LMFDB - Embedded newform 297.2.t.a.62.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			62.1
Character	$\chi$	$=$	297.62
Dual form			297.2.t.a.206.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14162 + 0.953512i) q^{2} +(2.33911 - 2.59784i) q^{4} +(1.18835 - 2.66909i) q^{5} +(0.273495 - 1.28669i) q^{7} +(-1.08356 + 3.33484i) q^{8} +6.84930i q^{10} +(-2.99913 - 1.41605i) q^{11} +(-5.87678 - 0.617674i) q^{13} +(0.641155 + 3.01640i) q^{14} +(-0.128435 - 1.22198i) q^{16} +(-3.07734 + 2.23582i) q^{17} +(-2.83716 - 0.921851i) q^{19} +(-4.15418 - 9.33044i) q^{20} +(7.77324 + 0.172942i) q^{22} +(-0.0733618 + 0.0423554i) q^{23} +(-2.36619 - 2.62792i) q^{25} +(13.1748 - 4.28075i) q^{26} +(-2.70289 - 3.72021i) q^{28} +(4.30718 + 0.915520i) q^{29} +(0.269516 - 2.56428i) q^{31} +(-2.06622 - 3.57881i) q^{32} +(4.45863 - 7.72257i) q^{34} +(-3.10929 - 2.25903i) q^{35} +(-2.11787 - 6.51815i) q^{37} +(6.95514 - 0.731014i) q^{38} +(7.61334 + 6.85508i) q^{40} +(4.42142 - 0.939802i) q^{41} +(-2.93163 - 1.69258i) q^{43} +(-10.6940 + 4.47897i) q^{44} +(0.116727 - 0.160661i) q^{46} +(-3.53111 + 3.17942i) q^{47} +(4.81404 + 2.14335i) q^{49} +(7.57326 + 3.37183i) q^{50} +(-15.3510 + 13.8221i) q^{52} +(2.46224 - 3.38898i) q^{53} +(-7.34360 + 6.32218i) q^{55} +(3.99457 + 2.30627i) q^{56} +(-10.0973 + 2.14625i) q^{58} +(-10.4314 - 9.39248i) q^{59} +(9.76570 - 1.02642i) q^{61} +(1.86787 + 5.74871i) q^{62} +(9.82561 + 7.13872i) q^{64} +(-8.63232 + 14.9516i) q^{65} +(1.89207 + 3.27716i) q^{67} +(-1.38993 + 13.2243i) q^{68} +(8.81295 + 1.87325i) q^{70} +(2.61027 + 3.59273i) q^{71} +(8.30569 - 2.69868i) q^{73} +(10.7508 + 11.9400i) q^{74} +(-9.03125 + 5.21419i) q^{76} +(-2.64228 + 3.47168i) q^{77} +(-2.26254 - 5.08174i) q^{79} +(-3.41421 - 1.10934i) q^{80} +(-8.57291 + 6.22858i) q^{82} +(-0.131905 - 1.25499i) q^{83} +(2.31063 + 10.8706i) q^{85} +(7.89234 + 0.829519i) q^{86} +(7.97204 - 8.46726i) q^{88} -13.6071i q^{89} +(-2.40203 + 7.39268i) q^{91} +(-0.0615683 + 0.289656i) q^{92} +(4.53068 - 10.1761i) q^{94} +(-5.83206 + 6.47716i) q^{95} +(-12.5821 + 5.60189i) q^{97} -12.3536 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−2.14162	+	0.953512i	−1.51436	+	0.674235i	−0.984745	−	0.174005i	$-0.944329\pi$
$2$	−2.14162	+	0.953512i	−1.51436	+	0.674235i	−0.529612	+	0.848240i	$0.677662\pi$
$3$		0			0
$3$		0			0
$4$	2.33911	−	2.59784i	1.16955	−	1.29892i
$5$	1.18835	−	2.66909i	0.531448	−	1.19365i	−0.425914	−	0.904764i	$-0.640047\pi$
$5$	1.18835	−	2.66909i	0.531448	−	1.19365i	0.957363	−	0.288889i	$-0.0932859\pi$
$6$		0			0
$7$	0.273495	−	1.28669i	0.103372	−	0.486325i	−0.895755	−	0.444547i	$-0.853365\pi$
$7$	0.273495	−	1.28669i	0.103372	−	0.486325i	0.999127	−	0.0417775i	$-0.0133021\pi$
$8$	−1.08356	+	3.33484i	−0.383095	+	1.17904i
$9$		0			0
$10$			6.84930i			2.16594i
$11$	−2.99913	−	1.41605i	−0.904272	−	0.426956i
$11$	−2.99913	−	1.41605i	−0.904272	−	0.426956i
$12$		0			0
$13$	−5.87678	−	0.617674i	−1.62992	−	0.171312i	−0.755052	−	0.655665i	$-0.772388\pi$
$13$	−5.87678	−	0.617674i	−1.62992	−	0.171312i	−0.874873	+	0.484353i	$0.839055\pi$
$14$	0.641155	+	3.01640i	0.171356	+	0.806166i
$15$		0			0
$16$	−0.128435	−	1.22198i	−0.0321089	−	0.305495i
$17$	−3.07734	+	2.23582i	−0.746365	+	0.542266i	−0.894698	−	0.446671i	$-0.852609\pi$
$17$	−3.07734	+	2.23582i	−0.746365	+	0.542266i	0.148333	+	0.988938i	$0.452609\pi$
$18$		0			0
$19$	−2.83716	−	0.921851i	−0.650890	−	0.211487i	−0.0350836	−	0.999384i	$-0.511170\pi$
$19$	−2.83716	−	0.921851i	−0.650890	−	0.211487i	−0.615807	+	0.787897i	$0.711170\pi$
$20$	−4.15418	−	9.33044i	−0.928902	−	2.08635i
$21$		0			0
$22$	7.77324	+	0.172942i	1.65726	+	0.0368713i
$23$	−0.0733618	+	0.0423554i	−0.0152970	+	0.00883172i	−0.507629	−	0.861576i	$-0.669478\pi$
$23$	−0.0733618	+	0.0423554i	−0.0152970	+	0.00883172i	0.492332	+	0.870407i	$0.336145\pi$
$24$		0			0
$25$	−2.36619	−	2.62792i	−0.473239	−	0.525585i
$26$	13.1748	−	4.28075i	2.58379	−	0.839525i
$27$		0			0
$28$	−2.70289	−	3.72021i	−0.510799	−	0.703054i
$29$	4.30718	+	0.915520i	0.799824	+	0.170008i	0.589653	−	0.807657i	$-0.299265\pi$
$29$	4.30718	+	0.915520i	0.799824	+	0.170008i	0.210171	+	0.977665i	$0.432598\pi$
$30$		0			0
$31$	0.269516	−	2.56428i	0.0484066	−	0.460558i	−0.943291	−	0.331967i	$-0.892288\pi$
$31$	0.269516	−	2.56428i	0.0484066	−	0.460558i	0.991698	−	0.128591i	$-0.0410455\pi$
$32$	−2.06622	−	3.57881i	−0.365260	−	0.632649i
$33$		0			0
$34$	4.45863	−	7.72257i	0.764649	−	1.32441i
$35$	−3.10929	−	2.25903i	−0.525566	−	0.381846i
$36$		0			0
$37$	−2.11787	−	6.51815i	−0.348176	−	1.07158i	−0.959861	−	0.280475i	$-0.909508\pi$
$37$	−2.11787	−	6.51815i	−0.348176	−	1.07158i	0.611685	−	0.791102i	$-0.290492\pi$
$38$	6.95514	−	0.731014i	1.12827	−	0.118586i
$39$		0			0
$40$	7.61334	+	6.85508i	1.20377	+	1.08388i
$41$	4.42142	−	0.939802i	0.690510	−	0.146772i	0.150726	−	0.988576i	$-0.451839\pi$
$41$	4.42142	−	0.939802i	0.690510	−	0.146772i	0.539785	+	0.841803i	$0.318506\pi$
$42$		0			0
$43$	−2.93163	−	1.69258i	−0.447069	−	0.258116i	0.259522	−	0.965737i	$-0.416435\pi$
$43$	−2.93163	−	1.69258i	−0.447069	−	0.258116i	−0.706592	+	0.707621i	$0.749768\pi$
$44$	−10.6940	+	4.47897i	−1.61218	+	0.675230i
$45$		0			0
$46$	0.116727	−	0.160661i	0.0172104	−	0.0236881i
$47$	−3.53111	+	3.17942i	−0.515065	+	0.463766i	−0.885199	−	0.465212i	$-0.845978\pi$
$47$	−3.53111	+	3.17942i	−0.515065	+	0.463766i	0.370135	+	0.928978i	$0.379312\pi$
$48$		0			0
$49$	4.81404	+	2.14335i	0.687719	+	0.306192i
$50$	7.57326	+	3.37183i	1.07102	+	0.476849i
$51$		0			0
$52$	−15.3510	+	13.8221i	−2.12880	+	1.91678i
$53$	2.46224	−	3.38898i	0.338215	−	0.465512i	−0.605704	−	0.795690i	$-0.707109\pi$
$53$	2.46224	−	3.38898i	0.338215	−	0.465512i	0.943919	+	0.330177i	$0.107109\pi$
$54$		0			0
$55$	−7.34360	+	6.32218i	−0.990211	+	0.852482i
$56$	3.99457	+	2.30627i	0.533797	+	0.308188i
$57$		0			0
$58$	−10.0973	+	2.14625i	−1.32584	+	0.281817i
$59$	−10.4314	−	9.39248i	−1.35805	−	1.22280i	−0.950923	−	0.309428i	$-0.899863\pi$
$59$	−10.4314	−	9.39248i	−1.35805	−	1.22280i	−0.407131	−	0.913370i	$-0.633471\pi$
$60$		0			0
$61$	9.76570	−	1.02642i	1.25037	−	0.131419i	0.543893	−	0.839155i	$-0.316950\pi$
$61$	9.76570	−	1.02642i	1.25037	−	0.131419i	0.706478	+	0.707735i	$0.250283\pi$
$62$	1.86787	+	5.74871i	0.237219	+	0.730086i
$63$		0			0
$64$	9.82561	+	7.13872i	1.22820	+	0.892340i
$65$	−8.63232	+	14.9516i	−1.07071	+	1.85452i
$66$		0			0
$67$	1.89207	+	3.27716i	0.231153	+	0.400369i	0.958148	−	0.286274i	$-0.0924168\pi$
$67$	1.89207	+	3.27716i	0.231153	+	0.400369i	−0.726995	+	0.686643i	$0.759083\pi$
$68$	−1.38993	+	13.2243i	−0.168553	+	1.60368i
$69$		0			0
$70$	8.81295	+	1.87325i	1.05335	+	0.223896i
$71$	2.61027	+	3.59273i	0.309782	+	0.426379i	0.935313	−	0.353821i	$-0.115118\pi$
$71$	2.61027	+	3.59273i	0.309782	+	0.426379i	−0.625531	+	0.780199i	$0.715118\pi$
$72$		0			0
$73$	8.30569	−	2.69868i	0.972108	−	0.315857i	0.220441	−	0.975400i	$-0.429250\pi$
$73$	8.30569	−	2.69868i	0.972108	−	0.315857i	0.751667	+	0.659543i	$0.229250\pi$
$74$	10.7508	+	11.9400i	1.24976	+	1.38800i
$75$		0			0
$76$	−9.03125	+	5.21419i	−1.03596	+	0.598109i
$77$	−2.64228	+	3.47168i	−0.301115	+	0.395635i
$78$		0			0
$79$	−2.26254	−	5.08174i	−0.254555	−	0.571740i	0.740388	−	0.672180i	$-0.234642\pi$
$79$	−2.26254	−	5.08174i	−0.254555	−	0.571740i	−0.994943	+	0.100439i	$0.967975\pi$
$80$	−3.41421	−	1.10934i	−0.381720	−	0.124028i
$81$		0			0
$82$	−8.57291	+	6.22858i	−0.946719	+	0.687832i
$83$	−0.131905	−	1.25499i	−0.0144784	−	0.137753i	0.984895	−	0.173154i	$-0.0553958\pi$
