LMFDB - Embedded newform 845.2.f.f.408.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			408.5
Character	$\chi$	$=$	845.408
Dual form			845.2.f.f.437.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.37242i q^{2} +(1.65235 + 1.65235i) q^{3} -3.62837 q^{4} +(-0.598181 + 2.15457i) q^{5} +(3.92008 - 3.92008i) q^{6} -3.73834 q^{7} +3.86318i q^{8} +2.46055i q^{9} +(5.11155 + 1.41914i) q^{10} +(-1.27726 - 1.27726i) q^{11} +(-5.99536 - 5.99536i) q^{12} +8.86890i q^{14} +(-4.54852 + 2.57171i) q^{15} +1.90834 q^{16} +(-0.272435 - 0.272435i) q^{17} +5.83745 q^{18} +(-3.87278 - 3.87278i) q^{19} +(2.17042 - 7.81759i) q^{20} +(-6.17706 - 6.17706i) q^{21} +(-3.03020 + 3.03020i) q^{22} +(-6.53419 + 6.53419i) q^{23} +(-6.38334 + 6.38334i) q^{24} +(-4.28436 - 2.57765i) q^{25} +(0.891365 - 0.891365i) q^{27} +13.5641 q^{28} -0.764574i q^{29} +(6.10117 + 10.7910i) q^{30} +(-3.27268 + 3.27268i) q^{31} +3.19898i q^{32} -4.22098i q^{33} +(-0.646330 + 0.646330i) q^{34} +(2.23620 - 8.05452i) q^{35} -8.92778i q^{36} +1.15622 q^{37} +(-9.18786 + 9.18786i) q^{38} +(-8.32350 - 2.31088i) q^{40} +(2.15688 - 2.15688i) q^{41} +(-14.6546 + 14.6546i) q^{42} +(-1.33870 + 1.33870i) q^{43} +(4.63438 + 4.63438i) q^{44} +(-5.30143 - 1.47185i) q^{45} +(15.5018 + 15.5018i) q^{46} +1.94248 q^{47} +(3.15325 + 3.15325i) q^{48} +6.97517 q^{49} +(-6.11526 + 10.1643i) q^{50} -0.900318i q^{51} +(-1.18715 - 1.18715i) q^{53} +(-2.11469 - 2.11469i) q^{54} +(3.51599 - 1.98792i) q^{55} -14.4419i q^{56} -12.7984i q^{57} -1.81389 q^{58} +(-4.50612 + 4.50612i) q^{59} +(16.5037 - 9.33112i) q^{60} -3.71664 q^{61} +(7.76418 + 7.76418i) q^{62} -9.19836i q^{63} +11.4060 q^{64} -10.0139 q^{66} +11.0561i q^{67} +(0.988496 + 0.988496i) q^{68} -21.5936 q^{69} +(-19.1087 - 5.30521i) q^{70} +(-7.84488 + 7.84488i) q^{71} -9.50554 q^{72} -4.49691i q^{73} -2.74303i q^{74} +(-2.82009 - 11.3385i) q^{75} +(14.0519 + 14.0519i) q^{76} +(4.77484 + 4.77484i) q^{77} +7.15052i q^{79} +(-1.14153 + 4.11165i) q^{80} +10.3273 q^{81} +(-5.11702 - 5.11702i) q^{82} +11.4388 q^{83} +(22.4127 + 22.4127i) q^{84} +(0.749946 - 0.424015i) q^{85} +(3.17596 + 3.17596i) q^{86} +(1.26335 - 1.26335i) q^{87} +(4.93430 - 4.93430i) q^{88} +(-1.63827 + 1.63827i) q^{89} +(-3.49185 + 12.5772i) q^{90} +(23.7085 - 23.7085i) q^{92} -10.8153 q^{93} -4.60838i q^{94} +(10.6608 - 6.02756i) q^{95} +(-5.28585 + 5.28585i) q^{96} -0.882970i q^{97} -16.5480i q^{98} +(3.14277 - 3.14277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{3} - 80 q^{4} - 12 q^{10} + 64 q^{12} + 80 q^{16} + 8 q^{17} + 24 q^{22} + 36 q^{23} - 48 q^{25} - 64 q^{27} - 4 q^{30} + 80 q^{35} + 28 q^{38} - 24 q^{40} - 56 q^{42} + 76 q^{43} - 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) $ 72 * q - 4 * q^3 - 80 * q^4 - 12 * q^10 + 64 * q^12 + 80 * q^16 + 8 * q^17 + 24 * q^22 + 36 * q^23 - 48 * q^25 - 64 * q^27 - 4 * q^30 + 80 * q^35 + 28 * q^38 - 24 * q^40 - 56 * q^42 + 76 * q^43 - 76 * q^48 + 8 * q^49 - 16 * q^53 + 12 * q^55 + 8 * q^61 + 148 * q^62 - 120 * q^64 + 40 * q^66 - 48 * q^68 - 40 * q^69 - 164 * q^75 + 172 * q^77 + 16 * q^81 + 44 * q^82 + 20 * q^87 + 124 * q^88 - 300 * q^90 - 4 * q^92 - 92 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	2.37242i		−	1.67755i	−0.544475	−	0.838777i	$-0.683271\pi$
$2$		−	2.37242i		−	1.67755i	0.544475	−	0.838777i	$-0.316729\pi$
$3$	1.65235	+	1.65235i	0.953987	+	0.953987i	0.998987	−	0.0449999i	$-0.0143287\pi$
$3$	1.65235	+	1.65235i	0.953987	+	0.953987i	−0.0449999	+	0.998987i	$0.514329\pi$
$4$	−3.62837			−1.81419
$5$	−0.598181	+	2.15457i	−0.267515	+	0.963554i
$5$	−0.598181	+	2.15457i	−0.267515	+	0.963554i
$6$	3.92008	−	3.92008i	1.60036	−	1.60036i
$7$	−3.73834			−1.41296			−0.706479	−	0.707734i	$-0.749718\pi$
$7$	−3.73834			−1.41296			−0.706479	+	0.707734i	$0.749718\pi$
$8$			3.86318i			1.36584i
$9$			2.46055i			0.820183i
$10$	5.11155	+	1.41914i	1.61641	+	0.448770i
$11$	−1.27726	−	1.27726i	−0.385109	−	0.385109i	0.487830	−	0.872939i	$-0.337789\pi$
$11$	−1.27726	−	1.27726i	−0.385109	−	0.385109i	−0.872939	+	0.487830i	$0.837789\pi$
$12$	−5.99536	−	5.99536i	−1.73071	−	1.73071i
$13$		0			0
$13$		0			0
$14$			8.86890i			2.37031i
$15$	−4.54852	+	2.57171i	−1.17442	+	0.664012i
$16$	1.90834			0.477085
$17$	−0.272435	−	0.272435i	−0.0660752	−	0.0660752i	0.673297	−	0.739372i	$-0.264878\pi$
$17$	−0.272435	−	0.272435i	−0.0660752	−	0.0660752i	−0.739372	+	0.673297i	$0.764878\pi$
$18$	5.83745			1.37590
$19$	−3.87278	−	3.87278i	−0.888477	−	0.888477i	0.105900	−	0.994377i	$-0.466228\pi$
$19$	−3.87278	−	3.87278i	−0.888477	−	0.888477i	−0.994377	+	0.105900i	$0.966228\pi$
$20$	2.17042	−	7.81759i	0.485321	−	1.74807i
$21$	−6.17706	−	6.17706i	−1.34794	−	1.34794i
$22$	−3.03020	+	3.03020i	−0.646041	+	0.646041i
$23$	−6.53419	+	6.53419i	−1.36247	+	1.36247i	−0.491718	+	0.870755i	$0.663631\pi$
$23$	−6.53419	+	6.53419i	−1.36247	+	1.36247i	−0.870755	+	0.491718i	$0.836369\pi$
$24$	−6.38334	+	6.38334i	−1.30299	+	1.30299i
$25$	−4.28436	−	2.57765i	−0.856872	−	0.515529i
$26$		0			0
$27$	0.891365	−	0.891365i	0.171543	−	0.171543i
$28$	13.5641			2.56337
$29$		−	0.764574i		−	0.141978i	−0.997477	−	0.0709889i	$-0.977385\pi$
$29$		−	0.764574i		−	0.141978i	0.997477	−	0.0709889i	$-0.0226155\pi$
$30$	6.10117	+	10.7910i	1.11392	+	1.97016i
$31$	−3.27268	+	3.27268i	−0.587792	+	0.587792i	−0.937033	−	0.349241i	$-0.886439\pi$
$31$	−3.27268	+	3.27268i	−0.587792	+	0.587792i	0.349241	+	0.937033i	$0.386439\pi$
$32$			3.19898i			0.565506i
$33$		−	4.22098i		−	0.734779i
$34$	−0.646330	+	0.646330i	−0.110845	+	0.110845i
$35$	2.23620	−	8.05452i	0.377987	−	1.36146i
$36$		−	8.92778i		−	1.48796i
$37$	1.15622			0.190081			0.0950403	−	0.995473i	$-0.469702\pi$
$37$	1.15622			0.190081			0.0950403	+	0.995473i	$0.469702\pi$
$38$	−9.18786	+	9.18786i	−1.49047	+	1.49047i
$39$		0			0
$40$	−8.32350	−	2.31088i	−1.31606	−	0.365382i
$41$	2.15688	−	2.15688i	0.336848	−	0.336848i	−0.518332	−	0.855180i	$-0.673447\pi$
$41$	2.15688	−	2.15688i	0.336848	−	0.336848i	0.855180	+	0.518332i	$0.173447\pi$
$42$	−14.6546	+	14.6546i	−2.26125	+	2.26125i
$43$	−1.33870	+	1.33870i	−0.204150	+	0.204150i	−0.801775	−	0.597626i	$-0.796111\pi$
$43$	−1.33870	+	1.33870i	−0.204150	+	0.204150i	0.597626	+	0.801775i	$0.296111\pi$
$44$	4.63438	+	4.63438i	0.698660	+	0.698660i
$45$	−5.30143	−	1.47185i	−0.790290	−	0.219411i
$46$	15.5018	+	15.5018i	2.28562	+	2.28562i
$47$	1.94248			0.283340			0.141670	−	0.989914i	$-0.454753\pi$
$47$	1.94248			0.283340			0.141670	+	0.989914i	$0.454753\pi$
$48$	3.15325	+	3.15325i	0.455133	+	0.455133i
$49$	6.97517			0.996453
$50$	−6.11526	+	10.1643i	−0.864828	+	1.43745i
$51$		−	0.900318i		−	0.126070i
$52$		0			0
$53$	−1.18715	−	1.18715i	−0.163068	−	0.163068i	0.620856	−	0.783924i	$-0.286785\pi$
$53$	−1.18715	−	1.18715i	−0.163068	−	0.163068i	−0.783924	+	0.620856i	$0.786785\pi$
$54$	−2.11469	−	2.11469i	−0.287773	−	0.287773i
$55$	3.51599	−	1.98792i	0.474096	−	0.268051i
$56$		−	14.4419i		−	1.92988i
$57$		−	12.7984i		−	1.69519i
$58$	−1.81389			−0.238175
$59$	−4.50612	+	4.50612i	−0.586647	+	0.586647i	−0.936722	−	0.350075i	$-0.886156\pi$
$59$	−4.50612	+	4.50612i	−0.586647	+	0.586647i	0.350075	+	0.936722i	$0.386156\pi$
$60$	16.5037	−	9.33112i	2.13062	−	1.20464i
$61$	−3.71664			−0.475867			−0.237933	−	0.971281i	$-0.576470\pi$
$61$	−3.71664			−0.475867			−0.237933	+	0.971281i	$0.576470\pi$
$62$	7.76418	+	7.76418i	0.986052	+	0.986052i
$63$		−	9.19836i		−	1.15888i
$64$	11.4060			1.42575
$65$		0			0
$66$	−10.0139			−1.23263
$67$			11.0561i			1.35072i	0.737487	+	0.675361i	$0.236012\pi$
$67$			11.0561i			1.35072i	−0.737487	+	0.675361i	$0.763988\pi$
$68$	0.988496	+	0.988496i	0.119873	+	0.119873i
$69$	−21.5936			−2.59956
$70$	−19.1087	−	5.30521i	−2.28393	−	0.634094i
$71$	−7.84488	+	7.84488i	−0.931016	+	0.931016i	−0.997770	−	0.0667534i	$-0.978736\pi$
$71$	−7.84488	+	7.84488i	−0.931016	+	0.931016i	0.0667534	+	0.997770i	$0.478736\pi$
$72$	−9.50554			−1.12024
$73$		−	4.49691i		−	0.526323i	−0.964752	−	0.263161i	$-0.915235\pi$
$73$		−	4.49691i		−	0.526323i	0.964752	−	0.263161i	$-0.0847652\pi$
