LMFDB - Embedded newform 820.2.y.a.137.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			137.5
Character	$\chi$	$=$	820.137
Dual form			820.2.y.a.413.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.04447 - 0.846849i) q^{3} +(2.12876 + 0.684393i) q^{5} +(1.81325 - 4.37757i) q^{7} +(1.34140 + 1.34140i) q^{9} +(-0.881451 + 0.365109i) q^{11} +(3.32754 + 1.37831i) q^{13} +(-3.77261 - 3.20196i) q^{15} +(2.21596 - 0.917880i) q^{17} +(-4.27371 - 1.77023i) q^{19} +(-7.41429 + 7.41429i) q^{21} +(0.410884 + 0.410884i) q^{23} +(4.06321 + 2.91381i) q^{25} +(0.934048 + 2.25499i) q^{27} +(1.92379 - 0.796858i) q^{29} -2.06873i q^{31} +2.11130 q^{33} +(6.85595 - 8.07781i) q^{35} +(-4.84468 - 4.84468i) q^{37} +(-5.63586 - 5.63586i) q^{39} +(1.96004 - 6.09576i) q^{41} -7.06541 q^{43} +(1.93747 + 3.77357i) q^{45} +(8.68032 - 3.59551i) q^{47} +(-10.9255 - 10.9255i) q^{49} -5.30778 q^{51} +(-0.821734 + 1.98384i) q^{53} +(-2.12627 + 0.173969i) q^{55} +(7.23837 + 7.23837i) q^{57} -6.82043i q^{59} +(-5.25030 - 5.25030i) q^{61} +(8.30439 - 3.43979i) q^{63} +(6.14022 + 5.21144i) q^{65} +(10.4450 - 4.32646i) q^{67} +(-0.492085 - 1.18800i) q^{69} +(-2.24583 - 5.42190i) q^{71} +5.58085 q^{73} +(-5.83957 - 9.39815i) q^{75} +4.52065i q^{77} +(1.44471 + 3.48785i) q^{79} -11.0924i q^{81} +(-6.06087 + 6.06087i) q^{83} +(5.34543 - 0.437356i) q^{85} -4.60795 q^{87} +(-1.93175 + 0.800159i) q^{89} +(12.0673 - 12.0673i) q^{91} +(-1.75190 + 4.22946i) q^{93} +(-7.88615 - 6.69328i) q^{95} +(-5.64811 - 13.6357i) q^{97} +(-1.67214 - 0.692623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−2.04447	−	0.846849i	−1.18038	−	0.488929i	−0.295768	−	0.955260i	$-0.595576\pi$
$3$	−2.04447	−	0.846849i	−1.18038	−	0.488929i	−0.884610	+	0.466331i	$0.845576\pi$
$4$		0			0
$5$	2.12876	+	0.684393i	0.952009	+	0.306070i
$5$	2.12876	+	0.684393i	0.952009	+	0.306070i
$6$		0			0
$7$	1.81325	−	4.37757i	0.685344	−	1.65457i	−0.0686134	−	0.997643i	$-0.521858\pi$
$7$	1.81325	−	4.37757i	0.685344	−	1.65457i	0.753957	−	0.656923i	$-0.228142\pi$
$8$		0			0
$9$	1.34140	+	1.34140i	0.447135	+	0.447135i
$10$		0			0
$11$	−0.881451	+	0.365109i	−0.265767	+	0.110084i	−0.511588	−	0.859231i	$-0.670943\pi$
$11$	−0.881451	+	0.365109i	−0.265767	+	0.110084i	0.245821	+	0.969315i	$0.420943\pi$
$12$		0			0
$13$	3.32754	+	1.37831i	0.922895	+	0.382275i	0.792979	−	0.609250i	$-0.208529\pi$
$13$	3.32754	+	1.37831i	0.922895	+	0.382275i	0.129916	+	0.991525i	$0.458529\pi$
$14$		0			0
$15$	−3.77261	−	3.20196i	−0.974084	−	0.826743i
$16$		0			0
$17$	2.21596	−	0.917880i	0.537449	−	0.222619i	−0.0974134	−	0.995244i	$-0.531057\pi$
$17$	2.21596	−	0.917880i	0.537449	−	0.222619i	0.634862	+	0.772625i	$0.281057\pi$
$18$		0			0
$19$	−4.27371	−	1.77023i	−0.980455	−	0.406118i	−0.165861	−	0.986149i	$-0.553040\pi$
$19$	−4.27371	−	1.77023i	−0.980455	−	0.406118i	−0.814594	+	0.580031i	$0.803040\pi$
$20$		0			0
$21$	−7.41429	+	7.41429i	−1.61793	+	1.61793i
$22$		0			0
$23$	0.410884	+	0.410884i	0.0856751	+	0.0856751i	0.748646	−	0.662970i	$-0.230705\pi$
$23$	0.410884	+	0.410884i	0.0856751	+	0.0856751i	−0.662970	+	0.748646i	$0.730705\pi$
$24$		0			0
$25$	4.06321	+	2.91381i	0.812642	+	0.582763i
$26$		0			0
$27$	0.934048	+	2.25499i	0.179758	+	0.433973i
$28$		0			0
$29$	1.92379	−	0.796858i	0.357238	−	0.147973i	−0.196844	−	0.980435i	$-0.563069\pi$
$29$	1.92379	−	0.796858i	0.357238	−	0.147973i	0.554082	+	0.832462i	$0.313069\pi$
$30$		0			0
$31$		−	2.06873i		−	0.371554i	−0.982592	−	0.185777i	$-0.940520\pi$
$31$		−	2.06873i		−	0.371554i	0.982592	−	0.185777i	$-0.0594803\pi$
$32$		0			0
$33$	2.11130			0.367530
$34$		0			0
$35$	6.85595	−	8.07781i	1.15887	−	1.36540i
$36$		0			0
$37$	−4.84468	−	4.84468i	−0.796461	−	0.796461i	0.186075	−	0.982536i	$-0.440423\pi$
$37$	−4.84468	−	4.84468i	−0.796461	−	0.796461i	−0.982536	+	0.186075i	$0.940423\pi$
$38$		0			0
$39$	−5.63586	−	5.63586i	−0.902459	−	0.902459i
$40$		0			0
$41$	1.96004	−	6.09576i	0.306106	−	0.951997i
$41$	1.96004	−	6.09576i	0.306106	−	0.951997i
$42$		0			0
$43$	−7.06541			−1.07747			−0.538733	−	0.842477i	$-0.681097\pi$
$43$	−7.06541			−1.07747			−0.538733	+	0.842477i	$0.681097\pi$
$44$		0			0
$45$	1.93747	+	3.77357i	0.288822	+	0.562531i
$46$		0			0
$47$	8.68032	−	3.59551i	1.26616	−	0.524459i	0.354362	−	0.935108i	$-0.384698\pi$
$47$	8.68032	−	3.59551i	1.26616	−	0.524459i	0.911793	+	0.410650i	$0.134698\pi$
$48$		0			0
$49$	−10.9255	−	10.9255i	−1.56079	−	1.56079i
$50$		0			0
$51$	−5.30778			−0.743237
$52$		0			0
$53$	−0.821734	+	1.98384i	−0.112874	+	0.272502i	−0.970214	−	0.242248i	$-0.922115\pi$
$53$	−0.821734	+	1.98384i	−0.112874	+	0.272502i	0.857340	+	0.514750i	$0.172115\pi$
$54$		0			0
$55$	−2.12627	+	0.173969i	−0.286707	+	0.0234580i
$56$		0			0
$57$	7.23837	+	7.23837i	0.958745	+	0.958745i
$58$		0			0
$59$		−	6.82043i		−	0.887945i	−0.896041	−	0.443972i	$-0.853569\pi$
$59$		−	6.82043i		−	0.887945i	0.896041	−	0.443972i	$-0.146431\pi$
$60$		0			0
$61$	−5.25030	−	5.25030i	−0.672232	−	0.672232i	0.285998	−	0.958230i	$-0.407675\pi$
$61$	−5.25030	−	5.25030i	−0.672232	−	0.672232i	−0.958230	+	0.285998i	$0.907675\pi$
$62$		0			0
$63$	8.30439	−	3.43979i	1.04625	−	0.433373i
$64$		0			0
$65$	6.14022	+	5.21144i	0.761601	+	0.646400i
$66$		0			0
$67$	10.4450	−	4.32646i	1.27606	−	0.528562i	0.361259	−	0.932465i	$-0.382347\pi$
$67$	10.4450	−	4.32646i	1.27606	−	0.528562i	0.914801	+	0.403904i	$0.132347\pi$
$68$		0			0
$69$	−0.492085	−	1.18800i	−0.0592400	−	0.143018i
$70$		0			0
$71$	−2.24583	−	5.42190i	−0.266530	−	0.643461i	0.732785	−	0.680460i	$-0.238220\pi$
$71$	−2.24583	−	5.42190i	−0.266530	−	0.643461i	−0.999315	+	0.0369990i	$0.988220\pi$
$72$		0			0
$73$	5.58085			0.653190			0.326595	−	0.945164i	$-0.394099\pi$
$73$	5.58085			0.653190			0.326595	+	0.945164i	$0.394099\pi$
$74$		0			0
$75$	−5.83957	−	9.39815i	−0.674296	−	1.08520i
$76$		0			0
$77$			4.52065i			0.515176i
$78$		0			0
$79$	1.44471	+	3.48785i	0.162543	+	0.392414i	0.984076	−	0.177747i	$-0.0568809\pi$
$79$	1.44471	+	3.48785i	0.162543	+	0.392414i	−0.821533	+	0.570161i	$0.806881\pi$
$80$		0			0
$81$		−	11.0924i		−	1.23249i
$82$		0			0
$83$	−6.06087	+	6.06087i	−0.665267	+	0.665267i	−0.956617	−	0.291350i	$-0.905896\pi$
$83$	−6.06087	+	6.06087i	−0.665267	+	0.665267i	0.291350	+	0.956617i	$0.405896\pi$
$84$		0			0
$85$	5.34543	−	0.437356i	0.579793	−	0.0474379i
$86$		0			0
$87$	−4.60795			−0.494024
$88$		0			0
