LMFDB - Embedded newform 300.3.l.g.107.9

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			107.9
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.770813 - 1.84549i) q^{2} +(-2.78107 + 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(4.21989 + 4.26527i) q^{6} +(4.75159 - 4.75159i) q^{7} +(7.41783 + 2.99596i) q^{8} +(6.46869 - 6.25748i) q^{9} +O(q^{10})$	\(q+(-0.770813 - 1.84549i) q^{2} +(-2.78107 + 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(4.21989 + 4.26527i) q^{6} +(4.75159 - 4.75159i) q^{7} +(7.41783 + 2.99596i) q^{8} +(6.46869 - 6.25748i) q^{9} -11.9496 q^{11} +(4.61879 - 11.0755i) 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} +(-16.5343 - 7.11458i) q^{18} -1.48848 q^{19} +(-7.86889 + 18.5601i) q^{21} +(9.21092 + 22.0529i) q^{22} +(-11.6030 + 11.6030i) q^{23} +(-24.0000 + 0.0132009i) q^{24} +(-11.0504 - 4.53911i) q^{26} +(-10.9501 + 24.6799i) q^{27} +(0.158538 + 26.8786i) q^{28} -39.3671 q^{29} +43.6522i q^{31} +(-29.3804 + 12.6805i) q^{32} +(33.2327 - 13.4435i) q^{33} +(24.4691 + 10.0510i) q^{34} +(-0.385062 + 35.9979i) q^{36} +(-49.1693 - 49.1693i) q^{37} +(1.14734 + 2.74698i) q^{38} +(-6.99465 + 16.4981i) q^{39} +27.0663i q^{41} +(40.3180 + 0.215630i) 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} +(18.5239 + 44.2817i) q^{48} +3.84477i q^{49} +(15.4883 - 36.5318i) q^{51} +(0.140924 + 23.8923i) q^{52} +(-14.6333 - 14.6333i) q^{53} +(53.9870 + 1.18482i) q^{54} +(49.4821 - 21.0109i) q^{56} +(4.13957 - 1.67456i) q^{57} +(30.3447 + 72.6517i) q^{58} -61.7260i q^{59} -84.6009 q^{61} +(80.5598 - 33.6477i) q^{62} +(1.00356 - 60.4695i) q^{63} +(46.0485 + 44.4470i) q^{64} +(-50.4261 - 50.9683i) q^{66} +(-65.7467 + 65.7467i) q^{67} +(-0.312049 - 52.9050i) q^{68} +(19.2152 - 45.3223i) q^{69} +14.2794 q^{71} +(66.7308 - 27.0370i) 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} +(35.8386 + 0.191673i) q^{78} -9.32721 q^{79} +(2.68783 - 80.9554i) q^{81} +(49.9507 - 20.8630i) q^{82} +(-12.7500 + 12.7500i) q^{83} +(-30.6797 - 74.5728i) q^{84} +(9.50762 - 23.1463i) q^{86} +(109.483 - 44.2885i) q^{87} +(-88.6403 - 35.8005i) q^{88} +52.4342 q^{89} -40.1384i q^{91} +(-0.387136 - 65.6353i) q^{92} +(-49.1093 - 121.400i) q^{93} +(-16.1213 + 39.2471i) q^{94} +(67.4431 - 68.3186i) q^{96} +(-6.90848 - 6.90848i) q^{97} +(7.09551 - 2.96360i) 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 $

$2$	−0.770813	−	1.84549i	−0.385406	−	0.922747i
$2$	−0.770813	−	1.84549i	−0.385406	−	0.922747i
$3$	−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
$6$	4.21989	+	4.26527i	0.703315	+	0.710878i
$7$	4.75159	−	4.75159i	0.678799	−	0.678799i	−0.280930	−	0.959728i	$-0.590643\pi$
$7$	4.75159	−	4.75159i	0.678799	−	0.678799i	0.959728	+	0.280930i	$0.0906428\pi$
$8$	7.41783	+	2.99596i	0.927229	+	0.374495i
$9$	6.46869	−	6.25748i	0.718743	−	0.695276i
$10$		0			0
$11$	−11.9496			−1.08633			−0.543164	−	0.839626i	$-0.682774\pi$
$11$	−11.9496			−1.08633			−0.543164	+	0.839626i	$0.682774\pi$
$12$	4.61879	−	11.0755i	0.384899	−	0.922959i
$13$	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	$0.377184\pi$
$18$	−16.5343	−	7.11458i	−0.918572	−	0.395254i
$19$	−1.48848			−0.0783411			−0.0391706	−	0.999233i	$-0.512472\pi$
$19$	−1.48848			−0.0783411			−0.0391706	+	0.999233i	$0.512472\pi$
$20$		0			0
$21$	−7.86889	+	18.5601i	−0.374709	+	0.883815i
$22$	9.21092	+	22.0529i	0.418678	+	1.00241i
$23$	−11.6030	+	11.6030i	−0.504478	+	0.504478i	−0.912826	−	0.408348i	$-0.866105\pi$
$23$	−11.6030	+	11.6030i	−0.504478	+	0.504478i	0.408348	+	0.912826i	$0.366105\pi$
$24$	−24.0000	+	0.0132009i	−1.00000	+	0.000550037i
$25$		0			0
$26$	−11.0504	−	4.53911i	−0.425017	−	0.174581i
$27$	−10.9501	+	24.6799i	−0.405560	+	0.914069i
$28$	0.158538	+	26.8786i	0.00566206	+	0.959950i
$29$	−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	$0.248635\pi$
$31$			43.6522i			1.40813i	−0.710133	+	0.704067i	$0.751365\pi$
$32$	−29.3804	+	12.6805i	−0.918136	+	0.396264i
$33$	33.2327	−	13.4435i	1.00705	−	0.407378i
$34$	24.4691	+	10.0510i	0.719679	+	0.295617i
$35$		0			0
$36$	−0.385062	+	35.9979i	−0.0106962	+	0.999943i
$37$	−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	$-0.638872\pi$
$38$	1.14734	+	2.74698i	0.0301932	+	0.0722890i
$39$	−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	$0.892925\pi$
$42$	40.3180	+	0.215630i	0.959953	+	0.00513405i
$43$	8.84693	+	8.84693i	0.205742	+	0.205742i	0.802455	−	0.596713i	$-0.203527\pi$
$43$	8.84693	+	8.84693i	0.205742	+	0.205742i	−0.596713	+	0.802455i	$0.703527\pi$
$44$	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	0.529278	−	0.848448i	$-0.322463\pi$
$47$	−15.0010	−	15.0010i	−0.319170	−	0.319170i	−0.848448	+	0.529278i	$0.822463\pi$
$48$	18.5239	+	44.2817i	0.385914	+	0.922535i
$49$			3.84477i			0.0784648i
$50$		0			0
$51$	15.4883	−	36.5318i	0.303692	−	0.716309i
$52$	0.140924	+	23.8923i	0.00271008	+	0.459468i
$53$	−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	$0.812546\pi$
$54$	53.9870	+	1.18482i	0.999759	+	0.0219410i
$55$		0			0
$56$	49.4821	−	21.0109i	0.883608	−	0.375195i
$57$	4.13957	−	1.67456i	0.0726240	−	0.0293783i
$58$	30.3447	+	72.6517i	0.523184	+	1.25262i
$59$		−	61.7260i		−	1.04620i	−0.852270	−	0.523102i	$-0.824775\pi$
$59$		−	61.7260i		−	1.04620i	0.852270	−	0.523102i	$-0.175225\pi$
$60$		0			0
$61$	−84.6009			−1.38690			−0.693450	−	0.720505i	$-0.743910\pi$
$61$	−84.6009			−1.38690			−0.693450	+	0.720505i	$0.743910\pi$
$62$	80.5598	−	33.6477i	1.29935	−	0.542704i
$63$	1.00356	−	60.4695i	0.0159295	−	0.959834i
$64$	46.0485	+	44.4470i	0.719507	+	0.694485i
$65$		0			0
$66$	−50.4261	−	50.9683i	−0.764031	−	0.772248i
$67$	−65.7467	+	65.7467i	−0.981293	+	0.981293i	−0.999828	−	0.0185347i	$-0.994100\pi$
$67$	−65.7467	+	65.7467i	−0.981293	+	0.981293i	0.0185347	+	0.999828i	$0.494100\pi$
$68$	−0.312049	−	52.9050i	−0.00458896	−	0.778014i
$69$	19.2152	−	45.3223i	0.278481	−	0.656844i
$70$		0			0
$71$	14.2794			0.201118			0.100559	−	0.994931i	$-0.467937\pi$
$71$	14.2794			0.201118			0.100559	+	0.994931i	$0.467937\pi$
$72$	66.7308	−	27.0370i	0.926817	−	0.375514i
$73$	−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
$78$	35.8386	+	0.191673i	0.459470	+	0.00245735i
$79$	−9.32721			−0.118066			−0.0590330	−	0.998256i	$-0.518802\pi$