$74$		−	2.74303i		−	0.318870i
$75$	−2.82009	−	11.3385i	−0.325636	−	1.30925i
$76$	14.0519	+	14.0519i	1.61186	+	1.61186i
$77$	4.77484	+	4.77484i	0.544144	+	0.544144i
$78$		0			0
$79$			7.15052i			0.804496i	0.915531	+	0.402248i	$0.131771\pi$
$79$			7.15052i			0.804496i	−0.915531	+	0.402248i	$0.868229\pi$
$80$	−1.14153	+	4.11165i	−0.127627	+	0.459697i
$81$	10.3273			1.14748
$82$	−5.11702	−	5.11702i	−0.565080	−	0.565080i
$83$	11.4388			1.25557			0.627783	−	0.778388i	$-0.283962\pi$
$83$	11.4388			1.25557			0.627783	+	0.778388i	$0.283962\pi$
$84$	22.4127	+	22.4127i	2.44542	+	2.44542i
$85$	0.749946	−	0.424015i	0.0813431	−	0.0459909i
$86$	3.17596	+	3.17596i	0.342472	+	0.342472i
$87$	1.26335	−	1.26335i	0.135445	−	0.135445i
$88$	4.93430	−	4.93430i	0.525998	−	0.525998i
$89$	−1.63827	+	1.63827i	−0.173656	+	0.173656i	−0.788584	−	0.614927i	$-0.789185\pi$
$89$	−1.63827	+	1.63827i	−0.173656	+	0.173656i	0.614927	+	0.788584i	$0.289185\pi$
$90$	−3.49185	+	12.5772i	−0.368074	+	1.32575i
$91$		0			0
$92$	23.7085	−	23.7085i	2.47178	−	2.47178i
$93$	−10.8153			−1.12149
$94$		−	4.60838i		−	0.475318i
$95$	10.6608	−	6.02756i	1.09378	−	0.618415i
$96$	−5.28585	+	5.28585i	−0.539485	+	0.539485i
$97$		−	0.882970i		−	0.0896520i	−0.998995	−	0.0448260i	$-0.985727\pi$
$97$		−	0.882970i		−	0.0896520i	0.998995	−	0.0448260i	$-0.0142733\pi$
$98$		−	16.5480i		−	1.67160i
$99$	3.14277	−	3.14277i	0.315860	−	0.315860i
$100$	15.5452	+	9.35266i	1.55452	+	0.935266i
$101$		−	7.94189i		−	0.790248i	−0.918628	−	0.395124i	$-0.870702\pi$
$101$		−	7.94189i		−	0.790248i	0.918628	−	0.395124i	$-0.129298\pi$
$102$	−2.13593			−0.211489
$103$	10.7428	−	10.7428i	1.05852	−	1.05852i	0.0603388	−	0.998178i	$-0.480782\pi$
$103$	10.7428	−	10.7428i	1.05852	−	1.05852i	0.998178	−	0.0603388i	$-0.0192181\pi$
$104$		0			0
$105$	17.0039	−	9.61392i	1.65941	−	0.938222i
$106$	−2.81643	+	2.81643i	−0.273556	+	0.273556i
$107$	7.38827	−	7.38827i	0.714251	−	0.714251i	−0.253170	−	0.967422i	$-0.581473\pi$
$107$	7.38827	−	7.38827i	0.714251	−	0.714251i	0.967422	+	0.253170i	$0.0814733\pi$
$108$	−3.23420	+	3.23420i	−0.311211	+	0.311211i
$109$	4.13475	+	4.13475i	0.396037	+	0.396037i	0.876833	−	0.480796i	$-0.159652\pi$
$109$	4.13475	+	4.13475i	0.396037	+	0.396037i	−0.480796	+	0.876833i	$0.659652\pi$
$110$	−4.71618	−	8.34140i	−0.449670	−	0.795321i
$111$	1.91048	+	1.91048i	0.181334	+	0.181334i
$112$	−7.13401			−0.674101
$113$	−10.3692	−	10.3692i	−0.975452	−	0.975452i	0.0242536	−	0.999706i	$-0.492279\pi$
$113$	−10.3692	−	10.3692i	−0.975452	−	0.975452i	−0.999706	+	0.0242536i	$0.992279\pi$
$114$	−30.3632			−2.84377
$115$	−10.1698	−	17.9870i	−0.948334	−	1.67730i
$116$			2.77416i			0.257574i
$117$		0			0
$118$	10.6904	+	10.6904i	0.984132	+	0.984132i
$119$	1.01845	+	1.01845i	0.0933616	+	0.0933616i
$120$	−9.93497	−	17.5718i	−0.906935	−	1.60407i
$121$		−	7.73720i		−	0.703382i
$122$			8.81743i			0.798292i
$123$	7.12785			0.642697
$124$	11.8745	−	11.8745i	1.06636	−	1.06636i
$125$	8.11655	−	7.68906i	0.725966	−	0.687730i
$126$	−21.8224			−1.94409
$127$	4.97319	+	4.97319i	0.441300	+	0.441300i	0.892449	−	0.451149i	$-0.148986\pi$
$127$	4.97319	+	4.97319i	0.441300	+	0.441300i	−0.451149	+	0.892449i	$0.648986\pi$
$128$		−	20.6619i		−	1.82627i
$129$	−4.42401			−0.389513
$130$		0			0
$131$	−9.34748			−0.816693			−0.408347	−	0.912827i	$-0.633895\pi$
$131$	−9.34748			−0.816693			−0.408347	+	0.912827i	$0.633895\pi$
$132$			15.3153i			1.33302i
$133$	14.4778	+	14.4778i	1.25538	+	1.25538i
$134$	26.2298			2.26591
$135$	1.38731	+	2.45371i	0.119401	+	0.211181i
$136$	1.05247	−	1.05247i	0.0902482	−	0.0902482i
$137$	13.6982			1.17032			0.585158	−	0.810919i	$-0.301032\pi$
$137$	13.6982			1.17032			0.585158	+	0.810919i	$0.301032\pi$
$138$			51.2290i			4.36090i
$139$			8.98600i			0.762182i	0.924537	+	0.381091i	$0.124452\pi$
$139$			8.98600i			0.762182i	−0.924537	+	0.381091i	$0.875548\pi$
$140$	−8.11377	+	29.2248i	−0.685739	+	2.46994i
$141$	3.20967	+	3.20967i	0.270303	+	0.270303i
$142$	18.6113	+	18.6113i	1.56183	+	1.56183i
$143$		0			0
$144$			4.69556i			0.391297i
$145$	1.64733	+	0.457353i	0.136803	+	0.0379811i
$146$	−10.6685			−0.882935
$147$	11.5255	+	11.5255i	0.950603	+	0.950603i
$148$	−4.19518			−0.344842
$149$	−8.98770	−	8.98770i	−0.736301	−	0.736301i	0.235559	−	0.971860i	$-0.424308\pi$
$149$	−8.98770	−	8.98770i	−0.736301	−	0.736301i	−0.971860	+	0.235559i	$0.924308\pi$
$150$	−26.8996	+	6.69044i	−2.19634	+	0.546272i
$151$	−2.96123	−	2.96123i	−0.240981	−	0.240981i	0.576275	−	0.817256i	$-0.304506\pi$
$151$	−2.96123	−	2.96123i	−0.240981	−	0.240981i	−0.817256	+	0.576275i	$0.804506\pi$
$152$	14.9612	−	14.9612i	1.21352	−	1.21352i
$153$	0.670340	−	0.670340i	0.0541938	−	0.0541938i
$154$	11.3279	−	11.3279i	0.912830	−	0.912830i
$155$	−5.09358	−	9.00889i	−0.409126	−	0.723612i
$156$		0			0
$157$	−13.0366	+	13.0366i	−1.04044	+	1.04044i	−0.0412907	+	0.999147i	$0.513147\pi$
$157$	−13.0366	+	13.0366i	−1.04044	+	1.04044i	−0.999147	+	0.0412907i	$0.986853\pi$
$158$	16.9640			1.34959
$159$		−	3.92320i		−	0.311130i
$160$	−6.89244	−	1.91357i	−0.544895	−	0.151281i
$161$	24.4270	−	24.4270i	1.92512	−	1.92512i
$162$		−	24.5008i		−	1.92496i
$163$			15.8438i			1.24098i	0.784213	+	0.620492i	$0.213067\pi$
$163$			15.8438i			1.24098i	−0.784213	+	0.620492i	$0.786933\pi$
$164$	−7.82595	+	7.82595i	−0.611104	+	0.611104i
$165$	9.09441	+	2.52491i	0.707999	+	0.196564i
$166$		−	27.1375i		−	2.10628i
$167$	12.4834			0.965991			0.482996	−	0.875623i	$-0.339549\pi$
$167$	12.4834			0.965991			0.482996	+	0.875623i	$0.339549\pi$
$168$	23.8631	−	23.8631i	1.84108	−	1.84108i
$169$		0			0
$170$	−1.00594	−	1.77919i	−0.0771523	−	0.136457i
$171$	9.52916	−	9.52916i	0.728713	−	0.728713i
$172$	4.85730	−	4.85730i	0.370366	−	0.370366i
$173$	−11.4282	+	11.4282i	−0.868870	+	0.868870i	−0.992347	−	0.123477i	$-0.960595\pi$
$173$	−11.4282	+	11.4282i	−0.868870	+	0.868870i	0.123477	+	0.992347i	$0.460595\pi$
$174$	−2.99719	−	2.99719i	−0.227216	−	0.227216i
$175$	16.0164	+	9.63612i	1.21072	+	0.728422i
$176$	−2.43745	−	2.43745i	−0.183730	−	0.183730i
$177$	−14.8914			−1.11931
$178$	3.88666	+	3.88666i	0.291318	+	0.291318i
$179$	−18.4481			−1.37888			−0.689438	−	0.724345i	$-0.742142\pi$
$179$	−18.4481			−1.37888			−0.689438	+	0.724345i	$0.742142\pi$
$180$	19.2356	+	5.34043i	1.43373	+	0.398052i
$181$		−	2.18983i		−	0.162769i	−0.996683	−	0.0813844i	$-0.974066\pi$
$181$		−	2.18983i		−	0.162769i	0.996683	−	0.0813844i	$-0.0259342\pi$
$182$		0			0
$183$	−6.14120	−	6.14120i	−0.453971	−	0.453971i
$184$	−25.2427	−	25.2427i	−1.86092	−	1.86092i
$185$	−0.691626	+	2.49115i	−0.0508493	+	0.183153i
$186$			25.6583i			1.88136i
$187$			0.695942i			0.0508923i
$188$	−7.04805			−0.514032
$189$	−3.33222	+	3.33222i	−0.242384	+	0.242384i
$190$	−14.2999	−	25.2919i	−1.03742	−	1.83487i
$191$	8.14632			0.589447			0.294724	−	0.955583i	$-0.404772\pi$
$191$	8.14632			0.589447			0.294724	+	0.955583i	$0.404772\pi$
$192$	18.8468	+	18.8468i	1.36015	+	1.36015i
$193$			23.2471i			1.67336i	0.547691	+	0.836681i	$0.315507\pi$
$193$			23.2471i			1.67336i	−0.547691	+	0.836681i	$0.684493\pi$
$194$	−2.09477			−0.150396
$195$		0			0
$196$	−25.3085			−1.80775
$197$		−	22.0689i		−	1.57234i	−0.618008	−	0.786172i	$-0.712060\pi$
$197$		−	22.0689i		−	1.57234i	0.618008	−	0.786172i	$-0.287940\pi$
$198$	−7.45596	−	7.45596i	−0.529872	−	0.529872i
$199$	8.13701			0.576817			0.288409	−	0.957507i	$-0.406874\pi$
$199$	8.13701			0.576817			0.288409	+	0.957507i	$0.406874\pi$
$200$	9.95792	−	16.5513i	0.704131	−	1.17035i
$201$	−18.2687	+	18.2687i	−1.28857	+	1.28857i
$202$	−18.8415			−1.32568
$203$			2.85823i			0.200609i
$204$			3.26669i			0.228714i
$205$	3.35694	+	5.93735i	0.234459	+	0.414683i
$206$	−25.4864	−	25.4864i	−1.77572	−	1.77572i
$207$	−16.0777	−	16.0777i	−1.11748	−	1.11748i
$208$		0			0
$209$			9.89312i			0.684321i
$210$	−22.8082	−	40.3404i	−1.57392	−	2.78375i
$211$	−24.7734			−1.70547			−0.852737	−	0.522340i	$-0.825059\pi$
$211$	−24.7734			−1.70547			−0.852737	+	0.522340i	$0.825059\pi$
