LMFDB - Embedded newform 690.2.w.a.217.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.10
Character	$\chi$	$=$	690.217
Dual form			690.2.w.a.283.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.842847 - 2.07114i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.76897 - 2.05801i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.842847 - 2.07114i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.76897 - 2.05801i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-2.12599 + 0.692946i) q^{10} +(2.64636 + 2.29308i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(0.489708 - 0.896834i) q^{13} +(-1.78389 - 3.90618i) q^{14} +(-1.26384 - 1.84465i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.373122 - 0.279315i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(-0.218004 + 1.51625i) q^{19} +(0.539515 + 2.17001i) q^{20} +(3.24537 - 2.81213i) q^{21} +(2.47603 - 2.47603i) q^{22} +(-1.03924 - 4.68188i) q^{23} +1.00000i q^{24} +(-3.57922 + 3.49130i) q^{25} +(-0.859613 - 0.552440i) q^{26} +(0.800541 - 0.599278i) q^{27} +(-4.02349 + 1.50068i) q^{28} +(-7.70426 + 1.10771i) q^{29} +(-1.93011 + 1.12902i) q^{30} +(4.48357 - 2.88141i) q^{31} +(0.349464 - 0.936950i) q^{32} +(3.07331 + 1.67815i) q^{33} +(-0.305222 + 0.352245i) q^{34} +(-7.43908 - 6.07146i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.546607 + 0.203874i) q^{37} +(1.49684 + 0.325617i) q^{38} +(0.287881 - 0.980433i) q^{39} +(2.20297 - 0.383333i) q^{40} +(-3.64571 + 7.98298i) q^{41} +(-2.57344 - 3.43772i) q^{42} +(-0.635179 - 2.91987i) q^{43} +(-2.29308 - 2.64636i) q^{44} +(-1.62706 - 1.53384i) q^{45} +(-4.74409 + 0.702595i) q^{46} +(-0.989385 - 0.989385i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(6.18520 - 9.62437i) q^{49} +(3.22707 + 3.81917i) q^{50} +(-0.423967 - 0.193619i) q^{51} +(-0.612357 + 0.818013i) q^{52} +(-5.43578 - 9.95488i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(2.51881 - 7.41369i) q^{55} +(1.20983 + 4.12029i) q^{56} +(0.109281 + 1.52794i) q^{57} +(0.555267 + 7.76365i) q^{58} +(0.205474 + 0.699779i) q^{59} +(0.988453 + 2.00573i) q^{60} +(3.11627 + 4.84901i) q^{61} +(-2.55422 - 4.67770i) q^{62} +(2.57344 - 3.43772i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-2.27022 - 0.258359i) q^{65} +(1.89313 - 2.94576i) q^{66} +(11.8224 + 0.845557i) q^{67} +(0.329573 + 0.329573i) q^{68} +(-2.01070 - 4.35397i) q^{69} +(-6.58668 + 6.98700i) q^{70} +(9.63328 + 11.1174i) q^{71} +(0.212565 + 0.977147i) q^{72} +(1.88888 + 2.52325i) q^{73} +(0.242349 - 0.530670i) q^{74} +(-2.75529 + 4.17233i) q^{75} +(0.431571 - 1.46979i) q^{76} +(14.6932 + 3.19631i) q^{77} +(-0.957398 - 0.357091i) q^{78} +(-8.14319 + 2.39106i) q^{79} +(-0.225199 - 2.22470i) q^{80} +(0.654861 - 0.755750i) q^{81} +(7.70256 + 4.20592i) q^{82} +(-3.42938 + 9.19453i) q^{83} +(-3.61255 + 2.32164i) q^{84} +(-0.264016 + 1.00821i) q^{85} +(-2.95775 + 0.425260i) q^{86} +(-7.29273 + 2.72005i) q^{87} +(-2.80320 + 2.09845i) q^{88} +(-1.85091 - 1.18951i) q^{89} +(-1.64601 + 1.51349i) q^{90} -4.38796i q^{91} +(0.362365 + 4.78212i) q^{92} +(3.76862 - 3.76862i) q^{93} +(-1.05745 + 0.916282i) q^{94} +(3.32411 - 0.826453i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.94979 + 13.2709i) q^{97} +(-9.15860 - 6.85604i) q^{98} +(3.35979 + 0.986524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$2$	0.0713392	−	0.997452i	0.0504444	−	0.705305i
$3$	0.977147	−	0.212565i	0.564156	−	0.122725i
$3$	0.977147	−	0.212565i	0.564156	−	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−0.842847	−	2.07114i	−0.376933	−	0.926241i
$5$	−0.842847	−	2.07114i	−0.376933	−	0.926241i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	3.76897	−	2.05801i	1.42453	−	0.777855i	0.432241	−	0.901758i	$-0.357723\pi$
$7$	3.76897	−	2.05801i	1.42453	−	0.777855i	0.992294	+	0.123903i	$0.0395413\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	−2.12599	+	0.692946i	−0.672296	+	0.219129i
$11$	2.64636	+	2.29308i	0.797907	+	0.691391i	0.955135	−	0.296172i	$-0.0957101\pi$
$11$	2.64636	+	2.29308i	0.797907	+	0.691391i	−0.157227	+	0.987562i	$0.550256\pi$
$12$	−0.997452	+	0.0713392i	−0.287940	+	0.0205938i
$13$	0.489708	−	0.896834i	0.135821	−	0.248737i	−0.800912	−	0.598782i	$-0.795652\pi$
$13$	0.489708	−	0.896834i	0.135821	−	0.248737i	0.936733	+	0.350045i	$0.113834\pi$
$14$	−1.78389	−	3.90618i	−0.476765	−	1.04397i
$15$	−1.26384	−	1.84465i	−0.326321	−	0.476285i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−0.373122	−	0.279315i	−0.0904953	−	0.0677439i	0.553072	−	0.833133i	$-0.313455\pi$
$17$	−0.373122	−	0.279315i	−0.0904953	−	0.0677439i	−0.643567	+	0.765390i	$0.722546\pi$
$18$	−0.349464	−	0.936950i	−0.0823695	−	0.220841i
$19$	−0.218004	+	1.51625i	−0.0500136	+	0.347852i	0.949414	+	0.314027i	$0.101678\pi$
$19$	−0.218004	+	1.51625i	−0.0500136	+	0.347852i	−0.999428	+	0.0338256i	$0.989231\pi$
$20$	0.539515	+	2.17001i	0.120639	+	0.485228i
$21$	3.24537	−	2.81213i	0.708198	−	0.613657i
$22$	2.47603	−	2.47603i	0.527891	−	0.527891i
$23$	−1.03924	−	4.68188i	−0.216697	−	0.976239i
$23$	−1.03924	−	4.68188i	−0.216697	−	0.976239i
$24$			1.00000i			0.204124i
$25$	−3.57922	+	3.49130i	−0.715844	+	0.698261i
$26$	−0.859613	−	0.552440i	−0.168584	−	0.108342i
$27$	0.800541	−	0.599278i	0.154064	−	0.115331i
$28$	−4.02349	+	1.50068i	−0.760368	+	0.283603i
$29$	−7.70426	+	1.10771i	−1.43064	+	0.205696i	−0.813688	−	0.581302i	$-0.802544\pi$
$29$	−7.70426	+	1.10771i	−1.43064	+	0.205696i	−0.616957	+	0.786997i	$0.711635\pi$
$30$	−1.93011	+	1.12902i	−0.352388	+	0.206130i
$31$	4.48357	−	2.88141i	0.805273	−	0.517517i	−0.0720599	−	0.997400i	$-0.522957\pi$
$31$	4.48357	−	2.88141i	0.805273	−	0.517517i	0.877332	+	0.479883i	$0.159321\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	3.07331	+	1.67815i	0.534995	+	0.292129i
$34$	−0.305222	+	0.352245i	−0.0523451	+	0.0604095i
$35$	−7.43908	−	6.07146i	−1.25743	−	1.02626i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	0.546607	+	0.203874i	0.0898616	+	0.0335167i	0.393993	−	0.919113i	$-0.371093\pi$
$37$	0.546607	+	0.203874i	0.0898616	+	0.0335167i	−0.304131	+	0.952630i	$0.598366\pi$
$38$	1.49684	+	0.325617i	0.242819	+	0.0528221i
$39$	0.287881	−	0.980433i	0.0460979	−	0.156995i
$40$	2.20297	−	0.383333i	0.348319	−	0.0606103i
$41$	−3.64571	+	7.98298i	−0.569364	+	1.24673i	0.377772	+	0.925899i	$0.376690\pi$
$41$	−3.64571	+	7.98298i	−0.569364	+	1.24673i	−0.947136	+	0.320834i	$0.896037\pi$
$42$	−2.57344	−	3.43772i	−0.397091	−	0.530451i
$43$	−0.635179	−	2.91987i	−0.0968639	−	0.445276i	−0.999877	−	0.0156639i	$-0.995014\pi$
$43$	−0.635179	−	2.91987i	−0.0968639	−	0.445276i	0.903013	−	0.429612i	$-0.141350\pi$
$44$	−2.29308	−	2.64636i	−0.345695	−	0.398954i
$45$	−1.62706	−	1.53384i	−0.242548	−	0.228652i
$46$	−4.74409	+	0.702595i	−0.699477	+	0.103592i
$47$	−0.989385	−	0.989385i	−0.144317	−	0.144317i	0.631257	−	0.775574i	$-0.282539\pi$
$47$	−0.989385	−	0.989385i	−0.144317	−	0.144317i	−0.775574	+	0.631257i	$0.782539\pi$
$48$	0.997452	+	0.0713392i	0.143970	+	0.0102969i
$49$	6.18520	−	9.62437i	0.883601	−	1.37491i
$50$	3.22707	+	3.81917i	0.456377	+	0.540112i
$51$	−0.423967	−	0.193619i	−0.0593673	−	0.0271121i
$52$	−0.612357	+	0.818013i	−0.0849186	+	0.113438i
$53$	−5.43578	−	9.95488i	−0.746662	−	1.36741i	−0.923666	−	0.383198i	$-0.874823\pi$
$53$	−5.43578	−	9.95488i	−0.746662	−	1.36741i	0.177004	−	0.984210i	$-0.443359\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	2.51881	−	7.41369i	0.339637	−	0.999662i
$56$	1.20983	+	4.12029i	0.161670	+	0.550597i
$57$	0.109281	+	1.52794i	0.0144746	+	0.202381i
$58$	0.555267	+	7.76365i	0.0729102	+	1.01942i
$59$	0.205474	+	0.699779i	0.0267504	+	0.0911035i	0.971786	−	0.235863i	$-0.0757917\pi$
$59$	0.205474	+	0.699779i	0.0267504	+	0.0911035i	−0.945036	+	0.326967i	$0.893974\pi$
$60$	0.988453	+	2.00573i	0.127609	+	0.258939i
$61$	3.11627	+	4.84901i	0.398997	+	0.620852i	0.981383	−	0.192061i	$-0.0615171\pi$
$61$	3.11627	+	4.84901i	0.398997	+	0.620852i	−0.582386	+	0.812912i	$0.697881\pi$
$62$	−2.55422	−	4.67770i	−0.324386	−	0.594069i
$63$	2.57344	−	3.43772i	0.324223	−	0.433112i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−2.27022	−	0.258359i	−0.281586	−	0.0320455i
$66$	1.89313	−	2.94576i	0.233028	−	0.362598i
$67$	11.8224	+	0.845557i	1.44434	+	0.103301i	0.771379	−	0.636377i	$-0.219568\pi$
$67$	11.8224	+	0.845557i	1.44434	+	0.103301i	0.672961	+	0.739678i	$0.265022\pi$
$68$	0.329573	+	0.329573i	0.0399666	+	0.0399666i
$69$	−2.01070	−	4.35397i	−0.242060	−	0.524157i
$70$	−6.58668	+	6.98700i	−0.787259	+	0.835106i
$71$	9.63328	+	11.1174i	1.14326	+	1.31939i	0.940356	+	0.340193i	$0.110492\pi$
$71$	9.63328	+	11.1174i	1.14326	+	1.31939i	0.202904	+	0.979199i	$0.434962\pi$
$72$	0.212565	+	0.977147i	0.0250511	+	0.115158i
$73$	1.88888	+	2.52325i	0.221076	+	0.295324i	0.897343	−	0.441333i	$-0.145494\pi$
$73$	1.88888	+	2.52325i	0.221076	+	0.295324i	−0.676267	+	0.736657i	$0.736403\pi$
$74$	0.242349	−	0.530670i	0.0281725	−	0.0616891i
$75$	−2.75529	+	4.17233i	−0.318154	+	0.481780i
$76$	0.431571	−	1.46979i	0.0495046	−	0.168597i
$77$	14.6932	+	3.19631i	1.67445	+	0.364254i
$78$	−0.957398	−	0.357091i	−0.108404	−	0.0404326i
$79$	−8.14319	+	2.39106i	−0.916181	+	0.269015i	−0.705640	−	0.708570i	$-0.749341\pi$
$79$	−8.14319	+	2.39106i	−0.916181	+	0.269015i	−0.210540	+	0.977585i	$0.567522\pi$
