LMFDB - Embedded newform 605.2.e.c.362.8

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			362.8
Character	$\chi$	$=$	605.362
Dual form			605.2.e.c.483.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.503119 + 0.503119i) q^{2} +(-1.98889 + 1.98889i) q^{3} +1.49374i q^{4} +(-1.36457 + 1.77143i) q^{5} -2.00130i q^{6} +(2.43291 - 2.43291i) q^{7} +(-1.75777 - 1.75777i) q^{8} -4.91135i q^{9} +O(q^{10})$	\(q+(-0.503119 + 0.503119i) q^{2} +(-1.98889 + 1.98889i) q^{3} +1.49374i q^{4} +(-1.36457 + 1.77143i) q^{5} -2.00130i q^{6} +(2.43291 - 2.43291i) q^{7} +(-1.75777 - 1.75777i) q^{8} -4.91135i q^{9} +(-0.204700 - 1.57778i) q^{10} +(-2.97088 - 2.97088i) q^{12} +(-2.88910 - 2.88910i) q^{13} +2.44809i q^{14} +(-0.809203 - 6.23714i) q^{15} -1.21875 q^{16} +(0.334956 - 0.334956i) q^{17} +(2.47099 + 2.47099i) q^{18} -4.06565 q^{19} +(-2.64606 - 2.03831i) q^{20} +9.67756i q^{21} +(0.771754 - 0.771754i) q^{23} +6.99201 q^{24} +(-1.27592 - 4.83446i) q^{25} +2.90713 q^{26} +(3.80145 + 3.80145i) q^{27} +(3.63414 + 3.63414i) q^{28} +2.39345 q^{29} +(3.54515 + 2.73090i) q^{30} +3.82833 q^{31} +(4.12871 - 4.12871i) q^{32} +0.337046i q^{34} +(0.989858 + 7.62959i) q^{35} +7.33628 q^{36} +(-3.60132 - 3.60132i) q^{37} +(2.04551 - 2.04551i) q^{38} +11.4922 q^{39} +(5.51236 - 0.715170i) q^{40} +8.48673i q^{41} +(-4.86897 - 4.86897i) q^{42} +(-7.82382 - 7.82382i) q^{43} +(8.70010 + 6.70186i) q^{45} +0.776569i q^{46} +(2.80844 + 2.80844i) q^{47} +(2.42395 - 2.42395i) q^{48} -4.83808i q^{49} +(3.07425 + 1.79037i) q^{50} +1.33238i q^{51} +(4.31558 - 4.31558i) q^{52} +(-3.61137 + 3.61137i) q^{53} -3.82517 q^{54} -8.55298 q^{56} +(8.08612 - 8.08612i) q^{57} +(-1.20419 + 1.20419i) q^{58} +7.63165i q^{59} +(9.31668 - 1.20874i) q^{60} -3.34380i q^{61} +(-1.92611 + 1.92611i) q^{62} +(-11.9489 - 11.9489i) q^{63} +1.71698i q^{64} +(9.06022 - 1.17547i) q^{65} +(-1.52319 - 1.52319i) q^{67} +(0.500338 + 0.500338i) q^{68} +3.06986i q^{69} +(-4.33661 - 3.34058i) q^{70} -10.8467 q^{71} +(-8.63301 + 8.63301i) q^{72} +(-3.02758 - 3.02758i) q^{73} +3.62379 q^{74} +(12.1529 + 7.07755i) q^{75} -6.07303i q^{76} +(-5.78195 + 5.78195i) q^{78} -6.48154 q^{79} +(1.66306 - 2.15892i) q^{80} -0.387281 q^{81} +(-4.26984 - 4.26984i) q^{82} +(-7.68119 - 7.68119i) q^{83} -14.4558 q^{84} +(0.136281 + 1.05042i) q^{85} +7.87263 q^{86} +(-4.76031 + 4.76031i) q^{87} -14.3621i q^{89} +(-7.74902 + 1.00535i) q^{90} -14.0579 q^{91} +(1.15280 + 1.15280i) q^{92} +(-7.61412 + 7.61412i) q^{93} -2.82596 q^{94} +(5.54785 - 7.20201i) q^{95} +16.4231i q^{96} +(-0.0994772 - 0.0994772i) q^{97} +(2.43413 + 2.43413i) 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.503119	+	0.503119i	−0.355759	+	0.355759i	−0.862247	−	0.506488i	$-0.830943\pi$
$2$	−0.503119	+	0.503119i	−0.355759	+	0.355759i	0.506488	+	0.862247i	$0.330943\pi$
$3$	−1.98889	+	1.98889i	−1.14828	+	1.14828i	−0.161395	+	0.986890i	$0.551599\pi$
$3$	−1.98889	+	1.98889i	−1.14828	+	1.14828i	−0.986890	+	0.161395i	$0.948401\pi$
$4$			1.49374i			0.746871i
$5$	−1.36457	+	1.77143i	−0.610253	+	0.792207i
$5$	−1.36457	+	1.77143i	−0.610253	+	0.792207i
$6$		−	2.00130i		−	0.817026i
$7$	2.43291	−	2.43291i	0.919553	−	0.919553i	−0.0774441	−	0.996997i	$-0.524676\pi$
$7$	2.43291	−	2.43291i	0.919553	−	0.919553i	0.996997	+	0.0774441i	$0.0246759\pi$
$8$	−1.75777	−	1.75777i	−0.621465	−	0.621465i
$9$		−	4.91135i		−	1.63712i
$10$	−0.204700	−	1.57778i	−0.0647319	−	0.498938i
$11$		0			0
$11$		0			0
$12$	−2.97088	−	2.97088i	−0.857620	−	0.857620i
$13$	−2.88910	−	2.88910i	−0.801294	−	0.801294i	0.182004	−	0.983298i	$-0.441742\pi$
$13$	−2.88910	−	2.88910i	−0.801294	−	0.801294i	−0.983298	+	0.182004i	$0.941742\pi$
$14$			2.44809i			0.654279i
$15$	−0.809203	−	6.23714i	−0.208935	−	1.61042i
$16$	−1.21875			−0.304687
$17$	0.334956	−	0.334956i	0.0812389	−	0.0812389i	−0.665320	−	0.746559i	$-0.731705\pi$
$17$	0.334956	−	0.334956i	0.0812389	−	0.0812389i	0.746559	+	0.665320i	$0.231705\pi$
$18$	2.47099	+	2.47099i	0.582419	+	0.582419i
$19$	−4.06565			−0.932724			−0.466362	−	0.884594i	$-0.654436\pi$
$19$	−4.06565			−0.932724			−0.466362	+	0.884594i	$0.654436\pi$
$20$	−2.64606	−	2.03831i	−0.591676	−	0.455780i
$21$			9.67756i			2.11182i
$22$		0			0
$23$	0.771754	−	0.771754i	0.160922	−	0.160922i	−0.622053	−	0.782975i	$-0.713701\pi$
$23$	0.771754	−	0.771754i	0.160922	−	0.160922i	0.782975	+	0.622053i	$0.213701\pi$
$24$	6.99201			1.42724
$25$	−1.27592	−	4.83446i	−0.255184	−	0.966893i
$26$	2.90713			0.570135
$27$	3.80145	+	3.80145i	0.731590	+	0.731590i
$28$	3.63414	+	3.63414i	0.686787	+	0.686787i
$29$	2.39345			0.444453			0.222226	−	0.974995i	$-0.428668\pi$
$29$	2.39345			0.444453			0.222226	+	0.974995i	$0.428668\pi$
$30$	3.54515	+	2.73090i	0.647253	+	0.498592i
$31$	3.82833			0.687589			0.343795	−	0.939045i	$-0.388288\pi$
$31$	3.82833			0.687589			0.343795	+	0.939045i	$0.388288\pi$
$32$	4.12871	−	4.12871i	0.729860	−	0.729860i
$33$		0			0
$34$			0.337046i			0.0578030i
$35$	0.989858	+	7.62959i	0.167317	+	1.28964i
$36$	7.33628			1.22271
$37$	−3.60132	−	3.60132i	−0.592054	−	0.592054i	0.346132	−	0.938186i	$-0.387495\pi$
$37$	−3.60132	−	3.60132i	−0.592054	−	0.592054i	−0.938186	+	0.346132i	$0.887495\pi$
$38$	2.04551	−	2.04551i	0.331825	−	0.331825i
$39$	11.4922			1.84023
$40$	5.51236	−	0.715170i	0.871580	−	0.113078i
$41$			8.48673i			1.32540i	0.748883	+	0.662702i	$0.230590\pi$
$41$			8.48673i			1.32540i	−0.748883	+	0.662702i	$0.769410\pi$
$42$	−4.86897	−	4.86897i	−0.751298	−	0.751298i
$43$	−7.82382	−	7.82382i	−1.19312	−	1.19312i	−0.976186	−	0.216935i	$-0.930394\pi$
$43$	−7.82382	−	7.82382i	−1.19312	−	1.19312i	−0.216935	−	0.976186i	$-0.569606\pi$
$44$		0			0
$45$	8.70010	+	6.70186i	1.29693	+	0.999054i
$46$			0.776569i			0.114499i
$47$	2.80844	+	2.80844i	0.409653	+	0.409653i	0.881618	−	0.471964i	$-0.156455\pi$
$47$	2.80844	+	2.80844i	0.409653	+	0.409653i	−0.471964	+	0.881618i	$0.656455\pi$
$48$	2.42395	−	2.42395i	0.349867	−	0.349867i
$49$		−	4.83808i		−	0.691154i
$50$	3.07425	+	1.79037i	0.434765	+	0.253197i
$51$			1.33238i			0.186571i
$52$	4.31558	−	4.31558i	0.598463	−	0.598463i
$53$	−3.61137	+	3.61137i	−0.496059	+	0.496059i	−0.910209	−	0.414150i	$-0.864079\pi$
$53$	−3.61137	+	3.61137i	−0.496059	+	0.496059i	0.414150	+	0.910209i	$0.364079\pi$
$54$	−3.82517			−0.520539
$55$		0			0
$56$	−8.55298			−1.14294
$57$	8.08612	−	8.08612i	1.07103	−	1.07103i
$58$	−1.20419	+	1.20419i	−0.158118	+	0.158118i
$59$			7.63165i			0.993557i	0.867877	+	0.496778i	$0.165484\pi$
$59$			7.63165i			0.993557i	−0.867877	+	0.496778i	$0.834516\pi$
$60$	9.31668	−	1.20874i	1.20278	−	0.156048i
$61$		−	3.34380i		−	0.428130i	−0.976819	−	0.214065i	$-0.931330\pi$
$61$		−	3.34380i		−	0.428130i	0.976819	−	0.214065i	$-0.0686705\pi$
$62$	−1.92611	+	1.92611i	−0.244616	+	0.244616i
$63$	−11.9489	−	11.9489i	−1.50541	−	1.50541i
$64$			1.71698i			0.214622i
$65$	9.06022	−	1.17547i	1.12378	−	0.145799i
$66$		0			0
$67$	−1.52319	−	1.52319i	−0.186087	−	0.186087i	0.607915	−	0.794002i	$-0.292006\pi$
$67$	−1.52319	−	1.52319i	−0.186087	−	0.186087i	−0.794002	+	0.607915i	$0.792006\pi$
$68$	0.500338	+	0.500338i	0.0606750	+	0.0606750i
$69$			3.06986i			0.369568i
$70$	−4.33661	−	3.34058i	−0.518324	−	0.399275i
$71$	−10.8467			−1.28726			−0.643631	−	0.765336i	$-0.722573\pi$
$71$	−10.8467			−1.28726			−0.643631	+	0.765336i	$0.722573\pi$
$72$	−8.63301	+	8.63301i	−1.01741	+	1.01741i
$73$	−3.02758	−	3.02758i	−0.354351	−	0.354351i	0.507375	−	0.861726i	$-0.330616\pi$
$73$	−3.02758	−	3.02758i	−0.354351	−	0.354351i	−0.861726	+	0.507375i	$0.830616\pi$
$74$	3.62379			0.421257
$75$	12.1529	+	7.07755i	1.40329	+	0.817245i
$76$		−	6.07303i		−	0.696624i
$77$		0			0
$78$	−5.78195	+	5.78195i	−0.654677	+	0.654677i
$79$	−6.48154			−0.729230			−0.364615	−	0.931158i	$-0.618799\pi$
$79$	−6.48154			−0.729230			−0.364615	+	0.931158i	$0.618799\pi$
$80$	1.66306	−	2.15892i	0.185936	−	0.241375i
