LMFDB - Embedded newform 690.2.n.a.89.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.19
Character	$\chi$	$=$	690.89
Dual form			690.2.n.a.659.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(1.27489 - 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.23188 - 0.136714i) q^{5} +(-1.34195 - 1.09506i) q^{6} +(-1.96759 + 1.26449i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.250714 - 2.98951i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(1.27489 - 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.23188 - 0.136714i) q^{5} +(-1.34195 - 1.09506i) q^{6} +(-1.96759 + 1.26449i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.250714 - 2.98951i) q^{9} +(-0.452953 - 2.18971i) q^{10} +(-0.590477 + 4.10685i) q^{11} +(-0.892935 + 1.48414i) q^{12} +(2.60370 - 4.05144i) q^{13} +(1.53164 + 1.76761i) q^{14} +(2.68513 - 2.79107i) q^{15} +(0.841254 - 0.540641i) q^{16} +(2.07397 - 7.06329i) q^{17} +(-2.99476 + 0.177289i) q^{18} +(-1.43678 - 4.89322i) q^{19} +(-2.10296 + 0.759971i) q^{20} +(-1.02591 + 3.91900i) q^{21} +4.14909 q^{22} +(0.585811 - 4.75992i) q^{23} +(1.59611 + 0.672631i) q^{24} +(4.96262 - 0.610262i) q^{25} +(-4.38075 - 2.00062i) q^{26} +(-3.18542 - 4.10526i) q^{27} +(1.53164 - 1.76761i) q^{28} +(-0.892286 + 3.03885i) q^{29} +(-3.14480 - 2.26059i) q^{30} +(0.520682 + 1.14014i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(4.06229 + 5.92811i) q^{33} +(-7.28655 - 1.04765i) q^{34} +(-4.21856 + 3.09120i) q^{35} +(0.601683 + 2.93904i) q^{36} +(-1.29334 - 1.49260i) q^{37} +(-4.63894 + 2.11853i) q^{38} +(-1.43067 - 8.21788i) q^{39} +(1.05152 + 1.97340i) q^{40} +(8.22539 + 7.12734i) q^{41} +(4.02511 + 0.457739i) q^{42} +(-2.57950 + 5.64832i) q^{43} +(-0.590477 - 4.10685i) q^{44} +(0.150857 - 6.70651i) q^{45} +(-4.79484 + 0.0975584i) q^{46} +6.75447 q^{47} +(0.438635 - 1.67559i) q^{48} +(-0.635439 + 1.39142i) q^{49} +(-1.31030 - 4.82526i) q^{50} +(-5.63727 - 11.4366i) q^{51} +(-1.35681 + 4.62088i) q^{52} +(7.10060 + 11.0487i) q^{53} +(-3.61014 + 3.73723i) q^{54} +(-0.756409 + 9.24675i) q^{55} +(-1.96759 - 1.26449i) q^{56} +(-7.56881 - 4.55379i) q^{57} +(3.13490 + 0.450731i) q^{58} +(-1.99640 + 3.10646i) q^{59} +(-1.79002 + 3.43450i) q^{60} +(-5.51656 + 2.51933i) q^{61} +(1.05443 - 0.677641i) q^{62} +(3.28691 + 6.19915i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(5.25727 - 9.39831i) q^{65} +(5.28965 - 4.86460i) q^{66} +(0.160946 + 1.11941i) q^{67} +7.36148i q^{68} +(-4.83393 - 6.75523i) q^{69} +(3.66010 + 3.73570i) q^{70} +(0.381400 - 0.0548370i) q^{71} +(2.82350 - 1.01383i) q^{72} +(-4.69578 - 15.9924i) q^{73} +(-1.29334 + 1.49260i) q^{74} +(5.61131 - 6.59645i) q^{75} +(2.75716 + 4.29022i) q^{76} +(-4.03127 - 8.82726i) q^{77} +(-7.93062 + 2.58563i) q^{78} +(-3.72151 + 5.79078i) q^{79} +(1.80367 - 1.32166i) q^{80} +(-8.87428 - 1.49902i) q^{81} +(5.88420 - 9.15600i) q^{82} +(-12.0367 + 10.4298i) q^{83} +(-0.119753 - 4.04929i) q^{84} +(3.66320 - 16.0480i) q^{85} +(5.95793 + 1.74940i) q^{86} +(2.42533 + 4.92037i) q^{87} +(-3.98102 + 1.16893i) q^{88} +(-6.45448 + 14.1333i) q^{89} +(-6.65971 + 0.805115i) q^{90} +11.2639i q^{91} +(0.778942 + 4.73215i) q^{92} +(2.00057 + 0.843078i) q^{93} +(-0.961261 - 6.68572i) q^{94} +(-3.87570 - 10.7247i) q^{95} +(-1.72096 - 0.195709i) q^{96} +(-5.68611 + 6.56212i) q^{97} +(1.46769 + 0.430952i) q^{98} +(12.1294 + 2.79488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	1.27489	−	1.17245i	0.736061	−	0.676915i
$3$	1.27489	−	1.17245i	0.736061	−	0.676915i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	2.23188	−	0.136714i	0.998129	−	0.0611406i
$5$	2.23188	−	0.136714i	0.998129	−	0.0611406i
$6$	−1.34195	−	1.09506i	−0.547851	−	0.447057i
$7$	−1.96759	+	1.26449i	−0.743679	+	0.477933i	−0.856801	−	0.515648i	$-0.827551\pi$
$7$	−1.96759	+	1.26449i	−0.743679	+	0.477933i	0.113122	+	0.993581i	$0.463915\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	0.250714	−	2.98951i	0.0835714	−	0.996502i
$10$	−0.452953	−	2.18971i	−0.143236	−	0.692447i
$11$	−0.590477	+	4.10685i	−0.178035	+	1.23826i	0.683266	+	0.730169i	$0.260559\pi$
$11$	−0.590477	+	4.10685i	−0.178035	+	1.23826i	−0.861302	+	0.508094i	$0.830350\pi$
$12$	−0.892935	+	1.48414i	−0.257768	+	0.428434i
$13$	2.60370	−	4.05144i	0.722137	−	1.12367i	−0.265071	−	0.964229i	$-0.585395\pi$
$13$	2.60370	−	4.05144i	0.722137	−	1.12367i	0.987208	−	0.159438i	$-0.0509683\pi$
$14$	1.53164	+	1.76761i	0.409348	+	0.472413i
$15$	2.68513	−	2.79107i	0.693297	−	0.720652i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	2.07397	−	7.06329i	0.503011	−	1.71310i	−0.180872	−	0.983507i	$-0.557892\pi$
$17$	2.07397	−	7.06329i	0.503011	−	1.71310i	0.683883	−	0.729592i	$-0.260290\pi$
$18$	−2.99476	+	0.177289i	−0.705871	+	0.0417874i
$19$	−1.43678	−	4.89322i	−0.329620	−	1.12258i	−0.943000	−	0.332794i	$-0.892009\pi$
$19$	−1.43678	−	4.89322i	−0.329620	−	1.12258i	0.613380	−	0.789788i	$-0.289809\pi$
$20$	−2.10296	+	0.759971i	−0.470236	+	0.169935i
$21$	−1.02591	+	3.91900i	−0.223873	+	0.855196i
$22$	4.14909			0.884588
$23$	0.585811	−	4.75992i	0.122150	−	0.992512i
$23$	0.585811	−	4.75992i	0.122150	−	0.992512i
$24$	1.59611	+	0.672631i	0.325805	+	0.137300i
$25$	4.96262	−	0.610262i	0.992524	−	0.122052i
$26$	−4.38075	−	2.00062i	−0.859135	−	0.392354i
$27$	−3.18542	−	4.10526i	−0.613034	−	0.790057i
$28$	1.53164	−	1.76761i	0.289453	−	0.334046i
$29$	−0.892286	+	3.03885i	−0.165693	+	0.564300i	0.834224	+	0.551426i	$0.185916\pi$
$29$	−0.892286	+	3.03885i	−0.165693	+	0.564300i	−0.999917	+	0.0128738i	$0.995902\pi$
$30$	−3.14480	−	2.26059i	−0.574159	−	0.412725i
$31$	0.520682	+	1.14014i	0.0935173	+	0.204774i	0.950610	−	0.310388i	$-0.100459\pi$
$31$	0.520682	+	1.14014i	0.0935173	+	0.204774i	−0.857093	+	0.515162i	$0.827732\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	4.06229	+	5.92811i	0.707154	+	1.03195i
$34$	−7.28655	−	1.04765i	−1.24963	−	0.179670i
$35$	−4.21856	+	3.09120i	−0.713066	+	0.522508i
$36$	0.601683	+	2.93904i	0.100280	+	0.489841i
$37$	−1.29334	−	1.49260i	−0.212624	−	0.245381i	0.639412	−	0.768864i	$-0.279178\pi$
$37$	−1.29334	−	1.49260i	−0.212624	−	0.245381i	−0.852036	+	0.523483i	$0.824632\pi$
$38$	−4.63894	+	2.11853i	−0.752535	+	0.343671i
$39$	−1.43067	−	8.21788i	−0.229091	−	1.31591i
$40$	1.05152	+	1.97340i	0.166260	+	0.312022i
$41$	8.22539	+	7.12734i	1.28459	+	1.11310i	0.987393	+	0.158288i	$0.0505974\pi$
$41$	8.22539	+	7.12734i	1.28459	+	1.11310i	0.297197	+	0.954816i	$0.403948\pi$
$42$	4.02511	+	0.457739i	0.621088	+	0.0706306i
$43$	−2.57950	+	5.64832i	−0.393370	+	0.861360i	0.604530	+	0.796583i	$0.293361\pi$
$43$	−2.57950	+	5.64832i	−0.393370	+	0.861360i	−0.997900	+	0.0647776i	$0.979366\pi$
$44$	−0.590477	−	4.10685i	−0.0890177	−	0.619132i
$45$	0.150857	−	6.70651i	0.0224884	−	0.999747i
$46$	−4.79484	+	0.0975584i	−0.706960	+	0.0143842i
$47$	6.75447			0.985240			0.492620	−	0.870244i	$-0.336039\pi$
$47$	6.75447			0.985240			0.492620	+	0.870244i	$0.336039\pi$
$48$	0.438635	−	1.67559i	0.0633115	−	0.241850i
$49$	−0.635439	+	1.39142i	−0.0907771	+	0.198774i
$50$	−1.31030	−	4.82526i	−0.185305	−	0.682394i
$51$	−5.63727	−	11.4366i	−0.789376	−	1.60144i
$52$	−1.35681	+	4.62088i	−0.188156	+	0.640800i
$53$	7.10060	+	11.0487i	0.975342	+	1.51766i	0.850828	+	0.525445i	$0.176101\pi$
$53$	7.10060	+	11.0487i	0.975342	+	1.51766i	0.124515	+	0.992218i	$0.460263\pi$
$54$	−3.61014	+	3.73723i	−0.491278	+	0.508573i
$55$	−0.756409	+	9.24675i	−0.101994	+	1.24683i
$56$	−1.96759	−	1.26449i	−0.262930	−	0.168975i
$57$	−7.56881	−	4.55379i	−1.00251	−	0.603164i
$58$	3.13490	+	0.450731i	0.411633	+	0.0591839i
$59$	−1.99640	+	3.10646i	−0.259909	+	0.404427i	−0.946543	−	0.322577i	$-0.895451\pi$
$59$	−1.99640	+	3.10646i	−0.259909	+	0.404427i	0.686634	+	0.727003i	$0.259087\pi$
$60$	−1.79002	+	3.43450i	−0.231091	+	0.443392i
$61$	−5.51656	+	2.51933i	−0.706323	+	0.322567i	−0.735990	−	0.676993i	$-0.763283\pi$
$61$	−5.51656	+	2.51933i	−0.706323	+	0.322567i	0.0296663	+	0.999560i	$0.490556\pi$
$62$	1.05443	−	0.677641i	0.133913	−	0.0860604i
$63$	3.28691	+	6.19915i	0.414111	+	0.781019i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	5.25727	−	9.39831i	0.652085	−	1.16572i
$66$	5.28965	−	4.86460i	0.651111	−	0.598791i
$67$	0.160946	+	1.11941i	0.0196627	+	0.136757i	0.997288	−	0.0735963i	$-0.0234476\pi$
$67$	0.160946	+	1.11941i	0.0196627	+	0.136757i	−0.977625	+	0.210353i	$0.932539\pi$
$68$			7.36148i			0.892710i
$69$	−4.83393	−	6.75523i	−0.581936	−	0.813234i
$70$	3.66010	+	3.73570i	0.437466	+	0.446501i
$71$	0.381400	−	0.0548370i	0.0452638	−	0.00650796i	−0.119646	−	0.992817i	$-0.538176\pi$
$71$	0.381400	−	0.0548370i	0.0452638	−	0.00650796i	0.164910	+	0.986309i	$0.447267\pi$
$72$	2.82350	−	1.01383i	0.332753	−	0.119481i
$73$	−4.69578	−	15.9924i	−0.549599	−	1.87176i	−0.486347	−	0.873766i	$-0.661671\pi$
$73$	−4.69578	−	15.9924i	−0.549599	−	1.87176i	−0.0632528	−	0.997998i	$-0.520147\pi$
$74$	−1.29334	+	1.49260i	−0.150348	+	0.173511i
$75$	5.61131	−	6.59645i	0.647939	−	0.761692i
$76$	2.75716	+	4.29022i	0.316268	+	0.492122i
$77$	−4.03127	−	8.82726i	−0.459406	−	1.00596i
$78$	−7.93062	+	2.58563i	−0.897966	+	0.292765i
$79$	−3.72151	+	5.79078i	−0.418702	+	0.651513i	−0.984974	−	0.172706i	$-0.944749\pi$
$79$	−3.72151	+	5.79078i	−0.418702	+	0.651513i	0.566271	+	0.824219i	$0.308385\pi$
