i	1.26832	+	0.422511i
$651$	−0.308173	−	0.198050i	−0.0120782	−	0.00776221i
$652$	−8.27881	−	3.78081i	−0.324223	−	0.148068i
$653$	−16.6921	−	14.4638i	−0.653211	−	0.566011i	0.263946	−	0.964538i	$-0.414976\pi$
$653$	−16.6921	−	14.4638i	−0.653211	−	0.566011i	−0.917157	+	0.398527i	$0.869522\pi$
$654$	−12.2692	+	7.88494i	−0.479764	+	0.308326i
$655$	−13.8624	−	2.24824i	−0.541649	−	0.0878460i
$656$	−0.978435	−	6.80517i	−0.0382015	−	0.265697i
$657$	−8.26054	−	12.8536i	−0.322274	−	0.501468i
$658$	−0.277964	−	0.240857i	−0.0108362	−	0.00938960i
$659$	−11.4773	+	25.1318i	−0.447092	+	0.978994i	0.543150	+	0.839635i	$0.317231\pi$
$659$	−11.4773	+	25.1318i	−0.447092	+	0.978994i	−0.990242	+	0.139359i	$0.955496\pi$
$660$	3.15602	+	3.77740i	0.122848	+	0.147035i
$661$	−11.7442	+	3.44840i	−0.456795	+	0.134127i	−0.502032	−	0.864849i	$-0.667414\pi$
$661$	−11.7442	+	3.44840i	−0.456795	+	0.134127i	0.0452368	+	0.998976i	$0.485596\pi$
$662$	−20.3346	+	17.6200i	−0.790325	+	0.684820i
$663$	−6.35021	+	21.6268i	−0.246622	+	0.839916i
$664$	1.53398	+	3.35894i	0.0595298	+	0.130352i
$665$	−0.168302	+	0.351654i	−0.00652646	+	0.0136365i
$666$	0.895413			0.0346966
$667$	22.5314	+	13.4777i	0.872420	+	0.521859i
$668$			19.2956i			0.746571i
$669$	−3.61954	+	25.1745i	−0.139940	+	0.973301i
$670$	16.3630	−	2.05305i	0.632159	−	0.0793164i
$671$	−19.8687	−	5.83399i	−0.767024	−	0.225219i
$672$	−0.0367131	+	0.0318121i	−0.00141624	+	0.00122718i
$673$	−8.03264	−	27.3567i	−0.309636	−	1.05452i	−0.956455	−	0.291879i	$-0.905719\pi$
$673$	−8.03264	−	27.3567i	−0.309636	−	1.05452i	0.646820	−	0.762643i	$-0.276099\pi$
$674$	20.6025	+	13.2404i	0.793579	+	0.510002i
$675$	2.55021	+	4.30075i	0.0981575	+	0.165536i
$676$	−21.9154	+	25.2917i	−0.842898	+	0.972756i
$677$	23.7432	+	36.9451i	0.912525	+	1.41992i	0.907557	+	0.419929i	$0.137945\pi$
$677$	23.7432	+	36.9451i	0.912525	+	1.41992i	0.00496851	+	0.999988i	$0.498418\pi$
$678$	−11.7167	+	1.68461i	−0.449977	+	0.0646969i
$679$	−0.0519303	−	0.361183i	−0.00199290	−	0.0138609i
$680$	1.95518	+	7.13064i	0.0749776	+	0.273448i
$681$	−2.87108	+	3.31340i	−0.110020	+	0.126970i
$682$	−15.0999	−	6.89590i	−0.578205	−	0.264058i
$683$	2.22489	−	3.46200i	0.0851331	−	0.132470i	−0.796075	−	0.605197i	$-0.793094\pi$
$683$	2.22489	−	3.46200i	0.0851331	−	0.132470i	0.881209	+	0.472728i	$0.156731\pi$
$684$	−3.44362	+	1.01114i	−0.131670	+	0.0386618i
$685$	−18.5697	−	42.6765i	−0.709510	−	1.63059i
$686$	0.652439	+	0.191573i	0.0249102	+	0.00731430i
$687$	−12.8613	+	5.87355i	−0.490688	+	0.224090i
$688$	9.97470	+	1.43415i	0.380282	+	0.0546763i
$689$	−67.8247			−2.58392
$690$	−10.6352	−	1.37592i	−0.404874	−	0.0523802i
$691$	−4.96477			−0.188869			−0.0944344	−	0.995531i	$-0.530104\pi$
$691$	−4.96477			−0.188869			−0.0944344	+	0.995531i	$0.530104\pi$
$692$	−14.7786	−	2.12485i	−0.561800	−	0.0807746i
$693$	−0.0972733	+	0.0444232i	−0.00369511	+	0.00168750i
$694$	10.0388	+	2.94767i	0.381069	+	0.111892i
$695$	7.66553	−	3.33547i	0.290770	−	0.126522i
$696$	5.25274	−	1.54234i	0.199105	−	0.0584624i
$697$	12.2907	−	19.1247i	0.465542	−	0.724398i
$698$	−6.57760	−	3.00389i	−0.248966	−	0.113699i
$699$	6.58382	−	7.59813i	0.249023	−	0.287388i
$700$	−0.00873396	+	0.242735i	−0.000330113	+	0.00917452i
$701$	0.877438	+	6.10272i	0.0331404	+	0.230496i	0.999659	−	0.0260987i	$-0.00830841\pi$
$701$	0.877438	+	6.10272i	0.0331404	+	0.230496i	−0.966519	+	0.256595i	$0.917399\pi$
$702$	−6.74719	+	0.970100i	−0.254656	+	0.0366140i
