LMFDB - Embedded newform 690.2.n.a.659.12

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			659.12
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.0512012 + 1.73129i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.182307 - 2.22862i) q^{5} +(-1.72096 - 0.195709i) q^{6} +(1.96759 + 1.26449i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.99476 + 0.177289i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.0512012 + 1.73129i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.182307 - 2.22862i) q^{5} +(-1.72096 - 0.195709i) q^{6} +(1.96759 + 1.26449i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.99476 + 0.177289i) q^{9} +(2.17999 + 0.497618i) q^{10} +(0.590477 + 4.10685i) q^{11} +(0.438635 - 1.67559i) q^{12} +(-2.60370 - 4.05144i) q^{13} +(-1.53164 + 1.76761i) q^{14} +(3.86774 + 0.201519i) q^{15} +(0.841254 + 0.540641i) q^{16} +(2.07397 + 7.06329i) q^{17} +(0.250714 - 2.98951i) q^{18} +(-1.43678 + 4.89322i) q^{19} +(-0.802799 + 2.08699i) q^{20} +(-2.08847 + 3.47122i) q^{21} -4.14909 q^{22} +(0.585811 + 4.75992i) q^{23} +(1.59611 + 0.672631i) q^{24} +(-4.93353 - 0.812589i) q^{25} +(4.38075 - 2.00062i) q^{26} +(-0.460274 - 5.17573i) q^{27} +(-1.53164 - 1.76761i) q^{28} +(0.892286 + 3.03885i) q^{29} +(-0.749905 + 3.79969i) q^{30} +(0.520682 - 1.14014i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-7.07994 + 1.23256i) q^{33} +(-7.28655 + 1.04765i) q^{34} +(3.17679 - 4.15449i) q^{35} +(2.92340 + 0.673613i) q^{36} +(1.29334 - 1.49260i) q^{37} +(-4.63894 - 2.11853i) q^{38} +(6.88092 - 4.71521i) q^{39} +(-1.95149 - 1.09164i) q^{40} +(-8.22539 + 7.12734i) q^{41} +(-3.13867 - 2.56121i) 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} +(-0.892935 + 1.48414i) q^{48} +(-0.635439 - 1.39142i) q^{49} +(1.50643 - 4.76767i) q^{50} +(-12.1224 + 3.95230i) q^{51} +(1.35681 + 4.62088i) q^{52} +(7.10060 - 11.0487i) q^{53} +(5.18855 + 0.280994i) q^{54} +(9.26028 - 0.567240i) q^{55} +(1.96759 - 1.26449i) q^{56} +(-8.54517 - 2.23695i) q^{57} +(-3.13490 + 0.450731i) q^{58} +(1.99640 + 3.10646i) q^{59} +(-3.65429 - 1.28302i) q^{60} +(-5.51656 - 2.51933i) q^{61} +(1.05443 + 0.677641i) q^{62} +(-6.11663 - 3.43802i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-9.50381 + 5.06407i) q^{65} +(-0.212438 - 7.18329i) q^{66} +(-0.160946 + 1.11941i) q^{67} -7.36148i q^{68} +(-8.21082 + 1.25793i) q^{69} +(3.66010 + 3.73570i) q^{70} +(-0.381400 - 0.0548370i) q^{71} +(-1.08280 + 2.79778i) q^{72} +(4.69578 - 15.9924i) q^{73} +(1.29334 + 1.49260i) q^{74} +(1.15423 - 8.58299i) q^{75} +(2.75716 - 4.29022i) q^{76} +(-4.03127 + 8.82726i) q^{77} +(3.68796 + 7.48193i) q^{78} +(-3.72151 - 5.79078i) q^{79} +(1.35825 - 1.77627i) q^{80} +(8.93714 - 1.06187i) q^{81} +(-5.88420 - 9.15600i) q^{82} +(-12.0367 - 10.4298i) q^{83} +(2.98182 - 2.74222i) q^{84} +(16.1195 - 3.33441i) q^{85} +(-5.95793 + 1.74940i) q^{86} +(-5.21545 + 1.70040i) q^{87} +(3.98102 + 1.16893i) q^{88} +(6.45448 + 14.1333i) q^{89} +(-6.61678 - 1.10376i) q^{90} -11.2639i q^{91} +(0.778942 - 4.73215i) q^{92} +(2.00057 + 0.843078i) q^{93} +(-0.961261 + 6.68572i) q^{94} +(10.6432 + 4.09411i) q^{95} +(-1.34195 - 1.09506i) q^{96} +(5.68611 + 6.56212i) q^{97} +(1.46769 - 0.430952i) q^{98} +(-2.49643 - 12.1943i) 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
$3$	0.0512012	+	1.73129i	0.0295610	+	0.999563i
$3$	0.0512012	+	1.73129i	0.0295610	+	0.999563i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.182307	−	2.22862i	0.0815303	−	0.996671i
$5$	0.182307	−	2.22862i	0.0815303	−	0.996671i
$6$	−1.72096	−	0.195709i	−0.702578	−	0.0798978i
$7$	1.96759	+	1.26449i	0.743679	+	0.477933i	0.856801	−	0.515648i	$-0.172449\pi$
$7$	1.96759	+	1.26449i	0.743679	+	0.477933i	−0.113122	+	0.993581i	$0.536085\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−2.99476	+	0.177289i	−0.998252	+	0.0590962i
$10$	2.17999	+	0.497618i	0.689375	+	0.157361i
$11$	0.590477	+	4.10685i	0.178035	+	1.23826i	0.861302	+	0.508094i	$0.169650\pi$
$11$	0.590477	+	4.10685i	0.178035	+	1.23826i	−0.683266	+	0.730169i	$0.739441\pi$
$12$	0.438635	−	1.67559i	0.126623	−	0.483701i
$13$	−2.60370	−	4.05144i	−0.722137	−	1.12367i	−0.987208	−	0.159438i	$-0.949032\pi$
$13$	−2.60370	−	4.05144i	−0.722137	−	1.12367i	0.265071	−	0.964229i	$-0.414605\pi$
$14$	−1.53164	+	1.76761i	−0.409348	+	0.472413i
$15$	3.86774	+	0.201519i	0.998645	+	0.0520321i
$16$	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	$0.557892\pi$
$18$	0.250714	−	2.98951i	0.0590939	−	0.704633i
$19$	−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	$0.892009\pi$
$20$	−0.802799	+	2.08699i	−0.179511	+	0.466664i
$21$	−2.08847	+	3.47122i	−0.455741	+	0.757482i
$22$	−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
$25$	−4.93353	−	0.812589i	−0.986706	−	0.162518i
$26$	4.38075	−	2.00062i	0.859135	−	0.392354i
$27$	−0.460274	−	5.17573i	−0.0885798	−	0.996069i
$28$	−1.53164	−	1.76761i	−0.289453	−	0.334046i
$29$	0.892286	+	3.03885i	0.165693	+	0.564300i	0.999917	+	0.0128738i	$0.00409797\pi$
$29$	0.892286	+	3.03885i	0.165693	+	0.564300i	−0.834224	+	0.551426i	$0.814084\pi$
$30$	−0.749905	+	3.79969i	−0.136913	+	0.693725i
$31$	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
$33$	−7.07994	+	1.23256i	−1.23246	+	0.214562i
$34$	−7.28655	+	1.04765i	−1.24963	+	0.179670i
$35$	3.17679	−	4.15449i	0.536975	−	0.702237i
$36$	2.92340	+	0.673613i	0.487233	+	0.112269i
$37$	1.29334	−	1.49260i	0.212624	−	0.245381i	−0.639412	−	0.768864i	$-0.720822\pi$
$37$	1.29334	−	1.49260i	0.212624	−	0.245381i	0.852036	+	0.523483i	$0.175368\pi$
$38$	−4.63894	−	2.11853i	−0.752535	−	0.343671i
$39$	6.88092	−	4.71521i	1.10183	−	0.755038i
$40$	−1.95149	−	1.09164i	−0.308558	−	0.172603i
$41$	−8.22539	+	7.12734i	−1.28459	+	1.11310i	−0.297197	+	0.954816i	$0.596052\pi$
$41$	−8.22539	+	7.12734i	−1.28459	+	1.11310i	−0.987393	+	0.158288i	$0.949403\pi$
$42$	−3.13867	−	2.56121i	−0.484307	−	0.395204i
$43$	2.57950	+	5.64832i	0.393370	+	0.861360i	0.997900	+	0.0647776i	$0.0206338\pi$
$43$	2.57950	+	5.64832i	0.393370	+	0.861360i	−0.604530	+	0.796583i	$0.706639\pi$
$44$	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	$0.336039\pi$
$48$	−0.892935	+	1.48414i	−0.128884	+	0.214217i
$49$	−0.635439	−	1.39142i	−0.0907771	−	0.198774i
$50$	1.50643	−	4.76767i	0.213042	−	0.674250i
$51$	−12.1224	+	3.95230i	−1.69748	+	0.553432i
$52$	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	$-0.176101\pi$
$54$	5.18855	+	0.280994i	0.706072	+	0.0382384i
$55$	9.26028	−	0.567240i	1.24866	−	0.0764866i
$56$	1.96759	−	1.26449i	0.262930	−	0.168975i
$57$	−8.54517	−	2.23695i	−1.13184	−	0.296291i
$58$	−3.13490	+	0.450731i	−0.411633	+	0.0591839i
$59$	1.99640	+	3.10646i	0.259909	+	0.404427i	0.946543	−	0.322577i	$-0.104549\pi$
$59$	1.99640	+	3.10646i	0.259909	+	0.404427i	−0.686634	+	0.727003i	$0.740913\pi$
$60$	−3.65429	−	1.28302i	−0.471767	−	0.165638i
$61$	−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
$63$	−6.11663	−	3.43802i	−0.770623	−	0.433149i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−9.50381	+	5.06407i	−1.17880	+	0.628120i
$66$	−0.212438	−	7.18329i	−0.0261493	−	0.884202i
$67$	−0.160946	+	1.11941i	−0.0196627	+	0.136757i	−0.997288	−	0.0735963i	$-0.976552\pi$
$67$	−0.160946	+	1.11941i	−0.0196627	+	0.136757i	0.977625	+	0.210353i	$0.0674615\pi$
$68$		−	7.36148i		−	0.892710i
$69$	−8.21082	+	1.25793i	−0.988467	+	0.151436i
$70$	3.66010	+	3.73570i	0.437466	+	0.446501i
$71$	−0.381400	−	0.0548370i	−0.0452638	−	0.00650796i	0.119646	−	0.992817i	$-0.461824\pi$
$71$	−0.381400	−	0.0548370i	−0.0452638	−	0.00650796i	−0.164910	+	0.986309i	$0.552733\pi$
