LMFDB - Embedded newform 552.2.t.a.451.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			451.8
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.620217 - 1.27096i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.23066 + 1.57654i) q^{4} +(0.514647 + 3.57945i) q^{5} +(0.554369 - 1.30103i) q^{6} +(0.174714 - 0.382571i) q^{7} +(2.76699 + 0.586321i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.620217 - 1.27096i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.23066 + 1.57654i) q^{4} +(0.514647 + 3.57945i) q^{5} +(0.554369 - 1.30103i) q^{6} +(0.174714 - 0.382571i) q^{7} +(2.76699 + 0.586321i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(4.23013 - 2.87413i) q^{10} +(0.516403 - 1.75871i) q^{11} +(-1.99738 + 0.102341i) q^{12} +(-5.06987 + 2.31533i) q^{13} +(-0.594591 + 0.0152228i) q^{14} +(-2.36814 + 2.73298i) q^{15} +(-0.970945 - 3.88037i) q^{16} +(0.555053 - 0.863679i) q^{17} +(1.34629 - 0.433028i) q^{18} +(3.08157 + 4.79502i) q^{19} +(-6.27649 - 3.59373i) q^{20} +(0.403541 - 0.118490i) q^{21} +(-2.55552 + 0.434454i) q^{22} +(-4.11034 - 2.47085i) q^{23} +(1.36888 + 2.47511i) q^{24} +(-7.75010 + 2.27564i) q^{25} +(6.08711 + 5.00758i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.388123 + 0.746258i) q^{28} +(-3.86352 + 6.01175i) q^{29} +(4.94226 + 1.31476i) q^{30} +(5.29576 + 4.58880i) q^{31} +(-4.32958 + 3.64070i) q^{32} +(1.66731 - 0.761437i) q^{33} +(-1.44195 - 0.169780i) q^{34} +(1.45931 + 0.428491i) q^{35} +(-1.38535 - 1.44250i) q^{36} +(-1.07805 + 7.49802i) q^{37} +(4.18302 - 6.89049i) q^{38} +(-5.06987 - 2.31533i) q^{39} +(-0.674684 + 10.2060i) q^{40} +(-1.68222 - 11.7001i) q^{41} +(-0.400879 - 0.439393i) q^{42} +(-2.37662 + 2.05935i) q^{43} +(2.13715 + 2.97850i) q^{44} -3.61625 q^{45} +(-0.591040 + 6.75653i) q^{46} +3.17246i q^{47} +(2.29675 - 3.27489i) q^{48} +(4.46819 + 5.15657i) q^{49} +(7.69898 + 8.43865i) q^{50} +(1.01621 - 0.146109i) q^{51} +(2.58909 - 10.8422i) q^{52} +(5.08685 - 11.1387i) q^{53} +(1.20889 + 0.733882i) q^{54} +(6.56096 + 0.943323i) q^{55} +(0.707741 - 0.956130i) q^{56} +(-1.60583 + 5.46896i) q^{57} +(10.0369 + 1.18177i) q^{58} +(-0.527440 - 1.15493i) q^{59} +(-1.39427 - 7.09684i) q^{60} +(7.14409 - 8.24471i) q^{61} +(2.54765 - 9.57673i) q^{62} +(0.353812 + 0.227381i) q^{63} +(7.31245 + 3.24469i) q^{64} +(-10.8968 - 16.9558i) q^{65} +(-2.00185 - 1.64683i) q^{66} +(1.57128 + 5.35128i) q^{67} +(0.678541 + 1.93796i) q^{68} +(-0.824356 - 4.72445i) q^{69} +(-0.360493 - 2.12047i) q^{70} +(1.19475 + 4.06895i) q^{71} +(-0.974137 + 2.65538i) q^{72} +(-1.18394 + 0.760875i) q^{73} +(10.1983 - 3.28024i) q^{74} +(-6.79505 - 4.36691i) q^{75} +(-11.3519 - 1.04283i) q^{76} +(-0.582606 - 0.504831i) q^{77} +(0.201734 + 7.87960i) q^{78} +(-0.967941 - 2.11949i) q^{79} +(13.3899 - 5.47246i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-13.8270 + 9.39465i) q^{82} +(15.9003 + 2.28611i) q^{83} +(-0.309818 + 0.782019i) q^{84} +(3.37715 + 1.54229i) q^{85} +(4.09137 + 1.74333i) q^{86} +(-7.07345 + 1.01701i) q^{87} +(2.46005 - 4.56354i) q^{88} +(-4.62959 + 4.01157i) q^{89} +(2.24286 + 4.59610i) q^{90} +2.34411i q^{91} +(8.95383 - 3.43933i) q^{92} +7.00729i q^{93} +(4.03207 - 1.96762i) q^{94} +(-15.5776 + 13.4980i) q^{95} +(-5.58673 - 0.887930i) q^{96} +(-8.56412 + 1.23133i) q^{97} +(3.78252 - 8.87707i) q^{98} +(1.66731 + 0.761437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	−0.620217	−	1.27096i	−0.438560	−	0.898702i
$2$	−0.620217	−	1.27096i	−0.438560	−	0.898702i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	−1.23066	+	1.57654i	−0.615331	+	0.788269i
$5$	0.514647	+	3.57945i	0.230157	+	1.60078i	0.697423	+	0.716660i	$0.254330\pi$
$5$	0.514647	+	3.57945i	0.230157	+	1.60078i	−0.467266	+	0.884117i	$0.654761\pi$
$6$	0.554369	−	1.30103i	0.226320	−	0.531143i
$7$	0.174714	−	0.382571i	0.0660357	−	0.144598i	−0.873736	−	0.486400i	$-0.838310\pi$
$7$	0.174714	−	0.382571i	0.0660357	−	0.144598i	0.939772	+	0.341802i	$0.111037\pi$
$8$	2.76699	+	0.586321i	0.978278	+	0.207296i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	4.23013	−	2.87413i	1.33768	−	0.908879i
$11$	0.516403	−	1.75871i	0.155701	−	0.530270i	−0.844283	−	0.535898i	$-0.819973\pi$
$11$	0.516403	−	1.75871i	0.155701	−	0.530270i	0.999984	+	0.00562785i	$0.00179141\pi$
$12$	−1.99738	+	0.102341i	−0.576594	+	0.0295433i
$13$	−5.06987	+	2.31533i	−1.40613	+	0.642158i	−0.966652	−	0.256095i	$-0.917564\pi$
$13$	−5.06987	+	2.31533i	−1.40613	+	0.642158i	−0.439478	+	0.898253i	$0.644837\pi$
$14$	−0.594591	+	0.0152228i	−0.158911	+	0.00406845i
$15$	−2.36814	+	2.73298i	−0.611452	+	0.705653i
$16$	−0.970945	−	3.88037i	−0.242736	−	0.970092i
$17$	0.555053	−	0.863679i	0.134620	−	0.209473i	−0.767398	−	0.641171i	$-0.778449\pi$
$17$	0.555053	−	0.863679i	0.134620	−	0.209473i	0.902018	+	0.431698i	$0.142085\pi$
$18$	1.34629	−	0.433028i	0.317323	−	0.102066i
$19$	3.08157	+	4.79502i	0.706961	+	1.10005i	0.990017	+	0.140949i	$0.0450153\pi$
$19$	3.08157	+	4.79502i	0.706961	+	1.10005i	−0.283056	+	0.959103i	$0.591348\pi$
$20$	−6.27649	−	3.59373i	−1.40347	−	0.803581i
$21$	0.403541	−	0.118490i	0.0880599	−	0.0258567i
$22$	−2.55552	+	0.434454i	−0.544839	+	0.0926260i
$23$	−4.11034	−	2.47085i	−0.857065	−	0.515208i
$23$	−4.11034	−	2.47085i	−0.857065	−	0.515208i
$24$	1.36888	+	2.47511i	0.279422	+	0.505230i
$25$	−7.75010	+	2.27564i	−1.55002	+	0.455127i
$26$	6.08711	+	5.00758i	1.19378	+	0.982067i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.388123	+	0.746258i	0.0733484	+	0.141030i
$29$	−3.86352	+	6.01175i	−0.717437	+	1.11635i	0.270682	+	0.962669i	$0.412751\pi$
$29$	−3.86352	+	6.01175i	−0.717437	+	1.11635i	−0.988120	+	0.153686i	$0.950886\pi$
$30$	4.94226	+	1.31476i	0.902330	+	0.240042i
$31$	5.29576	+	4.58880i	0.951146	+	0.824173i	0.984520	−	0.175270i	$-0.0560799\pi$
$31$	5.29576	+	4.58880i	0.951146	+	0.824173i	−0.0333744	+	0.999443i	$0.510625\pi$
$32$	−4.32958	+	3.64070i	−0.765370	+	0.643591i
$33$	1.66731	−	0.761437i	0.290242	−	0.132549i
$34$	−1.44195	−	0.169780i	−0.247293	−	0.0291169i
$35$	1.45931	+	0.428491i	0.246668	+	0.0724282i
$36$	−1.38535	−	1.44250i	−0.230892	−	0.240417i
$37$	−1.07805	+	7.49802i	−0.177231	+	1.23267i	0.685904	+	0.727692i	$0.259407\pi$
$37$	−1.07805	+	7.49802i	−0.177231	+	1.23267i	−0.863134	+	0.504974i	$0.831502\pi$
$38$	4.18302	−	6.89049i	0.678575	−	1.11779i
$39$	−5.06987	−	2.31533i	−0.811830	−	0.370750i
$40$	−0.674684	+	10.2060i	−0.106677	+	1.61372i
$41$	−1.68222	−	11.7001i	−0.262719	−	1.82725i	−0.512193	−	0.858871i	$-0.671167\pi$
$41$	−1.68222	−	11.7001i	−0.262719	−	1.82725i	0.249474	−	0.968382i	$-0.419742\pi$
$42$	−0.400879	−	0.439393i	−0.0618570	−	0.0677999i
$43$	−2.37662	+	2.05935i	−0.362431	+	0.314048i	−0.816972	−	0.576678i	$-0.804349\pi$
$43$	−2.37662	+	2.05935i	−0.362431	+	0.314048i	0.454541	+	0.890726i	$0.349803\pi$
$44$	2.13715	+	2.97850i	0.322188	+	0.449026i
$45$	−3.61625			−0.539079
$46$	−0.591040	+	6.75653i	−0.0871441	+	0.996196i
$47$			3.17246i			0.462752i	0.972864	+	0.231376i	$0.0743227\pi$
$47$			3.17246i			0.462752i	−0.972864	+	0.231376i	$0.925677\pi$
$48$	2.29675	−	3.27489i	0.331508	−	0.472690i
$49$	4.46819	+	5.15657i	0.638313	+	0.736652i
$50$	7.69898	+	8.43865i	1.08880	+	1.19341i
$51$	1.01621	−	0.146109i	0.142298	−	0.0204593i
$52$	2.58909	−	10.8422i	0.359042	−	1.50355i
$53$	5.08685	−	11.1387i	0.698733	−	1.53001i	−0.142768	−	0.989756i	$-0.545600\pi$
$53$	5.08685	−	11.1387i	0.698733	−	1.53001i	0.841501	−	0.540256i	$-0.181673\pi$
$54$	1.20889	+	0.733882i	0.164509	+	0.0998687i
$55$	6.56096	+	0.943323i	0.884679	+	0.127198i
$56$	0.707741	−	0.956130i	0.0945759	−	0.127768i
$57$	−1.60583	+	5.46896i	−0.212698	+	0.724382i
$58$	10.0369	+	1.18177i	1.31791	+	0.155174i
$59$	−0.527440	−	1.15493i	−0.0686668	−	0.150359i	0.872187	−	0.489173i	$-0.162702\pi$
$59$	−0.527440	−	1.15493i	−0.0686668	−	0.150359i	−0.940853	+	0.338814i	$0.889974\pi$
$60$	−1.39427	−	7.09684i	−0.179999	−	0.916198i
$61$	7.14409	−	8.24471i	0.914706	−	1.05563i	−0.0835442	−	0.996504i	$-0.526624\pi$
$61$	7.14409	−	8.24471i	0.914706	−	1.05563i	0.998251	−	0.0591234i	$-0.0188306\pi$
$62$	2.54765	−	9.57673i	0.323551	−	1.21625i
$63$	0.353812	+	0.227381i	0.0445761	+	0.0286473i
$64$	7.31245	+	3.24469i	0.914057	+	0.405586i
$65$	−10.8968	−	16.9558i	−1.35158	−	2.10310i
$66$	−2.00185	−	1.64683i	−0.246411	−	0.202710i
$67$	1.57128	+	5.35128i	0.191962	+	0.653763i	0.998076	+	0.0620024i	$0.0197487\pi$
$67$	1.57128	+	5.35128i	0.191962	+	0.653763i	−0.806114	+	0.591760i	$0.798433\pi$
$68$	0.678541	+	1.93796i	0.0822852	+	0.235012i
$69$	−0.824356	−	4.72445i	−0.0992408	−	0.568757i
$70$	−0.360493	−	2.12047i	−0.0430872	−	0.253445i
$71$	1.19475	+	4.06895i	0.141791	+	0.482896i	0.999513	−	0.0312186i	$-0.00993880\pi$
$71$	1.19475	+	4.06895i	0.141791	+	0.482896i	−0.857722	+	0.514115i	$0.828121\pi$
$72$	−0.974137	+	2.65538i	−0.114803	+	0.312940i
$73$	−1.18394	+	0.760875i	−0.138570	+	0.0890537i	−0.608089	−	0.793869i	$-0.708064\pi$
$73$	−1.18394	+	0.760875i	−0.138570	+	0.0890537i	0.469519	+	0.882922i	$0.344427\pi$
$74$	10.1983	−	3.28024i	1.18553	−	0.381320i
$75$	−6.79505	−	4.36691i	−0.784624	−	0.504248i
$76$	−11.3519	−	1.04283i	−1.30215	−	0.119621i
$77$	−0.582606	−	0.504831i	−0.0663942	−	0.0575309i
$78$	0.201734	+	7.87960i	0.0228419	+	0.892189i