$81$	−0.387281			−0.0430312
$82$	−4.26984	−	4.26984i	−0.471525	−	0.471525i
$83$	−7.68119	−	7.68119i	−0.843120	−	0.843120i	0.146143	−	0.989263i	$-0.453314\pi$
$83$	−7.68119	−	7.68119i	−0.843120	−	0.843120i	−0.989263	+	0.146143i	$0.953314\pi$
$84$	−14.4558			−1.57725
$85$	0.136281	+	1.05042i	0.0147818	+	0.113934i
$86$	7.87263			0.848927
$87$	−4.76031	+	4.76031i	−0.510358	+	0.510358i
$88$		0			0
$89$		−	14.3621i		−	1.52238i	−0.648532	−	0.761188i	$-0.724617\pi$
$89$		−	14.3621i		−	1.52238i	0.648532	−	0.761188i	$-0.275383\pi$
$90$	−7.74902	+	1.00535i	−0.816819	+	0.105974i
$91$	−14.0579			−1.47366
$92$	1.15280	+	1.15280i	0.120188	+	0.120188i
$93$	−7.61412	+	7.61412i	−0.789548	+	0.789548i
$94$	−2.82596			−0.291476
$95$	5.54785	−	7.20201i	0.569197	−	0.738910i
$96$			16.4231i			1.67618i
$97$	−0.0994772	−	0.0994772i	−0.0101004	−	0.0101004i	0.702039	−	0.712139i	$-0.252273\pi$
$97$	−0.0994772	−	0.0994772i	−0.0101004	−	0.0101004i	−0.712139	+	0.702039i	$0.752273\pi$
$98$	2.43413	+	2.43413i	0.245884	+	0.245884i
$99$		0			0
$100$	7.22144	−	1.90589i	0.722144	−	0.190589i
$101$		−	0.0797258i		−	0.00793301i	−0.999992	−	0.00396651i	$-0.998737\pi$
$101$		−	0.0797258i		−	0.00793301i	0.999992	−	0.00396651i	$-0.00126258\pi$
$102$	−0.670347	−	0.670347i	−0.0663742	−	0.0663742i
$103$	−3.74170	+	3.74170i	−0.368680	+	0.368680i	−0.866996	−	0.498315i	$-0.833952\pi$
$103$	−3.74170	+	3.74170i	−0.368680	+	0.368680i	0.498315	+	0.866996i	$0.333952\pi$
$104$			10.1568i			0.995952i
$105$	−17.1431	−	13.2057i	−1.67300	−	1.28874i
$106$		−	3.63390i		−	0.352955i
$107$	3.66752	−	3.66752i	0.354552	−	0.354552i	−0.507248	−	0.861800i	$-0.669337\pi$
$107$	3.66752	−	3.66752i	0.354552	−	0.354552i	0.861800	+	0.507248i	$0.169337\pi$
$108$	−5.67839	+	5.67839i	−0.546403	+	0.546403i
$109$	18.0760			1.73137			0.865686	−	0.500588i	$-0.166883\pi$
$109$	18.0760			1.73137			0.865686	+	0.500588i	$0.166883\pi$
$110$		0			0
$111$	14.3253			1.35969
$112$	−2.96510	+	2.96510i	−0.280176	+	0.280176i
$113$	7.51745	−	7.51745i	0.707182	−	0.707182i	−0.258760	−	0.965942i	$-0.583314\pi$
$113$	7.51745	−	7.51745i	0.707182	−	0.707182i	0.965942	+	0.258760i	$0.0833137\pi$
$114$			8.13657i			0.762059i
$115$	0.313997	+	2.42022i	0.0292804	+	0.225686i
$116$			3.57520i			0.331949i
$117$	−14.1894	+	14.1894i	−1.31181	+	1.31181i
$118$	−3.83963	−	3.83963i	−0.353467	−	0.353467i
$119$		−	1.62984i		−	0.149407i
$120$	−9.54106	+	12.3858i	−0.870976	+	1.13067i
$121$		0			0
$122$	1.68233	+	1.68233i	0.152311	+	0.152311i
$123$	−16.8791	−	16.8791i	−1.52194	−	1.52194i
$124$			5.71854i			0.513540i
$125$	10.3050	+	4.33675i	0.921705	+	0.387891i
$126$	12.0234			1.07113
$127$	2.22210	−	2.22210i	0.197179	−	0.197179i	−0.601610	−	0.798790i	$-0.705474\pi$
$127$	2.22210	−	2.22210i	0.197179	−	0.197179i	0.798790	+	0.601610i	$0.205474\pi$
$128$	7.39358	+	7.39358i	0.653507	+	0.653507i
$129$	31.1214			2.74008
$130$	−3.96697	+	5.14977i	−0.347926	+	0.451665i
$131$			7.60121i			0.664120i	0.943258	+	0.332060i	$0.107744\pi$
$131$			7.60121i			0.664120i	−0.943258	+	0.332060i	$0.892256\pi$
$132$		0			0
$133$	−9.89135	+	9.89135i	−0.857689	+	0.857689i
$134$	1.53269			0.132404
$135$	−11.9213	+	1.54667i	−1.02602	+	0.133116i
$136$	−1.17755			−0.100974
$137$	−10.9148	−	10.9148i	−0.932516	−	0.932516i	0.0653470	−	0.997863i	$-0.479185\pi$
$137$	−10.9148	−	10.9148i	−0.932516	−	0.932516i	−0.997863	+	0.0653470i	$0.979185\pi$
$138$	−1.54451	−	1.54451i	−0.131477	−	0.131477i
$139$	−11.2280			−0.952350			−0.476175	−	0.879351i	$-0.657977\pi$
$139$	−11.2280			−0.952350			−0.476175	+	0.879351i	$0.657977\pi$
$140$	−11.3966	+	1.47859i	−0.963191	+	0.124964i
$141$	−11.1714			−0.940797
$142$	5.45716	−	5.45716i	0.457955	−	0.457955i
$143$		0			0
$144$			5.98569i			0.498808i
$145$	−3.26602	+	4.23983i	−0.271228	+	0.352099i
$146$	3.04646			0.252127
$147$	9.62239	+	9.62239i	0.793642	+	0.793642i
$148$	5.37945	−	5.37945i	0.442188	−	0.442188i
$149$	−15.6857			−1.28502			−0.642512	−	0.766276i	$-0.722108\pi$
$149$	−15.6857			−1.28502			−0.642512	+	0.766276i	$0.722108\pi$
$150$	−9.67519	+	2.55349i	−0.789976	+	0.208491i
$151$		−	23.5811i		−	1.91900i	−0.281706	−	0.959501i	$-0.590900\pi$
$151$		−	23.5811i		−	1.91900i	0.281706	−	0.959501i	$-0.409100\pi$
$152$	7.14647	+	7.14647i	0.579656	+	0.579656i
$153$	−1.64509	−	1.64509i	−0.132997	−	0.132997i
$154$		0			0
$155$	−5.22402	+	6.78162i	−0.419603	+	0.544713i
$156$			17.1664i			1.37441i
$157$	−6.24987	−	6.24987i	−0.498794	−	0.498794i	0.412268	−	0.911062i	$-0.364737\pi$
$157$	−6.24987	−	6.24987i	−0.498794	−	0.498794i	−0.911062	+	0.412268i	$0.864737\pi$
$158$	3.26099	−	3.26099i	0.259430	−	0.259430i
$159$		−	14.3652i		−	1.13923i
$160$	1.67982	+	12.9476i	0.132801	+	1.02360i
$161$		−	3.75521i		−	0.295952i
$162$	0.194848	−	0.194848i	0.0153087	−	0.0153087i
$163$	−11.5177	+	11.5177i	−0.902139	+	0.902139i	−0.995621	−	0.0934823i	$-0.970200\pi$
$163$	−11.5177	+	11.5177i	−0.902139	+	0.902139i	0.0934823	+	0.995621i	$0.470200\pi$
$164$	−12.6770			−0.989905
$165$		0			0
$166$	7.72912			0.599896
$167$	8.38275	−	8.38275i	0.648677	−	0.648677i	−0.303996	−	0.952673i	$-0.598321\pi$
$167$	8.38275	−	8.38275i	0.648677	−	0.648677i	0.952673	+	0.303996i	$0.0983211\pi$
$168$	17.0109	−	17.0109i	1.31242	−	1.31242i
$169$			3.69385i			0.284143i
$170$	−0.597053	−	0.459922i	−0.0457919	−	0.0352744i
$171$			19.9678i			1.52698i
$172$	11.6868	−	11.6868i	0.891107	−	0.891107i
$173$	9.06040	+	9.06040i	0.688849	+	0.688849i	0.961978	−	0.273128i	$-0.0880583\pi$
$173$	9.06040	+	9.06040i	0.688849	+	0.688849i	−0.273128	+	0.961978i	$0.588058\pi$
$174$		−	4.79000i		−	0.363129i
$175$	−14.8660	−	8.65761i	−1.12376	−	0.654454i
$176$		0			0
$177$	−15.1785	−	15.1785i	−1.14089	−	1.14089i
$178$	7.22583	+	7.22583i	0.541599	+	0.541599i
$179$		−	11.3921i		−	0.851488i	−0.904844	−	0.425744i	$-0.860012\pi$
$179$		−	11.3921i		−	0.851488i	0.904844	−	0.425744i	$-0.139988\pi$
$180$	−10.0108	+	12.9957i	−0.746164	+	0.968642i
$181$	22.9507			1.70591			0.852956	−	0.521982i	$-0.174807\pi$
$181$	22.9507			1.70591			0.852956	+	0.521982i	$0.174807\pi$
$182$	7.07278	−	7.07278i	0.524269	−	0.524269i
$183$	6.65045	+	6.65045i	0.491615	+	0.491615i
$184$	−2.71313			−0.200015
$185$	11.2937	−	1.46524i	0.830332	−	0.107727i
$186$		−	7.66163i		−	0.561778i
$187$		0			0
$188$	−4.19509	+	4.19509i	−0.305958	+	0.305958i
$189$	18.4972			1.34547
$190$	0.832240	+	6.41470i	0.0603770	+	0.465371i
$191$	−26.9325			−1.94877			−0.974383	−	0.224894i	$-0.927797\pi$
$191$	−26.9325			−1.94877			−0.974383	+	0.224894i	$0.927797\pi$
$192$	−3.41488	−	3.41488i	−0.246447	−	0.246447i
$193$	8.17685	+	8.17685i	0.588582	+	0.588582i	0.937247	−	0.348665i	$-0.113365\pi$
$193$	8.17685	+	8.17685i	0.588582	+	0.588582i	−0.348665	+	0.937247i	$0.613365\pi$
$194$	0.100098			0.00718660
$195$	−15.6819	+	20.3576i	−1.12300	+	1.45784i
$196$	7.22684			0.516203
$197$	−12.3434	+	12.3434i	−0.879430	+	0.879430i	−0.993476	−	0.114045i	$-0.963619\pi$
$197$	−12.3434	+	12.3434i	−0.879430	+	0.879430i	0.114045	+	0.993476i	$0.463619\pi$
$198$		0			0
$199$		−	0.739593i		−	0.0524284i	−0.999656	−	0.0262142i	$-0.991655\pi$
$199$		−	0.739593i		−	0.0524284i	0.999656	−	0.0262142i	$-0.00834519\pi$
$200$	−6.25510	+	10.7406i	−0.442302	+	0.759478i
$201$	6.05889			0.427361
$202$	0.0401116	+	0.0401116i	0.00282224	+	0.00282224i
$203$	5.82305	−	5.82305i	0.408698	−	0.408698i
$204$	−1.99023			−0.139344
$205$	−15.0336	−	11.5807i	−1.04999	−	0.808831i
$206$		−	3.76504i		−	0.262323i
$207$	−3.79035	−	3.79035i	−0.263448	−	0.263448i
$208$	3.52109	+	3.52109i	0.244144	+	0.244144i
$209$		0			0
$210$	15.2691	−	1.98100i	1.05367	−	0.136702i
$211$		−	1.25606i		−	0.0864705i	−0.999065	−	0.0432352i	$-0.986234\pi$
$211$		−	1.25606i		−	0.0864705i	0.999065	−	0.0432352i	$-0.0137665\pi$
$212$	−5.39445	−	5.39445i	−0.370492	−	0.370492i
$213$	21.5728	−	21.5728i	1.47814	−	1.47814i
$214$			3.69040i			0.252270i
