LMFDB - Embedded newform 690.2.w.b.7.1

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			7.1
Character	$\chi$	$=$	690.7
Dual form			690.2.w.b.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.95274 + 1.08941i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.32241 - 2.42181i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.95274 + 1.08941i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.32241 - 2.42181i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.87005 - 1.22594i) q^{10} +(1.06157 - 0.919855i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-0.373337 + 0.203857i) q^{13} +(-1.14627 + 2.50998i) q^{14} +(-0.649426 - 2.13968i) q^{15} +(0.959493 - 0.281733i) q^{16} +(3.65418 + 4.88142i) q^{17} +(0.936950 + 0.349464i) q^{18} +(-1.15607 - 8.04065i) q^{19} +(-1.77783 + 1.35622i) q^{20} +(2.08536 + 1.80698i) q^{21} +(-0.993243 + 0.993243i) q^{22} +(-2.54521 - 4.06472i) q^{23} -1.00000i q^{24} +(2.62639 - 4.25466i) q^{25} +(0.357843 - 0.229972i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.964288 - 2.58536i) q^{28} +(5.63176 + 0.809725i) q^{29} +(0.800414 + 2.08790i) q^{30} +(5.70892 + 3.66890i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(0.673180 + 1.23284i) q^{33} +(-3.99311 - 4.60829i) q^{34} +(0.0560165 + 6.16980i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(1.21628 + 3.26096i) q^{37} +(1.72674 + 7.93769i) q^{38} +(-0.119840 - 0.408138i) q^{39} +(1.67654 - 1.47960i) q^{40} +(-1.16152 - 2.54337i) q^{41} +(-2.20896 - 1.65361i) q^{42} +(2.34544 + 0.510219i) q^{43} +(0.919855 - 1.06157i) q^{44} +(2.22883 - 0.179762i) q^{45} +(2.82870 + 3.87279i) q^{46} +(9.19442 + 9.19442i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(-0.331909 - 0.516460i) q^{49} +(-2.31617 + 4.43118i) q^{50} +(-5.54661 + 2.53305i) q^{51} +(-0.340525 + 0.254914i) q^{52} +(-2.54165 - 1.38785i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(-1.07087 + 2.95272i) q^{55} +(-0.777394 + 2.64756i) q^{56} +(8.10264 + 0.579512i) q^{57} +(-5.67518 - 0.405897i) q^{58} +(2.60440 - 8.86977i) q^{59} +(-0.947324 - 2.02548i) q^{60} +(6.21286 - 9.66741i) q^{61} +(-5.95611 - 3.25228i) q^{62} +(-2.20896 + 1.65361i) q^{63} +(0.909632 - 0.415415i) q^{64} +(0.506946 - 0.804796i) q^{65} +(-0.759415 - 1.18167i) q^{66} +(0.616464 + 8.61929i) q^{67} +(4.31169 + 4.31169i) q^{68} +(4.51285 - 1.62302i) q^{69} +(-0.496022 - 6.15009i) q^{70} +(3.18033 - 3.67030i) q^{71} +(0.977147 + 0.212565i) q^{72} +(5.68363 + 4.25471i) q^{73} +(-1.44581 - 3.16589i) q^{74} +(3.59915 + 3.47076i) q^{75} +(-2.28861 - 7.79429i) q^{76} +(-0.823885 - 3.78734i) q^{77} +(0.148651 + 0.398549i) q^{78} +(4.39954 + 1.29182i) q^{79} +(-1.56672 + 1.59543i) q^{80} +(0.654861 + 0.755750i) q^{81} +(1.34000 + 2.45403i) q^{82} +(-3.65752 + 1.36418i) q^{83} +(2.32130 + 1.49181i) q^{84} +(-12.4535 - 5.55125i) q^{85} +(-2.37586 - 0.341597i) q^{86} +(-1.98834 + 5.33094i) q^{87} +(-0.841780 + 1.12449i) q^{88} +(-0.0406320 + 0.0261126i) q^{89} +(-2.21033 + 0.338307i) q^{90} +1.17373i q^{91} +(-3.09777 - 3.66112i) q^{92} +(-4.79857 + 4.79857i) q^{93} +(-9.82692 - 8.51507i) q^{94} +(11.0170 + 14.4419i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-2.63322 - 0.982139i) q^{97} +(0.367907 + 0.491466i) q^{98} +(-1.34776 + 0.395738i) 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} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−1.95274	+	1.08941i	−0.873292	+	0.487197i
$5$	−1.95274	+	1.08941i	−0.873292	+	0.487197i
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	1.32241	−	2.42181i	0.499823	−	0.915358i	−0.498988	−	0.866609i	$-0.666295\pi$
$7$	1.32241	−	2.42181i	0.499823	−	0.915358i	0.998811	−	0.0487487i	$-0.0155233\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	1.87005	−	1.22594i	0.591361	−	0.387676i
$11$	1.06157	−	0.919855i	0.320075	−	0.277347i	−0.479972	−	0.877284i	$-0.659353\pi$
$11$	1.06157	−	0.919855i	0.320075	−	0.277347i	0.800047	+	0.599937i	$0.204808\pi$
$12$	−0.0713392	+	0.997452i	−0.0205938	+	0.287940i
$13$	−0.373337	+	0.203857i	−0.103545	+	0.0565399i	−0.530187	−	0.847881i	$-0.677878\pi$
$13$	−0.373337	+	0.203857i	−0.103545	+	0.0565399i	0.426642	+	0.904421i	$0.359696\pi$
$14$	−1.14627	+	2.50998i	−0.306353	+	0.670820i
$15$	−0.649426	−	2.13968i	−0.167681	−	0.552464i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	3.65418	+	4.88142i	0.886270	+	1.18392i	0.982070	+	0.188517i	$0.0603681\pi$
$17$	3.65418	+	4.88142i	0.886270	+	1.18392i	−0.0958003	+	0.995401i	$0.530541\pi$
$18$	0.936950	+	0.349464i	0.220841	+	0.0823695i
$19$	−1.15607	−	8.04065i	−0.265221	−	1.84465i	−0.491861	−	0.870674i	$-0.663683\pi$
$19$	−1.15607	−	8.04065i	−0.265221	−	1.84465i	0.226640	−	0.973979i	$-0.427226\pi$
$20$	−1.77783	+	1.35622i	−0.397534	+	0.303260i
$21$	2.08536	+	1.80698i	0.455064	+	0.394315i
$22$	−0.993243	+	0.993243i	−0.211760	+	0.211760i
$23$	−2.54521	−	4.06472i	−0.530713	−	0.847552i
$23$	−2.54521	−	4.06472i	−0.530713	−	0.847552i
$24$		−	1.00000i		−	0.204124i
$25$	2.62639	−	4.25466i	0.525277	−	0.850931i
$26$	0.357843	−	0.229972i	0.0701787	−	0.0451011i
$27$	0.599278	−	0.800541i	0.115331	−	0.154064i
$28$	0.964288	−	2.58536i	0.182233	−	0.488586i
$29$	5.63176	+	0.809725i	1.04579	+	0.150362i	0.643732	−	0.765251i	$-0.277385\pi$
$29$	5.63176	+	0.809725i	1.04579	+	0.150362i	0.402060	+	0.915613i	$0.368294\pi$
$30$	0.800414	+	2.08790i	0.146135	+	0.381197i
$31$	5.70892	+	3.66890i	1.02535	+	0.658954i	0.941322	−	0.337510i	$-0.109585\pi$
$31$	5.70892	+	3.66890i	1.02535	+	0.658954i	0.0840297	+	0.996463i	$0.473221\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	0.673180	+	1.23284i	0.117186	+	0.214610i
$34$	−3.99311	−	4.60829i	−0.684813	−	0.790316i
$35$	0.0560165	+	6.16980i	0.00946852	+	1.04289i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	1.21628	+	3.26096i	0.199955	+	0.536099i	0.997766	−	0.0668083i	$-0.0212816\pi$
$37$	1.21628	+	3.26096i	0.199955	+	0.536099i	−0.797811	+	0.602907i	$0.794009\pi$
$38$	1.72674	+	7.93769i	0.280114	+	1.28766i
$39$	−0.119840	−	0.408138i	−0.0191898	−	0.0653544i
$40$	1.67654	−	1.47960i	0.265085	−	0.233945i
$41$	−1.16152	−	2.54337i	−0.181399	−	0.397208i	0.796987	−	0.603997i	$-0.206426\pi$
$41$	−1.16152	−	2.54337i	−0.181399	−	0.397208i	−0.978386	+	0.206788i	$0.933699\pi$
$42$	−2.20896	−	1.65361i	−0.340850	−	0.255157i
$43$	2.34544	+	0.510219i	0.357676	+	0.0778077i	0.387813	−	0.921738i	$-0.373231\pi$
$43$	2.34544	+	0.510219i	0.357676	+	0.0778077i	−0.0301368	+	0.999546i	$0.509594\pi$
$44$	0.919855	−	1.06157i	0.138673	−	0.160038i
$45$	2.22883	−	0.179762i	0.332254	−	0.0267973i
$46$	2.82870	+	3.87279i	0.417069	+	0.571011i
$47$	9.19442	+	9.19442i	1.34114	+	1.34114i	0.894923	+	0.446221i	$0.147231\pi$
$47$	9.19442	+	9.19442i	1.34114	+	1.34114i	0.446221	+	0.894923i	$0.352769\pi$
$48$	0.0713392	+	0.997452i	0.0102969	+	0.143970i
$49$	−0.331909	−	0.516460i	−0.0474155	−	0.0737800i
$50$	−2.31617	+	4.43118i	−0.327556	+	0.626663i
$51$	−5.54661	+	2.53305i	−0.776681	+	0.354698i
$52$	−0.340525	+	0.254914i	−0.0472223	+	0.0353502i
$53$	−2.54165	−	1.38785i	−0.349123	−	0.190635i	0.295113	−	0.955462i	$-0.404643\pi$
$53$	−2.54165	−	1.38785i	−0.349123	−	0.190635i	−0.644236	+	0.764827i	$0.722825\pi$
$54$	−0.540641	+	0.841254i	−0.0735719	+	0.114480i
$55$	−1.07087	+	2.95272i	−0.144396	+	0.398144i
$56$	−0.777394	+	2.64756i	−0.103884	+	0.353795i
$57$	8.10264	+	0.579512i	1.07322	+	0.0767583i
$58$	−5.67518	−	0.405897i	−0.745187	−	0.0532968i
$59$	2.60440	−	8.86977i	0.339064	−	1.15475i	−0.596802	−	0.802389i	$-0.703562\pi$
$59$	2.60440	−	8.86977i	0.339064	−	1.15475i	0.935866	−	0.352357i	$-0.114620\pi$
$60$	−0.947324	−	2.02548i	−0.122299	−	0.261489i
$61$	6.21286	−	9.66741i	0.795476	−	1.23778i	−0.172069	−	0.985085i	$-0.555045\pi$
$61$	6.21286	−	9.66741i	0.795476	−	1.23778i	0.967545	−	0.252700i	$-0.0813184\pi$
$62$	−5.95611	−	3.25228i	−0.756426	−	0.413040i
$63$	−2.20896	+	1.65361i	−0.278303	+	0.208335i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	0.506946	−	0.804796i	0.0628789	−	0.0998227i
$66$	−0.759415	−	1.18167i	−0.0934775	−	0.145454i
$67$	0.616464	+	8.61929i	0.0753131	+	1.05301i	0.884829	+	0.465916i	$0.154275\pi$
$67$	0.616464	+	8.61929i	0.0753131	+	1.05301i	−0.809516	+	0.587098i	$0.800270\pi$
$68$	4.31169	+	4.31169i	0.522869	+	0.522869i
$69$	4.51285	−	1.62302i	0.543283	−	0.195389i
$70$	−0.496022	−	6.15009i	−0.0592860	−	0.735076i
$71$	3.18033	−	3.67030i	0.377436	−	0.435585i	−0.534970	−	0.844871i	$-0.679677\pi$
$71$	3.18033	−	3.67030i	0.377436	−	0.435585i	0.912406	+	0.409287i	$0.134222\pi$
$72$	0.977147	+	0.212565i	0.115158	+	0.0250511i
$73$	5.68363	+	4.25471i	0.665219	+	0.497977i	0.877714	−	0.479186i	$-0.159068\pi$
$73$	5.68363	+	4.25471i	0.665219	+	0.497977i	−0.212495	+	0.977162i	$0.568159\pi$
$74$	−1.44581	−	3.16589i	−0.168072	−	0.368027i
$75$	3.59915	+	3.47076i	0.415593	+	0.400769i
$76$	−2.28861	−	7.79429i	−0.262521	−	0.894066i
$77$	−0.823885	−	3.78734i	−0.0938904	−	0.431607i
$78$	0.148651	+	0.398549i	0.0168314	+	0.0451268i
$79$	4.39954	+	1.29182i	0.494986	+	0.145341i	0.519692	−	0.854354i	$-0.326047\pi$
$79$	4.39954	+	1.29182i	0.494986	+	0.145341i	−0.0247057	+	0.999695i	$0.507865\pi$
$80$	−1.56672	+	1.59543i	−0.175164	+	0.178374i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	1.34000	+	2.45403i	0.147979	+	0.271003i