$79$	−0.967941	−	2.11949i	−0.108902	−	0.238462i	0.847333	−	0.531062i	$-0.178207\pi$
$79$	−0.967941	−	2.11949i	−0.108902	−	0.238462i	−0.956235	+	0.292600i	$0.905480\pi$
$80$	13.3899	−	5.47246i	1.49703	−	0.611840i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−13.8270	+	9.39465i	−1.52694	+	1.03747i
$83$	15.9003	+	2.28611i	1.74528	+	0.250934i	0.939809	−	0.341700i	$-0.111003\pi$
$83$	15.9003	+	2.28611i	1.74528	+	0.250934i	0.805472	+	0.592634i	$0.201912\pi$
$84$	−0.309818	+	0.782019i	−0.0338039	+	0.0853253i
$85$	3.37715	+	1.54229i	0.366303	+	0.167285i
$86$	4.09137	+	1.74333i	0.441183	+	0.187988i
$87$	−7.07345	+	1.01701i	−0.758353	+	0.109035i
$88$	2.46005	−	4.56354i	0.262242	−	0.486475i
$89$	−4.62959	+	4.01157i	−0.490736	+	0.425225i	−0.864754	−	0.502196i	$-0.832525\pi$
$89$	−4.62959	+	4.01157i	−0.490736	+	0.425225i	0.374018	+	0.927422i	$0.377980\pi$
$90$	2.24286	+	4.59610i	0.236418	+	0.484472i
$91$			2.34411i			0.245729i
$92$	8.95383	−	3.43933i	0.933501	−	0.358575i
$93$			7.00729i			0.726622i
$94$	4.03207	−	1.96762i	0.415876	−	0.202944i
$95$	−15.5776	+	13.4980i	−1.59823	+	1.38487i
$96$	−5.58673	−	0.887930i	−0.570194	−	0.0906239i
$97$	−8.56412	+	1.23133i	−0.869555	+	0.125023i	−0.562628	−	0.826710i	$-0.690210\pi$
$97$	−8.56412	+	1.23133i	−0.869555	+	0.125023i	−0.306927	+	0.951733i	$0.599301\pi$
$98$	3.78252	−	8.87707i	0.382093	−	0.896719i
$99$	1.66731	+	0.761437i	0.167571	+	0.0765273i
$100$	5.95012	−	15.0189i	0.595012	−	1.50189i
$101$	9.39962	+	1.35146i	0.935297	+	0.134475i	0.593078	−	0.805145i	$-0.297912\pi$
$101$	9.39962	+	1.35146i	0.935297	+	0.134475i	0.342219	+	0.939620i	$0.388822\pi$
$102$	−0.815967	−	1.20094i	−0.0807928	−	0.118910i
$103$	5.91264	+	1.73611i	0.582590	+	0.171064i	0.559730	−	0.828675i	$-0.310905\pi$
$103$	5.91264	+	1.73611i	0.582590	+	0.171064i	0.0228596	+	0.999739i	$0.492723\pi$
$104$	−15.3858	+	3.43393i	−1.50870	+	0.336724i
$105$	0.631810	+	1.38347i	0.0616584	+	0.135013i
$106$	−17.3117	+	0.443215i	−1.68146	+	0.0430488i
$107$	4.37985	+	3.79516i	0.423416	+	0.366892i	0.840349	−	0.542045i	$-0.182350\pi$
$107$	4.37985	+	3.79516i	0.423416	+	0.366892i	−0.416934	+	0.908937i	$0.636895\pi$
$108$	0.182957	−	1.99161i	0.0176051	−	0.191643i
$109$	−5.61245	−	3.60690i	−0.537575	−	0.345478i	0.243515	−	0.969897i	$-0.421700\pi$
$109$	−5.61245	−	3.60690i	−0.537575	−	0.345478i	−0.781090	+	0.624419i	$0.785336\pi$
$110$	−2.87030	−	8.92376i	−0.273672	−	0.850847i
$111$	−6.37260	+	4.09542i	−0.604860	+	0.388720i
$112$	−1.65415	−	0.306500i	−0.156303	−	0.0289616i
$113$	1.58157	+	5.38632i	0.148781	+	0.506703i	0.999831	−	0.0183826i	$-0.00585168\pi$
$113$	1.58157	+	5.38632i	0.148781	+	0.506703i	−0.851050	+	0.525085i	$0.824033\pi$
$114$	7.94678	−	1.35100i	0.744284	−	0.126533i
$115$	6.72890	−	15.9844i	0.627473	−	1.49055i
$116$	−4.72307	−	13.4894i	−0.438526	−	1.25246i
$117$	−1.57025	−	5.34778i	−0.145170	−	0.494402i
$118$	−1.14074	+	1.38666i	−0.105014	+	0.127653i
$119$	−0.233443	−	0.363244i	−0.0213996	−	0.0332985i
$120$	−8.15503	+	6.17364i	−0.744449	+	0.563574i
$121$	6.42741	+	4.13065i	0.584310	+	0.375513i
$122$	−14.9096	−	3.96631i	−1.34985	−	0.359093i
$123$	7.74074	−	8.93329i	0.697959	−	0.805488i
$124$	−13.7517	+	2.70170i	−1.23494	+	0.242620i
$125$	−4.62284	−	10.1226i	−0.413480	−	0.905394i
$126$	0.0695514	−	0.590706i	0.00619613	−	0.0526242i
$127$	3.02357	−	10.2974i	0.268299	−	0.913742i	−0.709590	−	0.704615i	$-0.751120\pi$
$127$	3.02357	−	10.2974i	0.268299	−	0.913742i	0.977889	−	0.209127i	$-0.0670622\pi$
$128$	−0.411451	−	11.3062i	−0.0363675	−	0.999338i
$129$	−3.11271	−	0.447540i	−0.274059	−	0.0394037i
$130$	−14.7916	+	24.3656i	−1.29731	+	2.13701i
$131$	7.59926	−	16.6401i	0.663951	−	1.45385i	−0.214843	−	0.976649i	$-0.568924\pi$
$131$	7.59926	−	16.6401i	0.663951	−	1.45385i	0.878794	−	0.477201i	$-0.158349\pi$
$132$	−0.851465	+	3.56565i	−0.0741105	+	0.310350i
$133$	2.37283	−	0.341161i	0.205750	−	0.0295824i
$134$	5.82671	−	5.31598i	0.503351	−	0.459231i
$135$	−2.36814	−	2.73298i	−0.203817	−	0.235218i
$136$	2.04222	−	2.06435i	0.175119	−	0.177017i
$137$		−	0.896885i		−	0.0766261i	−0.999266	−	0.0383130i	$-0.987802\pi$
$137$		−	0.896885i		−	0.0766261i	0.999266	−	0.0383130i	$-0.0121984\pi$
$138$	−5.49329	+	3.97791i	−0.467620	+	0.338622i
$139$	1.59991			0.135703			0.0678514	−	0.997695i	$-0.478386\pi$
$139$	1.59991			0.135703			0.0678514	+	0.997695i	$0.478386\pi$
$140$	−2.47144	+	1.77332i	−0.208875	+	0.149873i
$141$	−2.39759	+	2.07752i	−0.201913	+	0.174959i
$142$	4.43046	−	4.04211i	0.371796	−	0.339207i
$143$	1.45390	+	10.1121i	0.121581	+	0.845613i
$144$	3.97905	−	0.408828i	0.331588	−	0.0340690i
$145$	−23.5071	−	10.7353i	−1.95216	−	0.891520i
$146$	1.70134	+	1.03283i	0.140804	+	0.0854780i
$147$	−0.971030	+	6.75367i	−0.0800892	+	0.557033i
$148$	−10.4942	−	10.9271i	−0.862617	−	0.898203i
$149$	−3.03705	−	0.891759i	−0.248805	−	0.0730558i	0.154952	−	0.987922i	$-0.450478\pi$
$149$	−3.03705	−	0.891759i	−0.248805	−	0.0730558i	−0.403757	+	0.914866i	$0.632296\pi$
$150$	−1.33575	+	11.3446i	−0.109064	+	0.926286i
$151$	5.05420	−	2.30818i	0.411305	−	0.187837i	−0.199006	−	0.979998i	$-0.563771\pi$
$151$	5.05420	−	2.30818i	0.411305	−	0.187837i	0.610312	+	0.792161i	$0.291044\pi$
$152$	5.71525	+	15.0745i	0.463568	+	1.22271i
$153$	0.775896	+	0.672318i	0.0627275	+	0.0543537i
$154$	−0.280276	+	1.05357i	−0.0225853	+	0.0848993i
$155$	−13.6999	+	21.3175i	−1.10040	+	1.71226i
$156$	9.88951	−	5.14346i	0.791795	−	0.411806i
$157$	−6.42113	+	4.12661i	−0.512462	+	0.329339i	−0.771184	−	0.636613i	$-0.780335\pi$
$157$	−6.42113	+	4.12661i	−0.512462	+	0.329339i	0.258722	+	0.965952i	$0.416699\pi$
$158$	−2.09345	+	2.54476i	−0.166546	+	0.202450i
$159$	11.7492	−	3.44988i	0.931773	−	0.273593i
$160$	−15.2599	−	13.6238i	−1.20640	−	1.07706i
$161$	−1.66341	+	1.14080i	−0.131095	+	0.0899078i
$162$	0.237024	+	1.39421i	0.0186224	+	0.109539i
$163$	−3.54312	+	1.04035i	−0.277519	+	0.0814868i	−0.417530	−	0.908663i	$-0.637104\pi$
$163$	−3.54312	+	1.04035i	−0.277519	+	0.0814868i	0.140012	+	0.990150i	$0.455286\pi$
$164$	20.5159	+	11.7468i	1.60203	+	0.917271i
$165$	3.58360	+	5.57619i	0.278983	+	0.434106i
$166$	−6.95607	−	21.6264i	−0.539896	−	1.67854i
$167$	0.978343	−	1.52233i	0.0757065	−	0.117802i	−0.801336	−	0.598215i	$-0.795877\pi$
$167$	0.978343	−	1.52233i	0.0757065	−	0.117802i	0.877042	+	0.480413i	$0.159513\pi$
$168$	1.18607	−	0.0912567i	0.0915070	−	0.00704061i
$169$	11.8297	−	13.6522i	0.909974	−	1.05017i
$170$	−0.134379	−	5.24876i	−0.0103064	−	0.402562i
$171$	−5.18476	+	2.36780i	−0.396489	+	0.181070i
$172$	−0.321834	−	6.28119i	−0.0245396	−	0.478936i
$173$	−0.426922	+	1.45396i	−0.0324583	+	0.110543i	−0.974129	−	0.225993i	$-0.927437\pi$
$173$	−0.426922	+	1.45396i	−0.0324583	+	0.110543i	0.941671	+	0.336536i	$0.109255\pi$
$174$	5.67965	+	8.35928i	0.430573	+	0.633715i
$175$	−0.483461	+	3.36255i	−0.0365462	+	0.254185i
$176$	−7.32583	−	0.296226i	−0.552205	−	0.0223289i
$177$	0.527440	−	1.15493i	0.0396448	−	0.0868101i
$178$	7.96988	+	3.39597i	0.597368	+	0.254539i
$179$	2.99107	+	20.8033i	0.223563	+	1.55491i	0.724405	+	0.689375i	$0.242115\pi$
$179$	2.99107	+	20.8033i	0.223563	+	1.55491i	−0.500842	+	0.865539i	$0.666976\pi$
$180$	4.45038	−	5.70116i	0.331712	−	0.424939i
$181$	−10.0184	−	11.5618i	−0.744662	−	0.859385i	0.249378	−	0.968406i	$-0.419774\pi$
$181$	−10.0184	−	11.5618i	−0.744662	−	0.859385i	−0.994039	+	0.109021i	$0.965228\pi$
$182$	2.97926	−	1.45385i	0.220837	−	0.107767i
$183$	10.9093			0.806440
$184$	−9.92455	−	9.24680i	−0.731648	−	0.681683i
$185$	−27.3936			−2.01401
$186$	8.90596	−	4.34604i	0.653017	−	0.318667i
$187$	−1.23233	−	1.42218i	−0.0901167	−	0.104000i
$188$	−5.00151	−	3.90423i	−0.364773	−	0.284745i
$189$	0.0598544	+	0.416296i	0.00435377	+	0.0302811i
$190$	26.8169	+	11.4267i	1.94550	+	0.828980i
$191$	11.2219	−	24.5726i	0.811991	−	1.77801i	0.213388	−	0.976968i	$-0.431550\pi$
$191$	11.2219	−	24.5726i	0.811991	−	1.77801i	0.598604	−	0.801045i	$-0.295722\pi$
$192$	2.33647	+	7.65120i	0.168620	+	0.552178i
$193$	−0.929388	+	6.46404i	−0.0668988	+	0.465292i	0.928643	+	0.370974i	$0.120976\pi$
$193$	−0.929388	+	6.46404i	−0.0668988	+	0.465292i	−0.995542	+	0.0943178i	$0.969933\pi$
$194$	6.87659	+	10.1209i	0.493710	+	0.726640i
$195$	5.67842	−	19.3389i	0.406640	−	1.38489i
$196$	−13.6284	+	0.698285i	−0.973454	+	0.0498775i
$197$	3.20510	−	1.46372i	0.228354	−	0.104286i	−0.297953	−	0.954581i	$-0.596304\pi$
$197$	3.20510	−	1.46372i	0.228354	−	0.104286i	0.526307	+	0.850295i	$0.323576\pi$
$198$	−0.0663436	−	2.59134i	−0.00471483	−	0.184158i
$199$	−1.96670	+	2.26970i	−0.139416	+	0.160895i	−0.821164	−	0.570693i	$-0.806675\pi$
$199$	−1.96670	+	2.26970i	−0.139416	+	0.160895i	0.681748	+	0.731587i	$0.261220\pi$
$200$	−22.7787	+	1.75261i	−1.61070	+	0.123928i
$201$	−3.01526	+	4.69183i	−0.212680	+	0.330937i
$202$	−4.11216	−	12.7847i	−0.289330	−	0.899529i
$203$	1.62491	+	2.52841i	0.114046	+	0.177459i
$204$	−1.02026	+	1.78190i	−0.0714326	+	0.124758i
$205$	41.0142	−	12.0429i	2.86456	−	0.841109i
$206$	−1.46060	−	8.59147i	−0.101765	−	0.598596i
$207$	3.03066	−	3.71686i	0.210646	−	0.258340i
$208$	13.9069	+	17.4249i	0.964271	+	1.20820i
$209$	10.0244	−	2.94342i	0.693399	−	0.203600i
$210$	1.36647	−	1.66106i	0.0942956	−	0.114624i
$211$	20.9986	−	13.4950i	1.44560	−	0.929031i	0.446181	−	0.894943i	$-0.352784\pi$