$83$	−0.131905	−	1.25499i	−0.0144784	−	0.137753i	−0.999373	+	0.0354010i	$0.988729\pi$
$84$		0			0
$85$	2.31063	+	10.8706i	0.250623	+	1.17909i
$86$	7.89234	+	0.829519i	0.851053	+	0.0894493i
$87$		0			0
$88$	7.97204	−	8.46726i	0.849822	−	0.902613i
$89$		−	13.6071i		−	1.44234i	−0.692756	−	0.721172i	$-0.743604\pi$
$89$		−	13.6071i		−	1.44234i	0.692756	−	0.721172i	$-0.256396\pi$
$90$		0			0
$91$	−2.40203	+	7.39268i	−0.251801	+	0.774964i
$92$	−0.0615683	+	0.289656i	−0.00641894	+	0.0301987i
$93$		0			0
$94$	4.53068	−	10.1761i	0.467304	−	1.04958i
$95$	−5.83206	+	6.47716i	−0.598357	+	0.664542i
$96$		0			0
$97$	−12.5821	+	5.60189i	−1.27751	+	0.568786i	−0.929541	−	0.368718i	$-0.879797\pi$
$97$	−12.5821	+	5.60189i	−1.27751	+	0.568786i	−0.347973	+	0.937504i	$0.613130\pi$
$98$	−12.3536			−1.24790
$99$		0			0
$100$	−12.3617			−1.23617
$101$	11.4215	−	5.08518i	1.13648	−	0.505994i	0.249765	−	0.968307i	$-0.419647\pi$
$101$	11.4215	−	5.08518i	1.13648	−	0.505994i	0.886717	+	0.462312i	$0.152980\pi$
$102$		0			0
$103$	4.00544	−	4.44849i	0.394668	−	0.438323i	−0.512759	−	0.858532i	$-0.671377\pi$
$103$	4.00544	−	4.44849i	0.394668	−	0.438323i	0.907427	+	0.420209i	$0.138043\pi$
$104$	8.42766	−	18.9288i	0.826400	−	1.85612i
$105$		0			0
$106$	−2.04175	+	9.60570i	−0.198313	+	0.932988i
$107$	−0.951472	+	2.92833i	−0.0919823	+	0.283092i	−0.986455	−	0.164029i	$-0.947551\pi$
$107$	−0.951472	+	2.92833i	−0.0919823	+	0.283092i	0.894473	+	0.447122i	$0.147551\pi$
$108$		0			0
$109$		−	9.98777i		−	0.956655i	−0.878181	−	0.478328i	$-0.841243\pi$
$109$		−	9.98777i		−	0.956655i	0.878181	−	0.478328i	$-0.158757\pi$
$110$	9.69896	−	20.5419i	0.924760	−	1.95860i
$111$		0			0
$112$	−1.60744	−	0.168949i	−0.151889	−	0.0159642i
$113$	−0.980147	−	4.61123i	−0.0922045	−	0.433788i	−0.999900	−	0.0141581i	$-0.995493\pi$
$113$	−0.980147	−	4.61123i	−0.0922045	−	0.433788i	0.907695	−	0.419630i	$-0.137840\pi$
$114$		0			0
$115$	0.0258706	+	0.246142i	0.00241245	+	0.0229529i
$116$	12.4533	−	9.04787i	1.15626	−	0.840074i
$117$		0			0
$118$	31.2960	+	10.1687i	2.88103	+	0.936104i
$119$	2.03518	+	4.57109i	0.186565	+	0.419031i
$120$		0			0
$121$	6.98959	+	8.49386i	0.635417	+	0.772169i
$122$	−19.9358	+	11.5099i	−1.80490	+	1.04206i
$123$		0			0
$124$	−6.03116	−	6.69828i	−0.541614	−	0.601523i
$125$	4.06738	−	1.32157i	0.363797	−	0.118205i
$126$		0			0
$127$	−1.75209	−	2.41154i	−0.155473	−	0.213990i	0.724174	−	0.689617i	$-0.242221\pi$
$127$	−1.75209	−	2.41154i	−0.155473	−	0.213990i	−0.879647	+	0.475627i	$0.842221\pi$
$128$	−19.7653	−	4.20125i	−1.74703	−	0.371342i
$129$		0			0
$130$	4.23063	−	40.2518i	0.371051	−	3.53031i
$131$	−3.89251	−	6.74202i	−0.340090	−	0.589053i	0.644359	−	0.764723i	$-0.277124\pi$
$131$	−3.89251	−	6.74202i	−0.340090	−	0.589053i	−0.984449	+	0.175670i	$0.943791\pi$
$132$		0			0
$133$	−1.96209	+	3.39844i	−0.170135	+	0.294682i
$134$	−7.17692	−	5.21434i	−0.619991	−	0.450450i
$135$		0			0
$136$	−4.12163	−	12.6851i	−0.353427	−	1.08774i
$137$	6.24749	−	0.656638i	0.533759	−	0.0561004i	0.166185	−	0.986095i	$-0.446855\pi$
$137$	6.24749	−	0.656638i	0.533759	−	0.0561004i	0.367574	+	0.929994i	$0.380188\pi$
$138$		0			0
$139$	−0.389804	−	0.350981i	−0.0330628	−	0.0297699i	0.652434	−	0.757846i	$-0.273748\pi$
$139$	−0.389804	−	0.350981i	−0.0330628	−	0.0297699i	−0.685496	+	0.728076i	$0.740415\pi$
$140$	−13.1416	+	2.79333i	−1.11067	+	0.236079i
$141$		0			0
$142$	−9.01593	−	5.20535i	−0.756600	−	0.436823i
$143$	16.7506	+	10.1743i	1.40075	+	0.850819i
$144$		0			0
$145$	7.56206	−	10.4083i	0.627995	−	0.864361i
$146$	−15.2144	+	13.6991i	−1.25916	+	1.13375i
$147$		0			0
$148$	−21.8870	−	9.74474i	−1.79910	−	0.801013i
$149$	8.78506	+	3.91136i	0.719700	+	0.320431i	0.733703	−	0.679471i	$-0.237791\pi$
$149$	8.78506	+	3.91136i	0.719700	+	0.320431i	−0.0140024	+	0.999902i	$0.504457\pi$
$150$		0			0
$151$	7.43581	−	6.69523i	0.605118	−	0.544850i	−0.308604	−	0.951191i	$-0.599862\pi$
$151$	7.43581	−	6.69523i	0.605118	−	0.544850i	0.913722	+	0.406340i	$0.133195\pi$
$152$	6.14845	−	8.46262i	0.498705	−	0.686409i
$153$		0			0
$154$	2.34847	−	9.95448i	0.189245	−	0.802155i
$155$	−6.52400	−	3.76663i	−0.524021	−	0.302543i
$156$		0			0
$157$	−3.20990	+	0.682286i	−0.256178	+	0.0544524i	−0.334210	−	0.942498i	$-0.608470\pi$
$157$	−3.20990	+	0.682286i	−0.256178	+	0.0544524i	0.0780322	+	0.996951i	$0.475136\pi$
$158$	9.69100	+	8.72582i	0.770975	+	0.694189i
$159$		0			0
$160$	−12.0076	+	1.26205i	−0.949281	+	0.0997734i
$161$	0.0344344	+	0.105978i	0.00271381	+	0.00835225i
$162$		0			0
$163$	−7.00394	−	5.08866i	−0.548591	−	0.398575i	0.278675	−	0.960386i	$-0.410105\pi$
$163$	−7.00394	−	5.08866i	−0.548591	−	0.398575i	−0.827266	+	0.561811i	$0.810105\pi$
$164$	7.90072	−	13.6844i	0.616942	−	1.06858i
$165$		0			0
$166$	1.47914	+	2.56194i	0.114803	+	0.198845i
$167$	−2.07396	+	19.7324i	−0.160488	+	1.52694i	0.557084	+	0.830456i	$0.311920\pi$
$167$	−2.07396	+	19.7324i	−0.160488	+	1.52694i	−0.717572	+	0.696484i	$0.754747\pi$
$168$		0			0
$169$	21.4391	+	4.55701i	1.64916	+	0.350540i
$170$	−15.3138	−	21.0776i	−1.17451	−	1.61658i
$171$		0			0
$172$	−11.2544	+	3.65679i	−0.858143	+	0.278828i
$173$	−4.67277	−	5.18963i	−0.355264	−	0.394561i	0.538849	−	0.842402i	$-0.318859\pi$
$173$	−4.67277	−	5.18963i	−0.355264	−	0.394561i	−0.894113	+	0.447842i	$0.852193\pi$
$174$		0			0
$175$	−4.02848	+	2.32584i	−0.304524	+	0.175817i
$176$	−1.34520	+	3.84676i	−0.101398	+	0.289960i
$177$		0			0
$178$	12.9745	+	29.1412i	0.972479	+	2.18422i
$179$	14.8154	+	4.81380i	1.10735	+	0.359800i	0.804928	−	0.593373i	$-0.202204\pi$
$179$	14.8154	+	4.81380i	1.10735	+	0.359800i	0.302424	+	0.953173i	$0.402204\pi$
$180$		0			0
$181$	−13.0927	+	9.51241i	−0.973173	+	0.707052i	−0.956173	−	0.292804i	$-0.905412\pi$
$181$	−13.0927	+	9.51241i	−0.973173	+	0.707052i	−0.0170005	+	0.999855i	$0.505412\pi$
$182$	−1.90477	−	18.1227i	−0.141191	−	1.34334i
$183$		0			0
$184$	−0.0617571	−	0.290544i	−0.00455279	−	0.0214192i
$185$	−19.9143	−	2.09308i	−1.46413	−	0.153886i
$186$		0			0
$187$	12.3954	−	2.34784i	0.906441	−	0.171691i
$188$			16.6103i			1.21143i
$189$		0			0
$190$	6.31403	−	19.4326i	0.458068	−	1.40979i
$191$	−3.06051	+	14.3986i	−0.221451	+	1.04184i	0.717171	+	0.696897i	$0.245436\pi$
$191$	−3.06051	+	14.3986i	−0.221451	+	1.04184i	−0.938622	+	0.344947i	$0.887897\pi$
$192$		0			0
$193$	2.78690	−	6.25948i	0.200606	−	0.450567i	−0.785029	−	0.619459i	$-0.787352\pi$
$193$	2.78690	−	6.25948i	0.200606	−	0.450567i	0.985635	+	0.168891i	$0.0540187\pi$
$194$	21.6046	−	23.9943i	1.55112	−	1.72269i
$195$		0			0
$196$	16.8286	−	7.49258i	1.20204	−	0.535184i
$197$	−8.81639			−0.628141			−0.314071	−	0.949400i	$-0.601693\pi$
$197$	−8.81639			−0.628141			−0.314071	+	0.949400i	$0.601693\pi$
$198$		0			0
$199$	8.40540			0.595843			0.297921	−	0.954590i	$-0.403707\pi$
$199$	8.40540			0.595843			0.297921	+	0.954590i	$0.403707\pi$
$200$	11.3276	−	5.04338i	0.800983	−	0.356621i
$201$		0			0
$202$	−19.6118	+	21.7811i	−1.37988	+	1.53251i
$203$	2.35599	−	5.29164i	0.165358	−	0.371400i
$204$		0			0
$205$	2.74580	−	12.9180i	0.191775	−	0.902231i
$206$	−4.33646	+	13.3462i	−0.302135	+	0.929877i
$207$		0			0
$208$			7.26065i			0.503435i
$209$	7.20364	+	6.78233i	0.498286	+	0.469143i
$210$		0			0
$211$	−17.3243	−	1.82086i	−1.19265	−	0.125353i	−0.512674	−	0.858583i	$-0.671345\pi$
$211$	−17.3243	−	1.82086i	−1.19265	−	0.125353i	−0.679980	+	0.733230i	$0.738012\pi$
$212$	−3.04459	−	14.3237i	−0.209104	−	0.983755i
$213$		0			0
$214$	−0.754504	−	7.17862i	−0.0515768	−	0.490721i
$215$	−8.00146	+	5.81340i	−0.545695	+	0.396471i
