LMFDB - Embedded newform 690.2.w.a.7.11

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			7.11
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.24397 - 1.85810i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(0.294639 - 0.539591i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.24397 - 1.85810i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(0.294639 - 0.539591i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.10824 - 1.94211i) q^{10} +(-0.0136216 + 0.0118032i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(2.55823 - 1.39690i) q^{13} +(0.255394 - 0.559236i) q^{14} +(1.55121 + 1.61051i) q^{15} +(0.959493 - 0.281733i) q^{16} +(2.52854 + 3.37773i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(-0.208338 - 1.44903i) q^{19} +(0.966872 - 2.01622i) q^{20} +(0.464630 + 0.402604i) q^{21} +(-0.0127449 + 0.0127449i) q^{22} +(0.868851 - 4.71647i) q^{23} +1.00000i q^{24} +(-1.90508 - 4.62284i) q^{25} +(2.45206 - 1.57584i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.214848 - 0.576030i) q^{28} +(1.75151 + 0.251830i) q^{29} +(1.66215 + 1.49574i) q^{30} +(-2.35626 - 1.51428i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-0.00863796 - 0.0158192i) q^{33} +(2.76306 + 3.18874i) q^{34} +(-0.636093 - 1.21870i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(3.04312 + 8.15892i) q^{37} +(-0.311180 - 1.43047i) q^{38} +(0.821185 + 2.79670i) q^{39} +(0.820572 - 2.08006i) q^{40} +(4.04979 + 8.86780i) q^{41} +(0.492167 + 0.368432i) q^{42} +(-9.90459 - 2.15461i) q^{43} +(-0.0118032 + 0.0136216i) q^{44} +(-1.90344 + 1.17343i) q^{45} +(0.530168 - 4.76644i) q^{46} +(1.44422 + 1.44422i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(3.58014 + 5.57081i) q^{49} +(-2.23002 - 4.47516i) q^{50} +(-3.83802 + 1.75277i) q^{51} +(2.33339 - 1.74676i) q^{52} +(-1.02310 - 0.558655i) q^{53} +(0.540641 - 0.841254i) q^{54} +(0.00498667 + 0.0399931i) q^{55} +(0.173207 - 0.589890i) q^{56} +(1.46020 + 0.104435i) q^{57} +(1.76502 + 0.126236i) q^{58} +(-0.309071 + 1.05260i) q^{59} +(1.76462 + 1.37335i) q^{60} +(4.01893 - 6.25357i) q^{61} +(-2.45829 - 1.34233i) q^{62} +(-0.492167 + 0.368432i) q^{63} +(0.909632 - 0.415415i) q^{64} +(0.586778 - 6.49115i) q^{65} +(-0.00974449 - 0.0151627i) q^{66} +(-0.188015 - 2.62879i) q^{67} +(2.98351 + 2.98351i) q^{68} +(4.42400 + 1.85155i) q^{69} +(-0.721414 - 1.17022i) q^{70} +(-8.80307 + 10.1593i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(-10.3492 - 7.74734i) q^{73} +(3.61742 + 7.92104i) q^{74} +(4.92215 - 0.878890i) q^{75} +(-0.412436 - 1.40463i) q^{76} +(0.00235544 + 0.0108278i) q^{77} +(1.01861 + 2.73099i) q^{78} +(-0.217136 - 0.0637570i) q^{79} +(0.670092 - 2.13330i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.67209 + 8.55630i) q^{82} +(-4.39699 + 1.63999i) q^{83} +(0.517197 + 0.332382i) q^{84} +(9.42160 - 0.496488i) q^{85} +(-10.0331 - 1.44254i) q^{86} +(-0.618386 + 1.65796i) q^{87} +(-0.0108014 + 0.0144289i) q^{88} +(-1.41759 + 0.911027i) q^{89} +(-1.81488 + 1.30623i) q^{90} -1.79198i q^{91} +(0.188784 - 4.79211i) q^{92} +(1.98053 - 1.98053i) q^{93} +(1.54357 + 1.33751i) q^{94} +(-2.95160 - 1.41543i) q^{95} +(0.142315 + 0.989821i) q^{96} +(-12.0907 - 4.50962i) q^{97} +(3.96843 + 5.30121i) q^{98} +(0.0172939 - 0.00507793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.24397	−	1.85810i	0.556320	−	0.830968i
$5$	1.24397	−	1.85810i	0.556320	−	0.830968i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	0.294639	−	0.539591i	0.111363	−	0.203946i	−0.816053	−	0.577976i	$-0.803843\pi$
$7$	0.294639	−	0.539591i	0.111363	−	0.203946i	0.927417	+	0.374030i	$0.122024\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	1.10824	−	1.94211i	0.350458	−	0.614149i
$11$	−0.0136216	+	0.0118032i	−0.00410707	+	0.00355879i	−0.656912	−	0.753967i	$-0.728138\pi$
$11$	−0.0136216	+	0.0118032i	−0.00410707	+	0.00355879i	0.652805	+	0.757526i	$0.273592\pi$
$12$	−0.0713392	+	0.997452i	−0.0205938	+	0.287940i
$13$	2.55823	−	1.39690i	0.709525	−	0.387430i	−0.0835911	−	0.996500i	$-0.526639\pi$
$13$	2.55823	−	1.39690i	0.709525	−	0.387430i	0.793117	+	0.609070i	$0.208457\pi$
$14$	0.255394	−	0.559236i	0.0682570	−	0.149462i
$15$	1.55121	+	1.61051i	0.400522	+	0.415831i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	2.52854	+	3.37773i	0.613261	+	0.819221i	0.994443	−	0.105279i	$-0.0335736\pi$
$17$	2.52854	+	3.37773i	0.613261	+	0.819221i	−0.381182	+	0.924500i	$0.624483\pi$
$18$	−0.936950	−	0.349464i	−0.220841	−	0.0823695i
$19$	−0.208338	−	1.44903i	−0.0477961	−	0.332429i	−0.999664	−	0.0259206i	$-0.991748\pi$
$19$	−0.208338	−	1.44903i	−0.0477961	−	0.332429i	0.951868	−	0.306509i	$-0.0991608\pi$
$20$	0.966872	−	2.01622i	0.216199	−	0.450841i
$21$	0.464630	+	0.402604i	0.101391	+	0.0878554i
$22$	−0.0127449	+	0.0127449i	−0.00271721	+	0.00271721i
$23$	0.868851	−	4.71647i	0.181168	−	0.983452i
$23$	0.868851	−	4.71647i	0.181168	−	0.983452i
$24$			1.00000i			0.204124i
$25$	−1.90508	−	4.62284i	−0.381017	−	0.924568i
$26$	2.45206	−	1.57584i	0.480888	−	0.309048i
$27$	0.599278	−	0.800541i	0.115331	−	0.154064i
$28$	0.214848	−	0.576030i	0.0406025	−	0.108859i
$29$	1.75151	+	0.251830i	0.325248	+	0.0467636i	0.303005	−	0.952989i	$-0.402010\pi$
$29$	1.75151	+	0.251830i	0.325248	+	0.0467636i	0.0222430	+	0.999753i	$0.492919\pi$
$30$	1.66215	+	1.49574i	0.303466	+	0.273084i
$31$	−2.35626	−	1.51428i	−0.423197	−	0.271972i	0.311661	−	0.950194i	$-0.399115\pi$
$31$	−2.35626	−	1.51428i	−0.423197	−	0.271972i	−0.734858	+	0.678221i	$0.762751\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	−0.00863796	−	0.0158192i	−0.00150368	−	0.00275378i
$34$	2.76306	+	3.18874i	0.473861	+	0.546865i
$35$	−0.636093	−	1.21870i	−0.107519	−	0.205999i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	3.04312	+	8.15892i	0.500286	+	1.34132i	0.904430	+	0.426623i	$0.140297\pi$
$37$	3.04312	+	8.15892i	0.500286	+	1.34132i	−0.404144	+	0.914696i	$0.632430\pi$
$38$	−0.311180	−	1.43047i	−0.0504800	−	0.232053i
$39$	0.821185	+	2.79670i	0.131495	+	0.447830i
$40$	0.820572	−	2.08006i	0.129744	−	0.328887i
$41$	4.04979	+	8.86780i	0.632471	+	1.38492i	0.906092	+	0.423081i	$0.139051\pi$
$41$	4.04979	+	8.86780i	0.632471	+	1.38492i	−0.273621	+	0.961838i	$0.588221\pi$
$42$	0.492167	+	0.368432i	0.0759431	+	0.0568503i
$43$	−9.90459	−	2.15461i	−1.51044	−	0.328575i	−0.620335	−	0.784337i	$-0.713003\pi$
$43$	−9.90459	−	2.15461i	−1.51044	−	0.328575i	−0.890102	+	0.455762i	$0.849367\pi$
$44$	−0.0118032	+	0.0136216i	−0.00177940	+	0.00205353i
$45$	−1.90344	+	1.17343i	−0.283748	+	0.174924i
$46$	0.530168	−	4.76644i	0.0781690	−	0.702773i
$47$	1.44422	+	1.44422i	0.210662	+	0.210662i	0.804548	−	0.593887i	$-0.202407\pi$
$47$	1.44422	+	1.44422i	0.210662	+	0.210662i	−0.593887	+	0.804548i	$0.702407\pi$
$48$	0.0713392	+	0.997452i	0.0102969	+	0.143970i
$49$	3.58014	+	5.57081i	0.511448	+	0.795829i
$50$	−2.23002	−	4.47516i	−0.315372	−	0.632883i
$51$	−3.83802	+	1.75277i	−0.537431	+	0.245436i
$52$	2.33339	−	1.74676i	0.323583	−	0.242231i
$53$	−1.02310	−	0.558655i	−0.140534	−	0.0767371i	0.407444	−	0.913230i	$-0.366420\pi$
$53$	−1.02310	−	0.558655i	−0.140534	−	0.0767371i	−0.547977	+	0.836493i	$0.684602\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	0.00498667	+	0.0399931i	0.000672402	+	0.00539267i
$56$	0.173207	−	0.589890i	0.0231458	−	0.0788273i
$57$	1.46020	+	0.104435i	0.193408	+	0.0138328i
$58$	1.76502	+	0.126236i	0.231758	+	0.0165757i
$59$	−0.309071	+	1.05260i	−0.0402376	+	0.137037i	−0.977162	−	0.212495i	$-0.931841\pi$
$59$	−0.309071	+	1.05260i	−0.0402376	+	0.137037i	0.936925	+	0.349532i	$0.113659\pi$
$60$	1.76462	+	1.37335i	0.227812	+	0.177299i
$61$	4.01893	−	6.25357i	0.514571	−	0.800688i	−0.482601	−	0.875840i	$-0.660308\pi$
$61$	4.01893	−	6.25357i	0.514571	−	0.800688i	0.997172	+	0.0751526i	$0.0239444\pi$
$62$	−2.45829	−	1.34233i	−0.312203	−	0.170476i
$63$	−0.492167	+	0.368432i	−0.0620072	+	0.0464180i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	0.586778	−	6.49115i	0.0727808	−	0.805128i
$66$	−0.00974449	−	0.0151627i	−0.00119946	−	0.00186640i
$67$	−0.188015	−	2.62879i	−0.0229697	−	0.321158i	−0.995926	−	0.0901705i	$-0.971259\pi$
$67$	−0.188015	−	2.62879i	−0.0229697	−	0.321158i	0.972957	−	0.230988i	$-0.0741957\pi$
$68$	2.98351	+	2.98351i	0.361803	+	0.361803i
$69$	4.42400	+	1.85155i	0.532587	+	0.222901i
$70$	−0.721414	−	1.17022i	−0.0862254	−	0.139868i
$71$	−8.80307	+	10.1593i	−1.04473	+	1.20569i	−0.0665837	+	0.997781i	$0.521210\pi$
$71$	−8.80307	+	10.1593i	−1.04473	+	1.20569i	−0.978149	+	0.207905i	$0.933336\pi$
$72$	−0.977147	−	0.212565i	−0.115158	−	0.0250511i
$73$	−10.3492	−	7.74734i	−1.21129	−	0.906758i	−0.213749	−	0.976889i	$-0.568568\pi$
$73$	−10.3492	−	7.74734i	−1.21129	−	0.906758i	−0.997538	+	0.0701305i	$0.977658\pi$
$74$	3.61742	+	7.92104i	0.420516	+	0.920802i
$75$	4.92215	−	0.878890i	0.568361	−	0.101485i
$76$	−0.412436	−	1.40463i	−0.0473096	−	0.161122i
$77$	0.00235544	+	0.0108278i	0.000268427	+	0.00123394i
$78$	1.01861	+	2.73099i	0.115335	+	0.309224i
$79$	−0.217136	−	0.0637570i	−0.0244297	−	0.00717322i	0.269495	−	0.963002i	$-0.413143\pi$
$79$	−0.217136	−	0.0637570i	−0.0244297	−	0.00717322i	−0.293925	+	0.955829i	$0.594961\pi$
$80$	0.670092	−	2.13330i	0.0749185	−	0.238510i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	4.67209	+	8.55630i	0.515946	+	0.944885i
$83$	−4.39699	+	1.63999i	−0.482633	+	0.180013i	−0.578991	−	0.815334i	$-0.696553\pi$
