LMFDB - Embedded newform 690.2.w.b.493.1

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			493.1
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.1

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.997452	−	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	0.998811	+	0.0487487i	$0.0155233\pi$
$7$	1.32241	+	2.42181i	0.499823	+	0.915358i	−0.498988	+	0.866609i	$0.666295\pi$
$8$	−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	0.800047	−	0.599937i	$-0.204808\pi$
$11$	1.06157	+	0.919855i	0.320075	+	0.277347i	−0.479972	+	0.877284i	$0.659353\pi$
$12$	−0.0713392	−	0.997452i	−0.0205938	−	0.287940i
$13$	−0.373337	−	0.203857i	−0.103545	−	0.0565399i	0.426642	−	0.904421i	$-0.359696\pi$
$13$	−0.373337	−	0.203857i	−0.103545	−	0.0565399i	−0.530187	+	0.847881i	$0.677878\pi$
$14$	−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	−0.0958003	−	0.995401i	$-0.530541\pi$
$17$	3.65418	−	4.88142i	0.886270	−	1.18392i	0.982070	−	0.188517i	$-0.0603681\pi$
$18$	0.936950	−	0.349464i	0.220841	−	0.0823695i
$19$	−1.15607	+	8.04065i	−0.265221	+	1.84465i	0.226640	+	0.973979i	$0.427226\pi$
$19$	−1.15607	+	8.04065i	−0.265221	+	1.84465i	−0.491861	+	0.870674i	$0.663683\pi$
$20$	−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	0.402060	−	0.915613i	$-0.368294\pi$
$29$	5.63176	−	0.809725i	1.04579	−	0.150362i	0.643732	+	0.765251i	$0.277385\pi$
$30$	0.800414	−	2.08790i	0.146135	−	0.381197i
$31$	5.70892	−	3.66890i	1.02535	−	0.658954i	0.0840297	−	0.996463i	$-0.473221\pi$
$31$	5.70892	−	3.66890i	1.02535	−	0.658954i	0.941322	+	0.337510i	$0.109585\pi$
$32$	−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	−0.797811	−	0.602907i	$-0.794009\pi$
$37$	1.21628	−	3.26096i	0.199955	−	0.536099i	0.997766	+	0.0668083i	$0.0212816\pi$
$38$	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	−0.978386	−	0.206788i	$-0.933699\pi$
$41$	−1.16152	+	2.54337i	−0.181399	+	0.397208i	0.796987	+	0.603997i	$0.206426\pi$
$42$	−2.20896	+	1.65361i	−0.340850	+	0.255157i
$43$	2.34544	−	0.510219i	0.357676	−	0.0778077i	−0.0301368	−	0.999546i	$-0.509594\pi$
$43$	2.34544	−	0.510219i	0.357676	−	0.0778077i	0.387813	+	0.921738i	$0.373231\pi$
$44$	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	0.446221	−	0.894923i	$-0.352769\pi$
$47$	9.19442	−	9.19442i	1.34114	−	1.34114i	0.894923	−	0.446221i	$-0.147231\pi$
$48$	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	−0.644236	−	0.764827i	$-0.722825\pi$
$53$	−2.54165	+	1.38785i	−0.349123	+	0.190635i	0.295113	+	0.955462i	$0.404643\pi$
$54$	−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	0.935866	+	0.352357i	$0.114620\pi$
$59$	2.60440	+	8.86977i	0.339064	+	1.15475i	−0.596802	+	0.802389i	$0.703562\pi$
$60$	−0.947324	+	2.02548i	−0.122299	+	0.261489i
$61$	6.21286	+	9.66741i	0.795476	+	1.23778i	0.967545	+	0.252700i	$0.0813184\pi$
$61$	6.21286	+	9.66741i	0.795476	+	1.23778i	−0.172069	+	0.985085i	$0.555045\pi$
$62$	−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	−0.809516	−	0.587098i	$-0.800270\pi$
$67$	0.616464	−	8.61929i	0.0753131	−	1.05301i	0.884829	−	0.465916i	$-0.154275\pi$
$68$	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	0.912406	−	0.409287i	$-0.134222\pi$
$71$	3.18033	+	3.67030i	0.377436	+	0.435585i	−0.534970	+	0.844871i	$0.679677\pi$
$72$	0.977147	−	0.212565i	0.115158	−	0.0250511i
$73$	5.68363	−	4.25471i	0.665219	−	0.497977i	−0.212495	−	0.977162i	$-0.568159\pi$
$73$	5.68363	−	4.25471i	0.665219	−	0.497977i	0.877714	+	0.479186i	$0.159068\pi$
$74$	−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	−0.0247057	−	0.999695i	$-0.507865\pi$
$79$	4.39954	−	1.29182i	0.494986	−	0.145341i	0.519692	+	0.854354i	$0.326047\pi$
$80$	−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	0.140618	−	0.990064i	$-0.455091\pi$
$83$	−3.65752	−	1.36418i	−0.401464	−	0.149739i	−0.542082	+	0.840325i	$0.682364\pi$
