LMFDB - Embedded newform 819.2.s.e.289.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.7
Root			$0.857510 - 1.48525i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.e.802.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.71502 q^{2} +0.941295 q^{4} +(-1.22863 + 2.12806i) q^{5} +(-2.38702 - 1.14112i) q^{7} -1.81570 q^{8} +O(q^{10})$	\(q+1.71502 q^{2} +0.941295 q^{4} +(-1.22863 + 2.12806i) q^{5} +(-2.38702 - 1.14112i) q^{7} -1.81570 q^{8} +(-2.10713 + 3.64966i) q^{10} +(-0.519081 + 0.899075i) q^{11} +(-3.36305 + 1.29996i) q^{13} +(-4.09378 - 1.95704i) q^{14} -4.99655 q^{16} -3.01950 q^{17} +(-1.59671 - 2.76558i) q^{19} +(-1.15651 + 2.00313i) q^{20} +(-0.890235 + 1.54193i) q^{22} +3.47202 q^{23} +(-0.519081 - 0.899075i) q^{25} +(-5.76770 + 2.22946i) q^{26} +(-2.24689 - 1.07413i) q^{28} +(4.01417 + 6.95275i) q^{29} +(-3.48074 - 6.02882i) q^{31} -4.93779 q^{32} -5.17850 q^{34} +(5.36113 - 3.67769i) q^{35} +2.82664 q^{37} +(-2.73838 - 4.74302i) q^{38} +(2.23083 - 3.86391i) q^{40} +(2.54107 + 4.40125i) q^{41} +(-3.21838 + 5.57439i) q^{43} +(-0.488608 + 0.846294i) q^{44} +5.95458 q^{46} +(-4.88951 + 8.46887i) q^{47} +(4.39569 + 5.44774i) q^{49} +(-0.890235 - 1.54193i) q^{50} +(-3.16562 + 1.22365i) q^{52} +(-5.90947 - 10.2355i) q^{53} +(-1.27552 - 2.20927i) q^{55} +(4.33411 + 2.07193i) q^{56} +(6.88438 + 11.9241i) q^{58} -8.94141 q^{59} +(1.30446 + 2.25940i) q^{61} +(-5.96954 - 10.3396i) q^{62} +1.52470 q^{64} +(1.36557 - 8.75393i) q^{65} +(5.61000 - 9.71681i) q^{67} -2.84224 q^{68} +(9.19445 - 6.30731i) q^{70} +(1.63013 - 2.82347i) q^{71} +(7.50717 + 13.0028i) q^{73} +4.84774 q^{74} +(-1.50297 - 2.60322i) q^{76} +(2.26501 - 1.55377i) q^{77} +(-0.211818 + 0.366880i) q^{79} +(6.13893 - 10.6329i) q^{80} +(4.35798 + 7.54824i) q^{82} +1.34088 q^{83} +(3.70986 - 6.42567i) q^{85} +(-5.51958 + 9.56019i) q^{86} +(0.942496 - 1.63245i) q^{88} -5.30493 q^{89} +(9.51106 + 0.734615i) q^{91} +3.26819 q^{92} +(-8.38560 + 14.5243i) q^{94} +7.84707 q^{95} +(2.92406 - 5.06463i) q^{97} +(7.53871 + 9.34298i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31} + 6 q^{32} - 68 q^{34} - 8 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} - 4 q^{46} - 5 q^{47} + 7 q^{49} + 7 q^{50} - 18 q^{52} - 36 q^{53} - 15 q^{55} + 51 q^{56} + 20 q^{58} - 34 q^{59} - 22 q^{61} + 6 q^{62} - 20 q^{64} + 24 q^{65} + 26 q^{67} + 10 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} + 30 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} + 28 q^{80} - q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} + 24 q^{88} + 40 q^{89} - 10 q^{91} + 94 q^{92} - 20 q^{94} + 7 q^{97} - 18 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.71502			1.21270			0.606351	−	0.795197i	$-0.292633\pi$
$2$	1.71502			1.21270			0.606351	+	0.795197i	$0.292633\pi$
$3$		0			0
$3$		0			0
$4$	0.941295			0.470647
$5$	−1.22863	+	2.12806i	−0.549462	+	0.951695i	0.448850	+	0.893607i	$0.351834\pi$
$5$	−1.22863	+	2.12806i	−0.549462	+	0.951695i	−0.998311	+	0.0580883i	$0.981500\pi$
$6$		0			0
$7$	−2.38702	−	1.14112i	−0.902207	−	0.431302i
$7$	−2.38702	−	1.14112i	−0.902207	−	0.431302i
$8$	−1.81570			−0.641947
$9$		0			0
$10$	−2.10713	+	3.64966i	−0.666334	+	1.15412i
$11$	−0.519081	+	0.899075i	−0.156509	+	0.271081i	−0.933607	−	0.358298i	$-0.883357\pi$
$11$	−0.519081	+	0.899075i	−0.156509	+	0.271081i	0.777099	+	0.629379i	$0.216691\pi$
$12$		0			0
$13$	−3.36305	+	1.29996i	−0.932742	+	0.360544i
$13$	−3.36305	+	1.29996i	−0.932742	+	0.360544i
$14$	−4.09378	−	1.95704i	−1.09411	−	0.523042i
$15$		0			0
$16$	−4.99655			−1.24914
$17$	−3.01950			−0.732336			−0.366168	−	0.930549i	$-0.619331\pi$
$17$	−3.01950			−0.732336			−0.366168	+	0.930549i	$0.619331\pi$
$18$		0			0
$19$	−1.59671	−	2.76558i	−0.366310	−	0.634467i	0.622676	−	0.782480i	$-0.286046\pi$
$19$	−1.59671	−	2.76558i	−0.366310	−	0.634467i	−0.988985	+	0.148013i	$0.952712\pi$
$20$	−1.15651	+	2.00313i	−0.258603	+	0.447913i
$21$		0			0
$22$	−0.890235	+	1.54193i	−0.189799	+	0.328741i
$23$	3.47202			0.723965			0.361983	−	0.932185i	$-0.382100\pi$
$23$	3.47202			0.723965			0.361983	+	0.932185i	$0.382100\pi$
$24$		0			0
$25$	−0.519081	−	0.899075i	−0.103816	−	0.179815i
$26$	−5.76770	+	2.22946i	−1.13114	+	0.437233i
$27$		0			0
$28$	−2.24689	−	1.07413i	−0.424621	−	0.202991i
$29$	4.01417	+	6.95275i	0.745413	+	1.29109i	0.950002	+	0.312245i	$0.101081\pi$
$29$	4.01417	+	6.95275i	0.745413	+	1.29109i	−0.204589	+	0.978848i	$0.565586\pi$
$30$		0			0
$31$	−3.48074	−	6.02882i	−0.625160	−	1.08281i	−0.988510	−	0.151156i	$-0.951700\pi$
$31$	−3.48074	−	6.02882i	−0.625160	−	1.08281i	0.363350	−	0.931653i	$-0.381633\pi$
$32$	−4.93779			−0.872886
$33$		0			0
$34$	−5.17850			−0.888106
$35$	5.36113	−	3.67769i	0.906197	−	0.621643i
$36$		0			0
$37$	2.82664			0.464696			0.232348	−	0.972633i	$-0.425359\pi$
$37$	2.82664			0.464696			0.232348	+	0.972633i	$0.425359\pi$
$38$	−2.73838	−	4.74302i	−0.444225	−	0.769419i
$39$		0			0
$40$	2.23083	−	3.86391i	0.352725	−	0.610938i
$41$	2.54107	+	4.40125i	0.396848	+	0.687360i	0.993335	−	0.115262i	$-0.0367708\pi$
$41$	2.54107	+	4.40125i	0.396848	+	0.687360i	−0.596487	+	0.802622i	$0.703437\pi$
$42$		0			0
$43$	−3.21838	+	5.57439i	−0.490798	+	0.850087i	−0.999944	−	0.0105935i	$-0.996628\pi$
$43$	−3.21838	+	5.57439i	−0.490798	+	0.850087i	0.509146	+	0.860680i	$0.329961\pi$
$44$	−0.488608	+	0.846294i	−0.0736605	+	0.127584i
$45$		0			0
$46$	5.95458			0.877955
$47$	−4.88951	+	8.46887i	−0.713208	+	1.23531i	0.250439	+	0.968132i	$0.419425\pi$
$47$	−4.88951	+	8.46887i	−0.713208	+	1.23531i	−0.963647	+	0.267180i	$0.913908\pi$
$48$		0			0
$49$	4.39569	+	5.44774i	0.627956	+	0.778249i
$50$	−0.890235	−	1.54193i	−0.125898	−	0.218062i
$51$		0			0
$52$	−3.16562	+	1.22365i	−0.438993	+	0.169689i
$53$	−5.90947	−	10.2355i	−0.811728	−	1.40595i	−0.911654	−	0.410959i	$-0.865194\pi$
$53$	−5.90947	−	10.2355i	−0.811728	−	1.40595i	0.0999257	−	0.994995i	$-0.468139\pi$
$54$		0			0
$55$	−1.27552	−	2.20927i	−0.171991	−	0.297898i
$56$	4.33411	+	2.07193i	0.579170	+	0.276873i
$57$		0			0
$58$	6.88438	+	11.9241i	0.903964	+	1.56571i
$59$	−8.94141			−1.16407			−0.582036	−	0.813163i	$-0.697744\pi$
$59$	−8.94141			−1.16407			−0.582036	+	0.813163i	$0.697744\pi$
$60$		0			0
$61$	1.30446	+	2.25940i	0.167019	+	0.289286i	0.937371	−	0.348334i	$-0.113252\pi$
$61$	1.30446	+	2.25940i	0.167019	+	0.289286i	−0.770351	+	0.637620i	$0.779919\pi$
$62$	−5.96954	−	10.3396i	−0.758133	−	1.31312i
$63$		0			0
$64$	1.52470			0.190588
$65$	1.36557	−	8.75393i	0.169378	−	1.08579i
$66$		0			0
$67$	5.61000	−	9.71681i	0.685371	−	1.18710i	−0.287949	−	0.957646i	$-0.592973\pi$
$67$	5.61000	−	9.71681i	0.685371	−	1.18710i	0.973320	−	0.229452i	$-0.0736933\pi$
$68$	−2.84224			−0.344672
$69$		0			0
$70$	9.19445	−	6.30731i	1.09895	−	0.753867i
$71$	1.63013	−	2.82347i	0.193461	−	0.335085i	−0.752934	−	0.658096i	$-0.771362\pi$
$71$	1.63013	−	2.82347i	0.193461	−	0.335085i	0.946395	+	0.323012i	$0.104695\pi$
$72$		0			0
$73$	7.50717	+	13.0028i	0.878648	+	1.52186i	0.852825	+	0.522196i	$0.174887\pi$
$73$	7.50717	+	13.0028i	0.878648	+	1.52186i	0.0258228	+	0.999667i	$0.491779\pi$
$74$	4.84774			0.563538
$75$		0			0
