LMFDB - Embedded newform 552.2.t.b.451.15

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			451.15
Character	$\chi$	$=$	552.451
Dual form			552.2.t.b.235.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.614348 + 1.27380i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.24515 + 1.56512i) q^{4} +(-0.254111 - 1.76738i) q^{5} +(0.560365 - 1.29846i) q^{6} +(0.304414 - 0.666574i) q^{7} +(-2.75861 - 0.624555i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.614348 + 1.27380i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.24515 + 1.56512i) q^{4} +(-0.254111 - 1.76738i) q^{5} +(0.560365 - 1.29846i) q^{6} +(0.304414 - 0.666574i) q^{7} +(-2.75861 - 0.624555i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(2.09518 - 1.40947i) q^{10} +(0.680911 - 2.31897i) q^{11} +(1.99824 - 0.0839098i) q^{12} +(-2.99026 + 1.36561i) q^{13} +(1.03610 - 0.0217443i) q^{14} +(-1.16929 + 1.34943i) q^{15} +(-0.899186 - 3.89762i) q^{16} +(3.85213 - 5.99403i) q^{17} +(-1.34827 + 0.426813i) q^{18} +(-3.08682 - 4.80319i) q^{19} +(3.08256 + 1.80295i) q^{20} +(-0.703112 + 0.206452i) q^{21} +(3.37223 - 0.557307i) q^{22} +(4.44247 - 1.80677i) q^{23} +(1.33450 + 2.49382i) q^{24} +(1.73841 - 0.510442i) q^{25} +(-3.57658 - 2.97005i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.664225 + 1.30643i) q^{28} +(-2.86784 + 4.46245i) q^{29} +(-2.43726 - 0.660425i) q^{30} +(-6.46576 - 5.60261i) q^{31} +(4.41240 - 3.53988i) q^{32} +(-2.19846 + 1.00400i) q^{33} +(10.0018 + 1.22444i) q^{34} +(-1.25544 - 0.368632i) q^{35} +(-1.37198 - 1.45522i) q^{36} +(0.948235 - 6.59512i) q^{37} +(4.22194 - 6.88283i) q^{38} +(2.99026 + 1.36561i) q^{39} +(-0.402833 + 5.03422i) q^{40} +(0.759579 + 5.28299i) q^{41} +(-0.694936 - 0.768794i) q^{42} +(5.68665 - 4.92751i) q^{43} +(2.78162 + 3.95318i) q^{44} +1.78555 q^{45} +(5.03070 + 4.54885i) q^{46} +8.18846i q^{47} +(-2.35679 + 3.23196i) q^{48} +(4.23237 + 4.88442i) q^{49} +(1.71819 + 1.90080i) q^{50} +(-7.05259 + 1.01401i) q^{51} +(1.58600 - 6.38050i) q^{52} +(-4.33438 + 9.49097i) q^{53} +(1.20549 + 0.739451i) q^{54} +(-4.27152 - 0.614153i) q^{55} +(-1.25607 + 1.64870i) q^{56} +(-1.60857 + 5.47828i) q^{57} +(-7.44613 - 0.911572i) q^{58} +(-3.51432 - 7.69529i) q^{59} +(-0.656074 - 3.51032i) q^{60} +(-0.167353 + 0.193136i) q^{61} +(3.16441 - 11.6781i) q^{62} +(0.616467 + 0.396179i) q^{63} +(7.21986 + 3.44581i) q^{64} +(3.17340 + 4.93791i) q^{65} +(-2.62952 - 2.18360i) q^{66} +(-1.33288 - 4.53936i) q^{67} +(4.58487 + 13.4925i) q^{68} +(-4.27467 - 2.17421i) q^{69} +(-0.301715 - 1.82566i) q^{70} +(0.666125 + 2.26861i) q^{71} +(1.01079 - 2.64165i) q^{72} +(-13.1263 + 8.43579i) q^{73} +(8.98343 - 2.84383i) q^{74} +(-1.52418 - 0.979532i) q^{75} +(11.3611 + 1.14947i) q^{76} +(-1.33849 - 1.15981i) q^{77} +(0.0975454 + 4.64797i) q^{78} +(-3.31296 - 7.25437i) q^{79} +(-6.66009 + 2.57963i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-6.26285 + 4.21315i) q^{82} +(-4.54852 - 0.653978i) q^{83} +(0.552361 - 1.35752i) q^{84} +(-11.5726 - 5.28503i) q^{85} +(9.77026 + 4.21647i) q^{86} +(5.25053 - 0.754912i) q^{87} +(-3.32669 + 5.97187i) q^{88} +(11.4479 - 9.91962i) q^{89} +(1.09695 + 2.27445i) q^{90} +2.40894i q^{91} +(-2.70375 + 9.20270i) q^{92} +8.55543i q^{93} +(-10.4305 + 5.03056i) q^{94} +(-7.70466 + 6.67613i) q^{95} +(-5.56477 - 1.01654i) q^{96} +(-1.40732 + 0.202343i) q^{97} +(-3.62164 + 8.39194i) q^{98} +(2.19846 + 1.00400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9	$ 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9} - 4 q^{12} - 4 q^{16} - 44 q^{17} + 4 q^{18} + 55 q^{20} + 4 q^{24} - 24 q^{25} - 24 q^{27} + 4 q^{32} - 55 q^{34} + 7 q^{36} + 22 q^{38} + 11 q^{40} - 44 q^{42} + 77 q^{44} - 48 q^{46} + 51 q^{48} + 8 q^{49} - 33 q^{50} + 165 q^{52} - 7 q^{54} - 22 q^{56} - 59 q^{58} + 11 q^{60} + 29 q^{62} - 4 q^{64} + 55 q^{66} + 132 q^{70} + 4 q^{72} - 144 q^{73} - 66 q^{74} - 24 q^{75} - 55 q^{76} - 24 q^{81} - 26 q^{82} - 44 q^{84} - 110 q^{86} - 198 q^{88} - 47 q^{92} - 73 q^{94} + 4 q^{96} + 53 q^{98}+O(q^{100}) $ 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9 - 4 * q^12 - 4 * q^16 - 44 * q^17 + 4 * q^18 + 55 * q^20 + 4 * q^24 - 24 * q^25 - 24 * q^27 + 4 * q^32 - 55 * q^34 + 7 * q^36 + 22 * q^38 + 11 * q^40 - 44 * q^42 + 77 * q^44 - 48 * q^46 + 51 * q^48 + 8 * q^49 - 33 * q^50 + 165 * q^52 - 7 * q^54 - 22 * q^56 - 59 * q^58 + 11 * q^60 + 29 * q^62 - 4 * q^64 + 55 * q^66 + 132 * q^70 + 4 * q^72 - 144 * q^73 - 66 * q^74 - 24 * q^75 - 55 * q^76 - 24 * q^81 - 26 * q^82 - 44 * q^84 - 110 * q^86 - 198 * q^88 - 47 * q^92 - 73 * q^94 + 4 * q^96 + 53 * 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 $

$2$	0.614348	+	1.27380i	0.434410	+	0.900715i
$2$	0.614348	+	1.27380i	0.434410	+	0.900715i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	−1.24515	+	1.56512i	−0.622577	+	0.782559i
$5$	−0.254111	−	1.76738i	−0.113642	−	0.790396i	−0.964326	−	0.264719i	$-0.914721\pi$
$5$	−0.254111	−	1.76738i	−0.113642	−	0.790396i	0.850684	−	0.525678i	$-0.176188\pi$
$6$	0.560365	−	1.29846i	0.228768	−	0.530093i
$7$	0.304414	−	0.666574i	0.115058	−	0.251941i	−0.843338	−	0.537383i	$-0.819413\pi$
$7$	0.304414	−	0.666574i	0.115058	−	0.251941i	0.958396	+	0.285442i	$0.0921402\pi$
$8$	−2.75861	−	0.624555i	−0.975316	−	0.220814i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	2.09518	−	1.40947i	0.662555	−	0.445715i
$11$	0.680911	−	2.31897i	0.205302	−	0.699195i	−0.790886	−	0.611964i	$-0.790380\pi$
$11$	0.680911	−	2.31897i	0.205302	−	0.699195i	0.996188	−	0.0872316i	$-0.0278020\pi$
$12$	1.99824	−	0.0839098i	0.576842	−	0.0242227i
$13$	−2.99026	+	1.36561i	−0.829350	+	0.378751i	−0.784413	−	0.620239i	$-0.787036\pi$
$13$	−2.99026	+	1.36561i	−0.829350	+	0.378751i	−0.0449365	+	0.998990i	$0.514309\pi$
$14$	1.03610	−	0.0217443i	0.276910	−	0.00581142i
$15$	−1.16929	+	1.34943i	−0.301909	+	0.348422i
$16$	−0.899186	−	3.89762i	−0.224796	−	0.974406i
$17$	3.85213	−	5.99403i	0.934279	−	1.45377i	0.0436435	−	0.999047i	$-0.486103\pi$
$17$	3.85213	−	5.99403i	0.934279	−	1.45377i	0.890635	−	0.454719i	$-0.150260\pi$
$18$	−1.34827	+	0.426813i	−0.317790	+	0.100601i
$19$	−3.08682	−	4.80319i	−0.708165	−	1.10193i	−0.989808	−	0.142407i	$-0.954516\pi$
$19$	−3.08682	−	4.80319i	−0.708165	−	1.10193i	0.281643	−	0.959519i	$-0.409121\pi$
$20$	3.08256	+	1.80295i	0.689282	+	0.403151i
$21$	−0.703112	+	0.206452i	−0.153432	+	0.0450516i
$22$	3.37223	−	0.557307i	0.718961	−	0.118818i
$23$	4.44247	−	1.80677i	0.926320	−	0.376738i
$23$	4.44247	−	1.80677i	0.926320	−	0.376738i
$24$	1.33450	+	2.49382i	0.272403	+	0.509048i
$25$	1.73841	−	0.510442i	0.347681	−	0.102088i
$26$	−3.57658	−	2.97005i	−0.701425	−	0.582475i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	0.664225	+	1.30643i	0.125527	+	0.246892i
$29$	−2.86784	+	4.46245i	−0.532545	+	0.828655i	−0.998420	−	0.0561949i	$-0.982103\pi$
$29$	−2.86784	+	4.46245i	−0.532545	+	0.828655i	0.465875	+	0.884850i	$0.345740\pi$
$30$	−2.43726	−	0.660425i	−0.444981	−	0.120577i
$31$	−6.46576	−	5.60261i	−1.16129	−	1.00626i	−0.999812	−	0.0193822i	$-0.993830\pi$
$31$	−6.46576	−	5.60261i	−1.16129	−	1.00626i	−0.161473	−	0.986877i	$-0.551624\pi$
$32$	4.41240	−	3.53988i	0.780009	−	0.625769i
$33$	−2.19846	+	1.00400i	−0.382703	+	0.174775i
$34$	10.0018	+	1.22444i	1.71529	+	0.209989i
$35$	−1.25544	−	0.368632i	−0.212209	−	0.0623102i
$36$	−1.37198	−	1.45522i	−0.228664	−	0.242537i
$37$	0.948235	−	6.59512i	0.155889	−	1.08423i	−0.750221	−	0.661187i	$-0.770053\pi$
$37$	0.948235	−	6.59512i	0.155889	−	1.08423i	0.906110	−	0.423043i	$-0.139038\pi$
$38$	4.22194	−	6.88283i	0.684889	−	1.11654i
$39$	2.99026	+	1.36561i	0.478825	+	0.218672i
$40$	−0.402833	+	5.03422i	−0.0636935	+	0.795980i
$41$	0.759579	+	5.28299i	0.118626	+	0.825065i	0.959071	+	0.283167i	$0.0913850\pi$
$41$	0.759579	+	5.28299i	0.118626	+	0.825065i	−0.840444	+	0.541898i	$0.817706\pi$
$42$	−0.694936	−	0.768794i	−0.107231	−	0.118627i
$43$	5.68665	−	4.92751i	0.867205	−	0.751438i	−0.102753	−	0.994707i	$-0.532765\pi$
$43$	5.68665	−	4.92751i	0.867205	−	0.751438i	0.969959	+	0.243269i	$0.0782198\pi$
$44$	2.78162	+	3.95318i	0.419345	+	0.595964i
$45$	1.78555			0.266175
$46$	5.03070	+	4.54885i	0.741736	+	0.670692i
$47$			8.18846i			1.19441i	0.802089	+	0.597205i	$0.203722\pi$
$47$			8.18846i			1.19441i	−0.802089	+	0.597205i	$0.796278\pi$
$48$	−2.35679	+	3.23196i	−0.340173	+	0.466493i
$49$	4.23237	+	4.88442i	0.604625	+	0.697774i
$50$	1.71819	+	1.90080i	0.242989	+	0.268814i
$51$	−7.05259	+	1.01401i	−0.987561	+	0.141990i
$52$	1.58600	−	6.38050i	0.219939	−	0.884817i
$53$	−4.33438	+	9.49097i	−0.595373	+	1.30369i	0.336767	+	0.941588i	$0.390667\pi$
$53$	−4.33438	+	9.49097i	−0.595373	+	1.30369i	−0.932140	+	0.362097i	$0.882061\pi$
$54$	1.20549	+	0.739451i	0.164047	+	0.100626i
$55$	−4.27152	−	0.614153i	−0.575972	−	0.0828123i
$56$	−1.25607	+	1.64870i	−0.167850	+	0.220316i
$57$	−1.60857	+	5.47828i	−0.213060	+	0.725616i
$58$	−7.44613	−	0.911572i	−0.977725	−	0.119695i
$59$	−3.51432	−	7.69529i	−0.457525	−	1.00184i	−0.988045	−	0.154168i	$-0.950730\pi$
$59$	−3.51432	−	7.69529i	−0.457525	−	1.00184i	0.530519	−	0.847673i	$-0.321997\pi$
$60$	−0.656074	−	3.51032i	−0.0846989	−	0.453181i
$61$	−0.167353	+	0.193136i	−0.0214273	+	0.0247285i	−0.766362	−	0.642409i	$-0.777935\pi$
$61$	−0.167353	+	0.193136i	−0.0214273	+	0.0247285i	0.744935	+	0.667137i	$0.232481\pi$
$62$	3.16441	−	11.6781i	0.401880	−	1.48312i
$63$	0.616467	+	0.396179i	0.0776675	+	0.0499139i
$64$	7.21986	+	3.44581i	0.902483	+	0.430726i
$65$	3.17340	+	4.93791i	0.393612	+	0.612473i
$66$	−2.62952	−	2.18360i	−0.323672	−	0.268783i
