LMFDB - Embedded newform 621.2.s.a.251.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [621,2,Mod(17,621)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("621.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(621, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 21])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 621 = 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	621.s (of order $66$, degree $20$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.95870996552$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	no (minimal twist has level 207)
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			251.22
Character	$\chi$	$=$	621.251
Dual form			621.2.s.a.287.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19334 + 2.31476i) q^{2} +(-2.77395 + 3.89546i) q^{4} +(0.904406 + 3.72801i) q^{5} +(2.50349 - 0.866468i) q^{7} +(-7.17183 - 1.03115i) q^{8} +(-7.55020 + 6.54229i) q^{10} +(-0.0853862 - 1.79248i) q^{11} +(-1.08344 + 3.13039i) q^{13} +(4.99320 + 4.76100i) q^{14} +(-3.04337 - 8.79325i) q^{16} +(0.919155 - 2.01267i) q^{17} +(5.33902 - 2.43825i) q^{19} +(-17.0311 - 6.81823i) q^{20} +(4.04726 - 2.33669i) q^{22} +(-0.537967 - 4.76556i) q^{23} +(-8.63596 + 4.45214i) q^{25} +(-8.53903 + 1.22773i) q^{26} +(-3.56927 + 12.1558i) q^{28} +(-0.362435 + 0.258089i) q^{29} +(3.86186 - 1.54606i) q^{31} +(6.72245 - 7.05030i) q^{32} +(5.75572 - 0.274179i) q^{34} +(5.49438 + 8.54942i) q^{35} +(-2.15828 - 7.35043i) q^{37} +(12.0153 + 9.44890i) q^{38} +(-2.64209 - 27.6693i) q^{40} +(-2.19367 + 0.532178i) q^{41} +(0.297622 - 0.743424i) q^{43} +(7.21938 + 4.63962i) q^{44} +(10.3892 - 6.93222i) q^{46} +(-2.64028 - 1.52437i) q^{47} +(0.0143456 - 0.0112815i) q^{49} +(-20.6113 - 14.6773i) q^{50} +(-9.18893 - 12.9040i) q^{52} +(-1.12878 + 1.30268i) q^{53} +(6.60515 - 1.93945i) q^{55} +(-18.8481 + 3.63267i) q^{56} +(-1.02992 - 0.530963i) q^{58} +(10.9766 + 3.79905i) q^{59} +(2.64020 - 3.35729i) q^{61} +(8.18729 + 7.09433i) q^{62} +(6.48578 + 1.90440i) q^{64} +(-12.6500 - 1.20793i) q^{65} +(-2.17994 - 0.103843i) q^{67} +(5.29059 + 9.16356i) q^{68} +(-13.2332 + 22.9206i) q^{70} +(-8.51253 + 13.2458i) q^{71} +(1.67838 + 3.67515i) q^{73} +(14.4389 - 13.7675i) q^{74} +(-5.31205 + 27.5615i) q^{76} +(-1.76689 - 4.41347i) q^{77} +(0.836762 + 4.34153i) q^{79} +(30.0289 - 19.2984i) q^{80} +(-3.84966 - 4.44275i) q^{82} +(3.00389 - 12.3822i) q^{83} +(8.33454 + 1.60635i) q^{85} +(2.07601 - 0.198235i) q^{86} +(-1.23594 + 12.9434i) q^{88} +(-0.218032 - 1.51645i) q^{89} +8.77569i q^{91} +(20.0564 + 11.1238i) q^{92} +(0.377786 - 7.93071i) q^{94} +(13.9185 + 17.6988i) q^{95} +(9.85700 + 10.3377i) q^{97} +(0.0432332 + 0.0197440i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) $ 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/621\mathbb{Z}\right)^\times$.

$n$	$28$	$461$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.19334	+	2.31476i	0.843821	+	1.63678i	0.768699	+	0.639610i	$0.220904\pi$
$2$	1.19334	+	2.31476i	0.843821	+	1.63678i	0.0751219	+	0.997174i	$0.476065\pi$
$3$		0			0
$3$		0			0
$4$	−2.77395	+	3.89546i	−1.38697	+	1.94773i
$5$	0.904406	+	3.72801i	0.404463	+	1.66722i	0.701745	+	0.712429i	$0.252405\pi$
$5$	0.904406	+	3.72801i	0.404463	+	1.66722i	−0.297282	+	0.954790i	$0.596080\pi$
$6$		0			0
$7$	2.50349	−	0.866468i	0.946232	−	0.327494i	0.189990	−	0.981786i	$-0.439154\pi$
$7$	2.50349	−	0.866468i	0.946232	−	0.327494i	0.756242	+	0.654292i	$0.227033\pi$
$8$	−7.17183	−	1.03115i	−2.53562	−	0.364568i
$9$		0			0
$10$	−7.55020	+	6.54229i	−2.38758	+	2.06885i
$11$	−0.0853862	−	1.79248i	−0.0257449	−	0.540452i	−0.974493	−	0.224418i	$-0.927952\pi$
$11$	−0.0853862	−	1.79248i	−0.0257449	−	0.540452i	0.948748	−	0.316034i	$-0.102351\pi$
$12$		0			0
$13$	−1.08344	+	3.13039i	−0.300492	+	0.868215i	0.689145	+	0.724623i	$0.257986\pi$
$13$	−1.08344	+	3.13039i	−0.300492	+	0.868215i	−0.989637	+	0.143591i	$0.954135\pi$
$14$	4.99320	+	4.76100i	1.33449	+	1.27243i
$15$		0			0
$16$	−3.04337	−	8.79325i	−0.760843	−	2.19831i
$17$	0.919155	−	2.01267i	0.222928	−	0.488144i	−0.764812	−	0.644254i	$-0.777168\pi$
$17$	0.919155	−	2.01267i	0.222928	−	0.488144i	0.987740	+	0.156110i	$0.0498954\pi$
$18$		0			0
$19$	5.33902	−	2.43825i	1.22486	−	0.559373i	0.305271	−	0.952266i	$-0.401253\pi$
$19$	5.33902	−	2.43825i	1.22486	−	0.559373i	0.919584	+	0.392893i	$0.128526\pi$
$20$	−17.0311	−	6.81823i	−3.80827	−	1.52460i
$21$		0			0
$22$	4.04726	−	2.33669i	0.862880	−	0.498184i
$23$	−0.537967	−	4.76556i	−0.112174	−	0.993689i
$23$	−0.537967	−	4.76556i	−0.112174	−	0.993689i
$24$		0			0
$25$	−8.63596	+	4.45214i	−1.72719	+	0.890429i
$26$	−8.53903	+	1.22773i	−1.67464	+	0.240777i
$27$		0			0
$28$	−3.56927	+	12.1558i	−0.674528	+	2.29723i
$29$	−0.362435	+	0.258089i	−0.0673025	+	0.0479259i	−0.613213	−	0.789918i	$-0.710123\pi$
$29$	−0.362435	+	0.258089i	−0.0673025	+	0.0479259i	0.545910	+	0.837844i	$0.316184\pi$
$30$		0			0
$31$	3.86186	−	1.54606i	0.693611	−	0.277680i	0.00205010	−	0.999998i	$-0.499347\pi$
$31$	3.86186	−	1.54606i	0.693611	−	0.277680i	0.691561	+	0.722318i	$0.256923\pi$
$32$	6.72245	−	7.05030i	1.18837	−	1.24633i
$33$		0			0
$34$	5.75572	−	0.274179i	0.987097	−	0.0470212i
$35$	5.49438	+	8.54942i	0.928720	+	1.44512i
$36$		0			0
$37$	−2.15828	−	7.35043i	−0.354819	−	1.20840i	−0.922773	−	0.385343i	$-0.874083\pi$
$37$	−2.15828	−	7.35043i	−0.354819	−	1.20840i	0.567954	−	0.823060i	$-0.307735\pi$
$38$	12.0153	+	9.44890i	1.94913	+	1.53281i
$39$		0			0
$40$	−2.64209	−	27.6693i	−0.417752	−	4.37489i
$41$	−2.19367	+	0.532178i	−0.342593	+	0.0831122i	−0.403364	−	0.915040i	$-0.632159\pi$
$41$	−2.19367	+	0.532178i	−0.342593	+	0.0831122i	0.0607710	+	0.998152i	$0.480644\pi$
$42$		0			0
$43$	0.297622	−	0.743424i	0.0453869	−	0.113371i	−0.903942	−	0.427654i	$-0.859340\pi$
$43$	0.297622	−	0.743424i	0.0453869	−	0.113371i	0.949329	+	0.314283i	$0.101764\pi$
$44$	7.21938	+	4.63962i	1.08836	+	0.699448i
$45$		0			0
$46$	10.3892	−	6.93222i	1.53180	−	1.02210i
$47$	−2.64028	−	1.52437i	−0.385124	−	0.222352i	0.294921	−	0.955522i	$-0.404707\pi$
$47$	−2.64028	−	1.52437i	−0.385124	−	0.222352i	−0.680045	+	0.733170i	$0.738040\pi$
$48$		0			0
$49$	0.0143456	−	0.0112815i	0.00204937	−	0.00161164i
$50$	−20.6113	−	14.6773i	−2.91488	−	2.07568i
$51$		0			0
$52$	−9.18893	−	12.9040i	−1.27427	−	1.78947i
$53$	−1.12878	+	1.30268i	−0.155050	+	0.178937i	−0.827960	−	0.560787i	$-0.810499\pi$
$53$	−1.12878	+	1.30268i	−0.155050	+	0.178937i	0.672910	+	0.739724i	$0.265044\pi$
$54$		0			0
$55$	6.60515	−	1.93945i	0.890639	−	0.261515i
$56$	−18.8481	+	3.63267i	−2.51868	+	0.485436i
$57$		0			0
$58$	−1.02992	−	0.530963i	−0.135236	−	0.0697188i
$59$	10.9766	+	3.79905i	1.42904	+	0.494595i	0.928569	−	0.371160i	$-0.121040\pi$
$59$	10.9766	+	3.79905i	1.42904	+	0.494595i	0.500469	+	0.865755i	$0.333161\pi$
$60$		0			0
$61$	2.64020	−	3.35729i	0.338043	−	0.429857i	−0.587077	−	0.809531i	$-0.699721\pi$
$61$	2.64020	−	3.35729i	0.338043	−	0.429857i	0.925120	+	0.379674i	$0.123964\pi$
$62$	8.18729	+	7.09433i	1.03979	+	0.900980i
$63$		0			0
$64$	6.48578	+	1.90440i	0.810723	+	0.238050i
$65$	−12.6500	−	1.20793i	−1.56904	−	0.149825i
$66$		0			0
$67$	−2.17994	−	0.103843i	−0.266322	−	0.0126865i	−0.0860037	−	0.996295i	$-0.527410\pi$
$67$	−2.17994	−	0.103843i	−0.266322	−	0.0126865i	−0.180318	+	0.983608i	$0.557713\pi$
$68$	5.29059	+	9.16356i	0.641578	+	1.11125i
$69$		0			0
$70$	−13.2332	+	22.9206i	−1.58167	+	2.73953i
$71$	−8.51253	+	13.2458i	−1.01025	+	1.57198i	−0.205250	+	0.978710i	$0.565801\pi$
$71$	−8.51253	+	13.2458i	−1.01025	+	1.57198i	−0.805002	+	0.593272i	$0.797836\pi$
$72$		0			0
$73$	1.67838	+	3.67515i	0.196440	+	0.430144i	0.982061	−	0.188565i	$-0.0603835\pi$