$703$	1.73742	+	2.70348i	0.0655282	+	0.101964i
$704$	−1.44156	+	1.66365i	−0.0543310	+	0.0627013i
$705$	−12.5933	−	11.3150i	−0.474291	−	0.426147i
$706$	−18.3472	−	11.7911i	−0.690508	−	0.443762i
$707$	0.0429715	+	0.146347i	0.00161611	+	0.00550396i
$708$	3.10803	−	2.69313i	0.116807	−	0.101214i
$709$	13.2615	+	3.89393i	0.498046	+	0.146239i	0.521101	−	0.853495i	$-0.325521\pi$
$709$	13.2615	+	3.89393i	0.498046	+	0.146239i	−0.0230557	+	0.999734i	$0.507340\pi$
$710$	−2.87438	−	22.9091i	−0.107874	−	0.859763i
$711$	1.10208	−	7.66513i	0.0413312	−	0.287465i
$712$			1.51082i			0.0566205i
$713$	34.3549	−	11.2981i	1.28660	−	0.423116i
$714$	−0.160630			−0.00601144
$715$	−14.4851	+	30.2656i	−0.541714	+	1.13187i
$716$	−1.59835	−	3.49990i	−0.0597331	−	0.130797i
$717$	−3.27538	+	11.1549i	−0.122321	+	0.416588i
$718$	−9.89826	+	8.57689i	−0.369400	+	0.320087i
$719$	16.3481	−	4.80025i	0.609683	−	0.179019i	0.0377062	−	0.999289i	$-0.487995\pi$
$719$	16.3481	−	4.80025i	0.609683	−	0.179019i	0.571977	+	0.820270i	$0.306177\pi$
$720$	−1.71597	+	1.43369i	−0.0639503	+	0.0534304i
$721$	−0.240625	+	0.526896i	−0.00896136	+	0.0196226i
$722$	4.62450	+	4.00715i	0.172106	+	0.149131i
$723$	9.89893	+	15.4030i	0.368145	+	0.572845i
$724$	−1.08221	−	7.52696i	−0.0402201	−	0.279737i
$725$	12.2589	−	24.4739i	0.455285	−	0.908938i
$726$	5.17721	−	3.32719i	0.192144	−	0.123484i
$727$	−19.1704	−	16.6112i	−0.710990	−	0.616076i	0.222393	−	0.974957i	$-0.428613\pi$
$727$	−19.1704	−	16.6112i	−0.710990	−	0.616076i	−0.933383	+	0.358881i	$0.883159\pi$
$728$	−0.301214	−	0.137560i	−0.0111637	−	0.00509831i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	0.614360	−	34.1597i	0.0227385	−	1.26431i
$731$	21.8211	+	25.1829i	0.807083	+	0.931423i
$732$	2.65021	−	9.02579i	0.0979547	−	0.333603i
$733$	−21.3284	+	9.74033i	−0.787781	+	0.359767i	−0.768339	−	0.640044i	$-0.778916\pi$
$733$	−21.3284	+	9.74033i	−0.787781	+	0.359767i	−0.0194422	+	0.999811i	$0.506189\pi$
$734$	2.18008	−	15.1628i	0.0804683	−	0.559670i
$735$	14.9317	+	4.67758i	0.550763	+	0.172535i
$736$	−0.154031	−	4.79336i	−0.00567765	−	0.176685i
$737$			16.2351i			0.598028i
$738$	6.80517	+	0.978435i	0.250502	+	0.0360167i
$739$	17.0087	+	37.2439i	0.625676	+	1.37004i	0.911318	+	0.411703i	$0.135066\pi$
$739$	17.0087	+	37.2439i	0.625676	+	1.37004i	−0.285642	+	0.958336i	$0.592207\pi$
$740$	1.66462	+	1.11259i	0.0611928	+	0.0408995i
$741$	−16.0210	−	18.4892i	−0.588544	−	0.679216i
$742$	−0.136177	−	0.463775i	−0.00499920	−	0.0170257i
$743$	−15.8987	+	24.7389i	−0.583268	+	0.907583i	−0.999999	−	0.00144726i	$-0.999539\pi$
$743$	−15.8987	+	24.7389i	−0.583268	+	0.907583i	0.416731	+	0.909030i	$0.363176\pi$
$744$	3.13261	−	6.85945i	0.114847	−	0.251480i
$745$	5.53760	+	8.96722i	0.202882	+	0.328534i
$746$	6.14741	−	3.95070i	0.225073	−	0.144646i
$747$	−3.65505	+	0.525517i	−0.133731	+	0.0192277i
$748$	−7.20487	+	1.03590i	−0.263436	+	0.0378764i
$749$	0.576314	−	0.370375i	0.0210581	−	0.0135332i
$750$	−0.602875	+	11.1641i	−0.0220139	+	0.407654i
$751$	−20.7300	+	45.3924i	−0.756448	+	1.65639i	−0.00202877	+	0.999998i	$0.500646\pi$
$751$	−20.7300	+	45.3924i	−0.756448	+	1.65639i	−0.754419	+	0.656393i	$0.772081\pi$
$752$	4.09333	−	6.36935i	0.149268	−	0.232266i
$753$	3.30642	+	11.2606i	0.120493	+	0.410360i
$754$	24.4377	+	28.2026i	0.889967	+	1.02708i
$755$	4.31737	−	6.45954i	0.157125	−	0.235087i
$756$	−0.0201802	−	0.0441885i	−0.000733947	−	0.00160712i