$212$	4.30744	+	4.30744i	0.295836	+	0.295836i
$213$	−25.9250			−1.77635
$214$	−17.5281	−	17.5281i	−1.19819	−	1.19819i
$215$	−2.08354	−	3.68511i	−0.142096	−	0.251322i
$216$	3.44350	+	3.44350i	0.234301	+	0.234301i
$217$	12.2344	−	12.2344i	0.830525	−	0.830525i
$218$	9.80935	−	9.80935i	0.664373	−	0.664373i
$219$	7.43048	−	7.43048i	0.502105	−	0.502105i
$220$	−12.7573	+	7.21291i	−0.860098	+	0.486295i
$221$		0			0
$222$	4.53245	−	4.53245i	0.304198	−	0.304198i
$223$	−29.5220			−1.97694			−0.988469	−	0.151425i	$-0.951614\pi$
$223$	−29.5220			−1.97694			−0.988469	+	0.151425i	$0.951614\pi$
$224$		−	11.9589i		−	0.799036i
$225$	6.34243	−	10.5419i	0.422828	−	0.702792i
$226$	−24.6001	+	24.6001i	−1.63637	+	1.63637i
$227$			7.86679i			0.522137i	0.965320	+	0.261068i	$0.0840748\pi$
$227$			7.86679i			0.522137i	−0.965320	+	0.261068i	$0.915925\pi$
$228$			46.4374i			3.07539i
$229$	−12.4410	+	12.4410i	−0.822125	+	0.822125i	−0.986412	−	0.164288i	$-0.947467\pi$
$229$	−12.4410	+	12.4410i	−0.822125	+	0.822125i	0.164288	+	0.986412i	$0.447467\pi$
$230$	−42.6727	+	24.1269i	−2.81376	+	1.59088i
$231$			15.7795i			1.03821i
$232$	2.95369			0.193919
$233$	−1.52992	+	1.52992i	−0.100228	+	0.100228i	−0.755443	−	0.655214i	$-0.772578\pi$
$233$	−1.52992	+	1.52992i	−0.100228	+	0.100228i	0.655214	+	0.755443i	$0.272578\pi$
$234$		0			0
$235$	−1.16196	+	4.18522i	−0.0757976	+	0.273013i
$236$	16.3499	−	16.3499i	1.06429	−	1.06429i
$237$	−11.8152	+	11.8152i	−0.767479	+	0.767479i
$238$	2.41620	−	2.41620i	0.156619	−	0.156619i
$239$	−7.05936	−	7.05936i	−0.456632	−	0.456632i	0.440916	−	0.897548i	$-0.354654\pi$
$239$	−7.05936	−	7.05936i	−0.456632	−	0.456632i	−0.897548	+	0.440916i	$0.854654\pi$
$240$	−8.68012	+	4.90769i	−0.560299	+	0.316790i
$241$	−10.2476	−	10.2476i	−0.660104	−	0.660104i	0.295300	−	0.955405i	$-0.404580\pi$
$241$	−10.2476	−	10.2476i	−0.660104	−	0.660104i	−0.955405	+	0.295300i	$0.904580\pi$
$242$	−18.3559			−1.17996
$243$	14.3903	+	14.3903i	0.923141	+	0.923141i
$244$	13.4854			0.863311
$245$	−4.17241	+	15.0285i	−0.266566	+	0.960136i
$246$		−	16.9102i		−	1.07816i
$247$		0			0
$248$	−12.6430	−	12.6430i	−0.802829	−	0.802829i
$249$	18.9009	+	18.9009i	1.19779	+	1.19779i
$250$	−18.2417	−	19.2559i	−1.15370	−	1.21785i
$251$		−	17.7643i		−	1.12127i	−0.828062	−	0.560636i	$-0.810557\pi$
$251$		−	17.7643i		−	1.12127i	0.828062	−	0.560636i	$-0.189443\pi$
$252$			33.3751i			2.10243i
$253$	16.6918			1.04940
$254$	11.7985	−	11.7985i	0.740304	−	0.740304i
$255$	1.93980	+	0.538553i	0.121475	+	0.0337255i
$256$	−26.2066			−1.63791
$257$	6.37449	+	6.37449i	0.397630	+	0.397630i	0.877396	−	0.479767i	$-0.159279\pi$
$257$	6.37449	+	6.37449i	0.397630	+	0.397630i	−0.479767	+	0.877396i	$0.659279\pi$
$258$			10.4956i			0.653428i
$259$	−4.32232			−0.268576
$260$		0			0
$261$	1.88127			0.116448
$262$			22.1761i			1.37005i
$263$	−3.01414	−	3.01414i	−0.185860	−	0.185860i	0.608044	−	0.793904i	$-0.291955\pi$
$263$	−3.01414	−	3.01414i	−0.185860	−	0.185860i	−0.793904	+	0.608044i	$0.791955\pi$
$264$	16.3064			1.00359
$265$	3.26794	−	1.84768i	0.200748	−	0.113502i
$266$	34.3473	−	34.3473i	2.10597	−	2.10597i
$267$	−5.41401			−0.331332
$268$		−	40.1158i		−	2.45046i
$269$			1.79761i			0.109602i	0.998497	+	0.0548011i	$0.0174525\pi$
$269$			1.79761i			0.109602i	−0.998497	+	0.0548011i	$0.982548\pi$
$270$	5.82122	−	3.29129i	0.354268	−	0.200301i
$271$	2.08531	+	2.08531i	0.126674	+	0.126674i	0.767601	−	0.640928i	$-0.221450\pi$
$271$	2.08531	+	2.08531i	0.126674	+	0.126674i	−0.640928	+	0.767601i	$0.721450\pi$
$272$	−0.519898	−	0.519898i	−0.0315235	−	0.0315235i
$273$		0			0
$274$		−	32.4979i		−	1.96327i
$275$	2.17992	+	8.76459i	0.131454	+	0.528524i
$276$	78.3496			4.71609
$277$	20.1491	+	20.1491i	1.21064	+	1.21064i	0.970815	+	0.239829i	$0.0770914\pi$
$277$	20.1491	+	20.1491i	1.21064	+	1.21064i	0.239829	+	0.970815i	$0.422909\pi$
$278$	21.3186			1.27860
$279$	−8.05260	−	8.05260i	−0.482097	−	0.482097i
$280$	31.1161	+	8.63885i	1.85954	+	0.516270i
$281$	2.57874	+	2.57874i	0.153835	+	0.153835i	0.779828	−	0.625993i	$-0.215306\pi$
$281$	2.57874	+	2.57874i	0.153835	+	0.153835i	−0.625993	+	0.779828i	$0.715306\pi$
$282$	7.61468	−	7.61468i	0.453447	−	0.453447i
$283$	5.52077	−	5.52077i	0.328176	−	0.328176i	−0.523717	−	0.851892i	$-0.675455\pi$
$283$	5.52077	−	5.52077i	0.328176	−	0.328176i	0.851892	+	0.523717i	$0.175455\pi$
$284$	28.4641	−	28.4641i	1.68904	−	1.68904i
$285$	27.5751	+	7.65576i	1.63341	+	0.453488i
$286$		0			0
$287$	−8.06314	+	8.06314i	−0.475952	+	0.475952i
$288$	−7.87125			−0.463818
$289$		−	16.8516i		−	0.991268i
$290$	1.08503	−	3.90815i	0.0637154	−	0.229495i
$291$	1.45898	−	1.45898i	0.0855269	−	0.0855269i
$292$			16.3164i			0.954848i
$293$		−	22.5598i		−	1.31796i	−0.752161	−	0.658979i	$-0.770988\pi$
$293$		−	22.5598i		−	1.31796i	0.752161	−	0.658979i	$-0.229012\pi$
$294$	27.3432	−	27.3432i	1.59469	−	1.59469i
$295$	−7.01329	−	12.4042i	−0.408329	−	0.722203i
$296$			4.46667i			0.259620i
$297$	−2.27701			−0.132126
$298$	−21.3226	+	21.3226i	−1.23518	+	1.23518i
$299$		0			0
$300$	10.2323	+	41.1402i	0.590765	+	2.37523i
$301$	5.00451	−	5.00451i	0.288455	−	0.288455i
$302$	−7.02528	+	7.02528i	−0.404259	+	0.404259i
$303$	13.1228	−	13.1228i	0.753886	−	0.753886i
$304$	−7.39057	−	7.39057i	−0.423878	−	0.423878i
$305$	2.22322	−	8.00777i	0.127301	−	0.458523i
$306$	−1.59033	−	1.59033i	−0.0909129	−	0.0909129i
$307$	−20.4085			−1.16477			−0.582387	−	0.812912i	$-0.697881\pi$
$307$	−20.4085			−1.16477			−0.582387	+	0.812912i	$0.697881\pi$
$308$	−17.3249	−	17.3249i	−0.987177	−	0.987177i
$309$	35.5017			2.01962
$310$	−21.3729	+	12.0841i	−1.21390	+	0.686331i
$311$			21.3762i			1.21213i	0.795413	+	0.606067i	$0.207254\pi$
$311$			21.3762i			1.21213i	−0.795413	+	0.606067i	$0.792746\pi$
$312$		0			0
$313$	−5.22723	−	5.22723i	−0.295461	−	0.295461i	0.543772	−	0.839233i	$-0.316996\pi$
$313$	−5.22723	−	5.22723i	−0.295461	−	0.295461i	−0.839233	+	0.543772i	$0.816996\pi$
$314$	30.9284	+	30.9284i	1.74539	+	1.74539i
$315$	19.8185	+	5.50228i	1.11665	+	0.310019i
$316$		−	25.9447i		−	1.45951i
$317$			25.8830i			1.45373i	0.686779	+	0.726867i	$0.259024\pi$
$317$			25.8830i			1.45373i	−0.686779	+	0.726867i	$0.740976\pi$
$318$	−9.30747			−0.521937
$319$	−0.976562	+	0.976562i	−0.0546770	+	0.0546770i
$320$	−6.82285	+	24.5751i	−0.381409	+	1.37379i
$321$	24.4161			1.36277
$322$	−57.9511	−	57.9511i	−3.22949	−	3.22949i
$323$			2.11016i			0.117413i
$324$	−37.4715			−2.08175
$325$		0			0
$326$	37.5882			2.08182
$327$			13.6641i			0.755628i
$328$	8.33241	+	8.33241i	0.460080	+	0.460080i
$329$	−7.26165			−0.400348
$330$	5.99015	−	21.5757i	0.329747	−	1.18771i
$331$	−7.44156	+	7.44156i	−0.409025	+	0.409025i	−0.881398	−	0.472374i	$-0.843397\pi$
$331$	−7.44156	+	7.44156i	−0.409025	+	0.409025i	0.472374	+	0.881398i	$0.343397\pi$
$332$	−41.5041			−2.27783
$333$			2.84492i			0.155901i
$334$		−	29.6158i		−	1.62050i
$335$	−23.8212	−	6.61357i	−1.30149	−	0.361338i
$336$	−11.7879	−	11.7879i	−0.643084	−	0.643084i
$337$	−6.67935	−	6.67935i	−0.363847	−	0.363847i	0.501380	−	0.865227i	$-0.332826\pi$
$337$	−6.67935	−	6.67935i	−0.363847	−	0.363847i	−0.865227	+	0.501380i	$0.832826\pi$
$338$		0			0
$339$		−	34.2672i		−	1.86114i
$340$	−2.72108	+	1.53849i	−0.147572	+	0.0834361i
$341$	8.36016			0.452728
$342$	−22.6072	−	22.6072i	−1.22246	−	1.22246i
$343$	0.0928245			0.00501205
$344$	−5.17164	−	5.17164i	−0.278836	−	0.278836i
$345$	12.9169	−	46.5249i	0.695421	−	2.50482i
$346$	27.1125	+	27.1125i	1.45758	+	1.45758i
$347$	−5.03872	+	5.03872i	−0.270492	+	0.270492i	−0.829298	−	0.558806i	$-0.811260\pi$
$347$	−5.03872	+	5.03872i	−0.270492	+	0.270492i	0.558806	+	0.829298i	$0.311260\pi$
$348$	−4.58389	+	4.58389i	−0.245722	+	0.245722i
$349$	−23.0603	+	23.0603i	−1.23439	+	1.23439i	−0.272125	+	0.962262i	$0.587726\pi$
$349$	−23.0603	+	23.0603i	−1.23439	+	1.23439i	−0.962262	+	0.272125i	$0.912274\pi$
$350$	22.8609	−	37.9976i	1.22197	−	2.03106i
$351$		0			0
$352$	4.08594	−	4.08594i	0.217781	−	0.217781i
$353$	12.9205			0.687688			0.343844	−	0.939027i	$-0.388271\pi$
