LMFDB - Embedded newform 690.2.w.b.7.2

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			7.2
Character	$\chi$	$=$	690.7
Dual form			690.2.w.b.493.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.89440 - 1.18796i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.244741 - 0.448210i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.89440 - 1.18796i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.244741 - 0.448210i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.97432 + 1.04979i) q^{10} +(-1.95533 + 1.69430i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(3.92447 - 2.14292i) q^{13} +(-0.212143 + 0.464528i) q^{14} +(1.56350 - 1.59859i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-0.573049 - 0.765504i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.787868 + 5.47974i) q^{19} +(-2.04418 - 0.906269i) q^{20} +(0.385944 + 0.334422i) q^{21} +(1.82947 - 1.82947i) q^{22} +(-0.985708 + 4.69344i) q^{23} -1.00000i q^{24} +(2.17749 + 4.50095i) q^{25} +(-3.76159 + 2.41743i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.178463 - 0.478478i) q^{28} +(9.80565 + 1.40984i) q^{29} +(-1.44547 + 1.70605i) q^{30} +(-1.87207 - 1.20311i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-1.23994 - 2.27079i) q^{33} +(0.626199 + 0.722672i) q^{34} +(-0.996094 + 0.558345i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.327944 + 0.879252i) q^{37} +(-1.17678 - 5.40957i) q^{38} +(1.25974 + 4.29029i) q^{39} +(2.10363 + 0.758130i) q^{40} +(3.97618 + 8.70662i) q^{41} +(-0.408818 - 0.306037i) q^{42} +(-0.920644 - 0.200274i) q^{43} +(-1.69430 + 1.95533i) q^{44} +(1.22971 + 1.86757i) q^{45} +(0.648370 - 4.75180i) q^{46} +(-5.32050 - 5.32050i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(3.64349 + 5.66938i) q^{49} +(-2.49304 - 4.33414i) q^{50} +(0.869820 - 0.397233i) q^{51} +(3.57955 - 2.67962i) q^{52} +(-2.72917 - 1.49024i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(5.71693 - 0.886826i) q^{55} +(-0.143874 + 0.489991i) q^{56} +(-5.52198 - 0.394940i) q^{57} +(-9.88124 - 0.706721i) q^{58} +(-3.62935 + 12.3604i) q^{59} +(1.32008 - 1.80482i) q^{60} +(-2.08617 + 3.24614i) q^{61} +(1.95313 + 1.06649i) q^{62} +(-0.408818 + 0.306037i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-9.98021 - 0.602571i) q^{65} +(1.39878 + 2.17655i) q^{66} +(0.439415 + 6.14383i) q^{67} +(-0.676159 - 0.676159i) q^{68} +(-4.37665 - 1.96084i) q^{69} +(0.953724 - 0.627983i) q^{70} +(-5.17574 + 5.97313i) q^{71} +(0.977147 + 0.212565i) q^{72} +(2.38663 + 1.78661i) q^{73} +(-0.389834 - 0.853616i) q^{74} +(-4.86095 + 1.17098i) q^{75} +(1.55970 + 5.31184i) q^{76} +(0.280853 + 1.29106i) q^{77} +(-1.56260 - 4.18949i) q^{78} +(13.7008 + 4.02292i) q^{79} +(-2.15235 - 0.606127i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-4.58717 - 8.40078i) q^{82} +(14.0560 - 5.24261i) q^{83} +(0.429608 + 0.276093i) q^{84} +(0.176194 + 2.13093i) q^{85} +(0.932586 + 0.134086i) q^{86} +(-3.46196 + 9.28188i) q^{87} +(1.55049 - 2.07121i) q^{88} +(1.23189 - 0.791689i) q^{89} +(-1.35981 - 1.77509i) q^{90} -2.28345i q^{91} +(-0.307729 + 4.78595i) q^{92} +(1.57355 - 1.57355i) q^{93} +(5.68650 + 4.92738i) q^{94} +(5.01719 - 11.3168i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-6.31543 - 2.35553i) q^{97} +(-4.03866 - 5.39502i) q^{98} +(2.48246 - 0.728917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$3$	−0.212565	+	0.977147i	−0.122725	+	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−1.89440	−	1.18796i	−0.847201	−	0.531273i
$5$	−1.89440	−	1.18796i	−0.847201	−	0.531273i
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	0.244741	−	0.448210i	0.0925035	−	0.169407i	−0.827330	−	0.561716i	$-0.810142\pi$
$7$	0.244741	−	0.448210i	0.0925035	−	0.169407i	0.919834	+	0.392308i	$0.128323\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	1.97432	+	1.04979i	0.624335	+	0.331973i
$11$	−1.95533	+	1.69430i	−0.589553	+	0.510850i	−0.897769	−	0.440466i	$-0.854813\pi$
$11$	−1.95533	+	1.69430i	−0.589553	+	0.510850i	0.308217	+	0.951316i	$0.400268\pi$
$12$	−0.0713392	+	0.997452i	−0.0205938	+	0.287940i
$13$	3.92447	−	2.14292i	1.08845	−	0.594339i	0.168234	−	0.985747i	$-0.446194\pi$
$13$	3.92447	−	2.14292i	1.08845	−	0.594339i	0.920217	+	0.391408i	$0.128012\pi$
$14$	−0.212143	+	0.464528i	−0.0566975	+	0.124150i
$15$	1.56350	−	1.59859i	0.403693	−	0.412753i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−0.573049	−	0.765504i	−0.138985	−	0.185662i	0.725648	−	0.688066i	$-0.241540\pi$
$17$	−0.573049	−	0.765504i	−0.138985	−	0.185662i	−0.864633	+	0.502404i	$0.832449\pi$
$18$	0.936950	+	0.349464i	0.220841	+	0.0823695i
$19$	0.787868	+	5.47974i	0.180749	+	1.25714i	0.854997	+	0.518633i	$0.173559\pi$
$19$	0.787868	+	5.47974i	0.180749	+	1.25714i	−0.674248	+	0.738505i	$0.735532\pi$
$20$	−2.04418	−	0.906269i	−0.457093	−	0.202648i
$21$	0.385944	+	0.334422i	0.0842198	+	0.0729769i
$22$	1.82947	−	1.82947i	0.390045	−	0.390045i
$23$	−0.985708	+	4.69344i	−0.205534	+	0.978650i
$23$	−0.985708	+	4.69344i	−0.205534	+	0.978650i
$24$		−	1.00000i		−	0.204124i
$25$	2.17749	+	4.50095i	0.435499	+	0.900189i
$26$	−3.76159	+	2.41743i	−0.737709	+	0.474097i
$27$	0.599278	−	0.800541i	0.115331	−	0.154064i
$28$	0.178463	−	0.478478i	0.0337264	−	0.0904239i
$29$	9.80565	+	1.40984i	1.82086	+	0.261801i	0.966276	−	0.257507i	$-0.0829011\pi$
$29$	9.80565	+	1.40984i	1.82086	+	0.261801i	0.854587	+	0.519308i	$0.173810\pi$
$30$	−1.44547	+	1.70605i	−0.263906	+	0.311481i
$31$	−1.87207	−	1.20311i	−0.336234	−	0.216084i	0.361618	−	0.932326i	$-0.382224\pi$
$31$	−1.87207	−	1.20311i	−0.336234	−	0.216084i	−0.697852	+	0.716242i	$0.745861\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	−1.23994	−	2.27079i	−0.215847	−	0.395294i
$34$	0.626199	+	0.722672i	0.107392	+	0.123937i
$35$	−0.996094	+	0.558345i	−0.168371	+	0.0943776i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	0.327944	+	0.879252i	0.0539137	+	0.144548i	0.961115	−	0.276149i	$-0.0890583\pi$
$37$	0.327944	+	0.879252i	0.0539137	+	0.144548i	−0.907201	+	0.420697i	$0.861786\pi$
$38$	−1.17678	−	5.40957i	−0.190899	−	0.877548i
$39$	1.25974	+	4.29029i	0.201720	+	0.686996i
$40$	2.10363	+	0.758130i	0.332612	+	0.119871i
$41$	3.97618	+	8.70662i	0.620975	+	1.35974i	0.914808	+	0.403888i	$0.132342\pi$
$41$	3.97618	+	8.70662i	0.620975	+	1.35974i	−0.293834	+	0.955857i	$0.594931\pi$
$42$	−0.408818	−	0.306037i	−0.0630819	−	0.0472225i
$43$	−0.920644	−	0.200274i	−0.140397	−	0.0305415i	0.141818	−	0.989893i	$-0.454705\pi$
$43$	−0.920644	−	0.200274i	−0.140397	−	0.0305415i	−0.282214	+	0.959351i	$0.591069\pi$
$44$	−1.69430	+	1.95533i	−0.255425	+	0.294776i
$45$	1.22971	+	1.86757i	0.183314	+	0.278401i
$46$	0.648370	−	4.75180i	0.0955970	−	0.700615i
$47$	−5.32050	−	5.32050i	−0.776074	−	0.776074i	0.203086	−	0.979161i	$-0.434903\pi$
$47$	−5.32050	−	5.32050i	−0.776074	−	0.776074i	−0.979161	+	0.203086i	$0.934903\pi$
$48$	0.0713392	+	0.997452i	0.0102969	+	0.143970i
$49$	3.64349	+	5.66938i	0.520499	+	0.809912i
$50$	−2.49304	−	4.33414i	−0.352569	−	0.612940i
$51$	0.869820	−	0.397233i	0.121799	−	0.0556238i
$52$	3.57955	−	2.67962i	0.496394	−	0.371596i
$53$	−2.72917	−	1.49024i	−0.374881	−	0.204700i	0.280752	−	0.959780i	$-0.409416\pi$
$53$	−2.72917	−	1.49024i	−0.374881	−	0.204700i	−0.655633	+	0.755080i	$0.727598\pi$
$54$	−0.540641	+	0.841254i	−0.0735719	+	0.114480i
$55$	5.71693	−	0.886826i	0.770871	−	0.119580i
$56$	−0.143874	+	0.489991i	−0.0192260	+	0.0654777i
$57$	−5.52198	−	0.394940i	−0.731405	−	0.0523111i
$58$	−9.88124	−	0.706721i	−1.29747	−	0.0927970i
$59$	−3.62935	+	12.3604i	−0.472501	+	1.60919i	0.286486	+	0.958084i	$0.407513\pi$
$59$	−3.62935	+	12.3604i	−0.472501	+	1.60919i	−0.758987	+	0.651106i	$0.774305\pi$
$60$	1.32008	−	1.80482i	0.170422	−	0.233002i
$61$	−2.08617	+	3.24614i	−0.267106	+	0.415625i	−0.948735	−	0.316073i	$-0.897636\pi$
$61$	−2.08617	+	3.24614i	−0.267106	+	0.415625i	0.681629	+	0.731698i	$0.261272\pi$
$62$	1.95313	+	1.06649i	0.248048	+	0.135444i
$63$	−0.408818	+	0.306037i	−0.0515062	+	0.0385570i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−9.98021	−	0.602571i	−1.23789	−	0.0747397i
$66$	1.39878	+	2.17655i	0.172178	+	0.267914i
$67$	0.439415	+	6.14383i	0.0536831	+	0.750588i	0.950998	+	0.309197i	$0.100060\pi$
$67$	0.439415	+	6.14383i	0.0536831	+	0.750588i	−0.897315	+	0.441391i	$0.854485\pi$
$68$	−0.676159	−	0.676159i	−0.0819963	−	0.0819963i
$69$	−4.37665	−	1.96084i	−0.526887	−	0.236058i
$70$	0.953724	−	0.627983i	0.113992	−	0.0750583i
$71$	−5.17574	+	5.97313i	−0.614248	+	0.708880i	−0.974604	−	0.223935i	$-0.928110\pi$
$71$	−5.17574	+	5.97313i	−0.614248	+	0.708880i	0.360356	+	0.932815i	$0.382655\pi$
$72$	0.977147	+	0.212565i	0.115158	+	0.0250511i
$73$	2.38663	+	1.78661i	0.279334	+	0.209107i	0.729754	−	0.683710i	$-0.239635\pi$
$73$	2.38663	+	1.78661i	0.279334	+	0.209107i	−0.450420	+	0.892817i	$0.648726\pi$
$74$	−0.389834	−	0.853616i	−0.0453172	−	0.0992309i
$75$	−4.86095	+	1.17098i	−0.561294	+	0.135214i
$76$	1.55970	+	5.31184i	0.178909	+	0.609310i
$77$	0.280853	+	1.29106i	0.0320062	+	0.147130i
$78$	−1.56260	−	4.18949i	−0.176929	−	0.474366i
$79$	13.7008	+	4.02292i	1.54146	+	0.452613i	0.938535	−	0.345185i	$-0.112184\pi$
$79$	13.7008	+	4.02292i	1.54146	+	0.452613i	0.602925	+	0.797798i	$0.294002\pi$
$80$	−2.15235	−	0.606127i	−0.240640	−	0.0677671i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	−4.58717	−	8.40078i	−0.506568	−	0.927710i
