LMFDB - Embedded newform 300.3.l.g.107.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(107,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("300.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.l (of order $4$, degree $2$, 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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.19
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.84549 + 0.770813i) q^{2} +(2.78107 - 1.12501i) q^{3} +(2.81170 + 2.84506i) q^{4} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(2.99596 + 7.41783i) q^{8} +(6.46869 - 6.25748i) q^{9} +O(q^{10})$	\(q+(1.84549 + 0.770813i) q^{2} +(2.78107 - 1.12501i) q^{3} +(2.81170 + 2.84506i) q^{4} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(2.99596 + 7.41783i) q^{8} +(6.46869 - 6.25748i) q^{9} +11.9496 q^{11} +(11.0203 + 4.74911i) q^{12} +(4.22368 - 4.22368i) q^{13} +(-12.4316 + 5.10644i) q^{14} +(-0.188739 + 15.9989i) q^{16} +(-9.35253 + 9.35253i) q^{17} +(16.7613 - 6.56200i) q^{18} +1.48848 q^{19} +(-7.86889 + 18.5601i) q^{21} +(22.0529 + 9.21092i) q^{22} +(11.6030 - 11.6030i) q^{23} +(16.6771 + 17.2590i) q^{24} +(11.0504 - 4.53911i) q^{26} +(10.9501 - 24.6799i) q^{27} +(-26.8786 - 0.158538i) q^{28} -39.3671 q^{29} -43.6522i q^{31} +(-12.6805 + 29.3804i) q^{32} +(33.2327 - 13.4435i) q^{33} +(-24.4691 + 10.0510i) q^{34} +(35.9909 + 0.809673i) q^{36} +(-49.1693 - 49.1693i) q^{37} +(2.74698 + 1.14734i) q^{38} +(6.99465 - 16.4981i) q^{39} +27.0663i q^{41} +(-28.8284 + 28.1871i) q^{42} +(-8.84693 - 8.84693i) q^{43} +(33.5987 + 33.9974i) q^{44} +(30.3570 - 12.4695i) q^{46} +(15.0010 + 15.0010i) q^{47} +(17.4741 + 44.7063i) q^{48} +3.84477i q^{49} +(-15.4883 + 36.5318i) q^{51} +(23.8923 + 0.140924i) q^{52} +(-14.6333 - 14.6333i) q^{53} +(39.2319 - 37.1060i) q^{54} +(-49.4821 - 21.0109i) q^{56} +(4.13957 - 1.67456i) q^{57} +(-72.6517 - 30.3447i) q^{58} +61.7260i q^{59} -84.6009 q^{61} +(33.6477 - 80.5598i) q^{62} +(-1.00356 + 60.4695i) q^{63} +(-46.0485 + 44.4470i) q^{64} +(71.6932 + 0.806325i) q^{66} +(65.7467 - 65.7467i) q^{67} +(-52.9050 - 0.312049i) q^{68} +(19.2152 - 45.3223i) q^{69} -14.2794 q^{71} +(65.7969 + 29.2365i) q^{72} +(-16.0903 + 16.0903i) q^{73} +(-52.8413 - 128.642i) q^{74} +(4.18516 + 4.23482i) q^{76} +(-56.7797 + 56.7797i) q^{77} +(25.6255 - 25.0555i) q^{78} +9.32721 q^{79} +(2.68783 - 80.9554i) q^{81} +(-20.8630 + 49.9507i) q^{82} +(12.7500 - 12.7500i) q^{83} +(-74.9296 + 29.7979i) q^{84} +(-9.50762 - 23.1463i) q^{86} +(-109.483 + 44.2885i) q^{87} +(35.8005 + 88.6403i) q^{88} +52.4342 q^{89} +40.1384i q^{91} +(65.6353 + 0.387136i) q^{92} +(-49.1093 - 121.400i) q^{93} +(16.1213 + 39.2471i) q^{94} +(-2.21192 + 95.9745i) q^{96} +(-6.90848 - 6.90848i) q^{97} +(-2.96360 + 7.09551i) q^{98} +(77.2983 - 74.7745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.84549	+	0.770813i	0.922747	+	0.385406i
$2$	1.84549	+	0.770813i	0.922747	+	0.385406i
$3$	2.78107	−	1.12501i	0.927023	−	0.375005i
$3$	2.78107	−	1.12501i	0.927023	−	0.375005i
$4$	2.81170	+	2.84506i	0.702924	+	0.711265i
$5$		0			0
$5$		0			0
$6$	5.99962	+	0.0674770i	0.999937	+	0.0112462i
$7$	−4.75159	+	4.75159i	−0.678799	+	0.678799i	−0.959728	−	0.280930i	$-0.909357\pi$
$7$	−4.75159	+	4.75159i	−0.678799	+	0.678799i	0.280930	+	0.959728i	$0.409357\pi$
$8$	2.99596	+	7.41783i	0.374495	+	0.927229i
$9$	6.46869	−	6.25748i	0.718743	−	0.695276i
$10$		0			0
$11$	11.9496			1.08633			0.543164	−	0.839626i	$-0.317226\pi$
$11$	11.9496			1.08633			0.543164	+	0.839626i	$0.317226\pi$
$12$	11.0203	+	4.74911i	0.918354	+	0.395759i
$13$	4.22368	−	4.22368i	0.324899	−	0.324899i	−0.525744	−	0.850643i	$-0.676213\pi$
$13$	4.22368	−	4.22368i	0.324899	−	0.324899i	0.850643	+	0.525744i	$0.176213\pi$
$14$	−12.4316	+	5.10644i	−0.887973	+	0.364746i
$15$		0			0
$16$	−0.188739	+	15.9989i	−0.0117962	+	0.999930i
$17$	−9.35253	+	9.35253i	−0.550149	+	0.550149i	−0.926484	−	0.376335i	$-0.877184\pi$
$17$	−9.35253	+	9.35253i	−0.550149	+	0.550149i	0.376335	+	0.926484i	$0.377184\pi$
$18$	16.7613	−	6.56200i	0.931182	−	0.364555i
$19$	1.48848			0.0783411			0.0391706	−	0.999233i	$-0.487528\pi$
$19$	1.48848			0.0783411			0.0391706	+	0.999233i	$0.487528\pi$
$20$		0			0
$21$	−7.86889	+	18.5601i	−0.374709	+	0.883815i
$22$	22.0529	+	9.21092i	1.00241	+	0.418678i
$23$	11.6030	−	11.6030i	0.504478	−	0.504478i	−0.408348	−	0.912826i	$-0.633895\pi$
$23$	11.6030	−	11.6030i	0.504478	−	0.504478i	0.912826	+	0.408348i	$0.133895\pi$
$24$	16.6771	+	17.2590i	0.694880	+	0.719125i
$25$		0			0
$26$	11.0504	−	4.53911i	0.425017	−	0.174581i
$27$	10.9501	−	24.6799i	0.405560	−	0.914069i
$28$	−26.8786	−	0.158538i	−0.959950	−	0.00566206i
$29$	−39.3671			−1.35749			−0.678743	−	0.734376i	$-0.737475\pi$
$29$	−39.3671			−1.35749			−0.678743	+	0.734376i	$0.737475\pi$
$30$		0			0
$31$		−	43.6522i		−	1.40813i	−0.710133	−	0.704067i	$-0.751365\pi$
$31$		−	43.6522i		−	1.40813i	0.710133	−	0.704067i	$-0.248635\pi$
$32$	−12.6805	+	29.3804i	−0.396264	+	0.918136i
$33$	33.2327	−	13.4435i	1.00705	−	0.407378i
$34$	−24.4691	+	10.0510i	−0.719679	+	0.295617i
$35$		0			0
$36$	35.9909	+	0.809673i	0.999747	+	0.0224909i
$37$	−49.1693	−	49.1693i	−1.32890	−	1.32890i	−0.906330	−	0.422571i	$-0.861128\pi$
$37$	−49.1693	−	49.1693i	−1.32890	−	1.32890i	−0.422571	−	0.906330i	$-0.638872\pi$
$38$	2.74698	+	1.14734i	0.0722890	+	0.0301932i
$39$	6.99465	−	16.4981i	0.179350	−	0.423027i
$40$		0			0
$41$			27.0663i			0.660153i	0.943954	+	0.330077i	$0.107075\pi$
$41$			27.0663i			0.660153i	−0.943954	+	0.330077i	$0.892925\pi$
$42$	−28.8284	+	28.1871i	−0.686390	+	0.671122i
$43$	−8.84693	−	8.84693i	−0.205742	−	0.205742i	0.596713	−	0.802455i	$-0.296473\pi$
$43$	−8.84693	−	8.84693i	−0.205742	−	0.205742i	−0.802455	+	0.596713i	$0.796473\pi$
$44$	33.5987	+	33.9974i	0.763606	+	0.772668i
$45$		0			0
$46$	30.3570	−	12.4695i	0.659935	−	0.271077i
$47$	15.0010	+	15.0010i	0.319170	+	0.319170i	0.848448	−	0.529278i	$-0.177537\pi$
$47$	15.0010	+	15.0010i	0.319170	+	0.319170i	−0.529278	+	0.848448i	$0.677537\pi$
$48$	17.4741	+	44.7063i	0.364043	+	0.931382i
$49$			3.84477i			0.0784648i
$50$		0			0
$51$	−15.4883	+	36.5318i	−0.303692	+	0.716309i
$52$	23.8923	+	0.140924i	0.459468	+	0.00271008i
$53$	−14.6333	−	14.6333i	−0.276100	−	0.276100i	0.555450	−	0.831550i	$-0.312546\pi$
$53$	−14.6333	−	14.6333i	−0.276100	−	0.276100i	−0.831550	+	0.555450i	$0.812546\pi$
$54$	39.2319	−	37.1060i	0.726517	−	0.687149i
$55$		0			0
$56$	−49.4821	−	21.0109i	−0.883608	−	0.375195i
$57$	4.13957	−	1.67456i	0.0726240	−	0.0293783i
$58$	−72.6517	−	30.3447i	−1.25262	−	0.523184i
$59$			61.7260i			1.04620i	0.852270	+	0.523102i	$0.175225\pi$
$59$			61.7260i			1.04620i	−0.852270	+	0.523102i	$0.824775\pi$
$60$		0			0
$61$	−84.6009			−1.38690			−0.693450	−	0.720505i	$-0.743910\pi$
$61$	−84.6009			−1.38690			−0.693450	+	0.720505i	$0.743910\pi$
$62$	33.6477	−	80.5598i	0.542704	−	1.29935i
$63$	−1.00356	+	60.4695i	−0.0159295	+	0.959834i
$64$	−46.0485	+	44.4470i	−0.719507	+	0.694485i
$65$		0			0
$66$	71.6932	+	0.806325i	1.08626	+	0.0122170i
$67$	65.7467	−	65.7467i	0.981293	−	0.981293i	−0.0185347	−	0.999828i	$-0.505900\pi$
$67$	65.7467	−	65.7467i	0.981293	−	0.981293i	0.999828	+	0.0185347i	$0.00590012\pi$
$68$	−52.9050	−	0.312049i	−0.778014	−	0.00458896i
$69$	19.2152	−	45.3223i	0.278481	−	0.656844i
$70$		0			0
$71$	−14.2794			−0.201118			−0.100559	−	0.994931i	$-0.532063\pi$
$71$	−14.2794			−0.201118			−0.100559	+	0.994931i	$0.532063\pi$
$72$	65.7969	+	29.2365i	0.913845	+	0.406062i
$73$	−16.0903	+	16.0903i	−0.220415	+	0.220415i	−0.808673	−	0.588258i	$-0.799814\pi$
$73$	−16.0903	+	16.0903i	−0.220415	+	0.220415i	0.588258	+	0.808673i	$0.299814\pi$
$74$	−52.8413	−	128.642i	−0.714072	−	1.73841i
$75$		0			0
$76$	4.18516	+	4.23482i	0.0550678	+	0.0557213i
$77$	−56.7797	+	56.7797i	−0.737399	+	0.737399i
$78$	25.6255	−	25.0555i	0.328532	−	0.321224i
$79$	9.32721			0.118066			0.0590330	−	0.998256i	$-0.481198\pi$
