LMFDB - Embedded newform 833.2.g.e.540.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(344,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("833.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.g (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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 62x^{12} + 563x^{8} + 910x^{4} + 289 $ x^16 + 62x^12 + 563x^8 + 910*x^4 + 289
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			540.3
Root			$0.787063 - 0.787063i$ of defining polynomial
Character	$\chi$	$=$	833.540
Dual form			833.2.g.e.344.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71208i q^{2} +(-0.787063 - 0.787063i) q^{3} -0.931205 q^{4} +(-2.50697 - 2.50697i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} -1.76106i q^{9} +O(q^{10})$	\(q-1.71208i q^{2} +(-0.787063 - 0.787063i) q^{3} -0.931205 q^{4} +(-2.50697 - 2.50697i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} -1.76106i q^{9} +(-4.29212 + 4.29212i) q^{10} +(3.87748 - 3.87748i) q^{11} +(0.732917 + 0.732917i) q^{12} +3.78474 q^{13} +3.94628i q^{15} -4.99527 q^{16} +(-3.74726 - 1.71990i) q^{17} -3.01508 q^{18} -3.92421i q^{19} +(2.33450 + 2.33450i) q^{20} +(-6.63855 - 6.63855i) q^{22} +(-0.643281 + 0.643281i) q^{23} +(-1.44021 + 1.44021i) q^{24} +7.56975i q^{25} -6.47976i q^{26} +(-3.74726 + 3.74726i) q^{27} +(1.69227 + 1.69227i) q^{29} +6.75633 q^{30} +(6.74493 + 6.74493i) q^{31} +4.89256i q^{32} -6.10365 q^{33} +(-2.94460 + 6.41559i) q^{34} +1.63991i q^{36} +(7.58956 + 7.58956i) q^{37} -6.71855 q^{38} +(-2.97883 - 2.97883i) q^{39} +(-4.58739 + 4.58739i) q^{40} +(-3.45091 + 3.45091i) q^{41} -1.18522i q^{43} +(-3.61073 + 3.61073i) q^{44} +(-4.41493 + 4.41493i) q^{45} +(1.10135 + 1.10135i) q^{46} +2.69502 q^{47} +(3.93159 + 3.93159i) q^{48} +12.9600 q^{50} +(1.59566 + 4.30300i) q^{51} -3.52437 q^{52} -1.33691i q^{53} +(6.41559 + 6.41559i) q^{54} -19.4414 q^{55} +(-3.08860 + 3.08860i) q^{57} +(2.89729 - 2.89729i) q^{58} -11.2481i q^{59} -3.67479i q^{60} +(6.25422 - 6.25422i) q^{61} +(11.5478 - 11.5478i) q^{62} -1.61410 q^{64} +(-9.48821 - 9.48821i) q^{65} +10.4499i q^{66} -0.430248 q^{67} +(3.48946 + 1.60158i) q^{68} +1.01260 q^{69} +(-1.60366 - 1.60366i) q^{71} -3.22250 q^{72} +(6.70745 + 6.70745i) q^{73} +(12.9939 - 12.9939i) q^{74} +(5.95787 - 5.95787i) q^{75} +3.65425i q^{76} +(-5.09998 + 5.09998i) q^{78} +(-4.82986 + 4.82986i) q^{79} +(12.5230 + 12.5230i) q^{80} +0.615464 q^{81} +(5.90821 + 5.90821i) q^{82} +3.11707i q^{83} +(5.08251 + 13.7060i) q^{85} -2.02918 q^{86} -2.66384i q^{87} +(-7.09525 - 7.09525i) q^{88} +2.93381 q^{89} +(7.55869 + 7.55869i) q^{90} +(0.599026 - 0.599026i) q^{92} -10.6174i q^{93} -4.61409i q^{94} +(-9.83787 + 9.83787i) q^{95} +(3.85075 - 3.85075i) q^{96} +(-8.64179 - 8.64179i) q^{97} +(-6.82850 - 6.82850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 28 q^{4}+O(q^{10}) $ 16 * q - 28 * q^4	$ 16 q - 28 q^{4} - 12 q^{11} + 20 q^{16} + 52 q^{18} - 4 q^{22} - 8 q^{23} + 12 q^{29} - 20 q^{30} + 32 q^{37} - 28 q^{39} + 12 q^{44} + 72 q^{46} + 56 q^{51} - 36 q^{57} - 28 q^{58} - 36 q^{64} - 8 q^{65} - 96 q^{67} - 24 q^{71} - 160 q^{72} + 88 q^{74} - 116 q^{78} - 36 q^{79} + 40 q^{81} - 52 q^{85} - 20 q^{86} - 48 q^{88} + 120 q^{92} - 84 q^{95} - 48 q^{99}+O(q^{100}) $ 16 * q - 28 * q^4 - 12 * q^11 + 20 * q^16 + 52 * q^18 - 4 * q^22 - 8 * q^23 + 12 * q^29 - 20 * q^30 + 32 * q^37 - 28 * q^39 + 12 * q^44 + 72 * q^46 + 56 * q^51 - 36 * q^57 - 28 * q^58 - 36 * q^64 - 8 * q^65 - 96 * q^67 - 24 * q^71 - 160 * q^72 + 88 * q^74 - 116 * q^78 - 36 * q^79 + 40 * q^81 - 52 * q^85 - 20 * q^86 - 48 * q^88 + 120 * q^92 - 84 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.71208i		−	1.21062i	−0.795990	−	0.605310i	$-0.793049\pi$
$2$		−	1.71208i		−	1.21062i	0.795990	−	0.605310i	$-0.206951\pi$
$3$	−0.787063	−	0.787063i	−0.454411	−	0.454411i	0.442405	−	0.896816i	$-0.354126\pi$
$3$	−0.787063	−	0.787063i	−0.454411	−	0.454411i	−0.896816	+	0.442405i	$0.854126\pi$
$4$	−0.931205			−0.465602
$5$	−2.50697	−	2.50697i	−1.12115	−	1.12115i	−0.991569	−	0.129580i	$-0.958637\pi$
$5$	−2.50697	−	2.50697i	−1.12115	−	1.12115i	−0.129580	−	0.991569i	$-0.541363\pi$
$6$	−1.34751	+	1.34751i	−0.550119	+	0.550119i
$7$		0			0
$7$		0			0
$8$		−	1.82986i		−	0.646953i
$9$		−	1.76106i		−	0.587021i
$10$	−4.29212	+	4.29212i	−1.35729	+	1.35729i
$11$	3.87748	−	3.87748i	1.16911	−	1.16911i	0.186686	−	0.982420i	$-0.440225\pi$
$11$	3.87748	−	3.87748i	1.16911	−	1.16911i	0.982420	−	0.186686i	$-0.0597746\pi$
$12$	0.732917	+	0.732917i	0.211575	+	0.211575i
$13$	3.78474			1.04970			0.524849	−	0.851195i	$-0.324122\pi$
$13$	3.78474			1.04970			0.524849	+	0.851195i	$0.324122\pi$
$14$		0			0
$15$			3.94628i			1.01893i
$16$	−4.99527			−1.24882
$17$	−3.74726	−	1.71990i	−0.908843	−	0.417138i
$17$	−3.74726	−	1.71990i	−0.908843	−	0.417138i
$18$	−3.01508			−0.710660
$19$		−	3.92421i		−	0.900276i	−0.892959	−	0.450138i	$-0.851375\pi$
$19$		−	3.92421i		−	0.900276i	0.892959	−	0.450138i	$-0.148625\pi$
$20$	2.33450	+	2.33450i	0.522010	+	0.522010i
$21$		0			0
$22$	−6.63855	−	6.63855i	−1.41534	−	1.41534i
$23$	−0.643281	+	0.643281i	−0.134133	+	0.134133i	−0.770986	−	0.636852i	$-0.780236\pi$
$23$	−0.643281	+	0.643281i	−0.134133	+	0.134133i	0.636852	+	0.770986i	$0.280236\pi$
$24$	−1.44021	+	1.44021i	−0.293983	+	0.293983i
$25$			7.56975i			1.51395i
$26$		−	6.47976i		−	1.27079i
$27$	−3.74726	+	3.74726i	−0.721160	+	0.721160i
$28$		0			0
$29$	1.69227	+	1.69227i	0.314246	+	0.314246i	0.846552	−	0.532306i	$-0.178674\pi$
$29$	1.69227	+	1.69227i	0.314246	+	0.314246i	−0.532306	+	0.846552i	$0.678674\pi$
$30$	6.75633			1.23353
$31$	6.74493	+	6.74493i	1.21143	+	1.21143i	0.970558	+	0.240868i	$0.0774322\pi$
$31$	6.74493	+	6.74493i	1.21143	+	1.21143i	0.240868	+	0.970558i	$0.422568\pi$
$32$			4.89256i			0.864890i
$33$	−6.10365			−1.06251
$34$	−2.94460	+	6.41559i	−0.504995	+	1.10026i
$35$		0			0
$36$			1.63991i			0.273318i
$37$	7.58956	+	7.58956i	1.24772	+	1.24772i	0.956726	+	0.290990i	$0.0939846\pi$
$37$	7.58956	+	7.58956i	1.24772	+	1.24772i	0.290990	+	0.956726i	$0.406015\pi$
$38$	−6.71855			−1.08989
$39$	−2.97883	−	2.97883i	−0.476994	−	0.476994i
$40$	−4.58739	+	4.58739i	−0.725331	+	0.725331i
$41$	−3.45091	+	3.45091i	−0.538941	+	0.538941i	−0.923218	−	0.384277i	$-0.874451\pi$
$41$	−3.45091	+	3.45091i	−0.538941	+	0.538941i	0.384277	+	0.923218i	$0.374451\pi$
$42$		0			0
$43$		−	1.18522i		−	0.180744i	−0.995908	−	0.0903719i	$-0.971194\pi$
$43$		−	1.18522i		−	0.180744i	0.995908	−	0.0903719i	$-0.0288056\pi$
$44$	−3.61073	+	3.61073i	−0.544338	+	0.544338i
$45$	−4.41493	+	4.41493i	−0.658138	+	0.658138i
$46$	1.10135	+	1.10135i	0.162385	+	0.162385i
$47$	2.69502			0.393110			0.196555	−	0.980493i	$-0.437025\pi$
$47$	2.69502			0.393110			0.196555	+	0.980493i	$0.437025\pi$
$48$	3.93159	+	3.93159i	0.567476	+	0.567476i
$49$		0			0
$50$	12.9600			1.83282
$51$	1.59566	+	4.30300i	0.223436	+	0.602540i
$52$	−3.52437			−0.488742
$53$		−	1.33691i		−	0.183639i	−0.995776	−	0.0918195i	$-0.970732\pi$
$53$		−	1.33691i		−	0.183639i	0.995776	−	0.0918195i	$-0.0292683\pi$
$54$	6.41559	+	6.41559i	0.873051	+	0.873051i
$55$	−19.4414			−2.62148
$56$		0			0
$57$	−3.08860	+	3.08860i	−0.409096	+	0.409096i
$58$	2.89729	−	2.89729i	0.380433	−	0.380433i
$59$		−	11.2481i		−	1.46437i	−0.681103	−	0.732187i	$-0.738500\pi$
$59$		−	11.2481i		−	1.46437i	0.681103	−	0.732187i	$-0.261500\pi$
$60$		−	3.67479i		−	0.474414i
$61$	6.25422	−	6.25422i	0.800771	−	0.800771i	−0.182445	−	0.983216i	$-0.558401\pi$
$61$	6.25422	−	6.25422i	0.800771	−	0.800771i	0.983216	+	0.182445i	$0.0584011\pi$
$62$	11.5478	−	11.5478i	1.46658	−	1.46658i
$63$		0			0
