LMFDB - Embedded newform 552.2.t.a.451.12

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			451.12
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.165371 + 1.40451i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.94530 + 0.464531i) q^{4} +(-0.514647 - 3.57945i) q^{5} +(-0.953164 + 1.04474i) q^{6} +(-0.174714 + 0.382571i) q^{7} +(-0.974137 - 2.65538i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.165371 + 1.40451i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.94530 + 0.464531i) q^{4} +(-0.514647 - 3.57945i) q^{5} +(-0.953164 + 1.04474i) q^{6} +(-0.174714 + 0.382571i) q^{7} +(-0.974137 - 2.65538i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(4.94226 - 1.31476i) q^{10} +(0.516403 - 1.75871i) q^{11} +(-1.62497 - 1.16596i) q^{12} +(5.06987 - 2.31533i) q^{13} +(-0.566217 - 0.182122i) q^{14} +(2.36814 - 2.73298i) q^{15} +(3.56842 - 1.80731i) q^{16} +(0.555053 - 0.863679i) q^{17} +(-1.41375 - 0.0361949i) q^{18} +(3.08157 + 4.79502i) q^{19} +(2.66391 + 6.72404i) 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} +(4.09032 + 6.73781i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.162156 - 0.825376i) q^{28} +(3.86352 - 6.01175i) q^{29} +(4.23013 + 2.87413i) q^{30} +(-5.29576 - 4.58880i) q^{31} +(3.12850 + 4.71301i) q^{32} +(1.66731 - 0.761437i) q^{33} +(1.30484 + 0.636750i) q^{34} +(1.45931 + 0.428491i) q^{35} +(-0.182957 - 1.99161i) q^{36} +(1.07805 - 7.49802i) q^{37} +(-6.22505 + 5.12106i) q^{38} +(5.06987 + 2.31533i) q^{39} +(-9.00346 + 4.85345i) q^{40} +(-1.68222 - 11.7001i) q^{41} +(-0.233155 - 0.547183i) q^{42} +(-2.37662 + 2.05935i) q^{43} +(-0.187587 + 3.66111i) q^{44} +3.61625 q^{45} +(-2.79061 + 6.18163i) q^{46} -3.17246i q^{47} +(3.70269 + 1.51330i) q^{48} +(4.46819 + 5.15657i) q^{49} +(-4.47780 - 10.5088i) q^{50} +(1.01621 - 0.146109i) q^{51} +(-8.78690 + 6.85915i) q^{52} +(-5.08685 + 11.1387i) q^{53} +(-0.898455 - 1.09214i) q^{54} +(-6.56096 - 0.943323i) q^{55} +(1.18607 + 0.0912567i) q^{56} +(-1.60583 + 5.46896i) q^{57} +(9.08249 + 4.43219i) q^{58} +(-0.527440 - 1.15493i) q^{59} +(-3.33720 + 6.41656i) q^{60} +(-7.14409 + 8.24471i) q^{61} +(5.56926 - 8.19681i) q^{62} +(-0.353812 - 0.227381i) q^{63} +(-6.10211 + 5.17341i) q^{64} +(-10.8968 - 16.9558i) q^{65} +(1.34517 + 2.21584i) 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} +(2.76699 - 0.586321i) q^{72} +(-1.18394 + 0.760875i) q^{73} +(10.7093 + 0.274181i) q^{74} +(-6.79505 - 4.36691i) q^{75} +(-8.22203 - 7.89628i) q^{76} +(0.582606 + 0.504831i) q^{77} +(-2.41350 + 7.50359i) q^{78} +(0.967941 + 2.11949i) q^{79} +(-8.30564 - 11.8428i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(16.1548 - 4.29757i) q^{82} +(15.9003 + 2.28611i) q^{83} +(0.729968 - 0.417957i) q^{84} +(-3.37715 - 1.54229i) q^{85} +(-3.28541 - 2.99743i) q^{86} +(7.07345 - 1.01701i) q^{87} +(-5.17309 + 0.341974i) q^{88} +(-4.62959 + 4.01157i) q^{89} +(0.598024 + 5.07907i) q^{90} +2.34411i q^{91} +(-9.14365 - 2.89718i) q^{92} -7.00729i q^{93} +(4.45576 - 0.524634i) q^{94} +(15.5776 - 13.4980i) q^{95} +(-1.51312 + 5.45073i) q^{96} +(-8.56412 + 1.23133i) q^{97} +(-6.50355 + 7.12837i) 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 $

$2$	0.165371	+	1.40451i	0.116935	+	0.993140i
$2$	0.165371	+	1.40451i	0.116935	+	0.993140i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	−1.94530	+	0.464531i	−0.972652	+	0.232266i
$5$	−0.514647	−	3.57945i	−0.230157	−	1.60078i	−0.697423	−	0.716660i	$-0.745670\pi$
$5$	−0.514647	−	3.57945i	−0.230157	−	1.60078i	0.467266	−	0.884117i	$-0.345239\pi$
$6$	−0.953164	+	1.04474i	−0.389128	+	0.426513i
$7$	−0.174714	+	0.382571i	−0.0660357	+	0.144598i	−0.939772	−	0.341802i	$-0.888963\pi$
$7$	−0.174714	+	0.382571i	−0.0660357	+	0.144598i	0.873736	+	0.486400i	$0.161690\pi$
$8$	−0.974137	−	2.65538i	−0.344409	−	0.938820i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	4.94226	−	1.31476i	1.56288	−	0.415765i
$11$	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	$0.00179141\pi$
$12$	−1.62497	−	1.16596i	−0.469089	−	0.336584i
$13$	5.06987	−	2.31533i	1.40613	−	0.642158i	0.439478	−	0.898253i	$-0.355163\pi$
$13$	5.06987	−	2.31533i	1.40613	−	0.642158i	0.966652	+	0.256095i	$0.0824360\pi$
$14$	−0.566217	−	0.182122i	−0.151328	−	0.0486741i
$15$	2.36814	−	2.73298i	0.611452	−	0.705653i
$16$	3.56842	−	1.80731i	0.892105	−	0.451828i
$17$	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	$0.142085\pi$
$18$	−1.41375	−	0.0361949i	−0.333224	−	0.00853122i
$19$	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	$0.591348\pi$
$20$	2.66391	+	6.72404i	0.595668	+	1.50354i
$21$	−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
$26$	4.09032	+	6.73781i	0.802178	+	1.32139i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	0.162156	−	0.825376i	0.0306446	−	0.155981i
$29$	3.86352	−	6.01175i	0.717437	−	1.11635i	−0.270682	−	0.962669i	$-0.587249\pi$
$29$	3.86352	−	6.01175i	0.717437	−	1.11635i	0.988120	−	0.153686i	$-0.0491143\pi$
$30$	4.23013	+	2.87413i	0.772312	+	0.524741i
$31$	−5.29576	−	4.58880i	−0.951146	−	0.824173i	0.0333744	−	0.999443i	$-0.489375\pi$
$31$	−5.29576	−	4.58880i	−0.951146	−	0.824173i	−0.984520	+	0.175270i	$0.943920\pi$
$32$	3.12850	+	4.71301i	0.553046	+	0.833151i
$33$	1.66731	−	0.761437i	0.290242	−	0.132549i
$34$	1.30484	+	0.636750i	0.223778	+	0.109202i
$35$	1.45931	+	0.428491i	0.246668	+	0.0724282i
$36$	−0.182957	−	1.99161i	−0.0304929	−	0.331936i
$37$	1.07805	−	7.49802i	0.177231	−	1.23267i	−0.685904	−	0.727692i	$-0.740593\pi$
$37$	1.07805	−	7.49802i	0.177231	−	1.23267i	0.863134	−	0.504974i	$-0.168498\pi$
$38$	−6.22505	+	5.12106i	−1.00984	+	0.830745i
$39$	5.06987	+	2.31533i	0.811830	+	0.370750i
$40$	−9.00346	+	4.85345i	−1.42357	+	0.767398i
$41$	−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	$-0.419742\pi$
$42$	−0.233155	−	0.547183i	−0.0359766	−	0.0844322i
$43$	−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	$0.349803\pi$
$44$	−0.187587	+	3.66111i	−0.0282797	+	0.551932i
$45$	3.61625			0.539079
$46$	−2.79061	+	6.18163i	−0.411452	+	0.911431i
$47$		−	3.17246i		−	0.462752i	−0.972864	−	0.231376i	$-0.925677\pi$
$47$		−	3.17246i		−	0.462752i	0.972864	−	0.231376i	$-0.0743227\pi$
$48$	3.70269	+	1.51330i	0.534438	+	0.218426i
$49$	4.46819	+	5.15657i	0.638313	+	0.736652i
$50$	−4.47780	−	10.5088i	−0.633256	−	1.48617i
$51$	1.01621	−	0.146109i	0.142298	−	0.0204593i
$52$	−8.78690	+	6.85915i	−1.21852	+	0.951192i
$53$	−5.08685	+	11.1387i	−0.698733	+	1.53001i	0.142768	+	0.989756i	$0.454400\pi$
$53$	−5.08685	+	11.1387i	−0.698733	+	1.53001i	−0.841501	+	0.540256i	$0.818327\pi$
$54$	−0.898455	−	1.09214i	−0.122264	−	0.148622i
$55$	−6.56096	−	0.943323i	−0.884679	−	0.127198i
$56$	1.18607	+	0.0912567i	0.158495	+	0.0121947i
$57$	−1.60583	+	5.46896i	−0.212698	+	0.724382i
$58$	9.08249	+	4.43219i	1.19259	+	0.581974i
$59$	−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	$0.889974\pi$
$60$	−3.33720	+	6.41656i	−0.430831	+	0.828374i
$61$	−7.14409	+	8.24471i	−0.914706	+	1.05563i	0.0835442	+	0.996504i	$0.473376\pi$
$61$	−7.14409	+	8.24471i	−0.914706	+	1.05563i	−0.998251	+	0.0591234i	$0.981169\pi$
$62$	5.56926	−	8.19681i	0.707296	−	1.04100i
$63$	−0.353812	−	0.227381i	−0.0445761	−	0.0286473i
$64$	−6.10211	+	5.17341i	−0.762764	+	0.646677i
$65$	−10.8968	−	16.9558i	−1.35158	−	2.10310i
$66$	1.34517	+	2.21584i	0.165579	+	0.272751i
$67$	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	0.857722	−	0.514115i	$-0.171879\pi$
$71$	−1.19475	−	4.06895i	−0.141791	−	0.482896i	−0.999513	+	0.0312186i	$0.990061\pi$
$72$	2.76699	−	0.586321i	0.326093	−	0.0690986i
$73$	−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	$0.344427\pi$
$74$	10.7093	+	0.274181i	1.24493	+	0.0318729i
$75$	−6.79505	−	4.36691i	−0.784624	−	0.504248i
$76$	−8.22203	−	7.89628i	−0.943131	−	0.905766i
