LMFDB - Embedded newform 690.2.n.b.89.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.6
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-1.27489 + 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.182307 - 2.22862i) q^{5} +(-1.34195 - 1.09506i) q^{6} +(1.96759 - 1.26449i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.250714 - 2.98951i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-1.27489 + 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.182307 - 2.22862i) 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} +(2.17999 - 0.497618i) 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} +(2.84538 + 2.62751i) 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} +(0.802799 + 2.08699i) q^{20} +(-1.02591 + 3.91900i) q^{21} -4.14909 q^{22} +(-0.585811 + 4.75992i) q^{23} +(1.59611 + 0.672631i) q^{24} +(-4.93353 + 0.812589i) 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} +(-2.19583 + 3.19035i) 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} +(-3.17679 - 4.15449i) 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} +(-1.95149 + 1.09164i) 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} +(-6.70819 - 0.0137386i) q^{45} +(-4.79484 + 0.0975584i) q^{46} -6.75447 q^{47} +(-0.438635 + 1.67559i) q^{48} +(-0.635439 + 1.39142i) q^{49} +(-1.50643 - 4.76767i) 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} +(9.26028 + 0.567240i) 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} +(-3.47038 - 1.71945i) 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} +(9.50381 + 5.06407i) 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} +(5.33701 - 6.82029i) 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} +(-1.35825 - 1.77627i) 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} +(16.1195 + 3.33441i) 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} +(-0.941076 - 6.64187i) 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} +(-1.72096 - 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} - 102 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 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	−1.27489	+	1.17245i	−0.736061	+	0.676915i
$3$	−1.27489	+	1.17245i	−0.736061	+	0.676915i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.182307	−	2.22862i	−0.0815303	−	0.996671i
$5$	−0.182307	−	2.22862i	−0.0815303	−	0.996671i
$6$	−1.34195	−	1.09506i	−0.547851	−	0.447057i
$7$	1.96759	−	1.26449i	0.743679	−	0.477933i	−0.113122	−	0.993581i	$-0.536085\pi$
$7$	1.96759	−	1.26449i	0.743679	−	0.477933i	0.856801	+	0.515648i	$0.172449\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	0.250714	−	2.98951i	0.0835714	−	0.996502i
$10$	2.17999	−	0.497618i	0.689375	−	0.157361i
$11$	−0.590477	+	4.10685i	−0.178035	+	1.23826i	0.683266	+	0.730169i	$0.260559\pi$
$11$	−0.590477	+	4.10685i	−0.178035	+	1.23826i	−0.861302	+	0.508094i	$0.830350\pi$
$12$	0.892935	−	1.48414i	0.257768	−	0.428434i
$13$	−2.60370	+	4.05144i	−0.722137	+	1.12367i	0.265071	+	0.964229i	$0.414605\pi$
$13$	−2.60370	+	4.05144i	−0.722137	+	1.12367i	−0.987208	+	0.159438i	$0.949032\pi$
$14$	1.53164	+	1.76761i	0.409348	+	0.472413i
$15$	2.84538	+	2.62751i	0.734673	+	0.678421i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−2.07397	+	7.06329i	−0.503011	+	1.71310i	0.180872	+	0.983507i	$0.442108\pi$
$17$	−2.07397	+	7.06329i	−0.503011	+	1.71310i	−0.683883	+	0.729592i	$0.739710\pi$
$18$	2.99476	−	0.177289i	0.705871	−	0.0417874i
$19$	−1.43678	−	4.89322i	−0.329620	−	1.12258i	−0.943000	−	0.332794i	$-0.892009\pi$
$19$	−1.43678	−	4.89322i	−0.329620	−	1.12258i	0.613380	−	0.789788i	$-0.289809\pi$
$20$	0.802799	+	2.08699i	0.179511	+	0.466664i
$21$	−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
$25$	−4.93353	+	0.812589i	−0.986706	+	0.162518i
$26$	−4.38075	−	2.00062i	−0.859135	−	0.392354i
$27$	3.18542	+	4.10526i	0.613034	+	0.790057i
$28$	−1.53164	+	1.76761i	−0.289453	+	0.334046i
$29$	−0.892286	+	3.03885i	−0.165693	+	0.564300i	0.834224	+	0.551426i	$0.185916\pi$
$29$	−0.892286	+	3.03885i	−0.165693	+	0.564300i	−0.999917	+	0.0128738i	$0.995902\pi$
$30$	−2.19583	+	3.19035i	−0.400902	+	0.582475i
$31$	0.520682	+	1.14014i	0.0935173	+	0.204774i	0.950610	−	0.310388i	$-0.100459\pi$
$31$	0.520682	+	1.14014i	0.0935173	+	0.204774i	−0.857093	+	0.515162i	$0.827732\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	−4.06229	−	5.92811i	−0.707154	−	1.03195i
$34$	−7.28655	−	1.04765i	−1.24963	−	0.179670i
$35$	−3.17679	−	4.15449i	−0.536975	−	0.702237i
$36$	0.601683	+	2.93904i	0.100280	+	0.489841i
$37$	1.29334	+	1.49260i	0.212624	+	0.245381i	0.852036	−	0.523483i	$-0.175368\pi$
$37$	1.29334	+	1.49260i	0.212624	+	0.245381i	−0.639412	+	0.768864i	$0.720822\pi$
$38$	4.63894	−	2.11853i	0.752535	−	0.343671i
$39$	−1.43067	−	8.21788i	−0.229091	−	1.31591i
$40$	−1.95149	+	1.09164i	−0.308558	+	0.172603i
$41$	8.22539	+	7.12734i	1.28459	+	1.11310i	0.987393	+	0.158288i	$0.0505974\pi$
$41$	8.22539	+	7.12734i	1.28459	+	1.11310i	0.297197	+	0.954816i	$0.403948\pi$
$42$	−4.02511	−	0.457739i	−0.621088	−	0.0706306i
$43$	2.57950	−	5.64832i	0.393370	−	0.861360i	−0.604530	−	0.796583i	$-0.706639\pi$
$43$	2.57950	−	5.64832i	0.393370	−	0.861360i	0.997900	−	0.0647776i	$-0.0206338\pi$
$44$	−0.590477	−	4.10685i	−0.0890177	−	0.619132i
$45$	−6.70819	−	0.0137386i	−0.999998	−	0.00204803i
$46$	−4.79484	+	0.0975584i	−0.706960	+	0.0143842i
$47$	−6.75447			−0.985240			−0.492620	−	0.870244i	$-0.663961\pi$
$47$	−6.75447			−0.985240			−0.492620	+	0.870244i	$0.663961\pi$
$48$	−0.438635	+	1.67559i	−0.0633115	+	0.241850i
$49$	−0.635439	+	1.39142i	−0.0907771	+	0.198774i
$50$	−1.50643	−	4.76767i	−0.213042	−	0.674250i
$51$	−5.63727	−	11.4366i	−0.789376	−	1.60144i
$52$	1.35681	−	4.62088i	0.188156	−	0.640800i
$53$	−7.10060	−	11.0487i	−0.975342	−	1.51766i	−0.850828	−	0.525445i	$-0.823899\pi$
$53$	−7.10060	−	11.0487i	−0.975342	−	1.51766i	−0.124515	−	0.992218i	$-0.539737\pi$
$54$	−3.61014	+	3.73723i	−0.491278	+	0.508573i
$55$	9.26028	+	0.567240i	1.24866	+	0.0764866i
$56$	−1.96759	−	1.26449i	−0.262930	−	0.168975i
$57$	7.56881	+	4.55379i	1.00251	+	0.603164i
$58$	−3.13490	−	0.450731i	−0.411633	−	0.0591839i
$59$	−1.99640	+	3.10646i	−0.259909	+	0.404427i	−0.946543	−	0.322577i	$-0.895451\pi$
$59$	−1.99640	+	3.10646i	−0.259909	+	0.404427i	0.686634	+	0.727003i	$0.259087\pi$
$60$	−3.47038	−	1.71945i	−0.448024	−	0.221980i
$61$	−5.51656	+	2.51933i	−0.706323	+	0.322567i	−0.735990	−	0.676993i	$-0.763283\pi$
$61$	−5.51656	+	2.51933i	−0.706323	+	0.322567i	0.0296663	+	0.999560i	$0.490556\pi$
$62$	−1.05443	+	0.677641i	−0.133913	+	0.0860604i
$63$	−3.28691	−	6.19915i	−0.414111	−	0.781019i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	9.50381	+	5.06407i	1.17880	+	0.628120i
$66$	5.28965	−	4.86460i	0.651111	−	0.598791i
$67$	−0.160946	−	1.11941i	−0.0196627	−	0.136757i	0.977625	−	0.210353i	$-0.0674615\pi$
$67$	−0.160946	−	1.11941i	−0.0196627	−	0.136757i	−0.997288	+	0.0735963i	$0.976552\pi$
$68$		−	7.36148i		−	0.892710i
$69$	−4.83393	−	6.75523i	−0.581936	−	0.813234i
$70$	3.66010	−	3.73570i	0.437466	−	0.446501i
$71$	0.381400	−	0.0548370i	0.0452638	−	0.00650796i	−0.119646	−	0.992817i	$-0.538176\pi$
$71$	0.381400	−	0.0548370i	0.0452638	−	0.00650796i	0.164910	+	0.986309i	$0.447267\pi$
$72$	−2.82350	+	1.01383i	−0.332753	+	0.119481i
$73$	4.69578	+	15.9924i	0.549599	+	1.87176i	0.486347	+	0.873766i	$0.338329\pi$
$73$	4.69578	+	15.9924i	0.549599	+	1.87176i	0.0632528	+	0.997998i	$0.479853\pi$
$74$	−1.29334	+	1.49260i	−0.150348	+	0.173511i