$73$	1.67838	+	3.67515i	0.196440	+	0.430144i	−0.785621	+	0.618708i	$0.787656\pi$
$74$	14.4389	−	13.7675i	1.67849	−	1.60044i
$75$		0			0
$76$	−5.31205	+	27.5615i	−0.609334	+	3.16152i
$77$	−1.76689	−	4.41347i	−0.201355	−	0.502962i
$78$		0			0
$79$	0.836762	+	4.34153i	0.0941431	+	0.488461i	0.998142	+	0.0609266i	$0.0194055\pi$
$79$	0.836762	+	4.34153i	0.0941431	+	0.488461i	−0.903999	+	0.427534i	$0.859382\pi$
$80$	30.0289	−	19.2984i	3.35733	−	2.15763i
$81$		0			0
$82$	−3.84966	−	4.44275i	−0.425124	−	0.490619i
$83$	3.00389	−	12.3822i	0.329720	−	1.35912i	−0.529843	−	0.848096i	$-0.677749\pi$
$83$	3.00389	−	12.3822i	0.329720	−	1.35912i	0.859563	−	0.511029i	$-0.170736\pi$
$84$		0			0
$85$	8.33454	+	1.60635i	0.904008	+	0.174233i
$86$	2.07601	−	0.198235i	0.223862	−	0.0213763i
$87$		0			0
$88$	−1.23594	+	12.9434i	−0.131752	+	1.37977i
$89$	−0.218032	−	1.51645i	−0.0231114	−	0.160743i	0.974997	−	0.222217i	$-0.0713292\pi$
$89$	−0.218032	−	1.51645i	−0.0231114	−	0.160743i	−0.998109	+	0.0614733i	$0.980420\pi$
$90$		0			0
$91$			8.77569i			0.919942i
$92$	20.0564	+	11.1238i	2.09102	+	1.15973i
$93$		0			0
$94$	0.377786	−	7.93071i	0.0389657	−	0.817990i
$95$	13.9185	+	17.6988i	1.42800	+	1.81586i
$96$		0			0
$97$	9.85700	+	10.3377i	1.00083	+	1.04964i	0.998767	+	0.0496395i	$0.0158072\pi$
$97$	9.85700	+	10.3377i	1.00083	+	1.04964i	0.00206002	+	0.999998i	$0.499344\pi$
$98$	0.0432332	+	0.0197440i	0.00436722	+	0.00199444i
$99$		0			0
$100$	6.61252	−	45.9911i	0.661252	−	4.59911i
$101$	−7.42557	−	1.80142i	−0.738872	−	0.179248i	−0.151377	−	0.988476i	$-0.548371\pi$
$101$	−7.42557	−	1.80142i	−0.738872	−	0.179248i	−0.587495	+	0.809228i	$0.699886\pi$
$102$		0			0
$103$	−6.77663	+	13.1448i	−0.667722	+	1.29520i	0.274944	+	0.961460i	$0.411341\pi$
$103$	−6.77663	+	13.1448i	−0.667722	+	1.29520i	−0.942666	+	0.333739i	$0.891690\pi$
$104$	10.9982	−	21.3335i	1.07846	−	2.09192i
$105$		0			0
$106$	−4.36242	−	1.05831i	−0.423715	−	0.102792i
$107$	0.219990	−	1.53007i	0.0212673	−	0.147917i	−0.976421	−	0.215876i	$-0.930739\pi$
$107$	0.219990	−	1.53007i	0.0212673	−	0.147917i	0.997688	+	0.0679585i	$0.0216485\pi$
$108$		0			0
$109$	8.60283	+	3.92878i	0.824001	+	0.376309i	0.782362	−	0.622824i	$-0.214015\pi$
$109$	8.60283	+	3.92878i	0.824001	+	0.376309i	0.0416393	+	0.999133i	$0.486742\pi$
$110$	12.3716	+	12.9749i	1.17958	+	1.23711i
$111$		0			0
$112$	−15.2381	−	19.3769i	−1.43987	−	1.83094i
$113$	−0.151342	+	3.17705i	−0.0142370	+	0.298872i	0.980507	+	0.196482i	$0.0629518\pi$
$113$	−0.151342	+	3.17705i	−0.0142370	+	0.298872i	−0.994744	+	0.102390i	$0.967351\pi$
$114$		0			0
$115$	17.2795	−	6.31555i	1.61133	−	0.588928i
$116$		−	2.12778i		−	0.197559i
$117$		0			0
$118$	4.30500	+	29.9419i	0.396307	+	2.75638i
$119$	0.557186	−	5.83512i	0.0510772	−	0.534905i
$120$		0			0
$121$	7.74451	−	0.739511i	0.704046	−	0.0672283i
$122$	10.9220	+	2.10504i	0.988831	+	0.190582i
$123$		0			0
$124$	−4.69000	+	19.3324i	−0.421174	+	1.73610i
$125$	−11.8474	−	13.6726i	−1.05966	−	1.22291i
$126$		0			0
$127$	0.209143	−	0.134408i	0.0185585	−	0.0119268i	−0.531329	−	0.847166i	$-0.678307\pi$
$127$	0.209143	−	0.134408i	0.0185585	−	0.0119268i	0.549887	+	0.835239i	$0.314671\pi$
$128$	−0.355671	−	1.84540i	−0.0314372	−	0.163111i
$129$		0			0
$130$	−12.2997	−	30.7233i	−1.07876	−	2.69461i
$131$	0.0338851	−	0.175813i	0.00296056	−	0.0153608i	−0.980418	−	0.196926i	$-0.936904\pi$
$131$	0.0338851	−	0.175813i	0.00296056	−	0.0153608i	0.983379	+	0.181565i	$0.0581163\pi$
$132$		0			0
$133$	11.2535	−	10.7302i	0.975806	−	0.930429i
$134$	−2.36104	−	5.16996i	−0.203963	−	0.446617i
$135$		0			0
$136$	−8.66739	+	13.4867i	−0.743222	+	1.15648i
$137$	3.65084	−	6.32345i	0.311913	−	0.540249i	−0.666864	−	0.745180i	$-0.732364\pi$
$137$	3.65084	−	6.32345i	0.311913	−	0.540249i	0.978776	+	0.204931i	$0.0656970\pi$
$138$		0			0
$139$	−10.6526	−	18.4508i	−0.903542	−	1.56498i	−0.822863	−	0.568240i	$-0.807625\pi$
$139$	−10.6526	−	18.4508i	−0.903542	−	1.56498i	−0.0806786	−	0.996740i	$-0.525709\pi$
$140$	−48.5451	−	2.31249i	−4.10281	−	0.195441i
$141$		0			0
$142$	−40.8192	−	3.89776i	−3.42547	−	0.327092i
$143$	5.70367	+	1.67475i	0.476965	+	0.140049i
$144$		0			0
$145$	−1.28995	−	1.11775i	−0.107124	−	0.0928237i
$146$	−6.50421	+	8.27077i	−0.538292	+	0.684494i
$147$		0			0
$148$	34.6203	+	11.9822i	2.84577	+	0.984930i
$149$	−10.9253	−	5.63237i	−0.895034	−	0.461422i	−0.0516077	−	0.998667i	$-0.516435\pi$
$149$	−10.9253	−	5.63237i	−0.895034	−	0.461422i	−0.843426	+	0.537246i	$0.819465\pi$
$150$		0			0
$151$	−2.53066	+	0.487744i	−0.205942	+	0.0396921i	−0.291179	−	0.956669i	$-0.594047\pi$
$151$	−2.53066	+	0.487744i	−0.205942	+	0.0396921i	0.0852368	+	0.996361i	$0.472835\pi$
$152$	−40.8047	+	11.9814i	−3.30970	+	0.971816i
$153$		0			0
$154$	8.10764	−	9.35671i	0.653332	−	0.753985i
$155$	9.25642	+	12.9988i	0.743493	+	1.04409i
$156$		0			0
$157$	11.9694	+	8.52340i	0.955265	+	0.680241i	0.947509	−	0.319729i	$-0.103592\pi$
$157$	11.9694	+	8.52340i	0.955265	+	0.680241i	0.00775580	+	0.999970i	$0.497531\pi$
$158$	−9.05108	+	7.11785i	−0.720065	+	0.566266i
$159$		0			0
$160$	32.3635	+	18.6850i	2.55856	+	1.47718i
$161$	−5.47601	−	11.4644i	−0.431570	−	0.903524i
$162$		0			0
$163$	−9.01920	−	5.79629i	−0.706438	−	0.454000i	0.137457	−	0.990508i	$-0.456107\pi$
$163$	−9.01920	−	5.79629i	−0.706438	−	0.454000i	−0.843896	+	0.536507i	$0.819743\pi$
$164$	4.01204	−	10.0216i	0.313287	−	0.782554i
$165$		0			0
$166$	32.2466	−	7.82293i	2.50282	−	0.607178i
$167$	−0.493577	−	5.16897i	−0.0381941	−	0.399987i	−0.994272	−	0.106875i	$-0.965915\pi$
$167$	−0.493577	−	5.16897i	−0.0381941	−	0.399987i	0.956078	−	0.293111i	$-0.0946907\pi$
$168$		0			0
$169$	1.59317	+	1.25288i	0.122552	+	0.0963757i
$170$	6.22765	+	21.2094i	0.477639	+	1.62669i
$171$		0			0
$172$	2.07039	+	3.22159i	0.157866	+	0.245644i
$173$	9.36625	−	0.446170i	0.712103	−	0.0339216i	0.311595	−	0.950215i	$-0.399137\pi$
$173$	9.36625	−	0.446170i	0.712103	−	0.0339216i	0.400508	+	0.916293i	$0.368834\pi$
$174$		0			0
$175$	−17.7624	+	18.6287i	−1.34271	+	1.40820i
$176$	−15.5018	+	6.20600i	−1.16849	+	0.467794i
$177$		0			0
$178$	3.25003	−	2.31434i	0.243600	−	0.173467i
$179$	2.41548	−	8.22638i	0.180542	−	0.614869i	−0.818636	−	0.574313i	$-0.805269\pi$
$179$	2.41548	−	8.22638i	0.180542	−	0.614869i	0.999177	−	0.0405554i	$-0.0129127\pi$
$180$		0			0
$181$	−21.5546	+	3.09908i	−1.60214	+	0.230353i	−0.884663	−	0.466231i	$-0.845612\pi$
$181$	−21.5546	+	3.09908i	−1.60214	+	0.230353i	−0.717476	+	0.696583i	$0.754703\pi$
$182$	−20.3136	+	10.4724i	−1.50575	+	0.776266i
$183$		0			0
$184$	−1.05582	+	34.7325i	−0.0778358	+	2.56052i
$185$	25.4505	−	14.6939i	1.87116	−	1.08032i
$186$		0			0
$187$	−3.68614	−	1.47571i	−0.269557	−	0.107915i
$188$	13.2621	−	6.05660i	0.967238	−	0.441723i
$189$		0			0
$190$	−24.3590	+	53.3387i	−1.76718	+	3.86959i
$191$	0.871549	+	2.51818i	0.0630631	+	0.182209i	0.972131	−	0.234440i	$-0.0753257\pi$
$191$	0.871549	+	2.51818i	0.0630631	+	0.182209i	−0.909067	+	0.416649i	$0.863204\pi$
$192$		0			0
$193$	−11.5652	−	11.0274i	−0.832481	−	0.793769i	0.148287	−	0.988944i	$-0.452624\pi$
$193$	−11.5652	−	11.0274i	−0.832481	−	0.793769i	−0.980768	+	0.195175i	$0.937472\pi$
$194$	−12.1666	+	35.1531i	−0.873511	+	2.52384i
$195$		0			0
$196$	0.00415276	+	0.0871771i	0.000296625	+	0.00622693i
$197$	−10.8321	+	9.38607i	−0.771755	+	0.668730i	−0.948943	−	0.315447i	$-0.897845\pi$
$197$	−10.8321	+	9.38607i	−0.771755	+	0.668730i	0.177188	+	0.984177i	$0.443300\pi$
$198$		0			0
$199$	14.1618	+	2.03616i	1.00390	+	0.144339i	0.624610	−	0.780937i	$-0.285258\pi$
$199$	14.1618	+	2.03616i	1.00390	+	0.144339i	0.379293	+	0.925277i	$0.376167\pi$
$200$	66.5264	−	23.0250i	4.70413	−	1.62812i
$201$		0			0
$202$	−4.69139	−	19.3382i	−0.330085	−	1.36063i