$84$	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	0.538486	−	0.842635i	$-0.318997\pi$
$89$	−0.0406320	−	0.0261126i	−0.00430698	−	0.00276793i	−0.542793	+	0.839867i	$0.682633\pi$
$90$	−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	−0.479570	−	0.877503i	$-0.659207\pi$
$97$	−2.63322	+	0.982139i	−0.267363	+	0.0997211i	0.212208	+	0.977225i	$0.431935\pi$
$98$	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	0.890683	+	0.454624i	$0.150226\pi$
$101$	6.54239	+	14.3258i	0.650992	+	1.42547i	−0.239691	+	0.970849i	$0.577046\pi$
$102$	5.35178	+	2.92229i	0.529905	+	0.289350i
$103$	1.22367	+	17.1092i	0.120572	+	1.68582i	0.593590	+	0.804768i	$0.297710\pi$
$103$	1.22367	+	17.1092i	0.120572	+	1.68582i	−0.473018	+	0.881053i	$0.656835\pi$
$104$	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	0.155486	−	0.987838i	$-0.450306\pi$
$107$	−1.17346	−	0.255271i	−0.113443	−	0.0246779i	−0.268928	+	0.963160i	$0.586669\pi$
$108$	0.479249	+	0.877679i	0.0461158	+	0.0844547i
$109$	−1.13944	−	7.92495i	−0.109138	−	0.759073i	−0.968735	−	0.248099i	$-0.920194\pi$
$109$	−1.13944	−	7.92495i	−0.109138	−	0.759073i	0.859596	−	0.510974i	$-0.170715\pi$
$110$	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	−0.407262	−	0.913311i	$-0.633516\pi$
$113$	−9.99612	−	0.714937i	−0.940356	−	0.0672556i	−0.533094	+	0.846056i	$0.678971\pi$
$114$	−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	0.548464	+	0.836174i	$0.315213\pi$
$127$	1.40397	+	19.6301i	0.124583	+	1.74189i	−0.423881	+	0.905718i	$0.639333\pi$
$128$	−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	−0.0570048	−	0.998374i	$-0.518155\pi$
$131$	−7.37918	−	2.16672i	−0.644722	−	0.189307i	−0.587717	+	0.809066i	$0.699973\pi$
$132$	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	0.542558	−	0.840018i	$-0.317456\pi$
$137$	−3.48169	−	3.48169i	−0.297461	−	0.297461i	−0.840018	+	0.542558i	$0.817456\pi$
$138$	−4.38556	−	1.94083i	−0.373324	−	0.165215i
$139$			21.3396i			1.81000i	0.425410	+	0.905001i	$0.360130\pi$
$139$			21.3396i			1.81000i	−0.425410	+	0.905001i	$0.639870\pi$
$140$	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	−0.999991	−	0.00423317i	$-0.998653\pi$
$149$	−10.4181	+	12.0232i	−0.853487	+	0.984977i	0.146504	+	0.989210i	$0.453198\pi$
$150$	−3.83758	+	3.20515i	−0.313337	+	0.261700i
$151$	10.6427	−	3.12498i	0.866091	−	0.254307i	0.181639	−	0.983365i	$-0.441860\pi$
$151$	10.6427	−	3.12498i	0.866091	−	0.254307i	0.684452	+	0.729058i	$0.260042\pi$
$152$	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	−0.0991019	−	0.995077i	$-0.531597\pi$
$157$	10.3716	−	7.76412i	0.827747	−	0.619644i	0.926849	+	0.375433i	$0.122506\pi$
$158$	−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	−0.828675	−	0.559730i	$-0.810905\pi$
$163$	0.909317	−	12.7139i	0.0712232	−	0.995831i	0.899898	−	0.436100i	$-0.143641\pi$
$164$	−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	0.740427	−	0.672136i	$-0.234623\pi$
$167$	3.93009	+	2.94203i	0.304120	+	0.227661i	−0.436308	+	0.899798i	$0.643714\pi$
$168$	−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	−0.816894	−	0.576789i	$-0.804306\pi$
$173$	−20.3001	+	1.45189i	−1.54339	+	0.110385i	−0.726493	+	0.687174i	$0.758851\pi$
$174$	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	−0.515971	−	0.856606i	$-0.672569\pi$
$179$	−20.0852	−	9.17261i	−1.50124	−	0.685593i	−0.985269	+	0.171013i	$0.945296\pi$
$180$	2.18056	+	0.495128i	0.162529	+	0.0369046i
$181$	−5.00103	+	7.78176i	−0.371724	+	0.578414i	−0.975841	−	0.218482i	$-0.929890\pi$
$181$	−5.00103	+	7.78176i	−0.371724	+	0.578414i	0.604117	+	0.796896i	$0.293526\pi$
$182$	−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	0.815776	+	0.578369i	$0.196310\pi$
$191$	−2.53171	+	8.62222i	−0.183188	+	0.623882i	−0.998964	+	0.0455131i	$0.985508\pi$
$192$	0.212565	−	0.977147i	0.0153406	−	0.0705195i
$193$	5.20476	−	13.9545i	0.374647	−	1.00447i	−0.603649	−	0.797251i	$-0.706287\pi$
