LMFDB - Embedded newform 605.2.e.c.483.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.20
Character	$\chi$	$=$	605.483
Dual form			605.2.e.c.362.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91757 + 1.91757i) q^{2} +(0.831561 + 0.831561i) q^{3} +5.35415i q^{4} +(1.62695 - 1.53396i) q^{5} +3.18915i q^{6} +(0.383282 + 0.383282i) q^{7} +(-6.43181 + 6.43181i) q^{8} -1.61701i q^{9} +O(q^{10})$	\(q+(1.91757 + 1.91757i) q^{2} +(0.831561 + 0.831561i) q^{3} +5.35415i q^{4} +(1.62695 - 1.53396i) q^{5} +3.18915i q^{6} +(0.383282 + 0.383282i) q^{7} +(-6.43181 + 6.43181i) q^{8} -1.61701i q^{9} +(6.06127 + 0.178306i) q^{10} +(-4.45230 + 4.45230i) q^{12} +(-1.46382 + 1.46382i) q^{13} +1.46994i q^{14} +(2.62849 + 0.0773230i) q^{15} -13.9586 q^{16} +(-3.33920 - 3.33920i) q^{17} +(3.10074 - 3.10074i) q^{18} +2.45931 q^{19} +(8.21306 + 8.71092i) q^{20} +0.637445i q^{21} +(2.08092 + 2.08092i) q^{23} -10.6969 q^{24} +(0.293919 - 4.99135i) q^{25} -5.61395 q^{26} +(3.83933 - 3.83933i) q^{27} +(-2.05215 + 2.05215i) q^{28} +0.102937 q^{29} +(4.89204 + 5.18858i) q^{30} -5.44125 q^{31} +(-13.9030 - 13.9030i) q^{32} -12.8063i q^{34} +(1.21152 + 0.0356397i) q^{35} +8.65773 q^{36} +(5.74503 - 5.74503i) q^{37} +(4.71591 + 4.71591i) q^{38} -2.43451 q^{39} +(-0.598065 + 20.3304i) q^{40} +3.50547i q^{41} +(-1.22234 + 1.22234i) q^{42} +(-5.15006 + 5.15006i) q^{43} +(-2.48044 - 2.63080i) q^{45} +7.98062i q^{46} +(1.47326 - 1.47326i) q^{47} +(-11.6074 - 11.6074i) q^{48} -6.70619i q^{49} +(10.1349 - 9.00766i) q^{50} -5.55350i q^{51} +(-7.83750 - 7.83750i) q^{52} +(-0.224800 - 0.224800i) q^{53} +14.7244 q^{54} -4.93040 q^{56} +(2.04507 + 2.04507i) q^{57} +(0.197389 + 0.197389i) q^{58} -2.79138i q^{59} +(-0.413999 + 14.0733i) q^{60} -9.29408i q^{61} +(-10.4340 - 10.4340i) q^{62} +(0.619773 - 0.619773i) q^{63} -25.4026i q^{64} +(-0.136114 + 4.62700i) q^{65} +(-10.6041 + 10.6041i) q^{67} +(17.8786 - 17.8786i) q^{68} +3.46082i q^{69} +(2.25483 + 2.39152i) q^{70} +11.5983 q^{71} +(10.4003 + 10.4003i) q^{72} +(-6.90968 + 6.90968i) q^{73} +22.0330 q^{74} +(4.39502 - 3.90620i) q^{75} +13.1675i q^{76} +(-4.66834 - 4.66834i) q^{78} +12.8575 q^{79} +(-22.7099 + 21.4120i) q^{80} +1.53422 q^{81} +(-6.72198 + 6.72198i) q^{82} +(-3.83250 + 3.83250i) q^{83} -3.41297 q^{84} +(-10.5549 - 0.310497i) q^{85} -19.7512 q^{86} +(0.0855986 + 0.0855986i) q^{87} +2.37467i q^{89} +(0.288323 - 9.80115i) q^{90} -1.12211 q^{91} +(-11.1416 + 11.1416i) q^{92} +(-4.52473 - 4.52473i) q^{93} +5.65016 q^{94} +(4.00118 - 3.77250i) q^{95} -23.1223i q^{96} +(-1.97796 + 1.97796i) q^{97} +(12.8596 - 12.8596i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) $ 40 * q + 8 * q^3 - 4 * q^5	$ 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) $ 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.91757	+	1.91757i	1.35593	+	1.35593i	0.878876	+	0.477051i	$0.158294\pi$
$2$	1.91757	+	1.91757i	1.35593	+	1.35593i	0.477051	+	0.878876i	$0.341706\pi$
$3$	0.831561	+	0.831561i	0.480102	+	0.480102i	0.905164	−	0.425062i	$-0.139748\pi$
$3$	0.831561	+	0.831561i	0.480102	+	0.480102i	−0.425062	+	0.905164i	$0.639748\pi$
$4$			5.35415i			2.67707i
$5$	1.62695	−	1.53396i	0.727593	−	0.686009i
$5$	1.62695	−	1.53396i	0.727593	−	0.686009i
$6$			3.18915i			1.30197i
$7$	0.383282	+	0.383282i	0.144867	+	0.144867i	0.775821	−	0.630954i	$-0.217336\pi$
$7$	0.383282	+	0.383282i	0.144867	+	0.144867i	−0.630954	+	0.775821i	$0.717336\pi$
$8$	−6.43181	+	6.43181i	−2.27399	+	2.27399i
$9$		−	1.61701i		−	0.539005i
$10$	6.06127	+	0.178306i	1.91674	+	0.0563853i
$11$		0			0
$11$		0			0
$12$	−4.45230	+	4.45230i	−1.28527	+	1.28527i
$13$	−1.46382	+	1.46382i	−0.405990	+	0.405990i	−0.880338	−	0.474347i	$-0.842684\pi$
$13$	−1.46382	+	1.46382i	−0.405990	+	0.405990i	0.474347	+	0.880338i	$0.342684\pi$
$14$			1.46994i			0.392858i
$15$	2.62849	+	0.0773230i	0.678673	+	0.0199647i
$16$	−13.9586			−3.48965
$17$	−3.33920	−	3.33920i	−0.809876	−	0.809876i	0.174739	−	0.984615i	$-0.444092\pi$
$17$	−3.33920	−	3.33920i	−0.809876	−	0.809876i	−0.984615	+	0.174739i	$0.944092\pi$
$18$	3.10074	−	3.10074i	0.730851	−	0.730851i
$19$	2.45931			0.564205			0.282103	−	0.959384i	$-0.408968\pi$
$19$	2.45931			0.564205			0.282103	+	0.959384i	$0.408968\pi$
$20$	8.21306	+	8.71092i	1.83650	+	1.94782i
$21$			0.637445i			0.139102i
$22$		0			0
$23$	2.08092	+	2.08092i	0.433902	+	0.433902i	0.889953	−	0.456051i	$-0.150737\pi$
$23$	2.08092	+	2.08092i	0.433902	+	0.433902i	−0.456051	+	0.889953i	$0.650737\pi$
$24$	−10.6969			−2.18349
$25$	0.293919	−	4.99135i	0.0587837	−	0.998271i
$26$	−5.61395			−1.10099
$27$	3.83933	−	3.83933i	0.738879	−	0.738879i
$28$	−2.05215	+	2.05215i	−0.387820	+	0.387820i
$29$	0.102937			0.0191150			0.00955749	−	0.999954i	$-0.496958\pi$
$29$	0.102937			0.0191150			0.00955749	+	0.999954i	$0.496958\pi$
$30$	4.89204	+	5.18858i	0.893160	+	0.947301i
$31$	−5.44125			−0.977277			−0.488638	−	0.872486i	$-0.662506\pi$
$31$	−5.44125			−0.977277			−0.488638	+	0.872486i	$0.662506\pi$
$32$	−13.9030	−	13.9030i	−2.45772	−	2.45772i
$33$		0			0
$34$		−	12.8063i		−	2.19626i
$35$	1.21152	+	0.0356397i	0.204784	+	0.00602420i
$36$	8.65773			1.44296
$37$	5.74503	−	5.74503i	0.944478	−	0.944478i	−0.0540599	−	0.998538i	$-0.517216\pi$
$37$	5.74503	−	5.74503i	0.944478	−	0.944478i	0.998538	+	0.0540599i	$0.0172162\pi$
$38$	4.71591	+	4.71591i	0.765021	+	0.765021i
$39$	−2.43451			−0.389833
$40$	−0.598065	+	20.3304i	−0.0945624	+	3.21451i
$41$			3.50547i			0.547462i	0.961806	+	0.273731i	$0.0882579\pi$
$41$			3.50547i			0.547462i	−0.961806	+	0.273731i	$0.911742\pi$
$42$	−1.22234	+	1.22234i	−0.188612	+	0.188612i
$43$	−5.15006	+	5.15006i	−0.785378	+	0.785378i	−0.980733	−	0.195355i	$-0.937414\pi$
$43$	−5.15006	+	5.15006i	−0.785378	+	0.785378i	0.195355	+	0.980733i	$0.437414\pi$
$44$		0			0
$45$	−2.48044	−	2.63080i	−0.369762	−	0.392176i
$46$			7.98062i			1.17668i
$47$	1.47326	−	1.47326i	0.214897	−	0.214897i	−0.591447	−	0.806344i	$-0.701443\pi$
$47$	1.47326	−	1.47326i	0.214897	−	0.214897i	0.806344	+	0.591447i	$0.201443\pi$
$48$	−11.6074	−	11.6074i	−1.67539	−	1.67539i
$49$		−	6.70619i		−	0.958027i
$50$	10.1349	−	9.00766i	1.43329	−	1.27388i
$51$		−	5.55350i		−	0.777645i
$52$	−7.83750	−	7.83750i	−1.08687	−	1.08687i
$53$	−0.224800	−	0.224800i	−0.0308786	−	0.0308786i	0.691499	−	0.722378i	$-0.256951\pi$
$53$	−0.224800	−	0.224800i	−0.0308786	−	0.0308786i	−0.722378	+	0.691499i	$0.756951\pi$
$54$	14.7244			2.00373
$55$		0			0
$56$	−4.93040			−0.658852
$57$	2.04507	+	2.04507i	0.270876	+	0.270876i
$58$	0.197389	+	0.197389i	0.0259185	+	0.0259185i
$59$		−	2.79138i		−	0.363407i	−0.983353	−	0.181704i	$-0.941839\pi$
$59$		−	2.79138i		−	0.363407i	0.983353	−	0.181704i	$-0.0581611\pi$
$60$	−0.413999	+	14.0733i	−0.0534470	+	1.81686i
$61$		−	9.29408i		−	1.18998i	−0.803731	−	0.594992i	$-0.797155\pi$
$61$		−	9.29408i		−	1.18998i	0.803731	−	0.594992i	$-0.202845\pi$
$62$	−10.4340	−	10.4340i	−1.32512	−	1.32512i
$63$	0.619773	−	0.619773i	0.0780840	−	0.0780840i
$64$		−	25.4026i		−	3.17532i
$65$	−0.136114	+	4.62700i	−0.0168829	+	0.573909i
$66$		0			0
$67$	−10.6041	+	10.6041i	−1.29550	+	1.29550i	−0.364167	+	0.931334i	$0.618646\pi$
$67$	−10.6041	+	10.6041i	−1.29550	+	1.29550i	−0.931334	+	0.364167i	$0.881354\pi$
$68$	17.8786	−	17.8786i	2.16810	−	2.16810i
$69$			3.46082i			0.416634i
$70$	2.25483	+	2.39152i	0.269504	+	0.285841i
$71$	11.5983			1.37647			0.688234	−	0.725489i	$-0.258386\pi$
$71$	11.5983			1.37647			0.688234	+	0.725489i	$0.258386\pi$
$72$	10.4003	+	10.4003i	1.22569	+	1.22569i
$73$	−6.90968	+	6.90968i	−0.808717	+	0.808717i	−0.984440	−	0.175723i	$-0.943774\pi$
$73$	−6.90968	+	6.90968i	−0.808717	+	0.808717i	0.175723	+	0.984440i	$0.443774\pi$
$74$	22.0330			2.56128
$75$	4.39502	−	3.90620i	0.507494	−	0.451049i
$76$			13.1675i			1.51042i
$77$		0			0
$78$	−4.66834	−	4.66834i	−0.528585	−	0.528585i
$79$	12.8575			1.44658			0.723289	−	0.690546i	$-0.242630\pi$
