LMFDB - Embedded newform 684.2.cf.b.127.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(91,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 11]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("684.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cf (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.8
Character	$\chi$	$=$	684.127
Dual form			684.2.cf.b.307.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02960 - 0.969499i) q^{2} +(0.120142 - 1.99639i) q^{4} +(-0.162908 - 0.923898i) q^{5} +(-2.27351 - 1.31261i) q^{7} +(-1.81180 - 2.17195i) q^{8} +(-1.06345 - 0.793304i) q^{10} +(-5.14137 + 2.96837i) q^{11} +(-1.39481 - 3.83220i) q^{13} +(-3.61337 + 0.852704i) q^{14} +(-3.97113 - 0.479699i) q^{16} +(-2.94059 + 2.46745i) q^{17} +(4.31383 + 0.625180i) q^{19} +(-1.86403 + 0.214229i) q^{20} +(-2.41571 + 8.04079i) q^{22} +(0.401333 + 0.0707658i) q^{23} +(3.87141 - 1.40908i) q^{25} +(-5.15140 - 2.59336i) q^{26} +(-2.89362 + 4.38110i) q^{28} +(4.15634 - 4.95333i) q^{29} +(3.66403 - 6.34629i) q^{31} +(-4.55373 + 3.35611i) q^{32} +(-0.635435 + 5.39138i) q^{34} +(-0.842345 + 2.31432i) q^{35} -2.51566i q^{37} +(5.04762 - 3.53857i) q^{38} +(-1.71151 + 2.02775i) q^{40} +(1.57709 - 4.33302i) q^{41} +(-11.3090 + 1.99407i) q^{43} +(5.30833 + 10.6208i) q^{44} +(0.481818 - 0.316231i) q^{46} +(-2.45354 + 2.92401i) q^{47} +(-0.0541088 - 0.0937192i) q^{49} +(2.61990 - 5.20412i) q^{50} +(-7.81813 + 2.32417i) q^{52} +(4.84195 + 0.853766i) q^{53} +(3.58005 + 4.26653i) q^{55} +(1.26821 + 7.31614i) q^{56} +(-0.522897 - 9.12951i) q^{58} +(1.21047 - 1.01570i) q^{59} +(1.11276 - 6.31077i) q^{61} +(-2.38025 - 10.0864i) q^{62} +(-1.43476 + 7.87029i) q^{64} +(-3.31333 + 1.91295i) q^{65} +(-2.22499 - 1.86699i) q^{67} +(4.57270 + 6.16701i) q^{68} +(1.37646 + 3.19948i) q^{70} +(-1.17754 - 6.67818i) q^{71} +(11.1504 + 4.05843i) q^{73} +(-2.43893 - 2.59011i) q^{74} +(1.76637 - 8.53697i) q^{76} +15.5853 q^{77} +(-4.29071 - 1.56169i) q^{79} +(0.203737 + 3.74707i) q^{80} +(-2.57709 - 5.99025i) q^{82} +(-0.641515 - 0.370379i) q^{83} +(2.75872 + 2.31484i) q^{85} +(-9.71042 + 13.0171i) q^{86} +(15.7623 + 5.78873i) q^{88} +(-5.87516 - 16.1419i) q^{89} +(-1.85908 + 10.5434i) q^{91} +(0.189493 - 0.792714i) q^{92} +(0.308673 + 5.38926i) q^{94} +(-0.125156 - 4.08739i) q^{95} +(2.43876 + 2.90640i) q^{97} +(-0.146571 - 0.0440346i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.02960	−	0.969499i	0.728035	−	0.685540i
$2$	1.02960	−	0.969499i	0.728035	−	0.685540i
$3$		0			0
$3$		0			0
$4$	0.120142	−	1.99639i	0.0600708	−	0.998194i
$5$	−0.162908	−	0.923898i	−0.0728547	−	0.413180i	−0.999322	−	0.0368055i	$-0.988282\pi$
$5$	−0.162908	−	0.923898i	−0.0728547	−	0.413180i	0.926468	−	0.376374i	$-0.122829\pi$
$6$		0			0
$7$	−2.27351	−	1.31261i	−0.859305	−	0.496120i	0.00447442	−	0.999990i	$-0.498576\pi$
$7$	−2.27351	−	1.31261i	−0.859305	−	0.496120i	−0.863780	+	0.503870i	$0.831909\pi$
$8$	−1.81180	−	2.17195i	−0.640568	−	0.767901i
$9$		0			0
$10$	−1.06345	−	0.793304i	−0.336292	−	0.250865i
$11$	−5.14137	+	2.96837i	−1.55018	+	0.894998i	−0.552057	+	0.833807i	$0.686157\pi$
$11$	−5.14137	+	2.96837i	−1.55018	+	0.894998i	−0.998126	+	0.0611917i	$0.980510\pi$
$12$		0			0
$13$	−1.39481	−	3.83220i	−0.386850	−	1.06286i	−0.968411	−	0.249358i	$-0.919780\pi$
$13$	−1.39481	−	3.83220i	−0.386850	−	1.06286i	0.581562	−	0.813502i	$-0.302442\pi$
$14$	−3.61337	+	0.852704i	−0.965714	+	0.227895i
$15$		0			0
$16$	−3.97113	−	0.479699i	−0.992783	−	0.119925i
$17$	−2.94059	+	2.46745i	−0.713198	+	0.598444i	−0.925495	−	0.378761i	$-0.876350\pi$
$17$	−2.94059	+	2.46745i	−0.713198	+	0.598444i	0.212296	+	0.977205i	$0.431906\pi$
$18$		0			0
$19$	4.31383	+	0.625180i	0.989661	+	0.143426i
$19$	4.31383	+	0.625180i	0.989661	+	0.143426i
$20$	−1.86403	+	0.214229i	−0.416810	+	0.0479031i
$21$		0			0
$22$	−2.41571	+	8.04079i	−0.515031	+	1.71430i
$23$	0.401333	+	0.0707658i	0.0836836	+	0.0147557i	0.215333	−	0.976541i	$-0.430916\pi$
$23$	0.401333	+	0.0707658i	0.0836836	+	0.0147557i	−0.131650	+	0.991296i	$0.542027\pi$
$24$		0			0
$25$	3.87141	−	1.40908i	0.774283	−	0.281816i
$26$	−5.15140	−	2.59336i	−1.01027	−	0.508599i
$27$		0			0
$28$	−2.89362	+	4.38110i	−0.546843	+	0.827951i
$29$	4.15634	−	4.95333i	0.771813	−	0.919811i	−0.226720	−	0.973960i	$-0.572800\pi$
$29$	4.15634	−	4.95333i	0.771813	−	0.919811i	0.998533	+	0.0541493i	$0.0172447\pi$
$30$		0			0
$31$	3.66403	−	6.34629i	0.658080	−	1.13983i	−0.323032	−	0.946388i	$-0.604702\pi$
$31$	3.66403	−	6.34629i	0.658080	−	1.13983i	0.981112	−	0.193440i	$-0.0619644\pi$
$32$	−4.55373	+	3.35611i	−0.804994	+	0.593283i
$33$		0			0
$34$	−0.635435	+	5.39138i	−0.108976	+	0.924614i
$35$	−0.842345	+	2.31432i	−0.142382	+	0.391192i
$36$		0			0
$37$		−	2.51566i		−	0.413571i	−0.978386	−	0.206786i	$-0.933700\pi$
$37$		−	2.51566i		−	0.413571i	0.978386	−	0.206786i	$-0.0663003\pi$
$38$	5.04762	−	3.53857i	0.818832	−	0.574033i
$39$		0			0
$40$	−1.71151	+	2.02775i	−0.270613	+	0.320615i
$41$	1.57709	−	4.33302i	0.246300	−	0.676703i	−0.753514	−	0.657431i	$-0.771643\pi$
$41$	1.57709	−	4.33302i	0.246300	−	0.676703i	0.999814	−	0.0192719i	$-0.00613482\pi$
$42$		0			0
$43$	−11.3090	+	1.99407i	−1.72460	+	0.304093i	−0.946178	−	0.323648i	$-0.895091\pi$
$43$	−11.3090	+	1.99407i	−1.72460	+	0.304093i	−0.778422	+	0.627741i	$0.783980\pi$
$44$	5.30833	+	10.6208i	0.800261	+	1.60115i
$45$		0			0
$46$	0.481818	−	0.316231i	0.0710402	−	0.0466258i
$47$	−2.45354	+	2.92401i	−0.357886	+	0.426511i	−0.914705	−	0.404122i	$-0.867577\pi$
$47$	−2.45354	+	2.92401i	−0.357886	+	0.426511i	0.556819	+	0.830634i	$0.312022\pi$
$48$		0			0
$49$	−0.0541088	−	0.0937192i	−0.00772983	−	0.0133885i
$50$	2.61990	−	5.20412i	0.370509	−	0.735974i
$51$		0			0
$52$	−7.81813	+	2.32417i	−1.08418	+	0.322304i
$53$	4.84195	+	0.853766i	0.665092	+	0.117274i	0.495995	−	0.868326i	$-0.334804\pi$
$53$	4.84195	+	0.853766i	0.665092	+	0.117274i	0.169098	+	0.985599i	$0.445915\pi$
$54$		0			0
$55$	3.58005	+	4.26653i	0.482733	+	0.575299i
$56$	1.26821	+	7.31614i	0.169472	+	0.977660i
$57$		0			0
$58$	−0.522897	−	9.12951i	−0.0686597	−	1.19876i
$59$	1.21047	−	1.01570i	0.157589	−	0.132233i	−0.560584	−	0.828098i	$-0.689423\pi$
$59$	1.21047	−	1.01570i	0.157589	−	0.132233i	0.718173	+	0.695865i	$0.244979\pi$
$60$		0			0
$61$	1.11276	−	6.31077i	0.142474	−	0.808012i	−0.826886	−	0.562369i	$-0.809890\pi$
$61$	1.11276	−	6.31077i	0.142474	−	0.808012i	0.969360	−	0.245643i	$-0.0789989\pi$
$62$	−2.38025	−	10.0864i	−0.302292	−	1.28097i
$63$		0			0
$64$	−1.43476	+	7.87029i	−0.179345	+	0.983786i
$65$	−3.31333	+	1.91295i	−0.410969	+	0.237273i
$66$		0			0
$67$	−2.22499	−	1.86699i	−0.271826	−	0.228089i	0.496677	−	0.867936i	$-0.334554\pi$
$67$	−2.22499	−	1.86699i	−0.271826	−	0.228089i	−0.768503	+	0.639846i	$0.778998\pi$
$68$	4.57270	+	6.16701i	0.554521	+	0.747859i
$69$		0			0
$70$	1.37646	+	3.19948i	0.164518	+	0.382410i
$71$	−1.17754	−	6.67818i	−0.139749	−	0.792555i	−0.971434	−	0.237308i	$-0.923735\pi$
$71$	−1.17754	−	6.67818i	−0.139749	−	0.792555i	0.831686	−	0.555247i	$-0.187376\pi$
$72$		0			0
$73$	11.1504	+	4.05843i	1.30506	+	0.475003i	0.898642	−	0.438684i	$-0.144555\pi$
$73$	11.1504	+	4.05843i	1.30506	+	0.475003i	0.406419	+	0.913687i	$0.366777\pi$
$74$	−2.43893	−	2.59011i	−0.283519	−	0.301094i
$75$		0			0
$76$	1.76637	−	8.53697i	0.202617	−	0.979258i
$77$	15.5853			1.77611
$78$		0			0
$79$	−4.29071	−	1.56169i	−0.482742	−	0.175704i	0.0891737	−	0.996016i	$-0.471577\pi$
$79$	−4.29071	−	1.56169i	−0.482742	−	0.175704i	−0.571916	+	0.820312i	$0.693800\pi$
