LMFDB - Embedded newform 690.2.w.a.493.11

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			493.11
Character	$\chi$	$=$	690.493
Dual form			690.2.w.a.7.11

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

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

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
$5$	1.24397	+	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	0.927417	−	0.374030i	$-0.122024\pi$
$7$	0.294639	+	0.539591i	0.111363	+	0.203946i	−0.816053	+	0.577976i	$0.803843\pi$
$8$	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	0.652805	−	0.757526i	$-0.273592\pi$
$11$	−0.0136216	−	0.0118032i	−0.00410707	−	0.00355879i	−0.656912	+	0.753967i	$0.728138\pi$
$12$	−0.0713392	−	0.997452i	−0.0205938	−	0.287940i
$13$	2.55823	+	1.39690i	0.709525	+	0.387430i	0.793117	−	0.609070i	$-0.208457\pi$
$13$	2.55823	+	1.39690i	0.709525	+	0.387430i	−0.0835911	+	0.996500i	$0.526639\pi$
$14$	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	−0.381182	−	0.924500i	$-0.624483\pi$
$17$	2.52854	−	3.37773i	0.613261	−	0.819221i	0.994443	+	0.105279i	$0.0335736\pi$
$18$	−0.936950	+	0.349464i	−0.220841	+	0.0823695i
$19$	−0.208338	+	1.44903i	−0.0477961	+	0.332429i	0.951868	+	0.306509i	$0.0991608\pi$
$19$	−0.208338	+	1.44903i	−0.0477961	+	0.332429i	−0.999664	+	0.0259206i	$0.991748\pi$
$20$	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	0.0222430	−	0.999753i	$-0.492919\pi$
$29$	1.75151	−	0.251830i	0.325248	−	0.0467636i	0.303005	+	0.952989i	$0.402010\pi$
$30$	1.66215	−	1.49574i	0.303466	−	0.273084i
$31$	−2.35626	+	1.51428i	−0.423197	+	0.271972i	−0.734858	−	0.678221i	$-0.762751\pi$
$31$	−2.35626	+	1.51428i	−0.423197	+	0.271972i	0.311661	+	0.950194i	$0.399115\pi$
$32$	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	−0.404144	−	0.914696i	$-0.632430\pi$
$37$	3.04312	−	8.15892i	0.500286	−	1.34132i	0.904430	−	0.426623i	$-0.140297\pi$
$38$	−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	−0.273621	−	0.961838i	$-0.588221\pi$
$41$	4.04979	−	8.86780i	0.632471	−	1.38492i	0.906092	−	0.423081i	$-0.139051\pi$
$42$	0.492167	−	0.368432i	0.0759431	−	0.0568503i
$43$	−9.90459	+	2.15461i	−1.51044	+	0.328575i	−0.890102	−	0.455762i	$-0.849367\pi$
$43$	−9.90459	+	2.15461i	−1.51044	+	0.328575i	−0.620335	+	0.784337i	$0.713003\pi$
$44$	−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	−0.593887	−	0.804548i	$-0.702407\pi$
$47$	1.44422	−	1.44422i	0.210662	−	0.210662i	0.804548	+	0.593887i	$0.202407\pi$
$48$	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	−0.547977	−	0.836493i	$-0.684602\pi$
$53$	−1.02310	+	0.558655i	−0.140534	+	0.0767371i	0.407444	+	0.913230i	$0.366420\pi$
$54$	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	0.936925	−	0.349532i	$-0.113659\pi$
$59$	−0.309071	−	1.05260i	−0.0402376	−	0.137037i	−0.977162	+	0.212495i	$0.931841\pi$
$60$	1.76462	−	1.37335i	0.227812	−	0.177299i
$61$	4.01893	+	6.25357i	0.514571	+	0.800688i	0.997172	−	0.0751526i	$-0.0239444\pi$
$61$	4.01893	+	6.25357i	0.514571	+	0.800688i	−0.482601	+	0.875840i	$0.660308\pi$
$62$	−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	0.972957	+	0.230988i	$0.0741957\pi$
$67$	−0.188015	+	2.62879i	−0.0229697	+	0.321158i	−0.995926	+	0.0901705i	$0.971259\pi$
$68$	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	−0.978149	−	0.207905i	$-0.933336\pi$
$71$	−8.80307	−	10.1593i	−1.04473	−	1.20569i	−0.0665837	−	0.997781i	$-0.521210\pi$
$72$	−0.977147	+	0.212565i	−0.115158	+	0.0250511i
$73$	−10.3492	+	7.74734i	−1.21129	+	0.906758i	−0.997538	−	0.0701305i	$-0.977658\pi$
$73$	−10.3492	+	7.74734i	−1.21129	+	0.906758i	−0.213749	+	0.976889i	$0.568568\pi$
$74$	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	−0.293925	−	0.955829i	$-0.594961\pi$
$79$	−0.217136	+	0.0637570i	−0.0244297	+	0.00717322i	0.269495	+	0.963002i	$0.413143\pi$
$80$	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	0.0963582	−	0.995347i	$-0.469281\pi$
