LMFDB - Embedded newform 819.2.s.f.802.2

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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369$ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.2
Root			$1.14017 - 1.97483i$ of defining polynomial
Character	$\chi$	$=$	819.802
Dual form			819.2.s.f.289.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28034 q^{2} +3.19995 q^{4} +(1.46862 + 2.54373i) q^{5} +(0.102378 - 2.64377i) q^{7} -2.73629 q^{8} +(-3.34896 - 5.80057i) q^{10} +(-2.58477 - 4.47696i) q^{11} +(-0.364757 + 3.58705i) q^{13} +(-0.233457 + 6.02869i) q^{14} -0.160234 q^{16} -5.05291 q^{17} +(-1.12929 + 1.95599i) q^{19} +(4.69952 + 8.13980i) q^{20} +(5.89416 + 10.2090i) q^{22} -5.23204 q^{23} +(-1.81371 + 3.14143i) q^{25} +(0.831769 - 8.17970i) q^{26} +(0.327604 - 8.45992i) q^{28} +(-0.216901 + 0.375683i) q^{29} +(-1.34122 + 2.32306i) q^{31} +5.83796 q^{32} +11.5224 q^{34} +(6.87539 - 3.62228i) q^{35} -4.24772 q^{37} +(2.57517 - 4.46033i) q^{38} +(-4.01857 - 6.96037i) q^{40} +(-0.269622 + 0.466999i) q^{41} +(-4.66348 - 8.07739i) q^{43} +(-8.27113 - 14.3260i) q^{44} +11.9308 q^{46} +(4.87054 + 8.43603i) q^{47} +(-6.97904 - 0.541328i) q^{49} +(4.13587 - 7.16354i) q^{50} +(-1.16720 + 11.4784i) q^{52} +(-0.377571 + 0.653972i) q^{53} +(7.59211 - 13.1499i) q^{55} +(-0.280135 + 7.23411i) q^{56} +(0.494607 - 0.856685i) q^{58} +3.64771 q^{59} +(-3.47734 + 6.02293i) q^{61} +(3.05843 - 5.29736i) q^{62} -12.9921 q^{64} +(-9.66019 + 4.34019i) q^{65} +(6.68012 + 11.5703i) q^{67} -16.1691 q^{68} +(-15.6782 + 8.26003i) q^{70} +(-3.90487 - 6.76343i) q^{71} +(-7.94401 + 13.7594i) q^{73} +9.68624 q^{74} +(-3.61368 + 6.25908i) q^{76} +(-12.1007 + 6.37520i) q^{77} +(-7.79235 - 13.4967i) q^{79} +(-0.235324 - 0.407593i) q^{80} +(0.614830 - 1.06492i) q^{82} -13.2349 q^{83} +(-7.42083 - 12.8532i) q^{85} +(10.6343 + 18.4192i) q^{86} +(7.07267 + 12.2502i) q^{88} +4.00286 q^{89} +(9.44600 + 1.33157i) q^{91} -16.7423 q^{92} +(-11.1065 - 19.2370i) q^{94} -6.63403 q^{95} +(2.69653 + 4.67053i) q^{97} +(15.9146 + 1.23441i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 32 q^{4} + 3 q^{7} + 12 q^{8} - 4 q^{10} + 8 q^{11} - 5 q^{13} + 9 q^{14} + 40 q^{16} + 7 q^{19} - 12 q^{20} - 9 q^{22} - 28 q^{23} - 32 q^{25} - 13 q^{26} - 23 q^{28} + 9 q^{29} - 9 q^{31} + 34 q^{32}+ \cdots + 76 q^{98}+O(q^{100})$ 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8 - 4 * q^10 + 8 * q^11 - 5 * q^13 + 9 * q^14 + 40 * q^16 + 7 * q^19 - 12 * q^20 - 9 * q^22 - 28 * q^23 - 32 * q^25 - 13 * q^26 - 23 * q^28 + 9 * q^29 - 9 * q^31 + 34 * q^32 + 12 * q^34 - 10 * q^35 - 36 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 + 20 * q^46 - 13 * q^47 - 3 * q^49 - 5 * q^50 - 44 * q^52 + 6 * q^53 - 19 * q^55 + 23 * q^56 - 30 * q^59 - 22 * q^62 + 72 * q^64 + 6 * q^65 - 22 * q^67 + 78 * q^68 + 30 * q^70 + 11 * q^71 - 6 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 - 48 * q^80 - 13 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 - 12 * q^88 + 4 * q^89 + 30 * q^91 - 66 * q^92 - 44 * q^94 - 72 * q^95 + 21 * q^97 + 76 * q^98

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	−2.28034			−1.61244			−0.806222	−	0.591614i	$-0.798491\pi$
$2$	−2.28034			−1.61244			−0.806222	+	0.591614i	$0.798491\pi$
$3$		0			0
$3$		0			0
$4$	3.19995			1.59997
$5$	1.46862	+	2.54373i	0.656788	+	1.13759i	0.981442	+	0.191758i	$0.0614188\pi$
$5$	1.46862	+	2.54373i	0.656788	+	1.13759i	−0.324654	+	0.945833i	$0.605248\pi$
$6$		0			0
$7$	0.102378	−	2.64377i	0.0386952	−	0.999251i
$7$	0.102378	−	2.64377i	0.0386952	−	0.999251i
$8$	−2.73629			−0.967423
$9$		0			0
$10$	−3.34896	−	5.80057i	−1.05903	−	1.83430i
$11$	−2.58477	−	4.47696i	−0.779338	−	1.34985i	−0.932324	−	0.361624i	$-0.882222\pi$
$11$	−2.58477	−	4.47696i	−0.779338	−	1.34985i	0.152986	−	0.988228i	$-0.451111\pi$
$12$		0			0
$13$	−0.364757	+	3.58705i	−0.101165	+	0.994870i
$13$	−0.364757	+	3.58705i	−0.101165	+	0.994870i
$14$	−0.233457	+	6.02869i	−0.0623939	+	1.61124i
$15$		0			0
$16$	−0.160234			−0.0400586
$17$	−5.05291			−1.22551			−0.612756	−	0.790272i	$-0.709939\pi$
$17$	−5.05291			−1.22551			−0.612756	+	0.790272i	$0.709939\pi$
$18$		0			0
$19$	−1.12929	+	1.95599i	−0.259078	+	0.448736i	−0.965995	−	0.258560i	$-0.916752\pi$
$19$	−1.12929	+	1.95599i	−0.259078	+	0.448736i	0.706917	+	0.707296i	$0.250085\pi$
$20$	4.69952	+	8.13980i	1.05084	+	1.82011i
$21$		0			0
$22$	5.89416	+	10.2090i	1.25664	+	2.17656i
$23$	−5.23204			−1.09096			−0.545478	−	0.838125i	$-0.683652\pi$
$23$	−5.23204			−1.09096			−0.545478	+	0.838125i	$0.683652\pi$
$24$		0			0
$25$	−1.81371	+	3.14143i	−0.362742	+	0.628287i
$26$	0.831769	−	8.17970i	0.163123	−	1.60417i
$27$		0			0
$28$	0.327604	−	8.45992i	0.0619114	−	1.59878i
$29$	−0.216901	+	0.375683i	−0.0402775	+	0.0697626i	−0.885461	−	0.464713i	$-0.846158\pi$
$29$	−0.216901	+	0.375683i	−0.0402775	+	0.0697626i	0.845184	+	0.534476i	$0.179491\pi$
$30$		0			0
$31$	−1.34122	+	2.32306i	−0.240890	+	0.417234i	−0.960968	−	0.276659i	$-0.910773\pi$
$31$	−1.34122	+	2.32306i	−0.240890	+	0.417234i	0.720078	+	0.693893i	$0.244106\pi$
$32$	5.83796			1.03202
$33$		0			0
$34$	11.5224			1.97607
$35$	6.87539	−	3.62228i	1.16215	−	0.612277i
$36$		0			0
$37$	−4.24772			−0.698321			−0.349160	−	0.937063i	$-0.613533\pi$
$37$	−4.24772			−0.698321			−0.349160	+	0.937063i	$0.613533\pi$
$38$	2.57517	−	4.46033i	0.417748	−	0.723561i
$39$		0			0
$40$	−4.01857	−	6.96037i	−0.635392	−	1.10053i
$41$	−0.269622	+	0.466999i	−0.0421079	+	0.0729330i	−0.886311	−	0.463090i	$-0.846741\pi$
$41$	−0.269622	+	0.466999i	−0.0421079	+	0.0729330i	0.844203	+	0.536023i	$0.180074\pi$
$42$		0			0
$43$	−4.66348	−	8.07739i	−0.711175	−	1.23179i	−0.964416	−	0.264388i	$-0.914830\pi$
$43$	−4.66348	−	8.07739i	−0.711175	−	1.23179i	0.253242	−	0.967403i	$-0.418503\pi$
$44$	−8.27113	−	14.3260i	−1.24692	−	2.15973i
$45$		0			0
$46$	11.9308			1.75910
$47$	4.87054	+	8.43603i	0.710442	+	1.23052i	0.964691	+	0.263383i	$0.0848382\pi$
$47$	4.87054	+	8.43603i	0.710442	+	1.23052i	−0.254250	+	0.967139i	$0.581828\pi$
$48$		0			0
$49$	−6.97904	−	0.541328i	−0.997005	−	0.0773325i
$50$	4.13587	−	7.16354i	0.584900	−	1.01308i
$51$		0			0
$52$	−1.16720	+	11.4784i	−0.161862	+	1.59176i
$53$	−0.377571	+	0.653972i	−0.0518634	+	0.0898300i	−0.890792	−	0.454412i	$-0.849849\pi$
$53$	−0.377571	+	0.653972i	−0.0518634	+	0.0898300i	0.838928	+	0.544242i	$0.183183\pi$
$54$		0			0
$55$	7.59211	−	13.1499i	1.02372	−	1.77313i
$56$	−0.280135	+	7.23411i	−0.0374347	+	0.966698i
$57$		0			0
$58$	0.494607	−	0.856685i	0.0649451	−	0.112488i
$59$	3.64771			0.474891			0.237445	−	0.971401i	$-0.423690\pi$
$59$	3.64771			0.474891			0.237445	+	0.971401i	$0.423690\pi$
$60$		0			0
$61$	−3.47734	+	6.02293i	−0.445228	+	0.771157i	−0.998068	−	0.0621304i	$-0.980211\pi$
$61$	−3.47734	+	6.02293i	−0.445228	+	0.771157i	0.552841	+	0.833287i	$0.313544\pi$
$62$	3.05843	−	5.29736i	0.388422	−	0.672766i
$63$		0			0