$211$	20.9986	−	13.4950i	1.44560	−	0.929031i	0.999419	−	0.0340880i	$-0.0108526\pi$
$212$	11.3003	+	21.7275i	0.776109	+	1.49225i
$213$	−2.29271	+	3.56753i	−0.157094	+	0.244443i
$214$	2.10703	−	7.92042i	0.144033	−	0.541429i
$215$	−8.59445	−	7.44714i	−0.586137	−	0.507890i
$216$	−2.64473	+	1.00270i	−0.179951	+	0.0682253i
$217$	2.68078	−	1.22427i	0.181983	−	0.0831090i
$218$	−1.10328	+	9.37024i	−0.0747235	+	0.634633i
$219$	−1.35035	−	0.396498i	−0.0912482	−	0.0267929i
$220$	−9.56150	+	9.18269i	−0.644636	+	0.619097i
$221$	−0.814343	+	5.66388i	−0.0547786	+	0.380994i
$222$	9.15749	+	5.55925i	0.614611	+	0.373112i
$223$	4.99327	+	2.28035i	0.334374	+	0.152703i	0.575525	−	0.817784i	$-0.304798\pi$
$223$	4.99327	+	2.28035i	0.334374	+	0.152703i	−0.241151	+	0.970488i	$0.577525\pi$
$224$	0.636385	+	2.29245i	0.0425203	+	0.153171i
$225$	−1.14952	−	7.99507i	−0.0766345	−	0.533005i
$226$	5.86487	−	5.35079i	0.390125	−	0.355929i
$227$	3.88255	−	3.36425i	0.257694	−	0.223293i	−0.516426	−	0.856332i	$-0.672738\pi$
$227$	3.88255	−	3.36425i	0.257694	−	0.223293i	0.774120	+	0.633038i	$0.218193\pi$
$228$	−6.64579	−	9.26210i	−0.440128	−	0.613397i
$229$	16.1245			1.06554			0.532768	−	0.846261i	$-0.321152\pi$
$229$	16.1245			1.06554			0.532768	+	0.846261i	$0.321152\pi$
$230$	−24.4888	+	1.36163i	−1.61474	+	0.0897831i
$231$		−	0.770899i		−	0.0507214i
$232$	−14.2151	+	14.3692i	−0.933269	+	0.943383i
$233$	−17.0202	−	19.6423i	−1.11503	−	1.28681i	−0.953982	−	0.299865i	$-0.903058\pi$
$233$	−17.0202	−	19.6423i	−1.11503	−	1.28681i	−0.161047	−	0.986947i	$-0.551487\pi$
$234$	−5.82290	+	5.31250i	−0.380655	+	0.347289i
$235$	−11.3557	+	1.63270i	−0.740762	+	0.106505i
$236$	2.46990	+	0.589802i	0.160777	+	0.0383928i
$237$	0.967941	−	2.11949i	0.0628745	−	0.137676i
$238$	−0.316882	+	0.521985i	−0.0205404	+	0.0338353i
$239$	22.8951	+	3.29182i	1.48096	+	0.212930i	0.834920	−	0.550371i	$-0.185514\pi$
$239$	22.8951	+	3.29182i	1.48096	+	0.212930i	0.646043	+	0.763301i	$0.276423\pi$
$240$	12.9043	+	6.53569i	0.832970	+	0.421877i
$241$	−7.76480	+	26.4445i	−0.500175	+	1.70344i	0.191729	+	0.981448i	$0.438591\pi$
$241$	−7.76480	+	26.4445i	−0.500175	+	1.70344i	−0.691903	+	0.721990i	$0.743227\pi$
$242$	1.26348	−	10.7309i	0.0812197	−	0.689806i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	4.20616	+	21.4094i	0.269272	+	1.37059i
$245$	−16.1581	+	18.6474i	−1.03230	+	1.19134i
$246$	−16.1548	−	4.29757i	−1.02999	−	0.274003i
$247$	−26.7252	−	17.1753i	−1.70049	−	1.09284i
$248$	11.9628	+	15.8022i	0.759638	+	1.00344i
$249$	8.68473	+	13.5137i	0.550373	+	0.856396i
$250$	−9.99824	+	12.1537i	−0.632344	+	0.768665i
$251$	5.10963	+	17.4018i	0.322517	+	1.09839i	0.948031	+	0.318179i	$0.103071\pi$
$251$	5.10963	+	17.4018i	0.322517	+	1.09839i	−0.625513	+	0.780213i	$0.715110\pi$
$252$	−0.793898	+	0.277969i	−0.0500109	+	0.0175104i
$253$	−6.46809	+	5.95293i	−0.406645	+	0.374257i
$254$	−14.9628	+	2.54376i	−0.938847	+	0.159610i
$255$	1.04598	+	3.56226i	0.0655015	+	0.223078i
$256$	−14.1145	+	7.53525i	−0.882158	+	0.470953i
$257$	19.6384	−	12.6208i	1.22501	−	0.787267i	0.241904	−	0.970300i	$-0.422228\pi$
$257$	19.6384	−	12.6208i	1.22501	−	0.787267i	0.983107	+	0.183034i	$0.0585917\pi$
$258$	1.36175	+	4.23369i	0.0847789	+	0.263578i
$259$	2.68017	+	1.72244i	0.166538	+	0.107027i
$260$	40.1417	+	3.68757i	2.48948	+	0.228693i
$261$	−5.40073	−	4.67975i	−0.334296	−	0.289670i
$262$	−25.8620	+	0.662120i	−1.59776	+	0.0409059i
$263$	−8.52535	−	18.6679i	−0.525696	−	1.15111i	−0.967238	−	0.253873i	$-0.918296\pi$
$263$	−8.52535	−	18.6679i	−0.525696	−	1.15111i	0.441542	−	0.897241i	$-0.354432\pi$
$264$	5.05988	−	1.12931i	0.311414	−	0.0695039i
$265$	42.4881	+	12.4756i	2.61003	+	0.766373i
$266$	−1.90527	−	2.80416i	−0.116819	−	0.171934i
$267$	−6.06348	−	0.871797i	−0.371079	−	0.0533531i
$268$	−10.3702	−	4.10843i	−0.633461	−	0.250963i
$269$	−3.47782	−	1.58827i	−0.212047	−	0.0968385i	0.306560	−	0.951851i	$-0.400822\pi$
$269$	−3.47782	−	1.58827i	−0.212047	−	0.0968385i	−0.518607	+	0.855013i	$0.673549\pi$
$270$	−2.00474	+	4.70485i	−0.122005	+	0.286328i
$271$	18.5390	−	2.66550i	1.12616	−	0.161918i	0.446038	−	0.895014i	$-0.352835\pi$
$271$	18.5390	−	2.66550i	1.12616	−	0.161918i	0.680125	+	0.733096i	$0.261925\pi$
$272$	−3.89032	−	1.31523i	−0.235885	−	0.0797472i
$273$	−1.77156	+	1.53506i	−0.107220	+	0.0929062i
$274$	−1.13990	+	0.556264i	−0.0688640	+	0.0336051i
$275$			14.8053i			0.892793i
$276$	8.46278	+	4.51457i	0.509400	+	0.271745i
$277$			23.8555i			1.43334i	0.697414	+	0.716668i	$0.254334\pi$
$277$			23.8555i			1.43334i	−0.697414	+	0.716668i	$0.745666\pi$
$278$	−0.992293	−	2.03342i	−0.0595138	−	0.121956i
$279$	−5.29576	+	4.58880i	−0.317049	+	0.274724i
$280$	3.78665	+	2.04125i	0.226296	+	0.121988i
$281$	−16.6275	+	2.39068i	−0.991915	+	0.142616i	−0.619119	−	0.785297i	$-0.712510\pi$
$281$	−16.6275	+	2.39068i	−0.991915	+	0.142616i	−0.372796	+	0.927913i	$0.621601\pi$
$282$	4.12747	+	1.75872i	0.245787	+	0.104730i
$283$	−2.71789	−	1.24122i	−0.161562	−	0.0737828i	0.332993	−	0.942929i	$-0.391942\pi$
$283$	−2.71789	−	1.24122i	−0.161562	−	0.0737828i	−0.494555	+	0.869147i	$0.664669\pi$
$284$	−7.88520	−	3.12393i	−0.467900	−	0.185371i
$285$	−20.4023	−	2.93341i	−1.20853	−	0.173760i
$286$	11.9503	−	8.11951i	0.706634	−	0.480117i
$287$	−4.77003	−	1.40061i	−0.281566	−	0.0826752i
$288$	−2.98748	−	4.80364i	−0.176039	−	0.283057i
$289$	6.62420	+	14.5050i	0.389659	+	0.853233i
$290$	0.935363	+	36.5347i	0.0549264	+	2.14539i
$291$	−6.53889	−	5.66598i	−0.383316	−	0.332145i
$292$	0.257486	−	2.80291i	0.0150683	−	0.164028i
$293$	−10.6698	−	6.85705i	−0.623335	−	0.400593i	0.190502	−	0.981687i	$-0.438989\pi$
$293$	−10.6698	−	6.85705i	−0.623335	−	0.400593i	−0.813837	+	0.581094i	$0.802625\pi$
$294$	9.18587	−	2.95460i	0.535731	−	0.172316i
$295$	3.86257	−	2.48232i	0.224888	−	0.144527i
$296$	−7.37921	+	20.1148i	−0.428908	+	1.16915i
$297$	0.516403	+	1.75871i	0.0299647	+	0.102051i
$298$	0.750245	+	4.41305i	0.0434605	+	0.255641i
$299$	26.5598	+	3.01009i	1.53599	+	0.174078i
$300$	15.2470	−	5.33846i	0.880286	−	0.308216i
$301$	0.372618	+	1.26902i	0.0214774	+	0.0731452i
$302$	−6.06830	−	4.99210i	−0.349191	−	0.287263i
$303$	5.13408	+	7.98878i	0.294945	+	0.458943i
$304$	15.6144	−	16.6133i	0.895547	−	0.952840i
$305$	33.1882	+	21.3287i	1.90035	+	1.22128i
$306$	0.373263	−	1.40311i	0.0213380	−	0.0802106i
$307$	4.93534	−	5.69569i	0.281675	−	0.325070i	−0.597228	−	0.802072i	$-0.703731\pi$
$307$	4.93534	−	5.69569i	0.281675	−	0.325070i	0.878902	+	0.477002i	$0.158277\pi$
$308$	1.51288	−	0.297225i	0.0862042	−	0.0169360i
$309$	2.55989	+	5.60538i	0.145627	+	0.318879i
$310$	35.5905	+	4.19053i	2.02141	+	0.238006i
$311$	5.23408	−	17.8256i	0.296798	−	1.01080i	−0.667198	−	0.744881i	$-0.732506\pi$
$311$	5.23408	−	17.8256i	0.296798	−	1.01080i	0.963995	−	0.265919i	$-0.0856754\pi$
$312$	−12.6708	−	9.37908i	−0.717340	−	0.530986i
$313$	−3.14861	−	0.452702i	−0.177970	−	0.0255883i	0.0527535	−	0.998608i	$-0.483200\pi$
$313$	−3.14861	−	0.452702i	−0.177970	−	0.0255883i	−0.230724	+	0.973019i	$0.574109\pi$
$314$	9.22724	+	5.60158i	0.520723	+	0.316116i
$315$	−0.631810	+	1.38347i	−0.0355985	+	0.0779498i
$316$	4.53267	+	1.08238i	0.254983	+	0.0608889i
$317$	11.1965	−	1.60981i	0.628858	−	0.0904161i	0.179485	−	0.983761i	$-0.442557\pi$
$317$	11.1965	−	1.60981i	0.628858	−	0.0904161i	0.449372	+	0.893345i	$0.351648\pi$
$318$	−11.6717	−	12.7931i	−0.654517	−	0.717400i
$319$	8.57778	+	9.89928i	0.480263	+	0.554253i
$320$	−7.85086	+	27.8444i	−0.438876	+	1.55655i
$321$			5.79537i			0.323466i
$322$	2.48159	+	1.40658i	0.138293	+	0.0783854i
$323$	5.85179			0.325602
$324$	1.62497	−	1.16596i	0.0902763	−	0.0647755i
$325$	34.0232	−	29.4813i	1.88727	−	1.63533i
$326$	3.51975	+	3.85791i	0.194941	+	0.213670i
$327$	−0.949458	−	6.60362i	−0.0525051	−	0.365181i
$328$	2.20534	−	33.3604i	0.121769	−	1.84202i
$329$	1.21369	+	0.554274i	0.0669130	+	0.0305581i
$330$	4.86448	−	8.01304i	0.267781	−	0.441104i
$331$	−2.98666	+	20.7727i	−0.164162	+	1.14177i	0.726522	+	0.687144i	$0.241136\pi$
$331$	−2.98666	+	20.7727i	−0.164162	+	1.14177i	−0.890683	+	0.454625i	$0.849773\pi$
$332$	−23.1720	+	22.2539i	−1.27173	+	1.22134i
$333$	−7.26828	−	2.13416i	−0.398299	−	0.116951i
$334$	−2.54160	−	0.299256i	−0.139070	−	0.0163745i
$335$	−18.3460	+	8.37832i	−1.00235	+	0.457756i
$336$	−0.851602	−	1.45084i	−0.0464587	−	0.0791498i
$337$	9.58180	+	8.30268i	0.521954	+	0.452276i	0.875554	−	0.483121i	$-0.160497\pi$
$337$	9.58180	+	8.30268i	0.521954	+	0.452276i	−0.353599	+	0.935397i	$0.615042\pi$
$338$	−24.6883	−	6.56768i	−1.34286	−	0.357235i
$339$	−3.03500	+	4.72256i	−0.164839	+	0.256494i
$340$	−6.58761	+	3.42616i	−0.357263	+	0.185810i
$341$	10.8051	−	6.94401i	0.585129	−	0.376039i
$342$	6.22505	+	5.12106i	0.336612	+	0.276915i
$343$	5.57819	−	1.63791i	0.301194	−	0.0884386i
$344$	−7.78352	+	4.30474i	−0.419659	+	0.232096i
$345$	16.4867	−	5.38216i	0.887612	−	0.289766i
$346$	2.11271	−	0.359173i	0.113580	−	0.0193093i
$347$	−31.5108	+	9.25240i	−1.69159	+	0.496695i	−0.978823	−	0.204708i	$-0.934375\pi$
$347$	−31.5108	+	9.25240i	−1.69159	+	0.496695i	−0.712765	+	0.701403i	$0.752557\pi$
$348$	7.10166	−	12.4031i	0.380689	−	0.664879i
$349$	−16.0400	−	24.9587i	−0.858601	−	1.33601i	−0.940649	−	0.339381i	$-0.889782\pi$