$89$	−1.93175	+	0.800159i	−0.204766	+	0.0848167i	−0.482709	−	0.875781i	$-0.660347\pi$
$89$	−1.93175	+	0.800159i	−0.204766	+	0.0848167i	0.277944	+	0.960597i	$0.410347\pi$
$90$		0			0
$91$	12.0673	−	12.0673i	1.26500	−	1.26500i
$92$		0			0
$93$	−1.75190	+	4.22946i	−0.181664	+	0.438575i
$94$		0			0
$95$	−7.88615	−	6.69328i	−0.809102	−	0.686716i
$96$		0			0
$97$	−5.64811	−	13.6357i	−0.573479	−	1.38450i	−0.898576	−	0.438819i	$-0.855397\pi$
$97$	−5.64811	−	13.6357i	−0.573479	−	1.38450i	0.325097	−	0.945681i	$-0.394603\pi$
$98$		0			0
$99$	−1.67214	−	0.692623i	−0.168056	−	0.0696112i
$100$		0			0
$101$	−6.75684	+	16.3124i	−0.672330	+	1.62315i	0.105310	+	0.994439i	$0.466417\pi$
$101$	−6.75684	+	16.3124i	−0.672330	+	1.62315i	−0.777640	+	0.628710i	$0.783583\pi$
$102$		0			0
$103$			8.01025i			0.789273i	0.918837	+	0.394636i	$0.129129\pi$
$103$			8.01025i			0.789273i	−0.918837	+	0.394636i	$0.870871\pi$
$104$		0			0
$105$	−20.8575	+	10.7089i	−2.03548	+	1.04508i
$106$		0			0
$107$	3.11465	−	3.11465i	0.301105	−	0.301105i	−0.540341	−	0.841446i	$-0.681705\pi$
$107$	3.11465	−	3.11465i	0.301105	−	0.301105i	0.841446	+	0.540341i	$0.181705\pi$
$108$		0			0
$109$	−5.14641	+	12.4245i	−0.492936	+	1.19005i	0.460282	+	0.887773i	$0.347748\pi$
$109$	−5.14641	+	12.4245i	−0.492936	+	1.19005i	−0.953219	+	0.302281i	$0.902252\pi$
$110$		0			0
$111$	5.80212	+	14.0075i	0.550712	+	1.32954i
$112$		0			0
$113$	3.54373	+	3.54373i	0.333366	+	0.333366i	0.853863	−	0.520497i	$-0.174253\pi$
$113$	3.54373	+	3.54373i	0.333366	+	0.333366i	−0.520497	+	0.853863i	$0.674253\pi$
$114$		0			0
$115$	0.593465	+	1.15588i	0.0553409	+	0.107786i
$116$		0			0
$117$	2.61470	+	6.31246i	0.241730	+	0.583587i
$118$		0			0
$119$		−	11.3649i		−	1.04181i
$120$		0			0
$121$	−7.13452	+	7.13452i	−0.648593	+	0.648593i
$122$		0			0
$123$	−9.16943	+	10.8028i	−0.826780	+	0.974053i
$124$		0			0
$125$	6.65540	+	8.98364i	0.595277	+	0.803521i
$126$		0			0
$127$	−2.45936	+	2.45936i	−0.218232	+	0.218232i	−0.807753	−	0.589521i	$-0.799317\pi$
$127$	−2.45936	+	2.45936i	−0.218232	+	0.218232i	0.589521	+	0.807753i	$0.299317\pi$
$128$		0			0
$129$	14.4451	+	5.98334i	1.27182	+	0.526804i
$130$		0			0
$131$	12.7798	−	12.7798i	1.11658	−	1.11658i	0.124340	−	0.992240i	$-0.460319\pi$
$131$	12.7798	−	12.7798i	1.11658	−	1.11658i	0.992240	−	0.124340i	$-0.0396812\pi$
$132$		0			0
$133$	−15.4986	+	15.4986i	−1.34390	+	1.34390i
$134$		0			0
$135$	0.445060	+	5.43959i	0.0383047	+	0.468165i
$136$		0			0
$137$	10.7739	−	4.46268i	0.920474	−	0.381273i	0.128417	−	0.991720i	$-0.459010\pi$
$137$	10.7739	−	4.46268i	0.920474	−	0.381273i	0.792057	+	0.610447i	$0.209010\pi$
$138$		0			0
$139$			2.58764i			0.219481i	0.993960	+	0.109741i	$0.0350020\pi$
$139$			2.58764i			0.219481i	−0.993960	+	0.109741i	$0.964998\pi$
$140$		0			0
$141$	−20.7916			−1.75096
$142$		0			0
$143$	−3.43630			−0.287358
$144$		0			0
$145$	4.64064	−	0.379691i	0.385384	−	0.0315316i
$146$		0			0
$147$	13.0847	+	31.5892i	1.07921	+	2.60543i
$148$		0			0
$149$	8.35679	+	3.46150i	0.684615	+	0.283577i	0.697755	−	0.716337i	$-0.254183\pi$
$149$	8.35679	+	3.46150i	0.684615	+	0.283577i	−0.0131398	+	0.999914i	$0.504183\pi$
$150$		0			0
$151$	3.68922	−	1.52812i	0.300224	−	0.124357i	−0.227486	−	0.973781i	$-0.573051\pi$
$151$	3.68922	−	1.52812i	0.300224	−	0.124357i	0.527710	+	0.849424i	$0.323051\pi$
$152$		0			0
$153$	4.20374	+	1.74125i	0.339852	+	0.140771i
$154$		0			0
$155$	1.41582	−	4.40382i	0.113722	−	0.353723i
$156$		0			0
$157$	21.7267	+	8.99950i	1.73398	+	0.718238i	0.999202	+	0.0399303i	$0.0127136\pi$
$157$	21.7267	+	8.99950i	1.73398	+	0.718238i	0.734778	+	0.678308i	$0.237286\pi$
$158$		0			0
$159$	3.36003	−	3.36003i	0.266468	−	0.266468i
$160$		0			0
$161$	2.54371	−	1.05364i	0.200472	−	0.0830383i
$162$		0			0
$163$	5.14086	+	5.14086i	0.402664	+	0.402664i	0.879171	−	0.476507i	$-0.158097\pi$
$163$	5.14086	+	5.14086i	0.402664	+	0.402664i	−0.476507	+	0.879171i	$0.658097\pi$
$164$		0			0
$165$	4.49444	+	1.44496i	0.349891	+	0.112490i
$166$		0			0
$167$	−8.02898	+	19.3837i	−0.621301	+	1.49995i	0.228876	+	0.973456i	$0.426495\pi$
$167$	−8.02898	+	19.3837i	−0.621301	+	1.49995i	−0.850177	+	0.526497i	$0.823505\pi$
$168$		0			0
$169$	−0.0195886	−	0.0195886i	−0.00150681	−	0.00150681i
$170$		0			0
$171$	−3.35818	−	8.10735i	−0.256806	−	0.619985i
$172$		0			0
$173$		−	26.0789i		−	1.98274i	−0.131076	−	0.991372i	$-0.541843\pi$
$173$		−	26.0789i		−	1.98274i	0.131076	−	0.991372i	$-0.458157\pi$
$174$		0			0
$175$	20.1230	−	12.5035i	1.52116	−	0.945178i
$176$		0			0
$177$	−5.77588	+	13.9442i	−0.434142	+	1.04811i
$178$		0			0
$179$	−5.44075	+	13.1351i	−0.406660	+	0.981765i	0.579350	+	0.815079i	$0.303307\pi$
$179$	−5.44075	+	13.1351i	−0.406660	+	0.981765i	−0.986010	+	0.166686i	$0.946693\pi$
$180$		0			0
$181$	−5.81420	+	14.0367i	−0.432166	+	1.04334i	0.546421	+	0.837511i	$0.315990\pi$
$181$	−5.81420	+	14.0367i	−0.432166	+	1.04334i	−0.978587	+	0.205831i	$0.934010\pi$
$182$		0			0
$183$	6.28789	+	15.1803i	0.464814	+	1.12216i
$184$		0			0
$185$	−6.99748	−	13.6288i	−0.514465	−	1.00201i
$186$		0			0
$187$	−1.61813	+	1.61813i	−0.118329	+	0.118329i
$188$		0			0
$189$	11.5651			0.841234
$190$		0			0
$191$	13.8761	+	5.74768i	1.00404	+	0.415887i	0.823277	−	0.567639i	$-0.192143\pi$
$191$	13.8761	+	5.74768i	1.00404	+	0.415887i	0.180763	+	0.983527i	$0.442143\pi$
$192$		0			0
$193$	−1.72640	−	0.715099i	−0.124269	−	0.0514740i	0.319682	−	0.947525i	$-0.396424\pi$
$193$	−1.72640	−	0.715099i	−0.124269	−	0.0514740i	−0.443952	+	0.896051i	$0.646424\pi$
$194$		0			0
$195$	−8.14023	−	15.8545i	−0.582934	−	1.13537i
$196$		0			0
$197$			15.3718i			1.09519i	0.836743	+	0.547596i	$0.184457\pi$
$197$			15.3718i			1.09519i	−0.836743	+	0.547596i	$0.815543\pi$
$198$		0			0
$199$	−6.31798	+	15.2530i	−0.447870	+	1.08125i	0.525248	+	0.850949i	$0.323972\pi$
$199$	−6.31798	+	15.2530i	−0.447870	+	1.08125i	−0.973118	+	0.230305i	$0.926028\pi$
$200$		0			0
$201$	−25.0184			−1.76466
$202$		0			0
$203$		−	9.86641i		−	0.692486i
$204$		0			0
$205$	8.34434	−	11.6349i	0.582794	−	0.812620i
$206$		0			0
$207$			1.10232i			0.0766166i
$208$		0			0
$209$	4.41339			0.305280
$210$		0			0
$211$	−4.03466	+	9.74053i	−0.277757	+	0.670566i	−0.999773	−	0.0213111i	$-0.993216\pi$
$211$	−4.03466	+	9.74053i	−0.277757	+	0.670566i	0.722015	+	0.691877i	$0.243216\pi$
$212$		0			0
$213$			12.9868i			0.889842i
$214$		0			0
$215$	−15.0405	−	4.83552i	−1.02576	−	0.329780i