$64$	−12.9921			−1.62401
$65$	−9.66019	+	4.34019i	−1.19820	+	0.538334i
$66$		0			0
$67$	6.68012	+	11.5703i	0.816107	+	1.41354i	0.908530	+	0.417819i	$0.137205\pi$
$67$	6.68012	+	11.5703i	0.816107	+	1.41354i	−0.0924236	+	0.995720i	$0.529461\pi$
$68$	−16.1691			−1.96079
$69$		0			0
$70$	−15.6782	+	8.26003i	−1.87391	+	0.987262i
$71$	−3.90487	−	6.76343i	−0.463423	−	0.802672i	0.535706	−	0.844404i	$-0.320045\pi$
$71$	−3.90487	−	6.76343i	−0.463423	−	0.802672i	−0.999129	+	0.0417329i	$0.986712\pi$
$72$		0			0
$73$	−7.94401	+	13.7594i	−0.929776	+	1.61042i	−0.146083	+	0.989272i	$0.546667\pi$
$73$	−7.94401	+	13.7594i	−0.929776	+	1.61042i	−0.783694	+	0.621147i	$0.786667\pi$
$74$	9.68624			1.12600
$75$		0			0
$76$	−3.61368	+	6.25908i	−0.414517	+	0.717965i
$77$	−12.1007	+	6.37520i	−1.37900	+	0.726521i
$78$		0			0
$79$	−7.79235	−	13.4967i	−0.876708	−	1.51850i	−0.854932	−	0.518740i	$-0.826401\pi$
$79$	−7.79235	−	13.4967i	−0.876708	−	1.51850i	−0.0217756	−	0.999763i	$-0.506932\pi$
$80$	−0.235324	−	0.407593i	−0.0263100	−	0.0455703i
$81$		0			0
$82$	0.614830	−	1.06492i	0.0678966	−	0.117600i
$83$	−13.2349			−1.45272			−0.726360	−	0.687315i	$-0.758789\pi$
$83$	−13.2349			−1.45272			−0.726360	+	0.687315i	$0.758789\pi$
$84$		0			0
$85$	−7.42083	−	12.8532i	−0.804902	−	1.39413i
$86$	10.6343	+	18.4192i	1.14673	+	1.98619i
$87$		0			0
$88$	7.07267	+	12.2502i	0.753949	+	1.30588i
$89$	4.00286			0.424303			0.212151	−	0.977237i	$-0.431953\pi$
$89$	4.00286			0.424303			0.212151	+	0.977237i	$0.431953\pi$
$90$		0			0
$91$	9.44600	+	1.33157i	0.990210	+	0.139586i
$92$	−16.7423			−1.74550
$93$		0			0
$94$	−11.1065	−	19.2370i	−1.14555	−	1.98415i
$95$	−6.63403			−0.680637
$96$		0			0
$97$	2.69653	+	4.67053i	0.273791	+	0.474220i	0.969829	−	0.243784i	$-0.0783889\pi$
$97$	2.69653	+	4.67053i	0.273791	+	0.474220i	−0.696038	+	0.718005i	$0.745056\pi$
$98$	15.9146	+	1.23441i	1.60761	+	0.124694i
$99$		0			0
$100$	−5.80377	+	10.0524i	−0.580377	+	1.00524i
$101$	−1.57620	−	2.73006i	−0.156838	−	0.271651i	0.776889	−	0.629638i	$-0.216797\pi$
$101$	−1.57620	−	2.73006i	−0.156838	−	0.271651i	−0.933727	+	0.357987i	$0.883463\pi$
$102$		0			0
$103$	−6.59727	−	11.4268i	−0.650048	−	1.12592i	−0.983111	−	0.183012i	$-0.941415\pi$
$103$	−6.59727	−	11.4268i	−0.650048	−	1.12592i	0.333062	−	0.942905i	$-0.391918\pi$
$104$	0.998078	−	9.81520i	0.0978696	−	0.962460i
$105$		0			0
$106$	0.860990	−	1.49128i	0.0836267	−	0.144846i
$107$	−5.86701			−0.567185			−0.283593	−	0.958945i	$-0.591526\pi$
$107$	−5.86701			−0.567185			−0.283593	+	0.958945i	$0.591526\pi$
$108$		0			0
$109$	2.74399	−	4.75273i	0.262826	−	0.455229i	−0.704166	−	0.710036i	$-0.748679\pi$
$109$	2.74399	−	4.75273i	0.262826	−	0.455229i	0.966992	+	0.254807i	$0.0820120\pi$
$110$	−17.3126	+	29.9863i	−1.65069	+	2.85908i
$111$		0			0
$112$	−0.0164045	+	0.423623i	−0.00155008	+	0.0400286i
$113$	−0.794808	−	1.37665i	−0.0747692	−	0.129504i	0.826217	−	0.563352i	$-0.190489\pi$
$113$	−0.794808	−	1.37665i	−0.0747692	−	0.129504i	−0.900986	+	0.433848i	$0.857155\pi$
$114$		0			0
$115$	−7.68390	−	13.3089i	−0.716527	−	1.24106i
$116$	−0.694071	+	1.20217i	−0.0644428	+	0.111618i
$117$		0			0
$118$	−8.31800			−0.765734
$119$	−0.517307	+	13.3587i	−0.0474215	+	1.22459i
$120$		0			0
$121$	−7.86209	+	13.6175i	−0.714735	+	1.23796i
$122$	7.92951	−	13.7343i	0.717904	−	1.24345i
$123$		0			0
$124$	−4.29183	+	7.43367i	−0.385418	+	0.667563i
$125$	4.03162			0.360599
$126$		0			0
$127$	0.348278	−	0.603236i	0.0309047	−	0.0535285i	−0.850159	−	0.526525i	$-0.823494\pi$
$127$	0.348278	−	0.603236i	0.0309047	−	0.0535285i	0.881064	+	0.472997i	$0.156828\pi$
$128$	17.9504			1.58660
$129$		0			0
$130$	22.0285	−	9.89710i	1.93203	−	0.868033i
$131$	−3.35469	−	5.81049i	−0.293101	−	0.507665i	0.681441	−	0.731873i	$-0.261354\pi$
$131$	−3.35469	−	5.81049i	−0.293101	−	0.507665i	−0.974541	+	0.224208i	$0.928020\pi$
$132$		0			0
$133$	5.05558	+	3.18584i	0.438375	+	0.276248i
$134$	−15.2329	−	26.3842i	−1.31593	−	2.27925i
$135$		0			0
$136$	13.8262			1.18559
$137$	−12.4993			−1.06789			−0.533944	−	0.845520i	$-0.679291\pi$
$137$	−12.4993			−1.06789			−0.533944	+	0.845520i	$0.679291\pi$
$138$		0			0
$139$	−0.657614	−	1.13902i	−0.0557781	−	0.0966105i	0.836788	−	0.547527i	$-0.184431\pi$
$139$	−0.657614	−	1.13902i	−0.0557781	−	0.0966105i	−0.892566	+	0.450916i	$0.851097\pi$
$140$	22.0009	−	11.5911i	1.85941	−	0.979627i
$141$		0			0
$142$	8.90442	+	15.4229i	0.747243	+	1.29426i
$143$	17.0019	−	7.63871i	1.42177	−	0.638781i
$144$		0			0
$145$	−1.27418			−0.105815
$146$	18.1150	−	31.3762i	1.49921	−	2.59671i
$147$		0			0
$148$	−13.5925			−1.11729
$149$	10.5964	−	18.3534i	0.868088	−	1.50357i	0.00413964	−	0.999991i	$-0.498682\pi$
$149$	10.5964	−	18.3534i	0.868088	−	1.50357i	0.863948	−	0.503581i	$-0.167984\pi$
$150$		0			0
$151$	7.90358	−	13.6894i	0.643185	−	1.11403i	−0.341533	−	0.939870i	$-0.610946\pi$
$151$	7.90358	−	13.6894i	0.643185	−	1.11403i	0.984718	−	0.174159i	$-0.0557205\pi$
$152$	3.09007	−	5.35216i	0.250638	−	0.434117i
$153$		0			0
$154$	27.5936	−	14.5376i	2.22356	−	1.17147i
$155$	−7.87898			−0.632855
$156$		0			0
$157$	−2.76205	+	4.78402i	−0.220436	+	0.381806i	−0.954940	−	0.296798i	$-0.904081\pi$
$157$	−2.76205	+	4.78402i	−0.220436	+	0.381806i	0.734505	+	0.678604i	$0.237415\pi$
$158$	17.7692	+	30.7772i	1.41364	+	2.44850i
$159$		0			0
$160$	8.57376	+	14.8502i	0.677815	+	1.17401i
$161$	−0.535646	+	13.8323i	−0.0422148	+	1.09014i
$162$		0			0
$163$	1.57435	−	2.72685i	0.123313	−	0.213584i	−0.797759	−	0.602976i	$-0.793982\pi$
$163$	1.57435	−	2.72685i	0.123313	−	0.213584i	0.921072	+	0.389392i	$0.127315\pi$
$164$	−0.862777	+	1.49437i	−0.0673715	+	0.116691i
$165$		0			0
$166$	30.1801			2.34243
$167$	−6.71152	+	11.6247i	−0.519353	+	0.899546i	0.480394	+	0.877053i	$0.340494\pi$
$167$	−6.71152	+	11.6247i	−0.519353	+	0.899546i	−0.999747	+	0.0224932i	$0.992840\pi$
$168$		0			0
$169$	−12.7339	−	2.61680i	−0.979531	−	0.201293i
$170$	16.9220	+	29.3098i	1.29786	+	2.24796i
$171$		0			0
$172$	−14.9229	−	25.8472i	−1.13786	−	1.97083i
$173$	−6.42442	+	11.1274i	−0.488439	+	0.846002i	−0.999912	−	0.0132981i	$-0.995767\pi$
$173$	−6.42442	+	11.1274i	−0.488439	+	0.846002i	0.511472	+	0.859300i	$0.329100\pi$
$174$		0			0
$175$	8.11955	+	5.11664i	0.613780	+	0.386782i
$176$	0.414169	+	0.717362i	0.0312192	+	0.0540732i
$177$		0			0
$178$	−9.12788			−0.684164
$179$	9.33314	+	16.1655i	0.697591	+	1.20826i	0.969299	+	0.245884i	$0.0790782\pi$
$179$	9.33314	+	16.1655i	0.697591	+	1.20826i	−0.271708	+	0.962380i	$0.587588\pi$
$180$		0			0
$181$	0.878433			0.0652934			0.0326467	−	0.999467i	$-0.489606\pi$
$181$	0.878433			0.0652934			0.0326467	+	0.999467i	$0.489606\pi$
$182$	−21.5401	−	3.03643i	−1.59666	−	0.225075i
$183$		0			0
$184$	14.3164			1.05542
$185$	−6.23830	−	10.8051i	−0.458649	−	0.794403i
$186$		0			0
$187$	13.0606	+	22.6217i	0.955088	+	1.65426i
$188$	15.5855	+	26.9948i	1.13669	+	1.96880i
$189$		0			0