$83$	−4.39699	−	1.63999i	−0.482633	−	0.180013i	−0.578991	+	0.815334i	$0.696553\pi$
$84$	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	0.463348	−	0.886176i	$-0.346648\pi$
$89$	−1.41759	−	0.911027i	−0.150264	−	0.0965687i	−0.613612	+	0.789607i	$0.710284\pi$
$90$	−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	−0.877843	−	0.478948i	$-0.841018\pi$
$97$	−12.0907	+	4.50962i	−1.22763	+	0.457882i	−0.349786	+	0.936830i	$0.613746\pi$
$98$	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	−0.768329	−	0.640055i	$-0.778912\pi$
$101$	−7.52637	−	16.4804i	−0.748902	−	1.63987i	0.0194277	−	0.999811i	$-0.493816\pi$
$102$	−3.70320	−	2.02210i	−0.366672	−	0.200218i
$103$	0.306591	+	4.28670i	0.0302093	+	0.422381i	0.989943	+	0.141469i	$0.0451825\pi$
$103$	0.306591	+	4.28670i	0.0302093	+	0.422381i	−0.959733	+	0.280913i	$0.909363\pi$
$104$	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	−0.119735	−	0.992806i	$-0.538204\pi$
$107$	−6.63134	−	1.44256i	−0.641075	−	0.139457i	−0.521341	+	0.853349i	$0.674568\pi$
$108$	0.479249	+	0.877679i	0.0461158	+	0.0844547i
$109$	0.531525	+	3.69684i	0.0509109	+	0.354093i	0.999314	+	0.0370268i	$0.0117887\pi$
$109$	0.531525	+	3.69684i	0.0509109	+	0.354093i	−0.948403	+	0.317066i	$0.897302\pi$
$110$	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	0.343688	−	0.939084i	$-0.388324\pi$
$113$	5.84904	+	0.418332i	0.550232	+	0.0393533i	0.206544	+	0.978437i	$0.433778\pi$
$114$	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	0.960101	+	0.279653i	$0.0902195\pi$
$127$	0.558640	+	7.81080i	0.0495712	+	0.693097i	−0.910530	+	0.413443i	$0.864326\pi$
$128$	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	−0.200911	−	0.979610i	$-0.564390\pi$
$131$	−10.2958	−	3.02311i	−0.899545	−	0.264130i	−0.698634	+	0.715479i	$0.746208\pi$
$132$	−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	0.846570	−	0.532278i	$-0.178664\pi$
$137$	3.67869	+	3.67869i	0.314292	+	0.314292i	−0.532278	+	0.846570i	$0.678664\pi$
$138$	4.54481	−	1.53123i	0.386880	−	0.130347i
$139$			0.208568i			0.0176905i	0.999961	+	0.00884525i	$0.00281557\pi$
$139$			0.208568i			0.0176905i	−0.999961	+	0.00884525i	$0.997184\pi$
$140$	−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	−0.652822	−	0.757511i	$-0.726415\pi$
$149$	2.31784	−	2.67493i	0.189885	−	0.219139i	0.842707	+	0.538372i	$0.180961\pi$
$150$	4.84691	+	1.22779i	0.395748	+	0.100249i
$151$	8.43988	−	2.47817i	0.686828	−	0.201671i	0.0803447	−	0.996767i	$-0.474398\pi$
$151$	8.43988	−	2.47817i	0.686828	−	0.201671i	0.606483	+	0.795096i	$0.292580\pi$
$152$	−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	−0.943598	−	0.331094i	$-0.892582\pi$
$157$	−11.1737	+	8.36452i	−0.891757	+	0.667561i	0.0518404	+	0.998655i	$0.483491\pi$
$158$	−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	−0.999188	−	0.0402993i	$-0.987169\pi$
$163$	−0.0566236	+	0.791701i	−0.00443510	+	0.0620108i	0.994753	+	0.102310i	$0.0326234\pi$
$164$	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	0.0707254	−	0.997496i	$-0.477469\pi$
$167$	−11.1969	−	8.38187i	−0.866439	−	0.648608i	−0.937165	+	0.348888i	$0.886559\pi$
$168$	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	0.497784	−	0.867301i	$-0.334147\pi$
$173$	14.6515	−	1.04789i	1.11393	−	0.0796699i	0.616147	+	0.787631i	$0.288693\pi$
$174$	−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	0.238922	−	0.971039i	$-0.423206\pi$
$179$	−4.52854	−	2.06812i	−0.338479	−	0.154578i	−0.577401	+	0.816460i	$0.695933\pi$
$180$	−1.71707	−	1.43237i	−0.127983	−	0.106762i
$181$	−13.2807	+	20.6652i	−0.987146	+	1.53603i	−0.150264	+	0.988646i	$0.548012\pi$
$181$	−13.2807	+	20.6652i	−0.987146	+	1.53603i	−0.836882	+	0.547383i	$0.815624\pi$
$182$	−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	−0.875340	−	0.483508i	$-0.839363\pi$
$191$	1.69225	−	5.76327i	0.122447	−	0.417016i	0.997787	+	0.0664921i	$0.0211807\pi$