$193$	5.20476	−	13.9545i	0.374647	−	1.00447i	0.978295	−	0.207216i	$-0.0664403\pi$
$194$	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	−0.996835	−	0.0795010i	$-0.974667\pi$
$197$	−5.48829	+	10.0511i	−0.391025	+	0.716108i	0.605810	+	0.795609i	$0.292849\pi$
$198$	1.31609	+	0.490877i	0.0935307	+	0.0348851i
$199$	−12.2869	+	7.89633i	−0.870997	+	0.559756i	−0.898057	−	0.439878i	$-0.855022\pi$
$199$	−12.2869	+	7.89633i	−0.870997	+	0.559756i	0.0270606	+	0.999634i	$0.491385\pi$
$200$	−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	−0.996363	−	0.0852082i	$-0.972844\pi$
$211$	−0.237553	+	1.65221i	−0.0163538	+	0.113743i	0.980009	+	0.198951i	$0.0637536\pi$
$212$	−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	0.859430	−	0.511253i	$-0.170819\pi$
$223$	−0.527236	−	0.965561i	−0.0353064	−	0.0646588i	−0.894737	+	0.446594i	$0.852637\pi$
$224$	−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	1.00000		0.000683157i	$-0.000217456\pi$
$227$	1.35726	+	6.23920i	0.0900842	+	0.414110i	−0.909916	+	0.414793i	$0.863854\pi$
$228$	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	0.999951	+	0.00985959i	$0.00313846\pi$
$233$	1.44186	+	6.62813i	0.0944594	+	0.434223i	−0.905492	+	0.424363i	$0.860498\pi$
$234$	−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	0.728037	−	0.685538i	$-0.240433\pi$
$239$	26.6353	−	12.1639i	1.72289	−	0.786820i	0.994858	−	0.101282i	$-0.0322943\pi$
$240$	−1.22594	+	1.87005i	−0.0791339	+	0.120711i
$241$	−0.709128	−	0.614463i	−0.0456789	−	0.0395810i	0.631722	−	0.775195i	$-0.282348\pi$
$241$	−0.709128	−	0.614463i	−0.0456789	−	0.0395810i	−0.677401	+	0.735614i	$0.736894\pi$
$242$	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	0.0586411	−	0.998279i	$-0.481323\pi$
$251$	16.7160	−	14.4845i	1.05510	−	0.914253i	0.996464	+	0.0840257i	$0.0267778\pi$
$252$	−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	0.813457	−	0.581625i	$-0.197583\pi$
$257$	0.420247	+	0.561384i	0.0262143	+	0.0350182i	−0.787243	+	0.616643i	$0.788492\pi$
$258$	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	−0.844563	−	0.535456i	$-0.820140\pi$
$263$	1.01353	−	1.85614i	0.0624969	−	0.114454i	0.907060	+	0.421002i	$0.138321\pi$
$264$	−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	−0.995529	−	0.0944531i	$-0.969890\pi$
$269$	−1.75446	+	5.97516i	−0.106972	+	0.364312i	0.888558	+	0.458765i	$0.151708\pi$
$270$	0.139264	+	2.23173i	0.00847532	+	0.135819i
$271$	13.5030	−	29.5675i	0.820251	−	1.79610i	0.265429	−	0.964130i	$-0.414486\pi$
$271$	13.5030	−	29.5675i	0.820251	−	1.79610i	0.554822	−	0.831969i	$-0.312786\pi$
$272$	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	−0.862152	−	0.506649i	$-0.830884\pi$
$277$	−5.91674	+	5.91674i	−0.355503	+	0.355503i	0.506649	+	0.862152i	$0.330884\pi$
$278$	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	0.852954	−	0.521987i	$-0.174809\pi$
$281$	17.0485	+	7.78579i	1.01703	+	0.464461i	0.164075	+	0.986448i	$0.447536\pi$
$282$	10.4093	+	7.79233i	0.619867	+	0.464027i
$283$	2.59168	−	1.41517i	0.154060	−	0.0841229i	−0.400370	−	0.916354i	$-0.631118\pi$
$283$	2.59168	−	1.41517i	0.154060	−	0.0841229i	0.554429	+	0.832231i	$0.312937\pi$
$284$	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	0.946698	−	0.322121i	$-0.104396\pi$
$293$	15.4798	+	11.5881i	0.904341	+	0.676981i	−0.0423574	+	0.999103i	$0.513487\pi$
$294$	−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	−0.944866	−	0.327457i	$-0.893808\pi$
$307$	0.887368	−	4.07917i	0.0506448	−	0.232810i	0.995511	+	0.0946464i	$0.0301721\pi$
$308$	−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	0.0598156	−	0.998209i	$-0.480949\pi$
$311$	18.3292	−	21.1530i	1.03935	−	1.19948i	0.979536	−	0.201267i	$-0.0645058\pi$
$312$	0.203857	−	0.373337i	0.0115412	−	0.0211360i
$313$	10.4637	+	3.90278i	0.591446	+	0.220598i	0.627324	−	0.778758i	$-0.284150\pi$