$83$	−3.65752	+	1.36418i	−0.401464	+	0.149739i	−0.542082	−	0.840325i	$-0.682364\pi$
$83$	−3.65752	+	1.36418i	−0.401464	+	0.149739i	0.140618	+	0.990064i	$0.455091\pi$
$84$	2.32130	+	1.49181i	0.253274	+	0.162770i
$85$	−12.4535	−	5.55125i	−1.35077	−	0.602117i
$86$	−2.37586	−	0.341597i	−0.256196	−	0.0368354i
$87$	−1.98834	+	5.33094i	−0.213172	+	0.571536i
$88$	−0.841780	+	1.12449i	−0.0897340	+	0.119871i
$89$	−0.0406320	+	0.0261126i	−0.00430698	+	0.00276793i	−0.542793	−	0.839867i	$-0.682633\pi$
$89$	−0.0406320	+	0.0261126i	−0.00430698	+	0.00276793i	0.538486	+	0.842635i	$0.318997\pi$
$90$	−2.21033	+	0.338307i	−0.232989	+	0.0356607i
$91$			1.17373i			0.123041i
$92$	−3.09777	−	3.66112i	−0.322965	−	0.381698i
$93$	−4.79857	+	4.79857i	−0.497589	+	0.497589i
$94$	−9.82692	−	8.51507i	−1.01357	−	0.878263i
$95$	11.0170	+	14.4419i	1.13033	+	1.48171i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	−2.63322	−	0.982139i	−0.267363	−	0.0997211i	0.212208	−	0.977225i	$-0.431935\pi$
$97$	−2.63322	−	0.982139i	−0.267363	−	0.0997211i	−0.479570	+	0.877503i	$0.659207\pi$
$98$	0.367907	+	0.491466i	0.0371642	+	0.0496456i
$99$	−1.34776	+	0.395738i	−0.135455	+	0.0397731i
$100$	1.99415	−	4.58512i	0.199415	−	0.458512i
$101$	6.54239	−	14.3258i	0.650992	−	1.42547i	−0.239691	−	0.970849i	$-0.577046\pi$
$101$	6.54239	−	14.3258i	0.650992	−	1.42547i	0.890683	−	0.454624i	$-0.150226\pi$
$102$	5.35178	−	2.92229i	0.529905	−	0.289350i
$103$	1.22367	−	17.1092i	0.120572	−	1.68582i	−0.473018	−	0.881053i	$-0.656835\pi$
$103$	1.22367	−	17.1092i	0.120572	−	1.68582i	0.593590	−	0.804768i	$-0.297710\pi$
$104$	0.321472	−	0.278557i	0.0315229	−	0.0273148i
$105$	−6.04071	−	1.25675i	−0.589513	−	0.122646i
$106$	2.63418	+	1.20299i	0.255855	+	0.116845i
$107$	−1.17346	+	0.255271i	−0.113443	+	0.0246779i	−0.268928	−	0.963160i	$-0.586669\pi$
$107$	−1.17346	+	0.255271i	−0.113443	+	0.0246779i	0.155486	+	0.987838i	$0.450306\pi$
$108$	0.479249	−	0.877679i	0.0461158	−	0.0844547i
$109$	−1.13944	+	7.92495i	−0.109138	+	0.759073i	0.859596	+	0.510974i	$0.170715\pi$
$109$	−1.13944	+	7.92495i	−0.109138	+	0.759073i	−0.968735	+	0.248099i	$0.920194\pi$
$110$	0.857499	−	3.02159i	0.0817593	−	0.288097i
$111$	−3.44498	+	0.495313i	−0.326983	+	0.0470130i
$112$	0.586538	−	2.69627i	0.0554227	−	0.254774i
$113$	−9.99612	+	0.714937i	−0.940356	+	0.0672556i	−0.533094	−	0.846056i	$-0.678971\pi$
$113$	−9.99612	+	0.714937i	−0.940356	+	0.0672556i	−0.407262	+	0.913311i	$0.633516\pi$
$114$	−8.12334			−0.760820
$115$	9.39826	+	5.16457i	0.876392	+	0.481598i
$116$	5.68967			0.528273
$117$	0.424285	−	0.0303454i	0.0392251	−	0.00280544i
$118$	−1.96500	+	9.03297i	−0.180893	+	0.831552i
$119$	16.6542	−	2.39451i	1.52669	−	0.219504i
$120$	1.08941	+	1.95274i	0.0994488	+	0.178260i
$121$	−1.28467	+	8.93506i	−0.116788	+	0.812278i
$122$	−5.50737	+	10.0860i	−0.498614	+	0.913143i
$123$	2.73215	−	0.594343i	0.246350	−	0.0535901i
$124$	6.17295	+	2.81909i	0.554347	+	0.253162i
$125$	−0.493599	+	11.1694i	−0.0441488	+	0.999025i
$126$	2.08536	−	1.80698i	0.185779	−	0.160978i
$127$	1.40397	−	19.6301i	0.124583	−	1.74189i	−0.423881	−	0.905718i	$-0.639333\pi$
$127$	1.40397	−	19.6301i	0.124583	−	1.74189i	0.548464	−	0.836174i	$-0.315213\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	−0.997118	+	2.18338i	−0.0877913	+	0.192236i
$130$	−0.448241	+	0.838911i	−0.0393133	+	0.0735773i
$131$	−7.37918	+	2.16672i	−0.644722	+	0.189307i	−0.587717	−	0.809066i	$-0.699973\pi$
$131$	−7.37918	+	2.16672i	−0.644722	+	0.189307i	−0.0570048	+	0.998374i	$0.518155\pi$
$132$	0.841780	+	1.12449i	0.0732675	+	0.0978739i
$133$	−21.0017	−	7.83324i	−1.82108	−	0.679228i
$134$	−1.22979	−	8.55335i	−0.106237	−	0.738897i
$135$	−0.298118	+	2.21611i	−0.0256579	+	0.190732i
$136$	−4.60829	−	3.99311i	−0.395158	−	0.342406i
$137$	−3.48169	+	3.48169i	−0.297461	+	0.297461i	−0.840018	−	0.542558i	$-0.817456\pi$
$137$	−3.48169	+	3.48169i	−0.297461	+	0.297461i	0.542558	+	0.840018i	$0.317456\pi$
$138$	−4.38556	+	1.94083i	−0.373324	+	0.165215i
$139$		−	21.3396i		−	1.81000i	−0.425410	−	0.905001i	$-0.639870\pi$
$139$		−	21.3396i		−	1.81000i	0.425410	−	0.905001i	$-0.360130\pi$
$140$	0.933501	+	6.09903i	0.0788952	+	0.515462i
$141$	−10.9387	+	7.02988i	−0.921206	+	0.592023i
$142$	−2.91039	+	3.88783i	−0.244235	+	0.326260i
$143$	−0.208804	+	0.559824i	−0.0174610	+	0.0468149i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	−11.8795	+	4.55410i	−0.986537	+	0.378197i
$146$	−5.97268	−	3.83841i	−0.494302	−	0.317669i
$147$	0.575210	−	0.214542i	0.0474425	−	0.0176951i
$148$	1.66798	+	3.05468i	0.137107	+	0.251093i
$149$	−10.4181	−	12.0232i	−0.853487	−	0.984977i	0.146504	−	0.989210i	$-0.453198\pi$
$149$	−10.4181	−	12.0232i	−0.853487	−	0.984977i	−0.999991	+	0.00423317i	$0.998653\pi$
$150$	−3.83758	−	3.20515i	−0.313337	−	0.261700i
$151$	10.6427	+	3.12498i	0.866091	+	0.254307i	0.684452	−	0.729058i	$-0.260042\pi$
$151$	10.6427	+	3.12498i	0.866091	+	0.254307i	0.181639	+	0.983365i	$0.441860\pi$
$152$	2.83882	+	7.61116i	0.230258	+	0.617347i
$153$	−1.29615	−	5.95830i	−0.104787	−	0.481700i
$154$	1.09197	+	3.71891i	0.0879936	+	0.299679i
$155$	−15.1450	−	0.945072i	−1.21647	−	0.0759100i
$156$	−0.176704	−	0.386929i	−0.0141477	−	0.0309791i
$157$	10.3716	+	7.76412i	0.827747	+	0.619644i	0.926849	−	0.375433i	$-0.122506\pi$
$157$	10.3716	+	7.76412i	0.827747	+	0.619644i	−0.0991019	+	0.995077i	$0.531597\pi$
$158$	−4.48048	−	0.974669i	−0.356448	−	0.0775405i
$159$	1.89640	−	2.18856i	0.150394	−	0.173564i
$160$	1.44891	−	1.70313i	0.114546	−	0.134644i
$161$	−13.2098	+	0.788797i	−1.04108	+	0.0621659i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	0.909317	+	12.7139i	0.0712232	+	0.995831i	0.899898	+	0.436100i	$0.143641\pi$
$163$	0.909317	+	12.7139i	0.0712232	+	0.995831i	−0.828675	+	0.559730i	$0.810905\pi$
$164$	−1.51166	−	2.35219i	−0.118041	−	0.183675i
$165$	−2.65761	−	1.67404i	−0.206895	−	0.130324i
$166$	3.55088	−	1.62163i	0.275602	−	0.125863i
$167$	3.93009	−	2.94203i	0.304120	−	0.227661i	−0.436308	−	0.899798i	$-0.643714\pi$
$167$	3.93009	−	2.94203i	0.304120	−	0.227661i	0.740427	+	0.672136i	$0.234623\pi$
$168$	−2.42181	−	1.32241i	−0.186847	−	0.102026i
$169$	−6.93051	+	10.7841i	−0.533116	+	0.829545i
$170$	12.8178	+	4.64868i	0.983081	+	0.356537i
$171$	−2.28861	+	7.79429i	−0.175014	+	0.596044i
$172$	2.39418	+	0.171235i	0.182554	+	0.0130565i
$173$	−20.3001	−	1.45189i	−1.54339	−	0.110385i	−0.726493	−	0.687174i	$-0.758851\pi$
$173$	−20.3001	−	1.45189i	−1.54339	−	0.110385i	−0.816894	+	0.576789i	$0.804306\pi$
$174$	1.60297	−	5.45920i	0.121521	−	0.413861i
$175$	−6.83081	−	11.9870i	−0.516361	−	0.906131i
$176$	0.759415	−	1.18167i	0.0572431	−	0.0890719i
$177$	8.11346	+	4.43029i	0.609845	+	0.333001i
$178$	0.0386656	−	0.0289447i	0.00289811	−	0.00216950i
$179$	−20.0852	+	9.17261i	−1.50124	+	0.685593i	−0.985269	−	0.171013i	$-0.945296\pi$
$179$	−20.0852	+	9.17261i	−1.50124	+	0.685593i	−0.515971	+	0.856606i	$0.672569\pi$
$180$	2.18056	−	0.495128i	0.162529	−	0.0369046i
$181$	−5.00103	−	7.78176i	−0.371724	−	0.578414i	0.604117	−	0.796896i	$-0.293526\pi$
$181$	−5.00103	−	7.78176i	−0.371724	−	0.578414i	−0.975841	+	0.218482i	$0.929890\pi$
$182$	−0.0837332	−	1.17074i	−0.00620671	−	0.0867812i
$183$	8.12584	+	8.12584i	0.600679	+	0.600679i
$184$	3.35106	+	3.43080i	0.247043	+	0.252922i
$185$	−5.92759	−	5.04279i	−0.435805	−	0.370753i
$186$	4.44402	−	5.12867i	0.325851	−	0.376052i
$187$	8.36936	+	1.82064i	0.612028	+	0.133139i
$188$	10.4093	+	7.79233i	0.759179	+	0.568314i
$189$	−1.14627	−	2.50998i	−0.0833787	−	0.182574i
$190$	−12.0193	−	13.6191i	−0.871968	−	0.988036i
$191$	−2.53171	−	8.62222i	−0.183188	−	0.623882i	−0.998964	−	0.0455131i	$-0.985508\pi$
$191$	−2.53171	−	8.62222i	−0.183188	−	0.623882i	0.815776	−	0.578369i	$-0.196310\pi$
$192$	0.212565	+	0.977147i	0.0153406	+	0.0705195i
$193$	5.20476	+	13.9545i	0.374647	+	1.00447i	0.978295	+	0.207216i	$0.0664403\pi$
$193$	5.20476	+	13.9545i	0.374647	+	1.00447i	−0.603649	+	0.797251i	$0.706287\pi$
$194$	2.69657	+	0.791785i	0.193603	+	0.0568469i
$195$	0.678645	+	0.666433i	0.0485988	+	0.0477242i
$196$	−0.402030	−	0.463968i	−0.0287164	−	0.0331405i
$197$	−5.48829	−	10.0511i	−0.391025	−	0.716108i	0.605810	−	0.795609i	$-0.292849\pi$
$197$	−5.48829	−	10.0511i	−0.391025	−	0.716108i	−0.996835	+	0.0795010i	$0.974667\pi$
$198$	1.31609	−	0.490877i	0.0935307	−	0.0348851i
$199$	−12.2869	−	7.89633i	−0.870997	−	0.559756i	0.0270606	−	0.999634i	$-0.491385\pi$
$199$	−12.2869	−	7.89633i	−0.870997	−	0.559756i	−0.898057	+	0.439878i	$0.855022\pi$
$200$	−1.66197	+	4.71570i	−0.117519	+	0.333450i
$201$	−8.55335	−	1.22979i	−0.603307	−	0.0867425i
$202$	−5.50373	+	14.7561i	−0.387241	+	1.03823i
$203$	9.40848	−	12.5683i	0.660346	−	0.882119i
$204$	−5.12967	+	3.29664i	−0.359148	+	0.230811i
$205$	5.03892	+	3.70118i	0.351933	+	0.258502i
$206$			17.1529i			1.19510i
$207$	0.626659	+	4.75471i	0.0435558	+	0.330475i
$208$	−0.300781	+	0.300781i	−0.0208554	+	0.0208554i
$209$	−8.62348	−	7.47229i	−0.596499	−	0.516869i
$210$	6.11497	+	0.822608i	0.421973	+	0.0567653i
$211$	−0.237553	−	1.65221i	−0.0163538	−	0.113743i	0.980009	−	0.198951i	$-0.0637536\pi$
$211$	−0.237553	−	1.65221i	−0.0163538	−	0.113743i	−0.996363	+	0.0852082i	$0.972844\pi$
$212$	−2.71329	−	1.01201i	−0.186350	−	0.0695049i
$213$	2.91039	+	3.88783i	0.199417	+	0.266390i
$214$	1.15226	−	0.338334i	0.0787668	−	0.0231280i