$72$	−1.08280	+	2.79778i	−0.127609	+	0.329721i
$73$	4.69578	−	15.9924i	0.549599	−	1.87176i	0.0632528	−	0.997998i	$-0.479853\pi$
$73$	4.69578	−	15.9924i	0.549599	−	1.87176i	0.486347	−	0.873766i	$-0.338329\pi$
$74$	1.29334	+	1.49260i	0.150348	+	0.173511i
$75$	1.15423	−	8.58299i	0.133279	−	0.991079i
$76$	2.75716	−	4.29022i	0.316268	−	0.492122i
$77$	−4.03127	+	8.82726i	−0.459406	+	1.00596i
$78$	3.68796	+	7.48193i	0.417579	+	0.847162i
$79$	−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	$0.944749\pi$
$80$	1.35825	−	1.77627i	0.151857	−	0.198594i
$81$	8.93714	−	1.06187i	0.993015	−	0.117986i
$82$	−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	$-0.611273\pi$
$84$	2.98182	−	2.74222i	0.325344	−	0.299201i
$85$	16.1195	−	3.33441i	1.74841	−	0.361667i
$86$	−5.95793	+	1.74940i	−0.642460	+	0.188643i
$87$	−5.21545	+	1.70040i	−0.559155	+	0.182302i
$88$	3.98102	+	1.16893i	0.424378	+	0.124609i
$89$	6.45448	+	14.1333i	0.684174	+	1.49813i	0.858159	+	0.513383i	$0.171608\pi$
$89$	6.45448	+	14.1333i	0.684174	+	1.49813i	−0.173986	+	0.984748i	$0.555665\pi$
$90$	−6.61678	−	1.10376i	−0.697469	−	0.116346i
$91$		−	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
$95$	10.6432	+	4.09411i	1.09197	+	0.420047i
$96$	−1.34195	−	1.09506i	−0.136963	−	0.111764i
$97$	5.68611	+	6.56212i	0.577337	+	0.666283i	0.967030	−	0.254662i	$-0.0819642\pi$
$97$	5.68611	+	6.56212i	0.577337	+	0.666283i	−0.389693	+	0.920945i	$0.627419\pi$
$98$	1.46769	−	0.430952i	0.148259	−	0.0435327i
$99$	−2.49643	−	12.1943i	−0.250901	−	1.22558i
$100$	4.50475	+	2.16961i	0.450475	+	0.216961i
$101$	−2.88426	−	2.49923i	−0.286995	−	0.248683i	0.499450	−	0.866343i	$-0.333535\pi$
$101$	−2.88426	−	2.49923i	−0.286995	−	0.248683i	−0.786445	+	0.617660i	$0.788081\pi$
$102$	−2.18687	−	12.5615i	−0.216532	−	1.24378i
$103$	1.59510	+	11.0942i	0.157170	+	1.09314i	0.903817	+	0.427920i	$0.140754\pi$
$103$	1.59510	+	11.0942i	0.157170	+	1.09314i	−0.746647	+	0.665221i	$0.768337\pi$
$104$	−4.76694	+	0.685382i	−0.467437	+	0.0672072i
$105$	7.35530	+	5.28723i	0.717804	+	0.515981i
$106$	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	$0.456183\pi$
$108$	−1.01654	+	5.09575i	−0.0978167	+	0.490339i
$109$	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	$0.869240\pi$
$110$	−0.756409	+	9.24675i	−0.0721208	+	0.881643i
$111$	2.65034	+	2.16273i	0.251560	+	0.205278i
$112$	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
$115$	10.7149	−	0.437785i	0.999166	−	0.0408236i
$116$		−	3.16714i		−	0.294062i
$117$	8.51573	+	11.6715i	0.787280	+	1.07903i
$118$	−3.35896	+	1.53398i	−0.309217	+	0.141215i
$119$	−4.85076	+	16.5202i	−0.444668	+	1.51440i
$120$	1.79002	−	3.43450i	0.163406	−	0.313526i
$121$	−5.96317	+	1.75094i	−0.542106	+	0.159177i
$122$	3.27877	−	5.10187i	0.296846	−	0.461902i
$123$	−12.7607	−	13.8756i	−1.15059	−	1.25112i
$124$	−0.820804	+	0.947258i	−0.0737104	+	0.0850663i
$125$	−2.71037	+	10.8468i	−0.242423	+	0.970171i
$126$	4.27351	−	5.56509i	0.380715	−	0.495778i
$127$	1.45735	−	0.209535i	0.129319	−	0.0185932i	−0.0773516	−	0.997004i	$-0.524646\pi$
$127$	1.45735	−	0.209535i	0.129319	−	0.0185932i	0.206670	+	0.978411i	$0.433737\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−9.64682	+	4.75507i	−0.849355	+	0.418661i
$130$	−3.65999	−	10.1278i	−0.321002	−	0.888264i
$131$	−1.40959	+	2.19337i	−0.123157	+	0.191635i	−0.897357	−	0.441305i	$-0.854516\pi$
$131$	−1.40959	+	2.19337i	−0.123157	+	0.191635i	0.774201	+	0.632940i	$0.218152\pi$
$132$	7.14040	+	0.812012i	0.621492	+	0.0706766i
$133$	−9.01443	+	7.81105i	−0.781651	+	0.677304i
$134$	−1.08511	−	0.318616i	−0.0937389	−	0.0275242i
$135$	−11.6187	+	0.0822044i	−0.999975	+	0.00707503i
$136$	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	$0.875280\pi$
$138$	−0.0765994	−	8.30627i	−0.00652058	−	0.707077i
$139$	−1.72575			−0.146376			−0.0731880	−	0.997318i	$-0.523317\pi$
$139$	−1.72575			−0.146376			−0.0731880	+	0.997318i	$0.523317\pi$
$140$	−4.21856	+	3.09120i	−0.356533	+	0.261254i
$141$	0.345837	+	11.6940i	0.0291247	+	0.984810i
$142$	0.108558	−	0.369714i	0.00910996	−	0.0310257i
$143$	15.1012	−	13.0853i	1.26283	−	1.09425i
$144$	−2.61520	−	1.46994i	−0.217933	−	0.122495i
$145$	6.93512	−	1.43457i	0.575930	−	0.119134i
$146$	15.1613	+	6.92393i	1.25476	+	0.573029i
$147$	2.37642	−	1.17137i	0.196004	−	0.0966134i
$148$	−1.66147	+	1.06776i	−0.136572	+	0.0877693i
$149$	−2.78753	−	19.3877i	−0.228363	−	1.58830i	−0.705003	−	0.709204i	$-0.749054\pi$
$149$	−2.78753	−	19.3877i	−0.228363	−	1.58830i	0.476640	−	0.879099i	$-0.341855\pi$
$150$	8.33137	+	2.36397i	0.680253	+	0.193017i
$151$	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
$153$	−7.46327	−	20.7851i	−0.603370	−	1.68038i
$154$	−8.16370	−	5.24649i	−0.657850	−	0.422774i
$155$	−2.44601	−	1.36826i	−0.196468	−	0.109901i
$156$	−7.93062	+	2.58563i	−0.634958	+	0.207016i
$157$	21.4105	+	6.28669i	1.70874	+	0.501732i	0.982588	−	0.185798i	$-0.0594871\pi$
$157$	21.4105	+	6.28669i	1.70874	+	0.501732i	0.726155	+	0.687531i	$0.241305\pi$
$158$	6.26146	−	2.85951i	0.498135	−	0.227491i
$159$	19.4922	+	11.7275i	1.54583	+	0.930053i
$160$	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	$-0.467459\pi$
$163$	−1.02510	−	0.147387i	−0.0802918	−	0.0115442i	−0.182344	+	0.983235i	$0.558368\pi$
$164$	9.90021	−	4.52127i	0.773077	−	0.353052i
$165$	1.45620	+	16.0032i	0.113365	+	1.24585i
$166$	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	$0.491774\pi$
$168$	2.28995	+	3.34173i	0.176674	+	0.257820i
$169$	−4.23451	+	9.27227i	−0.325731	+	0.713252i
$170$	1.00642	+	16.4300i	0.0771889	+	1.26012i
$171$	3.43529	−	14.9087i	0.262703	−	1.14010i
$172$	−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	$0.999311\pi$
$174$	−0.940859	−	5.40436i	−0.0713263	−	0.409703i
$175$	−8.67964	−	7.83725i	−0.656119	−	0.592441i
$176$	−1.72359	+	3.77414i	−0.129921	+	0.284487i
$177$	−5.27598	+	3.61541i	−0.396567	+	0.271751i
$178$	−14.9081	+	4.37740i	−1.11741	+	0.328100i
$179$	12.0244	−	10.4192i	0.898750	−	0.778771i	−0.0771436	−	0.997020i	$-0.524580\pi$
$179$	12.0244	−	10.4192i	0.898750	−	0.778771i	0.975893	+	0.218249i	$0.0700345\pi$
$180$	2.03419	−	6.39235i	0.151619	−	0.476457i
$181$	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
$186$	−1.11921	+	1.86022i	−0.0820642	+	0.136398i
$187$	−27.7833	+	12.6882i	−2.03171	+	0.927852i
$188$	−6.48086	−	1.90295i	−0.472666	−	0.138787i
$189$	5.63904	−	10.7657i	0.410180	−	0.783091i
$190$	−5.56713	+	9.95223i	−0.403882	+	0.722010i
$191$	−9.29975	−	5.97659i	−0.672906	−	0.432451i	0.159066	−	0.987268i	$-0.449152\pi$
$191$	−9.29975	−	5.97659i	−0.672906	−	0.432451i	−0.831972	+	0.554817i	$0.812788\pi$
$192$	1.27489	−	1.17245i	0.0920076	−	0.0846144i
$193$	3.75659	+	3.25511i	0.270406	+	0.234308i	0.779499	−	0.626404i	$-0.215474\pi$
$193$	3.75659	+	3.25511i	0.270406	+	0.234308i	−0.509093	+	0.860711i	$0.670019\pi$
$194$	−7.30455	+	4.69435i	−0.524436	+	0.337035i
$195$	−9.25399	−	16.1946i	−0.662692	−	1.15972i
$196$	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	$0.0827294\pi$
$198$	12.4255	−	0.735586i	0.883042	−	0.0522758i
$199$	−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	$0.672299\pi$
$200$	−2.78862	+	4.15013i	−0.197185	+	0.293459i
$201$	−1.94626	−	0.221330i	−0.137279	−	0.0156114i
$202$	2.88426	−	2.49923i	0.202936	−	0.175845i
$203$	−2.08695	+	7.10750i	−0.146475	+	0.498848i
$204$	12.7449	−	0.376917i	0.892320	−	0.0263894i
$205$	14.3846	+	19.6307i	1.00467	+	1.37107i
$206$	−11.2083			−0.780916
$207$	−2.59824	−	14.1509i	−0.180590	−	0.983558i
$208$		−	4.81596i		−	0.333926i
$209$	−20.9441	−	3.01131i	−1.44874	−	0.208297i