$80$	−0.225199	−	2.22470i	−0.0251780	−	0.248729i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	7.70256	+	4.20592i	0.850606	+	0.464466i
$83$	−3.42938	+	9.19453i	−0.376424	+	1.00923i	0.601242	+	0.799067i	$0.294673\pi$
$83$	−3.42938	+	9.19453i	−0.376424	+	1.00923i	−0.977666	+	0.210164i	$0.932600\pi$
$84$	−3.61255	+	2.32164i	−0.394161	+	0.253312i
$85$	−0.264016	+	1.00821i	−0.0286366	+	0.109355i
$86$	−2.95775	+	0.425260i	−0.318942	+	0.0458569i
$87$	−7.29273	+	2.72005i	−0.781863	+	0.291620i
$88$	−2.80320	+	2.09845i	−0.298822	+	0.223696i
$89$	−1.85091	−	1.18951i	−0.196196	−	0.126087i	0.438855	−	0.898558i	$-0.355384\pi$
$89$	−1.85091	−	1.18951i	−0.196196	−	0.126087i	−0.635050	+	0.772471i	$0.719021\pi$
$90$	−1.64601	+	1.51349i	−0.173504	+	0.159536i
$91$		−	4.38796i		−	0.459983i
$92$	0.362365	+	4.78212i	0.0377792	+	0.498571i
$93$	3.76862	−	3.76862i	0.390787	−	0.390787i
$94$	−1.05745	+	0.916282i	−0.109067	+	0.0945073i
$95$	3.32411	−	0.826453i	0.341047	−	0.0847923i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	4.94979	+	13.2709i	0.502575	+	1.34746i	0.902414	+	0.430871i	$0.141794\pi$
$97$	4.94979	+	13.2709i	0.502575	+	1.34746i	−0.399838	+	0.916586i	$0.630934\pi$
$98$	−9.15860	−	6.85604i	−0.925158	−	0.692565i
$99$	3.35979	+	0.986524i	0.337672	+	0.0991494i
$100$	4.03965	−	2.94639i	0.403965	−	0.294639i
$101$	−8.23439	−	18.0308i	−0.819352	−	1.79413i	−0.560354	−	0.828253i	$-0.689335\pi$
$101$	−8.23439	−	18.0308i	−0.819352	−	1.79413i	−0.258998	−	0.965878i	$-0.583392\pi$
$102$	−0.223372	+	0.409075i	−0.0221171	+	0.0405044i
$103$	4.70851	−	0.336759i	0.463943	−	0.0331819i	0.162588	−	0.986694i	$-0.448016\pi$
$103$	4.70851	−	0.336759i	0.463943	−	0.0331819i	0.301355	+	0.953512i	$0.402561\pi$
$104$	0.772243	+	0.669153i	0.0757247	+	0.0656158i
$105$	−8.55966	−	4.35141i	−0.835337	−	0.424654i
$106$	−10.3173	+	4.71176i	−1.00211	+	0.457646i
$107$	−1.86494	+	8.57301i	−0.180291	+	0.828784i	0.794781	+	0.606896i	$0.207586\pi$
$107$	−1.86494	+	8.57301i	−0.180291	+	0.828784i	−0.975072	+	0.221888i	$0.928778\pi$
$108$	−0.877679	+	0.479249i	−0.0844547	+	0.0461158i
$109$	0.941118	+	6.54562i	0.0901427	+	0.626957i	0.983942	+	0.178489i	$0.0571209\pi$
$109$	0.941118	+	6.54562i	0.0901427	+	0.626957i	−0.893799	+	0.448467i	$0.851970\pi$
$110$	−7.21511	−	3.04128i	−0.687934	−	0.289975i
$111$	0.577452	+	0.0830250i	0.0548093	+	0.00788039i
$112$	4.19610	−	0.912807i	0.396495	−	0.0862521i
$113$	−1.23404	+	17.2541i	−0.116088	+	1.62313i	0.521847	+	0.853039i	$0.325243\pi$
$113$	−1.23404	+	17.2541i	−0.116088	+	1.62313i	−0.637936	+	0.770090i	$0.720211\pi$
$114$	1.53185			0.143470
$115$	−8.82089	+	6.09852i	−0.822552	+	0.568690i
$116$	7.78348			0.722678
$117$	0.0728961	−	1.01922i	0.00673925	−	0.0942270i
$118$	0.712655	−	0.155029i	0.0656052	−	0.0142715i
$119$	−1.98112	−	0.284842i	−0.181609	−	0.0261114i
$120$	2.07114	−	0.842847i	0.189068	−	0.0769411i
$121$	0.179522	+	1.24860i	0.0163202	+	0.113510i
$122$	5.05896	−	2.76240i	0.458017	−	0.250096i
$123$	−1.86549	+	8.57550i	−0.168205	+	0.773226i
$124$	−4.84800	+	2.21401i	−0.435363	+	0.198824i
$125$	10.2477	+	4.47042i	0.916582	+	0.399846i
$126$	−3.24537	−	2.81213i	−0.289121	−	0.250524i
$127$	−12.1271	+	0.867350i	−1.07611	+	0.0769649i	−0.598125	−	0.801403i	$-0.704087\pi$
$127$	−12.1271	+	0.867350i	−1.07611	+	0.0769649i	−0.477985	+	0.878368i	$0.658633\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	−1.24133	−	2.71813i	−0.109293	−	0.239318i
$130$	−0.419656	+	2.24600i	−0.0368063	+	0.196987i
$131$	−1.92181	−	0.564295i	−0.167910	−	0.0493027i	0.196697	−	0.980464i	$-0.436978\pi$
$131$	−1.92181	−	0.564295i	−0.167910	−	0.0493027i	−0.364607	+	0.931162i	$0.618797\pi$
$132$	−2.80320	−	2.09845i	−0.243987	−	0.182647i
$133$	2.29881	+	6.16336i	0.199333	+	0.534431i
$134$	1.68681	−	11.7320i	0.145718	−	1.01349i
$135$	−1.91592	−	1.15293i	−0.164896	−	0.0992285i
$136$	0.352245	−	0.305222i	0.0302048	−	0.0261726i
$137$	14.3078	−	14.3078i	1.22240	−	1.22240i	0.255622	−	0.966777i	$-0.417720\pi$
$137$	14.3078	−	14.3078i	1.22240	−	1.22240i	0.966777	−	0.255622i	$-0.0822802\pi$
$138$	−4.48632	+	1.69497i	−0.381901	+	0.144285i
$139$			3.17705i			0.269474i	0.990881	+	0.134737i	$0.0430189\pi$
$139$			3.17705i			0.269474i	−0.990881	+	0.134737i	$0.956981\pi$
$140$	6.49931	+	7.06835i	0.549292	+	0.597384i
$141$	−1.17708	−	0.756466i	−0.0991283	−	0.0637059i
$142$	11.7763	−	8.81563i	0.988245	−	0.739791i
$143$	3.35246	−	1.25040i	0.280347	−	0.104564i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	8.78772	+	15.0229i	0.729780	+	1.24759i
$146$	2.65157	−	1.70406i	0.219445	−	0.141029i
$147$	3.99805	−	10.7192i	0.329753	−	0.884103i
$148$	−0.512029	−	0.279589i	−0.0420885	−	0.0229821i
$149$	8.12511	−	9.37688i	0.665635	−	0.768184i	−0.318052	−	0.948073i	$-0.603029\pi$
$149$	8.12511	−	9.37688i	0.665635	−	0.768184i	0.983687	+	0.179890i	$0.0575740\pi$
$150$	3.96514	+	3.04592i	0.323753	+	0.248699i
$151$	12.6768	−	3.72225i	1.03163	−	0.302913i	0.278254	−	0.960508i	$-0.410244\pi$
$151$	12.6768	−	3.72225i	1.03163	−	0.302913i	0.753372	+	0.657595i	$0.228426\pi$
$152$	−1.43526	−	0.535325i	−0.116415	−	0.0434206i
$153$	−0.455435	−	0.0990739i	−0.0368198	−	0.00800965i
$154$	4.23637	−	14.4278i	0.341377	−	1.16262i
$155$	−9.74677	−	6.85749i	−0.782879	−	0.550807i
$156$	−0.424481	+	0.929484i	−0.0339857	+	0.0744183i
$157$	4.03037	+	5.38395i	0.321659	+	0.429686i	0.932003	−	0.362450i	$-0.118060\pi$
$157$	4.03037	+	5.38395i	0.321659	+	0.429686i	−0.610344	+	0.792136i	$0.708969\pi$
$158$	1.80404	+	8.29302i	0.143521	+	0.659757i
$159$	−7.42762	−	8.57193i	−0.589048	−	0.679798i
$160$	−2.23510	+	0.0659171i	−0.176700	+	0.00521120i
$161$	−13.5522	−	15.5071i	−1.06807	−	1.22213i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	1.29032	+	0.0922857i	0.101066	+	0.00722838i	0.121781	−	0.992557i	$-0.461140\pi$
$163$	1.29032	+	0.0922857i	0.101066	+	0.00722838i	−0.0207146	+	0.999785i	$0.506594\pi$
$164$	4.74469	−	7.38289i	0.370498	−	0.576507i
$165$	0.885358	−	7.77968i	0.0689250	−	0.605647i
$166$	8.92646	+	4.07658i	0.692827	+	0.316404i
$167$	−1.08387	+	1.44788i	−0.0838720	+	0.112040i	−0.840515	−	0.541789i	$-0.817747\pi$
$167$	−1.08387	+	1.44788i	−0.0838720	+	0.112040i	0.756643	+	0.653829i	$0.226838\pi$
$168$	2.05801	+	3.76897i	0.158779	+	0.290782i
$169$	6.46383	+	10.0579i	0.497218	+	0.773686i
$170$	0.986803	+	0.335268i	0.0756843	+	0.0257139i
$171$	0.431571	+	1.46979i	0.0330030	+	0.112398i
$172$	0.213173	+	2.98055i	0.0162543	+	0.227265i
$173$	0.695733	+	9.72762i	0.0528956	+	0.739577i	0.952821	+	0.303533i	$0.0981663\pi$
$173$	0.695733	+	9.72762i	0.0528956	+	0.739577i	−0.899925	+	0.436044i	$0.856379\pi$
$174$	2.19286	+	7.46820i	0.166240	+	0.566163i
$175$	−6.30481	+	20.5247i	−0.476599	+	1.55152i
$176$	1.89313	+	2.94576i	0.142700	+	0.222045i
$177$	0.349527	+	0.640111i	0.0262721	+	0.0481137i
$178$	−1.31852	+	1.76133i	−0.0988271	+	0.132018i
$179$	−17.9069	−	8.17780i	−1.33842	−	0.611238i	−0.387846	−	0.921724i	$-0.626781\pi$
$179$	−17.9069	−	8.17780i	−1.33842	−	0.611238i	−0.950578	+	0.310486i	$0.899508\pi$
$180$	1.39221	+	1.74978i	0.103769	+	0.130421i
$181$	−1.30004	+	2.02290i	−0.0966311	+	0.150361i	−0.886203	−	0.463297i	$-0.846666\pi$
$181$	−1.30004	+	2.02290i	−0.0966311	+	0.150361i	0.789572	+	0.613658i	$0.210303\pi$
$182$	−4.37678	−	0.313034i	−0.324429	−	0.0232036i
$183$	4.07578	+	4.07578i	0.301290	+	0.301290i
$184$	4.79579	−	0.0202895i	0.353550	−	0.00149576i
$185$	−0.0384553	−	1.30393i	−0.00282729	−	0.0958670i
$186$	−3.49016	−	4.02786i	−0.255911	−	0.295337i
$187$	−0.346921	−	1.59477i	−0.0253693	−	0.116621i
$188$	0.838511	+	1.12012i	0.0611547	+	0.0816931i
$189$	1.78389	−	3.90618i	0.129759	−	0.284133i
$190$	−0.587208	−	3.37460i	−0.0426005	−	0.244819i
$191$	−0.0241154	+	0.0821296i	−0.00174493	+	0.00594269i	−0.960361	−	0.278760i	$-0.910077\pi$
$191$	−0.0241154	+	0.0821296i	−0.00174493	+	0.00594269i	0.958616	+	0.284703i	$0.0918948\pi$
$192$	−0.977147	−	0.212565i	−0.0705195	−	0.0153406i
$193$	20.6081	+	7.68643i	1.48341	+	0.553282i	0.955233	−	0.295855i	$-0.0956047\pi$
$193$	20.6081	+	7.68643i	1.48341	+	0.553282i	0.528173	+	0.849137i	$0.322877\pi$
$194$	13.5902	−	3.99045i	0.975720	−	0.286497i
$195$	−2.27325	+	0.230114i	−0.162791	+	0.0164788i
$196$	−7.49194	+	8.64616i	−0.535138	+	0.617583i
$197$	21.5771	+	11.7820i	1.53731	+	0.839432i	0.999992	−	0.00395021i	$-0.00125740\pi$
$197$	21.5771	+	11.7820i	1.53731	+	0.839432i	0.537313	+	0.843383i	$0.319439\pi$
$198$	1.22370	−	3.28086i	0.0869643	−	0.233160i
$199$	−13.6796	+	8.79136i	−0.969723	+	0.623203i	−0.926672	−	0.375870i	$-0.877344\pi$
$199$	−13.6796	+	8.79136i	−0.969723	+	0.623203i	−0.0430505	+	0.999073i	$0.513708\pi$
$200$	−2.65070	−	4.23955i	−0.187433	−	0.299782i
$201$	11.7320	−	1.68681i	0.827511	−	0.118978i
$202$	−18.5723	+	6.92710i	−1.30674	+	0.487389i
$203$	−26.7574	+	20.0303i	−1.87800	+	1.40585i
$204$	0.392097	+	0.251986i	0.0274523	+	0.0176425i
$205$	19.6066	+	0.822324i	1.36939	+	0.0574336i
$206$		−	4.72054i		−	0.328895i
$207$	−2.89025	−	3.82707i	−0.200886	−	0.266000i
$208$	0.722539	−	0.722539i	0.0500991	−	0.0500991i
$209$	−4.05381	+	3.51265i	−0.280408	+	0.242975i
$210$	−4.95096	+	8.22742i	−0.341649	+	0.567746i
$211$	−0.0604568	+	0.420486i	−0.00416201	+	0.0289474i	−0.991797	−	0.127826i	$-0.959200\pi$
$211$	−0.0604568	+	0.420486i	−0.00416201	+	0.0289474i	0.987635	+	0.156773i	$0.0501092\pi$
$212$	3.96372	+	10.6271i	0.272230	+	0.729876i
