LMFDB - Embedded newform 816.2.cj.c.209.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [816,2,Mod(65,816)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(816, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 0, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("816.65"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.cj (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,8,0,0,0,16,0,-8,0,0] 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:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			209.3
Character	$\chi$	$=$	816.209
Dual form			816.2.cj.c.449.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.706330 - 1.58149i) q^{3} +(3.00087 + 0.596910i) q^{5} +(0.464975 + 2.33759i) q^{7} +(-2.00219 - 2.23410i) q^{9} +(0.172899 - 0.258762i) q^{11} +(1.45541 + 1.45541i) q^{13} +(3.06361 - 4.32421i) q^{15} +(2.58814 - 3.20960i) q^{17} +(-0.427451 - 1.03196i) q^{19} +(4.02529 + 0.915758i) q^{21} +(4.71932 + 3.15335i) q^{23} +(4.02951 + 1.66908i) q^{25} +(-4.94741 + 1.58843i) q^{27} +(-1.62296 + 8.15918i) q^{29} +(5.25259 - 3.50967i) q^{31} +(-0.287105 - 0.456210i) q^{33} +7.29234i q^{35} +(-6.02262 - 9.01349i) q^{37} +(3.32972 - 1.27371i) q^{39} +(-5.42232 + 1.07857i) q^{41} +(1.13048 - 2.72921i) q^{43} +(-4.67476 - 7.89938i) q^{45} +(-4.50710 + 4.50710i) q^{47} +(1.21904 - 0.504943i) q^{49} +(-3.24785 - 6.36015i) q^{51} +(5.31572 - 2.20184i) q^{53} +(0.673306 - 0.673306i) q^{55} +(-1.93395 - 0.0528956i) q^{57} +(-0.337607 + 0.815054i) q^{59} +(-3.27882 + 0.652199i) q^{61} +(4.29144 - 5.71911i) q^{63} +(3.49876 + 5.23626i) q^{65} -2.49028i q^{67} +(8.32038 - 5.23624i) q^{69} +(0.997325 - 0.666391i) q^{71} +(-0.197828 + 0.994547i) q^{73} +(5.48579 - 5.19369i) q^{75} +(0.685274 + 0.283850i) q^{77} +(-11.0957 - 7.41392i) q^{79} +(-0.982433 + 8.94622i) q^{81} +(-1.56322 - 3.77396i) q^{83} +(9.68252 - 8.08669i) q^{85} +(11.7573 + 8.32976i) q^{87} +(-0.687749 - 0.687749i) q^{89} +(-2.72543 + 4.07889i) q^{91} +(-1.84043 - 10.7859i) q^{93} +(-0.666738 - 3.35192i) q^{95} +(-6.12098 - 1.21754i) q^{97} +(-0.924280 + 0.131817i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} - 16 q^{15} + 16 q^{19} + 16 q^{21} + 16 q^{25} + 8 q^{27} - 16 q^{31} + 16 q^{37} + 24 q^{39} - 16 q^{43} - 40 q^{45} - 48 q^{49} + 40 q^{51} + 48 q^{55}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 - 16 * q^15 + 16 * q^19 + 16 * q^21 + 16 * q^25 + 8 * q^27 - 16 * q^31 + 16 * q^37 + 24 * q^39 - 16 * q^43 - 40 * q^45 - 48 * q^49 + 40 * q^51 + 48 * q^55 + 8 * q^57 - 32 * q^61 - 64 * q^63 + 80 * q^69 + 48 * q^73 - 88 * q^75 - 16 * q^79 + 48 * q^81 + 56 * q^87 - 16 * q^91 - 72 * q^93 - 16 * q^97 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	0.706330	−	1.58149i	0.407800	−	0.913071i
$3$	0.706330	−	1.58149i	0.407800	−	0.913071i
$4$		0			0
$5$	3.00087	+	0.596910i	1.34203	+	0.266946i	0.813300	−	0.581845i	$-0.197669\pi$
$5$	3.00087	+	0.596910i	1.34203	+	0.266946i	0.528729	+	0.848791i	$0.322669\pi$
$6$		0			0
$7$	0.464975	+	2.33759i	0.175744	+	0.883525i	0.963535	+	0.267582i	$0.0862248\pi$
$7$	0.464975	+	2.33759i	0.175744	+	0.883525i	−0.787791	+	0.615943i	$0.788775\pi$
$8$		0			0
$9$	−2.00219	−	2.23410i	−0.667398	−	0.744701i
$10$		0			0
$11$	0.172899	−	0.258762i	0.0521312	−	0.0780198i	−0.804488	−	0.593968i	$-0.797560\pi$
$11$	0.172899	−	0.258762i	0.0521312	−	0.0780198i	0.856620	+	0.515949i	$0.172560\pi$
$12$		0			0
$13$	1.45541	+	1.45541i	0.403659	+	0.403659i	0.879520	−	0.475861i	$-0.157864\pi$
$13$	1.45541	+	1.45541i	0.403659	+	0.403659i	−0.475861	+	0.879520i	$0.657864\pi$
$14$		0			0
$15$	3.06361	−	4.32421i	0.791020	−	1.11651i
$16$		0			0
$17$	2.58814	−	3.20960i	0.627717	−	0.778442i
$17$	2.58814	−	3.20960i	0.627717	−	0.778442i
$18$		0			0
$19$	−0.427451	−	1.03196i	−0.0980640	−	0.236747i	0.867233	−	0.497903i	$-0.165896\pi$
$19$	−0.427451	−	1.03196i	−0.0980640	−	0.236747i	−0.965297	+	0.261156i	$0.915896\pi$
$20$		0			0
$21$	4.02529	+	0.915758i	0.878390	+	0.199835i
$22$		0			0
$23$	4.71932	+	3.15335i	0.984047	+	0.657519i	0.939880	−	0.341505i	$-0.110937\pi$
$23$	4.71932	+	3.15335i	0.984047	+	0.657519i	0.0441670	+	0.999024i	$0.485937\pi$
$24$		0			0
$25$	4.02951	+	1.66908i	0.805902	+	0.333816i
$26$		0			0
$27$	−4.94741	+	1.58843i	−0.952130	+	0.305693i
$28$		0			0
$29$	−1.62296	+	8.15918i	−0.301376	+	1.51512i	0.472242	+	0.881469i	$0.343445\pi$
$29$	−1.62296	+	8.15918i	−0.301376	+	1.51512i	−0.773618	+	0.633652i	$0.781555\pi$
$30$		0			0
$31$	5.25259	−	3.50967i	0.943394	−	0.630355i	0.0141803	−	0.999899i	$-0.495486\pi$
$31$	5.25259	−	3.50967i	0.943394	−	0.630355i	0.929213	+	0.369544i	$0.120486\pi$
$32$		0			0
$33$	−0.287105	−	0.456210i	−0.0499785	−	0.0794159i
$34$		0			0
$35$			7.29234i			1.23263i
$36$		0			0
$37$	−6.02262	−	9.01349i	−0.990113	−	1.48181i	−0.872419	−	0.488758i	$-0.837450\pi$
$37$	−6.02262	−	9.01349i	−0.990113	−	1.48181i	−0.117694	−	0.993050i	$-0.537550\pi$
$38$		0			0
$39$	3.32972	−	1.27371i	0.533182	−	0.203957i
$40$		0			0
$41$	−5.42232	+	1.07857i	−0.846824	+	0.168444i	−0.599386	−	0.800460i	$-0.704589\pi$
$41$	−5.42232	+	1.07857i	−0.846824	+	0.168444i	−0.247438	+	0.968904i	$0.579589\pi$
$42$		0			0
$43$	1.13048	−	2.72921i	0.172396	−	0.416201i	−0.813939	−	0.580950i	$-0.802681\pi$
$43$	1.13048	−	2.72921i	0.172396	−	0.416201i	0.986336	+	0.164749i	$0.0526813\pi$
$44$		0			0
$45$	−4.67476	−	7.89938i	−0.696873	−	1.17757i
$46$		0			0
$47$	−4.50710	+	4.50710i	−0.657428	+	0.657428i	−0.954771	−	0.297343i	$-0.903900\pi$
$47$	−4.50710	+	4.50710i	−0.657428	+	0.657428i	0.297343	+	0.954771i	$0.403900\pi$
$48$		0			0
$49$	1.21904	−	0.504943i	0.174148	−	0.0721347i
$50$		0			0
$51$	−3.24785	−	6.36015i	−0.454790	−	0.890599i
$52$		0			0
$53$	5.31572	−	2.20184i	0.730170	−	0.302447i	0.0135484	−	0.999908i	$-0.495687\pi$
$53$	5.31572	−	2.20184i	0.730170	−	0.302447i	0.716622	+	0.697462i	$0.245687\pi$
$54$		0			0
$55$	0.673306	−	0.673306i	0.0907886	−	0.0907886i
$56$		0			0
$57$	−1.93395	−	0.0528956i	−0.256158	−	0.00700620i
$58$		0			0
$59$	−0.337607	+	0.815054i	−0.0439526	+	0.106111i	−0.944331	−	0.328996i	$-0.893290\pi$
$59$	−0.337607	+	0.815054i	−0.0439526	+	0.106111i	0.900379	+	0.435107i	$0.143290\pi$
$60$		0			0
$61$	−3.27882	+	0.652199i	−0.419810	+	0.0835055i	−0.400475	−	0.916308i	$-0.631155\pi$
$61$	−3.27882	+	0.652199i	−0.419810	+	0.0835055i	−0.0193351	+	0.999813i	$0.506155\pi$
$62$		0			0
$63$	4.29144	−	5.71911i	0.540671	−	0.720540i
$64$		0			0
$65$	3.49876	+	5.23626i	0.433967	+	0.649478i
$66$		0			0
$67$		−	2.49028i		−	0.304236i	−0.988362	−	0.152118i	$-0.951391\pi$
$67$		−	2.49028i		−	0.304236i	0.988362	−	0.152118i	$-0.0486095\pi$
$68$		0			0
$69$	8.32038	−	5.23624i	1.00166	−	0.630369i
$70$		0			0
$71$	0.997325	−	0.666391i	0.118361	−	0.0790861i	−0.494981	−	0.868904i	$-0.664825\pi$
$71$	0.997325	−	0.666391i	0.118361	−	0.0790861i	0.613342	+	0.789818i	$0.289825\pi$
$72$		0			0
$73$	−0.197828	+	0.994547i	−0.0231540	+	0.116403i	−0.990634	−	0.136545i	$-0.956400\pi$
$73$	−0.197828	+	0.994547i	−0.0231540	+	0.116403i	0.967480	+	0.252948i	$0.0814001\pi$
$74$		0			0
$75$	5.48579	−	5.19369i	0.633444	−	0.599716i
$76$		0			0
