LMFDB - Embedded newform 552.2.t.a.451.6

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			451.6
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908250 - 1.08401i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.350163 + 1.96911i) q^{4} +(0.0443320 + 0.308336i) q^{5} +(0.224464 - 1.39629i) q^{6} +(0.778998 - 1.70577i) q^{7} +(2.45257 - 1.40886i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.908250 - 1.08401i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.350163 + 1.96911i) q^{4} +(0.0443320 + 0.308336i) q^{5} +(0.224464 - 1.39629i) q^{6} +(0.778998 - 1.70577i) q^{7} +(2.45257 - 1.40886i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.293975 - 0.328103i) q^{10} +(-0.132235 + 0.450351i) q^{11} +(-1.71746 + 1.02486i) q^{12} +(4.84409 - 2.21222i) q^{13} +(-2.55660 + 0.704820i) q^{14} +(-0.203994 + 0.235421i) q^{15} +(-3.75477 - 1.37902i) q^{16} +(-3.35182 + 5.21553i) q^{17} +(1.20224 - 0.744735i) q^{18} +(-0.457964 - 0.712606i) q^{19} +(-0.622670 - 0.0206734i) q^{20} +(1.79927 - 0.528313i) q^{21} +(0.608289 - 0.265687i) q^{22} +(4.73817 - 0.741431i) q^{23} +(2.67084 + 0.930922i) q^{24} +(4.70436 - 1.38132i) q^{25} +(-6.79772 - 3.24180i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(3.08606 + 2.13123i) q^{28} +(0.704877 - 1.09681i) q^{29} +(0.440476 + 0.00731016i) q^{30} +(4.98874 + 4.32277i) q^{31} +(1.91540 + 5.32271i) q^{32} +(-0.426949 + 0.194981i) q^{33} +(8.69799 - 1.10360i) q^{34} +(0.560484 + 0.164573i) q^{35} +(-1.89923 - 0.626832i) q^{36} +(0.124525 - 0.866090i) q^{37} +(-0.356527 + 1.14366i) q^{38} +(4.84409 + 2.21222i) q^{39} +(0.543130 + 0.693759i) q^{40} +(1.07436 + 7.47237i) q^{41} +(-2.20688 - 1.47059i) q^{42} +(7.10478 - 6.15633i) q^{43} +(-0.840487 - 0.418082i) q^{44} -0.311507 q^{45} +(-5.10717 - 4.46283i) q^{46} -2.81845i q^{47} +(-1.41666 - 3.74073i) q^{48} +(2.28122 + 2.63267i) q^{49} +(-5.77011 - 3.84499i) q^{50} +(-6.13661 + 0.882311i) q^{51} +(2.65988 + 10.3132i) q^{52} +(1.73474 - 3.79855i) q^{53} +(1.35013 + 0.420892i) q^{54} +(-0.144722 - 0.0208079i) q^{55} +(-0.492641 - 5.28102i) q^{56} +(0.238649 - 0.812764i) q^{57} +(-1.82916 + 0.232083i) q^{58} +(-2.13105 - 4.66635i) q^{59} +(-0.392138 - 0.484121i) q^{60} +(-8.17481 + 9.43424i) q^{61} +(0.154907 - 9.33400i) q^{62} +(1.57754 + 1.01382i) q^{63} +(4.03022 - 6.91067i) q^{64} +(0.896856 + 1.39554i) q^{65} +(0.599138 + 0.285726i) q^{66} +(1.44273 + 4.91350i) q^{67} +(-9.09626 - 8.42638i) q^{68} +(3.66318 + 3.09534i) q^{69} +(-0.330661 - 0.757045i) q^{70} +(-2.07446 - 7.06497i) q^{71} +(1.04548 + 2.62811i) q^{72} +(4.75400 - 3.05521i) q^{73} +(-1.05195 + 0.651640i) q^{74} +(4.12464 + 2.65074i) q^{75} +(1.56356 - 0.652252i) q^{76} +(0.665184 + 0.576385i) q^{77} +(-2.00157 - 7.26030i) q^{78} +(-5.11164 - 11.1929i) q^{79} +(0.258744 - 1.21887i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(7.12434 - 7.95140i) q^{82} +(-9.65749 - 1.38854i) q^{83} +(0.410267 + 3.72795i) q^{84} +(-1.75673 - 0.802271i) q^{85} +(-13.1264 - 2.11018i) q^{86} +(1.29051 - 0.185547i) q^{87} +(0.310167 + 1.29082i) q^{88} +(-0.723050 + 0.626526i) q^{89} +(0.282926 + 0.337677i) q^{90} -9.98620i q^{91} +(-0.199176 + 9.58959i) q^{92} +6.60105i q^{93} +(-3.05523 + 2.55985i) q^{94} +(0.199420 - 0.172798i) q^{95} +(-2.76832 + 4.93320i) q^{96} +(-9.74665 + 1.40136i) q^{97} +(0.781926 - 4.86400i) q^{98} +(-0.426949 - 0.194981i) 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 $

$2$	−0.908250	−	1.08401i	−0.642230	−	0.766512i
$2$	−0.908250	−	1.08401i	−0.642230	−	0.766512i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	−0.350163	+	1.96911i	−0.175082	+	0.984554i
$5$	0.0443320	+	0.308336i	0.0198259	+	0.137892i	0.997330	−	0.0730231i	$-0.0232647\pi$
$5$	0.0443320	+	0.308336i	0.0198259	+	0.137892i	−0.977504	+	0.210915i	$0.932356\pi$
$6$	0.224464	−	1.39629i	0.0916371	−	0.570032i
$7$	0.778998	−	1.70577i	0.294433	−	0.644719i	−0.703380	−	0.710814i	$-0.748327\pi$
$7$	0.778998	−	1.70577i	0.294433	−	0.644719i	0.997813	+	0.0660949i	$0.0210540\pi$
$8$	2.45257	−	1.40886i	0.867115	−	0.498108i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.293975	−	0.328103i	0.0929632	−	0.103755i
$11$	−0.132235	+	0.450351i	−0.0398704	+	0.135786i	−0.977023	−	0.213133i	$-0.931633\pi$
$11$	−0.132235	+	0.450351i	−0.0398704	+	0.135786i	0.937153	+	0.348919i	$0.113451\pi$
$12$	−1.71746	+	1.02486i	−0.495788	+	0.295850i
$13$	4.84409	−	2.21222i	1.34351	−	0.613560i	0.391655	−	0.920112i	$-0.371903\pi$
$13$	4.84409	−	2.21222i	1.34351	−	0.613560i	0.951854	+	0.306552i	$0.0991754\pi$
$14$	−2.55660	+	0.704820i	−0.683279	+	0.188371i
$15$	−0.203994	+	0.235421i	−0.0526709	+	0.0607855i
$16$	−3.75477	−	1.37902i	−0.938693	−	0.344755i
$17$	−3.35182	+	5.21553i	−0.812935	+	1.26495i	0.148223	+	0.988954i	$0.452645\pi$
$17$	−3.35182	+	5.21553i	−0.812935	+	1.26495i	−0.961158	+	0.275998i	$0.910992\pi$
$18$	1.20224	−	0.744735i	0.283370	−	0.175536i
$19$	−0.457964	−	0.712606i	−0.105064	−	0.163483i	0.784741	−	0.619824i	$-0.212796\pi$
$19$	−0.457964	−	0.712606i	−0.105064	−	0.163483i	−0.889805	+	0.456341i	$0.849160\pi$
$20$	−0.622670	−	0.0206734i	−0.139233	−	0.00462271i
$21$	1.79927	−	0.528313i	0.392632	−	0.115287i
$22$	0.608289	−	0.265687i	0.129688	−	0.0566447i
$23$	4.73817	−	0.741431i	0.987977	−	0.154599i
$23$	4.73817	−	0.741431i	0.987977	−	0.154599i
$24$	2.67084	+	0.930922i	0.545183	+	0.190024i
$25$	4.70436	−	1.38132i	0.940872	−	0.276265i
$26$	−6.79772	−	3.24180i	−1.33314	−	0.635769i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	3.08606	+	2.13123i	0.583211	+	0.402764i
$29$	0.704877	−	1.09681i	0.130892	−	0.203673i	−0.769621	−	0.638501i	$-0.779555\pi$
$29$	0.704877	−	1.09681i	0.130892	−	0.203673i	0.900513	+	0.434829i	$0.143191\pi$
$30$	0.440476	+	0.00731016i	0.0804196	+	0.00133465i
$31$	4.98874	+	4.32277i	0.896004	+	0.776392i	0.975398	−	0.220452i	$-0.0707531\pi$
$31$	4.98874	+	4.32277i	0.896004	+	0.776392i	−0.0793942	+	0.996843i	$0.525299\pi$
$32$	1.91540	+	5.32271i	0.338598	+	0.940931i
$33$	−0.426949	+	0.194981i	−0.0743222	+	0.0339418i
$34$	8.69799	−	1.10360i	1.49169	−	0.189265i
$35$	0.560484	+	0.164573i	0.0947391	+	0.0278179i
$36$	−1.89923	−	0.626832i	−0.316539	−	0.104472i
$37$	0.124525	−	0.866090i	0.0204718	−	0.142384i	−0.977022	−	0.213138i	$-0.931631\pi$
$37$	0.124525	−	0.866090i	0.0204718	−	0.142384i	0.997494	+	0.0707541i	$0.0225406\pi$
$38$	−0.356527	+	1.14366i	−0.0578364	+	0.185527i
$39$	4.84409	+	2.21222i	0.775675	+	0.354239i
$40$	0.543130	+	0.693759i	0.0858764	+	0.109693i
$41$	1.07436	+	7.47237i	0.167787	+	1.16699i	0.883445	+	0.468536i	$0.155218\pi$
$41$	1.07436	+	7.47237i	0.167787	+	1.16699i	−0.715657	+	0.698452i	$0.753873\pi$
$42$	−2.20688	−	1.47059i	−0.340529	−	0.226917i
$43$	7.10478	−	6.15633i	1.08347	−	0.938831i	0.0851256	−	0.996370i	$-0.472871\pi$
$43$	7.10478	−	6.15633i	1.08347	−	0.938831i	0.998343	+	0.0575391i	$0.0183254\pi$
$44$	−0.840487	−	0.418082i	−0.126708	−	0.0630282i
$45$	−0.311507			−0.0464367
$46$	−5.10717	−	4.46283i	−0.753011	−	0.658008i
$47$		−	2.81845i		−	0.411113i	−0.978645	−	0.205556i	$-0.934100\pi$
$47$		−	2.81845i		−	0.411113i	0.978645	−	0.205556i	$-0.0659004\pi$
$48$	−1.41666	−	3.74073i	−0.204477	−	0.539928i
$49$	2.28122	+	2.63267i	0.325889	+	0.376096i
$50$	−5.77011	−	3.84499i	−0.816016	−	0.543764i
$51$	−6.13661	+	0.882311i	−0.859297	+	0.123548i
$52$	2.65988	+	10.3132i	0.368859	+	1.43018i
$53$	1.73474	−	3.79855i	0.238285	−	0.521771i	−0.752275	−	0.658849i	$-0.771044\pi$
$53$	1.73474	−	3.79855i	0.238285	−	0.521771i	0.990560	+	0.137077i	$0.0437709\pi$
$54$	1.35013	+	0.420892i	0.183729	+	0.0572761i
$55$	−0.144722	−	0.0208079i	−0.0195143	−	0.00280573i
$56$	−0.492641	−	5.28102i	−0.0658320	−	0.705705i
$57$	0.238649	−	0.812764i	0.0316098	−	0.107653i
$58$	−1.82916	+	0.232083i	−0.240181	+	0.0304740i
$59$	−2.13105	−	4.66635i	−0.277439	−	0.607507i	0.718697	−	0.695323i	$-0.244739\pi$
$59$	−2.13105	−	4.66635i	−0.277439	−	0.607507i	−0.996137	+	0.0878155i	$0.972011\pi$
$60$	−0.392138	−	0.484121i	−0.0506249	−	0.0624998i
$61$	−8.17481	+	9.43424i	−1.04668	+	1.20793i	−0.0690441	+	0.997614i	$0.521995\pi$
$61$	−8.17481	+	9.43424i	−1.04668	+	1.20793i	−0.977633	+	0.210317i	$0.932551\pi$
$62$	0.154907	−	9.33400i	0.0196732	−	1.18542i
$63$	1.57754	+	1.01382i	0.198752	+	0.127730i
$64$	4.03022	−	6.91067i	0.503777	−	0.863834i
$65$	0.896856	+	1.39554i	0.111241	+	0.173095i
$66$	0.599138	+	0.285726i	0.0737487	+	0.0351704i
$67$	1.44273	+	4.91350i	0.176258	+	0.600279i	0.999470	+	0.0325458i	$0.0103615\pi$
$67$	1.44273	+	4.91350i	0.176258	+	0.600279i	−0.823212	+	0.567734i	$0.807820\pi$
$68$	−9.09626	−	8.42638i	−1.10308	−	1.02185i
$69$	3.66318	+	3.09534i	0.440995	+	0.372635i
$70$	−0.330661	−	0.757045i	−0.0395215	−	0.0904841i
$71$	−2.07446	−	7.06497i	−0.246193	−	0.838457i	−0.986158	−	0.165811i	$-0.946976\pi$
$71$	−2.07446	−	7.06497i	−0.246193	−	0.838457i	0.739964	−	0.672646i	$-0.234842\pi$
$72$	1.04548	+	2.62811i	0.123211	+	0.309726i
$73$	4.75400	−	3.05521i	0.556413	−	0.357585i	−0.232015	−	0.972712i	$-0.574532\pi$
$73$	4.75400	−	3.05521i	0.556413	−	0.357585i	0.788428	+	0.615127i	$0.210895\pi$
$74$	−1.05195	+	0.651640i	−0.122287	+	0.0757516i
$75$	4.12464	+	2.65074i	0.476272	+	0.306081i
$76$	1.56356	−	0.652252i	0.179353	−	0.0748184i
$77$	0.665184	+	0.576385i	0.0758047	+	0.0656852i
$78$	−2.00157	−	7.26030i	−0.226633	−	0.822067i