$83$	14.0560	−	5.24261i	1.54284	−	0.575451i	0.573081	−	0.819499i	$-0.305748\pi$
$83$	14.0560	−	5.24261i	1.54284	−	0.575451i	0.969763	+	0.244048i	$0.0784754\pi$
$84$	0.429608	+	0.276093i	0.0468741	+	0.0301242i
$85$	0.176194	+	2.13093i	0.0191109	+	0.231132i
$86$	0.932586	+	0.134086i	0.100563	+	0.0144588i
$87$	−3.46196	+	9.28188i	−0.371161	+	0.995122i
$88$	1.55049	−	2.07121i	0.165283	−	0.220792i
$89$	1.23189	−	0.791689i	0.130580	−	0.0839189i	−0.473720	−	0.880676i	$-0.657089\pi$
$89$	1.23189	−	0.791689i	0.130580	−	0.0839189i	0.604300	+	0.796757i	$0.293453\pi$
$90$	−1.35981	−	1.77509i	−0.143336	−	0.187110i
$91$		−	2.28345i		−	0.239370i
$92$	−0.307729	+	4.78595i	−0.0320830	+	0.498970i
$93$	1.57355	−	1.57355i	0.163169	−	0.163169i
$94$	5.68650	+	4.92738i	0.586518	+	0.508221i
$95$	5.01719	−	11.3168i	0.514752	−	1.16108i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	−6.31543	−	2.35553i	−0.641235	−	0.239168i	0.00774950	−	0.999970i	$-0.497533\pi$
$97$	−6.31543	−	2.35553i	−0.641235	−	0.239168i	−0.648984	+	0.760802i	$0.724806\pi$
$98$	−4.03866	−	5.39502i	−0.407966	−	0.544979i
$99$	2.48246	−	0.728917i	0.249497	−	0.0732589i
$100$	2.79588	+	4.14524i	0.279588	+	0.414524i
$101$	5.92946	−	12.9837i	0.590004	−	1.29193i	−0.345436	−	0.938442i	$-0.612269\pi$
$101$	5.92946	−	12.9837i	0.590004	−	1.29193i	0.935440	−	0.353485i	$-0.115004\pi$
$102$	−0.839265	+	0.458274i	−0.0830997	+	0.0453758i
$103$	0.0631063	−	0.882342i	0.00621805	−	0.0869397i	−0.993395	−	0.114741i	$-0.963396\pi$
$103$	0.0631063	−	0.882342i	0.00621805	−	0.0869397i	0.999613	+	0.0278015i	$0.00885064\pi$
$104$	−3.37927	+	2.92815i	−0.331365	+	0.287129i
$105$	−0.333850	−	1.09201i	−0.0325805	−	0.106570i
$106$	2.82853	+	1.29175i	0.274731	+	0.125466i
$107$	−13.4013	+	2.91527i	−1.29555	+	0.281830i	−0.806920	−	0.590661i	$-0.798867\pi$
$107$	−13.4013	+	2.91527i	−1.29555	+	0.281830i	−0.488631	+	0.872491i	$0.662503\pi$
$108$	0.479249	−	0.877679i	0.0461158	−	0.0844547i
$109$	0.195647	−	1.36075i	0.0187396	−	0.130337i	−0.978304	−	0.207174i	$-0.933573\pi$
$109$	0.195647	−	1.36075i	0.0187396	−	0.130337i	0.997044	+	0.0768377i	$0.0244823\pi$
$110$	−5.63910	+	1.29241i	−0.537667	+	0.123226i
$111$	−0.928868	+	0.133551i	−0.0881642	+	0.0126761i
$112$	0.108552	−	0.499006i	0.0102572	−	0.0471516i
$113$	18.2410	−	1.30462i	1.71597	−	0.122729i	0.821602	−	0.570061i	$-0.193081\pi$
$113$	18.2410	−	1.30462i	1.71597	−	0.122729i	0.894368	+	0.447333i	$0.147626\pi$
$114$	5.53609			0.518502
$115$	7.44295	−	7.72026i	0.694059	−	0.719918i
$116$	9.90648			0.919794
$117$	−4.46002	+	0.318987i	−0.412329	+	0.0294904i
$118$	2.73832	−	12.5878i	0.252083	−	1.15881i
$119$	−0.483355	+	0.0694960i	−0.0443091	+	0.00637069i
$120$	−1.18796	+	1.89440i	−0.108446	+	0.172934i
$121$	−0.612815	+	4.26222i	−0.0557105	+	0.387475i
$122$	1.84927	−	3.38669i	0.167425	−	0.306617i
$123$	−9.35284	+	2.03459i	−0.843317	+	0.183452i
$124$	−2.02423	−	0.924437i	−0.181782	−	0.0830169i
$125$	1.22192	−	11.1134i	0.109291	−	0.994010i
$126$	0.385944	−	0.334422i	0.0343826	−	0.0297927i
$127$	−0.707018	+	9.88540i	−0.0627377	+	0.877187i	0.864481	+	0.502666i	$0.167647\pi$
$127$	−0.707018	+	9.88540i	−0.0627377	+	0.877187i	−0.927218	+	0.374521i	$0.877807\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	0.391394	−	0.857033i	0.0344603	−	0.0754576i
$130$	9.99777	−	0.110945i	0.876862	−	0.00973050i
$131$	−4.72860	+	1.38844i	−0.413140	+	0.121309i	−0.481696	−	0.876338i	$-0.659979\pi$
$131$	−4.72860	+	1.38844i	−0.413140	+	0.121309i	0.0685560	+	0.997647i	$0.478161\pi$
$132$	−1.55049	−	2.07121i	−0.134953	−	0.180276i
$133$	2.64890	+	0.987988i	0.229689	+	0.0856694i
$134$	−0.876591	−	6.09683i	−0.0757260	−	0.526686i
$135$	−2.08628	+	0.804625i	−0.179559	+	0.0692511i
$136$	0.722672	+	0.626199i	0.0619687	+	0.0536961i
$137$	−5.79056	+	5.79056i	−0.494721	+	0.494721i	−0.909790	−	0.415069i	$-0.863757\pi$
$137$	−5.79056	+	5.79056i	−0.494721	+	0.494721i	0.415069	+	0.909790i	$0.363757\pi$
$138$	4.50539	+	1.64362i	0.383524	+	0.139914i
$139$		−	8.01319i		−	0.679670i	−0.940485	−	0.339835i	$-0.889629\pi$
$139$		−	8.01319i		−	0.679670i	0.940485	−	0.339835i	$-0.110371\pi$
$140$	−0.906494	+	0.694421i	−0.0766128	+	0.0586893i
$141$	6.32986	−	4.06795i	0.533070	−	0.342584i
$142$	4.73644	−	6.32714i	0.397473	−	0.530962i
$143$	−4.04286	+	10.8393i	−0.338081	+	0.906430i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	−16.9010	−	14.3195i	−1.40355	−	1.18917i
$146$	−2.50801	−	1.61180i	−0.207564	−	0.133393i
$147$	−6.31430	+	2.35511i	−0.520795	+	0.194246i
$148$	0.449737	+	0.823631i	0.0369681	+	0.0677021i
$149$	−12.3890	−	14.2977i	−1.01495	−	1.17132i	−0.985139	−	0.171760i	$-0.945055\pi$
$149$	−12.3890	−	14.2977i	−1.01495	−	1.17132i	−0.0298115	−	0.999556i	$-0.509491\pi$
$150$	4.76502	−	1.51478i	0.389063	−	0.123681i
$151$	1.99256	+	0.585069i	0.162152	+	0.0476122i	0.361801	−	0.932255i	$-0.382162\pi$
$151$	1.99256	+	0.585069i	0.162152	+	0.0476122i	−0.199649	+	0.979868i	$0.563980\pi$
$152$	−1.93466	−	5.18704i	−0.156922	−	0.420724i
$153$	0.203262	+	0.934380i	0.0164327	+	0.0755401i
$154$	−0.372241	−	1.26774i	−0.0299960	−	0.102157i
$155$	2.11720	+	4.50311i	0.170058	+	0.361699i
$156$	1.85749	+	4.06734i	0.148718	+	0.325648i
$157$	−6.77069	−	5.06848i	−0.540360	−	0.404509i	0.293936	−	0.955825i	$-0.405035\pi$
$157$	−6.77069	−	5.06848i	−0.540360	−	0.404509i	−0.834296	+	0.551317i	$0.814126\pi$
$158$	−13.9529	−	3.03526i	−1.11003	−	0.241472i
$159$	2.03631	−	2.35003i	0.161490	−	0.186369i
$160$	2.19011	+	0.451036i	0.173143	+	0.0356575i
$161$	1.86240	+	1.59048i	0.146778	+	0.125348i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−1.07253	−	14.9960i	−0.0840073	−	1.17458i	−0.848232	−	0.529625i	$-0.822333\pi$
$163$	−1.07253	−	14.9960i	−0.0840073	−	1.17458i	0.764224	−	0.644951i	$-0.223122\pi$
$164$	5.17479	+	8.05213i	0.404083	+	0.628765i
$165$	−0.348662	+	5.77479i	−0.0271433	+	0.449567i
$166$	−13.6462	+	6.23199i	−1.05915	+	0.483696i
$167$	15.2464	−	11.4133i	1.17980	−	0.883191i	0.184776	−	0.982781i	$-0.440844\pi$
$167$	15.2464	−	11.4133i	1.17980	−	0.883191i	0.995029	+	0.0995898i	$0.0317531\pi$
$168$	−0.448210	−	0.244741i	−0.0345802	−	0.0188822i
$169$	3.78099	−	5.88334i	0.290846	−	0.452565i
$170$	−0.327764	−	2.11293i	−0.0251383	−	0.162054i
$171$	1.55970	−	5.31184i	0.119273	−	0.406206i
$172$	−0.939775	−	0.0672140i	−0.0716572	−	0.00512502i
$173$	20.9356	+	1.49734i	1.59170	+	0.113841i	0.838855	−	0.544356i	$-0.183226\pi$
$173$	20.9356	+	1.49734i	1.59170	+	0.113841i	0.752846	+	0.658196i	$0.228680\pi$
$174$	2.79098	−	9.50520i	0.211584	−	0.720588i
$175$	2.55029	+	0.125593i	0.192784	+	0.00949395i
$176$	−1.39878	+	2.17655i	−0.105437	+	0.164063i
$177$	−11.3065	−	6.17380i	−0.849847	−	0.464051i
$178$	−1.17228	+	0.877555i	−0.0878658	+	0.0657755i
$179$	−4.54563	+	2.07592i	−0.339757	+	0.155162i	−0.577985	−	0.816048i	$-0.696161\pi$
$179$	−4.54563	+	2.07592i	−0.339757	+	0.155162i	0.238228	+	0.971209i	$0.423433\pi$
$180$	1.48297	+	1.67355i	0.110534	+	0.124739i
$181$	−6.78877	−	10.5635i	−0.504605	−	0.785181i	0.491727	−	0.870749i	$-0.336366\pi$
$181$	−6.78877	−	10.5635i	−0.504605	−	0.785181i	−0.996332	+	0.0855684i	$0.972729\pi$
$182$	0.162899	+	2.27763i	0.0120749	+	0.168829i
$183$	−2.72851	−	2.72851i	−0.201697	−	0.201697i
$184$	−0.0344808	−	4.79571i	−0.00254196	−	0.353544i
$185$	0.423261	−	2.05524i	0.0311188	−	0.151104i
$186$	−1.45728	+	1.68180i	−0.106853	+	0.123315i
$187$	2.41749	+	0.525893i	0.176784	+	0.0384571i
$188$	−6.02353	−	4.50916i	−0.439311	−	0.328864i
$189$	−0.212143	−	0.464528i	−0.0154311	−	0.0337894i
$190$	−4.19707	+	11.6459i	−0.304488	+	0.844879i
$191$	3.78068	+	12.8758i	0.273560	+	0.931660i	0.975606	+	0.219529i	$0.0704519\pi$
$191$	3.78068	+	12.8758i	0.273560	+	0.931660i	−0.702046	+	0.712132i	$0.747730\pi$
$192$	0.212565	+	0.977147i	0.0153406	+	0.0705195i
$193$	−1.68287	−	4.51194i	−0.121135	−	0.324776i	0.862203	−	0.506564i	$-0.169084\pi$
$193$	−1.68287	−	4.51194i	−0.121135	−	0.324776i	−0.983338	+	0.181787i	$0.941812\pi$
$194$	6.46738	+	1.89899i	0.464331	+	0.136340i
$195$	2.71025	−	9.62405i	0.194085	−	0.689192i
$196$	4.41324	+	5.09315i	0.315232	+	0.363797i
$197$	−6.49645	−	11.8974i	−0.462853	−	0.847651i	−0.999991	−	0.00415738i	$-0.998677\pi$
$197$	−6.49645	−	11.8974i	−0.462853	−	0.847651i	0.537139	−	0.843494i	$-0.319505\pi$
$198$	−2.42414	+	0.904157i	−0.172276	+	0.0642556i
$199$	−6.41867	−	4.12503i	−0.455008	−	0.292416i	0.292992	−	0.956115i	$-0.405349\pi$
$199$	−6.41867	−	4.12503i	−0.455008	−	0.292416i	−0.748000	+	0.663699i	$0.768985\pi$
$200$	−3.08448	−	3.93523i	−0.218105	−	0.278263i
$201$	−6.09683	−	0.876591i	−0.430037	−	0.0618300i
$202$	−4.98811	+	13.3736i	−0.350962	+	0.940966i
$203$	3.03175	−	4.04995i	0.212787	−	0.284250i
$204$	0.804434	−	0.516978i	0.0563217	−	0.0361957i
$205$	2.81066	−	21.2174i	0.196305	−	1.48188i
$206$			0.884596i			0.0616327i
$207$	2.84636	−	3.85983i	0.197835	−	0.268276i
$208$	3.16177	−	3.16177i	0.219229	−	0.219229i
$209$	−10.8249	−	9.37979i	−0.748771	−	0.648814i
$210$	0.410903	+	1.06542i	0.0283550	+	0.0735207i
$211$	−2.24097	−	15.5863i	−0.154275	−	1.07300i	−0.908950	−	0.416905i	$-0.863115\pi$
$211$	−2.24097	−	15.5863i	−0.154275	−	1.07300i	0.754676	−	0.656098i	$-0.227794\pi$
$212$	−2.91348	−	1.08667i	−0.200099	−	0.0746329i
$213$	−4.73644	−	6.32714i	−0.324535	−	0.433529i