$79$	−9.32721			−0.118066			−0.0590330	+	0.998256i	$0.518802\pi$
$80$		0			0
$81$	2.68783	−	80.9554i	0.0331831	−	0.999449i
$82$	49.9507	−	20.8630i	0.609154	−	0.254427i
$83$	−12.7500	+	12.7500i	−0.153615	+	0.153615i	−0.779730	−	0.626116i	$-0.784644\pi$
$83$	−12.7500	+	12.7500i	−0.153615	+	0.153615i	0.626116	+	0.779730i	$0.284644\pi$
$84$	−30.6797	−	74.5728i	−0.365234	−	0.887772i
$85$		0			0
$86$	9.50762	−	23.1463i	0.110554	−	0.269143i
$87$	109.483	−	44.2885i	1.25842	−	0.509063i
$88$	−88.6403	−	35.8005i	−1.00728	−	0.406824i
$89$	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
$92$	−0.387136	−	65.6353i	−0.00420800	−	0.713427i
$93$	−49.1093	−	121.400i	−0.528057	−	1.30537i
$94$	−16.1213	+	39.2471i	−0.171503	+	0.417523i
$95$		0			0
$96$	67.4431	−	68.3186i	0.702533	−	0.711652i
$97$	−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	$0.766037\pi$
$98$	7.09551	−	2.96360i	0.0724031	−	0.0302408i
$99$	−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	$-0.0236689\pi$
$102$	−79.3577	−	0.424424i	−0.778017	−	0.00416102i
$103$	−10.0417	−	10.0417i	−0.0974926	−	0.0974926i	0.656678	−	0.754171i	$-0.271961\pi$
$103$	−10.0417	−	10.0417i	−0.0974926	−	0.0974926i	−0.754171	+	0.656678i	$0.771961\pi$
$104$	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	0.775409	−	0.631459i	$-0.217544\pi$
$107$	15.4027	+	15.4027i	0.143950	+	0.143950i	−0.631459	+	0.775409i	$0.717544\pi$
$108$	−39.4273	−	100.546i	−0.365068	−	0.930981i
$109$		−	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
$112$	−76.9170	−	75.1234i	−0.686759	−	0.670744i
$113$	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	$0.683135\pi$
$114$	−6.28123	−	6.34877i	−0.0550985	−	0.0556910i
$115$		0			0
$116$	110.688	−	112.002i	0.954209	−	0.965532i
$117$	0.892063	−	53.7513i	0.00762447	−	0.459413i
$118$	−113.915	+	47.5792i	−0.965382	+	0.403214i
$119$			88.8788i			0.746881i
$120$		0			0
$121$	21.7934			0.180110
$122$	65.2114	+	156.130i	0.534520	+	1.27976i
$123$	−30.4500	−	75.2732i	−0.247561	−	0.611977i
$124$	−124.193	−	122.737i	−1.00156	−	0.989812i
$125$		0			0
$126$	−112.370	+	44.7586i	−0.891823	+	0.355227i
$127$	11.9832	−	11.9832i	0.0943557	−	0.0943557i	−0.658353	−	0.752709i	$-0.728747\pi$
$127$	11.9832	−	11.9832i	0.0943557	−	0.0943557i	0.752709	+	0.658353i	$0.228747\pi$
$128$	46.5320	−	119.243i	0.363531	−	0.931582i
$129$	−34.5568	−	14.6510i	−0.267882	−	0.113574i
$130$		0			0
$131$	−228.815			−1.74668			−0.873341	−	0.487109i	$-0.838051\pi$
$131$	−228.815			−1.74668			−0.873341	+	0.487109i	$0.838051\pi$
$132$	−55.1927	+	132.348i	−0.418127	+	1.00264i
$133$	−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	$-0.0465042\pi$
$138$	−98.4533	−	0.526552i	−0.713430	−	0.00381559i
$139$	220.188			1.58409			0.792043	−	0.610465i	$-0.209018\pi$
$139$	220.188			1.58409			0.792043	+	0.610465i	$0.209018\pi$
$140$		0			0
$141$	58.5950	+	24.8424i	0.415568	+	0.176187i
$142$	−11.0067	−	26.3525i	−0.0775123	−	0.185581i
$143$	−50.4714	+	50.4714i	−0.352947	+	0.352947i
$144$	−101.334	−	102.311i	−0.703706	−	0.710491i
$145$		0			0
$146$	42.0971	+	17.2919i	0.288337	+	0.118438i
$147$	−4.32542	−	10.6926i	−0.0294247	−	0.0727386i
$148$	278.139	−	1.64054i	1.87932	−	0.0110848i
$149$	−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	$-0.869050\pi$
$151$		−	120.766i		−	0.799772i	0.916565	−	0.399886i	$-0.130950\pi$
$152$	−11.0413	−	4.45943i	−0.0726402	−	0.0293383i
$153$	−1.97530	+	119.022i	−0.0129105	+	0.777921i
$154$	148.553	+	61.0201i	0.964630	+	0.396234i
$155$		0			0
$156$	−27.2711	−	66.2877i	−0.174815	−	0.424921i
$157$	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	$0.637076\pi$
$158$	7.18953	+	17.2133i	0.0455034	+	0.108945i
$159$	57.1589	+	24.2336i	0.359490	+	0.152412i
$160$		0			0
$161$			110.265i			0.684878i
$162$	−151.474	+	57.4411i	−0.935028	+	0.354575i
$163$	179.764	+	179.764i	1.10285	+	1.10285i	0.994065	+	0.108783i	$0.0346955\pi$
$163$	179.764	+	179.764i	1.10285	+	1.10285i	0.108783	+	0.994065i	$0.465305\pi$
$164$	−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	0.516191	−	0.856474i	$-0.327349\pi$
$167$	−56.8272	−	56.8272i	−0.340283	−	0.340283i	−0.856474	+	0.516191i	$0.827349\pi$
$168$	−113.975	+	114.101i	−0.678425	+	0.679172i
$169$			133.321i			0.788882i
$170$		0			0
$171$	−9.62852	+	9.31414i	−0.0563071	+	0.0544687i
$172$	−50.0449	+	0.295179i	−0.290959	+	0.00171616i
$173$	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	$0.570538\pi$
$174$	−166.125	−	167.911i	−0.954740	−	0.965007i
$175$		0			0
$176$	2.25536	+	191.181i	0.0128145	+	1.08625i
$177$	69.4427	+	171.664i	0.392331	+	0.969855i
$178$	−40.4170	−	96.7670i	−0.227062	−	0.543635i
$179$		−	213.930i		−	1.19514i	−0.801816	−	0.597571i	$-0.796133\pi$
$179$		−	213.930i		−	1.19514i	0.801816	−	0.597571i	$-0.203867\pi$
$180$		0			0
$181$	155.404			0.858588			0.429294	−	0.903165i	$-0.358762\pi$
$181$	155.404			0.858588			0.429294	+	0.903165i	$0.358762\pi$
$182$	−74.0752	+	30.9392i	−0.407007	+	0.169996i
$183$	235.281	−	95.1771i	1.28569	−	0.520094i
$184$	−120.831	+	51.3070i	−0.656691	+	0.278842i
$185$		0			0
$186$	−186.188	+	184.207i	−1.00101	+	0.990362i
$187$	111.759	−	111.759i	0.597643	−	0.597643i
$188$	84.8569	−	0.500511i	0.451366	−	0.00266229i
$189$	65.2381	+	169.299i	0.345175	+	0.895762i
$190$		0			0
$191$	−102.576			−0.537047			−0.268524	−	0.963273i	$-0.586536\pi$
$191$	−102.576			−0.537047			−0.268524	+	0.963273i	$0.586536\pi$
$192$	−178.068	−	71.8050i	−0.927435	−	0.373985i
$193$	−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	$0.360068\pi$
$198$	197.578	+	85.0165i	0.997871	+	0.429376i
$199$	−185.280			−0.931058			−0.465529	−	0.885033i	$-0.654136\pi$
$199$	−185.280			−0.931058			−0.465529	+	0.885033i	$0.654136\pi$
$200$		0			0
$201$	108.880	−	256.812i	0.541692	−	1.27767i
$202$	−27.6943	+	11.5672i	−0.137101	+	0.0572632i
$203$	−187.056	+	187.056i	−0.921459	+	0.921459i
$204$	60.3867	+	146.781i	0.296013	+	0.719516i
$205$		0			0
$206$	−10.7917	+	26.2723i	−0.0523868	+	0.127535i
$207$	−2.45061	+	147.662i	−0.0118387	+	0.713342i
$208$	−68.3714	−	66.7771i	−0.328709	−	0.321044i
$209$	17.7868			0.0851042
$210$		0			0
$211$			270.850i			1.28365i	0.766850	+	0.641826i	$0.221823\pi$
$211$			270.850i			1.28365i	−0.766850	+	0.641826i	$0.778177\pi$