$77$	0.685274	+	0.283850i	0.0780942	+	0.0323477i
$78$		0			0
$79$	−11.0957	−	7.41392i	−1.24836	−	0.834131i	−0.257147	−	0.966372i	$-0.582783\pi$
$79$	−11.0957	−	7.41392i	−1.24836	−	0.834131i	−0.991218	+	0.132242i	$0.957783\pi$
$80$		0			0
$81$	−0.982433	+	8.94622i	−0.109159	+	0.994024i
$82$		0			0
$83$	−1.56322	−	3.77396i	−0.171586	−	0.414246i	0.814570	−	0.580065i	$-0.196973\pi$
$83$	−1.56322	−	3.77396i	−0.171586	−	0.414246i	−0.986156	+	0.165820i	$0.946973\pi$
$84$		0			0
$85$	9.68252	−	8.08669i	1.05022	−	0.877125i
$86$		0			0
$87$	11.7573	+	8.32976i	1.26051	+	0.893044i
$88$		0			0
$89$	−0.687749	−	0.687749i	−0.0729012	−	0.0729012i	0.669716	−	0.742617i	$-0.266416\pi$
$89$	−0.687749	−	0.687749i	−0.0729012	−	0.0729012i	−0.742617	+	0.669716i	$0.766416\pi$
$90$		0			0
$91$	−2.72543	+	4.07889i	−0.285703	+	0.427584i
$92$		0			0
$93$	−1.84043	−	10.7859i	−0.190843	−	1.11844i
$94$		0			0
$95$	−0.666738	−	3.35192i	−0.0684059	−	0.343900i
$96$		0			0
$97$	−6.12098	−	1.21754i	−0.621491	−	0.123622i	−0.125706	−	0.992068i	$-0.540120\pi$
$97$	−6.12098	−	1.21754i	−0.621491	−	0.123622i	−0.495785	+	0.868445i	$0.665120\pi$
$98$		0			0
$99$	−0.924280	+	0.131817i	−0.0928937	+	0.0132481i
$100$		0			0
$101$	−3.89961			−0.388026			−0.194013	−	0.980999i	$-0.562150\pi$
$101$	−3.89961			−0.388026			−0.194013	+	0.980999i	$0.562150\pi$
$102$		0			0
$103$	8.34664			0.822419			0.411210	−	0.911541i	$-0.365106\pi$
$103$	8.34664			0.822419			0.411210	+	0.911541i	$0.365106\pi$
$104$		0			0
$105$	11.5327	+	5.15080i	1.12548	+	0.502667i
$106$		0			0
$107$	−5.14612	−	1.02363i	−0.497494	−	0.0989577i	−0.0600352	−	0.998196i	$-0.519121\pi$
$107$	−5.14612	−	1.02363i	−0.497494	−	0.0989577i	−0.437459	+	0.899239i	$0.644121\pi$
$108$		0			0
$109$	−0.476511	−	2.39558i	−0.0456415	−	0.229455i	0.951231	−	0.308479i	$-0.0998198\pi$
$109$	−0.476511	−	2.39558i	−0.0456415	−	0.229455i	−0.996873	+	0.0790234i	$0.974820\pi$
$110$		0			0
$111$	−18.5087	+	3.15819i	−1.75676	+	0.299762i
$112$		0			0
$113$	−4.29629	+	6.42985i	−0.404161	+	0.604870i	−0.976596	−	0.215080i	$-0.930999\pi$
$113$	−4.29629	+	6.42985i	−0.404161	+	0.604870i	0.572435	+	0.819950i	$0.305999\pi$
$114$		0			0
$115$	12.2798	+	12.2798i	1.14510	+	1.14510i
$116$		0			0
$117$	0.337523	−	6.16557i	0.0312040	−	0.570007i
$118$		0			0
$119$	8.70614	+	4.55763i	0.798091	+	0.417797i
$120$		0			0
$121$	4.17245	+	10.0732i	0.379314	+	0.915745i
$122$		0			0
$123$	−2.12421	+	9.33714i	−0.191534	+	0.841902i
$124$		0			0
$125$	−1.62433	−	1.08534i	−0.145284	−	0.0970757i
$126$		0			0
$127$	−11.7962	−	4.88615i	−1.04674	−	0.433576i	−0.208016	−	0.978125i	$-0.566701\pi$
$127$	−11.7962	−	4.88615i	−1.04674	−	0.433576i	−0.838729	+	0.544550i	$0.816701\pi$
$128$		0			0
$129$	−3.51772	−	3.71556i	−0.309718	−	0.327137i
$130$		0			0
$131$	−2.00825	+	10.0962i	−0.175462	+	0.882107i	0.788289	+	0.615305i	$0.210967\pi$
$131$	−2.00825	+	10.0962i	−0.175462	+	0.882107i	−0.963751	+	0.266802i	$0.914033\pi$
$132$		0			0
$133$	2.21354	−	1.47904i	0.191938	−	0.128249i
$134$		0			0
$135$	−15.7947	+	1.81350i	−1.35939	+	0.156081i
$136$		0			0
$137$			19.0290i			1.62576i	0.582434	+	0.812878i	$0.302100\pi$
$137$			19.0290i			1.62576i	−0.582434	+	0.812878i	$0.697900\pi$
$138$		0			0
$139$	−1.03770	−	1.55303i	−0.0880167	−	0.131726i	0.784849	−	0.619688i	$-0.212741\pi$
$139$	−1.03770	−	1.55303i	−0.0880167	−	0.131726i	−0.872865	+	0.487961i	$0.837741\pi$
$140$		0			0
$141$	3.94441	+	10.3114i	0.332179	+	0.868378i
$142$		0			0
$143$	0.628247	−	0.124966i	0.0525366	−	0.0104502i
$144$		0			0
$145$	−9.74058	+	23.5158i	−0.808911	+	1.95288i
$146$		0			0
$147$	0.0624850	−	2.28455i	0.00515367	−	0.188426i
$148$		0			0
$149$	−5.87087	+	5.87087i	−0.480960	+	0.480960i	−0.905438	−	0.424478i	$-0.860458\pi$
$149$	−5.87087	+	5.87087i	−0.480960	+	0.480960i	0.424478	+	0.905438i	$0.360458\pi$
$150$		0			0
$151$	−14.9344	+	6.18603i	−1.21534	+	0.503412i	−0.895927	−	0.444202i	$-0.853487\pi$
$151$	−14.9344	+	6.18603i	−1.21534	+	0.503412i	−0.319418	+	0.947614i	$0.603487\pi$
$152$		0			0
$153$	−12.3525	+	0.644061i	−0.998643	+	0.0520693i
$154$		0			0
$155$	17.8573	−	7.39673i	1.43433	−	0.594120i
$156$		0			0
$157$	3.33169	−	3.33169i	0.265898	−	0.265898i	−0.561547	−	0.827445i	$-0.689794\pi$
$157$	3.33169	−	3.33169i	0.265898	−	0.265898i	0.827445	+	0.561547i	$0.189794\pi$
$158$		0			0
$159$	0.272471	−	9.96197i	0.0216083	−	0.790035i
$160$		0			0
$161$	−5.17687	+	12.4981i	−0.407994	+	0.984986i
$162$		0			0
$163$	3.23758	−	0.643995i	0.253587	−	0.0504416i	−0.0666598	−	0.997776i	$-0.521234\pi$
$163$	3.23758	−	0.643995i	0.253587	−	0.0504416i	0.320247	+	0.947334i	$0.396234\pi$
$164$		0			0
$165$	−0.589248	−	1.54040i	−0.0458729	−	0.119920i
$166$		0			0
$167$	3.69262	+	5.52640i	0.285743	+	0.427645i	0.946378	−	0.323063i	$-0.104712\pi$
$167$	3.69262	+	5.52640i	0.285743	+	0.427645i	−0.660634	+	0.750708i	$0.729712\pi$
$168$		0			0
$169$		−	8.76354i		−	0.674118i
$170$		0			0
$171$	−1.44966	+	3.02115i	−0.110858	+	0.231033i
$172$		0			0
$173$	12.5940	−	8.41505i	0.957505	−	0.639784i	0.0245198	−	0.999699i	$-0.492194\pi$
$173$	12.5940	−	8.41505i	0.957505	−	0.639784i	0.932985	+	0.359915i	$0.117194\pi$
$174$		0			0
$175$	−2.02799	+	10.1954i	−0.153302	+	0.770701i
$176$		0			0
$177$	1.05054	+	1.10962i	0.0789631	+	0.0834040i
$178$		0			0
$179$	−17.6614	−	7.31558i	−1.32007	−	0.546792i	−0.392266	−	0.919852i	$-0.628309\pi$
$179$	−17.6614	−	7.31558i	−1.32007	−	0.546792i	−0.927807	+	0.373059i	$0.878309\pi$
$180$		0			0
$181$	−6.27270	−	4.19128i	−0.466246	−	0.311535i	0.300164	−	0.953888i	$-0.402959\pi$
$181$	−6.27270	−	4.19128i	−0.466246	−	0.311535i	−0.766410	+	0.642352i	$0.777959\pi$
$182$		0			0
$183$	−1.28449	+	5.64608i	−0.0949522	+	0.417370i
$184$		0			0
$185$	−12.6929	−	30.6433i	−0.933197	−	2.25294i
$186$		0			0
$187$	−0.383034	−	1.22465i	−0.0280103	−	0.0895554i
$188$		0			0
$189$	−6.01351	−	10.8264i	−0.437419	−	0.787507i
$190$		0			0
$191$	11.3186	+	11.3186i	0.818985	+	0.818985i	0.985961	−	0.166976i	$-0.0534002\pi$
$191$	11.3186	+	11.3186i	0.818985	+	0.818985i	−0.166976	+	0.985961i	$0.553400\pi$
$192$		0			0
$193$	−6.02621	+	9.01886i	−0.433776	+	0.649192i	−0.982381	−	0.186890i	$-0.940159\pi$
$193$	−6.02621	+	9.01886i	−0.433776	+	0.649192i	0.548605	+	0.836082i	$0.315159\pi$
$194$		0			0
$195$	10.7523	−	1.83470i	0.769991	−	0.131386i
$196$		0			0
$197$	−1.09663	−	5.51314i	−0.0781318	−	0.392795i	−0.999986	−	0.00525859i	$-0.998326\pi$
$197$	−1.09663	−	5.51314i	−0.0781318	−	0.392795i	0.921854	−	0.387536i	$-0.126674\pi$
$198$		0			0
$199$	8.28425	+	1.64784i	0.587255	+	0.116812i	0.479770	−	0.877394i	$-0.340720\pi$
$199$	8.28425	+	1.64784i	0.587255	+	0.116812i	0.107485	+	0.994207i	$0.465720\pi$
$200$		0			0
$201$	−3.93835	−	1.75896i	−0.277790	−	0.124068i
$202$		0			0
$203$	−19.8274			−1.39161
$204$		0			0
$205$	−16.9155			−1.18143
$206$		0			0
$207$	−2.40409	−	16.8571i	−0.167096	−	1.17165i
$208$		0			0
$209$	−0.340938	−	0.0678168i	−0.0235832	−	0.00469098i
$210$		0			0
$211$	2.32730	+	11.7002i	0.160218	+	0.805472i	0.974393	+	0.224852i	$0.0721898\pi$
$211$	2.32730	+	11.7002i	0.160218	+	0.805472i	−0.814175	+	0.580620i	$0.802810\pi$