$190$	15.1278			1.09749
$191$	−7.97565	+	13.8142i	−0.577097	+	0.999562i	0.418713	+	0.908119i	$0.362481\pi$
$191$	−7.97565	+	13.8142i	−0.577097	+	0.999562i	−0.995810	+	0.0914434i	$0.970852\pi$
$192$		0			0
$193$	−1.97533	−	3.42137i	−0.142187	−	0.246276i	0.786133	−	0.618058i	$-0.212080\pi$
$193$	−1.97533	−	3.42137i	−0.142187	−	0.246276i	−0.928320	+	0.371782i	$0.878747\pi$
$194$	−6.14900	−	10.6504i	−0.441473	−	0.764653i
$195$		0			0
$196$	−22.3325	−	1.73222i	−1.59518	−	0.123730i
$197$	6.72353	−	11.6455i	0.479032	−	0.829708i	−0.520679	−	0.853753i	$-0.674321\pi$
$197$	6.72353	−	11.6455i	0.479032	−	0.829708i	0.999711	+	0.0240448i	$0.00765444\pi$
$198$		0			0
$199$	20.8291			1.47654			0.738268	−	0.674508i	$-0.235644\pi$
$199$	20.8291			1.47654			0.738268	+	0.674508i	$0.235644\pi$
$200$	4.96282	−	8.59586i	0.350925	−	0.607819i
$201$		0			0
$202$	3.59427	+	6.22546i	0.252892	+	0.438022i
$203$	0.971014	+	0.611897i	0.0681518	+	0.0429468i
$204$		0			0
$205$	−1.58389			−0.110624
$206$	15.0440	+	26.0570i	1.04817	+	1.81548i
$207$		0			0
$208$	0.0584466	−	0.574769i	0.00405254	−	0.0398531i
$209$	11.6759			0.807636
$210$		0			0
$211$	7.17814	−	12.4329i	0.494164	−	0.855917i	−0.505814	−	0.862643i	$-0.668808\pi$
$211$	7.17814	−	12.4329i	0.494164	−	0.855917i	0.999977	+	0.00672604i	$0.00214098\pi$
$212$	−1.20821	+	2.09268i	−0.0829800	+	0.143726i
$213$		0			0
$214$	13.3788			0.914554
$215$	13.6978	−	23.7253i	0.934182	−	1.61805i
$216$		0			0
$217$	6.00432	+	3.78370i	0.407600	+	0.256855i
$218$	−6.25722	+	10.8378i	−0.423793	+	0.734030i
$219$		0			0
$220$	24.2943	−	42.0790i	1.63792	−	2.83697i
$221$	1.84308	−	18.1251i	0.123979	−	1.21922i
$222$		0			0
$223$	0.596931	−	1.03392i	0.0399735	−	0.0692361i	−0.845346	−	0.534218i	$-0.820606\pi$
$223$	0.596931	−	1.03392i	0.0399735	−	0.0692361i	0.885320	+	0.464982i	$0.153939\pi$
$224$	0.597679	−	15.4342i	0.0399341	−	1.03124i
$225$		0			0
$226$	1.81243	+	3.13922i	0.120561	+	0.208818i
$227$	15.8887			1.05457			0.527286	−	0.849688i	$-0.323210\pi$
$227$	15.8887			1.05457			0.527286	+	0.849688i	$0.323210\pi$
$228$		0			0
$229$	−4.39323	−	7.60931i	−0.290313	−	0.502837i	0.683571	−	0.729884i	$-0.260426\pi$
$229$	−4.39323	−	7.60931i	−0.290313	−	0.502837i	−0.973884	+	0.227047i	$0.927093\pi$
$230$	17.5219	+	30.3488i	1.15536	+	2.00114i
$231$		0			0
$232$	0.593502	−	1.02798i	0.0389653	−	0.0674899i
$233$	−2.86714	−	4.96604i	−0.187833	−	0.325336i	0.756695	−	0.653769i	$-0.226813\pi$
$233$	−2.86714	−	4.96604i	−0.187833	−	0.325336i	−0.944527	+	0.328432i	$0.893480\pi$
$234$		0			0
$235$	−14.3060	+	24.7787i	−0.933220	+	1.61638i
$236$	11.6725			0.759813
$237$		0			0
$238$	1.17964	−	30.4625i	0.0764644	−	1.97459i
$239$	11.5411			0.746532			0.373266	−	0.927724i	$-0.378238\pi$
$239$	11.5411			0.746532			0.373266	+	0.927724i	$0.378238\pi$
$240$		0			0
$241$	−5.66060			−0.364631			−0.182316	−	0.983240i	$-0.558359\pi$
$241$	−5.66060			−0.364631			−0.182316	+	0.983240i	$0.558359\pi$
$242$	17.9282	−	31.0526i	1.15247	−	1.99614i
$243$		0			0
$244$	−11.1273	+	19.2730i	−0.712352	+	1.23383i
$245$	−8.87258	−	18.5478i	−0.566849	−	1.18498i
$246$		0			0
$247$	−6.60434	−	4.76430i	−0.420224	−	0.303145i
$248$	3.66996	−	6.35655i	0.233043	−	0.403642i
$249$		0			0
$250$	−9.19346			−0.581445
$251$	−12.1872	−	21.1088i	−0.769249	−	1.33238i	−0.937971	−	0.346715i	$-0.887297\pi$
$251$	−12.1872	−	21.1088i	−0.769249	−	1.33238i	0.168721	−	0.985664i	$-0.446036\pi$
$252$		0			0
$253$	13.5236	+	23.4236i	0.850223	+	1.47263i
$254$	−0.794193	+	1.37558i	−0.0498321	+	0.0863117i
$255$		0			0
$256$	−14.9488			−0.934303
$257$	−4.60536			−0.287275			−0.143637	−	0.989630i	$-0.545880\pi$
$257$	−4.60536			−0.287275			−0.143637	+	0.989630i	$0.545880\pi$
$258$		0			0
$259$	−0.434873	+	11.2300i	−0.0270217	+	0.697798i
$260$	−30.9121	+	13.8884i	−1.91709	+	0.861320i
$261$		0			0
$262$	7.64983	+	13.2499i	0.472608	+	0.818581i
$263$	11.4912	+	19.9033i	0.708576	+	1.22729i	0.965385	+	0.260828i	$0.0839955\pi$
$263$	11.4912	+	19.9033i	0.708576	+	1.22729i	−0.256809	+	0.966462i	$0.582671\pi$
$264$		0			0
$265$	−2.21804			−0.136253
$266$	−11.5284	−	7.26480i	−0.706854	−	0.445434i
$267$		0			0
$268$	21.3760	+	37.0244i	1.30575	+	2.26162i
$269$	−14.0049			−0.853896			−0.426948	−	0.904276i	$-0.640411\pi$
$269$	−14.0049			−0.853896			−0.426948	+	0.904276i	$0.640411\pi$
$270$		0			0
$271$	−19.1060			−1.16061			−0.580303	−	0.814401i	$-0.697066\pi$
$271$	−19.1060			−1.16061			−0.580303	+	0.814401i	$0.697066\pi$
$272$	0.809651			0.0490923
$273$		0			0
$274$	28.5027			1.72191
$275$	18.7521			1.13079
$276$		0			0
$277$	12.9200			0.776285			0.388142	−	0.921599i	$-0.373117\pi$
$277$	12.9200			0.776285			0.388142	+	0.921599i	$0.373117\pi$
$278$	1.49958	+	2.59735i	0.0899390	+	0.155779i
$279$		0			0
$280$	−18.8130	+	9.91159i	−1.12429	+	0.592331i
$281$	19.6264			1.17082			0.585408	−	0.810739i	$-0.300934\pi$
$281$	19.6264			1.17082			0.585408	+	0.810739i	$0.300934\pi$
$282$		0			0
$283$	−1.63363	−	2.82954i	−0.0971095	−	0.168199i	0.813378	−	0.581736i	$-0.197626\pi$
$283$	−1.63363	−	2.82954i	−0.0971095	−	0.168199i	−0.910487	+	0.413538i	$0.864293\pi$
$284$	−12.4954	−	21.6426i	−0.741464	−	1.28425i
$285$		0			0
$286$	−38.7701	+	17.4189i	−2.29252	+	1.03000i
$287$	1.20704	+	0.760629i	0.0712490	+	0.0448985i
$288$		0			0
$289$	8.53194			0.501879
$290$	2.90557			0.170621
$291$		0			0
$292$	−25.4204	+	44.0295i	−1.48762	+	2.57663i
$293$	−9.50947	−	16.4709i	−0.555549	−	0.962239i	−0.997861	−	0.0653778i	$-0.979175\pi$
$293$	−9.50947	−	16.4709i	−0.555549	−	0.962239i	0.442311	−	0.896862i	$-0.354159\pi$
$294$		0			0
$295$	5.35710	+	9.27878i	0.311903	+	0.540231i
$296$	11.6230			0.675572
$297$		0			0
$298$	−24.1633	+	41.8521i	−1.39974	+	2.42442i
$299$	1.90842	−	18.7676i	0.110367	−	1.08536i
$300$		0			0
$301$	−21.8322	+	11.5022i	−1.25839	+	0.662978i
$302$	−18.0229	+	31.2165i	−1.03710	+	1.79631i
$303$		0			0
$304$	0.180952	−	0.313418i	0.0103783	−	0.0179757i
$305$	−20.4276			−1.16968
$306$		0			0
$307$	−8.30660			−0.474083			−0.237041	−	0.971500i	$-0.576178\pi$
$307$	−8.30660			−0.474083			−0.237041	+	0.971500i	$0.576178\pi$
$308$	−38.7215	+	20.4003i	−2.20636	+	1.16241i
$309$		0			0
$310$	17.9668			1.02044
$311$	−5.42853	+	9.40250i	−0.307824	+	0.533167i	−0.977886	−	0.209138i	$-0.932934\pi$
$311$	−5.42853	+	9.40250i	−0.307824	+	0.533167i	0.670062	+	0.742305i	$0.266267\pi$
$312$		0			0
$313$	0.566928	+	0.981949i	0.0320447	+	0.0555030i	0.881603	−	0.471992i	$-0.156465\pi$
$313$	0.566928	+	0.981949i	0.0320447	+	0.0555030i	−0.849558	+	0.527495i	$0.823131\pi$
$314$	6.29842	−	10.9092i	0.355440	−	0.615641i
$315$		0			0
$316$	−24.9351	−	43.1889i	−1.40271	−	2.42956i
$317$	4.98712	+	8.63795i	0.280105	+	0.485155i	0.971410	−	0.237407i	$-0.0762975\pi$
$317$	4.98712	+	8.63795i	0.280105	+	0.485155i	−0.691306	+	0.722562i	$0.742964\pi$
$318$		0			0
$319$	2.24256			0.125559
$320$	−19.0804	−	33.0483i	−1.06663	−	1.84746i
$321$		0			0