$349$	−16.0400	−	24.9587i	−0.858601	−	1.33601i	0.0820477	−	0.996628i	$-0.473854\pi$
$350$	4.57350	−	1.47105i	0.244464	−	0.0786310i
$351$	3.01329	−	4.68876i	0.160837	−	0.250268i
$352$	4.16711	+	9.49454i	0.222108	+	0.506060i
$353$	0.993198	−	1.14621i	0.0528626	−	0.0610067i	−0.728702	−	0.684830i	$-0.759876\pi$
$353$	0.993198	−	1.14621i	0.0528626	−	0.0610067i	0.781565	+	0.623824i	$0.214422\pi$
$354$	−1.79500	+	0.0459556i	−0.0954030	+	0.00244251i
$355$	−13.9497	+	6.37062i	−0.740374	+	0.338118i
$356$	−0.626924	−	12.2356i	−0.0332269	−	0.648486i
$357$	0.121649	−	0.414298i	0.00643834	−	0.0219270i
$358$	24.5850	−	16.7041i	1.29936	−	0.882839i
$359$	−1.45080	+	10.0905i	−0.0765701	+	0.532557i	0.915047	+	0.403347i	$0.132153\pi$
$359$	−1.45080	+	10.0905i	−0.0765701	+	0.532557i	−0.991617	+	0.129210i	$0.958756\pi$
$360$	−10.0061	−	2.12029i	−0.527369	−	0.111749i
$361$	−5.60322	+	12.2693i	−0.294906	+	0.645755i
$362$	−8.48103	+	19.9038i	−0.445753	+	1.04612i
$363$	1.08733	+	7.56251i	0.0570698	+	0.396929i
$364$	−3.69557	−	2.88480i	−0.193701	−	0.151205i
$365$	−3.33282	−	3.84628i	−0.174448	−	0.201324i
$366$	−6.76615	−	13.8653i	−0.353672	−	0.724749i
$367$	−27.3567			−1.42801			−0.714003	−	0.700143i	$-0.753120\pi$
$367$	−27.3567			−1.42801			−0.714003	+	0.700143i	$0.753120\pi$
$368$	−5.59690	+	18.3487i	−0.291758	+	0.956492i
$369$	11.8204			0.615347
$370$	16.9900	+	34.8160i	0.883266	+	1.81000i
$371$	−3.37258	−	3.89216i	−0.175095	−	0.202071i
$372$	−11.0473	−	8.62360i	−0.572774	−	0.447113i
$373$	2.40226	+	16.7081i	0.124384	+	0.865110i	0.952497	+	0.304549i	$0.0985056\pi$
$373$	2.40226	+	16.7081i	0.124384	+	0.865110i	−0.828113	+	0.560562i	$0.810585\pi$
$374$	−1.04322	+	2.44830i	−0.0539436	+	0.126598i
$375$	4.62284	−	10.1226i	0.238723	−	0.522730i
$376$	−1.86008	+	8.77818i	−0.0959265	+	0.452700i
$377$	5.66834	−	39.4242i	0.291934	−	2.03045i
$378$	0.491972	−	0.334266i	0.0253043	−	0.0171928i
$379$	5.80051	−	19.7547i	0.297952	−	1.01473i	−0.665399	−	0.746488i	$-0.731738\pi$
$379$	5.80051	−	19.7547i	0.297952	−	1.01473i	0.963351	−	0.268244i	$-0.0864434\pi$
$380$	−2.10946	−	41.1702i	−0.108213	−	2.11199i
$381$	9.76224	−	4.45826i	0.500135	−	0.228404i
$382$	−38.1908	+	0.977762i	−1.95401	+	0.0500267i
$383$	−14.6701	+	16.9302i	−0.749607	+	0.865093i	−0.994530	−	0.104450i	$-0.966692\pi$
$383$	−14.6701	+	16.9302i	−0.749607	+	0.865093i	0.244923	+	0.969543i	$0.421237\pi$
$384$	8.27523	−	7.71496i	0.422294	−	0.393702i
$385$	1.50718	−	2.34522i	0.0768130	−	0.119523i
$386$	8.79193	−	2.82789i	0.447498	−	0.143936i
$387$	−1.70016	−	2.64550i	−0.0864241	−	0.134479i
$388$	8.59829	−	15.0170i	0.436512	−	0.762374i
$389$	−7.50380	+	2.20331i	−0.380458	+	0.111712i	−0.466369	−	0.884590i	$-0.654438\pi$
$389$	−7.50380	+	2.20331i	−0.380458	+	0.111712i	0.0859112	+	0.996303i	$0.472620\pi$
$390$	−28.1008	+	4.77730i	−1.42294	+	0.241908i
$391$	−4.41548	+	2.17856i	−0.223300	+	0.110175i
$392$	9.34003	+	16.8880i	0.471743	+	0.852971i
$393$	17.5522	−	5.15379i	0.885391	−	0.259974i
$394$	−3.84818	−	3.16572i	−0.193869	−	0.159487i
$395$	7.08847	−	4.55548i	0.356659	−	0.229211i
$396$	−3.25233	+	1.69151i	−0.163436	+	0.0850017i
$397$	−2.81836	+	4.38545i	−0.141449	+	0.220100i	−0.904749	−	0.425945i	$-0.859942\pi$
$397$	−2.81836	+	4.38545i	−0.141449	+	0.220100i	0.763300	+	0.646045i	$0.223578\pi$
$398$	4.10447	+	1.09189i	0.205739	+	0.0547315i
$399$	1.81170	+	1.56985i	0.0906986	+	0.0785908i
$400$	16.3552	+	27.8637i	0.817761	+	1.39319i
$401$	6.97947	−	3.18742i	0.348538	−	0.159172i	−0.233451	−	0.972369i	$-0.575002\pi$
$401$	6.97947	−	3.18742i	0.348538	−	0.159172i	0.581989	+	0.813197i	$0.302275\pi$
$402$	7.83323	+	0.922307i	0.390686	+	0.0460005i
$403$	−37.4734	−	11.0032i	−1.86668	−	0.548108i
$404$	−13.6984	+	13.1557i	−0.681520	+	0.654519i
$405$	0.514647	−	3.57945i	0.0255730	−	0.177864i
$406$	2.20570	−	3.63335i	0.109467	−	0.180320i
$407$	12.6301	+	5.76797i	0.626051	+	0.285908i
$408$	2.89750	+	0.191543i	0.143448	+	0.00948280i
$409$	0.480882	+	3.34461i	0.0237781	+	0.165380i	0.998250	−	0.0591272i	$-0.0188318\pi$
$409$	0.480882	+	3.34461i	0.0237781	+	0.165380i	−0.974472	+	0.224508i	$0.927923\pi$
$410$	−40.7437	−	44.6581i	−2.01219	−	2.20551i
$411$	0.677821	−	0.587335i	0.0334344	−	0.0289711i
$412$	−10.0135	+	7.18494i	−0.493330	+	0.353977i
$413$	−0.533994			−0.0262761
$414$	−6.60364	−	1.54658i	−0.324551	−	0.0760102i
$415$			58.0907i			2.85156i
$416$	13.5210	−	28.4823i	0.662922	−	1.39646i
$417$	1.04772	+	1.20913i	0.0513070	+	0.0592115i
$418$	−9.95823	−	10.9150i	−0.487073	−	0.533868i
$419$	−1.22688	+	0.176399i	−0.0599370	+	0.00861763i	−0.172218	−	0.985059i	$-0.555093\pi$
$419$	−1.22688	+	0.176399i	−0.0599370	+	0.00861763i	0.112281	+	0.993676i	$0.464184\pi$
$420$	−2.95864	−	0.706512i	−0.144367	−	0.0344743i
$421$	−8.25319	+	18.0720i	−0.402236	+	0.880773i	0.594803	+	0.803872i	$0.297230\pi$
$421$	−8.25319	+	18.0720i	−0.402236	+	0.880773i	−0.997039	+	0.0769019i	$0.975497\pi$
$422$	−30.1752	−	18.3184i	−1.46890	−	0.891728i
$423$	−3.14017	−	0.451489i	−0.152680	−	0.0219521i
$424$	20.6061	−	27.8380i	1.00072	−	1.35193i
$425$	−2.33630	+	7.95670i	−0.113327	+	0.385957i
$426$	5.95616	+	0.701295i	0.288577	+	0.0339779i
$427$	−1.90601	−	4.17358i	−0.0922384	−	0.201974i
$428$	−11.3733	+	2.23444i	−0.549750	+	0.108006i
$429$	−6.69009	+	7.72078i	−0.323001	+	0.372763i
$430$	−4.13456	+	15.5420i	−0.199386	+	0.749503i
$431$	19.2795	+	12.3902i	0.928662	+	0.596815i	0.915159	−	0.403094i	$-0.132065\pi$
$431$	19.2795	+	12.3902i	0.928662	+	0.596815i	0.0135036	+	0.999909i	$0.495702\pi$
$432$	2.91470	+	2.73944i	0.140233	+	0.131801i
$433$	−11.9789	−	18.6395i	−0.575669	−	0.895758i	0.424283	−	0.905529i	$-0.360526\pi$
$433$	−11.9789	−	18.6395i	−0.575669	−	0.895758i	−0.999952	+	0.00977131i	$0.996890\pi$
$434$	−3.21866	−	2.64784i	−0.154501	−	0.127101i
$435$	−7.28065	−	24.7956i	−0.349080	−	1.18886i
$436$	12.5934	−	4.40936i	0.603116	−	0.211170i
$437$	−0.818533	−	27.3232i	−0.0391557	−	1.30705i
$438$	0.333578	+	1.96215i	0.0159390	+	0.0937552i
$439$	−8.68928	−	29.5930i	−0.414717	−	1.41240i	−0.856905	−	0.515474i	$-0.827616\pi$
$439$	−8.68928	−	29.5930i	−0.414717	−	1.41240i	0.442189	−	0.896922i	$-0.354202\pi$
$440$	17.6010	+	6.45699i	0.839095	+	0.307825i
$441$	−5.73997	+	3.68885i	−0.273332	+	0.175660i
$442$	7.70361	−	2.47784i	0.366423	−	0.117859i
$443$	−19.8718	−	12.7708i	−0.944137	−	0.606760i	−0.0245718	−	0.999698i	$-0.507822\pi$
$443$	−19.8718	−	12.7708i	−0.944137	−	0.606760i	−0.919565	+	0.392938i	$0.871459\pi$
$444$	1.38592	−	15.0867i	0.0657731	−	0.715984i
$445$	−16.7418	−	14.5068i	−0.793637	−	0.687690i
$446$	−0.198686	−	7.76054i	−0.00940804	−	0.367472i
$447$	−1.31490	−	2.87923i	−0.0621927	−	0.136183i
$448$	2.51891	−	2.23064i	0.119007	−	0.105388i
$449$	−1.92741	−	0.565940i	−0.0909603	−	0.0267083i	0.235936	−	0.971769i	$-0.424185\pi$
$449$	−1.92741	−	0.565940i	−0.0909603	−	0.0267083i	−0.326896	+	0.945060i	$0.606003\pi$
$450$	−9.44844	+	6.41967i	−0.445404	+	0.302626i
$451$	−21.4458	−	3.08344i	−1.00984	−	0.145193i
$452$	−10.4381	−	4.13534i	−0.490968	−	0.194510i
$453$	5.05420	+	2.30818i	0.237467	+	0.108448i
$454$	−6.68384	−	2.84799i	−0.313688	−	0.133663i
$455$	−8.39060	+	1.20639i	−0.393357	+	0.0565562i
$456$	−7.64989	+	14.1910i	−0.358239	+	0.664556i
$457$	23.0762	−	19.9956i	1.07946	−	0.935355i	0.0813397	−	0.996686i	$-0.474080\pi$
$457$	23.0762	−	19.9956i	1.07946	−	0.935355i	0.998117	+	0.0613314i	$0.0195347\pi$
$458$	−10.0007	−	20.4935i	−0.467301	−	0.957599i
$459$			1.02666i			0.0479203i
$460$	16.9189	+	30.2797i	0.788850	+	1.41180i
$461$			25.7500i			1.19930i	0.800264	+	0.599648i	$0.204693\pi$
$461$			25.7500i			1.19930i	−0.800264	+	0.599648i	$0.795307\pi$
$462$	−0.979779	+	0.478125i	−0.0455834	+	0.0222444i
$463$	8.32083	−	7.21004i	0.386702	−	0.335079i	−0.439716	−	0.898137i	$-0.644921\pi$
$463$	8.32083	−	7.21004i	0.386702	−	0.335079i	0.826417	+	0.563058i	$0.190375\pi$
$464$	27.0791	+	9.15480i	1.25711	+	0.425001i
$465$	−25.0822	+	3.60628i	−1.16316	+	0.167237i
$466$	−14.4083	+	33.8144i	−0.667454	+	1.56642i
$467$	−30.8912	−	14.1075i	−1.42947	−	0.652819i	−0.457780	−	0.889065i	$-0.651355\pi$
$467$	−30.8912	−	14.1075i	−1.42947	−	0.652819i	−0.971693	+	0.236247i	$0.924083\pi$
$468$	10.3634	+	4.10574i	0.479049	+	0.189788i
$469$	2.32177	+	0.333820i	0.107209	+	0.0154144i
$470$	9.11807	+	13.4199i	0.420585	+	0.619015i
$471$	−7.32363	−	2.15041i	−0.337455	−	0.0990857i
$472$	−0.782259	−	3.50494i	−0.0360064	−	0.161328i
$473$	2.39450	+	5.24323i	0.110099	+	0.241084i
$474$	−3.29412	+	0.0843362i	−0.151304	+	0.00387369i
$475$	−34.7942	−	30.1493i	−1.59647	−	1.38335i
$476$	0.859957	+	0.0789989i	0.0394160	+	0.00362091i
$477$	10.3013	+	6.62027i	0.471666	+	0.303121i
$478$	−10.0162	−	31.1404i	−0.458130	−	1.42433i
$479$	−9.24167	+	5.93926i	−0.422263	+	0.271372i	−0.734469	−	0.678643i	$-0.762569\pi$
$479$	−9.24167	+	5.93926i	−0.422263	+	0.271372i	0.312206	+	0.950014i	$0.398932\pi$
$480$	0.303103	−	20.4544i	0.0138347	−	0.933610i
$481$	−11.8948	−	40.5101i	−0.542357	−	1.84710i
$482$	38.4256	−	6.53259i	1.75024	−	0.297552i
$483$	−1.95146	−	0.510054i	−0.0887946	−	0.0232083i
$484$	−14.4221	+	5.04963i	−0.655550	+	0.229529i
$485$	−8.81499	−	30.0211i	−0.400268	−	1.36319i
$486$	−0.898455	+	1.09214i	−0.0407548	+	0.0495406i