$212$	82.7770	−	0.488243i	0.390458	−	0.00230303i
$213$	−39.7120	+	16.0645i	−0.186441	+	0.0754203i
$214$	16.5530	−	40.2982i	0.0773504	−	0.188309i
$215$		0			0
$216$	−155.166	+	150.265i	−0.718360	+	0.695671i
$217$	207.417	+	207.417i	0.955840	+	0.955840i
$218$	−28.9666	+	12.0985i	−0.132874	+	0.0554979i
$219$	26.6464	−	62.8500i	0.121673	−	0.286986i
$220$		0			0
$221$			79.0043i			0.357485i
$222$	2.23134	−	417.210i	0.0100511	−	1.87932i
$223$	−173.313	−	173.313i	−0.777190	−	0.777190i	0.202162	−	0.979352i	$-0.435203\pi$
$223$	−173.313	−	173.313i	−0.777190	−	0.777190i	−0.979352	+	0.202162i	$0.935203\pi$
$224$	−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	0.142773	−	0.989755i	$-0.454398\pi$
$227$	−192.265	−	192.265i	−0.846983	−	0.846983i	−0.989755	+	0.142773i	$0.954398\pi$
$228$	−6.87497	+	16.4857i	−0.0301534	+	0.0723056i
$229$		−	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
$232$	−292.018	−	117.942i	−1.25870	−	0.508371i
$233$	−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	$0.899115\pi$
$234$	−99.8853	+	39.7859i	−0.426860	+	0.170025i
$235$		0			0
$236$	175.614	+	173.555i	0.744128	+	0.735402i
$237$	25.9396	−	10.4932i	0.109450	−	0.0442753i
$238$	164.025	−	68.5089i	0.689182	−	0.287853i
$239$		−	214.211i		−	0.896278i	−0.893964	−	0.448139i	$-0.852087\pi$
$239$		−	214.211i		−	0.896278i	0.893964	−	0.448139i	$-0.147913\pi$
$240$		0			0
$241$	167.934			0.696821			0.348411	−	0.937342i	$-0.386722\pi$
$241$	167.934			0.696821			0.348411	+	0.937342i	$0.386722\pi$
$242$	−16.7986	−	40.2195i	−0.0694157	−	0.166196i
$243$	83.6009	+	228.166i	0.344037	+	0.938956i
$244$	237.872	−	240.695i	0.974885	−	0.986453i
$245$		0			0
$246$	−115.445	+	114.217i	−0.469289	+	0.464296i
$247$	−6.28687	+	6.28687i	−0.0254529	+	0.0254529i
$248$	−130.780	+	323.805i	−0.527339	+	1.30566i
$249$	21.1147	−	49.8027i	0.0847982	−	0.200011i
$250$		0			0
$251$	−166.809			−0.664578			−0.332289	−	0.943178i	$-0.607821\pi$
$251$	−166.809			−0.664578			−0.332289	+	0.943178i	$0.607821\pi$
$252$	169.218	+	172.877i	0.671499	+	0.686020i
$253$	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	$0.264298\pi$
$258$	−0.401479	+	75.0676i	−0.00155612	+	0.290960i
$259$	−467.265			−1.80411
$260$		0			0
$261$	−254.653	+	246.339i	−0.975683	+	0.943827i
$262$	176.374	+	422.277i	0.673183	+	1.61175i
$263$	121.290	−	121.290i	0.461180	−	0.461180i	−0.437862	−	0.899042i	$-0.644264\pi$
$263$	121.290	−	121.290i	0.461180	−	0.461180i	0.899042	+	0.437862i	$0.144264\pi$
$264$	286.791	−	0.157746i	1.08633	−	0.000597521i
$265$		0			0
$266$	18.5042	+	7.60085i	0.0695648	+	0.0285746i
$267$	−145.823	+	58.9892i	−0.546154	+	0.220933i
$268$	−2.19365	−	371.913i	−0.00818526	−	1.38773i
$269$	−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	$-0.808413\pi$
$271$		−	306.881i		−	1.13240i	0.824268	−	0.566200i	$-0.191587\pi$
$272$	151.395	+	147.865i	0.556600	+	0.543621i
$273$	45.1563	+	111.628i	0.165408	+	0.408893i
$274$	−406.796	−	167.096i	−1.48466	−	0.609841i
$275$		0			0
$276$	74.9173	+	182.101i	0.271439	+	0.659786i
$277$	−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	$0.773256\pi$
$278$	−169.724	−	406.356i	−0.610517	−	1.46171i
$279$	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	$-0.0239928\pi$
$282$	0.680754	−	127.286i	0.00241402	−	0.451368i
$283$	−341.834	−	341.834i	−1.20789	−	1.20789i	−0.971708	−	0.236185i	$-0.924103\pi$
$283$	−341.834	−	341.834i	−1.20789	−	1.20789i	−0.236185	−	0.971708i	$-0.575897\pi$
$284$	−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
$288$	−110.705	+	265.873i	−0.384391	+	0.923170i
$289$			114.060i			0.394672i
$290$		0			0
$291$	26.9851	+	11.4408i	0.0927322	+	0.0393155i
$292$	−0.536856	−	91.0189i	−0.00183855	−	0.311708i
$293$	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	$0.541018\pi$
$294$	−16.3990	+	16.2245i	−0.0557789	+	0.0551854i
$295$		0			0
$296$	−217.421	−	512.039i	−0.734529	−	1.72986i
$297$	130.850	−	294.915i	0.440571	−	0.992979i
$298$	18.7264	+	44.8351i	0.0628403	+	0.150453i
$299$			98.0148i			0.327809i
$300$		0			0
$301$	84.0739			0.279315
$302$	−222.872	+	93.0877i	−0.737987	+	0.308237i
$303$	16.8825	+	41.7340i	0.0557177	+	0.137736i
$304$	0.280934	+	23.8140i	0.000924125	+	0.0783357i
$305$		0			0
$306$	221.177	−	88.0982i	0.722800	−	0.287903i
$307$	281.593	−	281.593i	0.917240	−	0.917240i	−0.0795878	−	0.996828i	$-0.525360\pi$
$307$	281.593	−	281.593i	0.917240	−	0.917240i	0.996828	+	0.0795878i	$0.0253604\pi$
$308$	−1.89447	−	321.189i	−0.00615086	−	1.04282i
$309$	39.2239	+	16.6297i	0.126938	+	0.0538177i
$310$		0			0
$311$	318.688			1.02472			0.512360	−	0.858771i	$-0.328771\pi$
$311$	318.688			1.02472			0.512360	+	0.858771i	$0.328771\pi$
$312$	−101.313	+	101.424i	−0.324720	+	0.325077i
$313$	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	$0.254788\pi$
$318$	0.664069	−	124.166i	0.00208827	−	0.390459i
$319$	470.422			1.47468
$320$		0			0
$321$	−60.1642	−	25.5077i	−0.187427	−	0.0794633i
$322$	203.494	−	84.9940i	0.631969	−	0.263956i
$323$	13.9211	−	13.9211i	0.0430993	−	0.0430993i
$324$	222.766	+	235.269i	0.687548	+	0.726139i
$325$		0			0
$326$	193.189	−	470.319i	0.592605	−	1.44270i
$327$	17.6580	+	43.6512i	0.0540001	+	0.133490i
$328$	−81.0894	+	200.773i	−0.247224	+	0.612113i
$329$	−142.557			−0.433304
$330$		0			0
$331$			278.406i			0.841105i	0.907268	+	0.420553i	$0.138164\pi$
$331$			278.406i			0.841105i	−0.907268	+	0.420553i	$0.861836\pi$
$332$	−0.425407	−	72.1238i	−0.00128135	−	0.217240i
$333$	−625.737	−	10.3848i	−1.87909	−	0.0311856i
$334$	−61.0711	+	148.677i	−0.182848	+	0.445142i
$335$		0			0
$336$	298.426	+	122.391i	0.888173	+	0.364258i
$337$	−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	$0.952344\pi$
$338$	246.043	−	102.766i	0.727938	−	0.304040i
$339$	−130.163	−	55.1849i	−0.383961	−	0.162787i
$340$		0			0
$341$		−	521.627i		−	1.52970i
$342$	24.6110	+	10.5899i	0.0719619	+	0.0309647i
$343$	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	0.653289	−	0.757109i	$-0.273389\pi$
$347$	−36.0256	−	36.0256i	−0.103820	−	0.103820i	−0.757109	+	0.653289i	$0.773389\pi$
$348$	−181.828	+	436.010i	−0.522495	+	1.25290i
$349$		−	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
$352$	351.084	−	151.527i	0.997398	−	0.430474i