$64$	−1.61410			−0.201763
$65$	−9.48821	−	9.48821i	−1.17687	−	1.17687i
$66$			10.4499i			1.28630i
$67$	−0.430248			−0.0525631			−0.0262816	−	0.999655i	$-0.508367\pi$
$67$	−0.430248			−0.0525631			−0.0262816	+	0.999655i	$0.508367\pi$
$68$	3.48946	+	1.60158i	0.423160	+	0.194220i
$69$	1.01260			0.121903
$70$		0			0
$71$	−1.60366	−	1.60366i	−0.190320	−	0.190320i	0.605514	−	0.795834i	$-0.292967\pi$
$71$	−1.60366	−	1.60366i	−0.190320	−	0.190320i	−0.795834	+	0.605514i	$0.792967\pi$
$72$	−3.22250			−0.379775
$73$	6.70745	+	6.70745i	0.785048	+	0.785048i	0.980678	−	0.195630i	$-0.0626752\pi$
$73$	6.70745	+	6.70745i	0.785048	+	0.785048i	−0.195630	+	0.980678i	$0.562675\pi$
$74$	12.9939	−	12.9939i	1.51051	−	1.51051i
$75$	5.95787	−	5.95787i	0.687956	−	0.687956i
$76$			3.65425i			0.419171i
$77$		0			0
$78$	−5.09998	+	5.09998i	−0.577459	+	0.577459i
$79$	−4.82986	+	4.82986i	−0.543402	+	0.543402i	−0.924524	−	0.381123i	$-0.875538\pi$
$79$	−4.82986	+	4.82986i	−0.543402	+	0.543402i	0.381123	+	0.924524i	$0.375538\pi$
$80$	12.5230	+	12.5230i	1.40011	+	1.40011i
$81$	0.615464			0.0683848
$82$	5.90821	+	5.90821i	0.652453	+	0.652453i
$83$			3.11707i			0.342143i	0.985259	+	0.171072i	$0.0547229\pi$
$83$			3.11707i			0.342143i	−0.985259	+	0.171072i	$0.945277\pi$
$84$		0			0
$85$	5.08251	+	13.7060i	0.551275	+	1.48662i
$86$	−2.02918			−0.218812
$87$		−	2.66384i		−	0.285594i
$88$	−7.09525	−	7.09525i	−0.756356	−	0.756356i
$89$	2.93381			0.310983			0.155492	−	0.987837i	$-0.450304\pi$
$89$	2.93381			0.310983			0.155492	+	0.987837i	$0.450304\pi$
$90$	7.55869	+	7.55869i	0.796756	+	0.796756i
$91$		0			0
$92$	0.599026	−	0.599026i	0.0624528	−	0.0624528i
$93$		−	10.6174i		−	1.10097i
$94$		−	4.61409i		−	0.475907i
$95$	−9.83787	+	9.83787i	−1.00934	+	1.00934i
$96$	3.85075	−	3.85075i	0.393016	−	0.393016i
$97$	−8.64179	−	8.64179i	−0.877441	−	0.877441i	0.115828	−	0.993269i	$-0.463048\pi$
$97$	−8.64179	−	8.64179i	−0.877441	−	0.877441i	−0.993269	+	0.115828i	$0.963048\pi$
$98$		0			0
$99$	−6.82850	−	6.82850i	−0.686290	−	0.686290i
$100$		−	7.04899i		−	0.704899i
$101$	13.6605			1.35927			0.679636	−	0.733549i	$-0.262138\pi$
$101$	13.6605			1.35927			0.679636	+	0.733549i	$0.262138\pi$
$102$	7.36706	−	2.73188i	0.729448	−	0.270497i
$103$	−3.47099			−0.342006			−0.171003	−	0.985270i	$-0.554701\pi$
$103$	−3.47099			−0.342006			−0.171003	+	0.985270i	$0.554701\pi$
$104$		−	6.92554i		−	0.679105i
$105$		0			0
$106$	−2.28889			−0.222317
$107$	5.99527	+	5.99527i	0.579584	+	0.579584i	0.934789	−	0.355204i	$-0.115589\pi$
$107$	5.99527	+	5.99527i	0.579584	+	0.579584i	−0.355204	+	0.934789i	$0.615589\pi$
$108$	3.48946	−	3.48946i	0.335774	−	0.335774i
$109$	−3.74696	+	3.74696i	−0.358894	+	0.358894i	−0.863405	−	0.504511i	$-0.831673\pi$
$109$	−3.74696	+	3.74696i	−0.358894	+	0.358894i	0.504511	+	0.863405i	$0.331673\pi$
$110$			33.2852i			3.17362i
$111$		−	11.9469i		−	1.13395i
$112$		0			0
$113$	6.45333	−	6.45333i	0.607078	−	0.607078i	−0.335103	−	0.942181i	$-0.608771\pi$
$113$	6.45333	−	6.45333i	0.607078	−	0.607078i	0.942181	+	0.335103i	$0.108771\pi$
$114$	5.28792	+	5.28792i	0.495259	+	0.495259i
$115$	3.22536			0.300767
$116$	−1.57585	−	1.57585i	−0.146314	−	0.146314i
$117$		−	6.66517i		−	0.616195i
$118$	−19.2576			−1.77280
$119$		0			0
$120$	7.22114			0.659197
$121$		−	19.0698i		−	1.73362i
$122$	−10.7077	−	10.7077i	−0.969430	−	0.969430i
$123$	5.43216			0.489801
$124$	−6.28091	−	6.28091i	−0.564043	−	0.564043i
$125$	6.44228	−	6.44228i	0.576215	−	0.576215i
$126$		0			0
$127$			0.446266i			0.0395997i	0.999804	+	0.0197999i	$0.00630290\pi$
$127$			0.446266i			0.0395997i	−0.999804	+	0.0197999i	$0.993697\pi$
$128$			12.5486i			1.10915i
$129$	−0.932840	+	0.932840i	−0.0821319	+	0.0821319i
$130$	−16.2445	+	16.2445i	−1.42474	+	1.42474i
$131$	0.0311801	+	0.0311801i	0.00272422	+	0.00272422i	0.708468	−	0.705743i	$-0.249387\pi$
$131$	0.0311801	+	0.0311801i	0.00272422	+	0.00272422i	−0.705743	+	0.708468i	$0.749387\pi$
$132$	5.68375			0.494707
$133$		0			0
$134$			0.736617i			0.0636340i
$135$	18.7885			1.61706
$136$	−3.14718	+	6.85695i	−0.269868	+	0.587979i
$137$	1.92414			0.164390			0.0821951	−	0.996616i	$-0.473807\pi$
$137$	1.92414			0.164390			0.0821951	+	0.996616i	$0.473807\pi$
$138$		−	1.73366i		−	0.147579i
$139$	4.26435	+	4.26435i	0.361698	+	0.361698i	0.864438	−	0.502740i	$-0.167675\pi$
$139$	4.26435	+	4.26435i	0.361698	+	0.361698i	−0.502740	+	0.864438i	$0.667675\pi$
$140$		0			0
$141$	−2.12115	−	2.12115i	−0.178633	−	0.178633i
$142$	−2.74560	+	2.74560i	−0.230405	+	0.230405i
$143$	14.6753	−	14.6753i	1.22721	−	1.22721i
$144$			8.79698i			0.733082i
$145$		−	8.48492i		−	0.704634i
$146$	11.4837	−	11.4837i	0.950395	−	0.950395i
$147$		0			0
$148$	−7.06743	−	7.06743i	−0.580939	−	0.580939i
$149$	−19.1730			−1.57072			−0.785358	−	0.619042i	$-0.787521\pi$
$149$	−19.1730			−1.57072			−0.785358	+	0.619042i	$0.787521\pi$
$150$	−10.2003	−	10.2003i	−0.832853	−	0.832853i
$151$		−	22.3643i		−	1.81998i	−0.414626	−	0.909992i	$-0.636088\pi$
$151$		−	22.3643i		−	1.81998i	0.414626	−	0.909992i	$-0.363912\pi$
$152$	−7.18076			−0.582436
$153$	−3.02886	+	6.59916i	−0.244869	+	0.533510i
$154$		0			0
$155$		−	33.8186i		−	2.71638i
$156$	2.77390	+	2.77390i	0.222090	+	0.222090i
$157$	3.00878			0.240127			0.120063	−	0.992766i	$-0.461690\pi$
$157$	3.00878			0.240127			0.120063	+	0.992766i	$0.461690\pi$
$158$	8.26909	+	8.26909i	0.657853	+	0.657853i
$159$	−1.05223	+	1.05223i	−0.0834476	+	0.0834476i
$160$	12.2655	−	12.2655i	0.969671	−	0.969671i
$161$		0			0
$162$		−	1.05372i		−	0.0827881i
$163$	−10.4590	+	10.4590i	−0.819215	+	0.819215i	−0.985994	−	0.166779i	$-0.946663\pi$
$163$	−10.4590	+	10.4590i	−0.819215	+	0.819215i	0.166779	+	0.985994i	$0.446663\pi$
$164$	3.21350	−	3.21350i	0.250932	−	0.250932i
$165$	15.3016	+	15.3016i	1.19123	+	1.19123i
$166$	5.33666			0.414205
$167$	9.61691	+	9.61691i	0.744179	+	0.744179i	0.973379	−	0.229200i	$-0.0736110\pi$
$167$	9.61691	+	9.61691i	0.744179	+	0.744179i	−0.229200	+	0.973379i	$0.573611\pi$
$168$		0			0
$169$	1.32426			0.101866
$170$	23.4657	−	8.70164i	1.79974	−	0.667385i
$171$	−6.91079			−0.528481
$172$			1.10368i			0.0841547i
$173$	6.11475	+	6.11475i	0.464896	+	0.464896i	0.900256	−	0.435360i	$-0.143379\pi$
$173$	6.11475	+	6.11475i	0.464896	+	0.464896i	−0.435360	+	0.900256i	$0.643379\pi$
$174$	−4.56070			−0.345746
$175$		0			0
$176$	−19.3691	+	19.3691i	−1.46000	+	1.46000i
$177$	−8.85294	+	8.85294i	−0.665428	+	0.665428i
$178$		−	5.02291i		−	0.376483i
$179$			10.7073i			0.800304i	0.916449	+	0.400152i	$0.131043\pi$
$179$			10.7073i			0.800304i	−0.916449	+	0.400152i	$0.868957\pi$
$180$	4.11120	−	4.11120i	0.306431	−	0.306431i
$181$	11.4187	−	11.4187i	0.848747	−	0.848747i	−0.141230	−	0.989977i	$-0.545106\pi$
$181$	11.4187	−	11.4187i	0.848747	−	0.848747i	0.989977	+	0.141230i	$0.0451056\pi$
$182$		0			0
$183$	−9.84493			−0.727758
$184$	1.17711	+	1.17711i	0.0867779	+	0.0867779i
$185$		−	38.0535i		−	2.79775i
$186$	−18.1778			−1.33286
$187$	−21.1988	+	7.86103i	−1.55021	+	0.574856i
$188$	−2.50962			−0.183033
$189$		0			0
$190$	16.8432	+	16.8432i	1.22193	+	1.22193i
$191$	−13.8544			−1.00247			−0.501235	−	0.865311i	$-0.667121\pi$
$191$	−13.8544			−1.00247			−0.501235	+	0.865311i	$0.667121\pi$
$192$	1.27040	+	1.27040i	0.0916832	+	0.0916832i
$193$	10.7483	−	10.7483i	0.773681	−	0.773681i	−0.205067	−	0.978748i	$-0.565741\pi$
$193$	10.7483	−	10.7483i	0.773681	−	0.773681i	0.978748	+	0.205067i	$0.0657412\pi$
$194$	−14.7954	+	14.7954i	−1.06225	+	1.06225i
$195$			14.9356i			1.06956i
$196$		0			0
$197$	−16.0288	+	16.0288i	−1.14200	+	1.14200i	−0.153921	+	0.988083i	$0.549190\pi$
$197$	−16.0288	+	16.0288i	−1.14200	+	1.14200i	−0.988083	+	0.153921i	$0.950810\pi$