$210$	−6.28019	+	6.52798i	−0.433374	+	0.450473i
$211$	−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
$213$	0.0754109	−	0.663123i	0.00516707	−	0.0454364i
$214$	−5.99851	+	9.33386i	−0.410049	+	0.638049i
$215$	13.0582	−	4.71900i	0.890564	−	0.321833i
$216$	−4.89921	−	1.73139i	−0.333349	−	0.117806i
$217$	2.46618	−	1.58492i	0.167415	−	0.107591i
$218$	−2.58082	+	0.371066i	−0.174795	+	0.0251317i
$219$	27.9279	+	7.31095i	1.88719	+	0.494028i
$220$	−9.04499	−	2.06466i	−0.609813	−	0.139199i
$221$	23.2165	−	26.7933i	1.56171	−	1.80231i
$222$	−2.51790	+	2.31558i	−0.168991	+	0.155411i
$223$	−1.38258	+	2.15134i	−0.0925847	+	0.144065i	−0.884456	−	0.466623i	$-0.845471\pi$
$223$	−1.38258	+	2.15134i	−0.0925847	+	0.144065i	0.791872	+	0.610688i	$0.209107\pi$
$224$	−2.24414	+	0.658938i	−0.149943	+	0.0440272i
$225$	14.9188	+	1.55885i	0.994585	+	0.103923i
$226$	−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	$0.328662\pi$
$228$	7.56881	+	4.55379i	0.501256	+	0.301582i
$229$		−	13.0423i		−	0.861861i	−0.902385	−	0.430930i	$-0.858185\pi$
$229$		−	13.0423i		−	0.861861i	0.902385	−	0.430930i	$-0.141815\pi$
$230$	−1.09156	+	10.6681i	−0.0719750	+	0.703434i
$231$	−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	$0.864069\pi$
$234$	−12.7646	+	6.76803i	−0.834447	+	0.442440i
$235$	1.23139	−	15.0532i	0.0803270	−	0.981960i
$236$	−1.04034	−	3.54308i	−0.0677204	−	0.230635i
$237$	9.83499	−	6.73952i	0.638851	−	0.437779i
$238$	−15.6617	−	7.15245i	−1.01520	−	0.463624i
$239$	−17.2040	−	14.9073i	−1.11283	−	0.964275i	−0.113262	−	0.993565i	$-0.536130\pi$
$239$	−17.2040	−	14.9073i	−1.11283	−	0.964275i	−0.999571	+	0.0292902i	$0.990675\pi$
$240$	3.14480	+	2.26059i	0.202996	+	0.145920i
$241$	−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
$243$	2.29601	+	15.4184i	0.147289	+	0.989094i
$244$	4.58333	+	3.97147i	0.293417	+	0.254248i
$245$	−3.21679	+	1.16249i	−0.205513	+	0.0742687i
$246$	15.5504	−	10.6561i	0.991460	−	0.679407i
$247$	23.5655	−	6.91947i	1.49944	−	0.440275i
$248$	−0.820804	−	0.947258i	−0.0521211	−	0.0601510i
$249$	17.4408	−	21.3730i	1.10527	−	1.35446i
$250$	−10.3507	−	4.22645i	−0.654636	−	0.267304i
$251$	−0.707153	+	4.91836i	−0.0446351	+	0.310444i	0.955257	+	0.295776i	$0.0955782\pi$
$251$	−0.707153	+	4.91836i	−0.0446351	+	0.310444i	−0.999892	+	0.0146680i	$0.995331\pi$
$252$	4.90026	+	5.02201i	0.308688	+	0.316357i
$253$	−19.2024	+	5.21646i	−1.20724	+	0.327956i
$254$			1.47233i			0.0923823i
$255$	6.59817	+	27.7369i	0.413194	+	1.73695i
$256$	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	$0.866794\pi$
$258$	−3.33379	−	10.2253i	−0.207553	−	0.636602i
$259$	4.43214	−	1.30140i	0.275400	−	0.0808648i
$260$	10.5456	−	2.18140i	0.654007	−	0.135285i
$261$	−3.21093	−	8.94242i	−0.198752	−	0.553522i
$262$	−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	$-0.381994\pi$
$264$	−1.81993	+	6.95216i	−0.112009	+	0.427876i
$265$	−23.3290	−	17.8388i	−1.43309	−	1.09583i
$266$	−6.44866	−	10.0343i	−0.395393	−	0.615243i
$267$	−24.1385	+	11.8982i	−1.47725	+	0.728161i
$268$	0.469800	−	1.02872i	0.0286976	−	0.0628389i
$269$	−4.99311	+	7.76944i	−0.304436	+	0.473711i	−0.959440	−	0.281914i	$-0.909031\pi$
$269$	−4.99311	+	7.76944i	−0.304436	+	0.473711i	0.655004	+	0.755625i	$0.272667\pi$
$270$	1.57214	−	11.5121i	0.0956774	−	0.700604i
$271$	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
$273$	19.5012	−	0.576727i	1.18027	−	0.0349051i
$274$	−8.84838	−	1.27221i	−0.534550	−	0.0768568i
$275$	0.424053	−	20.7411i	0.0255714	−	1.25074i
$276$	8.23263	+	1.10629i	0.495546	+	0.0665906i
$277$		−	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
$279$	−1.35718	+	3.50674i	−0.0812525	+	0.209943i
$280$	−2.45937	−	4.61554i	−0.146976	−	0.275831i
$281$	7.87946	+	9.09338i	0.470049	+	0.542466i	0.940425	−	0.340000i	$-0.110427\pi$
$281$	7.87946	+	9.09338i	0.470049	+	0.542466i	−0.470376	+	0.882466i	$0.655882\pi$
$282$	−11.6242	−	1.32191i	−0.692209	−	0.0787185i
$283$	14.1573	+	9.09834i	0.841564	+	0.540840i	0.888933	−	0.458037i	$-0.151447\pi$
$283$	14.1573	+	9.09834i	0.841564	+	0.540840i	−0.0473690	+	0.998877i	$0.515084\pi$
$284$	0.350501	+	0.160068i	0.0207984	+	0.00949832i
$285$	−6.54316	+	18.6362i	−0.387584	+	1.10391i
$286$	10.8030	+	16.8098i	0.638794	+	0.993983i
$287$	−25.1967	+	3.62273i	−1.48731	+	0.213843i
$288$	1.82716	−	2.37939i	0.107667	−	0.140207i
$289$	−31.2874	+	20.1072i	−1.84043	+	1.18277i
$290$	0.432994	+	7.06869i	0.0254263	+	0.415088i
$291$	−11.0698	+	10.1803i	−0.648925	+	0.596781i
$292$	−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	$0.835928\pi$
$294$	0.821252	+	2.51893i	0.0478964	+	0.146907i
$295$	7.28709	−	3.88289i	0.424271	−	0.226071i
$296$	−0.820440	−	1.79651i	−0.0476871	−	0.104420i
$297$	20.9842	−	4.94642i	1.21763	−	0.287021i
$298$	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
$303$	4.17922	−	5.12147i	0.240090	−	0.294221i
$304$	−3.85417	+	3.33966i	−0.221052	+	0.191542i
$305$	−6.62035	+	11.8350i	−0.379080	+	0.677673i
$306$	21.6357	−	4.42927i	1.23683	−	0.253205i
$307$	−12.9762	−	5.92604i	−0.740592	−	0.338217i	0.00914055	−	0.999958i	$-0.497090\pi$
$307$	−12.9762	−	5.92604i	−0.740592	−	0.338217i	−0.749732	+	0.661741i	$0.769818\pi$
$308$	6.35490	−	7.33395i	0.362104	−	0.417891i
$309$	−19.1256	+	3.32962i	−1.08802	+	0.189416i
$310$	1.70244	−	2.22639i	0.0966919	−	0.126450i
$311$	11.3575	−	1.63297i	0.644026	−	0.0925970i	0.187440	−	0.982276i	$-0.439981\pi$
$311$	11.3575	−	1.63297i	0.644026	−	0.0925970i	0.456586	+	0.889679i	$0.349072\pi$
$312$	−1.43067	−	8.21788i	−0.0809958	−	0.465246i
$313$	6.95776	−	8.02969i	0.393276	−	0.453865i	−0.524236	−	0.851573i	$-0.675649\pi$
$313$	6.95776	−	8.02969i	0.393276	−	0.453865i	0.917512	+	0.397708i	$0.130194\pi$
$314$	−9.26973	+	20.2979i	−0.523121	+	1.14548i
$315$	−8.77715	+	13.0049i	−0.494537	+	0.732743i
$316$	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	$0.560130\pi$
$318$	−14.3822	+	17.6248i	−0.806512	+	0.988349i
$319$	−11.9532	+	5.45886i	−0.669253	+	0.305637i
$320$	−1.80367	+	1.32166i	−0.100828	+	0.0738830i
$321$	−7.46296	+	17.7091i	−0.416542	+	0.988427i
$322$	−9.31091	−	6.25499i	−0.518877	−	0.348577i
$323$	−37.5421			−2.08890
$324$	−8.87428	−	1.49902i	−0.493016	−	0.0832790i
$325$	9.55328	+	22.1036i	0.529921	+	1.22609i
$326$	0.291773	−	0.993687i	0.0161598	−	0.0550353i
$327$	−4.29364	+	1.39986i	−0.237439	+	0.0774125i
$328$	3.06631	+	10.4429i	0.169309	+	0.576612i
$329$	13.2900	+	8.54098i	0.732702	+	0.470879i
$330$	−16.0476	−	0.836121i	−0.883390	−	0.0460270i
$331$	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
$333$	−3.60863	+	4.69926i	−0.197751	+	0.257518i
$334$	−0.944738	−	6.57080i	−0.0516938	−	0.359538i
$335$	2.46539	+	0.562764i	0.134699	+	0.0307471i
$336$	−3.63361	+	1.79107i	−0.198230	+	0.0977106i
$337$	2.17083	−	4.75346i	0.118253	−	0.258938i	−0.841245	−	0.540655i	$-0.818177\pi$
$337$	2.17083	−	4.75346i	0.118253	−	0.258938i	0.959498	+	0.281717i	$0.0909039\pi$
$338$	−8.57526	−	5.51099i	−0.466433	−	0.299758i
$339$	−1.71389	+	15.0710i	−0.0930858	+	0.818547i
$340$	−16.4060	−	1.34205i	−0.889738	−	0.0727830i
$341$	4.98982	+	1.46514i	0.270214	+	0.0793419i
$342$	14.2681	+	5.52206i	0.771530	+	0.298599i
$343$	2.83915	−	19.7467i	0.153300	−	1.06622i
$344$	6.20945			0.334791
$345$	1.30655	+	18.5282i	0.0703422	+	0.997523i
$346$	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	$0.953680\pi$
$348$	5.48325	−	0.162161i	0.293933	−	0.00869276i
$349$	−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	$0.646805\pi$
$350$	8.99272	−	7.47594i	0.480681	−	0.399606i
$351$	−19.7707	+	15.3408i	−1.05528	+	0.818833i