$67$	−1.33288	−	4.53936i	−0.162837	−	0.554571i	−0.999971	−	0.00757423i	$-0.997589\pi$
$67$	−1.33288	−	4.53936i	−0.162837	−	0.554571i	0.837134	−	0.546997i	$-0.184229\pi$
$68$	4.58487	+	13.4925i	0.555997	+	1.63621i
$69$	−4.27467	−	2.17421i	−0.514610	−	0.261744i
$70$	−0.301715	−	1.82566i	−0.0360618	−	0.218208i
$71$	0.666125	+	2.26861i	0.0790545	+	0.269235i	0.989530	−	0.144328i	$-0.0461022\pi$
$71$	0.666125	+	2.26861i	0.0790545	+	0.269235i	−0.910475	+	0.413563i	$0.864284\pi$
$72$	1.01079	−	2.64165i	0.119123	−	0.311321i
$73$	−13.1263	+	8.43579i	−1.53632	+	0.987334i	−0.547740	+	0.836648i	$0.684512\pi$
$73$	−13.1263	+	8.43579i	−1.53632	+	0.987334i	−0.988582	+	0.150686i	$0.951852\pi$
$74$	8.98343	−	2.84383i	1.04430	−	0.330589i
$75$	−1.52418	−	0.979532i	−0.175997	−	0.113107i
$76$	11.3611	+	1.14947i	1.30321	+	0.131853i
$77$	−1.33849	−	1.15981i	−0.152535	−	0.132172i
$78$	0.0975454	+	4.64797i	0.0110448	+	0.526279i
$79$	−3.31296	−	7.25437i	−0.372737	−	0.816181i	−0.999322	−	0.0368272i	$-0.988275\pi$
$79$	−3.31296	−	7.25437i	−0.372737	−	0.816181i	0.626584	−	0.779354i	$-0.284452\pi$
$80$	−6.66009	+	2.57963i	−0.744620	+	0.288411i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−6.26285	+	4.21315i	−0.691616	+	0.465265i
$83$	−4.54852	−	0.653978i	−0.499265	−	0.0717835i	−0.111918	−	0.993717i	$-0.535699\pi$
$83$	−4.54852	−	0.653978i	−0.499265	−	0.0717835i	−0.387347	+	0.921934i	$0.626608\pi$
$84$	0.552361	−	1.35752i	0.0602675	−	0.148117i
$85$	−11.5726	−	5.28503i	−1.25522	−	0.573242i
$86$	9.77026	+	4.21647i	1.05355	+	0.454674i
$87$	5.25053	−	0.754912i	0.562916	−	0.0809351i
$88$	−3.32669	+	5.97187i	−0.354626	+	0.636603i
$89$	11.4479	−	9.91962i	1.21347	−	1.05148i	0.216298	−	0.976327i	$-0.430602\pi$
$89$	11.4479	−	9.91962i	1.21347	−	1.05148i	0.997172	−	0.0751506i	$-0.0239438\pi$
$90$	1.09695	+	2.27445i	0.115629	+	0.239748i
$91$			2.40894i			0.252526i
$92$	−2.70375	+	9.20270i	−0.281885	+	0.959448i
$93$			8.55543i			0.887157i
$94$	−10.4305	+	5.03056i	−1.07582	+	0.518863i
$95$	−7.70466	+	6.67613i	−0.790481	+	0.684956i
$96$	−5.56477	−	1.01654i	−0.567952	−	0.103750i
$97$	−1.40732	+	0.202343i	−0.142892	+	0.0205448i	−0.213390	−	0.976967i	$-0.568450\pi$
$97$	−1.40732	+	0.202343i	−0.142892	+	0.0205448i	0.0704975	+	0.997512i	$0.477541\pi$
$98$	−3.62164	+	8.39194i	−0.365841	+	0.847714i
$99$	2.19846	+	1.00400i	0.220954	+	0.100906i
$100$	−1.36568	+	3.35639i	−0.136568	+	0.335639i
$101$	12.8550	+	1.84826i	1.27912	+	0.183909i	0.748176	−	0.663500i	$-0.230930\pi$
$101$	12.8550	+	1.84826i	1.27912	+	0.183909i	0.530940	+	0.847409i	$0.321839\pi$
$102$	−5.62440	−	8.36067i	−0.556898	−	0.827830i
$103$	−11.1369	−	3.27008i	−1.09735	−	0.322210i	−0.317549	−	0.948242i	$-0.602860\pi$
$103$	−11.1369	−	3.27008i	−1.09735	−	0.322210i	−0.779798	+	0.626032i	$0.784678\pi$
$104$	9.10187	−	1.89959i	0.892512	−	0.186271i
$105$	0.543548	+	1.19020i	0.0530449	+	0.116152i
$106$	−14.7525	+	0.309605i	−1.43289	+	0.0300715i
$107$	5.23879	+	4.53944i	0.506453	+	0.438844i	0.870233	−	0.492641i	$-0.163968\pi$
$107$	5.23879	+	4.53944i	0.506453	+	0.438844i	−0.363780	+	0.931485i	$0.618514\pi$
$108$	−0.201323	+	1.98984i	−0.0193724	+	0.191473i
$109$	3.31263	+	2.12890i	0.317292	+	0.203911i	0.689586	−	0.724203i	$-0.257792\pi$
$109$	3.31263	+	2.12890i	0.317292	+	0.203911i	−0.372294	+	0.928115i	$0.621429\pi$
$110$	−1.84189	−	5.81839i	−0.175618	−	0.554762i
$111$	−5.60522	+	3.60225i	−0.532024	+	0.341911i
$112$	−2.87178	−	0.587118i	−0.271358	−	0.0554775i
$113$	3.93621	+	13.4055i	0.370287	+	1.26108i	0.908362	+	0.418185i	$0.137334\pi$
$113$	3.93621	+	13.4055i	0.370287	+	1.26108i	−0.538075	+	0.842897i	$0.680848\pi$
$114$	−7.96648	+	1.31657i	−0.746129	+	0.123308i
$115$	−4.32213	−	7.39242i	−0.403041	−	0.689346i
$116$	−3.41335	−	10.0449i	−0.316922	−	0.932649i
$117$	−0.926149	−	3.15417i	−0.0856225	−	0.291603i
$118$	7.64327	−	9.20414i	0.703620	−	0.847309i
$119$	−2.82282	−	4.39240i	−0.258768	−	0.402651i
$120$	4.06841	−	2.99227i	0.371393	−	0.273156i
$121$	4.33981	+	2.78903i	0.394528	+	0.253548i
$122$	−0.348830	−	0.0945224i	−0.0315816	−	0.00855766i
$123$	3.49520	−	4.03368i	0.315152	−	0.363704i
$124$	16.8196	−	3.14356i	1.51045	−	0.282300i
$125$	−5.05262	−	11.0637i	−0.451920	−	0.989567i
$126$	−0.125930	+	1.02865i	−0.0112187	+	0.0916394i
$127$	−2.19557	+	7.47742i	−0.194825	+	0.663514i	0.802901	+	0.596113i	$0.203289\pi$
$127$	−2.19557	+	7.47742i	−0.194825	+	0.663514i	−0.997726	+	0.0674012i	$0.978529\pi$
$128$	0.0462224	+	11.3136i	0.00408552	+	0.999992i
$129$	−7.44792	−	1.07085i	−0.655753	−	0.0942831i
$130$	−4.34036	+	7.07589i	−0.380675	+	0.620597i
$131$	−1.67053	+	3.65794i	−0.145955	+	0.319596i	−0.968463	−	0.249157i	$-0.919847\pi$
$131$	−1.67053	+	3.65794i	−0.145955	+	0.319596i	0.822509	+	0.568753i	$0.192574\pi$
$132$	1.16604	−	4.69099i	0.101491	−	0.408298i
$133$	−4.14135	+	0.595437i	−0.359101	+	0.0516309i
$134$	4.96341	−	4.48657i	0.428773	−	0.387581i
$135$	−1.16929	−	1.34943i	−0.100636	−	0.116141i
$136$	−14.3701	+	14.1293i	−1.23223	+	1.21158i
$137$		−	9.86383i		−	0.842724i	−0.906892	−	0.421362i	$-0.861552\pi$
$137$		−	9.86383i		−	0.842724i	0.906892	−	0.421362i	$-0.138448\pi$
$138$	0.143387	−	6.78081i	0.0122059	−	0.577221i
$139$	−4.59149			−0.389445			−0.194722	−	0.980858i	$-0.562381\pi$
$139$	−4.59149			−0.389445			−0.194722	+	0.980858i	$0.562381\pi$
$140$	2.14017	−	1.50592i	0.180878	−	0.127273i
$141$	6.18842	−	5.36230i	0.521159	−	0.451587i
$142$	−2.48054	+	2.24223i	−0.208162	+	0.188164i
$143$	1.13070	+	7.86418i	0.0945538	+	0.657636i
$144$	3.98592	−	0.335344i	0.332160	−	0.0279453i
$145$	8.61558	+	3.93461i	0.715485	+	0.326751i
$146$	−18.8097	−	11.5379i	−1.55670	−	0.954882i
$147$	0.919782	−	6.39723i	0.0758624	−	0.527634i
$148$	9.14143	+	9.69603i	0.751421	+	0.797009i
$149$	12.0981	+	3.55232i	0.991113	+	0.291017i	0.736804	−	0.676106i	$-0.236334\pi$
$149$	12.0981	+	3.55232i	0.991113	+	0.291017i	0.254309	+	0.967123i	$0.418152\pi$
$150$	0.311354	−	2.54328i	0.0254220	−	0.207658i
$151$	17.7649	−	8.11296i	1.44569	−	0.660223i	0.470662	−	0.882314i	$-0.344015\pi$
$151$	17.7649	−	8.11296i	1.44569	−	0.660223i	0.975026	+	0.222090i	$0.0712880\pi$
$152$	5.51548	+	15.1780i	0.447365	+	1.23110i
$153$	5.38480	+	4.66596i	0.435336	+	0.377220i
$154$	0.655068	−	2.41749i	0.0527869	−	0.194807i
$155$	−8.25893	+	12.8511i	−0.663373	+	1.03223i
$156$	−5.86067	+	2.97972i	−0.469229	+	0.238569i
$157$	−10.8216	+	6.95459i	−0.863654	+	0.555037i	−0.895805	−	0.444446i	$-0.853400\pi$
$157$	−10.8216	+	6.95459i	−0.863654	+	0.555037i	0.0321517	+	0.999483i	$0.489764\pi$
$158$	7.20534	−	8.67677i	0.573226	−	0.690287i
$159$	10.0112	−	2.93956i	0.793941	−	0.233122i
$160$	−7.37755	−	6.89885i	−0.583247	−	0.545402i
$161$	0.148004	−	3.51125i	0.0116643	−	0.276725i
$162$	−0.230590	−	1.39529i	−0.0181169	−	0.109624i
$163$	18.3772	−	5.39602i	1.43941	−	0.422649i	0.533385	−	0.845872i	$-0.320920\pi$
$163$	18.3772	−	5.39602i	1.43941	−	0.422649i	0.906025	+	0.423223i	$0.139101\pi$
$164$	−9.21430	−	5.38930i	−0.719516	−	0.420834i
$165$	2.33311	+	3.63039i	0.181632	+	0.282625i
$166$	−1.96133	−	6.19569i	−0.152229	−	0.480879i
$167$	7.03954	−	10.9537i	0.544736	−	0.847626i	−0.454330	−	0.890833i	$-0.650121\pi$
$167$	7.03954	−	10.9537i	0.544736	−	0.847626i	0.999066	+	0.0432076i	$0.0137577\pi$
$168$	2.06855	−	0.130389i	0.159592	−	0.0100598i
$169$	−1.43640	+	1.65769i	−0.110492	+	0.127515i
$170$	−0.377510	−	17.9881i	−0.0289537	−	1.37962i
$171$	5.19360	−	2.37184i	0.397164	−	0.181379i
$172$	0.631380	+	15.0358i	0.0481423	+	1.14647i
$173$	2.55028	−	8.68545i	0.193894	−	0.660343i	−0.803949	−	0.594698i	$-0.797271\pi$
$173$	2.55028	−	8.68545i	0.193894	−	0.660343i	0.997843	−	0.0656445i	$-0.0209103\pi$
$174$	4.18726	+	6.22436i	0.317435	+	0.471868i
$175$	0.188948	−	1.31416i	0.0142831	−	0.0993415i
$176$	−9.65073	−	0.568750i	−0.727451	−	0.0428711i
$177$	−3.51432	+	7.69529i	−0.264152	+	0.578413i
$178$	19.6686	+	8.48823i	1.47423	+	0.636219i
$179$	0.553217	+	3.84771i	0.0413494	+	0.287591i	0.999996	+	0.00299057i	$0.000951929\pi$
$179$	0.553217	+	3.84771i	0.0413494	+	0.287591i	−0.958646	+	0.284601i	$0.908139\pi$
$180$	−2.22329	+	2.79460i	−0.165714	+	0.208297i
$181$	−7.41254	−	8.55452i	−0.550970	−	0.635853i	0.410139	−	0.912023i	$-0.365480\pi$
$181$	−7.41254	−	8.55452i	−0.550970	−	0.635853i	−0.961109	+	0.276170i	$0.910935\pi$
$182$	−3.06852	+	1.47993i	−0.227454	+	0.109700i
$183$	0.255555			0.0188912
$184$	−13.3835	+	2.20961i	−0.986643	+	0.162895i
$185$	−11.8970			−0.874687
$186$	−10.8979	+	5.25601i	−0.799076	+	0.385389i
$187$	−11.2770	−	13.0144i	−0.824657	−	0.951705i
$188$	−12.8159	−	10.1959i	−0.934696	−	0.743612i
$189$	−0.104288	−	0.725337i	−0.00758582	−	0.0527605i
$190$	−13.2374	−	5.71276i	−0.960343	−	0.414447i
$191$	3.99534	−	8.74857i	0.289092	−	0.633024i	−0.708244	−	0.705968i	$-0.750512\pi$
$191$	3.99534	−	8.74857i	0.289092	−	0.633024i	0.997336	+	0.0729441i	$0.0232395\pi$
$192$	−2.12384	−	7.71293i	−0.153275	−	0.556633i
$193$	−2.78508	+	19.3706i	−0.200474	+	1.39433i	0.602406	+	0.798190i	$0.294209\pi$
$193$	−2.78508	+	19.3706i	−0.200474	+	1.39433i	−0.802881	+	0.596140i	$0.796700\pi$
$194$	−1.12233	−	1.66835i	−0.0805787	−	0.119780i
$195$	1.65369	−	5.63194i	0.118423	−	0.403312i
$196$	−12.9146	+	0.542310i	−0.922474	+	0.0387364i
$197$	0.0366925	−	0.0167569i	0.00261423	−	0.00119388i	−0.414107	−	0.910228i	$-0.635906\pi$
$197$	0.0366925	−	0.0167569i	0.00261423	−	0.00119388i	0.416722	+	0.909034i	$0.363179\pi$
$198$	0.0717160	+	3.41722i	0.00509664	+	0.242851i
$199$	−2.19562	+	2.53388i	−0.155643	+	0.179622i	−0.828216	−	0.560409i	$-0.810644\pi$
