LMFDB - Embedded newform 675.2.r.a.496.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] 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("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			496.22
Character	$\chi$	$=$	675.496
Dual form			675.2.r.a.181.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39878 - 0.297321i) q^{2} +(0.0411076 - 0.0183023i) q^{4} +(-1.76390 - 1.37429i) q^{5} +(1.92019 + 3.32586i) q^{7} +(-2.26178 + 1.64328i) q^{8} +(-2.87591 - 1.39789i) q^{10} +(5.11325 - 1.08686i) q^{11} +(3.28926 + 0.699153i) q^{13} +(3.67477 + 4.08125i) q^{14} +(-2.73539 + 3.03795i) q^{16} +(3.90998 - 2.84077i) q^{17} +(-1.90903 + 1.38699i) q^{19} +(-0.0976621 - 0.0242104i) q^{20} +(6.82920 - 3.04055i) q^{22} +(3.12041 + 3.46556i) q^{23} +(1.22265 + 4.84821i) q^{25} +4.80884 q^{26} +(0.139805 + 0.101574i) q^{28} +(-0.768054 + 7.30754i) q^{29} +(-0.0679615 - 0.646611i) q^{31} +(-0.127249 + 0.220402i) q^{32} +(4.62460 - 5.13614i) q^{34} +(1.18369 - 8.50536i) q^{35} +(0.315262 + 0.970276i) q^{37} +(-2.25794 + 2.50769i) q^{38} +(6.24790 + 0.209769i) q^{40} +(-3.66775 - 0.779604i) q^{41} +(-2.34851 - 4.06773i) q^{43} +(0.190302 - 0.138262i) q^{44} +(5.39516 + 3.91981i) q^{46} +(1.24854 - 11.8791i) q^{47} +(-3.87423 + 6.71036i) q^{49} +(3.15170 + 6.41808i) q^{50} +(0.148010 - 0.0314604i) q^{52} +(-2.92011 - 2.12158i) q^{53} +(-10.5129 - 5.10999i) q^{55} +(-9.80838 - 4.36697i) q^{56} +(1.09834 + 10.4500i) q^{58} +(-7.61268 - 1.61813i) q^{59} +(6.44432 - 1.36978i) q^{61} +(-0.287314 - 0.884263i) q^{62} +(2.41404 - 7.42965i) q^{64} +(-4.84107 - 5.75363i) q^{65} +(0.106476 + 1.01305i) q^{67} +(0.108737 - 0.188339i) q^{68} +(-0.873097 - 12.2491i) q^{70} +(2.82082 + 2.04945i) q^{71} +(-1.38140 + 4.25150i) q^{73} +(0.729467 + 1.26347i) q^{74} +(-0.0530904 + 0.0919553i) q^{76} +(13.4331 + 14.9190i) q^{77} +(-0.171432 + 1.63107i) q^{79} +(8.99997 - 1.59942i) q^{80} -5.36219 q^{82} +(-10.3261 - 4.59747i) q^{83} +(-10.8008 - 0.362630i) q^{85} +(-4.49448 - 4.99162i) q^{86} +(-9.77907 + 10.8608i) q^{88} +(0.935178 - 2.87818i) q^{89} +(3.99070 + 12.2821i) q^{91} +(0.191700 + 0.0853504i) q^{92} +(-1.78546 - 16.9875i) q^{94} +(5.27345 + 0.177052i) q^{95} +(-1.69408 + 16.1181i) q^{97} +(-3.42408 + 10.5382i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.39878	−	0.297321i	0.989090	−	0.210238i	0.315165	−	0.949037i	$-0.397940\pi$
$2$	1.39878	−	0.297321i	0.989090	−	0.210238i	0.673925	+	0.738799i	$0.264607\pi$
$3$		0			0
$3$		0			0
$4$	0.0411076	−	0.0183023i	0.0205538	−	0.00915114i
$5$	−1.76390	−	1.37429i	−0.788838	−	0.614601i
$5$	−1.76390	−	1.37429i	−0.788838	−	0.614601i
$6$		0			0
$7$	1.92019	+	3.32586i	0.725762	+	1.25706i	0.958660	+	0.284556i	$0.0918460\pi$
$7$	1.92019	+	3.32586i	0.725762	+	1.25706i	−0.232897	+	0.972501i	$0.574821\pi$
$8$	−2.26178	+	1.64328i	−0.799662	+	0.580988i
$9$		0			0
$10$	−2.87591	−	1.39789i	−0.909444	−	0.442052i
$11$	5.11325	−	1.08686i	1.54170	−	0.327699i	0.642865	−	0.765979i	$-0.277745\pi$
$11$	5.11325	−	1.08686i	1.54170	−	0.327699i	0.898839	+	0.438280i	$0.144412\pi$
$12$		0			0
$13$	3.28926	+	0.699153i	0.912276	+	0.193910i	0.640059	−	0.768326i	$-0.278910\pi$
$13$	3.28926	+	0.699153i	0.912276	+	0.193910i	0.272217	+	0.962236i	$0.412243\pi$
$14$	3.67477	+	4.08125i	0.982125	+	1.09076i
$15$		0			0
$16$	−2.73539	+	3.03795i	−0.683847	+	0.759489i
$17$	3.90998	−	2.84077i	0.948309	−	0.688987i	−0.00209712	−	0.999998i	$-0.500668\pi$
$17$	3.90998	−	2.84077i	0.948309	−	0.688987i	0.950406	+	0.311011i	$0.100668\pi$
$18$		0			0
$19$	−1.90903	+	1.38699i	−0.437961	+	0.318197i	−0.784824	−	0.619719i	$-0.787247\pi$
$19$	−1.90903	+	1.38699i	−0.437961	+	0.318197i	0.346863	+	0.937916i	$0.387247\pi$
$20$	−0.0976621	−	0.0242104i	−0.0218379	−	0.00541362i
$21$		0			0
$22$	6.82920	−	3.04055i	1.45599	−	0.648248i
$23$	3.12041	+	3.46556i	0.650650	+	0.722620i	0.974724	−	0.223412i	$-0.0717194\pi$
$23$	3.12041	+	3.46556i	0.650650	+	0.722620i	−0.324074	+	0.946032i	$0.605053\pi$
$24$		0			0
$25$	1.22265	+	4.84821i	0.244531	+	0.969641i
$26$	4.80884			0.943090
$27$		0			0
$28$	0.139805	+	0.101574i	0.0264207	+	0.0191957i
$29$	−0.768054	+	7.30754i	−0.142624	+	1.35698i	0.655824	+	0.754913i	$0.272321\pi$
$29$	−0.768054	+	7.30754i	−0.142624	+	1.35698i	−0.798448	+	0.602063i	$0.794346\pi$
$30$		0			0
$31$	−0.0679615	−	0.646611i	−0.0122062	−	0.116135i	0.986722	−	0.162417i	$-0.0519291\pi$
$31$	−0.0679615	−	0.646611i	−0.0122062	−	0.116135i	−0.998928	+	0.0462828i	$0.985262\pi$
$32$	−0.127249	+	0.220402i	−0.0224947	+	0.0389619i
$33$		0			0
$34$	4.62460	−	5.13614i	0.793112	−	0.880840i
$35$	1.18369	−	8.50536i	0.200080	−	1.43767i
$36$		0			0
$37$	0.315262	+	0.970276i	0.0518287	+	0.159512i	0.973621	−	0.228172i	$-0.0732749\pi$
$37$	0.315262	+	0.970276i	0.0518287	+	0.159512i	−0.921792	+	0.387685i	$0.873275\pi$
$38$	−2.25794	+	2.50769i	−0.366286	+	0.406801i
$39$		0			0
$40$	6.24790	+	0.209769i	0.987880	+	0.0331674i
$41$	−3.66775	−	0.779604i	−0.572806	−	0.121754i	−0.0876036	−	0.996155i	$-0.527921\pi$
$41$	−3.66775	−	0.779604i	−0.572806	−	0.121754i	−0.485203	+	0.874402i	$0.661254\pi$
$42$		0			0
$43$	−2.34851	−	4.06773i	−0.358144	−	0.620324i	0.629507	−	0.776995i	$-0.283257\pi$
$43$	−2.34851	−	4.06773i	−0.358144	−	0.620324i	−0.987651	+	0.156671i	$0.949924\pi$
$44$	0.190302	−	0.138262i	0.0286890	−	0.0208438i
$45$		0			0
$46$	5.39516	+	3.91981i	0.795473	+	0.577945i
$47$	1.24854	−	11.8791i	0.182118	−	1.73274i	−0.397281	−	0.917697i	$-0.630046\pi$
$47$	1.24854	−	11.8791i	0.182118	−	1.73274i	0.579400	−	0.815044i	$-0.303287\pi$
$48$		0			0
$49$	−3.87423	+	6.71036i	−0.553461	+	0.958623i
$50$	3.15170	+	6.41808i	0.445718	+	0.907653i
$51$		0			0
$52$	0.148010	−	0.0314604i	0.0205252	−	0.00436277i
$53$	−2.92011	−	2.12158i	−0.401108	−	0.291422i	0.368884	−	0.929475i	$-0.379740\pi$
$53$	−2.92011	−	2.12158i	−0.401108	−	0.291422i	−0.769992	+	0.638054i	$0.779740\pi$
$54$		0			0
$55$	−10.5129	−	5.10999i	−1.41756	−	0.689031i
$56$	−9.80838	−	4.36697i	−1.31070	−	0.583561i
$57$		0			0
$58$	1.09834	+	10.4500i	0.144220	+	1.37216i
$59$	−7.61268	−	1.61813i	−0.991087	−	0.210662i	−0.316288	−	0.948663i	$-0.602437\pi$
$59$	−7.61268	−	1.61813i	−0.991087	−	0.210662i	−0.674799	+	0.738001i	$0.735770\pi$
$60$		0			0
$61$	6.44432	−	1.36978i	0.825110	−	0.175383i	0.224041	−	0.974580i	$-0.428075\pi$
$61$	6.44432	−	1.36978i	0.825110	−	0.175383i	0.601069	+	0.799197i	$0.294742\pi$
$62$	−0.287314	−	0.884263i	−0.0364890	−	0.112301i
$63$		0			0
$64$	2.41404	−	7.42965i	0.301755	−	0.928707i
$65$	−4.84107	−	5.75363i	−0.600461	−	0.713650i
$66$		0			0
$67$	0.106476	+	1.01305i	0.0130081	+	0.123764i	0.999099	−	0.0424441i	$-0.0135144\pi$
$67$	0.106476	+	1.01305i	0.0130081	+	0.123764i	−0.986091	+	0.166208i	$0.946848\pi$
$68$	0.108737	−	0.188339i	0.0131863	−	0.0228394i
$69$		0			0
$70$	−0.873097	−	12.2491i	−0.104355	−	1.46405i
$71$	2.82082	+	2.04945i	0.334770	+	0.243225i	0.742452	−	0.669899i	$-0.233663\pi$
$71$	2.82082	+	2.04945i	0.334770	+	0.243225i	−0.407682	+	0.913124i	$0.633663\pi$
$72$		0			0
$73$	−1.38140	+	4.25150i	−0.161680	+	0.497601i	−0.998776	−	0.0494551i	$-0.984252\pi$
$73$	−1.38140	+	4.25150i	−0.161680	+	0.497601i	0.837096	+	0.547056i	$0.184252\pi$
$74$	0.729467	+	1.26347i	0.0847988	+	0.146876i
$75$		0			0
$76$	−0.0530904	+	0.0919553i	−0.00608989	+	0.0105480i
$77$	13.4331	+	14.9190i	1.53085	+	1.70018i
$78$		0			0
$79$	−0.171432	+	1.63107i	−0.0192877	+	0.183510i	−0.999924	−	0.0123278i	$-0.996076\pi$
$79$	−0.171432	+	1.63107i	−0.0192877	+	0.183510i	0.980636	+	0.195838i	$0.0627425\pi$
$80$	8.99997	−	1.59942i	1.00623	−	0.178821i
$81$		0			0
$82$	−5.36219			−0.592154
