LMFDB - Embedded newform 819.2.s.e.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-1.27528 + 2.20885i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.e.802.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.55056 q^{2} +4.50537 q^{4} +(1.39351 - 2.41363i) q^{5} +(-2.46231 - 0.968004i) q^{7} -6.39011 q^{8} +(-3.55423 + 6.15611i) q^{10} +(-1.38373 + 2.39670i) q^{11} +(2.99297 + 2.01050i) q^{13} +(6.28028 + 2.46895i) q^{14} +7.28763 q^{16} +5.88680 q^{17} +(-1.70037 - 2.94513i) q^{19} +(6.27828 - 10.8743i) q^{20} +(3.52930 - 6.11292i) q^{22} +7.34492 q^{23} +(-1.38373 - 2.39670i) q^{25} +(-7.63376 - 5.12791i) q^{26} +(-11.0936 - 4.36122i) q^{28} +(-1.56328 - 2.70768i) q^{29} +(1.93352 + 3.34896i) q^{31} -5.80735 q^{32} -15.0147 q^{34} +(-5.76765 + 4.59418i) q^{35} +5.84347 q^{37} +(4.33691 + 7.51175i) q^{38} +(-8.90467 + 15.4233i) q^{40} +(-3.24124 - 5.61400i) q^{41} +(2.99197 - 5.18224i) q^{43} +(-6.23423 + 10.7980i) q^{44} -18.7337 q^{46} +(-3.95673 + 6.85325i) q^{47} +(5.12594 + 4.76705i) q^{49} +(3.52930 + 6.11292i) q^{50} +(13.4845 + 9.05806i) q^{52} +(-6.34471 - 10.9894i) q^{53} +(3.85649 + 6.67963i) q^{55} +(15.7344 + 6.18565i) q^{56} +(3.98724 + 6.90611i) q^{58} -2.73648 q^{59} +(-4.77631 - 8.27282i) q^{61} +(-4.93157 - 8.54173i) q^{62} +0.236742 q^{64} +(9.02334 - 4.42227i) q^{65} +(4.34033 - 7.51767i) q^{67} +26.5222 q^{68} +(14.7108 - 11.7177i) q^{70} +(1.57062 - 2.72039i) q^{71} +(-4.80291 - 8.31889i) q^{73} -14.9041 q^{74} +(-7.66082 - 13.2689i) q^{76} +(5.72719 - 4.56195i) q^{77} +(-1.88112 + 3.25819i) q^{79} +(10.1554 - 17.5896i) q^{80} +(8.26699 + 14.3189i) q^{82} -4.82088 q^{83} +(8.20331 - 14.2086i) q^{85} +(-7.63120 + 13.2176i) q^{86} +(8.84221 - 15.3151i) q^{88} -1.75557 q^{89} +(-5.42345 - 7.84769i) q^{91} +33.0916 q^{92} +(10.0919 - 17.4797i) q^{94} -9.47794 q^{95} +(8.48637 - 14.6988i) q^{97} +(-13.0740 - 12.1587i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

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 $

$2$	−2.55056			−1.80352			−0.901760	−	0.432237i	$-0.857725\pi$
$2$	−2.55056			−1.80352			−0.901760	+	0.432237i	$0.857725\pi$
$3$		0			0
$3$		0			0
$4$	4.50537			2.25269
$5$	1.39351	−	2.41363i	0.623196	−	1.07941i	−0.365691	−	0.930736i	$-0.619167\pi$
$5$	1.39351	−	2.41363i	0.623196	−	1.07941i	0.988887	−	0.148671i	$-0.0474995\pi$
$6$		0			0
$7$	−2.46231	−	0.968004i	−0.930666	−	0.365871i
$7$	−2.46231	−	0.968004i	−0.930666	−	0.365871i
$8$	−6.39011			−2.25924
$9$		0			0
$10$	−3.55423	+	6.15611i	−1.12395	+	1.94673i
$11$	−1.38373	+	2.39670i	−0.417211	+	0.722631i	−0.995658	−	0.0930893i	$-0.970326\pi$
$11$	−1.38373	+	2.39670i	−0.417211	+	0.722631i	0.578447	+	0.815720i	$0.303659\pi$
$12$		0			0
$13$	2.99297	+	2.01050i	0.830101	+	0.557613i
$13$	2.99297	+	2.01050i	0.830101	+	0.557613i
$14$	6.28028	+	2.46895i	1.67847	+	0.659856i
$15$		0			0
$16$	7.28763			1.82191
$17$	5.88680			1.42776			0.713880	−	0.700268i	$-0.246936\pi$
$17$	5.88680			1.42776			0.713880	+	0.700268i	$0.246936\pi$
$18$		0			0
$19$	−1.70037	−	2.94513i	−0.390093	−	0.675660i	0.602369	−	0.798218i	$-0.294224\pi$
$19$	−1.70037	−	2.94513i	−0.390093	−	0.675660i	−0.992461	+	0.122558i	$0.960890\pi$
$20$	6.27828	−	10.8743i	1.40386	−	2.43157i
$21$		0			0
$22$	3.52930	−	6.11292i	0.752449	−	1.30328i
$23$	7.34492			1.53152			0.765761	−	0.643126i	$-0.222363\pi$
$23$	7.34492			1.53152			0.765761	+	0.643126i	$0.222363\pi$
$24$		0			0
$25$	−1.38373	−	2.39670i	−0.276747	−	0.479339i
$26$	−7.63376	−	5.12791i	−1.49710	−	1.00567i
$27$		0			0
$28$	−11.0936	−	4.36122i	−2.09650	−	0.824193i
$29$	−1.56328	−	2.70768i	−0.290294	−	0.502803i	0.683585	−	0.729871i	$-0.260420\pi$
$29$	−1.56328	−	2.70768i	−0.290294	−	0.502803i	−0.973879	+	0.227067i	$0.927086\pi$
$30$		0			0
$31$	1.93352	+	3.34896i	0.347271	+	0.601491i	0.985764	−	0.168137i	$-0.0537751\pi$
$31$	1.93352	+	3.34896i	0.347271	+	0.601491i	−0.638493	+	0.769628i	$0.720442\pi$
$32$	−5.80735			−1.02660
$33$		0			0
$34$	−15.0147			−2.57499
$35$	−5.76765	+	4.59418i	−0.974911	+	0.776558i
$36$		0			0
$37$	5.84347			0.960660			0.480330	−	0.877088i	$-0.340517\pi$
$37$	5.84347			0.960660			0.480330	+	0.877088i	$0.340517\pi$
$38$	4.33691	+	7.51175i	0.703540	+	1.21857i
$39$		0			0
$40$	−8.90467	+	15.4233i	−1.40795	+	2.43865i
$41$	−3.24124	−	5.61400i	−0.506197	−	0.876759i	−0.999974	−	0.00717054i	$-0.997718\pi$
$41$	−3.24124	−	5.61400i	−0.506197	−	0.876759i	0.493777	−	0.869588i	$-0.335616\pi$
$42$		0			0
$43$	2.99197	−	5.18224i	0.456271	−	0.790284i	−0.542489	−	0.840063i	$-0.682518\pi$
$43$	2.99197	−	5.18224i	0.456271	−	0.790284i	0.998760	+	0.0497783i	$0.0158515\pi$
$44$	−6.23423	+	10.7980i	−0.939846	+	1.62786i
$45$		0			0
$46$	−18.7337			−2.76213
$47$	−3.95673	+	6.85325i	−0.577148	+	0.999650i	0.418656	+	0.908145i	$0.362501\pi$
$47$	−3.95673	+	6.85325i	−0.577148	+	0.999650i	−0.995805	+	0.0915053i	$0.970832\pi$
$48$		0			0
$49$	5.12594	+	4.76705i	0.732277	+	0.681007i
$50$	3.52930	+	6.11292i	0.499118	+	0.864498i
$51$		0			0
$52$	13.4845	+	9.05806i	1.86996	+	1.25613i
$53$	−6.34471	−	10.9894i	−0.871513	−	1.50951i	−0.860431	−	0.509567i	$-0.829806\pi$
$53$	−6.34471	−	10.9894i	−0.871513	−	1.50951i	−0.0110819	−	0.999939i	$-0.503528\pi$
$54$		0			0
$55$	3.85649	+	6.67963i	0.520009	+	0.900682i
$56$	15.7344	+	6.18565i	2.10260	+	0.826592i
$57$		0			0
$58$	3.98724	+	6.90611i	0.523551	+	0.906816i
$59$	−2.73648			−0.356260			−0.178130	−	0.984007i	$-0.557005\pi$
$59$	−2.73648			−0.356260			−0.178130	+	0.984007i	$0.557005\pi$
$60$		0			0
$61$	−4.77631	−	8.27282i	−0.611544	−	1.05923i	−0.990980	−	0.134008i	$-0.957215\pi$
$61$	−4.77631	−	8.27282i	−0.611544	−	1.05923i	0.379436	−	0.925218i	$-0.376118\pi$
$62$	−4.93157	−	8.54173i	−0.626310	−	1.08480i
$63$		0			0
$64$	0.236742			0.0295928
$65$	9.02334	−	4.42227i	1.11921	−	0.548515i
$66$		0			0
$67$	4.34033	−	7.51767i	0.530255	−	0.918429i	−0.469121	−	0.883134i	$-0.655429\pi$
$67$	4.34033	−	7.51767i	0.530255	−	0.918429i	0.999377	−	0.0352957i	$-0.0112373\pi$
$68$	26.5222			3.21629
$69$		0			0
$70$	14.7108	−	11.7177i	1.75827	−	1.40054i
$71$	1.57062	−	2.72039i	0.186398	−	0.322851i	−0.757649	−	0.652663i	$-0.773652\pi$
$71$	1.57062	−	2.72039i	0.186398	−	0.322851i	0.944047	+	0.329812i	$0.106985\pi$
$72$		0			0
$73$	−4.80291	−	8.31889i	−0.562138	−	0.973652i	−0.997310	−	0.0733045i	$-0.976646\pi$
$73$	−4.80291	−	8.31889i	−0.562138	−	0.973652i	0.435171	−	0.900348i	$-0.356688\pi$
$74$	−14.9041			−1.73257
$75$		0			0
$76$	−7.66082	−	13.2689i	−0.878756	−	1.52205i
$77$	5.72719	−	4.56195i	0.652674	−	0.519882i
$78$		0			0
$79$	−1.88112	+	3.25819i	−0.211642	+	0.366575i	−0.952229	−	0.305386i	$-0.901215\pi$
$79$	−1.88112	+	3.25819i	−0.211642	+	0.366575i	0.740586	+	0.671961i	$0.234548\pi$
$80$	10.1554	−	17.5896i	1.13541	−	1.96658i
$81$		0			0
$82$	8.26699	+	14.3189i	0.912937	+	1.58125i
$83$	−4.82088			−0.529161			−0.264580	−	0.964364i	$-0.585233\pi$
$83$	−4.82088			−0.529161			−0.264580	+	0.964364i	$0.585233\pi$