$322$	1.22145	−	31.5424i	0.0680690	−	1.75779i
$323$	5.70622	−	9.88347i	0.317503	−	0.549931i
$324$		0			0
$325$	−10.6069	−	7.65173i	−0.588367	−	0.424441i
$326$	−3.59005	+	6.21815i	−0.198835	+	0.344392i
$327$		0			0
$328$	0.737763	−	1.27784i	0.0407362	−	0.0705571i
$329$	22.8016	−	12.0129i	1.25709	−	0.662294i
$330$		0			0
$331$	0.827569	−	1.43339i	0.0454873	−	0.0787863i	−0.842385	−	0.538876i	$-0.818849\pi$
$331$	0.827569	−	1.43339i	0.0454873	−	0.0787863i	0.887873	+	0.460089i	$0.152183\pi$
$332$	−42.3510			−2.32431
$333$		0			0
$334$	15.3045	−	26.5083i	0.837428	−	1.45047i
$335$	−19.6212	+	33.9849i	−1.07202	+	1.85679i
$336$		0			0
$337$	−12.4081			−0.675913			−0.337956	−	0.941162i	$-0.609736\pi$
$337$	−12.4081			−0.675913			−0.337956	+	0.941162i	$0.609736\pi$
$338$	29.0376	+	5.96720i	1.57944	+	0.324573i
$339$		0			0
$340$	−23.7463	−	41.1297i	−1.28782	−	2.23057i
$341$	13.8670			0.750939
$342$		0			0
$343$	−2.14565	+	18.3955i	−0.115854	+	0.993266i
$344$	12.7606	+	22.1021i	0.688007	+	1.19166i
$345$		0			0
$346$	14.6498	−	25.3743i	0.787581	−	1.36413i
$347$	−13.2452			−0.711041			−0.355521	−	0.934668i	$-0.615696\pi$
$347$	−13.2452			−0.711041			−0.355521	+	0.934668i	$0.615696\pi$
$348$		0			0
$349$	17.5068	−	30.3227i	0.937119	−	1.62314i	0.166307	−	0.986074i	$-0.446816\pi$
$349$	17.5068	−	30.3227i	0.937119	−	1.62314i	0.770812	−	0.637063i	$-0.219851\pi$
$350$	−18.5153	−	11.6677i	−0.989685	−	0.623663i
$351$		0			0
$352$	−15.0898	−	26.1363i	−0.804289	−	1.39307i
$353$	11.5541	+	20.0123i	0.614964	+	1.06515i	0.990391	+	0.138297i	$0.0441628\pi$
$353$	11.5541	+	20.0123i	0.614964	+	1.06515i	−0.375427	+	0.926852i	$0.622504\pi$
$354$		0			0
$355$	11.4696	−	19.8659i	0.608741	−	1.05437i
$356$	12.8089			0.678873
$357$		0			0
$358$	−21.2827	−	36.8628i	−1.12483	−	1.94826i
$359$	6.44458	+	11.1623i	0.340132	+	0.589126i	0.984457	−	0.175626i	$-0.0561949\pi$
$359$	6.44458	+	11.1623i	0.340132	+	0.589126i	−0.644325	+	0.764752i	$0.722862\pi$
$360$		0			0
$361$	6.94939	+	12.0367i	0.365758	+	0.633511i
$362$	−2.00312			−0.105282
$363$		0			0
$364$	30.2267	+	4.26095i	1.58431	+	0.223334i
$365$	−46.6670			−2.44266
$366$		0			0
$367$	13.2465	+	22.9436i	0.691460	+	1.19764i	0.971360	+	0.237614i	$0.0763655\pi$
$367$	13.2465	+	22.9436i	0.691460	+	1.19764i	−0.279900	+	0.960029i	$0.590301\pi$
$368$	0.838353			0.0437022
$369$		0			0
$370$	14.2254	+	24.6392i	0.739545	+	1.28093i
$371$	1.69030	+	1.06516i	0.0877558	+	0.0553005i
$372$		0			0
$373$	6.18549	−	10.7136i	0.320273	−	0.554729i	−0.660271	−	0.751027i	$-0.729559\pi$
$373$	6.18549	−	10.7136i	0.320273	−	0.554729i	0.980544	+	0.196298i	$0.0628921\pi$
$374$	−29.7827	−	51.5851i	−1.54002	−	2.66740i
$375$		0			0
$376$	−13.3272	−	23.0834i	−0.687298	−	1.19043i
$377$	−1.26848	−	0.915067i	−0.0653300	−	0.0471284i
$378$		0			0
$379$	−14.0179	+	24.2797i	−0.720050	+	1.24716i	0.240929	+	0.970543i	$0.422548\pi$
$379$	−14.0179	+	24.2797i	−0.720050	+	1.24716i	−0.960979	+	0.276621i	$0.910785\pi$
$380$	−21.2285			−1.08900
$381$		0			0
$382$	18.1872	−	31.5011i	0.930537	−	1.61174i
$383$	−13.1452	+	22.7681i	−0.671687	+	1.16340i	0.305739	+	0.952115i	$0.401097\pi$
$383$	−13.1452	+	22.7681i	−0.671687	+	1.16340i	−0.977426	+	0.211280i	$0.932237\pi$
$384$		0			0
$385$	−33.9881	−	21.4181i	−1.73219	−	1.09157i
$386$	4.50442	+	7.80188i	0.229269	+	0.397105i
$387$		0			0
$388$	8.62875	+	14.9454i	0.438059	+	0.758740i
$389$	13.4205	−	23.2449i	0.680445	−	1.17856i	−0.294400	−	0.955682i	$-0.595120\pi$
$389$	13.4205	−	23.2449i	0.680445	−	1.17856i	0.974845	−	0.222883i	$-0.0715467\pi$
$390$		0			0
$391$	26.4371			1.33698
$392$	19.0966	+	1.48123i	0.964526	+	0.0748133i
$393$		0			0
$394$	−15.3319	+	26.5557i	−0.772412	+	1.33786i
$395$	22.8881	−	39.6433i	1.15162	−	1.99467i
$396$		0			0
$397$	−12.2621	+	21.2386i	−0.615419	+	1.06594i	0.374892	+	0.927068i	$0.377680\pi$
$397$	−12.2621	+	21.2386i	−0.615419	+	1.06594i	−0.990311	+	0.138868i	$0.955654\pi$
$398$	−47.4974			−2.38083
$399$		0			0
$400$	0.290618	−	0.503366i	0.0145309	−	0.0251683i
$401$	−3.16570			−0.158088			−0.0790438	−	0.996871i	$-0.525187\pi$
$401$	−3.16570			−0.158088			−0.0790438	+	0.996871i	$0.525187\pi$
$402$		0			0
$403$	−7.84372	−	5.65838i	−0.390724	−	0.281864i
$404$	−5.04376	−	8.73605i	−0.250936	−	0.434635i
$405$		0			0
$406$	−2.21424	−	1.39533i	−0.109891	−	0.0692492i
$407$	10.9794	+	19.0169i	0.544228	+	0.942630i
$408$		0			0
$409$	19.0685			0.942876			0.471438	−	0.881899i	$-0.343735\pi$
$409$	19.0685			0.942876			0.471438	+	0.881899i	$0.343735\pi$
$410$	3.61181			0.178375
$411$		0			0
$412$	−21.1109	−	36.5652i	−1.04006	−	1.80144i
$413$	0.373445	−	9.64369i	0.0183760	−	0.474535i
$414$		0			0
$415$	−19.4371	−	33.6660i	−0.954129	−	1.65260i
$416$	−2.12943	+	20.9411i	−0.104404	+	1.02672i
$417$		0			0
$418$	−26.6249			−1.30227
$419$	−7.80534	+	13.5192i	−0.381316	+	0.660458i	−0.991251	−	0.131993i	$-0.957862\pi$
$419$	−7.80534	+	13.5192i	−0.381316	+	0.660458i	0.609935	+	0.792452i	$0.291196\pi$
$420$		0			0
$421$	−18.0525			−0.879827			−0.439913	−	0.898040i	$-0.644991\pi$
$421$	−18.0525			−0.879827			−0.439913	+	0.898040i	$0.644991\pi$
$422$	−16.3686	+	28.3512i	−0.796811	+	1.38012i
$423$		0			0
$424$	1.03314	−	1.78945i	0.0501738	−	0.0869036i
$425$	9.16451	−	15.8734i	0.444544	−	0.769973i
$426$		0			0
$427$	15.5672	+	9.80990i	0.753351	+	0.474734i
$428$	−18.7741			−0.907481
$429$		0			0
$430$	−31.2356	+	54.1017i	−1.50632	+	2.60902i
$431$	−8.75826	−	15.1698i	−0.421871	−	0.730701i	0.574252	−	0.818679i	$-0.305293\pi$
$431$	−8.75826	−	15.1698i	−0.421871	−	0.730701i	−0.996122	+	0.0879774i	$0.971960\pi$
$432$		0			0
$433$	−3.02961	−	5.24744i	−0.145594	−	0.252176i	0.784001	−	0.620760i	$-0.213176\pi$
$433$	−3.02961	−	5.24744i	−0.145594	−	0.252176i	−0.929594	+	0.368584i	$0.879843\pi$
$434$	−13.6919	−	8.62813i	−0.657232	−	0.414163i
$435$		0			0
$436$	8.78061	−	15.2085i	0.420515	−	0.728354i
$437$	5.90851	−	10.2338i	0.282642	−	0.489551i
$438$		0			0
$439$	23.3824			1.11598			0.557990	−	0.829848i	$-0.311573\pi$
$439$	23.3824			1.11598			0.557990	+	0.829848i	$0.311573\pi$
$440$	−20.7742	+	35.9819i	−0.990370	+	1.71537i
$441$		0			0
$442$	−4.20286	+	41.3313i	−0.199910	+	1.96593i
$443$	−4.44712	−	7.70264i	−0.211289	−	0.365963i	0.740829	−	0.671693i	$-0.234433\pi$
$443$	−4.44712	−	7.70264i	−0.211289	−	0.365963i	−0.952118	+	0.305730i	$0.901099\pi$
$444$		0			0
$445$	5.87870	+	10.1822i	0.278677	+	0.482683i
$446$	−1.36121	+	2.35768i	−0.0644550	+	0.111639i
$447$		0			0
$448$	−1.33010	+	34.3480i	−0.0628414	+	1.62279i
$449$	19.3671	+	33.5448i	0.913989	+	1.58308i	0.808375	+	0.588668i	$0.200348\pi$
$449$	19.3671	+	33.5448i	0.913989	+	1.58308i	0.105614	+	0.994407i	$0.466319\pi$
$450$		0			0
$451$	2.78765			0.131265
$452$	−2.54334	−	4.40520i	−0.119629	−	0.207203i
$453$		0			0
$454$	−36.2317			−1.70044
$455$	10.4855	+	25.9836i	0.491566	+	1.21813i
$456$		0			0
$457$	22.4003			1.04784			0.523920	−	0.851767i	$-0.324469\pi$