$80$	1.80367	−	1.32166i	0.201656	−	0.147766i
$81$	−8.87428	−	1.49902i	−0.986032	−	0.166558i
$82$	5.88420	−	9.15600i	0.649801	−	1.01111i
$83$	−12.0367	+	10.4298i	−1.32120	+	1.14482i	−0.342498	+	0.939519i	$0.611273\pi$
$83$	−12.0367	+	10.4298i	−1.32120	+	1.14482i	−0.978698	+	0.205304i	$0.934182\pi$
$84$	−0.119753	−	4.04929i	−0.0130662	−	0.441813i
$85$	3.66320	−	16.0480i	0.397330	−	1.74065i
$86$	5.95793	+	1.74940i	0.642460	+	0.188643i
$87$	2.42533	+	4.92037i	0.260023	+	0.527520i
$88$	−3.98102	+	1.16893i	−0.424378	+	0.124609i
$89$	−6.45448	+	14.1333i	−0.684174	+	1.49813i	0.173986	+	0.984748i	$0.444335\pi$
$89$	−6.45448	+	14.1333i	−0.684174	+	1.49813i	−0.858159	+	0.513383i	$0.828392\pi$
$90$	−6.65971	+	0.805115i	−0.701995	+	0.0848665i
$91$			11.2639i			1.18078i
$92$	0.778942	+	4.73215i	0.0812103	+	0.493361i
$93$	2.00057	+	0.843078i	0.207449	+	0.0874231i
$94$	−0.961261	−	6.68572i	−0.0991465	−	0.689579i
$95$	−3.87570	−	10.7247i	−0.397638	−	1.10033i
$96$	−1.72096	−	0.195709i	−0.175645	−	0.0199744i
$97$	−5.68611	+	6.56212i	−0.577337	+	0.666283i	−0.967030	−	0.254662i	$-0.918036\pi$
$97$	−5.68611	+	6.56212i	−0.577337	+	0.666283i	0.389693	+	0.920945i	$0.372581\pi$
$98$	1.46769	+	0.430952i	0.148259	+	0.0435327i
$99$	12.1294	+	2.79488i	1.21905	+	0.280896i
$100$	−4.58967	+	1.98367i	−0.458967	+	0.198367i
$101$	2.88426	−	2.49923i	0.286995	−	0.248683i	−0.499450	−	0.866343i	$-0.666465\pi$
$101$	2.88426	−	2.49923i	0.286995	−	0.248683i	0.786445	+	0.617660i	$0.211919\pi$
$102$	−10.5179	+	7.20749i	−1.04143	+	0.713647i
$103$	−1.59510	+	11.0942i	−0.157170	+	1.09314i	0.746647	+	0.665221i	$0.231663\pi$
$103$	−1.59510	+	11.0942i	−0.157170	+	1.09314i	−0.903817	+	0.427920i	$0.859246\pi$
$104$	4.76694	+	0.685382i	0.467437	+	0.0672072i
$105$	−1.75394	+	8.88701i	−0.171167	+	0.867283i
$106$	9.92577	−	8.60073i	0.964076	−	0.835377i
$107$	10.0925	−	4.60910i	0.975682	−	0.445579i	0.137221	−	0.990541i	$-0.456183\pi$
$107$	10.0925	−	4.60910i	0.975682	−	0.445579i	0.838461	+	0.544962i	$0.183456\pi$
$108$	4.21297	+	3.04153i	0.405393	+	0.292671i
$109$	0.734577	−	2.50174i	0.0703597	−	0.239623i	−0.916803	−	0.399339i	$-0.869240\pi$
$109$	0.734577	−	2.50174i	0.0703597	−	0.239623i	0.987163	+	0.159716i	$0.0510578\pi$
$110$	9.26028	−	0.567240i	0.882933	−	0.0540842i
$111$	−3.39887	−	0.386523i	−0.322607	−	0.0366871i
$112$	−0.971605	+	2.12752i	−0.0918080	+	0.201032i
$113$	8.66822	−	1.24630i	0.815437	−	0.117242i	0.278038	−	0.960570i	$-0.410316\pi$
$113$	8.66822	−	1.24630i	0.815437	−	0.117242i	0.537399	+	0.843328i	$0.319407\pi$
$114$	−3.43028	+	8.13984i	−0.321275	+	0.762366i
$115$	0.656714	−	10.7037i	0.0612389	−	0.998123i
$116$		−	3.16714i		−	0.294062i
$117$	−11.4590	−	8.79954i	−1.05939	−	0.813517i
$118$	3.35896	+	1.53398i	0.309217	+	0.141215i
$119$	4.85076	+	16.5202i	0.444668	+	1.51440i
$120$	3.65429	+	1.28302i	0.333590	+	0.117124i
$121$	−5.96317	−	1.75094i	−0.542106	−	0.159177i
$122$	3.27877	+	5.10187i	0.296846	+	0.461902i
$123$	18.8430	−	0.557261i	1.69901	−	0.0502466i
$124$	−0.820804	−	0.947258i	−0.0737104	−	0.0850663i
$125$	10.9926	−	2.04050i	0.983204	−	0.182507i
$126$	5.66827	−	4.13568i	0.504970	−	0.368436i
$127$	−1.45735	−	0.209535i	−0.129319	−	0.0185932i	0.0773516	−	0.997004i	$-0.475354\pi$
$127$	−1.45735	−	0.209535i	−0.129319	−	0.0185932i	−0.206670	+	0.978411i	$0.566263\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	3.33379	+	10.2253i	0.293524	+	0.900292i
$130$	−10.0508	−	3.86624i	−0.881517	−	0.339092i
$131$	1.40959	+	2.19337i	0.123157	+	0.191635i	0.897357	−	0.441305i	$-0.145484\pi$
$131$	1.40959	+	2.19337i	0.123157	+	0.191635i	−0.774201	+	0.632940i	$0.781848\pi$
$132$	−5.56788	−	4.54350i	−0.484622	−	0.395461i
$133$	9.01443	+	7.81105i	0.781651	+	0.677304i
$134$	1.08511	−	0.318616i	0.0937389	−	0.0275242i
$135$	−7.67073	−	8.72696i	−0.660191	−	0.751098i
$136$	7.28655	−	1.04765i	0.624816	−	0.0898350i
$137$		−	8.93937i		−	0.763742i	−0.924216	−	0.381871i	$-0.875280\pi$
$137$		−	8.93937i		−	0.763742i	0.924216	−	0.381871i	$-0.124720\pi$
$138$	−5.99853	+	5.74609i	−0.510629	+	0.489140i
$139$	−1.72575			−0.146376			−0.0731880	−	0.997318i	$-0.523317\pi$
$139$	−1.72575			−0.146376			−0.0731880	+	0.997318i	$0.523317\pi$
$140$	3.17679	−	4.15449i	0.268487	−	0.351118i
$141$	8.61124	−	7.91929i	0.725197	−	0.666924i
$142$	−0.108558	−	0.369714i	−0.00910996	−	0.0310257i
$143$	15.1012	+	13.0853i	1.26283	+	1.09425i
$144$	−1.40533	−	2.65048i	−0.117111	−	0.220873i
$145$	−1.57603	+	6.90435i	−0.130882	+	0.573375i
$146$	−15.1613	+	6.92393i	−1.25476	+	0.573029i
$147$	0.821252	+	2.51893i	0.0677357	+	0.207758i
$148$	1.66147	+	1.06776i	0.136572	+	0.0877693i
$149$	2.78753	−	19.3877i	0.228363	−	1.58830i	−0.476640	−	0.879099i	$-0.658145\pi$
$149$	2.78753	−	19.3877i	0.228363	−	1.58830i	0.705003	−	0.709204i	$-0.250946\pi$
$150$	−7.32788	−	4.61543i	−0.598319	−	0.376848i
$151$	10.1818	+	6.54342i	0.828580	+	0.532496i	0.884826	−	0.465921i	$-0.154277\pi$
$151$	10.1818	+	6.54342i	0.828580	+	0.532496i	−0.0562462	+	0.998417i	$0.517913\pi$
$152$	3.85417	−	3.33966i	0.312614	−	0.270882i
$153$	−20.5958	−	7.97101i	−1.66507	−	0.644418i
$154$	−8.16370	+	5.24649i	−0.657850	+	0.422774i
$155$	1.31798	+	2.47347i	0.105862	+	0.198673i
$156$	3.68796	+	7.48193i	0.295273	+	0.599034i
$157$	−21.4105	+	6.28669i	−1.70874	+	0.501732i	−0.982588	−	0.185798i	$-0.940513\pi$
$157$	−21.4105	+	6.28669i	−1.70874	+	0.501732i	−0.726155	+	0.687531i	$0.758695\pi$
$158$	6.26146	+	2.85951i	0.498135	+	0.227491i
$159$	22.0066	+	5.76088i	1.74524	+	0.456868i
$160$	−1.56490	−	1.59722i	−0.123716	−	0.126271i
$161$	4.86625	+	10.1063i	0.383514	+	0.796490i
$162$	−0.220822	+	8.99729i	−0.0173494	+	0.706894i
$163$	1.02510	−	0.147387i	0.0802918	−	0.0115442i	−0.102052	−	0.994779i	$-0.532541\pi$
$163$	1.02510	−	0.147387i	0.0802918	−	0.0115442i	0.182344	+	0.983235i	$0.441632\pi$
$164$	−9.90021	−	4.52127i	−0.773077	−	0.353052i
$165$	9.87703	+	12.6755i	0.768926	+	0.986786i
$166$	12.0367	+	10.4298i	0.934227	+	0.809512i
$167$	−6.36947	−	1.87024i	−0.492884	−	0.144724i	0.0258390	−	0.999666i	$-0.491774\pi$
$167$	−6.36947	−	1.87024i	−0.492884	−	0.144724i	−0.518723	+	0.854942i	$0.673592\pi$
$168$	−3.99103	+	0.694808i	−0.307914	+	0.0536056i
$169$	−4.23451	−	9.27227i	−0.325731	−	0.713252i
$170$	−16.4060	−	1.34205i	−1.25828	−	0.102931i
$171$	−14.9885	+	3.06846i	−1.14620	+	0.234651i
$172$	0.883697	−	6.14625i	0.0673813	−	0.468647i
$173$	−0.524760	+	3.64979i	−0.0398968	+	0.277488i	−0.999998	−	0.00216564i	$-0.999311\pi$
$173$	−0.524760	+	3.64979i	−0.0398968	+	0.277488i	0.960101	+	0.279654i	$0.0902197\pi$
$174$	4.52513	−	3.10089i	0.343049	−	0.235078i
$175$	−8.99272	+	7.47594i	−0.679786	+	0.565128i
$176$	1.72359	+	3.77414i	0.129921	+	0.284487i
$177$	1.09697	+	6.30109i	0.0824535	+	0.473619i
$178$	14.9081	+	4.37740i	1.11741	+	0.328100i
$179$	−12.0244	−	10.4192i	−0.898750	−	0.778771i	0.0771436	−	0.997020i	$-0.475420\pi$
$179$	−12.0244	−	10.4192i	−0.898750	−	0.778771i	−0.975893	+	0.218249i	$0.929965\pi$
$180$	1.74470	+	6.47735i	0.130042	+	0.482793i
$181$	6.62705	+	3.02647i	0.492585	+	0.224956i	0.646190	−	0.763176i	$-0.276361\pi$
$181$	6.62705	+	3.02647i	0.492585	+	0.224956i	−0.153606	+	0.988132i	$0.549089\pi$
$182$	11.1493	−	1.60302i	0.826440	−	0.118824i
$183$	−4.07924	+	9.67978i	−0.301546	+	0.715550i
$184$	4.57313	−	1.44447i	0.337136	−	0.106488i
$185$	−3.09065	−	3.15449i	−0.227229	−	0.231922i
$186$	0.549786	−	2.10019i	0.0403122	−	0.153993i
$187$	27.7833	+	12.6882i	2.03171	+	0.927852i
$188$	−6.48086	+	1.90295i	−0.472666	+	0.138787i
$189$	11.4587	+	4.04952i	0.833495	+	0.294559i
$190$	−10.0639	+	5.36253i	−0.730115	+	0.389039i
$191$	9.29975	−	5.97659i	0.672906	−	0.432451i	−0.159066	−	0.987268i	$-0.550848\pi$
$191$	9.29975	−	5.97659i	0.672906	−	0.432451i	0.831972	+	0.554817i	$0.187212\pi$
$192$	0.0512012	+	1.73129i	0.00369513	+	0.124945i
$193$	−3.75659	+	3.25511i	−0.270406	+	0.234308i	−0.779499	−	0.626404i	$-0.784526\pi$
$193$	−3.75659	+	3.25511i	−0.270406	+	0.234308i	0.509093	+	0.860711i	$0.329981\pi$
$194$	7.30455	+	4.69435i	0.524436	+	0.337035i
$195$	−4.31659	−	18.1458i	−0.309118	−	1.29944i
$196$	0.217692	−	1.51408i	0.0155494	−	0.108149i
$197$	15.9181	+	10.2299i	1.13412	+	0.728852i	0.966415	−	0.256986i	$-0.0827294\pi$
$197$	15.9181	+	10.2299i	1.13412	+	0.728852i	0.167701	+	0.985838i	$0.446366\pi$
$198$	1.04023	−	12.4037i	0.0739263	−	0.881494i
$199$	−2.89119	+	1.32036i	−0.204951	+	0.0935980i	−0.515246	−	0.857042i	$-0.672299\pi$
$199$	−2.89119	+	1.32036i	−0.204951	+	0.0935980i	0.310295	+	0.950640i	$0.399572\pi$
$200$	2.61666	+	4.26064i	0.185026	+	0.301273i
$201$	1.51764	+	1.23842i	0.107046	+	0.0873516i
$202$	−2.88426	−	2.49923i	−0.202936	−	0.175845i
$203$	−2.08695	−	7.10750i	−0.146475	−	0.498848i
$204$	8.63098	+	9.38511i	0.604289	+	0.657089i
$205$	19.3325	+	14.7829i	1.35024	+	1.03248i
$206$	11.2083			0.780916
$207$	−14.0829	−	2.94467i	−0.978831	−	0.204668i
$208$		−	4.81596i		−	0.333926i
$209$	20.9441	−	3.01131i	1.44874	−	0.208297i
$210$	9.04617	+	0.471329i	0.624245	+	0.0325248i
$211$	−5.95073	+	1.74729i	−0.409665	+	0.120288i	−0.480070	−	0.877230i	$-0.659389\pi$
$211$	−5.95073	+	1.74729i	−0.409665	+	0.120288i	0.0704055	+	0.997518i	$0.477571\pi$
$212$	−9.92577	−	8.60073i	−0.681705	−	0.590700i
$213$	0.421951	−	0.517084i	0.0289116	−	0.0354300i