$77$	0.582606	+	0.504831i	0.0663942	+	0.0575309i
$78$	−2.41350	+	7.50359i	−0.273275	+	0.849614i
$79$	0.967941	+	2.11949i	0.108902	+	0.238462i	0.956235	−	0.292600i	$-0.0945205\pi$
$79$	0.967941	+	2.11949i	0.108902	+	0.238462i	−0.847333	+	0.531062i	$0.821793\pi$
$80$	−8.30564	−	11.8428i	−0.928599	−	1.32407i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	16.1548	−	4.29757i	1.78400	−	0.474587i
$83$	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	$0.201912\pi$
$84$	0.729968	−	0.417957i	0.0796460	−	0.0456029i
$85$	−3.37715	−	1.54229i	−0.366303	−	0.167285i
$86$	−3.28541	−	2.99743i	−0.354275	−	0.323221i
$87$	7.07345	−	1.01701i	0.758353	−	0.109035i
$88$	−5.17309	+	0.341974i	−0.551453	+	0.0364545i
$89$	−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	$0.377980\pi$
$90$	0.598024	+	5.07907i	0.0630373	+	0.535381i
$91$			2.34411i			0.245729i
$92$	−9.14365	−	2.89718i	−0.953292	−	0.302051i
$93$		−	7.00729i		−	0.726622i
$94$	4.45576	−	0.524634i	0.459577	−	0.0541119i
$95$	15.5776	−	13.4980i	1.59823	−	1.38487i
$96$	−1.51312	+	5.45073i	−0.154433	+	0.556313i
$97$	−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	$0.599301\pi$
$98$	−6.50355	+	7.12837i	−0.656957	+	0.720074i
$99$	1.66731	+	0.761437i	0.167571	+	0.0765273i
$100$	14.0192	−	8.02697i	1.40192	−	0.802697i
$101$	−9.39962	−	1.35146i	−0.935297	−	0.134475i	−0.342219	−	0.939620i	$-0.611178\pi$
$101$	−9.39962	−	1.35146i	−0.935297	−	0.134475i	−0.593078	+	0.805145i	$0.702088\pi$
$102$	0.373263	+	1.40311i	0.0369585	+	0.138929i
$103$	−5.91264	−	1.73611i	−0.582590	−	0.171064i	−0.0228596	−	0.999739i	$-0.507277\pi$
$103$	−5.91264	−	1.73611i	−0.582590	−	0.171064i	−0.559730	+	0.828675i	$0.689095\pi$
$104$	−11.0868	−	11.2070i	−1.08715	−	1.09894i
$105$	0.631810	+	1.38347i	0.0616584	+	0.135013i
$106$	−16.4856	−	5.30253i	−1.60122	−	0.515027i
$107$	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	$0.636895\pi$
$108$	1.38535	−	1.44250i	0.133305	−	0.138805i
$109$	5.61245	+	3.60690i	0.537575	+	0.345478i	0.781090	−	0.624419i	$-0.214664\pi$
$109$	5.61245	+	3.60690i	0.537575	+	0.345478i	−0.243515	+	0.969897i	$0.578300\pi$
$110$	0.239915	−	9.37094i	0.0228750	−	0.893484i
$111$	6.37260	−	4.09542i	0.604860	−	0.388720i
$112$	0.0679701	+	1.68094i	0.00642257	+	0.158833i
$113$	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
$118$	1.53489	−	0.931788i	0.141298	−	0.0857781i
$119$	0.233443	+	0.363244i	0.0213996	+	0.0332985i
$120$	−9.56401	−	3.62603i	−0.873070	−	0.331009i
$121$	6.42741	+	4.13065i	0.584310	+	0.375513i
$122$	−12.7612	−	8.67051i	−1.15535	−	0.784991i
$123$	7.74074	−	8.93329i	0.697959	−	0.805488i
$124$	12.4335	+	6.46657i	1.11656	+	0.580715i
$125$	4.62284	+	10.1226i	0.413480	+	0.905394i
$126$	0.260849	−	0.534535i	0.0232383	−	0.0476202i
$127$	−3.02357	+	10.2974i	−0.268299	+	0.913742i	0.709590	+	0.704615i	$0.248880\pi$
$127$	−3.02357	+	10.2974i	−0.268299	+	0.913742i	−0.977889	+	0.209127i	$0.932938\pi$
$128$	−8.27523	−	7.71496i	−0.731434	−	0.681912i
$129$	−3.11271	−	0.447540i	−0.274059	−	0.0394037i
$130$	22.0125	−	18.1087i	1.93063	−	1.58824i
$131$	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	$-0.158349\pi$
$132$	−2.88972	+	2.25575i	−0.251518	+	0.196337i
$133$	−2.37283	+	0.341161i	−0.205750	+	0.0295824i
$134$	−7.25609	+	3.09182i	−0.626831	+	0.267093i
$135$	2.36814	+	2.73298i	0.203817	+	0.235218i
$136$	−2.83410	−	0.632536i	−0.243022	−	0.0542395i
$137$		−	0.896885i		−	0.0766261i	−0.999266	−	0.0383130i	$-0.987802\pi$
$137$		−	0.896885i		−	0.0766261i	0.999266	−	0.0383130i	$-0.0121984\pi$
$138$	−6.49922	+	1.93911i	−0.553250	+	0.165068i
$139$	1.59991			0.135703			0.0678514	−	0.997695i	$-0.478386\pi$
$139$	1.59991			0.135703			0.0678514	+	0.997695i	$0.478386\pi$
$140$	−3.03784	−	0.155652i	−0.256745	−	0.0131550i
$141$	2.39759	−	2.07752i	0.201913	−	0.174959i
$142$	5.51731	−	2.35093i	0.463003	−	0.197286i
$143$	−1.45390	−	10.1121i	−0.121581	−	0.845613i
$144$	1.28108	+	3.78931i	0.106756	+	0.315776i
$145$	−23.5071	−	10.7353i	−1.95216	−	0.891520i
$146$	−1.26445	−	1.53704i	−0.104646	−	0.127206i
$147$	−0.971030	+	6.75367i	−0.0800892	+	0.557033i
$148$	1.38592	+	15.0867i	0.113922	+	1.24012i
$149$	3.03705	+	0.891759i	0.248805	+	0.0730558i	0.403757	−	0.914866i	$-0.367704\pi$
$149$	3.03705	+	0.891759i	0.248805	+	0.0730558i	−0.154952	+	0.987922i	$0.549522\pi$
$150$	5.00967	−	10.2659i	0.409038	−	0.838206i
$151$	−5.05420	+	2.30818i	−0.411305	+	0.187837i	−0.610312	−	0.792161i	$-0.708956\pi$
$151$	−5.05420	+	2.30818i	−0.411305	+	0.187837i	0.199006	+	0.979998i	$0.436229\pi$
$152$	9.73073	−	12.8537i	0.789267	−	1.04258i
$153$	0.775896	+	0.672318i	0.0627275	+	0.0543537i
$154$	−0.612695	+	0.901762i	−0.0493724	+	0.0726660i
$155$	−13.6999	+	21.3175i	−1.10040	+	1.71226i
$156$	−10.9380	−	2.14891i	−0.875740	−	0.172051i
$157$	6.42113	−	4.12661i	0.512462	−	0.329339i	−0.258722	−	0.965952i	$-0.583301\pi$
$157$	6.42113	−	4.12661i	0.512462	−	0.329339i	0.771184	+	0.636613i	$0.219665\pi$
$158$	−2.81678	+	1.70999i	−0.224091	+	0.136039i
$159$	−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	$0.455286\pi$
$164$	8.70751	+	21.9789i	0.679942	+	1.71626i
$165$	−3.58360	−	5.57619i	−0.278983	−	0.434106i
$166$	−0.581427	+	22.7102i	−0.0451275	+	1.76265i
$167$	−0.978343	+	1.52233i	−0.0757065	+	0.117802i	−0.877042	−	0.480413i	$-0.840487\pi$
$167$	−0.978343	+	1.52233i	−0.0757065	+	0.117802i	0.801336	+	0.598215i	$0.204123\pi$
$168$	0.707741	+	0.956130i	0.0546034	+	0.0737670i
$169$	11.8297	−	13.6522i	0.909974	−	1.05017i
$170$	1.60768	−	4.99829i	0.123304	−	0.383352i
$171$	−5.18476	+	2.36780i	−0.396489	+	0.181070i
$172$	3.66661	−	5.11008i	0.279577	−	0.389640i
$173$	0.426922	−	1.45396i	0.0324583	−	0.110543i	−0.941671	−	0.336536i	$-0.890745\pi$
$173$	0.426922	−	1.45396i	0.0324583	−	0.110543i	0.974129	+	0.225993i	$0.0725628\pi$
$174$	2.59814	+	9.76655i	0.196965	+	0.740400i
$175$	0.483461	−	3.36255i	0.0365462	−	0.254185i
$176$	−1.33579	−	7.20911i	−0.100689	−	0.543407i
$177$	0.527440	−	1.15493i	0.0396448	−	0.0868101i
$178$	−6.39989	−	5.83892i	−0.479692	−	0.437646i
$179$	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	$0.666976\pi$
$180$	−7.03471	+	1.67986i	−0.524337	+	0.125210i
$181$	10.0184	+	11.5618i	0.744662	+	0.859385i	0.994039	−	0.109021i	$-0.0347715\pi$
$181$	10.0184	+	11.5618i	0.744662	+	0.859385i	−0.249378	+	0.968406i	$0.580226\pi$
$182$	−3.29232	+	0.387648i	−0.244043	+	0.0287343i
$183$	−10.9093			−0.806440
$184$	2.55702	−	13.3215i	0.188506	−	0.982072i
$185$	−27.3936			−2.01401
$186$	9.84182	−	1.15880i	0.721637	−	0.0849676i
$187$	−1.23233	−	1.42218i	−0.0901167	−	0.104000i
$188$	1.47371	+	6.17141i	0.107481	+	0.450096i
$189$	−0.0598544	−	0.416296i	−0.00435377	−	0.0302811i
$190$	21.5342	+	19.6467i	1.56226	+	1.42532i
$191$	−11.2219	+	24.5726i	−0.811991	+	1.77801i	−0.213388	+	0.976968i	$0.568450\pi$
$191$	−11.2219	+	24.5726i	−0.811991	+	1.77801i	−0.598604	+	0.801045i	$0.704278\pi$
$192$	−7.90584	−	1.22381i	−0.570555	−	0.0883206i
$193$	−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	$0.969933\pi$
$194$	−3.14568	−	11.8248i	−0.225847	−	0.848970i
$195$	5.67842	−	19.3389i	0.406640	−	1.38489i
$196$	−11.0874	−	7.95548i	−0.791956	−	0.568248i
$197$	−3.20510	+	1.46372i	−0.228354	+	0.104286i	−0.526307	−	0.850295i	$-0.676424\pi$
$197$	−3.20510	+	1.46372i	−0.228354	+	0.104286i	0.297953	+	0.954581i	$0.403696\pi$
$198$	−0.793721	+	2.46768i	−0.0564073	+	0.175370i
$199$	1.96670	−	2.26970i	0.139416	−	0.160895i	−0.681748	−	0.731587i	$-0.738780\pi$
$199$	1.96670	−	2.26970i	0.139416	−	0.160895i	0.821164	+	0.570693i	$0.193325\pi$
$200$	13.5923	+	18.3627i	0.961124	+	1.29844i
$201$	−3.01526	+	4.69183i	−0.212680	+	0.330937i
$202$	0.343717	−	13.4254i	0.0241838	−	0.944605i
$203$	1.62491	+	2.52841i	0.114046	+	0.177459i
$204$	−1.90896	+	0.756286i	−0.133654	+	0.0529506i
