LMFDB - Embedded newform 300.3.l.g.107.2

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			107.2
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84549 - 0.770813i) q^{2} +(-1.12501 + 2.78107i) q^{3} +(2.81170 + 2.84506i) q^{4} +(4.21989 - 4.26527i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(-2.99596 - 7.41783i) q^{8} +(-6.46869 - 6.25748i) q^{9} +O(q^{10})$	\(q+(-1.84549 - 0.770813i) q^{2} +(-1.12501 + 2.78107i) q^{3} +(2.81170 + 2.84506i) q^{4} +(4.21989 - 4.26527i) q^{6} +(-4.75159 + 4.75159i) q^{7} +(-2.99596 - 7.41783i) q^{8} +(-6.46869 - 6.25748i) q^{9} -11.9496 q^{11} +(-11.0755 + 4.61879i) 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} +(7.11458 + 16.5343i) q^{18} +1.48848 q^{19} +(-7.86889 - 18.5601i) q^{21} +(22.0529 + 9.21092i) q^{22} +(-11.6030 + 11.6030i) q^{23} +(24.0000 + 0.0132009i) q^{24} +(-11.0504 + 4.53911i) q^{26} +(24.6799 - 10.9501i) q^{27} +(-26.8786 - 0.158538i) q^{28} +39.3671 q^{29} -43.6522i q^{31} +(12.6805 - 29.3804i) q^{32} +(13.4435 - 33.2327i) q^{33} +(-24.4691 + 10.0510i) q^{34} +(-0.385062 - 35.9979i) q^{36} +(-49.1693 - 49.1693i) q^{37} +(-2.74698 - 1.14734i) q^{38} +(6.99465 + 16.4981i) q^{39} -27.0663i q^{41} +(0.215630 + 40.3180i) 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} +(-44.2817 - 18.5239i) q^{48} +3.84477i q^{49} +(15.4883 + 36.5318i) q^{51} +(23.8923 + 0.140924i) q^{52} +(14.6333 + 14.6333i) q^{53} +(-53.9870 + 1.18482i) q^{54} +(49.4821 + 21.0109i) q^{56} +(-1.67456 + 4.13957i) q^{57} +(-72.6517 - 30.3447i) q^{58} -61.7260i q^{59} -84.6009 q^{61} +(-33.6477 + 80.5598i) q^{62} +(60.4695 - 1.00356i) q^{63} +(-46.0485 + 44.4470i) q^{64} +(-50.4261 + 50.9683i) q^{66} +(65.7467 - 65.7467i) q^{67} +(52.9050 + 0.312049i) q^{68} +(-19.2152 - 45.3223i) q^{69} +14.2794 q^{71} +(-27.0370 + 66.7308i) 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} +(-0.191673 - 35.8386i) q^{78} +9.32721 q^{79} +(2.68783 + 80.9554i) q^{81} +(-20.8630 + 49.9507i) q^{82} +(-12.7500 + 12.7500i) q^{83} +(30.6797 - 74.5728i) q^{84} +(9.50762 + 23.1463i) q^{86} +(-44.2885 + 109.483i) q^{87} +(35.8005 + 88.6403i) q^{88} -52.4342 q^{89} +40.1384i q^{91} +(-65.6353 - 0.387136i) q^{92} +(121.400 + 49.1093i) q^{93} +(16.1213 + 39.2471i) q^{94} +(67.4431 + 68.3186i) 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
$3$	−1.12501	+	2.78107i	−0.375005	+	0.927023i
$3$	−1.12501	+	2.78107i	−0.375005	+	0.927023i
$4$	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	−0.959728	−	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	$-0.682774\pi$
$11$	−11.9496			−1.08633			−0.543164	+	0.839626i	$0.682774\pi$
$12$	−11.0755	+	4.61879i	−0.922959	+	0.384899i
$13$	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	−0.376335	−	0.926484i	$-0.622816\pi$
$17$	9.35253	−	9.35253i	0.550149	−	0.550149i	0.926484	+	0.376335i	$0.122816\pi$
$18$	7.11458	+	16.5343i	0.395254	+	0.918572i
$19$	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	−0.912826	−	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
$27$	24.6799	−	10.9501i	0.914069	−	0.405560i
$28$	−26.8786	−	0.158538i	−0.959950	−	0.00566206i
$29$	39.3671			1.35749			0.678743	−	0.734376i	$-0.262525\pi$
$29$	39.3671			1.35749			0.678743	+	0.734376i	$0.262525\pi$
$30$		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
$33$	13.4435	−	33.2327i	0.407378	−	1.00705i
$34$	−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	$-0.638872\pi$
$38$	−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	$-0.892925\pi$
$41$		−	27.0663i		−	0.660153i	0.943954	−	0.330077i	$-0.107075\pi$
$42$	0.215630	+	40.3180i	0.00513405	+	0.959953i
$43$	−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	0.529278	−	0.848448i	$-0.322463\pi$
$47$	−15.0010	−	15.0010i	−0.319170	−	0.319170i	−0.848448	+	0.529278i	$0.822463\pi$
$48$	−44.2817	−	18.5239i	−0.922535	−	0.385914i
$49$			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	0.831550	−	0.555450i	$-0.187454\pi$
