LMFDB - Embedded newform 819.2.s.g.289.12

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			289.12
Character	$\chi$	$=$	819.289
Dual form			819.2.s.g.802.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.09380 q^{2} -0.803600 q^{4} +(-0.179458 + 0.310830i) q^{5} +(2.59911 + 0.494573i) q^{7} -3.06658 q^{8} +(-0.196291 + 0.339986i) q^{10} +(0.697132 - 1.20747i) q^{11} +(3.19831 - 1.66457i) q^{13} +(2.84291 + 0.540964i) q^{14} -1.74703 q^{16} +6.02773 q^{17} +(-0.0503215 - 0.0871594i) q^{19} +(0.144212 - 0.249783i) q^{20} +(0.762523 - 1.32073i) q^{22} -2.30972 q^{23} +(2.43559 + 4.21857i) q^{25} +(3.49832 - 1.82071i) q^{26} +(-2.08865 - 0.397439i) q^{28} +(4.04339 + 7.00337i) q^{29} +(2.94949 + 5.10866i) q^{31} +4.22226 q^{32} +6.59314 q^{34} +(-0.620159 + 0.719128i) q^{35} +5.28441 q^{37} +(-0.0550417 - 0.0953350i) q^{38} +(0.550322 - 0.953185i) q^{40} +(-5.97937 - 10.3566i) q^{41} +(5.43548 - 9.41454i) q^{43} +(-0.560215 + 0.970321i) q^{44} -2.52638 q^{46} +(-4.67269 + 8.09334i) q^{47} +(6.51079 + 2.57090i) q^{49} +(2.66405 + 4.61427i) q^{50} +(-2.57017 + 1.33765i) q^{52} +(-5.20881 - 9.02192i) q^{53} +(0.250211 + 0.433379i) q^{55} +(-7.97039 - 1.51665i) q^{56} +(4.42267 + 7.66029i) q^{58} -9.03407 q^{59} +(-0.812845 - 1.40789i) q^{61} +(3.22615 + 5.58786i) q^{62} +8.11236 q^{64} +(-0.0565649 + 1.29285i) q^{65} +(3.12115 - 5.40599i) q^{67} -4.84389 q^{68} +(-0.678331 + 0.786582i) q^{70} +(2.36071 - 4.08886i) q^{71} +(-1.63045 - 2.82402i) q^{73} +5.78010 q^{74} +(0.0404384 + 0.0700413i) q^{76} +(2.40911 - 2.79356i) q^{77} +(-3.65397 + 6.32887i) q^{79} +(0.313517 - 0.543028i) q^{80} +(-6.54024 - 11.3280i) q^{82} +8.23791 q^{83} +(-1.08172 + 1.87360i) q^{85} +(5.94534 - 10.2976i) q^{86} +(-2.13781 + 3.70280i) q^{88} -11.8662 q^{89} +(9.13604 - 2.74460i) q^{91} +1.85609 q^{92} +(-5.11099 + 8.85250i) q^{94} +0.0361224 q^{95} +(-3.37036 + 5.83763i) q^{97} +(7.12151 + 2.81206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.09380			0.773434			0.386717	−	0.922198i	$-0.373609\pi$
$2$	1.09380			0.773434			0.386717	+	0.922198i	$0.373609\pi$
$3$		0			0
$3$		0			0
$4$	−0.803600			−0.401800
$5$	−0.179458	+	0.310830i	−0.0802560	+	0.139007i	−0.903360	−	0.428883i	$-0.858907\pi$
$5$	−0.179458	+	0.310830i	−0.0802560	+	0.139007i	0.823104	+	0.567891i	$0.192240\pi$
$6$		0			0
$7$	2.59911	+	0.494573i	0.982373	+	0.186931i
$7$	2.59911	+	0.494573i	0.982373	+	0.186931i
$8$	−3.06658			−1.08420
$9$		0			0
$10$	−0.196291	+	0.339986i	−0.0620727	+	0.107513i
$11$	0.697132	−	1.20747i	0.210193	−	0.364065i	−0.741582	−	0.670863i	$-0.765924\pi$
$11$	0.697132	−	1.20747i	0.210193	−	0.364065i	0.951775	+	0.306797i	$0.0992574\pi$
$12$		0			0
$13$	3.19831	−	1.66457i	0.887053	−	0.461668i
$13$	3.19831	−	1.66457i	0.887053	−	0.461668i
$14$	2.84291	+	0.540964i	0.759801	+	0.144579i
$15$		0			0
$16$	−1.74703			−0.436757
$17$	6.02773			1.46194			0.730970	−	0.682409i	$-0.239068\pi$
$17$	6.02773			1.46194			0.730970	+	0.682409i	$0.239068\pi$
$18$		0			0
$19$	−0.0503215	−	0.0871594i	−0.0115445	−	0.0199957i	0.860195	−	0.509965i	$-0.170341\pi$
$19$	−0.0503215	−	0.0871594i	−0.0115445	−	0.0199957i	−0.871740	+	0.489969i	$0.837008\pi$
$20$	0.144212	−	0.249783i	0.0322468	−	0.0558532i
$21$		0			0
$22$	0.762523	−	1.32073i	0.162570	−	0.281580i
$23$	−2.30972			−0.481611			−0.240805	−	0.970573i	$-0.577412\pi$
$23$	−2.30972			−0.481611			−0.240805	+	0.970573i	$0.577412\pi$
$24$		0			0
$25$	2.43559	+	4.21857i	0.487118	+	0.843713i
$26$	3.49832	−	1.82071i	0.686077	−	0.357070i
$27$		0			0
$28$	−2.08865	−	0.397439i	−0.394718	−	0.0751089i
$29$	4.04339	+	7.00337i	0.750840	+	1.30049i	0.947416	+	0.320004i	$0.103684\pi$
$29$	4.04339	+	7.00337i	0.750840	+	1.30049i	−0.196577	+	0.980488i	$0.562982\pi$
$30$		0			0
$31$	2.94949	+	5.10866i	0.529744	+	0.917543i	0.999398	+	0.0346927i	$0.0110452\pi$
$31$	2.94949	+	5.10866i	0.529744	+	0.917543i	−0.469654	+	0.882850i	$0.655621\pi$
$32$	4.22226			0.746397
$33$		0			0
$34$	6.59314			1.13071
$35$	−0.620159	+	0.719128i	−0.104826	+	0.121555i
$36$		0			0
$37$	5.28441			0.868752			0.434376	−	0.900732i	$-0.356969\pi$
$37$	5.28441			0.868752			0.434376	+	0.900732i	$0.356969\pi$
$38$	−0.0550417	−	0.0953350i	−0.00892895	−	0.0154654i
$39$		0			0
$40$	0.550322	−	0.953185i	0.0870135	−	0.150712i
$41$	−5.97937	−	10.3566i	−0.933821	−	1.61743i	−0.776723	−	0.629843i	$-0.783119\pi$
$41$	−5.97937	−	10.3566i	−0.933821	−	1.61743i	−0.157098	−	0.987583i	$-0.550214\pi$
$42$		0			0
$43$	5.43548	−	9.41454i	0.828904	−	1.43570i	−0.0699953	−	0.997547i	$-0.522298\pi$
$43$	5.43548	−	9.41454i	0.828904	−	1.43570i	0.898899	−	0.438156i	$-0.144368\pi$
$44$	−0.560215	+	0.970321i	−0.0844556	+	0.146281i
$45$		0			0
$46$	−2.52638			−0.372494
$47$	−4.67269	+	8.09334i	−0.681582	+	1.18054i	0.292916	+	0.956138i	$0.405375\pi$
$47$	−4.67269	+	8.09334i	−0.681582	+	1.18054i	−0.974498	+	0.224397i	$0.927959\pi$
$48$		0			0
$49$	6.51079	+	2.57090i	0.930114	+	0.367272i
$50$	2.66405	+	4.61427i	0.376754	+	0.652556i
$51$		0			0
$52$	−2.57017	+	1.33765i	−0.356418	+	0.185498i
$53$	−5.20881	−	9.02192i	−0.715485	−	1.23926i	−0.962772	−	0.270314i	$-0.912873\pi$
$53$	−5.20881	−	9.02192i	−0.715485	−	1.23926i	0.247288	−	0.968942i	$-0.420461\pi$
$54$		0			0
$55$	0.250211	+	0.433379i	0.0337385	+	0.0584368i
$56$	−7.97039	−	1.51665i	−1.06509	−	0.202671i
$57$		0			0
$58$	4.42267	+	7.66029i	0.580725	+	1.00584i
$59$	−9.03407			−1.17614			−0.588068	−	0.808811i	$-0.700111\pi$
$59$	−9.03407			−1.17614			−0.588068	+	0.808811i	$0.700111\pi$
$60$		0			0
$61$	−0.812845	−	1.40789i	−0.104074	−	0.180262i	0.809285	−	0.587416i	$-0.199855\pi$
$61$	−0.812845	−	1.40789i	−0.104074	−	0.180262i	−0.913360	+	0.407154i	$0.866521\pi$
$62$	3.22615	+	5.58786i	0.409722	+	0.709659i
$63$		0			0
$64$	8.11236			1.01405
$65$	−0.0565649	+	1.29285i	−0.00701601	+	0.160358i
$66$		0			0
$67$	3.12115	−	5.40599i	0.381309	−	0.660447i	−0.609941	−	0.792447i	$-0.708807\pi$
$67$	3.12115	−	5.40599i	0.381309	−	0.660447i	0.991250	+	0.132000i	$0.0421400\pi$
$68$	−4.84389			−0.587408
$69$		0			0
$70$	−0.678331	+	0.786582i	−0.0810760	+	0.0940146i
$71$	2.36071	−	4.08886i	0.280164	−	0.485259i	−0.691261	−	0.722605i	$-0.742944\pi$
$71$	2.36071	−	4.08886i	0.280164	−	0.485259i	0.971425	+	0.237347i	$0.0762777\pi$
$72$		0			0
$73$	−1.63045	−	2.82402i	−0.190830	−	0.330527i	0.754696	−	0.656075i	$-0.227784\pi$
$73$	−1.63045	−	2.82402i	−0.190830	−	0.330527i	−0.945525	+	0.325548i	$0.894451\pi$
$74$	5.78010			0.671923
$75$		0			0
$76$	0.0404384	+	0.0700413i	0.00463860	+	0.00803429i
$77$	2.40911	−	2.79356i	0.274543	−	0.318356i
$78$		0			0
$79$	−3.65397	+	6.32887i	−0.411104	+	0.712053i	−0.995011	−	0.0997675i	$-0.968190\pi$
$79$	−3.65397	+	6.32887i	−0.411104	+	0.712053i	0.583907	+	0.811821i	$0.301523\pi$
$80$	0.313517	−	0.543028i	0.0350523	−	0.0607124i
$81$		0			0
$82$	−6.54024	−	11.3280i	−0.722249	−	1.25097i
$83$	8.23791			0.904228			0.452114	−	0.891960i	$-0.350670\pi$
$83$	8.23791			0.904228			0.452114	+	0.891960i	$0.350670\pi$
$84$		0			0
$85$	−1.08172	+	1.87360i	−0.117329	+	0.203220i