$83$	−4.39699	+	1.63999i	−0.482633	+	0.180013i	0.0963582	+	0.995347i	$0.469281\pi$
$84$	0.517197	+	0.332382i	0.0564308	+	0.0362659i
$85$	9.42160	−	0.496488i	1.02192	−	0.0538517i
$86$	−10.0331	−	1.44254i	−1.08189	−	0.155553i
$87$	−0.618386	+	1.65796i	−0.0662979	+	0.177752i
$88$	−0.0108014	+	0.0144289i	−0.00115143	+	0.00153813i
$89$	−1.41759	+	0.911027i	−0.150264	+	0.0965687i	−0.613612	−	0.789607i	$-0.710284\pi$
$89$	−1.41759	+	0.911027i	−0.150264	+	0.0965687i	0.463348	+	0.886176i	$0.346648\pi$
$90$	−1.81488	+	1.30623i	−0.191305	+	0.137688i
$91$		−	1.79198i		−	0.187850i
$92$	0.188784	−	4.79211i	0.0196820	−	0.499612i
$93$	1.98053	−	1.98053i	0.205372	−	0.205372i
$94$	1.54357	+	1.33751i	0.159207	+	0.137954i
$95$	−2.95160	−	1.41543i	−0.302828	−	0.145220i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	−12.0907	−	4.50962i	−1.22763	−	0.457882i	−0.349786	−	0.936830i	$-0.613746\pi$
$97$	−12.0907	−	4.50962i	−1.22763	−	0.457882i	−0.877843	+	0.478948i	$0.841018\pi$
$98$	3.96843	+	5.30121i	0.400872	+	0.535503i
$99$	0.0172939	−	0.00507793i	0.00173810	−	0.000510352i
$100$	−2.54359	−	4.30467i	−0.254359	−	0.430467i
$101$	−7.52637	+	16.4804i	−0.748902	+	1.63987i	0.0194277	+	0.999811i	$0.493816\pi$
$101$	−7.52637	+	16.4804i	−0.748902	+	1.63987i	−0.768329	+	0.640055i	$0.778912\pi$
$102$	−3.70320	+	2.02210i	−0.366672	+	0.200218i
$103$	0.306591	−	4.28670i	0.0302093	−	0.422381i	−0.959733	−	0.280913i	$-0.909363\pi$
$103$	0.306591	−	4.28670i	0.0302093	−	0.422381i	0.989943	−	0.141469i	$-0.0451825\pi$
$104$	2.20283	−	1.90877i	0.216006	−	0.187170i
$105$	1.32606	−	0.362502i	0.129411	−	0.0353766i
$106$	−1.06035	−	0.484244i	−0.102990	−	0.0470340i
$107$	−6.63134	+	1.44256i	−0.641075	+	0.139457i	−0.521341	−	0.853349i	$-0.674568\pi$
$107$	−6.63134	+	1.44256i	−0.641075	+	0.139457i	−0.119735	+	0.992806i	$0.538204\pi$
$108$	0.479249	−	0.877679i	0.0461158	−	0.0844547i
$109$	0.531525	−	3.69684i	0.0509109	−	0.354093i	−0.948403	−	0.317066i	$-0.897302\pi$
$109$	0.531525	−	3.69684i	0.0509109	−	0.354093i	0.999314	−	0.0370268i	$-0.0117887\pi$
$110$	0.00782704	+	0.0395355i	0.000746279	+	0.00376956i
$111$	−8.61933	+	1.23927i	−0.818110	+	0.117627i
$112$	0.130684	−	0.600743i	0.0123484	−	0.0567649i
$113$	5.84904	−	0.418332i	0.550232	−	0.0393533i	0.206544	−	0.978437i	$-0.433778\pi$
$113$	5.84904	−	0.418332i	0.550232	−	0.0393533i	0.343688	+	0.939084i	$0.388324\pi$
$114$	1.46393			0.137109
$115$	−7.68286	−	7.48156i	−0.716430	−	0.697659i
$116$	1.76952			0.164296
$117$	−2.90734	+	0.207937i	−0.268784	+	0.0192238i
$118$	−0.233192	+	1.07197i	−0.0214671	+	0.0986825i
$119$	2.56760	−	0.369165i	0.235372	−	0.0338413i
$120$	1.85810	+	1.24397i	0.169621	+	0.113558i
$121$	−1.56542	+	10.8877i	−0.142311	+	0.989792i
$122$	3.56256	−	6.52434i	0.322539	−	0.590686i
$123$	−9.52599	+	2.07225i	−0.858930	+	0.186849i
$124$	−2.54778	−	1.16353i	−0.228798	−	0.104488i
$125$	−10.9596	−	2.21083i	−0.980254	−	0.197743i
$126$	−0.464630	+	0.402604i	−0.0413925	+	0.0358668i
$127$	0.558640	−	7.81080i	0.0495712	−	0.693097i	−0.910530	−	0.413443i	$-0.864326\pi$
$127$	0.558640	−	7.81080i	0.0495712	−	0.693097i	0.960101	−	0.279653i	$-0.0902195\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	4.21075	−	9.22025i	0.370736	−	0.811798i
$130$	0.122209	−	6.51647i	0.0107185	−	0.571532i
$131$	−10.2958	+	3.02311i	−0.899545	+	0.264130i	−0.698634	−	0.715479i	$-0.746208\pi$
$131$	−10.2958	+	3.02311i	−0.899545	+	0.264130i	−0.200911	+	0.979610i	$0.564390\pi$
$132$	−0.0108014	−	0.0144289i	−0.000940137	−	0.00125588i
$133$	−0.843266	−	0.314522i	−0.0731204	−	0.0272725i
$134$	−0.375072	−	2.60868i	−0.0324013	−	0.225356i
$135$	−0.742004	−	2.10937i	−0.0638615	−	0.181545i
$136$	3.18874	+	2.76306i	0.273433	+	0.236931i
$137$	3.67869	−	3.67869i	0.314292	−	0.314292i	−0.532278	−	0.846570i	$-0.678664\pi$
$137$	3.67869	−	3.67869i	0.314292	−	0.314292i	0.846570	+	0.532278i	$0.178664\pi$
$138$	4.54481	+	1.53123i	0.386880	+	0.130347i
$139$		−	0.208568i		−	0.0176905i	−0.999961	−	0.00884525i	$-0.997184\pi$
$139$		−	0.208568i		−	0.0176905i	0.999961	−	0.00884525i	$-0.00281557\pi$
$140$	−0.803058	−	1.11577i	−0.0678708	−	0.0943001i
$141$	−1.71821	+	1.10423i	−0.144699	+	0.0929926i
$142$	−8.05589	+	10.7614i	−0.676035	+	0.903077i
$143$	−0.0183593	+	0.0492233i	−0.00153528	+	0.00411626i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	2.64675	−	2.94122i	0.219801	−	0.244255i
$146$	−10.8756	−	6.98930i	−0.900068	−	0.578438i
$147$	−6.20451	+	2.31416i	−0.511739	+	0.190869i
$148$	4.17328	+	7.64280i	0.343042	+	0.628234i
$149$	2.31784	+	2.67493i	0.189885	+	0.219139i	0.842707	−	0.538372i	$-0.180961\pi$
$149$	2.31784	+	2.67493i	0.189885	+	0.219139i	−0.652822	+	0.757511i	$0.726415\pi$
$150$	4.84691	−	1.22779i	0.395748	−	0.100249i
$151$	8.43988	+	2.47817i	0.686828	+	0.201671i	0.606483	−	0.795096i	$-0.292580\pi$
$151$	8.43988	+	2.47817i	0.686828	+	0.201671i	0.0803447	+	0.996767i	$0.474398\pi$
$152$	−0.511590	−	1.37162i	−0.0414954	−	0.111253i
$153$	−0.896880	−	4.12289i	−0.0725084	−	0.333316i
$154$	0.00312188	+	0.0106321i	0.000251568	+	0.000856763i
$155$	−5.74480	+	2.49446i	−0.461434	+	0.200360i
$156$	1.21084	+	2.65137i	0.0969446	+	0.212279i
$157$	−11.1737	−	8.36452i	−0.891757	−	0.667561i	0.0518404	−	0.998655i	$-0.483491\pi$
$157$	−11.1737	−	8.36452i	−0.891757	−	0.667561i	−0.943598	+	0.331094i	$0.892582\pi$
$158$	−0.221131	−	0.0481042i	−0.0175923	−	0.00382696i
$159$	0.763363	−	0.880968i	0.0605386	−	0.0698653i
$160$	0.516196	−	2.17567i	0.0408089	−	0.172002i
$161$	−2.28897	−	1.85848i	−0.180396	−	0.146469i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−0.0566236	−	0.791701i	−0.00443510	−	0.0620108i	0.994753	−	0.102310i	$-0.0326234\pi$
$163$	−0.0566236	−	0.791701i	−0.00443510	−	0.0620108i	−0.999188	+	0.0402993i	$0.987169\pi$
$164$	5.27059	+	8.20120i	0.411564	+	0.640406i
$165$	−0.0401391	−	0.00362844i	−0.00312483	−	0.000282474i
$166$	−4.26879	+	1.94949i	−0.331323	+	0.151310i
$167$	−11.1969	+	8.38187i	−0.866439	+	0.648608i	−0.937165	−	0.348888i	$-0.886559\pi$
$167$	−11.1969	+	8.38187i	−0.866439	+	0.648608i	0.0707254	+	0.997496i	$0.477469\pi$
$168$	0.539591	+	0.294639i	0.0416304	+	0.0227319i
$169$	−2.43512	+	3.78911i	−0.187317	+	0.291470i
$170$	9.36218	−	1.16735i	0.718046	−	0.0895318i
$171$	−0.412436	+	1.40463i	−0.0315397	+	0.107414i
$172$	−10.1104	−	0.723111i	−0.770912	−	0.0551367i
$173$	14.6515	+	1.04789i	1.11393	+	0.0796699i	0.616147	−	0.787631i	$-0.288693\pi$
$173$	14.6515	+	1.04789i	1.11393	+	0.0796699i	0.497784	+	0.867301i	$0.334147\pi$
$174$	−0.498533	+	1.69785i	−0.0377937	+	0.128713i
$175$	−3.05576	−	0.334104i	−0.230993	−	0.0252559i
$176$	−0.00974449	+	0.0151627i	−0.000734518	+	0.00114293i
$177$	−0.962846	−	0.525754i	−0.0723720	−	0.0395181i
$178$	−1.34898	+	1.00984i	−0.101111	+	0.0756904i
$179$	−4.52854	+	2.06812i	−0.338479	+	0.154578i	−0.577401	−	0.816460i	$-0.695933\pi$
$179$	−4.52854	+	2.06812i	−0.338479	+	0.154578i	0.238922	+	0.971039i	$0.423206\pi$
$180$	−1.71707	+	1.43237i	−0.127983	+	0.106762i
$181$	−13.2807	−	20.6652i	−0.987146	−	1.53603i	−0.836882	−	0.547383i	$-0.815624\pi$
$181$	−13.2807	−	20.6652i	−0.987146	−	1.53603i	−0.150264	−	0.988646i	$-0.548012\pi$
$182$	−0.127838	−	1.78741i	−0.00947601	−	0.132492i
$183$	5.25637	+	5.25637i	0.388562	+	0.388562i
$184$	−0.153563	−	4.79337i	−0.0113208	−	0.353372i
$185$	18.9457	+	4.49502i	1.39291	+	0.330480i
$186$	1.83420	−	2.11678i	0.134490	−	0.155210i
$187$	−0.0743108	−	0.0161653i	−0.00543414	−	0.00118213i
$188$	1.63506	+	1.22399i	0.119249	+	0.0892685i
$189$	−0.255394	−	0.559236i	−0.0185772	−	0.0406784i
$190$	−3.04506	−	1.20126i	−0.220912	−	0.0871484i
$191$	1.69225	+	5.76327i	0.122447	+	0.417016i	0.997787	−	0.0664921i	$-0.0211807\pi$
$191$	1.69225	+	5.76327i	0.122447	+	0.417016i	−0.875340	+	0.483508i	$0.839363\pi$
$192$	0.212565	+	0.977147i	0.0153406	+	0.0705195i
$193$	−5.53130	−	14.8300i	−0.398152	−	1.06749i	−0.969136	−	0.246525i	$-0.920711\pi$
$193$	−5.53130	−	14.8300i	−0.398152	−	1.06749i	0.570985	−	0.820961i	$-0.306562\pi$
$194$	−12.3817	−	3.63558i	−0.888951	−	0.261020i
$195$	6.21808	+	1.95316i	0.445286	+	0.139869i
$196$	4.33651	+	5.00460i	0.309751	+	0.357471i
$197$	8.02314	+	14.6933i	0.571625	+	1.04685i	0.990330	+	0.138731i	$0.0443022\pi$
$197$	8.02314	+	14.6933i	0.571625	+	1.04685i	−0.418705	+	0.908122i	$0.637516\pi$
$198$	0.0168875	−	0.00629873i	0.00120015	−	0.000447631i
$199$	16.3014	+	10.4763i	1.15557	+	0.742642i	0.970741	−	0.240128i	$-0.0771893\pi$
$199$	16.3014	+	10.4763i	1.15557	+	0.742642i	0.184833	+	0.982770i	$0.440826\pi$
$200$	−2.84420	−	4.11224i	−0.201115	−	0.290779i
$201$	2.60868	+	0.375072i	0.184002	+	0.0264555i
$202$	−6.33149	+	16.9754i	−0.445482	+	1.19438i
$203$	0.651949	−	0.870902i	0.0457579	−	0.0611253i
$204$	−3.54951	+	2.28113i	−0.248516	+	0.159711i
$205$	21.5151	+	3.50635i	1.50268	+	0.244894i
$206$		−	4.29765i		−	0.299432i
$207$	−2.74963	+	3.92932i	−0.191112	+	0.273107i
$208$	2.06105	−	2.06105i	0.142908	−	0.142908i
$209$	0.0199410	+	0.0172790i	0.00137935	+	0.00119521i
$210$	1.29682	−	0.456179i	0.0894894	−	0.0314793i
$211$	0.225867	+	1.57094i	0.0155493	+	0.108148i	0.996118	−	0.0880283i	$-0.0280566\pi$
$211$	0.225867	+	1.57094i	0.0155493	+	0.108148i	−0.980569	+	0.196176i	$0.937148\pi$
$212$	−1.09219	−	0.407366i	−0.0750120	−	0.0279780i
$213$	−8.05589	−	10.7614i	−0.551980	−	0.737360i
$214$	−6.51153	+	1.91196i	−0.445119	+	0.130699i