$353$	−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	$0.892237\pi$
$354$	263.278	−	260.477i	0.743724	−	0.735811i
$355$		0			0
$356$	−147.429	+	149.178i	−0.414126	+	0.419041i
$357$	−99.9899	−	247.178i	−0.280084	−	0.692375i
$358$	−394.807	+	164.900i	−1.10281	+	0.460615i
$359$			473.986i			1.32030i	0.751136	+	0.660148i	$0.229506\pi$
$359$			473.986i			1.32030i	−0.751136	+	0.660148i	$0.770494\pi$
$360$		0			0
$361$	−358.784			−0.993863
$362$	−119.788	−	286.798i	−0.330905	−	0.792260i
$363$	−60.6088	+	24.5178i	−0.166966	+	0.0675422i
$364$	114.196	+	112.857i	0.313726	+	0.310047i
$365$		0			0
$366$	−357.006	−	360.846i	−0.975427	−	0.985917i
$367$	−249.323	+	249.323i	−0.679354	+	0.679354i	−0.959854	−	0.280500i	$-0.909500\pi$
$367$	−249.323	+	249.323i	−0.679354	+	0.679354i	0.280500	+	0.959854i	$0.409500\pi$
$368$	187.825	+	183.445i	0.510394	+	0.498492i
$369$	169.367	+	175.083i	0.458989	+	0.474481i
$370$		0			0
$371$	−139.063			−0.374833
$372$	483.470	+	201.620i	1.29965	+	0.541989i
$373$	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
$378$	262.154	−	250.894i	0.693529	−	0.663742i
$379$	60.0656			0.158484			0.0792422	−	0.996855i	$-0.474750\pi$
$379$	60.0656			0.158484			0.0792422	+	0.996855i	$0.474750\pi$
$380$		0			0
$381$	−19.8448	+	46.8073i	−0.0520861	+	0.122854i
$382$	79.0669	+	189.303i	0.206981	+	0.495559i
$383$	375.372	−	375.372i	0.980084	−	0.980084i	−0.0197220	−	0.999806i	$-0.506278\pi$
$383$	375.372	−	375.372i	0.980084	−	0.980084i	0.999806	+	0.0197220i	$0.00627811\pi$
$384$	4.74093	+	383.971i	0.0123462	+	0.999924i
$385$		0			0
$386$	361.607	+	148.535i	0.936806	+	0.384805i
$387$	112.587	+	1.86852i	0.290924	+	0.00482821i
$388$	39.0796	−	0.230503i	0.100721	−	0.000594079i
$389$	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
$392$	−11.5188	+	28.5199i	−0.0293846	+	0.0727548i
$393$	636.351	−	257.421i	1.61921	−	0.655014i
$394$	247.053	+	101.480i	0.627039	+	0.257564i
$395$		0			0
$396$	4.60135	−	430.162i	0.0116196	−	1.08627i
$397$	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	$0.677989\pi$
$398$	142.817	+	341.934i	0.358836	+	0.859131i
$399$	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	$0.781619\pi$
$402$	−557.871	−	2.98363i	−1.38774	−	0.00742196i
$403$	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
$408$	224.337	−	224.584i	0.549846	−	0.550451i
$409$		−	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
$412$	56.8037	−	0.335045i	0.137873	−	0.000813215i
$413$	−293.297	−	293.297i	−0.710162	−	0.710162i
$414$	274.398	−	109.297i	0.662796	−	0.264002i
$415$		0			0
$416$	−70.5351	+	177.652i	−0.169556	+	0.427047i
$417$	−612.358	+	247.715i	−1.46848	+	0.594040i
$418$	−13.7103	−	32.8254i	−0.0327997	−	0.0785297i
$419$		−	283.902i		−	0.677571i	−0.940864	−	0.338786i	$-0.889984\pi$
$419$		−	283.902i		−	0.677571i	0.940864	−	0.338786i	$-0.110016\pi$
$420$		0			0
$421$	−468.185			−1.11208			−0.556039	−	0.831156i	$-0.687679\pi$
$421$	−468.185			−1.11208			−0.556039	+	0.831156i	$0.687679\pi$
$422$	499.853	−	208.775i	1.18449	−	0.494728i
$423$	−190.905	−	3.16828i	−0.451312	−	0.00749003i
$424$	−64.7066	−	152.388i	−0.152610	−	0.359406i
$425$		0			0
$426$	60.2575	+	60.9055i	0.141449	+	0.142971i
$427$	−401.989	+	401.989i	−0.941425	+	0.941425i
$428$	−87.1293	+	0.513914i	−0.203573	+	0.00120073i
$429$	83.5834	−	197.145i	0.194833	−	0.459546i
$430$		0			0
$431$	849.775			1.97164			0.985818	−	0.167821i	$-0.0536730\pi$
$431$	849.775			1.97164			0.985818	+	0.167821i	$0.0536730\pi$
$432$	396.917	+	170.532i	0.918789	+	0.394749i
$433$	−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
$438$	−136.529	−	0.730188i	−0.311709	−	0.00166710i
$439$	−55.5775			−0.126600			−0.0633001	−	0.997995i	$-0.520163\pi$
$439$	−55.5775			−0.126600			−0.0633001	+	0.997995i	$0.520163\pi$
$440$		0			0
$441$	24.0586	+	24.8706i	0.0545547	+	0.0563960i
$442$	145.802	−	60.8975i	0.329868	−	0.137777i
$443$	−543.074	+	543.074i	−1.22590	+	1.22590i	−0.260398	+	0.965501i	$0.583854\pi$
$443$	−543.074	+	543.074i	−1.22590	+	1.22590i	−0.965501	+	0.260398i	$0.916146\pi$
$444$	−771.678	+	317.473i	−1.73801	+	0.715028i
$445$		0			0
$446$	−186.257	+	453.441i	−0.417616	+	1.01668i
$447$	67.5643	−	27.3315i	0.151150	−	0.0611443i
$448$	429.998	−	7.60946i	0.959816	−	0.0169854i
$449$	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
$452$	−188.501	+	1.11183i	−0.417037	+	0.00245981i
$453$	135.863	+	335.857i	0.299918	+	0.741407i
$454$	−206.624	+	503.024i	−0.455118	+	1.10798i
$455$		0			0
$456$	35.7235	−	0.0196493i	0.0783411	−	4.30905e-5i
$457$	−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	$-0.505732\pi$
$458$	−137.797	+	57.5539i	−0.300866	+	0.125663i
$459$	−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	$-0.0240843\pi$
$462$	−481.785	−	2.57670i	−1.04282	−	0.00557727i
$463$	−453.386	−	453.386i	−0.979236	−	0.979236i	0.0205531	−	0.999789i	$-0.493457\pi$
$463$	−453.386	−	453.386i	−0.979236	−	0.979236i	−0.999789	+	0.0205531i	$0.993457\pi$
$464$	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	0.0675833	−	0.997714i	$-0.478471\pi$
$467$	−434.371	−	434.371i	−0.930130	−	0.930130i	−0.997714	+	0.0675833i	$0.978471\pi$
$468$	150.418	+	153.670i	0.321405	+	0.328355i
$469$			624.802i			1.33220i
$470$		0			0
$471$	−301.261	−	127.725i	−0.639619	−	0.271178i
$472$	184.929	−	457.873i	0.391798	−	0.970071i
$473$	−105.717	−	105.717i	−0.223504	−	0.223504i
$474$	−39.3598	−	39.7831i	−0.0830376	−	0.0839305i
$475$		0			0
$476$	−252.866	−	249.900i	−0.531230	−	0.525000i
$477$	−186.226	−	3.09063i	−0.390411	−	0.00647930i
$478$	−395.324	+	165.116i	−0.827038	+	0.345431i
$479$			307.039i			0.641000i	0.947248	+	0.320500i	$0.103851\pi$
$479$			307.039i			0.641000i	−0.947248	+	0.320500i	$0.896149\pi$
$480$		0			0
$481$	−415.351			−0.863516
$482$	−129.446	−	309.921i	−0.268559	−	0.642990i
$483$	−124.050	−	306.656i	−0.256832	−	0.634898i
$484$	−61.2763	+	62.0034i	−0.126604	+	0.128106i
$485$		0			0
$486$	356.639	−	330.158i	0.733825	−	0.679338i
$487$	250.434	−	250.434i	0.514237	−	0.514237i	−0.401585	−	0.915822i	$-0.631540\pi$
$487$	250.434	−	250.434i	0.514237	−	0.514237i	0.915822	+	0.401585i	$0.131540\pi$
$488$	−627.555	−	253.461i	−1.28597	−	0.519386i
$489$	−702.174	−	297.700i	−1.43594	−	0.608793i