$76$	−1.50297	−	2.60322i	−0.172403	−	0.298610i
$77$	2.26501	−	1.55377i	0.258121	−	0.177069i
$78$		0			0
$79$	−0.211818	+	0.366880i	−0.0238314	+	0.0412773i	−0.877695	−	0.479219i	$-0.840920\pi$
$79$	−0.211818	+	0.366880i	−0.0238314	+	0.0412773i	0.853864	+	0.520497i	$0.174253\pi$
$80$	6.13893	−	10.6329i	0.686354	−	1.18880i
$81$		0			0
$82$	4.35798	+	7.54824i	0.481258	+	0.833564i
$83$	1.34088			0.147181			0.0735904	−	0.997289i	$-0.476554\pi$
$83$	1.34088			0.147181			0.0735904	+	0.997289i	$0.476554\pi$
$84$		0			0
$85$	3.70986	−	6.42567i	0.402391	−	0.696961i
$86$	−5.51958	+	9.56019i	−0.595192	+	1.03090i
$87$		0			0
$88$	0.942496	−	1.63245i	0.100470	−	0.174020i
$89$	−5.30493			−0.562322			−0.281161	−	0.959661i	$-0.590719\pi$
$89$	−5.30493			−0.562322			−0.281161	+	0.959661i	$0.590719\pi$
$90$		0			0
$91$	9.51106	+	0.734615i	0.997030	+	0.0770086i
$92$	3.26819			0.340732
$93$		0			0
$94$	−8.38560	+	14.5243i	−0.864909	+	1.49807i
$95$	7.84707			0.805092
$96$		0			0
$97$	2.92406	−	5.06463i	0.296894	−	0.514235i	−0.678530	−	0.734573i	$-0.737383\pi$
$97$	2.92406	−	5.06463i	0.296894	−	0.514235i	0.975424	+	0.220338i	$0.0707159\pi$
$98$	7.53871	+	9.34298i	0.761524	+	0.943784i
$99$		0			0
$100$	−0.488608	−	0.846294i	−0.0488608	−	0.0846294i
$101$	−9.26437	+	16.0464i	−0.921840	+	1.59667i	−0.125273	+	0.992122i	$0.539981\pi$
$101$	−9.26437	+	16.0464i	−0.921840	+	1.59667i	−0.796567	+	0.604551i	$0.793353\pi$
$102$		0			0
$103$	−1.01571	+	1.75926i	−0.100081	+	0.173345i	−0.911718	−	0.410817i	$-0.865243\pi$
$103$	−1.01571	+	1.75926i	−0.100081	+	0.173345i	0.811637	+	0.584162i	$0.198577\pi$
$104$	6.10629	−	2.36034i	0.598771	−	0.231450i
$105$		0			0
$106$	−10.1349	−	17.5541i	−0.984385	−	1.70500i
$107$	2.43666			0.235561			0.117781	−	0.993040i	$-0.462422\pi$
$107$	2.43666			0.235561			0.117781	+	0.993040i	$0.462422\pi$
$108$		0			0
$109$	−7.85642	−	13.6077i	−0.752508	−	1.30338i	−0.946604	−	0.322400i	$-0.895510\pi$
$109$	−7.85642	−	13.6077i	−0.752508	−	1.30338i	0.194095	−	0.980983i	$-0.437823\pi$
$110$	−2.18754	−	3.78894i	−0.208574	−	0.361261i
$111$		0			0
$112$	11.9269	+	5.70166i	1.12698	+	0.538756i
$113$	−2.52708	+	4.37702i	−0.237727	+	0.411756i	−0.960062	−	0.279788i	$-0.909736\pi$
$113$	−2.52708	+	4.37702i	−0.237727	+	0.411756i	0.722335	+	0.691544i	$0.243069\pi$
$114$		0			0
$115$	−4.26584	+	7.38864i	−0.397791	+	0.688995i
$116$	3.77852	+	6.54458i	0.350826	+	0.607649i
$117$		0			0
$118$	−15.3347			−1.41167
$119$	7.20760	+	3.44561i	0.660719	+	0.315858i
$120$		0			0
$121$	4.96111	+	8.59289i	0.451010	+	0.781172i
$122$	2.23718	+	3.87491i	0.202545	+	0.350818i
$123$		0			0
$124$	−3.27640	−	5.67490i	−0.294230	−	0.509621i
$125$	−9.73529			−0.870751
$126$		0			0
$127$	1.84246	+	3.19124i	0.163492	+	0.283177i	0.936119	−	0.351684i	$-0.114391\pi$
$127$	1.84246	+	3.19124i	0.163492	+	0.283177i	−0.772627	+	0.634861i	$0.781058\pi$
$128$	12.4905			1.10401
$129$		0			0
$130$	2.34198	−	15.0132i	0.205405	−	1.31674i
$131$	0.924144	−	1.60066i	0.0807428	−	0.139851i	−0.822826	−	0.568293i	$-0.807604\pi$
$131$	0.924144	−	1.60066i	0.0807428	−	0.139851i	0.903569	+	0.428442i	$0.140937\pi$
$132$		0			0
$133$	0.655512	+	8.42351i	0.0568401	+	0.730411i
$134$	9.62127	−	16.6645i	0.831151	−	1.43960i
$135$		0			0
$136$	5.48251			0.470121
$137$	−2.81519			−0.240518			−0.120259	−	0.992743i	$-0.538372\pi$
$137$	−2.81519			−0.240518			−0.120259	+	0.992743i	$0.538372\pi$
$138$		0			0
$139$	1.87848	−	3.25363i	0.159331	−	0.275969i	−0.775297	−	0.631597i	$-0.782400\pi$
$139$	1.87848	−	3.25363i	0.159331	−	0.275969i	0.934628	+	0.355628i	$0.115733\pi$
$140$	5.04641	−	3.46179i	0.426499	−	0.292574i
$141$		0			0
$142$	2.79571	−	4.84232i	0.234611	−	0.406358i
$143$	0.576934	−	3.69842i	0.0482457	−	0.309277i
$144$		0			0
$145$	−19.7278			−1.63830
$146$	12.8750	+	22.3001i	1.06554	+	1.84557i
$147$		0			0
$148$	2.66070			0.218708
$149$	3.36841	+	5.83426i	0.275951	+	0.477961i	0.970375	−	0.241605i	$-0.0776739\pi$
$149$	3.36841	+	5.83426i	0.275951	+	0.477961i	−0.694424	+	0.719567i	$0.744341\pi$
$150$		0			0
$151$	−2.70020	−	4.67689i	−0.219739	−	0.380600i	0.734989	−	0.678079i	$-0.237187\pi$
$151$	−2.70020	−	4.67689i	−0.219739	−	0.380600i	−0.954728	+	0.297479i	$0.903854\pi$
$152$	2.89914	+	5.02146i	0.235151	+	0.407294i
$153$		0			0
$154$	3.88453	−	2.66475i	0.313025	−	0.214732i
$155$	17.1062			1.37401
$156$		0			0
$157$	−5.82721	−	10.0930i	−0.465062	−	0.805512i	0.534142	−	0.845395i	$-0.320635\pi$
$157$	−5.82721	−	10.0930i	−0.465062	−	0.805512i	−0.999204	+	0.0398832i	$0.987301\pi$
$158$	−0.363273	+	0.629207i	−0.0289004	+	0.0500570i
$159$		0			0
$160$	6.06673	−	10.5079i	0.479617	−	0.830722i
$161$	−8.28776	−	3.96198i	−0.653167	−	0.312248i
$162$		0			0
$163$	−12.1258	−	21.0025i	−0.949766	−	1.64504i	−0.745915	−	0.666041i	$-0.767987\pi$
$163$	−12.1258	−	21.0025i	−0.949766	−	1.64504i	−0.203851	−	0.979002i	$-0.565346\pi$
$164$	2.39189	+	4.14288i	0.186775	+	0.323504i
$165$		0			0
$166$	2.29964			0.178487
$167$	−8.23216	−	14.2585i	−0.637024	−	1.10336i	−0.986083	−	0.166257i	$-0.946832\pi$
$167$	−8.23216	−	14.2585i	−0.637024	−	1.10336i	0.349059	−	0.937101i	$-0.386501\pi$
$168$		0			0
$169$	9.62021	−	8.74366i	0.740016	−	0.672589i
$170$	6.36248	−	11.0201i	0.487980	−	0.845207i
$171$		0			0
$172$	−3.02944	+	5.24714i	−0.230993	+	0.400091i
$173$	−10.0203	−	17.3556i	−0.761827	−	1.31952i	−0.941908	−	0.335871i	$-0.890969\pi$
$173$	−10.0203	−	17.3556i	−0.761827	−	1.31952i	0.180081	−	0.983652i	$-0.442364\pi$
$174$		0			0
$175$	0.213104	+	2.73844i	0.0161091	+	0.207007i
$176$	2.59362	−	4.49228i	0.195501	−	0.338618i
$177$		0			0
$178$	−9.09806			−0.681929
$179$	−5.04757	+	8.74265i	−0.377273	+	0.653456i	−0.990664	−	0.136323i	$-0.956472\pi$
$179$	−5.04757	+	8.74265i	−0.377273	+	0.653456i	0.613391	+	0.789779i	$0.289805\pi$
$180$		0			0
$181$	19.8959			1.47885			0.739426	−	0.673238i	$-0.235097\pi$
$181$	19.8959			1.47885			0.739426	+	0.673238i	$0.235097\pi$
$182$	16.3117	+	1.25988i	1.20910	+	0.0933885i
$183$		0			0
$184$	−6.30414			−0.464748
$185$	−3.47290	+	6.01524i	−0.255333	+	0.442249i
$186$		0			0
$187$	1.56737	−	2.71476i	0.114617	−	0.198523i
$188$	−4.60246	+	7.97170i	−0.335669	+	0.581396i
$189$		0			0
$190$	13.4579			0.976337
$191$	7.63868	+	13.2306i	0.552715	+	0.957331i	0.998077	+	0.0619803i	$0.0197416\pi$
$191$	7.63868	+	13.2306i	0.552715	+	0.957331i	−0.445362	+	0.895350i	$0.646925\pi$
$192$		0			0
$193$	−12.8340	+	22.2292i	−0.923814	+	1.60009i	−0.130355	+	0.991467i	$0.541612\pi$
$193$	−12.8340	+	22.2292i	−0.923814	+	1.60009i	−0.793458	+	0.608625i	$0.791722\pi$
$194$	5.01483	−	8.68594i	0.360044	−	0.623614i
$195$		0			0
$196$	4.13764	+	5.12793i	0.295546	+	0.366281i
$197$	−7.84255	−	13.5837i	−0.558759	−	0.967798i	−0.997600	−	0.0692340i	$-0.977944\pi$
$197$	−7.84255	−	13.5837i	−0.558759	−	0.967798i	0.438842	−	0.898564i	$-0.355389\pi$
$198$		0			0
$199$	−5.75089			−0.407670			−0.203835	−	0.979005i	$-0.565341\pi$
$199$	−5.75089			−0.407670			−0.203835	+	0.979005i	$0.565341\pi$
$200$	0.942496	+	1.63245i	0.0666445	+	0.115432i
$201$		0			0
$202$	−15.8886	+	27.5198i	−1.11792	+	1.93629i
$203$	−1.64798	−	21.1770i	−0.115665	−	1.48633i
