LMFDB - Embedded newform 605.2.e.b.362.15

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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.15
Character	$\chi$	$=$	605.362
Dual form			605.2.e.b.483.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72010 - 1.72010i) q^{2} +(0.422864 - 0.422864i) q^{3} -3.91750i q^{4} +(-0.759172 - 2.10325i) q^{5} -1.45474i q^{6} +(1.82555 - 1.82555i) q^{7} +(-3.29830 - 3.29830i) q^{8} +2.64237i q^{9} +O(q^{10})$	\(q+(1.72010 - 1.72010i) q^{2} +(0.422864 - 0.422864i) q^{3} -3.91750i q^{4} +(-0.759172 - 2.10325i) q^{5} -1.45474i q^{6} +(1.82555 - 1.82555i) q^{7} +(-3.29830 - 3.29830i) q^{8} +2.64237i q^{9} +(-4.92366 - 2.31195i) q^{10} +(-1.65657 - 1.65657i) q^{12} +(1.98612 + 1.98612i) q^{13} -6.28027i q^{14} +(-1.21041 - 0.568362i) q^{15} -3.51181 q^{16} +(-0.667728 + 0.667728i) q^{17} +(4.54515 + 4.54515i) q^{18} -4.14980 q^{19} +(-8.23948 + 2.97406i) q^{20} -1.54392i q^{21} +(0.104710 - 0.104710i) q^{23} -2.78946 q^{24} +(-3.84732 + 3.19345i) q^{25} +6.83265 q^{26} +(2.38596 + 2.38596i) q^{27} +(-7.15160 - 7.15160i) q^{28} -6.94005 q^{29} +(-3.05968 + 1.10440i) q^{30} +9.06250 q^{31} +(0.555921 - 0.555921i) q^{32} +2.29712i q^{34} +(-5.22550 - 2.45368i) q^{35} +10.3515 q^{36} +(5.37272 + 5.37272i) q^{37} +(-7.13807 + 7.13807i) q^{38} +1.67972 q^{39} +(-4.43317 + 9.44111i) q^{40} +3.44754i q^{41} +(-2.65570 - 2.65570i) q^{42} +(-3.91833 - 3.91833i) q^{43} +(5.55757 - 2.00601i) q^{45} -0.360222i q^{46} +(-0.747616 - 0.747616i) q^{47} +(-1.48502 + 1.48502i) q^{48} +0.334721i q^{49} +(-1.12471 + 12.1108i) q^{50} +0.564716i q^{51} +(7.78062 - 7.78062i) q^{52} +(2.91513 - 2.91513i) q^{53} +8.20817 q^{54} -12.0424 q^{56} +(-1.75480 + 1.75480i) q^{57} +(-11.9376 + 11.9376i) q^{58} -6.48185i q^{59} +(-2.22656 + 4.74180i) q^{60} -9.52525i q^{61} +(15.5884 - 15.5884i) q^{62} +(4.82379 + 4.82379i) q^{63} -8.93610i q^{64} +(2.66950 - 5.68511i) q^{65} +(2.94509 + 2.94509i) q^{67} +(2.61582 + 2.61582i) q^{68} -0.0885557i q^{69} +(-13.2090 + 4.76780i) q^{70} +1.26606 q^{71} +(8.71533 - 8.71533i) q^{72} +(-1.25255 - 1.25255i) q^{73} +18.4832 q^{74} +(-0.276494 + 2.97729i) q^{75} +16.2568i q^{76} +(2.88928 - 2.88928i) q^{78} -4.34195 q^{79} +(2.66607 + 7.38621i) q^{80} -5.90925 q^{81} +(5.93012 + 5.93012i) q^{82} +(5.86295 + 5.86295i) q^{83} -6.04831 q^{84} +(1.91132 + 0.897478i) q^{85} -13.4799 q^{86} +(-2.93470 + 2.93470i) q^{87} +4.23092i q^{89} +(6.10903 - 13.0101i) q^{90} +7.25153 q^{91} +(-0.410200 - 0.410200i) q^{92} +(3.83220 - 3.83220i) q^{93} -2.57195 q^{94} +(3.15041 + 8.72806i) q^{95} -0.470158i q^{96} +(10.1990 + 10.1990i) q^{97} +(0.575755 + 0.575755i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) $ 32 * q - 4 * q^3 + 8 * q^5	$ 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * 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 $

$2$	1.72010	−	1.72010i	1.21630	−	1.21630i	0.247376	−	0.968920i	$-0.420432\pi$
$2$	1.72010	−	1.72010i	1.21630	−	1.21630i	0.968920	−	0.247376i	$-0.0795683\pi$
$3$	0.422864	−	0.422864i	0.244141	−	0.244141i	−0.574420	−	0.818561i	$-0.694772\pi$
$3$	0.422864	−	0.422864i	0.244141	−	0.244141i	0.818561	+	0.574420i	$0.194772\pi$
$4$		−	3.91750i		−	1.95875i
$5$	−0.759172	−	2.10325i	−0.339512	−	0.940602i
$5$	−0.759172	−	2.10325i	−0.339512	−	0.940602i
$6$		−	1.45474i		−	0.593894i
$7$	1.82555	−	1.82555i	0.689994	−	0.689994i	−0.272237	−	0.962230i	$-0.587763\pi$
$7$	1.82555	−	1.82555i	0.689994	−	0.689994i	0.962230	+	0.272237i	$0.0877633\pi$
$8$	−3.29830	−	3.29830i	−1.16612	−	1.16612i
$9$			2.64237i			0.880791i
$10$	−4.92366	−	2.31195i	−1.55700	−	0.731103i
$11$		0			0
$11$		0			0
$12$	−1.65657	−	1.65657i	−0.478210	−	0.478210i
$13$	1.98612	+	1.98612i	0.550850	+	0.550850i	0.926686	−	0.375836i	$-0.122644\pi$
$13$	1.98612	+	1.98612i	0.550850	+	0.550850i	−0.375836	+	0.926686i	$0.622644\pi$
$14$		−	6.28027i		−	1.67847i
$15$	−1.21041	−	0.568362i	−0.312528	−	0.146750i
$16$	−3.51181			−0.877953
$17$	−0.667728	+	0.667728i	−0.161948	+	0.161948i	−0.783429	−	0.621481i	$-0.786531\pi$
$17$	−0.667728	+	0.667728i	−0.161948	+	0.161948i	0.621481	+	0.783429i	$0.286531\pi$
$18$	4.54515	+	4.54515i	1.07130	+	1.07130i
$19$	−4.14980			−0.952028			−0.476014	−	0.879438i	$-0.657919\pi$
$19$	−4.14980			−0.952028			−0.476014	+	0.879438i	$0.657919\pi$
$20$	−8.23948	+	2.97406i	−1.84240	+	0.665019i
$21$		−	1.54392i		−	0.336911i
$22$		0			0
$23$	0.104710	−	0.104710i	0.0218334	−	0.0218334i	−0.696106	−	0.717939i	$-0.745086\pi$
$23$	0.104710	−	0.104710i	0.0218334	−	0.0218334i	0.717939	+	0.696106i	$0.245086\pi$
$24$	−2.78946			−0.569396
$25$	−3.84732	+	3.19345i	−0.769463	+	0.638691i
$26$	6.83265			1.33999
$27$	2.38596	+	2.38596i	0.459177	+	0.459177i
$28$	−7.15160	−	7.15160i	−1.35153	−	1.35153i
$29$	−6.94005			−1.28873			−0.644367	−	0.764716i	$-0.722879\pi$
$29$	−6.94005			−1.28873			−0.644367	+	0.764716i	$0.722879\pi$
$30$	−3.05968	+	1.10440i	−0.558618	+	0.201634i
$31$	9.06250			1.62767			0.813836	−	0.581094i	$-0.197375\pi$
$31$	9.06250			1.62767			0.813836	+	0.581094i	$0.197375\pi$
$32$	0.555921	−	0.555921i	0.0982739	−	0.0982739i
$33$		0			0
$34$			2.29712i			0.393953i
$35$	−5.22550	−	2.45368i	−0.883270	−	0.414748i
$36$	10.3515			1.72525
$37$	5.37272	+	5.37272i	0.883269	+	0.883269i	0.993865	−	0.110596i	$-0.0352761\pi$
$37$	5.37272	+	5.37272i	0.883269	+	0.883269i	−0.110596	+	0.993865i	$0.535276\pi$
$38$	−7.13807	+	7.13807i	−1.15795	+	1.15795i
$39$	1.67972			0.268970
$40$	−4.43317	+	9.44111i	−0.700945	+	1.49277i
$41$			3.44754i			0.538415i	0.963082	+	0.269207i	$0.0867617\pi$
$41$			3.44754i			0.538415i	−0.963082	+	0.269207i	$0.913238\pi$
$42$	−2.65570	−	2.65570i	−0.409783	−	0.409783i
$43$	−3.91833	−	3.91833i	−0.597540	−	0.597540i	0.342117	−	0.939657i	$-0.388856\pi$
$43$	−3.91833	−	3.91833i	−0.597540	−	0.597540i	−0.939657	+	0.342117i	$0.888856\pi$
$44$		0			0
$45$	5.55757	−	2.00601i	0.828473	−	0.299039i
$46$		−	0.360222i		−	0.0531118i
$47$	−0.747616	−	0.747616i	−0.109051	−	0.109051i	0.650476	−	0.759527i	$-0.274569\pi$
$47$	−0.747616	−	0.747616i	−0.109051	−	0.109051i	−0.759527	+	0.650476i	$0.774569\pi$
$48$	−1.48502	+	1.48502i	−0.214344	+	0.214344i
$49$			0.334721i			0.0478173i
$50$	−1.12471	+	12.1108i	−0.159058	+	1.71273i
$51$			0.564716i			0.0790760i
$52$	7.78062	−	7.78062i	1.07898	−	1.07898i
$53$	2.91513	−	2.91513i	0.400425	−	0.400425i	−0.477958	−	0.878383i	$-0.658623\pi$
$53$	2.91513	−	2.91513i	0.400425	−	0.400425i	0.878383	+	0.477958i	$0.158623\pi$
$54$	8.20817			1.11699
$55$		0			0
$56$	−12.0424			−1.60924
$57$	−1.75480	+	1.75480i	−0.232429	+	0.232429i
$58$	−11.9376	+	11.9376i	−1.56748	+	1.56748i
$59$		−	6.48185i		−	0.843865i	−0.906627	−	0.421932i	$-0.861352\pi$
$59$		−	6.48185i		−	0.843865i	0.906627	−	0.421932i	$-0.138648\pi$
$60$	−2.22656	+	4.74180i	−0.287447	+	0.612164i
$61$		−	9.52525i		−	1.21958i	−0.792562	−	0.609792i	$-0.791253\pi$
$61$		−	9.52525i		−	1.21958i	0.792562	−	0.609792i	$-0.208747\pi$
$62$	15.5884	−	15.5884i	1.97973	−	1.97973i
$63$	4.82379	+	4.82379i	0.607740	+	0.607740i
$64$		−	8.93610i		−	1.11701i
$65$	2.66950	−	5.68511i	0.331111	−	0.705151i
$66$		0			0
$67$	2.94509	+	2.94509i	0.359801	+	0.359801i	0.863739	−	0.503939i	$-0.168116\pi$
$67$	2.94509	+	2.94509i	0.359801	+	0.359801i	−0.503939	+	0.863739i	$0.668116\pi$
$68$	2.61582	+	2.61582i	0.317215	+	0.317215i
$69$		−	0.0885557i		−	0.0106609i
$70$	−13.2090	+	4.76780i	−1.57877	+	0.569861i
$71$	1.26606			0.150254			0.0751268	−	0.997174i	$-0.476064\pi$
$71$	1.26606			0.150254			0.0751268	+	0.997174i	$0.476064\pi$
$72$	8.71533	−	8.71533i	1.02711	−	1.02711i
$73$	−1.25255	−	1.25255i	−0.146600	−	0.146600i	0.629997	−	0.776597i	$-0.283056\pi$
$73$	−1.25255	−	1.25255i	−0.146600	−	0.146600i	−0.776597	+	0.629997i	$0.783056\pi$
$74$	18.4832			2.14863
$75$	−0.276494	+	2.97729i	−0.0319268	+	0.343788i
$76$			16.2568i			1.86479i
$77$		0			0
$78$	2.88928	−	2.88928i	0.327147	−	0.327147i
$79$	−4.34195			−0.488508			−0.244254	−	0.969711i	$-0.578543\pi$
$79$	−4.34195			−0.488508			−0.244254	+	0.969711i	$0.578543\pi$