$457$	22.4003			1.04784			0.523920	+	0.851767i	$0.324469\pi$
$458$	10.0181	+	17.3518i	0.468113	+	0.810796i
$459$		0			0
$460$	−24.5881	−	42.5878i	−1.14642	−	1.98567i
$461$	1.40367	+	2.43123i	0.0653755	+	0.113234i	0.896860	−	0.442314i	$-0.145842\pi$
$461$	1.40367	+	2.43123i	0.0653755	+	0.113234i	−0.831485	+	0.555547i	$0.812509\pi$
$462$		0			0
$463$	37.7530			1.75453			0.877266	−	0.480004i	$-0.159365\pi$
$463$	37.7530			1.75453			0.877266	+	0.480004i	$0.159365\pi$
$464$	0.0347550	−	0.0601974i	0.00161346	−	0.00279459i
$465$		0			0
$466$	6.53806	+	11.3243i	0.302870	+	0.524586i
$467$	8.04389	+	13.9324i	0.372227	+	0.644716i	0.989908	−	0.141713i	$-0.0452609\pi$
$467$	8.04389	+	13.9324i	0.372227	+	0.644716i	−0.617681	+	0.786429i	$0.711928\pi$
$468$		0			0
$469$	31.2731	−	16.4762i	1.44406	−	0.760798i
$470$	32.6225	−	56.5038i	1.50476	−	2.60633i
$471$		0			0
$472$	−9.98116			−0.459420
$473$	−24.1081	+	41.7564i	−1.10849	+	1.91996i
$474$		0			0
$475$	−4.09642	−	7.09520i	−0.187956	−	0.325550i
$476$	−1.65536	+	42.7473i	−0.0758731	+	1.95932i
$477$		0			0
$478$	−26.3176			−1.20374
$479$	4.27425	+	7.40322i	0.195295	+	0.338262i	0.946997	−	0.321241i	$-0.104100\pi$
$479$	4.27425	+	7.40322i	0.195295	+	0.338262i	−0.751702	+	0.659503i	$0.770767\pi$
$480$		0			0
$481$	1.54938	−	15.2368i	0.0706458	−	0.694738i
$482$	12.9081			0.587948
$483$		0			0
$484$	−25.1583	+	43.5754i	−1.14356	+	1.98070i
$485$	−7.92037	+	13.7185i	−0.359646	+	0.622925i
$486$		0			0
$487$	−35.5761			−1.61211			−0.806054	−	0.591842i	$-0.798401\pi$
$487$	−35.5761			−1.61211			−0.806054	+	0.591842i	$0.798401\pi$
$488$	9.51499	−	16.4804i	0.430723	−	0.746035i
$489$		0			0
$490$	20.2325	+	42.2953i	0.914011	+	1.91071i
$491$	−15.6990	+	27.1914i	−0.708485	+	1.22713i	0.256934	+	0.966429i	$0.417288\pi$
$491$	−15.6990	+	27.1914i	−0.708485	+	1.22713i	−0.965419	+	0.260703i	$0.916046\pi$
$492$		0			0
$493$	1.09598	−	1.89829i	0.0493605	−	0.0854949i
$494$	15.0601	+	10.8642i	0.677587	+	0.488804i
$495$		0			0
$496$	0.214909	−	0.372234i	0.00964972	−	0.0167138i
$497$	−18.2807	+	9.63115i	−0.820003	+	0.432016i
$498$		0			0
$499$	2.14606	+	3.71708i	0.0960708	+	0.166399i	0.910055	−	0.414488i	$-0.136039\pi$
$499$	2.14606	+	3.71708i	0.0960708	+	0.166399i	−0.813984	+	0.580887i	$0.802706\pi$
$500$	12.9010			0.576949
$501$		0			0
$502$	27.7909	+	48.1353i	1.24037	+	2.14839i
$503$	−7.83439	−	13.5696i	−0.349318	−	0.605037i	0.636810	−	0.771021i	$-0.280253\pi$
$503$	−7.83439	−	13.5696i	−0.349318	−	0.605037i	−0.986129	+	0.165984i	$0.946920\pi$
$504$		0			0
$505$	4.62969	−	8.01886i	0.206019	−	0.356835i
$506$	−30.8385	−	53.4138i	−1.37094	−	2.37453i
$507$		0			0
$508$	1.11447	−	1.93032i	0.0494467	−	0.0856442i
$509$	−1.70373			−0.0755165			−0.0377583	−	0.999287i	$-0.512022\pi$
$509$	−1.70373			−0.0755165			−0.0377583	+	0.999287i	$0.512022\pi$
$510$		0			0
$511$	35.5635	+	22.4108i	1.57324	+	0.991396i
$512$	−1.81234			−0.0800947
$513$		0			0
$514$	10.5018			0.463214
$515$	19.3778	−	33.5633i	0.853888	−	1.47898i
$516$		0			0
$517$	25.1785	−	43.6104i	1.10735	−	1.91798i
$518$	0.991658	−	25.6082i	0.0435710	−	1.12516i
$519$		0			0
$520$	26.4330	−	11.8760i	1.15916	−	0.520797i
$521$	−8.39696	+	14.5440i	−0.367878	+	0.637183i	−0.989234	−	0.146346i	$-0.953249\pi$
$521$	−8.39696	+	14.5440i	−0.367878	+	0.637183i	0.621356	+	0.783528i	$0.286582\pi$
$522$		0			0
$523$	−7.49051			−0.327537			−0.163769	−	0.986499i	$-0.552365\pi$
$523$	−7.49051			−0.327537			−0.163769	+	0.986499i	$0.552365\pi$
$524$	−10.7348	−	18.5933i	−0.468953	−	0.812251i
$525$		0			0
$526$	−26.2038	−	45.3863i	−1.14254	−	1.97894i
$527$	6.77706	−	11.7382i	0.295214	−	0.511325i
$528$		0			0
$529$	4.37426			0.190185
$530$	5.05788			0.219700
$531$		0			0
$532$	16.1776	+	10.1945i	0.701388	+	0.441989i
$533$	−1.57681	−	1.13749i	−0.0682990	−	0.0492702i
$534$		0			0
$535$	−8.61643	−	14.9241i	−0.372521	−	0.645225i
$536$	−18.2787	−	31.6597i	−0.789521	−	1.36749i
$537$		0			0
$538$	31.9360			1.37686
$539$	15.6157	+	32.6440i	0.672617	+	1.40608i
$540$		0			0
$541$	4.78963	+	8.29588i	0.205922	+	0.356668i	0.950426	−	0.310950i	$-0.100647\pi$
$541$	4.78963	+	8.29588i	0.205922	+	0.356668i	−0.744504	+	0.667618i	$0.767314\pi$
$542$	43.5681			1.87141
$543$		0			0
$544$	−29.4987			−1.26475
$545$	16.1195			0.690485
$546$		0			0
$547$	−30.1843			−1.29059			−0.645293	−	0.763935i	$-0.723265\pi$
$547$	−30.1843			−1.29059			−0.645293	+	0.763935i	$0.723265\pi$
$548$	−39.9971			−1.70859
$549$		0			0
$550$	−42.7611			−1.82334
$551$	−0.489889	−	0.848513i	−0.0208700	−	0.0361479i
$552$		0			0
$553$	−36.4801	+	19.2194i	−1.55129	+	0.817292i
$554$	−29.4619			−1.25172
$555$		0			0
$556$	−2.10433	−	3.64480i	−0.0892434	−	0.154574i
$557$	−2.33571	−	4.04557i	−0.0989673	−	0.171416i	0.812290	−	0.583254i	$-0.198221\pi$
$557$	−2.33571	−	4.04557i	−0.0989673	−	0.171416i	−0.911257	+	0.411837i	$0.864887\pi$
$558$		0			0
$559$	30.6751	−	13.7819i	1.29742	−	0.582912i
$560$	−1.10167	+	0.580414i	−0.0465542	+	0.0245270i
$561$		0			0
$562$	−44.7550			−1.88787
$563$	14.3818			0.606120			0.303060	−	0.952971i	$-0.401992\pi$
$563$	14.3818			0.606120			0.303060	+	0.952971i	$0.401992\pi$
$564$		0			0
$565$	2.33455	−	4.04355i	0.0982151	−	0.170114i
$566$	3.72524	+	6.45231i	0.156584	+	0.271211i
$567$		0			0
$568$	10.6848	+	18.5067i	0.448326	+	0.776523i
$569$	14.5756			0.611040			0.305520	−	0.952186i	$-0.401170\pi$
$569$	14.5756			0.611040			0.305520	+	0.952186i	$0.401170\pi$
$570$		0			0
$571$	−12.9575	+	22.4430i	−0.542254	+	0.939211i	0.456520	+	0.889713i	$0.349096\pi$
$571$	−12.9575	+	22.4430i	−0.542254	+	0.939211i	−0.998774	+	0.0494981i	$0.984238\pi$
$572$	54.4051	−	24.4435i	2.27479	−	1.02203i
$573$		0			0
$574$	−2.75245	−	1.73449i	−0.114885	−	0.0723963i
$575$	9.48940	−	16.4361i	0.395735	−	0.685433i
$576$		0			0
$577$	11.7875	−	20.4165i	0.490719	−	0.849950i	−0.509224	−	0.860634i	$-0.670068\pi$
$577$	11.7875	−	20.4165i	0.490719	−	0.849950i	0.999943	+	0.0106839i	$0.00340085\pi$
$578$	−19.4557			−0.809251
$579$		0			0
$580$	−4.07731			−0.169301
$581$	−1.35496	+	34.9900i	−0.0562133	+	1.45163i
$582$		0			0
$583$	3.90374			0.161676
$584$	21.7371	−	37.6497i	0.899487	−	1.55796i
$585$		0			0
$586$	21.6848	+	37.5592i	0.895791	+	1.55156i
$587$	23.7561	−	41.1468i	0.980521	−	1.69831i	0.320160	−	0.947364i	$-0.396263\pi$
$587$	23.7561	−	41.1468i	0.980521	−	1.69831i	0.660361	−	0.750948i	$-0.270403\pi$
$588$		0			0
$589$	−3.02926	−	5.24683i	−0.124818	−	0.216192i
$590$	−12.2160	−	21.1588i	−0.502925	−	0.871092i
$591$		0			0
$592$	0.680631			0.0279738
$593$	2.36887	+	4.10300i	0.0972779	+	0.168490i	0.910557	−	0.413384i	$-0.135653\pi$
$593$	2.36887	+	4.10300i	0.0972779	+	0.168490i	−0.813279	+	0.581874i	$0.802320\pi$
$594$		0			0
$595$	−34.7408	+	18.3031i	−1.42423	+	0.750353i
$596$	33.9078	−	58.7300i	1.38892	−	2.40568i
$597$		0			0
$598$	−4.35185	+	42.7965i	−0.177960	+	1.75008i