$204$		0			0
$205$	−12.4882			−0.872210
$206$	−1.74196	+	3.01717i	−0.121368	+	0.210216i
$207$		0			0
$208$	16.8037	−	6.49532i	1.16512	−	0.450369i
$209$	3.31528			0.229323
$210$		0			0
$211$	10.3771	+	17.9736i	0.714387	+	1.23735i	0.963196	+	0.268802i	$0.0866276\pi$
$211$	10.3771	+	17.9736i	0.714387	+	1.23735i	−0.248809	+	0.968553i	$0.580039\pi$
$212$	−5.56255	−	9.63462i	−0.382038	−	0.661708i
$213$		0			0
$214$	4.17893			0.285666
$215$	−7.90841	−	13.6978i	−0.539349	−	0.934180i
$216$		0			0
$217$	1.42898	+	18.3628i	0.0970058	+	1.24655i
$218$	−13.4739	−	23.3375i	−0.912569	−	1.58062i
$219$		0			0
$220$	−1.20064	−	2.07957i	−0.0809472	−	0.140205i
$221$	10.1547	−	3.92523i	0.683081	−	0.264039i
$222$		0			0
$223$	5.68668	+	9.84963i	0.380809	+	0.659580i	0.991178	−	0.132537i	$-0.0423123\pi$
$223$	5.68668	+	9.84963i	0.380809	+	0.659580i	−0.610369	+	0.792117i	$0.708979\pi$
$224$	11.7866	+	5.63460i	0.787524	+	0.376478i
$225$		0			0
$226$	−4.33399	+	7.50668i	−0.288292	+	0.499337i
$227$	5.42928			0.360354			0.180177	−	0.983634i	$-0.442333\pi$
$227$	5.42928			0.360354			0.180177	+	0.983634i	$0.442333\pi$
$228$		0			0
$229$	−8.67170	+	15.0198i	−0.573042	+	0.992538i	0.423209	+	0.906032i	$0.360903\pi$
$229$	−8.67170	+	15.0198i	−0.573042	+	0.992538i	−0.996251	+	0.0865059i	$0.972430\pi$
$230$	−7.31599	+	12.6717i	−0.482402	+	0.835545i
$231$		0			0
$232$	−7.28853	−	12.6241i	−0.478516	−	0.828813i
$233$	−10.0164	+	17.3490i	−0.656199	+	1.13657i	0.325393	+	0.945579i	$0.394504\pi$
$233$	−10.0164	+	17.3490i	−0.656199	+	1.13657i	−0.981592	+	0.190991i	$0.938830\pi$
$234$		0			0
$235$	−12.0148	−	20.8103i	−0.783761	−	1.35751i
$236$	−8.41650			−0.547867
$237$		0			0
$238$	12.3612	+	5.90929i	0.801256	+	0.383042i
$239$	8.30497			0.537204			0.268602	−	0.963251i	$-0.413438\pi$
$239$	8.30497			0.537204			0.268602	+	0.963251i	$0.413438\pi$
$240$		0			0
$241$	20.5906			1.32636			0.663178	−	0.748461i	$-0.269207\pi$
$241$	20.5906			1.32636			0.663178	+	0.748461i	$0.269207\pi$
$242$	8.50840	+	14.7370i	0.546941	+	0.947329i
$243$		0			0
$244$	1.22788	+	2.12676i	0.0786073	+	0.136152i
$245$	−16.9938	+	2.66101i	−1.08569	+	0.170006i
$246$		0			0
$247$	8.96494	+	7.22512i	0.570426	+	0.459723i
$248$	6.31999	+	10.9465i	0.401320	+	0.695106i
$249$		0			0
$250$	−16.6962			−1.05596
$251$	−5.22288	+	9.04629i	−0.329665	+	0.570997i	−0.982445	−	0.186550i	$-0.940269\pi$
$251$	−5.22288	+	9.04629i	−0.329665	+	0.570997i	0.652780	+	0.757547i	$0.273603\pi$
$252$		0			0
$253$	−1.80226	+	3.12160i	−0.113307	+	0.196253i
$254$	3.15986	+	5.47304i	0.198267	+	0.343409i
$255$		0			0
$256$	18.3720			1.14825
$257$	−7.23377			−0.451230			−0.225615	−	0.974216i	$-0.572439\pi$
$257$	−7.23377			−0.451230			−0.225615	+	0.974216i	$0.572439\pi$
$258$		0			0
$259$	−6.74723	−	3.22553i	−0.419252	−	0.200425i
$260$	1.28540	−	8.24003i	0.0797173	−	0.511025i
$261$		0			0
$262$	1.58493	−	2.74517i	0.0979170	−	0.169597i
$263$	−0.853104	+	1.47762i	−0.0526047	+	0.0911139i	−0.891129	−	0.453751i	$-0.850086\pi$
$263$	−0.853104	+	1.47762i	−0.0526047	+	0.0911139i	0.838524	+	0.544865i	$0.183419\pi$
$264$		0			0
$265$	29.0423			1.78405
$266$	1.12422	+	14.4465i	0.0689301	+	0.885771i
$267$		0			0
$268$	5.28067	−	9.14638i	0.322568	−	0.558704i
$269$	−21.9883			−1.34065			−0.670324	−	0.742068i	$-0.733845\pi$
$269$	−21.9883			−1.34065			−0.670324	+	0.742068i	$0.733845\pi$
$270$		0			0
$271$	−23.6502			−1.43665			−0.718324	−	0.695709i	$-0.755090\pi$
$271$	−23.6502			−1.43665			−0.718324	+	0.695709i	$0.755090\pi$
$272$	15.0871			0.914790
$273$		0			0
$274$	−4.82810			−0.291676
$275$	1.07778			0.0649926
$276$		0			0
$277$	−29.9287			−1.79824			−0.899119	−	0.437703i	$-0.855792\pi$
$277$	−29.9287			−1.79824			−0.899119	+	0.437703i	$0.855792\pi$
$278$	3.22164	−	5.58004i	0.193221	−	0.334669i
$279$		0			0
$280$	−9.73422	+	6.67758i	−0.581731	+	0.399062i
$281$	27.8636			1.66220			0.831102	−	0.556120i	$-0.187711\pi$
$281$	27.8636			1.66220			0.831102	+	0.556120i	$0.187711\pi$
$282$		0			0
$283$	9.70377	−	16.8074i	0.576829	−	0.999097i	−0.419011	−	0.907981i	$-0.637623\pi$
$283$	9.70377	−	16.8074i	0.576829	−	0.999097i	0.995840	−	0.0911161i	$-0.0290434\pi$
$284$	1.53444	−	2.65772i	0.0910520	−	0.157707i
$285$		0			0
$286$	0.989454	−	6.34286i	0.0585077	−	0.375061i
$287$	−1.04321	−	13.4055i	−0.0615787	−	0.791303i
$288$		0			0
$289$	−7.88262			−0.463683
$290$	−33.8335			−1.98677
$291$		0			0
$292$	7.06646	+	12.2395i	0.413533	+	0.716261i
$293$	2.20711	−	3.82282i	0.128940	−	0.223331i	−0.794326	−	0.607492i	$-0.792176\pi$
$293$	2.20711	−	3.82282i	0.128940	−	0.223331i	0.923266	+	0.384160i	$0.125509\pi$
$294$		0			0
$295$	10.9857	−	19.0278i	0.639613	−	1.10784i
$296$	−5.13233			−0.298311
$297$		0			0
$298$	5.77690	+	10.0059i	0.334647	+	0.579625i
$299$	−11.6766	+	4.51348i	−0.675273	+	0.261021i
$300$		0			0
$301$	14.0434	−	9.63361i	0.809446	−	0.555272i
$302$	−4.63090	−	8.02096i	−0.266479	−	0.461554i
$303$		0			0
$304$	7.97803	+	13.8184i	0.457571	+	0.792537i
$305$	−6.41083			−0.367083
$306$		0			0
$307$	−9.06995			−0.517649			−0.258825	−	0.965924i	$-0.583335\pi$
$307$	−9.06995			−0.517649			−0.258825	+	0.965924i	$0.583335\pi$
$308$	2.13204	−	1.46256i	0.121484	−	0.0833370i
$309$		0			0
$310$	29.3375			1.66626
$311$	11.8691	+	20.5579i	0.673037	+	1.16573i	0.977039	+	0.213062i	$0.0683437\pi$
$311$	11.8691	+	20.5579i	0.673037	+	1.16573i	−0.304002	+	0.952671i	$0.598323\pi$
$312$		0			0
$313$	−6.48059	+	11.2247i	−0.366304	+	0.634458i	−0.988985	−	0.148019i	$-0.952710\pi$
$313$	−6.48059	+	11.2247i	−0.366304	+	0.634458i	0.622680	+	0.782476i	$0.286044\pi$
$314$	−9.99379	−	17.3098i	−0.563982	−	0.976846i
$315$		0			0
$316$	−0.199384	+	0.345342i	−0.0112162	+	0.0194270i
$317$	−15.7012	+	27.1953i	−0.881867	+	1.52744i	−0.0326048	+	0.999468i	$0.510380\pi$
$317$	−15.7012	+	27.1953i	−0.881867	+	1.52744i	−0.849263	+	0.527971i	$0.822953\pi$
$318$		0			0
$319$	−8.33472			−0.466655
$320$	−1.87330	+	3.24465i	−0.104721	+	0.181381i
$321$		0			0
$322$	−14.2137	−	6.79488i	−0.792097	−	0.378664i
$323$	4.82126	+	8.35066i	0.268262	+	0.464643i
$324$		0			0
$325$	2.91446	+	2.34885i	0.161665	+	0.130291i
$326$	−20.7960	−	36.0197i	−1.15178	−	1.99495i
$327$		0			0
$328$	−4.61382	−	7.99136i	−0.254755	−	0.441249i
$329$	21.3353	−	14.6358i	1.17625	−	0.806899i
$330$		0			0
$331$	5.76165	+	9.97948i	0.316689	+	0.548522i	0.979795	−	0.200004i	$-0.0640955\pi$
$331$	5.76165	+	9.97948i	0.316689	+	0.548522i	−0.663106	+	0.748526i	$0.730762\pi$
$332$	1.26216			0.0692702
$333$		0			0
$334$	−14.1183	−	24.4537i	−0.772520	−	1.33804i
$335$	13.7853	+	23.8768i	0.753170	+	1.30453i
$336$		0			0
$337$	−17.7823			−0.968665			−0.484332	−	0.874884i	$-0.660937\pi$
$337$	−17.7823			−0.968665			−0.484332	+	0.874884i	$0.660937\pi$
$338$	16.4989	−	14.9956i	0.897419	−	0.815651i
$339$		0			0
$340$	3.49207	−	6.04844i	0.189384	−	0.328023i
$341$	7.22715			0.391372
$342$		0			0
$343$	−4.27608	−	18.0199i	−0.230886	−	0.972981i
$344$	5.84361	−	10.1214i	0.315066	−	0.545711i
$345$		0			0
$346$	−17.1850	−	29.7652i	−0.923869	−	1.60019i
$347$	12.3200			0.661373			0.330687	−	0.943741i	$-0.392720\pi$
$347$	12.3200			0.661373			0.330687	+	0.943741i	$0.392720\pi$