$80$	0.203737	+	3.74707i	0.0227785	+	0.418935i
$81$		0			0
$82$	−2.57709	−	5.99025i	−0.284592	−	0.661512i
$83$	−0.641515	−	0.370379i	−0.0704154	−	0.0406543i	0.464379	−	0.885637i	$-0.346278\pi$
$83$	−0.641515	−	0.370379i	−0.0704154	−	0.0406543i	−0.534794	+	0.844982i	$0.679611\pi$
$84$		0			0
$85$	2.75872	+	2.31484i	0.299225	+	0.251080i
$86$	−9.71042	+	13.0171i	−1.04710	+	1.40367i
$87$		0			0
$88$	15.7623	+	5.78873i	1.68027	+	0.617080i
$89$	−5.87516	−	16.1419i	−0.622766	−	1.71103i	−0.700114	−	0.714031i	$-0.746868\pi$
$89$	−5.87516	−	16.1419i	−0.622766	−	1.71103i	0.0773486	−	0.997004i	$-0.475355\pi$
$90$		0			0
$91$	−1.85908	+	10.5434i	−0.194885	+	1.10525i
$92$	0.189493	−	0.792714i	0.0197560	−	0.0826461i
$93$		0			0
$94$	0.308673	+	5.38926i	0.0318371	+	0.555860i
$95$	−0.125156	−	4.08739i	−0.0128407	−	0.419357i
$96$		0			0
$97$	2.43876	+	2.90640i	0.247618	+	0.295100i	0.875509	−	0.483201i	$-0.160526\pi$
$97$	2.43876	+	2.90640i	0.247618	+	0.295100i	−0.627891	+	0.778301i	$0.716082\pi$
$98$	−0.146571	−	0.0440346i	−0.0148059	−	0.00444817i
$99$		0			0
$100$	−2.34795	−	7.89814i	−0.234795	−	0.789814i
$101$	−9.11983	+	3.31935i	−0.907457	+	0.330287i	−0.753237	−	0.657749i	$-0.771509\pi$
$101$	−9.11983	+	3.31935i	−0.907457	+	0.330287i	−0.154220	+	0.988037i	$0.549286\pi$
$102$		0			0
$103$	7.76969	+	13.4575i	0.765570	+	1.32601i	0.939945	+	0.341327i	$0.110876\pi$
$103$	7.76969	+	13.4575i	0.765570	+	1.32601i	−0.174374	+	0.984679i	$0.555790\pi$
$104$	−5.79625	+	9.97263i	−0.568369	+	0.977897i
$105$		0			0
$106$	5.81298	−	3.81523i	0.564607	−	0.370568i
$107$	8.60129	−	14.8979i	0.831518	−	1.44023i	−0.0653163	−	0.997865i	$-0.520806\pi$
$107$	8.60129	−	14.8979i	0.831518	−	1.44023i	0.896834	−	0.442367i	$-0.145861\pi$
$108$		0			0
$109$	−3.11205	+	0.548739i	−0.298081	+	0.0525597i	−0.320688	−	0.947185i	$-0.603914\pi$
$109$	−3.11205	+	0.548739i	−0.298081	+	0.0525597i	0.0226078	+	0.999744i	$0.492803\pi$
$110$	7.82241	+	0.921958i	0.745837	+	0.0879053i
$111$		0			0
$112$	8.39874	+	6.30315i	0.793606	+	0.595591i
$113$			19.3153i			1.81703i	0.417850	+	0.908516i	$0.362784\pi$
$113$			19.3153i			1.81703i	−0.417850	+	0.908516i	$0.637216\pi$
$114$		0			0
$115$		−	0.382319i		−	0.0356514i
$116$	−9.38942	−	8.89277i	−0.871786	−	0.825673i
$117$		0			0
$118$	0.261570	−	2.21931i	0.0240795	−	0.204304i
$119$	9.92426	−	1.74991i	0.909755	−	0.160414i
$120$		0			0
$121$	12.1225	−	20.9968i	1.10204	−	1.90880i
$122$	−4.97260	−	7.57638i	−0.450198	−	0.685933i
$123$		0			0
$124$	−12.2295	−	8.07729i	−1.09824	−	0.725362i
$125$	−4.27791	−	7.40955i	−0.382628	−	0.662731i
$126$		0			0
$127$	13.9783	−	5.08769i	1.24037	−	0.451459i	0.363236	−	0.931697i	$-0.381672\pi$
$127$	13.9783	−	5.08769i	1.24037	−	0.451459i	0.877138	+	0.480238i	$0.159450\pi$
$128$	6.15301	+	9.49423i	0.543855	+	0.839179i
$129$		0			0
$130$	−1.55679	+	5.18185i	−0.136540	+	0.454478i
$131$	2.07131	+	2.46849i	0.180971	+	0.215673i	0.848902	−	0.528551i	$-0.177264\pi$
$131$	2.07131	+	2.46849i	0.180971	+	0.215673i	−0.667931	+	0.744223i	$0.732820\pi$
$132$		0			0
$133$	−8.98691	−	7.08373i	−0.779264	−	0.614237i
$134$	−4.10089	+	0.234881i	−0.354263	+	0.0202906i
$135$		0			0
$136$	10.6869	+	1.91630i	0.916398	+	0.164322i
$137$	−1.36502	+	7.74139i	−0.116621	+	0.661391i	0.869314	+	0.494261i	$0.164561\pi$
$137$	−1.36502	+	7.74139i	−0.116621	+	0.661391i	−0.985935	+	0.167130i	$0.946550\pi$
$138$		0			0
$139$	−0.00238476	−	0.00655208i	−0.000202273	−	0.000555740i	0.939591	−	0.342298i	$-0.111205\pi$
$139$	−0.00238476	−	0.00655208i	−0.000202273	−	0.000555740i	−0.939794	+	0.341742i	$0.888983\pi$
$140$	4.51909	+	1.95969i	0.381933	+	0.165624i
$141$		0			0
$142$	−7.68689	−	5.73421i	−0.645070	−	0.481204i
$143$	18.5466	+	15.5625i	1.55095	+	1.30140i
$144$		0			0
$145$	−5.25348	−	3.03310i	−0.436277	−	0.251885i
$146$	15.4151	−	6.63180i	1.27576	−	0.548852i
$147$		0			0
$148$	−5.02223	−	0.302235i	−0.412824	−	0.0248436i
$149$	10.8510	+	3.94945i	0.888950	+	0.323552i	0.745816	−	0.666152i	$-0.232060\pi$
$149$	10.8510	+	3.94945i	0.888950	+	0.323552i	0.143134	+	0.989703i	$0.454282\pi$
$150$		0			0
$151$	−3.85210			−0.313480			−0.156740	−	0.987640i	$-0.550098\pi$
$151$	−3.85210			−0.313480			−0.156740	+	0.987640i	$0.550098\pi$
$152$	−6.45794	−	10.5021i	−0.523808	−	0.851836i
$153$		0			0
$154$	16.0466	−	15.1099i	1.29307	−	1.21759i
$155$	−6.46023	−	2.35133i	−0.518898	−	0.188863i
$156$		0			0
$157$	3.30340	+	18.7345i	0.263640	+	1.49518i	0.772880	+	0.634553i	$0.218816\pi$
$157$	3.30340	+	18.7345i	0.263640	+	1.49518i	−0.509240	+	0.860625i	$0.670073\pi$
$158$	−5.93176	+	2.55193i	−0.471905	+	0.203020i
$159$		0			0
$160$	3.84255	+	3.66045i	0.303780	+	0.289384i
$161$	−0.819545	−	0.687680i	−0.0645892	−	0.0541968i
$162$		0			0
$163$	−5.72920	+	3.30775i	−0.448745	+	0.259083i	−0.707300	−	0.706913i	$-0.750087\pi$
$163$	−5.72920	+	3.30775i	−0.448745	+	0.259083i	0.258555	+	0.965997i	$0.416754\pi$
$164$	−8.46091	−	3.66906i	−0.660686	−	0.286505i
$165$		0			0
$166$	−1.01958	+	0.240607i	−0.0791350	+	0.0186747i
$167$	−0.143711	+	0.815026i	−0.0111207	+	0.0630686i	−0.989863	−	0.142025i	$-0.954639\pi$
$167$	−0.143711	+	0.815026i	−0.0111207	+	0.0630686i	0.978742	+	0.205093i	$0.0657498\pi$
$168$		0			0
$169$	−2.78168	+	2.33410i	−0.213975	+	0.179546i
$170$	5.08460	−	0.291223i	0.389971	−	0.0223358i
$171$		0			0
$172$	2.62227	+	22.8166i	0.199946	+	1.73975i
$173$	−3.66715	−	4.37034i	−0.278808	−	0.332271i	0.608408	−	0.793624i	$-0.291808\pi$
$173$	−3.66715	−	4.37034i	−0.278808	−	0.332271i	−0.887216	+	0.461354i	$0.847364\pi$
$174$		0			0
$175$	−10.6513	−	1.87810i	−0.805160	−	0.141971i
$176$	21.8410	−	9.32149i	1.64633	−	0.702634i
$177$		0			0
$178$	−21.6986	−	10.9237i	−1.62638	−	0.818763i
$179$	−2.18671	−	3.78750i	−0.163442	−	0.283091i	0.772659	−	0.634822i	$-0.218926\pi$
$179$	−2.18671	−	3.78750i	−0.163442	−	0.283091i	−0.936101	+	0.351731i	$0.885593\pi$
$180$		0			0
$181$	−5.17743	+	6.17022i	−0.384835	+	0.458628i	−0.923334	−	0.383998i	$-0.874547\pi$
$181$	−5.17743	+	6.17022i	−0.384835	+	0.458628i	0.538499	+	0.842626i	$0.318992\pi$
$182$	8.30768	+	12.6578i	0.615807	+	0.938259i
$183$		0			0
$184$	−0.573434	−	0.999889i	−0.0422741	−	0.0737128i
$185$	−2.32421	+	0.409821i	−0.170879	+	0.0301306i
$186$		0			0
$187$	7.79437	−	21.4149i	0.569981	−	1.56601i
$188$	5.54270	+	5.24951i	0.404243	+	0.382860i
$189$		0			0
$190$	−4.09158	−	4.08703i	−0.296834	−	0.296504i
$191$			3.21322i			0.232501i	0.993220	+	0.116250i	$0.0370875\pi$
$191$			3.21322i			0.232501i	−0.993220	+	0.116250i	$0.962913\pi$
$192$		0			0
$193$	−2.03628	+	5.59463i	−0.146575	+	0.402711i	−0.991153	−	0.132721i	$-0.957629\pi$
$193$	−2.03628	+	5.59463i	−0.146575	+	0.402711i	0.844579	+	0.535431i	$0.179851\pi$
$194$	5.32869	+	0.628046i	0.382578	+	0.0450911i
$195$		0			0
$196$	−0.193601	+	0.0967626i	−0.0138286	+	0.00691162i
$197$	6.98997	−	12.1070i	0.498015	−	0.862587i	−0.501982	−	0.864878i	$-0.667396\pi$
$197$	6.98997	−	12.1070i	0.498015	−	0.862587i	0.999997	+	0.00229054i	$0.000729101\pi$
$198$		0			0
$199$	6.33587	−	7.55079i	0.449138	−	0.535261i	−0.493204	−	0.869914i	$-0.664174\pi$
$199$	6.33587	−	7.55079i	0.449138	−	0.535261i	0.942342	+	0.334652i	$0.108619\pi$
$200$	−10.0747	−	5.85556i	−0.712388	−	0.414051i
$201$		0			0
$202$	−6.17165	+	12.2593i	−0.434236	+	0.862559i
$203$	−15.9513	+	5.80578i	−1.11956	+	0.407486i
$204$		0			0
$205$	−4.26018	−	0.751186i	−0.297544	−	0.0524651i
$206$	21.0467	+	6.32309i	1.46639	+	0.440551i
$207$		0			0
$208$	3.70066	+	15.8872i	0.256594	+	1.10158i
$209$	−24.0348	+	9.59078i	−1.66252	+	0.663408i
$210$		0			0