$214$	13.1592	−	3.86388i	0.899542	−	0.264129i
$215$	1.50615	+	1.47309i	0.102719	+	0.100464i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	−0.997417	+	0.544631i	−0.0677091	+	0.0369720i
$218$	−0.0980733	+	1.37124i	−0.00664236	+	0.0928724i
$219$	−2.25309	+	1.95232i	−0.152250	+	0.131925i
$220$	5.53253	−	1.69140i	0.373003	−	0.114034i
$221$	−3.88932	−	1.77619i	−0.261624	−	0.119480i
$222$	0.916974	−	0.199475i	0.0615432	−	0.0133879i
$223$	−5.62381	+	10.2992i	−0.376598	+	0.689687i	−0.995394	−	0.0958638i	$-0.969439\pi$
$223$	−5.62381	+	10.2992i	−0.376598	+	0.689687i	0.618797	+	0.785551i	$0.287620\pi$
$224$	−0.0726768	+	0.505479i	−0.00485593	+	0.0337737i
$225$	−0.110956	−	4.99877i	−0.00739706	−	0.333251i
$226$	−18.1015	+	2.60260i	−1.20409	+	0.173122i
$227$	−2.91698	+	13.4091i	−0.193607	+	0.889996i	0.773135	+	0.634241i	$0.218687\pi$
$227$	−2.91698	+	13.4091i	−0.193607	+	0.889996i	−0.966742	+	0.255754i	$0.917676\pi$
$228$	−5.52198	+	0.394940i	−0.365702	+	0.0261555i
$229$	8.33186			0.550585			0.275292	−	0.961361i	$-0.411225\pi$
$229$	8.33186			0.550585			0.275292	+	0.961361i	$0.411225\pi$
$230$	−6.87323	+	8.23157i	−0.453207	+	0.542773i
$231$	−1.32126			−0.0869323
$232$	−9.88124	+	0.706721i	−0.648735	+	0.0463985i
$233$	0.940730	−	4.32447i	0.0616293	−	0.283305i	−0.936010	−	0.351973i	$-0.885511\pi$
$233$	0.940730	−	4.32447i	0.0616293	−	0.283305i	0.997640	+	0.0686673i	$0.0218747\pi$
$234$	4.42590	−	0.636349i	0.289330	−	0.0415994i
$235$	3.75860	+	16.3997i	0.245184	+	1.06980i
$236$	−1.83333	+	12.7511i	−0.119340	+	0.830027i
$237$	−6.84329	+	12.5326i	−0.444520	+	0.814077i
$238$	0.477166	−	0.103801i	0.0309301	−	0.00672842i
$239$	22.6919	+	10.3630i	1.46782	+	0.670330i	0.979335	−	0.202244i	$-0.0648234\pi$
$239$	22.6919	+	10.3630i	1.46782	+	0.670330i	0.488482	+	0.872574i	$0.337551\pi$
$240$	1.04979	−	1.97432i	0.0677637	−	0.127442i
$241$	−13.2575	+	11.4877i	−0.853990	+	0.739986i	−0.967317	−	0.253571i	$-0.918395\pi$
$241$	−13.2575	+	11.4877i	−0.853990	+	0.739986i	0.113327	+	0.993558i	$0.463849\pi$
$242$	0.307190	−	4.29508i	0.0197469	−	0.276098i
$243$	−0.877679	+	0.479249i	−0.0563031	+	0.0307438i
$244$	−1.60296	+	3.50999i	−0.102619	+	0.224704i
$245$	−0.167213	−	15.0684i	−0.0106829	−	0.962685i
$246$	9.18386	−	2.69663i	0.585542	−	0.171931i
$247$	14.8346	+	19.8167i	0.943903	+	1.26091i
$248$	2.08503	+	0.777674i	0.132399	+	0.0493824i
$249$	2.13499	+	14.8492i	0.135299	+	0.941027i
$250$	−0.425983	+	11.1722i	−0.0269416	+	0.706593i
$251$	−14.1158	−	12.2314i	−0.890979	−	0.772038i	0.0835019	−	0.996508i	$-0.473390\pi$
$251$	−14.1158	−	12.2314i	−0.890979	−	0.772038i	−0.974481	+	0.224470i	$0.927935\pi$
$252$	−0.361103	+	0.361103i	−0.0227473	+	0.0227473i
$253$	−6.02471	−	10.8473i	−0.378770	−	0.681963i
$254$		−	9.91065i		−	0.621849i
$255$	−2.11968	−	0.280794i	−0.132740	−	0.0175840i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	12.9691	−	17.3247i	0.808990	−	1.08068i	−0.186180	−	0.982516i	$-0.559611\pi$
$257$	12.9691	−	17.3247i	0.808990	−	1.08068i	0.995170	−	0.0981683i	$-0.0312984\pi$
$258$	−0.329257	+	0.882771i	−0.0204986	+	0.0549589i
$259$	0.474351	+	0.0682014i	0.0294747	+	0.00423783i
$260$	−9.96438	+	0.823895i	−0.617965	+	0.0510958i
$261$	−8.33387	−	5.35585i	−0.515853	−	0.331519i
$262$	4.61750	−	1.72224i	0.285270	−	0.106400i
$263$	5.49488	+	10.0631i	0.338829	+	0.620518i	0.990426	−	0.138047i	$-0.0440825\pi$
$263$	5.49488	+	10.0631i	0.338829	+	0.620518i	−0.651597	+	0.758565i	$0.725901\pi$
$264$	1.69430	+	1.95533i	0.104277	+	0.120342i
$265$	3.39979	+	6.06527i	0.208848	+	0.372586i
$266$	−2.71263	−	0.796500i	−0.166322	−	0.0488366i
$267$	0.511739	+	1.37203i	0.0313179	+	0.0839666i
$268$	1.30930	+	6.01876i	0.0799783	+	0.367654i
$269$	5.98518	+	20.3837i	0.364923	+	1.24281i	0.913543	+	0.406742i	$0.133335\pi$
$269$	5.98518	+	20.3837i	0.364923	+	1.24281i	−0.548620	+	0.836072i	$0.684847\pi$
$270$	2.02357	−	0.951409i	0.123150	−	0.0579009i
$271$	11.4494	+	25.0706i	0.695500	+	1.52293i	0.845344	+	0.534222i	$0.179395\pi$
$271$	11.4494	+	25.0706i	0.695500	+	1.52293i	−0.149844	+	0.988710i	$0.547877\pi$
$272$	−0.765504	−	0.573049i	−0.0464155	−	0.0347462i
$273$	2.23126	+	0.485381i	0.135042	+	0.0293766i
$274$	5.36271	−	6.18890i	0.323973	−	0.373885i
$275$	−11.8837	−	5.11149i	−0.716612	−	0.308235i
$276$	−4.61116	−	1.31802i	−0.277559	−	0.0793357i
$277$	−3.82464	−	3.82464i	−0.229800	−	0.229800i	0.582809	−	0.812609i	$-0.301954\pi$
$277$	−3.82464	−	3.82464i	−0.229800	−	0.229800i	−0.812609	+	0.582809i	$0.801954\pi$
$278$	0.571655	+	7.99278i	0.0342856	+	0.479375i
$279$	1.20311	+	1.87207i	0.0720281	+	0.112078i
$280$	0.854645	−	0.757320i	0.0510748	−	0.0452585i
$281$	6.86060	−	3.13313i	0.409269	−	0.186907i	−0.200132	−	0.979769i	$-0.564137\pi$
$281$	6.86060	−	3.13313i	0.409269	−	0.186907i	0.609401	+	0.792862i	$0.291410\pi$
$282$	−6.02353	+	4.50916i	−0.358696	+	0.268516i
$283$	−9.58838	−	5.23565i	−0.569970	−	0.311227i	0.168296	−	0.985736i	$-0.446173\pi$
$283$	−9.58838	−	5.23565i	−0.569970	−	0.311227i	−0.738266	+	0.674509i	$0.764355\pi$
$284$	−4.27300	+	6.64892i	−0.253556	+	0.394541i
$285$	9.99166	+	7.30808i	0.591855	+	0.432893i
$286$	3.25929	−	11.1001i	0.192726	−	0.656364i
$287$	4.87553	+	0.348705i	0.287793	+	0.0205834i
$288$	0.997452	+	0.0713392i	0.0587754	+	0.00420370i
$289$	4.53184	−	15.4340i	0.266579	−	0.907885i
$290$	17.8795	+	13.0774i	1.04992	+	0.767929i
$291$	3.64414	−	5.67040i	0.213624	−	0.332405i
$292$	2.61660	+	1.42877i	0.153125	+	0.0836125i
$293$	−15.9812	+	11.9634i	−0.933630	+	0.698907i	−0.953658	−	0.300893i	$-0.902715\pi$
$293$	−15.9812	+	11.9634i	−0.933630	+	0.698907i	0.0200281	+	0.999799i	$0.493624\pi$
$294$	6.13020	−	2.79957i	0.357521	−	0.163274i
$295$	21.5591	−	19.1040i	1.25522	−	1.11228i
$296$	−0.507348	−	0.789449i	−0.0294890	−	0.0458858i
$297$	0.184573	+	2.58067i	0.0107100	+	0.149746i
$298$	13.3775	+	13.3775i	0.774936	+	0.774936i
$299$	6.18929	+	20.5315i	0.357936	+	1.18737i
$300$	−4.64482	+	1.85085i	−0.268169	+	0.106859i
$301$	−0.315084	+	0.363627i	−0.0181612	+	0.0209591i
$302$	−2.02922	−	0.441430i	−0.116769	−	0.0254015i
$303$	11.4266	+	8.55384i	0.656441	+	0.491405i
$304$	2.29977	+	5.03580i	0.131901	+	0.288823i
$305$	7.80832	−	3.67119i	0.447103	−	0.210212i
$306$	−0.269402	−	0.917499i	−0.0154007	−	0.0524499i
$307$	2.07106	+	9.52053i	0.118202	+	0.543365i	0.997719	+	0.0674988i	$0.0215019\pi$
$307$	2.07106	+	9.52053i	0.118202	+	0.543365i	−0.879517	+	0.475867i	$0.842134\pi$
$308$	0.461732	+	1.23795i	0.0263096	+	0.0705388i
$309$	0.848763	+	0.249219i	0.0482845	+	0.0141776i
$310$	−2.43306	−	4.34060i	−0.138188	−	0.246529i
$311$	11.5872	+	13.3723i	0.657048	+	0.758274i	0.982292	−	0.187356i	$-0.0599919\pi$
$311$	11.5872	+	13.3723i	0.657048	+	0.758274i	−0.325244	+	0.945630i	$0.605446\pi$
$312$	−2.14292	−	3.92447i	−0.121319	−	0.222179i
$313$	−22.1611	+	8.26566i	−1.25262	+	0.467203i	−0.886224	−	0.463256i	$-0.846681\pi$
$313$	−22.1611	+	8.26566i	−1.25262	+	0.467203i	−0.366395	+	0.930459i	$0.619408\pi$
$314$	7.11502	+	4.57255i	0.401524	+	0.258044i
$315$	1.13802	−	0.0940964i	0.0641204	−	0.00530173i
$316$	14.1339	+	2.03214i	0.795092	+	0.114317i
$317$	−4.63391	+	12.4240i	−0.260266	+	0.697801i	0.739432	+	0.673231i	$0.235094\pi$
$317$	−4.63391	+	12.4240i	−0.260266	+	0.697801i	−0.999698	+	0.0245693i	$0.992179\pi$
$318$	−1.86348	+	2.48931i	−0.104498	+	0.139594i
$319$	−21.5619	+	13.8570i	−1.20724	+	0.775844i
$320$	−2.21670	−	0.293647i	−0.123917	−	0.0164153i
$321$		−	13.7147i		−	0.765480i
$322$	−1.97112	−	1.45357i	−0.109846	−	0.0810042i
$323$	3.74327	−	3.74327i	0.208281	−	0.208281i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	18.1907	+	12.9976i	1.00904	+	0.720978i
$326$	2.13960	+	14.8813i	0.118502	+	0.824197i
$327$	1.28807	+	0.480425i	0.0712304	+	0.0265676i
$328$	−5.73603	−	7.66245i	−0.316720	−	0.423088i
$329$	−3.68685	+	1.08256i	−0.203262	+	0.0596832i
$330$	−0.0641953	−	5.78495i	−0.00353383	−	0.318451i
$331$	2.10640	−	4.61237i	0.115778	−	0.253519i	−0.842868	−	0.538121i	$-0.819134\pi$
$331$	2.10640	−	4.61237i	0.115778	−	0.253519i	0.958646	+	0.284602i	$0.0918616\pi$
$332$	13.1668	−	7.18962i	0.722622	−	0.394582i
$333$	0.0669461	−	0.936029i	0.00366862	−	0.0512941i
$334$	−14.3934	+	12.4719i	−0.787570	+	0.682434i
$335$	6.46621	−	12.1609i	0.353287	−	0.664419i
$336$	0.464528	+	0.212143i	0.0253421	+	0.0115733i
$337$	−32.6223	+	7.09654i	−1.77705	+	0.386573i	−0.976979	−	0.213334i	$-0.931568\pi$
$337$	−32.6223	+	7.09654i	−1.77705	+	0.386573i	−0.800069	+	0.599907i	$0.795204\pi$
$338$	−3.35165	+	6.13808i	−0.182306	+	0.333868i
$339$	−2.60260	+	18.1015i	−0.141354	+	0.983137i
$340$	0.477663	+	2.08416i	0.0259049	+	0.113030i
$341$	5.69893	−	0.819382i	0.308614	−	0.0443720i
$342$	−1.17678	+	5.40957i	−0.0636330	+	0.292516i
$343$	6.99841	−	0.500537i	0.377879	−	0.0270264i
$344$	0.942176			0.0507987
$345$	5.96172	+	8.91392i	0.320968	+	0.479909i
$346$	−20.9890			−1.12838
$347$	30.4296	−	2.17637i	1.63355	−	0.116834i	0.775826	−	0.630947i	$-0.217333\pi$
$347$	30.4296	−	2.17637i	1.63355	−	0.116834i	0.857722	+	0.514113i	$0.171879\pi$
$348$	−2.10577	+	9.68009i	−0.112881	+	0.518907i
$349$	−18.2585	+	2.62518i	−0.977357	+	0.140523i	−0.612440	−	0.790517i	$-0.709812\pi$
$349$	−18.2585	+	2.62518i	−0.977357	+	0.140523i	−0.364917	+	0.931040i	$0.618903\pi$
$350$	−2.55275	+	0.0566626i	−0.136450	+	0.00302874i