$79$	12.8575			1.44658			0.723289	+	0.690546i	$0.242630\pi$
$80$	−22.7099	+	21.4120i	−2.53904	+	2.39393i
$81$	1.53422			0.170469
$82$	−6.72198	+	6.72198i	−0.742319	+	0.742319i
$83$	−3.83250	+	3.83250i	−0.420672	+	0.420672i	−0.885435	−	0.464763i	$-0.846139\pi$
$83$	−3.83250	+	3.83250i	−0.420672	+	0.420672i	0.464763	+	0.885435i	$0.346139\pi$
$84$	−3.41297			−0.372386
$85$	−10.5549	−	0.310497i	−1.14484	−	0.0336782i
$86$	−19.7512			−2.12983
$87$	0.0855986	+	0.0855986i	0.00917713	+	0.00917713i
$88$		0			0
$89$			2.37467i			0.251715i	0.992048	+	0.125857i	$0.0401682\pi$
$89$			2.37467i			0.251715i	−0.992048	+	0.125857i	$0.959832\pi$
$90$	0.288323	−	9.80115i	0.0303920	−	1.03313i
$91$	−1.12211			−0.117629
$92$	−11.1416	+	11.1416i	−1.16159	+	1.16159i
$93$	−4.52473	−	4.52473i	−0.469192	−	0.469192i
$94$	5.65016			0.582770
$95$	4.00118	−	3.77250i	0.410512	−	0.387050i
$96$		−	23.1223i		−	2.35991i
$97$	−1.97796	+	1.97796i	−0.200831	+	0.200831i	−0.800356	−	0.599525i	$-0.795356\pi$
$97$	−1.97796	+	1.97796i	−0.200831	+	0.200831i	0.599525	+	0.800356i	$0.295356\pi$
$98$	12.8596	−	12.8596i	1.29901	−	1.29901i
$99$		0			0
$100$	26.7244	+	1.57368i	2.67244	+	0.157368i
$101$			14.5348i			1.44627i	0.690706	+	0.723135i	$0.257300\pi$
$101$			14.5348i			1.44627i	−0.690706	+	0.723135i	$0.742700\pi$
$102$	10.6492	−	10.6492i	1.05443	−	1.05443i
$103$	−2.09836	−	2.09836i	−0.206758	−	0.206758i	0.596130	−	0.802888i	$-0.296704\pi$
$103$	−2.09836	−	2.09836i	−0.206758	−	0.206758i	−0.802888	+	0.596130i	$0.796704\pi$
$104$		−	18.8300i		−	1.84643i
$105$	0.977816	+	1.03709i	0.0954251	+	0.101210i
$106$		−	0.862139i		−	0.0837383i
$107$	1.17699	+	1.17699i	0.113784	+	0.113784i	0.761706	−	0.647922i	$-0.224362\pi$
$107$	1.17699	+	1.17699i	0.113784	+	0.113784i	−0.647922	+	0.761706i	$0.724362\pi$
$108$	20.5563	+	20.5563i	1.97803	+	1.97803i
$109$	−9.24354			−0.885371			−0.442685	−	0.896677i	$-0.645974\pi$
$109$	−9.24354			−0.885371			−0.442685	+	0.896677i	$0.645974\pi$
$110$		0			0
$111$	9.55469			0.906891
$112$	−5.35008	−	5.35008i	−0.505535	−	0.505535i
$113$	7.77171	+	7.77171i	0.731101	+	0.731101i	0.970838	−	0.239737i	$-0.0770611\pi$
$113$	7.77171	+	7.77171i	0.731101	+	0.731101i	−0.239737	+	0.970838i	$0.577061\pi$
$114$			7.84312i			0.734576i
$115$	6.57761	+	0.193495i	0.613365	+	0.0180435i
$116$			0.551141i			0.0511722i
$117$	2.36702	+	2.36702i	0.218831	+	0.218831i
$118$	5.35267	−	5.35267i	0.492753	−	0.492753i
$119$		−	2.55971i		−	0.234649i
$120$	−17.4033	+	16.4086i	−1.58869	+	1.49789i
$121$		0			0
$122$	17.8220	−	17.8220i	1.61353	−	1.61353i
$123$	−2.91501	+	2.91501i	−0.262838	+	0.262838i
$124$		−	29.1332i		−	2.61624i
$125$	−7.17836	−	8.57153i	−0.642052	−	0.766661i
$126$	2.37691			0.211752
$127$	4.82946	+	4.82946i	0.428545	+	0.428545i	0.888133	−	0.459587i	$-0.152003\pi$
$127$	4.82946	+	4.82946i	0.428545	+	0.428545i	−0.459587	+	0.888133i	$0.652003\pi$
$128$	20.9053	−	20.9053i	1.84779	−	1.84779i
$129$	−8.56518			−0.754122
$130$	−9.13360	+	8.61159i	−0.801070	+	0.755286i
$131$		−	20.5992i		−	1.79976i	−0.436141	−	0.899878i	$-0.643655\pi$
$131$		−	20.5992i		−	1.79976i	0.436141	−	0.899878i	$-0.356345\pi$
$132$		0			0
$133$	0.942611	+	0.942611i	0.0817347	+	0.0817347i
$134$	−40.6683			−3.51321
$135$	0.357002	−	12.1358i	0.0307258	−	1.04448i
$136$	42.9542			3.68330
$137$	−4.69687	+	4.69687i	−0.401281	+	0.401281i	−0.878684	−	0.477403i	$-0.841578\pi$
$137$	−4.69687	+	4.69687i	−0.401281	+	0.401281i	0.477403	+	0.878684i	$0.341578\pi$
$138$	−6.63637	+	6.63637i	−0.564926	+	0.564926i
$139$	6.25764			0.530766			0.265383	−	0.964143i	$-0.414502\pi$
$139$	6.25764			0.530766			0.265383	+	0.964143i	$0.414502\pi$
$140$	−0.190820	+	6.48666i	−0.0161272	+	0.548223i
$141$	2.45021			0.206345
$142$	22.2406	+	22.2406i	1.86639	+	1.86639i
$143$		0			0
$144$			22.5712i			1.88094i
$145$	0.167474	−	0.157902i	0.0139079	−	0.0131130i
$146$	−26.4996			−2.19312
$147$	5.57660	−	5.57660i	0.459950	−	0.459950i
$148$	30.7598	+	30.7598i	2.52844	+	2.52844i
$149$	−17.9764			−1.47268			−0.736342	−	0.676610i	$-0.763448\pi$
$149$	−17.9764			−1.47268			−0.736342	+	0.676610i	$0.763448\pi$
$150$	15.9182	+	0.937351i	1.29971	+	0.0765344i
$151$			3.83556i			0.312134i	0.987746	+	0.156067i	$0.0498815\pi$
$151$			3.83556i			0.312134i	−0.987746	+	0.156067i	$0.950118\pi$
$152$	−15.8178	+	15.8178i	−1.28300	+	1.28300i
$153$	−5.39954	+	5.39954i	−0.436527	+	0.436527i
$154$		0			0
$155$	−8.85262	+	8.34667i	−0.711060	+	0.670420i
$156$		−	13.0347i		−	1.04361i
$157$	−0.523576	+	0.523576i	−0.0417859	+	0.0417859i	−0.727691	−	0.685905i	$-0.759406\pi$
$157$	−0.523576	+	0.523576i	−0.0417859	+	0.0417859i	0.685905	+	0.727691i	$0.259406\pi$
$158$	24.6551	+	24.6551i	1.96145	+	1.96145i
$159$		−	0.373869i		−	0.0296498i
$160$	−43.9460	−	1.29277i	−3.47424	−	0.102203i
$161$			1.59516i			0.125716i
$162$	2.94198	+	2.94198i	0.231144	+	0.231144i
$163$	7.37800	+	7.37800i	0.577890	+	0.577890i	0.934321	−	0.356432i	$-0.116007\pi$
$163$	7.37800	+	7.37800i	0.577890	+	0.577890i	−0.356432	+	0.934321i	$0.616007\pi$
$164$	−18.7688			−1.46560
$165$		0			0
$166$	−14.6982			−1.14080
$167$	−10.9811	−	10.9811i	−0.849745	−	0.849745i	0.140356	−	0.990101i	$-0.455175\pi$
$167$	−10.9811	−	10.9811i	−0.849745	−	0.849745i	−0.990101	+	0.140356i	$0.955175\pi$
$168$	−4.09992	−	4.09992i	−0.316316	−	0.316316i
$169$			8.71447i			0.670344i
$170$	−19.6444	−	20.8352i	−1.50666	−	1.59799i
$171$		−	3.97675i		−	0.304109i
$172$	−27.5742	−	27.5742i	−2.10251	−	2.10251i
$173$	8.78660	−	8.78660i	0.668033	−	0.668033i	−0.289228	−	0.957260i	$-0.593398\pi$
$173$	8.78660	−	8.78660i	0.668033	−	0.668033i	0.957260	+	0.289228i	$0.0933985\pi$
$174$			0.328282i			0.0248870i
$175$	2.02575	−	1.80044i	0.153132	−	0.136101i
$176$		0			0
$177$	2.32120	−	2.32120i	0.174472	−	0.174472i
$178$	−4.55360	+	4.55360i	−0.341307	+	0.341307i
$179$			22.2415i			1.66241i	0.555970	+	0.831203i	$0.312347\pi$
$179$			22.2415i			1.66241i	−0.555970	+	0.831203i	$0.687653\pi$
$180$	14.0857	−	13.2806i	1.04988	−	0.989880i
$181$	−18.0176			−1.33924			−0.669619	−	0.742705i	$-0.733543\pi$
$181$	−18.0176			−1.33924			−0.669619	+	0.742705i	$0.733543\pi$
$182$	−2.15173	−	2.15173i	−0.159497	−	0.159497i
$183$	7.72859	−	7.72859i	0.571314	−	0.571314i
$184$	−26.7682			−1.97338
$185$	0.534205	−	18.1595i	0.0392755	−	1.33512i
$186$		−	17.3530i		−	1.27238i
$187$		0			0
$188$	7.88805	+	7.88805i	0.575296	+	0.575296i
$189$	2.94309			0.214078
$190$	14.9066	+	0.438511i	1.08144	+	0.0318129i
$191$	−20.8165			−1.50623			−0.753114	−	0.657890i	$-0.771449\pi$
$191$	−20.8165			−1.50623			−0.753114	+	0.657890i	$0.771449\pi$
$192$	21.1238	−	21.1238i	1.52448	−	1.52448i
$193$	5.19338	−	5.19338i	0.373828	−	0.373828i	−0.495041	−	0.868869i	$-0.664847\pi$
$193$	5.19338	−	5.19338i	0.373828	−	0.373828i	0.868869	+	0.495041i	$0.164847\pi$
$194$	−7.58574			−0.544625
$195$	−3.96082	+	3.73444i	−0.283640	+	0.267429i
$196$	35.9059			2.56471
$197$	4.06649	+	4.06649i	0.289725	+	0.289725i	0.836972	−	0.547246i	$-0.184324\pi$
$197$	4.06649	+	4.06649i	0.289725	+	0.289725i	−0.547246	+	0.836972i	$0.684324\pi$
$198$		0			0
$199$		−	11.0726i		−	0.784913i	−0.919771	−	0.392456i	$-0.871625\pi$
$199$		−	11.0726i		−	0.784913i	0.919771	−	0.392456i	$-0.128375\pi$
$200$	30.2130	+	33.9939i	2.13638	+	2.40373i
$201$	−17.6359			−1.24394
$202$	−27.8716	+	27.8716i	−1.96104	+	1.96104i
$203$	0.0394540	+	0.0394540i	0.00276913	+	0.00276913i
$204$	29.7343			2.08181
$205$	5.37726	+	5.70322i	0.375564	+	0.398330i
$206$		−	8.04751i		−	0.560697i
$207$	3.36488	−	3.36488i	0.233875	−	0.233875i
$208$	20.4329	−	20.4329i	1.41676	−	1.41676i
$209$		0			0
$210$	−0.113660	+	3.86372i	−0.00784330	+	0.266622i
$211$		−	20.9798i		−	1.44431i	−0.691730	−	0.722156i	$-0.743151\pi$
$211$		−	20.9798i		−	1.44431i	0.691730	−	0.722156i	$-0.256849\pi$
$212$	1.20361	−	1.20361i	0.0826644	−	0.0826644i
$213$	9.64471	+	9.64471i	0.660844	+	0.660844i