$198$	−11.6909	+	11.6909i	−0.830836	+	0.830836i
$199$	−8.30316	−	8.30316i	−0.588596	−	0.588596i	0.348655	−	0.937251i	$-0.386638\pi$
$199$	−8.30316	−	8.30316i	−0.588596	−	0.588596i	−0.937251	+	0.348655i	$0.886638\pi$
$200$	13.8516			0.979455
$201$	0.338632	+	0.338632i	0.0238853	+	0.0238853i
$202$		−	23.3879i		−	1.64556i
$203$		0			0
$204$	−1.48588	−	4.00697i	−0.104033	−	0.280544i
$205$	17.3026			1.20847
$206$			5.94259i			0.414040i
$207$	1.13286	+	1.13286i	0.0787391	+	0.0787391i
$208$	−18.9058			−1.31088
$209$	−15.2161	−	15.2161i	−1.05252	−	1.05252i
$210$		0			0
$211$	15.4623	−	15.4623i	1.06447	−	1.06447i	0.0666961	−	0.997773i	$-0.478754\pi$
$211$	15.4623	−	15.4623i	1.06447	−	1.06447i	0.997773	−	0.0666961i	$-0.0212458\pi$
$212$			1.24494i			0.0855027i
$213$			2.52437i			0.172967i
$214$	10.2644	−	10.2644i	0.701657	−	0.701657i
$215$	−2.97130	+	2.97130i	−0.202641	+	0.202641i
$216$	6.85695	+	6.85695i	0.466557	+	0.466557i
$217$		0			0
$218$	6.41508	+	6.41508i	0.434484	+	0.434484i
$219$		−	10.5584i		−	0.713469i
$220$	18.1040			1.22057
$221$	−14.1824	−	6.50939i	−0.954011	−	0.437869i
$222$	−20.4540			−1.37279
$223$			24.5325i			1.64282i	0.570341	+	0.821408i	$0.306811\pi$
$223$			24.5325i			1.64282i	−0.570341	+	0.821408i	$0.693189\pi$
$224$		0			0
$225$	13.3308			0.888721
$226$	−11.0486	−	11.0486i	−0.734942	−	0.734942i
$227$	−7.83465	+	7.83465i	−0.520004	+	0.520004i	−0.917573	−	0.397568i	$-0.869854\pi$
$227$	−7.83465	+	7.83465i	−0.520004	+	0.520004i	0.397568	+	0.917573i	$0.369854\pi$
$228$	2.87612	−	2.87612i	0.190476	−	0.190476i
$229$		−	28.4018i		−	1.87684i	−0.345493	−	0.938421i	$-0.612288\pi$
$229$		−	28.4018i		−	1.87684i	0.345493	−	0.938421i	$-0.387712\pi$
$230$		−	5.52207i		−	0.364114i
$231$		0			0
$232$	3.09661	−	3.09661i	0.203303	−	0.203303i
$233$	2.93257	+	2.93257i	0.192119	+	0.192119i	0.796611	−	0.604492i	$-0.206624\pi$
$233$	2.93257	+	2.93257i	0.192119	+	0.192119i	−0.604492	+	0.796611i	$0.706624\pi$
$234$	−11.4113			−0.745979
$235$	−6.75633	−	6.75633i	−0.440734	−	0.440734i
$236$			10.4743i			0.681816i
$237$	7.60281			0.493855
$238$		0			0
$239$	17.2805			1.11778			0.558890	−	0.829242i	$-0.311227\pi$
$239$	17.2805			1.11778			0.558890	+	0.829242i	$0.311227\pi$
$240$		−	19.7127i		−	1.27245i
$241$	0.265171	+	0.265171i	0.0170811	+	0.0170811i	0.715596	−	0.698515i	$-0.246155\pi$
$241$	0.265171	+	0.265171i	0.0170811	+	0.0170811i	−0.698515	+	0.715596i	$0.746155\pi$
$242$	−32.6489			−2.09875
$243$	10.7574	+	10.7574i	0.690085	+	0.690085i
$244$	−5.82396	+	5.82396i	−0.372841	+	0.372841i
$245$		0			0
$246$		−	9.30027i		−	0.592964i
$247$		−	14.8521i		−	0.945019i
$248$	12.3423	−	12.3423i	0.783736	−	0.783736i
$249$	2.45333	−	2.45333i	0.155474	−	0.155474i
$250$	−11.0297	−	11.0297i	−0.697578	−	0.697578i
$251$	15.6012			0.984737			0.492369	−	0.870387i	$-0.336131\pi$
$251$	15.6012			0.984737			0.492369	+	0.870387i	$0.336131\pi$
$252$		0			0
$253$			4.98862i			0.313632i
$254$	0.764041			0.0479402
$255$	6.78722	−	14.7877i	0.425032	−	0.926043i
$256$	18.2559			1.14100
$257$		−	21.0927i		−	1.31573i	−0.753138	−	0.657863i	$-0.771461\pi$
$257$		−	21.0927i		−	1.31573i	0.753138	−	0.657863i	$-0.228539\pi$
$258$	1.59709	+	1.59709i	0.0994306	+	0.0994306i
$259$		0			0
$260$	8.83547	+	8.83547i	0.547953	+	0.547953i
$261$	2.98019	−	2.98019i	0.184469	−	0.184469i
$262$	0.0533827	−	0.0533827i	0.00329799	−	0.00329799i
$263$		−	10.6033i		−	0.653826i	−0.945054	−	0.326913i	$-0.893992\pi$
$263$		−	10.6033i		−	0.653826i	0.945054	−	0.326913i	$-0.106008\pi$
$264$			11.1688i			0.687393i
$265$	−3.35159	+	3.35159i	−0.205887	+	0.205887i
$266$		0			0
$267$	−2.30909	−	2.30909i	−0.141314	−	0.141314i
$268$	0.400649			0.0244735
$269$	−19.7552	−	19.7552i	−1.20450	−	1.20450i	−0.972785	−	0.231711i	$-0.925568\pi$
$269$	−19.7552	−	19.7552i	−1.20450	−	1.20450i	−0.231711	−	0.972785i	$-0.574432\pi$
$270$		−	32.1673i		−	1.95764i
$271$	−2.88043			−0.174974			−0.0874868	−	0.996166i	$-0.527884\pi$
$271$	−2.88043			−0.174974			−0.0874868	+	0.996166i	$0.527884\pi$
$272$	18.7186	+	8.59137i	1.13498	+	0.520928i
$273$		0			0
$274$		−	3.29427i		−	0.199014i
$275$	29.3516	+	29.3516i	1.76997	+	1.76997i
$276$	−0.942942			−0.0567584
$277$	−5.07016	−	5.07016i	−0.304636	−	0.304636i	0.538188	−	0.842825i	$-0.319109\pi$
$277$	−5.07016	−	5.07016i	−0.304636	−	0.304636i	−0.842825	+	0.538188i	$0.819109\pi$
$278$	7.30089	−	7.30089i	0.437879	−	0.437879i
$279$	11.8783	−	11.8783i	0.711133	−	0.711133i
$280$		0			0
$281$			20.3361i			1.21315i	0.795026	+	0.606575i	$0.207457\pi$
$281$			20.3361i			1.21315i	−0.795026	+	0.606575i	$0.792543\pi$
$282$	−3.63158	+	3.63158i	−0.216257	+	0.216257i
$283$	−2.18423	+	2.18423i	−0.129839	+	0.129839i	−0.769040	−	0.639201i	$-0.779265\pi$
$283$	−2.18423	+	2.18423i	−0.129839	+	0.129839i	0.639201	+	0.769040i	$0.279265\pi$
$284$	1.49334	+	1.49334i	0.0886134	+	0.0886134i
$285$	15.4860			0.917314
$286$	−25.1252	−	25.1252i	−1.48568	−	1.48568i
$287$		0			0
$288$	8.61611			0.507709
$289$	11.0839	+	12.8898i	0.651992	+	0.758226i
$290$	−14.5268			−0.853044
$291$			13.6033i			0.797438i
$292$	−6.24601	−	6.24601i	−0.365520	−	0.365520i
$293$	20.4376			1.19398			0.596989	−	0.802249i	$-0.296364\pi$
$293$	20.4376			1.19398			0.596989	+	0.802249i	$0.296364\pi$
$294$		0			0
$295$	−28.1985	+	28.1985i	−1.64178	+	1.64178i
$296$	13.8878	−	13.8878i	0.807214	−	0.807214i
$297$			29.0599i			1.68622i
$298$			32.8257i			1.90154i
$299$	−2.43465	+	2.43465i	−0.140799	+	0.140799i
$300$	−5.54800	+	5.54800i	−0.320314	+	0.320314i
$301$		0			0
$302$	−38.2894			−2.20331
$303$	−10.7517	−	10.7517i	−0.617669	−	0.617669i
$304$			19.6025i			1.12428i
$305$	−31.3582			−1.79557
$306$	11.2983	+	5.18564i	0.645879	+	0.296443i
$307$	−24.4776			−1.39701			−0.698504	−	0.715606i	$-0.746151\pi$
$307$	−24.4776			−1.39701			−0.698504	+	0.715606i	$0.746151\pi$
$308$		0			0
$309$	2.73188	+	2.73188i	0.155411	+	0.155411i
$310$	−57.9001			−3.28850
$311$	0.318553	+	0.318553i	0.0180635	+	0.0180635i	0.716081	−	0.698017i	$-0.245934\pi$
$311$	0.318553	+	0.318553i	0.0180635	+	0.0180635i	−0.698017	+	0.716081i	$0.745934\pi$
$312$	−5.45084	+	5.45084i	−0.308593	+	0.308593i
$313$	−12.0045	+	12.0045i	−0.678534	+	0.678534i	−0.959668	−	0.281135i	$-0.909289\pi$
$313$	−12.0045	+	12.0045i	−0.678534	+	0.678534i	0.281135	+	0.959668i	$0.409289\pi$
$314$		−	5.15126i		−	0.290702i
$315$		0			0
$316$	4.49759	−	4.49759i	0.253009	−	0.253009i
$317$	3.31101	−	3.31101i	0.185965	−	0.185965i	−0.607984	−	0.793949i	$-0.708022\pi$
$317$	3.31101	−	3.31101i	0.185965	−	0.185965i	0.793949	+	0.607984i	$0.208022\pi$
$318$	1.80150	+	1.80150i	0.101023	+	0.101023i
$319$	13.1235			0.734774
$320$	4.04650	+	4.04650i	0.226206	+	0.226206i
$321$		−	9.43731i		−	0.526739i
$322$		0			0
$323$	−6.74927	+	14.7050i	−0.375539	+	0.818210i
$324$	−0.573122			−0.0318401
$325$			28.6496i			1.58919i
$326$	17.9067	+	17.9067i	0.991758	+	0.991758i
$327$	5.89819			0.326170
$328$	6.31467	+	6.31467i	0.348669	+	0.348669i
$329$		0			0
$330$	26.1976	−	26.1976i	1.44213	−	1.44213i
$331$			34.5038i			1.89650i	0.317521	+	0.948251i	$0.397150\pi$
$331$			34.5038i			1.89650i	−0.317521	+	0.948251i	$0.602850\pi$
$332$		−	2.90263i		−	0.159303i
$333$	13.3657	−	13.3657i	0.732436	−	0.732436i
$334$	16.4649	−	16.4649i	0.900919	−	0.900919i
$335$	1.07862	+	1.07862i	0.0589311	+	0.0589311i
$336$		0			0
$337$	−19.0302	−	19.0302i	−1.03664	−	1.03664i	−0.999303	−	0.0373355i	$-0.988113\pi$
$337$	−19.0302	−	19.0302i	−1.03664	−	1.03664i	−0.0373355	−	0.999303i	$-0.511887\pi$
$338$		−	2.26724i		−	0.123322i
$339$	−10.1584			−0.551726
$340$	−4.73285	−	12.7631i	−0.256675	−	0.692175i
$341$	52.3068			2.83257
$342$			11.8318i			0.639790i
