LMFDB - Embedded newform 690.2.w.a.217.8

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			217.8
Character	$\chi$	$=$	690.217
Dual form			690.2.w.a.283.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.72850 - 1.41855i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.29243 + 2.34384i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.72850 - 1.41855i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.29243 + 2.34384i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-1.53824 + 1.62290i) q^{10} +(1.50612 + 1.30506i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-0.133687 + 0.244830i) q^{13} +(2.03165 + 4.44870i) q^{14} +(-1.99054 - 1.01871i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-2.43486 - 1.82271i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(-0.800012 + 5.56421i) q^{19} +(1.50903 + 1.65010i) q^{20} +(-3.69611 + 3.20270i) q^{21} +(1.40918 - 1.40918i) q^{22} +(0.205848 + 4.79141i) q^{23} +1.00000i q^{24} +(0.975443 + 4.90393i) q^{25} +(0.234669 + 0.150813i) q^{26} +(0.800541 - 0.599278i) q^{27} +(4.58230 - 1.70911i) q^{28} +(1.36321 - 0.196000i) q^{29} +(-1.15812 + 1.91279i) q^{30} +(-4.02938 + 2.58953i) q^{31} +(0.349464 - 0.936950i) q^{32} +(1.74912 + 0.955089i) q^{33} +(-1.99177 + 2.29863i) q^{34} +(10.7443 + 2.03768i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-8.75718 - 3.26626i) q^{37} +(5.49296 + 1.19492i) q^{38} +(-0.0785898 + 0.267652i) q^{39} +(1.75355 - 1.38747i) q^{40} +(-3.49392 + 7.65063i) q^{41} +(2.93086 + 3.91517i) q^{42} +(-0.412041 - 1.89412i) q^{43} +(-1.30506 - 1.50612i) q^{44} +(-2.16159 - 0.572311i) q^{45} +(4.79389 + 0.136492i) q^{46} +(1.51427 + 1.51427i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(9.14684 - 14.2328i) q^{49} +(4.96102 - 0.623115i) q^{50} +(-2.76666 - 1.26349i) q^{51} +(0.167169 - 0.223312i) q^{52} +(-2.56140 - 4.69085i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-0.752043 - 4.39231i) q^{55} +(-1.37786 - 4.69255i) q^{56} +(0.401028 + 5.60710i) q^{57} +(-0.0982503 - 1.37372i) q^{58} +(1.00990 + 3.43939i) q^{59} +(1.82530 + 1.29162i) q^{60} +(-8.04008 - 12.5106i) q^{61} +(2.29548 + 4.20385i) q^{62} +(-2.93086 + 3.91517i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(0.578382 - 0.233547i) q^{65} +(1.07744 - 1.67652i) q^{66} +(-14.5583 - 1.04123i) q^{67} +(2.15068 + 2.15068i) q^{68} +(1.21963 + 4.63816i) q^{69} +(2.79897 - 10.5716i) q^{70} +(-2.87789 - 3.32126i) q^{71} +(0.212565 + 0.977147i) q^{72} +(2.88765 + 3.85745i) q^{73} +(-3.88267 + 8.50186i) q^{74} +(1.99556 + 4.58451i) q^{75} +(1.58374 - 5.39372i) q^{76} +(-9.52378 - 2.07177i) q^{77} +(0.261364 + 0.0974836i) q^{78} +(7.25291 - 2.12965i) q^{79} +(-1.25883 - 1.84806i) q^{80} +(0.654861 - 0.755750i) q^{81} +(7.38188 + 4.03081i) q^{82} +(1.54072 - 4.13083i) q^{83} +(4.11428 - 2.64409i) q^{84} +(1.62306 + 6.60453i) q^{85} +(-1.91869 + 0.275866i) q^{86} +(1.29039 - 0.481292i) q^{87} +(-1.59539 + 1.19429i) q^{88} +(1.70958 + 1.09868i) q^{89} +(-0.725058 + 2.11525i) q^{90} -1.36426i q^{91} +(0.478136 - 4.77194i) q^{92} +(-3.38685 + 3.38685i) q^{93} +(1.61844 - 1.40238i) q^{94} +(9.27592 - 8.48289i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.74617 + 12.7250i) q^{97} +(-13.5440 - 10.1389i) q^{98} +(1.91216 + 0.561461i) 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
$5$	−1.72850	−	1.41855i	−0.773010	−	0.634394i
$5$	−1.72850	−	1.41855i	−0.773010	−	0.634394i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−4.29243	+	2.34384i	−1.62238	+	0.885889i	−0.628217	+	0.778038i	$0.716215\pi$
$7$	−4.29243	+	2.34384i	−1.62238	+	0.885889i	−0.994167	+	0.107851i	$0.965603\pi$
$8$	−0.212565	+	0.977147i	−0.0751532	+	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	−1.53824	+	1.62290i	−0.486435	+	0.513206i
$11$	1.50612	+	1.30506i	0.454113	+	0.393491i	0.851664	−	0.524089i	$-0.175594\pi$
$11$	1.50612	+	1.30506i	0.454113	+	0.393491i	−0.397550	+	0.917580i	$0.630140\pi$
$12$	−0.997452	+	0.0713392i	−0.287940	+	0.0205938i
$13$	−0.133687	+	0.244830i	−0.0370782	+	0.0679036i	−0.895561	−	0.444938i	$-0.853226\pi$
$13$	−0.133687	+	0.244830i	−0.0370782	+	0.0679036i	0.858483	+	0.512842i	$0.171407\pi$
$14$	2.03165	+	4.44870i	0.542982	+	1.18896i
$15$	−1.99054	−	1.01871i	−0.513954	−	0.263030i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−2.43486	−	1.82271i	−0.590540	−	0.442073i	0.261755	−	0.965134i	$-0.415699\pi$
$17$	−2.43486	−	1.82271i	−0.590540	−	0.442073i	−0.852295	+	0.523061i	$0.824790\pi$
$18$	−0.349464	−	0.936950i	−0.0823695	−	0.220841i
$19$	−0.800012	+	5.56421i	−0.183535	+	1.27652i	0.664785	+	0.747034i	$0.268523\pi$
$19$	−0.800012	+	5.56421i	−0.183535	+	1.27652i	−0.848321	+	0.529482i	$0.822386\pi$
$20$	1.50903	+	1.65010i	0.337429	+	0.368974i
$21$	−3.69611	+	3.20270i	−0.806557	+	0.698886i
$22$	1.40918	−	1.40918i	0.300439	−	0.300439i
$23$	0.205848	+	4.79141i	0.0429223	+	0.999078i
$23$	0.205848	+	4.79141i	0.0429223	+	0.999078i
$24$			1.00000i			0.204124i
$25$	0.975443	+	4.90393i	0.195089	+	0.980786i
$26$	0.234669	+	0.150813i	0.0460224	+	0.0295768i
$27$	0.800541	−	0.599278i	0.154064	−	0.115331i
$28$	4.58230	−	1.70911i	0.865973	−	0.322991i
$29$	1.36321	−	0.196000i	0.253142	−	0.0363963i	−0.0145757	−	0.999894i	$-0.504640\pi$
$29$	1.36321	−	0.196000i	0.253142	−	0.0363963i	0.267717	+	0.963498i	$0.413731\pi$
$30$	−1.15812	+	1.91279i	−0.211442	+	0.349226i
$31$	−4.02938	+	2.58953i	−0.723698	+	0.465093i	−0.849922	−	0.526909i	$-0.823351\pi$
$31$	−4.02938	+	2.58953i	−0.723698	+	0.465093i	0.126223	+	0.992002i	$0.459714\pi$
$32$	0.349464	−	0.936950i	0.0617771	−	0.165631i
$33$	1.74912	+	0.955089i	0.304482	+	0.166260i
$34$	−1.99177	+	2.29863i	−0.341586	+	0.394211i
$35$	10.7443	+	2.03768i	1.81612	+	0.344430i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−8.75718	−	3.26626i	−1.43967	−	0.536970i	−0.496137	−	0.868244i	$-0.665249\pi$
$37$	−8.75718	−	3.26626i	−1.43967	−	0.536970i	−0.943534	+	0.331275i	$0.892521\pi$
$38$	5.49296	+	1.19492i	0.891076	+	0.193842i
$39$	−0.0785898	+	0.267652i	−0.0125844	+	0.0428586i
$40$	1.75355	−	1.38747i	0.277261	−	0.219378i
$41$	−3.49392	+	7.65063i	−0.545659	+	1.19483i	0.413120	+	0.910676i	$0.364439\pi$
$41$	−3.49392	+	7.65063i	−0.545659	+	1.19483i	−0.958780	+	0.284151i	$0.908288\pi$
$42$	2.93086	+	3.91517i	0.452242	+	0.604124i
$43$	−0.412041	−	1.89412i	−0.0628357	−	0.288851i	0.934997	−	0.354656i	$-0.115402\pi$
$43$	−0.412041	−	1.89412i	−0.0628357	−	0.288851i	−0.997832	+	0.0658051i	$0.979038\pi$
$44$	−1.30506	−	1.50612i	−0.196746	−	0.227057i
$45$	−2.16159	−	0.572311i	−0.322230	−	0.0853151i
$46$	4.79389	+	0.136492i	0.706820	+	0.0201246i
$47$	1.51427	+	1.51427i	0.220879	+	0.220879i	0.808868	−	0.587990i	$-0.200080\pi$
$47$	1.51427	+	1.51427i	0.220879	+	0.220879i	−0.587990	+	0.808868i	$0.700080\pi$
$48$	0.997452	+	0.0713392i	0.143970	+	0.0102969i
$49$	9.14684	−	14.2328i	1.30669	−	2.03325i
$50$	4.96102	−	0.623115i	0.701594	−	0.0881218i
$51$	−2.76666	−	1.26349i	−0.387410	−	0.176924i
$52$	0.167169	−	0.223312i	0.0231822	−	0.0309678i
$53$	−2.56140	−	4.69085i	−0.351835	−	0.644337i	0.640494	−	0.767963i	$-0.278730\pi$
$53$	−2.56140	−	4.69085i	−0.351835	−	0.644337i	−0.992329	+	0.123626i	$0.960548\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−0.752043	−	4.39231i	−0.101405	−	0.592260i
$56$	−1.37786	−	4.69255i	−0.184124	−	0.627068i
$57$	0.401028	+	5.60710i	0.0531174	+	0.742679i
$58$	−0.0982503	−	1.37372i	−0.0129009	−	0.180378i
$59$	1.00990	+	3.43939i	0.131477	+	0.447770i	0.998746	−	0.0500704i	$-0.0159446\pi$
$59$	1.00990	+	3.43939i	0.131477	+	0.447770i	−0.867268	+	0.497841i	$0.834126\pi$
$60$	1.82530	+	1.29162i	0.235645	+	0.166748i
$61$	−8.04008	−	12.5106i	−1.02943	−	1.60182i	−0.772107	−	0.635493i	$-0.780797\pi$
$61$	−8.04008	−	12.5106i	−1.02943	−	1.60182i	−0.257320	−	0.966326i	$-0.582839\pi$
$62$	2.29548	+	4.20385i	0.291526	+	0.533889i
$63$	−2.93086	+	3.91517i	−0.369254	+	0.493265i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	0.578382	−	0.233547i	0.0717395	−	0.0289680i
$66$	1.07744	−	1.67652i	0.132623	−	0.206366i
$67$	−14.5583	−	1.04123i	−1.77858	−	0.127207i	−0.856981	−	0.515347i	$-0.827663\pi$
$67$	−14.5583	−	1.04123i	−1.77858	−	0.127207i	−0.921600	+	0.388141i	$0.873118\pi$
$68$	2.15068	+	2.15068i	0.260808	+	0.260808i
$69$	1.21963	+	4.63816i	0.146826	+	0.558368i
$70$	2.79897	−	10.5716i	0.334541	−	1.26355i
$71$	−2.87789	−	3.32126i	−0.341543	−	0.394161i	0.558829	−	0.829283i	$-0.311251\pi$
$71$	−2.87789	−	3.32126i	−0.341543	−	0.394161i	−0.900372	+	0.435122i	$0.856705\pi$
$72$	0.212565	+	0.977147i	0.0250511	+	0.115158i
$73$	2.88765	+	3.85745i	0.337974	+	0.451481i	0.937041	−	0.349218i	$-0.113553\pi$
$73$	2.88765	+	3.85745i	0.337974	+	0.451481i	−0.599067	+	0.800699i	$0.704462\pi$
$74$	−3.88267	+	8.50186i	−0.451351	+	0.988321i
$75$	1.99556	+	4.58451i	0.230427	+	0.529374i
$76$	1.58374	−	5.39372i	0.181667	−	0.618702i
$77$	−9.52378	−	2.07177i	−1.08534	−	0.236100i
$78$	0.261364	+	0.0974836i	0.0295936	+	0.0110378i
$79$	7.25291	−	2.12965i	0.816016	−	0.239604i	0.153016	−	0.988224i	$-0.451101\pi$
$79$	7.25291	−	2.12965i	0.816016	−	0.239604i	0.663000	+	0.748620i	$0.269283\pi$
$80$	−1.25883	−	1.84806i	−0.140742	−	0.206620i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	7.38188	+	4.03081i	0.815192	+	0.445129i