$75$	5.33701	−	6.82029i	0.616265	−	0.787539i
$76$	2.75716	+	4.29022i	0.316268	+	0.492122i
$77$	4.03127	+	8.82726i	0.459406	+	1.00596i
$78$	7.93062	−	2.58563i	0.897966	−	0.292765i
$79$	−3.72151	+	5.79078i	−0.418702	+	0.651513i	−0.984974	−	0.172706i	$-0.944749\pi$
$79$	−3.72151	+	5.79078i	−0.418702	+	0.651513i	0.566271	+	0.824219i	$0.308385\pi$
$80$	−1.35825	−	1.77627i	−0.151857	−	0.198594i
$81$	−8.87428	−	1.49902i	−0.986032	−	0.166558i
$82$	−5.88420	+	9.15600i	−0.649801	+	1.01111i
$83$	12.0367	−	10.4298i	1.32120	−	1.14482i	0.342498	−	0.939519i	$-0.388727\pi$
$83$	12.0367	−	10.4298i	1.32120	−	1.14482i	0.978698	−	0.205304i	$-0.0658185\pi$
$84$	−0.119753	−	4.04929i	−0.0130662	−	0.441813i
$85$	16.1195	+	3.33441i	1.74841	+	0.361667i
$86$	5.95793	+	1.74940i	0.642460	+	0.188643i
$87$	−2.42533	−	4.92037i	−0.260023	−	0.527520i
$88$	3.98102	−	1.16893i	0.424378	−	0.124609i
$89$	−6.45448	+	14.1333i	−0.684174	+	1.49813i	0.173986	+	0.984748i	$0.444335\pi$
$89$	−6.45448	+	14.1333i	−0.684174	+	1.49813i	−0.858159	+	0.513383i	$0.828392\pi$
$90$	−0.941076	−	6.64187i	−0.0991981	−	0.700114i
$91$			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
$96$	−1.72096	−	0.195709i	−0.175645	−	0.0199744i
$97$	5.68611	−	6.56212i	0.577337	−	0.666283i	−0.389693	−	0.920945i	$-0.627419\pi$
$97$	5.68611	−	6.56212i	0.577337	−	0.666283i	0.967030	+	0.254662i	$0.0819642\pi$
$98$	−1.46769	−	0.430952i	−0.148259	−	0.0435327i
$99$	12.1294	+	2.79488i	1.21905	+	0.280896i
$100$	4.50475	−	2.16961i	0.450475	−	0.216961i
$101$	2.88426	−	2.49923i	0.286995	−	0.248683i	−0.499450	−	0.866343i	$-0.666465\pi$
$101$	2.88426	−	2.49923i	0.286995	−	0.248683i	0.786445	+	0.617660i	$0.211919\pi$
$102$	10.5179	−	7.20749i	1.04143	−	0.713647i
$103$	1.59510	−	11.0942i	0.157170	−	1.09314i	−0.746647	−	0.665221i	$-0.768337\pi$
$103$	1.59510	−	11.0942i	0.157170	−	1.09314i	0.903817	−	0.427920i	$-0.140754\pi$
$104$	4.76694	+	0.685382i	0.467437	+	0.0672072i
$105$	8.92101	+	1.57191i	0.870601	+	0.153403i
$106$	9.92577	−	8.60073i	0.964076	−	0.835377i
$107$	−10.0925	+	4.60910i	−0.975682	+	0.445579i	−0.838461	−	0.544962i	$-0.816544\pi$
$107$	−10.0925	+	4.60910i	−0.975682	+	0.445579i	−0.137221	+	0.990541i	$0.543817\pi$
$108$	−4.21297	−	3.04153i	−0.405393	−	0.292671i
$109$	0.734577	−	2.50174i	0.0703597	−	0.239623i	−0.916803	−	0.399339i	$-0.869240\pi$
$109$	0.734577	−	2.50174i	0.0703597	−	0.239623i	0.987163	+	0.159716i	$0.0510578\pi$
$110$	0.756409	+	9.24675i	0.0721208	+	0.881643i
$111$	−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	$-0.680593\pi$
$113$	−8.66822	+	1.24630i	−0.815437	+	0.117242i	−0.278038	+	0.960570i	$0.589684\pi$
$114$	−3.43028	+	8.13984i	−0.321275	+	0.762366i
$115$	10.7149	+	0.437785i	0.999166	+	0.0408236i
$116$		−	3.16714i		−	0.294062i
$117$	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
$120$	1.20806	−	3.67975i	0.110280	−	0.335914i
$121$	−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
$125$	2.71037	+	10.8468i	0.242423	+	0.970171i
$126$	5.66827	−	4.13568i	0.504970	−	0.368436i
$127$	1.45735	+	0.209535i	0.129319	+	0.0185932i	0.206670	−	0.978411i	$-0.433737\pi$
$127$	1.45735	+	0.209535i	0.129319	+	0.0185932i	−0.0773516	+	0.997004i	$0.524646\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	3.33379	+	10.2253i	0.293524	+	0.900292i
$130$	−3.65999	+	10.1278i	−0.321002	+	0.888264i
$131$	1.40959	+	2.19337i	0.123157	+	0.191635i	0.897357	−	0.441305i	$-0.145484\pi$
$131$	1.40959	+	2.19337i	0.123157	+	0.191635i	−0.774201	+	0.632940i	$0.781848\pi$
$132$	5.56788	+	4.54350i	0.484622	+	0.395461i
$133$	−9.01443	−	7.81105i	−0.781651	−	0.677304i
$134$	1.08511	−	0.318616i	0.0937389	−	0.0275242i
$135$	8.56835	−	7.84751i	0.737446	−	0.675406i
$136$	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	$0.523317\pi$
$140$	4.21856	+	3.09120i	0.356533	+	0.261254i
$141$	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
$145$	6.93512	+	1.43457i	0.575930	+	0.119134i
$146$	−15.1613	+	6.92393i	−1.25476	+	0.573029i
$147$	−0.821252	−	2.51893i	−0.0677357	−	0.207758i
$148$	−1.66147	−	1.06776i	−0.136572	−	0.0877693i
$149$	2.78753	−	19.3877i	0.228363	−	1.58830i	−0.476640	−	0.879099i	$-0.658145\pi$
$149$	2.78753	−	19.3877i	0.228363	−	1.58830i	0.705003	−	0.709204i	$-0.250946\pi$
$150$	7.51040	+	4.31206i	0.613222	+	0.352078i
$151$	10.1818	+	6.54342i	0.828580	+	0.532496i	0.884826	−	0.465921i	$-0.154277\pi$
$151$	10.1818	+	6.54342i	0.828580	+	0.532496i	−0.0562462	+	0.998417i	$0.517913\pi$
$152$	−3.85417	+	3.33966i	−0.312614	+	0.270882i
$153$	20.5958	+	7.97101i	1.66507	+	0.644418i
$154$	−8.16370	+	5.24649i	−0.657850	+	0.422774i
$155$	2.44601	−	1.36826i	0.196468	−	0.109901i
$156$	3.68796	+	7.48193i	0.295273	+	0.599034i
$157$	21.4105	−	6.28669i	1.70874	−	0.501732i	0.726155	−	0.687531i	$-0.241305\pi$
$157$	21.4105	−	6.28669i	1.70874	−	0.501732i	0.982588	+	0.185798i	$0.0594871\pi$
$158$	−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	$-0.558368\pi$
$163$	−1.02510	+	0.147387i	−0.0802918	+	0.0115442i	0.102052	+	0.994779i	$0.467459\pi$
$164$	−9.90021	−	4.52127i	−0.773077	−	0.353052i
$165$	−12.4709	+	10.1341i	−0.970862	+	0.788936i
$166$	12.0367	+	10.4298i	0.934227	+	0.809512i
$167$	6.36947	+	1.87024i	0.492884	+	0.144724i	0.518723	−	0.854942i	$-0.326408\pi$
$167$	6.36947	+	1.87024i	0.492884	+	0.144724i	−0.0258390	+	0.999666i	$0.508226\pi$
$168$	3.99103	−	0.694808i	0.307914	−	0.0536056i
$169$	−4.23451	−	9.27227i	−0.325731	−	0.713252i
$170$	−1.00642	+	16.4300i	−0.0771889	+	1.26012i
$171$	−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	$-0.909780\pi$
$173$	0.524760	−	3.64979i	0.0398968	−	0.277488i	0.999998	+	0.00216564i	$0.000689346\pi$
$174$	4.52513	−	3.10089i	0.343049	−	0.235078i
$175$	−8.67964	+	7.83725i	−0.656119	+	0.592441i
$176$	1.72359	+	3.77414i	0.129921	+	0.284487i
$177$	−1.09697	−	6.30109i	−0.0824535	−	0.473619i
$178$	−14.9081	−	4.37740i	−1.11741	−	0.328100i
$179$	−12.0244	−	10.4192i	−0.898750	−	0.778771i	0.0771436	−	0.997020i	$-0.475420\pi$
$179$	−12.0244	−	10.4192i	−0.898750	−	0.778771i	−0.975893	+	0.218249i	$0.929965\pi$
$180$	6.44033	−	1.87673i	0.480034	−	0.139883i
$181$	6.62705	+	3.02647i	0.492585	+	0.224956i	0.646190	−	0.763176i	$-0.276361\pi$
$181$	6.62705	+	3.02647i	0.492585	+	0.224956i	−0.153606	+	0.988132i	$0.549089\pi$
$182$	−11.1493	+	1.60302i	−0.826440	+	0.118824i
$183$	4.07924	−	9.67978i	0.301546	−	0.715550i
$184$	4.57313	−	1.44447i	0.337136	−	0.106488i
$185$	3.09065	−	3.15449i	0.227229	−	0.231922i
$186$	0.549786	−	2.10019i	0.0403122	−	0.153993i
$187$	−27.7833	−	12.6882i	−2.03171	−	0.927852i
$188$	6.48086	−	1.90295i	0.472666	−	0.138787i
$189$	11.4587	+	4.04952i	0.833495	+	0.294559i
$190$	−5.56713	−	9.95223i	−0.403882	−	0.722010i
$191$	9.29975	−	5.97659i	0.672906	−	0.432451i	−0.159066	−	0.987268i	$-0.550848\pi$
$191$	9.29975	−	5.97659i	0.672906	−	0.432451i	0.831972	+	0.554817i	$0.187212\pi$
$192$	−0.0512012	−	1.73129i	−0.00369513	−	0.124945i
$193$	3.75659	−	3.25511i	0.270406	−	0.234308i	−0.509093	−	0.860711i	$-0.670019\pi$
$193$	3.75659	−	3.25511i	0.270406	−	0.234308i	0.779499	+	0.626404i	$0.215474\pi$
$194$	7.30455	+	4.69435i	0.524436	+	0.337035i
$195$	−18.0537	+	4.68661i	−1.29285	+	0.335615i
$196$	0.217692	−	1.51408i	0.0155494	−	0.108149i
$197$	−15.9181	−	10.2299i	−1.13412	−	0.728852i	−0.167701	−	0.985838i	$-0.553634\pi$
$197$	−15.9181	−	10.2299i	−1.13412	−	0.728852i	−0.966415	+	0.256986i	$0.917271\pi$
$198$	−1.04023	+	12.4037i	−0.0739263	+	0.881494i
$199$	−2.89119	+	1.32036i	−0.204951	+	0.0935980i	−0.515246	−	0.857042i	$-0.672299\pi$