$216$		0			0
$217$	−3.22573	−	1.04810i	−0.218977	−	0.0711499i
$218$	9.52347	+	21.3901i	0.645011	+	1.44872i
$219$		0			0
$220$	−0.753457	+	33.8658i	−0.0507981	+	2.28323i
$221$	19.4659	−	11.2386i	1.30942	−	0.755992i
$222$		0			0
$223$	11.4680	+	12.7365i	0.767953	+	0.852899i	0.992586	−	0.121545i	$-0.0387848\pi$
$223$	11.4680	+	12.7365i	0.767953	+	0.852899i	−0.224633	+	0.974444i	$0.572118\pi$
$224$	−5.16993	+	1.67981i	−0.345431	+	0.112237i
$225$		0			0
$226$	6.49597	+	8.94094i	0.432106	+	0.594742i
$227$	−16.9143	−	3.59525i	−1.12264	−	0.238625i	−0.391051	−	0.920369i	$-0.627888\pi$
$227$	−16.9143	−	3.59525i	−1.12264	−	0.238625i	−0.731591	+	0.681744i	$0.761222\pi$
$228$		0			0
$229$	−1.65196	+	15.7173i	−0.109164	+	1.03863i	0.793584	+	0.608461i	$0.208213\pi$
$229$	−1.65196	+	15.7173i	−0.109164	+	1.03863i	−0.902748	+	0.430169i	$0.858454\pi$
$230$	−0.290105	−	0.502476i	−0.0191290	−	0.0331323i
$231$		0			0
$232$	−7.72018	+	13.3718i	−0.506855	+	0.877898i
$233$	2.75423	+	2.00107i	0.180436	+	0.131094i	0.674337	−	0.738424i	$-0.264430\pi$
$233$	2.75423	+	2.00107i	0.180436	+	0.131094i	−0.493901	+	0.869518i	$0.664430\pi$
$234$		0			0
$235$	4.28995	+	13.2031i	0.279846	+	0.861276i
$236$	−48.8004	+	5.12912i	−3.17663	+	0.333878i
$237$		0			0
$238$	−8.71717	−	7.84898i	−0.565051	−	0.508774i
$239$	5.67923	−	1.20716i	0.367359	−	0.0780845i	−0.0205337	−	0.999789i	$-0.506537\pi$
$239$	5.67923	−	1.20716i	0.367359	−	0.0780845i	0.387892	+	0.921705i	$0.373203\pi$
$240$		0			0
$241$	−2.60691	−	1.50510i	−0.167926	−	0.0969521i	0.413681	−	0.910422i	$-0.364243\pi$
$241$	−2.60691	−	1.50510i	−0.167926	−	0.0969521i	−0.581608	+	0.813470i	$0.697576\pi$
$242$	−23.0681	−	11.5260i	−1.48287	−	0.740918i
$243$		0			0
$244$	20.1765	−	27.7706i	1.29167	−	1.77783i
$245$	11.4416	−	10.3020i	0.730975	−	0.658173i
$246$		0			0
$247$	16.1040	+	7.16995i	1.02467	+	0.456213i
$248$	8.25942	+	3.67733i	0.524474	+	0.233511i
$249$		0			0
$250$	−7.45066	+	6.70860i	−0.471221	+	0.424289i
$251$	−9.41803	+	12.9628i	−0.594461	+	0.818205i	−0.995187	−	0.0979925i	$-0.968758\pi$
$251$	−9.41803	+	12.9628i	−0.594461	+	0.818205i	0.400726	+	0.916198i	$0.368758\pi$
$252$		0			0
$253$	0.279999	−	0.0231455i	0.0176034	−	0.00145514i
$254$	6.05175	+	3.49398i	0.379721	+	0.219232i
$255$		0			0
$256$	22.5764	−	4.79876i	1.41103	−	0.299923i
$257$	9.24660	+	8.32568i	0.576787	+	0.519341i	0.905084	−	0.425233i	$-0.139808\pi$
$257$	9.24660	+	8.32568i	0.576787	+	0.519341i	−0.328297	+	0.944575i	$0.606475\pi$
$258$		0			0
$259$	−8.96609	+	0.942374i	−0.557126	+	0.0585563i
$260$	18.6500	+	57.3988i	1.15662	+	3.55972i
$261$		0			0
$262$	14.7649	+	10.7273i	0.912178	+	0.662736i
$263$	7.64365	−	13.2392i	0.471328	−	0.816363i	−0.528134	−	0.849161i	$-0.677108\pi$
$263$	7.64365	−	13.2392i	0.471328	−	0.816363i	0.999462	+	0.0327974i	$0.0104416\pi$
$264$		0			0
$265$	−6.11948	−	10.5992i	−0.375917	−	0.651107i
$266$	0.961605	−	9.14906i	0.0589598	−	0.560965i
$267$		0			0
$268$	12.9393	+	2.75033i	0.790393	+	0.168003i
$269$	−1.18129	−	1.62591i	−0.0720247	−	0.0991335i	0.771485	−	0.636248i	$-0.219514\pi$
$269$	−1.18129	−	1.62591i	−0.0720247	−	0.0991335i	−0.843509	+	0.537114i	$0.819514\pi$
$270$		0			0
$271$	−20.2438	+	6.57759i	−1.22972	+	0.399560i	−0.850613	−	0.525792i	$-0.823769\pi$
$271$	−20.2438	+	6.57759i	−1.22972	+	0.399560i	−0.379107	+	0.925353i	$0.623769\pi$
$272$	3.12737	+	3.47330i	0.189625	+	0.210600i
$273$		0			0
$274$	−12.7537	+	7.36333i	−0.770477	+	0.444835i
$275$	3.37525	+	11.2321i	0.203535	+	0.677324i
$276$		0			0
$277$	10.0411	+	22.5527i	0.603311	+	1.35506i	0.914451	+	0.404696i	$0.132623\pi$
$277$	10.0411	+	22.5527i	0.603311	+	1.35506i	−0.311140	+	0.950364i	$0.600711\pi$
$278$	1.16948	+	0.379987i	0.0701407	+	0.0227901i
$279$		0			0
$280$	10.9026	−	7.92121i	0.651555	−	0.473383i
$281$	−1.36140	−	12.9528i	−0.0812140	−	0.772700i	−0.957017	−	0.290031i	$-0.906334\pi$
$281$	−1.36140	−	12.9528i	−0.0812140	−	0.772700i	0.875803	−	0.482669i	$-0.160332\pi$
$282$		0			0
$283$	−4.11013	−	19.3366i	−0.244322	−	1.14944i	−0.913658	−	0.406484i	$-0.866755\pi$
$283$	−4.11013	−	19.3366i	−0.244322	−	1.14944i	0.669336	−	0.742960i	$-0.266579\pi$
$284$	15.4390	+	1.62271i	0.916138	+	0.0962900i
$285$		0			0
$286$	−45.5748	−	5.81767i	−2.69489	−	0.344006i
$287$		−	5.94605i		−	0.350984i
$288$		0			0
$289$	−0.782142	+	2.40719i	−0.0460084	+	0.141599i
$290$	−6.27066	+	29.5012i	−0.368226	+	1.73237i
$291$		0			0
$292$	12.4171	−	27.8894i	0.726659	−	1.63210i
$293$	2.96594	−	3.29401i	0.173272	−	0.192438i	−0.650254	−	0.759717i	$-0.725337\pi$
$293$	2.96594	−	3.29401i	0.173272	−	0.192438i	0.823525	+	0.567279i	$0.192004\pi$
$294$		0			0
$295$	−37.4656	+	16.6808i	−2.18133	+	0.971191i
$296$	24.0318			1.39682
$297$		0			0
$298$	−22.5438			−1.30593
$299$	0.457293	−	0.203600i	0.0264459	−	0.0117745i
$300$		0			0
$301$	−2.97962	+	3.30920i	−0.171742	+	0.190739i
$302$	−9.54072	+	21.4288i	−0.549007	+	1.23309i
$303$		0			0
$304$	−0.762092	+	3.58536i	−0.0437090	+	0.205635i
$305$	8.86552	−	27.2853i	0.507638	−	1.56235i
$306$		0			0
$307$			11.0942i			0.633182i	0.948562	+	0.316591i	$0.102538\pi$
$307$			11.0942i			0.633182i	−0.948562	+	0.316591i	$0.897462\pi$
$308$	2.83832	+	14.9848i	0.161728	+	0.853841i
$309$		0			0
$310$	17.5635	+	1.84600i	0.997539	+	0.104846i
$311$	−1.63132	−	7.67477i	−0.0925038	−	0.435196i	−0.999889	−	0.0148963i	$-0.995258\pi$
$311$	−1.63132	−	7.67477i	−0.0925038	−	0.435196i	0.907385	−	0.420300i	$-0.138075\pi$
$312$		0			0
$313$	−3.38103	−	32.1683i	−0.191107	−	1.81826i	−0.498734	−	0.866755i	$-0.666202\pi$
$313$	−3.38103	−	32.1683i	−0.191107	−	1.81826i	0.307627	−	0.951507i	$-0.400465\pi$
$314$	6.22384	−	4.52188i	0.351232	−	0.255185i
$315$		0			0
$316$	−18.4939	−	6.00902i	−1.04036	−	0.338034i
$317$	−4.89317	−	10.9902i	−0.274828	−	0.617273i	0.722417	−	0.691458i	$-0.243031\pi$
$317$	−4.89317	−	10.9902i	−0.274828	−	0.617273i	−0.997245	+	0.0741845i	$0.976365\pi$
$318$		0			0
$319$	−11.6214	−	8.84496i	−0.650673	−	0.495223i
$320$	30.7302	−	17.7421i	1.71787	−	0.991813i
$321$		0			0
$322$	−0.174797	−	0.194132i	−0.00974106	−	0.0108185i
$323$	10.7920	−	3.50654i	0.600484	−	0.195109i
$324$		0			0
$325$	12.2824	+	16.9053i	0.681305	+	0.937735i
$326$	19.8519	+	4.21966i	1.09950	+	0.233705i
$327$		0			0
$328$	−1.65677	+	15.7631i	−0.0914796	+	0.870370i
$329$	3.12520	+	5.41301i	0.172298	+	0.298429i
$330$		0			0
$331$	15.0373	−	26.0453i	0.826524	−	1.43158i	−0.0742249	−	0.997242i	$-0.523648\pi$
$331$	15.0373	−	26.0453i	0.826524	−	1.43158i	0.900749	−	0.434340i	$-0.143018\pi$
$332$	−3.56880	−	2.59289i	−0.195863	−	0.142303i
$333$		0			0
$334$	−14.3735	−	44.2370i	−0.786481	−	2.42054i
$335$	10.9955	−	1.15567i	0.600748	−	0.0631411i
$336$		0			0
$337$	16.3466	+	14.7186i	0.890459	+	0.801772i	0.980977	−	0.194122i	$-0.0621859\pi$
$337$	16.3466	+	14.7186i	0.890459	+	0.801772i	−0.0905188	+	0.995895i	$0.528853\pi$
$338$	−50.2596	+	10.6830i	−2.73376	+	0.581079i
$339$		0			0
$340$	33.6450	+	19.4250i	1.82466	+	1.05347i
$341$	−4.43947	+	7.30896i	−0.240411	+	0.395802i
$342$		0			0
$343$	9.48682	−	13.0575i	0.512240	−	0.705038i
$344$	8.82106	−	7.94252i	0.475600	−	0.428232i
$345$		0			0
$346$	14.9557	+	6.65870i	0.804023	+	0.357974i
$347$	13.8520	+	6.16730i	0.743613	+	0.331078i	0.743333	−	0.668922i	$-0.233244\pi$
$347$	13.8520	+	6.16730i	0.743613	+	0.331078i	0.000280702		1.00000i	$0.499911\pi$
$348$		0			0
$349$	13.9680	−	12.5769i	0.747692	−	0.673225i	−0.204451	−	0.978877i	$-0.565541\pi$
$349$	13.9680	−	12.5769i	0.747692	−	0.673225i	0.952143	+	0.305652i	$0.0988743\pi$