$757$	27.4702	+	3.94962i	0.998421	+	0.143551i	0.622100	−	0.782938i	$-0.286280\pi$
$757$	27.4702	+	3.94962i	0.998421	+	0.143551i	0.376321	+	0.926489i	$0.377189\pi$
$758$			7.47013i			0.271328i
$759$	2.64743	−	10.2199i	0.0960958	−	0.370957i
$760$	−7.65826	−	2.39907i	−0.277794	−	0.0870235i
$761$	−0.774850	+	5.38920i	−0.0280883	+	0.195358i	−0.999034	−	0.0439410i	$-0.986009\pi$
$761$	−0.774850	+	5.38920i	−0.0280883	+	0.195358i	0.970946	+	0.239299i	$0.0769177\pi$
$762$	16.1356	−	7.36888i	0.584531	−	0.266946i
$763$	0.199604	−	0.679790i	0.00722616	−	0.0246100i
$764$	−0.291665	−	0.336600i	−0.0105521	−	0.0121777i
$765$	−7.39264	−	0.132956i	−0.267281	−	0.00480704i
$766$	−7.14963	−	4.59479i	−0.258327	−	0.166017i
$767$	25.5000	+	11.6454i	0.920750	+	0.420492i
$768$	−0.755750	−	0.654861i	−0.0272708	−	0.0236303i
$769$	0.957350	−	0.615252i	0.0345229	−	0.0221865i	−0.523266	−	0.852170i	$-0.675286\pi$
$769$	0.957350	−	0.615252i	0.0345229	−	0.0221865i	0.557788	+	0.829983i	$0.311650\pi$
$770$	−0.236034	−	0.0382807i	−0.00850608	−	0.00137954i
$771$	−0.708456	−	4.92742i	−0.0255144	−	0.177457i
$772$	−9.54882	−	14.8583i	−0.343670	−	0.534760i
$773$	−11.7513	−	10.1825i	−0.422664	−	0.366240i	0.417404	−	0.908721i	$-0.362940\pi$
$773$	−11.7513	−	10.1825i	−0.422664	−	0.366240i	−0.840068	+	0.542480i	$0.817485\pi$
$774$	−4.18625	+	9.16661i	−0.150472	+	0.329487i
$775$	−14.4196	−	34.8383i	−0.517969	−	1.25143i
$776$	7.20724	−	2.11624i	0.258725	−	0.0759685i
$777$	−0.0328734	+	0.0284850i	−0.00117933	+	0.00102189i
$778$	−3.87506	+	13.1972i	−0.138928	+	0.473144i
$779$	10.2503	+	22.4451i	0.367256	+	0.804178i
$780$	−13.7488	−	6.58018i	−0.492286	−	0.235608i
$781$	22.7300			0.813343
$782$	9.99451	−	12.3120i	0.357403	−	0.440278i
$783$			5.47450i			0.195643i
$784$	−0.995868	+	6.92641i	−0.0355667	+	0.247372i
$785$	−2.06861	−	16.4870i	−0.0738318	−	0.588446i
$786$	6.02606	+	1.76941i	0.214942	+	0.0631128i
$787$	1.88040	−	1.62937i	0.0670290	−	0.0580809i	−0.620702	−	0.784047i	$-0.713152\pi$
$787$	1.88040	−	1.62937i	0.0670290	−	0.0580809i	0.687731	+	0.725966i	$0.258607\pi$
$788$	−5.16050	−	17.5751i	−0.183835	−	0.626086i
$789$	−9.45125	−	6.07395i	−0.336473	−	0.216238i
$790$	11.5731	−	12.8805i	0.411751	−	0.458269i
$791$	0.376565	−	0.434580i	0.0133891	−	0.0154519i
$792$	−1.19013	−	1.85187i	−0.0422893	−	0.0658035i
$793$	63.4697	−	9.12557i	2.25388	−	0.324058i
$794$	0.330323	+	2.29745i	0.0117227	+	0.0815333i
$795$	−5.88333	−	21.4568i	−0.208660	−	0.760996i
$796$	1.14419	−	1.32047i	0.0405548	−	0.0468027i
$797$	−0.965475	−	0.440918i	−0.0341989	−	0.0156181i	0.398242	−	0.917280i	$-0.369620\pi$
$797$	−0.965475	−	0.440918i	−0.0341989	−	0.0156181i	−0.432441	+	0.901662i	$0.642348\pi$
$798$	0.0942595	−	0.146671i	0.00333675	−	0.00519209i
$799$	24.0212	−	7.05326i	0.849809	−	0.249526i
$800$	−4.97149	+	0.533153i	−0.175769	+	0.0188498i
$801$	−1.44963	−	0.425648i	−0.0512200	−	0.0150395i
$802$	−34.7143	+	15.8535i	−1.22581	+	0.559806i
$803$	33.2921	+	4.78668i	1.17485	+	0.168918i
$804$	−7.37515			−0.260101
$805$	0.434221	−	0.287813i	0.0153043	−	0.0101441i
$806$	51.4032			1.81060
$807$	17.3083	+	2.48856i	0.609281	+	0.0876014i
$808$	−2.85605	+	1.30431i	−0.100475	+	0.0458856i
$809$	−39.6425	−	11.6401i	−1.39376	−	0.409244i	−0.503221	−	0.864158i	$-0.667852\pi$
$809$	−39.6425	−	11.6401i	−1.39376	−	0.409244i	−0.890535	+	0.454914i	$0.849670\pi$
$810$	−0.892171	−	2.05037i	−0.0313477	−	0.0720428i