$86$	5.94534	−	10.2976i	0.641102	−	1.11042i
$87$		0			0
$88$	−2.13781	+	3.70280i	−0.227891	+	0.394719i
$89$	−11.8662			−1.25782			−0.628909	−	0.777479i	$-0.716498\pi$
$89$	−11.8662			−1.25782			−0.628909	+	0.777479i	$0.716498\pi$
$90$		0			0
$91$	9.13604	−	2.74460i	0.957717	−	0.287712i
$92$	1.85609			0.193511
$93$		0			0
$94$	−5.11099	+	8.85250i	−0.527159	+	0.913066i
$95$	0.0361224			0.00370608
$96$		0			0
$97$	−3.37036	+	5.83763i	−0.342208	+	0.592722i	−0.984842	−	0.173451i	$-0.944508\pi$
$97$	−3.37036	+	5.83763i	−0.342208	+	0.592722i	0.642635	+	0.766173i	$0.277841\pi$
$98$	7.12151	+	2.81206i	0.719381	+	0.284061i
$99$		0			0
$100$	−1.95724	−	3.39004i	−0.195724	−	0.339004i
$101$	−7.06616	+	12.2390i	−0.703109	+	1.21782i	0.264260	+	0.964451i	$0.414872\pi$
$101$	−7.06616	+	12.2390i	−0.703109	+	1.21782i	−0.967370	+	0.253370i	$0.918461\pi$
$102$		0			0
$103$	−3.40155	+	5.89166i	−0.335165	+	0.580523i	−0.983516	−	0.180818i	$-0.942125\pi$
$103$	−3.40155	+	5.89166i	−0.335165	+	0.580523i	0.648352	+	0.761341i	$0.275459\pi$
$104$	−9.80789	+	5.10453i	−0.961742	+	0.500540i
$105$		0			0
$106$	−5.69740	−	9.86818i	−0.553380	−	0.958482i
$107$	−18.0865			−1.74849			−0.874246	−	0.485483i	$-0.838644\pi$
$107$	−18.0865			−1.74849			−0.874246	+	0.485483i	$0.838644\pi$
$108$		0			0
$109$	−0.968032	−	1.67668i	−0.0927207	−	0.160597i	0.815934	−	0.578145i	$-0.196223\pi$
$109$	−0.968032	−	1.67668i	−0.0927207	−	0.160597i	−0.908655	+	0.417548i	$0.862890\pi$
$110$	0.273681	+	0.474030i	0.0260945	+	0.0451970i
$111$		0			0
$112$	−4.54072	−	0.864032i	−0.429058	−	0.0816434i
$113$	0.793136	−	1.37375i	0.0746119	−	0.129232i	−0.826306	−	0.563222i	$-0.809562\pi$
$113$	0.793136	−	1.37375i	0.0746119	−	0.129232i	0.900917	+	0.433990i	$0.142895\pi$
$114$		0			0
$115$	0.414498	−	0.717931i	0.0386521	−	0.0669474i
$116$	−3.24927	−	5.62791i	−0.301687	−	0.522538i
$117$		0			0
$118$	−9.88147			−0.909663
$119$	15.6668	+	2.98116i	1.43617	+	0.273282i
$120$		0			0
$121$	4.52801	+	7.84275i	0.411638	+	0.712977i
$122$	−0.889090	−	1.53995i	−0.0804944	−	0.139420i
$123$		0			0
$124$	−2.37021	−	4.10532i	−0.212851	−	0.368669i
$125$	−3.54292			−0.316888
$126$		0			0
$127$	−7.35093	−	12.7322i	−0.652290	−	1.12980i	−0.982566	−	0.185915i	$-0.940475\pi$
$127$	−7.35093	−	12.7322i	−0.652290	−	1.12980i	0.330276	−	0.943884i	$-0.392858\pi$
$128$	0.428789			0.0378999
$129$		0			0
$130$	−0.0618707	+	1.41412i	−0.00542642	+	0.124027i
$131$	3.10064	−	5.37046i	0.270904	−	0.469220i	−0.698190	−	0.715913i	$-0.746011\pi$
$131$	3.10064	−	5.37046i	0.270904	−	0.469220i	0.969094	+	0.246693i	$0.0793440\pi$
$132$		0			0
$133$	−0.0876847	−	0.251425i	−0.00760323	−	0.0218013i
$134$	3.41392	−	5.91307i	0.294917	−	0.510812i
$135$		0			0
$136$	−18.4845			−1.58504
$137$	−5.65097			−0.482795			−0.241398	−	0.970426i	$-0.577606\pi$
$137$	−5.65097			−0.482795			−0.241398	+	0.970426i	$0.577606\pi$
$138$		0			0
$139$	−8.97874	+	15.5516i	−0.761567	+	1.31907i	0.180476	+	0.983579i	$0.442236\pi$
$139$	−8.97874	+	15.5516i	−0.761567	+	1.31907i	−0.942043	+	0.335493i	$0.891097\pi$
$140$	0.498360	−	0.577891i	0.0421191	−	0.0488407i
$141$		0			0
$142$	2.58214	−	4.47240i	0.216689	−	0.375316i
$143$	0.219735	−	5.02228i	0.0183752	−	0.419985i
$144$		0			0
$145$	−2.90247			−0.241037
$146$	−1.78339	−	3.08891i	−0.147594	−	0.255640i
$147$		0			0
$148$	−4.24656			−0.349065
$149$	11.1029	+	19.2308i	0.909584	+	1.57545i	0.814642	+	0.579964i	$0.196933\pi$
$149$	11.1029	+	19.2308i	0.909584	+	1.57545i	0.0949421	+	0.995483i	$0.469733\pi$
$150$		0			0
$151$	−6.95630	−	12.0487i	−0.566095	−	0.980506i	−0.996947	−	0.0780832i	$-0.975120\pi$
$151$	−6.95630	−	12.0487i	−0.566095	−	0.980506i	0.430851	−	0.902423i	$-0.358213\pi$
$152$	0.154315	+	0.267281i	0.0125166	+	0.0216794i
$153$		0			0
$154$	2.63508	−	3.05560i	0.212341	−	0.246227i
$155$	−2.11723			−0.170060
$156$		0			0
$157$	−6.11973	−	10.5997i	−0.488408	−	0.845947i	0.511503	−	0.859281i	$-0.329089\pi$
$157$	−6.11973	−	10.5997i	−0.488408	−	0.845947i	−0.999911	+	0.0133340i	$0.995756\pi$
$158$	−3.99672	+	6.92252i	−0.317962	+	0.550726i
$159$		0			0
$160$	−0.757717	+	1.31241i	−0.0599028	+	0.103755i
$161$	−6.00324	−	1.14233i	−0.473121	−	0.0900280i
$162$		0			0
$163$	7.77814	+	13.4721i	0.609231	+	1.05522i	0.991367	+	0.131113i	$0.0418549\pi$
$163$	7.77814	+	13.4721i	0.609231	+	1.05522i	−0.382137	+	0.924106i	$0.624812\pi$
$164$	4.80502	+	8.32255i	0.375209	+	0.649882i
$165$		0			0
$166$	9.01063			0.699361
$167$	−0.0298989	−	0.0517864i	−0.00231365	−	0.00400735i	0.864866	−	0.502002i	$-0.167403\pi$
$167$	−0.0298989	−	0.0517864i	−0.00231365	−	0.00400735i	−0.867180	+	0.497995i	$0.834070\pi$
$168$		0			0
$169$	7.45843	−	10.6476i	0.573725	−	0.819048i
$170$	−1.18319	+	2.04935i	−0.0907465	+	0.157178i
$171$		0			0
$172$	−4.36796	+	7.56552i	−0.333054	+	0.576866i
$173$	−7.32243	−	12.6828i	−0.556714	−	0.964257i	−0.997768	−	0.0667767i	$-0.978728\pi$
$173$	−7.32243	−	12.6828i	−0.556714	−	0.964257i	0.441054	−	0.897481i	$-0.354605\pi$
$174$		0			0
$175$	4.24399	+	12.1691i	0.320815	+	0.919898i
$176$	−1.21791	+	2.10948i	−0.0918033	+	0.159008i
$177$		0			0
$178$	−12.9793			−0.972840
$179$	12.4461	−	21.5573i	0.930268	−	1.61127i	0.147406	−	0.989076i	$-0.452908\pi$
$179$	12.4461	−	21.5573i	0.930268	−	1.61127i	0.782862	−	0.622195i	$-0.213759\pi$
$180$		0			0
$181$	10.8716			0.808081			0.404040	−	0.914741i	$-0.367605\pi$
$181$	10.8716			0.808081			0.404040	+	0.914741i	$0.367605\pi$
$182$	9.99300	−	3.00205i	0.740731	−	0.222527i
$183$		0			0
$184$	7.08295			0.522162
$185$	−0.948329	+	1.64255i	−0.0697226	+	0.120763i
$186$		0			0
$187$	4.20213	−	7.27829i	0.307290	−	0.532242i
$188$	3.75498	−	6.50381i	0.273860	−	0.474339i
$189$		0			0
$190$	0.0395107			0.00286640
$191$	3.02442	+	5.23844i	0.218839	+	0.379040i	0.954453	−	0.298360i	$-0.0964397\pi$
$191$	3.02442	+	5.23844i	0.218839	+	0.379040i	−0.735614	+	0.677401i	$0.763106\pi$
$192$		0			0
$193$	2.29217	−	3.97016i	0.164994	−	0.285778i	−0.771659	−	0.636036i	$-0.780573\pi$
$193$	2.29217	−	3.97016i	0.164994	−	0.285778i	0.936653	+	0.350258i	$0.113906\pi$
$194$	−3.68650	+	6.38520i	−0.264675	+	0.458431i
$195$		0			0
$196$	−5.23208	−	2.06598i	−0.373720	−	0.147570i
$197$	3.85123	+	6.67053i	0.274389	+	0.475256i	0.969981	−	0.243182i	$-0.0781911\pi$
$197$	3.85123	+	6.67053i	0.274389	+	0.475256i	−0.695592	+	0.718437i	$0.744858\pi$
$198$		0			0
$199$	−4.37138			−0.309879			−0.154940	−	0.987924i	$-0.549518\pi$
$199$	−4.37138			−0.309879			−0.154940	+	0.987924i	$0.549518\pi$
$200$	−7.46893	−	12.9366i	−0.528133	−	0.914753i
$201$		0			0
$202$	−7.72897	+	13.3870i	−0.543809	+	0.941904i
$203$	7.04557	+	20.2023i	0.494502	+	1.41792i
$204$		0			0
$205$	4.29218			0.299779
$206$	−3.72062	+	6.44430i	−0.259228	+	0.448996i
$207$		0			0
$208$	−5.58754	+	2.90804i	−0.387426	+	0.201637i
$209$	−0.140323			−0.00970634
$210$		0			0
$211$	0.357428	+	0.619084i	0.0246064	+	0.0426195i	0.878066	−	0.478539i	$-0.158833\pi$
$211$	0.357428	+	0.619084i	0.0246064	+	0.0426195i	−0.853460	+	0.521158i	$0.825500\pi$
$212$	4.18580	+	7.25001i	0.287482	+	0.497933i