$192$	0.212565	−	0.977147i	0.0153406	−	0.0705195i
$193$	−5.53130	+	14.8300i	−0.398152	+	1.06749i	0.570985	+	0.820961i	$0.306562\pi$
$193$	−5.53130	+	14.8300i	−0.398152	+	1.06749i	−0.969136	+	0.246525i	$0.920711\pi$
$194$	−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	−0.418705	−	0.908122i	$-0.637516\pi$
$197$	8.02314	−	14.6933i	0.571625	−	1.04685i	0.990330	−	0.138731i	$-0.0443022\pi$
$198$	0.0168875	+	0.00629873i	0.00120015	+	0.000447631i
$199$	16.3014	−	10.4763i	1.15557	−	0.742642i	0.184833	−	0.982770i	$-0.440826\pi$
$199$	16.3014	−	10.4763i	1.15557	−	0.742642i	0.970741	+	0.240128i	$0.0771893\pi$
$200$	−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	−0.980569	−	0.196176i	$-0.937148\pi$
$211$	0.225867	−	1.57094i	0.0155493	−	0.108148i	0.996118	+	0.0880283i	$0.0280566\pi$
$212$	−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	−0.993807	−	0.111120i	$-0.964556\pi$
$223$	−8.21317	−	15.0413i	−0.549994	−	1.00724i	0.443813	−	0.896120i	$-0.353626\pi$
$224$	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	0.886548	+	0.462637i	$0.153097\pi$
$227$	4.10264	+	18.8595i	0.272302	+	1.25175i	−0.614246	+	0.789115i	$0.710540\pi$
$228$	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	−0.944940	−	0.327243i	$-0.893880\pi$
$233$	−3.37852	−	15.5308i	−0.221334	−	1.01746i	0.723606	−	0.690213i	$-0.242483\pi$
$234$	−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	0.0612836	−	0.998120i	$-0.480481\pi$
$239$	13.2295	−	6.04171i	0.855745	−	0.390806i	0.794461	+	0.607315i	$0.207753\pi$
$240$	1.94211	−	1.10824i	0.125363	−	0.0715368i
$241$	1.63837	+	1.41966i	0.105537	+	0.0914482i	0.706031	−	0.708181i	$-0.250484\pi$
$241$	1.63837	+	1.41966i	0.105537	+	0.0914482i	−0.600494	+	0.799629i	$0.705029\pi$
$242$	−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	0.150899	−	0.988549i	$-0.451783\pi$
$251$	18.2331	−	15.7990i	1.15086	−	0.997227i	0.999962	−	0.00867741i	$-0.00276214\pi$
$252$	−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	0.990756	−	0.135654i	$-0.0433135\pi$
$257$	9.32166	+	12.4523i	0.581469	+	0.776752i	−0.409287	+	0.912406i	$0.634223\pi$
$258$	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	−0.916016	−	0.401142i	$-0.868613\pi$
$263$	−1.35119	+	2.47452i	−0.0833181	+	0.152586i	0.832698	+	0.553728i	$0.186795\pi$
$264$	−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	−0.832503	−	0.554020i	$-0.813093\pi$
$269$	2.74506	−	9.34880i	0.167369	−	0.570007i	0.999872	−	0.0159863i	$-0.00508881\pi$
$270$	−0.890594	+	2.05106i	−0.0541998	+	0.124823i
$271$	−7.61637	+	16.6775i	−0.462662	+	1.01309i	0.524211	+	0.851588i	$0.324360\pi$
$271$	−7.61637	+	16.6775i	−0.462662	+	1.01309i	−0.986873	+	0.161499i	$0.948367\pi$
$272$	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	−0.609446	−	0.792827i	$-0.708608\pi$
$277$	3.05207	−	3.05207i	0.183381	−	0.183381i	0.792827	+	0.609446i	$0.208608\pi$
$278$	−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	−0.106523	−	0.994310i	$-0.533972\pi$
$281$	−15.5516	−	7.10218i	−0.927731	−	0.423680i	−0.821207	+	0.570630i	$0.806699\pi$
$282$	−1.63506	−	1.22399i	−0.0973662	−	0.0728874i
$283$	3.99262	−	2.18013i	0.237336	−	0.129595i	−0.356180	−	0.934417i	$-0.615921\pi$
$283$	3.99262	−	2.18013i	0.237336	−	0.129595i	0.593516	+	0.804822i	$0.297739\pi$
$284$	−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	0.519130	−	0.854695i	$-0.326256\pi$
$293$	−2.64782	−	1.98213i	−0.154687	−	0.115798i	−0.673818	+	0.738897i	$0.735347\pi$
$294$	−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	0.852235	+	0.523158i	$0.175246\pi$
$307$	−2.45848	+	11.3015i	−0.140313	+	0.645009i	−0.992549	+	0.121850i	$0.961117\pi$
$308$	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	−0.643193	−	0.765704i	$-0.722391\pi$
$311$	3.63731	−	4.19768i	0.206253	−	0.238029i	0.849446	+	0.527675i	$0.176936\pi$
$312$	1.39690	−	2.55823i	0.0790839	−	0.144831i
$313$	7.22248	+	2.69385i	0.408239	+	0.152265i	0.545190	−	0.838313i	$-0.316458\pi$