$83$	1.54072	−	4.13083i	0.169116	−	0.453418i	−0.824550	−	0.565789i	$-0.808572\pi$
$83$	1.54072	−	4.13083i	0.169116	−	0.453418i	0.993666	+	0.112371i	$0.0358445\pi$
$84$	4.11428	−	2.64409i	0.448905	−	0.288494i
$85$	1.62306	+	6.60453i	0.176045	+	0.716362i
$86$	−1.91869	+	0.275866i	−0.206898	+	0.0297474i
$87$	1.29039	−	0.481292i	0.138345	−	0.0515999i
$88$	−1.59539	+	1.19429i	−0.170069	+	0.127312i
$89$	1.70958	+	1.09868i	0.181215	+	0.116460i	0.628103	−	0.778130i	$-0.283832\pi$
$89$	1.70958	+	1.09868i	0.181215	+	0.116460i	−0.446889	+	0.894590i	$0.647468\pi$
$90$	−0.725058	+	2.11525i	−0.0764279	+	0.222967i
$91$		−	1.36426i		−	0.143013i
$92$	0.478136	−	4.77194i	0.0498491	−	0.497509i
$93$	−3.38685	+	3.38685i	−0.351200	+	0.351200i
$94$	1.61844	−	1.40238i	0.166929	−	0.144645i
$95$	9.27592	−	8.48289i	0.951689	−	0.870326i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	4.74617	+	12.7250i	0.481900	+	1.29202i	0.919583	+	0.392895i	$0.128527\pi$
$97$	4.74617	+	12.7250i	0.481900	+	1.29202i	−0.437683	+	0.899129i	$0.644201\pi$
$98$	−13.5440	−	10.1389i	−1.36815	−	1.02418i
$99$	1.91216	+	0.561461i	0.192179	+	0.0564290i
$100$	−0.267612	−	4.99283i	−0.0267612	−	0.499283i
$101$	6.27379	+	13.7377i	0.624266	+	1.36695i	0.912376	+	0.409354i	$0.134246\pi$
$101$	6.27379	+	13.7377i	0.624266	+	1.36695i	−0.288110	+	0.957597i	$0.593027\pi$
$102$	−1.45764	+	2.66948i	−0.144328	+	0.264318i
$103$	−6.10371	+	0.436546i	−0.601416	+	0.0430141i	−0.368728	−	0.929537i	$-0.620207\pi$
$103$	−6.10371	+	0.436546i	−0.601416	+	0.0430141i	−0.232688	+	0.972551i	$0.574752\pi$
$104$	−0.210818	−	0.182674i	−0.0206724	−	0.0179127i
$105$	10.9319	−	0.292762i	1.06685	−	0.0285706i
$106$	−4.86162	+	2.22023i	−0.472202	+	0.215648i
$107$	−0.182406	+	0.838508i	−0.0176339	+	0.0810616i	−0.985123	−	0.171852i	$-0.945025\pi$
$107$	−0.182406	+	0.838508i	−0.0176339	+	0.0810616i	0.967489	+	0.252913i	$0.0813887\pi$
$108$	−0.877679	+	0.479249i	−0.0844547	+	0.0461158i
$109$	−0.651483	−	4.53117i	−0.0624008	−	0.434007i	−0.996942	−	0.0781509i	$-0.975098\pi$
$109$	−0.651483	−	4.53117i	−0.0624008	−	0.434007i	0.934541	−	0.355856i	$-0.115811\pi$
$110$	−4.43477	+	0.436783i	−0.422839	+	0.0416456i
$111$	−9.25134	−	1.33014i	−0.878099	−	0.126252i
$112$	−4.77889	+	1.03958i	−0.451563	+	0.0982314i
$113$	0.324808	−	4.54141i	0.0305553	−	0.427219i	−0.959033	−	0.283294i	$-0.908573\pi$
$113$	0.324808	−	4.54141i	0.0305553	−	0.427219i	0.989589	−	0.143926i	$-0.0459726\pi$
$114$	5.62143			0.526495
$115$	6.44104	−	8.57397i	0.600630	−	0.799527i
$116$	−1.37723			−0.127872
$117$	−0.0199002	+	0.278241i	−0.00183977	+	0.0257234i
$118$	3.50267	−	0.761960i	0.322447	−	0.0701441i
$119$	14.7236	+	2.11694i	1.34971	+	0.194059i
$120$	1.41855	−	1.72850i	0.129495	−	0.157790i
$121$	−1.00025	−	6.95686i	−0.0909314	−	0.632442i
$122$	−13.0523	+	7.12710i	−1.18170	+	0.645257i
$123$	−1.78782	+	8.21847i	−0.161202	+	0.741035i
$124$	4.35690	−	1.98973i	0.391261	−	0.178683i
$125$	5.27040	−	9.86017i	0.471399	−	0.881920i
$126$	3.69611	+	3.20270i	0.329276	+	0.285319i
$127$	−14.2215	+	1.01714i	−1.26195	+	0.0902566i	−0.686227	−	0.727387i	$-0.740734\pi$
$127$	−14.2215	+	1.01714i	−1.26195	+	0.0902566i	−0.575725	+	0.817644i	$0.695280\pi$
$128$	−0.479249	+	0.877679i	−0.0423600	+	0.0775766i
$129$	−0.805250	−	1.76325i	−0.0708983	−	0.155246i
$130$	−0.191691	−	0.593569i	−0.0168124	−	0.0520595i
$131$	15.7201	+	4.61585i	1.37348	+	0.403289i	0.883493	−	0.468443i	$-0.155185\pi$
$131$	15.7201	+	4.61585i	1.37348	+	0.403289i	0.489982	+	0.871732i	$0.337003\pi$
$132$	−1.59539	−	1.19429i	−0.138861	−	0.103950i
$133$	−9.60763	−	25.7590i	−0.833087	−	2.23359i
$134$	−2.07716	+	14.4469i	−0.179439	+	1.24803i
$135$	−2.23384	−	0.0997532i	−0.192258	−	0.00858539i
$136$	2.29863	−	1.99177i	0.197106	−	0.170793i
$137$	−3.33155	+	3.33155i	−0.284633	+	0.284633i	−0.834954	−	0.550320i	$-0.814506\pi$
$137$	−3.33155	+	3.33155i	−0.284633	+	0.284633i	0.550320	+	0.834954i	$0.314506\pi$
$138$	4.71335	−	0.885642i	0.401227	−	0.0753908i
$139$			1.19039i			0.100968i	0.998725	+	0.0504838i	$0.0160763\pi$
$139$			1.19039i			0.100968i	−0.998725	+	0.0504838i	$0.983924\pi$
$140$	−10.3450	−	3.54601i	−0.874309	−	0.299693i
$141$	1.80154	+	1.15778i	0.151717	+	0.0975028i
$142$	−3.51811	+	2.63362i	−0.295233	+	0.221009i
$143$	−0.520868	+	0.194274i	−0.0435572	+	0.0162460i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	−2.63435	−	1.59499i	−0.218770	−	0.132457i
$146$	4.05363	−	2.60511i	0.335480	−	0.215600i
$147$	5.91241	−	15.8518i	0.487648	−	1.30743i
$148$	8.20321	+	4.47929i	0.674299	+	0.368195i
$149$	−7.75232	+	8.94665i	−0.635094	+	0.732938i	−0.978499	−	0.206249i	$-0.933874\pi$
$149$	−7.75232	+	8.94665i	−0.635094	+	0.732938i	0.343405	+	0.939187i	$0.388420\pi$
$150$	4.71519	−	1.66342i	0.384994	−	0.135817i
$151$	9.50239	−	2.79015i	0.773293	−	0.227059i	0.128801	−	0.991670i	$-0.458887\pi$
$151$	9.50239	−	2.79015i	0.773293	−	0.227059i	0.644492	+	0.764611i	$0.277069\pi$
$152$	−5.26699	−	1.96449i	−0.427210	−	0.159341i
$153$	−2.97201	−	0.646521i	−0.240273	−	0.0522681i
$154$	−2.74591	+	9.35172i	−0.221272	+	0.753583i
$155$	10.6382	+	1.23987i	0.854478	+	0.0995886i
$156$	0.115881	−	0.253743i	0.00927788	−	0.0203157i
$157$	9.31251	+	12.4401i	0.743219	+	0.992824i	0.999655	+	0.0262631i	$0.00836077\pi$
$157$	9.31251	+	12.4401i	0.743219	+	0.992824i	−0.256436	+	0.966561i	$0.582548\pi$
$158$	−1.60680	−	7.38636i	−0.127830	−	0.587627i
$159$	−3.49997	−	4.03918i	−0.277566	−	0.320328i
$160$	−1.93316	+	1.12379i	−0.152830	+	0.0888433i
$161$	−12.1139	−	20.0843i	−0.954709	−	1.58286i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−1.26431	−	0.0904249i	−0.0990281	−	0.00708263i	0.0217372	−	0.999764i	$-0.493080\pi$
$163$	−1.26431	−	0.0904249i	−0.0990281	−	0.00708263i	−0.120765	+	0.992681i	$0.538535\pi$
$164$	4.54716	−	7.07552i	0.355073	−	0.552505i
$165$	−1.66851	−	4.13208i	−0.129893	−	0.321682i
$166$	−4.01039	−	1.83148i	−0.311267	−	0.142151i
$167$	6.99218	−	9.34047i	0.541072	−	0.722787i	−0.443790	−	0.896131i	$-0.646366\pi$
$167$	6.99218	−	9.34047i	0.541072	−	0.722787i	0.984861	+	0.173344i	$0.0554572\pi$
$168$	−2.34384	−	4.29243i	−0.180831	−	0.331168i
$169$	6.98626	+	10.8708i	0.537405	+	0.836218i
$170$	6.70349	−	1.14776i	0.514134	−	0.0880291i
$171$	1.58374	+	5.39372i	0.121112	+	0.412468i
$172$	0.138285	+	1.93348i	0.0105442	+	0.147427i
$173$	−0.578769	−	8.09225i	−0.0440030	−	0.615242i	−0.970832	−	0.239760i	$-0.922931\pi$
$173$	−0.578769	−	8.09225i	−0.0440030	−	0.615242i	0.926829	−	0.375483i	$-0.122523\pi$
$174$	−0.388010	−	1.32144i	−0.0294149	−	0.100178i
$175$	−15.6810	−	18.7635i	−1.18538	−	1.41838i
$176$	1.07744	+	1.67652i	0.0812148	+	0.126373i
$177$	1.71791	+	3.14612i	0.129126	+	0.236477i
$178$	1.21784	−	1.62684i	0.0912808	−	0.121937i
$179$	−14.0404	−	6.41204i	−1.04943	−	0.479259i	−0.185381	−	0.982667i	$-0.559352\pi$
$179$	−14.0404	−	6.41204i	−1.04943	−	0.479259i	−0.864049	+	0.503408i	$0.832079\pi$
$180$	2.05814	+	0.874111i	0.153404	+	0.0651524i
$181$	−4.57070	+	7.11216i	−0.339738	+	0.528642i	−0.968519	−	0.248940i	$-0.919918\pi$
$181$	−4.57070	+	7.11216i	−0.339738	+	0.528642i	0.628781	+	0.777582i	$0.283554\pi$
$182$	−1.36078	−	0.0973249i	−0.100868	−	0.00721420i
$183$	−10.5157	−	10.5157i	−0.777340	−	0.777340i
$184$	−4.72567	−	0.817344i	−0.348381	−	0.0602554i
$185$	10.5035	+	18.0682i	0.772230	+	1.32840i
$186$	3.13661	+	3.61984i	0.229987	+	0.265420i
$187$	−1.28844	−	5.92288i	−0.0942203	−	0.433124i
$188$	−1.28335	−	1.71436i	−0.0935981	−	0.125032i
$189$	−2.03165	+	4.44870i	−0.147781	+	0.323595i
$190$	−7.79954	−	9.85745i	−0.565838	−	0.715134i
$191$	−4.74498	+	16.1599i	−0.343334	+	1.16929i	0.589133	+	0.808036i	$0.299469\pi$
$191$	−4.74498	+	16.1599i	−0.343334	+	1.16929i	−0.932468	+	0.361254i	$0.882349\pi$
$192$	−0.977147	−	0.212565i	−0.0705195	−	0.0153406i
$193$	−18.1696	−	6.77690i	−1.30787	−	0.487812i	−0.403667	−	0.914906i	$-0.632264\pi$
$193$	−18.1696	−	6.77690i	−1.30787	−	0.487812i	−0.904207	+	0.427094i	$0.859537\pi$
$194$	13.0311	−	3.82629i	0.935581	−	0.274711i
$195$	0.515520	−	0.351154i	0.0369172	−	0.0251467i
$196$	−11.0793	+	12.7862i	−0.791376	+	0.913297i
$197$	−12.7168	−	6.94387i	−0.906031	−	0.494730i	−0.0425401	−	0.999095i	$-0.513545\pi$
$197$	−12.7168	−	6.94387i	−0.906031	−	0.494730i	−0.863491	+	0.504364i	$0.831727\pi$
$198$	0.696443	−	1.86723i	0.0494940	−	0.132699i
$199$	−15.9551	+	10.2537i	−1.13102	+	0.726865i	−0.965773	−	0.259387i	$-0.916480\pi$
$199$	−15.9551	+	10.2537i	−1.13102	+	0.726865i	−0.165250	+	0.986252i	$0.552843\pi$
$200$	−4.99920	−	0.0892541i	−0.353497	−	0.00631122i
$201$	−14.4469	+	2.07716i	−1.01901	+	0.146511i
$202$	14.1503	−	5.27777i	0.995609	−	0.371343i
$203$	−5.39208	+	4.03646i	−0.378450	+	0.283304i
$204$	2.55869	+	1.64437i	0.179144	+	0.115129i
$205$	16.8920	−	8.26783i	1.17979	−	0.577450i
$206$			6.11930i			0.426352i
$207$	2.17767	+	4.27291i	0.151359	+	0.296988i
$208$	−0.197249	+	0.197249i	−0.0136767	+	0.0136767i
$209$	−8.46656	+	7.33632i	−0.585644	+	0.507464i
$210$	0.487859	−	10.9250i	0.0336654	−	0.753893i
$211$	2.08477	−	14.4999i	0.143522	−	0.998215i	−0.783013	−	0.622006i	$-0.786318\pi$
$211$	2.08477	−	14.4999i	0.143522	−	0.998215i	0.926535	−	0.376210i	$-0.122773\pi$
$212$	1.86775	+	5.00762i	0.128277	+	0.343925i
$213$	−3.51811	−	2.63362i	−0.241057	−	0.180453i
$214$	0.823359	+	0.241760i	0.0562837	+	0.0165264i