$348$		0			0
$349$	−4.29722	−	7.44301i	−0.230025	−	0.398415i	0.727790	−	0.685800i	$-0.240548\pi$
$349$	−4.29722	−	7.44301i	−0.230025	−	0.398415i	−0.957815	+	0.287385i	$0.907214\pi$
$350$	0.365477	+	4.69648i	0.0195356	+	0.251037i
$351$		0			0
$352$	2.56311	−	4.43944i	0.136614	−	0.236623i
$353$	14.5824	−	25.2575i	0.776144	−	1.34432i	−0.158005	−	0.987438i	$-0.550506\pi$
$353$	14.5824	−	25.2575i	0.776144	−	1.34432i	0.934149	−	0.356882i	$-0.116160\pi$
$354$		0			0
$355$	4.00567	+	6.93803i	0.212599	+	0.368232i
$356$	−4.99350			−0.264655
$357$		0			0
$358$	−8.65668	+	14.9938i	−0.457520	+	0.792448i
$359$	1.79924	−	3.11637i	0.0949602	−	0.164476i	−0.814632	−	0.579979i	$-0.803061\pi$
$359$	1.79924	−	3.11637i	0.0949602	−	0.164476i	0.909592	+	0.415503i	$0.136394\pi$
$360$		0			0
$361$	4.40106	−	7.62286i	0.231635	−	0.401203i
$362$	34.1219			1.79341
$363$		0			0
$364$	8.95271	+	0.691489i	0.469250	+	0.0362439i
$365$	−36.8943			−1.93113
$366$		0			0
$367$	−15.5328	+	26.9035i	−0.810803	+	1.40435i	0.101500	+	0.994836i	$0.467636\pi$
$367$	−15.5328	+	26.9035i	−0.810803	+	1.40435i	−0.912303	+	0.409516i	$0.865697\pi$
$368$	−17.3481			−0.904333
$369$		0			0
$370$	−5.95610	+	10.3163i	−0.309643	+	0.536317i
$371$	2.42607	+	31.1757i	0.125956	+	1.61856i
$372$		0			0
$373$	11.7312	+	20.3191i	0.607421	+	1.05208i	0.991664	+	0.128852i	$0.0411292\pi$
$373$	11.7312	+	20.3191i	0.607421	+	1.05208i	−0.384243	+	0.923232i	$0.625537\pi$
$374$	2.68806	−	4.65586i	0.138996	−	0.240749i
$375$		0			0
$376$	8.87788	−	15.3769i	0.457842	−	0.793005i
$377$	−22.5381	−	18.1642i	−1.16077	−	0.935502i
$378$		0			0
$379$	4.67032	+	8.08923i	0.239898	+	0.415516i	0.960685	−	0.277641i	$-0.0895526\pi$
$379$	4.67032	+	8.08923i	0.239898	+	0.415516i	−0.720787	+	0.693157i	$0.756219\pi$
$380$	7.38640			0.378914
$381$		0			0
$382$	13.1005	+	22.6907i	0.670279	+	1.16096i
$383$	5.84067	+	10.1163i	0.298444	+	0.516921i	0.975780	−	0.218753i	$-0.0701989\pi$
$383$	5.84067	+	10.1163i	0.298444	+	0.516921i	−0.677336	+	0.735674i	$0.736866\pi$
$384$		0			0
$385$	0.523653	+	6.72908i	0.0266878	+	0.342946i
$386$	−22.0106	+	38.1235i	−1.12031	+	1.94044i
$387$		0			0
$388$	2.75241	−	4.76731i	0.139732	−	0.242023i
$389$	−9.34341	−	16.1833i	−0.473730	−	0.820524i	0.525818	−	0.850597i	$-0.323759\pi$
$389$	−9.34341	−	16.1833i	−0.473730	−	0.820524i	−0.999548	+	0.0300730i	$0.990426\pi$
$390$		0			0
$391$	−10.4838			−0.530186
$392$	−7.98127	−	9.89147i	−0.403115	−	0.499595i
$393$		0			0
$394$	−13.4501	−	23.2963i	−0.677608	−	1.17365i
$395$	−0.520495	−	0.901523i	−0.0261889	−	0.0453605i
$396$		0			0
$397$	−4.72206	−	8.17885i	−0.236993	−	0.410485i	0.722857	−	0.690998i	$-0.242829\pi$
$397$	−4.72206	−	8.17885i	−0.236993	−	0.410485i	−0.959850	+	0.280513i	$0.909495\pi$
$398$	−9.86289			−0.494382
$399$		0			0
$400$	2.59362	+	4.49228i	0.129681	+	0.224614i
$401$	−10.3724			−0.517975			−0.258987	−	0.965881i	$-0.583389\pi$
$401$	−10.3724			−0.517975			−0.258987	+	0.965881i	$0.583389\pi$
$402$		0			0
$403$	19.5431	+	15.7504i	0.973513	+	0.784584i
$404$	−8.72050	+	15.1044i	−0.433861	+	0.751470i
$405$		0			0
$406$	−2.82632	−	36.3189i	−0.140268	−	1.80248i
$407$	−1.46725	+	2.54136i	−0.0727291	+	0.125970i
$408$		0			0
$409$	22.8870			1.13169			0.565844	−	0.824512i	$-0.308550\pi$
$409$	22.8870			1.13169			0.565844	+	0.824512i	$0.308550\pi$
$410$	−21.4174			−1.05773
$411$		0			0
$412$	−0.956082	+	1.65598i	−0.0471028	+	0.0815844i
$413$	21.3433	+	10.2032i	1.05023	+	0.502067i
$414$		0			0
$415$	−1.64745	+	2.85347i	−0.0808702	+	0.140071i
$416$	16.6060	−	6.41893i	0.814178	−	0.314714i
$417$		0			0
$418$	5.68577			0.278100
$419$	−4.33086	−	7.50127i	−0.211576	−	0.366461i	0.740632	−	0.671911i	$-0.234526\pi$
$419$	−4.33086	−	7.50127i	−0.211576	−	0.366461i	−0.952208	+	0.305450i	$0.901193\pi$
$420$		0			0
$421$	−1.15030			−0.0560620			−0.0280310	−	0.999607i	$-0.508924\pi$
$421$	−1.15030			−0.0560620			−0.0280310	+	0.999607i	$0.508924\pi$
$422$	17.7969	+	30.8251i	0.866339	+	1.50054i
$423$		0			0
$424$	10.7298	+	18.5846i	0.521087	+	0.902549i
$425$	1.56737	+	2.71476i	0.0760284	+	0.131685i
$426$		0			0
$427$	−0.535535	−	6.88177i	−0.0259163	−	0.333032i
$428$	2.29362			0.110866
$429$		0			0
$430$	−13.5631	−	23.4919i	−0.654070	−	1.13288i
$431$	4.38024	−	7.58680i	0.210989	−	0.365443i	−0.741036	−	0.671466i	$-0.765665\pi$
$431$	4.38024	−	7.58680i	0.210989	−	0.365443i	0.952024	+	0.306023i	$0.0989983\pi$
$432$		0			0
$433$	0.463102	−	0.802117i	0.0222553	−	0.0385473i	−0.854683	−	0.519150i	$-0.826249\pi$
$433$	0.463102	−	0.802117i	0.0222553	−	0.0385473i	0.876939	+	0.480603i	$0.159582\pi$
$434$	2.45074	+	31.4926i	0.117639	+	1.51170i
$435$		0			0
$436$	−7.39520	−	12.8089i	−0.354166	−	0.613434i
$437$	−5.54379	−	9.60213i	−0.265195	−	0.459332i
$438$		0			0
$439$	12.4084			0.592219			0.296109	−	0.955154i	$-0.404311\pi$
$439$	12.4084			0.592219			0.296109	+	0.955154i	$0.404311\pi$
$440$	2.31597	+	4.01137i	0.110409	+	0.191235i
$441$		0			0
$442$	17.4156	−	6.73185i	0.828374	−	0.320201i
$443$	1.61468	−	2.79670i	0.0767156	−	0.132875i	−0.825115	−	0.564964i	$-0.808890\pi$
$443$	1.61468	−	2.79670i	0.0767156	−	0.132875i	0.901831	+	0.432089i	$0.142223\pi$
$444$		0			0
$445$	6.51782	−	11.2892i	0.308974	−	0.535159i
$446$	9.75278	+	16.8923i	0.461808	+	0.799874i
$447$		0			0
$448$	−3.63949	−	1.73986i	−0.171950	−	0.0822009i
$449$	9.94344	−	17.2225i	0.469260	−	0.812782i	−0.530123	−	0.847921i	$-0.677854\pi$
$449$	9.94344	−	17.2225i	0.469260	−	0.812782i	0.999382	+	0.0351392i	$0.0111875\pi$
$450$		0			0
$451$	−5.27608			−0.248441
$452$	−2.37872	+	4.12007i	−0.111886	+	0.193792i
$453$		0			0
$454$	9.31132			0.437002
$455$	−13.2489	+	19.3375i	−0.621119	+	0.906556i
$456$		0			0
$457$	−0.0789744			−0.00369427			−0.00184713	−	0.999998i	$-0.500588\pi$
$457$	−0.0789744			−0.00369427			−0.00184713	+	0.999998i	$0.500588\pi$
$458$	−14.8721	+	25.7593i	−0.694929	+	1.20365i
$459$		0			0
$460$	−4.01541	+	6.95489i	−0.187219	+	0.324273i
$461$	−2.45979	+	4.26049i	−0.114564	+	0.198431i	−0.917605	−	0.397493i	$-0.869880\pi$
$461$	−2.45979	+	4.26049i	−0.114564	+	0.198431i	0.803041	+	0.595923i	$0.203214\pi$
$462$		0			0
$463$	1.24837			0.0580166			0.0290083	−	0.999579i	$-0.490765\pi$
$463$	1.24837			0.0580166			0.0290083	+	0.999579i	$0.490765\pi$
$464$	−20.0570	−	34.7398i	−0.931124	−	1.61275i
$465$		0			0
$466$	−17.1784	+	29.7539i	−0.795774	+	1.37832i
$467$	14.3411	−	24.8395i	0.663628	−	1.14944i	−0.316028	−	0.948750i	$-0.602349\pi$
$467$	14.3411	−	24.8395i	0.663628	−	1.14944i	0.979655	−	0.200687i	$-0.0643173\pi$
$468$		0			0
$469$	−24.4792	+	16.7925i	−1.13035	+	0.775406i
$470$	−20.6057	−	35.6901i	−0.950468	−	1.64626i
$471$		0			0
$472$	16.2349			0.747273
$473$	−3.34120	−	5.78712i	−0.153628	−	0.266092i
$474$		0			0
$475$	−1.65764	+	2.87112i	−0.0760577	+	0.131736i
$476$	6.78447	+	3.24333i	0.310966	+	0.148658i
$477$		0			0
$478$	14.2432			0.651468
$479$	−3.48936	+	6.04374i	−0.159433	+	0.276146i	−0.934664	−	0.355532i	$-0.884300\pi$
$479$	−3.48936	+	6.04374i	−0.159433	+	0.276146i	0.775232	+	0.631677i	$0.217633\pi$
$480$		0			0
$481$	−9.50612	+	3.67451i	−0.433442	+	0.167543i
$482$	35.3133			1.60848