$79$	9.32721			0.118066			0.0590330	+	0.998256i	$0.481198\pi$
$80$		0			0
$81$	2.68783	−	80.9554i	0.0331831	−	0.999449i
$82$	−20.8630	+	49.9507i	−0.254427	+	0.609154i
$83$	12.7500	−	12.7500i	0.153615	−	0.153615i	−0.626116	−	0.779730i	$-0.715356\pi$
$83$	12.7500	−	12.7500i	0.153615	−	0.153615i	0.779730	+	0.626116i	$0.215356\pi$
$84$	−74.9296	+	29.7979i	−0.892019	+	0.354737i
$85$		0			0
$86$	−9.50762	−	23.1463i	−0.110554	−	0.269143i
$87$	−109.483	+	44.2885i	−1.25842	+	0.509063i
$88$	35.8005	+	88.6403i	0.406824	+	1.00728i
$89$	52.4342			0.589148			0.294574	−	0.955629i	$-0.404822\pi$
$89$	52.4342			0.589148			0.294574	+	0.955629i	$0.404822\pi$
$90$		0			0
$91$			40.1384i			0.441082i
$92$	65.6353	+	0.387136i	0.713427	+	0.00420800i
$93$	−49.1093	−	121.400i	−0.528057	−	1.30537i
$94$	16.1213	+	39.2471i	0.171503	+	0.417523i
$95$		0			0
$96$	−2.21192	+	95.9745i	−0.0230408	+	0.999735i
$97$	−6.90848	−	6.90848i	−0.0712214	−	0.0712214i	0.670599	−	0.741820i	$-0.266037\pi$
$97$	−6.90848	−	6.90848i	−0.0712214	−	0.0712214i	−0.741820	+	0.670599i	$0.766037\pi$
$98$	−2.96360	+	7.09551i	−0.0302408	+	0.0724031i
$99$	77.2983	−	74.7745i	0.780791	−	0.755298i
$100$		0			0
$101$		−	15.0065i		−	0.148579i	−0.997237	−	0.0742894i	$-0.976331\pi$
$101$		−	15.0065i		−	0.148579i	0.997237	−	0.0742894i	$-0.0236689\pi$
$102$	−56.7427	+	55.4806i	−0.556301	+	0.543927i
$103$	10.0417	+	10.0417i	0.0974926	+	0.0974926i	0.754171	−	0.656678i	$-0.228039\pi$
$103$	10.0417	+	10.0417i	0.0974926	+	0.0974926i	−0.656678	+	0.754171i	$0.728039\pi$
$104$	43.9845	+	18.6766i	0.422928	+	0.179583i
$105$		0			0
$106$	−15.7261	−	38.2852i	−0.148360	−	0.361181i
$107$	−15.4027	−	15.4027i	−0.143950	−	0.143950i	0.631459	−	0.775409i	$-0.282456\pi$
$107$	−15.4027	−	15.4027i	−0.143950	−	0.143950i	−0.775409	+	0.631459i	$0.782456\pi$
$108$	101.004	−	38.2385i	0.935223	−	0.354060i
$109$		−	15.6958i		−	0.143998i	−0.997405	−	0.0719992i	$-0.977062\pi$
$109$		−	15.6958i		−	0.143998i	0.997405	−	0.0719992i	$-0.0229379\pi$
$110$		0			0
$111$	−192.059	−	81.4271i	−1.73027	−	0.733577i
$112$	−75.1234	−	76.9170i	−0.670744	−	0.686759i
$113$	33.3231	+	33.3231i	0.294895	+	0.294895i	0.839010	−	0.544116i	$-0.183135\pi$
$113$	33.3231	+	33.3231i	0.294895	+	0.294895i	−0.544116	+	0.839010i	$0.683135\pi$
$114$	8.93032	+	0.100438i	0.0783362	+	0.000881038i
$115$		0			0
$116$	−110.688	−	112.002i	−0.954209	−	0.965532i
$117$	0.892063	−	53.7513i	0.00762447	−	0.459413i
$118$	−47.5792	+	113.915i	−0.403214	+	0.965382i
$119$		−	88.8788i		−	0.746881i
$120$		0			0
$121$	21.7934			0.180110
$122$	−156.130	−	65.2114i	−1.27976	−	0.534520i
$123$	30.4500	+	75.2732i	0.247561	+	0.611977i
$124$	124.193	−	122.737i	1.00156	−	0.989812i
$125$		0			0
$126$	−48.4628	+	110.823i	−0.384625	+	0.879545i
$127$	−11.9832	+	11.9832i	−0.0943557	+	0.0943557i	−0.752709	−	0.658353i	$-0.771253\pi$
$127$	−11.9832	+	11.9832i	−0.0943557	+	0.0943557i	0.658353	+	0.752709i	$0.271253\pi$
$128$	−119.243	+	46.5320i	−0.931582	+	0.363531i
$129$	−34.5568	−	14.6510i	−0.267882	−	0.113574i
$130$		0			0
$131$	228.815			1.74668			0.873341	−	0.487109i	$-0.161949\pi$
$131$	228.815			1.74668			0.873341	+	0.487109i	$0.161949\pi$
$132$	131.688	+	56.7501i	0.997635	+	0.429925i
$133$	−7.07265	+	7.07265i	−0.0531778	+	0.0531778i
$134$	172.013	−	70.6567i	1.28368	−	0.527289i
$135$		0			0
$136$	−97.3953	−	41.3557i	−0.716142	−	0.304086i
$137$	155.485	−	155.485i	1.13492	−	1.13492i	0.145578	−	0.989347i	$-0.453496\pi$
$137$	155.485	−	155.485i	1.13492	−	1.13492i	0.989347	−	0.145578i	$-0.0465042\pi$
$138$	70.3965	−	68.8306i	0.510120	−	0.498773i
$139$	−220.188			−1.58409			−0.792043	−	0.610465i	$-0.790982\pi$
$139$	−220.188			−1.58409			−0.792043	+	0.610465i	$0.790982\pi$
$140$		0			0
$141$	58.5950	+	24.8424i	0.415568	+	0.176187i
$142$	−26.3525	−	11.0067i	−0.185581	−	0.0775123i
$143$	50.4714	−	50.4714i	0.352947	−	0.352947i
$144$	98.8919	+	104.673i	0.686749	+	0.726895i
$145$		0			0
$146$	−42.0971	+	17.2919i	−0.288337	+	0.118438i
$147$	4.32542	+	10.6926i	0.0294247	+	0.0727386i
$148$	1.64054	−	278.139i	0.0110848	−	1.87932i
$149$	−24.2943			−0.163049			−0.0815247	−	0.996671i	$-0.525979\pi$
$149$	−24.2943			−0.163049			−0.0815247	+	0.996671i	$0.525979\pi$
$150$		0			0
$151$			120.766i			0.799772i	0.916565	+	0.399886i	$0.130950\pi$
$151$			120.766i			0.799772i	−0.916565	+	0.399886i	$0.869050\pi$
$152$	4.45943	+	11.0413i	0.0293383	+	0.0726402i
$153$	−1.97530	+	119.022i	−0.0129105	+	0.777921i
$154$	−148.553	+	61.0201i	−0.964630	+	0.396234i
$155$		0			0
$156$	66.6048	−	26.4873i	0.426954	−	0.169790i
$157$	77.1260	+	77.1260i	0.491249	+	0.491249i	0.908700	−	0.417451i	$-0.137076\pi$
$157$	77.1260	+	77.1260i	0.491249	+	0.491249i	−0.417451	+	0.908700i	$0.637076\pi$
$158$	17.2133	+	7.18953i	0.108945	+	0.0455034i
$159$	−57.1589	−	24.2336i	−0.359490	−	0.152412i
$160$		0			0
$161$			110.265i			0.684878i
$162$	67.3618	−	147.331i	0.415814	−	0.909450i
$163$	−179.764	−	179.764i	−1.10285	−	1.10285i	−0.994065	−	0.108783i	$-0.965305\pi$
$163$	−179.764	−	179.764i	−1.10285	−	1.10285i	−0.108783	−	0.994065i	$-0.534695\pi$
$164$	−77.0052	+	76.1022i	−0.469544	+	0.464038i
$165$		0			0
$166$	33.3580	−	13.7022i	0.200952	−	0.0825434i
$167$	56.8272	+	56.8272i	0.340283	+	0.340283i	0.856474	−	0.516191i	$-0.172651\pi$
$167$	56.8272	+	56.8272i	0.340283	+	0.340283i	−0.516191	+	0.856474i	$0.672651\pi$
$168$	−161.251	−	2.76485i	−0.959825	−	0.0164575i
$169$			133.321i			0.788882i
$170$		0			0
$171$	9.62852	−	9.31414i	0.0563071	−	0.0544687i
$172$	0.295179	−	50.0449i	0.00171616	−	0.290959i
$173$	130.746	+	130.746i	0.755756	+	0.755756i	0.975547	−	0.219791i	$-0.0705377\pi$
$173$	130.746	+	130.746i	0.755756	+	0.755756i	−0.219791	+	0.975547i	$0.570538\pi$
$174$	−236.188	−	2.65637i	−1.35740	−	0.0152665i
$175$		0			0
$176$	−2.25536	+	191.181i	−0.0128145	+	1.08625i
$177$	69.4427	+	171.664i	0.392331	+	0.969855i
$178$	96.7670	+	40.4170i	0.543635	+	0.227062i
$179$			213.930i			1.19514i	0.801816	+	0.597571i	$0.203867\pi$
$179$			213.930i			1.19514i	−0.801816	+	0.597571i	$0.796133\pi$
$180$		0			0
$181$	155.404			0.858588			0.429294	−	0.903165i	$-0.358762\pi$
$181$	155.404			0.858588			0.429294	+	0.903165i	$0.358762\pi$
$182$	−30.9392	+	74.0752i	−0.169996	+	0.407007i
$183$	−235.281	+	95.1771i	−1.28569	+	0.520094i
$184$	120.831	+	51.3070i	0.656691	+	0.278842i
$185$		0			0
$186$	2.94552	−	261.897i	0.0158361	−	1.40805i
$187$	−111.759	+	111.759i	−0.597643	+	0.597643i
$188$	−0.500511	+	84.8569i	−0.00266229	+	0.451366i
$189$	65.2381	+	169.299i	0.345175	+	0.895762i
$190$		0			0
$191$	102.576			0.537047			0.268524	−	0.963273i	$-0.413464\pi$
$191$	102.576			0.537047			0.268524	+	0.963273i	$0.413464\pi$
$192$	−78.0605	+	175.415i	−0.406565	+	0.913622i
$193$	−138.213	+	138.213i	−0.716129	+	0.716129i	−0.967810	−	0.251681i	$-0.919017\pi$
$193$	−138.213	+	138.213i	−0.716129	+	0.716129i	0.251681	+	0.967810i	$0.419017\pi$
$194$	−7.42441	−	18.0747i	−0.0382701	−	0.0931685i
$195$		0			0
$196$	−10.9386	+	10.8103i	−0.0558093	+	0.0551548i
$197$	−94.4283	+	94.4283i	−0.479331	+	0.479331i	−0.904918	−	0.425586i	$-0.860068\pi$
$197$	−94.4283	+	94.4283i	−0.479331	+	0.479331i	0.425586	+	0.904918i	$0.360068\pi$
$198$	200.291	−	78.4134i	1.01157	−	0.396027i
$199$	185.280			0.931058			0.465529	−	0.885033i	$-0.345864\pi$
$199$	185.280			0.931058			0.465529	+	0.885033i	$0.345864\pi$
$200$		0			0
$201$	108.880	−	256.812i	0.541692	−	1.27767i
$202$	11.5672	−	27.6943i	0.0572632	−	0.137101i
$203$	187.056	−	187.056i	0.921459	−	0.921459i
$204$	−147.483	+	58.6510i	−0.722958	+	0.287505i
$205$		0			0
$206$	10.7917	+	26.2723i	0.0523868	+	0.127535i
$207$	2.45061	−	147.662i	0.0118387	−	0.713342i
$208$	66.7771	+	68.3714i	0.321044	+	0.328709i
$209$	17.7868			0.0851042
$210$		0			0
$211$		−	270.850i		−	1.28365i	−0.766850	−	0.641826i	$-0.778177\pi$
$211$		−	270.850i		−	1.28365i	0.766850	−	0.641826i	$-0.221823\pi$
$212$	0.488243	−	82.7770i	0.00230303	−	0.390458i