$313$	7.22248	+	2.69385i	0.408239	+	0.152265i	−0.136951	+	0.990578i	$0.543730\pi$
$314$	−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	0.898505	+	0.438963i	$0.144654\pi$
$317$	9.02545	+	24.1982i	0.506920	+	1.35910i	−0.391585	+	0.920142i	$0.628073\pi$
$318$	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	0.994905	−	0.100818i	$-0.0321460\pi$
$331$	4.86105	+	10.6442i	0.267188	+	0.585059i	−0.727717	+	0.685877i	$0.759419\pi$
$332$	−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	0.226277	−	0.974063i	$-0.427345\pi$
$337$	0.504184	+	0.109678i	0.0274646	+	0.00597457i	−0.198812	+	0.980038i	$0.563708\pi$
$338$	−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	0.234930	−	0.972012i	$-0.424514\pi$
$347$	6.13116	+	0.438509i	0.329138	+	0.0235404i	0.0942074	+	0.995553i	$0.469968\pi$
$348$	−0.376140	−	1.72909i	−0.0201632	−	0.0926887i
$349$	6.64224	+	0.955009i	0.355551	+	0.0511205i	0.317776	−	0.948166i	$-0.397064\pi$
$349$	6.64224	+	0.955009i	0.355551	+	0.0511205i	0.0377747	+	0.999286i	$0.487973\pi$
$350$	−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	−0.116878	−	0.993146i	$-0.537289\pi$
$353$	−11.9449	−	2.59845i	−0.635761	−	0.138301i	−0.518884	+	0.854845i	$0.673652\pi$
$354$	−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	0.827374	−	0.561651i	$-0.189834\pi$
$359$	−2.63193	−	5.76312i	−0.138908	−	0.304166i	−0.966282	+	0.257485i	$0.917106\pi$
$360$	−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	−0.998902	−	0.0468593i	$-0.985079\pi$
$367$	−20.0339	−	20.0339i	−1.04576	−	1.04576i	−0.0468593	−	0.998902i	$-0.514921\pi$
$368$	−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	−0.980583	−	0.196105i	$-0.937171\pi$
$373$	−7.10590	−	19.0517i	−0.367929	−	0.986457i	0.612653	−	0.790352i	$-0.290102\pi$
$374$	−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	0.190589	−	0.981670i	$-0.438960\pi$
$379$	22.0989	−	25.5035i	1.13514	−	1.31003i	0.944554	−	0.328355i	$-0.106494\pi$
$380$	−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	0.500137	+	0.865946i	$0.333283\pi$
$383$	−6.15549	+	28.2963i	−0.314531	+	1.44587i	−0.814668	+	0.579928i	$0.803081\pi$
$384$	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	0.933790	−	0.357822i	$-0.116481\pi$
$389$	8.81064	+	10.1680i	0.446717	+	0.515539i	−0.487072	+	0.873362i	$0.661935\pi$
$390$	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	0.842334	−	0.538955i	$-0.181181\pi$
$397$	11.2082	+	8.39036i	0.562524	+	0.421100i	−0.279811	+	0.960055i	$0.590272\pi$
$398$	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	0.989914	−	0.141668i	$-0.0452467\pi$
$401$	1.61309	+	5.49367i	0.0805537	+	0.274341i	−0.909360	+	0.416009i	$0.863428\pi$
$402$	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	−0.330303	−	0.943875i	$-0.607151\pi$
$409$	−25.4807	−	11.6366i	−1.25994	−	0.575395i	−0.929636	+	0.368480i	$0.879878\pi$
$410$	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	−0.854436	−	0.519557i	$-0.826097\pi$
$419$	2.00101	−	4.38161i	0.0977559	−	0.214056i	0.952192	+	0.305502i	$0.0988242\pi$
$420$	1.26098	+	0.547531i	0.0615294	+	0.0267168i
$421$	1.48573	−	5.05993i	0.0724101	−	0.246606i	−0.915332	−	0.402700i	$-0.868072\pi$
$421$	1.48573	−	5.05993i	0.0724101	−	0.246606i	0.987742	+	0.156094i	$0.0498901\pi$
$422$	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	0.474780	−	0.880105i	$-0.342528\pi$
$431$	24.4618	−	3.51707i	1.17828	−	0.169411i	0.703502	+	0.710693i	$0.251619\pi$
$432$	0.349464	+	0.936950i	0.0168136	+	0.0450790i
$433$	24.1739	+	32.2926i	1.16172	+	1.55188i	0.777793	+	0.628521i	$0.216339\pi$
$433$	24.1739	+	32.2926i	1.16172	+	1.55188i	0.383932	+	0.923361i	$0.374570\pi$
$434$	−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	−0.848461	−	0.529259i	$-0.822470\pi$
$439$	−9.33086	+	8.08524i	−0.445338	+	0.385887i	0.403123	+	0.915146i	$0.367925\pi$