$343$		0			0
$344$	−2.16878			−0.116933
$345$	−2.53857	−	2.53857i	−0.136672	−	0.136672i
$346$	10.4689	−	10.4689i	0.562812	−	0.562812i
$347$	−11.6966	+	11.6966i	−0.627907	+	0.627907i	−0.947541	−	0.319634i	$-0.896440\pi$
$347$	−11.6966	+	11.6966i	−0.627907	+	0.627907i	0.319634	+	0.947541i	$0.396440\pi$
$348$			2.48058i			0.132973i
$349$			10.1340i			0.542461i	0.962514	+	0.271231i	$0.0874306\pi$
$349$			10.1340i			0.542461i	−0.962514	+	0.271231i	$0.912569\pi$
$350$		0			0
$351$	−14.1824	+	14.1824i	−0.757000	+	0.757000i
$352$	18.9708	+	18.9708i	1.01115	+	1.01115i
$353$	0.797547			0.0424491			0.0212246	−	0.999775i	$-0.493244\pi$
$353$	0.797547			0.0424491			0.0212246	+	0.999775i	$0.493244\pi$
$354$	15.1569	+	15.1569i	0.805581	+	0.805581i
$355$			8.04067i			0.426754i
$356$	−2.73198			−0.144795
$357$		0			0
$358$	18.3318			0.968865
$359$		−	20.7329i		−	1.09424i	−0.837055	−	0.547119i	$-0.815724\pi$
$359$		−	20.7329i		−	1.09424i	0.837055	−	0.547119i	$-0.184276\pi$
$360$	8.07869	+	8.07869i	0.425784	+	0.425784i
$361$	3.60055			0.189502
$362$	−19.5497	−	19.5497i	−1.02751	−	1.02751i
$363$	−15.0091	+	15.0091i	−0.787774	+	0.787774i
$364$		0			0
$365$		−	33.6307i		−	1.76031i
$366$			16.8553i			0.881039i
$367$	−3.45988	+	3.45988i	−0.180604	+	0.180604i	−0.791619	−	0.611015i	$-0.790762\pi$
$367$	−3.45988	+	3.45988i	−0.180604	+	0.180604i	0.611015	+	0.791619i	$0.290762\pi$
$368$	3.21336	−	3.21336i	0.167508	−	0.167508i
$369$	6.07727	+	6.07727i	0.316370	+	0.316370i
$370$	−65.1505			−3.38702
$371$		0			0
$372$			9.88695i			0.512614i
$373$	6.65171			0.344412			0.172206	−	0.985061i	$-0.444910\pi$
$373$	6.65171			0.344412			0.172206	+	0.985061i	$0.444910\pi$
$374$	13.4587	+	36.2940i	0.695932	+	1.87672i
$375$	−10.1410			−0.523677
$376$		−	4.93151i		−	0.254323i
$377$	6.40480	+	6.40480i	0.329864	+	0.329864i
$378$		0			0
$379$	−4.33788	−	4.33788i	−0.222822	−	0.222822i	0.586864	−	0.809686i	$-0.300362\pi$
$379$	−4.33788	−	4.33788i	−0.222822	−	0.222822i	−0.809686	+	0.586864i	$0.800362\pi$
$380$	9.16107	−	9.16107i	0.469953	−	0.469953i
$381$	0.351240	−	0.351240i	0.0179945	−	0.0179945i
$382$			23.7198i			1.21361i
$383$			28.9723i			1.48041i	0.672379	+	0.740207i	$0.265273\pi$
$383$			28.9723i			1.48041i	−0.672379	+	0.740207i	$0.734727\pi$
$384$	9.87652	−	9.87652i	0.504009	−	0.504009i
$385$		0			0
$386$	−18.4019	−	18.4019i	−0.936634	−	0.936634i
$387$	−2.08724			−0.106100
$388$	8.04728	+	8.04728i	0.408539	+	0.408539i
$389$		−	10.2248i		−	0.518420i	−0.965821	−	0.259210i	$-0.916538\pi$
$389$		−	10.2248i		−	0.518420i	0.965821	−	0.259210i	$-0.0834621\pi$
$390$	25.5710			1.29484
$391$	3.51692	−	1.30416i	0.177858	−	0.0659541i
$392$		0			0
$393$		−	0.0490814i		−	0.00247583i
$394$	27.4425	+	27.4425i	1.38253	+	1.38253i
$395$	24.2166			1.21847
$396$	6.35873	+	6.35873i	0.319538	+	0.319538i
$397$	3.33631	−	3.33631i	0.167445	−	0.167445i	−0.618411	−	0.785855i	$-0.712223\pi$
$397$	3.33631	−	3.33631i	0.167445	−	0.167445i	0.785855	+	0.618411i	$0.212223\pi$
$398$	−14.2156	+	14.2156i	−0.712566	+	0.712566i
$399$		0			0
$400$		−	37.8129i		−	1.89065i
$401$	−5.33652	+	5.33652i	−0.266493	+	0.266493i	−0.827685	−	0.561192i	$-0.810343\pi$
$401$	−5.33652	+	5.33652i	−0.266493	+	0.266493i	0.561192	+	0.827685i	$0.310343\pi$
$402$	0.579764	−	0.579764i	0.0289160	−	0.0289160i
$403$	25.5278	+	25.5278i	1.27163	+	1.27163i
$404$	−12.7207			−0.632880
$405$	−1.54295	−	1.54295i	−0.0766696	−	0.0766696i
$406$		0			0
$407$	58.8568			2.91742
$408$	7.87388	−	2.91983i	0.389815	−	0.144553i
$409$	11.3008			0.558791			0.279395	−	0.960176i	$-0.409866\pi$
$409$	11.3008			0.558791			0.279395	+	0.960176i	$0.409866\pi$
$410$		−	29.6234i		−	1.46299i
$411$	−1.51442	−	1.51442i	−0.0747007	−	0.0747007i
$412$	3.23220			0.159239
$413$		0			0
$414$	1.93954	−	1.93954i	0.0953232	−	0.0953232i
$415$	7.81439	−	7.81439i	0.383593	−	0.383593i
$416$			18.5171i			0.907874i
$417$		−	6.71263i		−	0.328719i
$418$	−26.0511	+	26.0511i	−1.27420	+	1.27420i
$419$	−20.0293	+	20.0293i	−0.978497	+	0.978497i	−0.999774	−	0.0212763i	$-0.993227\pi$
$419$	−20.0293	+	20.0293i	−0.978497	+	0.978497i	0.0212763	+	0.999774i	$0.493227\pi$
$420$		0			0
$421$	35.8374			1.74661			0.873304	−	0.487176i	$-0.161973\pi$
$421$	35.8374			1.74661			0.873304	+	0.487176i	$0.161973\pi$
$422$	−26.4727	−	26.4727i	−1.28867	−	1.28867i
$423$		−	4.74611i		−	0.230764i
$424$	−2.44636			−0.118806
$425$	13.0192	−	28.3658i	0.631526	−	1.37594i
$426$	4.32191			0.209397
$427$		0			0
$428$	−5.58282	−	5.58282i	−0.269856	−	0.269856i
$429$	−23.1007			−1.11531
$430$	5.08708	+	5.08708i	0.245321	+	0.245321i
$431$	3.91140	−	3.91140i	0.188405	−	0.188405i	−0.606601	−	0.795006i	$-0.707467\pi$
$431$	3.91140	−	3.91140i	0.188405	−	0.188405i	0.795006	+	0.606601i	$0.207467\pi$
$432$	18.7186	−	18.7186i	0.900597	−	0.900597i
$433$		−	2.97397i		−	0.142920i	−0.997443	−	0.0714599i	$-0.977234\pi$
$433$		−	2.97397i		−	0.142920i	0.997443	−	0.0714599i	$-0.0227658\pi$
$434$		0			0
$435$	−6.67816	+	6.67816i	−0.320193	+	0.320193i
$436$	3.48919	−	3.48919i	0.167102	−	0.167102i
$437$	2.52437	+	2.52437i	0.120757	+	0.120757i
$438$	−18.0767			−0.863740
$439$	1.26188	+	1.26188i	0.0602261	+	0.0602261i	0.736578	−	0.676352i	$-0.236440\pi$
$439$	1.26188	+	1.26188i	0.0602261	+	0.0602261i	−0.676352	+	0.736578i	$0.736440\pi$
$440$			35.5751i			1.69598i
$441$		0			0
$442$	−11.1446	+	24.2813i	−0.530093	+	1.15495i
$443$	−8.70125			−0.413409			−0.206704	−	0.978403i	$-0.566274\pi$
$443$	−8.70125			−0.413409			−0.206704	+	0.978403i	$0.566274\pi$
$444$			11.1250i			0.527971i
$445$	−7.35496	−	7.35496i	−0.348659	−	0.348659i
$446$	42.0015			1.98883
$447$	15.0904	+	15.0904i	0.713750	+	0.713750i
$448$		0			0
$449$	−12.5684	+	12.5684i	−0.593139	+	0.593139i	−0.938478	−	0.345339i	$-0.887764\pi$
$449$	−12.5684	+	12.5684i	−0.593139	+	0.593139i	0.345339	+	0.938478i	$0.387764\pi$
$450$		−	22.8234i		−	1.07590i
$451$			26.7617i			1.26016i
$452$	−6.00937	+	6.00937i	−0.282657	+	0.282657i
$453$	−17.6021	+	17.6021i	−0.827021	+	0.827021i
$454$	13.4135	+	13.4135i	0.629528	+	0.629528i
$455$		0			0
$456$	5.65171	+	5.65171i	0.264666	+	0.264666i
$457$		−	22.4208i		−	1.04880i	−0.851472	−	0.524400i	$-0.824290\pi$
$457$		−	22.4208i		−	1.04880i	0.851472	−	0.524400i	$-0.175710\pi$
$458$	−48.6260			−2.27214
$459$	20.4869	−	7.59702i	0.956244	−	0.354598i
$460$	−3.00347			−0.140038
$461$		−	24.0555i		−	1.12038i	−0.828365	−	0.560189i	$-0.810729\pi$
$461$		−	24.0555i		−	1.12038i	0.828365	−	0.560189i	$-0.189271\pi$
$462$		0			0
$463$	−0.665002			−0.0309053			−0.0154526	−	0.999881i	$-0.504919\pi$
$463$	−0.665002			−0.0309053			−0.0154526	+	0.999881i	$0.504919\pi$
$464$	−8.45333	−	8.45333i	−0.392436	−	0.392436i
$465$	−26.6174	+	26.6174i	−1.23435	+	1.23435i
$466$	5.02078	−	5.02078i	0.232583	−	0.232583i
$467$		−	20.5935i		−	0.952954i	−0.879187	−	0.476477i	$-0.841914\pi$
$467$		−	20.5935i		−	0.952954i	0.879187	−	0.476477i	$-0.158086\pi$
$468$			6.20664i			0.286902i
$469$		0			0
$470$	−11.5674	+	11.5674i	−0.533562	+	0.533562i
$471$	−2.36810	−	2.36810i	−0.109116	−	0.109116i
$472$	−20.5824			−0.947381
$473$	−4.59566	−	4.59566i	−0.211308	−	0.211308i
$474$		−	13.0166i		−	0.597871i
$475$	29.7053			1.36297
$476$		0			0
$477$	−2.35439			−0.107800
$478$		−	29.5855i		−	1.35321i
$479$	6.54363	+	6.54363i	0.298986	+	0.298986i	0.840617	−	0.541631i	$-0.182193\pi$
$479$	6.54363	+	6.54363i	0.298986	+	0.298986i	−0.541631	+	0.840617i	$0.682193\pi$
$480$	−19.3074			−0.881258
$481$	28.7245	+	28.7245i	1.30973	+	1.30973i
$482$	0.453992	−	0.453992i	0.0206788	−	0.0206788i
$483$		0			0
$484$			17.7579i			0.807175i
$485$			43.3294i			1.96748i
$486$	18.4174	−	18.4174i	0.835431	−	0.835431i