$214$			4.51392i			0.308565i
$215$	−0.478881	+	16.2789i	−0.0326594	+	1.11021i
$216$			49.3876i			3.36040i
$217$	−2.08553	−	2.08553i	−0.141575	−	0.141575i
$218$	−17.7251	−	17.7251i	−1.20050	−	1.20050i
$219$	−11.4916			−0.776533
$220$		0			0
$221$	9.77598			0.657603
$222$	18.3218	+	18.3218i	1.22968	+	1.22968i
$223$	8.16639	+	8.16639i	0.546862	+	0.546862i	0.925532	−	0.378670i	$-0.123618\pi$
$223$	8.16639	+	8.16639i	0.546862	+	0.546862i	−0.378670	+	0.925532i	$0.623618\pi$
$224$		−	10.6575i		−	0.712085i
$225$	−8.07109	−	0.475271i	−0.538073	−	0.0316847i
$226$			29.8056i			1.98264i
$227$	10.6518	+	10.6518i	0.706985	+	0.706985i	0.965900	−	0.258915i	$-0.0833649\pi$
$227$	10.6518	+	10.6518i	0.706985	+	0.706985i	−0.258915	+	0.965900i	$0.583365\pi$
$228$	−10.9496	+	10.9496i	−0.725155	+	0.725155i
$229$		−	2.74244i		−	0.181226i	−0.995886	−	0.0906129i	$-0.971117\pi$
$229$		−	2.74244i		−	0.181226i	0.995886	−	0.0906129i	$-0.0288826\pi$
$230$	12.2420	+	12.9841i	0.807212	+	0.856144i
$231$		0			0
$232$	−0.662073	+	0.662073i	−0.0434672	+	0.0434672i
$233$	2.95822	−	2.95822i	0.193799	−	0.193799i	−0.603536	−	0.797335i	$-0.706242\pi$
$233$	2.95822	−	2.95822i	0.193799	−	0.193799i	0.797335	+	0.603536i	$0.206242\pi$
$234$			9.07784i			0.593437i
$235$	0.136992	−	4.65685i	0.00893636	−	0.303779i
$236$	14.9455			0.972867
$237$	10.6918	+	10.6918i	0.694504	+	0.694504i
$238$	4.90843	−	4.90843i	0.318166	−	0.318166i
$239$	−0.245754			−0.0158965			−0.00794824	−	0.999968i	$-0.502530\pi$
$239$	−0.245754			−0.0158965			−0.00794824	+	0.999968i	$0.502530\pi$
$240$	−36.6900	−	1.07932i	−2.36833	−	0.0696699i
$241$		−	15.5425i		−	1.00118i	−0.865684	−	0.500591i	$-0.833116\pi$
$241$		−	15.5425i		−	1.00118i	0.865684	−	0.500591i	$-0.166884\pi$
$242$		0			0
$243$	−10.2422	−	10.2422i	−0.657036	−	0.657036i
$244$	49.7619			3.18568
$245$	−10.2870	−	10.9106i	−0.657215	−	0.697054i
$246$	−11.1795			−0.712777
$247$	−3.59999	+	3.59999i	−0.229062	+	0.229062i
$248$	34.9971	−	34.9971i	2.22232	−	2.22232i
$249$	−6.37391			−0.403930
$250$	2.67151	−	30.2015i	0.168961	−	1.91011i
$251$	4.88048			0.308053			0.154027	−	0.988067i	$-0.450776\pi$
$251$	4.88048			0.308053			0.154027	+	0.988067i	$0.450776\pi$
$252$	3.31835	+	3.31835i	0.209037	+	0.209037i
$253$		0			0
$254$			18.5217i			1.16215i
$255$	−8.51886	−	9.03525i	−0.533472	−	0.565810i
$256$	29.3696			1.83560
$257$	5.59507	−	5.59507i	0.349011	−	0.349011i	−0.510730	−	0.859741i	$-0.670625\pi$
$257$	5.59507	−	5.59507i	0.349011	−	0.349011i	0.859741	+	0.510730i	$0.170625\pi$
$258$	−16.4243	−	16.4243i	−1.02253	−	1.02253i
$259$	4.40394			0.273647
$260$	−24.7736	−	0.728774i	−1.53640	−	0.0451966i
$261$		−	0.166451i		−	0.0103031i
$262$	39.5003	−	39.5003i	2.44034	−	2.44034i
$263$	1.02839	−	1.02839i	0.0634133	−	0.0634133i	−0.674689	−	0.738102i	$-0.735722\pi$
$263$	1.02839	−	1.02839i	0.0634133	−	0.0634133i	0.738102	+	0.674689i	$0.235722\pi$
$264$		0			0
$265$	−0.710572	−	0.0209031i	−0.0436501	−	0.00128407i
$266$			3.61504i			0.221653i
$267$	−1.97469	+	1.97469i	−0.120849	+	0.120849i
$268$	−56.7761	−	56.7761i	−3.46815	−	3.46815i
$269$			23.1174i			1.40949i	0.709458	+	0.704747i	$0.248940\pi$
$269$			23.1174i			1.40949i	−0.709458	+	0.704747i	$0.751060\pi$
$270$	23.9558	−	22.5866i	1.45790	−	1.37458i
$271$		−	26.0865i		−	1.58464i	−0.610106	−	0.792320i	$-0.708873\pi$
$271$		−	26.0865i		−	1.58464i	0.610106	−	0.792320i	$-0.291127\pi$
$272$	46.6106	+	46.6106i	2.82618	+	2.82618i
$273$	−0.933103	−	0.933103i	−0.0564740	−	0.0564740i
$274$	−18.0132			−1.08821
$275$		0			0
$276$	−18.5298			−1.11536
$277$	−14.6511	−	14.6511i	−0.880298	−	0.880298i	0.113266	−	0.993565i	$-0.463869\pi$
$277$	−14.6511	−	14.6511i	−0.880298	−	0.880298i	−0.993565	+	0.113266i	$0.963869\pi$
$278$	11.9995	+	11.9995i	0.719680	+	0.719680i
$279$			8.79857i			0.526757i
$280$	−8.02150	+	7.56304i	−0.479376	+	0.451978i
$281$		−	22.6736i		−	1.35260i	−0.736628	−	0.676298i	$-0.763583\pi$
$281$		−	22.6736i		−	1.35260i	0.736628	−	0.676298i	$-0.236417\pi$
$282$	4.69845	+	4.69845i	0.279789	+	0.279789i
$283$	4.13198	−	4.13198i	0.245621	−	0.245621i	−0.573550	−	0.819171i	$-0.694434\pi$
$283$	4.13198	−	4.13198i	0.245621	−	0.245621i	0.819171	+	0.573550i	$0.194434\pi$
$284$			62.0991i			3.68490i
$285$	6.46428	+	0.190162i	0.382911	+	0.0112642i
$286$		0			0
$287$	−1.34358	+	1.34358i	−0.0793092	+	0.0793092i
$288$	−22.4813	+	22.4813i	−1.32472	+	1.32472i
$289$			5.30056i			0.311798i
$290$	0.623930	+	0.0183543i	0.0366384	+	0.00107780i
$291$	−3.28958			−0.192839
$292$	−36.9955	−	36.9955i	−2.16499	−	2.16499i
$293$	−11.9309	+	11.9309i	−0.697010	+	0.697010i	−0.963764	−	0.266755i	$-0.914049\pi$
$293$	−11.9309	+	11.9309i	−0.697010	+	0.697010i	0.266755	+	0.963764i	$0.414049\pi$
$294$	21.3870			1.24732
$295$	−4.28188	−	4.54143i	−0.249300	−	0.264412i
$296$			73.9019i			4.29546i
$297$		0			0
$298$	−34.4710	−	34.4710i	−1.99685	−	1.99685i
$299$	−6.09219			−0.352320
$300$	20.9144	+	23.5316i	1.20749	+	1.35860i
$301$	−3.94786			−0.227551
$302$	−7.35496	+	7.35496i	−0.423230	+	0.423230i
$303$	−12.0866	+	12.0866i	−0.694357	+	0.694357i
$304$	−34.3286			−1.96888
$305$	−14.2568	−	15.1210i	−0.816340	−	0.865825i
$306$	−20.7080			−1.18380
$307$	−16.0581	−	16.0581i	−0.916486	−	0.916486i	0.0802861	−	0.996772i	$-0.474417\pi$
$307$	−16.0581	−	16.0581i	−0.916486	−	0.916486i	−0.996772	+	0.0802861i	$0.974417\pi$
$308$		0			0
$309$		−	3.48983i		−	0.198530i
$310$	−32.9808	−	0.970207i	−1.87319	−	0.0551041i
$311$	−3.53177			−0.200268			−0.100134	−	0.994974i	$-0.531927\pi$
$311$	−3.53177			−0.200268			−0.100134	+	0.994974i	$0.531927\pi$
$312$	15.6583	−	15.6583i	0.886476	−	0.886476i
$313$	−8.38436	−	8.38436i	−0.473912	−	0.473912i	0.429266	−	0.903178i	$-0.358772\pi$
$313$	−8.38436	−	8.38436i	−0.473912	−	0.473912i	−0.903178	+	0.429266i	$0.858772\pi$
$314$	−2.00799			−0.113317
$315$	0.0576298	−	1.95905i	0.00324707	−	0.110380i
$316$			68.8407i			3.87259i
$317$	−7.20481	+	7.20481i	−0.404662	+	0.404662i	−0.879872	−	0.475210i	$-0.842372\pi$
$317$	−7.20481	+	7.20481i	−0.404662	+	0.404662i	0.475210	+	0.879872i	$0.342372\pi$
$318$	0.716921	−	0.716921i	0.0402029	−	0.0402029i
$319$		0			0
$320$	−38.9666	−	41.3287i	−2.17830	−	2.31034i
$321$			1.95748i			0.109256i
$322$	−3.05883	+	3.05883i	−0.170462	+	0.170462i
$323$	−8.21215	−	8.21215i	−0.456936	−	0.456936i
$324$			8.21446i			0.456359i
$325$	6.87619	+	7.73668i	0.381423	+	0.429154i
$326$			28.2957i			1.56715i
$327$	−7.68657	−	7.68657i	−0.425068	−	0.425068i
$328$	−22.5465	−	22.5465i	−1.24492	−	1.24492i
$329$	1.12935			0.0622630
$330$		0			0
$331$	11.6382			0.639694			0.319847	−	0.947469i	$-0.396369\pi$
$331$	11.6382			0.639694			0.319847	+	0.947469i	$0.396369\pi$
$332$	−20.5198	−	20.5198i	−1.12617	−	1.12617i
$333$	−9.28980	−	9.28980i	−0.509078	−	0.509078i
$334$		−	42.1141i		−	2.30438i
$335$	−0.986030	+	33.5187i	−0.0538726	+	1.83132i
$336$		−	8.89783i		−	0.485416i
$337$	18.8969	+	18.8969i	1.02938	+	1.02938i	0.999555	+	0.0298219i	$0.00949400\pi$
$337$	18.8969	+	18.8969i	1.02938	+	1.02938i	0.0298219	+	0.999555i	$0.490506\pi$
$338$	−16.7106	+	16.7106i	−0.908937	+	0.908937i
$339$			12.9253i			0.702006i
$340$	1.66245	−	56.5126i	0.0901589	−	3.06483i
$341$		0			0
$342$	7.62569	−	7.62569i	0.412350	−	0.412350i
$343$	5.25334	−	5.25334i	0.283654	−	0.283654i
$344$		−	66.2485i		−	3.57188i
$345$	5.30878	+	5.63058i	0.285815	+	0.303140i
$346$	33.6978			1.81161
$347$	19.8035	+	19.8035i	1.06311	+	1.06311i	0.997870	+	0.0652398i	$0.0207812\pi$
$347$	19.8035	+	19.8035i	1.06311	+	1.06311i	0.0652398	+	0.997870i	$0.479219\pi$
$348$	−0.458307	+	0.458307i	−0.0245679	+	0.0245679i
$349$	18.6294			0.997208			0.498604	−	0.866830i	$-0.333846\pi$
$349$	18.6294			0.997208			0.498604	+	0.866830i	$0.333846\pi$
$350$	7.33699	+	0.432043i	0.392179	+	0.0230937i
$351$			11.2402i			0.599955i
$352$		0			0
$353$	22.8366	+	22.8366i	1.21547	+	1.21547i	0.969201	+	0.246270i	$0.0792049\pi$