$83$	−10.3261	−	4.59747i	−1.13344	−	0.504638i	−0.247704	−	0.968836i	$-0.579676\pi$
$83$	−10.3261	−	4.59747i	−1.13344	−	0.504638i	−0.885731	+	0.464198i	$0.846343\pi$
$84$		0			0
$85$	−10.8008	−	0.362630i	−1.17151	−	0.0393328i
$86$	−4.49448	−	4.99162i	−0.484652	−	0.538261i
$87$		0			0
$88$	−9.77907	+	10.8608i	−1.04245	+	1.15776i
$89$	0.935178	−	2.87818i	0.0991286	−	0.305087i	−0.889179	−	0.457559i	$-0.848724\pi$
$89$	0.935178	−	2.87818i	0.0991286	−	0.305087i	0.988308	+	0.152473i	$0.0487237\pi$
$90$		0			0
$91$	3.99070	+	12.2821i	0.418339	+	1.28752i
$92$	0.191700	+	0.0853504i	0.0199861	+	0.00889839i
$93$		0			0
$94$	−1.78546	−	16.9875i	−0.184156	−	1.75212i
$95$	5.27345	+	0.177052i	0.541044	+	0.0181652i
$96$		0			0
$97$	−1.69408	+	16.1181i	−0.172008	+	1.63654i	0.479243	+	0.877682i	$0.340911\pi$
$97$	−1.69408	+	16.1181i	−0.172008	+	1.63654i	−0.651251	+	0.758862i	$0.725755\pi$
$98$	−3.42408	+	10.5382i	−0.345885	+	1.06452i
$99$		0			0
$100$	0.138994	+	0.176921i	0.0138994	+	0.0176921i
$101$	2.79104	+	4.83422i	0.277719	+	0.481023i	0.970817	−	0.239820i	$-0.0770884\pi$
$101$	2.79104	+	4.83422i	0.277719	+	0.481023i	−0.693099	+	0.720843i	$0.743755\pi$
$102$		0			0
$103$	0.569374	−	0.253501i	0.0561020	−	0.0249782i	−0.378494	−	0.925604i	$-0.623558\pi$
$103$	0.569374	−	0.253501i	0.0561020	−	0.0249782i	0.434596	+	0.900626i	$0.356891\pi$
$104$	−8.58850	+	3.82385i	−0.842172	+	0.374959i
$105$		0			0
$106$	−4.71539	−	2.09943i	−0.457999	−	0.203914i
$107$	−8.51791			−0.823458			−0.411729	−	0.911306i	$-0.635075\pi$
$107$	−8.51791			−0.823458			−0.411729	+	0.911306i	$0.635075\pi$
$108$		0			0
$109$	−3.14970	−	9.69377i	−0.301686	−	0.928495i	−0.980893	−	0.194548i	$-0.937676\pi$
$109$	−3.14970	−	9.69377i	−0.301686	−	0.928495i	0.679207	−	0.733947i	$-0.262324\pi$
$110$	−16.2246	−	4.02208i	−1.54695	−	0.383490i
$111$		0			0
$112$	−15.3563	−	3.26407i	−1.45103	−	0.308426i
$113$	−6.20262	−	1.31841i	−0.583494	−	0.124025i	−0.0932987	−	0.995638i	$-0.529741\pi$
$113$	−6.20262	−	1.31841i	−0.583494	−	0.124025i	−0.490195	+	0.871613i	$0.663074\pi$
$114$		0			0
$115$	−0.741384	−	10.4012i	−0.0691344	−	0.969920i
$116$	0.102172	+	0.314453i	0.00948642	+	0.0291962i
$117$		0			0
$118$	−11.1296			−1.02456
$119$	16.9559	+	7.54924i	1.55434	+	0.692038i
$120$		0			0
$121$	14.9151	−	6.64063i	1.35592	−	0.603694i
$122$	8.60695	−	3.83206i	0.779236	−	0.346938i
$123$		0			0
$124$	−0.0146282	−	0.0253368i	−0.00131365	−	0.00227531i
$125$	4.50621	−	10.2320i	0.403047	−	0.915179i
$126$		0			0
$127$	4.60449	−	14.1712i	0.408583	−	1.25749i	−0.509284	−	0.860599i	$-0.670090\pi$
$127$	4.60449	−	14.1712i	0.408583	−	1.25749i	0.917867	−	0.396889i	$-0.129910\pi$
$128$	1.22094	−	11.6164i	0.107917	−	1.02676i
$129$		0			0
$130$	−8.48228	−	6.60873i	−0.743946	−	0.579624i
$131$	−1.40768	−	13.3932i	−0.122989	−	1.17017i	−0.865703	−	0.500558i	$-0.833128\pi$
$131$	−1.40768	−	13.3932i	−0.122989	−	1.17017i	0.742714	−	0.669609i	$-0.233538\pi$
$132$		0			0
$133$	−8.27862	−	3.68588i	−0.717847	−	0.319606i
$134$	0.450138	+	1.38538i	0.0388860	+	0.119679i
$135$		0			0
$136$	−4.17535	+	12.8504i	−0.358033	+	1.10191i
$137$	−6.11073	+	6.78665i	−0.522075	+	0.579823i	−0.945300	−	0.326201i	$-0.894231\pi$
$137$	−6.11073	+	6.78665i	−0.522075	+	0.579823i	0.423225	+	0.906024i	$0.360898\pi$
$138$		0			0
$139$	7.85045	+	8.71881i	0.665866	+	0.739520i	0.977559	−	0.210664i	$-0.0675625\pi$
$139$	7.85045	+	8.71881i	0.665866	+	0.739520i	−0.311692	+	0.950183i	$0.600896\pi$
$140$	−0.107009	−	0.371299i	−0.00904391	−	0.0313805i
$141$		0			0
$142$	4.55506	+	2.02805i	0.382253	+	0.170190i
$143$	17.5787			1.47000
$144$		0			0
$145$	11.3974	−	11.8342i	0.946507	−	0.982778i
$146$	−0.668217	+	6.35766i	−0.0553020	+	0.526163i
$147$		0			0
$148$	0.0307179	+	0.0341157i	0.00252500	+	0.00280429i
$149$	4.73317	−	8.19809i	0.387756	−	0.671614i	−0.604391	−	0.796688i	$-0.706584\pi$
$149$	4.73317	−	8.19809i	0.387756	−	0.671614i	0.992147	+	0.125074i	$0.0399169\pi$
$150$		0			0
$151$	7.67377	+	13.2914i	0.624482	+	1.08164i	0.988641	+	0.150298i	$0.0480234\pi$
$151$	7.67377	+	13.2914i	0.624482	+	1.08164i	−0.364158	+	0.931337i	$0.618643\pi$
$152$	2.03859	−	6.27414i	0.165352	−	0.508900i
$153$		0			0
$154$	23.2258	+	16.8745i	1.87159	+	1.35979i
$155$	−0.768753	+	1.23395i	−0.0617478	+	0.0991134i
$156$		0			0
$157$	10.9037	−	18.8858i	0.870210	−	1.50725i	0.00843010	−	0.999964i	$-0.497317\pi$
$157$	10.9037	−	18.8858i	0.870210	−	1.50725i	0.861780	−	0.507283i	$-0.169350\pi$
$158$	0.245154	+	2.33249i	0.0195034	+	0.185563i
$159$		0			0
$160$	0.527351	−	0.213889i	0.0416907	−	0.0169094i
$161$	−5.53422	+	17.0326i	−0.436157	+	1.34235i
$162$		0			0
$163$	−3.56614	−	10.9754i	−0.279321	−	0.859663i	−0.988044	−	0.154175i	$-0.950728\pi$
$163$	−3.56614	−	10.9754i	−0.279321	−	0.859663i	0.708722	−	0.705488i	$-0.249272\pi$
$164$	−0.165041	+	0.0350805i	−0.0128875	+	0.00273933i
$165$		0			0
$166$	−15.8109	−	3.36071i	−1.22716	−	0.260842i
$167$	−0.441309	−	4.19878i	−0.0341495	−	0.324911i	−0.998238	−	0.0593312i	$-0.981103\pi$
$167$	−0.441309	−	4.19878i	−0.0341495	−	0.324911i	0.964089	−	0.265580i	$-0.0855635\pi$
$168$		0			0
$169$	−1.54569	−	0.688185i	−0.118899	−	0.0529373i
$170$	−15.2159	+	2.70407i	−1.16700	+	0.207393i
$171$		0			0
$172$	−0.170990	−	0.124232i	−0.0130379	−	0.00947258i
$173$	−9.65824	+	2.05292i	−0.734302	+	0.156081i	−0.559861	−	0.828587i	$-0.689145\pi$
$173$	−9.65824	+	2.05292i	−0.734302	+	0.156081i	−0.174441	+	0.984668i	$0.555812\pi$
$174$		0			0
$175$	−13.7767	+	13.3758i	−1.04142	+	1.01112i
$176$	−10.6849	+	18.5068i	−0.805405	+	1.39500i
$177$		0			0
$178$	0.452369	−	4.30400i	0.0339065	−	0.322599i
$179$	2.85965	+	2.07766i	0.213740	+	0.155292i	0.689504	−	0.724281i	$-0.257828\pi$
$179$	2.85965	+	2.07766i	0.213740	+	0.155292i	−0.475764	+	0.879573i	$0.657828\pi$
$180$		0			0
$181$	12.3513	−	8.97372i	0.918062	−	0.667011i	−0.0249788	−	0.999688i	$-0.507952\pi$
$181$	12.3513	−	8.97372i	0.918062	−	0.667011i	0.943041	+	0.332677i	$0.107952\pi$
$182$	9.23386	+	15.9935i	0.684459	+	1.18552i
$183$		0			0
$184$	−12.7526	−	2.71065i	−0.940134	−	0.199832i
$185$	0.777352	−	2.14473i	0.0571520	−	0.157683i
$186$		0			0
$187$	16.9052	−	18.7751i	1.23623	−	1.37297i
$188$	−0.166090	−	0.511171i	−0.0121133	−	0.0372810i
$189$		0			0
$190$	7.42906	−	1.32025i	0.538960	−	0.0957808i
$191$	−12.4128	+	13.7858i	−0.898157	+	0.997505i	0.101839	+	0.994801i	$0.467527\pi$
$191$	−12.4128	+	13.7858i	−0.898157	+	0.997505i	−0.999996	+	0.00270389i	$0.999139\pi$
$192$		0			0
$193$	−5.82208	+	10.0841i	−0.419082	+	0.725872i	−0.995847	−	0.0910384i	$-0.970981\pi$
$193$	−5.82208	+	10.0841i	−0.419082	+	0.725872i	0.576765	+	0.816910i	$0.304315\pi$
$194$	2.42259	+	23.0494i	0.173932	+	1.65485i
$195$		0			0
$196$	−0.0364453	+	0.346754i	−0.00260324	+	0.0247681i
$197$	−6.93084	−	5.03555i	−0.493802	−	0.358768i	0.312843	−	0.949805i	$-0.398719\pi$
$197$	−6.93084	−	5.03555i	−0.493802	−	0.358768i	−0.806645	+	0.591037i	$0.798719\pi$
$198$		0			0
$199$	17.3700			1.23133			0.615663	−	0.788010i	$-0.288888\pi$
$199$	17.3700			1.23133			0.615663	+	0.788010i	$0.288888\pi$
$200$	−10.7324	−	8.95644i	−0.758892	−	0.633316i
$201$		0			0
$202$	5.34137	+	5.93220i	0.375818	+	0.417388i
$203$	−25.7787	+	11.4774i	−1.80931	+	0.805556i
$204$		0			0
$205$	5.39813	+	6.41569i	0.377021	+	0.448091i
$206$	0.721060	−	0.523881i	0.0502386	−	0.0365005i
$207$		0			0
$208$	−11.1214	+	8.08016i	−0.771129	+	0.560258i
$209$	−8.25388	+	9.16686i	−0.570933	+	0.634085i
$210$		0			0
$211$	−3.14108	−	3.48852i	−0.216241	−	0.240160i	0.625259	−	0.780418i	$-0.284993\pi$
$211$	−3.14108	−	3.48852i	−0.216241	−	0.240160i	−0.841500	+	0.540258i	$0.818327\pi$