$214$	−5.99851	−	9.33386i	−0.410049	−	0.638049i
$215$	−4.98494	+	12.9590i	−0.339970	+	0.883800i
$216$	2.41100	−	4.60294i	0.164048	−	0.313190i
$217$	−2.46618	−	1.58492i	−0.167415	−	0.107591i
$218$	−2.58082	−	0.371066i	−0.174795	−	0.0251317i
$219$	−24.7369	−	14.8830i	−1.67156	−	1.00570i
$220$	−1.87934	−	9.08530i	−0.126705	−	0.612531i
$221$	−23.2165	−	26.7933i	−1.56171	−	1.80231i
$222$	0.101122	+	3.41929i	0.00678685	+	0.229487i
$223$	1.38258	+	2.15134i	0.0925847	+	0.144065i	0.884456	−	0.466623i	$-0.154529\pi$
$223$	1.38258	+	2.15134i	0.0925847	+	0.144065i	−0.791872	+	0.610688i	$0.790893\pi$
$224$	2.24414	+	0.658938i	0.149943	+	0.0440272i
$225$	−0.580182	−	14.9888i	−0.0386788	−	0.999252i
$226$	−2.46723	−	8.40262i	−0.164118	−	0.558934i
$227$	3.00561	+	1.37261i	0.199489	+	0.0911036i	0.512655	−	0.858595i	$-0.328662\pi$
$227$	3.00561	+	1.37261i	0.199489	+	0.0911036i	−0.313165	+	0.949699i	$0.601389\pi$
$228$	8.54517	+	2.23695i	0.565918	+	0.148146i
$229$			13.0423i			0.861861i	0.902385	+	0.430930i	$0.141815\pi$
$229$			13.0423i			0.861861i	−0.902385	+	0.430930i	$0.858185\pi$
$230$	−10.6882	+	0.873263i	−0.704758	+	0.0575812i
$231$	−15.4890	−	6.52735i	−1.01910	−	0.429468i
$232$	−3.13490	+	0.450731i	−0.205816	+	0.0295919i
$233$	−0.0172536	+	0.0377800i	−0.00113032	+	0.00247505i	−0.910196	−	0.414177i	$-0.864069\pi$
$233$	−0.0172536	+	0.0377800i	−0.00113032	+	0.00247505i	0.909066	+	0.416652i	$0.136797\pi$
$234$	−7.07918	+	12.5947i	−0.462781	+	0.823340i
$235$	15.0752	−	0.923433i	0.983397	−	0.0602382i
$236$	1.04034	−	3.54308i	0.0677204	−	0.230635i
$237$	2.04488	+	11.7459i	0.132829	+	0.762980i
$238$	15.6617	−	7.15245i	1.01520	−	0.463624i
$239$	17.2040	−	14.9073i	1.11283	−	0.964275i	0.113262	−	0.993565i	$-0.463870\pi$
$239$	17.2040	−	14.9073i	1.11283	−	0.964275i	0.999571	+	0.0292902i	$0.00932468\pi$
$240$	0.749905	−	3.79969i	0.0484061	−	0.245269i
$241$	−0.846017	−	0.121639i	−0.0544968	−	0.00783545i	0.115013	−	0.993364i	$-0.463309\pi$
$241$	−0.846017	−	0.121639i	−0.0544968	−	0.00783545i	−0.169509	+	0.985529i	$0.554218\pi$
$242$	−0.884475	+	6.15166i	−0.0568562	+	0.395443i
$243$	−13.0713	+	8.49357i	−0.838525	+	0.544863i
$244$	4.58333	−	3.97147i	0.293417	−	0.254248i
$245$	−1.22800	+	3.19236i	−0.0784541	+	0.203952i
$246$	−3.23322	−	18.5719i	−0.206143	−	1.18410i
$247$	−23.5655	−	6.91947i	−1.49944	−	0.440275i
$248$	−0.820804	+	0.947258i	−0.0521211	+	0.0601510i
$249$	−3.11701	+	27.4094i	−0.197533	+	1.73700i
$250$	−3.58413	−	10.5903i	−0.226680	−	0.669788i
$251$	0.707153	+	4.91836i	0.0446351	+	0.310444i	0.999892	+	0.0146680i	$0.00466914\pi$
$251$	0.707153	+	4.91836i	0.0446351	+	0.310444i	−0.955257	+	0.295776i	$0.904422\pi$
$252$	−4.90026	−	5.02201i	−0.308688	−	0.316357i
$253$	19.2024	+	5.21646i	1.20724	+	0.327956i
$254$			1.47233i			0.0923823i
$255$	−14.1453	−	24.7544i	−0.885812	−	1.55018i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−23.4483	+	6.88505i	−1.46267	+	0.429478i	−0.913708	−	0.406371i	$-0.866794\pi$
$257$	−23.4483	+	6.88505i	−1.46267	+	0.429478i	−0.548959	+	0.835849i	$0.684976\pi$
$258$	9.64682	−	4.75507i	0.600585	−	0.296038i
$259$	4.43214	+	1.30140i	0.275400	+	0.0808648i
$260$	−2.39651	+	10.4988i	−0.148625	+	0.651105i
$261$	8.86094	+	3.42938i	0.548479	+	0.212273i
$262$	1.97044	−	1.70739i	0.121734	−	0.105483i
$263$	−10.3149	+	16.0503i	−0.636046	+	0.989706i	0.362292	+	0.932065i	$0.381994\pi$
$263$	−10.3149	+	16.0503i	−0.636046	+	0.989706i	−0.998337	+	0.0576416i	$0.981642\pi$
$264$	−3.70486	+	6.15782i	−0.228019	+	0.378988i
$265$	17.3582	+	23.6888i	1.06631	+	1.45519i
$266$	6.44866	−	10.0343i	0.395393	−	0.615243i
$267$	8.34188	+	25.5861i	0.510515	+	1.56584i
$268$	−0.469800	−	1.02872i	−0.0286976	−	0.0628389i
$269$	4.99311	+	7.76944i	0.304436	+	0.473711i	0.959440	−	0.281914i	$-0.0909694\pi$
$269$	4.99311	+	7.76944i	0.304436	+	0.473711i	−0.655004	+	0.755625i	$0.727333\pi$
$270$	−7.54648	+	8.83463i	−0.459264	+	0.537658i
$271$	9.17490	−	10.5884i	0.557335	−	0.643199i	−0.405241	−	0.914210i	$-0.632812\pi$
$271$	9.17490	−	10.5884i	0.557335	−	0.643199i	0.962576	+	0.271011i	$0.0873578\pi$
$272$	−2.07397	−	7.06329i	−0.125753	−	0.428275i
$273$	13.2064	+	14.3603i	0.799289	+	0.869127i
$274$	−8.84838	+	1.27221i	−0.534550	+	0.0768568i
$275$	−0.424053	+	20.7411i	−0.0255714	+	1.25074i
$276$	6.54129	+	5.11972i	0.393739	+	0.308171i
$277$		−	18.1513i		−	1.09060i	−0.838240	−	0.545302i	$-0.816415\pi$
$277$		−	18.1513i		−	1.09060i	0.838240	−	0.545302i	$-0.183585\pi$
$278$	0.245599	+	1.70818i	0.0147301	+	0.102450i
$279$	3.53898	−	1.27073i	0.211873	−	0.0760769i
$280$	−4.56431	−	2.55320i	−0.272770	−	0.152583i
$281$	−7.87946	+	9.09338i	−0.470049	+	0.542466i	−0.940425	−	0.340000i	$-0.889573\pi$
$281$	−7.87946	+	9.09338i	−0.470049	+	0.542466i	0.470376	+	0.882466i	$0.344118\pi$
$282$	−9.06419	−	7.39656i	−0.539764	−	0.440458i
$283$	−14.1573	+	9.09834i	−0.841564	+	0.540840i	−0.888933	−	0.458037i	$-0.848553\pi$
$283$	−14.1573	+	9.09834i	−0.841564	+	0.540840i	0.0473690	+	0.998877i	$0.484916\pi$
$284$	−0.350501	+	0.160068i	−0.0207984	+	0.00949832i
$285$	−17.5153	−	9.12876i	−1.03752	−	0.540741i
$286$	10.8030	−	16.8098i	0.638794	−	0.993983i
$287$	−25.1967	−	3.62273i	−1.48731	−	0.213843i
$288$	−2.42350	+	1.76823i	−0.142806	+	0.104194i
$289$	−31.2874	−	20.1072i	−1.84043	−	1.18277i
$290$	7.05836	+	0.577393i	0.414481	+	0.0339057i
$291$	0.444577	+	15.0327i	0.0260616	+	0.881233i
$292$	9.01113	+	14.0216i	0.527337	+	0.820552i
$293$	2.19741	−	7.48370i	0.128374	−	0.437203i	−0.870072	−	0.492925i	$-0.835928\pi$
$293$	2.19741	−	7.48370i	0.128374	−	0.437203i	0.998446	+	0.0557220i	$0.0177460\pi$
$294$	2.37642	−	1.17137i	0.138596	−	0.0683160i
$295$	−4.03104	+	7.20619i	−0.234696	+	0.419561i
$296$	0.820440	−	1.79651i	0.0476871	−	0.104420i
$297$	18.7406	−	10.6580i	1.08744	−	0.618439i
$298$	−19.5871			−1.13465
$299$	−17.7592	−	14.7668i	−1.02704	−	0.853986i
$300$	−3.52558	+	7.91014i	−0.203550	+	0.456692i
$301$	−2.06686	−	14.3753i	−0.119132	−	0.828580i
$302$	5.02780	−	11.0094i	0.289318	−	0.633517i
$303$	0.746908	−	6.56791i	0.0429088	−	0.377317i
$304$	−3.85417	−	3.33966i	−0.221052	−	0.191542i
$305$	−11.9679	+	6.37705i	−0.685280	+	0.365149i
$306$	−4.95879	+	21.5205i	−0.283475	+	1.23025i
$307$	12.9762	−	5.92604i	0.740592	−	0.338217i	−0.00914055	−	0.999958i	$-0.502910\pi$
$307$	12.9762	−	5.92604i	0.740592	−	0.338217i	0.749732	+	0.661741i	$0.230182\pi$
$308$	6.35490	+	7.33395i	0.362104	+	0.417891i
$309$	10.9738	+	16.0141i	0.624277	+	0.911009i
$310$	2.26072	−	1.65657i	0.128400	−	0.0940869i
$311$	−11.3575	−	1.63297i	−0.644026	−	0.0925970i	−0.187440	−	0.982276i	$-0.560019\pi$
$311$	−11.3575	−	1.63297i	−0.644026	−	0.0925970i	−0.456586	+	0.889679i	$0.650928\pi$
$312$	6.88092	−	4.71521i	0.389555	−	0.266946i
$313$	−6.95776	−	8.02969i	−0.393276	−	0.453865i	0.524236	−	0.851573i	$-0.324351\pi$
$313$	−6.95776	−	8.02969i	−0.393276	−	0.453865i	−0.917512	+	0.397708i	$0.869806\pi$
$314$	9.26973	+	20.2979i	0.523121	+	1.14548i
$315$	8.18351	+	13.3864i	0.461088	+	0.754239i
$316$	1.93931	−	6.60468i	0.109095	−	0.371542i
$317$	14.4422	−	16.6672i	0.811153	−	0.936121i	−0.187784	−	0.982210i	$-0.560130\pi$
$317$	14.4422	−	16.6672i	0.811153	−	0.936121i	0.998937	+	0.0460894i	$0.0146759\pi$
$318$	2.57037	−	22.6025i	0.144139	−	1.26749i
$319$	−11.9532	−	5.45886i	−0.669253	−	0.305637i
$320$	−1.35825	+	1.77627i	−0.0759286	+	0.0992968i
$321$	7.46296	−	17.7091i	0.416542	−	0.988427i
$322$	9.31091	−	6.25499i	0.518877	−	0.348577i
$323$	−37.5421			−2.08890
$324$	8.93714	−	1.06187i	0.496508	−	0.0589930i
$325$	10.4487	−	21.6947i	0.579592	−	1.20340i
$326$	−0.291773	−	0.993687i	−0.0161598	−	0.0550353i
$327$	−1.99666	−	4.05071i	−0.110416	−	0.224005i
$328$	−3.06631	+	10.4429i	−0.169309	+	0.576612i
$329$	−13.2900	+	8.54098i	−0.732702	+	0.470879i
$330$	11.1408	−	11.5804i	0.613282	−	0.637480i
$331$	12.3913	+	14.3004i	0.681090	+	0.786019i	0.986069	−	0.166340i	$-0.0531948\pi$
$331$	12.3913	+	14.3004i	0.681090	+	0.786019i	−0.304979	+	0.952359i	$0.598649\pi$
$332$	8.61068	−	13.3985i	0.472572	−	0.735337i
$333$	−4.78639	+	3.49224i	−0.262292	+	0.191374i
$334$	−0.944738	+	6.57080i	−0.0516938	+	0.359538i
$335$	0.512252	+	2.47638i	0.0279873	+	0.135299i
$336$	1.25572	+	3.85152i	0.0685050	+	0.210118i
$337$	−2.17083	−	4.75346i	−0.118253	−	0.258938i	0.841245	−	0.540655i	$-0.181823\pi$
$337$	−2.17083	−	4.75346i	−0.118253	−	0.258938i	−0.959498	+	0.281717i	$0.909096\pi$
$338$	−8.57526	+	5.51099i	−0.466433	+	0.299758i
$339$	9.58984	−	11.7520i	0.520848	−	0.638279i
$340$	1.00642	+	16.4300i	0.0545808	+	0.891040i
$341$	−4.98982	+	1.46514i	−0.270214	+	0.0793419i
$342$	5.17032	+	14.3993i	0.279579	+	0.778624i
$343$	−2.83915	−	19.7467i	−0.153300	−	1.06622i
$344$	−6.20945			−0.334791
$345$	−11.7123	−	14.4160i	−0.630569	−	0.776133i
$346$	3.68732			0.198232
$347$	−1.50759	−	10.4855i	−0.0809314	−	0.562890i	−0.989431	−	0.145005i	$-0.953680\pi$
$347$	−1.50759	−	10.4855i	−0.0809314	−	0.562890i	0.908500	−	0.417886i	$-0.137229\pi$
$348$	−3.71332	−	4.03777i	−0.199055	−	0.216447i
$349$	−6.26294	+	1.83896i	−0.335247	+	0.0984375i	−0.445024	−	0.895519i	$-0.646805\pi$
$349$	−6.26294	+	1.83896i	−0.335247	+	0.0984375i	0.109776	+	0.993956i	$0.464987\pi$
$350$	8.67964	+	7.83725i	0.463946	+	0.418919i
$351$	−24.9261	+	2.21666i	−1.33046	+	0.118317i