$215$	−16.3245	+	15.7235i	−1.11332	+	1.07233i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−1.51134	+	0.825253i	−0.102596	+	0.0560218i
$218$	0.266442	−	3.72534i	0.0180457	−	0.252312i
$219$	9.77018	−	8.46591i	0.660208	−	0.572073i
$220$	0.0106275	+	0.0388763i	0.000716507	+	0.00262104i
$221$	11.1869	+	5.10891i	0.752515	+	0.343662i
$222$	−8.50896	+	1.85101i	−0.571084	+	0.124232i
$223$	−8.21317	+	15.0413i	−0.549994	+	1.00724i	0.443813	+	0.896120i	$0.353626\pi$
$223$	−8.21317	+	15.0413i	−0.549994	+	1.00724i	−0.993807	+	0.111120i	$0.964556\pi$
$224$	0.0874942	−	0.608535i	0.00584595	−	0.0406595i
$225$	−0.187473	+	4.99648i	−0.0124982	+	0.333099i
$226$	5.80430	−	0.834532i	0.386096	−	0.0555122i
$227$	4.10264	−	18.8595i	0.272302	−	1.25175i	−0.614246	−	0.789115i	$-0.710540\pi$
$227$	4.10264	−	18.8595i	0.272302	−	1.25175i	0.886548	−	0.462637i	$-0.153097\pi$
$228$	1.46020	−	0.104435i	0.0967038	−	0.00691639i
$229$	25.5479			1.68825			0.844127	−	0.536143i	$-0.180119\pi$
$229$	25.5479			1.68825			0.844127	+	0.536143i	$0.180119\pi$
$230$	−8.19701	−	6.91441i	−0.540495	−	0.455922i
$231$	−0.0110810			−0.000729077
$232$	1.76502	−	0.126236i	0.115879	−	0.00828783i
$233$	−3.37852	+	15.5308i	−0.221334	+	1.01746i	0.723606	+	0.690213i	$0.242483\pi$
$233$	−3.37852	+	15.5308i	−0.221334	+	1.01746i	−0.944940	+	0.327243i	$0.893880\pi$
$234$	−2.88510	+	0.414815i	−0.188605	+	0.0271173i
$235$	4.48008	−	0.886944i	0.292248	−	0.0578579i
$236$	−0.156125	+	1.08587i	−0.0101628	+	0.0706842i
$237$	0.108456	−	0.198621i	0.00704494	−	0.0129019i
$238$	2.53472	−	0.551395i	0.164302	−	0.0357417i
$239$	13.2295	+	6.04171i	0.855745	+	0.390806i	0.794461	−	0.607315i	$-0.207753\pi$
$239$	13.2295	+	6.04171i	0.855745	+	0.390806i	0.0612836	+	0.998120i	$0.480481\pi$
$240$	1.94211	+	1.10824i	0.125363	+	0.0715368i
$241$	1.63837	−	1.41966i	0.105537	−	0.0914482i	−0.600494	−	0.799629i	$-0.705029\pi$
$241$	1.63837	−	1.41966i	0.105537	−	0.0914482i	0.706031	+	0.708181i	$0.250484\pi$
$242$	−0.784708	+	10.9716i	−0.0504429	+	0.705284i
$243$	−0.877679	+	0.479249i	−0.0563031	+	0.0307438i
$244$	3.08804	−	6.76187i	0.197692	−	0.432884i
$245$	14.8047	+	0.277646i	0.945838	+	0.0177382i
$246$	−9.35389	+	2.74655i	−0.596382	+	0.175114i
$247$	−2.55712	−	3.41591i	−0.162706	−	0.217349i
$248$	−2.62430	−	0.978813i	−0.166643	−	0.0621547i
$249$	−0.667866	−	4.64511i	−0.0423243	−	0.294372i
$250$	−11.0894	−	1.42335i	−0.701353	−	0.0900208i
$251$	18.2331	+	15.7990i	1.15086	+	0.997227i	0.999962	+	0.00867741i	$0.00276214\pi$
$251$	18.2331	+	15.7990i	1.15086	+	0.997227i	0.150899	+	0.988549i	$0.451783\pi$
$252$	−0.434724	+	0.434724i	−0.0273851	+	0.0273851i
$253$	0.0438342	+	0.0745011i	0.00275583	+	0.00468384i
$254$		−	7.83075i		−	0.491345i
$255$	−1.51756	+	9.31182i	−0.0950335	+	0.583129i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	9.32166	−	12.4523i	0.581469	−	0.776752i	−0.409287	−	0.912406i	$-0.634223\pi$
$257$	9.32166	−	12.4523i	0.581469	−	0.776752i	0.990756	+	0.135654i	$0.0433135\pi$
$258$	3.54225	−	9.49715i	0.220531	−	0.591267i
$259$	5.29910	+	0.761896i	0.329270	+	0.0473419i
$260$	−0.342982	−	6.50859i	−0.0212708	−	0.403645i
$261$	−1.48862	−	0.956677i	−0.0921432	−	0.0592168i
$262$	−10.0539	+	3.74990i	−0.621130	+	0.231669i
$263$	−1.35119	−	2.47452i	−0.0833181	−	0.152586i	0.832698	−	0.553728i	$-0.186795\pi$
$263$	−1.35119	−	2.47452i	−0.0833181	−	0.152586i	−0.916016	+	0.401142i	$0.868613\pi$
$264$	−0.0118032	−	0.0136216i	−0.000726436	−	0.000838351i
$265$	−2.31074	+	1.20607i	−0.141948	+	0.0740885i
$266$	−0.863555	−	0.253563i	−0.0529479	−	0.0155469i
$267$	−0.588878	−	1.57884i	−0.0360387	−	0.0966236i
$268$	−0.560218	−	2.57528i	−0.0342207	−	0.157310i
$269$	2.74506	+	9.34880i	0.167369	+	0.570007i	0.999872	+	0.0159863i	$0.00508881\pi$
$269$	2.74506	+	9.34880i	0.167369	+	0.570007i	−0.832503	+	0.554020i	$0.813093\pi$
$270$	−0.890594	−	2.05106i	−0.0541998	−	0.124823i
$271$	−7.61637	−	16.6775i	−0.462662	−	1.01309i	−0.986873	−	0.161499i	$-0.948367\pi$
$271$	−7.61637	−	16.6775i	−0.462662	−	1.01309i	0.524211	−	0.851588i	$-0.324360\pi$
$272$	3.37773	+	2.52854i	0.204805	+	0.153315i
$273$	1.75103	+	0.380913i	0.105977	+	0.0230539i
$274$	3.40688	−	3.93175i	0.205817	−	0.237526i
$275$	0.0805145	+	0.0404844i	0.00485521	+	0.00244130i
$276$	4.64247	+	1.20311i	0.279444	+	0.0724185i
$277$	3.05207	+	3.05207i	0.183381	+	0.183381i	0.792827	−	0.609446i	$-0.208608\pi$
$277$	3.05207	+	3.05207i	0.183381	+	0.183381i	−0.609446	+	0.792827i	$0.708608\pi$
$278$	−0.0148791	−	0.208036i	−0.000892387	−	0.0124772i
$279$	1.51428	+	2.35626i	0.0906575	+	0.141066i
$280$	−0.880611	−	1.05564i	−0.0526265	−	0.0630866i
$281$	−15.5516	+	7.10218i	−0.927731	+	0.423680i	−0.821207	−	0.570630i	$-0.806699\pi$
$281$	−15.5516	+	7.10218i	−0.927731	+	0.423680i	−0.106523	+	0.994310i	$0.533972\pi$
$282$	−1.63506	+	1.22399i	−0.0973662	+	0.0728874i
$283$	3.99262	+	2.18013i	0.237336	+	0.129595i	0.593516	−	0.804822i	$-0.297739\pi$
$283$	3.99262	+	2.18013i	0.237336	+	0.129595i	−0.356180	+	0.934417i	$0.615921\pi$
$284$	−7.26765	+	11.3087i	−0.431256	+	0.671047i
$285$	2.01049	−	2.58328i	0.119091	−	0.153020i
$286$	−0.0148010	+	0.0504076i	−0.000875202	+	0.00298066i
$287$	5.97821	+	0.427570i	0.352883	+	0.0252387i
$288$	−0.997452	−	0.0713392i	−0.0587754	−	0.00420370i
$289$	−0.226121	+	0.770097i	−0.0133012	+	0.0452998i
$290$	2.43019	−	3.12255i	0.142705	−	0.183362i
$291$	6.97663	−	10.8558i	0.408977	−	0.636381i
$292$	−11.3465	−	6.19564i	−0.664001	−	0.362572i
$293$	−2.64782	+	1.98213i	−0.154687	+	0.115798i	−0.673818	−	0.738897i	$-0.735347\pi$
$293$	−2.64782	+	1.98213i	−0.154687	+	0.115798i	0.519130	+	0.854695i	$0.326256\pi$
$294$	−6.02361	+	2.75089i	−0.351304	+	0.160435i
$295$	1.57136	+	1.88369i	0.0914882	+	0.109672i
$296$	4.70788	+	7.32560i	0.273640	+	0.425792i
$297$	0.00128581	+	0.0179780i	7.46105e−5	+	0.00104319i
$298$	2.50276	+	2.50276i	0.144981	+	0.144981i
$299$	−4.36571	−	13.2795i	−0.252476	−	0.767974i
$300$	4.74697	−	1.57044i	0.274066	−	0.0906693i
$301$	−4.08089	+	4.70960i	−0.235219	+	0.271457i
$302$	8.59517	+	1.86976i	0.494596	+	0.107593i
$303$	−14.5040	−	10.8575i	−0.833232	−	0.623749i
$304$	−0.608137	−	1.33163i	−0.0348790	−	0.0763744i
$305$	−6.62035	−	15.2468i	−0.379080	−	0.873030i
$306$	−1.18872	−	4.04840i	−0.0679545	−	0.231432i
$307$	−2.45848	−	11.3015i	−0.140313	−	0.645009i	−0.992549	−	0.121850i	$-0.961117\pi$
$307$	−2.45848	−	11.3015i	−0.140313	−	0.645009i	0.852235	−	0.523158i	$-0.175246\pi$
$308$	0.00387241	+	0.0103823i	0.000220651	+	0.000591589i
$309$	4.12357	+	1.21079i	0.234582	+	0.0688794i
$310$	−5.55221	+	2.89794i	−0.315344	+	0.164592i
$311$	3.63731	+	4.19768i	0.206253	+	0.238029i	0.849446	−	0.527675i	$-0.176936\pi$
$311$	3.63731	+	4.19768i	0.206253	+	0.238029i	−0.643193	+	0.765704i	$0.722391\pi$
$312$	1.39690	+	2.55823i	0.0790839	+	0.144831i
$313$	7.22248	−	2.69385i	0.408239	−	0.152265i	−0.136951	−	0.990578i	$-0.543730\pi$
$313$	7.22248	−	2.69385i	0.408239	−	0.152265i	0.545190	+	0.838313i	$0.316458\pi$
$314$	−11.7419	−	7.54608i	−0.662636	−	0.425850i
$315$	0.0723429	+	1.37281i	0.00407606	+	0.0773493i
$316$	−0.224000	−	0.0322063i	−0.0126010	−	0.00181175i
$317$	9.02545	−	24.1982i	0.506920	−	1.35910i	−0.391585	−	0.920142i	$-0.628073\pi$
$317$	9.02545	−	24.1982i	0.506920	−	1.35910i	0.898505	−	0.438963i	$-0.144654\pi$
$318$	0.698571	−	0.933181i	0.0391739	−	0.0523302i
$319$	−0.0268308	+	0.0172431i	−0.00150224	+	0.000965429i
$320$	0.359671	−	2.20695i	0.0201062	−	0.123372i
$321$		−	6.78643i		−	0.378781i
$322$	−2.41572	−	1.69045i	−0.134623	−	0.0942052i
$323$	4.36763	−	4.36763i	0.243021	−	0.243021i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	−11.3313	−	9.16508i	−0.628547	−	0.508387i
$326$	−0.112959	−	0.785644i	−0.00625620	−	0.0435128i
$327$	3.49937	+	1.30520i	0.193516	+	0.0721776i
$328$	5.84223	+	7.80430i	0.322583	+	0.430920i
$329$	1.20481	−	0.353765i	0.0664235	−	0.0195037i
$330$	−0.0402957		0.000755703i	−0.00221821		4.16001e-5i
$331$	4.86105	−	10.6442i	0.267188	−	0.585059i	−0.727717	−	0.685877i	$-0.759419\pi$
$331$	4.86105	−	10.6442i	0.267188	−	0.585059i	0.994905	+	0.100818i	$0.0321460\pi$
$332$	−4.11884	+	2.24906i	−0.226051	+	0.123433i
$333$	0.621219	−	8.68578i	0.0340426	−	0.475978i
$334$	−10.5704	+	9.15928i	−0.578385	+	0.501174i
$335$	−5.11845	−	2.92079i	−0.279651	−	0.159580i
$336$	0.559236	+	0.255394i	0.0305088	+	0.0139329i
$337$	0.504184	−	0.109678i	0.0274646	−	0.00597457i	−0.198812	−	0.980038i	$-0.563708\pi$
$337$	0.504184	−	0.109678i	0.0274646	−	0.00597457i	0.226277	+	0.974063i	$0.427345\pi$
$338$	−2.15860	+	3.95318i	−0.117412	+	0.215025i
$339$	−0.834532	+	5.80430i	−0.0453255	+	0.315246i
$340$	9.25504	−	1.83227i	0.501925	−	0.0993687i
$341$	0.0499694	−	0.00718451i	0.00270599	−	0.000389063i
$342$	−0.311180	+	1.43047i	−0.0168267	+	0.0773510i
$343$	8.35339	−	0.597446i	0.451041	−	0.0322591i
$344$	−10.1362			−0.546509
$345$	8.94369	−	5.91696i	0.481512	−	0.318559i
$346$	14.6889			0.789680
$347$	6.13116	−	0.438509i	0.329138	−	0.0235404i	0.0942074	−	0.995553i	$-0.469968\pi$
$347$	6.13116	−	0.438509i	0.329138	−	0.0235404i	0.234930	+	0.972012i	$0.424514\pi$
$348$	−0.376140	+	1.72909i	−0.0201632	+	0.0926887i
$349$	6.64224	−	0.955009i	0.355551	−	0.0511205i	0.0377747	−	0.999286i	$-0.487973\pi$
$349$	6.64224	−	0.955009i	0.355551	−	0.0511205i	0.317776	+	0.948166i	$0.397064\pi$
$350$	−3.07180	−	0.115257i	−0.164195	−	0.00616076i
$351$	0.414815	−	2.88510i	0.0221412	−	0.153995i