$353$	22.8366	+	22.8366i	1.21547	+	1.21547i	0.246270	+	0.969201i	$0.420795\pi$
$354$	8.90214			0.473143
$355$	18.8699	−	17.7914i	1.00151	−	0.944269i
$356$	−12.7144			−0.673859
$357$	2.12856	−	2.12856i	0.112655	−	0.112655i
$358$	−42.6496	+	42.6496i	−2.25410	+	2.25410i
$359$	−33.2038			−1.75243			−0.876214	−	0.481922i	$-0.839939\pi$
$359$	−33.2038			−1.75243			−0.876214	+	0.481922i	$0.839939\pi$
$360$	32.8745	+	0.967079i	1.73264	+	0.0509696i
$361$	−12.9518			−0.681672
$362$	−34.5500	−	34.5500i	−1.81591	−	1.81591i
$363$		0			0
$364$		−	6.00795i		−	0.314902i
$365$	−0.642500	+	21.8409i	−0.0336300	+	1.14320i
$366$	29.6402			1.54932
$367$	−13.6277	+	13.6277i	−0.711360	+	0.711360i	−0.966820	−	0.255460i	$-0.917773\pi$
$367$	−13.6277	+	13.6277i	−0.711360	+	0.711360i	0.255460	+	0.966820i	$0.417773\pi$
$368$	−29.0467	−	29.0467i	−1.51417	−	1.51417i
$369$	5.66839			0.295085
$370$	35.8466	−	33.7978i	1.86357	−	1.75706i
$371$		−	0.172324i		−	0.00894659i
$372$	24.2260	−	24.2260i	1.25606	−	1.25606i
$373$	−14.7456	+	14.7456i	−0.763498	+	0.763498i	−0.976953	−	0.213455i	$-0.931528\pi$
$373$	−14.7456	+	14.7456i	−0.763498	+	0.763498i	0.213455	+	0.976953i	$0.431528\pi$
$374$		0			0
$375$	1.15851	−	13.0970i	0.0598251	−	0.676326i
$376$			18.9515i			0.977347i
$377$	−0.150682	+	0.150682i	−0.00776049	+	0.00776049i
$378$	5.64358	+	5.64358i	0.290274	+	0.290274i
$379$		−	12.8178i		−	0.658404i	−0.944260	−	0.329202i	$-0.893220\pi$
$379$		−	12.8178i		−	0.658404i	0.944260	−	0.329202i	$-0.106780\pi$
$380$	20.1985	+	21.4229i	1.03616	+	1.09897i
$381$			8.03198i			0.411491i
$382$	−39.9171	−	39.9171i	−2.04233	−	2.04233i
$383$	17.5018	+	17.5018i	0.894300	+	0.894300i	0.994924	−	0.100624i	$-0.0320841\pi$
$383$	17.5018	+	17.5018i	0.894300	+	0.894300i	−0.100624	+	0.994924i	$0.532084\pi$
$384$	34.7681			1.77425
$385$		0			0
$386$	19.9173			1.01377
$387$	8.32773	+	8.32773i	0.423322	+	0.423322i
$388$	−10.5903	−	10.5903i	−0.537640	−	0.537640i
$389$			6.09407i			0.308982i	0.987994	+	0.154491i	$0.0493737\pi$
$389$			6.09407i			0.308982i	−0.987994	+	0.154491i	$0.950626\pi$
$390$	−14.7562	−	0.434088i	−0.747209	−	0.0219809i
$391$		−	13.8972i		−	0.702814i
$392$	43.1329	+	43.1329i	2.17854	+	2.17854i
$393$	17.1294	−	17.1294i	0.864066	−	0.864066i
$394$			15.5955i			0.785692i
$395$	20.9184	−	19.7229i	1.05252	−	0.992365i
$396$		0			0
$397$	5.37603	−	5.37603i	0.269815	−	0.269815i	−0.559211	−	0.829026i	$-0.688896\pi$
$397$	5.37603	−	5.37603i	0.269815	−	0.269815i	0.829026	+	0.559211i	$0.188896\pi$
$398$	21.2324	−	21.2324i	1.06428	−	1.06428i
$399$			1.56768i			0.0784820i
$400$	−4.10269	+	69.6723i	−0.205135	+	3.48361i
$401$	−10.7055			−0.534605			−0.267302	−	0.963613i	$-0.586132\pi$
$401$	−10.7055			−0.534605			−0.267302	+	0.963613i	$0.586132\pi$
$402$	−33.8182	−	33.8182i	−1.68670	−	1.68670i
$403$	7.96500	−	7.96500i	0.396765	−	0.396765i
$404$	−77.8217			−3.87177
$405$	2.49610	−	2.35344i	0.124032	−	0.116943i
$406$			0.151312i			0.00750947i
$407$		0			0
$408$	35.7191	+	35.7191i	1.76836	+	1.76836i
$409$	4.52307			0.223652			0.111826	−	0.993728i	$-0.464330\pi$
$409$	4.52307			0.223652			0.111826	+	0.993728i	$0.464330\pi$
$410$	−0.625047	+	21.2476i	−0.0308689	+	1.04934i
$411$	−7.81147			−0.385311
$412$	11.2349	−	11.2349i	0.553506	−	0.553506i
$413$	1.06989	−	1.06989i	0.0526457	−	0.0526457i
$414$	12.9048			0.634235
$415$	−0.356367	+	12.1142i	−0.0174934	+	0.594662i
$416$	40.7028			1.99562
$417$	5.20361	+	5.20361i	0.254822	+	0.254822i
$418$		0			0
$419$			8.57378i			0.418857i	0.977824	+	0.209428i	$0.0671603\pi$
$419$			8.57378i			0.418857i	−0.977824	+	0.209428i	$0.932840\pi$
$420$	−5.55273	+	5.23537i	−0.270945	+	0.255460i
$421$	−25.1023			−1.22341			−0.611707	−	0.791085i	$-0.709517\pi$
$421$	−25.1023			−1.22341			−0.611707	+	0.791085i	$0.709517\pi$
$422$	40.2303	−	40.2303i	1.95838	−	1.95838i
$423$	−2.38228	−	2.38228i	−0.115831	−	0.115831i
$424$	2.89174			0.140435
$425$	−17.6486	+	15.6857i	−0.856083	+	0.760868i
$426$			36.9888i			1.79211i
$427$	3.56225	−	3.56225i	0.172390	−	0.172390i
$428$	−6.30178	+	6.30178i	−0.304608	+	0.304608i
$429$		0			0
$430$	−32.1342	+	30.2976i	−1.54965	+	1.46108i
$431$			9.30270i			0.448095i	0.974578	+	0.224048i	$0.0719271\pi$
$431$			9.30270i			0.448095i	−0.974578	+	0.224048i	$0.928073\pi$
$432$	−53.5916	+	53.5916i	−2.57843	+	2.57843i
$433$	23.3858	+	23.3858i	1.12385	+	1.12385i	0.991157	+	0.132694i	$0.0423629\pi$
$433$	23.3858	+	23.3858i	1.12385	+	1.12385i	0.132694	+	0.991157i	$0.457637\pi$
$434$		−	7.99831i		−	0.383931i
$435$	0.270569	+	0.00795942i	0.0129728	+	0.000381625i
$436$		−	49.4913i		−	2.37020i
$437$	5.11764	+	5.11764i	0.244810	+	0.244810i
$438$	−22.0360	−	22.0360i	−1.05292	−	1.05292i
$439$	33.4407			1.59604			0.798018	−	0.602633i	$-0.205882\pi$
$439$	33.4407			1.59604			0.798018	+	0.602633i	$0.205882\pi$
$440$		0			0
$441$	−10.8440			−0.516381
$442$	18.7461	+	18.7461i	0.891662	+	0.891662i
$443$	19.8562	+	19.8562i	0.943395	+	0.943395i	0.998482	−	0.0550870i	$-0.0175436\pi$
$443$	19.8562	+	19.8562i	0.943395	+	0.943395i	−0.0550870	+	0.998482i	$0.517544\pi$
$444$			51.1572i			2.42781i
$445$	3.64266	+	3.86347i	0.172679	+	0.183146i
$446$			31.3193i			1.48301i
$447$	−14.9485	−	14.9485i	−0.707038	−	0.707038i
$448$	9.73635	−	9.73635i	0.460000	−	0.460000i
$449$			6.67204i			0.314873i	0.987529	+	0.157436i	$0.0503229\pi$
$449$			6.67204i			0.314873i	−0.987529	+	0.157436i	$0.949677\pi$
$450$	−14.5655	−	16.3882i	−0.686625	−	0.772549i
$451$		0			0
$452$	−41.6109	+	41.6109i	−1.95721	+	1.95721i
$453$	−3.18950	+	3.18950i	−0.149856	+	0.149856i
$454$			40.8512i			1.91724i
$455$	−1.82562	+	1.72128i	−0.0855862	+	0.0806947i
$456$	−26.3070			−1.23194
$457$	11.7933	+	11.7933i	0.551665	+	0.551665i	0.926921	−	0.375256i	$-0.122445\pi$
$457$	11.7933	+	11.7933i	0.551665	+	0.551665i	−0.375256	+	0.926921i	$0.622445\pi$
$458$	5.25883	−	5.25883i	0.245729	−	0.245729i
$459$	−25.6406			−1.19680
$460$	−1.03600	+	35.2175i	−0.0483039	+	1.64202i
$461$			20.7236i			0.965194i	0.875842	+	0.482597i	$0.160306\pi$
$461$			20.7236i			0.965194i	−0.875842	+	0.482597i	$0.839694\pi$
$462$		0			0
$463$	−19.1545	−	19.1545i	−0.890187	−	0.890187i	0.104353	−	0.994540i	$-0.466723\pi$
$463$	−19.1545	−	19.1545i	−0.890187	−	0.890187i	−0.994540	+	0.104353i	$0.966723\pi$
$464$	−1.43686			−0.0667045
$465$	−14.3023	−	0.420734i	−0.663251	−	0.0195111i
$466$	11.3452			0.525555
$467$	22.5244	−	22.5244i	1.04230	−	1.04230i	0.0432386	−	0.999065i	$-0.486232\pi$
$467$	22.5244	−	22.5244i	1.04230	−	1.04230i	0.999065	−	0.0432386i	$-0.0137676\pi$
$468$	−12.6734	+	12.6734i	−0.585826	+	0.585826i
$469$	−8.12875			−0.375351
$470$	9.19252	−	8.66713i	0.424019	−	0.399785i
$471$	−0.870770			−0.0401229
$472$	17.9536	+	17.9536i	0.826383	+	0.826383i
$473$		0			0
$474$			41.0044i			1.88339i
$475$	0.722838	−	12.2753i	0.0331661	−	0.563230i
$476$	13.7051			0.628171
$477$	−0.363505	+	0.363505i	−0.0166437	+	0.0166437i
$478$	−0.471250	−	0.471250i	−0.0215545	−	0.0215545i
$479$	−14.3874			−0.657379			−0.328689	−	0.944438i	$-0.606607\pi$
$479$	−14.3874			−0.657379			−0.328689	+	0.944438i	$0.606607\pi$
$480$	−35.4687	−	37.6188i	−1.61892	−	1.71705i
$481$			16.8194i			0.766898i
$482$	29.8039	−	29.8039i	1.35753	−	1.35753i
$483$	−1.32647	+	1.32647i	−0.0603566	+	0.0603566i
$484$		0			0
$485$	−0.183921	+	6.25215i	−0.00835144	+	0.283895i
$486$		−	39.2802i		−	1.78179i
$487$	9.69050	−	9.69050i	0.439118	−	0.439118i	−0.452597	−	0.891715i	$-0.649502\pi$
$487$	9.69050	−	9.69050i	0.439118	−	0.439118i	0.891715	+	0.452597i	$0.149502\pi$
$488$	59.7777	+	59.7777i	2.70601	+	2.70601i
$489$			12.2705i			0.554892i
$490$	1.19575	−	40.6480i	0.0540187	−	1.83629i
$491$		−	24.3127i		−	1.09722i	−0.836079	−	0.548608i	$-0.815158\pi$
$491$		−	24.3127i		−	1.09722i	0.836079	−	0.548608i	$-0.184842\pi$
$492$	−15.6074	−	15.6074i	−0.703636	−	0.703636i
$493$	−0.343729	−	0.343729i	−0.0154808	−	0.0154808i