$212$		0			0
$213$	−0.349447	−	2.04795i	−0.0239437	−	0.140323i
$214$		0			0
$215$	5.02150	−	7.51521i	0.342464	−	0.512533i
$216$		0			0
$217$	10.6465	+	10.6465i	0.722731	+	0.722731i
$218$		0			0
$219$	1.43313	+	1.01534i	0.0968420	+	0.0686103i
$220$		0			0
$221$	8.43812	−	0.904474i	0.567609	−	0.0608415i
$222$		0			0
$223$	2.08637	+	5.03695i	0.139714	+	0.337299i	0.978213	−	0.207604i	$-0.0665665\pi$
$223$	2.08637	+	5.03695i	0.139714	+	0.337299i	−0.838499	+	0.544903i	$0.816566\pi$
$224$		0			0
$225$	−4.33897	−	12.3442i	−0.289265	−	0.822944i
$226$		0			0
$227$	−20.1039	−	13.4330i	−1.33434	−	0.891579i	−0.335614	−	0.942000i	$-0.608944\pi$
$227$	−20.1039	−	13.4330i	−1.33434	−	0.891579i	−0.998728	+	0.0504205i	$0.983944\pi$
$228$		0			0
$229$	−6.34884	−	2.62978i	−0.419543	−	0.173781i	0.162917	−	0.986640i	$-0.447910\pi$
$229$	−6.34884	−	2.62978i	−0.419543	−	0.173781i	−0.582460	+	0.812859i	$0.697910\pi$
$230$		0			0
$231$	0.932934	−	0.883259i	0.0613826	−	0.0581142i
$232$		0			0
$233$	−1.91961	+	9.65051i	−0.125758	+	0.632226i	0.865567	+	0.500792i	$0.166958\pi$
$233$	−1.91961	+	9.65051i	−0.125758	+	0.632226i	−0.991325	+	0.131434i	$0.958042\pi$
$234$		0			0
$235$	−16.2155	+	10.8349i	−1.05779	+	0.706789i
$236$		0			0
$237$	−19.5622	+	12.3110i	−1.27070	+	0.799687i
$238$		0			0
$239$			15.3938i			0.995745i	0.867250	+	0.497872i	$0.165885\pi$
$239$			15.3938i			0.995745i	−0.867250	+	0.497872i	$0.834115\pi$
$240$		0			0
$241$	8.31553	+	12.4451i	0.535650	+	0.801657i	0.996302	−	0.0859240i	$-0.0273842\pi$
$241$	8.31553	+	12.4451i	0.535650	+	0.801657i	−0.460652	+	0.887581i	$0.652384\pi$
$242$		0			0
$243$	13.4544	+	7.87269i	0.863100	+	0.505033i
$244$		0			0
$245$	3.95958	−	0.787610i	0.252968	−	0.0503185i
$246$		0			0
$247$	0.879808	−	2.12405i	0.0559809	−	0.135150i
$248$		0			0
$249$	−7.07261	−	0.193444i	−0.448209	−	0.0122590i
$250$		0			0
$251$	18.8524	−	18.8524i	1.18995	−	1.18995i	0.212869	−	0.977081i	$-0.431719\pi$
$251$	18.8524	−	18.8524i	1.18995	−	1.18995i	0.977081	−	0.212869i	$-0.0682809\pi$
$252$		0			0
$253$	1.63194	−	0.675970i	0.102599	−	0.0424979i
$254$		0			0
$255$	−5.94993	−	21.0246i	−0.372599	−	1.31661i
$256$		0			0
$257$	2.18812	−	0.906350i	0.136491	−	0.0565366i	−0.313392	−	0.949624i	$-0.601465\pi$
$257$	2.18812	−	0.906350i	0.136491	−	0.0565366i	0.449884	+	0.893087i	$0.351465\pi$
$258$		0			0
$259$	18.2695	−	18.2695i	1.13521	−	1.13521i
$260$		0			0
$261$	21.4779	−	12.7104i	1.32945	−	0.786754i
$262$		0			0
$263$	−12.1218	+	29.2646i	−0.747461	+	1.80453i	−0.175055	+	0.984559i	$0.556010\pi$
$263$	−12.1218	+	29.2646i	−0.747461	+	1.80453i	−0.572405	+	0.819971i	$0.693990\pi$
$264$		0			0
$265$	17.2661	−	3.43444i	1.06065	−	0.210976i
$266$		0			0
$267$	−1.57344	+	0.601887i	−0.0962931	+	0.0368349i
$268$		0			0
$269$	10.6861	+	15.9929i	0.651546	+	0.975107i	0.999296	+	0.0375200i	$0.0119458\pi$
$269$	10.6861	+	15.9929i	0.651546	+	0.975107i	−0.347750	+	0.937587i	$0.613054\pi$
$270$		0			0
$271$		−	14.1909i		−	0.862033i	−0.902344	−	0.431017i	$-0.858155\pi$
$271$		−	14.1909i		−	0.862033i	0.902344	−	0.431017i	$-0.141845\pi$
$272$		0			0
$273$	4.52566	+	7.19127i	0.273905	+	0.435236i
$274$		0			0
$275$	1.12859	−	0.754103i	0.0680568	−	0.0454741i
$276$		0			0
$277$	−3.04146	+	15.2905i	−0.182744	+	0.918715i	0.775191	+	0.631727i	$0.217654\pi$
$277$	−3.04146	+	15.2905i	−0.182744	+	0.918715i	−0.957934	+	0.286987i	$0.907346\pi$
$278$		0			0
$279$	−18.3577	−	4.70779i	−1.09905	−	0.281848i
$280$		0			0
$281$	2.87379	+	1.19036i	0.171436	+	0.0710112i	0.466751	−	0.884389i	$-0.345424\pi$
$281$	2.87379	+	1.19036i	0.171436	+	0.0710112i	−0.295315	+	0.955400i	$0.595424\pi$
$282$		0			0
$283$	6.70804	+	4.48217i	0.398752	+	0.266437i	0.738738	−	0.673993i	$-0.235422\pi$
$283$	6.70804	+	4.48217i	0.398752	+	0.266437i	−0.339986	+	0.940431i	$0.610422\pi$
$284$		0			0
$285$	−5.77195	−	1.31313i	−0.341901	−	0.0777829i
$286$		0			0
$287$	−5.04249	−	12.1736i	−0.297649	−	0.718587i
$288$		0			0
$289$	−3.60303	−	16.6138i	−0.211943	−	0.977282i
$290$		0			0
$291$	−6.24895	+	8.82025i	−0.366320	+	0.517052i
$292$		0			0
$293$	−8.86520	−	8.86520i	−0.517910	−	0.517910i	0.399028	−	0.916939i	$-0.369348\pi$
$293$	−8.86520	−	8.86520i	−0.517910	−	0.517910i	−0.916939	+	0.399028i	$0.869348\pi$
$294$		0			0
$295$	−1.49963	+	2.24435i	−0.0873117	+	0.130671i
$296$		0			0
$297$	−0.444380	+	1.55484i	−0.0257855	+	0.0902211i
$298$		0			0
$299$	2.27914	+	11.4580i	0.131806	+	0.662634i
$300$		0			0
$301$	6.90542	+	1.37357i	0.398022	+	0.0791714i
$302$		0			0
$303$	−2.75441	+	6.16718i	−0.158237	+	0.354295i
$304$		0			0
$305$	−10.2286			−0.585689
$306$		0			0
$307$	−18.0205			−1.02849			−0.514243	−	0.857645i	$-0.671927\pi$
$307$	−18.0205			−1.02849			−0.514243	+	0.857645i	$0.671927\pi$
$308$		0			0
$309$	5.89549	−	13.2001i	0.335383	−	0.750927i
$310$		0			0
$311$	−10.5180	−	2.09217i	−0.596424	−	0.118636i	−0.112358	−	0.993668i	$-0.535840\pi$
$311$	−10.5180	−	2.09217i	−0.596424	−	0.118636i	−0.484065	+	0.875032i	$0.660840\pi$
$312$		0			0
$313$	−3.99371	−	20.0777i	−0.225738	−	1.13486i	−0.912846	−	0.408305i	$-0.866120\pi$
$313$	−3.99371	−	20.0777i	−0.225738	−	1.13486i	0.687108	−	0.726556i	$-0.258880\pi$
$314$		0			0
$315$	16.2918	−	14.6007i	0.917941	−	0.822656i
$316$		0			0
$317$	4.70443	−	7.04068i	0.264227	−	0.395444i	−0.675505	−	0.737356i	$-0.736074\pi$
$317$	4.70443	−	7.04068i	0.264227	−	0.395444i	0.939732	+	0.341911i	$0.111074\pi$
$318$		0			0
$319$	1.83068	+	1.83068i	0.102498	+	0.102498i
$320$		0			0
$321$	−5.25371	+	7.41549i	−0.293233	+	0.413892i
$322$		0			0
$323$	−4.41847	−	1.29891i	−0.245850	−	0.0722732i
$324$		0			0
$325$	3.43541	+	8.29381i	0.190562	+	0.460058i
$326$		0			0
$327$	−4.12515	−	0.938477i	−0.228121	−	0.0518979i
$328$		0			0
$329$	−12.6314	−	8.44005i	−0.696393	−	0.465315i
$330$		0			0
$331$	−13.8877	−	5.75246i	−0.763335	−	0.316184i	−0.0331656	−	0.999450i	$-0.510559\pi$
$331$	−13.8877	−	5.75246i	−0.763335	−	0.316184i	−0.730169	+	0.683266i	$0.760559\pi$
$332$		0			0
$333$	−8.07860	+	31.5019i	−0.442705	+	1.72629i
$334$		0			0
$335$	1.48647	−	7.47301i	0.0812148	−	0.408294i
$336$		0			0
$337$	−22.9447	+	15.3312i	−1.24988	+	0.835143i	−0.991399	−	0.130873i	$-0.958222\pi$
$337$	−22.9447	+	15.3312i	−1.24988	+	0.835143i	−0.258481	+	0.966016i	$0.583222\pi$
$338$		0			0
$339$	7.13412	+	11.3361i	0.387472	+	0.615694i
$340$		0			0
$341$		−	1.96599i		−	0.106465i
$342$		0			0
$343$	11.0161	+	16.4868i	0.594815	+	0.890204i
$344$		0			0
$345$	28.0939	−	10.7467i	1.51253	−	0.578585i
$346$		0			0
$347$	16.6581	−	3.31350i	0.894252	−	0.177878i	0.273488	−	0.961875i	$-0.411823\pi$
$347$	16.6581	−	3.31350i	0.894252	−	0.177878i	0.620764	+	0.783997i	$0.286823\pi$
$348$		0			0
$349$	13.5795	−	32.7838i	0.726894	−	1.75488i	0.0742177	−	0.997242i	$-0.476354\pi$
$349$	13.5795	−	32.7838i	0.726894	−	1.75488i	0.652677	−	0.757636i	$-0.273646\pi$
$350$		0			0
$351$	−9.51236	−	4.88872i	−0.507732	−	0.260940i
$352$		0			0
$353$	16.3117	−	16.3117i	0.868187	−	0.868187i	−0.124085	−	0.992272i	$-0.539600\pi$
$353$	16.3117	−	16.3117i	0.868187	−	0.868187i	0.992272	+	0.124085i	$0.0395995\pi$
$354$		0			0
$355$	3.39062	−	1.40444i	0.179955	−	0.0745399i