$215$	24.5354	−	3.18321i	1.67330	−	0.217093i
$216$		−	13.3642i		−	0.909315i
$217$	9.31398	−	9.31398i	0.632274	−	0.632274i
$218$	−9.09441	+	9.09441i	−0.615951	+	0.615951i
$219$	12.0430			0.813791
$220$		0			0
$221$	−1.93545			−0.130192
$222$	−7.20731	+	7.20731i	−0.483723	+	0.483723i
$223$	−11.5866	+	11.5866i	−0.775899	+	0.775899i	−0.979131	−	0.203231i	$-0.934856\pi$
$223$	−11.5866	+	11.5866i	−0.775899	+	0.775899i	0.203231	+	0.979131i	$0.434856\pi$
$224$		−	20.0896i		−	1.34229i
$225$	−23.7437	+	6.26647i	−1.58291	+	0.417765i
$226$			7.56435i			0.503173i
$227$	−9.88513	+	9.88513i	−0.656099	+	0.656099i	−0.954455	−	0.298356i	$-0.903562\pi$
$227$	−9.88513	+	9.88513i	−0.656099	+	0.656099i	0.298356	+	0.954455i	$0.403562\pi$
$228$	12.0786	+	12.0786i	0.799923	+	0.799923i
$229$		−	9.48652i		−	0.626887i	−0.949607	−	0.313444i	$-0.898517\pi$
$229$		−	9.48652i		−	0.626887i	0.949607	−	0.313444i	$-0.101483\pi$
$230$	−1.37564	−	1.05968i	−0.0907068	−	0.0698732i
$231$		0			0
$232$	−4.20714	−	4.20714i	−0.276212	−	0.276212i
$233$	0.392688	+	0.392688i	0.0257258	+	0.0257258i	0.719853	−	0.694127i	$-0.244209\pi$
$233$	0.392688	+	0.392688i	0.0257258	+	0.0257258i	−0.694127	+	0.719853i	$0.744209\pi$
$234$		−	14.2779i		−	0.933377i
$235$	−8.80726	+	1.14265i	−0.574522	+	0.0745382i
$236$	−11.3997			−0.742059
$237$	12.8911	−	12.8911i	0.837364	−	0.837364i
$238$	0.820002	+	0.820002i	0.0531529	+	0.0531529i
$239$	−10.0508			−0.650129			−0.325065	−	0.945692i	$-0.605386\pi$
$239$	−10.0508			−0.650129			−0.325065	+	0.945692i	$0.605386\pi$
$240$	0.986214	+	7.60150i	0.0636599	+	0.490675i
$241$		−	24.0480i		−	1.54906i	−0.632534	−	0.774532i	$-0.717985\pi$
$241$		−	24.0480i		−	1.54906i	0.632534	−	0.774532i	$-0.282015\pi$
$242$		0			0
$243$	−10.6341	+	10.6341i	−0.682178	+	0.682178i
$244$	4.99478			0.319758
$245$	8.57031	+	6.60188i	0.547537	+	0.421779i
$246$	16.9844			1.08289
$247$	11.7461	+	11.7461i	0.747386	+	0.747386i
$248$	−6.72933	−	6.72933i	−0.427313	−	0.427313i
$249$	30.5541			1.93628
$250$	−7.36654	+	3.00273i	−0.465901	+	0.189910i
$251$	−1.76457			−0.111379			−0.0556894	−	0.998448i	$-0.517736\pi$
$251$	−1.76457			−0.111379			−0.0556894	+	0.998448i	$0.517736\pi$
$252$	17.8485	−	17.8485i	1.12435	−	1.12435i
$253$		0			0
$254$			2.23596i			0.140297i
$255$	−2.36022	−	1.81812i	−0.147803	−	0.113855i
$256$	−10.8737			−0.679604
$257$	19.8363	+	19.8363i	1.23735	+	1.23735i	0.961078	+	0.276276i	$0.0891004\pi$
$257$	19.8363	+	19.8363i	1.23735	+	1.23735i	0.276276	+	0.961078i	$0.410900\pi$
$258$	−15.6578	+	15.6578i	−0.974810	+	0.974810i
$259$	−17.5234			−1.08885
$260$	1.75584	+	13.5336i	0.108893	+	0.839320i
$261$		−	11.7551i		−	0.727620i
$262$	−3.82431	−	3.82431i	−0.236267	−	0.236267i
$263$	2.00212	+	2.00212i	0.123456	+	0.123456i	0.766135	−	0.642679i	$-0.222177\pi$
$263$	2.00212	+	2.00212i	0.123456	+	0.123456i	−0.642679	+	0.766135i	$0.722177\pi$
$264$		0			0
$265$	−1.46933	−	11.3252i	−0.0902601	−	0.695703i
$266$		−	9.95306i		−	0.610261i
$267$	28.5645	+	28.5645i	1.74812	+	1.74812i
$268$	2.27525	−	2.27525i	0.138983	−	0.138983i
$269$			7.76303i			0.473321i	0.971592	+	0.236660i	$0.0760528\pi$
$269$			7.76303i			0.473321i	−0.971592	+	0.236660i	$0.923947\pi$
$270$	5.21970	−	6.77601i	0.317661	−	0.412375i
$271$			10.8971i			0.661953i	0.943639	+	0.330976i	$0.107378\pi$
$271$			10.8971i			0.661953i	−0.943639	+	0.330976i	$0.892622\pi$
$272$	−0.408227	+	0.408227i	−0.0247524	+	0.0247524i
$273$	27.9595	−	27.9595i	1.69218	−	1.69218i
$274$	10.9829			0.663502
$275$		0			0
$276$	−4.58558			−0.276020
$277$	16.3370	−	16.3370i	0.981596	−	0.981596i	−0.0182379	−	0.999834i	$-0.505806\pi$
$277$	16.3370	−	16.3370i	0.981596	−	0.981596i	0.999834	+	0.0182379i	$0.00580562\pi$
$278$	5.64904	−	5.64904i	0.338807	−	0.338807i
$279$		−	18.8023i		−	1.12566i
$280$	11.6711	−	15.1510i	0.697482	−	0.905445i
$281$		−	26.2130i		−	1.56374i	−0.623442	−	0.781870i	$-0.714266\pi$
$281$		−	26.2130i		−	1.56374i	0.623442	−	0.781870i	$-0.285734\pi$
$282$	5.62052	−	5.62052i	0.334697	−	0.334697i
$283$	−10.3957	−	10.3957i	−0.617959	−	0.617959i	0.327049	−	0.945008i	$-0.393946\pi$
$283$	−10.3957	−	10.3957i	−0.617959	−	0.617959i	−0.945008	+	0.327049i	$0.893946\pi$
$284$		−	16.2021i		−	0.961418i
$285$	3.28994	+	25.3580i	0.194879	+	1.50208i
$286$		0			0
$287$	20.6474	+	20.6474i	1.21878	+	1.21878i
$288$	−20.2775	−	20.2775i	−1.19487	−	1.19487i
$289$			16.7756i			0.986800i
$290$	−0.489940	−	3.77634i	−0.0287703	−	0.221754i
$291$	0.395698			0.0231962
$292$	4.52242	−	4.52242i	0.264654	−	0.264654i
$293$	4.74424	+	4.74424i	0.277161	+	0.277161i	0.831975	−	0.554814i	$-0.187210\pi$
$293$	4.74424	+	4.74424i	0.277161	+	0.277161i	−0.554814	+	0.831975i	$0.687210\pi$
$294$	−9.68243			−0.564691
$295$	−13.5189	−	10.4139i	−0.787102	−	0.606321i
$296$			12.6606i			0.735882i
$297$		0			0
$298$	7.89179	−	7.89179i	0.457159	−	0.457159i
$299$	−4.45936			−0.257891
$300$	−10.5720	+	18.1532i	−0.610376	+	1.04808i
$301$	−38.0692			−2.19427
$302$	11.8641	+	11.8641i	0.682702	+	0.682702i
$303$	0.158566	+	0.158566i	0.00910936	+	0.00910936i
$304$	4.95500			0.284189
$305$	5.92331	+	4.56284i	0.339168	+	0.261268i
$306$	1.65535			0.0946301
$307$	−12.1734	+	12.1734i	−0.694775	+	0.694775i	−0.963279	−	0.268503i	$-0.913471\pi$
$307$	−12.1734	+	12.1734i	−0.694775	+	0.694775i	0.268503	+	0.963279i	$0.413471\pi$
$308$		0			0
$309$		−	14.8836i		−	0.846700i
$310$	−0.783661	−	6.04027i	−0.0445090	−	0.343064i
$311$	−15.6822			−0.889254			−0.444627	−	0.895716i	$-0.646664\pi$
$311$	−15.6822			−0.889254			−0.444627	+	0.895716i	$0.646664\pi$
$312$	−20.2007	−	20.2007i	−1.14364	−	1.14364i
$313$	−8.73934	+	8.73934i	−0.493977	+	0.493977i	−0.909557	−	0.415580i	$-0.863579\pi$
$313$	−8.73934	+	8.73934i	−0.493977	+	0.493977i	0.415580	+	0.909557i	$0.363579\pi$
$314$	6.28887			0.354901
$315$	37.4715	−	4.86154i	2.11128	−	0.273917i
$316$		−	9.68175i		−	0.544641i
$317$	−5.15371	−	5.15371i	−0.289461	−	0.289461i	0.547406	−	0.836867i	$-0.315615\pi$
$317$	−5.15371	−	5.15371i	−0.289461	−	0.289461i	−0.836867	+	0.547406i	$0.815615\pi$
$318$	7.22741	+	7.22741i	0.405293	+	0.405293i
$319$		0			0
$320$	−3.04150	−	2.34293i	−0.170025	−	0.130974i
$321$			14.5886i			0.814254i
$322$	1.88932	+	1.88932i	0.105288	+	0.105288i
$323$	−1.36182	+	1.36182i	−0.0757734	+	0.0757734i
$324$		−	0.578497i		−	0.0321387i
$325$	−10.2810	+	17.6535i	−0.570288	+	0.979242i
$326$		−	11.5896i		−	0.641888i
$327$	−35.9512	+	35.9512i	−1.98811	+	1.98811i
$328$	14.9177	−	14.9177i	0.823693	−	0.823693i
$329$	13.6654			0.753396
$330$		0			0
$331$	27.2490			1.49774			0.748871	−	0.662716i	$-0.230596\pi$
$331$	27.2490			1.49774			0.748871	+	0.662716i	$0.230596\pi$
$332$	11.4737	−	11.4737i	0.629702	−	0.629702i
$333$	−17.6873	+	17.6873i	−0.969261	+	0.969261i
$334$			8.43505i			0.461545i
$335$	4.77671	−	0.619727i	0.260979	−	0.0338593i
$336$		−	11.7945i		−	0.643443i
$337$	1.56864	−	1.56864i	0.0854492	−	0.0854492i	−0.663090	−	0.748539i	$-0.730755\pi$
$337$	1.56864	−	1.56864i	0.0854492	−	0.0854492i	0.748539	+	0.663090i	$0.230755\pi$
$338$	−1.85845	−	1.85845i	−0.101086	−	0.101086i
$339$			29.9027i			1.62409i
$340$	−1.56906	+	0.203569i	−0.0850942	+	0.0110401i
$341$		0			0
$342$	−10.0462	−	10.0462i	−0.543236	−	0.543236i
$343$	5.25976	+	5.25976i	0.284000	+	0.284000i
$344$			27.5049i			1.48297i
$345$	−5.43804	−	4.18903i	−0.292774	−	0.225530i
$346$	−9.11693			−0.490129
$347$	−14.2401	+	14.2401i	−0.764448	+	0.764448i	−0.977123	−	0.212675i	$-0.931782\pi$
$347$	−14.2401	+	14.2401i	−0.764448	+	0.764448i	0.212675	+	0.977123i	$0.431782\pi$
$348$	−7.11067	−	7.11067i	−0.381172	−	0.381172i
$349$	6.67832			0.357482			0.178741	−	0.983896i	$-0.442798\pi$
$349$	6.67832			0.357482			0.178741	+	0.983896i	$0.442798\pi$
$350$	11.8352	−	3.12356i	0.632617	−	0.166961i
$351$		−	21.9656i		−	1.17244i
$352$		0			0
$353$	7.96284	−	7.96284i	0.423819	−	0.423819i	−0.462697	−	0.886516i	$-0.653118\pi$