$351$	0.636349	−	4.42590i	0.0339658	−	0.236237i
$352$	1.23994	−	2.27079i	0.0660893	−	0.121033i
$353$	−3.74833	+	0.815400i	−0.199504	+	0.0433993i	−0.311207	−	0.950342i	$-0.600733\pi$
$353$	−3.74833	+	0.815400i	−0.199504	+	0.0433993i	0.111703	+	0.993742i	$0.464369\pi$
$354$	11.7181	+	5.35148i	0.622810	+	0.284428i
$355$	16.9008	−	5.16690i	0.897000	−	0.274230i
$356$	1.10668	−	0.958948i	0.0586542	−	0.0508241i
$357$	0.0348367	−	0.487081i	0.00184376	−	0.0257791i
$358$	4.38596	−	2.39491i	0.231805	−	0.126575i
$359$	−5.71286	+	12.5094i	−0.301513	+	0.660222i	−0.998375	−	0.0569836i	$-0.981852\pi$
$359$	−5.71286	+	12.5094i	−0.301513	+	0.660222i	0.696862	+	0.717205i	$0.254579\pi$
$360$	−1.59859	−	1.56350i	−0.0842529	−	0.0824035i
$361$	−11.1764	+	3.28170i	−0.588233	+	0.172721i
$362$	7.52506	+	10.0523i	0.395509	+	0.528338i
$363$	−4.03456	−	1.50481i	−0.211759	−	0.0789821i
$364$	−0.324968	−	2.26020i	−0.0170330	−	0.118467i
$365$	−2.39881	−	6.21978i	−0.125559	−	0.325558i
$366$	2.91621	+	2.52691i	0.152432	+	0.132084i
$367$	−0.954106	+	0.954106i	−0.0498040	+	0.0498040i	−0.731570	−	0.681766i	$-0.761212\pi$
$367$	−0.954106	+	0.954106i	−0.0498040	+	0.0498040i	0.681766	+	0.731570i	$0.261212\pi$
$368$	0.376515	+	4.78103i	0.0196272	+	0.249228i
$369$		−	9.57158i		−	0.498277i
$370$	−0.275564	+	2.08020i	−0.0143259	+	0.108144i
$371$	−1.33588	+	0.858520i	−0.0693556	+	0.0445721i
$372$	1.33359	−	1.78147i	0.0691436	−	0.0923650i
$373$	−6.87339	+	18.4283i	−0.355891	+	0.954179i	0.628442	+	0.777857i	$0.283693\pi$
$373$	−6.87339	+	18.4283i	−0.355891	+	0.954179i	−0.984332	+	0.176323i	$0.943580\pi$
$374$	−2.44885	−	0.352091i	−0.126627	−	0.0182062i
$375$	10.5997	+	3.55631i	0.547364	+	0.183647i
$376$	6.32986	+	4.06795i	0.326438	+	0.209789i
$377$	41.5031	−	15.4799i	2.13752	−	0.797253i
$378$	0.244741	+	0.448210i	0.0125881	+	0.0230534i
$379$	−13.6774	−	15.7846i	−0.702561	−	0.810798i	0.286535	−	0.958070i	$-0.407496\pi$
$379$	−13.6774	−	15.7846i	−0.702561	−	0.810798i	−0.989096	+	0.147271i	$0.952951\pi$
$380$	3.35557	−	11.9156i	0.172137	−	0.611257i
$381$	−9.50920	−	2.79215i	−0.487171	−	0.143046i
$382$	−4.68959	−	12.5733i	−0.239940	−	0.643305i
$383$	3.89270	+	17.8945i	0.198908	+	0.914364i	0.963051	+	0.269318i	$0.0867982\pi$
$383$	3.89270	+	17.8945i	0.198908	+	0.914364i	−0.764144	+	0.645046i	$0.776838\pi$
$384$	−0.281733	−	0.959493i	−0.0143771	−	0.0489639i
$385$	1.00168	−	2.77943i	0.0510505	−	0.141653i
$386$	2.00046	+	4.38039i	0.101821	+	0.222956i
$387$	0.754250	+	0.564625i	0.0383407	+	0.0287015i
$388$	−6.58638	−	1.43278i	−0.334373	−	0.0727383i
$389$	12.2630	−	14.1522i	0.621757	−	0.717545i	−0.354283	−	0.935138i	$-0.615275\pi$
$389$	12.2630	−	14.1522i	0.621757	−	0.717545i	0.976040	+	0.217593i	$0.0698205\pi$
$390$	−2.01677	+	9.79287i	−0.102123	+	0.495881i
$391$	4.15770	−	1.93501i	0.210264	−	0.0978575i
$392$	−4.76534	−	4.76534i	−0.240686	−	0.240686i
$393$	−0.351576	−	4.91567i	−0.0177347	−	0.247963i
$394$	7.32864	+	11.4036i	0.369212	+	0.574504i
$395$	−21.1757	−	23.8970i	−1.06546	−	1.20239i
$396$	2.35346	−	1.07479i	0.118266	−	0.0540102i
$397$	−13.2784	+	9.94011i	−0.666425	+	0.498880i	−0.878110	−	0.478458i	$-0.841196\pi$
$397$	−13.2784	+	9.94011i	−0.666425	+	0.498880i	0.211685	+	0.977338i	$0.432105\pi$
$398$	6.69660	+	3.65662i	0.335670	+	0.183290i
$399$	−1.52847	+	2.37835i	−0.0765194	+	0.119066i
$400$	3.35735	+	3.70516i	0.167868	+	0.185258i
$401$	−1.06254	+	3.61867i	−0.0530605	+	0.180708i	−0.981760	−	0.190127i	$-0.939110\pi$
$401$	−1.06254	+	3.61867i	−0.0530605	+	0.180708i	0.928699	+	0.370834i	$0.120928\pi$
$402$	6.14383	+	0.439415i	0.306426	+	0.0219160i
$403$	−9.92504	−	0.709853i	−0.494401	−	0.0353603i
$404$	4.02133	−	13.6954i	0.200069	−	0.681372i
$405$	−0.342766	−	2.20964i	−0.0170322	−	0.109798i
$406$	−2.73511	+	4.25591i	−0.135741	+	0.211217i
$407$	−2.13095	−	1.16359i	−0.105627	−	0.0576769i
$408$	−0.765504	+	0.573049i	−0.0378981	+	0.0283701i
$409$	8.12539	−	3.71074i	0.401775	−	0.183484i	−0.204271	−	0.978914i	$-0.565482\pi$
$409$	8.12539	−	3.71074i	0.401775	−	0.183484i	0.606045	+	0.795430i	$0.292755\pi$
$410$	−1.28987	+	21.3638i	−0.0637023	+	1.05508i
$411$	−4.42736	−	6.88910i	−0.218385	−	0.339814i
$412$	−0.0631063	−	0.882342i	−0.00310903	−	0.0434699i
$413$	4.65182	+	4.65182i	0.228901	+	0.228901i
$414$	−2.56375	+	4.05305i	−0.126001	+	0.199196i
$415$	−32.8556	−	6.76638i	−1.61282	−	0.332148i
$416$	−2.92815	+	3.37927i	−0.143565	+	0.165682i
$417$	7.83007	+	1.70333i	0.383440	+	0.0834123i
$418$	11.4664	+	8.58365i	0.560841	+	0.419840i
$419$	−11.2504	−	24.6350i	−0.549620	−	1.20350i	−0.956959	−	0.290223i	$-0.906271\pi$
$419$	−11.2504	−	24.6350i	−0.549620	−	1.20350i	0.407339	−	0.913277i	$-0.366457\pi$
$420$	−0.485862	−	1.03339i	−0.0237076	−	0.0504242i
$421$	5.35924	+	18.2519i	0.261193	+	0.889543i	0.980776	+	0.195136i	$0.0625149\pi$
$421$	5.35924	+	18.2519i	0.261193	+	0.889543i	−0.719583	+	0.694407i	$0.755667\pi$
$422$	3.34717	+	15.3867i	0.162938	+	0.749012i
$423$	2.62948	+	7.04991i	0.127850	+	0.342778i
$424$	2.98358	+	0.876057i	0.144895	+	0.0425451i
$425$	2.19768	−	4.24614i	0.106603	−	0.205968i
$426$	5.17574	+	5.97313i	0.250766	+	0.289399i
$427$	0.944381	+	1.72950i	0.0457018	+	0.0836966i
$428$	−12.8500	+	4.79280i	−0.621127	+	0.231669i
$429$	−9.73224	−	6.25453i	−0.469877	−	0.301972i
$430$	−1.60740	−	1.36189i	−0.0775157	−	0.0656761i
$431$	−33.2619	−	4.78233i	−1.60217	−	0.230357i	−0.717493	−	0.696566i	$-0.754710\pi$
$431$	−33.2619	−	4.78233i	−1.60217	−	0.230357i	−0.884675	+	0.466209i	$0.845619\pi$
$432$	0.349464	−	0.936950i	0.0168136	−	0.0450790i
$433$	11.3800	−	15.2020i	0.546890	−	0.730560i	−0.438901	−	0.898535i	$-0.644632\pi$
$433$	11.3800	−	15.2020i	0.546890	−	0.730560i	0.985791	+	0.167976i	$0.0537230\pi$
$434$	0.956022	−	0.614398i	0.0458905	−	0.0294921i
$435$	17.5849	−	13.4709i	0.843129	−	0.645880i
$436$		−	1.37475i		−	0.0658385i
$437$	−26.4954	−	1.70361i	−1.26745	−	0.0814949i
$438$	2.10808	−	2.10808i	0.100728	−	0.100728i
$439$	−1.66718	−	1.44462i	−0.0795701	−	0.0689479i	0.614168	−	0.789176i	$-0.289492\pi$
$439$	−1.66718	−	1.44462i	−0.0795701	−	0.0689479i	−0.693738	+	0.720228i	$0.744037\pi$
$440$	−5.39777	+	2.08178i	−0.257329	+	0.0992449i
$441$	−0.959090	−	6.67061i	−0.0456709	−	0.317648i
$442$	4.00613	+	1.49421i	0.190552	+	0.0710722i
$443$	11.5896	+	15.4819i	0.550637	+	0.735565i	0.986376	−	0.164508i	$-0.0526037\pi$
$443$	11.5896	+	15.4819i	0.550637	+	0.735565i	−0.435739	+	0.900073i	$0.643513\pi$
$444$	−0.900407	+	0.264383i	−0.0427314	+	0.0125471i
$445$	−3.27419	+	0.0363336i	−0.155212	+	0.00172238i
$446$	4.87474	−	10.6742i	0.230826	−	0.505437i
$447$	16.6045	−	9.06672i	0.785364	−	0.428841i
$448$	0.0364312	−	0.509375i	0.00172121	−	0.0240657i
$449$	−15.6185	+	13.5335i	−0.737083	+	0.638686i	−0.940261	−	0.340456i	$-0.889419\pi$
$449$	−15.6185	+	13.5335i	−0.737083	+	0.638686i	0.203177	+	0.979142i	$0.434873\pi$
$450$	0.467281	+	4.97812i	0.0220278	+	0.234671i
$451$	−22.5263	−	10.2874i	−1.06072	−	0.484416i
$452$	17.8697	−	3.88731i	0.840519	−	0.182844i
$453$	−0.995247	+	1.82266i	−0.0467608	+	0.0856360i
$454$	1.95295	−	13.5831i	0.0916565	−	0.637485i
$455$	−2.71265	+	4.32576i	−0.127171	+	0.202795i
$456$	5.47974	−	0.787868i	0.256612	−	0.0368953i
$457$	−4.44081	+	20.4141i	−0.207732	+	0.954931i	0.748685	+	0.662926i	$0.230686\pi$
$457$	−4.44081	+	20.4141i	−0.207732	+	0.954931i	−0.956417	+	0.292004i	$0.905678\pi$
$458$	−8.31063	+	0.594388i	−0.388330	+	0.0277739i
$459$	−0.956233			−0.0446331
$460$	6.26849	−	8.70092i	0.292270	−	0.405683i
$461$	28.2217			1.31442			0.657209	−	0.753709i	$-0.271737\pi$
$461$	28.2217			1.31442			0.657209	+	0.753709i	$0.271737\pi$
$462$	1.31789	−	0.0942573i	0.0613138	−	0.00438525i
$463$	−0.245614	+	1.12907i	−0.0114147	+	0.0524723i	−0.982502	−	0.186252i	$-0.940366\pi$
$463$	−0.245614	+	1.12907i	−0.0114147	+	0.0524723i	0.971087	+	0.238725i	$0.0767294\pi$
$464$	9.80565	−	1.40984i	0.455216	−	0.0654502i
$465$	−4.85024	+	1.11161i	−0.224925	+	0.0515498i
$466$	−0.629829	+	4.38056i	−0.0291763	+	0.202925i
$467$	5.81066	−	10.6414i	0.268885	−	0.492426i	−0.707994	−	0.706218i	$-0.750400\pi$
$467$	5.81066	−	10.6414i	0.268885	−	0.492426i	0.976879	+	0.213792i	$0.0685815\pi$
$468$	−4.36923	+	0.950467i	−0.201968	+	0.0439354i
$469$	2.86127	+	1.30670i	0.132121	+	0.0603377i
$470$	−4.91896	−	16.0898i	−0.226895	−	0.742166i
$471$	6.39186	−	5.53858i	0.294521	−	0.255204i
$472$	0.919009	−	12.8494i	0.0423008	−	0.591443i
$473$	2.13948	−	1.16825i	0.0983735	−	0.0537160i
$474$	5.93179	−	12.9888i	0.272456	−	0.596596i
$475$	−22.9484	+	15.4782i	−1.05295	+	0.710190i
$476$	−0.468545	+	0.137577i	−0.0214757	+	0.00630584i
$477$	1.86348	+	2.48931i	0.0853227	+	0.113978i
$478$	−23.3734	−	8.71782i	−1.06907	−	0.398744i
$479$	−4.80678	−	33.4319i	−0.219627	−	1.52754i	−0.739418	−	0.673247i	$-0.764899\pi$
$479$	−4.80678	−	33.4319i	−0.219627	−	1.52754i	0.519791	−	0.854294i	$-0.326010\pi$
$480$	−0.906269	+	2.04418i	−0.0413653	+	0.0933037i
$481$	3.17117	+	2.74784i	0.144593	+	0.125291i
$482$	12.4042	−	12.4042i	0.564995	−	0.564995i
$483$	−1.95002	+	1.48176i	−0.0887289	+	0.0674224i
$484$			4.30605i			0.195730i
$485$	9.16566	+	11.9648i	0.416191	+	0.543294i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	−1.98095	+	2.64624i	−0.0897655	+	0.119913i	−0.843176	−	0.537638i	$-0.819317\pi$
$487$	−1.98095	+	2.64624i	−0.0897655	+	0.119913i	0.753410	+	0.657551i	$0.228408\pi$