$215$	−1.97469	+	3.85850i	−0.134673	+	0.263147i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	11.2264	−	20.5596i	0.762096	−	1.39568i
$218$	−4.56610	+	0.326574i	−0.309255	+	0.0221184i
$219$	3.64162	+	3.15548i	0.246078	+	0.213228i
$220$	0.119297	+	4.45463i	0.00804300	+	0.300331i
$221$	0.771765	−	0.352453i	0.0519145	−	0.0237086i
$222$	−1.98674	+	9.13288i	−0.133341	+	0.612959i
$223$	7.28085	−	3.97564i	0.487562	−	0.266229i	−0.216611	−	0.976258i	$-0.569500\pi$
$223$	7.28085	−	3.97564i	0.487562	−	0.266229i	0.704172	+	0.710029i	$0.251318\pi$
$224$	0.696013	+	4.84088i	0.0465043	+	0.323445i
$225$	2.92446	+	4.05556i	0.194964	+	0.270370i
$226$	−4.50666	−	0.647960i	−0.299779	−	0.0431017i
$227$	11.4158	−	2.48336i	0.757695	−	0.164826i	0.182909	−	0.983130i	$-0.441449\pi$
$227$	11.4158	−	2.48336i	0.757695	−	0.164826i	0.574786	+	0.818303i	$0.305085\pi$
$228$	0.401028	−	5.60710i	0.0265587	−	0.371339i
$229$	−15.2432			−1.00730			−0.503648	−	0.863909i	$-0.668009\pi$
$229$	−15.2432			−1.00730			−0.503648	+	0.863909i	$0.668009\pi$
$230$	−8.09263	−	7.03629i	−0.533612	−	0.463959i
$231$	−9.74652			−0.641274
$232$	−0.0982503	+	1.37372i	−0.00645045	+	0.0901890i
$233$	13.6747	−	2.97475i	0.895860	−	0.194883i	0.259014	−	0.965873i	$-0.416602\pi$
$233$	13.6747	−	2.97475i	0.895860	−	0.194883i	0.636846	+	0.770991i	$0.280239\pi$
$234$	0.276112	+	0.0396990i	0.0180500	+	0.00259520i
$235$	−0.469355	−	4.76548i	−0.0306173	−	0.310866i
$236$	−0.510140	−	3.54810i	−0.0332073	−	0.230962i
$237$	6.63447	−	3.62269i	0.430955	−	0.235319i
$238$	3.16191	−	14.5351i	0.204956	−	0.942169i
$239$	1.45787	−	0.665786i	0.0943016	−	0.0430661i	−0.367706	−	0.929942i	$-0.619857\pi$
$239$	1.45787	−	0.665786i	0.0943016	−	0.0430661i	0.462007	+	0.886876i	$0.347129\pi$
$240$	−1.62290	−	1.53824i	−0.104758	−	0.0992932i
$241$	18.6512	+	16.1613i	1.20143	+	1.04104i	0.998080	+	0.0619357i	$0.0197274\pi$
$241$	18.6512	+	16.1613i	1.20143	+	1.04104i	0.203347	+	0.979107i	$0.434818\pi$
$242$	−7.01049	+	0.501400i	−0.450652	+	0.0322312i
$243$	0.479249	−	0.877679i	0.0307438	−	0.0563031i
$244$	6.17780	+	13.5275i	0.395493	+	0.866009i
$245$	−36.0002	+	11.6261i	−2.29997	+	0.742766i
$246$	8.06999	+	2.36956i	0.514524	+	0.151078i
$247$	−1.25533	−	0.939731i	−0.0798750	−	0.0597936i
$248$	−1.67384	−	4.48774i	−0.106289	−	0.284972i
$249$	0.627439	−	4.36393i	0.0397623	−	0.276553i
$250$	−9.45906	−	5.96039i	−0.598243	−	0.376968i
$251$	19.8769	−	17.2235i	1.25462	−	1.08713i	0.262102	−	0.965040i	$-0.415584\pi$
$251$	19.8769	−	17.2235i	1.25462	−	1.08713i	0.992518	−	0.122095i	$-0.0389611\pi$
$252$	3.45822	−	3.45822i	0.217847	−	0.217847i
$253$	−5.94306	+	7.48510i	−0.373637	+	0.470584i
$254$			14.2578i			0.894614i
$255$	2.98986	+	6.10859i	0.187232	+	0.382535i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−14.7100	+	11.0118i	−0.917584	+	0.686894i	−0.949890	−	0.312584i	$-0.898806\pi$
$257$	−14.7100	+	11.0118i	−0.917584	+	0.686894i	0.0323067	+	0.999478i	$0.489715\pi$
$258$	−1.81620	+	0.677409i	−0.113072	+	0.0421737i
$259$	45.2451	−	6.50527i	2.81140	−	0.404218i
$260$	−0.605732	+	0.148858i	−0.0375659	+	0.00923178i
$261$	1.15860	−	0.744585i	0.0717154	−	0.0460887i
$262$	5.72555	−	15.3508i	0.353726	−	0.948376i
$263$	23.5006	+	12.8323i	1.44911	+	0.791273i	0.995019	−	0.0996838i	$-0.0317831\pi$
$263$	23.5006	+	12.8323i	1.44911	+	0.791273i	0.454089	+	0.890957i	$0.349965\pi$
$264$	−1.30506	+	1.50612i	−0.0803211	+	0.0926955i
$265$	−2.22681	+	11.7416i	−0.136792	+	0.721281i
$266$	−26.3788	+	7.74552i	−1.61739	+	0.474908i
$267$	1.90405	+	0.710173i	0.116526	+	0.0434619i
$268$	14.2620	+	3.10250i	0.871187	+	0.189515i
$269$	4.67026	−	15.9054i	0.284751	−	0.969772i	−0.685581	−	0.727996i	$-0.740452\pi$
$269$	4.67026	−	15.9054i	0.284751	−	0.969772i	0.970332	−	0.241776i	$-0.0777300\pi$
$270$	−0.258859	+	2.22103i	−0.0157537	+	0.135168i
$271$	−4.23459	+	9.27246i	−0.257233	+	0.563262i	−0.993553	−	0.113372i	$-0.963835\pi$
$271$	−4.23459	+	9.27246i	−0.257233	+	0.563262i	0.736320	+	0.676634i	$0.236562\pi$
$272$	−1.82271	−	2.43486i	−0.110518	−	0.147635i
$273$	−0.289994	−	1.33308i	−0.0175512	−	0.0806816i
$274$	3.08539	+	3.56073i	0.186395	+	0.215112i
$275$	−4.93080	+	8.65894i	−0.297338	+	0.522154i
$276$	−0.547139	−	4.76452i	−0.0329339	−	0.286790i
$277$	−11.1432	−	11.1432i	−0.669530	−	0.669530i	0.288077	−	0.957607i	$-0.406984\pi$
$277$	−11.1432	−	11.1432i	−0.669530	−	0.669530i	−0.957607	+	0.288077i	$0.906984\pi$
$278$	1.18736	+	0.0849215i	0.0712129	+	0.00509325i
$279$	−2.58953	+	4.02938i	−0.155031	+	0.241233i
$280$	−4.27498	+	10.0656i	−0.255479	+	0.601537i
$281$	15.9541	+	7.28602i	0.951745	+	0.434647i	0.829906	−	0.557903i	$-0.188394\pi$
$281$	15.9541	+	7.28602i	0.951745	+	0.434647i	0.121838	+	0.992550i	$0.461121\pi$
$282$	1.28335	−	1.71436i	0.0764226	−	0.102089i
$283$	13.2037	+	24.1808i	0.784881	+	1.43740i	0.896216	+	0.443619i	$0.146305\pi$
$283$	13.2037	+	24.1808i	0.784881	+	1.43740i	−0.111335	+	0.993783i	$0.535513\pi$
$284$	2.37593	+	3.69702i	0.140986	+	0.219378i
$285$	7.26077	−	10.2608i	0.430091	−	0.607796i
$286$	0.156621	+	0.533400i	0.00926117	+	0.0315406i
$287$	−2.93445	−	41.0289i	−0.173215	−	2.42186i
$288$	−0.0713392	−	0.997452i	−0.00420370	−	0.0587754i
$289$	−2.18319	−	7.43527i	−0.128423	−	0.437369i
$290$	−1.77886	+	2.51385i	−0.104458	+	0.147618i
$291$	7.34259	+	11.4253i	0.430430	+	0.669762i
$292$	−2.30929	−	4.22914i	−0.135141	−	0.247492i
$293$	16.8901	−	22.5626i	0.986732	−	1.31812i	0.0389366	−	0.999242i	$-0.487603\pi$
$293$	16.8901	−	22.5626i	0.986732	−	1.31812i	0.947796	−	0.318878i	$-0.103306\pi$
$294$	−15.3896	−	7.02820i	−0.897541	−	0.409893i
$295$	3.13333	−	7.37758i	0.182430	−	0.429539i
$296$	5.05309	−	7.86276i	0.293705	−	0.457013i
$297$	1.98781	+	0.142171i	0.115344	+	0.00824959i
$298$	8.37081	+	8.37081i	0.484908	+	0.484908i
$299$	−1.20060	−	0.590153i	−0.0694325	−	0.0341294i
$300$	−1.32280	−	4.82185i	−0.0763719	−	0.278389i
$301$	6.20818	+	7.16463i	0.357834	+	0.412962i
$302$	−2.10515	−	9.67722i	−0.121138	−	0.556862i
$303$	9.05058	+	12.0902i	0.519942	+	0.694561i
$304$	−2.33522	+	5.11343i	−0.133934	+	0.293275i
$305$	−3.84960	+	33.0299i	−0.220427	+	1.89128i
$306$	−0.856895	+	2.91832i	−0.0489854	+	0.166829i
$307$	19.7134	+	4.28838i	1.12510	+	0.244751i	0.736356	−	0.676594i	$-0.236545\pi$
$307$	19.7134	+	4.28838i	1.12510	+	0.244751i	0.388745	+	0.921345i	$0.372909\pi$
$308$	9.13200	+	3.40606i	0.520344	+	0.194078i
$309$	−5.87142	+	1.72401i	−0.334014	+	0.0980752i
$310$	1.99563	−	10.5226i	0.113344	−	0.597644i
$311$	−3.65443	+	4.21744i	−0.207224	+	0.239149i	−0.849842	−	0.527037i	$-0.823303\pi$
$311$	−3.65443	+	4.21744i	−0.207224	+	0.239149i	0.642618	+	0.766187i	$0.277848\pi$
$312$	−0.244830	−	0.133687i	−0.0138608	−	0.00756855i
$313$	−5.99833	+	16.0822i	−0.339046	+	0.909017i	0.649804	+	0.760102i	$0.274851\pi$
$313$	−5.99833	+	16.0822i	−0.339046	+	0.909017i	−0.988850	+	0.148915i	$0.952422\pi$
$314$	13.0727	−	8.40132i	0.737735	−	0.474114i
$315$	10.6199	−	2.60982i	0.598361	−	0.147047i
$316$	−7.48217	+	1.07577i	−0.420905	+	0.0605170i
$317$	−27.1630	+	10.1313i	−1.52563	+	0.569030i	−0.965734	−	0.259535i	$-0.916431\pi$
$317$	−27.1630	+	10.1313i	−1.52563	+	0.569030i	−0.559894	+	0.828565i	$0.689158\pi$
$318$	−4.27857	+	3.20290i	−0.239931	+	0.179610i
$319$	2.30895	+	1.48387i	0.129277	+	0.0830810i
$320$	0.983015	+	2.00840i	0.0549522	+	0.112273i
$321$			0.858119i			0.0478955i
$322$	−20.8973	+	10.6502i	−1.16456	+	0.593514i
$323$	12.0899	−	12.0899i	0.672699	−	0.672699i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	−1.33103	−	0.416775i	−0.0738324	−	0.0231185i
$326$	−0.180389	+	1.25463i	−0.00999083	+	0.0694877i
$327$	−1.59976	−	4.28913i	−0.0884671	−	0.237190i
$328$	−6.73310	−	5.04033i	−0.371773	−	0.278306i
$329$	−10.0491	−	2.95068i	−0.554024	−	0.162676i
$330$	−4.24058	+	1.36948i	−0.233436	+	0.0753874i
$331$	12.7284	+	27.8713i	0.699617	+	1.53195i	0.840435	+	0.541912i	$0.182299\pi$
$331$	12.7284	+	27.8713i	0.699617	+	1.53195i	−0.140818	+	0.990035i	$0.544973\pi$
$332$	−2.11292	+	3.86952i	−0.115961	+	0.212367i
$333$	−9.32266	+	0.666770i	−0.510879	+	0.0365388i
$334$	−8.81785	−	7.64071i	−0.482491	−	0.418081i
$335$	23.6871	+	22.4514i	1.29416	+	1.22665i
$336$	−4.44870	+	2.03165i	−0.242696	+	0.110836i
$337$	0.297107	−	1.36578i	0.0161844	−	0.0743986i	−0.968346	−	0.249611i	$-0.919697\pi$
$337$	0.297107	−	1.36578i	0.0161844	−	0.0743986i	0.984531	+	0.175212i	$0.0560610\pi$
$338$	11.3415	−	6.19294i	0.616898	−	0.336852i
$339$	−0.647960	−	4.50666i	−0.0351924	−	0.244768i
$340$	−0.666613	−	6.76829i	−0.0361521	−	0.367062i
$341$	−9.44824	−	1.35845i	−0.511651	−	0.0735643i
$342$	5.49296	−	1.19492i	0.297025	−	0.0646139i
$343$	−3.46052	+	48.3844i	−0.186851	+	2.61251i
$344$	1.93842			0.104513
$345$	4.47131	−	9.74717i	0.240727	−	0.524770i
$346$	−8.11292			−0.436153
$347$	0.657605	−	9.19452i	0.0353021	−	0.493588i	−0.948788	−	0.315915i	$-0.897689\pi$
$347$	0.657605	−	9.19452i	0.0353021	−	0.493588i	0.984090	−	0.177673i	$-0.0568569\pi$
$348$	−1.34575	+	0.292751i	−0.0721399	+	0.0156931i
$349$	32.8330	+	4.72067i	1.75751	+	0.252692i	0.944254	−	0.329217i	$-0.106785\pi$
$349$	32.8330	+	4.72067i	1.75751	+	0.252692i	0.813254	+	0.581909i	$0.197694\pi$
$350$	−19.8343	+	14.3025i	−1.06019	+	0.764502i
$351$	0.0396990	+	0.276112i	0.00211897	+	0.0147378i
$352$	1.74912	−	0.955089i	0.0932281	−	0.0509064i