$353$	7.96284	−	7.96284i	0.423819	−	0.423819i	0.886516	+	0.462697i	$0.153118\pi$
$354$	15.2732			0.811761
$355$	14.8010	−	19.2141i	0.785555	−	1.01978i
$356$	21.4532			1.13702
$357$	3.24156	+	3.24156i	0.171562	+	0.171562i
$358$	5.73160	+	5.73160i	0.302925	+	0.302925i
$359$	−0.495594			−0.0261564			−0.0130782	−	0.999914i	$-0.504163\pi$
$359$	−0.495594			−0.0261564			−0.0130782	+	0.999914i	$0.504163\pi$
$360$	−3.51245	−	27.0731i	−0.185122	−	1.42688i
$361$	−2.47050			−0.130026
$362$	−11.5469	+	11.5469i	−0.606894	+	0.606894i
$363$		0			0
$364$		−	20.9988i		−	1.10064i
$365$	9.49446	−	1.23181i	0.496963	−	0.0644757i
$366$	−6.69194			−0.349793
$367$	−8.97027	−	8.97027i	−0.468244	−	0.468244i	0.433101	−	0.901345i	$-0.357419\pi$
$367$	−8.97027	−	8.97027i	−0.468244	−	0.468244i	−0.901345	+	0.433101i	$0.857419\pi$
$368$	−0.940573	+	0.940573i	−0.0490308	+	0.0490308i
$369$	41.6812			2.16984
$370$	−4.94490	+	6.41929i	−0.257073	+	0.333723i
$371$			17.5722i			0.912305i
$372$	−11.3735	−	11.3735i	−0.589690	−	0.589690i
$373$	−9.16115	−	9.16115i	−0.474346	−	0.474346i	0.428972	−	0.903318i	$-0.358876\pi$
$373$	−9.16115	−	9.16115i	−0.474346	−	0.474346i	−0.903318	+	0.428972i	$0.858876\pi$
$374$		0			0
$375$	−29.1207	+	11.8701i	−1.50379	+	0.612971i
$376$		−	9.87319i		−	0.509171i
$377$	−6.91493	−	6.91493i	−0.356137	−	0.356137i
$378$	−9.30628	+	9.30628i	−0.478663	+	0.478663i
$379$			7.02914i			0.361063i	0.983569	+	0.180531i	$0.0577817\pi$
$379$			7.02914i			0.361063i	−0.983569	+	0.180531i	$0.942218\pi$
$380$	10.7579	+	8.28705i	0.551871	+	0.425117i
$381$			8.83901i			0.452836i
$382$	13.5503	−	13.5503i	0.693292	−	0.693292i
$383$	−12.0918	+	12.0918i	−0.617865	+	0.617865i	−0.944983	−	0.327119i	$-0.893922\pi$
$383$	−12.0918	+	12.0918i	−0.617865	+	0.617865i	0.327119	+	0.944983i	$0.393922\pi$
$384$	−29.4100			−1.50082
$385$		0			0
$386$	−8.22786			−0.418787
$387$	−38.4255	+	38.4255i	−1.95328	+	1.95328i
$388$	0.148593	−	0.148593i	0.00754368	−	0.00754368i
$389$		−	15.3124i		−	0.776370i	−0.921582	−	0.388185i	$-0.873102\pi$
$389$		−	15.3124i		−	0.776370i	0.921582	−	0.388185i	$-0.126898\pi$
$390$	−2.35246	−	18.1322i	−0.119121	−	0.918158i
$391$		−	0.517008i		−	0.0261462i
$392$	−8.50423	+	8.50423i	−0.429528	+	0.429528i
$393$	−15.1179	−	15.1179i	−0.762599	−	0.762599i
$394$		−	12.4204i		−	0.625731i
$395$	8.84449	−	11.4816i	0.445015	−	0.577701i
$396$		0			0
$397$	10.8782	+	10.8782i	0.545960	+	0.545960i	0.925270	−	0.379310i	$-0.123839\pi$
$397$	10.8782	+	10.8782i	0.545960	+	0.545960i	−0.379310	+	0.925270i	$0.623839\pi$
$398$	0.372104	+	0.372104i	0.0186519	+	0.0186519i
$399$		−	39.3456i		−	1.96974i
$400$	1.55502	+	5.89199i	0.0777511	+	0.294600i
$401$	14.4828			0.723239			0.361619	−	0.932326i	$-0.382224\pi$
$401$	14.4828			0.723239			0.361619	+	0.932326i	$0.382224\pi$
$402$	−3.04835	+	3.04835i	−0.152038	+	0.152038i
$403$	−11.0605	−	11.0605i	−0.550961	−	0.550961i
$404$	0.119090			0.00592494
$405$	0.528470	−	0.686040i	0.0262599	−	0.0340896i
$406$			5.85937i			0.290796i
$407$		0			0
$408$	2.34202	−	2.34202i	0.115947	−	0.115947i
$409$	−10.9654			−0.542202			−0.271101	−	0.962551i	$-0.587388\pi$
$409$	−10.9654			−0.542202			−0.271101	+	0.962551i	$0.587388\pi$
$410$	13.3902	−	1.73724i	0.661294	−	0.0857959i
$411$	43.4167			2.14159
$412$	−5.58913	−	5.58913i	−0.275357	−	0.275357i
$413$	18.5671	+	18.5671i	0.913628	+	0.913628i
$414$	3.81400			0.187448
$415$	24.0882	−	3.12519i	1.18244	−	0.153409i
$416$	−23.8566			−1.16966
$417$	22.3313	−	22.3313i	1.09357	−	1.09357i
$418$		0			0
$419$			6.85633i			0.334954i	0.985876	+	0.167477i	$0.0535620\pi$
$419$			6.85633i			0.334954i	−0.985876	+	0.167477i	$0.946438\pi$
$420$	19.7259	−	25.6074i	0.962523	−	1.24951i
$421$	19.7835			0.964187			0.482094	−	0.876120i	$-0.339876\pi$
$421$	19.7835			0.964187			0.482094	+	0.876120i	$0.339876\pi$
$422$	0.631946	+	0.631946i	0.0307627	+	0.0307627i
$423$	13.7932	−	13.7932i	0.670650	−	0.670650i
$424$	12.6959			0.616567
$425$	−2.04671	−	1.19196i	−0.0992801	−	0.0578184i
$426$			21.7074i			1.05173i
$427$	−8.13516	−	8.13516i	−0.393688	−	0.393688i
$428$	5.47832	+	5.47832i	0.264805	+	0.264805i
$429$		0			0
$430$	−10.7427	+	13.9458i	−0.518060	+	0.672526i
$431$			2.12747i			0.102477i	0.998686	+	0.0512383i	$0.0163168\pi$
$431$			2.12747i			0.102477i	−0.998686	+	0.0512383i	$0.983683\pi$
$432$	−4.63301	−	4.63301i	−0.222906	−	0.222906i
$433$	−12.0190	+	12.0190i	−0.577598	+	0.577598i	−0.934241	−	0.356643i	$-0.883921\pi$
$433$	−12.0190	+	12.0190i	−0.577598	+	0.577598i	0.356643	+	0.934241i	$0.383921\pi$
$434$			9.37209i			0.449875i
$435$	−1.93679	−	14.9283i	−0.0928619	−	0.715757i
$436$			27.0009i			1.29311i
$437$	−3.13768	+	3.13768i	−0.150096	+	0.150096i
$438$	−6.05907	+	6.05907i	−0.289514	+	0.289514i
$439$	−41.8416			−1.99699			−0.998496	−	0.0548171i	$-0.982542\pi$
$439$	−41.8416			−1.99699			−0.998496	+	0.0548171i	$0.982542\pi$
$440$		0			0
$441$	−23.7615			−1.13150
$442$	0.973762	−	0.973762i	0.0463171	−	0.0463171i
$443$	17.2399	−	17.2399i	0.819094	−	0.819094i	−0.166883	−	0.985977i	$-0.553370\pi$
$443$	17.2399	−	17.2399i	0.819094	−	0.819094i	0.985977	+	0.166883i	$0.0533702\pi$
$444$			21.3982i			1.01551i
$445$	25.4414	+	19.5980i	1.20604	+	0.929034i
$446$		−	11.6589i		−	0.552067i
$447$	31.1971	−	31.1971i	1.47557	−	1.47557i
$448$	4.17725	+	4.17725i	0.197356	+	0.197356i
$449$		−	1.70856i		−	0.0806317i	−0.999187	−	0.0403159i	$-0.987164\pi$
$449$		−	1.70856i		−	0.0806317i	0.999187	−	0.0403159i	$-0.0128364\pi$
$450$	8.79314	−	15.0987i	0.414513	−	0.711760i
$451$		0			0
$452$	11.2291	+	11.2291i	0.528174	+	0.528174i
$453$	46.9001	+	46.9001i	2.20356	+	2.20356i
$454$		−	9.94680i		−	0.466826i
$455$	19.1829	−	24.9025i	0.899307	−	1.16745i
$456$	−28.4271			−1.33122
$457$	−1.38353	+	1.38353i	−0.0647190	+	0.0647190i	−0.738725	−	0.674006i	$-0.764572\pi$
$457$	−1.38353	+	1.38353i	−0.0647190	+	0.0647190i	0.674006	+	0.738725i	$0.264572\pi$
$458$	4.77285	+	4.77285i	0.223021	+	0.223021i
$459$	2.54664			0.118867
$460$	−3.61518	+	0.469031i	−0.168559	+	0.0218687i
$461$			22.4717i			1.04661i	0.852144	+	0.523307i	$0.175302\pi$
$461$			22.4717i			1.04661i	−0.852144	+	0.523307i	$0.824698\pi$
$462$		0			0
$463$	−4.93273	+	4.93273i	−0.229244	+	0.229244i	−0.812377	−	0.583133i	$-0.801827\pi$
$463$	−4.93273	+	4.93273i	−0.229244	+	0.229244i	0.583133	+	0.812377i	$0.301827\pi$
$464$	−2.91701			−0.135419
$465$	−3.09790	−	23.8779i	−0.143662	−	1.10731i
$466$	−0.395138			−0.0183044
$467$	−14.6910	−	14.6910i	−0.679820	−	0.679820i	0.280139	−	0.959959i	$-0.409619\pi$
$467$	−14.6910	−	14.6910i	−0.679820	−	0.679820i	−0.959959	+	0.280139i	$0.909619\pi$
$468$	−21.1953	−	21.1953i	−0.979753	−	0.979753i
$469$	−7.41155			−0.342233
$470$	3.85621	−	5.00599i	0.177874	−	0.230909i
$471$	24.8606			1.14552
$472$	13.4147	−	13.4147i	0.617461	−	0.617461i
$473$		0			0
$474$			12.9715i			0.595800i
$475$	5.18743	+	19.6552i	0.238016	+	0.901844i
$476$	2.43455			0.111588
$477$	17.7367	+	17.7367i	0.812106	+	0.812106i
$478$	5.05673	−	5.05673i	0.231290	−	0.231290i
$479$	−20.2576			−0.925592			−0.462796	−	0.886465i	$-0.653154\pi$
$479$	−20.2576			−0.925592			−0.462796	+	0.886465i	$0.653154\pi$
$480$	−29.0923	−	22.4104i	−1.32788	−	1.02289i
$481$			20.8092i			0.948818i
$482$	12.0990	+	12.0990i	0.551094	+	0.551094i
$483$	7.46869	+	7.46869i	0.339837	+	0.339837i
$484$		0			0
$485$	0.311960	−	0.0404735i	0.0141654	−	0.00183781i
$486$		−	10.7004i		−	0.485382i
$487$	−14.4921	−	14.4921i	−0.656700	−	0.656700i	0.297898	−	0.954598i	$-0.403714\pi$
$487$	−14.4921	−	14.4921i	−0.656700	−	0.656700i	−0.954598	+	0.297898i	$0.903714\pi$
$488$	−5.87763	+	5.87763i	−0.266068	+	0.266068i
$489$		−	45.8150i		−	2.07182i
$490$	−7.63342	+	0.990356i	−0.344843	+	0.0447397i
$491$		−	12.2278i		−	0.551834i	−0.961181	−	0.275917i	$-0.911018\pi$
$491$		−	12.2278i		−	0.551834i	0.961181	−	0.275917i	$-0.0889815\pi$
$492$	25.2131	−	25.2131i	1.13669	−	1.13669i
