LMFDB - Embedded newform 819.2.s.g.289.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [36,0,0,44,0,0,4,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.8
Character	$\chi$	$=$	819.289
Dual form			819.2.s.g.802.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.883334 q^{2} -1.21972 q^{4} +(-0.803460 + 1.39163i) q^{5} +(0.969010 + 2.46191i) q^{7} +2.84409 q^{8} +(0.709724 - 1.22928i) q^{10} +(2.72405 - 4.71819i) q^{11} +(-3.59111 + 0.322418i) q^{13} +(-0.855960 - 2.17469i) q^{14} -0.0728419 q^{16} +4.79892 q^{17} +(2.78511 + 4.82396i) q^{19} +(0.979997 - 1.69740i) q^{20} +(-2.40625 + 4.16774i) q^{22} -7.52514 q^{23} +(1.20890 + 2.09388i) q^{25} +(3.17215 - 0.284803i) q^{26} +(-1.18192 - 3.00285i) q^{28} +(0.471280 + 0.816281i) q^{29} +(-0.198822 - 0.344370i) q^{31} -5.62384 q^{32} -4.23905 q^{34} +(-4.20464 - 0.629543i) q^{35} -3.86353 q^{37} +(-2.46019 - 4.26117i) q^{38} +(-2.28511 + 3.95793i) q^{40} +(2.37243 + 4.10917i) q^{41} +(-5.30416 + 9.18707i) q^{43} +(-3.32258 + 5.75487i) q^{44} +6.64722 q^{46} +(-0.143183 + 0.247999i) q^{47} +(-5.12204 + 4.77124i) q^{49} +(-1.06787 - 1.84960i) q^{50} +(4.38015 - 0.393259i) q^{52} +(-0.0573682 - 0.0993647i) q^{53} +(4.37733 + 7.58176i) q^{55} +(2.75595 + 7.00190i) q^{56} +(-0.416298 - 0.721049i) q^{58} +9.23340 q^{59} +(5.19136 + 8.99170i) q^{61} +(0.175626 + 0.304194i) q^{62} +5.11341 q^{64} +(2.43662 - 5.25656i) q^{65} +(-2.38954 + 4.13881i) q^{67} -5.85334 q^{68} +(3.71411 + 0.556097i) q^{70} +(-6.93681 + 12.0149i) q^{71} +(-3.63370 - 6.29375i) q^{73} +3.41279 q^{74} +(-3.39706 - 5.88388i) q^{76} +(14.2554 + 2.13440i) q^{77} +(-2.55189 + 4.42000i) q^{79} +(0.0585256 - 0.101369i) q^{80} +(-2.09565 - 3.62977i) q^{82} -2.73115 q^{83} +(-3.85574 + 6.67834i) q^{85} +(4.68535 - 8.11526i) q^{86} +(7.74744 - 13.4190i) q^{88} -4.28738 q^{89} +(-4.27358 - 8.52857i) q^{91} +9.17857 q^{92} +(0.126478 - 0.219066i) q^{94} -8.95091 q^{95} +(0.544831 - 0.943675i) q^{97} +(4.52447 - 4.21460i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) $ 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

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 $

$2$	−0.883334			−0.624612			−0.312306	−	0.949982i	$-0.601101\pi$
$2$	−0.883334			−0.624612			−0.312306	+	0.949982i	$0.601101\pi$
$3$		0			0
$3$		0			0
$4$	−1.21972			−0.609860
$5$	−0.803460	+	1.39163i	−0.359318	+	0.622358i	−0.987847	−	0.155429i	$-0.950324\pi$
$5$	−0.803460	+	1.39163i	−0.359318	+	0.622358i	0.628529	+	0.777786i	$0.283657\pi$
$6$		0			0
$7$	0.969010	+	2.46191i	0.366251	+	0.930516i
$7$	0.969010	+	2.46191i	0.366251	+	0.930516i
$8$	2.84409			1.00554
$9$		0			0
$10$	0.709724	−	1.22928i	0.224435	−	0.388732i
$11$	2.72405	−	4.71819i	0.821332	−	1.42259i	−0.0833590	−	0.996520i	$-0.526565\pi$
$11$	2.72405	−	4.71819i	0.821332	−	1.42259i	0.904691	−	0.426069i	$-0.140102\pi$
$12$		0			0
$13$	−3.59111	+	0.322418i	−0.995994	+	0.0894225i
$13$	−3.59111	+	0.322418i	−0.995994	+	0.0894225i
$14$	−0.855960	−	2.17469i	−0.228765	−	0.581211i
$15$		0			0
$16$	−0.0728419			−0.0182105
$17$	4.79892			1.16391			0.581954	−	0.813222i	$-0.302288\pi$
$17$	4.79892			1.16391			0.581954	+	0.813222i	$0.302288\pi$
$18$		0			0
$19$	2.78511	+	4.82396i	0.638949	+	1.10669i	0.985664	+	0.168721i	$0.0539638\pi$
$19$	2.78511	+	4.82396i	0.638949	+	1.10669i	−0.346715	+	0.937971i	$0.612703\pi$
$20$	0.979997	−	1.69740i	0.219134	−	0.379551i
$21$		0			0
$22$	−2.40625	+	4.16774i	−0.513013	+	0.888565i
$23$	−7.52514			−1.56910			−0.784550	−	0.620065i	$-0.787106\pi$
$23$	−7.52514			−1.56910			−0.784550	+	0.620065i	$0.787106\pi$
$24$		0			0
$25$	1.20890	+	2.09388i	0.241781	+	0.418776i
$26$	3.17215	−	0.284803i	0.622109	−	0.0558544i
$27$		0			0
$28$	−1.18192	−	3.00285i	−0.223362	−	0.567485i
$29$	0.471280	+	0.816281i	0.0875145	+	0.151580i	0.906460	−	0.422292i	$-0.138774\pi$
$29$	0.471280	+	0.816281i	0.0875145	+	0.151580i	−0.818945	+	0.573871i	$0.805441\pi$
$30$		0			0
$31$	−0.198822	−	0.344370i	−0.0357095	−	0.0618506i	0.847618	−	0.530606i	$-0.178036\pi$
$31$	−0.198822	−	0.344370i	−0.0357095	−	0.0618506i	−0.883328	+	0.468756i	$0.844702\pi$
$32$	−5.62384			−0.994163
$33$		0			0
$34$	−4.23905			−0.726991
$35$	−4.20464	−	0.629543i	−0.710715	−	0.106412i
$36$		0			0
$37$	−3.86353			−0.635161			−0.317580	−	0.948231i	$-0.602870\pi$
$37$	−3.86353			−0.635161			−0.317580	+	0.948231i	$0.602870\pi$
$38$	−2.46019	−	4.26117i	−0.399095	−	0.691253i
$39$		0			0
$40$	−2.28511	+	3.95793i	−0.361308	+	0.625804i
$41$	2.37243	+	4.10917i	0.370511	+	0.641744i	0.989644	−	0.143542i	$-0.0458492\pi$
$41$	2.37243	+	4.10917i	0.370511	+	0.641744i	−0.619133	+	0.785286i	$0.712516\pi$
$42$		0			0
$43$	−5.30416	+	9.18707i	−0.808877	+	1.40102i	0.104766	+	0.994497i	$0.466591\pi$
$43$	−5.30416	+	9.18707i	−0.808877	+	1.40102i	−0.913643	+	0.406519i	$0.866743\pi$
$44$	−3.32258	+	5.75487i	−0.500898	+	0.867580i
$45$		0			0
$46$	6.64722			0.980079
$47$	−0.143183	+	0.247999i	−0.0208853	+	0.0361744i	−0.876279	−	0.481804i	$-0.839982\pi$
$47$	−0.143183	+	0.247999i	−0.0208853	+	0.0361744i	0.855394	+	0.517978i	$0.173315\pi$
$48$		0			0
$49$	−5.12204	+	4.77124i	−0.731720	+	0.681605i
$50$	−1.06787	−	1.84960i	−0.151019	−	0.261573i
$51$		0			0
$52$	4.38015	−	0.393259i	0.607417	−	0.0545352i
$53$	−0.0573682	−	0.0993647i	−0.00788013	−	0.0136488i	0.862058	−	0.506809i	$-0.169175\pi$
$53$	−0.0573682	−	0.0993647i	−0.00788013	−	0.0136488i	−0.869939	+	0.493160i	$0.835842\pi$
$54$		0			0
$55$	4.37733	+	7.58176i	0.590239	+	1.02232i
$56$	2.75595	+	7.00190i	0.368279	+	0.935669i
$57$		0			0
$58$	−0.416298	−	0.721049i	−0.0546626	−	0.0946784i
$59$	9.23340			1.20209			0.601043	−	0.799217i	$-0.294752\pi$
$59$	9.23340			1.20209			0.601043	+	0.799217i	$0.294752\pi$
$60$		0			0
$61$	5.19136	+	8.99170i	0.664686	+	1.15127i	0.979370	+	0.202073i	$0.0647678\pi$
$61$	5.19136	+	8.99170i	0.664686	+	1.15127i	−0.314685	+	0.949196i	$0.601899\pi$
$62$	0.175626	+	0.304194i	0.0223046	+	0.0386326i
$63$		0			0
$64$	5.11341			0.639176
$65$	2.43662	−	5.25656i	0.302226	−	0.651996i
$66$		0			0
$67$	−2.38954	+	4.13881i	−0.291929	+	0.505636i	−0.974266	−	0.225402i	$-0.927630\pi$
$67$	−2.38954	+	4.13881i	−0.291929	+	0.505636i	0.682337	+	0.731038i	$0.260964\pi$
$68$	−5.85334			−0.709821
$69$		0			0
$70$	3.71411	+	0.556097i	0.443921	+	0.0664663i
$71$	−6.93681	+	12.0149i	−0.823248	+	1.42591i	0.0800027	+	0.996795i	$0.474507\pi$
$71$	−6.93681	+	12.0149i	−0.823248	+	1.42591i	−0.903251	+	0.429113i	$0.858826\pi$
$72$		0			0
$73$	−3.63370	−	6.29375i	−0.425292	−	0.736628i	0.571156	−	0.820842i	$-0.306495\pi$
$73$	−3.63370	−	6.29375i	−0.425292	−	0.736628i	−0.996448	+	0.0842143i	$0.973162\pi$
$74$	3.41279			0.396729
$75$		0			0
$76$	−3.39706	−	5.88388i	−0.389669	−	0.674927i
$77$	14.2554	+	2.13440i	1.62456	+	0.243237i
$78$		0			0
$79$	−2.55189	+	4.42000i	−0.287110	+	0.497289i	−0.973119	−	0.230304i	$-0.926028\pi$
$79$	−2.55189	+	4.42000i	−0.287110	+	0.497289i	0.686009	+	0.727593i	$0.259361\pi$
$80$	0.0585256	−	0.101369i	0.00654336	−	0.0113334i
$81$		0			0
$82$	−2.09565	−	3.62977i	−0.231426	−	0.400841i