$494$	−13.8065			−0.621182
$495$		0			0
$496$	75.9521			3.41035
$497$	4.44543	+	4.44543i	0.199405	+	0.199405i
$498$	−12.2224	−	12.2224i	−0.547700	−	0.547700i
$499$			12.4196i			0.555978i	0.960584	+	0.277989i	$0.0896678\pi$
$499$			12.4196i			0.555978i	−0.960584	+	0.277989i	$0.910332\pi$
$500$	45.8932	−	38.4340i	2.05241	−	1.71882i
$501$		−	18.2629i		−	0.815928i
$502$	9.35866	+	9.35866i	0.417697	+	0.417697i
$503$	−8.90701	+	8.90701i	−0.397144	+	0.397144i	−0.877224	−	0.480081i	$-0.840607\pi$
$503$	−8.90701	+	8.90701i	−0.397144	+	0.397144i	0.480081	+	0.877224i	$0.340607\pi$
$504$			7.97252i			0.355124i
$505$	22.2959	+	23.6474i	0.992155	+	1.05230i
$506$		0			0
$507$	−7.24661	+	7.24661i	−0.321833	+	0.321833i
$508$	−25.8576	+	25.8576i	−1.14725	+	1.14725i
$509$		−	20.3598i		−	0.902434i	−0.892414	−	0.451217i	$-0.850990\pi$
$509$		−	20.3598i		−	0.902434i	0.892414	−	0.451217i	$-0.149010\pi$
$510$	0.990223	−	33.6612i	0.0438478	−	1.49054i
$511$	−5.29671			−0.234313
$512$	14.5077	+	14.5077i	0.641154	+	0.641154i
$513$	9.44211	−	9.44211i	0.416879	−	0.416879i
$514$	21.4579			0.946467
$515$	−6.63273	−	0.195117i	−0.292273	−	0.00859789i
$516$		−	45.8592i		−	2.01884i
$517$		0			0
$518$	8.44486	+	8.44486i	0.371046	+	0.371046i
$519$	14.6132			0.641447
$520$	−28.8845	−	30.6354i	−1.26667	−	1.34345i
$521$	−2.59336			−0.113617			−0.0568085	−	0.998385i	$-0.518092\pi$
$521$	−2.59336			−0.113617			−0.0568085	+	0.998385i	$0.518092\pi$
$522$	0.319181	−	0.319181i	0.0139702	−	0.0139702i
$523$	25.8572	−	25.8572i	1.13066	−	1.13066i	0.140591	−	0.990068i	$-0.455100\pi$
$523$	25.8572	−	25.8572i	1.13066	−	1.13066i	0.990068	−	0.140591i	$-0.0449001\pi$
$524$	110.291			4.81808
$525$	3.18171	+	0.187357i	0.138861	+	0.00817693i
$526$	3.94402			0.171968
$527$	18.1694	+	18.1694i	0.791473	+	0.791473i
$528$		0			0
$529$		−	14.3395i		−	0.623458i
$530$	−1.32249	−	1.40265i	−0.0574452	−	0.0609274i
$531$	−4.51370			−0.195878
$532$	−5.04688	+	5.04688i	−0.218810	+	0.218810i
$533$	−5.13137	−	5.13137i	−0.222264	−	0.222264i
$534$	−7.57319			−0.327724
$535$	3.72036	+	0.109443i	0.160845	+	0.00473164i
$536$		−	136.407i		−	5.89191i
$537$	−18.4951	+	18.4951i	−0.798124	+	0.798124i
$538$	−44.3293	+	44.3293i	−1.91117	+	1.91117i
$539$		0			0
$540$	64.9767	+	1.91144i	2.79615	+	0.0822552i
$541$			16.1923i			0.696161i	0.937465	+	0.348080i	$0.113166\pi$
$541$			16.1923i			0.696161i	−0.937465	+	0.348080i	$0.886834\pi$
$542$	50.0226	−	50.0226i	2.14865	−	2.14865i
$543$	−14.9827	−	14.9827i	−0.642970	−	0.642970i
$544$			92.8496i			3.98089i
$545$	−15.0388	+	14.1792i	−0.644190	+	0.607372i
$546$		−	3.57858i		−	0.153149i
$547$	24.8996	+	24.8996i	1.06463	+	1.06463i	0.997762	+	0.0668672i	$0.0213004\pi$
$547$	24.8996	+	24.8996i	1.06463	+	1.06463i	0.0668672	+	0.997762i	$0.478700\pi$
$548$	−25.1477	−	25.1477i	−1.07426	−	1.07426i
$549$	−15.0287			−0.641407
$550$		0			0
$551$	0.253155			0.0107848
$552$	−22.2594	−	22.2594i	−0.947422	−	0.947422i
$553$	4.92804	+	4.92804i	0.209561	+	0.209561i
$554$		−	56.1889i		−	2.38724i
$555$	15.5450	−	14.6565i	0.659848	−	0.622135i
$556$			33.5043i			1.42090i
$557$	0.190250	+	0.190250i	0.00806114	+	0.00806114i	0.711126	−	0.703065i	$-0.248186\pi$
$557$	0.190250	+	0.190250i	0.00806114	+	0.00806114i	−0.703065	+	0.711126i	$0.748186\pi$
$558$	−16.8719	+	16.8719i	−0.714243	+	0.714243i
$559$		−	15.0775i		−	0.637711i
$560$	−16.9111	−	0.497480i	−0.714625	−	0.0210223i
$561$		0			0
$562$	43.4783	−	43.4783i	1.83402	−	1.83402i
$563$	−22.2138	+	22.2138i	−0.936198	+	0.936198i	−0.998083	−	0.0618853i	$-0.980289\pi$
$563$	−22.2138	+	22.2138i	−0.936198	+	0.936198i	0.0618853	+	0.998083i	$0.480289\pi$
$564$			13.1188i			0.552401i
$565$	24.5657	+	0.722656i	1.03349	+	0.0304024i
$566$	15.8467			0.666087
$567$	0.588040	+	0.588040i	0.0246954	+	0.0246954i
$568$	−74.5982	+	74.5982i	−3.13007	+	3.13007i
$569$	39.9312			1.67400			0.837001	−	0.547201i	$-0.184307\pi$
$569$	39.9312			1.67400			0.837001	+	0.547201i	$0.184307\pi$
$570$	12.0311	+	12.7604i	0.503925	+	0.534472i
$571$		−	15.4289i		−	0.645678i	−0.946454	−	0.322839i	$-0.895363\pi$
$571$		−	15.4289i		−	0.645678i	0.946454	−	0.322839i	$-0.104637\pi$
$572$		0			0
$573$	−17.3102	−	17.3102i	−0.723142	−	0.723142i
$574$	−5.15283			−0.215075
$575$	10.9982	−	9.77499i	0.458658	−	0.407645i
$576$	−41.0763			−1.71151
$577$	11.3556	−	11.3556i	0.472739	−	0.472739i	−0.430061	−	0.902800i	$-0.641508\pi$
$577$	11.3556	−	11.3556i	0.472739	−	0.472739i	0.902800	+	0.430061i	$0.141508\pi$
$578$	−10.1642	+	10.1642i	−0.422775	+	0.422775i
$579$	8.63722			0.358951
$580$	0.845430	+	0.896678i	0.0351046	+	0.0372325i
$581$	−2.93786			−0.121883
$582$	−6.30801	−	6.30801i	−0.261475	−	0.261475i
$583$		0			0
$584$		−	88.8835i		−	3.67803i
$585$	7.48192	+	0.220098i	0.309340	+	0.00909994i
$586$	−45.7566			−1.89019
$587$	3.99363	−	3.99363i	0.164835	−	0.164835i	−0.619870	−	0.784705i	$-0.712815\pi$
$587$	3.99363	−	3.99363i	0.164835	−	0.164835i	0.784705	+	0.619870i	$0.212815\pi$
$588$	29.8579	+	29.8579i	1.23132	+	1.23132i
$589$	−13.3817			−0.551385
$590$	0.497721	−	16.9193i	0.0204908	−	0.696557i
$591$			6.76306i			0.278195i
$592$	−80.1926	+	80.1926i	−3.29590	+	3.29590i
$593$	11.8944	−	11.8944i	0.488443	−	0.488443i	−0.419372	−	0.907814i	$-0.637750\pi$
$593$	11.8944	−	11.8944i	0.488443	−	0.488443i	0.907814	+	0.419372i	$0.137750\pi$
$594$		0			0
$595$	−3.92650	−	4.16452i	−0.160971	−	0.170729i
$596$		−	96.2483i		−	3.94248i
$597$	9.20750	−	9.20750i	0.376838	−	0.376838i
$598$	−11.6822	−	11.6822i	−0.477720	−	0.477720i
$599$			10.0028i			0.408703i	0.978898	+	0.204351i	$0.0655085\pi$
$599$			10.0028i			0.408703i	−0.978898	+	0.204351i	$0.934491\pi$
$600$	−3.14401	+	53.3919i	−0.128354	+	2.17972i
$601$			17.7104i			0.722423i	0.932484	+	0.361212i	$0.117637\pi$
$601$			17.7104i			0.722423i	−0.932484	+	0.361212i	$0.882363\pi$
$602$	−7.57029	−	7.57029i	−0.308542	−	0.308542i
$603$	17.1470	+	17.1470i	0.698281	+	0.698281i
$604$	−20.5362			−0.835605
$605$		0			0
$606$	−46.3538			−1.88299
$607$	9.79881	+	9.79881i	0.397721	+	0.397721i	0.877429	−	0.479707i	$-0.159257\pi$
$607$	9.79881	+	9.79881i	0.397721	+	0.397721i	−0.479707	+	0.877429i	$0.659257\pi$
$608$	−34.1917	−	34.1917i	−1.38666	−	1.38666i
$609$			0.0656168i			0.00265893i
$610$	1.65719	−	56.3339i	0.0670977	−	2.28089i
$611$			4.31317i			0.174492i
$612$	−28.9099	−	28.9099i	−1.16861	−	1.16861i
$613$	−2.16963	+	2.16963i	−0.0876303	+	0.0876303i	−0.749563	−	0.661933i	$-0.769736\pi$
$613$	−2.16963	+	2.16963i	−0.0876303	+	0.0876303i	0.661933	+	0.749563i	$0.269736\pi$
$614$		−	61.5852i		−	2.48537i
$615$	−0.271054	+	9.21408i	−0.0109299	+	0.371548i
$616$		0			0
$617$	−4.11926	+	4.11926i	−0.165835	+	0.165835i	−0.785146	−	0.619311i	$-0.787412\pi$
$617$	−4.11926	+	4.11926i	−0.165835	+	0.165835i	0.619311	+	0.785146i	$0.287412\pi$
$618$	6.69199	−	6.69199i	0.269191	−	0.269191i
$619$		−	3.75376i		−	0.150876i	−0.997150	−	0.0754382i	$-0.975964\pi$
$619$		−	3.75376i		−	0.150876i	0.997150	−	0.0754382i	$-0.0240356\pi$
$620$	−44.6893	−	47.3982i	−1.79476	−	1.90356i
$621$	15.9787			0.641202
$622$	−6.77241	−	6.77241i	−0.271549	−	0.271549i
$623$	−0.910170	+	0.910170i	−0.0364652	+	0.0364652i
$624$	33.9823			1.36038
$625$	−24.8272	−	2.93410i	−0.993089	−	0.117364i
$626$		−	32.1552i		−	1.28518i
$627$		0			0
$628$	−2.80330	−	2.80330i	−0.111864	−	0.111864i
$629$	−38.3677			−1.52982
$630$	3.86712	−	3.64610i	0.154070	−	0.145264i
$631$	18.5828			0.739771			0.369885	−	0.929077i	$-0.379397\pi$
$631$	18.5828			0.739771			0.369885	+	0.929077i	$0.379397\pi$
$632$	−82.6968	+	82.6968i	−3.28950	+	3.28950i
$633$	17.4460	−	17.4460i	0.693417	−	0.693417i
$634$	−27.6314			−1.09738
$635$	15.2655	+	0.449070i	0.605793	+	0.0178208i
$636$	2.00175			0.0793746
$637$	9.81665	+	9.81665i	0.388950	+	0.388950i
$638$		0			0
$639$		−	18.7546i		−	0.741922i
$640$	1.94389	−	66.0798i	0.0768390	−	2.61203i
$641$	25.4126			1.00374			0.501869	−	0.864944i	$-0.332646\pi$