$215$	−5.13587	+	1.55881i	−0.350263	+	0.106310i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	16.4349	−	8.97413i	1.11567	−	0.609203i
$218$	0.571174	−	7.98605i	0.0386848	−	0.540884i
$219$	−5.36562	+	4.64934i	−0.362575	+	0.314173i
$220$	−0.639757	+	3.07506i	−0.0431324	+	0.207321i
$221$	−2.35935	−	1.07748i	−0.158707	−	0.0724792i
$222$	3.40087	−	0.739813i	0.228251	−	0.0496530i
$223$	−0.527236	+	0.965561i	−0.0353064	+	0.0646588i	−0.894737	−	0.446594i	$-0.852637\pi$
$223$	−0.527236	+	0.965561i	−0.0353064	+	0.0646588i	0.859430	+	0.511253i	$0.170819\pi$
$224$	−0.392694	+	2.73125i	−0.0262380	+	0.182489i
$225$	−4.15649	+	2.77913i	−0.277100	+	0.185275i
$226$	9.91965	−	1.42623i	0.659845	−	0.0948714i
$227$	1.35726	−	6.23920i	0.0900842	−	0.414110i	−0.909916	−	0.414793i	$-0.863854\pi$
$227$	1.35726	−	6.23920i	0.0900842	−	0.414110i	1.00000		0.000683157i	$0.000217456\pi$
$228$	8.10264	−	0.579512i	0.536610	−	0.0383791i
$229$	−19.0008			−1.25561			−0.627803	−	0.778373i	$-0.716045\pi$
$229$	−19.0008			−1.25561			−0.627803	+	0.778373i	$0.716045\pi$
$230$	−9.74275	−	4.48094i	−0.642418	−	0.295465i
$231$	3.87592			0.255017
$232$	−5.67518	+	0.405897i	−0.372594	+	0.0266484i
$233$	1.44186	−	6.62813i	0.0944594	−	0.434223i	−0.905492	−	0.424363i	$-0.860498\pi$
$233$	1.44186	−	6.62813i	0.0944594	−	0.434223i	0.999951	−	0.00985959i	$-0.00313846\pi$
$234$	−0.421039	+	0.0605362i	−0.0275242	+	0.00395738i
$235$	−27.9708	−	7.93785i	−1.82461	−	0.517808i
$236$	1.31559	−	9.15013i	0.0856377	−	0.595623i
$237$	−2.19749	+	4.02440i	−0.142742	+	0.261413i
$238$	−16.4409	+	3.57650i	−1.06571	+	0.231830i
$239$	26.6353	+	12.1639i	1.72289	+	0.786820i	0.994858	+	0.101282i	$0.0322943\pi$
$239$	26.6353	+	12.1639i	1.72289	+	0.786820i	0.728037	+	0.685538i	$0.240433\pi$
$240$	−1.22594	−	1.87005i	−0.0791339	−	0.120711i
$241$	−0.709128	+	0.614463i	−0.0456789	+	0.0395810i	−0.677401	−	0.735614i	$-0.736894\pi$
$241$	−0.709128	+	0.614463i	−0.0456789	+	0.0395810i	0.631722	+	0.775195i	$0.282348\pi$
$242$	0.643974	−	9.00394i	0.0413962	−	0.578795i
$243$	−0.877679	+	0.479249i	−0.0563031	+	0.0307438i
$244$	4.77381	−	10.4532i	0.305612	−	0.669197i
$245$	1.21077	+	0.646928i	0.0773530	+	0.0413307i
$246$	−2.68279	+	0.787738i	−0.171048	+	0.0502243i
$247$	2.07075	+	2.76620i	0.131759	+	0.176009i
$248$	−6.35833	−	2.37153i	−0.403754	−	0.150593i
$249$	−0.555546	−	3.86391i	−0.0352063	−	0.244865i
$250$	−0.304478	−	11.1762i	−0.0192569	−	0.706845i
$251$	16.7160	+	14.4845i	1.05510	+	0.914253i	0.996464	−	0.0840257i	$-0.0267778\pi$
$251$	16.7160	+	14.4845i	1.05510	+	0.914253i	0.0586411	+	0.998279i	$0.481323\pi$
$252$	−1.95114	+	1.95114i	−0.122910	+	0.122910i
$253$	−6.44086	−	1.97375i	−0.404934	−	0.124089i
$254$			19.6803i			1.23485i
$255$	8.07157	−	10.9889i	0.505461	−	0.688152i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.420247	−	0.561384i	0.0262143	−	0.0350182i	−0.787243	−	0.616643i	$-0.788492\pi$
$257$	0.420247	−	0.561384i	0.0262143	−	0.0350182i	0.813457	+	0.581625i	$0.197583\pi$
$258$	0.838816	−	2.24895i	0.0522224	−	0.140014i
$259$	9.50584	+	1.36673i	0.590664	+	0.0849247i
$260$	0.387252	−	0.868750i	0.0240163	−	0.0538776i
$261$	−4.78646	−	3.07607i	−0.296274	−	0.190404i
$262$	7.20581	−	2.68763i	0.445176	−	0.166042i
$263$	1.01353	+	1.85614i	0.0624969	+	0.114454i	0.907060	−	0.421002i	$-0.138321\pi$
$263$	1.01353	+	1.85614i	0.0624969	+	0.114454i	−0.844563	+	0.535456i	$0.820140\pi$
$264$	−0.919855	−	1.06157i	−0.0566131	−	0.0653351i
$265$	6.47512	−	0.0587885i	0.397763	−	0.00361135i
$266$	21.5070	+	6.31503i	1.31868	+	0.387200i
$267$	−0.0168789	−	0.0452540i	−0.00103297	−	0.00276950i
$268$	1.83684	+	8.44383i	0.112203	+	0.515789i
$269$	−1.75446	−	5.97516i	−0.106972	−	0.364312i	0.888558	−	0.458765i	$-0.151708\pi$
$269$	−1.75446	−	5.97516i	−0.106972	−	0.364312i	−0.995529	+	0.0944531i	$0.969890\pi$
$270$	0.139264	−	2.23173i	0.00847532	−	0.135819i
$271$	13.5030	+	29.5675i	0.820251	+	1.79610i	0.554822	+	0.831969i	$0.312786\pi$
$271$	13.5030	+	29.5675i	0.820251	+	1.79610i	0.265429	+	0.964130i	$0.414486\pi$
$272$	4.88142	+	3.65418i	0.295979	+	0.221567i
$273$	−1.14691	−	0.249495i	−0.0694141	−	0.0151001i
$274$	3.22443	−	3.72120i	0.194795	−	0.224806i
$275$	−1.12558	−	6.93250i	−0.0678747	−	0.418046i
$276$	4.23593	−	2.24875i	0.254973	−	0.135359i
$277$	−5.91674	−	5.91674i	−0.355503	−	0.355503i	0.506649	−	0.862152i	$-0.330884\pi$
$277$	−5.91674	−	5.91674i	−0.355503	−	0.355503i	−0.862152	+	0.506649i	$0.830884\pi$
$278$	1.52235	+	21.2852i	0.0913045	+	1.27660i
$279$	−3.66890	−	5.70892i	−0.219651	−	0.341784i
$280$	−1.36622	−	6.01689i	−0.0816474	−	0.359578i
$281$	17.0485	−	7.78579i	1.01703	−	0.464461i	0.164075	−	0.986448i	$-0.447536\pi$
$281$	17.0485	−	7.78579i	1.01703	−	0.464461i	0.852954	+	0.521987i	$0.174809\pi$
$282$	10.4093	−	7.79233i	0.619867	−	0.464027i
$283$	2.59168	+	1.41517i	0.154060	+	0.0841229i	0.554429	−	0.832231i	$-0.312937\pi$
$283$	2.59168	+	1.41517i	0.154060	+	0.0841229i	−0.400370	+	0.916354i	$0.631118\pi$
$284$	2.62562	−	4.08555i	0.155802	−	0.242433i
$285$	−16.4537	+	7.69543i	−0.974632	+	0.455838i
$286$	0.168334	−	0.573294i	0.00995381	−	0.0338996i
$287$	−7.69557	−	0.550398i	−0.454255	−	0.0324890i
$288$	0.997452	+	0.0713392i	0.0587754	+	0.00420370i
$289$	−5.68573	+	19.3638i	−0.334455	+	1.13905i
$290$	11.5243	−	5.38996i	0.676732	−	0.316510i
$291$	1.51942	−	2.36427i	0.0890703	−	0.138596i
$292$	6.23129	+	3.40254i	0.364659	+	0.199119i
$293$	15.4798	−	11.5881i	0.904341	−	0.676981i	−0.0423574	−	0.999103i	$-0.513487\pi$
$293$	15.4798	−	11.5881i	0.904341	−	0.676981i	0.946698	+	0.322121i	$0.104396\pi$
$294$	−0.558439	+	0.255030i	−0.0325688	+	0.0148737i
$295$	4.57707	+	20.1576i	0.266487	+	1.17362i
$296$	−1.88165	−	2.92790i	−0.109369	−	0.170181i
$297$	−0.100207	−	1.40108i	−0.00581460	−	0.0812988i
$298$	11.2493	+	11.2493i	0.651656	+	0.651656i
$299$	1.77884	+	0.998649i	0.102873	+	0.0577534i
$300$	4.05645	+	2.92322i	0.234199	+	0.168772i
$301$	4.33728	−	5.00549i	0.249997	−	0.288511i
$302$	−10.8385	−	2.35778i	−0.623687	−	0.135675i
$303$	12.6078	+	9.43805i	0.724297	+	0.542202i
$304$	−3.37456	−	7.38925i	−0.193544	−	0.423802i
$305$	−1.60037	+	25.6463i	−0.0916370	+	1.46850i
$306$	1.71791	+	5.85065i	0.0982061	+	0.334459i
$307$	0.887368	+	4.07917i	0.0506448	+	0.232810i	0.995511	−	0.0946464i	$-0.0301721\pi$
$307$	0.887368	+	4.07917i	0.0506448	+	0.232810i	−0.944866	+	0.327457i	$0.893808\pi$
$308$	−1.35449	−	3.63154i	−0.0771795	−	0.206926i
$309$	16.4581	+	4.83253i	0.936268	+	0.274913i
$310$	15.1738	−	0.137765i	0.861813	−	0.00782453i
$311$	18.3292	+	21.1530i	1.03935	+	1.19948i	0.979536	+	0.201267i	$0.0645058\pi$
$311$	18.3292	+	21.1530i	1.03935	+	1.19948i	0.0598156	+	0.998209i	$0.480949\pi$
$312$	0.203857	+	0.373337i	0.0115412	+	0.0211360i
$313$	10.4637	−	3.90278i	0.591446	−	0.220598i	−0.0358782	−	0.999356i	$-0.511423\pi$
$313$	10.4637	−	3.90278i	0.591446	−	0.220598i	0.627324	+	0.778758i	$0.284150\pi$
$314$	−10.8991	−	7.00443i	−0.615072	−	0.395283i
$315$	2.51207	−	5.63552i	0.141539	−	0.317526i
$316$	4.53860	+	0.652552i	0.255316	+	0.0367089i
$317$	4.67732	−	12.5404i	0.262704	−	0.704338i	−0.736894	−	0.676008i	$-0.763708\pi$
$317$	4.67732	−	12.5404i	0.262704	−	0.704338i	0.999599	−	0.0283297i	$-0.00901884\pi$
$318$	−1.73544	+	2.31827i	−0.0973184	+	0.130002i
$319$	6.72333	−	4.32082i	0.376434	−	0.241920i
$320$	−1.32372	+	1.80216i	−0.0739981	+	0.100744i
$321$		−	1.20090i		−	0.0670279i
$322$	13.1198	−	1.72916i	0.731140	−	0.0963624i
$323$	35.0253	−	35.0253i	1.94886	−	1.94886i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	−0.113184	+	2.12383i	−0.00627831	+	0.117809i
$326$	−1.81400	−	12.6167i	−0.100468	−	0.698772i
$327$	−7.50164	−	2.79797i	−0.414842	−	0.154728i
$328$	1.67561	+	2.23835i	0.0925200	+	0.123592i
$329$	34.4259	−	10.1084i	1.89796	−	0.557292i
$330$	2.77026	+	1.48019i	0.152498	+	0.0814817i
$331$	−6.38596	+	13.9833i	−0.351004	+	0.768591i	0.648966	+	0.760818i	$0.275202\pi$
$331$	−6.38596	+	13.9833i	−0.351004	+	0.768591i	−0.999970	+	0.00777386i	$0.997525\pi$
$332$	−3.42614	+	1.87082i	−0.188034	+	0.102674i
$333$	0.248289	−	3.47154i	0.0136062	−	0.190239i
$334$	−3.71020	+	3.21491i	−0.203013	+	0.175912i
$335$	−10.5937	−	16.1597i	−0.578796	−	0.882896i
$336$	2.50998	+	1.14627i	0.136930	+	0.0625341i
$337$	13.0993	−	2.84957i	0.713563	−	0.155226i	0.158892	−	0.987296i	$-0.449208\pi$
$337$	13.0993	−	2.84957i	0.713563	−	0.155226i	0.554671	+	0.832070i	$0.312844\pi$
$338$	6.14352	−	11.2510i	0.334164	−	0.611975i
$339$	1.42623	−	9.91965i	0.0774622	−	0.538761i
$340$	−13.1168	−	3.72242i	−0.711357	−	0.201877i
$341$	9.43526	−	1.35659i	0.510948	−	0.0734633i
$342$	1.72674	−	7.93769i	0.0933714	−	0.429221i
$343$	17.5764	−	1.25709i	0.949038	−	0.0678765i
$344$	−2.40029			−0.129415
$345$	−7.04428	+	8.08567i	−0.379251	+	0.435318i
$346$	20.3519			1.09413
$347$	−16.8424	+	1.20459i	−0.904147	+	0.0646659i	−0.515665	−	0.856790i	$-0.672455\pi$
$347$	−16.8424	+	1.20459i	−0.904147	+	0.0646659i	−0.388482	+	0.921456i	$0.627001\pi$
$348$	−1.20943	+	5.55965i	−0.0648321	+	0.298028i
$349$	−12.2393	+	1.75974i	−0.655154	+	0.0941970i	−0.461872	−	0.886946i	$-0.652822\pi$
$349$	−12.2393	+	1.75974i	−0.655154	+	0.0941970i	−0.193282	+	0.981143i	$0.561913\pi$
$350$	7.66855	+	11.4691i	0.409901	+	0.613052i
$351$	−0.0605362	+	0.421039i	−0.00323119	+	0.0224734i