$83$	−2.73115			−0.299782			−0.149891	−	0.988703i	$-0.547892\pi$
$83$	−2.73115			−0.299782			−0.149891	+	0.988703i	$0.547892\pi$
$84$		0			0
$85$	−3.85574	+	6.67834i	−0.418214	+	0.724367i
$86$	4.68535	−	8.11526i	0.505234	−	0.875091i
$87$		0			0
$88$	7.74744	−	13.4190i	0.825880	−	1.43047i
$89$	−4.28738			−0.454461			−0.227230	−	0.973841i	$-0.572967\pi$
$89$	−4.28738			−0.454461			−0.227230	+	0.973841i	$0.572967\pi$
$90$		0			0
$91$	−4.27358	−	8.52857i	−0.447993	−	0.894037i
$92$	9.17857			0.956932
$93$		0			0
$94$	0.126478	−	0.219066i	0.0130452	−	0.0225950i
$95$	−8.95091			−0.918344
$96$		0			0
$97$	0.544831	−	0.943675i	0.0553192	−	0.0958157i	−0.837040	−	0.547142i	$-0.815716\pi$
$97$	0.544831	−	0.943675i	0.0553192	−	0.0958157i	0.892359	+	0.451326i	$0.149049\pi$
$98$	4.52447	−	4.21460i	0.457041	−	0.425739i
$99$		0			0
$100$	−1.47452	−	2.55395i	−0.147452	−	0.255395i
$101$	−4.59397	+	7.95699i	−0.457117	+	0.791750i	−0.998807	−	0.0488281i	$-0.984451\pi$
$101$	−4.59397	+	7.95699i	−0.457117	+	0.791750i	0.541690	+	0.840578i	$0.317785\pi$
$102$		0			0
$103$	7.28534	−	12.6186i	0.717846	−	1.24335i	−0.244006	−	0.969774i	$-0.578462\pi$
$103$	7.28534	−	12.6186i	0.717846	−	1.24335i	0.961852	−	0.273571i	$-0.0882050\pi$
$104$	−10.2134	+	0.916984i	−1.00151	+	0.0899177i
$105$		0			0
$106$	0.0506753	+	0.0877723i	0.00492202	+	0.00852520i
$107$	0.290702			0.0281032			0.0140516	−	0.999901i	$-0.495527\pi$
$107$	0.290702			0.0281032			0.0140516	+	0.999901i	$0.495527\pi$
$108$		0			0
$109$	1.08666	+	1.88215i	0.104083	+	0.180278i	0.913363	−	0.407145i	$-0.133476\pi$
$109$	1.08666	+	1.88215i	0.104083	+	0.180278i	−0.809280	+	0.587423i	$0.800142\pi$
$110$	−3.86665	−	6.69723i	−0.368670	−	0.638556i
$111$		0			0
$112$	−0.0705845	−	0.179331i	−0.00666961	−	0.0169451i
$113$	6.13563	−	10.6272i	0.577191	−	0.999725i	−0.418609	−	0.908167i	$-0.637482\pi$
$113$	6.13563	−	10.6272i	0.577191	−	0.999725i	0.995800	−	0.0915578i	$-0.0291846\pi$
$114$		0			0
$115$	6.04615	−	10.4722i	0.563807	−	0.976542i
$116$	−0.574830	−	0.995635i	−0.0533716	−	0.0924424i
$117$		0			0
$118$	−8.15618			−0.750837
$119$	4.65020	+	11.8145i	0.426283	+	1.08304i
$120$		0			0
$121$	−9.34089	−	16.1789i	−0.849172	−	1.47081i
$122$	−4.58571	−	7.94268i	−0.415170	−	0.719096i
$123$		0			0
$124$	0.242507	+	0.420035i	0.0217778	+	0.0377202i
$125$	−11.9198			−1.06614
$126$		0			0
$127$	3.64434	+	6.31219i	0.323383	+	0.560116i	0.981184	−	0.193076i	$-0.0618464\pi$
$127$	3.64434	+	6.31219i	0.323383	+	0.560116i	−0.657801	+	0.753192i	$0.728513\pi$
$128$	6.73082			0.594926
$129$		0			0
$130$	−2.15235	+	4.64330i	−0.188774	+	0.407244i
$131$	−10.5108	+	18.2052i	−0.918329	+	1.59059i	−0.116376	+	0.993205i	$0.537128\pi$
$131$	−10.5108	+	18.2052i	−0.918329	+	1.59059i	−0.801953	+	0.597388i	$0.796205\pi$
$132$		0			0
$133$	−9.17737	+	11.5312i	−0.795779	+	0.999879i
$134$	2.11077	−	3.65595i	0.182342	−	0.315826i
$135$		0			0
$136$	13.6485			1.17035
$137$	−0.545710			−0.0466232			−0.0233116	−	0.999728i	$-0.507421\pi$
$137$	−0.545710			−0.0466232			−0.0233116	+	0.999728i	$0.507421\pi$
$138$		0			0
$139$	1.17958	−	2.04308i	0.100050	−	0.173292i	−0.811655	−	0.584137i	$-0.801433\pi$
$139$	1.17958	−	2.04308i	0.100050	−	0.173292i	0.911705	+	0.410845i	$0.134766\pi$
$140$	5.12849	+	0.767866i	0.433437	+	0.0648965i
$141$		0			0
$142$	6.12753	−	10.6132i	0.514210	−	0.890639i
$143$	−8.26112	+	17.8218i	−0.690830	+	1.49033i
$144$		0			0
$145$	−1.51462			−0.125782
$146$	3.20977	+	5.55948i	0.265642	+	0.460106i
$147$		0			0
$148$	4.71243			0.387359
$149$	7.50416	+	12.9976i	0.614765	+	1.06480i	0.990426	+	0.138047i	$0.0440824\pi$
$149$	7.50416	+	12.9976i	0.614765	+	1.06480i	−0.375661	+	0.926757i	$0.622584\pi$
$150$		0			0
$151$	−3.49582	−	6.05495i	−0.284486	−	0.492744i	0.687998	−	0.725712i	$-0.258490\pi$
$151$	−3.49582	−	6.05495i	−0.284486	−	0.492744i	−0.972484	+	0.232968i	$0.925156\pi$
$152$	7.92111	+	13.7198i	0.642487	+	1.11282i
$153$		0			0
$154$	−12.5923	−	1.88539i	−1.01472	−	0.151929i
$155$	0.638982			0.0513243
$156$		0			0
$157$	2.04859	+	3.54826i	0.163495	+	0.283182i	0.936120	−	0.351681i	$-0.114390\pi$
$157$	2.04859	+	3.54826i	0.163495	+	0.283182i	−0.772625	+	0.634863i	$0.781057\pi$
$158$	2.25417	−	3.90434i	0.179332	−	0.310612i
$159$		0			0
$160$	4.51853	−	7.82632i	0.357221	−	0.618725i
$161$	−7.29194	−	18.5263i	−0.574685	−	1.46007i
$162$		0			0
$163$	−1.29159	−	2.23711i	−0.101166	−	0.175224i	0.811000	−	0.585047i	$-0.198924\pi$
$163$	−1.29159	−	2.23711i	−0.101166	−	0.175224i	−0.912165	+	0.409823i	$0.865590\pi$
$164$	−2.89370	−	5.01203i	−0.225960	−	0.391374i
$165$		0			0
$166$	2.41252			0.187248
$167$	−9.57784	−	16.5893i	−0.741155	−	1.28372i	−0.951970	−	0.306193i	$-0.900945\pi$
$167$	−9.57784	−	16.5893i	−0.741155	−	1.28372i	0.210814	−	0.977526i	$-0.432389\pi$
$168$		0			0
$169$	12.7921	−	2.31567i	0.984007	−	0.178129i
$170$	3.40591	−	5.89920i	0.261221	−	0.452448i
$171$		0			0
$172$	6.46959	−	11.2057i	0.493302	−	0.854424i
$173$	−3.56228	−	6.17004i	−0.270835	−	0.469100i	0.698241	−	0.715863i	$-0.253966\pi$
$173$	−3.56228	−	6.17004i	−0.270835	−	0.469100i	−0.969076	+	0.246763i	$0.920633\pi$
$174$		0			0
$175$	−3.98352	+	5.00521i	−0.301126	+	0.378358i
$176$	−0.198425	+	0.343682i	−0.0149568	+	0.0259060i
$177$		0			0
$178$	3.78719			0.283862
$179$	12.1275	−	21.0054i	0.906450	−	1.57002i	0.0874919	−	0.996165i	$-0.472115\pi$
$179$	12.1275	−	21.0054i	0.906450	−	1.57002i	0.818958	−	0.573853i	$-0.194552\pi$
$180$		0			0
$181$	21.6218			1.60714			0.803569	−	0.595212i	$-0.202932\pi$
$181$	21.6218			1.60714			0.803569	+	0.595212i	$0.202932\pi$
$182$	3.77500	+	7.53358i	0.279822	+	0.558426i
$183$		0			0
$184$	−21.4022			−1.57779
$185$	3.10419	−	5.37662i	0.228225	−	0.395297i
$186$		0			0
$187$	13.0725	−	22.6422i	0.955955	−	1.65576i
$188$	0.174643	−	0.302490i	0.0127371	−	0.0220613i
$189$		0			0
$190$	7.90665			0.573609
$191$	−1.77703	−	3.07790i	−0.128581	−	0.222709i	0.794546	−	0.607204i	$-0.207709\pi$
$191$	−1.77703	−	3.07790i	−0.128581	−	0.222709i	−0.923127	+	0.384495i	$0.874376\pi$
$192$		0			0
$193$	−9.27331	+	16.0618i	−0.667507	+	1.15616i	0.311091	+	0.950380i	$0.399305\pi$
$193$	−9.27331	+	16.0618i	−0.667507	+	1.15616i	−0.978599	+	0.205777i	$0.934028\pi$
$194$	−0.481268	+	0.833581i	−0.0345530	+	0.0598476i
$195$		0			0
$196$	6.24746	−	5.81958i	0.446247	−	0.415684i
$197$	−5.77712	−	10.0063i	−0.411603	−	0.712917i	0.583462	−	0.812140i	$-0.301698\pi$
$197$	−5.77712	−	10.0063i	−0.411603	−	0.712917i	−0.995065	+	0.0992233i	$0.968364\pi$
$198$		0			0
$199$	3.48474			0.247026			0.123513	−	0.992343i	$-0.460584\pi$
$199$	3.48474			0.247026			0.123513	+	0.992343i	$0.460584\pi$
$200$	3.43823	+	5.95519i	0.243119	+	0.421095i
$201$		0			0
$202$	4.05801	−	7.02869i	0.285521	−	0.494537i
$203$	−1.55294	+	1.95124i	−0.108995	+	0.136950i
$204$		0			0
$205$	−7.62461			−0.532526
$206$	−6.43539	+	11.1464i	−0.448375	+	0.776608i
$207$		0			0
$208$	0.261583	−	0.0234855i	0.0181375	−	0.00162843i
$209$	30.3471			2.09916
$210$		0			0
$211$	8.69054	+	15.0525i	0.598282	+	1.03625i	0.993075	+	0.117484i	$0.0374829\pi$