$199$	−2.89119	+	1.32036i	−0.204951	+	0.0935980i	0.310295	+	0.950640i	$0.399572\pi$
$200$	2.78862	+	4.15013i	0.197185	+	0.293459i
$201$	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
$205$	14.3846	−	19.6307i	1.00467	−	1.37107i
$206$	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
$210$	−0.286320	+	9.05391i	−0.0197580	+	0.624779i
$211$	−5.95073	+	1.74729i	−0.409665	+	0.120288i	−0.480070	−	0.877230i	$-0.659389\pi$
$211$	−5.95073	+	1.74729i	−0.409665	+	0.120288i	0.0704055	+	0.997518i	$0.477571\pi$
$212$	9.92577	+	8.60073i	0.681705	+	0.590700i
$213$	−0.421951	+	0.517084i	−0.0289116	+	0.0354300i
$214$	−5.99851	−	9.33386i	−0.410049	−	0.638049i
$215$	−13.0582	−	4.71900i	−0.890564	−	0.321833i
$216$	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
$220$	−9.04499	+	2.06466i	−0.609813	+	0.139199i
$221$	−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	$-0.209107\pi$
$223$	−1.38258	−	2.15134i	−0.0925847	−	0.144065i	−0.884456	+	0.466623i	$0.845471\pi$
$224$	2.24414	+	0.658938i	0.149943	+	0.0440272i
$225$	1.19233	+	14.9525i	0.0794890	+	0.996836i
$226$	−2.46723	−	8.40262i	−0.164118	−	0.558934i
$227$	−3.00561	−	1.37261i	−0.199489	−	0.0911036i	0.313165	−	0.949699i	$-0.398611\pi$
$227$	−3.00561	−	1.37261i	−0.199489	−	0.0911036i	−0.512655	+	0.858595i	$0.671338\pi$
$228$	−8.54517	−	2.23695i	−0.565918	−	0.148146i
$229$			13.0423i			0.861861i	0.902385	+	0.430930i	$0.141815\pi$
$229$			13.0423i			0.861861i	−0.902385	+	0.430930i	$0.858185\pi$
$230$	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	$-0.863203\pi$
$233$	0.0172536	−	0.0377800i	0.00113032	−	0.00247505i	0.910196	+	0.414177i	$0.135931\pi$
$234$	−7.07918	+	12.5947i	−0.462781	+	0.823340i
$235$	1.23139	+	15.0532i	0.0803270	+	0.981960i
$236$	1.04034	−	3.54308i	0.0677204	−	0.230635i
$237$	−2.04488	−	11.7459i	−0.132829	−	0.762980i
$238$	−15.6617	+	7.15245i	−1.01520	+	0.463624i
$239$	17.2040	−	14.9073i	1.11283	−	0.964275i	0.113262	−	0.993565i	$-0.463870\pi$
$239$	17.2040	−	14.9073i	1.11283	−	0.964275i	0.999571	+	0.0292902i	$0.00932468\pi$
$240$	3.81422	+	0.672079i	0.246207	+	0.0433825i
$241$	−0.846017	−	0.121639i	−0.0544968	−	0.00783545i	0.115013	−	0.993364i	$-0.463309\pi$
$241$	−0.846017	−	0.121639i	−0.0544968	−	0.00783545i	−0.169509	+	0.985529i	$0.554218\pi$
$242$	0.884475	−	6.15166i	0.0568562	−	0.395443i
$243$	13.0713	−	8.49357i	0.838525	−	0.544863i
$244$	4.58333	−	3.97147i	0.293417	−	0.254248i
$245$	3.21679	+	1.16249i	0.205513	+	0.0742687i
$246$	−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
$250$	−10.3507	+	4.22645i	−0.654636	+	0.267304i
$251$	0.707153	+	4.91836i	0.0446351	+	0.310444i	0.999892	+	0.0146680i	$0.00466914\pi$
$251$	0.707153	+	4.91836i	0.0446351	+	0.310444i	−0.955257	+	0.295776i	$0.904422\pi$
$252$	4.90026	+	5.02201i	0.308688	+	0.316357i
$253$	−19.2024	−	5.21646i	−1.20724	−	0.327956i
$254$			1.47233i			0.0923823i
$255$	−24.4601	+	14.6483i	−1.53175	+	0.917314i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	23.4483	−	6.88505i	1.46267	−	0.429478i	0.548959	−	0.835849i	$-0.315024\pi$
$257$	23.4483	−	6.88505i	1.46267	−	0.429478i	0.913708	+	0.406371i	$0.133206\pi$
$258$	−9.64682	+	4.75507i	−0.600585	+	0.296038i
$259$	4.43214	+	1.30140i	0.275400	+	0.0808648i
$260$	−10.5456	−	2.18140i	−0.654007	−	0.135285i
$261$	8.86094	+	3.42938i	0.548479	+	0.212273i
$262$	−1.97044	+	1.70739i	−0.121734	+	0.105483i
$263$	10.3149	−	16.0503i	0.636046	−	0.989706i	−0.362292	−	0.932065i	$-0.618006\pi$
$263$	10.3149	−	16.0503i	0.636046	−	0.989706i	0.998337	−	0.0576416i	$-0.0183581\pi$
$264$	−3.70486	+	6.15782i	−0.228019	+	0.378988i
$265$	−23.3290	+	17.8388i	−1.43309	+	1.09583i
$266$	6.44866	−	10.0343i	0.395393	−	0.615243i
$267$	−8.34188	−	25.5861i	−0.510515	−	1.56584i
$268$	0.469800	+	1.02872i	0.0286976	+	0.0628389i
$269$	4.99311	+	7.76944i	0.304436	+	0.473711i	0.959440	−	0.281914i	$-0.0909694\pi$
$269$	4.99311	+	7.76944i	0.304436	+	0.473711i	−0.655004	+	0.755625i	$0.727333\pi$
$270$	8.98704	+	7.36431i	0.546934	+	0.448178i
$271$	9.17490	−	10.5884i	0.557335	−	0.643199i	−0.405241	−	0.914210i	$-0.632812\pi$
$271$	9.17490	−	10.5884i	0.557335	−	0.643199i	0.962576	+	0.271011i	$0.0873578\pi$
$272$	2.07397	+	7.06329i	0.125753	+	0.428275i
$273$	−13.2064	−	14.3603i	−0.799289	−	0.869127i
$274$	−8.84838	+	1.27221i	−0.534550	+	0.0768568i
$275$	−0.424053	−	20.7411i	−0.0255714	−	1.25074i
$276$	6.54129	+	5.11972i	0.393739	+	0.308171i
$277$			18.1513i			1.09060i	0.838240	+	0.545302i	$0.183585\pi$
$277$			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
$280$	−2.45937	+	4.61554i	−0.146976	+	0.275831i
$281$	−7.87946	+	9.09338i	−0.470049	+	0.542466i	−0.940425	−	0.340000i	$-0.889573\pi$
$281$	−7.87946	+	9.09338i	−0.470049	+	0.542466i	0.470376	+	0.882466i	$0.344118\pi$
$282$	9.06419	+	7.39656i	0.539764	+	0.440458i
$283$	14.1573	−	9.09834i	0.841564	−	0.540840i	−0.0473690	−	0.998877i	$-0.515084\pi$
$283$	14.1573	−	9.09834i	0.841564	−	0.540840i	0.888933	+	0.458037i	$0.151447\pi$
$284$	−0.350501	+	0.160068i	−0.0207984	+	0.00949832i
$285$	8.76883	−	17.6982i	0.519421	−	1.04835i
$286$	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
$290$	−0.432994	+	7.06869i	−0.0254263	+	0.415088i
$291$	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	$-0.982254\pi$
$293$	−2.19741	+	7.48370i	−0.128374	+	0.437203i	0.870072	+	0.492925i	$0.164072\pi$
$294$	2.37642	−	1.17137i	0.138596	−	0.0683160i
$295$	7.28709	+	3.88289i	0.424271	+	0.226071i
$296$	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
$300$	−3.19932	+	8.04763i	−0.184713	+	0.464630i
$301$	−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
$305$	6.62035	+	11.8350i	0.379080	+	0.677673i
$306$	−4.95879	+	21.5205i	−0.283475	+	1.23025i
$307$	−12.9762	+	5.92604i	−0.740592	+	0.338217i	−0.749732	−	0.661741i	$-0.769818\pi$
$307$	−12.9762	+	5.92604i	−0.740592	+	0.338217i	0.00914055	+	0.999958i	$0.497090\pi$
$308$	−6.35490	−	7.33395i	−0.362104	−	0.417891i
$309$	10.9738	+	16.0141i	0.624277	+	0.911009i
$310$	1.70244	+	2.22639i	0.0966919	+	0.126450i
$311$	−11.3575	−	1.63297i	−0.644026	−	0.0925970i	−0.187440	−	0.982276i	$-0.560019\pi$
$311$	−11.3575	−	1.63297i	−0.644026	−	0.0925970i	−0.456586	+	0.889679i	$0.650928\pi$
$312$	−6.88092	+	4.71521i	−0.389555	+	0.266946i
$313$	6.95776	+	8.02969i	0.393276	+	0.453865i	0.917512	−	0.397708i	$-0.130194\pi$
$313$	6.95776	+	8.02969i	0.393276	+	0.453865i	−0.524236	+	0.851573i	$0.675649\pi$
$314$	9.26973	+	20.2979i	0.523121	+	1.14548i
$315$	−13.2163	+	8.45543i	−0.744656	+	0.476409i
$316$	1.93931	−	6.60468i	0.109095	−	0.371542i
$317$	−14.4422	+	16.6672i	−0.811153	+	0.936121i	−0.998937	−	0.0460894i	$-0.985324\pi$
$317$	−14.4422	+	16.6672i	−0.811153	+	0.936121i	0.187784	+	0.982210i	$0.439870\pi$
$318$	−2.57037	+	22.6025i	−0.144139	+	1.26749i
$319$	−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
$324$	8.93714	−	1.06187i	0.496508	−	0.0589930i
$325$	9.55328	−	22.1036i	0.529921	−	1.22609i
$326$	−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
$330$	−11.8057	−	10.9018i	−0.649883	−	0.600123i
$331$	12.3913	+	14.3004i	0.681090	+	0.786019i	0.986069	−	0.166340i	$-0.0531948\pi$
$331$	12.3913	+	14.3004i	0.681090	+	0.786019i	−0.304979	+	0.952359i	$0.598649\pi$
$332$	−8.61068	+	13.3985i	−0.472572	+	0.735337i
$333$	4.78639	−	3.49224i	0.262292	−	0.191374i
$334$	−0.944738	+	6.57080i	−0.0516938	+	0.359538i
$335$	−2.46539	+	0.562764i	−0.134699	+	0.0307471i
$336$	1.25572	+	3.85152i	0.0685050	+	0.210118i
$337$	2.17083	+	4.75346i	0.118253	+	0.258938i	0.959498	−	0.281717i	$-0.0909039\pi$