$203$	−0.683728	+	0.960162i	−0.0479883	+	0.0673902i
$204$		0			0
$205$	−3.96793	−	7.69671i	−0.277132	−	0.537562i
$206$	−38.5140			−2.68340
$207$		0			0
$208$	30.8236			2.13723
$209$	−4.82638	−	9.36188i	−0.333848	−	0.647575i
$210$		0			0
$211$	5.51685	−	7.74732i	0.379795	−	0.533348i	−0.579790	−	0.814766i	$-0.696865\pi$
$211$	5.51685	−	7.74732i	0.379795	−	0.533348i	0.959585	+	0.281418i	$0.0908048\pi$
$212$	−1.94337	−	8.01068i	−0.133471	−	0.550176i
$213$		0			0
$214$	3.80426	−	1.31667i	0.260054	−	0.0900056i
$215$	3.04066	+	0.437181i	0.207372	+	0.0298155i
$216$		0			0
$217$	8.32855	−	7.21673i	0.565379	−	0.489903i
$218$	1.17193	+	24.6019i	0.0793733	+	1.66625i
$219$		0			0
$220$	−10.7673	+	31.1101i	−0.725931	+	2.09744i
$221$	5.30459	+	5.05792i	0.356825	+	0.340232i
$222$		0			0
$223$	−2.21277	−	6.39338i	−0.148178	−	0.428132i	0.846347	−	0.532632i	$-0.178797\pi$
$223$	−2.21277	−	6.39338i	−0.148178	−	0.428132i	−0.994525	+	0.104500i	$0.966676\pi$
$224$	10.7208	−	23.4752i	0.716311	−	1.56850i
$225$		0			0
$226$	−7.53472	+	3.44099i	−0.501202	+	0.228891i
$227$	−1.11066	−	0.444642i	−0.0737172	−	0.0295119i	0.334511	−	0.942392i	$-0.391429\pi$
$227$	−1.11066	−	0.444642i	−0.0737172	−	0.0295119i	−0.408228	+	0.912880i	$0.633853\pi$
$228$		0			0
$229$	−9.02087	+	5.20820i	−0.596116	+	0.344168i	−0.767512	−	0.641035i	$-0.778506\pi$
$229$	−9.02087	+	5.20820i	−0.596116	+	0.344168i	0.171396	+	0.985202i	$0.445172\pi$
$230$	35.2394	+	32.4614i	2.32362	+	2.14044i
$231$		0			0
$232$	2.86545	−	1.47724i	0.188126	−	0.0969857i
$233$	26.8065	−	3.85420i	1.75615	−	0.252497i	0.812390	−	0.583115i	$-0.198166\pi$
$233$	26.8065	−	3.85420i	1.75615	−	0.252497i	0.943765	+	0.330618i	$0.107257\pi$
$234$		0			0
$235$	3.29497	−	11.2216i	0.214940	−	0.732019i
$236$	−45.2477	+	32.2207i	−2.94537	+	2.09739i
$237$		0			0
$238$	14.1718	−	5.67355i	0.918624	−	0.367761i
$239$	8.87358	−	9.30634i	0.573984	−	0.601977i	−0.371185	−	0.928559i	$-0.621048\pi$
$239$	8.87358	−	9.30634i	0.573984	−	0.601977i	0.945169	+	0.326582i	$0.105897\pi$
$240$		0			0
$241$	−12.7455	+	0.607142i	−0.821009	+	0.0391095i	−0.453882	−	0.891062i	$-0.649961\pi$
$241$	−12.7455	+	0.607142i	−0.821009	+	0.0391095i	−0.367126	+	0.930171i	$0.619658\pi$
$242$	10.9537	+	17.0442i	0.704127	+	1.09564i
$243$		0			0
$244$	5.75442	+	19.5977i	0.368389	+	1.25462i
$245$	0.0550319	+	0.0432775i	0.00351586	+	0.00276490i
$246$		0			0
$247$	1.84817	+	19.3549i	0.117596	+	1.23152i
$248$	−29.2909	+	7.10588i	−1.85997	+	0.451224i
$249$		0			0
$250$	17.5108	−	43.7399i	1.10748	−	2.76635i
$251$	−15.2592	−	9.80651i	−0.963154	−	0.618982i	−0.0382851	−	0.999267i	$-0.512189\pi$
$251$	−15.2592	−	9.80651i	−0.963154	−	0.618982i	−0.924869	+	0.380285i	$0.875826\pi$
$252$		0			0
$253$	−8.49623	+	1.37121i	−0.534153	+	0.0862071i
$254$	0.560703	+	0.323722i	0.0351816	+	0.0203121i
$255$		0			0
$256$	14.4740	−	11.3825i	0.904626	−	0.711406i
$257$	−19.1620	−	13.6452i	−1.19529	−	0.851163i	−0.203506	−	0.979074i	$-0.565234\pi$
$257$	−19.1620	−	13.6452i	−1.19529	−	0.851163i	−0.991786	+	0.127910i	$0.959173\pi$
$258$		0			0
$259$	−11.7722	−	16.5317i	−0.731486	−	1.02723i
$260$	39.7959	−	45.9269i	2.46804	−	2.84827i
$261$		0			0
$262$	0.447401	−	0.131369i	0.0276405	−	0.00811599i
$263$	−3.06444	+	0.590623i	−0.188962	+	0.0364194i	−0.282854	−	0.959163i	$-0.591281\pi$
$263$	−3.06444	+	0.590623i	−0.188962	+	0.0364194i	0.0938923	+	0.995582i	$0.470069\pi$
$264$		0			0
$265$	−5.87728	−	3.02995i	−0.361039	−	0.186128i
$266$	38.2673	+	13.2444i	2.34632	+	0.812068i
$267$		0			0
$268$	6.45155	−	8.20381i	0.394091	−	0.501128i
$269$	−20.5579	−	17.8135i	−1.25344	−	1.08611i	−0.992689	−	0.120703i	$-0.961485\pi$
$269$	−20.5579	−	17.8135i	−1.25344	−	1.08611i	−0.260749	−	0.965407i	$-0.583969\pi$
$270$		0			0
$271$	−28.1936	−	8.27839i	−1.71264	−	0.502876i	−0.729229	−	0.684270i	$-0.760121\pi$
$271$	−28.1936	−	8.27839i	−1.71264	−	0.502876i	−0.983410	+	0.181394i	$0.941939\pi$
$272$	−20.4952	−	1.95706i	−1.24270	−	0.118664i
$273$		0			0
$274$	18.9940	+	0.904795i	1.14747	+	0.0546607i
$275$	8.71776	+	15.0996i	0.525701	+	0.910540i
$276$		0			0
$277$	7.61253	−	13.1853i	0.457393	−	0.792227i	−0.541430	−	0.840746i	$-0.682117\pi$
$277$	7.61253	−	13.1853i	0.457393	−	0.792227i	0.998822	+	0.0485189i	$0.0154501\pi$
$278$	29.9971	−	46.6764i	1.79911	−	2.79947i
$279$		0			0
$280$	−30.5890	−	66.9805i	−1.82804	−	4.00285i
$281$	7.85844	−	7.49301i	0.468795	−	0.446995i	−0.418487	−	0.908223i	$-0.637439\pi$
$281$	7.85844	−	7.49301i	0.468795	−	0.446995i	0.887282	+	0.461228i	$0.152591\pi$
$282$		0			0
$283$	2.88826	−	14.9857i	0.171689	−	0.890808i	−0.789255	−	0.614066i	$-0.789533\pi$
$283$	2.88826	−	14.9857i	0.171689	−	0.890808i	0.960944	−	0.276743i	$-0.0892549\pi$
$284$	−27.9850	−	69.9033i	−1.66061	−	4.14800i
$285$		0			0
$286$	2.92979	+	15.2012i	0.173242	+	0.898865i
$287$	−5.03072	+	3.23305i	−0.296954	+	0.190841i
$288$		0			0
$289$	7.92665	+	9.14784i	0.466273	+	0.538108i
$290$	1.04797	−	4.31978i	0.0615387	−	0.253666i
$291$		0			0
$292$	−18.9721	−	3.65658i	−1.11026	−	0.213985i
$293$	−20.7282	+	1.97930i	−1.21095	+	0.115632i	−0.680928	−	0.732350i	$-0.738424\pi$
$293$	−20.7282	+	1.97930i	−1.21095	+	0.115632i	−0.530025	+	0.847982i	$0.677817\pi$
$294$		0			0
$295$	−4.23558	+	44.3570i	−0.246605	+	2.58256i
$296$	7.89940	+	54.9415i	0.459143	+	3.19341i
$297$		0			0
$298$		−	32.0108i		−	1.85433i
$299$	15.5009	+	3.47915i	0.896442	+	0.201204i
$300$		0			0
$301$	0.100942	−	2.11904i	0.00581821	−	0.122139i
$302$	−4.14896	−	5.27583i	−0.238746	−	0.303590i
$303$		0			0
$304$	−37.6887	−	39.5268i	−2.16160	−	2.26702i
$305$	14.9038	+	6.80635i	0.853391	+	0.389731i
$306$		0			0
$307$	−0.243859	+	1.69608i	−0.0139178	+	0.0968002i	−0.995596	−	0.0937445i	$-0.970116\pi$
$307$	−0.243859	+	1.69608i	−0.0139178	+	0.0968002i	0.981679	+	0.190545i	$0.0610254\pi$
$308$	22.0938	+	5.35989i	1.25891	+	0.305408i
$309$		0			0
$310$	−19.0431	+	36.9385i	−1.08158	+	2.09796i
$311$	−8.57366	+	16.6306i	−0.486168	+	0.943034i	0.510375	+	0.859952i	$0.329507\pi$
$311$	−8.57366	+	16.6306i	−0.486168	+	0.943034i	−0.996543	+	0.0830819i	$0.973524\pi$
$312$		0			0
$313$	−3.68935	−	0.895026i	−0.208534	−	0.0505899i	0.130131	−	0.991497i	$-0.458460\pi$
$313$	−3.68935	−	0.895026i	−0.208534	−	0.0505899i	−0.338665	+	0.940907i	$0.609975\pi$
$314$	−5.44600	+	37.8777i	−0.307335	+	2.13756i
$315$		0			0
$316$	−19.2334	−	8.78361i	−1.08196	−	0.494117i
$317$	4.08419	+	4.28337i	0.229391	+	0.240578i	0.828363	−	0.560192i	$-0.189273\pi$
$317$	4.08419	+	4.28337i	0.229391	+	0.240578i	−0.598972	+	0.800770i	$0.704424\pi$
$318$		0			0
$319$	0.493565	+	0.627619i	0.0276343	+	0.0351399i
$320$	−1.23384	+	25.9014i	−0.0689736	+	1.44793i
$321$		0			0
$322$	20.0027	−	26.3567i	1.11471	−	1.46880i
$323$		−	12.9868i		−	0.722605i
$324$		0			0
$325$	−4.58043	−	31.8576i	−0.254076	−	1.76714i
$326$	2.65403	−	27.7943i	0.146993	−	1.53938i
$327$		0			0
$328$	16.2814	−	1.55468i	0.898988	−	0.0858429i
$329$	−7.93074	−	1.52852i	−0.437236	−	0.0842703i
$330$		0			0
$331$	0.894900	−	3.68883i	0.0491881	−	0.202756i	−0.941915	−	0.335851i	$-0.890976\pi$
$331$	0.894900	−	3.68883i	0.0491881	−	0.202756i	0.991103	+	0.133094i	$0.0424914\pi$
$332$	39.9018	+	46.0492i	2.18990	+	2.52728i
$333$		0			0
$334$	11.3759	−	7.31087i	0.622463	−	0.400033i
$335$	−1.58442	−	8.22075i	−0.0865661	−	0.449148i
$336$		0			0
$337$	−4.84211	−	12.0950i	−0.263767	−	0.658857i	0.736070	−	0.676905i	$-0.236679\pi$
$337$	−4.84211	−	12.0950i	−0.263767	−	0.658857i	−0.999837	+	0.0180477i	$0.994255\pi$
$338$	−0.998929	+	5.18294i	−0.0543346	+	0.281915i
$339$		0			0
$340$	−29.3771	+	28.0110i	−1.59319	+	1.51911i
$341$	−3.10102	−	6.79029i	−0.167930	−	0.367715i
$342$		0			0