$199$	−2.19562	+	2.53388i	−0.155643	+	0.179622i	0.672573	+	0.740031i	$0.265189\pi$
$200$	−5.11439	+	0.322381i	−0.361642	+	0.0227958i
$201$	−2.55777	+	3.97997i	−0.180411	+	0.280726i
$202$	5.54309	+	17.5102i	0.390010	+	1.23201i
$203$	2.10154	+	3.27006i	0.147499	+	0.229513i
$204$	7.19452	−	12.3007i	0.503717	−	0.861224i
$205$	9.14403	−	2.68493i	0.638647	−	0.187524i
$206$	−2.67647	−	16.1951i	−0.186478	−	1.12837i
$207$	1.15615	+	4.65439i	0.0803582	+	0.323502i
$208$	8.01142	+	10.4270i	0.555492	+	0.722981i
$209$	−13.2403	+	3.88770i	−0.915850	+	0.268918i
$210$	−1.18216	+	1.42357i	−0.0815768	+	0.0982359i
$211$	−11.9973	+	7.71023i	−0.825932	+	0.530794i	−0.883983	−	0.467520i	$-0.845148\pi$
$211$	−11.9973	+	7.71023i	−0.825932	+	0.530794i	0.0580511	+	0.998314i	$0.481511\pi$
$212$	−9.45752	−	18.6015i	−0.649545	−	1.27756i
$213$	1.27829	−	1.98905i	0.0875867	−	0.136287i
$214$	−2.56392	+	9.46199i	−0.175266	+	0.646808i
$215$	−10.1538	−	8.79833i	−0.692484	−	0.600041i
$216$	−2.65835	+	0.966008i	−0.180878	+	0.0657285i
$217$	−5.70283	+	2.60440i	−0.387133	+	0.176798i
$218$	−0.676692	+	5.52752i	−0.0458313	+	0.374371i
$219$	14.9713	+	4.39596i	1.01166	+	0.297052i
$220$	6.27993	−	5.92072i	0.423392	−	0.399175i
$221$	−3.33339	+	23.1842i	−0.224228	+	1.55954i
$222$	−8.03212	−	4.92691i	−0.539081	−	0.330673i
$223$	3.56778	+	1.62935i	0.238916	+	0.109109i	0.531275	−	0.847199i	$-0.321713\pi$
$223$	3.56778	+	1.62935i	0.238916	+	0.109109i	−0.292359	+	0.956309i	$0.594440\pi$
$224$	−1.01640	−	4.01878i	−0.0679110	−	0.268516i
$225$	0.257846	+	1.79336i	0.0171897	+	0.119557i
$226$	−14.6578	+	13.2496i	−0.975020	+	0.881349i
$227$	−1.76403	+	1.52854i	−0.117083	+	0.101453i	−0.711434	−	0.702752i	$-0.751954\pi$
$227$	−1.76403	+	1.52854i	−0.117083	+	0.101453i	0.594352	+	0.804205i	$0.297409\pi$
$228$	−6.57124	−	9.33890i	−0.435191	−	0.618484i
$229$	18.3520			1.21274			0.606368	−	0.795184i	$-0.292626\pi$
$229$	18.3520			1.21274			0.606368	+	0.795184i	$0.292626\pi$
$230$	6.76119	−	10.0471i	0.445820	−	0.662484i
$231$			1.77107i			0.116528i
$232$	10.6983	−	10.5190i	0.702378	−	0.690608i
$233$	−8.67837	−	10.0154i	−0.568539	−	0.656129i	0.396562	−	0.918008i	$-0.370203\pi$
$233$	−8.67837	−	10.0154i	−0.568539	−	0.656129i	−0.965101	+	0.261879i	$0.915658\pi$
$234$	3.44882	−	3.11749i	0.225456	−	0.203797i
$235$	14.4721	−	2.08078i	0.944057	−	0.135735i
$236$	16.4199	+	4.08149i	1.06884	+	0.265682i
$237$	−3.31296	+	7.25437i	−0.215200	+	0.471222i
$238$	3.86086	−	6.29419i	0.250262	−	0.407992i
$239$	27.2287	+	3.91490i	1.76128	+	0.253234i	0.945614	−	0.325290i	$-0.105462\pi$
$239$	27.2287	+	3.91490i	1.76128	+	0.253234i	0.815665	+	0.578524i	$0.196371\pi$
$240$	6.31098	+	3.34406i	0.407372	+	0.215858i
$241$	3.89118	−	13.2521i	0.250653	−	0.853646i	−0.734004	−	0.679145i	$-0.762351\pi$
$241$	3.89118	−	13.2521i	0.250653	−	0.853646i	0.984657	−	0.174501i	$-0.0558311\pi$
$242$	−0.886521	+	7.24150i	−0.0569877	+	0.465501i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	−0.0938998	−	0.502410i	−0.00601132	−	0.0321635i
$245$	7.55713	−	8.72139i	0.482807	−	0.557189i
$246$	7.28538	+	1.97412i	0.464499	+	0.125865i
$247$	15.7897	+	10.1474i	1.00467	+	0.645664i
$248$	14.3374	+	19.4937i	0.910424	+	1.23785i
$249$	2.48440	+	3.86581i	0.157443	+	0.244986i
$250$	10.9889	−	13.2330i	0.695000	−	0.836929i
$251$	5.37827	+	18.3167i	0.339473	+	1.15614i	0.935545	+	0.353209i	$0.114909\pi$
$251$	5.37827	+	18.3167i	0.339473	+	1.15614i	−0.596071	+	0.802932i	$0.703272\pi$
$252$	−1.38766	+	0.471539i	−0.0874146	+	0.0297042i
$253$	−1.16492	−	11.5322i	−0.0732381	−	0.725024i
$254$	−10.8736	+	1.79701i	−0.682271	+	0.112755i
$255$	3.58428	+	12.2069i	0.224456	+	0.764428i
$256$	−14.3829	+	7.00937i	−0.898933	+	0.438086i
$257$	13.6875	−	8.79644i	0.853805	−	0.548707i	−0.0389545	−	0.999241i	$-0.512403\pi$
$257$	13.6875	−	8.79644i	0.853805	−	0.548707i	0.892759	+	0.450534i	$0.148766\pi$
$258$	−3.21156	−	10.1451i	−0.199943	−	0.631604i
$259$	−4.10748	−	2.63972i	−0.255226	−	0.164024i
$260$	−11.6798	−	1.18171i	−0.724350	−	0.0732865i
$261$	−4.00889	−	3.47372i	−0.248144	−	0.215018i
$262$	−5.68579	+	0.119326i	−0.351269	+	0.00737198i
$263$	0.968677	+	2.12111i	0.0597312	+	0.130793i	0.937144	−	0.348944i	$-0.113459\pi$
$263$	0.968677	+	2.12111i	0.0597312	+	0.130793i	−0.877413	+	0.479737i	$0.840732\pi$
$264$	6.69175	−	1.39659i	0.411849	−	0.0859545i
$265$	17.8756	+	5.24874i	1.09809	+	0.322427i
$266$	−3.30270	−	4.90947i	−0.202502	−	0.301019i
$267$	−14.9935	−	2.15574i	−0.917587	−	0.131929i
$268$	8.76427	+	3.56609i	0.535363	+	0.217834i
$269$	11.6111	+	5.30262i	0.707943	+	0.323307i	0.736643	−	0.676282i	$-0.236410\pi$
$269$	11.6111	+	5.30262i	0.707943	+	0.323307i	−0.0287007	+	0.999588i	$0.509137\pi$
$270$	1.00056	−	2.31847i	0.0608922	−	0.141097i
$271$	16.8764	−	2.42646i	1.02517	−	0.147397i	0.390838	−	0.920459i	$-0.372185\pi$
$271$	16.8764	−	2.42646i	1.02517	−	0.147397i	0.634330	+	0.773062i	$0.281276\pi$
$272$	−26.8263	−	9.62440i	−1.62658	−	0.583565i
$273$	1.82056	−	1.57752i	0.110185	−	0.0954760i
$274$	12.5646	−	6.05982i	0.759055	−	0.366087i
$275$		−	4.37888i		−	0.264056i
$276$	8.72552	−	3.98313i	0.525214	−	0.239756i
$277$			1.75816i			0.105637i	0.998604	+	0.0528187i	$0.0168205\pi$
$277$			1.75816i			0.105637i	−0.998604	+	0.0528187i	$0.983179\pi$
$278$	−2.82077	−	5.84866i	−0.169179	−	0.350779i
$279$	6.46576	−	5.60261i	0.387095	−	0.335420i
$280$	3.23305	+	1.80101i	0.193212	+	0.107631i
$281$	20.5947	−	2.96107i	1.22858	−	0.176643i	0.502696	−	0.864463i	$-0.332342\pi$
$281$	20.5947	−	2.96107i	1.22858	−	0.176643i	0.725881	+	0.687821i	$0.241432\pi$
$282$	10.6324	+	4.58852i	0.633148	+	0.273243i
$283$	22.5738	+	10.3091i	1.34188	+	0.612814i	0.951445	−	0.307818i	$-0.0995988\pi$
$283$	22.5738	+	10.3091i	1.34188	+	0.612814i	0.390431	+	0.920632i	$0.372326\pi$
$284$	−4.38008	−	1.78221i	−0.259910	−	0.105755i
$285$	10.0910	+	1.45086i	0.597737	+	0.0859416i
$286$	−9.32279	+	6.27163i	−0.551268	+	0.370849i
$287$	3.75273	+	1.10190i	0.221517	+	0.0650432i
$288$	2.87590	+	4.87126i	0.169464	+	0.287042i
$289$	−14.0274	−	30.7158i	−0.825144	−	1.80681i
$290$	0.281049	+	13.3918i	0.0165038	+	0.786393i
$291$	1.07452	+	0.931079i	0.0629896	+	0.0545808i
$292$	3.14131	−	31.0481i	0.183831	−	1.81695i
$293$	−12.4093	−	7.97500i	−0.724961	−	0.465904i	0.125398	−	0.992107i	$-0.459979\pi$
$293$	−12.4093	−	7.97500i	−0.724961	−	0.465904i	−0.850360	+	0.526202i	$0.823616\pi$
$294$	8.71388	−	2.75850i	0.508204	−	0.160879i
$295$	−12.7075	+	8.16659i	−0.739857	+	0.475477i
$296$	−6.73482	+	17.6011i	−0.391454	+	1.02304i
$297$	−0.680911	−	2.31897i	−0.0395105	−	0.134560i
$298$	2.90747	+	17.5929i	0.168425	+	1.01913i
$299$	−10.8168	+	11.4694i	−0.625553	+	0.663293i
$300$	3.43092	−	1.16586i	0.198084	−	0.0673107i
$301$	−1.55345	−	5.29058i	−0.0895396	−	0.304944i
$302$	21.2482	+	17.6448i	1.22269	+	1.01535i
$303$	−7.02138	−	10.9255i	−0.403368	−	0.627653i
$304$	−15.9454	+	16.3502i	−0.914531	+	0.937749i
$305$	0.383870	+	0.246698i	0.0219803	+	0.0141259i
$306$	−2.63538	+	9.72571i	−0.150654	+	0.555982i
$307$	−0.579831	+	0.669161i	−0.0330927	+	0.0381910i	−0.772055	−	0.635556i	$-0.780771\pi$
$307$	−0.579831	+	0.669161i	−0.0330927	+	0.0381910i	0.738962	+	0.673747i	$0.235316\pi$
$308$	3.48185	−	0.650753i	0.198397	−	0.0370801i
$309$	4.82173	+	10.5581i	0.274299	+	0.600630i
$310$	−21.4437	−	2.62518i	−1.21792	−	0.149100i
$311$	2.01628	−	6.86683i	0.114333	−	0.389382i	−0.882366	−	0.470563i	$-0.844051\pi$
$311$	2.01628	−	6.86683i	0.114333	−	0.389382i	0.996699	+	0.0811806i	$0.0258691\pi$
$312$	−7.39607	−	5.63476i	−0.418720	−	0.319006i
$313$	−3.99733	−	0.574729i	−0.225942	−	0.0324856i	0.0284137	−	0.999596i	$-0.490954\pi$
$313$	−3.99733	−	0.574729i	−0.225942	−	0.0324856i	−0.254356	+	0.967111i	$0.581864\pi$
$314$	−15.5070	−	9.51200i	−0.875109	−	0.536793i
$315$	0.543548	−	1.19020i	0.0306255	−	0.0670604i
$316$	15.4791	+	3.84763i	0.870767	+	0.216446i
$317$	25.6535	−	3.68842i	1.44084	−	0.207162i	0.622829	−	0.782358i	$-0.285983\pi$
$317$	25.6535	−	3.68842i	1.44084	−	0.207162i	0.818016	+	0.575196i	$0.195074\pi$
$318$	9.89479	+	10.9464i	0.554872	+	0.613845i
$319$	8.39553	+	9.68896i	0.470060	+	0.542478i
$320$	4.25541	−	13.6359i	0.237884	−	0.762267i
$321$		−	6.93191i		−	0.386902i
$322$	4.56357	−	1.96860i	0.254318	−	0.109706i
$323$	−40.6813			−2.26357
$324$	1.63566	−	1.15092i	0.0908700	−	0.0639399i
$325$	−4.50123	+	3.90034i	−0.249683	+	0.216352i
$326$	18.1634	+	20.0939i	1.00598	+	1.11290i
$327$	−0.560397	−	3.89765i	−0.0309900	−	0.215540i
$328$	1.20414	−	15.0481i	0.0664872	−	0.830893i
$329$	5.45822	+	2.49268i	0.300921	+	0.137426i
$330$	−3.19106	+	5.20224i	−0.175662	+	0.286374i
$331$	2.22622	−	15.4837i	0.122364	−	0.851062i	−0.832501	−	0.554023i	$-0.813092\pi$
$331$	2.22622	−	15.4837i	0.122364	−	0.851062i	0.954865	−	0.297039i	$-0.0959991\pi$
$332$	6.68716	−	6.30466i	0.367005	−	0.346013i
$333$	6.39304	+	1.87717i	0.350336	+	0.102868i
$334$	18.2776	+	2.23759i	1.00011	+	0.122435i
$335$	−7.68408	+	3.50920i	−0.419826	+	0.191728i
$336$	1.43690	+	2.55483i	0.0783894	+	0.139377i
$337$	−9.47722	−	8.21206i	−0.516257	−	0.447339i	0.357351	−	0.933970i	$-0.383680\pi$
$337$	−9.47722	−	8.21206i	−0.516257	−	0.447339i	−0.873608	+	0.486631i	$0.838226\pi$
$338$	−2.99403	−	0.811292i	−0.162854	−	0.0441285i
$339$	7.55352	−	11.7535i	0.410251	−	0.638363i
$340$	22.6813	−	11.5318i	1.23007	−	0.625400i
$341$	−17.3949	+	11.1790i	−0.941986	+	0.605378i
$342$	6.21193	+	5.15849i	0.335903	+	0.278939i
$343$	9.46601	−	2.77947i	0.511116	−	0.150077i
$344$	−18.7647	+	10.0414i	−1.01173	+	0.541399i
$345$	−2.75642	+	8.10745i	−0.148401	+	0.436491i
$346$	12.6303	−	2.08733i	0.679010	−	0.112216i