$350$	6.40977	−	8.82229i	0.342616	−	0.471571i
$351$		0			0
$352$	1.12910	+	13.6592i	0.0601815	+	0.728037i
$353$	−7.65781	−	4.42124i	−0.407584	−	0.235319i	0.282167	−	0.959365i	$-0.408947\pi$
$353$	−7.65781	−	4.42124i	−0.407584	−	0.235319i	−0.689751	+	0.724046i	$0.742280\pi$
$354$		0			0
$355$	12.6912	−	2.69761i	0.673581	−	0.143174i
$356$	−35.3490	−	31.8283i	−1.87349	−	1.68690i
$357$		0			0
$358$	−36.3189	+	3.81727i	−1.91952	+	0.201749i
$359$	−5.57195	−	17.1487i	−0.294076	−	0.905074i	−0.983530	−	0.180744i	$-0.942149\pi$
$359$	−5.57195	−	17.1487i	−0.294076	−	0.905074i	0.689454	−	0.724330i	$-0.257851\pi$
$360$		0			0
$361$	−8.17163	−	5.93703i	−0.430086	−	0.312476i
$362$	18.9695	−	32.8561i	0.997012	−	1.72688i
$363$		0			0
$364$	13.5864	+	23.5324i	0.712122	+	1.23343i
$365$	2.66709	−	25.3756i	0.139602	−	1.32822i
$366$		0			0
$367$	−30.6339	−	6.51144i	−1.59908	−	0.339894i	−0.679767	−	0.733428i	$-0.737919\pi$
$367$	−30.6339	−	6.51144i	−1.59908	−	0.339894i	−0.919310	+	0.393534i	$0.871253\pi$
$368$	0.0611798	+	0.0842068i	0.00318922	+	0.00438958i
$369$		0			0
$370$	44.6447	−	14.5059i	2.32097	−	0.754128i
$371$	−3.68717	−	4.09502i	−0.191428	−	0.212603i
$372$		0			0
$373$	−2.91679	+	1.68401i	−0.151026	+	0.0871948i	−0.573609	−	0.819130i	$-0.694457\pi$
$373$	−2.91679	+	1.68401i	−0.151026	+	0.0871948i	0.422583	+	0.906324i	$0.361124\pi$
$374$	−24.3076	+	16.8474i	−1.25692	+	0.871156i
$375$		0			0
$376$	−6.77672	−	15.2208i	−0.349483	−	0.784951i
$377$	−24.7469	−	8.04074i	−1.27453	−	0.414119i
$378$		0			0
$379$	−19.5313	+	14.1903i	−1.00326	+	0.728908i	−0.962784	−	0.270273i	$-0.912886\pi$
$379$	−19.5313	+	14.1903i	−1.00326	+	0.728908i	−0.0404716	+	0.999181i	$0.512886\pi$
$380$	3.18482	+	30.3015i	0.163378	+	1.55444i
$381$		0			0
$382$	−7.17475	−	33.7546i	−0.367092	−	1.72703i
$383$	8.99961	+	0.945897i	0.459859	+	0.0483331i	0.331626	−	0.943411i	$-0.392403\pi$
$383$	8.99961	+	0.945897i	0.459859	+	0.0483331i	0.128233	+	0.991744i	$0.459070\pi$
$384$		0			0
$385$	6.12627	+	11.1781i	0.312224	+	0.569687i
$386$			16.0628i			0.817575i
$387$		0			0
$388$	−14.8779	+	45.7896i	−0.755313	+	2.32461i
$389$	5.42389	−	25.5174i	0.275002	−	1.29378i	−0.596191	−	0.802842i	$-0.703320\pi$
$389$	5.42389	−	25.5174i	0.275002	−	1.29378i	0.871193	−	0.490940i	$-0.163347\pi$
$390$		0			0
$391$	0.131060	−	0.294366i	0.00662800	−	0.0148867i
$392$	−12.3640	+	13.7316i	−0.624476	+	0.693551i
$393$		0			0
$394$	18.8814	−	8.40653i	0.951230	−	0.423515i
$395$	−16.2523			−0.817742
$396$		0			0
$397$	19.8829			0.997896			0.498948	−	0.866632i	$-0.333720\pi$
$397$	19.8829			0.997896			0.498948	+	0.866632i	$0.333720\pi$
$398$	−18.0012	+	8.01465i	−0.902319	+	0.401738i
$399$		0			0
$400$	−2.90737	+	3.22896i	−0.145369	+	0.161448i
$401$	−4.04140	+	9.07713i	−0.201818	+	0.453290i	−0.985893	−	0.167375i	$-0.946471\pi$
$401$	−4.04140	+	9.07713i	−0.201818	+	0.453290i	0.784075	+	0.620666i	$0.213137\pi$
$402$		0			0
$403$	−3.16778	+	14.9032i	−0.157798	+	0.742382i
$404$	13.5056	−	41.5660i	0.671929	−	2.06799i
$405$		0			0
$406$			13.5792i			0.673922i
$407$	−2.87825	+	22.5478i	−0.142670	+	1.11765i
$408$		0			0
$409$	−0.00153409		0.000161240i	−7.58560e−5		7.97279e-6i	0.104491	−	0.994526i	$-0.466679\pi$
$409$	−0.00153409		0.000161240i	−7.58560e−5		7.97279e-6i	−0.104566	+	0.994518i	$0.533345\pi$
$410$	6.43698	+	30.2836i	0.317900	+	1.49560i
$411$		0			0
$412$	−2.18732	−	20.8110i	−0.107762	−	1.02528i
$413$	−14.9382	+	10.8532i	−0.735061	+	0.534053i
$414$		0			0
$415$	−3.50643	−	1.13931i	−0.172124	−	0.0559264i
$416$	9.93220	+	22.3081i	0.486966	+	1.09374i
$417$		0			0
$418$	−21.8945	−	7.65643i	−1.07090	−	0.374488i
$419$	−13.3723	+	7.72050i	−0.653279	+	0.377171i	−0.789711	−	0.613478i	$-0.789770\pi$
$419$	−13.3723	+	7.72050i	−0.653279	+	0.377171i	0.136432	+	0.990649i	$0.456436\pi$
$420$		0			0
$421$	16.4032	+	18.2176i	0.799444	+	0.887872i	0.995696	−	0.0926811i	$-0.0295437\pi$
$421$	16.4032	+	18.2176i	0.799444	+	0.887872i	−0.196252	+	0.980553i	$0.562877\pi$
$422$	38.8383	−	12.6193i	1.89062	−	0.614300i
$423$		0			0
$424$	8.63374	+	11.8833i	0.419292	+	0.577105i
$425$	13.1572	+	2.79664i	0.638216	+	0.135657i
$426$		0			0
$427$	1.35019	−	12.8462i	0.0653403	−	0.621671i
$428$	5.38174	+	9.32145i	0.260136	+	0.450569i
$429$		0			0
$430$	11.5930	−	20.0796i	0.559062	−	0.968324i
$431$	−9.71012	−	7.05482i	−0.467720	−	0.339818i	0.328832	−	0.944388i	$-0.393345\pi$
$431$	−9.71012	−	7.05482i	−0.467720	−	0.339818i	−0.796552	+	0.604570i	$0.793345\pi$
$432$		0			0
$433$	0.277208	+	0.853159i	0.0133218	+	0.0410002i	0.957496	−	0.288445i	$-0.0931383\pi$
$433$	0.277208	+	0.853159i	0.0133218	+	0.0410002i	−0.944175	+	0.329445i	$0.893138\pi$
$434$	7.90768	−	0.831131i	0.379581	−	0.0398955i
$435$		0			0
$436$	−25.9466	−	23.3625i	−1.24262	−	1.11886i
$437$	0.247185	−	0.0525408i	0.0118245	−	0.00251337i
$438$		0			0
$439$	−3.76825	−	2.17560i	−0.179849	−	0.103836i	0.407373	−	0.913262i	$-0.366445\pi$
$439$	−3.76825	−	2.17560i	−0.179849	−	0.103836i	−0.587222	+	0.809426i	$0.699778\pi$
$440$	−13.1263	−	31.3402i	−0.625770	−	1.49408i
$441$		0			0
$442$	−30.9724	+	42.6299i	−1.47321	+	2.02770i
$443$	28.5708	−	25.7253i	1.35744	−	1.22225i	0.406205	−	0.913782i	$-0.366852\pi$
$443$	28.5708	−	25.7253i	1.35744	−	1.22225i	0.951236	−	0.308464i	$-0.0998149\pi$
$444$		0			0
$445$	−36.3184	−	16.1700i	−1.72166	−	0.766532i
$446$	−36.7045	−	16.3419i	−1.73801	−	0.773812i
$447$		0			0
$448$	11.8726	−	10.6901i	0.560928	−	0.505062i
$449$	−10.6492	+	14.6573i	−0.502566	+	0.691723i	−0.982644	−	0.185503i	$-0.940608\pi$
$449$	−10.6492	+	14.6573i	−0.502566	+	0.691723i	0.480078	+	0.877226i	$0.340608\pi$
$450$		0			0
$451$	−14.5912	−	3.44237i	−0.687075	−	0.162095i
$452$	−14.2719	−	8.23989i	−0.671294	−	0.387572i
$453$		0			0
$454$	39.6522	−	8.42834i	1.86097	−	0.395561i
$455$	16.8773	+	15.1964i	0.791218	+	0.712416i
$456$		0			0
$457$	32.0269	−	3.36616i	1.49816	−	0.157462i	0.680320	−	0.732915i	$-0.261841\pi$
$457$	32.0269	−	3.36616i	1.49816	−	0.157462i	0.817835	+	0.575453i	$0.195174\pi$
$458$	−11.4488	−	35.2358i	−0.534967	−	1.64646i
$459$		0			0
$460$	0.699953	+	0.508545i	0.0326355	+	0.0237111i
$461$	−19.5476	+	33.8574i	−0.910420	+	1.57689i	−0.0969489	+	0.995289i	$0.530908\pi$
$461$	−19.5476	+	33.8574i	−0.910420	+	1.57689i	−0.813471	+	0.581605i	$0.802425\pi$
$462$		0			0
$463$	8.51825	+	14.7540i	0.395877	+	0.685679i	0.993213	−	0.116313i	$-0.0371074\pi$
$463$	8.51825	+	14.7540i	0.395877	+	0.685679i	−0.597336	+	0.801991i	$0.703774\pi$
$464$	0.565554	−	5.38088i	0.0262552	−	0.249801i
$465$		0			0
$466$	−7.80657	−	1.65934i	−0.361633	−	0.0768674i
$467$	13.3070	+	18.3156i	0.615776	+	0.847543i	0.997037	−	0.0769242i	$-0.0245100\pi$
$467$	13.3070	+	18.3156i	0.615776	+	0.847543i	−0.381261	+	0.924468i	$0.624510\pi$
$468$		0			0
$469$	4.73418	−	1.53823i	0.218604	−	0.0710287i
$470$	−21.7768	−	24.1856i	−1.00449	−	1.11560i
$471$		0			0
$472$	42.6255	−	24.6098i	1.96200	−	1.13276i
$473$	6.39557	+	9.22761i	0.294069	+	0.424286i
$474$		0			0
$475$	4.29073	+	9.63713i	0.196872	+	0.442182i
$476$	16.6355	+	5.40519i	0.762485	+	0.247746i
$477$		0			0
$478$	−11.0117	+	8.00049i	−0.503665	+	0.365934i
$479$	1.42153	+	13.5250i	0.0649513	+	0.617971i	0.977781	+	0.209630i	$0.0672259\pi$
$479$	1.42153	+	13.5250i	0.0649513	+	0.617971i	−0.912829	+	0.408341i	$0.866107\pi$
$480$		0			0
$481$	8.42019	+	39.6139i	0.383927	+	1.80624i
$482$	7.01816	+	0.737638i	0.319668	+	0.0335985i
$483$		0			0
$484$	38.4151	+	1.71019i	1.74614	+	0.0777359i
$485$			40.2397i			1.82719i
$486$		0			0
$487$	2.70549	−	8.32664i	0.122597	−	0.377316i	−0.870858	−	0.491534i	$-0.836436\pi$