$213$	11.7763	+	8.81563i	0.806899	+	0.604037i
$214$	8.41813	+	2.47178i	0.575451	+	0.168968i
$215$	−5.51210	+	3.77655i	−0.375922	+	0.257558i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	10.9684	−	20.0872i	0.744585	−	1.36361i
$218$	6.59608	−	0.471761i	0.446743	−	0.0319517i
$219$	2.38207	+	2.06407i	0.160965	+	0.139477i
$220$	−3.54825	+	6.97976i	−0.239223	+	0.470576i
$221$	−0.433220	+	0.197845i	−0.0291416	+	0.0133085i
$222$	0.124008	−	0.570058i	0.00832290	−	0.0382598i
$223$	7.43040	−	4.05731i	0.497577	−	0.271697i	−0.210804	−	0.977528i	$-0.567608\pi$
$223$	7.43040	−	4.05731i	0.497577	−	0.271697i	0.708380	+	0.705831i	$0.249426\pi$
$224$	−0.611134	−	4.25053i	−0.0408331	−	0.284001i
$225$	−1.80543	+	4.66266i	−0.120362	+	0.310844i
$226$	17.1221	+	2.46179i	1.13895	+	0.163756i
$227$	−4.83296	+	1.05135i	−0.320775	+	0.0697803i	−0.370070	−	0.929004i	$-0.620666\pi$
$227$	−4.83296	+	1.05135i	−0.320775	+	0.0697803i	0.0492948	+	0.998784i	$0.484303\pi$
$228$	0.109281	−	1.52794i	0.00723728	−	0.101190i
$229$	−17.0077			−1.12390			−0.561949	−	0.827172i	$-0.689948\pi$
$229$	−17.0077			−1.12390			−0.561949	+	0.827172i	$0.689948\pi$
$230$	5.45371	+	9.23347i	0.359607	+	0.608837i
$231$	15.0369			0.989353
$232$	0.555267	−	7.76365i	0.0364551	−	0.509709i
$233$	23.7042	−	5.15653i	1.55291	−	0.337815i	0.647405	−	0.762146i	$-0.275854\pi$
$233$	23.7042	−	5.15653i	1.55291	−	0.337815i	0.905507	+	0.424331i	$0.139491\pi$
$234$	−1.01142	−	0.145421i	−0.0661188	−	0.00950645i
$235$	−1.21525	+	2.88305i	−0.0792743	+	0.188070i
$236$	−0.103793	−	0.721899i	−0.00675637	−	0.0469916i
$237$	−7.44884	+	4.06737i	−0.483854	+	0.264204i
$238$	−0.425447	+	1.95575i	−0.0275776	+	0.126772i
$239$	21.6988	−	9.90953i	1.40358	−	0.640994i	0.437497	−	0.899220i	$-0.355865\pi$
$239$	21.6988	−	9.90953i	1.40358	−	0.640994i	0.966085	+	0.258226i	$0.0831378\pi$
$240$	−0.692946	−	2.12599i	−0.0447295	−	0.137232i
$241$	−20.0686	−	17.3895i	−1.29273	−	1.12016i	−0.985709	−	0.168456i	$-0.946122\pi$
$241$	−20.0686	−	17.3895i	−1.29273	−	1.12016i	−0.307022	−	0.951702i	$-0.599333\pi$
$242$	1.25823	−	0.0899904i	0.0808821	−	0.00578480i
$243$	0.479249	−	0.877679i	0.0307438	−	0.0563031i
$244$	−2.39446	−	5.24314i	−0.153290	−	0.335658i
$245$	−25.1466	−	4.69854i	−1.60655	−	0.300179i
$246$	8.42056	+	2.47250i	0.536876	+	0.157641i
$247$	1.25307	+	0.938036i	0.0797309	+	0.0596858i
$248$	1.86251	+	4.99359i	0.118270	+	0.317093i
$249$	−1.39657	+	9.71338i	−0.0885042	+	0.615560i
$250$	5.19009	−	9.90268i	0.328250	−	0.626300i
$251$	−12.3253	+	10.6799i	−0.777964	+	0.674110i	−0.950441	−	0.310904i	$-0.899368\pi$
$251$	−12.3253	+	10.6799i	−0.777964	+	0.674110i	0.172477	+	0.985014i	$0.444823\pi$
$252$	−3.03649	+	3.03649i	−0.191281	+	0.191281i
$253$	7.98572	−	14.7730i	0.502058	−	0.928770i
$254$			12.1581i			0.762868i
$255$	−0.0436727	+	1.04129i	−0.00273489	+	0.0652079i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	3.84358	−	2.87727i	0.239756	−	0.179479i	−0.472643	−	0.881254i	$-0.656700\pi$
$257$	3.84358	−	2.87727i	0.239756	−	0.179479i	0.712398	+	0.701775i	$0.247609\pi$
$258$	−2.79976	+	1.04426i	−0.174305	+	0.0650125i
$259$	2.47972	−	0.356529i	0.154082	−	0.0221537i
$260$	2.21034	+	0.578815i	0.137079	+	0.0358966i
$261$	−6.54788	+	4.20807i	−0.405304	+	0.260473i
$262$	−0.699958	+	1.87666i	−0.0432436	+	0.115941i
$263$	0.778721	+	0.425214i	0.0480180	+	0.0262198i	0.503079	−	0.864241i	$-0.332201\pi$
$263$	0.778721	+	0.425214i	0.0480180	+	0.0262198i	−0.455061	+	0.890460i	$0.650382\pi$
$264$	−2.29308	+	2.64636i	−0.141129	+	0.162872i
$265$	−16.0364	+	19.6487i	−0.985108	+	1.20701i
$266$	6.31165	−	1.85327i	0.386992	−	0.113631i
$267$	−2.06146	−	0.768884i	−0.126159	−	0.0470549i
$268$	−11.5818	−	2.51946i	−0.707469	−	0.153900i
$269$	−1.30709	+	4.45155i	−0.0796948	+	0.271416i	−0.989695	−	0.143193i	$-0.954263\pi$
$269$	−1.30709	+	4.45155i	−0.0796948	+	0.271416i	0.910000	+	0.414608i	$0.136081\pi$
$270$	−1.28667	+	1.82879i	−0.0783045	+	0.111297i
$271$	0.660947	−	1.44727i	0.0401496	−	0.0879155i	−0.888494	−	0.458887i	$-0.848248\pi$
$271$	0.660947	−	1.44727i	0.0401496	−	0.0879155i	0.928644	+	0.370972i	$0.120975\pi$
$272$	−0.279315	−	0.373122i	−0.0169360	−	0.0226238i
$273$	−0.932728	−	4.28768i	−0.0564513	−	0.259502i
$274$	−13.2506	−	15.2921i	−0.800501	−	0.923827i
$275$	−17.4777	+	1.03180i	−1.05395	+	0.0622198i
$276$	1.37060	+	4.59581i	0.0825003	+	0.276635i
$277$	−12.3269	−	12.3269i	−0.740654	−	0.740654i	0.232050	−	0.972704i	$-0.425457\pi$
$277$	−12.3269	−	12.3269i	−0.740654	−	0.740654i	−0.972704	+	0.232050i	$0.925457\pi$
$278$	3.16895	+	0.226648i	0.190061	+	0.0135934i
$279$	2.88141	−	4.48357i	0.172506	−	0.268424i
$280$	7.51399	−	5.97850i	0.449047	−	0.357283i
$281$	0.989054	+	0.451686i	0.0590020	+	0.0269453i	0.444697	−	0.895681i	$-0.353311\pi$
$281$	0.989054	+	0.451686i	0.0590020	+	0.0269453i	−0.385695	+	0.922626i	$0.626038\pi$
$282$	−0.838511	+	1.12012i	−0.0499326	+	0.0667021i
$283$	−8.11537	−	14.8622i	−0.482409	−	0.883466i	−0.999619	−	0.0276072i	$-0.991211\pi$
$283$	−8.11537	−	14.8622i	−0.482409	−	0.883466i	0.517210	−	0.855858i	$-0.326971\pi$
$284$	−7.95305	−	12.3752i	−0.471927	−	0.734333i
$285$	3.07247	−	1.51416i	0.181997	−	0.0896909i
$286$	−1.00805	−	3.43312i	−0.0596075	−	0.203005i
$287$	2.68852	+	37.5905i	0.158699	+	2.21890i
$288$	−0.0713392	−	0.997452i	−0.00420370	−	0.0587754i
$289$	−4.72825	−	16.1029i	−0.278132	−	0.947232i
$290$	15.6116	−	7.69360i	0.916744	−	0.451784i
$291$	7.65761	+	11.9155i	0.448897	+	0.698497i
$292$	−1.51056	−	2.76638i	−0.0883986	−	0.161890i
$293$	−6.98130	+	9.32593i	−0.407852	+	0.544827i	−0.956692	−	0.291101i	$-0.905979\pi$
$293$	−6.98130	+	9.32593i	−0.407852	+	0.544827i	0.548840	+	0.835927i	$0.315069\pi$
$294$	−10.4066	−	4.75256i	−0.606928	−	0.277175i
$295$	1.27616	−	1.01537i	0.0743007	−	0.0591172i
$296$	−0.315404	+	0.490779i	−0.0183325	+	0.0285259i
$297$	3.49271	+	0.249804i	0.202668	+	0.0144951i
$298$	−8.77335	−	8.77335i	−0.508226	−	0.508226i
$299$	−4.70779	−	1.36072i	−0.272259	−	0.0786928i
$300$	3.32103	−	3.73775i	0.191740	−	0.215799i
$301$	−8.40310	−	9.69769i	−0.484346	−	0.558966i
$302$	−2.80841	−	12.9101i	−0.161606	−	0.742891i
$303$	−11.8789	−	15.8684i	−0.682426	−	0.911615i
$304$	−0.636352	+	1.39342i	−0.0364973	+	0.0799179i
$305$	7.41642	−	10.5412i	0.424663	−	0.603587i
$306$	−0.131312	+	0.447207i	−0.00750660	+	0.0255651i
$307$	−31.9818	−	6.95721i	−1.82530	−	0.397069i	−0.836701	−	0.547660i	$-0.815519\pi$
$307$	−31.9818	−	6.95721i	−1.82530	−	0.397069i	−0.988596	+	0.150591i	$0.951882\pi$
$308$	−14.0888	−	5.25484i	−0.802783	−	0.299423i
$309$	4.52932	−	1.32993i	0.257664	−	0.0756570i
$310$	−7.53535	+	9.23272i	−0.427979	+	0.524383i
$311$	22.1693	−	25.5847i	1.25710	−	1.45077i	0.416488	−	0.909141i	$-0.363261\pi$
$311$	22.1693	−	25.5847i	1.25710	−	1.45077i	0.840615	−	0.541633i	$-0.182194\pi$
$312$	0.896834	+	0.489708i	0.0507732	+	0.0277243i
$313$	4.18891	−	11.2309i	0.236771	−	0.634809i	−0.763164	−	0.646205i	$-0.776355\pi$
$313$	4.18891	−	11.2309i	0.236771	−	0.634809i	0.999935	+	0.0113966i	$0.00362773\pi$
$314$	5.65775	−	3.63602i	0.319286	−	0.205192i
$315$	−9.28900	−	2.43248i	−0.523376	−	0.137055i
$316$	8.40059	−	1.20782i	0.472570	−	0.0679453i
$317$	−10.7824	+	4.02163i	−0.605600	+	0.225877i	−0.633512	−	0.773733i	$-0.718387\pi$
$317$	−10.7824	+	4.02163i	−0.605600	+	0.225877i	0.0279114	+	0.999610i	$0.491114\pi$
$318$	−9.07997	+	6.79718i	−0.509179	+	0.381167i
$319$	−22.9283	−	14.7351i	−1.28374	−	0.825008i
$320$	−0.0937008	+	2.23410i	−0.00523804	+	0.124890i
$321$			8.77351i			0.489690i
$322$	−16.4343	+	12.4114i	−0.915851	+	0.691662i
$323$	0.504855	−	0.504855i	0.0280909	−	0.0280909i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	1.37835	+	4.91968i	0.0764569	+	0.272895i
$326$	0.184101	−	1.28045i	0.0101964	−	0.0709177i
$327$	2.31098	+	6.19598i	0.127798	+	0.342639i
$328$	−7.02560	−	5.25929i	−0.387924	−	0.290396i
$329$	−5.76512	−	1.69279i	−0.317842	−	0.0933267i
$330$	−7.69669	−	1.43810i	−0.423689	−	0.0791647i
$331$	2.85749	+	6.25704i	0.157062	+	0.343918i	0.971761	−	0.235966i	$-0.0758253\pi$
$331$	2.85749	+	6.25704i	0.157062	+	0.343918i	−0.814699	+	0.579884i	$0.803098\pi$
$332$	4.70300	−	8.61289i	0.258110	−	0.472694i
$333$	0.581903	−	0.0416186i	0.0318881	−	0.00228068i
$334$	1.36686	+	1.18439i	0.0747915	+	0.0648072i
$335$	−8.21324	−	25.1985i	−0.448737	−	1.37674i
$336$	3.90618	−	1.78389i	0.213100	−	0.0973193i
$337$	4.52532	−	20.8025i	0.246510	−	1.13319i	−0.672853	−	0.739776i	$-0.734931\pi$
$337$	4.52532	−	20.8025i	0.246510	−	1.13319i	0.919363	−	0.393411i	$-0.128705\pi$
$338$	10.4934	−	5.72984i	0.570767	−	0.311662i
$339$	2.46179	+	17.1221i	0.133706	+	0.929945i
$340$	0.404811	−	0.960371i	0.0219540	−	0.0520834i
$341$	18.4724	+	2.65594i	1.00034	+	0.143827i
$342$	1.49684	−	0.325617i	0.0809397	−	0.0176074i
$343$	1.36034	−	19.0200i	0.0734514	−	1.02698i
$344$	2.98816			0.161111
$345$	−7.32297	+	7.83417i	−0.394255	+	0.421777i
$346$	9.75247			0.524296
$347$	−1.94684	+	27.2204i	−0.104512	+	1.46127i	0.626778	+	0.779198i	$0.284373\pi$
$347$	−1.94684	+	27.2204i	−0.104512	+	1.46127i	−0.731290	+	0.682067i	$0.761081\pi$
$348$	7.60561	−	1.65450i	0.407703	−	0.0886904i
$349$	−0.0222219	−	0.00319503i	−0.00118951	−	0.000171026i	0.141720	−	0.989907i	$-0.454737\pi$
$349$	−0.0222219	−	0.00319503i	−0.00118951	−	0.000171026i	−0.142910	+	0.989736i	$0.545646\pi$