$347$	−0.951142	+	0.279281i	−0.0510600	+	0.0149926i	−0.307163	−	0.951657i	$-0.599380\pi$
$347$	−0.951142	+	0.279281i	−0.0510600	+	0.0149926i	0.256103	+	0.966650i	$0.417561\pi$
$348$	−5.35619	+	9.15767i	−0.287122	+	0.490903i
$349$	−0.248640	−	0.386891i	−0.0133094	−	0.0207098i	0.834535	−	0.550955i	$-0.185736\pi$
$349$	−0.248640	−	0.386891i	−0.0133094	−	0.0207098i	−0.847844	+	0.530245i	$0.822100\pi$
$350$	1.79007	−	0.566671i	0.0956831	−	0.0302898i
$351$	−1.77727	+	2.76548i	−0.0948635	+	0.147610i
$352$	−5.20443	−	12.6426i	−0.277397	−	0.673850i
$353$	19.6888	−	22.7221i	1.04793	−	1.20937i	0.0706302	−	0.997503i	$-0.477499\pi$
$353$	19.6888	−	22.7221i	1.04793	−	1.20937i	0.977298	−	0.211871i	$-0.0679556\pi$
$354$	−11.9613	+	0.251028i	−0.635736	+	0.0133420i
$355$	3.84023	−	1.75378i	0.203818	−	0.0930807i
$356$	1.27104	+	30.2687i	0.0673649	+	1.60424i
$357$	−1.47100	+	5.00976i	−0.0778535	+	0.265145i
$358$	−4.56136	+	3.06852i	−0.241075	+	0.162176i
$359$	1.65227	−	11.4918i	0.0872035	−	0.606514i	−0.898620	−	0.438728i	$-0.855429\pi$
$359$	1.65227	−	11.4918i	0.0872035	−	0.606514i	0.985823	−	0.167786i	$-0.0536617\pi$
$360$	−4.92565	−	1.11518i	−0.259604	−	0.0587750i
$361$	−5.64926	+	12.3701i	−0.297329	+	0.651060i
$362$	6.34291	−	14.6976i	0.333376	−	0.772487i
$363$	−0.734166	−	5.10623i	−0.0385337	−	0.268008i
$364$	−3.77028	−	2.99950i	−0.197616	−	0.157217i
$365$	18.2448	+	21.0556i	0.954976	+	1.10210i
$366$	0.157000	+	0.325527i	0.00820650	+	0.0170156i
$367$	−25.4620			−1.32911			−0.664554	−	0.747241i	$-0.731378\pi$
$367$	−25.4620			−1.32911			−0.664554	+	0.747241i	$0.731378\pi$
$368$	−11.0367	−	15.6905i	−0.575329	−	0.817922i
$369$	−5.33732			−0.277850
$370$	−7.30891	−	15.1545i	−0.379972	−	0.787844i
$371$	5.00699	+	5.77838i	0.259950	+	0.299998i
$372$	−13.3903	−	10.6528i	−0.694252	−	0.552323i
$373$	−0.760038	−	5.28618i	−0.0393533	−	0.273708i	0.960638	−	0.277802i	$-0.0896059\pi$
$373$	−0.760038	−	5.28618i	−0.0393533	−	0.273708i	−0.999992	+	0.00409395i	$0.998697\pi$
$374$	9.64975	−	22.3601i	0.498977	−	1.15621i
$375$	−5.05262	+	11.0637i	−0.260916	+	0.571327i
$376$	5.11414	−	22.5888i	0.263742	−	1.16493i
$377$	2.48165	−	17.2602i	0.127811	−	0.888947i
$378$	0.859868	−	0.578451i	0.0442269	−	0.0297523i
$379$	−1.00526	+	3.42360i	−0.0516367	+	0.175858i	−0.981274	−	0.192618i	$-0.938302\pi$
$379$	−1.00526	+	3.42360i	−0.0516367	+	0.175858i	0.929637	+	0.368476i	$0.120120\pi$
$380$	−0.855437	−	20.3715i	−0.0438830	−	1.04504i
$381$	7.08885	−	3.23737i	0.363173	−	0.165856i
$382$	13.5985	−	0.285387i	0.695759	−	0.0146017i
$383$	−24.6566	+	28.4552i	−1.25989	+	1.45400i	−0.423472	+	0.905909i	$0.639189\pi$
$383$	−24.6566	+	28.4552i	−1.25989	+	1.45400i	−0.836422	+	0.548086i	$0.815357\pi$
$384$	8.51999	−	7.44377i	0.434784	−	0.379864i
$385$	−1.70969	+	2.66033i	−0.0871340	+	0.135583i
$386$	−26.3854	+	8.35267i	−1.34298	+	0.425140i
$387$	4.06806	+	6.33002i	0.206791	+	0.321773i
$388$	1.43565	−	2.45458i	0.0728838	−	0.124612i
$389$	1.92753	−	0.565975i	0.0977298	−	0.0286961i	−0.232502	−	0.972596i	$-0.574691\pi$
$389$	1.92753	−	0.565975i	0.0977298	−	0.0286961i	0.330232	+	0.943900i	$0.392873\pi$
$390$	8.18993	−	1.35350i	0.414713	−	0.0685370i
$391$	6.28313	−	33.5882i	0.317751	−	1.69863i
$392$	−8.62488	−	16.1176i	−0.435622	−	0.814059i
$393$	3.85845	−	1.13294i	0.194633	−	0.0571495i
$394$	0.0438869	+	0.0364445i	0.00221099	+	0.00183605i
$395$	−11.9794	+	7.69867i	−0.602748	+	0.387362i
$396$	−4.30881	+	2.19071i	−0.216526	+	0.110087i
$397$	−14.4963	+	22.5567i	−0.727549	+	1.13209i	0.258561	+	0.965995i	$0.416752\pi$
$397$	−14.4963	+	22.5567i	−0.727549	+	1.13209i	−0.986110	+	0.166093i	$0.946885\pi$
$398$	−4.57653	−	1.24010i	−0.229401	−	0.0621608i
$399$	3.16201	+	2.73990i	0.158299	+	0.137167i
$400$	−3.55266	−	6.31667i	−0.177633	−	0.315834i
$401$	−19.0618	+	8.70525i	−0.951903	+	0.434720i	−0.829963	−	0.557818i	$-0.811639\pi$
$401$	−19.0618	+	8.70525i	−0.951903	+	0.434720i	−0.121940	+	0.992538i	$0.538911\pi$
$402$	−6.64107	−	0.813014i	−0.331226	−	0.0405495i
$403$	26.9853	+	7.92360i	1.34423	+	0.394703i
$404$	−18.8991	+	17.8182i	−0.940268	+	0.886486i
$405$	−0.254111	+	1.76738i	−0.0126269	+	0.0878218i
$406$	−2.87434	+	4.68591i	−0.142651	+	0.232558i
$407$	−14.6482	−	6.68961i	−0.726085	−	0.331592i
$408$	20.0887	+	1.60747i	0.994537	+	0.0795819i
$409$	−1.63345	−	11.3609i	−0.0807690	−	0.561761i	−0.989517	−	0.144416i	$-0.953870\pi$
$409$	−1.63345	−	11.3609i	−0.0807690	−	0.561761i	0.908748	−	0.417345i	$-0.137039\pi$
$410$	9.03769	+	9.99822i	0.446340	+	0.493777i
$411$	−7.45459	+	6.45944i	−0.367708	+	0.318621i
$412$	18.9852	−	13.3587i	0.935331	−	0.658138i
$413$	−6.19929			−0.305047
$414$	−5.21850	+	4.33212i	−0.256475	+	0.212912i
$415$			8.20514i			0.402775i
$416$	−8.36013	+	16.6108i	−0.409889	+	0.814410i
$417$	3.00679	+	3.47002i	0.147243	+	0.169927i
$418$	−13.0863	−	14.4771i	−0.640073	−	0.708100i
$419$	2.86265	−	0.411587i	0.139850	−	0.0201073i	−0.0720345	−	0.997402i	$-0.522949\pi$
$419$	2.86265	−	0.411587i	0.139850	−	0.0201073i	0.211884	+	0.977295i	$0.432040\pi$
$420$	−2.53961	−	0.631271i	−0.123920	−	0.0308029i
$421$	11.8500	−	25.9479i	0.577534	−	1.26462i	−0.365154	−	0.930947i	$-0.618984\pi$
$421$	11.8500	−	25.9479i	0.577534	−	1.26462i	0.942688	−	0.333675i	$-0.108289\pi$
$422$	−17.1919	−	10.5455i	−0.836887	−	0.513347i
$423$	−8.10511	−	1.16534i	−0.394084	−	0.0566607i
$424$	17.8845	−	23.4748i	0.868548	−	1.14004i
$425$	3.63696	−	12.3864i	0.176419	−	0.600827i
$426$	3.31897	+	0.406316i	0.160805	+	0.0196861i
$427$	0.0777946	+	0.170346i	0.00376474	+	0.00824364i
$428$	−13.6279	+	2.54703i	−0.658727	+	0.123115i
$429$	5.20290	−	6.00447i	0.251199	−	0.289899i
$430$	4.96937	−	18.3392i	0.239645	−	0.884395i
$431$	0.396883	+	0.255061i	0.0191172	+	0.0122859i	0.550165	−	0.835056i	$-0.314565\pi$
$431$	0.396883	+	0.255061i	0.0191172	+	0.0122859i	−0.531047	+	0.847342i	$0.678201\pi$
$432$	−2.86366	−	2.79275i	−0.137778	−	0.134366i
$433$	6.97508	+	10.8534i	0.335201	+	0.521583i	0.967410	−	0.253215i	$-0.0814880\pi$
$433$	6.97508	+	10.8534i	0.335201	+	0.521583i	−0.632209	+	0.774798i	$0.717852\pi$
$434$	−6.82101	−	5.66428i	−0.327419	−	0.271894i
$435$	−2.66843	−	9.08784i	−0.127941	−	0.435729i
$436$	−7.45671	+	2.53385i	−0.357111	+	0.121349i
$437$	−22.3914	−	15.7608i	−1.07113	−	0.753943i
$438$	3.59797	+	21.7711i	0.171918	+	1.04026i
$439$	−4.00784	−	13.6494i	−0.191284	−	0.651452i	−0.998155	−	0.0607246i	$-0.980659\pi$
$439$	−4.00784	−	13.6494i	−0.191284	−	0.651452i	0.806871	−	0.590728i	$-0.201159\pi$
$440$	11.3999	+	4.36201i	0.543469	+	0.207951i
$441$	−5.43703	+	3.49417i	−0.258906	+	0.166389i
$442$	−31.5800	+	9.99709i	−1.50211	+	0.475513i
$443$	4.67268	+	3.00295i	0.222006	+	0.142674i	0.646916	−	0.762561i	$-0.276058\pi$
$443$	4.67268	+	3.00295i	0.222006	+	0.142674i	−0.424911	+	0.905235i	$0.639695\pi$
$444$	1.34140	−	13.2582i	0.0636602	−	0.629206i
$445$	−20.4408	−	17.7120i	−0.968985	−	0.839630i
$446$	0.116385	+	5.54564i	0.00551097	+	0.262594i
$447$	−5.23790	−	11.4694i	−0.247744	−	0.542484i
$448$	4.49472	−	3.76362i	0.212355	−	0.177814i
$449$	−21.5110	−	6.31621i	−1.01517	−	0.298080i	−0.268502	−	0.963279i	$-0.586529\pi$
$449$	−21.5110	−	6.31621i	−1.01517	−	0.298080i	−0.746666	+	0.665199i	$0.768347\pi$
$450$	−2.12598	+	1.43019i	−0.100220	+	0.0674198i
$451$	12.7683	+	1.83580i	0.601236	+	0.0864447i
$452$	−25.8823	−	10.5313i	−1.21740	−	0.495349i
$453$	−17.7649	−	8.11296i	−0.834668	−	0.381180i
$454$	−3.03079	−	1.30797i	−0.142242	−	0.0613861i
$455$	4.25752	−	0.612139i	0.199595	−	0.0286975i
$456$	7.85890	−	14.1078i	0.368027	−	0.660659i
$457$	−9.82683	+	8.51500i	−0.459680	+	0.398315i	−0.853682	−	0.520795i	$-0.825636\pi$
$457$	−9.82683	+	8.51500i	−0.459680	+	0.398315i	0.394002	+	0.919110i	$0.371090\pi$
$458$	11.2745	+	23.3769i	0.526824	+	1.09233i
$459$		−	7.12512i		−	0.332572i
$460$	16.9517	+	2.44004i	0.790378	+	0.113768i
$461$		−	20.7779i		−	0.967725i	−0.875144	−	0.483862i	$-0.839234\pi$
$461$		−	20.7779i		−	0.967725i	0.875144	−	0.483862i	$-0.160766\pi$
$462$	−2.25600	+	1.08805i	−0.104959	+	0.0506209i
$463$	−28.6614	+	24.8352i	−1.33201	+	1.15419i	−0.356483	+	0.934302i	$0.616024\pi$
$463$	−28.6614	+	24.8352i	−1.33201	+	1.15419i	−0.975525	+	0.219890i	$0.929430\pi$
$464$	19.9717	+	7.16519i	0.927161	+	0.332636i
$465$	15.1207	−	2.17403i	0.701205	−	0.100818i
$466$	7.42609	−	17.2075i	0.344007	−	0.797121i
$467$	28.8645	+	13.1820i	1.33569	+	0.609989i	0.949887	−	0.312593i	$-0.101198\pi$
$467$	28.8645	+	13.1820i	1.33569	+	0.609989i	0.385802	+	0.922582i	$0.373925\pi$
$468$	6.08985	+	2.47790i	0.281503	+	0.114541i
$469$	−3.43157	−	0.493385i	−0.158455	−	0.0227824i
$470$	11.5414	+	17.1563i	0.532366	+	0.791362i
$471$	12.3425	+	3.62410i	0.568714	+	0.166990i
$472$	4.88851	+	23.4232i	0.225012	+	1.07814i
$473$	−7.55464	−	16.5424i	−0.347363	−	0.760618i
$474$	−11.2760	+	0.236645i	−0.517922	+	0.0108695i
$475$	−7.81790	−	6.77425i	−0.358710	−	0.310824i
$476$	10.3895	+	1.05116i	0.476201	+	0.0481799i
$477$	−8.77752	−	5.64097i	−0.401895	−	0.258282i
$478$	11.7411	+	37.0892i	0.537025	+	1.69642i
$479$	1.48269	−	0.952865i	0.0677457	−	0.0435375i	−0.506330	−	0.862340i	$-0.668998\pi$
$479$	1.48269	−	0.952865i	0.0677457	−	0.0435375i	0.574075	+	0.818803i	$0.305362\pi$
$480$	−0.382537	+	10.0934i	−0.0174603	+	0.460697i
$481$	6.17087	+	21.0160i	0.281367	+	0.958249i
$482$	19.2712	−	3.18483i	0.877778	−	0.145065i
$483$	−2.75055	+	2.18752i	−0.125154	+	0.0995358i
$484$	−9.76889	+	3.31955i	−0.444040	+	0.150888i
$485$	0.715233	+	2.43586i	0.0324771	+	0.110607i
$486$	−0.903484	+	1.08799i	−0.0409828	+	0.0493521i
