LMFDB - Embedded newform 504.2.bk.b.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.1
Character	$\chi$	$=$	504.451
Dual form			504.2.bk.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40711 + 0.141583i) q^{2} +(1.95991 - 0.398446i) q^{4} +(-1.91923 - 3.32420i) q^{5} +(1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +O(q^{10})$	\(q+(-1.40711 + 0.141583i) q^{2} +(1.95991 - 0.398446i) q^{4} +(-1.91923 - 3.32420i) q^{5} +(1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +(3.17121 + 4.40578i) q^{10} +(1.28125 - 2.21918i) q^{11} -5.99175 q^{13} +(-1.88836 + 3.23018i) q^{14} +(3.68248 - 1.56183i) q^{16} +(3.53425 + 2.04050i) q^{17} +(-2.05318 + 1.18541i) q^{19} +(-5.08602 - 5.75041i) q^{20} +(-1.48865 + 3.30403i) q^{22} +(-6.53773 + 3.77456i) q^{23} +(-4.86686 + 8.42964i) q^{25} +(8.43104 - 0.848331i) q^{26} +(2.19979 - 4.81258i) q^{28} +2.70568i q^{29} +(2.90258 - 5.02742i) q^{31} +(-4.96052 + 2.71905i) q^{32} +(-5.26197 - 2.37081i) q^{34} +(-10.0989 - 1.07147i) q^{35} +(3.61144 - 2.08507i) q^{37} +(2.72122 - 1.95869i) q^{38} +(7.97074 + 7.37136i) q^{40} -5.96293i q^{41} -8.06098 q^{43} +(1.62690 - 4.85990i) q^{44} +(8.66488 - 6.23685i) q^{46} +(0.204145 + 0.353590i) q^{47} +(-2.15004 - 6.66163i) q^{49} +(5.65470 - 12.5505i) q^{50} +(-11.7433 + 2.38739i) q^{52} +(4.41436 + 2.54863i) q^{53} -9.83600 q^{55} +(-2.41396 + 7.08327i) q^{56} +(-0.383078 - 3.80718i) q^{58} +(-9.05639 - 5.22871i) q^{59} +(-1.34535 - 2.33021i) q^{61} +(-3.37245 + 7.48508i) q^{62} +(6.59502 - 4.52832i) q^{64} +(11.4995 + 19.9178i) q^{65} +(2.38045 - 4.12307i) q^{67} +(7.73983 + 2.59098i) q^{68} +(14.3620 + 0.0778363i) q^{70} -1.21482i q^{71} +(-6.65046 - 3.83964i) q^{73} +(-4.78648 + 3.44523i) q^{74} +(-3.55173 + 3.14137i) q^{76} +(-2.75147 - 6.19628i) q^{77} +(-8.89433 + 5.13514i) q^{79} +(-12.2594 - 9.24378i) q^{80} +(0.844250 + 8.39049i) q^{82} -4.49449i q^{83} -15.6647i q^{85} +(11.3427 - 1.14130i) q^{86} +(-1.60115 + 7.06875i) q^{88} +(3.35682 - 1.93806i) q^{89} +(-9.33056 + 12.8159i) q^{91} +(-11.3094 + 10.0027i) q^{92} +(-0.337316 - 0.468635i) q^{94} +(7.88105 + 4.55013i) q^{95} +1.20561i q^{97} +(3.96851 + 9.06923i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4}+O(q^{10}) $ 32 * q + 2 * q^4	$ 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) $ 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.40711	+	0.141583i	−0.994976	+	0.100114i
$2$	−1.40711	+	0.141583i	−0.994976	+	0.100114i
$3$		0			0
$3$		0			0
$4$	1.95991	−	0.398446i	0.979954	−	0.199223i
$5$	−1.91923	−	3.32420i	−0.858304	−	1.48663i	−0.873546	−	0.486742i	$-0.838185\pi$