$213$	−39.7120	+	16.0645i	−0.186441	+	0.0754203i
$214$	−16.5530	−	40.2982i	−0.0773504	−	0.188309i
$215$		0			0
$216$	215.877	+	7.28629i	0.999431	+	0.0337328i
$217$	207.417	+	207.417i	0.955840	+	0.955840i
$218$	12.0985	−	28.9666i	0.0554979	−	0.132874i
$219$	−26.6464	+	62.8500i	−0.121673	+	0.286986i
$220$		0			0
$221$			79.0043i			0.357485i
$222$	−291.679	−	298.315i	−1.31387	−	1.34376i
$223$	173.313	+	173.313i	0.777190	+	0.777190i	0.979352	−	0.202162i	$-0.0647968\pi$
$223$	173.313	+	173.313i	0.777190	+	0.777190i	−0.202162	+	0.979352i	$0.564797\pi$
$224$	−79.3511	−	199.856i	−0.354246	−	0.892214i
$225$		0			0
$226$	35.8117	+	87.1835i	0.158459	+	0.385768i
$227$	192.265	+	192.265i	0.846983	+	0.846983i	0.989755	−	0.142773i	$-0.0456019\pi$
$227$	192.265	+	192.265i	0.846983	+	0.846983i	−0.142773	+	0.989755i	$0.545602\pi$
$228$	16.4034	+	7.06896i	0.0719449	+	0.0310042i
$229$		−	74.6665i		−	0.326054i	−0.986622	−	0.163027i	$-0.947874\pi$
$229$		−	74.6665i		−	0.326054i	0.986622	−	0.163027i	$-0.0521258\pi$
$230$		0			0
$231$	−94.0303	+	221.786i	−0.407058	+	0.960113i
$232$	−117.942	−	292.018i	−0.508371	−	1.25870i
$233$	−148.778	−	148.778i	−0.638532	−	0.638532i	0.311661	−	0.950193i	$-0.399115\pi$
$233$	−148.778	−	148.778i	−0.638532	−	0.638532i	−0.950193	+	0.311661i	$0.899115\pi$
$234$	43.0785	−	98.5101i	0.184096	−	0.420983i
$235$		0			0
$236$	−175.614	+	173.555i	−0.744128	+	0.735402i
$237$	25.9396	−	10.4932i	0.109450	−	0.0442753i
$238$	68.5089	−	164.025i	0.287853	−	0.689182i
$239$			214.211i			0.896278i	0.893964	+	0.448139i	$0.147913\pi$
$239$			214.211i			0.896278i	−0.893964	+	0.448139i	$0.852087\pi$
$240$		0			0
$241$	167.934			0.696821			0.348411	−	0.937342i	$-0.386722\pi$
$241$	167.934			0.696821			0.348411	+	0.937342i	$0.386722\pi$
$242$	40.2195	+	16.7986i	0.166196	+	0.0694157i
$243$	−83.6009	−	228.166i	−0.344037	−	0.938956i
$244$	−237.872	−	240.695i	−0.974885	−	0.986453i
$245$		0			0
$246$	−1.82635	+	162.387i	−0.00742420	+	0.660112i
$247$	6.28687	−	6.28687i	0.0254529	−	0.0254529i
$248$	323.805	−	130.780i	1.30566	−	0.527339i
$249$	21.1147	−	49.8027i	0.0847982	−	0.200011i
$250$		0			0
$251$	166.809			0.664578			0.332289	−	0.943178i	$-0.392179\pi$
$251$	166.809			0.664578			0.332289	+	0.943178i	$0.392179\pi$
$252$	−174.861	+	167.167i	−0.693894	+	0.663360i
$253$	138.651	−	138.651i	0.548029	−	0.548029i
$254$	−31.3516	+	12.8781i	−0.123432	+	0.0507011i
$255$		0			0
$256$	−255.929	−	6.03922i	−0.999722	−	0.0235907i
$257$	−16.3199	+	16.3199i	−0.0635014	+	0.0635014i	−0.738144	−	0.674643i	$-0.764298\pi$
$257$	−16.3199	+	16.3199i	−0.0635014	+	0.0635014i	0.674643	+	0.738144i	$0.264298\pi$
$258$	−52.4812	−	53.6752i	−0.203416	−	0.208043i
$259$	467.265			1.80411
$260$		0			0
$261$	−254.653	+	246.339i	−0.975683	+	0.943827i
$262$	422.277	+	176.374i	1.61175	+	0.673183i
$263$	−121.290	+	121.290i	−0.461180	+	0.461180i	−0.899042	−	0.437862i	$-0.855736\pi$
$263$	−121.290	+	121.290i	−0.461180	+	0.461180i	0.437862	+	0.899042i	$0.355736\pi$
$264$	199.285	+	206.239i	0.754869	+	0.781207i
$265$		0			0
$266$	−18.5042	+	7.60085i	−0.0695648	+	0.0285746i
$267$	145.823	−	58.9892i	0.546154	−	0.220933i
$268$	371.913	+	2.19365i	1.38773	+	0.00818526i
$269$	−174.671			−0.649336			−0.324668	−	0.945828i	$-0.605253\pi$
$269$	−174.671			−0.649336			−0.324668	+	0.945828i	$0.605253\pi$
$270$		0			0
$271$			306.881i			1.13240i	0.824268	+	0.566200i	$0.191587\pi$
$271$			306.881i			1.13240i	−0.824268	+	0.566200i	$0.808413\pi$
$272$	−147.865	−	151.395i	−0.543621	−	0.556600i
$273$	45.1563	+	111.628i	0.165408	+	0.408893i
$274$	406.796	−	167.096i	1.48466	−	0.609841i
$275$		0			0
$276$	182.972	−	72.7640i	0.662942	−	0.263638i
$277$	−28.5949	−	28.5949i	−0.103231	−	0.103231i	0.653605	−	0.756836i	$-0.273256\pi$
$277$	−28.5949	−	28.5949i	−0.103231	−	0.103231i	−0.756836	+	0.653605i	$0.773256\pi$
$278$	−406.356	−	169.724i	−1.46171	−	0.610517i
$279$	−273.153	−	282.372i	−0.979042	−	1.01209i
$280$		0			0
$281$		−	42.3210i		−	0.150609i	−0.997161	−	0.0753043i	$-0.976007\pi$
$281$		−	42.3210i		−	0.150609i	0.997161	−	0.0753043i	$-0.0239928\pi$
$282$	88.9879	+	91.0124i	0.315560	+	0.322739i
$283$	341.834	+	341.834i	1.20789	+	1.20789i	0.971708	+	0.236185i	$0.0758971\pi$
$283$	341.834	+	341.834i	1.20789	+	1.20789i	0.236185	+	0.971708i	$0.424103\pi$
$284$	−40.1493	−	40.6257i	−0.141371	−	0.143048i
$285$		0			0
$286$	132.049	−	54.2407i	0.461709	−	0.189653i
$287$	−128.608	−	128.608i	−0.448111	−	0.448111i
$288$	101.821	+	269.400i	0.353546	+	0.935417i
$289$			114.060i			0.394672i
$290$		0			0
$291$	−26.9851	−	11.4408i	−0.0927322	−	0.0393155i
$292$	−91.0189	−	0.536856i	−0.311708	−	0.00183855i
$293$	252.918	+	252.918i	0.863203	+	0.863203i	0.991709	−	0.128506i	$-0.0410181\pi$
$293$	252.918	+	252.918i	0.863203	+	0.863203i	−0.128506	+	0.991709i	$0.541018\pi$
$294$	−0.259434	+	23.0672i	−0.000882428	+	0.0784598i
$295$		0			0
$296$	217.421	−	512.039i	0.734529	−	1.72986i
$297$	130.850	−	294.915i	0.440571	−	0.992979i
$298$	−44.8351	−	18.7264i	−0.150453	−	0.0628403i
$299$		−	98.0148i		−	0.327809i
$300$		0			0
$301$	84.0739			0.279315
$302$	−93.0877	+	222.872i	−0.308237	+	0.737987i
$303$	−16.8825	−	41.7340i	−0.0557177	−	0.137736i
$304$	−0.280934	+	23.8140i	−0.000924125	+	0.0783357i
$305$		0			0
$306$	−95.3890	+	218.132i	−0.311729	+	0.712848i
$307$	−281.593	+	281.593i	−0.917240	+	0.917240i	−0.996828	−	0.0795878i	$-0.974640\pi$
$307$	−281.593	+	281.593i	−0.917240	+	0.917240i	0.0795878	+	0.996828i	$0.474640\pi$
$308$	−321.189	−	1.89447i	−1.04282	−	0.00615086i
$309$	39.2239	+	16.6297i	0.126938	+	0.0538177i
$310$		0			0
$311$	−318.688			−1.02472			−0.512360	−	0.858771i	$-0.671229\pi$
$311$	−318.688			−1.02472			−0.512360	+	0.858771i	$0.671229\pi$
$312$	143.335	+	2.45768i	0.459409	+	0.00787716i
$313$	165.571	−	165.571i	0.528979	−	0.528979i	−0.391289	−	0.920268i	$-0.627971\pi$
$313$	165.571	−	165.571i	0.528979	−	0.528979i	0.920268	+	0.391289i	$0.127971\pi$
$314$	82.8859	+	201.785i	0.263968	+	0.642629i
$315$		0			0
$316$	26.2253	+	26.5365i	0.0829914	+	0.0839762i
$317$	−6.74356	+	6.74356i	−0.0212731	+	0.0212731i	−0.717663	−	0.696390i	$-0.754788\pi$
$317$	−6.74356	+	6.74356i	−0.0212731	+	0.0212731i	0.696390	+	0.717663i	$0.254788\pi$
$318$	−86.8069	−	88.7817i	−0.272978	−	0.279188i
$319$	−470.422			−1.47468
$320$		0			0
$321$	−60.1642	−	25.5077i	−0.187427	−	0.0794633i
$322$	−84.9940	+	203.494i	−0.263956	+	0.631969i
$323$	−13.9211	+	13.9211i	−0.0430993	+	0.0430993i
$324$	237.880	−	219.975i	0.734199	−	0.678935i
$325$		0			0
$326$	−193.189	−	470.319i	−0.592605	−	1.44270i
$327$	−17.6580	−	43.6512i	−0.0540001	−	0.133490i
$328$	−200.773	+	81.0894i	−0.612113	+	0.247224i
$329$	−142.557			−0.433304
$330$		0			0
$331$		−	278.406i		−	0.841105i	−0.907268	−	0.420553i	$-0.861836\pi$
$331$		−	278.406i		−	0.841105i	0.907268	−	0.420553i	$-0.138164\pi$
$332$	72.1238	+	0.425407i	0.217240	+	0.00128135i
$333$	−625.737	−	10.3848i	−1.87909	−	0.0311856i
$334$	61.0711	+	148.677i	0.182848	+	0.445142i
$335$		0			0
$336$	−295.456	−	129.397i	−0.879333	−	0.385109i
$337$	−282.964	−	282.964i	−0.839656	−	0.839656i	0.149157	−	0.988813i	$-0.452344\pi$
$337$	−282.964	−	282.964i	−0.839656	−	0.839656i	−0.988813	+	0.149157i	$0.952344\pi$
$338$	−102.766	+	246.043i	−0.304040	+	0.727938i
$339$	130.163	+	55.1849i	0.383961	+	0.162787i
$340$		0			0
$341$		−	521.627i		−	1.52970i
$342$	24.9488	−	9.76741i	0.0729498	−	0.0285597i
$343$	−251.097	−	251.097i	−0.732060	−	0.732060i
$344$	39.1200	−	92.1300i	0.113721	−	0.267820i
$345$		0			0
$346$	140.510	+	342.071i	0.406098	+	0.988644i
$347$	36.0256	+	36.0256i	0.103820	+	0.103820i	0.757109	−	0.653289i	$-0.226611\pi$
$347$	36.0256	+	36.0256i	0.103820	+	0.103820i	−0.653289	+	0.757109i	$0.726611\pi$
$348$	−433.835	−	186.959i	−1.24665	−	0.537238i
$349$		−	382.830i		−	1.09693i	−0.836173	−	0.548467i	$-0.815212\pi$
$349$		−	382.830i		−	1.09693i	0.836173	−	0.548467i	$-0.184788\pi$
$350$		0			0
$351$	−57.9901	−	150.490i	−0.165214	−	0.428745i