$80$	2.66607	+	7.38621i	0.298075	+	0.825804i
$81$	−5.90925			−0.656583
$82$	5.93012	+	5.93012i	0.654872	+	0.654872i
$83$	5.86295	+	5.86295i	0.643543	+	0.643543i	0.951425	−	0.307882i	$-0.0996202\pi$
$83$	5.86295	+	5.86295i	0.643543	+	0.643543i	−0.307882	+	0.951425i	$0.599620\pi$
$84$	−6.04831			−0.659924
$85$	1.91132	+	0.897478i	0.207312	+	0.0973452i
$86$	−13.4799			−1.45357
$87$	−2.93470	+	2.93470i	−0.314632	+	0.314632i
$88$		0			0
$89$			4.23092i			0.448477i	0.974534	+	0.224238i	$0.0719894\pi$
$89$			4.23092i			0.448477i	−0.974534	+	0.224238i	$0.928011\pi$
$90$	6.10903	−	13.0101i	0.643949	−	1.37139i
$91$	7.25153			0.760167
$92$	−0.410200	−	0.410200i	−0.0427663	−	0.0427663i
$93$	3.83220	−	3.83220i	0.397381	−	0.397381i
$94$	−2.57195			−0.265276
$95$	3.15041	+	8.72806i	0.323225	+	0.895480i
$96$		−	0.470158i		−	0.0479853i
$97$	10.1990	+	10.1990i	1.03555	+	1.03555i	0.999344	+	0.0362058i	$0.0115272\pi$
$97$	10.1990	+	10.1990i	1.03555	+	1.03555i	0.0362058	+	0.999344i	$0.488473\pi$
$98$	0.575755	+	0.575755i	0.0581600	+	0.0581600i
$99$		0			0
$100$	12.5104	+	15.0719i	1.25104	+	1.50719i
$101$			1.93517i			0.192557i	0.995354	+	0.0962785i	$0.0306939\pi$
$101$			1.93517i			0.192557i	−0.995354	+	0.0962785i	$0.969306\pi$
$102$	0.971369	+	0.971369i	0.0961798	+	0.0961798i
$103$	1.21570	−	1.21570i	0.119786	−	0.119786i	−0.644673	−	0.764459i	$-0.723006\pi$
$103$	1.21570	−	1.21570i	0.119786	−	0.119786i	0.764459	+	0.644673i	$0.223006\pi$
$104$		−	13.1016i		−	1.28472i
$105$	−3.24725	+	1.17210i	−0.316899	+	0.114385i
$106$		−	10.0287i		−	0.974069i
$107$	−2.94087	+	2.94087i	−0.284305	+	0.284305i	−0.834823	−	0.550518i	$-0.814430\pi$
$107$	−2.94087	+	2.94087i	−0.284305	+	0.284305i	0.550518	+	0.834823i	$0.314430\pi$
$108$	9.34698	−	9.34698i	0.899414	−	0.899414i
$109$	3.22321			0.308728			0.154364	−	0.988014i	$-0.450667\pi$
$109$	3.22321			0.308728			0.154364	+	0.988014i	$0.450667\pi$
$110$		0			0
$111$	4.54385			0.431284
$112$	−6.41099	+	6.41099i	−0.605782	+	0.605782i
$113$	−7.88651	+	7.88651i	−0.741900	+	0.741900i	−0.972944	−	0.231043i	$-0.925786\pi$
$113$	−7.88651	+	7.88651i	−0.741900	+	0.741900i	0.231043	+	0.972944i	$0.425786\pi$
$114$			6.03686i			0.565404i
$115$	−0.299723	−	0.140738i	−0.0279493	−	0.0131239i
$116$			27.1876i			2.52431i
$117$	−5.24807	+	5.24807i	−0.485184	+	0.485184i
$118$	−11.1494	−	11.1494i	−1.02639	−	1.02639i
$119$			2.43794i			0.223486i
$120$	2.11768	+	5.86693i	0.193317	+	0.535575i
$121$		0			0
$122$	−16.3844	−	16.3844i	−1.48337	−	1.48337i
$123$	1.45784	+	1.45784i	0.131449	+	0.131449i
$124$		−	35.5023i		−	3.18820i
$125$	9.63741	+	5.66749i	0.861996	+	0.506915i
$126$	16.5948			1.47838
$127$	−1.67941	+	1.67941i	−0.149023	+	0.149023i	−0.777682	−	0.628658i	$-0.783604\pi$
$127$	−1.67941	+	1.67941i	−0.149023	+	0.149023i	0.628658	+	0.777682i	$0.283604\pi$
$128$	−14.2592	−	14.2592i	−1.26034	−	1.26034i
$129$	−3.31384			−0.291768
$130$	−5.18716	−	14.3708i	−0.454944	−	1.26040i
$131$		−	3.12466i		−	0.273003i	−0.990640	−	0.136501i	$-0.956414\pi$
$131$		−	3.12466i		−	0.273003i	0.990640	−	0.136501i	$-0.0435858\pi$
$132$		0			0
$133$	−7.57567	+	7.57567i	−0.656894	+	0.656894i
$134$	10.1317			0.875248
$135$	3.20691	−	6.82961i	0.276007	−	0.587799i
$136$	4.40473			0.377702
$137$	−11.6927	−	11.6927i	−0.998971	−	0.998971i	0.00102829	−	0.999999i	$-0.499673\pi$
$137$	−11.6927	−	11.6927i	−0.998971	−	0.998971i	−0.999999	+	0.00102829i	$0.999673\pi$
$138$	−0.152325	−	0.152325i	−0.0129668	−	0.0129668i
$139$	−4.32047			−0.366458			−0.183229	−	0.983070i	$-0.558655\pi$
$139$	−4.32047			−0.366458			−0.183229	+	0.983070i	$0.558655\pi$
$140$	−9.61231	+	20.4709i	−0.812388	+	1.73011i
$141$	−0.632279			−0.0532475
$142$	2.17775	−	2.17775i	0.182753	−	0.182753i
$143$		0			0
$144$		−	9.27951i		−	0.773293i
$145$	5.26869	+	14.5967i	0.437541	+	1.21219i
$146$	−4.30904			−0.356619
$147$	0.141542	+	0.141542i	0.0116742	+	0.0116742i
$148$	21.0476	−	21.0476i	1.73010	−	1.73010i
$149$	8.44467			0.691814			0.345907	−	0.938269i	$-0.387571\pi$
$149$	8.44467			0.691814			0.345907	+	0.938269i	$0.387571\pi$
$150$	4.64564	+	5.59684i	0.379315	+	0.456980i
$151$			11.9323i			0.971039i	0.874226	+	0.485520i	$0.161370\pi$
$151$			11.9323i			0.971039i	−0.874226	+	0.485520i	$0.838630\pi$
$152$	13.6873	+	13.6873i	1.11018	+	1.11018i
$153$	−1.76439	−	1.76439i	−0.142642	−	0.142642i
$154$		0			0
$155$	−6.87999	−	19.0607i	−0.552614	−	1.53099i
$156$		−	6.58029i		−	0.526845i
$157$	−0.962739	−	0.962739i	−0.0768350	−	0.0768350i	0.667645	−	0.744480i	$-0.267302\pi$
$157$	−0.962739	−	0.962739i	−0.0768350	−	0.0768350i	−0.744480	+	0.667645i	$0.767302\pi$
$158$	−7.46860	+	7.46860i	−0.594170	+	0.594170i
$159$		−	2.46541i		−	0.195520i
$160$	−1.59128	−	0.747201i	−0.125802	−	0.0590714i
$161$		−	0.382305i		−	0.0301299i
$162$	−10.1645	+	10.1645i	−0.798599	+	0.798599i
$163$	−16.2235	+	16.2235i	−1.27072	+	1.27072i	−0.325007	+	0.945712i	$0.605367\pi$
$163$	−16.2235	+	16.2235i	−1.27072	+	1.27072i	−0.945712	+	0.325007i	$0.894633\pi$
$164$	13.5057			1.05462
$165$		0			0
$166$	20.1698			1.56548
$167$	−10.1543	+	10.1543i	−0.785766	+	0.785766i	−0.980797	−	0.195031i	$-0.937519\pi$
$167$	−10.1543	+	10.1543i	−0.785766	+	0.785766i	0.195031	+	0.980797i	$0.437519\pi$
$168$	−5.09231	+	5.09231i	−0.392880	+	0.392880i
$169$		−	5.11066i		−	0.393128i
$170$	4.83142	−	1.74391i	0.370553	−	0.133752i
$171$		−	10.9653i		−	0.838538i
$172$	−15.3501	+	15.3501i	−1.17043	+	1.17043i
$173$	−15.7696	−	15.7696i	−1.19894	−	1.19894i	−0.974485	−	0.224454i	$-0.927940\pi$
$173$	−15.7696	−	15.7696i	−1.19894	−	1.19894i	−0.224454	−	0.974485i	$-0.572060\pi$
$174$			10.0960i			0.765372i
$175$	−1.19366	+	12.8533i	−0.0902321	+	0.971618i
$176$		0			0
$177$	−2.74094	−	2.74094i	−0.206022	−	0.206022i
$178$	7.27762	+	7.27762i	0.545480	+	0.545480i
$179$			4.36821i			0.326495i	0.986585	+	0.163248i	$0.0521970\pi$
$179$			4.36821i			0.326495i	−0.986585	+	0.163248i	$0.947803\pi$
$180$	−7.85856	−	21.7718i	−0.585743	−	1.62277i
$181$	9.43978			0.701654			0.350827	−	0.936440i	$-0.385901\pi$
$181$	9.43978			0.701654			0.350827	+	0.936440i	$0.385901\pi$
$182$	12.4734	−	12.4734i	0.924587	−	0.924587i
$183$	−4.02788	−	4.02788i	−0.297750	−	0.297750i
$184$	−0.690726			−0.0509210
$185$	7.22135	−	15.3790i	0.530924	−	1.13068i
$186$		−	13.1836i		−	0.966665i
$187$		0			0
$188$	−2.92879	+	2.92879i	−0.213604	+	0.213604i
$189$	8.71137			0.633659
$190$	20.4322	+	9.59412i	1.48231	+	0.696031i
$191$	−6.47277			−0.468353			−0.234177	−	0.972194i	$-0.575239\pi$
$191$	−6.47277			−0.468353			−0.234177	+	0.972194i	$0.575239\pi$
$192$	−3.77875	−	3.77875i	−0.272708	−	0.272708i
$193$	0.711801	+	0.711801i	0.0512366	+	0.0512366i	0.732261	−	0.681024i	$-0.238465\pi$
$193$	0.711801	+	0.711801i	0.0512366	+	0.0512366i	−0.681024	+	0.732261i	$0.738465\pi$
$194$	35.0866			2.51907
$195$	−1.27519	−	3.53286i	−0.0913185	−	0.252993i
$196$	1.31127			0.0936622
$197$	−17.3425	+	17.3425i	−1.23560	+	1.23560i	−0.273821	+	0.961781i	$0.588287\pi$
$197$	−17.3425	+	17.3425i	−1.23560	+	1.23560i	−0.961781	+	0.273821i	$0.911713\pi$
$198$		0			0
$199$		−	3.25580i		−	0.230797i	−0.993319	−	0.115399i	$-0.963185\pi$
$199$		−	3.25580i		−	0.230797i	0.993319	−	0.115399i	$-0.0368146\pi$
$200$	23.2226	+	2.15663i	1.64208	+	0.152497i
$201$	2.49075			0.175684
$202$	3.32870	+	3.32870i	0.234206	+	0.234206i
$203$	−12.6694	+	12.6694i	−0.889219	+	0.889219i
$204$	2.21227			0.154890
$205$	7.25103	−	2.61727i	0.506434	−	0.182798i
$206$		−	4.18224i		−	0.291391i
$207$	0.276682	+	0.276682i	0.0192307	+	0.0192307i
$208$	−6.97487	−	6.97487i	−0.483621	−	0.483621i
$209$		0			0
$210$	−3.56947	+	7.60173i	−0.246317	+	0.524569i
$211$		−	24.8414i		−	1.71015i	−0.518505	−	0.855075i	$-0.673511\pi$
$211$		−	24.8414i		−	1.71015i	0.518505	−	0.855075i	$-0.326489\pi$
$212$	−11.4200	−	11.4200i	−0.784332	−	0.784332i
$213$	0.535370	−	0.535370i	0.0366830	−	0.0366830i
$214$			10.1172i			0.691597i
$215$	−5.26654	+	11.2159i	−0.359175	+	0.764919i
$216$		−	15.7392i		−	1.07092i
$217$	16.5441	−	16.5441i	1.12308	−	1.12308i
$218$	5.54426	−	5.54426i	0.375504	−	0.375504i