$641$	25.4126			1.00374			0.501869	+	0.864944i	$0.332646\pi$
$642$	−3.75360	+	3.75360i	−0.148143	+	0.148143i
$643$	11.6189	+	11.6189i	0.458203	+	0.458203i	0.898065	−	0.439862i	$-0.144973\pi$
$643$	11.6189	+	11.6189i	0.458203	+	0.458203i	−0.439862	+	0.898065i	$0.644973\pi$
$644$	−8.54072			−0.336552
$645$	−13.9351	+	13.1387i	−0.548694	+	0.517335i
$646$		−	31.4947i		−	1.23914i
$647$	−2.79794	+	2.79794i	−0.109999	+	0.109999i	−0.759964	−	0.649965i	$-0.774783\pi$
$647$	−2.79794	+	2.79794i	−0.109999	+	0.109999i	0.649965	+	0.759964i	$0.274783\pi$
$648$	−9.86783	+	9.86783i	−0.387645	+	0.387645i
$649$		0			0
$650$	−1.65004	+	28.0212i	−0.0647201	+	1.09908i
$651$		−	3.46849i		−	0.135941i
$652$	−39.5029	+	39.5029i	−1.54705	+	1.54705i
$653$	1.41713	+	1.41713i	0.0554566	+	0.0554566i	0.734291	−	0.678835i	$-0.237515\pi$
$653$	1.41713	+	1.41713i	0.0554566	+	0.0554566i	−0.678835	+	0.734291i	$0.737515\pi$
$654$		−	29.4791i		−	1.15272i
$655$	−31.5983	−	33.5137i	−1.23465	−	1.30949i
$656$		−	48.9314i		−	1.91045i
$657$	11.1731	+	11.1731i	0.435902	+	0.435902i
$658$	2.16561	+	2.16561i	0.0844241	+	0.0844241i
$659$	27.2915			1.06312			0.531562	−	0.847019i	$-0.321605\pi$
$659$	27.2915			1.06312			0.531562	+	0.847019i	$0.321605\pi$
$660$		0			0
$661$	11.7092			0.455435			0.227717	−	0.973727i	$-0.426874\pi$
$661$	11.7092			0.455435			0.227717	+	0.973727i	$0.426874\pi$
$662$	22.3171	+	22.3171i	0.867378	+	0.867378i
$663$	8.12932	+	8.12932i	0.315717	+	0.315717i
$664$		−	49.2998i		−	1.91320i
$665$	2.97951	+	0.0876491i	0.115540	+	0.00339889i
$666$		−	35.6277i		−	1.38054i
$667$	0.214204	+	0.214204i	0.00829403	+	0.00829403i
$668$	58.7945	−	58.7945i	2.27483	−	2.27483i
$669$			13.5817i			0.525099i
$670$	−66.1652	+	62.3837i	−2.55619	+	2.41009i
$671$		0			0
$672$	8.86236	−	8.86236i	0.341873	−	0.341873i
$673$	27.7908	−	27.7908i	1.07126	−	1.07126i	0.0739999	−	0.997258i	$-0.476424\pi$
$673$	27.7908	−	27.7908i	1.07126	−	1.07126i	0.997258	−	0.0739999i	$-0.0235765\pi$
$674$			72.4721i			2.79152i
$675$	−18.0350	−	20.2919i	−0.694167	−	0.781035i
$676$	−46.6585			−1.79456
$677$	−1.06466	−	1.06466i	−0.0409183	−	0.0409183i	0.686352	−	0.727270i	$-0.259211\pi$
$677$	−1.06466	−	1.06466i	−0.0409183	−	0.0409183i	−0.727270	+	0.686352i	$0.759211\pi$
$678$	−24.7852	+	24.7852i	−0.951868	+	0.951868i
$679$	−1.51623			−0.0581876
$680$	69.8843	−	65.8902i	2.67994	−	2.52677i
$681$			17.7152i			0.678850i
$682$		0			0
$683$	9.30069	+	9.30069i	0.355881	+	0.355881i	0.862292	−	0.506411i	$-0.169028\pi$
$683$	9.30069	+	9.30069i	0.355881	+	0.355881i	−0.506411	+	0.862292i	$0.669028\pi$
$684$	21.2921			0.814123
$685$	−0.436741	+	14.8464i	−0.0166870	+	0.567252i
$686$	20.1473			0.769227
$687$	2.28051	−	2.28051i	0.0870068	−	0.0870068i
$688$	71.8877	−	71.8877i	2.74069	−	2.74069i
$689$	0.658133			0.0250729
$690$	−0.617086	+	20.9770i	−0.0234921	+	0.798580i
$691$	18.1730			0.691333			0.345667	−	0.938357i	$-0.387653\pi$
$691$	18.1730			0.691333			0.345667	+	0.938357i	$0.387653\pi$
$692$	47.0447	+	47.0447i	1.78837	+	1.78837i
$693$		0			0
$694$			75.9493i			2.88300i
$695$	10.1809	−	9.59899i	0.386182	−	0.364110i
$696$	−1.10111			−0.0417374
$697$	11.7055	−	11.7055i	0.443376	−	0.443376i
$698$	35.7231	+	35.7231i	1.35214	+	1.35214i
$699$	4.91987			0.186087
$700$	9.63983	+	10.8462i	0.364351	+	0.409946i
$701$		−	3.77621i		−	0.142626i	−0.997454	−	0.0713128i	$-0.977281\pi$
$701$		−	3.77621i		−	0.142626i	0.997454	−	0.0713128i	$-0.0227189\pi$
$702$	−21.5538	+	21.5538i	−0.813495	+	0.813495i
$703$	14.1288	−	14.1288i	0.532879	−	0.532879i
$704$		0			0
$705$	3.98637	−	3.75853i	0.150135	−	0.141555i
$706$			87.5816i			3.29618i
$707$	−5.57095	+	5.57095i	−0.209517	+	0.209517i
$708$	12.4281	+	12.4281i	0.467075	+	0.467075i
$709$		−	37.4880i		−	1.40789i	−0.710254	−	0.703946i	$-0.751420\pi$
$709$		−	37.4880i		−	1.40789i	0.710254	−	0.703946i	$-0.248580\pi$
$710$	70.3005	+	2.06805i	2.63833	+	0.0776126i
$711$		−	20.7907i		−	0.779712i
$712$	−15.2735	−	15.2735i	−0.572397	−	0.572397i
$713$	−11.3228	−	11.3228i	−0.424042	−	0.424042i
$714$	8.16331			0.305504
$715$		0			0
$716$	−119.084			−4.45038
$717$	−0.204359	−	0.204359i	−0.00763193	−	0.00763193i
$718$	−63.6706	−	63.6706i	−2.37616	−	2.37616i
$719$			13.2722i			0.494969i	0.968892	+	0.247485i	$0.0796040\pi$
$719$			13.2722i			0.494969i	−0.968892	+	0.247485i	$0.920396\pi$
$720$	34.6234	+	36.7222i	1.29034	+	1.36856i
$721$		−	1.60853i		−	0.0599048i
$722$	−24.8359	−	24.8359i	−0.924298	−	0.924298i
$723$	12.9245	−	12.9245i	0.480669	−	0.480669i
$724$		−	96.4689i		−	3.58524i
$725$	0.0302552	−	0.513796i	0.00112365	−	0.0190819i
$726$		0			0
$727$	11.3623	−	11.3623i	0.421405	−	0.421405i	−0.464282	−	0.885687i	$-0.653688\pi$
$727$	11.3623	−	11.3623i	0.421405	−	0.421405i	0.885687	+	0.464282i	$0.153688\pi$
$728$	7.21721	−	7.21721i	0.267487	−	0.267487i
$729$		−	21.6367i		−	0.801358i
$730$	−43.1135	+	40.6494i	−1.59570	+	1.50450i
$731$	34.3942			1.27212
$732$	41.3800	+	41.3800i	1.52945	+	1.52945i
$733$	4.02676	−	4.02676i	0.148732	−	0.148732i	−0.628819	−	0.777551i	$-0.716462\pi$
$733$	4.02676	−	4.02676i	0.148732	−	0.148732i	0.777551	+	0.628819i	$0.216462\pi$
$734$	−52.2641			−1.92910
$735$	0.518543	−	17.6271i	0.0191267	−	0.650187i
$736$		−	57.8619i		−	2.13282i
$737$		0			0
$738$	10.8695	+	10.8695i	0.400113	+	0.400113i
$739$	9.61651			0.353749			0.176875	−	0.984233i	$-0.443401\pi$
$739$	9.61651			0.353749			0.176875	+	0.984233i	$0.443401\pi$
$740$	97.2288	+	2.86021i	3.57420	+	0.105143i
$741$	−5.98722			−0.219946
$742$	0.330442	−	0.330442i	0.0121309	−	0.0121309i
$743$	−24.8273	+	24.8273i	−0.910826	+	0.910826i	−0.996337	−	0.0855114i	$-0.972748\pi$
$743$	−24.8273	+	24.8273i	−0.910826	+	0.910826i	0.0855114	+	0.996337i	$0.472748\pi$
$744$	58.2044			2.13388
$745$	−29.2467	+	27.5751i	−1.07151	+	1.01027i
$746$	−56.5514			−2.07049
$747$	6.19721	+	6.19721i	0.226744	+	0.226744i
$748$		0			0
$749$			0.902239i			0.0329671i
$750$	27.3359	−	22.8929i	0.998166	−	0.835929i
$751$	49.4018			1.80270			0.901348	−	0.433096i	$-0.142579\pi$
$751$	49.4018			1.80270			0.901348	+	0.433096i	$0.142579\pi$
$752$	−20.5646	+	20.5646i	−0.749916	+	0.749916i
$753$	4.05841	+	4.05841i	0.147897	+	0.147897i
$754$	−0.577885			−0.0210453
$755$	5.88361	+	6.24026i	0.214126	+	0.227106i
$756$			15.7577i			0.573103i
$757$	−26.1873	+	26.1873i	−0.951795	+	0.951795i	−0.998890	−	0.0470950i	$-0.985004\pi$
$757$	−26.1873	+	26.1873i	−0.951795	+	0.951795i	0.0470950	+	0.998890i	$0.485004\pi$
$758$	24.5789	−	24.5789i	0.892747	−	0.892747i
$759$		0			0
$760$	−1.47083	+	49.9988i	−0.0533526	+	1.81365i
$761$			46.7158i			1.69345i	0.532034	+	0.846723i	$0.321428\pi$
$761$			46.7158i			1.69345i	−0.532034	+	0.846723i	$0.678572\pi$
$762$	−15.4019	+	15.4019i	−0.557951	+	0.557951i
$763$	−3.54288	−	3.54288i	−0.128261	−	0.128261i
$764$		−	111.454i		−	4.03228i
$765$	−0.502079	+	17.0675i	−0.0181527	+	0.617075i
$766$			67.1218i			2.42521i
$767$	4.08608	+	4.08608i	0.147540	+	0.147540i
$768$	24.4226	+	24.4226i	0.881275	+	0.881275i
$769$	−4.05122			−0.146091			−0.0730453	−	0.997329i	$-0.523272\pi$
$769$	−4.05122			−0.146091			−0.0730453	+	0.997329i	$0.523272\pi$
$770$		0			0
$771$	9.30529			0.335122
$772$	27.8061	+	27.8061i	1.00076	+	1.00076i
$773$	−4.03017	−	4.03017i	−0.144955	−	0.144955i	0.630905	−	0.775860i	$-0.282684\pi$
$773$	−4.03017	−	4.03017i	−0.144955	−	0.144955i	−0.775860	+	0.630905i	$0.782684\pi$
$774$			31.9380i			1.14799i
$775$	−1.59928	+	27.1592i	−0.0574480	+	0.975587i
$776$		−	25.4437i		−	0.913375i
$777$	3.66214	+	3.66214i	0.131379	+	0.131379i
$778$	−11.6858	+	11.6858i	−0.418957	+	0.418957i
$779$			8.62105i			0.308881i
$780$	−19.9948	−	21.2068i	−0.715927	−	0.759325i
$781$		0			0
$782$	26.6489	−	26.6489i	0.952964	−	0.952964i
$783$	0.395210	−	0.395210i	0.0141236	−	0.0141236i
$784$			93.6090i			3.34318i
$785$	−0.0486849	+	1.65498i	−0.00173764	+	0.0590686i