$5$	−1.91923	−	3.32420i	−0.858304	−	1.48663i	0.0152419	−	0.999884i	$-0.495148\pi$
$6$		0			0
$7$	1.55724	−	2.13893i	0.588580	−	0.808439i
$7$	1.55724	−	2.13893i	0.588580	−	0.808439i
$8$	−2.70139	+	0.838146i	−0.955086	+	0.296330i
$9$		0			0
$10$	3.17121	+	4.40578i	1.00282	+	1.39323i
$11$	1.28125	−	2.21918i	0.386310	−	0.669109i	−0.605640	−	0.795739i	$-0.707083\pi$
$11$	1.28125	−	2.21918i	0.386310	−	0.669109i	0.991950	+	0.126630i	$0.0404161\pi$
$12$		0			0
$13$	−5.99175			−1.66181			−0.830906	−	0.556413i	$-0.812177\pi$
$13$	−5.99175			−1.66181			−0.830906	+	0.556413i	$0.812177\pi$
$14$	−1.88836	+	3.23018i	−0.504686	+	0.863303i
$15$		0			0
$16$	3.68248	−	1.56183i	0.920620	−	0.390459i
$17$	3.53425	+	2.04050i	0.857181	+	0.494894i	0.863067	−	0.505089i	$-0.168540\pi$
$17$	3.53425	+	2.04050i	0.857181	+	0.494894i	−0.00588636	+	0.999983i	$0.501874\pi$
$18$		0			0
$19$	−2.05318	+	1.18541i	−0.471033	+	0.271951i	−0.716672	−	0.697410i	$-0.754335\pi$
$19$	−2.05318	+	1.18541i	−0.471033	+	0.271951i	0.245639	+	0.969361i	$0.421002\pi$
$20$	−5.08602	−	5.75041i	−1.13727	−	1.28583i
$21$		0			0
$22$	−1.48865	+	3.30403i	−0.317382	+	0.704422i
$23$	−6.53773	+	3.77456i	−1.36321	+	0.787050i	−0.990050	−	0.140716i	$-0.955059\pi$
$23$	−6.53773	+	3.77456i	−1.36321	+	0.787050i	−0.373161	+	0.927767i	$0.621726\pi$
$24$		0			0
$25$	−4.86686	+	8.42964i	−0.973371	+	1.68593i
$26$	8.43104	−	0.848331i	1.65346	−	0.166371i
$27$		0			0
$28$	2.19979	−	4.81258i	0.415721	−	0.909492i
$29$			2.70568i			0.502431i	0.967931	+	0.251216i	$0.0808303\pi$
$29$			2.70568i			0.502431i	−0.967931	+	0.251216i	$0.919170\pi$
$30$		0			0
$31$	2.90258	−	5.02742i	0.521319	−	0.902951i	−0.478373	−	0.878156i	$-0.658773\pi$
$31$	2.90258	−	5.02742i	0.521319	−	0.902951i	0.999693	−	0.0247947i	$-0.00789320\pi$
$32$	−4.96052	+	2.71905i	−0.876905	+	0.480664i
$33$		0			0
$34$	−5.26197	−	2.37081i	−0.902420	−	0.406591i
$35$	−10.0989	−	1.07147i	−1.70703	−	0.181111i
$36$		0			0
$37$	3.61144	−	2.08507i	0.593717	−	0.342783i	−0.172849	−	0.984948i	$-0.555297\pi$
$37$	3.61144	−	2.08507i	0.593717	−	0.342783i	0.766566	+	0.642166i	$0.221964\pi$
$38$	2.72122	−	1.95869i	0.441440	−	0.317742i
$39$		0			0
$40$	7.97074	+	7.37136i	1.26028	+	1.16551i
$41$		−	5.96293i		−	0.931253i	−0.884981	−	0.465627i	$-0.845829\pi$
$41$		−	5.96293i		−	0.931253i	0.884981	−	0.465627i	$-0.154171\pi$
$42$		0			0
$43$	−8.06098			−1.22929			−0.614644	−	0.788805i	$-0.710700\pi$
$43$	−8.06098			−1.22929			−0.614644	+	0.788805i	$0.710700\pi$
$44$	1.62690	−	4.85990i	0.245264	−	0.732658i
$45$		0			0
$46$	8.66488	−	6.23685i	1.27757	−	0.919573i
$47$	0.204145	+	0.353590i	0.0297776	+	0.0515763i	0.880530	−	0.473990i	$-0.157187\pi$