$211$	11.1612	−	9.36536i	0.768369	−	0.644738i	−0.171922	−	0.985111i	$-0.554998\pi$
$211$	11.1612	−	9.36536i	0.768369	−	0.644738i	0.940291	+	0.340373i	$0.110553\pi$
$212$	2.28617	−	9.56383i	0.157015	−	0.656847i
$213$		0			0
$214$	−5.58761	−	23.6778i	−0.381961	−	1.61858i
$215$	3.68464	+	10.1235i	0.251291	+	0.690415i
$216$		0			0
$217$	−16.6604	+	9.61889i	−1.13098	+	0.652973i
$218$	−2.67216	+	3.58211i	−0.180981	+	0.242611i
$219$		0			0
$220$	8.94777	−	6.63457i	0.603258	−	0.447303i
$221$	13.5573	+	7.82731i	0.911963	+	0.526522i
$222$		0			0
$223$	0.947405	+	5.37300i	0.0634429	+	0.359803i	0.999958	+	0.00917516i	$0.00292059\pi$
$223$	0.947405	+	5.37300i	0.0634429	+	0.359803i	−0.936515	+	0.350628i	$0.885968\pi$
$224$	14.7582	−	1.65287i	0.986075	−	0.110437i
$225$		0			0
$226$	18.7262	+	19.8870i	1.24565	+	1.32286i
$227$	4.73837			0.314497			0.157248	−	0.987559i	$-0.449738\pi$
$227$	4.73837			0.314497			0.157248	+	0.987559i	$0.449738\pi$
$228$		0			0
$229$	−25.7074			−1.69879			−0.849397	−	0.527755i	$-0.823034\pi$
$229$	−25.7074			−1.69879			−0.849397	+	0.527755i	$0.823034\pi$
$230$	−0.370658	−	0.393634i	−0.0244405	−	0.0259555i
$231$		0			0
$232$	−18.2889	−	0.0529289i	−1.20072	−	0.00347495i
$233$	−2.50999	−	14.2349i	−0.164435	−	0.932556i	−0.949645	−	0.313327i	$-0.898556\pi$
$233$	−2.50999	−	14.2349i	−0.164435	−	0.932556i	0.785210	−	0.619229i	$-0.212555\pi$
$234$		0			0
$235$	3.10119	+	1.79047i	0.202300	+	0.116798i
$236$	−1.88231	−	2.53859i	−0.122528	−	0.165248i
$237$		0			0
$238$	8.52145	−	11.4233i	0.552363	−	0.740460i
$239$	13.1429	−	7.58808i	0.850146	−	0.490832i	−0.0105542	−	0.999944i	$-0.503360\pi$
$239$	13.1429	−	7.58808i	0.850146	−	0.490832i	0.860700	+	0.509112i	$0.170026\pi$
$240$		0			0
$241$	−1.91914	−	5.27279i	−0.123623	−	0.339650i	0.862408	−	0.506214i	$-0.168955\pi$
$241$	−1.91914	−	5.27279i	−0.123623	−	0.339650i	−0.986031	+	0.166563i	$0.946733\pi$
$242$	−7.87507	−	33.3710i	−0.506229	−	2.14517i
$243$		0			0
$244$	−12.4651	−	2.97969i	−0.797994	−	0.190755i
$245$	−0.0777723	+	0.0652587i	−0.00496869	+	0.00416922i
$246$		0			0
$247$	−3.62114	−	17.4035i	−0.230408	−	1.10736i
$248$	−20.4223	+	3.54010i	−1.29682	+	0.224797i
$249$		0			0
$250$	−11.5881	−	3.48143i	−0.732895	−	0.220185i
$251$	−20.4595	−	3.60756i	−1.29139	−	0.227707i	−0.514580	−	0.857442i	$-0.672052\pi$
$251$	−20.4595	−	3.60756i	−1.29139	−	0.227707i	−0.776810	+	0.629735i	$0.783163\pi$
$252$		0			0
$253$	−2.27346	+	0.827472i	−0.142931	+	0.0520227i
$254$	9.45952	−	18.7902i	0.593543	−	1.17900i
$255$		0			0
$256$	15.5398	+	3.80989i	0.971236	+	0.238118i
$257$	10.5434	−	12.5652i	0.657681	−	0.783793i	−0.329370	−	0.944201i	$-0.606836\pi$
$257$	10.5434	−	12.5652i	0.657681	−	0.783793i	0.987051	+	0.160408i	$0.0512809\pi$
$258$		0			0
$259$	−3.30208	+	5.71936i	−0.205181	+	0.355384i
$260$	3.42093	+	6.84453i	0.212157	+	0.424480i
$261$		0			0
$262$	4.52581	+	0.533417i	0.279605	+	0.0329546i
$263$	4.15539	−	11.4168i	0.256232	−	0.703992i	−0.743159	−	0.669114i	$-0.766674\pi$
$263$	4.15539	−	11.4168i	0.256232	−	0.703992i	0.999392	−	0.0348776i	$-0.0111041\pi$
$264$		0			0
$265$		−	4.61255i		−	0.283347i
$266$	−16.1206	+	1.41941i	−0.988416	+	0.0870299i
$267$		0			0
$268$	−3.99455	+	4.21765i	−0.244006	+	0.257634i
$269$	−5.91660	+	16.2557i	−0.360741	+	0.991129i	0.618027	+	0.786157i	$0.287932\pi$
$269$	−5.91660	+	16.2557i	−0.360741	+	0.991129i	−0.978768	+	0.204972i	$0.934290\pi$
$270$		0			0
$271$	6.08103	−	1.07225i	0.369396	−	0.0651345i	0.0141312	−	0.999900i	$-0.495502\pi$
$271$	6.08103	−	1.07225i	0.369396	−	0.0651345i	0.355265	+	0.934766i	$0.384391\pi$
$272$	12.8611	−	8.38797i	0.779819	−	0.508595i
$273$		0			0
$274$	6.09985	+	9.29389i	0.368506	+	0.561465i
$275$	−15.7217	+	18.7364i	−0.948055	+	1.12985i
$276$		0			0
$277$	13.7725	+	23.8547i	0.827511	+	1.43329i	0.899985	+	0.435920i	$0.143577\pi$
$277$	13.7725	+	23.8547i	0.827511	+	1.43329i	−0.0724748	+	0.997370i	$0.523090\pi$
$278$	−0.00880758	−	0.00443398i	−0.000528243	−	0.000265932i
$279$		0			0
$280$	6.55276	−	2.36356i	0.391603	−	0.141250i
$281$	−7.27059	−	1.28200i	−0.433727	−	0.0764778i	−0.0474780	−	0.998872i	$-0.515118\pi$
$281$	−7.27059	−	1.28200i	−0.433727	−	0.0764778i	−0.386249	+	0.922394i	$0.626230\pi$
$282$		0			0
$283$	5.57965	+	6.64957i	0.331676	+	0.395276i	0.905948	−	0.423388i	$-0.139159\pi$
$283$	5.57965	+	6.64957i	0.331676	+	0.395276i	−0.574272	+	0.818664i	$0.694715\pi$
$284$	−13.4737	+	1.54851i	−0.799518	+	0.0918870i
$285$		0			0
$286$	34.1833	−	1.95787i	2.02130	−	0.115771i
$287$	−9.27308	+	7.78104i	−0.547373	+	0.459300i
$288$		0			0
$289$	−0.393247	+	2.23021i	−0.0231321	+	0.131189i
$290$	−8.34955	+	1.97037i	−0.490302	+	0.115704i
$291$		0			0
$292$	9.44183	−	21.7730i	0.552541	−	1.27417i
$293$	−8.59522	+	4.96245i	−0.502138	+	0.289910i	−0.729596	−	0.683878i	$-0.760292\pi$
$293$	−8.59522	+	4.96245i	−0.502138	+	0.289910i	0.227458	+	0.973788i	$0.426959\pi$
$294$		0			0
$295$	−1.13560	−	0.952881i	−0.0661171	−	0.0554789i
$296$	−5.46389	+	4.55786i	−0.317582	+	0.264921i
$297$		0			0
$298$	15.0012	−	6.45372i	0.868995	−	0.373854i
$299$	−0.288593	−	1.63669i	−0.0166897	−	0.0946522i
$300$		0			0
$301$	28.3284	+	10.3107i	1.63282	+	0.594299i
$302$	−3.96611	+	3.73461i	−0.228224	+	0.214903i
$303$		0			0
$304$	−16.8309	−	4.55201i	−0.965318	−	0.261076i
$305$	−6.01179			−0.344234
$306$		0			0
$307$	−23.6159	−	8.59549i	−1.34783	−	0.490571i	−0.435562	−	0.900159i	$-0.643450\pi$
$307$	−23.6159	−	8.59549i	−1.34783	−	0.490571i	−0.912271	+	0.409588i	$0.865672\pi$
$308$	1.87244	−	31.1143i	0.106692	−	1.77290i
$309$		0			0
$310$	−8.93105	+	3.84226i	−0.507249	+	0.218226i
$311$	17.9579	+	10.3680i	1.01830	+	0.587916i	0.913611	−	0.406589i	$-0.133282\pi$
$311$	17.9579	+	10.3680i	1.01830	+	0.587916i	0.104689	+	0.994505i	$0.466615\pi$
$312$		0			0
$313$	13.2291	+	11.1005i	0.747752	+	0.627439i	0.934907	−	0.354892i	$-0.115482\pi$
$313$	13.2291	+	11.1005i	0.747752	+	0.627439i	−0.187155	+	0.982330i	$0.559927\pi$
$314$	21.5643	+	16.0864i	1.21694	+	0.907806i
$315$		0			0
$316$	−3.63323	+	8.37829i	−0.204385	+	0.471316i
$317$	1.69445	+	4.65547i	0.0951699	+	0.261477i	0.978138	−	0.207955i	$-0.0666808\pi$
$317$	1.69445	+	4.65547i	0.0951699	+	0.261477i	−0.882968	+	0.469432i	$0.844459\pi$
$318$		0			0
$319$	−6.66595	+	37.8045i	−0.373222	+	2.11665i
$320$	7.50508	+	0.0434405i	0.419547	+	0.00242840i
$321$		0			0
$322$	−1.51051	+	0.0865150i	−0.0841772	+	0.00482129i
$323$	−14.2278	+	8.80576i	−0.791657	+	0.489966i
$324$		0			0
$325$	−10.7997	−	12.8706i	−0.599062	−	0.713934i
$326$	−2.69190	+	8.96011i	−0.149091	+	0.496255i
$327$		0			0
$328$	−12.2685	+	4.42519i	−0.677413	+	0.244340i
$329$	9.41623	−	3.42723i	0.519134	−	0.188949i
$330$		0			0
$331$	−6.79791	−	11.7743i	−0.373647	−	0.647175i	0.616477	−	0.787373i	$-0.288559\pi$
$331$	−6.79791	−	11.7743i	−0.373647	−	0.647175i	−0.990123	+	0.140198i	$0.955226\pi$
$332$	−0.816492	+	1.23621i	−0.0448108	+	0.0678461i
$333$		0			0
$334$	0.642203	+	0.978477i	0.0351398	+	0.0535399i
$335$	−1.36244	+	2.35981i	−0.0744380	+	0.128930i
$336$		0			0
$337$	−7.24750	+	1.27793i	−0.394797	+	0.0696133i	−0.367522	−	0.930015i	$-0.619794\pi$
$337$	−7.24750	+	1.27793i	−0.394797	+	0.0696133i	−0.0272743	+	0.999628i	$0.508683\pi$
$338$	−0.601095	+	5.10002i	−0.0326952	+	0.277405i
$339$		0			0
$340$	4.95275	−	5.22936i	0.268601	−	0.283602i
$341$			43.5049i			2.35592i
$342$		0			0
$343$			18.6606i			1.00758i
$344$	24.8206	+	20.9497i	1.33824	+	1.12953i
$345$		0			0
$346$	−8.01273	−	0.944390i	−0.430767	−	0.0507707i
$347$	7.29437	−	1.28619i	0.391582	−	0.0690465i	0.0256094	−	0.999672i	$-0.491847\pi$