$79$	−5.11164	−	11.1929i	−0.575104	−	1.25930i	−0.944035	−	0.329846i	$-0.893003\pi$
$79$	−5.11164	−	11.1929i	−0.575104	−	1.25930i	0.368931	−	0.929457i	$-0.379724\pi$
$80$	0.258744	−	1.21887i	0.0289285	−	0.136273i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	7.12434	−	7.95140i	0.786752	−	0.878085i
$83$	−9.65749	−	1.38854i	−1.06005	−	0.152412i	−0.409831	−	0.912161i	$-0.634412\pi$
$83$	−9.65749	−	1.38854i	−1.06005	−	0.152412i	−0.650216	+	0.759750i	$0.725322\pi$
$84$	0.410267	+	3.72795i	0.0447638	+	0.406752i
$85$	−1.75673	−	0.802271i	−0.190544	−	0.0870186i
$86$	−13.1264	−	2.11018i	−1.41546	−	0.227547i
$87$	1.29051	−	0.185547i	0.138357	−	0.0198928i
$88$	0.310167	+	1.29082i	0.0330639	+	0.137602i
$89$	−0.723050	+	0.626526i	−0.0766432	+	0.0664117i	−0.692340	−	0.721572i	$-0.743420\pi$
$89$	−0.723050	+	0.626526i	−0.0766432	+	0.0664117i	0.615697	+	0.787983i	$0.288875\pi$
$90$	0.282926	+	0.337677i	0.0298230	+	0.0355943i
$91$		−	9.98620i		−	1.04684i
$92$	−0.199176	+	9.58959i	−0.0207656	+	0.999784i
$93$			6.60105i			0.684497i
$94$	−3.05523	+	2.55985i	−0.315123	+	0.264029i
$95$	0.199420	−	0.172798i	0.0204600	−	0.0177287i
$96$	−2.76832	+	4.93320i	−0.282540	+	0.503492i
$97$	−9.74665	+	1.40136i	−0.989622	+	0.142286i	−0.618068	−	0.786125i	$-0.712084\pi$
$97$	−9.74665	+	1.40136i	−0.989622	+	0.142286i	−0.371555	+	0.928411i	$0.621175\pi$
$98$	0.781926	−	4.86400i	0.0789864	−	0.491338i
$99$	−0.426949	−	0.194981i	−0.0429099	−	0.0195963i
$100$	1.07268	+	9.74708i	0.107268	+	0.974708i
$101$	−12.9015	−	1.85496i	−1.28375	−	0.184575i	−0.533539	−	0.845776i	$-0.679138\pi$
$101$	−12.9015	−	1.85496i	−1.28375	−	0.184575i	−0.750209	+	0.661200i	$0.770047\pi$
$102$	6.53001	+	5.85080i	0.646568	+	0.579315i
$103$	2.90292	+	0.852375i	0.286034	+	0.0839870i	0.421602	−	0.906781i	$-0.361468\pi$
$103$	2.90292	+	0.852375i	0.286034	+	0.0839870i	−0.135569	+	0.990768i	$0.543286\pi$
$104$	8.76377	−	12.2503i	0.859358	−	1.20124i
$105$	0.242663	+	0.531358i	0.0236815	+	0.0518552i
$106$	−5.69326	+	1.56956i	−0.552978	+	0.152449i
$107$	−1.62974	−	1.41218i	−0.157553	−	0.136520i	0.572517	−	0.819893i	$-0.305967\pi$
$107$	−1.62974	−	1.41218i	−0.157553	−	0.136520i	−0.730070	+	0.683372i	$0.760513\pi$
$108$	−0.770004	−	1.84583i	−0.0740937	−	0.177615i
$109$	−3.89793	−	2.50505i	−0.373354	−	0.239940i	0.340485	−	0.940250i	$-0.389409\pi$
$109$	−3.89793	−	2.50505i	−0.373354	−	0.239940i	−0.713839	+	0.700310i	$0.753045\pi$
$110$	0.108888	+	0.175779i	0.0103820	+	0.0167599i
$111$	0.736093	−	0.473059i	0.0698669	−	0.0449007i
$112$	−5.27724	+	5.33051i	−0.498652	+	0.503686i
$113$	5.21792	+	17.7706i	0.490860	+	1.67172i	0.716565	+	0.697521i	$0.245713\pi$
$113$	5.21792	+	17.7706i	0.490860	+	1.67172i	−0.225705	+	0.974196i	$0.572468\pi$
$114$	−1.09780	+	0.479494i	−0.102818	+	0.0449088i
$115$	0.438663	+	1.42808i	0.0409055	+	0.133169i
$116$	1.91292	+	1.77204i	0.177610	+	0.164530i
$117$	1.50032	+	5.10962i	0.138705	+	0.472384i
$118$	−3.12285	+	6.54830i	−0.287482	+	0.602820i
$119$	6.28542	+	9.78031i	0.576184	+	0.896559i
$120$	−0.168633	+	0.864786i	−0.0153940	+	0.0789438i
$121$	9.06846	+	5.82794i	0.824405	+	0.529813i
$122$	17.6516	+	0.292946i	1.59810	+	0.0265221i
$123$	−4.94368	+	5.70531i	−0.445756	+	0.514430i
$124$	−10.2589	+	8.30969i	−0.921273	+	0.746232i
$125$	1.28149	+	2.80607i	0.114620	+	0.250982i
$126$	−0.333805	−	2.63088i	−0.0297377	−	0.234377i
$127$	1.48683	−	5.06367i	0.131935	−	0.449328i	−0.866853	−	0.498565i	$-0.833861\pi$
$127$	1.48683	−	5.06367i	0.131935	−	0.449328i	0.998787	+	0.0492367i	$0.0156789\pi$
$128$	−11.1517	+	1.90781i	−0.985680	+	0.168628i
$129$	9.30528	+	1.33790i	0.819285	+	0.117795i
$130$	0.698207	−	2.23970i	0.0612368	−	0.196435i
$131$	6.19500	−	13.5652i	0.541259	−	1.18519i	−0.419486	−	0.907762i	$-0.637790\pi$
$131$	6.19500	−	13.5652i	0.541259	−	1.18519i	0.960746	−	0.277431i	$-0.0894830\pi$
$132$	−0.234437	−	0.908983i	−0.0204051	−	0.0791168i
$133$	−1.57229	+	0.226061i	−0.136335	+	0.0196020i
$134$	4.01593	−	6.02663i	0.346923	−	0.520621i
$135$	−0.203994	−	0.235421i	−0.0175570	−	0.0202618i
$136$	−0.872615	+	17.5137i	−0.0748261	+	1.50179i
$137$			22.0585i			1.88459i	0.334790	+	0.942293i	$0.391335\pi$
$137$			22.0585i			1.88459i	−0.334790	+	0.942293i	$0.608665\pi$
$138$	0.0282996	−	6.78227i	0.00240902	−	0.577345i
$139$	−14.5306			−1.23247			−0.616233	−	0.787564i	$-0.711342\pi$
$139$	−14.5306			−1.23247			−0.616233	+	0.787564i	$0.711342\pi$
$140$	−0.520323	+	1.04603i	−0.0439753	+	0.0884053i
$141$	2.13004	−	1.84569i	0.179382	−	0.155435i
$142$	−5.77438	+	8.66550i	−0.484575	+	0.727193i
$143$	0.355719	+	2.47408i	0.0297467	+	0.206893i
$144$	1.89934	−	3.52030i	0.158278	−	0.293358i
$145$	0.369435	+	0.168715i	0.0306799	+	0.0140110i
$146$	−7.62970	−	2.37850i	−0.631439	−	0.196846i
$147$	−0.495757	+	3.44807i	−0.0408893	+	0.284392i
$148$	1.66182	+	0.548476i	0.136601	+	0.0450844i
$149$	−9.37869	−	2.75383i	−0.768332	−	0.225603i	−0.126001	−	0.992030i	$-0.540214\pi$
$149$	−9.37869	−	2.75383i	−0.768332	−	0.225603i	−0.642331	+	0.766428i	$0.722032\pi$
$150$	−0.872765	−	6.87869i	−0.0712610	−	0.561643i
$151$	−18.6825	+	8.53203i	−1.52036	+	0.694326i	−0.988320	−	0.152391i	$-0.951303\pi$
$151$	−18.6825	+	8.53203i	−1.52036	+	0.694326i	−0.532042	+	0.846718i	$0.678575\pi$
$152$	−2.12715	−	1.10251i	−0.172535	−	0.0894253i
$153$	−4.68543	−	4.05995i	−0.378795	−	0.328227i
$154$	0.0206549	−	1.24457i	0.00166442	−	0.100290i
$155$	−1.11170	+	1.72984i	−0.0892942	+	0.138944i
$156$	−6.05233	+	8.76390i	−0.484574	+	0.701673i
$157$	1.64325	−	1.05606i	0.131146	−	0.0842824i	−0.473423	−	0.880835i	$-0.656982\pi$
$157$	1.64325	−	1.05606i	0.131146	−	0.0842824i	0.604569	+	0.796553i	$0.293345\pi$
$158$	−7.49062	+	15.7071i	−0.595922	+	1.24959i
$159$	4.00677	−	1.17649i	0.317757	−	0.0933020i
$160$	−1.55627	+	0.826553i	−0.123034	+	0.0653448i
$161$	2.42632	−	8.65979i	0.191221	−	0.682487i
$162$	0.566058	+	1.29599i	0.0444737	+	0.101822i
$163$	−19.9802	+	5.86672i	−1.56497	+	0.459517i	−0.945532	−	0.325528i	$-0.894458\pi$
$163$	−19.9802	+	5.86672i	−1.56497	+	0.459517i	−0.619439	+	0.785045i	$0.712640\pi$
$164$	−15.0901	−	0.501009i	−1.17834	−	0.0391222i
$165$	−0.0790471	−	0.123000i	−0.00615381	−	0.00957552i
$166$	7.26622	+	11.7300i	0.563968	+	0.910422i
$167$	−7.22219	+	11.2380i	−0.558870	+	0.869619i	−0.999607	−	0.0280171i	$-0.991081\pi$
$167$	−7.22219	+	11.2380i	−0.558870	+	0.869619i	0.440737	+	0.897636i	$0.354717\pi$
$168$	3.66851	−	3.83064i	0.283032	−	0.295541i
$169$	10.0581	−	11.6077i	0.773700	−	0.892897i
$170$	0.725878	+	2.63298i	0.0556723	+	0.201940i
$171$	0.770528	−	0.351888i	0.0589237	−	0.0269096i
$172$	9.63464	+	16.1458i	0.734634	+	1.23111i
$173$	3.43076	−	11.6841i	0.260836	−	0.888326i	−0.720080	−	0.693891i	$-0.755895\pi$
$173$	3.43076	−	11.6841i	0.260836	−	0.888326i	0.980916	−	0.194434i	$-0.0622870\pi$
$174$	−1.37324	−	1.23041i	−0.104105	−	0.0932768i
$175$	1.30847	−	9.10059i	0.0989108	−	0.687940i
$176$	1.11756	−	1.50861i	0.0842389	−	0.113716i
$177$	2.13105	−	4.66635i	0.160180	−	0.350745i
$178$	1.33587	+	0.214752i	0.100128	+	0.0160963i
$179$	−1.76601	−	12.2829i	−0.131998	−	0.918067i	−0.942945	−	0.332948i	$-0.891957\pi$
$179$	−1.76601	−	12.2829i	−0.131998	−	0.918067i	0.810947	−	0.585119i	$-0.198952\pi$
$180$	0.109078	−	0.613390i	0.00813021	−	0.0457194i
$181$	−6.89728	−	7.95988i	−0.512670	−	0.591653i	0.439110	−	0.898433i	$-0.355294\pi$
$181$	−6.89728	−	7.95988i	−0.512670	−	0.591653i	−0.951780	+	0.306780i	$0.900748\pi$
$182$	−10.8252	+	9.06997i	−0.802414	+	0.672311i
$183$	−12.4833			−0.922791
$184$	10.5761	−	8.49384i	0.779683	−	0.626174i
$185$	0.272567			0.0200395
$186$	7.15561	−	5.99540i	0.524675	−	0.439604i
$187$	−1.90559	−	2.19917i	−0.139351	−	0.160819i
$188$	5.54982	+	0.986916i	0.404763	+	0.0719783i
$189$	0.266873	+	1.85614i	0.0194121	+	0.135014i
$190$	−0.368438	−	0.0592293i	−0.0267293	−	0.00429695i
$191$	10.2174	−	22.3729i	0.739302	−	1.61884i	−0.0453981	−	0.998969i	$-0.514456\pi$
$191$	10.2174	−	22.3729i	0.739302	−	1.61884i	0.784700	−	0.619876i	$-0.212817\pi$
$192$	7.86197	−	1.47969i	0.567389	−	0.106787i
$193$	1.48062	−	10.2979i	0.106577	−	0.741261i	−0.864524	−	0.502592i	$-0.832380\pi$
$193$	1.48062	−	10.2979i	0.106577	−	0.741261i	0.971101	−	0.238669i	$-0.0767111\pi$
$194$	10.3715	+	9.29270i	0.744629	+	0.667177i
$195$	−0.467359	+	1.59168i	−0.0334683	+	0.113983i
$196$	−5.98281	+	3.57011i	−0.427344	+	0.255008i
$197$	−8.62974	+	3.94107i	−0.614844	+	0.280790i	−0.698394	−	0.715714i	$-0.746101\pi$
$197$	−8.62974	+	3.94107i	−0.614844	+	0.280790i	0.0835499	+	0.996504i	$0.473374\pi$
$198$	0.176415	+	0.639909i	0.0125372	+	0.0454763i
$199$	−5.27291	+	6.08526i	−0.373787	+	0.431373i	−0.911211	−	0.411939i	$-0.864852\pi$
$199$	−5.27291	+	6.08526i	−0.373787	+	0.431373i	0.537425	+	0.843312i	$0.319397\pi$
$200$	9.59168	−	10.0156i	0.678235	−	0.708209i
$201$	−2.76859	+	4.30800i	−0.195281	+	0.303863i
$202$	9.70700	+	15.6702i	0.682982	+	1.10255i
$203$	−1.32181	−	2.05677i	−0.0927726	−	0.144357i
$204$	0.411449	−	12.3926i	0.0288072	−	0.867656i
$205$	−2.25637	+	0.662530i	−0.157592	+	0.0462731i
$206$	−1.71260	−	3.92097i	−0.119322	−	0.273187i
$207$	0.0595720	+	4.79546i	0.00414054	+	0.333308i
$208$	−21.2391	+	1.62630i	−1.47267	+	0.112763i
$209$	0.381482	−	0.112013i	0.0263877	−	0.00774812i
$210$	0.355599	−	0.745655i	0.0245387	−	0.0514551i