$53$	14.6333	+	14.6333i	0.276100	+	0.276100i	−0.555450	+	0.831550i	$0.687454\pi$
$54$	−53.9870	+	1.18482i	−0.999759	+	0.0219410i
$55$		0			0
$56$	49.4821	+	21.0109i	0.883608	+	0.375195i
$57$	−1.67456	+	4.13957i	−0.0293783	+	0.0726240i
$58$	−72.6517	−	30.3447i	−1.25262	−	0.523184i
$59$		−	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	$0.743910\pi$
$62$	−33.6477	+	80.5598i	−0.542704	+	1.29935i
$63$	60.4695	−	1.00356i	0.959834	−	0.0159295i
$64$	−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	−0.0185347	−	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	$-0.467937\pi$
$71$	14.2794			0.201118			0.100559	+	0.994931i	$0.467937\pi$
$72$	−27.0370	+	66.7308i	−0.375514	+	0.926817i
$73$	−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
$78$	−0.191673	−	35.8386i	−0.00245735	−	0.459470i
$79$	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	−0.779730	−	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
$87$	−44.2885	+	109.483i	−0.509063	+	1.25842i
$88$	35.8005	+	88.6403i	0.406824	+	1.00728i
$89$	−52.4342			−0.589148			−0.294574	−	0.955629i	$-0.595178\pi$
$89$	−52.4342			−0.589148			−0.294574	+	0.955629i	$0.595178\pi$
$90$		0			0
$91$			40.1384i			0.441082i
$92$	−65.6353	−	0.387136i	−0.713427	−	0.00420800i
$93$	121.400	+	49.1093i	1.30537	+	0.528057i
$94$	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	$0.766037\pi$
$98$	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	$0.0236689\pi$
$101$			15.0065i			0.148579i	−0.997237	+	0.0742894i	$0.976331\pi$
$102$	−0.424424	−	79.3577i	−0.00416102	−	0.778017i
$103$	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	0.775409	−	0.631459i	$-0.217544\pi$
$107$	15.4027	+	15.4027i	0.143950	+	0.143950i	−0.631459	+	0.775409i	$0.717544\pi$
$108$	100.546	+	39.4273i	0.930981	+	0.365068i
$109$		−	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	0.544116	−	0.839010i	$-0.316865\pi$
$113$	−33.3231	−	33.3231i	−0.294895	−	0.294895i	−0.839010	+	0.544116i	$0.816865\pi$
$114$	6.28123	−	6.34877i	0.0550985	−	0.0556910i
$115$		0			0
$116$	110.688	+	112.002i	0.954209	+	0.965532i
$117$	−53.7513	+	0.892063i	−0.459413	+	0.00762447i
$118$	−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
$123$	75.2732	+	30.4500i	0.611977	+	0.247561i
$124$	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	−0.752709	−	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	$-0.838051\pi$
$131$	−228.815			−1.74668			−0.873341	+	0.487109i	$0.838051\pi$
$132$	132.348	−	55.1927i	1.00264	−	0.418127i
$133$	−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	$0.546504\pi$
$137$	−155.485	+	155.485i	−1.13492	+	1.13492i	−0.989347	+	0.145578i	$0.953496\pi$
$138$	0.526552	+	98.4533i	0.00381559	+	0.713430i
$139$	−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
$144$	101.334	−	102.311i	0.703706	−	0.710491i
$145$		0			0
$146$	42.0971	−	17.2919i	0.288337	−	0.118438i
$147$	−10.6926	−	4.32542i	−0.0727386	−	0.0294247i
$148$	1.64054	−	278.139i	0.0110848	−	1.87932i
$149$	24.2943			0.163049			0.0815247	−	0.996671i	$-0.474021\pi$
$149$	24.2943			0.163049			0.0815247	+	0.996671i	$0.474021\pi$
$150$		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
$153$	−119.022	+	1.97530i	−0.777921	+	0.0129105i
$154$	−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	$0.637076\pi$
$158$	−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
$162$	57.4411	−	151.474i	0.354575	−	0.935028i
$163$	−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	0.516191	−	0.856474i	$-0.327349\pi$
$167$	−56.8272	−	56.8272i	−0.340283	−	0.340283i	−0.856474	+	0.516191i	$0.827349\pi$
$168$	−114.101	+	113.975i	−0.679172	+	0.678425i
$169$			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	0.219791	−	0.975547i	$-0.429462\pi$
$173$	−130.746	−	130.746i	−0.755756	−	0.755756i	−0.975547	+	0.219791i	$0.929462\pi$
$174$	166.125	−	167.911i	0.954740	−	0.965007i
$175$		0			0