$347$	7.29437	−	1.28619i	0.391582	−	0.0690465i	0.365973	+	0.930625i	$0.380736\pi$
$348$		0			0
$349$	−10.0951	+	17.4851i	−0.540376	+	0.935958i	0.458507	+	0.888691i	$0.348385\pi$
$349$	−10.0951	+	17.4851i	−0.540376	+	0.935958i	−0.998882	+	0.0472671i	$0.984949\pi$
$350$	−12.7873	+	8.39270i	−0.683512	+	0.448609i
$351$		0			0
$352$	13.4503	−	30.7722i	0.716901	−	1.64016i
$353$	10.6908	+	18.5171i	0.569016	+	0.985564i	0.996664	+	0.0816189i	$0.0260090\pi$
$353$	10.6908	+	18.5171i	0.569016	+	0.985564i	−0.427648	+	0.903945i	$0.640658\pi$
$354$		0			0
$355$	−5.97813	+	2.17586i	−0.317286	+	0.115483i
$356$	−32.9313	+	9.78979i	−1.74535	+	0.518858i
$357$		0			0
$358$	−5.92341	−	1.77958i	−0.313062	−	0.0940537i
$359$	−13.3436	−	15.9023i	−0.704248	−	0.839290i	0.288752	−	0.957404i	$-0.406760\pi$
$359$	−13.3436	−	15.9023i	−0.704248	−	0.839290i	−0.993000	+	0.118114i	$0.962315\pi$
$360$		0			0
$361$	18.2183	+	5.39384i	0.958858	+	0.283887i
$362$	0.651357	+	11.3723i	0.0342345	+	0.597717i
$363$		0			0
$364$	20.8253	+	4.97814i	1.09154	+	0.260926i
$365$	1.93308	−	10.9630i	0.101182	−	0.573831i
$366$		0			0
$367$	−3.99066	−	10.9643i	−0.208311	−	0.572330i	0.790904	−	0.611940i	$-0.209611\pi$
$367$	−3.99066	−	10.9643i	−0.208311	−	0.572330i	−0.999215	+	0.0396103i	$0.987388\pi$
$368$	−1.55980	−	0.473539i	−0.0813101	−	0.0246849i
$369$		0			0
$370$	−1.99568	+	2.67527i	−0.103750	+	0.139081i
$371$	−9.88754	−	8.29663i	−0.513336	−	0.430740i
$372$		0			0
$373$	−22.7922	−	13.1591i	−1.18013	−	0.681351i	−0.224089	−	0.974569i	$-0.571941\pi$
$373$	−22.7922	−	13.1591i	−1.18013	−	0.681351i	−0.956046	+	0.293218i	$0.905274\pi$
$374$	−12.7366	−	29.6053i	−0.658595	−	1.53085i
$375$		0			0
$376$	10.7961	+	0.0312446i	0.556769	+	0.00161132i
$377$	−24.7794	−	9.01898i	−1.27621	−	0.464501i
$378$		0			0
$379$	15.1616			0.778798			0.389399	−	0.921069i	$-0.372683\pi$
$379$	15.1616			0.778798			0.389399	+	0.921069i	$0.372683\pi$
$380$	−8.17505	−	0.241206i	−0.419371	−	0.0123736i
$381$		0			0
$382$	3.11522	+	3.30833i	0.159388	+	0.169269i
$383$	−29.2153	−	10.6335i	−1.49283	−	0.543346i	−0.538637	−	0.842538i	$-0.681060\pi$
$383$	−29.2153	−	10.6335i	−1.49283	−	0.543346i	−0.954193	+	0.299193i	$0.903283\pi$
$384$		0			0
$385$	−2.53897	−	14.3992i	−0.129398	−	0.733851i
$386$	3.32745	+	7.73439i	0.169363	+	0.393670i
$387$		0			0
$388$	6.09530	−	4.51953i	0.309442	−	0.229444i
$389$	−26.2800	−	22.0515i	−1.33245	−	1.11806i	−0.983499	−	0.180913i	$-0.942095\pi$
$389$	−26.2800	−	22.0515i	−1.33245	−	1.11806i	−0.348947	−	0.937142i	$-0.613461\pi$
$390$		0			0
$391$	−1.35477	+	0.782175i	−0.0685135	+	0.0395563i
$392$	−0.105519	+	0.287322i	−0.00532954	+	0.0145120i
$393$		0			0
$394$	−4.54086	−	19.2421i	−0.228765	−	0.969403i
$395$	−0.743851	+	4.21859i	−0.0374272	+	0.212260i
$396$		0			0
$397$	−6.93811	+	5.82177i	−0.348214	+	0.292186i	−0.800072	−	0.599904i	$-0.795206\pi$
$397$	−6.93811	+	5.82177i	−0.348214	+	0.292186i	0.451859	+	0.892090i	$0.350761\pi$
$398$	−0.797097	−	13.9169i	−0.0399548	−	0.697591i
$399$		0			0
$400$	−16.0498	+	3.73853i	−0.802492	+	0.186926i
$401$	5.10512	+	6.08405i	0.254938	+	0.303823i	0.878300	−	0.478110i	$-0.158678\pi$
$401$	5.10512	+	6.08405i	0.254938	+	0.303823i	−0.623362	+	0.781933i	$0.714234\pi$
$402$		0			0
$403$	−29.4309	−	5.18945i	−1.46606	−	0.258505i
$404$	5.53103	+	18.6055i	0.275179	+	0.925659i
$405$		0			0
$406$	−10.7947	+	21.4424i	−0.535731	+	1.06417i
$407$	7.46741	+	12.9339i	0.370146	+	0.641111i
$408$		0			0
$409$	−17.5748	+	20.9449i	−0.869020	+	1.03566i	0.130005	+	0.991513i	$0.458501\pi$
$409$	−17.5748	+	20.9449i	−0.869020	+	1.03566i	−0.999025	+	0.0441446i	$0.985944\pi$
$410$	−5.11455	+	3.35683i	−0.252590	+	0.165782i
$411$		0			0
$412$	27.7999	−	13.8945i	1.36960	−	0.684533i
$413$	−4.08522	+	0.720335i	−0.201021	+	0.0354454i
$414$		0			0
$415$	−0.237684	+	0.653032i	−0.0116675	+	0.0320561i
$416$	19.2129	+	12.7697i	0.941988	+	0.626085i
$417$		0			0
$418$	−15.4479	+	33.1764i	−0.755582	+	1.62271i
$419$		−	13.4784i		−	0.658462i	−0.944249	−	0.329231i	$-0.893211\pi$
$419$		−	13.4784i		−	0.658462i	0.944249	−	0.329231i	$-0.106789\pi$
$420$		0			0
$421$	13.2512	−	36.4074i	0.645825	−	1.77439i	0.0132242	−	0.999913i	$-0.495790\pi$
$421$	13.2512	−	36.4074i	0.645825	−	1.77439i	0.632601	−	0.774478i	$-0.281987\pi$
$422$	2.41183	−	20.4633i	0.117406	−	0.996139i
$423$		0			0
$424$	−6.91830	−	12.0633i	−0.335982	−	0.585847i
$425$	−7.90742	+	13.6960i	−0.383566	+	0.664356i
$426$		0			0
$427$	−10.8135	+	12.8870i	−0.523300	+	0.623644i
$428$	−28.7086	−	18.9614i	−1.38768	−	0.916532i
$429$		0			0
$430$	13.6084	+	6.85084i	0.656255	+	0.330377i
$431$	37.1856	−	13.5345i	1.79117	−	0.651932i	0.792029	−	0.610484i	$-0.209025\pi$
$431$	37.1856	−	13.5345i	1.79117	−	0.651932i	0.999141	−	0.0414488i	$-0.0131973\pi$
$432$		0			0
$433$	35.8179	+	6.31566i	1.72130	+	0.303511i	0.945052	−	0.326919i	$-0.106011\pi$
$433$	35.8179	+	6.31566i	1.72130	+	0.303511i	0.776246	+	0.630431i	$0.217122\pi$
$434$	−7.82801	+	26.0558i	−0.375756	+	1.25072i
$435$		0			0
$436$	0.721609	+	6.27879i	0.0345588	+	0.300700i
$437$	1.68704	+	0.556177i	0.0807021	+	0.0266055i
$438$		0			0
$439$	8.70974	−	7.30834i	0.415693	−	0.348808i	−0.410829	−	0.911713i	$-0.634761\pi$
$439$	8.70974	−	7.30834i	0.415693	−	0.348808i	0.826522	+	0.562905i	$0.190316\pi$
$440$	2.78038	−	15.5058i	0.132550	−	0.739210i
$441$		0			0
$442$	21.5471	−	5.08482i	1.02489	−	0.241860i
$443$	−7.73933	−	21.2636i	−0.367707	−	1.01027i	−0.976231	−	0.216731i	$-0.930461\pi$
$443$	−7.73933	−	21.2636i	−0.367707	−	1.01027i	0.608525	−	0.793535i	$-0.291762\pi$
$444$		0			0
$445$	−13.9563	+	8.05769i	−0.661594	+	0.381971i
$446$	6.18457	+	4.61352i	0.292848	+	0.218456i
$447$		0			0
$448$	13.5926	−	16.0099i	0.642188	−	0.756396i
$449$	26.6431	+	15.3824i	1.25737	+	0.725941i	0.972562	−	0.232644i	$-0.0747378\pi$
$449$	26.6431	+	15.3824i	1.25737	+	0.725941i	0.284805	+	0.958585i	$0.408071\pi$
$450$		0			0
$451$	4.75361	+	26.9590i	0.223839	+	1.26945i
$452$	38.5609	+	2.32057i	1.81375	+	0.109151i
$453$		0			0
$454$	4.87862	−	4.59385i	0.228965	−	0.215600i
$455$	10.0439			0.470863
$456$		0			0
$457$	−24.2691			−1.13526			−0.567631	−	0.823283i	$-0.692140\pi$
$457$	−24.2691			−1.13526			−0.567631	+	0.823283i	$0.692140\pi$
$458$	−26.4683	+	24.9233i	−1.23678	+	1.16459i
$459$		0			0
$460$	−0.763257	−	0.0459324i	−0.0355870	−	0.00214161i
$461$	−6.43606	−	36.5007i	−0.299757	−	1.70001i	−0.647212	−	0.762310i	$-0.724065\pi$
$461$	−6.43606	−	36.5007i	−0.299757	−	1.70001i	0.347455	−	0.937697i	$-0.387046\pi$
$462$		0			0
$463$	18.1684	+	10.4895i	0.844355	+	0.487489i	0.858742	−	0.512408i	$-0.171246\pi$
$463$	18.1684	+	10.4895i	0.844355	+	0.487489i	−0.0143872	+	0.999896i	$0.504580\pi$
$464$	−18.8815	+	17.6765i	−0.876551	+	0.820613i
$465$		0			0
$466$	−16.3850	−	12.2227i	−0.759019	−	0.566207i
$467$	−34.2174	+	19.7554i	−1.58339	+	0.914172i	−0.589032	+	0.808110i	$0.700491\pi$
$467$	−34.2174	+	19.7554i	−1.58339	+	0.914172i	−0.994360	+	0.106062i	$0.966176\pi$
$468$		0			0
$469$	2.60791	+	7.16517i	0.120422	+	0.330857i
$470$	4.92885	−	1.16314i	0.227351	−	0.0536515i
$471$		0			0
$472$	−4.39918	−	0.788828i	−0.202489	−	0.0363087i
$473$	52.2244	−	43.8215i	2.40128	−	2.01491i
$474$		0			0
$475$	17.5816	−	3.65820i	0.806697	−	0.167850i
$476$	−2.30119	−	20.0229i	−0.105475	−	0.917748i
$477$		0			0
$478$	6.17530	−	20.5547i	0.282451	−	0.940152i
$479$	12.6442	+	2.22951i	0.577728	+	0.101869i	0.454874	−	0.890556i	$-0.349684\pi$
$479$	12.6442	+	2.22951i	0.577728	+	0.101869i	0.122854	+	0.992425i	$0.460795\pi$
$480$		0			0