$487$	−0.312500	−	0.486260i	−0.0141607	−	0.0220346i	0.834101	−	0.551612i	$-0.185987\pi$
$487$	−0.312500	−	0.486260i	−0.0141607	−	0.0220346i	−0.848262	+	0.529577i	$0.822351\pi$
$488$	0.582285	−	0.428265i	0.0263588	−	0.0193866i
$489$	−16.1125	−	10.3549i	−0.728634	−	0.468264i
$490$	15.7520	+	4.26833i	0.711605	+	0.192824i
$491$	−20.9589	+	24.1879i	−0.945862	+	1.09158i	0.0498201	+	0.998758i	$0.484135\pi$
$491$	−20.9589	+	24.1879i	−0.945862	+	1.09158i	−0.995682	+	0.0928251i	$0.970410\pi$
$492$	1.96112	+	10.4929i	0.0884139	+	0.473058i
$493$	15.7007	+	34.3798i	0.707126	+	1.54839i
$494$	−3.22546	+	26.3470i	−0.145120	+	1.18541i
$495$	1.21580	−	4.14064i	0.0546463	−	0.186108i
$496$	−16.0230	+	30.2389i	−0.719452	+	1.35777i
$497$	1.71498	+	0.246577i	0.0769273	+	0.0110605i
$498$	−3.39799	+	5.53959i	−0.152268	+	0.248235i
$499$	−9.14772	+	20.0307i	−0.409508	+	0.896698i	0.586709	+	0.809798i	$0.300423\pi$
$499$	−9.14772	+	20.0307i	−0.409508	+	0.896698i	−0.996217	+	0.0869000i	$0.972304\pi$
$500$	23.6073	+	5.86806i	1.05575	+	0.262427i
$501$	−12.8882	+	1.85304i	−0.575802	+	0.0827879i
$502$	−20.0278	+	18.1037i	−0.893883	+	0.808007i
$503$	−24.5086	−	28.2844i	−1.09278	−	1.26114i	−0.962972	−	0.269601i	$-0.913108\pi$
$503$	−24.5086	−	28.2844i	−1.09278	−	1.26114i	−0.129812	−	0.991539i	$-0.541437\pi$
$504$	−1.45316	−	1.47792i	−0.0647287	−	0.0658319i
$505$		−	23.1893i		−	1.03191i
$506$	13.9741	−	8.56867i	0.621225	−	0.380924i
$507$	2.19344			0.0974143
$508$	−8.96923	−	12.7469i	−0.397945	−	0.565551i
$509$	6.37985	−	5.52817i	0.282782	−	0.245032i	−0.501907	−	0.864922i	$-0.667368\pi$
$509$	6.37985	−	5.52817i	0.282782	−	0.245032i	0.784689	+	0.619890i	$0.212823\pi$
$510$	−13.3473	+	12.0650i	−0.591026	+	0.534246i
$511$	1.62723	+	11.3177i	0.0719846	+	0.500664i
$512$	−17.7647	−	14.0148i	−0.785096	−	0.619374i
$513$	−5.19360	−	2.37184i	−0.229303	−	0.104719i
$514$	19.6139	+	12.0312i	0.865130	+	0.530672i
$515$	−2.94947	+	20.5140i	−0.129969	+	0.903955i
$516$	10.9498	−	10.3235i	0.482039	−	0.454467i
$517$	18.9888	+	5.57561i	0.835126	+	0.245215i
$518$	0.839061	−	6.85383i	0.0368662	−	0.301140i
$519$	−8.23411	+	3.76039i	−0.361437	+	0.165063i
$520$	−5.67019	−	15.6037i	−0.248654	−	0.684269i
$521$	4.13075	+	3.57932i	0.180972	+	0.156813i	0.740636	−	0.671907i	$-0.234524\pi$
$521$	4.13075	+	3.57932i	0.180972	+	0.156813i	−0.559664	+	0.828719i	$0.689070\pi$
$522$	1.96199	−	7.24061i	0.0858739	−	0.316913i
$523$	−18.1656	+	28.2662i	−0.794325	+	1.23599i	0.173615	+	0.984814i	$0.444455\pi$
$523$	−18.1656	+	28.2662i	−0.794325	+	1.23599i	−0.967940	+	0.251181i	$0.919181\pi$
$524$	−3.64505	−	7.16927i	−0.159235	−	0.313191i
$525$	−1.11691	+	0.717797i	−0.0487461	+	0.0313272i
$526$	−2.10677	+	2.53700i	−0.0918595	+	0.110619i
$527$	−58.4892	+	17.1740i	−2.54783	+	0.748110i
$528$	5.89005	+	7.66599i	0.256332	+	0.333619i
$529$	16.4711	−	16.0531i	0.716137	−	0.697960i
$530$	4.29595	+	25.9945i	0.186604	+	1.12913i
$531$	8.11710	−	2.38340i	0.352252	−	0.103431i
$532$	4.22469	−	7.22312i	0.183164	−	0.313162i
$533$	−9.48583	−	14.7602i	−0.410877	−	0.639337i
$534$	−6.46523	−	20.4232i	−0.279778	−	0.883796i
$535$	6.69168	−	10.4125i	0.289306	−	0.450170i
$536$	0.841807	+	13.3548i	0.0363605	+	0.576839i
$537$	2.54562	−	2.93781i	0.109852	−	0.126776i
$538$	0.378766	+	18.0479i	0.0163298	+	0.778102i
$539$	14.2087	−	6.48889i	0.612011	−	0.279496i
$540$	3.56796	−	0.149825i	0.153541	−	0.00644746i
$541$	5.17569	−	17.6268i	0.222520	−	0.757834i	−0.770244	−	0.637750i	$-0.779865\pi$
$541$	5.17569	−	17.6268i	0.222520	−	0.757834i	0.992764	−	0.120084i	$-0.0383165\pi$
$542$	13.4588	+	20.0065i	0.578105	+	0.859354i
$543$	−1.61090	+	11.2040i	−0.0691303	+	0.480812i
$544$	−4.22104	−	40.0841i	−0.180976	−	1.71859i
$545$	2.92079	−	6.39565i	0.125113	−	0.273959i
$546$	3.12791	+	1.34989i	0.133862	+	0.0577698i
$547$	2.29583	+	15.9678i	0.0981624	+	0.682735i	0.978175	+	0.207784i	$0.0666251\pi$
$547$	2.29583	+	15.9678i	0.0981624	+	0.682735i	−0.880012	+	0.474951i	$0.842466\pi$
$548$	15.4381	+	12.2820i	0.659481	+	0.524660i
$549$	−0.167353	−	0.193136i	−0.00714245	−	0.00824282i
$550$	5.57783	−	2.69015i	0.237840	−	0.114709i
$551$	30.2865			1.29025
$552$	10.4342	+	8.66757i	0.444110	+	0.368916i
$553$	−5.84409			−0.248516
$554$	−2.23955	+	1.08012i	−0.0951492	+	0.0458899i
$555$	7.79090	+	8.99117i	0.330705	+	0.381654i
$556$	5.71711	−	7.18622i	0.242459	−	0.304764i
$557$	2.06836	+	14.3857i	0.0876391	+	0.609543i	0.985552	+	0.169371i	$0.0541735\pi$
$557$	2.06836	+	14.3857i	0.0876391	+	0.609543i	−0.897913	+	0.440172i	$0.854917\pi$
$558$	11.1089	+	4.79416i	0.470276	+	0.202953i
$559$	−10.2755	+	22.5003i	−0.434609	+	0.951660i
$560$	−0.307910	+	5.22472i	−0.0130116	+	0.220785i
$561$	−2.45073	+	17.0452i	−0.103470	+	0.719649i
$562$	16.4241	+	24.4145i	0.692810	+	1.02986i
$563$	−11.6541	+	39.6902i	−0.491161	+	1.67274i	0.224643	+	0.974441i	$0.427878\pi$
$563$	−11.6541	+	39.6902i	−0.491161	+	1.67274i	−0.715805	+	0.698301i	$0.753940\pi$
$564$	0.687092	+	16.3625i	0.0289318	+	0.688985i
$565$	22.6923	−	10.3632i	0.954674	−	0.435985i
$566$	0.736382	+	35.0881i	0.0309524	+	1.47486i
$567$	−0.479879	+	0.553810i	−0.0201530	+	0.0232578i
$568$	−0.420706	−	6.67426i	−0.0176524	−	0.280046i
$569$	−3.99635	+	6.21845i	−0.167536	+	0.260691i	−0.914862	−	0.403766i	$-0.867701\pi$
$569$	−3.99635	+	6.21845i	−0.167536	+	0.260691i	0.747326	+	0.664457i	$0.231337\pi$
$570$	4.35125	+	13.7452i	0.182254	+	0.575725i
$571$	−13.5242	−	21.0441i	−0.565972	−	0.880670i	0.433821	−	0.900999i	$-0.357165\pi$
$571$	−13.5242	−	21.0441i	−0.565972	−	0.880670i	−0.999793	+	0.0203294i	$0.993529\pi$
$572$	−13.7163	−	8.02244i	−0.573506	−	0.335435i
$573$	−9.22811	+	2.70962i	−0.385510	+	0.113196i
$574$	0.901877	+	5.45720i	0.0376436	+	0.227779i
$575$	6.80057	−	5.40854i	0.283604	−	0.225552i
$576$	−4.43823	+	6.65598i	−0.184926	+	0.277333i
$577$	18.3322	−	5.38281i	0.763178	−	0.224089i	0.123095	−	0.992395i	$-0.460718\pi$
$577$	18.3322	−	5.38281i	0.763178	−	0.224089i	0.640083	+	0.768306i	$0.278900\pi$
$578$	30.5082	−	36.7384i	1.26897	−	1.52812i
$579$	16.4632	−	10.5803i	0.684187	−	0.439700i
$580$	−16.8858	+	8.58521i	−0.701147	+	0.356482i
$581$	−1.82056	+	2.83285i	−0.0755296	+	0.117526i
$582$	−0.525882	+	1.94074i	−0.0217985	+	0.0804461i
$583$	19.0579	+	16.5138i	0.789299	+	0.683932i
$584$	41.4791	−	15.0729i	1.71642	−	0.623722i
$585$	−5.33928	+	2.43837i	−0.220752	+	0.100814i
$586$	2.53493	−	20.7065i	0.104717	−	0.855377i
$587$	12.6646	+	3.71867i	0.522725	+	0.153486i	0.532442	−	0.846467i	$-0.321275\pi$
$587$	12.6646	+	3.71867i	0.522725	+	0.153486i	−0.00971612	+	0.999953i	$0.503093\pi$
$588$	8.86714	+	9.40510i	0.365675	+	0.387860i
$589$	−6.95176	+	48.3505i	−0.286442	+	1.99225i
$590$	−18.2094	−	11.1697i	−0.749671	−	0.459849i
$591$	−0.0366925	−	0.0167569i	−0.00150933	−	0.000689286i
$592$	−26.5579	+	2.23437i	−1.09152	+	0.0918321i
$593$	1.67488	+	11.6491i	0.0687793	+	0.478370i	0.994878	+	0.101088i	$0.0322323\pi$
$593$	1.67488	+	11.6491i	0.0687793	+	0.478370i	−0.926098	+	0.377282i	$0.876859\pi$
$594$	2.53560	−	2.29200i	0.104037	−	0.0940419i
$595$	−7.04573	+	6.10516i	−0.288847	+	0.250287i
$596$	−20.6238	+	14.5117i	−0.844782	+	0.594424i
$597$	3.35280			0.137221
$598$	−21.2551	−	6.73231i	−0.869184	−	0.275305i
$599$			14.9823i			0.612161i	0.952006	+	0.306081i	$0.0990177\pi$
$599$			14.9823i			0.612161i	−0.952006	+	0.306081i	$0.900982\pi$
$600$	3.59285	+	3.65408i	0.146678	+	0.149177i
$601$	2.46472	+	2.84444i	0.100538	+	0.116027i	0.803789	−	0.594915i	$-0.202814\pi$
$601$	2.46472	+	2.84444i	0.100538	+	0.116027i	−0.703251	+	0.710942i	$0.748269\pi$
$602$	5.78480	−	5.22905i	0.235771	−	0.213120i
$603$	4.68285	−	0.673292i	0.190700	−	0.0274186i
$604$	−9.42230	+	37.9060i	−0.383388	+	1.54238i
$605$	3.82648	−	8.37881i	0.155568	−	0.340647i
$606$	9.60336	−	15.6559i	0.390110	−	0.635978i
$607$	25.4769	+	3.66302i	1.03407	+	0.148677i	0.638393	−	0.769710i	$-0.279599\pi$
$607$	25.4769	+	3.66302i	1.03407	+	0.148677i	0.395681	+	0.918388i	$0.370509\pi$
$608$	−30.6230	−	10.2666i	−1.24193	−	0.416365i
$609$	1.09513	−	3.72967i	0.0443769	−	0.151134i
$610$	−0.0784155	+	0.640534i	−0.00317495	+	0.0259344i
$611$	−11.1822	−	24.4856i	−0.452384	−	0.990583i
$612$	−14.0077	+	2.61802i	−0.566227	+	0.105827i
$613$	−19.6480	+	22.6750i	−0.793575	+	0.915835i	−0.998011	−	0.0630452i	$-0.979919\pi$
$613$	−19.6480	+	22.6750i	−0.793575	+	0.915835i	0.204435	+	0.978880i	$0.434464\pi$
$614$	−1.20860	−	0.327494i	−0.0487751	−	0.0132166i
$615$	−8.01720	−	5.15234i	−0.323285	−	0.207763i
$616$	2.96800	+	4.03541i	0.119584	+	0.162591i
$617$	−16.7527	−	26.0678i	−0.674440	−	1.04945i	−0.994770	−	0.102143i	$-0.967430\pi$
$617$	−16.7527	−	26.0678i	−0.674440	−	1.04945i	0.320330	−	0.947306i	$-0.396206\pi$
$618$	−10.4868	+	12.6283i	−0.421839	+	0.507985i
$619$	−4.43110	−	15.0909i	−0.178101	−	0.606556i	−0.999352	−	0.0359892i	$-0.988542\pi$
$619$	−4.43110	−	15.0909i	−0.178101	−	0.606556i	0.821251	−	0.570567i	$-0.193276\pi$
$620$	−9.82991	−	28.9278i	−0.394779	−	1.16177i
$621$	2.76043	−	3.92174i	0.110772	−	0.157374i
$622$	9.98570	−	1.65027i	0.400390	−	0.0661699i
$623$	−3.12728	−	10.6505i	−0.125292	−	0.426704i
$624$	2.63382	−	12.8829i	0.105437	−	0.515727i
$625$	−10.6489	+	6.84365i	−0.425957	+	0.273746i
$626$	−1.72366	−	5.44490i	−0.0688912	−	0.217622i
$627$	11.6087	+	7.46044i	0.463606	+	0.297941i
$628$	2.58974	−	25.5965i	0.103342	−	1.02141i
$629$	−35.8786	−	31.0890i	−1.43057	−	1.23960i
$630$	1.85002	−	0.0388257i	0.0737064	−	0.00154685i
$631$	−16.3166	−	35.7284i	−0.649555	−	1.42233i	−0.891943	−	0.452147i	$-0.850658\pi$
$631$	−16.3166	−	35.7284i	−0.649555	−	1.42233i	0.242389	−	0.970179i	$-0.422069\pi$