$343$	−9.99971	+	15.5599i	−0.539934	+	0.840153i
$344$	−2.90108	+	5.02481i	−0.156416	+	0.270920i
$345$		0			0
$346$	12.2099	+	21.1482i	0.656410	+	1.13694i
$347$	34.9011	+	1.66255i	1.87359	+	0.0892501i	0.953307	−	0.302002i	$-0.0976550\pi$
$347$	34.9011	+	1.66255i	1.87359	+	0.0892501i	0.920283	+	0.391252i	$0.127958\pi$
$348$		0			0
$349$	16.3206	+	1.55843i	0.873623	+	0.0834209i	0.522228	−	0.852806i	$-0.325101\pi$
$349$	16.3206	+	1.55843i	0.873623	+	0.0834209i	0.351396	+	0.936227i	$0.385707\pi$
$350$	−64.3177	−	18.8854i	−3.43793	−	1.00947i
$351$		0			0
$352$	−13.2115	−	11.4478i	−0.704176	−	0.610172i
$353$	19.4996	−	24.7958i	1.03786	−	1.31975i	0.0917905	−	0.995778i	$-0.470741\pi$
$353$	19.4996	−	24.7958i	1.03786	−	1.31975i	0.946068	−	0.323967i	$-0.105017\pi$
$354$		0			0
$355$	−57.0791	−	19.7553i	−3.02945	−	1.04850i
$356$	6.51208	+	3.35721i	0.345139	+	0.177932i
$357$		0			0
$358$	21.9246	−	4.22563i	1.15875	−	0.223331i
$359$	−24.3292	+	7.14369i	−1.28404	+	0.377030i	−0.851391	−	0.524531i	$-0.824241\pi$
$359$	−24.3292	+	7.14369i	−1.28404	+	0.377030i	−0.432653	+	0.901560i	$0.642423\pi$
$360$		0			0
$361$	10.1177	−	11.6765i	0.532512	−	0.614551i
$362$	−32.8956	−	46.1955i	−1.72896	−	2.42798i
$363$		0			0
$364$	−34.1854	−	24.3433i	−1.79180	−	1.27593i
$365$	−12.1831	+	9.58086i	−0.637691	+	0.501485i
$366$		0			0
$367$	22.8849	+	13.2126i	1.19458	+	0.689694i	0.959343	−	0.282243i	$-0.0910785\pi$
$367$	22.8849	+	13.2126i	1.19458	+	0.689694i	0.235242	+	0.971937i	$0.424412\pi$
$368$	−40.2675	+	19.2339i	−2.09909	+	1.00263i
$369$		0			0
$370$	64.3841	+	41.3771i	3.34717	+	2.15109i
$371$	−1.69716	+	4.23930i	−0.0881122	+	0.220094i
$372$		0			0
$373$	27.5314	−	6.67904i	1.42552	−	0.345828i	0.552501	−	0.833512i	$-0.313673\pi$
$373$	27.5314	−	6.67904i	1.42552	−	0.345828i	0.873020	+	0.487684i	$0.162158\pi$
$374$	−0.982917	−	10.2936i	−0.0508254	−	0.532268i
$375$		0			0
$376$	17.3638	+	13.6550i	0.895468	+	0.704204i
$377$	−0.415243	−	1.41419i	−0.0213861	−	0.0728344i
$378$		0			0
$379$	10.7760	+	16.7677i	0.553524	+	0.861300i	0.999429	−	0.0337799i	$-0.0107545\pi$
$379$	10.7760	+	16.7677i	0.553524	+	0.861300i	−0.445905	+	0.895080i	$0.647118\pi$
$380$	−107.554	+	5.12343i	−5.51740	+	0.262826i
$381$		0			0
$382$	−4.78892	+	5.02248i	−0.245023	+	0.256972i
$383$	16.0786	−	6.43689i	0.821577	−	0.328910i	0.0774905	−	0.996993i	$-0.475309\pi$
$383$	16.0786	−	6.43689i	0.821577	−	0.328910i	0.744086	+	0.668083i	$0.232885\pi$
$384$		0			0
$385$	14.8555	−	10.5785i	0.757106	−	0.539133i
$386$	11.7246	−	39.9302i	0.596764	−	2.03239i
$387$		0			0
$388$	−67.6130	+	9.72129i	−3.43253	+	0.493524i
$389$	5.04145	−	2.59905i	0.255611	−	0.131777i	−0.325659	−	0.945487i	$-0.605586\pi$
$389$	5.04145	−	2.59905i	0.255611	−	0.131777i	0.581270	+	0.813710i	$0.302556\pi$
$390$		0			0
$391$	−10.0860	−	3.29754i	−0.510069	−	0.166764i
$392$	−0.114517	+	0.0661165i	−0.00578399	+	0.00333939i
$393$		0			0
$394$	−34.6529	−	13.8729i	−1.74579	−	0.698909i
$395$	−15.4285	+	7.04597i	−0.776293	+	0.354521i
$396$		0			0
$397$	6.66528	−	14.5949i	0.334521	−	0.732499i	−0.665381	−	0.746504i	$-0.731731\pi$
$397$	6.66528	−	14.5949i	0.334521	−	0.732499i	0.999902	+	0.0140053i	$0.00445816\pi$
$398$	12.1867	+	35.2110i	0.610862	+	1.76497i
$399$		0			0
$400$	65.4312	+	62.3886i	3.27156	+	3.11943i
$401$	2.00823	−	5.80239i	0.100286	−	0.289757i	−0.883686	−	0.468080i	$-0.844946\pi$
$401$	2.00823	−	5.80239i	0.100286	−	0.289757i	0.983972	+	0.178323i	$0.0570671\pi$
$402$		0			0
$403$	0.655670	+	13.7642i	0.0326613	+	0.685644i
$404$	27.6155	−	23.9290i	1.37392	−	1.19051i
$405$		0			0
$406$	−3.03847	−	0.436866i	−0.150797	−	0.0216813i
$407$	−12.9912	+	4.49629i	−0.643949	+	0.222873i
$408$		0			0
$409$	5.04888	+	20.8118i	0.249651	+	1.02908i	0.949246	+	0.314535i	$0.101849\pi$
$409$	5.04888	+	20.8118i	0.249651	+	1.02908i	−0.699595	+	0.714540i	$0.746636\pi$
$410$	13.0810	−	18.3696i	0.646023	−	0.907212i
$411$		0			0
$412$	−32.4072	−	62.8612i	−1.59659	−	3.09695i
$413$	30.7717			1.51418
$414$		0			0
$415$	48.8778			2.39932
$416$	14.7869	+	28.6825i	0.724985	+	1.40627i
$417$		0			0
$418$	15.9110	−	22.3439i	0.778232	−	1.09287i
$419$	3.26276	+	13.4493i	0.159396	+	0.657041i	0.994298	+	0.106641i	$0.0340096\pi$
$419$	3.26276	+	13.4493i	0.159396	+	0.657041i	−0.834901	+	0.550400i	$0.814475\pi$
$420$		0			0
$421$	19.1830	−	6.63930i	0.934922	−	0.323580i	0.183212	−	0.983073i	$-0.441351\pi$
$421$	19.1830	−	6.63930i	0.934922	−	0.323580i	0.751710	+	0.659494i	$0.229229\pi$
$422$	24.5167	+	3.52497i	1.19345	+	0.171593i
$423$		0			0
$424$	9.43867	−	8.17866i	0.458382	−	0.397191i
$425$	1.02291	+	21.4735i	0.0496184	+	1.04162i
$426$		0			0
$427$	3.70075	−	10.6926i	0.179092	−	0.517451i
$428$	5.35007	+	5.10128i	0.258606	+	0.246580i
$429$		0			0
$430$	2.61658	+	7.56012i	0.126183	+	0.364582i
$431$	−7.12729	+	15.6066i	−0.343309	+	0.751743i	−0.999997	−	0.00241981i	$-0.999230\pi$
$431$	−7.12729	+	15.6066i	−0.343309	+	0.751743i	0.656688	+	0.754163i	$0.271957\pi$
$432$		0			0
$433$	−21.2797	+	9.71810i	−1.02264	+	0.467022i	−0.854891	−	0.518808i	$-0.826376\pi$
$433$	−21.2797	+	9.71810i	−1.02264	+	0.467022i	−0.167745	+	0.985830i	$0.553649\pi$
$434$	26.6438	+	10.6666i	1.27894	+	0.512012i
$435$		0			0
$436$	−39.1682	+	22.6138i	−1.87582	+	1.08300i
$437$	−14.4918	−	24.1317i	−0.693239	−	1.15438i
$438$		0			0
$439$	1.01209	−	0.521771i	0.0483046	−	0.0249028i	−0.433905	−	0.900959i	$-0.642865\pi$
$439$	1.01209	−	0.521771i	0.0483046	−	0.0249028i	0.482210	+	0.876056i	$0.339834\pi$
$440$	−49.3709	+	7.09846i	−2.35367	+	0.338406i
$441$		0			0
$442$	−5.37768	+	18.3147i	−0.255790	+	0.871142i
$443$	−23.0851	+	16.4388i	−1.09681	+	0.781033i	−0.977313	−	0.211802i	$-0.932067\pi$
$443$	−23.0851	+	16.4388i	−1.09681	+	0.781033i	−0.119495	+	0.992835i	$0.538127\pi$
$444$		0			0
$445$	5.45615	−	2.18431i	0.258646	−	0.103546i
$446$	12.1586	−	12.7515i	0.575725	−	0.603803i
$447$		0			0
$448$	17.8872	−	0.852073i	0.845092	−	0.0402567i
$449$	17.8738	+	27.8121i	0.843516	+	1.31254i	0.948085	+	0.318018i	$0.103017\pi$
$449$	17.8738	+	27.8121i	0.843516	+	1.31254i	−0.104569	+	0.994518i	$0.533346\pi$
$450$		0			0
$451$	1.14123	+	3.88666i	0.0537382	+	0.183015i
$452$	−11.9563	−	9.40252i	−0.562376	−	0.442257i
$453$		0			0
$454$	−0.296160	−	3.10153i	−0.0138995	−	0.145562i
$455$	−32.7159	+	7.93679i	−1.53374	+	0.372082i
$456$		0			0
$457$	−8.73113	+	21.8093i	−0.408425	+	1.02020i	0.571460	+	0.820630i	$0.306377\pi$
$457$	−8.73113	+	21.8093i	−0.408425	+	1.02020i	−0.979884	+	0.199566i	$0.936047\pi$
$458$	−22.8208	−	14.6660i	−1.06634	−	0.685297i
$459$		0			0
$460$	−23.3305	+	84.8308i	−1.08779	+	3.95526i
$461$	2.99383	+	1.72849i	0.139437	+	0.0805038i	0.568095	−	0.822963i	$-0.307680\pi$
$461$	2.99383	+	1.72849i	0.139437	+	0.0805038i	−0.428659	+	0.903466i	$0.641014\pi$
$462$		0			0
$463$	−30.0270	+	23.6135i	−1.39547	+	1.09741i	−0.413057	+	0.910705i	$0.635539\pi$
$463$	−30.0270	+	23.6135i	−1.39547	+	1.09741i	−0.982416	+	0.186707i	$0.940218\pi$
$464$	3.37246	+	2.40152i	0.156563	+	0.111488i
$465$		0			0
$466$	40.9109	+	57.4514i	1.89516	+	2.66138i
$467$	22.8932	−	26.4201i	1.05937	−	1.22258i	0.0852940	−	0.996356i	$-0.472817\pi$
$467$	22.8932	−	26.4201i	1.05937	−	1.22258i	0.974076	−	0.226222i	$-0.0726375\pi$
$468$		0			0
$469$	−5.54744	+	1.62887i	−0.256157	+	0.0752145i
$470$	29.9075	−	5.76419i	1.37953	−	0.265882i
$471$		0			0
$472$	−74.8052	−	38.5648i	−3.44319	−	1.77509i
$473$	−1.35798	−	0.470002i	−0.0624401	−	0.0216107i
$474$		0			0
$475$	−35.2521	+	44.8267i	−1.61748	+	2.05679i
$476$	21.1849	+	18.3568i	0.971008	+	0.841383i
$477$		0			0
$478$	32.1312	+	9.43457i	1.46965	+	0.431527i
$479$	20.3430	+	1.94252i	0.929497	+	0.0887562i	0.548809	−	0.835948i	$-0.315081\pi$