$490$		0			0
$491$	−291.754			−0.594203			−0.297102	−	0.954846i	$-0.596020\pi$
$491$	−291.754			−0.594203			−0.297102	+	0.954846i	$0.596020\pi$
$492$	299.773	+	125.013i	0.609294	+	0.254092i
$493$	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
$498$	−108.186	−	0.578605i	−0.217241	−	0.00116186i
$499$	−421.977			−0.845646			−0.422823	−	0.906212i	$-0.638961\pi$
$499$	−421.977			−0.845646			−0.422823	+	0.906212i	$0.638961\pi$
$500$		0			0
$501$	221.972	+	94.1089i	0.443057	+	0.187842i
$502$	128.579	+	307.845i	0.256133	+	0.613238i
$503$	288.062	−	288.062i	0.572688	−	0.572688i	−0.360191	−	0.932879i	$-0.617288\pi$
$503$	288.062	−	288.062i	0.572688	−	0.572688i	0.932879	+	0.360191i	$0.117288\pi$
$504$	188.608	−	445.546i	0.374223	−	0.884021i
$505$		0			0
$506$	−362.755	−	149.006i	−0.716906	−	0.294478i
$507$	−149.988	−	370.775i	−0.295834	−	0.731311i
$508$	0.399821	+	67.7859i	0.000787049	+	0.133437i
$509$	−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
$512$	208.418	+	467.660i	0.407067	+	0.913398i
$513$	16.2990	−	36.7355i	0.0317720	−	0.0716091i
$514$	42.6977	+	17.5386i	0.0830695	+	0.0341219i
$515$		0			0
$516$	138.846	−	57.1221i	0.269082	−	0.110702i
$517$	179.256	+	179.256i	0.346723	+	0.346723i
$518$	360.174	+	862.335i	0.695316	+	1.66474i
$519$	−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	$0.967572\pi$
$522$	650.907	+	280.080i	1.24695	+	0.536552i
$523$	229.588	+	229.588i	0.438982	+	0.438982i	0.891669	−	0.452687i	$-0.149535\pi$
$523$	229.588	+	229.588i	0.438982	+	0.438982i	−0.452687	+	0.891669i	$0.649535\pi$
$524$	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
$528$	−221.353	−	529.149i	−0.419229	−	1.00218i
$529$			259.741i			0.491004i
$530$		0			0
$531$	−386.250	−	399.286i	−0.727400	−	0.751952i
$532$	−0.235980	−	40.0083i	−0.000443572	−	0.0752035i
$533$	114.319	+	114.319i	0.214483	+	0.214483i
$534$	221.267	+	223.646i	0.414357	+	0.418813i
$535$		0			0
$536$	−684.672	+	290.724i	−1.27737	+	0.542395i
$537$	240.675	+	594.955i	0.448184	+	1.10792i
$538$	134.639	+	322.355i	0.250258	+	0.599173i
$539$		−	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	$0.0730021\pi$
$542$	−566.346	+	236.547i	−1.04492	+	0.436434i
$543$	−432.190	+	174.832i	−0.795931	+	0.321975i
$544$	156.186	−	393.375i	0.287107	−	0.723116i
$545$		0			0
$546$	171.201	−	169.380i	0.313555	−	0.310219i
$547$	−559.528	+	559.528i	−1.02290	+	1.02290i	−0.0231709	+	0.999732i	$0.507376\pi$
$547$	−559.528	+	559.528i	−1.02290	+	1.02290i	−0.999732	+	0.0231709i	$0.992624\pi$
$548$	5.18778	+	879.539i	0.00946675	+	1.60500i
$549$	−547.256	+	529.388i	−0.996824	+	0.964278i
$550$		0			0
$551$	58.5972			0.106347
$552$	278.319	−	278.625i	0.504201	−	0.504756i
$553$	−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	$-0.0363340\pi$
$558$	310.567	−	721.758i	0.556571	−	1.29347i
$559$	74.7332			0.133691
$560$		0			0
$561$	−185.079	+	436.541i	−0.329910	+	0.778147i
$562$	−78.1032	+	32.6216i	−0.138974	+	0.0580455i
$563$	170.898	−	170.898i	0.303550	−	0.303550i	−0.538851	−	0.842401i	$-0.681142\pi$
$563$	170.898	−	170.898i	0.303550	−	0.303550i	0.842401	+	0.538851i	$0.181142\pi$
$564$	−235.430	+	96.8571i	−0.417428	+	0.171732i
$565$		0			0
$566$	−367.362	+	894.342i	−0.649050	+	1.58011i
$567$	−371.895	−	397.438i	−0.655900	−	0.700949i
$568$	105.922	+	42.7805i	0.186483	+	0.0753177i
$569$	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	$0.137712\pi$
$571$			478.800i			0.838529i	−0.907864	+	0.419265i	$0.862288\pi$
$572$	−1.68399	−	285.504i	−0.00294404	−	0.499134i
$573$	285.271	−	115.399i	0.497855	−	0.201395i
$574$	138.212	−	336.478i	0.240788	−	0.586198i
$575$		0			0
$576$	576.000	−	0.633642i	0.999999	−	0.00110007i
$577$	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	$0.686111\pi$
$578$	210.498	−	87.9192i	0.364183	−	0.152109i
$579$	228.888	−	539.871i	0.395316	−	0.932419i
$580$		0			0
$581$			121.166i			0.208547i
$582$	0.313511	−	58.6195i	0.000538679	−	0.100721i
$583$	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	$0.145474\pi$
$587$	785.786	+	785.786i	1.33865	+	1.33865i	0.441275	+	0.897372i	$0.354526\pi$
$588$	42.5828	+	17.7582i	0.0724197	+	0.0302010i
$589$		−	64.9754i		−	0.110315i
$590$		0			0
$591$	156.378	−	368.845i	0.264600	−	0.624103i
$592$	−777.374	+	795.935i	−1.31313	+	1.34448i
$593$	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	$0.469676\pi$
$594$	−645.124	−	14.1581i	−1.08607	−	0.0238352i
$595$		0			0
$596$	68.3083	−	69.1189i	0.114611	−	0.115971i
$597$	515.278	−	208.443i	0.863112	−	0.349151i
$598$	180.886	−	75.5510i	0.302484	−	0.126340i
$599$			300.352i			0.501423i	0.968062	+	0.250711i	$0.0806645\pi$
$599$			300.352i			0.501423i	−0.968062	+	0.250711i	$0.919336\pi$
$600$		0			0
$601$	7.74118			0.0128805			0.00644025	−	0.999979i	$-0.497950\pi$
$601$	7.74118			0.0128805			0.00644025	+	0.999979i	$0.497950\pi$
$602$	−64.8053	−	155.158i	−0.107650	−	0.257737i
$603$	−13.8860	+	836.703i	−0.0230282	+	1.38757i
$604$	343.585	+	339.556i	0.568850	+	0.562179i
$605$		0			0
$606$	64.0066	−	63.3256i	0.105621	−	0.104498i
$607$	424.929	−	424.929i	0.700047	−	0.700047i	−0.264373	−	0.964421i	$-0.585165\pi$
$607$	424.929	−	424.929i	0.700047	−	0.700047i	0.964421	+	0.264373i	$0.0851650\pi$
$608$	43.7321	−	18.8746i	0.0719278	−	0.0310438i
$609$	309.775	−	730.657i	0.508662	−	1.19977i
$610$		0			0
$611$	−126.719			−0.207396
$612$	−333.071	−	340.273i	−0.544233	−	0.556002i
$613$	−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	$0.428865\pi$
$618$	0.455701	−	85.2058i	0.000737380	−	0.137873i
$619$	667.181			1.07784			0.538918	−	0.842358i	$-0.318833\pi$
$619$	667.181			1.07784			0.538918	+	0.842358i	$0.318833\pi$
$620$		0			0
$621$	−159.306	−	413.414i	−0.256532	−	0.665724i
$622$	−245.649	−	588.137i	−0.394934	−	0.945558i
$623$	249.146	−	249.146i	0.399913	−	0.399913i
$624$	265.271	+	108.793i	0.425113	+	0.174347i
$625$		0			0
$626$	−433.183	−	177.936i	−0.691986	−	0.284242i
$627$	−49.4663	+	20.0104i	−0.0788936	+	0.0319145i
$628$	−436.283	+	2.57333i	−0.694718	+	0.00409765i
$629$	919.715			1.46219
$630$		0			0
$631$			736.830i			1.16772i	0.811855	+	0.583859i	$0.198458\pi$
$631$			736.830i			1.16772i	−0.811855	+	0.583859i	$0.801542\pi$
$632$	−69.1877	−	27.9439i	−0.109474	−	0.0442151i