$352$	−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	$0.0470593\pi$
$354$	−2.82776	−	5.73680i	−0.150294	−	0.304907i
$355$	−0.191743	+	0.840000i	−0.0101767	+	0.0445825i
$356$	−2.21121	−	15.3793i	−0.117194	−	0.815100i
$357$	−28.8496	−	7.55224i	−1.52688	−	0.399707i
$358$	8.60193	+	13.3849i	0.454626	+	0.707412i
$359$	15.6130	−	18.0183i	0.824021	−	0.950971i	−0.175417	−	0.984494i	$-0.556127\pi$
$359$	15.6130	−	18.0183i	0.824021	−	0.950971i	0.999438	+	0.0335237i	$0.0106729\pi$
$360$	6.03779	+	2.92321i	0.318219	+	0.154067i
$361$	−5.89545	−	3.78878i	−0.310287	−	0.199409i
$362$	2.05254	+	6.99031i	0.107879	+	0.367402i
$363$	−3.33672	−	10.2343i	−0.175132	−	0.537164i
$364$	−3.17342	+	10.8077i	−0.166332	+	0.566476i
$365$	−34.7849	−	13.3806i	−1.82072	−	0.700375i
$366$	9.00072	+	5.41530i	0.470475	+	0.283062i
$367$	−11.9447			−0.623508			−0.311754	−	0.950163i	$-0.600917\pi$
$367$	−11.9447			−0.623508			−0.311754	+	0.950163i	$0.600917\pi$
$368$	−2.08059	+	4.32101i	−0.108458	+	0.225248i
$369$	23.3695	−	22.8029i	1.21657	−	1.18707i
$370$	3.56222	−	2.61026i	0.185191	−	0.135701i
$371$	27.9421	−	12.7607i	1.45068	−	0.662505i
$372$	−1.68201	−	1.37255i	−0.0872081	−	0.0711635i
$373$	−3.67482	−	4.24097i	−0.190275	−	0.219589i	0.652594	−	0.757708i	$-0.273681\pi$
$373$	−3.67482	−	4.24097i	−0.190275	−	0.219589i	−0.842869	+	0.538119i	$0.819135\pi$
$374$	−8.60507	−	29.3062i	−0.444958	−	1.51539i
$375$	−18.9178	−	4.13708i	−0.976913	−	0.213638i
$376$	2.80591	−	6.14408i	0.144704	−	0.316857i
$377$	9.98846	−	11.5273i	0.514432	−	0.593686i
$378$	9.85362	+	7.11376i	0.506816	+	0.365893i
$379$	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	$0.145994\pi$
$380$	−9.05864	−	6.92681i	−0.464699	−	0.355338i
$381$	0.437384	+	2.51237i	0.0224079	+	0.128712i
$382$	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	$0.425534\pi$
$384$	0.979081	+	1.42878i	0.0499635	+	0.0729119i
$385$	18.9377	+	10.5935i	0.965155	+	0.539893i
$386$	−3.75659	+	3.25511i	−0.191206	+	0.165681i
$387$	−8.72636	−	16.4580i	−0.443586	−	0.836608i
$388$	−3.60702	−	7.89828i	−0.183119	−	0.400974i
$389$	1.32775	−	9.23471i	0.0673196	−	0.468218i	−0.928078	−	0.372386i	$-0.878540\pi$
$389$	1.32775	−	9.23471i	0.0673196	−	0.468218i	0.995398	−	0.0958322i	$-0.0305512\pi$
$390$	17.3467	−	6.85507i	0.878387	−	0.347120i
$391$	−32.4057	+	14.0097i	−1.63883	+	0.708500i
$392$	−1.52965			−0.0772590
$393$	−3.86954	−	2.32811i	−0.195192	−	0.117438i
$394$	7.86042	+	17.2119i	0.396002	+	0.867124i
$395$	−13.5839	+	7.23814i	−0.683481	+	0.364190i
$396$	−1.04023	+	12.4037i	−0.0522738	+	0.623310i
$397$	−5.07738	−	17.2920i	−0.254826	−	0.867859i	−0.983177	−	0.182655i	$-0.941531\pi$
$397$	−5.07738	−	17.2920i	−0.254826	−	0.867859i	0.728351	−	0.685204i	$-0.240287\pi$
$398$	1.71838	−	2.67386i	0.0861347	−	0.134028i
$399$	−13.9848	−	15.2067i	−0.700114	−	0.761287i
$400$	−3.71103	−	3.35086i	−0.185551	−	0.167543i
$401$	−17.3106	+	11.1248i	−0.864449	+	0.555548i	−0.896050	−	0.443953i	$-0.853576\pi$
$401$	−17.3106	+	11.1248i	−0.864449	+	0.555548i	0.0316008	+	0.999501i	$0.489939\pi$
$402$	0.496059	−	1.89495i	0.0247412	−	0.0945116i
$403$	−5.97489	+	0.859060i	−0.297630	+	0.0427928i
$404$	2.06332	+	3.21058i	0.102654	+	0.159732i
$405$	−0.737210	−	20.1111i	−0.0366322	−	0.999329i
$406$	−6.73815	−	3.07721i	−0.334409	−	0.152719i
$407$	6.89357	+	4.43023i	0.341701	+	0.219598i
$408$	−1.44071	+	12.6688i	−0.0713256	+	0.627199i
$409$	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	$0.743651\pi$
$410$	−21.4780	+	11.4445i	−1.06072	+	0.565202i
$411$	−15.4767	+	0.457707i	−0.763409	+	0.0225770i
$412$	1.59510	−	11.0942i	0.0785850	−	0.546571i
$413$			8.63667i			0.424983i
$414$	14.3767	−	0.557907i	0.706575	−	0.0274196i
$415$	−25.4385	+	24.9238i	−1.24873	+	1.22346i
$416$	4.76694	+	0.685382i	0.233718	+	0.0336036i
$417$	−0.0883604	−	2.98778i	−0.00432703	−	0.146312i
$418$	5.96132	−	20.3024i	0.291578	−	0.993022i
$419$	14.6560	+	16.9140i	0.715994	+	0.826301i	0.990819	−	0.135193i	$-0.0431656\pi$
$419$	14.6560	+	16.9140i	0.715994	+	0.826301i	−0.274826	+	0.961494i	$0.588620\pi$
$420$	−5.56777	−	7.14529i	−0.271679	−	0.348654i
$421$	−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
$423$	−20.2280	+	1.19749i	−0.983519	+	0.0582240i
$424$	−7.10060	−	11.0487i	−0.344836	−	0.536575i
$425$	−4.49243	−	36.5322i	−0.217915	−	1.77207i
$426$	0.645641	+	0.169016i	0.0312814	+	0.00818883i
$427$	−7.66865	−	11.9327i	−0.371112	−	0.577462i
$428$	−8.38518	−	7.26580i	−0.405313	−	0.351206i
$429$	23.4277	+	25.4747i	1.13110	+	1.22993i
$430$	2.81259	+	13.5969i	0.135635	+	0.655701i
$431$	−17.7323	+	5.20668i	−0.854136	+	0.250797i	−0.679354	−	0.733810i	$-0.737740\pi$
$431$	−17.7323	+	5.20668i	−0.854136	+	0.250797i	−0.174781	+	0.984607i	$0.555922\pi$
$432$	2.41100	−	4.60294i	0.115999	−	0.221459i
$433$	−20.6839	−	6.07334i	−0.994004	−	0.291866i	−0.256011	−	0.966674i	$-0.582408\pi$
$433$	−20.6839	−	6.07334i	−0.994004	−	0.291866i	−0.737993	+	0.674808i	$0.764226\pi$
$434$	1.21781	+	2.66664i	0.0584569	+	0.128003i
$435$	2.83874	+	11.9333i	0.136107	+	0.572157i
$436$		−	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	$0.970025\pi$
$440$	3.33088	−	8.65909i	0.158793	−	0.412806i
$441$	2.14967	+	4.05430i	0.102365	+	0.193062i
$442$	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	$0.560567\pi$
$444$	−1.93367	−	2.82182i	−0.0917681	−	0.133917i
$445$	32.6746	−	11.8080i	1.54892	−	0.559753i
$446$	−1.93268	−	1.67468i	−0.0915152	−	0.0792984i
$447$	33.4231	−	5.81871i	1.58086	−	0.275216i
$448$	−0.332857	−	2.31507i	−0.0157260	−	0.109377i
$449$	36.4667	−	5.24312i	1.72097	−	0.247438i	0.790150	−	0.612914i	$-0.210003\pi$
$449$	36.4667	−	5.24312i	1.72097	−	0.247438i	0.930821	+	0.365476i	$0.119094\pi$
$450$	−3.66615	+	14.5451i	−0.172824	+	0.685662i
$451$	−34.1279	−	29.5720i	−1.60702	−	1.39249i
$452$	−7.96597	−	3.63794i	−0.374688	−	0.171114i
$453$	11.8499	+	17.2926i	0.556757	+	0.812477i
$454$	0.930900	+	3.17036i	0.0436893	+	0.148792i
$455$	−25.1031	−	2.05350i	−1.17685	−	0.0962695i
$456$	−5.58459	+	6.84370i	−0.261522	+	0.320485i
$457$	2.34541	+	5.13574i	0.109714	+	0.240240i	0.956523	−	0.291657i	$-0.0942067\pi$
$457$	2.34541	+	5.13574i	0.109714	+	0.240240i	−0.846809	+	0.531897i	$0.821479\pi$
$458$	12.9096	+	1.85612i	0.603224	+	0.0867306i
$459$	35.6030	−	13.9853i	1.66181	−	0.652780i
$460$	−10.4042	−	2.59868i	−0.485097	−	0.121164i
$461$			15.4684i			0.720434i	0.932869	+	0.360217i	$0.117297\pi$
$461$			15.4684i			0.720434i	−0.932869	+	0.360217i	$0.882703\pi$
$462$	8.66522	−	14.4024i	0.403143	−	0.670060i
$463$	−17.5125	+	7.99767i	−0.813873	+	0.371683i	−0.778464	−	0.627690i	$-0.784001\pi$
$463$	−17.5125	+	7.99767i	−0.813873	+	0.371683i	−0.0354090	+	0.999373i	$0.511273\pi$
$464$	−0.892286	+	3.03885i	−0.0414234	+	0.141075i
$465$	2.24362	−	4.30481i	0.104045	−	0.199631i
$466$	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	$0.121330\pi$
$468$	−4.88255	−	13.5979i	−0.225696	−	0.628561i
$469$	−1.73216	+	1.99901i	−0.0799835	+	0.0923059i
$470$	14.7247	+	3.36114i	0.679200	+	0.155038i
$471$	−9.78786	+	37.3897i	−0.451001	+	1.72283i
$472$	3.65507	−	0.525520i	0.168238	−	0.0241890i
$473$	−21.6737	+	13.9288i	−0.996557	+	0.640448i
$474$	5.27125	+	10.6940i	0.242117	+	0.491193i
$475$	11.0646	−	22.9733i	0.507677	−	1.05409i
$476$	9.30854	−	14.4844i	0.426656	−	0.663890i
$477$	−19.3058	+	34.3472i	−0.883950	+	1.57265i
$478$	17.2040	−	14.9073i	0.786892	−	0.681845i
$479$	−32.5854	−	9.56793i	−1.48886	−	0.437170i	−0.566686	−	0.823934i	$-0.691775\pi$
$479$	−32.5854	−	9.56793i	−1.48886	−	0.437170i	−0.922179	+	0.386764i	$0.873593\pi$