$352$	−0.00863796	+	0.0158192i	−0.000460405	+	0.000843169i
$353$	−11.9449	+	2.59845i	−0.635761	+	0.138301i	−0.518884	−	0.854845i	$-0.673652\pi$
$353$	−11.9449	+	2.59845i	−0.635761	+	0.138301i	−0.116878	+	0.993146i	$0.537289\pi$
$354$	−0.997900	−	0.455726i	−0.0530378	−	0.0242215i
$355$	7.92624	+	28.9948i	0.420681	+	1.53889i
$356$	−1.27350	+	1.10350i	−0.0674956	+	0.0584853i
$357$	−0.185054	+	2.58740i	−0.00979411	+	0.136940i
$358$	−4.36947	+	2.38591i	−0.230933	+	0.126099i
$359$	−2.63193	+	5.76312i	−0.138908	+	0.304166i	−0.966282	−	0.257485i	$-0.917106\pi$
$359$	−2.63193	+	5.76312i	−0.138908	+	0.304166i	0.827374	+	0.561651i	$0.189834\pi$
$360$	−1.61051	+	1.55121i	−0.0848812	+	0.0817561i
$361$	16.1741	−	4.74914i	0.851268	−	0.249955i
$362$	−14.7211	−	19.6651i	−0.773723	−	1.03357i
$363$	−10.3061	−	3.84399i	−0.540932	−	0.201757i
$364$	−0.255025	−	1.77374i	−0.0133670	−	0.0929692i
$365$	−27.2695	+	9.59248i	−1.42735	+	0.502094i
$366$	5.61796	+	4.86799i	0.293656	+	0.254454i
$367$	−20.0339	+	20.0339i	−1.04576	+	1.04576i	−0.0468593	+	0.998902i	$0.514921\pi$
$367$	−20.0339	+	20.0339i	−1.04576	+	1.04576i	−0.998902	+	0.0468593i	$0.985079\pi$
$368$	−0.495127	−	4.77020i	−0.0258103	−	0.248664i
$369$		−	9.74878i		−	0.507501i
$370$	19.2181	+	3.13200i	0.999099	+	0.162825i
$371$	−0.602890	+	0.387454i	−0.0313005	+	0.0201156i
$372$	1.67851	−	2.24223i	0.0870269	−	0.116254i
$373$	−7.10590	+	19.0517i	−0.367929	+	0.986457i	0.612653	+	0.790352i	$0.290102\pi$
$373$	−7.10590	+	19.0517i	−0.367929	+	0.986457i	−0.980583	+	0.196105i	$0.937171\pi$
$374$	−0.0752747	−	0.0108229i	−0.00389236	−	0.000559637i
$375$	4.48993	−	10.2392i	0.231859	−	0.528748i
$376$	1.71821	+	1.10423i	0.0886099	+	0.0569461i
$377$	4.83256	−	1.80245i	0.248889	−	0.0928309i
$378$	−0.294639	−	0.539591i	−0.0151546	−	0.0277536i
$379$	22.0989	+	25.5035i	1.13514	+	1.31003i	0.944554	+	0.328355i	$0.106494\pi$
$379$	22.0989	+	25.5035i	1.13514	+	1.31003i	0.190589	+	0.981670i	$0.438960\pi$
$380$	−3.12300	−	0.980965i	−0.160206	−	0.0503224i
$381$	7.51355	+	2.20618i	0.384931	+	0.113026i
$382$	2.09908	+	5.62786i	0.107398	+	0.287946i
$383$	−6.15549	−	28.2963i	−0.314531	−	1.44587i	−0.814668	−	0.579928i	$-0.803081\pi$
$383$	−6.15549	−	28.2963i	−0.314531	−	1.44587i	0.500137	−	0.865946i	$-0.333283\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	0.0230492	+	0.00909277i	0.00117470	+	0.000463410i
$386$	−6.57517	−	14.3976i	−0.334667	−	0.732819i
$387$	8.11448	+	6.07442i	0.412482	+	0.308780i
$388$	−12.6095	−	2.74302i	−0.640149	−	0.139256i
$389$	8.81064	−	10.1680i	0.446717	−	0.515539i	−0.487072	−	0.873362i	$-0.661935\pi$
$389$	8.81064	−	10.1680i	0.446717	−	0.515539i	0.933790	+	0.357822i	$0.116481\pi$
$390$	6.34157	+	1.50459i	0.321118	+	0.0761880i
$391$	18.1279	−	8.99104i	0.916768	−	0.454696i
$392$	4.68248	+	4.68248i	0.236501	+	0.236501i
$393$	−0.765499	−	10.7031i	−0.0386143	−	0.539899i
$394$	9.05090	+	14.0835i	0.455978	+	0.709515i
$395$	−0.388578	+	0.324150i	−0.0195515	+	0.0163097i
$396$	0.0163952	−	0.00748742i	0.000823888	−	0.000376257i
$397$	11.2082	−	8.39036i	0.562524	−	0.421100i	−0.279811	−	0.960055i	$-0.590272\pi$
$397$	11.2082	−	8.39036i	0.562524	−	0.421100i	0.842334	+	0.538955i	$0.181181\pi$
$398$	17.0072	+	9.28664i	0.852495	+	0.465497i
$399$	0.486583	−	0.757138i	0.0243596	−	0.0379043i
$400$	−3.13032	−	3.89886i	−0.156516	−	0.194943i
$401$	1.61309	−	5.49367i	0.0805537	−	0.274341i	−0.909360	−	0.416009i	$-0.863428\pi$
$401$	1.61309	−	5.49367i	0.0805537	−	0.274341i	0.989914	+	0.141668i	$0.0452467\pi$
$402$	2.62879	+	0.188015i	0.131112	+	0.00937734i
$403$	−8.14316	−	0.582410i	−0.405640	−	0.0290119i
$404$	−5.10435	+	17.3838i	−0.253951	+	0.864877i
$405$	2.21889	−	0.276669i	0.110257	−	0.0137478i
$406$	0.588159	−	0.915193i	0.0291898	−	0.0454203i
$407$	−0.137753	−	0.0752190i	−0.00682818	−	0.00372847i
$408$	−3.37773	+	2.52854i	−0.167223	+	0.125181i
$409$	−25.4807	+	11.6366i	−1.25994	+	0.575395i	−0.929636	−	0.368480i	$-0.879878\pi$
$409$	−25.4807	+	11.6366i	−1.25994	+	0.575395i	−0.330303	+	0.943875i	$0.607151\pi$
$410$	21.7104	+	1.96255i	1.07220	+	0.0969233i
$411$	2.81266	+	4.37658i	0.138738	+	0.215881i
$412$	−0.306591	−	4.28670i	−0.0151047	−	0.211191i
$413$	0.476909	+	0.476909i	0.0234671	+	0.0234671i
$414$	−2.46231	+	4.11546i	−0.121016	+	0.202264i
$415$	−2.42245	+	10.2102i	−0.118913	+	0.501197i
$416$	1.90877	−	2.20283i	0.0935850	−	0.108003i
$417$	0.203801	+	0.0443343i	0.00998020	+	0.00217106i
$418$	0.0211229	+	0.0158124i	0.00103315	+	0.000773409i
$419$	2.00101	+	4.38161i	0.0977559	+	0.214056i	0.952192	−	0.305502i	$-0.0988242\pi$
$419$	2.00101	+	4.38161i	0.0977559	+	0.214056i	−0.854436	+	0.519557i	$0.826097\pi$
$420$	1.26098	−	0.547531i	0.0615294	−	0.0267168i
$421$	1.48573	+	5.05993i	0.0724101	+	0.246606i	0.987742	−	0.156094i	$-0.0498901\pi$
$421$	1.48573	+	5.05993i	0.0724101	+	0.246606i	−0.915332	+	0.402700i	$0.868072\pi$
$422$	0.337361	+	1.55082i	0.0164225	+	0.0754929i
$423$	−0.713759	−	1.91366i	−0.0347042	−	0.0930455i
$424$	−1.11847	−	0.328412i	−0.0543177	−	0.0159491i
$425$	10.7977	−	18.1239i	0.523763	−	0.879139i
$426$	−8.80307	−	10.1593i	−0.426510	−	0.492219i
$427$	−2.19024	−	4.01112i	−0.105993	−	0.194112i
$428$	−6.35854	+	2.37161i	−0.307352	+	0.114636i
$429$	−0.0441958	−	0.0284029i	−0.00213379	−	0.00137131i
$430$	−15.1612	+	16.8480i	−0.731138	+	0.812482i
$431$	24.4618	+	3.51707i	1.17828	+	0.169411i	0.703502	−	0.710693i	$-0.251619\pi$
$431$	24.4618	+	3.51707i	1.17828	+	0.169411i	0.474780	+	0.880105i	$0.342528\pi$
$432$	0.349464	−	0.936950i	0.0168136	−	0.0450790i
$433$	24.1739	−	32.2926i	1.16172	−	1.55188i	0.383932	−	0.923361i	$-0.374570\pi$
$433$	24.1739	−	32.2926i	1.16172	−	1.55188i	0.777793	−	0.628521i	$-0.216339\pi$
$434$	−1.44861	+	0.930968i	−0.0695357	+	0.0446879i
$435$	2.31140	+	3.21147i	0.110823	+	0.153978i
$436$		−	3.73486i		−	0.178867i
$437$	−7.01530	−	0.276365i	−0.335587	−	0.0132203i
$438$	9.14134	−	9.14134i	0.436790	−	0.436790i
$439$	−9.33086	−	8.08524i	−0.445338	−	0.385887i	0.403123	−	0.915146i	$-0.367925\pi$
$439$	−9.33086	−	8.08524i	−0.445338	−	0.385887i	−0.848461	+	0.529259i	$0.822470\pi$
$440$	0.0133738	+	0.0380191i	0.000637573	+	0.00181249i
$441$	−0.942413	−	6.55463i	−0.0448768	−	0.312125i
$442$	11.5229	+	4.29782i	0.548089	+	0.204427i
$443$	7.58563	+	10.1332i	0.360404	+	0.481444i	0.943694	−	0.330821i	$-0.107326\pi$
$443$	7.58563	+	10.1332i	0.360404	+	0.481444i	−0.583289	+	0.812264i	$0.698235\pi$
$444$	−8.35523	+	2.45332i	−0.396522	+	0.116429i
$445$	−0.0706518	+	3.76731i	−0.00334922	+	0.178588i
$446$	−7.11921	+	15.5889i	−0.337104	+	0.738155i
$447$	−3.10649	+	1.69627i	−0.146932	+	0.0802309i
$448$	0.0438588	−	0.613227i	0.00207214	−	0.0289722i
$449$	6.70209	−	5.80739i	0.316291	−	0.274068i	−0.482217	−	0.876052i	$-0.660168\pi$
$449$	6.70209	−	5.80739i	0.316291	−	0.274068i	0.798508	+	0.601984i	$0.205623\pi$
$450$	0.169449	+	4.99713i	0.00798792	+	0.235567i
$451$	−0.159833	−	0.0729932i	−0.00752624	−	0.00343712i
$452$	5.72997	−	1.24648i	0.269515	−	0.0586295i
$453$	−4.21557	+	7.72023i	−0.198065	+	0.362728i
$454$	2.74676	−	19.1042i	0.128912	−	0.896603i
$455$	−3.32968	−	2.22917i	−0.156098	−	0.104505i
$456$	1.44903	−	0.208338i	0.0678568	−	0.00975634i
$457$	3.43892	−	15.8085i	0.160866	−	0.739489i	−0.824059	−	0.566504i	$-0.808295\pi$
$457$	3.43892	−	15.8085i	0.160866	−	0.739489i	0.984925	−	0.172984i	$-0.0553409\pi$
$458$	25.4828	−	1.82257i	1.19073	−	0.0851630i
$459$	4.21931			0.196941
$460$	−8.66939	−	6.31202i	−0.404213	−	0.294299i
$461$	32.3954			1.50881			0.754403	−	0.656412i	$-0.227927\pi$
$461$	32.3954			1.50881			0.754403	+	0.656412i	$0.227927\pi$
$462$	−0.0110528		0.000790510i	−0.000514221		3.67778e-5i
$463$	−8.53834	+	39.2501i	−0.396810	+	1.82411i	0.152271	+	0.988339i	$0.451341\pi$
$463$	−8.53834	+	39.2501i	−0.396810	+	1.82411i	−0.549082	+	0.835769i	$0.685022\pi$
$464$	1.75151	−	0.251830i	0.0813120	−	0.0116909i
$465$	−1.21631	−	6.14375i	−0.0564050	−	0.284910i
$466$	−2.26195	+	15.7322i	−0.104783	+	0.728782i
$467$	12.7779	−	23.4009i	0.591289	−	1.08286i	−0.395131	−	0.918625i	$-0.629301\pi$
$467$	12.7779	−	23.4009i	0.591289	−	1.08286i	0.986420	−	0.164240i	$-0.0525172\pi$
$468$	−2.84816	+	0.619578i	−0.131656	+	0.0286400i
$469$	−1.47387	−	0.673094i	−0.0680570	−	0.0310806i
$470$	4.40539	−	1.20429i	0.203206	−	0.0555497i
$471$	10.5485	−	9.14033i	0.486049	−	0.421164i
$472$	−0.0782617	+	1.09424i	−0.00360229	+	0.0503666i
$473$	0.160348	−	0.0875564i	0.00737279	−	0.00402585i
$474$	0.0940097	−	0.205853i	0.00431801	−	0.00945512i
$475$	−6.30171	+	3.72363i	−0.289142	+	0.170852i
$476$	2.48893	−	0.730816i	0.114080	−	0.0334969i
$477$	0.698571	+	0.933181i	0.0319853	+	0.0427274i
$478$	13.6268	+	5.08253i	0.623275	+	0.232470i
$479$	−4.20032	−	29.2139i	−0.191917	−	1.33481i	−0.826926	−	0.562310i	$-0.809913\pi$
$479$	−4.20032	−	29.2139i	−0.191917	−	1.33481i	0.635009	−	0.772505i	$-0.280996\pi$
$480$	2.01622	+	0.966872i	0.0920276	+	0.0441315i
$481$	19.1822	+	16.6215i	0.874633	+	0.757874i
$482$	1.53292	−	1.53292i	0.0698227	−	0.0698227i
$483$	2.30256	−	1.84161i	0.104770	−	0.0837961i
$484$			10.9997i			0.499985i
$485$	−23.4198	+	16.8560i	−1.06344	+	0.765392i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−19.1072	+	25.5243i	−0.865832	+	1.15662i	0.120642	+	0.992696i	$0.461505\pi$
$487$	−19.1072	+	25.5243i	−0.865832	+	1.15662i	−0.986474	+	0.163920i	$0.947586\pi$
$488$	2.59779	−	6.96494i	0.117596	−	0.315288i