$488$	1.34847	−	3.61540i	0.0610426	−	0.163662i
$489$	14.8813	+	2.13960i	0.672954	+	0.0967562i
$490$	1.24175	+	15.0181i	0.0560968	+	0.678448i
$491$	−6.96785	−	4.47796i	−0.314455	−	0.202088i	0.373887	−	0.927474i	$-0.378025\pi$
$491$	−6.96785	−	4.47796i	−0.314455	−	0.202088i	−0.688342	+	0.725387i	$0.741661\pi$
$492$	−8.96809	+	3.34492i	−0.404313	+	0.150801i
$493$	−4.53988	−	8.31417i	−0.204466	−	0.374451i
$494$	−16.2105	−	18.7079i	−0.729346	−	0.841710i
$495$	−5.56870	−	1.56821i	−0.250295	−	0.0704859i
$496$	−2.13519	−	0.626949i	−0.0958730	−	0.0281508i
$497$	1.41050	+	3.78169i	0.0632695	+	0.169632i
$498$	−3.18887	−	14.6590i	−0.142897	−	0.656886i
$499$	0.967518	+	3.29506i	0.0433121	+	0.147507i	0.978310	−	0.207145i	$-0.0664173\pi$
$499$	0.967518	+	3.29506i	0.0433121	+	0.147507i	−0.934998	+	0.354653i	$0.884599\pi$
$500$	−0.372119	−	11.1741i	−0.0166417	−	0.499723i
$501$	7.91165	+	17.3241i	0.353466	+	0.773983i
$502$	14.9524	+	11.1932i	0.667357	+	0.499577i
$503$	5.31757	+	1.15677i	0.237099	+	0.0515776i	0.329544	−	0.944140i	$-0.393105\pi$
$503$	5.31757	+	1.15677i	0.237099	+	0.0515776i	−0.0924458	+	0.995718i	$0.529468\pi$
$504$	0.334422	−	0.385944i	0.0148963	−	0.0171913i
$505$	−26.6569	+	17.5523i	−1.18622	+	0.781069i
$506$	6.78320	+	10.3899i	0.301550	+	0.461885i
$507$	4.94518	+	4.94518i	0.219623	+	0.219623i
$508$	0.707018	+	9.88540i	0.0313688	+	0.438594i
$509$	8.98107	+	13.9748i	0.398079	+	0.619423i	0.981207	−	0.192957i	$-0.0618079\pi$
$509$	8.98107	+	13.9748i	0.398079	+	0.619423i	−0.583128	+	0.812380i	$0.698172\pi$
$510$	2.13431	+	0.128863i	0.0945090	+	0.00570613i
$511$	1.38488	−	0.632455i	0.0612636	−	0.0279782i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	4.85891	+	2.65316i	0.214526	+	0.117140i
$514$	−11.7001	+	18.2057i	−0.516070	+	0.803021i
$515$	−1.16774	+	1.59654i	−0.0514566	+	0.0703519i
$516$	0.265442	−	0.904011i	0.0116854	−	0.0397969i
$517$	19.4178	+	1.38879i	0.853995	+	0.0610789i
$518$	−0.478008	−	0.0341878i	−0.0210025	−	0.00150213i
$519$	−5.91329	+	20.1388i	−0.259565	+	0.883997i
$520$	9.88022	−	1.53265i	0.433276	−	0.0672110i
$521$	−0.510724	+	0.794703i	−0.0223752	+	0.0348166i	−0.852261	−	0.523117i	$-0.824769\pi$
$521$	−0.510724	+	0.794703i	−0.0223752	+	0.0348166i	0.829886	+	0.557933i	$0.188406\pi$
$522$	8.69471	+	4.74767i	0.380557	+	0.207800i
$523$	12.0923	−	9.05216i	0.528758	−	0.395823i	−0.301275	−	0.953537i	$-0.597412\pi$
$523$	12.0923	−	9.05216i	0.528758	−	0.395823i	0.830033	+	0.557714i	$0.188321\pi$
$524$	−4.48287	+	2.04726i	−0.195835	+	0.0894350i
$525$	−0.664827	+	2.46531i	−0.0290154	+	0.107595i
$526$	−6.19877	−	9.64547i	−0.270279	−	0.420563i
$527$	0.151805	+	2.12252i	0.00661274	+	0.0924582i
$528$	−1.82947	−	1.82947i	−0.0796176	−	0.0796176i
$529$	−21.0568	−	9.25272i	−0.915511	−	0.402292i
$530$	−3.82382	−	5.80727i	−0.166096	−	0.252252i
$531$	8.43608	−	9.73575i	0.366095	−	0.422496i
$532$	2.76254	+	0.600954i	0.119771	+	0.0260547i
$533$	34.2620	+	25.6482i	1.48405	+	1.11095i
$534$	−0.608315	−	1.33202i	−0.0263243	−	0.0576423i
$535$	28.8506	+	10.3975i	1.24732	+	0.449524i
$536$	−1.73534	−	5.91002i	−0.0749552	−	0.255274i
$537$	−1.06224	−	4.88302i	−0.0458389	−	0.210718i
$538$	−7.42408	−	19.9047i	−0.320075	−	0.858154i
$539$	−16.7298	−	4.91233i	−0.720605	−	0.211589i
$540$	−1.95054	+	1.09334i	−0.0839378	+	0.0470500i
$541$	−20.9339	−	24.1590i	−0.900019	−	1.03868i	−0.999049	−	0.0435928i	$-0.986120\pi$
$541$	−20.9339	−	24.1590i	−0.900019	−	1.03868i	0.0990304	−	0.995084i	$-0.468426\pi$
$542$	−13.2087	−	24.1900i	−0.567363	−	1.03905i
$543$	11.7652	−	4.38818i	0.504892	−	0.188315i
$544$	0.804434	+	0.516978i	0.0344898	+	0.0221653i
$545$	−1.98716	+	2.34539i	−0.0851205	+	0.100465i
$546$	−2.26020	−	0.324968i	−0.0967278	−	0.0139074i
$547$	−4.36522	+	11.7036i	−0.186643	+	0.500410i	−0.996246	−	0.0865682i	$-0.972410\pi$
$547$	−4.36522	+	11.7036i	−0.186643	+	0.500410i	0.809603	+	0.586978i	$0.199683\pi$
$548$	−4.90754	+	6.55570i	−0.209640	+	0.280046i
$549$	3.24614	−	2.08617i	0.138542	−	0.0890354i
$550$	12.2180	+	4.25070i	0.520979	+	0.181250i
$551$			54.8432i			2.33640i
$552$	4.69344	+	0.985708i	0.199766	+	0.0419545i
$553$	5.15626	−	5.15626i	0.219266	−	0.219266i
$554$	4.08774	+	3.54205i	0.173671	+	0.150487i
$555$	1.91830	+	0.850461i	0.0814273	+	0.0361000i
$556$	−1.14040	−	7.93163i	−0.0483636	−	0.336376i
$557$	−7.66305	−	2.85817i	−0.324694	−	0.121105i	0.181831	−	0.983330i	$-0.441798\pi$
$557$	−7.66305	−	2.85817i	−0.324694	−	0.121105i	−0.506525	+	0.862225i	$0.669070\pi$
$558$	−1.33359	−	1.78147i	−0.0564555	−	0.0754157i
$559$	−4.04221	+	1.18690i	−0.170967	+	0.0502005i
$560$	−0.798441	+	0.816360i	−0.0337403	+	0.0344975i
$561$	−1.02775	+	2.25046i	−0.0433916	+	0.0950143i
$562$	−6.61961	+	3.61458i	−0.279231	+	0.152472i
$563$	−1.37028	+	19.1590i	−0.0577504	+	0.807456i	0.883218	+	0.468962i	$0.155372\pi$
$563$	−1.37028	+	19.1590i	−0.0577504	+	0.807456i	−0.940969	+	0.338494i	$0.890083\pi$
$564$	5.68650	−	4.92738i	0.239445	−	0.207480i
$565$	−36.1056	−	19.1982i	−1.51897	−	0.807672i
$566$	9.93746	+	4.53829i	0.417703	+	0.190758i
$567$	0.499006	−	0.108552i	0.0209563	−	0.00455876i
$568$	3.78778	−	6.93681i	0.158932	−	0.291062i
$569$	−2.41925	+	16.8262i	−0.101420	+	0.705392i	0.874142	+	0.485670i	$0.161424\pi$
$569$	−2.41925	+	16.8262i	−0.101420	+	0.705392i	−0.975562	+	0.219722i	$0.929485\pi$
$570$	−10.4876	−	6.57666i	−0.439275	−	0.275466i
$571$	17.6978	−	2.54456i	0.740629	−	0.106486i	0.238335	−	0.971183i	$-0.423398\pi$
$571$	17.6978	−	2.54456i	0.740629	−	0.106486i	0.502294	+	0.864697i	$0.332489\pi$
$572$	−2.45911	+	11.3044i	−0.102821	+	0.472659i
$573$	−13.3852	+	0.957328i	−0.559174	+	0.0399929i
$574$	−4.88798			−0.204020
$575$	−23.2713	+	5.78331i	−0.970480	+	0.241181i
$576$	−1.00000			−0.0416667
$577$	−29.5159	+	2.11102i	−1.22876	+	0.0878829i	−0.670581	−	0.741836i	$-0.733955\pi$
$577$	−29.5159	+	2.11102i	−1.22876	+	0.0878829i	−0.558182	+	0.829719i	$0.688501\pi$
$578$	−3.41924	+	15.7180i	−0.142222	+	0.653783i
$579$	4.76654	−	0.685326i	0.198091	−	0.0284812i
$580$	−18.7668	−	11.7685i	−0.779250	−	0.488662i
$581$	1.09029	−	7.58311i	0.0452327	−	0.314601i
$582$	−3.23034	+	5.91592i	−0.133902	+	0.245223i
$583$	7.86134	−	1.71013i	0.325583	−	0.0708263i
$584$	−2.71186	−	1.23846i	−0.112218	−	0.0512480i
$585$	8.82800	+	4.69405i	0.364993	+	0.194075i
$586$	15.0870	−	13.0730i	0.623238	−	0.540039i
$587$	3.36319	−	47.0236i	0.138814	−	1.94087i	−0.161171	−	0.986927i	$-0.551527\pi$
$587$	3.36319	−	47.0236i	0.138814	−	1.94087i	0.299985	−	0.953944i	$-0.403018\pi$
$588$	−5.91486	+	3.22976i	−0.243925	+	0.133193i
$589$	5.11777	−	11.2063i	0.210874	−	0.461749i
$590$	−20.1413	+	20.5934i	−0.829206	+	0.847816i
$591$	13.0064	−	3.81902i	0.535011	−	0.157093i
$592$	0.562374	+	0.751244i	0.0231134	+	0.0308759i
$593$	−40.6406	−	15.1582i	−1.66891	−	0.622471i	−0.675528	−	0.737334i	$-0.736084\pi$
$593$	−40.6406	−	15.1582i	−1.66891	−	0.622471i	−0.993381	+	0.114863i	$0.963357\pi$
$594$	−0.368206	−	2.56093i	−0.0151077	−	0.105076i
$595$	0.998226	+	0.442554i	0.0409233	+	0.0181430i
$596$	−14.2977	−	12.3890i	−0.585658	−	0.507475i
$597$	5.39515	−	5.39515i	0.220809	−	0.220809i
$598$	−7.63822	−	20.0377i	−0.312350	−	0.819402i
$599$		−	16.3972i		−	0.669972i	−0.942223	−	0.334986i	$-0.891268\pi$
$599$		−	16.3972i		−	0.669972i	0.942223	−	0.334986i	$-0.108732\pi$
$600$	4.50095	−	2.17749i	0.183750	−	0.0888958i
$601$	33.4782	−	21.5151i	1.36560	−	0.877620i	0.366988	−	0.930226i	$-0.380389\pi$
$601$	33.4782	−	21.5151i	1.36560	−	0.877620i	0.998615	+	0.0526062i	$0.0167528\pi$
$602$	0.288341	−	0.385178i	0.0117519	−	0.0156987i
$603$	2.15253	−	5.77116i	0.0876579	−	0.235020i
$604$	2.05554	+	0.295542i	0.0836389	+	0.0120255i
$605$	6.22428	−	7.34635i	0.253053	−	0.298672i
$606$	−12.0077	−	7.71688i	−0.487780	−	0.313477i
$607$	28.4723	−	10.6196i	1.15566	−	0.431037i	0.302734	−	0.953075i	$-0.402101\pi$
$607$	28.4723	−	10.6196i	1.15566	−	0.431037i	0.852922	+	0.522038i	$0.174828\pi$
$608$	−2.65316	−	4.85891i	−0.107600	−	0.197055i
$609$	3.31295	+	3.82334i	0.134247	+	0.154930i
$610$	−7.52653	+	4.21888i	−0.304740	+	0.170817i
$611$	−32.2815	−	9.47871i	−1.30597	−	0.383468i
$612$	0.334169	+	0.895942i	0.0135080	+	0.0362163i
$613$	−10.3132	−	47.4088i	−0.416545	−	1.91483i	−0.403662	−	0.914908i	$-0.632263\pi$
$613$	−10.3132	−	47.4088i	−0.416545	−	1.91483i	−0.0128825	−	0.999917i	$-0.504101\pi$
$614$	−2.74497	−	9.34853i	−0.110778	−	0.377276i
$615$	20.1350	+	7.25650i	0.811922	+	0.292610i
$616$	−0.548870	−	1.20186i	−0.0221146	−	0.0484242i
$617$	2.91434	+	2.18165i	0.117327	+	0.0878298i	0.656330	−	0.754474i	$-0.272108\pi$
$617$	2.91434	+	2.18165i	0.117327	+	0.0878298i	−0.539003	+	0.842304i	$0.681199\pi$
$618$	−0.864380	−	0.188034i	−0.0347705	−	0.00756385i
$619$	10.2446	−	11.8229i	0.411764	−	0.475201i	−0.511546	−	0.859256i	$-0.670927\pi$
$619$	10.2446	−	11.8229i	0.411764	−	0.475201i	0.923310	+	0.384055i	$0.125473\pi$
$620$	2.73651	+	4.15597i	0.109901	+	0.166908i
$621$	3.16658	+	3.60177i	0.127070	+	0.144534i
$622$	−12.5116	−	12.5116i	−0.501670	−	0.501670i
$623$	−0.0533482	−	0.745906i	−0.00213735	−	0.0298841i
$624$	2.41743	+	3.76159i	0.0967746	+	0.150584i
$625$	−15.5171	+	19.6016i	−0.620682	+	0.784062i
$626$	21.5150	−	9.82556i	0.859911	−	0.392708i
$627$	11.4664	−	8.58365i	0.457925	−	0.342798i
$628$	−7.42310	−	4.05332i	−0.296214	−	0.161745i
$629$	0.485143	−	0.754897i	0.0193439	−	0.0300997i