$216$		0			0
$217$	−9.05600	−	3.75112i	−0.614762	−	0.254643i
$218$		0			0
$219$	−11.4099	−	4.72614i	−0.771011	−	0.319363i
$220$		0			0
$221$	8.63882			0.581110
$222$		0			0
$223$	−7.54584	+	7.54584i	−0.505307	+	0.505307i	−0.913082	−	0.407775i	$-0.866305\pi$
$223$	−7.54584	+	7.54584i	−0.505307	+	0.505307i	0.407775	+	0.913082i	$0.366305\pi$
$224$		0			0
$225$	1.54181	+	9.35901i	0.102787	+	0.623934i
$226$		0			0
$227$	8.85987	+	21.3896i	0.588050	+	1.41968i	0.885364	+	0.464899i	$0.153909\pi$
$227$	8.85987	+	21.3896i	0.588050	+	1.41968i	−0.297314	+	0.954780i	$0.596091\pi$
$228$		0			0
$229$	4.35571	−	10.5156i	0.287833	−	0.694891i	−0.712141	−	0.702036i	$-0.752274\pi$
$229$	4.35571	−	10.5156i	0.287833	−	0.694891i	0.999974	+	0.00714511i	$0.00227438\pi$
$230$		0			0
$231$	3.82831	−	9.24235i	0.251884	−	0.608102i
$232$		0			0
$233$	10.4285	−	25.1766i	0.683194	−	1.64938i	−0.0748674	−	0.997193i	$-0.523853\pi$
$233$	10.4285	−	25.1766i	0.683194	−	1.64938i	0.758062	−	0.652183i	$-0.226147\pi$
$234$		0			0
$235$	20.9390	−	1.71321i	1.36591	−	0.111757i
$236$		0			0
$237$		−	8.35427i		−	0.542668i
$238$		0			0
$239$	−5.92992	−	14.3161i	−0.383575	−	0.926031i	−0.991268	−	0.131860i	$-0.957905\pi$
$239$	−5.92992	−	14.3161i	−0.383575	−	0.926031i	0.607694	−	0.794172i	$-0.292095\pi$
$240$		0			0
$241$	−10.0865	−	10.0865i	−0.649730	−	0.649730i	0.303198	−	0.952928i	$-0.401946\pi$
$241$	−10.0865	−	10.0865i	−0.649730	−	0.649730i	−0.952928	+	0.303198i	$0.901946\pi$
$242$		0			0
$243$	−6.59142	+	15.9131i	−0.422840	+	1.02083i
$244$		0			0
$245$	−15.7804	−	30.7351i	−1.00817	−	1.96359i
$246$		0			0
$247$	−11.7810	−	11.7810i	−0.749608	−	0.749608i
$248$		0			0
$249$	17.5239	−	7.25865i	1.11053	−	0.459999i
$250$		0			0
$251$	−10.2125	+	10.2125i	−0.644608	+	0.644608i	−0.951685	−	0.307077i	$-0.900649\pi$
$251$	−10.2125	+	10.2125i	−0.644608	+	0.644608i	0.307077	+	0.951685i	$0.400649\pi$
$252$		0			0
$253$	−0.512191	−	0.212156i	−0.0322012	−	0.0133382i
$254$		0			0
$255$	−11.2990	−	3.63261i	−0.707568	−	0.227483i
$256$		0			0
$257$	7.43369	+	3.07914i	0.463701	+	0.192071i	0.602288	−	0.798279i	$-0.294256\pi$
$257$	7.43369	+	3.07914i	0.463701	+	0.192071i	−0.138587	+	0.990350i	$0.544256\pi$
$258$		0			0
$259$	−29.9926	+	12.4233i	−1.86365	+	0.771948i
$260$		0			0
$261$	3.64948	+	1.51166i	0.225897	+	0.0935697i
$262$		0			0
$263$	−11.4992	−	27.7616i	−0.709072	−	1.71185i	−0.702307	−	0.711875i	$-0.747846\pi$
$263$	−11.4992	−	27.7616i	−0.709072	−	1.71185i	−0.00676556	−	0.999977i	$-0.502154\pi$
$264$		0			0
$265$	−3.10700	+	3.66073i	−0.190861	+	0.224877i
$266$		0			0
$267$	4.62704			0.283170
$268$		0			0
$269$	−9.31129			−0.567719			−0.283860	−	0.958866i	$-0.591615\pi$
$269$	−9.31129			−0.567719			−0.283860	+	0.958866i	$0.591615\pi$
$270$		0			0
$271$			7.53080i			0.457463i	0.973489	+	0.228732i	$0.0734579\pi$
$271$			7.53080i			0.457463i	−0.973489	+	0.228732i	$0.926542\pi$
$272$		0			0
$273$	−34.8906	+	14.4522i	−2.11167	+	0.874684i
$274$		0			0
$275$	−4.64538	−	1.08487i	−0.280127	−	0.0654201i
$276$		0			0
$277$	19.2375	−	19.2375i	1.15587	−	1.15587i	0.170516	−	0.985355i	$-0.445457\pi$
$277$	19.2375	−	19.2375i	1.15587	−	1.15587i	0.985355	−	0.170516i	$-0.0545435\pi$
$278$		0			0
$279$	2.77500	−	2.77500i	0.166135	−	0.166135i
$280$		0			0
$281$	15.9980	+	6.62659i	0.954361	+	0.395309i	0.804868	−	0.593454i	$-0.202236\pi$
$281$	15.9980	+	6.62659i	0.954361	+	0.395309i	0.149493	+	0.988763i	$0.452236\pi$
$282$		0			0
$283$	13.5450	−	13.5450i	0.805167	−	0.805167i	−0.178731	−	0.983898i	$-0.557199\pi$
$283$	13.5450	−	13.5450i	0.805167	−	0.805167i	0.983898	+	0.178731i	$0.0571992\pi$
$284$		0			0
$285$	10.4548	+	20.3626i	0.619291	+	1.20618i
$286$		0			0
$287$	−23.1306	−	19.6333i	−1.36536	−	1.15892i
$288$		0			0
$289$	−7.95285	+	7.95285i	−0.467815	+	0.467815i
$290$		0			0
$291$			32.6610i			1.91462i
$292$		0			0
$293$	0.880478	+	2.12566i	0.0514381	+	0.124183i	0.947510	−	0.319727i	$-0.103591\pi$
$293$	0.880478	+	2.12566i	0.0514381	+	0.124183i	−0.896072	+	0.443909i	$0.853591\pi$
$294$		0			0
$295$	4.66786	−	14.5190i	0.271773	−	0.845331i
$296$		0			0
$297$	−1.64664	−	1.64664i	−0.0955475	−	0.0955475i
$298$		0			0
$299$	0.800907	+	1.93356i	0.0463176	+	0.111821i
$300$		0			0
$301$	−12.8114	+	30.9293i	−0.738434	+	1.78274i
$302$		0			0
$303$	27.6284	−	27.6284i	1.58721	−	1.58721i
$304$		0			0
$305$	−7.58334	−	14.7699i	−0.434221	−	0.845721i
$306$		0			0
$307$			34.6172i			1.97571i	0.155393	+	0.987853i	$0.450336\pi$
$307$			34.6172i			1.97571i	−0.155393	+	0.987853i	$0.549664\pi$
$308$		0			0
$309$	6.78347	−	16.3767i	0.385898	−	0.931641i
$310$		0			0
$311$	−3.68078	−	1.52463i	−0.208718	−	0.0864537i	0.275875	−	0.961193i	$-0.411032\pi$
$311$	−3.68078	−	1.52463i	−0.208718	−	0.0864537i	−0.484593	+	0.874740i	$0.661032\pi$
$312$		0			0
$313$	−1.31952	−	3.18560i	−0.0745835	−	0.180061i	0.882191	−	0.470892i	$-0.156068\pi$
$313$	−1.31952	−	3.18560i	−0.0745835	−	0.180061i	−0.956774	+	0.290832i	$0.906068\pi$
$314$		0			0
$315$	20.0322	−	1.63901i	1.12869	−	0.0923478i
$316$		0			0
$317$	5.57131	−	13.4503i	0.312916	−	0.755446i	−0.686678	−	0.726961i	$-0.740932\pi$
$317$	5.57131	−	13.4503i	0.312916	−	0.755446i	0.999594	−	0.0284845i	$-0.00906812\pi$
$318$		0			0
$319$	−1.40478	+	1.40478i	−0.0786527	+	0.0786527i
$320$		0			0
$321$	−9.00548	+	3.73019i	−0.502637	+	0.208199i
$322$		0			0
$323$	−11.0952			−0.617354
$324$		0			0
$325$	9.50437	+	15.2962i	0.527207	+	0.848482i
$326$		0			0
$327$	21.0434	−	21.0434i	1.16370	−	1.16370i
$328$		0			0
$329$		−	44.5183i		−	2.45437i
$330$		0			0
$331$	−11.4155	−	27.5594i	−0.627452	−	1.51480i	−0.842778	−	0.538261i	$-0.819081\pi$
$331$	−11.4155	−	27.5594i	−0.627452	−	1.51480i	0.215326	−	0.976542i	$-0.430919\pi$
$332$		0			0
$333$		−	12.9974i		−	0.712250i
$334$		0			0
$335$	25.1959	−	2.06150i	1.37660	−	0.112632i
$336$		0			0
$337$	−15.0203			−0.818210			−0.409105	−	0.912487i	$-0.634159\pi$
$337$	−15.0203			−0.818210			−0.409105	+	0.912487i	$0.634159\pi$
$338$		0			0
$339$	−4.24406	−	10.2461i	−0.230506	−	0.556490i
$340$		0			0
$341$	0.755311	+	1.82348i	0.0409024	+	0.0987471i
$342$		0			0
$343$	−36.9949	+	15.3238i	−1.99754	+	0.827407i
$344$		0			0
$345$	−0.234471	−	2.86574i	−0.0126235	−	0.154286i
$346$		0			0
$347$	20.9512	−	8.67826i	1.12472	−	0.465873i	0.258736	−	0.965948i	$-0.416694\pi$
$347$	20.9512	−	8.67826i	1.12472	−	0.465873i	0.865982	+	0.500075i	$0.166694\pi$