$487$	2.70549	−	8.32664i	0.122597	−	0.377316i	0.993456	+	0.114218i	$0.0364362\pi$
$488$	−7.15875	+	33.6793i	−0.324061	+	1.52459i
$489$		0			0
$490$	−14.6804	+	32.9728i	−0.663194	+	1.48956i
$491$	−22.4667	+	24.9518i	−1.01391	+	1.12606i	−0.0219175	+	0.999760i	$0.506977\pi$
$491$	−22.4667	+	24.9518i	−1.01391	+	1.12606i	−0.991992	+	0.126301i	$0.959690\pi$
$492$		0			0
$493$	−15.3016	+	6.81272i	−0.689150	+	0.306829i
$494$	−41.3253			−1.85931
$495$		0			0
$496$	−3.16812			−0.142253
$497$	5.33664	−	2.37603i	0.239381	−	0.106579i
$498$		0			0
$499$	1.50346	−	1.66976i	0.0673042	−	0.0747489i	−0.708552	−	0.705658i	$-0.750651\pi$
$499$	1.50346	−	1.66976i	0.0673042	−	0.0747489i	0.775857	+	0.630909i	$0.217318\pi$
$500$	6.08080	−	13.6577i	0.271942	−	0.610791i
$501$		0			0
$502$	7.80969	−	36.7417i	0.348563	−	1.63986i
$503$	5.15181	−	15.8556i	0.229708	−	0.706968i	−0.768072	−	0.640364i	$-0.778784\pi$
$503$	5.15181	−	15.8556i	0.229708	−	0.706968i	0.997779	−	0.0666040i	$-0.0212164\pi$
$504$		0			0
$505$		−	36.5280i		−	1.62547i
$506$	−0.577584	+	0.316552i	−0.0256767	+	0.0140724i
$507$		0			0
$508$	−10.3631	−	1.08921i	−0.459789	−	0.0483258i
$509$	2.17684	+	10.2412i	0.0964869	+	0.453935i	0.999694	+	0.0247305i	$0.00787277\pi$
$509$	2.17684	+	10.2412i	0.0964869	+	0.453935i	−0.903207	+	0.429205i	$0.858794\pi$
$510$		0			0
$511$	−1.20081	−	11.4250i	−0.0531208	−	0.505411i
$512$	−11.0790	+	8.04940i	−0.489629	+	0.355737i
$513$		0			0
$514$	−27.7414	−	9.01372i	−1.22362	−	0.397578i
$515$	−7.11354	−	15.9773i	−0.313460	−	0.704043i
$516$		0			0
$517$	15.0925	−	4.53528i	0.663767	−	0.199461i
$518$	18.3034	−	10.5675i	0.804207	−	0.464309i
$519$		0			0
$520$	−40.5077	−	44.9883i	−1.77638	−	1.97287i
$521$	5.99155	−	1.94677i	0.262494	−	0.0852896i	−0.174813	−	0.984602i	$-0.555932\pi$
$521$	5.99155	−	1.94677i	0.262494	−	0.0852896i	0.437308	+	0.899312i	$0.355932\pi$
$522$		0			0
$523$	−12.7364	−	17.5301i	−0.556923	−	0.766538i	0.434008	−	0.900909i	$-0.357099\pi$
$523$	−12.7364	−	17.5301i	−0.556923	−	0.766538i	−0.990931	+	0.134370i	$0.957099\pi$
$524$	−26.6197	−	5.65819i	−1.16289	−	0.247179i
$525$		0			0
$526$	−3.74609	+	35.6417i	−0.163337	+	1.55405i
$527$	4.90387	+	8.49375i	0.213616	+	0.369994i
$528$		0			0
$529$	−11.4964	+	19.9124i	−0.499844	+	0.865755i
$530$	23.2121	+	16.8646i	1.00827	+	0.732551i
$531$		0			0
$532$	4.23907	+	13.0465i	0.183787	+	0.565638i
$533$	−26.5642	+	2.79201i	−1.15062	+	0.120935i
$534$		0			0
$535$	6.68529	+	6.01946i	0.289030	+	0.260244i
$536$	−12.9790	+	2.75877i	−0.560606	+	0.119161i
$537$		0			0
$538$	4.08021	+	2.35571i	0.175910	+	0.101562i
$539$	−11.4028	−	13.2451i	−0.491155	−	0.570507i
$540$		0			0
$541$	13.1964	−	18.1633i	0.567357	−	0.780899i	−0.424882	−	0.905249i	$-0.639684\pi$
$541$	13.1964	−	18.1633i	0.567357	−	0.780899i	0.992238	+	0.124349i	$0.0396844\pi$
$542$	37.0827	−	33.3894i	1.59284	−	1.43420i
$543$		0			0
$544$	14.3600	+	6.39351i	0.615682	+	0.274119i
$545$	−26.6583	−	11.8690i	−1.14191	−	0.508413i
$546$		0			0
$547$	17.4107	−	15.6767i	0.744430	−	0.670287i	−0.206935	−	0.978355i	$-0.566349\pi$
$547$	17.4107	−	15.6767i	0.744430	−	0.670287i	0.951365	+	0.308067i	$0.0996822\pi$
$548$	12.9077	−	17.7659i	0.551390	−	0.758923i
$549$		0			0
$550$	−17.9385	−	20.8367i	−0.764901	−	0.888480i
$551$	−11.3762	−	6.56806i	−0.484643	−	0.279809i
$552$		0			0
$553$	−7.15744	+	1.52136i	−0.304365	+	0.0646948i
$554$	−43.0085	−	38.7251i	−1.82726	−	1.64527i
$555$		0			0
$556$	−1.82359	+	0.191667i	−0.0773373	+	0.00812848i
$557$	−1.09525	−	3.37084i	−0.0464074	−	0.142827i	0.925168	−	0.379558i	$-0.123924\pi$
$557$	−1.09525	−	3.37084i	−0.0464074	−	0.142827i	−0.971575	+	0.236731i	$0.923924\pi$
$558$		0			0
$559$	16.1831	+	11.7577i	0.684471	+	0.497297i
$560$	−2.36115	+	4.08964i	−0.0997770	+	0.172819i
$561$		0			0
$562$	15.2663	+	26.4419i	0.643968	+	1.11539i
$563$	1.92867	−	18.3501i	0.0812837	−	0.773363i	−0.875628	−	0.482985i	$-0.839552\pi$
$563$	1.92867	−	18.3501i	0.0812837	−	0.773363i	0.956912	−	0.290378i	$-0.0937809\pi$
$564$		0			0
$565$	−13.4725	−	2.86368i	−0.566794	−	0.120476i
$566$	27.2401	+	37.4927i	1.14499	+	1.57594i
$567$		0			0
$568$	−14.8096	+	4.81192i	−0.621395	+	0.201904i
$569$	9.58925	+	10.6499i	0.402002	+	0.446469i	0.909824	−	0.414993i	$-0.136216\pi$
$569$	9.58925	+	10.6499i	0.402002	+	0.446469i	−0.507822	+	0.861462i	$0.669549\pi$
$570$		0			0
$571$	34.7935	−	20.0880i	1.45606	−	0.840658i	0.457247	−	0.889340i	$-0.348835\pi$
$571$	34.7935	−	20.0880i	1.45606	−	0.840658i	0.998814	+	0.0486820i	$0.0155021\pi$
$572$	65.6126	−	19.7165i	2.74340	−	0.824389i
$573$		0			0
$574$	5.66963	+	12.7342i	0.236646	+	0.531515i
$575$	0.284895	+	0.0925680i	0.0118809	+	0.00386035i
$576$		0			0
$577$	24.3026	−	17.6568i	1.01173	−	0.735064i	0.0471580	−	0.998887i	$-0.484984\pi$
$577$	24.3026	−	17.6568i	1.01173	−	0.735064i	0.964571	+	0.263823i	$0.0849836\pi$
$578$	−0.620228	−	5.90107i	−0.0257981	−	0.245452i
$579$		0			0
$580$	−9.35060	−	43.9911i	−0.388263	−	1.82663i
$581$	−1.65086	−	0.173513i	−0.0684893	−	0.00719852i
$582$		0			0
$583$	−12.1836	+	6.67734i	−0.504591	+	0.276547i
$584$			30.6223i			1.26716i
$585$		0			0
$586$	−3.21104	+	9.88258i	−0.132647	+	0.408246i
$587$	2.54166	−	11.9576i	0.104906	−	0.493542i	−0.894055	−	0.447957i	$-0.852152\pi$
$587$	2.54166	−	11.9576i	0.104906	−	0.493542i	0.998960	−	0.0455844i	$-0.0145150\pi$
$588$		0			0
$589$	−3.12854	+	7.02682i	−0.128909	+	0.289535i
$590$	64.3319	−	71.4478i	2.64850	−	2.94146i
$591$		0			0
$592$	−7.69305	+	3.42517i	−0.316182	+	0.140773i
$593$	26.0062			1.06795			0.533973	−	0.845502i	$-0.320699\pi$
$593$	26.0062			1.06795			0.533973	+	0.845502i	$0.320699\pi$
$594$		0			0
$595$	14.6191			0.599327
$596$	30.7103	−	13.6731i	1.25794	−	0.560072i
$597$		0			0
$598$	−0.785214	+	0.872068i	−0.0321098	+	0.0356615i
$599$	6.73721	−	15.1320i	0.275275	−	0.618277i	−0.722013	−	0.691880i	$-0.756783\pi$
$599$	6.73721	−	15.1320i	0.275275	−	0.618277i	0.997288	+	0.0736024i	$0.0234496\pi$
$600$		0			0
$601$	−6.92358	+	32.5729i	−0.282419	+	1.32868i	0.576723	+	0.816940i	$0.304331\pi$
$601$	−6.92358	+	32.5729i	−0.282419	+	1.32868i	−0.859142	+	0.511737i	$0.829002\pi$
$602$	3.22586	−	9.92816i	0.131476	−	0.404642i
$603$		0			0
$604$		−	34.9779i		−	1.42323i
$605$	30.9770	−	8.56212i	1.25939	−	0.348100i
$606$		0			0
$607$	−44.3554	−	4.66194i	−1.80033	−	0.189222i	−0.855724	−	0.517433i	$-0.826888\pi$
$607$	−44.3554	−	4.66194i	−1.80033	−	0.189222i	−0.944605	+	0.328211i	$0.893554\pi$
$608$	2.56309	+	12.0584i	0.103947	+	0.489033i
$609$		0			0
$610$	7.03023	+	66.8882i	0.284646	+	2.70822i
$611$	22.7154	−	16.5037i	0.918966	−	0.667668i
$612$		0			0
$613$	−11.7116	−	3.80532i	−0.473026	−	0.153695i	0.0627963	−	0.998026i	$-0.479998\pi$
$613$	−11.7116	−	3.80532i	−0.473026	−	0.153695i	−0.535822	+	0.844331i	$0.679998\pi$
$614$	−10.5785	−	23.7597i	−0.426913	−	0.958863i
$615$		0			0
$616$	−8.71446	−	12.5733i	−0.351116	−	0.506594i
$617$	13.5088	−	7.79934i	0.543846	−	0.313989i	−0.202790	−	0.979222i	$-0.565001\pi$
$617$	13.5088	−	7.79934i	0.543846	−	0.313989i	0.746636	+	0.665233i	$0.231668\pi$
$618$		0			0
$619$	−24.7627	−	27.5018i	−0.995297	−	1.10539i	−0.994431	−	0.105390i	$-0.966391\pi$
$619$	−24.7627	−	27.5018i	−0.995297	−	1.10539i	−0.000866293	−	1.00000i	$-0.500276\pi$
$620$	−25.0455	+	8.13776i	−1.00585	+	0.326820i
$621$		0			0
$622$	10.8117	+	14.8810i	0.433508	+	0.596673i
$623$	−17.5081	−	3.72147i	−0.701448	−	0.149097i
$624$		0			0
$625$	3.15428	−	30.0109i	0.126171	−	1.20044i
$626$	37.9138	+	65.6686i	1.51534	+	2.62465i