$353$	12.9205			0.687688			0.343844	+	0.939027i	$0.388271\pi$
$354$			35.3287i			1.87770i
$355$	−12.2097	−	21.5950i	−0.648024	−	1.14614i
$356$	5.94425	−	5.94425i	0.315045	−	0.315045i
$357$			3.36569i			0.178131i
$358$			43.7666i			2.31314i
$359$	12.5304	−	12.5304i	0.661330	−	0.661330i	−0.294364	−	0.955693i	$-0.595108\pi$
$359$	12.5304	−	12.5304i	0.661330	−	0.661330i	0.955693	+	0.294364i	$0.0951077\pi$
$360$	5.68603	−	20.4804i	0.299680	−	1.07941i
$361$			10.9968i			0.578781i
$362$	−5.19520			−0.273053
$363$	12.7846	−	12.7846i	0.671017	−	0.671017i
$364$		0			0
$365$	9.68891	+	2.68996i	0.507140	+	0.140799i
$366$	−14.5695	+	14.5695i	−0.761561	+	0.761561i
$367$	−24.6452	+	24.6452i	−1.28647	+	1.28647i	−0.349552	+	0.936917i	$0.613666\pi$
$367$	−24.6452	+	24.6452i	−1.28647	+	1.28647i	−0.936917	+	0.349552i	$0.886334\pi$
$368$	−12.4694	+	12.4694i	−0.650015	+	0.650015i
$369$	5.30710	+	5.30710i	0.276277	+	0.276277i
$370$	5.91005	+	1.64083i	0.307249	+	0.0853025i
$371$	4.43799	+	4.43799i	0.230409	+	0.230409i
$372$	39.2418			2.03459
$373$	10.5600	+	10.5600i	0.546778	+	0.546778i	0.925507	−	0.378730i	$-0.123639\pi$
$373$	10.5600	+	10.5600i	0.546778	+	0.546778i	−0.378730	+	0.925507i	$0.623639\pi$
$374$	1.65107			0.0853746
$375$	26.1165	+	0.706362i	1.34865	+	0.0364764i
$376$			7.50416i			0.386997i
$377$		0			0
$378$	7.90543	+	7.90543i	0.406611	+	0.406611i
$379$	−22.9029	−	22.9029i	−1.17644	−	1.17644i	−0.980645	−	0.195796i	$-0.937271\pi$
$379$	−22.9029	−	22.9029i	−1.17644	−	1.17644i	−0.195796	−	0.980645i	$-0.562729\pi$
$380$	−38.6814	+	21.8702i	−1.98431	+	1.12192i
$381$			16.4350i			0.841988i
$382$		−	19.3265i		−	0.988829i
$383$	32.2292			1.64684			0.823418	−	0.567435i	$-0.192064\pi$
$383$	32.2292			1.64684			0.823418	+	0.567435i	$0.192064\pi$
$384$	34.1407	−	34.1407i	1.74224	−	1.74224i
$385$	−13.1440	+	7.43152i	−0.669878	+	0.378745i
$386$	55.1518			2.80715
$387$	−3.29394	−	3.29394i	−0.167440	−	0.167440i
$388$			3.20374i			0.162645i
$389$	11.7818			0.597359			0.298679	−	0.954354i	$-0.403454\pi$
$389$	11.7818			0.597359			0.298679	+	0.954354i	$0.403454\pi$
$390$		0			0
$391$	3.56028			0.180051
$392$			26.9463i			1.36100i
$393$	−15.4454	−	15.4454i	−0.779115	−	0.779115i
$394$	−52.3567			−2.63769
$395$	−15.4063	−	4.27730i	−0.775175	−	0.215214i
$396$	−11.4031	+	11.4031i	−0.573029	+	0.573029i
$397$	8.14777			0.408925			0.204462	−	0.978874i	$-0.434455\pi$
$397$	8.14777			0.408925			0.204462	+	0.978874i	$0.434455\pi$
$398$		−	19.3044i		−	0.967642i
$399$			47.8448i			2.39523i
$400$	−8.17601	−	4.91902i	−0.408800	−	0.245951i
$401$	−11.6766	−	11.6766i	−0.583101	−	0.583101i	0.352653	−	0.935754i	$-0.385280\pi$
$401$	−11.6766	−	11.6766i	−0.583101	−	0.583101i	−0.935754	+	0.352653i	$0.885280\pi$
$402$	43.3409	+	43.3409i	2.16165	+	2.16165i
$403$		0			0
$404$			28.8161i			1.43366i
$405$	−6.17762	+	22.2510i	−0.306968	+	1.10566i
$406$	6.78093			0.336532
$407$	−1.47679	−	1.47679i	−0.0732018	−	0.0732018i
$408$	3.47809			0.172191
$409$	2.98672	+	2.98672i	0.147684	+	0.147684i	0.777082	−	0.629399i	$-0.216699\pi$
$409$	2.98672	+	2.98672i	0.147684	+	0.147684i	−0.629399	+	0.777082i	$0.716699\pi$
$410$	14.0859	−	7.96408i	0.695652	−	0.393318i
$411$	22.6343	+	22.6343i	1.11647	+	1.11647i
$412$	−38.9788	+	38.9788i	−1.92035	+	1.92035i
$413$	16.8454	−	16.8454i	0.828908	−	0.828908i
$414$	−38.1430	+	38.1430i	−1.87463	+	1.87463i
$415$	−6.84245	+	24.6456i	−0.335882	+	1.20981i
$416$		0			0
$417$	−14.8481	+	14.8481i	−0.727112	+	0.727112i
$418$	23.4706			1.14799
$419$		−	17.0792i		−	0.834371i	−0.908821	−	0.417186i	$-0.863017\pi$
$419$		−	17.0792i		−	0.834371i	0.908821	−	0.417186i	$-0.136983\pi$
$420$	−61.6965	+	34.8829i	−3.01048	+	1.70211i
$421$	9.26544	−	9.26544i	0.451570	−	0.451570i	−0.444305	−	0.895875i	$-0.646549\pi$
$421$	9.26544	−	9.26544i	0.451570	−	0.451570i	0.895875	+	0.444305i	$0.146549\pi$
$422$			58.7730i			2.86102i
$423$			4.77957i			0.232391i
$424$	4.58619	−	4.58619i	0.222725	−	0.222725i
$425$	0.464968	+	1.86945i	0.0225543	+	0.0906817i
$426$			61.5051i			2.97993i
$427$	13.8941			0.672380
$428$	−26.8074	+	26.8074i	−1.29578	+	1.29578i
$429$		0			0
$430$	−8.74262	+	4.94303i	−0.421607	+	0.238374i
$431$	−7.57641	+	7.57641i	−0.364943	+	0.364943i	−0.865629	−	0.500686i	$-0.833081\pi$
$431$	−7.57641	+	7.57641i	−0.364943	+	0.364943i	0.500686	+	0.865629i	$0.333081\pi$
$432$	1.70103	−	1.70103i	0.0818406	−	0.0818406i
$433$	−3.61077	+	3.61077i	−0.173522	+	0.173522i	−0.788525	−	0.615003i	$-0.789155\pi$
$433$	−3.61077	+	3.61077i	−0.173522	+	0.173522i	0.615003	+	0.788525i	$0.289155\pi$
$434$	−29.0251	−	29.0251i	−1.39325	−	1.39325i
$435$	1.96626	+	3.47768i	0.0942750	+	0.166742i
$436$	−15.0024	−	15.0024i	−0.718485	−	0.718485i
$437$	50.6109			2.42105
$438$	−17.6282	−	17.6282i	−0.842309	−	0.842309i
$439$	−20.2393			−0.965969			−0.482985	−	0.875629i	$-0.660447\pi$
$439$	−20.2393			−0.965969			−0.482985	+	0.875629i	$0.660447\pi$
$440$	7.67969	+	13.5829i	0.366115	+	0.647539i
$441$			17.1627i			0.817273i
$442$		0			0
$443$	2.66083	+	2.66083i	0.126420	+	0.126420i	0.767486	−	0.641066i	$-0.221508\pi$
$443$	2.66083	+	2.66083i	0.126420	+	0.126420i	−0.641066	+	0.767486i	$0.721508\pi$
$444$	−6.93192	−	6.93192i	−0.328974	−	0.328974i
$445$	−2.54979	−	4.50975i	−0.120872	−	0.213783i
$446$			70.0385i			3.31642i
$447$		−	29.7017i		−	1.40484i
$448$	−42.6395			−2.01453
$449$	−21.7913	+	21.7913i	−1.02839	+	1.02839i	−0.0288081	+	0.999585i	$0.509171\pi$
$449$	−21.7913	+	21.7913i	−1.02839	+	1.02839i	−0.999585	+	0.0288081i	$0.990829\pi$
$450$	−25.0097	−	15.0469i	−1.17897	−	0.709317i
$451$	−5.50980			−0.259446
$452$	37.6233	+	37.6233i	1.76965	+	1.76965i
$453$		−	9.78600i		−	0.459786i
$454$	18.6633			0.875913
$455$		0			0
$456$	49.4426			2.31536
$457$		−	10.1798i		−	0.476191i	−0.971242	−	0.238096i	$-0.923477\pi$
$457$		−	10.1798i		−	0.476191i	0.971242	−	0.238096i	$-0.0765232\pi$
$458$	29.5153	+	29.5153i	1.37916	+	1.37916i
$459$	−0.485678			−0.0226695
$460$	36.8996	+	65.2635i	1.72045	+	3.04293i
$461$	13.6308	−	13.6308i	0.634848	−	0.634848i	−0.314432	−	0.949280i	$-0.601814\pi$
$461$	13.6308	−	13.6308i	0.634848	−	0.634848i	0.949280	+	0.314432i	$0.101814\pi$
$462$	37.4355			1.74166
$463$		−	16.7929i		−	0.780432i	−0.920723	−	0.390216i	$-0.872400\pi$
$463$		−	16.7929i		−	0.780432i	0.920723	−	0.390216i	$-0.127600\pi$
$464$		−	1.45907i		−	0.0677354i
$465$	6.46949	−	23.3023i	0.300015	−	1.08062i
$466$	3.62961	+	3.62961i	0.168139	+	0.168139i
$467$	−9.75781	−	9.75781i	−0.451538	−	0.451538i	0.444327	−	0.895865i	$-0.353443\pi$
$467$	−9.75781	−	9.75781i	−0.451538	−	0.451538i	−0.895865	+	0.444327i	$0.853443\pi$
$468$		0			0
$469$		−	41.3316i		−	1.90851i
$470$	9.92909	+	2.75665i	0.457995	+	0.127155i
$471$	−43.0823			−1.98513
$472$	−17.4080	−	17.4080i	−0.801266	−	0.801266i
$473$	3.41974			0.157240
$474$	28.0306	+	28.0306i	1.28749	+	1.28749i
$475$	6.60972	+	26.5750i	0.303275	+	1.21935i
$476$	−3.69533	−	3.69533i	−0.169375	−	0.169375i
$477$	2.92105	−	2.92105i	0.133746	−	0.133746i
$478$	−16.7478	+	16.7478i	−0.766025	+	0.766025i
$479$	−9.77217	+	9.77217i	−0.446502	+	0.446502i	−0.894190	−	0.447688i	$-0.852248\pi$
$479$	−9.77217	+	9.77217i	−0.446502	+	0.446502i	0.447688	+	0.894190i	$0.352248\pi$
$480$	−8.22685	−	14.5506i	−0.375503	−	0.664143i
$481$		0			0
$482$	−24.3115	+	24.3115i	−1.10736	+	1.10736i
$483$	80.7241			3.67307
$484$			28.0734i			1.27607i
$485$	1.90242	+	0.528176i	0.0863846	+	0.0239832i
$486$	34.1399	−	34.1399i	1.54862	−	1.54862i
$487$			20.4592i			0.927095i	0.886072	+	0.463547i	$0.153424\pi$
$487$			20.4592i			0.927095i	−0.886072	+	0.463547i	$0.846576\pi$
$488$		−	14.3580i		−	0.649958i
$489$	−26.1796	+	26.1796i	−1.18388	+	1.18388i
$490$	35.6539	+	9.89871i	1.61068	+	0.447178i
$491$		−	10.1889i		−	0.459817i	−0.973212	−	0.229908i	$-0.926157\pi$
$491$		−	10.1889i		−	0.459817i	0.973212	−	0.229908i	$-0.0738427\pi$
$492$	−25.8625			−1.16597
$493$	−0.208297	+	0.208297i	−0.00938121	+	0.00938121i
$494$		0			0
$495$	4.89137	+	8.65126i	0.219851	+	0.388845i
$496$	−6.24539	+	6.24539i	−0.280426	+	0.280426i