$352$	−151.527	+	351.084i	−0.430474	+	0.997398i
$353$	−215.726	−	215.726i	−0.611121	−	0.611121i	0.332117	−	0.943238i	$-0.392237\pi$
$353$	−215.726	−	215.726i	−0.611121	−	0.611121i	−0.943238	+	0.332117i	$0.892237\pi$
$354$	−4.16509	+	370.333i	−0.0117658	+	1.04614i
$355$		0			0
$356$	147.429	+	149.178i	0.414126	+	0.419041i
$357$	−99.9899	−	247.178i	−0.280084	−	0.692375i
$358$	−164.900	+	394.807i	−0.460615	+	1.10281i
$359$		−	473.986i		−	1.32030i	−0.751136	−	0.660148i	$-0.770494\pi$
$359$		−	473.986i		−	1.32030i	0.751136	−	0.660148i	$-0.229506\pi$
$360$		0			0
$361$	−358.784			−0.993863
$362$	286.798	+	119.788i	0.792260	+	0.330905i
$363$	60.6088	−	24.5178i	0.166966	−	0.0675422i
$364$	−114.196	+	112.857i	−0.313726	+	0.310047i
$365$		0			0
$366$	−507.573	−	5.70862i	−1.38681	−	0.0155973i
$367$	249.323	−	249.323i	0.679354	−	0.679354i	−0.280500	−	0.959854i	$-0.590500\pi$
$367$	249.323	−	249.323i	0.679354	−	0.679354i	0.959854	+	0.280500i	$0.0905004\pi$
$368$	183.445	+	187.825i	0.498492	+	0.510394i
$369$	169.367	+	175.083i	0.458989	+	0.474481i
$370$		0			0
$371$	139.063			0.374833
$372$	207.309	−	481.058i	0.557283	−	1.29317i
$373$	108.084	−	108.084i	0.289769	−	0.289769i	−0.547220	−	0.836989i	$-0.684314\pi$
$373$	108.084	−	108.084i	0.289769	−	0.289769i	0.836989	+	0.547220i	$0.184314\pi$
$374$	−292.396	+	120.105i	−0.781808	+	0.321138i
$375$		0			0
$376$	−66.3324	+	156.217i	−0.176416	+	0.415471i
$377$	−166.274	+	166.274i	−0.441045	+	0.441045i
$378$	−10.1013	+	362.727i	−0.0267230	+	0.959594i
$379$	−60.0656			−0.158484			−0.0792422	−	0.996855i	$-0.525250\pi$
$379$	−60.0656			−0.158484			−0.0792422	+	0.996855i	$0.525250\pi$
$380$		0			0
$381$	−19.8448	+	46.8073i	−0.0520861	+	0.122854i
$382$	189.303	+	79.0669i	0.495559	+	0.206981i
$383$	−375.372	+	375.372i	−0.980084	+	0.980084i	−0.999806	−	0.0197220i	$-0.993722\pi$
$383$	−375.372	+	375.372i	−0.980084	+	0.980084i	0.0197220	+	0.999806i	$0.493722\pi$
$384$	−279.273	+	263.558i	−0.727272	+	0.686349i
$385$		0			0
$386$	−361.607	+	148.535i	−0.936806	+	0.384805i
$387$	−112.587	−	1.86852i	−0.290924	−	0.00482821i
$388$	0.230503	−	39.0796i	0.000594079	−	0.100721i
$389$	464.374			1.19376			0.596882	−	0.802329i	$-0.296406\pi$
$389$	464.374			1.19376			0.596882	+	0.802329i	$0.296406\pi$
$390$		0			0
$391$			217.035i			0.555076i
$392$	−28.5199	+	11.5188i	−0.0727548	+	0.0293846i
$393$	636.351	−	257.421i	1.61921	−	0.655014i
$394$	−247.053	+	101.480i	−0.627039	+	0.257564i
$395$		0			0
$396$	430.077	+	9.67529i	1.08605	+	0.0244325i
$397$	125.935	+	125.935i	0.317215	+	0.317215i	0.847697	−	0.530481i	$-0.177989\pi$
$397$	125.935	+	125.935i	0.317215	+	0.317215i	−0.530481	+	0.847697i	$0.677989\pi$
$398$	341.934	+	142.817i	0.859131	+	0.358836i
$399$	−11.7127	+	27.6264i	−0.0293551	+	0.0692390i
$400$		0			0
$401$			508.065i			1.26699i	0.773745	+	0.633497i	$0.218381\pi$
$401$			508.065i			1.26699i	−0.773745	+	0.633497i	$0.781619\pi$
$402$	398.891	−	390.019i	0.992267	−	0.970196i
$403$	−184.373	−	184.373i	−0.457501	−	0.457501i
$404$	42.6943	−	42.1936i	0.105679	−	0.104440i
$405$		0			0
$406$	489.397	−	201.026i	1.20541	−	0.495138i
$407$	−587.555	−	587.555i	−1.44362	−	1.44362i
$408$	−317.389	−	5.44205i	−0.777914	−	0.0133384i
$409$		−	583.921i		−	1.42768i	−0.700309	−	0.713840i	$-0.746954\pi$
$409$		−	583.921i		−	1.42768i	0.700309	−	0.713840i	$-0.253046\pi$
$410$		0			0
$411$	257.491	−	607.336i	0.626499	−	1.47770i
$412$	−0.335045	+	56.8037i	−0.000813215	+	0.137873i
$413$	−293.297	−	293.297i	−0.710162	−	0.710162i
$414$	118.342	−	270.620i	0.285851	−	0.653671i
$415$		0			0
$416$	70.5351	+	177.652i	0.169556	+	0.427047i
$417$	−612.358	+	247.715i	−1.46848	+	0.594040i
$418$	32.8254	+	13.7103i	0.0785297	+	0.0327997i
$419$			283.902i			0.677571i	0.940864	+	0.338786i	$0.110016\pi$
$419$			283.902i			0.677571i	−0.940864	+	0.338786i	$0.889984\pi$
$420$		0			0
$421$	−468.185			−1.11208			−0.556039	−	0.831156i	$-0.687679\pi$
$421$	−468.185			−1.11208			−0.556039	+	0.831156i	$0.687679\pi$
$422$	208.775	−	499.853i	0.494728	−	1.18449i
$423$	190.905	+	3.16828i	0.451312	+	0.00749003i
$424$	64.7066	−	152.388i	0.152610	−	0.359406i
$425$		0			0
$426$	−85.6710	−	0.963531i	−0.201106	−	0.00226181i
$427$	401.989	−	401.989i	0.941425	−	0.941425i
$428$	0.513914	−	87.1293i	0.00120073	−	0.203573i
$429$	83.5834	−	197.145i	0.194833	−	0.459546i
$430$		0			0
$431$	−849.775			−1.97164			−0.985818	−	0.167821i	$-0.946327\pi$
$431$	−849.775			−1.97164			−0.985818	+	0.167821i	$0.946327\pi$
$432$	392.783	+	179.848i	0.909221	+	0.416314i
$433$	−153.887	+	153.887i	−0.355398	+	0.355398i	−0.862113	−	0.506715i	$-0.830859\pi$
$433$	−153.887	+	153.887i	−0.355398	+	0.355398i	0.506715	+	0.862113i	$0.330859\pi$
$434$	222.907	+	542.667i	0.513612	+	1.25039i
$435$		0			0
$436$	44.6556	−	44.1319i	0.102421	−	0.101220i
$437$	17.2708	−	17.2708i	0.0395214	−	0.0395214i
$438$	−97.6214	+	95.4499i	−0.222880	+	0.217922i
$439$	55.5775			0.126600			0.0633001	−	0.997995i	$-0.479837\pi$
$439$	55.5775			0.126600			0.0633001	+	0.997995i	$0.479837\pi$
$440$		0			0
$441$	24.0586	+	24.8706i	0.0545547	+	0.0563960i
$442$	−60.8975	+	145.802i	−0.137777	+	0.329868i
$443$	543.074	−	543.074i	1.22590	−	1.22590i	0.260398	−	0.965501i	$-0.416146\pi$
$443$	543.074	−	543.074i	1.22590	−	1.22590i	0.965501	−	0.260398i	$-0.0838539\pi$
$444$	−308.348	−	775.369i	−0.694477	−	1.74633i
$445$		0			0
$446$	186.257	+	453.441i	0.417616	+	1.01668i
$447$	−67.5643	+	27.3315i	−0.151150	+	0.0611443i
$448$	7.60946	−	429.998i	0.0169854	−	0.959816i
$449$	36.3462			0.0809493			0.0404746	−	0.999181i	$-0.487113\pi$
$449$	36.3462			0.0809493			0.0404746	+	0.999181i	$0.487113\pi$
$450$		0			0
$451$			323.432i			0.717144i
$452$	−1.11183	+	188.501i	−0.00245981	+	0.417037i
$453$	135.863	+	335.857i	0.299918	+	0.741407i
$454$	206.624	+	503.024i	0.455118	+	1.10798i
$455$		0			0
$456$	24.8236	+	25.6897i	0.0544377	+	0.0563371i
$457$	−465.155	−	465.155i	−1.01784	−	1.01784i	−0.999838	−	0.0180061i	$-0.994268\pi$
$457$	−465.155	−	465.155i	−1.01784	−	1.01784i	−0.0180061	−	0.999838i	$-0.505732\pi$
$458$	57.5539	−	137.797i	0.125663	−	0.300866i
$459$	128.408	+	333.230i	0.279756	+	0.725992i
$460$		0			0
$461$		−	69.6948i		−	0.151182i	−0.997139	−	0.0755909i	$-0.975916\pi$
$461$		−	69.6948i		−	0.151182i	0.997139	−	0.0755909i	$-0.0240843\pi$
$462$	−344.488	+	336.825i	−0.745645	+	0.729059i
$463$	453.386	+	453.386i	0.979236	+	0.979236i	0.999789	−	0.0205531i	$-0.00654273\pi$
$463$	453.386	+	453.386i	0.979236	+	0.979236i	−0.0205531	+	0.999789i	$0.506543\pi$
$464$	7.43010	−	629.830i	0.0160131	−	1.35739i
$465$		0			0
$466$	−159.889	−	389.249i	−0.343109	−	0.835298i
$467$	434.371	+	434.371i	0.930130	+	0.930130i	0.997714	−	0.0675833i	$-0.0215288\pi$
$467$	434.371	+	434.371i	0.930130	+	0.930130i	−0.0675833	+	0.997714i	$0.521529\pi$
$468$	155.434	−	148.594i	0.332124	−	0.317509i
$469$			624.802i			1.33220i
$470$		0			0
$471$	301.261	+	127.725i	0.639619	+	0.271178i
$472$	−457.873	+	184.929i	−0.970071	+	0.391798i
$473$	−105.717	−	105.717i	−0.223504	−	0.223504i
$474$	55.9597	+	0.629373i	0.118059	+	0.00132779i
$475$		0			0
$476$	252.866	−	249.900i	0.531230	−	0.525000i
$477$	−186.226	−	3.09063i	−0.390411	−	0.00647930i
$478$	−165.116	+	395.324i	−0.345431	+	0.827038i
$479$		−	307.039i		−	0.641000i	−0.947248	−	0.320500i	$-0.896149\pi$
$479$		−	307.039i		−	0.641000i	0.947248	−	0.320500i	$-0.103851\pi$
$480$		0			0
$481$	−415.351			−0.863516
$482$	309.921	+	129.446i	0.642990	+	0.268559i
$483$	124.050	+	306.656i	0.256832	+	0.634898i
$484$	61.2763	+	62.0034i	0.126604	+	0.128106i
$485$		0			0
$486$	21.5886	−	485.520i	0.0444210	−	0.999013i
$487$	−250.434	+	250.434i	−0.514237	+	0.514237i	−0.915822	−	0.401585i	$-0.868460\pi$
$487$	−250.434	+	250.434i	−0.514237	+	0.514237i	0.401585	+	0.915822i	$0.368460\pi$
$488$	−253.461	−	627.555i	−0.519386	−	1.28597i
$489$	−702.174	−	297.700i	−1.43594	−	0.608793i
$490$		0			0