$348$		0			0
$349$	23.5083	+	23.5083i	1.25837	+	1.25837i	0.951871	+	0.306499i	$0.0991577\pi$
$349$	23.5083	+	23.5083i	1.25837	+	1.25837i	0.306499	+	0.951871i	$0.400842\pi$
$350$		0			0
$351$			8.79100i			0.469229i
$352$		0			0
$353$	13.0214	+	13.0214i	0.693059	+	0.693059i	0.962904	−	0.269844i	$-0.0869723\pi$
$353$	13.0214	+	13.0214i	0.693059	+	0.693059i	−0.269844	+	0.962904i	$0.586972\pi$
$354$		0			0
$355$	−1.07010	−	13.0789i	−0.0567952	−	0.694158i
$356$		0			0
$357$	−9.62432	+	23.2352i	−0.509373	+	1.22974i
$358$		0			0
$359$	35.6560			1.88185			0.940926	−	0.338614i	$-0.109958\pi$
$359$	35.6560			1.88185			0.940926	+	0.338614i	$0.109958\pi$
$360$		0			0
$361$	1.69583	+	1.69583i	0.0892542	+	0.0892542i
$362$		0			0
$363$	20.6282	−	8.54449i	1.08270	−	0.448469i
$364$		0			0
$365$	11.8803	+	3.81950i	0.621842	+	0.199922i
$366$		0			0
$367$	−4.56215			−0.238142			−0.119071	−	0.992886i	$-0.537992\pi$
$367$	−4.56215			−0.238142			−0.119071	+	0.992886i	$0.537992\pi$
$368$		0			0
$369$	10.8061	−	5.54767i	0.562542	−	0.288800i
$370$		0			0
$371$	7.19440	+	7.19440i	0.373515	+	0.373515i
$372$		0			0
$373$	9.50451	+	9.50451i	0.492125	+	0.492125i	0.908975	−	0.416850i	$-0.136866\pi$
$373$	9.50451	+	9.50451i	0.492125	+	0.492125i	−0.416850	+	0.908975i	$0.636866\pi$
$374$		0			0
$375$	−5.99900	−	24.0029i	−0.309787	−	1.23951i
$376$		0			0
$377$	7.49980			0.386259
$378$		0			0
$379$			35.2748i			1.81194i	0.423337	+	0.905972i	$0.360859\pi$
$379$			35.2748i			1.81194i	−0.423337	+	0.905972i	$0.639141\pi$
$380$		0			0
$381$	7.11079	−	2.94539i	0.364297	−	0.150897i
$382$		0			0
$383$	5.20336	+	12.5620i	0.265879	+	0.641889i	0.999281	−	0.0379059i	$-0.0120687\pi$
$383$	5.20336	+	12.5620i	0.265879	+	0.641889i	−0.733402	+	0.679795i	$0.762069\pi$
$384$		0			0
$385$	−3.09390	+	9.62336i	−0.157680	+	0.490452i
$386$		0			0
$387$	−9.47757	−	9.47757i	−0.481772	−	0.481772i
$388$		0			0
$389$	−11.6500	+	11.6500i	−0.590676	+	0.590676i	−0.937814	−	0.347138i	$-0.887154\pi$
$389$	−11.6500	+	11.6500i	−0.590676	+	0.590676i	0.347138	+	0.937814i	$0.387154\pi$
$390$		0			0
$391$	1.28764	+	0.533359i	0.0651189	+	0.0269731i
$392$		0			0
$393$	−36.9506	+	15.3055i	−1.86391	+	0.772058i
$394$		0			0
$395$	0.688385	+	8.41353i	0.0346364	+	0.423331i
$396$		0			0
$397$	10.5821	+	4.38326i	0.531101	+	0.219989i	0.632086	−	0.774899i	$-0.282199\pi$
$397$	10.5821	+	4.38326i	0.531101	+	0.219989i	−0.100984	+	0.994888i	$0.532199\pi$
$398$		0			0
$399$	44.8115	−	18.5615i	2.24338	−	0.929238i
$400$		0			0
$401$	15.4759	+	15.4759i	0.772830	+	0.772830i	0.978600	−	0.205770i	$-0.0659700\pi$
$401$	15.4759	+	15.4759i	0.772830	+	0.772830i	−0.205770	+	0.978600i	$0.565970\pi$
$402$		0			0
$403$	2.85136	−	6.88378i	0.142036	−	0.342906i
$404$		0			0
$405$	7.59154	−	23.6130i	0.377227	−	1.17334i
$406$		0			0
$407$	6.03919	+	2.50151i	0.299351	+	0.123995i
$408$		0			0
$409$	−34.5850			−1.71012			−0.855058	−	0.518532i	$-0.826479\pi$
$409$	−34.5850			−1.71012			−0.855058	+	0.518532i	$0.826479\pi$
$410$		0			0
$411$	−25.8061			−1.27292
$412$		0			0
$413$	−29.8569	−	12.3671i	−1.46916	−	0.608547i
$414$		0			0
$415$	−17.0501	+	8.75410i	−0.836958	+	0.429722i
$416$		0			0
$417$	2.19134	−	5.29037i	0.107311	−	0.259071i
$418$		0			0
$419$	−8.17907	−	8.17907i	−0.399574	−	0.399574i	0.478509	−	0.878083i	$-0.341177\pi$
$419$	−8.17907	−	8.17907i	−0.399574	−	0.399574i	−0.878083	+	0.478509i	$0.841177\pi$
$420$		0			0
$421$	−17.3852	+	7.20118i	−0.847302	+	0.350964i	−0.763729	−	0.645537i	$-0.776633\pi$
$421$	−17.3852	+	7.20118i	−0.847302	+	0.350964i	−0.0835737	+	0.996502i	$0.526633\pi$
$422$		0			0
$423$	16.4668	+	6.82079i	0.800645	+	0.331638i
$424$		0			0
$425$	11.6784	+	2.72735i	0.566487	+	0.132296i
$426$		0			0
$427$	−32.5037	+	13.4635i	−1.57296	+	0.651542i
$428$		0			0
$429$	7.02543	+	2.91003i	0.339191	+	0.140498i
$430$		0			0
$431$	−7.46649	+	7.46649i	−0.359648	+	0.359648i	−0.863683	−	0.504035i	$-0.831848\pi$
$431$	−7.46649	+	7.46649i	−0.359648	+	0.359648i	0.504035	+	0.863683i	$0.331848\pi$
$432$		0			0
$433$	9.67998	+	9.67998i	0.465190	+	0.465190i	0.900352	−	0.435162i	$-0.143309\pi$
$433$	9.67998	+	9.67998i	0.465190	+	0.465190i	−0.435162	+	0.900352i	$0.643309\pi$
$434$		0			0
$435$	−9.80920	−	3.15365i	−0.470315	−	0.151206i
$436$		0			0
$437$	−1.02864	−	2.48335i	−0.0492064	−	0.118795i
$438$		0			0
$439$	18.8403	−	7.80393i	0.899201	−	0.372461i	0.115288	−	0.993332i	$-0.463221\pi$
$439$	18.8403	−	7.80393i	0.899201	−	0.372461i	0.783913	+	0.620871i	$0.213221\pi$
$440$		0			0
$441$		−	29.3111i		−	1.39576i
$442$		0			0
$443$	6.49575			0.308623			0.154311	−	0.988022i	$-0.450684\pi$
$443$	6.49575			0.308623			0.154311	+	0.988022i	$0.450684\pi$
$444$		0			0
$445$	−4.65986	+	0.381264i	−0.220898	+	0.0180736i
$446$		0			0
$447$	−14.1539	−	14.1539i	−0.669456	−	0.669456i
$448$		0			0
$449$	12.9909	+	12.9909i	0.613078	+	0.613078i	0.943747	−	0.330669i	$-0.107274\pi$
$449$	12.9909	+	12.9909i	0.613078	+	0.613078i	−0.330669	+	0.943747i	$0.607274\pi$
$450$		0			0
$451$	0.497940	+	6.08874i	0.0234471	+	0.286707i
$452$		0			0
$453$	−8.83660			−0.415180
$454$		0			0
$455$	33.9472	−	17.4296i	1.59147	−	0.817113i
$456$		0			0
$457$	15.0860	−	6.24882i	0.705692	−	0.292307i	−0.000828363	−	1.00000i	$-0.500264\pi$
$457$	15.0860	−	6.24882i	0.705692	−	0.292307i	0.706521	+	0.707692i	$0.250264\pi$
$458$		0			0
$459$	4.13962	+	4.13962i	0.193221	+	0.193221i
$460$		0			0
$461$	−1.96245			−0.0914004			−0.0457002	−	0.998955i	$-0.514552\pi$
$461$	−1.96245			−0.0914004			−0.0457002	+	0.998955i	$0.514552\pi$
$462$		0			0
$463$	−14.3426	+	34.6260i	−0.666555	+	1.60921i	0.120779	+	0.992679i	$0.461461\pi$
$463$	−14.3426	+	34.6260i	−0.666555	+	1.60921i	−0.787334	+	0.616527i	$0.788539\pi$
$464$		0			0
$465$	−6.62399	+	7.80451i	−0.307180	+	0.361925i
$466$		0			0
$467$	−12.6295	−	12.6295i	−0.584423	−	0.584423i	0.351692	−	0.936116i	$-0.385606\pi$
$467$	−12.6295	−	12.6295i	−0.584423	−	0.584423i	−0.936116	+	0.351692i	$0.885606\pi$
$468$		0			0
$469$		−	53.5687i		−	2.47357i
$470$		0			0
$471$	−36.7985	−	36.7985i	−1.69559	−	1.69559i
$472$		0			0
$473$	6.22781	−	2.57964i	0.286355	−	0.118612i
$474$		0			0
$475$	−12.2069	−	19.6456i	−0.560089	−	0.901401i
$476$		0			0
$477$	−3.76341	+	1.55886i	−0.172315	+	0.0713751i
$478$		0			0
$479$	2.55351	+	6.16471i	0.116673	+	0.281673i	0.971418	−	0.237375i	$-0.0762869\pi$