$497$	29.3268	−	29.3268i	1.31549	−	1.31549i
$498$	44.8408	−	44.8408i	2.00936	−	2.00936i
$499$	7.90149	+	7.90149i	0.353719	+	0.353719i	0.861491	−	0.507772i	$-0.169531\pi$
$499$	7.90149	+	7.90149i	0.353719	+	0.353719i	−0.507772	+	0.861491i	$0.669531\pi$
$500$	−29.4499	+	27.8988i	−1.31704	+	1.24767i
$501$	20.6269	+	20.6269i	0.921543	+	0.921543i
$502$	−42.1443			−1.88099
$503$	10.0106	+	10.0106i	0.446349	+	0.446349i	0.894139	−	0.447790i	$-0.147789\pi$
$503$	10.0106	+	10.0106i	0.446349	+	0.446349i	−0.447790	+	0.894139i	$0.647789\pi$
$504$	35.5349			1.58285
$505$	17.1114	+	4.75069i	0.761446	+	0.211403i
$506$		−	39.5998i		−	1.76043i
$507$		0			0
$508$	−18.0446	−	18.0446i	−0.800600	−	0.800600i
$509$	−16.3943	−	16.3943i	−0.726665	−	0.726665i	0.243289	−	0.969954i	$-0.421774\pi$
$509$	−16.3943	−	16.3943i	−0.726665	−	0.726665i	−0.969954	+	0.243289i	$0.921774\pi$
$510$	1.27767	−	4.60202i	0.0565764	−	0.203781i
$511$			16.8110i			0.743673i
$512$			20.8492i			0.921415i
$513$	−6.90412			−0.304824
$514$	15.1230	−	15.1230i	0.667045	−	0.667045i
$515$	16.7200	+	29.5722i	0.736769	+	1.30311i
$516$	16.0520			0.706648
$517$	−2.48106	−	2.48106i	−0.109117	−	0.109117i
$518$			10.2544i			0.450551i
$519$	−37.7669			−1.65778
$520$		0			0
$521$	−35.0306			−1.53472			−0.767359	−	0.641218i	$-0.778429\pi$
$521$	−35.0306			−1.53472			−0.767359	+	0.641218i	$0.778429\pi$
$522$		−	4.46316i		−	0.195347i
$523$	28.5551	+	28.5551i	1.24863	+	1.24863i	0.956327	+	0.292298i	$0.0944199\pi$
$523$	28.5551	+	28.5551i	1.24863	+	1.24863i	0.292298	+	0.956327i	$0.405580\pi$
$524$	33.9161			1.48163
$525$	10.5425	+	42.3870i	0.460111	+	1.84992i
$526$	−7.15081	+	7.15081i	−0.311790	+	0.311790i
$527$	1.78319			0.0776769
$528$		−	8.05506i		−	0.350551i
$529$		−	62.3912i		−	2.71266i
$530$	−4.38346	−	7.75293i	−0.190405	−	0.336766i
$531$	−11.0875	−	11.0875i	−0.481158	−	0.481158i
$532$	−52.5307	−	52.5307i	−2.27749	−	2.27749i
$533$		0			0
$534$			12.8443i			0.555827i
$535$	11.4990	+	20.3381i	0.497147	+	0.879292i
$536$	−42.7118			−1.84487
$537$	−30.4828	−	30.4828i	−1.31543	−	1.31543i
$538$	4.26468			0.183864
$539$	−8.90912	−	8.90912i	−0.383743	−	0.383743i
$540$	−5.03368	−	8.90296i	−0.216615	−	0.383122i
$541$	16.7846	+	16.7846i	0.721626	+	0.721626i	0.968936	−	0.247310i	$-0.0795467\pi$
$541$	16.7846	+	16.7846i	0.721626	+	0.721626i	−0.247310	+	0.968936i	$0.579547\pi$
$542$	4.94723	−	4.94723i	0.212502	−	0.212502i
$543$	3.61838	−	3.61838i	0.155279	−	0.155279i
$544$	0.871515	−	0.871515i	0.0373659	−	0.0373659i
$545$	−11.3819	+	6.43528i	−0.487549	+	0.275657i
$546$		0			0
$547$	10.0151	−	10.0151i	0.428216	−	0.428216i	−0.459804	−	0.888020i	$-0.652080\pi$
$547$	10.0151	−	10.0151i	0.428216	−	0.428216i	0.888020	+	0.459804i	$0.152080\pi$
$548$	−49.7022			−2.12317
$549$		−	9.14497i		−	0.390298i
$550$	20.7933	−	5.17168i	0.886628	−	0.220521i
$551$	−2.96103	+	2.96103i	−0.126144	+	0.126144i
$552$		−	83.4199i		−	3.55059i
$553$		−	26.7310i		−	1.13672i
$554$	47.8022	−	47.8022i	2.03092	−	2.03092i
$555$	−5.25907	+	2.97345i	−0.223235	+	0.126216i
$556$		−	32.6045i		−	1.38274i
$557$	−17.9619			−0.761072			−0.380536	−	0.924766i	$-0.624260\pi$
$557$	−17.9619			−0.761072			−0.380536	+	0.924766i	$0.624260\pi$
$558$	−19.1041	+	19.1041i	−0.808743	+	0.808743i
$559$		0			0
$560$	4.26743	−	15.3707i	0.180332	−	0.649532i
$561$	−1.14994	+	1.14994i	−0.0485506	+	0.0485506i
$562$	6.11785	−	6.11785i	0.258066	−	0.258066i
$563$	10.6362	−	10.6362i	0.448262	−	0.448262i	−0.446514	−	0.894777i	$-0.647335\pi$
$563$	10.6362	−	10.6362i	0.448262	−	0.448262i	0.894777	+	0.446514i	$0.147335\pi$
$564$	−11.6459	−	11.6459i	−0.490380	−	0.490380i
$565$	28.5438	−	16.1385i	1.20085	−	0.678953i
$566$	−13.0976	−	13.0976i	−0.550532	−	0.550532i
$567$	−38.6071			−1.62135
$568$	−30.3062	−	30.3062i	−1.27162	−	1.27162i
$569$	−21.9520			−0.920277			−0.460138	−	0.887847i	$-0.652200\pi$
$569$	−21.9520			−0.920277			−0.460138	+	0.887847i	$0.652200\pi$
$570$	18.1627	−	65.4197i	0.760751	−	2.74013i
$571$		−	12.0101i		−	0.502606i	−0.967908	−	0.251303i	$-0.919141\pi$
$571$		−	12.0101i		−	0.502606i	0.967908	−	0.251303i	$-0.0808590\pi$
$572$		0			0
$573$	13.4606	+	13.4606i	0.562325	+	0.562325i
$574$	19.1291	+	19.1291i	0.798435	+	0.798435i
$575$	44.8376	−	11.1520i	1.86986	−	0.465070i
$576$			28.0650i			1.16938i
$577$			21.1801i			0.881741i	0.897571	+	0.440870i	$0.145330\pi$
$577$			21.1801i			0.881741i	−0.897571	+	0.440870i	$0.854670\pi$
$578$	−39.9790			−1.66291
$579$	−38.4124	+	38.4124i	−1.59637	+	1.59637i
$580$	−5.97712	−	1.65945i	−0.248186	−	0.0689048i
$581$	−42.7619			−1.77406
$582$	−3.46131	−	3.46131i	−0.143476	−	0.143476i
$583$			3.03262i			0.125598i
$584$	17.3724			0.718873
$585$		0			0
$586$	−53.5214			−2.21095
$587$		−	34.5014i		−	1.42403i	−0.702166	−	0.712013i	$-0.747784\pi$
$587$		−	34.5014i		−	1.42403i	0.702166	−	0.712013i	$-0.252216\pi$
$588$	−41.8186	−	41.8186i	−1.72457	−	1.72457i
$589$	25.3488			1.04448
$590$	−29.4280	+	16.6385i	−1.21153	+	0.684994i
$591$	36.4656	−	36.4656i	1.50000	−	1.50000i
$592$	2.20645			0.0906845
$593$		−	28.3656i		−	1.16483i	−0.812890	−	0.582417i	$-0.802107\pi$
$593$		−	28.3656i		−	1.16483i	0.812890	−	0.582417i	$-0.197893\pi$
$594$			5.40203i			0.221648i
$595$	−2.80355	+	1.58511i	−0.114934	+	0.0649833i
$596$	32.6107	+	32.6107i	1.33579	+	1.33579i
$597$	13.4452	+	13.4452i	0.550276	+	0.550276i
$598$		0			0
$599$			3.01612i			0.123235i	0.998100	+	0.0616176i	$0.0196259\pi$
$599$			3.01612i			0.123235i	−0.998100	+	0.0616176i	$0.980374\pi$
$600$	43.8025	−	10.8945i	1.78823	−	0.444767i
$601$	13.5808			0.553973			0.276986	−	0.960874i	$-0.410664\pi$
$601$	13.5808			0.553973			0.276986	+	0.960874i	$0.410664\pi$
$602$	−11.8728	−	11.8728i	−0.483899	−	0.483899i
$603$	−27.2042			−1.10784
$604$	10.7444	+	10.7444i	0.437185	+	0.437185i
$605$	16.6704	+	4.62824i	0.677746	+	0.188165i
$606$	−31.1328	−	31.1328i	−1.26468	−	1.26468i
$607$	−25.3551	+	25.3551i	−1.02913	+	1.02913i	−0.0295695	+	0.999563i	$0.509414\pi$
$607$	−25.3551	+	25.3551i	−1.02913	+	1.02913i	−0.999563	+	0.0295695i	$0.990586\pi$
$608$	12.3890	−	12.3890i	0.502438	−	0.502438i
$609$	−4.72282	+	4.72282i	−0.191378	+	0.191378i
$610$	−18.9978	−	5.27442i	−0.769198	−	0.213555i
$611$		0			0
$612$	−2.43224	+	2.43224i	−0.0983175	+	0.0983175i
$613$	4.50152			0.181815			0.0909074	−	0.995859i	$-0.471023\pi$
$613$	4.50152			0.181815			0.0909074	+	0.995859i	$0.471023\pi$
$614$			48.4175i			1.95397i
$615$	−4.26374	+	15.3575i	−0.171931	+	0.619273i
$616$	−18.4461	+	18.4461i	−0.743213	+	0.743213i
$617$		−	38.4700i		−	1.54874i	−0.632731	−	0.774372i	$-0.718066\pi$
$617$		−	38.4700i		−	1.54874i	0.632731	−	0.774372i	$-0.281934\pi$
$618$		−	84.2250i		−	3.38803i
$619$	5.85514	−	5.85514i	0.235338	−	0.235338i	−0.579578	−	0.814916i	$-0.696783\pi$
$619$	5.85514	−	5.85514i	0.235338	−	0.235338i	0.814916	+	0.579578i	$0.196783\pi$
$620$	18.4814	+	32.6876i	0.742230	+	1.31277i
$621$			11.6487i			0.467446i
$622$	50.7134			2.03342
$623$	6.12441	−	6.12441i	0.245369	−	0.245369i
$624$		0			0
$625$	11.7115	+	22.0871i	0.468459	+	0.883485i
$626$	−12.4012	+	12.4012i	−0.495651	+	0.495651i
$627$	−16.3469	+	16.3469i	−0.652834	+	0.652834i
$628$	47.3018	−	47.3018i	1.88755	−	1.88755i
$629$	−0.314994	−	0.314994i	−0.0125596	−	0.0125596i
$630$	13.0537	−	47.0179i	0.520073	−	1.87324i
$631$	−26.4142	−	26.4142i	−1.05153	−	1.05153i	−0.998598	−	0.0529351i	$-0.983142\pi$
$631$	−26.4142	−	26.4142i	−1.05153	−	1.05153i	−0.0529351	−	0.998598i	$-0.516858\pi$
$632$	−27.6237			−1.09881
$633$	−40.9345	−	40.9345i	−1.62700	−	1.62700i
$634$	61.4053			2.43872
$635$	−13.6900	+	7.74023i	−0.543270	+	0.307162i
$636$			14.2348i			0.564448i
$637$		0			0
$638$	2.31681	+	2.31681i	0.0917235	+	0.0917235i
$639$	−19.3027	−	19.3027i	−0.763603	−	0.763603i
$640$	44.5174	+	12.3595i	1.75971	+	0.488553i
$641$		−	3.43214i		−	0.135561i	−0.997700	−	0.0677806i	$-0.978408\pi$
$641$		−	3.43214i		−	0.135561i	0.997700	−	0.0677806i	$-0.0215918\pi$
$642$		−	57.9252i		−	2.28613i
$643$	16.4627			0.649227			0.324614	−	0.945847i	$-0.394766\pi$