$479$	20.3430	+	1.94252i	0.929497	+	0.0887562i	0.380688	+	0.924704i	$0.375687\pi$
$480$		0			0
$481$	25.3481	+	1.20748i	1.15577	+	0.0550563i
$482$	−16.6151	−	28.7782i	−0.756798	−	1.31081i
$483$		0			0
$484$	−18.6021	+	32.2198i	−0.845551	+	1.46454i
$485$	−29.6245	+	46.0966i	−1.34518	+	2.09314i
$486$		0			0
$487$	−0.0167778	−	0.0367382i	−0.000760273	−	0.00166477i	0.909251	−	0.416247i	$-0.136655\pi$
$487$	−0.0167778	−	0.0367382i	−0.000760273	−	0.00166477i	−0.910012	+	0.414582i	$0.863928\pi$
$488$	−22.3969	+	21.3554i	−1.01386	+	0.966716i
$489$		0			0
$490$	−0.0345053	+	0.179031i	−0.00155879	+	0.00808778i
$491$	11.4600	+	28.6257i	0.517183	+	1.29186i	0.925406	+	0.378977i	$0.123724\pi$
$491$	11.4600	+	28.6257i	0.517183	+	1.29186i	−0.408223	+	0.912882i	$0.633852\pi$
$492$		0			0
$493$	0.186313	+	0.966685i	0.00839112	+	0.0435373i
$494$	−42.5966	+	27.3752i	−1.91651	+	1.23167i
$495$		0			0
$496$	−25.3480	−	29.2531i	−1.13816	−	1.31350i
$497$	−9.83405	+	40.5365i	−0.441117	+	1.81831i
$498$		0			0
$499$	−6.18830	−	1.19270i	−0.277026	−	0.0533925i	0.0488456	−	0.998806i	$-0.484446\pi$
$499$	−6.18830	−	1.19270i	−0.277026	−	0.0533925i	−0.325872	+	0.945414i	$0.605658\pi$
$500$	86.1249	−	8.22393i	3.85162	−	0.367786i
$501$		0			0
$502$	4.49025	−	47.0241i	0.200410	−	2.09879i
$503$	−1.47746	−	10.2760i	−0.0658768	−	0.458183i	−0.995884	−	0.0906409i	$-0.971108\pi$
$503$	−1.47746	−	10.2760i	−0.0658768	−	0.458183i	0.930007	−	0.367542i	$-0.119801\pi$
$504$		0			0
$505$		−	29.3119i		−	1.30436i
$506$	−13.3129	−	18.0304i	−0.591832	−	0.801550i
$507$		0			0
$508$	−0.0565701	+	1.18755i	−0.00250989	+	0.0526891i
$509$	−6.83816	−	8.69542i	−0.303096	−	0.385418i	0.610517	−	0.792003i	$-0.290962\pi$
$509$	−6.83816	−	8.69542i	−0.303096	−	0.385418i	−0.913613	+	0.406585i	$0.866719\pi$
$510$		0			0
$511$	7.38622	+	7.74645i	0.326747	+	0.342683i
$512$	40.2012	+	18.3593i	1.77666	+	0.811373i
$513$		0			0
$514$	8.71855	−	60.6388i	0.384559	−	2.67466i
$515$	−55.1330	−	13.3751i	−2.42945	−	0.589378i
$516$		0			0
$517$	−2.50695	+	4.86280i	−0.110255	+	0.213866i
$518$	24.2187	−	46.9777i	1.06411	−	2.06408i
$519$		0			0
$520$	89.4782	+	21.7072i	3.92388	+	0.951923i
$521$	−0.289337	+	2.01239i	−0.0126761	+	0.0881642i	−0.995177	−	0.0980915i	$-0.968726\pi$
$521$	−0.289337	+	2.01239i	−0.0126761	+	0.0881642i	0.982501	+	0.186256i	$0.0596353\pi$
$522$		0			0
$523$	−11.5481	−	5.27386i	−0.504965	−	0.230610i	0.146610	−	0.989194i	$-0.453164\pi$
$523$	−11.5481	−	5.27386i	−0.504965	−	0.230610i	−0.651574	+	0.758585i	$0.725891\pi$
$524$	0.590876	+	0.619693i	0.0258125	+	0.0270714i
$525$		0			0
$526$	−5.02409	−	6.38864i	−0.219061	−	0.278558i
$527$	0.437951	−	9.19372i	0.0190774	−	0.400485i
$528$		0			0
$529$	−22.4212	+	5.12743i	−0.974834	+	0.222932i
$530$		−	17.2203i		−	0.748002i
$531$		0			0
$532$	10.5825	+	73.6028i	0.458809	+	3.19109i
$533$	0.710780	−	7.44362i	0.0307873	−	0.322419i
$534$		0			0
$535$	5.90307	−	0.563674i	0.255212	−	0.0243698i
$536$	15.5271	+	2.99260i	0.670667	+	0.129260i
$537$		0			0
$538$	16.7015	−	68.8443i	0.720051	−	2.96809i
$539$	−0.0214468	−	0.0247509i	−0.000923777	−	0.00106610i
$540$		0			0
$541$	4.54887	−	2.92338i	0.195571	−	0.125686i	−0.439190	−	0.898394i	$-0.644735\pi$
$541$	4.54887	−	2.92338i	0.195571	−	0.125686i	0.634762	+	0.772708i	$0.281098\pi$
$542$	−14.4821	−	75.1405i	−0.622061	−	3.22756i
$543$		0			0
$544$	−8.01095	−	20.0104i	−0.343466	−	0.857938i
$545$	−6.86609	+	35.6247i	−0.294111	+	1.52599i
$546$		0			0
$547$	10.6017	−	10.1087i	0.453294	−	0.432215i	−0.428720	−	0.903437i	$-0.641035\pi$
$547$	10.6017	−	10.1087i	0.453294	−	0.432215i	0.882015	+	0.471222i	$0.156187\pi$
$548$	14.5055	+	31.7626i	0.619645	+	1.35683i
$549$		0			0
$550$	−24.5487	+	38.1985i	−1.04676	+	1.62879i
$551$	−1.30576	+	2.26165i	−0.0556274	+	0.0963494i
$552$		0			0
$553$	5.85663	+	10.1440i	0.249049	+	0.431366i
$554$	39.6052	+	1.88663i	1.68266	+	0.0801551i
$555$		0			0
$556$	101.424	+	9.68485i	4.30135	+	0.410729i
$557$	−29.7304	−	8.72965i	−1.25972	−	0.369887i	−0.417329	−	0.908755i	$-0.637034\pi$
$557$	−29.7304	−	8.72965i	−1.25972	−	0.369887i	−0.842390	+	0.538868i	$0.818852\pi$
$558$		0			0
$559$	2.00475	+	1.73713i	0.0847920	+	0.0734727i
$560$	58.4557	−	74.3325i	2.47021	−	3.14112i
$561$		0			0
$562$	26.7223	+	9.24869i	1.12721	+	0.390133i
$563$	9.44881	+	4.87120i	0.398220	+	0.205297i	0.645691	−	0.763599i	$-0.276569\pi$
$563$	9.44881	+	4.87120i	0.398220	+	0.205297i	−0.247471	+	0.968895i	$0.579600\pi$
$564$		0			0
$565$	−11.9810	+	2.30914i	−0.504043	+	0.0971463i
$566$	38.1351	−	11.1975i	1.60294	−	0.470665i
$567$		0			0
$568$	74.7088	−	86.2186i	3.13471	−	3.61765i
$569$	13.7824	+	19.3547i	0.577790	+	0.811392i	0.995255	−	0.0973007i	$-0.0310209\pi$
$569$	13.7824	+	19.3547i	0.577790	+	0.811392i	−0.417465	+	0.908693i	$0.637081\pi$
$570$		0			0
$571$	−7.19014	−	5.12008i	−0.300898	−	0.214269i	0.419628	−	0.907696i	$-0.362160\pi$
$571$	−7.19014	−	5.12008i	−0.300898	−	0.214269i	−0.720526	+	0.693427i	$0.756100\pi$
$572$	−22.3456	+	17.5728i	−0.934316	+	0.734754i
$573$		0			0
$574$	−13.4871	−	7.78679i	−0.562941	−	0.325014i
$575$	25.8628	+	38.7601i	1.07855	+	1.61641i
$576$		0			0
$577$	−30.3039	−	19.4751i	−1.26157	−	0.810760i	−0.273069	−	0.961994i	$-0.588039\pi$
$577$	−30.3039	−	19.4751i	−1.26157	−	0.810760i	−0.988498	+	0.151235i	$0.951675\pi$
$578$	−11.7159	+	29.2648i	−0.487316	+	1.21726i
$579$		0			0
$580$	7.93238	−	1.92437i	0.329374	−	0.0799053i
$581$	−3.20856	−	33.6016i	−0.133114	−	1.39403i
$582$		0			0
$583$	2.43141	+	1.91208i	0.100699	+	0.0791902i
$584$	−8.24744	−	28.0882i	−0.341282	−	1.16230i
$585$		0			0
$586$	−29.3175	−	45.6189i	−1.21109	−	1.88450i
$587$	−6.46343	+	0.307891i	−0.266774	+	0.0127080i	−0.180543	−	0.983567i	$-0.557785\pi$
$587$	−6.46343	+	0.307891i	−0.266774	+	0.0127080i	−0.0862313	+	0.996275i	$0.527482\pi$
$588$		0			0
$589$	16.8489	−	17.6706i	0.694247	−	0.728105i
$590$	−107.730	+	43.1287i	−4.43519	+	1.77558i
$591$		0			0
$592$	−58.0657	+	41.3484i	−2.38648	+	1.69941i
$593$	−3.77109	+	12.8432i	−0.154860	+	0.527405i	−0.999974	−	0.00718076i	$-0.997714\pi$
$593$	−3.77109	+	12.8432i	−0.154860	+	0.527405i	0.845114	+	0.534586i	$0.179532\pi$
$594$		0			0
$595$	22.2573	−	3.20012i	0.912461	−	0.131192i
$596$	52.2468	−	26.9351i	2.14011	−	1.10331i
$597$		0			0
$598$	10.4445	+	40.0328i	0.427109	+	1.63706i
$599$	−1.02406	+	0.591240i	−0.0418419	+	0.0241574i	−0.520775	−	0.853694i	$-0.674357\pi$
$599$	−1.02406	+	0.591240i	−0.0418419	+	0.0241574i	0.478933	+	0.877851i	$0.341024\pi$
$600$		0			0
$601$	−30.2389	−	12.1058i	−1.23347	−	0.493807i	−0.338937	−	0.940809i	$-0.610067\pi$
$601$	−30.2389	−	12.1058i	−1.23347	−	0.493807i	−0.894533	+	0.447003i	$0.852491\pi$
$602$	5.02553	−	2.29508i	0.204825	−	0.0935405i
$603$		0			0
$604$	5.11992	−	11.2111i	0.208327	−	0.456172i
$605$	9.76109	+	28.2028i	0.396845	+	1.14661i
$606$		0			0
$607$	17.9570	+	17.1219i	0.728851	+	0.694958i	0.960636	−	0.277809i	$-0.0896083\pi$
$607$	17.9570	+	17.1219i	0.728851	+	0.694958i	−0.231786	+	0.972767i	$0.574457\pi$
$608$	18.7009	−	54.0327i	0.758422	−	2.19132i
$609$		0			0
$610$	2.03030	+	42.6212i	0.0822043	+	1.72568i
$611$	7.63244	−	6.61355i	0.308776	−	0.267556i
$612$		0			0
$613$	−26.4982	−	3.80986i	−1.07025	−	0.153879i	−0.415401	−	0.909638i	$-0.636359\pi$
$613$	−26.4982	−	3.80986i	−1.07025	−	0.153879i	−0.654849	+	0.755760i	$0.727268\pi$
$614$	−4.21702	+	1.45953i	−0.170185	+	0.0589017i
$615$		0			0
$616$	8.12085	+	33.4746i	0.327198	+	1.34873i
$617$	7.73635	−	10.8642i	0.311454	−	0.437376i	−0.628945	−	0.777450i	$-0.716513\pi$
$617$	7.73635	−	10.8642i	0.311454	−	0.437376i	0.940399	+	0.340074i	$0.110452\pi$
$618$		0			0
$619$	0.404571	+	0.784759i	0.0162611	+	0.0315421i	0.896826	−	0.442383i	$-0.145867\pi$
