LMFDB - Embedded newform 690.2.n.a.659.19

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			659.19
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.19

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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	0.113122	−	0.993581i	$-0.463915\pi$
$7$	−1.96759	−	1.26449i	−0.743679	−	0.477933i	−0.856801	+	0.515648i	$0.827551\pi$
$8$	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	−0.861302	−	0.508094i	$-0.830350\pi$
$11$	−0.590477	−	4.10685i	−0.178035	−	1.23826i	0.683266	−	0.730169i	$-0.260559\pi$
$12$	−0.892935	−	1.48414i	−0.257768	−	0.428434i
$13$	2.60370	+	4.05144i	0.722137	+	1.12367i	0.987208	+	0.159438i	$0.0509683\pi$
$13$	2.60370	+	4.05144i	0.722137	+	1.12367i	−0.265071	+	0.964229i	$0.585395\pi$
$14$	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	0.683883	+	0.729592i	$0.260290\pi$
$17$	2.07397	+	7.06329i	0.503011	+	1.71310i	−0.180872	+	0.983507i	$0.557892\pi$
$18$	−2.99476	−	0.177289i	−0.705871	−	0.0417874i
$19$	−1.43678	+	4.89322i	−0.329620	+	1.12258i	0.613380	+	0.789788i	$0.289809\pi$
$19$	−1.43678	+	4.89322i	−0.329620	+	1.12258i	−0.943000	+	0.332794i	$0.892009\pi$
$20$	−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	−0.999917	−	0.0128738i	$-0.995902\pi$
$29$	−0.892286	−	3.03885i	−0.165693	−	0.564300i	0.834224	−	0.551426i	$-0.185916\pi$
$30$	−3.14480	+	2.26059i	−0.574159	+	0.412725i
$31$	0.520682	−	1.14014i	0.0935173	−	0.204774i	−0.857093	−	0.515162i	$-0.827732\pi$
$31$	0.520682	−	1.14014i	0.0935173	−	0.204774i	0.950610	+	0.310388i	$0.100459\pi$
$32$	−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	−0.852036	−	0.523483i	$-0.824632\pi$
$37$	−1.29334	+	1.49260i	−0.212624	+	0.245381i	0.639412	+	0.768864i	$0.279178\pi$
$38$	−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	0.297197	−	0.954816i	$-0.403948\pi$
$41$	8.22539	−	7.12734i	1.28459	−	1.11310i	0.987393	−	0.158288i	$-0.0505974\pi$
$42$	4.02511	−	0.457739i	0.621088	−	0.0706306i
$43$	−2.57950	−	5.64832i	−0.393370	−	0.861360i	−0.997900	−	0.0647776i	$-0.979366\pi$
$43$	−2.57950	−	5.64832i	−0.393370	−	0.861360i	0.604530	−	0.796583i	$-0.293361\pi$
$44$	−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	0.124515	−	0.992218i	$-0.460263\pi$
$53$	7.10060	−	11.0487i	0.975342	−	1.51766i	0.850828	−	0.525445i	$-0.176101\pi$
$54$	−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	0.686634	−	0.727003i	$-0.259087\pi$
$59$	−1.99640	−	3.10646i	−0.259909	−	0.404427i	−0.946543	+	0.322577i	$0.895451\pi$
$60$	−1.79002	−	3.43450i	−0.231091	−	0.443392i
$61$	−5.51656	−	2.51933i	−0.706323	−	0.322567i	0.0296663	−	0.999560i	$-0.490556\pi$
$61$	−5.51656	−	2.51933i	−0.706323	−	0.322567i	−0.735990	+	0.676993i	$0.763283\pi$
$62$	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	−0.977625	−	0.210353i	$-0.932539\pi$
$67$	0.160946	−	1.11941i	0.0196627	−	0.136757i	0.997288	+	0.0735963i	$0.0234476\pi$
$68$		−	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	0.164910	−	0.986309i	$-0.447267\pi$
$71$	0.381400	+	0.0548370i	0.0452638	+	0.00650796i	−0.119646	+	0.992817i	$0.538176\pi$
$72$	2.82350	+	1.01383i	0.332753	+	0.119481i
$73$	−4.69578	+	15.9924i	−0.549599	+	1.87176i	−0.0632528	+	0.997998i	$0.520147\pi$
$73$	−4.69578	+	15.9924i	−0.549599	+	1.87176i	−0.486347	+	0.873766i	$0.661671\pi$
$74$	−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	0.566271	−	0.824219i	$-0.308385\pi$
$79$	−3.72151	−	5.79078i	−0.418702	−	0.651513i	−0.984974	+	0.172706i	$0.944749\pi$
$80$	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	−0.978698	−	0.205304i	$-0.934182\pi$
$83$	−12.0367	−	10.4298i	−1.32120	−	1.14482i	−0.342498	−	0.939519i	$-0.611273\pi$
$84$	−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	−0.858159	−	0.513383i	$-0.828392\pi$
$89$	−6.45448	−	14.1333i	−0.684174	−	1.49813i	0.173986	−	0.984748i	$-0.444335\pi$