$213$		0			0
$214$	−19.7831			−1.35234
$215$	1.95088	+	3.37902i	0.133049	+	0.230447i
$216$		0			0
$217$	5.13945	+	14.7367i	0.348889	+	1.00040i
$218$	−1.05883	−	1.83395i	−0.0717133	−	0.124211i
$219$		0			0
$220$	−0.201070	−	0.348263i	−0.0135561	−	0.0234799i
$221$	19.2786	−	10.0336i	1.29682	−	0.674931i
$222$		0			0
$223$	−12.1944	−	21.1213i	−0.816596	−	1.41439i	−0.908176	−	0.418588i	$-0.862525\pi$
$223$	−12.1944	−	21.1213i	−0.816596	−	1.41439i	0.0915802	−	0.995798i	$-0.470808\pi$
$224$	10.9741	+	2.08822i	0.733241	+	0.139525i
$225$		0			0
$226$	0.867533	−	1.50261i	0.0577074	−	0.0999522i
$227$	16.5604			1.09915			0.549575	−	0.835445i	$-0.314790\pi$
$227$	16.5604			1.09915			0.549575	+	0.835445i	$0.314790\pi$
$228$		0			0
$229$	−2.41260	+	4.17874i	−0.159429	+	0.276139i	−0.934663	−	0.355535i	$-0.884299\pi$
$229$	−2.41260	+	4.17874i	−0.159429	+	0.276139i	0.775234	+	0.631674i	$0.217632\pi$
$230$	0.453378	−	0.785274i	0.0298949	−	0.0517794i
$231$		0			0
$232$	−12.3994	−	21.4764i	−0.814060	−	1.40999i
$233$	6.70488	−	11.6132i	0.439251	−	0.760805i	−0.558381	−	0.829585i	$-0.688577\pi$
$233$	6.70488	−	11.6132i	0.439251	−	0.760805i	0.997632	+	0.0687796i	$0.0219105\pi$
$234$		0			0
$235$	−1.67710	−	2.90483i	−0.109402	−	0.189490i
$236$	7.25978			0.472572
$237$		0			0
$238$	17.1363	+	3.26079i	1.11078	+	0.211366i
$239$	5.50569			0.356134			0.178067	−	0.984018i	$-0.443016\pi$
$239$	5.50569			0.356134			0.178067	+	0.984018i	$0.443016\pi$
$240$		0			0
$241$	−20.4391			−1.31660			−0.658299	−	0.752757i	$-0.728724\pi$
$241$	−20.4391			−1.31660			−0.658299	+	0.752757i	$0.728724\pi$
$242$	4.95275	+	8.57841i	0.318375	+	0.551441i
$243$		0			0
$244$	0.653202	+	1.13138i	0.0418170	+	0.0724291i
$245$	−1.96753	+	1.56238i	−0.125701	+	0.0998169i
$246$		0			0
$247$	−0.306027	−	0.195000i	−0.0194720	−	0.0124075i
$248$	−9.04484	−	15.6661i	−0.574348	−	0.994800i
$249$		0			0
$250$	−3.87525			−0.245092
$251$	−9.68127	+	16.7685i	−0.611077	+	1.05842i	0.379983	+	0.924994i	$0.375930\pi$
$251$	−9.68127	+	16.7685i	−0.611077	+	1.05842i	−0.991059	+	0.133422i	$0.957403\pi$
$252$		0			0
$253$	−1.61018	+	2.78892i	−0.101231	+	0.175338i
$254$	−8.04046	−	13.9265i	−0.504503	−	0.873825i
$255$		0			0
$256$	−15.7557			−0.984732
$257$	0.718316			0.0448073			0.0224037	−	0.999749i	$-0.492868\pi$
$257$	0.718316			0.0448073			0.0224037	+	0.999749i	$0.492868\pi$
$258$		0			0
$259$	13.7348	+	2.61353i	0.853439	+	0.162397i
$260$	0.0454555	−	1.03894i	0.00281903	−	0.0644321i
$261$		0			0
$262$	3.39148	−	5.87422i	0.209526	−	0.362910i
$263$	−10.5364	+	18.2496i	−0.649702	+	1.12532i	0.333492	+	0.942753i	$0.391773\pi$
$263$	−10.5364	+	18.2496i	−0.649702	+	1.12532i	−0.983194	+	0.182564i	$0.941560\pi$
$264$		0			0
$265$	3.73904			0.229688
$266$	−0.0959096	−	0.275009i	−0.00588059	−	0.0168619i
$267$		0			0
$268$	−2.50816	+	4.34425i	−0.153210	+	0.265368i
$269$	10.1981			0.621792			0.310896	−	0.950444i	$-0.399371\pi$
$269$	10.1981			0.621792			0.310896	+	0.950444i	$0.399371\pi$
$270$		0			0
$271$	−25.6733			−1.55954			−0.779771	−	0.626065i	$-0.784665\pi$
$271$	−25.6733			−1.55954			−0.779771	+	0.626065i	$0.784665\pi$
$272$	−10.5306			−0.638512
$273$		0			0
$274$	−6.18104			−0.373410
$275$	6.79171			0.409555
$276$		0			0
$277$	3.97623			0.238908			0.119454	−	0.992840i	$-0.461886\pi$
$277$	3.97623			0.238908			0.119454	+	0.992840i	$0.461886\pi$
$278$	−9.82095	+	17.0104i	−0.589022	+	1.02022i
$279$		0			0
$280$	1.90177	−	2.20526i	0.113652	−	0.131790i
$281$	9.12206			0.544177			0.272088	−	0.962272i	$-0.412286\pi$
$281$	9.12206			0.544177			0.272088	+	0.962272i	$0.412286\pi$
$282$		0			0
$283$	−10.4761	+	18.1452i	−0.622742	+	1.07862i	0.366231	+	0.930524i	$0.380648\pi$
$283$	−10.4761	+	18.1452i	−0.622742	+	1.07862i	−0.988973	+	0.148097i	$0.952685\pi$
$284$	−1.89706	+	3.28581i	−0.112570	+	0.194977i
$285$		0			0
$286$	0.240346	−	5.49338i	0.0142120	−	0.324830i
$287$	−10.4190	−	29.8752i	−0.615014	−	1.76348i
$288$		0			0
$289$	19.3336			1.13727
$290$	−3.17473			−0.186426
$291$		0			0
$292$	1.31023	+	2.26938i	0.0766753	+	0.132806i
$293$	9.84030	−	17.0439i	0.574876	−	0.995715i	−0.421179	−	0.906978i	$-0.638383\pi$
$293$	9.84030	−	17.0439i	0.574876	−	0.995715i	0.996055	−	0.0887375i	$-0.0282832\pi$
$294$		0			0
$295$	1.62123	−	2.80806i	0.0943919	−	0.163492i
$296$	−16.2051			−0.941901
$297$		0			0
$298$	12.1444	+	21.0346i	0.703503	+	1.21850i
$299$	−7.38722	+	3.84469i	−0.427214	+	0.222344i
$300$		0			0
$301$	18.7836	−	21.7812i	1.08267	−	1.25545i
$302$	−7.60880	−	13.1788i	−0.437837	−	0.758357i
$303$		0			0
$304$	0.0879130	+	0.152270i	0.00504216	+	0.00873327i
$305$	0.583485			0.0334103
$306$		0			0
$307$	−14.0883			−0.804061			−0.402031	−	0.915626i	$-0.631696\pi$
$307$	−14.0883			−0.804061			−0.402031	+	0.915626i	$0.631696\pi$
$308$	−1.93596	+	2.24491i	−0.110311	+	0.127916i
$309$		0			0
$310$	−2.31583			−0.131530
$311$	−0.493701	−	0.855116i	−0.0279952	−	0.0484892i	0.851688	−	0.524049i	$-0.175579\pi$
$311$	−0.493701	−	0.855116i	−0.0279952	−	0.0484892i	−0.879684	+	0.475559i	$0.842246\pi$
$312$		0			0
$313$	1.34562	−	2.33069i	0.0760591	−	0.131738i	−0.825487	−	0.564421i	$-0.809100\pi$
$313$	1.34562	−	2.33069i	0.0760591	−	0.131738i	0.901546	+	0.432683i	$0.142433\pi$
$314$	−6.69377	−	11.5939i	−0.377751	−	0.654284i
$315$		0			0
$316$	2.93633	−	5.08588i	0.165182	−	0.286103i
$317$	3.19625	−	5.53606i	0.179519	−	0.310936i	−0.762197	−	0.647345i	$-0.775879\pi$
$317$	3.19625	−	5.53606i	0.179519	−	0.310936i	0.941716	+	0.336409i	$0.109213\pi$
$318$		0			0
$319$	11.2751			0.631285
$320$	−1.45583	+	2.52157i	−0.0813832	+	0.140960i
$321$		0			0
$322$	−6.56634	−	1.24948i	−0.365928	−	0.0696307i
$323$	−0.303325	−	0.525374i	−0.0168774	−	0.0292326i
$324$		0			0
$325$	14.8119	+	9.43809i	0.821615	+	0.523531i
$326$	8.50773	+	14.7358i	0.471200	+	0.816142i
$327$		0			0
$328$	18.3362	+	31.7593i	1.01245	+	1.75361i
$329$	−16.1476	+	18.7245i	−0.890247	+	1.03232i
$330$		0			0
$331$	−8.63916	−	14.9635i	−0.474851	−	0.822467i	0.524734	−	0.851266i	$-0.324165\pi$
$331$	−8.63916	−	14.9635i	−0.474851	−	0.822467i	−0.999585	+	0.0287997i	$0.990832\pi$
$332$	−6.61999			−0.363319
$333$		0			0
$334$	−0.0327034	−	0.0566440i	−0.00178945	−	0.00309942i
$335$	1.12023	+	1.94029i	0.0612046	+	0.106010i
$336$		0			0
$337$	32.8157			1.78759			0.893793	−	0.448480i	$-0.148034\pi$
$337$	32.8157			1.78759			0.893793	+	0.448480i	$0.148034\pi$
$338$	8.15804	−	11.6464i	0.443739	−	0.633479i
$339$		0			0
$340$	0.869273	−	1.50563i	0.0471430	−	0.0816540i
$341$	8.22473			0.445394
$342$		0			0
$343$	15.6508	+	9.90214i	0.845064	+	0.534665i
$344$	−16.6683	+	28.8704i	−0.898697	+	1.55659i
$345$		0			0
$346$	−8.00928	−	13.8725i	−0.430582	−	0.745789i
$347$	−24.5955			−1.32036			−0.660179	−	0.751108i	$-0.729519\pi$
$347$	−24.5955			−1.32036			−0.660179	+	0.751108i	$0.729519\pi$
$348$		0			0
$349$	5.72238	+	9.91146i	0.306312	+	0.530548i	0.977553	−	0.210691i	$-0.0675715\pi$
$349$	5.72238	+	9.91146i	0.306312	+	0.530548i	−0.671240	+	0.741240i	$0.734238\pi$
$350$	4.64208	+	13.3106i	0.248129	+	0.711481i