$211$	8.69054	+	15.0525i	0.598282	+	1.03625i	−0.394793	+	0.918770i	$0.629184\pi$
$212$	0.0699732	+	0.121197i	0.00480578	+	0.00832386i
$213$		0			0
$214$	−0.256787			−0.0175536
$215$	−8.52336	−	14.7629i	−0.581289	−	1.00682i
$216$		0			0
$217$	0.655148	−	0.823180i	0.0444744	−	0.0558811i
$218$	−0.959886	−	1.66257i	−0.0650117	−	0.112604i
$219$		0			0
$220$	−5.33912	−	9.24763i	−0.359963	−	0.623475i
$221$	−17.2334	+	1.54725i	−1.15925	+	0.104080i
$222$		0			0
$223$	−12.3847	−	21.4509i	−0.829341	−	1.43646i	−0.898556	−	0.438859i	$-0.855383\pi$
$223$	−12.3847	−	21.4509i	−0.829341	−	1.43646i	0.0692152	−	0.997602i	$-0.477950\pi$
$224$	−5.44955	−	13.8454i	−0.364114	−	0.925085i
$225$		0			0
$226$	−5.41981	+	9.38739i	−0.360520	+	0.624440i
$227$	1.77646			0.117908			0.0589538	−	0.998261i	$-0.481224\pi$
$227$	1.77646			0.117908			0.0589538	+	0.998261i	$0.481224\pi$
$228$		0			0
$229$	−11.5552	+	20.0142i	−0.763589	+	1.32258i	0.177400	+	0.984139i	$0.443231\pi$
$229$	−11.5552	+	20.0142i	−0.763589	+	1.32258i	−0.940989	+	0.338437i	$0.890102\pi$
$230$	−5.34078	+	9.25050i	−0.352160	+	0.609960i
$231$		0			0
$232$	1.34036	+	2.32158i	0.0879991	+	0.152419i
$233$	−12.6393	+	21.8920i	−0.828031	+	1.43419i	0.0715498	+	0.997437i	$0.477206\pi$
$233$	−12.6393	+	21.8920i	−0.828031	+	1.43419i	−0.899581	+	0.436755i	$0.856128\pi$
$234$		0			0
$235$	−0.230083	−	0.398515i	−0.0150090	−	0.0259963i
$236$	−11.2622			−0.733104
$237$		0			0
$238$	−4.10768	−	10.4362i	−0.266261	−	0.676476i
$239$	21.6715			1.40181			0.700906	−	0.713254i	$-0.252779\pi$
$239$	21.6715			1.40181			0.700906	+	0.713254i	$0.252779\pi$
$240$		0			0
$241$	16.6386			1.07179			0.535894	−	0.844285i	$-0.319975\pi$
$241$	16.6386			1.07179			0.535894	+	0.844285i	$0.319975\pi$
$242$	8.25113	+	14.2914i	0.530403	+	0.918684i
$243$		0			0
$244$	−6.33201	−	10.9674i	−0.405365	−	0.702113i
$245$	−2.52446	−	10.9615i	−0.161282	−	0.700305i
$246$		0			0
$247$	−11.5570	−	16.4254i	−0.735352	−	1.04512i
$248$	−0.565468	−	0.979419i	−0.0359072	−	0.0621932i
$249$		0			0
$250$	10.5292			0.665925
$251$	14.3915	−	24.9268i	0.908384	−	1.57337i	0.0920752	−	0.995752i	$-0.470650\pi$
$251$	14.3915	−	24.9268i	0.908384	−	1.57337i	0.816309	−	0.577616i	$-0.196017\pi$
$252$		0			0
$253$	−20.4989	+	35.5051i	−1.28875	+	2.23218i
$254$	−3.21917	−	5.57577i	−0.201989	−	0.349855i
$255$		0			0
$256$	−16.1724			−1.01077
$257$	30.3644			1.89408			0.947038	−	0.321121i	$-0.104059\pi$
$257$	30.3644			1.89408			0.947038	+	0.321121i	$0.104059\pi$
$258$		0			0
$259$	−3.74380	−	9.51168i	−0.232628	−	0.591027i
$260$	−2.97200	+	6.41153i	−0.184316	+	0.397626i
$261$		0			0
$262$	9.28451	−	16.0812i	0.573599	−	0.993503i
$263$	9.30715	−	16.1204i	0.573903	−	0.994030i	−0.422257	−	0.906476i	$-0.638762\pi$
$263$	9.30715	−	16.1204i	0.573903	−	0.994030i	0.996160	−	0.0875532i	$-0.0279048\pi$
$264$		0			0
$265$	0.184372			0.0113259
$266$	8.10668	−	10.1859i	0.497053	−	0.624536i
$267$		0			0
$268$	2.91457	−	5.04819i	0.178036	−	0.308367i
$269$	0.0363342			0.00221534			0.00110767	−	0.999999i	$-0.499647\pi$
$269$	0.0363342			0.00221534			0.00110767	+	0.999999i	$0.499647\pi$
$270$		0			0
$271$	11.0401			0.670636			0.335318	−	0.942105i	$-0.391156\pi$
$271$	11.0401			0.670636			0.335318	+	0.942105i	$0.391156\pi$
$272$	−0.349562			−0.0211953
$273$		0			0
$274$	0.482045			0.0291214
$275$	13.1724			0.794328
$276$		0			0
$277$	19.6810			1.18252			0.591258	−	0.806482i	$-0.298631\pi$
$277$	19.6810			1.18252			0.591258	+	0.806482i	$0.298631\pi$
$278$	−1.04196	+	1.80473i	−0.0624926	+	0.108240i
$279$		0			0
$280$	−11.9584	−	1.79048i	−0.714650	−	0.107001i
$281$	−23.2580			−1.38746			−0.693729	−	0.720236i	$-0.744033\pi$
$281$	−23.2580			−1.38746			−0.693729	+	0.720236i	$0.744033\pi$
$282$		0			0
$283$	1.33837	−	2.31813i	0.0795581	−	0.137799i	−0.823501	−	0.567314i	$-0.807982\pi$
$283$	1.33837	−	2.31813i	0.0795581	−	0.137799i	0.903059	+	0.429516i	$0.141316\pi$
$284$	8.46097	−	14.6548i	0.502066	−	0.869604i
$285$		0			0
$286$	7.29734	−	15.7426i	0.431500	−	0.930881i
$287$	−7.81751	+	9.82254i	−0.461453	+	0.579806i
$288$		0			0
$289$	6.02960			0.354682
$290$	1.33792			0.0785651
$291$		0			0
$292$	4.43209	+	7.67661i	0.259369	+	0.449240i
$293$	−12.8781	+	22.3056i	−0.752349	+	1.30311i	0.194333	+	0.980936i	$0.437746\pi$
$293$	−12.8781	+	22.3056i	−0.752349	+	1.30311i	−0.946682	+	0.322170i	$0.895588\pi$
$294$		0			0
$295$	−7.41867	+	12.8495i	−0.431932	+	0.748128i
$296$	−10.9882			−0.638678
$297$		0			0
$298$	−6.62868	−	11.4812i	−0.383989	−	0.665089i
$299$	27.0236	−	2.42624i	1.56281	−	0.140313i
$300$		0			0
$301$	−27.7576	−	4.15602i	−1.59992	−	0.239549i
$302$	3.08798	+	5.34854i	0.177693	+	0.307774i
$303$		0			0
$304$	−0.202873	−	0.351386i	−0.0116356	−	0.0201534i
$305$	−16.6842			−0.955335
$306$		0			0
$307$	17.3467			0.990028			0.495014	−	0.868885i	$-0.335163\pi$
$307$	17.3467			0.990028			0.495014	+	0.868885i	$0.335163\pi$
$308$	−17.3876	−	2.60337i	−0.990751	−	0.148341i
$309$		0			0
$310$	−0.564435			−0.0320578
$311$	8.58893	+	14.8765i	0.487034	+	0.843567i	0.999889	−	0.0149083i	$-0.00474562\pi$
$311$	8.58893	+	14.8765i	0.487034	+	0.843567i	−0.512855	+	0.858475i	$0.671412\pi$
$312$		0			0
$313$	−1.53678	+	2.66179i	−0.0868641	+	0.150453i	−0.906184	−	0.422884i	$-0.861018\pi$
$313$	−1.53678	+	2.66179i	−0.0868641	+	0.150453i	0.819320	+	0.573337i	$0.194351\pi$
$314$	−1.80959	−	3.13430i	−0.102121	−	0.176879i
$315$		0			0
$316$	3.11259	−	5.39116i	0.175097	−	0.303277i
$317$	−1.19776	+	2.07459i	−0.0672731	+	0.116520i	−0.897700	−	0.440607i	$-0.854763\pi$
$317$	−1.19776	+	2.07459i	−0.0672731	+	0.116520i	0.830427	+	0.557128i	$0.188097\pi$
$318$		0			0
$319$	5.13516			0.287514
$320$	−4.10842	+	7.11600i	−0.229668	+	0.397796i
$321$		0			0
$322$	6.44122	+	16.3649i	0.358955	+	0.911979i
$323$	13.3655	+	23.1498i	0.743678	+	1.28809i
$324$		0			0
$325$	−5.01640	−	7.12958i	−0.278260	−	0.395478i
$326$	1.14091	+	1.97611i	0.0631892	+	0.109447i
$327$		0			0
$328$	6.74740	+	11.6868i	0.372563	+	0.645298i
$329$	−0.749298	−	0.112189i	−0.0413102	−	0.00618519i
$330$		0			0
$331$	12.3711	+	21.4274i	0.679977	+	1.17775i	0.974987	+	0.222261i	$0.0713436\pi$
$331$	12.3711	+	21.4274i	0.679977	+	1.17775i	−0.295010	+	0.955494i	$0.595323\pi$
$332$	3.33124			0.182825
$333$		0			0
$334$	8.46044	+	14.6539i	0.462934	+	0.801826i
$335$	−3.83981	−	6.65074i	−0.209791	−	0.363369i
$336$		0			0
$337$	25.9308			1.41254			0.706271	−	0.707941i	$-0.250376\pi$
$337$	25.9308			1.41254			0.706271	+	0.707941i	$0.250376\pi$
$338$	−11.2997	+	2.04551i	−0.614622	+	0.111261i
$339$		0			0
$340$	4.70292	−	8.14570i	0.255052	−	0.441763i
$341$	−2.16640			−0.117317
$342$		0			0
$343$	−16.7097	−	7.98664i	−0.902238	−	0.431238i
$344$	−15.0855	+	26.1289i	−0.813356	+	1.40877i
$345$		0			0
$346$	3.14668	+	5.45021i	0.169167	+	0.293005i
$347$	−14.5655			−0.781919			−0.390959	−	0.920408i	$-0.627857\pi$
$347$	−14.5655			−0.781919			−0.390959	+	0.920408i	$0.627857\pi$
$348$		0			0
$349$	2.29742	+	3.97924i	0.122978	+	0.213004i	0.920941	−	0.389703i	$-0.127422\pi$