$356$		0			0
$357$	13.3572	−	10.5494i	0.706940	−	0.558336i
$358$		0			0
$359$	14.5670	−	6.03383i	0.768814	−	0.318453i	0.0364222	−	0.999336i	$-0.488404\pi$
$359$	14.5670	−	6.03383i	0.768814	−	0.318453i	0.732392	+	0.680883i	$0.238404\pi$
$360$		0			0
$361$	12.5528	−	12.5528i	0.660674	−	0.660674i
$362$		0			0
$363$	18.8777	+	0.516327i	0.990825	+	0.0271002i
$364$		0			0
$365$	−1.18731	+	2.86642i	−0.0621466	+	0.150035i
$366$		0			0
$367$	−17.1344	+	3.40824i	−0.894408	+	0.177909i	−0.620834	−	0.783942i	$-0.713206\pi$
$367$	−17.1344	+	3.40824i	−0.894408	+	0.177909i	−0.273574	+	0.961851i	$0.588206\pi$
$368$		0			0
$369$	13.2662	+	9.95452i	0.690609	+	0.518212i
$370$		0			0
$371$	7.61868	+	11.4022i	0.395542	+	0.591971i
$372$		0			0
$373$			9.88473i			0.511812i	0.966702	+	0.255906i	$0.0823738\pi$
$373$			9.88473i			0.511812i	−0.966702	+	0.255906i	$0.917626\pi$
$374$		0			0
$375$	−2.86376	+	1.80224i	−0.147884	+	0.0930672i
$376$		0			0
$377$	−14.2371	+	9.51290i	−0.733246	+	0.489939i
$378$		0			0
$379$	4.33652	−	21.8012i	0.222752	−	1.11985i	−0.693872	−	0.720099i	$-0.744096\pi$
$379$	4.33652	−	21.8012i	0.222752	−	1.11985i	0.916624	−	0.399751i	$-0.130904\pi$
$380$		0			0
$381$	−16.0594	+	15.2043i	−0.822748	+	0.778940i
$382$		0			0
$383$	17.3935	+	7.20462i	0.888765	+	0.368139i	0.779890	−	0.625917i	$-0.215275\pi$
$383$	17.3935	+	7.20462i	0.888765	+	0.368139i	0.108875	+	0.994055i	$0.465275\pi$
$384$		0			0
$385$	1.88698	+	1.26084i	0.0961696	+	0.0642585i
$386$		0			0
$387$	−8.36078	+	2.93881i	−0.425002	+	0.149388i
$388$		0			0
$389$	4.70975	+	11.3703i	0.238794	+	0.576499i	0.997159	−	0.0753313i	$-0.0240014\pi$
$389$	4.70975	+	11.3703i	0.238794	+	0.576499i	−0.758365	+	0.651830i	$0.774001\pi$
$390$		0			0
$391$	22.3353	−	6.98581i	1.12954	−	0.353287i
$392$		0			0
$393$	14.5485	+	10.3073i	0.733873	+	0.519933i
$394$		0			0
$395$	−28.8713	−	28.8713i	−1.45267	−	1.45267i
$396$		0			0
$397$	−3.63413	+	5.43887i	−0.182392	+	0.272969i	−0.911387	−	0.411550i	$-0.864988\pi$
$397$	−3.63413	+	5.43887i	−0.182392	+	0.272969i	0.728995	+	0.684519i	$0.239988\pi$
$398$		0			0
$399$	−0.775590	−	4.54537i	−0.0388281	−	0.227553i
$400$		0			0
$401$	−1.04712	−	5.26423i	−0.0522907	−	0.262883i	0.945792	−	0.324772i	$-0.105288\pi$
$401$	−1.04712	−	5.26423i	−0.0522907	−	0.262883i	−0.998083	+	0.0618889i	$0.980288\pi$
$402$		0			0
$403$	12.7527	+	2.53667i	0.635259	+	0.126361i
$404$		0			0
$405$	−8.28824	+	26.2600i	−0.411846	+	1.30487i
$406$		0			0
$407$	−3.37366			−0.167226
$408$		0			0
$409$	29.6457			1.46589			0.732943	−	0.680290i	$-0.238146\pi$
$409$	29.6457			1.46589			0.732943	+	0.680290i	$0.238146\pi$
$410$		0			0
$411$	30.0941	+	13.4407i	1.48443	+	0.662983i
$412$		0			0
$413$	−2.06224	−	0.410205i	−0.101476	−	0.0201849i
$414$		0			0
$415$	−2.43832	−	12.2583i	−0.119692	−	0.601734i
$416$		0			0
$417$	−3.18906	+	0.544158i	−0.156169	+	0.0266475i
$418$		0			0
$419$	−15.8338	+	23.6969i	−0.773530	+	1.15767i	0.210137	+	0.977672i	$0.432609\pi$
$419$	−15.8338	+	23.6969i	−0.773530	+	1.15767i	−0.983667	+	0.179998i	$0.942391\pi$
$420$		0			0
$421$	−10.1384	−	10.1384i	−0.494115	−	0.494115i	0.415485	−	0.909600i	$-0.363612\pi$
$421$	−10.1384	−	10.1384i	−0.494115	−	0.494115i	−0.909600	+	0.415485i	$0.863612\pi$
$422$		0			0
$423$	19.0934	+	1.04523i	0.928353	+	0.0508210i
$424$		0			0
$425$	15.7860	−	8.61329i	0.765734	−	0.417806i
$426$		0			0
$427$	−3.04914	−	7.36128i	−0.147558	−	0.356237i
$428$		0			0
$429$	0.246118	−	1.08183i	0.0118827	−	0.0522313i
$430$		0			0
$431$	14.2217	+	9.50263i	0.685035	+	0.457726i	0.848759	−	0.528781i	$-0.177351\pi$
$431$	14.2217	+	9.50263i	0.685035	+	0.457726i	−0.163724	+	0.986506i	$0.552351\pi$
$432$		0			0
$433$	−24.9557	−	10.3370i	−1.19929	−	0.496763i	−0.308522	−	0.951217i	$-0.599835\pi$
$433$	−24.9557	−	10.3370i	−1.19929	−	0.496763i	−0.890770	+	0.454454i	$0.849835\pi$
$434$		0			0
$435$	30.3099	+	32.0146i	1.45325	+	1.53498i
$436$		0			0
$437$	1.23685	−	6.21805i	0.0591664	−	0.297450i
$438$		0			0
$439$	3.58289	−	2.39401i	0.171002	−	0.114260i	−0.467124	−	0.884192i	$-0.654710\pi$
$439$	3.58289	−	2.39401i	0.171002	−	0.114260i	0.638126	+	0.769932i	$0.279710\pi$
$440$		0			0
$441$	−3.56885	−	1.71247i	−0.169945	−	0.0815460i
$442$		0			0
$443$		−	18.4676i		−	0.877421i	−0.898628	−	0.438711i	$-0.855435\pi$
$443$		−	18.4676i		−	0.877421i	0.898628	−	0.438711i	$-0.144565\pi$
$444$		0			0
$445$	−1.65332	−	2.47437i	−0.0783748	−	0.117296i
$446$		0			0
$447$	5.13792	+	13.4315i	0.243015	+	0.635287i
$448$		0			0
$449$	34.5644	−	6.87529i	1.63120	−	0.324465i	0.707243	−	0.706971i	$-0.249939\pi$
$449$	34.5644	−	6.87529i	1.63120	−	0.324465i	0.923953	+	0.382506i	$0.124939\pi$
$450$		0			0
$451$	−0.658424	+	1.58958i	−0.0310040	+	0.0748502i
$452$		0			0
$453$	−0.765501	+	27.9879i	−0.0359664	+	1.31499i
$454$		0			0
$455$	−10.6134	+	10.6134i	−0.497563	+	0.497563i
$456$		0			0
$457$	−7.09930	+	2.94063i	−0.332091	+	0.137557i	−0.542498	−	0.840057i	$-0.682521\pi$
$457$	−7.09930	+	2.94063i	−0.332091	+	0.137557i	0.210406	+	0.977614i	$0.432521\pi$
$458$		0			0
$459$	−7.70640	+	19.9903i	−0.359704	+	0.933066i
$460$		0			0
$461$	28.6159	−	11.8531i	1.33278	−	0.552054i	0.401330	−	0.915933i	$-0.368548\pi$
$461$	28.6159	−	11.8531i	1.33278	−	0.552054i	0.931446	+	0.363879i	$0.118548\pi$
$462$		0			0
$463$	13.2795	−	13.2795i	0.617149	−	0.617149i	−0.327650	−	0.944799i	$-0.606257\pi$
$463$	13.2795	−	13.2795i	0.617149	−	0.617149i	0.944799	+	0.327650i	$0.106257\pi$
$464$		0			0
$465$	0.915321	−	33.4656i	0.0424470	−	1.55193i
$466$		0			0
$467$	−4.24049	+	10.2375i	−0.196227	+	0.473733i	−0.991113	−	0.133026i	$-0.957531\pi$
$467$	−4.24049	+	10.2375i	−0.196227	+	0.473733i	0.794886	+	0.606759i	$0.207531\pi$
$468$		0			0
$469$	5.82126	−	1.15792i	0.268801	−	0.0534678i
$470$		0			0
$471$	−2.91575	−	7.62229i	−0.134351	−	0.351217i
$472$		0			0
$473$	−0.510759	−	0.764404i	−0.0234847	−	0.0351473i
$474$		0			0
$475$		−	4.87173i		−	0.223531i
$476$		0			0
$477$	−15.5623	−	7.46735i	−0.712547	−	0.341906i
$478$		0			0
$479$	33.4090	−	22.3232i	1.52650	−	1.01997i	0.542855	−	0.839826i	$-0.317343\pi$
$479$	33.4090	−	22.3232i	1.52650	−	1.01997i	0.983640	−	0.180145i	$-0.0576569\pi$
$480$		0			0
$481$	4.35295	−	21.8838i	0.198478	−	0.997814i
$482$		0			0
$483$	16.1089	+	17.0149i	0.732982	+	0.774205i
$484$		0			0
$485$	−17.6415	−	7.30734i	−0.801058	−	0.331809i
$486$		0			0
$487$	33.7348	+	22.5409i	1.52867	+	1.02143i	0.983038	+	0.183400i	$0.0587105\pi$
$487$	33.7348	+	22.5409i	1.52867	+	1.02143i	0.545632	+	0.838025i	$0.316290\pi$
$488$		0			0
$489$	1.26833	−	5.57506i	0.0573560	−	0.252113i
$490$		0			0
$491$	−12.9778	−	31.3311i	−0.585679	−	1.41395i	−0.887597	−	0.460620i	$-0.847627\pi$
$491$	−12.9778	−	31.3311i	−0.585679	−	1.41395i	0.301918	−	0.953334i	$-0.402373\pi$
$492$		0			0
$493$	21.9872	+	26.3262i	0.990254	+	1.18567i
$494$		0			0
$495$	−2.85233	−	0.156145i	−0.128203	−	0.00701821i
$496$		0			0
$497$	2.02148	+	2.02148i	0.0906757	+	0.0906757i
$498$		0			0
$499$	−0.488815	+	0.731563i	−0.0218824	+	0.0327493i	−0.842250	−	0.539088i	$-0.818769\pi$
$499$	−0.488815	+	0.731563i	−0.0218824	+	0.0327493i	0.820367	+	0.571837i	$0.193769\pi$