$811$	2.52326	−	0.740896i	0.0886037	−	0.0260164i	−0.237130	−	0.971478i	$-0.576207\pi$
$811$	2.52326	−	0.740896i	0.0886037	−	0.0260164i	0.325734	+	0.945461i	$0.394389\pi$
$812$	−0.143779	+	0.223725i	−0.00504566	+	0.00785121i
$813$	0.673068	+	0.307380i	0.0236055	+	0.0107803i
$814$	−1.29079	+	1.48966i	−0.0452423	+	0.0522124i
$815$	19.6267	−	5.38150i	0.687492	−	0.188506i
$816$	−0.470582	−	3.27297i	−0.0164737	−	0.114577i
$817$	−35.7992	+	5.14715i	−1.25246	+	0.180076i
$818$	−18.4046	−	28.6381i	−0.643501	−	1.00131i
$819$	0.216849	−	0.250258i	0.00757733	−	0.00874471i
$820$	11.4355	+	10.2747i	0.399343	+	0.358807i
$821$	2.27938	+	1.46487i	0.0795509	+	0.0511242i	0.579812	−	0.814751i	$-0.303126\pi$
$821$	2.27938	+	1.46487i	0.0795509	+	0.0511242i	−0.500261	+	0.865875i	$0.666763\pi$
$822$	5.86399	+	19.9709i	0.204530	+	0.696565i
$823$	27.2141	−	23.5812i	0.948624	−	0.821987i	−0.0355181	−	0.999369i	$-0.511308\pi$
$823$	27.2141	−	23.5812i	0.948624	−	0.821987i	0.984142	+	0.177382i	$0.0567627\pi$
$824$	−11.4408	−	3.35933i	−0.398561	−	0.117028i
$825$	−10.8312	−	1.95715i	−0.377095	−	0.0681391i
$826$	−0.0284316	+	0.197746i	−0.000989261	+	0.00688046i
$827$		−	39.1629i		−	1.36183i	−0.732363	−	0.680915i	$-0.761582\pi$
$827$		−	39.1629i		−	1.36183i	0.732363	−	0.680915i	$-0.238418\pi$
$828$	4.64259	+	1.20265i	0.161341	+	0.0417951i
$829$	−11.3597			−0.394540			−0.197270	−	0.980349i	$-0.563208\pi$
$829$	−11.3597			−0.394540			−0.197270	+	0.980349i	$0.563208\pi$
$830$	−7.44793	−	3.56458i	−0.258521	−	0.123728i
$831$	−11.0036	−	24.0946i	−0.381711	−	0.835831i
$832$	1.92045	−	6.54045i	0.0665796	−	0.226749i
$833$	−17.4870	+	15.1525i	−0.605887	+	0.525004i
$834$	−3.58716	+	1.05329i	−0.124213	+	0.0364723i
$835$	−27.6639	−	33.1106i	−0.957350	−	1.14584i
$836$	3.28201	−	7.18660i	0.113511	−	0.248554i
$837$	5.69904	+	4.93825i	0.196988	+	0.170691i
$838$	16.4035	+	25.5243i	0.566648	+	0.881721i
$839$	−3.89731	−	27.1064i	−0.134550	−	0.935817i	−0.939518	−	0.342499i	$-0.888727\pi$
$839$	−3.89731	−	27.1064i	−0.134550	−	0.935817i	0.804968	−	0.593318i	$-0.202182\pi$
$840$	0.0173898	−	0.107224i	0.000600005	−	0.00369957i
$841$	0.816134	−	0.524498i	0.0281426	−	0.0180861i
$842$	−3.92200	−	3.39843i	−0.135161	−	0.117118i
$843$	1.58892	+	0.725637i	0.0547254	+	0.0249923i
$844$	−5.49304	−	3.53016i	−0.189078	−	0.121513i
$845$	1.34562	−	74.8194i	0.0462908	−	2.57387i
$846$	4.95812	+	5.72197i	0.170464	+	0.196726i
$847$	−0.0842265	+	0.286849i	−0.00289406	+	0.00985625i
$848$	9.05082	−	4.13337i	0.310806	−	0.141940i
$849$	−4.33176	+	30.1280i	−0.148666	+	1.03399i
$850$	−13.5781	−	9.43282i	−0.465726	−	0.323543i
$851$	−0.137921	−	4.29204i	−0.00472788	−	0.147129i
$852$			10.3256i			0.353749i
$853$	39.4165	+	5.66724i	1.34960	+	0.194043i	0.778915	−	0.627129i	$-0.215770\pi$
$853$	39.4165	+	5.66724i	1.34960	+	0.194043i	0.570681	+	0.821172i	$0.306679\pi$
$854$	0.189832	+	0.415674i	0.00649591	+	0.0142241i
$855$	4.45947	−	6.67215i	0.152511	−	0.228183i
$856$	9.23503	+	10.6578i	0.315647	+	0.364276i
$857$	10.8766	+	37.0423i	0.371537	+	1.26534i	0.907125	+	0.420861i	$0.138272\pi$
$857$	10.8766	+	37.0423i	0.371537	+	1.26534i	−0.535588	+	0.844480i	$0.679910\pi$
$858$	8.11259	−	12.6234i	0.276959	−	0.430957i
$859$	8.89908	−	19.4863i	0.303633	−	0.664863i	−0.694895	−	0.719111i	$-0.744549\pi$
$859$	8.89908	−	19.4863i	0.303633	−	0.664863i	0.998527	+	0.0542485i	$0.0172763\pi$
$860$	−19.1724	+	11.8397i	−0.653772	+	0.403729i
$861$	−0.280965	+	0.180565i	−0.00957526	+	0.00615364i