$481$	−9.64049	+	3.50885i	−0.439569	+	0.159990i
$482$	−7.08791	−	3.56825i	−0.322845	−	0.162529i
$483$		0			0
$484$	−40.4613	−	26.7238i	−1.83915	−	1.21472i
$485$	2.28792	−	2.72664i	0.103889	−	0.123810i
$486$		0			0
$487$	16.9204	−	29.3070i	0.766736	−	1.32803i	−0.172587	−	0.984994i	$-0.555213\pi$
$487$	16.9204	−	29.3070i	0.766736	−	1.32803i	0.939324	−	0.343032i	$-0.111454\pi$
$488$	−15.7228	+	9.01700i	−0.711738	+	0.408180i
$489$		0			0
$490$	−0.0168059	+	0.142590i	−0.000759212	+	0.00644157i
$491$	11.0221	−	30.2830i	0.497420	−	1.36665i	−0.396339	−	0.918104i	$-0.629720\pi$
$491$	11.0221	−	30.2830i	0.497420	−	1.36665i	0.893759	−	0.448547i	$-0.148058\pi$
$492$		0			0
$493$			24.8213i			1.11789i
$494$	−20.6010	−	14.4079i	−0.926881	−	0.648240i
$495$		0			0
$496$	−17.5947	+	23.4443i	−0.790024	+	1.05268i
$497$	−6.08870	+	16.7286i	−0.273115	+	0.750378i
$498$		0			0
$499$	−13.9952	+	2.46774i	−0.626513	+	0.110471i	−0.477885	−	0.878422i	$-0.658597\pi$
$499$	−13.9952	+	2.46774i	−0.626513	+	0.110471i	−0.148627	+	0.988893i	$0.547485\pi$
$500$	−15.3063	+	7.65017i	−0.684519	+	0.342126i
$501$		0			0
$502$	−24.5625	+	16.1211i	−1.09628	+	0.719520i
$503$	9.64008	−	11.4886i	0.429830	−	0.512251i	−0.507043	−	0.861921i	$-0.669262\pi$
$503$	9.64008	−	11.4886i	0.429830	−	0.512251i	0.936873	+	0.349669i	$0.113706\pi$
$504$		0			0
$505$	4.55243	+	7.88505i	0.202581	+	0.350880i
$506$	−1.53852	+	3.05608i	−0.0683953	+	0.135859i
$507$		0			0
$508$	−8.47762	−	28.5174i	−0.376134	−	1.26525i
$509$	17.9890	+	3.17194i	0.797348	+	0.140594i	0.557457	−	0.830206i	$-0.311777\pi$
$509$	17.9890	+	3.17194i	0.797348	+	0.140594i	0.239891	+	0.970800i	$0.422888\pi$
$510$		0			0
$511$	−20.0235	−	23.8631i	−0.885786	−	1.05564i
$512$	19.6934	−	11.1432i	0.870334	−	0.492462i
$513$		0			0
$514$	−1.32644	−	23.1589i	−0.0585066	−	1.02150i
$515$	11.1676	−	9.37074i	0.492104	−	0.412924i
$516$		0			0
$517$	3.93500	−	22.3165i	0.173061	−	0.981478i
$518$	2.14511	+	9.09000i	0.0942507	+	0.399392i
$519$		0			0
$520$	10.1579	+	3.73052i	0.445455	+	0.163594i
$521$	5.73358	−	3.31029i	0.251193	−	0.145026i	−0.369117	−	0.929383i	$-0.620340\pi$
$521$	5.73358	−	3.31029i	0.251193	−	0.145026i	0.620310	+	0.784356i	$0.287007\pi$
$522$		0			0
$523$	4.96107	+	4.16283i	0.216932	+	0.182028i	0.744778	−	0.667313i	$-0.232555\pi$
$523$	4.96107	+	4.16283i	0.216932	+	0.182028i	−0.527845	+	0.849341i	$0.677000\pi$
$524$	5.17691	−	3.83857i	0.226154	−	0.167688i
$525$		0			0
$526$	−6.79024	−	15.7834i	−0.296068	−	0.688188i
$527$	4.88473	+	27.7027i	0.212782	+	1.20675i
$528$		0			0
$529$	−21.4569	−	7.80966i	−0.932907	−	0.339551i
$530$	−4.47186	−	4.74907i	−0.194245	−	0.206286i
$531$		0			0
$532$	−15.2216	+	17.0903i	−0.659939	+	0.740959i
$533$	−18.8047			−0.814522
$534$		0			0
$535$	−15.1653	−	5.51973i	−0.655654	−	0.238639i
$536$	−0.0237752	+	8.21520i	−0.00102693	+	0.354842i
$537$		0			0
$538$	9.66820	+	22.4730i	0.416826	+	0.968879i
$539$	0.556387	+	0.321230i	0.0239653	+	0.0138364i
$540$		0			0
$541$	−28.8161	−	24.1796i	−1.23890	−	1.03956i	−0.997609	−	0.0691090i	$-0.977984\pi$
$541$	−28.8161	−	24.1796i	−1.23890	−	1.03956i	−0.241292	−	0.970453i	$-0.577571\pi$
$542$	5.22147	−	6.99954i	0.224281	−	0.300656i
$543$		0			0
$544$	5.10963	−	21.1051i	0.219074	−	0.904872i
$545$	1.01396	+	2.78583i	0.0434332	+	0.119332i
$546$		0			0
$547$	−1.80391	+	10.2305i	−0.0771298	+	0.437425i	0.921649	+	0.388024i	$0.126842\pi$
$547$	−1.80391	+	10.2305i	−0.0771298	+	0.437425i	−0.998779	+	0.0494007i	$0.984269\pi$
$548$	15.2908	+	3.65516i	0.653191	+	0.156141i
$549$		0			0
$550$	1.97790	+	34.5332i	0.0843380	+	1.47250i
$551$	21.0265	−	18.7694i	0.895758	−	0.799603i
$552$		0			0
$553$	7.70506	+	9.18254i	0.327653	+	0.390481i
$554$	37.3073	+	11.2083i	1.58503	+	0.476195i
$555$		0			0
$556$	−0.0133670	+	0.00397373i	−0.000566887	+	0.000168524i
$557$	−32.8112	+	11.9423i	−1.39026	+	0.506012i	−0.925271	−	0.379306i	$-0.876163\pi$
$557$	−32.8112	+	11.9423i	−1.39026	+	0.506012i	−0.464985	+	0.885318i	$0.653940\pi$
$558$		0			0
$559$	23.4155	+	40.5568i	0.990370	+	1.71537i
$560$	4.45524	−	8.78641i	0.188268	−	0.371294i
$561$		0			0
$562$	−8.72868	+	5.72889i	−0.368197	+	0.241659i
$563$	−10.3868	+	17.9905i	−0.437753	+	0.758210i	−0.997516	−	0.0704427i	$-0.977559\pi$
$563$	−10.3868	+	17.9905i	−0.437753	+	0.758210i	0.559763	+	0.828653i	$0.310892\pi$
$564$		0			0
$565$	17.8454	−	3.14662i	0.750761	−	0.132379i
$566$	12.1916	+	1.43691i	0.512449	+	0.0603979i
$567$		0			0
$568$	−12.3712	+	14.6571i	−0.519085	+	0.614998i
$569$			0.315660i			0.0132332i	0.999978	+	0.00661658i	$0.00210614\pi$
$569$			0.315660i			0.0132332i	−0.999978	+	0.00661658i	$0.997894\pi$
$570$		0			0
$571$		−	21.2742i		−	0.890299i	−0.895456	−	0.445150i	$-0.853150\pi$
$571$		−	21.2742i		−	0.890299i	0.895456	−	0.445150i	$-0.146850\pi$
$572$	33.2969	−	35.1565i	1.39221	−	1.46997i
$573$		0			0
$574$	−2.00383	+	17.0016i	−0.0836382	+	0.709633i
$575$	1.65344	−	0.291546i	0.0689532	−	0.0121583i
$576$		0			0
$577$	11.4507	−	19.8332i	0.476699	−	0.825667i	−0.522944	−	0.852367i	$-0.675166\pi$
$577$	11.4507	−	19.8332i	0.476699	−	0.825667i	0.999643	+	0.0266997i	$0.00849980\pi$
$578$	1.75730	+	2.67747i	0.0730942	+	0.111368i
$579$		0			0
$580$	−6.68640	+	10.1236i	−0.277638	+	0.420359i
$581$	0.972325	+	1.68412i	0.0403389	+	0.0698689i
$582$		0			0
$583$	−27.4286	+	9.98318i	−1.13597	+	0.413461i
$584$	−11.3876	−	31.5713i	−0.471224	−	1.30643i
$585$		0			0
$586$	−4.03852	+	13.4424i	−0.166830	+	0.555300i
$587$	9.56479	+	11.3989i	0.394781	+	0.470482i	0.926421	−	0.376488i	$-0.122869\pi$
$587$	9.56479	+	11.3989i	0.394781	+	0.470482i	−0.531640	+	0.846970i	$0.678424\pi$
$588$		0			0
$589$	19.7736	−	25.0862i	0.814757	−	1.03366i
$590$	−2.09303	+	0.119879i	−0.0861686	+	0.00493535i
$591$		0			0
$592$	−1.20676	+	9.99000i	−0.0495974	+	0.410587i
$593$	0.999120	−	5.66629i	0.0410289	−	0.232687i	−0.957397	−	0.288776i	$-0.906752\pi$
$593$	0.999120	−	5.66629i	0.0410289	−	0.232687i	0.998426	+	0.0560888i	$0.0178630\pi$
$594$		0			0
$595$	−3.23348	−	8.88393i	−0.132560	−	0.364205i
$596$	9.18829	−	21.1884i	0.376367	−	0.867909i
$597$		0			0
$598$	−1.88390	−	1.40534i	−0.0770386	−	0.0574687i
$599$	−12.8004	−	10.7408i	−0.523008	−	0.438856i	0.342671	−	0.939456i	$-0.388669\pi$
$599$	−12.8004	−	10.7408i	−0.523008	−	0.438856i	−0.865679	+	0.500599i	$0.833113\pi$
$600$		0			0
$601$	−2.32187	−	1.34053i	−0.0947110	−	0.0546814i	0.451896	−	0.892070i	$-0.350748\pi$
$601$	−2.32187	−	1.34053i	−0.0947110	−	0.0546814i	−0.546607	+	0.837389i	$0.684081\pi$
$602$	39.1631	−	16.8485i	1.59617	−	0.686695i
$603$		0			0
$604$	−0.462798	+	7.69029i	−0.0188310	+	0.312914i
$605$	−21.3737	−	7.77940i	−0.868965	−	0.316277i
$606$		0			0
$607$	35.3587			1.43517			0.717583	−	0.696473i	$-0.245248\pi$
$607$	35.3587			1.43517			0.717583	+	0.696473i	$0.245248\pi$
$608$	−21.7422	+	11.6308i	−0.881764	+	0.471692i
$609$		0			0
$610$	−6.18972	+	5.82843i	−0.250615	+	0.235986i
$611$	14.6276	+	5.32402i	0.591770	+	0.215387i
$612$		0			0
$613$	−4.31337	−	24.4623i	−0.174215	−	0.988024i	−0.939046	−	0.343792i	$-0.888288\pi$
$613$	−4.31337	−	24.4623i	−0.174215	−	0.988024i	0.764831	−	0.644232i	$-0.222823\pi$
$614$	−32.6482	+	14.0457i	−1.31758	+	0.566840i
$615$		0			0
$616$	−28.2374	−	33.8505i	−1.13772	−	1.36387i
$617$	2.84603	+	2.38810i	0.114577	+	0.0961415i	0.698276	−	0.715829i	$-0.253951\pi$
$617$	2.84603	+	2.38810i	0.114577	+	0.0961415i	−0.583699	+	0.811970i	$0.698395\pi$
$618$		0			0
$619$	−30.3051	+	17.4967i	−1.21807	+	0.703250i	−0.964504	−	0.264069i	$-0.914935\pi$
$619$	−30.3051	+	17.4967i	−1.21807	+	0.703250i	−0.253562	+	0.967319i	$0.581602\pi$