$487$	−6.72951	−	10.4713i	−0.304943	−	0.474501i	0.654634	−	0.755946i	$-0.272823\pi$
$487$	−6.72951	−	10.4713i	−0.304943	−	0.474501i	−0.959577	+	0.281445i	$0.909186\pi$
$488$	24.6017	−	18.6243i	1.11366	−	0.843083i
$489$	−3.10650	−	1.99642i	−0.140481	−	0.0902814i
$490$	33.7216	+	8.97078i	1.52339	+	0.405259i
$491$	−2.98824	+	3.44862i	−0.134858	+	0.155634i	−0.819161	−	0.573563i	$-0.805561\pi$
$491$	−2.98824	+	3.44862i	−0.134858	+	0.155634i	0.684304	+	0.729197i	$0.260106\pi$
$492$	4.55744	+	23.1974i	0.205465	+	1.04582i
$493$	3.04777	+	6.67368i	0.137265	+	0.300567i
$494$	−5.25357	+	44.6190i	−0.236369	+	2.00750i
$495$	−1.86744	+	6.35993i	−0.0839353	+	0.285858i
$496$	12.6643	−	25.0050i	0.568646	−	1.12276i
$497$	1.76540	+	0.253826i	0.0791891	+	0.0113857i
$498$	11.7889	−	19.4194i	0.528274	−	0.870202i
$499$	−3.25624	+	7.13017i	−0.145769	+	0.319190i	−0.968407	−	0.249376i	$-0.919775\pi$
$499$	−3.25624	+	7.13017i	−0.145769	+	0.319190i	0.822637	+	0.568566i	$0.192502\pi$
$500$	21.6478	+	5.16942i	0.968121	+	0.231184i
$501$	1.79118	−	0.257533i	0.0800240	−	0.0115057i
$502$	18.9479	−	17.2870i	0.845685	−	0.771558i
$503$	3.48132	+	4.01766i	0.155225	+	0.179139i	0.828035	−	0.560676i	$-0.189459\pi$
$503$	3.48132	+	4.01766i	0.155225	+	0.179139i	−0.672811	+	0.739815i	$0.734913\pi$
$504$	0.845676	+	0.836609i	0.0376694	+	0.0372655i
$505$			34.3409i			1.52815i
$506$	11.5775	+	4.52856i	0.514684	+	0.201319i
$507$	18.0644			0.802268
$508$	12.5132	+	17.4393i	0.555182	+	0.773745i
$509$	2.93351	−	2.54190i	0.130026	−	0.112668i	−0.587420	−	0.809282i	$-0.699856\pi$
$509$	2.93351	−	2.54190i	0.130026	−	0.112668i	0.717446	+	0.696614i	$0.245311\pi$
$510$	3.87875	−	3.53877i	0.171754	−	0.156699i
$511$	0.0842365	+	0.585878i	0.00372640	+	0.0259177i
$512$	18.3311	+	13.2655i	0.810126	+	0.586256i
$513$	−5.18476	−	2.36780i	−0.228913	−	0.104541i
$514$	−28.2206	−	17.1319i	−1.24476	−	0.755656i
$515$	−3.17138	+	22.0575i	−0.139748	+	0.971968i
$516$	4.53625	−	4.35653i	0.199697	−	0.191786i
$517$	5.57943	+	1.63827i	0.245383	+	0.0720510i
$518$	0.526860	−	4.47467i	0.0231489	−	0.196606i
$519$	−1.37841	+	0.629497i	−0.0605053	+	0.0276318i
$520$	−20.2098	−	53.3054i	−0.886259	−	2.33760i
$521$	−1.81021	−	1.56856i	−0.0793069	−	0.0687199i	0.614305	−	0.789068i	$-0.289436\pi$
$521$	−1.81021	−	1.56856i	−0.0793069	−	0.0687199i	−0.693612	+	0.720349i	$0.743982\pi$
$522$	−2.59814	+	9.76655i	−0.113718	+	0.427470i
$523$	15.5053	−	24.1268i	0.678002	−	1.05499i	−0.316328	−	0.948650i	$-0.602450\pi$
$523$	15.5053	−	24.1268i	0.678002	−	1.05499i	0.994330	−	0.106341i	$-0.0339136\pi$
$524$	16.8816	+	32.4588i	0.737475	+	1.41797i
$525$	−2.85784	+	1.83662i	−0.124726	+	0.0801568i
$526$	−18.4385	+	22.4135i	−0.803959	+	0.977276i
$527$	6.90267	−	2.02681i	0.300685	−	0.0882891i
$528$	−4.57353	−	5.73048i	−0.199037	−	0.249387i
$529$	10.7898	+	20.3121i	0.469122	+	0.883134i
$530$	−10.4959	−	61.7382i	−0.455912	−	2.68174i
$531$	1.21824	−	0.357707i	0.0528671	−	0.0155232i
$532$	−2.38229	+	4.16070i	−0.103285	+	0.180389i
$533$	35.6184	+	55.4232i	1.54280	+	2.40065i
$534$	2.65266	+	8.24712i	0.114792	+	0.356888i
$535$	−11.3305	+	17.6306i	−0.489860	+	0.762237i
$536$	1.21014	+	15.7282i	0.0522700	+	0.679355i
$537$	−13.7634	+	15.8838i	−0.593933	+	0.685435i
$538$	0.138385	+	5.40524i	0.00596621	+	0.233036i
$539$	11.3763	−	5.19537i	0.490011	−	0.223780i
$540$	7.22303	−	0.370091i	0.310830	−	0.0159262i
$541$	−2.54903	+	8.68120i	−0.109591	+	0.373234i	−0.995966	−	0.0897355i	$-0.971398\pi$
$541$	−2.54903	+	8.68120i	−0.109591	+	0.373234i	0.886374	+	0.462969i	$0.153216\pi$
$542$	−14.8859	−	21.9091i	−0.639406	−	0.941075i
$543$	2.17721	−	15.1428i	0.0934329	−	0.649840i
$544$	0.741249	+	5.76015i	0.0317808	+	0.246965i
$545$	10.0223	−	21.9457i	0.429307	−	0.940052i
$546$	3.04975	+	1.29950i	0.130517	+	0.0556135i
$547$	2.39531	+	16.6598i	0.102416	+	0.712320i	0.974732	+	0.223377i	$0.0717082\pi$
$547$	2.39531	+	16.6598i	0.102416	+	0.712320i	−0.872316	+	0.488943i	$0.837383\pi$
$548$	1.41397	+	1.10376i	0.0604020	+	0.0471504i
$549$	7.14409	+	8.24471i	0.304902	+	0.351876i
$550$	18.8169	−	9.18250i	0.802355	−	0.391543i
$551$	−40.7321			−1.73525
$552$	0.489061	−	13.5558i	0.0208158	−	0.576975i
$553$	−0.979969			−0.0416725
$554$	30.3193	−	14.7956i	1.28814	−	0.628604i
$555$	−17.9390	−	20.7027i	−0.761467	−	0.878779i
$556$	−1.96895	+	2.52232i	−0.0835021	+	0.106970i
$557$	−2.59722	−	18.0640i	−0.110048	−	0.765398i	−0.967870	−	0.251451i	$-0.919092\pi$
$557$	−2.59722	−	18.0640i	−0.110048	−	0.765398i	0.857822	−	0.513946i	$-0.171817\pi$
$558$	9.11668	+	3.88462i	0.385940	+	0.164449i
$559$	7.28107	−	15.9433i	0.307956	−	0.674330i
$560$	0.245797	−	6.07869i	0.0103868	−	0.256871i
$561$	0.267810	−	1.86266i	0.0113070	−	0.0786416i
$562$	13.3511	+	19.6501i	0.563183	+	0.828891i
$563$	−13.3313	+	45.4021i	−0.561845	+	1.91347i	−0.208225	+	0.978081i	$0.566769\pi$
$563$	−13.3313	+	45.4021i	−0.561845	+	1.91347i	−0.353620	+	0.935389i	$0.615049\pi$
$564$	−0.324674	−	6.33662i	−0.0136712	−	0.266820i
$565$	−18.4661	+	8.43318i	−0.776874	+	0.354787i
$566$	0.108147	+	4.22415i	0.00454575	+	0.177554i
$567$	−0.275420	+	0.317851i	−0.0115665	+	0.0133485i
$568$	0.920153	+	11.9593i	0.0386088	+	0.501799i
$569$	−11.0346	+	17.1701i	−0.462593	+	0.719808i	−0.991676	−	0.128762i	$-0.958900\pi$
$569$	−11.0346	+	17.1701i	−0.462593	+	0.719808i	0.529083	+	0.848570i	$0.322536\pi$
$570$	8.92562	+	27.7498i	0.373853	+	1.16231i
$571$	18.0111	+	28.0259i	0.753742	+	1.17285i	0.980042	+	0.198789i	$0.0637007\pi$
$571$	18.0111	+	28.0259i	0.753742	+	1.17285i	−0.226300	+	0.974058i	$0.572663\pi$
$572$	−17.7313	−	10.1524i	−0.741383	−	0.424493i
$573$	25.9196	−	7.61067i	1.08281	−	0.317940i
$574$	1.17834	+	6.93118i	0.0491831	+	0.289302i
$575$	37.4783	+	9.79571i	1.56295	+	0.408509i
$576$	−4.25233	+	6.77626i	−0.177181	+	0.282344i
$577$	35.2904	−	10.3622i	1.46916	−	0.431384i	0.553332	−	0.832961i	$-0.313356\pi$
$577$	35.2904	−	10.3622i	1.46916	−	0.431384i	0.915825	+	0.401577i	$0.131538\pi$
$578$	14.3267	−	17.4153i	0.595914	−	0.724381i
$579$	−5.49381	+	3.53066i	−0.228315	+	0.146729i
$580$	45.8539	−	23.8483i	1.90398	−	0.990245i
$581$	3.65260	−	5.68356i	0.151535	−	0.235794i
$582$	−3.14568	+	11.8248i	−0.130393	+	0.490153i
$583$	−16.9628	−	14.6983i	−0.702526	−	0.608742i
$584$	−3.72208	+	1.41116i	−0.154021	+	0.0583942i
$585$	18.3339	−	8.37283i	0.758015	−	0.346174i
$586$	−2.09743	+	17.8137i	−0.0866442	+	0.735877i
$587$	−25.6865	−	7.54225i	−1.06020	−	0.311302i	−0.295267	−	0.955415i	$-0.595409\pi$
$587$	−25.6865	−	7.54225i	−1.06020	−	0.311302i	−0.764930	+	0.644113i	$0.777227\pi$
$588$	−9.45240	−	9.84234i	−0.389810	−	0.405891i
$589$	−5.68412	+	39.5339i	−0.234210	+	1.62897i
$590$	−5.55056	−	3.36958i	−0.228513	−	0.138723i
$591$	3.20510	+	1.46372i	0.131840	+	0.0602094i
$592$	30.1418	−	3.09692i	1.23882	−	0.127283i
$593$	1.36692	+	9.50712i	0.0561325	+	0.390410i	0.998448	+	0.0556853i	$0.0177344\pi$
$593$	1.36692	+	9.50712i	0.0561325	+	0.390410i	−0.942316	+	0.334725i	$0.891357\pi$
$594$	1.91496	−	1.74711i	0.0785717	−	0.0716846i
$595$	1.18007	−	1.02254i	0.0483782	−	0.0419199i
$596$	5.14348	−	3.69058i	0.210685	−	0.151172i
$597$	−3.00324			−0.122914
$598$	−12.6471	−	35.6232i	−0.517179	−	1.45674i
$599$		−	30.8462i		−	1.26034i	−0.776456	−	0.630172i	$-0.782985\pi$
$599$		−	30.8462i		−	1.26034i	0.776456	−	0.630172i	$-0.217015\pi$
$600$	−16.2414	−	16.0673i	−0.663053	−	0.655944i
$601$	−6.76253	−	7.80438i	−0.275849	−	0.318347i	0.600872	−	0.799345i	$-0.294820\pi$
$601$	−6.76253	−	7.80438i	−0.275849	−	0.318347i	−0.876722	+	0.480998i	$0.840275\pi$
$602$	1.38177	−	1.26065i	0.0563166	−	0.0513803i
$603$	−5.52043	+	0.793718i	−0.224809	+	0.0323227i
$604$	−2.58108	+	10.8087i	−0.105023	+	0.439801i
$605$	−11.4776	+	25.1324i	−0.466630	+	1.02178i
$606$	6.96915	−	11.4800i	0.283102	−	0.466342i
$607$	14.1422	+	2.03334i	0.574013	+	0.0825305i	0.423207	−	0.906033i	$-0.360904\pi$
$607$	14.1422	+	2.03334i	0.574013	+	0.0825305i	0.150805	+	0.988563i	$0.451813\pi$
$608$	−30.7991	−	9.54135i	−1.24907	−	0.386953i
$609$	−0.846753	+	2.88378i	−0.0343122	+	0.116857i
$610$	6.52404	−	55.4092i	0.264150	−	2.24345i
$611$	−7.34532	−	16.0840i	−0.297160	−	0.650689i
$612$	−2.01480	+	0.395834i	−0.0814434	+	0.0160006i
$613$	−26.0134	+	30.0211i	−1.05067	+	1.21254i	−0.0741223	+	0.997249i	$0.523616\pi$
$613$	−26.0134	+	30.0211i	−1.05067	+	1.21254i	−0.976550	+	0.215291i	$0.930930\pi$
$614$	−10.3000	−	2.74004i	−0.415672	−	0.110579i
$615$	35.9600	+	23.1101i	1.45005	+	0.931888i
$616$	−1.31607	−	1.73846i	−0.0530261	−	0.0700444i
$617$	2.98873	+	4.65055i	0.120322	+	0.187224i	0.896190	−	0.443671i	$-0.146324\pi$
$617$	2.98873	+	4.65055i	0.120322	+	0.187224i	−0.775868	+	0.630895i	$0.782688\pi$
$618$	5.53651	−	6.73007i	0.222711	−	0.270723i
$619$	−6.81784	−	23.2194i	−0.274032	−	0.933267i	−0.975395	−	0.220463i	$-0.929243\pi$
$619$	−6.81784	−	23.2194i	−0.274032	−	0.933267i	0.701363	−	0.712804i	$-0.252575\pi$
$620$	−16.7479	−	47.8330i	−0.672610	−	1.92102i
$621$	4.79368	−	0.143606i	0.192364	−	0.00576271i
$622$	−25.9019	+	4.40348i	−1.03857	+	0.176563i
$623$	0.725852	+	2.47202i	0.0290806	+	0.0990395i
$624$	−4.06178	+	21.9210i	−0.162601	+	0.877544i
$625$	−0.121021	+	0.0777752i	−0.00484082	+	0.00311101i
$626$	1.37746	+	4.28253i	0.0550544	+	0.171164i
$627$	8.78904	+	5.64838i	0.351001	+	0.225574i