$350$	20.0226	+	7.75296i	1.07025	+	0.414413i
$351$	−0.145421	−	1.01142i	−0.00776199	−	0.0539858i
$352$	3.07331	−	1.67815i	0.163808	−	0.0894460i
$353$	1.76953	−	8.13441i	0.0941828	−	0.432951i	−0.905775	−	0.423759i	$-0.860710\pi$
$353$	1.76953	−	8.13441i	0.0941828	−	0.432951i	0.999958	−	0.00919220i	$-0.00292601\pi$
$354$	0.663415	−	0.302971i	0.0352601	−	0.0161027i
$355$	14.9063	−	29.3221i	0.791142	−	1.55626i
$356$	1.66278	+	1.44081i	0.0881274	+	0.0763628i
$357$	−1.99639	+	0.142785i	−0.105660	+	0.00755696i
$358$	−9.43443	+	17.2779i	−0.498625	+	0.913164i
$359$	5.55506	+	12.1639i	0.293185	+	0.641985i	0.997706	−	0.0676982i	$-0.0215655\pi$
$359$	5.55506	+	12.1639i	0.293185	+	0.641985i	−0.704521	+	0.709683i	$0.748838\pi$
$360$	1.84465	−	1.26384i	0.0972213	−	0.0666101i
$361$	15.9789	+	4.69182i	0.840993	+	0.246938i
$362$	1.92500	+	1.44104i	0.101176	+	0.0757393i
$363$	0.440830	+	1.18191i	0.0231376	+	0.0620342i
$364$	−0.624472	+	4.34330i	−0.0327312	+	0.227651i
$365$	3.63395	−	6.03884i	0.190210	−	0.316087i
$366$	4.35616	−	3.77463i	0.227700	−	0.197303i
$367$	−11.7369	+	11.7369i	−0.612661	+	0.612661i	−0.943639	−	0.330978i	$-0.892622\pi$
$367$	−11.7369	+	11.7369i	−0.612661	+	0.612661i	0.330978	+	0.943639i	$0.392622\pi$
$368$	0.321890	−	4.78502i	0.0167797	−	0.249436i
$369$			8.77606i			0.456863i
$370$	−1.30335	−	0.0546641i	−0.0677581	−	0.00284185i
$371$	−40.9745	−	26.3327i	−2.12729	−	1.36713i
$372$	−4.26659	+	3.19393i	−0.221212	+	0.165597i
$373$	−26.2412	+	9.78748i	−1.35872	+	0.506776i	−0.920025	−	0.391860i	$-0.871832\pi$
$373$	−26.2412	+	9.78748i	−1.35872	+	0.506776i	−0.438695	+	0.898636i	$0.644559\pi$
$374$	−1.61545	+	0.232267i	−0.0835331	+	0.0120102i
$375$	10.9638	+	2.18995i	0.566166	+	0.113088i
$376$	1.17708	−	0.756466i	0.0607035	−	0.0390117i
$377$	−2.77941	+	7.45189i	−0.143147	+	0.383792i
$378$	−3.76897	−	2.05801i	−0.193855	−	0.105853i
$379$	−12.4163	+	14.3291i	−0.637781	+	0.736038i	−0.978981	−	0.203952i	$-0.934621\pi$
$379$	−12.4163	+	14.3291i	−0.637781	+	0.736038i	0.341200	+	0.939991i	$0.389167\pi$
$380$	−3.40789	+	0.344970i	−0.174821	+	0.0176966i
$381$	−11.6656	+	3.42534i	−0.597648	+	0.175485i
$382$	0.0802000	+	0.0299130i	0.00410339	+	0.00153048i
$383$	−20.0411	−	4.35968i	−1.02405	−	0.222769i	−0.330982	−	0.943637i	$-0.607380\pi$
$383$	−20.0411	−	4.35968i	−1.02405	−	0.222769i	−0.693073	+	0.720868i	$0.743744\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	−5.76413	−	33.1257i	−0.293767	−	1.68824i
$386$	9.13702	−	20.0073i	0.465062	−	1.01834i
$387$	−1.79074	−	2.39215i	−0.0910283	−	0.121600i
$388$	−3.01076	−	13.8403i	−0.152848	−	0.702633i
$389$	9.85952	+	11.3785i	0.499897	+	0.576912i	0.948483	−	0.316827i	$-0.102618\pi$
$389$	9.85952	+	11.3785i	0.499897	+	0.576912i	−0.448586	+	0.893740i	$0.648072\pi$
$390$	0.0673557	+	2.28388i	0.00341069	+	0.115649i
$391$	−0.919956	+	2.03719i	−0.0465242	+	0.103025i
$392$	8.08966	+	8.08966i	0.408589	+	0.408589i
$393$	−1.99784	−	0.142889i	−0.100778	−	0.00720778i
$394$	13.2913	−	20.6816i	0.669604	−	1.04192i
$395$	11.8157	+	14.8504i	0.594511	+	0.747203i
$396$	−3.18520	−	1.45463i	−0.160062	−	0.0730980i
$397$	9.16160	−	12.2385i	0.459808	−	0.614231i	−0.509384	−	0.860539i	$-0.670127\pi$
$397$	9.16160	−	12.2385i	0.459808	−	0.614231i	0.969192	+	0.246308i	$0.0792175\pi$
$398$	7.79307	+	14.2719i	0.390631	+	0.715388i
$399$	3.55640	+	5.53386i	0.178042	+	0.277040i
$400$	−4.41785	+	2.34150i	−0.220892	+	0.117075i
$401$	−6.20905	−	21.1461i	−0.310065	−	1.05599i	−0.956188	−	0.292752i	$-0.905429\pi$
$401$	−6.20905	−	21.1461i	−0.310065	−	1.05599i	0.646123	−	0.763233i	$-0.276389\pi$
$402$	−0.845557	−	11.8224i	−0.0421725	−	0.589649i
$403$	−0.388509	−	5.43207i	−0.0193530	−	0.270591i
$404$	5.58452	+	19.0191i	0.277840	+	0.946238i
$405$	−2.11721	−	0.719325i	−0.105205	−	0.0357436i
$406$	18.0705	+	28.1182i	0.896822	+	1.39548i
$407$	0.979018	+	1.79294i	0.0485281	+	0.0888727i
$408$	0.279315	−	0.373122i	0.0138282	−	0.0184723i
$409$	−22.3803	−	10.2208i	−1.10664	−	0.505384i	−0.223596	−	0.974682i	$-0.571780\pi$
$409$	−22.3803	−	10.2208i	−1.10664	−	0.505384i	−0.883040	+	0.469298i	$0.844507\pi$
$410$	2.21895	−	19.4980i	0.109586	−	0.962938i
$411$	10.9395	−	17.0222i	0.539605	−	0.839642i
$412$	−4.70851	−	0.336759i	−0.231972	−	0.0165909i
$413$	2.21458	+	2.21458i	0.108972	+	0.108972i
$414$	−4.02350	+	2.60987i	−0.197744	+	0.128268i
$415$	21.9336	−	0.646861i	1.07668	−	0.0317532i
$416$	−0.669153	−	0.772243i	−0.0328079	−	0.0378623i
$417$	0.675330	+	3.10444i	0.0330711	+	0.152025i
$418$	3.21450	+	4.29407i	0.157226	+	0.210030i
$419$	−3.51016	+	7.68619i	−0.171483	+	0.375495i	−0.975787	−	0.218723i	$-0.929811\pi$
$419$	−3.51016	+	7.68619i	−0.171483	+	0.375495i	0.804304	+	0.594218i	$0.202538\pi$
$420$	7.85326	+	5.52529i	0.383200	+	0.269606i
$421$	−10.5814	+	36.0371i	−0.515708	+	1.75634i	0.128728	+	0.991680i	$0.458911\pi$
$421$	−10.5814	+	36.0371i	−0.515708	+	1.75634i	−0.644435	+	0.764659i	$0.722908\pi$
$422$	0.415102	+	0.0902998i	0.0202068	+	0.00439573i
$423$	−1.31098	−	0.488971i	−0.0637421	−	0.0237746i
$424$	10.8828	−	3.19549i	0.528518	−	0.155187i
$425$	2.31066	−	0.302950i	0.112083	−	0.0146953i
$426$	9.63328	−	11.1174i	0.466734	−	0.538639i
$427$	21.7244	+	11.8624i	1.05132	+	0.574063i
$428$	3.06603	−	8.22034i	0.148202	−	0.397345i
$429$	3.01005	−	1.93444i	0.145327	−	0.0933958i
$430$	3.37370	+	5.76747i	0.162694	+	0.278132i
$431$	−30.0560	+	4.32140i	−1.44775	+	0.208155i	−0.820938	−	0.571018i	$-0.806549\pi$
$431$	−30.0560	+	4.32140i	−1.44775	+	0.208155i	−0.626809	+	0.779173i	$0.715640\pi$
$432$	0.936950	−	0.349464i	0.0450790	−	0.0168136i
$433$	7.96127	−	5.95973i	0.382594	−	0.286407i	−0.390619	−	0.920552i	$-0.627739\pi$
$433$	7.96127	−	5.95973i	0.382594	−	0.286407i	0.773213	+	0.634146i	$0.218648\pi$
$434$	−19.2535	−	12.3735i	−0.924199	−	0.593946i
$435$	11.7802	+	12.8117i	0.564820	+	0.614272i
$436$		−	6.61293i		−	0.316702i
$437$	7.32547	−	0.555088i	0.350425	−	0.0265534i
$438$	2.22875	−	2.22875i	0.106494	−	0.106494i
$439$	−2.35093	+	2.03709i	−0.112204	+	0.0972250i	−0.709156	−	0.705052i	$-0.750924\pi$
$439$	−2.35093	+	2.03709i	−0.112204	+	0.0972250i	0.596952	+	0.802277i	$0.296378\pi$
$440$	6.70885	+	4.03714i	0.319832	+	0.192463i
$441$	1.62815	−	11.3241i	0.0775311	−	0.539241i
$442$	0.166435	+	0.446231i	0.00791653	+	0.0212250i
$443$	−17.4201	−	13.0405i	−0.827656	−	0.619575i	0.0991687	−	0.995071i	$-0.468382\pi$
$443$	−17.4201	−	13.0405i	−0.827656	−	0.619575i	−0.926824	+	0.375495i	$0.877473\pi$
$444$	−0.559758	−	0.164360i	−0.0265650	−	0.00780018i
$445$	−0.903598	+	4.83606i	−0.0428347	+	0.229251i
$446$	−3.51689	−	7.70092i	−0.166530	−	0.364649i
$447$	5.94623	−	10.8897i	0.281247	−	0.515065i
$448$	−4.28330	+	0.306348i	−0.202367	+	0.0144736i
$449$	9.15725	+	7.93480i	0.432157	+	0.374466i	0.843603	−	0.536968i	$-0.180430\pi$
$449$	9.15725	+	7.93480i	0.432157	+	0.374466i	−0.411445	+	0.911434i	$0.634976\pi$
$450$	4.52198	+	2.13346i	0.213168	+	0.100572i
$451$	−27.9535	+	12.7659i	−1.31628	+	0.601124i
$452$	3.67699	−	16.9029i	0.172951	−	0.795043i
$453$	11.5959	−	6.33184i	0.544823	−	0.297496i
$454$	0.703888	+	4.89565i	0.0330351	+	0.229764i
$455$	−9.08807	+	3.69838i	−0.426055	+	0.173383i
$456$	−1.51625	−	0.218004i	−0.0710051	−	0.0102090i
$457$	−26.4220	+	5.74776i	−1.23597	+	0.268869i	−0.782641	−	0.622474i	$-0.786128\pi$
$457$	−26.4220	+	5.74776i	−1.23597	+	0.268869i	−0.453330	+	0.891343i	$0.649764\pi$
$458$	−1.21331	+	16.9643i	−0.0566944	+	0.792692i
$459$	−0.466087			−0.0217551
$460$	9.59901	−	4.78111i	0.447556	−	0.222920i
$461$	−24.6984			−1.15032			−0.575160	−	0.818041i	$-0.695060\pi$
$461$	−24.6984			−1.15032			−0.575160	+	0.818041i	$0.695060\pi$
$462$	1.07272	−	14.9985i	0.0499073	−	0.697796i
$463$	19.4951	−	4.24089i	0.906012	−	0.197091i	0.264664	−	0.964341i	$-0.414739\pi$
$463$	19.4951	−	4.24089i	0.906012	−	0.197091i	0.641348	+	0.767250i	$0.278375\pi$
$464$	−7.70426	−	1.10771i	−0.357661	−	0.0514239i
$465$	−10.9817	−	4.62895i	−0.509263	−	0.214663i
$466$	−3.45235	−	24.0116i	−0.159927	−	1.11232i
$467$	−24.8775	+	13.5841i	−1.15119	+	0.628598i	−0.937391	−	0.348279i	$-0.886766\pi$
$467$	−24.8775	+	13.5841i	−1.15119	+	0.628598i	−0.213801	+	0.976877i	$0.568584\pi$
$468$	−0.217204	+	0.998473i	−0.0100403	+	0.0461544i
$469$	46.2985	−	21.1438i	2.13787	−	0.976331i
$470$	2.78901	+	1.41783i	0.128648	+	0.0653996i
$471$	5.08271	+	4.40419i	0.234199	+	0.202934i
$472$	−0.727464	+	0.0520292i	−0.0334842	+	0.00239484i
$473$	5.01460	−	9.18355i	0.230571	−	0.422260i
$474$	3.52562	+	7.72002i	0.161937	+	0.354592i
$475$	−4.51342	−	6.18812i	−0.207090	−	0.283930i
$476$	1.92041	+	0.563885i	0.0880221	+	0.0258456i
$477$	−9.07997	−	6.79718i	−0.415743	−	0.311221i
$478$	−8.33630	−	22.3505i	−0.381294	−	1.02229i
$479$	0.0829013	−	0.576591i	0.00378786	−	0.0263451i	−0.987840	−	0.155475i	$-0.950309\pi$
$479$	0.0829013	−	0.576591i	0.00378786	−	0.0263451i	0.991628	+	0.129130i	$0.0412183\pi$
$480$	−2.17001	+	0.539515i	−0.0990467	+	0.0246254i
$481$	0.450519	−	0.390377i	0.0205419	−	0.0177997i
$482$	−18.7769	+	18.7769i	−0.855264	+	0.855264i
$483$	−16.5388	−	12.2719i	−0.752540	−	0.558392i
$484$		−	1.26144i		−	0.0573384i
$485$	23.3140	−	21.4370i	1.05863	−	0.973406i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	−26.9669	+	20.1871i	−1.22199	+	0.914767i	−0.998206	−	0.0598731i	$-0.980930\pi$
$487$	−26.9669	+	20.1871i	−1.22199	+	0.914767i	−0.223779	+	0.974640i	$0.571839\pi$