$633$	−304.711	−	753.254i	−0.481375	−	1.18997i
$634$	17.6432	+	7.24718i	0.0278284	+	0.0114309i
$635$		0			0
$636$	−229.659	+	94.4831i	−0.361100	+	0.148558i
$637$	16.2391	+	16.2391i	0.0254931	+	0.0254931i
$638$	−362.607	−	868.160i	−0.568350	−	1.36075i
$639$	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	$-0.0925895\pi$
$642$	−0.698985	+	130.694i	−0.00108876	+	0.203574i
$643$	376.586	+	376.586i	0.585670	+	0.585670i	0.936456	−	0.350786i	$-0.114086\pi$
$643$	376.586	+	376.586i	0.585670	+	0.585670i	−0.350786	+	0.936456i	$0.614086\pi$
$644$	−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	0.905474	−	0.424402i	$-0.139515\pi$
$647$	311.254	+	311.254i	0.481073	+	0.481073i	−0.424402	+	0.905474i	$0.639515\pi$
$648$	262.477	−	592.461i	0.405057	−	0.914292i
$649$			737.603i			1.13652i
$650$		0			0
$651$	−810.189	−	343.494i	−1.24453	−	0.527641i
$652$	−1016.88	+	5.99787i	−1.55964	+	0.00919919i
$653$	−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	$0.766474\pi$
$654$	66.9470	−	66.2347i	0.102365	−	0.101276i
$655$		0			0
$656$	433.030	−	5.10846i	0.660107	−	0.00778728i
$657$	−3.39835	+	204.768i	−0.00517253	+	0.311671i
$658$	109.885	+	263.088i	0.166998	+	0.399830i
$659$			471.784i			0.715909i	0.933739	+	0.357954i	$0.116526\pi$
$659$			471.784i			0.715909i	−0.933739	+	0.357954i	$0.883474\pi$
$660$		0			0
$661$	86.9863			0.131598			0.0657990	−	0.997833i	$-0.479040\pi$
$661$	86.9863			0.131598			0.0657990	+	0.997833i	$0.479040\pi$
$662$	513.796	−	214.599i	0.776127	−	0.324167i
$663$	−88.8809	−	219.716i	−0.134059	−	0.331397i
$664$	−132.776	+	56.3790i	−0.199964	+	0.0849082i
$665$		0			0
$666$	463.161	+	1162.80i	0.695437	+	1.74594i
$667$	456.776	−	456.776i	0.684822	−	0.684822i
$668$	321.458	−	1.89605i	0.481224	−	0.00283840i
$669$	676.976	+	287.016i	1.01192	+	0.429023i
$670$		0			0
$671$	1010.95			1.50663
$672$	−4.15973	−	645.084i	−0.00619007	−	0.959946i
$673$	−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	$0.398260\pi$
$678$	−1.51222	+	282.752i	−0.00223042	+	0.417038i
$679$	−65.6525			−0.0966900
$680$		0			0
$681$	751.003	+	318.401i	1.10279	+	0.467550i
$682$	−962.659	+	402.077i	−1.41152	+	0.589555i
$683$	371.280	−	371.280i	0.543602	−	0.543602i	−0.380981	−	0.924583i	$-0.624414\pi$
$683$	371.280	−	371.280i	0.543602	−	0.543602i	0.924583	+	0.380981i	$0.124414\pi$
$684$	0.573158	−	53.5823i	0.000837950	−	0.0783366i
$685$		0			0
$686$	269.849	−	656.946i	0.393366	−	0.957647i
$687$	84.0008	+	207.653i	0.122272	+	0.302260i
$688$	139.871	−	143.211i	0.203301	−	0.208155i
$689$	−123.613			−0.179409
$690$		0			0
$691$		−	112.536i		−	0.162860i	−0.996679	−	0.0814301i	$-0.974051\pi$
$691$		−	112.536i		−	0.162860i	0.996679	−	0.0814301i	$-0.0259487\pi$
$692$	−739.597	+	4.36236i	−1.06878	+	0.00630398i
$693$	−11.9922	+	722.588i	−0.0173047	+	1.04270i
$694$	−38.7160	+	94.2540i	−0.0557868	+	0.135813i
$695$		0			0
$696$	944.810	−	0.519680i	1.35749	−	0.000746667i
$697$	−253.138	−	253.138i	−0.363183	−	0.363183i
$698$	−706.510	+	295.090i	−1.01219	+	0.422765i
$699$	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	$-0.122370\pi$
$702$	233.028	−	223.020i	0.331949	−	0.317692i
$703$	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
$708$	−683.647	−	285.099i	−0.965603	−	0.402683i
$709$		−	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
$712$	388.948	+	157.091i	0.546275	+	0.220633i
$713$	−506.496	−	506.496i	−0.710373	−	0.710373i
$714$	−379.092	+	375.059i	−0.530941	+	0.525292i
$715$		0			0
$716$	608.645	+	601.507i	0.850063	+	0.840094i
$717$	240.990	+	595.734i	0.336109	+	0.830871i
$718$	874.739	−	365.355i	1.21830	−	0.508850i
$719$		−	313.578i		−	0.436131i	−0.975934	−	0.218065i	$-0.930025\pi$
$719$		−	313.578i		−	0.436131i	0.975934	−	0.218065i	$-0.0699746\pi$
$720$		0			0
$721$	−95.4285			−0.132356
$722$	276.556	+	662.134i	0.383041	+	0.917084i
$723$	−467.036	+	188.928i	−0.645969	+	0.261311i
$724$	−436.950	+	442.135i	−0.603522	+	0.610684i
$725$		0			0
$726$	91.9656	+	92.9546i	0.126674	+	0.128037i
$727$	318.387	−	318.387i	0.437946	−	0.437946i	−0.453374	−	0.891320i	$-0.649780\pi$
$727$	318.387	−	318.387i	0.437946	−	0.437946i	0.891320	+	0.453374i	$0.149780\pi$
$728$	120.253	−	297.740i	0.165183	−	0.408984i
$729$	−489.190	−	540.494i	−0.671043	−	0.741419i
$730$		0			0
$731$	−165.482			−0.226378
$732$	−390.753	+	936.997i	−0.533816	+	1.28005i
$733$	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
$738$	192.565	−	447.522i	0.260928	−	0.606398i
$739$	376.922			0.510043			0.255022	−	0.966935i	$-0.417917\pi$
$739$	376.922			0.510043			0.255022	+	0.966935i	$0.417917\pi$
$740$		0			0
$741$	10.4114	−	24.5570i	0.0140505	−	0.0331404i
$742$	107.191	+	256.640i	0.144463	+	0.345876i
$743$	−139.469	+	139.469i	−0.187710	+	0.187710i	−0.794705	−	0.606995i	$-0.792375\pi$
$743$	−139.469	+	139.469i	−0.187710	+	0.187710i	0.606995	+	0.794705i	$0.292375\pi$
$744$	−0.576247	−	1047.65i	−0.000774526	−	1.40813i
$745$		0			0
$746$	−282.780	−	116.156i	−0.379062	−	0.155705i
$747$	−2.69287	+	162.259i	−0.00360491	+	0.217214i
$748$	3.72887	+	632.194i	0.00498512	+	0.845180i
$749$	146.375			0.195427
$750$		0			0
$751$		−	387.240i		−	0.515633i	−0.966194	−	0.257816i	$-0.916997\pi$
$751$		−	387.240i		−	0.515633i	0.966194	−	0.257816i	$-0.0830029\pi$
$752$	−237.168	+	242.830i	−0.315382	+	0.322912i
$753$	463.908	−	187.663i	0.616079	−	0.249220i
$754$	435.024	+	178.692i	0.576955	+	0.236992i
$755$		0			0
$756$	−665.096	−	290.411i	−0.879756	−	0.384141i
$757$	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	$0.496295\pi$
$758$	−46.2993	−	110.851i	−0.0610809	−	0.146241i
$759$	−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	$-0.269315\pi$
$762$	101.679	+	0.543804i	0.133437	+	0.000713654i
$763$	−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
$768$	704.961	−	304.719i	0.917918	−	0.396769i
$769$			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
$772$	−4.61150	−	781.836i	−0.00597345	−	1.01274i
$773$	−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	$0.849413\pi$
$774$	−83.3355	−	209.220i	−0.107669	−	0.270310i
$775$		0			0
$776$	−30.5484	−	71.9434i	−0.0393665	−	0.0927106i
$777$	1299.50	−	525.680i	1.67245	−	0.676550i
$778$	−357.946	−	857.000i	−0.460084	−	1.10154i
$779$		−	40.2877i		−	0.0517171i
$780$		0			0