$619$	0.404571	+	0.784759i	0.0162611	+	0.0315421i	−0.880565	+	0.473925i	$0.842837\pi$
$620$	−76.3132			−3.06481
$621$		0			0
$622$	−48.7272			−1.95378
$623$	−1.85980	−	3.60750i	−0.0745112	−	0.144531i
$624$		0			0
$625$	12.0775	−	16.9604i	0.483098	−	0.678417i
$626$	−2.33089	−	9.60804i	−0.0931609	−	0.384015i
$627$		0			0
$628$	−66.4051	+	22.9830i	−2.64985	+	0.917123i
$629$	−16.7778	−	2.41228i	−0.668973	−	0.0961838i
$630$		0			0
$631$	−5.95890	+	5.16342i	−0.237220	+	0.205552i	−0.765356	−	0.643608i	$-0.777437\pi$
$631$	−5.95890	+	5.16342i	−0.237220	+	0.205552i	0.528135	+	0.849160i	$0.322891\pi$
$632$	−1.52433	−	31.9996i	−0.0606345	−	1.27287i
$633$		0			0
$634$	−5.04115	+	14.5655i	−0.200210	+	0.578468i
$635$	0.690226	+	0.658130i	0.0273908	+	0.0261171i
$636$		0			0
$637$	0.0197730	+	0.0571302i	0.000783433	+	0.00226358i
$638$	−0.863797	+	1.89145i	−0.0341980	+	0.0748833i
$639$		0			0
$640$	6.55799	−	2.99493i	0.259227	−	0.118385i
$641$	−37.5848	−	15.0467i	−1.48451	−	0.594309i	−0.519024	−	0.854760i	$-0.673704\pi$
$641$	−37.5848	−	15.0467i	−1.48451	−	0.594309i	−0.965487	+	0.260451i	$0.916129\pi$
$642$		0			0
$643$	−6.46771	+	3.73413i	−0.255061	+	0.147260i	−0.622080	−	0.782954i	$-0.713712\pi$
$643$	−6.46771	+	3.73413i	−0.255061	+	0.147260i	0.367018	+	0.930214i	$0.380379\pi$
$644$	59.8494	+	10.4701i	2.35840	+	0.412581i
$645$		0			0
$646$	30.0614	−	15.4977i	1.18275	−	0.609749i
$647$	32.7053	−	4.70232i	1.28578	−	0.184867i	0.534679	−	0.845055i	$-0.320433\pi$
$647$	32.7053	−	4.70232i	1.28578	−	0.184867i	0.751100	+	0.660188i	$0.229524\pi$
$648$		0			0
$649$	5.87246	−	19.9998i	0.230514	−	0.785060i
$650$	68.2767	−	48.6196i	2.67803	−	1.90702i
$651$		0			0
$652$	47.5980	−	19.0554i	1.86408	−	0.746266i
$653$	−22.0717	+	23.1482i	−0.863734	+	0.905858i	−0.996355	−	0.0853088i	$-0.972812\pi$
$653$	−22.0717	+	23.1482i	−0.863734	+	0.905858i	0.132621	+	0.991167i	$0.457661\pi$
$654$		0			0
$655$	0.686078	−	0.0326819i	0.0268073	−	0.00127699i
$656$	11.3557	+	17.6698i	0.443366	+	0.689891i
$657$		0			0
$658$	−5.92592	−	20.1818i	−0.231016	−	0.786770i
$659$	8.78200	+	6.90624i	0.342098	+	0.269029i	0.774395	−	0.632702i	$-0.218054\pi$
$659$	8.78200	+	6.90624i	0.342098	+	0.269029i	−0.432297	+	0.901731i	$0.642297\pi$
$660$		0			0
$661$	2.83114	+	29.6490i	0.110119	+	1.15321i	0.866532	+	0.499121i	$0.166344\pi$
$661$	2.83114	+	29.6490i	0.110119	+	1.15321i	−0.756414	+	0.654093i	$0.773050\pi$
$662$	9.60668	−	2.33056i	0.373374	−	0.0905797i
$663$		0			0
$664$	−34.3114	+	85.7057i	−1.33154	+	3.32603i
$665$	50.1802	+	32.2489i	1.94591	+	1.25056i
$666$		0			0
$667$	1.42492	+	1.58836i	0.0551730	+	0.0615017i
$668$	21.5047	+	12.4157i	0.832041	+	0.480379i
$669$		0			0
$670$	17.1383	−	13.4777i	0.662112	−	0.520691i
$671$	−6.24330	−	4.44583i	−0.241020	−	0.171629i
$672$		0			0
$673$	−14.0259	−	19.6966i	−0.540659	−	0.759250i	0.450378	−	0.892838i	$-0.351289\pi$
$673$	−14.0259	−	19.6966i	−0.540659	−	0.759250i	−0.991037	+	0.133588i	$0.957350\pi$
$674$	22.2188	−	25.6418i	0.855836	−	0.987687i
$675$		0			0
$676$	−9.29994	+	2.73071i	−0.357690	+	0.105027i
$677$	45.2015	−	8.71187i	1.73723	−	0.334824i	0.780361	−	0.625329i	$-0.215035\pi$
$677$	45.2015	−	8.71187i	1.73723	−	0.334824i	0.956874	+	0.290505i	$0.0938233\pi$
$678$		0			0
$679$	33.6343	+	17.3397i	1.29076	+	0.665435i
$680$	−58.1175	−	20.1147i	−2.22870	−	0.771362i
$681$		0			0
$682$	12.0173	−	15.2813i	0.460167	−	0.585150i
$683$	0.675703	+	0.585500i	0.0258551	+	0.0224035i	0.667692	−	0.744437i	$-0.267282\pi$
$683$	0.675703	+	0.585500i	0.0258551	+	0.0224035i	−0.641837	+	0.766841i	$0.721828\pi$
$684$		0			0
$685$	26.8757	+	7.89143i	1.02687	+	0.301516i
$686$	−47.9505	−	4.57872i	−1.83076	−	0.174816i
$687$		0			0
$688$	−7.44288	−	0.354548i	−0.283757	−	0.0135170i
$689$	−2.85494	−	4.94490i	−0.108764	−	0.188386i
$690$		0			0
$691$	−5.62405	+	9.74115i	−0.213949	+	0.370571i	−0.952947	−	0.303137i	$-0.901966\pi$
$691$	−5.62405	+	9.74115i	−0.213949	+	0.370571i	0.738998	+	0.673708i	$0.235299\pi$
$692$	−24.2434	+	37.7235i	−0.921597	+	1.43403i
$693$		0			0
$694$	37.8006	+	82.7718i	1.43489	+	3.14198i
$695$	59.1507	−	56.4001i	2.24371	−	2.13938i
$696$		0			0
$697$	−0.945222	+	4.90428i	−0.0358028	+	0.185763i
$698$	15.8687	+	39.6381i	0.600640	+	1.50033i
$699$		0			0
$700$	−23.2954	−	120.868i	−0.880482	−	4.56838i
$701$	19.2081	−	12.3443i	0.725479	−	0.466237i	−0.125060	−	0.992149i	$-0.539912\pi$
$701$	19.2081	−	12.3443i	0.725479	−	0.466237i	0.850539	+	0.525912i	$0.176276\pi$
$702$		0			0
$703$	−29.4453	−	33.9817i	−1.11055	−	1.28164i
$704$	2.85979	−	11.7882i	0.107782	−	0.444285i
$705$		0			0
$706$	80.6660	+	15.5471i	3.03591	+	0.585123i
$707$	−20.1508	+	1.92416i	−0.757847	+	0.0723656i
$708$		0			0
$709$	0.301620	−	3.15871i	0.0113276	−	0.118628i	−0.988039	−	0.154201i	$-0.950720\pi$
$709$	0.301620	−	3.15871i	0.0113276	−	0.118628i	0.999367	+	0.0355733i	$0.0113257\pi$
$710$	−22.3862	−	155.700i	−0.840140	−	5.84330i
$711$		0			0
$712$			11.1005i			0.416010i
$713$	−9.44539	−	17.5722i	−0.353733	−	0.658085i
$714$		0			0
$715$	−1.08505	+	22.7780i	−0.0405786	+	0.851849i
$716$	25.3451	+	32.2290i	0.947193	+	1.20445i
$717$		0			0
$718$	−45.5690	−	47.7914i	−1.70062	−	1.78356i
$719$	7.99664	+	3.65194i	0.298224	+	0.136194i	0.558908	−	0.829230i	$-0.311221\pi$
$719$	7.99664	+	3.65194i	0.298224	+	0.136194i	−0.260683	+	0.965424i	$0.583948\pi$
$720$		0			0
$721$	−5.57569	+	38.7798i	−0.207649	+	1.44423i
$722$	39.1022	+	9.48609i	1.45523	+	0.353036i
$723$		0			0
$724$	47.7189	−	92.5617i	1.77346	−	3.44003i
$725$	1.98092	−	3.84246i	0.0735697	−	0.142705i
$726$		0			0
$727$	−42.6376	−	10.3438i	−1.58134	−	0.383629i	−0.653596	−	0.756844i	$-0.726740\pi$
$727$	−42.6376	−	10.3438i	−1.58134	−	0.383629i	−0.927745	+	0.373215i	$0.878256\pi$
$728$	9.04908	−	62.9377i	0.335381	−	2.33263i
$729$		0			0
$730$	−36.7160	−	16.7676i	−1.35892	−	0.620598i
$731$	−1.22270	−	1.28234i	−0.0452233	−	0.0474289i
$732$		0			0
$733$	−21.4708	−	27.3024i	−0.793043	−	1.00844i	−0.999550	−	0.0299915i	$-0.990452\pi$
$733$	−21.4708	−	27.3024i	−0.793043	−	1.00844i	0.206507	−	0.978445i	$-0.433790\pi$
$734$	−3.27451	+	68.7404i	−0.120864	+	2.53726i
$735$		0			0
$736$	−37.2151	−	28.2434i	−1.37177	−	1.04107i
$737$			3.91635i			0.144261i
$738$		0			0
$739$	5.64224	+	39.2426i	0.207553	+	1.44356i	0.781108	+	0.624396i	$0.214655\pi$
$739$	5.64224	+	39.2426i	0.207553	+	1.44356i	−0.573555	+	0.819167i	$0.694436\pi$
$740$	−13.3590	+	139.902i	−0.491086	+	5.14289i
$741$		0			0
$742$	−11.8383	+	1.13042i	−0.434597	+	0.0414990i
$743$	−37.4594	−	7.21971i	−1.37425	−	0.264865i	−0.551931	−	0.833890i	$-0.686109\pi$
$743$	−37.4594	−	7.21971i	−1.37425	−	0.264865i	−0.822321	+	0.569024i	$0.807321\pi$
$744$		0			0
$745$	11.1167	−	45.8235i	0.407283	−	1.67884i
$746$	48.3148	+	55.7583i	1.76893	+	2.04146i
$747$		0			0
$748$	15.9737	−	10.2657i	0.584057	−	0.375351i
$749$	−0.775008	−	4.02113i	−0.0283182	−	0.146929i
$750$		0			0
$751$	2.97584	+	7.43329i	0.108590	+	0.271244i	0.972703	−	0.232053i	$-0.0745443\pi$
$751$	2.97584	+	7.43329i	0.108590	+	0.271244i	−0.864113	+	0.503297i	$0.832120\pi$
$752$	−5.36877	+	27.8558i	−0.195779	+	1.01580i
$753$		0			0
$754$	2.77798	−	2.64880i	0.101168	−	0.0964636i
$755$	−4.10706	−	8.99321i	−0.149471	−	0.327296i
$756$		0			0
$757$	−23.3456	+	36.3264i	−0.848509	+	1.32031i	0.0971909	+	0.995266i	$0.469014\pi$
$757$	−23.3456	+	36.3264i	−0.848509	+	1.32031i	−0.945700	+	0.325040i	$0.894622\pi$
$758$	−25.9539	+	44.9535i	−0.942688	+	1.63278i
$759$		0			0
$760$	−81.5707	−	141.285i	−2.95888	−	5.12493i
$761$	5.38610	+	0.256572i	0.195246	+	0.00930071i	0.144977	−	0.989435i	$-0.453689\pi$
$761$	5.38610	+	0.256572i	0.195246	+	0.00930071i	0.0502689	+	0.998736i	$0.483992\pi$
$762$		0			0