$90$	−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	0.389693	−	0.920945i	$-0.372581\pi$
$97$	−5.68611	−	6.56212i	−0.577337	−	0.666283i	−0.967030	+	0.254662i	$0.918036\pi$
$98$	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	0.786445	−	0.617660i	$-0.211919\pi$
$101$	2.88426	+	2.49923i	0.286995	+	0.248683i	−0.499450	+	0.866343i	$0.666465\pi$
$102$	−10.5179	−	7.20749i	−1.04143	−	0.713647i
$103$	−1.59510	−	11.0942i	−0.157170	−	1.09314i	−0.903817	−	0.427920i	$-0.859246\pi$
$103$	−1.59510	−	11.0942i	−0.157170	−	1.09314i	0.746647	−	0.665221i	$-0.231663\pi$
$104$	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	0.838461	−	0.544962i	$-0.183456\pi$
$107$	10.0925	+	4.60910i	0.975682	+	0.445579i	0.137221	+	0.990541i	$0.456183\pi$
$108$	4.21297	−	3.04153i	0.405393	−	0.292671i
$109$	0.734577	+	2.50174i	0.0703597	+	0.239623i	0.987163	−	0.159716i	$-0.0510578\pi$
$109$	0.734577	+	2.50174i	0.0703597	+	0.239623i	−0.916803	+	0.399339i	$0.869240\pi$
$110$	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	0.537399	−	0.843328i	$-0.319407\pi$
$113$	8.66822	+	1.24630i	0.815437	+	0.117242i	0.278038	+	0.960570i	$0.410316\pi$
$114$	−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	−0.206670	−	0.978411i	$-0.566263\pi$
$127$	−1.45735	+	0.209535i	−0.129319	+	0.0185932i	0.0773516	+	0.997004i	$0.475354\pi$
$128$	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	−0.774201	−	0.632940i	$-0.781848\pi$
$131$	1.40959	−	2.19337i	0.123157	−	0.191635i	0.897357	+	0.441305i	$0.145484\pi$
$132$	−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	$0.124720\pi$
$137$			8.93937i			0.763742i	−0.924216	+	0.381871i	$0.875280\pi$
$138$	−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	0.705003	+	0.709204i	$0.250946\pi$
$149$	2.78753	+	19.3877i	0.228363	+	1.58830i	−0.476640	+	0.879099i	$0.658145\pi$
$150$	−7.32788	+	4.61543i	−0.598319	+	0.376848i
$151$	10.1818	−	6.54342i	0.828580	−	0.532496i	−0.0562462	−	0.998417i	$-0.517913\pi$
$151$	10.1818	−	6.54342i	0.828580	−	0.532496i	0.884826	+	0.465921i	$0.154277\pi$
$152$	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	−0.726155	−	0.687531i	$-0.758695\pi$
$157$	−21.4105	−	6.28669i	−1.70874	−	0.501732i	−0.982588	+	0.185798i	$0.940513\pi$
$158$	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	0.182344	−	0.983235i	$-0.441632\pi$
$163$	1.02510	+	0.147387i	0.0802918	+	0.0115442i	−0.102052	+	0.994779i	$0.532541\pi$
$164$	−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	−0.518723	−	0.854942i	$-0.673592\pi$
$167$	−6.36947	+	1.87024i	−0.492884	+	0.144724i	0.0258390	+	0.999666i	$0.491774\pi$
$168$	−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	0.960101	−	0.279654i	$-0.0902197\pi$
$173$	−0.524760	−	3.64979i	−0.0398968	−	0.277488i	−0.999998	+	0.00216564i	$0.999311\pi$
$174$	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	−0.975893	−	0.218249i	$-0.929965\pi$
$179$	−12.0244	+	10.4192i	−0.898750	+	0.778771i	0.0771436	+	0.997020i	$0.475420\pi$
$180$	1.74470	−	6.47735i	0.130042	−	0.482793i
$181$	6.62705	−	3.02647i	0.492585	−	0.224956i	−0.153606	−	0.988132i	$-0.549089\pi$
$181$	6.62705	−	3.02647i	0.492585	−	0.224956i	0.646190	+	0.763176i	$0.276361\pi$
$182$	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	0.831972	−	0.554817i	$-0.187212\pi$
$191$	9.29975	+	5.97659i	0.672906	+	0.432451i	−0.159066	+	0.987268i	$0.550848\pi$
$192$	0.0512012	−	1.73129i	0.00369513	−	0.124945i
$193$	−3.75659	−	3.25511i	−0.270406	−	0.234308i	0.509093	−	0.860711i	$-0.329981\pi$
$193$	−3.75659	−	3.25511i	−0.270406	−	0.234308i	−0.779499	+	0.626404i	$0.784526\pi$
$194$	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	0.167701	−	0.985838i	$-0.446366\pi$
$197$	15.9181	−	10.2299i	1.13412	−	0.728852i	0.966415	+	0.256986i	$0.0827294\pi$