$353$	−0.375503	+	1.72616i	−0.0199860	+	0.0918741i	−0.986059	−	0.166393i	$-0.946788\pi$
$353$	−0.375503	+	1.72616i	−0.0199860	+	0.0918741i	0.966073	+	0.258267i	$0.0831515\pi$
$354$	3.26066	−	1.48909i	0.173302	−	0.0791444i
$355$	0.263071	+	9.82324i	0.0139623	+	0.521363i
$356$	−1.53582	−	1.33079i	−0.0813981	−	0.0705318i
$357$	14.8371	−	1.06117i	0.785264	−	0.0561632i
$358$	−7.39734	+	13.5472i	−0.390961	+	0.715992i
$359$	14.9637	+	32.7660i	0.789755	+	1.72932i	0.677352	+	0.735659i	$0.263128\pi$
$359$	14.9637	+	32.7660i	0.789755	+	1.72932i	0.112403	+	0.993663i	$0.464145\pi$
$360$	1.01871	−	1.99054i	0.0536907	−	0.104910i
$361$	−12.0900	−	3.54995i	−0.636317	−	0.186839i
$362$	6.76796	+	5.06643i	0.355716	+	0.266286i
$363$	−2.45617	−	6.58526i	−0.128916	−	0.345636i
$364$	−0.194154	+	1.35037i	−0.0101764	+	0.0707786i
$365$	0.480666	−	10.7639i	0.0251592	−	0.563408i
$366$	−11.2390	+	9.73869i	−0.587474	+	0.509049i
$367$	6.79128	−	6.79128i	0.354502	−	0.354502i	−0.507280	−	0.861781i	$-0.669349\pi$
$367$	6.79128	−	6.79128i	0.354502	−	0.354502i	0.861781	+	0.507280i	$0.169349\pi$
$368$	−1.15239	+	4.65532i	−0.0600723	+	0.242675i
$369$			8.41068i			0.437843i
$370$	18.7715	−	9.18773i	0.975883	−	0.477647i
$371$	21.9892	+	14.1316i	1.14162	+	0.733676i
$372$	3.83438	−	2.87038i	0.198803	−	0.148822i
$373$	−23.1405	+	8.63094i	−1.19817	+	0.446893i	−0.867778	−	0.496952i	$-0.834453\pi$
$373$	−23.1405	+	8.63094i	−1.19817	+	0.446893i	−0.330389	+	0.943845i	$0.607180\pi$
$374$	−5.99971	+	0.862627i	−0.310237	+	0.0446054i
$375$	3.05403	−	10.7551i	0.157709	−	0.555393i
$376$	−1.80154	+	1.15778i	−0.0929076	+	0.0597081i
$377$	−0.134257	+	0.359957i	−0.00691459	+	0.0185387i
$378$	4.29243	+	2.34384i	0.220779	+	0.120554i
$379$	−9.71585	+	11.2127i	−0.499069	+	0.575957i	−0.948266	−	0.317476i	$-0.897165\pi$
$379$	−9.71585	+	11.2127i	−0.499069	+	0.575957i	0.449197	+	0.893433i	$0.351710\pi$
$380$	−10.3887	+	7.07645i	−0.532931	+	0.363014i
$381$	−13.6803	+	4.01689i	−0.700861	+	0.205791i
$382$	15.7802	+	5.88572i	0.807387	+	0.301140i
$383$	−2.92508	−	0.636313i	−0.149465	−	0.0325141i	0.137210	−	0.990542i	$-0.456186\pi$
$383$	−2.92508	−	0.636313i	−0.149465	−	0.0325141i	−0.286675	+	0.958028i	$0.592550\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	13.5230	+	17.0910i	0.689195	+	0.871039i
$386$	−8.05583	+	17.6398i	−0.410031	+	0.897843i
$387$	−1.16165	−	1.55179i	−0.0590502	−	0.0788818i
$388$	−2.88691	−	13.2709i	−0.146560	−	0.673728i
$389$	15.7625	+	18.1909i	0.799189	+	0.922313i	0.998336	−	0.0576563i	$-0.0183627\pi$
$389$	15.7625	+	18.1909i	0.799189	+	0.922313i	−0.199148	+	0.979970i	$0.563817\pi$
$390$	−0.313483	−	0.539258i	−0.0158738	−	0.0273064i
$391$	8.23216	−	12.0416i	0.416318	−	0.608971i
$392$	11.9632	+	11.9632i	0.604232	+	0.604232i
$393$	16.3421	+	1.16881i	0.824348	+	0.0589585i
$394$	−7.83338	+	12.1890i	−0.394640	+	0.614072i
$395$	−15.5577	−	6.60750i	−0.782792	−	0.332459i
$396$	−1.81279	−	0.827875i	−0.0910963	−	0.0416023i
$397$	−19.9254	+	26.6173i	−1.00003	+	1.33588i	−0.0587424	+	0.998273i	$0.518709\pi$
$397$	−19.9254	+	26.6173i	−1.00003	+	1.33588i	−0.941286	+	0.337609i	$0.890382\pi$
$398$	9.08934	+	16.6459i	0.455608	+	0.834383i
$399$	−14.8635	−	23.1281i	−0.744108	−	1.15785i
$400$	−0.445666	+	4.98010i	−0.0222833	+	0.249005i
$401$	−8.24920	−	28.0942i	−0.411945	−	1.40296i	−0.860613	−	0.509259i	$-0.829920\pi$
$401$	−8.24920	−	28.0942i	−0.411945	−	1.40296i	0.448668	−	0.893699i	$-0.351899\pi$
$402$	1.04123	+	14.5583i	0.0519319	+	0.726103i
$403$	−0.0953166	−	1.33270i	−0.00474806	−	0.0663865i
$404$	−4.25486	−	14.4907i	−0.211687	−	0.720940i
$405$	−2.20400	+	0.377364i	−0.109517	+	0.0187514i
$406$	3.64151	+	5.66630i	0.180725	+	0.281214i
$407$	−8.92672	−	16.3481i	−0.442481	−	0.810343i
$408$	1.82271	−	2.43486i	0.0902378	−	0.120544i
$409$	−23.9524	−	10.9387i	−1.18437	−	0.540884i	−0.276859	−	0.960911i	$-0.589293\pi$
$409$	−23.9524	−	10.9387i	−1.18437	−	0.540884i	−0.907512	+	0.420027i	$0.862021\pi$
$410$	−7.04170	−	17.4388i	−0.347765	−	0.861242i
$411$	−2.54724	+	3.96358i	−0.125646	+	0.195509i
$412$	6.10371	+	0.436546i	0.300708	+	0.0215071i
$413$	−12.3963	−	12.3963i	−0.609981	−	0.609981i
$414$	4.41738	−	1.86730i	0.217102	−	0.0917726i
$415$	−8.52292	+	4.95457i	−0.418374	+	0.243210i
$416$	0.182674	+	0.210818i	0.00895635	+	0.0103362i
$417$	0.253036	+	1.16319i	0.0123912	+	0.0569615i
$418$	6.71363	+	8.96836i	0.328374	+	0.438657i
$419$	5.20648	−	11.4006i	0.254353	−	0.556956i	−0.738780	−	0.673947i	$-0.764598\pi$
$419$	5.20648	−	11.4006i	0.254353	−	0.556956i	0.993133	+	0.116991i	$0.0373249\pi$
$420$	−10.8623	−	1.26599i	−0.530027	−	0.0617741i
$421$	4.66714	−	15.8948i	0.227462	−	0.774666i	−0.764107	−	0.645090i	$-0.776820\pi$
$421$	4.66714	−	15.8948i	0.227462	−	0.774666i	0.991569	−	0.129576i	$-0.0413618\pi$
$422$	−14.3142	−	3.11387i	−0.696806	−	0.151581i
$423$	2.00648	+	0.748377i	0.0975583	+	0.0363874i
$424$	5.12811	−	1.50575i	0.249043	−	0.0731256i
$425$	6.56339	−	13.7183i	0.318371	−	0.665437i
$426$	−2.87789	+	3.32126i	−0.139434	+	0.160916i
$427$	63.8343	+	34.8562i	3.08916	+	1.68681i
$428$	0.299882	−	0.804014i	0.0144953	−	0.0388635i
$429$	−0.467669	+	0.300553i	−0.0225793	+	0.0145108i
$430$	3.70779	+	2.24492i	0.178806	+	0.108260i
$431$	−19.7481	+	2.83935i	−0.951233	+	0.136767i	−0.600425	−	0.799681i	$-0.705002\pi$
$431$	−19.7481	+	2.83935i	−0.951233	+	0.136767i	−0.350808	+	0.936448i	$0.614093\pi$
$432$	0.936950	−	0.349464i	0.0450790	−	0.0168136i
$433$	−30.0531	+	22.4975i	−1.44426	+	1.08116i	−0.463464	+	0.886116i	$0.653394\pi$
$433$	−30.0531	+	22.4975i	−1.44426	+	1.08116i	−0.980795	+	0.195043i	$0.937515\pi$
$434$	−19.7063	−	12.6645i	−0.945933	−	0.607915i
$435$	−2.91318	−	0.998570i	−0.139676	−	0.0478778i
$436$			4.57776i			0.219235i
$437$	−26.8251	−	2.68781i	−1.28322	−	0.128575i
$438$	3.40723	−	3.40723i	0.162804	−	0.162804i
$439$	−22.8921	+	19.8361i	−1.09258	+	0.946726i	−0.998805	−	0.0488675i	$-0.984439\pi$
$439$	−22.8921	+	19.8361i	−1.09258	+	0.946726i	−0.0937747	+	0.995593i	$0.529893\pi$
$440$	4.45179	+	0.198797i	0.212231	+	0.00947727i
$441$	2.40775	−	16.7463i	0.114655	−	0.797443i
$442$	−0.296498	−	0.794942i	−0.0141030	−	0.0378116i
$443$	−5.45656	−	4.08473i	−0.259249	−	0.194071i	0.461745	−	0.887013i	$-0.347224\pi$
$443$	−5.45656	−	4.08473i	−0.259249	−	0.194071i	−0.720994	+	0.692941i	$0.756314\pi$
$444$	8.96788	+	2.63321i	0.425597	+	0.124966i
$445$	−1.39648	−	4.32418i	−0.0661994	−	0.204986i
$446$	−3.44610	−	7.54592i	−0.163178	−	0.357309i
$447$	−5.67340	+	10.3901i	−0.268343	+	0.491433i
$448$	4.87819	−	0.348895i	0.230473	−	0.0164838i
$449$	−10.2132	−	8.84983i	−0.481993	−	0.417649i	0.379677	−	0.925119i	$-0.376035\pi$
$449$	−10.2132	−	8.84983i	−0.481993	−	0.417649i	−0.861669	+	0.507470i	$0.830581\pi$
$450$	4.25385	−	2.62769i	0.200528	−	0.123870i
$451$	−15.2468	+	6.96300i	−0.717945	+	0.327875i
$452$	−0.967811	+	4.44896i	−0.0455220	+	0.209261i
$453$	8.69214	−	4.74627i	0.408392	−	0.222999i
$454$	−1.66264	−	11.5639i	−0.0780315	−	0.542721i
$455$	−1.93526	+	2.35812i	−0.0907265	+	0.110550i
$456$	−5.56421	−	0.800012i	−0.260568	−	0.0374640i
$457$	−6.49086	+	1.41200i	−0.303630	+	0.0660506i	−0.361799	−	0.932256i	$-0.617837\pi$
$457$	−6.49086	+	1.41200i	−0.303630	+	0.0660506i	0.0581693	+	0.998307i	$0.481474\pi$
$458$	−1.08743	+	15.2043i	−0.0508125	+	0.710452i
$459$	−3.04152			−0.141966
$460$	−7.59568	+	7.57005i	−0.354151	+	0.352955i
$461$	38.0333			1.77139			0.885693	−	0.464271i	$-0.153683\pi$
$461$	38.0333			1.77139			0.885693	+	0.464271i	$0.153683\pi$
$462$	−0.695309	+	9.72169i	−0.0323487	+	0.452294i
$463$	17.6659	−	3.84298i	0.821003	−	0.178598i	0.217603	−	0.976037i	$-0.430176\pi$
$463$	17.6659	−	3.84298i	0.821003	−	0.178598i	0.603400	+	0.797439i	$0.293812\pi$
$464$	1.36321	+	0.196000i	0.0632854	+	0.00909907i
$465$	10.6586	−	1.04977i	0.494281	−	0.0486820i
$466$	−1.99163	−	13.8521i	−0.0922605	−	0.641686i
$467$	3.83530	−	2.09423i	0.177476	−	0.0969095i	−0.388055	−	0.921636i	$-0.626853\pi$
$467$	3.83530	−	2.09423i	0.177476	−	0.0969095i	0.565531	+	0.824727i	$0.308671\pi$
$468$	0.0592954	−	0.272577i	0.00274093	−	0.0125999i
$469$	64.9310	−	29.6530i	2.99823	−	1.36925i
$470$	−4.78682	+	0.128193i	−0.220800	+	0.00591311i
$471$	11.7440	+	10.1762i	0.541135	+	0.468897i
$472$	−3.57546	+	0.255722i	−0.164574	+	0.0117705i
$473$	1.85137	−	3.39052i	0.0851259	−	0.155896i
$474$	−3.14017	−	6.87600i	−0.144233	−	0.315825i
$475$	−28.0668	+	1.50436i	−1.28779	+	0.0690249i
$476$	−14.2725	−	4.19078i	−0.654178	−	0.192084i
$477$	−4.27857	−	3.20290i	−0.195902	−	0.146651i
$478$	−0.560087	−	1.50165i	−0.0256178	−	0.0686839i
$479$	5.15566	−	35.8584i	0.235568	−	1.63841i	−0.437776	−	0.899084i	$-0.644234\pi$
$479$	5.15566	−	35.8584i	0.235568	−	1.63841i	0.673344	−	0.739329i	$-0.264857\pi$
$480$	−1.65010	+	1.50903i	−0.0753165	+	0.0688774i
$481$	1.97040	−	1.70736i	0.0898426	−	0.0778490i
$482$	17.4507	−	17.4507i	0.794858	−	0.794858i
$483$	−16.1063	−	17.0503i	−0.732861	−	0.775816i
$484$			7.02840i			0.319473i
$485$	9.84722	−	28.7278i	0.447139	−	1.30446i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	−0.481773	+	0.360651i	−0.0218312	+	0.0163427i	−0.610138	−	0.792295i	$-0.708886\pi$
$487$	−0.481773	+	0.360651i	−0.0218312	+	0.0163427i	0.588306	+	0.808638i	$0.299795\pi$
$488$	13.9337	−	5.19702i	0.630751	−	0.235258i