$337$	2.17083	+	4.75346i	0.118253	+	0.258938i	−0.841245	+	0.540655i	$0.818177\pi$
$338$	8.57526	−	5.51099i	0.466433	−	0.299758i
$339$	9.58984	−	11.7520i	0.520848	−	0.638279i
$340$	−16.4060	+	1.34205i	−0.889738	+	0.0727830i
$341$	−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
$345$	−14.1736	+	12.0045i	−0.763081	+	0.646302i
$346$	3.68732			0.198232
$347$	1.50759	+	10.4855i	0.0809314	+	0.562890i	0.989431	+	0.145005i	$0.0463197\pi$
$347$	1.50759	+	10.4855i	0.0809314	+	0.562890i	−0.908500	+	0.417886i	$0.862771\pi$
$348$	3.71332	+	4.03777i	0.199055	+	0.216447i
$349$	−6.26294	+	1.83896i	−0.335247	+	0.0984375i	−0.445024	−	0.895519i	$-0.646805\pi$
$349$	−6.26294	+	1.83896i	−0.335247	+	0.0984375i	0.109776	+	0.993956i	$0.464987\pi$
$350$	−8.99272	−	7.47594i	−0.480681	−	0.399606i
$351$	−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	$-0.225668\pi$
$353$	−4.32225	−	9.46440i	−0.230050	−	0.503739i	−0.989091	+	0.147303i	$0.952941\pi$
$354$	6.08084	−	1.98255i	0.323193	−	0.105371i
$355$	−0.191743	−	0.840000i	−0.0101767	−	0.0445825i
$356$	2.21121	−	15.3793i	0.117194	−	0.815100i
$357$	−25.5533	−	15.3742i	−1.35242	−	0.813689i
$358$	8.60193	−	13.3849i	0.454626	−	0.707412i
$359$	−15.6130	−	18.0183i	−0.824021	−	0.950971i	0.175417	−	0.984494i	$-0.443873\pi$
$359$	−15.6130	−	18.0183i	−0.824021	−	0.950971i	−0.999438	+	0.0335237i	$0.989327\pi$
$360$	2.77419	+	6.10769i	0.146212	+	0.321904i
$361$	−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
$365$	34.7849	−	13.3806i	1.82072	−	0.700375i
$366$	10.1618	+	2.66015i	0.531165	+	0.139048i
$367$	−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
$372$	2.15705	+	0.245302i	0.111838	+	0.0127183i
$373$	−3.67482	+	4.24097i	−0.190275	+	0.219589i	−0.842869	−	0.538119i	$-0.819135\pi$
$373$	−3.67482	+	4.24097i	−0.190275	+	0.219589i	0.652594	+	0.757708i	$0.273681\pi$
$374$	8.60507	−	29.3062i	0.444958	−	1.51539i
$375$	−16.1728	−	10.6508i	−0.835162	−	0.550005i
$376$	2.80591	+	6.14408i	0.144704	+	0.316857i
$377$	−9.98846	−	11.5273i	−0.514432	−	0.593686i
$378$	−2.37757	+	11.9183i	−0.122289	+	0.613013i
$379$	31.7764	+	4.56875i	1.63224	+	0.234681i	0.896649	−	0.442742i	$-0.145994\pi$
$379$	31.7764	+	4.56875i	1.63224	+	0.234681i	0.735593	+	0.677423i	$0.236903\pi$
$380$	9.05864	−	6.92681i	0.464699	−	0.355338i
$381$	−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	$-0.847193\pi$
$383$	−21.8950	+	9.99910i	−1.11878	+	0.510930i	−0.231813	+	0.972760i	$0.574466\pi$
$384$	1.70639	−	0.297069i	0.0870786	−	0.0151597i
$385$	18.9377	−	10.5935i	0.965155	−	0.539893i
$386$	3.75659	+	3.25511i	0.191206	+	0.165681i
$387$	−16.2390	−	9.12754i	−0.825473	−	0.463979i
$388$	−3.60702	+	7.89828i	−0.183119	+	0.400974i
$389$	−1.32775	−	9.23471i	−0.0673196	−	0.468218i	−0.995398	−	0.0958322i	$-0.969449\pi$
$389$	−1.32775	−	9.23471i	−0.0673196	−	0.468218i	0.928078	−	0.372386i	$-0.121460\pi$
$390$	−7.20822	−	17.2030i	−0.365002	−	0.871108i
$391$	−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
$395$	13.5839	+	7.23814i	0.683481	+	0.364190i
$396$	−12.4255	+	0.735586i	−0.624405	+	0.0369646i
$397$	−5.07738	+	17.2920i	−0.254826	+	0.867859i	0.728351	+	0.685204i	$0.240287\pi$
$397$	−5.07738	+	17.2920i	−0.254826	+	0.867859i	−0.983177	+	0.182655i	$0.941531\pi$
$398$	−1.71838	−	2.67386i	−0.0861347	−	0.134028i
$399$	20.6505	−	0.610718i	1.03382	−	0.0305742i
$400$	−3.71103	+	3.35086i	−0.185551	+	0.167543i
$401$	17.3106	+	11.1248i	0.864449	+	0.555548i	0.896050	−	0.443953i	$-0.146424\pi$
$401$	17.3106	+	11.1248i	0.864449	+	0.555548i	−0.0316008	+	0.999501i	$0.510061\pi$
$402$	−1.00983	+	1.67844i	−0.0503660	+	0.0837128i
$403$	−5.97489	−	0.859060i	−0.297630	−	0.0427928i
$404$	−2.06332	+	3.21058i	−0.102654	+	0.159732i
$405$	−1.72291	+	20.0507i	−0.0856121	+	0.996329i
$406$	−6.73815	+	3.07721i	−0.334409	+	0.152719i
$407$	−6.89357	+	4.43023i	−0.341701	+	0.219598i
$408$	−8.06127	+	9.87877i	−0.399092	+	0.489072i
$409$	2.41616	−	2.78840i	0.119471	−	0.137877i	−0.692863	−	0.721069i	$-0.743651\pi$
$409$	2.41616	−	2.78840i	0.119471	−	0.137877i	0.812334	+	0.583192i	$0.198196\pi$
$410$	21.4780	+	11.4445i	1.06072	+	0.565202i
$411$	−10.4810	−	11.3968i	−0.516989	−	0.562161i
$412$	1.59510	+	11.0942i	0.0785850	+	0.546571i
$413$			8.63667i			0.424983i
$414$	−0.910483	+	14.3587i	−0.0447478	+	0.705689i
$415$	−25.4385	−	24.9238i	−1.24873	−	1.22346i
$416$	−4.76694	+	0.685382i	−0.233718	+	0.0336036i
$417$	2.20015	−	2.02336i	0.107742	−	0.0990841i
$418$	5.96132	+	20.3024i	0.291578	+	0.993022i
$419$	−14.6560	+	16.9140i	−0.715994	+	0.826301i	−0.990819	−	0.135193i	$-0.956834\pi$
$419$	−14.6560	+	16.9140i	−0.715994	+	0.826301i	0.274826	+	0.961494i	$0.411380\pi$
$420$	−9.00250	+	1.00510i	−0.439277	+	0.0490439i
$421$	−7.44651	−	11.5870i	−0.362921	−	0.564715i	0.610993	−	0.791636i	$-0.290770\pi$
$421$	−7.44651	−	11.5870i	−0.362921	−	0.564715i	−0.973913	+	0.226921i	$0.927134\pi$
$422$	−2.57638	−	5.64149i	−0.125416	−	0.274623i
$423$	−1.69344	+	20.1925i	−0.0823379	+	0.981794i
$424$	−7.10060	+	11.0487i	−0.344836	+	0.536575i
$425$	4.49243	−	36.5322i	0.217915	−	1.77207i
$426$	−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
$430$	2.81259	−	13.5969i	0.135635	−	0.655701i
$431$	17.7323	+	5.20668i	0.854136	+	0.250797i	0.679354	−	0.733810i	$-0.262260\pi$
$431$	17.7323	+	5.20668i	0.854136	+	0.250797i	0.174781	+	0.984607i	$0.444078\pi$
$432$	4.89921	+	1.73139i	0.235713	+	0.0833018i
$433$	−20.6839	+	6.07334i	−0.994004	+	0.291866i	−0.737993	−	0.674808i	$-0.764226\pi$
$433$	−20.6839	+	6.07334i	−0.994004	+	0.291866i	−0.256011	+	0.966674i	$0.582408\pi$
$434$	−1.21781	+	2.66664i	−0.0584569	+	0.128003i
$435$	−10.5235	+	6.30217i	−0.504564	+	0.302166i
$436$			2.60736i			0.124870i
$437$	24.1330	−	3.97245i	1.15444	−	0.190028i
$438$	11.2111	−	26.6032i	0.535686	−	1.27115i
$439$	−1.40002	−	9.73732i	−0.0668191	−	0.464737i	−0.995569	−	0.0940309i	$-0.970025\pi$
$439$	−1.40002	−	9.73732i	−0.0668191	−	0.464737i	0.928750	−	0.370706i	$-0.120884\pi$
$440$	−3.33088	−	8.65909i	−0.158793	−	0.412806i
$441$	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	$-0.257615\pi$
$443$	18.5033	+	5.43306i	0.879119	+	0.258133i	0.189130	+	0.981952i	$0.439433\pi$
$444$	3.37009	−	0.586708i	0.159937	−	0.0278439i
$445$	32.6746	+	11.8080i	1.54892	+	0.559753i
$446$	1.93268	−	1.67468i	0.0915152	−	0.0792984i
$447$	19.1773	+	27.9855i	0.907057	+	1.32367i
$448$	−0.332857	+	2.31507i	−0.0157260	+	0.109377i
$449$	−36.4667	−	5.24312i	−1.72097	−	0.247438i	−0.790150	−	0.612914i	$-0.789997\pi$
$449$	−36.4667	−	5.24312i	−1.72097	−	0.247438i	−0.930821	+	0.365476i	$0.880906\pi$
$450$	−14.6307	+	3.30817i	−0.689696	+	0.155948i
$451$	−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
$455$	25.1031	−	2.05350i	1.17685	−	0.0962695i
$456$	0.998075	−	8.77654i	0.0467391	−	0.410999i
$457$	2.34541	−	5.13574i	0.109714	−	0.240240i	−0.846809	−	0.531897i	$-0.821479\pi$
$457$	2.34541	−	5.13574i	0.109714	−	0.240240i	0.956523	+	0.291657i	$0.0942067\pi$
$458$	−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	$0.882703\pi$
$462$	4.25660	−	16.2603i	0.198035	−	0.756496i
$463$	−17.5125	−	7.99767i	−0.813873	−	0.371683i	−0.0354090	−	0.999373i	$-0.511273\pi$
$463$	−17.5125	−	7.99767i	−0.813873	−	0.371683i	−0.778464	+	0.627690i	$0.784001\pi$
$464$	0.892286	+	3.03885i	0.0414234	+	0.141075i
$465$	−1.51418	+	4.61221i	−0.0702186	+	0.213886i
$466$	0.0398509	+	0.0117013i	0.00184606	+	0.000542051i
$467$	−4.41370	−	6.86784i	−0.204241	−	0.317806i	0.723989	−	0.689811i	$-0.242307\pi$