$630$	−1.12841	+	0.175042i	−0.0449570	+	0.00697385i
$631$	0.929400	−	3.16524i	0.0369988	−	0.126006i	−0.938923	−	0.344128i	$-0.888175\pi$
$631$	0.929400	−	3.16524i	0.0369988	−	0.126006i	0.975922	+	0.218121i	$0.0699929\pi$
$632$	−14.2428	−	1.01867i	−0.566549	−	0.0405204i
$633$	15.7064	+	1.12335i	0.624274	+	0.0446490i
$634$	3.73578	−	12.7229i	0.148367	−	0.505291i
$635$	13.0829	−	17.8870i	0.519177	−	0.709823i
$636$	1.68114	−	2.61591i	0.0666616	−	0.103727i
$637$	26.4478	+	14.4416i	1.04790	+	0.572197i
$638$	20.5184	−	15.3599i	0.812333	−	0.608105i
$639$	7.18935	−	3.28327i	0.284406	−	0.129884i
$640$	2.23200	+	0.134761i	0.0882277	+	0.00532688i
$641$	13.2639	+	20.6390i	0.523892	+	0.815192i	0.997862	−	0.0653486i	$-0.0208160\pi$
$641$	13.2639	+	20.6390i	0.523892	+	0.815192i	−0.473970	+	0.880541i	$0.657180\pi$
$642$	0.978396	+	13.6798i	0.0386142	+	0.539897i
$643$	5.25766	+	5.25766i	0.207342	+	0.207342i	0.803137	−	0.595795i	$-0.203163\pi$
$643$	5.25766	+	5.25766i	0.207342	+	0.207342i	−0.595795	+	0.803137i	$0.703163\pi$
$644$	2.06980	+	1.30925i	0.0815614	+	0.0515915i
$645$	−1.75958	+	1.15860i	−0.0692833	+	0.0456199i
$646$	−3.46669	+	4.00078i	−0.136395	+	0.157409i
$647$	1.81166	+	0.394103i	0.0712237	+	0.0154938i	0.248036	−	0.968751i	$-0.420215\pi$
$647$	1.81166	+	0.394103i	0.0712237	+	0.0154938i	−0.176812	+	0.984245i	$0.556579\pi$
$648$	−0.800541	−	0.599278i	−0.0314482	−	0.0235419i
$649$	−13.8457	−	30.3179i	−0.543491	−	1.19008i
$650$	−19.0716	−	11.6668i	−0.748048	−	0.457609i
$651$	−0.320168	−	1.09039i	−0.0125484	−	0.0427359i
$652$	−3.19577	−	14.6907i	−0.125156	−	0.575332i
$653$	−10.4772	−	28.0904i	−0.410004	−	1.09926i	−0.963804	−	0.266613i	$-0.914095\pi$
$653$	−10.4772	−	28.0904i	−0.410004	−	1.09926i	0.553799	−	0.832650i	$-0.313177\pi$
$654$	−1.31906	−	0.387311i	−0.0515793	−	0.0151451i
$655$	10.6073	+	2.98713i	0.414460	+	0.116717i
$656$	6.26805	+	7.23372i	0.244726	+	0.282429i
$657$	−1.42877	−	2.61660i	−0.0557417	−	0.102083i
$658$	3.60022	−	1.34281i	0.140351	−	0.0523483i
$659$	−33.1899	−	21.3299i	−1.29290	−	0.830893i	−0.300476	−	0.953789i	$-0.597145\pi$
$659$	−33.1899	−	21.3299i	−1.29290	−	0.830893i	−0.992420	+	0.122896i	$0.960782\pi$
$660$	0.476725	+	5.76563i	0.0185565	+	0.224427i
$661$	36.6470	+	5.26905i	1.42540	+	0.204942i	0.811460	−	0.584407i	$-0.198673\pi$
$661$	36.6470	+	5.26905i	1.42540	+	0.204942i	0.613944	+	0.789350i	$0.289582\pi$
$662$	−1.77199	+	4.75089i	−0.0688703	+	0.184648i
$663$	2.56234	−	3.42288i	0.0995130	−	0.132934i
$664$	−12.6204	+	8.11061i	−0.489765	+	0.314753i
$665$	−3.84438	−	5.01843i	−0.149079	−	0.194606i
$666$			0.938420i			0.0363630i
$667$	−16.2825	+	44.6325i	−0.630461	+	1.72818i
$668$	13.4670	−	13.4670i	0.521052	−	0.521052i
$669$	−8.86843	−	7.68454i	−0.342873	−	0.297102i
$670$	−5.58218	+	12.5912i	−0.215659	+	0.486440i
$671$	−1.42080	−	9.88185i	−0.0548492	−	0.381485i
$672$	−0.478478	−	0.178463i	−0.0184577	−	0.00688437i
$673$	21.6966	+	28.9832i	0.836341	+	1.11722i	0.991599	+	0.129347i	$0.0412880\pi$
$673$	21.6966	+	28.9832i	0.836341	+	1.11722i	−0.155259	+	0.987874i	$0.549621\pi$
$674$	32.0329	−	9.40571i	1.23386	−	0.362294i
$675$	4.90812	+	0.954145i	0.188913	+	0.0367250i
$676$	2.90522	−	6.36155i	0.111739	−	0.244675i
$677$	35.6255	−	19.4530i	1.36920	−	0.747639i	0.384702	−	0.923041i	$-0.374304\pi$
$677$	35.6255	−	19.4530i	1.36920	−	0.747639i	0.984497	+	0.175402i	$0.0561225\pi$
$678$	1.30462	−	18.2410i	0.0501037	−	0.700542i
$679$	−2.60142	+	2.25414i	−0.0998333	+	0.0865061i
$680$	−0.625129	−	2.04478i	−0.0239726	−	0.0784137i
$681$	−12.4826	−	5.70063i	−0.478336	−	0.218449i
$682$	−5.62595	+	1.22385i	−0.215429	+	0.0468637i
$683$	−4.53598	+	8.30703i	−0.173565	+	0.317860i	−0.949952	−	0.312396i	$-0.898868\pi$
$683$	−4.53598	+	8.30703i	−0.173565	+	0.317860i	0.776387	+	0.630256i	$0.217050\pi$
$684$	0.787868	−	5.47974i	0.0301249	−	0.209523i
$685$	17.8486	−	4.09066i	0.681960	−	0.156296i
$686$	−6.94488	+	0.998522i	−0.265157	+	0.0381238i
$687$	−1.77106	+	8.14145i	−0.0675703	+	0.310616i
$688$	−0.939775	+	0.0672140i	−0.0358286	+	0.00256251i
$689$	−13.9040			−0.529701
$690$	−6.58244	−	8.46590i	−0.250589	−	0.322291i
$691$	−19.2792			−0.733417			−0.366708	−	0.930336i	$-0.619515\pi$
$691$	−19.2792			−0.733417			−0.366708	+	0.930336i	$0.619515\pi$
$692$	20.9356	−	1.49734i	0.795851	−	0.0569204i
$693$	0.280853	−	1.29106i	0.0106687	−	0.0490434i
$694$	−30.1968	+	4.34165i	−1.14626	+	0.164807i
$695$	−9.51937	+	15.1802i	−0.361090	+	0.575817i
$696$	1.40984	−	9.80565i	0.0534398	−	0.371682i
$697$	4.38640	−	8.03310i	0.166147	−	0.304275i
$698$	18.0247	−	3.92104i	0.682246	−	0.148414i
$699$	4.02567	+	1.83846i	0.152265	+	0.0695371i
$700$	2.54221	−	0.238630i	0.0960864	−	0.00901935i
$701$	−18.4328	+	15.9721i	−0.696196	+	0.603257i	−0.929358	−	0.369181i	$-0.879638\pi$
$701$	−18.4328	+	15.9721i	−0.696196	+	0.603257i	0.233161	+	0.972438i	$0.425093\pi$
$702$	−0.318987	+	4.46002i	−0.0120394	+	0.168333i
$703$	−4.55969	+	2.48978i	−0.171972	+	0.0939039i
$704$	−1.07479	+	2.35346i	−0.0405076	+	0.0886994i
$705$	−16.8239	+	0.186694i	−0.633623	+	0.00703129i
$706$	3.68061	−	1.08072i	0.138522	−	0.0406736i
$707$	−4.36825	−	5.83529i	−0.164285	−	0.219459i
$708$	−12.0700	−	4.50188i	−0.453619	−	0.169191i
$709$	−4.57919	−	31.8490i	−0.171975	−	1.19611i	−0.874705	−	0.484656i	$-0.838945\pi$
$709$	−4.57919	−	31.8490i	−0.171975	−	1.19611i	0.702730	−	0.711457i	$-0.251964\pi$
$710$	−16.4891	+	6.35942i	−0.618825	+	0.238665i
$711$	−10.7915	−	9.35089i	−0.404713	−	0.350686i
$712$	−1.03545	+	1.03545i	−0.0388053	+	0.0388053i
$713$	7.49202	−	7.60054i	0.280578	−	0.284642i
$714$			0.488326i			0.0182751i
$715$	20.5355	−	15.7312i	0.767984	−	0.588315i
$716$	−4.20393	+	2.70170i	−0.157108	+	0.100967i
$717$	−14.9497	+	19.9705i	−0.558308	+	0.745812i
$718$	4.80589	−	12.8851i	0.179354	−	0.480867i
$719$	−30.0763	−	4.32432i	−1.12166	−	0.161270i	−0.443562	−	0.896244i	$-0.646285\pi$
$719$	−30.0763	−	4.32432i	−1.12166	−	0.161270i	−0.678095	+	0.734974i	$0.737194\pi$
$720$	1.70605	+	1.44547i	0.0635808	+	0.0538695i
$721$	−0.380030	−	0.244230i	−0.0141530	−	0.00909561i
$722$	10.9138	−	4.07065i	0.406171	−	0.151494i
$723$	−8.40707	−	15.3964i	−0.312662	−	0.572598i
$724$	−8.22301	−	9.48986i	−0.305606	−	0.352688i
$725$	15.0061	+	47.2046i	0.557313	+	1.75314i
$726$	4.13163	+	1.21316i	0.153339	+	0.0450244i
$727$	−12.5990	−	33.7793i	−0.467272	−	1.25280i	−0.930411	−	0.366519i	$-0.880550\pi$
$727$	−12.5990	−	33.7793i	−0.467272	−	1.25280i	0.463139	−	0.886286i	$-0.346723\pi$
$728$	0.485381	+	2.23126i	0.0179894	+	0.0826961i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	2.83641	+	6.03280i	0.104980	+	0.223284i
$731$	0.374264	+	0.819523i	0.0138426	+	0.0303112i
$732$	−3.08904	−	2.31243i	−0.114174	−	0.0854698i
$733$	49.3396	+	10.7332i	1.82240	+	0.396439i	0.987966	−	0.154670i	$-0.0494316\pi$
$733$	49.3396	+	10.7332i	1.82240	+	0.396439i	0.834433	+	0.551109i	$0.185795\pi$
$734$	0.883610	−	1.01974i	0.0326147	−	0.0376393i
$735$	14.7596	+	3.03963i	0.544416	+	0.112118i
$736$	−0.716630	−	4.74199i	−0.0264153	−	0.174792i
$737$	−11.2687	−	11.2687i	−0.415087	−	0.415087i
$738$	0.682829	+	9.54719i	0.0251353	+	0.351437i
$739$	11.0980	+	17.2688i	0.408246	+	0.635243i	0.983112	−	0.183004i	$-0.0585822\pi$
$739$	11.0980	+	17.2688i	0.408246	+	0.635243i	−0.574866	+	0.818247i	$0.694946\pi$
$740$	0.126462	−	2.09456i	0.00464884	−	0.0769974i
$741$	−22.5172	+	10.2832i	−0.827188	+	0.377764i
$742$	1.27123	−	0.951633i	0.0466684	−	0.0349355i
$743$	2.11168	+	1.15307i	0.0774702	+	0.0423019i	0.517517	−	0.855673i	$-0.326856\pi$
$743$	2.11168	+	1.15307i	0.0774702	+	0.0423019i	−0.440047	+	0.897975i	$0.645038\pi$
$744$	−1.20311	+	1.87207i	−0.0441080	+	0.0686334i
$745$	6.48464	+	41.8033i	0.237579	+	1.53155i
$746$	5.54122	−	18.8717i	0.202878	−	0.690940i
$747$	−14.9636	−	1.07022i	−0.547490	−	0.0391573i
$748$	2.46773	+	0.176495i	0.0902290	+	0.00645330i
$749$	−1.97319	+	6.72007i	−0.0720988	+	0.245546i
$750$	−10.8264	−	2.79107i	−0.395322	−	0.101916i
$751$	−17.9335	+	27.9051i	−0.654404	+	1.01827i	0.342490	+	0.939521i	$0.388730\pi$
$751$	−17.9335	+	27.9051i	−0.654404	+	1.01827i	−0.996894	+	0.0787511i	$0.974907\pi$
$752$	−6.60394	−	3.60602i	−0.240821	−	0.131498i
$753$	14.9524	−	11.1932i	0.544895	−	0.407903i
$754$	−40.2931	+	18.4012i	−1.46739	+	0.670133i
$755$	−3.07966	−	3.47544i	−0.112080	−	0.126484i
$756$	−0.276093	−	0.429608i	−0.0100414	−	0.0156247i
$757$	−0.000540604	−	0.00755862i	−1.96486e−5	−	0.000274723i	0.997442	−	0.0714765i	$-0.0227711\pi$
$757$	−0.000540604	−	0.00755862i	−1.96486e−5	−	0.000274723i	−0.997462	+	0.0712018i	$0.977317\pi$
$758$	14.7686	+	14.7686i	0.536420	+	0.536420i
$759$	11.8800	−	3.58127i	0.431218	−	0.129992i
$760$	−2.49698	+	12.1246i	−0.0905748	+	0.439806i
$761$	23.5684	−	27.1994i	0.854354	−	0.985977i	−0.145640	−	0.989338i	$-0.546524\pi$
$761$	23.5684	−	27.1994i	0.854354	−	0.985977i	0.999994	+	0.00336050i	$0.00106968\pi$
$762$	9.68416	+	2.10666i	0.350820	+	0.0763162i
$763$	−0.562021	−	0.420724i	−0.0203465	−	0.0152312i
$764$	5.57461	+	12.2067i	0.201682	+	0.441623i
$765$	0.724949	−	2.01156i	0.0262106	−	0.0727279i
$766$	−5.15936	−	17.5712i	−0.186415	−	0.634872i
$767$	12.2442	+	56.2855i	0.442111	+	2.03235i
$768$	0.349464	+	0.936950i	0.0126102	+	0.0338093i
$769$	50.4681	+	14.8188i	1.81993	+	0.534379i	0.999312	−	0.0371009i	$-0.0118123\pi$