$352$	3.49043	−	2.24317i	0.186041	−	0.119561i
$353$	4.32225	+	9.46440i	0.230050	+	0.503739i	0.989091	−	0.147303i	$-0.0470593\pi$
$353$	4.32225	+	9.46440i	0.230050	+	0.503739i	−0.759041	+	0.651042i	$0.774332\pi$
$354$	6.08084	−	1.98255i	0.323193	−	0.105371i
$355$	0.843743	−	0.174533i	0.0447813	−	0.00926324i
$356$	2.21121	−	15.3793i	0.117194	−	0.815100i
$357$	25.5533	+	15.3742i	1.35242	+	0.813689i
$358$	−8.60193	+	13.3849i	−0.454626	+	0.707412i
$359$	−15.6130	−	18.0183i	−0.824021	−	0.950971i	0.175417	−	0.984494i	$-0.443873\pi$
$359$	−15.6130	−	18.0183i	−0.824021	−	0.950971i	−0.999438	+	0.0335237i	$0.989327\pi$
$360$	6.16312	−	2.64876i	0.324825	−	0.139602i
$361$	−5.89545	+	3.78878i	−0.310287	+	0.199409i
$362$	2.05254	−	6.99031i	0.107879	−	0.367402i
$363$	−9.65531	+	4.75926i	−0.506772	+	0.249796i
$364$	−3.17342	−	10.8077i	−0.166332	−	0.566476i
$365$	−12.6668	−	35.0511i	−0.663012	−	1.83466i
$366$	10.1618	+	2.66015i	0.531165	+	0.139048i
$367$	11.9447			0.623508			0.311754	−	0.950163i	$-0.399083\pi$
$367$	11.9447			0.623508			0.311754	+	0.950163i	$0.399083\pi$
$368$	−2.08059	−	4.32101i	−0.108458	−	0.225248i
$369$	23.3695	−	22.8029i	1.21657	−	1.18707i
$370$	−2.68253	+	3.50812i	−0.139458	+	0.182379i
$371$	−27.9421	−	12.7607i	−1.45068	−	0.662505i
$372$	−2.15705	−	0.245302i	−0.111838	−	0.0127183i
$373$	3.67482	−	4.24097i	0.190275	−	0.219589i	−0.652594	−	0.757708i	$-0.726319\pi$
$373$	3.67482	−	4.24097i	0.190275	−	0.219589i	0.842869	+	0.538119i	$0.180865\pi$
$374$	8.60507	−	29.3062i	0.444958	−	1.51539i
$375$	11.6220	−	15.4897i	0.600156	−	0.799883i
$376$	2.80591	+	6.14408i	0.144704	+	0.316857i
$377$	9.98846	+	11.5273i	0.514432	+	0.593686i
$378$	2.37757	−	11.9183i	0.122289	−	0.613013i
$379$	31.7764	+	4.56875i	1.63224	+	0.234681i	0.896649	−	0.442742i	$-0.145994\pi$
$379$	31.7764	+	4.56875i	1.63224	+	0.234681i	0.735593	+	0.677423i	$0.236903\pi$
$380$	6.74020	+	9.19834i	0.345765	+	0.471865i
$381$	−2.10363	+	1.44153i	−0.107772	+	0.0738520i
$382$	−7.23925	−	8.35454i	−0.370392	−	0.427455i
$383$	21.8950	−	9.99910i	1.11878	−	0.510930i	0.231813	−	0.972760i	$-0.425534\pi$
$383$	21.8950	−	9.99910i	1.11878	−	0.510930i	0.886968	+	0.461830i	$0.152807\pi$
$384$	1.70639	−	0.297069i	0.0870786	−	0.0151597i
$385$	−10.2041	−	19.1503i	−0.520052	−	0.975989i
$386$	3.75659	+	3.25511i	0.191206	+	0.165681i
$387$	16.2390	+	9.12754i	0.825473	+	0.463979i
$388$	3.60702	−	7.89828i	0.183119	−	0.400974i
$389$	−1.32775	−	9.23471i	−0.0673196	−	0.468218i	−0.995398	−	0.0958322i	$-0.969449\pi$
$389$	−1.32775	−	9.23471i	−0.0673196	−	0.468218i	0.928078	−	0.372386i	$-0.121460\pi$
$390$	−17.3467	+	6.85507i	−0.878387	+	0.347120i
$391$	−32.4057	−	14.0097i	−1.63883	−	0.708500i
$392$	−1.52965			−0.0772590
$393$	4.36870	+	1.14363i	0.220372	+	0.0576887i
$394$	7.86042	−	17.2119i	0.396002	−	0.867124i
$395$	−7.51429	+	13.4331i	−0.378085	+	0.675894i
$396$	−12.4255	+	0.735586i	−0.624405	+	0.0369646i
$397$	5.07738	−	17.2920i	0.254826	−	0.867859i	−0.728351	−	0.685204i	$-0.759713\pi$
$397$	5.07738	−	17.2920i	0.254826	−	0.867859i	0.983177	−	0.182655i	$-0.0584690\pi$
$398$	1.71838	+	2.67386i	0.0861347	+	0.134028i
$399$	20.6505	−	0.610718i	1.03382	−	0.0305742i
$400$	3.84489	−	3.19638i	0.192244	−	0.159819i
$401$	17.3106	+	11.1248i	0.864449	+	0.555548i	0.896050	−	0.443953i	$-0.146424\pi$
$401$	17.3106	+	11.1248i	0.864449	+	0.555548i	−0.0316008	+	0.999501i	$0.510061\pi$
$402$	1.00983	−	1.67844i	0.0503660	−	0.0837128i
$403$	5.97489	+	0.859060i	0.297630	+	0.0427928i
$404$	−2.06332	+	3.21058i	−0.102654	+	0.159732i
$405$	−20.0113	−	2.13240i	−0.994370	−	0.105960i
$406$	−6.73815	+	3.07721i	−0.334409	+	0.152719i
$407$	6.89357	−	4.43023i	0.341701	−	0.219598i
$408$	8.06127	−	9.87877i	0.399092	−	0.489072i
$409$	2.41616	−	2.78840i	0.119471	−	0.137877i	−0.692863	−	0.721069i	$-0.743651\pi$
$409$	2.41616	−	2.78840i	0.119471	−	0.137877i	0.812334	+	0.583192i	$0.198196\pi$
$410$	11.8811	−	21.2396i	0.586766	−	1.04895i
$411$	−10.4810	−	11.3968i	−0.516989	−	0.562161i
$412$	−1.59510	−	11.0942i	−0.0785850	−	0.546571i
$413$		−	8.63667i		−	0.424983i
$414$	−0.910483	+	14.3587i	−0.0447478	+	0.705689i
$415$	−25.4385	+	24.9238i	−1.24873	+	1.22346i
$416$	−4.76694	+	0.685382i	−0.233718	+	0.0336036i
$417$	−2.20015	+	2.02336i	−0.107742	+	0.0990841i
$418$	−5.96132	−	20.3024i	−0.291578	−	0.993022i
$419$	−14.6560	+	16.9140i	−0.715994	+	0.826301i	−0.990819	−	0.135193i	$-0.956834\pi$
$419$	−14.6560	+	16.9140i	−0.715994	+	0.826301i	0.274826	+	0.961494i	$0.411380\pi$
$420$	−0.820872	−	9.02117i	−0.0400544	−	0.440188i
$421$	−7.44651	−	11.5870i	−0.362921	−	0.564715i	0.610993	−	0.791636i	$-0.290770\pi$
$421$	−7.44651	−	11.5870i	−0.362921	−	0.564715i	−0.973913	+	0.226921i	$0.927134\pi$
$422$	2.57638	+	5.64149i	0.125416	+	0.274623i
$423$	1.69344	−	20.1925i	0.0823379	−	0.981794i
$424$	−7.10060	+	11.0487i	−0.344836	+	0.536575i
$425$	5.98186	−	36.3181i	0.290163	−	1.76168i
$426$	−0.571871	−	0.344067i	−0.0277072	−	0.0166701i
$427$	7.66865	−	11.9327i	0.371112	−	0.577462i
$428$	−8.38518	+	7.26580i	−0.405313	+	0.351206i
$429$	34.5944	−	1.02309i	1.67023	−	0.0493954i
$430$	13.5366	+	3.08994i	0.652791	+	0.149010i
$431$	17.7323	+	5.20668i	0.854136	+	0.250797i	0.679354	−	0.733810i	$-0.262260\pi$
$431$	17.7323	+	5.20668i	0.854136	+	0.250797i	0.174781	+	0.984607i	$0.444078\pi$
$432$	−4.89921	−	1.73139i	−0.235713	−	0.0833018i
$433$	20.6839	−	6.07334i	0.994004	−	0.291866i	0.256011	−	0.966674i	$-0.417592\pi$
$433$	20.6839	−	6.07334i	0.994004	−	0.291866i	0.737993	+	0.674808i	$0.235774\pi$
$434$	−1.21781	+	2.66664i	−0.0584569	+	0.128003i
$435$	6.08575	+	10.6501i	0.291789	+	0.510635i
$436$			2.60736i			0.124870i
$437$	−24.1330	+	3.97245i	−1.15444	+	0.190028i
$438$	−11.2111	+	26.6032i	−0.535686	+	1.27115i
$439$	−1.40002	−	9.73732i	−0.0668191	−	0.464737i	−0.995569	−	0.0940309i	$-0.970025\pi$
$439$	−1.40002	−	9.73732i	−0.0668191	−	0.464737i	0.928750	−	0.370706i	$-0.120884\pi$
$440$	−8.72537	+	3.15319i	−0.415965	+	0.150322i
$441$	4.00034	+	2.24850i	0.190492	+	0.107071i
$442$	−23.2165	+	26.7933i	−1.10430	+	1.27443i
$443$	−18.5033	−	5.43306i	−0.879119	−	0.258133i	−0.189130	−	0.981952i	$-0.560567\pi$
$443$	−18.5033	−	5.43306i	−0.879119	−	0.258133i	−0.689989	+	0.723820i	$0.742385\pi$
$444$	3.37009	−	0.586708i	0.159937	−	0.0278439i
$445$	−12.4734	+	32.4264i	−0.591297	+	1.53716i
$446$	1.93268	−	1.67468i	0.0915152	−	0.0792984i
$447$	−19.1773	−	27.9855i	−0.907057	−	1.32367i
$448$	0.332857	−	2.31507i	0.0157260	−	0.109377i
$449$	−36.4667	−	5.24312i	−1.72097	−	0.247438i	−0.790150	−	0.612914i	$-0.789997\pi$
$449$	−36.4667	−	5.24312i	−1.72097	−	0.247438i	−0.930821	+	0.365476i	$0.880906\pi$
$450$	−14.7536	+	2.70740i	−0.695493	+	0.127628i
$451$	−34.1279	+	29.5720i	−1.60702	+	1.39249i
$452$	−7.96597	+	3.63794i	−0.374688	+	0.171114i
$453$	20.6525	−	3.59545i	0.970340	−	0.168929i
$454$	0.930900	−	3.17036i	0.0436893	−	0.148792i
$455$	1.53994	+	25.1398i	0.0721936	+	1.17857i
$456$	0.998075	−	8.77654i	0.0467391	−	0.410999i
$457$	−2.34541	+	5.13574i	−0.109714	+	0.240240i	−0.956523	−	0.291657i	$-0.905793\pi$
$457$	−2.34541	+	5.13574i	−0.109714	+	0.240240i	0.846809	+	0.531897i	$0.178521\pi$
$458$	12.9096	−	1.85612i	0.603224	−	0.0867306i
$459$	−35.6030	+	13.9853i	−1.66181	+	0.652780i
$460$	2.38546	+	10.4551i	0.111223	+	0.487473i
$461$			15.4684i			0.720434i	0.932869	+	0.360217i	$0.117297\pi$
$461$			15.4684i			0.720434i	−0.932869	+	0.360217i	$0.882703\pi$
$462$	−4.25660	+	16.2603i	−0.198035	+	0.756496i
$463$	17.5125	+	7.99767i	0.813873	+	0.371683i	0.778464	−	0.627690i	$-0.215999\pi$
$463$	17.5125	+	7.99767i	0.813873	+	0.371683i	0.0354090	+	0.999373i	$0.488727\pi$
$464$	0.892286	+	3.03885i	0.0414234	+	0.141075i
$465$	4.58030	+	1.60815i	0.212406	+	0.0745760i
$466$	0.0398509	+	0.0117013i	0.00184606	+	0.000542051i
$467$	4.41370	+	6.86784i	0.204241	+	0.317806i	0.928231	−	0.372006i	$-0.121330\pi$
$467$	4.41370	+	6.86784i	0.204241	+	0.317806i	−0.723989	+	0.689811i	$0.757693\pi$
$468$	13.4740	+	5.21472i	0.622834	+	0.241050i
$469$	−1.73216	−	1.99901i	−0.0799835	−	0.0923059i
$470$	−3.05946	−	14.7903i	−0.141122	−	0.682227i
$471$	−19.9253	+	33.1176i	−0.918109	+	1.52598i
$472$	−3.65507	−	0.525520i	−0.168238	−	0.0241890i
$473$	−21.6737	−	13.9288i	−0.996557	−	0.640448i
$474$	11.3353	−	3.69568i	0.520650	−	0.169748i
$475$	−10.1163	−	23.4064i	−0.464169	−	1.07396i
$476$	−9.30854	−	14.4844i	−0.426656	−	0.663890i
$477$	34.8105	−	18.4572i	1.59386	−	0.845097i
$478$	−17.2040	−	14.9073i	−0.786892	−	0.681845i
$479$	32.5854	−	9.56793i	1.48886	−	0.437170i	0.566686	−	0.823934i	$-0.308225\pi$
$479$	32.5854	−	9.56793i	1.48886	−	0.437170i	0.922179	+	0.386764i	$0.126407\pi$
$480$	−3.86774	−	0.201519i	−0.176537	−	0.00919806i
$481$	−9.41465	+	1.35362i	−0.429271	+	0.0617198i
$482$			0.854717i			0.0389313i
$483$	18.0531	+	7.17906i	0.821446	+	0.326658i
$484$	6.21492			0.282496
$485$	−11.7936	+	15.4233i	−0.535520	+	0.700335i
$486$	10.2674	+	11.7295i	0.465737	+	0.532061i
$487$	4.71268	+	16.0499i	0.213552	+	0.727291i	0.994689	+	0.102931i	$0.0328220\pi$
$487$	4.71268	+	16.0499i	0.213552	+	0.727291i	−0.781137	+	0.624360i	$0.785360\pi$
$488$	−4.58333	−	3.97147i	−0.207477	−	0.179780i
$489$	1.13409	−	1.38978i	0.0512852	−	0.0628480i
$490$	3.33463	+	0.761181i	0.150643	+	0.0343867i