$480$	−2.68513	+	2.79107i	−0.122559	+	0.127394i
$481$	−9.41465	−	1.35362i	−0.429271	−	0.0617198i
$482$		−	0.854717i		−	0.0389313i
$483$	−17.7462	−	7.90745i	−0.807479	−	0.359801i
$484$	6.21492			0.282496
$485$	15.6611	−	11.4759i	0.711135	−	0.521093i
$486$	−15.5883	+	0.0783637i	−0.707098	+	0.00355465i
$487$	−4.71268	+	16.0499i	−0.213552	+	0.727291i	0.781137	+	0.624360i	$0.214640\pi$
$487$	−4.71268	+	16.0499i	−0.213552	+	0.727291i	−0.994689	+	0.102931i	$0.967178\pi$
$488$	−4.58333	+	3.97147i	−0.207477	+	0.179780i
$489$	0.202683	−	1.78229i	0.00916566	−	0.0805979i
$490$	−0.692860	−	3.34949i	−0.0313002	−	0.151315i
$491$	29.8520	+	13.6330i	1.34720	+	0.615247i	0.952774	−	0.303680i	$-0.0982152\pi$
$491$	29.8520	+	13.6330i	1.34720	+	0.615247i	0.394429	+	0.918927i	$0.370942\pi$
$492$	8.33456	+	16.9087i	0.375751	+	0.762302i
$493$	−19.6137	+	12.6049i	−0.883356	+	0.567698i
$494$	3.49531	+	24.3104i	0.157261	+	1.09378i
$495$	−27.6317	+	3.34049i	−1.24195	+	0.150144i
$496$	1.05443	−	0.677641i	0.0473453	−	0.0304270i
$497$	−0.681097	−	0.590174i	−0.0305514	−	0.0264729i
$498$	18.6734	+	20.3050i	0.836775	+	0.909888i
$499$	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	$0.604227\pi$
$500$	5.65649	−	9.64386i	0.252966	−	0.431287i
$501$	−3.56407	−	10.9317i	−0.159231	−	0.488391i
$502$	−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	$0.415596\pi$
$504$	−5.66827	+	4.13568i	−0.252485	+	0.184218i
$505$	−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	$-0.920127\pi$
$509$	−31.9324	+	14.5830i	−1.41538	+	0.646381i	−0.446696	+	0.894686i	$0.647399\pi$
$510$	−28.3936	+	2.58364i	−1.25729	+	0.114406i
$511$	29.4616	−	25.5286i	1.30330	−	1.12932i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	25.9873	+	5.18415i	1.14737	+	0.228886i
$514$	10.1520	−	22.2298i	0.447786	−	0.980516i
$515$	25.0155	−	1.53233i	1.10232	−	0.0675225i
$516$	10.5957	−	1.84463i	0.466450	−	0.0812055i
$517$	3.98835	+	27.7396i	0.175408	+	1.21999i
$518$	0.657389	+	4.57224i	0.0288840	+	0.200893i
$519$	6.29199	−	1.09539i	0.276188	−	0.0480822i
$520$	0.658411	+	10.7487i	0.0288732	+	0.471360i
$521$	−12.7175	+	27.8474i	−0.557162	+	1.22001i	0.396194	+	0.918167i	$0.370331\pi$
$521$	−12.7175	+	27.8474i	−0.557162	+	1.22001i	−0.953356	+	0.301848i	$0.902396\pi$
$522$	9.30836	−	1.90561i	0.407416	−	0.0834064i
$523$	20.3869	−	5.98613i	0.891456	−	0.261755i	0.196240	−	0.980556i	$-0.437127\pi$
$523$	20.3869	−	5.98613i	0.891456	−	0.261755i	0.695216	+	0.718801i	$0.255309\pi$
$524$	1.97044	−	1.70739i	0.0860789	−	0.0745878i
$525$	13.1242	−	15.4283i	0.572786	−	0.673346i
$526$	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
$531$	−6.52947	−	8.94915i	−0.283355	−	0.388360i
$532$	10.8499	−	4.95499i	0.470403	−	0.214826i
$533$	50.2925	+	14.7672i	2.17841	+	0.639639i
$534$	−8.34188	−	25.5861i	−0.360988	−	1.10722i
$535$	12.1119	−	21.6522i	0.523643	−	0.936105i
$536$	0.951387	+	0.611420i	0.0410937	+	0.0264093i
$537$	18.6544	+	20.2844i	0.804999	+	0.875335i
$538$	−6.97976	−	6.04800i	−0.300919	−	0.260748i
$539$	5.33914	−	3.43126i	0.229973	−	0.147795i
$540$	11.1712	+	3.19448i	0.480731	+	0.137469i
$541$	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
$543$	5.57902	+	11.3184i	0.239419	+	0.485719i
$544$	−6.69624	−	3.05807i	−0.287099	−	0.131114i
$545$	5.70936	−	1.18101i	0.244562	−	0.0505889i
$546$	−2.20445	+	19.3848i	−0.0943418	+	0.829591i
$547$	13.7006	−	11.8717i	0.585797	−	0.507596i	−0.310781	−	0.950482i	$-0.600591\pi$
$547$	13.7006	−	11.8717i	0.585797	−	0.507596i	0.896578	+	0.442885i	$0.146045\pi$
$548$	2.51851	−	8.57727i	0.107586	−	0.366403i
$549$	16.9674	+	6.56675i	0.724151	+	0.280262i
$550$	20.4696	+	3.37150i	0.872828	+	0.143761i
$551$	−16.1518			−0.688089
$552$	−2.26665	+	7.99139i	−0.0964750	+	0.340136i
$553$		−	16.0997i		−	0.684629i
$554$	17.9665	+	2.58319i	0.763323	+	0.109749i
$555$	5.30310	−	5.51234i	0.225104	−	0.233986i
$556$	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	$0.0652968\pi$
$558$	−3.27790	−	1.84243i	−0.138764	−	0.0779963i
$559$	16.1676	−	25.1572i	0.683815	−	1.06404i
$560$	4.91857	−	1.77748i	0.207847	−	0.0751122i
$561$	−23.3895	−	47.4513i	−0.987506	−	2.00340i
$562$	−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	$0.501880\pi$
$564$	2.96274	−	11.3177i	0.124754	−	0.476562i
$565$	4.35782	−	19.0910i	0.183335	−	0.803164i
$566$	−11.0205	+	12.7184i	−0.463227	+	0.534593i
$567$	18.9273	+	9.21162i	0.794874	+	0.386852i
$568$	−0.208321	+	0.324153i	−0.00874094	+	0.0136012i
$569$	−9.35550	+	2.74702i	−0.392203	+	0.115161i	−0.471887	−	0.881659i	$-0.656427\pi$
$569$	−9.35550	+	2.74702i	−0.392203	+	0.115161i	0.0796842	+	0.996820i	$0.474609\pi$
$570$	−17.5153	−	9.12876i	−0.733634	−	0.382362i
$571$	−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
$573$	9.87107	−	16.4066i	0.412370	−	0.685396i
$574$		−	25.4558i		−	1.06250i
$575$	0.977742	−	23.9592i	0.0407746	−	0.999168i
$576$	2.09513	+	2.14719i	0.0872973	+	0.0894661i
$577$	24.8903	+	3.57868i	1.03620	+	0.148982i	0.639360	−	0.768907i	$-0.279199\pi$
$577$	24.8903	+	3.57868i	1.03620	+	0.148982i	0.396836	+	0.917890i	$0.370108\pi$
$578$	−15.4499	−	33.8305i	−0.642629	−	1.40716i
$579$	−5.44320	+	6.67043i	−0.226212	+	0.277214i
$580$	−7.05836	−	0.577393i	−0.293083	−	0.0239749i
$581$	−10.4948	−	35.7419i	−0.435397	−	1.48282i
$582$	−8.50130	−	12.4060i	−0.352390	−	0.514244i
$583$	49.5683	+	22.6371i	2.05291	+	0.937533i
$584$	−12.5965	−	10.9149i	−0.521245	−	0.451662i
$585$	27.5638	−	16.8506i	1.13962	−	0.696685i
$586$	−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	$-0.410733\pi$
$588$	−2.61017	+	0.454411i	−0.107642	+	0.0187396i
$589$	4.83083	+	4.18594i	0.199051	+	0.172478i
$590$	2.80631	+	7.76551i	0.115534	+	0.319701i
$591$	18.5260	+	27.0351i	0.762059	+	1.11207i
$592$	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	$0.603947\pi$
$594$	1.90972	+	21.4745i	0.0783566	+	0.881111i
$595$	35.9329	+	13.8223i	1.47311	+	0.566658i
$596$	−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	$0.963123\pi$
$600$	−7.32788	−	4.61543i	−0.299159	−	0.188424i
$601$	−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
$603$	0.283537	−	3.38088i	0.0115465	−	0.137680i
$604$	−11.6128	+	3.40983i	−0.472519	+	0.138744i
$605$	2.81507	+	13.6089i	0.114449	+	0.553279i
$606$	4.47458	+	4.86554i	0.181767	+	0.197649i
$607$	24.4841	+	21.2156i	0.993779	+	0.861114i	0.990309	−	0.138880i	$-0.0443502\pi$
$607$	24.4841	+	21.2156i	0.993779	+	0.861114i	0.00346955	+	0.999994i	$0.498896\pi$
$608$	−2.75716	−	4.29022i	−0.111818	−	0.173992i
$609$	−12.4120	−	3.24921i	−0.502960	−	0.131665i
$610$	−10.7724	−	8.23726i	−0.436162	−	0.333517i
$611$	−17.5866	−	27.3653i	−0.711479	−	1.10708i
$612$	1.30511	+	22.0458i	0.0527558	+	0.891150i
$613$	−3.45586	+	7.56728i	−0.139581	+	0.305640i	−0.966494	−	0.256691i	$-0.917368\pi$
$613$	−3.45586	+	7.56728i	−0.139581	+	0.305640i	0.826913	+	0.562330i	$0.190095\pi$
$614$	7.71243	−	12.0008i	0.311248	−	0.484312i
$615$	−33.2500	+	25.9091i	−1.34077	+	1.04476i
$616$	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	$-0.0450821\pi$
$618$	−0.573876	−	19.4048i	−0.0230847	−	0.780575i
$619$	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
$621$	24.3664	−	5.22287i	0.977790	−	0.209586i
$622$			11.4743i			0.460078i
$623$	−5.17174	+	35.9703i	−0.207202	+	1.44112i
$624$	8.33784	−	0.246583i	0.333781	−	0.00987121i
$625$	23.6794	+	8.01786i	0.947176	+	0.320715i
$626$	6.95776	+	8.02969i	0.278088	+	0.320931i
$627$	4.14110	−	36.4146i	0.165380	−	1.45426i
$628$	−18.7721	−	12.0641i	−0.749086	−	0.481409i
$629$	13.2250	+	6.03965i	0.527315	+	0.240817i
$630$	−11.6234	−	10.5386i	−0.463088	−	0.419868i