$205$	−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
$210$	−1.83862	+	1.11617i	−0.126877	+	0.0770231i
$211$	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	$-0.0108526\pi$
$212$	4.72123	−	24.0311i	0.324255	−	1.65046i
$213$	2.29271	−	3.56753i	0.157094	−	0.244443i
$214$	−4.60604	+	6.77916i	−0.314863	+	0.463414i
$215$	8.59445	+	7.44714i	0.586137	+	0.507890i
$216$	2.25510	+	1.70719i	0.153440	+	0.116160i
$217$	2.68078	−	1.22427i	0.181983	−	0.0831090i
$218$	−4.13780	+	8.47922i	−0.280247	+	0.574286i
$219$	−1.35035	−	0.396498i	−0.0912482	−	0.0267929i
$220$	13.2013	−	1.21272i	0.890029	−	0.0817615i
$221$	0.814343	−	5.66388i	0.0547786	−	0.380994i
$222$	6.80591	+	8.27312i	0.456783	+	0.555256i
$223$	−4.99327	−	2.28035i	−0.334374	−	0.152703i	0.241151	−	0.970488i	$-0.422475\pi$
$223$	−4.99327	−	2.28035i	−0.334374	−	0.152703i	−0.575525	+	0.817784i	$0.695202\pi$
$224$	−2.34965	+	0.373443i	−0.156993	+	0.0249517i
$225$	−1.14952	−	7.99507i	−0.0766345	−	0.533005i
$226$	−7.30360	+	3.11207i	−0.485829	+	0.207012i
$227$	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	$0.218193\pi$
$228$	0.583329	−	11.3848i	0.0386319	−	0.753974i
$229$	−16.1245			−1.06554			−0.532768	−	0.846261i	$-0.678848\pi$
$229$	−16.1245			−1.06554			−0.532768	+	0.846261i	$0.678848\pi$
$230$	23.5630	+	6.80747i	1.55370	+	0.448871i
$231$			0.770899i			0.0507214i
$232$	−19.7271	−	4.40285i	−1.29515	−	0.289061i
$233$	−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	$-0.551487\pi$
$234$	−7.25134	+	3.08980i	−0.474035	+	0.201987i
$235$	−11.3557	+	1.63270i	−0.740762	+	0.106505i
$236$	1.56253	+	2.00168i	0.101712	+	0.130299i
$237$	−0.967941	+	2.11949i	−0.0628745	+	0.137676i
$238$	−0.471575	+	0.387943i	−0.0305677	+	0.0251466i
$239$	−22.8951	−	3.29182i	−1.48096	−	0.212930i	−0.646043	−	0.763301i	$-0.723577\pi$
$239$	−22.8951	−	3.29182i	−1.48096	−	0.212930i	−0.834920	+	0.550371i	$0.814486\pi$
$240$	3.51118	−	14.0324i	0.226646	−	0.905787i
$241$	−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	$0.743227\pi$
$242$	−4.73863	+	9.71046i	−0.304611	+	0.624212i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	10.0675	−	19.3571i	0.644505	−	1.23921i
$245$	16.1581	−	18.6474i	1.03230	−	1.19134i
$246$	13.8270	+	9.39465i	0.881578	+	0.598981i
$247$	26.7252	+	17.1753i	1.70049	+	1.09284i
$248$	−7.02623	+	18.5324i	−0.446166	+	1.17681i
$249$	8.68473	+	13.5137i	0.550373	+	0.856396i
$250$	−13.4528	+	8.16683i	−0.850833	+	0.516515i
$251$	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
$256$	9.46726	−	12.8985i	0.591704	−	0.806155i
$257$	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	$0.0585917\pi$
$258$	0.113823	−	4.44584i	0.00708629	−	0.276786i
$259$	2.68017	+	1.72244i	0.166538	+	0.107027i
$260$	29.0741	+	27.9222i	1.80310	+	1.73166i
$261$	5.40073	+	4.67975i	0.334296	+	0.289670i
$262$	24.6279	+	7.92147i	1.52151	+	0.489390i
$263$	8.52535	+	18.6679i	0.525696	+	1.15111i	0.967238	+	0.253873i	$0.0817044\pi$
$263$	8.52535	+	18.6679i	0.525696	+	1.15111i	−0.441542	+	0.897241i	$0.645568\pi$
$264$	−3.64610	−	3.68561i	−0.224402	−	0.226834i
$265$	42.4881	+	12.4756i	2.61003	+	0.766373i
$266$	−0.871561	−	3.27624i	−0.0534388	−	0.200879i
$267$	−6.06348	−	0.871797i	−0.371079	−	0.0533531i
$268$	−5.54245	−	9.67996i	−0.338559	−	0.591298i
$269$	3.47782	+	1.58827i	0.212047	+	0.0968385i	0.518607	−	0.855013i	$-0.326451\pi$
$269$	3.47782	+	1.58827i	0.212047	+	0.0968385i	−0.306560	+	0.951851i	$0.599178\pi$
$270$	−3.44688	+	3.77804i	−0.209771	+	0.229924i
$271$	−18.5390	+	2.66550i	−1.12616	+	0.161918i	−0.680125	−	0.733096i	$-0.738075\pi$
$271$	−18.5390	+	2.66550i	−1.12616	+	0.161918i	−0.446038	+	0.895014i	$0.647165\pi$
$272$	0.419726	−	4.08512i	0.0254497	−	0.247697i
$273$	−1.77156	+	1.53506i	−0.107220	+	0.0929062i
$274$	1.25969	−	0.148319i	0.0761004	−	0.00896027i
$275$			14.8053i			0.892793i
$276$	−3.79828	−	8.80756i	−0.228630	−	0.530153i
$277$		−	23.8555i		−	1.43334i	−0.697414	−	0.716668i	$-0.745666\pi$
$277$		−	23.8555i		−	1.43334i	0.697414	−	0.716668i	$-0.254334\pi$
$278$	0.264579	+	2.24709i	0.0158684	+	0.134772i
$279$	5.29576	−	4.58880i	0.317049	−	0.274724i
$280$	−0.283757	−	4.29243i	−0.0169577	−	0.256521i
$281$	−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	$0.621601\pi$
$282$	3.31440	+	3.02388i	0.197369	+	0.180069i
$283$	−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	$0.664669\pi$
$284$	4.21431	+	7.36035i	0.250074	+	0.436757i
$285$	20.4023	+	2.93341i	1.20853	+	0.173760i
$286$	13.9621	−	3.71426i	0.825595	−	0.219629i
$287$	4.77003	+	1.40061i	0.281566	+	0.0826752i
$288$	−5.11027	+	2.42593i	−0.301126	+	0.142949i
$289$	6.62420	+	14.5050i	0.389659	+	0.853233i
$290$	11.1905	−	34.7913i	0.657128	−	2.04301i
$291$	−6.53889	−	5.66598i	−0.383316	−	0.332145i
$292$	1.94968	−	2.03011i	0.114097	−	0.118803i
$293$	10.6698	+	6.85705i	0.623335	+	0.400593i	0.813837	−	0.581094i	$-0.197375\pi$
$293$	10.6698	+	6.85705i	0.623335	+	0.400593i	−0.190502	+	0.981687i	$0.561011\pi$
$294$	−9.64618	−	0.246962i	−0.562577	−	0.0144031i
$295$	−3.86257	+	2.48232i	−0.224888	+	0.144527i
$296$	−20.9603	+	4.44145i	−1.21829	+	0.258154i
$297$	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
$302$	−4.07768	−	6.71698i	−0.234644	−	0.386519i
$303$	−5.13408	−	7.98878i	−0.294945	−	0.458943i
$304$	19.6624	+	11.5413i	1.12772	+	0.661938i
$305$	33.1882	+	21.3287i	1.90035	+	1.22128i
$306$	−0.815967	+	1.20094i	−0.0466457	+	0.0686530i
$307$	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	$0.158277\pi$
$308$	−1.36786	−	0.711412i	−0.0779409	−	0.0405365i
$309$	−2.55989	−	5.60538i	−0.145627	−	0.318879i
$310$	−32.2062	−	15.7164i	−1.82919	−	0.892631i
$311$	−5.23408	+	17.8256i	−0.296798	+	1.01080i	0.667198	+	0.744881i	$0.267494\pi$
$311$	−5.23408	+	17.8256i	−0.296798	+	1.01080i	−0.963995	+	0.265919i	$0.914325\pi$
$312$	1.20935	−	15.7179i	0.0684657	−	0.889851i
$313$	−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	$0.574109\pi$
$314$	6.85774	+	8.33613i	0.387005	+	0.470435i
$315$	−0.631810	+	1.38347i	−0.0355985	+	0.0779498i
$316$	−2.86751	−	3.67342i	−0.161310	−	0.206646i
$317$	−11.1965	+	1.60981i	−0.628858	+	0.0904161i	−0.449372	−	0.893345i	$-0.648352\pi$
$317$	−11.1965	+	1.60981i	−0.628858	+	0.0904161i	−0.179485	+	0.983761i	$0.557443\pi$
$318$	−6.78838	−	15.9314i	−0.380673	−	0.893388i
$319$	−8.57778	−	9.89928i	−0.480263	−	0.554253i
$320$	21.6584	+	19.1797i	1.21074	+	1.07218i
$321$			5.79537i			0.323466i
$322$	−1.87735	−	2.14762i	−0.104621	−	0.119682i
$323$	5.85179			0.325602
$324$	1.99738	+	0.102341i	0.110966	+	0.00568562i
$325$	−34.0232	+	29.4813i	−1.88727	+	1.63533i
$326$	−2.04712	−	4.80431i	−0.113379	−	0.266086i
$327$	0.949458	+	6.60362i	0.0525051	+	0.365181i
$328$	−29.4296	+	15.8645i	−1.62498	+	0.875969i
$329$	1.21369	+	0.554274i	0.0669130	+	0.0305581i
$330$	7.23919	−	5.95534i	0.398505	−	0.327831i
$331$	−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	$0.849773\pi$
$332$	−31.9928	+	2.93899i	−1.75584	+	0.161298i
$333$	7.26828	+	2.13416i	0.398299	+	0.116951i
$334$	−2.29992	−	1.12234i	−0.125846	−	0.0614120i
$335$	18.3460	−	8.37832i	1.00235	−	0.457756i
$336$	−1.22586	+	1.15215i	−0.0668759	+	0.0628548i
$337$	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	$0.615042\pi$
$338$	21.1309	+	14.3572i	1.14937	+	0.780930i
$339$	−3.03500	+	4.72256i	−0.164839	+	0.256494i
$340$	7.28602	+	1.43144i	0.395140	+	0.0776305i
$341$	−10.8051	+	6.94401i	−0.585129	+	0.376039i
$342$	−4.18302	−	6.89049i	−0.226192	−	0.372595i
$343$	−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	$0.752557\pi$
$348$	−13.2876	+	5.26423i	−0.712289	+	0.282192i
$349$	16.0400	+	24.9587i	0.858601	+	1.33601i	0.940649	+	0.339381i	$0.110218\pi$
$349$	16.0400	+	24.9587i	0.858601	+	1.33601i	−0.0820477	+	0.996628i	$0.526146\pi$
$350$	4.80268	+	0.122959i	0.256714	+	0.00657241i