$351$		0			0
$352$	2.94347	−	5.09824i	0.156888	−	0.271737i
$353$	−0.435031	+	0.753497i	−0.0231544	+	0.0401046i	−0.877370	−	0.479814i	$-0.840704\pi$
$353$	−0.435031	+	0.753497i	−0.0231544	+	0.0401046i	0.854216	+	0.519918i	$0.174038\pi$
$354$		0			0
$355$	0.847294	+	1.46756i	0.0449697	+	0.0778898i
$356$	9.53571			0.505392
$357$		0			0
$358$	13.6136	−	23.5794i	0.719501	−	1.24621i
$359$	−3.03021	+	5.24849i	−0.159929	+	0.277004i	−0.934843	−	0.355062i	$-0.884460\pi$
$359$	−3.03021	+	5.24849i	−0.159929	+	0.277004i	0.774914	+	0.632067i	$0.217793\pi$
$360$		0			0
$361$	9.49494	−	16.4457i	0.499733	−	0.865564i
$362$	11.8914			0.624997
$363$		0			0
$364$	−7.34172	+	2.20556i	−0.384811	+	0.115603i
$365$	1.17039			0.0612608
$366$		0			0
$367$	−10.3629	+	17.9491i	−0.540941	+	0.936938i	0.457909	+	0.888999i	$0.348599\pi$
$367$	−10.3629	+	17.9491i	−0.540941	+	0.936938i	−0.998850	+	0.0479388i	$0.984735\pi$
$368$	4.03515			0.210347
$369$		0			0
$370$	−1.03728	+	1.79663i	−0.0539258	+	0.0934022i
$371$	−9.07629	−	26.0251i	−0.471217	−	1.35116i
$372$		0			0
$373$	12.4934	+	21.6392i	0.646884	+	1.12044i	0.983863	+	0.178924i	$0.0572617\pi$
$373$	12.4934	+	21.6392i	0.646884	+	1.12044i	−0.336979	+	0.941512i	$0.609405\pi$
$374$	4.59629	−	7.96100i	0.237668	−	0.411654i
$375$		0			0
$376$	14.3292	−	24.8189i	0.738971	−	1.27994i
$377$	24.5896	+	15.6685i	1.26643	+	0.806967i
$378$		0			0
$379$	−9.67343	−	16.7549i	−0.496890	−	0.860640i	0.503103	−	0.864226i	$-0.332192\pi$
$379$	−9.67343	−	16.7549i	−0.496890	−	0.860640i	−0.999994	+	0.00358685i	$0.998858\pi$
$380$	−0.0290279			−0.00148910
$381$		0			0
$382$	3.30811	+	5.72981i	0.169258	+	0.293163i
$383$	−5.68759	−	9.85119i	−0.290622	−	0.503372i	0.683335	−	0.730105i	$-0.260529\pi$
$383$	−5.68759	−	9.85119i	−0.290622	−	0.503372i	−0.973957	+	0.226733i	$0.927196\pi$
$384$		0			0
$385$	0.435991	+	1.25015i	0.0222201	+	0.0637135i
$386$	2.50718	−	4.34256i	0.127612	−	0.221030i
$387$		0			0
$388$	2.70842	−	4.69112i	0.137499	−	0.238156i
$389$	0.870373	+	1.50753i	0.0441297	+	0.0764348i	0.887247	−	0.461295i	$-0.152615\pi$
$389$	0.870373	+	1.50753i	0.0441297	+	0.0764348i	−0.843117	+	0.537730i	$0.819282\pi$
$390$		0			0
$391$	−13.9224			−0.704086
$392$	−19.9659	−	7.88388i	−1.00843	−	0.398196i
$393$		0			0
$394$	4.21248	+	7.29623i	0.212222	+	0.367579i
$395$	−1.31147	−	2.27153i	−0.0659871	−	0.114293i
$396$		0			0
$397$	−3.64462	−	6.31267i	−0.182918	−	0.316824i	0.759955	−	0.649976i	$-0.225221\pi$
$397$	−3.64462	−	6.31267i	−0.182918	−	0.316824i	−0.942873	+	0.333152i	$0.891888\pi$
$398$	−4.78142			−0.239671
$399$		0			0
$400$	−4.25504	−	7.36995i	−0.212752	−	0.368497i
$401$	−28.7557			−1.43599			−0.717996	−	0.696048i	$-0.754940\pi$
$401$	−28.7557			−1.43599			−0.717996	+	0.696048i	$0.754940\pi$
$402$		0			0
$403$	17.9371	+	11.4295i	0.893511	+	0.569343i
$404$	5.67837	−	9.83522i	0.282509	−	0.489321i
$405$		0			0
$406$	7.70645	+	22.0973i	0.382465	+	1.09667i
$407$	3.68393	−	6.38076i	0.182606	−	0.316283i
$408$		0			0
$409$	−15.4719			−0.765037			−0.382518	−	0.923948i	$-0.624943\pi$
$409$	−15.4719			−0.765037			−0.382518	+	0.923948i	$0.624943\pi$
$410$	4.69479			0.231859
$411$		0			0
$412$	2.73349	−	4.73454i	0.134669	−	0.233254i
$413$	−23.4806	−	4.46801i	−1.15540	−	0.219856i
$414$		0			0
$415$	−1.47836	+	2.56059i	−0.0725697	+	0.125694i
$416$	13.5041	−	7.02824i	0.662094	−	0.344588i
$417$		0			0
$418$	−0.153485			−0.00750721
$419$	5.20699	+	9.01877i	0.254378	+	0.440596i	0.964726	−	0.263254i	$-0.0847959\pi$
$419$	5.20699	+	9.01877i	0.254378	+	0.440596i	−0.710348	+	0.703850i	$0.751463\pi$
$420$		0			0
$421$	32.3268			1.57551			0.787755	−	0.615989i	$-0.211243\pi$
$421$	32.3268			1.57551			0.787755	+	0.615989i	$0.211243\pi$
$422$	0.390955	+	0.677154i	0.0190314	+	0.0329633i
$423$		0			0
$424$	15.9732	+	27.6664i	0.775728	+	1.34360i
$425$	14.6811	+	25.4284i	0.712137	+	1.23346i
$426$		0			0
$427$	−1.41637	−	4.06127i	−0.0685431	−	0.196539i
$428$	14.5343			0.702544
$429$		0			0
$430$	2.13387	+	3.69598i	0.102905	+	0.178236i
$431$	−3.47837	+	6.02472i	−0.167547	+	0.290201i	−0.937557	−	0.347832i	$-0.886918\pi$
$431$	−3.47837	+	6.02472i	−0.167547	+	0.290201i	0.770010	+	0.638032i	$0.220251\pi$
$432$		0			0
$433$	2.67170	−	4.62751i	0.128393	−	0.222384i	−0.794661	−	0.607054i	$-0.792351\pi$
$433$	2.67170	−	4.62751i	0.128393	−	0.222384i	0.923054	+	0.384670i	$0.125685\pi$
$434$	5.62154	+	16.1191i	0.269842	+	0.773740i
$435$		0			0
$436$	0.777911	+	1.34738i	0.0372552	+	0.0645279i
$437$	0.116229	+	0.201314i	0.00555998	+	0.00963016i
$438$		0			0
$439$	−26.8157			−1.27984			−0.639921	−	0.768441i	$-0.721033\pi$
$439$	−26.8157			−1.27984			−0.639921	+	0.768441i	$0.721033\pi$
$440$	−0.767293	−	1.32899i	−0.0365793	−	0.0633572i
$441$		0			0
$442$	21.0869	−	10.9747i	1.00300	−	0.522015i
$443$	1.50193	−	2.60143i	0.0713590	−	0.123597i	−0.828138	−	0.560524i	$-0.810600\pi$
$443$	1.50193	−	2.60143i	0.0713590	−	0.123597i	0.899497	+	0.436927i	$0.143933\pi$
$444$		0			0
$445$	2.12949	−	3.68838i	0.100947	−	0.174846i
$446$	−13.3382	−	23.1025i	−0.631583	−	1.09393i
$447$		0			0
$448$	21.0850	+	4.01216i	0.996171	+	0.189557i
$449$	−14.9445	+	25.8846i	−0.705273	+	1.22157i	0.261320	+	0.965252i	$0.415842\pi$
$449$	−14.9445	+	25.8846i	−0.705273	+	1.22157i	−0.966593	+	0.256317i	$0.917491\pi$
$450$		0			0
$451$	−16.6736			−0.785131
$452$	−0.637364	+	1.10395i	−0.0299791	+	0.0519253i
$453$		0			0
$454$	18.1137			0.850119
$455$	−0.786428	+	3.33229i	−0.0368683	+	0.156220i
$456$		0			0
$457$	1.37753			0.0644383			0.0322192	−	0.999481i	$-0.489743\pi$
$457$	1.37753			0.0644383			0.0322192	+	0.999481i	$0.489743\pi$
$458$	−2.63890	+	4.57071i	−0.123308	+	0.213575i
$459$		0			0
$460$	−0.333090	+	0.576930i	−0.0155304	+	0.0268995i
$461$	−0.314876	+	0.545381i	−0.0146652	+	0.0254009i	−0.873265	−	0.487246i	$-0.838002\pi$
$461$	−0.314876	+	0.545381i	−0.0146652	+	0.0254009i	0.858600	+	0.512647i	$0.171335\pi$
$462$		0			0
$463$	−2.39950			−0.111514			−0.0557572	−	0.998444i	$-0.517757\pi$
$463$	−2.39950			−0.111514			−0.0557572	+	0.998444i	$0.517757\pi$
$464$	−7.06392	−	12.2351i	−0.327934	−	0.567999i
$465$		0			0
$466$	7.33380	−	12.7025i	0.339732	−	0.588432i
$467$	14.2387	−	24.6622i	0.658889	−	1.14123i	−0.322014	−	0.946735i	$-0.604360\pi$
$467$	14.2387	−	24.6622i	0.658889	−	1.14123i	0.980904	−	0.194495i	$-0.0623067\pi$
$468$		0			0
$469$	10.7859	−	12.5072i	0.498046	−	0.577527i
$470$	−1.83442	−	3.17730i	−0.0846153	−	0.146558i
$471$		0			0
$472$	27.7037			1.27517
$473$	−7.57850	−	13.1263i	−0.348460	−	0.603550i
$474$		0			0
$475$	0.245125	−	0.424569i	0.0112471	−	0.0194806i
$476$	−12.5898	−	2.39566i	−0.577053	−	0.109805i
$477$		0			0
$478$	6.02213			0.275446
$479$	−0.776598	+	1.34511i	−0.0354836	+	0.0614595i	−0.883222	−	0.468955i	$-0.844631\pi$
$479$	−0.776598	+	1.34511i	−0.0354836	+	0.0614595i	0.847738	+	0.530415i	$0.177964\pi$
$480$		0			0
$481$	16.9012	−	8.79627i	0.770629	−	0.401075i
$482$	−22.3563			−1.01830
$483$		0			0
$484$	−3.63871	−	6.30244i	−0.165396	−	0.286474i
$485$	−1.20967	−	2.09522i	−0.0549284	−	0.0951389i