$352$	−0.673180	+	1.23284i	−0.0358806	+	0.0657105i
$353$	−1.79599	+	0.390694i	−0.0955911	+	0.0207946i	−0.260106	−	0.965580i	$-0.583758\pi$
$353$	−1.79599	+	0.390694i	−0.0955911	+	0.0207946i	0.164515	+	0.986375i	$0.447394\pi$
$354$	−8.40884	−	3.84019i	−0.446925	−	0.204104i
$355$	−2.21191	+	10.6318i	−0.117396	+	0.564278i
$356$	−0.0365022	+	0.0316293i	−0.00193461	+	0.00167635i
$357$	−1.20031	+	16.7826i	−0.0635273	+	0.888228i
$358$	19.3797	−	10.5821i	1.02425	−	0.559281i
$359$	−12.4367	+	27.2326i	−0.656386	+	1.43728i	0.229467	+	0.973317i	$0.426302\pi$
$359$	−12.4367	+	27.2326i	−0.656386	+	1.43728i	−0.885852	+	0.463968i	$0.846425\pi$
$360$	−2.13968	+	0.649426i	−0.112771	+	0.0342277i
$361$	−45.0853	+	13.2382i	−2.37291	+	0.696749i
$362$	5.54344	+	7.40516i	0.291357	+	0.389207i
$363$	−8.45779	−	3.15459i	−0.443919	−	0.165573i
$364$	0.167040	+	1.16179i	0.00875525	+	0.0608941i
$365$	−15.7338	−	2.11656i	−0.823543	−	0.110786i
$366$	−8.68482	−	7.52544i	−0.453963	−	0.393361i
$367$	6.98787	−	6.98787i	0.364764	−	0.364764i	−0.500799	−	0.865563i	$-0.666961\pi$
$367$	6.98787	−	6.98787i	0.364764	−	0.364764i	0.865563	+	0.500799i	$0.166961\pi$
$368$	−3.58727	−	3.18300i	−0.186999	−	0.165925i
$369$			2.79605i			0.145556i
$370$	6.27223	+	4.60708i	0.326078	+	0.239510i
$371$	−6.72220	+	4.32010i	−0.348999	+	0.224288i
$372$	−4.06682	+	5.43264i	−0.210855	+	0.281669i
$373$	−4.23068	+	11.3429i	−0.219056	+	0.587313i	−0.999270	−	0.0382002i	$-0.987838\pi$
$373$	−4.23068	+	11.3429i	−0.219056	+	0.587313i	0.780214	+	0.625513i	$0.215110\pi$
$374$	−8.47792	−	1.21894i	−0.438383	−	0.0630299i
$375$	−10.8093	−	2.85655i	−0.558188	−	0.147512i
$376$	−10.9387	−	7.02988i	−0.564121	−	0.362539i
$377$	−2.26761	+	0.845776i	−0.116788	+	0.0435597i
$378$	1.32241	+	2.42181i	0.0680173	+	0.124564i
$379$	0.0468847	+	0.0541079i	0.00240831	+	0.00277933i	0.756952	−	0.653470i	$-0.226687\pi$
$379$	0.0468847	+	0.0541079i	0.00240831	+	0.00277933i	−0.754544	+	0.656249i	$0.772142\pi$
$380$	12.9602	+	12.7270i	0.664844	+	0.652881i
$381$	18.8831	+	5.54457i	0.967409	+	0.284057i
$382$	3.14036	+	8.41964i	0.160675	+	0.430786i
$383$	−6.99109	−	32.1375i	−0.357228	−	1.64215i	−0.708380	−	0.705832i	$-0.750573\pi$
$383$	−6.99109	−	32.1375i	−0.357228	−	1.64215i	0.351152	−	0.936319i	$-0.385790\pi$
$384$	−0.281733	−	0.959493i	−0.0143771	−	0.0489639i
$385$	5.73479	+	6.49814i	0.292272	+	0.331176i
$386$	−6.18700	−	13.5476i	−0.314910	−	0.689557i
$387$	−1.92153	−	1.43844i	−0.0976770	−	0.0731201i
$388$	−2.74619	−	0.597397i	−0.139417	−	0.0303282i
$389$	21.2818	−	24.5605i	1.07903	−	1.24527i	0.111164	−	0.993802i	$-0.464542\pi$
$389$	21.2818	−	24.5605i	1.07903	−	1.24527i	0.967866	−	0.251465i	$-0.0809124\pi$
$390$	−0.724459	−	0.616321i	−0.0366844	−	0.0312086i
$391$	10.5409	−	27.2774i	0.533077	−	1.37948i
$392$	0.434105	+	0.434105i	0.0219256	+	0.0219256i
$393$	−0.548649	−	7.67111i	−0.0276757	−	0.386956i
$394$	6.19134	+	9.63392i	0.311915	+	0.485350i
$395$	−9.99847	+	2.27029i	−0.503077	+	0.114231i
$396$	−1.27772	+	0.583516i	−0.0642079	+	0.0293228i
$397$	−20.2616	+	15.1677i	−1.01690	+	0.761244i	−0.971334	−	0.237717i	$-0.923601\pi$
$397$	−20.2616	+	15.1677i	−1.01690	+	0.761244i	−0.0455684	+	0.998961i	$0.514510\pi$
$398$	12.8189	+	6.99967i	0.642555	+	0.350862i
$399$	12.1185	−	18.8567i	0.606682	−	0.944015i
$400$	1.32132	−	4.82225i	0.0660662	−	0.241113i
$401$	2.09126	−	7.12219i	0.104433	−	0.355665i	−0.890653	−	0.454684i	$-0.849752\pi$
$401$	2.09126	−	7.12219i	0.104433	−	0.355665i	0.995086	+	0.0990188i	$0.0315704\pi$
$402$	8.61929	+	0.616464i	0.429891	+	0.0307464i
$403$	−2.87928	−	0.205930i	−0.143427	−	0.0102581i
$404$	4.43702	−	15.1111i	0.220750	−	0.751805i
$405$	−2.10209	−	0.762373i	−0.104454	−	0.0378826i
$406$	−8.48790	+	13.2074i	−0.421247	+	0.655474i
$407$	4.29077	+	2.34294i	0.212686	+	0.116135i
$408$	4.88142	−	3.65418i	0.241666	−	0.180909i
$409$	−3.86292	+	1.76414i	−0.191009	+	0.0872309i	−0.508624	−	0.860989i	$-0.669845\pi$
$409$	−3.86292	+	1.76414i	−0.191009	+	0.0872309i	0.317614	+	0.948220i	$0.397118\pi$
$410$	−5.29012	−	3.33228i	−0.261260	−	0.164570i
$411$	−2.66203	−	4.14220i	−0.131308	−	0.204320i
$412$	−1.22367	−	17.1092i	−0.0602861	−	0.842910i
$413$	−18.0368	−	18.0368i	−0.887533	−	0.887533i
$414$	−0.964260	−	4.69789i	−0.0473908	−	0.230889i
$415$	5.65603	−	6.64842i	0.277643	−	0.326358i
$416$	0.278557	−	0.321472i	0.0136574	−	0.0157615i
$417$	20.8519	+	4.53606i	1.02112	+	0.222132i
$418$	9.13458	+	6.83806i	0.446787	+	0.334460i
$419$	−4.65611	−	10.1954i	−0.227466	−	0.498080i	0.761144	−	0.648583i	$-0.224638\pi$
$419$	−4.65611	−	10.1954i	−0.227466	−	0.498080i	−0.988610	+	0.150503i	$0.951911\pi$
$420$	−6.15808	−	0.384275i	−0.300483	−	0.0187507i
$421$	−3.47897	−	11.8483i	−0.169555	−	0.577450i	−0.999799	−	0.0200507i	$-0.993617\pi$
$421$	−3.47897	−	11.8483i	−0.169555	−	0.577450i	0.830244	−	0.557400i	$-0.188201\pi$
$422$	0.354815	+	1.63106i	0.0172721	+	0.0793986i
$423$	−4.54404	−	12.1830i	−0.220939	−	0.592360i
$424$	2.77858	+	0.815864i	0.134940	+	0.0396218i
$425$	30.3660	−	2.72681i	1.47297	−	0.132269i
$426$	−3.18033	−	3.67030i	−0.154088	−	0.177827i
$427$	−15.1967	−	27.8306i	−0.735418	−	1.34682i
$428$	−1.12519	+	0.419673i	−0.0543880	+	0.0202857i
$429$	−0.502646	−	0.323031i	−0.0242680	−	0.0155961i
$430$	5.01158	−	1.92123i	0.241680	−	0.0926499i
$431$	−1.08505	−	0.156007i	−0.0522651	−	0.00751459i	0.116133	−	0.993234i	$-0.462950\pi$
$431$	−1.08505	−	0.156007i	−0.0522651	−	0.00751459i	−0.168398	+	0.985719i	$0.553859\pi$
$432$	0.349464	−	0.936950i	0.0168136	−	0.0450790i
$433$	−11.4843	+	15.3412i	−0.551898	+	0.737250i	−0.986570	−	0.163339i	$-0.947773\pi$
$433$	−11.4843	+	15.3412i	−0.551898	+	0.737250i	0.434672	+	0.900589i	$0.356864\pi$
$434$	−15.7528	+	10.1237i	−0.756159	+	0.485954i
$435$	−1.92485	−	12.5760i	−0.0922897	−	0.602975i
$436$			8.00645i			0.383439i
$437$	−29.7405	+	25.1642i	−1.42268	+	1.20377i
$438$	5.02027	−	5.02027i	0.239878	−	0.239878i
$439$	9.52773	+	8.25583i	0.454734	+	0.394029i	0.851889	−	0.523722i	$-0.175457\pi$
$439$	9.52773	+	8.25583i	0.454734	+	0.394029i	−0.397155	+	0.917751i	$0.630003\pi$
$440$	0.418754	−	3.11287i	0.0199633	−	0.148400i
$441$	0.0873695	+	0.607668i	0.00416045	+	0.0289366i
$442$	2.43021	+	0.906421i	0.115593	+	0.0431141i
$443$	5.03645	+	6.72791i	0.239289	+	0.319653i	0.904069	−	0.427386i	$-0.140566\pi$
$443$	5.03645	+	6.72791i	0.239289	+	0.319653i	−0.664780	+	0.747039i	$0.731475\pi$
$444$	−3.33942	+	0.980543i	−0.158482	+	0.0465345i
$445$	0.0508964	−	0.0952558i	0.00241272	−	0.00451556i
$446$	0.457011	−	1.00071i	0.0216401	−	0.0473852i
$447$	13.9629	−	7.62434i	0.660425	−	0.360619i
$448$	0.196849	−	2.75230i	0.00930022	−	0.130034i
$449$	−26.3276	+	22.8130i	−1.24248	+	1.07661i	−0.248319	+	0.968678i	$0.579878\pi$
$449$	−26.3276	+	22.8130i	−1.24248	+	1.07661i	−0.994158	+	0.107934i	$0.965576\pi$
$450$	3.94764	−	3.06857i	0.186094	−	0.144654i
$451$	−3.57257	−	1.63154i	−0.168226	−	0.0768261i
$452$	−9.79263	+	2.13026i	−0.460607	+	0.100199i
$453$	−5.31583	+	9.73522i	−0.249760	+	0.457401i
$454$	−0.908698	+	6.32013i	−0.0426473	+	0.296618i
$455$	−1.27867	−	2.29200i	−0.0599451	−	0.107450i
$456$	−8.04065	+	1.15607i	−0.376538	+	0.0541380i
$457$	−3.74870	+	17.2325i	−0.175357	+	0.806102i	0.802471	+	0.596691i	$0.203518\pi$
$457$	−3.74870	+	17.2325i	−0.175357	+	0.806102i	−0.977828	+	0.209411i	$0.932845\pi$
$458$	18.9523	−	1.35550i	0.885585	−	0.0633383i
$459$	6.09765			0.284614
$460$	10.0376	+	3.77449i	0.468005	+	0.175986i
$461$	6.58334			0.306617			0.153308	−	0.988178i	$-0.451007\pi$
$461$	6.58334			0.306617			0.153308	+	0.988178i	$0.451007\pi$
$462$	−3.86604	+	0.276505i	−0.179864	+	0.0128642i
$463$	−4.87369	+	22.4040i	−0.226499	+	1.04120i	0.713667	+	0.700485i	$0.247033\pi$
$463$	−4.87369	+	22.4040i	−0.226499	+	1.04120i	−0.940166	+	0.340716i	$0.889331\pi$
$464$	5.63176	−	0.809725i	0.261448	−	0.0375905i
$465$	4.14276	−	14.5980i	0.192116	−	0.676964i
$466$	−0.965342	+	6.71410i	−0.0447186	+	0.311025i
$467$	−0.970033	+	1.77648i	−0.0448878	+	0.0822058i	−0.899160	−	0.437620i	$-0.855821\pi$
$467$	−0.970033	+	1.77648i	−0.0448878	+	0.0822058i	0.854272	+	0.519826i	$0.174003\pi$
$468$	0.415647	−	0.0904186i	0.0192133	−	0.00417960i
$469$	21.6895	+	9.90526i	1.00153	+	0.457382i
$470$	28.4658	+	5.92221i	1.31303	+	0.273171i
$471$	−9.79133	+	8.48424i	−0.451161	+	0.390933i
$472$	−0.659476	+	9.22067i	−0.0303548	+	0.424416i
$473$	2.95917	−	1.61583i	0.136063	−	0.0742960i
$474$	1.90479	−	4.17091i	0.0874899	−	0.191576i
$475$	−37.2465	−	16.1992i	−1.70899	−	0.743269i
$476$	16.1439	−	4.74027i	0.739954	−	0.217270i
$477$	1.73544	+	2.31827i	0.0794602	+	0.106146i
$478$	−27.4352	−	10.2328i	−1.25486	−	0.468038i
$479$	0.648613	+	4.51120i	0.0296359	+	0.206122i	0.999259	−	0.0384803i	$-0.0122517\pi$
$479$	0.648613	+	4.51120i	0.0296359	+	0.206122i	−0.969623	+	0.244602i	$0.921343\pi$
$480$	1.35622	+	1.77783i	0.0619028	+	0.0811462i
$481$	−1.11885	−	0.969491i	−0.0510153	−	0.0442050i
$482$	0.663486	−	0.663486i	0.0302209	−	0.0302209i
$483$	2.03717	−	13.0756i	0.0926943	−	0.594958i
$484$			9.02694i			0.410315i
$485$	6.21194	−	0.950782i	0.282070	−	0.0431728i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	14.7176	−	19.6605i	0.666920	−	0.890901i	−0.331702	−	0.943384i	$-0.607623\pi$
$487$	14.7176	−	19.6605i	0.666920	−	0.890901i	0.998622	+	0.0524833i	$0.0167136\pi$