$491$	−29.8520	+	13.6330i	−1.34720	+	0.615247i	−0.952774	−	0.303680i	$-0.901785\pi$
$491$	−29.8520	+	13.6330i	−1.34720	+	0.615247i	−0.394429	+	0.918927i	$0.629058\pi$
$492$	−17.9227	+	5.84337i	−0.808018	+	0.263439i
$493$	19.6137	+	12.6049i	0.883356	+	0.567698i
$494$	−3.49531	+	24.3104i	−0.157261	+	1.09378i
$495$	27.4536	+	4.57958i	1.23395	+	0.205837i
$496$	1.05443	+	0.677641i	0.0473453	+	0.0304270i
$497$	−0.681097	+	0.590174i	−0.0305514	+	0.0264729i
$498$	27.5740	−	0.815471i	1.23562	−	0.0365421i
$499$	9.07107	−	5.82962i	0.406077	−	0.260970i	−0.321620	−	0.946869i	$-0.604227\pi$
$499$	9.07107	−	5.82962i	0.406077	−	0.260970i	0.727697	+	0.685899i	$0.240591\pi$
$500$	−9.97241	+	5.05480i	−0.445980	+	0.226058i
$501$	−10.3132	+	5.08353i	−0.460759	+	0.227115i
$502$	4.76766	−	1.39991i	0.212791	−	0.0624811i
$503$	−6.63077	−	3.02817i	−0.295651	−	0.135019i	0.262067	−	0.965050i	$-0.415596\pi$
$503$	−6.63077	−	3.02817i	−0.295651	−	0.135019i	−0.557718	+	0.830030i	$0.688323\pi$
$504$	−4.27351	+	5.56509i	−0.190357	+	0.247889i
$505$	6.09566	−	5.97231i	0.271253	−	0.265764i
$506$	2.43058	−	19.7493i	0.108053	−	0.877964i
$507$	−16.2698	−	6.85642i	−0.722569	−	0.304504i
$508$	1.45735	−	0.209535i	0.0646593	−	0.00929660i
$509$	31.9324	+	14.5830i	1.41538	+	0.646381i	0.968682	−	0.248304i	$-0.0798733\pi$
$509$	31.9324	+	14.5830i	1.41538	+	0.646381i	0.446696	+	0.894686i	$0.352601\pi$
$510$	−22.4894	+	17.5242i	−0.995846	+	0.775986i
$511$	29.4616	+	25.5286i	1.30330	+	1.12932i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−15.5112	+	21.4853i	−0.684835	+	0.948599i
$514$	10.1520	+	22.2298i	0.447786	+	0.980516i
$515$	−2.04335	+	24.9790i	−0.0900407	+	1.10071i
$516$	−6.07956	−	8.87191i	−0.267638	−	0.390564i
$517$	−3.98835	+	27.7396i	−0.175408	+	1.21999i
$518$	0.657389	−	4.57224i	0.0288840	−	0.200893i
$519$	3.61019	+	5.26835i	0.158470	+	0.231255i
$520$	10.7330	+	0.877984i	0.470671	+	0.0385022i
$521$	12.7175	+	27.8474i	0.557162	+	1.22001i	0.953356	+	0.301848i	$0.0976035\pi$
$521$	12.7175	+	27.8474i	0.557162	+	1.22001i	−0.396194	+	0.918167i	$0.629669\pi$
$522$	2.13343	−	9.25880i	0.0933776	−	0.405247i
$523$	−20.3869	−	5.98613i	−0.891456	−	0.261755i	−0.196240	−	0.980556i	$-0.562873\pi$
$523$	−20.3869	−	5.98613i	−0.891456	−	0.261755i	−0.695216	+	0.718801i	$0.744691\pi$
$524$	−1.97044	−	1.70739i	−0.0860789	−	0.0745878i
$525$	−2.69960	+	20.0746i	−0.117820	+	0.876126i
$526$	17.3549	+	7.92573i	0.756711	+	0.345578i
$527$	9.13298	−	1.31312i	0.397839	−	0.0572006i
$528$	6.62240	+	2.79080i	0.288203	+	0.121454i
$529$	−22.3137	−	5.57683i	−0.970159	−	0.242471i
$530$	20.9773	−	20.5528i	0.911197	−	0.892758i
$531$	8.78625	+	6.74708i	0.381291	+	0.292798i
$532$	−10.8499	−	4.95499i	−0.470403	−	0.214826i
$533$	50.2925	−	14.7672i	2.17841	−	0.639639i
$534$	24.1385	−	11.8982i	1.04457	−	0.514888i
$535$	21.8952	−	11.6668i	0.946613	−	0.504399i
$536$	−0.951387	+	0.611420i	−0.0410937	+	0.0264093i
$537$	−27.5460	+	0.814643i	−1.18870	+	0.0351545i
$538$	6.97976	−	6.04800i	0.300919	−	0.260748i
$539$	−5.33914	−	3.43126i	−0.229973	−	0.147795i
$540$	9.81868	+	6.21237i	0.422529	+	0.267338i
$541$	0.666518	−	4.63574i	0.0286559	−	0.199306i	−0.970464	−	0.241245i	$-0.922444\pi$
$541$	0.666518	−	4.63574i	0.0286559	−	0.199306i	0.999120	+	0.0419388i	$0.0133535\pi$
$542$	−11.7863	−	7.57462i	−0.506267	−	0.325358i
$543$	11.9972	−	3.91146i	0.514848	−	0.167857i
$544$	−6.69624	+	3.05807i	−0.287099	+	0.131114i
$545$	1.29747	−	5.68402i	0.0555774	−	0.243477i
$546$	12.3347	−	15.1157i	0.527876	−	0.646892i
$547$	−13.7006	−	11.8717i	−0.585797	−	0.507596i	0.310781	−	0.950482i	$-0.399409\pi$
$547$	−13.7006	−	11.8717i	−0.585797	−	0.507596i	−0.896578	+	0.442885i	$0.853955\pi$
$548$	2.51851	+	8.57727i	0.107586	+	0.366403i
$549$	6.14847	+	17.1234i	0.262410	+	0.730810i
$550$	20.5903	−	2.53203i	0.877975	−	0.107966i
$551$	16.1518			0.688089
$552$	4.13669	−	7.20332i	0.176069	−	0.306594i
$553$		−	16.0997i		−	0.684629i
$554$	−17.9665	+	2.58319i	−0.763323	+	0.109749i
$555$	−7.63874	−	0.397999i	−0.324246	−	0.0168941i
$556$	1.65584	−	0.486199i	0.0702234	−	0.0206194i
$557$	21.6358	+	18.7475i	0.916737	+	0.794357i	0.979033	−	0.203700i	$-0.0652968\pi$
$557$	21.6358	+	18.7475i	0.916737	+	0.794357i	−0.0622960	+	0.998058i	$0.519842\pi$
$558$	−1.76145	−	3.32212i	−0.0745681	−	0.140636i
$559$	16.1676	+	25.1572i	0.683815	+	1.06404i
$560$	−1.87765	+	4.88121i	−0.0793451	+	0.206269i
$561$	50.2970	−	16.3984i	2.12354	−	0.692342i
$562$	10.1222	+	6.50514i	0.426979	+	0.274403i
$563$	−6.95926	−	1.00059i	−0.293298	−	0.0421699i	−0.00590472	−	0.999983i	$-0.501880\pi$
$563$	−6.95926	−	1.00059i	−0.293298	−	0.0421699i	−0.287393	+	0.957813i	$0.592789\pi$
$564$	−6.03130	+	10.0246i	−0.253964	+	0.422110i
$565$	19.1761	−	3.96667i	0.806743	−	0.166879i
$566$	11.0205	+	12.7184i	0.463227	+	0.534593i
$567$	19.3565	−	8.27201i	0.812895	−	0.347392i
$568$	0.208321	+	0.324153i	0.00874094	+	0.0136012i
$569$	9.35550	+	2.74702i	0.392203	+	0.115161i	0.471887	−	0.881659i	$-0.343573\pi$
$569$	9.35550	+	2.74702i	0.392203	+	0.115161i	−0.0796842	+	0.996820i	$0.525391\pi$
$570$	−6.54316	+	18.6362i	−0.274063	+	0.780582i
$571$	−5.33238	−	18.1604i	−0.223153	−	0.759989i	−0.992616	−	0.121298i	$-0.961294\pi$
$571$	−5.33238	−	18.1604i	−0.223153	−	0.759989i	0.769463	−	0.638691i	$-0.220524\pi$
$572$	−18.1761	−	8.30075i	−0.759981	−	0.347072i
$573$	4.84895	−	18.5230i	0.202568	−	0.773811i
$574$			25.4558i			1.06250i
$575$	0.00236189	−	23.9792i	9.84975e−5	−	1.00000i
$576$	2.09513	+	2.14719i	0.0872973	+	0.0894661i
$577$	−24.8903	+	3.57868i	−1.03620	+	0.148982i	−0.639360	−	0.768907i	$-0.720801\pi$
$577$	−24.8903	+	3.57868i	−1.03620	+	0.148982i	−0.396836	+	0.917890i	$0.629892\pi$
$578$	−15.4499	+	33.8305i	−0.642629	+	1.40716i
$579$	−0.972807	+	8.55434i	−0.0404285	+	0.355506i
$580$	−0.432994	−	7.06869i	−0.0179791	−	0.293511i
$581$	10.4948	−	35.7419i	0.435397	−	1.48282i
$582$	14.8164	−	2.57943i	0.614161	−	0.106921i
$583$	−49.5683	+	22.6371i	−2.05291	+	0.937533i
$584$	12.5965	−	10.9149i	0.521245	−	0.451662i
$585$	−26.7782	−	18.0729i	−1.10714	−	0.747224i
$586$	−7.72025	−	1.11000i	−0.318921	−	0.0458539i
$587$	−6.28755	+	43.7309i	−0.259515	+	1.80497i	0.276778	+	0.960934i	$0.410733\pi$
$587$	−6.28755	+	43.7309i	−0.259515	+	1.80497i	−0.536293	+	0.844032i	$0.680176\pi$
$588$	−1.49765	−	2.18553i	−0.0617621	−	0.0901296i
$589$	4.83083	−	4.18594i	0.199051	−	0.172478i
$590$	7.70652	+	2.96446i	0.317273	+	0.122045i
$591$	32.2880	−	5.62109i	1.32815	−	0.231221i
$592$	−1.89499	−	0.556419i	−0.0778835	−	0.0228687i
$593$	16.1300	−	18.6150i	0.662379	−	0.764426i	−0.320785	−	0.947152i	$-0.603947\pi$
$593$	16.1300	−	18.6150i	0.662379	−	0.764426i	0.983164	+	0.182726i	$0.0584922\pi$
$594$	−13.2166	−	17.0331i	−0.542282	−	0.698875i
$595$	13.0849	+	36.2079i	0.536428	+	1.48438i
$596$	2.78753	+	19.3877i	0.114182	+	0.794151i
$597$	−2.13790	+	5.07310i	−0.0874985	+	0.207628i
$598$	−12.0891	+	19.6800i	−0.494359	+	0.804776i
$599$			5.65818i			0.231187i	0.993297	+	0.115594i	$0.0368770\pi$
$599$			5.65818i			0.231187i	−0.993297	+	0.115594i	$0.963123\pi$
$600$	8.33137	+	2.36397i	0.340127	+	0.0965085i
$601$	−3.82773	+	8.38156i	−0.156136	+	0.341891i	−0.971493	−	0.237068i	$-0.923814\pi$
$601$	−3.82773	+	8.38156i	−0.156136	+	0.341891i	0.815357	+	0.578959i	$0.196541\pi$
$602$	−13.9349	+	4.09164i	−0.567943	+	0.166763i
$603$	3.38682	−	0.200499i	0.137922	−	0.00816494i
$604$	−11.6128	−	3.40983i	−0.472519	−	0.138744i
$605$	−13.5485	−	3.09265i	−0.550824	−	0.125734i
$606$	−6.60736	+	0.195406i	−0.268406	+	0.00793782i
$607$	−24.4841	+	21.2156i	−0.993779	+	0.861114i	−0.990309	−	0.138880i	$-0.955650\pi$
$607$	−24.4841	+	21.2156i	−0.993779	+	0.861114i	−0.00346955	+	0.999994i	$0.501104\pi$
$608$	−2.75716	+	4.29022i	−0.111818	+	0.173992i
$609$	−10.9938	−	6.61446i	−0.445493	−	0.268032i
$610$	8.01535	+	10.9385i	0.324532	+	0.442888i
$611$	17.5866	−	27.3653i	0.711479	−	1.10708i
$612$	22.0072	+	1.84563i	0.889588	+	0.0746051i
$613$	3.45586	+	7.56728i	0.139581	+	0.305640i	0.966494	−	0.256691i	$-0.0826322\pi$
$613$	3.45586	+	7.56728i	0.139581	+	0.305640i	−0.826913	+	0.562330i	$0.809905\pi$
$614$	−7.71243	−	12.0008i	−0.311248	−	0.484312i
$615$	41.9792	−	3.81985i	1.69276	−	0.154031i
$616$	6.35490	−	7.33395i	0.256046	−	0.295493i
$617$	5.79932	+	19.7507i	0.233472	+	0.795132i	0.989987	+	0.141156i	$0.0450821\pi$
$617$	5.79932	+	19.7507i	0.233472	+	0.795132i	−0.756515	+	0.653976i	$0.773100\pi$
$618$	14.2893	−	13.1411i	0.574802	−	0.528614i
$619$	3.01004	−	0.432778i	0.120984	−	0.0173948i	−0.0815570	−	0.996669i	$-0.525989\pi$
$619$	3.01004	−	0.432778i	0.120984	−	0.0173948i	0.202541	+	0.979274i	$0.435080\pi$
$620$	−1.96144	−	2.00196i	−0.0787735	−	0.0804005i
$621$	−21.4067	+	12.7574i	−0.859023	+	0.511938i
$622$			11.4743i			0.460078i
$623$	−5.17174	−	35.9703i	−0.207202	−	1.44112i
$624$	−5.64648	−	6.13984i	−0.226040	−	0.245790i
$625$	24.2552	−	6.05699i	0.970206	−	0.242280i
$626$	−6.95776	+	8.02969i	−0.278088	+	0.320931i
$627$	23.1709	−	28.3951i	0.925358	−	1.13399i
$628$	18.7721	−	12.0641i	0.749086	−	0.481409i
$629$	−13.2250	+	6.03965i	−0.527315	+	0.240817i
$630$	12.0855	−	10.0053i	0.481499	−	0.398621i
$631$	8.35360	−	12.9985i	0.332552	−	0.517460i	−0.634203	−	0.773167i	$-0.718672\pi$
$631$	8.35360	−	12.9985i	0.332552	−	0.517460i	0.966755	+	0.255706i	$0.0823080\pi$