$483$		0			0
$484$	4.66987	+	8.08844i	0.212267	+	0.367657i
$485$	7.18521	+	12.4451i	0.326263	+	0.565105i
$486$		0			0
$487$	−1.92831			−0.0873803			−0.0436901	−	0.999045i	$-0.513911\pi$
$487$	−1.92831			−0.0873803			−0.0436901	+	0.999045i	$0.513911\pi$
$488$	−2.36852	−	4.10239i	−0.107218	−	0.185707i
$489$		0			0
$490$	−29.1447	+	4.56368i	−1.31662	+	0.206166i
$491$	−14.6968	−	25.4556i	−0.663256	−	1.14879i	−0.979755	−	0.200200i	$-0.935841\pi$
$491$	−14.6968	−	25.4556i	−0.663256	−	1.14879i	0.316499	−	0.948593i	$-0.397493\pi$
$492$		0			0
$493$	−12.1208	−	20.9938i	−0.545893	−	0.945514i
$494$	15.3751	+	12.3912i	0.691756	+	0.557508i
$495$		0			0
$496$	17.3917	+	30.1233i	0.780911	+	1.35258i
$497$	−7.11308	+	4.87950i	−0.319065	+	0.218876i
$498$		0			0
$499$	−9.92902	+	17.1976i	−0.444484	+	0.769869i	−0.998016	−	0.0629592i	$-0.979946\pi$
$499$	−9.92902	+	17.1976i	−0.444484	+	0.769869i	0.553532	+	0.832828i	$0.313280\pi$
$500$	−9.16378			−0.409817
$501$		0			0
$502$	−8.95734	+	15.5146i	−0.399786	+	0.692449i
$503$	−13.3790	+	23.1731i	−0.596540	+	1.03324i	0.396787	+	0.917911i	$0.370125\pi$
$503$	−13.3790	+	23.1731i	−0.596540	+	1.03324i	−0.993328	+	0.115327i	$0.963208\pi$
$504$		0			0
$505$	−22.7650	−	39.4302i	−1.01303	−	1.75462i
$506$	−3.09091	+	5.35361i	−0.137408	+	0.237997i
$507$		0			0
$508$	1.73430	+	3.00389i	0.0769471	+	0.133276i
$509$	−5.92930			−0.262811			−0.131406	−	0.991329i	$-0.541949\pi$
$509$	−5.92930			−0.262811			−0.131406	+	0.991329i	$0.541949\pi$
$510$		0			0
$511$	−3.08200	−	39.6045i	−0.136339	−	1.75200i
$512$	6.52743			0.288474
$513$		0			0
$514$	−12.4061			−0.547208
$515$	−2.49587	−	4.32297i	−0.109981	−	0.190493i
$516$		0			0
$517$	−5.07610	−	8.79206i	−0.223247	−	0.386674i
$518$	−11.5716	−	5.53185i	−0.508428	−	0.243055i
$519$		0			0
$520$	−2.47947	+	15.8945i	−0.108732	+	0.697021i
$521$	16.7414	+	28.9969i	0.733453	+	1.27038i	0.955399	+	0.295319i	$0.0954259\pi$
$521$	16.7414	+	28.9969i	0.733453	+	1.27038i	−0.221946	+	0.975059i	$0.571241\pi$
$522$		0			0
$523$	41.4546			1.81268			0.906341	−	0.422547i	$-0.138864\pi$
$523$	41.4546			1.81268			0.906341	+	0.422547i	$0.138864\pi$
$524$	0.869892	−	1.50670i	0.0380014	−	0.0658203i
$525$		0			0
$526$	−1.46309	+	2.53415i	−0.0637938	+	0.110494i
$527$	10.5101	+	18.2040i	0.457827	+	0.792980i
$528$		0			0
$529$	−10.9451			−0.475874
$530$	49.8081			2.16353
$531$		0			0
$532$	0.617030	+	7.92900i	0.0267516	+	0.343766i
$533$	−14.2672	−	11.4984i	−0.617980	−	0.498049i
$534$		0			0
$535$	−2.99377	+	5.18536i	−0.129432	+	0.224183i
$536$	−10.1861	+	17.6428i	−0.439972	+	0.762054i
$537$		0			0
$538$	−37.7103			−1.62581
$539$	−7.17965	+	1.12424i	−0.309249	+	0.0484244i
$540$		0			0
$541$	−14.7605	+	25.5660i	−0.634606	+	1.09917i	0.351993	+	0.936003i	$0.385504\pi$
$541$	−14.7605	+	25.5660i	−0.634606	+	1.09917i	−0.986599	+	0.163166i	$0.947829\pi$
$542$	−40.5606			−1.74223
$543$		0			0
$544$	14.9097			0.639246
$545$	38.6106			1.65390
$546$		0			0
$547$	34.6619			1.48203			0.741017	−	0.671486i	$-0.234344\pi$
$547$	34.6619			1.48203			0.741017	+	0.671486i	$0.234344\pi$
$548$	−2.64992			−0.113199
$549$		0			0
$550$	1.84842			0.0788167
$551$	12.8189	−	22.2030i	0.546104	−	0.945879i
$552$		0			0
$553$	0.924268	−	0.634039i	0.0393039	−	0.0269621i
$554$	−51.3283			−2.18073
$555$		0			0
$556$	1.76821	−	3.06262i	0.0749887	−	0.129884i
$557$	−7.52422	+	13.0323i	−0.318812	+	0.552198i	−0.980240	−	0.197810i	$-0.936617\pi$
$557$	−7.52422	+	13.0323i	−0.318812	+	0.552198i	0.661429	+	0.750008i	$0.269950\pi$
$558$		0			0
$559$	3.57707	−	22.9307i	0.151294	−	0.969866i
$560$	−26.7872	+	18.3758i	−1.13197	+	0.776518i
$561$		0			0
$562$	47.7867			2.01576
$563$	1.45745			0.0614242			0.0307121	−	0.999528i	$-0.490223\pi$
$563$	1.45745			0.0614242			0.0307121	+	0.999528i	$0.490223\pi$
$564$		0			0
$565$	−6.20970	−	10.7555i	−0.261244	−	0.452488i
$566$	16.6422	−	28.8251i	0.699522	−	1.21161i
$567$		0			0
$568$	−2.95984	+	5.12659i	−0.124192	+	0.215107i
$569$	−4.10651			−0.172154			−0.0860770	−	0.996288i	$-0.527433\pi$
$569$	−4.10651			−0.172154			−0.0860770	+	0.996288i	$0.527433\pi$
$570$		0			0
$571$	16.1753	+	28.0165i	0.676916	+	1.17245i	0.975905	+	0.218197i	$0.0700175\pi$
$571$	16.1753	+	28.0165i	0.676916	+	1.17245i	−0.298988	+	0.954257i	$0.596649\pi$
$572$	0.543065	−	3.48130i	0.0227067	−	0.145560i
$573$		0			0
$574$	−1.78913	−	22.9907i	−0.0746767	−	0.959615i
$575$	−1.80226	−	3.12160i	−0.0751593	−	0.130180i
$576$		0			0
$577$	3.24107	+	5.61369i	0.134927	+	0.233701i	0.925570	−	0.378577i	$-0.123587\pi$
$577$	3.24107	+	5.61369i	0.134927	+	0.233701i	−0.790642	+	0.612278i	$0.790253\pi$
$578$	−13.5188			−0.562310
$579$		0			0
$580$	−18.5696			−0.771063
$581$	−3.20070	−	1.53010i	−0.132788	−	0.0634794i
$582$		0			0
$583$	12.2700			0.508170
$584$	−13.6308	−	23.6092i	−0.564046	−	0.976956i
$585$		0			0
$586$	3.78523	−	6.55621i	0.156366	−	0.270835i
$587$	−8.72720	−	15.1159i	−0.360210	−	0.623902i	0.627785	−	0.778387i	$-0.283962\pi$
$587$	−8.72720	−	15.1159i	−0.360210	−	0.623902i	−0.987995	+	0.154485i	$0.950628\pi$
$588$		0			0
$589$	−11.1154	+	19.2525i	−0.458004	+	0.793286i
$590$	18.8407	−	32.6331i	0.775660	−	1.34348i
$591$		0			0
$592$	−14.1234			−0.580470
$593$	5.07543	−	8.79090i	0.208423	−	0.360999i	−0.742795	−	0.669519i	$-0.766500\pi$
$593$	5.07543	−	8.79090i	0.208423	−	0.360999i	0.951218	+	0.308520i	$0.0998337\pi$
$594$		0			0
$595$	−16.1879	+	11.1048i	−0.663641	+	0.455251i
$596$	3.17067	+	5.49176i	0.129876	+	0.224951i
$597$		0			0
$598$	−20.0255	+	7.74071i	−0.818905	+	0.316541i
$599$	5.29665	+	9.17406i	0.216415	+	0.374842i	0.953709	−	0.300730i	$-0.0972302\pi$
$599$	5.29665	+	9.17406i	0.216415	+	0.374842i	−0.737294	+	0.675572i	$0.763897\pi$
$600$		0			0
$601$	5.08203	+	8.80234i	0.207300	+	0.359055i	0.950863	−	0.309611i	$-0.100199\pi$
$601$	5.08203	+	8.80234i	0.207300	+	0.359055i	−0.743563	+	0.668666i	$0.766866\pi$
$602$	24.0846	−	16.5218i	0.981617	−	0.673380i
$603$		0			0
$604$	−2.54169	−	4.40233i	−0.103420	−	0.179128i
$605$	−24.3815			−0.991251
$606$		0			0
$607$	−16.2239	−	28.1006i	−0.658508	−	1.14057i	−0.981002	−	0.193998i	$-0.937854\pi$
$607$	−16.2239	−	28.1006i	−0.658508	−	1.14057i	0.322494	−	0.946572i	$-0.395479\pi$
$608$	7.88420	+	13.6558i	0.319746	+	0.553817i
$609$		0			0
$610$	−10.9947			−0.445163
$611$	5.43446	−	34.8374i	0.219855	−	1.40937i
$612$		0			0
$613$	4.91821	−	8.51859i	0.198645	−	0.344063i	−0.749445	−	0.662067i	$-0.769679\pi$
$613$	4.91821	−	8.51859i	0.198645	−	0.344063i	0.948089	+	0.318004i	$0.103013\pi$
$614$	−15.5551			−0.627755
$615$		0			0
$616$	−4.11258	+	2.82119i	−0.165700	+	0.113669i
$617$	−17.6661	+	30.5985i	−0.711208	+	1.23185i	0.253195	+	0.967415i	$0.418518\pi$
$617$	−17.6661	+	30.5985i	−0.711208	+	1.23185i	−0.964404	+	0.264434i	$0.914815\pi$
$618$		0			0
$619$	−17.5126	−	30.3327i	−0.703892	−	1.21918i	−0.967090	−	0.254434i	$-0.918111\pi$
$619$	−17.5126	−	30.3327i	−0.703892	−	1.21918i	0.263198	−	0.964742i	$-0.415223\pi$
$620$	16.1020			0.646672
$621$		0			0
$622$	20.3558	+	35.2573i	0.816193	+	1.41369i
$623$	12.6630	+	6.05356i	0.507331	+	0.242531i
$624$		0			0
$625$	14.5565	−	25.2126i	0.582261	−	1.00850i