$176$	2.25536	−	191.181i	0.0128145	−	1.08625i
$177$	171.664	+	69.4427i	0.969855	+	0.392331i
$178$	96.7670	+	40.4170i	0.543635	+	0.227062i
$179$		−	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	$0.358762\pi$
$182$	30.9392	−	74.0752i	0.169996	−	0.407007i
$183$	95.1771	−	235.281i	0.520094	−	1.28569i
$184$	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
$188$	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	$-0.586536\pi$
$191$	−102.576			−0.537047			−0.268524	+	0.963273i	$0.586536\pi$
$192$	−71.8050	−	178.068i	−0.373985	−	0.927435i
$193$	−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	−0.425586	−	0.904918i	$-0.639932\pi$
$197$	94.4283	−	94.4283i	0.479331	−	0.479331i	0.904918	+	0.425586i	$0.139932\pi$
$198$	−85.0165	−	197.578i	−0.429376	−	0.997871i
$199$	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
$204$	−60.3867	+	146.781i	−0.296013	+	0.719516i
$205$		0			0
$206$	−10.7917	−	26.2723i	−0.0523868	−	0.127535i
$207$	147.662	−	2.45061i	0.713342	−	0.0118387i
$208$	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
$213$	−16.0645	+	39.7120i	−0.0754203	+	0.186441i
$214$	−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
$218$	−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
$222$	−417.210	+	2.23134i	−1.87932	+	0.0100511i
$223$	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	0.142773	−	0.989755i	$-0.454398\pi$
$227$	−192.265	−	192.265i	−0.846983	−	0.846983i	−0.989755	+	0.142773i	$0.954398\pi$
$228$	−16.4857	+	6.87497i	−0.0723056	+	0.0301534i
$229$		−	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	0.950193	−	0.311661i	$-0.100885\pi$
$233$	148.778	+	148.778i	0.638532	+	0.638532i	−0.311661	+	0.950193i	$0.600885\pi$
$234$	99.8853	+	39.7859i	0.426860	+	0.170025i
$235$		0			0
$236$	175.614	−	173.555i	0.744128	−	0.735402i
$237$	−10.4932	+	25.9396i	−0.0442753	+	0.109450i
$238$	68.5089	−	164.025i	0.287853	−	0.689182i
$239$		−	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	$0.386722\pi$
$242$	−40.2195	−	16.7986i	−0.166196	−	0.0694157i
$243$	−228.166	−	83.6009i	−0.938956	−	0.344037i
$244$	−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
$248$	−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	$-0.607821\pi$
$251$	−166.809			−0.664578			−0.332289	+	0.943178i	$0.607821\pi$
$252$	172.877	+	169.218i	0.686020	+	0.671499i
$253$	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	−0.674643	−	0.738144i	$-0.735702\pi$
$257$	16.3199	−	16.3199i	0.0635014	−	0.0635014i	0.738144	+	0.674643i	$0.235702\pi$
$258$	−75.0676	+	0.401479i	−0.290960	+	0.00155612i
$259$	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	−0.437862	−	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
$267$	58.9892	−	145.823i	0.220933	−	0.546154i
$268$	371.913	+	2.19365i	1.38773	+	0.00818526i
$269$	174.671			0.649336			0.324668	−	0.945828i	$-0.394747\pi$
$269$	174.671			0.649336			0.324668	+	0.945828i	$0.394747\pi$
$270$		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
$273$	−111.628	−	45.1563i	−0.408893	−	0.165408i
$274$	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	$0.773256\pi$
$278$	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	$0.0239928\pi$
$281$			42.3210i			0.150609i	−0.997161	+	0.0753043i	$0.976007\pi$
$282$	−127.286	+	0.680754i	−0.451368	+	0.00241402i
$283$	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
$288$	−265.873	+	110.705i	−0.923170	+	0.384391i
$289$			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	0.128506	−	0.991709i	$-0.458982\pi$
$293$	−252.918	−	252.918i	−0.863203	−	0.863203i	−0.991709	+	0.128506i	$0.958982\pi$
$294$	16.3990	+	16.2245i	0.0557789	+	0.0551854i
$295$		0			0
$296$	−217.421	+	512.039i	−0.734529	+	1.72986i
$297$	−294.915	+	130.850i	−0.992979	+	0.440571i
$298$	−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
$303$	−41.7340	−	16.8825i	−0.137736	−	0.0557177i
$304$	−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	−0.996828	−	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	$-0.328771\pi$