$212$	−0.158868	−	0.0337685i	−0.0109111	−	0.00231923i
$213$		0			0
$214$	−11.9147	+	2.53255i	−0.814474	+	0.173122i
$215$	−1.44772	+	10.4026i	−0.0987340	+	0.709450i
$216$		0			0
$217$	2.02004	−	1.46764i	0.137129	−	0.0996301i
$218$	−7.28791	−	12.6230i	−0.493599	−	0.854939i
$219$		0			0
$220$	−0.525684	−	0.0176495i	−0.0354416	−	0.00118993i
$221$	14.8471	−	6.61034i	0.998721	−	0.444659i
$222$		0			0
$223$	−15.4209	+	3.27781i	−1.03266	+	0.219499i	−0.692915	−	0.721019i	$-0.743674\pi$
$223$	−15.4209	+	3.27781i	−1.03266	+	0.219499i	−0.339745	+	0.940518i	$0.610341\pi$
$224$	−0.977368			−0.0653032
$225$		0			0
$226$	−9.06813			−0.603203
$227$	7.05368	−	1.49931i	0.468169	−	0.0995124i	0.0322143	−	0.999481i	$-0.489744\pi$
$227$	7.05368	−	1.49931i	0.468169	−	0.0995124i	0.435955	+	0.899969i	$0.356411\pi$
$228$		0			0
$229$	9.43095	−	4.19893i	0.623215	−	0.277473i	−0.0707365	−	0.997495i	$-0.522535\pi$
$229$	9.43095	−	4.19893i	0.623215	−	0.277473i	0.693951	+	0.720022i	$0.255868\pi$
$230$	−4.12954	−	14.3287i	−0.272294	−	0.944804i
$231$		0			0
$232$	−10.2712	−	17.7902i	−0.674337	−	1.16799i
$233$	10.0148	−	7.27620i	0.656094	−	0.476680i	−0.209248	−	0.977863i	$-0.567102\pi$
$233$	10.0148	−	7.27620i	0.656094	−	0.476680i	0.865341	+	0.501183i	$0.167102\pi$
$234$		0			0
$235$	−18.5276	+	19.2376i	−1.20861	+	1.25492i
$236$	−0.342555	+	0.0728122i	−0.0222984	+	0.00473967i
$237$		0			0
$238$	25.9622	+	5.51843i	1.68288	+	0.357707i
$239$	−10.7186	−	11.9042i	−0.693326	−	0.770016i	0.288973	−	0.957337i	$-0.406686\pi$
$239$	−10.7186	−	11.9042i	−0.693326	−	0.770016i	−0.982299	+	0.187321i	$0.940020\pi$
$240$		0			0
$241$	−1.95862	+	2.17526i	−0.126166	+	0.140121i	−0.802918	−	0.596090i	$-0.796720\pi$
$241$	−1.95862	+	2.17526i	−0.126166	+	0.140121i	0.676752	+	0.736211i	$0.263387\pi$
$242$	18.8886	−	13.7234i	1.21421	−	0.882173i
$243$		0			0
$244$	0.239840	−	0.174254i	0.0153542	−	0.0111555i
$245$	16.0557	−	6.51206i	1.02576	−	0.416041i
$246$		0			0
$247$	−7.24900	+	3.22746i	−0.461243	+	0.205358i
$248$	1.21628	+	1.35081i	0.0772338	+	0.0857768i
$249$		0			0
$250$	3.26102	−	15.6522i	0.206245	−	0.989930i
$251$	4.72015			0.297933			0.148967	−	0.988842i	$-0.452405\pi$
$251$	4.72015			0.297933			0.148967	+	0.988842i	$0.452405\pi$
$252$		0			0
$253$	19.7220	+	14.3289i	1.23991	+	0.900849i
$254$	2.22731	−	21.1914i	0.139754	−	1.32967i
$255$		0			0
$256$	−0.112829	−	1.07349i	−0.00705179	−	0.0670933i
$257$	10.6050	−	18.3684i	0.661523	−	1.14579i	−0.318692	−	0.947858i	$-0.603244\pi$
$257$	10.6050	−	18.3684i	0.661523	−	1.14579i	0.980215	−	0.197934i	$-0.0634230\pi$
$258$		0			0
$259$	−2.62164	+	2.91163i	−0.162901	+	0.180920i
$260$	−0.304309	−	0.147915i	−0.0188725	−	0.00917331i
$261$		0			0
$262$	−5.95111	−	18.3156i	−0.367661	−	1.13154i
$263$	4.94948	−	5.49696i	0.305198	−	0.338957i	−0.570962	−	0.820976i	$-0.693430\pi$
$263$	4.94948	−	5.49696i	0.305198	−	0.338957i	0.876161	+	0.482019i	$0.160096\pi$
$264$		0			0
$265$	2.23509	+	7.75532i	0.137301	+	0.476406i
$266$	−12.6759	−	2.69434i	−0.777209	−	0.165201i
$267$		0			0
$268$	0.0229181	+	0.0396953i	0.00139994	+	0.00242478i
$269$	−22.6424	+	16.4507i	−1.38053	+	1.00301i	−0.383700	+	0.923458i	$0.625350\pi$
$269$	−22.6424	+	16.4507i	−1.38053	+	1.00301i	−0.996830	+	0.0795565i	$0.974650\pi$
$270$		0			0
$271$	−16.6545	−	12.1002i	−1.01169	−	0.735034i	−0.0471255	−	0.998889i	$-0.515006\pi$
$271$	−16.6545	−	12.1002i	−1.01169	−	0.735034i	−0.964562	+	0.263855i	$0.915006\pi$
$272$	−2.06519	+	19.6489i	−0.125220	+	1.19139i
$273$		0			0
$274$	−6.52978	+	11.3099i	−0.394479	+	0.683257i
$275$	11.5210	+	23.4613i	0.694745	+	1.41477i
$276$		0			0
$277$	2.66279	−	0.565994i	0.159992	−	0.0340073i	−0.127219	−	0.991875i	$-0.540605\pi$
$277$	2.66279	−	0.565994i	0.159992	−	0.0340073i	0.287211	+	0.957867i	$0.407272\pi$
$278$	13.5734	+	9.86163i	0.814077	+	0.591461i
$279$		0			0
$280$	11.2995	+	21.1824i	0.675272	+	1.26589i
$281$	21.9561	+	9.77547i	1.30979	+	0.583156i	0.938474	−	0.345351i	$-0.112240\pi$
$281$	21.9561	+	9.77547i	1.30979	+	0.583156i	0.371316	+	0.928507i	$0.378907\pi$
$282$		0			0
$283$	−0.805482	−	7.66365i	−0.0478809	−	0.455557i	−0.992027	−	0.126028i	$-0.959777\pi$
$283$	−0.805482	−	7.66365i	−0.0478809	−	0.455557i	0.944146	−	0.329528i	$-0.106890\pi$
$284$	0.153467	+	0.0326204i	0.00910657	+	0.00193566i
$285$		0			0
$286$	24.5888	−	5.22651i	1.45397	−	0.309050i
$287$	−4.44991	−	13.6954i	−0.262670	−	0.808415i
$288$		0			0
$289$	1.96470	−	6.04671i	0.115570	−	0.355689i
$290$	12.4240	−	19.9422i	0.729563	−	1.17105i
$291$		0			0
$292$	0.0210263	+	0.200052i	0.00123047	+	0.0117071i
$293$	13.7967	−	23.8965i	0.806010	−	1.39605i	−0.109597	−	0.993976i	$-0.534956\pi$
$293$	13.7967	−	23.8965i	0.806010	−	1.39605i	0.915607	−	0.402074i	$-0.131711\pi$
$294$		0			0
$295$	11.2042	+	13.3162i	0.652334	+	0.775302i
$296$	−2.30749	−	1.67649i	−0.134120	−	0.0974441i
$297$		0			0
$298$	4.18322	−	12.8746i	0.242327	−	0.745807i
$299$	7.84086	+	13.5808i	0.453449	+	0.785397i
$300$		0			0
$301$	9.01914	−	15.6216i	0.519855	−	0.900415i
$302$	14.6857	+	16.3102i	0.845070	+	0.938545i
$303$		0			0
$304$	1.00832	−	9.59348i	0.0578309	−	0.550224i
$305$	−13.2496	−	6.44021i	−0.758669	−	0.368765i
$306$		0			0
$307$	−29.8034			−1.70097			−0.850485	−	0.526000i	$-0.823691\pi$
$307$	−29.8034			−1.70097			−0.850485	+	0.526000i	$0.823691\pi$
$308$	0.825255	+	0.367427i	0.0470233	+	0.0209361i
$309$		0			0
$310$	−0.708441	+	1.95460i	−0.0402367	+	0.111014i
$311$	3.70318	+	4.11280i	0.209988	+	0.233215i	0.838933	−	0.544234i	$-0.183180\pi$
$311$	3.70318	+	4.11280i	0.209988	+	0.233215i	−0.628945	+	0.777450i	$0.716513\pi$
$312$		0			0
$313$	3.83120	−	4.25498i	0.216552	−	0.240506i	−0.625075	−	0.780565i	$-0.714932\pi$
$313$	3.83120	−	4.25498i	0.216552	−	0.240506i	0.841627	+	0.540059i	$0.181598\pi$
$314$	9.63679	−	29.6590i	0.543836	−	1.67375i
$315$		0			0
$316$	0.0228051	+	0.0701870i	0.00128289	+	0.00394833i
$317$	−10.6366	−	4.73570i	−0.597409	−	0.265984i	0.0856755	−	0.996323i	$-0.472695\pi$
$317$	−10.6366	−	4.73570i	−0.597409	−	0.265984i	−0.683084	+	0.730340i	$0.739362\pi$
$318$		0			0
$319$	4.01499	+	38.2001i	0.224796	+	2.13879i
$320$	−14.4686	+	9.78754i	−0.808820	+	0.547140i
$321$		0			0
$322$	−2.67704	+	25.4703i	−0.149186	+	1.41941i
$323$	−3.52414	+	10.8462i	−0.196089	+	0.603498i
$324$		0			0
$325$	0.631986	+	16.8018i	0.0350563	+	0.931998i
$326$	−8.25148	−	14.2920i	−0.457007	−	0.791560i
$327$		0			0
$328$	9.57677	−	4.26385i	0.528789	−	0.235432i
$329$	41.9056	−	18.6576i	2.31033	−	1.02862i
$330$		0			0
$331$	−18.2816	−	8.13951i	−1.00485	−	0.447388i	−0.162725	−	0.986671i	$-0.552028\pi$
$331$	−18.2816	−	8.13951i	−1.00485	−	0.447388i	−0.842124	+	0.539284i	$0.818695\pi$
$332$	−0.508625			−0.0279144
$333$		0			0
$334$	−1.86568	−	5.74198i	−0.102086	−	0.314187i
$335$	1.20441	−	1.93324i	0.0658040	−	0.105624i
$336$		0			0
$337$	3.88794	+	0.826407i	0.211790	+	0.0450173i	0.312584	−	0.949890i	$-0.398805\pi$
$337$	3.88794	+	0.826407i	0.211790	+	0.0450173i	−0.100795	+	0.994907i	$0.532139\pi$
$338$	−2.36670	−	0.503057i	−0.128731	−	0.0273627i
$339$		0			0
$340$	−0.450633	+	0.182773i	−0.0244390	+	0.00991226i
$341$	−1.05028	−	3.23242i	−0.0568757	−	0.175045i
$342$		0			0
$343$	−2.87436			−0.155201
$344$	11.9963	+	5.34108i	0.646795	+	0.287972i
$345$		0			0
$346$	−12.8994	+	5.74319i	−0.693477	+	0.308756i
$347$	−33.5579	+	14.9409i	−1.80148	+	0.802072i	−0.832882	+	0.553451i	$0.813311\pi$
$347$	−33.5579	+	14.9409i	−1.80148	+	0.802072i	−0.968601	+	0.248620i	$0.920023\pi$
$348$		0			0
$349$	5.56763	+	9.64341i	0.298028	+	0.516200i	0.975685	−	0.219179i	$-0.0703377\pi$