$626$	−11.1143	+	19.2506i	−0.444218	+	0.769409i
$627$		0			0
$628$	−5.48512	−	9.50051i	−0.218880	−	0.379112i
$629$	−8.53503			−0.340314
$630$		0			0
$631$	−10.2980	+	17.8367i	−0.409959	+	0.710069i	−0.994885	−	0.101017i	$-0.967790\pi$
$631$	−10.2980	+	17.8367i	−0.409959	+	0.710069i	0.584926	+	0.811087i	$0.301124\pi$
$632$	0.384599	−	0.666145i	0.0152985	−	0.0264978i
$633$		0			0
$634$	−26.9279	+	46.6405i	−1.06944	+	1.85233i
$635$	−9.05484			−0.359330
$636$		0			0
$637$	−21.8648	−	12.6068i	−0.866314	−	0.499499i
$638$	−14.2942			−0.565913
$639$		0			0
$640$	−15.3462	+	26.5804i	−0.606612	+	1.05068i
$641$	35.0768			1.38545			0.692725	−	0.721202i	$-0.256410\pi$
$641$	35.0768			1.38545			0.692725	+	0.721202i	$0.256410\pi$
$642$		0			0
$643$	−12.4615	+	21.5840i	−0.491435	+	0.851190i	−0.999951	−	0.00986235i	$-0.996861\pi$
$643$	−12.4615	+	21.5840i	−0.491435	+	0.851190i	0.508517	+	0.861052i	$0.330194\pi$
$644$	−7.80122	−	3.72939i	−0.307411	−	0.146959i
$645$		0			0
$646$	8.26855	+	14.3215i	0.325322	+	0.563474i
$647$	−1.67759	+	2.90567i	−0.0659528	+	0.114234i	−0.897116	−	0.441795i	$-0.854342\pi$
$647$	−1.67759	+	2.90567i	−0.0659528	+	0.114234i	0.831163	+	0.556028i	$0.187675\pi$
$648$		0			0
$649$	4.64131	−	8.03899i	0.182188	−	0.315558i
$650$	4.99835	+	4.02832i	0.196052	+	0.158004i
$651$		0			0
$652$	−11.4140	−	19.7695i	−0.447005	−	0.774235i
$653$	−5.09251			−0.199285			−0.0996426	−	0.995023i	$-0.531770\pi$
$653$	−5.09251			−0.199285			−0.0996426	+	0.995023i	$0.531770\pi$
$654$		0			0
$655$	2.27087	+	3.93326i	0.0887302	+	0.153685i
$656$	−12.6966	−	21.9911i	−0.495718	−	0.858608i
$657$		0			0
$658$	36.5905	−	25.1007i	1.42645	−	0.978529i
$659$	16.9148	−	29.2973i	0.658907	−	1.14126i	−0.321992	−	0.946742i	$-0.604352\pi$
$659$	16.9148	−	29.2973i	0.658907	−	1.14126i	0.980899	−	0.194518i	$-0.0623143\pi$
$660$		0			0
$661$	−16.9507	+	29.3595i	−0.659306	+	1.14195i	0.321490	+	0.946913i	$0.395816\pi$
$661$	−16.9507	+	29.3595i	−0.659306	+	1.14195i	−0.980796	+	0.195038i	$0.937517\pi$
$662$	9.88135	+	17.1150i	0.384050	+	0.665194i
$663$		0			0
$664$	−2.43464			−0.0944823
$665$	−18.7311	−	8.95444i	−0.726360	−	0.347238i
$666$		0			0
$667$	13.9373	+	24.1400i	0.539653	+	0.934706i
$668$	−7.74889	−	13.4215i	−0.299813	−	0.519292i
$669$		0			0
$670$	23.6420	+	40.9492i	0.913372	+	1.58201i
$671$	−2.70849			−0.104560
$672$		0			0
$673$	−7.46805	−	12.9350i	−0.287872	−	0.498609i	0.685430	−	0.728139i	$-0.259614\pi$
$673$	−7.46805	−	12.9350i	−0.287872	−	0.498609i	−0.973302	+	0.229530i	$0.926281\pi$
$674$	−30.4970			−1.17470
$675$		0			0
$676$	9.05545	−	8.23036i	0.348287	−	0.316552i
$677$	−10.8470	+	18.7875i	−0.416883	+	0.722063i	−0.995624	−	0.0934485i	$-0.970211\pi$
$677$	−10.8470	+	18.7875i	−0.416883	+	0.722063i	0.578741	+	0.815512i	$0.303544\pi$
$678$		0			0
$679$	−12.7591	+	8.75265i	−0.489651	+	0.335896i
$680$	−6.73600	+	11.6671i	−0.258314	+	0.447412i
$681$		0			0
$682$	12.3947			0.474618
$683$	−23.2958			−0.891389			−0.445694	−	0.895185i	$-0.647043\pi$
$683$	−23.2958			−0.891389			−0.445694	+	0.895185i	$0.647043\pi$
$684$		0			0
$685$	3.45883	−	5.99087i	0.132155	−	0.228900i
$686$	−7.33356	−	30.9044i	−0.279996	−	1.17994i
$687$		0			0
$688$	16.0808	−	27.8527i	0.613074	−	1.06188i
$689$	33.1796	+	26.7404i	1.26404	+	1.01873i
$690$		0			0
$691$	31.3451			1.19242			0.596212	−	0.802827i	$-0.296672\pi$
$691$	31.3451			1.19242			0.596212	+	0.802827i	$0.296672\pi$
$692$	−9.43202	−	16.3367i	−0.358552	−	0.621030i
$693$		0			0
$694$	21.1291			0.802049
$695$	4.61594	+	7.99504i	0.175093	+	0.303269i
$696$		0			0
$697$	−7.67275	−	13.2896i	−0.290626	−	0.503379i
$698$	−7.36983	−	12.7649i	−0.278952	−	0.483159i
$699$		0			0
$700$	0.200593	+	2.57768i	0.00758171	+	0.0974271i
$701$	36.5409			1.38013			0.690066	−	0.723746i	$-0.257581\pi$
$701$	36.5409			1.38013			0.690066	+	0.723746i	$0.257581\pi$
$702$		0			0
$703$	−4.51331	−	7.81728i	−0.170223	−	0.294834i
$704$	−0.791443	+	1.37082i	−0.0298286	+	0.0516647i
$705$		0			0
$706$	25.0091	−	43.3171i	0.941232	−	1.63026i
$707$	40.4250	−	27.7312i	1.52034	−	1.04294i
$708$		0			0
$709$	−16.4689	−	28.5249i	−0.618502	−	1.07128i	−0.989759	−	0.142746i	$-0.954407\pi$
$709$	−16.4689	−	28.5249i	−0.618502	−	1.07128i	0.371258	−	0.928530i	$-0.378927\pi$
$710$	6.86981	+	11.8989i	0.257819	+	0.446556i
$711$		0			0
$712$	9.63217			0.360981
$713$	−12.0852	−	20.9322i	−0.452594	−	0.783916i
$714$		0			0
$715$	7.16160	+	5.77175i	0.267829	+	0.215851i
$716$	−4.75125	+	8.22941i	−0.177563	+	0.307547i
$717$		0			0
$718$	3.08573	−	5.34465i	0.115159	−	0.199460i
$719$	4.29318	+	7.43600i	0.160109	+	0.277316i	0.934907	−	0.354892i	$-0.115482\pi$
$719$	4.29318	+	7.43600i	0.160109	+	0.277316i	−0.774799	+	0.632208i	$0.782149\pi$
$720$		0			0
$721$	4.43204	−	3.04034i	0.165058	−	0.113228i
$722$	7.54790	−	13.0734i	0.280904	−	0.486540i
$723$		0			0
$724$	18.7279			0.696017
$725$	4.16736	−	7.21808i	0.154772	−	0.268073i
$726$		0			0
$727$	31.5760			1.17109			0.585545	−	0.810640i	$-0.300881\pi$
$727$	31.5760			1.17109			0.585545	+	0.810640i	$0.300881\pi$
$728$	−17.2693	−	1.33384i	−0.640041	−	0.0494355i
$729$		0			0
$730$	−63.2744			−2.34189
$731$	9.71789	−	16.8319i	0.359429	−	0.622549i
$732$		0			0
$733$	7.35414	−	12.7377i	0.271631	−	0.470479i	−0.697648	−	0.716440i	$-0.745770\pi$
$733$	7.35414	−	12.7377i	0.271631	−	0.470479i	0.969280	+	0.245961i	$0.0791035\pi$
$734$	−26.6390	+	46.1401i	−0.983263	+	1.70306i
$735$		0			0
$736$	−17.1441			−0.631939
$737$	5.82409	+	10.0876i	0.214533	+	0.371583i
$738$		0			0
$739$	7.08297	−	12.2681i	0.260551	−	0.451288i	−0.705837	−	0.708374i	$-0.749429\pi$
$739$	7.08297	−	12.2681i	0.260551	−	0.451288i	0.966389	+	0.257086i	$0.0827624\pi$
$740$	−3.26902	+	5.66211i	−0.120172	+	0.208143i
$741$		0			0
$742$	4.16077	+	53.4670i	0.152747	+	1.96283i
$743$	21.4265	+	37.1119i	0.786063	+	1.36150i	0.928362	+	0.371678i	$0.121217\pi$
$743$	21.4265	+	37.1119i	0.786063	+	1.36150i	−0.142298	+	0.989824i	$0.545449\pi$
$744$		0			0
$745$	−16.5542			−0.606498
$746$	20.1193	+	34.8477i	0.736621	+	1.27586i
$747$		0			0
$748$	1.47535	−	2.55539i	0.0539442	−	0.0934342i
$749$	−5.81636	−	2.78052i	−0.212525	−	0.101598i
$750$		0			0
$751$	−0.620656			−0.0226481			−0.0113240	−	0.999936i	$-0.503605\pi$
$751$	−0.620656			−0.0226481			−0.0113240	+	0.999936i	$0.503605\pi$
$752$	24.4307	−	42.3152i	0.890895	−	1.54308i
$753$		0			0
$754$	−38.6534	−	31.1519i	−1.40767	−	1.13449i
$755$	13.2702			0.482954
$756$		0			0
$757$	2.21558	+	3.83750i	0.0805266	+	0.139476i	0.903476	−	0.428638i	$-0.141006\pi$
$757$	2.21558	+	3.83750i	0.0805266	+	0.139476i	−0.822950	+	0.568114i	$0.807673\pi$
$758$	8.00970	+	13.8732i	0.290925	+	0.503897i
$759$		0			0
$760$	−14.2479			−0.516827
$761$	10.5022	+	18.1903i	0.380704	+	0.659399i	0.991163	−	0.132649i	$-0.0423482\pi$
$761$	10.5022	+	18.1903i	0.380704	+	0.659399i	−0.610459	+	0.792048i	$0.709015\pi$
$762$		0			0
$763$	3.22538	+	41.4469i	0.116766	+	1.50048i
$764$	7.19024	+	12.4539i	0.260134	+	0.450565i
$765$		0			0
$766$	10.0169	+	17.3497i	0.361924	+	0.626871i
$767$	30.0704	−	11.6235i	1.08578	−	0.419699i
$768$		0			0
$769$	−5.85570	−	10.1424i	−0.211162	−	0.365743i	0.740917	−	0.671597i	$-0.234391\pi$