$349$	2.29742	+	3.97924i	0.122978	+	0.213004i	−0.797963	+	0.602707i	$0.794089\pi$
$350$	3.51878	−	4.42127i	0.188087	−	0.236327i
$351$		0			0
$352$	−15.3196	+	26.5343i	−0.816538	+	1.41428i
$353$	0.425776	−	0.737465i	0.0226618	−	0.0392513i	−0.854472	−	0.519497i	$-0.826119\pi$
$353$	0.425776	−	0.737465i	0.0226618	−	0.0392513i	0.877134	+	0.480246i	$0.159453\pi$
$354$		0			0
$355$	−11.1469	−	19.3070i	−0.591616	−	1.02471i
$356$	5.22940			0.277158
$357$		0			0
$358$	−10.7126	+	18.5548i	−0.566180	+	0.980652i
$359$	−4.81661	+	8.34262i	−0.254211	+	0.440307i	−0.964681	−	0.263421i	$-0.915149\pi$
$359$	−4.81661	+	8.34262i	−0.254211	+	0.440307i	0.710470	+	0.703728i	$0.248482\pi$
$360$		0			0
$361$	−6.01371	+	10.4161i	−0.316511	+	0.548214i
$362$	−19.0993			−1.00384
$363$		0			0
$364$	5.21257	+	10.4025i	0.273213	+	0.545238i
$365$	11.6781			0.611261
$366$		0			0
$367$	12.1901	−	21.1138i	0.636316	−	1.10213i	−0.349919	−	0.936780i	$-0.613791\pi$
$367$	12.1901	−	21.1138i	0.636316	−	1.10213i	0.986235	−	0.165351i	$-0.0528758\pi$
$368$	0.548146			0.0285741
$369$		0			0
$370$	−2.74204	+	4.74935i	−0.142552	+	0.246907i
$371$	0.189037	−	0.237521i	0.00981431	−	0.0123315i
$372$		0			0
$373$	8.85917	+	15.3445i	0.458710	+	0.794510i	0.998893	−	0.0470380i	$-0.0149782\pi$
$373$	8.85917	+	15.3445i	0.458710	+	0.794510i	−0.540183	+	0.841548i	$0.681645\pi$
$374$	−11.5474	+	20.0006i	−0.597101	+	1.03421i
$375$		0			0
$376$	−0.407224	+	0.705333i	−0.0210010	+	0.0363747i
$377$	−1.95560	−	2.77940i	−0.100719	−	0.143147i
$378$		0			0
$379$	−0.0992792	−	0.171957i	−0.00509963	−	0.00883282i	0.863464	−	0.504410i	$-0.168290\pi$
$379$	−0.0992792	−	0.171957i	−0.00509963	−	0.00883282i	−0.868564	+	0.495577i	$0.834957\pi$
$380$	10.9176			0.560062
$381$		0			0
$382$	1.56971	+	2.71881i	0.0803132	+	0.139107i
$383$	−14.7402	−	25.5308i	−0.753191	−	1.30456i	−0.946269	−	0.323381i	$-0.895180\pi$
$383$	−14.7402	−	25.5308i	−0.753191	−	1.30456i	0.193078	−	0.981183i	$-0.438153\pi$
$384$		0			0
$385$	−14.4240	+	18.1234i	−0.735113	+	0.923655i
$386$	8.19143	−	14.1880i	0.416933	−	0.722149i
$387$		0			0
$388$	−0.664542	+	1.15102i	−0.0337370	+	0.0584342i
$389$	−4.94238	−	8.56045i	−0.250589	−	0.434032i	0.713099	−	0.701063i	$-0.247291\pi$
$389$	−4.94238	−	8.56045i	−0.250589	−	0.434032i	−0.963688	+	0.267031i	$0.913957\pi$
$390$		0			0
$391$	−36.1125			−1.82629
$392$	−14.5675	+	13.5698i	−0.735772	+	0.685380i
$393$		0			0
$394$	5.10313	+	8.83888i	0.257092	+	0.445296i
$395$	−4.10068	−	7.10259i	−0.206328	−	0.357370i
$396$		0			0
$397$	6.17210	+	10.6904i	0.309769	+	0.536535i	0.978312	−	0.207138i	$-0.0664151\pi$
$397$	6.17210	+	10.6904i	0.309769	+	0.536535i	−0.668543	+	0.743673i	$0.733082\pi$
$398$	−3.07819			−0.154296
$399$		0			0
$400$	−0.0880588	−	0.152522i	−0.00440294	−	0.00762612i
$401$	6.81721			0.340435			0.170218	−	0.985407i	$-0.445553\pi$
$401$	6.81721			0.340435			0.170218	+	0.985407i	$0.445553\pi$
$402$		0			0
$403$	0.825022	+	1.17257i	0.0410973	+	0.0584096i
$404$	5.60336	−	9.70530i	0.278778	−	0.482857i
$405$		0			0
$406$	1.37176	−	1.72359i	0.0680795	−	0.0855405i
$407$	−10.5244	+	18.2289i	−0.521678	+	0.903572i
$408$		0			0
$409$	−4.79971			−0.237330			−0.118665	−	0.992934i	$-0.537862\pi$
$409$	−4.79971			−0.237330			−0.118665	+	0.992934i	$0.537862\pi$
$410$	6.73508			0.332622
$411$		0			0
$412$	−8.88607	+	15.3911i	−0.437785	+	0.758267i
$413$	8.94725	+	22.7318i	0.440266	+	1.11856i
$414$		0			0
$415$	2.19437	−	3.80076i	0.107717	−	0.186572i
$416$	20.1958	−	1.81322i	0.990180	−	0.0889006i
$417$		0			0
$418$	−26.8067			−1.31116
$419$	−3.90401	−	6.76195i	−0.190724	−	0.330343i	0.754767	−	0.655993i	$-0.227750\pi$
$419$	−3.90401	−	6.76195i	−0.190724	−	0.330343i	−0.945490	+	0.325651i	$0.894417\pi$
$420$		0			0
$421$	−6.33152			−0.308579			−0.154290	−	0.988026i	$-0.549309\pi$
$421$	−6.33152			−0.308579			−0.154290	+	0.988026i	$0.549309\pi$
$422$	−7.67666	−	13.2964i	−0.373694	−	0.647257i
$423$		0			0
$424$	−0.163160	−	0.282602i	−0.00792377	−	0.0137244i
$425$	5.80142	+	10.0484i	0.281410	+	0.487417i
$426$		0			0
$427$	−17.1063	+	21.4937i	−0.827832	+	1.04015i
$428$	−0.354575			−0.0171390
$429$		0			0
$430$	7.52898	+	13.0406i	0.363080	+	0.628872i
$431$	−1.70489	+	2.95296i	−0.0821218	+	0.142239i	−0.904161	−	0.427192i	$-0.859503\pi$
$431$	−1.70489	+	2.95296i	−0.0821218	+	0.142239i	0.822039	+	0.569431i	$0.192836\pi$
$432$		0			0
$433$	−7.48575	+	12.9657i	−0.359742	+	0.623092i	−0.987918	−	0.154980i	$-0.950469\pi$
$433$	−7.48575	+	12.9657i	−0.359742	+	0.623092i	0.628175	+	0.778072i	$0.283802\pi$
$434$	−0.578715	+	0.727144i	−0.0277792	+	0.0349040i
$435$		0			0
$436$	−1.32542	−	2.29570i	−0.0634763	−	0.109944i
$437$	−20.9584	−	36.3010i	−1.00258	−	1.73651i
$438$		0			0
$439$	22.9999			1.09773			0.548863	−	0.835913i	$-0.315061\pi$
$439$	22.9999			1.09773			0.548863	+	0.835913i	$0.315061\pi$
$440$	12.4495	+	21.5632i	0.593508	+	1.02799i
$441$		0			0
$442$	15.2229	−	1.36674i	0.724078	−	0.0650094i
$443$	8.44703	−	14.6307i	0.401331	−	0.695125i	−0.592556	−	0.805529i	$-0.701881\pi$
$443$	8.44703	−	14.6307i	0.401331	−	0.695125i	0.993887	+	0.110404i	$0.0352145\pi$
$444$		0			0
$445$	3.44474	−	5.96646i	0.163296	−	0.282837i
$446$	10.9398	+	18.9483i	0.518016	+	0.897230i
$447$		0			0
$448$	4.95495	+	12.5888i	0.234099	+	0.594764i
$449$	7.11000	−	12.3149i	0.335542	−	0.581175i	−0.648047	−	0.761600i	$-0.724414\pi$
$449$	7.11000	−	12.3149i	0.335542	−	0.581175i	0.983589	+	0.180425i	$0.0577473\pi$
$450$		0			0
$451$	25.8505			1.21725
$452$	−7.48375	+	12.9622i	−0.352006	+	0.609692i
$453$		0			0
$454$	−1.56920			−0.0736464
$455$	15.3023	+	0.905104i	0.717383	+	0.0424319i
$456$		0			0
$457$	−30.2116			−1.41324			−0.706619	−	0.707594i	$-0.749780\pi$
$457$	−30.2116			−1.41324			−0.706619	+	0.707594i	$0.749780\pi$
$458$	10.2071	−	17.6792i	0.476947	−	0.826096i
$459$		0			0
$460$	−7.37462	+	12.7732i	−0.343843	+	0.595554i
$461$	1.39657	−	2.41893i	0.0650447	−	0.112661i	−0.831669	−	0.555272i	$-0.812614\pi$
$461$	1.39657	−	2.41893i	0.0650447	−	0.112661i	0.896714	+	0.442611i	$0.145948\pi$
$462$		0			0
$463$	−30.4337			−1.41437			−0.707186	−	0.707027i	$-0.750036\pi$
$463$	−30.4337			−1.41437			−0.707186	+	0.707027i	$0.750036\pi$
$464$	−0.0343289	−	0.0594595i	−0.00159368	−	0.00276034i
$465$		0			0
$466$	11.1648	−	19.3379i	0.517198	−	0.895813i
$467$	1.78815	−	3.09716i	0.0827456	−	0.143320i	−0.821683	−	0.569945i	$-0.806964\pi$
$467$	1.78815	−	3.09716i	0.0827456	−	0.143320i	0.904428	+	0.426626i	$0.140298\pi$
$468$		0			0
$469$	−12.5049	−	1.87230i	−0.577422	−	0.0864548i
$470$	0.203240	+	0.352022i	0.00937477	+	0.0162376i
$471$		0			0
$472$	26.2606			1.20874
$473$	28.8976	+	50.0521i	1.32871	+	2.30140i
$474$		0			0
$475$	−6.73386	+	11.6634i	−0.308971	+	0.535153i
$476$	−5.67194	−	14.4104i	−0.259973	−	0.660500i
$477$		0			0
$478$	−19.1432			−0.875588
$479$	12.8645	−	22.2820i	0.587795	−	1.01809i	−0.406725	−	0.913551i	$-0.633329\pi$
$479$	12.8645	−	22.2820i	0.587795	−	1.01809i	0.994521	−	0.104541i	$-0.0333373\pi$
$480$		0			0
$481$	13.8744	−	1.24567i	0.632616	−	0.0567977i
$482$	−14.6975			−0.669452
$483$		0			0