$211$	17.8532	−	11.4735i	1.22906	−	0.789871i	0.245319	−	0.969442i	$-0.421107\pi$
$211$	17.8532	−	11.4735i	1.22906	−	0.789871i	0.983745	+	0.179571i	$0.0574710\pi$
$212$	6.87232	+	4.74601i	0.471993	+	0.325957i
$213$	3.98086	−	6.19434i	0.272764	−	0.424429i
$214$	−0.0506057	+	3.04927i	−0.00345934	+	0.208444i
$215$	2.21319	+	1.91774i	0.150938	+	0.130789i
$216$	−1.30155	+	2.51117i	−0.0885590	+	0.170863i
$217$	11.2598	−	5.14220i	0.764368	−	0.349075i
$218$	0.824795	+	6.50062i	0.0558622	+	0.440277i
$219$	5.42218	+	1.59210i	0.366397	+	0.107584i
$220$	0.0916492	−	0.277687i	0.00617899	−	0.0187216i
$221$	−4.69860	+	32.6795i	−0.316062	+	2.19826i
$222$	−1.18136	−	0.368279i	−0.0792876	−	0.0247172i
$223$	−15.3216	−	6.99714i	−1.02601	−	0.468563i	−0.169957	−	0.985452i	$-0.554363\pi$
$223$	−15.3216	−	6.99714i	−1.02601	−	0.468563i	−0.856053	+	0.516889i	$0.827090\pi$
$224$	10.5714	+	0.879153i	0.706331	+	0.0587409i
$225$	0.697764	+	4.85306i	0.0465176	+	0.323537i
$226$	14.5244	−	21.7964i	0.966146	−	1.44988i
$227$	5.67202	−	4.91484i	0.376465	−	0.326209i	−0.445991	−	0.895038i	$-0.647149\pi$
$227$	5.67202	−	4.91484i	0.376465	−	0.326209i	0.822456	+	0.568828i	$0.192603\pi$
$228$	1.51685	+	0.754525i	0.100456	+	0.0499697i
$229$	3.57873			0.236489			0.118244	−	0.992985i	$-0.462273\pi$
$229$	3.57873			0.236489			0.118244	+	0.992985i	$0.462273\pi$
$230$	1.14964	−	1.77257i	0.0758050	−	0.116880i
$231$			0.880164i			0.0579106i
$232$	0.183508	−	3.68308i	0.0120479	−	0.241806i
$233$	−8.56290	−	9.88211i	−0.560974	−	0.647399i	0.402430	−	0.915451i	$-0.368166\pi$
$233$	−8.56290	−	9.88211i	−0.560974	−	0.647399i	−0.963404	+	0.268052i	$0.913620\pi$
$234$	4.17622	−	6.26717i	0.273008	−	0.409698i
$235$	0.869029	−	0.124947i	0.0566892	−	0.00815067i
$236$	9.93477	−	2.56229i	0.646698	−	0.166791i
$237$	5.11164	−	11.1929i	0.332037	−	0.727059i
$238$	4.89323	−	15.6964i	0.317181	−	1.01745i
$239$	15.2475	+	2.19226i	0.986277	+	0.141805i	0.616533	−	0.787329i	$-0.288537\pi$
$239$	15.2475	+	2.19226i	0.986277	+	0.141805i	0.369743	+	0.929134i	$0.379446\pi$
$240$	1.09060	−	0.602642i	0.0703979	−	0.0389003i
$241$	−0.622886	+	2.12135i	−0.0401236	+	0.136648i	−0.977119	−	0.212693i	$-0.931777\pi$
$241$	−0.622886	+	2.12135i	−0.0401236	+	0.136648i	0.936995	+	0.349342i	$0.113595\pi$
$242$	−1.91887	−	15.1235i	−0.123350	−	0.972178i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	−15.7145	−	19.4006i	−1.00602	−	1.24200i
$245$	−0.710616	+	0.820095i	−0.0453996	+	0.0523939i
$246$	10.6747	+	0.177158i	0.680595	+	0.0112952i
$247$	−3.79486	−	2.43881i	−0.241461	−	0.155178i
$248$	18.3254	+	3.57345i	1.16366	+	0.226915i
$249$	−5.27492	−	8.20794i	−0.334285	−	0.520157i
$250$	1.87790	−	3.93776i	0.118769	−	0.249046i
$251$	−1.87434	−	6.38342i	−0.118307	−	0.402918i	0.878951	−	0.476912i	$-0.158244\pi$
$251$	−1.87434	−	6.38342i	−0.118307	−	0.402918i	−0.997259	+	0.0739935i	$0.976426\pi$
$252$	−2.54873	+	2.75135i	−0.160555	+	0.173318i
$253$	−0.292648	+	2.23189i	−0.0183986	+	0.140317i
$254$	−6.83949	+	2.98734i	−0.429148	+	0.187442i
$255$	−0.544097	−	1.85302i	−0.0340727	−	0.116041i
$256$	12.1966	+	10.3558i	0.762289	+	0.647237i
$257$	−12.6229	+	8.11225i	−0.787395	+	0.506028i	−0.871480	−	0.490430i	$-0.836840\pi$
$257$	−12.6229	+	8.11225i	−0.787395	+	0.506028i	0.0840850	+	0.996459i	$0.473203\pi$
$258$	−7.00123	−	11.3022i	−0.435877	−	0.703643i
$259$	−1.38034	−	0.887092i	−0.0857703	−	0.0551212i
$260$	−3.06201	+	1.27734i	−0.189898	+	0.0792173i
$261$	0.985332	+	0.853795i	0.0609905	+	0.0528486i
$262$	−20.3314	+	5.60510i	−1.25608	+	0.346284i
$263$	5.68542	+	12.4493i	0.350578	+	0.767658i	0.999974	+	0.00720813i	$0.00229444\pi$
$263$	5.68542	+	12.4493i	0.350578	+	0.767658i	−0.649396	+	0.760450i	$0.724978\pi$
$264$	−0.772421	+	1.07972i	−0.0475392	+	0.0664519i
$265$	1.24814	+	0.366486i	0.0766724	+	0.0225130i
$266$	1.67309	+	1.49906i	0.102584	+	0.0919134i
$267$	−0.946994	−	0.136157i	−0.0579551	−	0.00833269i
$268$	−10.1804	+	1.12037i	−0.621867	+	0.0684376i
$269$	15.4893	+	7.07373i	0.944400	+	0.431293i	0.827258	−	0.561822i	$-0.189899\pi$
$269$	15.4893	+	7.07373i	0.944400	+	0.431293i	0.117142	+	0.993115i	$0.462627\pi$
$270$	−0.0699221	+	0.434953i	−0.00425532	+	0.0264704i
$271$	7.84495	−	1.12793i	0.476547	−	0.0685171i	0.100144	−	0.994973i	$-0.468070\pi$
$271$	7.84495	−	1.12793i	0.476547	−	0.0685171i	0.376403	+	0.926456i	$0.377161\pi$
$272$	19.7776	−	14.9609i	1.19919	−	0.907138i
$273$	7.54707	−	6.53957i	0.456769	−	0.395793i
$274$	23.9117	−	20.0346i	1.44456	−	1.21034i
$275$			2.30127i			0.138772i
$276$	−7.37776	+	6.12932i	−0.444089	+	0.368942i
$277$			20.9386i			1.25808i	0.777374	+	0.629038i	$0.216551\pi$
$277$			20.9386i			1.25808i	−0.777374	+	0.629038i	$0.783449\pi$
$278$	13.1974	+	15.7513i	0.791527	+	0.944700i
$279$	−4.98874	+	4.32277i	−0.298668	+	0.258797i
$280$	1.60649	−	0.386017i	0.0960060	−	0.0230689i
$281$	−4.42816	+	0.636674i	−0.264162	+	0.0379808i	−0.273123	−	0.961979i	$-0.588057\pi$
$281$	−4.42816	+	0.636674i	−0.264162	+	0.0379808i	0.00896104	+	0.999960i	$0.497148\pi$
$282$	−3.93536	−	0.632640i	−0.234347	−	0.0376732i
$283$	−3.93525	−	1.79717i	−0.233926	−	0.106831i	0.295003	−	0.955496i	$-0.404679\pi$
$283$	−3.93525	−	1.79717i	−0.233926	−	0.106831i	−0.528930	+	0.848666i	$0.677406\pi$
$284$	14.6381	−	1.61095i	0.868610	−	0.0955921i
$285$	0.261184	+	0.0375526i	0.0154712	+	0.00222442i
$286$	2.35885	−	2.63268i	0.139482	−	0.155674i
$287$	13.5830	+	3.98834i	0.801781	+	0.235424i
$288$	−5.54112	+	1.13840i	−0.326514	+	0.0670810i
$289$	−8.90502	−	19.4993i	−0.523825	−	1.14702i
$290$	−0.152650	−	0.553708i	−0.00896392	−	0.0325148i
$291$	−7.44177	−	6.44833i	−0.436244	−	0.378008i
$292$	4.35136	+	10.4310i	0.254644	+	0.610425i
$293$	−16.2589	−	10.4490i	−0.949857	−	0.610436i	−0.0286838	−	0.999589i	$-0.509132\pi$
$293$	−16.2589	−	10.4490i	−0.949857	−	0.610436i	−0.921173	+	0.389152i	$0.872768\pi$
$294$	4.18802	−	2.59430i	0.244250	−	0.151303i
$295$	1.34433	−	0.863949i	0.0782700	−	0.0503011i
$296$	−0.914794	−	2.29959i	−0.0531713	−	0.133661i
$297$	−0.132235	−	0.450351i	−0.00767306	−	0.0261320i
$298$	5.53301	+	12.6678i	0.320519	+	0.733824i
$299$	21.3119	−	14.0734i	1.23250	−	0.813888i
$300$	−6.66389	+	7.19366i	−0.384740	+	0.415326i
$301$	−4.96665	−	16.9149i	−0.286273	−	0.974956i
$302$	26.2172	+	12.5029i	1.50863	+	0.719459i
$303$	−7.04681	−	10.9650i	−0.404829	−	0.629926i
$304$	0.736854	+	3.30721i	0.0422614	+	0.189682i
$305$	−3.27132	−	2.10235i	−0.187315	−	0.120380i
$306$	−0.145489	+	8.76651i	−0.00831707	+	0.501148i
$307$	11.6088	−	13.3972i	0.662547	−	0.764621i	−0.320644	−	0.947200i	$-0.603899\pi$
$307$	11.6088	−	13.3972i	0.662547	−	0.764621i	0.983191	+	0.182579i	$0.0584446\pi$
$308$	−1.36789	+	1.10799i	−0.0779426	+	0.0631336i
$309$	1.25683	+	2.75207i	0.0714985	+	0.156560i
$310$	2.88488	−	0.366032i	0.163850	−	0.0207892i
$311$	0.149480	−	0.509084i	0.00847626	−	0.0288675i	−0.955146	−	0.296134i	$-0.904302\pi$
$311$	0.149480	−	0.509084i	0.00847626	−	0.0288675i	0.963623	+	0.267267i	$0.0861205\pi$
$312$	14.9972	−	1.39902i	0.849049	−	0.0792038i
$313$	−20.9994	−	3.01926i	−1.18696	−	0.170659i	−0.479583	−	0.877496i	$-0.659212\pi$
$313$	−20.9994	−	3.01926i	−1.18696	−	0.170659i	−0.707376	+	0.706838i	$0.750121\pi$
$314$	−2.63726	−	0.822144i	−0.148829	−	0.0463963i
$315$	−0.242663	+	0.531358i	−0.0136725	+	0.0299386i
$316$	23.8300	−	6.14602i	1.34054	−	0.345740i
$317$	6.60554	−	0.949734i	0.371004	−	0.0533424i	0.0457089	−	0.998955i	$-0.485445\pi$
$317$	6.60554	−	0.949734i	0.371004	−	0.0533424i	0.325295	+	0.945612i	$0.394536\pi$
$318$	−4.91448	−	3.27483i	−0.275590	−	0.183644i
$319$	0.400741	+	0.462480i	0.0224372	+	0.0258939i
$320$	2.30948	+	0.936298i	0.129104	+	0.0523406i
$321$		−	2.15646i		−	0.120362i
$322$	−11.5910	+	5.23510i	−0.645942	+	0.291741i
$323$	5.25163			0.292209
$324$	0.890741	−	1.79069i	0.0494856	−	0.0994829i
$325$	19.7325	−	17.0983i	1.09456	−	0.948446i
$326$	24.5066	+	16.3303i	1.35730	+	0.904454i
$327$	−0.659413	−	4.58632i	−0.0364656	−	0.253624i
$328$	13.1625	+	16.8129i	0.726777	+	0.928336i
$329$	−4.80761	−	2.19556i	−0.265052	−	0.121045i
$330$	−0.0615386	+	0.197403i	−0.00338759	+	0.0108667i
$331$	−1.90096	+	13.2214i	−0.104486	+	0.726716i	0.868473	+	0.495737i	$0.165102\pi$
$331$	−1.90096	+	13.2214i	−0.104486	+	0.726716i	−0.972959	+	0.230979i	$0.925807\pi$
$332$	6.11588	−	18.5304i	0.335652	−	1.01699i
$333$	0.839553	+	0.246515i	0.0460072	+	0.0135089i
$334$	18.7416	−	2.37793i	1.02550	−	0.130115i
$335$	−1.45105	+	0.662672i	−0.0792793	+	0.0362056i
$336$	−7.48439	−	0.497530i	−0.408307	−	0.0271425i
$337$	−18.5031	−	16.0330i	−1.00793	−	0.873374i	−0.0159601	−	0.999873i	$-0.505080\pi$
$337$	−18.5031	−	16.0330i	−1.00793	−	0.873374i	−0.991967	+	0.126499i	$0.959626\pi$
$338$	−21.7181	−	0.360434i	−1.18131	−	0.0196050i
$339$	−10.0131	+	15.5807i	−0.543837	+	0.846227i
$340$	2.19490	−	3.17826i	0.119035	−	0.172366i
$341$	−2.60645	+	1.67506i	−0.141147	+	0.0907098i
$342$	−1.08128	−	0.515659i	−0.0584691	−	0.0278836i
$343$	18.8627	−	5.53858i	1.01849	−	0.299055i
$344$	8.75157	−	25.1085i	0.471853	−	1.35376i
$345$	−0.792008	+	1.26671i	−0.0426403	+	0.0681975i
$346$	−15.7817	+	6.89310i	−0.848429	+	0.370575i
$347$	−5.70115	+	1.67401i	−0.306054	+	0.0898655i	−0.431153	−	0.902279i	$-0.641893\pi$
$347$	−5.70115	+	1.67401i	−0.306054	+	0.0898655i	0.125099	+	0.992144i	$0.460075\pi$
$348$	−0.0865265	+	2.60613i	−0.00463831	+	0.139703i