$491$	291.754			0.594203			0.297102	−	0.954846i	$-0.403980\pi$
$491$	291.754			0.594203			0.297102	+	0.954846i	$0.403980\pi$
$492$	−128.541	+	298.277i	−0.261262	+	0.606255i
$493$	368.182	−	368.182i	0.746819	−	0.746819i
$494$	16.4484	−	6.75638i	0.0332963	−	0.0136769i
$495$		0			0
$496$	698.386	+	8.23886i	1.40804	+	0.0166106i
$497$	67.8498	−	67.8498i	0.136519	−	0.136519i
$498$	77.3557	−	75.6350i	0.155333	−	0.151877i
$499$	421.977			0.845646			0.422823	−	0.906212i	$-0.361039\pi$
$499$	421.977			0.845646			0.422823	+	0.906212i	$0.361039\pi$
$500$		0			0
$501$	221.972	+	94.1089i	0.443057	+	0.187842i
$502$	307.845	+	128.579i	0.613238	+	0.256133i
$503$	−288.062	+	288.062i	−0.572688	+	0.572688i	−0.932879	−	0.360191i	$-0.882712\pi$
$503$	−288.062	+	288.062i	−0.572688	+	0.572688i	0.360191	+	0.932879i	$0.382712\pi$
$504$	−451.560	+	173.720i	−0.895952	+	0.344682i
$505$		0			0
$506$	362.755	−	149.006i	0.716906	−	0.294478i
$507$	149.988	+	370.775i	0.295834	+	0.731311i
$508$	−67.7859	−	0.399821i	−0.133437	−	0.000787049i
$509$	−808.790			−1.58898			−0.794489	−	0.607278i	$-0.792261\pi$
$509$	−808.790			−1.58898			−0.794489	+	0.607278i	$0.792261\pi$
$510$		0			0
$511$		−	152.909i		−	0.299235i
$512$	−467.660	−	208.418i	−0.913398	−	0.407067i
$513$	16.2990	−	36.7355i	0.0317720	−	0.0716091i
$514$	−42.6977	+	17.5386i	−0.0830695	+	0.0341219i
$515$		0			0
$516$	−55.4803	−	139.510i	−0.107520	−	0.270369i
$517$	179.256	+	179.256i	0.346723	+	0.346723i
$518$	862.335	+	360.174i	1.66474	+	0.695316i
$519$	510.704	+	216.522i	0.984015	+	0.417191i
$520$		0			0
$521$			105.970i			0.203397i	0.994815	+	0.101699i	$0.0324277\pi$
$521$			105.970i			0.203397i	−0.994815	+	0.101699i	$0.967572\pi$
$522$	−659.842	+	258.327i	−1.26407	+	0.494879i
$523$	−229.588	−	229.588i	−0.438982	−	0.438982i	0.452687	−	0.891669i	$-0.350465\pi$
$523$	−229.588	−	229.588i	−0.438982	−	0.438982i	−0.891669	+	0.452687i	$0.850465\pi$
$524$	643.359	+	650.994i	1.22778	+	1.24235i
$525$		0			0
$526$	−317.332	+	130.348i	−0.603294	+	0.247810i
$527$	408.258	+	408.258i	0.774684	+	0.774684i
$528$	208.809	+	534.224i	0.395471	+	1.01179i
$529$			259.741i			0.491004i
$530$		0			0
$531$	386.250	+	399.286i	0.727400	+	0.751952i
$532$	−40.0083	−	0.235980i	−0.0752035	−	0.000443572i
$533$	114.319	+	114.319i	0.214483	+	0.214483i
$534$	314.585	+	3.53811i	0.589111	+	0.00662566i
$535$		0			0
$536$	684.672	+	290.724i	1.27737	+	0.542395i
$537$	240.675	+	594.955i	0.448184	+	1.10792i
$538$	−322.355	−	134.639i	−0.599173	−	0.250258i
$539$			45.9436i			0.0852385i
$540$		0			0
$541$	1053.67			1.94763			0.973816	−	0.227338i	$-0.0730021\pi$
$541$	1053.67			1.94763			0.973816	+	0.227338i	$0.0730021\pi$
$542$	−236.547	+	566.346i	−0.436434	+	1.04492i
$543$	432.190	−	174.832i	0.795931	−	0.321975i
$544$	−156.186	−	393.375i	−0.287107	−	0.723116i
$545$		0			0
$546$	−2.70842	+	240.815i	−0.00496048	+	0.441054i
$547$	559.528	−	559.528i	1.02290	−	1.02290i	0.0231709	−	0.999732i	$-0.492624\pi$
$547$	559.528	−	559.528i	1.02290	−	1.02290i	0.999732	−	0.0231709i	$-0.00737620\pi$
$548$	879.539	+	5.18778i	1.60500	+	0.00946675i
$549$	−547.256	+	529.388i	−0.996824	+	0.964278i
$550$		0			0
$551$	−58.5972			−0.106347
$552$	393.761	+	6.75155i	0.713335	+	0.0122311i
$553$	−44.3191	+	44.3191i	−0.0801430	+	0.0801430i
$554$	−30.7304	−	74.8131i	−0.0554701	−	0.135042i
$555$		0			0
$556$	−619.101	−	626.448i	−1.11349	−	1.12671i
$557$	616.817	−	616.817i	1.10739	−	1.10739i	0.113899	−	0.993492i	$-0.463666\pi$
$557$	616.817	−	616.817i	1.10739	−	1.10739i	0.993492	−	0.113899i	$-0.0363340\pi$
$558$	−286.446	−	731.666i	−0.513343	−	1.31123i
$559$	−74.7332			−0.133691
$560$		0			0
$561$	−185.079	+	436.541i	−0.329910	+	0.778147i
$562$	32.6216	−	78.1032i	0.0580455	−	0.138974i
$563$	−170.898	+	170.898i	−0.303550	+	0.303550i	−0.842401	−	0.538851i	$-0.818858\pi$
$563$	−170.898	+	170.898i	−0.303550	+	0.303550i	0.538851	+	0.842401i	$0.318858\pi$
$564$	94.0732	+	236.556i	0.166796	+	0.419425i
$565$		0			0
$566$	367.362	+	894.342i	0.649050	+	1.58011i
$567$	371.895	+	397.438i	0.655900	+	0.700949i
$568$	−42.7805	−	105.922i	−0.0753177	−	0.186483i
$569$	609.836			1.07177			0.535884	−	0.844291i	$-0.319978\pi$
$569$	609.836			1.07177			0.535884	+	0.844291i	$0.319978\pi$
$570$		0			0
$571$		−	478.800i		−	0.838529i	−0.907864	−	0.419265i	$-0.862288\pi$
$571$		−	478.800i		−	0.838529i	0.907864	−	0.419265i	$-0.137712\pi$
$572$	285.504	+	1.68399i	0.499134	+	0.00294404i
$573$	285.271	−	115.399i	0.497855	−	0.201395i
$574$	−138.212	−	336.478i	−0.240788	−	0.586198i
$575$		0			0
$576$	−19.7467	+	575.661i	−0.0342826	+	0.999412i
$577$	162.684	+	162.684i	0.281947	+	0.281947i	0.833885	−	0.551938i	$-0.186111\pi$
$577$	162.684	+	162.684i	0.281947	+	0.281947i	−0.551938	+	0.833885i	$0.686111\pi$
$578$	−87.9192	+	210.498i	−0.152109	+	0.364183i
$579$	−228.888	+	539.871i	−0.395316	+	0.932419i
$580$		0			0
$581$			121.166i			0.208547i
$582$	−40.9821	−	41.9144i	−0.0704159	−	0.0720179i
$583$	−174.862	−	174.862i	−0.299935	−	0.299935i
$584$	−167.561	−	71.1493i	−0.286919	−	0.121831i
$585$		0			0
$586$	271.807	+	661.712i	0.463834	+	1.12920i
$587$	−785.786	−	785.786i	−1.33865	−	1.33865i	−0.897372	−	0.441275i	$-0.854526\pi$
$587$	−785.786	−	785.786i	−1.33865	−	1.33865i	−0.441275	−	0.897372i	$-0.645474\pi$
$588$	−18.2593	+	42.3704i	−0.0310532	+	0.0720585i
$589$		−	64.9754i		−	0.110315i
$590$		0			0
$591$	−156.378	+	368.845i	−0.264600	+	0.624103i
$592$	795.935	−	777.374i	1.34448	−	1.31313i
$593$	646.718	+	646.718i	1.09059	+	1.09059i	0.995466	+	0.0951217i	$0.0303240\pi$
$593$	646.718	+	646.718i	1.09059	+	1.09059i	0.0951217	+	0.995466i	$0.469676\pi$
$594$	468.806	−	443.403i	0.789236	−	0.746470i
$595$		0			0
$596$	−68.3083	−	69.1189i	−0.114611	−	0.115971i
$597$	515.278	−	208.443i	0.863112	−	0.349151i
$598$	75.5510	−	180.886i	0.126340	−	0.302484i
$599$		−	300.352i		−	0.501423i	−0.968062	−	0.250711i	$-0.919336\pi$
$599$		−	300.352i		−	0.501423i	0.968062	−	0.250711i	$-0.0806645\pi$
$600$		0			0
$601$	7.74118			0.0128805			0.00644025	−	0.999979i	$-0.497950\pi$
$601$	7.74118			0.0128805			0.00644025	+	0.999979i	$0.497950\pi$
$602$	155.158	+	64.8053i	0.257737	+	0.107650i
$603$	13.8860	−	836.703i	0.0230282	−	1.38757i
$604$	−343.585	+	339.556i	−0.568850	+	0.562179i
$605$		0			0
$606$	1.01259	−	90.0331i	0.00167094	−	0.148569i
$607$	−424.929	+	424.929i	−0.700047	+	0.700047i	−0.964421	−	0.264373i	$-0.914835\pi$
$607$	−424.929	+	424.929i	−0.700047	+	0.700047i	0.264373	+	0.964421i	$0.414835\pi$
$608$	−18.8746	+	43.7321i	−0.0310438	+	0.0719278i
$609$	309.775	−	730.657i	0.508662	−	1.19977i
$610$		0			0
$611$	126.719			0.207396
$612$	−344.178	+	329.033i	−0.562383	+	0.537636i
$613$	−714.397	+	714.397i	−1.16541	+	1.16541i	−0.182138	+	0.983273i	$0.558302\pi$
$613$	−714.397	+	714.397i	−1.16541	+	1.16541i	−0.983273	+	0.182138i	$0.941698\pi$
$614$	−736.733	+	302.622i	−1.19989	+	0.492870i
$615$		0			0
$616$	−591.292	−	251.073i	−0.959889	−	0.407586i
$617$	−464.917	+	464.917i	−0.753513	+	0.753513i	−0.975133	−	0.221620i	$-0.928865\pi$
$617$	−464.917	+	464.917i	−0.753513	+	0.753513i	0.221620	+	0.975133i	$0.428865\pi$
$618$	59.5691	+	60.9242i	0.0963901	+	0.0985829i
$619$	−667.181			−1.07784			−0.538918	−	0.842358i	$-0.681167\pi$
$619$	−667.181			−1.07784			−0.538918	+	0.842358i	$0.681167\pi$
$620$		0			0
$621$	−159.306	−	413.414i	−0.256532	−	0.665724i
$622$	−588.137	−	245.649i	−0.945558	−	0.394934i
$623$	−249.146	+	249.146i	−0.399913	+	0.399913i
$624$	262.630	+	115.020i	0.420882	+	0.184328i
$625$		0			0
$626$	433.183	−	177.936i	0.691986	−	0.284242i
$627$	49.4663	−	20.0104i	0.0788936	−	0.0319145i
$628$	−2.57333	+	436.283i	−0.00409765	+	0.694718i
$629$	919.715			1.46219
$630$		0			0
$631$		−	736.830i		−	1.16772i	−0.811855	−	0.583859i	$-0.801542\pi$
$631$		−	736.830i		−	1.16772i	0.811855	−	0.583859i	$-0.198458\pi$
$632$	27.9439	+	69.1877i	0.0442151	+	0.109474i
$633$	−304.711	−	753.254i	−0.481375	−	1.18997i