$311$	318.688			1.02472			0.512360	+	0.858771i	$0.328771\pi$
$312$	101.424	−	101.313i	0.325077	−	0.324720i
$313$	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	−0.696390	−	0.717663i	$-0.745212\pi$
$317$	6.74356	−	6.74356i	0.0212731	−	0.0212731i	0.717663	+	0.696390i	$0.245212\pi$
$318$	124.166	−	0.664069i	0.390459	−	0.00208827i
$319$	−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
$324$	−222.766	+	235.269i	−0.687548	+	0.726139i
$325$		0			0
$326$	193.189	+	470.319i	0.592605	+	1.44270i
$327$	43.6512	+	17.6580i	0.133490	+	0.0540001i
$328$	−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
$333$	10.3848	+	625.737i	0.0311856	+	1.87909i
$334$	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	$0.952344\pi$
$338$	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
$342$	10.5899	+	24.6110i	0.0309647	+	0.0719619i
$343$	−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	$0.773389\pi$
$348$	−436.010	+	181.828i	−1.25290	+	0.522495i
$349$		−	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	0.943238	−	0.332117i	$-0.107763\pi$
$353$	215.726	+	215.726i	0.611121	+	0.611121i	−0.332117	+	0.943238i	$0.607763\pi$
$354$	−263.278	−	260.477i	−0.743724	−	0.735811i
$355$		0			0
$356$	−147.429	−	149.178i	−0.414126	−	0.419041i
$357$	−247.178	−	99.9899i	−0.692375	−	0.280084i
$358$	−164.900	+	394.807i	−0.460615	+	1.10281i
$359$			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
$362$	−286.798	−	119.788i	−0.792260	−	0.330905i
$363$	−24.5178	+	60.6088i	−0.0675422	+	0.166966i
$364$	−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	−0.280500	−	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
$372$	201.620	+	483.470i	0.541989	+	1.29965i
$373$	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
$378$	250.894	−	262.154i	0.663742	−	0.693529i
$379$	−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	−0.0197220	−	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
$387$	1.86852	+	112.587i	0.00482821	+	0.290924i
$388$	0.230503	−	39.0796i	0.000594079	−	0.100721i
$389$	−464.374			−1.19376			−0.596882	−	0.802329i	$-0.703594\pi$
$389$	−464.374			−1.19376			−0.596882	+	0.802329i	$0.703594\pi$
$390$		0			0
$391$			217.035i			0.555076i
$392$	28.5199	−	11.5188i	0.0727548	−	0.0293846i
$393$	257.421	−	636.351i	0.655014	−	1.61921i
$394$	−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	$0.677989\pi$
$398$	−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	$-0.781619\pi$
$401$		−	508.065i		−	1.26699i	0.773745	−	0.633497i	$-0.218381\pi$
$402$	−2.98363	−	557.871i	−0.00742196	−	1.38774i
$403$	−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
$408$	224.584	−	224.337i	0.550451	−	0.549846i
$409$		−	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
$414$	−274.398	−	109.297i	−0.662796	−	0.264002i
$415$		0			0
$416$	−70.5351	−	177.652i	−0.169556	−	0.427047i
$417$	247.715	−	612.358i	0.594040	−	1.46848i
$418$	32.8254	+	13.7103i	0.0785297	+	0.0327997i
$419$		−	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	$0.687679\pi$
$422$	−208.775	+	499.853i	−0.494728	+	1.18449i
$423$	3.16828	+	190.905i	0.00749003	+	0.451312i
$424$	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
$428$	−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	$-0.0536730\pi$
$431$	849.775			1.97164			0.985818	+	0.167821i	$0.0536730\pi$
$432$	170.532	+	396.917i	0.394749	+	0.918789i
$433$	−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
$438$	0.730188	+	136.529i	0.00166710	+	0.311709i
$439$	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	$0.583854\pi$
$443$	−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
$447$	−27.3315	+	67.5643i	−0.0611443	+	0.151150i
$448$	7.60946	−	429.998i	0.0169854	−	0.959816i
$449$	−36.3462			−0.0809493			−0.0404746	−	0.999181i	$-0.512887\pi$
$449$	−36.3462			−0.0809493			−0.0404746	+	0.999181i	$0.512887\pi$
$450$		0			0