$862$	12.8868	−	1.85285i	0.438927	−	0.0631082i
$863$	−15.7264	+	2.26111i	−0.535332	+	0.0769691i	−0.404679	−	0.914459i	$-0.632617\pi$
$863$	−15.7264	+	2.26111i	−0.535332	+	0.0769691i	−0.130653	+	0.991428i	$0.541707\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	28.4060	−	17.5418i	0.965833	−	0.596439i
$866$	16.4423	−	36.0037i	0.558734	−	1.22346i
$867$	−3.27966	+	5.10325i	−0.111383	+	0.173315i
$868$	0.103206	+	0.351487i	0.00350303	+	0.0119302i
$869$	11.1634	+	12.8832i	0.378692	+	0.437034i
$870$	−6.80228	+	10.1774i	−0.230619	+	0.345046i
$871$	−20.8843	−	45.7302i	−0.707636	−	1.54951i
$872$	14.4360	+	2.07558i	0.488864	+	0.0702881i
$873$			7.51151i			0.254226i
$874$	5.37717	+	16.3507i	0.181885	+	0.553072i
$875$	−0.333019	−	0.429047i	−0.0112581	−	0.0145044i
$876$	−2.17445	+	15.1236i	−0.0734679	+	0.510980i
$877$	17.8308	−	8.14306i	0.602104	−	0.274972i	−0.0909524	−	0.995855i	$-0.528991\pi$
$877$	17.8308	−	8.14306i	0.602104	−	0.274972i	0.693056	+	0.720884i	$0.256264\pi$
$878$	−6.55806	+	22.3347i	−0.221324	+	0.753759i
$879$	11.2117	+	12.9390i	0.378161	+	0.436421i
$880$	0.0885132	−	4.92152i	0.00298378	−	0.165904i
$881$	−2.58567	−	1.66171i	−0.0871134	−	0.0559844i	0.496359	−	0.868117i	$-0.334670\pi$
$881$	−2.58567	−	1.66171i	−0.0871134	−	0.0559844i	−0.583472	+	0.812133i	$0.698306\pi$
$882$	−6.36528	−	2.90692i	−0.214330	−	0.0978812i
$883$	−13.7744	−	11.9356i	−0.463545	−	0.401664i	0.391532	−	0.920164i	$-0.371945\pi$
$883$	−13.7744	−	11.9356i	−0.463545	−	0.401664i	−0.855078	+	0.518500i	$0.826491\pi$
$884$	18.9617	−	12.1860i	0.637752	−	0.409858i
$885$	−1.47217	+	9.07726i	−0.0494866	+	0.305129i
$886$	−2.78405	−	19.3635i	−0.0935321	−	0.650530i
$887$	−15.2379	−	23.7106i	−0.511638	−	0.796125i	0.485297	−	0.874349i	$-0.338711\pi$
$887$	−15.2379	−	23.7106i	−0.511638	−	0.796125i	−0.996936	+	0.0782244i	$0.975075\pi$
$888$	−0.676708	−	0.586371i	−0.0227088	−	0.0196773i
$889$	−0.357968	+	0.783841i	−0.0120059	+	0.0262892i
$890$	−2.16605	−	2.59252i	−0.0726062	−	0.0869015i
$891$	2.11216	−	0.620186i	0.0707600	−	0.0207770i
$892$	19.2212	−	16.6553i	0.643574	−	0.557660i
$893$	−7.65558	+	26.0725i	−0.256184	+	0.872484i
$894$	−1.95798	−	4.28737i	−0.0654845	−	0.143391i
$895$	7.76047	+	3.71417i	0.259404	+	0.124151i
$896$	0.0485784			0.00162289
$897$	5.68931	+	32.1923i	0.189960	+	1.07487i
$898$			5.23270i			0.174618i
$899$	5.87514	−	40.8625i	0.195947	−	1.36284i
$900$	0.889075	−	4.92032i	0.0296358	−	0.164011i
$901$	31.5681	+	9.26923i	1.05169	+	0.308803i
$902$	−11.4379	+	9.91096i	−0.380839	+	0.329999i
$903$	−0.137919	−	0.469708i	−0.00458965	−	0.0156309i
$904$	9.95807	+	6.39966i	0.331200	+	0.212850i
$905$	12.6484	+	11.3644i	0.420445	+	0.377767i
$906$	−2.27540	+	2.62595i	−0.0755951	+	0.0872414i
$907$	−20.5916	−	32.0411i	−0.683732	−	1.06391i	−0.993581	−	0.113122i	$-0.963915\pi$
$907$	−20.5916	−	32.0411i	−0.683732	−	1.06391i	0.309850	−	0.950786i	$-0.399721\pi$
$908$	4.33964	−	0.623946i	0.144016	−	0.0207064i
$909$	−0.446838	−	3.10783i	−0.0148207	−	0.103080i
$910$	0.714091	−	0.195799i	0.0236719	−	0.00649068i
$911$	27.3992	−	31.6204i	0.907776	−	1.04763i	−0.0908834	−	0.995862i	$-0.528969\pi$
$911$	27.3992	−	31.6204i	0.907776	−	1.04763i	0.998659	−	0.0517675i	$-0.0164855\pi$
$912$	3.26467	+	1.49092i	0.108104	+	0.0493694i
$913$	4.39471	−	6.83830i	0.145444	−	0.226315i
$914$	−2.59188	+	0.761044i	−0.0857317	+	0.0251731i
$915$	8.39250	+	19.2875i	0.277448	+	0.637626i