$84$		0			0
$85$	8.20331	−	14.2086i	0.889774	−	1.54113i
$86$	−7.63120	+	13.2176i	−0.822894	+	1.42529i
$87$		0			0
$88$	8.84221	−	15.3151i	0.942582	−	1.63260i
$89$	−1.75557			−0.186091			−0.0930453	−	0.995662i	$-0.529660\pi$
$89$	−1.75557			−0.186091			−0.0930453	+	0.995662i	$0.529660\pi$
$90$		0			0
$91$	−5.42345	−	7.84769i	−0.568532	−	0.822661i
$92$	33.0916			3.45004
$93$		0			0
$94$	10.0919	−	17.4797i	1.04090	−	1.80289i
$95$	−9.47794			−0.972416
$96$		0			0
$97$	8.48637	−	14.6988i	0.861660	−	1.49244i	−0.00866511	−	0.999962i	$-0.502758\pi$
$97$	8.48637	−	14.6988i	0.861660	−	1.49244i	0.870325	−	0.492477i	$-0.163908\pi$
$98$	−13.0740	−	12.1587i	−1.32068	−	1.22821i
$99$		0			0
$100$	−6.23423	−	10.7980i	−0.623423	−	1.07980i
$101$	−0.921364	+	1.59585i	−0.0916791	+	0.158793i	−0.908218	−	0.418498i	$-0.862557\pi$
$101$	−0.921364	+	1.59585i	−0.0916791	+	0.158793i	0.816539	+	0.577291i	$0.195890\pi$
$102$		0			0
$103$	−2.38506	+	4.13105i	−0.235007	+	0.407045i	−0.959275	−	0.282474i	$-0.908845\pi$
$103$	−2.38506	+	4.13105i	−0.235007	+	0.407045i	0.724267	+	0.689519i	$0.242178\pi$
$104$	−19.1254	−	12.8473i	−1.87540	−	1.25978i
$105$		0			0
$106$	16.1826	+	28.0291i	1.57179	+	2.72242i
$107$	12.0754			1.16738			0.583688	−	0.811978i	$-0.301609\pi$
$107$	12.0754			1.16738			0.583688	+	0.811978i	$0.301609\pi$
$108$		0			0
$109$	3.40885	+	5.90430i	0.326508	+	0.565529i	0.981816	−	0.189832i	$-0.0607945\pi$
$109$	3.40885	+	5.90430i	0.326508	+	0.565529i	−0.655308	+	0.755362i	$0.727461\pi$
$110$	−9.83622	−	17.0368i	−0.937846	−	1.62440i
$111$		0			0
$112$	−17.9444	−	7.05446i	−1.69559	−	0.666583i
$113$	2.72463	−	4.71920i	0.256312	−	0.443945i	−0.708939	−	0.705270i	$-0.750826\pi$
$113$	2.72463	−	4.71920i	0.256312	−	0.443945i	0.965251	+	0.261325i	$0.0841593\pi$
$114$		0			0
$115$	10.2352	−	17.7279i	0.954438	−	1.65314i
$116$	−7.04316	−	12.1991i	−0.653941	−	1.13266i
$117$		0			0
$118$	6.97958			0.642522
$119$	−14.4951	−	5.69845i	−1.32877	−	0.522376i
$120$		0			0
$121$	1.67057	+	2.89350i	0.151870	+	0.263046i
$122$	12.1823	+	21.1003i	1.10293	+	1.91034i
$123$		0			0
$124$	8.71124	+	15.0883i	0.782292	+	1.35497i
$125$	6.22211			0.556523
$126$		0			0
$127$	−0.886520	−	1.53550i	−0.0786660	−	0.136253i	0.824009	−	0.566577i	$-0.191733\pi$
$127$	−0.886520	−	1.53550i	−0.0786660	−	0.136253i	−0.902675	+	0.430324i	$0.858399\pi$
$128$	11.0109			0.973233
$129$		0			0
$130$	−23.0146	+	11.2793i	−2.01851	+	0.989258i
$131$	3.50734	−	6.07490i	0.306438	−	0.530766i	−0.671143	−	0.741328i	$-0.734196\pi$
$131$	3.50734	−	6.07490i	0.306438	−	0.530766i	0.977580	+	0.210562i	$0.0675295\pi$
$132$		0			0
$133$	1.33595	+	8.89780i	0.115841	+	0.771537i
$134$	−11.0703	+	19.1743i	−0.956326	+	1.65641i
$135$		0			0
$136$	−37.6173			−3.22566
$137$	19.6574			1.67945			0.839725	−	0.543013i	$-0.182716\pi$
$137$	19.6574			1.67945			0.839725	+	0.543013i	$0.182716\pi$
$138$		0			0
$139$	−9.17342	+	15.8888i	−0.778079	+	1.34767i	0.154968	+	0.987919i	$0.450472\pi$
$139$	−9.17342	+	15.8888i	−0.778079	+	1.34767i	−0.933048	+	0.359753i	$0.882861\pi$
$140$	−25.9854	+	20.6985i	−2.19617	+	1.74934i
$141$		0			0
$142$	−4.00596	+	6.93852i	−0.336173	+	0.582268i
$143$	−8.96004	+	4.39125i	−0.749276	+	0.367215i
$144$		0			0
$145$	−8.71377			−0.723640
$146$	12.2501	+	21.2178i	1.01383	+	1.75600i
$147$		0			0
$148$	26.3270			2.16407
$149$	−4.40145	−	7.62354i	−0.360581	−	0.624545i	0.627476	−	0.778636i	$-0.284088\pi$
$149$	−4.40145	−	7.62354i	−0.360581	−	0.624545i	−0.988057	+	0.154092i	$0.950755\pi$
$150$		0			0
$151$	−4.83567	−	8.37562i	−0.393521	−	0.681598i	0.599390	−	0.800457i	$-0.295410\pi$
$151$	−4.83567	−	8.37562i	−0.393521	−	0.681598i	−0.992911	+	0.118859i	$0.962076\pi$
$152$	10.8656	+	18.8197i	0.881314	+	1.52648i
$153$		0			0
$154$	−14.6076	+	11.6355i	−1.17711	+	0.937618i
$155$	10.7775			0.865672
$156$		0			0
$157$	−5.76601	−	9.98702i	−0.460177	−	0.797051i	0.538792	−	0.842439i	$-0.318881\pi$
$157$	−5.76601	−	9.98702i	−0.460177	−	0.797051i	−0.998969	+	0.0453882i	$0.985548\pi$
$158$	4.79791	−	8.31023i	0.381701	−	0.661126i
$159$		0			0
$160$	−8.09259	+	14.0168i	−0.639775	+	1.10812i
$161$	−18.0855	−	7.10991i	−1.42533	−	0.560339i
$162$		0			0
$163$	6.08521	+	10.5399i	0.476631	+	0.825548i	0.999641	−	0.0267776i	$-0.00852461\pi$
$163$	6.08521	+	10.5399i	0.476631	+	0.825548i	−0.523011	+	0.852326i	$0.675191\pi$
$164$	−14.6030	−	25.2931i	−1.14030	−	1.97506i
$165$		0			0
$166$	12.2960			0.954352
$167$	−4.54697	−	7.87559i	−0.351855	−	0.609431i	0.634719	−	0.772743i	$-0.281116\pi$
$167$	−4.54697	−	7.87559i	−0.351855	−	0.609431i	−0.986575	+	0.163311i	$0.947782\pi$
$168$		0			0
$169$	4.91577	+	12.0348i	0.378136	+	0.925750i
$170$	−20.9231	+	36.2398i	−1.60473	+	2.77947i
$171$		0			0
$172$	13.4799	−	23.3479i	1.02783	−	1.78026i
$173$	−0.673648	−	1.16679i	−0.0512165	−	0.0887096i	0.839281	−	0.543699i	$-0.182977\pi$
$173$	−0.673648	−	1.16679i	−0.0512165	−	0.0887096i	−0.890497	+	0.454989i	$0.849643\pi$
$174$		0			0
$175$	1.08717	+	7.24087i	0.0821822	+	0.547358i
$176$	−10.0841	+	17.4662i	−0.760121	+	1.31657i
$177$		0			0
$178$	4.47770			0.335618
$179$	−2.97996	+	5.16145i	−0.222733	+	0.385785i	−0.955637	−	0.294547i	$-0.904831\pi$
$179$	−2.97996	+	5.16145i	−0.222733	+	0.385785i	0.732904	+	0.680332i	$0.238164\pi$
$180$		0			0
$181$	10.4495			0.776707			0.388354	−	0.921510i	$-0.373044\pi$
$181$	10.4495			0.776707			0.388354	+	0.921510i	$0.373044\pi$
$182$	13.8329	+	20.0160i	1.02536	+	1.48369i
$183$		0			0
$184$	−46.9348			−3.46008
$185$	8.14292	−	14.1040i	0.598680	−	1.03694i
$186$		0			0
$187$	−8.14577	+	14.1089i	−0.595677	+	1.03174i
$188$	−17.8265	+	30.8765i	−1.30013	+	2.25190i
$189$		0			0
$190$	24.1741			1.75377
$191$	−0.329057	−	0.569943i	−0.0238097	−	0.0412396i	0.853875	−	0.520478i	$-0.174246\pi$
$191$	−0.329057	−	0.569943i	−0.0238097	−	0.0412396i	−0.877685	+	0.479238i	$0.840913\pi$
$192$		0			0
$193$	−4.39278	+	7.60853i	−0.316200	+	0.547674i	−0.979692	−	0.200510i	$-0.935740\pi$
$193$	−4.39278	+	7.60853i	−0.316200	+	0.547674i	0.663492	+	0.748183i	$0.269074\pi$
$194$	−21.6450	+	37.4903i	−1.55402	+	2.69165i
$195$		0			0
$196$	23.0943	+	21.4773i	1.64959	+	1.53410i
$197$	9.29781	+	16.1043i	0.662442	+	1.14738i	0.979972	+	0.199135i	$0.0638131\pi$
$197$	9.29781	+	16.1043i	0.662442	+	1.14738i	−0.317530	+	0.948248i	$0.602854\pi$
$198$		0			0
$199$	15.2257			1.07932			0.539659	−	0.841884i	$-0.318553\pi$
$199$	15.2257			1.07932			0.539659	+	0.841884i	$0.318553\pi$
$200$	8.84221	+	15.3151i	0.625238	+	1.08294i
$201$		0			0
$202$	2.35000	−	4.07031i	0.165345	−	0.286386i
$203$	1.22823	+	8.18041i	0.0862051	+	0.574152i
$204$		0			0
$205$	−18.0668			−1.26184
$206$	6.08326	−	10.5365i	0.423841	−	0.734113i
$207$		0			0
$208$	21.8117	+	14.6518i	1.51237	+	1.01592i
$209$	9.41145			0.651004
$210$		0			0
$211$	−10.5945	−	18.3503i	−0.729357	−	1.26328i	−0.957155	−	0.289575i	$-0.906486\pi$
$211$	−10.5945	−	18.3503i	−0.729357	−	1.26328i	0.227798	−	0.973708i	$-0.426847\pi$