$627$		0			0
$628$	−5.73584	+	9.93476i	−0.228885	+	0.396440i
$629$	21.0908	+	15.3234i	0.840947	+	0.610984i
$630$		0			0
$631$	13.3328	+	41.0343i	0.530772	+	1.63355i	0.752611	+	0.658465i	$0.228794\pi$
$631$	13.3328	+	41.0343i	0.530772	+	1.63355i	−0.221840	+	0.975083i	$0.571206\pi$
$632$	19.3984	−	2.03885i	0.771626	−	0.0811012i
$633$		0			0
$634$	20.9587	+	18.8713i	0.832375	+	0.749474i
$635$	−8.51872	+	1.81071i	−0.338055	+	0.0718559i
$636$		0			0
$637$	−26.9671	−	15.5695i	−1.06848	−	0.616885i
$638$	33.3224	+	7.86144i	1.31925	+	0.311238i
$639$		0			0
$640$	−34.7017	+	47.7629i	−1.37171	+	1.88799i
$641$	−36.9064	+	33.2307i	−1.45771	+	1.31253i	−0.598279	+	0.801288i	$0.704148\pi$
$641$	−36.9064	+	33.2307i	−1.45771	+	1.31253i	−0.859436	+	0.511244i	$0.829185\pi$
$642$		0			0
$643$	30.3009	+	13.4908i	1.19495	+	0.532027i	0.905164	−	0.425063i	$-0.139748\pi$
$643$	30.3009	+	13.4908i	1.19495	+	0.532027i	0.289789	+	0.957091i	$0.406415\pi$
$644$	0.355860	+	0.158439i	0.0140229	+	0.00624338i
$645$		0			0
$646$	−19.7689	+	17.8000i	−0.777798	+	0.700332i
$647$	−25.8770	+	35.6166i	−1.01733	+	1.40023i	−0.103268	+	0.994654i	$0.532930\pi$
$647$	−25.8770	+	35.6166i	−1.01733	+	1.40023i	−0.914060	+	0.405578i	$0.867070\pi$
$648$		0			0
$649$	17.9849	+	42.9407i	0.705970	+	1.68557i
$650$	−42.4236	−	24.4933i	−1.66399	−	0.960706i
$651$		0			0
$652$	−29.6025	+	6.29221i	−1.15932	+	0.246422i
$653$	5.08933	+	4.58246i	0.199161	+	0.179325i	0.762677	−	0.646780i	$-0.223885\pi$
$653$	5.08933	+	4.58246i	0.199161	+	0.179325i	−0.563516	+	0.826105i	$0.690552\pi$
$654$		0			0
$655$	−22.6207	+	2.37753i	−0.883865	+	0.0928980i
$656$	−1.71629	−	5.28219i	−0.0670098	−	0.206235i
$657$		0			0
$658$	−11.8544	−	8.61271i	−0.462132	−	0.335759i
$659$	5.89894	−	10.2173i	0.229790	−	0.398008i	−0.727956	−	0.685624i	$-0.759529\pi$
$659$	5.89894	−	10.2173i	0.229790	−	0.398008i	0.957746	+	0.287616i	$0.0928627\pi$
$660$		0			0
$661$	−22.4153	−	38.8245i	−0.871855	−	1.51010i	−0.860076	−	0.510167i	$-0.829584\pi$
$661$	−22.4153	−	38.8245i	−0.871855	−	1.51010i	−0.0117796	−	0.999931i	$-0.503750\pi$
$662$	−7.36965	+	70.1176i	−0.286430	+	2.72520i
$663$		0			0
$664$	4.32812	+	0.919970i	0.167963	+	0.0357017i
$665$	6.73908	+	9.27555i	0.261330	+	0.359690i
$666$		0			0
$667$	−0.354760	+	0.115268i	−0.0137364	+	0.00446321i
$668$	46.4104	+	51.5440i	1.79567	+	1.99430i
$669$		0			0
$670$	−22.4462	+	12.9593i	−0.867174	+	0.500663i
$671$	−30.7421	−	10.7504i	−1.18679	−	0.415014i
$672$		0			0
$673$	−15.4591	−	34.7218i	−0.595906	−	1.33843i	−0.919820	−	0.392340i	$-0.871666\pi$
$673$	−15.4591	−	34.7218i	−0.595906	−	1.33843i	0.323914	−	0.946086i	$-0.395001\pi$
$674$	−49.0427	−	15.9349i	−1.88906	−	0.613791i
$675$		0			0
$676$	61.9866	−	45.0359i	2.38410	−	1.73215i
$677$	2.80398	+	26.6781i	0.107766	+	1.02532i	0.906088	+	0.423090i	$0.139055\pi$
$677$	2.80398	+	26.6781i	0.107766	+	1.02532i	−0.798322	+	0.602231i	$0.794279\pi$
$678$		0			0
$679$	3.76679	+	17.7214i	0.144556	+	0.680083i
$680$	−38.7556	−	4.07338i	−1.48621	−	0.156207i
$681$		0			0
$682$	2.53849	−	19.8861i	0.0972036	−	0.761479i
$683$		−	4.41371i		−	0.168886i	−0.996428	−	0.0844429i	$-0.973089\pi$
$683$		−	4.41371i		−	0.168886i	0.996428	−	0.0844429i	$-0.0269111\pi$
$684$		0			0
$685$	5.67161	−	17.4554i	0.216701	−	0.666938i
$686$	−7.86673	+	37.0100i	−0.300353	+	1.41305i
$687$		0			0
$688$	−1.69177	+	3.79979i	−0.0644983	+	0.144866i
$689$	−16.5633	+	18.3954i	−0.631012	+	0.700810i
$690$		0			0
$691$	15.1260	−	6.73452i	0.575420	−	0.256193i	−0.0983290	−	0.995154i	$-0.531350\pi$
$691$	15.1260	−	6.73452i	0.575420	−	0.256193i	0.673749	+	0.738961i	$0.264683\pi$
$692$	−24.4119			−0.928003
$693$		0			0
$694$	−35.5463			−1.34932
$695$	−1.40003	+	0.623332i	−0.0531060	+	0.0236443i
$696$		0			0
$697$	−11.5050	+	12.7776i	−0.435783	+	0.483986i
$698$	−17.9221	+	40.2537i	−0.678361	+	1.52362i
$699$		0			0
$700$	−3.38087	+	15.9057i	−0.127785	+	0.601180i
$701$	−3.17601	+	9.77475i	−0.119956	+	0.369187i	−0.992948	−	0.118547i	$-0.962176\pi$
$701$	−3.17601	+	9.77475i	−0.119956	+	0.369187i	0.872992	+	0.487734i	$0.162176\pi$
$702$		0			0
$703$			20.4454i			0.771114i
$704$	−19.3595	−	35.3236i	−0.729639	−	1.33131i
$705$		0			0
$706$	20.6159	+	2.16681i	0.775888	+	0.0815491i
$707$	−3.41934	−	16.0867i	−0.128598	−	0.605004i
$708$		0			0
$709$	5.03050	+	47.8620i	0.188924	+	1.79749i	0.520288	+	0.853991i	$0.325825\pi$
$709$	5.03050	+	47.8620i	0.188924	+	1.79749i	−0.331363	+	0.943503i	$0.607509\pi$
$710$	−24.6077	+	17.8785i	−0.923509	+	0.670969i
$711$		0			0
$712$	45.3774	+	14.7440i	1.70059	+	0.552555i
$713$	0.0888389	+	0.199535i	0.00332704	+	0.00747266i
$714$		0			0
$715$	47.0618	−	32.6181i	1.76001	−	1.21985i
$716$	47.1602	−	27.2279i	1.76246	−	1.01756i
$717$		0			0
$718$	28.2845	+	31.4132i	1.05557	+	1.17233i
$719$	−46.0534	+	14.9636i	−1.71750	+	0.558050i	−0.991553	−	0.129700i	$-0.958598\pi$
$719$	−46.0534	+	14.9636i	−1.71750	+	0.558050i	−0.725947	+	0.687750i	$0.758598\pi$
$720$		0			0
$721$	−4.62838	−	6.37042i	−0.172370	−	0.237247i
$722$	23.1616	+	4.92315i	0.861985	+	0.183221i
$723$		0			0
$724$	−5.91351	+	56.2633i	−0.219774	+	2.09101i
$725$	−7.78571	−	13.4852i	−0.289154	−	0.500829i
$726$		0			0
$727$	−14.4674	+	25.0583i	−0.536568	+	0.929363i	0.462518	+	0.886610i	$0.346946\pi$
$727$	−14.4674	+	25.0583i	−0.536568	+	0.929363i	−0.999086	+	0.0427527i	$0.986387\pi$
$728$	−22.0507	−	16.0208i	−0.817253	−	0.593769i
$729$		0			0
$730$	18.4841	+	56.8881i	0.684126	+	2.10552i
$731$	12.8059	−	1.34596i	0.473645	−	0.0497820i
$732$		0			0
$733$	−12.4546	−	11.2142i	−0.460021	−	0.414205i	0.406263	−	0.913756i	$-0.366832\pi$
$733$	−12.4546	−	11.2142i	−0.460021	−	0.414205i	−0.866284	+	0.499551i	$0.833498\pi$
$734$	71.8151	−	15.2648i	2.65074	−	0.563433i
$735$		0			0
$736$	0.303164	+	0.175032i	0.0111748	+	0.00645175i
$737$	−1.03394	−	12.5079i	−0.0380855	−	0.460735i
$738$		0			0
$739$	16.0114	−	22.0378i	0.588990	−	0.810675i	−0.405655	−	0.914026i	$-0.632957\pi$
$739$	16.0114	−	22.0378i	0.588990	−	0.810675i	0.994645	+	0.103351i	$0.0329566\pi$
$740$	−52.0191	+	46.8382i	−1.91226	+	1.72181i
$741$		0			0
$742$	11.8012	+	5.25423i	0.433235	+	0.192889i
$743$	40.4729	+	18.0197i	1.48481	+	0.661078i	0.979423	−	0.201818i	$-0.0646848\pi$
$743$	40.4729	+	18.0197i	1.48481	+	0.661078i	0.505382	+	0.862896i	$0.331351\pi$
$744$		0			0
$745$	20.8795	−	18.8000i	0.764967	−	0.688779i
$746$	4.64095	−	6.38772i	0.169917	−	0.233871i
$747$		0			0
$748$	22.8948	−	37.6931i	0.837118	−	1.37820i
$749$	3.50764	+	2.02514i	0.128166	+	0.0739970i
$750$		0			0
$751$	−27.6504	+	5.87728i	−1.00898	+	0.214465i	−0.682614	−	0.730779i	$-0.739157\pi$
$751$	−27.6504	+	5.87728i	−1.00898	+	0.214465i	−0.326364	+	0.945244i	$0.605824\pi$
$752$	4.33872	+	3.90660i	0.158217	+	0.142459i
$753$		0			0
$754$	60.6654	−	6.37619i	2.20930	−	0.232207i
$755$	−9.03379	−	27.8031i	−0.328773	−	1.01186i
$756$		0			0
$757$	−13.9254	−	10.1174i	−0.506129	−	0.367724i	0.305224	−	0.952280i	$-0.401269\pi$
$757$	−13.9254	−	10.1174i	−0.506129	−	0.367724i	−0.811353	+	0.584556i	$0.801269\pi$
$758$	28.2980	−	49.0137i	1.02783	−	1.78026i
$759$		0			0
$760$	−15.2809	−	26.4674i	−0.554298	−	0.960072i
$761$	5.06226	−	48.1642i	0.183507	−	1.74595i	−0.384678	−	0.923051i	$-0.625688\pi$
$761$	5.06226	−	48.1642i	0.183507	−	1.74595i	0.568185	−	0.822901i	$-0.307646\pi$
$762$		0			0
$763$	−12.8512	−	2.73161i	−0.465245	−	0.0988909i
$764$	30.2463	+	41.6305i	1.09427	+	1.50614i
$765$		0			0
$766$	−20.1757	+	6.55549i	−0.728978	+	0.236859i
$767$	55.5016	+	61.6407i	2.00405	+	2.22572i
$768$		0			0