$198$	1.04023	+	12.4037i	0.0739263	+	0.881494i
$199$	−2.89119	−	1.32036i	−0.204951	−	0.0935980i	0.310295	−	0.950640i	$-0.399572\pi$
$199$	−2.89119	−	1.32036i	−0.204951	−	0.0935980i	−0.515246	+	0.857042i	$0.672299\pi$
$200$	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	0.0704055	−	0.997518i	$-0.477571\pi$
$211$	−5.95073	−	1.74729i	−0.409665	−	0.120288i	−0.480070	+	0.877230i	$0.659389\pi$
$212$	−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	−0.791872	−	0.610688i	$-0.790893\pi$
$223$	1.38258	−	2.15134i	0.0925847	−	0.144065i	0.884456	+	0.466623i	$0.154529\pi$
$224$	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	−0.313165	−	0.949699i	$-0.601389\pi$
$227$	3.00561	−	1.37261i	0.199489	−	0.0911036i	0.512655	+	0.858595i	$0.328662\pi$
$228$	8.54517	−	2.23695i	0.565918	−	0.148146i
$229$		−	13.0423i		−	0.861861i	−0.902385	−	0.430930i	$-0.858185\pi$
$229$		−	13.0423i		−	0.861861i	0.902385	−	0.430930i	$-0.141815\pi$
$230$	−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	0.909066	−	0.416652i	$-0.136797\pi$
$233$	−0.0172536	−	0.0377800i	−0.00113032	−	0.00247505i	−0.910196	+	0.414177i	$0.864069\pi$
$234$	−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	0.999571	−	0.0292902i	$-0.00932468\pi$
$239$	17.2040	+	14.9073i	1.11283	+	0.964275i	0.113262	+	0.993565i	$0.463870\pi$
$240$	0.749905	+	3.79969i	0.0484061	+	0.245269i
$241$	−0.846017	+	0.121639i	−0.0544968	+	0.00783545i	−0.169509	−	0.985529i	$-0.554218\pi$
$241$	−0.846017	+	0.121639i	−0.0544968	+	0.00783545i	0.115013	+	0.993364i	$0.463309\pi$
$242$	−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	−0.955257	−	0.295776i	$-0.904422\pi$
$251$	0.707153	−	4.91836i	0.0446351	−	0.310444i	0.999892	−	0.0146680i	$-0.00466914\pi$
$252$	−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	−0.548959	−	0.835849i	$-0.684976\pi$
$257$	−23.4483	−	6.88505i	−1.46267	−	0.429478i	−0.913708	+	0.406371i	$0.866794\pi$
$258$	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	−0.998337	−	0.0576416i	$-0.981642\pi$
$263$	−10.3149	−	16.0503i	−0.636046	−	0.989706i	0.362292	−	0.932065i	$-0.381994\pi$
$264$	−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	−0.655004	−	0.755625i	$-0.727333\pi$
$269$	4.99311	−	7.76944i	0.304436	−	0.473711i	0.959440	+	0.281914i	$0.0909694\pi$
$270$	−7.54648	−	8.83463i	−0.459264	−	0.537658i
$271$	9.17490	+	10.5884i	0.557335	+	0.643199i	0.962576	−	0.271011i	$-0.0873578\pi$
$271$	9.17490	+	10.5884i	0.557335	+	0.643199i	−0.405241	+	0.914210i	$0.632812\pi$
$272$	−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	$0.183585\pi$
$277$			18.1513i			1.09060i	−0.838240	+	0.545302i	$0.816415\pi$
$278$	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	0.470376	−	0.882466i	$-0.344118\pi$
$281$	−7.87946	−	9.09338i	−0.470049	−	0.542466i	−0.940425	+	0.340000i	$0.889573\pi$
$282$	−9.06419	+	7.39656i	−0.539764	+	0.440458i
$283$	−14.1573	−	9.09834i	−0.841564	−	0.540840i	0.0473690	−	0.998877i	$-0.484916\pi$
$283$	−14.1573	−	9.09834i	−0.841564	−	0.540840i	−0.888933	+	0.458037i	$0.848553\pi$
$284$	−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	0.998446	−	0.0557220i	$-0.0177460\pi$
$293$	2.19741	+	7.48370i	0.128374	+	0.437203i	−0.870072	+	0.492925i	$0.835928\pi$
$294$	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	0.749732	−	0.661741i	$-0.230182\pi$
$307$	12.9762	+	5.92604i	0.740592	+	0.338217i	−0.00914055	+	0.999958i	$0.502910\pi$
$308$	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	−0.456586	−	0.889679i	$-0.650928\pi$
$311$	−11.3575	+	1.63297i	−0.644026	+	0.0925970i	−0.187440	+	0.982276i	$0.560019\pi$
$312$	6.88092	+	4.71521i	0.389555	+	0.266946i
$313$	−6.95776	+	8.02969i	−0.393276	+	0.453865i	−0.917512	−	0.397708i	$-0.869806\pi$
$313$	−6.95776	+	8.02969i	−0.393276	+	0.453865i	0.524236	+	0.851573i	$0.324351\pi$