$47$	0.204145	+	0.353590i	0.0297776	+	0.0515763i	−0.850753	+	0.525566i	$0.823853\pi$
$48$		0			0
$49$	−2.15004	−	6.66163i	−0.307148	−	0.951662i
$50$	5.65470	−	12.5505i	0.799695	−	1.77491i
$51$		0			0
$52$	−11.7433	+	2.38739i	−1.62850	+	0.331071i
$53$	4.41436	+	2.54863i	0.606359	+	0.350082i	0.771539	−	0.636182i	$-0.219487\pi$
$53$	4.41436	+	2.54863i	0.606359	+	0.350082i	−0.165180	+	0.986263i	$0.552821\pi$
$54$		0			0
$55$	−9.83600			−1.32629
$56$	−2.41396	+	7.08327i	−0.322580	+	0.946542i
$57$		0			0
$58$	−0.383078	−	3.80718i	−0.0503006	−	0.499907i
$59$	−9.05639	−	5.22871i	−1.17904	−	0.680720i	−0.223249	−	0.974761i	$-0.571666\pi$
$59$	−9.05639	−	5.22871i	−1.17904	−	0.680720i	−0.955793	+	0.294041i	$0.905000\pi$
$60$		0			0
$61$	−1.34535	−	2.33021i	−0.172254	−	0.298353i	0.766954	−	0.641703i	$-0.221772\pi$
$61$	−1.34535	−	2.33021i	−0.172254	−	0.298353i	−0.939208	+	0.343350i	$0.888438\pi$
$62$	−3.37245	+	7.48508i	−0.428302	+	0.950606i
$63$		0			0
$64$	6.59502	−	4.52832i	0.824378	−	0.566040i
$65$	11.4995	+	19.9178i	1.42634	+	2.47049i
$66$		0			0
$67$	2.38045	−	4.12307i	0.290819	−	0.503713i	−0.683185	−	0.730245i	$-0.739406\pi$
$67$	2.38045	−	4.12307i	0.290819	−	0.503713i	0.974004	+	0.226533i	$0.0727390\pi$
$68$	7.73983	+	2.59098i	0.938592	+	0.314203i
$69$		0			0
$70$	14.3620	+	0.0778363i	1.71658	+	0.00930322i
$71$		−	1.21482i		−	0.144172i	−0.997398	−	0.0720860i	$-0.977034\pi$
$71$		−	1.21482i		−	0.144172i	0.997398	−	0.0720860i	$-0.0229656\pi$
$72$		0			0
$73$	−6.65046	−	3.83964i	−0.778377	−	0.449396i	0.0574778	−	0.998347i	$-0.481694\pi$
$73$	−6.65046	−	3.83964i	−0.778377	−	0.449396i	−0.835855	+	0.548951i	$0.815027\pi$
$74$	−4.78648	+	3.44523i	−0.556417	+	0.400500i
$75$		0			0
$76$	−3.55173	+	3.14137i	−0.407412	+	0.360340i
$77$	−2.75147	−	6.19628i	−0.313560	−	0.706132i
$78$		0			0
$79$	−8.89433	+	5.13514i	−1.00069	+	0.577749i	−0.908452	−	0.417988i	$-0.862735\pi$
$79$	−8.89433	+	5.13514i	−1.00069	+	0.577749i	−0.0922379	+	0.995737i	$0.529402\pi$
$80$	−12.2594	−	9.24378i	−1.37064	−	1.03349i
$81$		0			0
$82$	0.844250	+	8.39049i	0.0932319	+	0.926574i
$83$		−	4.49449i		−	0.493335i	−0.969100	−	0.246667i	$-0.920664\pi$
$83$		−	4.49449i		−	0.493335i	0.969100	−	0.246667i	$-0.0793355\pi$
$84$		0			0
$85$		−	15.6647i		−	1.69908i
$86$	11.3427	−	1.14130i	1.22311	−	0.123069i
$87$		0			0
$88$	−1.60115	+	7.06875i	−0.170683	+	0.753531i
$89$	3.35682	−	1.93806i	0.355822	−	0.205434i	−0.311424	−	0.950271i	$-0.600806\pi$
$89$	3.35682	−	1.93806i	0.355822	−	0.205434i	0.667247	+	0.744837i	$0.267473\pi$
$90$		0			0
$91$	−9.33056	+	12.8159i	−0.978109	+	1.34347i