$488$	−4.01593	+	10.7671i	−0.181792	+	0.487404i
$489$	−12.6167	−	1.81400i	−0.570545	−	0.0820320i
$490$	−1.25383	−	0.558905i	−0.0566424	−	0.0252488i
$491$	8.64445	+	5.55545i	0.390118	+	0.250714i	0.720966	−	0.692970i	$-0.243698\pi$
$491$	8.64445	+	5.55545i	0.390118	+	0.250714i	−0.330848	+	0.943684i	$0.607335\pi$
$492$	2.61976	−	0.977119i	0.118108	−	0.0440519i
$493$	16.6269	+	30.4499i	0.748837	+	1.37139i
$494$	−2.26281	−	2.61143i	−0.101809	−	0.117494i
$495$	2.20070	−	2.24103i	0.0989142	−	0.100727i
$496$	6.51131	+	1.91189i	0.292367	+	0.0858466i
$497$	−4.68307	−	12.5558i	−0.210064	−	0.563204i
$498$	0.829779	+	3.81443i	0.0371833	+	0.170929i
$499$	10.4187	+	35.4829i	0.466406	+	1.58843i	0.771577	+	0.636136i	$0.219468\pi$
$499$	10.4187	+	35.4829i	0.466406	+	1.58843i	−0.305171	+	0.952298i	$0.598713\pi$
$500$	1.10100	+	11.1260i	0.0492383	+	0.497570i
$501$	2.03940	+	4.46565i	0.0911135	+	0.199511i
$502$	−17.7067	−	13.2551i	−0.790290	−	0.591604i
$503$	−18.4263	−	4.00839i	−0.821587	−	0.178725i	−0.217925	−	0.975965i	$-0.569929\pi$
$503$	−18.4263	−	4.00839i	−0.821587	−	0.178725i	−0.603662	+	0.797240i	$0.706292\pi$
$504$	1.80698	−	2.08536i	0.0804892	−	0.0928895i
$505$	2.83107	+	35.1019i	0.125981	+	1.56202i
$506$	6.56526	+	1.50924i	0.291861	+	0.0670939i
$507$	−9.06445	−	9.06445i	−0.402566	−	0.402566i
$508$	−1.40397	−	19.6301i	−0.0622913	−	0.870946i
$509$	18.3847	+	28.6071i	0.814887	+	1.26799i	0.960398	+	0.278632i	$0.0898810\pi$
$509$	18.3847	+	28.6071i	0.814887	+	1.26799i	−0.145511	+	0.989357i	$0.546483\pi$
$510$	−7.26706	+	11.5367i	−0.321791	+	0.510855i
$511$	17.8202	−	8.13820i	0.788318	−	0.360013i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	−7.12968	−	3.89310i	−0.314783	−	0.171885i
$514$	−0.379127	+	0.589933i	−0.0167226	+	0.0260208i
$515$	16.2494	+	34.7429i	0.716033	+	1.53096i
$516$	−0.676241	+	2.30306i	−0.0297698	+	0.101387i
$517$	18.2180	+	1.30298i	0.801229	+	0.0573050i
$518$	−9.57912	−	0.685112i	−0.420882	−	0.0301021i
$519$	5.73380	−	19.5275i	0.251686	−	0.857164i
$520$	−0.324289	+	0.894163i	−0.0142210	+	0.0392117i
$521$	2.70606	−	4.21071i	0.118555	−	0.184474i	−0.776904	−	0.629619i	$-0.783211\pi$
$521$	2.70606	−	4.21071i	0.118555	−	0.184474i	0.895459	+	0.445144i	$0.146848\pi$
$522$	4.99371	+	2.72677i	0.218569	+	0.119347i
$523$	−31.9286	+	23.9014i	−1.39614	+	1.04514i	−0.404717	+	0.914442i	$0.632630\pi$
$523$	−31.9286	+	23.9014i	−1.39614	+	1.04514i	−0.991423	+	0.130695i	$0.958279\pi$
$524$	−6.99571	+	3.19484i	−0.305609	+	0.139567i
$525$	13.1650	−	4.12668i	0.574570	−	0.180103i
$526$	−1.14336	−	1.77911i	−0.0498529	−	0.0775727i
$527$	2.95201	+	41.2744i	0.128591	+	1.79794i
$528$	0.993243	+	0.993243i	0.0432253	+	0.0432253i
$529$	−10.0438	+	20.6911i	−0.436688	+	0.899613i
$530$	−6.45442	+	0.520568i	−0.280362	+	0.0226120i
$531$	−6.05368	+	6.98632i	−0.262707	+	0.303180i
$532$	−21.9027	−	4.76465i	−0.949604	−	0.206574i
$533$	0.952124	+	0.712751i	0.0412411	+	0.0308727i
$534$	0.0200643	+	0.0439346i	0.000868265	+	0.00190124i
$535$	2.01337	−	1.77685i	0.0870455	−	0.0768200i
$536$	−2.43454	−	8.29128i	−0.105156	−	0.358129i
$537$	−4.69357	−	21.5760i	−0.202542	−	0.931072i
$538$	2.17626	+	5.83477i	0.0938251	+	0.251555i
$539$	−0.827412	−	0.242950i	−0.0356392	−	0.0104646i
$540$	0.0203007	+	2.23598i	0.000873605	+	0.0962211i
$541$	7.96628	+	9.19358i	0.342497	+	0.395263i	0.900700	−	0.434442i	$-0.143054\pi$
$541$	7.96628	+	9.19358i	0.342497	+	0.395263i	−0.558203	+	0.829705i	$0.688509\pi$
$542$	−15.5780	−	28.5289i	−0.669131	−	1.22542i
$543$	8.66697	−	3.23261i	0.371935	−	0.138725i
$544$	−5.12967	−	3.29664i	−0.219933	−	0.141342i
$545$	−6.40848	−	16.7167i	−0.274509	−	0.716064i
$546$	1.16179	+	0.167040i	0.0497199	+	0.00714864i
$547$	0.627785	−	1.68316i	0.0268421	−	0.0719665i	−0.922837	−	0.385190i	$-0.874136\pi$
$547$	0.627785	−	1.68316i	0.0268421	−	0.0719665i	0.949680	+	0.313223i	$0.101409\pi$
$548$	−2.95075	+	3.94174i	−0.126050	+	0.168383i
$549$	−9.66741	+	6.21286i	−0.412595	+	0.265159i
$550$	1.61727	+	6.83454i	0.0689605	+	0.291426i
$551$		−	46.2191i		−	1.96900i
$552$	−4.06472	+	2.54521i	−0.173006	+	0.108331i
$553$	8.94652	−	8.94652i	0.380445	−	0.380445i
$554$	6.32376	+	5.47957i	0.268671	+	0.232805i
$555$	6.18755	−	4.72020i	0.262647	−	0.200361i
$556$	−3.03694	−	21.1224i	−0.128795	−	0.895789i
$557$	−35.9555	−	13.4107i	−1.52348	−	0.568229i	−0.558261	−	0.829665i	$-0.688531\pi$
$557$	−35.9555	−	13.4107i	−1.52348	−	0.568229i	−0.965221	+	0.261436i	$0.915804\pi$
$558$	4.06682	+	5.43264i	0.172162	+	0.229982i
$559$	−0.979651	+	0.287651i	−0.0414348	+	0.0121664i
$560$	1.79198	+	5.90410i	0.0757250	+	0.249494i
$561$	−3.55807	+	7.79109i	−0.150222	+	0.328940i
$562$	−16.4496	+	8.98218i	−0.693886	+	0.378890i
$563$	−0.388006	+	5.42504i	−0.0163525	+	0.228638i	0.982703	+	0.185188i	$0.0592894\pi$
$563$	−0.388006	+	5.42504i	−0.0163525	+	0.228638i	−0.999056	+	0.0434499i	$0.986165\pi$
$564$	−9.82692	+	8.51507i	−0.413788	+	0.358549i
$565$	18.7410	−	12.2859i	0.788438	−	0.516873i
$566$	−2.68604	−	1.22667i	−0.112903	−	0.0515609i
$567$	2.69627	−	0.586538i	0.113233	−	0.0246323i
$568$	−2.32747	+	4.26245i	−0.0976587	+	0.178849i
$569$	−0.175779	+	1.22257i	−0.00736904	+	0.0512528i	−0.993174	−	0.116641i	$-0.962787\pi$
$569$	−0.175779	+	1.22257i	−0.00736904	+	0.0512528i	0.985805	+	0.167894i	$0.0536965\pi$
$570$	15.8628	−	8.84962i	0.664418	−	0.370670i
$571$	18.9867	−	2.72988i	0.794570	−	0.114242i	0.266937	−	0.963714i	$-0.413989\pi$
$571$	18.9867	−	2.72988i	0.794570	−	0.114242i	0.527633	+	0.849472i	$0.323079\pi$
$572$	−0.127007	+	0.583842i	−0.00531043	+	0.0244117i
$573$	8.96333	−	0.641070i	0.374448	−	0.0267811i
$574$	7.71523			0.322027
$575$	−23.9787	+	0.153473i	−0.999980	+	0.00640025i
$576$	−1.00000			−0.0416667
$577$	21.3344	−	1.52587i	0.888162	−	0.0635226i	0.380202	−	0.924903i	$-0.375854\pi$
$577$	21.3344	−	1.52587i	0.888162	−	0.0635226i	0.507960	+	0.861381i	$0.330400\pi$
$578$	4.28984	−	19.7201i	0.178434	−	0.820247i
$579$	−14.7419	+	2.11957i	−0.612654	+	0.0880864i
$580$	−11.1105	+	6.19837i	−0.461336	+	0.257373i
$581$	−1.53294	+	10.6618i	−0.0635969	+	0.442326i
$582$	−1.34689	+	2.46664i	−0.0558303	+	0.102246i
$583$	−3.97476	+	0.864656i	−0.164618	+	0.0358104i
$584$	−6.45815	−	2.94934i	−0.267240	−	0.122044i
$585$	−0.795459	+	0.521475i	−0.0328882	+	0.0215603i
$586$	−14.6137	+	12.6628i	−0.603686	+	0.523097i
$587$	0.414204	−	5.79133i	0.0170960	−	0.239034i	−0.981718	−	0.190342i	$-0.939040\pi$
$587$	0.414204	−	5.79133i	0.0170960	−	0.239034i	0.998814	−	0.0486918i	$-0.0155052\pi$
$588$	0.538822	−	0.294219i	0.0222207	−	0.0121334i
$589$	22.9004	−	50.1449i	0.943596	−	2.06619i
$590$	−6.00344	−	19.7797i	−0.247158	−	0.814318i
$591$	10.9880	−	3.22636i	0.451985	−	0.132715i
$592$	2.08573	+	2.78621i	0.0857229	+	0.114512i
$593$	−15.5862	−	5.81334i	−0.640047	−	0.238725i	0.00842413	−	0.999965i	$-0.497318\pi$
$593$	−15.5862	−	5.81334i	−0.640047	−	0.238725i	−0.648471	+	0.761239i	$0.724591\pi$
$594$	0.199904	+	1.39036i	0.00820214	+	0.0570471i
$595$	−29.9127	+	22.8190i	−1.22630	+	0.935489i
$596$	−12.0232	−	10.4181i	−0.492488	−	0.426744i
$597$	10.3276	−	10.3276i	0.422682	−	0.422682i
$598$	−1.84555	−	0.869203i	−0.0754703	−	0.0355444i
$599$			14.2196i			0.580996i	0.956876	+	0.290498i	$0.0938210\pi$
$599$			14.2196i			0.580996i	−0.956876	+	0.290498i	$0.906179\pi$
$600$	−4.25466	−	2.62639i	−0.173696	−	0.107222i
$601$	−14.9018	+	9.57678i	−0.607856	+	0.390645i	−0.808052	−	0.589111i	$-0.799478\pi$
$601$	−14.9018	+	9.57678i	−0.607856	+	0.390645i	0.200197	+	0.979756i	$0.435842\pi$
$602$	−3.96914	+	5.30215i	−0.161770	+	0.216100i
$603$	3.01983	−	8.09647i	0.122977	−	0.329714i
$604$	10.9791	+	1.57856i	0.446733	+	0.0642306i
$605$	−7.22529	−	18.8474i	−0.293750	−	0.766254i
$606$	−13.2489	−	8.51457i	−0.538201	−	0.345881i
$607$	2.24214	−	0.836274i	0.0910055	−	0.0339433i	−0.303549	−	0.952816i	$-0.598172\pi$
$607$	2.24214	−	0.836274i	0.0910055	−	0.0339433i	0.394555	+	0.918873i	$0.370899\pi$
$608$	3.89310	+	7.12968i	0.157886	+	0.289147i
$609$	10.2811	+	11.8650i	0.416612	+	0.480796i
$610$	−0.233289	−	25.6951i	−0.00944561	−	1.04036i
$611$	−5.30697	−	1.55827i	−0.214697	−	0.0630407i
$612$	−2.13091	−	5.71319i	−0.0861369	−	0.230942i
$613$	−0.373970	−	1.71911i	−0.0151045	−	0.0694343i	0.968978	−	0.247148i	$-0.0794935\pi$
$613$	−0.373970	−	1.71911i	−0.0151045	−	0.0694343i	−0.984082	+	0.177714i	$0.943130\pi$
$614$	−1.17611	−	4.00547i	−0.0474640	−	0.161648i
$615$	−4.68770	+	4.13702i	−0.189026	+	0.166821i
$616$	1.61011	+	3.52566i	0.0648733	+	0.142053i
$617$	3.96048	+	2.96478i	0.159443	+	0.119357i	0.676020	−	0.736883i	$-0.263703\pi$
$617$	3.96048	+	2.96478i	0.159443	+	0.119357i	−0.516577	+	0.856241i	$0.672794\pi$
$618$	−16.7609	−	3.64611i	−0.674223	−	0.146668i
$619$	−3.47128	+	4.00607i	−0.139523	+	0.161018i	−0.821210	−	0.570626i	$-0.806701\pi$
$619$	−3.47128	+	4.00607i	−0.139523	+	0.161018i	0.681688	+	0.731643i	$0.261246\pi$
$620$	−15.1253	+	1.21990i	−0.607447	+	0.0489923i
$621$	−4.77926	−	0.398349i	−0.191785	−	0.0159852i
$622$	−19.7915	−	19.7915i	−0.793567	−	0.793567i
$623$	0.00950765	+	0.132934i	0.000380916	+	0.00532590i
$624$	−0.229972	−	0.357843i	−0.00920623	−	0.0143252i
$625$	−11.2042	−	22.3487i	−0.448168	−	0.893950i
$626$	−10.1587	+	4.63931i	−0.406022	+	0.185424i
$627$	9.13458	−	6.83806i	0.364800	−	0.273086i
$628$	11.3710	+	6.20905i	0.453753	+	0.247768i