$769$	−8.98495	+	5.18746i	−0.324006	+	0.187065i	−0.653177	−	0.757206i	$-0.726564\pi$
$769$	−8.98495	+	5.18746i	−0.324006	+	0.187065i	0.329171	+	0.944270i	$0.393231\pi$
$770$	−23.7786	−	18.0977i	−0.856921	−	0.652197i
$771$		0			0
$772$	−9.74228	−	21.8815i	−0.350632	−	0.787533i
$773$	7.58873	+	2.46573i	0.272947	+	0.0886860i	0.442293	−	0.896871i	$-0.354165\pi$
$773$	7.58873	+	2.46573i	0.272947	+	0.0886860i	−0.169345	+	0.985557i	$0.554165\pi$
$774$		0			0
$775$	−7.37646	+	5.35931i	−0.264970	+	0.192512i
$776$	−5.04806	−	48.0291i	−0.181215	−	1.72415i
$777$		0			0
$778$	12.7152	+	59.8204i	0.455863	+	2.14466i
$779$	−13.4107	−	1.40952i	−0.480487	−	0.0505012i
$780$		0			0
$781$	−2.74105	−	14.4714i	−0.0980826	−	0.517826i
$782$			0.755389i			0.0270126i
$783$		0			0
$784$	2.00084	−	6.15795i	0.0714585	−	0.219927i
$785$	−1.99342	+	9.37832i	−0.0711483	+	0.334727i
$786$		0			0
$787$	7.20028	−	16.1721i	0.256662	−	0.576473i	−0.738551	−	0.674197i	$-0.764490\pi$
$787$	7.20028	−	16.1721i	0.256662	−	0.576473i	0.995214	+	0.0977243i	$0.0311563\pi$
$788$	−20.6225	+	22.9036i	−0.734645	+	0.815906i
$789$		0			0
$790$	34.8063	−	15.4968i	1.23835	−	0.551351i
$791$	−6.20131			−0.220493
$792$		0			0
$793$	−58.0249			−2.06052
$794$	−42.5818	+	18.9586i	−1.51117	+	0.672816i
$795$		0			0
$796$	19.6611	−	21.8359i	0.696870	−	0.773952i
$797$	12.7980	−	28.7448i	0.453329	−	1.01819i	−0.531878	−	0.846821i	$-0.678513\pi$
$797$	12.7980	−	28.7448i	0.453329	−	1.01819i	0.985206	−	0.171372i	$-0.0548199\pi$
$798$		0			0
$799$	3.75781	−	17.6791i	0.132942	−	0.625441i
$800$	−4.51574	+	13.8980i	−0.159656	+	0.491370i
$801$		0			0
$802$		−	23.2933i		−	0.822516i
$803$	−28.7314	−	3.66759i	−1.01391	−	0.129426i
$804$		0			0
$805$	0.323785	+	0.0340312i	0.0114119	+	0.00119944i
$806$	−7.42621	−	34.9376i	−0.261577	−	1.23062i
$807$		0			0
$808$	4.58244	+	43.5990i	0.161210	+	1.53381i
$809$	17.3896	−	12.6343i	0.611384	−	0.444197i	−0.238517	−	0.971138i	$-0.576661\pi$
$809$	17.3896	−	12.6343i	0.611384	−	0.444197i	0.849902	+	0.526942i	$0.176661\pi$
$810$		0			0
$811$	31.2311	+	10.1476i	1.09667	+	0.356331i	0.800822	−	0.598903i	$-0.204396\pi$
$811$	31.2311	+	10.1476i	1.09667	+	0.356331i	0.295852	+	0.955234i	$0.404396\pi$
$812$	−8.23592	−	18.4982i	−0.289024	−	0.649159i
$813$		0			0
$814$	−15.3355	−	51.0334i	−0.537508	−	1.78872i
$815$	−21.9053	+	12.6470i	−0.767308	+	0.443005i
$816$		0			0
$817$	6.75722	+	7.50465i	0.236405	+	0.262554i
$818$	0.00343919	−	0.00111746i	0.000120249	−	3.90711e-5i
$819$		0			0
$820$	−27.1361	−	37.3497i	−0.947635	−	1.30431i
$821$	−54.8274	−	11.6539i	−1.91349	−	0.406725i	−0.913491	−	0.406859i	$-0.866624\pi$
$821$	−54.8274	−	11.6539i	−1.91349	−	0.406725i	−1.00000		0.000133485i	$0.999958\pi$
$822$		0			0
$823$	−5.58299	+	53.1186i	−0.194611	+	1.85160i	0.265971	+	0.963981i	$0.414308\pi$
$823$	−5.58299	+	53.1186i	−0.194611	+	1.85160i	−0.460581	+	0.887617i	$0.652359\pi$
$824$	10.4949	+	18.1777i	0.365607	+	0.633250i
$825$		0			0
$826$	21.6433	−	37.4873i	0.753067	−	1.30435i
$827$	−15.2821	−	11.1031i	−0.531410	−	0.386092i	0.289475	−	0.957186i	$-0.406519\pi$
$827$	−15.2821	−	11.1031i	−0.531410	−	0.386092i	−0.820885	+	0.571094i	$0.806519\pi$
$828$		0			0
$829$	−8.51237	−	26.1984i	−0.295647	−	0.909907i	−0.983003	−	0.183587i	$-0.941229\pi$
$829$	−8.51237	−	26.1984i	−0.295647	−	0.909907i	0.687357	−	0.726320i	$-0.258771\pi$
$830$	8.59579	−	0.903454i	0.298364	−	0.0313594i
$831$		0			0
$832$	−53.3335	−	48.0217i	−1.84901	−	1.66485i
$833$	−19.6066	+	4.16751i	−0.679328	+	0.144396i
$834$		0			0
$835$	50.2030	+	28.9847i	1.73735	+	1.00306i
$836$	34.4695	−	2.84934i	1.19215	−	0.0985464i
$837$		0			0
$838$	21.2768	−	29.2850i	0.734996	−	1.01164i
$839$	2.67098	−	2.40496i	0.0922124	−	0.0830284i	−0.621735	−	0.783227i	$-0.713572\pi$
$839$	2.67098	−	2.40496i	0.0922124	−	0.0830284i	0.713948	+	0.700199i	$0.246905\pi$
$840$		0			0
$841$	−8.77918	−	3.90874i	−0.302730	−	0.134784i
$842$	−52.5002	−	23.3746i	−1.80928	−	0.805542i
$843$		0			0
$844$	−45.2537	+	40.7466i	−1.55770	+	1.40256i
$845$	37.6403	−	51.8074i	1.29487	−	1.78223i
$846$		0			0
$847$	12.8406	−	6.67044i	0.441209	−	0.229199i
$848$	−4.45751	−	2.57355i	−0.153072	−	0.0883759i
$849$		0			0
$850$	−30.8443	+	6.55616i	−1.05795	+	0.224874i
$851$	0.431450	+	0.388479i	0.0147899	+	0.0133169i
$852$		0			0
$853$	−13.6404	+	1.43367i	−0.467039	+	0.0490878i	−0.335126	−	0.942173i	$-0.608779\pi$
$853$	−13.6404	+	1.43367i	−0.467039	+	0.0490878i	−0.131914	+	0.991261i	$0.542112\pi$
$854$	9.35741	+	28.7991i	0.320204	+	0.985486i
$855$		0			0
$856$	−8.73455	−	6.34602i	−0.298541	−	0.216902i
$857$	1.82655	−	3.16368i	0.0623939	−	0.108069i	−0.833141	−	0.553060i	$-0.813460\pi$
$857$	1.82655	−	3.16368i	0.0623939	−	0.108069i	0.895535	+	0.444991i	$0.146793\pi$
$858$		0			0
$859$	−12.4493	−	21.5628i	−0.424764	−	0.735713i	0.571634	−	0.820509i	$-0.306310\pi$
$859$	−12.4493	−	21.5628i	−0.424764	−	0.735713i	−0.996398	+	0.0847953i	$0.972976\pi$
$860$	−3.61397	+	34.3847i	−0.123235	+	1.17251i
$861$		0			0
$862$	27.5223	+	5.85004i	0.937413	+	0.199253i
$863$	4.84824	+	6.67303i	0.165036	+	0.227152i	0.883523	−	0.468388i	$-0.155165\pi$
$863$	4.84824	+	6.67303i	0.165036	+	0.227152i	−0.718487	+	0.695540i	$0.755165\pi$
$864$		0			0
$865$	−19.4045	+	6.30490i	−0.659773	+	0.214373i
$866$	−1.40717	−	1.56282i	−0.0478177	−	0.0531069i
$867$		0			0
$868$	−10.2681	+	5.92831i	−0.348523	+	0.201220i
$869$	−0.410364	+	18.4447i	−0.0139206	+	0.625693i
$870$		0			0
$871$	−9.09506	−	20.4278i	−0.308174	−	0.692171i
$872$	33.3076	+	10.8223i	1.12794	+	0.366490i
$873$		0			0
$874$	−0.479279	+	0.348216i	−0.0162118	+	0.0117786i
$875$	−0.588049	−	5.59492i	−0.0198797	−	0.189143i
$876$		0			0
$877$	−2.06685	−	9.72376i	−0.0697925	−	0.328348i	0.929375	−	0.369136i	$-0.120346\pi$
$877$	−2.06685	−	9.72376i	−0.0697925	−	0.328348i	−0.999168	+	0.0407882i	$0.987013\pi$
$878$	10.1446	+	1.06624i	0.342365	+	0.0359840i
$879$		0			0
$880$	8.66877	+	8.16176i	0.292224	+	0.275133i
$881$		−	46.2212i		−	1.55723i	−0.627501	−	0.778616i	$-0.715922\pi$
$881$		−	46.2212i		−	1.55723i	0.627501	−	0.778616i	$-0.284078\pi$
$882$		0			0
$883$	9.04674	−	27.8430i	0.304447	−	0.936991i	−0.675436	−	0.737419i	$-0.736045\pi$
$883$	9.04674	−	27.8430i	0.304447	−	0.936991i	0.979883	−	0.199573i	$-0.0639554\pi$
$884$	16.3366	−	76.8575i	0.549458	−	2.58500i
$885$		0			0
$886$	−36.6586	+	82.3366i	−1.23157	+	2.76615i
$887$	33.5199	−	37.2277i	1.12549	−	1.24998i	0.160687	−	0.987005i	$-0.448629\pi$
$887$	33.5199	−	37.2277i	1.12549	−	1.24998i	0.964802	−	0.262977i	$-0.0847044\pi$
$888$		0			0
$889$	−3.58211	+	1.59486i	−0.120140	+	0.0534898i
$890$	93.1987			3.12403
$891$		0			0
$892$	59.9122			2.00601
$893$	12.9493	−	5.76539i	0.433331	−	0.192932i
$894$		0			0
$895$	30.4544	−	33.8230i	1.01798	−	1.13058i
$896$	−10.8115	+	24.2829i	−0.361185	+	0.811235i
$897$		0			0
$898$	8.83058	−	41.5446i	0.294680	−	1.38636i
$899$	3.50850	−	10.7981i	0.117015	−	0.360136i
$900$		0			0
$901$			15.9342i			0.530845i
$902$	34.5313	−	6.54066i	1.14977	−	0.217780i
$903$		0			0
$904$	16.4398	+	1.72789i	0.546778	+	0.0574687i
$905$	9.83068	+	46.2497i	0.326783	+	1.53739i
$906$		0			0
$907$	−1.45510	−	13.8443i	−0.0483158	−	0.459694i	−0.991755	−	0.128148i	$-0.959097\pi$
$907$	−1.45510	−	13.8443i	−0.0483158	−	0.459694i	0.943439	−	0.331546i	$-0.107570\pi$
$908$	−48.9042	+	35.5310i	−1.62294	+	1.17914i
$909$		0			0
$910$	−50.6347	−	16.4522i	−1.67852	−	0.545385i
$911$	−5.64577	−	12.6806i	−0.187053	−	0.420127i	0.795540	−	0.605901i	$-0.207187\pi$
$911$	−5.64577	−	12.6806i	−0.187053	−	0.420127i	−0.982592	+	0.185774i	$0.940521\pi$