$486$		0			0
$487$	−39.8616			−1.80630			−0.903150	−	0.429325i	$-0.858752\pi$
$487$	−39.8616			−1.80630			−0.903150	+	0.429325i	$0.858752\pi$
$488$	2.49265	+	4.31740i	0.112837	+	0.195440i
$489$		0			0
$490$	−2.15208	+	1.70893i	−0.0972212	+	0.0772018i
$491$	4.23463	+	7.33460i	0.191106	+	0.331006i	0.945617	−	0.325282i	$-0.105459\pi$
$491$	4.23463	+	7.33460i	0.191106	+	0.331006i	−0.754511	+	0.656288i	$0.772126\pi$
$492$		0			0
$493$	24.3725	+	42.2144i	1.09768	+	1.90124i
$494$	−0.334732	−	0.213291i	−0.0150603	−	0.00959641i
$495$		0			0
$496$	−5.15283	−	8.92497i	−0.231369	−	0.400743i
$497$	8.15799	−	9.45988i	0.365936	−	0.424334i
$498$		0			0
$499$	−2.39601	+	4.15001i	−0.107260	+	0.185780i	−0.914659	−	0.404225i	$-0.867541\pi$
$499$	−2.39601	+	4.15001i	−0.107260	+	0.185780i	0.807399	+	0.590006i	$0.200874\pi$
$500$	2.84709			0.127326
$501$		0			0
$502$	−10.5894	+	18.3413i	−0.472627	+	0.818614i
$503$	12.2637	−	21.2413i	0.546810	−	0.947103i	−0.451681	−	0.892180i	$-0.649175\pi$
$503$	12.2637	−	21.2413i	0.546810	−	0.947103i	0.998491	−	0.0549230i	$-0.0174913\pi$
$504$		0			0
$505$	−2.53615	−	4.39275i	−0.112857	−	0.195475i
$506$	−1.76122	+	3.05052i	−0.0782957	+	0.135612i
$507$		0			0
$508$	5.90721	+	10.2316i	0.262090	+	0.453953i
$509$	23.3353			1.03432			0.517160	−	0.855889i	$-0.326989\pi$
$509$	23.3353			1.03432			0.517160	+	0.855889i	$0.326989\pi$
$510$		0			0
$511$	−2.84104	−	8.14633i	−0.125680	−	0.360372i
$512$	−18.0912			−0.799525
$513$		0			0
$514$	0.785695			0.0346555
$515$	−1.22087	−	2.11461i	−0.0537979	−	0.0931808i
$516$		0			0
$517$	6.51497	+	11.2843i	0.286528	+	0.496281i
$518$	15.0231	+	2.85868i	0.660079	+	0.125603i
$519$		0			0
$520$	0.173461	−	3.96463i	0.00760675	−	0.173861i
$521$	3.14111	+	5.44057i	0.137615	+	0.238356i	0.926593	−	0.376065i	$-0.122723\pi$
$521$	3.14111	+	5.44057i	0.137615	+	0.238356i	−0.788979	+	0.614421i	$0.789390\pi$
$522$		0			0
$523$	−10.2487			−0.448145			−0.224072	−	0.974573i	$-0.571935\pi$
$523$	−10.2487			−0.448145			−0.224072	+	0.974573i	$0.571935\pi$
$524$	−2.49167	+	4.31571i	−0.108849	+	0.188532i
$525$		0			0
$526$	−11.5247	+	19.9614i	−0.502502	+	0.870358i
$527$	17.7787	+	30.7937i	0.774454	+	1.34139i
$528$		0			0
$529$	−17.6652			−0.768051
$530$	4.08977			0.177648
$531$		0			0
$532$	0.0704634	+	0.202045i	0.00305498	+	0.00875977i
$533$	−36.3631	−	23.1705i	−1.57506	−	1.00363i
$534$		0			0
$535$	3.24577	−	5.62184i	0.140327	−	0.243053i
$536$	−9.57125	+	16.5779i	−0.413415	+	0.716056i
$537$		0			0
$538$	11.1547			0.480915
$539$	7.64317	−	6.06932i	0.329214	−	0.261424i
$540$		0			0
$541$	8.03065	−	13.9095i	0.345264	−	0.598016i	−0.640137	−	0.768261i	$-0.721123\pi$
$541$	8.03065	−	13.9095i	0.345264	−	0.598016i	0.985402	+	0.170245i	$0.0544559\pi$
$542$	−28.0815			−1.20620
$543$		0			0
$544$	25.4507			1.09119
$545$	0.694884			0.0297655
$546$		0			0
$547$	−16.1258			−0.689490			−0.344745	−	0.938696i	$-0.612035\pi$
$547$	−16.1258			−0.689490			−0.344745	+	0.938696i	$0.612035\pi$
$548$	4.54112			0.193987
$549$		0			0
$550$	7.42878			0.316764
$551$	0.406940	−	0.704840i	0.0173362	−	0.0300272i
$552$		0			0
$553$	−12.6272	+	14.6423i	−0.536963	+	0.622654i
$554$	4.34920			0.184780
$555$		0			0
$556$	7.21532	−	12.4973i	0.305998	−	0.530003i
$557$	−11.4268	+	19.7919i	−0.484170	+	0.838608i	−0.999835	−	0.0181829i	$-0.994212\pi$
$557$	−11.4268	+	19.7919i	−0.484170	+	0.838608i	0.515664	+	0.856791i	$0.327545\pi$
$558$		0			0
$559$	1.71326	−	39.1584i	0.0724631	−	1.65622i
$560$	1.08344	−	1.25634i	0.0457835	−	0.0530899i
$561$		0			0
$562$	9.97772			0.420885
$563$	24.6555			1.03910			0.519552	−	0.854439i	$-0.326099\pi$
$563$	24.6555			1.03910			0.519552	+	0.854439i	$0.326099\pi$
$564$		0			0
$565$	0.284669	+	0.493061i	0.0119761	+	0.0207432i
$566$	−11.4588	+	19.8472i	−0.481650	+	0.834242i
$567$		0			0
$568$	−7.23930	+	12.5388i	−0.303754	+	0.526118i
$569$	32.0516			1.34367			0.671836	−	0.740700i	$-0.265506\pi$
$569$	32.0516			1.34367			0.671836	+	0.740700i	$0.265506\pi$
$570$		0			0
$571$	4.67070	+	8.08988i	0.195463	+	0.338551i	0.947052	−	0.321080i	$-0.104046\pi$
$571$	4.67070	+	8.08988i	0.195463	+	0.338551i	−0.751590	+	0.659631i	$0.770713\pi$
$572$	−0.176579	+	4.03591i	−0.00738314	+	0.168750i
$573$		0			0
$574$	−11.3963	−	32.6775i	−0.475672	−	1.36393i
$575$	−5.62554	−	9.74372i	−0.234601	−	0.406341i
$576$		0			0
$577$	−9.66471	−	16.7398i	−0.402347	−	0.696886i	0.591662	−	0.806186i	$-0.298472\pi$
$577$	−9.66471	−	16.7398i	−0.402347	−	0.696886i	−0.994009	+	0.109301i	$0.965139\pi$
$578$	21.1471			0.879603
$579$		0			0
$580$	2.33243			0.0968488
$581$	21.4113	+	4.07425i	0.888289	+	0.169028i
$582$		0			0
$583$	−14.5249			−0.601560
$584$	4.99990	+	8.66008i	0.206897	+	0.358357i
$585$		0			0
$586$	10.7633	−	18.6426i	0.444629	−	0.770120i
$587$	3.06856	+	5.31490i	0.126653	+	0.219369i	0.922378	−	0.386289i	$-0.126243\pi$
$587$	3.06856	+	5.31490i	0.126653	+	0.219369i	−0.795725	+	0.605658i	$0.792910\pi$
$588$		0			0
$589$	0.296846	−	0.514151i	0.0122313	−	0.0211852i
$590$	1.77331	−	3.07146i	0.0730059	−	0.126450i
$591$		0			0
$592$	−9.23201			−0.379433
$593$	9.09996	−	15.7616i	0.373691	−	0.647251i	−0.616439	−	0.787402i	$-0.711425\pi$
$593$	9.09996	−	15.7616i	0.373691	−	0.647251i	0.990130	+	0.140151i	$0.0447588\pi$
$594$		0			0
$595$	−3.73816	+	4.33471i	−0.153249	+	0.177706i
$596$	−8.92229	−	15.4539i	−0.365471	−	0.633014i
$597$		0			0
$598$	−8.08015	+	4.20532i	−0.330422	+	0.171969i
$599$	15.2172	+	26.3570i	0.621758	+	1.07692i	0.989158	+	0.146854i	$0.0469146\pi$
$599$	15.2172	+	26.3570i	0.621758	+	1.07692i	−0.367400	+	0.930063i	$0.619752\pi$
$600$		0			0
$601$	14.3890	+	24.9224i	0.586938	+	1.01661i	0.994631	+	0.103487i	$0.0330000\pi$
$601$	14.3890	+	24.9224i	0.586938	+	1.01661i	−0.407693	+	0.913119i	$0.633667\pi$
$602$	20.5455	−	23.8243i	0.837374	−	0.971006i
$603$		0			0
$604$	5.59008	+	9.68231i	0.227457	+	0.393967i
$605$	−3.25035			−0.132145
$606$		0			0
$607$	−2.78147	−	4.81764i	−0.112896	−	0.195542i	0.804041	−	0.594574i	$-0.202679\pi$
$607$	−2.78147	−	4.81764i	−0.112896	−	0.195542i	−0.916937	+	0.399032i	$0.869346\pi$
$608$	−0.212471	−	0.368010i	−0.00861682	−	0.0149248i
$609$		0			0
$610$	0.638216			0.0258406
$611$	−1.47283	+	33.6631i	−0.0595842	+	1.36186i
$612$		0			0
$613$	2.68005	−	4.64198i	0.108246	−	0.187488i	−0.806814	−	0.590806i	$-0.798810\pi$
$613$	2.68005	−	4.64198i	0.108246	−	0.187488i	0.915060	+	0.403318i	$0.132143\pi$
$614$	−15.4098			−0.621888
$615$		0			0
$616$	−7.38772	+	8.56669i	−0.297660	+	0.345162i
$617$	21.9459	−	38.0114i	0.883508	−	1.53028i	0.0360931	−	0.999348i	$-0.488509\pi$
$617$	21.9459	−	38.0114i	0.883508	−	1.53028i	0.847415	−	0.530932i	$-0.178158\pi$
$618$		0			0
$619$	−13.8858	−	24.0510i	−0.558119	−	0.966691i	−0.997654	−	0.0684651i	$-0.978190\pi$
$619$	−13.8858	−	24.0510i	−0.558119	−	0.966691i	0.439534	−	0.898226i	$-0.355144\pi$
$620$	1.70141			0.0683303
$621$		0			0
$622$	−0.540011	−	0.935326i	−0.0216525	−	0.0375032i
$623$	−30.8417	−	5.86872i	−1.23565	−	0.235125i
$624$		0			0
$625$	−11.5421	+	19.9916i	−0.461686	+	0.799663i