$643$	16.4627			0.649227			0.324614	+	0.945847i	$0.394766\pi$
$644$	−88.6302	+	88.6302i	−3.49252	+	3.49252i
$645$	2.64636	−	9.53185i	0.104200	−	0.375316i
$646$	5.00619			0.196966
$647$	13.4904	+	13.4904i	0.530364	+	0.530364i	0.920681	−	0.390317i	$-0.127635\pi$
$647$	13.4904	+	13.4904i	0.530364	+	0.530364i	−0.390317	+	0.920681i	$0.627635\pi$
$648$			39.8964i			1.56728i
$649$	11.5110			0.451846
$650$		0			0
$651$	40.4311			1.58462
$652$		−	57.4872i		−	2.25137i
$653$	−27.0722	−	27.0722i	−1.05942	−	1.05942i	−0.998120	−	0.0612973i	$-0.980476\pi$
$653$	−27.0722	−	27.0722i	−1.05942	−	1.05942i	−0.0612973	−	0.998120i	$-0.519524\pi$
$654$	32.4171			1.26761
$655$	5.59149	−	20.1398i	0.218477	−	0.786928i
$656$	4.11605	−	4.11605i	0.160705	−	0.160705i
$657$	11.0649			0.431681
$658$			17.2277i			0.671605i
$659$			39.2882i			1.53045i	0.643763	+	0.765225i	$0.277372\pi$
$659$			39.2882i			1.53045i	−0.643763	+	0.765225i	$0.722628\pi$
$660$	−32.9979	−	9.16131i	−1.28444	−	0.356604i
$661$	19.1671	+	19.1671i	0.745515	+	0.745515i	0.973633	−	0.228119i	$-0.0732574\pi$
$661$	19.1671	+	19.1671i	0.745515	+	0.745515i	−0.228119	+	0.973633i	$0.573257\pi$
$662$	17.6545	+	17.6545i	0.686161	+	0.686161i
$663$		0			0
$664$			44.1900i			1.71490i
$665$	−39.8537	+	22.5331i	−1.54546	+	0.873794i
$666$	6.74935			0.261532
$667$	4.99587	+	4.99587i	0.193441	+	0.193441i
$668$	−45.2943			−1.75249
$669$	−48.7808	−	48.7808i	−1.88597	−	1.88597i
$670$	−15.6902	+	56.5140i	−0.606164	+	2.18332i
$671$	4.74713	+	4.74713i	0.183261	+	0.183261i
$672$	19.7603	−	19.7603i	0.762270	−	0.762270i
$673$	−5.02239	+	5.02239i	−0.193599	+	0.193599i	−0.797249	−	0.603650i	$-0.793712\pi$
$673$	−5.02239	+	5.02239i	−0.193599	+	0.193599i	0.603650	+	0.797249i	$0.293712\pi$
$674$	−15.8462	+	15.8462i	−0.610373	+	0.610373i
$675$	−6.11655	+	1.52130i	−0.235426	+	0.0585550i
$676$		0			0
$677$	19.2265	−	19.2265i	0.738933	−	0.738933i	−0.233439	−	0.972372i	$-0.574998\pi$
$677$	19.2265	−	19.2265i	0.738933	−	0.738933i	0.972372	+	0.233439i	$0.0749978\pi$
$678$	−81.2961			−3.12216
$679$			3.30084i			0.126675i
$680$	1.63805	+	2.89718i	0.0628163	+	0.111102i
$681$	−12.9987	+	12.9987i	−0.498112	+	0.498112i
$682$		−	19.8338i		−	0.759475i
$683$		−	4.61676i		−	0.176655i	−0.996091	−	0.0883277i	$-0.971848\pi$
$683$		−	4.61676i		−	0.176655i	0.996091	−	0.0883277i	$-0.0281523\pi$
$684$	−34.5753	+	34.5753i	−1.32202	+	1.32202i
$685$	−8.19401	+	29.5138i	−0.313077	+	1.12766i
$686$		−	0.220219i		−	0.00840798i
$687$	−41.1139			−1.56859
$688$	−2.55469	+	2.55469i	−0.0973967	+	0.0973967i
$689$		0			0
$690$	−110.377	−	30.6442i	−4.20197	−	1.16661i
$691$	7.48635	−	7.48635i	0.284794	−	0.284794i	−0.550223	−	0.835018i	$-0.685457\pi$
$691$	7.48635	−	7.48635i	0.284794	−	0.284794i	0.835018	+	0.550223i	$0.185457\pi$
$692$	41.4658	−	41.4658i	1.57629	−	1.57629i
$693$	−11.7487	+	11.7487i	−0.446297	+	0.446297i
$694$	11.9539	+	11.9539i	0.453766	+	0.453766i
$695$	−19.3610	−	5.37525i	−0.734404	−	0.203895i
$696$	4.88054	+	4.88054i	0.184996	+	0.184996i
$697$	−1.17522			−0.0445146
$698$	54.7086	+	54.7086i	2.07075	+	2.07075i
$699$	−5.05594			−0.191233
$700$	−58.1134	−	34.9634i	−2.19648	−	1.32149i
$701$		−	48.9646i		−	1.84937i	−0.380735	−	0.924684i	$-0.624329\pi$
$701$		−	48.9646i		−	1.84937i	0.380735	−	0.924684i	$-0.375671\pi$
$702$		0			0
$703$	−4.47777	−	4.47777i	−0.168882	−	0.168882i
$704$	−14.5685	−	14.5685i	−0.549070	−	0.549070i
$705$	−8.83542	+	4.99550i	−0.332761	+	0.188141i
$706$		−	30.6528i		−	1.15363i
$707$			29.6895i			1.11659i
$708$	54.0316			2.03063
$709$	17.4186	−	17.4186i	0.654169	−	0.654169i	−0.299825	−	0.953994i	$-0.596928\pi$
$709$	17.4186	−	17.4186i	0.654169	−	0.654169i	0.953994	+	0.299825i	$0.0969284\pi$
$710$	−51.2324	+	28.9665i	−1.92272	+	1.08709i
$711$	−17.5942			−0.659834
$712$	−6.32893	−	6.32893i	−0.237187	−	0.237187i
$713$		−	42.7687i		−	1.60170i
$714$	7.98484			0.298825
$715$		0			0
$716$	66.9366			2.50154
$717$		−	23.3291i		−	0.871242i
$718$	−29.7274	−	29.7274i	−1.10942	−	1.10942i
$719$	−46.6034			−1.73801			−0.869007	−	0.494799i	$-0.835242\pi$
$719$	−46.6034			−1.73801			−0.869007	+	0.494799i	$0.835242\pi$
$720$	−10.1169	−	2.80879i	−0.377035	−	0.104678i
$721$	−40.1601	+	40.1601i	−1.49564	+	1.49564i
$722$	26.0891			0.970937
$723$		−	33.8652i		−	1.25946i
$724$			7.94552i			0.295293i
$725$	−1.97080	+	3.27571i	−0.0731937	+	0.121657i
$726$	−30.3304	−	30.3304i	−1.12567	−	1.12567i
$727$	16.4412	+	16.4412i	0.609770	+	0.609770i	0.942886	−	0.333116i	$-0.108100\pi$
$727$	16.4412	+	16.4412i	0.609770	+	0.609770i	−0.333116	+	0.942886i	$0.608100\pi$
$728$		0			0
$729$			16.5738i			0.613846i
$730$	6.38172	−	22.9861i	0.236198	−	0.850755i
$731$	0.729418			0.0269785
$732$	22.2826	+	22.2826i	0.823588	+	0.823588i
$733$	−30.6968			−1.13381			−0.566907	−	0.823782i	$-0.691860\pi$
$733$	−30.6968			−1.13381			−0.566907	+	0.823782i	$0.691860\pi$
$734$	58.4687	+	58.4687i	2.15812	+	2.15812i
$735$	−31.7267	+	17.9381i	−1.17026	+	0.661657i
$736$	−20.9028	−	20.9028i	−0.770486	−	0.770486i
$737$	14.1216	−	14.1216i	0.520176	−	0.520176i
$738$	12.5907	−	12.5907i	0.463469	−	0.463469i
$739$	24.4091	−	24.4091i	0.897902	−	0.897902i	−0.0973480	−	0.995250i	$-0.531036\pi$
$739$	24.4091	−	24.4091i	0.897902	−	0.897902i	0.995250	+	0.0973480i	$0.0310360\pi$
$740$	2.50948	−	9.03881i	0.0922502	−	0.332273i
$741$		0			0
$742$	10.5288	−	10.5288i	0.386523	−	0.386523i
$743$	−0.307988			−0.0112990			−0.00564949	−	0.999984i	$-0.501798\pi$
$743$	−0.307988			−0.0112990			−0.00564949	+	0.999984i	$0.501798\pi$
$744$		−	41.7813i		−	1.53178i
$745$	24.7409	−	13.9884i	0.906437	−	0.512494i
$746$	25.0528	−	25.0528i	0.917249	−	0.917249i
$747$			28.1456i			1.02979i
$748$		−	2.52514i		−	0.0923282i
$749$	−27.6199	+	27.6199i	−1.00921	+	1.00921i
$750$	1.67579	−	61.9592i	0.0611911	−	2.26243i
$751$			20.9010i			0.762690i	0.924433	+	0.381345i	$0.124539\pi$
$751$			20.9010i			0.762690i	−0.924433	+	0.381345i	$0.875461\pi$
$752$	3.70691			0.135177
$753$	29.3529	−	29.3529i	1.06968	−	1.06968i
$754$		0			0
$755$	8.15153	−	4.60883i	0.296665	−	0.167733i
$756$	12.0905	−	12.0905i	0.439729	−	0.439729i
$757$	−23.7489	+	23.7489i	−0.863168	+	0.863168i	−0.991705	−	0.128536i	$-0.958972\pi$
$757$	−23.7489	+	23.7489i	−0.863168	+	0.863168i	0.128536	+	0.991705i	$0.458972\pi$
$758$	−54.3352	+	54.3352i	−1.97354	+	1.97354i
$759$	27.5807	+	27.5807i	1.00112	+	1.00112i
$760$	23.2855	+	41.1846i	0.844656	+	1.49392i
$761$	33.9474	+	33.9474i	1.23059	+	1.23059i	0.963736	+	0.266856i	$0.0859850\pi$
$761$	33.9474	+	33.9474i	1.23059	+	1.23059i	0.266856	+	0.963736i	$0.414015\pi$
$762$	38.9906			1.41248
$763$	−15.4571	−	15.4571i	−0.559584	−	0.559584i
$764$	−29.5579			−1.06937
$765$	1.04331	+	1.84528i	0.0377210	+	0.0667162i
$766$		−	76.4612i		−	2.76266i
$767$		0			0
$768$	−43.3025	−	43.3025i	−1.56255	−	1.56255i
$769$	16.5558	+	16.5558i	0.597016	+	0.597016i	0.939517	−	0.342502i	$-0.111274\pi$
$769$	16.5558	+	16.5558i	0.597016	+	0.597016i	−0.342502	+	0.939517i	$0.611274\pi$
$770$	17.6307	+	31.1830i	0.635365	+	1.12376i
$771$			21.0658i			0.758667i
$772$		−	84.3490i		−	3.03579i
$773$	−26.8939			−0.967307			−0.483653	−	0.875260i	$-0.660690\pi$
$773$	−26.8939			−0.967307			−0.483653	+	0.875260i	$0.660690\pi$
$774$	−7.81460	+	7.81460i	−0.280890	+	0.280890i
$775$	22.4572	−	5.58553i	0.806686	−	0.200638i
$776$	3.41107			0.122450
$777$	−7.14201	−	7.14201i	−0.256218	−	0.256218i
$778$		−	27.9513i		−	1.00210i
$779$	−16.7062			−0.598563
$780$		0			0
$781$	20.0399			0.717086
$782$		−	8.44649i		−	0.302046i
$783$	−0.681514	−	0.681514i	−0.0243553	−	0.0243553i
$784$	13.3110			0.475392
$785$	−20.2901	−	35.8867i	−0.724186	−	1.28085i
$786$	−36.6428	+	36.6428i	−1.30701	+	1.30701i
$787$	1.45463			0.0518521			0.0259261	−	0.999664i	$-0.491747\pi$
$787$	1.45463			0.0518521			0.0259261	+	0.999664i	$0.491747\pi$
$788$			80.0741i			2.85252i
$789$		−	9.96087i		−	0.354616i
$790$	−10.1476	+	36.5502i	−0.361034	+	1.30040i
$791$	38.7636	+	38.7636i	1.37827	+	1.37827i
$792$	12.1411	+	12.1411i	0.431414	+	0.431414i
$793$		0			0