$219$	−1.05932			−0.0715822
$220$		0			0
$221$	−2.65237			−0.178418
$222$	7.81589	−	7.81589i	0.524568	−	0.524568i
$223$	13.8522	−	13.8522i	0.927615	−	0.927615i	−0.0699369	−	0.997551i	$-0.522280\pi$
$223$	13.8522	−	13.8522i	0.927615	−	0.927615i	0.997551	+	0.0699369i	$0.0222798\pi$
$224$		−	2.02973i		−	0.135617i
$225$	−8.43830	−	10.1660i	−0.562553	−	0.677736i
$226$			27.1312i			1.80474i
$227$	0.723313	−	0.723313i	0.0480079	−	0.0480079i	−0.682695	−	0.730703i	$-0.739192\pi$
$227$	0.723313	−	0.723313i	0.0480079	−	0.0480079i	0.730703	+	0.682695i	$0.239192\pi$
$228$	6.87443	+	6.87443i	0.455270	+	0.455270i
$229$		−	0.101849i		−	0.00673036i	−0.999994	−	0.00336518i	$-0.998929\pi$
$229$		−	0.101849i		−	0.00673036i	0.999994	−	0.00336518i	$-0.00107117\pi$
$230$	−0.757637	+	0.273470i	−0.0499571	+	0.0180321i
$231$		0			0
$232$	22.8903	+	22.8903i	1.50282	+	1.50282i
$233$	−15.1321	−	15.1321i	−0.991339	−	0.991339i	0.00862392	−	0.999963i	$-0.497255\pi$
$233$	−15.1321	−	15.1321i	−0.991339	−	0.991339i	−0.999963	+	0.00862392i	$0.997255\pi$
$234$			18.0544i			1.18025i
$235$	−1.00485	+	2.13999i	−0.0655494	+	0.139598i
$236$	−25.3926			−1.65292
$237$	−1.83605	+	1.83605i	−0.119265	+	0.119265i
$238$	4.19351	+	4.19351i	0.271825	+	0.271825i
$239$	8.66369			0.560408			0.280204	−	0.959941i	$-0.409598\pi$
$239$	8.66369			0.560408			0.280204	+	0.959941i	$0.409598\pi$
$240$	4.25075	+	1.99598i	0.274385	+	0.128840i
$241$			10.6492i			0.685976i	0.939340	+	0.342988i	$0.111439\pi$
$241$			10.6492i			0.685976i	−0.939340	+	0.342988i	$0.888561\pi$
$242$		0			0
$243$	−9.65667	+	9.65667i	−0.619476	+	0.619476i
$244$	−37.3152			−2.38886
$245$	0.704003	−	0.254111i	0.0449771	−	0.0162346i
$246$	5.01526			0.319762
$247$	−8.24199	−	8.24199i	−0.524425	−	0.524425i
$248$	−29.8908	−	29.8908i	−1.89807	−	1.89807i
$249$	4.95846			0.314230
$250$	26.3260	−	6.82867i	1.66500	−	0.431883i
$251$	−9.39306			−0.592885			−0.296442	−	0.955051i	$-0.595800\pi$
$251$	−9.39306			−0.592885			−0.296442	+	0.955051i	$0.595800\pi$
$252$	18.8972	−	18.8972i	1.19041	−	1.19041i
$253$		0			0
$254$			5.77750i			0.362513i
$255$	1.18774	−	0.428716i	0.0743791	−	0.0268473i
$256$	−31.1822			−1.94889
$257$	−13.0389	−	13.0389i	−0.813345	−	0.813345i	0.171789	−	0.985134i	$-0.445045\pi$
$257$	−13.0389	−	13.0389i	−0.813345	−	0.813345i	−0.985134	+	0.171789i	$0.945045\pi$
$258$	−5.70015	+	5.70015i	−0.354876	+	0.354876i
$259$	19.6163			1.21890
$260$	−22.2714	−	10.4578i	−1.38121	−	0.648563i
$261$		−	18.3382i		−	1.13511i
$262$	−5.37473	−	5.37473i	−0.332052	−	0.332052i
$263$	11.8928	+	11.8928i	0.733342	+	0.733342i	0.971280	−	0.237938i	$-0.0764717\pi$
$263$	11.8928	+	11.8928i	0.733342	+	0.733342i	−0.237938	+	0.971280i	$0.576472\pi$
$264$		0			0
$265$	−8.34434	−	3.91817i	−0.512589	−	0.240691i
$266$			26.0618i			1.59795i
$267$	1.78910	+	1.78910i	0.109491	+	0.109491i
$268$	11.5374	−	11.5374i	0.704760	−	0.704760i
$269$			28.4567i			1.73503i	0.497408	+	0.867517i	$0.334285\pi$
$269$			28.4567i			1.73503i	−0.497408	+	0.867517i	$0.665715\pi$
$270$	−6.23141	−	17.2638i	−0.379232	−	1.05064i
$271$			29.6823i			1.80307i	0.432707	+	0.901535i	$0.357558\pi$
$271$			29.6823i			1.80307i	−0.432707	+	0.901535i	$0.642442\pi$
$272$	2.34493	−	2.34493i	0.142182	−	0.142182i
$273$	3.06641	−	3.06641i	0.185587	−	0.185587i
$274$	−40.2251			−2.43009
$275$		0			0
$276$	−0.346917			−0.0208820
$277$	−8.78206	+	8.78206i	−0.527663	+	0.527663i	−0.919875	−	0.392212i	$-0.871710\pi$
$277$	−8.78206	+	8.78206i	−0.527663	+	0.527663i	0.392212	+	0.919875i	$0.371710\pi$
$278$	−7.43165	+	7.43165i	−0.445721	+	0.445721i
$279$			23.9465i			1.43364i
$280$	9.14227	+	25.3282i	0.546355	+	1.51365i
$281$		−	21.8750i		−	1.30495i	−0.757809	−	0.652477i	$-0.773730\pi$
$281$		−	21.8750i		−	1.30495i	0.757809	−	0.652477i	$-0.226270\pi$
$282$	−1.08759	+	1.08759i	−0.0647647	+	0.0647647i
$283$	19.2316	+	19.2316i	1.14320	+	1.14320i	0.987862	+	0.155336i	$0.0496462\pi$
$283$	19.2316	+	19.2316i	1.14320	+	1.14320i	0.155336	+	0.987862i	$0.450354\pi$
$284$		−	4.95979i		−	0.294309i
$285$	5.02297	+	2.35859i	0.297535	+	0.139711i
$286$		0			0
$287$	6.29366	+	6.29366i	0.371503	+	0.371503i
$288$	1.46895	+	1.46895i	0.0865587	+	0.0865587i
$289$			16.1083i			0.947546i
$290$	34.1704	+	16.0451i	2.00656	+	0.942198i
$291$	8.62556			0.505640
$292$	−4.90688	+	4.90688i	−0.287153	+	0.287153i
$293$	−14.2215	−	14.2215i	−0.830829	−	0.830829i	0.156801	−	0.987630i	$-0.449882\pi$
$293$	−14.2215	−	14.2215i	−0.830829	−	0.830829i	−0.987630	+	0.156801i	$0.949882\pi$
$294$	0.486932			0.0283984
$295$	−13.6329	+	4.92083i	−0.793740	+	0.286502i
$296$		−	35.4416i		−	2.06000i
$297$		0			0
$298$	14.5257	−	14.5257i	0.841450	−	0.841450i
$299$	0.415931			0.0240539
$300$	11.6635	+	1.08317i	0.673394	+	0.0625367i
$301$	−14.3062			−0.824598
$302$	20.5248	+	20.5248i	1.18107	+	1.18107i
$303$	0.818315	+	0.818315i	0.0470110	+	0.0470110i
$304$	14.5733			0.835836
$305$	−20.0340	+	7.23130i	−1.14714	+	0.414063i
$306$	−6.06985			−0.346990
$307$	14.6921	−	14.6921i	0.838520	−	0.838520i	−0.150144	−	0.988664i	$-0.547974\pi$
$307$	14.6921	−	14.6921i	0.838520	−	0.838520i	0.988664	+	0.150144i	$0.0479738\pi$
$308$		0			0
$309$		−	1.02815i		−	0.0584893i
$310$	−44.6206	−	20.9520i	−2.53428	−	1.19000i
$311$	23.2789			1.32003			0.660013	−	0.751254i	$-0.270551\pi$
$311$	23.2789			1.32003			0.660013	+	0.751254i	$0.270551\pi$
$312$	−5.54020	−	5.54020i	−0.313652	−	0.313652i
$313$	−9.91219	+	9.91219i	−0.560270	+	0.560270i	−0.929384	−	0.369114i	$-0.879661\pi$
$313$	−9.91219	+	9.91219i	−0.560270	+	0.560270i	0.369114	+	0.929384i	$0.379661\pi$
$314$	−3.31202			−0.186908
$315$	6.48355	−	13.8077i	0.365306	−	0.777976i
$316$			17.0096i			0.956865i
$317$	−20.8597	−	20.8597i	−1.17160	−	1.17160i	−0.981829	−	0.189767i	$-0.939227\pi$
$317$	−20.8597	−	20.8597i	−1.17160	−	1.17160i	−0.189767	−	0.981829i	$-0.560773\pi$
$318$	−4.24076	−	4.24076i	−0.237810	−	0.237810i
$319$		0			0
$320$	−18.7949	+	6.78404i	−1.05066	+	0.379239i
$321$			2.48718i			0.138821i
$322$	−0.657604	−	0.657604i	−0.0366468	−	0.0366468i
$323$	2.77093	−	2.77093i	0.154179	−	0.154179i
$324$			23.1495i			1.28608i
$325$	−13.9838	−	1.29865i	−0.775682	−	0.0720360i
$326$			55.8120i			3.09114i
$327$	1.36298	−	1.36298i	0.0753730	−	0.0753730i
$328$	11.3710	−	11.3710i	0.627859	−	0.627859i
$329$	−2.72962			−0.150489
$330$		0			0
$331$	2.18560			0.120131			0.0600657	−	0.998194i	$-0.480869\pi$
$331$	2.18560			0.120131			0.0600657	+	0.998194i	$0.480869\pi$
$332$	22.9681	−	22.9681i	1.26054	−	1.26054i
$333$	−14.1967	+	14.1967i	−0.777975	+	0.777975i
$334$			34.9330i			1.91145i
$335$	3.95844	−	8.43010i	0.216272	−	0.460586i
$336$			5.42195i			0.295792i
$337$	−1.27421	+	1.27421i	−0.0694108	+	0.0694108i	−0.740960	−	0.671549i	$-0.765629\pi$
$337$	−1.27421	+	1.27421i	−0.0694108	+	0.0694108i	0.671549	+	0.740960i	$0.265629\pi$
$338$	−8.79086	−	8.79086i	−0.478160	−	0.478160i
$339$			6.66984i			0.362256i
$340$	3.51587	−	7.48759i	0.190675	−	0.406072i
$341$		0			0
$342$	−18.8614	−	18.8614i	−1.01991	−	1.01991i
$343$	13.3899	+	13.3899i	0.722987	+	0.722987i
$344$			25.8476i			1.39361i
$345$	−0.186255	+	0.0672290i	−0.0100276	+	0.00361949i
$346$	−54.2505			−2.91653
$347$	−15.1832	+	15.1832i	−0.815077	+	0.815077i	−0.985390	−	0.170313i	$-0.945522\pi$
$347$	−15.1832	+	15.1832i	−0.815077	+	0.815077i	0.170313	+	0.985390i	$0.445522\pi$
$348$	11.4967	+	11.4967i	0.616286	+	0.616286i
$349$	−10.6564			−0.570423			−0.285212	−	0.958465i	$-0.592064\pi$
$349$	−10.6564			−0.570423			−0.285212	+	0.958465i	$0.592064\pi$
$350$	20.0558	+	24.1622i	1.07203	+	1.29152i
$351$			9.47758i			0.505876i
$352$		0			0
$353$	−7.73857	+	7.73857i	−0.411883	+	0.411883i	−0.882394	−	0.470511i	$-0.844069\pi$
$353$	−7.73857	+	7.73857i	−0.411883	+	0.411883i	0.470511	+	0.882394i	$0.344069\pi$
$354$	−9.42939			−0.501166
$355$	−0.961156	−	2.66284i	−0.0510129	−	0.141329i
$356$	16.5746			0.878454
$357$	1.03092	+	1.03092i	0.0545620	+	0.0545620i
$358$	7.51377	+	7.51377i	0.397115	+	0.397115i
$359$	−3.27419			−0.172805			−0.0864025	−	0.996260i	$-0.527537\pi$