$487$	1.08588	−	1.08588i	0.0492058	−	0.0492058i	−0.682076	−	0.731282i	$-0.738923\pi$
$487$	1.08588	−	1.08588i	0.0492058	−	0.0492058i	0.731282	+	0.682076i	$0.238923\pi$
$488$	−11.4443	−	11.4443i	−0.518061	−	0.518061i
$489$	16.4638			0.744521
$490$		0			0
$491$			14.6140i			0.659521i	0.944065	+	0.329760i	$0.106968\pi$
$491$			14.6140i			0.659521i	−0.944065	+	0.329760i	$0.893032\pi$
$492$	−5.05845			−0.228053
$493$	−3.43083	−	9.25190i	−0.154517	−	0.416685i
$494$	−25.4280			−1.14406
$495$			34.2376i			1.53887i
$496$	−33.6928	−	33.6928i	−1.51285	−	1.51285i
$497$		0			0
$498$	−4.20029	−	4.20029i	−0.188220	−	0.188220i
$499$	14.0490	−	14.0490i	0.628919	−	0.628919i	−0.318877	−	0.947796i	$-0.603306\pi$
$499$	14.0490	−	14.0490i	0.628919	−	0.628919i	0.947796	+	0.318877i	$0.103306\pi$
$500$	−5.99908	+	5.99908i	−0.268287	+	0.268287i
$501$		−	15.1382i		−	0.676326i
$502$		−	26.7104i		−	1.19214i
$503$	−25.4194	+	25.4194i	−1.13339	+	1.13339i	−0.143786	+	0.989609i	$0.545928\pi$
$503$	−25.4194	+	25.4194i	−1.13339	+	1.13339i	−0.989609	+	0.143786i	$0.954072\pi$
$504$		0			0
$505$	−34.2465	−	34.2465i	−1.52395	−	1.52395i
$506$	8.54090			0.379689
$507$	−1.04228	−	1.04228i	−0.0462892	−	0.0462892i
$508$		−	0.415565i		−	0.0184377i
$509$	−8.06864			−0.357636			−0.178818	−	0.983882i	$-0.557227\pi$
$509$	−8.06864			−0.357636			−0.178818	+	0.983882i	$0.557227\pi$
$510$	−25.3177	−	11.6202i	−1.12109	−	0.514552i
$511$		0			0
$512$		−	6.15837i		−	0.272164i
$513$	14.7050	+	14.7050i	0.649243	+	0.649243i
$514$	−36.1123			−1.59284
$515$	8.70164	+	8.70164i	0.383440	+	0.383440i
$516$	0.868664	−	0.868664i	0.0382408	−	0.0382408i
$517$	10.4499	−	10.4499i	0.459587	−	0.459587i
$518$		0			0
$519$		−	9.62539i		−	0.422508i
$520$	−17.3621	+	17.3621i	−0.761378	+	0.761378i
$521$	5.42273	−	5.42273i	0.237574	−	0.237574i	−0.578271	−	0.815845i	$-0.696272\pi$
$521$	5.42273	−	5.42273i	0.237574	−	0.237574i	0.815845	+	0.578271i	$0.196272\pi$
$522$	−5.10232	−	5.10232i	−0.223322	−	0.223322i
$523$	−32.6947			−1.42964			−0.714819	−	0.699310i	$-0.753491\pi$
$523$	−32.6947			−1.42964			−0.714819	+	0.699310i	$0.753491\pi$
$524$	−0.0290350	−	0.0290350i	−0.00126840	−	0.00126840i
$525$		0			0
$526$	−18.1536			−0.791535
$527$	−13.6744	−	36.8756i	−0.595665	−	1.60633i
$528$	30.4894			1.32688
$529$			22.1724i			0.964017i
$530$	5.73818	+	5.73818i	0.249251	+	0.249251i
$531$	−19.8086			−0.859619
$532$		0			0
$533$	−13.0608	+	13.0608i	−0.565725	+	0.565725i
$534$	−3.95335	+	3.95335i	−0.171078	+	0.171078i
$535$		−	30.0599i		−	1.29960i
$536$			0.787293i			0.0340059i
$537$	8.42735	−	8.42735i	0.363667	−	0.363667i
$538$	−33.8224	+	33.8224i	−1.45819	+	1.45819i
$539$		0			0
$540$	−17.4959			−0.752905
$541$	−14.4440	−	14.4440i	−0.620994	−	0.620994i	0.324791	−	0.945786i	$-0.394706\pi$
$541$	−14.4440	−	14.4440i	−0.620994	−	0.620994i	−0.945786	+	0.324791i	$0.894706\pi$
$542$			4.93151i			0.211827i
$543$	−17.9745			−0.771360
$544$	8.41472	−	18.3337i	0.360778	−	0.786050i
$545$	18.7870			0.804746
$546$		0			0
$547$	30.6169	+	30.6169i	1.30908	+	1.30908i	0.922077	+	0.387007i	$0.126491\pi$
$547$	30.6169	+	30.6169i	1.30908	+	1.30908i	0.387007	+	0.922077i	$0.373509\pi$
$548$	−1.79177			−0.0765405
$549$	−11.0141	−	11.0141i	−0.470070	−	0.470070i
$550$	50.2522	−	50.2522i	2.14276	−	2.14276i
$551$	6.64082	−	6.64082i	0.282909	−	0.282909i
$552$		−	1.85292i		−	0.0788657i
$553$		0			0
$554$	−8.68050	+	8.68050i	−0.368799	+	0.368799i
$555$	−29.9505	+	29.9505i	−1.27133	+	1.27133i
$556$	−3.97098	−	3.97098i	−0.168407	−	0.168407i
$557$	21.2160			0.898951			0.449476	−	0.893293i	$-0.351611\pi$
$557$	21.2160			0.898951			0.449476	+	0.893293i	$0.351611\pi$
$558$	−20.3365	−	20.3365i	−0.860912	−	0.860912i
$559$		−	4.48573i		−	0.189726i
$560$		0			0
$561$	22.8719	+	10.4977i	0.965654	+	0.443212i
$562$	34.8170			1.46866
$563$			17.8118i			0.750677i	0.926888	+	0.375339i	$0.122474\pi$
$563$			17.8118i			0.750677i	−0.926888	+	0.375339i	$0.877526\pi$
$564$	1.97523	+	1.97523i	0.0831721	+	0.0831721i
$565$	−32.3566			−1.36125
$566$	3.73957	+	3.73957i	0.157186	+	0.157186i
$567$		0			0
$568$	−2.93448	+	2.93448i	−0.123128	+	0.123128i
$569$		−	20.9185i		−	0.876950i	−0.898743	−	0.438475i	$-0.855519\pi$
$569$		−	20.9185i		−	0.876950i	0.898743	−	0.438475i	$-0.144481\pi$
$570$		−	26.5133i		−	1.11052i
$571$	−19.0298	+	19.0298i	−0.796371	+	0.796371i	−0.982521	−	0.186151i	$-0.940399\pi$
$571$	−19.0298	+	19.0298i	−0.796371	+	0.796371i	0.186151	+	0.982521i	$0.440399\pi$
$572$	−13.6657	+	13.6657i	−0.571391	+	0.571391i
$573$	10.9043	+	10.9043i	0.455533	+	0.455533i
$574$		0			0
$575$	−4.86947	−	4.86947i	−0.203071	−	0.203071i
$576$			2.84253i			0.118439i
$577$	−4.09850			−0.170623			−0.0853113	−	0.996354i	$-0.527188\pi$
$577$	−4.09850			−0.170623			−0.0853113	+	0.996354i	$0.527188\pi$
$578$	22.0684	−	18.9764i	0.917923	−	0.789315i
$579$	−16.9192			−0.703138
$580$			7.90119i			0.328079i
$581$		0			0
$582$	23.2898			0.965395
$583$	−5.18385	−	5.18385i	−0.214693	−	0.214693i
$584$	12.2737	−	12.2737i	0.507889	−	0.507889i
$585$	−16.7094	+	16.7094i	−0.690847	+	0.690847i
$586$		−	34.9908i		−	1.44545i
$587$			30.1079i			1.24269i	0.783538	+	0.621344i	$0.213413\pi$
$587$			30.1079i			1.24269i	−0.783538	+	0.621344i	$0.786587\pi$
$588$		0			0
$589$	26.4686	−	26.4686i	1.09062	−	1.09062i
$590$	48.2780	+	48.2780i	1.98758	+	1.98758i
$591$	25.2313			1.03788
$592$	−37.9119	−	37.9119i	−1.55817	−	1.55817i
$593$			16.8436i			0.691683i	0.938293	+	0.345842i	$0.112407\pi$
$593$			16.8436i			0.691683i	−0.938293	+	0.345842i	$0.887593\pi$
$594$	49.7527			2.04138
$595$		0			0
$596$	17.8540			0.731329
$597$			13.0702i			0.534929i
$598$	4.16831	+	4.16831i	0.170455	+	0.170455i
$599$	−6.37653			−0.260538			−0.130269	−	0.991479i	$-0.541584\pi$
$599$	−6.37653			−0.260538			−0.130269	+	0.991479i	$0.541584\pi$
$600$	−10.9021	−	10.9021i	−0.445075	−	0.445075i
$601$	22.6980	−	22.6980i	0.925870	−	0.925870i	−0.0715659	−	0.997436i	$-0.522800\pi$
$601$	22.6980	−	22.6980i	0.925870	−	0.925870i	0.997436	+	0.0715659i	$0.0227996\pi$
$602$		0			0
$603$			0.757694i			0.0308557i
$604$			20.8258i			0.847389i
$605$	−47.8072	+	47.8072i	−1.94364	+	1.94364i
$606$	−18.4077	+	18.4077i	−0.747762	+	0.747762i
$607$	9.88359	+	9.88359i	0.401163	+	0.401163i	0.878643	−	0.477480i	$-0.158450\pi$
$607$	9.88359	+	9.88359i	0.401163	+	0.401163i	−0.477480	+	0.878643i	$0.658450\pi$
$608$	19.1994			0.778640
$609$		0			0
$610$			53.6877i			2.17375i
$611$	10.2000			0.412646
$612$	2.82049	−	6.14517i	0.114011	−	0.248404i
$613$	−30.9977			−1.25199			−0.625993	−	0.779828i	$-0.715306\pi$
$613$	−30.9977			−1.25199			−0.625993	+	0.779828i	$0.715306\pi$
$614$			41.9075i			1.69125i
$615$	−13.6182	−	13.6182i	−0.549140	−	0.549140i
$616$		0			0
$617$	−22.1042	−	22.1042i	−0.889883	−	0.889883i	0.104629	−	0.994511i	$-0.466635\pi$
$617$	−22.1042	−	22.1042i	−0.889883	−	0.889883i	−0.994511	+	0.104629i	$0.966635\pi$
$618$	4.67719	−	4.67719i	0.188144	−	0.188144i
$619$	−4.96117	+	4.96117i	−0.199406	+	0.199406i	−0.799745	−	0.600339i	$-0.795032\pi$
$619$	−4.96117	+	4.96117i	−0.199406	+	0.199406i	0.600339	+	0.799745i	$0.295032\pi$
$620$			31.4921i			1.26475i
$621$		−	4.82108i		−	0.193463i
$622$	0.545387	−	0.545387i	0.0218680	−	0.0218680i
$623$		0			0
$624$	14.8800	+	14.8800i	0.595679	+	0.595679i
$625$	5.54761			0.221904
$626$	20.5526	+	20.5526i	0.821447	+	0.821447i
$627$			23.9520i			0.956552i
$628$	−2.80179			−0.111804
$629$	−15.3867	−	41.4933i	−0.613509	−	1.65445i
$630$		0			0
$631$		−	12.0354i		−	0.479123i	−0.970881	−	0.239562i	$-0.922996\pi$
$631$		−	12.0354i		−	0.479123i	0.970881	−	0.239562i	$-0.0770037\pi$
$632$	8.83796	+	8.83796i	0.351555	+	0.351555i
$633$	−24.3396			−0.967413