$212$	−28.5853	−	49.5112i	−1.96325	−	3.40044i
$213$		0			0
$214$	−30.7991			−2.10539
$215$	−8.33867	−	14.4430i	−0.568692	−	0.985004i
$216$		0			0
$217$	−1.51913	−	10.1178i	−0.103125	−	0.686843i
$218$	−8.69448	−	15.0593i	−0.588865	−	1.01994i
$219$		0			0
$220$	17.3749	+	30.0942i	1.17142	+	2.02895i
$221$	17.6190	+	11.8354i	1.18518	+	0.796137i
$222$		0			0
$223$	−0.453274	−	0.785093i	−0.0303534	−	0.0525737i	0.850450	−	0.526056i	$-0.176330\pi$
$223$	−0.453274	−	0.785093i	−0.0303534	−	0.0525737i	−0.880803	+	0.473483i	$0.842997\pi$
$224$	14.2995	+	5.62154i	0.955425	+	0.375605i
$225$		0			0
$226$	−6.94935	+	12.0366i	−0.462264	+	0.800664i
$227$	−1.92809			−0.127972			−0.0639859	−	0.997951i	$-0.520381\pi$
$227$	−1.92809			−0.127972			−0.0639859	+	0.997951i	$0.520381\pi$
$228$		0			0
$229$	5.05578	−	8.75686i	0.334095	−	0.578670i	−0.649216	−	0.760604i	$-0.724903\pi$
$229$	5.05578	−	8.75686i	0.334095	−	0.578670i	0.983311	+	0.181935i	$0.0582360\pi$
$230$	−26.1055	+	45.2161i	−1.72135	+	2.98146i
$231$		0			0
$232$	9.98953	+	17.3024i	0.655845	+	1.13596i
$233$	−13.1134	+	22.7130i	−0.859085	+	1.48798i	0.0137178	+	0.999906i	$0.495633\pi$
$233$	−13.1134	+	22.7130i	−0.859085	+	1.48798i	−0.872803	+	0.488073i	$0.837700\pi$
$234$		0			0
$235$	11.0275	+	19.1001i	0.719353	+	1.24596i
$236$	−12.3289			−0.802542
$237$		0			0
$238$	36.9708	+	14.5343i	2.39646	+	0.942116i
$239$	−28.0556			−1.81476			−0.907382	−	0.420306i	$-0.861923\pi$
$239$	−28.0556			−1.81476			−0.907382	+	0.420306i	$0.861923\pi$
$240$		0			0
$241$	−4.45249			−0.286810			−0.143405	−	0.989664i	$-0.545805\pi$
$241$	−4.45249			−0.286810			−0.143405	+	0.989664i	$0.545805\pi$
$242$	−4.26088	−	7.38007i	−0.273900	−	0.474409i
$243$		0			0
$244$	−21.5191	−	37.2721i	−1.37762	−	2.38610i
$245$	18.6489	−	5.72918i	1.19144	−	0.366024i
$246$		0			0
$247$	0.832025	−	12.2333i	0.0529405	−	0.778387i
$248$	−12.3554	−	21.4002i	−0.784570	−	1.35892i
$249$		0			0
$250$	−15.8699			−1.00370
$251$	−1.55413	+	2.69183i	−0.0980956	+	0.169907i	−0.910896	−	0.412635i	$-0.864608\pi$
$251$	−1.55413	+	2.69183i	−0.0980956	+	0.169907i	0.812801	+	0.582542i	$0.197942\pi$
$252$		0			0
$253$	−10.1634	+	17.6035i	−0.638968	+	1.10672i
$254$	2.26113	+	3.91638i	0.141876	+	0.245736i
$255$		0			0
$256$	−28.5574			−1.78484
$257$	25.9854			1.62092			0.810461	−	0.585793i	$-0.199217\pi$
$257$	25.9854			1.62092			0.810461	+	0.585793i	$0.199217\pi$
$258$		0			0
$259$	−14.3884	−	5.65650i	−0.894053	−	0.351478i
$260$	40.6535	−	19.9240i	2.52122	−	1.23563i
$261$		0			0
$262$	−8.94570	+	15.4944i	−0.552667	+	0.957247i
$263$	6.39028	−	11.0683i	0.394042	−	0.682500i	−0.598937	−	0.800796i	$-0.704410\pi$
$263$	6.39028	−	11.0683i	0.394042	−	0.682500i	0.992978	+	0.118296i	$0.0377432\pi$
$264$		0			0
$265$	−35.3656			−2.17249
$266$	−3.40741	−	22.6944i	−0.208922	−	1.39148i
$267$		0			0
$268$	19.5548	−	33.8699i	1.19450	−	2.06893i
$269$	−1.95749			−0.119350			−0.0596751	−	0.998218i	$-0.519006\pi$
$269$	−1.95749			−0.119350			−0.0596751	+	0.998218i	$0.519006\pi$
$270$		0			0
$271$	26.9218			1.63538			0.817692	−	0.575656i	$-0.195253\pi$
$271$	26.9218			1.63538			0.817692	+	0.575656i	$0.195253\pi$
$272$	42.9009			2.60125
$273$		0			0
$274$	−50.1376			−3.02892
$275$	7.65887			0.461847
$276$		0			0
$277$	−23.1556			−1.39129			−0.695643	−	0.718388i	$-0.744880\pi$
$277$	−23.1556			−1.39129			−0.695643	+	0.718388i	$0.744880\pi$
$278$	23.3974	−	40.5254i	1.40328	−	2.43055i
$279$		0			0
$280$	36.8559	−	29.3573i	2.20256	−	1.75443i
$281$	26.9347			1.60679			0.803396	−	0.595446i	$-0.203024\pi$
$281$	26.9347			1.60679			0.803396	+	0.595446i	$0.203024\pi$
$282$		0			0
$283$	−7.62216	+	13.2020i	−0.453091	+	0.784776i	−0.998576	−	0.0533442i	$-0.983012\pi$
$283$	−7.62216	+	13.2020i	−0.453091	+	0.784776i	0.545486	+	0.838120i	$0.316345\pi$
$284$	7.07621	−	12.2564i	0.419896	−	0.727281i
$285$		0			0
$286$	22.8531	−	11.2002i	1.35133	−	0.662279i
$287$	2.54657	+	16.9609i	0.150319	+	1.00117i
$288$		0			0
$289$	17.6545			1.03850
$290$	22.2250			1.30510
$291$		0			0
$292$	−21.6389	−	37.4797i	−1.26632	−	2.19333i
$293$	2.04388	−	3.54010i	0.119405	−	0.206815i	−0.800127	−	0.599830i	$-0.795235\pi$
$293$	2.04388	−	3.54010i	0.119405	−	0.206815i	0.919532	+	0.393015i	$0.128568\pi$
$294$		0			0
$295$	−3.81332	+	6.60486i	−0.222020	+	0.384550i
$296$	−37.3404			−2.17037
$297$		0			0
$298$	11.2262	+	19.4443i	0.650315	+	1.12638i
$299$	21.9831	+	14.7670i	1.27132	+	0.853996i
$300$		0			0
$301$	−12.3836	+	9.86404i	−0.713778	+	0.568554i
$302$	12.3337	+	21.3625i	0.709723	+	1.22928i
$303$		0			0
$304$	−12.3917	−	21.4631i	−0.710713	−	1.23099i
$305$	−26.6233			−1.52445
$306$		0			0
$307$	1.04296			0.0595250			0.0297625	−	0.999557i	$-0.490525\pi$
$307$	1.04296			0.0595250			0.0297625	+	0.999557i	$0.490525\pi$
$308$	25.8031	−	20.5533i	1.47027	−	1.17113i
$309$		0			0
$310$	−27.4888			−1.56126
$311$	3.88724	+	6.73290i	0.220425	+	0.381788i	0.954937	−	0.296808i	$-0.0959221\pi$
$311$	3.88724	+	6.73290i	0.220425	+	0.381788i	−0.734512	+	0.678596i	$0.762589\pi$
$312$		0			0
$313$	−12.1950	+	21.1224i	−0.689304	+	1.19391i	0.282759	+	0.959191i	$0.408750\pi$
$313$	−12.1950	+	21.1224i	−0.689304	+	1.19391i	−0.972063	+	0.234719i	$0.924583\pi$
$314$	14.7066	+	25.4725i	0.829939	+	1.43750i
$315$		0			0
$316$	−8.47514	+	14.6794i	−0.476764	+	0.825779i
$317$	5.38045	−	9.31922i	0.302196	−	0.523419i	−0.674437	−	0.738333i	$-0.735614\pi$
$317$	5.38045	−	9.31922i	0.302196	−	0.523419i	0.976633	+	0.214913i	$0.0689468\pi$
$318$		0			0
$319$	8.65265			0.484455
$320$	0.329903	−	0.571408i	0.0184421	−	0.0319427i
$321$		0			0
$322$	46.1281	+	18.1343i	2.57062	+	1.01058i
$323$	−10.0098	−	17.3374i	−0.556958	−	0.964680i
$324$		0			0
$325$	0.677087	−	9.95524i	0.0375580	−	0.552217i
$326$	−15.5207	−	26.8827i	−0.859613	−	1.48889i
$327$		0			0
$328$	20.7119	+	35.8741i	1.14362	+	1.98081i
$329$	16.3767	−	13.0447i	0.902875	−	0.719178i
$330$		0			0
$331$	11.4845	+	19.8918i	0.631248	+	1.09335i	0.987297	+	0.158886i	$0.0507902\pi$
$331$	11.4845	+	19.8918i	0.631248	+	1.09335i	−0.356049	+	0.934467i	$0.615876\pi$
$332$	−21.7199			−1.19203
$333$		0			0
$334$	11.5973	+	20.0872i	0.634578	+	1.09912i
$335$	−12.0966	−	20.9519i	−0.660906	−	1.14472i
$336$		0			0
$337$	6.99034			0.380788			0.190394	−	0.981708i	$-0.439023\pi$
$337$	6.99034			0.380788			0.190394	+	0.981708i	$0.439023\pi$
$338$	−12.5380	−	30.6954i	−0.681976	−	1.66961i
$339$		0			0
$340$	36.9590	−	64.0148i	2.00438	−	3.47169i
$341$	−10.7019			−0.579541
$342$		0			0
$343$	−8.00712	−	16.6999i	−0.432344	−	0.901709i
$344$	−19.1190	+	33.1151i	−1.03083	+	1.78545i
$345$		0			0
$346$	1.71818	+	2.97598i	0.0923701	+	0.159990i
$347$	2.15384			0.115624			0.0578120	−	0.998327i	$-0.481588\pi$
$347$	2.15384			0.115624			0.0578120	+	0.998327i	$0.481588\pi$
$348$		0			0
$349$	−0.756384	−	1.31010i	−0.0404883	−	0.0701278i	0.845071	−	0.534654i	$-0.179558\pi$
$349$	−0.756384	−	1.31010i	−0.0404883	−	0.0701278i	−0.885559	+	0.464526i	$0.846225\pi$