$359$	−3.27419			−0.172805			−0.0864025	+	0.996260i	$0.527537\pi$
$360$	−24.9469	−	11.7141i	−1.31482	−	0.617386i
$361$	−1.77919			−0.0936418
$362$	16.2374	−	16.2374i	0.853418	−	0.853418i
$363$		0			0
$364$		−	28.4079i		−	1.48898i
$365$	−1.68353	+	3.58534i	−0.0881199	+	0.187665i
$366$	−13.8567			−0.724303
$367$	12.8904	+	12.8904i	0.672873	+	0.672873i	0.958377	−	0.285504i	$-0.0921610\pi$
$367$	12.8904	+	12.8904i	0.672873	+	0.672873i	−0.285504	+	0.958377i	$0.592161\pi$
$368$	−0.367720	+	0.367720i	−0.0191687	+	0.0191687i
$369$	−9.10968			−0.474231
$370$	−14.0319	−	38.8749i	−0.729486	−	2.02101i
$371$		−	10.6435i		−	0.552581i
$372$	−15.0127	−	15.0127i	−0.778370	−	0.778370i
$373$	−12.4917	−	12.4917i	−0.646795	−	0.646795i	0.305422	−	0.952217i	$-0.401202\pi$
$373$	−12.4917	−	12.4917i	−0.646795	−	0.646795i	−0.952217	+	0.305422i	$0.901202\pi$
$374$		0			0
$375$	6.47189	−	1.67874i	0.334207	−	0.0866895i
$376$			4.93172i			0.254334i
$377$	−13.7838	−	13.7838i	−0.709900	−	0.709900i
$378$	14.9844	−	14.9844i	0.770717	−	0.770717i
$379$		−	22.0633i		−	1.13332i	−0.823953	−	0.566658i	$-0.808236\pi$
$379$		−	22.0633i		−	1.13332i	0.823953	−	0.566658i	$-0.191764\pi$
$380$	34.1922	−	12.3417i	1.75402	−	0.633117i
$381$			1.42032i			0.0727652i
$382$	−11.1338	+	11.1338i	−0.569656	+	0.569656i
$383$	13.9228	−	13.9228i	0.711419	−	0.711419i	−0.255413	−	0.966832i	$-0.582211\pi$
$383$	13.9228	−	13.9228i	0.711419	−	0.711419i	0.966832	+	0.255413i	$0.0822114\pi$
$384$	−12.0594			−0.615402
$385$		0			0
$386$	2.44874			0.124638
$387$	10.3537	−	10.3537i	0.526308	−	0.526308i
$388$	39.9545	−	39.9545i	2.02838	−	2.02838i
$389$		−	17.1206i		−	0.868051i	−0.900901	−	0.434025i	$-0.857093\pi$
$389$		−	17.1206i		−	0.868051i	0.900901	−	0.434025i	$-0.142907\pi$
$390$	−8.27034	−	3.88342i	−0.418785	−	0.196645i
$391$			0.139835i			0.00707175i
$392$	1.10401	−	1.10401i	0.0557610	−	0.0557610i
$393$	−1.32131	−	1.32131i	−0.0666510	−	0.0666510i
$394$			59.6617i			3.00571i
$395$	3.29629	+	9.13221i	0.165854	+	0.459491i
$396$		0			0
$397$	5.24887	+	5.24887i	0.263433	+	0.263433i	0.826447	−	0.563014i	$-0.190358\pi$
$397$	5.24887	+	5.24887i	0.263433	+	0.263433i	−0.563014	+	0.826447i	$0.690358\pi$
$398$	−5.60030	−	5.60030i	−0.280718	−	0.280718i
$399$			6.40695i			0.320749i
$400$	13.5110	−	11.2148i	0.675552	−	0.560740i
$401$	12.2753			0.612998			0.306499	−	0.951871i	$-0.400842\pi$
$401$	12.2753			0.612998			0.306499	+	0.951871i	$0.400842\pi$
$402$	4.28434	−	4.28434i	0.213683	−	0.213683i
$403$	17.9992	+	17.9992i	0.896604	+	0.896604i
$404$	7.58104			0.377171
$405$	4.48613	+	12.4286i	0.222918	+	0.617583i
$406$			43.5854i			2.16311i
$407$		0			0
$408$	1.86260	−	1.86260i	0.0922125	−	0.0922125i
$409$	26.7590			1.32315			0.661574	−	0.749880i	$-0.269889\pi$
$409$	26.7590			1.32315			0.661574	+	0.749880i	$0.269889\pi$
$410$	7.97054	−	16.9745i	0.393637	−	0.838310i
$411$	−9.88880			−0.487779
$412$	−4.76249	−	4.76249i	−0.234631	−	0.234631i
$413$	−11.8329	−	11.8329i	−0.582261	−	0.582261i
$414$	0.951841			0.0467804
$415$	7.88026	−	16.7822i	0.386827	−	0.823808i
$416$	2.20825			0.108268
$417$	−1.82697	+	1.82697i	−0.0894672	+	0.0894672i
$418$		0			0
$419$		−	14.2401i		−	0.695676i	−0.937555	−	0.347838i	$-0.886916\pi$
$419$		−	14.2401i		−	0.695676i	0.937555	−	0.347838i	$-0.113084\pi$
$420$	4.59170	+	12.7211i	0.224052	+	0.620726i
$421$	−6.90619			−0.336587			−0.168294	−	0.985737i	$-0.553826\pi$
$421$	−6.90619			−0.336587			−0.168294	+	0.985737i	$0.553826\pi$
$422$	−42.7297	−	42.7297i	−2.08005	−	2.08005i
$423$	1.97548	−	1.97548i	0.0960511	−	0.0960511i
$424$	−19.2300			−0.933889
$425$	0.436602	−	4.70132i	0.0211783	−	0.228047i
$426$		−	1.84178i		−	0.0892347i
$427$	−17.3888	−	17.3888i	−0.841505	−	0.841505i
$428$	11.5209	+	11.5209i	0.556882	+	0.556882i
$429$		0			0
$430$	10.2335	+	28.3515i	0.493505	+	1.36723i
$431$		−	7.13930i		−	0.343888i	−0.985107	−	0.171944i	$-0.944995\pi$
$431$		−	7.13930i		−	0.343888i	0.985107	−	0.171944i	$-0.0550048\pi$
$432$	−8.37902	−	8.37902i	−0.403136	−	0.403136i
$433$	11.8812	−	11.8812i	0.570975	−	0.570975i	−0.361426	−	0.932401i	$-0.617710\pi$
$433$	11.8812	−	11.8812i	0.570975	−	0.570975i	0.932401	+	0.361426i	$0.117710\pi$
$434$		−	56.9149i		−	2.73200i
$435$	8.40034	+	3.94446i	0.402765	+	0.189122i
$436$		−	12.6269i		−	0.604721i
$437$	−0.434523	+	0.434523i	−0.0207861	+	0.0207861i
$438$	−1.82214	+	1.82214i	−0.0870651	+	0.0870651i
$439$	−0.772934			−0.0368901			−0.0184451	−	0.999830i	$-0.505872\pi$
$439$	−0.772934			−0.0368901			−0.0184451	+	0.999830i	$0.505872\pi$
$440$		0			0
$441$	−0.884459			−0.0421171
$442$	−4.56235	+	4.56235i	−0.217009	+	0.217009i
$443$	13.2864	−	13.2864i	0.631257	−	0.631257i	−0.317127	−	0.948383i	$-0.602718\pi$
$443$	13.2864	−	13.2864i	0.631257	−	0.631257i	0.948383	+	0.317127i	$0.102718\pi$
$444$		−	17.8006i		−	0.844777i
$445$	8.89868	−	3.21200i	0.421838	−	0.152263i
$446$		−	47.6545i		−	2.25651i
$447$	3.57094	−	3.57094i	0.168900	−	0.168900i
$448$	−16.3133	−	16.3133i	−0.770732	−	0.770732i
$449$			0.713384i			0.0336667i	0.999858	+	0.0168333i	$0.00535847\pi$
$449$			0.713384i			0.0336667i	−0.999858	+	0.0168333i	$0.994642\pi$
$450$	−32.0014	−	2.97190i	−1.50856	−	0.140097i
$451$		0			0
$452$	30.8954	+	30.8954i	1.45320	+	1.45320i
$453$	5.04575	+	5.04575i	0.237070	+	0.237070i
$454$		−	2.48834i		−	0.116784i
$455$	−5.50515	−	15.2518i	−0.258086	−	0.715014i
$456$	11.5757			0.542081
$457$	−13.6790	+	13.6790i	−0.639876	+	0.639876i	−0.950525	−	0.310649i	$-0.899454\pi$
$457$	−13.6790	+	13.6790i	−0.639876	+	0.639876i	0.310649	+	0.950525i	$0.399454\pi$
$458$	−0.175190	−	0.175190i	−0.00818611	−	0.00818611i
$459$	−3.18634			−0.148725
$460$	−0.551340	+	1.17416i	−0.0257064	+	0.0547457i
$461$		−	36.5277i		−	1.70126i	−0.525761	−	0.850632i	$-0.676219\pi$
$461$		−	36.5277i		−	1.70126i	0.525761	−	0.850632i	$-0.323781\pi$
$462$		0			0
$463$	−17.1422	+	17.1422i	−0.796664	+	0.796664i	−0.982568	−	0.185904i	$-0.940479\pi$
$463$	−17.1422	+	17.1422i	−0.796664	+	0.796664i	0.185904	+	0.982568i	$0.440479\pi$
$464$	24.3721			1.13145
$465$	−10.9694	−	5.15078i	−0.508693	−	0.238862i
$466$	−52.0576			−2.41152
$467$	10.4791	+	10.4791i	0.484917	+	0.484917i	0.906698	−	0.421781i	$-0.138595\pi$
$467$	10.4791	+	10.4791i	0.484917	+	0.484917i	−0.421781	+	0.906698i	$0.638595\pi$
$468$	20.5593	+	20.5593i	0.950354	+	0.950354i
$469$	10.7528			0.496520
$470$	1.95255	+	5.40945i	0.0900645	+	0.249520i
$471$	−0.814215			−0.0375171
$472$	−21.3791	+	21.3791i	−0.984051	+	0.984051i
$473$		0			0
$474$			6.31640i			0.290122i
$475$	15.9656	−	13.2522i	0.732551	−	0.608052i
$476$	9.55065			0.437753
$477$	7.70287	+	7.70287i	0.352690	+	0.352690i
$478$	14.9024	−	14.9024i	0.681621	−	0.681621i
$479$	27.5860			1.26044			0.630218	−	0.776418i	$-0.282965\pi$
$479$	27.5860			1.26044			0.630218	+	0.776418i	$0.282965\pi$
$480$	−0.988859	+	0.356930i	−0.0451350	+	0.0162916i
$481$			21.3417i			0.973098i
$482$	18.3177	+	18.3177i	0.834349	+	0.834349i
$483$	−0.161663	−	0.161663i	−0.00735592	−	0.00735592i
$484$		0			0
$485$	13.7082	−	29.1938i	0.622459	−	1.32562i
$486$			33.2209i			1.50693i
$487$	−27.5034	−	27.5034i	−1.24630	−	1.24630i	−0.957342	−	0.288958i	$-0.906691\pi$
$487$	−27.5034	−	27.5034i	−1.24630	−	1.24630i	−0.288958	−	0.957342i	$-0.593309\pi$
$488$	−31.4171	+	31.4171i	−1.42219	+	1.42219i
$489$			13.7206i			0.620468i
$490$	0.773859	−	1.64805i	0.0349594	−	0.0744515i
$491$		−	18.8013i		−	0.848490i	−0.905547	−	0.424245i	$-0.860539\pi$
$491$		−	18.8013i		−	0.848490i	0.905547	−	0.424245i	$-0.139461\pi$
$492$	5.71109	−	5.71109i	0.257476	−	0.257476i
$493$	4.63406	−	4.63406i	0.208708	−	0.208708i
$494$	−28.3541			−1.27571
$495$		0			0
$496$	−31.8258			−1.42902
$497$	2.31126	−	2.31126i	0.103674	−	0.103674i
$498$	8.52906	−	8.52906i	0.382196	−	0.382196i
$499$		−	5.23972i		−	0.234562i	−0.993099	−	0.117281i	$-0.962582\pi$
$499$		−	5.23972i		−	0.234562i	0.993099	−	0.117281i	$-0.0374178\pi$
$500$	22.2024	−	37.7545i	0.992921	−	1.68843i
$501$			8.58780i			0.383675i
$502$	−16.1570	+	16.1570i	−0.721123	+	0.721123i