$451$			323.432i			0.717144i
$452$	1.11183	−	188.501i	0.00245981	−	0.417037i
$453$	−335.857	−	135.863i	−0.741407	−	0.299918i
$454$	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	$-0.505732\pi$
$458$	−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	$0.0240843\pi$
$461$			69.6948i			0.151182i	−0.997139	+	0.0755909i	$0.975916\pi$
$462$	−2.57670	−	481.785i	−0.00557727	−	1.04282i
$463$	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	0.0675833	−	0.997714i	$-0.478471\pi$
$467$	−434.371	−	434.371i	−0.930130	−	0.930130i	−0.997714	+	0.0675833i	$0.978471\pi$
$468$	−153.670	−	150.418i	−0.328355	−	0.321405i
$469$			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
$474$	39.3598	−	39.7831i	0.0830376	−	0.0839305i
$475$		0			0
$476$	−252.866	+	249.900i	−0.531230	+	0.525000i
$477$	−3.09063	−	186.226i	−0.00647930	−	0.390411i
$478$	−165.116	+	395.324i	−0.345431	+	0.827038i
$479$			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
$482$	−309.921	−	129.446i	−0.642990	−	0.268559i
$483$	306.656	+	124.050i	0.634898	+	0.256832i
$484$	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	−0.915822	−	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	$-0.596020\pi$
$491$	−291.754			−0.594203			−0.297102	+	0.954846i	$0.596020\pi$
$492$	125.013	+	299.773i	0.254092	+	0.609294i
$493$	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
$498$	0.578605	+	108.186i	0.00116186	+	0.217241i
$499$	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	−0.360191	−	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
$507$	−370.775	−	149.988i	−0.731311	−	0.295834i
$508$	−67.7859	−	0.399821i	−0.133437	−	0.000787049i
$509$	808.790			1.58898			0.794489	−	0.607278i	$-0.207739\pi$
$509$	808.790			1.58898			0.794489	+	0.607278i	$0.207739\pi$
$510$		0			0
$511$		−	152.909i		−	0.299235i
$512$	467.660	+	208.418i	0.913398	+	0.407067i
$513$	36.7355	−	16.2990i	0.0716091	−	0.0317720i
$514$	−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
$518$	−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	$-0.967572\pi$
$521$		−	105.970i		−	0.203397i	0.994815	−	0.101699i	$-0.0324277\pi$
$522$	280.080	+	650.907i	0.536552	+	1.24695i
$523$	−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
$528$	529.149	+	221.353i	1.00218	+	0.419229i
$529$			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
$534$	−221.267	+	223.646i	−0.414357	+	0.418813i
$535$		0			0
$536$	−684.672	−	290.724i	−1.27737	−	0.542395i
$537$	594.955	+	240.675i	1.10792	+	0.448184i
$538$	−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
$543$	−174.832	+	432.190i	−0.321975	+	0.795931i
$544$	−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	$-0.492624\pi$
$547$	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
$552$	−278.625	+	278.319i	−0.504756	+	0.504201i
$553$	−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	$0.536334\pi$
$557$	−616.817	+	616.817i	−1.10739	+	1.10739i	−0.993492	+	0.113899i	$0.963666\pi$
$558$	721.758	−	310.567i	1.29347	−	0.556571i
$559$	−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	−0.538851	−	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
$567$	−397.438	−	371.895i	−0.700949	−	0.655900i
$568$	−42.7805	−	105.922i	−0.0753177	−	0.186483i
$569$	−609.836			−1.07177			−0.535884	−	0.844291i	$-0.680022\pi$
$569$	−609.836			−1.07177			−0.535884	+	0.844291i	$0.680022\pi$
$570$		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
$573$	115.399	−	285.271i	0.201395	−	0.497855i
$574$	−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	$0.686111\pi$
$578$	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
$582$	−58.6195	+	0.313511i	−0.100721	+	0.000538679i
$583$	−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	$0.354526\pi$
$588$	−17.7582	−	42.5828i	−0.0302010	−	0.0724197i
$589$		−	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	$-0.969676\pi$
$593$	−646.718	−	646.718i	−1.09059	−	1.09059i	−0.0951217	−	0.995466i	$-0.530324\pi$