$349$	5.56763	+	9.64341i	0.298028	+	0.516200i	−0.677657	+	0.735378i	$0.737004\pi$
$350$	−15.2938	+	22.8060i	−0.817486	+	1.21903i
$351$		0			0
$352$	−0.411112	+	1.26527i	−0.0219124	+	0.0674393i
$353$	−0.311118	+	2.96009i	−0.0165592	+	0.157550i	−0.999677	−	0.0254251i	$-0.991906\pi$
$353$	−0.311118	+	2.96009i	−0.0165592	+	0.157550i	0.983118	+	0.182975i	$0.0585727\pi$
$354$		0			0
$355$	−2.15910	−	7.49164i	−0.114593	−	0.397615i
$356$	−0.0142344	−	0.135431i	−0.000754420	−	0.00717783i
$357$		0			0
$358$	4.61777	+	2.05596i	0.244057	+	0.108661i
$359$	−0.714480	−	2.19894i	−0.0377088	−	0.116056i	0.930430	−	0.366469i	$-0.119433\pi$
$359$	−0.714480	−	2.19894i	−0.0377088	−	0.116056i	−0.968139	+	0.250413i	$0.919433\pi$
$360$		0			0
$361$	−4.15068	+	12.7745i	−0.218457	+	0.672341i
$362$	14.6087	−	16.2246i	0.767815	−	0.852745i
$363$		0			0
$364$	0.388839	+	0.431849i	0.0203807	+	0.0226351i
$365$	8.27944	−	5.60077i	0.433366	−	0.293158i
$366$		0			0
$367$	−15.4758	−	6.89027i	−0.807830	−	0.359669i	−0.0390939	−	0.999236i	$-0.512447\pi$
$367$	−15.4758	−	6.89027i	−0.807830	−	0.359669i	−0.768736	+	0.639567i	$0.779114\pi$
$368$	−19.0637			−0.993766
$369$		0			0
$370$	0.449676	−	3.23113i	0.0233775	−	0.167979i
$371$	1.44894	−	13.7857i	0.0752250	−	0.715718i
$372$		0			0
$373$	−16.8689	−	18.7348i	−0.873437	−	0.970050i	0.126322	−	0.991989i	$-0.459683\pi$
$373$	−16.8689	−	18.7348i	−0.873437	−	0.970050i	−0.999759	+	0.0219391i	$0.993016\pi$
$374$	18.0645	−	31.2886i	0.934094	−	1.61790i
$375$		0			0
$376$	16.6967	+	28.9196i	0.861069	+	1.49141i
$377$	−7.63542	+	23.4994i	−0.393244	+	1.21028i
$378$		0			0
$379$	19.7932	+	14.3806i	1.01671	+	0.738681i	0.965605	−	0.260012i	$-0.0837266\pi$
$379$	19.7932	+	14.3806i	1.01671	+	0.738681i	0.0511021	+	0.998693i	$0.483727\pi$
$380$	0.220019	−	0.0892379i	0.0112867	−	0.00457781i
$381$		0			0
$382$	−13.2640	+	22.9739i	−0.678645	+	1.17545i
$383$	−0.000525732	−	0.00500201i	−2.68637e−5	−	0.000255591i	0.994508	−	0.104656i	$-0.0333742\pi$
$383$	−0.000525732	−	0.00500201i	−2.68637e−5	−	0.000255591i	−0.994535	+	0.104401i	$0.966708\pi$
$384$		0			0
$385$	−3.19160	−	44.7766i	−0.162659	−	2.28203i
$386$	−5.14561	+	15.8365i	−0.261904	+	0.806059i
$387$		0			0
$388$	0.225358	+	0.693582i	0.0114408	+	0.0352113i
$389$	10.1990	−	2.16786i	0.517109	−	0.109915i	0.0580377	−	0.998314i	$-0.481516\pi$
$389$	10.1990	−	2.16786i	0.517109	−	0.109915i	0.459071	+	0.888400i	$0.348182\pi$
$390$		0			0
$391$	22.0456	+	4.68593i	1.11489	+	0.236978i
$392$	−2.26435	−	21.5439i	−0.114367	−	1.08813i
$393$		0			0
$394$	−11.1919	−	4.98297i	−0.563841	−	0.251038i
$395$	2.54395	−	2.64144i	0.128000	−	0.132905i
$396$		0			0
$397$	−4.80180	−	3.48871i	−0.240996	−	0.175094i	0.460731	−	0.887540i	$-0.347587\pi$
$397$	−4.80180	−	3.48871i	−0.240996	−	0.175094i	−0.701727	+	0.712446i	$0.747587\pi$
$398$	24.2969	−	5.16446i	1.21789	−	0.258871i
$399$		0			0
$400$	−18.0731	−	9.54735i	−0.903653	−	0.477368i
$401$	−9.95507	+	17.2427i	−0.497133	+	0.861059i	−0.999995	−	0.00330780i	$-0.998947\pi$
$401$	−9.95507	+	17.2427i	−0.497133	+	0.861059i	0.502862	+	0.864367i	$0.332280\pi$
$402$		0			0
$403$	0.228537	−	2.17438i	0.0113842	−	0.108314i
$404$	0.203210	+	0.147641i	0.0101101	+	0.00734540i
$405$		0			0
$406$	−32.6463	+	23.7190i	−1.62021	+	1.17715i
$407$	2.66656	+	4.61862i	0.132177	+	0.228937i
$408$		0			0
$409$	4.78216	+	1.01648i	0.236463	+	0.0502617i	0.324619	−	0.945845i	$-0.394764\pi$
$409$	4.78216	+	1.01648i	0.236463	+	0.0502617i	−0.0881559	+	0.996107i	$0.528097\pi$
$410$	9.45833	+	7.36920i	0.467114	+	0.363939i
$411$		0			0
$412$	0.0187659	−	0.0208417i	0.000924531	−	0.00102680i
$413$	−9.23611	−	28.4258i	−0.454479	−	1.39874i
$414$		0			0
$415$	11.8959	+	22.3005i	0.583946	+	1.09469i
$416$	−0.572650	+	0.635993i	−0.0280765	+	0.0311821i
$417$		0			0
$418$	−8.81990	+	15.2765i	−0.431395	+	0.747199i
$419$	1.33241	+	12.6770i	0.0650923	+	0.619312i	0.977632	+	0.210323i	$0.0674517\pi$
$419$	1.33241	+	12.6770i	0.0650923	+	0.619312i	−0.912540	+	0.408988i	$0.865882\pi$
$420$		0			0
$421$	1.83515	−	17.4603i	0.0894397	−	0.850962i	−0.854191	−	0.519960i	$-0.825947\pi$
$421$	1.83515	−	17.4603i	0.0894397	−	0.850962i	0.943630	−	0.331001i	$-0.107387\pi$
$422$	−5.43091	−	3.94579i	−0.264372	−	0.192078i
$423$		0			0
$424$	10.0910			0.490063
$425$	18.5532	+	15.4831i	0.899961	+	0.751041i
$426$		0			0
$427$	16.9300	+	18.8027i	0.819300	+	0.909925i
$428$	−0.350151	+	0.155897i	−0.0169252	+	0.00753558i
$429$		0			0
$430$	1.06785	+	14.9814i	0.0514964	+	0.722468i
$431$	−23.8727	+	17.3445i	−1.14991	+	0.835456i	−0.988469	−	0.151427i	$-0.951613\pi$
$431$	−23.8727	+	17.3445i	−1.14991	+	0.835456i	−0.161438	+	0.986883i	$0.551613\pi$
$432$		0			0
$433$	15.9668	−	11.6006i	0.767316	−	0.557488i	−0.133830	−	0.991004i	$-0.542727\pi$
$433$	15.9668	−	11.6006i	0.767316	−	0.557488i	0.901146	+	0.433517i	$0.142727\pi$
$434$	2.38924	−	2.65352i	0.114687	−	0.127373i
$435$		0			0
$436$	−0.306895	−	0.340841i	−0.0146976	−	0.0163233i
$437$	−10.7636	−	2.28788i	−0.514895	−	0.109444i
$438$		0			0
$439$	−12.0097	+	2.55274i	−0.573192	+	0.121836i	−0.485383	−	0.874302i	$-0.661320\pi$
$439$	−12.0097	+	2.55274i	−0.573192	+	0.121836i	−0.0878087	+	0.996137i	$0.527986\pi$
$440$	32.1751	−	5.71796i	1.53389	−	0.272593i
$441$		0			0
$442$	18.8024	−	13.6608i	0.894341	−	0.649777i
$443$	11.4062	+	19.7562i	0.541926	+	0.938643i	0.998793	+	0.0491085i	$0.0156380\pi$
$443$	11.4062	+	19.7562i	0.541926	+	0.938643i	−0.456868	+	0.889535i	$0.651029\pi$
$444$		0			0
$445$	−5.60501	+	3.79161i	−0.265703	+	0.179739i
$446$	−20.5960	+	9.16991i	−0.975247	+	0.434208i
$447$		0			0
$448$	29.3454	−	6.23756i	1.38644	−	0.294697i
$449$	4.10374			0.193668			0.0968338	−	0.995301i	$-0.469128\pi$
$449$	4.10374			0.193668			0.0968338	+	0.995301i	$0.469128\pi$
$450$		0			0
$451$	−19.6015			−0.922997
$452$	−0.279105	+	0.0593256i	−0.0131280	+	0.00279044i
$453$		0			0
$454$	9.42080	−	4.19441i	0.442140	−	0.196853i
$455$	9.84001	−	27.1487i	0.461307	−	1.27275i
$456$		0			0
$457$	9.06472	+	15.7006i	0.424030	+	0.734441i	0.996329	−	0.0856035i	$-0.0272818\pi$
$457$	9.06472	+	15.7006i	0.424030	+	0.734441i	−0.572299	+	0.820045i	$0.693948\pi$
$458$	11.9434	−	8.67742i	0.558080	−	0.405469i
$459$		0			0
$460$	−0.220843	−	0.414001i	−0.0102968	−	0.0193029i
$461$	23.0180	−	4.89262i	1.07205	−	0.227872i	0.362113	−	0.932134i	$-0.382055\pi$
$461$	23.0180	−	4.89262i	1.07205	−	0.227872i	0.709940	+	0.704262i	$0.248722\pi$
$462$		0			0
$463$	3.50086	+	0.744131i	0.162699	+	0.0345827i	0.288541	−	0.957468i	$-0.406830\pi$
$463$	3.50086	+	0.744131i	0.162699	+	0.0345827i	−0.125842	+	0.992050i	$0.540163\pi$
$464$	−20.0991	−	22.3223i	−0.933075	−	1.03629i
$465$		0			0
$466$	11.8452	−	13.1555i	0.548720	−	0.609415i
$467$	−12.8399	+	9.32877i	−0.594162	+	0.431684i	−0.843802	−	0.536655i	$-0.819688\pi$
$467$	−12.8399	+	9.32877i	−0.594162	+	0.431684i	0.249640	+	0.968339i	$0.419688\pi$
$468$		0			0
$469$	−3.16481	+	2.29937i	−0.146137	+	0.106175i
$470$	−20.1964	+	32.4179i	−0.931589	+	1.49532i
$471$		0			0
$472$	19.8773	−	8.84994i	0.914927	−	0.407352i
$473$	−16.4296	−	18.2469i	−0.755432	−	0.838992i
$474$		0			0
$475$	−9.05849	−	7.55955i	−0.415632	−	0.346856i
$476$	0.835184			0.0382806
$477$		0			0
$478$	−18.5323	−	13.4645i	−0.847648	−	0.615852i
$479$	−1.76013	+	16.7466i	−0.0804226	+	0.765170i	0.877777	+	0.479069i	$0.159026\pi$
$479$	−1.76013	+	16.7466i	−0.0804226	+	0.765170i	−0.958200	+	0.286100i	$0.907641\pi$
$480$		0			0
$481$	0.358606	+	3.41191i	0.0163510	+	0.155569i
$482$	−2.09293	+	3.62506i	−0.0953304	+	0.165117i
$483$		0			0
$484$	0.491585	−	0.545961i	0.0223448	−	0.0248164i