$503$	9.32841	+	9.32841i	0.415933	+	0.415933i	0.883799	−	0.467866i	$-0.154977\pi$
$503$	9.32841	+	9.32841i	0.415933	+	0.415933i	−0.467866	+	0.883799i	$0.654977\pi$
$504$		−	31.8206i		−	1.41740i
$505$	4.07015	−	1.46913i	0.181119	−	0.0653754i
$506$		0			0
$507$	−2.16111	−	2.16111i	−0.0959784	−	0.0959784i
$508$	6.57907	+	6.57907i	0.291899	+	0.291899i
$509$			5.59580i			0.248030i	0.992280	+	0.124015i	$0.0395770\pi$
$509$			5.59580i			0.248030i	−0.992280	+	0.124015i	$0.960423\pi$
$510$	1.30560	−	2.78047i	0.0578127	−	0.123121i
$511$	−4.57320			−0.202307
$512$	−25.1183	+	25.1183i	−1.11008	+	1.11008i
$513$	−9.90123	−	9.90123i	−0.437150	−	0.437150i
$514$	−44.8565			−1.97854
$515$	−3.47984	−	1.63399i	−0.153340	−	0.0720023i
$516$			12.9820i			0.571500i
$517$		0			0
$518$	33.7421	−	33.7421i	1.48254	−	1.48254i
$519$	−13.3368			−0.585419
$520$	−27.5560	+	9.94638i	−1.20841	+	0.436178i
$521$	19.0771			0.835783			0.417891	−	0.908497i	$-0.362769\pi$
$521$	19.0771			0.835783			0.417891	+	0.908497i	$0.362769\pi$
$522$	−31.5436	−	31.5436i	−1.38062	−	1.38062i
$523$	24.8184	+	24.8184i	1.08523	+	1.08523i	0.996012	+	0.0892197i	$0.0284373\pi$
$523$	24.8184	+	24.8184i	1.08523	+	1.08523i	0.0892197	+	0.996012i	$0.471563\pi$
$524$	−12.2409			−0.534744
$525$	4.93044	+	5.93995i	0.215182	+	0.259241i
$526$	40.9137			1.78392
$527$	−6.05128	+	6.05128i	−0.263598	+	0.263598i
$528$		0			0
$529$			22.9781i			0.999047i
$530$	−21.0928	+	7.61347i	−0.916211	+	0.330708i
$531$	17.1275			0.743268
$532$	29.6777	+	29.6777i	1.28669	+	1.28669i
$533$	−6.84722	+	6.84722i	−0.296586	+	0.296586i
$534$	6.15488			0.266348
$535$	8.41801	+	3.95276i	0.363942	+	0.170893i
$536$		−	19.4276i		−	0.839144i
$537$	1.84716	+	1.84716i	0.0797108	+	0.0797108i
$538$	48.9484	+	48.9484i	2.11031	+	2.11031i
$539$		0			0
$540$	−26.7550	−	12.5631i	−1.15135	−	0.540628i
$541$		−	2.54081i		−	0.109238i	−0.998507	−	0.0546189i	$-0.982606\pi$
$541$		−	2.54081i		−	0.109238i	0.998507	−	0.0546189i	$-0.0173944\pi$
$542$	51.0565	+	51.0565i	2.19307	+	2.19307i
$543$	3.99174	−	3.99174i	0.171302	−	0.171302i
$544$			0.742408i			0.0318305i
$545$	−2.44697	−	6.77922i	−0.104817	−	0.290390i
$546$		−	10.5491i		−	0.451459i
$547$	−10.4825	+	10.4825i	−0.448199	+	0.448199i	−0.894755	−	0.446556i	$-0.852650\pi$
$547$	−10.4825	+	10.4825i	−0.448199	+	0.448199i	0.446556	+	0.894755i	$0.352650\pi$
$548$	−45.8060	+	45.8060i	−1.95674	+	1.95674i
$549$	25.1693			1.07420
$550$		0			0
$551$	28.7998			1.22691
$552$	−0.292083	+	0.292083i	−0.0124319	+	0.0124319i
$553$	−7.92646	+	7.92646i	−0.337067	+	0.337067i
$554$			30.2121i			1.28359i
$555$	−3.44957	−	9.55686i	−0.146426	−	0.405666i
$556$			16.9255i			0.717799i
$557$	9.02363	−	9.02363i	0.382343	−	0.382343i	−0.489602	−	0.871946i	$-0.662858\pi$
$557$	9.02363	−	9.02363i	0.382343	−	0.382343i	0.871946	+	0.489602i	$0.162858\pi$
$558$	41.1904	+	41.1904i	1.74373	+	1.74373i
$559$		−	15.5645i		−	0.658310i
$560$	18.3510	+	8.61687i	0.775470	+	0.364129i
$561$		0			0
$562$	−37.6272	−	37.6272i	−1.58721	−	1.58721i
$563$	−23.7106	−	23.7106i	−0.999281	−	0.999281i	0.000718770	−	1.00000i	$-0.499771\pi$
$563$	−23.7106	−	23.7106i	−0.999281	−	0.999281i	−1.00000		0.000718770i	$0.999771\pi$
$564$			2.47696i			0.104299i
$565$	22.5745	+	10.6001i	0.949717	+	0.445949i
$566$	66.1605			2.78093
$567$	−10.7876	+	10.7876i	−0.453038	+	0.453038i
$568$	−4.17584	−	4.17584i	−0.175214	−	0.175214i
$569$	−8.31880			−0.348742			−0.174371	−	0.984680i	$-0.555789\pi$
$569$	−8.31880			−0.348742			−0.174371	+	0.984680i	$0.555789\pi$
$570$	12.6970	−	4.58302i	0.531820	−	0.191961i
$571$		−	45.2601i		−	1.89408i	−0.321118	−	0.947039i	$-0.604059\pi$
$571$		−	45.2601i		−	1.89408i	0.321118	−	0.947039i	$-0.395941\pi$
$572$		0			0
$573$	−2.73710	+	2.73710i	−0.114344	+	0.114344i
$574$	21.6515			0.903715
$575$	−0.0684655	+	0.737236i	−0.00285521	+	0.0307449i
$576$	23.6125			0.983855
$577$	16.2169	+	16.2169i	0.675117	+	0.675117i	0.958891	−	0.283774i	$-0.0915866\pi$
$577$	16.2169	+	16.2169i	0.675117	+	0.675117i	−0.283774	+	0.958891i	$0.591587\pi$
$578$	27.7079	+	27.7079i	1.15250	+	1.15250i
$579$	0.601990			0.0250178
$580$	57.1824	−	20.6401i	2.37437	−	0.857033i
$581$	21.4062			0.888081
$582$	14.8369	−	14.8369i	0.615007	−	0.615007i
$583$		0			0
$584$			8.26259i			0.341908i
$585$	15.0222	+	7.05381i	0.621091	+	0.291639i
$586$	−48.9249			−2.02107
$587$	7.13944	+	7.13944i	0.294676	+	0.294676i	0.838924	−	0.544248i	$-0.183185\pi$
$587$	7.13944	+	7.13944i	0.294676	+	0.294676i	−0.544248	+	0.838924i	$0.683185\pi$
$588$	0.554489	−	0.554489i	0.0228668	−	0.0228668i
$589$	−37.6075			−1.54959
$590$	−14.9857	+	31.9144i	−0.616952	+	1.31389i
$591$			14.6670i			0.603321i
$592$	−18.8680	−	18.8680i	−0.775468	−	0.775468i
$593$	−9.47168	−	9.47168i	−0.388955	−	0.388955i	0.485359	−	0.874315i	$-0.338689\pi$
$593$	−9.47168	−	9.47168i	−0.388955	−	0.388955i	−0.874315	+	0.485359i	$0.838689\pi$
$594$		0			0
$595$	5.12760	−	1.85082i	0.210211	−	0.0758761i
$596$		−	33.0820i		−	1.35509i
$597$	−1.37676	−	1.37676i	−0.0563470	−	0.0563470i
$598$	0.715444	−	0.715444i	0.0292567	−	0.0292567i
$599$			40.0090i			1.63472i	0.576125	+	0.817362i	$0.304564\pi$
$599$			40.0090i			1.63472i	−0.576125	+	0.817362i	$0.695436\pi$
$600$	10.7319	−	8.90802i	0.438130	−	0.363668i
$601$		−	36.3601i		−	1.48316i	−0.670864	−	0.741580i	$-0.734077\pi$
$601$		−	36.3601i		−	1.48316i	0.670864	−	0.741580i	$-0.265923\pi$
$602$	−24.6082	+	24.6082i	−1.00295	+	1.00295i
$603$	−7.78204	+	7.78204i	−0.316909	+	0.316909i
$604$	46.7449			1.90202
$605$		0			0
$606$	2.81517			0.114358
$607$	−17.6282	+	17.6282i	−0.715506	+	0.715506i	−0.967681	−	0.252176i	$-0.918854\pi$
$607$	−17.6282	+	17.6282i	−0.715506	+	0.715506i	0.252176	+	0.967681i	$0.418854\pi$
$608$	−2.30696	+	2.30696i	−0.0935595	+	0.0935595i
$609$			10.7149i			0.434189i
$610$	−22.0219	+	46.8990i	−0.891641	+	1.89889i
$611$		−	2.96971i		−	0.120142i
$612$	−6.91198	+	6.91198i	−0.279400	+	0.279400i
$613$	−8.26677	−	8.26677i	−0.333892	−	0.333892i	0.520171	−	0.854062i	$-0.325868\pi$
$613$	−8.26677	−	8.26677i	−0.333892	−	0.333892i	−0.854062	+	0.520171i	$0.825868\pi$
$614$		−	50.5437i		−	2.03978i
$615$	1.95945	−	4.17295i	0.0790126	−	0.168270i
$616$		0			0
$617$	6.18386	+	6.18386i	0.248953	+	0.248953i	0.820541	−	0.571588i	$-0.193672\pi$
$617$	6.18386	+	6.18386i	0.248953	+	0.248953i	−0.571588	+	0.820541i	$0.693672\pi$
$618$	−1.76852	−	1.76852i	−0.0711403	−	0.0711403i
$619$			1.09866i			0.0441588i	0.999756	+	0.0220794i	$0.00702866\pi$
$619$			1.09866i			0.0441588i	−0.999756	+	0.0220794i	$0.992971\pi$
$620$	−74.6703	+	26.9524i	−2.99883	+	1.08243i
$621$	0.499664			0.0200508
$622$	40.0421	−	40.0421i	1.60554	−	1.60554i
$623$	7.72377	+	7.72377i	0.309446	+	0.309446i
$624$	−5.89884			−0.236143
$625$	4.60369	−	24.5725i	0.184148	−	0.982899i
$626$			34.1000i			1.36291i
$627$		0			0
$628$	−3.77153	+	3.77153i	−0.150501	+	0.150501i
$629$	−7.17502			−0.286087
$630$	−12.5983	−	34.9030i	−0.501929	−	1.39057i
$631$	−3.26083			−0.129812			−0.0649059	−	0.997891i	$-0.520675\pi$
$631$	−3.26083			−0.129812			−0.0649059	+	0.997891i	$0.520675\pi$
$632$	14.3210	+	14.3210i	0.569661	+	0.569661i
$633$	−10.5045	−	10.5045i	−0.417517	−	0.417517i
$634$	−71.7616			−2.85002
$635$	4.80717	+	2.25725i	0.190767	+	0.0895763i
$636$	−9.65825			−0.382974
$637$	−0.664797	+	0.664797i	−0.0263402	+	0.0263402i
$638$		0			0
$639$			3.34540i			0.132342i
$640$	−19.1654	+	40.8157i	−0.757580	+	1.61338i
$641$	−8.91236			−0.352017			−0.176009	−	0.984389i	$-0.556319\pi$
$641$	−8.91236			−0.352017			−0.176009	+	0.984389i	$0.556319\pi$
$642$	4.27820	+	4.27820i	0.168847	+	0.168847i
$643$	26.2341	−	26.2341i	1.03457	−	1.03457i	0.0351926	−	0.999381i	$-0.488796\pi$
$643$	26.2341	−	26.2341i	1.03457	−	1.03457i	0.999381	−	0.0351926i	$-0.0112045\pi$
$644$	−1.49768			−0.0590169
$645$	2.51578	+	6.96984i	0.0990586	+	0.274437i
$646$		−	9.53258i		−	0.375054i
$647$	15.5930	+	15.5930i	0.613023	+	0.613023i	0.943733	−	0.330709i	$-0.107288\pi$
$647$	15.5930	+	15.5930i	0.613023	+	0.613023i	−0.330709	+	0.943733i	$0.607288\pi$