$628$	1.39648	−	15.2016i	0.0557256	−	0.606610i
$629$	5.87750	+	5.09289i	0.234351	+	0.203067i
$630$	2.15019	−	0.0550493i	0.0856657	−	0.00219322i
$631$	−2.10750	−	4.61478i	−0.0838982	−	0.183711i	0.863033	−	0.505147i	$-0.168562\pi$
$631$	−2.10750	−	4.61478i	−0.0838982	−	0.183711i	−0.946931	+	0.321436i	$0.895835\pi$
$632$	−1.43558	−	6.43214i	−0.0571042	−	0.255857i
$633$	23.9499	+	7.03233i	0.951924	+	0.279510i
$634$	−8.99026	−	13.2318i	−0.357049	−	0.525503i
$635$	38.4149	+	5.52322i	1.52445	+	0.219182i
$636$	−9.02044	+	22.7687i	−0.357684	+	0.902839i
$637$	−34.5923	−	15.7978i	−1.37060	−	0.625931i
$638$	7.26147	−	17.0417i	0.287484	−	0.674687i
$639$	−4.19757	+	0.603519i	−0.166053	+	0.0238749i
$640$	40.2583	−	7.29148i	1.59135	−	0.288221i
$641$	−11.9749	+	10.3763i	−0.472980	+	0.409840i	−0.858463	−	0.512875i	$-0.828580\pi$
$641$	−11.9749	+	10.3763i	−0.472980	+	0.409840i	0.385483	+	0.922715i	$0.374035\pi$
$642$	7.36566	−	3.59439i	0.290700	−	0.141859i
$643$		−	34.8441i		−	1.37412i	−0.726601	−	0.687060i	$-0.758901\pi$
$643$		−	34.8441i		−	1.37412i	0.726601	−	0.687060i	$-0.241099\pi$
$644$	0.248574	−	4.02637i	0.00979520	−	0.158661i
$645$		−	11.3721i		−	0.447776i
$646$	−3.62938	−	7.43737i	−0.142796	−	0.292619i
$647$	−10.7696	+	9.33188i	−0.423395	+	0.366874i	−0.840342	−	0.542057i	$-0.817646\pi$
$647$	−10.7696	+	9.33188i	−0.423395	+	0.366874i	0.416946	+	0.908931i	$0.363100\pi$
$648$	−2.48972	−	1.34212i	−0.0978055	−	0.0527235i
$649$	−2.30356	+	0.331202i	−0.0904226	+	0.0130008i
$650$	−58.5712	−	24.9572i	−2.29735	−	0.978902i
$651$	2.68078	+	1.22427i	0.105068	+	0.0479830i
$652$	2.72022	−	6.86619i	0.106532	−	0.268901i
$653$	−13.5793	−	1.95241i	−0.531399	−	0.0764036i	−0.128608	−	0.991696i	$-0.541051\pi$
$653$	−13.5793	−	1.95241i	−0.531399	−	0.0764036i	−0.402791	+	0.915292i	$0.631960\pi$
$654$	−7.80405	+	5.30240i	−0.305162	+	0.207340i
$655$	63.4731	+	18.6374i	2.48010	+	0.728223i
$656$	−43.7674	+	17.8878i	−1.70883	+	0.698402i
$657$	−0.584637	−	1.28018i	−0.0228089	−	0.0499445i
$658$	−0.0482936	−	1.88632i	−0.00188268	−	0.0735364i
$659$	2.18840	+	1.89626i	0.0852481	+	0.0738679i	0.696442	−	0.717613i	$-0.254765\pi$
$659$	2.18840	+	1.89626i	0.0852481	+	0.0738679i	−0.611194	+	0.791481i	$0.709311\pi$
$660$	−13.2013	−	1.21272i	−0.513859	−	0.0472050i
$661$	−11.6029	−	7.45675i	−0.451301	−	0.290034i	0.295178	−	0.955442i	$-0.404621\pi$
$661$	−11.6029	−	7.45675i	−0.451301	−	0.290034i	−0.746479	+	0.665408i	$0.768257\pi$
$662$	28.2535	−	9.08765i	1.09810	−	0.353201i
$663$	−4.81375	+	3.09361i	−0.186951	+	0.120146i
$664$	42.6555	+	15.6483i	1.65535	+	0.607272i
$665$	2.44233	+	8.31782i	0.0947096	+	0.322551i
$666$	1.79549	+	10.5613i	0.0695737	+	0.409242i
$667$	30.7345	−	15.1642i	1.19005	−	0.587159i
$668$	1.19601	+	3.41587i	0.0462748	+	0.132164i
$669$	1.54652	+	5.26697i	0.0597920	+	0.203633i
$670$	22.0270	+	18.1205i	0.850976	+	0.700058i
$671$	−10.8108	−	16.8219i	−0.417347	−	0.649404i
$672$	−1.31578	+	1.98219i	−0.0507572	+	0.0764645i
$673$	−24.2752	−	15.6007i	−0.935739	−	0.601363i	−0.0185552	−	0.999828i	$-0.505907\pi$
$673$	−24.2752	−	15.6007i	−0.935739	−	0.601363i	−0.917184	+	0.398465i	$0.869543\pi$
$674$	4.60955	−	17.3275i	0.177553	−	0.667431i
$675$	5.28950	−	6.10441i	0.203593	−	0.234959i
$676$	6.96484	+	35.4511i	0.267878	+	1.36350i
$677$	14.5243	+	31.8038i	0.558214	+	1.22232i	0.952839	+	0.303476i	$0.0981471\pi$
$677$	14.5243	+	31.8038i	0.558214	+	1.22232i	−0.394625	+	0.918842i	$0.629126\pi$
$678$	7.88453	+	0.928347i	0.302804	+	0.0356529i
$679$	−1.02520	+	3.49151i	−0.0393436	+	0.133992i
$680$	8.44025	+	6.24760i	0.323669	+	0.239584i
$681$	5.08506	+	0.731122i	0.194860	+	0.0280166i
$682$	−15.5270	−	9.42601i	−0.594561	−	0.360941i
$683$	−3.77707	+	8.27062i	−0.144525	+	0.316467i	−0.968026	−	0.250848i	$-0.919290\pi$
$683$	−3.77707	+	8.27062i	−0.144525	+	0.316467i	0.823501	+	0.567315i	$0.192018\pi$
$684$	2.64776	−	11.0879i	0.101240	−	0.423958i
$685$	3.21035	−	0.461579i	0.122661	−	0.0176360i
$686$	−5.54140	−	6.07378i	−0.211572	−	0.231898i
$687$	10.5593	+	12.1861i	0.402862	+	0.464928i
$688$	10.2986	+	7.22264i	0.392631	+	0.275361i
$689$			68.2493i			2.60009i
$690$	−17.0658	−	17.6157i	−0.649684	−	0.670619i
$691$	−8.79461			−0.334563			−0.167281	−	0.985909i	$-0.553499\pi$
$691$	−8.79461			−0.334563			−0.167281	+	0.985909i	$0.553499\pi$
$692$	−1.76683	−	2.46239i	−0.0671648	−	0.0936062i
$693$	0.582606	−	0.504831i	0.0221314	−	0.0191770i
$694$	31.3029	+	34.3103i	1.18824	+	1.30240i
$695$	0.823389	+	5.72680i	0.0312329	+	0.217230i
$696$	−20.1684	−	1.33326i	−0.764483	−	0.0505372i
$697$	−11.0389	−	5.04128i	−0.418127	−	0.190952i
$698$	−21.7732	+	35.8660i	−0.824127	+	1.35755i
$699$	3.69884	−	25.7260i	0.139903	−	0.973046i
$700$	−4.70621	−	4.90035i	−0.177878	−	0.185216i
$701$	−28.1446	−	8.26401i	−1.06301	−	0.312127i	−0.296947	−	0.954894i	$-0.595968\pi$
$701$	−28.1446	−	8.26401i	−1.06301	−	0.312127i	−0.766062	+	0.642767i	$0.777786\pi$
$702$	−7.82811	−	0.921703i	−0.295453	−	0.0347875i
$703$	−39.2752	+	17.9364i	−1.48129	+	0.676484i
$704$	9.48263	−	11.1849i	0.357390	−	0.421547i
$705$	−8.67029	−	7.51285i	−0.326542	−	0.282950i
$706$	−2.07278	−	0.551412i	−0.0780103	−	0.0207527i
$707$	2.15928	−	3.35990i	0.0812079	−	0.126362i
$708$	1.17170	+	2.25286i	0.0440350	+	0.0846677i
$709$	−28.4219	+	18.2656i	−1.06741	+	0.685980i	−0.951615	−	0.307294i	$-0.900577\pi$
$709$	−28.4219	+	18.2656i	−1.06741	+	0.685980i	−0.115791	+	0.993274i	$0.536940\pi$
$710$	16.7486	+	13.7783i	0.628565	+	0.517091i
$711$	2.23567	−	0.656453i	0.0838443	−	0.0246189i
$712$	−15.1621	+	8.38553i	−0.568224	+	0.314261i
$713$	−10.4291	−	31.9465i	−0.390574	−	1.19641i
$714$	−0.602004	+	0.102344i	−0.0225294	+	0.00383014i
$715$	−35.4473	+	10.4083i	−1.32566	+	0.389248i
$716$	−36.4782	−	20.8863i	−1.36326	−	0.780558i
$717$	12.5053	+	19.4587i	0.467020	+	0.726698i
$718$	13.7244	−	4.41441i	0.512191	−	0.164744i
$719$	−6.96862	+	10.8434i	−0.259886	+	0.404390i	−0.946536	−	0.322598i	$-0.895444\pi$
$719$	−6.96862	+	10.8434i	−0.259886	+	0.404390i	0.686650	+	0.726988i	$0.259080\pi$
$720$	3.51118	+	14.0324i	0.130854	+	0.522957i
$721$	1.69721	−	1.95868i	0.0632072	−	0.0729450i
$722$	19.0690	−	0.488206i	0.709675	−	0.0181691i
$723$	−25.0703	+	11.4492i	−0.932373	+	0.425801i
$724$	30.5570	−	1.56567i	1.13564	−	0.0581876i
$725$	16.2621	−	55.3836i	0.603959	−	2.05690i
$726$	8.93725	−	6.07234i	0.331692	−	0.225366i
$727$	−0.697629	+	4.85211i	−0.0258736	+	0.179955i	−0.998660	−	0.0517482i	$-0.983521\pi$
$727$	−0.697629	+	4.85211i	−0.0258736	+	0.179955i	0.972787	+	0.231703i	$0.0744298\pi$
$728$	−1.37440	+	6.48612i	−0.0509386	+	0.240391i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−2.82138	+	6.62140i	−0.104424	+	0.245069i
$731$	0.459470	+	3.19568i	0.0169941	+	0.118197i
$732$	−13.4257	+	17.1990i	−0.496227	+	0.635692i
$733$	−13.0496	−	15.0600i	−0.481998	−	0.556256i	0.461712	−	0.887030i	$-0.347236\pi$
$733$	−13.0496	−	15.0600i	−0.481998	−	0.556256i	−0.943710	+	0.330775i	$0.892690\pi$
$734$	16.9671	+	34.7691i	0.626266	+	1.28335i
$735$	−24.6741			−0.910118
$736$	26.7917	−	4.26676i	0.987555	−	0.157275i
$737$	10.2227			0.376560
$738$	−7.33124	−	15.0233i	−0.269867	−	0.553014i
$739$	29.2067	+	33.7063i	1.07438	+	1.23991i	0.969414	+	0.245430i	$0.0789291\pi$
$739$	29.2067	+	33.7063i	1.07438	+	1.23991i	0.104970	+	0.994475i	$0.466525\pi$
$740$	33.7122	−	43.1870i	1.23928	−	1.58759i
$741$	−4.52111	−	31.4450i	−0.166087	−	1.15516i
$742$	−2.85504	+	6.70038i	−0.104812	+	0.245979i
$743$	11.1203	−	24.3500i	0.407963	−	0.893314i	−0.588438	−	0.808543i	$-0.700257\pi$
$743$	11.1203	−	24.3500i	0.407963	−	0.893314i	0.996400	−	0.0847714i	$-0.0270160\pi$
$744$	−4.10852	+	19.3891i	−0.150626	+	0.710839i
$745$	1.62899	−	11.3299i	0.0596818	−	0.415096i
$746$	19.7453	−	13.4158i	0.722927	−	0.491187i
$747$	−4.52569	+	15.4131i	−0.165586	+	0.563935i
$748$	3.75870	−	0.192587i	0.137432	−	0.00704168i
$749$	2.21714	−	1.01253i	0.0810124	−	0.0369971i
$750$	−15.7326	+	0.402786i	−0.574472	+	0.0147077i
$751$	18.8039	−	21.7009i	0.686165	−	0.791877i	−0.300649	−	0.953735i	$-0.597203\pi$
$751$	18.8039	−	21.7009i	0.686165	−	0.791877i	0.986814	+	0.161858i	$0.0517486\pi$
$752$	12.3103	−	3.08029i	0.448912	−	0.112327i
$753$	−9.80531	+	15.2574i	−0.357326	+	0.556009i
$754$	−53.6220	+	17.2473i	−1.95280	+	0.628111i
$755$	10.8631	+	16.9034i	0.395350	+	0.615176i
$756$	−0.729968	−	0.417957i	−0.0265487	−	0.0152010i
$757$	−47.2201	+	13.8651i	−1.71624	+	0.503935i	−0.984161	−	0.177279i	$-0.943270\pi$
$757$	−47.2201	+	13.8651i	−1.71624	+	0.503935i	−0.732084	+	0.681214i	$0.761452\pi$
$758$	−28.7050	+	4.88002i	−1.04261	+	0.177250i
$759$	−8.73462	−	0.989919i	−0.317047	−	0.0359318i
$760$	−51.0172	+	28.2155i	−1.85059	+	1.02348i
$761$	−13.9742	+	4.10320i	−0.506565	+	0.148741i	−0.525022	−	0.851089i	$-0.675943\pi$
$761$	−13.9742	+	4.10320i	−0.506565	+	0.148741i	0.0184568	+	0.999830i	$0.494125\pi$
$762$	−11.7210	−	9.64229i	−0.424606	−	0.349303i
$763$	−2.36047	+	1.51698i	−0.0854547	+	0.0549184i
$764$	24.9293	+	47.9324i	0.901909	+	1.73413i
$765$	−2.00721	+	3.12328i	−0.0725709	+	0.112923i
$766$	30.6162	+	8.14466i	1.10621	+	0.294279i
$767$	5.34811	+	4.63416i	0.193109	+	0.167330i
$768$	−14.9378	−	5.73251i	−0.539022	−	0.206854i
$769$	29.0072	−	13.2472i	1.04603	−	0.477705i	0.183133	−	0.983088i	$-0.441376\pi$