$488$	−5.40060	+	2.01432i	−0.244474	+	0.0911840i
$489$	1.28045	−	0.184101i	0.0579040	−	0.00832535i
$490$	−6.48050	+	24.7473i	−0.292759	+	1.11797i
$491$	10.6704	−	6.85744i	0.481548	−	0.309472i	−0.277250	−	0.960798i	$-0.589423\pi$
$491$	10.6704	−	6.85744i	0.481548	−	0.309472i	0.758798	+	0.651326i	$0.225787\pi$
$492$	3.06692	−	8.22272i	0.138267	−	0.370709i
$493$	3.18402	+	1.73861i	0.143401	+	0.0783030i
$494$	1.02504	−	1.18296i	0.0461187	−	0.0532238i
$495$	−0.788565	−	7.79008i	−0.0354433	−	0.350138i
$496$	5.11374	−	1.50153i	0.229614	−	0.0674207i
$497$	59.1872	+	22.0757i	2.65491	+	0.990230i
$498$	9.58900	+	2.08596i	0.429693	+	0.0934740i
$499$	−1.86240	+	6.34274i	−0.0833723	+	0.283940i	−0.990618	−	0.136661i	$-0.956363\pi$
$499$	−1.86240	+	6.34274i	−0.0833723	+	0.283940i	0.907246	+	0.420601i	$0.138181\pi$
$500$	−9.50719	−	5.88331i	−0.425174	−	0.263110i
$501$	−0.751328	+	1.64518i	−0.0335669	+	0.0735012i
$502$	9.77342	+	13.0558i	0.436209	+	0.582707i
$503$	5.52875	+	25.4152i	0.246515	+	1.13321i	0.919357	+	0.393424i	$0.128710\pi$
$503$	5.52875	+	25.4152i	0.246515	+	1.13321i	−0.672842	+	0.739786i	$0.734927\pi$
$504$	2.81213	+	3.24537i	0.125262	+	0.144560i
$505$	−30.4039	+	32.2517i	−1.35296	+	1.43518i
$506$	−14.1657	−	9.01927i	−0.629741	−	0.400955i
$507$	8.45408	+	8.45408i	0.375459	+	0.375459i
$508$	12.1271	+	0.867350i	0.538055	+	0.0384824i
$509$	13.9127	−	21.6486i	0.616671	−	0.959559i	−0.382692	−	0.923876i	$-0.625003\pi$
$509$	13.9127	−	21.6486i	0.616671	−	0.959559i	0.999363	−	0.0356827i	$-0.0113606\pi$
$510$	1.03552	+	0.117846i	0.0458535	+	0.00521831i
$511$	12.3120	+	5.62269i	0.544650	+	0.248733i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	0.734135	+	1.34447i	0.0324129	+	0.0593597i
$514$	−2.59574	−	4.03905i	−0.114493	−	0.178155i
$515$	−4.66603	−	9.46813i	−0.205610	−	0.417216i
$516$	0.841862	+	2.86712i	0.0370609	+	0.126218i
$517$	−0.349526	−	4.88701i	−0.0153721	−	0.214930i
$518$	−0.178720	−	2.49883i	−0.00785251	−	0.109792i
$519$	2.74759	+	9.35743i	0.120606	+	0.410745i
$520$	0.735024	−	2.16342i	0.0322329	−	0.0948720i
$521$	22.9511	+	35.7126i	1.00551	+	1.56460i	0.812133	+	0.583473i	$0.198306\pi$
$521$	22.9511	+	35.7126i	1.00551	+	1.56460i	0.193373	+	0.981125i	$0.438057\pi$
$522$	3.73023	+	6.83140i	0.163268	+	0.299002i
$523$	24.0380	−	32.1110i	1.05111	−	1.40412i	0.140872	−	0.990028i	$-0.455009\pi$
$523$	24.0380	−	32.1110i	1.05111	−	1.40412i	0.910237	−	0.414089i	$-0.135900\pi$
$524$	1.82194	+	0.832054i	0.0795920	+	0.0363485i
$525$	−1.79789	+	21.3958i	−0.0784664	+	0.933789i
$526$	0.479684	−	0.746403i	0.0209152	−	0.0325447i
$527$	−2.47774	−	0.177211i	−0.107932	−	0.00771945i
$528$	2.47603	+	2.47603i	0.107755	+	0.107755i
$529$	−20.8399	+	9.73123i	−0.906085	+	0.423097i
$530$	18.4546	+	17.3973i	0.801617	+	0.755689i
$531$	0.477604	+	0.551185i	0.0207263	+	0.0239194i
$532$	−1.39828	−	6.42778i	−0.0606231	−	0.278680i
$533$	5.37408	+	7.17893i	0.232777	+	0.310954i
$534$	−0.913987	+	2.00135i	−0.0395521	+	0.0866070i
$535$	19.3277	−	3.36318i	0.835611	−	0.145403i
$536$	−3.33927	+	11.3725i	−0.144235	+	0.491218i
$537$	−19.2360	−	4.18453i	−0.830094	−	0.180576i
$538$	4.34696	+	1.62133i	0.187411	+	0.0699005i
$539$	38.4377	−	11.2863i	1.65563	−	0.486137i
$540$	1.73234	+	1.41386i	0.0745480	+	0.0608428i
$541$	−0.709833	+	0.819190i	−0.0305181	+	0.0352197i	−0.770803	−	0.637073i	$-0.780145\pi$
$541$	−0.709833	+	0.819190i	−0.0305181	+	0.0352197i	0.740285	+	0.672293i	$0.234690\pi$
$542$	−1.39643	−	0.762510i	−0.0599819	−	0.0327526i
$543$	−0.840330	+	2.25301i	−0.0360620	+	0.0966860i
$544$	−0.392097	+	0.251986i	−0.0168110	+	0.0108038i
$545$	12.7637	−	7.46614i	0.546735	−	0.319814i
$546$	−4.34330	+	0.624472i	−0.185876	+	0.0267249i
$547$	22.6986	−	8.46613i	0.970521	−	0.361986i	0.186318	−	0.982490i	$-0.440345\pi$
$547$	22.6986	−	8.46613i	0.970521	−	0.361986i	0.784203	+	0.620504i	$0.213072\pi$
$548$	−16.1984	+	12.1260i	−0.691961	+	0.517996i
$549$	4.84901	+	3.11627i	0.206951	+	0.132999i
$550$	−0.217678	+	17.5068i	−0.00928184	+	0.746493i
$551$		−	11.9231i		−	0.507941i
$552$	4.68188	−	1.03924i	0.199274	−	0.0442332i
$553$	−25.7706	+	25.7706i	−1.09588	+	1.09588i
$554$	−13.1749	+	11.4161i	−0.559749	+	0.485025i
$555$	−0.314747	−	1.26596i	−0.0133603	−	0.0537370i
$556$	0.452141	−	3.14471i	0.0191751	−	0.133365i
$557$	3.00168	+	8.04781i	0.127185	+	0.340997i	0.984899	−	0.173131i	$-0.0553884\pi$
$557$	3.00168	+	8.04781i	0.127185	+	0.340997i	−0.857714	+	0.514128i	$0.828116\pi$
$558$	−4.26659	−	3.19393i	−0.180619	−	0.135210i
$559$	−2.92969	−	0.860235i	−0.123913	−	0.0363841i
$560$	−5.42722	−	7.92135i	−0.229342	−	0.334738i
$561$	−0.677985	−	1.48458i	−0.0286245	−	0.0626790i
$562$	0.521093	−	0.954311i	0.0219810	−	0.0402552i
$563$	11.2685	−	0.805941i	0.474912	−	0.0339664i	0.168168	−	0.985758i	$-0.446215\pi$
$563$	11.2685	−	0.805941i	0.474912	−	0.0339664i	0.306744	+	0.951792i	$0.400760\pi$
$564$	1.05745	+	0.916282i	0.0445265	+	0.0385825i
$565$	36.7757	−	11.9867i	1.54717	−	0.504284i
$566$	−15.4033	+	7.03444i	−0.647448	+	0.295679i
$567$	0.912807	−	4.19610i	0.0383343	−	0.176220i
$568$	−12.9110	+	7.04995i	−0.541735	+	0.295809i
$569$	−1.18613	−	8.24969i	−0.0497250	−	0.345845i	−0.999462	−	0.0327962i	$-0.989559\pi$
$569$	−1.18613	−	8.24969i	−0.0497250	−	0.345845i	0.949737	−	0.313049i	$-0.101350\pi$
$570$	−1.29111	−	3.17266i	−0.0540787	−	0.132888i
$571$	−34.7345	−	4.99406i	−1.45359	−	0.208995i	−0.630184	−	0.776446i	$-0.717021\pi$
$571$	−34.7345	−	4.99406i	−1.45359	−	0.208995i	−0.823407	+	0.567451i	$0.807930\pi$
$572$	−3.49629	+	0.760570i	−0.146187	+	0.0318010i
$573$	−0.00610641	+	0.0853788i	−0.000255099	+	0.00356675i
$574$	37.6865			1.57300
$575$	20.0655	+	13.1291i	0.836791	+	0.547523i
$576$	−1.00000			−0.0416667
$577$	3.39185	−	47.4243i	0.141205	−	1.97430i	−0.0723927	−	0.997376i	$-0.523063\pi$
$577$	3.39185	−	47.4243i	0.141205	−	1.97430i	0.213597	−	0.976922i	$-0.431482\pi$
$578$	−16.3992	+	3.56743i	−0.682118	+	0.148386i
$579$	21.7710	+	3.13020i	0.904773	+	0.130087i
$580$	−6.56028	−	16.1207i	−0.272401	−	0.669374i
$581$	5.99722	+	41.7116i	0.248807	+	1.73049i
$582$	12.4314	−	6.78806i	0.515298	−	0.281374i
$583$	8.44236	−	38.8089i	0.349647	−	1.60730i
$584$	−2.86709	+	1.30936i	−0.118641	+	0.0541816i
$585$	−2.17239	+	0.708070i	−0.0898171	+	0.0292751i
$586$	8.80413	+	7.62882i	0.363695	+	0.315144i
$587$	−39.4954	+	2.82476i	−1.63015	+	0.116591i	−0.856195	−	0.516652i	$-0.827178\pi$
$587$	−39.4954	+	2.82476i	−1.63015	+	0.116591i	−0.773953	+	0.633243i	$0.781723\pi$
$588$	−5.48285	+	10.0411i	−0.226109	+	0.414088i
$589$	3.39152	+	7.42638i	0.139745	+	0.305999i
$590$	−0.921744	−	1.34534i	−0.0379476	−	0.0553868i
$591$	23.5885	+	6.92619i	0.970299	+	0.284906i
$592$	0.467028	+	0.349612i	0.0191947	+	0.0143690i
$593$	5.05562	+	13.5547i	0.207610	+	0.556623i	0.998465	−	0.0553797i	$-0.0176369\pi$
$593$	5.05562	+	13.5547i	0.207610	+	0.556623i	−0.790856	+	0.612003i	$0.790364\pi$
$594$	0.498335	−	3.46599i	0.0204469	−	0.142211i
$595$	1.07983	+	4.34324i	0.0442688	+	0.178056i
$596$	−9.37688	+	8.12511i	−0.384092	+	0.332818i
$597$	−11.4983	+	11.4983i	−0.470593	+	0.470593i
$598$	−1.69311	+	4.59872i	−0.0692363	+	0.188056i
$599$		−	4.80779i		−	0.196441i	−0.995165	−	0.0982204i	$-0.968685\pi$
$599$		−	4.80779i		−	0.196441i	0.995165	−	0.0982204i	$-0.0313150\pi$
$600$	−3.49130	−	3.57922i	−0.142532	−	0.146121i
$601$	−23.1937	−	14.9057i	−0.946089	−	0.608015i	−0.0259743	−	0.999663i	$-0.508269\pi$
$601$	−23.1937	−	14.9057i	−0.946089	−	0.608015i	−0.920115	+	0.391648i	$0.871905\pi$
$602$	−10.2725	+	7.68986i	−0.418674	+	0.313415i
$603$	11.1053	−	4.14207i	0.452244	−	0.168678i
$604$	−13.0775	+	1.88026i	−0.532117	+	0.0765069i
$605$	2.43472	−	1.42420i	0.0989855	−	0.0579019i
$606$	−16.6754	+	10.7166i	−0.677391	+	0.435333i
$607$	7.92208	−	21.2399i	0.321547	−	0.862102i	−0.671134	−	0.741336i	$-0.734192\pi$
$607$	7.92208	−	21.2399i	0.321547	−	0.862102i	0.992681	−	0.120766i	$-0.0385350\pi$
$608$	1.34447	+	0.734135i	0.0545254	+	0.0297731i
$609$	−21.8882	+	25.2603i	−0.886953	+	1.02360i
$610$	−9.98525	−	8.14952i	−0.404291	−	0.329965i
$611$	−1.37182	+	0.402804i	−0.0554981	+	0.0162957i
$612$	0.436700	+	0.162881i	0.0176525	+	0.00658406i
$613$	−6.58784	−	1.43310i	−0.266080	−	0.0578823i	0.0775457	−	0.996989i	$-0.475292\pi$
$613$	−6.58784	−	1.43310i	−0.266080	−	0.0578823i	−0.343626	+	0.939107i	$0.611655\pi$
$614$	−9.22104	+	31.4040i	−0.372131	+	1.26736i
$615$	19.3333	−	3.36416i	0.779596	−	0.135656i
$616$	−6.24654	+	13.6780i	−0.251680	+	0.551103i
$617$	12.4121	+	16.5807i	0.499694	+	0.667513i	0.977496	−	0.210955i	$-0.0676573\pi$
$617$	12.4121	+	16.5807i	0.499694	+	0.667513i	−0.477802	+	0.878468i	$0.658566\pi$
$618$	−1.00342	−	4.61266i	−0.0403636	−	0.185548i
$619$	20.9512	+	24.1789i	0.842099	+	0.971834i	0.999878	−	0.0156407i	$-0.00497879\pi$
$619$	20.9512	+	24.1789i	0.842099	+	0.971834i	−0.157779	+	0.987474i	$0.550433\pi$
$620$	8.67163	+	8.17480i	0.348261	+	0.328308i
$621$	−3.63770	−	3.12524i	−0.145976	−	0.125412i
$622$	−23.9380	−	23.9380i	−0.959825	−	0.959825i
$623$	−9.42402	−	0.674019i	−0.377566	−	0.0270040i
$624$	0.552440	−	0.859613i	0.0221153	−	0.0344121i
$625$	0.621600	−	24.9923i	0.0248640	−	0.999691i
$626$	−10.9035	−	4.97944i	−0.435790	−	0.199019i
$627$	−3.21450	+	4.29407i	−0.128375	+	0.171489i
$628$	−3.22313	−	5.90273i	−0.128617	−	0.235545i