$632$	−6.81345	−	0.979626i	−0.271024	−	0.0389674i
$633$	−5.53794	+	9.20455i	−0.220113	+	0.365848i
$634$	−18.5528	−	11.9232i	−0.736828	−	0.473530i
$635$	−3.28127	−	0.268417i	−0.130213	−	0.0106518i
$636$	−22.7382	+	0.672460i	−0.901630	+	0.0266648i
$637$	3.98275	+	6.19728i	0.157802	+	0.245545i
$638$	−3.70217	+	12.6084i	−0.146570	+	0.499173i
$639$	−0.0683132	−	1.15395i	−0.00270243	−	0.0456494i
$640$	1.95149	+	1.09164i	0.0771396	+	0.0431507i
$641$	−6.34196	+	13.8870i	−0.250492	+	0.548502i	−0.992551	−	0.121834i	$-0.961123\pi$
$641$	−6.34196	+	13.8870i	−0.250492	+	0.548502i	0.742058	+	0.670336i	$0.233850\pi$
$642$	−18.5910	−	4.86673i	−0.733727	−	0.192074i
$643$	−40.8285			−1.61012			−0.805059	−	0.593194i	$-0.797867\pi$
$643$	−40.8285			−1.61012			−0.805059	+	0.593194i	$0.797867\pi$
$644$	−7.51641	−	8.32596i	−0.296188	−	0.328089i
$645$	8.83858	+	22.3660i	0.348019	+	0.880661i
$646$	5.34279	+	37.1599i	0.210209	+	1.46204i
$647$	−1.73917	+	3.80826i	−0.0683740	+	0.149718i	−0.940733	−	0.339147i	$-0.889862\pi$
$647$	−1.73917	+	3.80826i	−0.0683740	+	0.149718i	0.872359	+	0.488865i	$0.162589\pi$
$648$	−2.32295	−	8.69505i	−0.0912542	−	0.341574i
$649$	−11.5789	−	10.0332i	−0.454513	−	0.393838i
$650$	−22.9609	−	7.25491i	−0.900600	−	0.284561i
$651$	−5.00236	+	0.870874i	−0.196058	+	0.0341322i
$652$	−0.942050	+	0.430220i	−0.0368935	+	0.0168487i
$653$	−28.5889	−	32.9934i	−1.11877	−	1.29113i	−0.952327	−	0.305079i	$-0.901317\pi$
$653$	−28.5889	−	32.9934i	−1.11877	−	1.29113i	−0.166443	−	0.986051i	$-0.553228\pi$
$654$	−3.72533	+	2.55281i	−0.145672	+	0.0998229i
$655$	3.44591	+	4.70263i	0.134643	+	0.183747i
$656$	10.7730	+	1.54892i	0.420614	+	0.0604752i
$657$	−48.9865	+	10.0285i	−1.91115	+	0.391251i
$658$	10.3454	+	11.9392i	0.403306	+	0.465440i
$659$	−6.61988	−	14.4955i	−0.257874	−	0.564665i	0.735770	−	0.677231i	$-0.236820\pi$
$659$	−6.61988	−	14.4955i	−0.257874	−	0.564665i	−0.993644	+	0.112566i	$0.964093\pi$
$660$	−13.0480	−	9.37936i	−0.507894	−	0.365091i
$661$	−10.1310	+	34.5031i	−0.394051	+	1.34201i	0.488815	+	0.872388i	$0.337429\pi$
$661$	−10.1310	+	34.5031i	−0.394051	+	1.34201i	−0.882865	+	0.469626i	$0.844389\pi$
$662$	12.3913	−	14.3004i	0.481603	−	0.555800i
$663$	−61.0124	−	6.93838i	−2.36952	−	0.269464i
$664$	−14.4875	−	6.61623i	−0.562225	−	0.256760i
$665$	21.1871	+	16.2010i	0.821599	+	0.628246i
$666$	4.13787	+	4.24067i	0.160339	+	0.164323i
$667$	13.9420	+	6.02740i	0.539835	+	0.233382i
$668$	6.63837			0.256846
$669$	4.28500	+	1.12172i	0.165667	+	0.0433683i
$670$	2.37827	−	0.859464i	0.0918807	−	0.0332040i
$671$	−7.08912	−	24.1433i	−0.273672	−	0.932043i
$672$	3.63361	−	1.79107i	0.140170	−	0.0690918i
$673$	−3.21079	+	10.9349i	−0.123767	+	0.421511i	−0.997944	−	0.0640967i	$-0.979583\pi$
$673$	−3.21079	+	10.9349i	−0.123767	+	0.421511i	0.874177	+	0.485608i	$0.161402\pi$
$674$	−4.39614	+	2.82523i	−0.169333	+	0.108824i
$675$	−18.3133	−	18.4289i	−0.704879	−	0.709328i
$676$	6.67528	+	7.70368i	0.256742	+	0.296296i
$677$	−4.19917	+	6.53403i	−0.161387	+	0.251123i	−0.912524	−	0.409023i	$-0.865869\pi$
$677$	−4.19917	+	6.53403i	−0.161387	+	0.251123i	0.751137	+	0.660146i	$0.229506\pi$
$678$	−12.9971	−	7.81975i	−0.499152	−	0.300316i
$679$	2.89018	−	20.1016i	0.110915	−	0.771429i
$680$	16.1195	−	3.33441i	0.618155	−	0.127869i
$681$	5.44115	−	1.77399i	0.208505	−	0.0679794i
$682$	2.16036	+	4.73052i	0.0827243	+	0.181141i
$683$	20.9750	−	13.4798i	0.802585	−	0.515790i	−0.0738735	−	0.997268i	$-0.523536\pi$
$683$	20.9750	−	13.4798i	0.802585	−	0.515790i	0.876458	+	0.481478i	$0.159900\pi$
$684$	13.5169	−	7.16692i	0.516832	−	0.274034i
$685$	−1.22214	−	19.9517i	−0.0466956	−	0.762313i
$686$	−19.1417	+	5.62051i	−0.730834	+	0.214592i
$687$	15.2915	+	16.6276i	0.583407	+	0.634382i
$688$	0.883697	+	6.14625i	0.0336906	+	0.234324i
$689$	63.2512			2.40968
$690$	−12.6025	+	13.6447i	−0.479767	+	0.519445i
$691$	−16.5361			−0.629062			−0.314531	−	0.949247i	$-0.601847\pi$
$691$	−16.5361			−0.629062			−0.314531	+	0.949247i	$0.601847\pi$
$692$	−0.524760	−	3.64979i	−0.0199484	−	0.138744i
$693$	−27.3998	+	9.83839i	−1.04083	+	0.373730i
$694$	−10.1642	+	2.98448i	−0.385828	+	0.113289i
$695$	−3.85167	+	0.235935i	−0.146102	+	0.00894951i
$696$	−3.46821	+	4.25016i	−0.131462	+	0.161102i
$697$	67.4017	−	43.3164i	2.55302	−	1.64073i
$698$	2.71155	+	5.93748i	0.102634	+	0.224737i
$699$	0.0222988	+	0.0683945i	0.000843417	+	0.00258692i
$700$	6.52224	−	9.70666i	0.246517	−	0.366877i
$701$	3.47838	−	24.1927i	0.131377	−	0.913744i	−0.812386	−	0.583120i	$-0.801832\pi$
$701$	3.47838	−	24.1927i	0.131377	−	0.913744i	0.943763	−	0.330624i	$-0.107259\pi$
$702$	5.74145	+	24.3569i	0.216697	+	0.919292i
$703$	−5.44536	+	8.47314i	−0.205376	+	0.319571i
$704$	−2.71707	−	3.13567i	−0.102404	−	0.118180i
$705$	18.1366	−	18.8522i	0.683064	−	0.710016i
$706$	8.75294	−	5.62517i	0.329421	−	0.211706i
$707$	−2.51479	+	8.56459i	−0.0945784	+	0.322104i
$708$	−2.82776	−	5.73680i	−0.106274	−	0.215602i
$709$	4.91152	+	16.7271i	0.184456	+	0.628199i	0.998853	+	0.0478907i	$0.0152499\pi$
$709$	4.91152	+	16.7271i	0.184456	+	0.628199i	−0.814397	+	0.580309i	$0.802932\pi$
$710$	−0.292833	−	0.810317i	−0.0109898	−	0.0304106i
$711$	16.3785	+	12.5773i	0.614243	+	0.471685i
$712$	−15.5374			−0.582290
$713$	5.73197	−	1.81050i	0.214664	−	0.0678038i
$714$	11.5811	−	27.4812i	0.433412	−	1.02846i
$715$	35.4932	+	27.1403i	1.32737	+	1.01499i
$716$	14.4728	+	6.60951i	0.540874	+	0.247009i
$717$	4.45514	−	39.1761i	0.166380	−	1.46306i
$718$	−15.6130	+	18.0183i	−0.582671	+	0.672438i
$719$	2.19385	−	7.47155i	0.0818166	−	0.278642i	−0.908416	−	0.418068i	$-0.862707\pi$
$719$	2.19385	−	7.47155i	0.0818166	−	0.278642i	0.990233	+	0.139426i	$0.0445257\pi$
$720$	−3.49890	−	5.72343i	−0.130396	−	0.213300i
$721$	−10.8900	−	23.8458i	−0.405565	−	0.888063i
$722$	4.58922	+	5.29625i	0.170793	+	0.197106i
$723$	−1.22120	+	0.836838i	−0.0454169	+	0.0311223i
$724$	−7.21126	−	1.03682i	−0.268004	−	0.0385332i
$725$	−2.57358	+	15.6252i	−0.0955805	+	0.580304i
$726$	6.08491	+	8.87972i	0.225832	+	0.329557i
$727$	−4.52057	−	5.21702i	−0.167659	−	0.193489i	0.665702	−	0.746217i	$-0.268132\pi$
$727$	−4.52057	−	5.21702i	−0.167659	−	0.193489i	−0.833361	+	0.552729i	$0.813587\pi$
$728$	−10.2460	+	4.67921i	−0.379743	+	0.173423i
$729$	−6.70625	+	26.1539i	−0.248379	+	0.968663i
$730$	−32.8917	+	17.5262i	−1.21738	+	0.648673i
$731$	34.5459	+	29.9342i	1.27773	+	1.10716i
$732$	1.18690	−	10.4369i	0.0438690	−	0.385760i
$733$	15.6214	−	34.2061i	0.576989	−	1.26343i	−0.366003	−	0.930614i	$-0.619274\pi$
$733$	15.6214	−	34.2061i	0.576989	−	1.26343i	0.942992	−	0.332816i	$-0.107999\pi$
$734$	−1.69991	−	11.8231i	−0.0627448	−	0.436399i
$735$	2.17731	+	5.50969i	0.0803115	+	0.203228i
$736$	−3.98093	+	2.67436i	−0.146739	+	0.0985781i
$737$	−4.69227			−0.172842
$738$	−25.8966	−	19.8864i	−0.953269	−	0.732028i
$739$	−2.79524	+	6.12073i	−0.102825	+	0.225155i	−0.954051	−	0.299644i	$-0.903132\pi$
$739$	−2.79524	+	6.12073i	−0.102825	+	0.225155i	0.851226	+	0.524799i	$0.175859\pi$
$740$	3.85418	+	2.15597i	0.141682	+	0.0792550i
$741$	−38.1563	+	18.8079i	−1.40171	+	0.690924i
$742$	−8.65428	+	29.4738i	−0.317709	+	1.08202i
$743$	−19.2016	−	29.8783i	−0.704440	−	1.09613i	−0.990446	−	0.137902i	$-0.955964\pi$
$743$	−19.2016	−	29.8783i	−0.704440	−	1.09613i	0.286006	−	0.958228i	$-0.407672\pi$
$744$	0.0641757	+	2.17001i	0.00235280	+	0.0795564i
$745$	3.57087	−	43.6522i	0.130826	−	1.59929i
$746$	−4.72078	−	3.03386i	−0.172840	−	0.111078i
$747$	28.1623	+	38.5986i	1.03040	+	1.41225i
$748$	−30.2325	−	4.34678i	−1.10541	−	0.158934i
$749$	−14.0298	+	21.8308i	−0.512637	+	0.797678i
$750$	−16.9860	−	9.29927i	−0.620240	−	0.339561i
$751$	17.5657	−	8.02199i	0.640982	−	0.292727i	−0.0682859	−	0.997666i	$-0.521753\pi$
$751$	17.5657	−	8.02199i	0.640982	−	0.292727i	0.709268	+	0.704939i	$0.249026\pi$
$752$	5.68222	−	3.65174i	0.207209	−	0.133165i
$753$	6.66808	+	5.44129i	0.242999	+	0.198292i
$754$	9.98846	−	11.5273i	0.363758	−	0.419800i
$755$	23.6191	+	13.2122i	0.859587	+	0.480840i
$756$	−12.1354	−	0.657210i	−0.441360	−	0.0239025i
$757$	2.79276	+	19.4241i	0.101505	+	0.705981i	0.975492	+	0.220033i	$0.0706165\pi$
$757$	2.79276	+	19.4241i	0.101505	+	0.705981i	−0.873988	+	0.485948i	$0.838474\pi$
$758$		−	32.1031i		−	1.16604i
$759$	30.5971	−	15.8634i	1.11060	−	0.575806i
$760$	8.14548	−	7.98065i	0.295468	−	0.289489i
$761$	15.0024	−	2.15702i	0.543838	−	0.0781921i	0.135080	−	0.990835i	$-0.456871\pi$
$761$	15.0024	−	2.15702i	0.543838	−	0.0781921i	0.408758	+	0.912643i	$0.365962\pi$
$762$	1.72624	+	1.87707i	0.0625350	+	0.0679990i
$763$	1.71809	+	5.85127i	0.0621989	+	0.211830i
$764$	−7.23925	+	8.35454i	−0.261907	+	0.302256i
$765$	−47.0571	−	14.9746i	−1.70135	−	0.541409i
$766$	−13.0133	−	20.2491i	−0.470190	−	0.731629i
$767$	7.38760	+	16.1766i	0.266751	+	0.584103i
$768$	−0.536889	−	1.64674i	−0.0193733	−	0.0594216i
$769$	−5.21934	+	8.12145i	−0.188214	+	0.292867i	−0.922518	−	0.385954i	$-0.873872\pi$
$769$	−5.21934	+	8.12145i	−0.188214	+	0.292867i	0.734304	+	0.678821i	$0.237509\pi$
$770$	−17.5032	+	12.8257i	−0.630770	+	0.462205i
$771$	−21.8218	+	36.2698i	−0.785892	+	1.30622i
$772$	2.68736	−	4.18161i	0.0967200	−	0.150499i
$773$	−14.3883	+	12.4675i	−0.517510	+	0.448425i	−0.874037	−	0.485860i	$-0.838506\pi$