$769$	29.0072	−	13.2472i	1.04603	−	0.477705i	0.862895	+	0.505384i	$0.168649\pi$
$770$	−3.91545	−	0.461016i	−0.141103	−	0.0166139i
$771$	22.3986	+	6.57683i	0.806667	+	0.236859i
$772$	−9.04704	−	9.42026i	−0.325610	−	0.339043i
$773$	−2.32399	+	16.1637i	−0.0835882	+	0.581368i	0.904382	+	0.426724i	$0.140332\pi$
$773$	−2.32399	+	16.1637i	−0.0835882	+	0.581368i	−0.987970	+	0.154645i	$0.950577\pi$
$774$	−2.30785	+	3.80162i	−0.0829540	+	0.136646i
$775$	−51.4851	−	23.5124i	−1.84940	−	0.844592i
$776$	−24.4188	−	1.61424i	−0.876583	−	0.0579477i
$777$	0.453404	+	3.15350i	0.0162658	+	0.113131i
$778$	7.45430	+	8.17047i	0.267250	+	0.292926i
$779$	50.9184	−	44.1210i	1.82434	−	1.58080i
$780$	23.5003	+	32.7519i	0.841447	+	1.17271i
$781$	7.77307			0.278142
$782$	5.50741	+	4.26070i	0.196945	+	0.152362i
$783$		−	7.14618i		−	0.255384i
$784$	15.6710	−	22.3450i	0.559679	−	0.798035i
$785$	−18.0756	−	20.8603i	−0.645145	−	0.744537i
$786$	−17.4364	−	19.1116i	−0.621936	−	0.681688i
$787$	−48.7297	+	7.00627i	−1.73703	+	0.249747i	−0.936778	−	0.349923i	$-0.886208\pi$
$787$	−48.7297	+	7.00627i	−1.73703	+	0.249747i	−0.800247	+	0.599670i	$0.795299\pi$
$788$	−1.63678	+	6.85431i	−0.0583080	+	0.244175i
$789$	8.52535	−	18.6679i	0.303511	−	0.664596i
$790$	−10.1862	−	6.18375i	−0.362409	−	0.220008i
$791$	2.33697	+	0.336006i	0.0830931	+	0.0119470i
$792$	4.16699	+	3.08447i	0.148068	+	0.109602i
$793$	−17.1303	+	58.3406i	−0.608316	+	2.07174i
$794$	7.32172	+	0.862080i	0.259838	+	0.0305941i
$795$	18.3954	+	40.2802i	0.652416	+	1.42859i
$796$	−1.15792	−	5.89382i	−0.0410413	−	0.208901i
$797$	4.69897	−	5.42290i	0.166446	−	0.192089i	−0.666399	−	0.745595i	$-0.732165\pi$
$797$	4.69897	−	5.42290i	0.166446	−	0.192089i	0.832845	+	0.553507i	$0.186711\pi$
$798$	0.871561	−	3.27624i	0.0308529	−	0.115978i
$799$	2.73999	+	1.76089i	0.0969339	+	0.0622957i
$800$	25.2698	−	38.0684i	0.893423	−	1.34592i
$801$	−3.31187	−	5.15338i	−0.117019	−	0.182086i
$802$	−8.37985	−	6.89371i	−0.295903	−	0.243425i
$803$	0.726763	+	2.47513i	0.0256469	+	0.0873454i
$804$	−3.68609	−	10.5277i	−0.129998	−	0.371284i
$805$	−4.93951	−	5.36697i	−0.174095	−	0.189161i
$806$	9.25708	+	54.4515i	0.326067	+	1.91797i
$807$	−1.07716	−	3.66846i	−0.0379177	−	0.129136i
$808$	25.2163	+	9.25067i	0.887105	+	0.325438i
$809$	15.6635	−	10.0663i	0.550700	−	0.353913i	−0.235511	−	0.971872i	$-0.575676\pi$
$809$	15.6635	−	10.0663i	0.550700	−	0.353913i	0.786211	+	0.617958i	$0.212040\pi$
$810$	−4.86851	+	1.56594i	−0.171062	+	0.0550215i
$811$	40.6152	+	26.1018i	1.42619	+	0.916558i	0.999928	+	0.0119593i	$0.00380686\pi$
$811$	40.6152	+	26.1018i	1.42619	+	0.916558i	0.426264	+	0.904599i	$0.359830\pi$
$812$	−5.98584	−	0.549882i	−0.210062	−	0.0192971i
$813$	14.1549	+	12.2653i	0.496434	+	0.430163i
$814$	−0.502561	−	19.6297i	−0.0176147	−	0.688021i
$815$	−5.54734	−	12.1470i	−0.194315	−	0.425490i
$816$	−1.55364	−	3.80140i	−0.0543882	−	0.133075i
$817$	−17.1983	−	5.04989i	−0.601694	−	0.176673i
$818$	3.95260	−	2.68557i	0.138200	−	0.0938986i
$819$	−2.32025	−	0.333601i	−0.0810760	−	0.0116570i
$820$	−31.4886	+	79.4811i	−1.09963	+	2.77560i
$821$	29.8540	+	13.6339i	1.04191	+	0.475826i	0.861496	−	0.507764i	$-0.169528\pi$
$821$	29.8540	+	13.6339i	1.04191	+	0.475826i	0.180417	+	0.983590i	$0.442255\pi$
$822$	−1.16687	−	0.497205i	−0.0406994	−	0.0173420i
$823$	36.1080	−	5.19154i	1.25864	−	0.180966i	0.519475	−	0.854486i	$-0.326127\pi$
$823$	36.1080	−	5.19154i	1.25864	−	0.180966i	0.739169	+	0.673520i	$0.235218\pi$
$824$	15.3423	+	8.27050i	0.534474	+	0.288116i
$825$	−11.1891	+	9.69541i	−0.389554	+	0.337551i
$826$	0.331193	+	0.678684i	0.0115237	+	0.0236144i
$827$		−	46.8065i		−	1.62762i	−0.581131	−	0.813810i	$-0.697390\pi$
$827$		−	46.8065i		−	1.62762i	0.581131	−	0.813810i	$-0.302610\pi$
$828$	2.13006	+	9.35216i	0.0740246	+	0.325010i
$829$			9.96741i			0.346182i	0.984906	+	0.173091i	$0.0553755\pi$
$829$			9.96741i			0.346182i	−0.984906	+	0.173091i	$0.944624\pi$
$830$	73.8307	−	36.0288i	2.56270	−	1.25058i
$831$	−18.0288	+	15.6220i	−0.625411	+	0.541922i
$832$	−44.5858	+	0.480612i	−1.54573	+	0.0166622i
$833$	6.93370	−	0.996916i	0.240238	−	0.0345411i
$834$	0.886942	−	2.08153i	0.0307123	−	0.0720775i
$835$	5.95261	+	2.71846i	0.205998	+	0.0940763i
$836$	−7.69618	+	19.4261i	−0.266178	+	0.671867i
$837$	−6.93597	−	0.997241i	−0.239742	−	0.0344697i
$838$	0.985126	+	1.44990i	0.0340306	+	0.0500861i
$839$	18.8587	+	5.53743i	0.651076	+	0.191173i	0.590560	−	0.806994i	$-0.298907\pi$
$839$	18.8587	+	5.53743i	0.651076	+	0.191173i	0.0605166	+	0.998167i	$0.480725\pi$
$840$	0.937054	+	4.19850i	0.0323314	+	0.144862i
$841$	−9.16735	−	20.0737i	−0.316116	−	0.692197i
$842$	28.0874	−	0.719096i	0.967957	−	0.0247817i
$843$	−12.6955	−	11.0007i	−0.437255	−	0.378884i
$844$	−4.56680	+	49.7127i	−0.157196	+	1.71118i
$845$	54.9552	+	35.3176i	1.89052	+	1.21496i
$846$	1.37377	+	4.27105i	0.0472311	+	0.146842i
$847$	2.70322	−	1.73726i	0.0928839	−	0.0596928i
$848$	−48.1612	−	8.92385i	−1.65386	−	0.306446i
$849$	−0.841789	−	2.86687i	−0.0288901	−	0.0983908i
$850$	11.5616	−	1.96555i	0.396561	−	0.0674177i
$851$	22.9576	−	28.1557i	0.786978	−	0.965165i
$852$	−2.80280	−	8.00497i	−0.0960222	−	0.274246i
$853$	−6.72879	−	22.9162i	−0.230390	−	0.784635i	−0.990817	−	0.135212i	$-0.956829\pi$
$853$	−6.72879	−	22.9162i	−0.230390	−	0.784635i	0.760427	−	0.649423i	$-0.224990\pi$
$854$	−4.12230	+	5.01099i	−0.141062	+	0.171472i
$855$	−11.1437	−	17.3400i	−0.381108	−	0.593015i
$856$	9.89381	+	13.0692i	0.338163	+	0.446695i
$857$	13.8267	+	8.88590i	0.472312	+	0.303537i	0.755058	−	0.655658i	$-0.227609\pi$
$857$	13.8267	+	8.88590i	0.472312	+	0.303537i	−0.282745	+	0.959195i	$0.591245\pi$
$858$	13.9621	+	3.71426i	0.476658	+	0.126803i
$859$	15.4736	−	17.8575i	0.527954	−	0.609291i	−0.427651	−	0.903944i	$-0.640659\pi$
$859$	15.4736	−	17.8575i	0.527954	−	0.609291i	0.955604	+	0.294653i	$0.0952041\pi$
$860$	22.3176	−	4.38458i	0.761022	−	0.149513i
$861$	−2.06520	−	4.52215i	−0.0703817	−	0.154115i
$862$	3.78991	−	32.1881i	0.129085	−	1.09633i
$863$	−7.10103	+	24.1839i	−0.241722	+	0.823229i	0.745857	+	0.666106i	$0.232040\pi$
$863$	−7.10103	+	24.1839i	−0.241722	+	0.823229i	−0.987579	+	0.157123i	$0.949778\pi$
$864$	1.67397	−	5.40350i	0.0569495	−	0.183831i
$865$	−5.42409	−	0.779867i	−0.184425	−	0.0265163i
$866$	−16.2605	+	26.7852i	−0.552554	+	0.910198i
$867$	−6.62420	+	14.5050i	−0.224970	+	0.492615i
$868$	−1.36902	+	5.73302i	−0.0464677	+	0.194591i
$869$	−4.22742	+	0.607811i	−0.143405	+	0.0206186i
$870$	−26.9986	+	24.6321i	−0.915337	+	0.835105i
$871$	−20.3562	−	23.4923i	−0.689743	−	0.796006i
$872$	−13.4148	−	13.2710i	−0.454282	−	0.449411i
$873$		−	8.65219i		−	0.292832i
$874$	−34.2190	+	17.9867i	−1.15747	+	0.608408i
$875$	−4.68029			−0.158223
$876$	2.28692	−	1.64092i	0.0772678	−	0.0554416i
$877$	33.8589	−	29.3389i	1.14333	−	0.990704i	0.143333	−	0.989674i	$-0.454218\pi$
$877$	33.8589	−	29.3389i	1.14333	−	0.990704i	0.999999	−	0.00102918i	$-0.000327600\pi$
$878$	−32.2221	+	29.3978i	−1.08744	+	0.992127i
$879$	−1.80501	−	12.5541i	−0.0608813	−	0.423439i
$880$	−2.70989	−	26.3749i	−0.0913503	−	0.889096i
$881$	−4.86434	−	2.22147i	−0.163884	−	0.0748431i	0.331784	−	0.943355i	$-0.392349\pi$
$881$	−4.86434	−	2.22147i	−0.163884	−	0.0748431i	−0.495668	+	0.868512i	$0.665077\pi$
$882$	8.24840	+	5.00736i	0.277738	+	0.168607i
$883$	5.06085	−	35.1990i	0.170311	−	1.18454i	−0.707916	−	0.706297i	$-0.750364\pi$
$883$	5.06085	−	35.1990i	0.170311	−	1.18454i	0.878227	−	0.478244i	$-0.158726\pi$
$884$	−7.92714	−	8.25416i	−0.266618	−	0.277617i
$885$	4.40546	+	1.29356i	0.148088	+	0.0434826i
$886$	−3.90634	+	33.1768i	−0.131236	+	1.11460i
$887$	29.7022	−	13.5645i	0.997301	−	0.455452i	0.151216	−	0.988501i	$-0.451681\pi$
$887$	29.7022	−	13.5645i	0.997301	−	0.455452i	0.846085	+	0.533048i	$0.178954\pi$
$888$	−20.0341	+	7.59559i	−0.672302	+	0.254891i
$889$	−3.41120	−	2.95582i	−0.114408	−	0.0991351i
$890$	−8.05402	+	30.2755i	−0.269971	+	1.01484i
$891$	−0.990970	+	1.54198i	−0.0331987	+	0.0516582i
$892$	−9.74008	+	5.06574i	−0.326122	+	0.169613i
$893$	−15.2120	+	9.77617i	−0.509051	+	0.327147i
$894$	−2.84385	+	3.45693i	−0.0951127	+	0.115617i
$895$	−72.9250	+	21.4127i	−2.43761	+	0.715748i
$896$	−4.39731	−	1.81795i	−0.146904	−	0.0607334i
$897$	15.1181	+	22.0437i	0.504777	+	0.736018i
$898$	0.476130	+	2.80066i	0.0158887	+	0.0934594i
$899$	−48.0470	+	14.1079i	−1.60246	+	0.470524i
$900$	14.0192	+	8.02697i	0.467307	+	0.267566i
$901$	−6.79675	−	10.5760i	−0.226433	−	0.352336i
$902$	9.38213	+	29.1691i	0.312391	+	0.971224i
$903$	−0.715050	+	1.11264i	−0.0237954	+	0.0370263i
$904$	1.21806	+	15.8312i	0.0405122	+	0.526538i
$905$	36.2291	−	41.8106i	1.20430	−	1.38983i
$906$	−0.201110	−	7.85525i	−0.00668144	−	0.260973i
$907$	−25.5671	+	11.6761i	−0.848940	+	0.387698i	−0.791883	−	0.610673i	$-0.790899\pi$
$907$	−25.5671	+	11.6761i	−0.848940	+	0.387698i	−0.0570573	+	0.998371i	$0.518172\pi$
$908$	0.525763	+	10.2612i	0.0174480	+	0.340531i
$909$	−2.67541	+	9.11161i	−0.0887378	+	0.302213i
$910$	6.73726	+	9.91587i	0.223338	+	0.328708i
$911$	−1.15563	+	8.03756i	−0.0382876	+	0.266296i	−0.999969	−	0.00787329i	$-0.997494\pi$
$911$	−1.15563	+	8.03756i	−0.0382876	+	0.266296i	0.961681	+	0.274169i	$0.0884029\pi$
$912$	22.7808	+	0.921160i	0.754347	+	0.0305027i