$92$	−11.3094	+	10.0027i	−1.17909	+	1.04286i
$93$		0			0
$94$	−0.337316	−	0.468635i	−0.0347915	−	0.0483360i
$95$	7.88105	+	4.55013i	0.808578	+	0.466833i
$96$		0			0
$97$			1.20561i			0.122411i	0.998125	+	0.0612055i	$0.0194945\pi$
$97$			1.20561i			0.122411i	−0.998125	+	0.0612055i	$0.980505\pi$
$98$	3.96851	+	9.06923i	0.400880	+	0.916131i
$99$		0			0
$100$	−6.17984	+	18.4605i	−0.617984	+	1.84605i
$101$	6.74188	−	11.6773i	0.670842	−	1.16193i	−0.306824	−	0.951766i	$-0.599266\pi$
$101$	6.74188	−	11.6773i	0.670842	−	1.16193i	0.977666	−	0.210166i	$-0.0674003\pi$
$102$		0			0
$103$	2.63098	+	4.55700i	0.259239	+	0.449014i	0.966038	−	0.258399i	$-0.0831951\pi$
$103$	2.63098	+	4.55700i	0.259239	+	0.449014i	−0.706800	+	0.707414i	$0.749862\pi$
$104$	16.1861	−	5.02196i	1.58717	−	0.492444i
$105$		0			0
$106$	−6.57233	−	2.96120i	−0.638361	−	0.287617i
$107$	1.74917	+	3.02965i	0.169098	+	0.292887i	0.938103	−	0.346356i	$-0.112581\pi$
$107$	1.74917	+	3.02965i	0.169098	+	0.292887i	−0.769005	+	0.639243i	$0.779248\pi$
$108$		0			0
$109$	14.9576	+	8.63578i	1.43268	+	0.827158i	0.997324	−	0.0731016i	$-0.0232897\pi$
$109$	14.9576	+	8.63578i	1.43268	+	0.827158i	0.435354	+	0.900259i	$0.356623\pi$
$110$	13.8403	−	1.39261i	1.31962	−	0.132780i
$111$		0			0
$112$	2.39384	−	10.3087i	0.226196	−	0.974082i
$113$	11.7160			1.10215			0.551075	−	0.834456i	$-0.314218\pi$
$113$	11.7160			1.10215			0.551075	+	0.834456i	$0.314218\pi$
$114$		0			0
$115$	25.0948	+	14.4885i	2.34010	+	1.35106i
$116$	1.07806	+	5.30288i	0.100096	+	0.492360i
$117$		0			0
$118$	13.4836	+	6.07513i	1.24127	+	0.559261i
$119$	9.86814	−	4.38197i	0.904611	−	0.401694i
$120$		0			0
$121$	2.21682	+	3.83964i	0.201529	+	0.349058i
$122$	2.22297	+	3.08838i	0.201258	+	0.279609i
$123$		0			0
$124$	3.68564	−	11.0098i	0.330980	−	0.988709i
$125$	18.1701			1.62518
$126$		0			0
$127$		−	10.4857i		−	0.930459i	−0.885190	−	0.465229i	$-0.845972\pi$
$127$		−	10.4857i		−	0.930459i	0.885190	−	0.465229i	$-0.154028\pi$
$128$	−8.63878	+	7.30558i	−0.763567	+	0.645728i
$129$		0			0
$130$	−19.0011	−	26.3983i	−1.66651	−	2.31528i
$131$	1.93929	−	1.11965i	0.169437	−	0.0978243i	−0.412884	−	0.910784i	$-0.635478\pi$
$131$	1.93929	−	1.11965i	0.169437	−	0.0978243i	0.582320	+	0.812960i	$0.302145\pi$
$132$		0			0
$133$	−0.661790	+	6.23757i	−0.0573845	+	0.540866i
$134$	−2.76580	+	6.13863i	−0.238929	+	0.530297i
$135$		0			0
$136$	−11.2576	−	2.54997i	−0.965333	−	0.218658i
$137$	2.84029	−	4.91953i	0.242662	−	0.420303i	−0.718809	−	0.695207i	$-0.755313\pi$
$137$	2.84029	−	4.91953i	0.242662	−	0.420303i	0.961472	+	0.274904i	$0.0886460\pi$
$138$		0			0