$313$	10.4637	+	3.90278i	0.591446	+	0.220598i	−0.0358782	+	0.999356i	$0.511423\pi$
$314$	−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	0.999599	+	0.0283297i	$0.00901884\pi$
$317$	4.67732	+	12.5404i	0.262704	+	0.704338i	−0.736894	+	0.676008i	$0.763708\pi$
$318$	−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	−0.999970	−	0.00777386i	$-0.997525\pi$
$331$	−6.38596	−	13.9833i	−0.351004	−	0.768591i	0.648966	−	0.760818i	$-0.275202\pi$
$332$	−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	0.554671	−	0.832070i	$-0.312844\pi$
$337$	13.0993	+	2.84957i	0.713563	+	0.155226i	0.158892	+	0.987296i	$0.449208\pi$
$338$	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	−0.388482	−	0.921456i	$-0.627001\pi$
$347$	−16.8424	−	1.20459i	−0.904147	−	0.0646659i	−0.515665	+	0.856790i	$0.672455\pi$
$348$	−1.20943	−	5.55965i	−0.0648321	−	0.298028i
$349$	−12.2393	−	1.75974i	−0.655154	−	0.0941970i	−0.193282	−	0.981143i	$-0.561913\pi$
$349$	−12.2393	−	1.75974i	−0.655154	−	0.0941970i	−0.461872	+	0.886946i	$0.652822\pi$
$350$	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	0.164515	−	0.986375i	$-0.447394\pi$
$353$	−1.79599	−	0.390694i	−0.0955911	−	0.0207946i	−0.260106	+	0.965580i	$0.583758\pi$
$354$	−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	−0.885852	−	0.463968i	$-0.846425\pi$
$359$	−12.4367	−	27.2326i	−0.656386	−	1.43728i	0.229467	−	0.973317i	$-0.426302\pi$
$360$	−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	0.865563	−	0.500799i	$-0.166961\pi$
$367$	6.98787	+	6.98787i	0.364764	+	0.364764i	−0.500799	+	0.865563i	$0.666961\pi$
$368$	−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	0.780214	−	0.625513i	$-0.215110\pi$
$373$	−4.23068	−	11.3429i	−0.219056	−	0.587313i	−0.999270	+	0.0382002i	$0.987838\pi$
$374$	−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	−0.754544	−	0.656249i	$-0.772142\pi$
$379$	0.0468847	−	0.0541079i	0.00240831	−	0.00277933i	0.756952	+	0.653470i	$0.226687\pi$
$380$	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	0.351152	+	0.936319i	$0.385790\pi$
$383$	−6.99109	+	32.1375i	−0.357228	+	1.64215i	−0.708380	+	0.705832i	$0.750573\pi$
$384$	−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	0.967866	+	0.251465i	$0.0809124\pi$
$389$	21.2818	+	24.5605i	1.07903	+	1.24527i	0.111164	+	0.993802i	$0.464542\pi$
$390$	−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	−0.0455684	−	0.998961i	$-0.514510\pi$
$397$	−20.2616	−	15.1677i	−1.01690	−	0.761244i	−0.971334	+	0.237717i	$0.923601\pi$
$398$	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	0.995086	−	0.0990188i	$-0.0315704\pi$
$401$	2.09126	+	7.12219i	0.104433	+	0.355665i	−0.890653	+	0.454684i	$0.849752\pi$
$402$	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	0.317614	−	0.948220i	$-0.397118\pi$
$409$	−3.86292	−	1.76414i	−0.191009	−	0.0872309i	−0.508624	+	0.860989i	$0.669845\pi$
$410$	−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	−0.988610	−	0.150503i	$-0.951911\pi$
$419$	−4.65611	+	10.1954i	−0.227466	+	0.498080i	0.761144	+	0.648583i	$0.224638\pi$
$420$	−6.15808	+	0.384275i	−0.300483	+	0.0187507i
$421$	−3.47897	+	11.8483i	−0.169555	+	0.577450i	0.830244	+	0.557400i	$0.188201\pi$
$421$	−3.47897	+	11.8483i	−0.169555	+	0.577450i	−0.999799	+	0.0200507i	$0.993617\pi$
$422$	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	−0.168398	−	0.985719i	$-0.553859\pi$
$431$	−1.08505	+	0.156007i	−0.0522651	+	0.00751459i	0.116133	+	0.993234i	$0.462950\pi$
$432$	0.349464	+	0.936950i	0.0168136	+	0.0450790i
$433$	−11.4843	−	15.3412i	−0.551898	−	0.737250i	0.434672	−	0.900589i	$-0.356864\pi$
$433$	−11.4843	−	15.3412i	−0.551898	−	0.737250i	−0.986570	+	0.163339i	$0.947773\pi$
$434$	−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	−0.397155	−	0.917751i	$-0.630003\pi$
$439$	9.52773	−	8.25583i	0.454734	−	0.394029i	0.851889	+	0.523722i	$0.175457\pi$