$634$	−5.66870	−	5.66870i	−0.225133	−	0.225133i
$635$	1.11877	−	1.11877i	0.0443972	−	0.0443972i
$636$	0.979845	−	0.979845i	0.0388534	−	0.0388534i
$637$		0			0
$638$		−	22.4684i		−	0.889533i
$639$	−2.82416	+	2.82416i	−0.111722	+	0.111722i
$640$	31.4589	−	31.4589i	1.24352	−	1.24352i
$641$	27.1348	+	27.1348i	1.07176	+	1.07176i	0.997218	+	0.0745423i	$0.0237496\pi$
$641$	27.1348	+	27.1348i	1.07176	+	1.07176i	0.0745423	+	0.997218i	$0.476250\pi$
$642$	−16.1574			−0.637681
$643$	4.98124	+	4.98124i	0.196441	+	0.196441i	0.798472	−	0.602031i	$-0.205642\pi$
$643$	4.98124	+	4.98124i	0.196441	+	0.196441i	−0.602031	+	0.798472i	$0.705642\pi$
$644$		0			0
$645$	4.67719			0.184164
$646$	25.1761	+	11.5553i	0.990542	+	0.454635i
$647$	−45.4370			−1.78631			−0.893156	−	0.449747i	$-0.851514\pi$
$647$	−45.4370			−1.78631			−0.893156	+	0.449747i	$0.851514\pi$
$648$		−	1.12621i		−	0.0442418i
$649$	−43.6142	−	43.6142i	−1.71201	−	1.71201i
$650$	49.0502			1.92391
$651$		0			0
$652$	9.73950	−	9.73950i	0.381428	−	0.381428i
$653$	2.02405	−	2.02405i	0.0792074	−	0.0792074i	−0.666393	−	0.745601i	$-0.732163\pi$
$653$	2.02405	−	2.02405i	0.0792074	−	0.0792074i	0.745601	+	0.666393i	$0.232163\pi$
$654$		−	10.0981i		−	0.394869i
$655$		−	0.156335i		−	0.00610850i
$656$	17.2382	−	17.2382i	0.673039	−	0.673039i
$657$	11.8122	−	11.8122i	0.460840	−	0.460840i
$658$		0			0
$659$	−3.39527			−0.132261			−0.0661305	−	0.997811i	$-0.521065\pi$
$659$	−3.39527			−0.132261			−0.0661305	+	0.997811i	$0.521065\pi$
$660$	−14.2490	−	14.2490i	−0.554640	−	0.554640i
$661$			15.0572i			0.585656i	0.956165	+	0.292828i	$0.0945963\pi$
$661$			15.0572i			0.585656i	−0.956165	+	0.292828i	$0.905404\pi$
$662$	59.0732			2.29595
$663$	6.03914	+	16.2857i	0.234541	+	0.632486i
$664$	5.70380			0.221350
$665$		0			0
$666$	−22.8831	−	22.8831i	−0.886702	−	0.886702i
$667$	−2.17721			−0.0843018
$668$	−8.95531	−	8.95531i	−0.346492	−	0.346492i
$669$	19.3086	−	19.3086i	0.746514	−	0.746514i
$670$	1.84667	−	1.84667i	0.0713432	−	0.0713432i
$671$		−	48.5013i		−	1.87237i
$672$		0			0
$673$	16.6305	−	16.6305i	0.641060	−	0.641060i	−0.309756	−	0.950816i	$-0.600247\pi$
$673$	16.6305	−	16.6305i	0.641060	−	0.641060i	0.950816	+	0.309756i	$0.100247\pi$
$674$	−32.5811	+	32.5811i	−1.25498	+	1.25498i
$675$	−28.3658	−	28.3658i	−1.09180	−	1.09180i
$676$	−1.23316			−0.0474292
$677$	−26.7743	−	26.7743i	−1.02902	−	1.02902i	−0.999566	−	0.0294529i	$-0.990624\pi$
$677$	−26.7743	−	26.7743i	−1.02902	−	1.02902i	−0.0294529	−	0.999566i	$-0.509376\pi$
$678$			17.3919i			0.667931i
$679$		0			0
$680$	25.0800	−	9.30027i	0.961775	−	0.356649i
$681$	12.3327			0.472591
$682$		−	89.5531i		−	3.42917i
$683$	16.6107	+	16.6107i	0.635592	+	0.635592i	0.949465	−	0.313873i	$-0.101627\pi$
$683$	16.6107	+	16.6107i	0.635592	+	0.635592i	−0.313873	+	0.949465i	$0.601627\pi$
$684$	6.43536			0.246062
$685$	−4.82375	−	4.82375i	−0.184306	−	0.184306i
$686$		0			0
$687$	−22.3540	+	22.3540i	−0.852858	+	0.852858i
$688$			5.92047i			0.225716i
$689$		−	5.05986i		−	0.192765i
$690$	−4.34622	+	4.34622i	−0.165458	+	0.165458i
$691$	−6.03978	+	6.03978i	−0.229764	+	0.229764i	−0.812594	−	0.582830i	$-0.801945\pi$
$691$	−6.03978	+	6.03978i	−0.229764	+	0.229764i	0.582830	+	0.812594i	$0.301945\pi$
$692$	−5.69408	−	5.69408i	−0.216457	−	0.216457i
$693$		0			0
$694$	20.0255	+	20.0255i	0.760157	+	0.760157i
$695$		−	21.3812i		−	0.811034i
$696$	−4.87446			−0.184766
$697$	18.8667	−	6.99621i	0.714626	−	0.265000i
$698$	17.3502			0.656715
$699$		−	4.61623i		−	0.174602i
$700$		0			0
$701$	−9.16499			−0.346157			−0.173078	−	0.984908i	$-0.555371\pi$
$701$	−9.16499			−0.346157			−0.173078	+	0.984908i	$0.555371\pi$
$702$	24.2813	+	24.2813i	0.916440	+	0.916440i
$703$	29.7831	−	29.7831i	1.12329	−	1.12329i
$704$	−6.25865	+	6.25865i	−0.235882	+	0.235882i
$705$			10.6353i			0.400549i
$706$		−	1.36546i		−	0.0513898i
$707$		0			0
$708$	8.24390	−	8.24390i	0.309825	−	0.309825i
$709$	1.04370	+	1.04370i	0.0391971	+	0.0391971i	0.726434	−	0.687237i	$-0.241176\pi$
$709$	1.04370	+	1.04370i	0.0391971	+	0.0391971i	−0.687237	+	0.726434i	$0.741176\pi$
$710$	13.7662			0.516637
$711$	8.50569	+	8.50569i	0.318988	+	0.318988i
$712$		−	5.36846i		−	0.201192i
$713$	−8.67777			−0.324985
$714$		0			0
$715$	−73.5808			−2.75177
$716$		−	9.97073i		−	0.372624i
$717$	−13.6008	−	13.6008i	−0.507932	−	0.507932i
$718$	−35.4962			−1.32471
$719$	−7.89648	−	7.89648i	−0.294489	−	0.294489i	0.544362	−	0.838851i	$-0.316772\pi$
$719$	−7.89648	−	7.89648i	−0.294489	−	0.294489i	−0.838851	+	0.544362i	$0.816772\pi$
$720$	22.0537	−	22.0537i	0.821894	−	0.821894i
$721$		0			0
$722$		−	6.16441i		−	0.229416i
$723$		−	0.417412i		−	0.0155237i
$724$	−10.6332	+	10.6332i	−0.395179	+	0.395179i
$725$	−12.8101	+	12.8101i	−0.475753	+	0.475753i
$726$	25.6967	+	25.6967i	0.953695	+	0.953695i
$727$	29.4789			1.09331			0.546656	−	0.837357i	$-0.315901\pi$
$727$	29.4789			1.09331			0.546656	+	0.837357i	$0.315901\pi$
$728$		0			0
$729$		−	18.7798i		−	0.695549i
$730$	−57.5783			−2.13107
$731$	−2.03846	+	4.44131i	−0.0753950	+	0.164268i
$732$	9.16765			0.338846
$733$			14.4608i			0.534123i	0.963679	+	0.267062i	$0.0860527\pi$
$733$			14.4608i			0.534123i	−0.963679	+	0.267062i	$0.913947\pi$
$734$	5.92358	+	5.92358i	0.218643	+	0.218643i
$735$		0			0
$736$	−3.14729	−	3.14729i	−0.116011	−	0.116011i
$737$	−1.66828	+	1.66828i	−0.0614518	+	0.0614518i
$738$	10.4047	−	10.4047i	0.383004	−	0.383004i
$739$		−	18.0495i		−	0.663963i	−0.943286	−	0.331982i	$-0.892283\pi$
$739$		−	18.0495i		−	0.663963i	0.943286	−	0.331982i	$-0.107717\pi$
$740$			35.4356i			1.30264i
$741$	−11.6896	+	11.6896i	−0.429427	+	0.429427i
$742$		0			0
$743$	22.5374	+	22.5374i	0.826816	+	0.826816i	0.987075	−	0.160259i	$-0.0512331\pi$
$743$	22.5374	+	22.5374i	0.826816	+	0.826816i	−0.160259	+	0.987075i	$0.551233\pi$
$744$	−19.4283			−0.712276
$745$	48.0661	+	48.0661i	1.76101	+	1.76101i
$746$		−	11.3882i		−	0.416953i
$747$	5.48936			0.200845
$748$	19.7404	−	7.32023i	0.721782	−	0.267654i
$749$		0			0
$750$			17.3621i			0.633974i
$751$	−27.9002	−	27.9002i	−1.01809	−	1.01809i	−0.999833	−	0.0182586i	$-0.994188\pi$
$751$	−27.9002	−	27.9002i	−1.01809	−	1.01809i	−0.0182586	−	0.999833i	$-0.505812\pi$
$752$	−13.4624			−0.490922
$753$	−12.2791	−	12.2791i	−0.447475	−	0.447475i
$754$	10.9655	−	10.9655i	0.399340	−	0.399340i
$755$	−56.0666	+	56.0666i	−2.04047	+	2.04047i
$756$		0			0
$757$			11.7657i			0.427633i	0.976874	+	0.213816i	$0.0685894\pi$
$757$			11.7657i			0.427633i	−0.976874	+	0.213816i	$0.931411\pi$
$758$	−7.42678	+	7.42678i	−0.269753	+	0.269753i
$759$	3.92636	−	3.92636i	0.142518	−	0.142518i
$760$	18.0019	+	18.0019i	0.652998	+	0.652998i
$761$	−26.3966			−0.956877			−0.478439	−	0.878121i	$-0.658797\pi$
$761$	−26.3966			−0.956877			−0.478439	+	0.878121i	$0.658797\pi$
$762$	−0.601349	−	0.601349i	−0.0217846	−	0.0217846i
$763$		0			0
$764$	12.9013			0.466752
$765$	24.1371	−	8.95062i	0.872679	−	0.323610i
$766$	49.6028			1.79222
$767$		−	42.5710i		−	1.53715i
$768$	−14.3686	−	14.3686i	−0.518481	−	0.518481i
$769$	14.6383			0.527871			0.263936	−	0.964540i	$-0.414979\pi$
$769$	14.6383			0.527871			0.263936	+	0.964540i	$0.414979\pi$
$770$		0			0
$771$	−16.6013	+	16.6013i	−0.597880	+	0.597880i
$772$	−10.0089	+	10.0089i	−0.360228	+	0.360228i
$773$		−	17.9450i		−	0.645438i	−0.946495	−	0.322719i	$-0.895403\pi$
$773$		−	17.9450i		−	0.645438i	0.946495	−	0.322719i	$-0.104597\pi$
$774$			3.57351i			0.128447i
$775$	−51.0575	+	51.0575i	−1.83404	+	1.83404i
$776$	−15.8133	+	15.8133i	−0.567663	+	0.567663i
$777$		0			0
$778$	−17.5057			−0.627609
$779$	13.5421	+	13.5421i	0.485196	+	0.485196i
$780$		−	13.9081i		−	0.497991i
$781$	−12.4364			−0.445008