$794$		−	19.3299i		−	0.685994i
$795$	8.45282	+	2.34678i	0.299790	+	0.0832318i
$796$	−29.5241			−1.04645
$797$	8.79879	+	8.79879i	0.311669	+	0.311669i	0.845556	−	0.533887i	$-0.179269\pi$
$797$	8.79879	+	8.79879i	0.311669	+	0.311669i	−0.533887	+	0.845556i	$0.679269\pi$
$798$	113.508			4.01813
$799$	−0.529200	−	0.529200i	−0.0187218	−	0.0187218i
$800$	8.24585	−	13.7056i	0.291535	−	0.484566i
$801$	−4.03104	−	4.03104i	−0.142430	−	0.142430i
$802$	−27.7018	+	27.7018i	−0.978183	+	0.978183i
$803$	−5.74373	+	5.74373i	−0.202692	+	0.202692i
$804$	66.2855	−	66.2855i	2.33771	−	2.33771i
$805$	38.0180	+	67.2415i	1.33996	+	2.36995i
$806$		0			0
$807$	−2.97029	+	2.97029i	−0.104559	+	0.104559i
$808$	30.6810			1.07935
$809$			7.21727i			0.253746i	0.991919	+	0.126873i	$0.0404940\pi$
$809$			7.21727i			0.253746i	−0.991919	+	0.126873i	$0.959506\pi$
$810$	52.7887	+	14.6559i	1.85481	+	0.514956i
$811$	−15.0515	+	15.0515i	−0.528530	+	0.528530i	−0.920134	−	0.391604i	$-0.871920\pi$
$811$	−15.0515	+	15.0515i	−0.528530	+	0.528530i	0.391604	+	0.920134i	$0.371920\pi$
$812$		−	10.3707i		−	0.363942i
$813$			6.89134i			0.241690i
$814$	−3.50357	+	3.50357i	−0.122800	+	0.122800i
$815$	−34.1366	−	9.47747i	−1.19575	−	0.331981i
$816$		−	1.71811i		−	0.0601460i
$817$	10.3690			0.362765
$818$	7.08575	−	7.08575i	0.247747	−	0.247747i
$819$		0			0
$820$	−12.1802	−	21.5429i	−0.425352	−	0.752311i
$821$	−12.4012	+	12.4012i	−0.432805	+	0.432805i	−0.889581	−	0.456777i	$-0.849004\pi$
$821$	−12.4012	+	12.4012i	−0.432805	+	0.432805i	0.456777	+	0.889581i	$0.349004\pi$
$822$	53.6980	−	53.6980i	1.87293	−	1.87293i
$823$	−7.74299	+	7.74299i	−0.269904	+	0.269904i	−0.829061	−	0.559158i	$-0.811125\pi$
$823$	−7.74299	+	7.74299i	−0.269904	+	0.269904i	0.559158	+	0.829061i	$0.311125\pi$
$824$	41.5013	+	41.5013i	1.44576	+	1.44576i
$825$	−10.8802	+	18.0842i	−0.378800	+	0.629611i
$826$	−39.9644	−	39.9644i	−1.39054	−	1.39054i
$827$	1.86613			0.0648917			0.0324458	−	0.999473i	$-0.489670\pi$
$827$	1.86613			0.0648917			0.0324458	+	0.999473i	$0.489670\pi$
$828$	58.3358	+	58.3358i	2.02731	+	2.02731i
$829$	34.7843			1.20811			0.604055	−	0.796943i	$-0.293551\pi$
$829$	34.7843			1.20811			0.604055	+	0.796943i	$0.293551\pi$
$830$	58.4697	+	16.2331i	2.02951	+	0.563461i
$831$			66.5870i			2.30988i
$832$		0			0
$833$	−1.90028	−	1.90028i	−0.0658408	−	0.0658408i
$834$	35.2258	+	35.2258i	1.21977	+	1.21977i
$835$	−7.46731	+	26.8963i	−0.258417	+	0.930784i
$836$		−	35.8959i		−	1.24149i
$837$			5.83431i			0.201663i
$838$	−40.5189			−1.39970
$839$	13.7215	−	13.7215i	0.473718	−	0.473718i	−0.429397	−	0.903116i	$-0.641274\pi$
$839$	13.7215	−	13.7215i	0.473718	−	0.473718i	0.903116	+	0.429397i	$0.141274\pi$
$840$	37.1403	+	65.6892i	1.28146	+	2.26649i
$841$	28.4154			0.979842
$842$	−21.9815	−	21.9815i	−0.757533	−	0.757533i
$843$			8.52199i			0.293513i
$844$	89.8873			3.09405
$845$		0			0
$846$	11.3391			0.389848
$847$			28.9243i			0.993849i
$848$	−2.26549	−	2.26549i	−0.0777973	−	0.0777973i
$849$	18.2445			0.626151
$850$	4.43512	−	1.10310i	0.152123	−	0.0378360i
$851$	−7.55493	+	7.55493i	−0.258980	+	0.258980i
$852$	94.0657			3.22264
$853$			2.67051i			0.0914364i	0.998954	+	0.0457182i	$0.0145576\pi$
$853$			2.67051i			0.0914364i	−0.998954	+	0.0457182i	$0.985442\pi$
$854$		−	32.9625i		−	1.12795i
$855$	14.8311	+	26.2314i	0.507213	+	0.897096i
$856$	28.5422	+	28.5422i	0.975553	+	0.975553i
$857$	−17.5773	−	17.5773i	−0.600430	−	0.600430i	0.339996	−	0.940427i	$-0.389574\pi$
$857$	−17.5773	−	17.5773i	−0.600430	−	0.600430i	−0.940427	+	0.339996i	$0.889574\pi$
$858$		0			0
$859$			52.8699i			1.80390i	0.431844	+	0.901949i	$0.357863\pi$
$859$			52.8699i			1.80390i	−0.431844	+	0.901949i	$0.642137\pi$
$860$	7.55986	+	13.3709i	0.257789	+	0.455946i
$861$	−26.6463			−0.908104
$862$	17.9744	+	17.9744i	0.612211	+	0.612211i
$863$	−3.40127			−0.115780			−0.0578902	−	0.998323i	$-0.518437\pi$
$863$	−3.40127			−0.115780			−0.0578902	+	0.998323i	$0.518437\pi$
$864$	2.85146	+	2.85146i	0.0970087	+	0.0970087i
$865$	−17.7868	−	31.4590i	−0.604768	−	1.06964i
$866$	8.56625	+	8.56625i	0.291093	+	0.291093i
$867$	27.8447	−	27.8447i	0.945657	−	0.945657i
$868$	−44.3910	+	44.3910i	−1.50673	+	1.50673i
$869$	9.13309	−	9.13309i	0.309819	−	0.309819i
$870$	8.25052	−	4.66479i	0.279719	−	0.158151i
$871$		0			0
$872$	−15.9733	+	15.9733i	−0.540923	+	0.540923i
$873$	2.17259			0.0735311
$874$		−	120.070i		−	4.06144i
$875$	−30.3424	+	28.7443i	−1.02576	+	0.971735i
$876$	−26.9605	+	26.9605i	−0.910912	+	0.910912i
$877$		−	19.6750i		−	0.664379i	−0.943213	−	0.332189i	$-0.892213\pi$
$877$		−	19.6750i		−	0.664379i	0.943213	−	0.332189i	$-0.107787\pi$
$878$			48.0161i			1.62046i
$879$	37.2768	−	37.2768i	1.25732	−	1.25732i
$880$	6.70970	−	3.79362i	0.226184	−	0.127883i
$881$		−	2.38273i		−	0.0802762i	−0.999194	−	0.0401381i	$-0.987220\pi$
$881$		−	2.38273i		−	0.0802762i	0.999194	−	0.0401381i	$-0.0127798\pi$
$882$	40.7172			1.37102
$883$	−30.4180	+	30.4180i	−1.02365	+	1.02365i	−0.0239343	+	0.999714i	$0.507619\pi$
$883$	−30.4180	+	30.4180i	−1.02365	+	1.02365i	−0.999714	+	0.0239343i	$0.992381\pi$
$884$		0			0
$885$	8.90776	−	32.0846i	0.299431	−	1.07851i
$886$	6.31260	−	6.31260i	0.212076	−	0.212076i
$887$	−16.0566	+	16.0566i	−0.539127	+	0.539127i	−0.923272	−	0.384146i	$-0.874496\pi$
$887$	−16.0566	+	16.0566i	−0.539127	+	0.539127i	0.384146	+	0.923272i	$0.374496\pi$
$888$	−7.38052	+	7.38052i	−0.247674	+	0.247674i
$889$	−18.5915	−	18.5915i	−0.623538	−	0.623538i
$890$	−10.6990	+	6.04917i	−0.358632	+	0.202769i
$891$	−13.1907	−	13.1907i	−0.441906	−	0.441906i
$892$	107.117			3.58653
$893$	−7.52280	−	7.52280i	−0.251741	−	0.251741i
$894$	−70.4649			−2.35670
$895$	11.0353	−	39.7477i	0.368869	−	1.32862i
$896$			77.2410i			2.58044i
$897$		0			0
$898$	51.6980	+	51.6980i	1.72518	+	1.72518i
$899$	2.50221	+	2.50221i	0.0834533	+	0.0834533i
$900$	−23.0127	+	38.2498i	−0.767089	+	1.27499i
$901$			0.646845i			0.0215495i
$902$			13.0716i			0.435235i
$903$	16.5385			0.550365
$904$	40.0581	−	40.0581i	1.33231	−	1.33231i
$905$	4.71815	+	1.30992i	0.156837	+	0.0435431i
$906$	−23.2165			−0.771316
$907$	−16.3686	−	16.3686i	−0.543510	−	0.543510i	0.381046	−	0.924556i	$-0.375564\pi$
$907$	−16.3686	−	16.3686i	−0.543510	−	0.543510i	−0.924556	+	0.381046i	$0.875564\pi$
$908$		−	28.5436i		−	0.947253i
$909$	19.5414			0.648147
$910$		0			0
$911$	−23.7450			−0.786707			−0.393354	−	0.919387i	$-0.628685\pi$
$911$	−23.7450			−0.786707			−0.393354	+	0.919387i	$0.628685\pi$
$912$		−	24.4237i		−	0.808749i
$913$	−14.6103	−	14.6103i	−0.483530	−	0.483530i
$914$	−24.1508			−0.798837
$915$	16.9052	−	9.55812i	0.558869	−	0.315982i
$916$	45.1406	−	45.1406i	1.49149	−	1.49149i
$917$	34.9440			1.15395
$918$			1.15223i			0.0380293i
$919$		−	56.9671i		−	1.87917i	−0.342313	−	0.939586i	$-0.611210\pi$
$919$		−	56.9671i		−	1.87917i	0.342313	−	0.939586i	$-0.388790\pi$
$920$	69.4870	−	39.2876i	2.29092	−	1.29527i
$921$	−33.7221	−	33.7221i	−1.11118	−	1.11118i
$922$	−32.3379	−	32.3379i	−1.06499	−	1.06499i
$923$		0			0
$924$		−	57.2537i		−	1.88351i
$925$	−4.95364	−	2.98032i	−0.162875	−	0.0979922i
$926$	−39.8398			−1.30922
$927$	26.4331	+	26.4331i	0.868177	+	0.868177i
$928$	2.44586			0.0802892
$929$	20.6626	+	20.6626i	0.677918	+	0.677918i	0.959529	−	0.281611i	$-0.0908687\pi$
$929$	20.6626	+	20.6626i	0.677918	+	0.677918i	−0.281611	+	0.959529i	$0.590869\pi$
$930$	−55.2828	−	15.3483i	−1.81279	−	0.503292i
$931$	−27.0133	−	27.0133i	−0.885325	−	0.885325i
$932$	5.55112	−	5.55112i	0.181833	−	0.181833i
$933$	−35.3211	+	35.3211i	−1.15636	+	1.15636i
$934$	−23.1496	+	23.1496i	−0.757478	+	0.757478i
$935$	−1.49946	−	0.416299i	−0.0490375	−	0.0136144i
$936$		0			0
$937$	−1.77191	+	1.77191i	−0.0578859	+	0.0578859i	−0.735457	−	0.677571i	$-0.763033\pi$
$937$	−1.77191	+	1.77191i	−0.0578859	+	0.0578859i	0.677571	+	0.735457i	$0.263033\pi$
$938$	−98.0558			−3.20164
$939$		−	17.2745i		−	0.563731i
$940$	4.21601	−	15.1855i	0.137511	−	0.495297i
$941$	−15.5682	+	15.5682i	−0.507507	+	0.507507i	−0.913761	−	0.406253i	$-0.866835\pi$