$493$	0.801702	−	0.801702i	0.0361068	−	0.0361068i
$494$	−11.8194			−0.531779
$495$		0			0
$496$	−4.66577			−0.209499
$497$	−26.3889	+	26.3889i	−1.18370	+	1.18370i
$498$	−15.3723	+	15.3723i	−0.688851	+	0.688851i
$499$		−	17.4373i		−	0.780600i	−0.920688	−	0.390300i	$-0.872371\pi$
$499$		−	17.4373i		−	0.780600i	0.920688	−	0.390300i	$-0.127629\pi$
$500$	−6.47798	+	15.3930i	−0.289704	+	0.688395i
$501$			33.3447i			1.48973i
$502$	0.887791	−	0.887791i	0.0396240	−	0.0396240i
$503$	18.1510	+	18.1510i	0.809312	+	0.809312i	0.984530	−	0.175218i	$-0.0560629\pi$
$503$	18.1510	+	18.1510i	0.809312	+	0.809312i	−0.175218	+	0.984530i	$0.556063\pi$
$504$			42.0066i			1.87112i
$505$	0.141229	+	0.108791i	0.00628459	+	0.00484114i
$506$		0			0
$507$	−7.34666	−	7.34666i	−0.326277	−	0.326277i
$508$	3.31924	+	3.31924i	0.147268	+	0.147268i
$509$			39.5711i			1.75396i	0.480530	+	0.876978i	$0.340444\pi$
$509$			39.5711i			1.75396i	−0.480530	+	0.876978i	$0.659556\pi$
$510$	2.10220	−	0.272739i	0.0930872	−	0.0120771i
$511$	−14.7316			−0.651689
$512$	−9.31641	+	9.31641i	−0.411731	+	0.411731i
$513$	−15.4554	−	15.4554i	−0.682371	−	0.682371i
$514$	−19.9601			−0.880400
$515$	−1.52236	−	11.7339i	−0.0670830	−	0.517059i
$516$			46.4873i			2.04649i
$517$		0			0
$518$	8.81635	−	8.81635i	0.387368	−	0.387368i
$519$	−36.0402			−1.58199
$520$	−17.9920	−	13.8596i	−0.789000	−	0.607782i
$521$	8.59201			0.376423			0.188211	−	0.982129i	$-0.439731\pi$
$521$	8.59201			0.376423			0.188211	+	0.982129i	$0.439731\pi$
$522$	5.91420	+	5.91420i	0.258858	+	0.258858i
$523$	0.195667	+	0.195667i	0.00855593	+	0.00855593i	0.711372	−	0.702816i	$-0.248074\pi$
$523$	0.195667	+	0.195667i	0.00855593	+	0.00855593i	−0.702816	+	0.711372i	$0.748074\pi$
$524$	−11.3542			−0.496012
$525$	46.7858	−	12.3478i	2.04190	−	0.538901i
$526$	−2.01462			−0.0878414
$527$	1.28233	−	1.28233i	0.0558590	−	0.0558590i
$528$		0			0
$529$			21.8088i			0.948208i
$530$	6.43719	+	4.95869i	0.279614	+	0.215392i
$531$	37.4817			1.62657
$532$	−14.7751	−	14.7751i	−0.640583	−	0.640583i
$533$	24.5190	−	24.5190i	1.06204	−	1.06204i
$534$	−28.7427			−1.24382
$535$	1.49217	+	11.5013i	0.0645123	+	0.497245i
$536$			5.35482i			0.231293i
$537$	22.6577	+	22.6577i	0.977750	+	0.977750i
$538$	−3.90573	−	3.90573i	−0.168388	−	0.168388i
$539$		0			0
$540$	−2.31032	−	17.8074i	−0.0994204	−	0.766308i
$541$		−	32.6816i		−	1.40509i	−0.711639	−	0.702545i	$-0.752047\pi$
$541$		−	32.6816i		−	1.40509i	0.711639	−	0.702545i	$-0.247953\pi$
$542$	−5.48255	−	5.48255i	−0.235496	−	0.235496i
$543$	−45.6464	+	45.6464i	−1.95887	+	1.95887i
$544$		−	2.76588i		−	0.118586i
$545$	−24.6660	+	32.0204i	−1.05657	+	1.37160i
$546$			28.1339i			1.20402i
$547$	−15.1192	+	15.1192i	−0.646451	+	0.646451i	−0.952134	−	0.305682i	$-0.901115\pi$
$547$	−15.1192	+	15.1192i	−0.646451	+	0.646451i	0.305682	+	0.952134i	$0.401115\pi$
$548$	16.3039	−	16.3039i	0.696469	−	0.696469i
$549$	−16.4226			−0.700898
$550$		0			0
$551$	−9.73093			−0.414552
$552$	5.39611	−	5.39611i	0.229674	−	0.229674i
$553$	−15.7690	+	15.7690i	−0.670566	+	0.670566i
$554$			16.4389i			0.698423i
$555$	−19.5478	+	25.3762i	−0.829756	+	1.07716i
$556$		−	16.7718i		−	0.711282i
$557$	−31.2783	+	31.2783i	−1.32530	+	1.32530i	−0.415889	+	0.909415i	$0.636530\pi$
$557$	−31.2783	+	31.2783i	−1.32530	+	1.32530i	−0.909415	+	0.415889i	$0.863470\pi$
$558$	9.45979	+	9.45979i	0.400465	+	0.400465i
$559$			45.2076i			1.91208i
$560$	−1.20639	−	9.29854i	−0.0509792	−	0.392935i
$561$		0			0
$562$	13.1883	+	13.1883i	0.556314	+	0.556314i
$563$	−31.4299	−	31.4299i	−1.32461	−	1.32461i	−0.909996	−	0.414617i	$-0.863916\pi$
$563$	−31.4299	−	31.4299i	−1.32461	−	1.32461i	−0.414617	−	0.909996i	$-0.636084\pi$
$564$		−	16.6871i		−	0.702654i
$565$	3.05857	+	23.5747i	0.128675	+	0.991794i
$566$	10.4605			0.439689
$567$	−0.942218	+	0.942218i	−0.0395695	+	0.0395695i
$568$	19.0659	+	19.0659i	0.799988	+	0.799988i
$569$	−36.2705			−1.52054			−0.760269	−	0.649609i	$-0.774933\pi$
$569$	−36.2705			−1.52054			−0.760269	+	0.649609i	$0.774933\pi$
$570$	−14.4133	−	11.1029i	−0.603709	−	0.465049i
$571$			10.1812i			0.426071i	0.977044	+	0.213036i	$0.0683350\pi$
$571$			10.1812i			0.426071i	−0.977044	+	0.213036i	$0.931665\pi$
$572$		0			0
$573$	53.5657	−	53.5657i	2.23774	−	2.23774i
$574$	−20.7762			−0.867183
$575$	−4.71571	−	2.74632i	−0.196659	−	0.114530i
$576$	8.43267			0.351361
$577$	−3.43820	−	3.43820i	−0.143134	−	0.143134i	0.631909	−	0.775043i	$-0.282272\pi$
$577$	−3.43820	−	3.43820i	−0.143134	−	0.143134i	−0.775043	+	0.631909i	$0.782272\pi$
$578$	−8.44013	−	8.44013i	−0.351063	−	0.351063i
$579$	−32.5257			−1.35172
$580$	−6.33321	−	4.87859i	−0.262972	−	0.202573i
$581$	−37.3753			−1.55059
$582$	−0.199083	+	0.199083i	−0.00825226	+	0.00825226i
$583$		0			0
$584$			10.6436i			0.440434i
$585$	−5.77313	−	44.4979i	−0.238689	−	1.83976i
$586$	−4.77383			−0.197205
$587$	−11.4838	−	11.4838i	−0.473989	−	0.473989i	0.429214	−	0.903203i	$-0.358791\pi$
$587$	−11.4838	−	11.4838i	−0.473989	−	0.473989i	−0.903203	+	0.429214i	$0.858791\pi$
$588$	−14.3734	+	14.3734i	−0.592748	+	0.592748i
$589$	−15.5647			−0.641331
$590$	12.0411	−	1.56220i	0.495723	−	0.0643148i
$591$		−	49.0992i		−	2.01967i
$592$	4.38910	+	4.38910i	0.180391	+	0.180391i
$593$	−17.4863	−	17.4863i	−0.718078	−	0.718078i	0.250134	−	0.968211i	$-0.419525\pi$
$593$	−17.4863	−	17.4863i	−0.718078	−	0.718078i	−0.968211	+	0.250134i	$0.919525\pi$
$594$		0			0
$595$	2.88714	+	2.22402i	0.118361	+	0.0911759i
$596$		−	23.4304i		−	0.959747i
$597$	1.47097	+	1.47097i	0.0602027	+	0.0602027i
$598$	2.24359	−	2.24359i	0.0917472	−	0.0917472i
$599$			32.5486i			1.32990i	0.746887	+	0.664950i	$0.231547\pi$
$599$			32.5486i			1.32990i	−0.746887	+	0.664950i	$0.768453\pi$
$600$	−8.92123	−	33.8026i	−0.364208	−	1.37999i
$601$		−	14.4422i		−	0.589112i	−0.955634	−	0.294556i	$-0.904828\pi$
$601$		−	14.4422i		−	0.589112i	0.955634	−	0.294556i	$-0.0951717\pi$
$602$	19.1534	−	19.1534i	0.780633	−	0.780633i
$603$	−7.48090	+	7.48090i	−0.304646	+	0.304646i
$604$	35.2241			1.43325
$605$		0			0
$606$	−0.159555			−0.00648147
$607$	9.62524	−	9.62524i	0.390677	−	0.390677i	−0.484252	−	0.874929i	$-0.660908\pi$
$607$	9.62524	−	9.62524i	0.390677	−	0.390677i	0.874929	+	0.484252i	$0.160908\pi$
$608$	−16.7859	+	16.7859i	−0.680758	+	0.680758i
$609$			23.1628i			0.938603i
$610$	−5.27579	+	0.684477i	−0.213610	+	0.0277137i
$611$		−	16.2278i		−	0.656505i
$612$	2.45734	−	2.45734i	0.0993319	−	0.0993319i
$613$	−16.3254	−	16.3254i	−0.659376	−	0.659376i	0.295856	−	0.955232i	$-0.404395\pi$
$613$	−16.3254	−	16.3254i	−0.659376	−	0.659376i	−0.955232	+	0.295856i	$0.904395\pi$
$614$		−	12.2494i		−	0.494345i
$615$	52.9329	−	6.86748i	2.13446	−	0.276924i
$616$		0			0
$617$	−27.8255	−	27.8255i	−1.12021	−	1.12021i	−0.991709	−	0.128506i	$-0.958982\pi$
$617$	−27.8255	−	27.8255i	−1.12021	−	1.12021i	−0.128506	−	0.991709i	$-0.541018\pi$
$618$	7.48824	+	7.48824i	0.301221	+	0.301221i
$619$			12.9114i			0.518954i	0.965749	+	0.259477i	$0.0835502\pi$
$619$			12.9114i			0.518954i	−0.965749	+	0.259477i	$0.916450\pi$
$620$	−10.1300	−	7.80333i	−0.406830	−	0.313389i
$621$	5.86757			0.235457
$622$	7.89000	−	7.89000i	0.316360	−	0.316360i
$623$	−34.9416	−	34.9416i	−1.39990	−	1.39990i
$624$	−14.0061			−0.560693
$625$	−21.7441	+	12.3368i	−0.869763	+	0.493470i
$626$		−	8.79386i		−	0.351473i
$627$		0			0
$628$	9.33570	−	9.33570i	0.372535	−	0.372535i
$629$	−2.41257			−0.0961956
$630$	−16.4067	+	21.2986i	−0.653659	+	0.848556i
$631$	34.5944			1.37718			0.688591	−	0.725150i	$-0.258230\pi$
$631$	34.5944			1.37718			0.688591	+	0.725150i	$0.258230\pi$
$632$	11.3931	+	11.3931i	0.453191	+	0.453191i
$633$	2.49816	+	2.49816i	0.0992927	+	0.0992927i
$634$	5.18586			0.205957
$635$	0.904089	+	6.96849i	0.0358777	+	0.276536i
$636$	21.4579			0.850861
$637$	−13.9777	+	13.9777i	−0.553817	+	0.553817i
$638$		0			0
$639$			53.2717i			2.10740i