$594$	645.124	−	14.1581i	1.08607	−	0.0238352i
$595$		0			0
$596$	68.3083	+	69.1189i	0.114611	+	0.115971i
$597$	−208.443	+	515.278i	−0.349151	+	0.863112i
$598$	75.5510	−	180.886i	0.126340	−	0.302484i
$599$			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	$0.497950\pi$
$602$	−155.158	−	64.8053i	−0.257737	−	0.107650i
$603$	−836.703	+	13.8860i	−1.38757	+	0.0230282i
$604$	−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	−0.964421	−	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
$612$	−340.273	−	333.071i	−0.556002	−	0.544233i
$613$	−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	−0.221620	−	0.975133i	$-0.571135\pi$
$617$	464.917	−	464.917i	0.753513	−	0.753513i	0.975133	+	0.221620i	$0.0711345\pi$
$618$	85.2058	−	0.455701i	0.137873	−	0.000737380i
$619$	−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
$624$	−265.271	+	108.793i	−0.425113	+	0.174347i
$625$		0			0
$626$	−433.183	+	177.936i	−0.691986	+	0.284242i
$627$	20.0104	−	49.4663i	0.0319145	−	0.0788936i
$628$	−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
$633$	753.254	+	304.711i	1.18997	+	0.481375i
$634$	−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
$638$	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	$0.0925895\pi$
$641$			367.670i			0.573588i	−0.957992	+	0.286794i	$0.907410\pi$
$642$	130.694	−	0.698985i	0.203574	−	0.00108876i
$643$	−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	0.905474	−	0.424402i	$-0.139515\pi$
$647$	311.254	+	311.254i	0.481073	+	0.481073i	−0.424402	+	0.905474i	$0.639515\pi$
$648$	592.461	−	262.477i	0.914292	−	0.405057i
$649$			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	0.742740	−	0.669580i	$-0.233526\pi$
$653$	47.7734	+	47.7734i	0.0731598	+	0.0731598i	−0.669580	+	0.742740i	$0.733526\pi$
$654$	−66.9470	−	66.2347i	−0.102365	−	0.101276i
$655$		0			0
$656$	433.030	+	5.10846i	0.660107	+	0.00778728i
$657$	204.768	−	3.39835i	0.311671	−	0.00517253i
$658$	−263.088	−	109.885i	−0.399830	−	0.166998i
$659$			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	$0.479040\pi$
$662$	−214.599	+	513.796i	−0.324167	+	0.776127i
$663$	219.716	+	88.8809i	0.331397	+	0.134059i
$664$	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
$668$	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
$672$	−645.084	−	4.15973i	−0.959946	−	0.00619007i
$673$	−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	−0.314210	−	0.949353i	$-0.601740\pi$
$677$	429.992	−	429.992i	0.635143	−	0.635143i	0.949353	+	0.314210i	$0.101740\pi$
$678$	−282.752	+	1.51222i	−0.417038	+	0.00223042i
$679$	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	−0.380981	−	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
$687$	207.653	+	84.0008i	0.302260	+	0.122272i
$688$	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
$693$	−722.588	+	11.9922i	−1.04270	+	0.0173047i
$694$	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
$698$	−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	$0.122370\pi$
$701$			525.802i			0.750074i	−0.927010	+	0.375037i	$0.877630\pi$
$702$	−223.020	+	233.028i	−0.317692	+	0.331949i
$703$	−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
$708$	285.099	+	683.647i	0.402683	+	0.965603i
$709$		−	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
$714$	379.092	+	375.059i	0.530941	+	0.525292i
$715$		0			0
$716$	608.645	−	601.507i	0.850063	−	0.840094i
$717$	595.734	+	240.990i	0.830871	+	0.336109i
$718$	365.355	−	874.739i	0.508850	−	1.21830i
$719$		−	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
$722$	662.134	+	276.556i	0.917084	+	0.383041i
$723$	−188.928	+	467.036i	−0.261311	+	0.645969i
$724$	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	−0.891320	−	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
$732$	936.997	−	390.753i	1.28005	−	0.533816i
$733$	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
$738$	447.522	−	192.565i	0.606398	−	0.260928i