$632$	4.60841	+	22.0811i	0.183313	+	0.878340i
$633$	13.6836	+	4.01787i	0.543874	+	0.159696i
$634$	20.4585	+	30.4116i	0.812511	+	1.20780i
$635$	13.7734	+	1.98031i	0.546579	+	0.0785862i
$636$	−7.86475	+	19.3289i	−0.311857	+	0.766442i
$637$	−19.3261	−	8.82593i	−0.765728	−	0.349696i
$638$	−7.18406	+	16.6467i	−0.284420	+	0.659047i
$639$	−2.34032	+	0.336488i	−0.0925817	+	0.0133112i
$640$	19.9837	−	2.95660i	0.789925	−	0.116870i
$641$	−8.50172	+	7.36679i	−0.335798	+	0.290971i	−0.806395	−	0.591378i	$-0.798584\pi$
$641$	−8.50172	+	7.36679i	−0.335798	+	0.290971i	0.470597	+	0.882348i	$0.344039\pi$
$642$	8.82990	−	4.25861i	0.348488	−	0.168074i
$643$		−	33.5373i		−	1.32258i	−0.750129	−	0.661292i	$-0.770009\pi$
$643$		−	33.5373i		−	1.32258i	0.750129	−	0.661292i	$-0.229991\pi$
$644$	5.31123	+	4.60368i	0.209292	+	0.181411i
$645$			13.4354i			0.529019i
$646$	−24.9925	−	51.8200i	−0.983315	−	2.03883i
$647$	27.0931	−	23.4763i	1.06514	−	0.922949i	0.0679367	−	0.997690i	$-0.478358\pi$
$647$	27.0931	−	23.4763i	1.06514	−	0.922949i	0.997203	+	0.0747409i	$0.0238130\pi$
$648$	2.47091	+	1.37645i	0.0970665	+	0.0540719i
$649$	−20.2381	+	2.90979i	−0.794414	+	0.114219i
$650$	−7.73359	−	3.33752i	−0.303336	−	0.130908i
$651$	5.70283	+	2.60440i	0.223512	+	0.102074i
$652$	−14.4370	+	35.4813i	−0.565396	+	1.38955i
$653$	−42.2840	−	6.07952i	−1.65470	−	0.237910i	−0.749226	−	0.662314i	$-0.769575\pi$
$653$	−42.2840	−	6.07952i	−1.65470	−	0.237910i	−0.905473	+	0.424404i	$0.860484\pi$
$654$	4.62056	−	3.10835i	0.180678	−	0.121546i
$655$	6.88948	+	2.02293i	0.269194	+	0.0790425i
$656$	19.9081	−	7.71094i	0.777281	−	0.301062i
$657$	−6.48185	−	14.1933i	−0.252881	−	0.553732i
$658$	0.178053	+	8.48408i	0.00694121	+	0.330744i
$659$	19.7767	+	17.1366i	0.770392	+	0.667549i	0.948612	−	0.316442i	$-0.102488\pi$
$659$	19.7767	+	17.1366i	0.770392	+	0.667549i	−0.178219	+	0.983991i	$0.557034\pi$
$660$	−8.58706	−	0.868801i	−0.334251	−	0.0338180i
$661$	29.4897	+	18.9519i	1.14702	+	0.737142i	0.969043	−	0.246894i	$-0.0794098\pi$
$661$	29.4897	+	18.9519i	1.14702	+	0.737142i	0.177972	+	0.984035i	$0.443046\pi$
$662$	21.0909	−	6.67662i	0.819721	−	0.259494i
$663$	19.7044	−	12.6632i	0.765254	−	0.491799i
$664$	12.1391	+	4.64487i	0.471090	+	0.180256i
$665$	2.10473	+	7.16804i	0.0816178	+	0.277965i
$666$	1.53641	+	9.29671i	0.0595346	+	0.360240i
$667$	−4.67767	+	25.0058i	−0.181120	+	0.968230i
$668$	8.37858	+	24.6568i	0.324177	+	0.954000i
$669$	−1.10502	−	3.76334i	−0.0427224	−	0.145499i
$670$	−9.19073	−	7.63214i	−0.355069	−	0.294855i
$671$	0.333923	+	0.519594i	0.0128910	+	0.0200587i
$672$	−2.37159	+	3.39988i	−0.0914862	+	0.131153i
$673$	−37.6575	−	24.2010i	−1.45159	−	0.932880i	−0.999156	−	0.0410829i	$-0.986919\pi$
$673$	−37.6575	−	24.2010i	−1.45159	−	0.932880i	−0.452435	−	0.891798i	$-0.649444\pi$
$674$	4.63824	−	17.1172i	0.178658	−	0.659329i
$675$	1.18648	−	1.36927i	0.0456675	−	0.0527031i
$676$	−0.805948	−	4.31222i	−0.0309980	−	0.165855i
$677$	0.285385	+	0.624906i	0.0109682	+	0.0240171i	0.915037	−	0.403370i	$-0.132161\pi$
$677$	0.285385	+	0.624906i	0.0109682	+	0.0240171i	−0.904069	+	0.427387i	$0.859434\pi$
$678$	19.6122	+	2.40096i	0.753201	+	0.0922085i
$679$	−0.293533	+	0.999683i	−0.0112648	+	0.0383643i
$680$	28.6235	+	21.8070i	1.09766	+	0.836262i
$681$	2.31038	+	0.332183i	0.0885341	+	0.0127293i
$682$	−24.9264	−	15.2899i	−0.954481	−	0.585480i
$683$	−1.44475	+	3.16356i	−0.0552818	+	0.121050i	−0.935257	−	0.353969i	$-0.884832\pi$
$683$	−1.44475	+	3.16356i	−0.0552818	+	0.121050i	0.879975	+	0.475020i	$0.157559\pi$
$684$	−2.75462	+	11.0819i	−0.105326	+	0.423727i
$685$	−17.4331	+	2.50651i	−0.666086	+	0.0957687i
$686$	9.35592	+	10.3503i	0.357211	+	0.395176i
$687$	−12.0180	−	13.8695i	−0.458516	−	0.529156i
$688$	−24.3189	−	17.7337i	−0.927150	−	0.676090i
$689$		−	34.2996i		−	1.30671i
$690$	−12.0207	+	1.46966i	−0.457620	+	0.0559490i
$691$	0.0763029			0.00290270			0.00145135	−	0.999999i	$-0.499538\pi$
$691$	0.0763029			0.00290270			0.00145135	+	0.999999i	$0.499538\pi$
$692$	10.4183	+	14.8062i	0.396043	+	0.562848i
$693$	1.33849	−	1.15981i	0.0508449	−	0.0440574i
$694$	−0.940081	−	1.03999i	−0.0356850	−	0.0394776i
$695$	1.16675	+	8.11490i	0.0442572	+	0.307816i
$696$	−14.9556	−	1.19674i	−0.566892	−	0.0453621i
$697$	34.5924	+	15.7978i	1.31028	+	0.598385i
$698$	0.340072	−	0.554404i	0.0128719	−	0.0209845i
$699$	−1.88599	+	13.1174i	−0.0713347	+	0.496144i
$700$	1.82155	+	1.93206i	0.0688482	+	0.0730251i
$701$	12.1610	+	3.57079i	0.459314	+	0.134867i	0.503201	−	0.864170i	$-0.332156\pi$
$701$	12.1610	+	3.57079i	0.459314	+	0.134867i	−0.0438861	+	0.999037i	$0.513974\pi$
$702$	−4.61454	−	0.564922i	−0.174165	−	0.0213216i
$703$	−34.6046	+	15.8034i	−1.30514	+	0.596036i
$704$	12.9068	−	14.3963i	0.486443	−	0.542583i
$705$	−11.0498	−	9.57468i	−0.416158	−	0.360603i
$706$	41.0392	+	11.1204i	1.54453	+	0.418522i
$707$	5.14524	−	8.00615i	0.193507	−	0.301102i
$708$	−7.66816	−	15.0821i	−0.288187	−	0.566821i
$709$	−7.17540	+	4.61135i	−0.269478	+	0.173183i	−0.668400	−	0.743802i	$-0.733021\pi$
$709$	−7.17540	+	4.61135i	−0.269478	+	0.173183i	0.398922	+	0.916985i	$0.369384\pi$
$710$	4.59321	+	3.81428i	0.172380	+	0.143147i
$711$	7.65202	−	2.24684i	0.286973	−	0.0842629i
$712$	−37.7755	+	20.2146i	−1.41570	+	0.757573i
$713$	−38.8466	−	13.2073i	−1.45482	−	0.494617i
$714$	−7.28516	+	1.20397i	−0.272640	+	0.0450575i
$715$	13.6117	−	3.99675i	0.509048	−	0.149470i
$716$	−6.71096	−	3.92514i	−0.250800	−	0.146689i
$717$	−14.8723	−	23.1418i	−0.555418	−	0.864247i
$718$	15.6534	−	4.95529i	0.584178	−	0.184930i
$719$	−4.27710	+	6.65530i	−0.159509	+	0.248201i	−0.911804	−	0.410625i	$-0.865310\pi$
$719$	−4.27710	+	6.65530i	−0.159509	+	0.248201i	0.752295	+	0.658826i	$0.228947\pi$
$720$	−1.60554	−	6.95942i	−0.0598351	−	0.259362i
$721$	−5.56997	+	6.42809i	−0.207436	+	0.239394i
$722$	−19.2278	+	0.403527i	−0.715583	+	0.0150177i
$723$	−12.5635	+	5.73755i	−0.467241	+	0.213382i
$724$	22.6186	−	0.949796i	0.840613	−	0.0352989i
$725$	−2.70765	+	9.22142i	−0.100560	+	0.342475i
$726$	6.05331	−	4.07219i	0.224659	−	0.151133i
$727$	3.72111	−	25.8809i	0.138008	−	0.959870i	−0.796680	−	0.604401i	$-0.793412\pi$
$727$	3.72111	−	25.8809i	0.138008	−	0.959870i	0.934688	−	0.355468i	$-0.115679\pi$
$728$	1.50452	−	6.64534i	0.0557611	−	0.246293i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−15.6121	+	36.1757i	−0.577829	+	1.33892i
$731$	−7.62993	−	53.0673i	−0.282203	−	1.96277i
$732$	−0.318205	+	0.399973i	−0.0117612	+	0.0147834i
$733$	11.5066	+	13.2794i	0.425008	+	0.490485i	0.927356	−	0.374180i	$-0.122076\pi$
$733$	11.5066	+	13.2794i	0.425008	+	0.490485i	−0.502348	+	0.864665i	$0.667530\pi$
$734$	−15.6425	−	32.4336i	−0.577377	−	1.19715i
$735$	−11.5401			−0.425661
$736$	13.2062	−	23.6980i	0.486786	−	0.873521i
$737$	−11.4342			−0.421185
$738$	−3.27897	−	6.79870i	−0.120701	−	0.250263i
$739$	25.3632	+	29.2707i	0.933000	+	1.07674i	0.996892	+	0.0787828i	$0.0251033\pi$
$739$	25.3632	+	29.2707i	0.933000	+	1.07674i	−0.0638916	+	0.997957i	$0.520351\pi$
$740$	14.8136	−	18.6202i	0.544560	−	0.684494i
$741$	−2.67114	−	18.5782i	−0.0981267	−	0.682486i
$742$	−4.28449	+	9.92786i	−0.157288	+	0.364463i
$743$	0.784913	−	1.71872i	0.0287957	−	0.0630537i	−0.894688	−	0.446692i	$-0.852602\pi$
$743$	0.784913	−	1.71872i	0.0287957	−	0.0630537i	0.923483	+	0.383639i	$0.125329\pi$
$744$	5.34334	−	23.6011i	0.195896	−	0.865258i
$745$	3.20404	−	22.2846i	0.117387	−	0.816444i
$746$	6.26663	−	4.21569i	0.229438	−	0.154348i
$747$	1.29464	−	4.40915i	0.0473685	−	0.161322i
$748$	34.4106	−	1.44497i	1.25818	−	0.0528332i
$749$	4.62064	−	2.11017i	0.168834	−	0.0771041i
$750$	−17.1971	+	0.360909i	−0.627948	+	0.0131785i
$751$	−26.3575	+	30.4182i	−0.961798	+	1.10997i	0.0320790	+	0.999485i	$0.489787\pi$
$751$	−26.3575	+	30.4182i	−0.961798	+	1.10997i	−0.993877	+	0.110489i	$0.964758\pi$
$752$	31.9155	−	7.36294i	1.16384	−	0.268499i
$753$	10.3208	−	16.0595i	0.376112	−	0.585241i
$754$	23.5107	−	7.44265i	0.856211	−	0.271045i
$755$	−18.8529	−	29.3357i	−0.686129	−	1.06764i
$756$	1.26509	+	0.739933i	0.0460109	+	0.0269111i
$757$	47.2526	−	13.8746i	1.71743	−	0.504282i	0.733022	−	0.680205i	$-0.238109\pi$
$757$	47.2526	−	13.8746i	1.71743	−	0.504282i	0.984404	+	0.175923i	$0.0562910\pi$
$758$	−4.97857	+	0.822777i	−0.180830	+	0.0298846i
$759$	−7.95260	+	8.43238i	−0.288661	+	0.306076i
$760$	25.4238	−	13.6048i	0.922217	−	0.493500i
$761$	40.6103	−	11.9243i	1.47212	−	0.432254i	0.555334	−	0.831628i	$-0.312591\pi$
$761$	40.6103	−	11.9243i	1.47212	−	0.432254i	0.916788	+	0.399374i	$0.130772\pi$
$762$	8.47880	+	7.04094i	0.307154	+	0.255066i
$763$	2.42748	−	1.56005i	0.0878807	−	0.0564775i
$764$	8.71773	+	17.1465i	0.315396	+	0.620338i
$765$	6.87818	−	10.7027i	0.248681	−	0.386956i
$766$	−51.3941	−	13.9263i	−1.85695	−	0.503177i
$767$	21.0175	+	18.2117i	0.758897	+	0.657588i
$768$	14.7161	+	6.27973i	0.531023	+	0.226600i
$769$	−14.8719	+	6.79179i	−0.536296	+	0.244918i	−0.665103	−	0.746752i	$-0.731612\pi$
$769$	−14.8719	+	6.79179i	−0.536296	+	0.244918i	0.128807	+	0.991670i	$0.458885\pi$
$770$	−4.43909	−	0.543443i	−0.159974	−	0.0195843i
$771$	−15.6113	−	4.58390i	−0.562229	−	0.165085i
$772$	−26.8495	−	28.4784i	−0.966334	−	1.02496i
$773$	−6.81846	+	47.4234i	−0.245243	+	1.70570i	0.379764	+	0.925084i	$0.376005\pi$
$773$	−6.81846	+	47.4234i	−0.245243	+	1.70570i	−0.625007	+	0.780619i	$0.714904\pi$
$774$	−5.56401	+	9.07074i	−0.199994	+	0.326041i
$775$	−14.0999	−	6.43923i	−0.506485	−	0.231304i
$776$	4.00864	+	0.320767i	0.143902	+	0.0115149i
$777$	0.694862	+	4.83287i	0.0249280	+	0.173378i
$778$	1.90512	+	2.10759i	0.0683018	+	0.0755609i