$786$	65.6938			2.34322
$787$	17.0150	+	17.0150i	0.606520	+	0.606520i	0.942035	−	0.335515i	$-0.108910\pi$
$787$	17.0150	+	17.0150i	0.606520	+	0.606520i	−0.335515	+	0.942035i	$0.608910\pi$
$788$	−21.7726	+	21.7726i	−0.775615	+	0.775615i
$789$	1.71034			0.0608897
$790$	77.9325	+	2.29256i	2.77271	+	0.0815658i
$791$			5.95752i			0.211825i
$792$		0			0
$793$	13.6048	+	13.6048i	0.483122	+	0.483122i
$794$	20.6178			0.731699
$795$	−0.573502	−	0.608266i	−0.0203400	−	0.0215730i
$796$	59.2841			2.10127
$797$	0.744630	−	0.744630i	0.0263762	−	0.0263762i	−0.693796	−	0.720172i	$-0.744063\pi$
$797$	0.744630	−	0.744630i	0.0263762	−	0.0263762i	0.720172	+	0.693796i	$0.244063\pi$
$798$	−3.00613	+	3.00613i	−0.106416	+	0.106416i
$799$	−9.83904			−0.348080
$800$	−73.4809	+	65.3082i	−2.59794	+	2.30899i
$801$	3.83988			0.135676
$802$	−20.5285	−	20.5285i	−0.724885	−	0.724885i
$803$		0			0
$804$		−	94.4255i		−	3.33013i
$805$	2.44692	+	2.59524i	0.0862424	+	0.0914703i
$806$	30.5469			1.07597
$807$	−19.2235	+	19.2235i	−0.676701	+	0.676701i
$808$	−93.4853	−	93.4853i	−3.28880	−	3.28880i
$809$	10.2395			0.360001			0.180000	−	0.983667i	$-0.442390\pi$
$809$	10.2395			0.360001			0.180000	+	0.983667i	$0.442390\pi$
$810$	9.29933	+	0.273561i	0.326745	+	0.00961197i
$811$		−	42.6071i		−	1.49614i	−0.663622	−	0.748068i	$-0.730981\pi$
$811$		−	42.6071i		−	1.49614i	0.663622	−	0.748068i	$-0.269019\pi$
$812$	−0.211243	+	0.211243i	−0.00741316	+	0.00741316i
$813$	21.6925	−	21.6925i	0.760788	−	0.760788i
$814$		0			0
$815$	23.3212	+	0.686047i	0.816906	+	0.0240312i
$816$			77.5190i			2.71371i
$817$	−12.6656	+	12.6656i	−0.443114	+	0.443114i
$818$	8.67331	+	8.67331i	0.303255	+	0.303255i
$819$			1.81447i			0.0634027i
$820$	−30.5359	+	28.7906i	−1.06636	+	1.00541i
$821$			13.4680i			0.470038i	0.971991	+	0.235019i	$0.0755152\pi$
$821$			13.4680i			0.470038i	−0.971991	+	0.235019i	$0.924485\pi$
$822$	−14.9790	−	14.9790i	−0.522454	−	0.522454i
$823$	6.93121	+	6.93121i	0.241607	+	0.241607i	0.817515	−	0.575908i	$-0.195351\pi$
$823$	6.93121	+	6.93121i	0.241607	+	0.241607i	−0.575908	+	0.817515i	$0.695351\pi$
$824$	26.9925			0.940329
$825$		0			0
$826$	4.10317			0.142767
$827$	3.72124	+	3.72124i	0.129400	+	0.129400i	0.768841	−	0.639440i	$-0.220834\pi$
$827$	3.72124	+	3.72124i	0.129400	+	0.129400i	−0.639440	+	0.768841i	$0.720834\pi$
$828$	18.0161	+	18.0161i	0.626101	+	0.626101i
$829$		−	47.2538i		−	1.64119i	−0.571509	−	0.820596i	$-0.693642\pi$
$829$		−	47.2538i		−	1.64119i	0.571509	−	0.820596i	$-0.306358\pi$
$830$	−23.9132	+	22.5464i	−0.830038	+	0.782599i
$831$		−	24.3665i		−	0.845265i
$832$	37.1848	+	37.1848i	1.28915	+	1.28915i
$833$	−22.3933	+	22.3933i	−0.775883	+	0.775883i
$834$			19.9566i			0.691039i
$835$	−34.7103	−	1.02108i	−1.20120	−	0.0353361i
$836$		0			0
$837$	−20.8907	+	20.8907i	−0.722089	+	0.722089i
$838$	−16.4408	+	16.4408i	−0.567939	+	0.567939i
$839$		−	14.3454i		−	0.495260i	−0.968855	−	0.247630i	$-0.920348\pi$
$839$		−	14.3454i		−	0.495260i	0.968855	−	0.247630i	$-0.0796517\pi$
$840$	−12.9595	−	0.381233i	−0.447145	−	0.0131538i
$841$	−28.9894			−0.999635
$842$	−48.1355	−	48.1355i	−1.65886	−	1.65886i
$843$	18.8545	−	18.8545i	0.649383	−	0.649383i
$844$	112.329			3.86653
$845$	13.3677	+	14.1780i	0.459862	+	0.487738i
$846$		−	9.13639i		−	0.314116i
$847$		0			0
$848$	3.13789	+	3.13789i	0.107756	+	0.107756i
$849$	6.87198			0.235846
$850$	−63.9208	−	3.76401i	−2.19247	−	0.129105i
$851$	23.9099			0.819622
$852$	−51.6392	+	51.6392i	−1.76913	+	1.76913i
$853$	22.1481	−	22.1481i	0.758335	−	0.758335i	−0.217684	−	0.976019i	$-0.569850\pi$
$853$	22.1481	−	22.1481i	0.758335	−	0.758335i	0.976019	+	0.217684i	$0.0698503\pi$
$854$	13.6617			0.467495
$855$	−6.10018	−	6.46996i	−0.208622	−	0.221268i
$856$	−15.1404			−0.517487
$857$	−6.37606	−	6.37606i	−0.217802	−	0.217802i	0.589770	−	0.807572i	$-0.299219\pi$
$857$	−6.37606	−	6.37606i	−0.217802	−	0.217802i	−0.807572	+	0.589770i	$0.799219\pi$
$858$		0			0
$859$			15.0575i			0.513754i	0.966444	+	0.256877i	$0.0826936\pi$
$859$			15.0575i			0.513754i	−0.966444	+	0.256877i	$0.917306\pi$
$860$	−87.1596	−	2.56400i	−2.97212	−	0.0874317i
$861$	−2.23454			−0.0761530
$862$	−17.8386	+	17.8386i	−0.607584	+	0.607584i
$863$	5.52318	+	5.52318i	0.188011	+	0.188011i	0.794836	−	0.606825i	$-0.207557\pi$
$863$	5.52318	+	5.52318i	0.188011	+	0.188011i	−0.606825	+	0.794836i	$0.707557\pi$
$864$	−106.756			−3.63191
$865$	0.817026	−	27.7736i	0.0277797	−	0.944332i
$866$			89.6879i			3.04772i
$867$	−4.40774	+	4.40774i	−0.149695	+	0.149695i
$868$	11.1662	−	11.1662i	0.379007	−	0.379007i
$869$		0			0
$870$	0.503573	+	0.534098i	0.0170727	+	0.0181076i
$871$		−	31.0450i		−	1.05192i
$872$	59.4527	−	59.4527i	2.01332	−	2.01332i
$873$	3.19839	+	3.19839i	0.108249	+	0.108249i
$874$			19.6269i			0.663888i
$875$	0.533979	−	6.03665i	0.0180518	−	0.204076i
$876$		−	61.5279i		−	2.07884i
$877$	−6.07411	−	6.07411i	−0.205108	−	0.205108i	0.597076	−	0.802184i	$-0.296329\pi$
$877$	−6.07411	−	6.07411i	−0.205108	−	0.205108i	−0.802184	+	0.597076i	$0.796329\pi$
$878$	64.1248	+	64.1248i	2.16411	+	2.16411i
$879$	−19.8425			−0.669271
$880$		0			0
$881$	−13.8980			−0.468236			−0.234118	−	0.972208i	$-0.575220\pi$
$881$	−13.8980			−0.468236			−0.234118	+	0.972208i	$0.575220\pi$
$882$	−20.7941	−	20.7941i	−0.700175	−	0.700175i
$883$	−17.0750	−	17.0750i	−0.574619	−	0.574619i	0.358797	−	0.933416i	$-0.383187\pi$
$883$	−17.0750	−	17.0750i	−0.574619	−	0.574619i	−0.933416	+	0.358797i	$0.883187\pi$
$884$			52.3420i			1.76045i
$885$	0.215838	−	7.33712i	0.00725532	−	0.246634i
$886$			76.1511i			2.55835i
$887$	−23.5528	−	23.5528i	−0.790825	−	0.790825i	0.190803	−	0.981628i	$-0.438891\pi$
$887$	−23.5528	−	23.5528i	−0.790825	−	0.790825i	−0.981628	+	0.190803i	$0.938891\pi$
$888$	−61.4539	+	61.4539i	−2.06226	+	2.06226i
$889$			3.70209i			0.124164i
$890$	−0.423419	+	14.3935i	−0.0141930	+	0.482472i
$891$		0			0
$892$	−43.7241	+	43.7241i	−1.46399	+	1.46399i
$893$	3.62321	−	3.62321i	0.121246	−	0.121246i
$894$		−	57.3294i		−	1.91738i
$895$	34.1176	+	36.1857i	1.14042	+	1.20955i
$896$	16.0253			0.535366
$897$	−5.06602	−	5.06602i	−0.169150	−	0.169150i
$898$	−12.7941	+	12.7941i	−0.426944	+	0.426944i
$899$	−0.560107			−0.0186806
$900$	2.54467	−	43.2138i	0.0848223	−	1.44046i
$901$			1.50130i			0.0500157i
$902$		0			0
$903$	−3.28288	−	3.28288i	−0.109247	−	0.109247i
$904$	−99.9724			−3.32503
$905$	−29.3137	+	27.6383i	−0.974420	+	0.918729i
$906$	−12.2322			−0.406387
$907$	−21.2728	+	21.2728i	−0.706352	+	0.706352i	−0.965766	−	0.259414i	$-0.916471\pi$
$907$	−21.2728	+	21.2728i	−0.706352	+	0.706352i	0.259414	+	0.965766i	$0.416471\pi$
$908$	−57.0313	+	57.0313i	−1.89265	+	1.89265i
$909$	23.5030			0.779547
$910$	−6.80141	−	0.200079i	−0.225465	−	0.00663256i
$911$	14.4760			0.479612			0.239806	−	0.970821i	$-0.422916\pi$
$911$	14.4760			0.479612			0.239806	+	0.970821i	$0.422916\pi$
$912$	−28.5463	−	28.5463i	−0.945262	−	0.945262i
$913$		0			0
$914$			45.2288i			1.49604i
$915$	0.718646	−	24.4294i	0.0237577	−	0.807610i
$916$	14.6834			0.485155
$917$	7.89529	−	7.89529i	0.260725	−	0.260725i
$918$	−49.1676	−	49.1676i	−1.62277	−	1.62277i
$919$	−41.5573			−1.37085			−0.685425	−	0.728143i	$-0.740384\pi$
$919$	−41.5573			−1.37085			−0.685425	+	0.728143i	$0.740384\pi$
$920$	−43.5504	+	41.0614i	−1.43582	+	1.35375i
$921$		−	26.7066i		−	0.880013i
$922$	−39.7390	+	39.7390i	−1.30873	+	1.30873i
$923$	−16.9778	+	16.9778i	−0.558832	+	0.558832i
$924$		0			0
$925$	−26.9869	−	30.3641i	−0.887325	−	0.998365i
$926$		−	73.4603i		−	2.41406i
$927$	−3.39308	+	3.39308i	−0.111443	+	0.111443i
$928$	−1.43113	−	1.43113i	−0.0469792	−	0.0469792i
$929$			22.4718i			0.737275i	0.929573	+	0.368638i	$0.120176\pi$
$929$			22.4718i			0.737275i	−0.929573	+	0.368638i	$0.879824\pi$
$930$	−26.6188	−	28.2324i	−0.872864	−	0.925775i
$931$		−	16.4926i		−	0.540524i
$932$	15.8387	+	15.8387i	0.518814	+	0.518814i