$500$		0			0
$501$	11.3481	−	1.93636i	0.506997	−	0.0865104i
$502$		0			0
$503$	−0.915226	−	4.60115i	−0.0408079	−	0.205155i	0.955002	−	0.296598i	$-0.0958522\pi$
$503$	−0.915226	−	4.60115i	−0.0408079	−	0.205155i	−0.995810	+	0.0914427i	$0.970852\pi$
$504$		0			0
$505$	−11.7022	−	2.32772i	−0.520742	−	0.103582i
$506$		0			0
$507$	−13.8594	−	6.18995i	−0.615518	−	0.274905i
$508$		0			0
$509$	−23.4235			−1.03823			−0.519114	−	0.854705i	$-0.673738\pi$
$509$	−23.4235			−1.03823			−0.519114	+	0.854705i	$0.673738\pi$
$510$		0			0
$511$	−2.41683			−0.106914
$512$		0			0
$513$	3.75397	+	4.42655i	0.165742	+	0.195437i
$514$		0			0
$515$	25.0472	+	4.98219i	1.10371	+	0.219542i
$516$		0			0
$517$	0.386992	+	1.94554i	0.0170199	+	0.0855649i
$518$		0			0
$519$	−4.41275	−	25.8611i	−0.193698	−	1.13517i
$520$		0			0
$521$	1.87377	−	2.80429i	0.0820913	−	0.122858i	−0.788152	−	0.615481i	$-0.788962\pi$
$521$	1.87377	−	2.80429i	0.0820913	−	0.122858i	0.870243	+	0.492623i	$0.163962\pi$
$522$		0			0
$523$	−29.9264	−	29.9264i	−1.30859	−	1.30859i	−0.922433	−	0.386158i	$-0.873802\pi$
$523$	−29.9264	−	29.9264i	−1.30859	−	1.30859i	−0.386158	−	0.922433i	$-0.626198\pi$
$524$		0			0
$525$	14.6915	+	10.4086i	0.641188	+	0.454268i
$526$		0			0
$527$	2.32983	−	25.9422i	0.101489	−	1.13006i
$528$		0			0
$529$	3.52667	+	8.51414i	0.153334	+	0.370180i
$530$		0			0
$531$	2.49687	−	0.877650i	0.108355	−	0.0380868i
$532$		0			0
$533$	−9.46148	−	6.32196i	−0.409822	−	0.273834i
$534$		0			0
$535$	−14.8318	−	6.14353i	−0.641235	−	0.265608i
$536$		0			0
$537$	−24.0443	+	22.7640i	−1.03759	+	0.982339i
$538$		0			0
$539$	0.0801111	−	0.402746i	0.00345063	−	0.0173475i
$540$		0			0
$541$	26.5506	−	17.7405i	1.14150	−	0.762725i	0.166743	−	0.986000i	$-0.446675\pi$
$541$	26.5506	−	17.7405i	1.14150	−	0.762725i	0.974755	+	0.223275i	$0.0716749\pi$
$542$		0			0
$543$	−11.0590	+	6.95975i	−0.474589	+	0.298671i
$544$		0			0
$545$		−	7.47326i		−	0.320119i
$546$		0			0
$547$	−2.57308	−	3.85088i	−0.110017	−	0.164652i	0.772376	−	0.635166i	$-0.219068\pi$
$547$	−2.57308	−	3.85088i	−0.110017	−	0.164652i	−0.882392	+	0.470514i	$0.844068\pi$
$548$		0			0
$549$	8.02192	+	6.01940i	0.342367	+	0.256902i
$550$		0			0
$551$	9.11366	−	1.81282i	0.388255	−	0.0772287i
$552$		0			0
$553$	12.1715	−	29.3845i	0.517583	−	1.24956i
$554$		0			0
$555$	−57.4272	−	1.57070i	−2.43765	−	0.0666724i
$556$		0			0
$557$	11.8460	−	11.8460i	0.501933	−	0.501933i	−0.410105	−	0.912038i	$-0.634508\pi$
$557$	11.8460	−	11.8460i	0.501933	−	0.501933i	0.912038	+	0.410105i	$0.134508\pi$
$558$		0			0
$559$	5.61745	−	2.32682i	0.237593	−	0.0984141i
$560$		0			0
$561$	−2.20732	−	0.259245i	−0.0931930	−	0.0109453i
$562$		0			0
$563$	12.3385	−	5.11078i	0.520006	−	0.215394i	−0.107214	−	0.994236i	$-0.534193\pi$
$563$	12.3385	−	5.11078i	0.520006	−	0.215394i	0.627220	+	0.778842i	$0.284193\pi$
$564$		0			0
$565$	−16.7306	+	16.7306i	−0.703863	+	0.703863i
$566$		0			0
$567$	−21.3694	+	1.86325i	−0.897430	+	0.0782490i
$568$		0			0
$569$	−14.8059	+	35.7445i	−0.620694	+	1.49849i	0.230195	+	0.973144i	$0.426064\pi$
$569$	−14.8059	+	35.7445i	−0.620694	+	1.49849i	−0.850890	+	0.525345i	$0.823936\pi$
$570$		0			0
$571$	−19.3864	+	3.85620i	−0.811297	+	0.161377i	−0.583270	−	0.812278i	$-0.698227\pi$
$571$	−19.3864	+	3.85620i	−0.811297	+	0.161377i	−0.228026	+	0.973655i	$0.573227\pi$
$572$		0			0
$573$	25.8949	−	9.90553i	1.08177	−	0.413810i
$574$		0			0
$575$	13.7534	+	20.5834i	0.573555	+	0.858386i
$576$		0			0
$577$		−	34.4403i		−	1.43377i	−0.697192	−	0.716884i	$-0.745568\pi$
$577$		−	34.4403i		−	1.43377i	0.697192	−	0.716884i	$-0.254432\pi$
$578$		0			0
$579$	10.0067	+	15.9007i	0.415864	+	0.660809i
$580$		0			0
$581$	8.09510	−	5.40897i	0.335841	−	0.224402i
$582$		0			0
$583$	0.349331	−	1.75621i	0.0144678	−	0.0727346i
$584$		0			0
$585$	4.69315	−	18.3006i	0.194038	−	0.756636i
$586$		0			0
$587$	7.71494	+	3.19563i	0.318430	+	0.131898i	0.536173	−	0.844108i	$-0.319870\pi$
$587$	7.71494	+	3.19563i	0.318430	+	0.131898i	−0.217743	+	0.976006i	$0.569870\pi$
$588$		0			0
$589$	−5.86706	−	3.92024i	−0.241748	−	0.161531i
$590$		0			0
$591$	−9.49354	−	2.15979i	−0.390512	−	0.0888419i
$592$		0			0
$593$	0.0555800	+	0.134182i	0.00228240	+	0.00551019i	0.925017	−	0.379927i	$-0.124051\pi$
$593$	0.0555800	+	0.134182i	0.00228240	+	0.00551019i	−0.922734	+	0.385437i	$0.874051\pi$
$594$		0			0
$595$	23.4055	+	18.8736i	0.959531	+	0.773743i
$596$		0			0
$597$	8.45745	−	11.9375i	0.346140	−	0.488569i
$598$		0			0
$599$	−19.5023	−	19.5023i	−0.796842	−	0.796842i	0.185754	−	0.982596i	$-0.440527\pi$
$599$	−19.5023	−	19.5023i	−0.796842	−	0.796842i	−0.982596	+	0.185754i	$0.940527\pi$
$600$		0			0
$601$	−17.1815	+	25.7140i	−0.700849	+	1.04889i	0.294786	+	0.955563i	$0.404752\pi$
$601$	−17.1815	+	25.7140i	−0.700849	+	1.04889i	−0.995635	+	0.0933313i	$0.970248\pi$
$602$		0			0
$603$	−5.56355	+	4.98603i	−0.226565	+	0.203047i
$604$		0			0
$605$	6.50820	+	32.7189i	0.264596	+	1.33021i
$606$		0			0
$607$	9.07485	+	1.80510i	0.368337	+	0.0732668i	0.375788	−	0.926705i	$-0.377372\pi$
$607$	9.07485	+	1.80510i	0.368337	+	0.0732668i	−0.00745155	+	0.999972i	$0.502372\pi$
$608$		0			0
$609$	−14.0047	+	31.3568i	−0.567500	+	1.27064i
$610$		0			0
$611$	−13.1194			−0.530754
$612$		0			0
$613$	−19.1051			−0.771649			−0.385824	−	0.922572i	$-0.626083\pi$
$613$	−19.1051			−0.771649			−0.385824	+	0.922572i	$0.626083\pi$
$614$		0			0
$615$	−11.9479	+	26.7516i	−0.481786	+	1.07873i
$616$		0			0
$617$	−11.8884	−	2.36475i	−0.478610	−	0.0952014i	−0.0501108	−	0.998744i	$-0.515957\pi$
$617$	−11.8884	−	2.36475i	−0.478610	−	0.0952014i	−0.428499	+	0.903542i	$0.640957\pi$
$618$		0			0
$619$	−7.99128	−	40.1749i	−0.321197	−	1.61476i	−0.717441	−	0.696619i	$-0.754687\pi$
$619$	−7.99128	−	40.1749i	−0.321197	−	1.61476i	0.396244	−	0.918145i	$-0.370313\pi$
$620$		0			0
$621$	−28.3573	−	8.10463i	−1.13794	−	0.325228i
$622$		0			0
$623$	1.28789	−	1.92746i	0.0515981	−	0.0772220i
$624$		0			0
$625$	−19.6468	−	19.6468i	−0.785872	−	0.785872i
$626$		0			0
$627$	−0.348066	+	0.491287i	−0.0139004	+	0.0196201i
$628$		0			0
$629$	−44.5171	−	3.99801i	−1.77501	−	0.159411i
$630$		0			0
$631$	−2.60197	−	6.28172i	−0.103583	−	0.250071i	0.863588	−	0.504198i	$-0.168212\pi$
$631$	−2.60197	−	6.28172i	−0.103583	−	0.250071i	−0.967171	+	0.254127i	$0.918212\pi$
$632$		0			0
$633$	20.1475	+	4.58357i	0.800790	+	0.182181i
$634$		0			0
$635$	−32.4823	−	21.7040i	−1.28902	−	0.861296i
$636$		0			0
$637$	2.50911	+	1.03931i	0.0994145	+	0.0411788i
$638$		0			0
$639$	−3.48562	−	0.893882i	−0.137889	−	0.0353614i
$640$		0			0
$641$	3.06190	−	15.3932i	0.120938	−	0.607995i	−0.872014	−	0.489480i	$-0.837187\pi$
$641$	3.06190	−	15.3932i	0.120938	−	0.607995i	0.992952	−	0.118515i	$-0.0378134\pi$
$642$		0			0
$643$	−32.5931	+	21.7780i	−1.28535	+	0.858842i	−0.995173	−	0.0981314i	$-0.968713\pi$
$643$	−32.5931	+	21.7780i	−1.28535	+	0.858842i	−0.290175	+	0.956974i	$0.593713\pi$
$644$		0			0
$645$	−8.33836	−	13.2497i	−0.328323	−	0.521705i
$646$		0			0
$647$			26.5289i			1.04296i	0.853264	+	0.521479i	$0.174619\pi$
$647$			26.5289i			1.04296i	−0.853264	+	0.521479i	$0.825381\pi$