$631$	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
$633$	2.72039	−	10.3919i	0.108126	−	0.413042i
$634$	−18.5528	+	11.9232i	−0.736828	+	0.473530i
$635$	−0.201289	−	3.28608i	−0.00798792	−	0.130404i
$636$	−15.3986	−	16.7441i	−0.610594	−	0.663945i
$637$	−3.98275	+	6.19728i	−0.157802	+	0.245545i
$638$	−3.70217	−	12.6084i	−0.146570	−	0.499173i
$639$	1.15192	+	0.0966056i	0.0455693	+	0.00382166i
$640$	−1.05152	−	1.97340i	−0.0415649	−	0.0780055i
$641$	6.34196	+	13.8870i	0.250492	+	0.548502i	0.992551	−	0.121834i	$-0.0388774\pi$
$641$	6.34196	+	13.8870i	0.250492	+	0.548502i	−0.742058	+	0.670336i	$0.766150\pi$
$642$	−16.4668	−	9.90727i	−0.649892	−	0.391009i
$643$	40.8285			1.61012			0.805059	−	0.593194i	$-0.202133\pi$
$643$	40.8285			1.61012			0.805059	+	0.593194i	$0.202133\pi$
$644$	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	$0.889862\pi$
$648$	2.74671	−	8.57062i	0.107901	−	0.336686i
$649$	−11.5789	+	10.0332i	−0.454513	+	0.393838i
$650$	−23.2382	+	6.31037i	−0.911478	+	0.247513i
$651$	2.87023	+	4.18854i	0.112493	+	0.164162i
$652$	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	$0.901317\pi$
$654$	−0.774565	−	4.44915i	−0.0302879	−	0.173976i
$655$	4.63121	+	3.54132i	0.180956	+	0.138371i
$656$	−10.7730	+	1.54892i	−0.420614	+	0.0604752i
$657$	−11.2275	+	48.7257i	−0.438025	+	1.90097i
$658$	−10.3454	+	11.9392i	−0.403306	+	0.465440i
$659$	6.61988	−	14.4955i	0.257874	−	0.564665i	−0.735770	−	0.677231i	$-0.763180\pi$
$659$	6.61988	−	14.4955i	0.257874	−	0.564665i	0.993644	+	0.112566i	$0.0359070\pi$
$660$	3.11142	−	15.7652i	0.121112	−	0.613661i
$661$	−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
$663$	47.5757	+	38.8227i	1.84769	+	1.50775i
$664$	−14.4875	+	6.61623i	−0.562225	+	0.256760i
$665$	15.7645	+	21.5138i	0.611321	+	0.834269i
$666$	−4.13787	−	4.24067i	−0.160339	−	0.164323i
$667$	−13.9420	+	6.02740i	−0.539835	+	0.233382i
$668$	6.63837			0.256846
$669$	−3.79540	−	2.28351i	−0.146739	−	0.0882855i
$670$	−0.907898	+	2.36021i	−0.0350752	+	0.0911828i
$671$	7.08912	−	24.1433i	0.273672	−	0.932043i
$672$	−1.25572	−	3.85152i	−0.0484404	−	0.148576i
$673$	3.21079	+	10.9349i	0.123767	+	0.421511i	0.997944	−	0.0640967i	$-0.0204166\pi$
$673$	3.21079	+	10.9349i	0.123767	+	0.421511i	−0.874177	+	0.485608i	$0.838598\pi$
$674$	4.39614	+	2.82523i	0.169333	+	0.108824i
$675$	−1.93496	+	25.9086i	−0.0744768	+	0.997223i
$676$	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	$0.865869\pi$
$678$	−14.6737	−	3.84128i	−0.563541	−	0.147523i
$679$	2.89018	+	20.1016i	0.110915	+	0.771429i
$680$	3.66320	−	16.0480i	0.140477	−	0.615412i
$681$	2.53029	+	5.13331i	0.0969609	+	0.196709i
$682$	−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	$0.523536\pi$
$684$	−7.49641	+	13.3370i	−0.286633	+	0.509952i
$685$	19.9225	+	1.62971i	0.761200	+	0.0622682i
$686$	19.1417	+	5.62051i	0.730834	+	0.214592i
$687$	22.5801	−	0.667783i	0.861484	−	0.0254775i
$688$	−0.883697	+	6.14625i	−0.0336906	+	0.234324i
$689$	−63.2512			−2.40968
$690$	−18.5255	−	1.34358i	−0.705254	−	0.0511493i
$691$	−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
$693$	10.5077	−	27.1502i	0.399155	−	1.03135i
$694$	−10.1642	−	2.98448i	−0.385828	−	0.113289i
$695$	−0.314616	+	3.84604i	−0.0119341	+	0.145889i
$696$	−0.619837	+	5.45052i	−0.0234949	+	0.206601i
$697$	−67.4017	−	43.3164i	−2.55302	−	1.64073i
$698$	2.71155	−	5.93748i	0.102634	−	0.224737i
$699$	0.0645249	−	0.0318054i	0.00244056	−	0.00120299i
$700$	6.12005	+	9.96513i	0.231316	+	0.376646i
$701$	−3.47838	−	24.1927i	−0.131377	−	0.913744i	−0.943763	−	0.330624i	$-0.892741\pi$
$701$	−3.47838	−	24.1927i	−0.131377	−	0.913744i	0.812386	−	0.583120i	$-0.198168\pi$
$702$	−12.3710	−	21.7527i	−0.466914	−	0.821004i
$703$	5.44536	+	8.47314i	0.205376	+	0.319571i
$704$	2.71707	−	3.13567i	0.102404	−	0.118180i
$705$	26.1245	+	1.36116i	0.983906	+	0.0512641i
$706$	8.75294	+	5.62517i	0.329421	+	0.211706i
$707$	−2.51479	−	8.56459i	−0.0945784	−	0.322104i
$708$	6.08084	−	1.98255i	0.228532	−	0.0745086i
$709$	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	$-0.0152499\pi$
$710$	−0.804162	−	0.309336i	−0.0301796	−	0.0116092i
$711$	12.1716	+	16.6822i	0.456472	+	0.625631i
$712$	15.5374			0.582290
$713$	5.73197	+	1.81050i	0.214664	+	0.0678038i
$714$	11.5811	−	27.4812i	0.433412	−	1.02846i
$715$	−26.4092	−	36.0406i	−0.987647	−	1.34784i
$716$	−14.4728	+	6.60951i	−0.540874	+	0.247009i
$717$	24.9281	−	30.5484i	0.930957	−	1.14085i
$718$	15.6130	+	18.0183i	0.582671	+	0.672438i
$719$	−2.19385	−	7.47155i	−0.0818166	−	0.278642i	0.908416	−	0.418068i	$-0.137293\pi$
$719$	−2.19385	−	7.47155i	−0.0818166	−	0.278642i	−0.990233	+	0.139426i	$0.955474\pi$
$720$	−3.75272	+	5.56031i	−0.139856	+	0.207221i
$721$	−10.8900	+	23.8458i	−0.405565	+	0.888063i
$722$	4.58922	−	5.29625i	0.170793	−	0.197106i
$723$	−0.253910	−	1.45848i	−0.00944301	−	0.0542413i
$724$	−7.21126	+	1.03682i	−0.268004	+	0.0385332i
$725$	−1.93278	−	15.7173i	−0.0717818	−	0.583726i
$726$	10.6050	−	1.84626i	0.393590	−	0.0685211i
$727$	4.52057	−	5.21702i	0.167659	−	0.193489i	−0.665702	−	0.746217i	$-0.731868\pi$
$727$	4.52057	−	5.21702i	0.167659	−	0.193489i	0.833361	+	0.552729i	$0.186413\pi$
$728$	−10.2460	−	4.67921i	−0.379743	−	0.173423i
$729$	−26.5763	+	4.76451i	−0.984307	+	0.176463i
$730$	18.1949	−	32.5265i	0.673422	−	1.20386i
$731$	−34.5459	+	29.9342i	−1.27773	+	1.10716i
$732$	−6.64112	+	8.13843i	−0.245463	+	0.300805i
$733$	−15.6214	−	34.2061i	−0.576989	−	1.26343i	−0.942992	−	0.332816i	$-0.892001\pi$
$733$	−15.6214	−	34.2061i	−0.576989	−	1.26343i	0.366003	−	0.930614i	$-0.380726\pi$
$734$	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
$738$	19.2450	+	26.3768i	0.708419	+	0.970943i
$739$	−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	$0.903132\pi$
$740$	2.07674	+	3.89744i	0.0763423	+	0.143273i
$741$	13.1862	+	40.4446i	0.484408	+	1.48577i
$742$	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	$0.955964\pi$
$744$	1.59796	−	1.46955i	0.0585839	−	0.0538765i
$745$	−43.7161	+	2.67784i	−1.60163	+	0.0981083i
$746$	4.72078	−	3.03386i	0.172840	−	0.111078i
$747$	37.8960	+	29.1009i	1.38654	+	1.06474i
$748$	30.2325	−	4.34678i	1.10541	−	0.158934i
$749$	14.0298	+	21.8308i	0.512637	+	0.797678i
$750$	6.78726	−	18.1365i	0.247836	−	0.662252i
$751$	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
$753$	−8.55133	−	0.972464i	−0.311628	−	0.0354386i
$754$	9.98846	+	11.5273i	0.363758	+	0.419800i
$755$	−12.7266	−	23.8842i	−0.463169	−	0.869236i
$756$	−8.44367	+	8.74093i	−0.307093	+	0.317905i
$757$	−2.79276	+	19.4241i	−0.101505	+	0.705981i	0.873988	+	0.485948i	$0.161526\pi$
$757$	−2.79276	+	19.4241i	−0.101505	+	0.705981i	−0.975492	+	0.220033i	$0.929383\pi$
$758$			32.1031i			1.16604i
$759$	−10.0144	−	32.9779i	−0.363500	−	1.19702i
$760$	8.14548	−	7.98065i	0.295468	−	0.289489i
$761$	−15.0024	−	2.15702i	−0.543838	−	0.0781921i	−0.135080	−	0.990835i	$-0.543129\pi$
$761$	−15.0024	−	2.15702i	−0.543838	−	0.0781921i	−0.408758	+	0.912643i	$0.634038\pi$
$762$	−2.54904	+	0.0753852i	−0.0923420	+	0.00273092i
$763$	−1.71809	+	5.85127i	−0.0621989	+	0.211830i
$764$	7.23925	+	8.35454i	0.261907	+	0.302256i
$765$	−47.6829	+	12.8435i	−1.72398	+	0.464359i
$766$	−13.0133	+	20.2491i	−0.470190	+	0.731629i
$767$	7.38760	−	16.1766i	0.266751	−	0.584103i
$768$	−1.55357	+	0.765780i	−0.0560596	+	0.0276327i
$769$	−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	$0.873872\pi$
$770$	−13.1808	+	17.2373i	−0.475001	+	0.621191i
$771$	10.7195	−	40.9485i	0.386052	−	1.47472i
$772$	−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	$0.838506\pi$