$489$	−1.25463	+	0.180389i	−0.0567365	+	0.00815748i
$490$	9.02828	+	36.7379i	0.407856	+	1.65965i
$491$	7.29833	−	4.69035i	0.329369	−	0.211673i	−0.365496	−	0.930813i	$-0.619101\pi$
$491$	7.29833	−	4.69035i	0.329369	−	0.211673i	0.694865	+	0.719140i	$0.255464\pi$
$492$	2.93923	−	7.88039i	0.132511	−	0.355275i
$493$	−3.67648	−	2.00751i	−0.165580	−	0.0904136i
$494$	−1.02689	+	1.18510i	−0.0462020	+	0.0533200i
$495$	−2.50872	−	3.68298i	−0.112758	−	0.165538i
$496$	−4.59572	+	1.34942i	−0.206354	+	0.0605909i
$497$	20.1376	+	7.51095i	0.903297	+	0.336912i
$498$	−4.30805	−	0.937159i	−0.193048	−	0.0419951i
$499$	6.88494	−	23.4479i	0.308212	−	1.04967i	−0.649120	−	0.760686i	$-0.724863\pi$
$499$	6.88494	−	23.4479i	0.308212	−	1.04967i	0.957333	−	0.288989i	$-0.0933190\pi$
$500$	−6.62001	+	9.00975i	−0.296056	+	0.402928i
$501$	4.84693	−	10.6133i	0.216545	−	0.474167i
$502$	−15.7616	−	21.0550i	−0.703473	−	0.939730i
$503$	7.02451	+	32.2912i	0.313208	+	1.43979i	0.817335	+	0.576163i	$0.195451\pi$
$503$	7.02451	+	32.2912i	0.313208	+	1.43979i	−0.504127	+	0.863629i	$0.668186\pi$
$504$	−3.20270	−	3.69611i	−0.142660	−	0.164638i
$505$	8.64331	−	32.6453i	0.384622	−	1.45270i
$506$	7.04206	+	6.46190i	0.313058	+	0.287267i
$507$	9.13737	+	9.13737i	0.405805	+	0.405805i
$508$	14.2215	+	1.01714i	0.630976	+	0.0451283i
$509$	−12.1415	+	18.8925i	−0.538162	+	0.837396i	−0.998738	−	0.0502239i	$-0.984007\pi$
$509$	−12.1415	+	18.8925i	−0.538162	+	0.837396i	0.460576	+	0.887620i	$0.347643\pi$
$510$	6.30632	−	2.54646i	0.279249	−	0.112759i
$511$	−21.4363	−	9.78962i	−0.948285	−	0.433067i
$512$	0.599278	−	0.800541i	0.0264846	−	0.0353793i
$513$	2.69406	+	4.93381i	0.118946	+	0.217833i
$514$	9.93430	+	15.4581i	0.438183	+	0.681826i
$515$	11.1695	+	7.90383i	0.492188	+	0.348284i
$516$	0.546117	+	1.85990i	0.0240415	+	0.0818777i
$517$	0.304459	+	4.25689i	0.0133901	+	0.187218i
$518$	−3.26094	−	45.5939i	−0.143278	−	2.00328i
$519$	−2.28567	−	7.78429i	−0.100330	−	0.341692i
$520$	0.105266	+	0.614808i	0.00461623	+	0.0269611i
$521$	−12.8390	−	19.9778i	−0.562486	−	0.875245i	0.437223	−	0.899353i	$-0.355962\pi$
$521$	−12.8390	−	19.9778i	−0.562486	−	0.875245i	−0.999709	+	0.0241077i	$0.992326\pi$
$522$	−0.660035	−	1.20876i	−0.0288889	−	0.0529061i
$523$	−0.408658	+	0.545904i	−0.0178694	+	0.0238707i	−0.809387	−	0.587276i	$-0.800200\pi$
$523$	−0.408658	+	0.545904i	−0.0178694	+	0.0238707i	0.791518	+	0.611146i	$0.209291\pi$
$524$	−14.9032	−	6.80608i	−0.651051	−	0.297325i
$525$	−19.3111	−	15.0014i	−0.842808	−	0.654715i
$526$	14.4761	−	22.5253i	0.631188	−	0.982148i
$527$	14.5309	+	1.03927i	0.632978	+	0.0452715i
$528$	1.40918	+	1.40918i	0.0613269	+	0.0613269i
$529$	−22.9153	+	1.97261i	−0.996315	+	0.0857655i
$530$	11.5528	+	3.05877i	0.501823	+	0.132865i
$531$	2.34741	+	2.70905i	0.101869	+	0.117563i
$532$	5.84394	+	26.8642i	0.253367	+	1.16471i
$533$	−1.40601	−	1.87821i	−0.0609010	−	0.0813543i
$534$	0.844196	−	1.84853i	0.0365320	−	0.0799938i
$535$	1.50475	−	1.19061i	0.0650562	−	0.0514746i
$536$	4.11203	−	14.0043i	0.177613	−	0.604893i
$537$	−15.0825	−	3.28100i	−0.650859	−	0.141586i
$538$	−15.5318	−	5.79304i	−0.669621	−	0.249756i
$539$	32.3509	−	9.49909i	1.39345	−	0.409155i
$540$	2.19691	+	0.416647i	0.0945399	+	0.0179296i
$541$	−23.5002	+	27.1207i	−1.01035	+	1.16601i	−0.0242779	+	0.999705i	$0.507729\pi$
$541$	−23.5002	+	27.1207i	−1.01035	+	1.16601i	−0.986075	+	0.166304i	$0.946817\pi$
$542$	8.94674	+	4.88529i	0.384295	+	0.209841i
$543$	−2.95445	+	7.92119i	−0.126788	+	0.339931i
$544$	−2.55869	+	1.64437i	−0.109703	+	0.0705017i
$545$	−5.30159	+	8.75629i	−0.227095	+	0.375078i
$546$	−1.35037	+	0.194154i	−0.0577905	+	0.00830902i
$547$	−16.1218	+	6.01310i	−0.689316	+	0.257102i	−0.669620	−	0.742704i	$-0.733543\pi$
$547$	−16.1218	+	6.01310i	−0.689316	+	0.257102i	−0.0196969	+	0.999806i	$0.506270\pi$
$548$	3.77177	−	2.82351i	0.161122	−	0.120614i
$549$	−12.5106	−	8.04008i	−0.533940	−	0.343142i
$550$	8.28511	+	5.53596i	0.353278	+	0.236054i
$551$			7.74198i			0.329819i
$552$	−4.79141	+	0.205848i	−0.203936	+	0.00876148i
$553$	−26.1410	+	26.1410i	−1.11163	+	1.11163i
$554$	−11.9098	+	10.3199i	−0.505997	+	0.438449i
$555$	14.1041	+	15.4226i	0.598686	+	0.654654i
$556$	0.169410	−	1.17827i	0.00718459	−	0.0499699i
$557$	10.6047	+	28.4323i	0.449335	+	1.20471i	0.942331	+	0.334682i	$0.108629\pi$
$557$	10.6047	+	28.4323i	0.449335	+	1.20471i	−0.492996	+	0.870031i	$0.664098\pi$
$558$	3.83438	+	2.87038i	0.162322	+	0.121513i
$559$	0.518823	+	0.152340i	0.0219439	+	0.00644330i
$560$	9.73502	+	4.98216i	0.411380	+	0.210535i
$561$	−2.51800	−	5.51365i	−0.106310	−	0.232786i
$562$	8.40561	−	15.3937i	0.354569	−	0.649345i
$563$	−26.6912	+	1.90899i	−1.12490	+	0.0804544i	−0.621365	−	0.783521i	$-0.713422\pi$
$563$	−26.6912	+	1.90899i	−1.12490	+	0.0804544i	−0.503534	+	0.863975i	$0.667967\pi$
$564$	−1.61844	−	1.40238i	−0.0681485	−	0.0590510i
$565$	−7.00363	+	7.38908i	−0.294645	+	0.310861i
$566$	25.0612	−	11.4451i	1.05340	−	0.481071i
$567$	−1.03958	+	4.77889i	−0.0436584	+	0.200694i
$568$	3.85710	−	2.10614i	0.161840	−	0.0883715i
$569$	−4.97655	−	34.6126i	−0.208628	−	1.45104i	−0.777641	−	0.628709i	$-0.783584\pi$
$569$	−4.97655	−	34.6126i	−0.208628	−	1.45104i	0.569013	−	0.822329i	$-0.307325\pi$
$570$	−9.71665	−	7.97426i	−0.406986	−	0.334005i
$571$	11.5736	+	1.66403i	0.484339	+	0.0696375i	0.380159	−	0.924921i	$-0.375869\pi$
$571$	11.5736	+	1.66403i	0.484339	+	0.0696375i	0.104180	+	0.994558i	$0.466778\pi$
$572$	0.543215	−	0.118169i	0.0227129	−	0.00494090i
$573$	−1.20150	+	16.7992i	−0.0501935	+	0.701797i
$574$	−41.1337			−1.71689
$575$	−23.2959	+	5.68321i	−0.971508	+	0.237006i
$576$	−1.00000			−0.0416667
$577$	−0.0759827	+	1.06238i	−0.00316320	+	0.0442273i	−0.998789	−	0.0492080i	$-0.984330\pi$
$577$	−0.0759827	+	1.06238i	−0.00316320	+	0.0442273i	0.995625	+	0.0934353i	$0.0297848\pi$
$578$	−7.57207	+	1.64720i	−0.314957	+	0.0685147i
$579$	−19.1949	−	2.75980i	−0.797711	−	0.114694i
$580$	2.38054	+	1.95366i	0.0988466	+	0.0811214i
$581$	3.06859	+	21.3425i	0.127306	+	0.885435i
$582$	11.9200	−	6.50881i	0.494100	−	0.269799i
$583$	2.26407	−	10.4078i	0.0937683	−	0.431046i
$584$	−4.38311	+	2.00170i	−0.181374	+	0.0828309i
$585$	0.429096	−	0.452711i	0.0177409	−	0.0187173i
$586$	−21.3002	−	18.4567i	−0.879902	−	0.762439i
$587$	15.4478	−	1.10485i	0.637597	−	0.0456018i	0.251201	−	0.967935i	$-0.419174\pi$
$587$	15.4478	−	1.10485i	0.637597	−	0.0456018i	0.386396	+	0.922333i	$0.373720\pi$
$588$	−8.10818	+	14.8490i	−0.334376	+	0.612363i
$589$	−11.1851	−	24.4920i	−0.460874	−	1.00917i
$590$	−7.13525	−	3.65166i	−0.293754	−	0.150336i
$591$	−13.9022	−	4.08204i	−0.571858	−	0.167913i
$592$	−7.48224	−	5.60114i	−0.307518	−	0.230205i
$593$	−11.3018	−	30.3012i	−0.464107	−	1.24432i	−0.932619	−	0.360862i	$-0.882482\pi$
$593$	−11.3018	−	30.3012i	−0.464107	−	1.24432i	0.468512	−	0.883457i	$-0.344790\pi$
$594$	0.283617	−	1.97260i	0.0116370	−	0.0809369i
$595$	−22.4468	−	24.5453i	−0.920230	−	1.00626i
$596$	8.94665	−	7.75232i	0.366469	−	0.317547i
$597$	−13.4109	+	13.4109i	−0.548870	+	0.548870i
$598$	−0.674299	+	1.15544i	−0.0275741	+	0.0472495i
$599$			13.4493i			0.549523i	0.961512	+	0.274761i	$0.0885988\pi$
$599$			13.4493i			0.549523i	−0.961512	+	0.274761i	$0.911401\pi$
$600$	−4.90393	+	0.975443i	−0.200202	+	0.0398223i
$601$	6.59225	+	4.23658i	0.268904	+	0.172814i	0.668143	−	0.744033i	$-0.267089\pi$
$601$	6.59225	+	4.23658i	0.268904	+	0.172814i	−0.399239	+	0.916847i	$0.630726\pi$
$602$	7.58926	−	5.68125i	0.309315	−	0.231550i
$603$	−13.6753	+	5.10061i	−0.556899	+	0.207713i
$604$	−9.80275	+	1.40942i	−0.398868	+	0.0573486i
$605$	−8.13972	+	13.4439i	−0.330927	+	0.546570i
$606$	12.7050	−	8.16501i	0.516106	−	0.331681i
$607$	5.39649	−	14.4685i	0.219037	−	0.587260i	−0.780232	−	0.625490i	$-0.784899\pi$
$607$	5.39649	−	14.4685i	0.219037	−	0.587260i	0.999269	+	0.0382297i	$0.0121719\pi$
$608$	4.93381	+	2.69406i	0.200092	+	0.109259i
$609$	−4.41084	+	5.09038i	−0.178736	+	0.206273i
$610$	32.6711	+	6.19611i	1.32281	+	0.250873i
$611$	−0.573177	+	0.168300i	−0.0231883	+	0.00680869i
$612$	2.84975	+	1.06290i	0.115194	+	0.0429653i
$613$	19.8327	+	4.31434i	0.801036	+	0.174255i	0.594407	−	0.804165i	$-0.297387\pi$
$613$	19.8327	+	4.31434i	0.801036	+	0.174255i	0.206629	+	0.978419i	$0.433751\pi$
$614$	5.68379	−	19.3572i	0.229379	−	0.781193i
$615$	14.7485	−	11.6695i	0.594719	−	0.470561i
$616$	4.04885	−	8.86575i	0.163133	−	0.357211i
$617$	−7.06937	−	9.44357i	−0.284602	−	0.380184i	0.635344	−	0.772230i	$-0.280858\pi$
$617$	−7.06937	−	9.44357i	−0.284602	−	0.380184i	−0.919946	+	0.392046i	$0.871768\pi$
$618$	1.30075	+	5.97945i	0.0523239	+	0.240529i
$619$	0.388252	+	0.448067i	0.0156052	+	0.0180093i	0.763499	−	0.645810i	$-0.223480\pi$
$619$	0.388252	+	0.448067i	0.0156052	+	0.0180093i	−0.747893	+	0.663819i	$0.768935\pi$
$620$	−10.3534	−	2.74122i	−0.415804	−	0.110090i
$621$	3.03618	+	3.71236i	0.121838	+	0.148972i
$622$	3.94599	+	3.94599i	0.158220	+	0.158220i
$623$	−9.91335	−	0.709017i	−0.397170	−	0.0284062i
$624$	−0.150813	+	0.234669i	−0.00603734	+	0.00939428i
$625$	−23.0970	+	9.56700i	−0.923881	+	0.382680i
$626$	15.6133	+	7.13034i	0.624031	+	0.284986i
$627$	−6.71363	+	8.96836i	−0.268116	+	0.358162i
$628$	−7.44732	−	13.6387i	−0.297180	−	0.544245i
$629$	15.3691	+	23.9147i	0.612804	+	0.953542i
$630$	−1.84556	−	10.7790i	−0.0735287	−	0.429445i