$484$	11.3933	+	19.7337i	0.517876	+	0.896988i
$485$	0.875501	+	1.51641i	0.0397544	+	0.0688567i
$486$		0			0
$487$	−22.6393			−1.02589			−0.512943	−	0.858423i	$-0.671445\pi$
$487$	−22.6393			−1.02589			−0.512943	+	0.858423i	$0.671445\pi$
$488$	14.7647	+	25.5732i	0.668366	+	1.15764i
$489$		0			0
$490$	2.22994	+	9.68268i	0.100739	+	0.437419i
$491$	−15.4236	−	26.7144i	−0.696057	−	1.20561i	−0.969823	−	0.243810i	$-0.921603\pi$
$491$	−15.4236	−	26.7144i	−0.696057	−	1.20561i	0.273766	−	0.961796i	$-0.411731\pi$
$492$		0			0
$493$	2.26163	+	3.91726i	0.101859	+	0.176425i
$494$	10.2087	+	14.5091i	0.459310	+	0.652795i
$495$		0			0
$496$	0.0144826	+	0.0250846i	0.000650287	+	0.00112633i
$497$	−36.3015	−	5.43527i	−1.62835	−	0.243805i
$498$		0			0
$499$	8.82877	−	15.2919i	0.395230	−	0.684558i	−0.597901	−	0.801570i	$-0.703998\pi$
$499$	8.82877	−	15.2919i	0.395230	−	0.684558i	0.993131	+	0.117012i	$0.0373316\pi$
$500$	14.5389			0.650197
$501$		0			0
$502$	−12.7125	+	22.0187i	−0.567387	+	0.982744i
$503$	−8.29312	+	14.3641i	−0.369772	+	0.640464i	−0.989530	−	0.144329i	$-0.953897\pi$
$503$	−8.29312	+	14.3641i	−0.369772	+	0.640464i	0.619758	+	0.784793i	$0.287231\pi$
$504$		0			0
$505$	−7.38215	−	12.7863i	−0.328501	−	0.568981i
$506$	18.1074	−	31.3629i	0.804970	−	1.39425i
$507$		0			0
$508$	−4.44508	−	7.69911i	−0.197219	−	0.341593i
$509$	−6.15538			−0.272833			−0.136416	−	0.990652i	$-0.543558\pi$
$509$	−6.15538			−0.272833			−0.136416	+	0.990652i	$0.543558\pi$
$510$		0			0
$511$	11.9736	−	15.0446i	0.529680	−	0.665532i
$512$	0.823989			0.0364155
$513$		0			0
$514$	−26.8219			−1.18306
$515$	11.7070	+	20.2770i	0.515870	+	0.893514i
$516$		0			0
$517$	0.780072	+	1.35113i	0.0343075	+	0.0594224i
$518$	3.30703	+	8.40199i	0.145302	+	0.369162i
$519$		0			0
$520$	6.92998	−	14.9501i	0.303900	−	0.655606i
$521$	6.12942	+	10.6165i	0.268535	+	0.465116i	0.968484	−	0.249077i	$-0.0801272\pi$
$521$	6.12942	+	10.6165i	0.268535	+	0.465116i	−0.699949	+	0.714193i	$0.746794\pi$
$522$		0			0
$523$	38.1472			1.66806			0.834030	−	0.551719i	$-0.186028\pi$
$523$	38.1472			1.66806			0.834030	+	0.551719i	$0.186028\pi$
$524$	12.8202	−	22.2052i	0.560052	−	0.970039i
$525$		0			0
$526$	−8.22132	+	14.2397i	−0.358467	+	0.620883i
$527$	−0.954130	−	1.65260i	−0.0415626	−	0.0719885i
$528$		0			0
$529$	33.6278			1.46208
$530$	−0.162863			−0.00707430
$531$		0			0
$532$	11.1938	−	14.0648i	0.485314	−	0.609787i
$533$	−9.84451	−	13.9915i	−0.426413	−	0.606041i
$534$		0			0
$535$	−0.233568	+	0.404551i	−0.0100980	+	0.0174903i
$536$	−6.79607	+	11.7711i	−0.293546	+	0.508436i
$537$		0			0
$538$	−0.0320952			−0.00138372
$539$	8.55893	+	37.1639i	0.368659	+	1.60076i
$540$		0			0
$541$	−3.75677	+	6.50691i	−0.161516	+	0.279754i	−0.935413	−	0.353558i	$-0.884972\pi$
$541$	−3.75677	+	6.50691i	−0.161516	+	0.279754i	0.773897	+	0.633312i	$0.218305\pi$
$542$	−9.75207			−0.418887
$543$		0			0
$544$	−26.9883			−1.15711
$545$	−3.49236			−0.149596
$546$		0			0
$547$	−11.4681			−0.490342			−0.245171	−	0.969480i	$-0.578844\pi$
$547$	−11.4681			−0.490342			−0.245171	+	0.969480i	$0.578844\pi$
$548$	0.665614			0.0284336
$549$		0			0
$550$	−11.6357			−0.496147
$551$	−2.62514	+	4.54687i	−0.111835	+	0.193703i
$552$		0			0
$553$	−13.3545	−	1.99950i	−0.567890	−	0.0850276i
$554$	−17.3849			−0.738614
$555$		0			0
$556$	−1.43875	+	2.49199i	−0.0610167	+	0.105684i
$557$	−5.02210	+	8.69854i	−0.212793	+	0.368569i	−0.952588	−	0.304264i	$-0.901589\pi$
$557$	−5.02210	+	8.69854i	−0.212793	+	0.368569i	0.739794	+	0.672833i	$0.234923\pi$
$558$		0			0
$559$	16.0857	−	34.7019i	0.680354	−	1.46773i
$560$	0.306274	+	0.0458571i	0.0129425	+	0.00193782i
$561$		0			0
$562$	20.5446			0.866622
$563$	−45.0566			−1.89891			−0.949455	−	0.313904i	$-0.898363\pi$
$563$	−45.0566			−1.89891			−0.949455	+	0.313904i	$0.898363\pi$
$564$		0			0
$565$	9.85947	+	17.0771i	0.414791	+	0.718439i
$566$	−1.18223	+	2.04769i	−0.0496929	+	0.0860707i
$567$		0			0
$568$	−19.7289	+	34.1715i	−0.827807	+	1.43380i
$569$	−20.5201			−0.860247			−0.430124	−	0.902770i	$-0.641530\pi$
$569$	−20.5201			−0.860247			−0.430124	+	0.902770i	$0.641530\pi$
$570$		0			0
$571$	17.0886	+	29.5984i	0.715136	+	1.23865i	0.962907	+	0.269834i	$0.0869687\pi$
$571$	17.0886	+	29.5984i	0.715136	+	1.23865i	−0.247771	+	0.968819i	$0.579698\pi$
$572$	10.0763	−	21.7376i	0.421310	−	0.908896i
$573$		0			0
$574$	6.90547	−	8.67659i	0.288229	−	0.362154i
$575$	−9.09717	−	15.7568i	−0.379378	−	0.657102i
$576$		0			0
$577$	11.3112	+	19.5916i	0.470893	+	0.815610i	0.999446	−	0.0332901i	$-0.0105985\pi$
$577$	11.3112	+	19.5916i	0.470893	+	0.815610i	−0.528553	+	0.848900i	$0.677265\pi$
$578$	−5.32615			−0.221539
$579$		0			0
$580$	1.84741			0.0767096
$581$	−2.64651	−	6.72385i	−0.109796	−	0.278952i
$582$		0			0
$583$	−0.625096			−0.0258888
$584$	−10.3346	−	17.9000i	−0.427647	−	0.740707i
$585$		0			0
$586$	11.3757	−	19.7033i	0.469926	−	0.813935i
$587$	18.3617	+	31.8035i	0.757870	+	1.31267i	0.943935	+	0.330132i	$0.107093\pi$
$587$	18.3617	+	31.8035i	0.757870	+	1.31267i	−0.186065	+	0.982538i	$0.559573\pi$
$588$		0			0
$589$	1.10748	−	1.91822i	0.0456331	−	0.0790388i
$590$	6.55317	−	11.3504i	0.269790	−	0.467289i
$591$		0			0
$592$	0.281427			0.0115666
$593$	23.5959	−	40.8692i	0.968966	−	1.67830i	0.270407	−	0.962746i	$-0.412842\pi$
$593$	23.5959	−	40.8692i	0.968966	−	1.67830i	0.698559	−	0.715553i	$-0.253825\pi$
$594$		0			0
$595$	−20.1777	−	3.02112i	−0.827207	−	0.123854i
$596$	−9.15298	−	15.8534i	−0.374921	−	0.649381i
$597$		0			0
$598$	−23.8709	+	2.14318i	−0.976152	+	0.0876411i
$599$	−4.87939	−	8.45135i	−0.199366	−	0.345313i	0.748957	−	0.662619i	$-0.230555\pi$
$599$	−4.87939	−	8.45135i	−0.199366	−	0.345313i	−0.948323	+	0.317306i	$0.897222\pi$
$600$		0			0
$601$	7.60715	+	13.1760i	0.310302	+	0.537459i	0.978428	−	0.206590i	$-0.0662365\pi$
$601$	7.60715	+	13.1760i	0.310302	+	0.537459i	−0.668126	+	0.744048i	$0.732903\pi$
$602$	24.5192	+	3.67115i	0.999329	+	0.149625i
$603$		0			0
$604$	4.26393	+	7.38534i	0.173497	+	0.300505i
$605$	30.0201			1.22049
$606$		0			0
$607$	−2.58581	−	4.47875i	−0.104955	−	0.181787i	0.808765	−	0.588132i	$-0.200136\pi$
$607$	−2.58581	−	4.47875i	−0.104955	−	0.181787i	−0.913720	+	0.406345i	$0.866803\pi$
$608$	−15.6630	−	27.1291i	−0.635219	−	1.10023i
$609$		0			0
$610$	14.7377			0.596713
$611$	0.434224	−	0.936757i	0.0175668	−	0.0378971i
$612$		0			0
$613$	−12.5030	+	21.6558i	−0.504991	+	0.874670i	0.494993	+	0.868897i	$0.335171\pi$
$613$	−12.5030	+	21.6558i	−0.504991	+	0.874670i	−0.999983	+	0.00577250i	$0.998163\pi$
$614$	−15.3229			−0.618383
$615$		0			0
$616$	40.5437	+	6.07042i	1.63355	+	0.244584i
$617$	18.0868	−	31.3273i	0.728148	−	1.26119i	−0.229518	−	0.973304i	$-0.573715\pi$
$617$	18.0868	−	31.3273i	0.728148	−	1.26119i	0.957665	−	0.287884i	$-0.0929518\pi$
$618$		0			0
$619$	−18.3433	−	31.7715i	−0.737278	−	1.27700i	−0.953717	−	0.300706i	$-0.902778\pi$
$619$	−18.3433	−	31.7715i	−0.737278	−	1.27700i	0.216439	−	0.976296i	$-0.430556\pi$
$620$	−0.779380			−0.0313006
$621$		0			0
$622$	−7.58690	−	13.1409i	−0.304207	−	0.526902i