$763$	24.9413	+	2.38160i	0.902935	+	0.0862199i
$764$	−12.2271	−	3.59020i	−0.442361	−	0.129889i
$765$		0			0
$766$	34.0871	+	29.5367i	1.23162	+	1.06720i
$767$	−23.7851	+	30.2452i	−0.858829	+	1.09209i
$768$		0			0
$769$	28.6413	+	9.91287i	1.03283	+	0.357467i	0.790329	−	0.612683i	$-0.209910\pi$
$769$	28.6413	+	9.91287i	1.03283	+	0.357467i	0.242505	+	0.970150i	$0.422031\pi$
$770$	42.2145	+	21.7631i	1.52131	+	0.784288i
$771$		0			0
$772$	75.0380	−	14.4624i	2.70068	−	0.520513i
$773$	−5.06971	+	1.48860i	−0.182345	+	0.0535413i	−0.371630	−	0.928381i	$-0.621201\pi$
$773$	−5.06971	+	1.48860i	−0.182345	+	0.0535413i	0.189285	+	0.981922i	$0.439383\pi$
$774$		0			0
$775$	−26.4676	+	30.5453i	−0.950745	+	1.09722i
$776$	−60.0330	−	84.3045i	−2.15506	−	3.02636i
$777$		0			0
$778$	12.0324	+	8.56820i	0.431381	+	0.307185i
$779$	−10.4144	+	8.19001i	−0.373136	+	0.293438i
$780$		0			0
$781$	24.4696	+	14.1275i	0.875590	+	0.505522i
$782$	−4.40300	−	27.2817i	−0.157451	−	0.975593i
$783$		0			0
$784$	−0.142860	−	0.0918106i	−0.00510215	−	0.00327895i
$785$	−20.9501	+	52.3308i	−0.747741	+	1.86777i
$786$		0			0
$787$	−3.83849	+	0.931209i	−0.136828	+	0.0331940i	−0.303588	−	0.952803i	$-0.598185\pi$
$787$	−3.83849	+	0.931209i	−0.136828	+	0.0331940i	0.166760	+	0.985997i	$0.446669\pi$
$788$	−6.51541	−	68.2325i	−0.232102	−	2.43068i
$789$		0			0
$790$	−34.7213	−	27.3051i	−1.23533	−	0.971473i
$791$	2.37393	+	8.08486i	0.0844072	+	0.287465i
$792$		0			0
$793$	7.64913	+	11.9023i	0.271629	+	0.422662i
$794$	41.7378	−	1.98822i	1.48122	−	0.0705591i
$795$		0			0
$796$	−47.2158	+	49.5185i	−1.67352	+	1.75514i
$797$	8.60197	−	3.44371i	0.304697	−	0.121982i	−0.214275	−	0.976773i	$-0.568739\pi$
$797$	8.60197	−	3.44371i	0.304697	−	0.121982i	0.518973	+	0.854791i	$0.326315\pi$
$798$		0			0
$799$	−5.49486	+	3.91288i	−0.194394	+	0.138428i
$800$	−26.6658	+	90.8154i	−0.942779	+	3.21081i
$801$		0			0
$802$	15.8277	−	2.27567i	0.558894	−	0.0803568i
$803$	6.44431	−	3.32227i	0.227415	−	0.117240i
$804$		0			0
$805$	37.7870	−	30.7831i	1.33182	−	1.08496i
$806$	−31.0785	+	17.9432i	−1.09469	+	0.632021i
$807$		0			0
$808$	51.3974	+	20.5764i	1.80815	+	0.723876i
$809$	26.5830	−	12.1401i	0.934610	−	0.426822i	0.110899	−	0.993832i	$-0.464627\pi$
$809$	26.5830	−	12.1401i	0.934610	−	0.426822i	0.823711	+	0.567010i	$0.191900\pi$
$810$		0			0
$811$	8.15328	−	17.8532i	0.286300	−	0.626910i	−0.710768	−	0.703426i	$-0.751652\pi$
$811$	8.15328	−	17.8532i	0.286300	−	0.626910i	0.997068	+	0.0765163i	$0.0243797\pi$
$812$	−1.84365	−	5.32688i	−0.0646994	−	0.186937i
$813$		0			0
$814$	−25.9108	−	24.7059i	−0.908173	−	0.865941i
$815$	13.4516	−	38.8659i	0.471190	−	1.36141i
$816$		0			0
$817$	−0.223642	−	4.69483i	−0.00782425	−	0.164251i
$818$	−42.1492	+	36.5225i	−1.47371	+	1.27698i
$819$		0			0
$820$	40.9891	+	5.89334i	1.43140	+	0.205804i
$821$	11.0066	−	3.80944i	0.384135	−	0.132950i	−0.128174	−	0.991752i	$-0.540912\pi$
$821$	11.0066	−	3.80944i	0.384135	−	0.132950i	0.512309	+	0.858801i	$0.328790\pi$
$822$		0			0
$823$	1.08444	+	4.47010i	0.0378010	+	0.155818i	0.987584	−	0.157091i	$-0.0502116\pi$
$823$	1.08444	+	4.47010i	0.0378010	+	0.155818i	−0.949783	+	0.312909i	$0.898696\pi$
$824$	62.1552	−	87.2848i	2.16528	−	3.04071i
$825$		0			0
$826$	36.7212	+	71.2293i	1.27770	+	2.47838i
$827$	15.7706			0.548398			0.274199	−	0.961673i	$-0.411587\pi$
$827$	15.7706			0.548398			0.274199	+	0.961673i	$0.411587\pi$
$828$		0			0
$829$	−22.6475			−0.786580			−0.393290	−	0.919414i	$-0.628663\pi$
$829$	−22.6475			−0.786580			−0.393290	+	0.919414i	$0.628663\pi$
$830$	58.3280	+	113.141i	2.02459	+	3.92717i
$831$		0			0
$832$	−12.9885	+	18.2397i	−0.450294	+	0.632349i
$833$	−0.00952010	−	0.0392424i	−0.000329852	−	0.00135967i
$834$		0			0
$835$	18.8236	−	6.51491i	0.651417	−	0.225458i
$836$	49.8570	+	7.16835i	1.72434	+	0.247923i
$837$		0			0
$838$	−27.2383	+	23.6021i	−0.940933	+	0.815323i
$839$	1.64814	+	34.5987i	0.0569000	+	1.19448i	0.829100	+	0.559100i	$0.188853\pi$
$839$	1.64814	+	34.5987i	0.0569000	+	1.19448i	−0.772200	+	0.635379i	$0.780844\pi$
$840$		0			0
$841$	−9.42022	+	27.2179i	−0.324835	+	0.938550i
$842$	38.2603	+	36.4811i	1.31854	+	1.25722i
$843$		0			0
$844$	14.8760	+	42.9813i	0.512052	+	1.47948i
$845$	−3.22989	+	7.07248i	−0.111112	+	0.243301i
$846$		0			0
$847$	18.7476	−	8.56173i	0.644174	−	0.294185i
$848$	14.8901	+	5.96109i	0.511328	+	0.204705i
$849$		0			0
$850$	−48.4854	+	27.9931i	−1.66304	+	0.960155i
$851$	−33.8679	+	14.2397i	−1.16098	+	0.488131i
$852$		0			0
$853$	−5.17638	+	2.66861i	−0.177236	+	0.0913715i	−0.544561	−	0.838721i	$-0.683304\pi$
$853$	−5.17638	+	2.66861i	−0.177236	+	0.0913715i	0.367325	+	0.930093i	$0.380274\pi$
$854$	29.1671	−	4.19360i	0.998078	−	0.143502i
$855$		0			0
$856$	−3.15546	+	10.7465i	−0.107852	+	0.367309i
$857$	12.3086	−	8.76492i	0.420454	−	0.299404i	−0.350179	−	0.936683i	$-0.613879\pi$
$857$	12.3086	−	8.76492i	0.420454	−	0.299404i	0.770634	+	0.637279i	$0.219940\pi$
$858$		0			0
$859$	−24.4581	+	9.79156i	−0.834500	+	0.334084i	−0.749259	−	0.662277i	$-0.769590\pi$
$859$	−24.4581	+	9.79156i	−0.834500	+	0.334084i	−0.0852412	+	0.996360i	$0.527166\pi$
$860$	−10.1377	+	10.6321i	−0.345691	+	0.362551i
$861$		0			0
$862$	−44.6309	+	2.12603i	−1.52013	+	0.0724129i
$863$	−26.3014	−	40.9258i	−0.895312	−	1.39313i	−0.919358	−	0.393421i	$-0.871291\pi$
$863$	−26.3014	−	40.9258i	−0.895312	−	1.39313i	0.0240467	−	0.999711i	$-0.492345\pi$
$864$		0			0
$865$	10.1342	+	34.5140i	0.344574	+	1.17351i
$866$	−47.8890	−	37.6604i	−1.62734	−	1.27975i
$867$		0			0
$868$	5.00955	+	52.4624i	0.170035	+	1.78069i
$869$	7.71065	−	1.87058i	0.261566	−	0.0634552i
$870$		0			0
$871$	2.68690	−	6.71155i	0.0910422	−	0.227412i
$872$	−57.6468	−	37.0474i	−1.95217	−	1.25458i
$873$		0			0
$874$	38.5655	−	62.3426i	1.30450	−	2.10877i
$875$	−41.5066	−	23.9639i	−1.40318	−	0.810126i
$876$		0			0
$877$	−15.5380	+	12.2192i	−0.524681	+	0.412614i	−0.845057	−	0.534677i	$-0.820433\pi$
$877$	−15.5380	+	12.2192i	−0.524681	+	0.412614i	0.320376	+	0.947291i	$0.396191\pi$
$878$	2.41555	+	1.72011i	0.0815209	+	0.0580508i
$879$		0			0
$880$	−37.1560	−	52.1783i	−1.25253	−	1.75893i
$881$	−19.6113	+	22.6326i	−0.660721	+	0.762512i	−0.982895	−	0.184168i	$-0.941041\pi$
$881$	−19.6113	+	22.6326i	−0.660721	+	0.762512i	0.322174	+	0.946680i	$0.395586\pi$
$882$		0			0
$883$	48.1840	−	14.1481i	1.62152	−	0.476121i	0.660093	−	0.751184i	$-0.270517\pi$
$883$	48.1840	−	14.1481i	1.62152	−	0.476121i	0.961426	+	0.275062i	$0.0886985\pi$
$884$	−34.4176	+	6.63345i	−1.15759	+	0.223107i
$885$		0			0
$886$	−65.6005	−	33.8194i	−2.20389	−	1.13619i
$887$	−5.11936	−	1.77183i	−0.171891	−	0.0594921i	0.239767	−	0.970830i	$-0.422929\pi$
$887$	−5.11936	−	1.77183i	−0.171891	−	0.0594921i	−0.411658	+	0.911338i	$0.635050\pi$
$888$		0			0
$889$	0.407129	−	0.517706i	0.0136547	−	0.0173633i
$890$	11.5672	+	10.0231i	0.387734	+	0.335974i
$891$		0			0
$892$	31.0433	+	9.11513i	1.03941	+	0.305197i
$893$	−17.8133	−	1.70096i	−0.596099	−	0.0569205i
$894$		0			0
$895$	32.8526	+	1.56496i	1.09814	+	0.0523110i
$896$	−2.48940	−	4.31176i	−0.0831649	−	0.144046i
$897$		0			0
$898$	−43.0490	+	74.5630i	−1.43656	+	2.48820i
$899$	−1.00065	+	1.55705i	−0.0333737	+	0.0519305i
$900$		0			0
$901$	1.58434	+	3.46922i	0.0527820	+	0.115577i
$902$	−7.63481	+	7.27978i	−0.254212	+	0.242390i
$903$		0			0
$904$	4.36142	−	22.6292i	0.145059	−	0.752636i
$905$	−31.0475	−	77.5529i	−1.03205	−	2.57795i
$906$		0			0
$907$	3.12973	+	16.2386i	0.103921	+	0.539193i	0.996154	+	0.0876181i	$0.0279255\pi$
$907$	3.12973	+	16.2386i	0.103921	+	0.539193i	−0.892233	+	0.451575i	$0.850862\pi$
$908$	4.81300	−	3.09313i	0.159725	−	0.102649i
$909$		0			0
$910$	−57.4131	−	66.2582i	−1.90322	−	2.19644i