$485$	25.1391	−	26.1025i	1.14151	−	1.18525i
$486$		0			0
$487$	−3.07445	−	9.46219i	−0.139317	−	0.428773i	0.856920	−	0.515450i	$-0.172375\pi$
$487$	−3.07445	−	9.46219i	−0.139317	−	0.428773i	−0.996236	+	0.0866771i	$0.972375\pi$
$488$	−12.3247	+	13.6880i	−0.557914	+	0.619626i
$489$		0			0
$490$	20.5223	−	13.8827i	0.927104	−	0.627155i
$491$	11.4989	+	2.44418i	0.518940	+	0.110304i	0.459933	−	0.887953i	$-0.347873\pi$
$491$	11.4989	+	2.44418i	0.518940	+	0.110304i	0.0590068	+	0.998258i	$0.481207\pi$
$492$		0			0
$493$	17.7559	+	30.7542i	0.799688	+	1.38510i
$494$	−9.18019	+	6.66980i	−0.413036	+	0.300089i
$495$		0			0
$496$	2.15027	+	1.56227i	0.0965502	+	0.0701478i
$497$	−1.39967	+	13.3170i	−0.0627838	+	0.597348i
$498$		0			0
$499$	12.7440	−	22.0733i	0.570501	−	0.988137i	−0.426013	−	0.904717i	$-0.640082\pi$
$499$	12.7440	−	22.0733i	0.570501	−	0.988137i	0.996514	−	0.0834204i	$-0.0265844\pi$
$500$	−0.00202981	−	0.503087i	−9.07757e−5	−	0.0224987i
$501$		0			0
$502$	6.60247	−	1.40340i	0.294683	−	0.0626367i
$503$	3.86329	+	2.80684i	0.172256	+	0.125151i	0.670573	−	0.741844i	$-0.266048\pi$
$503$	3.86329	+	2.80684i	0.172256	+	0.125151i	−0.498317	+	0.866995i	$0.666048\pi$
$504$		0			0
$505$	1.72052	−	12.3628i	0.0765621	−	0.550135i
$506$	31.8471	+	14.1792i	1.41578	+	0.630344i
$507$		0			0
$508$	−0.0700851	−	0.666815i	−0.00310952	−	0.0295851i
$509$	−0.205186	−	0.0436136i	−0.00909471	−	0.00193314i	0.203362	−	0.979104i	$-0.434813\pi$
$509$	−0.205186	−	0.0436136i	−0.00909471	−	0.00193314i	−0.212457	+	0.977170i	$0.568146\pi$
$510$		0			0
$511$	−16.7924	+	3.56935i	−0.742854	+	0.157899i
$512$	6.74190	+	20.7494i	0.297953	+	0.917005i
$513$		0			0
$514$	9.37282	−	28.8466i	0.413417	−	1.27237i
$515$	−1.35270	−	0.335334i	−0.0596071	−	0.0147766i
$516$		0			0
$517$	−6.52673	−	62.0977i	−0.287045	−	2.73105i
$518$	−2.80142	+	4.85221i	−0.123088	+	0.213194i
$519$		0			0
$520$	20.4043	+	5.05822i	0.894787	+	0.221818i
$521$	10.5015	+	7.62978i	0.460079	+	0.334267i	0.793562	−	0.608489i	$-0.208224\pi$
$521$	10.5015	+	7.62978i	0.460079	+	0.334267i	−0.333484	+	0.942756i	$0.608224\pi$
$522$		0			0
$523$	11.1175	−	34.2162i	0.486136	−	1.49617i	−0.344194	−	0.938899i	$-0.611848\pi$
$523$	11.1175	−	34.2162i	0.486136	−	1.49617i	0.830329	−	0.557273i	$-0.188152\pi$
$524$	−0.302992	−	0.524797i	−0.0132363	−	0.0229259i
$525$		0			0
$526$	5.28890	−	9.16064i	0.230607	−	0.399423i
$527$	−2.10260	−	2.33517i	−0.0915906	−	0.101722i
$528$		0			0
$529$	0.130967	−	1.24606i	0.00569420	−	0.0541767i
$530$	5.43223	+	10.1835i	0.235961	+	0.442342i
$531$		0			0
$532$	−0.407774			−0.0176792
$533$	−11.5191	−	5.12864i	−0.498948	−	0.222146i
$534$		0			0
$535$	15.0247	+	11.7061i	0.649575	+	0.506098i
$536$	−1.90555	−	2.11633i	−0.0823073	−	0.0914116i
$537$		0			0
$538$	−26.7807	+	29.7430i	−1.15460	+	1.28231i
$539$	−12.5167	+	38.5225i	−0.539133	+	1.65928i
$540$		0			0
$541$	5.95413	+	18.3249i	0.255988	+	0.787850i	0.993633	+	0.112661i	$0.0359376\pi$
$541$	5.95413	+	18.3249i	0.255988	+	0.787850i	−0.737646	+	0.675188i	$0.764062\pi$
$542$	−26.8937	−	11.9738i	−1.15518	−	0.514320i
$543$		0			0
$544$	0.128569	+	1.22325i	0.00551235	+	0.0524465i
$545$	−7.76632	+	21.4274i	−0.332672	+	0.917849i
$546$		0			0
$547$	−4.57078	+	43.4881i	−0.195433	+	1.85942i	0.255435	+	0.966826i	$0.417781\pi$
$547$	−4.57078	+	43.4881i	−0.195433	+	1.85942i	−0.450868	+	0.892591i	$0.648885\pi$
$548$	−0.126986	+	0.390823i	−0.00542458	+	0.0166951i
$549$		0			0
$550$	23.0910	+	29.3918i	0.984603	+	1.25327i
$551$	−8.66924	−	15.0156i	−0.369322	−	0.639685i
$552$		0			0
$553$	−5.75389	+	2.56180i	−0.244680	+	0.108939i
$554$	3.55639	−	1.58341i	0.151097	−	0.0672726i
$555$		0			0
$556$	0.482287	+	0.214728i	0.0204535	+	0.00910650i
$557$	−42.9035			−1.81788			−0.908939	−	0.416929i	$-0.863106\pi$
$557$	−42.9035			−1.81788			−0.908939	+	0.416929i	$0.863106\pi$
$558$		0			0
$559$	−4.88088	−	15.0218i	−0.206439	−	0.635354i
$560$	22.6011	+	26.8614i	0.955069	+	1.13510i
$561$		0			0
$562$	33.6183	+	7.14578i	1.41810	+	0.301427i
$563$	15.5556	+	3.30645i	0.655591	+	0.139350i	0.523685	−	0.851912i	$-0.324557\pi$
$563$	15.5556	+	3.30645i	0.655591	+	0.139350i	0.131906	+	0.991262i	$0.457890\pi$
$564$		0			0
$565$	9.12891	+	10.8497i	0.384056	+	0.456452i
$566$	−3.40526	−	10.4803i	−0.143134	−	0.440520i
$567$		0			0
$568$	−9.74791			−0.409013
$569$	−21.5787	−	9.60744i	−0.904624	−	0.402765i	−0.0989287	−	0.995095i	$-0.531542\pi$
$569$	−21.5787	−	9.60744i	−0.904624	−	0.402765i	−0.805696	+	0.592330i	$0.798208\pi$
$570$		0			0
$571$	−1.06659	+	0.474875i	−0.0446353	+	0.0198729i	−0.428933	−	0.903336i	$-0.641110\pi$
$571$	−1.06659	+	0.474875i	−0.0446353	+	0.0198729i	0.384298	+	0.923209i	$0.374444\pi$
$572$	0.722618	−	0.321730i	0.0302142	−	0.0134522i
$573$		0			0
$574$	−10.2964	−	17.8339i	−0.429763	−	0.744372i
$575$	−12.9866	+	19.3656i	−0.541578	+	0.807600i
$576$		0			0
$577$	−10.2147	+	31.4377i	−0.425244	+	1.30877i	0.477516	+	0.878623i	$0.341537\pi$
$577$	−10.2147	+	31.4377i	−0.425244	+	1.30877i	−0.902760	+	0.430144i	$0.858463\pi$
$578$	0.950373	−	9.04219i	0.0395303	−	0.376106i
$579$		0			0
$580$	0.251929	−	0.695075i	0.0104608	−	0.0288614i
$581$	−4.53747	−	43.1711i	−0.188246	−	1.79104i
$582$		0			0
$583$	−17.2371	−	7.67445i	−0.713888	−	0.317843i
$584$	−3.86200	−	11.8860i	−0.159811	−	0.491847i
$585$		0			0
$586$	12.1936	−	37.5281i	0.503714	−	1.55027i
$587$	−2.46506	+	2.73772i	−0.101744	+	0.112998i	−0.791866	−	0.610695i	$-0.790890\pi$
$587$	−2.46506	+	2.73772i	−0.101744	+	0.112998i	0.690122	+	0.723693i	$0.257557\pi$
$588$		0			0
$589$	1.02658	+	1.14013i	0.0422996	+	0.0469784i
$590$	19.6315	+	15.2953i	0.808215	+	0.629698i
$591$		0			0
$592$	−3.81002	−	1.69633i	−0.156591	−	0.0697187i
$593$	−18.3600			−0.753956			−0.376978	−	0.926222i	$-0.623037\pi$
$593$	−18.3600			−0.753956			−0.376978	+	0.926222i	$0.623037\pi$
$594$		0			0
$595$	−19.5335	−	36.6184i	−0.800797	−	1.50121i
$596$	0.0445255	−	0.423631i	0.00182383	−	0.0173526i
$597$		0			0
$598$	15.0055	+	16.6653i	0.613622	+	0.681496i
$599$	−21.7553	+	37.6813i	−0.888897	+	1.53961i	−0.0477161	+	0.998861i	$0.515194\pi$
$599$	−21.7553	+	37.6813i	−0.888897	+	1.53961i	−0.841181	+	0.540754i	$0.818139\pi$
$600$		0			0
$601$	4.47712	+	7.75460i	0.182626	+	0.316317i	0.942774	−	0.333433i	$-0.108207\pi$
$601$	4.47712	+	7.75460i	0.182626	+	0.316317i	−0.760148	+	0.649750i	$0.774874\pi$
$602$	7.97120	−	24.5328i	0.324882	−	0.999884i
$603$		0			0
$604$	0.558712	+	0.405928i	0.0227337	+	0.0165170i
$605$	−35.4348	−	8.78430i	−1.44063	−	0.357132i
$606$		0			0
$607$	2.21210	−	3.83147i	0.0897864	−	0.155515i	−0.817634	−	0.575738i	$-0.804715\pi$
$607$	2.21210	−	3.83147i	0.0897864	−	0.155515i	0.907421	+	0.420223i	$0.138048\pi$
$608$	−0.0627731	−	0.597246i	−0.00254579	−	0.0242215i
$609$		0			0
$610$	−20.4481	−	5.06909i	−0.827920	−	0.205241i
$611$	12.4121	−	38.2004i	0.502138	−	1.54542i
$612$		0			0
$613$	−6.60377	−	20.3243i	−0.266724	−	0.820891i	−0.991291	−	0.131687i	$-0.957960\pi$
$613$	−6.60377	−	20.3243i	−0.266724	−	0.820891i	0.724568	−	0.689204i	$-0.242040\pi$
$614$	−41.6885	+	8.86117i	−1.68241	+	0.357608i
$615$		0			0
$616$	−54.8990	−	11.6691i	−2.21194	−	0.470163i
$617$	−3.36726	−	32.0374i	−0.135561	−	1.28978i	−0.824876	−	0.565314i	$-0.808755\pi$
$617$	−3.36726	−	32.0374i	−0.135561	−	1.28978i	0.689315	−	0.724462i	$-0.257912\pi$
$618$		0			0
$619$	−36.7704	−	16.3712i	−1.47793	−	0.658015i	−0.499822	−	0.866128i	$-0.666601\pi$
$619$	−36.7704	−	16.3712i	−1.47793	−	0.658015i	−0.978105	+	0.208113i	$0.933268\pi$
$620$	−0.00901746	+	0.0647948i	−0.000362150	+	0.00260222i
$621$		0			0
$622$	6.40277	+	4.65188i	0.256728	+	0.186524i