$599$	−1.07453	+	1.86114i	−0.0439041	+	0.0760441i	−0.887142	−	0.461496i	$-0.847313\pi$
$599$	−1.07453	+	1.86114i	−0.0439041	+	0.0760441i	0.843238	+	0.537540i	$0.180646\pi$
$600$		0			0
$601$	0.736182	−	1.27511i	0.0300295	−	0.0520126i	−0.850620	−	0.525781i	$-0.823773\pi$
$601$	0.736182	−	1.27511i	0.0300295	−	0.0520126i	0.880650	+	0.473768i	$0.157107\pi$
$602$	49.7848	−	26.2290i	2.02908	−	1.06901i
$603$		0			0
$604$	25.2910	−	43.8054i	1.02908	−	1.78242i
$605$	−46.1858			−1.87772
$606$		0			0
$607$	6.49295	−	11.2461i	0.263541	−	0.456466i	−0.703640	−	0.710557i	$-0.748443\pi$
$607$	6.49295	−	11.2461i	0.263541	−	0.456466i	0.967180	+	0.254091i	$0.0817763\pi$
$608$	−6.59277	+	11.4190i	−0.267372	+	0.463102i
$609$		0			0
$610$	46.5818			1.88604
$611$	−32.0371	+	14.3938i	−1.29608	+	0.582311i
$612$		0			0
$613$	20.0546	+	34.7356i	0.809997	+	1.40296i	0.912865	+	0.408262i	$0.133865\pi$
$613$	20.0546	+	34.7356i	0.809997	+	1.40296i	−0.102868	+	0.994695i	$0.532802\pi$
$614$	18.9419			0.764432
$615$		0			0
$616$	33.1109	−	17.4444i	1.33407	−	0.702853i
$617$	−8.82052	−	15.2776i	−0.355101	−	0.615052i	0.632035	−	0.774940i	$-0.282220\pi$
$617$	−8.82052	−	15.2776i	−0.355101	−	0.615052i	−0.987135	+	0.159888i	$0.948887\pi$
$618$		0			0
$619$	13.3825	−	23.1792i	0.537890	−	0.931652i	−0.461128	−	0.887334i	$-0.652555\pi$
$619$	13.3825	−	23.1792i	0.537890	−	0.931652i	0.999017	−	0.0443184i	$-0.0141116\pi$
$620$	−25.2123			−1.01255
$621$		0			0
$622$	12.3789	−	21.4409i	0.496349	−	0.859701i
$623$	0.409805	−	10.5826i	0.0164185	−	0.423985i
$624$		0			0
$625$	14.9895	+	25.9625i	0.599579	+	1.03850i
$626$	−1.29279	−	2.23918i	−0.0516702	−	0.0894955i
$627$		0			0
$628$	−8.83842	+	15.3086i	−0.352691	+	0.610880i
$629$	21.4634			0.855800
$630$		0			0
$631$	10.1224	+	17.5324i	0.402964	+	0.697955i	0.994082	−	0.108630i	$-0.0346465\pi$
$631$	10.1224	+	17.5324i	0.402964	+	0.697955i	−0.591118	+	0.806585i	$0.701313\pi$
$632$	21.3221	+	36.9309i	0.848147	+	1.46903i
$633$		0			0
$634$	−11.3723	−	19.6974i	−0.451653	−	0.782286i
$635$	2.04596			0.0811914
$636$		0			0
$637$	4.48742	−	24.8367i	0.177798	−	0.984067i
$638$	−5.11379			−0.202457
$639$		0			0
$640$	26.3623	+	45.6609i	1.04206	+	1.80491i
$641$	14.7765			0.583637			0.291819	−	0.956474i	$-0.405740\pi$
$641$	14.7765			0.583637			0.291819	+	0.956474i	$0.405740\pi$
$642$		0			0
$643$	4.74073	+	8.21118i	0.186956	+	0.323817i	0.944234	−	0.329276i	$-0.106804\pi$
$643$	4.74073	+	8.21118i	0.186956	+	0.323817i	−0.757278	+	0.653093i	$0.773471\pi$
$644$	−1.71404	+	44.2627i	−0.0675426	+	1.74419i
$645$		0			0
$646$	−13.0121	+	22.5377i	−0.511955	+	0.886732i
$647$	−24.9513	−	43.2169i	−0.980937	−	1.69903i	−0.658760	−	0.752353i	$-0.728919\pi$
$647$	−24.9513	−	43.2169i	−0.980937	−	1.69903i	−0.322177	−	0.946680i	$-0.604414\pi$
$648$		0			0
$649$	−9.42848	−	16.3306i	−0.370100	−	0.641033i
$650$	24.1874	+	17.4485i	0.948708	+	0.684388i
$651$		0			0
$652$	5.03784	−	8.72579i	0.197297	−	0.341728i
$653$	−41.4038			−1.62026			−0.810128	−	0.586252i	$-0.800603\pi$
$653$	−41.4038			−1.62026			−0.810128	+	0.586252i	$0.800603\pi$
$654$		0			0
$655$	9.85355	−	17.0668i	0.385010	−	0.666857i
$656$	0.0432028	−	0.0748294i	0.00168678	−	0.00292160i
$657$		0			0
$658$	−51.9953	+	27.3936i	−2.02699	+	1.06791i
$659$	−1.08993	−	1.88781i	−0.0424576	−	0.0735387i	0.844016	−	0.536318i	$-0.180185\pi$
$659$	−1.08993	−	1.88781i	−0.0424576	−	0.0735387i	−0.886473	+	0.462780i	$0.846852\pi$
$660$		0			0
$661$	−16.4283	−	28.4546i	−0.638986	−	1.10676i	−0.985656	−	0.168769i	$-0.946021\pi$
$661$	−16.4283	−	28.4546i	−0.638986	−	1.10676i	0.346669	−	0.937987i	$-0.387313\pi$
$662$	−1.88714	+	3.26862i	−0.0733457	+	0.127038i
$663$		0			0
$664$	36.2145			1.40539
$665$	−0.679178	+	17.5388i	−0.0263374	+	0.680127i
$666$		0			0
$667$	1.13483	−	1.96559i	0.0439409	−	0.0761079i
$668$	−21.4765	+	37.1984i	−0.830951	+	1.43925i
$669$		0			0
$670$	44.7429	−	77.4970i	1.72857	−	2.99397i
$671$	35.9525			1.38793
$672$		0			0
$673$	−5.61199	+	9.72024i	−0.216326	+	0.374688i	−0.953682	−	0.300817i	$-0.902741\pi$
$673$	−5.61199	+	9.72024i	−0.216326	+	0.374688i	0.737356	+	0.675505i	$0.236074\pi$
$674$	28.2947			1.08987
$675$		0			0
$676$	−40.7478	−	8.37363i	−1.56722	−	0.322063i
$677$	−10.0207	−	17.3564i	−0.385127	−	0.667059i	0.606660	−	0.794961i	$-0.292509\pi$
$677$	−10.0207	−	17.3564i	−0.385127	−	0.667059i	−0.991787	+	0.127902i	$0.959176\pi$
$678$		0			0
$679$	12.6239	−	6.65085i	0.484460	−	0.255236i
$680$	20.3055	+	35.1702i	0.778680	+	1.34871i
$681$		0			0
$682$	−31.6214			−1.21085
$683$	−14.6601			−0.560953			−0.280476	−	0.959861i	$-0.590492\pi$
$683$	−14.6601			−0.560953			−0.280476	+	0.959861i	$0.590492\pi$
$684$		0			0
$685$	−18.3568	−	31.7949i	−0.701376	−	1.21482i
$686$	4.89280	−	41.9481i	0.186808	−	1.60159i
$687$		0			0
$688$	0.747251	+	1.29428i	0.0284887	+	0.0493438i
$689$	−2.20811	−	1.59291i	−0.0841223	−	0.0606850i
$690$		0			0
$691$	28.9453			1.10113			0.550565	−	0.834792i	$-0.314412\pi$
$691$	28.9453			1.10113			0.550565	+	0.834792i	$0.314412\pi$
$692$	−20.5578	+	35.6071i	−0.781490	+	1.35358i
$693$		0			0
$694$	30.2036			1.14651
$695$	1.93157	−	3.34558i	0.0732688	−	0.126905i
$696$		0			0
$697$	1.36238	−	2.35971i	0.0516037	−	0.0893803i
$698$	−39.9215	+	69.1460i	−1.51105	+	2.61722i
$699$		0			0
$700$	25.9821	+	16.3730i	0.982032	+	0.618840i
$701$	37.6521			1.42210			0.711051	−	0.703141i	$-0.248220\pi$
$701$	37.6521			1.42210			0.711051	+	0.703141i	$0.248220\pi$
$702$		0			0
$703$	4.79692	−	8.30851i	0.180919	−	0.313362i
$704$	33.5815	+	58.1649i	1.26565	+	2.19217i
$705$		0			0
$706$	−26.3473	−	45.6349i	−0.991595	−	1.71749i
$707$	−7.37902	+	3.88761i	−0.277517	+	0.146209i
$708$		0			0
$709$	−11.2107	+	19.4175i	−0.421026	+	0.729239i	−0.996040	−	0.0889046i	$-0.971663\pi$
$709$	−11.2107	+	19.4175i	−0.421026	+	0.729239i	0.575014	+	0.818144i	$0.304997\pi$
$710$	−26.1545	+	45.3009i	−0.981560	+	1.70011i
$711$		0			0
$712$	−10.9530			−0.410480
$713$	7.01731	−	12.1543i	0.262800	−	0.455184i
$714$		0			0
$715$	44.4002	+	32.0298i	1.66047	+	1.19785i
$716$	29.8655	+	51.7286i	1.11613	+	1.93319i
$717$		0			0
$718$	−14.6958	−	25.4539i	−0.548444	−	0.949932i
$719$	4.18609	−	7.25051i	0.156115	−	0.270399i	−0.777350	−	0.629069i	$-0.783436\pi$
$719$	4.18609	−	7.25051i	0.156115	−	0.270399i	0.933464	+	0.358670i	$0.116770\pi$
$720$		0			0
$721$	−30.8853	+	16.2718i	−1.15023	+	0.605994i
$722$	−15.8470	−	27.4478i	−0.589763	−	1.02150i
$723$		0			0
$724$	2.81094			0.104468
$725$	−0.786789	−	1.36276i	−0.0292206	−	0.0506116i
$726$		0			0
$727$	20.0990			0.745432			0.372716	−	0.927945i	$-0.378427\pi$
$727$	20.0990			0.745432			0.372716	+	0.927945i	$0.378427\pi$
$728$	−25.8470	−	3.64355i	−0.957952	−	0.135039i
$729$		0			0
$730$	106.417			3.93866
$731$	23.5642	+	40.8144i	0.871553	+	1.50957i
$732$		0			0
$733$	5.77804	+	10.0079i	0.213417	+	0.369649i	0.952782	−	0.303656i	$-0.0982074\pi$
$733$	5.77804	+	10.0079i	0.213417	+	0.369649i	−0.739365	+	0.673305i	$0.764874\pi$