$782$	−2.23282	−	6.02123i	−0.0798454	−	0.215319i
$783$	−12.6827			−0.453244
$784$		0			0
$785$	−7.54291	−	7.54291i	−0.269218	−	0.269218i
$786$	−0.0840310			−0.00299729
$787$	−0.592701	−	0.592701i	−0.0211275	−	0.0211275i	0.696464	−	0.717592i	$-0.254756\pi$
$787$	−0.592701	−	0.592701i	−0.0211275	−	0.0211275i	−0.717592	+	0.696464i	$0.754756\pi$
$788$	14.9261	−	14.9261i	0.531720	−	0.531720i
$789$	−8.34544	+	8.34544i	−0.297106	+	0.297106i
$790$		−	41.4606i		−	1.47510i
$791$		0			0
$792$	−12.4952	+	12.4952i	−0.443997	+	0.443997i
$793$	23.6706	−	23.6706i	0.840568	−	0.840568i
$794$	−5.71202	−	5.71202i	−0.202712	−	0.202712i
$795$	5.27583			0.187114
$796$	7.73194	+	7.73194i	0.274051	+	0.274051i
$797$		−	17.3052i		−	0.612981i	−0.951874	−	0.306490i	$-0.900845\pi$
$797$		−	17.3052i		−	0.612981i	0.951874	−	0.306490i	$-0.0991547\pi$
$798$		0			0
$799$	−10.0989	−	4.63518i	−0.357275	−	0.163981i
$800$	−37.0355			−1.30940
$801$		−	5.16663i		−	0.182554i
$802$	9.13653	+	9.13653i	0.322622	+	0.322622i
$803$	52.0161			1.83561
$804$	−0.315336	−	0.315336i	−0.0111210	−	0.0111210i
$805$		0			0
$806$	43.7056	−	43.7056i	1.53946	−	1.53946i
$807$			31.0972i			1.09467i
$808$		−	24.9968i		−	0.879386i
$809$	22.2239	−	22.2239i	0.781352	−	0.781352i	−0.198707	−	0.980059i	$-0.563674\pi$
$809$	22.2239	−	22.2239i	0.781352	−	0.781352i	0.980059	+	0.198707i	$0.0636743\pi$
$810$	−2.64164	+	2.64164i	−0.0928178	+	0.0928178i
$811$	−23.4079	−	23.4079i	−0.821964	−	0.821964i	0.164426	−	0.986389i	$-0.447423\pi$
$811$	−23.4079	−	23.4079i	−0.821964	−	0.821964i	−0.986389	+	0.164426i	$0.947423\pi$
$812$		0			0
$813$	2.26708	+	2.26708i	0.0795099	+	0.0795099i
$814$		−	100.767i		−	3.53189i
$815$	52.4409			1.83692
$816$	−7.97073	−	21.4946i	−0.279031	−	0.752463i
$817$	−4.65104			−0.162719
$818$		−	19.3479i		−	0.676483i
$819$		0			0
$820$	−16.1123			−0.562665
$821$	15.2809	+	15.2809i	0.533307	+	0.533307i	0.921555	−	0.388248i	$-0.126920\pi$
$821$	15.2809	+	15.2809i	0.533307	+	0.533307i	−0.388248	+	0.921555i	$0.626920\pi$
$822$	−2.59280	+	2.59280i	−0.0904343	+	0.0904343i
$823$	−15.7187	+	15.7187i	−0.547920	+	0.547920i	−0.925839	−	0.377919i	$-0.876640\pi$
$823$	−15.7187	+	15.7187i	−0.547920	+	0.547920i	0.377919	+	0.925839i	$0.376640\pi$
$824$			6.35141i			0.221262i
$825$		−	46.2031i		−	1.60859i
$826$		0			0
$827$	31.0315	−	31.0315i	1.07907	−	1.07907i	0.0824786	−	0.996593i	$-0.473716\pi$
$827$	31.0315	−	31.0315i	1.07907	−	1.07907i	0.996593	−	0.0824786i	$-0.0262836\pi$
$828$	−1.05492	−	1.05492i	−0.0366611	−	0.0366611i
$829$	48.2425			1.67553			0.837765	−	0.546031i	$-0.183862\pi$
$829$	48.2425			1.67553			0.837765	+	0.546031i	$0.183862\pi$
$830$	−13.3788	−	13.3788i	−0.464386	−	0.464386i
$831$			7.98107i			0.276860i
$832$	−6.10895			−0.211790
$833$		0			0
$834$	−11.4925			−0.397954
$835$		−	48.2185i		−	1.66867i
$836$	14.1693	+	14.1693i	0.490055	+	0.490055i
$837$	−50.5500			−1.74726
$838$	34.2918	+	34.2918i	1.18459	+	1.18459i
$839$	−18.6559	+	18.6559i	−0.644073	+	0.644073i	−0.951554	−	0.307482i	$-0.900514\pi$
$839$	−18.6559	+	18.6559i	−0.644073	+	0.644073i	0.307482	+	0.951554i	$0.400514\pi$
$840$		0			0
$841$		−	23.2725i		−	0.802499i
$842$		−	61.3563i		−	2.11448i
$843$	16.0058	−	16.0058i	0.551269	−	0.551269i
$844$	−14.3986	+	14.3986i	−0.495619	+	0.495619i
$845$	−3.31988	−	3.31988i	−0.114207	−	0.114207i
$846$	−8.12570			−0.279367
$847$		0			0
$848$			6.67823i			0.229331i
$849$	3.43826			0.118001
$850$	−48.5644	−	22.2899i	−1.66575	−	0.764538i
$851$	−9.76443			−0.334720
$852$		−	2.35071i		−	0.0805338i
$853$	−12.6584	−	12.6584i	−0.433415	−	0.433415i	0.456374	−	0.889788i	$-0.349148\pi$
$853$	−12.6584	−	12.6584i	−0.433415	−	0.433415i	−0.889788	+	0.456374i	$0.849148\pi$
$854$		0			0
$855$	17.3251	+	17.3251i	0.592506	+	0.592506i
$856$	10.9705	−	10.9705i	0.374964	−	0.374964i
$857$	−16.8061	+	16.8061i	−0.574086	+	0.574086i	−0.933268	−	0.359182i	$-0.883056\pi$
$857$	−16.8061	+	16.8061i	−0.574086	+	0.574086i	0.359182	+	0.933268i	$0.383056\pi$
$858$			39.5502i			1.35022i
$859$			42.5275i			1.45102i	0.688211	+	0.725510i	$0.258396\pi$
$859$			42.5275i			1.45102i	−0.688211	+	0.725510i	$0.741604\pi$
$860$	2.76688	−	2.76688i	0.0943499	−	0.0943499i
$861$		0			0
$862$	−6.69661	−	6.69661i	−0.228087	−	0.228087i
$863$	35.7959			1.21851			0.609253	−	0.792976i	$-0.291470\pi$
$863$	35.7959			1.21851			0.609253	+	0.792976i	$0.291470\pi$
$864$	−18.3337	−	18.3337i	−0.623724	−	0.623724i
$865$		−	30.6589i		−	1.04244i
$866$	−5.09166			−0.173022
$867$	1.42141	−	18.8688i	0.0482735	−	0.640819i
$868$		0			0
$869$			37.4554i			1.27059i
$870$	11.4335	+	11.4335i	0.387633	+	0.387633i
$871$	−1.62838			−0.0551754
$872$	6.85641	+	6.85641i	0.232187	+	0.232187i
$873$	−15.2187	+	15.2187i	−0.515077	+	0.515077i
$874$	4.32191	−	4.32191i	0.146191	−	0.146191i
$875$		0			0
$876$			9.83200i			0.332193i
$877$	−15.0886	+	15.0886i	−0.509506	+	0.509506i	−0.914375	−	0.404869i	$-0.867317\pi$
$877$	−15.0886	+	15.0886i	−0.509506	+	0.509506i	0.404869	+	0.914375i	$0.367317\pi$
$878$	2.16043	−	2.16043i	0.0729109	−	0.0729109i
$879$	−16.0857	−	16.0857i	−0.542557	−	0.542557i
$880$	97.1152			3.27375
$881$	24.2562	+	24.2562i	0.817212	+	0.817212i	0.985703	−	0.168491i	$-0.0538895\pi$
$881$	24.2562	+	24.2562i	0.817212	+	0.817212i	−0.168491	+	0.985703i	$0.553890\pi$
$882$		0			0
$883$	25.3180			0.852018			0.426009	−	0.904719i	$-0.359919\pi$
$883$	25.3180			0.852018			0.426009	+	0.904719i	$0.359919\pi$
$884$	13.2067	+	6.06157i	0.444190	+	0.203873i
$885$	44.3880			1.49209
$886$			14.8972i			0.500481i
$887$	11.9511	+	11.9511i	0.401279	+	0.401279i	0.878684	−	0.477405i	$-0.158422\pi$
$887$	11.9511	+	11.9511i	0.401279	+	0.401279i	−0.477405	+	0.878684i	$0.658422\pi$
$888$	−21.8612			−0.733613
$889$		0			0
$890$	−12.5923	+	12.5923i	−0.422093	+	0.422093i
$891$	2.38645	−	2.38645i	0.0799491	−	0.0799491i
$892$		−	22.8448i		−	0.764899i
$893$		−	10.5758i		−	0.353907i
$894$	25.8359	−	25.8359i	0.864081	−	0.864081i
$895$	26.8429	−	26.8429i	0.897261	−	0.897261i
$896$		0			0
$897$	3.83245			0.127962
$898$	21.5180	+	21.5180i	0.718066	+	0.718066i
$899$			22.8285i			0.761372i
$900$	−12.4137			−0.413791
$901$	−2.29936	+	5.00975i	−0.0766027	+	0.166899i
$902$	45.8180			1.52557
$903$		0			0
$904$	−11.8087	−	11.8087i	−0.392751	−	0.392751i
$905$	−57.2527			−1.90314
$906$	30.1362	+	30.1362i	1.00121	+	1.00121i
$907$	−20.5548	+	20.5548i	−0.682512	+	0.682512i	−0.960566	−	0.278053i	$-0.910311\pi$
$907$	−20.5548	+	20.5548i	−0.682512	+	0.682512i	0.278053	+	0.960566i	$0.410311\pi$
$908$	7.29566	−	7.29566i	0.242115	−	0.242115i
$909$		−	24.0571i		−	0.797922i
$910$		0			0
$911$	33.6975	−	33.6975i	1.11645	−	1.11645i	0.124188	−	0.992259i	$-0.460367\pi$
$911$	33.6975	−	33.6975i	1.11645	−	1.11645i	0.992259	−	0.124188i	$-0.0396326\pi$
$912$	15.4284	−	15.4284i	0.510885	−	0.510885i
$913$	12.0864	+	12.0864i	0.400001	+	0.400001i
$914$	−38.3861			−1.26970
$915$	24.6809	+	24.6809i	0.815926	+	0.815926i
$916$			26.4479i			0.873862i
$917$		0			0
$918$	−13.0067	−	35.0750i	−0.429284	−	1.15765i
$919$	0.642431			0.0211918			0.0105959	−	0.999944i	$-0.496627\pi$
$919$	0.642431			0.0211918			0.0105959	+	0.999944i	$0.496627\pi$
$920$		−	5.90196i		−	0.194582i
$921$	19.2654	+	19.2654i	0.634816	+	0.634816i
$922$	−41.1849			−1.35635
$923$	−6.06946	−	6.06946i	−0.199779	−	0.199779i
$924$		0			0
$925$	−57.4511	+	57.4511i	−1.88898	+	1.88898i
$926$			1.13853i			0.0374146i
$927$			6.11263i			0.200765i
$928$	−8.27952	+	8.27952i	−0.271789	+	0.271789i
$929$	6.08987	−	6.08987i	0.199802	−	0.199802i	−0.600113	−	0.799915i	$-0.704878\pi$
$929$	6.08987	−	6.08987i	0.199802	−	0.199802i	0.799915	+	0.600113i	$0.204878\pi$