$351$	−3.01329	+	4.68876i	−0.160837	+	0.250268i
$352$	9.90437	−	3.06830i	0.527905	−	0.163541i
$353$	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	$0.214422\pi$
$354$	1.70934	+	0.549803i	0.0908504	+	0.0292217i
$355$	−13.9497	+	6.37062i	−0.740374	+	0.338118i
$356$	7.14247	−	9.95431i	0.378550	−	0.527577i
$357$	−0.121649	+	0.414298i	−0.00643834	+	0.0219270i
$358$	−28.7239	+	7.64126i	−1.51810	+	0.403853i
$359$	1.45080	−	10.0905i	0.0765701	−	0.532557i	−0.915047	−	0.403347i	$-0.867847\pi$
$359$	1.45080	−	10.0905i	0.0765701	−	0.532557i	0.991617	−	0.129210i	$-0.0412441\pi$
$360$	−3.52273	−	9.60254i	−0.185664	−	0.506098i
$361$	−5.60322	+	12.2693i	−0.294906	+	0.645755i
$362$	−14.5820	+	15.9830i	−0.766413	+	0.840045i
$363$	1.08733	+	7.56251i	0.0570698	+	0.396929i
$364$	−1.08891	−	4.56000i	−0.0570744	−	0.239009i
$365$	3.33282	+	3.84628i	0.174448	+	0.201324i
$366$	−1.80409	−	15.3223i	−0.0943011	−	0.800908i
$367$	27.3567			1.42801			0.714003	−	0.700143i	$-0.246880\pi$
$367$	27.3567			1.42801			0.714003	+	0.700143i	$0.246880\pi$
$368$	19.1330	+	1.38838i	0.997378	+	0.0723741i
$369$	11.8204			0.615347
$370$	−4.53010	−	38.4746i	−0.235509	−	2.00020i
$371$	−3.37258	−	3.89216i	−0.175095	−	0.202071i
$372$	3.25511	+	13.6313i	0.168769	+	0.706751i
$373$	−2.40226	−	16.7081i	−0.124384	−	0.865110i	−0.952497	−	0.304549i	$-0.901494\pi$
$373$	−2.40226	−	16.7081i	−0.124384	−	0.865110i	0.828113	−	0.560562i	$-0.189415\pi$
$374$	1.79368	−	1.96601i	0.0927489	−	0.101660i
$375$	−4.62284	+	10.1226i	−0.238723	+	0.522730i
$376$	−8.42411	+	3.09042i	−0.434440	+	0.159376i
$377$	5.66834	−	39.4242i	0.291934	−	2.03045i
$378$	0.574795	−	0.152910i	0.0295643	−	0.00786482i
$379$	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	$-0.0864434\pi$
$380$	−24.0329	+	33.4941i	−1.23286	+	1.71821i
$381$	−9.76224	+	4.45826i	−0.500135	+	0.228404i
$382$	−36.3683	−	11.6977i	−1.86077	−	0.598509i
$383$	14.6701	−	16.9302i	0.749607	−	0.865093i	−0.244923	−	0.969543i	$-0.578763\pi$
$383$	14.6701	−	16.9302i	0.749607	−	0.865093i	0.994530	+	0.104450i	$0.0333081\pi$
$384$	0.411451	−	11.3062i	0.0209968	−	0.576968i
$385$	1.50718	−	2.34522i	0.0768130	−	0.119523i
$386$	−9.23251	−	0.236371i	−0.469922	−	0.0120310i
$387$	−1.70016	−	2.64550i	−0.0864241	−	0.134479i
$388$	16.0878	−	6.37362i	0.816736	−	0.323572i
$389$	7.50380	−	2.20331i	0.380458	−	0.111712i	−0.0859112	−	0.996303i	$-0.527380\pi$
$389$	7.50380	−	2.20331i	0.380458	−	0.111712i	0.466369	+	0.884590i	$0.345562\pi$
$390$	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
$394$	−2.58584	−	4.25954i	−0.130273	−	0.214593i
$395$	7.08847	−	4.55548i	0.356659	−	0.229211i
$396$	−3.59714	−	0.706707i	−0.180763	−	0.0355134i
$397$	2.81836	−	4.38545i	0.141449	−	0.220100i	−0.763300	−	0.646045i	$-0.776422\pi$
$397$	2.81836	−	4.38545i	0.141449	−	0.220100i	0.904749	+	0.425945i	$0.140058\pi$
$398$	3.51305	+	2.38692i	0.176093	+	0.119645i
$399$	−1.81170	−	1.56985i	−0.0906986	−	0.0785908i
$400$	−23.5428	+	22.1273i	−1.17714	+	1.10636i
$401$	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	$0.302275\pi$
$402$	−7.08837	−	3.45907i	−0.353536	−	0.172523i
$403$	−37.4734	−	11.0032i	−1.86668	−	0.548108i
$404$	18.9129	−	1.73741i	0.940953	−	0.0864396i
$405$	−0.514647	+	3.57945i	−0.0255730	+	0.177864i
$406$	−3.28246	+	2.70033i	−0.162906	+	0.134015i
$407$	−12.6301	−	5.76797i	−0.626051	−	0.285908i
$408$	−1.37790	−	2.55609i	−0.0682162	−	0.126545i
$409$	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	$0.927923\pi$
$410$	−23.6969	−	55.6134i	−1.17031	−	2.74655i
$411$	0.677821	−	0.587335i	0.0334344	−	0.0289711i
$412$	12.3084	+	0.630652i	0.606390	+	0.0310700i
$413$	0.533994			0.0262761
$414$	−5.72156	−	3.64194i	−0.281199	−	0.178992i
$415$		−	58.0907i		−	2.85156i
$416$	26.7733	+	16.6508i	1.31267	+	0.816375i
$417$	1.04772	+	1.20913i	0.0513070	+	0.0592115i
$418$	5.79180	+	13.5926i	0.283286	+	0.664834i
$419$	−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	$0.464184\pi$
$420$	−1.87173	−	2.39778i	−0.0913311	−	0.117000i
$421$	8.25319	−	18.0720i	0.402236	−	0.880773i	−0.594803	−	0.803872i	$-0.702770\pi$
$421$	8.25319	−	18.0720i	0.402236	−	0.880773i	0.997039	−	0.0769019i	$-0.0245028\pi$
$422$	22.4264	+	27.2610i	1.09170	+	1.32705i
$423$	3.14017	+	0.451489i	0.152680	+	0.0219521i
$424$	34.5327	+	2.65697i	1.67706	+	0.129034i
$425$	−2.33630	+	7.95670i	−0.113327	+	0.385957i
$426$	5.38979	+	2.63018i	0.261136	+	0.127432i
$427$	−1.90601	−	4.17358i	−0.0922384	−	0.201974i
$428$	−10.2831	−	5.34817i	−0.497053	−	0.258513i
$429$	6.69009	−	7.72078i	0.323001	−	0.372763i
$430$	−9.03831	+	13.3025i	−0.435866	+	0.641506i
$431$	−19.2795	−	12.3902i	−0.928662	−	0.596815i	−0.0135036	−	0.999909i	$-0.504298\pi$
$431$	−19.2795	−	12.3902i	−0.928662	−	0.596815i	−0.915159	+	0.403094i	$0.867935\pi$
$432$	−2.02484	+	3.44964i	−0.0974202	+	0.165971i
$433$	−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	$0.996890\pi$
$434$	2.16283	+	3.56273i	0.103819	+	0.171017i
$435$	−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	$0.172384\pi$
$439$	8.68928	+	29.5930i	0.414717	+	1.41240i	−0.442189	+	0.896922i	$0.645798\pi$
$440$	3.88639	+	18.3408i	0.185276	+	0.874362i
$441$	−5.73997	+	3.68885i	−0.273332	+	0.175660i
$442$	8.08965	+	0.207112i	0.384785	+	0.00985129i
$443$	−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	$0.871459\pi$
$444$	−10.4942	+	10.9271i	−0.498032	+	0.518578i
$445$	16.7418	+	14.5068i	0.793637	+	0.687690i
$446$	2.37703	−	7.39020i	0.112556	−	0.349936i
$447$	1.31490	+	2.87923i	0.0621927	+	0.136183i
$448$	−0.913070	−	3.23836i	−0.0431385	−	0.152998i
$449$	−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	$0.606003\pi$
$450$	11.0391	−	2.93667i	0.520387	−	0.138436i
$451$	−21.4458	−	3.08344i	−1.00984	−	0.145193i
$452$	−5.57874	−	9.74335i	−0.262402	−	0.458289i
$453$	−5.05420	−	2.30818i	−0.237467	−	0.108448i
$454$	5.36719	+	4.89674i	0.251895	+	0.229815i
$455$	8.39060	−	1.20639i	0.393357	−	0.0565562i
$456$	16.0865	−	1.06342i	0.753319	−	0.0497992i
$457$	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	$0.0195347\pi$
$458$	−2.66653	−	22.6470i	−0.124599	−	1.05823i
$459$			1.02666i			0.0479203i
$460$	−5.66453	+	34.2202i	−0.264110	+	1.59553i
$461$		−	25.7500i		−	1.19930i	−0.800264	−	0.599648i	$-0.795307\pi$
$461$		−	25.7500i		−	1.19930i	0.800264	−	0.599648i	$-0.204693\pi$
$462$	−1.08274	+	0.127484i	−0.0503734	+	0.00593111i
$463$	−8.32083	+	7.21004i	−0.386702	+	0.335079i	−0.826417	−	0.563058i	$-0.809625\pi$
$463$	−8.32083	+	7.21004i	−0.386702	+	0.335079i	0.439716	+	0.898137i	$0.355079\pi$
$464$	2.92156	−	28.4350i	0.135630	−	1.32006i
$465$	−25.0822	+	3.60628i	−1.16316	+	0.167237i
$466$	24.7732	−	27.1533i	1.14760	−	1.25785i
$467$	−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	$0.924083\pi$
$468$	−5.53882	−	9.67362i	−0.256032	−	0.447163i
$469$	−2.32177	−	0.333820i	−0.107209	−	0.0154144i
$470$	−4.17104	−	15.6792i	−0.192396	−	0.723226i
$471$	7.32363	+	2.15041i	0.337455	+	0.0990857i
$472$	−2.55299	+	2.52562i	−0.117511	+	0.116251i
$473$	2.39450	+	5.24323i	0.110099	+	0.241084i
$474$	−3.13692	−	1.00898i	−0.144084	−	0.0463440i
$475$	−34.7942	−	30.1493i	−1.59647	−	1.38335i
$476$	−0.622855	−	0.598178i	−0.0285485	−	0.0274175i
$477$	−10.3013	−	6.62027i	−0.471666	−	0.303121i
$478$	0.837209	−	32.7009i	0.0382930	−	1.49570i
$479$	9.24167	−	5.93926i	0.422263	−	0.271372i	−0.312206	−	0.950014i	$-0.601068\pi$
$479$	9.24167	−	5.93926i	0.422263	−	0.271372i	0.734469	+	0.678643i	$0.237431\pi$
$480$	20.2893	+	2.61094i	0.926076	+	0.119173i
$481$	−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
$486$	1.20889	−	0.733882i	0.0548364	−	0.0332896i
$487$	6.72951	+	10.4713i	0.304943	+	0.474501i	0.959577	−	0.281445i	$-0.0908136\pi$
$487$	6.72951	+	10.4713i	0.304943	+	0.474501i	−0.654634	+	0.755946i	$0.727177\pi$