$781$	−170.633			−0.218481
$782$	−400.536	+	167.293i	−0.512195	+	0.213930i
$783$	431.074	−	971.574i	0.550541	−	1.24084i
$784$	61.5121	−	0.725658i	0.0784593	−	0.000925584i
$785$		0			0
$786$	−965.576	−	975.960i	−1.22847	−	1.24168i
$787$	−168.467	+	168.467i	−0.214063	+	0.214063i	−0.805991	−	0.591928i	$-0.798367\pi$
$787$	−168.467	+	168.467i	−0.214063	+	0.214063i	0.591928	+	0.805991i	$0.298367\pi$
$788$	−3.15062	−	534.158i	−0.00399825	−	0.677865i
$789$	−200.863	+	473.770i	−0.254580	+	0.600468i
$790$		0			0
$791$	316.676			0.400348
$792$	−797.407	+	323.082i	−1.00683	+	0.407932i
$793$	−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	$0.0579949\pi$
$798$	−60.0126	−	0.320962i	−0.0752037	−	0.000402208i
$799$	280.594			0.351182
$800$		0			0
$801$	339.180	−	328.106i	0.423446	−	0.409621i
$802$	937.631	−	391.623i	1.16912	−	0.488308i
$803$	192.273	−	192.273i	0.239443	−	0.239443i
$804$	424.508	+	1031.85i	0.527995	+	1.28339i
$805$		0			0
$806$	198.142	−	482.376i	0.245834	−	0.598482i
$807$	485.773	−	196.508i	0.601949	−	0.243504i
$808$	44.9587	−	111.315i	0.0556420	−	0.137767i
$809$	−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	$-0.577983\pi$
$811$		−	1573.57i		−	1.94028i	0.242547	−	0.970140i	$-0.422017\pi$
$812$	−6.24117	−	1058.13i	−0.00768617	−	1.30312i
$813$	345.245	+	853.456i	0.424656	+	1.04976i
$814$	631.434	−	1537.22i	0.775717	−	1.88848i
$815$		0			0
$816$	−587.391	−	240.901i	−0.719842	−	0.295221i
$817$	−13.1685	−	13.1685i	−0.0161181	−	0.0161181i
$818$	−1077.62	+	450.094i	−1.31739	+	0.550237i
$819$	−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	$0.781531\pi$
$822$	1319.31	+	7.05600i	1.60500	+	0.00858394i
$823$	309.894	+	309.894i	0.376542	+	0.376542i	0.869853	−	0.493311i	$-0.164214\pi$
$823$	309.894	+	309.894i	0.376542	+	0.376542i	−0.493311	+	0.869853i	$0.664214\pi$
$824$	−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	0.312292	−	0.949986i	$-0.398903\pi$
$827$	−527.373	−	527.373i	−0.637694	−	0.637694i	−0.949986	+	0.312292i	$0.898903\pi$
$828$	−413.216	−	422.152i	−0.499053	−	0.509845i
$829$		−	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
$832$	382.224	−	6.76404i	0.459404	−	0.00812986i
$833$	−35.9584	−	35.9584i	−0.0431673	−	0.0431673i
$834$	929.169	+	939.161i	1.11411	+	1.12609i
$835$		0			0
$836$	−50.0110	+	50.6045i	−0.0598218	+	0.0605317i
$837$	−1077.33	−	477.996i	−1.28713	−	0.571083i
$838$	−523.940	+	218.836i	−0.625227	+	0.261140i
$839$			1290.47i			1.53811i	0.639182	+	0.769055i	$0.279273\pi$
$839$			1290.47i			1.53811i	−0.639182	+	0.769055i	$0.720727\pi$
$840$		0			0
$841$	708.767			0.842767
$842$	360.883	+	864.032i	0.428602	+	1.02617i
$843$	47.6117	+	117.698i	0.0564789	+	0.139618i
$844$	−770.586	−	761.549i	−0.913017	−	0.902309i
$845$		0			0
$846$	141.305	+	354.756i	0.167027	+	0.419333i
$847$	103.553	−	103.553i	0.122259	−	0.122259i
$848$	−231.355	+	236.878i	−0.272824	+	0.279338i
$849$	1335.23	+	566.095i	1.57271	+	0.666779i
$850$		0			0
$851$	1141.02			1.34080
$852$	65.9535	−	158.152i	0.0774102	−	0.185624i
$853$	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	$0.257745\pi$
$858$	−428.258	−	2.29043i	−0.499135	−	0.00266949i
$859$	−1301.37			−1.51499			−0.757493	−	0.652843i	$-0.773576\pi$
$859$	−1301.37			−1.51499			−0.757493	+	0.652843i	$0.773576\pi$
$860$		0			0
$861$	−502.353	−	212.982i	−0.583453	−	0.247366i
$862$	−655.017	−	1568.25i	−0.759881	−	1.81932i
$863$	−7.00094	+	7.00094i	−0.00811233	+	0.00811233i	−0.711151	−	0.703039i	$-0.751826\pi$
$863$	−7.00094	+	7.00094i	−0.00811233	+	0.00811233i	0.703039	+	0.711151i	$0.251826\pi$
$864$	8.76628	−	863.956i	0.0101462	−	0.999949i
$865$		0			0
$866$	402.616	+	165.380i	0.464915	+	0.190970i
$867$	−128.319	−	317.210i	−0.148004	−	0.365870i
$868$	−1173.31	+	6.92052i	−1.35174	+	0.00797295i
$869$	111.457			0.128258
$870$		0			0
$871$			555.386i			0.637642i
$872$	47.0240	−	116.429i	0.0539267	−	0.133520i
$873$	−87.9184	−	1.45911i	−0.100708	−	0.00167137i
$874$	−45.1858	−	18.5606i	−0.0517000	−	0.0212364i
$875$		0			0
$876$	103.891	+	252.526i	0.118596	+	0.288271i
$877$	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	$0.738945\pi$
$878$	42.8398	+	102.568i	0.0487925	+	0.116820i
$879$	−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	$-0.120038\pi$
$882$	27.3539	−	63.5706i	0.0310135	−	0.0720755i
$883$	−799.685	−	799.685i	−0.905645	−	0.905645i	0.0902718	−	0.995917i	$-0.471226\pi$
$883$	−799.685	−	799.685i	−0.905645	−	0.905645i	−0.995917	+	0.0902718i	$0.971226\pi$
$884$	−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	0.646070	−	0.763278i	$-0.276412\pi$
$887$	−103.964	−	103.964i	−0.117209	−	0.117209i	−0.763278	+	0.646070i	$0.776412\pi$
$888$	1180.71	+	1179.41i	1.32963	+	1.32817i
$889$		−	113.878i		−	0.128097i
$890$		0			0
$891$	−32.1186	+	967.386i	−0.0360478	+	1.08573i
$892$	980.391	−	5.78263i	1.09909	−	0.00648277i
$893$	22.3287	+	22.3287i	0.0250041	+	0.0250041i
$894$	−102.519	−	103.622i	−0.114675	−	0.115908i
$895$		0			0
$896$	−345.491	−	787.692i	−0.385592	−	0.879121i
$897$	−110.268	−	272.586i	−0.122930	−	0.303886i
$898$	−28.0161	−	67.0767i	−0.0311984	−	0.0746957i
$899$		−	1718.46i		−	1.91152i
$900$		0			0
$901$	273.717			0.303792
$902$	−596.891	+	249.305i	−0.661742	+	0.276392i
$903$	−233.815	+	94.5843i	−0.258932	+	0.104745i
$904$	147.351	+	347.020i	0.162998	+	0.383872i
$905$		0			0
$906$	515.098	−	509.618i	0.568541	−	0.562492i
$907$	−695.991	+	695.991i	−0.767355	+	0.767355i	−0.977640	−	0.210285i	$-0.932561\pi$
$907$	−695.991	+	695.991i	−0.767355	+	0.767355i	0.210285	+	0.977640i	$0.432561\pi$
$908$	1087.60	−	6.41496i	1.19779	−	0.00706494i
$909$	−93.9027	−	97.0721i	−0.103303	−	0.106790i
$910$		0			0
$911$	−1074.43			−1.17939			−0.589696	−	0.807625i	$-0.700753\pi$
$911$	−1074.43			−1.17939			−0.589696	+	0.807625i	$0.700753\pi$
$912$	−27.5724	−	65.9124i	−0.0302329	−	0.0722724i
$913$	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
$918$	−515.996	+	493.834i	−0.562087	+	0.537946i
$919$	1186.92			1.29153			0.645766	−	0.763535i	$-0.276538\pi$
$919$	1186.92			1.29153			0.645766	+	0.763535i	$0.276538\pi$
$920$		0			0
$921$	−466.333	+	1099.92i	−0.506333	+	1.19427i
$922$	−128.621	+	53.7217i	−0.139503	+	0.0582665i
$923$	60.3116	−	60.3116i	0.0653431	−	0.0653431i