$314$	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	0.998937	−	0.0460894i	$-0.0146759\pi$
$317$	14.4422	+	16.6672i	0.811153	+	0.936121i	−0.187784	+	0.982210i	$0.560130\pi$
$318$	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	−0.304979	−	0.952359i	$-0.598649\pi$
$331$	12.3913	−	14.3004i	0.681090	−	0.786019i	0.986069	+	0.166340i	$0.0531948\pi$
$332$	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	−0.959498	−	0.281717i	$-0.909096\pi$
$337$	−2.17083	+	4.75346i	−0.118253	+	0.258938i	0.841245	+	0.540655i	$0.181823\pi$
$338$	−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	0.908500	+	0.417886i	$0.137229\pi$
$347$	−1.50759	+	10.4855i	−0.0809314	+	0.562890i	−0.989431	+	0.145005i	$0.953680\pi$
$348$	−3.71332	+	4.03777i	−0.199055	+	0.216447i
$349$	−6.26294	−	1.83896i	−0.335247	−	0.0984375i	0.109776	−	0.993956i	$-0.464987\pi$
$349$	−6.26294	−	1.83896i	−0.335247	−	0.0984375i	−0.445024	+	0.895519i	$0.646805\pi$
$350$	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	−0.759041	−	0.651042i	$-0.774332\pi$
$353$	4.32225	−	9.46440i	0.230050	−	0.503739i	0.989091	+	0.147303i	$0.0470593\pi$
$354$	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	−0.999438	−	0.0335237i	$-0.989327\pi$
$359$	−15.6130	+	18.0183i	−0.824021	+	0.950971i	0.175417	+	0.984494i	$0.443873\pi$
$360$	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	0.842869	−	0.538119i	$-0.180865\pi$
$373$	3.67482	+	4.24097i	0.190275	+	0.219589i	−0.652594	+	0.757708i	$0.726319\pi$
$374$	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	0.735593	−	0.677423i	$-0.236903\pi$
$379$	31.7764	−	4.56875i	1.63224	−	0.234681i	0.896649	+	0.442742i	$0.145994\pi$
$380$	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	0.886968	−	0.461830i	$-0.152807\pi$
$383$	21.8950	+	9.99910i	1.11878	+	0.510930i	0.231813	+	0.972760i	$0.425534\pi$
$384$	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	0.928078	+	0.372386i	$0.121460\pi$
$389$	−1.32775	+	9.23471i	−0.0673196	+	0.468218i	−0.995398	+	0.0958322i	$0.969449\pi$
$390$	−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	0.983177	+	0.182655i	$0.0584690\pi$
$397$	5.07738	+	17.2920i	0.254826	+	0.867859i	−0.728351	+	0.685204i	$0.759713\pi$
$398$	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	−0.0316008	−	0.999501i	$-0.510061\pi$
$401$	17.3106	−	11.1248i	0.864449	−	0.555548i	0.896050	+	0.443953i	$0.146424\pi$
$402$	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	0.812334	−	0.583192i	$-0.198196\pi$
$409$	2.41616	+	2.78840i	0.119471	+	0.137877i	−0.692863	+	0.721069i	$0.743651\pi$
$410$	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	0.274826	−	0.961494i	$-0.411380\pi$
$419$	−14.6560	−	16.9140i	−0.715994	−	0.826301i	−0.990819	+	0.135193i	$0.956834\pi$
$420$	−0.820872	+	9.02117i	−0.0400544	+	0.440188i
$421$	−7.44651	+	11.5870i	−0.362921	+	0.564715i	−0.973913	−	0.226921i	$-0.927134\pi$
$421$	−7.44651	+	11.5870i	−0.362921	+	0.564715i	0.610993	+	0.791636i	$0.290770\pi$
$422$	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	0.174781	−	0.984607i	$-0.444078\pi$
$431$	17.7323	−	5.20668i	0.854136	−	0.250797i	0.679354	+	0.733810i	$0.262260\pi$
$432$	−4.89921	+	1.73139i	−0.235713	+	0.0833018i
$433$	20.6839	+	6.07334i	0.994004	+	0.291866i	0.737993	−	0.674808i	$-0.235774\pi$
$433$	20.6839	+	6.07334i	0.994004	+	0.291866i	0.256011	+	0.966674i	$0.417592\pi$
$434$	−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	0.928750	+	0.370706i	$0.120884\pi$
$439$	−1.40002	+	9.73732i	−0.0668191	+	0.464737i	−0.995569	+	0.0940309i	$0.970025\pi$
$440$	−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	−0.689989	−	0.723820i	$-0.742385\pi$
$443$	−18.5033	+	5.43306i	−0.879119	+	0.258133i	−0.189130	+	0.981952i	$0.560567\pi$
$444$	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	−0.930821	−	0.365476i	$-0.880906\pi$