$479$	2.55351	+	6.16471i	0.116673	+	0.281673i	−0.854746	+	0.519047i	$0.826287\pi$
$480$		0			0
$481$	−9.44340	−	22.7984i	−0.430582	−	1.03952i
$482$		0			0
$483$	−6.09282			−0.277233
$484$		0			0
$485$	−2.69124	−	32.8927i	−0.122203	−	1.49358i
$486$		0			0
$487$		−	13.2572i		−	0.600742i	−0.953822	−	0.300371i	$-0.902889\pi$
$487$		−	13.2572i		−	0.600742i	0.953822	−	0.300371i	$-0.0971106\pi$
$488$		0			0
$489$	−6.15683	−	14.8639i	−0.278421	−	0.672169i
$490$		0			0
$491$			10.9386i			0.493652i	0.969060	+	0.246826i	$0.0793876\pi$
$491$			10.9386i			0.493652i	−0.969060	+	0.246826i	$0.920612\pi$
$492$		0			0
$493$	3.53161	−	3.53161i	0.159056	−	0.159056i
$494$		0			0
$495$	−3.08555	−	2.61883i	−0.138685	−	0.117708i
$496$		0			0
$497$	−27.8070			−1.24731
$498$		0			0
$499$	4.37824	−	1.81352i	0.195997	−	0.0811845i	−0.282526	−	0.959260i	$-0.591172\pi$
$499$	4.37824	−	1.81352i	0.195997	−	0.0811845i	0.478523	+	0.878075i	$0.341172\pi$
$500$		0			0
$501$	32.8301	−	32.8301i	1.46674	−	1.46674i
$502$		0			0
$503$	7.20310	−	17.3898i	0.321171	−	0.775374i	−0.678016	−	0.735047i	$-0.737160\pi$
$503$	7.20310	−	17.3898i	0.321171	−	0.775374i	0.999187	−	0.0403272i	$-0.0128400\pi$
$504$		0			0
$505$	−25.5478	+	30.1009i	−1.13686	+	1.33947i
$506$		0			0
$507$	0.0234598	+	0.0566370i	0.00104189	+	0.00251534i
$508$		0			0
$509$	23.9967	+	9.93975i	1.06363	+	0.440572i	0.844740	−	0.535177i	$-0.179755\pi$
$509$	23.9967	+	9.93975i	1.06363	+	0.440572i	0.218894	+	0.975749i	$0.429755\pi$
$510$		0			0
$511$	10.1195	−	24.4306i	0.447660	−	1.08075i
$512$		0			0
$513$		−	11.2906i		−	0.498494i
$514$		0			0
$515$	−5.48216	+	17.0519i	−0.241573	+	0.751395i
$516$		0			0
$517$	−6.33853	+	6.33853i	−0.278768	+	0.278768i
$518$		0			0
$519$	−22.0849	+	53.3177i	−0.969421	+	2.34039i
$520$		0			0
$521$	2.37897	+	5.74335i	0.104225	+	0.251621i	0.967386	−	0.253308i	$-0.0815187\pi$
$521$	2.37897	+	5.74335i	0.104225	+	0.251621i	−0.863161	+	0.504929i	$0.831519\pi$
$522$		0			0
$523$	28.1529	+	28.1529i	1.23104	+	1.23104i	0.963564	+	0.267477i	$0.0861900\pi$
$523$	28.1529	+	28.1529i	1.23104	+	1.23104i	0.267477	+	0.963564i	$0.413810\pi$
$524$		0			0
$525$	−51.7297	+	8.52197i	−2.25767	+	0.371929i
$526$		0			0
$527$	−1.89884	−	4.58421i	−0.0827149	−	0.199691i
$528$		0			0
$529$		−	22.6623i		−	0.985320i
$530$		0			0
$531$	9.14895	−	9.14895i	0.397031	−	0.397031i
$532$		0			0
$533$	14.9240	−	17.5824i	0.646429	−	0.761576i
$534$		0			0
$535$	8.76199	−	4.49869i	0.378814	−	0.194495i
$536$		0			0
$537$	22.2469	−	22.2469i	0.960026	−	0.960026i
$538$		0			0
$539$	13.6193	+	5.64130i	0.586625	+	0.242988i
$540$		0			0
$541$	6.83003	−	6.83003i	0.293646	−	0.293646i	−0.544873	−	0.838519i	$-0.683422\pi$
$541$	6.83003	−	6.83003i	0.293646	−	0.293646i	0.838519	+	0.544873i	$0.183422\pi$
$542$		0			0
$543$	23.7740	−	23.7740i	1.02024	−	1.02024i
$544$		0			0
$545$	−19.4587	+	22.9266i	−0.833520	+	0.982069i
$546$		0			0
$547$	−0.789217	+	0.326905i	−0.0337445	+	0.0139774i	−0.399492	−	0.916737i	$-0.630813\pi$
$547$	−0.789217	+	0.326905i	−0.0337445	+	0.0139774i	0.365747	+	0.930714i	$0.380813\pi$
$548$		0			0
$549$		−	14.0855i		−	0.601156i
$550$		0			0
$551$	−9.63231			−0.410350
$552$		0			0
$553$	17.8879			0.760672
$554$		0			0
$555$	2.76462	+	33.7896i	0.117352	+	1.43429i
$556$		0			0
$557$	13.9162	+	33.5967i	0.589649	+	1.42354i	0.883839	+	0.467792i	$0.154950\pi$
$557$	13.9162	+	33.5967i	0.589649	+	1.42354i	−0.294190	+	0.955747i	$0.595050\pi$
$558$		0			0
$559$	−23.5105	−	9.73835i	−0.994387	−	0.411888i
$560$		0			0
$561$	4.67854	−	1.93792i	0.197528	−	0.0818189i
$562$		0			0
$563$	14.1974	+	5.88077i	0.598351	+	0.247845i	0.661239	−	0.750176i	$-0.270031\pi$
$563$	14.1974	+	5.88077i	0.598351	+	0.247845i	−0.0628879	+	0.998021i	$0.520031\pi$
$564$		0			0
$565$	5.11843	+	9.96904i	0.215334	+	0.419401i
$566$		0			0
$567$	−48.5576	−	20.1132i	−2.03923	−	0.844676i
$568$		0			0
$569$	1.43427	−	1.43427i	0.0601277	−	0.0601277i	−0.676404	−	0.736531i	$-0.736462\pi$
$569$	1.43427	−	1.43427i	0.0601277	−	0.0601277i	0.736531	+	0.676404i	$0.236462\pi$
$570$		0			0
$571$	23.9088	−	9.90334i	1.00055	−	0.414442i	0.178552	−	0.983931i	$-0.442859\pi$
$571$	23.9088	−	9.90334i	1.00055	−	0.414442i	0.821999	+	0.569489i	$0.192859\pi$
$572$		0			0
$573$	−23.5020	−	23.5020i	−0.981808	−	0.981808i
$574$		0			0
$575$	0.472269	+	2.86675i	0.0196950	+	0.119552i
$576$		0			0
$577$	−6.80262	+	16.4230i	−0.283197	+	0.683697i	−0.999907	−	0.0136742i	$-0.995647\pi$
$577$	−6.80262	+	16.4230i	−0.283197	+	0.683697i	0.716710	+	0.697372i	$0.245647\pi$
$578$		0			0
$579$	2.92401	+	2.92401i	0.121518	+	0.121518i
$580$		0			0
$581$	15.5420	+	37.5218i	0.644792	+	1.55667i
$582$		0			0
$583$		−	2.04868i		−	0.0848477i
$584$		0			0
$585$	1.24587	+	15.2272i	0.0515103	+	0.629566i
$586$		0			0
$587$	12.4961	−	30.1683i	0.515770	−	1.24518i	−0.424709	−	0.905330i	$-0.639624\pi$
$587$	12.4961	−	30.1683i	0.515770	−	1.24518i	0.940480	−	0.339850i	$-0.110376\pi$
$588$		0			0
$589$	−3.66212	+	8.84113i	−0.150895	+	0.364293i
$590$		0			0
$591$	13.0176	−	31.4272i	0.535471	−	1.29274i
$592$		0			0
$593$	16.3002	+	39.3522i	0.669369	+	1.61600i	0.782669	+	0.622438i	$0.213858\pi$
$593$	16.3002	+	39.3522i	0.669369	+	1.61600i	−0.113300	+	0.993561i	$0.536142\pi$
$594$		0			0
$595$	7.77803	−	24.1930i	0.318868	−	0.991817i
$596$		0			0
$597$	25.8339	−	25.8339i	1.05731	−	1.05731i
$598$		0			0
$599$	−11.5079			−0.470199			−0.235099	−	0.971971i	$-0.575542\pi$
$599$	−11.5079			−0.470199			−0.235099	+	0.971971i	$0.575542\pi$
$600$		0			0
$601$	24.9899	+	10.3512i	1.01936	+	0.422233i	0.828861	−	0.559455i	$-0.188989\pi$
$601$	24.9899	+	10.3512i	1.01936	+	0.422233i	0.190499	+	0.981687i	$0.438989\pi$
$602$		0			0
$603$	19.8145	+	8.20744i	0.806909	+	0.334233i
$604$		0			0
$605$	−20.0705	+	10.3048i	−0.815981	+	0.418952i
$606$		0			0
$607$			21.5193i			0.873443i	0.899597	+	0.436722i	$0.143861\pi$
$607$			21.5193i			0.873443i	−0.899597	+	0.436722i	$0.856139\pi$
$608$		0			0
$609$	−8.35536	+	20.1716i	−0.338576	+	0.817396i
$610$		0			0
$611$	33.8399			1.36902
$612$		0			0
$613$		−	48.0920i		−	1.94242i	−0.238231	−	0.971209i	$-0.576568\pi$
$613$		−	48.0920i		−	1.94242i	0.238231	−	0.971209i	$-0.423432\pi$
$614$		0			0
$615$	−26.9128	+	16.7210i	−1.08523	+	0.674255i
$616$		0			0
$617$			3.88630i			0.156456i	0.996935	+	0.0782282i	$0.0249263\pi$
$617$			3.88630i			0.156456i	−0.996935	+	0.0782282i	$0.975074\pi$
$618$		0			0