$631$	2.69895	+	9.19177i	0.107443	+	0.365919i	0.995610	−	0.0936040i	$-0.0298387\pi$
$631$	2.69895	+	9.19177i	0.107443	+	0.365919i	−0.888166	+	0.459522i	$0.848021\pi$
$632$	0.539260	+	7.53985i	0.0214506	+	0.299919i
$633$	−1.04505	−	14.6117i	−0.0415370	−	0.580763i
$634$	8.16768	+	27.8166i	0.324380	+	1.10474i
$635$	26.0247	+	18.4157i	1.03276	+	0.730805i
$636$	2.88951	+	4.49617i	0.114577	+	0.178285i
$637$	2.26179	+	4.14216i	0.0896154	+	0.164118i
$638$	1.64481	−	2.19721i	0.0651187	−	0.0869885i
$639$	−3.99752	−	1.82561i	−0.158140	−	0.0722200i
$640$	2.07341	−	0.837233i	0.0819588	−	0.0330945i
$641$	15.2922	−	23.7951i	0.604004	−	0.939849i	−0.395765	−	0.918352i	$-0.629520\pi$
$641$	15.2922	−	23.7951i	0.604004	−	0.939849i	0.999769	−	0.0214968i	$-0.00684317\pi$
$642$	0.855932	+	0.0612175i	0.0337810	+	0.00241606i
$643$	15.3919	+	15.3919i	0.606997	+	0.606997i	0.942160	−	0.335163i	$-0.108791\pi$
$643$	15.3919	+	15.3919i	0.606997	+	0.606997i	−0.335163	+	0.942160i	$0.608791\pi$
$644$	9.13230	+	21.6039i	0.359863	+	0.851311i
$645$	−1.10938	+	4.19007i	−0.0436818	+	0.164984i
$646$	−11.1966	−	12.9216i	−0.440524	−	0.508392i
$647$	−6.79633	−	31.2422i	−0.267191	−	1.22826i	−0.893636	−	0.448793i	$-0.851854\pi$
$647$	−6.79633	−	31.2422i	−0.267191	−	1.22826i	0.626444	−	0.779466i	$-0.284510\pi$
$648$	0.599278	+	0.800541i	0.0235419	+	0.0314482i
$649$	−2.96759	+	6.49812i	−0.116488	+	0.255074i
$650$	−0.510668	+	1.29791i	−0.0200301	+	0.0509082i
$651$	6.59957	−	22.4761i	0.258658	−	0.880907i
$652$	1.23857	+	0.269434i	0.0485061	+	0.0105519i
$653$	34.5826	+	12.8986i	1.35332	+	0.504763i	0.918381	−	0.395697i	$-0.129497\pi$
$653$	34.5826	+	12.8986i	1.35332	+	0.504763i	0.434940	+	0.900459i	$0.356770\pi$
$654$	−4.39233	+	1.28970i	−0.171754	+	0.0504314i
$655$	−20.6245	−	30.2783i	−0.805866	−	1.18307i
$656$	−5.50783	+	6.35637i	−0.215044	+	0.248175i
$657$	4.22914	+	2.30929i	0.164995	+	0.0900939i
$658$	−3.66006	+	9.81299i	−0.142684	+	0.382550i
$659$	−34.9409	+	22.4551i	−1.36110	+	0.874728i	−0.998365	−	0.0571628i	$-0.981795\pi$
$659$	−34.9409	+	22.4551i	−1.36110	+	0.874728i	−0.362739	+	0.931891i	$0.618158\pi$
$660$	1.06347	+	4.32747i	0.0413956	+	0.168447i
$661$	47.2393	−	6.79199i	1.83740	−	0.264178i	0.865726	−	0.500518i	$-0.166857\pi$
$661$	47.2393	−	6.79199i	1.83740	−	0.264178i	0.971670	+	0.236341i	$0.0759482\pi$
$662$	28.7084	−	10.7077i	1.11578	−	0.416165i
$663$	0.679208	−	0.508449i	0.0263783	−	0.0197465i
$664$	3.70892	+	2.38358i	0.143934	+	0.0925009i
$665$	−19.9336	+	58.1535i	−0.772993	+	2.25509i
$666$			9.34648i			0.362169i
$667$	1.21973	+	6.49135i	0.0472281	+	0.251346i
$668$	−8.25030	+	8.25030i	−0.319214	+	0.319214i
$669$	6.26937	−	5.43244i	0.242388	−	0.210030i
$670$	24.0841	−	22.0250i	0.930448	−	0.850901i
$671$	4.21778	−	29.3353i	0.162826	−	1.13248i
$672$	1.70911	+	4.58230i	0.0659303	+	0.176766i
$673$	10.8835	+	8.14730i	0.419529	+	0.314055i	0.788103	−	0.615543i	$-0.211063\pi$
$673$	10.8835	+	8.14730i	0.419529	+	0.314055i	−0.368575	+	0.929598i	$0.620154\pi$
$674$	−1.34110	−	0.393783i	−0.0516573	−	0.0151680i
$675$	3.71970	+	3.34124i	0.143171	+	0.128604i
$676$	−5.36807	−	11.7544i	−0.206464	−	0.452094i
$677$	5.33462	−	9.76962i	0.205026	−	0.375477i	−0.754852	−	0.655895i	$-0.772291\pi$
$677$	5.33462	−	9.76962i	0.205026	−	0.375477i	0.959878	+	0.280418i	$0.0904731\pi$
$678$	−4.54141	+	0.324808i	−0.174412	+	0.0124742i
$679$	−50.1979	−	43.4967i	−1.92642	−	1.66925i
$680$	−6.79860	+	0.182070i	−0.260715	+	0.00698205i
$681$	10.6271	−	4.85322i	0.407230	−	0.185976i
$682$	−2.02902	+	9.32726i	−0.0776952	+	0.357159i
$683$	−9.17075	+	5.00761i	−0.350909	+	0.191611i	−0.645030	−	0.764157i	$-0.723155\pi$
$683$	−9.17075	+	5.00761i	−0.350909	+	0.191611i	0.294121	+	0.955768i	$0.404973\pi$
$684$	−0.800012	−	5.56421i	−0.0305892	−	0.212753i
$685$	10.4845	−	1.03263i	0.400594	−	0.0394547i
$686$	48.0143	+	6.90341i	1.83319	+	0.263573i
$687$	−14.8948	+	3.24017i	−0.568272	+	0.123620i
$688$	0.138285	−	1.93348i	0.00527209	−	0.0737134i
$689$	1.49089			0.0567982
$690$	−9.40336	−	5.15527i	−0.357980	−	0.196258i
$691$	−38.8202			−1.47679			−0.738394	−	0.674369i	$-0.764416\pi$
$691$	−38.8202			−1.47679			−0.738394	+	0.674369i	$0.764416\pi$
$692$	−0.578769	+	8.09225i	−0.0220015	+	0.307621i
$693$	−9.52378	+	2.07177i	−0.361779	+	0.0787001i
$694$	−9.12418	−	1.31186i	−0.346349	−	0.0497975i
$695$	1.68863	−	2.05759i	0.0640532	−	0.0780489i
$696$	0.196000	+	1.36321i	0.00742936	+	0.0516723i
$697$	22.4521	−	12.2598i	0.850435	−	0.464372i
$698$	7.05092	−	32.4125i	0.266881	−	1.22683i
$699$	12.7299	−	5.81354i	0.481488	−	0.219888i
$700$	12.8511	+	20.8041i	0.485727	+	0.786322i
$701$	14.2151	+	12.3174i	0.536896	+	0.465223i	0.880603	−	0.473854i	$-0.157138\pi$
$701$	14.2151	+	12.3174i	0.536896	+	0.465223i	−0.343708	+	0.939077i	$0.611683\pi$
$702$	0.278241	−	0.0199002i	0.0105015	−	0.000751084i
$703$	25.1800	−	46.1137i	0.949682	−	1.73921i
$704$	−0.827875	−	1.81279i	−0.0312017	−	0.0683222i
$705$	−1.47160	−	4.55681i	−0.0554238	−	0.171619i
$706$	1.69497	+	0.497689i	0.0637911	+	0.0187308i
$707$	−59.1288	−	44.2632i	−2.22377	−	1.66469i
$708$	−1.25269	−	3.35858i	−0.0470788	−	0.126223i
$709$	−0.727329	+	5.05869i	−0.0273154	+	0.189983i	−0.998911	−	0.0466665i	$-0.985140\pi$
$709$	−0.727329	+	5.05869i	−0.0273154	+	0.189983i	0.971595	+	0.236649i	$0.0760493\pi$
$710$	9.81698	+	0.438382i	0.368425	+	0.0164522i
$711$	5.71279	−	4.95016i	0.214246	−	0.185646i
$712$	−1.43697	+	1.43697i	−0.0538526	+	0.0538526i
$713$	−13.2369	−	18.7734i	−0.495727	−	0.703068i
$714$		−	14.8750i		−	0.556684i
$715$	1.17591	+	0.403074i	0.0439765	+	0.0150741i
$716$	12.9850	+	8.34494i	0.485271	+	0.311865i
$717$	1.28303	−	0.960463i	0.0479156	−	0.0358691i
$718$	33.7500	−	12.5881i	1.25954	−	0.469784i
$719$	−12.3343	+	1.77340i	−0.459991	+	0.0661367i	−0.368415	−	0.929661i	$-0.620100\pi$
$719$	−12.3343	+	1.77340i	−0.459991	+	0.0661367i	−0.0915760	+	0.995798i	$0.529190\pi$
$720$	−1.91279	−	1.15812i	−0.0712855	−	0.0431605i
$721$	25.1765	−	16.1800i	0.937622	−	0.602573i
$722$	−4.40340	+	11.8060i	−0.163877	+	0.439373i
$723$	21.6603	+	11.8274i	0.805554	+	0.439866i
$724$	5.53635	−	6.38928i	0.205757	−	0.237456i
$725$	2.29090	+	6.49389i	0.0850820	+	0.241177i
$726$	−6.74370	+	1.98013i	−0.250282	+	0.0734895i
$727$	−4.57949	−	1.70806i	−0.169844	−	0.0633485i	0.263104	−	0.964768i	$-0.415254\pi$
$727$	−4.57949	−	1.70806i	−0.169844	−	0.0633485i	−0.432948	+	0.901419i	$0.642527\pi$
$728$	1.33308	+	0.289994i	0.0494072	+	0.0107479i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	−10.7022	−	1.24733i	−0.396105	−	0.0461657i
$731$	−2.44918	+	5.36296i	−0.0905863	+	0.198356i
$732$	8.91209	+	11.9052i	0.329400	+	0.440027i
$733$	−7.08970	−	32.5908i	−0.261864	−	1.20377i	−0.900705	−	0.434430i	$-0.856950\pi$
$733$	−7.08970	−	32.5908i	−0.261864	−	1.20377i	0.638841	−	0.769338i	$-0.279414\pi$
$734$	−6.28949	−	7.25846i	−0.232149	−	0.267915i
$735$	−32.7062	+	19.0128i	−1.20638	+	0.701299i
$736$	4.56125	+	1.48156i	0.168130	+	0.0546109i
$737$	−20.5678	−	20.5678i	−0.757623	−	0.757623i
$738$	8.38925	+	0.600011i	0.308813	+	0.0220867i
$739$	−7.81964	+	12.1676i	−0.287650	+	0.447592i	−0.954764	−	0.297363i	$-0.903893\pi$
$739$	−7.81964	+	12.1676i	−0.287650	+	0.447592i	0.667114	+	0.744955i	$0.267529\pi$
$740$	−7.82518	−	19.3791i	−0.287659	−	0.712390i
$741$	−1.42640	−	0.651415i	−0.0524001	−	0.0239303i
$742$	15.6643	−	20.9250i	0.575054	−	0.768182i
$743$	−15.5564	−	28.4894i	−0.570709	−	1.04518i	−0.990494	−	0.137553i	$-0.956076\pi$
$743$	−15.5564	−	28.4894i	−0.570709	−	1.04518i	0.419785	−	0.907624i	$-0.362105\pi$
$744$	−2.58953	−	4.02938i	−0.0949366	−	0.147724i
$745$	26.0912	−	4.46727i	0.955906	−	0.163668i
$746$	6.95813	+	23.6972i	0.254755	+	0.867617i
$747$	−0.314521	−	4.39757i	−0.0115077	−	0.160899i
$748$	0.432415	+	6.04596i	0.0158107	+	0.221062i
$749$	−1.18236	−	4.02676i	−0.0432027	−	0.147135i
$750$	−10.5099	−	3.81351i	−0.383766	−	0.139250i
$751$	−5.98070	−	9.30615i	−0.218239	−	0.339586i	0.714821	−	0.699307i	$-0.246508\pi$
$751$	−5.98070	−	9.30615i	−0.218239	−	0.339586i	−0.933060	+	0.359721i	$0.882872\pi$
$752$	1.02631	+	1.87955i	0.0374257	+	0.0685401i
$753$	15.7616	−	21.0550i	0.574383	−	0.767286i
$754$	0.349462	+	0.159594i	0.0127267	+	0.00581207i
$755$	−20.3829	−	8.65681i	−0.741809	−	0.315053i
$756$	2.64409	−	4.11428i	0.0961645	−	0.149635i
$757$	15.3735	+	1.09953i	0.558758	+	0.0399632i	0.347863	−	0.937545i	$-0.386907\pi$
$757$	15.3735	+	1.09953i	0.558758	+	0.0399632i	0.210896	+	0.977509i	$0.432362\pi$
$758$	10.4910	+	10.4910i	0.381050	+	0.381050i
$759$	−4.21617	+	8.57733i	−0.153037	+	0.311337i
$760$	6.31729	+	10.8671i	0.229152	+	0.394191i
$761$	4.94377	+	5.70541i	0.179211	+	0.206821i	0.838247	−	0.545291i	$-0.183581\pi$
$761$	4.94377	+	5.70541i	0.179211	+	0.206821i	−0.659036	+	0.752112i	$0.729035\pi$
$762$	3.03071	+	13.9320i	0.109791	+	0.504702i
$763$	13.4168	+	17.9227i	0.485720	+	0.648846i
$764$	6.99647	−	15.3201i	0.253124	−	0.554263i
$765$	4.22001	+	5.33345i	0.152575	+	0.192831i
$766$	−0.843364	+	2.87224i	−0.0304720	+	0.103778i
$767$	−0.977076	−	0.212550i	−0.0352802	−	0.00767473i
$768$	0.936950	+	0.349464i	0.0338093	+	0.0126102i
$769$	3.97264	−	1.16647i	0.143257	−	0.0420640i	−0.209318	−	0.977848i	$-0.567124\pi$
$769$	3.97264	−	1.16647i	0.143257	−	0.0420640i	0.352575	+	0.935784i	$0.385306\pi$