$467$	−4.41370	−	6.86784i	−0.204241	−	0.317806i	−0.928231	+	0.372006i	$0.878670\pi$
$468$	−13.4740	−	5.21472i	−0.622834	−	0.241050i
$469$	−1.73216	−	1.99901i	−0.0799835	−	0.0923059i
$470$	−14.7247	+	3.36114i	−0.679200	+	0.155038i
$471$	−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
$475$	11.0646	+	22.9733i	0.507677	+	1.05409i
$476$	−9.30854	−	14.4844i	−0.426656	−	0.663890i
$477$	−34.8105	+	18.4572i	−1.59386	+	0.845097i
$478$	17.2040	+	14.9073i	0.786892	+	0.681845i
$479$	32.5854	−	9.56793i	1.48886	−	0.437170i	0.566686	−	0.823934i	$-0.308225\pi$
$479$	32.5854	−	9.56793i	1.48886	−	0.437170i	0.922179	+	0.386764i	$0.126407\pi$
$480$	−0.122418	+	3.87105i	−0.00558758	+	0.176688i
$481$	−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
$485$	−15.6611	−	11.4759i	−0.711135	−	0.521093i
$486$	10.2674	+	11.7295i	0.465737	+	0.532061i
$487$	−4.71268	−	16.0499i	−0.213552	−	0.727291i	−0.994689	−	0.102931i	$-0.967178\pi$
$487$	−4.71268	−	16.0499i	−0.213552	−	0.727291i	0.781137	−	0.624360i	$-0.214640\pi$
$488$	4.58333	+	3.97147i	0.207477	+	0.179780i
$489$	1.13409	−	1.38978i	0.0512852	−	0.0628480i
$490$	−0.692860	+	3.34949i	−0.0313002	+	0.151315i
$491$	−29.8520	+	13.6330i	−1.34720	+	0.615247i	−0.952774	−	0.303680i	$-0.901785\pi$
$491$	−29.8520	+	13.6330i	−1.34720	+	0.615247i	−0.394429	+	0.918927i	$0.629058\pi$
$492$	17.9227	−	5.84337i	0.808018	−	0.263439i
$493$	−19.6137	−	12.6049i	−0.883356	−	0.567698i
$494$	−3.49531	+	24.3104i	−0.157261	+	1.09378i
$495$	4.01745	−	27.5414i	0.180571	−	1.23790i
$496$	1.05443	+	0.677641i	0.0473453	+	0.0304270i
$497$	0.681097	−	0.590174i	0.0305514	−	0.0264729i
$498$	−27.5740	+	0.815471i	−1.23562	+	0.0365421i
$499$	9.07107	−	5.82962i	0.406077	−	0.260970i	−0.321620	−	0.946869i	$-0.604227\pi$
$499$	9.07107	−	5.82962i	0.406077	−	0.260970i	0.727697	+	0.685899i	$0.240591\pi$
$500$	−5.65649	−	9.64386i	−0.252966	−	0.431287i
$501$	−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	$-0.311677\pi$
$503$	6.63077	+	3.02817i	0.295651	+	0.135019i	−0.262067	+	0.965050i	$0.584404\pi$
$504$	−4.27351	+	5.56509i	−0.190357	+	0.247889i
$505$	−6.09566	−	5.97231i	−0.271253	−	0.265764i
$506$	2.43058	−	19.7493i	0.108053	−	0.877964i
$507$	16.2698	+	6.85642i	0.722569	+	0.304504i
$508$	−1.45735	+	0.209535i	−0.0646593	+	0.00929660i
$509$	31.9324	+	14.5830i	1.41538	+	0.646381i	0.968682	−	0.248304i	$-0.0798733\pi$
$509$	31.9324	+	14.5830i	1.41538	+	0.646381i	0.446696	+	0.894686i	$0.352601\pi$
$510$	−17.9803	−	22.1265i	−0.796180	−	0.979776i
$511$	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
$515$	−25.0155	−	1.53233i	−1.10232	−	0.0675225i
$516$	−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
$520$	0.658411	−	10.7487i	0.0288732	−	0.471360i
$521$	12.7175	+	27.8474i	0.557162	+	1.22001i	0.953356	+	0.301848i	$0.0976035\pi$
$521$	12.7175	+	27.8474i	0.557162	+	1.22001i	−0.396194	+	0.918167i	$0.629669\pi$
$522$	−2.13343	+	9.25880i	−0.0933776	+	0.405247i
$523$	20.3869	+	5.98613i	0.891456	+	0.261755i	0.695216	−	0.718801i	$-0.255309\pi$
$523$	20.3869	+	5.98613i	0.891456	+	0.261755i	0.196240	+	0.980556i	$0.437127\pi$
$524$	−1.97044	−	1.70739i	−0.0860789	−	0.0745878i
$525$	1.87683	−	20.1681i	0.0819117	−	0.880210i
$526$	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
$535$	12.1119	+	21.6522i	0.523643	+	0.936105i
$536$	−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
$540$	−6.01037	+	9.94362i	−0.258645	+	0.427905i
$541$	0.666518	−	4.63574i	0.0286559	−	0.199306i	−0.970464	−	0.241245i	$-0.922444\pi$
$541$	0.666518	−	4.63574i	0.0286559	−	0.199306i	0.999120	+	0.0419388i	$0.0133535\pi$
$542$	11.7863	+	7.57462i	0.506267	+	0.325358i
$543$	−11.9972	+	3.91146i	−0.514848	+	0.167857i
$544$	−6.69624	+	3.05807i	−0.287099	+	0.131114i
$545$	−5.70936	−	1.18101i	−0.244562	−	0.0505889i
$546$	12.3347	−	15.1157i	0.527876	−	0.646892i
$547$	13.7006	+	11.8717i	0.585797	+	0.507596i	0.896578	−	0.442885i	$-0.146045\pi$
$547$	13.7006	+	11.8717i	0.585797	+	0.507596i	−0.310781	+	0.950482i	$0.600591\pi$
$548$	−2.51851	−	8.57727i	−0.107586	−	0.366403i
$549$	6.14847	+	17.1234i	0.262410	+	0.730810i
$550$	20.4696	−	3.37150i	0.872828	−	0.143761i
$551$	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
$555$	−0.241774	+	7.64528i	−0.0102627	+	0.324524i
$556$	1.65584	−	0.486199i	0.0702234	−	0.0206194i
$557$	−21.6358	−	18.7475i	−0.916737	−	0.794357i	0.0622960	−	0.998058i	$-0.480158\pi$
$557$	−21.6358	−	18.7475i	−0.916737	−	0.794357i	−0.979033	+	0.203700i	$0.934703\pi$
$558$	1.76145	+	3.32212i	0.0745681	+	0.140636i
$559$	16.1676	+	25.1572i	0.683815	+	1.06404i
$560$	−4.91857	−	1.77748i	−0.207847	−	0.0751122i
$561$	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	$-0.407211\pi$
$563$	6.95926	+	1.00059i	0.293298	+	0.0421699i	0.00590472	+	0.999983i	$0.498120\pi$
$564$	−6.03130	+	10.0246i	−0.253964	+	0.422110i
$565$	4.35782	+	19.0910i	0.183335	+	0.803164i
$566$	11.0205	+	12.7184i	0.463227	+	0.534593i
$567$	−19.3565	+	8.27201i	−0.812895	+	0.347392i
$568$	−0.208321	−	0.324153i	−0.00874094	−	0.0136012i
$569$	9.35550	+	2.74702i	0.392203	+	0.115161i	0.471887	−	0.881659i	$-0.343573\pi$
$569$	9.35550	+	2.74702i	0.392203	+	0.115161i	−0.0796842	+	0.996820i	$0.525391\pi$
$570$	18.7660	+	6.16086i	0.786021	+	0.258050i
$571$	−5.33238	−	18.1604i	−0.223153	−	0.759989i	−0.992616	−	0.121298i	$-0.961294\pi$
$571$	−5.33238	−	18.1604i	−0.223153	−	0.759989i	0.769463	−	0.638691i	$-0.220524\pi$
$572$	18.1761	+	8.30075i	0.759981	+	0.347072i
$573$	−4.84895	+	18.5230i	−0.202568	+	0.773811i
$574$			25.4558i			1.06250i
$575$	−0.977742	−	23.9592i	−0.0407746	−	0.999168i
$576$	2.09513	+	2.14719i	0.0872973	+	0.0894661i
$577$	24.8903	−	3.57868i	1.03620	−	0.148982i	0.396836	−	0.917890i	$-0.370108\pi$
$577$	24.8903	−	3.57868i	1.03620	−	0.148982i	0.639360	+	0.768907i	$0.279199\pi$
$578$	15.4499	−	33.8305i	0.642629	−	1.40716i
$579$	−0.972807	+	8.55434i	−0.0404285	+	0.355506i
$580$	−7.05836	+	0.577393i	−0.293083	+	0.0239749i
$581$	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
$585$	17.5218	−	27.1421i	0.724437	−	1.12219i
$586$	−7.72025	−	1.11000i	−0.318921	−	0.0458539i
$587$	6.28755	−	43.7309i	0.259515	−	1.80497i	−0.276778	−	0.960934i	$-0.589267\pi$
$587$	6.28755	−	43.7309i	0.259515	−	1.80497i	0.536293	−	0.844032i	$-0.319824\pi$
$588$	1.49765	+	2.18553i	0.0617621	+	0.0901296i
$589$	4.83083	−	4.18594i	0.199051	−	0.172478i
$590$	−2.80631	+	7.76551i	−0.115534	+	0.319701i
$591$	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	$-0.941508\pi$
$593$	−16.1300	+	18.6150i	−0.662379	+	0.764426i	0.320785	+	0.947152i	$0.396053\pi$
$594$	−13.2166	−	17.0331i	−0.542282	−	0.698875i
$595$	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	$0.963123\pi$
$600$	−8.42103	−	2.02146i	−0.343787	−	0.0825259i
$601$	−3.82773	+	8.38156i	−0.156136	+	0.341891i	−0.971493	−	0.237068i	$-0.923814\pi$
$601$	−3.82773	+	8.38156i	−0.156136	+	0.341891i	0.815357	+	0.578959i	$0.196541\pi$
$602$	13.9349	−	4.09164i	0.567943	−	0.166763i
$603$	−3.38682	+	0.200499i	−0.137922	+	0.00816494i
$604$	−11.6128	−	3.40983i	−0.472519	−	0.138744i
$605$	−2.81507	+	13.6089i	−0.114449	+	0.553279i
$606$	−6.60736	+	0.195406i	−0.268406	+	0.00793782i
$607$	24.4841	−	21.2156i	0.993779	−	0.861114i	0.00346955	−	0.999994i	$-0.498896\pi$
$607$	24.4841	−	21.2156i	0.993779	−	0.861114i	0.990309	+	0.138880i	$0.0443502\pi$
$608$	2.75716	−	4.29022i	0.111818	−	0.173992i
$609$	−10.9938	−	6.61446i	−0.445493	−	0.268032i
$610$	−10.7724	+	8.23726i	−0.436162	+	0.333517i