$773$	−14.3883	+	12.4675i	−0.517510	+	0.448425i	0.356526	+	0.934285i	$0.383961\pi$
$774$	6.72359	−	17.3727i	0.241675	−	0.624447i
$775$	3.27973	+	5.34030i	0.117811	+	0.191829i
$776$	−8.33122	−	2.44627i	−0.299073	−	0.0878158i
$777$	7.17634	−	3.53733i	0.257450	−	0.126901i
$778$	−8.95176	+	2.62847i	−0.320936	+	0.0942353i
$779$	23.0576	−	50.4891i	0.826124	−	1.80896i
$780$	9.25399	+	16.1946i	0.331346	+	0.579860i
$781$			1.59873i			0.0572072i
$782$	−9.25526	+	34.0697i	−0.330967	+	1.21833i
$783$	15.3176	−	6.01693i	0.547405	−	0.215028i
$784$	0.217692	+	1.51408i	0.00777471	+	0.0540743i
$785$	−46.9263	+	16.9583i	−1.67487	+	0.605267i
$786$	0.510264	−	4.48699i	0.0182005	−	0.160046i
$787$	0.773676	−	0.892870i	0.0275786	−	0.0318274i	−0.741793	−	0.670629i	$-0.766024\pi$
$787$	0.773676	−	0.892870i	0.0275786	−	0.0318274i	0.769371	+	0.638802i	$0.220570\pi$
$788$	−18.1554	−	5.33090i	−0.646759	−	0.189905i
$789$	5.66780	+	32.5563i	0.201779	+	1.15903i
$790$	14.3658	+	5.52607i	0.511112	+	0.196609i
$791$	−15.4796	+	13.4131i	−0.550389	+	0.476915i
$792$	2.49643	+	12.1943i	0.0887069	+	0.433307i
$793$	−4.15657	+	28.9096i	−0.147604	+	1.02661i
$794$	−17.8385	−	2.56480i	−0.633066	−	0.0910212i
$795$	49.9039	+	9.84900i	1.76991	+	0.349308i
$796$	2.40209	−	2.08142i	0.0851397	−	0.0737740i
$797$	0.864647	−	0.394871i	0.0306274	−	0.0139871i	−0.400042	−	0.916497i	$-0.631005\pi$
$797$	0.864647	−	0.394871i	0.0306274	−	0.0139871i	0.430670	+	0.902510i	$0.358277\pi$
$798$	−3.54338	−	20.3534i	−0.125434	−	0.720504i
$799$	14.0086	−	47.7087i	0.495587	−	1.68781i
$800$	−3.71103	−	3.35086i	−0.131205	−	0.118471i
$801$	40.6335	+	22.8391i	1.43571	+	0.806981i
$802$	8.54805	−	18.7176i	0.301842	−	0.660942i
$803$	68.4510	−	9.84177i	2.41558	−	0.347309i
$804$	−1.80507	−	0.760690i	−0.0636598	−	0.0268275i
$805$	12.2426	+	21.8909i	0.431494	+	0.771551i
$806$		−	6.03633i		−	0.212621i
$807$	15.4750	+	4.05103i	0.544745	+	0.142603i
$808$	3.47154	+	1.58540i	0.122129	+	0.0557742i
$809$	0.951643	+	3.24100i	0.0334580	+	0.113947i	0.974529	−	0.224262i	$-0.0719970\pi$
$809$	0.951643	+	3.24100i	0.0334580	+	0.113947i	−0.941071	+	0.338209i	$0.890179\pi$
$810$	0.737210	+	20.1111i	0.0259029	+	0.706632i
$811$	−3.36442	−	0.987882i	−0.118141	−	0.0346892i	0.222128	−	0.975018i	$-0.428700\pi$
$811$	−3.36442	−	0.987882i	−0.118141	−	0.0346892i	−0.340268	+	0.940328i	$0.610518\pi$
$812$	4.00483	+	6.23163i	0.140542	+	0.218687i
$813$	−0.717352	−	24.2562i	−0.0251586	−	0.850703i
$814$	−5.36619	−	6.19291i	−0.188085	−	0.217061i
$815$	2.26775	−	0.469096i	0.0794357	−	0.0164317i
$816$	−10.9255	−	6.57332i	−0.382467	−	0.230112i
$817$	31.3446	+	4.50668i	1.09661	+	0.157669i
$818$	−3.10387	−	1.99474i	−0.108524	−	0.0697443i
$819$	33.6736	+	2.82403i	1.17665	+	0.0986795i
$820$	−22.7143	−	8.73746i	−0.793216	−	0.305125i
$821$	9.02626	+	14.0451i	0.315019	+	0.490179i	0.962269	−	0.272099i	$-0.0877177\pi$
$821$	9.02626	+	14.0451i	0.315019	+	0.490179i	−0.647251	+	0.762277i	$0.724081\pi$
$822$	−9.78916	+	11.9962i	−0.341436	+	0.418417i
$823$	15.3096	+	13.2659i	0.533660	+	0.462419i	0.879516	−	0.475868i	$-0.157866\pi$
$823$	15.3096	+	13.2659i	0.533660	+	0.462419i	−0.345857	+	0.938287i	$0.612412\pi$
$824$	−10.7542	+	3.15773i	−0.374642	+	0.110005i
$825$	23.7773	+	26.9399i	0.827820	+	0.937927i
$826$	−8.54876	+	1.22913i	−0.297449	+	0.0427668i
$827$			17.6281i			0.612991i	0.951872	+	0.306495i	$0.0991564\pi$
$827$			17.6281i			0.612991i	−0.951872	+	0.306495i	$0.900844\pi$
$828$	14.3421	−	1.14223i	0.498422	−	0.0396954i
$829$	−50.9519			−1.76963			−0.884817	−	0.465939i	$-0.845717\pi$
$829$	−50.9519			−1.76963			−0.884817	+	0.465939i	$0.845717\pi$
$830$	28.2904	+	21.6326i	0.981973	+	0.750878i
$831$	−21.2815	−	23.1409i	−0.738246	−	0.802750i
$832$	1.35681	+	4.62088i	0.0470390	+	0.160200i
$833$	8.51011	+	7.37405i	0.294858	+	0.255496i
$834$	2.31587	+	1.88980i	0.0801921	+	0.0654384i
$835$	−14.4716	−	3.30337i	−0.500811	−	0.114318i
$836$	−19.2474	+	8.78997i	−0.665684	+	0.304008i
$837$	3.02196	−	5.76934i	0.104454	−	0.199418i
$838$	18.8276	+	12.0997i	0.650387	+	0.417979i
$839$	−0.0889258	+	0.618492i	−0.00307006	+	0.0213527i	−0.991299	−	0.131630i	$-0.957979\pi$
$839$	−0.0889258	+	0.618492i	−0.00307006	+	0.0213527i	0.988229	+	0.152983i	$0.0488880\pi$
$840$	−8.81252	+	2.09636i	−0.304061	+	0.0723314i
$841$	15.9579	+	10.2555i	0.550273	+	0.353639i
$842$	−10.4093	+	9.01971i	−0.358728	+	0.310840i
$843$	0.616067	+	20.8314i	0.0212185	+	0.717471i
$844$	5.21741	−	3.35303i	0.179591	−	0.115416i
$845$	−10.7186	−	20.1157i	−0.368730	−	0.692002i
$846$	−20.2280	+	1.19749i	−0.695453	+	0.0411706i
$847$	13.9471	−	4.09524i	0.479229	−	0.140714i
$848$	11.9468	+	5.45593i	0.410255	+	0.187357i
$849$	−7.38170	+	28.1982i	−0.253339	+	0.967759i
$850$	−36.7997	−	0.752373i	−1.26222	−	0.0258062i
$851$	−7.86229	+	5.28182i	−0.269516	+	0.181059i
$852$	−0.259179	+	0.615016i	−0.00887934	+	0.0210701i
$853$	−40.6201	+	5.84029i	−1.39081	+	0.199968i	−0.796679	−	0.604403i	$-0.793412\pi$
$853$	−40.6201	+	5.84029i	−1.39081	+	0.199968i	−0.594127	+	0.804371i	$0.702503\pi$
$854$	−12.9026	−	5.89240i	−0.441517	−	0.201634i
$855$	−33.0332	+	8.89760i	−1.12971	+	0.304291i
$856$	8.38518	+	7.26580i	0.286599	+	0.248340i
$857$	−19.6281	−	5.76332i	−0.670483	−	0.196871i	−0.0712647	−	0.997457i	$-0.522703\pi$
$857$	−19.6281	−	5.76332i	−0.670483	−	0.196871i	−0.599218	+	0.800586i	$0.704522\pi$
$858$	−5.93598	−	34.0967i	−0.202651	−	1.16404i
$859$	8.13909	+	17.8221i	0.277702	+	0.608083i	0.996166	−	0.0874810i	$-0.0278817\pi$
$859$	8.13909	+	17.8221i	0.277702	+	0.608083i	−0.718464	+	0.695564i	$0.755154\pi$
$860$	1.13203	−	13.8385i	0.0386019	−	0.471890i
$861$	−36.3706	+	24.9233i	−1.23951	+	0.849383i
$862$	2.63011	−	18.2928i	0.0895819	−	0.623056i
$863$	6.54288	−	45.5068i	0.222722	−	1.54907i	−0.504953	−	0.863147i	$-0.668490\pi$
$863$	6.54288	−	45.5068i	0.222722	−	1.54907i	0.727676	−	0.685921i	$-0.240601\pi$
$864$	−1.01654	+	5.09575i	−0.0345834	+	0.173361i
$865$	−0.672226	+	8.21765i	−0.0228564	+	0.279409i
$866$	−8.95514	−	19.6090i	−0.304308	−	0.666342i
$867$	−63.4628	+	11.0484i	−2.15531	+	0.375223i
$868$	2.81281	+	0.825915i	0.0954729	+	0.0280334i
$869$	−21.5844	−	18.7030i	−0.732201	−	0.634456i
$870$	9.67564	−	7.53947i	0.328035	−	0.255612i
$871$	4.95426	+	2.26253i	0.167869	+	0.0766631i
$872$	2.58082	−	0.371066i	0.0873975	−	0.0125659i
$873$	18.1919	+	18.6439i	0.615703	+	0.631000i
$874$	7.36650	+	23.3220i	0.249176	+	0.788880i
$875$	−19.0487	+	17.9149i	−0.643962	+	0.605633i
$876$	27.9279	+	7.31095i	0.943596	+	0.247014i
$877$	−6.12197	−	2.79581i	−0.206724	−	0.0944078i	0.309362	−	0.950944i	$-0.399884\pi$
$877$	−6.12197	−	2.79581i	−0.206724	−	0.0944078i	−0.516086	+	0.856536i	$0.672612\pi$
$878$	−9.43897	+	2.77153i	−0.318550	+	0.0935347i
$879$	−5.97281	−	12.1173i	−0.201458	−	0.408706i
$880$	4.36284	+	8.18781i	0.147071	+	0.276011i
$881$	−33.9780	+	21.8363i	−1.14475	+	0.735684i	−0.968586	−	0.248677i	$-0.920004\pi$
$881$	−33.9780	+	21.8363i	−1.14475	+	0.735684i	−0.176160	+	0.984361i	$0.556368\pi$
$882$	1.65630	−	4.27962i	0.0557707	−	0.144102i
$883$	1.02468	−	0.887888i	0.0344832	−	0.0298798i	−0.637449	−	0.770493i	$-0.720010\pi$
$883$	1.02468	−	0.887888i	0.0344832	−	0.0298798i	0.671932	+	0.740613i	$0.265465\pi$
$884$	29.8246	+	19.1671i	1.00311	+	0.644659i
$885$	3.30977	+	13.9133i	0.111257	+	0.467692i
$886$	−2.74447	+	19.0882i	−0.0922021	+	0.641280i
$887$	−38.1701	−	24.5304i	−1.28163	−	0.823650i	−0.290538	−	0.956864i	$-0.593834\pi$
$887$	−38.1701	−	24.5304i	−1.28163	−	0.823650i	−0.991087	+	0.133213i	$0.957471\pi$
$888$	−1.06035	−	3.25229i	−0.0355830	−	0.109140i
$889$	3.13241	−	1.43053i	0.105058	−	0.0479783i
$890$	33.8715	+	7.73171i	1.13538	+	0.259167i
$891$	11.3963	−	35.5603i	0.381791	−	1.19131i
$892$	−1.93268	−	1.67468i	−0.0647110	−	0.0560724i
$893$	−9.70468	−	33.0511i	−0.324755	−	1.10601i
$894$	−24.9715	+	22.9649i	−0.835171	+	0.768061i
$895$	−28.2616	−	21.6106i	−0.944683	−	0.722364i
$896$	−2.33888			−0.0781364
$897$	−39.9545	+	1.99575i	−1.33404	+	0.0666362i
$898$			36.8417i			1.22942i
$899$	−3.92930	+	0.564947i	−0.131049	+	0.0188420i
$900$	4.77951	+	14.2182i	0.159317	+	0.473939i
$901$	92.7669	−	27.2388i	3.09051	−	0.907457i
$902$	34.1279	+	29.5720i	1.13633	+	0.984639i
$903$	−19.4894	−	15.9037i	−0.648567	−	0.529243i
$904$	4.73458	+	7.36715i	0.157470	+	0.245028i
$905$	15.2046	+	5.84872i	0.505417	+	0.194418i
$906$	−6.49801	−	19.9306i	−0.215882	−	0.662151i
$907$	−34.3109	−	22.0503i	−1.13927	−	0.732167i	−0.171799	−	0.985132i	$-0.554958\pi$
$907$	−34.3109	−	22.0503i	−1.13927	−	0.732167i	−0.967476	+	0.252965i	$0.918594\pi$
$908$	−3.27057	−	0.470237i	−0.108538	−	0.0156053i
$909$	−6.74833	−	9.24911i	−0.223828	−	0.306774i
$910$	24.6648	−	5.10204i	0.817629	−	0.169131i
$911$	1.31019	+	1.51204i	0.0434086	+	0.0500962i	0.777039	−	0.629453i	$-0.216721\pi$
$911$	1.31019	+	1.51204i	0.0434086	+	0.0500962i	−0.733630	+	0.679549i	$0.762175\pi$
$912$	−8.82925	+	0.261116i	−0.292366	+	0.00864641i
$913$	−35.7264	−	55.5914i	−1.18237	−	1.83981i
$914$	5.41725	+	1.59065i	0.179187	+	0.0526139i
$915$	−7.78104	+	22.1618i	−0.257233	+	0.732648i
$916$	−3.67445	−	12.5140i	−0.121407	−	0.413475i
$917$	−5.54699	−	2.53323i	−0.183178	−	0.0836545i
$918$	18.9098	+	33.2503i	0.624117	+	1.09742i
$919$			11.1166i			0.366703i	0.983047	+	0.183351i	$0.0586946\pi$