$349$	4.99799	+	7.77702i	0.267536	+	0.416294i	0.948865	−	0.315683i	$-0.102234\pi$
$349$	4.99799	+	7.77702i	0.267536	+	0.416294i	−0.681328	+	0.731978i	$0.738597\pi$
$350$	−11.0536	+	6.84722i	−0.590838	+	0.365999i
$351$	−2.87909	+	4.47995i	−0.153674	+	0.239122i
$352$	−2.65037	+	0.158754i	−0.141265	+	0.00846161i
$353$	10.0041	−	11.5454i	0.532466	−	0.614499i	−0.424242	−	0.905549i	$-0.639459\pi$
$353$	10.0041	−	11.5454i	0.532466	−	0.614499i	0.956708	+	0.291050i	$0.0940047\pi$
$354$	−6.99391	+	1.92813i	−0.371722	+	0.102479i
$355$	2.08642	−	0.952836i	0.110736	−	0.0505713i
$356$	−0.980513	−	1.64315i	−0.0519671	−	0.0870868i
$357$	−3.27539	+	11.1549i	−0.173352	+	0.590382i
$358$	−11.7108	+	13.0703i	−0.618936	+	0.690788i
$359$	−2.98020	+	20.7278i	−0.157289	+	1.09397i	0.746313	+	0.665595i	$0.231822\pi$
$359$	−2.98020	+	20.7278i	−0.157289	+	1.09397i	−0.903602	+	0.428373i	$0.859087\pi$
$360$	−0.763993	+	0.438870i	−0.0402660	+	0.0231305i
$361$	7.59481	−	16.6303i	0.399727	−	0.875280i
$362$	−2.36415	+	14.7063i	−0.124257	+	0.772946i
$363$	1.53411	+	10.6700i	0.0805199	+	0.560028i
$364$	19.6639	+	3.49680i	1.03067	+	0.183282i
$365$	1.15279	+	1.33039i	0.0603395	+	0.0696355i
$366$	11.3379	+	13.5320i	0.592644	+	0.707330i
$367$	−16.3586			−0.853913			−0.426957	−	0.904272i	$-0.640414\pi$
$367$	−16.3586			−0.853913			−0.426957	+	0.904272i	$0.640414\pi$
$368$	−18.8132	−	3.75012i	−0.980706	−	0.195489i
$369$	−7.54921			−0.392996
$370$	−0.247559	−	0.295466i	−0.0128700	−	0.0153605i
$371$	−5.12809	−	5.91813i	−0.266237	−	0.307254i
$372$	−12.9982	−	2.31144i	−0.673924	−	0.119843i
$373$	−3.75239	−	26.0985i	−0.194291	−	1.35133i	−0.820489	−	0.571662i	$-0.806299\pi$
$373$	−3.75239	−	26.0985i	−0.194291	−	1.35133i	0.626198	−	0.779664i	$-0.284610\pi$
$374$	−0.653173	+	4.06309i	−0.0337748	+	0.210097i
$375$	−1.28149	+	2.80607i	−0.0661758	+	0.144905i
$376$	−3.97080	−	6.91244i	−0.204778	−	0.356482i
$377$	0.988101	−	6.87240i	0.0508898	−	0.353946i
$378$	1.76969	−	1.97513i	0.0910231	−	0.101590i
$379$	−9.90556	+	33.7352i	−0.508814	+	1.73286i	0.157810	+	0.987469i	$0.449557\pi$
$379$	−9.90556	+	33.7352i	−0.508814	+	1.73286i	−0.666625	+	0.745394i	$0.732262\pi$
$380$	0.270429	+	0.453186i	0.0138727	+	0.0232480i
$381$	4.80053	−	2.19233i	0.245939	−	0.112316i
$382$	−33.5324	+	9.24444i	−1.71567	+	0.472987i
$383$	−3.59068	+	4.14387i	−0.183475	+	0.211742i	−0.840035	−	0.542532i	$-0.817466\pi$
$383$	−3.59068	+	4.14387i	−0.183475	+	0.211742i	0.656560	+	0.754274i	$0.272011\pi$
$384$	−8.74463	−	7.17854i	−0.446248	−	0.366328i
$385$	−0.148231	+	0.230652i	−0.00755457	+	0.0117551i
$386$	−12.5079	+	7.74809i	−0.636633	+	0.394367i
$387$	5.08255	+	7.90860i	0.258360	+	0.402017i
$388$	0.653496	−	19.6829i	0.0331762	−	0.999248i
$389$	23.3073	−	6.84364i	1.18173	−	0.346986i	0.368887	−	0.929474i	$-0.379739\pi$
$389$	23.3073	−	6.84364i	1.18173	−	0.346986i	0.812839	+	0.582488i	$0.197921\pi$
$390$	2.14988	−	0.939020i	0.108863	−	0.0475492i
$391$	−12.0145	+	27.1972i	−0.607601	+	1.37542i
$392$	9.30393	+	3.24289i	0.469919	+	0.163791i
$393$	14.3087	−	4.20142i	0.721779	−	0.211934i
$394$	12.1101	+	5.77526i	0.610100	+	0.290954i
$395$	3.22457	−	2.07231i	0.162246	−	0.104269i
$396$	0.533440	−	0.772433i	0.0268064	−	0.0388162i
$397$	−14.6414	+	22.7825i	−0.734831	+	1.14342i	0.249719	+	0.968318i	$0.419662\pi$
$397$	−14.6414	+	22.7825i	−0.734831	+	1.14342i	−0.984550	+	0.175101i	$0.943975\pi$
$398$	11.3856	+	0.188956i	0.570709	+	0.00947150i
$399$	−1.20048	−	1.04022i	−0.0600991	−	0.0520762i
$400$	−19.5687	−	1.30084i	−0.978433	−	0.0650420i
$401$	−14.3788	+	6.56656i	−0.718041	+	0.327918i	−0.740710	−	0.671825i	$-0.765511\pi$
$401$	−14.3788	+	6.56656i	−0.718041	+	0.327918i	0.0226690	+	0.999743i	$0.492784\pi$
$402$	7.18449	−	0.911565i	0.358330	−	0.0454647i
$403$	33.7288	+	9.90367i	1.68015	+	0.493337i
$404$	8.17024	−	24.7549i	0.406485	−	1.23160i
$405$	0.0443320	−	0.308336i	0.00220288	−	0.0153213i
$406$	−1.02903	+	3.30091i	−0.0510700	+	0.163822i
$407$	0.373578	+	0.170607i	0.0185176	+	0.00845670i
$408$	−13.8074	+	10.8096i	−0.683569	+	0.535153i
$409$	−2.29950	−	15.9933i	−0.113703	−	0.790820i	−0.964264	−	0.264944i	$-0.914647\pi$
$409$	−2.29950	−	15.9933i	−0.113703	−	0.790820i	0.850561	−	0.525876i	$-0.176263\pi$
$410$	2.76754	+	1.84419i	0.136679	+	0.0910780i
$411$	−16.6707	+	14.4453i	−0.822305	+	0.712532i
$412$	−2.69492	+	5.41770i	−0.132769	+	0.266911i
$413$	−9.61979			−0.473359
$414$	5.14423	−	4.42006i	0.252825	−	0.217234i
$415$		−	3.03931i		−	0.149194i
$416$	21.0534	+	21.5464i	1.03223	+	1.05640i
$417$	−9.51549	−	10.9815i	−0.465976	−	0.537765i
$418$	−0.467905	−	0.311795i	−0.0228860	−	0.0152504i
$419$	−8.50135	+	1.22231i	−0.415318	+	0.0597137i	−0.346807	−	0.937937i	$-0.612734\pi$
$419$	−8.50135	+	1.22231i	−0.415318	+	0.0597137i	−0.0685114	+	0.997650i	$0.521825\pi$
$420$	−1.13127	+	0.291768i	−0.0552004	+	0.0142368i
$421$	4.17298	−	9.13755i	0.203378	−	0.445337i	−0.780268	−	0.625445i	$-0.784917\pi$
$421$	4.17298	−	9.13755i	0.203378	−	0.445337i	0.983647	+	0.180108i	$0.0576448\pi$
$422$	−28.6526	−	8.93221i	−1.39479	−	0.434813i
$423$	2.78976	+	0.401107i	0.135643	+	0.0195025i
$424$	−1.09706	−	11.7602i	−0.0532778	−	0.571128i
$425$	−8.56382	+	29.1657i	−0.415406	+	1.41474i
$426$	−10.3304	+	1.31071i	−0.500508	+	0.0635042i
$427$	9.72445	+	21.2936i	0.470599	+	1.03047i
$428$	3.35141	−	2.71464i	0.161996	−	0.131217i
$429$	−1.63684	+	1.88901i	−0.0790272	+	0.0912022i
$430$	0.0687226	−	4.14091i	0.00331410	−	0.199692i
$431$	−24.4856	−	15.7359i	−1.17943	−	0.757974i	−0.204149	−	0.978940i	$-0.565443\pi$
$431$	−24.4856	−	15.7359i	−1.17943	−	0.757974i	−0.975282	+	0.220966i	$0.929079\pi$
$432$	3.90427	−	0.869879i	0.187844	−	0.0418521i
$433$	21.8102	+	33.9374i	1.04813	+	1.63093i	0.730771	+	0.682623i	$0.239161\pi$
$433$	21.8102	+	33.9374i	1.04813	+	1.63093i	0.317363	+	0.948304i	$0.397203\pi$
$434$	−15.8010	−	7.53540i	−0.758470	−	0.361711i
$435$	0.114422	+	0.389685i	0.00548611	+	0.0186840i
$436$	6.29763	−	6.79828i	0.301602	−	0.325578i
$437$	−2.69826	−	3.03690i	−0.129075	−	0.145275i
$438$	−3.19884	−	7.32373i	−0.152847	−	0.349941i
$439$	0.902938	+	3.07513i	0.0430949	+	0.146768i	0.978230	−	0.207523i	$-0.0665403\pi$
$439$	0.902938	+	3.07513i	0.0430949	+	0.146768i	−0.935135	+	0.354291i	$0.884722\pi$
$440$	−0.384256	+	0.152860i	−0.0183187	+	0.00728733i
$441$	−2.93053	+	1.88333i	−0.139549	+	0.0896826i
$442$	39.6924	−	24.5878i	1.88798	−	1.16952i
$443$	20.6826	+	13.2919i	0.982662	+	0.631519i	0.930180	−	0.367103i	$-0.119650\pi$
$443$	20.6826	+	13.2919i	0.982662	+	0.631519i	0.0524818	+	0.998622i	$0.483287\pi$
$444$	0.673750	+	1.61510i	0.0319748	+	0.0766490i
$445$	−0.225235	−	0.195167i	−0.0106772	−	0.00925181i
$446$	6.33086	+	22.9639i	0.299775	+	1.08737i
$447$	−4.06053	−	8.89131i	−0.192056	−	0.420545i
$448$	−8.64846	−	12.2580i	−0.408601	−	0.579136i
$449$	13.2564	+	3.89242i	0.625606	+	0.183695i	0.579144	−	0.815226i	$-0.303387\pi$
$449$	13.2564	+	3.89242i	0.625606	+	0.183695i	0.0464624	+	0.998920i	$0.485205\pi$
$450$	4.62703	−	5.16418i	0.218120	−	0.243442i
$451$	−3.50726	−	0.504268i	−0.165150	−	0.0237450i
$452$	−36.8193	+	4.05203i	−1.73184	+	0.190592i
$453$	−18.6825	−	8.53203i	−0.877782	−	0.400870i
$454$	−10.4794	−	1.68464i	−0.491821	−	0.0790641i
$455$	3.07911	−	0.442709i	0.144351	−	0.0207545i
$456$	−0.559768	−	2.32958i	−0.0262135	−	0.109093i
$457$	−19.1167	+	16.5647i	−0.894240	+	0.774863i	−0.975078	−	0.221864i	$-0.928786\pi$
$457$	−19.1167	+	16.5647i	−0.894240	+	0.774863i	0.0808379	+	0.996727i	$0.474240\pi$
$458$	−3.25038	−	3.87938i	−0.151880	−	0.181272i
$459$		−	6.19971i		−	0.289378i
$460$	−2.96565	+	0.363713i	−0.138274	+	0.0169582i
$461$		−	16.6199i		−	0.774067i	−0.922066	−	0.387034i	$-0.873500\pi$
$461$		−	16.6199i		−	0.774067i	0.922066	−	0.387034i	$-0.126500\pi$
$462$	0.954108	−	0.799409i	0.0443891	−	0.0371919i
$463$	−14.8365	+	12.8559i	−0.689511	+	0.597465i	−0.927509	−	0.373801i	$-0.878054\pi$
$463$	−14.8365	+	12.8559i	−0.689511	+	0.597465i	0.237998	+	0.971266i	$0.423509\pi$
$464$	−4.15918	+	3.14623i	−0.193085	+	0.146060i
$465$	−2.03534	+	0.292638i	−0.0943866	+	0.0135708i
$466$	−2.93507	+	18.2577i	−0.135965	+	0.845772i
$467$	20.3959	+	9.31448i	0.943809	+	0.431023i	0.827044	−	0.562137i	$-0.190021\pi$
$467$	20.3959	+	9.31448i	0.943809	+	0.431023i	0.116764	+	0.993160i	$0.462748\pi$
$468$	−10.5867	+	1.16509i	−0.489372	+	0.0538563i
$469$	9.50517	+	1.36664i	0.438908	+	0.0631054i
$470$	−0.924740	−	0.828554i	−0.0426551	−	0.0382183i
$471$	1.87422	+	0.550319i	0.0863593	+	0.0253574i
$472$	−11.8008	−	8.44221i	−0.543176	−	0.388584i
$473$	1.83301	+	4.01373i	0.0842819	+	0.184552i
$474$	−16.7759	+	4.62490i	−0.770543	+	0.212429i
$475$	−3.13877	−	2.71976i	−0.144017	−	0.124791i
$476$	−21.4594	+	8.95197i	−0.983590	+	0.410313i
$477$	3.51301	+	2.25767i	0.160850	+	0.103372i
$478$	−11.4721	−	18.5196i	−0.524721	−	0.847065i
$479$	5.70829	−	3.66849i	0.260818	−	0.167618i	−0.403696	−	0.914893i	$-0.632275\pi$
$479$	5.70829	−	3.66849i	0.260818	−	0.167618i	0.664515	+	0.747275i	$0.268638\pi$
$480$	−1.64381	−	0.634873i	−0.0750292	−	0.0289779i
$481$	−1.31277	−	4.47089i	−0.0598573	−	0.203855i
$482$	2.86531	−	1.25151i	0.130511	−	0.0570045i
$483$	8.13353	−	3.83727i	0.370089	−	0.174602i
$484$	−14.6513	+	15.8160i	−0.665968	+	0.718911i
$485$	−0.864178	−	2.94312i	−0.0392403	−	0.133640i
$486$	−0.608751	+	1.27649i	−0.0276135	+	0.0579027i