$648$	19.4905	+	19.4905i	0.765657	+	0.765657i
$649$		0			0
$650$	−26.2874	+	21.8198i	−1.03108	+	0.855842i
$651$		−	13.9918i		−	0.548381i
$652$	63.5554	+	63.5554i	2.48902	+	2.48902i
$653$	−34.3520	+	34.3520i	−1.34430	+	1.34430i	−0.452571	+	0.891729i	$0.649493\pi$
$653$	−34.3520	+	34.3520i	−1.34430	+	1.34430i	−0.891729	+	0.452571i	$0.850507\pi$
$654$		−	4.68893i		−	0.183352i
$655$	−6.57194	+	2.37215i	−0.256787	+	0.0926877i
$656$		−	12.1071i		−	0.472703i
$657$	3.30971	−	3.30971i	0.129124	−	0.129124i
$658$	−4.69523	+	4.69523i	−0.183039	+	0.183039i
$659$	47.3029			1.84266			0.921329	−	0.388783i	$-0.127104\pi$
$659$	47.3029			1.84266			0.921329	+	0.388783i	$0.127104\pi$
$660$		0			0
$661$	−26.7159			−1.03913			−0.519564	−	0.854432i	$-0.673906\pi$
$661$	−26.7159			−1.03913			−0.519564	+	0.854432i	$0.673906\pi$
$662$	3.75945	−	3.75945i	0.146115	−	0.146115i
$663$	−1.12159	+	1.12159i	−0.0435591	+	0.0435591i
$664$		−	38.6755i		−	1.50090i
$665$	21.6848	+	10.1823i	0.840899	+	0.394852i
$666$			48.8396i			1.89250i
$667$	−0.726689	+	0.726689i	−0.0281375	+	0.0281375i
$668$	39.7796	+	39.7796i	1.53912	+	1.53912i
$669$		−	11.7152i		−	0.452937i
$670$	−7.69172	−	21.3095i	−0.297157	−	0.823260i
$671$		0			0
$672$	−0.858297	−	0.858297i	−0.0331095	−	0.0331095i
$673$	9.35877	+	9.35877i	0.360754	+	0.360754i	0.864090	−	0.503337i	$-0.167894\pi$
$673$	9.35877	+	9.35877i	0.360754	+	0.360754i	−0.503337	+	0.864090i	$0.667894\pi$
$674$			4.38355i			0.168848i
$675$	−16.7990	−	1.56008i	−0.646592	−	0.0600477i
$676$	−20.0210			−0.770039
$677$	24.3176	−	24.3176i	0.934601	−	0.934601i	−0.0633884	−	0.997989i	$-0.520191\pi$
$677$	24.3176	−	24.3176i	0.934601	−	0.934601i	0.997989	+	0.0633884i	$0.0201907\pi$
$678$	11.4728	+	11.4728i	0.440610	+	0.440610i
$679$	37.2376			1.42905
$680$	−3.34395	−	9.26424i	−0.128234	−	0.355268i
$681$		−	0.611726i		−	0.0234414i
$682$		0			0
$683$	27.9495	−	27.9495i	1.06946	−	1.06946i	0.0720555	−	0.997401i	$-0.477044\pi$
$683$	27.9495	−	27.9495i	1.06946	−	1.06946i	0.997401	−	0.0720555i	$-0.0229559\pi$
$684$	−42.9566			−1.64249
$685$	−15.7158	+	33.4693i	−0.600471	+	1.27880i
$686$	46.0640			1.75873
$687$	−0.0430682	−	0.0430682i	−0.00164315	−	0.00164315i
$688$	13.7604	+	13.7604i	0.524612	+	0.524612i
$689$	11.5796			0.441148
$690$	−0.204736	+	0.436018i	−0.00779418	+	0.0165989i
$691$	3.27424			0.124558			0.0622790	−	0.998059i	$-0.480163\pi$
$691$	3.27424			0.124558			0.0622790	+	0.998059i	$0.480163\pi$
$692$	−61.7773	+	61.7773i	−2.34842	+	2.34842i
$693$		0			0
$694$			52.2333i			1.98275i
$695$	3.27998	+	9.08703i	0.124417	+	0.344691i
$696$	19.3590			0.733801
$697$	−2.30202	−	2.30202i	−0.0871951	−	0.0871951i
$698$	−18.3301	+	18.3301i	−0.693803	+	0.693803i
$699$	−12.7977			−0.484052
$700$	50.3528	+	4.67616i	1.90316	+	0.176742i
$701$		−	5.84293i		−	0.220685i	−0.993894	−	0.110342i	$-0.964805\pi$
$701$		−	5.84293i		−	0.220685i	0.993894	−	0.110342i	$-0.0351947\pi$
$702$	16.3024	+	16.3024i	0.615295	+	0.615295i
$703$	−22.2957	−	22.2957i	−0.840897	−	0.840897i
$704$		0			0
$705$	0.480009	+	1.32984i	0.0180782	+	0.0500847i
$706$			26.6223i			1.00194i
$707$	3.53276	+	3.53276i	0.132863	+	0.132863i
$708$	−10.7376	+	10.7376i	−0.403545	+	0.403545i
$709$		−	39.9834i		−	1.50161i	−0.660525	−	0.750804i	$-0.729666\pi$
$709$		−	39.9834i		−	1.50161i	0.660525	−	0.750804i	$-0.270334\pi$
$710$	−6.23364	−	2.92707i	−0.233944	−	0.109851i
$711$		−	11.4731i		−	0.430273i
$712$	13.9548	−	13.9548i	0.522980	−	0.522980i
$713$	0.948930	−	0.948930i	0.0355377	−	0.0355377i
$714$	3.54657			0.132727
$715$		0			0
$716$	17.1125			0.639523
$717$	3.66356	−	3.66356i	0.136818	−	0.136818i
$718$	−5.63193	+	5.63193i	−0.210182	+	0.210182i
$719$		−	20.1992i		−	0.753303i	−0.926355	−	0.376652i	$-0.877075\pi$
$719$		−	20.1992i		−	0.753303i	0.926355	−	0.376652i	$-0.122925\pi$
$720$	−19.5171	+	7.04474i	−0.727360	+	0.262542i
$721$		−	4.43864i		−	0.165303i
$722$	−3.06039	+	3.06039i	−0.113896	+	0.113896i
$723$	4.50317	+	4.50317i	0.167475	+	0.167475i
$724$		−	36.9804i		−	1.37436i
$725$	26.7006	−	22.1627i	0.991634	−	0.823103i
$726$		0			0
$727$	26.5141	+	26.5141i	0.983354	+	0.983354i	0.999864	−	0.0165102i	$-0.00525558\pi$
$727$	26.5141	+	26.5141i	0.983354	+	0.983354i	−0.0165102	+	0.999864i	$0.505256\pi$
$728$	−23.9177	−	23.9177i	−0.886448	−	0.886448i
$729$		−	9.56083i		−	0.354105i
$730$	3.27130	+	9.06298i	0.121076	+	0.335436i
$731$	5.23276			0.193541
$732$	−15.7792	+	15.7792i	−0.583217	+	0.583217i
$733$	−22.5549	−	22.5549i	−0.833084	−	0.833084i	0.154853	−	0.987938i	$-0.450510\pi$
$733$	−22.5549	−	22.5549i	−0.833084	−	0.833084i	−0.987938	+	0.154853i	$0.950510\pi$
$734$	44.3456			1.63683
$735$	0.190243	−	0.405152i	0.00701722	−	0.0149442i
$736$		−	0.116420i		−	0.00429131i
$737$		0			0
$738$	−15.6696	+	15.6696i	−0.576805	+	0.576805i
$739$	39.1674			1.44080			0.720399	−	0.693560i	$-0.243959\pi$
$739$	39.1674			1.44080			0.720399	+	0.693560i	$0.243959\pi$
$740$	−60.2471	−	28.2896i	−2.21473	−	1.03995i
$741$	−6.97048			−0.256067
$742$	−18.3078	−	18.3078i	−0.672102	−	0.672102i
$743$	4.79767	+	4.79767i	0.176009	+	0.176009i	0.789614	−	0.613604i	$-0.210281\pi$
$743$	4.79767	+	4.79767i	0.176009	+	0.176009i	−0.613604	+	0.789614i	$0.710281\pi$
$744$	−25.2795			−0.926791
$745$	−6.41095	−	17.7612i	−0.234879	−	0.650722i
$746$	−42.9739			−1.57339
$747$	−15.4921	+	15.4921i	−0.566826	+	0.566826i
$748$		0			0
$749$			10.7374i			0.392337i
$750$	8.24471	−	14.0199i	0.301054	−	0.511934i
$751$	−22.0927			−0.806175			−0.403088	−	0.915161i	$-0.632063\pi$
$751$	−22.0927			−0.806175			−0.403088	+	0.915161i	$0.632063\pi$
$752$	2.62549	+	2.62549i	0.0957416	+	0.0957416i
$753$	−3.97199	+	3.97199i	−0.144747	+	0.144747i
$754$	−47.4190			−1.72690
$755$	25.0967	−	9.05869i	0.913361	−	0.329679i
$756$		−	34.1268i		−	1.24118i
$757$	23.6558	+	23.6558i	0.859785	+	0.859785i	0.991312	−	0.131528i	$-0.0419883\pi$
$757$	23.6558	+	23.6558i	0.859785	+	0.859785i	−0.131528	+	0.991312i	$0.541988\pi$
$758$	−37.9511	−	37.9511i	−1.37845	−	1.37845i
$759$		0			0
$760$	18.3967	−	39.1787i	0.667320	−	1.42116i
$761$		−	26.0552i		−	0.944500i	−0.881465	−	0.472250i	$-0.843442\pi$
$761$		−	26.0552i		−	0.944500i	0.881465	−	0.472250i	$-0.156558\pi$
$762$	2.44310	+	2.44310i	0.0885040	+	0.0885040i
$763$	5.88414	−	5.88414i	0.213020	−	0.213020i
$764$			25.3571i			0.917387i
$765$	−2.37147	+	5.05041i	−0.0857407	+	0.182598i
$766$		−	47.8971i		−	1.73059i
$767$	12.8737	−	12.8737i	0.464843	−	0.464843i
$768$	−13.1858	+	13.1858i	−0.475803	+	0.475803i
$769$	−51.2907			−1.84959			−0.924794	−	0.380468i	$-0.875763\pi$
$769$	−51.2907			−1.84959			−0.924794	+	0.380468i	$0.875763\pi$
$770$		0			0
$771$	−11.0274			−0.397141
$772$	2.78848	−	2.78848i	0.100360	−	0.100360i
$773$	11.6775	−	11.6775i	0.420009	−	0.420009i	−0.465198	−	0.885207i	$-0.654017\pi$
$773$	11.6775	−	11.6775i	0.420009	−	0.420009i	0.885207	+	0.465198i	$0.154017\pi$
$774$		−	35.6188i		−	1.28029i
$775$	−34.8663	+	28.9407i	−1.25243	+	1.03958i
$776$		−	67.2786i		−	2.41516i
$777$	8.29504	−	8.29504i	0.297583	−	0.297583i
$778$	−29.4492	−	29.4492i	−1.05581	−	1.05581i
$779$		−	14.3066i		−	0.512586i
$780$	−13.8400	+	4.99557i	−0.495551	+	0.178870i
$781$		0			0
$782$	0.240530	+	0.240530i	0.00860135	+	0.00860135i
$783$	−16.5586	−	16.5586i	−0.591758	−	0.591758i
$784$		−	1.17548i		−	0.0419814i
$785$	−1.29400	+	2.75577i	−0.0461847	+	0.0983575i
$786$	−4.54556			−0.162135
$787$	3.13084	−	3.13084i	0.111602	−	0.111602i	−0.649100	−	0.760703i	$-0.724854\pi$
$787$	3.13084	−	3.13084i	0.111602	−	0.111602i	0.760703	+	0.649100i	$0.224854\pi$
$788$	67.9392	+	67.9392i	2.42023	+	2.42023i
$789$	10.0581			0.358077
$790$	21.3783	+	10.0384i	0.760605	+	0.357149i
$791$			28.7945i			1.02381i
$792$		0			0
$793$	18.9183	−	18.9183i	0.671808	−	0.671808i
$794$	18.0572			0.640825
$795$	−5.18537	+	1.87167i	−0.183906	+	0.0663813i
$796$	−12.7546			−0.452074
$797$	−13.5917	−	13.5917i	−0.481444	−	0.481444i	0.424149	−	0.905593i	$-0.360573\pi$
$797$	−13.5917	−	13.5917i	−0.481444	−	0.481444i	−0.905593	+	0.424149i	$0.860573\pi$
$798$	11.0206	+	11.0206i	0.390125	+	0.390125i