$913$	12.2315	−	26.7833i	0.404805	−	0.886400i
$914$	−39.7258	−	16.9272i	−1.31401	−	0.559901i
$915$	5.61444	+	39.0493i	0.185608	+	1.29093i
$916$	−19.8438	+	25.4209i	−0.655657	+	0.839929i
$917$	−5.03830	−	5.81451i	−0.166379	−	0.192012i
$918$	1.30484	−	0.636750i	0.0430660	−	0.0210159i
$919$	−6.57008			−0.216727			−0.108363	−	0.994111i	$-0.534561\pi$
$919$	−6.57008			−0.216727			−0.108363	+	0.994111i	$0.534561\pi$
$920$	27.9908	−	40.2832i	0.922828	−	1.32810i
$921$	7.53647			0.248335
$922$	32.7271	−	15.9706i	1.07781	−	0.525963i
$923$	−15.4782	−	17.8628i	−0.509472	−	0.587962i
$924$	1.21535	+	0.948715i	0.0399821	+	0.0312104i
$925$	−8.70774	−	60.5636i	−0.286309	−	1.99132i
$926$	−14.3244	−	6.10362i	−0.470728	−	0.200577i
$927$	−2.55989	+	5.60538i	−0.0840779	+	0.184105i
$928$	−5.15956	−	40.0943i	−0.169371	−	1.31616i
$929$	3.92310	−	27.2858i	0.128713	−	0.895217i	−0.818476	−	0.574541i	$-0.805181\pi$
$929$	3.92310	−	27.2858i	0.128713	−	0.895217i	0.947189	−	0.320676i	$-0.103910\pi$
$930$	20.1398	+	29.6417i	0.660411	+	0.971990i
$931$	−10.9568	+	37.3154i	−0.359094	+	1.22296i
$932$	51.9130	−	2.65990i	1.70047	−	0.0871279i
$933$	16.8993	−	7.71766i	0.553259	−	0.252665i
$934$	1.22918	+	48.0111i	0.0402201	+	1.57097i
$935$	4.45641	−	5.14297i	0.145740	−	0.168193i
$936$	−1.20935	−	15.7179i	−0.0395287	−	0.513756i
$937$	−13.5795	+	21.1300i	−0.443622	+	0.690289i	−0.989002	−	0.147900i	$-0.952749\pi$
$937$	−13.5795	+	21.1300i	−0.443622	+	0.690289i	0.545381	+	0.838188i	$0.316385\pi$
$938$	−1.01573	−	3.15790i	−0.0331647	−	0.103109i
$939$	−1.71977	−	2.67602i	−0.0561227	−	0.0873287i
$940$	11.4010	−	19.9119i	0.371859	−	0.649456i
$941$	43.3525	−	12.7294i	1.41325	−	0.414968i	0.516038	−	0.856565i	$-0.327406\pi$
$941$	43.3525	−	12.7294i	1.41325	−	0.414968i	0.897213	+	0.441597i	$0.145588\pi$
$942$	1.80916	+	10.6417i	0.0589456	+	0.346727i
$943$	−21.9947	+	52.2480i	−0.716247	+	1.70143i
$944$	−3.96945	+	3.16804i	−0.129195	+	0.103111i
$945$	−1.45931	+	0.428491i	−0.0474712	+	0.0139388i
$946$	5.17880	−	6.29525i	0.168377	−	0.204676i
$947$	−14.3730	+	9.23698i	−0.467060	+	0.300161i	−0.752922	−	0.658109i	$-0.771356\pi$
$947$	−14.3730	+	9.23698i	−0.467060	+	0.300161i	0.285862	+	0.958271i	$0.407720\pi$
$948$	2.15026	+	4.13438i	0.0698371	+	0.134278i
$949$	4.24077	−	6.59877i	0.137661	−	0.214205i
$950$	−16.7385	+	62.9210i	−0.543070	+	2.04143i
$951$	8.54876	+	7.40754i	0.277213	+	0.240206i
$952$	−0.432956	−	1.14196i	−0.0140322	−	0.0370113i
$953$	−44.0641	+	20.1234i	−1.42737	+	0.651860i	−0.971251	−	0.238056i	$-0.923490\pi$
$953$	−44.0641	+	20.1234i	−1.42737	+	0.651860i	−0.456123	+	0.889917i	$0.650762\pi$
$954$	2.02501	−	17.1986i	0.0655621	−	0.556824i
$955$	93.7317	+	27.5221i	3.03309	+	0.890595i
$956$	−33.3659	+	32.0439i	−1.07913	+	1.03638i
$957$	−1.86413	+	12.9653i	−0.0602587	+	0.419109i
$958$	13.2804	+	8.06213i	0.429070	+	0.260476i
$959$	−0.343122	−	0.156698i	−0.0110800	−	0.00506006i
$960$	−26.1846	+	12.3009i	−0.845105	+	0.397011i
$961$	2.57620	+	17.9179i	0.0831032	+	0.577995i
$962$	−44.1091	+	40.2428i	−1.42214	+	1.29748i
$963$	−4.37985	+	3.79516i	−0.141139	+	0.122297i
$964$	−32.1349	−	44.7857i	−1.03499	−	1.44245i
$965$	−23.6160			−0.760225
$966$	0.562074	+	2.79657i	0.0180844	+	0.0899781i
$967$		−	27.5700i		−	0.886590i	−0.896376	−	0.443295i	$-0.853809\pi$
$967$		−	27.5700i		−	0.886590i	0.896376	−	0.443295i	$-0.146191\pi$
$968$	15.3627	+	15.1980i	0.493776	+	0.488482i
$969$	3.83211	+	4.42249i	0.123105	+	0.142071i
$970$	−32.6883	+	29.8231i	−1.04956	+	0.957561i
$971$	55.7753	−	8.01928i	1.78992	−	0.257351i	0.834162	−	0.551520i	$-0.185952\pi$
$971$	55.7753	−	8.01928i	1.78992	−	0.257351i	0.955753	+	0.294169i	$0.0950428\pi$
$972$	1.94530	+	0.464531i	0.0623957	+	0.0148999i
$973$	0.279527	−	0.612079i	0.00896123	−	0.0196224i
$974$	−9.13484	+	15.0474i	−0.292699	+	0.482150i
$975$	44.5609	+	6.40689i	1.42709	+	0.205185i
$976$	−38.9291	−	19.7165i	−1.24609	−	0.631111i
$977$	6.53497	−	22.2561i	0.209072	−	0.712035i	−0.786462	−	0.617638i	$-0.788090\pi$
$977$	6.53497	−	22.2561i	0.209072	−	0.712035i	0.995535	−	0.0943966i	$-0.0300922\pi$
$978$	−0.610666	+	5.18644i	−0.0195269	+	0.165844i
$979$	4.66443	+	10.2137i	0.149076	+	0.326431i
$980$	−9.51326	−	48.4226i	−0.303890	−	1.54680i
$981$	4.36892	−	5.04201i	0.139489	−	0.160979i
$982$	6.23640	+	1.65904i	0.199012	+	0.0529420i
$983$	−3.66751	−	2.35697i	−0.116975	−	0.0751755i	0.480845	−	0.876806i	$-0.340330\pi$
$983$	−3.66751	−	2.35697i	−0.116975	−	0.0751755i	−0.597820	+	0.801630i	$0.703966\pi$
$984$	26.6563	−	20.1798i	0.849772	−	0.643307i
$985$	6.88880	+	10.7192i	0.219496	+	0.341542i
$986$	6.59168	−	8.01271i	0.209922	−	0.255177i
$987$	0.375906	+	1.28022i	0.0119652	+	0.0407498i
$988$	59.9672	−	20.9964i	1.90781	−	0.667985i
$989$	14.8571	−	2.59237i	0.472427	−	0.0824325i
$990$	9.24141	−	1.57110i	0.293711	−	0.0499327i
$991$	16.7346	+	56.9927i	0.531591	+	1.81043i	0.583932	+	0.811802i	$0.301513\pi$
$991$	16.7346	+	56.9927i	0.531591	+	1.81043i	−0.0523415	+	0.998629i	$0.516668\pi$
$992$	−39.6349	−	0.587328i	−1.25841	−	0.0186477i
$993$	−17.6548	+	11.3460i	−0.560257	+	0.360055i
$994$	−0.772330	−	2.40118i	−0.0244968	−	0.0761607i
$995$	−9.13642	−	5.87162i	−0.289644	−	0.186143i
$996$	−31.9928	−	2.93899i	−1.01373	−	0.0931253i
$997$	−26.6350	−	23.0793i	−0.843537	−	0.730929i	0.121626	−	0.992576i	$-0.461189\pi$
$997$	−26.6350	−	23.0793i	−0.843537	−	0.730929i	−0.965164	+	0.261647i	$0.915734\pi$
$998$	11.0817	−	0.283715i	0.350786	−	0.00898083i
$999$	−3.14682	−	6.89057i	−0.0995609	−	0.218008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.451.8	yes	240
8.3	odd	2	inner	552.2.t.a.451.12	yes	240
23.5	odd	22	inner	552.2.t.a.235.12	yes	240
184.51	even	22	inner	552.2.t.a.235.8	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.8	✓	240	184.51	even	22	inner
552.2.t.a.235.12	yes	240	23.5	odd	22	inner
552.2.t.a.451.8	yes	240	1.1	even	1	trivial
552.2.t.a.451.12	yes	240	8.3	odd	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.620217 - 1.27096i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.23066 + 1.57654i) q^{4} +(0.514647 + 3.57945i) q^{5} +(0.554369 - 1.30103i) q^{6} +(0.174714 - 0.382571i) q^{7} +(2.76699 + 0.586321i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.620217 - 1.27096i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.23066 + 1.57654i) q^{4} +(0.514647 + 3.57945i) q^{5} +(0.554369 - 1.30103i) q^{6} +(0.174714 - 0.382571i) q^{7} +(2.76699 + 0.586321i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(4.23013 - 2.87413i) q^{10} +(0.516403 - 1.75871i) q^{11} +(-1.99738 + 0.102341i) q^{12} +(-5.06987 + 2.31533i) q^{13} +(-0.594591 + 0.0152228i) q^{14} +(-2.36814 + 2.73298i) q^{15} +(-0.970945 - 3.88037i) q^{16} +(0.555053 - 0.863679i) q^{17} +(1.34629 - 0.433028i) q^{18} +(3.08157 + 4.79502i) q^{19} +(-6.27649 - 3.59373i) q^{20} +(0.403541 - 0.118490i) q^{21} +(-2.55552 + 0.434454i) q^{22} +(-4.11034 - 2.47085i) q^{23} +(1.36888 + 2.47511i) q^{24} +(-7.75010 + 2.27564i) q^{25} +(6.08711 + 5.00758i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.388123 + 0.746258i) q^{28} +(-3.86352 + 6.01175i) q^{29} +(4.94226 + 1.31476i) q^{30} +(5.29576 + 4.58880i) q^{31} +(-4.32958 + 3.64070i) q^{32} +(1.66731 - 0.761437i) q^{33} +(-1.44195 - 0.169780i) q^{34} +(1.45931 + 0.428491i) q^{35} +(-1.38535 - 1.44250i) q^{36} +(-1.07805 + 7.49802i) q^{37} +(4.18302 - 6.89049i) q^{38} +(-5.06987 - 2.31533i) q^{39} +(-0.674684 + 10.2060i) q^{40} +(-1.68222 - 11.7001i) q^{41} +(-0.400879 - 0.439393i) q^{42} +(-2.37662 + 2.05935i) q^{43} +(2.13715 + 2.97850i) q^{44} -3.61625 q^{45} +(-0.591040 + 6.75653i) q^{46} +3.17246i q^{47} +(2.29675 - 3.27489i) q^{48} +(4.46819 + 5.15657i) q^{49} +(7.69898 + 8.43865i) q^{50} +(1.01621 - 0.146109i) q^{51} +(2.58909 - 10.8422i) q^{52} +(5.08685 - 11.1387i) q^{53} +(1.20889 + 0.733882i) q^{54} +(6.56096 + 0.943323i) q^{55} +(0.707741 - 0.956130i) q^{56} +(-1.60583 + 5.46896i) q^{57} +(10.0369 + 1.18177i) q^{58} +(-0.527440 - 1.15493i) q^{59} +(-1.39427 - 7.09684i) q^{60} +(7.14409 - 8.24471i) q^{61} +(2.54765 - 9.57673i) q^{62} +(0.353812 + 0.227381i) q^{63} +(7.31245 + 3.24469i) q^{64} +(-10.8968 - 16.9558i) q^{65} +(-2.00185 - 1.64683i) q^{66} +(1.57128 + 5.35128i) q^{67} +(0.678541 + 1.93796i) q^{68} +(-0.824356 - 4.72445i) q^{69} +(-0.360493 - 2.12047i) q^{70} +(1.19475 + 4.06895i) q^{71} +(-0.974137 + 2.65538i) q^{72} +(-1.18394 + 0.760875i) q^{73} +(10.1983 - 3.28024i) q^{74} +(-6.79505 - 4.36691i) q^{75} +(-11.3519 - 1.04283i) q^{76} +(-0.582606 - 0.504831i) q^{77} +(0.201734 + 7.87960i) q^{78} +(-0.967941 - 2.11949i) q^{79} +(13.3899 - 5.47246i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-13.8270 + 9.39465i) q^{82} +(15.9003 + 2.28611i) q^{83} +(-0.309818 + 0.782019i) q^{84} +(3.37715 + 1.54229i) q^{85} +(4.09137 + 1.74333i) q^{86} +(-7.07345 + 1.01701i) q^{87} +(2.46005 - 4.56354i) q^{88} +(-4.62959 + 4.01157i) q^{89} +(2.24286 + 4.59610i) q^{90} +2.34411i q^{91} +(8.95383 - 3.43933i) q^{92} +7.00729i q^{93} +(4.03207 - 1.96762i) q^{94} +(-15.5776 + 13.4980i) q^{95} +(-5.58673 - 0.887930i) q^{96} +(-8.56412 + 1.23133i) q^{97} +(3.78252 - 8.87707i) q^{98} +(1.66731 + 0.761437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more