$619$	−1.90502			−0.0765692			−0.0382846	−	0.999267i	$-0.512189\pi$
$619$	−1.90502			−0.0765692			−0.0382846	+	0.999267i	$0.512189\pi$
$620$		0			0
$621$	−0.542754	+	1.31032i	−0.0217800	+	0.0525815i
$622$		0			0
$623$			9.90728i			0.396927i
$624$		0			0
$625$	8.01938	+	23.6789i	0.320775	+	0.947155i
$626$		0			0
$627$	−9.02306	−	3.73747i	−0.360346	−	0.149260i
$628$		0			0
$629$	−15.1824	−	6.28877i	−0.605364	−	0.250750i
$630$		0			0
$631$	−24.0530			−0.957535			−0.478767	−	0.877942i	$-0.658916\pi$
$631$	−24.0530			−0.957535			−0.478767	+	0.877942i	$0.658916\pi$
$632$		0			0
$633$	16.4975	−	16.4975i	0.655718	−	0.655718i
$634$		0			0
$635$	−6.91854	+	3.55220i	−0.274554	+	0.140965i
$636$		0			0
$637$	−21.2963	−	51.4139i	−0.843792	−	2.03709i
$638$		0			0
$639$	4.26040	−	10.2855i	0.168539	−	0.406889i
$640$		0			0
$641$	6.62859	−	16.0028i	0.261814	−	0.632074i	−0.737237	−	0.675634i	$-0.763870\pi$
$641$	6.62859	−	16.0028i	0.261814	−	0.632074i	0.999051	+	0.0435599i	$0.0138699\pi$
$642$		0			0
$643$	−9.56163	+	23.0838i	−0.377074	+	0.910337i	0.615438	+	0.788186i	$0.288979\pi$
$643$	−9.56163	+	23.0838i	−0.377074	+	0.910337i	−0.992511	+	0.122151i	$0.961021\pi$
$644$		0			0
$645$	26.6551	+	22.6232i	1.04954	+	0.890786i
$646$		0			0
$647$		−	15.5476i		−	0.611237i	−0.952154	−	0.305619i	$-0.901137\pi$
$647$		−	15.5476i		−	0.611237i	0.952154	−	0.305619i	$-0.0988633\pi$
$648$		0			0
$649$	2.49020	+	6.01188i	0.0977489	+	0.235987i
$650$		0			0
$651$	15.3381	+	15.3381i	0.601149	+	0.601149i
$652$		0			0
$653$	18.7937	−	45.3721i	0.735455	−	1.77555i	0.111968	−	0.993712i	$-0.464285\pi$
$653$	18.7937	−	45.3721i	0.735455	−	1.77555i	0.623487	−	0.781834i	$-0.285715\pi$
$654$		0			0
$655$	35.9516	−	18.4587i	1.40475	−	0.721242i
$656$		0			0
$657$	7.48618	+	7.48618i	0.292064	+	0.292064i
$658$		0			0
$659$	−24.8847	+	10.3076i	−0.969371	+	0.401527i	−0.810478	−	0.585769i	$-0.800793\pi$
$659$	−24.8847	+	10.3076i	−0.969371	+	0.401527i	−0.158893	+	0.987296i	$0.550793\pi$
$660$		0			0
$661$	−6.01328	+	6.01328i	−0.233889	+	0.233889i	−0.814314	−	0.580425i	$-0.802887\pi$
$661$	−6.01328	+	6.01328i	−0.233889	+	0.233889i	0.580425	+	0.814314i	$0.302887\pi$
$662$		0			0
$663$	−17.6619	−	7.31578i	−0.685930	−	0.284121i
$664$		0			0
$665$	−43.5999	+	22.3856i	−1.69073	+	0.868076i
$666$		0			0
$667$	1.11787	+	0.463036i	0.0432840	+	0.0179288i
$668$		0			0
$669$	21.8175	−	9.03710i	0.843513	−	0.349394i
$670$		0			0
$671$	6.54481	+	2.71095i	0.252660	+	0.104655i
$672$		0			0
$673$	3.39162	+	8.18808i	0.130737	+	0.315627i	0.975670	−	0.219245i	$-0.0703595\pi$
$673$	3.39162	+	8.18808i	0.130737	+	0.315627i	−0.844933	+	0.534873i	$0.820360\pi$
$674$		0			0
$675$	−2.77539	+	11.8842i	−0.106825	+	0.457421i
$676$		0			0
$677$	−31.8359			−1.22355			−0.611777	−	0.791030i	$-0.709545\pi$
$677$	−31.8359			−1.22355			−0.611777	+	0.791030i	$0.709545\pi$
$678$		0			0
$679$	−69.9329			−2.68378
$680$		0			0
$681$		−	51.2335i		−	1.96327i
$682$		0			0
$683$	−32.3607	+	13.4043i	−1.23825	+	0.512899i	−0.903167	−	0.429290i	$-0.858764\pi$
$683$	−32.3607	+	13.4043i	−1.23825	+	0.512899i	−0.335082	+	0.942189i	$0.608764\pi$
$684$		0			0
$685$	25.9892	−	2.12640i	0.992996	−	0.0812457i
$686$		0			0
$687$	−17.8103	+	17.8103i	−0.679504	+	0.679504i
$688$		0			0
$689$	−5.46871	+	5.46871i	−0.208341	+	0.208341i
$690$		0			0
$691$	−15.3976	−	6.37790i	−0.585753	−	0.242627i	0.0700696	−	0.997542i	$-0.477678\pi$
$691$	−15.3976	−	6.37790i	−0.585753	−	0.242627i	−0.655822	+	0.754915i	$0.727678\pi$
$692$		0			0
$693$	−6.06401	+	6.06401i	−0.230353	+	0.230353i
$694$		0			0
$695$	−1.77097	+	5.50847i	−0.0671766	+	0.208948i
$696$		0			0
$697$	−1.25181	−	15.3070i	−0.0474159	−	0.579795i
$698$		0			0
$699$	−42.6416	+	42.6416i	−1.61285	+	1.61285i
$700$		0			0
$701$		−	5.39909i		−	0.203921i	−0.994788	−	0.101960i	$-0.967488\pi$
$701$		−	5.39909i		−	0.203921i	0.994788	−	0.101960i	$-0.0325115\pi$
$702$		0			0
$703$	12.1286	+	29.2809i	0.457437	+	1.10435i
$704$		0			0
$705$	−44.2602	−	14.2296i	−1.66693	−	0.535918i
$706$		0			0
$707$	59.1571	+	59.1571i	2.22483	+	2.22483i
$708$		0			0
$709$	−6.17473	−	14.9071i	−0.231897	−	0.559849i	0.764503	−	0.644620i	$-0.222984\pi$
$709$	−6.17473	−	14.9071i	−0.231897	−	0.559849i	−0.996400	+	0.0847707i	$0.972984\pi$
$710$		0			0
$711$	−2.74067	+	6.61656i	−0.102783	+	0.248140i
$712$		0			0
$713$	0.850006	−	0.850006i	0.0318330	−	0.0318330i
$714$		0			0
$715$	−7.31505	−	2.35178i	−0.273567	−	0.0879516i
$716$		0			0
$717$			34.2907i			1.28061i
$718$		0			0
$719$	−10.3523	+	24.9927i	−0.386076	+	0.932069i	0.604687	+	0.796463i	$0.293298\pi$
$719$	−10.3523	+	24.9927i	−0.386076	+	0.932069i	−0.990763	+	0.135606i	$0.956702\pi$
$720$		0			0
$721$	35.0654	+	14.5246i	1.30590	+	0.540923i
$722$		0			0
$723$	12.0799	+	29.1634i	0.449255	+	1.08460i
$724$		0			0
$725$	10.1386	+	2.36775i	0.376540	+	0.0879360i
$726$		0			0
$727$	−1.49878	+	3.61838i	−0.0555868	+	0.134198i	−0.949233	−	0.314574i	$-0.898138\pi$
$727$	−1.49878	+	3.61838i	−0.0555868	+	0.134198i	0.893646	+	0.448772i	$0.148138\pi$
$728$		0			0
$729$	3.42151	−	3.42151i	0.126723	−	0.126723i
$730$		0			0
$731$	−15.6566	+	6.48520i	−0.579082	+	0.239864i
$732$		0			0
$733$	−38.6211			−1.42650			−0.713251	−	0.700908i	$-0.752778\pi$
$733$	−38.6211			−1.42650			−0.713251	+	0.700908i	$0.752778\pi$
$734$		0			0
$735$	6.23466	+	76.2008i	0.229969	+	2.81071i
$736$		0			0
$737$	−7.62713	+	7.62713i	−0.280949	+	0.280949i
$738$		0			0
$739$			17.8735i			0.657487i	0.944419	+	0.328743i	$0.106625\pi$
$739$			17.8735i			0.657487i	−0.944419	+	0.328743i	$0.893375\pi$
$740$		0			0
$741$	14.1092	+	34.0627i	0.518316	+	1.25133i
$742$		0			0
$743$		−	9.99751i		−	0.366773i	−0.983041	−	0.183387i	$-0.941294\pi$
$743$		−	9.99751i		−	0.366773i	0.983041	−	0.183387i	$-0.0587060\pi$
$744$		0			0
$745$	15.4205	+	13.0880i	0.564965	+	0.479508i
$746$		0			0
$747$	−16.2601			−0.594928
$748$		0			0
$749$	−7.98698	−	19.2823i	−0.291838	−	0.704559i
$750$		0			0
$751$	−10.5747	−	25.5296i	−0.385876	−	0.931587i	−0.990804	−	0.135307i	$-0.956798\pi$
$751$	−10.5747	−	25.5296i	−0.385876	−	0.931587i	0.604928	−	0.796280i	$-0.293202\pi$
$752$		0			0
$753$	29.5277	−	12.2308i	1.07605	−	0.445714i
$754$		0			0
$755$	8.89929	−	0.728129i	0.323878	−	0.0264993i
$756$		0			0
$757$	−4.81028	+	1.99248i	−0.174833	+	0.0724181i	−0.468383	−	0.883526i	$-0.655163\pi$
$757$	−4.81028	+	1.99248i	−0.174833	+	0.0724181i	0.293550	+	0.955944i	$0.405163\pi$