$626$	1.47184	−	2.54931i	0.0588266	−	0.101891i
$627$		0			0
$628$	4.91782	+	8.51791i	0.196242	+	0.339902i
$629$	31.8530			1.27006
$630$		0			0
$631$	0.265662	−	0.460140i	0.0105758	−	0.0183179i	−0.860689	−	0.509131i	$-0.829967\pi$
$631$	0.265662	−	0.460140i	0.0105758	−	0.0183179i	0.871265	+	0.490813i	$0.163300\pi$
$632$	11.2052	−	19.4080i	0.445719	−	0.772008i
$633$		0			0
$634$	3.49606	−	6.05535i	0.138846	−	0.240489i
$635$	5.27673			0.209401
$636$		0			0
$637$	25.1030	−	2.61510i	0.994618	−	0.103614i
$638$	12.3327			0.488257
$639$		0			0
$640$	−0.0769495	+	0.133280i	−0.00304169	+	0.00526837i
$641$	12.5249			0.494702			0.247351	−	0.968926i	$-0.420440\pi$
$641$	12.5249			0.494702			0.247351	+	0.968926i	$0.420440\pi$
$642$		0			0
$643$	−3.21981	+	5.57687i	−0.126977	+	0.219930i	−0.922504	−	0.385988i	$-0.873861\pi$
$643$	−3.21981	+	5.57687i	−0.126977	+	0.219930i	0.795527	+	0.605918i	$0.207194\pi$
$644$	4.82420	+	0.917974i	0.190100	+	0.0361732i
$645$		0			0
$646$	−0.331777	−	0.574654i	−0.0130536	−	0.0226095i
$647$	−8.25026	+	14.2899i	−0.324351	+	0.561793i	−0.981381	−	0.192072i	$-0.938479\pi$
$647$	−8.25026	+	14.2899i	−0.324351	+	0.561793i	0.657030	+	0.753865i	$0.271813\pi$
$648$		0			0
$649$	−6.29794	+	10.9084i	−0.247216	+	0.428190i
$650$	16.2012	+	10.3234i	0.635465	+	0.404917i
$651$		0			0
$652$	−6.25051	−	10.8262i	−0.244789	−	0.423987i
$653$	−16.4213			−0.642616			−0.321308	−	0.946975i	$-0.604122\pi$
$653$	−16.4213			−0.642616			−0.321308	+	0.946975i	$0.604122\pi$
$654$		0			0
$655$	1.11287	+	1.92754i	0.0434833	+	0.0753153i
$656$	10.4461	+	18.0932i	0.407853	+	0.706421i
$657$		0			0
$658$	−17.6623	+	20.4809i	−0.688547	+	0.798429i
$659$	−3.87927	+	6.71910i	−0.151115	+	0.261739i	−0.931638	−	0.363389i	$-0.881620\pi$
$659$	−3.87927	+	6.71910i	−0.151115	+	0.261739i	0.780523	+	0.625128i	$0.214953\pi$
$660$		0			0
$661$	−8.63548	+	14.9571i	−0.335881	+	0.581763i	−0.983654	−	0.180071i	$-0.942367\pi$
$661$	−8.63548	+	14.9571i	−0.335881	+	0.581763i	0.647773	+	0.761834i	$0.275701\pi$
$662$	−9.44952	−	16.3671i	−0.367266	−	0.636124i
$663$		0			0
$664$	−25.2622			−0.980364
$665$	0.0938861	+	0.0178651i	0.00364075	+	0.000692781i
$666$		0			0
$667$	−9.33912	−	16.1758i	−0.361612	−	0.626331i
$668$	0.0240268	+	0.0416156i	0.000929624	+	0.00161016i
$669$		0			0
$670$	1.22531	+	2.12229i	0.0473377	+	0.0819914i
$671$	−2.26664			−0.0875027
$672$		0			0
$673$	7.19912	+	12.4692i	0.277506	+	0.480654i	0.970764	−	0.240035i	$-0.0771589\pi$
$673$	7.19912	+	12.4692i	0.277506	+	0.480654i	−0.693258	+	0.720689i	$0.743826\pi$
$674$	35.8939			1.38258
$675$		0			0
$676$	−5.99359	+	8.55643i	−0.230523	+	0.329093i
$677$	0.606851	−	1.05110i	0.0233232	−	0.0403970i	−0.854128	−	0.520062i	$-0.825909\pi$
$677$	0.606851	−	1.05110i	0.0233232	−	0.0403970i	0.877451	+	0.479666i	$0.159242\pi$
$678$		0			0
$679$	−11.6471	+	13.5058i	−0.446974	+	0.518304i
$680$	3.31719	−	5.74554i	0.127209	−	0.220332i
$681$		0			0
$682$	8.99621			0.344483
$683$	0.196457			0.00751721			0.00375861	−	0.999993i	$-0.498804\pi$
$683$	0.196457			0.00751721			0.00375861	+	0.999993i	$0.498804\pi$
$684$		0			0
$685$	1.01411	−	1.75649i	0.0387472	−	0.0671121i
$686$	17.1189	+	10.8310i	0.653601	+	0.413528i
$687$		0			0
$688$	−9.49594	+	16.4474i	−0.362029	+	0.627053i
$689$	−31.6770	−	20.1845i	−1.20680	−	0.768969i
$690$		0			0
$691$	−37.3938			−1.42253			−0.711264	−	0.702925i	$-0.751877\pi$
$691$	−37.3938			−1.42253			−0.711264	+	0.702925i	$0.751877\pi$
$692$	5.88431	+	10.1919i	0.223688	+	0.387439i
$693$		0			0
$694$	−26.9026			−1.02121
$695$	−3.22261	−	5.58172i	−0.122241	−	0.211727i
$696$		0			0
$697$	−36.0421	−	62.4267i	−1.36519	−	2.36458i
$698$	6.25915	+	10.8412i	0.236912	+	0.410344i
$699$		0			0
$700$	−3.41047	−	9.77910i	−0.128904	−	0.369615i
$701$	1.21787			0.0459985			0.0229992	−	0.999735i	$-0.492678\pi$
$701$	1.21787			0.0459985			0.0229992	+	0.999735i	$0.492678\pi$
$702$		0			0
$703$	−0.265920	−	0.460587i	−0.0100294	−	0.0173714i
$704$	5.65539	−	9.79542i	0.213145	−	0.369179i
$705$		0			0
$706$	−0.475838	+	0.824175i	−0.0179084	+	0.0310182i
$707$	−24.4188	+	28.3157i	−0.918364	+	1.06492i
$708$		0			0
$709$	−12.0978	−	20.9541i	−0.454344	−	0.786946i	0.544306	−	0.838886i	$-0.316793\pi$
$709$	−12.0978	−	20.9541i	−0.454344	−	0.786946i	−0.998650	+	0.0519400i	$0.983460\pi$
$710$	0.926771	+	1.60521i	0.0347811	+	0.0602426i
$711$		0			0
$712$	36.3888			1.36373
$713$	−6.81250	−	11.7996i	−0.255130	−	0.441898i
$714$		0			0
$715$	1.52164	+	0.969588i	0.0569062	+	0.0362605i
$716$	−10.0017	+	17.3235i	−0.373782	+	0.647409i
$717$		0			0
$718$	−3.31445	+	5.74080i	−0.123694	+	0.214245i
$719$	11.1931	+	19.3871i	0.417433	+	0.723015i	0.995680	−	0.0928464i	$-0.0295965\pi$
$719$	11.1931	+	19.3871i	0.417433	+	0.723015i	−0.578248	+	0.815861i	$0.696263\pi$
$720$		0			0
$721$	−11.7549	+	13.6308i	−0.437775	+	0.507637i
$722$	10.3856	−	17.9883i	0.386511	−	0.669456i
$723$		0			0
$724$	−8.73643			−0.324687
$725$	−19.6961	+	34.1147i	−0.731495	+	1.26699i
$726$		0			0
$727$	−13.7293			−0.509190			−0.254595	−	0.967048i	$-0.581942\pi$
$727$	−13.7293			−0.509190			−0.254595	+	0.967048i	$0.581942\pi$
$728$	−28.0164	+	8.41654i	−1.03836	+	0.311938i
$729$		0			0
$730$	1.28017			0.0473812
$731$	32.7637	−	56.7483i	1.21181	−	2.09891i
$732$		0			0
$733$	−6.10146	+	10.5680i	−0.225362	+	0.390339i	−0.956428	−	0.291968i	$-0.905690\pi$
$733$	−6.10146	+	10.5680i	−0.225362	+	0.390339i	0.731066	+	0.682307i	$0.239023\pi$
$734$	−11.3350	+	19.6328i	−0.418382	+	0.724660i
$735$		0			0
$736$	−9.75225			−0.359473
$737$	−4.35171	−	7.53737i	−0.160297	−	0.277643i
$738$		0			0
$739$	14.8036	−	25.6406i	0.544559	−	0.943204i	−0.454076	−	0.890963i	$-0.650030\pi$
$739$	14.8036	−	25.6406i	0.544559	−	0.943204i	0.998635	−	0.0522406i	$-0.0166363\pi$
$740$	0.762078	−	1.31996i	0.0280145	−	0.0485226i
$741$		0			0
$742$	−9.92765	−	28.4663i	−0.364455	−	1.04503i
$743$	−8.70519	−	15.0778i	−0.319363	−	0.553152i	0.660993	−	0.750392i	$-0.270135\pi$
$743$	−8.70519	−	15.0778i	−0.319363	−	0.553152i	−0.980355	+	0.197240i	$0.936802\pi$
$744$		0			0
$745$	−7.97000			−0.291998
$746$	13.6653	+	23.6690i	0.500322	+	0.866583i
$747$		0			0
$748$	−3.37683	+	5.84884i	−0.123469	+	0.213855i
$749$	−47.0090	−	8.94512i	−1.71767	−	0.326848i
$750$		0			0
$751$	−29.9309			−1.09219			−0.546097	−	0.837722i	$-0.683887\pi$
$751$	−29.9309			−1.09219			−0.546097	+	0.837722i	$0.683887\pi$
$752$	8.16332	−	14.1393i	0.297686	−	0.515607i
$753$		0			0
$754$	26.8961	+	17.1382i	0.979500	+	0.624135i
$755$	4.99345			0.181730
$756$		0			0
$757$	13.7884	+	23.8822i	0.501147	+	0.868012i	0.999999	+	0.00132507i	$0.000421784\pi$
$757$	13.7884	+	23.8822i	0.501147	+	0.868012i	−0.498852	+	0.866687i	$0.666245\pi$
$758$	−10.5808	−	18.3265i	−0.384312	−	0.665648i
$759$		0			0
$760$	−0.110772			−0.00401813
$761$	−9.95601	−	17.2443i	−0.360905	−	0.625106i	0.627205	−	0.778854i	$-0.284199\pi$
$761$	−9.95601	−	17.2443i	−0.360905	−	0.625106i	−0.988110	+	0.153748i	$0.950866\pi$
$762$		0			0
$763$	−1.68679	−	4.83665i	−0.0610657	−	0.175098i