$769$	−5.85570	−	10.1424i	−0.211162	−	0.365743i	−0.952078	+	0.305854i	$0.901058\pi$
$770$	0.898075	+	11.5405i	0.0323644	+	0.415891i
$771$		0			0
$772$	−12.0806	+	20.9242i	−0.434790	+	0.753079i
$773$	−8.04150			−0.289233			−0.144616	−	0.989488i	$-0.546195\pi$
$773$	−8.04150			−0.289233			−0.144616	+	0.989488i	$0.546195\pi$
$774$		0			0
$775$	−3.61357	+	6.25890i	−0.129803	+	0.224826i
$776$	−5.30923	+	9.19585i	−0.190590	+	0.330112i
$777$		0			0
$778$	−16.0241	−	27.7546i	−0.574493	−	0.995052i
$779$	8.11467	−	14.0550i	0.290738	−	0.503573i
$780$		0			0
$781$	1.69234	+	2.93122i	0.0605568	+	0.104887i
$782$	−17.9799			−0.642958
$783$		0			0
$784$	−21.9633	−	27.2199i	−0.784404	−	0.972140i
$785$	28.6380			1.02214
$786$		0			0
$787$	44.1774			1.57475			0.787377	−	0.616472i	$-0.211439\pi$
$787$	44.1774			1.57475			0.787377	+	0.616472i	$0.211439\pi$
$788$	−7.38215	−	12.7863i	−0.262978	−	0.455492i
$789$		0			0
$790$	−0.892659	−	1.54613i	−0.0317594	−	0.0550088i
$791$	11.0269	−	7.56433i	0.392071	−	0.268957i
$792$		0			0
$793$	−7.32410	−	5.90272i	−0.260086	−	0.209612i
$794$	−8.09843	−	14.0269i	−0.287403	−	0.497796i
$795$		0			0
$796$	−5.41328			−0.191869
$797$	9.83025	−	17.0265i	0.348205	−	0.603109i	−0.637725	−	0.770264i	$-0.720125\pi$
$797$	9.83025	−	17.0265i	0.348205	−	0.603109i	0.985931	+	0.167155i	$0.0534579\pi$
$798$		0			0
$799$	14.7639	−	25.5718i	0.522308	−	0.904664i
$800$	2.56311	+	4.43944i	0.0906197	+	0.156958i
$801$		0			0
$802$	−17.7889			−0.628149
$803$	−15.5873			−0.550065
$804$		0			0
$805$	18.6139	−	12.7690i	0.656055	−	0.450048i
$806$	33.5169	+	27.0123i	1.18058	+	0.951466i
$807$		0			0
$808$	16.8213	−	29.1354i	0.591773	−	1.02498i
$809$	−0.436336	+	0.755756i	−0.0153407	+	0.0265710i	−0.873594	−	0.486656i	$-0.838217\pi$
$809$	−0.436336	+	0.755756i	−0.0153407	+	0.0265710i	0.858253	+	0.513227i	$0.171550\pi$
$810$		0			0
$811$	35.1149			1.23305			0.616526	−	0.787335i	$-0.288540\pi$
$811$	35.1149			1.23305			0.616526	+	0.787335i	$0.288540\pi$
$812$	−1.55123	−	19.9338i	−0.0544376	−	0.699538i
$813$		0			0
$814$	−2.51637	+	4.35848i	−0.0881987	+	0.152765i
$815$	59.5927			2.08744
$816$		0			0
$817$	20.5552			0.719136
$818$	39.2517			1.37240
$819$		0			0
$820$	−11.7550			−0.410503
$821$	20.2047			0.705151			0.352575	−	0.935783i	$-0.385306\pi$
$821$	20.2047			0.705151			0.352575	+	0.935783i	$0.385306\pi$
$822$		0			0
$823$	27.9427			0.974020			0.487010	−	0.873396i	$-0.338087\pi$
$823$	27.9427			0.974020			0.487010	+	0.873396i	$0.338087\pi$
$824$	1.84422	−	3.19429i	0.0642466	−	0.111278i
$825$		0			0
$826$	36.6042	+	17.4987i	1.27362	+	0.608858i
$827$	44.6141			1.55138			0.775692	−	0.631112i	$-0.217401\pi$
$827$	44.6141			1.55138			0.775692	+	0.631112i	$0.217401\pi$
$828$		0			0
$829$	14.0525	−	24.3397i	0.488065	−	0.845353i	−0.511841	−	0.859080i	$-0.671036\pi$
$829$	14.0525	−	24.3397i	0.488065	−	0.845353i	0.999906	+	0.0137273i	$0.00436966\pi$
$830$	−2.82541	+	4.89376i	−0.0980715	+	0.169865i
$831$		0			0
$832$	−5.12764	+	1.98205i	−0.177769	+	0.0687152i
$833$	−13.2728	−	16.4495i	−0.459875	−	0.569940i
$834$		0			0
$835$	40.4572			1.40008
$836$	3.12066			0.107930
$837$		0			0
$838$	−7.42751	−	12.8648i	−0.256579	−	0.444408i
$839$	−18.8751	+	32.6926i	−0.651640	+	1.12867i	0.331085	+	0.943601i	$0.392585\pi$
$839$	−18.8751	+	32.6926i	−0.651640	+	1.12867i	−0.982725	+	0.185072i	$0.940748\pi$
$840$		0			0
$841$	−17.7271	+	30.7043i	−0.611280	+	1.05877i
$842$	−1.97278			−0.0679865
$843$		0			0
$844$	9.76788	+	16.9185i	0.336224	+	0.582357i
$845$	6.78728	+	31.2151i	0.233490	+	1.07383i
$846$		0			0
$847$	−2.03674	−	26.1726i	−0.0699830	−	0.899301i
$848$	29.5270	+	51.1422i	1.01396	+	1.75623i
$849$		0			0
$850$	2.68806	+	4.65586i	0.0921998	+	0.159695i
$851$	9.81413			0.336424
$852$		0			0
$853$	7.52465			0.257639			0.128820	−	0.991668i	$-0.458881\pi$
$853$	7.52465			0.257639			0.128820	+	0.991668i	$0.458881\pi$
$854$	−0.918453	−	11.8024i	−0.0314288	−	0.403869i
$855$		0			0
$856$	−4.42425			−0.151218
$857$	−7.72284	−	13.3764i	−0.263807	−	0.456928i	0.703443	−	0.710751i	$-0.251645\pi$
$857$	−7.72284	−	13.3764i	−0.263807	−	0.456928i	−0.967250	+	0.253824i	$0.918312\pi$
$858$		0			0
$859$	4.27437	−	7.40343i	0.145840	−	0.252602i	−0.783846	−	0.620955i	$-0.786745\pi$
$859$	4.27437	−	7.40343i	0.145840	−	0.252602i	0.929686	+	0.368353i	$0.120078\pi$
$860$	−7.44414	−	12.8936i	−0.253843	−	0.439669i
$861$		0			0
$862$	7.51220	−	13.0115i	0.255866	−	0.443174i
$863$	27.6867	−	47.9548i	0.942468	−	1.63240i	0.181724	−	0.983350i	$-0.441832\pi$
$863$	27.6867	−	47.9548i	0.942468	−	1.63240i	0.760744	−	0.649052i	$-0.224834\pi$
$864$		0			0
$865$	49.2450			1.67438
$866$	0.794230	−	1.37565i	0.0269890	−	0.0467464i
$867$		0			0
$868$	1.34510	+	17.2848i	0.0456555	+	0.586686i
$869$	−0.219902	−	0.380881i	−0.00745966	−	0.0129205i
$870$		0			0
$871$	−6.23526	+	39.9709i	−0.211274	+	1.35436i
$872$	14.2649	+	24.7075i	0.483071	+	0.836703i
$873$		0			0
$874$	−9.50771	−	16.4678i	−0.321603	−	0.557033i
$875$	23.2383	+	11.1091i	0.785598	+	0.375557i
$876$		0			0
$877$	−24.5606	−	42.5402i	−0.829352	−	1.43648i	−0.898547	−	0.438877i	$-0.855376\pi$
$877$	−24.5606	−	42.5402i	−0.829352	−	1.43648i	0.0691950	−	0.997603i	$-0.477957\pi$
$878$	21.2806			0.718185
$879$		0			0
$880$	6.37321	+	11.0387i	0.214841	+	0.372115i
$881$	3.45324	+	5.98118i	0.116342	+	0.201511i	0.918316	−	0.395849i	$-0.129550\pi$
$881$	3.45324	+	5.98118i	0.116342	+	0.201511i	−0.801973	+	0.597360i	$0.796216\pi$
$882$		0			0
$883$	−25.4087			−0.855071			−0.427536	−	0.903998i	$-0.640618\pi$
$883$	−25.4087			−0.855071			−0.427536	+	0.903998i	$0.640618\pi$
$884$	9.55859	−	3.69480i	0.321490	−	0.124269i
$885$		0			0
$886$	2.76920	−	4.79640i	0.0930332	−	0.161138i
$887$	42.1860			1.41647			0.708234	−	0.705977i	$-0.249492\pi$
$887$	42.1860			1.41647			0.708234	+	0.705977i	$0.249492\pi$
$888$		0			0
$889$	−0.756405	−	9.72000i	−0.0253690	−	0.325998i
$890$	11.1782	−	19.3612i	0.374694	−	0.648989i
$891$		0			0
$892$	5.35285	+	9.27140i	0.179227	+	0.310429i
$893$	31.2284			1.04502
$894$		0			0
$895$	−12.4032	−	21.4830i	−0.414594	−	0.718098i
$896$	−29.8150	−	14.2531i	−0.996048	−	0.476163i
$897$		0			0
$898$	17.0532	−	29.5370i	0.569072	−	0.985662i
$899$	27.9446	−	48.4014i	0.932004	−	1.61428i
$900$		0			0
$901$	17.8436	+	30.9061i	0.594458	+	1.02963i
$902$	−9.04858			−0.301285
$903$		0			0
$904$	4.58841	−	7.94737i	0.152608	−	0.264325i
$905$	−24.4448	+	42.3396i	−0.812572	+	1.40742i
$906$		0			0
$907$	−13.6930	+	23.7169i	−0.454667	+	0.787507i	−0.998669	−	0.0515772i	$-0.983575\pi$
$907$	−13.6930	+	23.7169i	−0.454667	+	0.787507i	0.544002	+	0.839084i	$0.316909\pi$
$908$	5.11055			0.169599
$909$		0			0
$910$	−22.7222	+	33.1642i	−0.753232	+	1.09938i
$911$	−46.0844			−1.52685			−0.763423	−	0.645899i	$-0.776483\pi$
$911$	−46.0844			−1.52685			−0.763423	+	0.645899i	$0.776483\pi$
$912$		0			0
$913$	−0.696026	+	1.20555i	−0.0230351	+	0.0398980i
$914$	−0.135443			−0.00448005
$915$		0			0
$916$	−8.16262	+	14.1381i	−0.269701	+	0.467135i
$917$	−4.03250	+	2.76625i	−0.133165	+	0.0913497i
$918$		0			0