$449$	−36.4667	+	5.24312i	−1.72097	+	0.247438i	−0.790150	+	0.612914i	$0.789997\pi$
$450$	−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	0.846809	−	0.531897i	$-0.178521\pi$
$457$	−2.34541	−	5.13574i	−0.109714	−	0.240240i	−0.956523	+	0.291657i	$0.905793\pi$
$458$	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	$-0.882703\pi$
$461$		−	15.4684i		−	0.720434i	0.932869	−	0.360217i	$-0.117297\pi$
$462$	−4.25660	−	16.2603i	−0.198035	−	0.756496i
$463$	17.5125	−	7.99767i	0.813873	−	0.371683i	0.0354090	−	0.999373i	$-0.488727\pi$
$463$	17.5125	−	7.99767i	0.813873	−	0.371683i	0.778464	+	0.627690i	$0.215999\pi$
$464$	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	−0.723989	−	0.689811i	$-0.757693\pi$
$467$	4.41370	−	6.86784i	0.204241	−	0.317806i	0.928231	+	0.372006i	$0.121330\pi$
$468$	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	0.922179	−	0.386764i	$-0.126407\pi$
$479$	32.5854	+	9.56793i	1.48886	+	0.437170i	0.566686	+	0.823934i	$0.308225\pi$
$480$	−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	−0.781137	−	0.624360i	$-0.785360\pi$
$487$	4.71268	−	16.0499i	0.213552	−	0.727291i	0.994689	−	0.102931i	$-0.0328220\pi$
$488$	−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	−0.394429	−	0.918927i	$-0.629058\pi$
$491$	−29.8520	−	13.6330i	−1.34720	−	0.615247i	−0.952774	+	0.303680i	$0.901785\pi$
$492$	−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	0.727697	−	0.685899i	$-0.240591\pi$
$499$	9.07107	+	5.82962i	0.406077	+	0.260970i	−0.321620	+	0.946869i	$0.604227\pi$
$500$	−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	−0.557718	−	0.830030i	$-0.688323\pi$
$503$	−6.63077	+	3.02817i	−0.295651	+	0.135019i	0.262067	+	0.965050i	$0.415596\pi$
$504$	−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	0.446696	−	0.894686i	$-0.352601\pi$
$509$	31.9324	−	14.5830i	1.41538	−	0.646381i	0.968682	+	0.248304i	$0.0798733\pi$
$510$	−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	−0.396194	−	0.918167i	$-0.629669\pi$
$521$	12.7175	−	27.8474i	0.557162	−	1.22001i	0.953356	−	0.301848i	$-0.0976035\pi$
$522$	2.13343	+	9.25880i	0.0933776	+	0.405247i
$523$	−20.3869	+	5.98613i	−0.891456	+	0.261755i	−0.695216	−	0.718801i	$-0.744691\pi$
$523$	−20.3869	+	5.98613i	−0.891456	+	0.261755i	−0.196240	+	0.980556i	$0.562873\pi$
$524$	−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	0.999120	−	0.0419388i	$-0.0133535\pi$
$541$	0.666518	+	4.63574i	0.0286559	+	0.199306i	−0.970464	+	0.241245i	$0.922444\pi$
$542$	−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	−0.896578	−	0.442885i	$-0.853955\pi$
$547$	−13.7006	+	11.8717i	−0.585797	+	0.507596i	0.310781	+	0.950482i	$0.399409\pi$
$548$	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	−0.0622960	−	0.998058i	$-0.519842\pi$
$557$	21.6358	−	18.7475i	0.916737	−	0.794357i	0.979033	+	0.203700i	$0.0652968\pi$
$558$	−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	−0.287393	−	0.957813i	$-0.592789\pi$
$563$	−6.95926	+	1.00059i	−0.293298	+	0.0421699i	−0.00590472	+	0.999983i	$0.501880\pi$
$564$	−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	−0.0796842	−	0.996820i	$-0.525391\pi$
$569$	9.35550	−	2.74702i	0.392203	−	0.115161i	0.471887	+	0.881659i	$0.343573\pi$
$570$	−6.54316	−	18.6362i	−0.274063	−	0.780582i
$571$	−5.33238	+	18.1604i	−0.223153	+	0.759989i	0.769463	+	0.638691i	$0.220524\pi$
$571$	−5.33238	+	18.1604i	−0.223153	+	0.759989i	−0.992616	+	0.121298i	$0.961294\pi$
$572$	−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	−0.396836	−	0.917890i	$-0.629892\pi$
$577$	−24.8903	−	3.57868i	−1.03620	−	0.148982i	−0.639360	+	0.768907i	$0.720801\pi$
$578$	−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	−0.536293	−	0.844032i	$-0.680176\pi$
$587$	−6.28755	−	43.7309i	−0.259515	−	1.80497i	0.276778	−	0.960934i	$-0.410733\pi$