$440$	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	−0.583289	−	0.812264i	$-0.698235\pi$
$443$	7.58563	−	10.1332i	0.360404	−	0.481444i	0.943694	+	0.330821i	$0.107326\pi$
$444$	−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	0.798508	−	0.601984i	$-0.205623\pi$
$449$	6.70209	+	5.80739i	0.316291	+	0.274068i	−0.482217	+	0.876052i	$0.660168\pi$
$450$	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	0.984925	+	0.172984i	$0.0553409\pi$
$457$	3.43892	+	15.8085i	0.160866	+	0.739489i	−0.824059	+	0.566504i	$0.808295\pi$
$458$	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	−0.549082	−	0.835769i	$-0.685022\pi$
$463$	−8.53834	−	39.2501i	−0.396810	−	1.82411i	0.152271	−	0.988339i	$-0.451341\pi$
$464$	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	0.986420	+	0.164240i	$0.0525172\pi$
$467$	12.7779	+	23.4009i	0.591289	+	1.08286i	−0.395131	+	0.918625i	$0.629301\pi$
$468$	−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	0.635009	+	0.772505i	$0.280996\pi$
$479$	−4.20032	+	29.2139i	−0.191917	+	1.33481i	−0.826926	+	0.562310i	$0.809913\pi$
$480$	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	−0.986474	−	0.163920i	$-0.947586\pi$
$487$	−19.1072	−	25.5243i	−0.865832	−	1.15662i	0.120642	−	0.992696i	$-0.461505\pi$
$488$	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	−0.427048	−	0.904229i	$-0.640446\pi$
$491$	4.83201	−	3.10534i	0.218066	−	0.140142i	0.645113	+	0.764087i	$0.276810\pi$
$492$	−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	−0.416307	−	0.909224i	$-0.636676\pi$
$499$	9.50443	−	32.3691i	0.425477	−	1.44904i	0.841783	−	0.539816i	$-0.181506\pi$
$500$	−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	−0.719507	−	0.694485i	$-0.755632\pi$
$503$	−24.3451	+	5.29595i	−1.08549	+	0.236135i	−0.365987	+	0.930620i	$0.619269\pi$
$504$	−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	0.402998	+	0.915201i	$0.367968\pi$
$509$	−13.4669	+	20.9549i	−0.596909	+	0.928809i	−0.999907	+	0.0136081i	$0.995668\pi$
$510$	−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	0.515881	−	0.856660i	$-0.327465\pi$
$521$	−10.9030	−	16.9654i	−0.477669	−	0.743268i	−0.993550	+	0.113392i	$0.963828\pi$
$522$	−1.55307	+	0.848043i	−0.0679762	+	0.0371178i
$523$	3.22347	+	2.41306i	0.140953	+	0.105516i	0.667427	−	0.744675i	$-0.267396\pi$
$523$	3.22347	+	2.41306i	0.140953	+	0.105516i	−0.526475	+	0.850191i	$0.676486\pi$
$524$	−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	−0.961846	−	0.273590i	$-0.911789\pi$
$541$	−12.8893	+	14.8751i	−0.554156	+	0.639530i	0.407690	+	0.913120i	$0.366334\pi$
$542$	−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	0.906361	+	0.422504i	$0.138849\pi$
$547$	11.6487	+	31.2313i	0.498060	+	1.33535i	−0.408300	+	0.912848i	$0.633878\pi$
$548$	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	0.502896	−	0.864347i	$-0.332268\pi$
$557$	34.1973	−	12.7549i	1.44899	−	0.540444i	0.946090	+	0.323903i	$0.104995\pi$
$558$	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	0.438748	+	0.898610i	$0.355422\pi$
$563$	3.14038	+	43.9083i	0.132351	+	1.85051i	−0.306396	+	0.951904i	$0.599123\pi$
$564$	−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	0.999674	+	0.0255338i	$0.00812854\pi$
$569$	1.13752	+	7.91166i	0.0476875	+	0.331674i	−0.951986	+	0.306140i	$0.900962\pi$
$570$	1.82108	+	2.72012i	0.0762766	+	0.113933i
$571$	−26.9843	−	3.87975i	−1.12926	−	0.162363i	−0.447739	−	0.894164i	$-0.647771\pi$
$571$	−26.9843	−	3.87975i	−1.12926	−	0.162363i	−0.681518	+	0.731802i	$0.738680\pi$
$572$	−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	0.476048	−	0.879419i	$-0.342069\pi$
$577$	19.7474	+	1.41236i	0.822097	+	0.0587975i	0.346048	+	0.938217i	$0.387523\pi$
$578$	−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	0.798416	+	0.602106i	$0.205672\pi$
$587$	2.27297	+	31.7802i	0.0938153	+	1.31171i	−0.704601	+	0.709604i	$0.748874\pi$
$588$	−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	−0.773946	−	0.633251i	$-0.781720\pi$