$734$	−30.2064	−	52.3191i	−1.11494	−	1.93113i
$735$		0			0
$736$	−30.5444			−1.12588
$737$	34.5332	−	59.8132i	1.27205	−	2.20325i
$738$		0			0
$739$	−12.1325	−	21.0141i	−0.446300	−	0.773015i	0.551841	−	0.833949i	$-0.313925\pi$
$739$	−12.1325	−	21.0141i	−0.446300	−	0.773015i	−0.998142	+	0.0609342i	$0.980592\pi$
$740$	−19.9622	−	34.5756i	−0.733826	−	1.27102i
$741$		0			0
$742$	−3.85445	−	2.42893i	−0.141501	−	0.0891689i
$743$	−0.777681	+	1.34698i	−0.0285303	+	0.0494160i	−0.879938	−	0.475088i	$-0.842416\pi$
$743$	−0.777681	+	1.34698i	−0.0285303	+	0.0494160i	0.851408	+	0.524504i	$0.175749\pi$
$744$		0			0
$745$	62.2483			2.28060
$746$	−14.1050	+	24.4306i	−0.516422	+	0.894468i
$747$		0			0
$748$	41.7933	+	72.3881i	1.52811	+	2.64677i
$749$	−0.600653	+	15.5110i	−0.0219474	+	0.566761i
$750$		0			0
$751$	−35.3585			−1.29025			−0.645125	−	0.764077i	$-0.723195\pi$
$751$	−35.3585			−1.29025			−0.645125	+	0.764077i	$0.723195\pi$
$752$	−0.780429	−	1.35174i	−0.0284593	−	0.0492930i
$753$		0			0
$754$	2.89256	+	2.08666i	0.105341	+	0.0759918i
$755$	46.4295			1.68974
$756$		0			0
$757$	9.73684	−	16.8647i	0.353891	−	0.612958i	−0.633036	−	0.774122i	$-0.718192\pi$
$757$	9.73684	−	16.8647i	0.353891	−	0.612958i	0.986928	+	0.161164i	$0.0515249\pi$
$758$	31.9655	−	55.3659i	1.16104	−	2.01098i
$759$		0			0
$760$	18.1526			0.658464
$761$	8.81978	−	15.2763i	0.319717	−	0.553766i	−0.660712	−	0.750640i	$-0.729746\pi$
$761$	8.81978	−	15.2763i	0.319717	−	0.553766i	0.980429	+	0.196874i	$0.0630789\pi$
$762$		0			0
$763$	−12.2842	−	7.74105i	−0.444717	−	0.280245i
$764$	−25.5216	+	44.2048i	−0.923341	+	1.59927i
$765$		0			0
$766$	29.9754	−	51.9190i	1.08306	−	1.87591i
$767$	−1.33052	+	13.0845i	−0.0480425	+	0.472454i
$768$		0			0
$769$	−2.32077	+	4.01969i	−0.0836890	+	0.144954i	−0.904832	−	0.425769i	$-0.860004\pi$
$769$	−2.32077	+	4.01969i	−0.0836890	+	0.144954i	0.821143	+	0.570723i	$0.193337\pi$
$770$	77.5044	+	48.8404i	2.79306	+	1.76009i
$771$		0			0
$772$	−6.32095	−	10.9482i	−0.227496	−	0.394034i
$773$	−20.0445			−0.720949			−0.360475	−	0.932769i	$-0.617385\pi$
$773$	−20.0445			−0.720949			−0.360475	+	0.932769i	$0.617385\pi$
$774$		0			0
$775$	−4.86516	−	8.42670i	−0.174762	−	0.302696i
$776$	−7.37848	−	12.7799i	−0.264872	−	0.458772i
$777$		0			0
$778$	−30.6032	+	53.0063i	−1.09718	+	1.90037i
$779$	−0.608965	−	1.05476i	−0.0218184	−	0.0377906i
$780$		0			0
$781$	−20.1864	+	34.9638i	−0.722326	+	1.25110i
$782$	−60.2855			−2.15580
$783$		0			0
$784$	1.11828	+	0.0867393i	0.0399386	+	0.00309783i
$785$	−16.2257			−0.579119
$786$		0			0
$787$	−10.1166			−0.360620			−0.180310	−	0.983610i	$-0.557710\pi$
$787$	−10.1166			−0.360620			−0.180310	+	0.983610i	$0.557710\pi$
$788$	21.5150	−	37.2650i	0.766438	−	1.32751i
$789$		0			0
$790$	−52.1925	+	90.4001i	−1.85693	+	3.21629i
$791$	−3.72091	+	1.96035i	−0.132300	+	0.0697020i
$792$		0			0
$793$	−20.3362	−	14.6703i	−0.722159	−	0.520958i
$794$	27.9618	−	48.4313i	0.992328	−	1.71876i
$795$		0			0
$796$	66.6520			2.36242
$797$	4.44188	+	7.69357i	0.157340	+	0.272520i	0.933908	−	0.357512i	$-0.116375\pi$
$797$	4.44188	+	7.69357i	0.157340	+	0.272520i	−0.776569	+	0.630032i	$0.783042\pi$
$798$		0			0
$799$	−24.6104	−	42.6265i	−0.870655	−	1.50802i
$800$	−10.5884	+	18.3396i	−0.374355	+	0.648402i
$801$		0			0
$802$	7.21887			0.254907
$803$	82.1338			2.89844
$804$		0			0
$805$	−35.9723	+	18.9519i	−1.26786	+	0.667967i
$806$	17.8863	+	12.9030i	0.630020	+	0.454489i
$807$		0			0
$808$	4.31294	+	7.47022i	0.151729	+	0.262802i
$809$	−20.8784	−	36.1625i	−0.734047	−	1.27141i	−0.955140	−	0.296153i	$-0.904296\pi$
$809$	−20.8784	−	36.1625i	−0.734047	−	1.27141i	0.221094	−	0.975253i	$-0.429037\pi$
$810$		0			0
$811$	−31.3690			−1.10151			−0.550757	−	0.834666i	$-0.685661\pi$
$811$	−31.3690			−1.10151			−0.550757	+	0.834666i	$0.685661\pi$
$812$	3.10719	+	1.95804i	0.109041	+	0.0687137i
$813$		0			0
$814$	−25.0367	−	43.3649i	−0.877537	−	1.51994i
$815$	9.24851			0.323961
$816$		0			0
$817$	21.0658			0.736998
$818$	−43.4826			−1.52033
$819$		0			0
$820$	−5.06838			−0.176995
$821$	−30.5508			−1.06623			−0.533114	−	0.846043i	$-0.678978\pi$
$821$	−30.5508			−1.06623			−0.533114	+	0.846043i	$0.678978\pi$
$822$		0			0
$823$	3.34874			0.116730			0.0583650	−	0.998295i	$-0.481411\pi$
$823$	3.34874			0.116730			0.0583650	+	0.998295i	$0.481411\pi$
$824$	18.0520	+	31.2670i	0.628872	+	1.08924i
$825$		0			0
$826$	−0.851581	+	21.9909i	−0.0296303	+	0.765161i
$827$	48.2646			1.67833			0.839163	−	0.543880i	$-0.183045\pi$
$827$	48.2646			1.67833			0.839163	+	0.543880i	$0.183045\pi$
$828$		0			0
$829$	−24.9146	−	43.1534i	−0.865320	−	1.49878i	−0.866729	−	0.498780i	$-0.833782\pi$
$829$	−24.9146	−	43.1534i	−0.865320	−	1.49878i	0.00140835	−	0.999999i	$-0.499552\pi$
$830$	44.3231	+	76.7699i	1.53848	+	2.66472i
$831$		0			0
$832$	4.73894	−	46.6032i	0.164293	−	1.61568i
$833$	35.2645	+	2.73528i	1.22184	+	0.0947719i
$834$		0			0
$835$	−39.4268			−1.36442
$836$	37.3621			1.29220
$837$		0			0
$838$	17.7988	−	30.8285i	0.614850	−	1.06495i
$839$	−16.4441	−	28.4819i	−0.567712	−	0.983305i	−0.996792	−	0.0800390i	$-0.974496\pi$
$839$	−16.4441	−	28.4819i	−0.567712	−	0.983305i	0.429080	−	0.903266i	$-0.358838\pi$
$840$		0			0
$841$	14.4059	+	24.9518i	0.496755	+	0.860406i
$842$	41.1659			1.41867
$843$		0			0
$844$	22.9697	−	39.7846i	0.790649	−	1.36944i
$845$	−12.0449	−	36.2347i	−0.414356	−	1.24651i
$846$		0			0
$847$	35.1967	+	22.1797i	1.20937	+	0.762103i
$848$	0.0604999	−	0.104789i	0.00207757	−	0.00359846i
$849$		0			0
$850$	−20.8982	+	36.1967i	−0.716802	+	1.24154i
$851$	22.2242			0.761837
$852$		0			0
$853$	−17.9823			−0.615701			−0.307850	−	0.951435i	$-0.599610\pi$
$853$	−17.9823			−0.615701			−0.307850	+	0.951435i	$0.599610\pi$
$854$	−35.4986	−	22.3699i	−1.21474	−	0.765482i
$855$		0			0
$856$	16.0538			0.548708
$857$	−23.5502	+	40.7901i	−0.804459	+	1.39336i	0.112196	+	0.993686i	$0.464211\pi$
$857$	−23.5502	+	40.7901i	−0.804459	+	1.39336i	−0.916656	+	0.399678i	$0.869122\pi$
$858$		0			0
$859$	−13.8486	−	23.9866i	−0.472510	−	0.818411i	0.526995	−	0.849868i	$-0.323319\pi$
$859$	−13.8486	−	23.9866i	−0.472510	−	0.818411i	−0.999505	+	0.0314573i	$0.989985\pi$
$860$	43.8322	−	75.9197i	1.49467	−	2.58884i
$861$		0			0
$862$	19.9718	+	34.5922i	0.680242	+	1.17821i
$863$	−18.5569	−	32.1414i	−0.631683	−	1.09411i	−0.987208	−	0.159440i	$-0.949031\pi$
$863$	−18.5569	−	32.1414i	−0.631683	−	1.09411i	0.355525	−	0.934667i	$-0.384302\pi$
$864$		0			0
$865$	−37.7402			−1.28320
$866$	6.90854	+	11.9659i	0.234762	+	0.406619i
$867$		0			0
$868$	19.2135	+	12.1077i	0.652149	+	0.410961i
$869$	−40.2829	+	69.7720i	−1.36650	+	2.36685i
$870$		0			0
$871$	−43.9399	+	19.7416i	−1.48885	+	0.668919i
$872$	−7.50833	+	13.0048i	−0.254264	+	0.440399i
$873$		0			0
$874$	−13.4734	+	23.3366i	−0.455745	+	0.789373i
$875$	0.412749	−	10.6587i	0.0139535	−	0.360329i
$876$		0			0