$770$	18.0122	−	12.2693i	0.649114	−	0.442154i
$771$	−12.0331	+	13.8869i	−0.433361	+	0.500126i
$772$	17.0202	+	9.29372i	0.612569	+	0.334488i
$773$	−16.6443	+	44.6251i	−0.598654	+	1.60505i	0.184228	+	0.982884i	$0.441022\pi$
$773$	−16.6443	+	44.6251i	−0.598654	+	1.60505i	−0.782882	+	0.622170i	$0.786251\pi$
$774$	−1.63071	+	1.04799i	−0.0586145	+	0.0376692i
$775$	−16.6293	−	17.2339i	−0.597341	−	0.619059i
$776$	−13.4430	+	1.93282i	−0.482577	+	0.0693841i
$777$	42.8283	−	15.9741i	1.53646	−	0.573069i
$778$	19.2690	−	14.4246i	0.690827	−	0.517147i
$779$	−39.7745	−	25.5615i	−1.42507	−	0.915836i
$780$	−0.560247	+	0.274214i	−0.0200601	+	0.00981843i
$781$		−	8.75806i		−	0.313388i
$782$	−11.4237	−	9.07023i	−0.408509	−	0.324351i
$783$	0.973847	−	0.973847i	0.0348024	−	0.0348024i
$784$	12.7862	−	11.0793i	0.456648	−	0.395688i
$785$	1.55012	−	34.7129i	0.0553262	−	1.23896i
$786$	2.33166	−	16.2170i	0.0831675	−	0.578443i
$787$	10.0783	+	27.0209i	0.359251	+	0.963190i	0.983330	+	0.181829i	$0.0582017\pi$
$787$	10.0783	+	27.0209i	0.359251	+	0.963190i	−0.624079	+	0.781361i	$0.714526\pi$
$788$	11.5991	+	8.68297i	0.413201	+	0.309318i
$789$	25.6912	+	7.54362i	0.914632	+	0.268560i
$790$	−7.70054	+	15.0467i	−0.273973	+	0.535336i
$791$	9.25012	+	20.2549i	0.328896	+	0.720183i
$792$	−0.955089	+	1.74912i	−0.0339376	+	0.0621521i
$793$	4.13783	−	0.295943i	0.146939	−	0.0105093i
$794$	25.1280	+	21.7735i	0.891759	+	0.772713i
$795$	0.319935	+	11.9466i	0.0113469	+	0.423703i
$796$	17.2519	−	7.87868i	0.611478	−	0.279252i
$797$	6.64331	−	30.5388i	0.235318	−	1.08174i	−0.696144	−	0.717902i	$-0.745103\pi$
$797$	6.64331	−	30.5388i	0.235318	−	1.08174i	0.931462	−	0.363838i	$-0.118534\pi$
$798$	−24.1295	+	13.1757i	−0.854177	+	0.466416i
$799$	−0.926955	−	6.44711i	−0.0327933	−	0.228082i
$800$	4.93562	+	0.799806i	0.174500	+	0.0282774i
$801$	2.01149	+	0.289209i	0.0710726	+	0.0102187i
$802$	−28.6111	+	6.22397i	−1.01029	+	0.219776i
$803$	−0.685058	+	9.57837i	−0.0241752	+	0.338013i
$804$	14.5955			0.514744
$805$	−7.55164	+	51.8999i	−0.266160	+	1.82923i
$806$	−1.33610			−0.0470623
$807$	1.18258	−	16.5347i	0.0416290	−	0.582049i
$808$	−14.7573	+	3.21026i	−0.519161	+	0.112937i
$809$	−20.0206	−	2.87853i	−0.703887	−	0.101204i	−0.218929	−	0.975741i	$-0.570256\pi$
$809$	−20.0206	−	2.87853i	−0.703887	−	0.101204i	−0.484958	+	0.874537i	$0.661165\pi$
$810$	0.219171	+	2.22530i	0.00770088	+	0.0781891i
$811$	−3.26494	−	22.7082i	−0.114648	−	0.797392i	−0.963297	−	0.268437i	$-0.913493\pi$
$811$	−3.26494	−	22.7082i	−0.114648	−	0.797392i	0.848650	−	0.528955i	$-0.177416\pi$
$812$	5.91164	−	3.22800i	0.207458	−	0.113281i
$813$	−2.16681	+	9.96068i	−0.0759935	+	0.349336i
$814$	−16.9432	+	7.73772i	−0.593860	+	0.271207i
$815$	2.05708	+	1.94978i	0.0720565	+	0.0682978i
$816$	−2.29863	−	1.99177i	−0.0804680	−	0.0697259i
$817$	10.8689	−	0.777362i	0.380256	−	0.0271964i
$818$	−12.6196	+	23.1110i	−0.441233	+	0.808058i
$819$	−0.566733	−	1.24097i	−0.0198032	−	0.0433630i
$820$	−17.8967	+	5.77969i	−0.624981	+	0.201835i
$821$	35.5660	+	10.4431i	1.24126	+	0.364468i	0.835490	−	0.549506i	$-0.185184\pi$
$821$	35.5660	+	10.4431i	1.24126	+	0.364468i	0.405773	+	0.913974i	$0.367002\pi$
$822$	3.77177	+	2.82351i	0.131555	+	0.0984812i
$823$	10.8225	+	29.0163i	0.377249	+	1.01144i	0.977370	+	0.211535i	$0.0678463\pi$
$823$	10.8225	+	29.0163i	0.377249	+	1.01144i	−0.600121	+	0.799909i	$0.704881\pi$
$824$	0.870867	−	6.05701i	0.0303381	−	0.211006i
$825$	−2.97753	+	9.50917i	−0.103664	+	0.331067i
$826$	−13.2490	+	11.4804i	−0.460993	+	0.399453i
$827$	17.1328	−	17.1328i	0.595764	−	0.595764i	−0.343418	−	0.939183i	$-0.611585\pi$
$827$	17.1328	−	17.1328i	0.595764	−	0.595764i	0.939183	+	0.343418i	$0.111585\pi$
$828$	−1.54741	−	4.53933i	−0.0537761	−	0.157753i
$829$			0.451620i			0.0156854i	0.999969	+	0.00784270i	$0.00249644\pi$
$829$			0.451620i			0.0156854i	−0.999969	+	0.00784270i	$0.997504\pi$
$830$	4.33392	+	8.85466i	0.150433	+	0.307350i
$831$	−13.2572	−	8.51989i	−0.459887	−	0.295552i
$832$	0.223312	−	0.167169i	0.00774196	−	0.00579556i
$833$	−48.2135	+	17.9827i	−1.67050	+	0.623064i
$834$	1.17827	−	0.169410i	0.0408003	−	0.00586619i
$835$	−25.3359	+	6.22627i	−0.876785	+	0.215469i
$836$	9.42445	−	6.05673i	0.325951	−	0.209476i
$837$	−1.67384	+	4.48774i	−0.0578564	+	0.155119i
$838$	−11.0001	−	6.00653i	−0.379993	−	0.207492i
$839$	−31.2729	+	36.0909i	−1.07966	+	1.24600i	−0.112009	+	0.993707i	$0.535729\pi$
$839$	−31.2729	+	36.0909i	−1.07966	+	1.24600i	−0.967652	+	0.252288i	$0.918817\pi$
$840$	−2.03768	+	10.7443i	−0.0703065	+	0.370714i
$841$	−26.0054	+	7.63587i	−0.896737	+	0.263306i
$842$	−15.5214	−	5.78917i	−0.534902	−	0.199508i
$843$	17.1383	+	3.72821i	0.590274	+	0.128406i
$844$	−4.12711	+	14.0556i	−0.142061	+	0.483815i
$845$	3.34503	−	28.7006i	0.115073	−	0.987331i
$846$	0.889611	−	1.94798i	0.0305855	−	0.0669728i
$847$	20.5993	+	27.5174i	0.707799	+	0.945509i
$848$	−1.13608	−	5.22246i	−0.0390130	−	0.179340i
$849$	18.0420	+	20.8216i	0.619200	+	0.714594i
$850$	−13.2152	−	7.52532i	−0.453276	−	0.258116i
$851$	13.8473	−	42.6316i	0.474681	−	1.46139i
$852$	3.10749	+	3.10749i	0.106461	+	0.106461i
$853$	−9.31440	−	0.666179i	−0.318919	−	0.0228095i	−0.0890378	−	0.996028i	$-0.528379\pi$
$853$	−9.31440	−	0.666179i	−0.318919	−	0.0228095i	−0.229881	+	0.973219i	$0.573834\pi$
$854$	39.3213	−	61.1851i	1.34555	−	2.09371i
$855$	4.91375	−	11.5697i	0.168047	−	0.395674i
$856$	−0.780572	−	0.356475i	−0.0266794	−	0.0121841i
$857$	−16.5650	+	22.1283i	−0.565850	+	0.755887i	−0.988634	−	0.150343i	$-0.951962\pi$
$857$	−16.5650	+	22.1283i	−0.565850	+	0.755887i	0.422784	+	0.906231i	$0.361053\pi$
$858$	0.266424	+	0.487919i	0.00909555	+	0.0166573i
$859$	−25.1268	−	39.0981i	−0.857316	−	1.33401i	−0.941310	−	0.337544i	$-0.890404\pi$
$859$	−25.1268	−	39.0981i	−0.857316	−	1.33401i	0.0839936	−	0.996466i	$-0.473232\pi$
$860$	2.50371	−	3.53820i	0.0853759	−	0.120652i
$861$	−11.5887	−	39.4675i	−0.394942	−	1.34505i
$862$	1.42330	+	19.9004i	0.0484778	+	0.677809i
$863$	1.03282	+	14.4407i	0.0351576	+	0.491567i	0.984275	+	0.176644i	$0.0565242\pi$
$863$	1.03282	+	14.4407i	0.0351576	+	0.491567i	−0.949117	+	0.314923i	$0.898021\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−10.4788	+	14.8085i	−0.356291	+	0.503504i
$866$	20.2962	+	31.5815i	0.689692	+	1.07318i
$867$	−3.71378	−	6.80128i	−0.126127	−	0.230984i
$868$	−14.0380	+	18.7526i	−0.476482	+	0.636506i
$869$	13.7031	+	6.25800i	0.464846	+	0.212288i
$870$	−1.20385	+	2.83452i	−0.0408143	+	0.0960993i
$871$	2.20119	−	3.42511i	0.0745844	−	0.116056i
$872$	4.56610	+	0.326574i	0.154628	+	0.0110592i
$873$	9.60341	+	9.60341i	0.325026	+	0.325026i
$874$	−4.59464	+	26.5650i	−0.155416	+	0.898574i
$875$	0.487856	+	54.6770i	0.0164926	+	1.84842i
$876$	−3.15548	−	3.64162i	−0.106614	−	0.123039i
$877$	−3.30111	−	15.1749i	−0.111470	−	0.512422i	−0.998694	−	0.0510826i	$-0.983733\pi$
$877$	−3.30111	−	15.1749i	−0.111470	−	0.512422i	0.887224	−	0.461339i	$-0.152631\pi$
$878$	18.1525	+	24.2489i	0.612616	+	0.818359i
$879$	11.7081	−	25.6372i	0.394905	−	0.864722i
$880$	0.515878	−	4.42627i	0.0173902	−	0.149210i
$881$	9.48142	−	32.2907i	0.319437	−	1.08790i	−0.630689	−	0.776036i	$-0.717228\pi$
$881$	9.48142	−	32.2907i	0.319437	−	1.08790i	0.950126	−	0.311867i	$-0.100954\pi$
$882$	−16.5319	−	3.59629i	−0.556657	−	0.121093i
$883$	0.360208	+	0.134351i	0.0121220	+	0.00452126i	0.355518	−	0.934669i	$-0.384305\pi$
$883$	0.360208	+	0.134351i	0.0121220	+	0.00452126i	−0.343396	+	0.939191i	$0.611577\pi$
$884$	−0.814069	+	0.239032i	−0.0273801	+	0.00803952i
$885$	1.49351	−	7.87502i	0.0502037	−	0.264716i
$886$	−4.46359	+	5.15126i	−0.149957	+	0.173060i
$887$	42.3727	+	23.1373i	1.42274	+	0.776873i	0.992076	−	0.125640i	$-0.0400985\pi$
$887$	42.3727	+	23.1373i	1.42274	+	0.776873i	0.430661	+	0.902514i	$0.358280\pi$
$888$	3.26626	−	8.75718i	0.109608	−	0.293872i
$889$	58.6606	−	37.6989i	1.96741	−	1.26438i
$890$	−4.41279	+	1.08444i	−0.147917	+	0.0363504i
$891$	1.97260	−	0.283617i	0.0660847	−	0.00950154i
$892$	−7.77253	+	2.89900i	−0.260244	+	0.0970658i
$893$	−9.63714	+	7.21427i	−0.322495	+	0.241416i
$894$	9.95885	+	6.40017i	0.333074	+	0.214054i
$895$	15.1731	+	31.0002i	0.507181	+	1.03622i
$896$		−	4.89066i		−	0.163385i
$897$	−1.29861	−	0.321460i	−0.0433593	−	0.0107332i
$898$	−9.55588	+	9.55588i	−0.318884	+	0.318884i
$899$	−4.98534	+	4.31982i	−0.166270	+	0.144074i
$900$	−2.31753	−	4.43047i	−0.0772509	−	0.147682i
$901$	−2.31343	+	16.0902i	−0.0770715	+	0.536044i
$902$	5.85756	+	15.7047i	0.195035	+	0.522910i
$903$	7.58926	+	5.68125i	0.252555	+	0.189060i
$904$	4.36858	+	1.28273i	0.145297	+	0.0426630i
$905$	17.9894	−	5.80961i	0.597988	−	0.193118i
$906$	−4.11408	−	9.00859i	−0.136681	−	0.299290i
$907$	10.5798	−	19.3754i	0.351295	−	0.643349i	−0.640959	−	0.767575i	$-0.721463\pi$
$907$	10.5798	−	19.3754i	0.351295	−	0.643349i	0.992254	+	0.124226i	$0.0396448\pi$
$908$	−11.6530	+	0.833442i	−0.386720	+	0.0276588i
$909$	11.4137	+	9.89002i	0.378568	+	0.328031i
$910$	2.21405	+	2.09856i	0.0733951	+	0.0695665i
$911$	−35.2081	+	16.0790i	−1.16650	+	0.532721i	−0.902030	−	0.431673i	$-0.857923\pi$
$911$	−35.2081	+	16.0790i	−1.16650	+	0.532721i	−0.264467	+	0.964395i	$0.585196\pi$
$912$	−1.19492	+	5.49296i	−0.0395678	+	0.181890i
$913$	7.71151	−	4.21080i	0.255214	−	0.139357i