$588$	−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	0.983164	−	0.182726i	$-0.0584922\pi$
$593$	16.1300	+	18.6150i	0.662379	+	0.764426i	−0.320785	+	0.947152i	$0.603947\pi$
$594$	−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	$-0.963123\pi$
$599$		−	5.65818i		−	0.231187i	0.993297	−	0.115594i	$-0.0368770\pi$
$600$	8.33137	−	2.36397i	0.340127	−	0.0965085i
$601$	−3.82773	−	8.38156i	−0.156136	−	0.341891i	0.815357	−	0.578959i	$-0.196541\pi$
$601$	−3.82773	−	8.38156i	−0.156136	−	0.341891i	−0.971493	+	0.237068i	$0.923814\pi$
$602$	−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	−0.00346955	−	0.999994i	$-0.501104\pi$
$607$	−24.4841	−	21.2156i	−0.993779	−	0.861114i	−0.990309	+	0.138880i	$0.955650\pi$
$608$	−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	−0.826913	−	0.562330i	$-0.809905\pi$
$613$	3.45586	−	7.56728i	0.139581	−	0.305640i	0.966494	+	0.256691i	$0.0826322\pi$
$614$	−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	−0.756515	−	0.653976i	$-0.773100\pi$
$617$	5.79932	−	19.7507i	0.233472	−	0.795132i	0.989987	−	0.141156i	$-0.0450821\pi$
$618$	14.2893	+	13.1411i	0.574802	+	0.528614i
$619$	3.01004	+	0.432778i	0.120984	+	0.0173948i	0.202541	−	0.979274i	$-0.435080\pi$
$619$	3.01004	+	0.432778i	0.120984	+	0.0173948i	−0.0815570	+	0.996669i	$0.525989\pi$
$620$	−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	0.966755	−	0.255706i	$-0.0823080\pi$
$631$	8.35360	+	12.9985i	0.332552	+	0.517460i	−0.634203	+	0.773167i	$0.718672\pi$
$632$	−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	0.742058	−	0.670336i	$-0.233850\pi$
$641$	−6.34196	−	13.8870i	−0.250492	−	0.548502i	−0.992551	+	0.121834i	$0.961123\pi$
$642$	−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	0.872359	−	0.488865i	$-0.162589\pi$
$647$	−1.73917	−	3.80826i	−0.0683740	−	0.149718i	−0.940733	+	0.339147i	$0.889862\pi$
$648$	−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	−0.166443	+	0.986051i	$0.553228\pi$
$653$	−28.5889	+	32.9934i	−1.11877	+	1.29113i	−0.952327	+	0.305079i	$0.901317\pi$
$654$	−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	−0.993644	−	0.112566i	$-0.964093\pi$
$659$	−6.61988	+	14.4955i	−0.257874	+	0.564665i	0.735770	+	0.677231i	$0.236820\pi$
$660$	−13.0480	+	9.37936i	−0.507894	+	0.365091i
$661$	−10.1310	−	34.5031i	−0.394051	−	1.34201i	−0.882865	−	0.469626i	$-0.844389\pi$
$661$	−10.1310	−	34.5031i	−0.394051	−	1.34201i	0.488815	−	0.872388i	$-0.337429\pi$
$662$	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	0.874177	−	0.485608i	$-0.161402\pi$
$673$	−3.21079	−	10.9349i	−0.123767	−	0.421511i	−0.997944	+	0.0640967i	$0.979583\pi$
$674$	−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	0.751137	−	0.660146i	$-0.229506\pi$
$677$	−4.19917	−	6.53403i	−0.161387	−	0.251123i	−0.912524	+	0.409023i	$0.865869\pi$
$678$	−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	0.876458	−	0.481478i	$-0.159900\pi$
$683$	20.9750	+	13.4798i	0.802585	+	0.515790i	−0.0738735	+	0.997268i	$0.523536\pi$
$684$	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	0.943763	+	0.330624i	$0.107259\pi$
$701$	3.47838	+	24.1927i	0.131377	+	0.913744i	−0.812386	+	0.583120i	$0.801832\pi$
$702$	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	−0.814397	−	0.580309i	$-0.802932\pi$
$709$	4.91152	−	16.7271i	0.184456	−	0.628199i	0.998853	−	0.0478907i	$-0.0152499\pi$
$710$	−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	0.990233	−	0.139426i	$-0.0445257\pi$
$719$	2.19385	+	7.47155i	0.0818166	+	0.278642i	−0.908416	+	0.418068i	$0.862707\pi$
$720$	−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	−0.833361	−	0.552729i	$-0.813587\pi$
$727$	−4.52057	+	5.21702i	−0.167659	+	0.193489i	0.665702	+	0.746217i	$0.268132\pi$
$728$	−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	0.942992	+	0.332816i	$0.107999\pi$