$877$	−14.1491	+	24.5069i	−0.477780	+	0.827538i	−0.999676	−	0.0254707i	$-0.991892\pi$
$877$	−14.1491	+	24.5069i	−0.477780	+	0.827538i	0.521896	+	0.853009i	$0.325225\pi$
$878$	−53.3198			−1.79945
$879$		0			0
$880$	−1.21652	+	2.10707i	−0.0410088	+	0.0710293i
$881$	9.74919	−	16.8861i	0.328458	−	0.568907i	−0.653748	−	0.756713i	$-0.726804\pi$
$881$	9.74919	−	16.8861i	0.328458	−	0.568907i	0.982206	+	0.187806i	$0.0601376\pi$
$882$		0			0
$883$	36.8164			1.23897			0.619485	−	0.785009i	$-0.287342\pi$
$883$	36.8164			1.23897			0.619485	+	0.785009i	$0.287342\pi$
$884$	5.89777	−	57.9993i	0.198364	−	1.95073i
$885$		0			0
$886$	10.1409	+	17.5646i	0.340692	+	0.590095i
$887$	22.1839			0.744863			0.372432	−	0.928060i	$-0.378524\pi$
$887$	22.1839			0.744863			0.372432	+	0.928060i	$0.378524\pi$
$888$		0			0
$889$	−1.55916	−	0.982526i	−0.0522926	−	0.0329529i
$890$	−13.4054	−	23.2189i	−0.449351	−	0.778298i
$891$		0			0
$892$	1.91015	−	3.30847i	0.0639565	−	0.110776i
$893$	−22.0011			−0.736238
$894$		0			0
$895$	−27.4137	+	47.4820i	−0.916340	+	1.58715i
$896$	1.83772	−	47.4567i	0.0613941	−	1.58542i
$897$		0			0
$898$	−44.1635	−	76.4935i	−1.47376	−	2.55262i
$899$	−0.581823	−	1.00775i	−0.0194049	−	0.0336102i
$900$		0			0
$901$	1.90783	−	3.30446i	0.0635592	−	0.110088i
$902$	−6.35678			−0.211658
$903$		0			0
$904$	2.17482	+	3.76690i	0.0723335	+	0.125285i
$905$	1.29009	+	2.23450i	0.0428839	+	0.0742771i
$906$		0			0
$907$	23.3042	+	40.3640i	0.773803	+	1.34027i	0.935465	+	0.353420i	$0.114981\pi$
$907$	23.3042	+	40.3640i	0.773803	+	1.34027i	−0.161662	+	0.986846i	$0.551685\pi$
$908$	50.8431			1.68729
$909$		0			0
$910$	−23.9104	−	59.2515i	−0.792623	−	1.96417i
$911$	−0.542513			−0.0179743			−0.00898714	−	0.999960i	$-0.502861\pi$
$911$	−0.542513			−0.0179743			−0.00898714	+	0.999960i	$0.502861\pi$
$912$		0			0
$913$	34.2092	+	59.2521i	1.13216	+	1.96096i
$914$	−51.0802			−1.68958
$915$		0			0
$916$	−14.0581	−	24.3494i	−0.464493	−	0.804526i
$917$	−15.7051	+	8.27416i	−0.518626	+	0.273237i
$918$		0			0
$919$	−16.8311	+	29.1522i	−0.555205	+	0.961644i	0.442682	+	0.896679i	$0.354027\pi$
$919$	−16.8311	+	29.1522i	−0.555205	+	0.961644i	−0.997888	+	0.0649652i	$0.979306\pi$
$920$	21.0253	+	36.4170i	0.693185	+	1.20063i
$921$		0			0
$922$	−3.20085	−	5.54403i	−0.105414	−	0.182583i
$923$	25.6851	−	11.5400i	0.845436	−	0.379843i
$924$		0			0
$925$	7.70412	−	13.3439i	0.253310	−	0.438746i
$926$	−86.0897			−2.82908
$927$		0			0
$928$	−1.26626	+	2.19322i	−0.0415669	+	0.0719961i
$929$	−21.3392	+	36.9606i	−0.700116	+	1.21264i	0.268309	+	0.963333i	$0.413535\pi$
$929$	−21.3392	+	36.9606i	−0.700116	+	1.21264i	−0.968425	+	0.249304i	$0.919798\pi$
$930$		0			0
$931$	8.94021	−	13.0396i	0.293004	−	0.427357i
$932$	−9.17471	−	15.8911i	−0.300528	−	0.520529i
$933$		0			0
$934$	−18.3428	−	31.7707i	−0.600195	−	1.03957i
$935$	−38.3623	+	66.4454i	−1.25458	+	2.17300i
$936$		0			0
$937$	−10.2859			−0.336026			−0.168013	−	0.985785i	$-0.553735\pi$
$937$	−10.2859			−0.336026			−0.168013	+	0.985785i	$0.553735\pi$
$938$	−71.3134	+	37.5712i	−2.32846	+	1.22674i
$939$		0			0
$940$	−45.7784	+	79.2905i	−1.49313	+	2.58617i
$941$	−5.84119	+	10.1172i	−0.190417	+	0.329813i	−0.945389	−	0.325945i	$-0.894317\pi$
$941$	−5.84119	+	10.1172i	−0.190417	+	0.329813i	0.754971	+	0.655758i	$0.227651\pi$
$942$		0			0
$943$	1.41067	−	2.44336i	0.0459379	−	0.0795667i
$944$	−0.584488			−0.0190235
$945$		0			0
$946$	54.9746	−	95.2188i	1.78738	−	3.09583i
$947$	−31.8808			−1.03599			−0.517993	−	0.855385i	$-0.673321\pi$
$947$	−31.8808			−1.03599			−0.517993	+	0.855385i	$0.673321\pi$
$948$		0			0
$949$	−46.4582	−	33.5144i	−1.50810	−	1.08792i
$950$	9.34122	+	16.1795i	0.303069	+	0.524931i
$951$		0			0
$952$	1.41550	−	36.5533i	0.0458766	−	1.18470i
$953$	−3.72492	−	6.45175i	−0.120662	−	0.208993i	0.799367	−	0.600843i	$-0.205168\pi$
$953$	−3.72492	−	6.45175i	−0.120662	−	0.208993i	−0.920029	+	0.391850i	$0.871835\pi$
$954$		0			0
$955$	−46.8529			−1.51612
$956$	36.9309			1.19443
$957$		0			0
$958$	−9.74674	−	16.8818i	−0.314903	−	0.545428i
$959$	−1.27965	+	33.0453i	−0.0413222	+	1.06709i
$960$		0			0
$961$	11.9023	+	20.6153i	0.383944	+	0.665010i
$962$	−3.53312	+	34.7451i	−0.113912	+	1.12023i
$963$		0			0
$964$	−18.1136			−0.583401
$965$	5.80203	−	10.0494i	0.186774	−	0.323502i
$966$		0			0
$967$	−51.0981			−1.64320			−0.821602	−	0.570061i	$-0.806920\pi$
$967$	−51.0981			−1.64320			−0.821602	+	0.570061i	$0.806920\pi$
$968$	21.5129	−	37.2615i	0.691451	−	1.19763i
$969$		0			0
$970$	18.0611	−	31.2828i	0.579908	−	1.00443i
$971$	2.50917	−	4.34602i	0.0805232	−	0.139470i	−0.822952	−	0.568112i	$-0.807674\pi$
$971$	2.50917	−	4.34602i	0.0805232	−	0.139470i	0.903475	+	0.428641i	$0.141008\pi$
$972$		0			0
$973$	−3.07863	+	1.62197i	−0.0986964	+	0.0519979i
$974$	81.1256			2.59943
$975$		0			0
$976$	0.557189	−	0.965080i	0.0178352	−	0.0308915i
$977$	−13.8306	−	23.9553i	−0.442479	−	0.766396i	0.555394	−	0.831588i	$-0.312568\pi$
$977$	−13.8306	−	23.9553i	−0.442479	−	0.766396i	−0.997873	+	0.0651911i	$0.979234\pi$
$978$		0			0
$979$	−10.3465	−	17.9206i	−0.330675	−	0.572746i
$980$	−28.3918	−	59.3519i	−0.906943	−	1.89593i
$981$		0			0
$982$	35.7990	−	62.0057i	1.14239	−	1.97868i
$983$	−2.23464	+	3.87050i	−0.0712738	+	0.123450i	−0.899460	−	0.437003i	$-0.856040\pi$
$983$	−2.23464	+	3.87050i	−0.0712738	+	0.123450i	0.828186	+	0.560453i	$0.189373\pi$
$984$		0			0
$985$	39.4974			1.25849
$986$	−2.49921	+	4.32875i	−0.0795910	+	0.137856i
$987$		0			0
$988$	−21.1335	−	15.2455i	−0.672347	−	0.485024i
$989$	24.3995	+	42.2613i	0.775860	+	1.34383i
$990$		0			0
$991$	−5.21216	−	9.02772i	−0.165570	−	0.286775i	0.771288	−	0.636487i	$-0.219613\pi$
$991$	−5.21216	−	9.02772i	−0.165570	−	0.286775i	−0.936857	+	0.349712i	$0.886280\pi$
$992$	−7.82998	+	13.5619i	−0.248602	+	0.430592i
$993$		0			0
$994$	41.6863	−	21.9623i	1.32221	−	0.696601i
$995$	30.5901	+	52.9836i	0.969771	+	1.67969i
$996$		0			0
$997$	−14.5120			−0.459599			−0.229800	−	0.973238i	$-0.573807\pi$
$997$	−14.5120			−0.459599			−0.229800	+	0.973238i	$0.573807\pi$
$998$	−4.89374	−	8.47621i	−0.154909	−	0.268310i
$999$		0			0

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.f.802.2		20
3.2	odd	2		273.2.l.c.256.9	yes	20
7.2	even	3		819.2.n.f.100.9		20
13.3	even	3		819.2.n.f.172.9		20
21.2	odd	6		273.2.j.c.100.2	✓	20
39.29	odd	6		273.2.j.c.172.2	yes	20
91.16	even	3	inner	819.2.s.f.289.2		20
273.107	odd	6		273.2.l.c.16.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.2	✓	20	21.2	odd	6
273.2.j.c.172.2	yes	20	39.29	odd	6
273.2.l.c.16.9	yes	20	273.107	odd	6
273.2.l.c.256.9	yes	20	3.2	odd	2
819.2.n.f.100.9		20	7.2	even	3
819.2.n.f.172.9		20	13.3	even	3
819.2.s.f.289.2		20	91.16	even	3	inner
819.2.s.f.802.2		20	1.1	even	1	trivial

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	819.2.s.f.802.2

Level	$819$
Weight	$2$
Character	819.802
Analytic conductor	$6.540$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$