$779$	23.0305	−	19.9561i	0.825154	−	0.715000i
$780$	6.75556	+	9.60085i	0.241888	+	0.343766i
$781$	5.71442			0.204478
$782$	46.6449	−	12.6314i	1.66802	−	0.451698i
$783$			5.30452i			0.189568i
$784$	15.2319	−	20.8882i	0.543998	−	0.746007i
$785$	15.0413	+	17.3585i	0.536846	+	0.619553i
$786$	3.81358	+	4.21889i	0.136026	+	0.150483i
$787$	−18.2791	+	2.62814i	−0.651580	+	0.0936831i	−0.460175	−	0.887828i	$-0.652213\pi$
$787$	−18.2791	+	2.62814i	−0.651580	+	0.0936831i	−0.191405	+	0.981511i	$0.561304\pi$
$788$	−0.0194613	+	0.0782929i	−0.000693279	+	0.00278907i
$789$	0.968677	−	2.12111i	0.0344858	−	0.0755134i
$790$	−17.1661	−	10.5297i	−0.610743	−	0.374630i
$791$	10.1340	+	1.45705i	0.360323	+	0.0518067i
$792$	−5.43764	−	4.14272i	−0.193218	−	0.147205i
$793$	0.236682	−	0.806064i	0.00840482	−	0.0286242i
$794$	−37.6386	−	4.60780i	−1.33574	−	0.163525i
$795$	−7.73927	−	16.9466i	−0.274484	−	0.601035i
$796$	−1.23193	−	6.59146i	−0.0436648	−	0.233628i
$797$	−1.72856	+	1.99487i	−0.0612289	+	0.0706619i	−0.785538	−	0.618814i	$-0.787614\pi$
$797$	−1.72856	+	1.99487i	−0.0612289	+	0.0706619i	0.724309	+	0.689476i	$0.242159\pi$
$798$	−1.54752	+	5.71103i	−0.0547816	+	0.202168i
$799$	49.0819	+	31.5430i	1.73639	+	1.11591i
$800$	5.86363	−	8.40603i	0.207311	−	0.297198i
$801$	8.18946	+	12.7430i	0.289360	+	0.450253i
$802$	−22.7994	−	18.9330i	−0.805074	−	0.668547i
$803$	10.6245	+	36.1836i	0.374929	+	1.27689i
$804$	−3.04430	−	8.95889i	−0.107364	−	0.315956i
$805$	−6.24332	+	0.630667i	−0.220048	+	0.0222281i
$806$	6.48525	+	39.2418i	0.228433	+	1.38223i
$807$	−3.59621	−	12.2476i	−0.126593	−	0.431135i
$808$	−34.3075	−	13.1273i	−1.20693	−	0.461816i
$809$	5.37961	−	3.45726i	0.189137	−	0.121551i	−0.442645	−	0.896697i	$-0.645960\pi$
$809$	5.37961	−	3.45726i	0.189137	−	0.121551i	0.631782	+	0.775146i	$0.282324\pi$
$810$	−2.40741	+	0.762098i	−0.0845877	+	0.0267774i
$811$	26.0289	+	16.7278i	0.913999	+	0.587392i	0.910911	−	0.412604i	$-0.135380\pi$
$811$	26.0289	+	16.7278i	0.913999	+	0.587392i	0.00308862	+	0.999995i	$0.499017\pi$
$812$	−7.73477	−	0.782570i	−0.271437	−	0.0274628i
$813$	−12.8855	−	11.1653i	−0.451914	−	0.391585i
$814$	−0.477839	−	22.7687i	−0.0167483	−	0.798042i
$815$	−14.2067	−	31.1082i	−0.497637	−	1.08967i
$816$	10.2938	+	26.5766i	0.360356	+	0.930366i
$817$	−41.2214	−	12.1037i	−1.44215	−	0.423455i
$818$	13.4681	−	9.06025i	0.470900	−	0.316784i
$819$	−2.38442	−	0.342828i	−0.0833185	−	0.0119794i
$820$	−7.18349	+	17.6546i	−0.250858	+	0.616527i
$821$	7.21871	+	3.29668i	0.251935	+	0.115055i	0.537380	−	0.843340i	$-0.319414\pi$
$821$	7.21871	+	3.29668i	0.251935	+	0.115055i	−0.285445	+	0.958395i	$0.592141\pi$
$822$	−12.8078	−	5.52734i	−0.446722	−	0.192788i
$823$	32.6927	−	4.70051i	1.13960	−	0.163849i	0.453429	−	0.891292i	$-0.350201\pi$
$823$	32.6927	−	4.70051i	1.13960	−	0.163849i	0.686168	+	0.727443i	$0.259291\pi$
$824$	28.6799	+	15.9764i	0.999112	+	0.556566i
$825$	−3.30934	+	2.86756i	−0.115216	+	0.0998355i
$826$	−3.80852	−	7.89668i	−0.132515	−	0.274761i
$827$		−	20.3463i		−	0.707510i	−0.935338	−	0.353755i	$-0.884905\pi$
$827$		−	20.3463i		−	0.707510i	0.935338	−	0.353755i	$-0.115095\pi$
$828$	−8.72425	−	3.98591i	−0.303189	−	0.138520i
$829$		−	36.4365i		−	1.26549i	−0.774359	−	0.632747i	$-0.781927\pi$
$829$		−	36.4365i		−	1.26549i	0.774359	−	0.632747i	$-0.218073\pi$
$830$	−10.4517	+	5.04081i	−0.362785	+	0.174969i
$831$	1.32873	−	1.15135i	0.0460930	−	0.0399398i
$832$	−26.2949	−	0.444375i	−0.911612	−	0.0154059i
$833$	45.5810	−	6.55356i	1.57929	−	0.227067i
$834$	−2.57291	+	5.96185i	−0.0890925	+	0.206442i
$835$	−21.1482	−	9.65808i	−0.731865	−	0.334232i
$836$	10.4015	−	25.5634i	0.359743	−	0.884129i
$837$	−8.46835	−	1.21756i	−0.292709	−	0.0420852i
$838$	2.28294	+	3.39360i	0.0788629	+	0.117230i
$839$	7.18091	+	2.10851i	0.247913	+	0.0727937i	0.403328	−	0.915055i	$-0.367853\pi$
$839$	7.18091	+	2.10851i	0.247913	+	0.0727937i	−0.155415	+	0.987849i	$0.549672\pi$
$840$	−0.756089	−	3.62279i	−0.0260876	−	0.124998i
$841$	0.358116	+	0.784165i	0.0123488	+	0.0270402i
$842$	40.3325	−	0.846446i	1.38995	−	0.0291705i
$843$	−15.7245	−	13.6253i	−0.541580	−	0.469282i
$844$	2.87113	−	28.3777i	0.0988283	−	0.976800i
$845$	3.29478	+	2.11743i	0.113344	+	0.0728417i
$846$	−3.49494	−	11.0402i	−0.120159	−	0.379572i
$847$	3.18019	−	2.04379i	0.109273	−	0.0702254i
$848$	40.8896	+	8.35964i	1.40416	+	0.287071i
$849$	−6.99161	−	23.8112i	−0.239951	−	0.817199i
$850$	18.0122	−	2.97675i	0.617812	−	0.102102i
$851$	−7.70337	−	31.0119i	−0.264068	−	1.06307i
$852$	1.52144	+	4.47734i	0.0521236	+	0.153391i
$853$	0.226879	+	0.772680i	0.00776820	+	0.0264561i	0.963286	−	0.268478i	$-0.0865206\pi$
$853$	0.226879	+	0.772680i	0.00776820	+	0.0264561i	−0.955518	+	0.294934i	$0.904702\pi$
$854$	−0.169195	+	0.203747i	−0.00578973	+	0.00697208i
$855$	−5.51168	−	8.57635i	−0.188496	−	0.293305i
$856$	−11.6167	−	15.7945i	−0.397049	−	0.539843i
$857$	33.1333	+	21.2935i	1.13181	+	0.727371i	0.965937	−	0.258777i	$-0.0833193\pi$
$857$	33.1333	+	21.2935i	1.13181	+	0.727371i	0.165873	+	0.986147i	$0.446956\pi$
$858$	10.8449	+	2.93865i	0.370239	+	0.100324i
$859$	27.1048	−	31.2806i	0.924802	−	1.06728i	−0.0727497	−	0.997350i	$-0.523177\pi$
$859$	27.1048	−	31.2806i	0.924802	−	1.06728i	0.997552	−	0.0699286i	$-0.0222771\pi$
$860$	26.4135	−	4.93664i	0.900692	−	0.168338i
$861$	−1.62476	−	3.55772i	−0.0553715	−	0.121247i
$862$	−0.0810739	+	0.662248i	−0.00276139	+	0.0225563i
$863$	−1.75635	+	5.98159i	−0.0597869	+	0.203616i	−0.983970	−	0.178334i	$-0.942929\pi$
$863$	−1.75635	+	5.98159i	−0.0597869	+	0.203616i	0.924183	+	0.381950i	$0.124747\pi$
$864$	1.79814	−	5.36346i	0.0611739	−	0.182469i
$865$	−15.9985	−	2.30024i	−0.543967	−	0.0782106i
$866$	−9.54002	+	15.5527i	−0.324183	+	0.528501i
$867$	−14.0274	+	30.7158i	−0.476397	+	1.04316i
$868$	3.02471	−	12.1685i	0.102666	−	0.413025i
$869$	−19.0785	+	2.74307i	−0.647194	+	0.0930524i
$870$	9.93679	−	8.98216i	0.336889	−	0.304524i
$871$	10.1846	+	11.7537i	0.345093	+	0.398259i
$872$	−7.80864	−	7.94172i	−0.264434	−	0.268940i
$873$		−	1.42180i		−	0.0481205i
$874$	6.32013	−	38.2049i	0.213781	−	1.29230i
$875$	−8.91287			−0.301310
$876$	−25.5217	+	17.9581i	−0.862299	+	0.606750i
$877$	−19.5454	+	16.9362i	−0.660001	+	0.571894i	−0.919133	−	0.393948i	$-0.871109\pi$
$877$	−19.5454	+	16.9362i	−0.660001	+	0.571894i	0.259132	+	0.965842i	$0.416564\pi$
$878$	14.9245	−	13.4907i	0.503678	−	0.455289i
$879$	2.09929	+	14.6009i	0.0708072	+	0.492475i
$880$	1.44716	+	17.2010i	0.0487837	+	0.579847i
$881$	35.0113	+	15.9891i	1.17956	+	0.538687i	0.906046	−	0.423180i	$-0.139086\pi$
$881$	35.0113	+	15.9891i	1.17956	+	0.538687i	0.273515	+	0.961868i	$0.411814\pi$
$882$	−7.79111	−	4.77908i	−0.262340	−	0.160920i
$883$	−3.95699	+	27.5215i	−0.133163	+	0.926171i	0.808232	+	0.588865i	$0.200425\pi$
$883$	−3.95699	+	27.5215i	−0.133163	+	0.926171i	−0.941395	+	0.337306i	$0.890484\pi$
$884$	−32.1355	−	34.0851i	−1.08083	−	1.14640i
$885$	14.4935	+	4.25568i	0.487194	+	0.143053i
$886$	−0.954517	+	7.79693i	−0.0320676	+	0.261943i
$887$	−28.3611	+	12.9521i	−0.952273	+	0.434889i	−0.830096	−	0.557620i	$-0.811715\pi$
$887$	−28.3611	+	12.9521i	−0.952273	+	0.434889i	−0.122177	+	0.992508i	$0.538987\pi$
$888$	17.7124	−	6.43645i	0.594390	−	0.215993i
$889$	4.31590	+	3.73975i	0.144751	+	0.125427i
$890$	10.0039	−	36.9189i	0.335332	−	1.23752i
$891$	−1.30666	+	2.03320i	−0.0437747	+	0.0681148i
$892$	−6.99256	+	3.55520i	−0.234128	+	0.119037i
$893$	39.3307	−	25.2763i	1.31615	−	0.845839i
$894$	11.3919	−	13.7182i	0.381001	−	0.458807i
$895$	6.65978	−	1.95549i	0.222612	−	0.0653648i
$896$	7.55544	+	3.41322i	0.252409	+	0.114028i
$897$	15.7515	+	0.663947i	0.525927	+	0.0221685i
$898$	−5.16965	−	31.2812i	−0.172513	−	1.04387i
$899$	43.5441	−	12.7857i	1.45228	−	0.426427i
$900$	−3.12787	−	1.82945i	−0.104262	−	0.0609815i
$901$	40.1926	+	62.5409i	1.33901	+	2.08354i
$902$	5.50572	+	17.3921i	0.183320	+	0.579095i
$903$	−2.98106	+	4.63861i	−0.0992033	+	0.154363i
$904$	−2.48599	−	39.4389i	−0.0826829	−	1.31172i
$905$	−13.2355	+	15.2746i	−0.439962	+	0.507744i
$906$	−0.579509	−	27.6132i	−0.0192529	−	0.917387i
$907$	−38.7663	+	17.7040i	−1.28721	+	0.587850i	−0.937167	−	0.348882i	$-0.886561\pi$
$907$	−38.7663	+	17.7040i	−1.28721	+	0.587850i	−0.350046	+	0.936732i	$0.613834\pi$
$908$	−0.195857	−	4.66418i	−0.00649976	−	0.154786i
$909$	−3.65890	+	12.4611i	−0.121358	+	0.413308i
$910$	3.39534	+	5.04718i	0.112554	+	0.167312i
$911$	0.228660	−	1.59036i	0.00757583	−	0.0526911i	−0.985683	−	0.168610i	$-0.946072\pi$
$911$	0.228660	−	1.59036i	0.00757583	−	0.0526911i	0.993259	+	0.115919i	$0.0369813\pi$
$912$	22.7987	+	1.34360i	0.754940	+	0.0444911i
$913$	−4.61369	+	10.1026i	−0.152691	+	0.334346i
$914$	−16.8835	−	7.28629i	−0.558458	−	0.241009i
$915$	−0.0649393	−	0.451663i	−0.00214683	−	0.0149315i
$916$	−22.8511	+	28.7231i	−0.755021	+	0.949037i
$917$	1.92976	+	2.22706i	0.0637263	+	0.0735441i
$918$	9.07600	−	4.37730i	0.299553	−	0.144472i
$919$	−12.6758			−0.418137			−0.209069	−	0.977901i	$-0.567043\pi$
$919$	−12.6758			−0.418137			−0.209069	+	0.977901i	$0.567043\pi$
$920$	7.30611	+	23.0922i	0.240875	+	0.761327i
$921$	0.885427			0.0291758
$922$	26.4670	−	12.7649i	0.871645	−	0.420389i
$923$	−5.08993	−	5.87409i	−0.167537	−	0.193348i
$924$	−2.77194	−	2.20526i	−0.0911900	−	0.0725476i
$925$	−1.71801	−	11.9490i	−0.0564878	−	0.392881i
$926$	−49.2433	−	21.2515i	−1.61824	−	0.698368i
$927$	4.82173	−	10.5581i	0.158366	−	0.346774i
$928$	3.14249	+	29.8419i	0.103157	+	0.979608i
$929$	−6.56752	+	45.6781i	−0.215473	+	1.49865i	0.538992	+	0.842311i	$0.318805\pi$