$769$	50.4681	+	14.8188i	1.81993	+	0.534379i	0.820616	+	0.571480i	$0.193630\pi$
$770$	−0.800850	+	2.84381i	−0.0288606	+	0.102484i
$771$	14.1720	+	16.3553i	0.510391	+	0.589023i
$772$	−2.30785	−	4.22652i	−0.0830614	−	0.152116i
$773$	−4.13131	+	1.54090i	−0.148593	+	0.0554223i	−0.422660	−	0.906288i	$-0.638904\pi$
$773$	−4.13131	+	1.54090i	−0.148593	+	0.0554223i	0.274067	+	0.961711i	$0.411631\pi$
$774$	−0.792609	−	0.509379i	−0.0284897	−	0.0183092i
$775$	1.33870	−	11.0458i	0.0480875	−	0.396778i
$776$	6.67181	+	0.959261i	0.239504	+	0.0344355i
$777$	−0.167473	+	0.449013i	−0.00600807	+	0.0161083i
$778$	−11.2221	+	14.9910i	−0.402332	+	0.537453i
$779$	−44.5773	+	28.6481i	−1.59715	+	1.02642i
$780$	1.31302	−	9.91180i	0.0470135	−	0.354899i
$781$		−	20.4487i		−	0.731711i
$782$	−4.00907	+	2.22668i	−0.143364	+	0.0796261i
$783$	7.00494	−	7.00494i	0.250336	−	0.250336i
$784$	5.09315	+	4.41324i	0.181898	+	0.157616i
$785$	6.80523	+	17.6450i	0.242889	+	0.629779i
$786$	0.701360	+	4.87807i	0.0250167	+	0.173995i
$787$	9.77781	+	3.64693i	0.348541	+	0.129999i	0.517637	−	0.855601i	$-0.326812\pi$
$787$	9.77781	+	3.64693i	0.348541	+	0.129999i	−0.169095	+	0.985600i	$0.554085\pi$
$788$	−8.12349	−	10.8517i	−0.289387	−	0.386576i
$789$	−11.0012	+	3.23023i	−0.391652	+	0.114999i
$790$	22.8265	+	22.3255i	0.812131	+	0.794305i
$791$	3.87958	−	8.49510i	0.137942	−	0.302051i
$792$	−2.27079	+	1.23994i	−0.0806890	+	0.0440595i
$793$	−1.23087	+	17.2098i	−0.0437096	+	0.611140i
$794$	12.5355	−	10.8621i	0.444868	−	0.385480i
$795$	−6.64933	+	2.03283i	−0.235828	+	0.0720971i
$796$	−6.94039	−	3.16957i	−0.245996	−	0.112342i
$797$	28.8432	−	6.27446i	1.02168	−	0.222253i	0.329636	−	0.944108i	$-0.393074\pi$
$797$	28.8432	−	6.27446i	1.02168	−	0.222253i	0.692044	+	0.721855i	$0.256710\pi$
$798$	1.35491	−	2.48133i	0.0479633	−	0.0878381i
$799$	−1.02396	+	7.12177i	−0.0362249	+	0.251950i
$800$	−3.61312	−	3.45621i	−0.127743	−	0.122195i
$801$	−1.44945	+	0.208399i	−0.0512138	+	0.00736343i
$802$	0.801676	−	3.68525i	0.0283082	−	0.130131i
$803$	−7.69369	+	0.550264i	−0.271504	+	0.0194184i
$804$	−6.15952			−0.217230
$805$	−1.63870	−	5.22547i	−0.0577567	−	0.184174i
$806$	9.95039			0.350487
$807$	−21.1901	+	1.51554i	−0.745926	+	0.0533496i
$808$	−3.03407	+	13.9474i	−0.106738	+	0.490667i
$809$	−16.5923	+	2.38561i	−0.583354	+	0.0838736i	−0.427672	−	0.903934i	$-0.640666\pi$
$809$	−16.5923	+	2.38561i	−0.583354	+	0.0838736i	−0.155681	+	0.987807i	$0.549757\pi$
$810$	0.499526	+	2.17956i	0.0175516	+	0.0765819i
$811$	6.25692	−	43.5179i	0.219710	−	1.52812i	−0.519398	−	0.854532i	$-0.673844\pi$
$811$	6.25692	−	43.5179i	0.219710	−	1.52812i	0.739109	−	0.673586i	$-0.235247\pi$
$812$	2.42452	−	4.44019i	0.0850841	−	0.155820i
$813$	−26.9314	+	5.85857i	−0.944526	+	0.205469i
$814$	2.20853	+	1.00860i	0.0774090	+	0.0353515i
$815$	−15.7829	+	29.6825i	−0.552849	+	1.03973i
$816$	0.722672	−	0.626199i	0.0252986	−	0.0219214i
$817$	0.372103	−	5.20268i	0.0130182	−	0.182019i
$818$	−7.83997	+	4.28095i	−0.274118	+	0.149680i
$819$	−0.948578	+	2.07710i	−0.0331460	+	0.0725796i
$820$	−0.237490	−	21.4014i	−0.00829352	−	0.747369i
$821$	21.1582	−	6.21259i	0.738425	−	0.216821i	0.109173	−	0.994023i	$-0.465180\pi$
$821$	21.1582	−	6.21259i	0.738425	−	0.216821i	0.629252	+	0.777202i	$0.283362\pi$
$822$	4.90754	+	6.55570i	0.171170	+	0.228656i
$823$	−17.9552	−	6.69693i	−0.625878	−	0.233440i	0.0164569	−	0.999865i	$-0.494761\pi$
$823$	−17.9552	−	6.69693i	−0.625878	−	0.233440i	−0.642335	+	0.766424i	$0.722034\pi$
$824$	0.125891	+	0.875592i	0.00438562	+	0.0305027i
$825$	7.52073	−	10.5256i	0.261838	−	0.366453i
$826$	−4.97182	−	4.30811i	−0.172992	−	0.149898i
$827$	1.54670	−	1.54670i	0.0537839	−	0.0537839i	−0.679703	−	0.733487i	$-0.737891\pi$
$827$	1.54670	−	1.54670i	0.0537839	−	0.0537839i	0.733487	+	0.679703i	$0.237891\pi$
$828$	2.26807	−	4.22562i	0.0788211	−	0.146850i
$829$			28.5874i			0.992881i	0.868071	+	0.496441i	$0.165360\pi$
$829$			28.5874i			0.992881i	−0.868071	+	0.496441i	$0.834640\pi$
$830$	33.2546	+	4.40524i	1.15429	+	0.152908i
$831$	4.55022	−	2.92425i	0.157845	−	0.101441i
$832$	2.67962	−	3.57955i	0.0928991	−	0.124099i
$833$	2.25204	−	6.03794i	0.0780284	−	0.209202i
$834$	−7.93163	−	1.14040i	−0.274650	−	0.0394887i
$835$	−42.4414	+	3.50923i	−1.46875	+	0.121442i
$836$	−12.0496	−	7.74378i	−0.416743	−	0.267824i
$837$	−2.08503	+	0.777674i	−0.0720690	+	0.0268804i
$838$	12.9792	+	23.7697i	0.448359	+	0.821109i
$839$	2.17785	+	2.51338i	0.0751879	+	0.0867714i	0.792097	−	0.610395i	$-0.208989\pi$
$839$	2.17785	+	2.51338i	0.0751879	+	0.0867714i	−0.716909	+	0.697166i	$0.754444\pi$
$840$	0.558345	+	0.996094i	0.0192647	+	0.0343685i
$841$	66.3378	+	19.4785i	2.28751	+	0.671674i
$842$	−6.64766	−	17.8231i	−0.229094	−	0.614223i
$843$	1.60320	+	7.36981i	0.0552173	+	0.253830i
$844$	−4.43631	−	15.1087i	−0.152704	−	0.520063i
$845$	−14.1519	+	6.65372i	−0.486840	+	0.228895i
$846$	−3.12572	−	6.84436i	−0.107464	−	0.235314i
$847$	1.76039	+	1.31781i	0.0604877	+	0.0452805i
$848$	−3.03847	−	0.660979i	−0.104342	−	0.0226981i
$849$	7.15416	−	8.25634i	0.245530	−	0.283357i
$850$	−1.88917	+	4.39210i	−0.0647979	+	0.150648i
$851$	−4.44997	+	0.672500i	−0.152543	+	0.0230530i
$852$	−5.58868	−	5.58868i	−0.191465	−	0.191465i
$853$	1.32567	+	18.5353i	0.0453900	+	0.634635i	0.968327	+	0.249685i	$0.0803270\pi$
$853$	1.32567	+	18.5353i	0.0453900	+	0.634635i	−0.922937	+	0.384951i	$0.874218\pi$
$854$	−1.06536	−	1.65773i	−0.0364557	−	0.0567262i
$855$	−9.26495	+	8.20988i	−0.316855	+	0.280772i
$856$	12.4753	−	5.69729i	0.426398	−	0.194729i
$857$	−4.51030	+	3.37637i	−0.154069	+	0.115334i	−0.673531	−	0.739159i	$-0.735223\pi$
$857$	−4.51030	+	3.37637i	−0.154069	+	0.115334i	0.519462	+	0.854493i	$0.326132\pi$
$858$	10.1536	+	5.54431i	0.346639	+	0.189279i
$859$	15.0256	−	23.3804i	0.512669	−	0.797728i	−0.484351	−	0.874874i	$-0.660944\pi$
$859$	15.0256	−	23.3804i	0.512669	−	0.797728i	0.997020	+	0.0771458i	$0.0245807\pi$
$860$	1.70046	+	1.24375i	0.0579852	+	0.0424114i
$861$	−1.37710	+	4.68998i	−0.0469316	+	0.159834i
$862$	33.5183	+	2.39727i	1.14164	+	0.0816515i
$863$	11.1692	+	0.798835i	0.380203	+	0.0271926i	0.260133	−	0.965573i	$-0.416234\pi$
$863$	11.1692	+	0.798835i	0.380203	+	0.0271926i	0.120070	+	0.992765i	$0.461688\pi$
$864$	−0.281733	+	0.959493i	−0.00958474	+	0.0326426i
$865$	−37.8815	−	27.7072i	−1.28801	−	0.942073i
$866$	−10.2666	+	15.9751i	−0.348872	+	0.542855i
$867$	14.1180	+	7.70902i	0.479473	+	0.261812i
$868$	−0.909756	+	0.681035i	−0.0308791	+	0.0231158i
$869$	−33.6055	+	15.3471i	−1.13999	+	0.520616i
$870$	−16.5790	+	14.6911i	−0.562082	+	0.498074i
$871$	14.8902	+	23.1696i	0.504535	+	0.785072i
$872$	0.0980733	+	1.37124i	0.00332118	+	0.0464362i
$873$	4.76619	+	4.76619i	0.161311	+	0.161311i
$874$	26.5495	−	0.190889i	0.898049	−	0.00645691i
$875$	−4.68207	−	3.26757i	−0.158283	−	0.110464i
$876$	−1.95232	+	2.25309i	−0.0659627	+	0.0761250i
$877$	−26.1367	−	5.68570i	−0.882575	−	0.191992i	−0.251633	−	0.967823i	$-0.580968\pi$
$877$	−26.1367	−	5.68570i	−0.882575	−	0.191992i	−0.630942	+	0.775830i	$0.717331\pi$
$878$	1.76599	+	1.32200i	0.0595993	+	0.0446154i
$879$	−8.29291	−	18.1589i	−0.279713	−	0.612486i
$880$	5.23551	−	2.46155i	0.176489	−	0.0829788i
$881$	−11.5338	−	39.2805i	−0.388584	−	1.32339i	−0.889118	−	0.457678i	$-0.848681\pi$
$881$	−11.5338	−	39.2805i	−0.388584	−	1.32339i	0.500534	−	0.865717i	$-0.333137\pi$
$882$	1.43252	+	6.58520i	0.0482355	+	0.221735i
$883$	15.2454	+	40.8744i	0.513047	+	1.37553i	0.892804	+	0.450446i	$0.148735\pi$
$883$	15.2454	+	40.8744i	0.513047	+	1.37553i	−0.379757	+	0.925086i	$0.623992\pi$
$884$	−4.10252	−	1.20461i	−0.137983	−	0.0405153i
$885$	14.0847	+	25.1273i	0.473453	+	0.844645i
$886$	−12.6645	−	14.6156i	−0.425472	−	0.491021i
$887$	−20.6306	−	37.7820i	−0.692706	−	1.26860i	−0.952972	−	0.303060i	$-0.901992\pi$
$887$	−20.6306	−	37.7820i	−0.692706	−	1.26860i	0.260265	−	0.965537i	$-0.416190\pi$
$888$	0.879252	−	0.327944i	0.0295058	−	0.0110051i
$889$	4.25770	+	2.73626i	0.142799	+	0.0917711i
$890$	3.26326	−	0.269819i	0.109385	−	0.00904436i
$891$	−2.56093	−	0.368206i	−0.0857944	−	0.0123354i
$892$	−4.10083	+	10.9947i	−0.137306	+	0.368131i
$893$	24.9631	−	33.3468i	0.835358	−	1.11591i
$894$	−15.9153	+	10.2282i	−0.532289	+	0.342081i
$895$	11.0774	+	1.46742i	0.370275	+	0.0490504i
$896$			0.510677i			0.0170605i
$897$	−21.3780	+	1.68355i	−0.713789	+	0.0562122i
$898$	14.6132	−	14.6132i	0.487650	−	0.487650i
$899$	−16.6607	−	14.4366i	−0.555665	−	0.481486i
$900$	−0.821225	−	4.93210i	−0.0273742	−	0.164403i
$901$	0.423165	+	2.94317i	0.0140977	+	0.0980513i
$902$	23.2028	+	8.65421i	0.772570	+	0.288154i
$903$	−0.288341	−	0.385178i	−0.00959537	−	0.0128179i
$904$	−17.5468	+	5.15221i	−0.583599	+	0.171360i
$905$	0.311562	+	28.0763i	0.0103567	+	0.933289i
$906$	0.862684	−	1.88902i	0.0286608	−	0.0627583i
$907$	31.5744	−	17.2409i	1.04841	−	0.572475i	0.139826	−	0.990176i	$-0.455346\pi$
$907$	31.5744	−	17.2409i	1.04841	−	0.572475i	0.908585	+	0.417701i	$0.137164\pi$
$908$	−0.978969	+	13.6878i	−0.0324882	+	0.454245i
$909$	−10.7873	+	9.34721i	−0.357791	+	0.310027i
$910$	2.39714	−	4.50825i	0.0794644	−	0.149447i
$911$	52.5698	+	24.0078i	1.74171	+	0.795414i	0.990852	+	0.134957i	$0.0430895\pi$
$911$	52.5698	+	24.0078i	1.74171	+	0.795414i	0.750863	+	0.660458i	$0.229638\pi$
$912$	−5.40957	+	1.17678i	−0.179129	+	0.0389671i