$911$	−6.86130	+	28.2827i	−0.227325	+	0.937047i	0.737750	+	0.675074i	$0.235888\pi$
$911$	−6.86130	+	28.2827i	−0.227325	+	0.937047i	−0.965075	+	0.261973i	$0.915627\pi$
$912$		0			0
$913$	−22.4513	−	4.32714i	−0.743030	−	0.143207i
$914$	−60.9026	+	5.81549i	−2.01448	+	0.192359i
$915$		0			0
$916$	4.73506	−	49.5877i	0.156451	−	1.63843i
$917$	−0.0675048	−	0.469506i	−0.00222921	−	0.0155045i
$918$		0			0
$919$		−	30.9735i		−	1.02172i	−0.859663	−	0.510861i	$-0.829327\pi$
$919$		−	30.9735i		−	1.02172i	0.859663	−	0.510861i	$-0.170673\pi$
$920$	−130.438	+	27.4762i	−4.30042	+	0.905864i
$921$		0			0
$922$	−0.428375	+	8.99269i	−0.0141078	+	0.296159i
$923$	−32.2416	−	40.9985i	−1.06125	−	1.34948i
$924$		0			0
$925$	51.3640	+	53.8690i	1.68884	+	1.77120i
$926$	−90.4922	−	41.3264i	−2.97376	−	1.35807i
$927$		0			0
$928$	−0.616847	+	4.29027i	−0.0202490	+	0.140835i
$929$	−10.0362	−	2.43476i	−0.329277	−	0.0798818i	0.0677124	−	0.997705i	$-0.478430\pi$
$929$	−10.0362	−	2.43476i	−0.329277	−	0.0798818i	−0.396990	+	0.917823i	$0.629945\pi$
$930$		0			0
$931$	0.0490843	−	0.0952103i	0.00160867	−	0.00312039i
$932$	−59.3460	+	115.115i	−1.94394	+	3.77072i
$933$		0			0
$934$	88.4758	+	21.4640i	2.89502	+	0.702323i
$935$	2.16769	−	15.0766i	0.0708911	−	0.493059i
$936$		0			0
$937$	−49.8660	−	22.7730i	−1.62905	−	0.743962i	−0.629594	−	0.776924i	$-0.716779\pi$
$937$	−49.8660	−	22.7730i	−1.62905	−	0.743962i	−0.999457	+	0.0329618i	$0.989506\pi$
$938$	−10.3905	−	10.8972i	−0.339261	−	0.355806i
$939$		0			0
$940$	34.5734	+	43.9637i	1.12766	+	1.43394i
$941$	−2.29060	+	48.0856i	−0.0746715	+	1.56755i	0.581886	+	0.813271i	$0.302315\pi$
$941$	−2.29060	+	48.0856i	−0.0746715	+	1.56755i	−0.656557	+	0.754276i	$0.727988\pi$
$942$		0			0
$943$	3.71625	+	10.1678i	0.121018	+	0.331108i
$944$		−	108.082i		−	3.51778i
$945$		0			0
$946$	−0.532595	−	3.70428i	−0.0173162	−	0.120437i
$947$	−3.19103	+	33.4180i	−0.103694	+	1.08594i	0.782508	+	0.622640i	$0.213940\pi$
$947$	−3.19103	+	33.4180i	−0.103694	+	1.08594i	−0.886203	+	0.463298i	$0.846666\pi$
$948$		0			0
$949$	−13.3231	+	1.27220i	−0.432486	+	0.0412974i
$950$	−145.831	−	28.1066i	−4.73138	−	0.911900i
$951$		0			0
$952$	−10.0129	+	41.2739i	−0.324522	+	1.33770i
$953$	−39.2866	−	45.3391i	−1.27262	−	1.46868i	−0.814924	−	0.579568i	$-0.803221\pi$
$953$	−39.2866	−	45.3391i	−1.27262	−	1.46868i	−0.457693	−	0.889110i	$-0.651324\pi$
$954$		0			0
$955$	−8.59956	+	5.52660i	−0.278275	+	0.178837i
$956$	11.6377	+	60.3820i	0.376389	+	1.95289i
$957$		0			0
$958$	19.7797	+	49.4074i	0.639054	+	1.59628i
$959$	3.66080	−	18.9941i	0.118214	−	0.613350i
$960$		0			0
$961$	−9.91205	+	9.45112i	−0.319744	+	0.304875i
$962$	27.4540	+	60.1158i	0.885151	+	1.93821i
$963$		0			0
$964$	32.9902	−	51.3337i	1.06254	−	1.65335i
$965$	30.6506	−	53.0884i	0.986679	−	1.70898i
$966$		0			0
$967$	−8.46492	−	14.6617i	−0.272213	−	0.471487i	0.697215	−	0.716862i	$-0.254422\pi$
$967$	−8.46492	−	14.6617i	−0.272213	−	0.471487i	−0.969428	+	0.245375i	$0.921089\pi$
$968$	−56.3048	−	2.68213i	−1.80971	−	0.0862069i
$969$		0			0
$970$	−142.055	−	13.5646i	−4.56110	−	0.435533i
$971$	15.3885	+	4.51848i	0.493842	+	0.145005i	0.519164	−	0.854674i	$-0.326243\pi$
$971$	15.3885	+	4.51848i	0.493842	+	0.145005i	−0.0253229	+	0.999679i	$0.508061\pi$
$972$		0			0
$973$	−42.6558	−	36.9614i	−1.36748	−	1.18493i
$974$	0.0650186	−	0.0826778i	0.00208333	−	0.00264917i
$975$		0			0
$976$	−37.5566	−	12.9985i	−1.20216	−	0.416070i
$977$	−4.06958	−	2.09802i	−0.130197	−	0.0671215i	0.391897	−	0.920009i	$-0.371819\pi$
$977$	−4.06958	−	2.09802i	−0.130197	−	0.0671215i	−0.522095	+	0.852888i	$0.674849\pi$
$978$		0			0
$979$	−2.69958	+	0.520302i	−0.0862790	+	0.0166289i
$980$	−0.321241	+	0.0943250i	−0.0102617	+	0.00301310i
$981$		0			0
$982$	−52.5860	+	60.6875i	−1.67809	+	1.93661i
$983$	15.1105	+	21.2197i	0.481949	+	0.676803i	0.981932	−	0.189232i	$-0.0605999\pi$
$983$	15.1105	+	21.2197i	0.481949	+	0.676803i	−0.499983	+	0.866035i	$0.666660\pi$
$984$		0			0
$985$	−44.7880	−	31.8934i	−1.42706	−	1.01621i
$986$	−2.01531	+	1.58486i	−0.0641806	+	0.0504722i
$987$		0			0
$988$	−80.5231	−	46.4900i	−2.56178	−	1.47905i
$989$	−3.70294	−	1.01840i	−0.117747	−	0.0323832i
$990$		0			0
$991$	31.6171	+	20.3191i	1.00435	+	0.645456i	0.935925	−	0.352200i	$-0.114566\pi$
$991$	31.6171	+	20.3191i	1.00435	+	0.645456i	0.0684244	+	0.997656i	$0.478203\pi$
$992$	15.0610	−	37.6206i	0.478188	−	1.19446i
$993$		0			0
$994$	−105.568	+	25.6105i	−3.34841	+	0.812315i
$995$	5.21719	+	54.6369i	0.165396	+	1.73211i
$996$		0			0
$997$	2.90201	+	2.28216i	0.0919075	+	0.0722768i	0.663055	−	0.748570i	$-0.269259\pi$
$997$	2.90201	+	2.28216i	0.0919075	+	0.0722768i	−0.571148	+	0.820847i	$0.693502\pi$
$998$	−4.62396	−	15.7478i	−0.146369	−	0.498486i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	621.2.s.a.251.22		440
3.2	odd	2		207.2.o.a.182.1	yes	440
9.4	even	3		207.2.o.a.113.1	yes	440
9.5	odd	6	inner	621.2.s.a.44.22		440
23.11	odd	22	inner	621.2.s.a.494.22		440
69.11	even	22		207.2.o.a.11.1	✓	440
207.103	odd	66		207.2.o.a.149.1	yes	440
207.149	even	66	inner	621.2.s.a.287.22		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.1	✓	440	69.11	even	22
207.2.o.a.113.1	yes	440	9.4	even	3
207.2.o.a.149.1	yes	440	207.103	odd	66
207.2.o.a.182.1	yes	440	3.2	odd	2
621.2.s.a.44.22		440	9.5	odd	6	inner
621.2.s.a.251.22		440	1.1	even	1	trivial
621.2.s.a.287.22		440	207.149	even	66	inner
621.2.s.a.494.22		440	23.11	odd	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.s (of order \(66\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.19334 + 2.31476i) q^{2} +(-2.77395 + 3.89546i) q^{4} +(0.904406 + 3.72801i) q^{5} +(2.50349 - 0.866468i) q^{7} +(-7.17183 - 1.03115i) q^{8} +(-7.55020 + 6.54229i) q^{10} +(-0.0853862 - 1.79248i) q^{11} +(-1.08344 + 3.13039i) q^{13} +(4.99320 + 4.76100i) q^{14} +(-3.04337 - 8.79325i) q^{16} +(0.919155 - 2.01267i) q^{17} +(5.33902 - 2.43825i) q^{19} +(-17.0311 - 6.81823i) q^{20} +(4.04726 - 2.33669i) q^{22} +(-0.537967 - 4.76556i) q^{23} +(-8.63596 + 4.45214i) q^{25} +(-8.53903 + 1.22773i) q^{26} +(-3.56927 + 12.1558i) q^{28} +(-0.362435 + 0.258089i) q^{29} +(3.86186 - 1.54606i) q^{31} +(6.72245 - 7.05030i) q^{32} +(5.75572 - 0.274179i) q^{34} +(5.49438 + 8.54942i) q^{35} +(-2.15828 - 7.35043i) q^{37} +(12.0153 + 9.44890i) q^{38} +(-2.64209 - 27.6693i) q^{40} +(-2.19367 + 0.532178i) q^{41} +(0.297622 - 0.743424i) q^{43} +(7.21938 + 4.63962i) q^{44} +(10.3892 - 6.93222i) q^{46} +(-2.64028 - 1.52437i) q^{47} +(0.0143456 - 0.0112815i) q^{49} +(-20.6113 - 14.6773i) q^{50} +(-9.18893 - 12.9040i) q^{52} +(-1.12878 + 1.30268i) q^{53} +(6.60515 - 1.93945i) q^{55} +(-18.8481 + 3.63267i) q^{56} +(-1.02992 - 0.530963i) q^{58} +(10.9766 + 3.79905i) q^{59} +(2.64020 - 3.35729i) q^{61} +(8.18729 + 7.09433i) q^{62} +(6.48578 + 1.90440i) q^{64} +(-12.6500 - 1.20793i) q^{65} +(-2.17994 - 0.103843i) q^{67} +(5.29059 + 9.16356i) q^{68} +(-13.2332 + 22.9206i) q^{70} +(-8.51253 + 13.2458i) q^{71} +(1.67838 + 3.67515i) q^{73} +(14.4389 - 13.7675i) q^{74} +(-5.31205 + 27.5615i) q^{76} +(-1.76689 - 4.41347i) q^{77} +(0.836762 + 4.34153i) q^{79} +(30.0289 - 19.2984i) q^{80} +(-3.84966 - 4.44275i) q^{82} +(3.00389 - 12.3822i) q^{83} +(8.33454 + 1.60635i) q^{85} +(2.07601 - 0.198235i) q^{86} +(-1.23594 + 12.9434i) q^{88} +(-0.218032 - 1.51645i) q^{89} +8.77569i q^{91} +(20.0564 + 11.1238i) q^{92} +(0.377786 - 7.93071i) q^{94} +(13.9185 + 17.6988i) q^{95} +(9.85700 + 10.3377i) q^{97} +(0.0432332 + 0.0197440i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) \) 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Introduction

L-functions

Modular forms

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