$620$	−5.47031	+	12.6146i	−0.219693	+	0.506616i
$621$		0			0
$622$	28.5412	−	6.73532i	1.14440	−	0.270062i
$623$	−7.83076	+	44.4105i	−0.313733	+	1.77927i
$624$		0			0
$625$	9.63126	−	8.08159i	0.385251	−	0.323264i
$626$	24.3826	−	1.39652i	0.974524	−	0.0558163i
$627$		0			0
$628$	37.7983	−	4.34408i	1.50831	−	0.173347i
$629$	6.20725	+	7.39752i	0.247499	+	0.294958i
$630$		0			0
$631$	32.6231	+	5.75233i	1.29871	+	0.228997i	0.779904	−	0.625899i	$-0.215268\pi$
$631$	32.6231	+	5.75233i	1.29871	+	0.228997i	0.518801	+	0.854895i	$0.326379\pi$
$632$	4.38198	+	12.1487i	0.174306	+	0.483249i
$633$		0			0
$634$	6.25807	+	3.15049i	0.248540	+	0.125122i
$635$	−6.97769	−	12.0857i	−0.276901	−	0.479607i
$636$		0			0
$637$	−0.283679	+	0.338076i	−0.0112398	+	0.0133951i
$638$	29.7882	+	45.3861i	1.17933	+	1.79685i
$639$		0			0
$640$	7.76933	−	7.23144i	0.307110	−	0.285848i
$641$	−11.5354	+	2.03399i	−0.455619	+	0.0803379i	−0.396748	−	0.917928i	$-0.629861\pi$
$641$	−11.5354	+	2.03399i	−0.455619	+	0.0803379i	−0.0588712	+	0.998266i	$0.518750\pi$
$642$		0			0
$643$	14.1267	−	38.8127i	0.557101	−	1.53062i	−0.266720	−	0.963774i	$-0.585940\pi$
$643$	14.1267	−	38.8127i	0.557101	−	1.53062i	0.823822	−	0.566849i	$-0.191838\pi$
$644$	−1.47134	+	1.55351i	−0.0579788	+	0.0612169i
$645$		0			0
$646$	−6.11174	+	22.8603i	−0.240463	+	0.899425i
$647$			15.5407i			0.610967i	0.952197	+	0.305484i	$0.0988181\pi$
$647$			15.5407i			0.610967i	−0.952197	+	0.305484i	$0.901182\pi$
$648$		0			0
$649$	−3.20848	+	8.81521i	−0.125944	+	0.346027i
$650$	−23.5975	−	2.78122i	−0.925568	−	0.109089i
$651$		0			0
$652$	5.91525	+	11.8351i	0.231659	+	0.463498i
$653$	9.90157	−	17.1500i	0.387478	−	0.671132i	−0.604631	−	0.796506i	$-0.706679\pi$
$653$	9.90157	−	17.1500i	0.387478	−	0.671132i	0.992110	+	0.125373i	$0.0400128\pi$
$654$		0			0
$655$	1.94320	−	2.31581i	0.0759270	−	0.0904863i
$656$	−8.34137	+	16.4504i	−0.325676	+	0.642282i
$657$		0			0
$658$	6.37223	−	12.6577i	0.248416	−	0.493448i
$659$	−20.5503	+	7.47970i	−0.800526	+	0.291368i	−0.709705	−	0.704499i	$-0.751172\pi$
$659$	−20.5503	+	7.47970i	−0.800526	+	0.291368i	−0.0908217	+	0.995867i	$0.528949\pi$
$660$		0			0
$661$	39.3132	+	6.93199i	1.52911	+	0.269623i	0.874005	−	0.485917i	$-0.161514\pi$
$661$	39.3132	+	6.93199i	1.52911	+	0.269623i	0.655103	+	0.755540i	$0.272625\pi$
$662$	−18.4143	−	5.53224i	−0.715692	−	0.215017i
$663$		0			0
$664$	0.357851	+	2.06439i	0.0138873	+	0.0801139i
$665$	−5.08061	+	9.45699i	−0.197017	+	0.366726i
$666$		0			0
$667$	2.01860	−	1.69381i	0.0781605	−	0.0655845i
$668$	1.60984	+	0.384822i	0.0622867	+	0.0148892i
$669$		0			0
$670$	0.885075	+	3.75054i	0.0341934	+	0.144896i
$671$	13.0116	+	35.7491i	0.502308	+	1.38008i
$672$		0			0
$673$	22.9216	−	13.2338i	0.883561	−	0.510124i	0.0117304	−	0.999931i	$-0.496266\pi$
$673$	22.9216	−	13.2338i	0.883561	−	0.510124i	0.871831	+	0.489807i	$0.162933\pi$
$674$	−6.22306	+	8.34220i	−0.239703	+	0.321330i
$675$		0			0
$676$	4.32558	+	5.83373i	0.166369	+	0.224374i
$677$	20.4055	+	11.7811i	0.784248	+	0.452786i	0.837934	−	0.545772i	$-0.183764\pi$
$677$	20.4055	+	11.7811i	0.784248	+	0.452786i	−0.0536855	+	0.998558i	$0.517097\pi$
$678$		0			0
$679$	−1.72957	−	9.80886i	−0.0663747	−	0.376429i
$680$	0.0294783	−	10.1858i	0.00113044	−	0.390609i
$681$		0			0
$682$	42.1780	+	44.7925i	1.61508	+	1.71519i
$683$	−12.5259			−0.479292			−0.239646	−	0.970860i	$-0.577031\pi$
$683$	−12.5259			−0.479292			−0.239646	+	0.970860i	$0.577031\pi$
$684$		0			0
$685$	7.37462			0.281770
$686$	18.0915	+	19.2129i	0.690736	+	0.733554i
$687$		0			0
$688$	45.8659	−	2.49384i	1.74862	−	0.0950768i
$689$	−3.48178	−	19.7461i	−0.132645	−	0.752268i
$690$		0			0
$691$	17.6035	+	10.1634i	0.669667	+	0.386633i	0.795951	−	0.605362i	$-0.206971\pi$
$691$	17.6035	+	10.1634i	0.669667	+	0.386633i	−0.126283	+	0.991994i	$0.540305\pi$
$692$	−9.16547	+	6.79599i	−0.348419	+	0.258345i
$693$		0			0
$694$	6.26330	−	8.39615i	0.237752	−	0.318714i
$695$	−0.00566495	+	0.00327066i	−0.000214884	+	0.000124063i
$696$		0			0
$697$	6.05392	+	16.6330i	0.229309	+	0.630020i
$698$	6.55800	+	27.7898i	0.248224	+	1.05186i
$699$		0			0
$700$	−5.02909	+	21.0384i	−0.190082	+	0.795177i
$701$	18.7774	−	15.7561i	0.709211	−	0.595099i	−0.215167	−	0.976577i	$-0.569029\pi$
$701$	18.7774	−	15.7561i	0.709211	−	0.595099i	0.924378	+	0.381479i	$0.124585\pi$
$702$		0			0
$703$	1.57274	−	10.8521i	0.0593169	−	0.409295i
$704$	−15.9853	−	44.7230i	−0.602469	−	1.68556i
$705$		0			0
$706$	28.9596	+	8.70037i	1.08991	+	0.327443i
$707$	25.0910	+	4.42422i	0.943645	+	0.166390i
$708$		0			0
$709$	24.6478	−	8.97106i	0.925667	−	0.336915i	0.165176	−	0.986264i	$-0.447181\pi$
$709$	24.6478	−	8.97106i	0.925667	−	0.336915i	0.760491	+	0.649349i	$0.224958\pi$
$710$	−4.04557	+	8.03606i	−0.151828	+	0.301588i
$711$		0			0
$712$	−24.4148	+	42.0064i	−0.914982	+	1.57426i
$713$	1.91960	−	2.28769i	0.0718894	−	0.0856745i
$714$		0			0
$715$	11.3567	−	19.6704i	0.424718	−	0.735632i
$716$	−7.82403	+	3.91049i	−0.292398	+	0.146142i
$717$		0			0
$718$	−29.1558	−	3.43634i	−1.08808	−	0.128243i
$719$	−4.64524	+	12.7627i	−0.173238	+	0.475968i	−0.995677	−	0.0928858i	$-0.970391\pi$
$719$	−4.64524	+	12.7627i	−0.173238	+	0.475968i	0.822438	+	0.568854i	$0.192613\pi$
$720$		0			0
$721$		−	40.7943i		−	1.51926i
$722$	23.9868	−	12.1091i	0.892698	−	0.450656i
$723$		0			0
$724$	11.6961	+	11.0775i	0.434683	+	0.411690i
$725$	9.11127	−	25.0330i	0.338384	−	0.929703i
$726$		0			0
$727$	18.5330	−	3.26787i	0.687352	−	0.121199i	0.180945	−	0.983493i	$-0.442084\pi$
$727$	18.5330	−	3.26787i	0.687352	−	0.121199i	0.506407	+	0.862295i	$0.330973\pi$
$728$	26.2680	−	15.0646i	0.973556	−	0.558332i
$729$		0			0
$730$	−8.63835	−	13.1616i	−0.319720	−	0.487133i
$731$	28.3347	−	33.7680i	1.04800	−	1.24896i
$732$		0			0
$733$	11.3569	+	19.6706i	0.419475	+	0.726552i	0.995887	−	0.0906076i	$-0.0288809\pi$
$733$	11.3569	+	19.6706i	0.419475	+	0.726552i	−0.576412	+	0.817159i	$0.695548\pi$
$734$	−14.7386	−	7.41983i	−0.544012	−	0.273871i
$735$		0			0
$736$	−2.06506	+	1.02467i	−0.0761191	+	0.0377698i
$737$	16.9814	+	2.99429i	0.625520	+	0.110296i
$738$		0			0
$739$	−22.4003	−	26.6956i	−0.824008	−	0.982015i	0.175989	−	0.984392i	$-0.443688\pi$
$739$	−22.4003	−	26.6956i	−0.824008	−	0.982015i	−0.999997	+	0.00237743i	$0.999243\pi$
$740$	0.538927	+	4.68926i	0.0198114	+	0.172381i
$741$		0			0
$742$	−18.2238	+	1.04377i	−0.669015	+	0.0383182i
$743$	18.5624	−	15.5757i	0.680987	−	0.571416i	−0.235307	−	0.971921i	$-0.575610\pi$
$743$	18.5624	−	15.5757i	0.680987	−	0.571416i	0.916295	+	0.400505i	$0.131165\pi$
$744$		0			0
$745$	1.88117	−	10.6686i	0.0689207	−	0.390869i
$746$	−36.2245	+	8.54846i	−1.32627	+	0.312981i
$747$		0			0
$748$	−41.8159	−	18.1334i	−1.52894	−	0.663023i
$749$	−39.1102	+	22.5803i	−1.42906	+	0.825065i
$750$		0			0
$751$	25.2781	+	21.2109i	0.922412	+	0.773995i	0.974439	−	0.224650i	$-0.0721240\pi$
$751$	25.2781	+	21.2109i	0.922412	+	0.773995i	−0.0520279	+	0.998646i	$0.516568\pi$
$752$	11.1460	−	10.4347i	0.406452	−	0.380514i
$753$		0			0
$754$	−34.2567	+	14.7377i	−1.24756	+	0.536717i
$755$	0.627539	+	3.55895i	0.0228385	+	0.129523i
$756$		0			0
$757$	18.3827	+	6.69076i	0.668131	+	0.243180i	0.653743	−	0.756717i	$-0.273198\pi$
$757$	18.3827	+	6.69076i	0.668131	+	0.243180i	0.0143881	+	0.999896i	$0.495420\pi$
$758$	15.6103	−	14.6991i	0.566992	−	0.533897i
$759$		0			0
$760$	−8.65086	+	7.67736i	−0.313800	+	0.278487i
$761$	7.99819			0.289934			0.144967	−	0.989436i	$-0.453692\pi$
$761$	7.99819			0.289934			0.144967	+	0.989436i	$0.453692\pi$