$440$	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	−0.664780	−	0.747039i	$-0.731475\pi$
$443$	5.03645	−	6.72791i	0.239289	−	0.319653i	0.904069	+	0.427386i	$0.140566\pi$
$444$	−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	−0.994158	−	0.107934i	$-0.965576\pi$
$449$	−26.3276	−	22.8130i	−1.24248	−	1.07661i	−0.248319	−	0.968678i	$-0.579878\pi$
$450$	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	−0.977828	−	0.209411i	$-0.932845\pi$
$457$	−3.74870	−	17.2325i	−0.175357	−	0.806102i	0.802471	−	0.596691i	$-0.203518\pi$
$458$	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	−0.940166	−	0.340716i	$-0.889331\pi$
$463$	−4.87369	−	22.4040i	−0.226499	−	1.04120i	0.713667	−	0.700485i	$-0.247033\pi$
$464$	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	0.854272	−	0.519826i	$-0.174003\pi$
$467$	−0.970033	−	1.77648i	−0.0448878	−	0.0822058i	−0.899160	+	0.437620i	$0.855821\pi$
$468$	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	−0.969623	−	0.244602i	$-0.921343\pi$
$479$	0.648613	−	4.51120i	0.0296359	−	0.206122i	0.999259	+	0.0384803i	$0.0122517\pi$
$480$	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	0.998622	−	0.0524833i	$-0.0167136\pi$
$487$	14.7176	+	19.6605i	0.666920	+	0.890901i	−0.331702	+	0.943384i	$0.607623\pi$
$488$	−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	−0.330848	−	0.943684i	$-0.607335\pi$
$491$	8.64445	−	5.55545i	0.390118	−	0.250714i	0.720966	+	0.692970i	$0.243698\pi$
$492$	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	−0.305171	−	0.952298i	$-0.598713\pi$
$499$	10.4187	−	35.4829i	0.466406	−	1.58843i	0.771577	−	0.636136i	$-0.219468\pi$
$500$	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	−0.603662	−	0.797240i	$-0.706292\pi$
$503$	−18.4263	+	4.00839i	−0.821587	+	0.178725i	−0.217925	+	0.975965i	$0.569929\pi$
$504$	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	−0.145511	−	0.989357i	$-0.546483\pi$
$509$	18.3847	−	28.6071i	0.814887	−	1.26799i	0.960398	−	0.278632i	$-0.0898810\pi$
$510$	−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	0.895459	−	0.445144i	$-0.146848\pi$
$521$	2.70606	+	4.21071i	0.118555	+	0.184474i	−0.776904	+	0.629619i	$0.783211\pi$
$522$	4.99371	−	2.72677i	0.218569	−	0.119347i
$523$	−31.9286	−	23.9014i	−1.39614	−	1.04514i	−0.991423	−	0.130695i	$-0.958279\pi$
$523$	−31.9286	−	23.9014i	−1.39614	−	1.04514i	−0.404717	−	0.914442i	$-0.632630\pi$
$524$	−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	−0.558203	−	0.829705i	$-0.688509\pi$
$541$	7.96628	−	9.19358i	0.342497	−	0.395263i	0.900700	+	0.434442i	$0.143054\pi$
$542$	−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	0.949680	−	0.313223i	$-0.101409\pi$
$547$	0.627785	+	1.68316i	0.0268421	+	0.0719665i	−0.922837	+	0.385190i	$0.874136\pi$
$548$	−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	−0.965221	−	0.261436i	$-0.915804\pi$
$557$	−35.9555	+	13.4107i	−1.52348	+	0.568229i	−0.558261	+	0.829665i	$0.688531\pi$
$558$	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	−0.999056	−	0.0434499i	$-0.986165\pi$
$563$	−0.388006	−	5.42504i	−0.0163525	−	0.228638i	0.982703	−	0.185188i	$-0.0592894\pi$
$564$	−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	0.985805	−	0.167894i	$-0.0536965\pi$
$569$	−0.175779	−	1.22257i	−0.00736904	−	0.0512528i	−0.993174	+	0.116641i	$0.962787\pi$
$570$	15.8628	+	8.84962i	0.664418	+	0.370670i
$571$	18.9867	+	2.72988i	0.794570	+	0.114242i	0.527633	−	0.849472i	$-0.323079\pi$
$571$	18.9867	+	2.72988i	0.794570	+	0.114242i	0.266937	+	0.963714i	$0.413989\pi$
$572$	−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	0.507960	−	0.861381i	$-0.330400\pi$
$577$	21.3344	+	1.52587i	0.888162	+	0.0635226i	0.380202	+	0.924903i	$0.375854\pi$
$578$	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	0.998814	+	0.0486918i	$0.0155052\pi$