$629$	−0.147006	−	0.228745i	−0.00586151	−	0.00912068i
$630$	−3.08896	+	9.09180i	−0.123067	+	0.362226i
$631$	−5.91586	−	20.1476i	−0.235506	−	0.802061i	−0.989419	−	0.145087i	$-0.953654\pi$
$631$	−5.91586	−	20.1476i	−0.235506	−	0.802061i	0.753912	−	0.656975i	$-0.228164\pi$
$632$	−0.605454	−	8.46535i	−0.0240837	−	0.336734i
$633$	0.0303056	+	0.423728i	0.00120454	+	0.0168417i
$634$	3.24217	+	11.0418i	0.128763	+	0.438527i
$635$	12.0177	+	24.3859i	0.476909	+	0.967726i
$636$	6.13210	+	9.54174i	0.243154	+	0.378354i
$637$	−5.60251	−	10.2602i	−0.221980	−	0.406525i
$638$	−16.3333	+	21.8187i	−0.646640	+	0.863810i
$639$	13.3811	+	6.11093i	0.529347	+	0.241745i
$640$	2.22173	+	0.252841i	0.0878215	+	0.00999443i
$641$	−13.7283	+	21.3616i	−0.542233	+	0.843731i	−0.998947	−	0.0458824i	$-0.985390\pi$
$641$	−13.7283	+	21.3616i	−0.542233	+	0.843731i	0.456714	+	0.889614i	$0.349026\pi$
$642$	8.75116	+	0.625895i	0.345381	+	0.0247021i
$643$	21.0881	+	21.0881i	0.831635	+	0.831635i	0.987740	−	0.156105i	$-0.0498938\pi$
$643$	21.0881	+	21.0881i	0.831635	+	0.831635i	−0.156105	+	0.987740i	$0.549894\pi$
$644$	11.2074	+	17.2779i	0.441633	+	0.680845i
$645$	−4.58336	+	4.86192i	−0.180470	+	0.191438i
$646$	−0.467553	−	0.539585i	−0.0183956	−	0.0212297i
$647$	−1.70517	−	7.83855i	−0.0670372	−	0.308165i	0.931403	−	0.363989i	$-0.118585\pi$
$647$	−1.70517	−	7.83855i	−0.0670372	−	0.308165i	−0.998441	+	0.0558234i	$0.982222\pi$
$648$	0.599278	+	0.800541i	0.0235419	+	0.0314482i
$649$	−1.06090	+	2.32304i	−0.0416438	+	0.0911871i
$650$	5.00548	−	1.02387i	0.196331	−	0.0401594i
$651$	6.44793	−	21.9596i	0.252714	−	0.860666i
$652$	−1.26406	−	0.274979i	−0.0495043	−	0.0107690i
$653$	0.638588	+	0.238181i	0.0249899	+	0.00932074i	0.361928	−	0.932206i	$-0.382119\pi$
$653$	0.638588	+	0.238181i	0.0249899	+	0.00932074i	−0.336938	+	0.941527i	$0.609391\pi$
$654$	6.34506	−	1.86308i	0.248111	−	0.0728521i
$655$	0.451062	+	4.45595i	0.0176244	+	0.174109i
$656$	−5.74709	+	6.63250i	−0.224386	+	0.258956i
$657$	2.76638	+	1.51056i	0.107927	+	0.0589324i
$658$	−2.09976	+	5.62967i	−0.0818571	+	0.219467i
$659$	−32.5525	+	20.9202i	−1.26807	+	0.814937i	−0.989367	−	0.145441i	$-0.953540\pi$
$659$	−32.5525	+	20.9202i	−1.26807	+	0.814937i	−0.278700	+	0.960378i	$0.589903\pi$
$660$	−1.98351	+	7.57449i	−0.0772080	+	0.294837i
$661$	43.8092	−	6.29881i	1.70398	−	0.244995i	0.779548	−	0.626342i	$-0.215449\pi$
$661$	43.8092	−	6.29881i	1.70398	−	0.244995i	0.924432	+	0.381346i	$0.124540\pi$
$662$	6.44495	−	2.40384i	0.250490	−	0.0934279i
$663$	−0.381265	+	0.285411i	−0.0148071	+	0.0110845i
$664$	−8.25544	−	5.30545i	−0.320373	−	0.205891i
$665$	10.8276	−	9.95593i	0.419877	−	0.386074i
$666$		−	0.583390i		−	0.0226059i
$667$	13.1927	+	34.9192i	0.510825	+	1.35208i
$668$	1.27889	−	1.27889i	0.0494816	−	0.0494816i
$669$	6.39815	−	5.54403i	0.247367	−	0.214345i
$670$	−25.7203	+	6.39467i	−0.993661	+	0.247047i
$671$	−2.87241	+	19.9781i	−0.110888	+	0.771245i
$672$	−1.50068	−	4.02349i	−0.0578901	−	0.155209i
$673$	15.3984	+	11.5271i	0.593567	+	0.444338i	0.853357	−	0.521327i	$-0.174563\pi$
$673$	15.3984	+	11.5271i	0.593567	+	0.444338i	−0.259791	+	0.965665i	$0.583654\pi$
$674$	−20.4267	−	5.99782i	−0.786808	−	0.231028i
$675$	−0.773051	+	4.93988i	−0.0297548	+	0.190136i
$676$	−4.96665	−	10.8754i	−0.191025	−	0.418286i
$677$	11.4374	−	20.9461i	0.439576	−	0.805024i	−0.560151	−	0.828391i	$-0.689257\pi$
$677$	11.4374	−	20.9461i	0.439576	−	0.805024i	0.999727	+	0.0233669i	$0.00743859\pi$
$678$	17.2541	−	1.23404i	0.662640	−	0.0473929i
$679$	45.9673	+	39.8309i	1.76406	+	1.52857i
$680$	−0.929045	−	0.472292i	−0.0356273	−	0.0181116i
$681$	−4.49903	+	2.05464i	−0.172403	+	0.0787340i
$682$	3.96698	−	18.2359i	0.151904	−	0.698289i
$683$	33.5023	−	18.2936i	1.28193	−	0.699986i	0.313574	−	0.949564i	$-0.398474\pi$
$683$	33.5023	−	18.2936i	1.28193	−	0.699986i	0.968355	+	0.249577i	$0.0802917\pi$
$684$	−0.218004	−	1.51625i	−0.00833560	−	0.0579754i
$685$	−41.6927	−	17.5741i	−1.59300	−	0.671473i
$686$	−18.8745	−	2.71374i	−0.720632	−	0.103611i
$687$	−16.6190	+	3.61524i	−0.634054	+	0.137930i
$688$	0.213173	−	2.98055i	0.00812714	−	0.113632i
$689$	−11.5898			−0.441537
$690$	7.29179	+	7.86319i	0.277594	+	0.299347i
$691$	−15.7276			−0.598307			−0.299153	−	0.954205i	$-0.596704\pi$
$691$	−15.7276			−0.598307			−0.299153	+	0.954205i	$0.596704\pi$
$692$	0.695733	−	9.72762i	0.0264478	−	0.369789i
$693$	14.6932	−	3.19631i	0.558149	−	0.121418i
$694$	27.0121	+	3.88376i	1.02537	+	0.147425i
$695$	6.58010	−	2.67777i	0.249597	−	0.101573i
$696$	−1.10771	−	7.70426i	−0.0419875	−	0.292029i
$697$	3.59006	−	1.96032i	0.135983	−	0.0742525i
$698$	−0.00477219	+	0.0219374i	−0.000180630	+	0.000830343i
$699$	22.0664	−	10.0774i	0.834626	−	0.381161i
$700$	9.16160	−	19.4185i	0.346276	−	0.733950i
$701$	5.83026	+	5.05195i	0.220206	+	0.190809i	0.757977	−	0.652282i	$-0.226188\pi$
$701$	5.83026	+	5.05195i	0.220206	+	0.190809i	−0.537771	+	0.843091i	$0.680733\pi$
$702$	−1.01922	+	0.0728961i	−0.0384680	+	0.00275129i
$703$	−0.428287	+	0.784349i	−0.0161532	+	0.0295823i
$704$	−1.45463	−	3.18520i	−0.0548235	−	0.120047i
$705$	−0.574643	+	3.07549i	−0.0216423	+	0.115830i
$706$	−7.98745	−	2.34533i	−0.300612	−	0.0882676i
$707$	−68.1427	−	51.0110i	−2.56277	−	1.91847i
$708$	−0.254872	−	0.683338i	−0.00957868	−	0.0256814i
$709$	−4.22562	+	29.3898i	−0.158696	+	1.10376i	0.742343	+	0.670020i	$0.233715\pi$
$709$	−4.22562	+	29.3898i	−0.158696	+	1.10376i	−0.901039	+	0.433738i	$0.857194\pi$
$710$	−28.1840	−	16.9601i	−1.05773	−	0.636501i
$711$	−6.41403	+	5.55779i	−0.240545	+	0.208433i
$712$	1.55576	−	1.55576i	0.0583046	−	0.0583046i
$713$	−18.1499	−	17.9970i	−0.679721	−	0.673994i
$714$			2.00149i			0.0749038i
$715$	−5.41536	−	5.88950i	−0.202523	−	0.220255i
$716$	16.5608	+	10.6430i	0.618906	+	0.397747i
$717$	19.0965	−	14.2955i	0.713173	−	0.533875i
$718$	12.5292	−	4.67314i	0.467585	−	0.174400i
$719$	45.1501	−	6.49160i	1.68381	−	0.242096i	0.767068	−	0.641566i	$-0.221715\pi$
$719$	45.1501	−	6.49160i	1.68381	−	0.242096i	0.916746	+	0.399470i	$0.130806\pi$
$720$	−1.12902	−	1.93011i	−0.0420762	−	0.0719308i
$721$	17.0532	−	10.9594i	0.635093	−	0.408149i
$722$	5.81978	−	15.6034i	0.216590	−	0.580700i
$723$	−23.3064	−	12.7262i	−0.866773	−	0.473294i
$724$	1.57469	−	1.81729i	0.0585231	−	0.0675392i
$725$	23.7079	−	30.8626i	0.880489	−	1.14621i
$726$	1.21035	−	0.355390i	0.0449202	−	0.0131898i
$727$	−22.2906	−	8.31397i	−0.826714	−	0.308348i	−0.0997399	−	0.995014i	$-0.531801\pi$
$727$	−22.2906	−	8.31397i	−0.826714	−	0.308348i	−0.726974	+	0.686665i	$0.759074\pi$
$728$	4.28768	+	0.932728i	0.158912	+	0.0345692i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	−5.76421	−	4.05550i	−0.213343	−	0.150101i
$731$	−0.578566	+	1.26688i	−0.0213990	+	0.0468574i
$732$	−3.45425	−	4.61434i	−0.127673	−	0.170551i
$733$	5.64509	+	25.9501i	0.208506	+	0.958488i	0.955805	+	0.294000i	$0.0949866\pi$
$733$	5.64509	+	25.9501i	0.208506	+	0.958488i	−0.747299	+	0.664488i	$0.768650\pi$
$734$	10.8697	+	12.5443i	0.401208	+	0.463018i
$735$	−25.5706	+	0.754124i	−0.943187	+	0.0278163i
$736$	−4.74986	−	0.662429i	−0.175082	−	0.0244175i
$737$	29.3475	+	29.3475i	1.08103	+	1.08103i
$738$	8.75370	+	0.626077i	0.322228	+	0.0230462i
$739$	10.5595	−	16.4309i	0.388438	−	0.604421i	−0.590877	−	0.806761i	$-0.701218\pi$
$739$	10.5595	−	16.4309i	0.388438	−	0.604421i	0.979315	+	0.202340i	$0.0648547\pi$
$740$	−0.147505	+	1.29613i	−0.00542239	+	0.0476468i
$741$	1.42383	+	0.650240i	0.0523056	+	0.0238871i
$742$	−29.1887	+	38.9916i	−1.07155	+	1.43143i
$743$	−15.1633	−	27.7695i	−0.556286	−	1.01876i	−0.992882	−	0.119105i	$-0.961998\pi$
$743$	−15.1633	−	27.7695i	−0.556286	−	1.01876i	0.436595	−	0.899658i	$-0.356184\pi$
$744$	2.88141	+	4.48357i	0.105638	+	0.164376i
$745$	−26.2690	−	8.92495i	−0.962423	−	0.326985i
$746$	7.89051	+	26.8726i	0.288892	+	0.983876i
$747$	0.700070	+	9.78826i	0.0256142	+	0.358134i
$748$	0.116430	+	1.62791i	0.00425711	+	0.0595222i
$749$	10.6144	+	36.1495i	0.387843	+	1.32087i
$750$	2.96651	−	10.7796i	0.108322	−	0.393615i
$751$	−8.86939	−	13.8010i	−0.323649	−	0.503607i	0.640860	−	0.767658i	$-0.278578\pi$
$751$	−8.86939	−	13.8010i	−0.323649	−	0.503607i	−0.964509	+	0.264050i	$0.914941\pi$
$752$	−0.670566	−	1.22805i	−0.0244530	−	0.0447824i
$753$	−9.77342	+	13.0558i	−0.356163	+	0.475779i
$754$	7.23462	+	3.30394i	0.263469	+	0.120322i
$755$	−18.3939	−	23.1182i	−0.669423	−	0.841356i
$756$	−2.32164	+	3.61255i	−0.0844373	+	0.131387i
$757$	27.5217	+	1.96839i	1.00029	+	0.0715423i	0.561869	−	0.827226i	$-0.310082\pi$
$757$	27.5217	+	1.96839i	1.00029	+	0.0715423i	0.438424	+	0.898768i	$0.355537\pi$
$758$	13.4069	+	13.4069i	0.486959	+	0.486959i
$759$	4.66299	−	16.1329i	0.169256	−	0.585586i
$760$	0.100975	+	3.42382i	0.00366274	+	0.124195i
$761$	−0.00239754	−	0.00276691i	−8.69107e−5	−	0.000100300i	0.755706	−	0.654911i	$-0.227294\pi$
$761$	−0.00239754	−	0.00276691i	−8.69107e−5	−	0.000100300i	−0.755793	+	0.654811i	$0.772748\pi$
$762$	2.58439	+	11.8803i	0.0936227	+	0.430377i
$763$	17.0180	+	22.7334i	0.616093	+	0.823003i
$764$	0.0355582	−	0.0778617i	0.00128645	−	0.00281694i
$765$	0.178667	+	1.02677i	0.00645971	+	0.0371231i
$766$	−5.77830	+	19.6791i	−0.208778	+	0.711034i
$767$	0.728208	+	0.158412i	0.0262941	+	0.00571993i
$768$	0.936950	+	0.349464i	0.0338093	+	0.0126102i
$769$	−36.0384	+	10.5818i	−1.29958	+	0.381591i	−0.857082	−	0.515179i	$-0.827725\pi$