$350$	−2.77289	−	18.4683i	−0.148217	−	0.987171i
$351$		0			0
$352$	8.03582	−	13.9184i	0.428311	−	0.741856i
$353$	−16.1969	+	28.0538i	−0.862073	+	1.49315i	0.00785109	+	0.999969i	$0.497501\pi$
$353$	−16.1969	+	28.0538i	−0.862073	+	1.49315i	−0.869924	+	0.493185i	$0.835832\pi$
$354$		0			0
$355$	−4.37734	−	7.58177i	−0.232325	−	0.402399i
$356$	−7.90952			−0.419204
$357$		0			0
$358$	7.60058	−	13.1646i	0.401703	−	0.695771i
$359$	7.93156	−	13.7379i	0.418612	−	0.725057i	−0.577188	−	0.816611i	$-0.695850\pi$
$359$	7.93156	−	13.7379i	0.418612	−	0.725057i	0.995800	+	0.0915543i	$0.0291835\pi$
$360$		0			0
$361$	3.71746	−	6.43883i	0.195656	−	0.338886i
$362$	−26.6522			−1.40081
$363$		0			0
$364$	−24.4347	−	35.3567i	−1.28072	−	1.85320i
$365$	−26.7716			−1.40129
$366$		0			0
$367$	−6.29687	+	10.9065i	−0.328694	+	0.569315i	−0.982253	−	0.187561i	$-0.939942\pi$
$367$	−6.29687	+	10.9065i	−0.328694	+	0.569315i	0.653559	+	0.756876i	$0.273275\pi$
$368$	53.5271			2.79029
$369$		0			0
$370$	−20.7690	+	35.9730i	−1.07973	+	1.87015i
$371$	4.98490	+	33.2009i	0.258803	+	1.72371i
$372$		0			0
$373$	5.85178	+	10.1356i	0.302994	+	0.524800i	0.976813	−	0.214096i	$-0.0686806\pi$
$373$	5.85178	+	10.1356i	0.302994	+	0.524800i	−0.673819	+	0.738896i	$0.735347\pi$
$374$	20.7763	−	35.9856i	1.07432	−	1.86077i
$375$		0			0
$376$	25.2839	−	43.7930i	1.30392	−	2.25845i
$377$	0.764942	−	11.2470i	0.0393965	−	0.579249i
$378$		0			0
$379$	−16.4778	−	28.5403i	−0.846406	−	1.46602i	−0.884395	−	0.466740i	$-0.845428\pi$
$379$	−16.4778	−	28.5403i	−0.846406	−	1.46602i	0.0379888	−	0.999278i	$-0.487905\pi$
$380$	−42.7017			−2.19055
$381$		0			0
$382$	0.839280	+	1.45368i	0.0429413	+	0.0743765i
$383$	6.31803	+	10.9431i	0.322836	+	0.559169i	0.981072	−	0.193643i	$-0.0620304\pi$
$383$	6.31803	+	10.9431i	0.322836	+	0.559169i	−0.658236	+	0.752812i	$0.728697\pi$
$384$		0			0
$385$	−3.02996	−	20.1804i	−0.154421	−	1.02849i
$386$	11.2041	−	19.4060i	0.570272	−	0.987741i
$387$		0			0
$388$	38.2343	−	66.2237i	1.94105	−	3.36200i
$389$	0.0593906	+	0.102868i	0.00301122	+	0.00521559i	0.867527	−	0.497390i	$-0.165708\pi$
$389$	0.0593906	+	0.102868i	0.00301122	+	0.00521559i	−0.864516	+	0.502606i	$0.832375\pi$
$390$		0			0
$391$	43.2381			2.18664
$392$	−32.7553	−	30.4620i	−1.65439	−	1.53856i
$393$		0			0
$394$	−23.7147	−	41.0750i	−1.19473	−	2.06933i
$395$	5.24271	+	9.08064i	0.263789	+	0.456897i
$396$		0			0
$397$	−3.49151	−	6.04747i	−0.175234	−	0.303514i	0.765008	−	0.644020i	$-0.222735\pi$
$397$	−3.49151	−	6.04747i	−0.175234	−	0.303514i	−0.940242	+	0.340506i	$0.889401\pi$
$398$	−38.8340			−1.94657
$399$		0			0
$400$	−10.0841	−	17.4662i	−0.504207	−	0.873312i
$401$	19.1517			0.956389			0.478194	−	0.878254i	$-0.341291\pi$
$401$	19.1517			0.956389			0.478194	+	0.878254i	$0.341291\pi$
$402$		0			0
$403$	−0.946109	+	13.9107i	−0.0471291	+	0.692941i
$404$	−4.15109	+	7.18989i	−0.206524	+	0.357711i
$405$		0			0
$406$	−3.13269	−	20.8646i	−0.155473	−	1.03549i
$407$	−8.08580	+	14.0050i	−0.400798	+	0.694203i
$408$		0			0
$409$	11.6901			0.578039			0.289019	−	0.957323i	$-0.406671\pi$
$409$	11.6901			0.578039			0.289019	+	0.957323i	$0.406671\pi$
$410$	46.0805			2.27575
$411$		0			0
$412$	−10.7456	+	18.6119i	−0.529398	+	0.916944i
$413$	6.73807	+	2.64893i	0.331559	+	0.130345i
$414$		0			0
$415$	−6.71794	+	11.6358i	−0.329771	+	0.571180i
$416$	−17.3812	−	11.6757i	−0.852185	−	0.572447i
$417$		0			0
$418$	−24.0045			−1.17410
$419$	−7.89905	−	13.6816i	−0.385894	−	0.668388i	0.605999	−	0.795465i	$-0.292774\pi$
$419$	−7.89905	−	13.6816i	−0.385894	−	0.668388i	−0.991893	+	0.127078i	$0.959440\pi$
$420$		0			0
$421$	8.58170			0.418247			0.209123	−	0.977889i	$-0.432939\pi$
$421$	8.58170			0.418247			0.209123	+	0.977889i	$0.432939\pi$
$422$	27.0220	+	46.8035i	1.31541	+	2.27836i
$423$		0			0
$424$	40.5434	+	70.2232i	1.96896	+	3.41034i
$425$	−8.14577	−	14.1089i	−0.395128	−	0.684381i
$426$		0			0
$427$	3.75264	+	24.9937i	0.181603	+	1.20953i
$428$	54.4043			2.62973
$429$		0			0
$430$	21.2683	+	36.8378i	1.02565	+	1.77648i
$431$	−9.72232	+	16.8396i	−0.468308	+	0.811133i	−0.999344	−	0.0362164i	$-0.988469\pi$
$431$	−9.72232	+	16.8396i	−0.468308	+	0.811133i	0.531036	+	0.847349i	$0.321803\pi$
$432$		0			0
$433$	2.35409	−	4.07740i	0.113130	−	0.195948i	−0.803900	−	0.594764i	$-0.797246\pi$
$433$	2.35409	−	4.07740i	0.113130	−	0.195948i	0.917031	+	0.398816i	$0.130579\pi$
$434$	3.87463	+	25.8062i	0.185988	+	1.23874i
$435$		0			0
$436$	15.3581	+	26.6011i	0.735521	+	1.27396i
$437$	−12.4891	−	21.6318i	−0.597435	−	1.03479i
$438$		0			0
$439$	−20.6623			−0.986157			−0.493078	−	0.869985i	$-0.664128\pi$
$439$	−20.6623			−0.986157			−0.493078	+	0.869985i	$0.664128\pi$
$440$	−24.6434	−	42.6836i	−1.17483	−	2.03486i
$441$		0			0
$442$	−44.9385	−	30.1870i	−2.13751	−	1.43585i
$443$	−6.14100	+	10.6365i	−0.291768	+	0.505357i	−0.974228	−	0.225566i	$-0.927577\pi$
$443$	−6.14100	+	10.6365i	−0.291768	+	0.505357i	0.682460	+	0.730923i	$0.260910\pi$
$444$		0			0
$445$	−2.44641	+	4.23730i	−0.115971	+	0.200867i
$446$	1.15610	+	2.00243i	0.0547430	+	0.0948177i
$447$		0			0
$448$	−0.582933	−	0.229168i	−0.0275410	−	0.0108272i
$449$	−13.7884	+	23.8822i	−0.650714	+	1.12707i	0.332235	+	0.943196i	$0.392197\pi$
$449$	−13.7884	+	23.8822i	−0.650714	+	1.12707i	−0.982950	+	0.183874i	$0.941136\pi$
$450$		0			0
$451$	17.9401			0.844764
$452$	12.2755	−	21.2618i	0.577390	−	1.00007i
$453$		0			0
$454$	4.91771			0.230800
$455$	−26.4990	+	2.15437i	−1.24229	+	0.100999i
$456$		0			0
$457$	13.8786			0.649214			0.324607	−	0.945849i	$-0.394768\pi$
$457$	13.8786			0.649214			0.324607	+	0.945849i	$0.394768\pi$
$458$	−12.8951	+	22.3349i	−0.602547	+	1.04364i
$459$		0			0
$460$	46.1134	−	79.8708i	2.15005	−	3.72399i
$461$	12.2050	−	21.1396i	0.568441	−	0.984569i	−0.428279	−	0.903647i	$-0.640880\pi$
$461$	12.2050	−	21.1396i	0.568441	−	0.984569i	0.996720	−	0.0809228i	$-0.0257867\pi$
$462$		0			0
$463$	−11.6449			−0.541185			−0.270593	−	0.962694i	$-0.587220\pi$
$463$	−11.6449			−0.541185			−0.270593	+	0.962694i	$0.587220\pi$
$464$	−11.3926	−	19.7326i	−0.528888	−	0.916062i
$465$		0			0
$466$	33.4465	−	57.9310i	1.54938	−	2.68360i
$467$	−2.09483	+	3.62835i	−0.0969370	+	0.167900i	−0.910415	−	0.413695i	$-0.864238\pi$
$467$	−2.09483	+	3.62835i	−0.0969370	+	0.167900i	0.813478	+	0.581595i	$0.197571\pi$
$468$		0			0
$469$	−17.9644	+	14.3094i	−0.829517	+	0.660745i
$470$	−28.1263	−	48.7161i	−1.29737	−	2.24711i
$471$		0			0
$472$	17.4864			0.804879
$473$	8.28017	+	14.3417i	0.380723	+	0.659431i
$474$		0			0
$475$	−4.70573	+	8.15056i	−0.215914	+	0.373973i
$476$	−65.3060	−	25.6736i	−2.99329	−	1.17675i
$477$		0			0
$478$	71.5575			3.27297
$479$	−7.50423	+	12.9977i	−0.342877	+	0.593880i	−0.984966	−	0.172750i	$-0.944735\pi$
$479$	−7.50423	+	12.9977i	−0.342877	+	0.593880i	0.642089	+	0.766630i	$0.278068\pi$
$480$		0			0
$481$	17.4893	+	11.7483i	0.797445	+	0.535676i
$482$	11.3564			0.517268
$483$		0			0