$912$		0			0
$913$	−1.38153	+	3.95066i	−0.0457220	+	0.130748i
$914$	−65.3799	+	37.7471i	−2.16257	+	1.24856i
$915$		0			0
$916$	36.9670	+	41.0560i	1.22142	+	1.35653i
$917$	−9.73950	+	3.16456i	−0.321627	+	0.104503i
$918$		0			0
$919$	11.1835	+	15.3927i	0.368908	+	0.507759i	0.952604	−	0.304214i	$-0.0983938\pi$
$919$	11.1835	+	15.3927i	0.368908	+	0.507759i	−0.583695	+	0.811973i	$0.698394\pi$
$920$	−0.848878	−	0.180435i	−0.0279867	−	0.00594875i
$921$		0			0
$922$	9.58010	−	91.1486i	0.315504	−	3.00182i
$923$	−13.1208	−	22.7260i	−0.431878	−	0.748034i
$924$		0			0
$925$	−12.1179	+	20.9888i	−0.398434	+	0.690108i
$926$	−32.3111	−	23.4754i	−1.06181	−	0.771448i
$927$		0			0
$928$	−5.62314	−	17.3062i	−0.184588	−	0.568105i
$929$	−16.1053	+	1.69274i	−0.528398	+	0.0555369i	−0.364972	−	0.931019i	$-0.618921\pi$
$929$	−16.1053	+	1.69274i	−0.528398	+	0.0555369i	−0.163427	+	0.986555i	$0.552255\pi$
$930$		0			0
$931$	−11.6824	−	10.5189i	−0.382874	−	0.344741i
$932$	11.6409	−	2.47435i	0.381310	−	0.0810500i
$933$		0			0
$934$	−45.9628	−	26.5366i	−1.50395	−	0.868305i
$935$	8.46353	−	35.8745i	0.276787	−	1.17322i
$936$		0			0
$937$	−24.7387	+	34.0498i	−0.808177	+	1.11236i	0.183425	+	0.983034i	$0.441281\pi$
$937$	−24.7387	+	34.0498i	−0.808177	+	1.11236i	−0.991602	+	0.129326i	$0.958719\pi$
$938$	−8.67211	+	7.80840i	−0.283154	+	0.254953i
$939$		0			0
$940$	44.3342	+	19.7389i	1.44602	+	0.643811i
$941$	−0.386550	−	0.172103i	−0.0126012	−	0.00561040i	0.400426	−	0.916329i	$-0.368862\pi$
$941$	−0.386550	−	0.172103i	−0.0126012	−	0.00561040i	−0.413028	+	0.910719i	$0.635529\pi$
$942$		0			0
$943$	−0.284558	+	0.256217i	−0.00926647	+	0.00834357i
$944$	−10.1377	+	13.9533i	−0.329954	+	0.454142i
$945$		0			0
$946$	−22.4955	−	13.6638i	−0.731393	−	0.444249i
$947$	10.8999	+	6.29305i	0.354199	+	0.204497i	0.666533	−	0.745475i	$-0.267778\pi$
$947$	10.8999	+	6.29305i	0.354199	+	0.204497i	−0.312334	+	0.949972i	$0.601111\pi$
$948$		0			0
$949$	−50.4776	+	10.7293i	−1.63857	+	0.348289i
$950$	−18.3783	−	16.5479i	−0.596269	−	0.536883i
$951$		0			0
$952$	−17.4491	+	1.83397i	−0.565528	+	0.0594394i
$953$	16.7845	+	51.6574i	0.543703	+	1.67335i	0.724053	+	0.689745i	$0.242277\pi$
$953$	16.7845	+	51.6574i	0.543703	+	1.67335i	−0.180349	+	0.983603i	$0.557723\pi$
$954$		0			0
$955$	34.7941	+	25.2794i	1.12591	+	0.818022i
$956$	10.1483	−	17.5774i	0.328220	−	0.568494i
$957$		0			0
$958$	−15.9406	−	27.6099i	−0.515017	−	0.892036i
$959$	0.863768	−	8.21820i	0.0278925	−	0.265379i
$960$		0			0
$961$	23.8197	+	5.06303i	0.768377	+	0.163324i
$962$	−55.8052	−	76.8092i	−1.79923	−	2.47643i
$963$		0			0
$964$	−10.0079	+	3.25175i	−0.322332	+	0.104732i
$965$	−13.3953	−	14.8770i	−0.431210	−	0.478907i
$966$		0			0
$967$	−23.2525	+	13.4249i	−0.747751	+	0.431714i	−0.824881	−	0.565307i	$-0.808758\pi$
$967$	−23.2525	+	13.4249i	−0.747751	+	0.431714i	0.0771296	+	0.997021i	$0.475424\pi$
$968$	−35.8993	+	14.1056i	−1.15385	+	0.453372i
$969$		0			0
$970$	−38.3690	−	86.1782i	−1.23195	−	2.76702i
$971$	25.9476	+	8.43088i	0.832697	+	0.270560i	0.694181	−	0.719801i	$-0.255767\pi$
$971$	25.9476	+	8.43088i	0.832697	+	0.270560i	0.138516	+	0.990360i	$0.455767\pi$
$972$		0			0
$973$	−0.558215	+	0.405567i	−0.0178956	+	0.0130019i
$974$	2.14541	+	20.4123i	0.0687435	+	0.654051i
$975$		0			0
$976$	−2.50853	−	11.8017i	−0.0802960	−	0.377763i
$977$	−34.2567	−	3.60052i	−1.09597	−	0.115191i	−0.460754	−	0.887528i	$-0.652421\pi$
$977$	−34.2567	−	3.60052i	−1.09597	−	0.115191i	−0.635213	+	0.772337i	$0.719088\pi$
$978$		0			0
$979$	−19.2683	+	40.8094i	−0.615818	+	1.30427i
$980$		−	53.8209i		−	1.71925i
$981$		0			0
$982$	24.3234	−	74.8598i	0.776191	−	2.38887i
$983$	3.41126	−	16.0487i	0.108802	−	0.511875i	−0.889669	−	0.456606i	$-0.849065\pi$
$983$	3.41126	−	16.0487i	0.108802	−	0.511875i	0.998471	−	0.0552693i	$-0.0176017\pi$
$984$		0			0
$985$	−10.4770	+	23.5317i	−0.333825	+	0.749783i
$986$	26.2743	−	29.1806i	0.836744	−	0.929298i
$987$		0			0
$988$	56.2953	−	25.0643i	1.79099	−	0.797401i
$989$	0.286760			0.00911842
$990$		0			0
$991$	59.6539			1.89497			0.947484	−	0.319804i	$-0.103617\pi$
$991$	59.6539			1.89497			0.947484	+	0.319804i	$0.103617\pi$
$992$	−9.73393	+	4.33383i	−0.309053	+	0.137599i
$993$		0			0
$994$	−9.16351	+	10.1771i	−0.290649	+	0.322798i
$995$	9.98859	−	22.4347i	0.316660	−	0.711229i
$996$		0			0
$997$	−8.46698	+	39.8340i	−0.268152	+	1.26156i	0.613515	+	0.789683i	$0.289755\pi$
$997$	−8.46698	+	39.8340i	−0.268152	+	1.26156i	−0.881667	+	0.471873i	$0.843578\pi$
$998$	−1.62771	+	5.00958i	−0.0515243	+	0.158575i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.62.1		80
3.2	odd	2		99.2.p.a.29.10	✓	80
9.2	odd	6		891.2.k.a.161.2		80
9.4	even	3		99.2.p.a.95.10	yes	80
9.5	odd	6	inner	297.2.t.a.260.1		80
9.7	even	3		891.2.k.a.161.19		80
11.8	odd	10	inner	297.2.t.a.8.1		80
33.8	even	10		99.2.p.a.74.10	yes	80
99.41	even	30	inner	297.2.t.a.206.1		80
99.52	odd	30		891.2.k.a.404.2		80
99.74	even	30		891.2.k.a.404.19		80
99.85	odd	30		99.2.p.a.41.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.10	✓	80	3.2	odd	2
99.2.p.a.41.10	yes	80	99.85	odd	30
99.2.p.a.74.10	yes	80	33.8	even	10
99.2.p.a.95.10	yes	80	9.4	even	3
297.2.t.a.8.1		80	11.8	odd	10	inner
297.2.t.a.62.1		80	1.1	even	1	trivial
297.2.t.a.206.1		80	99.41	even	30	inner
297.2.t.a.260.1		80	9.5	odd	6	inner
891.2.k.a.161.2		80	9.2	odd	6
891.2.k.a.161.19		80	9.7	even	3
891.2.k.a.404.2		80	99.52	odd	30
891.2.k.a.404.19		80	99.74	even	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.14162 + 0.953512i) q^{2} +(2.33911 - 2.59784i) q^{4} +(1.18835 - 2.66909i) q^{5} +(0.273495 - 1.28669i) q^{7} +(-1.08356 + 3.33484i) q^{8} +6.84930i q^{10} +(-2.99913 - 1.41605i) q^{11} +(-5.87678 - 0.617674i) q^{13} +(0.641155 + 3.01640i) q^{14} +(-0.128435 - 1.22198i) q^{16} +(-3.07734 + 2.23582i) q^{17} +(-2.83716 - 0.921851i) q^{19} +(-4.15418 - 9.33044i) q^{20} +(7.77324 + 0.172942i) q^{22} +(-0.0733618 + 0.0423554i) q^{23} +(-2.36619 - 2.62792i) q^{25} +(13.1748 - 4.28075i) q^{26} +(-2.70289 - 3.72021i) q^{28} +(4.30718 + 0.915520i) q^{29} +(0.269516 - 2.56428i) q^{31} +(-2.06622 - 3.57881i) q^{32} +(4.45863 - 7.72257i) q^{34} +(-3.10929 - 2.25903i) q^{35} +(-2.11787 - 6.51815i) q^{37} +(6.95514 - 0.731014i) q^{38} +(7.61334 + 6.85508i) q^{40} +(4.42142 - 0.939802i) q^{41} +(-2.93163 - 1.69258i) q^{43} +(-10.6940 + 4.47897i) q^{44} +(0.116727 - 0.160661i) q^{46} +(-3.53111 + 3.17942i) q^{47} +(4.81404 + 2.14335i) q^{49} +(7.57326 + 3.37183i) q^{50} +(-15.3510 + 13.8221i) q^{52} +(2.46224 - 3.38898i) q^{53} +(-7.34360 + 6.32218i) q^{55} +(3.99457 + 2.30627i) q^{56} +(-10.0973 + 2.14625i) q^{58} +(-10.4314 - 9.39248i) q^{59} +(9.76570 - 1.02642i) q^{61} +(1.86787 + 5.74871i) q^{62} +(9.82561 + 7.13872i) q^{64} +(-8.63232 + 14.9516i) q^{65} +(1.89207 + 3.27716i) q^{67} +(-1.38993 + 13.2243i) q^{68} +(8.81295 + 1.87325i) q^{70} +(2.61027 + 3.59273i) q^{71} +(8.30569 - 2.69868i) q^{73} +(10.7508 + 11.9400i) q^{74} +(-9.03125 + 5.21419i) q^{76} +(-2.64228 + 3.47168i) q^{77} +(-2.26254 - 5.08174i) q^{79} +(-3.41421 - 1.10934i) q^{80} +(-8.57291 + 6.22858i) q^{82} +(-0.131905 - 1.25499i) q^{83} +(2.31063 + 10.8706i) q^{85} +(7.89234 + 0.829519i) q^{86} +(7.97204 - 8.46726i) q^{88} -13.6071i q^{89} +(-2.40203 + 7.39268i) q^{91} +(-0.0615683 + 0.289656i) q^{92} +(4.53068 - 10.1761i) q^{94} +(-5.83206 + 6.47716i) q^{95} +(-12.5821 + 5.60189i) q^{97} -12.3536 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

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