$916$	13.5663	+	3.98341i	0.448242	+	0.131616i
$917$	−0.277524	+	0.126741i	−0.00916465	+	0.00418535i
$918$	3.27297	+	0.470582i	0.108024	+	0.0155315i
$919$	56.6698			1.86937			0.934683	−	0.355483i	$-0.115683\pi$
$919$	56.6698			1.86937			0.934683	+	0.355483i	$0.115683\pi$
$920$	7.13649	+	8.00440i	0.235283	+	0.263897i
$921$	3.53707			0.116551
$922$	−0.427538	−	0.0614708i	−0.0140802	−	0.00202443i
$923$	−64.0246	+	29.2390i	−2.10739	+	0.962415i
$924$	0.102605	+	0.0301276i	0.00337547	+	0.000991126i
$925$	−4.45154	+	0.477392i	−0.146366	+	0.0156966i
$926$	4.72118	−	1.38626i	0.155148	−	0.0455554i
$927$	6.44652	−	10.0310i	0.211731	−	0.329460i
$928$	−4.97978	−	2.27419i	−0.163469	−	0.0746539i
$929$	8.42045	−	9.71772i	0.276266	−	0.318828i	−0.600612	−	0.799540i	$-0.705076\pi$
$929$	8.42045	−	9.71772i	0.276266	−	0.318828i	0.876878	+	0.480712i	$0.159622\pi$
$930$	4.45887	+	16.2618i	0.146212	+	0.533244i
$931$	−3.57417	−	24.8589i	−0.117139	−	0.814717i
$932$	−9.95143	+	1.43080i	−0.325970	+	0.0468674i
$933$	−12.3719	−	19.2511i	−0.405039	−	0.630253i
$934$	−19.1506	+	22.1010i	−0.626627	+	0.723166i
$935$	10.8781	−	12.1071i	0.355754	−	0.395945i
$936$	5.73447	+	3.68532i	0.187437	+	0.120458i
$937$	−4.07788	−	13.8880i	−0.133219	−	0.453701i	0.865681	−	0.500596i	$-0.166886\pi$
$937$	−4.07788	−	13.8880i	−0.133219	−	0.453701i	−0.998900	+	0.0468947i	$0.985067\pi$
$938$	0.270765	−	0.234619i	0.00884078	−	0.00766058i
$939$	5.50700	+	1.61700i	0.179714	+	0.0527689i
$940$	2.10764	+	16.7981i	0.0687438	+	0.547895i
$941$	3.51558	−	24.4514i	0.114605	−	0.797093i	−0.848737	−	0.528815i	$-0.822636\pi$
$941$	3.51558	−	24.4514i	0.114605	−	0.797093i	0.963342	−	0.268278i	$-0.0864545\pi$
$942$			7.43102i			0.242116i
$943$	3.64179	−	32.7703i	0.118593	−	1.06715i
$944$	−4.11252			−0.133851
$945$	0.0979810	+	0.0468938i	0.00318732	+	0.00152545i
$946$	−9.21531	−	20.1787i	−0.299616	−	0.656067i
$947$	−9.93852	+	33.8475i	−0.322959	+	1.09990i	0.624768	+	0.780811i	$0.285194\pi$
$947$	−9.93852	+	33.8475i	−0.322959	+	1.09990i	−0.947726	+	0.319085i	$0.896624\pi$
$948$	−5.85249	+	5.07121i	−0.190080	+	0.164705i
$949$	−99.9326	+	29.3429i	−3.24395	+	0.952510i
$950$	16.5808	−	6.86284i	0.537953	−	0.222660i
$951$	−8.90959	+	19.5093i	−0.288913	+	0.632632i
$952$	0.121396	+	0.105191i	0.00393448	+	0.00340925i
$953$	−2.75008	−	4.27921i	−0.0890839	−	0.138617i	0.793852	−	0.608111i	$-0.208073\pi$
$953$	−2.75008	−	4.27921i	−0.0890839	−	0.138617i	−0.882936	+	0.469494i	$0.844436\pi$
$954$	1.41603	+	9.84870i	0.0458456	+	0.318863i
$955$	0.983066	+	0.159436i	0.0318113	+	0.00515923i
$956$	9.78027	−	6.28540i	0.316317	−	0.203284i
$957$	−9.10766	−	7.89184i	−0.294409	−	0.255107i
$958$	−1.48443	−	0.677917i	−0.0479598	−	0.0219025i
$959$	−0.850601	−	0.546648i	−0.0274673	−	0.0176522i
$960$	2.23571	+	0.0402090i	0.0721571	+	0.00129774i
$961$	−16.9382	−	19.5477i	−0.546394	−	0.630572i
$962$	1.71960	−	5.85641i	0.0554420	−	0.188818i
$963$	−12.8279	+	5.85830i	−0.413373	+	0.188781i
$964$	2.60573	−	18.1233i	0.0839250	−	0.583711i
$965$	37.6876	+	11.8062i	1.21321	+	0.380056i
$966$	−0.208703	+	0.103537i	−0.00671490	+	0.00333126i
$967$			0.383893i			0.0123452i	0.999981	+	0.00617259i	$0.00196481\pi$
$967$			0.383893i			0.0123452i	−0.999981	+	0.00617259i	$0.998035\pi$
$968$	−6.09152	−	0.875828i	−0.195789	−	0.0281502i
$969$	4.92992	+	10.7950i	0.158372	+	0.346786i
$970$	−9.33335	+	13.9643i	−0.299676	+	0.448367i