$587$	0.414204	+	5.79133i	0.0170960	+	0.239034i	−0.981718	+	0.190342i	$0.939040\pi$
$588$	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	−0.648471	−	0.761239i	$-0.724591\pi$
$593$	−15.5862	+	5.81334i	−0.640047	+	0.238725i	0.00842413	+	0.999965i	$0.497318\pi$
$594$	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	$-0.906179\pi$
$599$		−	14.2196i		−	0.580996i	0.956876	−	0.290498i	$-0.0938210\pi$
$600$	−4.25466	+	2.62639i	−0.173696	+	0.107222i
$601$	−14.9018	−	9.57678i	−0.607856	−	0.390645i	0.200197	−	0.979756i	$-0.435842\pi$
$601$	−14.9018	−	9.57678i	−0.607856	−	0.390645i	−0.808052	+	0.589111i	$0.799478\pi$
$602$	−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	0.394555	−	0.918873i	$-0.370899\pi$
$607$	2.24214	+	0.836274i	0.0910055	+	0.0339433i	−0.303549	+	0.952816i	$0.598172\pi$
$608$	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	−0.984082	−	0.177714i	$-0.943130\pi$
$613$	−0.373970	+	1.71911i	−0.0151045	+	0.0694343i	0.968978	+	0.247148i	$0.0794935\pi$
$614$	−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	−0.516577	−	0.856241i	$-0.672794\pi$
$617$	3.96048	−	2.96478i	0.159443	−	0.119357i	0.676020	+	0.736883i	$0.263703\pi$
$618$	−16.7609	+	3.64611i	−0.674223	+	0.146668i
$619$	−3.47128	−	4.00607i	−0.139523	−	0.161018i	0.681688	−	0.731643i	$-0.261246\pi$
$619$	−3.47128	−	4.00607i	−0.139523	−	0.161018i	−0.821210	+	0.570626i	$0.806701\pi$
$620$	−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	0.845331	−	0.534243i	$-0.179403\pi$
$631$	−3.88451	−	13.2294i	−0.154640	−	0.526655i	−0.999971	+	0.00758712i	$0.997585\pi$
$632$	−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	0.398847	+	0.917017i	$0.369410\pi$
$641$	−15.2158	+	23.6763i	−0.600988	+	0.935156i	−0.999835	+	0.0181386i	$0.994226\pi$
$642$	0.0856715	−	1.19784i	0.00338118	−	0.0472751i
$643$	−23.3062	+	23.3062i	−0.919106	+	0.919106i	−0.996964	−	0.0778584i	$-0.975192\pi$
$643$	−23.3062	+	23.3062i	−0.919106	+	0.919106i	0.0778584	+	0.996964i	$0.475192\pi$
$644$	−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	−0.837011	−	0.547186i	$-0.815699\pi$
$647$	−34.8749	+	7.58657i	−1.37107	+	0.298259i	−0.534063	+	0.845445i	$0.679336\pi$
$648$	−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	−0.310573	−	0.950550i	$-0.600521\pi$
$653$	13.9683	−	37.4503i	0.546620	−	1.46555i	0.857193	−	0.514996i	$-0.172206\pi$
$654$	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	−0.118212	−	0.992988i	$-0.537716\pi$
$659$	18.8922	−	12.1413i	0.735936	−	0.472957i	0.854147	+	0.520031i	$0.174080\pi$
$660$	−2.86880	+	1.27879i	−0.111668	+	0.0497768i
$661$	−27.4770	+	3.95059i	−1.06873	+	0.153660i	−0.654160	−	0.756357i	$-0.726978\pi$
$661$	−27.4770	+	3.95059i	−1.06873	+	0.153660i	−0.414571	+	0.910017i	$0.636068\pi$
$662$	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	−0.00225987	+	0.999997i	$0.500719\pi$
$673$	−24.9334	+	33.3072i	−0.961114	+	1.28390i	−0.958854	+	0.283900i	$0.908372\pi$
$674$	−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	0.670393	−	0.742006i	$-0.266125\pi$
$677$	10.6320	+	5.80549i	0.408620	+	0.223123i	−0.261773	+	0.965129i	$0.584307\pi$
$678$	−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	−0.835769	−	0.549081i	$-0.814978\pi$
$683$	−22.1053	−	40.4828i	−0.845834	−	1.54903i	−0.0100652	−	0.999949i	$-0.503204\pi$
$684$	−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	−0.974614	−	0.223891i	$-0.928124\pi$
$701$	−35.3441	−	30.6258i	−1.33493	−	1.15672i	−0.360314	−	0.932831i	$-0.617331\pi$
$702$	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	−0.999652	−	0.0263701i	$-0.991605\pi$
$709$	−0.880387	+	6.12323i	−0.0330636	+	0.229963i	0.966589	+	0.256333i	$0.0825143\pi$
$710$	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	0.523816	−	0.851831i	$-0.324508\pi$
$719$	33.9576	−	4.88236i	1.26640	−	0.182081i	0.742587	+	0.669750i	$0.233599\pi$