$487$	5.26836	+	8.19772i	0.238732	+	0.371474i	0.939859	−	0.341562i	$-0.110956\pi$
$487$	5.26836	+	8.19772i	0.238732	+	0.371474i	−0.701127	+	0.713036i	$0.747320\pi$
$488$	−6.75778	+	34.6553i	−0.305910	+	1.56877i
$489$	−17.5180	−	11.2582i	−0.792193	−	0.509111i
$490$	1.53441	+	0.0254651i	0.0693176	+	0.00115040i
$491$	6.20354	−	7.15927i	0.279962	−	0.323093i	−0.598301	−	0.801272i	$-0.704157\pi$
$491$	6.20354	−	7.15927i	0.279962	−	0.323093i	0.878263	+	0.478178i	$0.158703\pi$
$492$	−9.50327	−	11.7324i	−0.428441	−	0.528939i
$493$	3.35783	+	7.35262i	0.151229	+	0.331145i
$494$	0.802985	+	6.32872i	0.0361280	+	0.284743i
$495$	0.0411921	−	0.140288i	0.00185145	−	0.00630546i
$496$	−12.7704	−	23.1106i	−0.573408	−	1.03769i
$497$	−13.6672	−	1.96504i	−0.613057	−	0.0881443i
$498$	−4.10655	+	13.1729i	−0.184019	+	0.590294i
$499$	−5.62343	+	12.3136i	−0.251739	+	0.551232i	−0.992741	−	0.120271i	$-0.961624\pi$
$499$	−5.62343	+	12.3136i	−0.251739	+	0.551232i	0.741002	+	0.671503i	$0.234351\pi$
$500$	−5.97418	+	1.54081i	−0.267174	+	0.0689070i
$501$	−13.2226	+	1.90112i	−0.590743	+	0.0849360i
$502$	−5.21733	+	7.82955i	−0.232861	+	0.349450i
$503$	13.4152	+	15.4819i	0.598153	+	0.690305i	0.971406	−	0.237424i	$-0.0763031\pi$
$503$	13.4152	+	15.4819i	0.598153	+	0.690305i	−0.373253	+	0.927730i	$0.621758\pi$
$504$	5.29737	+	0.263940i	0.235964	+	0.0117568i
$505$		−	4.06023i		−	0.180678i
$506$	2.68519	−	1.70988i	0.119371	−	0.0760133i
$507$	15.3591			0.682123
$508$	9.45028	+	4.70083i	0.419288	+	0.208566i
$509$	32.3353	−	28.0187i	1.43324	−	1.24191i	0.508633	−	0.860983i	$-0.330151\pi$
$509$	32.3353	−	28.0187i	1.43324	−	1.24191i	0.924606	−	0.380925i	$-0.124394\pi$
$510$	−1.51452	+	2.27282i	−0.0670642	+	0.100642i
$511$	−1.50812	−	10.4892i	−0.0667153	−	0.464015i
$512$	0.148227	−	22.6269i	0.00655079	−	0.999979i
$513$	0.770528	+	0.351888i	0.0340196	+	0.0155362i
$514$	20.2585	+	6.31543i	0.893566	+	0.278562i
$515$	−0.134126	+	0.932864i	−0.00591028	+	0.0411069i
$516$	−5.89283	+	17.8546i	−0.259418	+	0.786006i
$517$	1.26929	+	0.372698i	0.0558234	+	0.0163912i
$518$	0.292078	+	2.30201i	0.0128332	+	0.101144i
$519$	11.0769	−	5.05866i	0.486223	−	0.222051i
$520$	4.16572	+	2.15910i	0.182679	+	0.0946830i
$521$	−2.49644	−	2.16318i	−0.109371	−	0.0947707i	0.598459	−	0.801154i	$-0.295780\pi$
$521$	−2.49644	−	2.16318i	−0.109371	−	0.0947707i	−0.707830	+	0.706383i	$0.750326\pi$
$522$	0.0305960	−	1.84357i	0.00133915	−	0.0806909i
$523$	−0.996265	+	1.55022i	−0.0435636	+	0.0677863i	−0.862352	−	0.506309i	$-0.831010\pi$
$523$	−0.996265	+	1.55022i	−0.0435636	+	0.0677863i	0.818789	+	0.574095i	$0.194646\pi$
$524$	24.5420	+	16.9486i	1.07212	+	0.740404i
$525$	7.73463	−	4.97074i	0.337567	−	0.216941i
$526$	8.33144	−	17.4702i	0.363268	−	0.761735i
$527$	−39.2669	+	11.5298i	−1.71049	+	0.502246i
$528$	1.87198	−	0.143339i	0.0814673	−	0.00623802i
$529$	21.9006	−	7.02606i	0.952198	−	0.305481i
$530$	−0.736345	−	1.68585i	−0.0319848	−	0.0732288i
$531$	4.92214	−	1.44527i	0.213603	−	0.0627194i
$532$	0.105419	−	3.17517i	0.00457051	−	0.137661i
$533$	21.7348	+	33.8201i	0.941441	+	1.46491i
$534$	0.712512	+	1.15022i	0.0308334	+	0.0497748i
$535$	0.363176	−	0.565112i	0.0157015	−	0.0244319i
$536$	10.4608	+	10.0181i	0.451840	+	0.432716i
$537$	8.12630	−	9.37825i	0.350676	−	0.404702i
$538$	−6.40016	−	23.2153i	−0.275931	−	1.00088i
$539$	−1.48729	+	0.679220i	−0.0640619	+	0.0292561i
$540$	0.535001	−	0.319249i	0.0230228	−	0.0137383i
$541$	−4.28724	+	14.6010i	−0.184323	+	0.627746i	0.814542	+	0.580105i	$0.196989\pi$
$541$	−4.28724	+	14.6010i	−0.184323	+	0.627746i	−0.998865	+	0.0476410i	$0.984830\pi$
$542$	−8.34787	−	7.47958i	−0.358572	−	0.321275i
$543$	1.49892	−	10.4252i	0.0643249	−	0.447389i
$544$	−34.1808	−	7.85093i	−1.46549	−	0.336606i
$545$	0.599594	−	1.31293i	0.0256838	−	0.0562396i
$546$	−13.9436	−	2.24154i	−0.596731	−	0.0959292i
$547$	6.40631	+	44.5568i	0.273914	+	1.90511i	0.405997	+	0.913874i	$0.366924\pi$
$547$	6.40631	+	44.5568i	0.273914	+	1.90511i	−0.132083	+	0.991239i	$0.542167\pi$
$548$	−43.4356	−	7.72408i	−1.85548	−	0.329956i
$549$	−8.17481	−	9.43424i	−0.348892	−	0.402643i
$550$	2.49461	−	2.09013i	0.106370	−	0.0891236i
$551$	−1.10440			−0.0470491
$552$	13.3451	+	2.43063i	0.568006	+	0.103454i
$553$	−23.0745			−0.981227
$554$	22.6977	−	19.0175i	0.964331	−	0.807974i
$555$	0.178494	+	0.205993i	0.00757663	+	0.00874390i
$556$	5.08807	−	28.6122i	0.215782	−	1.21343i
$557$	−3.57404	−	24.8580i	−0.151437	−	1.05327i	−0.913813	−	0.406134i	$-0.866877\pi$
$557$	−3.57404	−	24.8580i	−0.151437	−	1.05327i	0.762376	−	0.647134i	$-0.224033\pi$
$558$	9.21695	+	1.48170i	0.390185	+	0.0627253i
$559$	20.7970	−	45.5392i	0.879621	−	1.92610i
$560$	−1.87754	−	1.39085i	−0.0793405	−	0.0587742i
$561$	0.414125	−	2.88030i	0.0174844	−	0.121607i
$562$	4.71204	+	4.22192i	0.198766	+	0.178091i
$563$	−3.71520	+	12.6528i	−0.156577	+	0.533252i	−0.999992	−	0.00401057i	$-0.998723\pi$
$563$	−3.71520	+	12.6528i	−0.156577	+	0.533252i	0.843415	+	0.537263i	$0.180542\pi$
$564$	2.88850	+	4.84057i	0.121628	+	0.203825i
$565$	−5.24799	+	2.39668i	−0.220785	+	0.100829i
$566$	1.62604	+	5.89813i	0.0683475	+	0.247917i
$567$	−1.22801	+	1.41720i	−0.0515717	+	0.0595169i
$568$	−15.0413	−	14.4047i	−0.631120	−	0.604408i
$569$	−0.745432	+	1.15991i	−0.0312501	+	0.0486262i	−0.856527	−	0.516102i	$-0.827383\pi$
$569$	−0.745432	+	1.15991i	−0.0312501	+	0.0486262i	0.825277	+	0.564728i	$0.191019\pi$
$570$	−0.196513	−	0.317234i	−0.00823103	−	0.0132875i
$571$	3.28083	+	5.10508i	0.137299	+	0.213641i	0.903093	−	0.429444i	$-0.141291\pi$
$571$	3.28083	+	5.10508i	0.137299	+	0.213641i	−0.765795	+	0.643085i	$0.777654\pi$
$572$	−4.99628	−	0.165883i	−0.208905	−	0.00693590i
$573$	23.5992	−	6.92936i	0.985872	−	0.289478i
$574$	−8.01339	−	18.3466i	−0.334472	−	0.765772i
$575$	21.2659	−	10.0329i	0.886850	−	0.418401i
$576$	6.26677	+	4.97269i	0.261115	+	0.207195i
$577$	−11.0780	+	3.25281i	−0.461185	+	0.135416i	−0.504068	−	0.863664i	$-0.668164\pi$
$577$	−11.0780	+	3.25281i	−0.461185	+	0.135416i	0.0428831	+	0.999080i	$0.486346\pi$
$578$	−13.0495	+	27.3634i	−0.542786	+	1.13817i
$579$	8.75226	−	5.62473i	0.363731	−	0.233756i
$580$	−0.461581	+	0.668379i	−0.0191661	+	0.0277529i
$581$	−9.89168	+	15.3918i	−0.410376	+	0.638558i
$582$	−0.231078	+	13.9237i	−0.00957847	+	0.577155i
$583$	1.48129	+	1.28355i	0.0613488	+	0.0531590i
$584$	7.35516	−	14.1908i	0.304358	−	0.587221i
$585$	−1.50897	+	0.689122i	−0.0623881	+	0.0284917i
$586$	3.44036	+	27.1152i	0.142120	+	1.12012i
$587$	1.14388	+	0.335873i	0.0472129	+	0.0138630i	0.305254	−	0.952271i	$-0.401259\pi$
$587$	1.14388	+	0.335873i	0.0472129	+	0.0138630i	−0.258041	+	0.966134i	$0.583077\pi$
$588$	−6.61602	−	2.18358i	−0.272840	−	0.0900495i
$589$	0.795766	−	5.53467i	0.0327890	−	0.228052i
$590$	−2.15752	−	0.672589i	−0.0888237	−	0.0276900i
$591$	−8.62974	−	3.94107i	−0.354980	−	0.162114i
$592$	−1.66192	+	3.08025i	−0.0683043	+	0.126597i
$593$	4.95302	+	34.4490i	0.203396	+	1.41465i	0.794112	+	0.607771i	$0.207936\pi$
$593$	4.95302	+	34.4490i	0.203396	+	1.41465i	−0.590716	+	0.806879i	$0.701155\pi$
$594$	−0.368084	+	0.552376i	−0.0151027	+	0.0226643i
$595$	−2.73698	+	2.37160i	−0.112205	+	0.0972262i
$596$	8.70666	−	17.5034i	0.356639	−	0.716965i
$597$	−8.05195			−0.329544
$598$	−34.6123	−	10.3202i	−1.41540	−	0.422023i
$599$			12.1335i			0.495762i	0.968791	+	0.247881i	$0.0797341\pi$
$599$			12.1335i			0.495762i	−0.968791	+	0.247881i	$0.920266\pi$
$600$	13.8505	+	0.690096i	0.565444	+	0.0281731i
$601$	17.9037	+	20.6619i	0.730306	+	0.842818i	0.992506	−	0.122195i	$-0.0389934\pi$
$601$	17.9037	+	20.6619i	0.730306	+	0.842818i	−0.262200	+	0.965014i	$0.584448\pi$
$602$	−13.8249	+	20.7468i	−0.563463	+	0.845578i
$603$	−5.06881	+	0.728785i	−0.206418	+	0.0296784i
$604$	−10.2585	−	39.7755i	−0.417414	−	1.61844i
$605$	−1.39494	+	3.05450i	−0.0567125	+	0.124183i
$606$	−5.48598	+	17.5978i	−0.222853	+	0.714863i
$607$	24.0530	+	3.45830i	0.976283	+	0.140368i	0.611946	−	0.790899i	$-0.290387\pi$
$607$	24.0530	+	3.45830i	0.976283	+	0.140368i	0.364336	+	0.931267i	$0.381296\pi$
$608$	2.91581	−	3.80253i	0.118252	−	0.154213i
$609$	0.688804	−	2.34585i	0.0279118	−	0.0950587i
$610$	0.692205	+	5.45561i	0.0280266	+	0.220891i
$611$	−6.23503	−	13.6528i	−0.252242	−	0.552333i
$612$	9.63514	−	7.80447i	0.389478	−	0.315477i
$613$	27.7709	−	32.0493i	1.12165	−	1.29446i	0.170633	−	0.985335i	$-0.445419\pi$
$613$	27.7709	−	32.0493i	1.12165	−	1.29446i	0.951022	−	0.309124i	$-0.100036\pi$
$614$	−25.0664	−	0.416003i	−1.01160	−	0.0167885i
$615$	−1.97832	−	1.27139i	−0.0797734	−	0.0512673i
$616$	2.44346	+	0.476474i	0.0984497	+	0.0191977i
$617$	−22.2749	−	34.6604i	−0.896753	−	1.39538i	−0.918419	−	0.395610i	$-0.870533\pi$
$617$	−22.2749	−	34.6604i	−0.896753	−	1.39538i	0.0216653	−	0.999765i	$-0.493103\pi$
$618$	1.84176	−	3.86199i	0.0740865	−	0.155352i
$619$	−5.99985	−	20.4336i	−0.241154	−	0.821296i	−0.987754	−	0.156022i	$-0.950133\pi$
$619$	−5.99985	−	20.4336i	−0.241154	−	0.821296i	0.746599	−	0.665274i	$-0.231685\pi$
$620$	−3.01697	−	2.79479i	−0.121165	−	0.112242i
$621$	−3.58516	+	3.18538i	−0.143867	+	0.127825i
$622$	−0.687618	+	0.300337i	−0.0275710	+	0.0120424i
$623$	0.505454	+	1.72142i	0.0202506	+	0.0689671i
$624$	−15.1378	−	14.9865i	−0.605995	−	0.599939i
$625$	19.8148	−	12.7342i	0.792591	−	0.509367i
$626$	15.7998	+	25.5059i	0.631488	+	1.01942i
$627$	0.334472	+	0.214952i	0.0133575	+	0.00858435i