$640$	−23.1862	+	3.00817i	−0.916517	+	0.118908i
$641$	14.4243			0.569726			0.284863	−	0.958568i	$-0.408052\pi$
$641$	14.4243			0.569726			0.284863	+	0.958568i	$0.408052\pi$
$642$	−7.33979	−	7.33979i	−0.289678	−	0.289678i
$643$	5.41176	−	5.41176i	0.213419	−	0.213419i	−0.592299	−	0.805718i	$-0.701780\pi$
$643$	5.41176	−	5.41176i	0.213419	−	0.213419i	0.805718	+	0.592299i	$0.201780\pi$
$644$	5.60932			0.221038
$645$	−42.4672	+	55.1293i	−1.67214	+	2.17071i
$646$		−	1.37031i		−	0.0539142i
$647$	32.2634	+	32.2634i	1.26840	+	1.26840i	0.946912	+	0.321493i	$0.104185\pi$
$647$	32.2634	+	32.2634i	1.26840	+	1.26840i	0.321493	+	0.946912i	$0.395815\pi$
$648$	0.680750	+	0.680750i	0.0267424	+	0.0267424i
$649$		0			0
$650$	−3.70926	−	14.0544i	−0.145489	−	0.551259i
$651$			37.0489i			1.45206i
$652$	−17.2045	−	17.2045i	−0.673781	−	0.673781i
$653$	−21.2370	+	21.2370i	−0.831069	+	0.831069i	−0.987663	−	0.156594i	$-0.949949\pi$
$653$	−21.2370	+	21.2370i	−0.831069	+	0.831069i	0.156594	+	0.987663i	$0.449949\pi$
$654$		−	36.1755i		−	1.41457i
$655$	−13.4650	−	10.3723i	−0.526121	−	0.405281i
$656$		−	10.3432i		−	0.403833i
$657$	−14.8695	+	14.8695i	−0.580113	+	0.580113i
$658$	−6.87531	+	6.87531i	−0.268027	+	0.268027i
$659$	19.2722			0.750739			0.375370	−	0.926875i	$-0.377516\pi$
$659$	19.2722			0.750739			0.375370	+	0.926875i	$0.377516\pi$
$660$		0			0
$661$	−8.42240			−0.327593			−0.163797	−	0.986494i	$-0.552374\pi$
$661$	−8.42240			−0.327593			−0.163797	+	0.986494i	$0.552374\pi$
$662$	−13.7095	+	13.7095i	−0.532835	+	0.532835i
$663$	3.84939	−	3.84939i	0.149498	−	0.149498i
$664$			27.0035i			1.04794i
$665$	−4.02442	−	31.0192i	−0.156060	−	1.20287i
$666$		−	17.7977i		−	0.689647i
$667$	1.84716	−	1.84716i	0.0715221	−	0.0715221i
$668$	12.5217	+	12.5217i	0.484478	+	0.484478i
$669$		−	46.0891i		−	1.78191i
$670$	−2.09146	+	2.71505i	−0.0808000	+	0.104892i
$671$		0			0
$672$	39.9559	+	39.9559i	1.54133	+	1.54133i
$673$	27.0776	+	27.0776i	1.04376	+	1.04376i	0.998997	+	0.0447675i	$0.0142547\pi$
$673$	27.0776	+	27.0776i	1.04376	+	1.04376i	0.0447675	+	0.998997i	$0.485745\pi$
$674$			1.57842i			0.0607987i
$675$	13.5276	−	23.2283i	0.520679	−	0.894058i
$676$	−5.51766			−0.212218
$677$	−10.8668	+	10.8668i	−0.417645	+	0.417645i	−0.884391	−	0.466746i	$-0.845426\pi$
$677$	−10.8668	+	10.8668i	−0.417645	+	0.417645i	0.466746	+	0.884391i	$0.345426\pi$
$678$	−15.0446	−	15.0446i	−0.577786	−	0.577786i
$679$	−0.484037			−0.0185757
$680$	1.60685	−	2.08595i	0.0616198	−	0.0799925i
$681$		−	39.3208i		−	1.50678i
$682$		0			0
$683$	−13.3701	+	13.3701i	−0.511594	+	0.511594i	−0.915015	−	0.403421i	$-0.867821\pi$
$683$	−13.3701	+	13.3701i	−0.511594	+	0.511594i	0.403421	+	0.915015i	$0.367821\pi$
$684$	−29.8268			−1.14045
$685$	34.2288	−	4.44083i	1.30782	−	0.169675i
$686$	−5.29257			−0.202071
$687$	18.8676	+	18.8676i	0.719845	+	0.719845i
$688$	9.53526	+	9.53526i	0.363528	+	0.363528i
$689$	20.8672			0.794978
$690$	4.84357	−	0.628402i	0.184391	−	0.0239228i
$691$	48.3363			1.83880			0.919400	−	0.393323i	$-0.128675\pi$
$691$	48.3363			1.83880			0.919400	+	0.393323i	$0.128675\pi$
$692$	−13.5339	+	13.5339i	−0.514482	+	0.514482i
$693$		0			0
$694$		−	14.3289i		−	0.543919i
$695$	15.3214	−	19.8897i	0.581174	−	0.754458i
$696$	16.7350			0.634340
$697$	2.84268	+	2.84268i	0.107674	+	0.107674i
$698$	−3.35999	+	3.35999i	−0.127178	+	0.127178i
$699$	−1.56202			−0.0590811
$700$	12.9322	−	22.2060i	0.488793	−	0.839306i
$701$		−	4.96673i		−	0.187591i	−0.995591	−	0.0937954i	$-0.970100\pi$
$701$		−	4.96673i		−	0.187591i	0.995591	−	0.0937954i	$-0.0298999\pi$
$702$	11.0513	+	11.0513i	0.417105	+	0.417105i
$703$	14.6417	+	14.6417i	0.552223	+	0.552223i
$704$		0			0
$705$	15.2440	−	19.7892i	0.574124	−	0.745306i
$706$			8.01252i			0.301555i
$707$	−0.193965	−	0.193965i	−0.00729482	−	0.00729482i
$708$	22.6728	−	22.6728i	0.852094	−	0.852094i
$709$			33.9415i			1.27470i	0.770574	+	0.637350i	$0.219969\pi$
$709$			33.9415i			1.27470i	−0.770574	+	0.637350i	$0.780031\pi$
$710$	2.22031	+	17.1136i	0.0833269	+	0.642263i
$711$			31.8331i			1.19383i
$712$	−25.2452	+	25.2452i	−0.946104	+	0.946104i
$713$	2.95453	−	2.95453i	0.110648	−	0.110648i
$714$	−3.26178			−0.122069
$715$		0			0
$716$	17.0169			0.635951
$717$	19.9898	−	19.9898i	0.746534	−	0.746534i
$718$	0.249343	−	0.249343i	0.00930540	−	0.00930540i
$719$			0.999925i			0.0372909i	0.999826	+	0.0186454i	$0.00593537\pi$
$719$			0.999925i			0.0372909i	−0.999826	+	0.0186454i	$0.994065\pi$
$720$	−10.6032	−	8.16787i	−0.395159	−	0.304399i
$721$			18.2064i			0.678042i
$722$	1.24295	−	1.24295i	0.0462580	−	0.0462580i
$723$	47.8287	+	47.8287i	1.77877	+	1.77877i
$724$			34.2824i			1.27410i
$725$	−3.05385	−	11.5711i	−0.113417	−	0.429738i
$726$		0			0
$727$	8.31564	+	8.31564i	0.308410	+	0.308410i	0.844293	−	0.535883i	$-0.180021\pi$
$727$	8.31564	+	8.31564i	0.308410	+	0.308410i	−0.535883	+	0.844293i	$0.680021\pi$
$728$	24.7105	+	24.7105i	0.915831	+	0.915831i
$729$		−	43.4619i		−	1.60970i
$730$	−4.15710	+	5.39659i	−0.153861	+	0.199737i
$731$	−5.24128			−0.193856
$732$	−9.93405	+	9.93405i	−0.367173	+	0.367173i
$733$	−9.48027	−	9.48027i	−0.350162	−	0.350162i	0.510008	−	0.860170i	$-0.329642\pi$
$733$	−9.48027	−	9.48027i	−0.350162	−	0.350162i	−0.860170	+	0.510008i	$0.829642\pi$
$734$	9.02623			0.333164
$735$	−30.1758	+	3.91499i	−1.11305	+	0.144407i
$736$		−	6.37270i		−	0.234901i
$737$		0			0
$738$	−20.9706	+	20.9706i	−0.771940	+	0.771940i
$739$	27.9159			1.02690			0.513452	−	0.858118i	$-0.328366\pi$
$739$	27.9159			1.02690			0.513452	+	0.858118i	$0.328366\pi$
$740$	2.18869	+	16.8699i	0.0804580	+	0.620151i
$741$	−46.7233			−1.71642
$742$	−8.84094	−	8.84094i	−0.324561	−	0.324561i
$743$	6.73618	+	6.73618i	0.247126	+	0.247126i	0.819790	−	0.572664i	$-0.194090\pi$
$743$	6.73618	+	6.73618i	0.247126	+	0.247126i	−0.572664	+	0.819790i	$0.694090\pi$
$744$	26.7677			0.981353
$745$	21.4042	−	27.7861i	0.784189	−	1.01800i
$746$	9.21830			0.337506
$747$	−37.7250	+	37.7250i	−1.38029	+	1.38029i
$748$		0			0
$749$		−	17.8455i		−	0.652059i
$750$	8.67912	−	20.6233i	0.316917	−	0.753057i
$751$	−5.23693			−0.191098			−0.0955492	−	0.995425i	$-0.530461\pi$
$751$	−5.23693			−0.191098			−0.0955492	+	0.995425i	$0.530461\pi$
$752$	−3.42278	−	3.42278i	−0.124816	−	0.124816i
$753$	3.50954	−	3.50954i	0.127895	−	0.127895i
$754$	6.95807			0.253398
$755$	41.7722	+	32.1780i	1.52025	+	1.17108i
$756$			27.6300i			1.00489i
$757$	−17.5005	−	17.5005i	−0.636068	−	0.636068i	0.313515	−	0.949583i	$-0.398493\pi$
$757$	−17.5005	−	17.5005i	−0.636068	−	0.636068i	−0.949583	+	0.313515i	$0.898493\pi$
$758$	−3.53650	−	3.53650i	−0.128451	−	0.128451i
$759$		0			0
$760$	−22.4113	+	2.90763i	−0.812943	+	0.105471i
$761$			12.9003i			0.467636i	0.972280	+	0.233818i	$0.0751220\pi$
$761$			12.9003i			0.467636i	−0.972280	+	0.233818i	$0.924878\pi$
$762$	−4.44708	−	4.44708i	−0.161101	−	0.161101i
$763$	43.9774	−	43.9774i	1.59209	−	1.59209i
$764$		−	40.2302i		−	1.45548i
$765$	5.15898	−	0.669324i	0.186523	−	0.0241995i
$766$		−	12.1673i		−	0.439622i
$767$	22.0486	−	22.0486i	0.796131	−	0.796131i
$768$	21.6265	−	21.6265i	0.780379	−	0.780379i
$769$	12.6310			0.455485			0.227743	−	0.973721i	$-0.426866\pi$
$769$	12.6310			0.455485			0.227743	+	0.973721i	$0.426866\pi$
$770$		0			0
$771$	−78.9043			−2.84167
$772$	−12.2141	+	12.2141i	−0.439595	+	0.439595i
$773$	13.0923	−	13.0923i	0.470896	−	0.470896i	−0.431308	−	0.902205i	$-0.641948\pi$
$773$	13.0923	−	13.0923i	0.470896	−	0.470896i	0.902205	+	0.431308i	$0.141948\pi$
$774$		−	38.6652i		−	1.38979i
$775$	−4.88464	−	18.5079i	−0.175461	−	0.664825i
$776$			0.349716i			0.0125541i
$777$	34.8520	−	34.8520i	1.25031	−	1.25031i
$778$	7.70397	+	7.70397i	0.276201	+	0.276201i
$779$		−	34.5041i		−	1.23624i
$780$	−30.4090	−	23.4247i	−1.08882	−	0.838738i
$781$		0			0
$782$	0.260117	+	0.260117i	0.00930176	+	0.00930176i
$783$	9.09859	+	9.09859i	0.325157	+	0.325157i