$488$	28.8522	+	10.9388i	1.30608	+	0.495176i
$489$	−3.10650	−	1.99642i	−0.140481	−	0.0902814i
$490$	28.8626	+	19.6105i	1.30388	+	0.885912i
$491$	−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	$0.260106\pi$
$492$	−10.9083	+	20.9738i	−0.491784	+	0.945571i
$493$	−3.04777	−	6.67368i	−0.137265	−	0.300567i
$494$	−19.7033	+	40.3762i	−0.886492	+	1.81661i
$495$	1.86744	−	6.35993i	0.0839353	−	0.285858i
$496$	−27.1909	−	6.80369i	−1.22091	−	0.305495i
$497$	1.76540	+	0.253826i	0.0791891	+	0.0113857i
$498$	−17.5440	+	14.4326i	−0.786163	+	0.646740i
$499$	−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	$0.192502\pi$
$500$	−13.6951	−	17.5441i	−0.612464	−	0.784597i
$501$	−1.79118	+	0.257533i	−0.0800240	+	0.0115057i
$502$	−23.5961	+	10.0543i	−1.05314	+	0.448745i
$503$	−3.48132	−	4.01766i	−0.155225	−	0.179139i	0.672811	−	0.739815i	$-0.265087\pi$
$503$	−3.48132	−	4.01766i	−0.155225	−	0.179139i	−0.828035	+	0.560676i	$0.810541\pi$
$504$	−0.259123	+	1.16101i	−0.0115422	+	0.0517154i
$505$			34.3409i			1.52815i
$506$	9.43059	+	8.10007i	0.419241	+	0.360092i
$507$	18.0644			0.802268
$508$	1.09833	−	21.4360i	0.0487306	−	0.951070i
$509$	−2.93351	+	2.54190i	−0.130026	+	0.112668i	−0.717446	−	0.696614i	$-0.754689\pi$
$509$	−2.93351	+	2.54190i	−0.130026	+	0.112668i	0.587420	+	0.809282i	$0.300144\pi$
$510$	4.83027	−	2.05818i	0.213888	−	0.0911377i
$511$	−0.0842365	−	0.585878i	−0.00372640	−	0.0259177i
$512$	19.6817	+	11.1638i	0.869816	+	0.493377i
$513$	−5.18476	−	2.36780i	−0.228913	−	0.104541i
$514$	20.9737	+	25.4953i	0.925112	+	1.12455i
$515$	−3.17138	+	22.0575i	−0.139748	+	0.971968i
$516$	6.26306	−	0.575349i	0.275716	−	0.0253283i
$517$	−5.57943	−	1.63827i	−0.245383	−	0.0720510i
$518$	−1.97596	+	4.04917i	−0.0868189	+	0.177910i
$519$	1.37841	−	0.629497i	0.0605053	−	0.0276318i
$520$	−34.4090	+	45.4524i	−1.50894	+	1.99322i
$521$	−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	$0.743982\pi$
$522$	−5.67965	+	8.35928i	−0.248591	+	0.365876i
$523$	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	$-0.0339136\pi$
$524$	−7.05305	+	35.9001i	−0.308114	+	1.56830i
$525$	2.85784	−	1.83662i	0.124726	−	0.0801568i
$526$	−24.8095	+	15.0611i	−1.08174	+	0.656695i
$527$	−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
$532$	4.45739	−	1.76591i	0.193252	−	0.0765621i
$533$	−35.6184	−	55.4232i	−1.54280	−	2.40065i
$534$	0.221724	−	8.66039i	0.00959493	−	0.374772i
$535$	11.3305	−	17.6306i	0.489860	−	0.762237i
$536$	12.6791	−	9.38522i	0.547652	−	0.405380i
$537$	−13.7634	+	15.8838i	−0.593933	+	0.685435i
$538$	−1.65561	+	5.14730i	−0.0713784	+	0.221916i
$539$	11.3763	−	5.19537i	0.490011	−	0.223780i
$540$	−5.87631	−	4.21641i	−0.252876	−	0.181445i
$541$	2.54903	−	8.68120i	0.109591	−	0.373234i	−0.886374	−	0.462969i	$-0.846784\pi$
$541$	2.54903	−	8.68120i	0.109591	−	0.373234i	0.995966	+	0.0897355i	$0.0286022\pi$
$542$	−6.80954	−	25.5974i	−0.292495	−	1.09950i
$543$	−2.17721	+	15.1428i	−0.0934329	+	0.649840i
$544$	5.80701	−	0.0860511i	0.248974	−	0.00368941i
$545$	10.0223	−	21.9457i	0.429307	−	0.940052i
$546$	−2.44898	−	2.23432i	−0.104807	−	0.0956199i
$547$	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	$0.837383\pi$
$548$	0.416631	+	1.74471i	0.0177976	+	0.0745305i
$549$	−7.14409	−	8.24471i	−0.304902	−	0.351876i
$550$	−20.7942	+	2.44837i	−0.886668	+	0.104399i
$551$	40.7321			1.73525
$552$	11.7422	−	6.79124i	0.499781	−	0.289055i
$553$	−0.979969			−0.0416725
$554$	33.5053	−	3.94501i	1.42350	−	0.167607i
$555$	−17.9390	−	20.7027i	−0.761467	−	0.878779i
$556$	−3.11232	+	0.743209i	−0.131992	+	0.0315191i
$557$	2.59722	+	18.0640i	0.110048	+	0.765398i	0.967870	+	0.251451i	$0.0809078\pi$
$557$	2.59722	+	18.0640i	0.110048	+	0.765398i	−0.857822	+	0.513946i	$0.828183\pi$
$558$	7.32079	+	6.67910i	0.309914	+	0.282749i
$559$	−7.28107	+	15.9433i	−0.307956	+	0.674330i
$560$	5.98184	−	1.10838i	0.252779	−	0.0468377i
$561$	0.267810	−	1.86266i	0.0113070	−	0.0786416i
$562$	−6.10745	−	22.9582i	−0.257627	−	0.968433i
$563$	−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	$0.615049\pi$
$564$	−3.69897	+	5.15517i	−0.155755	+	0.217072i
$565$	18.4661	−	8.43318i	0.776874	−	0.354787i
$566$	1.29385	−	4.02257i	0.0543844	−	0.169081i
$567$	0.275420	−	0.317851i	0.0115665	−	0.0133485i
$568$	−9.64078	+	7.13624i	−0.404518	+	0.299430i
$569$	−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	$0.322536\pi$
$570$	−0.746053	+	29.1403i	−0.0312487	+	1.22055i
$571$	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	$0.572663\pi$
$572$	7.52564	+	18.9957i	0.314663	+	0.794249i
$573$	−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	$0.131538\pi$
$578$	−19.2769	+	11.7025i	−0.801815	+	0.486758i
$579$	−5.49381	+	3.53066i	−0.228315	+	0.146729i
$580$	50.7153	+	9.96370i	2.10584	+	0.413720i
$581$	−3.65260	+	5.68356i	−0.151535	+	0.235794i
$582$	6.87659	−	10.1209i	0.285044	−	0.419526i
$583$	16.9628	+	14.6983i	0.702526	+	0.608742i
$584$	3.17374	+	2.40263i	0.131330	+	0.0994215i
$585$	18.3339	−	8.37283i	0.758015	−	0.346174i
$586$	−7.86633	+	16.1198i	−0.324955	+	0.665902i
$587$	−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	$0.777227\pi$
$588$	−1.24834	−	13.5890i	−0.0514806	−	0.560401i
$589$	5.68412	−	39.5339i	0.234210	−	1.62897i
$590$	−4.12521	−	5.01452i	−0.169832	−	0.206445i
$591$	−3.20510	−	1.46372i	−0.131840	−	0.0602094i
$592$	−9.70430	−	28.7045i	−0.398844	−	1.17975i
$593$	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	$0.891357\pi$
$594$	−2.38473	+	1.01613i	−0.0978465	+	0.0416924i
$595$	1.18007	−	1.02254i	0.0483782	−	0.0419199i
$596$	−6.32225	−	0.323937i	−0.258969	−	0.0132690i
$597$	3.00324			0.122914
$598$	0.164511	+	37.8013i	0.00672734	+	1.54581i
$599$			30.8462i			1.26034i	0.776456	+	0.630172i	$0.217015\pi$
$599$			30.8462i			1.26034i	−0.776456	+	0.630172i	$0.782985\pi$
$600$	−4.97652	+	22.2974i	−0.203165	+	0.910288i
$601$	−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	$0.840275\pi$
$602$	1.72074	−	0.733206i	0.0701319	−	0.0298833i
$603$	−5.52043	+	0.793718i	−0.224809	+	0.0323227i
$604$	8.75975	−	6.83795i	0.356429	−	0.278232i
$605$	11.4776	−	25.1324i	0.466630	−	1.02178i
$606$	10.3713	−	8.53198i	0.421305	−	0.346588i
$607$	−14.1422	−	2.03334i	−0.574013	−	0.0825305i	−0.150805	−	0.988563i	$-0.548187\pi$
$607$	−14.1422	−	2.03334i	−0.574013	−	0.0825305i	−0.423207	+	0.906033i	$0.639096\pi$
$608$	−12.9583	+	29.5247i	−0.525527	+	1.19738i
$609$	−0.846753	+	2.88378i	−0.0343122	+	0.116857i
$610$	−24.4681	+	50.1403i	−0.990685	+	2.03012i
$611$	−7.34532	−	16.0840i	−0.297160	−	0.650689i
$612$	−1.82167	−	0.947435i	−0.0736365	−	0.0382978i
$613$	26.0134	−	30.0211i	1.05067	−	1.21254i	0.0741223	−	0.997249i	$-0.476384\pi$
$613$	26.0134	−	30.0211i	1.05067	−	1.21254i	0.976550	−	0.215291i	$-0.0690701\pi$
$614$	8.81582	+	5.98984i	0.355777	+	0.241730i
$615$	−35.9600	−	23.1101i	−1.45005	−	0.931888i
$616$	0.772982	−	2.03882i	0.0311443	−	0.0821463i
$617$	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	$0.782688\pi$
$618$	7.44949	−	4.52237i	0.299663	−	0.181916i
$619$	−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
$624$	22.2760	−	0.900748i	0.891753	−	0.0360588i
$625$	−0.121021	+	0.0777752i	−0.00484082	+	0.00311101i
$626$	0.115136	−	4.49713i	0.00460175	−	0.179741i
$627$	8.78904	+	5.64838i	0.351001	+	0.225574i
$628$	−10.5741	+	11.0103i	−0.421953	+	0.439360i
$629$	−5.87750	−	5.09289i	−0.234351	−	0.203067i
$630$	−2.04759	−	0.658599i	−0.0815778	−	0.0262392i
$631$	2.10750	+	4.61478i	0.0838982	+	0.183711i	0.946931	−	0.321436i	$-0.104165\pi$
$631$	2.10750	+	4.61478i	0.0838982	+	0.183711i	−0.863033	+	0.505147i	$0.831438\pi$
$632$	4.68516	−	4.63493i	0.186366	−	0.184368i
$633$	23.9499	+	7.03233i	0.951924	+	0.279510i
$634$	−4.11258	−	15.4594i	−0.163331	−	0.613971i
$635$	38.4149	+	5.52322i	1.52445	+	0.219182i