$484$	7.52652	+	13.0363i	0.342115	+	0.592560i
$485$	−23.6517	−	40.9659i	−1.07397	−	1.86016i
$486$		0			0
$487$	6.60817			0.299445			0.149722	−	0.988728i	$-0.452162\pi$
$487$	6.60817			0.299445			0.149722	+	0.988728i	$0.452162\pi$
$488$	30.5212	+	52.8642i	1.38163	+	2.39305i
$489$		0			0
$490$	−47.5653	+	14.6126i	−2.14878	+	0.660131i
$491$	16.4555	+	28.5018i	0.742628	+	1.28627i	0.951295	+	0.308283i	$0.0997544\pi$
$491$	16.4555	+	28.5018i	0.742628	+	1.28627i	−0.208666	+	0.977987i	$0.566912\pi$
$492$		0			0
$493$	−9.20272	−	15.9396i	−0.414470	−	0.717883i
$494$	−2.12213	+	31.2018i	−0.0954792	+	1.40384i
$495$		0			0
$496$	14.0908	+	24.4060i	0.632696	+	1.09586i
$497$	−6.50069	+	5.17808i	−0.291596	+	0.232268i
$498$		0			0
$499$	−17.9199	+	31.0381i	−0.802204	+	1.38946i	0.115959	+	0.993254i	$0.463006\pi$
$499$	−17.9199	+	31.0381i	−0.802204	+	1.38946i	−0.918163	+	0.396203i	$0.870328\pi$
$500$	28.0329			1.25367
$501$		0			0
$502$	3.96390	−	6.86567i	0.176917	−	0.306430i
$503$	9.67700	−	16.7610i	0.431476	−	0.747338i	−0.565525	−	0.824731i	$-0.691326\pi$
$503$	9.67700	−	16.7610i	0.431476	−	0.747338i	0.997001	+	0.0773931i	$0.0246596\pi$
$504$		0			0
$505$	2.56786	+	4.44766i	0.114268	+	0.197918i
$506$	25.9224	−	44.8989i	1.15239	−	1.99600i
$507$		0			0
$508$	−3.99410	−	6.91799i	−0.177210	−	0.306936i
$509$	−10.4975			−0.465292			−0.232646	−	0.972561i	$-0.574738\pi$
$509$	−10.4975			−0.465292			−0.232646	+	0.972561i	$0.574738\pi$
$510$		0			0
$511$	3.77354	+	25.1329i	0.166932	+	1.11181i
$512$	50.8157			2.24576
$513$		0			0
$514$	−66.2773			−2.92337
$515$	6.64721	+	11.5133i	0.292911	+	0.507337i
$516$		0			0
$517$	−10.9501	−	18.9662i	−0.481585	−	0.834130i
$518$	36.6986	+	14.4273i	1.61244	+	0.633897i
$519$		0			0
$520$	−57.6601	+	28.2588i	−2.52856	+	1.23923i
$521$	−10.7923	−	18.6928i	−0.472818	−	0.818945i	0.526698	−	0.850053i	$-0.323430\pi$
$521$	−10.7923	−	18.6928i	−0.472818	−	0.818945i	−0.999516	+	0.0311074i	$0.990097\pi$
$522$		0			0
$523$	3.46379			0.151461			0.0757304	−	0.997128i	$-0.475871\pi$
$523$	3.46379			0.151461			0.0757304	+	0.997128i	$0.475871\pi$
$524$	15.8019	−	27.3697i	0.690308	−	1.19565i
$525$		0			0
$526$	−16.2988	+	28.2304i	−0.710662	+	1.23090i
$527$	11.3823	+	19.7147i	0.495819	+	0.858784i
$528$		0			0
$529$	30.9478			1.34556
$530$	90.2023			3.91814
$531$		0			0
$532$	6.01893	+	40.0879i	0.260954	+	1.73803i
$533$	1.58600	−	23.3191i	0.0686973	−	1.01006i
$534$		0			0
$535$	16.8272	−	29.1456i	0.727504	−	1.26007i
$536$	−27.7352	+	48.0387i	−1.19798	+	2.07496i
$537$		0			0
$538$	4.99270			0.215250
$539$	−18.5181	+	5.68899i	−0.797631	+	0.245042i
$540$		0			0
$541$	4.46427	−	7.73234i	0.191934	−	0.332439i	−0.753957	−	0.656924i	$-0.771857\pi$
$541$	4.46427	−	7.73234i	0.191934	−	0.332439i	0.945891	+	0.324484i	$0.105191\pi$
$542$	−68.6658			−2.94945
$543$		0			0
$544$	−34.1867			−1.46574
$545$	19.0010			0.813915
$546$		0			0
$547$	−3.62704			−0.155081			−0.0775405	−	0.996989i	$-0.524707\pi$
$547$	−3.62704			−0.155081			−0.0775405	+	0.996989i	$0.524707\pi$
$548$	88.5641			3.78327
$549$		0			0
$550$	−19.5344			−0.832951
$551$	−5.31632	+	9.20813i	−0.226483	+	0.392280i
$552$		0			0
$553$	7.78584	−	6.20175i	0.331088	−	0.263725i
$554$	59.0598			2.50921
$555$		0			0
$556$	−41.3297	+	71.5851i	−1.75277	+	3.03588i
$557$	−10.0223	+	17.3592i	−0.424660	+	0.735533i	−0.996389	−	0.0849101i	$-0.972940\pi$
$557$	−10.0223	+	17.3592i	−0.424660	+	0.735533i	0.571729	+	0.820443i	$0.306273\pi$
$558$		0			0
$559$	19.3738	−	9.49495i	0.819424	−	0.401593i
$560$	−42.0325	+	33.4807i	−1.77620	+	1.41482i
$561$		0			0
$562$	−68.6987			−2.89788
$563$	7.55430			0.318376			0.159188	−	0.987248i	$-0.449112\pi$
$563$	7.55430			0.318376			0.159188	+	0.987248i	$0.449112\pi$
$564$		0			0
$565$	−7.59360	−	13.1525i	−0.319465	−	0.553330i
$566$	19.4408	−	33.6725i	0.817158	−	1.41536i
$567$		0			0
$568$	−10.0364	+	17.3836i	−0.421119	+	0.729399i
$569$	−28.1656			−1.18076			−0.590381	−	0.807125i	$-0.701023\pi$
$569$	−28.1656			−1.18076			−0.590381	+	0.807125i	$0.701023\pi$
$570$		0			0
$571$	9.03604	+	15.6509i	0.378146	+	0.654969i	0.990793	−	0.135389i	$-0.0432283\pi$
$571$	9.03604	+	15.6509i	0.378146	+	0.654969i	−0.612646	+	0.790357i	$0.709895\pi$
$572$	−40.3683	+	19.7842i	−1.68788	+	0.827219i
$573$		0			0
$574$	−6.49519	−	43.2599i	−0.271104	−	1.80563i
$575$	−10.1634	−	17.6035i	−0.423843	−	0.734118i
$576$		0			0
$577$	21.5383	+	37.3054i	0.896651	+	1.55305i	0.831747	+	0.555154i	$0.187341\pi$
$577$	21.5383	+	37.3054i	0.896651	+	1.55305i	0.0649040	+	0.997892i	$0.479326\pi$
$578$	−45.0288			−1.87295
$579$		0			0
$580$	−39.2588			−1.63013
$581$	11.8705	+	4.66663i	0.492472	+	0.193605i
$582$		0			0
$583$	35.1175			1.45442
$584$	30.6911	+	53.1586i	1.27001	+	2.19972i
$585$		0			0
$586$	−5.21304	+	9.02925i	−0.215349	+	0.372995i
$587$	−2.26101	−	3.91619i	−0.0933220	−	0.161638i	0.815585	−	0.578637i	$-0.196415\pi$
$587$	−2.26101	−	3.91619i	−0.0933220	−	0.161638i	−0.908907	+	0.416999i	$0.863082\pi$
$588$		0			0
$589$	6.57542	−	11.3890i	0.270936	−	0.469274i
$590$	9.72610	−	16.8461i	0.400417	−	0.693543i
$591$		0			0
$592$	42.5850			1.75023
$593$	−1.43449	+	2.48460i	−0.0589073	+	0.102030i	−0.893975	−	0.448117i	$-0.852095\pi$
$593$	−1.43449	+	2.48460i	−0.0589073	+	0.102030i	0.835068	+	0.550147i	$0.185428\pi$
$594$		0			0
$595$	−33.9530	+	27.0450i	−1.39194	+	1.10874i
$596$	−19.8302	−	34.3469i	−0.812276	−	1.40690i
$597$		0			0
$598$	−56.0694	−	37.6641i	−2.29285	−	1.54020i
$599$	2.94653	+	5.10354i	0.120392	+	0.208525i	0.919922	−	0.392101i	$-0.128252\pi$
$599$	2.94653	+	5.10354i	0.120392	+	0.208525i	−0.799530	+	0.600626i	$0.794918\pi$
$600$		0			0
$601$	−9.46284	−	16.3901i	−0.385997	−	0.668567i	0.605910	−	0.795533i	$-0.292809\pi$
$601$	−9.46284	−	16.3901i	−0.385997	−	0.668567i	−0.991907	+	0.126967i	$0.959476\pi$
$602$	31.5851	−	25.1589i	1.28731	−	1.02540i
$603$		0			0
$604$	−21.7865	−	37.7353i	−0.886479	−	1.53543i
$605$	9.31179			0.378578
$606$		0			0
$607$	−21.9391	−	37.9997i	−0.890482	−	1.54236i	−0.839299	−	0.543671i	$-0.817034\pi$
$607$	−21.9391	−	37.9997i	−0.890482	−	1.54236i	−0.0511833	−	0.998689i	$-0.516299\pi$
$608$	9.87466	+	17.1034i	0.400470	+	0.693635i
$609$		0			0
$610$	67.9045			2.74937
$611$	−25.6209	+	12.5566i	−1.03651	+	0.507985i
$612$		0			0
$613$	−15.2913	+	26.4853i	−0.617610	+	1.06973i	0.372310	+	0.928108i	$0.378566\pi$
$613$	−15.2913	+	26.4853i	−0.617610	+	1.06973i	−0.989921	+	0.141624i	$0.954768\pi$
$614$	−2.66014			−0.107355
$615$		0			0
$616$	−36.5974	+	29.1513i	−1.47455	+	1.17454i
$617$	−22.1042	+	38.2856i	−0.889881	+	1.54132i	−0.0498659	+	0.998756i	$0.515879\pi$
$617$	−22.1042	+	38.2856i	−0.889881	+	1.54132i	−0.840015	+	0.542563i	$0.817454\pi$
$618$		0			0
$619$	0.184678	+	0.319871i	0.00742283	+	0.0128567i	0.869713	−	0.493558i	$-0.164304\pi$
$619$	0.184678	+	0.319871i	0.00742283	+	0.0128567i	−0.862290	+	0.506415i	$0.830971\pi$
$620$	48.5568			1.95009
$621$		0			0
$622$	−9.91466	−	17.1727i	−0.397542	−	0.688562i