$611$	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	$-0.190095\pi$
$613$	−3.45586	−	7.56728i	−0.139581	−	0.305640i	−0.966494	+	0.256691i	$0.917368\pi$
$614$	−7.71243	−	12.0008i	−0.311248	−	0.484312i
$615$	4.67714	+	41.8923i	0.188600	+	1.68926i
$616$	6.35490	−	7.33395i	0.256046	−	0.295493i
$617$	−5.79932	−	19.7507i	−0.233472	−	0.795132i	−0.989987	−	0.141156i	$-0.954918\pi$
$617$	−5.79932	−	19.7507i	−0.233472	−	0.795132i	0.756515	−	0.653976i	$-0.226900\pi$
$618$	−14.2893	+	13.1411i	−0.574802	+	0.528614i
$619$	3.01004	−	0.432778i	0.120984	−	0.0173948i	−0.0815570	−	0.996669i	$-0.525989\pi$
$619$	3.01004	−	0.432778i	0.120984	−	0.0173948i	0.202541	+	0.979274i	$0.435080\pi$
$620$	−1.96144	+	2.00196i	−0.0787735	+	0.0804005i
$621$	−21.4067	+	12.7574i	−0.859023	+	0.511938i
$622$		−	11.4743i		−	0.460078i
$623$	5.17174	+	35.9703i	0.207202	+	1.44112i
$624$	−5.64648	−	6.13984i	−0.226040	−	0.245790i
$625$	23.6794	−	8.01786i	0.947176	−	0.320715i
$626$	−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
$630$	−10.2502	−	11.8785i	−0.408379	−	0.473250i
$631$	8.35360	−	12.9985i	0.332552	−	0.517460i	−0.634203	−	0.773167i	$-0.718672\pi$
$631$	8.35360	−	12.9985i	0.332552	−	0.517460i	0.966755	+	0.255706i	$0.0823080\pi$
$632$	6.81345	+	0.979626i	0.271024	+	0.0389674i
$633$	5.53794	−	9.20455i	0.220113	−	0.365848i
$634$	−18.5528	−	11.9232i	−0.736828	−	0.473530i
$635$	0.201289	−	3.28608i	0.00798792	−	0.130404i
$636$	−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
$640$	−1.05152	+	1.97340i	−0.0415649	+	0.0780055i
$641$	−6.34196	+	13.8870i	−0.250492	+	0.548502i	−0.992551	−	0.121834i	$-0.961123\pi$
$641$	−6.34196	+	13.8870i	−0.250492	+	0.548502i	0.742058	+	0.670336i	$0.233850\pi$
$642$	18.5910	+	4.86673i	0.733727	+	0.192074i
$643$	40.8285			1.61012			0.805059	−	0.593194i	$-0.202133\pi$
$643$	40.8285			1.61012			0.805059	+	0.593194i	$0.202133\pi$
$644$	−7.51641	−	8.32596i	−0.296188	−	0.328089i
$645$	22.1807	−	9.29391i	0.873363	−	0.365948i
$646$	5.34279	+	37.1599i	0.210209	+	1.46204i
$647$	1.73917	−	3.80826i	0.0683740	−	0.149718i	−0.872359	−	0.488865i	$-0.837411\pi$
$647$	1.73917	−	3.80826i	0.0683740	−	0.149718i	0.940733	+	0.339147i	$0.110138\pi$
$648$	2.32295	+	8.69505i	0.0912542	+	0.341574i
$649$	−11.5789	−	10.0332i	−0.454513	−	0.393838i
$650$	23.2382	+	6.31037i	0.911478	+	0.247513i
$651$	−5.00236	+	0.870874i	−0.196058	+	0.0341322i
$652$	0.942050	−	0.430220i	0.0368935	−	0.0168487i
$653$	28.5889	+	32.9934i	1.11877	+	1.29113i	0.952327	+	0.305079i	$0.0986828\pi$
$653$	28.5889	+	32.9934i	1.11877	+	1.29113i	0.166443	+	0.986051i	$0.446772\pi$
$654$	−3.72533	+	2.55281i	−0.145672	+	0.0998229i
$655$	4.63121	−	3.54132i	0.180956	−	0.138371i
$656$	10.7730	+	1.54892i	0.420614	+	0.0604752i
$657$	48.9865	−	10.0285i	1.91115	−	0.391251i
$658$	−10.3454	−	11.9392i	−0.403306	−	0.465440i
$659$	−6.61988	−	14.4955i	−0.257874	−	0.564665i	0.735770	−	0.677231i	$-0.236820\pi$
$659$	−6.61988	−	14.4955i	−0.257874	−	0.564665i	−0.993644	+	0.112566i	$0.964093\pi$
$660$	9.11069	−	13.2370i	0.354633	−	0.515251i
$661$	−10.1310	+	34.5031i	−0.394051	+	1.34201i	0.488815	+	0.872388i	$0.337429\pi$
$661$	−10.1310	+	34.5031i	−0.394051	+	1.34201i	−0.882865	+	0.469626i	$0.844389\pi$
$662$	−12.3913	+	14.3004i	−0.481603	+	0.555800i
$663$	61.0124	+	6.93838i	2.36952	+	0.269464i
$664$	−14.4875	−	6.61623i	−0.562225	−	0.256760i
$665$	−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
$669$	4.28500	+	1.12172i	0.165667	+	0.0433683i
$670$	−0.907898	−	2.36021i	−0.0350752	−	0.0911828i
$671$	−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	$-0.838598\pi$
$673$	3.21079	−	10.9349i	0.123767	−	0.421511i	0.997944	+	0.0640967i	$0.0204166\pi$
$674$	−4.39614	+	2.82523i	−0.169333	+	0.108824i
$675$	−19.0512	−	17.6650i	−0.733282	−	0.679925i
$676$	6.67528	+	7.70368i	0.256742	+	0.296296i
$677$	4.19917	−	6.53403i	0.161387	−	0.251123i	−0.751137	−	0.660146i	$-0.770494\pi$
$677$	4.19917	−	6.53403i	0.161387	−	0.251123i	0.912524	+	0.409023i	$0.134131\pi$
$678$	12.9971	+	7.81975i	0.499152	+	0.300316i
$679$	2.89018	−	20.1016i	0.110915	−	0.771429i
$680$	−3.66320	−	16.0480i	−0.140477	−	0.615412i
$681$	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	$-0.840100\pi$
$683$	−20.9750	+	13.4798i	−0.802585	+	0.515790i	0.0738735	+	0.997268i	$0.476464\pi$
$684$	13.5169	−	7.16692i	0.516832	−	0.274034i
$685$	19.9225	−	1.62971i	0.761200	−	0.0622682i
$686$	−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
$690$	−13.8995	−	12.3209i	−0.529143	−	0.469049i
$691$	−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
$695$	0.314616	+	3.84604i	0.0119341	+	0.145889i
$696$	−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
$700$	6.12005	−	9.96513i	0.231316	−	0.376646i
$701$	3.47838	−	24.1927i	0.131377	−	0.913744i	−0.812386	−	0.583120i	$-0.801832\pi$
$701$	3.47838	−	24.1927i	0.131377	−	0.913744i	0.943763	−	0.330624i	$-0.107259\pi$
$702$	−5.74145	−	24.3569i	−0.216697	−	0.919292i
$703$	5.44536	−	8.47314i	0.205376	−	0.319571i
$704$	−2.71707	−	3.13567i	−0.102404	−	0.118180i
$705$	−19.2190	−	17.7475i	−0.723830	−	0.668408i
$706$	8.75294	−	5.62517i	0.329421	−	0.211706i
$707$	2.51479	−	8.56459i	0.0945784	−	0.322104i
$708$	2.82776	+	5.73680i	0.106274	+	0.215602i
$709$	4.91152	+	16.7271i	0.184456	+	0.628199i	0.998853	+	0.0478907i	$0.0152499\pi$
$709$	4.91152	+	16.7271i	0.184456	+	0.628199i	−0.814397	+	0.580309i	$0.802932\pi$
$710$	0.804162	−	0.309336i	0.0301796	−	0.0116092i
$711$	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
$715$	−26.4092	+	36.0406i	−0.987647	+	1.34784i
$716$	14.4728	+	6.60951i	0.540874	+	0.247009i
$717$	−4.45514	+	39.1761i	−0.166380	+	1.46306i
$718$	15.6130	−	18.0183i	0.582671	−	0.672438i
$719$	2.19385	−	7.47155i	0.0818166	−	0.278642i	−0.908416	−	0.418068i	$-0.862707\pi$
$719$	2.19385	−	7.47155i	0.0818166	−	0.278642i	0.990233	+	0.139426i	$0.0445257\pi$
$720$	−5.65072	+	3.61516i	−0.210590	+	0.134729i
$721$	−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
$725$	1.93278	−	15.7173i	0.0717818	−	0.583726i
$726$	6.08491	+	8.87972i	0.225832	+	0.329557i
$727$	4.52057	+	5.21702i	0.167659	+	0.193489i	0.833361	−	0.552729i	$-0.186413\pi$
$727$	4.52057	+	5.21702i	0.167659	+	0.193489i	−0.665702	+	0.746217i	$0.731868\pi$
$728$	10.2460	−	4.67921i	0.379743	−	0.173423i
$729$	−6.70625	+	26.1539i	−0.248379	+	0.968663i
$730$	18.1949	+	32.5265i	0.673422	+	1.20386i
$731$	34.5459	+	29.9342i	1.27773	+	1.10716i
$732$	−1.18690	+	10.4369i	−0.0438690	+	0.385760i
$733$	−15.6214	+	34.2061i	−0.576989	+	1.26343i	0.366003	+	0.930614i	$0.380726\pi$
$733$	−15.6214	+	34.2061i	−0.576989	+	1.26343i	−0.942992	+	0.332816i	$0.892001\pi$
$734$	−1.69991	−	11.8231i	−0.0627448	−	0.436399i
$735$	−5.46404	+	2.28948i	−0.201544	+	0.0844488i
$736$	−3.98093	+	2.67436i	−0.146739	+	0.0985781i
$737$	4.69227			0.172842
$738$	25.8966	+	19.8864i	0.953269	+	0.732028i
$739$	−2.79524	+	6.12073i	−0.102825	+	0.225155i	−0.954051	−	0.299644i	$-0.903132\pi$
$739$	−2.79524	+	6.12073i	−0.102825	+	0.225155i	0.851226	+	0.524799i	$0.175859\pi$
$740$	−2.07674	+	3.89744i	−0.0763423	+	0.143273i
$741$	−38.1563	+	18.8079i	−1.40171	+	0.690924i
$742$	8.65428	−	29.4738i	0.317709	−	1.08202i
$743$	19.2016	+	29.8783i	0.704440	+	1.09613i	0.990446	+	0.137902i	$0.0440359\pi$
$743$	19.2016	+	29.8783i	0.704440	+	1.09613i	−0.286006	+	0.958228i	$0.592328\pi$
$744$	0.0641757	+	2.17001i	0.00235280	+	0.0795564i
$745$	−43.7161	−	2.67784i	−1.60163	−	0.0981083i
$746$	−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