$914$	0.945350	+	6.57506i	0.0312694	+	0.217483i
$915$	3.25938	+	33.0933i	0.107752	+	1.09403i
$916$	15.0880	+	2.16933i	0.498522	+	0.0716766i
$917$	−78.2964	+	17.0323i	−2.58557	+	0.562457i
$918$	−0.216979	+	3.03377i	−0.00716139	+	0.100129i
$919$	−12.9002			−0.425538			−0.212769	−	0.977103i	$-0.568248\pi$
$919$	−12.9002			−0.425538			−0.212769	+	0.977103i	$0.568248\pi$
$920$	7.00889	+	8.11637i	0.231076	+	0.267589i
$921$	20.1744			0.664770
$922$	2.71326	−	37.9364i	0.0893566	−	1.24937i
$923$	1.19788	−	0.260583i	0.0394288	−	0.00857721i
$924$	9.64732	+	1.38707i	0.317373	+	0.0456314i
$925$	7.47537	−	46.1306i	0.245789	−	1.51677i
$926$	−2.57292	−	17.8950i	−0.0845513	−	0.588067i
$927$	−5.37078	+	2.93267i	−0.176400	+	0.0963214i
$928$	0.292751	−	1.34575i	0.00961001	−	0.0441765i
$929$	−49.6568	+	22.6775i	−1.62919	+	0.744025i	−0.999462	−	0.0327940i	$-0.989559\pi$
$929$	−49.6568	+	22.6775i	−1.62919	+	0.744025i	−0.629724	+	0.776819i	$0.716832\pi$
$930$	−0.286720	−	10.7063i	−0.00940193	−	0.351075i
$931$	71.8764	+	62.2813i	2.35565	+	2.04119i
$932$	−13.9589	+	0.998359i	−0.457238	+	0.0327023i
$933$	−2.67444	+	4.89787i	−0.0875571	+	0.160349i
$934$	−1.81529	−	3.97493i	−0.0593980	−	0.130064i
$935$	−6.17481	+	12.0654i	−0.201938	+	0.394582i
$936$	−0.267652	−	0.0785898i	−0.00874848	−	0.00256879i
$937$	22.2969	+	16.6912i	0.728407	+	0.545278i	0.897871	−	0.440258i	$-0.145113\pi$
$937$	22.2969	+	16.6912i	0.728407	+	0.545278i	−0.169465	+	0.985536i	$0.554204\pi$
$938$	−24.9453	−	66.8810i	−0.814493	−	2.18374i
$939$	−2.44274	+	16.9897i	−0.0797160	+	0.554437i
$940$	−0.213621	+	4.78377i	−0.00696756	+	0.156029i
$941$	−15.4959	+	13.4273i	−0.505152	+	0.437717i	−0.869782	−	0.493436i	$-0.835741\pi$
$941$	−15.4959	+	13.4273i	−0.505152	+	0.437717i	0.364630	+	0.931152i	$0.381195\pi$
$942$	10.9881	−	10.9881i	0.358012	−	0.358012i
$943$	−37.3765	−	15.1660i	−1.21715	−	0.493872i
$944$			3.58459i			0.116668i
$945$	9.82241	−	4.80759i	0.319523	−	0.156391i
$946$	−3.24981	−	2.08853i	−0.105660	−	0.0679039i
$947$	−7.94503	+	5.94758i	−0.258179	+	0.193270i	−0.720524	−	0.693430i	$-0.756099\pi$
$947$	−7.94503	+	5.94758i	−0.258179	+	0.193270i	0.462346	+	0.886700i	$0.347008\pi$
$948$	−7.08250	+	2.64164i	−0.230029	+	0.0857964i
$949$	−1.33046	+	0.191292i	−0.0431886	+	0.00620959i
$950$	−0.501735	+	28.1026i	−0.0162784	+	0.911770i
$951$	−24.3887	+	15.6737i	−0.790858	+	0.508253i
$952$	−5.19829	+	13.9371i	−0.168477	+	0.451705i
$953$	28.0491	+	15.3159i	0.908598	+	0.496132i	0.864351	−	0.502889i	$-0.167729\pi$
$953$	28.0491	+	15.3159i	0.908598	+	0.496132i	0.0442468	+	0.999021i	$0.485911\pi$
$954$	−3.49997	+	4.03918i	−0.113316	+	0.130773i
$955$	31.1253	−	21.2015i	1.00719	−	0.686063i
$956$	−1.53778	+	0.451533i	−0.0497354	+	0.0146036i
$957$	2.57161	+	0.959160i	0.0831282	+	0.0310052i
$958$	−35.3993	−	7.70064i	−1.14370	−	0.248796i
$959$	6.49180	−	22.1090i	0.209631	−	0.713938i
$960$	1.38747	+	1.75355i	0.0447803	+	0.0565956i
$961$	−3.34760	+	7.33021i	−0.107987	+	0.236458i
$962$	−1.56245	−	2.08718i	−0.0503753	−	0.0672935i
$963$	0.182406	+	0.838508i	0.00587796	+	0.0270205i
$964$	−16.1613	−	18.6512i	−0.520521	−	0.600714i
$965$	21.7928	+	37.4883i	0.701535	+	1.20679i
$966$	−18.1559	+	14.8489i	−0.584156	+	0.477755i
$967$	−14.1553	−	14.1553i	−0.455204	−	0.455204i	0.441874	−	0.897077i	$-0.354314\pi$
$967$	−14.1553	−	14.1553i	−0.455204	−	0.455204i	−0.897077	+	0.441874i	$0.854314\pi$
$968$	7.01049	+	0.501400i	0.225326	+	0.0161156i
$969$	9.24370	−	14.3835i	0.296950	−	0.462064i
$970$	−27.9521	−	11.8715i	−0.897488	−	0.381172i
$971$	−37.7870	−	17.2568i	−1.21264	−	0.553796i	−0.296649	−	0.954987i	$-0.595869\pi$
$971$	−37.7870	−	17.2568i	−1.21264	−	0.553796i	−0.915994	+	0.401191i	$0.868596\pi$
$972$	−0.599278	+	0.800541i	−0.0192218	+	0.0256774i
$973$	−2.79009	−	5.10966i	−0.0894460	−	0.163808i
$974$	0.325363	+	0.506274i	0.0104253	+	0.0162221i
$975$	−1.38921	−	0.124319i	−0.0444902	−	0.00398140i
$976$	−4.18975	−	14.2690i	−0.134111	−	0.456739i
$977$	−0.726825	−	10.1623i	−0.0232532	−	0.325122i	−0.995743	−	0.0921756i	$-0.970618\pi$
$977$	−0.726825	−	10.1623i	−0.0232532	−	0.325122i	0.972490	−	0.232946i	$-0.0748367\pi$
$978$	0.0904249	+	1.26431i	0.00289147	+	0.0404280i
$979$	1.14099	+	3.88585i	0.0364661	+	0.124192i
$980$	37.2883	−	6.38443i	1.19113	−	0.203943i
$981$	−2.47492	−	3.85106i	−0.0790183	−	0.122955i
$982$	−4.15775	−	7.61434i	−0.132679	−	0.242984i
$983$	25.1006	−	33.5305i	0.800585	−	1.06946i	−0.195469	−	0.980710i	$-0.562623\pi$
$983$	25.1006	−	33.5305i	0.800585	−	1.06946i	0.996054	−	0.0887470i	$-0.0282863\pi$
$984$	−7.65063	−	3.49392i	−0.243893	−	0.111382i
$985$	12.1307	+	30.0418i	0.386517	+	0.957212i
$986$	−2.26467	+	3.52389i	−0.0721218	+	0.112224i
$987$	−10.4467	−	0.747159i	−0.332521	−	0.0237823i
$988$	1.10882	+	1.10882i	0.0352762	+	0.0352762i
$989$	8.99071	−	2.36416i	0.285888	−	0.0751760i
$990$	−3.85257	+	2.23958i	−0.122443	+	0.0711786i
$991$	−29.3818	−	33.9084i	−0.933344	−	1.07714i	−0.996862	−	0.0791558i	$-0.974778\pi$
$991$	−29.3818	−	33.9084i	−0.933344	−	1.07714i	0.0635181	−	0.997981i	$-0.479768\pi$
$992$	1.01813	+	4.68027i	0.0323257	+	0.148599i
$993$	18.3620	+	24.5288i	0.582701	+	0.778397i
$994$	8.92842	−	19.5505i	0.283192	−	0.620105i
$995$	42.1237	+	4.90948i	1.33541	+	0.155641i
$996$	−1.24210	+	4.23022i	−0.0393576	+	0.134040i
$997$	−5.42208	−	1.17950i	−0.171719	−	0.0373552i	0.125884	−	0.992045i	$-0.459823\pi$
$997$	−5.42208	−	1.17950i	−0.171719	−	0.0373552i	−0.297603	+	0.954690i	$0.596187\pi$
$998$	−22.8970	−	8.54015i	−0.724793	−	0.270334i
$999$	−8.96788	+	2.63321i	−0.283731	+	0.0833110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.217.8	yes	240
5.3	odd	4	inner	690.2.w.a.493.1	yes	240
23.7	odd	22	inner	690.2.w.a.7.1	✓	240
115.53	even	44	inner	690.2.w.a.283.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.1	✓	240	23.7	odd	22	inner
690.2.w.a.217.8	yes	240	1.1	even	1	trivial
690.2.w.a.283.8	yes	240	115.53	even	44	inner
690.2.w.a.493.1	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)

\(f(q)\)	\(=\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.72850 - 1.41855i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.29243 + 2.34384i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.0713392 - 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.72850 - 1.41855i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.29243 + 2.34384i) q^{7} +(-0.212565 + 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-1.53824 + 1.62290i) q^{10} +(1.50612 + 1.30506i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-0.133687 + 0.244830i) q^{13} +(2.03165 + 4.44870i) q^{14} +(-1.99054 - 1.01871i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-2.43486 - 1.82271i) q^{17} +(-0.349464 - 0.936950i) q^{18} +(-0.800012 + 5.56421i) q^{19} +(1.50903 + 1.65010i) q^{20} +(-3.69611 + 3.20270i) q^{21} +(1.40918 - 1.40918i) q^{22} +(0.205848 + 4.79141i) q^{23} +1.00000i q^{24} +(0.975443 + 4.90393i) q^{25} +(0.234669 + 0.150813i) q^{26} +(0.800541 - 0.599278i) q^{27} +(4.58230 - 1.70911i) q^{28} +(1.36321 - 0.196000i) q^{29} +(-1.15812 + 1.91279i) q^{30} +(-4.02938 + 2.58953i) q^{31} +(0.349464 - 0.936950i) q^{32} +(1.74912 + 0.955089i) q^{33} +(-1.99177 + 2.29863i) q^{34} +(10.7443 + 2.03768i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-8.75718 - 3.26626i) q^{37} +(5.49296 + 1.19492i) q^{38} +(-0.0785898 + 0.267652i) q^{39} +(1.75355 - 1.38747i) q^{40} +(-3.49392 + 7.65063i) q^{41} +(2.93086 + 3.91517i) q^{42} +(-0.412041 - 1.89412i) q^{43} +(-1.30506 - 1.50612i) q^{44} +(-2.16159 - 0.572311i) q^{45} +(4.79389 + 0.136492i) q^{46} +(1.51427 + 1.51427i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(9.14684 - 14.2328i) q^{49} +(4.96102 - 0.623115i) q^{50} +(-2.76666 - 1.26349i) q^{51} +(0.167169 - 0.223312i) q^{52} +(-2.56140 - 4.69085i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-0.752043 - 4.39231i) q^{55} +(-1.37786 - 4.69255i) q^{56} +(0.401028 + 5.60710i) q^{57} +(-0.0982503 - 1.37372i) q^{58} +(1.00990 + 3.43939i) q^{59} +(1.82530 + 1.29162i) q^{60} +(-8.04008 - 12.5106i) q^{61} +(2.29548 + 4.20385i) q^{62} +(-2.93086 + 3.91517i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(0.578382 - 0.233547i) q^{65} +(1.07744 - 1.67652i) q^{66} +(-14.5583 - 1.04123i) q^{67} +(2.15068 + 2.15068i) q^{68} +(1.21963 + 4.63816i) q^{69} +(2.79897 - 10.5716i) q^{70} +(-2.87789 - 3.32126i) q^{71} +(0.212565 + 0.977147i) q^{72} +(2.88765 + 3.85745i) q^{73} +(-3.88267 + 8.50186i) q^{74} +(1.99556 + 4.58451i) q^{75} +(1.58374 - 5.39372i) q^{76} +(-9.52378 - 2.07177i) q^{77} +(0.261364 + 0.0974836i) q^{78} +(7.25291 - 2.12965i) q^{79} +(-1.25883 - 1.84806i) q^{80} +(0.654861 - 0.755750i) q^{81} +(7.38188 + 4.03081i) q^{82} +(1.54072 - 4.13083i) q^{83} +(4.11428 - 2.64409i) q^{84} +(1.62306 + 6.60453i) q^{85} +(-1.91869 + 0.275866i) q^{86} +(1.29039 - 0.481292i) q^{87} +(-1.59539 + 1.19429i) q^{88} +(1.70958 + 1.09868i) q^{89} +(-0.725058 + 2.11525i) q^{90} -1.36426i q^{91} +(0.478136 - 4.77194i) q^{92} +(-3.38685 + 3.38685i) q^{93} +(1.61844 - 1.40238i) q^{94} +(9.27592 - 8.48289i) q^{95} +(0.142315 - 0.989821i) q^{96} +(4.74617 + 12.7250i) q^{97} +(-13.5440 - 10.1389i) q^{98} +(1.91216 + 0.561461i) 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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