$784$			5.89640i			0.210586i
$785$	19.5996	−	2.54284i	0.699539	−	0.0907578i
$786$	15.2123			0.542603
$787$	33.4827	−	33.4827i	1.19353	−	1.19353i	0.217462	−	0.976069i	$-0.430222\pi$
$787$	33.4827	−	33.4827i	1.19353	−	1.19353i	0.976069	−	0.217462i	$-0.0697777\pi$
$788$	−18.4378	−	18.4378i	−0.656821	−	0.656821i
$789$	−7.96400			−0.283526
$790$	1.32677	+	10.2264i	0.0472045	+	0.363841i
$791$		−	36.5785i		−	1.30058i
$792$		0			0
$793$	−9.66060	+	9.66060i	−0.343058	+	0.343058i
$794$	−10.9460			−0.388460
$795$	25.4469	+	19.6023i	0.902509	+	0.695221i
$796$	1.10476			0.0391572
$797$	−22.0234	−	22.0234i	−0.780107	−	0.780107i	0.199741	−	0.979849i	$-0.435990\pi$
$797$	−22.0234	−	22.0234i	−0.780107	−	0.780107i	−0.979849	+	0.199741i	$0.935990\pi$
$798$	19.7955	+	19.7955i	0.700754	+	0.700754i
$799$	1.88141			0.0665596
$800$	−25.2280	−	14.6922i	−0.891945	−	0.519448i
$801$	−70.5371			−2.49230
$802$	−7.28660	+	7.28660i	−0.257299	+	0.257299i
$803$		0			0
$804$			9.05042i			0.319184i
$805$	6.65209	+	5.12424i	0.234455	+	0.180606i
$806$	11.1295			0.392019
$807$	−15.4398	−	15.4398i	−0.543507	−	0.543507i
$808$	−0.140140	+	0.140140i	−0.00493009	+	0.00493009i
$809$	44.2757			1.55665			0.778326	−	0.627861i	$-0.216069\pi$
$809$	44.2757			1.55665			0.778326	+	0.627861i	$0.216069\pi$
$810$	0.0792765	+	0.611044i	0.00278549	+	0.0214699i
$811$		−	2.49904i		−	0.0877532i	−0.999037	−	0.0438766i	$-0.986029\pi$
$811$		−	2.49904i		−	0.0877532i	0.999037	−	0.0438766i	$-0.0139708\pi$
$812$	8.69813	+	8.69813i	0.305244	+	0.305244i
$813$	−21.6731	−	21.6731i	−0.760110	−	0.760110i
$814$		0			0
$815$	−4.68613	−	36.1196i	−0.164148	−	1.26521i
$816$		−	1.62384i		−	0.0568457i
$817$	31.8089	+	31.8089i	1.11285	+	1.11285i
$818$	5.51689	−	5.51689i	0.192893	−	0.192893i
$819$			69.0430i			2.41256i
$820$	17.2986	−	22.4564i	0.604092	−	0.784210i
$821$		−	37.6724i		−	1.31478i	−0.753552	−	0.657388i	$-0.771661\pi$
$821$		−	37.6724i		−	1.31478i	0.753552	−	0.657388i	$-0.228339\pi$
$822$	−21.8438	+	21.8438i	−0.761889	+	0.761889i
$823$	6.31750	−	6.31750i	0.220214	−	0.220214i	−0.588374	−	0.808589i	$-0.700232\pi$
$823$	6.31750	−	6.31750i	0.220214	−	0.220214i	0.808589	+	0.588374i	$0.200232\pi$
$824$	13.1541			0.458244
$825$		0			0
$826$	−18.6829			−0.650063
$827$	20.8891	−	20.8891i	0.726387	−	0.726387i	−0.243511	−	0.969898i	$-0.578299\pi$
$827$	20.8891	−	20.8891i	0.726387	−	0.726387i	0.969898	+	0.243511i	$0.0782994\pi$
$828$	5.66180	−	5.66180i	0.196761	−	0.196761i
$829$		−	15.4972i		−	0.538240i	−0.963107	−	0.269120i	$-0.913267\pi$
$829$		−	15.4972i		−	0.538240i	0.963107	−	0.269120i	$-0.0867328\pi$
$830$	−10.5469	+	13.6916i	−0.366088	+	0.475241i
$831$			64.9849i			2.25430i
$832$	4.96053	−	4.96053i	0.171975	−	0.171975i
$833$	−1.62055	−	1.62055i	−0.0561486	−	0.0561486i
$834$			22.4706i			0.778094i
$835$	3.41062	+	26.2883i	0.118030	+	0.909743i
$836$		0			0
$837$	14.5532	+	14.5532i	0.503033	+	0.503033i
$838$	−3.44955	−	3.44955i	−0.119163	−	0.119163i
$839$		−	35.8907i		−	1.23908i	−0.784963	−	0.619542i	$-0.787318\pi$
$839$		−	35.8907i		−	1.23908i	0.784963	−	0.619542i	$-0.212682\pi$
$840$	6.92110	+	53.3461i	0.238801	+	1.84062i
$841$	−23.2714			−0.802462
$842$	−9.95345	+	9.95345i	−0.343018	+	0.343018i
$843$	52.1348	+	52.1348i	1.79562	+	1.79562i
$844$	1.87622			0.0645823
$845$	−6.54340	−	5.04051i	−0.225100	−	0.173399i
$846$			13.8793i			0.477180i
$847$		0			0
$848$	4.40134	−	4.40134i	0.151143	−	0.151143i
$849$	41.3517			1.41919
$850$	1.62944	−	0.430043i	0.0558892	−	0.0147504i
$851$	−5.55867			−0.190549
$852$	32.2242	+	32.2242i	1.10398	+	1.10398i
$853$	−6.84669	−	6.84669i	−0.234426	−	0.234426i	0.580111	−	0.814537i	$-0.303009\pi$
$853$	−6.84669	−	6.84669i	−0.234426	−	0.234426i	−0.814537	+	0.580111i	$0.803009\pi$
$854$	8.18592			0.280116
$855$	−35.3715	−	27.2474i	−1.20968	−	0.931841i
$856$	−12.8933			−0.440684
$857$	27.8084	−	27.8084i	0.949918	−	0.949918i	−0.0488861	−	0.998804i	$-0.515567\pi$
$857$	27.8084	−	27.8084i	0.949918	−	0.949918i	0.998804	+	0.0488861i	$0.0155671\pi$
$858$		0			0
$859$			27.0190i			0.921878i	0.887432	+	0.460939i	$0.152487\pi$
$859$			27.0190i			0.921878i	−0.887432	+	0.460939i	$0.847513\pi$
$860$	4.75490	+	36.6496i	0.162141	+	1.24974i
$861$	−82.1308			−2.79901
$862$	−1.07037	−	1.07037i	−0.0364570	−	0.0364570i
$863$	21.6891	−	21.6891i	0.738305	−	0.738305i	−0.233945	−	0.972250i	$-0.575164\pi$
$863$	21.6891	−	21.6891i	0.738305	−	0.738305i	0.972250	+	0.233945i	$0.0751636\pi$
$864$	31.3902			1.06792
$865$	−28.4134	+	3.68633i	−0.966083	+	0.125339i
$866$		−	12.0940i		−	0.410972i
$867$	−33.3648	−	33.3648i	−1.13313	−	1.13313i
$868$	13.9127	+	13.9127i	0.472227	+	0.472227i
$869$		0			0
$870$	8.48515	+	6.53628i	0.287674	+	0.221601i
$871$			8.80129i			0.298220i
$872$	−31.7735	−	31.7735i	−1.07599	−	1.07599i
$873$	−0.488567	+	0.488567i	−0.0165355	+	0.0165355i
$874$		−	3.15726i		−	0.106796i
$875$	35.6220	−	14.5202i	1.20424	−	0.490871i
$876$			17.9892i			0.607797i
$877$	−20.3642	+	20.3642i	−0.687652	+	0.687652i	−0.961712	−	0.274061i	$-0.911633\pi$
$877$	−20.3642	+	20.3642i	−0.687652	+	0.687652i	0.274061	+	0.961712i	$0.411633\pi$
$878$	21.0513	−	21.0513i	0.710448	−	0.710448i
$879$	−18.8715			−0.636520
$880$		0			0
$881$	27.4428			0.924572			0.462286	−	0.886731i	$-0.347029\pi$
$881$	27.4428			0.924572			0.462286	+	0.886731i	$0.347029\pi$
$882$	11.9549	−	11.9549i	0.402541	−	0.402541i
$883$	27.4325	−	27.4325i	0.923177	−	0.923177i	−0.0740760	−	0.997253i	$-0.523601\pi$
$883$	27.4325	−	27.4325i	0.923177	−	0.923177i	0.997253	+	0.0740760i	$0.0236007\pi$
$884$		−	2.89106i		−	0.0972369i
$885$	47.5997	−	6.17556i	1.60005	−	0.207589i
$886$			17.3475i			0.582800i
$887$	7.19261	−	7.19261i	0.241504	−	0.241504i	−0.575968	−	0.817472i	$-0.695375\pi$
$887$	7.19261	−	7.19261i	0.241504	−	0.241504i	0.817472	+	0.575968i	$0.195375\pi$
$888$	−25.1805	−	25.1805i	−0.845002	−	0.845002i
$889$		−	10.8123i		−	0.362634i
$890$	−22.6602	+	2.93992i	−0.759571	+	0.0985463i
$891$		0			0
$892$	−17.3075	−	17.3075i	−0.579497	−	0.579497i
$893$	−11.4181	−	11.4181i	−0.382094	−	0.382094i
$894$			31.3918i			1.04990i
$895$	20.1803	+	15.5453i	0.674554	+	0.519623i
$896$	35.9758			1.20187
$897$	8.86916	−	8.86916i	0.296133	−	0.296133i
$898$	0.859607	+	0.859607i	0.0286855	+	0.0286855i
$899$	9.16293			0.305601
$900$	−9.36049	−	35.4670i	−0.312016	−	1.18223i
$901$			2.41930i			0.0805986i
$902$		0			0
$903$	75.7154	−	75.7154i	2.51965	−	2.51965i
$904$	−26.4279			−0.878978
$905$	−31.3178	+	40.6555i	−1.04104	+	1.35144i
$906$	−47.1927			−1.56787
$907$	−16.4544	−	16.4544i	−0.546358	−	0.546358i	0.379027	−	0.925386i	$-0.376259\pi$
$907$	−16.4544	−	16.4544i	−0.546358	−	0.546358i	−0.925386	+	0.379027i	$0.876259\pi$
$908$	−14.7658	−	14.7658i	−0.490021	−	0.490021i
$909$	−0.391561			−0.0129873
$910$	2.87765	+	22.1802i	0.0953930	+	0.735266i
$911$	−16.5084			−0.546949			−0.273475	−	0.961879i	$-0.588173\pi$
$911$	−16.5084			−0.546949			−0.273475	+	0.961879i	$0.588173\pi$
$912$	−9.85494	+	9.85494i	−0.326330	+	0.326330i
$913$		0			0
$914$		−	1.39217i		−	0.0460488i
$915$	−20.8558	+	2.70582i	−0.689470	+	0.0894515i
$916$	14.1704			0.468204
$917$	18.4930	+	18.4930i	0.610694	+	0.610694i
$918$	−1.28126	+	1.28126i	−0.0422880	+	0.0422880i
$919$	−23.1496			−0.763635			−0.381817	−	0.924238i	$-0.624702\pi$
$919$	−23.1496			−0.763635			−0.381817	+	0.924238i	$0.624702\pi$
$920$	3.70225	−	4.80612i	0.122059	−	0.158453i
$921$		−	48.4232i		−	1.59560i
$922$	−11.3060	−	11.3060i	−0.372342	−	0.372342i
$923$	31.3371	+	31.3371i	1.03147	+	1.03147i
$924$		0			0
$925$	−12.8155	+	22.0055i	−0.421370	+	0.723535i
$926$		−	4.96351i		−	0.163111i
$927$	18.3768	+	18.3768i	0.603572	+	0.603572i
$928$	9.88188	−	9.88188i	0.324388	−	0.324388i
$929$			16.8820i			0.553881i	0.960887	+	0.276941i	$0.0893205\pi$
$929$			16.8820i			0.553881i	−0.960887	+	0.276941i	$0.910679\pi$
$930$	13.5720	+	10.4548i	0.445044	+	0.342826i