$629$	−11.4736	+	17.8533i	−0.457483	+	0.711858i
$630$	−2.10364	+	5.80037i	−0.0838110	+	0.231092i
$631$	−3.88451	+	13.2294i	−0.154640	+	0.526655i	−0.999971	−	0.00758712i	$-0.997585\pi$
$631$	−3.88451	+	13.2294i	−0.154640	+	0.526655i	0.845331	+	0.534243i	$0.179403\pi$
$632$	−4.57359	−	0.327109i	−0.181928	−	0.0130117i
$633$	1.66495	+	0.119080i	0.0661759	+	0.00473299i
$634$	−3.77078	+	12.8421i	−0.149757	+	0.510025i
$635$	18.6436	+	39.8620i	0.739848	+	1.58188i
$636$	1.56563	−	2.43617i	0.0620813	−	0.0966004i
$637$	0.229198	+	0.125152i	0.00908115	+	0.00495868i
$638$	−6.39796	+	4.78945i	−0.253298	+	0.189616i
$639$	−4.41763	+	2.01746i	−0.174759	+	0.0798097i
$640$	1.19178	−	1.89200i	0.0471093	−	0.0747878i
$641$	−15.2158	−	23.6763i	−0.600988	−	0.935156i	−0.999835	−	0.0181386i	$-0.994226\pi$
$641$	−15.2158	−	23.6763i	−0.600988	−	0.935156i	0.398847	−	0.917017i	$-0.369410\pi$
$642$	0.0856715	+	1.19784i	0.00338118	+	0.0472751i
$643$	−23.3062	−	23.3062i	−0.919106	−	0.919106i	0.0778584	−	0.996964i	$-0.475192\pi$
$643$	−23.3062	−	23.3062i	−0.919106	−	0.919106i	−0.996964	+	0.0778584i	$0.975192\pi$
$644$	−12.9631	+	2.66071i	−0.510816	+	0.104847i
$645$	−0.431481	−	5.34985i	−0.0169895	−	0.210650i
$646$	−32.4374	+	37.4347i	−1.27623	+	1.47285i
$647$	−34.8749	−	7.58657i	−1.37107	−	0.298259i	−0.534063	−	0.845445i	$-0.679336\pi$
$647$	−34.8749	−	7.58657i	−1.37107	−	0.298259i	−0.837011	+	0.547186i	$0.815699\pi$
$648$	−0.800541	−	0.599278i	−0.0314482	−	0.0235419i
$649$	−5.39415	−	11.8115i	−0.211739	−	0.463644i
$650$	−0.0386166	−	2.12649i	−0.00151467	−	0.0834079i
$651$	5.27555	+	17.9669i	0.206765	+	0.704178i
$652$	2.70944	+	12.4551i	0.106110	+	0.487779i
$653$	13.9683	+	37.4503i	0.546620	+	1.46555i	0.857193	+	0.514996i	$0.172206\pi$
$653$	13.9683	+	37.4503i	0.546620	+	1.46555i	−0.310573	+	0.950550i	$0.600521\pi$
$654$	7.68213	+	2.25568i	0.300395	+	0.0882040i
$655$	12.0492	−	12.2700i	0.470800	−	0.479428i
$656$	−1.83102	−	2.11311i	−0.0714894	−	0.0825032i
$657$	−3.40254	−	6.23129i	−0.132746	−	0.243106i
$658$	−33.6171	+	12.5385i	−1.31053	+	0.488802i
$659$	18.8922	+	12.1413i	0.735936	+	0.472957i	0.854147	−	0.520031i	$-0.174080\pi$
$659$	18.8922	+	12.1413i	0.735936	+	0.472957i	−0.118212	+	0.992988i	$0.537716\pi$
$660$	−2.86880	−	1.27879i	−0.111668	−	0.0497768i
$661$	−27.4770	−	3.95059i	−1.06873	−	0.153660i	−0.414571	−	0.910017i	$-0.636068\pi$
$661$	−27.4770	−	3.95059i	−1.06873	−	0.153660i	−0.654160	+	0.756357i	$0.726978\pi$
$662$	5.37213	−	14.4032i	0.208794	−	0.559798i
$663$	1.55437	−	2.07640i	0.0603669	−	0.0806407i
$664$	3.28395	−	2.11047i	0.127442	−	0.0819020i
$665$	49.5445	−	7.58314i	1.92125	−	0.294062i
$666$			3.48040i			0.134863i
$667$	−11.0427	−	24.9524i	−0.427575	−	0.966162i
$668$	3.47140	−	3.47140i	0.134312	−	0.134312i
$669$	−0.831423	−	0.720432i	−0.0321447	−	0.0278535i
$670$	11.7195	+	15.3627i	0.452765	+	0.593514i
$671$	−2.29723	−	15.9776i	−0.0886834	−	0.616807i
$672$	−2.58536	−	0.964288i	−0.0997323	−	0.0371982i
$673$	−24.9334	−	33.3072i	−0.961114	−	1.28390i	−0.958854	−	0.283900i	$-0.908372\pi$
$673$	−24.9334	−	33.3072i	−0.961114	−	1.28390i	−0.00225987	−	0.999997i	$-0.500719\pi$
$674$	−12.8626	+	3.77680i	−0.495449	+	0.145477i
$675$	−1.83209	−	4.65225i	−0.0705173	−	0.179065i
$676$	−5.32523	+	11.6606i	−0.204817	+	0.448486i
$677$	10.6320	−	5.80549i	0.408620	−	0.223123i	−0.261773	−	0.965129i	$-0.584307\pi$
$677$	10.6320	−	5.80549i	0.408620	−	0.223123i	0.670393	+	0.742006i	$0.266125\pi$
$678$	−0.714937	+	9.99612i	−0.0274570	+	0.383899i
$679$	−5.86074	+	5.07836i	−0.224914	+	0.194890i
$680$	13.3489	+	2.77720i	0.511908	+	0.106501i
$681$	5.80811	+	2.65248i	0.222567	+	0.101643i
$682$	−9.31445	+	2.02623i	−0.356669	+	0.0775885i
$683$	−22.1053	+	40.4828i	−0.845834	+	1.54903i	−0.0100652	+	0.999949i	$0.503204\pi$
$683$	−22.1053	+	40.4828i	−0.845834	+	1.54903i	−0.835769	+	0.549081i	$0.814978\pi$
$684$	−1.15607	+	8.04065i	−0.0442035	+	0.307442i
$685$	3.00586	−	10.5918i	0.114848	−	0.404692i
$686$	−17.4420	+	2.50778i	−0.665937	+	0.0957473i
$687$	4.03890	−	18.5665i	0.154094	−	0.708357i
$688$	2.39418	−	0.171235i	0.0912771	−	0.00652827i
$689$	1.23182			0.0469284
$690$	6.44951	−	8.56760i	0.245529	−	0.326163i
$691$	−23.4157			−0.890777			−0.445388	−	0.895337i	$-0.646934\pi$
$691$	−23.4157			−0.890777			−0.445388	+	0.895337i	$0.646934\pi$
$692$	−20.3001	+	1.45189i	−0.771693	+	0.0551926i
$693$	−0.823885	+	3.78734i	−0.0312968	+	0.143869i
$694$	16.7136	−	2.40305i	0.634438	−	0.0912184i
$695$	23.2475	+	41.6707i	0.881828	+	1.58066i
$696$	0.809725	−	5.63176i	0.0306925	−	0.213471i
$697$	8.17087	−	14.9638i	0.309494	−	0.566795i
$698$	12.0826	−	2.62840i	0.457332	−	0.0994865i
$699$	6.17016	+	2.81782i	0.233377	+	0.106580i
$700$	−8.46721	−	10.8929i	−0.320030	−	0.411711i
$701$	−35.3441	+	30.6258i	−1.33493	+	1.15672i	−0.360314	+	0.932831i	$0.617331\pi$
$701$	−35.3441	+	30.6258i	−1.33493	+	1.15672i	−0.974614	+	0.223891i	$0.928124\pi$
$702$	0.0303454	−	0.424285i	0.00114531	−	0.0160136i
$703$	24.8142	−	13.5496i	0.935884	−	0.511031i
$704$	0.583516	−	1.27772i	0.0219921	−	0.0481559i
$705$	13.7021	−	25.6442i	0.516049	−	0.965818i
$706$	1.76355	−	0.517824i	0.0663719	−	0.0194885i
$707$	−26.0427	−	34.7890i	−0.979437	−	1.30837i
$708$	8.66138	+	3.23053i	0.325514	+	0.121411i
$709$	−0.880387	−	6.12323i	−0.0330636	−	0.229963i	0.966589	−	0.256333i	$-0.0825143\pi$
$709$	−0.880387	−	6.12323i	−0.0330636	−	0.229963i	−0.999652	+	0.0263701i	$0.991605\pi$
$710$	1.44781	−	10.7625i	0.0543355	−	0.403910i
$711$	−3.46532	−	3.00271i	−0.129960	−	0.112611i
$712$	0.0341528	−	0.0341528i	0.00127993	−	0.00127993i
$713$	0.382645	−	32.5432i	0.0143302	−	1.21875i
$714$		−	16.8254i		−	0.629676i
$715$	−0.202137	−	1.32066i	−0.00755950	−	0.0493900i
$716$	−18.5754	+	11.9377i	−0.694194	+	0.446132i
$717$	−17.5477	+	23.4410i	−0.655331	+	0.875419i
$718$	10.4623	−	28.0505i	0.390449	−	1.04683i
$719$	33.9576	+	4.88236i	1.26640	+	0.182081i	0.742587	−	0.669750i	$-0.233599\pi$
$719$	33.9576	+	4.88236i	1.26640	+	0.182081i	0.523816	+	0.851831i	$0.324508\pi$
$720$	2.08790	−	0.800414i	0.0778115	−	0.0298297i
$721$	−39.8170	−	25.5888i	−1.48286	−	0.952979i
$722$	44.0260	−	16.4208i	1.63848	−	0.611120i
$723$	−0.449684	−	0.823535i	−0.0167239	−	0.0306276i
$724$	−6.05759	−	6.99083i	−0.225129	−	0.259812i
$725$	18.2363	−	21.8346i	0.677278	−	0.810915i
$726$	8.66128	+	2.54318i	0.321450	+	0.0943864i
$727$	−15.9016	−	42.6338i	−0.589758	−	1.58120i	−0.797696	−	0.603060i	$-0.793948\pi$
$727$	−15.9016	−	42.6338i	−0.589758	−	1.58120i	0.207938	−	0.978142i	$-0.433325\pi$
$728$	−0.249495	−	1.14691i	−0.00924690	−	0.0425073i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	15.8447	+	0.988735i	0.586438	+	0.0365947i
$731$	6.08007	+	13.3135i	0.224880	+	0.492418i
$732$	9.19955	+	6.88670i	0.340025	+	0.254540i
$733$	37.9294	+	8.25104i	1.40096	+	0.304759i	0.848682	−	0.528903i	$-0.177397\pi$
$733$	37.9294	+	8.25104i	1.40096	+	0.304759i	0.552274	+	0.833663i	$0.313760\pi$
$734$	−6.47156	+	7.46858i	−0.238870	+	0.275670i
$735$	−0.889511	+	1.04558i	−0.0328101	+	0.0385669i
$736$	3.80520	+	2.91898i	0.140262	+	0.107595i
$737$	8.58292	+	8.58292i	0.316156	+	0.316156i
$738$	−0.199468	−	2.78892i	−0.00734251	−	0.102662i
$739$	−9.94703	−	15.4779i	−0.365907	−	0.569363i	0.608667	−	0.793426i	$-0.291704\pi$
$739$	−9.94703	−	15.4779i	−0.365907	−	0.569363i	−0.974575	+	0.224062i	$0.928068\pi$
$740$	−6.58492	−	4.14788i	−0.242066	−	0.152479i
$741$	−3.14315	+	1.43543i	−0.115467	+	0.0527318i
$742$	6.39688	−	4.78865i	0.234837	−	0.175797i
$743$	−0.595079	−	0.324938i	−0.0218313	−	0.0119208i	0.468296	−	0.883572i	$-0.344868\pi$
$743$	−0.595079	−	0.324938i	−0.0218313	−	0.0119208i	−0.490128	+	0.871651i	$0.663050\pi$
$744$	3.66890	−	5.70892i	0.134508	−	0.209299i
$745$	33.4420	+	12.1285i	1.22522	+	0.444355i
$746$	3.41071	−	11.6158i	0.124875	−	0.425285i
$747$	3.89370	+	0.278483i	0.142463	+	0.0101891i
$748$	8.54328	+	0.611027i	0.312373	+	0.0223414i
$749$	−0.933575	+	3.17947i	−0.0341121	+	0.116175i
$750$	10.9855	+	2.07815i	0.401134	+	0.0758834i
$751$	11.1671	−	17.3764i	0.407494	−	0.634072i	−0.575481	−	0.817815i	$-0.695185\pi$
$751$	11.1671	−	17.3764i	0.407494	−	0.634072i	0.982974	+	0.183743i	$0.0588214\pi$
$752$	11.4123	+	6.23161i	0.416166	+	0.227244i
$753$	−17.7067	+	13.2551i	−0.645269	+	0.483042i
$754$	2.20150	−	1.00539i	0.0801738	−	0.0366142i
$755$	−24.1868	+	5.49196i	−0.880248	+	0.199873i
$756$	−1.49181	−	2.32130i	−0.0542565	−	0.0844248i
$757$	2.85418	+	39.9066i	0.103737	+	1.45043i	0.736685	+	0.676237i	$0.236390\pi$
$757$	2.85418	+	39.9066i	0.103737	+	1.45043i	−0.632948	+	0.774195i	$0.718155\pi$
$758$	−0.0506253	−	0.0506253i	−0.00183879	−	0.00183879i
$759$	3.29775	−	5.87412i	0.119701	−	0.213217i
$760$	−13.8351	−	11.7700i	−0.501852	−	0.426942i
$761$	−3.30561	+	3.81487i	−0.119828	+	0.138289i	−0.812494	−	0.582970i	$-0.801891\pi$
$761$	−3.30561	+	3.81487i	−0.119828	+	0.138289i	0.692666	+	0.721259i	$0.256436\pi$
$762$	−19.2305	−	4.18334i	−0.696648	−	0.151546i
$763$	17.6859	+	13.2395i	0.640273	+	0.479303i
$764$	−3.73301	−	8.17416i	−0.135056	−	0.295731i
$765$	9.02205	+	10.2230i	0.326193	+	0.369612i
$766$	9.26594	+	31.5569i	0.334792	+	1.14020i
$767$	0.835850	+	3.84234i	0.0301808	+	0.138739i
$768$	0.349464	+	0.936950i	0.0126102	+	0.0338093i
$769$	−5.69413	−	1.67195i	−0.205336	−	0.0602920i	0.177447	−	0.984130i	$-0.443216\pi$