$634$	−17.6432	+	7.24718i	−0.0278284	+	0.0114309i
$635$		0			0
$636$	−91.7675	−	230.758i	−0.144288	−	0.362827i
$637$	16.2391	+	16.2391i	0.0254931	+	0.0254931i
$638$	−868.160	−	362.607i	−1.36075	−	0.568350i
$639$	−92.3689	+	89.3531i	−0.144552	+	0.139833i
$640$		0			0
$641$		−	367.670i		−	0.573588i	−0.957992	−	0.286794i	$-0.907410\pi$
$641$		−	367.670i		−	0.573588i	0.957992	−	0.286794i	$-0.0925895\pi$
$642$	−91.3710	−	93.4497i	−0.142322	−	0.145560i
$643$	−376.586	−	376.586i	−0.585670	−	0.585670i	0.350786	−	0.936456i	$-0.385914\pi$
$643$	−376.586	−	376.586i	−0.585670	−	0.585670i	−0.936456	+	0.350786i	$0.885914\pi$
$644$	−313.712	+	310.033i	−0.487130	+	0.481417i
$645$		0			0
$646$	−36.4218	+	14.9607i	−0.0563805	+	0.0231590i
$647$	−311.254	−	311.254i	−0.481073	−	0.481073i	0.424402	−	0.905474i	$-0.360485\pi$
$647$	−311.254	−	311.254i	−0.481073	−	0.481073i	−0.905474	+	0.424402i	$0.860485\pi$
$648$	608.566	−	222.601i	0.939145	−	0.343520i
$649$			737.603i			1.13652i
$650$		0			0
$651$	810.189	+	343.494i	1.24453	+	0.527641i
$652$	5.99787	−	1016.88i	0.00919919	−	1.55964i
$653$	−47.7734	−	47.7734i	−0.0731598	−	0.0731598i	0.669580	−	0.742740i	$-0.266474\pi$
$653$	−47.7734	−	47.7734i	−0.0731598	−	0.0731598i	−0.742740	+	0.669580i	$0.766474\pi$
$654$	1.05911	−	94.1690i	0.00161943	−	0.143989i
$655$		0			0
$656$	−433.030	−	5.10846i	−0.660107	−	0.00778728i
$657$	−3.39835	+	204.768i	−0.00517253	+	0.311671i
$658$	−263.088	−	109.885i	−0.399830	−	0.166998i
$659$		−	471.784i		−	0.715909i	−0.933739	−	0.357954i	$-0.883474\pi$
$659$		−	471.784i		−	0.715909i	0.933739	−	0.357954i	$-0.116526\pi$
$660$		0			0
$661$	86.9863			0.131598			0.0657990	−	0.997833i	$-0.479040\pi$
$661$	86.9863			0.131598			0.0657990	+	0.997833i	$0.479040\pi$
$662$	214.599	−	513.796i	0.324167	−	0.776127i
$663$	88.8809	+	219.716i	0.134059	+	0.331397i
$664$	132.776	+	56.3790i	0.199964	+	0.0849082i
$665$		0			0
$666$	−1146.79	−	501.491i	−1.72191	−	0.752990i
$667$	−456.776	+	456.776i	−0.684822	+	0.684822i
$668$	−1.89605	+	321.458i	−0.00283840	+	0.481224i
$669$	676.976	+	287.016i	1.01192	+	0.429023i
$670$		0			0
$671$	−1010.95			−1.50663
$672$	−445.521	−	466.542i	−0.662978	−	0.694259i
$673$	−561.901	+	561.901i	−0.834920	+	0.834920i	−0.988185	−	0.153265i	$-0.951021\pi$
$673$	−561.901	+	561.901i	−0.834920	+	0.834920i	0.153265	+	0.988185i	$0.451021\pi$
$674$	−304.096	−	740.321i	−0.451181	−	1.09840i
$675$		0			0
$676$	−379.306	+	374.858i	−0.561104	+	0.554524i
$677$	−429.992	+	429.992i	−0.635143	+	0.635143i	−0.949353	−	0.314210i	$-0.898260\pi$
$677$	−429.992	+	429.992i	−0.635143	+	0.635143i	0.314210	+	0.949353i	$0.398260\pi$
$678$	197.677	+	202.175i	0.291560	+	0.298193i
$679$	65.6525			0.0966900
$680$		0			0
$681$	751.003	+	318.401i	1.10279	+	0.467550i
$682$	402.077	−	962.659i	0.589555	−	1.41152i
$683$	−371.280	+	371.280i	−0.543602	+	0.543602i	−0.924583	−	0.380981i	$-0.875586\pi$
$683$	−371.280	+	371.280i	−0.543602	+	0.543602i	0.380981	+	0.924583i	$0.375586\pi$
$684$	53.5718	+	1.20518i	0.0783213	+	0.00176196i
$685$		0			0
$686$	−269.849	−	656.946i	−0.393366	−	0.957647i
$687$	−84.0008	−	207.653i	−0.122272	−	0.302260i
$688$	143.211	−	139.871i	0.208155	−	0.203301i
$689$	−123.613			−0.179409
$690$		0			0
$691$			112.536i			0.162860i	0.996679	+	0.0814301i	$0.0259487\pi$
$691$			112.536i			0.162860i	−0.996679	+	0.0814301i	$0.974051\pi$
$692$	−4.36236	+	739.597i	−0.00630398	+	1.06878i
$693$	−11.9922	+	722.588i	−0.0173047	+	1.04270i
$694$	38.7160	+	94.2540i	0.0557868	+	0.135813i
$695$		0			0
$696$	−656.530	−	679.437i	−0.943290	−	0.976202i
$697$	−253.138	−	253.138i	−0.363183	−	0.363183i
$698$	295.090	−	706.510i	0.422765	−	1.01219i
$699$	−581.139	−	246.384i	−0.831386	−	0.352481i
$700$		0			0
$701$		−	525.802i		−	0.750074i	−0.927010	−	0.375037i	$-0.877630\pi$
$701$		−	525.802i		−	0.750074i	0.927010	−	0.375037i	$-0.122370\pi$
$702$	8.97902	−	322.427i	0.0127906	−	0.459298i
$703$	−73.1876	−	73.1876i	−0.104108	−	0.104108i
$704$	−550.262	+	531.125i	−0.781622	+	0.754439i
$705$		0			0
$706$	−231.836	−	564.405i	−0.328380	−	0.799440i
$707$	71.3046	+	71.3046i	0.100855	+	0.100855i
$708$	−293.144	+	680.236i	−0.414045	+	0.960786i
$709$		−	638.797i		−	0.900984i	−0.892781	−	0.450492i	$-0.851249\pi$
$709$		−	638.797i		−	0.900984i	0.892781	−	0.450492i	$-0.148751\pi$
$710$		0			0
$711$	60.3348	−	58.3649i	0.0848591	−	0.0820884i
$712$	157.091	+	388.948i	0.220633	+	0.546275i
$713$	−506.496	−	506.496i	−0.710373	−	0.710373i
$714$	5.99728	−	533.239i	0.00839955	−	0.746833i
$715$		0			0
$716$	−608.645	+	601.507i	−0.850063	+	0.840094i
$717$	240.990	+	595.734i	0.336109	+	0.830871i
$718$	365.355	−	874.739i	0.508850	−	1.21830i
$719$			313.578i			0.436131i	0.975934	+	0.218065i	$0.0699746\pi$
$719$			313.578i			0.436131i	−0.975934	+	0.218065i	$0.930025\pi$
$720$		0			0
$721$	−95.4285			−0.132356
$722$	−662.134	−	276.556i	−0.917084	−	0.383041i
$723$	467.036	−	188.928i	0.645969	−	0.261311i
$724$	436.950	+	442.135i	0.603522	+	0.610684i
$725$		0			0
$726$	130.752	+	1.47055i	0.180099	+	0.00202555i
$727$	−318.387	+	318.387i	−0.437946	+	0.437946i	−0.891320	−	0.453374i	$-0.850220\pi$
$727$	−318.387	+	318.387i	−0.437946	+	0.437946i	0.453374	+	0.891320i	$0.350220\pi$
$728$	−297.740	+	120.253i	−0.408984	+	0.165183i
$729$	−489.190	−	540.494i	−0.671043	−	0.741419i
$730$		0			0
$731$	165.482			0.226378
$732$	−932.323	−	401.779i	−1.27366	−	0.548878i
$733$	120.156	−	120.156i	0.163924	−	0.163924i	−0.620379	−	0.784303i	$-0.713021\pi$
$733$	120.156	−	120.156i	0.163924	−	0.163924i	0.784303	+	0.620379i	$0.213021\pi$
$734$	652.305	−	267.942i	0.888699	−	0.365044i
$735$		0			0
$736$	193.769	+	488.032i	0.263273	+	0.663086i
$737$	785.647	−	785.647i	1.06601	−	1.06601i
$738$	177.609	+	453.665i	0.240663	+	0.614723i
$739$	−376.922			−0.510043			−0.255022	−	0.966935i	$-0.582083\pi$
$739$	−376.922			−0.510043			−0.255022	+	0.966935i	$0.582083\pi$
$740$		0			0
$741$	10.4114	−	24.5570i	0.0140505	−	0.0331404i
$742$	256.640	+	107.191i	0.345876	+	0.144463i
$743$	139.469	−	139.469i	0.187710	−	0.187710i	−0.606995	−	0.794705i	$-0.707625\pi$
$743$	139.469	−	139.469i	0.187710	−	0.187710i	0.794705	+	0.606995i	$0.207625\pi$
$744$	753.393	−	727.993i	1.01263	−	0.978485i
$745$		0			0
$746$	282.780	−	116.156i	0.379062	−	0.155705i
$747$	2.69287	−	162.259i	0.00360491	−	0.217214i
$748$	−632.194	−	3.72887i	−0.845180	−	0.00498512i
$749$	146.375			0.195427
$750$		0			0
$751$			387.240i			0.515633i	0.966194	+	0.257816i	$0.0830029\pi$
$751$			387.240i			0.515633i	−0.966194	+	0.257816i	$0.916997\pi$
$752$	−242.830	+	237.168i	−0.322912	+	0.315382i
$753$	463.908	−	187.663i	0.616079	−	0.249220i
$754$	−435.024	+	178.692i	−0.576955	+	0.236992i
$755$		0			0
$756$	−298.236	+	661.624i	−0.394492	+	0.875163i
$757$	765.761	+	765.761i	1.01157	+	1.01157i	0.999932	+	0.0116408i	$0.00370545\pi$
$757$	765.761	+	765.761i	1.01157	+	1.01157i	0.0116408	+	0.999932i	$0.496295\pi$
$758$	−110.851	−	46.2993i	−0.146241	−	0.0610809i
$759$	229.614	−	541.584i	0.302522	−	0.713549i
$760$		0			0
$761$		−	1139.50i		−	1.49737i	−0.662925	−	0.748686i	$-0.730685\pi$
$761$		−	1139.50i		−	1.49737i	0.662925	−	0.748686i	$-0.269315\pi$
$762$	−72.7031	+	71.0859i	−0.0954108	+	0.0932886i
$763$	74.5802	+	74.5802i	0.0977460	+	0.0977460i
$764$	288.412	+	291.835i	0.377503	+	0.381983i
$765$		0			0
$766$	−982.088	+	403.405i	−1.28210	+	0.526639i
$767$	260.711	+	260.711i	0.339910	+	0.339910i
$768$	−718.550	+	271.128i	−0.935612	+	0.353031i
$769$			1312.74i			1.70708i	0.521031	+	0.853538i	$0.325548\pi$
$769$			1312.74i			1.70708i	−0.521031	+	0.853538i	$0.674452\pi$
$770$		0			0
$771$	−27.0266	+	63.7467i	−0.0350539	+	0.0826805i
$772$	−781.836	−	4.61150i	−1.01274	−	0.00597345i
$773$	−335.897	−	335.897i	−0.434537	−	0.434537i	0.455632	−	0.890168i	$-0.349413\pi$
$773$	−335.897	−	335.897i	−0.434537	−	0.434537i	−0.890168	+	0.455632i	$0.849413\pi$
$774$	−206.339	−	90.2322i	−0.266588	−	0.116579i
$775$		0			0