$799$	0.998408			0.0353211
$800$	−0.363495	+	3.91411i	−0.0128515	+	0.138385i
$801$	−11.1797			−0.395014
$802$	21.1147	−	21.1147i	0.745587	−	0.745587i
$803$		0			0
$804$		−	9.75751i		−	0.344121i
$805$	−0.804083	+	0.290235i	−0.0283402	+	0.0102295i
$806$	61.9209			2.18107
$807$	12.0333	+	12.0333i	0.423592	+	0.423592i
$808$	6.38278	−	6.38278i	0.224545	−	0.224545i
$809$	30.8922			1.08611			0.543056	−	0.839696i	$-0.317267\pi$
$809$	30.8922			1.08611			0.543056	+	0.839696i	$0.317267\pi$
$810$	29.0951	+	13.6619i	1.02230	+	0.480030i
$811$			25.0343i			0.879071i	0.898225	+	0.439536i	$0.144857\pi$
$811$			25.0343i			0.879071i	−0.898225	+	0.439536i	$0.855143\pi$
$812$	49.6325	+	49.6325i	1.74176	+	1.74176i
$813$	12.5516	+	12.5516i	0.440202	+	0.440202i
$814$		0			0
$815$	46.4383	+	21.8056i	1.62666	+	0.763816i
$816$		−	1.98318i		−	0.0694250i
$817$	16.2603	+	16.2603i	0.568875	+	0.568875i
$818$	46.0282	−	46.0282i	1.60934	−	1.60934i
$819$			19.1612i			0.669548i
$820$	−10.2532	−	28.4059i	−0.358056	−	0.991978i
$821$			22.7905i			0.795392i	0.917517	+	0.397696i	$0.130190\pi$
$821$			22.7905i			0.795392i	−0.917517	+	0.397696i	$0.869810\pi$
$822$	−17.0098	+	17.0098i	−0.593283	+	0.593283i
$823$	−12.4769	+	12.4769i	−0.434918	+	0.434918i	−0.890298	−	0.455379i	$-0.849504\pi$
$823$	−12.4769	+	12.4769i	−0.434918	+	0.434918i	0.455379	+	0.890298i	$0.349504\pi$
$824$	−8.01946			−0.279371
$825$		0			0
$826$	−40.7077			−1.41640
$827$	−11.7801	+	11.7801i	−0.409633	+	0.409633i	−0.881611	−	0.471977i	$-0.843540\pi$
$827$	−11.7801	+	11.7801i	−0.409633	+	0.409633i	0.471977	+	0.881611i	$0.343540\pi$
$828$	1.08390	−	1.08390i	0.0376681	−	0.0376681i
$829$		−	41.8329i		−	1.45292i	−0.687210	−	0.726459i	$-0.741165\pi$
$829$		−	41.8329i		−	1.45292i	0.687210	−	0.726459i	$-0.258835\pi$
$830$	−15.3123	−	42.4220i	−0.531498	−	1.47249i
$831$			7.42723i			0.257648i
$832$	17.7482	−	17.7482i	0.615307	−	0.615307i
$833$	−0.223503	−	0.223503i	−0.00774391	−	0.00774391i
$834$			6.28515i			0.217637i
$835$	29.0660	+	13.6482i	1.00587	+	0.472316i
$836$		0			0
$837$	21.6227	+	21.6227i	0.747390	+	0.747390i
$838$	−24.4945	−	24.4945i	−0.846147	−	0.846147i
$839$		−	51.9231i		−	1.79259i	−0.443463	−	0.896293i	$-0.646250\pi$
$839$		−	51.9231i		−	1.79259i	0.443463	−	0.896293i	$-0.353750\pi$
$840$	14.5763	+	6.84445i	0.502931	+	0.236156i
$841$	19.1643			0.660837
$842$	−11.8794	+	11.8794i	−0.409389	+	0.409389i
$843$	−9.25015	−	9.25015i	−0.318592	−	0.318592i
$844$	−97.3160			−3.34976
$845$	−10.7490	+	3.87987i	−0.369777	+	0.133472i
$846$		−	6.79605i		−	0.233653i
$847$		0			0
$848$	−10.2374	+	10.2374i	−0.351554	+	0.351554i
$849$	16.2647			0.558202
$850$	−7.33575	−	8.83775i	−0.251614	−	0.303132i
$851$	1.12515			0.0385696
$852$	−2.09731	−	2.09731i	−0.0718528	−	0.0718528i
$853$	−9.90313	−	9.90313i	−0.339077	−	0.339077i	0.516943	−	0.856020i	$-0.327070\pi$
$853$	−9.90313	−	9.90313i	−0.339077	−	0.339077i	−0.856020	+	0.516943i	$0.827070\pi$
$854$	−59.8211			−2.04704
$855$	−23.0628	+	8.32455i	−0.788730	+	0.284694i
$856$	19.3997			0.663069
$857$	10.2364	−	10.2364i	0.349669	−	0.349669i	−0.510317	−	0.859986i	$-0.670472\pi$
$857$	10.2364	−	10.2364i	0.349669	−	0.349669i	0.859986	+	0.510317i	$0.170472\pi$
$858$		0			0
$859$		−	56.0426i		−	1.91215i	−0.293125	−	0.956074i	$-0.594695\pi$
$859$		−	56.0426i		−	1.91215i	0.293125	−	0.956074i	$-0.405305\pi$
$860$	43.9384	+	20.6317i	1.49829	+	0.703535i
$861$	5.32272			0.181398
$862$	−12.2803	−	12.2803i	−0.418270	−	0.418270i
$863$	12.1881	−	12.1881i	0.414889	−	0.414889i	−0.468548	−	0.883438i	$-0.655223\pi$
$863$	12.1881	−	12.1881i	0.414889	−	0.414889i	0.883438	+	0.468548i	$0.155223\pi$
$864$	2.65281			0.0902503
$865$	−21.1955	+	45.1392i	−0.720670	+	1.53478i
$866$		−	40.8738i		−	1.38895i
$867$	6.81161	+	6.81161i	0.231334	+	0.231334i
$868$	−64.8114	−	64.8114i	−2.19984	−	2.19984i
$869$		0			0
$870$	21.2343	−	7.66456i	0.719910	−	0.259853i
$871$			11.6986i			0.396393i
$872$	−10.6311	−	10.6311i	−0.360015	−	0.360015i
$873$	−26.9495	+	26.9495i	−0.912103	+	0.912103i
$874$			1.49485i			0.0505640i
$875$	27.9399	−	7.24729i	0.944540	−	0.245003i
$876$			4.14988i			0.140212i
$877$	−4.98514	+	4.98514i	−0.168336	+	0.168336i	−0.786248	−	0.617911i	$-0.787979\pi$
$877$	−4.98514	+	4.98514i	−0.168336	+	0.168336i	0.617911	+	0.786248i	$0.287979\pi$
$878$	−1.32953	+	1.32953i	−0.0448693	+	0.0448693i
$879$	−12.0275			−0.405678
$880$		0			0
$881$	−46.6330			−1.57111			−0.785553	−	0.618794i	$-0.787622\pi$
$881$	−46.6330			−1.57111			−0.785553	+	0.618794i	$0.787622\pi$
$882$	−1.52136	+	1.52136i	−0.0512268	+	0.0512268i
$883$	7.78322	−	7.78322i	0.261926	−	0.261926i	−0.563910	−	0.825836i	$-0.690704\pi$
$883$	7.78322	−	7.78322i	0.261926	−	0.261926i	0.825836	+	0.563910i	$0.190704\pi$
$884$			10.3907i			0.349476i
$885$	−3.68403	+	7.84572i	−0.123837	+	0.263731i
$886$		−	45.7080i		−	1.53559i
$887$	−27.5613	+	27.5613i	−0.925417	+	0.925417i	−0.997405	−	0.0719884i	$-0.977066\pi$
$887$	−27.5613	+	27.5613i	−0.925417	+	0.925417i	0.0719884	+	0.997405i	$0.477066\pi$
$888$	−14.9870	−	14.9870i	−0.502930	−	0.502930i
$889$			6.13169i			0.205650i
$890$	9.78168	−	20.8316i	0.327883	−	0.698277i
$891$		0			0
$892$	−54.2662	−	54.2662i	−1.81697	−	1.81697i
$893$	3.10245	+	3.10245i	0.103820	+	0.103820i
$894$		−	12.2848i		−	0.410864i
$895$	9.18744	−	3.31622i	0.307102	−	0.110849i
$896$	−52.0617			−1.73926
$897$	0.175882	−	0.175882i	0.00587254	−	0.00587254i
$898$	1.22709	+	1.22709i	0.0409486	+	0.0409486i
$899$	−62.8942			−2.09764
$900$	−39.8255	+	33.0570i	−1.32752	+	1.10190i
$901$			3.89303i			0.129696i
$902$		0			0
$903$	−6.04959	+	6.04959i	−0.201318	+	0.201318i
$904$	52.0241			1.73030
$905$	−7.16642	−	19.8542i	−0.238220	−	0.659977i
$906$	17.3584			0.576695
$907$	19.8803	+	19.8803i	0.660114	+	0.660114i	0.955407	−	0.295293i	$-0.0954171\pi$
$907$	19.8803	+	19.8803i	0.660114	+	0.660114i	−0.295293	+	0.955407i	$0.595417\pi$
$908$	−2.83358	−	2.83358i	−0.0940356	−	0.0940356i
$909$	−5.11345			−0.169602
$910$	−35.7040	−	16.7652i	−1.18358	−	0.555760i
$911$	−29.4839			−0.976845			−0.488423	−	0.872607i	$-0.662428\pi$
$911$	−29.4839			−0.976845			−0.488423	+	0.872607i	$0.662428\pi$
$912$	6.16252	−	6.16252i	0.204061	−	0.204061i
$913$		0			0
$914$			47.0585i			1.55656i
$915$	−5.41379	+	11.5295i	−0.178974	+	0.381153i
$916$	−0.398993			−0.0131831
$917$	−5.70423	−	5.70423i	−0.188370	−	0.188370i
$918$	−5.48082	+	5.48082i	−0.180894	+	0.180894i
$919$	−40.7832			−1.34531			−0.672657	−	0.739955i	$-0.734847\pi$
$919$	−40.7832			−1.34531			−0.672657	+	0.739955i	$0.734847\pi$
$920$	0.524380	+	1.45277i	0.0172883	+	0.0478964i
$921$		−	12.4255i		−	0.409433i
$922$	−62.8314	−	62.8314i	−2.06924	−	2.06924i
$923$	2.51454	+	2.51454i	0.0827672	+	0.0827672i
$924$		0			0
$925$	−37.8281	−	3.51301i	−1.24378	−	0.115507i
$926$			58.9725i			1.93796i
$927$	3.21232	+	3.21232i	0.105507	+	0.105507i
$928$	−3.85812	+	3.85812i	−0.126649	+	0.126649i
$929$		−	51.2738i		−	1.68224i	−0.540849	−	0.841119i	$-0.681897\pi$
$929$		−	51.2738i		−	1.68224i	0.540849	−	0.841119i	$-0.318103\pi$
$930$	−27.7283	+	10.0086i	−0.909247	+	0.328194i
$931$		−	1.38903i		−	0.0455235i
$932$	−59.2801	+	59.2801i	−1.94179	+	1.94179i
$933$	9.84382	−	9.84382i	0.322272	−	0.322272i
$934$	36.0504			1.17960
$935$		0			0
$936$	34.6194			1.13157
$937$	2.17822	−	2.17822i	0.0711594	−	0.0711594i	−0.670631	−	0.741791i	$-0.733977\pi$
$937$	2.17822	−	2.17822i	0.0711594	−	0.0711594i	0.741791	+	0.670631i	$0.233977\pi$
$938$	18.4960	−	18.4960i	0.603915	−	0.603915i
$939$			8.38302i			0.273569i
$940$	8.38342	+	3.93652i	0.273437	+	0.128395i
$941$			28.4352i			0.926960i	0.886107	+	0.463480i	$0.153399\pi$
$941$			28.4352i			0.926960i	−0.886107	+	0.463480i	$0.846601\pi$
$942$	−1.40053	+	1.40053i	−0.0456318	+	0.0456318i
$943$	0.360990	+	0.360990i	0.0117555	+	0.0117555i
$944$			22.7630i			0.740873i
$945$	−6.61343	−	18.3222i	−0.215135	−	0.596021i
$946$		0			0
$947$	−40.6526	−	40.6526i	−1.32103	−	1.32103i	−0.912941	−	0.408091i	$-0.866195\pi$
$947$	−40.6526	−	40.6526i	−1.32103	−	1.32103i	−0.408091	−	0.912941i	$-0.633805\pi$