$774$	17.5324	−	6.29532i	0.630189	−	0.226280i
$775$	−3.49526	+	5.20179i	−0.125554	+	0.186854i
$776$	8.33122	−	2.44627i	0.299073	−	0.0878158i
$777$	2.48003	+	7.60671i	0.0889705	+	0.272889i
$778$	8.95176	+	2.62847i	0.320936	+	0.0942353i
$779$	−23.0576	−	50.4891i	−0.826124	−	1.80896i
$780$	4.31659	+	18.1458i	0.154559	+	0.649722i
$781$		−	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
$785$	17.9140	−	46.5698i	0.639376	−	1.66215i
$786$	2.85511	−	3.49882i	0.101838	−	0.124799i
$787$	−0.773676	−	0.892870i	−0.0275786	−	0.0318274i	0.741793	−	0.670629i	$-0.233976\pi$
$787$	−0.773676	−	0.892870i	−0.0275786	−	0.0318274i	−0.769371	+	0.638802i	$0.779430\pi$
$788$	−18.1554	+	5.33090i	−0.646759	+	0.189905i
$789$	27.2597	−	18.6800i	0.970472	−	0.665024i
$790$	−5.23127	−	14.4758i	−0.186120	−	0.515024i
$791$	15.4796	+	13.4131i	0.550389	+	0.476915i
$792$	−12.1294	−	2.79488i	−0.431000	−	0.0993117i
$793$	4.15657	+	28.9096i	0.147604	+	1.02661i
$794$	17.8385	−	2.56480i	0.633066	−	0.0910212i
$795$	29.6898	−	41.3028i	1.05299	−	1.46486i
$796$	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	$0.631005\pi$
$798$	17.0422	−	11.6783i	0.603286	−	0.413407i
$799$	14.0086	+	47.7087i	0.495587	+	1.68781i
$800$	3.84489	−	3.19638i	0.135937	−	0.113009i
$801$	−21.8353	−	41.1816i	−0.771512	−	1.45508i
$802$	−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
$805$	21.6360	+	12.6875i	0.762570	+	0.447175i
$806$		−	6.03633i		−	0.212621i
$807$	−13.7068	−	8.24674i	−0.482503	−	0.290299i
$808$	−3.47154	+	1.58540i	−0.122129	+	0.0557742i
$809$	−0.951643	+	3.24100i	−0.0334580	+	0.113947i	−0.974529	−	0.224262i	$-0.928003\pi$
$809$	−0.951643	+	3.24100i	−0.0334580	+	0.113947i	0.941071	+	0.338209i	$0.109821\pi$
$810$	20.0113	+	2.13240i	0.703126	+	0.0749250i
$811$	−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
$813$	−17.8619	+	16.4266i	−0.626443	+	0.576105i
$814$	−5.36619	+	6.19291i	−0.188085	+	0.217061i
$815$	−0.515352	+	2.25769i	−0.0180520	+	0.0790833i
$816$	−12.3348	−	3.22900i	−0.431805	−	0.113038i
$817$	−31.3446	+	4.50668i	−1.09661	+	0.157669i
$818$	−3.10387	+	1.99474i	−0.108524	+	0.0697443i
$819$	1.99697	+	33.7327i	0.0697797	+	1.17872i
$820$	−8.27134	−	22.8881i	−0.288848	−	0.799287i
$821$	−9.02626	+	14.0451i	−0.315019	+	0.490179i	−0.962269	−	0.272099i	$-0.912282\pi$
$821$	−9.02626	+	14.0451i	−0.315019	+	0.490179i	0.647251	+	0.762277i	$0.275919\pi$
$822$	1.74951	−	15.3843i	0.0610213	−	0.536589i
$823$	−15.3096	+	13.2659i	−0.533660	+	0.462419i	−0.879516	−	0.475868i	$-0.842134\pi$
$823$	−15.3096	+	13.2659i	−0.533660	+	0.462419i	0.345857	+	0.938287i	$0.387588\pi$
$824$	10.7542	+	3.15773i	0.374642	+	0.110005i
$825$	35.9306	−	0.327809i	1.25094	−	0.0114128i
$826$	−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	$-0.0991564\pi$
$828$	−1.49379	+	14.3097i	−0.0519126	+	0.497298i
$829$	−50.9519			−1.76963			−0.884817	−	0.465939i	$-0.845717\pi$
$829$	−50.9519			−1.76963			−0.884817	+	0.465939i	$0.845717\pi$
$830$	−21.0498	−	28.7266i	−0.730649	−	0.997116i
$831$	31.4252	−	0.929366i	1.09013	−	0.0322394i
$832$	−1.35681	+	4.62088i	−0.0470390	+	0.160200i
$833$	8.51011	−	7.37405i	0.294858	−	0.255496i
$834$	2.96994	+	0.337744i	0.102841	+	0.0116951i
$835$	3.00687	+	14.5361i	0.104057	+	0.503043i
$836$	19.2474	+	8.78997i	0.665684	+	0.304008i
$837$	−6.14068	−	2.17013i	−0.212253	−	0.0750108i
$838$	−18.8276	+	12.0997i	−0.650387	+	0.417979i
$839$	0.0889258	+	0.618492i	0.00307006	+	0.0213527i	0.991299	−	0.131630i	$-0.0420211\pi$
$839$	0.0889258	+	0.618492i	0.00307006	+	0.0213527i	−0.988229	+	0.152983i	$0.951112\pi$
$840$	7.86494	−	4.49422i	0.271366	−	0.155065i
$841$	15.9579	−	10.2555i	0.550273	−	0.353639i
$842$	−10.4093	−	9.01971i	−0.358728	−	0.310840i
$843$	−15.3399	+	14.1073i	−0.528333	+	0.485880i
$844$	5.21741	+	3.35303i	0.179591	+	0.115416i
$845$	19.8924	+	11.1275i	0.684320	+	0.382799i
$846$	1.69344	−	20.1925i	0.0582217	−	0.694233i
$847$	−13.9471	−	4.09524i	−0.479229	−	0.140714i
$848$	11.9468	−	5.45593i	0.410255	−	0.187357i
$849$	−15.0270	+	24.9763i	−0.515727	+	0.857184i
$850$	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	$-0.206588\pi$
$853$	40.6201	+	5.84029i	1.39081	+	0.199968i	0.594127	+	0.804371i	$0.297497\pi$
$854$	12.9026	−	5.89240i	0.441517	−	0.201634i
$855$	−32.5997	−	10.3739i	−1.11489	−	0.354781i
$856$	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	$0.522703\pi$
$858$	−28.5495	+	19.5638i	−0.974665	+	0.667898i
$859$	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	$0.0278817\pi$
$860$	−13.8588	+	0.848922i	−0.472581	+	0.0289480i
$861$	−7.56212	−	43.4373i	−0.257716	−	1.48034i
$862$	−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	$0.668490\pi$
$864$	4.21297	+	3.04153i	0.143328	+	0.103475i
$865$	−8.22967	+	0.504110i	−0.279817	+	0.0171403i
$866$	8.95514	−	19.6090i	0.304308	−	0.666342i
$867$	−36.4134	−	53.1381i	−1.23666	−	1.80467i
$868$	−2.81281	+	0.825915i	−0.0954729	+	0.0280334i
$869$	21.5844	−	18.7030i	0.732201	−	0.634456i
$870$	−12.2158	+	1.11157i	−0.414155	+	0.0376856i
$871$	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
$876$	−24.7369	−	14.8830i	−0.835782	−	0.502850i
$877$	6.12197	−	2.79581i	0.206724	−	0.0944078i	−0.309362	−	0.950944i	$-0.600116\pi$
$877$	6.12197	−	2.79581i	0.206724	−	0.0944078i	0.516086	+	0.856536i	$0.327388\pi$
$878$	−9.43897	−	2.77153i	−0.318550	−	0.0935347i
$879$	−12.8440	+	4.18754i	−0.433217	+	0.141242i
$880$	8.09692	+	4.52929i	0.272947	+	0.152682i
$881$	33.9780	+	21.8363i	1.14475	+	0.735684i	0.968586	−	0.248677i	$-0.0799959\pi$
$881$	33.9780	+	21.8363i	1.14475	+	0.735684i	0.176160	+	0.984361i	$0.443632\pi$
$882$	−4.31897	+	1.55080i	−0.145427	+	0.0522182i
$883$	−1.02468	−	0.887888i	−0.0344832	−	0.0298798i	0.637449	−	0.770493i	$-0.279990\pi$
$883$	−1.02468	−	0.887888i	−0.0344832	−	0.0298798i	−0.671932	+	0.740613i	$0.734535\pi$
$884$	−29.8246	+	19.1671i	−1.00311	+	0.644659i
$885$	7.09554	+	12.4173i	0.238514	+	0.417402i
$886$	−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	$0.593834\pi$
$888$	3.06828	−	1.51241i	0.102965	−	0.0507530i
$889$	3.13241	+	1.43053i	0.105058	+	0.0479783i
$890$	7.03773	+	34.0225i	0.235905	+	1.14044i
$891$	9.63813	+	36.0765i	0.322889	+	1.20861i
$892$	1.93268	−	1.67468i	0.0647110	−	0.0560724i
$893$	−9.70468	+	33.0511i	−0.324755	+	1.10601i
$894$	1.00288	+	33.9110i	0.0335414	+	1.13415i
$895$	−21.0284	−	28.6975i	−0.702903	−	0.959251i
$896$	2.33888			0.0781364
$897$	26.4750	+	29.9904i	0.883973	+	1.00135i
$898$			36.8417i			1.22942i
$899$	3.92930	+	0.564947i	0.131049	+	0.0188420i
$900$	−13.8753	−	5.69881i	−0.462510	−	0.189960i
$901$	92.7669	+	27.2388i	3.09051	+	0.907457i
$902$	34.1279	−	29.5720i	1.13633	−	0.984639i
$903$	−24.9937	−	2.84231i	−0.831740	−	0.0945861i
$904$	4.73458	−	7.36715i	0.157470	−	0.245028i
$905$	−5.53671	−	15.3209i	−0.184046	−	0.509285i
$906$	−18.8030	+	9.26830i	−0.624688	+	0.307919i
$907$	34.3109	−	22.0503i	1.13927	−	0.732167i	0.171799	−	0.985132i	$-0.445042\pi$
$907$	34.3109	−	22.0503i	1.13927	−	0.732167i	0.967476	+	0.252965i	$0.0814056\pi$
$908$	−3.27057	+	0.470237i	−0.108538	+	0.0156053i
$909$	9.08075	+	6.97324i	0.301190	+	0.231288i
$910$	5.60514	−	24.5553i	0.185808	−	0.814001i
$911$	−1.31019	+	1.51204i	−0.0434086	+	0.0500962i	−0.777039	−	0.629453i	$-0.783279\pi$
$911$	−1.31019	+	1.51204i	−0.0434086	+	0.0500962i	0.733630	+	0.679549i	$0.237825\pi$
$912$	−5.97927	−	6.50171i	−0.197993	−	0.215293i
$913$	35.7264	−	55.5914i	1.18237	−	1.83981i
$914$	−5.41725	+	1.59065i	−0.179187	+	0.0526139i
$915$	−20.8289	−	10.8558i	−0.688583	−	0.358882i
$916$	−3.67445	+	12.5140i	−0.121407	+	0.413475i