$739$	−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	−0.794705	−	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
$747$	162.259	−	2.69287i	0.217214	−	0.00360491i
$748$	−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
$753$	187.663	−	463.908i	0.249220	−	0.616079i
$754$	−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	$0.496295\pi$
$758$	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	$0.269315\pi$
$761$			1139.50i			1.49737i	−0.662925	+	0.748686i	$0.730685\pi$
$762$	0.543804	+	101.679i	0.000713654	+	0.133437i
$763$	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
$768$	304.719	−	704.961i	0.396769	−	0.917918i
$769$			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	0.890168	−	0.455632i	$-0.150587\pi$
$773$	335.897	+	335.897i	0.434537	+	0.434537i	−0.455632	+	0.890168i	$0.650587\pi$
$774$	83.3355	−	209.220i	0.107669	−	0.270310i
$775$		0			0
$776$	−30.5484	+	71.9434i	−0.0393665	+	0.0927106i
$777$	−525.680	+	1299.50i	−0.676550	+	1.67245i
$778$	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
$783$	971.574	−	431.074i	1.24084	−	0.550541i
$784$	−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	−0.591928	−	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
$792$	323.082	−	797.407i	0.407932	−	1.00683i
$793$	−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	−0.983448	−	0.181190i	$-0.942005\pi$
$797$	−639.400	+	639.400i	−0.802258	+	0.802258i	0.181190	+	0.983448i	$0.442005\pi$
$798$	0.320962	+	60.0126i	0.000402208	+	0.0752037i
$799$	−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
$804$	−424.508	+	1031.85i	−0.527995	+	1.28339i
$805$		0			0
$806$	198.142	+	482.376i	0.245834	+	0.598482i
$807$	−196.508	+	485.773i	−0.243504	+	0.601949i
$808$	111.315	−	44.9587i	0.137767	−	0.0556420i
$809$	857.503			1.05995			0.529977	−	0.848012i	$-0.322200\pi$
$809$	857.503			1.05995			0.529977	+	0.848012i	$0.322200\pi$
$810$		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
$813$	−853.456	−	345.245i	−1.04976	−	0.424656i
$814$	−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
$818$	−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	$-0.781531\pi$
$821$		−	1040.55i		−	1.26742i	0.773571	−	0.633710i	$-0.218469\pi$
$822$	7.05600	+	1319.31i	0.00858394	+	1.60500i
$823$	−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	0.312292	−	0.949986i	$-0.398903\pi$
$827$	−527.373	−	527.373i	−0.637694	−	0.637694i	−0.949986	+	0.312292i	$0.898903\pi$
$828$	422.152	+	413.216i	0.509845	+	0.499053i
$829$		−	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
$834$	−929.169	+	939.161i	−1.11411	+	1.12609i
$835$		0			0
$836$	−50.0110	−	50.6045i	−0.0598218	−	0.0605317i
$837$	−477.996	−	1077.33i	−0.571083	−	1.28713i
$838$	−218.836	+	523.940i	−0.261140	+	0.625227i
$839$			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
$842$	864.032	+	360.883i	1.02617	+	0.428602i
$843$	−117.698	−	47.6117i	−0.139618	−	0.0564789i
$844$	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
$848$	−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
$852$	−158.152	+	65.9535i	−0.185624	+	0.0774102i
$853$	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	−0.689694	−	0.724101i	$-0.742255\pi$
$857$	29.4871	−	29.4871i	0.0344074	−	0.0344074i	0.724101	+	0.689694i	$0.242255\pi$
$858$	2.29043	+	428.258i	0.00266949	+	0.499135i
$859$	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	−0.711151	−	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
$867$	−317.210	−	128.319i	−0.365870	−	0.148004i
$868$	−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
$873$	1.45911	+	87.9184i	0.00167137	+	0.100708i
$874$	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	$0.738945\pi$
$878$	−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	$0.120038\pi$
$881$			648.829i			0.736469i	−0.929733	+	0.368235i	$0.879962\pi$
$882$	−63.5706	+	27.3539i	−0.0720755	+	0.0310135i