$758$		0			0
$759$	0.867497	+	0.867497i	0.0314881	+	0.0314881i
$760$		0			0
$761$		−	31.5014i		−	1.14192i	−0.820977	−	0.570962i	$-0.806571\pi$
$761$		−	31.5014i		−	1.14192i	0.820977	−	0.570962i	$-0.193429\pi$
$762$		0			0
$763$	45.0575	+	45.0575i	1.63119	+	1.63119i
$764$		0			0
$765$	7.75704	+	6.58370i	0.280457	+	0.238034i
$766$		0			0
$767$	9.40070	−	22.6953i	0.339439	−	0.819479i
$768$		0			0
$769$	31.7177			1.14377			0.571885	−	0.820334i	$-0.306213\pi$
$769$	31.7177			1.14377			0.571885	+	0.820334i	$0.306213\pi$
$770$		0			0
$771$	−12.5904	−	12.5904i	−0.453433	−	0.453433i
$772$		0			0
$773$	−35.7325	+	14.8009i	−1.28521	+	0.532351i	−0.917554	−	0.397612i	$-0.869839\pi$
$773$	−35.7325	+	14.8009i	−1.28521	+	0.532351i	−0.367654	+	0.929963i	$0.619839\pi$
$774$		0			0
$775$	6.02789	−	8.40568i	0.216528	−	0.301941i
$776$		0			0
$777$	71.8397			2.57724
$778$		0			0
$779$	−19.1675	+	22.5818i	−0.686747	+	0.809076i
$780$		0			0
$781$	3.95917	+	3.95917i	0.141670	+	0.141670i
$782$		0			0
$783$	3.59382	+	3.59382i	0.128433	+	0.128433i
$784$		0			0
$785$	40.0917	+	34.0274i	1.43093	+	1.21449i
$786$		0			0
$787$	−50.5730			−1.80273			−0.901366	−	0.433058i	$-0.857434\pi$
$787$	−50.5730			−1.80273			−0.901366	+	0.433058i	$0.857434\pi$
$788$		0			0
$789$			66.4959i			2.36732i
$790$		0			0
$791$	21.9386	−	9.08726i	0.780047	−	0.323106i
$792$		0			0
$793$	−10.2340	−	24.7072i	−0.363421	−	0.877377i
$794$		0			0
$795$	9.45227	−	4.85310i	0.335237	−	0.172122i
$796$		0			0
$797$	−4.23854	−	4.23854i	−0.150137	−	0.150137i	0.628042	−	0.778179i	$-0.283856\pi$
$797$	−4.23854	−	4.23854i	−0.150137	−	0.150137i	−0.778179	+	0.628042i	$0.783856\pi$
$798$		0			0
$799$	15.9350	−	15.9350i	0.563739	−	0.563739i
$800$		0			0
$801$	−3.66460	−	1.51793i	−0.129482	−	0.0536333i
$802$		0			0
$803$	−4.91925	+	2.03762i	−0.173597	+	0.0719060i
$804$		0			0
$805$	6.13604	−	0.502043i	0.216267	−	0.0176947i
$806$		0			0
$807$	19.0367	+	7.88526i	0.670123	+	0.277574i
$808$		0			0
$809$	−14.4462	+	5.98380i	−0.507901	+	0.210379i	−0.621893	−	0.783102i	$-0.713636\pi$
$809$	−14.4462	+	5.98380i	−0.507901	+	0.210379i	0.113992	+	0.993482i	$0.463636\pi$
$810$		0			0
$811$	10.1692	+	10.1692i	0.357089	+	0.357089i	0.862739	−	0.505650i	$-0.168747\pi$
$811$	10.1692	+	10.1692i	0.357089	+	0.357089i	−0.505650	+	0.862739i	$0.668747\pi$
$812$		0			0
$813$	6.37745	−	15.3965i	0.223667	−	0.539980i
$814$		0			0
$815$	7.42528	+	14.4620i	0.260096	+	0.506583i
$816$		0			0
$817$	30.1955	+	12.5074i	1.05641	+	0.437578i
$818$		0			0
$819$	32.3743			1.13125
$820$		0			0
$821$	18.5070			0.645900			0.322950	−	0.946416i	$-0.395325\pi$
$821$	18.5070			0.645900			0.322950	+	0.946416i	$0.395325\pi$
$822$		0			0
$823$	−9.54807	−	3.95494i	−0.332825	−	0.137861i	0.210012	−	0.977699i	$-0.432650\pi$
$823$	−9.54807	−	3.95494i	−0.332825	−	0.137861i	−0.542837	+	0.839838i	$0.682650\pi$
$824$		0			0
$825$	8.57864	+	6.15192i	0.298670	+	0.214183i
$826$		0			0
$827$	9.30848	−	22.4727i	0.323687	−	0.781451i	−0.675346	−	0.737501i	$-0.736006\pi$
$827$	9.30848	−	22.4727i	0.323687	−	0.781451i	0.999034	−	0.0439499i	$-0.0139942\pi$
$828$		0			0
$829$	−14.3691	−	14.3691i	−0.499058	−	0.499058i	0.412087	−	0.911145i	$-0.364800\pi$
$829$	−14.3691	−	14.3691i	−0.499058	−	0.499058i	−0.911145	+	0.412087i	$0.864800\pi$
$830$		0			0
$831$	−55.6219	+	23.0394i	−1.92950	+	0.799226i
$832$		0			0
$833$	−34.2388	−	14.1822i	−1.18630	−	0.491383i
$834$		0			0
$835$	−30.3578	+	35.7681i	−1.05057	+	1.23781i
$836$		0			0
$837$	4.66496	−	1.93229i	0.161245	−	0.0667898i
$838$		0			0
$839$	1.92039	+	0.795452i	0.0662992	+	0.0274620i	0.415587	−	0.909554i	$-0.363576\pi$
$839$	1.92039	+	0.795452i	0.0662992	+	0.0274620i	−0.349287	+	0.937016i	$0.613576\pi$
$840$		0			0
$841$	−17.4401	+	17.4401i	−0.601384	+	0.601384i
$842$		0			0
$843$	−27.0958	−	27.0958i	−0.933229	−	0.933229i
$844$		0			0
$845$	−0.0282931	−	0.0551057i	−0.000973311	−	0.00189569i
$846$		0			0
$847$	18.2952	+	44.1686i	0.628631	+	1.51765i
$848$		0			0
$849$	−39.1630	+	16.2218i	−1.34407	+	0.556732i
$850$		0			0
$851$		−	3.98120i		−	0.136474i
$852$		0			0
$853$	−26.7502			−0.915910			−0.457955	−	0.888975i	$-0.651418\pi$
$853$	−26.7502			−0.915910			−0.457955	+	0.888975i	$0.651418\pi$
$854$		0			0
$855$	−1.60012	−	19.5569i	−0.0547230	−	0.668832i
$856$		0			0
$857$	−23.1376	−	23.1376i	−0.790364	−	0.790364i	0.191189	−	0.981553i	$-0.438766\pi$
$857$	−23.1376	−	23.1376i	−0.790364	−	0.790364i	−0.981553	+	0.191189i	$0.938766\pi$
$858$		0			0
$859$	−13.8292	−	13.8292i	−0.471847	−	0.471847i	0.430665	−	0.902512i	$-0.358279\pi$
$859$	−13.8292	−	13.8292i	−0.471847	−	0.471847i	−0.902512	+	0.430665i	$0.858279\pi$
$860$		0			0
$861$	30.6634	+	59.7280i	1.04501	+	2.03552i
$862$		0			0
$863$	32.3252			1.10036			0.550181	−	0.835046i	$-0.314559\pi$
$863$	32.3252			1.10036			0.550181	+	0.835046i	$0.314559\pi$
$864$		0			0
$865$	17.8482	−	55.5157i	0.606859	−	1.88759i
$866$		0			0
$867$	22.9943	−	9.52454i	0.780926	−	0.323470i
$868$		0			0
$869$	−2.54689	−	2.54689i	−0.0863973	−	0.0863973i
$870$		0			0
$871$	40.7194			1.37973
$872$		0			0
$873$	10.7146	−	25.8674i	0.362636	−	0.875480i
$874$		0			0
$875$	51.3944	−	12.8449i	1.73745	−	0.434237i
$876$		0			0
$877$	2.20192	+	2.20192i	0.0743537	+	0.0743537i	0.743306	−	0.668952i	$-0.233257\pi$
$877$	2.20192	+	2.20192i	0.0743537	+	0.0743537i	−0.668952	+	0.743306i	$0.733257\pi$
$878$		0			0
$879$		−	5.09150i		−	0.171732i
$880$		0			0
$881$	−3.19507	−	3.19507i	−0.107645	−	0.107645i	0.651233	−	0.758878i	$-0.274252\pi$
$881$	−3.19507	−	3.19507i	−0.107645	−	0.107645i	−0.758878	+	0.651233i	$0.774252\pi$
$882$		0			0
$883$	24.1133	−	9.98805i	0.811477	−	0.336125i	0.0619338	−	0.998080i	$-0.480273\pi$
$883$	24.1133	−	9.98805i	0.811477	−	0.336125i	0.749543	+	0.661955i	$0.230273\pi$
$884$		0			0
$885$	−21.8388	+	25.7308i	−0.734102	+	0.864933i
$886$		0			0
$887$	3.07272	−	1.27276i	0.103172	−	0.0427352i	−0.330501	−	0.943806i	$-0.607218\pi$
$887$	3.07272	−	1.27276i	0.103172	−	0.0427352i	0.433672	+	0.901071i	$0.357218\pi$
$888$		0			0
$889$	6.30658	+	15.2254i	0.211516	+	0.510644i
$890$		0			0
$891$	4.04992	+	9.77738i	0.135677	+	0.327554i
$892$		0			0
$893$	−43.4620			−1.45440
$894$		0			0
$895$	−20.5716	+	24.2379i	−0.687633	+	0.810183i
$896$		0			0
$897$		−	4.63136i		−	0.154637i
$898$		0			0
$899$	−1.64848	−	3.97979i	−0.0549800	−	0.132733i
$900$		0			0