$733$	15.6214	+	34.2061i	0.576989	+	1.26343i	−0.366003	+	0.930614i	$0.619274\pi$
$734$	−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	0.851226	−	0.524799i	$-0.175859\pi$
$739$	−2.79524	−	6.12073i	−0.102825	−	0.225155i	−0.954051	+	0.299644i	$0.903132\pi$
$740$	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	0.286006	+	0.958228i	$0.407672\pi$
$743$	−19.2016	+	29.8783i	−0.704440	+	1.09613i	−0.990446	+	0.137902i	$0.955964\pi$
$744$	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	0.709268	−	0.704939i	$-0.249026\pi$
$751$	17.5657	+	8.02199i	0.640982	+	0.292727i	−0.0682859	+	0.997666i	$0.521753\pi$
$752$	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	−0.873988	−	0.485948i	$-0.838474\pi$
$757$	2.79276	−	19.4241i	0.101505	−	0.705981i	0.975492	−	0.220033i	$-0.0706165\pi$
$758$			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	0.408758	−	0.912643i	$-0.365962\pi$
$761$	15.0024	+	2.15702i	0.543838	+	0.0781921i	0.135080	+	0.990835i	$0.456871\pi$
$762$	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	0.734304	−	0.678821i	$-0.237509\pi$
$769$	−5.21934	−	8.12145i	−0.188214	−	0.292867i	−0.922518	+	0.385954i	$0.873872\pi$
$770$	−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	0.356526	−	0.934285i	$-0.383961\pi$
$773$	−14.3883	−	12.4675i	−0.517510	−	0.448425i	−0.874037	+	0.485860i	$0.838506\pi$
$774$	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	0.769371	−	0.638802i	$-0.220570\pi$
$787$	0.773676	+	0.892870i	0.0275786	+	0.0318274i	−0.741793	+	0.670629i	$0.766024\pi$
$788$	−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	0.430670	−	0.902510i	$-0.358277\pi$
$797$	0.864647	+	0.394871i	0.0306274	+	0.0139871i	−0.400042	+	0.916497i	$0.631005\pi$
$798$	−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	−0.941071	−	0.338209i	$-0.890179\pi$
$809$	0.951643	−	3.24100i	0.0334580	−	0.113947i	0.974529	+	0.224262i	$0.0719970\pi$
$810$	0.737210	−	20.1111i	0.0259029	−	0.706632i
$811$	−3.36442	+	0.987882i	−0.118141	+	0.0346892i	−0.340268	−	0.940328i	$-0.610518\pi$
$811$	−3.36442	+	0.987882i	−0.118141	+	0.0346892i	0.222128	+	0.975018i	$0.428700\pi$
$812$	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	−0.647251	−	0.762277i	$-0.724081\pi$
$821$	9.02626	−	14.0451i	0.315019	−	0.490179i	0.962269	+	0.272099i	$0.0877177\pi$
$822$	−9.78916	−	11.9962i	−0.341436	−	0.418417i
$823$	15.3096	−	13.2659i	0.533660	−	0.462419i	−0.345857	−	0.938287i	$-0.612412\pi$
$823$	15.3096	−	13.2659i	0.533660	−	0.462419i	0.879516	+	0.475868i	$0.157866\pi$
$824$	−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	$-0.900844\pi$
$827$		−	17.6281i		−	0.612991i	0.951872	−	0.306495i	$-0.0991564\pi$
$828$	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	0.988229	−	0.152983i	$-0.0488880\pi$
$839$	−0.0889258	−	0.618492i	−0.00307006	−	0.0213527i	−0.991299	+	0.131630i	$0.957979\pi$
$840$	−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	−0.594127	−	0.804371i	$-0.702503\pi$
$853$	−40.6201	−	5.84029i	−1.39081	−	0.199968i	−0.796679	+	0.604403i	$0.793412\pi$
$854$	−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	−0.599218	−	0.800586i	$-0.704522\pi$
$857$	−19.6281	+	5.76332i	−0.670483	+	0.196871i	−0.0712647	+	0.997457i	$0.522703\pi$
$858$	−5.93598	+	34.0967i	−0.202651	+	1.16404i
$859$	8.13909	−	17.8221i	0.277702	−	0.608083i	−0.718464	−	0.695564i	$-0.755154\pi$
$859$	8.13909	−	17.8221i	0.277702	−	0.608083i	0.996166	+	0.0874810i	$0.0278817\pi$
$860$	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	0.727676	+	0.685921i	$0.240601\pi$
$863$	6.54288	+	45.5068i	0.222722	+	1.54907i	−0.504953	+	0.863147i	$0.668490\pi$
$864$	−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	−0.516086	−	0.856536i	$-0.672612\pi$
$877$	−6.12197	+	2.79581i	−0.206724	+	0.0944078i	0.309362	+	0.950944i	$0.399884\pi$