$883$	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	0.646070	−	0.763278i	$-0.276412\pi$
$887$	−103.964	−	103.964i	−0.117209	−	0.117209i	−0.763278	+	0.646070i	$0.776412\pi$
$888$	−1179.41	−	1180.71i	−1.32817	−	1.32963i
$889$		−	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
$894$	102.519	−	103.622i	0.114675	−	0.115908i
$895$		0			0
$896$	−345.491	+	787.692i	−0.385592	+	0.879121i
$897$	−272.586	−	110.268i	−0.303886	−	0.122930i
$898$	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
$903$	−94.5843	+	233.815i	−0.104745	+	0.258932i
$904$	−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	−0.210285	−	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	$-0.700753\pi$
$911$	−1074.43			−1.17939			−0.589696	+	0.807625i	$0.700753\pi$
$912$	−65.9124	−	27.5724i	−0.0722724	−	0.0302329i
$913$	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
$918$	−493.834	+	515.996i	−0.537946	+	0.562087i
$919$	−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
$924$	−366.611	+	891.117i	−0.396765	+	0.964412i
$925$		0			0
$926$	−487.245	−	1186.20i	−0.526183	−	1.28099i
$927$	−2.12087	−	127.793i	−0.00228788	−	0.137856i
$928$	499.193	−	1156.62i	0.537923	−	1.24636i
$929$	1085.41			1.16836			0.584182	−	0.811623i	$-0.301415\pi$
$929$	1085.41			1.16836			0.584182	+	0.811623i	$0.301415\pi$
$930$		0			0
$931$			5.72287i			0.00614702i
$932$	−4.96401	+	841.600i	−0.00532619	+	0.903005i
$933$	−358.528	+	886.293i	−0.384275	+	0.949939i
$934$	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	$0.676655\pi$
$938$	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	$-0.967293\pi$
$941$		−	193.039i		−	0.205142i	0.994726	−	0.102571i	$-0.0327069\pi$
$942$	654.427	−	3.50003i	0.694721	−	0.00371553i
$943$	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	$0.626026\pi$
$948$	−103.304	+	43.0804i	−0.108970	+	0.0454434i
$949$			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	0.604905	−	0.796298i	$-0.293211\pi$
$953$	−182.398	−	182.398i	−0.191393	−	0.191393i	−0.796298	+	0.604905i	$0.793211\pi$
$954$	−137.842	+	346.061i	−0.144488	+	0.362747i
$955$		0			0
$956$	609.442	−	602.295i	0.637492	−	0.630015i
$957$	529.231	−	1308.27i	0.553010	−	1.36706i
$958$	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
$963$	−3.25313	−	196.017i	−0.00337812	−	0.203549i
$964$	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	−0.199301	−	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	$-0.612142\pi$
$971$	−670.107			−0.690121			−0.345060	+	0.938580i	$0.612142\pi$
$972$	−403.685	−	884.207i	−0.415313	−	0.909678i
$973$	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	$-0.482187\pi$
$977$	1030.12	−	1030.12i	1.05437	−	1.05437i	0.998435	−	0.0559325i	$-0.0178132\pi$
$978$	−1525.33	+	8.15782i	−1.55964	+	0.00834133i
$979$	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	$0.540219\pi$
$983$	−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
$987$	−160.379	+	396.461i	−0.162491	+	0.401683i
$988$	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
$993$	774.266	+	313.210i	0.779724	+	0.315418i
$994$	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	$0.857122\pi$
$998$	−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.107.2		40
3.2	odd	2	inner	300.3.l.g.107.19		40
4.3	odd	2	inner	300.3.l.g.107.12		40
5.2	odd	4		60.3.l.a.23.12	yes	40
5.3	odd	4	inner	300.3.l.g.143.9		40
5.4	even	2		60.3.l.a.47.19	yes	40
12.11	even	2	inner	300.3.l.g.107.9		40
15.2	even	4		60.3.l.a.23.9	yes	40
15.8	even	4	inner	300.3.l.g.143.12		40
15.14	odd	2		60.3.l.a.47.2	yes	40
20.3	even	4	inner	300.3.l.g.143.19		40
20.7	even	4		60.3.l.a.23.2	✓	40
20.19	odd	2		60.3.l.a.47.9	yes	40
60.23	odd	4	inner	300.3.l.g.143.2		40
60.47	odd	4		60.3.l.a.23.19	yes	40
60.59	even	2		60.3.l.a.47.12	yes	40

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

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

Fields

Representations

Groups

Database

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