$750$	8.24075	−	17.5240i	0.300910	−	0.639885i
$751$	17.5657	−	8.02199i	0.640982	−	0.292727i	−0.0682859	−	0.997666i	$-0.521753\pi$
$751$	17.5657	−	8.02199i	0.640982	−	0.292727i	0.709268	+	0.704939i	$0.249026\pi$
$752$	−5.68222	+	3.65174i	−0.207209	+	0.133165i
$753$	−6.66808	−	5.44129i	−0.242999	−	0.198292i
$754$	9.98846	−	11.5273i	0.363758	−	0.419800i
$755$	12.7266	−	23.8842i	0.463169	−	0.869236i
$756$	−12.1354	−	0.657210i	−0.441360	−	0.0239025i
$757$	−2.79276	−	19.4241i	−0.101505	−	0.705981i	−0.975492	−	0.220033i	$-0.929383\pi$
$757$	−2.79276	−	19.4241i	−0.101505	−	0.705981i	0.873988	−	0.485948i	$-0.161526\pi$
$758$			32.1031i			1.16604i
$759$	30.5971	−	15.8634i	1.11060	−	0.575806i
$760$	8.14548	+	7.98065i	0.295468	+	0.289489i
$761$	15.0024	−	2.15702i	0.543838	−	0.0781921i	0.135080	−	0.990835i	$-0.456871\pi$
$761$	15.0024	−	2.15702i	0.543838	−	0.0781921i	0.408758	+	0.912643i	$0.365962\pi$
$762$	−1.72624	−	1.87707i	−0.0625350	−	0.0679990i
$763$	−1.71809	−	5.85127i	−0.0621989	−	0.211830i
$764$	−7.23925	+	8.35454i	−0.261907	+	0.302256i
$765$	14.0096	−	47.3534i	0.506519	−	1.71206i
$766$	−13.0133	−	20.2491i	−0.470190	−	0.731629i
$767$	−7.38760	−	16.1766i	−0.266751	−	0.584103i
$768$	0.536889	+	1.64674i	0.0193733	+	0.0594216i
$769$	−5.21934	+	8.12145i	−0.188214	+	0.292867i	−0.922518	−	0.385954i	$-0.873872\pi$
$769$	−5.21934	+	8.12145i	−0.188214	+	0.292867i	0.734304	+	0.678821i	$0.237509\pi$
$770$	13.1808	+	17.2373i	0.475001	+	0.621191i
$771$	−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	$-0.616039\pi$
$773$	14.3883	−	12.4675i	0.517510	−	0.448425i	0.874037	+	0.485860i	$0.161494\pi$
$774$	6.72359	−	17.3727i	0.241675	−	0.624447i
$775$	−3.49526	−	5.20179i	−0.125554	−	0.186854i
$776$	−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
$780$	16.0021	−	9.58309i	0.572966	−	0.343130i
$781$			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
$786$	0.510264	−	4.48699i	0.0182005	−	0.160046i
$787$	−0.773676	+	0.892870i	−0.0275786	+	0.0318274i	−0.769371	−	0.638802i	$-0.779430\pi$
$787$	−0.773676	+	0.892870i	−0.0275786	+	0.0318274i	0.741793	+	0.670629i	$0.233976\pi$
$788$	18.1554	+	5.33090i	0.646759	+	0.189905i
$789$	5.66780	+	32.5563i	0.201779	+	1.15903i
$790$	−5.23127	+	14.4758i	−0.186120	+	0.515024i
$791$	−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
$795$	8.82687	−	50.0948i	0.313057	−	1.77668i
$796$	2.40209	−	2.08142i	0.0851397	−	0.0737740i
$797$	−0.864647	+	0.394871i	−0.0306274	+	0.0139871i	−0.430670	−	0.902510i	$-0.641723\pi$
$797$	−0.864647	+	0.394871i	−0.0306274	+	0.0139871i	0.400042	+	0.916497i	$0.368995\pi$
$798$	3.54338	+	20.3534i	0.125434	+	0.720504i
$799$	14.0086	−	47.7087i	0.495587	−	1.68781i
$800$	−3.84489	−	3.19638i	−0.135937	−	0.113009i
$801$	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
$805$	21.6360	−	12.6875i	0.762570	−	0.447175i
$806$		−	6.03633i		−	0.212621i
$807$	−15.4750	−	4.05103i	−0.544745	−	0.142603i
$808$	−3.47154	−	1.58540i	−0.122129	−	0.0557742i
$809$	0.951643	+	3.24100i	0.0334580	+	0.113947i	0.974529	−	0.224262i	$-0.0719970\pi$
$809$	0.951643	+	3.24100i	0.0334580	+	0.113947i	−0.941071	+	0.338209i	$0.890179\pi$
$810$	−20.0918	+	1.14814i	−0.705955	+	0.0403416i
$811$	−3.36442	−	0.987882i	−0.118141	−	0.0346892i	0.222128	−	0.975018i	$-0.428700\pi$
$811$	−3.36442	−	0.987882i	−0.118141	−	0.0346892i	−0.340268	+	0.940328i	$0.610518\pi$
$812$	−4.00483	−	6.23163i	−0.140542	−	0.218687i
$813$	0.717352	+	24.2562i	0.0251586	+	0.850703i
$814$	−5.36619	−	6.19291i	−0.188085	−	0.217061i
$815$	0.515352	+	2.25769i	0.0180520	+	0.0790833i
$816$	−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
$820$	−8.27134	+	22.8881i	−0.288848	+	0.799287i
$821$	9.02626	+	14.0451i	0.315019	+	0.490179i	0.962269	−	0.272099i	$-0.0877177\pi$
$821$	9.02626	+	14.0451i	0.315019	+	0.490179i	−0.647251	+	0.762277i	$0.724081\pi$
$822$	9.78916	−	11.9962i	0.341436	−	0.418417i
$823$	−15.3096	−	13.2659i	−0.533660	−	0.462419i	0.345857	−	0.938287i	$-0.387588\pi$
$823$	−15.3096	−	13.2659i	−0.533660	−	0.462419i	−0.879516	+	0.475868i	$0.842134\pi$
$824$	−10.7542	+	3.15773i	−0.374642	+	0.110005i
$825$	24.8586	+	25.9455i	0.865464	+	0.903308i
$826$	−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	$0.845717\pi$
$830$	21.0498	−	28.7266i	0.730649	−	0.997116i
$831$	−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
$835$	3.00687	−	14.5361i	0.104057	−	0.503043i
$836$	−19.2474	+	8.78997i	−0.665684	+	0.304008i
$837$	−3.02196	+	5.76934i	−0.104454	+	0.199418i
$838$	−18.8276	−	12.0997i	−0.650387	−	0.417979i
$839$	−0.0889258	+	0.618492i	−0.00307006	+	0.0213527i	−0.991299	−	0.131630i	$-0.957979\pi$
$839$	−0.0889258	+	0.618492i	−0.00307006	+	0.0213527i	0.988229	+	0.152983i	$0.0488880\pi$
$840$	−2.27606	−	8.76783i	−0.0785315	−	0.302519i
$841$	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
$845$	−19.8924	+	11.1275i	−0.684320	+	0.382799i
$846$	−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	$-0.297497\pi$
$853$	40.6201	−	5.84029i	1.39081	−	0.199968i	0.796679	+	0.604403i	$0.206588\pi$
$854$	−12.9026	−	5.89240i	−0.441517	−	0.201634i
$855$	9.57096	+	32.8444i	0.327320	+	1.12325i
$856$	8.38518	+	7.26580i	0.286599	+	0.248340i
$857$	19.6281	+	5.76332i	0.670483	+	0.196871i	0.599218	−	0.800586i	$-0.295478\pi$
$857$	19.6281	+	5.76332i	0.670483	+	0.196871i	0.0712647	+	0.997457i	$0.477297\pi$
$858$	5.93598	+	34.0967i	0.202651	+	1.16404i
$859$	8.13909	+	17.8221i	0.277702	+	0.608083i	0.996166	−	0.0874810i	$-0.0278817\pi$
$859$	8.13909	+	17.8221i	0.277702	+	0.608083i	−0.718464	+	0.695564i	$0.755154\pi$
$860$	13.8588	+	0.848922i	0.472581	+	0.0289480i
$861$	−36.3706	+	24.9233i	−1.23951	+	0.849383i
$862$	−2.63011	+	18.2928i	−0.0895819	+	0.623056i
$863$	−6.54288	+	45.5068i	−0.222722	+	1.54907i	0.504953	+	0.863147i	$0.331510\pi$
$863$	−6.54288	+	45.5068i	−0.222722	+	1.54907i	−0.727676	+	0.685921i	$0.759399\pi$
$864$	−1.01654	+	5.09575i	−0.0345834	+	0.173361i
$865$	−8.22967	−	0.504110i	−0.279817	−	0.0171403i
$866$	−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
$870$	−7.73568	−	9.51950i	−0.262264	−	0.322741i
$871$	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	$-0.327388\pi$
$877$	6.12197	+	2.79581i	0.206724	+	0.0944078i	−0.309362	+	0.950944i	$0.600116\pi$
$878$	9.43897	−	2.77153i	0.318550	−	0.0935347i
$879$	−5.97281	−	12.1173i	−0.201458	−	0.408706i
$880$	8.09692	−	4.52929i	0.272947	−	0.152682i
$881$	−33.9780	+	21.8363i	−1.14475	+	0.735684i	−0.968586	−	0.248677i	$-0.920004\pi$
$881$	−33.9780	+	21.8363i	−1.14475	+	0.735684i	−0.176160	+	0.984361i	$0.556368\pi$
$882$	−1.65630	+	4.27962i	−0.0557707	+	0.144102i
$883$	−1.02468	+	0.887888i	−0.0344832	+	0.0298798i	−0.671932	−	0.740613i	$-0.734535\pi$
$883$	−1.02468	+	0.887888i	−0.0344832	+	0.0298798i	0.637449	+	0.770493i	$0.279990\pi$
$884$	29.8246	+	19.1671i	1.00311	+	0.644659i
$885$	−13.8428	+	3.59348i	−0.465320	+	0.120793i
$886$	−2.74447	+	19.0882i	−0.0922021	+	0.641280i
$887$	38.1701	+	24.5304i	1.28163	+	0.823650i	0.991087	−	0.133213i	$-0.0425295\pi$
$887$	38.1701	+	24.5304i	1.28163	+	0.823650i	0.290538	+	0.956864i	$0.406166\pi$
$888$	1.06035	+	3.25229i	0.0355830	+	0.109140i
$889$	3.13241	−	1.43053i	0.105058	−	0.0479783i
$890$	−7.03773	+	34.0225i	−0.235905	+	1.14044i
$891$	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
$895$	−21.0284	+	28.6975i	−0.702903	+	0.959251i
$896$	−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
$900$	−5.35665	−	14.0109i	−0.178555	−	0.467031i
$901$	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