$489$	0.785644	+	0.112959i	0.0355281	+	0.00510817i
$490$	14.7868	−	0.779217i	0.667999	−	0.0352014i
$491$	4.83201	+	3.10534i	0.218066	+	0.140142i	0.645113	−	0.764087i	$-0.276810\pi$
$491$	4.83201	+	3.10534i	0.218066	+	0.140142i	−0.427048	+	0.904229i	$0.640446\pi$
$492$	−9.13412	+	3.40685i	−0.411798	+	0.153593i
$493$	3.57816	+	6.55291i	0.161152	+	0.295128i
$494$	−2.79429	−	3.22479i	−0.125721	−	0.145090i
$495$	0.0120777	−	0.0384505i	0.000542852	−	0.00172822i
$496$	−2.68744	−	0.789104i	−0.120670	−	0.0354318i
$497$	2.88813	+	7.74338i	0.129550	+	0.347338i
$498$	−0.997543	−	4.58563i	−0.0447010	−	0.205487i
$499$	9.50443	+	32.3691i	0.425477	+	1.44904i	0.841783	+	0.539816i	$0.181506\pi$
$499$	9.50443	+	32.3691i	0.425477	+	1.44904i	−0.416307	+	0.909224i	$0.636676\pi$
$500$	−11.1627	−	0.628621i	−0.499209	−	0.0281128i
$501$	−5.81025	−	12.7227i	−0.259583	−	0.568407i
$502$	19.3137	+	14.4581i	0.862013	+	0.645295i
$503$	−24.3451	−	5.29595i	−1.08549	−	0.236135i	−0.365987	−	0.930620i	$-0.619269\pi$
$503$	−24.3451	−	5.29595i	−1.08549	−	0.236135i	−0.719507	+	0.694485i	$0.755632\pi$
$504$	−0.402604	+	0.464630i	−0.0179334	+	0.0206962i
$505$	21.2598	+	34.4859i	0.946048	+	1.53460i
$506$	0.0490374	+	0.0711841i	0.00217998	+	0.00316452i
$507$	−3.18490	−	3.18490i	−0.141446	−	0.141446i
$508$	−0.558640	−	7.81080i	−0.0247856	−	0.346548i
$509$	−13.4669	−	20.9549i	−0.596909	−	0.928809i	−0.999907	−	0.0136081i	$-0.995668\pi$
$509$	−13.4669	−	20.9549i	−0.596909	−	0.928809i	0.402998	−	0.915201i	$-0.367968\pi$
$510$	−0.849399	+	9.39636i	−0.0376120	+	0.416078i
$511$	−7.22969	+	3.30169i	−0.319823	+	0.146058i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	−1.28486	−	0.701585i	−0.0567278	−	0.0309757i
$514$	8.40957	−	13.0855i	0.370930	−	0.577179i
$515$	−7.58374	−	5.90220i	−0.334180	−	0.260082i
$516$	2.85571	−	9.72565i	0.125716	−	0.428148i
$517$	−0.0367190	−	0.00262620i	−0.00161490	−	0.000115500i
$518$	5.33996	+	0.381921i	0.234624	+	0.0167807i
$519$	−4.13834	+	14.0939i	−0.181653	+	0.618653i
$520$	−0.806425	−	6.46754i	−0.0353641	−	0.283620i
$521$	−10.9030	+	16.9654i	−0.477669	+	0.743268i	−0.993550	−	0.113392i	$-0.963828\pi$
$521$	−10.9030	+	16.9654i	−0.477669	+	0.743268i	0.515881	+	0.856660i	$0.327465\pi$
$522$	−1.55307	−	0.848043i	−0.0679762	−	0.0371178i
$523$	3.22347	−	2.41306i	0.140953	−	0.105516i	−0.526475	−	0.850191i	$-0.676486\pi$
$523$	3.22347	−	2.41306i	0.140953	−	0.105516i	0.667427	+	0.744675i	$0.267396\pi$
$524$	−9.76073	+	4.45758i	−0.426400	+	0.194730i
$525$	0.976016	−	2.91490i	0.0425968	−	0.127217i
$526$	−1.52428	−	2.37183i	−0.0664618	−	0.103417i
$527$	−0.843076	−	11.7877i	−0.0367250	−	0.513482i
$528$	−0.0127449	−	0.0127449i	−0.000554649	−	0.000554649i
$529$	−21.4902	−	8.19582i	−0.934356	−	0.356340i
$530$	−2.21881	+	1.36785i	−0.0963791	+	0.0594155i
$531$	0.718406	−	0.829085i	0.0311762	−	0.0359792i
$532$	−0.879443	−	0.191311i	−0.0381287	−	0.00829439i
$533$	22.7477	+	17.0287i	0.985313	+	0.737596i
$534$	−0.700011	−	1.53281i	−0.0302924	−	0.0663312i
$535$	−5.56875	+	14.1162i	−0.240758	+	0.610296i
$536$	−0.742509	−	2.52875i	−0.0320715	−	0.109225i
$537$	−1.05824	−	4.86466i	−0.0456665	−	0.209926i
$538$	3.40500	+	9.12915i	0.146800	+	0.393586i
$539$	−0.114520	−	0.0336262i	−0.00493274	−	0.00144838i
$540$	−1.03465	−	1.98230i	−0.0445241	−	0.0853046i
$541$	−12.8893	−	14.8751i	−0.554156	−	0.639530i	0.407690	−	0.913120i	$-0.366334\pi$
$541$	−12.8893	−	14.8751i	−0.554156	−	0.639530i	−0.961846	+	0.273590i	$0.911789\pi$
$542$	−8.78673	−	16.0917i	−0.377422	−	0.691197i
$543$	23.0159	−	8.58449i	0.987707	−	0.368396i
$544$	3.54951	+	2.28113i	0.152184	+	0.0978028i
$545$	−6.20790	−	5.58638i	−0.265917	−	0.239294i
$546$	1.77374	+	0.255025i	0.0759090	+	0.0109141i
$547$	11.6487	−	31.2313i	0.498060	−	1.33535i	−0.408300	−	0.912848i	$-0.633878\pi$
$547$	11.6487	−	31.2313i	0.498060	−	1.33535i	0.906361	−	0.422504i	$-0.138849\pi$
$548$	3.11771	−	4.16478i	0.133182	−	0.177911i
$549$	−6.25357	+	4.01893i	−0.266896	+	0.171524i
$550$	0.0831975	+	0.0346375i	0.00354755	+	0.00147695i
$551$		−	2.59045i		−	0.110357i
$552$	4.71647	+	0.868851i	0.200746	+	0.0369808i
$553$	−0.0983795	+	0.0983795i	−0.00418352	+	0.00418352i
$554$	3.26202	+	2.82656i	0.138590	+	0.120089i
$555$	−8.41948	+	17.5572i	−0.357387	+	0.745262i
$556$	−0.0296823	−	0.206445i	−0.00125881	−	0.00875522i
$557$	34.1973	+	12.7549i	1.44899	+	0.540444i	0.946090	−	0.323903i	$-0.104995\pi$
$557$	34.1973	+	12.7549i	1.44899	+	0.540444i	0.502896	+	0.864347i	$0.332268\pi$
$558$	1.67851	+	2.24223i	0.0710572	+	0.0949213i
$559$	−28.3480	+	8.32373i	−1.19899	+	0.352056i
$560$	−0.953675	−	0.990129i	−0.0403001	−	0.0418406i
$561$	0.0315918	−	0.0691763i	0.00133381	−	0.00292063i
$562$	−15.0053	+	8.19352i	−0.632961	+	0.345623i
$563$	3.14038	−	43.9083i	0.132351	−	1.85051i	−0.306396	−	0.951904i	$-0.599123\pi$
$563$	3.14038	−	43.9083i	0.132351	−	1.85051i	0.438748	−	0.898610i	$-0.355422\pi$
$564$	−1.54357	+	1.33751i	−0.0649961	+	0.0563195i
$565$	6.49872	−	11.3885i	0.273403	−	0.479118i
$566$	4.13797	+	1.88975i	0.173932	+	0.0794320i
$567$	0.600743	−	0.130684i	0.0252288	−	0.00548820i
$568$	−6.44238	+	11.7983i	−0.270316	+	0.495048i
$569$	1.13752	−	7.91166i	0.0476875	−	0.331674i	−0.951986	−	0.306140i	$-0.900962\pi$
$569$	1.13752	−	7.91166i	0.0476875	−	0.331674i	0.999674	−	0.0255338i	$-0.00812854\pi$
$570$	1.82108	−	2.72012i	0.0762766	−	0.113933i
$571$	−26.9843	+	3.87975i	−1.12926	+	0.162363i	−0.681518	−	0.731802i	$-0.738680\pi$
$571$	−26.9843	+	3.87975i	−1.12926	+	0.162363i	−0.447739	+	0.894164i	$0.647771\pi$
$572$	−0.0111673	+	0.0513350i	−0.000466926	+	0.00214643i
$573$	−5.99127	+	0.428504i	−0.250289	+	0.0179010i
$574$	5.99348			0.250163
$575$	−23.4587	+	4.96871i	−0.978297	+	0.207209i
$576$	−1.00000			−0.0416667
$577$	19.7474	−	1.41236i	0.822097	−	0.0587975i	0.346048	−	0.938217i	$-0.387523\pi$
$577$	19.7474	−	1.41236i	0.822097	−	0.0587975i	0.476048	+	0.879419i	$0.342069\pi$
$578$	−0.170607	+	0.784266i	−0.00709630	+	0.0326212i
$579$	15.6668	−	2.25255i	0.651092	−	0.0936129i
$580$	2.20123	−	3.28796i	0.0914013	−	0.136525i
$581$	−0.410600	+	2.85578i	−0.0170345	+	0.118478i
$582$	6.18441	−	11.3259i	0.256352	−	0.469473i
$583$	0.0205302	−	0.00446606i	0.000850272	−	0.000184965i
$584$	−11.7595	−	5.37040i	−0.486613	−	0.222229i
$585$	−3.23027	+	5.66080i	−0.133555	+	0.234045i
$586$	−2.49967	+	2.16598i	−0.103260	+	0.0894757i
$587$	2.27297	−	31.7802i	0.0938153	−	1.31171i	−0.704601	−	0.709604i	$-0.748874\pi$
$587$	2.27297	−	31.7802i	0.0938153	−	1.31171i	0.798416	−	0.602106i	$-0.205672\pi$
$588$	−5.81202	+	3.17360i	−0.239684	+	0.130877i
$589$	−1.70333	+	3.72977i	−0.0701844	+	0.153682i
$590$	1.70174	+	1.76679i	0.0700595	+	0.0727375i
$591$	−16.0629	+	4.71650i	−0.660741	+	0.194011i
$592$	5.21849	+	6.97108i	0.214479	+	0.286510i
$593$	−22.9919	−	8.57553i	−0.944164	−	0.352155i	−0.170218	−	0.985406i	$-0.554447\pi$
$593$	−22.9919	−	8.57553i	−0.944164	−	0.352155i	−0.773946	+	0.633251i	$0.781720\pi$
$594$	0.00256508	+	0.0178405i	0.000105246	+	0.000732004i
$595$	2.50807	−	5.23010i	0.102821	−	0.214413i
$596$	2.67493	+	2.31784i	0.109569	+	0.0949423i
$597$	−13.7020	+	13.7020i	−0.560784	+	0.560784i
$598$	−5.30194	−	12.9342i	−0.216813	−	0.528920i
$599$		−	14.9670i		−	0.611535i	−0.952106	−	0.305768i	$-0.901087\pi$
$599$		−	14.9670i		−	0.611535i	0.952106	−	0.305768i	$-0.0989131\pi$
$600$	4.62284	−	1.90508i	0.188727	−	0.0777747i
$601$	−31.3632	+	20.1559i	−1.27933	+	0.822176i	−0.990805	−	0.135296i	$-0.956801\pi$
$601$	−31.3632	+	20.1559i	−1.27933	+	0.822176i	−0.288526	+	0.957472i	$0.593165\pi$
$602$	−3.73451	+	4.98872i	−0.152207	+	0.203325i
$603$	−0.921016	+	2.46934i	−0.0375067	+	0.100559i
$604$	8.70666	+	1.25183i	0.354269	+	0.0509362i
$605$	18.2831	+	16.4527i	0.743316	+	0.668897i
$606$	−15.2416	−	9.79517i	−0.619147	−	0.397902i
$607$	−29.9092	+	11.1555i	−1.21398	+	0.452790i	−0.873203	−	0.487356i	$-0.837961\pi$
$607$	−29.9092	+	11.1555i	−1.21398	+	0.452790i	−0.340773	+	0.940146i	$0.610689\pi$
$608$	−0.701585	−	1.28486i	−0.0284530	−	0.0521078i
$609$	0.712418	+	0.822174i	0.0288686	+	0.0333162i
$610$	−7.69118	−	14.7357i	−0.311407	−	0.596630i
$611$	5.71209	+	1.67722i	0.231086	+	0.0678531i
$612$	−1.47450	−	3.95328i	−0.0596031	−	0.159802i
$613$	−1.90106	−	8.73904i	−0.0767831	−	0.352966i	0.922686	−	0.385553i	$-0.125989\pi$
$613$	−1.90106	−	8.73904i	−0.0767831	−	0.352966i	−0.999469	+	0.0325864i	$0.989626\pi$
$614$	−3.25846	−	11.0973i	−0.131501	−	0.447850i
$615$	−7.99958	+	20.2781i	−0.322574	+	0.817691i
$616$	0.00460322	+	0.0100796i	0.000185469	+	0.000406120i
$617$	10.3043	+	7.71373i	0.414837	+	0.310543i	0.786232	−	0.617932i	$-0.212029\pi$
$617$	10.3043	+	7.71373i	0.414837	+	0.310543i	−0.371394	+	0.928475i	$0.621120\pi$
$618$	4.19944	+	0.913532i	0.168926	+	0.0367476i
$619$	13.4371	−	15.5072i	0.540082	−	0.623287i	−0.418462	−	0.908234i	$-0.637431\pi$
$619$	13.4371	−	15.5072i	0.540082	−	0.623287i	0.958543	+	0.284947i	$0.0919760\pi$
$620$	−5.33133	+	3.28664i	−0.214111	+	0.131995i
$621$	−3.25505	−	3.52203i	−0.130621	−	0.141334i
$622$	3.92750	+	3.92750i	0.157479	+	0.157479i
$623$	0.0739060	+	1.03334i	0.00296098	+	0.0413999i
$624$	1.57584	+	2.45206i	0.0630842	+	0.0981609i
$625$	−17.7413	+	17.6138i	−0.709653	+	0.704552i
$626$	7.01190	−	3.20223i	0.280252	−	0.127987i
$627$	−0.0211229	+	0.0158124i	−0.000843566	+	0.000631486i
$628$	−12.2503	−	6.68920i	−0.488842	−	0.266928i