$941$	−15.5682	+	15.5682i	−0.507507	+	0.507507i	0.406253	+	0.913761i	$0.366835\pi$
$942$			102.209i			3.33016i
$943$			28.1869i			0.917891i
$944$	−8.59920	+	8.59920i	−0.279880	+	0.279880i
$945$	−5.18624	−	9.17279i	−0.168708	−	0.298391i
$946$		−	8.11306i		−	0.263778i
$947$	0.361869			0.0117591			0.00587957	−	0.999983i	$-0.498128\pi$
$947$	0.361869			0.0117591			0.00587957	+	0.999983i	$0.498128\pi$
$948$	42.8699	−	42.8699i	1.39235	−	1.39235i
$949$		0			0
$950$	63.0471	−	15.6810i	2.04552	−	0.508760i
$951$	−42.7679	+	42.7679i	−1.38684	+	1.38684i
$952$	−3.93447	+	3.93447i	−0.127517	+	0.127517i
$953$	−28.6611	+	28.6611i	−0.928423	+	0.928423i	−0.997604	−	0.0691813i	$-0.977961\pi$
$953$	−28.6611	+	28.6611i	−0.928423	+	0.928423i	0.0691813	+	0.997604i	$0.477961\pi$
$954$	−6.92996	−	6.92996i	−0.224366	−	0.224366i
$955$	−4.87298	+	17.5518i	−0.157686	+	0.567964i
$956$	25.6140	+	25.6140i	0.828415	+	0.828415i
$957$	−3.22725			−0.104322
$958$	23.1837	+	23.1837i	0.749031	+	0.749031i
$959$	−51.2085			−1.65361
$960$	−51.8805	+	29.3329i	−1.67443	+	0.946716i
$961$			9.57907i			0.309002i
$962$		0			0
$963$	18.1792	+	18.1792i	0.585817	+	0.585817i
$964$	37.1820	+	37.1820i	1.19755	+	1.19755i
$965$	−50.0875	−	13.9060i	−1.61237	−	0.447649i
$966$		−	191.511i		−	6.16178i
$967$			12.2654i			0.394430i	0.980360	+	0.197215i	$0.0631897\pi$
$967$			12.2654i			0.394430i	−0.980360	+	0.197215i	$0.936810\pi$
$968$	29.8902			0.960707
$969$	−3.48674	+	3.48674i	−0.112010	+	0.112010i
$970$	1.25305	−	4.51334i	0.0402332	−	0.144915i
$971$	22.6199			0.725907			0.362953	−	0.931807i	$-0.381768\pi$
$971$	22.6199			0.725907			0.362953	+	0.931807i	$0.381768\pi$
$972$	−52.2135	−	52.2135i	−1.67475	−	1.67475i
$973$		−	33.5927i		−	1.07693i
$974$	48.5378			1.55525
$975$		0			0
$976$	−7.09261			−0.227029
$977$		−	35.1692i		−	1.12516i	−0.826742	−	0.562581i	$-0.809808\pi$
$977$		−	35.1692i		−	1.12516i	0.826742	−	0.562581i	$-0.190192\pi$
$978$	62.1090	+	62.1090i	1.98603	+	1.98603i
$979$	4.18500			0.133753
$980$	15.1391	−	54.5290i	0.483600	−	1.74186i
$981$	−10.1737	+	10.1737i	−0.324823	+	0.324823i
$982$	−24.1722			−0.771367
$983$			12.2764i			0.391555i	0.980648	+	0.195778i	$0.0627231\pi$
$983$			12.2764i			0.391555i	−0.980648	+	0.195778i	$0.937277\pi$
$984$			27.5362i			0.877821i
$985$	47.5490	+	13.2012i	1.51504	+	0.420625i
$986$	0.494167	+	0.494167i	0.0157375	+	0.0157375i
$987$	−11.9988	−	11.9988i	−0.381927	−	0.381927i
$988$		0			0
$989$		−	17.4946i		−	0.556297i
$990$	20.5244	−	11.6044i	0.652309	−	0.368812i
$991$	33.1990			1.05460			0.527301	−	0.849679i	$-0.323204\pi$
$991$	33.1990			1.05460			0.527301	+	0.849679i	$0.323204\pi$
$992$	−10.4693	−	10.4693i	−0.332399	−	0.332399i
$993$	−24.5922			−0.780409
$994$	−69.5755	−	69.5755i	−2.20680	−	2.20680i
$995$	−4.86740	+	17.5318i	−0.154307	+	0.555795i
$996$	−68.5794	−	68.5794i	−2.17302	−	2.17302i
$997$	−26.5760	+	26.5760i	−0.841671	+	0.841671i	−0.989076	−	0.147405i	$-0.952908\pi$
$997$	−26.5760	+	26.5760i	−0.841671	+	0.841671i	0.147405	+	0.989076i	$0.452908\pi$
$998$	18.7456	−	18.7456i	0.593383	−	0.593383i
$999$	1.03061	−	1.03061i	0.0326070	−	0.0326070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.f.408.5	✓	72
5.2	odd	4		845.2.k.f.577.32	yes	72
13.2	odd	12		845.2.o.i.488.32		144
13.3	even	3		845.2.t.i.188.32		144
13.4	even	6		845.2.t.i.418.32		144
13.5	odd	4		845.2.k.f.268.5	yes	72
13.6	odd	12		845.2.o.i.258.32		144
13.7	odd	12		845.2.o.i.258.5		144
13.8	odd	4		845.2.k.f.268.32	yes	72
13.9	even	3		845.2.t.i.418.5		144
13.10	even	6		845.2.t.i.188.5		144
13.11	odd	12		845.2.o.i.488.5		144
13.12	even	2	inner	845.2.f.f.408.32	yes	72
65.2	even	12		845.2.t.i.657.32		144
65.7	even	12		845.2.t.i.427.32		144
65.12	odd	4		845.2.k.f.577.5	yes	72
65.17	odd	12		845.2.o.i.587.32		144
65.22	odd	12		845.2.o.i.587.5		144
65.32	even	12		845.2.t.i.427.5		144
65.37	even	12		845.2.t.i.657.5		144
65.42	odd	12		845.2.o.i.357.5		144
65.47	even	4	inner	845.2.f.f.437.32	yes	72
65.57	even	4	inner	845.2.f.f.437.5	yes	72
65.62	odd	12		845.2.o.i.357.32		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.f.f.408.5	✓	72	1.1	even	1	trivial
845.2.f.f.408.32	yes	72	13.12	even	2	inner
845.2.f.f.437.5	yes	72	65.57	even	4	inner
845.2.f.f.437.32	yes	72	65.47	even	4	inner
845.2.k.f.268.5	yes	72	13.5	odd	4
845.2.k.f.268.32	yes	72	13.8	odd	4
845.2.k.f.577.5	yes	72	65.12	odd	4
845.2.k.f.577.32	yes	72	5.2	odd	4
845.2.o.i.258.5		144	13.7	odd	12
845.2.o.i.258.32		144	13.6	odd	12
845.2.o.i.357.5		144	65.42	odd	12
845.2.o.i.357.32		144	65.62	odd	12
845.2.o.i.488.5		144	13.11	odd	12
845.2.o.i.488.32		144	13.2	odd	12
845.2.o.i.587.5		144	65.22	odd	12
845.2.o.i.587.32		144	65.17	odd	12
845.2.t.i.188.5		144	13.10	even	6
845.2.t.i.188.32		144	13.3	even	3
845.2.t.i.418.5		144	13.9	even	3
845.2.t.i.418.32		144	13.4	even	6
845.2.t.i.427.5		144	65.32	even	12
845.2.t.i.427.32		144	65.7	even	12
845.2.t.i.657.5		144	65.37	even	12
845.2.t.i.657.32		144	65.2	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.37242i q^{2} +(1.65235 + 1.65235i) q^{3} -3.62837 q^{4} +(-0.598181 + 2.15457i) q^{5} +(3.92008 - 3.92008i) q^{6} -3.73834 q^{7} +3.86318i q^{8} +2.46055i q^{9} +(5.11155 + 1.41914i) q^{10} +(-1.27726 - 1.27726i) q^{11} +(-5.99536 - 5.99536i) q^{12} +8.86890i q^{14} +(-4.54852 + 2.57171i) q^{15} +1.90834 q^{16} +(-0.272435 - 0.272435i) q^{17} +5.83745 q^{18} +(-3.87278 - 3.87278i) q^{19} +(2.17042 - 7.81759i) q^{20} +(-6.17706 - 6.17706i) q^{21} +(-3.03020 + 3.03020i) q^{22} +(-6.53419 + 6.53419i) q^{23} +(-6.38334 + 6.38334i) q^{24} +(-4.28436 - 2.57765i) q^{25} +(0.891365 - 0.891365i) q^{27} +13.5641 q^{28} -0.764574i q^{29} +(6.10117 + 10.7910i) q^{30} +(-3.27268 + 3.27268i) q^{31} +3.19898i q^{32} -4.22098i q^{33} +(-0.646330 + 0.646330i) q^{34} +(2.23620 - 8.05452i) q^{35} -8.92778i q^{36} +1.15622 q^{37} +(-9.18786 + 9.18786i) q^{38} +(-8.32350 - 2.31088i) q^{40} +(2.15688 - 2.15688i) q^{41} +(-14.6546 + 14.6546i) q^{42} +(-1.33870 + 1.33870i) q^{43} +(4.63438 + 4.63438i) q^{44} +(-5.30143 - 1.47185i) q^{45} +(15.5018 + 15.5018i) q^{46} +1.94248 q^{47} +(3.15325 + 3.15325i) q^{48} +6.97517 q^{49} +(-6.11526 + 10.1643i) q^{50} -0.900318i q^{51} +(-1.18715 - 1.18715i) q^{53} +(-2.11469 - 2.11469i) q^{54} +(3.51599 - 1.98792i) q^{55} -14.4419i q^{56} -12.7984i q^{57} -1.81389 q^{58} +(-4.50612 + 4.50612i) q^{59} +(16.5037 - 9.33112i) q^{60} -3.71664 q^{61} +(7.76418 + 7.76418i) q^{62} -9.19836i q^{63} +11.4060 q^{64} -10.0139 q^{66} +11.0561i q^{67} +(0.988496 + 0.988496i) q^{68} -21.5936 q^{69} +(-19.1087 - 5.30521i) q^{70} +(-7.84488 + 7.84488i) q^{71} -9.50554 q^{72} -4.49691i q^{73} -2.74303i q^{74} +(-2.82009 - 11.3385i) q^{75} +(14.0519 + 14.0519i) q^{76} +(4.77484 + 4.77484i) q^{77} +7.15052i q^{79} +(-1.14153 + 4.11165i) q^{80} +10.3273 q^{81} +(-5.11702 - 5.11702i) q^{82} +11.4388 q^{83} +(22.4127 + 22.4127i) q^{84} +(0.749946 - 0.424015i) q^{85} +(3.17596 + 3.17596i) q^{86} +(1.26335 - 1.26335i) q^{87} +(4.93430 - 4.93430i) q^{88} +(-1.63827 + 1.63827i) q^{89} +(-3.49185 + 12.5772i) q^{90} +(23.7085 - 23.7085i) q^{92} -10.8153 q^{93} -4.60838i q^{94} +(10.6608 - 6.02756i) q^{95} +(-5.28585 + 5.28585i) q^{96} -0.882970i q^{97} -16.5480i q^{98} +(3.14277 - 3.14277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{3} - 80 q^{4} - 12 q^{10} + 64 q^{12} + 80 q^{16} + 8 q^{17} + 24 q^{22} + 36 q^{23} - 48 q^{25} - 64 q^{27} - 4 q^{30} + 80 q^{35} + 28 q^{38} - 24 q^{40} - 56 q^{42} + 76 q^{43} - 76 q^{48}+ \cdots - 92 q^{95}+O(q^{100}) \) 72 * q - 4 * q^3 - 80 * q^4 - 12 * q^10 + 64 * q^12 + 80 * q^16 + 8 * q^17 + 24 * q^22 + 36 * q^23 - 48 * q^25 - 64 * q^27 - 4 * q^30 + 80 * q^35 + 28 * q^38 - 24 * q^40 - 56 * q^42 + 76 * q^43 - 76 * q^48 + 8 * q^49 - 16 * q^53 + 12 * q^55 + 8 * q^61 + 148 * q^62 - 120 * q^64 + 40 * q^66 - 48 * q^68 - 40 * q^69 - 164 * q^75 + 172 * q^77 + 16 * q^81 + 44 * q^82 + 20 * q^87 + 124 * q^88 - 300 * q^90 - 4 * q^92 - 92 * q^95

Introduction

L-functions

Modular forms

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