$919$			11.1166i			0.366703i	−0.983047	+	0.183351i	$0.941305\pi$
$920$	10.0092	−	3.84910i	0.329994	−	0.126901i
$921$	9.59532	−	22.7691i	0.316176	−	0.750266i
$922$	15.3109	−	2.20138i	0.504238	−	0.0724985i
$923$	0.770883	−	1.68800i	0.0253739	−	0.0555611i
$924$	16.7005	+	1.89920i	0.549407	+	0.0624790i
$925$	−7.32924	−	6.61791i	−0.240984	−	0.217596i
$926$	5.42398	−	18.4724i	0.178243	−	0.607040i
$927$	32.7662	+	7.55003i	1.07618	+	0.247975i
$928$	2.88093	−	1.31568i	0.0945712	−	0.0431892i
$929$	−27.9781	+	24.2432i	−0.917933	+	0.795394i	−0.979236	−	0.202725i	$-0.935020\pi$
$929$	−27.9781	+	24.2432i	−0.917933	+	0.795394i	0.0613023	+	0.998119i	$0.480475\pi$
$930$	0.939932	−	4.76254i	0.0308216	−	0.156170i
$931$	7.72150	+	1.11018i	0.253062	+	0.0363848i
$932$	0.00591081	−	0.0411106i	0.000193615	−	0.00134662i
$933$	−16.3942	+	11.2343i	−0.536723	+	0.367794i
$934$	6.16981	−	5.34617i	0.201882	−	0.174932i
$935$	63.7437	+	24.5202i	2.08464	+	0.801896i
$936$	3.24409	−	14.0789i	0.106036	−	0.460185i
$937$	26.5481	+	7.79523i	0.867289	+	0.254659i	0.684962	−	0.728579i	$-0.259819\pi$
$937$	26.5481	+	7.79523i	0.867289	+	0.254659i	0.182327	+	0.983238i	$0.441637\pi$
$938$	−1.73216	+	1.99901i	−0.0565569	+	0.0652701i
$939$	−18.2848	−	2.07937i	−0.596703	−	0.0678575i
$940$	−14.2044	+	5.13320i	−0.463296	+	0.167427i
$941$	2.01244	+	13.9968i	0.0656036	+	0.456283i	0.995973	+	0.0896584i	$0.0285775\pi$
$941$	2.01244	+	13.9968i	0.0656036	+	0.456283i	−0.930369	+	0.366624i	$0.880513\pi$
$942$	35.6162	+	15.0093i	1.16044	+	0.489031i
$943$	38.7441	−	34.9769i	1.26168	−	1.13901i
$944$			3.69265i			0.120186i
$945$	26.1280	+	7.47150i	0.849945	+	0.243048i
$946$	−10.7026	+	23.4354i	−0.347970	+	0.761949i
$947$	44.1059	−	12.9507i	1.43325	−	0.420840i	0.529284	−	0.848445i	$-0.322461\pi$
$947$	44.1059	−	12.9507i	1.43325	−	0.420840i	0.903966	+	0.427605i	$0.140642\pi$
$948$	−5.27125	−	10.6940i	−0.171202	−	0.347326i
$949$	−77.0185	−	22.6147i	−2.50013	−	0.734103i
$950$	−21.7284	+	13.3444i	−0.704963	+	0.432951i
$951$	−1.12918	−	38.1816i	−0.0366162	−	1.23812i
$952$	−13.0122	+	11.2751i	−0.421728	+	0.365429i
$953$	−7.98742	+	12.4287i	−0.258738	+	0.402604i	−0.946183	−	0.323632i	$-0.895096\pi$
$953$	−7.98742	+	12.4287i	−0.258738	+	0.402604i	0.687445	+	0.726236i	$0.258732\pi$
$954$	−23.2234	−	31.8295i	−0.751885	−	1.03052i
$955$	19.9389	−	14.6105i	0.645207	−	0.472783i
$956$	−12.3072	+	19.1504i	−0.398044	+	0.619368i
$957$	−21.6394	+	7.05512i	−0.699501	+	0.228060i
$958$	−14.1079	−	30.8921i	−0.455806	−	0.998077i
$959$	11.3038	+	17.5890i	0.365018	+	0.567979i
$960$	0.350968	+	3.85705i	0.0113274	+	0.124486i
$961$	19.2719	−	22.2409i	0.621674	−	0.717450i
$962$	2.67969	+	9.12618i	0.0863966	+	0.294240i
$963$	−11.2486	−	31.3272i	−0.362481	−	1.00951i
$964$	0.846017	−	0.121639i	0.0272484	−	0.00391773i
$965$	−7.93926	+	7.77860i	−0.255574	+	0.250402i
$966$	4.53676	−	18.8911i	0.145968	−	0.607810i
$967$		−	40.6173i		−	1.30616i	−0.757287	−	0.653082i	$-0.773476\pi$
$967$		−	40.6173i		−	1.30616i	0.757287	−	0.653082i	$-0.226524\pi$
$968$	−0.884475	−	6.15166i	−0.0284281	−	0.197722i
$969$	−47.8622	+	44.0162i	−1.53755	+	1.41401i
$970$	16.9447	+	9.47861i	0.544061	+	0.304340i
$971$	13.6438	−	15.7458i	0.437850	−	0.505306i	−0.493341	−	0.869836i	$-0.664225\pi$
$971$	13.6438	−	15.7458i	0.437850	−	0.505306i	0.931192	+	0.364529i	$0.118770\pi$
$972$	10.1489	−	11.8321i	0.325527	−	0.379516i
$973$	3.39556	−	2.18219i	0.108857	−	0.0699580i
$974$	15.2159	−	6.94885i	0.487548	−	0.222656i
$975$	−12.1149	−	39.9091i	−0.387988	−	1.27811i
$976$	−3.27877	+	5.10187i	−0.104951	+	0.163307i
$977$	−33.1411	−	4.76497i	−1.06028	−	0.152445i	−0.409957	−	0.912105i	$-0.634456\pi$
$977$	−33.1411	−	4.76497i	−1.06028	−	0.152445i	−0.650320	+	0.759660i	$0.725365\pi$
$978$	−1.53703	−	0.924757i	−0.0491488	−	0.0295705i
$979$	−54.2324	−	34.8530i	−1.73327	−	1.11391i
$980$	0.278866	−	3.40901i	0.00890806	−	0.108897i
$981$	−7.29480	−	2.82324i	−0.232905	−	0.0901393i
$982$	17.7426	+	27.6080i	0.566189	+	0.881007i
$983$	9.52862	−	32.4515i	0.303916	−	1.03504i	−0.656002	−	0.754759i	$-0.727754\pi$
$983$	9.52862	−	32.4515i	0.303916	−	1.03504i	0.959917	−	0.280283i	$-0.0904282\pi$
$984$	8.33456	+	16.9087i	0.265696	+	0.539029i
$985$	36.9259	+	20.6558i	1.17656	+	0.658148i
$986$	9.68533	−	21.2079i	0.308444	−	0.675398i
$987$	−6.92950	+	26.4708i	−0.220568	+	0.842573i
$988$	24.5604			0.781371
$989$	25.3744	+	15.5871i	0.806860	+	0.495640i
$990$	0.625917	−	27.8259i	0.0198929	−	0.884364i
$991$	−6.87067	−	47.7865i	−0.218254	−	1.51799i	−0.744480	−	0.667645i	$-0.767303\pi$
$991$	−6.87067	−	47.7865i	−0.218254	−	1.51799i	0.526226	−	0.850345i	$-0.323607\pi$
$992$	0.520682	−	1.14014i	0.0165317	−	0.0361993i
$993$	32.5642	+	3.70322i	1.03339	+	0.117518i
$994$	0.681097	+	0.590174i	0.0216031	+	0.0187192i
$995$	−6.27229	+	3.34216i	−0.198845	+	0.105954i
$996$	−4.73136	−	27.1772i	−0.149919	−	0.861144i
$997$	25.2514	−	11.5319i	0.799720	−	0.365220i	0.0267335	−	0.999643i	$-0.491489\pi$
$997$	25.2514	−	11.5319i	0.799720	−	0.365220i	0.772986	+	0.634423i	$0.218762\pi$
$998$	−7.06123	−	8.14910i	−0.223519	−	0.257955i
$999$	−2.00766	+	10.0640i	−0.0635194	+	0.318412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.89.19	yes	240
3.2	odd	2		690.2.n.b.89.13	yes	240
5.4	even	2		690.2.n.b.89.6	yes	240
15.14	odd	2	inner	690.2.n.a.89.12	✓	240
23.15	odd	22	inner	690.2.n.a.659.12	yes	240
69.38	even	22		690.2.n.b.659.6	yes	240
115.84	odd	22		690.2.n.b.659.13	yes	240
345.314	even	22	inner	690.2.n.a.659.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.12	✓	240	15.14	odd	2	inner
690.2.n.a.89.19	yes	240	1.1	even	1	trivial
690.2.n.a.659.12	yes	240	23.15	odd	22	inner
690.2.n.a.659.19	yes	240	345.314	even	22	inner
690.2.n.b.89.6	yes	240	5.4	even	2
690.2.n.b.89.13	yes	240	3.2	odd	2
690.2.n.b.659.6	yes	240	69.38	even	22
690.2.n.b.659.13	yes	240	115.84	odd	22

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.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(1.27489 - 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.23188 - 0.136714i) q^{5} +(-1.34195 - 1.09506i) q^{6} +(-1.96759 + 1.26449i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.250714 - 2.98951i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(1.27489 - 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.23188 - 0.136714i) q^{5} +(-1.34195 - 1.09506i) q^{6} +(-1.96759 + 1.26449i) q^{7} +(0.415415 + 0.909632i) q^{8} +(0.250714 - 2.98951i) q^{9} +(-0.452953 - 2.18971i) q^{10} +(-0.590477 + 4.10685i) q^{11} +(-0.892935 + 1.48414i) q^{12} +(2.60370 - 4.05144i) q^{13} +(1.53164 + 1.76761i) q^{14} +(2.68513 - 2.79107i) q^{15} +(0.841254 - 0.540641i) q^{16} +(2.07397 - 7.06329i) q^{17} +(-2.99476 + 0.177289i) q^{18} +(-1.43678 - 4.89322i) q^{19} +(-2.10296 + 0.759971i) q^{20} +(-1.02591 + 3.91900i) q^{21} +4.14909 q^{22} +(0.585811 - 4.75992i) q^{23} +(1.59611 + 0.672631i) q^{24} +(4.96262 - 0.610262i) q^{25} +(-4.38075 - 2.00062i) q^{26} +(-3.18542 - 4.10526i) q^{27} +(1.53164 - 1.76761i) q^{28} +(-0.892286 + 3.03885i) q^{29} +(-3.14480 - 2.26059i) q^{30} +(0.520682 + 1.14014i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(4.06229 + 5.92811i) q^{33} +(-7.28655 - 1.04765i) q^{34} +(-4.21856 + 3.09120i) q^{35} +(0.601683 + 2.93904i) q^{36} +(-1.29334 - 1.49260i) q^{37} +(-4.63894 + 2.11853i) q^{38} +(-1.43067 - 8.21788i) q^{39} +(1.05152 + 1.97340i) q^{40} +(8.22539 + 7.12734i) q^{41} +(4.02511 + 0.457739i) q^{42} +(-2.57950 + 5.64832i) q^{43} +(-0.590477 - 4.10685i) q^{44} +(0.150857 - 6.70651i) q^{45} +(-4.79484 + 0.0975584i) q^{46} +6.75447 q^{47} +(0.438635 - 1.67559i) q^{48} +(-0.635439 + 1.39142i) q^{49} +(-1.31030 - 4.82526i) q^{50} +(-5.63727 - 11.4366i) q^{51} +(-1.35681 + 4.62088i) q^{52} +(7.10060 + 11.0487i) q^{53} +(-3.61014 + 3.73723i) q^{54} +(-0.756409 + 9.24675i) q^{55} +(-1.96759 - 1.26449i) q^{56} +(-7.56881 - 4.55379i) q^{57} +(3.13490 + 0.450731i) q^{58} +(-1.99640 + 3.10646i) q^{59} +(-1.79002 + 3.43450i) q^{60} +(-5.51656 + 2.51933i) q^{61} +(1.05443 - 0.677641i) q^{62} +(3.28691 + 6.19915i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(5.25727 - 9.39831i) q^{65} +(5.28965 - 4.86460i) q^{66} +(0.160946 + 1.11941i) q^{67} +7.36148i q^{68} +(-4.83393 - 6.75523i) q^{69} +(3.66010 + 3.73570i) q^{70} +(0.381400 - 0.0548370i) q^{71} +(2.82350 - 1.01383i) q^{72} +(-4.69578 - 15.9924i) q^{73} +(-1.29334 + 1.49260i) q^{74} +(5.61131 - 6.59645i) q^{75} +(2.75716 + 4.29022i) q^{76} +(-4.03127 - 8.82726i) q^{77} +(-7.93062 + 2.58563i) q^{78} +(-3.72151 + 5.79078i) q^{79} +(1.80367 - 1.32166i) q^{80} +(-8.87428 - 1.49902i) q^{81} +(5.88420 - 9.15600i) q^{82} +(-12.0367 + 10.4298i) q^{83} +(-0.119753 - 4.04929i) q^{84} +(3.66320 - 16.0480i) q^{85} +(5.95793 + 1.74940i) q^{86} +(2.42533 + 4.92037i) q^{87} +(-3.98102 + 1.16893i) q^{88} +(-6.45448 + 14.1333i) q^{89} +(-6.65971 + 0.805115i) q^{90} +11.2639i q^{91} +(0.778942 + 4.73215i) q^{92} +(2.00057 + 0.843078i) q^{93} +(-0.961261 - 6.68572i) q^{94} +(-3.87570 - 10.7247i) q^{95} +(-1.72096 - 0.195709i) q^{96} +(-5.68611 + 6.56212i) q^{97} +(1.46769 + 0.430952i) q^{98} +(12.1294 + 2.79488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Introduction

L-functions

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