$764$	−2.43042	−	4.20961i	−0.0879296	−	0.152298i
$765$		0			0
$766$	−6.22109	−	10.7752i	−0.224777	−	0.389325i
$767$	−28.8938	+	15.0378i	−1.04329	+	0.542984i
$768$		0			0
$769$	−15.2251	−	26.3707i	−0.549032	−	0.950950i	−0.998341	−	0.0575744i	$-0.981663\pi$
$769$	−15.2251	−	26.3707i	−0.549032	−	0.950950i	0.449310	−	0.893376i	$-0.351670\pi$
$770$	0.476887	+	1.36741i	0.0171858	+	0.0492782i
$771$		0			0
$772$	−1.84199	+	3.19042i	−0.0662946	+	0.114826i
$773$	−42.8249			−1.54030			−0.770152	−	0.637860i	$-0.779820\pi$
$773$	−42.8249			−1.54030			−0.770152	+	0.637860i	$0.779820\pi$
$774$		0			0
$775$	−14.3675	+	24.8852i	−0.516095	+	0.893903i
$776$	10.3355	−	17.9016i	0.371022	−	0.642628i
$777$		0			0
$778$	0.952015	+	1.64894i	0.0341314	+	0.0591173i
$779$	−0.601782	+	1.04232i	−0.0215611	+	0.0373449i
$780$		0			0
$781$	−3.29145	−	5.70095i	−0.117777	−	0.203996i
$782$	−15.2283			−0.544564
$783$		0			0
$784$	−11.3745	−	4.49144i	−0.406233	−	0.160409i
$785$	4.39294			0.156791
$786$		0			0
$787$	9.49279			0.338382			0.169191	−	0.985583i	$-0.445885\pi$
$787$	9.49279			0.338382			0.169191	+	0.985583i	$0.445885\pi$
$788$	−3.09485	−	5.36044i	−0.110250	−	0.190958i
$789$		0			0
$790$	−1.43448	−	2.48460i	−0.0510367	−	0.0883981i
$791$	2.74087	−	3.17827i	0.0974542	−	0.113006i
$792$		0			0
$793$	−4.94326	−	3.14983i	−0.175540	−	0.111854i
$794$	−3.98649	−	6.90481i	−0.141475	−	0.245042i
$795$		0			0
$796$	3.51284			0.124509
$797$	−17.4248	+	30.1807i	−0.617219	+	1.06906i	0.372772	+	0.927923i	$0.378408\pi$
$797$	−17.4248	+	30.1807i	−0.617219	+	1.06906i	−0.989991	+	0.141132i	$0.954926\pi$
$798$		0			0
$799$	−28.1657	+	48.7845i	−0.996433	+	1.72587i
$800$	10.2837	+	17.8119i	0.363584	+	0.629745i
$801$		0			0
$802$	−31.4530			−1.11064
$803$	−4.54655			−0.160444
$804$		0			0
$805$	1.43240	−	1.66099i	0.0504853	−	0.0585421i
$806$	19.6196	+	12.5016i	0.691072	+	0.440350i
$807$		0			0
$808$	21.6689	−	37.5317i	0.762311	−	1.32036i
$809$	−0.448965	+	0.777630i	−0.0157848	+	0.0273400i	−0.873810	−	0.486268i	$-0.838358\pi$
$809$	−0.448965	+	0.777630i	−0.0157848	+	0.0273400i	0.858025	+	0.513608i	$0.171691\pi$
$810$		0			0
$811$	−33.9144			−1.19090			−0.595448	−	0.803394i	$-0.703026\pi$
$811$	−33.9144			−1.19090			−0.595448	+	0.803394i	$0.703026\pi$
$812$	−5.66182	−	16.2346i	−0.198691	−	0.569722i
$813$		0			0
$814$	4.02949	−	6.97928i	0.141234	−	0.244624i
$815$	−5.58339			−0.195578
$816$		0			0
$817$	−1.09409			−0.0382773
$818$	−16.9232			−0.591705
$819$		0			0
$820$	−3.44920			−0.120451
$821$	−18.6071			−0.649392			−0.324696	−	0.945818i	$-0.605262\pi$
$821$	−18.6071			−0.649392			−0.324696	+	0.945818i	$0.605262\pi$
$822$		0			0
$823$	15.6340			0.544967			0.272483	−	0.962160i	$-0.412155\pi$
$823$	15.6340			0.544967			0.272483	+	0.962160i	$0.412155\pi$
$824$	10.4311	−	18.0672i	0.363386	−	0.629402i
$825$		0			0
$826$	−25.6831	−	4.88711i	−0.893629	−	0.170044i
$827$	−15.1619			−0.527232			−0.263616	−	0.964628i	$-0.584915\pi$
$827$	−15.1619			−0.527232			−0.263616	+	0.964628i	$0.584915\pi$
$828$		0			0
$829$	1.81418	−	3.14226i	0.0630092	−	0.109135i	−0.832800	−	0.553574i	$-0.813264\pi$
$829$	1.81418	−	3.14226i	0.0630092	−	0.109135i	0.895809	+	0.444439i	$0.146597\pi$
$830$	−1.61703	+	2.80077i	−0.0561279	+	0.0972163i
$831$		0			0
$832$	25.9459	−	13.5036i	0.899512	−	0.468152i
$833$	39.2453	+	15.4967i	1.35977	+	0.536930i
$834$		0			0
$835$	0.0214624			0.000742736
$836$	0.112764			0.00390001
$837$		0			0
$838$	5.69541	+	9.86474i	0.196745	+	0.340772i
$839$	16.6905	−	28.9088i	0.576221	−	0.998044i	−0.419687	−	0.907669i	$-0.637860\pi$
$839$	16.6905	−	28.9088i	0.576221	−	0.998044i	0.995908	−	0.0903751i	$-0.0288066\pi$
$840$		0			0
$841$	−18.1981	+	31.5200i	−0.627520	+	1.08690i
$842$	35.3590			1.21855
$843$		0			0
$844$	−0.287229	−	0.497496i	−0.00988684	−	0.0171245i
$845$	1.97113	+	4.22910i	0.0678088	+	0.145486i
$846$		0			0
$847$	7.89002	+	22.6236i	0.271104	+	0.777358i
$848$	9.09992	+	15.7615i	0.312493	+	0.541253i
$849$		0			0
$850$	16.0582	+	27.8136i	0.550791	+	0.953998i
$851$	−12.2055			−0.418400
$852$		0			0
$853$	46.3694			1.58766			0.793829	−	0.608141i	$-0.208084\pi$
$853$	46.3694			1.58766			0.793829	+	0.608141i	$0.208084\pi$
$854$	−1.54923	−	4.44222i	−0.0530135	−	0.152010i
$855$		0			0
$856$	55.4638			1.89571
$857$	26.4952	+	45.8911i	0.905059	+	1.56761i	0.820837	+	0.571162i	$0.193507\pi$
$857$	26.4952	+	45.8911i	0.905059	+	1.56761i	0.0842219	+	0.996447i	$0.473160\pi$
$858$		0			0
$859$	12.5175	−	21.6809i	0.427090	−	0.739742i	−0.569523	−	0.821975i	$-0.692872\pi$
$859$	12.5175	−	21.6809i	0.427090	−	0.739742i	0.996613	+	0.0822337i	$0.0262054\pi$
$860$	−1.56773	−	2.71538i	−0.0534591	−	0.0925938i
$861$		0			0
$862$	−3.80465	+	6.58984i	−0.129587	+	0.224451i
$863$	25.2070	−	43.6597i	0.858055	−	1.48619i	−0.0157265	−	0.999876i	$-0.505006\pi$
$863$	25.2070	−	43.6597i	0.858055	−	1.48619i	0.873782	−	0.486319i	$-0.161661\pi$
$864$		0			0
$865$	5.25627			0.178719
$866$	2.92230	−	5.06158i	0.0993039	−	0.171999i
$867$		0			0
$868$	−4.13006	−	11.8424i	−0.140183	−	0.401959i
$869$	5.09460	+	8.82411i	0.172823	+	0.299337i
$870$		0			0
$871$	0.983782	−	22.4854i	0.0333342	−	0.761889i
$872$	2.96855	+	5.14168i	0.100528	+	0.174119i
$873$		0			0
$874$	0.127131	+	0.220198i	0.00430027	+	0.00744829i
$875$	−9.20845	−	1.75223i	−0.311303	−	0.0592363i
$876$		0			0
$877$	−5.74794	−	9.95573i	−0.194094	−	0.336181i	0.752509	−	0.658582i	$-0.228843\pi$
$877$	−5.74794	−	9.95573i	−0.194094	−	0.336181i	−0.946603	+	0.322401i	$0.895510\pi$
$878$	−29.3310			−0.989873
$879$		0			0
$880$	−0.437126	−	0.757124i	−0.0147355	−	0.0255227i
$881$	−14.6637	−	25.3983i	−0.494033	−	0.855691i	0.505943	−	0.862567i	$-0.331145\pi$
$881$	−14.6637	−	25.3983i	−0.494033	−	0.855691i	−0.999976	+	0.00687611i	$0.997811\pi$
$882$		0			0
$883$	4.23323			0.142460			0.0712298	−	0.997460i	$-0.477308\pi$
$883$	4.23323			0.142460			0.0712298	+	0.997460i	$0.477308\pi$
$884$	−15.4923	+	8.06298i	−0.521062	+	0.271187i
$885$		0			0
$886$	1.64282	−	2.84544i	0.0551915	−	0.0955945i
$887$	32.2206			1.08186			0.540930	−	0.841068i	$-0.318072\pi$
$887$	32.2206			1.08186			0.540930	+	0.841068i	$0.318072\pi$
$888$		0			0
$889$	−12.8089	−	36.7280i	−0.429597	−	1.23182i
$890$	2.32924	−	4.03435i	0.0780762	−	0.135232i
$891$		0			0
$892$	9.79940	+	16.9731i	0.328108	+	0.568300i
$893$	0.940548			0.0314742
$894$		0			0
$895$	4.46711	+	7.73726i	0.149319	+	0.258628i
$896$	1.11447	+	0.212067i	0.0372319	+	0.00708467i
$897$		0			0
$898$	−16.3463	+	28.3126i	−0.545482	+	0.944803i
$899$	−23.8519	+	41.3127i	−0.795505	+	1.37786i
$900$		0			0
$901$	−31.3973	−	54.3817i	−1.04600	−	1.81172i
$902$	−18.2376			−0.607247
$903$		0			0
$904$	−2.43221	+	4.21272i	−0.0808942	+	0.140113i
$905$	−1.95100	+	3.37922i	−0.0648533	+	0.112329i
$906$		0			0
$907$	−9.27541	+	16.0655i	−0.307985	+	0.533445i	−0.977921	−	0.208973i	$-0.932988\pi$
$907$	−9.27541	+	16.0655i	−0.307985	+	0.533445i	0.669937	+	0.742418i	$0.266321\pi$
$908$	−13.3079			−0.441638
$909$		0			0
$910$	−0.860196	+	3.64487i	−0.0285152	+	0.120826i