$905$	5.53671	−	15.3209i	0.184046	−	0.509285i
$906$	−6.49801	−	19.9306i	−0.215882	−	0.662151i
$907$	34.3109	+	22.0503i	1.13927	+	0.732167i	0.967476	−	0.252965i	$-0.0814056\pi$
$907$	34.3109	+	22.0503i	1.13927	+	0.732167i	0.171799	+	0.985132i	$0.445042\pi$
$908$	3.27057	+	0.470237i	0.108538	+	0.0156053i
$909$	−6.74833	−	9.24911i	−0.223828	−	0.306774i
$910$	5.60514	+	24.5553i	0.185808	+	0.814001i
$911$	1.31019	+	1.51204i	0.0434086	+	0.0500962i	0.777039	−	0.629453i	$-0.216721\pi$
$911$	1.31019	+	1.51204i	0.0434086	+	0.0500962i	−0.733630	+	0.679549i	$0.762175\pi$
$912$	8.82925	−	0.261116i	0.292366	−	0.00864641i
$913$	35.7264	+	55.5914i	1.18237	+	1.83981i
$914$	5.41725	+	1.59065i	0.179187	+	0.0526139i
$915$	−22.3163	−	7.32641i	−0.737753	−	0.242204i
$916$	−3.67445	−	12.5140i	−0.121407	−	0.413475i
$917$	5.54699	+	2.53323i	0.183178	+	0.0836545i
$918$	−18.9098	−	33.2503i	−0.624117	−	1.09742i
$919$			11.1166i			0.366703i	0.983047	+	0.183351i	$0.0586946\pi$
$919$			11.1166i			0.366703i	−0.983047	+	0.183351i	$0.941305\pi$
$920$	−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
$924$	16.7005	+	1.89920i	0.549407	+	0.0624790i
$925$	−7.59361	−	6.31281i	−0.249676	−	0.207564i
$926$	5.42398	−	18.4724i	0.178243	−	0.607040i
$927$	−32.7662	−	7.55003i	−1.07618	−	0.247975i
$928$	−2.88093	+	1.31568i	−0.0945712	+	0.0431892i
$929$	−27.9781	+	24.2432i	−0.917933	+	0.795394i	−0.979236	−	0.202725i	$-0.935020\pi$
$929$	−27.9781	+	24.2432i	−0.917933	+	0.795394i	0.0613023	+	0.998119i	$0.480475\pi$
$930$	−4.78076	−	0.842386i	−0.156767	−	0.0276229i
$931$	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
$935$	−23.2121	+	64.2316i	−0.759117	+	2.10060i
$936$	3.24409	−	14.0789i	0.106036	−	0.460185i
$937$	−26.5481	−	7.79523i	−0.867289	−	0.254659i	−0.182327	−	0.983238i	$-0.558363\pi$
$937$	−26.5481	−	7.79523i	−0.867289	−	0.254659i	−0.684962	+	0.728579i	$0.740181\pi$
$938$	1.73216	−	1.99901i	0.0565569	−	0.0652701i
$939$	−18.2848	−	2.07937i	−0.596703	−	0.0678575i
$940$	−5.42248	−	14.0965i	−0.176862	−	0.459777i
$941$	2.01244	+	13.9968i	0.0656036	+	0.456283i	0.995973	+	0.0896584i	$0.0285775\pi$
$941$	2.01244	+	13.9968i	0.0656036	+	0.456283i	−0.930369	+	0.366624i	$0.880513\pi$
$942$	−35.6162	−	15.0093i	−1.16044	−	0.489031i
$943$	−38.7441	+	34.9769i	−1.26168	+	1.13901i
$944$			3.69265i			0.120186i
$945$	6.93586	−	26.2753i	0.225624	−	0.854735i
$946$	−10.7026	+	23.4354i	−0.347970	+	0.761949i
$947$	−44.1059	+	12.9507i	−1.43325	+	0.420840i	−0.903966	−	0.427605i	$-0.859358\pi$
$947$	−44.1059	+	12.9507i	−1.43325	+	0.420840i	−0.529284	+	0.848445i	$0.677539\pi$
$948$	5.27125	+	10.6940i	0.171202	+	0.347326i
$949$	−77.0185	−	22.6147i	−2.50013	−	0.734103i
$950$	−21.1648	+	14.2214i	−0.686678	+	0.461403i
$951$	−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	$-0.741268\pi$
$953$	7.98742	−	12.4287i	0.258738	−	0.402604i	0.946183	+	0.323632i	$0.104904\pi$
$954$	−23.2234	−	31.8295i	−0.751885	−	1.03052i
$955$	−15.0150	−	19.6361i	−0.485873	−	0.635408i
$956$	−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
$960$	−3.84907	+	0.429736i	−0.124228	+	0.0138697i
$961$	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
$970$	9.13027	−	17.1349i	0.293155	−	0.550169i
$971$	13.6438	−	15.7458i	0.437850	−	0.505306i	−0.493341	−	0.869836i	$-0.664225\pi$
$971$	13.6438	−	15.7458i	0.437850	−	0.505306i	0.931192	+	0.364529i	$0.118770\pi$
$972$	−10.1489	+	11.8321i	−0.325527	+	0.379516i
$973$	−3.39556	+	2.18219i	−0.108857	+	0.0699580i
$974$	15.2159	−	6.94885i	0.487548	−	0.222656i
$975$	13.7360	+	39.3806i	0.439904	+	1.26119i
$976$	−3.27877	+	5.10187i	−0.104951	+	0.163307i
$977$	33.1411	+	4.76497i	1.06028	+	0.152445i	0.650320	−	0.759660i	$-0.274635\pi$
$977$	33.1411	+	4.76497i	1.06028	+	0.152445i	0.409957	+	0.912105i	$0.365544\pi$
$978$	1.53703	+	0.924757i	0.0491488	+	0.0295705i
$979$	−54.2324	−	34.8530i	−1.73327	−	1.11391i
$980$	−3.41400	−	0.209125i	−0.109056	−	0.00668026i
$981$	−7.29480	−	2.82324i	−0.232905	−	0.0901393i
$982$	−17.7426	−	27.6080i	−0.566189	−	0.881007i
$983$	−9.52862	+	32.4515i	−0.303916	+	1.03504i	0.656002	+	0.754759i	$0.272246\pi$
$983$	−9.52862	+	32.4515i	−0.303916	+	1.03504i	−0.959917	+	0.280283i	$0.909572\pi$
$984$	8.33456	+	16.9087i	0.265696	+	0.539029i
$985$	−19.8967	+	37.3404i	−0.633961	+	1.18976i
$986$	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
$990$	27.8329	+	0.0570027i	0.884586	+	0.00181166i
$991$	−6.87067	−	47.7865i	−0.218254	−	1.51799i	−0.744480	−	0.667645i	$-0.767303\pi$
$991$	−6.87067	−	47.7865i	−0.218254	−	1.51799i	0.526226	−	0.850345i	$-0.323607\pi$
$992$	−0.520682	+	1.14014i	−0.0165317	+	0.0361993i
$993$	−32.5642	−	3.70322i	−1.03339	−	0.117518i
$994$	0.681097	+	0.590174i	0.0216031	+	0.0187192i
$995$	3.46968	+	6.20266i	0.109996	+	0.196638i
$996$	−4.73136	−	27.1772i	−0.149919	−	0.861144i
$997$	−25.2514	+	11.5319i	−0.799720	+	0.365220i	−0.772986	−	0.634423i	$-0.781238\pi$
$997$	−25.2514	+	11.5319i	−0.799720	+	0.365220i	−0.0267335	+	0.999643i	$0.508511\pi$
$998$	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.b.89.6	yes	240
3.2	odd	2		690.2.n.a.89.12	✓	240
5.4	even	2		690.2.n.a.89.19	yes	240
15.14	odd	2	inner	690.2.n.b.89.13	yes	240
23.15	odd	22	inner	690.2.n.b.659.13	yes	240
69.38	even	22		690.2.n.a.659.19	yes	240
115.84	odd	22		690.2.n.a.659.12	yes	240
345.314	even	22	inner	690.2.n.b.659.6	yes	240

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.27489 + 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.182307 - 2.22862i) q^{5} +(-1.34195 - 1.09506i) q^{6} +(1.96759 - 1.26449i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.250714 - 2.98951i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-1.27489 + 1.17245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.182307 - 2.22862i) 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} +(2.17999 - 0.497618i) 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} +(2.84538 + 2.62751i) 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} +(0.802799 + 2.08699i) q^{20} +(-1.02591 + 3.91900i) q^{21} -4.14909 q^{22} +(-0.585811 + 4.75992i) q^{23} +(1.59611 + 0.672631i) q^{24} +(-4.93353 + 0.812589i) 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} +(-2.19583 + 3.19035i) 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} +(-3.17679 - 4.15449i) 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} +(-1.95149 + 1.09164i) 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} +(-6.70819 - 0.0137386i) q^{45} +(-4.79484 + 0.0975584i) q^{46} -6.75447 q^{47} +(-0.438635 + 1.67559i) q^{48} +(-0.635439 + 1.39142i) q^{49} +(-1.50643 - 4.76767i) 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} +(9.26028 + 0.567240i) 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} +(-3.47038 - 1.71945i) 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} +(9.50381 + 5.06407i) 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} +(5.33701 - 6.82029i) 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} +(-1.35825 - 1.77627i) 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} +(16.1195 + 3.33441i) 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} +(-0.941076 - 6.64187i) 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} +(-1.72096 - 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	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) \) 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 - 102 * 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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