$930$	45.5710	+	45.5710i	1.49433	+	1.49433i
$931$		0			0
$932$	−2.73082	−	2.73082i	−0.0894510	−	0.0894510i
$933$		−	0.501443i		−	0.0164165i
$934$	−35.2577			−1.15367
$935$	72.8521	+	33.4374i	2.38252	+	1.09352i
$936$	−12.1963			−0.398649
$937$		−	20.8080i		−	0.679766i	−0.940468	−	0.339883i	$-0.889612\pi$
$937$		−	20.8080i		−	0.679766i	0.940468	−	0.339883i	$-0.110388\pi$
$938$		0			0
$939$	18.8966			0.616666
$940$	6.29153	+	6.29153i	0.205207	+	0.205207i
$941$	−2.37017	+	2.37017i	−0.0772652	+	0.0772652i	−0.744683	−	0.667418i	$-0.767399\pi$
$941$	−2.37017	+	2.37017i	−0.0772652	+	0.0772652i	0.667418	+	0.744683i	$0.267399\pi$
$942$	−4.05437	+	4.05437i	−0.132098	+	0.132098i
$943$		−	4.43980i		−	0.144580i
$944$			56.1871i			1.82874i
$945$		0			0
$946$	−7.86811	+	7.86811i	−0.255814	+	0.255814i
$947$	8.49486	+	8.49486i	0.276046	+	0.276046i	0.831528	−	0.555482i	$-0.187466\pi$
$947$	8.49486	+	8.49486i	0.276046	+	0.276046i	−0.555482	+	0.831528i	$0.687466\pi$
$948$	−7.07977			−0.229940
$949$	25.3860	+	25.3860i	0.824063	+	0.824063i
$950$		−	50.8578i		−	1.65004i
$951$	−5.21194			−0.169009
$952$		0			0
$953$	13.0495			0.422716			0.211358	−	0.977409i	$-0.432211\pi$
$953$	13.0495			0.422716			0.211358	+	0.977409i	$0.432211\pi$
$954$			4.03089i			0.130505i
$955$	34.7325	+	34.7325i	1.12392	+	1.12392i
$956$	−16.0916			−0.520441
$957$	−10.3290	−	10.3290i	−0.333889	−	0.333889i
$958$	11.2032	−	11.2032i	0.361959	−	0.361959i
$959$		0			0
$960$		−	6.36969i		−	0.205581i
$961$			59.9883i			1.93511i
$962$	49.1786	−	49.1786i	1.58558	−	1.58558i
$963$	10.5580	−	10.5580i	0.340228	−	0.340228i
$964$	−0.246928	−	0.246928i	−0.00795302	−	0.00795302i
$965$	−53.8913			−1.73482
$966$		0			0
$967$		−	32.4078i		−	1.04216i	−0.853507	−	0.521082i	$-0.825529\pi$
$967$		−	32.4078i		−	1.04216i	0.853507	−	0.521082i	$-0.174471\pi$
$968$	−34.8950			−1.12157
$969$	16.8859	−	6.26169i	0.542453	−	0.201155i
$970$	74.1832			2.38188
$971$		−	24.9206i		−	0.799740i	−0.916572	−	0.399870i	$-0.869055\pi$
$971$		−	24.9206i		−	0.799740i	0.916572	−	0.399870i	$-0.130945\pi$
$972$	−10.0173	−	10.0173i	−0.321305	−	0.321305i
$973$		0			0
$974$	−1.85911	−	1.85911i	−0.0595696	−	0.0595696i
$975$	22.5490	−	22.5490i	0.722146	−	0.722146i
$976$	−31.2415	+	31.2415i	−1.00002	+	1.00002i
$977$		−	23.5906i		−	0.754731i	−0.926064	−	0.377365i	$-0.876830\pi$
$977$		−	23.5906i		−	0.754731i	0.926064	−	0.377365i	$-0.123170\pi$
$978$		−	28.1873i		−	0.901332i
$979$	11.3758	−	11.3758i	0.363572	−	0.363572i
$980$		0			0
$981$	6.59863	+	6.59863i	0.210678	+	0.210678i
$982$	25.0203			0.798430
$983$	−7.34127	−	7.34127i	−0.234150	−	0.234150i	0.580272	−	0.814422i	$-0.302946\pi$
$983$	−7.34127	−	7.34127i	−0.234150	−	0.234150i	−0.814422	+	0.580272i	$0.802946\pi$
$984$		−	9.94009i		−	0.316879i
$985$	80.3672			2.56071
$986$	−15.8400	+	5.87384i	−0.504447	+	0.187061i
$987$		0			0
$988$			13.8304i			0.440003i
$989$	0.762426	+	0.762426i	0.0242437	+	0.0242437i
$990$	58.6174			1.86298
$991$	−16.0590	−	16.0590i	−0.510132	−	0.510132i	0.404435	−	0.914567i	$-0.367468\pi$
$991$	−16.0590	−	16.0590i	−0.510132	−	0.510132i	−0.914567	+	0.404435i	$0.867468\pi$
$992$	−33.0000	+	33.0000i	−1.04775	+	1.04775i
$993$	27.1567	−	27.1567i	0.861792	−	0.861792i
$994$		0			0
$995$			41.6315i			1.31981i
$996$	−2.28455	+	2.28455i	−0.0723889	+	0.0723889i
$997$	−27.3633	+	27.3633i	−0.866605	+	0.866605i	−0.992095	−	0.125490i	$-0.959950\pi$
$997$	−27.3633	+	27.3633i	−0.866605	+	0.866605i	0.125490	+	0.992095i	$0.459950\pi$
$998$	−24.0529	−	24.0529i	−0.761382	−	0.761382i
$999$	−56.8801			−1.79961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.g.e.540.3	yes	16
7.2	even	3		833.2.o.e.557.4		32
7.3	odd	6		833.2.o.e.30.6		32
7.4	even	3		833.2.o.e.30.5		32
7.5	odd	6		833.2.o.e.557.3		32
7.6	odd	2	inner	833.2.g.e.540.4	yes	16
17.4	even	4	inner	833.2.g.e.344.5	✓	16
119.4	even	12		833.2.o.e.667.4		32
119.38	odd	12		833.2.o.e.667.3		32
119.55	odd	4	inner	833.2.g.e.344.6	yes	16
119.72	even	12		833.2.o.e.361.5		32
119.89	odd	12		833.2.o.e.361.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.g.e.344.5	✓	16	17.4	even	4	inner
833.2.g.e.344.6	yes	16	119.55	odd	4	inner
833.2.g.e.540.3	yes	16	1.1	even	1	trivial
833.2.g.e.540.4	yes	16	7.6	odd	2	inner
833.2.o.e.30.5		32	7.4	even	3
833.2.o.e.30.6		32	7.3	odd	6
833.2.o.e.361.5		32	119.72	even	12
833.2.o.e.361.6		32	119.89	odd	12
833.2.o.e.557.3		32	7.5	odd	6
833.2.o.e.557.4		32	7.2	even	3
833.2.o.e.667.3		32	119.38	odd	12
833.2.o.e.667.4		32	119.4	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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.71208i q^{2} +(-0.787063 - 0.787063i) q^{3} -0.931205 q^{4} +(-2.50697 - 2.50697i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} -1.76106i q^{9} +O(q^{10})\)	\(q-1.71208i q^{2} +(-0.787063 - 0.787063i) q^{3} -0.931205 q^{4} +(-2.50697 - 2.50697i) q^{5} +(-1.34751 + 1.34751i) q^{6} -1.82986i q^{8} -1.76106i q^{9} +(-4.29212 + 4.29212i) q^{10} +(3.87748 - 3.87748i) q^{11} +(0.732917 + 0.732917i) q^{12} +3.78474 q^{13} +3.94628i q^{15} -4.99527 q^{16} +(-3.74726 - 1.71990i) q^{17} -3.01508 q^{18} -3.92421i q^{19} +(2.33450 + 2.33450i) q^{20} +(-6.63855 - 6.63855i) q^{22} +(-0.643281 + 0.643281i) q^{23} +(-1.44021 + 1.44021i) q^{24} +7.56975i q^{25} -6.47976i q^{26} +(-3.74726 + 3.74726i) q^{27} +(1.69227 + 1.69227i) q^{29} +6.75633 q^{30} +(6.74493 + 6.74493i) q^{31} +4.89256i q^{32} -6.10365 q^{33} +(-2.94460 + 6.41559i) q^{34} +1.63991i q^{36} +(7.58956 + 7.58956i) q^{37} -6.71855 q^{38} +(-2.97883 - 2.97883i) q^{39} +(-4.58739 + 4.58739i) q^{40} +(-3.45091 + 3.45091i) q^{41} -1.18522i q^{43} +(-3.61073 + 3.61073i) q^{44} +(-4.41493 + 4.41493i) q^{45} +(1.10135 + 1.10135i) q^{46} +2.69502 q^{47} +(3.93159 + 3.93159i) q^{48} +12.9600 q^{50} +(1.59566 + 4.30300i) q^{51} -3.52437 q^{52} -1.33691i q^{53} +(6.41559 + 6.41559i) q^{54} -19.4414 q^{55} +(-3.08860 + 3.08860i) q^{57} +(2.89729 - 2.89729i) q^{58} -11.2481i q^{59} -3.67479i q^{60} +(6.25422 - 6.25422i) q^{61} +(11.5478 - 11.5478i) q^{62} -1.61410 q^{64} +(-9.48821 - 9.48821i) q^{65} +10.4499i q^{66} -0.430248 q^{67} +(3.48946 + 1.60158i) q^{68} +1.01260 q^{69} +(-1.60366 - 1.60366i) q^{71} -3.22250 q^{72} +(6.70745 + 6.70745i) q^{73} +(12.9939 - 12.9939i) q^{74} +(5.95787 - 5.95787i) q^{75} +3.65425i q^{76} +(-5.09998 + 5.09998i) q^{78} +(-4.82986 + 4.82986i) q^{79} +(12.5230 + 12.5230i) q^{80} +0.615464 q^{81} +(5.90821 + 5.90821i) q^{82} +3.11707i q^{83} +(5.08251 + 13.7060i) q^{85} -2.02918 q^{86} -2.66384i q^{87} +(-7.09525 - 7.09525i) q^{88} +2.93381 q^{89} +(7.55869 + 7.55869i) q^{90} +(0.599026 - 0.599026i) q^{92} -10.6174i q^{93} -4.61409i q^{94} +(-9.83787 + 9.83787i) q^{95} +(3.85075 - 3.85075i) q^{96} +(-8.64179 - 8.64179i) q^{97} +(-6.82850 - 6.82850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 28 q^{4}+O(q^{10}) \) 16 * q - 28 * q^4	\( 16 q - 28 q^{4} - 12 q^{11} + 20 q^{16} + 52 q^{18} - 4 q^{22} - 8 q^{23} + 12 q^{29} - 20 q^{30} + 32 q^{37} - 28 q^{39} + 12 q^{44} + 72 q^{46} + 56 q^{51} - 36 q^{57} - 28 q^{58} - 36 q^{64} - 8 q^{65} - 96 q^{67} - 24 q^{71} - 160 q^{72} + 88 q^{74} - 116 q^{78} - 36 q^{79} + 40 q^{81} - 52 q^{85} - 20 q^{86} - 48 q^{88} + 120 q^{92} - 84 q^{95} - 48 q^{99}+O(q^{100}) \) 16 * q - 28 * q^4 - 12 * q^11 + 20 * q^16 + 52 * q^18 - 4 * q^22 - 8 * q^23 + 12 * q^29 - 20 * q^30 + 32 * q^37 - 28 * q^39 + 12 * q^44 + 72 * q^46 + 56 * q^51 - 36 * q^57 - 28 * q^58 - 36 * q^64 - 8 * q^65 - 96 * q^67 - 24 * q^71 - 160 * q^72 + 88 * q^74 - 116 * q^78 - 36 * q^79 + 40 * q^81 - 52 * q^85 - 20 * q^86 - 48 * q^88 + 120 * q^92 - 84 * q^95 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more