$629$	−19.8640	+	30.9090i	−0.792030	+	1.23242i
$630$	0.170094	+	1.36416i	0.00677671	+	0.0543493i
$631$	−9.89244	+	33.6905i	−0.393812	+	1.34120i	0.489332	+	0.872097i	$0.337240\pi$
$631$	−9.89244	+	33.6905i	−0.393812	+	1.34120i	−0.883144	+	0.469102i	$0.844578\pi$
$632$	−0.225727	−	0.0161443i	−0.00897892	−	0.000642185i
$633$	−1.58305	−	0.113222i	−0.0629206	−	0.00450017i
$634$	7.27618	−	24.7804i	0.288974	−	0.984155i
$635$	−13.8183	−	10.7544i	−0.548364	−	0.426775i
$636$	0.630218	−	0.980639i	0.0249898	−	0.0388849i
$637$	16.9407	+	9.25031i	0.671214	+	0.366511i
$638$	−0.0255323	+	0.0191133i	−0.00101083	+	0.000756701i
$639$	12.2279	−	5.58429i	0.483727	−	0.220911i
$640$	0.201312	−	2.22699i	0.00795756	−	0.0880294i
$641$	−24.9721	−	38.8574i	−0.986340	−	1.53478i	−0.837878	−	0.545857i	$-0.816204\pi$
$641$	−24.9721	−	38.8574i	−0.986340	−	1.53478i	−0.148462	−	0.988918i	$-0.547432\pi$
$642$	−0.484138	−	6.76914i	−0.0191074	−	0.267156i
$643$	3.83532	+	3.83532i	0.151250	+	0.151250i	0.778676	−	0.627426i	$-0.215891\pi$
$643$	3.83532	+	3.83532i	0.151250	+	0.151250i	−0.627426	+	0.778676i	$0.715891\pi$
$644$	−2.53016	−	1.51381i	−0.0997022	−	0.0596525i
$645$	−11.8941	−	19.2937i	−0.468330	−	0.759688i
$646$	4.04492	−	4.66809i	0.159145	−	0.183663i
$647$	−35.3137	−	7.68203i	−1.38833	−	0.302012i	−0.544560	−	0.838722i	$-0.683303\pi$
$647$	−35.3137	−	7.68203i	−1.38833	−	0.302012i	−0.843767	+	0.536710i	$0.819667\pi$
$648$	0.800541	+	0.599278i	0.0314482	+	0.0235419i
$649$	−0.00821398	−	0.0179861i	−0.000322427	−	0.000706016i
$650$	−11.9562	−	8.33337i	−0.468962	−	0.326862i
$651$	−0.485135	−	1.65222i	−0.0190140	−	0.0647556i
$652$	−0.168718	−	0.775584i	−0.00660751	−	0.0303742i
$653$	15.7848	+	42.3207i	0.617707	+	1.65614i	0.747234	+	0.664561i	$0.231381\pi$
$653$	15.7848	+	42.3207i	0.617707	+	1.65614i	−0.129527	+	0.991576i	$0.541346\pi$
$654$	3.58357	+	1.05223i	0.140129	+	0.0411455i
$655$	−7.19037	+	22.8912i	−0.280951	+	0.894434i
$656$	6.38409	+	7.36764i	0.249257	+	0.287658i
$657$	6.19564	+	11.3465i	0.241715	+	0.442668i
$658$	1.17651	−	0.438814i	0.0458650	−	0.0171068i
$659$	−12.2866	−	7.89614i	−0.478619	−	0.307590i	0.278995	−	0.960293i	$-0.409999\pi$
$659$	−12.2866	−	7.89614i	−0.478619	−	0.307590i	−0.757614	+	0.652703i	$0.773635\pi$
$660$	−0.0402469	+	0.00212089i	−0.00156661	+	8.25553e-5i
$661$	−11.4725	−	1.64949i	−0.446227	−	0.0641578i	−0.0844615	−	0.996427i	$-0.526917\pi$
$661$	−11.4725	−	1.64949i	−0.446227	−	0.0641578i	−0.361766	+	0.932269i	$0.617826\pi$
$662$	4.08932	−	10.9639i	0.158936	−	0.426123i
$663$	−7.37011	+	9.84531i	−0.286231	+	0.382360i
$664$	−3.94790	+	2.53716i	−0.153208	+	0.0984610i
$665$	−1.63341	+	1.17562i	−0.0633409	+	0.0455885i
$666$		−	8.70796i		−	0.337427i
$667$	2.70955	−	8.04216i	0.104914	−	0.311394i
$668$	−9.89003	+	9.89003i	−0.382657	+	0.382657i
$669$	−12.9517	−	11.2227i	−0.500742	−	0.433896i
$670$	−5.31378	−	2.54820i	−0.205289	−	0.0984455i
$671$	0.0190678	+	0.132620i	0.000736106	+	0.00511973i
$672$	0.576030	+	0.214848i	0.0222208	+	0.00828795i
$673$	19.1478	+	25.5785i	0.738094	+	0.985978i	0.999783	+	0.0208260i	$0.00662960\pi$
$673$	19.1478	+	25.5785i	0.738094	+	0.985978i	−0.261689	+	0.965152i	$0.584279\pi$
$674$	0.495075	−	0.145367i	0.0190696	−	0.00559933i
$675$	−4.84245	−	1.24527i	−0.186386	−	0.0479304i
$676$	−1.87108	+	4.09710i	−0.0719647	+	0.157581i
$677$	19.5718	−	10.6870i	0.752204	−	0.410734i	−0.0569152	−	0.998379i	$-0.518126\pi$
$677$	19.5718	−	10.6870i	0.752204	−	0.410734i	0.809119	+	0.587645i	$0.199945\pi$
$678$	−0.418332	+	5.84904i	−0.0160659	+	0.224631i
$679$	−5.99575	+	5.19535i	−0.230096	+	0.199379i
$680$	9.10075	−	2.48785i	0.348998	−	0.0954046i
$681$	17.5565	+	8.01777i	0.672765	+	0.307241i
$682$	0.0493295	−	0.0107310i	0.00188893	−	0.000410911i
$683$	−7.71423	+	14.1276i	−0.295177	+	0.540576i	−0.982612	−	0.185670i	$-0.940555\pi$
$683$	−7.71423	+	14.1276i	−0.295177	+	0.540576i	0.687436	+	0.726245i	$0.258736\pi$
$684$	−0.208338	+	1.44903i	−0.00796602	+	0.0554049i
$685$	−2.25920	−	11.4116i	−0.0863198	−	0.436013i
$686$	8.28949	−	1.19185i	0.316494	−	0.0455050i
$687$	−5.43060	+	24.9641i	−0.207190	+	0.952439i
$688$	−10.1104	+	0.723111i	−0.385456	+	0.0275683i
$689$	−3.39771			−0.129442
$690$	8.49879	−	6.53992i	0.323543	−	0.248971i
$691$	5.17874			0.197009			0.0985043	−	0.995137i	$-0.468594\pi$
$691$	5.17874			0.197009			0.0985043	+	0.995137i	$0.468594\pi$
$692$	14.6515	−	1.04789i	0.556965	−	0.0398349i
$693$	0.00235544	−	0.0108278i	8.94756e−5	−	0.000411313i
$694$	6.08425	−	0.874784i	0.230955	−	0.0332063i
$695$	−0.387540	−	0.259452i	−0.0147002	−	0.00984157i
$696$	−0.251830	+	1.75151i	−0.00954558	+	0.0663910i
$697$	−19.7130	+	36.1017i	−0.746684	+	1.36745i
$698$	6.55718	−	1.42643i	0.248193	−	0.0539911i
$699$	−14.4577	−	6.60261i	−0.546841	−	0.249734i
$700$	−3.07220	+	0.104176i	−0.116118	+	0.00393749i
$701$	7.54152	−	6.53476i	0.284839	−	0.246815i	−0.500708	−	0.865616i	$-0.666927\pi$
$701$	7.54152	−	6.53476i	0.284839	−	0.246815i	0.785547	+	0.618802i	$0.212382\pi$
$702$	0.207937	−	2.90734i	0.00784808	−	0.109731i
$703$	11.1885	−	6.10938i	0.421982	−	0.230419i
$704$	−0.00748742	+	0.0163952i	−0.000282193	+	0.000617916i
$705$	−0.0856348	+	4.56623i	−0.00322519	+	0.171974i
$706$	−11.7291	+	3.44396i	−0.441429	+	0.129615i
$707$	6.67514	+	8.91694i	0.251044	+	0.335356i
$708$	−1.02787	−	0.383375i	−0.0386297	−	0.0144081i
$709$	−2.60866	−	18.1436i	−0.0979701	−	0.681397i	−0.978324	−	0.207080i	$-0.933604\pi$
$709$	−2.60866	−	18.1436i	−0.0979701	−	0.681397i	0.880354	−	0.474317i	$-0.157305\pi$
$710$	9.97451	+	28.3555i	0.374337	+	1.06416i
$711$	0.171028	+	0.148197i	0.00641407	+	0.00555782i
$712$	−1.19154	+	1.19154i	−0.0446547	+	0.0446547i
$713$	−9.18929	+	9.79757i	−0.344142	+	0.366922i
$714$			2.59401i			0.0970782i
$715$	0.0686234	+	0.0953457i	0.00256637	+	0.00356573i
$716$	−4.18812	+	2.69154i	−0.156518	+	0.100588i
$717$	−8.71577	+	11.6429i	−0.325496	+	0.434812i
$718$	−2.21409	+	5.93619i	−0.0826290	+	0.221537i
$719$	−46.7069	−	6.71544i	−1.74187	−	0.250444i	−0.803313	−	0.595557i	$-0.796931\pi$
$719$	−46.7069	−	6.71544i	−1.74187	−	0.250444i	−0.938561	+	0.345113i	$0.887840\pi$
$720$	−1.49574	+	1.66215i	−0.0557430	+	0.0619448i
$721$	−2.22273	−	1.42846i	−0.0827789	−	0.0531988i
$722$	15.7941	−	5.89089i	0.587795	−	0.219236i
$723$	1.03895	+	1.90270i	0.0386391	+	0.0707622i
$724$	−16.0865	−	18.5648i	−0.597849	−	0.689954i
$725$	−2.17261	−	8.57673i	−0.0806887	−	0.318532i
$726$	−10.5541	−	3.09897i	−0.391700	−	0.115013i
$727$	−2.03314	−	5.45106i	−0.0754050	−	0.202169i	0.893778	−	0.448509i	$-0.148045\pi$
$727$	−2.03314	−	5.45106i	−0.0754050	−	0.202169i	−0.969183	+	0.246340i	$0.920772\pi$
$728$	−0.380913	−	1.75103i	−0.0141176	−	0.0648974i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	−26.5157	+	11.5134i	−0.981390	+	0.426131i
$731$	−17.7665	−	38.9031i	−0.657116	−	1.43888i
$732$	5.95093	+	4.45481i	0.219953	+	0.164655i
$733$	−20.1360	−	4.38032i	−0.743741	−	0.161791i	−0.175300	−	0.984515i	$-0.556090\pi$
$733$	−20.1360	−	4.38032i	−0.743741	−	0.161791i	−0.568441	+	0.822724i	$0.692453\pi$
$734$	−18.5536	+	21.4121i	−0.684828	+	0.790333i
$735$	−3.41827	+	14.4074i	−0.126085	+	0.531423i
$736$	−0.834168	−	4.72273i	−0.0307478	−	0.174082i
$737$	0.0335892	+	0.0335892i	0.00123727	+	0.00123727i
$738$	−0.695470	−	9.72394i	−0.0256006	−	0.357943i
$739$	3.24449	+	5.04852i	0.119350	+	0.185713i	0.895788	−	0.444481i	$-0.146612\pi$
$739$	3.24449	+	5.04852i	0.119350	+	0.185713i	−0.776438	+	0.630194i	$0.782975\pi$
$740$	19.3925	+	1.75302i	0.712883	+	0.0644422i
$741$	3.88140	−	1.77258i	0.142587	−	0.0651173i
$742$	−0.573713	+	0.429476i	−0.0210617	+	0.0157666i
$743$	39.6133	+	21.6305i	1.45327	+	0.793546i	0.995431	−	0.0954887i	$-0.0304414\pi$
$743$	39.6133	+	21.6305i	1.45327	+	0.793546i	0.457840	+	0.889035i	$0.348623\pi$
$744$	1.51428	−	2.35626i	0.0555162	−	0.0863848i
$745$	7.85360	−	0.979251i	0.287734	−	0.0358770i
$746$	−5.72866	+	19.5100i	−0.209741	+	0.714313i
$747$	4.68092	+	0.334786i	0.171266	+	0.0122492i
$748$	−0.0758550	−	0.00542525i	−0.00277353	−	0.000198367i
$749$	−1.17546	+	4.00324i	−0.0429503	+	0.146275i
$750$	3.74804	−	10.5334i	0.136859	−	0.384625i
$751$	20.0032	−	31.1256i	0.729927	−	1.13579i	−0.255684	−	0.966760i	$-0.582301\pi$
$751$	20.0032	−	31.1256i	0.729927	−	1.13579i	0.985611	−	0.169028i	$-0.0540628\pi$
$752$	1.79261	+	0.978837i	0.0653696	+	0.0356945i
$753$	−19.3137	+	14.4581i	−0.703830	+	0.526881i
$754$	4.69166	−	2.14261i	0.170860	−	0.0780292i
$755$	15.1037	−	12.5994i	0.549678	−	0.458539i
$756$	−0.332382	−	0.517197i	−0.0120886	−	0.0188103i
$757$	−1.53158	−	21.4143i	−0.0556662	−	0.778315i	−0.946238	−	0.323472i	$-0.895150\pi$
$757$	−1.53158	−	21.4143i	−0.0556662	−	0.778315i	0.890572	−	0.454843i	$-0.150305\pi$
$758$	23.8620	+	23.8620i	0.866706	+	0.866706i
$759$	−0.0821161	+	0.0269961i	−0.00298063	+	0.000979897i
$760$	−3.18502	−	0.755673i	−0.115533	−	0.0274111i
$761$	−17.8697	+	20.6228i	−0.647777	+	0.747575i	−0.980730	−	0.195369i	$-0.937410\pi$
$761$	−17.8697	+	20.6228i	−0.647777	+	0.747575i	0.332952	+	0.942944i	$0.391955\pi$
$762$	7.65180	+	1.66455i	0.277195	+	0.0603001i
$763$	−1.83817	−	1.37604i	−0.0665464	−	0.0498160i
$764$	2.49522	+	5.46378i	0.0902740	+	0.197672i
$765$	−8.77644	−	3.46225i	−0.317313	−	0.125178i
$766$	−8.15844	−	27.7851i	−0.294776	−	1.00392i
$767$	0.679700	+	3.12453i	0.0245426	+	0.112820i
$768$	0.349464	+	0.936950i	0.0126102	+	0.0338093i