$878$	−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	−0.176160	−	0.984361i	$-0.556368\pi$
$881$	−33.9780	−	21.8363i	−1.14475	−	0.735684i	−0.968586	+	0.248677i	$0.920004\pi$
$882$	1.65630	+	4.27962i	0.0557707	+	0.144102i
$883$	1.02468	+	0.887888i	0.0344832	+	0.0298798i	0.671932	−	0.740613i	$-0.265465\pi$
$883$	1.02468	+	0.887888i	0.0344832	+	0.0298798i	−0.637449	+	0.770493i	$0.720010\pi$
$884$	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	−0.991087	−	0.133213i	$-0.957471\pi$
$887$	−38.1701	+	24.5304i	−1.28163	+	0.823650i	−0.290538	+	0.956864i	$0.593834\pi$
$888$	−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	−0.967476	−	0.252965i	$-0.918594\pi$
$907$	−34.3109	+	22.0503i	−1.13927	+	0.732167i	−0.171799	+	0.985132i	$0.554958\pi$
$908$	−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	−0.733630	−	0.679549i	$-0.762175\pi$
$911$	1.31019	−	1.51204i	0.0434086	−	0.0500962i	0.777039	+	0.629453i	$0.216721\pi$
$912$	−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	$-0.941305\pi$
$919$		−	11.1166i		−	0.366703i	0.983047	−	0.183351i	$-0.0586946\pi$
$920$	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	0.0613023	−	0.998119i	$-0.480475\pi$
$929$	−27.9781	−	24.2432i	−0.917933	−	0.795394i	−0.979236	+	0.202725i	$0.935020\pi$
$930$	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	0.182327	−	0.983238i	$-0.441637\pi$
$937$	26.5481	−	7.79523i	0.867289	−	0.254659i	0.684962	+	0.728579i	$0.259819\pi$
$938$	−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	−0.930369	−	0.366624i	$-0.880513\pi$
$941$	2.01244	−	13.9968i	0.0656036	−	0.456283i	0.995973	−	0.0896584i	$-0.0285775\pi$
$942$	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	0.903966	−	0.427605i	$-0.140642\pi$
$947$	44.1059	+	12.9507i	1.43325	+	0.420840i	0.529284	+	0.848445i	$0.322461\pi$
$948$	−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	0.687445	−	0.726236i	$-0.258732\pi$
$953$	−7.98742	−	12.4287i	−0.258738	−	0.402604i	−0.946183	+	0.323632i	$0.895096\pi$
$954$	−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	$0.226524\pi$
$967$			40.6173i			1.30616i	−0.757287	+	0.653082i	$0.773476\pi$
$968$	−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	0.931192	−	0.364529i	$-0.118770\pi$
$971$	13.6438	+	15.7458i	0.437850	+	0.505306i	−0.493341	+	0.869836i	$0.664225\pi$
$972$	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	−0.650320	−	0.759660i	$-0.725365\pi$
$977$	−33.1411	+	4.76497i	−1.06028	+	0.152445i	−0.409957	+	0.912105i	$0.634456\pi$
$978$	−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	0.959917	+	0.280283i	$0.0904282\pi$
$983$	9.52862	+	32.4515i	0.303916	+	1.03504i	−0.656002	+	0.754759i	$0.727754\pi$
$984$	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	0.526226	+	0.850345i	$0.323607\pi$
$991$	−6.87067	+	47.7865i	−0.218254	+	1.51799i	−0.744480	+	0.667645i	$0.767303\pi$
$992$	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	0.772986	−	0.634423i	$-0.218762\pi$
$997$	25.2514	+	11.5319i	0.799720	+	0.365220i	0.0267335	+	0.999643i	$0.491489\pi$
$998$	−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.659.19	yes	240
3.2	odd	2		690.2.n.b.659.13	yes	240
5.4	even	2		690.2.n.b.659.6	yes	240
15.14	odd	2	inner	690.2.n.a.659.12	yes	240
23.20	odd	22	inner	690.2.n.a.89.12	✓	240
69.20	even	22		690.2.n.b.89.6	yes	240
115.89	odd	22		690.2.n.b.89.13	yes	240
345.89	even	22	inner	690.2.n.a.89.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.12	✓	240	23.20	odd	22	inner
690.2.n.a.89.19	yes	240	345.89	even	22	inner
690.2.n.a.659.12	yes	240	15.14	odd	2	inner
690.2.n.a.659.19	yes	240	1.1	even	1	trivial
690.2.n.b.89.6	yes	240	69.20	even	22
690.2.n.b.89.13	yes	240	115.89	odd	22
690.2.n.b.659.6	yes	240	5.4	even	2
690.2.n.b.659.13	yes	240	3.2	odd	2

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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