$948$	7.19274	+	7.19274i	0.233609	+	0.233609i
$949$		−	4.97544i		−	0.161510i
$950$	4.66731	−	50.2575i	0.151428	−	1.63057i
$951$	−17.6416			−0.572068
$952$	8.04106	−	8.04106i	0.260612	−	0.260612i
$953$	13.5310	+	13.5310i	0.438313	+	0.438313i	0.891444	−	0.453131i	$-0.149693\pi$
$953$	13.5310	+	13.5310i	0.438313	+	0.438313i	−0.453131	+	0.891444i	$0.649693\pi$
$954$	26.4994			0.857951
$955$	4.91395	+	13.6139i	0.159012	+	0.440534i
$956$		−	33.9400i		−	1.09770i
$957$		0			0
$958$	47.4507	−	47.4507i	1.53306	−	1.53306i
$959$	−42.6911			−1.37857
$960$	−5.07894	+	10.8164i	−0.163922	+	0.349097i
$961$	51.1289			1.64932
$962$	36.7099	+	36.7099i	1.18357	+	1.18357i
$963$	−7.77087	−	7.77087i	−0.250413	−	0.250413i
$964$	41.7183			1.34366
$965$	0.956716	−	2.03747i	0.0307978	−	0.0655886i
$966$	−0.556154			−0.0178940
$967$	−12.6930	+	12.6930i	−0.408178	+	0.408178i	−0.881103	−	0.472925i	$-0.843198\pi$
$967$	−12.6930	+	12.6930i	−0.408178	+	0.408178i	0.472925	+	0.881103i	$0.343198\pi$
$968$		0			0
$969$		−	2.34346i		−	0.0752826i
$970$	−26.6367	−	73.7959i	−0.855254	−	2.36944i
$971$	−3.48594			−0.111869			−0.0559346	−	0.998434i	$-0.517814\pi$
$971$	−3.48594			−0.111869			−0.0559346	+	0.998434i	$0.517814\pi$
$972$	37.8300	+	37.8300i	1.21340	+	1.21340i
$973$	−7.88725	+	7.88725i	−0.252853	+	0.252853i
$974$	−94.6174			−3.03174
$975$	−6.46240	+	5.36410i	−0.206962	+	0.171789i
$976$			33.4509i			1.07074i
$977$	−18.2691	−	18.2691i	−0.584479	−	0.584479i	0.351652	−	0.936131i	$-0.385620\pi$
$977$	−18.2691	−	18.2691i	−0.584479	−	0.584479i	−0.936131	+	0.351652i	$0.885620\pi$
$978$	23.6009	+	23.6009i	0.754672	+	0.754672i
$979$		0			0
$980$	−0.995480	−	2.75793i	−0.0317994	−	0.0880989i
$981$			8.51693i			0.271925i
$982$	−32.3401	−	32.3401i	−1.03202	−	1.03202i
$983$	22.0803	−	22.0803i	0.704252	−	0.704252i	−0.261068	−	0.965320i	$-0.584075\pi$
$983$	22.0803	−	22.0803i	0.704252	−	0.704252i	0.965320	+	0.261068i	$0.0840748\pi$
$984$		−	9.61677i		−	0.306572i
$985$	49.6415	+	23.3097i	1.58171	+	0.742707i
$986$		−	15.9421i		−	0.507701i
$987$	−1.15426	+	1.15426i	−0.0367405	+	0.0367405i
$988$	−32.2880	+	32.2880i	−1.02722	+	1.02722i
$989$	−0.820573			−0.0260927
$990$		0			0
$991$	−19.5868			−0.622196			−0.311098	−	0.950378i	$-0.600697\pi$
$991$	−19.5868			−0.622196			−0.311098	+	0.950378i	$0.600697\pi$
$992$	5.03803	−	5.03803i	0.159958	−	0.159958i
$993$	0.924211	−	0.924211i	0.0293290	−	0.0293290i
$994$		−	7.95119i		−	0.252196i
$995$	−6.84775	+	2.47171i	−0.217088	+	0.0783585i
$996$		−	19.4248i		−	0.615498i
$997$	20.0210	−	20.0210i	0.634071	−	0.634071i	−0.315016	−	0.949086i	$-0.602010\pi$
$997$	20.0210	−	20.0210i	0.634071	−	0.634071i	0.949086	+	0.315016i	$0.102010\pi$
$998$	−9.01285	−	9.01285i	−0.285297	−	0.285297i
$999$			25.6381i			0.811154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.b.362.15		32
5.3	odd	4	inner	605.2.e.b.483.2		32
11.2	odd	10		605.2.m.e.282.4		32
11.3	even	5		605.2.m.c.112.1		32
11.4	even	5		605.2.m.d.457.4		32
11.5	even	5		605.2.m.e.602.1		32
11.6	odd	10		55.2.l.a.52.4	yes	32
11.7	odd	10		605.2.m.c.457.1		32
11.8	odd	10		605.2.m.d.112.4		32
11.9	even	5		55.2.l.a.7.1	✓	32
11.10	odd	2	inner	605.2.e.b.362.2		32
33.17	even	10		495.2.bj.a.217.1		32
33.20	odd	10		495.2.bj.a.172.4		32
44.31	odd	10		880.2.cm.a.337.3		32
44.39	even	10		880.2.cm.a.657.2		32
55.3	odd	20		605.2.m.c.233.1		32
55.8	even	20		605.2.m.d.233.4		32
55.9	even	10		275.2.bm.b.7.4		32
55.13	even	20		605.2.m.e.403.1		32
55.17	even	20		275.2.bm.b.118.4		32
55.18	even	20		605.2.m.c.578.1		32
55.28	even	20		55.2.l.a.8.1	yes	32
55.38	odd	20		605.2.m.e.118.4		32
55.39	odd	10		275.2.bm.b.107.1		32
55.42	odd	20		275.2.bm.b.18.1		32
55.43	even	4	inner	605.2.e.b.483.15		32
55.48	odd	20		605.2.m.d.578.4		32
55.53	odd	20		55.2.l.a.18.4	yes	32
165.53	even	20		495.2.bj.a.73.1		32
165.83	odd	20		495.2.bj.a.118.4		32
220.83	odd	20		880.2.cm.a.833.3		32
220.163	even	20		880.2.cm.a.513.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.1	✓	32	11.9	even	5
55.2.l.a.8.1	yes	32	55.28	even	20
55.2.l.a.18.4	yes	32	55.53	odd	20
55.2.l.a.52.4	yes	32	11.6	odd	10
275.2.bm.b.7.4		32	55.9	even	10
275.2.bm.b.18.1		32	55.42	odd	20
275.2.bm.b.107.1		32	55.39	odd	10
275.2.bm.b.118.4		32	55.17	even	20
495.2.bj.a.73.1		32	165.53	even	20
495.2.bj.a.118.4		32	165.83	odd	20
495.2.bj.a.172.4		32	33.20	odd	10
495.2.bj.a.217.1		32	33.17	even	10
605.2.e.b.362.2		32	11.10	odd	2	inner
605.2.e.b.362.15		32	1.1	even	1	trivial
605.2.e.b.483.2		32	5.3	odd	4	inner
605.2.e.b.483.15		32	55.43	even	4	inner
605.2.m.c.112.1		32	11.3	even	5
605.2.m.c.233.1		32	55.3	odd	20
605.2.m.c.457.1		32	11.7	odd	10
605.2.m.c.578.1		32	55.18	even	20
605.2.m.d.112.4		32	11.8	odd	10
605.2.m.d.233.4		32	55.8	even	20
605.2.m.d.457.4		32	11.4	even	5
605.2.m.d.578.4		32	55.48	odd	20
605.2.m.e.118.4		32	55.38	odd	20
605.2.m.e.282.4		32	11.2	odd	10
605.2.m.e.403.1		32	55.13	even	20
605.2.m.e.602.1		32	11.5	even	5
880.2.cm.a.337.3		32	44.31	odd	10
880.2.cm.a.513.2		32	220.163	even	20
880.2.cm.a.657.2		32	44.39	even	10
880.2.cm.a.833.3		32	220.83	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)

\(f(q)\)	\(=\)	\(q+(1.72010 - 1.72010i) q^{2} +(0.422864 - 0.422864i) q^{3} -3.91750i q^{4} +(-0.759172 - 2.10325i) q^{5} -1.45474i q^{6} +(1.82555 - 1.82555i) q^{7} +(-3.29830 - 3.29830i) q^{8} +2.64237i q^{9} +O(q^{10})\)	\(q+(1.72010 - 1.72010i) q^{2} +(0.422864 - 0.422864i) q^{3} -3.91750i q^{4} +(-0.759172 - 2.10325i) q^{5} -1.45474i q^{6} +(1.82555 - 1.82555i) q^{7} +(-3.29830 - 3.29830i) q^{8} +2.64237i q^{9} +(-4.92366 - 2.31195i) q^{10} +(-1.65657 - 1.65657i) q^{12} +(1.98612 + 1.98612i) q^{13} -6.28027i q^{14} +(-1.21041 - 0.568362i) q^{15} -3.51181 q^{16} +(-0.667728 + 0.667728i) q^{17} +(4.54515 + 4.54515i) q^{18} -4.14980 q^{19} +(-8.23948 + 2.97406i) q^{20} -1.54392i q^{21} +(0.104710 - 0.104710i) q^{23} -2.78946 q^{24} +(-3.84732 + 3.19345i) q^{25} +6.83265 q^{26} +(2.38596 + 2.38596i) q^{27} +(-7.15160 - 7.15160i) q^{28} -6.94005 q^{29} +(-3.05968 + 1.10440i) q^{30} +9.06250 q^{31} +(0.555921 - 0.555921i) q^{32} +2.29712i q^{34} +(-5.22550 - 2.45368i) q^{35} +10.3515 q^{36} +(5.37272 + 5.37272i) q^{37} +(-7.13807 + 7.13807i) q^{38} +1.67972 q^{39} +(-4.43317 + 9.44111i) q^{40} +3.44754i q^{41} +(-2.65570 - 2.65570i) q^{42} +(-3.91833 - 3.91833i) q^{43} +(5.55757 - 2.00601i) q^{45} -0.360222i q^{46} +(-0.747616 - 0.747616i) q^{47} +(-1.48502 + 1.48502i) q^{48} +0.334721i q^{49} +(-1.12471 + 12.1108i) q^{50} +0.564716i q^{51} +(7.78062 - 7.78062i) q^{52} +(2.91513 - 2.91513i) q^{53} +8.20817 q^{54} -12.0424 q^{56} +(-1.75480 + 1.75480i) q^{57} +(-11.9376 + 11.9376i) q^{58} -6.48185i q^{59} +(-2.22656 + 4.74180i) q^{60} -9.52525i q^{61} +(15.5884 - 15.5884i) q^{62} +(4.82379 + 4.82379i) q^{63} -8.93610i q^{64} +(2.66950 - 5.68511i) q^{65} +(2.94509 + 2.94509i) q^{67} +(2.61582 + 2.61582i) q^{68} -0.0885557i q^{69} +(-13.2090 + 4.76780i) q^{70} +1.26606 q^{71} +(8.71533 - 8.71533i) q^{72} +(-1.25255 - 1.25255i) q^{73} +18.4832 q^{74} +(-0.276494 + 2.97729i) q^{75} +16.2568i q^{76} +(2.88928 - 2.88928i) q^{78} -4.34195 q^{79} +(2.66607 + 7.38621i) q^{80} -5.90925 q^{81} +(5.93012 + 5.93012i) q^{82} +(5.86295 + 5.86295i) q^{83} -6.04831 q^{84} +(1.91132 + 0.897478i) q^{85} -13.4799 q^{86} +(-2.93470 + 2.93470i) q^{87} +4.23092i q^{89} +(6.10903 - 13.0101i) q^{90} +7.25153 q^{91} +(-0.410200 - 0.410200i) q^{92} +(3.83220 - 3.83220i) q^{93} -2.57195 q^{94} +(3.15041 + 8.72806i) q^{95} -0.470158i q^{96} +(10.1990 + 10.1990i) q^{97} +(0.575755 + 0.575755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5}+O(q^{10}) \) 32 * q - 4 * q^3 + 8 * q^5	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48} + 116 q^{53} - 80 q^{56} - 80 q^{58} + 104 q^{60} - 8 q^{67} - 80 q^{70} + 24 q^{71} - 76 q^{75} + 60 q^{78} + 8 q^{80} + 8 q^{81} - 20 q^{82} - 40 q^{86} + 80 q^{91} + 52 q^{92} + 32 q^{93} + 92 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Introduction

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