$776$	30.5484	−	71.9434i	0.0393665	−	0.0927106i
$777$	1299.50	−	525.680i	1.67245	−	0.676550i
$778$	857.000	+	357.946i	1.10154	+	0.460084i
$779$			40.2877i			0.0517171i
$780$		0			0
$781$	−170.633			−0.218481
$782$	−167.293	+	400.536i	−0.213930	+	0.512195i
$783$	−431.074	+	971.574i	−0.550541	+	1.24084i
$784$	−61.5121	−	0.725658i	−0.0784593	−	0.000925584i
$785$		0			0
$786$	1372.81	+	15.4398i	1.74657	+	0.0196435i
$787$	168.467	−	168.467i	0.214063	−	0.214063i	−0.591928	−	0.805991i	$-0.701633\pi$
$787$	168.467	−	168.467i	0.214063	−	0.214063i	0.805991	+	0.591928i	$0.201633\pi$
$788$	−534.158	−	3.15062i	−0.677865	−	0.00399825i
$789$	−200.863	+	473.770i	−0.254580	+	0.600468i
$790$		0			0
$791$	−316.676			−0.400348
$792$	786.247	+	349.365i	0.992737	+	0.441117i
$793$	−357.327	+	357.327i	−0.450602	+	0.450602i
$794$	135.339	+	329.483i	0.170453	+	0.414966i
$795$		0			0
$796$	520.952	+	527.134i	0.654463	+	0.662229i
$797$	639.400	−	639.400i	0.802258	−	0.802258i	−0.181190	−	0.983448i	$-0.557995\pi$
$797$	639.400	−	639.400i	0.802258	−	0.802258i	0.983448	+	0.181190i	$0.0579949\pi$
$798$	−42.9105	+	41.9560i	−0.0537725	+	0.0525764i
$799$	−280.594			−0.351182
$800$		0			0
$801$	339.180	−	328.106i	0.423446	−	0.409621i
$802$	−391.623	+	937.631i	−0.488308	+	1.16912i
$803$	−192.273	+	192.273i	−0.239443	+	0.239443i
$804$	1036.78	−	412.306i	1.28953	−	0.512819i
$805$		0			0
$806$	−198.142	−	482.376i	−0.245834	−	0.598482i
$807$	−485.773	+	196.508i	−0.601949	+	0.243504i
$808$	111.315	−	44.9587i	0.137767	−	0.0556420i
$809$	−857.503			−1.05995			−0.529977	−	0.848012i	$-0.677800\pi$
$809$	−857.503			−1.05995			−0.529977	+	0.848012i	$0.677800\pi$
$810$		0			0
$811$			1573.57i			1.94028i	0.242547	+	0.970140i	$0.422017\pi$
$811$			1573.57i			1.94028i	−0.242547	+	0.970140i	$0.577983\pi$
$812$	1058.13	+	6.24117i	1.30312	+	0.00768617i
$813$	345.245	+	853.456i	0.424656	+	1.04976i
$814$	−631.434	−	1537.22i	−0.775717	−	1.88848i
$815$		0			0
$816$	−581.544	−	254.691i	−0.712677	−	0.312121i
$817$	−13.1685	−	13.1685i	−0.0161181	−	0.0161181i
$818$	450.094	−	1077.62i	0.550237	−	1.31739i
$819$	251.165	+	259.643i	0.306673	+	0.317024i
$820$		0			0
$821$			1040.55i			1.26742i	0.773571	+	0.633710i	$0.218469\pi$
$821$			1040.55i			1.26742i	−0.773571	+	0.633710i	$0.781531\pi$
$822$	943.341	−	922.357i	1.14762	−	1.12209i
$823$	−309.894	−	309.894i	−0.376542	−	0.376542i	0.493311	−	0.869853i	$-0.335786\pi$
$823$	−309.894	−	309.894i	−0.376542	−	0.376542i	−0.869853	+	0.493311i	$0.835786\pi$
$824$	−44.4033	+	104.573i	−0.0538875	+	0.126908i
$825$		0			0
$826$	−315.201	−	767.355i	−0.381599	−	0.929001i
$827$	527.373	+	527.373i	0.637694	+	0.637694i	0.949986	−	0.312292i	$-0.101097\pi$
$827$	527.373	+	527.373i	0.637694	+	0.637694i	−0.312292	+	0.949986i	$0.601097\pi$
$828$	426.997	−	408.208i	0.515697	−	0.493004i
$829$		−	1067.23i		−	1.28737i	−0.765292	−	0.643683i	$-0.777406\pi$
$829$		−	1067.23i		−	1.28737i	0.765292	−	0.643683i	$-0.222594\pi$
$830$		0			0
$831$	−111.694	−	47.3548i	−0.134409	−	0.0569853i
$832$	−6.76404	+	382.224i	−0.00812986	+	0.459404i
$833$	−35.9584	−	35.9584i	−0.0431673	−	0.0431673i
$834$	−1321.04	−	14.8576i	−1.58399	−	0.0178149i
$835$		0			0
$836$	50.0110	+	50.6045i	0.0598218	+	0.0605317i
$837$	−1077.33	−	477.996i	−1.28713	−	0.571083i
$838$	−218.836	+	523.940i	−0.261140	+	0.625227i
$839$		−	1290.47i		−	1.53811i	−0.639182	−	0.769055i	$-0.720727\pi$
$839$		−	1290.47i		−	1.53811i	0.639182	−	0.769055i	$-0.279273\pi$
$840$		0			0
$841$	708.767			0.842767
$842$	−864.032	−	360.883i	−1.02617	−	0.428602i
$843$	−47.6117	−	117.698i	−0.0564789	−	0.139618i
$844$	770.586	−	761.549i	0.913017	−	0.902309i
$845$		0			0
$846$	349.872	+	152.999i	0.413560	+	0.180850i
$847$	−103.553	+	103.553i	−0.122259	+	0.122259i
$848$	236.878	−	231.355i	0.279338	−	0.272824i
$849$	1335.23	+	566.095i	1.57271	+	0.666779i
$850$		0			0
$851$	−1141.02			−1.34080
$852$	−157.363	−	67.8145i	−0.184698	−	0.0795944i
$853$	547.033	−	547.033i	0.641305	−	0.641305i	−0.309572	−	0.950876i	$-0.600186\pi$
$853$	547.033	−	547.033i	0.641305	−	0.641305i	0.950876	+	0.309572i	$0.100186\pi$
$854$	1051.73	−	432.010i	1.23153	−	0.505866i
$855$		0			0
$856$	68.1088	−	160.400i	0.0795664	−	0.187384i
$857$	−29.4871	+	29.4871i	−0.0344074	+	0.0344074i	−0.724101	−	0.689694i	$-0.757745\pi$
$857$	−29.4871	+	29.4871i	−0.0344074	+	0.0344074i	0.689694	+	0.724101i	$0.257745\pi$
$858$	306.215	−	299.404i	0.356894	−	0.348955i
$859$	1301.37			1.51499			0.757493	−	0.652843i	$-0.226424\pi$
$859$	1301.37			1.51499			0.757493	+	0.652843i	$0.226424\pi$
$860$		0			0
$861$	−502.353	−	212.982i	−0.583453	−	0.247366i
$862$	−1568.25	−	655.017i	−1.81932	−	0.759881i
$863$	7.00094	−	7.00094i	0.00811233	−	0.00811233i	−0.703039	−	0.711151i	$-0.748174\pi$
$863$	7.00094	−	7.00094i	0.00811233	−	0.00811233i	0.711151	+	0.703039i	$0.248174\pi$
$864$	586.251	+	634.670i	0.678531	+	0.734572i
$865$		0			0
$866$	−402.616	+	165.380i	−0.464915	+	0.190970i
$867$	128.319	+	317.210i	0.148004	+	0.365870i
$868$	−6.92052	+	1173.31i	−0.00797295	+	1.35174i
$869$	111.457			0.128258
$870$		0			0
$871$		−	555.386i		−	0.637642i
$872$	116.429	−	47.0240i	0.133520	−	0.0539267i
$873$	−87.9184	−	1.45911i	−0.100708	−	0.00167137i
$874$	45.1858	−	18.5606i	0.0517000	−	0.0212364i
$875$		0			0
$876$	−253.734	+	100.904i	−0.289650	+	0.115188i
$877$	43.0680	+	43.0680i	0.0491084	+	0.0491084i	0.731235	−	0.682126i	$-0.238945\pi$
$877$	43.0680	+	43.0680i	0.0491084	+	0.0491084i	−0.682126	+	0.731235i	$0.738945\pi$
$878$	102.568	+	42.8398i	0.116820	+	0.0487925i
$879$	987.920	+	418.847i	1.12391	+	0.476504i
$880$		0			0
$881$		−	648.829i		−	0.736469i	−0.929733	−	0.368235i	$-0.879962\pi$
$881$		−	648.829i		−	0.736469i	0.929733	−	0.368235i	$-0.120038\pi$
$882$	25.2294	+	64.4433i	0.0286048	+	0.0730650i
$883$	799.685	+	799.685i	0.905645	+	0.905645i	0.995917	−	0.0902718i	$-0.0287736\pi$
$883$	799.685	+	799.685i	0.905645	+	0.905645i	−0.0902718	+	0.995917i	$0.528774\pi$
$884$	−224.772	+	222.136i	−0.254267	+	0.251285i
$885$		0			0
$886$	1420.85	−	583.631i	1.60366	−	0.658726i
$887$	103.964	+	103.964i	0.117209	+	0.117209i	0.763278	−	0.646070i	$-0.223588\pi$
$887$	103.964	+	103.964i	0.117209	+	0.117209i	−0.646070	+	0.763278i	$0.723588\pi$
$888$	28.6106	−	1668.62i	0.0322192	−	1.87907i
$889$		−	113.878i		−	0.128097i
$890$		0			0
$891$	32.1186	−	967.386i	0.0360478	−	1.08573i
$892$	−5.78263	+	980.391i	−0.00648277	+	1.09909i
$893$	22.3287	+	22.3287i	0.0250041	+	0.0250041i
$894$	−145.757	−	1.63931i	−0.163039	−	0.00183368i
$895$		0			0
$896$	345.491	−	787.692i	0.385592	−	0.879121i
$897$	−110.268	−	272.586i	−0.122930	−	0.303886i
$898$	67.0767	+	28.0161i	0.0746957	+	0.0311984i
$899$			1718.46i			1.91152i
$900$		0			0
$901$	273.717			0.303792
$902$	−249.305	+	596.891i	−0.276392	+	0.661742i
$903$	233.815	−	94.5843i	0.258932	−	0.104745i
$904$	−147.351	+	347.020i	−0.162998	+	0.383872i
$905$		0			0
$906$	−8.14891	+	724.548i	−0.00899438	+	0.799722i
$907$	695.991	−	695.991i	0.767355	−	0.767355i	−0.210285	−	0.977640i	$-0.567439\pi$
$907$	695.991	−	695.991i	0.767355	−	0.767355i	0.977640	+	0.210285i	$0.0674393\pi$
$908$	−6.41496	+	1087.60i	−0.00706494	+	1.19779i
$909$	−93.9027	−	97.0721i	−0.103303	−	0.106790i
$910$		0			0
$911$	1074.43			1.17939			0.589696	−	0.807625i	$-0.299247\pi$
$911$	1074.43			1.17939			0.589696	+	0.807625i	$0.299247\pi$
$912$	26.0098	+	66.5445i	0.0285196	+	0.0729655i
$913$	152.358	−	152.358i	0.166876	−	0.166876i
$914$	−499.893	−	1216.99i	−0.546929	−	1.33150i
$915$		0			0
$916$	212.431	−	209.939i	0.231911	−	0.229191i
$917$	−1087.24	+	1087.24i	−1.18565	+	1.18565i
$918$	−19.8823	+	713.953i	−0.0216583	+	0.777727i
$919$	−1186.92			−1.29153			−0.645766	−	0.763535i	$-0.723462\pi$
$919$	−1186.92			−1.29153			−0.645766	+	0.763535i	$0.723462\pi$
$920$		0			0
$921$	−466.333	+	1099.92i	−0.506333	+	1.19427i
$922$	53.7217	−	128.621i	0.0582665	−	0.139503i
$923$	−60.3116	+	60.3116i	−0.0653431	+	0.0653431i