$911$	−28.2762			−0.936834			−0.468417	−	0.883508i	$-0.655175\pi$
$911$	−28.2762			−0.936834			−0.468417	+	0.883508i	$0.655175\pi$
$912$		0			0
$913$	5.74291	−	9.94701i	0.190063	−	0.329198i
$914$	1.50675			0.0498388
$915$		0			0
$916$	1.93876	−	3.35804i	0.0640585	−	0.110953i
$917$	10.7150	−	12.4250i	0.353841	−	0.410308i
$918$		0			0
$919$	−5.82981	−	10.0975i	−0.192308	−	0.333087i	0.753707	−	0.657211i	$-0.228264\pi$
$919$	−5.82981	−	10.0975i	−0.192308	−	0.333087i	−0.946015	+	0.324124i	$0.894930\pi$
$920$	−1.27109	+	2.20159i	−0.0419066	+	0.0725844i
$921$		0			0
$922$	−0.344411	+	0.596538i	−0.0113426	+	0.0196459i
$923$	0.744092	−	17.0070i	0.0244921	−	0.559793i
$924$		0			0
$925$	12.8707	+	22.2926i	0.423185	+	0.732978i
$926$	−2.62458			−0.0862490
$927$		0			0
$928$	17.0723	+	29.5700i	0.560425	+	0.970684i
$929$	−15.5093	−	26.8629i	−0.508843	−	0.881342i	−0.999948	−	0.0102410i	$-0.996740\pi$
$929$	−15.5093	−	26.8629i	−0.508843	−	0.881342i	0.491105	−	0.871101i	$-0.336593\pi$
$930$		0			0
$931$	−0.103555	−	0.696849i	−0.00339386	−	0.0228383i
$932$	−5.38804	+	9.33236i	−0.176491	+	0.305692i
$933$		0			0
$934$	15.5743	−	26.9755i	0.509607	−	0.882665i
$935$	1.50821	+	2.61229i	0.0493237	+	0.0854311i
$936$		0			0
$937$	−57.9467			−1.89304			−0.946518	−	0.322650i	$-0.895426\pi$
$937$	−57.9467			−1.89304			−0.946518	+	0.322650i	$0.895426\pi$
$938$	11.7976	−	13.6803i	0.385205	−	0.446679i
$939$		0			0
$940$	1.34772	+	2.33432i	0.0439578	+	0.0761371i
$941$	2.42774	+	4.20497i	0.0791421	+	0.137078i	0.902880	−	0.429893i	$-0.141449\pi$
$941$	2.42774	+	4.20497i	0.0791421	+	0.137078i	−0.823738	+	0.566971i	$0.808115\pi$
$942$		0			0
$943$	13.8107	+	23.9208i	0.449738	+	0.778969i
$944$	15.7828			0.513685
$945$		0			0
$946$	−8.28937	−	14.3576i	−0.269511	−	0.466806i
$947$	−35.9332			−1.16767			−0.583836	−	0.811872i	$-0.698449\pi$
$947$	−35.9332			−1.16767			−0.583836	+	0.811872i	$0.698449\pi$
$948$		0			0
$949$	−9.91546	−	6.31811i	−0.321869	−	0.205095i
$950$	0.268118	−	0.464394i	0.00869890	−	0.0150669i
$951$		0			0
$952$	−48.0434	−	9.14195i	−1.55710	−	0.296292i
$953$	−5.16994	+	8.95460i	−0.167471	+	0.290068i	−0.937530	−	0.347905i	$-0.886893\pi$
$953$	−5.16994	+	8.95460i	−0.167471	+	0.290068i	0.770059	+	0.637973i	$0.220227\pi$
$954$		0			0
$955$	−2.17102			−0.0702526
$956$	−4.42437			−0.143094
$957$		0			0
$958$	−0.849443	+	1.47128i	−0.0274443	+	0.0475348i
$959$	−14.6875	−	2.79482i	−0.474285	−	0.0902494i
$960$		0			0
$961$	−1.89897	+	3.28910i	−0.0612569	+	0.106100i
$962$	18.4866	−	9.62136i	0.596031	−	0.310205i
$963$		0			0
$964$	16.4249			0.529009
$965$	0.822696	+	1.42495i	0.0264835	+	0.0458708i
$966$		0			0
$967$	5.03117			0.161791			0.0808957	−	0.996723i	$-0.474222\pi$
$967$	5.03117			0.161791			0.0808957	+	0.996723i	$0.474222\pi$
$968$	−13.8855	−	24.0504i	−0.446297	−	0.773010i
$969$		0			0
$970$	−1.32314	−	2.29175i	−0.0424835	−	0.0735836i
$971$	−18.1391	−	31.4179i	−0.582112	−	1.00825i	−0.995229	−	0.0975697i	$-0.968893\pi$
$971$	−18.1391	−	31.4179i	−0.582112	−	1.00825i	0.413116	−	0.910678i	$-0.364440\pi$
$972$		0			0
$973$	−31.0282	+	35.9798i	−0.994719	+	1.15346i
$974$	−43.6006			−1.39705
$975$		0			0
$976$	1.42006	+	2.45962i	0.0454551	+	0.0787305i
$977$	9.99415	−	17.3104i	0.319741	−	0.553808i	−0.660693	−	0.750657i	$-0.729737\pi$
$977$	9.99415	−	17.3104i	0.319741	−	0.553808i	0.980434	+	0.196848i	$0.0630707\pi$
$978$		0			0
$979$	−8.27233	+	14.3281i	−0.264385	+	0.457928i
$980$	1.58110	−	1.25553i	0.0505065	−	0.0401064i
$981$		0			0
$982$	4.63185	+	8.02259i	0.147808	+	0.256011i
$983$	16.1375	+	27.9510i	0.514707	+	0.891499i	0.999854	+	0.0170667i	$0.00543275\pi$
$983$	16.1375	+	27.9510i	0.514707	+	0.891499i	−0.485147	+	0.874433i	$0.661234\pi$
$984$		0			0
$985$	−2.76454			−0.0880854
$986$	26.6587	+	46.1742i	0.848985	+	1.47049i
$987$		0			0
$988$	0.245923	+	0.156702i	0.00782386	+	0.00498535i
$989$	−12.5545	+	21.7450i	−0.399209	+	0.691450i
$990$		0			0
$991$	17.6360	−	30.5465i	0.560226	−	0.970340i	−0.437250	−	0.899340i	$-0.644048\pi$
$991$	17.6360	−	30.5465i	0.560226	−	0.970340i	0.997476	−	0.0710004i	$-0.0226191\pi$
$992$	12.4535	+	21.5701i	0.395399	+	0.684852i
$993$		0			0
$994$	8.92321	−	10.3472i	0.283027	−	0.328194i
$995$	0.784479	−	1.35876i	0.0248696	−	0.0430755i
$996$		0			0
$997$	35.1713			1.11389			0.556943	−	0.830551i	$-0.311974\pi$
$997$	35.1713			1.11389			0.556943	+	0.830551i	$0.311974\pi$
$998$	−2.62076	+	4.53929i	−0.0829587	+	0.143689i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.g.289.12	yes	36
3.2	odd	2	inner	819.2.s.g.289.7	yes	36
7.4	even	3		819.2.n.g.172.7	yes	36
13.9	even	3		819.2.n.g.100.7	✓	36
21.11	odd	6		819.2.n.g.172.12	yes	36
39.35	odd	6		819.2.n.g.100.12	yes	36
91.74	even	3	inner	819.2.s.g.802.12	yes	36
273.74	odd	6	inner	819.2.s.g.802.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.n.g.100.7	✓	36	13.9	even	3
819.2.n.g.100.12	yes	36	39.35	odd	6
819.2.n.g.172.7	yes	36	7.4	even	3
819.2.n.g.172.12	yes	36	21.11	odd	6
819.2.s.g.289.7	yes	36	3.2	odd	2	inner
819.2.s.g.289.12	yes	36	1.1	even	1	trivial
819.2.s.g.802.7	yes	36	273.74	odd	6	inner
819.2.s.g.802.12	yes	36	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+1.09380 q^{2} -0.803600 q^{4} +(-0.179458 + 0.310830i) q^{5} +(2.59911 + 0.494573i) q^{7} -3.06658 q^{8} +(-0.196291 + 0.339986i) q^{10} +(0.697132 - 1.20747i) q^{11} +(3.19831 - 1.66457i) q^{13} +(2.84291 + 0.540964i) q^{14} -1.74703 q^{16} +6.02773 q^{17} +(-0.0503215 - 0.0871594i) q^{19} +(0.144212 - 0.249783i) q^{20} +(0.762523 - 1.32073i) q^{22} -2.30972 q^{23} +(2.43559 + 4.21857i) q^{25} +(3.49832 - 1.82071i) q^{26} +(-2.08865 - 0.397439i) q^{28} +(4.04339 + 7.00337i) q^{29} +(2.94949 + 5.10866i) q^{31} +4.22226 q^{32} +6.59314 q^{34} +(-0.620159 + 0.719128i) q^{35} +5.28441 q^{37} +(-0.0550417 - 0.0953350i) q^{38} +(0.550322 - 0.953185i) q^{40} +(-5.97937 - 10.3566i) q^{41} +(5.43548 - 9.41454i) q^{43} +(-0.560215 + 0.970321i) q^{44} -2.52638 q^{46} +(-4.67269 + 8.09334i) q^{47} +(6.51079 + 2.57090i) q^{49} +(2.66405 + 4.61427i) q^{50} +(-2.57017 + 1.33765i) q^{52} +(-5.20881 - 9.02192i) q^{53} +(0.250211 + 0.433379i) q^{55} +(-7.97039 - 1.51665i) q^{56} +(4.42267 + 7.66029i) q^{58} -9.03407 q^{59} +(-0.812845 - 1.40789i) q^{61} +(3.22615 + 5.58786i) q^{62} +8.11236 q^{64} +(-0.0565649 + 1.29285i) q^{65} +(3.12115 - 5.40599i) q^{67} -4.84389 q^{68} +(-0.678331 + 0.786582i) q^{70} +(2.36071 - 4.08886i) q^{71} +(-1.63045 - 2.82402i) q^{73} +5.78010 q^{74} +(0.0404384 + 0.0700413i) q^{76} +(2.40911 - 2.79356i) q^{77} +(-3.65397 + 6.32887i) q^{79} +(0.313517 - 0.543028i) q^{80} +(-6.54024 - 11.3280i) q^{82} +8.23791 q^{83} +(-1.08172 + 1.87360i) q^{85} +(5.94534 - 10.2976i) q^{86} +(-2.13781 + 3.70280i) q^{88} -11.8662 q^{89} +(9.13604 - 2.74460i) q^{91} +1.85609 q^{92} +(-5.11099 + 8.85250i) q^{94} +0.0361224 q^{95} +(-3.37036 + 5.83763i) q^{97} +(7.12151 + 2.81206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) \) 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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