$593$	−22.9919	+	8.57553i	−0.944164	+	0.352155i	−0.170218	+	0.985406i	$0.554447\pi$
$594$	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	$0.0989131\pi$
$599$			14.9670i			0.611535i	−0.952106	+	0.305768i	$0.901087\pi$
$600$	4.62284	+	1.90508i	0.188727	+	0.0777747i
$601$	−31.3632	−	20.1559i	−1.27933	−	0.822176i	−0.288526	−	0.957472i	$-0.593165\pi$
$601$	−31.3632	−	20.1559i	−1.27933	−	0.822176i	−0.990805	+	0.135296i	$0.956801\pi$
$602$	−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	−0.340773	−	0.940146i	$-0.610689\pi$
$607$	−29.9092	−	11.1555i	−1.21398	−	0.452790i	−0.873203	+	0.487356i	$0.837961\pi$
$608$	−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	−0.999469	−	0.0325864i	$-0.989626\pi$
$613$	−1.90106	+	8.73904i	−0.0767831	+	0.352966i	0.922686	+	0.385553i	$0.125989\pi$
$614$	−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	−0.371394	−	0.928475i	$-0.621120\pi$
$617$	10.3043	−	7.71373i	0.414837	−	0.310543i	0.786232	+	0.617932i	$0.212029\pi$
$618$	4.19944	−	0.913532i	0.168926	−	0.0367476i
$619$	13.4371	+	15.5072i	0.540082	+	0.623287i	0.958543	−	0.284947i	$-0.0919760\pi$
$619$	13.4371	+	15.5072i	0.540082	+	0.623287i	−0.418462	+	0.908234i	$0.637431\pi$
$620$	−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	−0.883144	−	0.469102i	$-0.844578\pi$
$631$	−9.89244	−	33.6905i	−0.393812	−	1.34120i	0.489332	−	0.872097i	$-0.337240\pi$
$632$	−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	−0.148462	+	0.988918i	$0.547432\pi$
$641$	−24.9721	+	38.8574i	−0.986340	+	1.53478i	−0.837878	+	0.545857i	$0.816204\pi$
$642$	−0.484138	+	6.76914i	−0.0191074	+	0.267156i
$643$	3.83532	−	3.83532i	0.151250	−	0.151250i	−0.627426	−	0.778676i	$-0.715891\pi$
$643$	3.83532	−	3.83532i	0.151250	−	0.151250i	0.778676	+	0.627426i	$0.215891\pi$
$644$	−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	−0.843767	−	0.536710i	$-0.819667\pi$
$647$	−35.3137	+	7.68203i	−1.38833	+	0.302012i	−0.544560	+	0.838722i	$0.683303\pi$
$648$	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	−0.129527	−	0.991576i	$-0.541346\pi$
$653$	15.7848	−	42.3207i	0.617707	−	1.65614i	0.747234	−	0.664561i	$-0.231381\pi$
$654$	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	−0.757614	−	0.652703i	$-0.773635\pi$
$659$	−12.2866	+	7.89614i	−0.478619	+	0.307590i	0.278995	+	0.960293i	$0.409999\pi$
$660$	−0.0402469	−	0.00212089i	−0.00156661	−	8.25553e-5i
$661$	−11.4725	+	1.64949i	−0.446227	+	0.0641578i	−0.361766	−	0.932269i	$-0.617826\pi$
$661$	−11.4725	+	1.64949i	−0.446227	+	0.0641578i	−0.0844615	+	0.996427i	$0.526917\pi$
$662$	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	−0.261689	−	0.965152i	$-0.584279\pi$
$673$	19.1478	−	25.5785i	0.738094	−	0.985978i	0.999783	−	0.0208260i	$-0.00662960\pi$
$674$	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	0.809119	−	0.587645i	$-0.199945\pi$
$677$	19.5718	+	10.6870i	0.752204	+	0.410734i	−0.0569152	+	0.998379i	$0.518126\pi$
$678$	−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	0.687436	−	0.726245i	$-0.258736\pi$
$683$	−7.71423	−	14.1276i	−0.295177	−	0.540576i	−0.982612	+	0.185670i	$0.940555\pi$
$684$	−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	0.785547	−	0.618802i	$-0.212382\pi$
$701$	7.54152	+	6.53476i	0.284839	+	0.246815i	−0.500708	+	0.865616i	$0.666927\pi$
$702$	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	0.880354	+	0.474317i	$0.157305\pi$
$709$	−2.60866	+	18.1436i	−0.0979701	+	0.681397i	−0.978324	+	0.207080i	$0.933604\pi$
$710$	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	−0.938561	−	0.345113i	$-0.887840\pi$
$719$	−46.7069	+	6.71544i	−1.74187	+	0.250444i	−0.803313	+	0.595557i	$0.796931\pi$
$720$	−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	−0.969183	−	0.246340i	$-0.920772\pi$
$727$	−2.03314	+	5.45106i	−0.0754050	+	0.202169i	0.893778	+	0.448509i	$0.148045\pi$