$623$	11.3681	−	2.41637i	0.455455	−	0.0968099i
$624$		0			0
$625$	−22.0102	+	11.8554i	−0.880409	+	0.474215i
$626$	4.09393	−	7.09089i	0.163626	−	0.283409i
$627$		0			0
$628$	0.102572	−	0.975910i	0.00409308	−	0.0389431i
$629$	3.98900	+	2.89817i	0.159052	+	0.115558i
$630$		0			0
$631$	−0.646758	+	0.469897i	−0.0257470	+	0.0187063i	−0.600584	−	0.799561i	$-0.705065\pi$
$631$	−0.646758	+	0.469897i	−0.0257470	+	0.0187063i	0.574837	+	0.818268i	$0.305065\pi$
$632$	−2.29257	−	3.97084i	−0.0911934	−	0.157952i
$633$		0			0
$634$	−16.2863	−	3.46176i	−0.646811	−	0.137484i
$635$	−27.5971	+	18.6686i	−1.09516	+	0.740839i
$636$		0			0
$637$	−17.4349	+	19.3634i	−0.690796	+	0.767207i
$638$	16.9738	+	52.2399i	0.671999	+	2.06820i
$639$		0			0
$640$	−18.1180	+	18.8123i	−0.716175	+	0.743620i
$641$	19.2596	−	21.3900i	0.760709	−	0.844853i	−0.231054	−	0.972941i	$-0.574217\pi$
$641$	19.2596	−	21.3900i	0.760709	−	0.844853i	0.991763	+	0.128088i	$0.0408841\pi$
$642$		0			0
$643$	24.5329	−	42.4923i	0.967484	−	1.67573i	0.264695	−	0.964332i	$-0.414729\pi$
$643$	24.5329	−	42.4923i	0.967484	−	1.67573i	0.702789	−	0.711399i	$-0.251938\pi$
$644$	0.0842365	+	0.801456i	0.00331938	+	0.0315818i
$645$		0			0
$646$	−1.70472	+	16.2193i	−0.0670712	+	0.638139i
$647$	11.9156	+	8.65721i	0.468452	+	0.340350i	0.796838	−	0.604194i	$-0.206505\pi$
$647$	11.9156	+	8.65721i	0.468452	+	0.340350i	−0.328386	+	0.944544i	$0.606505\pi$
$648$		0			0
$649$	−40.6843			−1.59700
$650$	5.87955	+	23.3142i	0.230615	+	0.914460i
$651$		0			0
$652$	−0.347471	−	0.385905i	−0.0136080	−	0.0151132i
$653$	24.4047	−	10.8657i	0.955030	−	0.425207i	0.130766	−	0.991413i	$-0.458256\pi$
$653$	24.4047	−	10.8657i	0.955030	−	0.425207i	0.824263	+	0.566207i	$0.191590\pi$
$654$		0			0
$655$	−15.9231	+	25.5587i	−0.622167	+	0.998661i
$656$	12.4011	−	9.00994i	0.484182	−	0.351779i
$657$		0			0
$658$	53.0696	−	38.5573i	2.06887	−	1.50312i
$659$	3.60401	−	4.00266i	0.140392	−	0.155922i	−0.668848	−	0.743399i	$-0.733212\pi$
$659$	3.60401	−	4.00266i	0.140392	−	0.155922i	0.809240	+	0.587478i	$0.199879\pi$
$660$		0			0
$661$	−16.2515	−	18.0492i	−0.632111	−	0.702031i	0.338965	−	0.940799i	$-0.389923\pi$
$661$	−16.2515	−	18.0492i	−0.632111	−	0.702031i	−0.971077	+	0.238768i	$0.923256\pi$
$662$	−27.9921	−	5.94991i	−1.08794	−	0.231250i
$663$		0			0
$664$	30.9103	−	6.57019i	1.19955	−	0.254973i
$665$	9.53715	+	17.8787i	0.369835	+	0.693307i
$666$		0			0
$667$	−27.7214	+	20.1408i	−1.07338	+	0.779854i
$668$	−0.0949884	−	0.164525i	−0.00367521	−	0.00636565i
$669$		0			0
$670$	1.10992	−	3.06229i	0.0428799	−	0.118306i
$671$	31.4627	−	14.0081i	1.21460	−	0.540776i
$672$		0			0
$673$	−33.3569	+	7.09023i	−1.28581	+	0.273308i	−0.799601	−	0.600532i	$-0.794955\pi$
$673$	−33.3569	+	7.09023i	−1.28581	+	0.273308i	−0.486213	+	0.873840i	$0.661622\pi$
$674$	5.68410			0.218943
$675$		0			0
$676$	−0.0761349			−0.00292826
$677$	4.88333	−	1.03798i	0.187682	−	0.0398930i	−0.113112	−	0.993582i	$-0.536082\pi$
$677$	4.88333	−	1.03798i	0.187682	−	0.0398930i	0.300794	+	0.953689i	$0.402748\pi$
$678$		0			0
$679$	−56.8595	+	25.3155i	−2.18207	+	0.971519i
$680$	25.0251	−	16.9286i	0.959667	−	0.649183i
$681$		0			0
$682$	−2.43018	−	4.20919i	−0.0930563	−	0.161178i
$683$	−6.26357	+	4.55075i	−0.239669	+	0.174130i	−0.701136	−	0.713028i	$-0.747323\pi$
$683$	−6.26357	+	4.55075i	−0.239669	+	0.174130i	0.461467	+	0.887157i	$0.347323\pi$
$684$		0			0
$685$	20.1055	−	3.57303i	0.768192	−	0.136519i
$686$	−4.02062	+	0.854608i	−0.153508	+	0.0326291i
$687$		0			0
$688$	18.7817	+	3.99217i	0.716044	+	0.152200i
$689$	−8.12167	−	9.02003i	−0.309411	−	0.343636i
$690$		0			0
$691$	21.4759	−	23.8514i	0.816983	−	0.907351i	−0.180103	−	0.983648i	$-0.557643\pi$
$691$	21.4759	−	23.8514i	0.816983	−	0.907351i	0.997085	+	0.0762967i	$0.0243096\pi$
$692$	−0.359454	+	0.261158i	−0.0136644	+	0.00992775i
$693$		0			0
$694$	−42.4980	+	30.8766i	−1.61320	+	1.17206i
$695$	−1.86520	−	26.1679i	−0.0707512	−	0.992603i
$696$		0			0
$697$	−16.5555	+	7.37098i	−0.627084	+	0.279196i
$698$	10.6551	+	11.8337i	0.403301	+	0.447911i
$699$		0			0
$700$	−0.321520	+	0.801994i	−0.0121523	+	0.0303125i
$701$	2.23365			0.0843639			0.0421819	−	0.999110i	$-0.486569\pi$
$701$	2.23365			0.0843639			0.0421819	+	0.999110i	$0.486569\pi$
$702$		0			0
$703$	−1.94761	−	1.41502i	−0.0734553	−	0.0533684i
$704$	4.26864	−	40.6134i	0.160881	−	1.53068i
$705$		0			0
$706$	0.444910	+	4.23303i	0.0167444	+	0.159312i
$707$	−10.7186	+	18.5652i	−0.403115	+	0.698216i
$708$		0			0
$709$	27.4071	−	30.4387i	1.02930	−	1.14315i	0.0397092	−	0.999211i	$-0.487357\pi$
$709$	27.4071	−	30.4387i	1.02930	−	1.14315i	0.989587	−	0.143938i	$-0.0459765\pi$
$710$	−5.24754	−	9.83724i	−0.196936	−	0.369185i
$711$		0			0
$712$	2.61449	+	8.04659i	0.0979823	+	0.301559i
$713$	2.02880	−	2.25321i	0.0759793	−	0.0843835i
$714$		0			0
$715$	−31.0070	−	24.1582i	−1.15959	−	0.903466i
$716$	0.155579	+	0.0330694i	0.00581427	+	0.00123586i
$717$		0			0
$718$	−1.65319	−	2.86342i	−0.0616967	−	0.106862i
$719$	−11.5919	+	8.42199i	−0.432304	+	0.314087i	−0.782570	−	0.622563i	$-0.786091\pi$
$719$	−11.5919	+	8.42199i	−0.432304	+	0.314087i	0.350265	+	0.936650i	$0.386091\pi$
$720$		0			0
$721$	1.93641	+	1.40689i	0.0721158	+	0.0523952i
$722$	−2.00779	+	19.1028i	−0.0747221	+	0.710934i
$723$		0			0
$724$	0.343491	−	0.594944i	0.0127657	−	0.0221109i
$725$	−36.3676	+	5.21092i	−1.35066	+	0.193529i
$726$		0			0
$727$	33.4120	−	7.10195i	1.23918	−	0.263397i	0.458710	−	0.888586i	$-0.348312\pi$
$727$	33.4120	−	7.10195i	1.23918	−	0.263397i	0.780473	+	0.625189i	$0.214978\pi$
$728$	−29.2091	−	21.2217i	−1.08256	−	0.786527i
$729$		0			0
$730$	9.91593	−	10.2959i	0.367005	−	0.381069i
$731$	−20.7381	−	9.23319i	−0.767026	−	0.341502i
$732$		0			0
$733$	4.64837	+	44.2263i	0.171691	+	1.63353i	0.653266	+	0.757129i	$0.273398\pi$
$733$	4.64837	+	44.2263i	0.171691	+	1.63353i	−0.481574	+	0.876405i	$0.659935\pi$
$734$	−23.6959	−	5.03672i	−0.874632	−	0.185909i
$735$		0			0
$736$	−1.16089	+	0.246754i	−0.0427908	+	0.00909548i
$737$	1.64548	+	5.06426i	0.0606119	+	0.186544i
$738$		0			0
$739$	−6.83528	+	21.0368i	−0.251440	+	0.773852i	0.743071	+	0.669213i	$0.233369\pi$
$739$	−6.83528	+	21.0368i	−0.251440	+	0.773852i	−0.994510	+	0.104639i	$0.966631\pi$
$740$	−0.00729833	−	0.102392i	−0.000268292	−	0.00376400i
$741$		0			0
$742$	−2.07203	−	19.7140i	−0.0760665	−	0.723724i
$743$	−5.42519	+	9.39670i	−0.199031	+	0.344732i	−0.948214	−	0.317631i	$-0.897113\pi$
$743$	−5.42519	+	9.39670i	−0.199031	+	0.344732i	0.749184	+	0.662362i	$0.230446\pi$
$744$		0			0
$745$	−19.6154	+	7.95583i	−0.718651	+	0.291479i
$746$	−29.1662	−	21.1905i	−1.06785	−	0.775838i
$747$		0			0
$748$	0.351305	−	1.08120i	0.0128450	−	0.0395328i
$749$	−16.3560	−	28.3294i	−0.597635	−	1.03513i
$750$		0			0
$751$	7.68498	−	13.3108i	0.280429	−	0.485717i	−0.691062	−	0.722796i	$-0.742857\pi$
$751$	7.68498	−	13.3108i	0.280429	−	0.485717i	0.971490	+	0.237079i	$0.0761900\pi$
$752$	32.6728	+	36.2869i	1.19146	+	1.32325i
$753$		0			0
$754$	−3.69344	+	35.1408i	−0.134507	+	1.27975i
$755$	4.73045	−	33.9905i	0.172159	−	1.23704i
$756$		0			0
$757$	−32.9738			−1.19845			−0.599226	−	0.800580i	$-0.704525\pi$
$757$	−32.9738			−1.19845			−0.599226	+	0.800580i	$0.704525\pi$
$758$	31.9620	+	14.2304i	1.16091	+	0.516872i
$759$		0			0
$760$	−12.2184	+	8.26531i	−0.443206	+	0.299814i
$761$	21.4690	+	23.8438i	0.778251	+	0.864336i	0.993688	−	0.112182i	$-0.0357840\pi$
$761$	21.4690	+	23.8438i	0.778251	+	0.864336i	−0.215436	+	0.976518i	$0.569117\pi$
$762$		0			0
$763$	26.1921	−	29.0893i	0.948219	−	1.05310i
$764$	−0.257948	+	0.793883i	−0.00933224	+	0.0287217i
$765$		0			0