$919$	20.0638	+	34.7516i	0.661845	+	1.14635i	0.980130	+	0.198354i	$0.0635596\pi$
$919$	20.0638	+	34.7516i	0.661845	+	1.14635i	−0.318286	+	0.947995i	$0.603107\pi$
$920$	7.74548	−	13.4156i	0.255361	−	0.442298i
$921$		0			0
$922$	−4.21860	+	7.30683i	−0.138932	+	0.240638i
$923$	−1.81182	+	11.6146i	−0.0596367	+	0.382299i
$924$		0			0
$925$	−1.46725	−	2.54136i	−0.0482430	−	0.0835593i
$926$	2.14098			0.0703569
$927$		0			0
$928$	−19.8211	−	34.3312i	−0.650660	−	1.12698i
$929$	−23.5530	−	40.7950i	−0.772750	−	1.33844i	−0.936051	−	0.351865i	$-0.885548\pi$
$929$	−23.5530	−	40.7950i	−0.772750	−	1.33844i	0.163301	−	0.986576i	$-0.447786\pi$
$930$		0			0
$931$	8.04751	−	20.8551i	0.263746	−	0.683497i
$932$	−9.42842	+	16.3305i	−0.308838	+	0.534924i
$933$		0			0
$934$	24.5953	−	42.6003i	0.804783	−	1.39392i
$935$	3.85144	+	6.67088i	0.125955	+	0.218161i
$936$		0			0
$937$	43.2558			1.41310			0.706552	−	0.707661i	$-0.250249\pi$
$937$	43.2558			1.41310			0.706552	+	0.707661i	$0.250249\pi$
$938$	−41.9823	+	28.7995i	−1.37077	+	0.940337i
$939$		0			0
$940$	−11.3095	−	19.5886i	−0.368875	−	0.638910i
$941$	21.2053	+	36.7287i	0.691274	+	1.19732i	0.971421	+	0.237365i	$0.0762836\pi$
$941$	21.2053	+	36.7287i	0.691274	+	1.19732i	−0.280146	+	0.959957i	$0.590383\pi$
$942$		0			0
$943$	8.82262	+	15.2812i	0.287304	+	0.497625i
$944$	44.6762			1.45409
$945$		0			0
$946$	−5.73022	−	9.92503i	−0.186305	−	0.322691i
$947$	−43.8160			−1.42383			−0.711914	−	0.702266i	$-0.752172\pi$
$947$	−43.8160			−1.42383			−0.711914	+	0.702266i	$0.752172\pi$
$948$		0			0
$949$	−42.1501	−	33.9701i	−1.36825	−	1.10271i
$950$	−2.84289	+	4.92402i	−0.0922354	+	0.159756i
$951$		0			0
$952$	−13.0868	−	6.25620i	−0.424147	−	0.202765i
$953$	−8.09343	+	14.0182i	−0.262172	+	0.454095i	−0.966819	−	0.255463i	$-0.917772\pi$
$953$	−8.09343	+	14.0182i	−0.262172	+	0.454095i	0.704647	+	0.709558i	$0.251105\pi$
$954$		0			0
$955$	−37.5405			−1.21478
$956$	7.81742			0.252833
$957$		0			0
$958$	−5.98432	+	10.3651i	−0.193345	+	0.334883i
$959$	6.71990	+	3.21246i	0.216997	+	0.103736i
$960$		0			0
$961$	−8.73113	+	15.1228i	−0.281649	+	0.487831i
$962$	−16.3032	+	6.30187i	−0.525636	+	0.203180i
$963$		0			0
$964$	19.3818			0.624246
$965$	−31.5366	−	54.6231i	−1.01520	−	1.75838i
$966$		0			0
$967$	−42.5994			−1.36990			−0.684952	−	0.728588i	$-0.740177\pi$
$967$	−42.5994			−1.36990			−0.684952	+	0.728588i	$0.740177\pi$
$968$	−9.00789	−	15.6021i	−0.289525	−	0.501471i
$969$		0			0
$970$	12.3228	+	21.3437i	0.395661	+	0.685304i
$971$	1.50269	+	2.60273i	0.0482236	+	0.0835257i	0.889130	−	0.457655i	$-0.151311\pi$
$971$	1.50269	+	2.60273i	0.0482236	+	0.0835257i	−0.840906	+	0.541181i	$0.817977\pi$
$972$		0			0
$973$	−8.19675	+	5.62290i	−0.262776	+	0.180262i
$974$	−3.30710			−0.105966
$975$		0			0
$976$	−6.51782	−	11.2892i	−0.208630	−	0.361359i
$977$	−20.4223	+	35.3725i	−0.653368	+	1.13167i	0.328932	+	0.944354i	$0.393311\pi$
$977$	−20.4223	+	35.3725i	−0.653368	+	1.13167i	−0.982300	+	0.187313i	$0.940022\pi$
$978$		0			0
$979$	2.75369	−	4.76953i	0.0880083	−	0.152435i
$980$	−15.9962	+	2.50479i	−0.510979	+	0.0800126i
$981$		0			0
$982$	−25.2053	−	43.6568i	−0.804332	−	1.39314i
$983$	−30.1629	−	52.2437i	−0.962047	−	1.66631i	−0.717348	−	0.696715i	$-0.754644\pi$
$983$	−30.1629	−	52.2437i	−0.962047	−	1.66631i	−0.244699	−	0.969599i	$-0.578689\pi$
$984$		0			0
$985$	38.5425			1.22807
$986$	−20.7874	−	36.0048i	−0.662006	−	1.14663i
$987$		0			0
$988$	8.43865	+	6.80096i	0.268469	+	0.216367i
$989$	−11.1743	+	19.3544i	−0.355321	+	0.615433i
$990$		0			0
$991$	22.9595	−	39.7670i	0.729332	−	1.26324i	−0.227834	−	0.973700i	$-0.573164\pi$
$991$	22.9595	−	39.7670i	0.729332	−	1.26324i	0.957166	−	0.289540i	$-0.0935022\pi$
$992$	17.1872	+	29.7690i	0.545693	+	0.945168i
$993$		0			0
$994$	−12.1991	+	8.36845i	−0.386931	+	0.265431i
$995$	7.06574	−	12.2382i	0.223999	−	0.387978i
$996$		0			0
$997$	26.5770			0.841701			0.420850	−	0.907130i	$-0.361732\pi$
$997$	26.5770			0.841701			0.420850	+	0.907130i	$0.361732\pi$
$998$	−17.0285	+	29.4942i	−0.539027	+	0.933621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.e.289.7		16
3.2	odd	2		273.2.l.b.16.2	yes	16
7.4	even	3		819.2.n.e.172.2		16
13.9	even	3		819.2.n.e.100.2		16
21.11	odd	6		273.2.j.b.172.7	yes	16
39.35	odd	6		273.2.j.b.100.7	✓	16
91.74	even	3	inner	819.2.s.e.802.7		16
273.74	odd	6		273.2.l.b.256.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.7	✓	16	39.35	odd	6
273.2.j.b.172.7	yes	16	21.11	odd	6
273.2.l.b.16.2	yes	16	3.2	odd	2
273.2.l.b.256.2	yes	16	273.74	odd	6
819.2.n.e.100.2		16	13.9	even	3
819.2.n.e.172.2		16	7.4	even	3
819.2.s.e.289.7		16	1.1	even	1	trivial
819.2.s.e.802.7		16	91.74	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.71502 q^{2} +0.941295 q^{4} +(-1.22863 + 2.12806i) q^{5} +(-2.38702 - 1.14112i) q^{7} -1.81570 q^{8} +O(q^{10})\)	\(q+1.71502 q^{2} +0.941295 q^{4} +(-1.22863 + 2.12806i) q^{5} +(-2.38702 - 1.14112i) q^{7} -1.81570 q^{8} +(-2.10713 + 3.64966i) q^{10} +(-0.519081 + 0.899075i) q^{11} +(-3.36305 + 1.29996i) q^{13} +(-4.09378 - 1.95704i) q^{14} -4.99655 q^{16} -3.01950 q^{17} +(-1.59671 - 2.76558i) q^{19} +(-1.15651 + 2.00313i) q^{20} +(-0.890235 + 1.54193i) q^{22} +3.47202 q^{23} +(-0.519081 - 0.899075i) q^{25} +(-5.76770 + 2.22946i) q^{26} +(-2.24689 - 1.07413i) q^{28} +(4.01417 + 6.95275i) q^{29} +(-3.48074 - 6.02882i) q^{31} -4.93779 q^{32} -5.17850 q^{34} +(5.36113 - 3.67769i) q^{35} +2.82664 q^{37} +(-2.73838 - 4.74302i) q^{38} +(2.23083 - 3.86391i) q^{40} +(2.54107 + 4.40125i) q^{41} +(-3.21838 + 5.57439i) q^{43} +(-0.488608 + 0.846294i) q^{44} +5.95458 q^{46} +(-4.88951 + 8.46887i) q^{47} +(4.39569 + 5.44774i) q^{49} +(-0.890235 - 1.54193i) q^{50} +(-3.16562 + 1.22365i) q^{52} +(-5.90947 - 10.2355i) q^{53} +(-1.27552 - 2.20927i) q^{55} +(4.33411 + 2.07193i) q^{56} +(6.88438 + 11.9241i) q^{58} -8.94141 q^{59} +(1.30446 + 2.25940i) q^{61} +(-5.96954 - 10.3396i) q^{62} +1.52470 q^{64} +(1.36557 - 8.75393i) q^{65} +(5.61000 - 9.71681i) q^{67} -2.84224 q^{68} +(9.19445 - 6.30731i) q^{70} +(1.63013 - 2.82347i) q^{71} +(7.50717 + 13.0028i) q^{73} +4.84774 q^{74} +(-1.50297 - 2.60322i) q^{76} +(2.26501 - 1.55377i) q^{77} +(-0.211818 + 0.366880i) q^{79} +(6.13893 - 10.6329i) q^{80} +(4.35798 + 7.54824i) q^{82} +1.34088 q^{83} +(3.70986 - 6.42567i) q^{85} +(-5.51958 + 9.56019i) q^{86} +(0.942496 - 1.63245i) q^{88} -5.30493 q^{89} +(9.51106 + 0.734615i) q^{91} +3.26819 q^{92} +(-8.38560 + 14.5243i) q^{94} +7.84707 q^{95} +(2.92406 - 5.06463i) q^{97} +(7.53871 + 9.34298i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31} + 6 q^{32} - 68 q^{34} - 8 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} - 4 q^{46} - 5 q^{47} + 7 q^{49} + 7 q^{50} - 18 q^{52} - 36 q^{53} - 15 q^{55} + 51 q^{56} + 20 q^{58} - 34 q^{59} - 22 q^{61} + 6 q^{62} - 20 q^{64} + 24 q^{65} + 26 q^{67} + 10 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} + 30 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} + 28 q^{80} - q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} + 24 q^{88} + 40 q^{89} - 10 q^{91} + 94 q^{92} - 20 q^{94} + 7 q^{97} - 18 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more