$628$	1.50408	+	3.60554i	0.0600193	+	0.143877i
$629$	4.09973	+	3.55244i	0.163467	+	0.141645i
$630$	0.796397	−	0.219556i	0.0317292	−	0.00874733i
$631$	−4.17114	−	9.13352i	−0.166050	−	0.363600i	0.808254	−	0.588834i	$-0.200413\pi$
$631$	−4.17114	−	9.13352i	−0.166050	−	0.363600i	−0.974305	+	0.225234i	$0.927685\pi$
$632$	−28.3059	−	20.2499i	−1.12595	−	0.805497i
$633$	20.3625	+	5.97896i	0.809336	+	0.237642i
$634$	−7.02901	−	6.29789i	−0.279158	−	0.250121i
$635$	1.62723	+	0.233960i	0.0645745	+	0.00928441i
$636$	0.913620	+	8.30173i	0.0362274	+	0.329185i
$637$	16.8745	+	7.70633i	0.668592	+	0.305336i
$638$	0.137360	−	0.854455i	0.00543815	−	0.0338282i
$639$	7.28828	−	1.04790i	0.288320	−	0.0414542i
$640$	−1.08262	−	3.35389i	−0.0427945	−	0.132574i
$641$	26.1380	−	22.6487i	1.03239	−	0.894572i	0.0378879	−	0.999282i	$-0.487937\pi$
$641$	26.1380	−	22.6487i	1.03239	−	0.894572i	0.994503	+	0.104710i	$0.0333916\pi$
$642$	−2.33762	+	1.95860i	−0.0922586	+	0.0772998i
$643$			35.3854i			1.39547i	0.716358	+	0.697733i	$0.245808\pi$
$643$			35.3854i			1.39547i	−0.716358	+	0.697733i	$0.754192\pi$
$644$	16.2025	+	7.81002i	0.638466	+	0.307758i
$645$			2.92847i			0.115308i
$646$	−4.76979	−	5.69283i	−0.187665	−	0.223981i
$647$	−16.9998	+	14.7304i	−0.668330	+	0.579111i	−0.921532	−	0.388302i	$-0.873062\pi$
$647$	−16.9998	+	14.7304i	−0.668330	+	0.579111i	0.253202	+	0.967413i	$0.418516\pi$
$648$	−2.75015	+	0.660823i	−0.108036	+	0.0259596i
$649$	2.38330	−	0.342667i	0.0935527	−	0.0134508i
$650$	−36.4569	−	5.86073i	−1.42996	−	0.229877i
$651$	11.2598	+	5.14220i	0.441308	+	0.201539i
$652$	−4.55587	−	41.3975i	−0.178422	−	1.62125i
$653$	−22.5199	−	3.23788i	−0.881273	−	0.126708i	−0.313201	−	0.949687i	$-0.601401\pi$
$653$	−22.5199	−	3.23788i	−0.881273	−	0.126708i	−0.568072	+	0.822979i	$0.692311\pi$
$654$	−4.37271	+	4.88034i	−0.170987	+	0.190836i
$655$	4.45726	+	1.30877i	0.174160	+	0.0511379i
$656$	6.27054	−	29.5386i	0.244823	−	1.15329i
$657$	2.34755	+	5.14041i	0.0915865	+	0.200547i
$658$	1.98650	+	7.20563i	0.0774418	+	0.280905i
$659$	−2.05881	−	1.78397i	−0.0802000	−	0.0694937i	0.613838	−	0.789432i	$-0.289625\pi$
$659$	−2.05881	−	1.78397i	−0.0802000	−	0.0694937i	−0.694038	+	0.719938i	$0.744170\pi$
$660$	0.269879	−	0.112582i	0.0105050	−	0.00438226i
$661$	34.7239	+	22.3157i	1.35061	+	0.867981i	0.997707	−	0.0676807i	$-0.0215599\pi$
$661$	34.7239	+	22.3157i	1.35061	+	0.867981i	0.352898	+	0.935662i	$0.385196\pi$
$662$	16.0587	−	9.94771i	0.624140	−	0.386629i
$663$	−27.7744	+	17.8495i	−1.07867	+	0.693219i
$664$	−25.6419	+	10.2006i	−0.995100	+	0.395859i
$665$	−0.139406	−	0.474773i	−0.00540593	−	0.0184109i
$666$	−0.495299	−	1.13398i	−0.0191924	−	0.0439409i
$667$	2.52662	−	5.71950i	0.0978312	−	0.221460i
$668$	−19.5998	−	18.1564i	−0.758339	−	0.702492i
$669$	−4.74542	−	16.1614i	−0.183469	−	0.624837i
$670$	2.03626	+	0.971083i	0.0786676	+	0.0375162i
$671$	−3.16773	−	4.92908i	−0.122289	−	0.190285i
$672$	6.25837	+	8.56505i	0.241422	+	0.330404i
$673$	14.2336	+	9.14737i	0.548665	+	0.352605i	0.785419	−	0.618964i	$-0.212447\pi$
$673$	14.2336	+	9.14737i	0.548665	+	0.352605i	−0.236755	+	0.971569i	$0.576084\pi$
$674$	−0.574547	+	34.6195i	−0.0221307	+	1.33349i
$675$	−3.21076	+	3.70541i	−0.123582	+	0.142621i
$676$	19.3348	+	23.8700i	0.743645	+	0.918079i
$677$	−11.7942	−	25.8256i	−0.453287	−	0.992559i	−0.988967	−	0.148138i	$-0.952672\pi$
$677$	−11.7942	−	25.8256i	−0.453287	−	0.992559i	0.535680	−	0.844421i	$-0.320055\pi$
$678$	25.9841	−	3.29685i	0.997912	−	0.126615i
$679$	−5.20223	+	17.7172i	−0.199643	+	0.679922i
$680$	−5.43879	+	0.507360i	−0.208568	+	0.0194564i
$681$	7.42877	+	1.06810i	0.284671	+	0.0409295i
$682$	4.18310	+	1.30405i	0.160179	+	0.0499345i
$683$	15.2974	−	33.4966i	0.585338	−	1.28171i	−0.352880	−	0.935669i	$-0.614798\pi$
$683$	15.2974	−	33.4966i	0.585338	−	1.28171i	0.938218	−	0.346044i	$-0.112475\pi$
$684$	0.423095	+	1.64047i	0.0161775	+	0.0627250i
$685$	−6.80143	+	0.977899i	−0.259869	+	0.0373636i
$686$	−23.1359	−	15.4169i	−0.883333	−	0.588621i
$687$	2.34357	+	2.70462i	0.0894126	+	0.103188i
$688$	−35.1665	+	13.3180i	−1.34071	+	0.507743i
$689$		−	22.2382i		−	0.847207i
$690$	2.09247	−	0.291946i	0.0796591	−	0.0111142i
$691$	−28.3088			−1.07692			−0.538460	−	0.842651i	$-0.680994\pi$
$691$	−28.3088			−1.07692			−0.538460	+	0.842651i	$0.680994\pi$
$692$	21.8059	+	10.8469i	0.828937	+	0.412336i
$693$	−0.665184	+	0.576385i	−0.0252682	+	0.0218951i
$694$	6.99272	+	4.65970i	0.265440	+	0.176880i
$695$	−0.644169	−	4.48030i	−0.0244347	−	0.169947i
$696$	2.90366	−	2.27322i	0.110063	−	0.0861662i
$697$	−42.5734	−	19.4426i	−1.61258	−	0.736442i
$698$	3.89096	−	12.4814i	0.147275	−	0.472426i
$699$	1.86090	−	12.9428i	0.0703856	−	0.489542i
$700$	17.4619	+	5.76320i	0.659996	+	0.217829i
$701$	−17.9835	−	5.28043i	−0.679227	−	0.199439i	−0.0761194	−	0.997099i	$-0.524253\pi$
$701$	−17.9835	−	5.28043i	−0.679227	−	0.199439i	−0.603108	+	0.797660i	$0.706071\pi$
$702$	7.47126	−	0.947949i	0.281984	−	0.0357780i
$703$	−0.674209	+	0.307901i	−0.0254283	+	0.0116127i
$704$	2.57929	+	2.72885i	0.0972108	+	0.102847i
$705$	0.663522	+	0.574945i	0.0249897	+	0.0216537i
$706$	−21.6016	−	0.358500i	−0.812986	−	0.0134923i
$707$	−13.2144	+	20.5620i	−0.496977	+	0.773312i
$708$	8.44234	+	5.83026i	0.317282	+	0.219114i
$709$	−34.1558	+	21.9506i	−1.28275	+	0.824371i	−0.991224	−	0.132193i	$-0.957798\pi$
$709$	−34.1558	+	21.9506i	−1.28275	+	0.824371i	−0.291522	+	0.956564i	$0.594162\pi$
$710$	−2.92788	−	1.39629i	−0.109881	−	0.0524018i
$711$	11.8065	−	3.46669i	0.442777	−	0.130011i
$712$	−0.890643	+	2.55528i	−0.0333783	+	0.0957631i
$713$	26.8425	+	16.7832i	1.00526	+	0.628536i
$714$	15.0670	−	6.58092i	0.563867	−	0.246285i
$715$	−0.747077	+	0.219362i	−0.0279391	+	0.00820366i
$716$	24.8047	+	0.823547i	0.926997	+	0.0307774i
$717$	8.32817	+	12.9589i	0.311021	+	0.483959i
$718$	25.1759	−	15.5954i	0.939556	−	0.582016i
$719$	26.4306	−	41.1268i	0.985694	−	1.53377i	0.147023	−	0.989133i	$-0.453031\pi$
$719$	26.4306	−	41.1268i	0.985694	−	1.53377i	0.838672	−	0.544637i	$-0.183333\pi$
$720$	1.16964	+	0.429574i	0.0435898	+	0.0160093i
$721$	3.71532	−	4.28771i	0.138366	−	0.159683i
$722$	−24.9254	+	6.87162i	−0.927629	+	0.255735i
$723$	−2.01112	+	0.918446i	−0.0747942	+	0.0341574i
$724$	18.0890	−	10.7942i	0.672274	−	0.401164i
$725$	1.80095	−	6.13346i	0.0668854	−	0.227791i
$726$	10.1730	−	11.3540i	0.377556	−	0.421387i
$727$	−4.69455	+	32.6513i	−0.174111	+	1.21097i	0.695973	+	0.718068i	$0.254973\pi$
$727$	−4.69455	+	32.6513i	−0.174111	+	1.21097i	−0.870084	+	0.492903i	$0.835936\pi$
$728$	−14.0692	−	24.4919i	−0.521438	−	0.907729i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	0.395136	−	2.45796i	0.0146246	−	0.0909730i
$731$	8.29458	+	57.6901i	0.306786	+	2.13375i
$732$	4.37119	−	24.5809i	0.161564	−	0.908537i
$733$	6.39155	+	7.37624i	0.236077	+	0.272448i	0.861410	−	0.507911i	$-0.169582\pi$
$733$	6.39155	+	7.37624i	0.236077	+	0.272448i	−0.625332	+	0.780358i	$0.715037\pi$
$734$	14.8577	+	17.7329i	0.548409	+	0.654535i
$735$	−1.08514			−0.0400260
$736$	13.0219	+	23.7998i	0.479994	+	0.877272i
$737$	−2.40358			−0.0885371
$738$	6.85657	+	8.18343i	0.252394	+	0.301236i
$739$	−7.40802	−	8.54931i	−0.272508	−	0.314492i	0.602956	−	0.797775i	$-0.293990\pi$
$739$	−7.40802	−	8.54931i	−0.272508	−	0.314492i	−0.875464	+	0.483283i	$0.839444\pi$
$740$	−0.0954430	+	0.536714i	−0.00350855	+	0.0197300i
$741$	−0.641977	−	4.46504i	−0.0235836	−	0.164028i
$742$	−1.75773	+	10.9340i	−0.0645285	+	0.401402i
$743$	9.00423	−	19.7165i	0.330333	−	0.723329i	−0.669477	−	0.742833i	$-0.733482\pi$
$743$	9.00423	−	19.7165i	0.330333	−	0.723329i	0.999810	+	0.0195044i	$0.00620884\pi$
$744$	9.29996	+	16.1895i	0.340953	+	0.593537i
$745$	0.433329	−	3.01387i	0.0158759	−	0.110420i
$746$	−24.8829	+	27.7716i	−0.911028	+	1.01679i
$747$	2.74881	−	9.36158i	0.100574	−	0.342522i
$748$	4.99768	−	2.98225i	0.182733	−	0.109042i
$749$	−3.67841	+	1.67987i	−0.134406	+	0.0613812i
$750$	4.20572	−	1.15946i	0.153571	−	0.0423376i
$751$	6.20508	−	7.16105i	0.226427	−	0.261310i	−0.631157	−	0.775655i	$-0.717419\pi$
$751$	6.20508	−	7.16105i	0.226427	−	0.261310i	0.857583	+	0.514345i	$0.171965\pi$
$752$	−3.88669	+	10.5826i	−0.141733	+	0.385908i
$753$	3.59684	−	5.59679i	0.131076	−	0.203958i
$754$	−8.34720	+	5.17074i	−0.303987	+	0.188307i
$755$	−3.45897	−	5.38226i	−0.125885	−	0.195880i
$756$	−3.74839	−	0.124451i	−0.136328	−	0.00452624i
$757$	49.6636	−	14.5825i	1.80505	−	0.530012i	0.806897	−	0.590693i	$-0.201145\pi$
$757$	49.6636	−	14.5825i	1.80505	−	0.530012i	0.998157	+	0.0606809i	$0.0193272\pi$
$758$	45.5661	−	19.9023i	1.65504	−	0.722884i
$759$	−1.87839	+	1.24041i	−0.0681813	+	0.0450239i
$760$	0.245642	−	0.704754i	0.00891039	−	0.0255641i
$761$	10.9483	−	3.21472i	0.396876	−	0.116533i	−0.0772035	−	0.997015i	$-0.524599\pi$
$761$	10.9483	−	3.21472i	0.396876	−	0.116533i	0.474080	+	0.880482i	$0.342781\pi$
$762$	−6.73659	−	3.21265i	−0.244041	−	0.116382i
$763$	−7.30951	+	4.69754i	−0.264622	+	0.170062i
$764$	40.4769	+	27.9532i	1.46440	+	1.01131i
$765$	1.04411	−	1.62467i	0.0377500	−	0.0587402i
$766$	7.75324	+	0.128673i	0.280136	+	0.00464914i
$767$	−20.6460	−	17.8899i	−0.745484	−	0.645966i
$768$	0.160696	+	15.9992i	0.00579862	+	0.577321i
$769$	−29.4714	+	13.4591i	−1.06277	+	0.485349i	−0.868546	−	0.495609i	$-0.834945\pi$