$931$			19.6699i			0.644656i
$932$	−0.586574	+	0.586574i	−0.0192139	+	0.0192139i
$933$	31.1900	−	31.1900i	1.02112	−	1.02112i
$934$	14.7827			0.483705
$935$		0			0
$936$	49.8834			1.63049
$937$	−38.0770	+	38.0770i	−1.24392	+	1.24392i	−0.285559	+	0.958361i	$0.592179\pi$
$937$	−38.0770	+	38.0770i	−1.24392	+	1.24392i	−0.958361	+	0.285559i	$0.907821\pi$
$938$	3.72889	−	3.72889i	0.121753	−	0.121753i
$939$		−	34.7631i		−	1.13445i
$940$	−1.70682	−	13.1558i	−0.0556704	−	0.429094i
$941$		−	48.0751i		−	1.56720i	−0.621263	−	0.783602i	$-0.713380\pi$
$941$		−	48.0751i		−	1.56720i	0.621263	−	0.783602i	$-0.286620\pi$
$942$	−12.5078	+	12.5078i	−0.407528	+	0.407528i
$943$	6.54966	+	6.54966i	0.213286	+	0.213286i
$944$		−	9.30106i		−	0.302724i
$945$	−25.2406	+	32.7664i	−0.821077	+	1.06589i
$946$		0			0
$947$	−7.71234	−	7.71234i	−0.250617	−	0.250617i	0.570606	−	0.821224i	$-0.306708\pi$
$947$	−7.71234	−	7.71234i	−0.250617	−	0.250617i	−0.821224	+	0.570606i	$0.806708\pi$
$948$	19.2559	+	19.2559i	0.625403	+	0.625403i
$949$			17.4940i			0.567878i
$950$	−12.4988	−	7.27903i	−0.405516	−	0.236163i
$951$	20.5003			0.664767
$952$	−2.86488	+	2.86488i	−0.0928512	+	0.0928512i
$953$	−0.457301	−	0.457301i	−0.0148134	−	0.0148134i	0.699661	−	0.714475i	$-0.253334\pi$
$953$	−0.457301	−	0.457301i	−0.0148134	−	0.0148134i	−0.714475	+	0.699661i	$0.753334\pi$
$954$	−17.8473			−0.577828
$955$	36.7512	−	47.7090i	1.18924	−	1.54383i
$956$		−	15.0132i		−	0.485563i
$957$		0			0
$958$	10.1920	−	10.1920i	0.329288	−	0.329288i
$959$	−53.1095			−1.71499
$960$	10.7090	−	1.38938i	0.345632	−	0.0448422i
$961$	−16.3439			−0.527221
$962$	−10.4695	−	10.4695i	−0.337551	−	0.337551i
$963$	−18.0124	−	18.0124i	−0.580443	−	0.580443i
$964$	35.9214			1.15695
$965$	−25.6425	+	3.32685i	−0.825463	+	0.107095i
$966$	−7.51529			−0.241800
$967$	3.28535	−	3.28535i	0.105650	−	0.105650i	−0.652306	−	0.757956i	$-0.726198\pi$
$967$	3.28535	−	3.28535i	0.105650	−	0.105650i	0.757956	+	0.652306i	$0.226198\pi$
$968$		0			0
$969$		−	5.41700i		−	0.174019i
$970$	−0.136590	+	0.177316i	−0.00438564	+	0.00569328i
$971$	−46.0962			−1.47930			−0.739649	−	0.672992i	$-0.765009\pi$
$971$	−46.0962			−1.47930			−0.739649	+	0.672992i	$0.765009\pi$
$972$	−15.8846	−	15.8846i	−0.509499	−	0.509499i
$973$	−27.3168	+	27.3168i	−0.875736	+	0.875736i
$974$	14.5825			0.467254
$975$	−14.6631	−	55.5587i	−0.469595	−	1.77930i
$976$			4.07525i			0.130446i
$977$	37.9919	+	37.9919i	1.21547	+	1.21547i	0.969203	+	0.246265i	$0.0792033\pi$
$977$	37.9919	+	37.9919i	1.21547	+	1.21547i	0.246265	+	0.969203i	$0.420797\pi$
$978$	23.0504	+	23.0504i	0.737070	+	0.737070i
$979$		0			0
$980$	−9.86150	+	12.8018i	−0.315014	+	0.408939i
$981$		−	88.7777i		−	2.83445i
$982$	6.15206	+	6.15206i	0.196320	+	0.196320i
$983$	−11.0350	+	11.0350i	−0.351961	+	0.351961i	−0.860839	−	0.508878i	$-0.830061\pi$
$983$	−11.0350	+	11.0350i	−0.351961	+	0.351961i	0.508878	+	0.860839i	$0.330061\pi$
$984$			59.3393i			1.89167i
$985$	−5.02206	−	38.7088i	−0.160016	−	1.23337i
$986$			0.806704i			0.0256907i
$987$	−27.1789	+	27.1789i	−0.865113	+	0.865113i
$988$	−17.5456	+	17.5456i	−0.558201	+	0.558201i
$989$	−12.0761			−0.383998
$990$		0			0
$991$	7.83738			0.248962			0.124481	−	0.992222i	$-0.460273\pi$
$991$	7.83738			0.248962			0.124481	+	0.992222i	$0.460273\pi$
$992$	15.8061	−	15.8061i	0.501844	−	0.501844i
$993$	−54.1952	+	54.1952i	−1.71983	+	1.71983i
$994$		−	26.5536i		−	0.842228i
$995$	1.31014	+	1.00922i	0.0415341	+	0.0319946i
$996$			45.6399i			1.44615i
$997$	18.1683	−	18.1683i	0.575394	−	0.575394i	−0.358236	−	0.933631i	$-0.616622\pi$
$997$	18.1683	−	18.1683i	0.575394	−	0.575394i	0.933631	+	0.358236i	$0.116622\pi$
$998$	8.77303	+	8.77303i	0.277705	+	0.277705i
$999$		−	27.3805i		−	0.866281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.c.362.8	✓	40
5.3	odd	4	inner	605.2.e.c.483.13	yes	40
11.2	odd	10		605.2.m.g.282.8		160
11.3	even	5		605.2.m.g.112.13		160
11.4	even	5		605.2.m.g.457.8		160
11.5	even	5		605.2.m.g.602.13		160
11.6	odd	10		605.2.m.g.602.8		160
11.7	odd	10		605.2.m.g.457.13		160
11.8	odd	10		605.2.m.g.112.8		160
11.9	even	5		605.2.m.g.282.13		160
11.10	odd	2	inner	605.2.e.c.362.13	yes	40
55.3	odd	20		605.2.m.g.233.13		160
55.8	even	20		605.2.m.g.233.8		160
55.13	even	20		605.2.m.g.403.13		160
55.18	even	20		605.2.m.g.578.13		160
55.28	even	20		605.2.m.g.118.13		160
55.38	odd	20		605.2.m.g.118.8		160
55.43	even	4	inner	605.2.e.c.483.8	yes	40
55.48	odd	20		605.2.m.g.578.8		160
55.53	odd	20		605.2.m.g.403.8		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.8	✓	40	1.1	even	1	trivial
605.2.e.c.362.13	yes	40	11.10	odd	2	inner
605.2.e.c.483.8	yes	40	55.43	even	4	inner
605.2.e.c.483.13	yes	40	5.3	odd	4	inner
605.2.m.g.112.8		160	11.8	odd	10
605.2.m.g.112.13		160	11.3	even	5
605.2.m.g.118.8		160	55.38	odd	20
605.2.m.g.118.13		160	55.28	even	20
605.2.m.g.233.8		160	55.8	even	20
605.2.m.g.233.13		160	55.3	odd	20
605.2.m.g.282.8		160	11.2	odd	10
605.2.m.g.282.13		160	11.9	even	5
605.2.m.g.403.8		160	55.53	odd	20
605.2.m.g.403.13		160	55.13	even	20
605.2.m.g.457.8		160	11.4	even	5
605.2.m.g.457.13		160	11.7	odd	10
605.2.m.g.578.8		160	55.48	odd	20
605.2.m.g.578.13		160	55.18	even	20
605.2.m.g.602.8		160	11.6	odd	10
605.2.m.g.602.13		160	11.5	even	5

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)

\(f(q)\)	\(=\)	\(q+(-0.503119 + 0.503119i) q^{2} +(-1.98889 + 1.98889i) q^{3} +1.49374i q^{4} +(-1.36457 + 1.77143i) q^{5} -2.00130i q^{6} +(2.43291 - 2.43291i) q^{7} +(-1.75777 - 1.75777i) q^{8} -4.91135i q^{9} +O(q^{10})\)	\(q+(-0.503119 + 0.503119i) q^{2} +(-1.98889 + 1.98889i) q^{3} +1.49374i q^{4} +(-1.36457 + 1.77143i) q^{5} -2.00130i q^{6} +(2.43291 - 2.43291i) q^{7} +(-1.75777 - 1.75777i) q^{8} -4.91135i q^{9} +(-0.204700 - 1.57778i) q^{10} +(-2.97088 - 2.97088i) q^{12} +(-2.88910 - 2.88910i) q^{13} +2.44809i q^{14} +(-0.809203 - 6.23714i) q^{15} -1.21875 q^{16} +(0.334956 - 0.334956i) q^{17} +(2.47099 + 2.47099i) q^{18} -4.06565 q^{19} +(-2.64606 - 2.03831i) q^{20} +9.67756i q^{21} +(0.771754 - 0.771754i) q^{23} +6.99201 q^{24} +(-1.27592 - 4.83446i) q^{25} +2.90713 q^{26} +(3.80145 + 3.80145i) q^{27} +(3.63414 + 3.63414i) q^{28} +2.39345 q^{29} +(3.54515 + 2.73090i) q^{30} +3.82833 q^{31} +(4.12871 - 4.12871i) q^{32} +0.337046i q^{34} +(0.989858 + 7.62959i) q^{35} +7.33628 q^{36} +(-3.60132 - 3.60132i) q^{37} +(2.04551 - 2.04551i) q^{38} +11.4922 q^{39} +(5.51236 - 0.715170i) q^{40} +8.48673i q^{41} +(-4.86897 - 4.86897i) q^{42} +(-7.82382 - 7.82382i) q^{43} +(8.70010 + 6.70186i) q^{45} +0.776569i q^{46} +(2.80844 + 2.80844i) q^{47} +(2.42395 - 2.42395i) q^{48} -4.83808i q^{49} +(3.07425 + 1.79037i) q^{50} +1.33238i q^{51} +(4.31558 - 4.31558i) q^{52} +(-3.61137 + 3.61137i) q^{53} -3.82517 q^{54} -8.55298 q^{56} +(8.08612 - 8.08612i) q^{57} +(-1.20419 + 1.20419i) q^{58} +7.63165i q^{59} +(9.31668 - 1.20874i) q^{60} -3.34380i q^{61} +(-1.92611 + 1.92611i) q^{62} +(-11.9489 - 11.9489i) q^{63} +1.71698i q^{64} +(9.06022 - 1.17547i) q^{65} +(-1.52319 - 1.52319i) q^{67} +(0.500338 + 0.500338i) q^{68} +3.06986i q^{69} +(-4.33661 - 3.34058i) q^{70} -10.8467 q^{71} +(-8.63301 + 8.63301i) q^{72} +(-3.02758 - 3.02758i) q^{73} +3.62379 q^{74} +(12.1529 + 7.07755i) q^{75} -6.07303i q^{76} +(-5.78195 + 5.78195i) q^{78} -6.48154 q^{79} +(1.66306 - 2.15892i) q^{80} -0.387281 q^{81} +(-4.26984 - 4.26984i) q^{82} +(-7.68119 - 7.68119i) q^{83} -14.4558 q^{84} +(0.136281 + 1.05042i) q^{85} +7.87263 q^{86} +(-4.76031 + 4.76031i) q^{87} -14.3621i q^{89} +(-7.74902 + 1.00535i) q^{90} -14.0579 q^{91} +(1.15280 + 1.15280i) q^{92} +(-7.61412 + 7.61412i) q^{93} -2.82596 q^{94} +(5.54785 - 7.20201i) q^{95} +16.4231i q^{96} +(-0.0994772 - 0.0994772i) q^{97} +(2.43413 + 2.43413i) 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

Introduction

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