$623$	−4.15451	−	10.5551i	−0.166447	−	0.422883i
$624$		0			0
$625$	3.53259	−	6.11863i	0.141304	−	0.244745i
$626$	1.35749	−	2.35125i	0.0542563	−	0.0939747i
$627$		0			0
$628$	−2.49871	−	4.32789i	−0.0997092	−	0.172701i
$629$	−18.5408			−0.739268
$630$		0			0
$631$	22.2013	−	38.4537i	0.883818	−	1.53082i	0.0367564	−	0.999324i	$-0.488297\pi$
$631$	22.2013	−	38.4537i	0.883818	−	1.53082i	0.847062	−	0.531494i	$-0.178369\pi$
$632$	−7.25780	+	12.5709i	−0.288700	+	0.500043i
$633$		0			0
$634$	1.05803	−	1.83256i	0.0420196	−	0.0727801i
$635$	−11.7123			−0.464790
$636$		0			0
$637$	16.8555	−	18.7855i	0.667838	−	0.744307i
$638$	−4.53606			−0.179585
$639$		0			0
$640$	−5.40795	+	9.36684i	−0.213768	+	0.370257i
$641$	14.8405			0.586166			0.293083	−	0.956087i	$-0.405319\pi$
$641$	14.8405			0.586166			0.293083	+	0.956087i	$0.405319\pi$
$642$		0			0
$643$	9.38674	−	16.2583i	0.370177	−	0.641165i	−0.619416	−	0.785063i	$-0.712630\pi$
$643$	9.38674	−	16.2583i	0.370177	−	0.641165i	0.989592	+	0.143898i	$0.0459638\pi$
$644$	8.89413	+	22.5968i	0.350478	+	0.890441i
$645$		0			0
$646$	−11.8062	−	20.4490i	−0.464510	−	0.804555i
$647$	14.9328	−	25.8644i	0.587070	−	1.01684i	−0.407544	−	0.913186i	$-0.633615\pi$
$647$	14.9328	−	25.8644i	0.587070	−	1.01684i	0.994614	−	0.103649i	$-0.0330520\pi$
$648$		0			0
$649$	25.1522	−	43.5649i	0.987311	−	1.71007i
$650$	4.43116	+	6.29780i	0.173804	+	0.247020i
$651$		0			0
$652$	1.57538	+	2.72865i	0.0616968	+	0.106862i
$653$	33.8568			1.32492			0.662459	−	0.749098i	$-0.269513\pi$
$653$	33.8568			1.32492			0.662459	+	0.749098i	$0.269513\pi$
$654$		0			0
$655$	−16.8900	−	29.2543i	−0.659945	−	1.14306i
$656$	−0.172812	−	0.299320i	−0.00674719	−	0.0116865i
$657$		0			0
$658$	0.661881	+	0.0991005i	0.0258028	+	0.00386334i
$659$	−3.37349	+	5.84305i	−0.131412	+	0.227613i	−0.924221	−	0.381857i	$-0.875285\pi$
$659$	−3.37349	+	5.84305i	−0.131412	+	0.227613i	0.792809	+	0.609470i	$0.208618\pi$
$660$		0			0
$661$	5.07786	−	8.79511i	0.197506	−	0.342090i	−0.750213	−	0.661196i	$-0.770049\pi$
$661$	5.07786	−	8.79511i	0.197506	−	0.342090i	0.947719	+	0.319106i	$0.103383\pi$
$662$	−10.9278	−	18.9275i	−0.424722	−	0.735640i
$663$		0			0
$664$	−7.76763			−0.301442
$665$	−8.67352	−	22.0364i	−0.336345	−	0.854534i
$666$		0			0
$667$	−3.54645	−	6.14263i	−0.137319	−	0.237844i
$668$	11.6823	+	20.2343i	0.452001	+	0.782889i
$669$		0			0
$670$	3.39183	+	5.87483i	0.131038	+	0.226964i
$671$	56.5661			2.18371
$672$		0			0
$673$	−11.6435	−	20.1671i	−0.448823	−	0.777384i	0.549487	−	0.835502i	$-0.314823\pi$
$673$	−11.6435	−	20.1671i	−0.448823	−	0.777384i	−0.998310	+	0.0581183i	$0.981490\pi$
$674$	−22.9056			−0.882290
$675$		0			0
$676$	−15.6028	+	2.82447i	−0.600107	+	0.108634i
$677$	−2.93169	+	5.07783i	−0.112674	+	0.195157i	−0.916848	−	0.399238i	$-0.869275\pi$
$677$	−2.93169	+	5.07783i	−0.112674	+	0.195157i	0.804174	+	0.594394i	$0.202608\pi$
$678$		0			0
$679$	2.85119	+	0.426897i	0.109419	+	0.0163828i
$680$	−10.9661	+	18.9938i	−0.420529	+	0.728378i
$681$		0			0
$682$	1.91366			0.0732778
$683$	−22.1089			−0.845974			−0.422987	−	0.906136i	$-0.639018\pi$
$683$	−22.1089			−0.845974			−0.422987	+	0.906136i	$0.639018\pi$
$684$		0			0
$685$	0.438457	−	0.759429i	0.0167526	−	0.0290163i
$686$	14.7602	+	7.05488i	0.563549	+	0.269356i
$687$		0			0
$688$	0.386365	−	0.669204i	0.0147300	−	0.0255132i
$689$	0.238052	+	0.338333i	0.00906907	+	0.0128895i
$690$		0			0
$691$	−31.2183			−1.18760			−0.593801	−	0.804612i	$-0.702373\pi$
$691$	−31.2183			−1.18760			−0.593801	+	0.804612i	$0.702373\pi$
$692$	4.34498	+	7.52573i	0.165171	+	0.286085i
$693$		0			0
$694$	12.8662			0.488396
$695$	1.89548	+	3.28307i	0.0718998	+	0.124534i
$696$		0			0
$697$	11.3851	+	19.7195i	0.431241	+	0.746931i
$698$	−2.02939	−	3.51500i	−0.0768134	−	0.133045i
$699$		0			0
$700$	4.85878	−	6.10495i	0.183644	−	0.230745i
$701$	−8.38392			−0.316656			−0.158328	−	0.987387i	$-0.550610\pi$
$701$	−8.38392			−0.316656			−0.158328	+	0.987387i	$0.550610\pi$
$702$		0			0
$703$	−10.7604	−	18.6375i	−0.405835	−	0.702927i
$704$	13.9292	−	24.1261i	0.524976	−	0.909285i
$705$		0			0
$706$	−0.376102	+	0.651429i	−0.0141548	+	0.0245168i
$707$	−24.0410	−	3.59956i	−0.904156	−	0.135375i
$708$		0			0
$709$	0.0600423	+	0.103996i	0.00225494	+	0.00390566i	0.867151	−	0.498046i	$-0.165949\pi$
$709$	0.0600423	+	0.103996i	0.00225494	+	0.00390566i	−0.864896	+	0.501952i	$0.832616\pi$
$710$	9.84645	+	17.0545i	0.369531	+	0.640046i
$711$		0			0
$712$	−12.1937			−0.456977
$713$	1.49616	+	2.59143i	0.0560318	+	0.0970499i
$714$		0			0
$715$	−18.1640	−	25.8156i	−0.679293	−	0.965448i
$716$	−14.7921	+	25.6207i	−0.552808	+	0.957491i
$717$		0			0
$718$	4.25468	−	7.36932i	0.158783	−	0.275021i
$719$	4.99233	+	8.64698i	0.186183	+	0.322478i	0.943974	−	0.330019i	$-0.107055\pi$
$719$	4.99233	+	8.64698i	0.186183	+	0.322478i	−0.757792	+	0.652496i	$0.773722\pi$
$720$		0			0
$721$	38.1254	+	5.70835i	1.41986	+	0.212590i
$722$	5.31212	−	9.20086i	0.197697	−	0.342421i
$723$		0			0
$724$	−26.3726			−0.980129
$725$	−1.13946	+	1.97361i	−0.0423186	+	0.0732980i
$726$		0			0
$727$	18.5606			0.688375			0.344188	−	0.938901i	$-0.388154\pi$
$727$	18.5606			0.688375			0.344188	+	0.938901i	$0.388154\pi$
$728$	−12.1545	−	24.2560i	−0.450474	−	0.898988i
$729$		0			0
$730$	−10.3157			−0.381801
$731$	−25.4542	+	44.0880i	−0.941458	+	1.63065i
$732$		0			0
$733$	−1.70446	+	2.95222i	−0.0629558	+	0.109043i	−0.895785	−	0.444487i	$-0.853386\pi$
$733$	−1.70446	+	2.95222i	−0.0629558	+	0.109043i	0.832830	+	0.553529i	$0.186719\pi$
$734$	−10.7679	+	18.6505i	−0.397450	+	0.688404i
$735$		0			0
$736$	42.3202			1.55994
$737$	13.0185	+	22.5486i	0.479541	+	0.830590i
$738$		0			0
$739$	19.1586	−	33.1836i	0.704759	−	1.22068i	−0.262019	−	0.965063i	$-0.584388\pi$
$739$	19.1586	−	33.1836i	0.704759	−	1.22068i	0.966778	−	0.255616i	$-0.0822783\pi$
$740$	−3.78625	+	6.55797i	−0.139185	+	0.241076i
$741$		0			0
$742$	−0.166983	+	0.209811i	−0.00613013	+	0.00770239i
$743$	−0.536089	−	0.928533i	−0.0196672	−	0.0340646i	0.856024	−	0.516936i	$-0.172927\pi$
$743$	−0.536089	−	0.928533i	−0.0196672	−	0.0340646i	−0.875691	+	0.482871i	$0.839594\pi$
$744$		0			0
$745$	−24.1172			−0.883585
$746$	−7.82561	−	13.5544i	−0.286516	−	0.496260i
$747$		0			0
$748$	−15.9448	+	27.6172i	−0.582999	+	1.00978i
$749$	0.281693	+	0.715683i	0.0102928	+	0.0261505i
$750$		0			0
$751$	16.0446			0.585475			0.292737	−	0.956193i	$-0.405434\pi$
$751$	16.0446			0.585475			0.292737	+	0.956193i	$0.405434\pi$
$752$	0.0104297	−	0.0180648i	0.000380332	−	0.000658754i
$753$		0			0
$754$	1.72745	+	2.45514i	0.0629100	+	0.0894110i
$755$	11.2350			0.408884
$756$		0			0
$757$	−15.9500	−	27.6263i	−0.579714	−	1.00409i	−0.995512	−	0.0946374i	$-0.969831\pi$
$757$	−15.9500	−	27.6263i	−0.579714	−	1.00409i	0.415798	−	0.909457i	$-0.363503\pi$
$758$	0.0876968	+	0.151895i	0.00318529	+	0.00551708i
$759$		0			0
$760$	−25.4572			−0.923430
$761$	−20.4859	−	35.4826i	−0.742612	−	1.28624i	−0.951302	−	0.308261i	$-0.900253\pi$
$761$	−20.4859	−	35.4826i	−0.742612	−	1.28624i	0.208690	−	0.977982i	$-0.433080\pi$