$769$	−22.3027	−	6.54866i	−0.804256	−	0.236151i	−0.146332	−	0.989235i	$-0.546747\pi$
$769$	−22.3027	−	6.54866i	−0.804256	−	0.236151i	−0.657924	+	0.753085i	$0.728565\pi$
$770$	0.0236391	+	0.00742529i	0.000851895	+	0.000267589i
$771$	10.1862	+	11.7555i	0.366848	+	0.423366i
$772$	−7.58553	−	13.8919i	−0.273009	−	0.499979i
$773$	−20.1141	+	7.50217i	−0.723454	+	0.269834i	−0.684097	−	0.729391i	$-0.739804\pi$
$773$	−20.1141	+	7.50217i	−0.723454	+	0.269834i	−0.0393569	+	0.999225i	$0.512531\pi$
$774$	8.52715	+	5.48006i	0.306502	+	0.196977i
$775$	−2.51139	+	13.7775i	−0.0902119	+	0.494901i
$776$	−12.7730	−	1.83648i	−0.458525	−	0.0659259i
$777$	−1.87089	+	5.01605i	−0.0671178	+	0.179950i
$778$	8.06282	−	10.7707i	0.289066	−	0.386147i
$779$	12.0059	−	7.71575i	0.430158	−	0.276445i
$780$	6.43275	+	1.04836i	0.230329	+	0.0375372i
$781$		−	0.242290i		−	0.00866982i
$782$	17.4403	−	10.2614i	0.623664	−	0.366946i
$783$	1.25124	−	1.25124i	0.0447158	−	0.0447158i
$784$	5.00460	+	4.33651i	0.178736	+	0.154875i
$785$	−29.4418	+	10.3566i	−1.05082	+	0.369645i
$786$	−1.52710	−	10.6212i	−0.0544698	−	0.378846i
$787$	−2.25095	−	0.839559i	−0.0802375	−	0.0299271i	0.309025	−	0.951054i	$-0.399997\pi$
$787$	−2.25095	−	0.839559i	−0.0802375	−	0.0299271i	−0.389262	+	0.921127i	$0.627270\pi$
$788$	10.0325	+	13.4019i	0.357395	+	0.477423i
$789$	2.70519	−	0.794315i	0.0963073	−	0.0282784i
$790$	−0.364463	+	0.351044i	−0.0129670	+	0.0124896i
$791$	1.49763	−	3.27935i	0.0532495	−	0.116600i
$792$	0.0158192	−	0.00863796i	0.000562112	−	0.000306937i
$793$	1.54573	−	21.6121i	0.0548904	−	0.767468i
$794$	10.5811	−	9.16857i	0.375509	−	0.325380i
$795$	−0.687328	−	2.51430i	−0.0243770	−	0.0891731i
$796$	17.6264	+	8.04970i	0.624751	+	0.285314i
$797$	−34.5549	+	7.51697i	−1.22400	+	0.266265i	−0.777709	−	0.628624i	$-0.783618\pi$
$797$	−34.5549	+	7.51697i	−1.22400	+	0.266265i	−0.446290	+	0.894889i	$0.647255\pi$
$798$	0.431330	−	0.789921i	0.0152689	−	0.0279629i
$799$	−1.22643	+	8.52998i	−0.0433878	+	0.301769i
$800$	−3.40048	−	3.66561i	−0.120225	−	0.129599i
$801$	1.66794	−	0.239813i	0.0589336	−	0.00847338i
$802$	1.21706	−	5.59475i	0.0429760	−	0.197557i
$803$	0.232416	−	0.0166228i	0.00820180	−	0.000586604i
$804$	2.63551			0.0929472
$805$	−6.30065	+	1.94124i	−0.222069	+	0.0684198i
$806$	−8.16396			−0.287563
$807$	−9.71866	+	0.695092i	−0.342113	+	0.0244684i
$808$	−3.85120	+	17.7037i	−0.135485	+	0.622813i
$809$	2.64414	−	0.380171i	0.0929632	−	0.0133661i	−0.0956762	−	0.995413i	$-0.530501\pi$
$809$	2.64414	−	0.380171i	0.0929632	−	0.0133661i	0.188639	+	0.982046i	$0.439592\pi$
$810$	2.19350	−	0.434257i	0.0770716	−	0.0152582i
$811$	4.27969	−	29.7659i	0.150280	−	1.04522i	−0.765469	−	0.643473i	$-0.777493\pi$
$811$	4.27969	−	29.7659i	0.150280	−	1.04522i	0.915749	−	0.401750i	$-0.131598\pi$
$812$	0.521371	−	0.954820i	0.0182965	−	0.0335076i
$813$	17.9154	−	3.89725i	0.628319	−	0.136683i
$814$	−0.142768	−	0.0652002i	−0.00500403	−	0.00228527i
$815$	−1.54150	−	0.879639i	−0.0539964	−	0.0308124i
$816$	−3.18874	+	2.76306i	−0.111628	+	0.0967265i
$817$	−1.05858	+	14.8009i	−0.0370351	+	0.517818i
$818$	−24.5856	+	13.4248i	−0.859616	+	0.469386i
$819$	−0.744415	+	1.63004i	−0.0260120	+	0.0569583i
$820$	21.7951	+	0.408744i	0.761118	+	0.0142740i
$821$	−35.3838	+	10.3896i	−1.23490	+	0.362600i	−0.833098	−	0.553126i	$-0.813435\pi$
$821$	−35.3838	+	10.3896i	−1.23490	+	0.362600i	−0.401804	+	0.915726i	$0.631617\pi$
$822$	3.11771	+	4.16478i	0.108743	+	0.145263i
$823$	−45.2670	−	16.8837i	−1.57791	−	0.588530i	−0.600452	−	0.799661i	$-0.705013\pi$
$823$	−45.2670	−	16.8837i	−1.57791	−	0.588530i	−0.977458	+	0.211131i	$0.932285\pi$
$824$	−0.611620	−	4.25391i	−0.0213068	−	0.148192i
$825$	−0.0566738	+	0.0700689i	−0.00197313	+	0.00243949i
$826$	0.509716	+	0.441671i	0.0177353	+	0.0153677i
$827$	−12.3795	+	12.3795i	−0.430479	+	0.430479i	−0.888791	−	0.458312i	$-0.848454\pi$
$827$	−12.3795	+	12.3795i	−0.430479	+	0.430479i	0.458312	+	0.888791i	$0.348454\pi$
$828$	−2.16244	+	4.28064i	−0.0751500	+	0.148762i
$829$		−	39.5634i		−	1.37409i	−0.726614	−	0.687046i	$-0.758907\pi$
$829$		−	39.5634i		−	1.37409i	0.726614	−	0.687046i	$-0.241093\pi$
$830$	−1.68789	+	10.3570i	−0.0585876	+	0.359495i
$831$	−3.63108	+	2.33355i	−0.125961	+	0.0809501i
$832$	1.74676	−	2.33339i	0.0605578	−	0.0808958i
$833$	−9.76418	+	26.1788i	−0.338309	+	0.907041i
$834$	0.206445	+	0.0296823i	0.00714860	+	0.00102781i
$835$	1.64581	+	31.2317i	0.0569556	+	1.08082i
$836$	0.0221971	+	0.0142652i	0.000767702	+	0.000493372i
$837$	−2.62430	+	0.978813i	−0.0907090	+	0.0338327i
$838$	2.30850	+	4.22769i	0.0797457	+	0.146043i
$839$	−31.1642	−	35.9654i	−1.07591	−	1.24166i	−0.968912	−	0.247405i	$-0.920422\pi$
$839$	−31.1642	−	35.9654i	−1.07591	−	1.24166i	−0.106996	−	0.994259i	$-0.534123\pi$
$840$	1.21870	−	0.636093i	0.0420493	−	0.0219473i
$841$	−24.8209	−	7.28808i	−0.855894	−	0.251313i
$842$	1.84292	+	4.94105i	0.0635111	+	0.170280i
$843$	−3.63414	−	16.7059i	−0.125166	−	0.575381i
$844$	0.447136	+	1.52281i	0.0153911	+	0.0524171i
$845$	4.01135	+	9.23823i	0.137995	+	0.317805i
$846$	−0.848460	−	1.85787i	−0.0291707	−	0.0638748i
$847$	5.41368	+	4.05263i	0.186016	+	0.139250i
$848$	−1.13905	−	0.247785i	−0.0391151	−	0.00850896i
$849$	−2.97900	+	3.43795i	−0.102239	+	0.117990i
$850$	9.47720	−	18.8480i	0.325065	−	0.646482i
$851$	41.1253	−	7.26390i	1.40976	−	0.249003i
$852$	−9.50540	−	9.50540i	−0.325650	−	0.325650i
$853$	−1.08934	−	15.2309i	−0.0372982	−	0.521496i	−0.981416	−	0.191890i	$-0.938538\pi$
$853$	−1.08934	−	15.2309i	−0.0372982	−	0.521496i	0.944118	−	0.329607i	$-0.106916\pi$
$854$	−2.47081	−	3.84465i	−0.0845493	−	0.131561i
$855$	2.09688	+	2.51366i	0.0717118	+	0.0859653i
$856$	−6.17315	+	2.81918i	−0.210994	+	0.0963577i
$857$	42.7002	−	31.9650i	1.45861	−	1.09190i	0.482181	−	0.876072i	$-0.339845\pi$
$857$	42.7002	−	31.9650i	1.45861	−	1.09190i	0.976431	−	0.215831i	$-0.0692461\pi$
$858$	−0.0461094	−	0.0251777i	−0.00157415	−	0.000859551i
$859$	21.0424	−	32.7425i	0.717956	−	1.11716i	−0.270065	−	0.962842i	$-0.587045\pi$
$859$	21.0424	−	32.7425i	0.717956	−	1.11716i	0.988021	−	0.154319i	$-0.0493183\pi$
$860$	−13.9207	+	17.8866i	−0.474690	+	0.609930i
$861$	−1.68856	+	5.75071i	−0.0575459	+	0.195984i
$862$	24.6503	+	1.76303i	0.839594	+	0.0600489i
$863$	−5.44437	−	0.389389i	−0.185329	−	0.0132550i	−0.0216336	−	0.999766i	$-0.506887\pi$
$863$	−5.44437	−	0.389389i	−0.185329	−	0.0132550i	−0.163695	+	0.986511i	$0.552341\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	20.1731	−	25.9204i	0.685905	−	0.881319i
$866$	21.8086	−	33.9349i	0.741087	−	1.15315i
$867$	−0.704432	−	0.384649i	−0.0239238	−	0.0130634i
$868$	−1.37851	+	1.03194i	−0.0467897	+	0.0350263i
$869$	0.00371028	−	0.00169443i	0.000125863	−	5.74795e-5i
$870$	2.53461	+	3.03839i	0.0859314	+	0.103011i
$871$	−4.15315	−	6.46242i	−0.140724	−	0.218971i
$872$	−0.266442	−	3.72534i	−0.00902285	−	0.126156i
$873$	9.12477	+	9.12477i	0.308827	+	0.308827i
$874$	−7.01714	+	0.224805i	−0.237358	+	0.00760414i
$875$	−4.42206	+	5.26229i	−0.149493	+	0.177898i
$876$	8.46591	−	9.77018i	0.286037	−	0.330104i
$877$	22.1822	+	4.82545i	0.749041	+	0.162944i	0.570852	−	0.821053i	$-0.306613\pi$
$877$	22.1822	+	4.82545i	0.749041	+	0.162944i	0.178188	+	0.983996i	$0.442976\pi$
$878$	−9.88388	−	7.39898i	−0.333565	−	0.249704i
$879$	−1.37400	−	3.00864i	−0.0463439	−	0.101479i
$880$	0.0160520	+	0.0369682i	0.000541114	+	0.00124620i
$881$	3.73253	+	12.7118i	0.125752	+	0.428273i	0.998169	−	0.0604903i	$-0.0192664\pi$
$881$	3.73253	+	12.7118i	0.125752	+	0.428273i	−0.872417	+	0.488763i	$0.837448\pi$
$882$	−1.40761	−	6.47070i	−0.0473968	−	0.217880i
$883$	7.14373	+	19.1531i	0.240406	+	0.644553i	0.999983	−	0.00586467i	$-0.00186679\pi$
$883$	7.14373	+	19.1531i	0.240406	+	0.644553i	−0.759577	+	0.650417i	$0.774594\pi$
$884$	11.8002	+	3.46484i	0.396882	+	0.116535i
$885$	−2.17465	+	1.13504i	−0.0731002	+	0.0381541i
$886$	8.28920	+	9.56625i	0.278481	+	0.321384i
$887$	21.0778	+	38.6011i	0.707723	+	1.29610i	0.945767	+	0.324844i	$0.105312\pi$
$887$	21.0778	+	38.6011i	0.707723	+	1.29610i	−0.238044	+	0.971254i	$0.576506\pi$
$888$	−8.15892	+	3.04312i	−0.273796	+	0.102120i
$889$	−4.05004	−	2.60280i	−0.135834	−	0.0872952i
$890$	0.198285	+	3.76275i	0.00664652	+	0.126128i
$891$	−0.0178405	−	0.00256508i	−0.000597679	−	8.59333e-5i
$892$	−5.98897	+	16.0570i	−0.200526	+	0.537630i
$893$	1.79183	−	2.39360i	0.0599612	−	0.0800988i
$894$	−2.97756	+	1.91356i	−0.0995846	+	0.0639991i
$895$	−1.79060	+	10.9872i	−0.0598530	+	0.367260i
$896$		−	0.614793i		−	0.0205388i
$897$	13.9040	−	1.44318i	0.464242	−	0.0481864i
$898$	6.27072	−	6.27072i	0.209257	−	0.209257i
$899$	−3.74569	−	3.24566i	−0.124926	−	0.108249i
$900$	0.525509	+	4.97231i	0.0175170	+	0.165744i
$901$	−0.699962	−	4.86834i	−0.0233191	−	0.162188i
$902$	−0.164633	−	0.0614049i	−0.00548168	−	0.00204456i
$903$	−3.73451	−	4.98872i	−0.124277	−	0.166014i
$904$	5.62645	−	1.65207i	0.187133	−	0.0549472i
$905$	−54.9187	−	1.02994i	−1.82556	−	0.0342364i
$906$	−3.65407	+	8.00130i	−0.121398	+	0.265825i
$907$	37.1180	−	20.2680i	1.23248	−	0.672987i	0.274991	−	0.961447i	$-0.411325\pi$
$907$	37.1180	−	20.2680i	1.23248	−	0.672987i	0.957492	+	0.288460i	$0.0931433\pi$
$908$	1.37689	−	19.2514i	0.0456937	−	0.638882i
$909$	13.6925	−	11.8646i	0.454150	−	0.393523i
$910$	−3.48022	−	1.98595i	−0.115368	−	0.0658336i
$911$	−4.06297	−	1.85550i	−0.134612	−	0.0614753i	0.346970	−	0.937876i	$-0.387211\pi$