$648$		0			0
$649$	0.152533	+	0.228282i	0.00598746	+	0.00896087i
$650$		0			0
$651$	24.3572	−	9.31733i	0.954634	−	0.365175i
$652$		0			0
$653$	−31.6152	+	6.28866i	−1.23720	+	0.246094i	−0.769992	−	0.638054i	$-0.779740\pi$
$653$	−31.6152	+	6.28866i	−1.23720	+	0.246094i	−0.467207	+	0.884148i	$0.654740\pi$
$654$		0			0
$655$	−12.0530	+	29.0985i	−0.470950	+	1.13697i
$656$		0			0
$657$	2.61801	−	1.54931i	0.102138	−	0.0604443i
$658$		0			0
$659$	31.2044	−	31.2044i	1.21555	−	1.21555i	0.246379	−	0.969174i	$-0.420759\pi$
$659$	31.2044	−	31.2044i	1.21555	−	1.21555i	0.969174	−	0.246379i	$-0.0792407\pi$
$660$		0			0
$661$	1.00677	−	0.417016i	0.0391587	−	0.0162201i	−0.363018	−	0.931782i	$-0.618254\pi$
$661$	1.00677	−	0.417016i	0.0391587	−	0.0162201i	0.402177	+	0.915562i	$0.368254\pi$
$662$		0			0
$663$	4.52968	−	13.9836i	0.175918	−	0.543079i
$664$		0			0
$665$	7.52539	−	3.11712i	0.291822	−	0.120877i
$666$		0			0
$667$	−33.3880	+	33.3880i	−1.29279	+	1.29279i
$668$		0			0
$669$	9.43953	+	0.258182i	0.364953	+	0.00998188i
$670$		0			0
$671$	−0.398142	+	0.961201i	−0.0153701	+	0.0371067i
$672$		0			0
$673$	30.1550	−	5.99820i	1.16239	−	0.231214i	0.424048	−	0.905640i	$-0.360609\pi$
$673$	30.1550	−	5.99820i	1.16239	−	0.231214i	0.738342	+	0.674426i	$0.235609\pi$
$674$		0			0
$675$	−22.5869	−	1.85703i	−0.869369	−	0.0714772i
$676$		0			0
$677$	−6.61301	−	9.89706i	−0.254158	−	0.380375i	0.682347	−	0.731029i	$-0.260959\pi$
$677$	−6.61301	−	9.89706i	−0.254158	−	0.380375i	−0.936505	+	0.350654i	$0.885959\pi$
$678$		0			0
$679$		−	14.8744i		−	0.570829i
$680$		0			0
$681$	−35.4441	+	22.3059i	−1.35822	+	0.854764i
$682$		0			0
$683$	−31.5197	+	21.0608i	−1.20607	+	0.805869i	−0.985529	−	0.169509i	$-0.945782\pi$
$683$	−31.5197	+	21.0608i	−1.20607	+	0.805869i	−0.220540	+	0.975378i	$0.570782\pi$
$684$		0			0
$685$	−11.3586	+	57.1035i	−0.433989	+	2.18181i
$686$		0			0
$687$	−8.64333	+	8.18311i	−0.329764	+	0.312205i
$688$		0			0
$689$	10.9412	+	4.53198i	0.416826	+	0.172655i
$690$		0			0
$691$	11.3597	+	7.59031i	0.432143	+	0.288749i	0.752555	−	0.658529i	$-0.228821\pi$
$691$	11.3597	+	7.59031i	0.432143	+	0.288749i	−0.320412	+	0.947278i	$0.603821\pi$
$692$		0			0
$693$	−0.737902	−	2.09929i	−0.0280306	−	0.0797456i
$694$		0			0
$695$	−2.18699	−	5.27985i	−0.0829571	−	0.200276i
$696$		0			0
$697$	−10.5720	+	20.1949i	−0.400442	+	0.764938i
$698$		0			0
$699$	13.9063	+	9.85228i	0.525983	+	0.372647i
$700$		0			0
$701$	−19.2749	−	19.2749i	−0.728005	−	0.728005i	0.242217	−	0.970222i	$-0.422125\pi$
$701$	−19.2749	−	19.2749i	−0.728005	−	0.728005i	−0.970222	+	0.242217i	$0.922125\pi$
$702$		0			0
$703$	−6.72717	+	10.0679i	−0.253720	+	0.379719i
$704$		0			0
$705$	5.68168	+	33.2976i	0.213984	+	1.25406i
$706$		0			0
$707$	−1.81322	−	9.11568i	−0.0681932	−	0.342831i
$708$		0			0
$709$	29.7252	+	5.91272i	1.11635	+	0.222057i	0.718592	−	0.695432i	$-0.244787\pi$
$709$	29.7252	+	5.91272i	1.11635	+	0.222057i	0.397762	+	0.917488i	$0.369787\pi$
$710$		0			0
$711$	5.65232	+	39.6331i	0.211978	+	1.48636i
$712$		0			0
$713$	35.8559			1.34281
$714$		0			0
$715$	1.95988			0.0732953
$716$		0			0
$717$	24.3451	+	10.8731i	0.909186	+	0.406065i
$718$		0			0
$719$	0.877852	+	0.174616i	0.0327384	+	0.00651206i	0.211432	−	0.977393i	$-0.432187\pi$
$719$	0.877852	+	0.174616i	0.0327384	+	0.00651206i	−0.178694	+	0.983905i	$0.557187\pi$
$720$		0			0
$721$	3.88098	+	19.5110i	0.144535	+	0.726628i
$722$		0			0
$723$	25.5552	−	4.36056i	0.950408	−	0.162171i
$724$		0			0
$725$	−20.1580	+	30.1686i	−0.748651	+	1.12043i
$726$		0			0
$727$	30.4698	+	30.4698i	1.13006	+	1.13006i	0.990166	+	0.139898i	$0.0446774\pi$
$727$	30.4698	+	30.4698i	1.13006	+	1.13006i	0.139898	+	0.990166i	$0.455323\pi$
$728$		0			0
$729$	21.9538	−	15.7172i	0.813104	−	0.582119i
$730$		0			0
$731$	−5.83384	−	10.6920i	−0.215772	−	0.395457i
$732$		0			0
$733$	2.03359	+	4.90952i	0.0751123	+	0.181337i	0.956976	−	0.290168i	$-0.0937110\pi$
$733$	2.03359	+	4.90952i	0.0751123	+	0.181337i	−0.881864	+	0.471505i	$0.843711\pi$
$734$		0			0
$735$	1.55118	−	6.81833i	0.0572161	−	0.251498i
$736$		0			0
$737$	−0.644391	−	0.430569i	−0.0237365	−	0.0158602i
$738$		0			0
$739$	24.1993	+	10.0237i	0.890186	+	0.368727i	0.780438	−	0.625233i	$-0.214996\pi$
$739$	24.1993	+	10.0237i	0.890186	+	0.368727i	0.109747	+	0.993960i	$0.464996\pi$
$740$		0			0
$741$	−2.73771	−	2.89168i	−0.100572	−	0.106229i
$742$		0			0
$743$	1.23104	−	6.18886i	0.0451625	−	0.227047i	−0.951612	−	0.307303i	$-0.900574\pi$
$743$	1.23104	−	6.18886i	0.0451625	−	0.227047i	0.996774	+	0.0802553i	$0.0255736\pi$
$744$		0			0
$745$	−21.1221	+	14.1133i	−0.773853	+	0.517072i
$746$		0			0
$747$	−5.30153	+	11.0486i	−0.193973	+	0.404247i
$748$		0			0
$749$		−	12.5055i		−	0.456940i
$750$		0			0
$751$	−15.1572	−	22.6843i	−0.553093	−	0.827762i	0.444594	−	0.895732i	$-0.353348\pi$
$751$	−15.1572	−	22.6843i	−0.553093	−	0.827762i	−0.997687	+	0.0679697i	$0.978348\pi$
$752$		0			0
$753$	−16.4987	−	43.1307i	−0.601248	−	1.57177i
$754$		0			0
$755$	−48.5087	+	9.64897i	−1.76541	+	0.351162i
$756$		0			0
$757$	−5.39949	+	13.0355i	−0.196248	+	0.473784i	−0.991116	−	0.132997i	$-0.957540\pi$
$757$	−5.39949	+	13.0355i	−0.196248	+	0.473784i	0.794868	+	0.606782i	$0.207540\pi$
$758$		0			0
$759$	0.0836491	−	3.05834i	0.00303627	−	0.111011i
$760$		0			0
$761$	31.4843	−	31.4843i	1.14131	−	1.14131i	0.153094	−	0.988212i	$-0.451076\pi$
$761$	31.4843	−	31.4843i	1.14131	−	1.14131i	0.988212	−	0.153094i	$-0.0489239\pi$
$762$		0			0
$763$	5.37832	−	2.22777i	0.194708	−	0.0806508i
$764$		0			0
$765$	−37.4528	−	5.44061i	−1.35411	−	0.196706i
$766$		0			0
$767$	−1.67760	+	0.694885i	−0.0605746	+	0.0250908i
$768$		0			0
$769$	−16.1543	+	16.1543i	−0.582537	+	0.582537i	−0.935600	−	0.353062i	$-0.885140\pi$
$769$	−16.1543	+	16.1543i	−0.582537	+	0.582537i	0.353062	+	0.935600i	$0.385140\pi$
$770$		0			0
$771$	0.112158	−	4.10067i	0.00403927	−	0.147682i
$772$		0			0
$773$	−3.98178	+	9.61286i	−0.143215	+	0.345751i	−0.979169	−	0.203049i	$-0.934915\pi$
$773$	−3.98178	+	9.61286i	−0.143215	+	0.345751i	0.835954	+	0.548799i	$0.184915\pi$
$774$		0			0
$775$	27.0233	−	5.37527i	0.970705	−	0.193085i
$776$		0			0
$777$	−15.9886	−	41.7972i	−0.573588	−	1.49946i
$778$		0			0
$779$	3.43081	+	5.13457i	0.122922	+	0.183965i
$780$		0			0
$781$		−	0.373289i		−	0.0133573i
$782$		0			0
$783$	−4.93080	−	42.9448i	−0.176212	−	1.53472i
$784$		0			0
$785$	11.9867	−	8.00924i	0.427823	−	0.285862i
$786$		0			0
$787$	−7.55680	+	37.9906i	−0.269371	+	1.35422i	0.574865	+	0.818248i	$0.305054\pi$
$787$	−7.55680	+	37.9906i	−0.269371	+	1.35422i	−0.844236	+	0.535971i	$0.819946\pi$
$788$		0			0
$789$	37.7195	+	39.8409i	1.34285	+	1.41837i
$790$		0			0
$791$	−17.0280	−	7.05323i	−0.605446	−	0.250784i
$792$		0			0
$793$	−5.72127	−	3.82283i	−0.203168	−	0.135753i
$794$		0			0
$795$	6.76404	−	29.7319i	0.239896	−	1.05448i
$796$		0			0
$797$	−10.9971	−	26.5493i	−0.389537	−	0.940426i	−0.990038	−	0.140802i	$-0.955032\pi$
$797$	−10.9971	−	26.5493i	−0.389537	−	0.940426i	0.600501	−	0.799624i	$-0.294968\pi$
$798$		0			0
$799$	2.80096	+	26.1310i	0.0990908	+	0.924448i
$800$		0			0