$636$	21.2532	−	12.1689i	0.842745	−	0.482530i
$637$	34.5923	+	15.7978i	1.37060	+	0.625931i
$638$	12.4851	−	13.6846i	0.494291	−	0.541780i
$639$	4.19757	−	0.603519i	0.166053	−	0.0238749i
$640$	−23.3564	+	33.5912i	−0.923245	+	1.32781i
$641$	−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	$0.374035\pi$
$642$	−8.13966	+	0.958387i	−0.321247	+	0.0378245i
$643$		−	34.8441i		−	1.37412i	−0.726601	−	0.687060i	$-0.758901\pi$
$643$		−	34.8441i		−	1.37412i	0.726601	−	0.687060i	$-0.241099\pi$
$644$	2.70590	−	2.99191i	0.106627	−	0.117898i
$645$			11.3721i			0.447776i
$646$	0.967717	+	8.21890i	0.0380743	+	0.323368i
$647$	10.7696	−	9.33188i	0.423395	−	0.366874i	−0.416946	−	0.908931i	$-0.636900\pi$
$647$	10.7696	−	9.33188i	0.423395	−	0.366874i	0.840342	+	0.542057i	$0.182354\pi$
$648$	0.186570	+	2.82227i	0.00732915	+	0.110869i
$649$	−2.30356	+	0.331202i	−0.0904226	+	0.0130008i
$650$	−47.0332	−	42.9106i	−1.84479	−	1.68309i
$651$	2.68078	+	1.22427i	0.105068	+	0.0479830i
$652$	6.40917	−	3.66970i	0.251003	−	0.143716i
$653$	13.5793	+	1.95241i	0.531399	+	0.0764036i	0.402791	−	0.915292i	$-0.368040\pi$
$653$	13.5793	+	1.95241i	0.531399	+	0.0764036i	0.128608	+	0.991696i	$0.458949\pi$
$654$	−9.11785	+	2.42557i	−0.356536	+	0.0948474i
$655$	−63.4731	−	18.6374i	−2.48010	−	0.728223i
$656$	−27.1486	−	38.7107i	−1.05998	−	1.51140i
$657$	−0.584637	−	1.28018i	−0.0228089	−	0.0499445i
$658$	−0.577775	+	1.79630i	−0.0225240	+	0.0700273i
$659$	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	$0.709311\pi$
$660$	9.56150	+	9.18269i	0.372181	+	0.357436i
$661$	11.6029	+	7.45675i	0.451301	+	0.290034i	0.746479	−	0.665408i	$-0.231743\pi$
$661$	11.6029	+	7.45675i	0.451301	+	0.290034i	−0.295178	+	0.955442i	$0.595379\pi$
$662$	−29.6693	−	0.759596i	−1.15313	−	0.0295225i
$663$	4.81375	−	3.09361i	0.186951	−	0.120146i
$664$	−9.41853	−	44.4483i	−0.365510	−	1.72493i
$665$	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
$670$	14.8013	+	24.3816i	0.571825	+	0.941942i
$671$	10.8108	+	16.8219i	0.417347	+	0.649404i
$672$	−1.82092	−	1.53120i	−0.0702437	−	0.0590672i
$673$	−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	$0.869543\pi$
$674$	−10.0767	+	14.8308i	−0.388138	+	0.571260i
$675$	5.28950	−	6.10441i	0.203593	−	0.234959i
$676$	−16.6704	+	32.0529i	−0.641171	+	1.23280i
$677$	−14.5243	−	31.8038i	−0.558214	−	1.22232i	−0.952839	−	0.303476i	$-0.901853\pi$
$677$	−14.5243	−	31.8038i	−0.558214	−	1.22232i	0.394625	−	0.918842i	$-0.370874\pi$
$678$	−7.13479	−	3.48172i	−0.274010	−	0.133715i
$679$	1.02520	−	3.49151i	0.0393436	−	0.133992i
$680$	−0.805570	+	10.4700i	−0.0308922	+	0.401507i
$681$	5.08506	+	0.731122i	0.194860	+	0.0280166i
$682$	−11.5398	−	14.0275i	−0.441882	−	0.537142i
$683$	−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	$0.192018\pi$
$684$	8.98603	−	7.01458i	0.343589	−	0.268209i
$685$	−3.21035	+	0.461579i	−0.122661	+	0.0176360i
$686$	−3.22293	−	7.56377i	−0.123052	−	0.288786i
$687$	−10.5593	−	12.1861i	−0.402862	−	0.464928i
$688$	−4.75889	+	11.6439i	−0.181431	+	0.443920i
$689$			68.2493i			2.60009i
$690$	10.2857	+	22.2656i	0.391571	+	0.847639i
$691$	−8.79461			−0.334563			−0.167281	−	0.985909i	$-0.553499\pi$
$691$	−8.79461			−0.334563			−0.167281	+	0.985909i	$0.553499\pi$
$692$	−0.155082	+	3.02672i	−0.00589534	+	0.115059i
$693$	−0.582606	+	0.504831i	−0.0221314	+	0.0191770i
$694$	−18.2061	−	42.7272i	−0.691093	−	1.62190i
$695$	−0.823389	−	5.72680i	−0.0312329	−	0.217230i
$696$	−9.59105	−	17.7920i	−0.363548	−	0.674404i
$697$	−11.0389	−	5.04128i	−0.418127	−	0.190952i
$698$	−32.4023	+	26.6558i	−1.22644	+	1.00894i
$699$	3.69884	−	25.7260i	0.139903	−	0.973046i
$700$	0.621529	+	6.76576i	0.0234916	+	0.255722i
$701$	28.1446	+	8.26401i	1.06301	+	0.312127i	0.766062	−	0.642767i	$-0.222214\pi$
$701$	28.1446	+	8.26401i	1.06301	+	0.312127i	0.296947	+	0.954894i	$0.404032\pi$
$702$	−7.08373	−	3.45681i	−0.267358	−	0.130469i
$703$	39.2752	−	17.9364i	1.48129	−	0.676484i
$704$	5.94737	+	13.4034i	0.224150	+	0.505159i
$705$	−8.67029	−	7.51285i	−0.326542	−	0.282950i
$706$	1.77411	+	1.20541i	0.0667697	+	0.0453661i
$707$	2.15928	−	3.35990i	0.0812079	−	0.126362i
$708$	−0.489529	+	2.49171i	−0.0183976	+	0.0936441i
$709$	28.4219	−	18.2656i	1.06741	−	0.685980i	0.115791	−	0.993274i	$-0.463060\pi$
$709$	28.4219	−	18.2656i	1.06741	−	0.685980i	0.951615	+	0.307294i	$0.0994234\pi$
$710$	−11.2545	−	18.5390i	−0.422374	−	0.695757i
$711$	−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
$716$	−15.4823	−	39.0794i	−0.578602	−	1.46046i
$717$	−12.5053	−	19.4587i	−0.467020	−	0.726698i
$718$	14.4122	+	0.368981i	0.537857	+	0.0137702i
$719$	6.96862	−	10.8434i	0.259886	−	0.404390i	−0.686650	−	0.726988i	$-0.740920\pi$
$719$	6.96862	−	10.8434i	0.259886	−	0.404390i	0.946536	+	0.322598i	$0.104556\pi$
$720$	12.9043	−	6.53569i	0.480915	−	0.243571i
$721$	1.69721	−	1.95868i	0.0632072	−	0.0729450i
$722$	−18.1590	−	5.84079i	−0.675810	−	0.217372i
$723$	−25.0703	+	11.4492i	−0.932373	+	0.425801i
$724$	−24.8597	−	17.8375i	−0.923903	−	0.662924i
$725$	−16.2621	+	55.3836i	−0.603959	+	2.05690i
$726$	−10.4418	+	2.77778i	−0.387532	+	0.103093i
$727$	0.697629	−	4.85211i	0.0258736	−	0.179955i	−0.972787	−	0.231703i	$-0.925570\pi$
$727$	0.697629	−	4.85211i	0.0258736	−	0.179955i	0.998660	+	0.0517482i	$0.0164793\pi$
$728$	6.22450	−	2.28348i	0.230695	−	0.0846314i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−4.85099	+	5.31705i	−0.179543	+	0.196793i
$731$	0.459470	+	3.19568i	0.0169941	+	0.118197i
$732$	21.2220	−	5.06772i	0.784386	−	0.187308i
$733$	13.0496	+	15.0600i	0.481998	+	0.556256i	0.943710	−	0.330775i	$-0.107310\pi$
$733$	13.0496	+	15.0600i	0.481998	+	0.556256i	−0.461712	+	0.887030i	$0.652764\pi$
$734$	4.52400	+	38.4227i	0.166984	+	1.41821i
$735$	24.6741			0.910118
$736$	1.21406	+	27.1021i	0.0447509	+	0.998998i
$737$	10.2227			0.376560
$738$	1.95476	+	16.6019i	0.0719557	+	0.611126i
$739$	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	$0.466525\pi$
$740$	53.2888	−	12.7252i	1.95894	−	0.467786i
$741$	4.52111	+	31.4450i	0.166087	+	1.15516i
$742$	4.90886	−	5.38047i	0.180210	−	0.197523i
$743$	−11.1203	+	24.3500i	−0.407963	+	0.893314i	0.588438	+	0.808543i	$0.299743\pi$
$743$	−11.1203	+	24.3500i	−0.407963	+	0.893314i	−0.996400	+	0.0847714i	$0.972984\pi$
$744$	−18.6070	+	6.82606i	−0.682167	+	0.250255i
$745$	1.62899	−	11.3299i	0.0596818	−	0.415096i
$746$	23.0694	−	6.13703i	0.844631	−	0.224693i
$747$	−4.52569	+	15.4131i	−0.165586	+	0.563935i
$748$	3.05790	+	2.19412i	0.111808	+	0.0802250i
$749$	−2.21714	+	1.01253i	−0.0810124	+	0.0369971i
$750$	−14.9818	−	4.81885i	−0.547058	−	0.175959i
$751$	−18.8039	+	21.7009i	−0.686165	+	0.791877i	−0.986814	−	0.161858i	$-0.948251\pi$
$751$	−18.8039	+	21.7009i	−0.686165	+	0.791877i	0.300649	+	0.953735i	$0.402797\pi$
$752$	−5.73363	−	11.3207i	−0.209084	−	0.412823i
$753$	−9.80531	+	15.2574i	−0.357326	+	0.556009i
$754$	56.3091	+	1.44163i	2.05066	+	0.0525010i
$755$	10.8631	+	16.9034i	0.395350	+	0.615176i
$756$	0.309818	+	0.782019i	0.0112680	+	0.0284418i
$757$	47.2201	−	13.8651i	1.71624	−	0.503935i	0.732084	−	0.681214i	$-0.238548\pi$
$757$	47.2201	−	13.8651i	1.71624	−	0.503935i	0.984161	+	0.177279i	$0.0567296\pi$
$758$	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	$0.494125\pi$
$762$	−7.87608	−	12.9739i	−0.285320	−	0.469995i
$763$	−2.36047	+	1.51698i	−0.0854547	+	0.0549184i
$764$	10.4153	−	53.0142i	0.376814	−	1.91799i
$765$	2.00721	−	3.12328i	0.0725709	−	0.112923i
$766$	26.2047	+	17.8046i	0.946813	+	0.643305i
$767$	−5.34811	−	4.63416i	−0.193109	−	0.167330i
$768$	15.9478	−	1.29184i	0.575465	−	0.0466151i
$769$	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	$0.168649\pi$
$770$	3.54313	+	1.72902i	0.127685	+	0.0623096i
$771$	22.3986	+	6.57683i	0.806667	+	0.236859i
$772$	−1.19480	−	13.0063i	−0.0430020	−	0.468105i