$769$	−29.4714	+	13.4591i	−1.06277	+	0.485349i	−0.194221	+	0.980958i	$0.562218\pi$
$770$	0.384661	−	0.0488056i	0.0138622	−	0.00175883i
$771$	−14.3971	−	4.22736i	−0.518498	−	0.152245i
$772$	19.7593	+	6.52145i	0.711152	+	0.234712i
$773$	−4.83778	+	33.6475i	−0.174003	+	1.21022i	0.696318	+	0.717733i	$0.254820\pi$
$773$	−4.83778	+	33.6475i	−0.174003	+	1.21022i	−0.870321	+	0.492484i	$0.836089\pi$
$774$	3.95679	−	12.6925i	0.142224	−	0.456224i
$775$	29.4400	+	13.4448i	1.05751	+	0.482951i
$776$	−21.9300	+	17.1686i	−0.787243	+	0.616317i
$777$	−0.233513	−	1.62412i	−0.00837721	−	0.0582648i
$778$	−28.5874	−	19.0496i	−1.02491	−	0.682963i
$779$	4.83283	−	4.18767i	0.173154	−	0.150039i
$780$	−2.97054	−	1.47763i	−0.106362	−	0.0529076i
$781$	3.45604			0.123667
$782$	40.3943	−	11.6780i	1.44450	−	0.417604i
$783$			1.30378i			0.0465933i
$784$	−4.93497	−	13.0309i	−0.176249	−	0.465390i
$785$	0.398469	+	0.459857i	0.0142220	+	0.0164130i
$786$	−17.5503	−	11.6949i	−0.625998	−	0.417143i
$787$	0.437247	−	0.0628667i	0.0155862	−	0.00224096i	−0.134517	−	0.990911i	$-0.542948\pi$
$787$	0.437247	−	0.0628667i	0.0155862	−	0.00224096i	0.150104	+	0.988670i	$0.452039\pi$
$788$	−4.73858	−	18.3729i	−0.168805	−	0.654508i
$789$	−5.68542	+	12.4493i	−0.202406	+	0.443208i
$790$	−5.17513	−	1.61330i	−0.184123	−	0.0573987i
$791$	34.3772	+	4.94270i	1.22231	+	0.175742i
$792$	−1.32182	+	0.123307i	−0.0469689	+	0.00438151i
$793$	−18.7289	+	63.7848i	−0.665083	+	2.26506i
$794$	37.9945	−	4.82073i	1.34838	−	0.171081i
$795$	0.540384	+	1.18328i	0.0191654	+	0.0419664i
$796$	−10.1362	−	12.5138i	−0.359266	−	0.443538i
$797$	−11.1860	+	12.9093i	−0.396227	+	0.457270i	−0.918449	−	0.395539i	$-0.870558\pi$
$797$	−11.1860	+	12.9093i	−0.396227	+	0.457270i	0.522222	+	0.852809i	$0.325103\pi$
$798$	−0.0372765	+	2.24611i	−0.00131958	+	0.0795115i
$799$	14.6997	+	9.44692i	0.520038	+	0.334208i
$800$	16.3631	+	22.3942i	0.578524	+	0.791753i
$801$	−0.517249	−	0.804854i	−0.0182761	−	0.0284381i
$802$	20.1777	+	9.62267i	0.712501	+	0.339788i
$803$	0.747272	+	2.54498i	0.0263707	+	0.0898102i
$804$	−7.51347	−	6.96015i	−0.264979	−	0.245465i
$805$	2.77769	+	0.364215i	0.0979007	+	0.0128369i
$806$	−19.8985	−	45.5574i	−0.700895	−	1.60469i
$807$	4.79737	+	16.3384i	0.168876	+	0.575137i
$808$	−34.2553	+	13.6270i	−1.20510	+	0.479397i
$809$	−0.464433	+	0.298473i	−0.0163286	+	0.0104938i	−0.548780	−	0.835967i	$-0.684907\pi$
$809$	−0.464433	+	0.298473i	−0.0163286	+	0.0104938i	0.532451	+	0.846461i	$0.321271\pi$
$810$	−0.374505	+	0.231990i	−0.0131587	+	0.00815129i
$811$	−44.1413	−	28.3679i	−1.55001	−	0.996132i	−0.985298	−	0.170844i	$-0.945351\pi$
$811$	−44.1413	−	28.3679i	−1.55001	−	0.996132i	−0.564713	−	0.825288i	$-0.691013\pi$
$812$	4.51285	−	1.88257i	0.158370	−	0.0660653i
$813$	5.98979	+	5.19018i	0.210071	+	0.182028i
$814$	−0.154362	−	0.559918i	−0.00541039	−	0.0196251i
$815$	−2.69468	−	5.90054i	−0.0943907	−	0.206687i
$816$	24.2583	+	5.14962i	0.849210	+	0.180273i
$817$	−7.64077	−	2.24353i	−0.267317	−	0.0784913i
$818$	−15.2485	+	17.0186i	−0.533150	+	0.595043i
$819$	9.88456	+	1.42118i	0.345394	+	0.0496602i
$820$	−0.514496	−	4.67503i	−0.0179670	−	0.163259i
$821$	−2.20050	−	1.00493i	−0.0767978	−	0.0350724i	0.376646	−	0.926357i	$-0.377077\pi$
$821$	−2.20050	−	1.00493i	−0.0767978	−	0.0350724i	−0.453444	+	0.891285i	$0.649805\pi$
$822$	30.8000	+	4.95134i	1.07427	+	0.172698i
$823$	−2.42589	+	0.348791i	−0.0845613	+	0.0121581i	−0.184466	−	0.982839i	$-0.559055\pi$
$823$	−2.42589	+	0.348791i	−0.0845613	+	0.0121581i	0.0999043	+	0.994997i	$0.468146\pi$
$824$	8.32051	−	1.99931i	0.289859	−	0.0696491i
$825$	−1.73919	+	1.50701i	−0.0605507	+	0.0524675i
$826$	8.73718	+	10.4280i	0.304005	+	0.362835i
$827$		−	10.2810i		−	0.357505i	−0.983894	−	0.178752i	$-0.942794\pi$
$827$		−	10.2810i		−	0.357505i	0.983894	−	0.178752i	$-0.0572061\pi$
$828$	−9.46364	−	1.56189i	−0.328884	−	0.0542795i
$829$			33.3159i			1.15711i	0.815644	+	0.578554i	$0.196383\pi$
$829$			33.3159i			1.15711i	−0.815644	+	0.578554i	$0.803617\pi$
$830$	−3.29465	+	2.76045i	−0.114359	+	0.0958167i
$831$	−15.8243	+	13.7118i	−0.548939	+	0.475659i
$832$	4.23481	−	42.3916i	0.146816	−	1.46967i
$833$	−21.3770	+	3.07355i	−0.740670	+	0.106492i
$834$	−3.26159	+	20.2888i	−0.112940	+	0.702545i
$835$	−3.78524	−	1.72866i	−0.130994	−	0.0598228i
$836$	0.0869852	+	0.790402i	0.00300844	+	0.0273366i
$837$	−6.53386	−	0.939427i	−0.225843	−	0.0324713i
$838$	9.04635	+	8.10540i	0.312501	+	0.279996i
$839$	−43.1392	−	12.6668i	−1.48933	−	0.437307i	−0.567003	−	0.823716i	$-0.691897\pi$
$839$	−43.1392	−	12.6668i	−1.48933	−	0.437307i	−0.922328	+	0.386408i	$0.873716\pi$
$840$	1.34376	+	0.961315i	0.0463641	+	0.0331685i
$841$	11.3409	+	24.8331i	0.391065	+	0.856314i
$842$	−13.6953	+	3.77562i	−0.471972	+	0.130116i
$843$	−3.38100	−	2.92965i	−0.116448	−	0.100903i
$844$	16.3411	+	39.1725i	0.562485	+	1.34837i
$845$	4.02496	+	2.58668i	0.138463	+	0.0889846i
$846$	−2.09899	−	3.38844i	−0.0721649	−	0.116497i
$847$	17.0054	−	10.9287i	0.584313	−	0.375515i
$848$	−11.7518	+	11.8705i	−0.403560	+	0.407633i
$849$	−1.21883	−	4.15096i	−0.0418302	−	0.142460i
$850$	39.3940	−	17.2065i	1.35120	−	0.590177i
$851$	−0.0521253	−	4.19601i	−0.00178683	−	0.143837i
$852$	10.8034	+	10.0078i	0.370118	+	0.342861i
$853$	−4.01053	−	13.6586i	−0.137318	−	0.467662i	0.861905	−	0.507069i	$-0.169271\pi$
$853$	−4.01053	−	13.6586i	−0.137318	−	0.467662i	−0.999223	+	0.0394072i	$0.987453\pi$
$854$	14.2502	−	29.8813i	0.487634	−	1.02252i
$855$	0.142659	+	0.221982i	0.00487883	+	0.00759161i
$856$	−5.98662	−	1.16739i	−0.204618	−	0.0399006i
$857$	21.2621	+	13.6643i	0.726300	+	0.466765i	0.850823	−	0.525452i	$-0.176104\pi$
$857$	21.2621	+	13.6643i	0.726300	+	0.466765i	−0.124523	+	0.992217i	$0.539740\pi$
$858$	3.53437	+	0.0586564i	0.120661	+	0.00200250i
$859$	14.9939	−	17.3039i	0.511585	−	0.590400i	−0.439919	−	0.898038i	$-0.644993\pi$
$859$	14.9939	−	17.3039i	0.511585	−	0.590400i	0.951504	+	0.307637i	$0.0995383\pi$
$860$	−4.55121	+	3.68648i	−0.155195	+	0.125708i
$861$	5.88081	+	12.8772i	0.200418	+	0.438853i
$862$	5.18111	+	40.8349i	0.176469	+	1.39084i
$863$	6.56460	−	22.3570i	0.223462	−	0.761041i	−0.769082	−	0.639150i	$-0.779286\pi$
$863$	6.56460	−	22.3570i	0.223462	−	0.761041i	0.992544	−	0.121890i	$-0.0388956\pi$
$864$	−4.48901	−	3.44221i	−0.152719	−	0.117106i
$865$	3.75472	+	0.539847i	0.127664	+	0.0183554i
$866$	16.9794	−	54.4662i	0.576983	−	1.85084i
$867$	8.90502	−	19.4993i	0.302430	−	0.662230i
$868$	6.18276	+	23.9725i	0.209857	+	0.813678i
$869$	5.71669	−	0.821936i	0.193925	−	0.0278823i
$870$	0.318500	−	0.477967i	0.0107982	−	0.0162046i
$871$	17.8585	+	20.6098i	0.605112	+	0.698336i
$872$	−13.0892	−	0.652167i	−0.443257	−	0.0220851i
$873$		−	9.84688i		−	0.333266i
$874$	−0.841341	+	5.68321i	−0.0284588	+	0.192238i
$875$	5.78478			0.195561
$876$	−5.03366	+	10.1194i	−0.170071	+	0.341902i
$877$	9.90620	−	8.58377i	0.334509	−	0.289853i	−0.471368	−	0.881936i	$-0.656240\pi$
$877$	9.90620	−	8.58377i	0.334509	−	0.289853i	0.805877	+	0.592083i	$0.201694\pi$
$878$	2.51338	−	3.77178i	0.0848224	−	0.127291i
$879$	−2.75052	−	19.1303i	−0.0927729	−	0.645249i
$880$	0.514703	+	0.277703i	0.0173506	+	0.00936136i
$881$	−38.6567	−	17.6539i	−1.30238	−	0.594776i	−0.361137	−	0.932513i	$-0.617611\pi$
$881$	−38.6567	−	17.6539i	−1.30238	−	0.594776i	−0.941240	+	0.337737i	$0.890338\pi$
$882$	4.70321	+	1.46619i	0.158365	+	0.0493690i
$883$	−0.795838	+	5.53517i	−0.0267821	+	0.186273i	−0.998821	−	0.0485467i	$-0.984541\pi$
$883$	−0.795838	+	5.53517i	−0.0267821	+	0.186273i	0.972039	+	0.234820i	$0.0754501\pi$
$884$	−62.7041	−	20.6952i	−2.10897	−	0.696055i
$885$	1.53328	+	0.450211i	0.0515406	+	0.0151337i
$886$	−4.37641	−	34.4926i	−0.147028	−	1.15880i
$887$	−41.7136	+	19.0500i	−1.40061	+	0.639636i	−0.965419	−	0.260704i	$-0.916045\pi$
$887$	−41.7136	+	19.0500i	−1.40061	+	0.639636i	−0.435188	+	0.900340i	$0.643318\pi$
$888$	1.13885	−	2.19726i	0.0382172	−	0.0737354i
$889$	−7.47920	−	6.48077i	−0.250844	−	0.217358i
$890$	−0.00699386	+	0.421418i	−0.000234435	+	0.0141260i
$891$	0.253757	−	0.394854i	0.00850119	−	0.0132281i
$892$	19.1432	−	27.7197i	0.640961	−	0.928125i
$893$	−2.00844	+	1.29075i	−0.0672099	+	0.0431932i
$894$	−5.95031	+	12.4772i	−0.199008	+	0.417300i
$895$	3.70897	−	1.08905i	0.123977	−	0.0364030i
$896$	−5.43286	+	20.5084i	−0.181499	+	0.685136i
$897$	24.5923	+	6.89033i	0.821114	+	0.230061i
$898$	−7.82066	−	17.9053i	−0.260979	−	0.597509i
$899$	8.25770	−	2.42468i	0.275410	−	0.0808676i
$900$	−9.80053	−	0.325389i	−0.326684	−	0.0108463i
$901$	13.9969	+	21.7797i	0.466306	+	0.725586i
$902$	2.63884	+	4.25991i	0.0878637	+	0.141840i
$903$	9.53093	−	14.8304i	0.317170	−	0.493526i
$904$	37.8336	+	36.2323i	1.25833	+	1.20507i
$905$	2.14855	−	2.47956i	0.0714202	−	0.0824232i
$906$	7.71959	+	28.0013i	0.256466	+	0.930281i
$907$	10.5727	−	4.82837i	0.351059	−	0.160323i	−0.232078	−	0.972697i	$-0.574552\pi$
$907$	10.5727	−	4.82837i	0.351059	−	0.160323i	0.583137	+	0.812374i	$0.301825\pi$
$908$	7.69171	+	12.8898i	0.255258	+	0.427764i
$909$	3.67215	−	12.5062i	0.121798	−	0.414805i
$910$	−3.27650	−	2.93570i	−0.108615	−	0.0973174i
$911$	6.47908	−	45.0630i	0.214661	−	1.49300i	−0.542655	−	0.839955i	$-0.682581\pi$
$911$	6.47908	−	45.0630i	0.214661	−	1.49300i	0.757317	−	0.653048i	$-0.226510\pi$
$912$	−2.01689	+	2.72264i	−0.0667858	+	0.0901556i
$913$	1.90239	−	4.16565i	0.0629599	−	0.137863i