$728$	−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	−0.568441	−	0.822724i	$-0.692453\pi$
$733$	−20.1360	+	4.38032i	−0.743741	+	0.161791i	−0.175300	+	0.984515i	$0.556090\pi$
$734$	−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	−0.776438	−	0.630194i	$-0.782975\pi$
$739$	3.24449	−	5.04852i	0.119350	−	0.185713i	0.895788	+	0.444481i	$0.146612\pi$
$740$	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	0.457840	−	0.889035i	$-0.348623\pi$
$743$	39.6133	−	21.6305i	1.45327	−	0.793546i	0.995431	+	0.0954887i	$0.0304414\pi$
$744$	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	0.985611	+	0.169028i	$0.0540628\pi$
$751$	20.0032	+	31.1256i	0.729927	+	1.13579i	−0.255684	+	0.966760i	$0.582301\pi$
$752$	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	0.890572	+	0.454843i	$0.150305\pi$
$757$	−1.53158	+	21.4143i	−0.0556662	+	0.778315i	−0.946238	+	0.323472i	$0.895150\pi$
$758$	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	0.332952	−	0.942944i	$-0.391955\pi$
$761$	−17.8697	−	20.6228i	−0.647777	−	0.747575i	−0.980730	+	0.195369i	$0.937410\pi$
$762$	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	−0.657924	−	0.753085i	$-0.728565\pi$
$769$	−22.3027	+	6.54866i	−0.804256	+	0.236151i	−0.146332	+	0.989235i	$0.546747\pi$
$770$	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	−0.0393569	−	0.999225i	$-0.512531\pi$
$773$	−20.1141	−	7.50217i	−0.723454	−	0.269834i	−0.684097	+	0.729391i	$0.739804\pi$
$774$	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	−0.389262	−	0.921127i	$-0.627270\pi$
$787$	−2.25095	+	0.839559i	−0.0802375	+	0.0299271i	0.309025	+	0.951054i	$0.399997\pi$
$788$	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	−0.446290	−	0.894889i	$-0.647255\pi$
$797$	−34.5549	−	7.51697i	−1.22400	−	0.266265i	−0.777709	+	0.628624i	$0.783618\pi$
$798$	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	0.188639	−	0.982046i	$-0.439592\pi$
$809$	2.64414	+	0.380171i	0.0929632	+	0.0133661i	−0.0956762	+	0.995413i	$0.530501\pi$
$810$	2.19350	+	0.434257i	0.0770716	+	0.0152582i
$811$	4.27969	+	29.7659i	0.150280	+	1.04522i	0.915749	+	0.401750i	$0.131598\pi$
$811$	4.27969	+	29.7659i	0.150280	+	1.04522i	−0.765469	+	0.643473i	$0.777493\pi$
$812$	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	−0.401804	−	0.915726i	$-0.631617\pi$
$821$	−35.3838	−	10.3896i	−1.23490	−	0.362600i	−0.833098	+	0.553126i	$0.813435\pi$
$822$	3.11771	−	4.16478i	0.108743	−	0.145263i
$823$	−45.2670	+	16.8837i	−1.57791	+	0.588530i	−0.977458	−	0.211131i	$-0.932285\pi$
$823$	−45.2670	+	16.8837i	−1.57791	+	0.588530i	−0.600452	+	0.799661i	$0.705013\pi$
$824$	−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	0.458312	−	0.888791i	$-0.348454\pi$
$827$	−12.3795	−	12.3795i	−0.430479	−	0.430479i	−0.888791	+	0.458312i	$0.848454\pi$
$828$	−2.16244	−	4.28064i	−0.0751500	−	0.148762i
$829$			39.5634i			1.37409i	0.726614	+	0.687046i	$0.241093\pi$
$829$			39.5634i			1.37409i	−0.726614	+	0.687046i	$0.758907\pi$
$830$	−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	−0.106996	+	0.994259i	$0.534123\pi$
$839$	−31.1642	+	35.9654i	−1.07591	+	1.24166i	−0.968912	+	0.247405i	$0.920422\pi$
$840$	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	0.944118	+	0.329607i	$0.106916\pi$
$853$	−1.08934	+	15.2309i	−0.0372982	+	0.521496i	−0.981416	+	0.191890i	$0.938538\pi$
$854$	−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	0.976431	+	0.215831i	$0.0692461\pi$
$857$	42.7002	+	31.9650i	1.45861	+	1.09190i	0.482181	+	0.876072i	$0.339845\pi$
$858$	−0.0461094	+	0.0251777i	−0.00157415	+	0.000859551i
$859$	21.0424	+	32.7425i	0.717956	+	1.11716i	0.988021	+	0.154319i	$0.0493183\pi$
$859$	21.0424	+	32.7425i	0.717956	+	1.11716i	−0.270065	+	0.962842i	$0.587045\pi$
$860$	−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	−0.163695	−	0.986511i	$-0.552341\pi$
$863$	−5.44437	+	0.389389i	−0.185329	+	0.0132550i	−0.0216336	+	0.999766i	$0.506887\pi$