$913$	−18.6015	+	34.0660i	−0.615619	+	1.12742i
$914$	2.97317	−	20.6789i	0.0983438	−	0.683996i
$915$	1.92752	+	8.41024i	0.0637218	+	0.278034i
$916$	8.24705	−	1.18575i	0.272490	−	0.0391782i
$917$	−0.534970	+	2.45922i	−0.0176663	+	0.0812105i
$918$	0.953796	−	0.0682169i	0.0314800	−	0.00225149i
$919$	11.3200			0.373414			0.186707	−	0.982416i	$-0.440218\pi$
$919$	11.3200			0.373414			0.186707	+	0.982416i	$0.440218\pi$
$920$	−5.63180	+	9.12594i	−0.185675	+	0.300873i
$921$	−9.74319			−0.321049
$922$	−28.1498	+	2.01332i	−0.927065	+	0.0663050i
$923$	−7.51210	+	34.5325i	−0.247264	+	1.13665i
$924$	−1.30781	+	0.188034i	−0.0430237	+	0.00618588i
$925$	−3.24337	+	3.39062i	−0.106641	+	0.111483i
$926$	0.164441	−	1.14372i	0.00540388	−	0.0375848i
$927$	−0.423942	+	0.776391i	−0.0139241	+	0.0255000i
$928$	−9.68009	+	2.10577i	−0.317765	+	0.0691254i
$929$	34.4455	+	15.7307i	1.13012	+	0.516108i	0.890602	−	0.454784i	$-0.150283\pi$
$929$	34.4455	+	15.7307i	1.13012	+	0.516108i	0.239518	+	0.970892i	$0.423011\pi$
$930$	4.75859	−	1.45479i	0.156040	−	0.0477045i
$931$	−28.1962	+	24.4321i	−0.924092	+	0.800730i
$932$	0.315719	−	4.41433i	0.0103417	−	0.144596i
$933$	−15.5297	+	8.47987i	−0.508421	+	0.277619i
$934$	−5.03670	+	11.0288i	−0.164806	+	0.360875i
$935$	−3.95495	−	3.86814i	−0.129341	−	0.126502i
$936$	4.29029	−	1.25974i	0.140233	−	0.0411760i
$937$	25.7877	+	34.4483i	0.842448	+	1.12538i	0.990651	+	0.136421i	$0.0435601\pi$
$937$	25.7877	+	34.4483i	0.842448	+	1.12538i	−0.148203	+	0.988957i	$0.547349\pi$
$938$	−2.94720	−	1.09925i	−0.0962294	−	0.0358917i
$939$	−3.36609	−	23.4116i	−0.109848	−	0.764010i
$940$	6.05426	+	15.6979i	0.197468	+	0.512008i
$941$	−7.23763	−	6.27144i	−0.235940	−	0.204443i	0.528863	−	0.848707i	$-0.322618\pi$
$941$	−7.23763	−	6.27144i	−0.235940	−	0.204443i	−0.764803	+	0.644264i	$0.777164\pi$
$942$	−5.98046	+	5.98046i	−0.194854	+	0.194854i
$943$	−44.7833	+	10.0798i	−1.45835	+	0.328243i
$944$			12.8822i			0.419281i
$945$	−0.149958	+	1.13202i	−0.00487815	+	0.0368246i
$946$	−2.05069	+	1.31790i	−0.0666737	+	0.0428486i
$947$	1.18543	−	1.58355i	0.0385214	−	0.0514585i	−0.780867	−	0.624697i	$-0.785222\pi$
$947$	1.18543	−	1.58355i	0.0385214	−	0.0514585i	0.819388	+	0.573239i	$0.194313\pi$
$948$	−4.99007	+	13.3789i	−0.162070	+	0.434526i
$949$	13.1948	+	1.89713i	0.428322	+	0.0615834i
$950$	21.7858	−	17.0759i	0.706824	−	0.554016i
$951$	−11.1551	−	7.16892i	−0.361727	−	0.232468i
$952$	0.457537	−	0.170652i	0.0148288	−	0.00553087i
$953$	7.03334	+	12.8806i	0.227832	+	0.417244i	0.966440	−	0.256892i	$-0.0826983\pi$
$953$	7.03334	+	12.8806i	0.227832	+	0.417244i	−0.738608	+	0.674135i	$0.764517\pi$
$954$	−2.03631	−	2.35003i	−0.0659281	−	0.0760850i
$955$	8.13385	−	28.8832i	0.263205	−	0.934639i
$956$	23.9358	+	7.02817i	0.774138	+	0.227307i
$957$	−8.95702	−	24.0147i	−0.289539	−	0.776285i
$958$	7.17953	+	33.0038i	0.231960	+	1.06630i
$959$	1.17820	+	4.01258i	0.0380460	+	0.129573i
$960$	0.758130	−	2.10363i	0.0244685	−	0.0678942i
$961$	−10.8207	−	23.6940i	−0.349054	−	0.764322i
$962$	−3.35912	−	2.51461i	−0.108302	−	0.0810742i
$963$	13.4013	+	2.91527i	0.431850	+	0.0939432i
$964$	−11.4877	+	13.2575i	−0.369993	+	0.426995i
$965$	−2.17199	+	10.5466i	−0.0699189	+	0.339507i
$966$	1.83934	−	1.61710i	0.0591798	−	0.0520293i
$967$	−33.4598	−	33.4598i	−1.07600	−	1.07600i	−0.996864	−	0.0791316i	$-0.974785\pi$
$967$	−33.4598	−	33.4598i	−1.07600	−	1.07600i	−0.0791316	−	0.996864i	$-0.525215\pi$
$968$	−0.307190	−	4.29508i	−0.00987347	−	0.138049i
$969$	2.86204	+	4.45342i	0.0919419	+	0.143064i
$970$	−9.99587	−	11.2805i	−0.320948	−	0.362194i
$971$	27.7171	−	12.6580i	0.889485	−	0.406214i	0.0823651	−	0.996602i	$-0.473753\pi$
$971$	27.7171	−	12.6580i	0.889485	−	0.406214i	0.807119	+	0.590388i	$0.201025\pi$
$972$	−0.800541	+	0.599278i	−0.0256774	+	0.0192218i
$973$	−3.59159	−	1.96116i	−0.115141	−	0.0628718i
$974$	1.78712	−	2.78082i	0.0572632	−	0.0891032i
$975$	−16.5673	+	15.0121i	−0.530578	+	0.480772i
$976$	−1.08712	+	3.70239i	−0.0347978	+	0.118511i
$977$	−10.2979	−	0.736519i	−0.329458	−	0.0235633i	−0.0943696	−	0.995537i	$-0.530084\pi$
$977$	−10.2979	−	0.736519i	−0.329458	−	0.0235633i	−0.235089	+	0.971974i	$0.575538\pi$
$978$	−14.9960	−	1.07253i	−0.479519	−	0.0342958i
$979$	−1.06739	+	3.63521i	−0.0341140	+	0.116182i
$980$	−2.30997	−	14.8912i	−0.0737892	−	0.475683i
$981$	−0.743244	+	1.15651i	−0.0237300	+	0.0369246i
$982$	7.26955	+	3.96947i	0.231981	+	0.126671i
$983$	−17.1433	+	12.8333i	−0.546787	+	0.409320i	−0.836641	−	0.547751i	$-0.815484\pi$
$983$	−17.1433	+	12.8333i	−0.546787	+	0.409320i	0.289854	+	0.957071i	$0.406393\pi$
$984$	8.70662	−	3.97618i	0.277557	−	0.126756i
$985$	−1.82674	+	30.2559i	−0.0582049	+	0.964032i
$986$	5.12144	+	7.96911i	0.163100	+	0.253788i
$987$	−0.274120	−	3.83270i	−0.00872535	−	0.121996i
$988$	17.5038	+	17.5038i	0.556871	+	0.556871i
$989$	1.84746	−	4.12358i	0.0587458	−	0.131122i
$990$	5.66639	+	1.16695i	0.180090	+	0.0370881i
$991$	5.14416	−	5.93667i	0.163410	−	0.188585i	−0.668139	−	0.744036i	$-0.732909\pi$
$991$	5.14416	−	5.93667i	0.163410	−	0.188585i	0.831549	+	0.555451i	$0.187455\pi$
$992$	2.17448	+	0.473029i	0.0690397	+	0.0150187i
$993$	4.05922	+	3.03869i	0.128815	+	0.0964299i
$994$	−1.67669	−	3.67143i	−0.0531813	−	0.116451i
$995$	7.25915	+	15.4396i	0.230130	+	0.489468i
$996$	4.22651	+	14.3942i	0.133922	+	0.456097i
$997$	−0.692017	−	3.18115i	−0.0219164	−	0.100748i	0.964889	−	0.262657i	$-0.0845987\pi$
$997$	−0.692017	−	3.18115i	−0.0219164	−	0.100748i	−0.986806	+	0.161909i	$0.948235\pi$
$998$	−1.20012	−	3.21765i	−0.0379891	−	0.101853i
$999$	0.900407	+	0.264383i	0.0284876	+	0.00836472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.7.2	✓	240
5.3	odd	4	inner	690.2.w.b.283.8	yes	240
23.10	odd	22	inner	690.2.w.b.217.8	yes	240
115.33	even	44	inner	690.2.w.b.493.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.2	✓	240	1.1	even	1	trivial
690.2.w.b.217.8	yes	240	23.10	odd	22	inner
690.2.w.b.283.8	yes	240	5.3	odd	4	inner
690.2.w.b.493.2	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)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.89440 - 1.18796i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.244741 - 0.448210i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(-0.212565 + 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-1.89440 - 1.18796i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.244741 - 0.448210i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(1.97432 + 1.04979i) q^{10} +(-1.95533 + 1.69430i) q^{11} +(-0.0713392 + 0.997452i) q^{12} +(3.92447 - 2.14292i) q^{13} +(-0.212143 + 0.464528i) q^{14} +(1.56350 - 1.59859i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-0.573049 - 0.765504i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.787868 + 5.47974i) q^{19} +(-2.04418 - 0.906269i) q^{20} +(0.385944 + 0.334422i) q^{21} +(1.82947 - 1.82947i) q^{22} +(-0.985708 + 4.69344i) q^{23} -1.00000i q^{24} +(2.17749 + 4.50095i) q^{25} +(-3.76159 + 2.41743i) q^{26} +(0.599278 - 0.800541i) q^{27} +(0.178463 - 0.478478i) q^{28} +(9.80565 + 1.40984i) q^{29} +(-1.44547 + 1.70605i) q^{30} +(-1.87207 - 1.20311i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-1.23994 - 2.27079i) q^{33} +(0.626199 + 0.722672i) q^{34} +(-0.996094 + 0.558345i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.327944 + 0.879252i) q^{37} +(-1.17678 - 5.40957i) q^{38} +(1.25974 + 4.29029i) q^{39} +(2.10363 + 0.758130i) q^{40} +(3.97618 + 8.70662i) q^{41} +(-0.408818 - 0.306037i) q^{42} +(-0.920644 - 0.200274i) q^{43} +(-1.69430 + 1.95533i) q^{44} +(1.22971 + 1.86757i) q^{45} +(0.648370 - 4.75180i) q^{46} +(-5.32050 - 5.32050i) q^{47} +(0.0713392 + 0.997452i) q^{48} +(3.64349 + 5.66938i) q^{49} +(-2.49304 - 4.33414i) q^{50} +(0.869820 - 0.397233i) q^{51} +(3.57955 - 2.67962i) q^{52} +(-2.72917 - 1.49024i) q^{53} +(-0.540641 + 0.841254i) q^{54} +(5.71693 - 0.886826i) q^{55} +(-0.143874 + 0.489991i) q^{56} +(-5.52198 - 0.394940i) q^{57} +(-9.88124 - 0.706721i) q^{58} +(-3.62935 + 12.3604i) q^{59} +(1.32008 - 1.80482i) q^{60} +(-2.08617 + 3.24614i) q^{61} +(1.95313 + 1.06649i) q^{62} +(-0.408818 + 0.306037i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-9.98021 - 0.602571i) q^{65} +(1.39878 + 2.17655i) q^{66} +(0.439415 + 6.14383i) q^{67} +(-0.676159 - 0.676159i) q^{68} +(-4.37665 - 1.96084i) q^{69} +(0.953724 - 0.627983i) q^{70} +(-5.17574 + 5.97313i) q^{71} +(0.977147 + 0.212565i) q^{72} +(2.38663 + 1.78661i) q^{73} +(-0.389834 - 0.853616i) q^{74} +(-4.86095 + 1.17098i) q^{75} +(1.55970 + 5.31184i) q^{76} +(0.280853 + 1.29106i) q^{77} +(-1.56260 - 4.18949i) q^{78} +(13.7008 + 4.02292i) q^{79} +(-2.15235 - 0.606127i) q^{80} +(0.654861 + 0.755750i) q^{81} +(-4.58717 - 8.40078i) q^{82} +(14.0560 - 5.24261i) q^{83} +(0.429608 + 0.276093i) q^{84} +(0.176194 + 2.13093i) q^{85} +(0.932586 + 0.134086i) q^{86} +(-3.46196 + 9.28188i) q^{87} +(1.55049 - 2.07121i) q^{88} +(1.23189 - 0.791689i) q^{89} +(-1.35981 - 1.77509i) q^{90} -2.28345i q^{91} +(-0.307729 + 4.78595i) q^{92} +(1.57355 - 1.57355i) q^{93} +(5.68650 + 4.92738i) q^{94} +(5.01719 - 11.3168i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-6.31543 - 2.35553i) q^{97} +(-4.03866 - 5.39502i) q^{98} +(2.48246 - 0.728917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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