$914$	35.3190	+	5.67781i	1.16825	+	0.187805i
$915$	−0.553409	−	3.84905i	−0.0182951	−	0.127246i
$916$	−1.25314	+	7.04690i	−0.0414048	+	0.232836i
$917$	−18.3131	−	21.1344i	−0.604752	−	0.697921i
$918$	−6.72056	+	5.63089i	−0.221812	+	0.185847i
$919$	−48.6241			−1.60396			−0.801980	−	0.597351i	$-0.796220\pi$
$919$	−48.6241			−1.60396			−0.801980	+	0.597351i	$0.796220\pi$
$920$	3.08782	+	2.88445i	0.101802	+	0.0950977i
$921$	17.7271			0.584127
$922$	−18.0162	+	15.0950i	−0.593332	+	0.497129i
$923$	−25.6782	−	29.6342i	−0.845207	−	0.975421i
$924$	−1.73314	−	0.308201i	−0.0570161	−	0.0101391i
$925$	−0.610541	−	4.24641i	−0.0200745	−	0.139621i
$926$	27.4112	+	4.40657i	0.900789	+	0.144809i
$927$	−1.25683	+	2.75207i	−0.0412797	+	0.0903899i
$928$	7.18813	+	1.65103i	0.235962	+	0.0541976i
$929$	1.20672	−	8.39294i	0.0395913	−	0.275363i	−0.960403	−	0.278613i	$-0.910125\pi$
$929$	1.20672	−	8.39294i	0.0395913	−	0.275363i	0.999995	+	0.00324960i	$0.00103438\pi$
$930$	2.16582	+	1.94054i	0.0710201	+	0.0636330i
$931$	0.831339	−	2.83128i	0.0272460	−	0.0927915i
$932$	22.4574	−	13.4009i	0.735615	−	0.438962i
$933$	0.482629	−	0.220409i	0.0158006	−	0.00721587i
$934$	−8.42755	−	30.5693i	−0.275758	−	1.00026i
$935$	0.593605	−	0.685057i	0.0194130	−	0.0224038i
$936$	10.8784	+	10.4180i	0.355571	+	0.340522i
$937$	0.0936362	−	0.145701i	0.00305896	−	0.00475983i	−0.839721	−	0.543019i	$-0.817281\pi$
$937$	0.0936362	−	0.145701i	0.00305896	−	0.00475983i	0.842780	+	0.538259i	$0.180918\pi$
$938$	−7.15162	−	11.5450i	−0.233509	−	0.376956i
$939$	−11.4699	−	17.8475i	−0.374306	−	0.582432i
$940$	−0.0582669	+	1.75496i	−0.00190046	+	0.0572406i
$941$	−43.8407	+	12.8728i	−1.42917	+	0.419641i	−0.902596	−	0.430489i	$-0.858341\pi$
$941$	−43.8407	+	12.8728i	−1.42917	+	0.419641i	−0.526572	+	0.850131i	$0.676523\pi$
$942$	−1.10570	−	2.53150i	−0.0360258	−	0.0824807i
$943$	10.6308	+	34.6088i	0.346185	+	1.12702i
$944$	1.56663	+	20.4598i	0.0509894	+	0.665911i
$945$	−0.560484	+	0.164573i	−0.0182325	+	0.00535356i
$946$	2.68610	−	5.63248i	0.0873327	−	0.183128i
$947$	2.30546	−	1.48163i	0.0749173	−	0.0481464i	−0.502646	−	0.864492i	$-0.667640\pi$
$947$	2.30546	−	1.48163i	0.0749173	−	0.0481464i	0.577563	+	0.816346i	$0.304004\pi$
$948$	20.2502	+	13.9847i	0.657695	+	0.454203i
$949$	16.2700	−	25.3166i	0.528146	−	0.821812i
$950$	−0.0974631	+	5.87268i	−0.00316212	+	0.190535i
$951$	5.04347	+	4.37019i	0.163546	+	0.141713i
$952$	29.1945	+	15.1316i	0.946201	+	0.490419i
$953$	31.6468	−	14.4526i	1.02514	−	0.468166i	0.169388	−	0.985550i	$-0.445821\pi$
$953$	31.6468	−	14.4526i	1.02514	−	0.468166i	0.855754	+	0.517383i	$0.173094\pi$
$954$	−0.743346	−	5.85868i	−0.0240667	−	0.189682i
$955$	7.35132	+	2.15854i	0.237883	+	0.0698488i
$956$	−9.65589	+	29.2563i	−0.312294	+	0.946215i
$957$	−0.0870893	+	0.605719i	−0.00281520	+	0.0195801i
$958$	−9.16124	−	2.85594i	−0.295986	−	0.0922713i
$959$	37.6267	+	17.1835i	1.21503	+	0.554885i
$960$	0.804779	+	2.35853i	0.0259741	+	0.0761212i
$961$	1.78944	+	12.4458i	0.0577238	+	0.401478i
$962$	−3.65418	+	5.48375i	−0.117815	+	0.176803i
$963$	1.62974	−	1.41218i	0.0525176	−	0.0455068i
$964$	−3.95906	−	1.96935i	−0.127513	−	0.0634285i
$965$	3.24086			0.104327
$966$	−11.5469	−	5.33164i	−0.371516	−	0.171543i
$967$			32.2613i			1.03745i	0.854940	+	0.518727i	$0.173594\pi$
$967$			32.2613i			1.03745i	−0.854940	+	0.518727i	$0.826406\pi$
$968$	30.4518	+	1.51725i	0.978758	+	0.0487663i
$969$	3.43909	+	3.96892i	0.110479	+	0.127500i
$970$	−2.40549	+	3.60987i	−0.0772355	+	0.115906i
$971$	−55.9059	+	8.03805i	−1.79411	+	0.257953i	−0.957207	−	0.289405i	$-0.906543\pi$
$971$	−55.9059	+	8.03805i	−1.79411	+	0.257953i	−0.836899	+	0.547358i	$0.815634\pi$
$972$	1.93663	−	0.499477i	0.0621173	−	0.0160207i
$973$	−11.3193	+	24.7857i	−0.362879	+	0.794595i
$974$	4.10144	−	13.1565i	0.131419	−	0.421563i
$975$	25.8441	+	3.71583i	0.827675	+	0.119002i
$976$	43.7045	−	24.1502i	1.39895	−	0.773029i
$977$	15.7622	−	53.6812i	0.504279	−	1.71742i	−0.175936	−	0.984402i	$-0.556295\pi$
$977$	15.7622	−	53.6812i	0.504279	−	1.71742i	0.680214	−	0.733013i	$-0.261887\pi$
$978$	3.70678	+	29.2150i	0.118530	+	0.934192i
$979$	−0.186544	−	0.408475i	−0.00596199	−	0.0130549i
$980$	−1.36602	−	1.68645i	−0.0436360	−	0.0538716i
$981$	3.03429	−	3.50175i	0.0968773	−	0.111802i
$982$	−13.3951	−	0.222305i	−0.427455	−	0.00709405i
$983$	31.3054	+	20.1188i	0.998488	+	0.641689i	0.934389	−	0.356254i	$-0.115946\pi$
$983$	31.3054	+	20.1188i	0.998488	+	0.641689i	0.0640989	+	0.997944i	$0.479583\pi$
$984$	−4.08674	+	20.9576i	−0.130280	+	0.668105i
$985$	−1.59775	−	2.48615i	−0.0509085	−	0.0792152i
$986$	4.92058	−	10.3179i	0.156703	−	0.328590i
$987$	−1.48902	−	5.07114i	−0.0473960	−	0.161416i
$988$	6.13110	−	6.61851i	0.195056	−	0.210563i
$989$	29.0992	−	34.4374i	0.925300	−	1.09505i
$990$	−0.189486	+	0.0827634i	−0.00602226	+	0.00263039i
$991$	−3.74671	−	12.7601i	−0.119018	−	0.405338i	0.878335	−	0.478045i	$-0.158654\pi$
$991$	−3.74671	−	12.7601i	−0.119018	−	0.405338i	−0.997353	+	0.0727067i	$0.976836\pi$
$992$	−13.4534	+	34.8334i	−0.427146	+	1.10596i
$993$	−11.2370	+	7.22155i	−0.356594	+	0.229169i
$994$	10.2831	+	16.6001i	0.326160	+	0.526525i
$995$	−2.11006	−	1.35606i	−0.0668935	−	0.0429899i
$996$	18.0094	−	7.51277i	0.570650	−	0.238051i
$997$	−36.4817	−	31.6116i	−1.15539	−	1.00115i	−0.999911	−	0.0133085i	$-0.995764\pi$
$997$	−36.4817	−	31.6116i	−1.15539	−	1.00115i	−0.155475	−	0.987840i	$-0.549691\pi$
$998$	18.4556	−	5.08796i	0.584200	−	0.161056i
$999$	0.363486	+	0.795924i	0.0115002	+	0.0251819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.451.6	yes	240
8.3	odd	2	inner	552.2.t.a.451.10	yes	240
23.5	odd	22	inner	552.2.t.a.235.10	yes	240
184.51	even	22	inner	552.2.t.a.235.6	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.6	✓	240	184.51	even	22	inner
552.2.t.a.235.10	yes	240	23.5	odd	22	inner
552.2.t.a.451.6	yes	240	1.1	even	1	trivial
552.2.t.a.451.10	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)

\(f(q)\)	\(=\)	\(q+(-0.908250 - 1.08401i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.350163 + 1.96911i) q^{4} +(0.0443320 + 0.308336i) q^{5} +(0.224464 - 1.39629i) q^{6} +(0.778998 - 1.70577i) q^{7} +(2.45257 - 1.40886i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.908250 - 1.08401i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-0.350163 + 1.96911i) q^{4} +(0.0443320 + 0.308336i) q^{5} +(0.224464 - 1.39629i) q^{6} +(0.778998 - 1.70577i) q^{7} +(2.45257 - 1.40886i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.293975 - 0.328103i) q^{10} +(-0.132235 + 0.450351i) q^{11} +(-1.71746 + 1.02486i) q^{12} +(4.84409 - 2.21222i) q^{13} +(-2.55660 + 0.704820i) q^{14} +(-0.203994 + 0.235421i) q^{15} +(-3.75477 - 1.37902i) q^{16} +(-3.35182 + 5.21553i) q^{17} +(1.20224 - 0.744735i) q^{18} +(-0.457964 - 0.712606i) q^{19} +(-0.622670 - 0.0206734i) q^{20} +(1.79927 - 0.528313i) q^{21} +(0.608289 - 0.265687i) q^{22} +(4.73817 - 0.741431i) q^{23} +(2.67084 + 0.930922i) q^{24} +(4.70436 - 1.38132i) q^{25} +(-6.79772 - 3.24180i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(3.08606 + 2.13123i) q^{28} +(0.704877 - 1.09681i) q^{29} +(0.440476 + 0.00731016i) q^{30} +(4.98874 + 4.32277i) q^{31} +(1.91540 + 5.32271i) q^{32} +(-0.426949 + 0.194981i) q^{33} +(8.69799 - 1.10360i) q^{34} +(0.560484 + 0.164573i) q^{35} +(-1.89923 - 0.626832i) q^{36} +(0.124525 - 0.866090i) q^{37} +(-0.356527 + 1.14366i) q^{38} +(4.84409 + 2.21222i) q^{39} +(0.543130 + 0.693759i) q^{40} +(1.07436 + 7.47237i) q^{41} +(-2.20688 - 1.47059i) q^{42} +(7.10478 - 6.15633i) q^{43} +(-0.840487 - 0.418082i) q^{44} -0.311507 q^{45} +(-5.10717 - 4.46283i) q^{46} -2.81845i q^{47} +(-1.41666 - 3.74073i) q^{48} +(2.28122 + 2.63267i) q^{49} +(-5.77011 - 3.84499i) q^{50} +(-6.13661 + 0.882311i) q^{51} +(2.65988 + 10.3132i) q^{52} +(1.73474 - 3.79855i) q^{53} +(1.35013 + 0.420892i) q^{54} +(-0.144722 - 0.0208079i) q^{55} +(-0.492641 - 5.28102i) q^{56} +(0.238649 - 0.812764i) q^{57} +(-1.82916 + 0.232083i) q^{58} +(-2.13105 - 4.66635i) q^{59} +(-0.392138 - 0.484121i) q^{60} +(-8.17481 + 9.43424i) q^{61} +(0.154907 - 9.33400i) q^{62} +(1.57754 + 1.01382i) q^{63} +(4.03022 - 6.91067i) q^{64} +(0.896856 + 1.39554i) q^{65} +(0.599138 + 0.285726i) q^{66} +(1.44273 + 4.91350i) q^{67} +(-9.09626 - 8.42638i) q^{68} +(3.66318 + 3.09534i) q^{69} +(-0.330661 - 0.757045i) q^{70} +(-2.07446 - 7.06497i) q^{71} +(1.04548 + 2.62811i) q^{72} +(4.75400 - 3.05521i) q^{73} +(-1.05195 + 0.651640i) q^{74} +(4.12464 + 2.65074i) q^{75} +(1.56356 - 0.652252i) q^{76} +(0.665184 + 0.576385i) q^{77} +(-2.00157 - 7.26030i) q^{78} +(-5.11164 - 11.1929i) q^{79} +(0.258744 - 1.21887i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(7.12434 - 7.95140i) q^{82} +(-9.65749 - 1.38854i) q^{83} +(0.410267 + 3.72795i) q^{84} +(-1.75673 - 0.802271i) q^{85} +(-13.1264 - 2.11018i) q^{86} +(1.29051 - 0.185547i) q^{87} +(0.310167 + 1.29082i) q^{88} +(-0.723050 + 0.626526i) q^{89} +(0.282926 + 0.337677i) q^{90} -9.98620i q^{91} +(-0.199176 + 9.58959i) q^{92} +6.60105i q^{93} +(-3.05523 + 2.55985i) q^{94} +(0.199420 - 0.172798i) q^{95} +(-2.76832 + 4.93320i) q^{96} +(-9.74665 + 1.40136i) q^{97} +(0.781926 - 4.86400i) q^{98} +(-0.426949 - 0.194981i) 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

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