$933$	−2.93688	−	2.93688i	−0.0961491	−	0.0961491i
$934$	86.3841			2.82657
$935$		0			0
$936$	−30.4484			−0.995237
$937$	−34.0894	−	34.0894i	−1.11365	−	1.11365i	−0.992653	−	0.120998i	$-0.961391\pi$
$937$	−34.0894	−	34.0894i	−1.11365	−	1.11365i	−0.120998	−	0.992653i	$-0.538609\pi$
$938$	−15.5874	−	15.5874i	−0.508948	−	0.508948i
$939$		−	13.9442i		−	0.455052i
$940$	24.9334	+	0.733474i	0.813239	+	0.0239233i
$941$			39.3932i			1.28418i	0.766629	+	0.642091i	$0.221933\pi$
$941$			39.3932i			1.28418i	−0.766629	+	0.642091i	$0.778067\pi$
$942$	−1.66976	−	1.66976i	−0.0544038	−	0.0544038i
$943$	−7.29461	+	7.29461i	−0.237545	+	0.237545i
$944$			38.9638i			1.26816i
$945$	4.78825	−	4.51459i	0.155762	−	0.146860i
$946$		0			0
$947$	−29.4148	+	29.4148i	−0.955854	+	0.955854i	−0.999066	−	0.0432120i	$-0.986241\pi$
$947$	−29.4148	+	29.4148i	−0.955854	+	0.955854i	0.0432120	+	0.999066i	$0.486241\pi$
$948$	−57.2452	+	57.2452i	−1.85924	+	1.85924i
$949$		−	20.2290i		−	0.656663i
$950$	24.9248	−	22.1527i	0.808669	−	0.718727i
$951$	−11.9825			−0.388558
$952$	16.4636	+	16.4636i	0.533588	+	0.533588i
$953$	−15.1112	+	15.1112i	−0.489499	+	0.489499i	−0.908148	−	0.418649i	$-0.862504\pi$
$953$	−15.1112	+	15.1112i	−0.489499	+	0.489499i	0.418649	+	0.908148i	$0.362504\pi$
$954$	−1.39409			−0.0451354
$955$	−33.8673	+	31.9317i	−1.09592	+	1.03329i
$956$		−	1.31580i		−	0.0425561i
$957$		0			0
$958$	−27.5889	−	27.5889i	−0.891357	−	0.891357i
$959$	−3.60045			−0.116265
$960$	1.96420	−	66.7704i	0.0633944	−	2.15500i
$961$	−1.39284			−0.0449303
$962$	−32.2523	+	32.2523i	−1.03986	+	1.03986i
$963$	1.90321	−	1.90321i	0.0613301	−	0.0613301i
$964$	83.2169			2.68024
$965$	0.482909	−	16.4158i	0.0155454	−	0.528444i
$966$	−5.08721			−0.163678
$967$	−15.9838	−	15.9838i	−0.514004	−	0.514004i	0.401747	−	0.915751i	$-0.368403\pi$
$967$	−15.9838	−	15.9838i	−0.514004	−	0.514004i	−0.915751	+	0.401747i	$0.868403\pi$
$968$		0			0
$969$		−	13.6578i		−	0.438752i
$970$	−12.3416	+	11.6362i	−0.396265	+	0.373617i
$971$	−12.1244			−0.389091			−0.194545	−	0.980894i	$-0.562323\pi$
$971$	−12.1244			−0.389091			−0.194545	+	0.980894i	$0.562323\pi$
$972$	54.8381	−	54.8381i	1.75893	−	1.75893i
$973$	2.39844	+	2.39844i	0.0768905	+	0.0768905i
$974$	37.1644			1.19082
$975$	−0.715548	+	12.1515i	−0.0229159	+	0.389159i
$976$			129.732i			4.15263i
$977$	22.5657	−	22.5657i	0.721941	−	0.721941i	−0.247059	−	0.969000i	$-0.579464\pi$
$977$	22.5657	−	22.5657i	0.721941	−	0.721941i	0.969000	+	0.247059i	$0.0794643\pi$
$978$	−23.5296	+	23.5296i	−0.752392	+	0.752392i
$979$		0			0
$980$	58.4171	−	55.0783i	1.86606	−	1.75941i
$981$			14.9469i			0.477219i
$982$	46.6213	−	46.6213i	1.48775	−	1.48775i
$983$	−36.0906	−	36.0906i	−1.15111	−	1.15111i	−0.986330	−	0.164782i	$-0.947308\pi$
$983$	−36.0906	−	36.0906i	−1.15111	−	1.15111i	−0.164782	−	0.986330i	$-0.552692\pi$
$984$		−	37.4976i		−	1.19538i
$985$	12.8538	+	0.378124i	0.409556	+	0.0120480i
$986$		−	1.31825i		−	0.0419815i
$987$	0.939122	+	0.939122i	0.0298926	+	0.0298926i
$988$	−19.2749	−	19.2749i	−0.613216	−	0.613216i
$989$	−21.4338			−0.681554
$990$		0			0
$991$	7.38293			0.234526			0.117263	−	0.993101i	$-0.462588\pi$
$991$	7.38293			0.234526			0.117263	+	0.993101i	$0.462588\pi$
$992$	75.6494	+	75.6494i	2.40187	+	2.40187i
$993$	9.67787	+	9.67787i	0.307118	+	0.307118i
$994$			17.0488i			0.540756i
$995$	−16.9849	−	18.0145i	−0.538457	−	0.571097i
$996$		−	34.1269i		−	1.08135i
$997$	4.94080	+	4.94080i	0.156477	+	0.156477i	0.781003	−	0.624527i	$-0.214708\pi$
$997$	4.94080	+	4.94080i	0.156477	+	0.156477i	−0.624527	+	0.781003i	$0.714708\pi$
$998$	−23.8154	+	23.8154i	−0.753865	+	0.753865i
$999$		−	44.1141i		−	1.39571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.c.483.20	yes	40
5.2	odd	4	inner	605.2.e.c.362.1	✓	40
11.2	odd	10		605.2.m.g.403.20		160
11.3	even	5		605.2.m.g.233.20		160
11.4	even	5		605.2.m.g.578.1		160
11.5	even	5		605.2.m.g.118.1		160
11.6	odd	10		605.2.m.g.118.20		160
11.7	odd	10		605.2.m.g.578.20		160
11.8	odd	10		605.2.m.g.233.1		160
11.9	even	5		605.2.m.g.403.1		160
11.10	odd	2	inner	605.2.e.c.483.1	yes	40
55.2	even	20		605.2.m.g.282.1		160
55.7	even	20		605.2.m.g.457.20		160
55.17	even	20		605.2.m.g.602.1		160
55.27	odd	20		605.2.m.g.602.20		160
55.32	even	4	inner	605.2.e.c.362.20	yes	40
55.37	odd	20		605.2.m.g.457.1		160
55.42	odd	20		605.2.m.g.282.20		160
55.47	odd	20		605.2.m.g.112.20		160
55.52	even	20		605.2.m.g.112.1		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.1	✓	40	5.2	odd	4	inner
605.2.e.c.362.20	yes	40	55.32	even	4	inner
605.2.e.c.483.1	yes	40	11.10	odd	2	inner
605.2.e.c.483.20	yes	40	1.1	even	1	trivial
605.2.m.g.112.1		160	55.52	even	20
605.2.m.g.112.20		160	55.47	odd	20
605.2.m.g.118.1		160	11.5	even	5
605.2.m.g.118.20		160	11.6	odd	10
605.2.m.g.233.1		160	11.8	odd	10
605.2.m.g.233.20		160	11.3	even	5
605.2.m.g.282.1		160	55.2	even	20
605.2.m.g.282.20		160	55.42	odd	20
605.2.m.g.403.1		160	11.9	even	5
605.2.m.g.403.20		160	11.2	odd	10
605.2.m.g.457.1		160	55.37	odd	20
605.2.m.g.457.20		160	55.7	even	20
605.2.m.g.578.1		160	11.4	even	5
605.2.m.g.578.20		160	11.7	odd	10
605.2.m.g.602.1		160	55.17	even	20
605.2.m.g.602.20		160	55.27	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91757 + 1.91757i) q^{2} +(0.831561 + 0.831561i) q^{3} +5.35415i q^{4} +(1.62695 - 1.53396i) q^{5} +3.18915i q^{6} +(0.383282 + 0.383282i) q^{7} +(-6.43181 + 6.43181i) q^{8} -1.61701i q^{9} +O(q^{10})\)	\(q+(1.91757 + 1.91757i) q^{2} +(0.831561 + 0.831561i) q^{3} +5.35415i q^{4} +(1.62695 - 1.53396i) q^{5} +3.18915i q^{6} +(0.383282 + 0.383282i) q^{7} +(-6.43181 + 6.43181i) q^{8} -1.61701i q^{9} +(6.06127 + 0.178306i) q^{10} +(-4.45230 + 4.45230i) q^{12} +(-1.46382 + 1.46382i) q^{13} +1.46994i q^{14} +(2.62849 + 0.0773230i) q^{15} -13.9586 q^{16} +(-3.33920 - 3.33920i) q^{17} +(3.10074 - 3.10074i) q^{18} +2.45931 q^{19} +(8.21306 + 8.71092i) q^{20} +0.637445i q^{21} +(2.08092 + 2.08092i) q^{23} -10.6969 q^{24} +(0.293919 - 4.99135i) q^{25} -5.61395 q^{26} +(3.83933 - 3.83933i) q^{27} +(-2.05215 + 2.05215i) q^{28} +0.102937 q^{29} +(4.89204 + 5.18858i) q^{30} -5.44125 q^{31} +(-13.9030 - 13.9030i) q^{32} -12.8063i q^{34} +(1.21152 + 0.0356397i) q^{35} +8.65773 q^{36} +(5.74503 - 5.74503i) q^{37} +(4.71591 + 4.71591i) q^{38} -2.43451 q^{39} +(-0.598065 + 20.3304i) q^{40} +3.50547i q^{41} +(-1.22234 + 1.22234i) q^{42} +(-5.15006 + 5.15006i) q^{43} +(-2.48044 - 2.63080i) q^{45} +7.98062i q^{46} +(1.47326 - 1.47326i) q^{47} +(-11.6074 - 11.6074i) q^{48} -6.70619i q^{49} +(10.1349 - 9.00766i) q^{50} -5.55350i q^{51} +(-7.83750 - 7.83750i) q^{52} +(-0.224800 - 0.224800i) q^{53} +14.7244 q^{54} -4.93040 q^{56} +(2.04507 + 2.04507i) q^{57} +(0.197389 + 0.197389i) q^{58} -2.79138i q^{59} +(-0.413999 + 14.0733i) q^{60} -9.29408i q^{61} +(-10.4340 - 10.4340i) q^{62} +(0.619773 - 0.619773i) q^{63} -25.4026i q^{64} +(-0.136114 + 4.62700i) q^{65} +(-10.6041 + 10.6041i) q^{67} +(17.8786 - 17.8786i) q^{68} +3.46082i q^{69} +(2.25483 + 2.39152i) q^{70} +11.5983 q^{71} +(10.4003 + 10.4003i) q^{72} +(-6.90968 + 6.90968i) q^{73} +22.0330 q^{74} +(4.39502 - 3.90620i) q^{75} +13.1675i q^{76} +(-4.66834 - 4.66834i) q^{78} +12.8575 q^{79} +(-22.7099 + 21.4120i) q^{80} +1.53422 q^{81} +(-6.72198 + 6.72198i) q^{82} +(-3.83250 + 3.83250i) q^{83} -3.41297 q^{84} +(-10.5549 - 0.310497i) q^{85} -19.7512 q^{86} +(0.0855986 + 0.0855986i) q^{87} +2.37467i q^{89} +(0.288323 - 9.80115i) q^{90} -1.12211 q^{91} +(-11.1416 + 11.1416i) q^{92} +(-4.52473 - 4.52473i) q^{93} +5.65016 q^{94} +(4.00118 - 3.77250i) q^{95} -23.1223i q^{96} +(-1.97796 + 1.97796i) q^{97} +(12.8596 - 12.8596i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) 40 * q + 8 * q^3 - 4 * q^5	\( 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) \) 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

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