$929$	−6.56752	+	45.6781i	−0.215473	+	1.49865i	−0.754465	+	0.656340i	$0.772104\pi$
$930$	12.0586	+	17.9252i	0.395419	+	0.587790i
$931$	10.3962	−	35.4062i	0.340722	−	1.16039i
$932$	26.4811	−	1.11199i	0.867419	−	0.0364245i
$933$	−6.50999	+	2.97301i	−0.213128	+	0.0973321i
$934$	0.941588	+	44.8660i	0.0308097	+	1.46806i
$935$	−20.1357	+	23.2379i	−0.658508	+	0.759959i
$936$	0.584929	+	9.27956i	0.0191190	+	0.303312i
$937$	−12.7721	+	19.8739i	−0.417248	+	0.649250i	−0.984721	−	0.174142i	$-0.944285\pi$
$937$	−12.7721	+	19.8739i	−0.417248	+	0.649250i	0.567473	+	0.823392i	$0.307921\pi$
$938$	−1.47970	−	4.67426i	−0.0483140	−	0.152620i
$939$	2.18334	+	3.39735i	0.0712507	+	0.110868i
$940$	−14.7633	+	25.2414i	−0.481527	+	0.823285i
$941$	−4.29660	+	1.26159i	−0.140065	+	0.0411268i	−0.351014	−	0.936370i	$-0.614163\pi$
$941$	−4.29660	+	1.26159i	−0.140065	+	0.0411268i	0.210949	+	0.977497i	$0.432345\pi$
$942$	2.96622	+	17.9484i	0.0966448	+	0.584791i
$943$	12.9196	+	22.0972i	0.420719	+	0.719583i
$944$	−26.8333	+	20.6170i	−0.873349	+	0.671026i
$945$	−1.25544	+	0.368632i	−0.0408396	+	0.0119916i
$946$	16.4305	−	19.7859i	0.534203	−	0.643295i
$947$	21.8265	−	14.0271i	0.709267	−	0.455818i	−0.135621	−	0.990761i	$-0.543303\pi$
$947$	21.8265	−	14.0271i	0.709267	−	0.455818i	0.844888	+	0.534943i	$0.179667\pi$
$948$	−7.22880	−	14.2180i	−0.234781	−	0.461779i
$949$	27.7312	−	43.1507i	0.900194	−	1.40073i
$950$	3.82616	−	14.1202i	0.124137	−	0.458121i
$951$	−19.5870	−	16.9722i	−0.635152	−	0.550362i
$952$	5.04378	+	13.8799i	0.163470	+	0.449851i
$953$	0.455081	−	0.207828i	0.0147415	−	0.00673222i	−0.408031	−	0.912968i	$-0.633784\pi$
$953$	0.455081	−	0.207828i	0.0147415	−	0.00673222i	0.422772	+	0.906236i	$0.361057\pi$
$954$	1.79304	−	14.6464i	0.0580518	−	0.474193i
$955$	−16.4773	−	4.83817i	−0.533193	−	0.156559i
$956$	−40.0312	+	37.7415i	−1.29470	+	1.22065i
$957$	1.82452	−	12.6898i	0.0589785	−	0.410204i
$958$	2.12465	+	1.30326i	0.0686443	+	0.0421065i
$959$	−6.57498	−	3.00269i	−0.212317	−	0.0969620i
$960$	−13.0920	+	5.71356i	−0.422542	+	0.184404i
$961$	6.00503	+	41.7659i	0.193711	+	1.34729i
$962$	−22.9793	+	20.7716i	−0.740881	+	0.669705i
$963$	−5.23879	+	4.53944i	−0.168818	+	0.146281i
$964$	15.8960	+	22.5911i	0.511977	+	0.727611i
$965$	34.9430			1.12485
$966$	−4.47627	−	2.15976i	−0.144022	−	0.0694890i
$967$		−	3.57961i		−	0.115113i	−0.998342	−	0.0575563i	$-0.981669\pi$
$967$		−	3.57961i		−	0.115113i	0.998342	−	0.0575563i	$-0.0183309\pi$
$968$	−10.2299	−	10.4043i	−0.328803	−	0.334407i
$969$	26.6406	+	30.7449i	0.855819	+	0.987667i
$970$	−2.66341	+	2.40753i	−0.0855168	+	0.0773012i
$971$	42.3414	−	6.08777i	1.35880	−	0.195366i	0.575903	−	0.817518i	$-0.304651\pi$
$971$	42.3414	−	6.08777i	1.35880	−	0.195366i	0.782896	+	0.622153i	$0.213742\pi$
$972$	−1.94094	−	0.482458i	−0.0622556	−	0.0154749i
$973$	−1.39772	+	3.06057i	−0.0448087	+	0.0981173i
$974$	0.427416	−	0.696797i	0.0136953	−	0.0223268i
$975$	5.89536	+	0.847625i	0.188803	+	0.0271457i
$976$	0.903251	+	0.478614i	0.0289124	+	0.0153201i
$977$	6.65086	−	22.6507i	0.212780	−	0.724661i	−0.782060	−	0.623203i	$-0.785831\pi$
$977$	6.65086	−	22.6507i	0.212780	−	0.724661i	0.994840	−	0.101458i	$-0.0323508\pi$
$978$	3.29141	−	26.8857i	0.105248	−	0.859710i
$979$	−15.2083	−	33.3016i	−0.486060	−	1.06432i
$980$	4.24022	+	22.6873i	0.135449	+	0.724718i
$981$	−2.57866	+	2.97594i	−0.0823304	+	0.0950144i
$982$	−43.6867	−	11.8378i	−1.39410	−	0.377759i
$983$	−21.4240	−	13.7684i	−0.683319	−	0.439142i	0.152386	−	0.988321i	$-0.451304\pi$
$983$	−21.4240	−	13.7684i	−0.683319	−	0.439142i	−0.835705	+	0.549179i	$0.814941\pi$
$984$	−12.1611	+	8.94439i	−0.387683	+	0.285137i
$985$	−0.0389397	−	0.0605914i	−0.00124072	−	0.00193060i
$986$	−34.1475	+	41.1209i	−1.08748	+	1.30955i
$987$	−1.69053	−	5.75741i	−0.0538101	−	0.183260i
$988$	−35.5425	+	12.0776i	−1.13076	+	0.384240i
$989$	16.3599	−	32.1648i	0.520214	−	1.02278i
$990$	6.02129	−	0.995101i	0.191369	−	0.0316264i
$991$	7.98275	+	27.1867i	0.253580	+	0.863615i	0.983627	+	0.180218i	$0.0576802\pi$
$991$	7.98275	+	27.1867i	0.253580	+	0.863615i	−0.730046	+	0.683398i	$0.760502\pi$
$992$	−48.3621	−	1.83291i	−1.53550	−	0.0581951i
$993$	−13.1597	+	8.45721i	−0.417610	+	0.268382i
$994$	0.739503	+	2.33603i	0.0234556	+	0.0740944i
$995$	5.03625	+	3.23660i	0.159660	+	0.102607i
$996$	−9.14390	−	0.925140i	−0.289736	−	0.0293142i
$997$	34.9590	+	30.2922i	1.10716	+	0.959362i	0.999394	−	0.0348136i	$-0.0110838\pi$
$997$	34.9590	+	30.2922i	1.10716	+	0.959362i	0.107769	+	0.994176i	$0.465629\pi$
$998$	−31.1351	+	0.653422i	−0.985564	+	0.0206837i
$999$	−2.76788	−	6.06082i	−0.0875720	−	0.191756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.b.451.15	yes	240
8.3	odd	2	inner	552.2.t.b.451.12	yes	240
23.5	odd	22	inner	552.2.t.b.235.12	✓	240
184.51	even	22	inner	552.2.t.b.235.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.b.235.12	✓	240	23.5	odd	22	inner
552.2.t.b.235.15	yes	240	184.51	even	22	inner
552.2.t.b.451.12	yes	240	8.3	odd	2	inner
552.2.t.b.451.15	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)

\(f(q)\)	\(=\)	\(q+(0.614348 + 1.27380i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.24515 + 1.56512i) q^{4} +(-0.254111 - 1.76738i) q^{5} +(0.560365 - 1.29846i) q^{6} +(0.304414 - 0.666574i) q^{7} +(-2.75861 - 0.624555i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.614348 + 1.27380i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.24515 + 1.56512i) q^{4} +(-0.254111 - 1.76738i) q^{5} +(0.560365 - 1.29846i) q^{6} +(0.304414 - 0.666574i) q^{7} +(-2.75861 - 0.624555i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(2.09518 - 1.40947i) q^{10} +(0.680911 - 2.31897i) q^{11} +(1.99824 - 0.0839098i) q^{12} +(-2.99026 + 1.36561i) q^{13} +(1.03610 - 0.0217443i) q^{14} +(-1.16929 + 1.34943i) q^{15} +(-0.899186 - 3.89762i) q^{16} +(3.85213 - 5.99403i) q^{17} +(-1.34827 + 0.426813i) q^{18} +(-3.08682 - 4.80319i) q^{19} +(3.08256 + 1.80295i) q^{20} +(-0.703112 + 0.206452i) q^{21} +(3.37223 - 0.557307i) q^{22} +(4.44247 - 1.80677i) q^{23} +(1.33450 + 2.49382i) q^{24} +(1.73841 - 0.510442i) q^{25} +(-3.57658 - 2.97005i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.664225 + 1.30643i) q^{28} +(-2.86784 + 4.46245i) q^{29} +(-2.43726 - 0.660425i) q^{30} +(-6.46576 - 5.60261i) q^{31} +(4.41240 - 3.53988i) q^{32} +(-2.19846 + 1.00400i) q^{33} +(10.0018 + 1.22444i) q^{34} +(-1.25544 - 0.368632i) q^{35} +(-1.37198 - 1.45522i) q^{36} +(0.948235 - 6.59512i) q^{37} +(4.22194 - 6.88283i) q^{38} +(2.99026 + 1.36561i) q^{39} +(-0.402833 + 5.03422i) q^{40} +(0.759579 + 5.28299i) q^{41} +(-0.694936 - 0.768794i) q^{42} +(5.68665 - 4.92751i) q^{43} +(2.78162 + 3.95318i) q^{44} +1.78555 q^{45} +(5.03070 + 4.54885i) q^{46} +8.18846i q^{47} +(-2.35679 + 3.23196i) q^{48} +(4.23237 + 4.88442i) q^{49} +(1.71819 + 1.90080i) q^{50} +(-7.05259 + 1.01401i) q^{51} +(1.58600 - 6.38050i) q^{52} +(-4.33438 + 9.49097i) q^{53} +(1.20549 + 0.739451i) q^{54} +(-4.27152 - 0.614153i) q^{55} +(-1.25607 + 1.64870i) q^{56} +(-1.60857 + 5.47828i) q^{57} +(-7.44613 - 0.911572i) q^{58} +(-3.51432 - 7.69529i) q^{59} +(-0.656074 - 3.51032i) q^{60} +(-0.167353 + 0.193136i) q^{61} +(3.16441 - 11.6781i) q^{62} +(0.616467 + 0.396179i) q^{63} +(7.21986 + 3.44581i) q^{64} +(3.17340 + 4.93791i) q^{65} +(-2.62952 - 2.18360i) q^{66} +(-1.33288 - 4.53936i) q^{67} +(4.58487 + 13.4925i) q^{68} +(-4.27467 - 2.17421i) q^{69} +(-0.301715 - 1.82566i) q^{70} +(0.666125 + 2.26861i) q^{71} +(1.01079 - 2.64165i) q^{72} +(-13.1263 + 8.43579i) q^{73} +(8.98343 - 2.84383i) q^{74} +(-1.52418 - 0.979532i) q^{75} +(11.3611 + 1.14947i) q^{76} +(-1.33849 - 1.15981i) q^{77} +(0.0975454 + 4.64797i) q^{78} +(-3.31296 - 7.25437i) q^{79} +(-6.66009 + 2.57963i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-6.26285 + 4.21315i) q^{82} +(-4.54852 - 0.653978i) q^{83} +(0.552361 - 1.35752i) q^{84} +(-11.5726 - 5.28503i) q^{85} +(9.77026 + 4.21647i) q^{86} +(5.25053 - 0.754912i) q^{87} +(-3.32669 + 5.97187i) q^{88} +(11.4479 - 9.91962i) q^{89} +(1.09695 + 2.27445i) q^{90} +2.40894i q^{91} +(-2.70375 + 9.20270i) q^{92} +8.55543i q^{93} +(-10.4305 + 5.03056i) q^{94} +(-7.70466 + 6.67613i) q^{95} +(-5.56477 - 1.01654i) q^{96} +(-1.40732 + 0.202343i) q^{97} +(-3.62164 + 8.39194i) q^{98} +(2.19846 + 1.00400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9	\( 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9} - 4 q^{12} - 4 q^{16} - 44 q^{17} + 4 q^{18} + 55 q^{20} + 4 q^{24} - 24 q^{25} - 24 q^{27} + 4 q^{32} - 55 q^{34} + 7 q^{36} + 22 q^{38} + 11 q^{40} - 44 q^{42} + 77 q^{44} - 48 q^{46} + 51 q^{48} + 8 q^{49} - 33 q^{50} + 165 q^{52} - 7 q^{54} - 22 q^{56} - 59 q^{58} + 11 q^{60} + 29 q^{62} - 4 q^{64} + 55 q^{66} + 132 q^{70} + 4 q^{72} - 144 q^{73} - 66 q^{74} - 24 q^{75} - 55 q^{76} - 24 q^{81} - 26 q^{82} - 44 q^{84} - 110 q^{86} - 198 q^{88} - 47 q^{92} - 73 q^{94} + 4 q^{96} + 53 q^{98}+O(q^{100}) \) 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9 - 4 * q^12 - 4 * q^16 - 44 * q^17 + 4 * q^18 + 55 * q^20 + 4 * q^24 - 24 * q^25 - 24 * q^27 + 4 * q^32 - 55 * q^34 + 7 * q^36 + 22 * q^38 + 11 * q^40 - 44 * q^42 + 77 * q^44 - 48 * q^46 + 51 * q^48 + 8 * q^49 - 33 * q^50 + 165 * q^52 - 7 * q^54 - 22 * q^56 - 59 * q^58 + 11 * q^60 + 29 * q^62 - 4 * q^64 + 55 * q^66 + 132 * q^70 + 4 * q^72 - 144 * q^73 - 66 * q^74 - 24 * q^75 - 55 * q^76 - 24 * q^81 - 26 * q^82 - 44 * q^84 - 110 * q^86 - 198 * q^88 - 47 * q^92 - 73 * q^94 + 4 * q^96 + 53 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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