$917$	−5.54699	+	2.53323i	−0.183178	+	0.0836545i
$918$	8.77615	+	37.2310i	0.289656	+	1.22881i
$919$		−	11.1166i		−	0.366703i	−0.983047	−	0.183351i	$-0.941305\pi$
$919$		−	11.1166i		−	0.366703i	0.983047	−	0.183351i	$-0.0586946\pi$
$920$	4.05289	−	9.92845i	0.133620	−	0.327331i
$921$	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
$924$	13.0226	+	10.6267i	0.428412	+	0.349593i
$925$	−7.59361	+	6.31281i	−0.249676	+	0.207564i
$926$	−5.42398	−	18.4724i	−0.178243	−	0.607040i
$927$	−6.74381	−	32.9416i	−0.221496	−	1.08194i
$928$	−2.88093	−	1.31568i	−0.0945712	−	0.0431892i
$929$	27.9781	+	24.2432i	0.917933	+	0.795394i	0.979236	−	0.202725i	$-0.0649799\pi$
$929$	27.9781	+	24.2432i	0.917933	+	0.795394i	−0.0613023	+	0.998119i	$0.519525\pi$
$930$	3.94170	+	2.83342i	0.129253	+	0.0929116i
$931$	7.72150	−	1.11018i	0.253062	−	0.0363848i
$932$	0.00591081	+	0.0411106i	0.000193615	+	0.00134662i
$933$	3.40866	+	19.5796i	0.111595	+	0.641007i
$934$	6.16981	+	5.34617i	0.201882	+	0.174932i
$935$	23.2121	+	64.2316i	0.759117	+	2.10060i
$936$	14.1543	−	2.89768i	0.462648	−	0.0947135i
$937$	−26.5481	+	7.79523i	−0.867289	+	0.254659i	−0.684962	−	0.728579i	$-0.740181\pi$
$937$	−26.5481	+	7.79523i	−0.867289	+	0.254659i	−0.182327	+	0.983238i	$0.558363\pi$
$938$	−1.73216	−	1.99901i	−0.0565569	−	0.0652701i
$939$	14.2580	+	11.6348i	0.465292	+	0.379687i
$940$	−5.42248	+	14.0965i	−0.176862	+	0.459777i
$941$	−2.01244	+	13.9968i	−0.0656036	+	0.456283i	0.930369	+	0.366624i	$0.119487\pi$
$941$	−2.01244	+	13.9968i	−0.0656036	+	0.456283i	−0.995973	+	0.0896584i	$0.971422\pi$
$942$	−35.6162	−	15.0093i	−1.16044	−	0.489031i
$943$	−38.7441	−	34.9769i	−1.26168	−	1.13901i
$944$			3.69265i			0.120186i
$945$	−22.9647	−	14.5300i	−0.747042	−	0.472660i
$946$	−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	$0.322461\pi$
$948$	−11.3353	+	3.69568i	−0.368155	+	0.120030i
$949$	−77.0185	+	22.6147i	−2.50013	+	0.734103i
$950$	21.1648	+	14.2214i	0.686678	+	0.461403i
$951$	−28.1163	+	25.8570i	−0.911733	+	0.838472i
$952$	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	$0.895096\pi$
$954$	−31.2501	−	23.9974i	−1.01176	−	0.776943i
$955$	−15.0150	+	19.6361i	−0.485873	+	0.635408i
$956$	12.3072	+	19.1504i	0.398044	+	0.619368i
$957$	−10.0629	−	20.4151i	−0.325288	−	0.659925i
$958$	14.1079	−	30.8921i	0.455806	−	0.998077i
$959$	−11.3038	+	17.5890i	−0.365018	+	0.567979i
$960$	−2.38053	−	3.05501i	−0.0768313	−	0.0986000i
$961$	19.2719	+	22.2409i	0.621674	+	0.717450i
$962$	2.67969	−	9.12618i	0.0863966	−	0.294240i
$963$	−31.0418	−	12.0139i	−1.00031	−	0.387141i
$964$	0.846017	+	0.121639i	0.0272484	+	0.00391773i
$965$	7.93926	−	7.77860i	0.255574	−	0.250402i
$966$	10.3525	−	16.4402i	0.333086	−	0.528954i
$967$		−	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
$969$	−1.92220	−	64.9963i	−0.0617499	−	2.08798i
$970$	9.13027	+	17.1349i	0.293155	+	0.550169i
$971$	−13.6438	−	15.7458i	−0.437850	−	0.505306i	0.493341	−	0.869836i	$-0.335775\pi$
$971$	−13.6438	−	15.7458i	−0.437850	−	0.505306i	−0.931192	+	0.364529i	$0.881230\pi$
$972$	2.14087	−	15.4407i	0.0686686	−	0.495262i
$973$	−3.39556	−	2.18219i	−0.108857	−	0.0699580i
$974$	−15.2159	−	6.94885i	−0.487548	−	0.222656i
$975$	−37.7787	+	17.6713i	−1.20989	+	0.565934i
$976$	−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	$0.634456\pi$
$978$	1.73530	+	0.454267i	0.0554889	+	0.0145258i
$979$	−54.2324	+	34.8530i	−1.73327	+	1.11391i
$980$	3.41400	−	0.209125i	0.109056	−	0.00668026i
$981$	−2.64341	−	7.36187i	−0.0843976	−	0.235046i
$982$	−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	$0.727754\pi$
$984$	−17.9227	+	5.84337i	−0.571355	+	0.186280i
$985$	−19.8967	−	37.3404i	−0.633961	−	1.18976i
$986$	−9.68533	−	21.2079i	−0.308444	−	0.675398i
$987$	−14.1065	+	23.4462i	−0.449014	+	0.746302i
$988$	−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
$993$	25.3926	+	20.7209i	0.805810	+	0.657556i
$994$	0.681097	−	0.590174i	0.0216031	−	0.0187192i
$995$	−3.46968	+	6.20266i	−0.109996	+	0.196638i
$996$	−22.7558	+	15.5936i	−0.721046	+	0.494103i
$997$	−25.2514	−	11.5319i	−0.799720	−	0.365220i	−0.0267335	−	0.999643i	$-0.508511\pi$
$997$	−25.2514	−	11.5319i	−0.799720	−	0.365220i	−0.772986	+	0.634423i	$0.781238\pi$
$998$	−7.06123	+	8.14910i	−0.223519	+	0.257955i
$999$	−8.32056	−	6.00698i	−0.263251	−	0.190053i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.0512012 + 1.73129i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.182307 - 2.22862i) q^{5} +(-1.72096 - 0.195709i) q^{6} +(1.96759 + 1.26449i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.99476 + 0.177289i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.0512012 + 1.73129i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.182307 - 2.22862i) q^{5} +(-1.72096 - 0.195709i) q^{6} +(1.96759 + 1.26449i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.99476 + 0.177289i) q^{9} +(2.17999 + 0.497618i) q^{10} +(0.590477 + 4.10685i) q^{11} +(0.438635 - 1.67559i) q^{12} +(-2.60370 - 4.05144i) q^{13} +(-1.53164 + 1.76761i) q^{14} +(3.86774 + 0.201519i) q^{15} +(0.841254 + 0.540641i) q^{16} +(2.07397 + 7.06329i) q^{17} +(0.250714 - 2.98951i) q^{18} +(-1.43678 + 4.89322i) q^{19} +(-0.802799 + 2.08699i) q^{20} +(-2.08847 + 3.47122i) q^{21} -4.14909 q^{22} +(0.585811 + 4.75992i) q^{23} +(1.59611 + 0.672631i) q^{24} +(-4.93353 - 0.812589i) q^{25} +(4.38075 - 2.00062i) q^{26} +(-0.460274 - 5.17573i) q^{27} +(-1.53164 - 1.76761i) q^{28} +(0.892286 + 3.03885i) q^{29} +(-0.749905 + 3.79969i) q^{30} +(0.520682 - 1.14014i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-7.07994 + 1.23256i) q^{33} +(-7.28655 + 1.04765i) q^{34} +(3.17679 - 4.15449i) q^{35} +(2.92340 + 0.673613i) q^{36} +(1.29334 - 1.49260i) q^{37} +(-4.63894 - 2.11853i) q^{38} +(6.88092 - 4.71521i) q^{39} +(-1.95149 - 1.09164i) q^{40} +(-8.22539 + 7.12734i) q^{41} +(-3.13867 - 2.56121i) 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} +(-0.892935 + 1.48414i) q^{48} +(-0.635439 - 1.39142i) q^{49} +(1.50643 - 4.76767i) q^{50} +(-12.1224 + 3.95230i) q^{51} +(1.35681 + 4.62088i) q^{52} +(7.10060 - 11.0487i) q^{53} +(5.18855 + 0.280994i) q^{54} +(9.26028 - 0.567240i) q^{55} +(1.96759 - 1.26449i) q^{56} +(-8.54517 - 2.23695i) q^{57} +(-3.13490 + 0.450731i) q^{58} +(1.99640 + 3.10646i) q^{59} +(-3.65429 - 1.28302i) q^{60} +(-5.51656 - 2.51933i) q^{61} +(1.05443 + 0.677641i) q^{62} +(-6.11663 - 3.43802i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-9.50381 + 5.06407i) q^{65} +(-0.212438 - 7.18329i) q^{66} +(-0.160946 + 1.11941i) q^{67} -7.36148i q^{68} +(-8.21082 + 1.25793i) q^{69} +(3.66010 + 3.73570i) q^{70} +(-0.381400 - 0.0548370i) q^{71} +(-1.08280 + 2.79778i) q^{72} +(4.69578 - 15.9924i) q^{73} +(1.29334 + 1.49260i) q^{74} +(1.15423 - 8.58299i) q^{75} +(2.75716 - 4.29022i) q^{76} +(-4.03127 + 8.82726i) q^{77} +(3.68796 + 7.48193i) q^{78} +(-3.72151 - 5.79078i) q^{79} +(1.35825 - 1.77627i) q^{80} +(8.93714 - 1.06187i) q^{81} +(-5.88420 - 9.15600i) q^{82} +(-12.0367 - 10.4298i) q^{83} +(2.98182 - 2.74222i) q^{84} +(16.1195 - 3.33441i) q^{85} +(-5.95793 + 1.74940i) q^{86} +(-5.21545 + 1.70040i) q^{87} +(3.98102 + 1.16893i) q^{88} +(6.45448 + 14.1333i) q^{89} +(-6.61678 - 1.10376i) q^{90} -11.2639i q^{91} +(0.778942 - 4.73215i) q^{92} +(2.00057 + 0.843078i) q^{93} +(-0.961261 + 6.68572i) q^{94} +(10.6432 + 4.09411i) q^{95} +(-1.34195 - 1.09506i) q^{96} +(5.68611 + 6.56212i) q^{97} +(1.46769 - 0.430952i) q^{98} +(-2.49643 - 12.1943i) 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

Modular forms

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