$766$	−0.00222259	−	0.00684042i	−8.03054e−5	−	0.000247155i
$767$	−23.9088	−	10.6449i	−0.863295	−	0.384364i
$768$		0			0
$769$	4.43746	+	42.2196i	0.160019	+	1.52248i	0.720000	+	0.693974i	$0.244142\pi$
$769$	4.43746	+	42.2196i	0.160019	+	1.52248i	−0.559981	+	0.828505i	$0.689192\pi$
$770$	−17.7774	−	61.6838i	−0.640652	−	2.22293i
$771$		0			0
$772$	−0.0547689	+	0.521092i	−0.00197118	+	0.0187545i
$773$	−0.355723	+	1.09480i	−0.0127945	+	0.0393773i	−0.957250	−	0.289262i	$-0.906590\pi$
$773$	−0.355723	+	1.09480i	−0.0127945	+	0.0393773i	0.944455	+	0.328639i	$0.106590\pi$
$774$		0			0
$775$	3.05181	−	1.12007i	0.109624	−	0.0402342i
$776$	−22.6549	−	39.2395i	−0.813265	−	1.40862i
$777$		0			0
$778$	13.6216	−	6.06474i	0.488359	−	0.217431i
$779$	8.08313	−	3.59884i	0.289608	−	0.128942i
$780$		0			0
$781$	16.6510	+	7.41352i	0.595821	+	0.265276i
$782$	32.2302			1.15255
$783$		0			0
$784$	−9.78826	−	30.1252i	−0.349581	−	1.07590i
$785$	−45.1875	+	18.3277i	−1.61281	+	0.654142i
$786$		0			0
$787$	−10.0265	−	2.13121i	−0.357407	−	0.0759693i	0.0257087	−	0.999669i	$-0.491816\pi$
$787$	−10.0265	−	2.13121i	−0.357407	−	0.0759693i	−0.383116	+	0.923700i	$0.625149\pi$
$788$	−0.377072	−	0.0801492i	−0.0134326	−	0.00285520i
$789$		0			0
$790$	2.77309	−	4.45118i	0.0986620	−	0.158366i
$791$	−7.52535	−	23.1607i	−0.267571	−	0.823498i
$792$		0			0
$793$	22.1547			0.786737
$794$	−7.75396	−	3.45228i	−0.275178	−	0.122517i
$795$		0			0
$796$	0.714038	−	0.317910i	0.0253084	−	0.0112680i
$797$	44.1753	−	19.6681i	1.56477	−	0.696680i	0.572399	−	0.819975i	$-0.306013\pi$
$797$	44.1753	−	19.6681i	1.56477	−	0.696680i	0.992370	+	0.123295i	$0.0393461\pi$
$798$		0			0
$799$	−28.8639	−	49.9937i	−1.02113	−	1.76865i
$800$	−1.22414	−	0.347455i	−0.0432798	−	0.0122844i
$801$		0			0
$802$	−8.79839	+	27.0787i	−0.310682	+	0.956181i
$803$	−2.44266	+	23.2404i	−0.0861998	+	0.820136i
$804$		0			0
$805$	33.1695	−	22.4380i	1.16907	−	0.790837i
$806$	−0.326816	−	3.10944i	−0.0115116	−	0.109526i
$807$		0			0
$808$	−14.2567	−	6.34750i	−0.501550	−	0.223304i
$809$	4.53484	+	13.9568i	0.159436	+	0.490695i	0.998583	−	0.0532099i	$-0.0169452\pi$
$809$	4.53484	+	13.9568i	0.159436	+	0.490695i	−0.839147	+	0.543905i	$0.816945\pi$
$810$		0			0
$811$	8.81534	−	27.1308i	0.309549	−	0.952692i	−0.668392	−	0.743809i	$-0.733017\pi$
$811$	8.81534	−	27.1308i	0.309549	−	0.952692i	0.977941	−	0.208883i	$-0.0669829\pi$
$812$	−0.849636	+	0.943617i	−0.0298164	+	0.0331145i
$813$		0			0
$814$	5.10316	+	5.66764i	0.178866	+	0.198651i
$815$	−8.79314	+	24.2604i	−0.308010	+	0.849806i
$816$		0			0
$817$	10.1253	+	4.50806i	0.354238	+	0.157717i
$818$	6.99144			0.244450
$819$		0			0
$820$	0.339326	+	0.164936i	0.0118498	+	0.00575980i
$821$	−5.60308	+	53.3098i	−0.195549	+	1.86052i	0.253917	+	0.967226i	$0.418281\pi$
$821$	−5.60308	+	53.3098i	−0.195549	+	1.86052i	−0.449465	+	0.893298i	$0.648386\pi$
$822$		0			0
$823$	−1.36607	−	1.51717i	−0.0476181	−	0.0528852i	0.718865	−	0.695149i	$-0.244662\pi$
$823$	−1.36607	−	1.51717i	−0.0476181	−	0.0528852i	−0.766483	+	0.642264i	$0.777995\pi$
$824$	−0.871226	+	1.50901i	−0.0303506	+	0.0525688i
$825$		0			0
$826$	−21.3709	−	37.0155i	−0.743589	−	1.28793i
$827$	−13.2520	+	40.7853i	−0.460816	+	1.41824i	0.403354	+	0.915044i	$0.367844\pi$
$827$	−13.2520	+	40.7853i	−0.460816	+	1.41824i	−0.864170	+	0.503201i	$0.832156\pi$
$828$		0			0
$829$	30.3646	+	22.0611i	1.05460	+	0.766215i	0.973083	−	0.230456i	$-0.0740219\pi$
$829$	30.3646	+	22.0611i	1.05460	+	0.766215i	0.0815222	+	0.996672i	$0.474022\pi$
$830$	23.2702	+	27.6567i	0.807719	+	0.959978i
$831$		0			0
$832$	13.1349	−	22.7503i	0.455370	−	0.788723i
$833$	3.91441	+	37.2432i	0.135626	+	1.29040i
$834$		0			0
$835$	−4.99192	+	8.01269i	−0.172752	+	0.277291i
$836$	−0.171523	+	0.527892i	−0.00593223	+	0.0182575i
$837$		0			0
$838$	5.63288	+	17.3362i	0.194585	+	0.598870i
$839$	−0.761764	+	0.161918i	−0.0262990	+	0.00559003i	−0.221042	−	0.975264i	$-0.570946\pi$
$839$	−0.761764	+	0.161918i	−0.0262990	+	0.00559003i	0.194743	+	0.980854i	$0.437613\pi$
$840$		0			0
$841$	−24.4440	−	5.19573i	−0.842897	−	0.179163i
$842$	−2.62433	−	24.9688i	−0.0904402	−	0.860481i
$843$		0			0
$844$	−0.192970	−	0.0859159i	−0.00664231	−	0.00295735i
$845$	1.78067	+	3.33811i	0.0612568	+	0.114834i
$846$		0			0
$847$	50.7256	+	36.8543i	1.74295	+	1.26633i
$848$	14.4329	−	3.06781i	0.495627	−	0.105349i
$849$		0			0
$850$	30.5554	+	16.1413i	1.04804	+	0.553642i
$851$	−2.37881	+	4.12022i	−0.0815445	+	0.141239i
$852$		0			0
$853$	0.221478	−	2.10722i	0.00758327	−	0.0721500i	−0.990076	−	0.140535i	$-0.955118\pi$
$853$	0.221478	−	2.10722i	0.00758327	−	0.0721500i	0.997659	+	0.0683847i	$0.0217845\pi$
$854$	29.2718	+	21.2672i	1.00166	+	0.727750i
$855$		0			0
$856$	19.2657	−	13.9973i	0.658488	−	0.478419i
$857$	−2.95942	−	5.12586i	−0.101092	−	0.175096i	0.811043	−	0.584987i	$-0.198900\pi$
$857$	−2.95942	−	5.12586i	−0.101092	−	0.175096i	−0.912135	+	0.409890i	$0.865567\pi$
$858$		0			0
$859$	−30.2234	−	6.42418i	−1.03121	−	0.219190i	−0.338923	−	0.940814i	$-0.610063\pi$
$859$	−30.2234	−	6.42418i	−1.03121	−	0.219190i	−0.692285	+	0.721624i	$0.743396\pi$
$860$	0.130879	+	0.454122i	0.00446292	+	0.0154854i
$861$		0			0
$862$	−28.2359	+	31.3591i	−0.961717	+	1.06810i
$863$	−9.30552	−	28.6394i	−0.316764	−	0.974898i	−0.975022	−	0.222106i	$-0.928707\pi$
$863$	−9.30552	−	28.6394i	−0.316764	−	0.974898i	0.658259	−	0.752792i	$-0.271293\pi$
$864$		0			0
$865$	19.8574	+	9.65208i	0.675173	+	0.328180i
$866$	18.8850	−	20.9740i	0.641740	−	0.712724i
$867$		0			0
$868$	0.0561777	−	0.0973026i	0.00190679	−	0.00330266i
$869$	0.896161	+	8.52640i	0.0304002	+	0.289238i
$870$		0			0
$871$	−0.358051	+	3.40662i	−0.0121321	+	0.115429i
$872$	23.0535	+	16.7494i	0.780692	+	0.567206i
$873$		0			0
$874$	−15.7362			−0.532286
$875$	42.6830	−	4.66035i	1.44295	−	0.157549i
$876$		0			0
$877$	28.3653	+	31.5028i	0.957828	+	1.06378i	0.997913	+	0.0645791i	$0.0205705\pi$
$877$	28.3653	+	31.5028i	0.957828	+	1.06378i	−0.0400850	+	0.999196i	$0.512763\pi$
$878$	−16.0400	+	7.14147i	−0.541324	+	0.241013i
$879$		0			0
$880$	44.2808	−	17.9599i	1.49270	−	0.605428i
$881$	−0.943118	+	0.685215i	−0.0317744	+	0.0230855i	−0.603559	−	0.797318i	$-0.706251\pi$
$881$	−0.943118	+	0.685215i	−0.0317744	+	0.0230855i	0.571785	+	0.820404i	$0.306251\pi$
$882$		0			0
$883$	−13.1391	+	9.54614i	−0.442167	+	0.321253i	−0.786495	−	0.617596i	$-0.788107\pi$
$883$	−13.1391	+	9.54614i	−0.442167	+	0.321253i	0.344328	+	0.938849i	$0.388107\pi$
$884$	0.489343	−	0.543470i	0.0164584	−	0.0182789i
$885$		0			0
$886$	21.8288	+	24.2433i	0.733352	+	0.814469i
$887$	−28.4517	−	6.04760i	−0.955315	−	0.203058i	−0.296221	−	0.955119i	$-0.595727\pi$
$887$	−28.4517	−	6.04760i	−0.955315	−	0.203058i	−0.659094	+	0.752061i	$0.729060\pi$
$888$		0			0
$889$	55.9728	−	11.8974i	1.87727	−	0.399026i
$890$	−6.71288	+	6.97013i	−0.225016	+	0.233639i
$891$		0			0
$892$	−0.573925	+	0.416981i	−0.0192164	+	0.0139615i
$893$	14.0926	+	24.4092i	0.471592	+	0.816822i
$894$		0			0
$895$	−2.18882	−	7.59476i	−0.0731643	−	0.253865i
$896$	40.9791	−	18.2451i	1.36901	−	0.609525i
$897$		0			0
$898$	5.74025	−	1.22013i	0.191555	−	0.0407162i
$899$	4.77733			0.159333
$900$		0			0
$901$	−17.4445			−0.581160
$902$	−27.4182	+	5.82792i	−0.912927	+	0.194049i
$903$		0			0
$904$	16.1955	−	7.21071i	0.538655	−	0.239825i
$905$	−34.1188	−	1.14552i	−1.13415	−	0.0380782i
$906$		0			0
$907$	−2.44109	−	4.22810i	−0.0810552	−	0.140392i	0.822648	−	0.568551i	$-0.192496\pi$
$907$	−2.44109	−	4.22810i	−0.0810552	−	0.140392i	−0.903703	+	0.428159i	$0.859162\pi$
$908$	0.262519	−	0.190731i	0.00871200	−	0.00632964i
$909$		0			0