$769$	−5.69413	−	1.67195i	−0.205336	−	0.0602920i	−0.382783	+	0.923838i	$0.625034\pi$
$770$	−6.18375	−	6.07247i	−0.222847	−	0.218837i
$771$	0.459225	+	0.529973i	0.0165386	+	0.0190865i
$772$	7.13771	+	13.0717i	0.256892	+	0.470462i
$773$	5.57645	−	2.07991i	0.200571	−	0.0748091i	−0.247171	−	0.968972i	$-0.579501\pi$
$773$	5.57645	−	2.07991i	0.200571	−	0.0748091i	0.447742	+	0.894163i	$0.352228\pi$
$774$	2.01925	+	1.29770i	0.0725806	+	0.0466447i
$775$	30.6037	−	14.6535i	1.09932	−	0.526370i
$776$	2.78181	+	0.399964i	0.0998611	+	0.0143579i
$777$	−3.35611	+	8.99808i	−0.120400	+	0.322804i
$778$	−19.4755	+	26.0162i	−0.698229	+	0.932724i
$779$	−19.1076	+	12.2797i	−0.684601	+	0.439966i
$780$	0.766580	+	0.563068i	0.0274480	+	0.0201611i
$781$		−	6.82172i		−	0.244100i
$782$	−8.56811	+	27.9599i	−0.306395	+	0.999845i
$783$	4.02321	−	4.02321i	0.143778	−	0.143778i
$784$	−0.463968	−	0.402030i	−0.0165703	−	0.0143582i
$785$	−28.7114	−	3.86236i	−1.02475	−	0.137854i
$786$	1.09450	+	7.61243i	0.0390396	+	0.271526i
$787$	34.3193	+	12.8004i	1.22335	+	0.456286i	0.876394	−	0.481595i	$-0.159942\pi$
$787$	34.3193	+	12.8004i	1.22335	+	0.456286i	0.346957	+	0.937881i	$0.387215\pi$
$788$	−6.86285	−	9.16769i	−0.244479	−	0.326585i
$789$	−2.02916	+	0.595816i	−0.0722401	+	0.0212116i
$790$	9.81103	−	2.97779i	0.349061	−	0.105945i
$791$	−11.4875	+	25.1541i	−0.408449	+	0.894378i
$792$	1.23284	−	0.673180i	0.0438070	−	0.0239204i
$793$	−0.348720	+	4.87574i	−0.0123834	+	0.173143i
$794$	19.1280	−	16.5745i	0.678826	−	0.588206i
$795$	−1.31894	+	6.33964i	−0.0467780	+	0.224844i
$796$	−13.2856	−	6.06734i	−0.470896	−	0.215051i
$797$	14.8097	−	3.22166i	0.524588	−	0.114117i	0.0575300	−	0.998344i	$-0.481678\pi$
$797$	14.8097	−	3.22166i	0.524588	−	0.114117i	0.467058	+	0.884227i	$0.345314\pi$
$798$	−10.7424	+	19.6732i	−0.380276	+	0.696423i
$799$	−11.2837	+	78.4799i	−0.399189	+	2.77642i
$800$	−0.973942	+	4.90423i	−0.0344340	+	0.173391i
$801$	0.0478077	−	0.00687371i	0.00168920	−	0.000242871i
$802$	−1.57784	+	7.25323i	−0.0557156	+	0.256120i
$803$	9.94729	−	0.711444i	0.351032	−	0.0251063i
$804$	−8.64131			−0.304755
$805$	24.9359	−	15.9311i	0.878876	−	0.561498i
$806$	2.88664			0.101677
$807$	6.21154	−	0.444258i	0.218657	−	0.0156386i
$808$	−3.34770	+	15.3891i	−0.117772	+	0.541388i
$809$	33.2259	−	4.77717i	1.16816	−	0.167956i	0.469185	−	0.883100i	$-0.344548\pi$
$809$	33.2259	−	4.77717i	1.16816	−	0.167956i	0.698977	+	0.715144i	$0.253639\pi$
$810$	2.15112	+	0.610469i	0.0755827	+	0.0214497i
$811$	−0.994990	+	6.92031i	−0.0349388	+	0.243005i	−0.999805	−	0.0197361i	$-0.993717\pi$
$811$	−0.994990	+	6.92031i	−0.0349388	+	0.243005i	0.964866	+	0.262741i	$0.0846265\pi$
$812$	7.52407	−	13.7793i	0.264043	−	0.483559i
$813$	−31.7621	+	6.90942i	−1.11395	+	0.242324i
$814$	−4.44698	−	2.03087i	−0.155867	−	0.0711819i
$815$	−15.6263	−	23.8364i	−0.547365	−	0.834951i
$816$	−4.60829	+	3.99311i	−0.161323	+	0.139787i
$817$	1.39100	−	19.4487i	0.0486649	−	0.680424i
$818$	3.72722	−	2.03522i	0.130319	−	0.0711598i
$819$	0.487586	−	1.06767i	0.0170376	−	0.0373072i
$820$	5.51436	+	2.94640i	0.192570	+	0.102893i
$821$	14.8638	−	4.36441i	0.518751	−	0.152319i	−0.0118679	−	0.999930i	$-0.503778\pi$
$821$	14.8638	−	4.36441i	0.518751	−	0.152319i	0.530619	+	0.847611i	$0.321960\pi$
$822$	2.95075	+	3.94174i	0.102919	+	0.137484i
$823$	−22.4475	−	8.37247i	−0.782469	−	0.291846i	−0.0736945	−	0.997281i	$-0.523479\pi$
$823$	−22.4475	−	8.37247i	−0.782469	−	0.291846i	−0.708775	+	0.705435i	$0.750752\pi$
$824$	2.44111	+	16.9783i	0.0850402	+	0.591468i
$825$	7.01333	+	0.373757i	0.244173	+	0.0130126i
$826$	19.2776	+	16.7041i	0.670753	+	0.581211i
$827$	−31.2203	+	31.2203i	−1.08564	+	1.08564i	−0.0896649	+	0.995972i	$0.528580\pi$
$827$	−31.2203	+	31.2203i	−1.08564	+	1.08564i	−0.995972	+	0.0896649i	$0.971420\pi$
$828$	1.29695	+	4.61713i	0.0450720	+	0.160457i
$829$		−	1.81499i		−	0.0630373i	−0.999503	−	0.0315187i	$-0.989966\pi$
$829$		−	1.81499i		−	0.0630373i	0.999503	−	0.0315187i	$-0.0100344\pi$
$830$	−5.16732	+	7.03497i	−0.179360	+	0.244187i
$831$	7.03922	−	4.52383i	0.244188	−	0.156930i
$832$	−0.254914	+	0.340525i	−0.00883755	+	0.0118056i
$833$	1.30820	−	3.50742i	0.0453265	−	0.121525i
$834$	−21.1224	−	3.03694i	−0.731409	−	0.105161i
$835$	−4.46938	+	10.0265i	−0.154669	+	0.346981i
$836$	−9.59913	−	6.16898i	−0.331993	−	0.213359i
$837$	6.35833	−	2.37153i	0.219776	−	0.0819722i
$838$	5.37158	+	9.83731i	0.185558	+	0.339824i
$839$	−30.1662	−	34.8136i	−1.04145	−	1.20190i	−0.979002	−	0.203853i	$-0.934654\pi$
$839$	−30.1662	−	34.8136i	−1.04145	−	1.20190i	−0.0624512	−	0.998048i	$-0.519892\pi$
$840$	6.16980	−	0.0560165i	0.212878	−	0.00193275i
$841$	3.23577	+	0.950108i	0.111578	+	0.0327624i
$842$	4.31536	+	11.5699i	0.148717	+	0.398726i
$843$	3.98394	+	18.3139i	0.137214	+	0.630764i
$844$	−0.470269	−	1.60159i	−0.0161873	−	0.0551290i
$845$	1.78523	−	28.6086i	0.0614138	−	0.984167i
$846$	5.40159	+	11.8278i	0.185710	+	0.406649i
$847$	19.9401	+	14.9270i	0.685151	+	0.512898i
$848$	−2.82970	−	0.615563i	−0.0971723	−	0.0211385i
$849$	−1.93373	+	2.23164i	−0.0663654	+	0.0765897i
$850$	−30.0941	+	4.88615i	−1.03222	+	0.167593i
$851$	10.1592	−	13.2436i	0.348253	−	0.453986i
$852$	3.43407	+	3.43407i	0.117649	+	0.117649i
$853$	−0.495409	−	6.92673i	−0.0169625	−	0.237167i	−0.998859	−	0.0477501i	$-0.984795\pi$
$853$	−0.495409	−	6.92673i	−0.0169625	−	0.237167i	0.981897	−	0.189417i	$-0.0606597\pi$
$854$	17.1434	+	26.6756i	0.586634	+	0.912820i
$855$	−4.02209	−	17.7134i	−0.137553	−	0.605787i
$856$	1.09238	−	0.498874i	0.0373368	−	0.0170511i
$857$	−25.0262	+	18.7344i	−0.854879	+	0.639955i	−0.934143	−	0.356899i	$-0.883834\pi$
$857$	−25.0262	+	18.7344i	−0.854879	+	0.639955i	0.0792635	+	0.996854i	$0.474743\pi$
$858$	0.524410	+	0.286350i	0.0179031	+	0.00977582i
$859$	3.65630	−	5.68931i	0.124751	−	0.194117i	−0.773260	−	0.634089i	$-0.781375\pi$
$859$	3.65630	−	5.68931i	0.124751	−	0.194117i	0.898011	+	0.439972i	$0.145012\pi$
$860$	−4.86175	+	2.27386i	−0.165784	+	0.0775378i
$861$	2.17363	−	7.40271i	0.0740771	−	0.252284i
$862$	1.09342	+	0.0782027i	0.0372419	+	0.00266359i
$863$	34.3879	+	2.45947i	1.17058	+	0.0837214i	0.643055	−	0.765820i	$-0.277667\pi$
$863$	34.3879	+	2.45947i	1.17058	+	0.0837214i	0.527522	+	0.849541i	$0.323121\pi$
$864$	−0.281733	+	0.959493i	−0.00958474	+	0.0326426i
$865$	41.2225	−	19.2799i	1.40161	−	0.655536i
$866$	10.3606	−	16.1214i	0.352066	−	0.547826i
$867$	−17.7127	−	9.67186i	−0.601555	−	0.328474i
$868$	14.9904	−	11.2217i	0.508809	−	0.380890i
$869$	5.85870	−	2.67558i	0.198743	−	0.0907627i
$870$	2.81711	+	12.4067i	0.0955091	+	0.420626i
$871$	−1.98726	−	3.09223i	−0.0673356	−	0.104776i
$872$	−0.571174	−	7.98605i	−0.0193424	−	0.270442i
$873$	1.98726	+	1.98726i	0.0672587	+	0.0672587i
$874$	27.8696	−	27.2218i	0.942702	−	0.920791i
$875$	26.3975	+	15.9659i	0.892398	+	0.539748i
$876$	−4.64934	+	5.36562i	−0.157087	+	0.181288i
$877$	51.4183	+	11.1854i	1.73627	+	0.377703i	0.965702	−	0.259653i	$-0.0836081\pi$
$877$	51.4183	+	11.1854i	1.73627	+	0.377703i	0.770570	+	0.637356i	$0.219972\pi$
$878$	−10.0924	−	7.55509i	−0.340603	−	0.254972i
$879$	8.03275	+	17.5893i	0.270938	+	0.593272i
$880$	−0.195618	+	3.13481i	−0.00659427	+	0.105674i
$881$	13.3240	+	45.3773i	0.448896	+	1.52880i	0.804378	+	0.594117i	$0.202499\pi$
$881$	13.3240	+	45.3773i	0.448896	+	1.52880i	−0.355482	+	0.934683i	$0.615683\pi$
$882$	−0.130497	−	0.599887i	−0.00439408	−	0.0201993i
$883$	−12.3428	−	33.0924i	−0.415369	−	1.11365i	−0.961224	−	0.275769i	$-0.911068\pi$
$883$	−12.3428	−	33.0924i	−0.415369	−	1.11365i	0.545855	−	0.837880i	$-0.316205\pi$
$884$	−2.48868	−	0.730743i	−0.0837034	−	0.0245775i
$885$	−20.6699	+	0.187665i	−0.694810	+	0.00630828i
$886$	−5.50358	−	6.35147i	−0.184896	−	0.213382i
$887$	−5.10733	−	9.35337i	−0.171487	−	0.314055i	0.777774	−	0.628544i	$-0.216349\pi$
$887$	−5.10733	−	9.35337i	−0.171487	−	0.314055i	−0.949261	+	0.314489i	$0.898167\pi$
$888$	3.26096	−	1.21628i	0.109431	−	0.0408156i
$889$	−45.6838	−	29.3592i	−1.53218	−	0.984675i
$890$	−0.0439713	+	0.0986440i	−0.00147392	+	0.00330656i
$891$	1.39036	+	0.199904i	0.0465788	+	0.00669702i
$892$	−0.384456	+	1.03077i	−0.0128725	+	0.0345126i
$893$	63.2997	−	84.5586i	2.11825	−	2.82964i
$894$	−13.3835	+	8.60102i	−0.447610	+	0.287661i
$895$	29.2285	−	39.7927i	0.977001	−	1.33012i
$896$			2.75933i			0.0921828i
$897$	−1.35395	+	1.52591i	−0.0452070	+	0.0509487i
$898$	24.6331	−	24.6331i	0.822016	−	0.822016i
$899$	29.1805	+	25.2850i	0.973223	+	0.843302i
$900$	−3.71867	+	3.34237i	−0.123956	+	0.111412i
$901$	−2.51300	−	17.4783i	−0.0837202	−	0.582287i
$902$	3.67986	+	1.37252i	0.122526	+	0.0456998i
$903$	3.96914	+	5.30215i	0.132085	+	0.176445i
$904$	9.61571	−	2.82343i	0.319814	−	0.0939058i
$905$	18.2432	+	9.74759i	0.606425	+	0.324021i
$906$	4.60779	−	10.0896i	0.153083	−	0.335206i
$907$	−39.4031	+	21.5157i	−1.30836	+	0.714417i	−0.973681	−	0.227916i	$-0.926809\pi$
$907$	−39.4031	+	21.5157i	−1.30836	+	0.714417i	−0.334677	+	0.942333i	$0.608627\pi$
$908$	0.455509	−	6.36885i	0.0151166	−	0.211358i
$909$	−11.9023	+	10.3134i	−0.394775	+	0.342075i
$910$	1.43892	+	2.19494i	0.0476999	+	0.0727614i
$911$	−4.76006	−	2.17384i	−0.157708	−	0.0720227i	0.334997	−	0.942219i	$-0.391265\pi$
$911$	−4.76006	−	2.17384i	−0.157708	−	0.0720227i	−0.492705	+	0.870196i	$0.663992\pi$