$864$	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	0.178188	−	0.983996i	$-0.442976\pi$
$877$	22.1822	−	4.82545i	0.749041	−	0.162944i	0.570852	+	0.821053i	$0.306613\pi$
$878$	−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	−0.872417	−	0.488763i	$-0.837448\pi$
$881$	3.73253	−	12.7118i	0.125752	−	0.428273i	0.998169	+	0.0604903i	$0.0192664\pi$
$882$	−1.40761	+	6.47070i	−0.0473968	+	0.217880i
$883$	7.14373	−	19.1531i	0.240406	−	0.644553i	−0.759577	−	0.650417i	$-0.774594\pi$
$883$	7.14373	−	19.1531i	0.240406	−	0.644553i	0.999983	+	0.00586467i	$0.00186679\pi$
$884$	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	−0.238044	−	0.971254i	$-0.576506\pi$
$887$	21.0778	−	38.6011i	0.707723	−	1.29610i	0.945767	−	0.324844i	$-0.105312\pi$
$888$	−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	0.957492	−	0.288460i	$-0.0931433\pi$
$907$	37.1180	+	20.2680i	1.23248	+	0.672987i	0.274991	+	0.961447i	$0.411325\pi$
$908$	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	−0.481582	−	0.876401i	$-0.659938\pi$
$911$	−4.06297	+	1.85550i	−0.134612	+	0.0614753i	0.346970	+	0.937876i	$0.387211\pi$
$912$	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	0.699228	−	0.714899i	$-0.253527\pi$
$929$	51.7362	−	23.6271i	1.69741	−	0.775181i	0.998181	−	0.0602821i	$-0.0192000\pi$
$930$	−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	−0.474009	−	0.880520i	$-0.657193\pi$
$937$	15.4395	−	20.6248i	0.504388	−	0.673783i	0.978397	+	0.206737i	$0.0662844\pi$
$938$	−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	−0.352147	−	0.935945i	$-0.614548\pi$
$941$	16.0788	−	13.9324i	0.524155	−	0.454183i	0.876302	+	0.481762i	$0.160003\pi$
$942$	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	0.866772	−	0.498705i	$-0.166191\pi$
$947$	4.43353	+	5.92251i	0.144071	+	0.192456i	−0.722701	+	0.691160i	$0.757100\pi$
$948$	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	−0.781574	−	0.623813i	$-0.785583\pi$
$953$	5.11718	−	9.37141i	0.165762	−	0.303570i	0.947335	+	0.320243i	$0.103765\pi$
$954$	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	−0.214608	−	0.976700i	$-0.568847\pi$
$967$	23.6985	−	23.6985i	0.762093	−	0.762093i	0.976700	+	0.214608i	$0.0688473\pi$
$968$	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	0.587925	−	0.808916i	$-0.299945\pi$
$971$	11.2676	+	5.14576i	0.361596	+	0.165135i	−0.226329	+	0.974051i	$0.572672\pi$
$972$	−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	0.215359	−	0.976535i	$-0.430908\pi$
$977$	17.7384	−	1.26868i	0.567502	−	0.0405885i	0.352143	+	0.935946i	$0.385453\pi$
$978$	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	0.919030	+	0.394188i	$0.128974\pi$
$983$	48.7904	+	36.5240i	1.55617	+	1.16494i	0.637142	+	0.770747i	$0.280117\pi$
$984$	−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	0.976365	−	0.216128i	$-0.0693427\pi$
$991$	19.6274	+	22.6513i	0.623486	+	0.719541i	−0.352879	+	0.935669i	$0.614797\pi$
$992$	−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	0.852813	+	0.522217i	$0.174895\pi$
$997$	−4.41643	+	20.3020i	−0.139870	+	0.642971i	−0.992682	+	0.120754i	$0.961469\pi$
$998$	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.493.11	yes	240
5.2	odd	4	inner	690.2.w.a.217.6	yes	240
23.7	odd	22	inner	690.2.w.a.283.6	yes	240
115.7	even	44	inner	690.2.w.a.7.11	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.11	✓	240	115.7	even	44	inner
690.2.w.a.217.6	yes	240	5.2	odd	4	inner
690.2.w.a.283.6	yes	240	23.7	odd	22	inner
690.2.w.a.493.11	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)

\(f(q)\)	\(=\)	\(q+(0.997452 + 0.0713392i) q^{2} +(-0.212565 - 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.24397 + 1.85810i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.294639 + 0.539591i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(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

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