$801$	−0.159495	+	2.91351i	−0.00563547	+	0.102944i
$802$		0			0
$803$	0.223147	+	0.223147i	0.00787469	+	0.00787469i
$804$		0			0
$805$	−22.9953	+	34.4149i	−0.810478	+	1.21297i
$806$		0			0
$807$	32.8406	−	5.60368i	1.15604	−	0.197259i
$808$		0			0
$809$	−8.48221	−	42.6430i	−0.298219	−	1.49925i	−0.781569	−	0.623819i	$-0.785580\pi$
$809$	−8.48221	−	42.6430i	−0.298219	−	1.49925i	0.483350	−	0.875427i	$-0.339420\pi$
$810$		0			0
$811$	33.1881	+	6.60153i	1.16539	+	0.231811i	0.739624	−	0.673020i	$-0.235003\pi$
$811$	33.1881	+	6.60153i	1.16539	+	0.231811i	0.425770	+	0.904832i	$0.360003\pi$
$812$		0			0
$813$	−22.4426	−	10.0234i	−0.787098	−	0.351537i
$814$		0			0
$815$	10.1000			0.353786
$816$		0			0
$817$	−3.29966			−0.115440
$818$		0			0
$819$	14.5695	−	2.07785i	0.509100	−	0.0726059i
$820$		0			0
$821$	22.3951	+	4.45467i	0.781595	+	0.155469i	0.569732	−	0.821830i	$-0.307047\pi$
$821$	22.3951	+	4.45467i	0.781595	+	0.155469i	0.211863	+	0.977299i	$0.432047\pi$
$822$		0			0
$823$	1.56241	+	7.85479i	0.0544624	+	0.273801i	0.998415	−	0.0562801i	$-0.0179240\pi$
$823$	1.56241	+	7.85479i	0.0544624	+	0.273801i	−0.943953	+	0.330081i	$0.892924\pi$
$824$		0			0
$825$	−0.395442	−	2.31750i	−0.0137675	−	0.0806851i
$826$		0			0
$827$	−7.25454	+	10.8572i	−0.252265	+	0.377541i	−0.935890	−	0.352292i	$-0.885402\pi$
$827$	−7.25454	+	10.8572i	−0.252265	+	0.377541i	0.683625	+	0.729833i	$0.260402\pi$
$828$		0			0
$829$	24.5541	+	24.5541i	0.852800	+	0.852800i	0.990477	−	0.137678i	$-0.0439638\pi$
$829$	24.5541	+	24.5541i	0.852800	+	0.852800i	−0.137678	+	0.990477i	$0.543964\pi$
$830$		0			0
$831$	22.0334	+	15.6101i	0.764329	+	0.541510i
$832$		0			0
$833$	1.53439	−	5.21949i	0.0531633	−	0.180845i
$834$		0			0
$835$	7.78231	+	18.7881i	0.269318	+	0.650191i
$836$		0			0
$837$	−20.4119	+	25.7072i	−0.705538	+	0.888569i
$838$		0			0
$839$	26.1126	+	17.4479i	0.901507	+	0.602368i	0.917601	−	0.397503i	$-0.130123\pi$
$839$	26.1126	+	17.4479i	0.901507	+	0.602368i	−0.0160941	+	0.999870i	$0.505123\pi$
$840$		0			0
$841$	−37.1456	−	15.3862i	−1.28088	−	0.530560i
$842$		0			0
$843$	3.91239	−	3.70407i	0.134750	−	0.127575i
$844$		0			0
$845$	5.23104	−	26.2982i	0.179953	−	0.904686i
$846$		0			0
$847$	−21.6069	+	14.4373i	−0.742422	+	0.496070i
$848$		0			0
$849$	11.8266	−	7.44278i	0.405887	−	0.255436i
$850$		0			0
$851$		−	61.5290i		−	2.10919i
$852$		0			0
$853$	14.9568	+	22.3845i	0.512112	+	0.766430i	0.993950	−	0.109830i	$-0.0350307\pi$
$853$	14.9568	+	22.3845i	0.512112	+	0.766430i	−0.481838	+	0.876260i	$0.660031\pi$
$854$		0			0
$855$	−6.15359	+	8.20076i	−0.210448	+	0.280460i
$856$		0			0
$857$	−17.9881	+	3.57805i	−0.614462	+	0.122224i	−0.492502	−	0.870311i	$-0.663918\pi$
$857$	−17.9881	+	3.57805i	−0.614462	+	0.122224i	−0.121959	+	0.992535i	$0.538918\pi$
$858$		0			0
$859$	−3.04555	+	7.35261i	−0.103913	+	0.250868i	−0.967281	−	0.253706i	$-0.918350\pi$
$859$	−3.04555	+	7.35261i	−0.103913	+	0.250868i	0.863368	+	0.504574i	$0.168350\pi$
$860$		0			0
$861$	−22.8141	−	0.623991i	−0.777503	−	0.0212656i
$862$		0			0
$863$	−1.39363	+	1.39363i	−0.0474397	+	0.0474397i	−0.730429	−	0.682989i	$-0.760680\pi$
$863$	−1.39363	+	1.39363i	−0.0474397	+	0.0474397i	0.682989	+	0.730429i	$0.260680\pi$
$864$		0			0
$865$	42.8160	−	17.7350i	1.45579	−	0.603007i
$866$		0			0
$867$	−28.8194	−	6.03668i	−0.978759	−	0.205016i
$868$		0			0
$869$	−3.83688	+	1.58929i	−0.130157	+	0.0539130i
$870$		0			0
$871$	3.62439	−	3.62439i	0.122808	−	0.122808i
$872$		0			0
$873$	9.53528	+	16.1126i	0.322720	+	0.545330i
$874$		0			0
$875$	1.78181	−	4.30166i	0.0602360	−	0.145423i
$876$		0			0
$877$	−2.25554	+	0.448655i	−0.0761643	+	0.0151500i	−0.233025	−	0.972471i	$-0.574863\pi$
$877$	−2.25554	+	0.448655i	−0.0761643	+	0.0151500i	0.156861	+	0.987621i	$0.449863\pi$
$878$		0			0
$879$	−20.2819	+	7.75843i	−0.684093	+	0.261685i
$880$		0			0
$881$	12.3943	+	18.5493i	0.417573	+	0.624942i	0.979308	−	0.202375i	$-0.0648659\pi$
$881$	12.3943	+	18.5493i	0.417573	+	0.624942i	−0.561735	+	0.827317i	$0.689866\pi$
$882$		0			0
$883$		−	36.1867i		−	1.21778i	−0.793255	−	0.608890i	$-0.791615\pi$
$883$		−	36.1867i		−	1.21778i	0.793255	−	0.608890i	$-0.208385\pi$
$884$		0			0
$885$	2.49018	+	3.95689i	0.0837063	+	0.133009i
$886$		0			0
$887$	3.25224	−	2.17308i	0.109200	−	0.0729648i	−0.499771	−	0.866157i	$-0.666583\pi$
$887$	3.25224	−	2.17308i	0.109200	−	0.0729648i	0.608971	+	0.793193i	$0.291583\pi$
$888$		0			0
$889$	5.93686	−	29.8466i	0.199116	−	1.00102i
$890$		0			0
$891$	2.14508	+	1.80101i	0.0718630	+	0.0603362i
$892$		0			0
$893$	6.57770	+	2.72457i	0.220114	+	0.0911743i
$894$		0			0
$895$	−48.6327	−	32.4954i	−1.62561	−	1.08620i
$896$		0			0
$897$	19.7305	+	4.48871i	0.658782	+	0.149874i
$898$		0			0
$899$	20.1113	+	48.5529i	0.670748	+	1.61933i
$900$		0			0
$901$	6.69081	−	22.7600i	0.222903	−	0.758246i
$902$		0			0
$903$	7.04979	−	9.95062i	0.234602	−	0.331136i
$904$		0			0
$905$	−16.3217	−	16.3217i	−0.542552	−	0.542552i
$906$		0			0
$907$	16.6035	−	24.8490i	0.551311	−	0.825096i	−0.446249	−	0.894909i	$-0.647240\pi$
$907$	16.6035	−	24.8490i	0.551311	−	0.825096i	0.997560	+	0.0698131i	$0.0222403\pi$
$908$		0			0
$909$	7.80778	+	8.71213i	0.258968	+	0.288963i
$910$		0			0
$911$	−3.57313	−	17.9633i	−0.118383	−	0.595151i	−0.993744	−	0.111682i	$-0.964376\pi$
$911$	−3.57313	−	17.9633i	−0.118383	−	0.595151i	0.875361	−	0.483470i	$-0.160624\pi$
$912$		0			0
$913$	−1.24684	−	0.248012i	−0.0412643	−	0.00820799i
$914$		0			0
$915$	−7.22479	+	16.1764i	−0.238844	+	0.534776i
$916$		0			0
$917$	−24.5345			−0.810200
$918$		0			0
$919$	−18.9782			−0.626034			−0.313017	−	0.949747i	$-0.601340\pi$
$919$	−18.9782			−0.626034			−0.313017	+	0.949747i	$0.601340\pi$
$920$		0			0
$921$	−12.7284	+	28.4992i	−0.419417	+	0.939081i
$922$		0			0
$923$	2.42140	+	0.481646i	0.0797012	+	0.0158536i
$924$		0			0
$925$	−9.22400	−	46.3722i	−0.303283	−	1.52471i
$926$		0			0
$927$	−16.7116	−	18.6473i	−0.548881	−	0.612456i
$928$		0			0
$929$	−16.9777	+	25.4089i	−0.557019	+	0.833638i	−0.997956	−	0.0639000i	$-0.979646\pi$
$929$	−16.9777	+	25.4089i	−0.557019	+	0.833638i	0.440937	+	0.897538i	$0.354646\pi$
$930$		0			0
$931$	−1.04216	−	1.04216i	−0.0341554	−	0.0341554i
$932$		0			0
$933$	−10.7379	+	15.1564i	−0.351545	+	0.496197i
$934$		0			0
$935$	−0.418429	−	3.90366i	−0.0136841	−	0.127663i
$936$		0			0
$937$	14.2347	+	34.3655i	0.465026	+	1.12267i	0.966308	+	0.257388i	$0.0828618\pi$
$937$	14.2347	+	34.3655i	0.465026	+	1.12267i	−0.501282	+	0.865284i	$0.667138\pi$
$938$		0			0
$939$	−34.5735	−	7.86552i	−1.12826	−	0.256682i
$940$		0			0
$941$	37.1328	+	24.8113i	1.21049	+	0.808826i	0.986178	−	0.165690i	$-0.0529851\pi$
$941$	37.1328	+	24.8113i	1.21049	+	0.808826i	0.224316	+	0.974516i	$0.427985\pi$
$942$		0			0
$943$	−28.9908	−	12.0084i	−0.944069	−	0.391046i
$944$		0			0
$945$	−11.5834	−	36.0782i	−0.376807	−	1.17362i
$946$		0			0
$947$	−6.99454	+	35.1639i	−0.227292	+	1.14267i	0.683545	+	0.729908i	$0.260437\pi$
$947$	−6.99454	+	35.1639i	−0.227292	+	1.14267i	−0.910837	+	0.412766i	$0.864563\pi$
$948$		0			0
$949$	−1.73540	+	1.15956i	−0.0563334	+	0.0376408i
$950$		0			0
$951$	−7.81186	−	12.4130i	−0.253317	−	0.402521i
$952$		0			0