$623$	4.32277	+	1.69940i	0.173188	+	0.0680851i
$624$		0			0
$625$	15.5892	−	27.0013i	0.623569	−	1.08005i
$626$	31.1042	−	53.8741i	1.24317	−	2.15324i
$627$		0			0
$628$	−25.9780	−	44.9952i	−1.03664	−	1.79550i
$629$	34.3993			1.37159
$630$		0			0
$631$	6.70906	−	11.6204i	0.267083	−	0.462602i	−0.701024	−	0.713138i	$-0.747273\pi$
$631$	6.70906	−	11.6204i	0.267083	−	0.462602i	0.968107	+	0.250536i	$0.0806067\pi$
$632$	12.0206	−	20.8202i	0.478152	−	0.828184i
$633$		0			0
$634$	−13.7232	+	23.7693i	−0.545017	+	0.943998i
$635$	−4.94149			−0.196097
$636$		0			0
$637$	5.75762	+	24.5734i	0.228125	+	0.973632i
$638$	−22.0691			−0.873725
$639$		0			0
$640$	15.3437	−	26.5761i	0.606515	−	1.05051i
$641$	−43.0337			−1.69973			−0.849865	−	0.527000i	$-0.823317\pi$
$641$	−43.0337			−1.69973			−0.849865	+	0.527000i	$0.823317\pi$
$642$		0			0
$643$	14.6688	−	25.4071i	0.578482	−	1.00196i	−0.417172	−	0.908828i	$-0.636979\pi$
$643$	14.6688	−	25.4071i	0.578482	−	1.00196i	0.995654	−	0.0931324i	$-0.0296880\pi$
$644$	−81.4817	−	32.0328i	−3.21083	−	1.26227i
$645$		0			0
$646$	25.5305	+	44.2202i	1.00449	+	1.73982i
$647$	−9.00352	+	15.5945i	−0.353965	+	0.613085i	−0.986940	−	0.161087i	$-0.948500\pi$
$647$	−9.00352	+	15.5945i	−0.353965	+	0.613085i	0.632975	+	0.774172i	$0.281833\pi$
$648$		0			0
$649$	3.78656	−	6.55852i	0.148636	−	0.257445i
$650$	−1.72695	+	25.3915i	−0.0677366	+	0.995936i
$651$		0			0
$652$	27.4161	+	47.4862i	1.07370	+	1.85970i
$653$	−34.6541			−1.35612			−0.678059	−	0.735007i	$-0.737179\pi$
$653$	−34.6541			−1.35612			−0.678059	+	0.735007i	$0.737179\pi$
$654$		0			0
$655$	−9.77502	−	16.9308i	−0.381942	−	0.661543i
$656$	−23.6210	−	40.9127i	−0.922244	−	1.59737i
$657$		0			0
$658$	−41.7697	+	33.2713i	−1.62835	+	1.29705i
$659$	2.68796	−	4.65569i	0.104708	−	0.181360i	−0.808911	−	0.587931i	$-0.799942\pi$
$659$	2.68796	−	4.65569i	0.104708	−	0.181360i	0.913619	+	0.406572i	$0.133276\pi$
$660$		0			0
$661$	−20.2356	+	35.0490i	−0.787072	+	1.36325i	0.140681	+	0.990055i	$0.455071\pi$
$661$	−20.2356	+	35.0490i	−0.787072	+	1.36325i	−0.927753	+	0.373194i	$0.878263\pi$
$662$	−29.2921	−	50.7353i	−1.13847	−	1.97188i
$663$		0			0
$664$	30.8060			1.19550
$665$	23.3376	+	9.17469i	0.904994	+	0.355779i
$666$		0			0
$667$	−11.4822	−	19.8877i	−0.444591	−	0.770054i
$668$	−20.4858	−	35.4825i	−0.792620	−	1.37286i
$669$		0			0
$670$	30.8531	+	53.4391i	1.19196	+	2.06453i
$671$	26.4366			1.02057
$672$		0			0
$673$	13.1634	+	22.7996i	0.507411	+	0.878861i	0.999963	+	0.00857837i	$0.00273061\pi$
$673$	13.1634	+	22.7996i	0.507411	+	0.878861i	−0.492553	+	0.870283i	$0.663936\pi$
$674$	−17.8293			−0.686759
$675$		0			0
$676$	22.1474	+	54.2210i	0.851821	+	2.08542i
$677$	1.90262	−	3.29544i	0.0731236	−	0.126654i	−0.827145	−	0.561988i	$-0.810037\pi$
$677$	1.90262	−	3.29544i	0.0731236	−	0.126654i	0.900269	+	0.435335i	$0.143370\pi$
$678$		0			0
$679$	−35.1246	+	27.9782i	−1.34796	+	1.07371i
$680$	−52.4201	+	90.7942i	−2.01022	+	3.48180i
$681$		0			0
$682$	27.2959			1.04521
$683$	−10.3953			−0.397765			−0.198882	−	0.980023i	$-0.563731\pi$
$683$	−10.3953			−0.397765			−0.198882	+	0.980023i	$0.563731\pi$
$684$		0			0
$685$	27.3928	−	47.4458i	1.04663	−	1.81281i
$686$	20.4227	+	42.5941i	0.779741	+	1.62625i
$687$		0			0
$688$	21.8044	−	37.7663i	0.831284	−	1.43983i
$689$	3.10459	−	45.6469i	0.118275	−	1.73901i
$690$		0			0
$691$	−8.19915			−0.311910			−0.155955	−	0.987764i	$-0.549846\pi$
$691$	−8.19915			−0.311910			−0.155955	+	0.987764i	$0.549846\pi$
$692$	−3.03504	−	5.25684i	−0.115375	−	0.199835i
$693$		0			0
$694$	−5.49350			−0.208530
$695$	25.5665	+	44.2824i	0.969792	+	1.67973i
$696$		0			0
$697$	−19.0806	−	33.0485i	−0.722728	−	1.25180i
$698$	1.92921	+	3.34148i	0.0730215	+	0.126477i
$699$		0			0
$700$	4.89810	+	32.6228i	0.185131	+	1.23303i
$701$	−4.64503			−0.175440			−0.0877201	−	0.996145i	$-0.527958\pi$
$701$	−4.64503			−0.175440			−0.0877201	+	0.996145i	$0.527958\pi$
$702$		0			0
$703$	−9.93608	−	17.2098i	−0.374746	−	0.649080i
$704$	−0.327588	+	0.567400i	−0.0123464	+	0.0213847i
$705$		0			0
$706$	41.3112	−	71.5531i	1.55477	−	2.69293i
$707$	3.81347	−	3.03759i	0.143420	−	0.114240i
$708$		0			0
$709$	22.1987	+	38.4494i	0.833691	+	1.44400i	0.895091	+	0.445883i	$0.147110\pi$
$709$	22.1987	+	38.4494i	0.833691	+	1.44400i	−0.0614001	+	0.998113i	$0.519557\pi$
$710$	11.1647	+	19.3378i	0.419003	+	0.725734i
$711$		0			0
$712$	11.2183			0.420424
$713$	14.2016	+	24.5978i	0.531853	+	0.921196i
$714$		0			0
$715$	−1.88705	+	27.7454i	−0.0705718	+	1.03762i
$716$	−13.4258	+	23.2542i	−0.501747	+	0.869052i
$717$		0			0
$718$	−20.2299	+	35.0393i	−0.754975	+	1.30765i
$719$	−22.4689	−	38.9173i	−0.837949	−	1.45137i	−0.891606	−	0.452812i	$-0.850421\pi$
$719$	−22.4689	−	38.9173i	−0.837949	−	1.45137i	0.0536569	−	0.998559i	$-0.482912\pi$
$720$		0			0
$721$	9.87164	−	7.86318i	0.367639	−	0.292840i
$722$	−9.48161	+	16.4226i	−0.352869	+	0.611187i
$723$		0			0
$724$	47.0790			1.74968
$725$	−4.32632	+	7.49341i	−0.160676	+	0.278298i
$726$		0			0
$727$	−49.7876			−1.84652			−0.923260	−	0.384177i	$-0.874485\pi$
$727$	−49.7876			−1.84652			−0.923260	+	0.384177i	$0.874485\pi$
$728$	34.6564	+	50.1476i	1.28445	+	1.85859i
$729$		0			0
$730$	68.2827			2.52725
$731$	17.6131	−	30.5068i	0.651445	−	1.12834i
$732$		0			0
$733$	9.96819	−	17.2654i	0.368184	−	0.637713i	−0.621098	−	0.783733i	$-0.713313\pi$
$733$	9.96819	−	17.2654i	0.368184	−	0.637713i	0.989282	+	0.146020i	$0.0466465\pi$
$734$	16.0606	−	27.8177i	0.592807	−	1.02677i
$735$		0			0
$736$	−42.6545			−1.57227
$737$	12.0117	+	20.8049i	0.442457	+	0.766358i
$738$		0			0
$739$	−24.0236	+	41.6100i	−0.883721	+	1.53065i	−0.0365482	+	0.999332i	$0.511636\pi$
$739$	−24.0236	+	41.6100i	−0.883721	+	1.53065i	−0.847173	+	0.531318i	$0.821697\pi$
$740$	36.6869	−	63.5436i	1.34864	−	2.33591i
$741$		0			0
$742$	−12.7143	−	84.6810i	−0.466757	−	3.10874i
$743$	0.250266	+	0.433473i	0.00918137	+	0.0159026i	0.870580	−	0.492028i	$-0.163744\pi$
$743$	0.250266	+	0.433473i	0.00918137	+	0.0159026i	−0.861398	+	0.507930i	$0.830411\pi$
$744$		0			0
$745$	−24.5338			−0.898850
$746$	−14.9253	−	25.8514i	−0.546455	−	0.946488i
$747$		0			0
$748$	−36.6997	+	63.5657i	−1.34187	+	2.32419i
$749$	−29.7334	−	11.6891i	−1.08644	−	0.427109i
$750$		0			0
$751$	43.8051			1.59847			0.799235	−	0.601019i	$-0.205238\pi$
$751$	43.8051			1.59847			0.799235	+	0.601019i	$0.205238\pi$
$752$	−28.8352	+	49.9440i	−1.05151	+	1.82127i
$753$		0			0
$754$	−1.95103	+	28.6861i	−0.0710524	+	1.04469i
$755$	−26.9542			−0.980963
$756$		0			0
$757$	1.91271	+	3.31291i	0.0695186	+	0.120410i	0.898689	−	0.438585i	$-0.144520\pi$
$757$	1.91271	+	3.31291i	0.0695186	+	0.120410i	−0.829171	+	0.558995i	$0.811187\pi$
$758$	42.0276	+	72.7939i	1.52651	+	2.64399i
$759$		0			0
$760$	60.5651			2.19693
$761$	−2.86572	−	4.96357i	−0.103882	−	0.179929i	0.809399	−	0.587259i	$-0.199793\pi$
$761$	−2.86572	−	4.96357i	−0.103882	−	0.179929i	−0.913281	+	0.407330i	$0.866460\pi$