$912$	7.93769	−	1.72674i	0.262843	−	0.0571781i
$913$	−2.62786	+	4.81256i	−0.0869693	+	0.159272i
$914$	2.50980	−	17.4560i	0.0830167	−	0.577394i
$915$	−24.7200	−	7.01530i	−0.817217	−	0.231919i
$916$	−18.8074	+	2.70409i	−0.621412	+	0.0893456i
$917$	−4.51090	+	20.7363i	−0.148963	+	0.684771i
$918$	−6.08211	+	0.435001i	−0.200740	+	0.0143572i
$919$	51.6838			1.70489			0.852445	−	0.522817i	$-0.175119\pi$
$919$	51.6838			1.70489			0.852445	+	0.522817i	$0.175119\pi$
$920$	−10.2813	−	3.04880i	−0.338964	−	0.100516i
$921$	−4.17457			−0.137557
$922$	−6.56657	+	0.469650i	−0.216258	+	0.0154671i
$923$	−0.439118	+	2.01859i	−0.0144537	+	0.0664428i
$924$	3.83646	−	0.551600i	0.126210	−	0.0181463i
$925$	17.0687	+	3.38971i	0.561215	+	0.111453i
$926$	3.26299	−	22.6946i	0.107228	−	0.745790i
$927$	−8.22052	+	15.0548i	−0.269997	+	0.494463i
$928$	−5.55965	+	1.20943i	−0.182504	+	0.0397014i
$929$	53.3504	+	24.3643i	1.75037	+	0.799366i	0.988423	+	0.151725i	$0.0484829\pi$
$929$	53.3504	+	24.3643i	1.75037	+	0.799366i	0.761946	+	0.647641i	$0.224244\pi$
$930$	−3.09080	+	14.8563i	−0.101351	+	0.487157i
$931$	−3.76897	+	3.26583i	−0.123523	+	0.107033i
$932$	0.483904	−	6.76586i	0.0158508	−	0.221623i
$933$	−24.5657	+	13.4139i	−0.804246	+	0.439151i
$934$	0.840829	−	1.84116i	0.0275128	−	0.0602445i
$935$	−18.3266	+	5.56240i	−0.599344	+	0.181910i
$936$	−0.408138	+	0.119840i	−0.0133404	+	0.00391710i
$937$	9.29768	+	12.4203i	0.303742	+	0.405752i	0.926279	−	0.376839i	$-0.122989\pi$
$937$	9.29768	+	12.4203i	0.303742	+	0.405752i	−0.622537	+	0.782590i	$0.713898\pi$
$938$	−22.3409	−	8.33271i	−0.729455	−	0.272073i
$939$	1.58936	+	11.0542i	0.0518667	+	0.360741i
$940$	−28.8157	−	3.87640i	−0.939866	−	0.126434i
$941$	−12.9992	−	11.2639i	−0.423762	−	0.367192i	0.416717	−	0.909036i	$-0.363181\pi$
$941$	−12.9992	−	11.2639i	−0.423762	−	0.367192i	−0.840479	+	0.541844i	$0.817726\pi$
$942$	9.16113	−	9.16113i	0.298486	−	0.298486i
$943$	−7.38178	+	11.1947i	−0.240384	+	0.364549i
$944$		−	9.24423i		−	0.300874i
$945$	4.97275	+	3.65258i	0.161764	+	0.118818i
$946$	−2.83636	+	1.82282i	−0.0922180	+	0.0592649i
$947$	14.7108	−	19.6514i	0.478038	−	0.638584i	−0.495092	−	0.868840i	$-0.664866\pi$
$947$	14.7108	−	19.6514i	0.478038	−	0.638584i	0.973130	+	0.230257i	$0.0739566\pi$
$948$	−1.60239	+	4.29617i	−0.0520431	+	0.139533i
$949$	−2.98926	−	0.429791i	−0.0970356	−	0.0139516i
$950$	38.3072	+	13.5008i	1.24285	+	0.438023i
$951$	11.2596	+	7.23608i	0.365116	+	0.234646i
$952$	−15.7646	+	5.87989i	−0.510933	+	0.190568i
$953$	14.8184	+	27.1379i	0.480015	+	0.879082i	0.999694	+	0.0247207i	$0.00786966\pi$
$953$	14.8184	+	27.1379i	0.480015	+	0.879082i	−0.519679	+	0.854361i	$0.673949\pi$
$954$	−1.89640	−	2.18856i	−0.0613981	−	0.0708572i
$955$	14.3369	+	14.0789i	0.463930	+	0.455582i
$956$	28.0953	+	8.24953i	0.908667	+	0.266809i
$957$	2.79293	+	7.48814i	0.0902826	+	0.242057i
$958$	−0.968786	−	4.45344i	−0.0313000	−	0.143884i
$959$	3.82777	+	13.0362i	0.123605	+	0.420960i
$960$	−1.47960	−	1.67654i	−0.0477537	−	0.0541102i
$961$	6.25306	+	13.6923i	0.201711	+	0.441687i
$962$	1.18516	+	0.887203i	0.0382112	+	0.0286046i
$963$	1.17346	+	0.255271i	0.0378142	+	0.00822598i
$964$	−0.614463	+	0.709128i	−0.0197905	+	0.0228395i
$965$	−25.3657	−	21.5794i	−0.816549	−	0.694665i
$966$	−1.09918	+	13.1876i	−0.0353655	+	0.424303i
$967$	−28.2059	−	28.2059i	−0.907040	−	0.907040i	0.0889923	−	0.996032i	$-0.471635\pi$
$967$	−28.2059	−	28.2059i	−0.907040	−	0.907040i	−0.996032	+	0.0889923i	$0.971635\pi$
$968$	−0.643974	−	9.00394i	−0.0206981	−	0.289398i
$969$	26.7797	+	41.6700i	0.860288	+	1.33863i
$970$	−6.12828	+	1.39151i	−0.196767	+	0.0446788i
$971$	38.8011	−	17.7199i	1.24519	−	0.568657i	0.319728	−	0.947509i	$-0.396408\pi$
$971$	38.8011	−	17.7199i	1.24519	−	0.568657i	0.925457	+	0.378852i	$0.123681\pi$
$972$	−0.800541	+	0.599278i	−0.0256774	+	0.0192218i
$973$	−51.6804	−	28.2197i	−1.65680	−	0.904680i
$974$	−13.2776	+	20.6603i	−0.425441	+	0.661999i
$975$	−2.05123	−	0.562049i	−0.0656920	−	0.0180000i
$976$	3.23758	−	11.0262i	0.103632	−	0.352939i
$977$	−56.7624	−	4.05973i	−1.81599	−	0.129882i	−0.878466	−	0.477805i	$-0.841433\pi$
$977$	−56.7624	−	4.05973i	−1.81599	−	0.129882i	−0.937523	+	0.347922i	$0.886887\pi$
$978$	12.7139	+	0.909317i	0.406546	+	0.0290768i
$979$	−0.0191139	+	0.0650958i	−0.000610881	+	0.00208047i
$980$	1.29051	+	0.468034i	0.0412238	+	0.0149508i
$981$	4.32861	−	6.73545i	0.138202	−	0.215046i
$982$	−9.01874	−	4.92461i	−0.287800	−	0.157150i
$983$	−26.1387	+	19.5672i	−0.833694	+	0.624096i	−0.928472	−	0.371403i	$-0.878877\pi$
$983$	−26.1387	+	19.5672i	−0.833694	+	0.624096i	0.0947775	+	0.995498i	$0.469786\pi$
$984$	−2.54337	+	1.16152i	−0.0810798	+	0.0370279i
$985$	21.6669	+	13.6481i	0.690365	+	0.434865i
$986$	−18.7568	−	29.1861i	−0.597338	−	0.929476i
$987$	2.55960	+	35.7878i	0.0814729	+	1.13914i
$988$	2.44334	+	2.44334i	0.0777332	+	0.0777332i
$989$	−3.89574	−	10.8322i	−0.123877	−	0.344442i
$990$	−2.03522	+	2.39232i	−0.0646836	+	0.0760328i
$991$	−5.15430	+	5.94838i	−0.163732	+	0.188957i	−0.831687	−	0.555245i	$-0.812624\pi$
$991$	−5.15430	+	5.94838i	−0.163732	+	0.188957i	0.667955	+	0.744202i	$0.267170\pi$
$992$	−6.63112	−	1.44251i	−0.210538	−	0.0457998i
$993$	−12.3063	−	9.21238i	−0.390529	−	0.292346i
$994$	5.56686	+	12.1897i	0.176570	+	0.386634i
$995$	32.5955	+	2.03401i	1.03335	+	0.0644826i
$996$	−1.09978	−	3.74552i	−0.0348480	−	0.118681i
$997$	7.64404	+	35.1391i	0.242089	+	1.11287i	0.924287	+	0.381698i	$0.124661\pi$
$997$	7.64404	+	35.1391i	0.242089	+	1.11287i	−0.682198	+	0.731168i	$0.738976\pi$
$998$	−12.9235	−	34.6493i	−0.409086	−	1.09680i
$999$	3.33942	+	0.980543i	0.105655	+	0.0310230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.7.1	✓	240
5.3	odd	4	inner	690.2.w.b.283.7	yes	240
23.10	odd	22	inner	690.2.w.b.217.7	yes	240
115.33	even	44	inner	690.2.w.b.493.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.1	✓	240	1.1	even	1	trivial
690.2.w.b.217.7	yes	240	23.10	odd	22	inner
690.2.w.b.283.7	yes	240	5.3	odd	4	inner
690.2.w.b.493.1	yes	240	115.33	even	44	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)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.95274 + 1.08941i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.32241 - 2.42181i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.95274 + 1.08941i) q^{5} +(0.142315 - 0.989821i) q^{6} +(1.32241 - 2.42181i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.87005 - 1.22594i) q^{10} +(1.06157 - 0.919855i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(-0.373337 + 0.203857i) q^{13} +(-1.14627 + 2.50998i) q^{14} +(-0.649426 - 2.13968i) q^{15} +(0.959493 - 0.281733i) q^{16} +(3.65418 + 4.88142i) q^{17} +(0.936950 + 0.349464i) q^{18} +(-1.15607 - 8.04065i) q^{19} +(-1.77783 + 1.35622i) q^{20} +(2.08536 + 1.80698i) q^{21} +(-0.993243 + 0.993243i) q^{22} +(-2.54521 - 4.06472i) q^{23} -1.00000i q^{24} +(2.62639 - 4.25466i) q^{25} +(0.357843 - 0.229972i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.964288 - 2.58536i) q^{28} +(5.63176 + 0.809725i) q^{29} +(0.800414 + 2.08790i) q^{30} +(5.70892 + 3.66890i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(0.673180 + 1.23284i) q^{33} +(-3.99311 - 4.60829i) q^{34} +(0.0560165 + 6.16980i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(1.21628 + 3.26096i) q^{37} +(1.72674 + 7.93769i) q^{38} +(-0.119840 - 0.408138i) q^{39} +(1.67654 - 1.47960i) q^{40} +(-1.16152 - 2.54337i) q^{41} +(-2.20896 - 1.65361i) q^{42} +(2.34544 + 0.510219i) q^{43} +(0.919855 - 1.06157i) q^{44} +(2.22883 - 0.179762i) q^{45} +(2.82870 + 3.87279i) q^{46} +(9.19442 + 9.19442i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(-0.331909 - 0.516460i) q^{49} +(-2.31617 + 4.43118i) q^{50} +(-5.54661 + 2.53305i) q^{51} +(-0.340525 + 0.254914i) q^{52} +(-2.54165 - 1.38785i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(-1.07087 + 2.95272i) q^{55} +(-0.777394 + 2.64756i) q^{56} +(8.10264 + 0.579512i) q^{57} +(-5.67518 - 0.405897i) q^{58} +(2.60440 - 8.86977i) q^{59} +(-0.947324 - 2.02548i) q^{60} +(6.21286 - 9.66741i) q^{61} +(-5.95611 - 3.25228i) q^{62} +(-2.20896 + 1.65361i) q^{63} +(0.909632 - 0.415415i) q^{64} +(0.506946 - 0.804796i) q^{65} +(-0.759415 - 1.18167i) q^{66} +(0.616464 + 8.61929i) q^{67} +(4.31169 + 4.31169i) q^{68} +(4.51285 - 1.62302i) q^{69} +(-0.496022 - 6.15009i) q^{70} +(3.18033 - 3.67030i) q^{71} +(0.977147 + 0.212565i) q^{72} +(5.68363 + 4.25471i) q^{73} +(-1.44581 - 3.16589i) q^{74} +(3.59915 + 3.47076i) q^{75} +(-2.28861 - 7.79429i) q^{76} +(-0.823885 - 3.78734i) q^{77} +(0.148651 + 0.398549i) q^{78} +(4.39954 + 1.29182i) q^{79} +(-1.56672 + 1.59543i) q^{80} +(0.654861 + 0.755750i) q^{81} +(1.34000 + 2.45403i) q^{82} +(-3.65752 + 1.36418i) q^{83} +(2.32130 + 1.49181i) q^{84} +(-12.4535 - 5.55125i) q^{85} +(-2.37586 - 0.341597i) q^{86} +(-1.98834 + 5.33094i) q^{87} +(-0.841780 + 1.12449i) q^{88} +(-0.0406320 + 0.0261126i) q^{89} +(-2.21033 + 0.338307i) q^{90} +1.17373i q^{91} +(-3.09777 - 3.66112i) q^{92} +(-4.79857 + 4.79857i) q^{93} +(-9.82692 - 8.51507i) q^{94} +(11.0170 + 14.4419i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-2.63322 - 0.982139i) q^{97} +(0.367907 + 0.491466i) q^{98} +(-1.34776 + 0.395738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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