$762$		0			0
$763$	7.79556	+	2.83735i	0.282218	+	0.102719i
$764$	6.41484	+	0.386042i	0.232081	+	0.0139665i
$765$		0			0
$766$	−40.3891	+	17.3760i	−1.45932	+	0.627819i
$767$	−5.58073	−	3.22204i	−0.201509	−	0.116341i
$768$		0			0
$769$	9.49371	+	7.96617i	0.342352	+	0.287267i	0.797710	−	0.603041i	$-0.206044\pi$
$769$	9.49371	+	7.96617i	0.342352	+	0.287267i	−0.455358	+	0.890308i	$0.650489\pi$
$770$	−16.5741	−	12.3639i	−0.597290	−	0.445562i
$771$		0			0
$772$	10.9244	+	4.73735i	0.393178	+	0.170501i
$773$	11.5697	+	31.7874i	0.416132	+	1.14331i	0.953875	+	0.300204i	$0.0970547\pi$
$773$	11.5697	+	31.7874i	0.416132	+	1.14331i	−0.537743	+	0.843109i	$0.680723\pi$
$774$		0			0
$775$	5.24256	−	29.7320i	0.188318	−	1.06801i
$776$	1.89402	−	10.5627i	0.0679914	−	0.379178i
$777$		0			0
$778$	−48.4367	+	2.77423i	−1.73654	+	0.0994611i
$779$	9.51221	−	17.7059i	0.340810	−	0.634381i
$780$		0			0
$781$	25.8775	+	30.8397i	0.925971	+	1.10353i
$782$	−0.636546	+	2.11877i	−0.0227628	+	0.0757671i
$783$		0			0
$784$	0.169916	+	0.398127i	0.00606844	+	0.0142188i
$785$	16.7706	−	6.10401i	0.598570	−	0.217862i
$786$		0			0
$787$	−7.27170	−	12.5950i	−0.259208	−	0.448962i	0.706822	−	0.707392i	$-0.250128\pi$
$787$	−7.27170	−	12.5950i	−0.259208	−	0.448962i	−0.966030	+	0.258430i	$0.916795\pi$
$788$	−23.3305	−	15.4093i	−0.831113	−	0.548932i
$789$		0			0
$790$	3.32405	+	5.06461i	0.118264	+	0.180191i
$791$	25.3535	−	43.9135i	0.901466	−	1.56139i
$792$		0			0
$793$	−25.7362	+	4.53799i	−0.913920	+	0.161149i
$794$	−1.49926	+	12.7206i	−0.0532068	+	0.451436i
$795$		0			0
$796$	−14.3131	−	13.5560i	−0.507315	−	0.480480i
$797$			3.14479i			0.111394i	0.998448	+	0.0556971i	$0.0177381\pi$
$797$			3.14479i			0.111394i	−0.998448	+	0.0556971i	$0.982262\pi$
$798$		0			0
$799$		−	14.6523i		−	0.518362i
$800$	−12.9004	+	19.4095i	−0.456097	+	0.686229i
$801$		0			0
$802$	11.1547	+	1.31471i	0.393886	+	0.0464239i
$803$	−69.3755	+	12.2328i	−2.44821	+	0.431685i
$804$		0			0
$805$	−0.501835	+	0.869205i	−0.0176874	+	0.0306354i
$806$	−35.3331	+	23.1901i	−1.24456	+	0.816838i
$807$		0			0
$808$	23.7328	+	13.7939i	0.834916	+	0.485266i
$809$	7.09419	+	12.2875i	0.249419	+	0.432006i	0.963365	−	0.268195i	$-0.0864272\pi$
$809$	7.09419	+	12.2875i	0.249419	+	0.432006i	−0.713946	+	0.700201i	$0.753094\pi$
$810$		0			0
$811$	−5.23170	+	1.90418i	−0.183710	+	0.0668649i	−0.432237	−	0.901760i	$-0.642276\pi$
$811$	−5.23170	+	1.90418i	−0.183710	+	0.0668649i	0.248527	+	0.968625i	$0.420053\pi$
$812$	9.67419	+	32.5424i	0.339498	+	1.14202i
$813$		0			0
$814$	20.2279	+	6.07709i	0.708986	+	0.213002i
$815$	3.98936	+	4.75434i	0.139741	+	0.166537i
$816$		0			0
$817$	−50.0316	+	1.53197i	−1.75038	+	0.0535967i
$818$	2.21104	+	38.6036i	0.0773072	+	1.34974i
$819$		0			0
$820$	−2.01148	+	8.41473i	−0.0702441	+	0.293855i
$821$	4.88607	−	27.7103i	0.170525	−	0.967096i	−0.772658	−	0.634823i	$-0.781073\pi$
$821$	4.88607	−	27.7103i	0.170525	−	0.967096i	0.943183	−	0.332274i	$-0.107816\pi$
$822$		0			0
$823$	13.8813	+	38.1386i	0.483872	+	1.32943i	0.906148	+	0.422961i	$0.139009\pi$
$823$	13.8813	+	38.1386i	0.483872	+	1.32943i	−0.422276	+	0.906467i	$0.638769\pi$
$824$	15.1519	−	41.2577i	0.527843	−	1.43728i
$825$		0			0
$826$	−3.50777	+	4.70228i	−0.122051	+	0.163613i
$827$	28.7314	+	24.1085i	0.999088	+	0.838334i	0.986858	−	0.161591i	$-0.0516626\pi$
$827$	28.7314	+	24.1085i	0.999088	+	0.838334i	0.0122298	+	0.999925i	$0.496107\pi$
$828$		0			0
$829$	29.0901	+	16.7952i	1.01034	+	0.583320i	0.911291	−	0.411762i	$-0.135087\pi$
$829$	29.0901	+	16.7952i	1.01034	+	0.583320i	0.0990493	+	0.995083i	$0.468420\pi$
$830$	0.388395	+	0.902794i	0.0134814	+	0.0313364i
$831$		0			0
$832$	32.1617	−	5.47923i	1.11501	−	0.189958i
$833$	0.390359	+	0.142079i	0.0135252	+	0.00492275i
$834$		0			0
$835$	0.776413			0.0268689
$836$	16.2593	+	49.1350i	0.562341	+	1.69937i
$837$		0			0
$838$	−13.0673	−	13.8773i	−0.451402	−	0.479383i
$839$	2.98358	+	1.08593i	0.103005	+	0.0374906i	0.393008	−	0.919535i	$-0.371434\pi$
$839$	2.98358	+	1.08593i	0.103005	+	0.0374906i	−0.290004	+	0.957026i	$0.593657\pi$
$840$		0			0
$841$	−2.22455	−	12.6160i	−0.0767085	−	0.435035i
$842$	−21.6536	−	50.3321i	−0.746231	−	1.73456i
$843$		0			0
$844$	−17.3560	−	23.4073i	−0.597417	−	0.805711i
$845$	2.60963	+	2.18974i	0.0897741	+	0.0753294i
$846$		0			0
$847$	−55.1211	+	31.8242i	−1.89398	+	1.09349i
$848$	−18.8185	−	5.71309i	−0.646228	−	0.196188i
$849$		0			0
$850$	5.13685	+	21.7676i	0.176193	+	0.746624i
$851$	0.178022	−	1.00961i	0.00610253	−	0.0346091i
$852$		0			0
$853$	31.0068	−	26.0178i	1.06165	−	0.890833i	0.0673834	−	0.997727i	$-0.478535\pi$
$853$	31.0068	−	26.0178i	1.06165	−	0.890833i	0.994270	+	0.106894i	$0.0340905\pi$
$854$	1.36041	+	23.7520i	0.0465522	+	0.812778i
$855$		0			0
$856$	−47.9413	+	8.31036i	−1.63860	+	0.284042i
$857$	−4.59201	−	5.47255i	−0.156860	−	0.186939i	0.681891	−	0.731454i	$-0.261158\pi$
$857$	−4.59201	−	5.47255i	−0.156860	−	0.186939i	−0.838751	+	0.544515i	$0.816714\pi$
$858$		0			0
$859$	−33.5177	−	5.91007i	−1.14361	−	0.201649i	−0.430425	−	0.902626i	$-0.641636\pi$
$859$	−33.5177	−	5.91007i	−1.14361	−	0.201649i	−0.713184	+	0.700977i	$0.752747\pi$
$860$	20.6531	−	6.13973i	0.704264	−	0.209363i
$861$		0			0
$862$	25.1646	−	49.9865i	0.857109	−	1.70255i
$863$	3.20642	+	5.55368i	0.109148	+	0.189049i	0.915425	−	0.402488i	$-0.131854\pi$
$863$	3.20642	+	5.55368i	0.109148	+	0.189049i	−0.806277	+	0.591538i	$0.798521\pi$
$864$		0			0
$865$	−3.44034	+	4.10003i	−0.116975	+	0.139405i
$866$	43.0010	−	28.2228i	1.46123	−	0.959051i
$867$		0			0
$868$	17.2014	+	34.4163i	0.583855	+	1.16816i
$869$	26.6958	−	4.70719i	0.905593	−	0.159680i
$870$		0			0
$871$	−4.05124	+	11.1307i	−0.137271	+	0.377149i
$872$	6.83025	+	5.76503i	0.231302	+	0.195229i
$873$		0			0
$874$	2.27619	−	1.06295i	0.0769931	−	0.0359547i
$875$			22.4609i			0.759317i
$876$		0			0
$877$	2.85384	−	7.84086i	0.0963673	−	0.264767i	−0.882137	−	0.470993i	$-0.843896\pi$
$877$	2.85384	−	7.84086i	0.0963673	−	0.264767i	0.978504	+	0.206226i	$0.0661181\pi$
$878$	1.88209	−	15.9687i	0.0635176	−	0.538919i
$879$		0			0
$880$	−12.1702	−	18.6603i	−0.410257	−	0.629039i
$881$	9.44775	−	16.3640i	0.318303	−	0.551316i	−0.661831	−	0.749653i	$-0.730220\pi$
$881$	9.44775	−	16.3640i	0.318303	−	0.551316i	0.980134	+	0.198336i	$0.0635538\pi$
$882$		0			0
$883$	−7.40855	+	8.82916i	−0.249317	+	0.297125i	−0.876159	−	0.482021i	$-0.839903\pi$
$883$	−7.40855	+	8.82916i	−0.249317	+	0.297125i	0.626842	+	0.779146i	$0.284347\pi$
$884$	17.2552	−	26.1253i	0.580354	−	0.878688i
$885$		0			0
$886$	−28.5835	−	14.3897i	−0.960281	−	0.483432i
$887$	−15.5662	+	5.66563i	−0.522661	+	0.190233i	−0.589859	−	0.807507i	$-0.700817\pi$
$887$	−15.5662	+	5.66563i	−0.522661	+	0.190233i	0.0671973	+	0.997740i	$0.478594\pi$
$888$		0			0
$889$	−38.4579	−	6.78117i	−1.28984	−	0.227433i
$890$	−6.55747	+	21.8268i	−0.219807	+	0.731637i
$891$		0			0
$892$	10.8404	−	1.24587i	0.362964	−	0.0417147i
$893$	−12.4122	+	11.0798i	−0.415358	+	0.370772i
$894$		0			0
$895$	−3.14303	+	2.63731i	−0.105060	+	0.0881556i
$896$	−1.52670	−	29.6617i	−0.0510033	−	0.990928i
$897$		0			0
$898$	42.3449	−	9.99280i	1.41307	−	0.333464i
$899$	−16.2063	−	44.5265i	−0.540511	−	1.48504i
$900$		0			0
$901$	−16.3448	+	9.43668i	−0.544525	+	0.314381i
$902$	31.0311	+	23.1483i	1.03322	+	0.770755i
$903$		0			0
$904$	41.9520	−	34.9955i	1.39530	−	1.16393i
$905$	6.54409	+	3.77823i	0.217533	+	0.125593i
$906$		0			0
$907$	3.05694	+	17.3368i	0.101504	+	0.575658i	0.992559	+	0.121763i	$0.0388548\pi$
$907$	3.05694	+	17.3368i	0.101504	+	0.575658i	−0.891055	+	0.453895i	$0.850034\pi$