$971$	26.2237	+	30.2638i	0.841559	+	0.971211i	0.999869	−	0.0161788i	$-0.00515008\pi$
$971$	26.2237	+	30.2638i	0.841559	+	0.971211i	−0.158310	+	0.987389i	$0.550605\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	0.0981887	−	0.152785i	0.00314778	−	0.00489805i
$974$	2.30110	−	5.03871i	0.0737321	−	0.161451i
$975$	33.0264	−	8.42013i	1.05769	−	0.269660i
$976$	−7.91353	+	5.08572i	−0.253306	+	0.162790i
$977$	36.1707	−	5.20056i	1.15720	−	0.166381i	0.463133	−	0.886289i	$-0.346725\pi$
$977$	36.1707	−	5.20056i	1.15720	−	0.166381i	0.694070	+	0.719908i	$0.255816\pi$
$978$	−9.00864	+	1.29525i	−0.288065	+	0.0414174i
$979$	2.79786	−	1.79807i	0.0894199	−	0.0574667i
$980$	−8.22144	−	13.3133i	−0.262624	−	0.425276i
$981$	−6.05859	+	13.2665i	−0.193436	+	0.423566i
$982$	7.72949	−	12.0273i	0.246658	−	0.383807i
$983$	11.6627	+	39.7197i	0.371984	+	1.26686i	0.906681	+	0.421817i	$0.138608\pi$
$983$	11.6627	+	39.7197i	0.371984	+	1.26686i	−0.534697	+	0.845044i	$0.679574\pi$
$984$	−4.50226	−	5.19589i	−0.143527	−	0.165639i
$985$	34.0524	+	22.7596i	1.08500	+	0.725182i
$986$	−7.51989	−	16.4663i	−0.239482	−	0.524392i
$987$	−0.364056	−	0.0523433i	−0.0115880	−	0.00166611i
$988$			24.4647i			0.778325i
$989$	44.5836	+	18.6543i	1.41768	+	0.593171i
$990$	4.69723	+	1.47148i	0.149288	+	0.0467667i
$991$	−1.08353	+	7.53613i	−0.0344195	+	0.239393i	−0.999767	−	0.0215738i	$-0.993132\pi$
$991$	−1.08353	+	7.53613i	−0.0344195	+	0.239393i	0.965348	+	0.260967i	$0.0840414\pi$
$992$	−6.85945	+	3.13261i	−0.217788	+	0.0994604i
$993$	−7.58043	+	25.8166i	−0.240558	+	0.819264i
$994$	−0.328478	−	0.379084i	−0.0104187	−	0.0120238i
$995$	−0.0702543	+	3.90629i	−0.00222721	+	0.123838i
$996$	3.10644	+	1.99639i	0.0984314	+	0.0632580i
$997$	32.5512	+	14.8656i	1.03091	+	0.470800i	0.857735	−	0.514092i	$-0.171871\pi$
$997$	32.5512	+	14.8656i	1.03091	+	0.470800i	0.173172	+	0.984892i	$0.444598\pi$
$998$	−25.2094	−	21.8440i	−0.797988	−	0.691461i
$999$	0.753270	−	0.484097i	0.0238324	−	0.0153161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.a.169.1	yes	120
5.4	even	2	inner	690.2.r.a.169.10	yes	120
23.3	even	11	inner	690.2.r.a.49.10	yes	120
115.49	even	22	inner	690.2.r.a.49.1	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.a.49.1	✓	120	115.49	even	22	inner
690.2.r.a.49.10	yes	120	23.3	even	11	inner
690.2.r.a.169.1	yes	120	1.1	even	1	trivial
690.2.r.a.169.10	yes	120	5.4	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989821 - 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-2.05037 + 0.892171i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.0262635 + 0.0408667i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.989821 - 0.142315i) q^{2} +(-0.909632 + 0.415415i) q^{3} +(0.959493 + 0.281733i) q^{4} +(-2.05037 + 0.892171i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.0262635 + 0.0408667i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(0.654861 - 0.755750i) q^{9} +(2.15647 - 0.591291i) q^{10} +(0.313282 + 2.17892i) q^{11} +(-0.989821 + 0.142315i) q^{12} +(-3.68532 - 5.73447i) q^{13} +(0.0318121 - 0.0367131i) q^{14} +(1.49446 - 1.66330i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.931584 + 3.17268i) q^{17} +(-0.755750 + 0.654861i) q^{18} +(-3.44362 - 1.01114i) q^{19} +(-2.21867 + 0.278374i) q^{20} +(0.00691343 - 0.0480839i) q^{21} -2.20133i q^{22} +(3.25539 + 3.52171i) q^{23} +1.00000 q^{24} +(3.40806 - 3.65857i) q^{25} +(2.83171 + 6.20057i) q^{26} +(-0.281733 + 0.959493i) q^{27} +(-0.0367131 + 0.0318121i) q^{28} +(5.25274 - 1.54234i) q^{29} +(-1.71597 + 1.43369i) q^{30} +(3.13261 - 6.85945i) q^{31} +(-0.755750 - 0.654861i) q^{32} +(-1.19013 - 1.85187i) q^{33} +(-0.470582 - 3.27297i) q^{34} +(0.0173898 - 0.107224i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-0.676708 - 0.586371i) q^{37} +(3.26467 + 1.49092i) q^{38} +(5.73447 + 3.68532i) q^{39} +(2.23571 + 0.0402090i) q^{40} +(-4.50226 - 5.19589i) q^{41} +(-0.0136861 + 0.0466106i) q^{42} +(9.16661 - 4.18625i) q^{43} +(-0.313282 + 2.17892i) q^{44} +(-0.668452 + 2.13382i) q^{45} +(-2.72106 - 3.94915i) q^{46} -7.57126i q^{47} +(-0.989821 - 0.142315i) q^{48} +(2.90692 + 6.36528i) q^{49} +(-3.89404 + 3.13631i) q^{50} +(-2.16538 - 2.49898i) q^{51} +(-1.92045 - 6.54045i) q^{52} +(5.37936 - 8.37045i) q^{53} +(0.415415 - 0.909632i) q^{54} +(-2.58631 - 4.18810i) q^{55} +(0.0408667 - 0.0262635i) q^{56} +(3.55247 - 0.510768i) q^{57} +(-5.41878 + 0.779102i) q^{58} +(-3.45967 + 2.22339i) q^{59} +(1.90253 - 1.17489i) q^{60} +(-3.90774 + 8.55676i) q^{61} +(-4.07692 + 6.34382i) q^{62} +(0.0136861 + 0.0466106i) q^{63} +(0.654861 + 0.755750i) q^{64} +(12.6724 + 8.46987i) q^{65} +(0.914465 + 2.00240i) q^{66} +(7.30008 + 1.04959i) q^{67} +3.30662i q^{68} +(-4.42418 - 1.85112i) q^{69} +(-0.0324723 + 0.103657i) q^{70} +(1.46948 - 10.2205i) q^{71} +(-0.909632 + 0.415415i) q^{72} +(4.30464 - 14.6602i) q^{73} +(0.586371 + 0.676708i) q^{74} +(-1.58026 + 4.74371i) q^{75} +(-3.01926 - 1.94036i) q^{76} +(-0.0972733 - 0.0444232i) q^{77} +(-5.15162 - 4.46391i) q^{78} +(6.51463 - 4.18670i) q^{79} +(-2.20723 - 0.357974i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.71698 + 5.78374i) q^{82} +(-2.79071 - 2.41816i) q^{83} +(0.0201802 - 0.0441885i) q^{84} +(-4.74067 - 5.67405i) q^{85} +(-9.66907 + 2.83910i) q^{86} +(-4.13735 + 3.58503i) q^{87} +(0.620186 - 2.11216i) q^{88} +(-0.627619 - 1.37429i) q^{89} +(0.965321 - 2.01697i) q^{90} +0.331138 q^{91} +(2.13134 + 4.29620i) q^{92} +7.54091i q^{93} +(-1.07750 + 7.49419i) q^{94} +(7.96281 - 0.999086i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-5.67682 + 4.91899i) q^{97} +(-1.97146 - 6.71419i) q^{98} +(1.85187 + 1.19013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 12 q^{6} + 12 q^{9} + 18 q^{10} - 8 q^{14} - 4 q^{15} - 12 q^{16} + 22 q^{20} + 14 q^{21} + 120 q^{24} + 52 q^{25} + 16 q^{29} + 8 q^{31} - 36 q^{34} - 90 q^{35} - 12 q^{36} + 22 q^{39} + 4 q^{40} + 16 q^{41} - 4 q^{49} - 4 q^{50} + 8 q^{51} - 12 q^{54} - 56 q^{55} + 8 q^{56} + 138 q^{59} + 4 q^{60} - 36 q^{61} + 12 q^{64} + 52 q^{65} + 96 q^{70} + 8 q^{71} + 8 q^{74} - 4 q^{75} - 60 q^{79} - 12 q^{81} + 8 q^{84} + 24 q^{85} - 8 q^{86} - 104 q^{89} + 4 q^{90} - 144 q^{91} - 24 q^{94} - 14 q^{95} + 12 q^{96} - 44 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 12 * q^6 + 12 * q^9 + 18 * q^10 - 8 * q^14 - 4 * q^15 - 12 * q^16 + 22 * q^20 + 14 * q^21 + 120 * q^24 + 52 * q^25 + 16 * q^29 + 8 * q^31 - 36 * q^34 - 90 * q^35 - 12 * q^36 + 22 * q^39 + 4 * q^40 + 16 * q^41 - 4 * q^49 - 4 * q^50 + 8 * q^51 - 12 * q^54 - 56 * q^55 + 8 * q^56 + 138 * q^59 + 4 * q^60 - 36 * q^61 + 12 * q^64 + 52 * q^65 + 96 * q^70 + 8 * q^71 + 8 * q^74 - 4 * q^75 - 60 * q^79 - 12 * q^81 + 8 * q^84 + 24 * q^85 - 8 * q^86 - 104 * q^89 + 4 * q^90 - 144 * q^91 - 24 * q^94 - 14 * q^95 + 12 * q^96 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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