$773$	2.32399	−	16.1637i	0.0835882	−	0.581368i	−0.904382	−	0.426724i	$-0.859668\pi$
$773$	2.32399	−	16.1637i	0.0835882	−	0.581368i	0.987970	−	0.154645i	$-0.0494232\pi$
$774$	3.43448	−	2.82539i	0.123450	−	0.101556i
$775$	51.4851	+	23.5124i	1.84940	+	0.844592i
$776$	11.6123	+	21.5415i	0.416857	+	0.773296i
$777$	0.453404	+	3.15350i	0.0162658	+	0.113131i
$778$	4.33549	+	10.1748i	0.155435	+	0.364785i
$779$	50.9184	−	44.1210i	1.82434	−	1.58080i
$780$	−2.06272	+	40.2579i	−0.0738572	+	1.44146i
$781$	−7.77307			−0.278142
$782$	3.79001	+	5.84132i	0.135530	+	0.208885i
$783$			7.14618i			0.255384i
$784$	25.2639	+	10.3254i	0.902282	+	0.368764i
$785$	−18.0756	−	20.8603i	−0.645145	−	0.744537i
$786$	10.1412	+	23.8000i	0.361724	+	0.848916i
$787$	−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	$0.795299\pi$
$788$	5.55496	−	4.33625i	0.197887	−	0.154473i
$789$	−8.52535	+	18.6679i	−0.303511	+	0.664596i
$790$	7.57045	+	9.20249i	0.269345	+	0.327410i
$791$	−2.33697	−	0.336006i	−0.0830931	−	0.0119470i
$792$	0.397714	−	5.16910i	0.0141321	−	0.183676i
$793$	−17.1303	+	58.3406i	−0.608316	+	2.07174i
$794$	6.62550	+	3.23319i	0.235130	+	0.114742i
$795$	18.3954	+	40.2802i	0.652416	+	1.42859i
$796$	−2.77149	+	5.32885i	−0.0982330	+	0.188876i
$797$	−4.69897	+	5.42290i	−0.166446	+	0.192089i	−0.832845	−	0.553507i	$-0.813289\pi$
$797$	−4.69897	+	5.42290i	−0.166446	+	0.192089i	0.666399	+	0.745595i	$0.267835\pi$
$798$	1.90527	−	2.80416i	0.0674457	−	0.0992664i
$799$	−2.73999	−	1.76089i	−0.0969339	−	0.0622957i
$800$	−34.9713	−	29.4070i	−1.23642	−	1.03969i
$801$	−3.31187	−	5.15338i	−0.117019	−	0.182086i
$802$	5.63097	+	9.27564i	0.198836	+	0.327534i
$803$	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
$808$	5.56787	+	26.2761i	0.195877	+	0.924390i
$809$	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	$0.212040\pi$
$810$	−5.11248	−	0.130890i	−0.179634	−	0.00459900i
$811$	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	$0.359830\pi$
$812$	−4.33547	−	4.16370i	−0.152145	−	0.146117i
$813$	−14.1549	−	12.2653i	−0.496434	−	0.430163i
$814$	6.01253	−	18.6930i	0.210739	−	0.655189i
$815$	5.54734	+	12.1470i	0.194315	+	0.425490i
$816$	3.36219	−	2.35798i	0.117700	−	0.0825458i
$817$	−17.1983	−	5.04989i	−0.601694	−	0.176673i
$818$	−4.61802	+	1.22851i	−0.161465	+	0.0429537i
$819$	−2.32025	−	0.333601i	−0.0810760	−	0.0116570i
$820$	74.1908	−	42.4794i	2.59086	−	1.48345i
$821$	−29.8540	−	13.6339i	−1.04191	−	0.475826i	−0.180417	−	0.983590i	$-0.557745\pi$
$821$	−29.8540	−	13.6339i	−1.04191	−	0.475826i	−0.861496	+	0.507764i	$0.830472\pi$
$822$	0.937010	+	0.854878i	0.0326820	+	0.0298173i
$823$	−36.1080	+	5.19154i	−1.25864	+	0.180966i	−0.739169	−	0.673520i	$-0.764782\pi$
$823$	−36.1080	+	5.19154i	−1.25864	+	0.180966i	−0.519475	+	0.854486i	$0.673873\pi$
$824$	1.14969	+	17.3915i	0.0400514	+	0.605863i
$825$	−11.1891	+	9.69541i	−0.389554	+	0.337551i
$826$	0.0883073	+	0.750001i	0.00307260	+	0.0260959i
$827$		−	46.8065i		−	1.62762i	−0.581131	−	0.813810i	$-0.697390\pi$
$827$		−	46.8065i		−	1.62762i	0.581131	−	0.813810i	$-0.302610\pi$
$828$	4.16896	−	8.63827i	0.144881	−	0.300201i
$829$		−	9.96741i		−	0.346182i	−0.984906	−	0.173091i	$-0.944624\pi$
$829$		−	9.96741i		−	0.346182i	0.984906	−	0.173091i	$-0.0553755\pi$
$830$	81.5890	−	9.60652i	2.83200	−	0.333447i
$831$	18.0288	−	15.6220i	0.625411	−	0.541922i
$832$	−18.9588	+	40.3570i	−0.657277	+	1.39913i
$833$	6.93370	−	0.996916i	0.240238	−	0.0345411i
$834$	−1.52498	+	1.67149i	−0.0528057	+	0.0578789i
$835$	5.95261	+	2.71846i	0.205998	+	0.0940763i
$836$	−18.1331	+	10.3825i	−0.627147	+	0.359085i
$837$	6.93597	+	0.997241i	0.239742	+	0.0344697i
$838$	−0.450644	−	1.69399i	−0.0155672	−	0.0585181i
$839$	−18.8587	−	5.53743i	−0.651076	−	0.191173i	−0.0605166	−	0.998167i	$-0.519275\pi$
$839$	−18.8587	−	5.53743i	−0.651076	−	0.191173i	−0.590560	+	0.806994i	$0.701093\pi$
$840$	3.05818	−	3.02539i	0.105517	−	0.104386i
$841$	−9.16735	−	20.0737i	−0.316116	−	0.692197i
$842$	26.7471	+	8.60312i	0.921766	+	0.296483i
$843$	−12.6955	−	11.0007i	−0.437255	−	0.378884i
$844$	−34.5798	+	36.0063i	−1.19028	+	1.23939i
$845$	−54.9552	−	35.3176i	−1.89052	−	1.21496i
$846$	−0.114827	+	4.48507i	−0.00394784	+	0.154200i
$847$	−2.70322	+	1.73726i	−0.0928839	+	0.0596928i
$848$	1.97897	+	48.9409i	0.0679581	+	1.68064i
$849$	−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	$0.0431714\pi$
$853$	6.72879	+	22.9162i	0.230390	+	0.784635i	−0.760427	+	0.649423i	$0.775010\pi$
$854$	5.54665	−	3.36721i	0.189802	−	0.115223i
$855$	11.1437	+	17.3400i	0.381108	+	0.593015i
$856$	5.81103	−	15.3272i	0.198617	−	0.523872i
$857$	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	$0.591245\pi$
$858$	11.9503	+	8.11951i	0.407975	+	0.277196i
$859$	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	$0.0952041\pi$
$860$	−20.1783	−	10.4946i	−0.688073	−	0.357861i
$861$	2.06520	+	4.52215i	0.0703817	+	0.154115i
$862$	14.2139	−	29.1273i	0.484127	−	0.992080i
$863$	7.10103	−	24.1839i	0.241722	−	0.823229i	−0.745857	−	0.666106i	$-0.767960\pi$
$863$	7.10103	−	24.1839i	0.241722	−	0.823229i	0.987579	−	0.157123i	$-0.0502219\pi$
$864$	−5.17991	−	2.27344i	−0.176224	−	0.0773441i
$865$	−5.42409	−	0.779867i	−0.184425	−	0.0265163i
$866$	24.1985	−	19.9069i	0.822297	−	0.676465i
$867$	−6.62420	+	14.5050i	−0.224970	+	0.492615i
$868$	−4.64623	+	3.62689i	−0.157703	+	0.123105i
$869$	4.22742	−	0.607811i	0.143405	−	0.0206186i
$870$	33.6217	−	14.3262i	1.13988	−	0.485705i
$871$	20.3562	+	23.4923i	0.689743	+	0.796006i
$872$	4.11041	−	18.4168i	0.139196	−	0.623672i
$873$		−	8.65219i		−	0.292832i
$874$	−38.2405	+	5.66812i	−1.29350	+	0.191727i
$875$	−4.68029			−0.158223
$876$	2.81103	+	0.144031i	0.0949758	+	0.00486634i
$877$	−33.8589	+	29.3389i	−1.14333	+	0.990704i	−0.143333	+	0.989674i	$0.545782\pi$
$877$	−33.8589	+	29.3389i	−1.14333	+	0.990704i	−0.999999	+	0.00102918i	$0.999672\pi$
$878$	−40.1267	+	17.0980i	−1.35421	+	0.577030i
$879$	1.80501	+	12.5541i	0.0608813	+	0.423439i
$880$	−25.1171	+	8.49151i	−0.846699	+	0.286249i
$881$	−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	$0.665077\pi$
$882$	−6.13026	−	7.45182i	−0.206417	−	0.250916i
$883$	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	$-0.158726\pi$
$884$	1.04690	+	11.3963i	0.0352112	+	0.383298i
$885$	−4.40546	−	1.29356i	−0.148088	−	0.0434826i
$886$	14.6505	−	30.0221i	0.492194	−	1.00861i
$887$	−29.7022	+	13.5645i	−0.997301	+	0.455452i	−0.846085	−	0.533048i	$-0.821046\pi$
$887$	−29.7022	+	13.5645i	−0.997301	+	0.455452i	−0.151216	+	0.988501i	$0.548319\pi$
$888$	−17.0827	−	12.9322i	−0.573258	−	0.433976i
$889$	−3.41120	−	2.95582i	−0.114408	−	0.0991351i
$890$	−17.6064	+	25.9130i	−0.590168	+	0.868607i
$891$	−0.990970	+	1.54198i	−0.0331987	+	0.0516582i
$892$	10.7727	+	2.11644i	0.360697	+	0.0708638i
$893$	15.2120	−	9.77617i	0.509051	−	0.327147i
$894$	−3.82647	+	2.32293i	−0.127976	+	0.0776905i
$895$	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
$900$	5.95012	+	15.0189i	0.198337	+	0.500629i
$901$	6.79675	+	10.5760i	0.226433	+	0.352336i
$902$	0.784210	−	30.6308i	0.0261113	−	1.01989i
$903$	0.715050	−	1.11264i	0.0237954	−	0.0370263i
$904$	12.7621	−	9.44668i	0.424461	−	0.314192i
$905$	36.2291	−	41.8106i	1.20430	−	1.38983i
$906$	2.40604	−	7.48039i	0.0799354	−	0.248519i
$907$	−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	$0.518172\pi$
$908$	−5.98995	+	8.34806i	−0.198783	+	0.277040i
$909$	2.67541	−	9.11161i	0.0887378	−	0.302213i
$910$	3.08195	+	11.5852i	0.102166	+	0.384045i
$911$	1.15563	−	8.03756i	0.0382876	−	0.266296i	−0.961681	−	0.274169i	$-0.911597\pi$
$911$	1.15563	−	8.03756i	0.0382876	−	0.266296i	0.999969	+	0.00787329i	$0.00250617\pi$
$912$	4.15383	+	22.4178i	0.137547	+	0.742328i
$913$	12.2315	−	26.7833i	0.404805	−	0.886400i
$914$	31.9002	+	29.1040i	1.05516	+	0.962676i