$953$			38.2262i			1.23827i	0.785286	+	0.619134i	$0.212516\pi$
$953$			38.2262i			1.23827i	−0.785286	+	0.619134i	$0.787484\pi$
$954$		0			0
$955$	27.2094	+	40.7218i	0.880477	+	1.31773i
$956$		0			0
$957$	4.18826	−	1.60213i	0.135387	−	0.0517894i
$958$		0			0
$959$	−44.4819	+	8.84801i	−1.43640	+	0.285717i
$960$		0			0
$961$	3.40876	−	8.22947i	0.109960	−	0.265467i
$962$		0			0
$963$	8.01664	+	13.5465i	0.258333	+	0.436528i
$964$		0			0
$965$	−23.4673	+	23.4673i	−0.755439	+	0.755439i
$966$		0			0
$967$	−17.2448	+	7.14301i	−0.554554	+	0.229704i	−0.642319	−	0.766437i	$-0.722028\pi$
$967$	−17.2448	+	7.14301i	−0.554554	+	0.229704i	0.0877650	+	0.996141i	$0.472028\pi$
$968$		0			0
$969$	−5.17511	+	6.07030i	−0.166248	+	0.195006i
$970$		0			0
$971$	12.3249	−	5.10513i	0.395524	−	0.163831i	−0.176051	−	0.984381i	$-0.556333\pi$
$971$	12.3249	−	5.10513i	0.395524	−	0.163831i	0.571575	+	0.820550i	$0.306333\pi$
$972$		0			0
$973$	3.14784	−	3.14784i	0.100915	−	0.100915i
$974$		0			0
$975$	15.5431	+	0.425120i	0.497777	+	0.0136147i
$976$		0			0
$977$	−1.38266	+	3.33804i	−0.0442352	+	0.106793i	−0.944453	−	0.328647i	$-0.893407\pi$
$977$	−1.38266	+	3.33804i	−0.0442352	+	0.106793i	0.900218	+	0.435440i	$0.143407\pi$
$978$		0			0
$979$	−0.296875	+	0.0590521i	−0.00948816	+	0.00188731i
$980$		0			0
$981$	−4.39791	+	5.86100i	−0.140414	+	0.187127i
$982$		0			0
$983$	25.6445	+	38.3798i	0.817934	+	1.22412i	0.971747	+	0.236024i	$0.0758445\pi$
$983$	25.6445	+	38.3798i	0.817934	+	1.22412i	−0.153813	+	0.988100i	$0.549155\pi$
$984$		0			0
$985$		−	17.1988i		−	0.547999i
$986$		0			0
$987$	−22.2698	+	14.0150i	−0.708855	+	0.446101i
$988$		0			0
$989$	13.9412	−	9.31524i	0.443306	−	0.296208i
$990$		0			0
$991$	1.66369	−	8.36392i	0.0528488	−	0.265689i	−0.945323	−	0.326137i	$-0.894253\pi$
$991$	1.66369	−	8.36392i	0.0528488	−	0.265689i	0.998171	+	0.0604481i	$0.0192530\pi$
$992$		0			0
$993$	−18.9067	+	17.9000i	−0.599986	+	0.568040i
$994$		0			0
$995$	23.8763	+	9.88990i	0.756930	+	0.313531i
$996$		0			0
$997$	−11.0513	−	7.38423i	−0.349998	−	0.233861i	0.368127	−	0.929776i	$-0.379999\pi$
$997$	−11.0513	−	7.38423i	−0.349998	−	0.233861i	−0.718125	+	0.695915i	$0.754999\pi$
$998$		0			0
$999$	44.1137	+	35.0270i	1.39569	+	1.10820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.cj.c.209.3		32
3.2	odd	2	inner	816.2.cj.c.209.1		32
4.3	odd	2		51.2.i.a.5.2	✓	32
12.11	even	2		51.2.i.a.5.3	yes	32
17.7	odd	16	inner	816.2.cj.c.449.1		32
51.41	even	16	inner	816.2.cj.c.449.3		32
68.3	even	16		867.2.i.f.827.2		32
68.7	even	16		51.2.i.a.41.3	yes	32
68.11	even	16		867.2.i.c.503.2		32
68.15	odd	8		867.2.i.b.224.2		32
68.19	odd	8		867.2.i.i.224.2		32
68.23	even	16		867.2.i.d.503.2		32
68.27	even	16		867.2.i.h.653.3		32
68.31	even	16		867.2.i.g.827.2		32
68.39	even	16		867.2.i.b.329.3		32
68.43	odd	8		867.2.i.g.65.3		32
68.47	odd	4		867.2.i.c.131.3		32
68.55	odd	4		867.2.i.d.131.3		32
68.59	odd	8		867.2.i.f.65.3		32
68.63	even	16		867.2.i.i.329.3		32
68.67	odd	2		867.2.i.h.158.2		32
204.11	odd	16		867.2.i.c.503.3		32
204.23	odd	16		867.2.i.d.503.3		32
204.47	even	4		867.2.i.c.131.2		32
204.59	even	8		867.2.i.f.65.2		32
204.71	odd	16		867.2.i.f.827.3		32
204.83	even	8		867.2.i.b.224.3		32
204.95	odd	16		867.2.i.h.653.2		32
204.107	odd	16		867.2.i.b.329.2		32
204.131	odd	16		867.2.i.i.329.2		32
204.143	odd	16		51.2.i.a.41.2	yes	32
204.155	even	8		867.2.i.i.224.3		32
204.167	odd	16		867.2.i.g.827.3		32
204.179	even	8		867.2.i.g.65.2		32
204.191	even	4		867.2.i.d.131.2		32
204.203	even	2		867.2.i.h.158.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.5.2	✓	32	4.3	odd	2
51.2.i.a.5.3	yes	32	12.11	even	2
51.2.i.a.41.2	yes	32	204.143	odd	16
51.2.i.a.41.3	yes	32	68.7	even	16
816.2.cj.c.209.1		32	3.2	odd	2	inner
816.2.cj.c.209.3		32	1.1	even	1	trivial
816.2.cj.c.449.1		32	17.7	odd	16	inner
816.2.cj.c.449.3		32	51.41	even	16	inner
867.2.i.b.224.2		32	68.15	odd	8
867.2.i.b.224.3		32	204.83	even	8
867.2.i.b.329.2		32	204.107	odd	16
867.2.i.b.329.3		32	68.39	even	16
867.2.i.c.131.2		32	204.47	even	4
867.2.i.c.131.3		32	68.47	odd	4
867.2.i.c.503.2		32	68.11	even	16
867.2.i.c.503.3		32	204.11	odd	16
867.2.i.d.131.2		32	204.191	even	4
867.2.i.d.131.3		32	68.55	odd	4
867.2.i.d.503.2		32	68.23	even	16
867.2.i.d.503.3		32	204.23	odd	16
867.2.i.f.65.2		32	204.59	even	8
867.2.i.f.65.3		32	68.59	odd	8
867.2.i.f.827.2		32	68.3	even	16
867.2.i.f.827.3		32	204.71	odd	16
867.2.i.g.65.2		32	204.179	even	8
867.2.i.g.65.3		32	68.43	odd	8
867.2.i.g.827.2		32	68.31	even	16
867.2.i.g.827.3		32	204.167	odd	16
867.2.i.h.158.2		32	68.67	odd	2
867.2.i.h.158.3		32	204.203	even	2
867.2.i.h.653.2		32	204.95	odd	16
867.2.i.h.653.3		32	68.27	even	16
867.2.i.i.224.2		32	68.19	odd	8
867.2.i.i.224.3		32	204.155	even	8
867.2.i.i.329.2		32	204.131	odd	16
867.2.i.i.329.3		32	68.63	even	16

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.cj (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.706330 - 1.58149i) q^{3} +(3.00087 + 0.596910i) q^{5} +(0.464975 + 2.33759i) q^{7} +(-2.00219 - 2.23410i) q^{9} +(0.172899 - 0.258762i) q^{11} +(1.45541 + 1.45541i) q^{13} +(3.06361 - 4.32421i) q^{15} +(2.58814 - 3.20960i) q^{17} +(-0.427451 - 1.03196i) q^{19} +(4.02529 + 0.915758i) q^{21} +(4.71932 + 3.15335i) q^{23} +(4.02951 + 1.66908i) q^{25} +(-4.94741 + 1.58843i) q^{27} +(-1.62296 + 8.15918i) q^{29} +(5.25259 - 3.50967i) q^{31} +(-0.287105 - 0.456210i) q^{33} +7.29234i q^{35} +(-6.02262 - 9.01349i) q^{37} +(3.32972 - 1.27371i) q^{39} +(-5.42232 + 1.07857i) q^{41} +(1.13048 - 2.72921i) q^{43} +(-4.67476 - 7.89938i) q^{45} +(-4.50710 + 4.50710i) q^{47} +(1.21904 - 0.504943i) q^{49} +(-3.24785 - 6.36015i) q^{51} +(5.31572 - 2.20184i) q^{53} +(0.673306 - 0.673306i) q^{55} +(-1.93395 - 0.0528956i) q^{57} +(-0.337607 + 0.815054i) q^{59} +(-3.27882 + 0.652199i) q^{61} +(4.29144 - 5.71911i) q^{63} +(3.49876 + 5.23626i) q^{65} -2.49028i q^{67} +(8.32038 - 5.23624i) q^{69} +(0.997325 - 0.666391i) q^{71} +(-0.197828 + 0.994547i) q^{73} +(5.48579 - 5.19369i) q^{75} +(0.685274 + 0.283850i) q^{77} +(-11.0957 - 7.41392i) q^{79} +(-0.982433 + 8.94622i) q^{81} +(-1.56322 - 3.77396i) q^{83} +(9.68252 - 8.08669i) q^{85} +(11.7573 + 8.32976i) q^{87} +(-0.687749 - 0.687749i) q^{89} +(-2.72543 + 4.07889i) q^{91} +(-1.84043 - 10.7859i) q^{93} +(-0.666738 - 3.35192i) q^{95} +(-6.12098 - 1.21754i) q^{97} +(-0.924280 + 0.131817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 16 q^{7} - 8 q^{9} - 16 q^{13} - 16 q^{15} + 16 q^{19} + 16 q^{21} + 16 q^{25} + 8 q^{27} - 16 q^{31} + 16 q^{37} + 24 q^{39} - 16 q^{43} - 40 q^{45} - 48 q^{49} + 40 q^{51} + 48 q^{55}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 + 16 * q^7 - 8 * q^9 - 16 * q^13 - 16 * q^15 + 16 * q^19 + 16 * q^21 + 16 * q^25 + 8 * q^27 - 16 * q^31 + 16 * q^37 + 24 * q^39 - 16 * q^43 - 40 * q^45 - 48 * q^49 + 40 * q^51 + 48 * q^55 + 8 * q^57 - 32 * q^61 - 64 * q^63 + 80 * q^69 + 48 * q^73 - 88 * q^75 - 16 * q^79 + 48 * q^81 + 56 * q^87 - 16 * q^91 - 72 * q^93 - 16 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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