$910$	5.69216	−	40.9009i	0.188693	−	1.35585i
$911$	−49.9896	+	10.6256i	−1.65623	+	0.352042i	−0.938766	−	0.344555i	$-0.888030\pi$
$911$	−49.9896	+	10.6256i	−1.65623	+	0.352042i	−0.717462	+	0.696597i	$0.754696\pi$
$912$		0			0
$913$	−57.7967	−	12.2851i	−1.91279	−	0.406576i
$914$	17.3477	+	19.2666i	0.573811	+	0.637281i
$915$		0			0
$916$	0.310834	−	0.345216i	0.0102702	−	0.0114063i
$917$	41.8408	−	30.3991i	1.38170	−	1.00387i
$918$		0			0
$919$	−14.6917	+	10.6741i	−0.484634	+	0.352107i	−0.803117	−	0.595822i	$-0.796827\pi$
$919$	−14.6917	+	10.6741i	−0.484634	+	0.352107i	0.318483	+	0.947928i	$0.396827\pi$
$920$	18.7690	+	22.3071i	0.618796	+	0.735442i
$921$		0			0
$922$	30.7425	−	13.6874i	1.01245	−	0.450772i
$923$	7.84553	+	8.71335i	0.258239	+	0.286803i
$924$		0			0
$925$	−4.31864	+	2.71477i	−0.141996	+	0.0892610i
$926$	5.11819			0.168194
$927$		0			0
$928$	−1.51286	−	1.09916i	−0.0496622	−	0.0360817i
$929$	2.58266	−	24.5724i	0.0847343	−	0.806193i	−0.866801	−	0.498654i	$-0.833828\pi$
$929$	2.58266	−	24.5724i	0.0847343	−	0.806193i	0.951535	−	0.307539i	$-0.0995055\pi$
$930$		0			0
$931$	−1.91119	−	18.1838i	−0.0626368	−	0.595949i
$932$	0.278515	−	0.482401i	0.00912305	−	0.0158016i
$933$		0			0
$934$	−15.1867	+	16.8665i	−0.496923	+	0.551889i
$935$	−55.6215	+	9.88472i	−1.81902	+	0.323265i
$936$		0			0
$937$	−0.780220	−	2.40127i	−0.0254887	−	0.0784461i	0.937503	−	0.347977i	$-0.113131\pi$
$937$	−0.780220	−	2.40127i	−0.0254887	−	0.0784461i	−0.962992	+	0.269531i	$0.913131\pi$
$938$	−3.74323	+	4.15728i	−0.122221	+	0.135740i
$939$		0			0
$940$	−0.409533	+	1.12991i	−0.0133575	+	0.0368535i
$941$	4.08041	+	0.867319i	0.133018	+	0.0282738i	0.273939	−	0.961747i	$-0.411673\pi$
$941$	4.08041	+	0.867319i	0.133018	+	0.0282738i	−0.140922	+	0.990021i	$0.545007\pi$
$942$		0			0
$943$	−8.74311	−	15.1435i	−0.284715	−	0.493140i
$944$	25.7394	−	18.7008i	0.837747	−	0.608659i
$945$		0			0
$946$	−28.4066	−	20.6386i	−0.923577	−	0.671018i
$947$	5.72558	−	54.4752i	0.186056	−	1.77021i	−0.360475	−	0.932769i	$-0.617386\pi$
$947$	5.72558	−	54.4752i	0.186056	−	1.77021i	0.546532	−	0.837438i	$-0.315948\pi$
$948$		0			0
$949$	−7.51623	+	13.0185i	−0.243987	+	0.422598i
$950$	−14.9185	−	7.88090i	−0.484020	−	0.255690i
$951$		0			0
$952$	−50.7561	+	10.7885i	−1.64501	+	0.349659i
$953$	6.88510	+	5.00232i	0.223030	+	0.162041i	0.693690	−	0.720274i	$-0.255984\pi$
$953$	6.88510	+	5.00232i	0.223030	+	0.162041i	−0.470659	+	0.882315i	$0.655984\pi$
$954$		0			0
$955$	40.8405	−	7.25793i	1.32157	−	0.234861i
$956$	−0.658487	−	0.293177i	−0.0212970	−	0.00948204i
$957$		0			0
$958$	2.51705	+	23.9482i	0.0813223	+	0.773730i
$959$	−34.3052	−	7.29180i	−1.10777	−	0.235464i
$960$		0			0
$961$	29.9091	−	6.35737i	0.964809	−	0.205077i
$962$	1.51604	+	4.66590i	0.0488792	+	0.150435i
$963$		0			0
$964$	−0.0407017	+	0.125267i	−0.00131091	+	0.00403458i
$965$	24.1281	−	9.78613i	0.776709	−	0.315027i
$966$		0			0
$967$	4.97753	+	47.3581i	0.160067	+	1.52293i	0.719754	+	0.694229i	$0.244254\pi$
$967$	4.97753	+	47.3581i	0.160067	+	1.52293i	−0.559688	+	0.828704i	$0.689079\pi$
$968$	−22.8223	+	39.5294i	−0.733537	+	1.27052i
$969$		0			0
$970$	27.4034	−	43.9861i	0.879870	−	1.41231i
$971$	−4.89465	−	3.55617i	−0.157077	−	0.114123i	0.506471	−	0.862257i	$-0.330950\pi$
$971$	−4.89465	−	3.55617i	−0.157077	−	0.114123i	−0.663547	+	0.748134i	$0.730950\pi$
$972$		0			0
$973$	−13.9232	+	42.8512i	−0.446358	+	1.37375i
$974$	−7.11380	−	12.3215i	−0.227941	−	0.394805i
$975$		0			0
$976$	−13.4664	+	23.3244i	−0.431048	+	0.746597i
$977$	4.87939	+	5.41911i	0.156105	+	0.173373i	0.816124	−	0.577876i	$-0.196118\pi$
$977$	4.87939	+	5.41911i	0.156105	+	0.173373i	−0.660019	+	0.751249i	$0.729452\pi$
$978$		0			0
$979$	1.65363	−	15.7333i	0.0528504	−	0.502838i
$980$	0.540826	−	0.561552i	0.0172761	−	0.0179381i
$981$		0			0
$982$	16.8113			0.536469
$983$	22.0824	+	9.83170i	0.704318	+	0.313582i	0.727460	−	0.686150i	$-0.240701\pi$
$983$	22.0824	+	9.83170i	0.704318	+	0.313582i	−0.0231427	+	0.999732i	$0.507367\pi$
$984$		0			0
$985$	5.30497	+	18.4072i	0.169030	+	0.586501i
$986$	33.9806	+	37.7393i	1.08216	+	1.20186i
$987$		0			0
$988$	−0.238919	+	0.265346i	−0.00760102	+	0.00844179i
$989$	6.76869	−	20.8319i	0.215232	−	0.662415i
$990$		0			0
$991$	15.5428	+	47.8359i	0.493734	+	1.51956i	0.818920	+	0.573907i	$0.194573\pi$
$991$	15.5428	+	47.8359i	0.493734	+	1.51956i	−0.325186	+	0.945650i	$0.605427\pi$
$992$	0.151162	+	0.0673018i	0.00479941	+	0.00213683i
$993$		0			0
$994$	2.00158	+	19.0437i	0.0634862	+	0.604030i
$995$	−30.6388	−	23.8714i	−0.971316	−	0.756774i
$996$		0			0
$997$	4.05546	−	38.5851i	0.128438	−	1.22200i	−0.720479	−	0.693476i	$-0.756078\pi$
$997$	4.05546	−	38.5851i	0.128438	−	1.22200i	0.848917	−	0.528526i	$-0.177255\pi$
$998$	11.2633	−	34.6649i	0.356534	−	1.09730i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.496.22		224
3.2	odd	2		225.2.q.a.121.7	yes	224
9.2	odd	6		225.2.q.a.196.22	yes	224
9.7	even	3	inner	675.2.r.a.46.7		224
25.6	even	5	inner	675.2.r.a.631.7		224
75.56	odd	10		225.2.q.a.31.22	✓	224
225.56	odd	30		225.2.q.a.106.7	yes	224
225.106	even	15	inner	675.2.r.a.181.22		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.22	✓	224	75.56	odd	10
225.2.q.a.106.7	yes	224	225.56	odd	30
225.2.q.a.121.7	yes	224	3.2	odd	2
225.2.q.a.196.22	yes	224	9.2	odd	6
675.2.r.a.46.7		224	9.7	even	3	inner
675.2.r.a.181.22		224	225.106	even	15	inner
675.2.r.a.496.22		224	1.1	even	1	trivial
675.2.r.a.631.7		224	25.6	even	5	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39878 - 0.297321i) q^{2} +(0.0411076 - 0.0183023i) q^{4} +(-1.76390 - 1.37429i) q^{5} +(1.92019 + 3.32586i) q^{7} +(-2.26178 + 1.64328i) q^{8} +(-2.87591 - 1.39789i) q^{10} +(5.11325 - 1.08686i) q^{11} +(3.28926 + 0.699153i) q^{13} +(3.67477 + 4.08125i) q^{14} +(-2.73539 + 3.03795i) q^{16} +(3.90998 - 2.84077i) q^{17} +(-1.90903 + 1.38699i) q^{19} +(-0.0976621 - 0.0242104i) q^{20} +(6.82920 - 3.04055i) q^{22} +(3.12041 + 3.46556i) q^{23} +(1.22265 + 4.84821i) q^{25} +4.80884 q^{26} +(0.139805 + 0.101574i) q^{28} +(-0.768054 + 7.30754i) q^{29} +(-0.0679615 - 0.646611i) q^{31} +(-0.127249 + 0.220402i) q^{32} +(4.62460 - 5.13614i) q^{34} +(1.18369 - 8.50536i) q^{35} +(0.315262 + 0.970276i) q^{37} +(-2.25794 + 2.50769i) q^{38} +(6.24790 + 0.209769i) q^{40} +(-3.66775 - 0.779604i) q^{41} +(-2.34851 - 4.06773i) q^{43} +(0.190302 - 0.138262i) q^{44} +(5.39516 + 3.91981i) q^{46} +(1.24854 - 11.8791i) q^{47} +(-3.87423 + 6.71036i) q^{49} +(3.15170 + 6.41808i) q^{50} +(0.148010 - 0.0314604i) q^{52} +(-2.92011 - 2.12158i) q^{53} +(-10.5129 - 5.10999i) q^{55} +(-9.80838 - 4.36697i) q^{56} +(1.09834 + 10.4500i) q^{58} +(-7.61268 - 1.61813i) q^{59} +(6.44432 - 1.36978i) q^{61} +(-0.287314 - 0.884263i) q^{62} +(2.41404 - 7.42965i) q^{64} +(-4.84107 - 5.75363i) q^{65} +(0.106476 + 1.01305i) q^{67} +(0.108737 - 0.188339i) q^{68} +(-0.873097 - 12.2491i) q^{70} +(2.82082 + 2.04945i) q^{71} +(-1.38140 + 4.25150i) q^{73} +(0.729467 + 1.26347i) q^{74} +(-0.0530904 + 0.0919553i) q^{76} +(13.4331 + 14.9190i) q^{77} +(-0.171432 + 1.63107i) q^{79} +(8.99997 - 1.59942i) q^{80} -5.36219 q^{82} +(-10.3261 - 4.59747i) q^{83} +(-10.8008 - 0.362630i) q^{85} +(-4.49448 - 4.99162i) q^{86} +(-9.77907 + 10.8608i) q^{88} +(0.935178 - 2.87818i) q^{89} +(3.99070 + 12.2821i) q^{91} +(0.191700 + 0.0853504i) q^{92} +(-1.78546 - 16.9875i) q^{94} +(5.27345 + 0.177052i) q^{95} +(-1.69408 + 16.1181i) q^{97} +(-3.42408 + 10.5382i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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Database

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