$908$	0.569276	−	9.45963i	0.0188921	−	0.313929i
$909$		0			0
$910$	10.3411	−	9.73751i	0.342805	−	0.322795i
$911$	−30.1503			−0.998923			−0.499462	−	0.866336i	$-0.666469\pi$
$911$	−30.1503			−0.998923			−0.499462	+	0.866336i	$0.666469\pi$
$912$		0			0
$913$	4.39769			0.145542
$914$	−24.9874	+	23.5289i	−0.826510	+	0.778266i
$915$		0			0
$916$	−3.08853	+	51.3220i	−0.102048	+	1.69573i
$917$	−1.46897	−	8.33094i	−0.0485097	−	0.275112i
$918$		0			0
$919$	−11.6050	−	6.70014i	−0.382813	−	0.221017i	0.296228	−	0.955117i	$-0.404271\pi$
$919$	−11.6050	−	6.70014i	−0.382813	−	0.221017i	−0.679041	+	0.734100i	$0.737604\pi$
$920$	−0.830378	+	0.692685i	−0.0273768	+	0.0228371i
$921$		0			0
$922$	−42.0140	−	31.3413i	−1.38366	−	1.03217i
$923$	−23.9497	+	13.8274i	−0.788313	+	0.455133i
$924$		0			0
$925$	−3.54476	−	9.73915i	−0.116551	−	0.320221i
$926$	28.8757	−	6.81424i	0.948913	−	0.223930i
$927$		0			0
$928$	−2.30292	+	36.5053i	−0.0755971	+	1.19835i
$929$	−23.6357	+	19.8327i	−0.775461	+	0.650689i	−0.942101	−	0.335329i	$-0.891153\pi$
$929$	−23.6357	+	19.8327i	−0.775461	+	0.650689i	0.166640	+	0.986018i	$0.446708\pi$
$930$		0			0
$931$	−0.174825	−	0.438117i	−0.00572966	−	0.0143587i
$932$	−28.7199	+	3.30071i	−0.940750	+	0.108118i
$933$		0			0
$934$	−16.0773	+	53.5139i	−0.526064	+	1.75103i
$935$	−21.0549	−	3.71255i	−0.688569	−	0.121413i
$936$		0			0
$937$	−24.9043	+	9.06443i	−0.813588	+	0.296122i	−0.715105	−	0.699017i	$-0.753621\pi$
$937$	−24.9043	+	9.06443i	−0.813588	+	0.296122i	−0.0984830	+	0.995139i	$0.531399\pi$
$938$	9.63172	+	4.84887i	0.314487	+	0.158321i
$939$		0			0
$940$	3.94707	−	5.97608i	0.128739	−	0.194918i
$941$	19.3496	−	23.0600i	0.630780	−	0.751734i	−0.352104	−	0.935961i	$-0.614534\pi$
$941$	19.3496	−	23.0600i	0.630780	−	0.751734i	0.982884	+	0.184227i	$0.0589781\pi$
$942$		0			0
$943$	0.939566	−	1.62738i	0.0305965	−	0.0529947i
$944$	−5.29415	+	3.45282i	−0.172310	+	0.112380i
$945$		0			0
$946$	11.2852	−	95.7500i	0.366914	−	3.11310i
$947$	8.91757	−	24.5008i	0.289782	−	0.796170i	−0.706314	−	0.707898i	$-0.749643\pi$
$947$	8.91757	−	24.5008i	0.289782	−	0.796170i	0.996096	−	0.0882717i	$-0.0281344\pi$
$948$		0			0
$949$		−	48.3914i		−	1.57085i
$950$	14.5553	−	20.8118i	0.472236	−	0.675224i
$951$		0			0
$952$	−21.7815	−	18.3845i	−0.705942	−	0.595846i
$953$	0.413730	−	1.13671i	0.0134020	−	0.0368217i	−0.932811	−	0.360365i	$-0.882652\pi$
$953$	0.413730	−	1.13671i	0.0134020	−	0.0368217i	0.946213	+	0.323544i	$0.104874\pi$
$954$		0			0
$955$	2.96869	−	0.523460i	0.0960646	−	0.0169388i
$956$	−13.5697	−	27.1500i	−0.438877	−	0.878095i
$957$		0			0
$958$	15.1800	−	9.96305i	0.490442	−	0.321891i
$959$	13.2648	−	15.8084i	0.428343	−	0.510479i
$960$		0			0
$961$	−11.3503	−	19.6592i	−0.366138	−	0.634169i
$962$	−6.52399	+	12.9592i	−0.210342	+	0.417820i
$963$		0			0
$964$	−10.7571	+	3.19787i	−0.346463	+	0.102996i
$965$	5.50060	+	0.969904i	0.177071	+	0.0312223i
$966$		0			0
$967$	−22.9011	−	27.2925i	−0.736451	−	0.877668i	0.259667	−	0.965698i	$-0.416387\pi$
$967$	−22.9011	−	27.2925i	−0.736451	−	0.877668i	−0.996118	+	0.0880305i	$0.971943\pi$
$968$	−67.5675	+	11.7125i	−2.17170	+	0.376452i
$969$		0			0
$970$	−0.287837	−	5.02548i	−0.00924188	−	0.161358i
$971$	−10.6081	+	8.90129i	−0.340432	+	0.285656i	−0.796934	−	0.604066i	$-0.793546\pi$
$971$	−10.6081	+	8.90129i	−0.340432	+	0.285656i	0.456503	+	0.889722i	$0.349102\pi$
$972$		0			0
$973$	−0.00317855	+	0.0180265i	−0.000101900	+	0.000577902i
$974$	−10.9919	−	46.5787i	−0.352204	−	1.49248i
$975$		0			0
$976$	−7.44619	+	24.5271i	−0.238347	+	0.785094i
$977$	−6.07278	+	3.50612i	−0.194285	+	0.112171i	−0.593987	−	0.804475i	$-0.702447\pi$
$977$	−6.07278	+	3.50612i	−0.194285	+	0.112171i	0.399702	+	0.916645i	$0.369114\pi$
$978$		0			0
$979$	78.1215	+	65.5517i	2.49677	+	2.09504i
$980$	0.120938	+	0.163104i	0.00386322	+	0.00521016i
$981$		0			0
$982$	−18.0110	−	41.8652i	−0.574754	−	1.33597i
$983$	1.42112	+	8.05956i	0.0453266	+	0.257060i	0.999048	−	0.0436329i	$-0.0138932\pi$
$983$	1.42112	+	8.05956i	0.0453266	+	0.257060i	−0.953721	+	0.300693i	$0.902782\pi$
$984$		0			0
$985$	−12.3243	−	4.48570i	−0.392686	−	0.142926i
$986$	24.0642	+	25.5559i	0.766361	+	0.813866i
$987$		0			0
$988$	−35.1791	+	5.13833i	−1.11920	+	0.163472i
$989$	−4.67977			−0.148808
$990$		0			0
$991$	−50.4787	−	18.3727i	−1.60351	−	0.583629i	−0.623367	−	0.781929i	$-0.714236\pi$
$991$	−50.4787	−	18.3727i	−1.60351	−	0.583629i	−0.980141	+	0.198300i	$0.936458\pi$
$992$	4.61384	+	41.1962i	0.146490	+	1.30798i
$993$		0			0
$994$	9.94942	+	23.1267i	0.315577	+	0.733533i
$995$	−8.00833	−	4.62361i	−0.253881	−	0.146578i
$996$		0			0
$997$	8.97721	+	7.53277i	0.284311	+	0.238565i	0.773778	−	0.633456i	$-0.218364\pi$
$997$	8.97721	+	7.53277i	0.284311	+	0.238565i	−0.489467	+	0.872022i	$0.662809\pi$
$998$	−12.0170	+	16.1091i	−0.380391	+	0.509926i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.b.127.8		60
3.2	odd	2		228.2.w.b.127.3	yes	60
4.3	odd	2		684.2.cf.c.127.3		60
12.11	even	2		228.2.w.a.127.8	yes	60
19.3	odd	18		684.2.cf.c.307.3		60
57.41	even	18		228.2.w.a.79.8	✓	60
76.3	even	18	inner	684.2.cf.b.307.8		60
228.155	odd	18		228.2.w.b.79.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.8	✓	60	57.41	even	18
228.2.w.a.127.8	yes	60	12.11	even	2
228.2.w.b.79.3	yes	60	228.155	odd	18
228.2.w.b.127.3	yes	60	3.2	odd	2
684.2.cf.b.127.8		60	1.1	even	1	trivial
684.2.cf.b.307.8		60	76.3	even	18	inner
684.2.cf.c.127.3		60	4.3	odd	2
684.2.cf.c.307.3		60	19.3	odd	18

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02960 - 0.969499i) q^{2} +(0.120142 - 1.99639i) q^{4} +(-0.162908 - 0.923898i) q^{5} +(-2.27351 - 1.31261i) q^{7} +(-1.81180 - 2.17195i) q^{8} +(-1.06345 - 0.793304i) q^{10} +(-5.14137 + 2.96837i) q^{11} +(-1.39481 - 3.83220i) q^{13} +(-3.61337 + 0.852704i) q^{14} +(-3.97113 - 0.479699i) q^{16} +(-2.94059 + 2.46745i) q^{17} +(4.31383 + 0.625180i) q^{19} +(-1.86403 + 0.214229i) q^{20} +(-2.41571 + 8.04079i) q^{22} +(0.401333 + 0.0707658i) q^{23} +(3.87141 - 1.40908i) q^{25} +(-5.15140 - 2.59336i) q^{26} +(-2.89362 + 4.38110i) q^{28} +(4.15634 - 4.95333i) q^{29} +(3.66403 - 6.34629i) q^{31} +(-4.55373 + 3.35611i) q^{32} +(-0.635435 + 5.39138i) q^{34} +(-0.842345 + 2.31432i) q^{35} -2.51566i q^{37} +(5.04762 - 3.53857i) q^{38} +(-1.71151 + 2.02775i) q^{40} +(1.57709 - 4.33302i) q^{41} +(-11.3090 + 1.99407i) q^{43} +(5.30833 + 10.6208i) q^{44} +(0.481818 - 0.316231i) q^{46} +(-2.45354 + 2.92401i) q^{47} +(-0.0541088 - 0.0937192i) q^{49} +(2.61990 - 5.20412i) q^{50} +(-7.81813 + 2.32417i) q^{52} +(4.84195 + 0.853766i) q^{53} +(3.58005 + 4.26653i) q^{55} +(1.26821 + 7.31614i) q^{56} +(-0.522897 - 9.12951i) q^{58} +(1.21047 - 1.01570i) q^{59} +(1.11276 - 6.31077i) q^{61} +(-2.38025 - 10.0864i) q^{62} +(-1.43476 + 7.87029i) q^{64} +(-3.31333 + 1.91295i) q^{65} +(-2.22499 - 1.86699i) q^{67} +(4.57270 + 6.16701i) q^{68} +(1.37646 + 3.19948i) q^{70} +(-1.17754 - 6.67818i) q^{71} +(11.1504 + 4.05843i) q^{73} +(-2.43893 - 2.59011i) q^{74} +(1.76637 - 8.53697i) q^{76} +15.5853 q^{77} +(-4.29071 - 1.56169i) q^{79} +(0.203737 + 3.74707i) q^{80} +(-2.57709 - 5.99025i) q^{82} +(-0.641515 - 0.370379i) q^{83} +(2.75872 + 2.31484i) q^{85} +(-9.71042 + 13.0171i) q^{86} +(15.7623 + 5.78873i) q^{88} +(-5.87516 - 16.1419i) q^{89} +(-1.85908 + 10.5434i) q^{91} +(0.189493 - 0.792714i) q^{92} +(0.308673 + 5.38926i) q^{94} +(-0.125156 - 4.08739i) q^{95} +(2.43876 + 2.90640i) q^{97} +(-0.146571 - 0.0440346i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more