$924$	366.611	+	891.117i	0.396765	+	0.964412i
$925$		0			0
$926$	−487.245	+	1186.20i	−0.526183	+	1.28099i
$927$	−127.793	−	2.12087i	−0.137856	−	0.00228788i
$928$	1156.62	−	499.193i	1.24636	−	0.537923i
$929$	−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
$932$	841.600	−	4.96401i	0.903005	−	0.00532619i
$933$	−886.293	+	358.528i	−0.949939	+	0.384275i
$934$	−466.810	+	1136.45i	−0.499797	+	1.21675i
$935$		0			0
$936$	167.654	−	396.046i	0.179117	−	0.423126i
$937$	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	$0.676655\pi$
$938$	1153.07	−	481.606i	1.22928	−	0.513439i
$939$	−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	$0.967293\pi$
$942$	−3.50003	+	654.427i	−0.00371553	+	0.694721i
$943$	−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	0.922641	−	0.385659i	$-0.126026\pi$
$947$	508.522	+	508.522i	0.536982	+	0.536982i	−0.385659	+	0.922641i	$0.626026\pi$
$948$	−43.0804	+	103.304i	−0.0454434	+	0.108970i
$949$			135.921i			0.143225i
$950$		0			0
$951$	11.1677	−	26.3409i	0.0117431	−	0.0276981i
$952$	−266.277	+	659.288i	−0.279703	+	0.692529i
$953$	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	$0.706789\pi$
$954$	137.842	+	346.061i	0.144488	+	0.362747i
$955$		0			0
$956$	609.442	+	602.295i	0.637492	+	0.630015i
$957$	−1308.27	+	529.231i	−1.36706	+	0.553010i
$958$	566.639	−	236.670i	0.591481	−	0.247046i
$959$		−	1477.60i		−	1.54077i
$960$		0			0
$961$	−944.513			−0.982844
$962$	320.158	+	766.528i	0.332805	+	0.796807i
$963$	196.017	+	3.25313i	0.203549	+	0.00337812i
$964$	−472.179	+	477.782i	−0.489812	+	0.495625i
$965$		0			0
$966$	−470.312	+	465.308i	−0.486865	+	0.481685i
$967$	−754.876	+	754.876i	−0.780637	+	0.780637i	−0.979938	−	0.199301i	$-0.936133\pi$
$967$	−754.876	+	754.876i	−0.780637	+	0.780637i	0.199301	+	0.979938i	$0.436133\pi$
$968$	161.659	+	65.2920i	0.167004	+	0.0674504i
$969$	−23.0540	+	54.3768i	−0.0237916	+	0.0561164i
$970$		0			0
$971$	−670.107			−0.690121			−0.345060	−	0.938580i	$-0.612142\pi$
$971$	−670.107			−0.690121			−0.345060	+	0.938580i	$0.612142\pi$
$972$	−884.207	−	403.685i	−0.909678	−	0.415313i
$973$	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	$0.982187\pi$
$978$	−8.15782	+	1525.33i	−0.00834133	+	1.55964i
$979$	−626.569			−0.640009
$980$		0			0
$981$	−98.2164	−	101.531i	−0.100119	−	0.103498i
$982$	224.888	+	538.430i	0.229010	+	0.548299i
$983$	−1099.04	+	1099.04i	−1.11804	+	1.11804i	−0.126017	+	0.992028i	$0.540219\pi$
$983$	−1099.04	+	1099.04i	−1.11804	+	1.11804i	−0.992028	+	0.126017i	$0.959781\pi$
$984$	−0.357299	−	649.591i	−0.000363109	−	0.660153i
$985$		0			0
$986$	−963.277	−	395.678i	−0.976954	−	0.401296i
$987$	396.461	−	160.379i	0.401683	−	0.162491i
$988$	−0.209763	−	35.5633i	−0.000212310	−	0.0359952i
$989$	−205.302			−0.207585
$990$		0			0
$991$		−	893.875i		−	0.901993i	−0.892526	−	0.450996i	$-0.851069\pi$
$991$		−	893.875i		−	0.901993i	0.892526	−	0.450996i	$-0.148931\pi$
$992$	−553.530	−	1282.52i	−0.557994	−	1.29286i
$993$	−313.210	−	774.266i	−0.315418	−	0.779724i
$994$	−177.516	−	72.9169i	−0.178588	−	0.0733571i
$995$		0			0
$996$	82.3233	+	200.103i	0.0826540	+	0.200906i
$997$	−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	$0.857122\pi$
$998$	325.266	+	778.757i	0.325917	+	0.780317i
$999$	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.107.9		40
3.2	odd	2	inner	300.3.l.g.107.12		40
4.3	odd	2	inner	300.3.l.g.107.19		40
5.2	odd	4		60.3.l.a.23.19	yes	40
5.3	odd	4	inner	300.3.l.g.143.2		40
5.4	even	2		60.3.l.a.47.12	yes	40
12.11	even	2	inner	300.3.l.g.107.2		40
15.2	even	4		60.3.l.a.23.2	✓	40
15.8	even	4	inner	300.3.l.g.143.19		40
15.14	odd	2		60.3.l.a.47.9	yes	40
20.3	even	4	inner	300.3.l.g.143.12		40
20.7	even	4		60.3.l.a.23.9	yes	40
20.19	odd	2		60.3.l.a.47.2	yes	40
60.23	odd	4	inner	300.3.l.g.143.9		40
60.47	odd	4		60.3.l.a.23.12	yes	40
60.59	even	2		60.3.l.a.47.19	yes	40

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

\(f(q)\)	\(=\)	\(q+(-0.770813 - 1.84549i) q^{2} +(-2.78107 + 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(4.21989 + 4.26527i) q^{6} +(4.75159 - 4.75159i) q^{7} +(7.41783 + 2.99596i) q^{8} +(6.46869 - 6.25748i) q^{9} +O(q^{10})\)	\(q+(-0.770813 - 1.84549i) q^{2} +(-2.78107 + 1.12501i) q^{3} +(-2.81170 + 2.84506i) q^{4} +(4.21989 + 4.26527i) q^{6} +(4.75159 - 4.75159i) q^{7} +(7.41783 + 2.99596i) q^{8} +(6.46869 - 6.25748i) q^{9} -11.9496 q^{11} +(4.61879 - 11.0755i) 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} +(-16.5343 - 7.11458i) q^{18} -1.48848 q^{19} +(-7.86889 + 18.5601i) q^{21} +(9.21092 + 22.0529i) q^{22} +(-11.6030 + 11.6030i) q^{23} +(-24.0000 + 0.0132009i) q^{24} +(-11.0504 - 4.53911i) q^{26} +(-10.9501 + 24.6799i) q^{27} +(0.158538 + 26.8786i) q^{28} -39.3671 q^{29} +43.6522i q^{31} +(-29.3804 + 12.6805i) q^{32} +(33.2327 - 13.4435i) q^{33} +(24.4691 + 10.0510i) q^{34} +(-0.385062 + 35.9979i) q^{36} +(-49.1693 - 49.1693i) q^{37} +(1.14734 + 2.74698i) q^{38} +(-6.99465 + 16.4981i) q^{39} +27.0663i q^{41} +(40.3180 + 0.215630i) 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} +(18.5239 + 44.2817i) q^{48} +3.84477i q^{49} +(15.4883 - 36.5318i) q^{51} +(0.140924 + 23.8923i) q^{52} +(-14.6333 - 14.6333i) q^{53} +(53.9870 + 1.18482i) q^{54} +(49.4821 - 21.0109i) q^{56} +(4.13957 - 1.67456i) q^{57} +(30.3447 + 72.6517i) q^{58} -61.7260i q^{59} -84.6009 q^{61} +(80.5598 - 33.6477i) q^{62} +(1.00356 - 60.4695i) q^{63} +(46.0485 + 44.4470i) q^{64} +(-50.4261 - 50.9683i) q^{66} +(-65.7467 + 65.7467i) q^{67} +(-0.312049 - 52.9050i) q^{68} +(19.2152 - 45.3223i) q^{69} +14.2794 q^{71} +(66.7308 - 27.0370i) 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} +(35.8386 + 0.191673i) q^{78} -9.32721 q^{79} +(2.68783 - 80.9554i) q^{81} +(49.9507 - 20.8630i) q^{82} +(-12.7500 + 12.7500i) q^{83} +(-30.6797 - 74.5728i) q^{84} +(9.50762 - 23.1463i) q^{86} +(109.483 - 44.2885i) q^{87} +(-88.6403 - 35.8005i) q^{88} +52.4342 q^{89} -40.1384i q^{91} +(-0.387136 - 65.6353i) q^{92} +(-49.1093 - 121.400i) q^{93} +(-16.1213 + 39.2471i) q^{94} +(67.4431 - 68.3186i) q^{96} +(-6.90848 - 6.90848i) q^{97} +(7.09551 - 2.96360i) 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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