$762$		0			0
$763$	−2.67826	−	17.8380i	−0.0969594	−	0.645779i
$764$	−1.48252	−	2.56781i	−0.0536358	−	0.0928999i
$765$		0			0
$766$	−16.1145	−	27.9112i	−0.582242	−	1.00847i
$767$	−8.19022	−	5.50171i	−0.295732	−	0.198655i
$768$		0			0
$769$	8.50053	+	14.7234i	0.306537	+	0.530938i	0.977602	−	0.210461i	$-0.0674964\pi$
$769$	8.50053	+	14.7234i	0.306537	+	0.530938i	−0.671065	+	0.741398i	$0.734163\pi$
$770$	7.72810	+	51.4714i	0.278501	+	1.85490i
$771$		0			0
$772$	−19.7911	+	34.2792i	−0.712298	+	1.23374i
$773$	12.1864			0.438314			0.219157	−	0.975690i	$-0.429669\pi$
$773$	12.1864			0.438314			0.219157	+	0.975690i	$0.429669\pi$
$774$		0			0
$775$	5.35096	−	9.26813i	0.192212	−	0.332921i
$776$	−54.2288	+	93.9271i	−1.94670	+	3.37179i
$777$		0			0
$778$	−0.151480	−	0.262370i	−0.00543080	−	0.00940643i
$779$	−11.0226	+	19.0918i	−0.394927	+	0.684034i
$780$		0			0
$781$	4.34663	+	7.52858i	0.155535	+	0.269394i
$782$	−110.281			−3.94366
$783$		0			0
$784$	37.3559	+	34.7405i	1.33414	+	1.24073i
$785$	−32.1399			−1.14712
$786$		0			0
$787$	−4.62042			−0.164700			−0.0823501	−	0.996603i	$-0.526243\pi$
$787$	−4.62042			−0.164700			−0.0823501	+	0.996603i	$0.526243\pi$
$788$	41.8901	+	72.5558i	1.49227	+	2.58469i
$789$		0			0
$790$	−13.3719	−	23.1608i	−0.475750	−	0.824023i
$791$	−11.2771	+	8.98268i	−0.400967	+	0.319387i
$792$		0			0
$793$	2.33714	−	34.3631i	0.0829943	−	1.22027i
$794$	8.90531	+	15.4245i	0.316038	+	0.547393i
$795$		0			0
$796$	68.5972			2.43136
$797$	9.12087	−	15.7978i	0.323078	−	0.559587i	−0.658044	−	0.752980i	$-0.728616\pi$
$797$	9.12087	−	15.7978i	0.323078	−	0.559587i	0.981121	+	0.193393i	$0.0619491\pi$
$798$		0			0
$799$	−23.2925	+	40.3438i	−0.824029	+	1.42726i
$800$	8.03582	+	13.9184i	0.284109	+	0.492091i
$801$		0			0
$802$	−48.8475			−1.72487
$803$	26.5838			0.938122
$804$		0			0
$805$	−42.3629	+	33.7439i	−1.49310	+	1.18931i
$806$	2.41311	−	35.4801i	0.0849982	−	1.24973i
$807$		0			0
$808$	5.88762	−	10.1976i	0.207126	−	0.358752i
$809$	−17.2960	+	29.9576i	−0.608096	+	1.05325i	0.383457	+	0.923559i	$0.374733\pi$
$809$	−17.2960	+	29.9576i	−0.608096	+	1.05325i	−0.991554	+	0.129695i	$0.958600\pi$
$810$		0			0
$811$	−11.9774			−0.420582			−0.210291	−	0.977639i	$-0.567441\pi$
$811$	−11.9774			−0.420582			−0.210291	+	0.977639i	$0.567441\pi$
$812$	5.53365	+	36.8558i	0.194193	+	1.29338i
$813$		0			0
$814$	20.6233	−	35.7207i	0.722848	−	1.25201i
$815$	33.9192			1.18814
$816$		0			0
$817$	−20.3499			−0.711951
$818$	−29.8164			−1.04250
$819$		0			0
$820$	−81.3976			−2.84253
$821$	−21.1872			−0.739438			−0.369719	−	0.929144i	$-0.620546\pi$
$821$	−21.1872			−0.739438			−0.369719	+	0.929144i	$0.620546\pi$
$822$		0			0
$823$	19.9361			0.694930			0.347465	−	0.937693i	$-0.387043\pi$
$823$	19.9361			0.694930			0.347465	+	0.937693i	$0.387043\pi$
$824$	15.2408	−	26.3979i	0.530939	−	0.919614i
$825$		0			0
$826$	−17.1859	−	6.75626i	−0.597973	−	0.235080i
$827$	15.0299			0.522639			0.261320	−	0.965252i	$-0.415842\pi$
$827$	15.0299			0.522639			0.261320	+	0.965252i	$0.415842\pi$
$828$		0			0
$829$	−8.03587	+	13.9185i	−0.279097	+	0.483411i	−0.971161	−	0.238426i	$-0.923369\pi$
$829$	−8.03587	+	13.9185i	−0.279097	+	0.483411i	0.692063	+	0.721837i	$0.256702\pi$
$830$	17.1345	−	29.6779i	0.594749	−	1.03013i
$831$		0			0
$832$	0.708563	+	0.475971i	0.0245650	+	0.0165013i
$833$	30.1754	+	28.0627i	1.04552	+	0.972315i
$834$		0			0
$835$	−25.3450			−0.877100
$836$	42.4021			1.46651
$837$		0			0
$838$	20.1470	+	34.8957i	0.695967	+	1.20545i
$839$	−2.50930	+	4.34624i	−0.0866307	+	0.150049i	−0.906085	−	0.423096i	$-0.860943\pi$
$839$	−2.50930	+	4.34624i	−0.0866307	+	0.150049i	0.819454	+	0.573145i	$0.194277\pi$
$840$		0			0
$841$	9.61231	−	16.6490i	0.331459	−	0.574104i
$842$	−21.8882			−0.754316
$843$		0			0
$844$	−47.7323	−	82.6747i	−1.64301	−	2.84578i
$845$	35.8976	+	4.90570i	1.23491	+	0.168761i
$846$		0			0
$847$	−1.31253	−	8.74182i	−0.0450989	−	0.300372i
$848$	−46.2379	−	80.0864i	−1.58782	−	2.75018i
$849$		0			0
$850$	20.7763	+	35.9856i	0.712621	+	1.23430i
$851$	42.9198			1.47127
$852$		0			0
$853$	−4.22423			−0.144635			−0.0723175	−	0.997382i	$-0.523039\pi$
$853$	−4.22423			−0.144635			−0.0723175	+	0.997382i	$0.523039\pi$
$854$	−9.57136	−	63.7481i	−0.327525	−	2.18141i
$855$		0			0
$856$	−77.1633			−2.63739
$857$	−4.48428	−	7.76700i	−0.153180	−	0.265316i	0.779215	−	0.626757i	$-0.215618\pi$
$857$	−4.48428	−	7.76700i	−0.153180	−	0.265316i	−0.932395	+	0.361441i	$0.882285\pi$
$858$		0			0
$859$	18.3400	−	31.7658i	0.625753	−	1.08384i	−0.362642	−	0.931928i	$-0.618125\pi$
$859$	18.3400	−	31.7658i	0.625753	−	1.08384i	0.988395	−	0.151907i	$-0.0485414\pi$
$860$	−37.5688	−	65.0711i	−1.28109	−	2.21890i
$861$		0			0
$862$	24.7974	−	42.9503i	0.844602	−	1.46289i
$863$	10.4237	−	18.0544i	0.354828	−	0.614580i	−0.632261	−	0.774756i	$-0.717873\pi$
$863$	10.4237	−	18.0544i	0.354828	−	0.614580i	0.987088	+	0.160176i	$0.0512062\pi$
$864$		0			0
$865$	−3.75494			−0.127672
$866$	−6.00426	+	10.3997i	−0.204033	+	0.353395i
$867$		0			0
$868$	−6.84423	−	45.5846i	−0.232308	−	1.54724i
$869$	−5.20593	−	9.01694i	−0.176599	−	0.305879i
$870$		0			0
$871$	28.1048	−	13.7739i	0.952294	−	0.466712i
$872$	−21.7829	−	37.7291i	−0.737663	−	1.27767i
$873$		0			0
$874$	31.8543	+	55.1732i	1.07749	+	1.86626i
$875$	−15.3208	−	6.02303i	−0.517936	−	0.203615i
$876$		0			0
$877$	13.8100	+	23.9197i	0.466331	+	0.807709i	0.999261	−	0.0384504i	$-0.0122422\pi$
$877$	13.8100	+	23.9197i	0.466331	+	0.807709i	−0.532929	+	0.846160i	$0.678909\pi$
$878$	52.7004			1.77855
$879$		0			0
$880$	28.1047	+	48.6787i	0.947408	+	1.64096i
$881$	12.7092	+	22.0130i	0.428183	+	0.741635i	0.996712	−	0.0810283i	$-0.0258204\pi$
$881$	12.7092	+	22.0130i	0.428183	+	0.741635i	−0.568528	+	0.822664i	$0.692487\pi$
$882$		0			0
$883$	32.7921			1.10354			0.551771	−	0.833995i	$-0.313952\pi$
$883$	32.7921			1.10354			0.551771	+	0.833995i	$0.313952\pi$
$884$	79.3803	+	53.3230i	2.66985	+	1.79345i
$885$		0			0
$886$	15.6630	−	27.1291i	0.526209	−	0.911421i
$887$	7.93320			0.266371			0.133185	−	0.991091i	$-0.457479\pi$
$887$	7.93320			0.266371			0.133185	+	0.991091i	$0.457479\pi$
$888$		0			0
$889$	0.696519	+	4.63903i	0.0233605	+	0.155588i
$890$	6.23972	−	10.8075i	0.209156	−	0.362269i
$891$		0			0
$892$	−2.04217	−	3.53713i	−0.0683768	−	0.118432i
$893$	26.9117			0.900565
$894$		0			0
$895$	8.30521	+	14.3850i	0.277613	+	0.480839i
$896$	−27.1122	−	10.6586i	−0.905754	−	0.356078i
$897$		0			0
$898$	35.1682	−	60.9130i	1.17358	−	2.03269i
$899$	6.04527	−	10.4707i	0.201621	−	0.349218i
$900$		0			0
$901$	−37.3501	−	64.6922i	−1.24431	−	2.15521i
$902$	−45.7572			−1.52355
$903$		0			0
$904$	−17.4107	+	30.1562i	−0.579071	+	1.00298i
$905$	14.5615	−	25.2213i	0.484041	−	0.838384i
$906$		0			0
$907$	23.1186	−	40.0426i	0.767640	−	1.32959i	−0.171200	−	0.985236i	$-0.554764\pi$
$907$	23.1186	−	40.0426i	0.767640	−	1.32959i	0.938840	−	0.344355i	$-0.111902\pi$
$908$	−8.68676			−0.288280