$769$	−36.0384	+	10.5818i	−1.29958	+	0.381591i	−0.442497	+	0.896770i	$0.645907\pi$
$770$	−33.4525	+	3.38629i	−1.20554	+	0.122033i
$771$	3.14413	−	3.62852i	0.113233	−	0.130678i
$772$	−19.3045	−	10.5410i	−0.694783	−	0.379380i
$773$	12.1920	−	32.6880i	0.438516	−	1.17571i	−0.510333	−	0.859977i	$-0.670478\pi$
$773$	12.1920	−	32.6880i	0.438516	−	1.17571i	0.948849	−	0.315730i	$-0.102249\pi$
$774$	−2.51380	+	1.61552i	−0.0903567	+	0.0580687i
$775$	−5.98777	+	25.9667i	−0.215087	+	0.932752i
$776$	−14.0198	+	2.01574i	−0.503281	+	0.0723608i
$777$	2.34726	−	0.875483i	0.0842075	−	0.0314078i
$778$	12.0529	−	9.02267i	0.432116	−	0.323478i
$779$	−11.3094	−	7.26814i	−0.405203	−	0.260408i
$780$	2.28286	+	0.0957458i	0.0817396	+	0.00342825i
$781$			51.5105i			1.84319i
$782$	1.96637	+	1.06294i	0.0703172	+	0.0380108i
$783$	−5.50375	+	5.50375i	−0.196688	+	0.196688i
$784$	8.64616	−	7.49194i	0.308791	−	0.267569i
$785$	7.75391	−	12.8853i	0.276749	−	0.459896i
$786$	−0.285049	+	1.98256i	−0.0101674	+	0.0707156i
$787$	−10.8829	−	29.1783i	−0.387935	−	1.04009i	−0.973343	−	0.229354i	$-0.926339\pi$
$787$	−10.8829	−	29.1783i	−0.387935	−	1.04009i	0.585408	−	0.810739i	$-0.300934\pi$
$788$	−19.6807	−	14.7328i	−0.701097	−	0.524835i
$789$	0.851311	+	0.249967i	0.0303075	+	0.00889908i
$790$	15.6555	−	10.7262i	0.556996	−	0.381619i
$791$	30.8581	+	67.5697i	1.09719	+	2.40250i
$792$	−1.67815	+	3.07331i	−0.0596306	+	0.109205i
$793$	5.87482	−	0.420175i	0.208621	−	0.0149209i
$794$	−11.5537	−	10.0113i	−0.410026	−	0.355289i
$795$	−11.4933	+	22.6084i	−0.407625	+	0.801839i
$796$	14.7915	−	6.75506i	0.524272	−	0.239427i
$797$	−0.311722	+	1.43296i	−0.0110417	+	0.0507581i	−0.982338	−	0.187115i	$-0.940086\pi$
$797$	−0.311722	+	1.43296i	−0.0110417	+	0.0507581i	0.971296	+	0.237873i	$0.0764501\pi$
$798$	5.77347	−	3.15255i	0.204379	−	0.111599i
$799$	0.0928106	+	0.645512i	0.00328340	+	0.0228366i
$800$	2.02037	+	4.57363i	0.0714308	+	0.161702i
$801$	−2.17778	−	0.313118i	−0.0769482	−	0.0110635i
$802$	−21.5352	+	4.68469i	−0.760433	+	0.165422i
$803$	−0.787363	+	11.0088i	−0.0277854	+	0.388491i
$804$	−11.8526			−0.418010
$805$	−20.6948	+	41.1386i	−0.729395	+	1.44994i
$806$	−5.44594			−0.191825
$807$	−0.330976	+	4.62766i	−0.0116509	+	0.162901i
$808$	19.3691	−	4.21348i	0.681402	−	0.148230i
$809$	−20.1209	−	2.89295i	−0.707413	−	0.101711i	−0.220788	−	0.975322i	$-0.570863\pi$
$809$	−20.1209	−	2.89295i	−0.707413	−	0.101711i	−0.486625	+	0.873611i	$0.661772\pi$
$810$	−0.868532	+	2.06050i	−0.0305171	+	0.0723985i
$811$	−1.83964	−	12.7950i	−0.0645984	−	0.449292i	−0.996291	−	0.0860448i	$-0.972577\pi$
$811$	−1.83964	−	12.7950i	−0.0645984	−	0.449292i	0.931693	−	0.363247i	$-0.118332\pi$
$812$	29.3357	−	16.0185i	1.02948	−	0.562139i
$813$	0.338202	−	1.55469i	0.0118613	−	0.0545254i
$814$	1.85821	−	0.848617i	0.0651303	−	0.0297440i
$815$	−0.896409	−	2.75022i	−0.0313998	−	0.0963360i
$816$	−0.352245	−	0.305222i	−0.0123310	−	0.0106849i
$817$	4.56574	−	0.326548i	0.159735	−	0.0114245i
$818$	−11.7913	+	21.5942i	−0.412273	+	0.755022i
$819$	−1.82282	−	3.99143i	−0.0636946	−	0.139472i
$820$	−19.2900	−	3.60427i	−0.673637	−	0.125866i
$821$	−31.8952	−	9.36527i	−1.11315	−	0.326850i	−0.327085	−	0.944995i	$-0.606066\pi$
$821$	−31.8952	−	9.36527i	−1.11315	−	0.326850i	−0.786064	+	0.618145i	$0.787885\pi$
$822$	−16.1984	−	12.1260i	−0.564984	−	0.422942i
$823$	−10.0501	−	26.9453i	−0.350324	−	0.939255i	−0.985918	−	0.167231i	$-0.946517\pi$
$823$	−10.0501	−	26.9453i	−0.350324	−	0.939255i	0.635594	−	0.772024i	$-0.280755\pi$
$824$	−0.671802	+	4.67249i	−0.0234033	+	0.162774i
$825$	−16.8590	+	4.72338i	−0.586955	+	0.164447i
$826$	2.36692	−	2.05095i	0.0823557	−	0.0713616i
$827$	15.8409	−	15.8409i	0.550843	−	0.550843i	−0.375841	−	0.926684i	$-0.622646\pi$
$827$	15.8409	−	15.8409i	0.550843	−	0.550843i	0.926684	+	0.375841i	$0.122646\pi$
$828$	2.31618	+	4.19944i	0.0804930	+	0.145941i
$829$			50.3935i			1.75024i	0.483907	+	0.875120i	$0.339217\pi$
$829$			50.3935i			1.75024i	−0.483907	+	0.875120i	$0.660783\pi$
$830$	0.919511	−	21.9238i	0.0319167	−	0.760988i
$831$	−14.6655	−	9.42495i	−0.508741	−	0.326948i
$832$	−0.818013	+	0.612357i	−0.0283595	+	0.0212296i
$833$	−4.99607	+	1.86344i	−0.173103	+	0.0645643i
$834$	3.14471	−	0.452141i	0.108892	−	0.0156564i
$835$	3.91228	+	1.02450i	0.135390	+	0.0354542i
$836$	4.51245	−	2.89998i	0.156066	−	0.100298i
$837$	1.86251	−	4.99359i	0.0643779	−	0.172604i
$838$	7.41619	+	4.04955i	0.256188	+	0.139889i
$839$	5.47304	−	6.31622i	0.188950	−	0.218060i	−0.653368	−	0.757040i	$-0.726645\pi$
$839$	5.47304	−	6.31622i	0.188950	−	0.218060i	0.842319	+	0.538980i	$0.181190\pi$
$840$	6.07146	−	7.43908i	0.209485	−	0.256673i
$841$	30.3033	−	8.89785i	1.04494	−	0.306822i
$842$	35.1904	+	13.1253i	1.21274	+	0.452329i
$843$	1.06246	+	0.231125i	0.0365932	+	0.00796036i
$844$	0.119683	−	0.407602i	0.00411965	−	0.0140302i
$845$	15.3833	−	21.8648i	0.529202	−	0.752171i
$846$	−0.581250	+	1.27276i	−0.0199838	+	0.0437584i
$847$	3.24625	+	4.33649i	0.111543	+	0.149004i
$848$	−2.41098	−	11.0831i	−0.0827933	−	0.380594i
$849$	−11.0891	−	12.7975i	−0.380577	−	0.439209i
$850$	−0.137338	−	2.32638i	−0.00471066	−	0.0797943i
$851$	0.386454	−	2.77102i	0.0132475	−	0.0949894i
$852$	−10.4018	−	10.4018i	−0.356361	−	0.356361i
$853$	−10.0434	−	0.718321i	−0.343881	−	0.0245949i	−0.101669	−	0.994818i	$-0.532418\pi$
$853$	−10.0434	−	0.718321i	−0.343881	−	0.0245949i	−0.242212	+	0.970223i	$0.577873\pi$
$854$	13.3820	−	20.8228i	0.457923	−	0.712542i
$855$	2.68040	−	2.13265i	0.0916677	−	0.0729352i
$856$	−7.98067	−	3.64465i	−0.272774	−	0.124572i
$857$	−2.29939	+	3.07162i	−0.0785456	+	0.104925i	−0.838093	−	0.545527i	$-0.816329\pi$
$857$	−2.29939	+	3.07162i	−0.0785456	+	0.104925i	0.759548	+	0.650452i	$0.225420\pi$
$858$	−1.71478	−	3.14038i	−0.0585416	−	0.107211i
$859$	−10.0450	−	15.6303i	−0.342730	−	0.533298i	0.626511	−	0.779413i	$-0.284482\pi$
$859$	−10.0450	−	15.6303i	−0.342730	−	0.533298i	−0.969241	+	0.246115i	$0.920846\pi$
$860$	5.99345	−	2.95366i	0.204375	−	0.100719i
$861$	10.6175	+	36.1599i	0.361844	+	1.23233i
$862$	2.16622	+	30.2877i	0.0737817	+	1.03160i
$863$	−0.0303674	−	0.424591i	−0.00103372	−	0.0144533i	0.996909	−	0.0785639i	$-0.0250335\pi$
$863$	−0.0303674	−	0.424591i	−0.00103372	−	0.0144533i	−0.997943	+	0.0641107i	$0.979579\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	19.5608	−	9.63986i	0.665089	−	0.327765i
$866$	−5.37660	−	8.36615i	−0.182704	−	0.284293i
$867$	−8.04312	−	14.7299i	−0.273159	−	0.500253i
$868$	−13.7155	+	18.3217i	−0.465534	+	0.621881i
$869$	−27.0327	−	12.3454i	−0.917021	−	0.418790i
$870$	13.6194	−	10.8363i	0.461741	−	0.367384i
$871$	6.54787	−	10.1887i	0.221866	−	0.345230i
$872$	−6.59608	−	0.471761i	−0.223371	−	0.0159758i
$873$	10.0154	+	10.0154i	0.338971	+	0.338971i
$874$	−0.0310804	−	7.34641i	−0.00105131	−	0.248496i
$875$	47.8234	−	4.24104i	1.61673	−	0.143373i
$876$	−2.06407	−	2.38207i	−0.0697385	−	0.0804825i
$877$	7.27276	+	33.4323i	0.245584	+	1.12893i	0.920410	+	0.390954i	$0.127855\pi$
$877$	7.27276	+	33.4323i	0.245584	+	1.12893i	−0.674827	+	0.737976i	$0.735782\pi$
$878$	1.86419	+	2.49026i	0.0629133	+	0.0840423i
$879$	−4.83939	+	10.5968i	−0.163229	+	0.357421i
$880$	4.50546	−	6.40375i	0.151879	−	0.215870i
$881$	1.88608	−	6.42339i	0.0635436	−	0.216410i	−0.921600	−	0.388140i	$-0.873118\pi$
$881$	1.88608	−	6.42339i	0.0635436	−	0.216410i	0.985144	+	0.171731i	$0.0549358\pi$
$882$	−11.1791	−	2.43185i	−0.376418	−	0.0818848i
$883$	−0.418131	−	0.155955i	−0.0140712	−	0.00524830i	0.342419	−	0.939547i	$-0.388754\pi$
$883$	−0.418131	−	0.155955i	−0.0140712	−	0.00524830i	−0.356490	+	0.934299i	$0.616027\pi$
$884$	0.456967	−	0.134178i	0.0153695	−	0.00451288i
$885$	1.03116	−	1.26343i	0.0346620	−	0.0424699i
$886$	−14.2501	+	16.4454i	−0.478740	+	0.552496i
$887$	41.0543	+	22.4173i	1.37847	+	0.752700i	0.985949	−	0.167044i	$-0.0534223\pi$
$887$	41.0543	+	22.4173i	1.37847	+	0.752700i	0.392518	+	0.919744i	$0.371604\pi$
$888$	−0.203874	+	0.546607i	−0.00684156	+	0.0183429i
$889$	−43.9217	+	28.2268i	−1.47309	+	0.946696i
$890$	4.75927	+	1.24630i	0.159531	+	0.0417760i
$891$	3.46599	−	0.498335i	0.116115	−	0.0166948i
$892$	−7.93219	+	2.95855i	−0.265589	+	0.0990597i
$893$	1.71585	−	1.28447i	0.0574187	−	0.0429831i
$894$	−10.4378	−	6.70794i	−0.349091	−	0.224347i
$895$	−1.84458	+	43.9803i	−0.0616576	+	1.47010i
$896$			4.29424i			0.143461i
$897$	−4.88945	−	0.328915i	−0.163254	−	0.0109821i
$898$	8.56786	−	8.56786i	0.285913	−	0.285913i
$899$	−31.3508	+	27.1656i	−1.04561	+	0.906024i
$900$	2.45062	−	4.35826i	0.0816873	−	0.145275i
$901$	−0.752346	+	5.23268i	−0.0250643	+	0.174326i
$902$	10.7392	+	28.7930i	0.357577	+	0.958701i
$903$	−10.2725	−	7.68986i	−0.341846	−	0.255903i
$904$	−16.5975	−	4.87346i	−0.552024	−	0.162089i
$905$	5.28544	+	0.987563i	0.175694	+	0.0328277i
$906$	−5.48846	−	12.0181i	−0.182342	−	0.399273i
$907$	−4.26752	+	7.81537i	−0.141701	+	0.259505i	−0.938885	−	0.344230i	$-0.888140\pi$
$907$	−4.26752	+	7.81537i	−0.141701	+	0.259505i	0.797185	+	0.603736i	$0.206322\pi$
$908$	4.93339	−	0.352843i	0.163720	−	0.0117095i
$909$	−14.9805	−	12.9807i	−0.496873	−	0.430543i
$910$	3.04062	+	9.32875i	0.100796	+	0.309245i
$911$	−13.8066	+	6.30526i	−0.457433	+	0.208903i	−0.630786	−	0.775957i	$-0.717267\pi$
$911$	−13.8066	+	6.30526i	−0.457433	+	0.208903i	0.173352	+	0.984860i	$0.444540\pi$