$901$			5.15036i			0.171583i
$902$		0			0
$903$	52.3850	−	52.3850i	1.74326	−	1.74326i
$904$		0			0
$905$	−21.9837	+	25.9016i	−0.730762	+	0.860998i
$906$		0			0
$907$	−33.1688			−1.10135			−0.550676	−	0.834719i	$-0.685630\pi$
$907$	−33.1688			−1.10135			−0.550676	+	0.834719i	$0.685630\pi$
$908$		0			0
$909$	−30.9452	+	12.8179i	−1.02639	+	0.425144i
$910$		0			0
$911$	32.4282	−	32.4282i	1.07439	−	1.07439i	0.0773939	−	0.997001i	$-0.475340\pi$
$911$	32.4282	−	32.4282i	1.07439	−	1.07439i	0.997001	−	0.0773939i	$-0.0246599\pi$
$912$		0			0
$913$	3.12948	−	7.55524i	0.103571	−	0.250042i
$914$		0			0
$915$	2.99609	+	36.6186i	0.0990477	+	1.21057i
$916$		0			0
$917$	−32.7716	−	79.1177i	−1.08221	−	2.61270i
$918$		0			0
$919$	43.6564	+	18.0831i	1.44009	+	0.596506i	0.959821	−	0.280613i	$-0.0905379\pi$
$919$	43.6564	+	18.0831i	1.44009	+	0.596506i	0.480272	+	0.877119i	$0.340538\pi$
$920$		0			0
$921$	29.3155	−	70.7739i	0.965979	−	2.33208i
$922$		0			0
$923$		−	21.1371i		−	0.695735i
$924$		0			0
$925$	−5.56847	−	33.8015i	−0.183090	−	1.11139i
$926$		0			0
$927$	−10.7450	+	10.7450i	−0.352911	+	0.352911i
$928$		0			0
$929$	−19.8878	+	48.0135i	−0.652499	+	1.57527i	0.156641	+	0.987656i	$0.449934\pi$
$929$	−19.8878	+	48.0135i	−0.652499	+	1.57527i	−0.809140	+	0.587616i	$0.800066\pi$
$930$		0			0
$931$	27.3518	+	66.0331i	0.896419	+	2.16415i
$932$		0			0
$933$	6.23413	+	6.23413i	0.204096	+	0.204096i
$934$		0			0
$935$	−4.55205	+	2.33717i	−0.148868	+	0.0764336i
$936$		0			0
$937$	−18.2958	−	44.1700i	−0.597698	−	1.44297i	−0.875921	−	0.482454i	$-0.839745\pi$
$937$	−18.2958	−	44.1700i	−0.597698	−	1.44297i	0.278223	−	0.960517i	$-0.410255\pi$
$938$		0			0
$939$			7.63031i			0.249006i
$940$		0			0
$941$	0.0757829	−	0.0757829i	0.00247045	−	0.00247045i	−0.705870	−	0.708341i	$-0.749444\pi$
$941$	0.0757829	−	0.0757829i	0.00247045	−	0.00247045i	0.708341	+	0.705870i	$0.249444\pi$
$942$		0			0
$943$	3.30999	−	1.69930i	0.107788	−	0.0553368i
$944$		0			0
$945$	24.6192	+	7.91504i	0.800862	+	0.257476i
$946$		0			0
$947$	−19.5466	+	19.5466i	−0.635180	+	0.635180i	−0.949363	−	0.314182i	$-0.898270\pi$
$947$	−19.5466	+	19.5466i	−0.635180	+	0.635180i	0.314182	+	0.949363i	$0.398270\pi$
$948$		0			0
$949$	18.5705	+	7.69217i	0.602825	+	0.249698i
$950$		0			0
$951$	−22.7808	+	22.7808i	−0.738718	+	0.738718i
$952$		0			0
$953$	−7.80941	+	7.80941i	−0.252972	+	0.252972i	−0.822188	−	0.569216i	$-0.807247\pi$
$953$	−7.80941	+	7.80941i	−0.252972	+	0.252972i	0.569216	+	0.822188i	$0.307247\pi$
$954$		0			0
$955$	25.6052	+	21.7321i	0.828565	+	0.703235i
$956$		0			0
$957$	4.06168	−	1.68240i	0.131296	−	0.0543844i
$958$		0			0
$959$		−	55.2554i		−	1.78429i
$960$		0			0
$961$	26.7204			0.861947
$962$		0			0
$963$	8.35602			0.269269
$964$		0			0
$965$	−3.18568	−	2.70381i	−0.102551	−	0.0870388i
$966$		0			0
$967$	−20.4685	−	49.4153i	−0.658222	−	1.58909i	−0.800547	−	0.599270i	$-0.795458\pi$
$967$	−20.4685	−	49.4153i	−0.658222	−	1.58909i	0.142325	−	0.989820i	$-0.454542\pi$
$968$		0			0
$969$	22.6839	+	9.39597i	0.728711	+	0.301842i
$970$		0			0
$971$	−41.6076	+	17.2345i	−1.33525	+	0.553080i	−0.932149	−	0.362074i	$-0.882069\pi$
$971$	−41.6076	+	17.2345i	−1.33525	+	0.553080i	−0.403104	+	0.915154i	$0.632069\pi$
$972$		0			0
$973$	11.3276	+	4.69205i	0.363146	+	0.150420i
$974$		0			0
$975$	−6.47784	−	39.3215i	−0.207457	−	1.25930i
$976$		0			0
$977$	18.3585	+	7.60433i	0.587340	+	0.243284i	0.656506	−	0.754321i	$-0.272034\pi$
$977$	18.3585	+	7.60433i	0.587340	+	0.243284i	−0.0691660	+	0.997605i	$0.522034\pi$
$978$		0			0
$979$	1.41060	−	1.41060i	0.0450830	−	0.0450830i
$980$		0			0
$981$	−23.5697	+	9.76289i	−0.752523	+	0.311705i
$982$		0			0
$983$	22.0753	+	22.0753i	0.704091	+	0.704091i	0.965286	−	0.261195i	$-0.0841165\pi$
$983$	22.0753	+	22.0753i	0.704091	+	0.704091i	−0.261195	+	0.965286i	$0.584116\pi$
$984$		0			0
$985$	−10.5203	+	32.7228i	−0.335206	+	1.04263i
$986$		0			0
$987$	−37.7003	+	91.0165i	−1.20001	+	2.89709i
$988$		0			0
$989$	−2.90306	−	2.90306i	−0.0923120	−	0.0923120i
$990$		0			0
$991$	12.9983	+	31.3806i	0.412904	+	0.996838i	0.984354	+	0.176201i	$0.0563810\pi$
$991$	12.9983	+	31.3806i	0.412904	+	0.996838i	−0.571450	+	0.820637i	$0.693619\pi$
$992$		0			0
$993$			66.0118i			2.09482i
$994$		0			0
$995$	−23.8885	+	28.1459i	−0.757316	+	0.892284i
$996$		0			0
$997$	−2.39091	+	5.77216i	−0.0757208	+	0.182806i	−0.957207	−	0.289403i	$-0.906543\pi$
$997$	−2.39091	+	5.77216i	−0.0757208	+	0.182806i	0.881487	+	0.472209i	$0.156543\pi$
$998$		0			0
$999$	6.39955	−	15.4499i	0.202473	−	0.488813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.137.5	yes	84
5.3	odd	4		820.2.x.a.793.17	yes	84
41.3	odd	8		820.2.x.a.577.17	✓	84
205.3	even	8	inner	820.2.y.a.413.5	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.17	✓	84	41.3	odd	8
820.2.x.a.793.17	yes	84	5.3	odd	4
820.2.y.a.137.5	yes	84	1.1	even	1	trivial
820.2.y.a.413.5	yes	84	205.3	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04447 - 0.846849i) q^{3} +(2.12876 + 0.684393i) q^{5} +(1.81325 - 4.37757i) q^{7} +(1.34140 + 1.34140i) q^{9} +(-0.881451 + 0.365109i) q^{11} +(3.32754 + 1.37831i) q^{13} +(-3.77261 - 3.20196i) q^{15} +(2.21596 - 0.917880i) q^{17} +(-4.27371 - 1.77023i) q^{19} +(-7.41429 + 7.41429i) q^{21} +(0.410884 + 0.410884i) q^{23} +(4.06321 + 2.91381i) q^{25} +(0.934048 + 2.25499i) q^{27} +(1.92379 - 0.796858i) q^{29} -2.06873i q^{31} +2.11130 q^{33} +(6.85595 - 8.07781i) q^{35} +(-4.84468 - 4.84468i) q^{37} +(-5.63586 - 5.63586i) q^{39} +(1.96004 - 6.09576i) q^{41} -7.06541 q^{43} +(1.93747 + 3.77357i) q^{45} +(8.68032 - 3.59551i) q^{47} +(-10.9255 - 10.9255i) q^{49} -5.30778 q^{51} +(-0.821734 + 1.98384i) q^{53} +(-2.12627 + 0.173969i) q^{55} +(7.23837 + 7.23837i) q^{57} -6.82043i q^{59} +(-5.25030 - 5.25030i) q^{61} +(8.30439 - 3.43979i) q^{63} +(6.14022 + 5.21144i) q^{65} +(10.4450 - 4.32646i) q^{67} +(-0.492085 - 1.18800i) q^{69} +(-2.24583 - 5.42190i) q^{71} +5.58085 q^{73} +(-5.83957 - 9.39815i) q^{75} +4.52065i q^{77} +(1.44471 + 3.48785i) q^{79} -11.0924i q^{81} +(-6.06087 + 6.06087i) q^{83} +(5.34543 - 0.437356i) q^{85} -4.60795 q^{87} +(-1.93175 + 0.800159i) q^{89} +(12.0673 - 12.0673i) q^{91} +(-1.75190 + 4.22946i) q^{93} +(-7.88615 - 6.69328i) q^{95} +(-5.64811 - 13.6357i) q^{97} +(-1.67214 - 0.692623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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