$720$	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	0.207938	+	0.978142i	$0.433325\pi$
$727$	−15.9016	+	42.6338i	−0.589758	+	1.58120i	−0.797696	+	0.603060i	$0.793948\pi$
$728$	−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	0.552274	−	0.833663i	$-0.313760\pi$
$733$	37.9294	−	8.25104i	1.40096	−	0.304759i	0.848682	+	0.528903i	$0.177397\pi$
$734$	−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	−0.974575	−	0.224062i	$-0.928068\pi$
$739$	−9.94703	+	15.4779i	−0.365907	+	0.569363i	0.608667	+	0.793426i	$0.291704\pi$
$740$	−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	−0.490128	−	0.871651i	$-0.663050\pi$
$743$	−0.595079	+	0.324938i	−0.0218313	+	0.0119208i	0.468296	+	0.883572i	$0.344868\pi$
$744$	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	0.982974	−	0.183743i	$-0.0588214\pi$
$751$	11.1671	+	17.3764i	0.407494	+	0.634072i	−0.575481	+	0.817815i	$0.695185\pi$
$752$	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	−0.632948	−	0.774195i	$-0.718155\pi$
$757$	2.85418	−	39.9066i	0.103737	−	1.45043i	0.736685	−	0.676237i	$-0.236390\pi$
$758$	−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	0.692666	−	0.721259i	$-0.256436\pi$
$761$	−3.30561	−	3.81487i	−0.119828	−	0.138289i	−0.812494	+	0.582970i	$0.801891\pi$
$762$	−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	−0.382783	−	0.923838i	$-0.625034\pi$
$769$	−5.69413	+	1.67195i	−0.205336	+	0.0602920i	0.177447	+	0.984130i	$0.443216\pi$
$770$	−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	0.447742	−	0.894163i	$-0.352228\pi$
$773$	5.57645	+	2.07991i	0.200571	+	0.0748091i	−0.247171	+	0.968972i	$0.579501\pi$
$774$	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	0.346957	−	0.937881i	$-0.387215\pi$
$787$	34.3193	−	12.8004i	1.22335	−	0.456286i	0.876394	+	0.481595i	$0.159942\pi$
$788$	−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	0.467058	−	0.884227i	$-0.345314\pi$
$797$	14.8097	+	3.22166i	0.524588	+	0.114117i	0.0575300	+	0.998344i	$0.481678\pi$
$798$	−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	0.698977	−	0.715144i	$-0.253639\pi$
$809$	33.2259	+	4.77717i	1.16816	+	0.167956i	0.469185	+	0.883100i	$0.344548\pi$
$810$	2.15112	−	0.610469i	0.0755827	−	0.0214497i
$811$	−0.994990	−	6.92031i	−0.0349388	−	0.243005i	0.964866	−	0.262741i	$-0.0846265\pi$
$811$	−0.994990	−	6.92031i	−0.0349388	−	0.243005i	−0.999805	+	0.0197361i	$0.993717\pi$
$812$	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	0.530619	−	0.847611i	$-0.321960\pi$
$821$	14.8638	+	4.36441i	0.518751	+	0.152319i	−0.0118679	+	0.999930i	$0.503778\pi$
$822$	2.95075	−	3.94174i	0.102919	−	0.137484i
$823$	−22.4475	+	8.37247i	−0.782469	+	0.291846i	−0.708775	−	0.705435i	$-0.750752\pi$
$823$	−22.4475	+	8.37247i	−0.782469	+	0.291846i	−0.0736945	+	0.997281i	$0.523479\pi$
$824$	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	−0.995972	−	0.0896649i	$-0.971420\pi$
$827$	−31.2203	−	31.2203i	−1.08564	−	1.08564i	−0.0896649	−	0.995972i	$-0.528580\pi$
$828$	1.29695	−	4.61713i	0.0450720	−	0.160457i
$829$			1.81499i			0.0630373i	0.999503	+	0.0315187i	$0.0100344\pi$
$829$			1.81499i			0.0630373i	−0.999503	+	0.0315187i	$0.989966\pi$
$830$	−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	−0.0624512	+	0.998048i	$0.519892\pi$
$839$	−30.1662	+	34.8136i	−1.04145	+	1.20190i	−0.979002	+	0.203853i	$0.934654\pi$
$840$	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	0.981897	+	0.189417i	$0.0606597\pi$
$853$	−0.495409	+	6.92673i	−0.0169625	+	0.237167i	−0.998859	+	0.0477501i	$0.984795\pi$
$854$	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	0.0792635	−	0.996854i	$-0.474743\pi$
$857$	−25.0262	−	18.7344i	−0.854879	−	0.639955i	−0.934143	+	0.356899i	$0.883834\pi$
$858$	0.524410	−	0.286350i	0.0179031	−	0.00977582i
$859$	3.65630	+	5.68931i	0.124751	+	0.194117i	0.898011	−	0.439972i	$-0.145012\pi$
$859$	3.65630	+	5.68931i	0.124751	+	0.194117i	−0.773260	+	0.634089i	$0.781375\pi$