$912$	−0.325617	+	1.49684i	−0.0107823	+	0.0495653i
$913$	−30.1592	+	16.4682i	−0.998124	+	0.545017i
$914$	3.84819	+	26.7648i	0.127287	+	0.885299i
$915$	5.00624	−	11.8768i	0.165501	−	0.392634i
$916$	16.8346	+	2.42044i	0.556230	+	0.0799737i
$917$	−8.40458	+	1.82830i	−0.277544	+	0.0603759i
$918$	−0.0332503	+	0.464899i	−0.00109742	+	0.0153440i
$919$	10.4913			0.346076			0.173038	−	0.984915i	$-0.444642\pi$
$919$	10.4913			0.346076			0.173038	+	0.984915i	$0.444642\pi$
$920$	−4.08414	−	9.91563i	−0.134650	−	0.326909i
$921$	−32.7298			−1.07848
$922$	−1.76197	+	24.6355i	−0.0580272	+	0.811327i
$923$	14.6879	−	3.19517i	0.483460	−	0.105170i
$924$	−14.8838	−	2.13997i	−0.489641	−	0.0703998i
$925$	−2.66821	+	1.17866i	−0.0877302	+	0.0387542i
$926$	−2.83932	−	19.7479i	−0.0933060	−	0.648957i
$927$	4.14312	−	2.26231i	0.136078	−	0.0743041i
$928$	−1.65450	+	7.60561i	−0.0543116	+	0.249666i
$929$	30.9668	−	14.1421i	1.01599	−	0.463986i	0.163395	−	0.986561i	$-0.447756\pi$
$929$	30.9668	−	14.1421i	1.01599	−	0.463986i	0.852594	+	0.522575i	$0.175028\pi$
$930$	−5.40058	+	10.6235i	−0.177092	+	0.348358i
$931$	13.2446	+	11.4765i	0.434073	+	0.376127i
$932$	−24.1968	+	1.73059i	−0.792591	+	0.0566872i
$933$	16.2242	−	29.7124i	0.531156	−	0.972740i
$934$	11.7748	+	25.7832i	0.385282	+	0.843651i
$935$	−3.01058	+	2.06267i	−0.0984566	+	0.0674564i
$936$	0.980433	+	0.287881i	0.0320465	+	0.00940969i
$937$	−32.8555	−	24.5954i	−1.07334	−	0.803495i	−0.0920006	−	0.995759i	$-0.529326\pi$
$937$	−32.8555	−	24.5954i	−1.07334	−	0.803495i	−0.981343	+	0.192264i	$0.938417\pi$
$938$	−17.7870	−	47.6889i	−0.580768	−	1.55710i
$939$	1.70588	−	11.8647i	0.0556693	−	0.387189i
$940$	1.61318	−	2.68076i	0.0526163	−	0.0874367i
$941$	20.5427	−	17.8004i	0.669673	−	0.580275i	−0.252243	−	0.967664i	$-0.581168\pi$
$941$	20.5427	−	17.8004i	0.669673	−	0.580275i	0.921917	+	0.387389i	$0.126623\pi$
$942$	4.75557	−	4.75557i	0.154945	−	0.154945i
$943$	41.1641	+	8.77248i	1.34049	+	0.285671i
$944$			0.729322i			0.0237374i
$945$	−9.59378	−	0.402374i	−0.312086	−	0.0130892i
$946$	−8.80241	−	5.65697i	−0.286191	−	0.183924i
$947$	19.4921	−	14.5916i	0.633410	−	0.474164i	−0.233682	−	0.972313i	$-0.575078\pi$
$947$	19.4921	−	14.5916i	0.633410	−	0.474164i	0.867092	+	0.498149i	$0.165987\pi$
$948$	7.95187	−	2.96589i	0.258265	−	0.0963277i
$949$	3.18793	−	0.458355i	0.103485	−	0.0148788i
$950$	−6.49434	+	4.06046i	−0.210704	+	0.131739i
$951$	−9.68113	+	6.22169i	−0.313932	+	0.201752i
$952$	0.699449	−	1.87529i	0.0226693	−	0.0607786i
$953$	26.7055	+	14.5823i	0.865077	+	0.472368i	0.849548	−	0.527512i	$-0.176875\pi$
$953$	26.7055	+	14.5823i	0.865077	+	0.472368i	0.0155290	+	0.999879i	$0.495057\pi$
$954$	−7.42762	+	8.57193i	−0.240478	+	0.277526i
$955$	0.190427	−	0.0192763i	0.00616208	−	0.000623767i
$956$	−22.8883	+	6.72060i	−0.740259	+	0.217360i
$957$	−25.5365	−	9.52461i	−0.825477	−	0.307887i
$958$	−0.569208	−	0.123824i	−0.0183903	−	0.00400056i
$959$	24.4800	−	83.3713i	0.790501	−	2.69220i
$960$	0.383333	+	2.20297i	0.0123720	+	0.0711004i
$961$	−1.07803	+	2.36056i	−0.0347753	+	0.0761472i
$962$	−0.357243	−	0.477220i	−0.0115180	−	0.0153862i
$963$	1.86494	+	8.57301i	0.0600970	+	0.276261i
$964$	17.3895	+	20.0686i	0.560079	+	0.646366i
$965$	−1.44984	−	49.1607i	−0.0466720	−	1.58254i
$966$	−13.4205	+	15.6212i	−0.431799	+	0.502603i
$967$	26.8907	+	26.8907i	0.864746	+	0.864746i	0.991885	−	0.127139i	$-0.0405793\pi$
$967$	26.8907	+	26.8907i	0.864746	+	0.864746i	−0.127139	+	0.991885i	$0.540579\pi$
$968$	−1.25823	−	0.0899904i	−0.0404411	−	0.00289240i
$969$	0.386003	−	0.600632i	0.0124002	−	0.0192951i
$970$	−19.7192	−	24.7839i	−0.633146	−	0.795761i
$971$	−29.9838	−	13.6932i	−0.962227	−	0.439434i	−0.128560	−	0.991702i	$-0.541035\pi$
$971$	−29.9838	−	13.6932i	−0.962227	−	0.439434i	−0.833667	+	0.552267i	$0.813763\pi$
$972$	−0.599278	+	0.800541i	−0.0192218	+	0.0256774i
$973$	6.53840	+	11.9742i	0.209611	+	0.383875i
$974$	18.2119	+	28.3383i	0.583547	+	0.908017i
$975$	2.39260	+	4.51427i	0.0766246	+	0.144572i
$976$	1.62391	+	5.53054i	0.0519802	+	0.177028i
$977$	−2.65329	−	37.0978i	−0.0848862	−	1.18686i	−0.844159	−	0.536093i	$-0.819900\pi$
$977$	−2.65329	−	37.0978i	−0.0848862	−	1.18686i	0.759273	−	0.650772i	$-0.225555\pi$
$978$	−0.0922857	−	1.29032i	−0.00295097	−	0.0412600i
$979$	−2.17053	−	7.39215i	−0.0693704	−	0.236254i
$980$	24.2219	+	8.22944i	0.773741	+	0.262880i
$981$	3.57522	+	5.56315i	0.114148	+	0.177618i
$982$	−6.07876	−	11.1324i	−0.193981	−	0.355249i
$983$	3.34853	−	4.47312i	0.106802	−	0.142670i	−0.743956	−	0.668229i	$-0.767053\pi$
$983$	3.34853	−	4.47312i	0.106802	−	0.142670i	0.850757	+	0.525559i	$0.176144\pi$
$984$	−7.98298	−	3.64571i	−0.254488	−	0.116221i
$985$	6.21592	−	54.6196i	0.198056	−	1.74032i
$986$	1.96133	−	3.05188i	0.0624613	−	0.0971917i
$987$	−5.99320	−	0.428642i	−0.190766	−	0.0136438i
$988$	−1.10682	−	1.10682i	−0.0352126	−	0.0352126i
$989$	−13.0104	+	6.00829i	−0.413706	+	0.191053i
$990$	−7.82649	+	0.230817i	−0.248742	+	0.00733586i
$991$	2.78345	+	3.21227i	0.0884192	+	0.102041i	0.798235	−	0.602346i	$-0.205767\pi$
$991$	2.78345	+	3.21227i	0.0884192	+	0.102041i	−0.709816	+	0.704387i	$0.751222\pi$
$992$	−1.13289	−	5.20783i	−0.0359694	−	0.165349i
$993$	4.12222	+	5.50664i	0.130815	+	0.174748i
$994$	26.2418	−	57.4615i	0.832339	−	1.82257i
$995$	29.7379	+	20.9226i	0.942756	+	0.663291i
$996$	2.76472	−	9.41576i	0.0876034	−	0.298350i
$997$	−46.6348	−	10.1448i	−1.47694	−	0.321289i	−0.599268	−	0.800549i	$-0.704541\pi$
$997$	−46.6348	−	10.1448i	−1.47694	−	0.321289i	−0.877673	+	0.479260i	$0.840905\pi$
$998$	6.19372	+	2.31014i	0.196059	+	0.0731261i
$999$	0.559758	−	0.164360i	0.0177100	−	0.00520012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.217.10	yes	240
5.3	odd	4	inner	690.2.w.a.493.2	yes	240
23.7	odd	22	inner	690.2.w.a.7.2	✓	240
115.53	even	44	inner	690.2.w.a.283.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.2	✓	240	23.7	odd	22	inner
690.2.w.a.217.10	yes	240	1.1	even	1	trivial
690.2.w.a.283.10	yes	240	115.53	even	44	inner
690.2.w.a.493.2	yes	240	5.3	odd	4	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.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.842847 - 2.07114i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.76897 - 2.05801i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-0.842847 - 2.07114i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(3.76897 - 2.05801i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-2.12599 + 0.692946i) q^{10} +(2.64636 + 2.29308i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(0.489708 - 0.896834i) q^{13} +(-1.78389 - 3.90618i) q^{14} +(-1.26384 - 1.84465i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.373122 - 0.279315i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(-0.218004 + 1.51625i) q^{19} +(0.539515 + 2.17001i) q^{20} +(3.24537 - 2.81213i) q^{21} +(2.47603 - 2.47603i) q^{22} +(-1.03924 - 4.68188i) q^{23} +1.00000i q^{24} +(-3.57922 + 3.49130i) q^{25} +(-0.859613 - 0.552440i) q^{26} +(0.800541 - 0.599278i) q^{27} +(-4.02349 + 1.50068i) q^{28} +(-7.70426 + 1.10771i) q^{29} +(-1.93011 + 1.12902i) q^{30} +(4.48357 - 2.88141i) q^{31} +(0.349464 - 0.936950i) q^{32} +(3.07331 + 1.67815i) q^{33} +(-0.305222 + 0.352245i) q^{34} +(-7.43908 - 6.07146i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.546607 + 0.203874i) q^{37} +(1.49684 + 0.325617i) q^{38} +(0.287881 - 0.980433i) q^{39} +(2.20297 - 0.383333i) q^{40} +(-3.64571 + 7.98298i) q^{41} +(-2.57344 - 3.43772i) q^{42} +(-0.635179 - 2.91987i) q^{43} +(-2.29308 - 2.64636i) q^{44} +(-1.62706 - 1.53384i) q^{45} +(-4.74409 + 0.702595i) q^{46} +(-0.989385 - 0.989385i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(6.18520 - 9.62437i) q^{49} +(3.22707 + 3.81917i) q^{50} +(-0.423967 - 0.193619i) q^{51} +(-0.612357 + 0.818013i) q^{52} +(-5.43578 - 9.95488i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(2.51881 - 7.41369i) q^{55} +(1.20983 + 4.12029i) q^{56} +(0.109281 + 1.52794i) q^{57} +(0.555267 + 7.76365i) q^{58} +(0.205474 + 0.699779i) q^{59} +(0.988453 + 2.00573i) q^{60} +(3.11627 + 4.84901i) q^{61} +(-2.55422 - 4.67770i) q^{62} +(2.57344 - 3.43772i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-2.27022 - 0.258359i) q^{65} +(1.89313 - 2.94576i) q^{66} +(11.8224 + 0.845557i) q^{67} +(0.329573 + 0.329573i) q^{68} +(-2.01070 - 4.35397i) q^{69} +(-6.58668 + 6.98700i) q^{70} +(9.63328 + 11.1174i) q^{71} +(0.212565 + 0.977147i) q^{72} +(1.88888 + 2.52325i) q^{73} +(0.242349 - 0.530670i) q^{74} +(-2.75529 + 4.17233i) q^{75} +(0.431571 - 1.46979i) q^{76} +(14.6932 + 3.19631i) q^{77} +(-0.957398 - 0.357091i) q^{78} +(-8.14319 + 2.39106i) q^{79} +(-0.225199 - 2.22470i) q^{80} +(0.654861 - 0.755750i) q^{81} +(7.70256 + 4.20592i) q^{82} +(-3.42938 + 9.19453i) q^{83} +(-3.61255 + 2.32164i) q^{84} +(-0.264016 + 1.00821i) q^{85} +(-2.95775 + 0.425260i) q^{86} +(-7.29273 + 2.72005i) q^{87} +(-2.80320 + 2.09845i) q^{88} +(-1.85091 - 1.18951i) q^{89} +(-1.64601 + 1.51349i) q^{90} -4.38796i q^{91} +(0.362365 + 4.78212i) q^{92} +(3.76862 - 3.76862i) q^{93} +(-1.05745 + 0.916282i) q^{94} +(3.32411 - 0.826453i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.94979 + 13.2709i) q^{97} +(-9.15860 - 6.85604i) q^{98} +(3.35979 + 0.986524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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