$911$	−4.06297	−	1.85550i	−0.134612	−	0.0614753i	−0.481582	+	0.876401i	$0.659938\pi$
$912$	1.43047	−	0.311180i	0.0473676	−	0.0103042i
$913$	0.0405369	−	0.0742378i	0.00134158	−	0.00245691i
$914$	2.30240	−	16.0135i	0.0761565	−	0.529680i
$915$	16.3056	−	3.22811i	0.539048	−	0.106718i
$916$	25.2879	−	3.63585i	0.835535	−	0.120132i
$917$	−1.40229	+	6.44623i	−0.0463077	+	0.212873i
$918$	4.20856	−	0.301002i	0.138903	−	0.00993456i
$919$	−25.2599			−0.833246			−0.416623	−	0.909079i	$-0.636787\pi$
$919$	−25.2599			−0.833246			−0.416623	+	0.909079i	$0.636787\pi$
$920$	−9.09760	−	5.67747i	−0.299939	−	0.187181i
$921$	11.5658			0.381105
$922$	32.3129	−	2.31106i	1.06417	−	0.0761108i
$923$	−8.32879	+	38.2868i	−0.274145	+	1.26023i
$924$	−0.0109682	+	0.00157699i	−0.000360828	+	5.18792e-5i
$925$	31.9200	−	29.6113i	1.04952	−	0.973613i
$926$	−5.71651	+	39.7592i	−0.187856	+	1.30657i
$927$	−2.05965	+	3.77196i	−0.0676477	+	0.123887i
$928$	1.72909	−	0.376140i	0.0567600	−	0.0123474i
$929$	51.7362	+	23.6271i	1.69741	+	0.775181i	0.998181	+	0.0602821i	$0.0192000\pi$
$929$	51.7362	+	23.6271i	1.69741	+	0.775181i	0.699228	+	0.714899i	$0.253527\pi$
$930$	−1.65150	−	6.04133i	−0.0541549	−	0.198103i
$931$	7.32636	−	6.34832i	0.240112	−	0.208058i
$932$	−1.13387	+	15.8535i	−0.0371410	+	0.519299i
$933$	−4.87492	+	2.66191i	−0.159598	+	0.0871469i
$934$	11.0759	−	24.2528i	0.362415	−	0.793577i
$935$	−0.122477	+	0.117968i	−0.00400543	+	0.00385796i
$936$	−2.79670	+	0.821185i	−0.0914130	+	0.0268413i
$937$	15.4395	+	20.6248i	0.504388	+	0.673783i	0.978397	−	0.206737i	$-0.0662844\pi$
$937$	15.4395	+	20.6248i	0.504388	+	0.673783i	−0.474009	+	0.880520i	$0.657193\pi$
$938$	−1.51813	−	0.566234i	−0.0495688	−	0.0184882i
$939$	1.09703	+	7.63004i	0.0358004	+	0.248997i
$940$	4.30825	−	1.51550i	0.140520	−	0.0494301i
$941$	16.0788	+	13.9324i	0.524155	+	0.454183i	0.876302	−	0.481762i	$-0.160003\pi$
$941$	16.0788	+	13.9324i	0.524155	+	0.454183i	−0.352147	+	0.935945i	$0.614548\pi$
$942$	9.86956	−	9.86956i	0.321568	−	0.321568i
$943$	45.3434	−	11.3959i	1.47658	−	0.371102i
$944$			1.09704i			0.0357055i
$945$	−1.35682	−	0.221123i	−0.0441373	−	0.00719313i
$946$	0.153693	−	0.0987724i	0.00499699	−	0.00321137i
$947$	4.43353	−	5.92251i	0.144071	−	0.192456i	−0.722701	−	0.691160i	$-0.757100\pi$
$947$	4.43353	−	5.92251i	0.144071	−	0.192456i	0.866772	+	0.498705i	$0.166191\pi$
$948$	0.0790848	−	0.212035i	0.00256856	−	0.00688656i
$949$	−37.2980	−	5.36264i	−1.21074	−	0.174079i
$950$	−6.02001	+	4.16370i	−0.195315	+	0.135088i
$951$	21.7267	+	13.9629i	0.704535	+	0.452777i
$952$	2.43045	−	0.906512i	0.0787714	−	0.0293802i
$953$	5.11718	+	9.37141i	0.165762	+	0.303570i	0.947335	−	0.320243i	$-0.103765\pi$
$953$	5.11718	+	9.37141i	0.165762	+	0.303570i	−0.781574	+	0.623813i	$0.785583\pi$
$954$	0.763363	+	0.880968i	0.0247148	+	0.0285224i
$955$	12.8138	+	4.02496i	0.414646	+	0.130245i
$956$	13.9547	+	4.09746i	0.451326	+	0.132521i
$957$	−0.0111458	−	0.0298829i	−0.000360291	−	0.000965978i
$958$	−6.27371	−	28.8398i	−0.202694	−	0.931771i
$959$	−0.901103	−	3.06887i	−0.0290981	−	0.0990991i
$960$	2.08006	+	0.820572i	0.0671337	+	0.0264839i
$961$	−9.61893	−	21.0625i	−0.310288	−	0.679436i
$962$	20.3191	+	15.2107i	0.655114	+	0.490412i
$963$	6.63134	+	1.44256i	0.213692	+	0.0464858i
$964$	1.41966	−	1.63837i	0.0457241	−	0.0527684i
$965$	−34.4364	−	8.17033i	−1.10855	−	0.263012i
$966$	2.16532	−	2.00118i	0.0696680	−	0.0643869i
$967$	23.6985	+	23.6985i	0.762093	+	0.762093i	0.976700	−	0.214608i	$-0.0688473\pi$
$967$	23.6985	+	23.6985i	0.762093	+	0.762093i	−0.214608	+	0.976700i	$0.568847\pi$
$968$	0.784708	+	10.9716i	0.0252215	+	0.352642i
$969$	3.33941	+	5.19622i	0.107277	+	0.166927i
$970$	−22.1577	+	18.4838i	−0.711440	+	0.593480i
$971$	11.2676	−	5.14576i	0.361596	−	0.165135i	−0.226329	−	0.974051i	$-0.572672\pi$
$971$	11.2676	−	5.14576i	0.361596	−	0.165135i	0.587925	+	0.808916i	$0.299945\pi$
$972$	−0.800541	+	0.599278i	−0.0256774	+	0.0192218i
$973$	−0.112541	−	0.0614522i	−0.00360791	−	0.00197007i
$974$	−17.2377	+	26.8224i	−0.552331	+	0.859444i
$975$	11.3643	−	9.12415i	0.363948	−	0.292207i
$976$	2.09430	−	7.13252i	0.0670368	−	0.228306i
$977$	17.7384	+	1.26868i	0.567502	+	0.0405885i	0.352143	−	0.935946i	$-0.385453\pi$
$977$	17.7384	+	1.26868i	0.567502	+	0.0405885i	0.215359	+	0.976535i	$0.430908\pi$
$978$	0.791701	+	0.0566236i	0.0253158	+	0.00181062i
$979$	0.00855677	−	0.0291417i	0.000273475	−	0.000931372i
$980$	14.6935	−	1.83211i	0.469368	−	0.0585246i
$981$	−2.01922	+	3.14196i	−0.0644686	+	0.100315i
$982$	5.04123	+	2.75272i	0.160872	+	0.0878428i
$983$	48.7904	−	36.5240i	1.55617	−	1.16494i	0.637142	−	0.770747i	$-0.280117\pi$
$983$	48.7904	−	36.5240i	1.55617	−	1.16494i	0.919030	−	0.394188i	$-0.128974\pi$
$984$	−8.86780	+	4.04979i	−0.282695	+	0.129103i
$985$	37.2821	+	3.37018i	1.18791	+	0.107383i
$986$	4.03652	+	6.28095i	0.128549	+	0.200026i
$987$	0.0895790	+	1.25248i	0.00285133	+	0.0398668i
$988$	−3.01723	−	3.01723i	−0.0959908	−	0.0959908i
$989$	−18.7678	+	44.8427i	−0.596781	+	1.42591i
$990$	0.00930390	−	0.0392142i	0.000295697	−	0.00124631i
$991$	19.6274	−	22.6513i	0.623486	−	0.719541i	−0.352879	−	0.935669i	$-0.614797\pi$
$991$	19.6274	−	22.6513i	0.623486	−	0.719541i	0.976365	+	0.216128i	$0.0693427\pi$
$992$	−2.73689	−	0.595373i	−0.0868962	−	0.0189031i
$993$	9.36767	+	7.01255i	0.297274	+	0.222537i
$994$	3.43318	+	7.51762i	0.108894	+	0.238444i
$995$	39.7444	−	17.2575i	1.25998	−	0.547099i
$996$	−1.32214	−	4.50279i	−0.0418935	−	0.142676i
$997$	−4.41643	−	20.3020i	−0.139870	−	0.642971i	−0.992682	−	0.120754i	$-0.961469\pi$
$997$	−4.41643	−	20.3020i	−0.139870	−	0.642971i	0.852813	−	0.522217i	$-0.174895\pi$
$998$	11.7894	+	31.6086i	0.373187	+	1.00055i
$999$	8.35523	+	2.45332i	0.264348	+	0.0776195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.7.11	✓	240
5.3	odd	4	inner	690.2.w.a.283.6	yes	240
23.10	odd	22	inner	690.2.w.a.217.6	yes	240
115.33	even	44	inner	690.2.w.a.493.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.11	✓	240	1.1	even	1	trivial
690.2.w.a.217.6	yes	240	23.10	odd	22	inner
690.2.w.a.283.6	yes	240	5.3	odd	4	inner
690.2.w.a.493.11	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)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.24397 - 1.85810i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(0.294639 - 0.539591i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.24397 - 1.85810i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(0.294639 - 0.539591i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.10824 - 1.94211i) q^{10} +(-0.0136216 + 0.0118032i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(2.55823 - 1.39690i) q^{13} +(0.255394 - 0.559236i) q^{14} +(1.55121 + 1.61051i) q^{15} +(0.959493 - 0.281733i) q^{16} +(2.52854 + 3.37773i) q^{17} +(-0.936950 - 0.349464i) q^{18} +(-0.208338 - 1.44903i) q^{19} +(0.966872 - 2.01622i) q^{20} +(0.464630 + 0.402604i) q^{21} +(-0.0127449 + 0.0127449i) q^{22} +(0.868851 - 4.71647i) q^{23} +1.00000i q^{24} +(-1.90508 - 4.62284i) q^{25} +(2.45206 - 1.57584i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.214848 - 0.576030i) q^{28} +(1.75151 + 0.251830i) q^{29} +(1.66215 + 1.49574i) q^{30} +(-2.35626 - 1.51428i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-0.00863796 - 0.0158192i) q^{33} +(2.76306 + 3.18874i) q^{34} +(-0.636093 - 1.21870i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(3.04312 + 8.15892i) q^{37} +(-0.311180 - 1.43047i) q^{38} +(0.821185 + 2.79670i) q^{39} +(0.820572 - 2.08006i) q^{40} +(4.04979 + 8.86780i) q^{41} +(0.492167 + 0.368432i) q^{42} +(-9.90459 - 2.15461i) q^{43} +(-0.0118032 + 0.0136216i) q^{44} +(-1.90344 + 1.17343i) q^{45} +(0.530168 - 4.76644i) q^{46} +(1.44422 + 1.44422i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(3.58014 + 5.57081i) q^{49} +(-2.23002 - 4.47516i) q^{50} +(-3.83802 + 1.75277i) q^{51} +(2.33339 - 1.74676i) q^{52} +(-1.02310 - 0.558655i) q^{53} +(0.540641 - 0.841254i) q^{54} +(0.00498667 + 0.0399931i) q^{55} +(0.173207 - 0.589890i) q^{56} +(1.46020 + 0.104435i) q^{57} +(1.76502 + 0.126236i) q^{58} +(-0.309071 + 1.05260i) q^{59} +(1.76462 + 1.37335i) q^{60} +(4.01893 - 6.25357i) q^{61} +(-2.45829 - 1.34233i) q^{62} +(-0.492167 + 0.368432i) q^{63} +(0.909632 - 0.415415i) q^{64} +(0.586778 - 6.49115i) q^{65} +(-0.00974449 - 0.0151627i) q^{66} +(-0.188015 - 2.62879i) q^{67} +(2.98351 + 2.98351i) q^{68} +(4.42400 + 1.85155i) q^{69} +(-0.721414 - 1.17022i) q^{70} +(-8.80307 + 10.1593i) q^{71} +(-0.977147 - 0.212565i) q^{72} +(-10.3492 - 7.74734i) q^{73} +(3.61742 + 7.92104i) q^{74} +(4.92215 - 0.878890i) q^{75} +(-0.412436 - 1.40463i) q^{76} +(0.00235544 + 0.0108278i) q^{77} +(1.01861 + 2.73099i) q^{78} +(-0.217136 - 0.0637570i) q^{79} +(0.670092 - 2.13330i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.67209 + 8.55630i) q^{82} +(-4.39699 + 1.63999i) q^{83} +(0.517197 + 0.332382i) q^{84} +(9.42160 - 0.496488i) q^{85} +(-10.0331 - 1.44254i) q^{86} +(-0.618386 + 1.65796i) q^{87} +(-0.0108014 + 0.0144289i) q^{88} +(-1.41759 + 0.911027i) q^{89} +(-1.81488 + 1.30623i) q^{90} -1.79198i q^{91} +(0.188784 - 4.79211i) q^{92} +(1.98053 - 1.98053i) q^{93} +(1.54357 + 1.33751i) q^{94} +(-2.95160 - 1.41543i) q^{95} +(0.142315 + 0.989821i) q^{96} +(-12.0907 - 4.50962i) q^{97} +(3.96843 + 5.30121i) q^{98} +(0.0172939 - 0.00507793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more