$762$		0			0
$763$	−3.58071	+	4.49909i	−0.129631	+	0.162878i
$764$	2.16747	+	3.75418i	0.0784165	+	0.135821i
$765$		0			0
$766$	13.0206	+	22.5523i	0.470452	+	0.814847i
$767$	−33.1581	+	2.97701i	−1.19727	+	0.107494i
$768$		0			0
$769$	−19.0536	−	33.0018i	−0.687090	−	1.19008i	−0.972775	−	0.231752i	$-0.925554\pi$
$769$	−19.0536	−	33.0018i	−0.687090	−	1.19008i	0.285685	−	0.958324i	$-0.407779\pi$
$770$	12.7412	−	16.0090i	0.459160	−	0.576926i
$771$		0			0
$772$	11.3108	−	19.5910i	0.407086	−	0.705094i
$773$	31.7019			1.14024			0.570119	−	0.821562i	$-0.306897\pi$
$773$	31.7019			1.14024			0.570119	+	0.821562i	$0.306897\pi$
$774$		0			0
$775$	0.480713	−	0.832619i	0.0172677	−	0.0299086i
$776$	1.54955	−	2.68390i	0.0556256	−	0.0963463i
$777$		0			0
$778$	4.36577	+	7.56174i	0.156521	+	0.271102i
$779$	−13.2150	+	22.8890i	−0.473475	+	0.820083i
$780$		0			0
$781$	37.7924	+	65.4584i	1.35232	+	2.34229i
$782$	31.8994			1.14072
$783$		0			0
$784$	0.373099	−	0.347546i	0.0133250	−	0.0124124i
$785$	−6.58384			−0.234987
$786$		0			0
$787$	1.72653			0.0615442			0.0307721	−	0.999526i	$-0.490203\pi$
$787$	1.72653			0.0615442			0.0307721	+	0.999526i	$0.490203\pi$
$788$	7.04647	+	12.2048i	0.251020	+	0.434780i
$789$		0			0
$790$	3.62227	+	6.27396i	0.128875	+	0.223218i
$791$	32.1088	+	4.80751i	1.14166	+	0.170935i
$792$		0			0
$793$	−21.5418	−	30.6164i	−0.764972	−	1.08722i
$794$	−5.45202	−	9.44318i	−0.193485	−	0.335126i
$795$		0			0
$796$	−4.25040			−0.150652
$797$	−2.02629	+	3.50963i	−0.0717747	+	0.124317i	−0.899679	−	0.436552i	$-0.856200\pi$
$797$	−2.02629	+	3.50963i	−0.0717747	+	0.124317i	0.827904	+	0.560869i	$0.189533\pi$
$798$		0			0
$799$	−0.687121	+	1.19013i	−0.0243086	+	0.0421037i
$800$	−6.79867	−	11.7756i	−0.240369	−	0.416332i
$801$		0			0
$802$	−6.02187			−0.212640
$803$	−39.5935			−1.39722
$804$		0			0
$805$	31.6406	+	4.73740i	1.11518	+	0.166971i
$806$	−0.728770	−	1.03577i	−0.0256698	−	0.0364833i
$807$		0			0
$808$	−13.0657	+	22.6304i	−0.459649	+	0.796135i
$809$	−4.99676	+	8.65464i	−0.175677	+	0.304281i	−0.940395	−	0.340083i	$-0.889545\pi$
$809$	−4.99676	+	8.65464i	−0.175677	+	0.304281i	0.764719	+	0.644364i	$0.222878\pi$
$810$		0			0
$811$	47.3923			1.66417			0.832085	−	0.554648i	$-0.187147\pi$
$811$	47.3923			1.66417			0.832085	+	0.554648i	$0.187147\pi$
$812$	1.89415	−	2.37996i	0.0664717	−	0.0835203i
$813$		0			0
$814$	9.29661	−	16.1022i	0.325846	−	0.564382i
$815$	4.15098			0.145403
$816$		0			0
$817$	−59.0907			−2.06732
$818$	4.23975			0.148239
$819$		0			0
$820$	9.29989			0.324766
$821$	−33.8402			−1.18103			−0.590516	−	0.807026i	$-0.701076\pi$
$821$	−33.8402			−1.18103			−0.590516	+	0.807026i	$0.701076\pi$
$822$		0			0
$823$	−13.6533			−0.475924			−0.237962	−	0.971274i	$-0.576479\pi$
$823$	−13.6533			−0.475924			−0.237962	+	0.971274i	$0.576479\pi$
$824$	20.7202	−	35.8884i	0.721821	−	1.25023i
$825$		0			0
$826$	−7.90342	−	20.0798i	−0.274995	−	0.698666i
$827$	27.2276			0.946795			0.473398	−	0.880849i	$-0.343027\pi$
$827$	27.2276			0.946795			0.473398	+	0.880849i	$0.343027\pi$
$828$		0			0
$829$	−10.3268	+	17.8865i	−0.358665	+	0.621225i	−0.987738	−	0.156121i	$-0.950101\pi$
$829$	−10.3268	+	17.8865i	−0.358665	+	0.621225i	0.629073	+	0.777346i	$0.283434\pi$
$830$	−1.93836	+	3.35734i	−0.0672815	+	0.116535i
$831$		0			0
$832$	−18.3628	+	1.64865i	−0.636616	+	0.0571568i
$833$	−24.5802	+	22.8968i	−0.851655	+	0.793326i
$834$		0			0
$835$	30.7817			1.06524
$836$	−37.0150			−1.28019
$837$		0			0
$838$	3.44855	+	5.97306i	0.119128	+	0.206336i
$839$	−3.64540	+	6.31401i	−0.125853	+	0.217984i	−0.922066	−	0.387033i	$-0.873500\pi$
$839$	−3.64540	+	6.31401i	−0.125853	+	0.217984i	0.796213	+	0.605016i	$0.206833\pi$
$840$		0			0
$841$	14.0558	−	24.3453i	0.484682	−	0.839495i
$842$	5.59285			0.192742
$843$		0			0
$844$	−10.6000	−	18.3598i	−0.364868	−	0.631970i
$845$	−7.05537	+	19.6625i	−0.242712	+	0.676409i
$846$		0			0
$847$	30.7796	−	38.6740i	1.05760	−	1.32885i
$848$	0.00417881	+	0.00723792i	0.000143501	+	0.000248551i
$849$		0			0
$850$	−5.12460	−	8.87606i	−0.175772	−	0.304446i
$851$	29.0736			0.996631
$852$		0			0
$853$	−17.2736			−0.591437			−0.295718	−	0.955275i	$-0.595559\pi$
$853$	−17.2736			−0.591437			−0.295718	+	0.955275i	$0.595559\pi$
$854$	15.1106	−	18.9861i	0.517074	−	0.649693i
$855$		0			0
$856$	0.826782			0.0282588
$857$	13.7728	+	23.8552i	0.470470	+	0.814878i	0.999430	−	0.0337691i	$-0.0107511\pi$
$857$	13.7728	+	23.8552i	0.470470	+	0.814878i	−0.528960	+	0.848647i	$0.677418\pi$
$858$		0			0
$859$	17.7390	−	30.7248i	0.605246	−	1.04832i	−0.386767	−	0.922177i	$-0.626408\pi$
$859$	17.7390	−	30.7248i	0.605246	−	1.04832i	0.992013	−	0.126139i	$-0.0402584\pi$
$860$	10.3961	+	18.0066i	0.354505	+	0.614020i
$861$		0			0
$862$	1.50599	−	2.60845i	0.0512943	−	0.0888443i
$863$	4.15589	−	7.19822i	0.141468	−	0.245030i	−0.786581	−	0.617486i	$-0.788151\pi$
$863$	4.15589	−	7.19822i	0.141468	−	0.245030i	0.928050	+	0.372456i	$0.121484\pi$
$864$		0			0
$865$	11.4486			0.389264
$866$	6.61242	−	11.4530i	0.224699	−	0.389190i
$867$		0			0
$868$	−0.799098	+	1.00405i	−0.0271231	+	0.0340797i
$869$	13.9029	+	24.0806i	0.471625	+	0.816878i
$870$		0			0
$871$	7.24668	−	15.6333i	0.245544	−	0.529715i
$872$	3.09056	+	5.35302i	0.104660	+	0.181276i
$873$		0			0
$874$	18.5133	+	32.0659i	0.626220	+	1.08465i
$875$	−11.5504	−	29.3456i	−0.390476	−	0.992062i
$876$		0			0
$877$	−20.1954	−	34.9795i	−0.681952	−	1.18117i	−0.974384	−	0.224889i	$-0.927798\pi$
$877$	−20.1954	−	34.9795i	−0.681952	−	1.18117i	0.292433	−	0.956286i	$-0.405535\pi$
$878$	−20.3166			−0.685652
$879$		0			0
$880$	−0.318853	−	0.552270i	−0.0107485	−	0.0186170i
$881$	22.5508	+	39.0590i	0.759754	+	1.31593i	0.942976	+	0.332861i	$0.108014\pi$
$881$	22.5508	+	39.0590i	0.759754	+	1.31593i	−0.183222	+	0.983072i	$0.558653\pi$
$882$		0			0
$883$	20.9898			0.706363			0.353182	−	0.935555i	$-0.385100\pi$
$883$	20.9898			0.706363			0.353182	+	0.935555i	$0.385100\pi$
$884$	21.0200	−	1.88722i	0.706977	−	0.0634740i
$885$		0			0
$886$	−7.46155	+	12.9238i	−0.250676	+	0.434183i
$887$	45.7555			1.53632			0.768159	−	0.640259i	$-0.221173\pi$
$887$	45.7555			1.53632			0.768159	+	0.640259i	$0.221173\pi$
$888$		0			0
$889$	−12.0087	+	15.0886i	−0.402758	+	0.506057i
$890$	−3.04285	+	5.27038i	−0.101997	+	0.176663i
$891$		0			0
$892$	15.1059	+	26.1641i	0.505782	+	0.876040i
$893$	−1.59512			−0.0533786
$894$		0			0
$895$	19.4879	+	33.7540i	0.651409	+	1.12827i
$896$	6.52223	+	16.5707i	0.217892	+	0.553588i
$897$		0			0
$898$	−6.28051	+	10.8782i	−0.209583	+	0.363009i
$899$	0.187402	−	0.324589i	0.00625020	−	0.0108257i
$900$		0			0
$901$	−0.275305	−	0.476843i	−0.00917175	−	0.0158859i
$902$	−22.8346			−0.760309
$903$		0			0
$904$	17.4503	−	30.2248i	0.580387	−	1.00526i
$905$	−17.3723	+	30.0897i	−0.577474	+	1.00021i
$906$		0			0
$907$	−1.57210	+	2.72296i	−0.0522008	+	0.0904145i	−0.890945	−	0.454111i	$-0.849957\pi$
$907$	−1.57210	+	2.72296i	−0.0522008	+	0.0904145i	0.838744	+	0.544526i	$0.183290\pi$
$908$	−2.16678			−0.0719071
$909$		0			0
$910$	−13.5171	−	0.799510i	−0.448086	−	0.0265035i