$915$	5.61444	+	39.0493i	0.185608	+	1.29093i
$916$	31.3670	−	7.49033i	1.03640	−	0.247487i
$917$	5.03830	+	5.81451i	0.166379	+	0.192012i
$918$	−1.44195	+	0.169780i	−0.0475915	+	0.00560356i
$919$	6.57008			0.216727			0.108363	−	0.994111i	$-0.465439\pi$
$919$	6.57008			0.216727			0.108363	+	0.994111i	$0.465439\pi$
$920$	−48.9994	−	2.29686i	−1.61546	−	0.0757252i
$921$	7.53647			0.248335
$922$	36.1661	−	4.25830i	1.19107	−	0.140240i
$923$	−15.4782	−	17.8628i	−0.509472	−	0.587962i
$924$	−0.358107	−	1.49963i	−0.0117808	−	0.0493343i
$925$	8.70774	+	60.5636i	0.286309	+	1.99132i
$926$	−11.5026	−	10.4944i	−0.377999	−	0.344866i
$927$	2.55989	−	5.60538i	0.0840779	−	0.184105i
$928$	40.4205	−	0.598970i	1.32687	−	0.0196621i
$929$	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	$-0.103910\pi$
$930$	−9.21293	−	34.6319i	−0.302104	−	1.13562i
$931$	−10.9568	+	37.3154i	−0.359094	+	1.22296i
$932$	42.2339	+	30.3039i	1.38342	+	0.992638i
$933$	−16.8993	+	7.71766i	−0.553259	+	0.252665i
$934$	14.7057	−	45.7200i	0.481185	−	1.49600i
$935$	−4.45641	+	5.14297i	−0.145740	+	0.168193i
$936$	12.6708	−	9.37908i	0.414157	−	0.306565i
$937$	−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	$0.316385\pi$
$938$	0.0849003	−	3.31615i	0.00277209	−	0.108276i
$939$	−1.71977	−	2.67602i	−0.0561227	−	0.0873287i
$940$	21.3318	−	8.45116i	0.695766	−	0.275646i
$941$	−43.3525	+	12.7294i	−1.41325	+	0.414968i	−0.897213	−	0.441597i	$-0.854412\pi$
$941$	−43.3525	+	12.7294i	−1.41325	+	0.414968i	−0.516038	+	0.856565i	$0.672594\pi$
$942$	−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
$946$	−6.96819	+	4.23018i	−0.226555	+	0.137535i
$947$	−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	$0.407720\pi$
$948$	0.898368	−	4.57270i	0.0291776	−	0.148514i
$949$	−4.24077	+	6.59877i	−0.137661	+	0.214205i
$950$	36.5911	−	53.8547i	1.18717	−	1.74728i
$951$	−8.54876	−	7.40754i	−0.277213	−	0.240206i
$952$	0.737146	−	0.973729i	0.0238910	−	0.0315587i
$953$	−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	$0.650762\pi$
$954$	7.59470	−	15.5632i	0.245888	−	0.503876i
$955$	93.7317	+	27.5221i	3.03309	+	0.890595i
$956$	46.0672	−	4.23191i	1.48992	−	0.136870i
$957$	1.86413	−	12.9653i	0.0602587	−	0.419109i
$958$	9.87007	+	11.9979i	0.318887	+	0.387633i
$959$	0.343122	+	0.156698i	0.0110800	+	0.00506006i
$960$	−0.311833	+	28.9283i	−0.0100644	+	0.933658i
$961$	2.57620	+	17.9179i	0.0831032	+	0.577995i
$962$	54.9298	−	23.4056i	1.77101	−	0.754627i
$963$	−4.37985	+	3.79516i	−0.141139	+	0.122297i
$964$	2.82061	−	55.0496i	0.0908458	−	1.77303i
$965$	23.6160			0.760225
$966$	0.393661	−	2.82520i	0.0126658	−	0.0908993i
$967$			27.5700i			0.886590i	0.896376	+	0.443295i	$0.146191\pi$
$967$			27.5700i			0.886590i	−0.896376	+	0.443295i	$0.853809\pi$
$968$	4.70727	−	21.0911i	0.151297	−	0.677892i
$969$	3.83211	+	4.42249i	0.123105	+	0.142071i
$970$	−40.7072	+	17.3454i	−1.30703	+	0.556926i
$971$	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	$0.0950428\pi$
$972$	1.23066	+	1.57654i	0.0394735	+	0.0505675i
$973$	−0.279527	+	0.612079i	−0.00896123	+	0.0196224i
$974$	−13.5942	+	11.1833i	−0.435587	+	0.358337i
$975$	−44.5609	−	6.40689i	−1.42709	−	0.205185i
$976$	−10.5924	+	42.3322i	−0.339053	+	1.35502i
$977$	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	$-0.0300922\pi$
$978$	2.29028	−	4.69326i	0.0732350	−	0.150074i
$979$	4.66443	+	10.2137i	0.149076	+	0.326431i
$980$	−22.7701	+	43.7809i	−0.727365	+	1.39853i
$981$	−4.36892	+	5.04201i	−0.139489	+	0.160979i
$982$	−5.33779	−	3.62672i	−0.170336	−	0.115733i
$983$	3.66751	+	2.35697i	0.116975	+	0.0751755i	0.597820	−	0.801630i	$-0.296034\pi$
$983$	3.66751	+	2.35697i	0.116975	+	0.0751755i	−0.480845	+	0.876806i	$0.659670\pi$
$984$	−31.2618	−	11.8524i	−0.996591	−	0.377840i
$985$	6.88880	+	10.7192i	0.219496	+	0.341542i
$986$	8.86925	−	5.38426i	0.282454	−	0.171470i
$987$	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	$-0.698487\pi$
$991$	−16.7346	−	56.9927i	−0.531591	−	1.81043i	0.0523415	−	0.998629i	$-0.483332\pi$
$992$	5.05928	−	39.3150i	0.160632	−	1.24825i
$993$	−17.6548	+	11.3460i	−0.560257	+	0.360055i
$994$	−0.0645556	+	2.52150i	−0.00204758	+	0.0799772i
$995$	−9.13642	−	5.87162i	−0.289644	−	0.186143i
$996$	−23.1720	−	22.2539i	−0.734233	−	0.705143i
$997$	26.6350	+	23.0793i	0.843537	+	0.730929i	0.965164	−	0.261647i	$-0.0842655\pi$
$997$	26.6350	+	23.0793i	0.843537	+	0.730929i	−0.121626	+	0.992576i	$0.538811\pi$
$998$	−10.5529	−	3.39430i	−0.334046	−	0.107445i
$999$	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.451.12	yes	240
8.3	odd	2	inner	552.2.t.a.451.8	yes	240
23.5	odd	22	inner	552.2.t.a.235.8	✓	240
184.51	even	22	inner	552.2.t.a.235.12	yes	240

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.165371 + 1.40451i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.94530 + 0.464531i) q^{4} +(-0.514647 - 3.57945i) q^{5} +(-0.953164 + 1.04474i) q^{6} +(-0.174714 + 0.382571i) q^{7} +(-0.974137 - 2.65538i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.165371 + 1.40451i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.94530 + 0.464531i) q^{4} +(-0.514647 - 3.57945i) q^{5} +(-0.953164 + 1.04474i) q^{6} +(-0.174714 + 0.382571i) q^{7} +(-0.974137 - 2.65538i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(4.94226 - 1.31476i) q^{10} +(0.516403 - 1.75871i) q^{11} +(-1.62497 - 1.16596i) q^{12} +(5.06987 - 2.31533i) q^{13} +(-0.566217 - 0.182122i) q^{14} +(2.36814 - 2.73298i) q^{15} +(3.56842 - 1.80731i) q^{16} +(0.555053 - 0.863679i) q^{17} +(-1.41375 - 0.0361949i) q^{18} +(3.08157 + 4.79502i) q^{19} +(2.66391 + 6.72404i) 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} +(4.09032 + 6.73781i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(0.162156 - 0.825376i) q^{28} +(3.86352 - 6.01175i) q^{29} +(4.23013 + 2.87413i) q^{30} +(-5.29576 - 4.58880i) q^{31} +(3.12850 + 4.71301i) q^{32} +(1.66731 - 0.761437i) q^{33} +(1.30484 + 0.636750i) q^{34} +(1.45931 + 0.428491i) q^{35} +(-0.182957 - 1.99161i) q^{36} +(1.07805 - 7.49802i) q^{37} +(-6.22505 + 5.12106i) q^{38} +(5.06987 + 2.31533i) q^{39} +(-9.00346 + 4.85345i) q^{40} +(-1.68222 - 11.7001i) q^{41} +(-0.233155 - 0.547183i) q^{42} +(-2.37662 + 2.05935i) q^{43} +(-0.187587 + 3.66111i) q^{44} +3.61625 q^{45} +(-2.79061 + 6.18163i) q^{46} -3.17246i q^{47} +(3.70269 + 1.51330i) q^{48} +(4.46819 + 5.15657i) q^{49} +(-4.47780 - 10.5088i) q^{50} +(1.01621 - 0.146109i) q^{51} +(-8.78690 + 6.85915i) q^{52} +(-5.08685 + 11.1387i) q^{53} +(-0.898455 - 1.09214i) q^{54} +(-6.56096 - 0.943323i) q^{55} +(1.18607 + 0.0912567i) q^{56} +(-1.60583 + 5.46896i) q^{57} +(9.08249 + 4.43219i) q^{58} +(-0.527440 - 1.15493i) q^{59} +(-3.33720 + 6.41656i) q^{60} +(-7.14409 + 8.24471i) q^{61} +(5.56926 - 8.19681i) q^{62} +(-0.353812 - 0.227381i) q^{63} +(-6.10211 + 5.17341i) q^{64} +(-10.8968 - 16.9558i) q^{65} +(1.34517 + 2.21584i) 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} +(2.76699 - 0.586321i) q^{72} +(-1.18394 + 0.760875i) q^{73} +(10.7093 + 0.274181i) q^{74} +(-6.79505 - 4.36691i) q^{75} +(-8.22203 - 7.89628i) q^{76} +(0.582606 + 0.504831i) q^{77} +(-2.41350 + 7.50359i) q^{78} +(0.967941 + 2.11949i) q^{79} +(-8.30564 - 11.8428i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(16.1548 - 4.29757i) q^{82} +(15.9003 + 2.28611i) q^{83} +(0.729968 - 0.417957i) q^{84} +(-3.37715 - 1.54229i) q^{85} +(-3.28541 - 2.99743i) q^{86} +(7.07345 - 1.01701i) q^{87} +(-5.17309 + 0.341974i) q^{88} +(-4.62959 + 4.01157i) q^{89} +(0.598024 + 5.07907i) q^{90} +2.34411i q^{91} +(-9.14365 - 2.89718i) q^{92} -7.00729i q^{93} +(4.45576 - 0.524634i) q^{94} +(15.5776 - 13.4980i) q^{95} +(-1.51312 + 5.45073i) q^{96} +(-8.56412 + 1.23133i) q^{97} +(-6.50355 + 7.12837i) 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