$909$		0			0
$910$	67.5874	−	5.49486i	2.24050	−	0.182153i
$911$	21.5838			0.715102			0.357551	−	0.933894i	$-0.383612\pi$
$911$	21.5838			0.715102			0.357551	+	0.933894i	$0.383612\pi$
$912$		0			0
$913$	6.67082	−	11.5542i	0.220772	−	0.382388i
$914$	−35.3983			−1.17087
$915$		0			0
$916$	22.7781	−	39.4529i	0.752611	−	1.30356i
$917$	−14.5167	+	11.5632i	−0.479383	+	0.381849i
$918$		0			0
$919$	4.40489	+	7.62950i	0.145304	+	0.251674i	0.929486	−	0.368857i	$-0.120251\pi$
$919$	4.40489	+	7.62950i	0.145304	+	0.251674i	−0.784182	+	0.620530i	$0.786917\pi$
$920$	−65.4041	+	113.283i	−2.15631	+	3.73484i
$921$		0			0
$922$	−31.1295	+	53.9179i	−1.02520	+	1.77569i
$923$	10.1702	−	4.98432i	0.334755	−	0.164061i
$924$		0			0
$925$	−8.08580	−	14.0050i	−0.265859	−	0.460482i
$926$	29.7011			0.976039
$927$		0			0
$928$	9.07851	+	15.7244i	0.298017	+	0.516180i
$929$	−26.2347	−	45.4398i	−0.860733	−	1.49083i	−0.871223	−	0.490888i	$-0.836672\pi$
$929$	−26.2347	−	45.4398i	−0.860733	−	1.49083i	0.0104899	−	0.999945i	$-0.496661\pi$
$930$		0			0
$931$	5.32359	−	23.2023i	0.174474	−	0.760426i
$932$	−59.0806	+	102.331i	−1.93525	+	3.35195i
$933$		0			0
$934$	5.34299	−	9.25433i	0.174828	−	0.302811i
$935$	22.7024	+	39.3217i	0.742448	+	1.28596i
$936$		0			0
$937$	−19.3131			−0.630932			−0.315466	−	0.948937i	$-0.602161\pi$
$937$	−19.3131			−0.630932			−0.315466	+	0.948937i	$0.602161\pi$
$938$	45.8192	−	36.4970i	1.49605	−	1.19167i
$939$		0			0
$940$	49.6829	+	86.0532i	1.62048	+	2.80675i
$941$	8.45918	+	14.6517i	0.275761	+	0.477633i	0.970327	−	0.241797i	$-0.0777367\pi$
$941$	8.45918	+	14.6517i	0.275761	+	0.477633i	−0.694566	+	0.719429i	$0.744403\pi$
$942$		0			0
$943$	−23.8067	−	41.2343i	−0.775251	−	1.34277i
$944$	−19.9425			−0.649073
$945$		0			0
$946$	−21.1191	−	36.5793i	−0.686641	−	1.18930i
$947$	44.7022			1.45263			0.726313	−	0.687365i	$-0.241232\pi$
$947$	44.7022			1.45263			0.726313	+	0.687365i	$0.241232\pi$
$948$		0			0
$949$	2.35016	−	34.5545i	0.0762893	−	1.12169i
$950$	12.0023	−	20.7885i	0.389405	−	0.674468i
$951$		0			0
$952$	92.6255	+	36.4137i	3.00201	+	1.18018i
$953$	24.8774	−	43.0888i	0.805857	−	1.39578i	−0.109855	−	0.993948i	$-0.535038\pi$
$953$	24.8774	−	43.0888i	0.805857	−	1.39578i	0.915711	−	0.401837i	$-0.131628\pi$
$954$		0			0
$955$	−1.83417			−0.0593525
$956$	−126.401			−4.08809
$957$		0			0
$958$	19.1400	−	33.1515i	0.618386	−	1.07108i
$959$	−48.4027	−	19.0285i	−1.56301	−	0.614462i
$960$		0			0
$961$	8.02298	−	13.8962i	0.258806	−	0.448265i
$962$	−44.6076	−	29.9648i	−1.43821	−	0.966103i
$963$		0			0
$964$	−20.0601			−0.646094
$965$	12.2428	+	21.2051i	0.394109	+	0.682616i
$966$		0			0
$967$	1.92897			0.0620315			0.0310158	−	0.999519i	$-0.490126\pi$
$967$	1.92897			0.0620315			0.0310158	+	0.999519i	$0.490126\pi$
$968$	−10.6751	−	18.4898i	−0.343111	−	0.594285i
$969$		0			0
$970$	60.3251	+	104.486i	1.93692	+	3.35485i
$971$	−18.0616	−	31.2836i	−0.579624	−	1.00394i	−0.995522	−	0.0945270i	$-0.969866\pi$
$971$	−18.0616	−	31.2836i	−0.579624	−	1.00394i	0.415898	−	0.909411i	$-0.363467\pi$
$972$		0			0
$973$	37.9682	−	30.2433i	1.21721	−	0.969556i
$974$	−16.8546			−0.540055
$975$		0			0
$976$	−34.8080	−	60.2893i	−1.11418	−	1.92981i
$977$	16.4841	−	28.5513i	0.527373	−	0.913436i	−0.472118	−	0.881535i	$-0.656510\pi$
$977$	16.4841	−	28.5513i	0.527373	−	0.913436i	0.999491	−	0.0319012i	$-0.0101562\pi$
$978$		0			0
$979$	2.42925	−	4.20758i	0.0776391	−	0.134475i
$980$	84.0203	−	25.8121i	2.68393	−	0.824537i
$981$		0			0
$982$	−41.9709	−	72.6957i	−1.33935	−	2.31981i
$983$	−7.52903	−	13.0407i	−0.240139	−	0.415933i	0.720615	−	0.693336i	$-0.243860\pi$
$983$	−7.52903	−	13.0407i	−0.240139	−	0.415933i	−0.960754	+	0.277403i	$0.910526\pi$
$984$		0			0
$985$	51.8263			1.65132
$986$	23.4721	+	40.6549i	0.747504	+	1.29472i
$987$		0			0
$988$	3.74858	−	55.1156i	0.119258	−	1.75346i
$989$	21.9758	−	38.0631i	0.698789	−	1.21034i
$990$		0			0
$991$	−18.0676	+	31.2939i	−0.573935	+	0.994085i	0.422221	+	0.906493i	$0.361251\pi$
$991$	−18.0676	+	31.2939i	−0.573935	+	0.994085i	−0.996156	+	0.0875921i	$0.972083\pi$
$992$	−11.2286	−	19.4486i	−0.356510	−	0.617493i
$993$		0			0
$994$	16.5804	−	13.2070i	0.525899	−	0.418901i
$995$	21.2171	−	36.7491i	0.672627	−	1.16502i
$996$		0			0
$997$	3.81524			0.120830			0.0604149	−	0.998173i	$-0.480758\pi$
$997$	3.81524			0.120830			0.0604149	+	0.998173i	$0.480758\pi$
$998$	45.7058	−	79.1647i	1.44679	−	2.50591i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.e.289.1		16
3.2	odd	2		273.2.l.b.16.8	yes	16
7.4	even	3		819.2.n.e.172.8		16
13.9	even	3		819.2.n.e.100.8		16
21.11	odd	6		273.2.j.b.172.1	yes	16
39.35	odd	6		273.2.j.b.100.1	✓	16
91.74	even	3	inner	819.2.s.e.802.1		16
273.74	odd	6		273.2.l.b.256.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.1	✓	16	39.35	odd	6
273.2.j.b.172.1	yes	16	21.11	odd	6
273.2.l.b.16.8	yes	16	3.2	odd	2
273.2.l.b.256.8	yes	16	273.74	odd	6
819.2.n.e.100.8		16	13.9	even	3
819.2.n.e.172.8		16	7.4	even	3
819.2.s.e.289.1		16	1.1	even	1	trivial
819.2.s.e.802.1		16	91.74	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.55056 q^{2} +4.50537 q^{4} +(1.39351 - 2.41363i) q^{5} +(-2.46231 - 0.968004i) q^{7} -6.39011 q^{8} +(-3.55423 + 6.15611i) q^{10} +(-1.38373 + 2.39670i) q^{11} +(2.99297 + 2.01050i) q^{13} +(6.28028 + 2.46895i) q^{14} +7.28763 q^{16} +5.88680 q^{17} +(-1.70037 - 2.94513i) q^{19} +(6.27828 - 10.8743i) q^{20} +(3.52930 - 6.11292i) q^{22} +7.34492 q^{23} +(-1.38373 - 2.39670i) q^{25} +(-7.63376 - 5.12791i) q^{26} +(-11.0936 - 4.36122i) q^{28} +(-1.56328 - 2.70768i) q^{29} +(1.93352 + 3.34896i) q^{31} -5.80735 q^{32} -15.0147 q^{34} +(-5.76765 + 4.59418i) q^{35} +5.84347 q^{37} +(4.33691 + 7.51175i) q^{38} +(-8.90467 + 15.4233i) q^{40} +(-3.24124 - 5.61400i) q^{41} +(2.99197 - 5.18224i) q^{43} +(-6.23423 + 10.7980i) q^{44} -18.7337 q^{46} +(-3.95673 + 6.85325i) q^{47} +(5.12594 + 4.76705i) q^{49} +(3.52930 + 6.11292i) q^{50} +(13.4845 + 9.05806i) q^{52} +(-6.34471 - 10.9894i) q^{53} +(3.85649 + 6.67963i) q^{55} +(15.7344 + 6.18565i) q^{56} +(3.98724 + 6.90611i) q^{58} -2.73648 q^{59} +(-4.77631 - 8.27282i) q^{61} +(-4.93157 - 8.54173i) q^{62} +0.236742 q^{64} +(9.02334 - 4.42227i) q^{65} +(4.34033 - 7.51767i) q^{67} +26.5222 q^{68} +(14.7108 - 11.7177i) q^{70} +(1.57062 - 2.72039i) q^{71} +(-4.80291 - 8.31889i) q^{73} -14.9041 q^{74} +(-7.66082 - 13.2689i) q^{76} +(5.72719 - 4.56195i) q^{77} +(-1.88112 + 3.25819i) q^{79} +(10.1554 - 17.5896i) q^{80} +(8.26699 + 14.3189i) q^{82} -4.82088 q^{83} +(8.20331 - 14.2086i) q^{85} +(-7.63120 + 13.2176i) q^{86} +(8.84221 - 15.3151i) q^{88} -1.75557 q^{89} +(-5.42345 - 7.84769i) q^{91} +33.0916 q^{92} +(10.0919 - 17.4797i) q^{94} -9.47794 q^{95} +(8.48637 - 14.6988i) q^{97} +(-13.0740 - 12.1587i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31}+ \cdots - 18 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

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