$911$	−45.8072			−1.51766			−0.758829	−	0.651290i	$-0.774228\pi$
$911$	−45.8072			−1.51766			−0.758829	+	0.651290i	$0.774228\pi$
$912$		0			0
$913$	−7.43978	+	12.8861i	−0.246221	+	0.426467i
$914$	26.6869			0.882725
$915$		0			0
$916$	14.0941	−	24.4117i	0.465683	−	0.806586i
$917$	−55.0046	−	8.23559i	−1.81641	−	0.271963i
$918$		0			0
$919$	16.9149	+	29.2975i	0.557972	+	0.966437i	0.997666	+	0.0682886i	$0.0217539\pi$
$919$	16.9149	+	29.2975i	0.557972	+	0.966437i	−0.439693	+	0.898148i	$0.644913\pi$
$920$	17.1958	−	29.7840i	0.566929	−	0.981950i
$921$		0			0
$922$	−1.23364	+	2.13672i	−0.0406277	+	0.0703692i
$923$	21.0370	−	45.3834i	0.692442	−	1.49381i
$924$		0			0
$925$	−4.67063	−	8.08977i	−0.153569	−	0.265990i
$926$	26.8831			0.883434
$927$		0			0
$928$	−2.65040	−	4.59063i	−0.0870037	−	0.150695i
$929$	22.2364	+	38.5145i	0.729551	+	1.26362i	0.957073	+	0.289847i	$0.0936043\pi$
$929$	22.2364	+	38.5145i	0.729551	+	1.26362i	−0.227522	+	0.973773i	$0.573062\pi$
$930$		0			0
$931$	−37.2817	−	11.4201i	−1.22186	−	0.374277i
$932$	15.4165	−	26.7021i	0.504983	−	0.874656i
$933$		0			0
$934$	−1.57953	+	2.73583i	−0.0516839	+	0.0895191i
$935$	21.0064	+	36.3842i	0.686984	+	1.18989i
$936$		0			0
$937$	−2.05597			−0.0671657			−0.0335829	−	0.999436i	$-0.510692\pi$
$937$	−2.05597			−0.0671657			−0.0335829	+	0.999436i	$0.510692\pi$
$938$	11.0460	+	1.65387i	0.360664	+	0.0540007i
$939$		0			0
$940$	0.280637	+	0.486077i	0.00915337	+	0.0158541i
$941$	−10.6472	−	18.4415i	−0.347089	−	0.601176i	0.638642	−	0.769504i	$-0.279497\pi$
$941$	−10.6472	−	18.4415i	−0.347089	−	0.601176i	−0.985731	+	0.168328i	$0.946163\pi$
$942$		0			0
$943$	−17.8529	−	30.9221i	−0.581369	−	1.00696i
$944$	−0.672578			−0.0218906
$945$		0			0
$946$	−25.5262	−	44.2127i	−0.829929	−	1.43748i
$947$	−15.3455			−0.498661			−0.249331	−	0.968418i	$-0.580211\pi$
$947$	−15.3455			−0.498661			−0.249331	+	0.968418i	$0.580211\pi$
$948$		0			0
$949$	15.0782	+	21.4300i	0.489459	+	0.695646i
$950$	5.94825	−	10.3027i	0.192987	−	0.334263i
$951$		0			0
$952$	13.2256	+	33.6015i	0.428643	+	1.08903i
$953$	−12.2802	+	21.2700i	−0.397796	+	0.689002i	−0.993454	−	0.114236i	$-0.963558\pi$
$953$	−12.2802	+	21.2700i	−0.397796	+	0.689002i	0.595658	+	0.803238i	$0.296891\pi$
$954$		0			0
$955$	5.71108			0.184806
$956$	−26.4331			−0.854909
$957$		0			0
$958$	−11.3637	+	19.6825i	−0.367144	+	0.635912i
$959$	−0.528799	−	1.34349i	−0.0170758	−	0.0433836i
$960$		0			0
$961$	15.4209	−	26.7099i	0.497450	−	0.861608i
$962$	−12.2557	+	1.10034i	−0.395139	+	0.0354765i
$963$		0			0
$964$	−20.2945			−0.653641
$965$	−14.9015	−	25.8101i	−0.479695	−	0.830857i
$966$		0			0
$967$	−17.8067			−0.572625			−0.286313	−	0.958136i	$-0.592430\pi$
$967$	−17.8067			−0.572625			−0.286313	+	0.958136i	$0.592430\pi$
$968$	−26.5663	−	46.0142i	−0.853874	−	1.47895i
$969$		0			0
$970$	−0.773360	−	1.33950i	−0.0248311	−	0.0430087i
$971$	7.73741	+	13.4016i	0.248305	+	0.430077i	0.963056	−	0.269302i	$-0.0867931\pi$
$971$	7.73741	+	13.4016i	0.248305	+	0.430077i	−0.714750	+	0.699380i	$0.753460\pi$
$972$		0			0
$973$	6.17292	+	0.924244i	0.197895	+	0.0296299i
$974$	19.9981			0.640780
$975$		0			0
$976$	−0.378149	−	0.654973i	−0.0121042	−	0.0209652i
$977$	6.97273	−	12.0771i	0.223077	−	0.386381i	−0.732663	−	0.680591i	$-0.761723\pi$
$977$	6.97273	−	12.0771i	0.223077	−	0.386381i	0.955741	+	0.294210i	$0.0950564\pi$
$978$		0			0
$979$	−11.6790	+	20.2287i	−0.373263	+	0.646511i
$980$	3.07914	+	13.3700i	0.0983594	+	0.427088i
$981$		0			0
$982$	13.6242	+	23.5978i	0.434765	+	0.753036i
$983$	−10.0269	−	17.3671i	−0.319809	−	0.553926i	0.660639	−	0.750704i	$-0.270285\pi$
$983$	−10.0269	−	17.3671i	−0.319809	−	0.553926i	−0.980448	+	0.196778i	$0.936952\pi$
$984$		0			0
$985$	18.5667			0.591586
$986$	−1.99778	−	3.46025i	−0.0636222	−	0.110197i
$987$		0			0
$988$	14.0963	+	20.0344i	0.448462	+	0.637378i
$989$	39.9146	−	69.1340i	1.26921	−	2.19833i
$990$		0			0
$991$	16.3476	−	28.3148i	0.519297	−	0.899449i	−0.480451	−	0.877021i	$-0.659527\pi$
$991$	16.3476	−	28.3148i	0.519297	−	0.899449i	0.999748	−	0.0224278i	$-0.00713957\pi$
$992$	1.11814	+	1.93668i	0.0355011	+	0.0614896i
$993$		0			0
$994$	32.0664	+	4.80116i	1.01708	+	0.152283i
$995$	−2.79985	+	4.84948i	−0.0887611	+	0.153739i
$996$		0			0
$997$	−29.6606			−0.939362			−0.469681	−	0.882836i	$-0.655631\pi$
$997$	−29.6606			−0.939362			−0.469681	+	0.882836i	$0.655631\pi$
$998$	−7.79875	+	13.5078i	−0.246865	+	0.427583i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.g.289.8	yes	36
3.2	odd	2	inner	819.2.s.g.289.11	yes	36
7.4	even	3		819.2.n.g.172.11	yes	36
13.9	even	3		819.2.n.g.100.11	yes	36
21.11	odd	6		819.2.n.g.172.8	yes	36
39.35	odd	6		819.2.n.g.100.8	✓	36
91.74	even	3	inner	819.2.s.g.802.8	yes	36
273.74	odd	6	inner	819.2.s.g.802.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.n.g.100.8	✓	36	39.35	odd	6
819.2.n.g.100.11	yes	36	13.9	even	3
819.2.n.g.172.8	yes	36	21.11	odd	6
819.2.n.g.172.11	yes	36	7.4	even	3
819.2.s.g.289.8	yes	36	1.1	even	1	trivial
819.2.s.g.289.11	yes	36	3.2	odd	2	inner
819.2.s.g.802.8	yes	36	91.74	even	3	inner
819.2.s.g.802.11	yes	36	273.74	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.883334 q^{2} -1.21972 q^{4} +(-0.803460 + 1.39163i) q^{5} +(0.969010 + 2.46191i) q^{7} +2.84409 q^{8} +(0.709724 - 1.22928i) q^{10} +(2.72405 - 4.71819i) q^{11} +(-3.59111 + 0.322418i) q^{13} +(-0.855960 - 2.17469i) q^{14} -0.0728419 q^{16} +4.79892 q^{17} +(2.78511 + 4.82396i) q^{19} +(0.979997 - 1.69740i) q^{20} +(-2.40625 + 4.16774i) q^{22} -7.52514 q^{23} +(1.20890 + 2.09388i) q^{25} +(3.17215 - 0.284803i) q^{26} +(-1.18192 - 3.00285i) q^{28} +(0.471280 + 0.816281i) q^{29} +(-0.198822 - 0.344370i) q^{31} -5.62384 q^{32} -4.23905 q^{34} +(-4.20464 - 0.629543i) q^{35} -3.86353 q^{37} +(-2.46019 - 4.26117i) q^{38} +(-2.28511 + 3.95793i) q^{40} +(2.37243 + 4.10917i) q^{41} +(-5.30416 + 9.18707i) q^{43} +(-3.32258 + 5.75487i) q^{44} +6.64722 q^{46} +(-0.143183 + 0.247999i) q^{47} +(-5.12204 + 4.77124i) q^{49} +(-1.06787 - 1.84960i) q^{50} +(4.38015 - 0.393259i) q^{52} +(-0.0573682 - 0.0993647i) q^{53} +(4.37733 + 7.58176i) q^{55} +(2.75595 + 7.00190i) q^{56} +(-0.416298 - 0.721049i) q^{58} +9.23340 q^{59} +(5.19136 + 8.99170i) q^{61} +(0.175626 + 0.304194i) q^{62} +5.11341 q^{64} +(2.43662 - 5.25656i) q^{65} +(-2.38954 + 4.13881i) q^{67} -5.85334 q^{68} +(3.71411 + 0.556097i) q^{70} +(-6.93681 + 12.0149i) q^{71} +(-3.63370 - 6.29375i) q^{73} +3.41279 q^{74} +(-3.39706 - 5.88388i) q^{76} +(14.2554 + 2.13440i) q^{77} +(-2.55189 + 4.42000i) q^{79} +(0.0585256 - 0.101369i) q^{80} +(-2.09565 - 3.62977i) q^{82} -2.73115 q^{83} +(-3.85574 + 6.67834i) q^{85} +(4.68535 - 8.11526i) q^{86} +(7.74744 - 13.4190i) q^{88} -4.28738 q^{89} +(-4.27358 - 8.52857i) q^{91} +9.17857 q^{92} +(0.126478 - 0.219066i) q^{94} -8.95091 q^{95} +(0.544831 - 0.943675i) q^{97} +(4.52447 - 4.21460i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) \) 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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