$924$	−895.380	+	356.073i	−0.969026	+	0.385361i
$925$		0			0
$926$	487.245	+	1186.20i	0.526183	+	1.28099i
$927$	127.793	+	2.12087i	0.137856	+	0.00228788i
$928$	499.193	−	1156.62i	0.537923	−	1.24636i
$929$	−1085.41			−1.16836			−0.584182	−	0.811623i	$-0.698585\pi$
$929$	−1085.41			−1.16836			−0.584182	+	0.811623i	$0.698585\pi$
$930$		0			0
$931$			5.72287i			0.00614702i
$932$	4.96401	−	841.600i	0.00532619	−	0.903005i
$933$	−886.293	+	358.528i	−0.949939	+	0.384275i
$934$	466.810	+	1136.45i	0.499797	+	1.21675i
$935$		0			0
$936$	401.391	−	154.419i	0.428836	−	0.164978i
$937$	302.640	+	302.640i	0.322988	+	0.322988i	0.849912	−	0.526924i	$-0.176655\pi$
$937$	302.640	+	302.640i	0.322988	+	0.322988i	−0.526924	+	0.849912i	$0.676655\pi$
$938$	−481.606	+	1153.07i	−0.513439	+	1.22928i
$939$	274.194	−	646.732i	0.292006	−	0.688746i
$940$		0			0
$941$			193.039i			0.205142i	0.994726	+	0.102571i	$0.0327069\pi$
$941$			193.039i			0.205142i	−0.994726	+	0.102571i	$0.967293\pi$
$942$	457.523	+	467.931i	0.485693	+	0.496742i
$943$	314.050	+	314.050i	0.333033	+	0.333033i
$944$	−987.548	−	11.6501i	−1.04613	−	0.0123412i
$945$		0			0
$946$	−113.612	−	276.589i	−0.120098	−	0.292377i
$947$	−508.522	−	508.522i	−0.536982	−	0.536982i	0.385659	−	0.922641i	$-0.373974\pi$
$947$	−508.522	−	508.522i	−0.536982	−	0.536982i	−0.922641	+	0.385659i	$0.873974\pi$
$948$	102.788	+	44.2960i	0.108426	+	0.0467257i
$949$			135.921i			0.143225i
$950$		0			0
$951$	−11.1677	+	26.3409i	−0.0117431	+	0.0276981i
$952$	659.288	−	266.277i	0.692529	−	0.279703i
$953$	182.398	+	182.398i	0.191393	+	0.191393i	0.796298	−	0.604905i	$-0.206789\pi$
$953$	182.398	+	182.398i	0.191393	+	0.191393i	−0.604905	+	0.796298i	$0.706789\pi$
$954$	−341.296	−	149.249i	−0.357753	−	0.156446i
$955$		0			0
$956$	−609.442	+	602.295i	−0.637492	+	0.630015i
$957$	−1308.27	+	529.231i	−1.36706	+	0.553010i
$958$	236.670	−	566.639i	0.247046	−	0.591481i
$959$			1477.60i			1.54077i
$960$		0			0
$961$	−944.513			−0.982844
$962$	−766.528	−	320.158i	−0.796807	−	0.332805i
$963$	−196.017	−	3.25313i	−0.203549	−	0.00337812i
$964$	472.179	+	477.782i	0.489812	+	0.495625i
$965$		0			0
$966$	−7.44038	+	661.550i	−0.00770226	+	0.684835i
$967$	754.876	−	754.876i	0.780637	−	0.780637i	−0.199301	−	0.979938i	$-0.563867\pi$
$967$	754.876	−	754.876i	0.780637	−	0.780637i	0.979938	+	0.199301i	$0.0638673\pi$
$968$	65.2920	+	161.659i	0.0674504	+	0.167004i
$969$	−23.0540	+	54.3768i	−0.0237916	+	0.0561164i
$970$		0			0
$971$	670.107			0.690121			0.345060	−	0.938580i	$-0.387858\pi$
$971$	670.107			0.690121			0.345060	+	0.938580i	$0.387858\pi$
$972$	414.087	−	879.384i	0.426015	−	0.904716i
$973$	1046.24	−	1046.24i	1.07528	−	1.07528i
$974$	−655.211	+	269.136i	−0.672701	+	0.276321i
$975$		0			0
$976$	15.9675	−	1353.52i	0.0163601	−	1.38680i
$977$	−1030.12	+	1030.12i	−1.05437	+	1.05437i	−0.0559325	+	0.998435i	$0.517813\pi$
$977$	−1030.12	+	1030.12i	−1.05437	+	1.05437i	−0.998435	+	0.0559325i	$0.982187\pi$
$978$	−1066.39	−	1090.65i	−1.09038	−	1.11518i
$979$	626.569			0.640009
$980$		0			0
$981$	−98.2164	−	101.531i	−0.100119	−	0.103498i
$982$	538.430	+	224.888i	0.548299	+	0.229010i
$983$	1099.04	−	1099.04i	1.11804	−	1.11804i	0.126017	−	0.992028i	$-0.459781\pi$
$983$	1099.04	−	1099.04i	1.11804	−	1.11804i	0.992028	−	0.126017i	$-0.0402193\pi$
$984$	−467.137	+	451.388i	−0.474733	+	0.458728i
$985$		0			0
$986$	963.277	−	395.678i	0.976954	−	0.401296i
$987$	−396.461	+	160.379i	−0.401683	+	0.162491i
$988$	35.5633	+	0.209763i	0.0359952	+	0.000212310i
$989$	−205.302			−0.207585
$990$		0			0
$991$			893.875i			0.901993i	0.892526	+	0.450996i	$0.148931\pi$
$991$			893.875i			0.901993i	−0.892526	+	0.450996i	$0.851069\pi$
$992$	1282.52	+	553.530i	1.29286	+	0.557994i
$993$	−313.210	−	774.266i	−0.315418	−	0.779724i
$994$	177.516	−	72.9169i	0.178588	−	0.0733571i
$995$		0			0
$996$	201.060	−	79.9572i	0.201867	−	0.0802783i
$997$	−465.597	−	465.597i	−0.466998	−	0.466998i	0.433943	−	0.900940i	$-0.357122\pi$
$997$	−465.597	−	465.597i	−0.466998	−	0.466998i	−0.900940	+	0.433943i	$0.857122\pi$
$998$	778.757	+	325.266i	0.780317	+	0.325917i
$999$	−1751.90	+	675.082i	−1.75365	+	0.675758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.l.g.107.19		40
3.2	odd	2	inner	300.3.l.g.107.2		40
4.3	odd	2	inner	300.3.l.g.107.9		40
5.2	odd	4		60.3.l.a.23.9	yes	40
5.3	odd	4	inner	300.3.l.g.143.12		40
5.4	even	2		60.3.l.a.47.2	yes	40
12.11	even	2	inner	300.3.l.g.107.12		40
15.2	even	4		60.3.l.a.23.12	yes	40
15.8	even	4	inner	300.3.l.g.143.9		40
15.14	odd	2		60.3.l.a.47.19	yes	40
20.3	even	4	inner	300.3.l.g.143.2		40
20.7	even	4		60.3.l.a.23.19	yes	40
20.19	odd	2		60.3.l.a.47.12	yes	40
60.23	odd	4	inner	300.3.l.g.143.19		40
60.47	odd	4		60.3.l.a.23.2	✓	40
60.59	even	2		60.3.l.a.47.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.2	✓	40	60.47	odd	4
60.3.l.a.23.9	yes	40	5.2	odd	4
60.3.l.a.23.12	yes	40	15.2	even	4
60.3.l.a.23.19	yes	40	20.7	even	4
60.3.l.a.47.2	yes	40	5.4	even	2
60.3.l.a.47.9	yes	40	60.59	even	2
60.3.l.a.47.12	yes	40	20.19	odd	2
60.3.l.a.47.19	yes	40	15.14	odd	2
300.3.l.g.107.2		40	3.2	odd	2	inner
300.3.l.g.107.9		40	4.3	odd	2	inner
300.3.l.g.107.12		40	12.11	even	2	inner
300.3.l.g.107.19		40	1.1	even	1	trivial
300.3.l.g.143.2		40	20.3	even	4	inner
300.3.l.g.143.9		40	15.8	even	4	inner
300.3.l.g.143.12		40	5.3	odd	4	inner
300.3.l.g.143.19		40	60.23	odd	4	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84549 + 0.770813i) q^{2} +(2.78107 - 1.12501i) q^{3} +(2.81170 + 2.84506i) q^{4} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(2.99596 + 7.41783i) q^{8} +(6.46869 - 6.25748i) q^{9} +O(q^{10})\)	\(q+(1.84549 + 0.770813i) q^{2} +(2.78107 - 1.12501i) q^{3} +(2.81170 + 2.84506i) q^{4} +(5.99962 + 0.0674770i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(2.99596 + 7.41783i) q^{8} +(6.46869 - 6.25748i) q^{9} +11.9496 q^{11} +(11.0203 + 4.74911i) q^{12} +(4.22368 - 4.22368i) q^{13} +(-12.4316 + 5.10644i) q^{14} +(-0.188739 + 15.9989i) q^{16} +(-9.35253 + 9.35253i) q^{17} +(16.7613 - 6.56200i) q^{18} +1.48848 q^{19} +(-7.86889 + 18.5601i) q^{21} +(22.0529 + 9.21092i) q^{22} +(11.6030 - 11.6030i) q^{23} +(16.6771 + 17.2590i) q^{24} +(11.0504 - 4.53911i) q^{26} +(10.9501 - 24.6799i) q^{27} +(-26.8786 - 0.158538i) q^{28} -39.3671 q^{29} -43.6522i q^{31} +(-12.6805 + 29.3804i) q^{32} +(33.2327 - 13.4435i) q^{33} +(-24.4691 + 10.0510i) q^{34} +(35.9909 + 0.809673i) q^{36} +(-49.1693 - 49.1693i) q^{37} +(2.74698 + 1.14734i) q^{38} +(6.99465 - 16.4981i) q^{39} +27.0663i q^{41} +(-28.8284 + 28.1871i) q^{42} +(-8.84693 - 8.84693i) q^{43} +(33.5987 + 33.9974i) q^{44} +(30.3570 - 12.4695i) q^{46} +(15.0010 + 15.0010i) q^{47} +(17.4741 + 44.7063i) q^{48} +3.84477i q^{49} +(-15.4883 + 36.5318i) q^{51} +(23.8923 + 0.140924i) q^{52} +(-14.6333 - 14.6333i) q^{53} +(39.2319 - 37.1060i) q^{54} +(-49.4821 - 21.0109i) q^{56} +(4.13957 - 1.67456i) q^{57} +(-72.6517 - 30.3447i) q^{58} +61.7260i q^{59} -84.6009 q^{61} +(33.6477 - 80.5598i) q^{62} +(-1.00356 + 60.4695i) q^{63} +(-46.0485 + 44.4470i) q^{64} +(71.6932 + 0.806325i) q^{66} +(65.7467 - 65.7467i) q^{67} +(-52.9050 - 0.312049i) q^{68} +(19.2152 - 45.3223i) q^{69} -14.2794 q^{71} +(65.7969 + 29.2365i) q^{72} +(-16.0903 + 16.0903i) q^{73} +(-52.8413 - 128.642i) q^{74} +(4.18516 + 4.23482i) q^{76} +(-56.7797 + 56.7797i) q^{77} +(25.6255 - 25.0555i) q^{78} +9.32721 q^{79} +(2.68783 - 80.9554i) q^{81} +(-20.8630 + 49.9507i) q^{82} +(12.7500 - 12.7500i) q^{83} +(-74.9296 + 29.7979i) q^{84} +(-9.50762 - 23.1463i) q^{86} +(-109.483 + 44.2885i) q^{87} +(35.8005 + 88.6403i) q^{88} +52.4342 q^{89} +40.1384i q^{91} +(65.6353 + 0.387136i) q^{92} +(-49.1093 - 121.400i) q^{93} +(16.1213 + 39.2471i) q^{94} +(-2.21192 + 95.9745i) q^{96} +(-6.90848 - 6.90848i) q^{97} +(-2.96360 + 7.09551i) q^{98} +(77.2983 - 74.7745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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