$860$	−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	0.527522	−	0.849541i	$-0.323121\pi$
$863$	34.3879	−	2.45947i	1.17058	−	0.0837214i	0.643055	+	0.765820i	$0.277667\pi$
$864$	−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	0.770570	−	0.637356i	$-0.219972\pi$
$877$	51.4183	−	11.1854i	1.73627	−	0.377703i	0.965702	+	0.259653i	$0.0836081\pi$
$878$	−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	−0.355482	−	0.934683i	$-0.615683\pi$
$881$	13.3240	−	45.3773i	0.448896	−	1.52880i	0.804378	−	0.594117i	$-0.202499\pi$
$882$	−0.130497	+	0.599887i	−0.00439408	+	0.0201993i
$883$	−12.3428	+	33.0924i	−0.415369	+	1.11365i	0.545855	+	0.837880i	$0.316205\pi$
$883$	−12.3428	+	33.0924i	−0.415369	+	1.11365i	−0.961224	+	0.275769i	$0.911068\pi$
$884$	−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	−0.949261	−	0.314489i	$-0.898167\pi$
$887$	−5.10733	+	9.35337i	−0.171487	+	0.314055i	0.777774	+	0.628544i	$0.216349\pi$
$888$	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	−0.334677	−	0.942333i	$-0.608627\pi$
$907$	−39.4031	−	21.5157i	−1.30836	−	0.714417i	−0.973681	+	0.227916i	$0.926809\pi$
$908$	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	−0.492705	−	0.870196i	$-0.663992\pi$
$911$	−4.76006	+	2.17384i	−0.157708	+	0.0720227i	0.334997	+	0.942219i	$0.391265\pi$
$912$	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	0.761946	−	0.647641i	$-0.224244\pi$
$929$	53.3504	−	24.3643i	1.75037	−	0.799366i	0.988423	−	0.151725i	$-0.0484829\pi$
$930$	−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	−0.622537	−	0.782590i	$-0.713898\pi$
$937$	9.29768	−	12.4203i	0.303742	−	0.405752i	0.926279	+	0.376839i	$0.122989\pi$
$938$	−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	−0.840479	−	0.541844i	$-0.817726\pi$
$941$	−12.9992	+	11.2639i	−0.423762	+	0.367192i	0.416717	+	0.909036i	$0.363181\pi$
$942$	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	0.973130	−	0.230257i	$-0.0739566\pi$
$947$	14.7108	+	19.6514i	0.478038	+	0.638584i	−0.495092	+	0.868840i	$0.664866\pi$
$948$	−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	−0.519679	−	0.854361i	$-0.673949\pi$
$953$	14.8184	−	27.1379i	0.480015	−	0.879082i	0.999694	−	0.0247207i	$-0.00786966\pi$
$954$	−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	−0.996032	−	0.0889923i	$-0.971635\pi$
$967$	−28.2059	+	28.2059i	−0.907040	+	0.907040i	0.0889923	+	0.996032i	$0.471635\pi$
$968$	−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	0.925457	−	0.378852i	$-0.123681\pi$
$971$	38.8011	+	17.7199i	1.24519	+	0.568657i	0.319728	+	0.947509i	$0.396408\pi$
$972$	−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	−0.937523	−	0.347922i	$-0.886887\pi$
$977$	−56.7624	+	4.05973i	−1.81599	+	0.129882i	−0.878466	+	0.477805i	$0.841433\pi$
$978$	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	0.0947775	−	0.995498i	$-0.469786\pi$
$983$	−26.1387	−	19.5672i	−0.833694	−	0.624096i	−0.928472	+	0.371403i	$0.878877\pi$
$984$	−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	0.667955	−	0.744202i	$-0.267170\pi$
$991$	−5.15430	−	5.94838i	−0.163732	−	0.188957i	−0.831687	+	0.555245i	$0.812624\pi$
$992$	−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	−0.682198	−	0.731168i	$-0.738976\pi$
$997$	7.64404	−	35.1391i	0.242089	−	1.11287i	0.924287	−	0.381698i	$-0.124661\pi$
$998$	−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.493.1	yes	240
5.2	odd	4	inner	690.2.w.b.217.7	yes	240
23.7	odd	22	inner	690.2.w.b.283.7	yes	240
115.7	even	44	inner	690.2.w.b.7.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.1	✓	240	115.7	even	44	inner
690.2.w.b.217.7	yes	240	5.2	odd	4	inner
690.2.w.b.283.7	yes	240	23.7	odd	22	inner
690.2.w.b.493.1	yes	240	1.1	even	1	trivial

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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