$139$		−	15.0149i		−	1.27355i	−0.771050	−	0.636774i	$-0.780268\pi$
$139$		−	15.0149i		−	1.27355i	0.771050	−	0.636774i	$-0.219732\pi$
$140$	−20.2199	+	1.92389i	−1.70889	+	0.162598i
$141$		0			0
$142$	0.171997	+	1.70938i	0.0144337	+	0.143448i
$143$	−7.67690	+	13.2968i	−0.641975	+	1.11193i
$144$		0			0
$145$	8.99420	−	5.19280i	0.746927	−	0.431239i
$146$	9.90154	+	4.46120i	0.819457	+	0.369212i
$147$		0			0
$148$	6.24731	−	5.52550i	0.513526	−	0.454194i
$149$	−2.90342	+	1.67629i	−0.237858	+	0.137327i	−0.614192	−	0.789157i	$-0.710518\pi$
$149$	−2.90342	+	1.67629i	−0.237858	+	0.137327i	0.376334	+	0.926484i	$0.377185\pi$
$150$		0			0
$151$	6.37756	+	3.68209i	0.518998	+	0.299644i	0.736525	−	0.676411i	$-0.236465\pi$
$151$	6.37756	+	3.68209i	0.518998	+	0.299644i	−0.217526	+	0.976054i	$0.569799\pi$
$152$	4.55291	−	4.92311i	0.369290	−	0.399317i
$153$		0			0
$154$	4.74891	+	8.32928i	0.382678	+	0.671193i
$155$	−22.2828			−1.78980
$156$		0			0
$157$	−4.53219	+	7.84998i	−0.361708	+	0.626497i	−0.988242	−	0.152897i	$-0.951140\pi$
$157$	−4.53219	+	7.84998i	−0.361708	+	0.626497i	0.626534	+	0.779394i	$0.284473\pi$
$158$	11.7882	−	8.48499i	0.937822	−	0.675030i
$159$		0			0
$160$	18.5590	+	11.2713i	1.46722	+	0.891073i
$161$	−2.10727	+	19.8616i	−0.166076	+	1.56532i
$162$		0			0
$163$	−9.73371	−	16.8593i	−0.762403	−	1.32052i	−0.941609	−	0.336709i	$-0.890686\pi$
$163$	−9.73371	−	16.8593i	−0.762403	−	1.32052i	0.179206	−	0.983812i	$-0.442647\pi$
$164$	−2.37590	−	11.6868i	−0.185527	−	0.912585i
$165$		0			0
$166$	0.636345	+	6.32424i	0.0493899	+	0.490856i
$167$	−17.4579			−1.35094			−0.675468	−	0.737390i	$-0.736058\pi$
$167$	−17.4579			−1.35094			−0.675468	+	0.737390i	$0.736058\pi$
$168$		0			0
$169$	22.9011			1.76162
$170$	2.21786	+	22.0419i	0.170102	+	1.69054i
$171$		0			0
$172$	−15.7988	+	3.21186i	−1.20465	+	0.244902i
$173$	−1.76728	−	3.06101i	−0.134363	−	0.232724i	0.790991	−	0.611828i	$-0.209566\pi$
$173$	−1.76728	−	3.06101i	−0.134363	−	0.232724i	−0.925354	+	0.379104i	$0.876232\pi$
$174$		0			0
$175$	10.4516	+	23.5368i	0.790064	+	1.77921i
$176$	1.25217	−	10.1732i	0.0943858	−	0.766833i
$177$		0			0
$178$	−4.44901	+	3.20233i	−0.333468	+	0.240025i
$179$	4.69613	−	8.13393i	0.351005	−	0.607958i	−0.635421	−	0.772166i	$-0.719173\pi$
$179$	4.69613	−	8.13393i	0.351005	−	0.607958i	0.986426	+	0.164208i	$0.0525067\pi$
$180$		0			0
$181$	−0.0924470			−0.00687153			−0.00343577	−	0.999994i	$-0.501094\pi$
$181$	−0.0924470			−0.00687153			−0.00343577	+	0.999994i	$0.501094\pi$
$182$	11.3146	−	19.3545i	0.838694	−	1.43465i
$183$		0			0
$184$	14.4973	−	15.6761i	1.06876	−	1.15566i
$185$	−13.8623	−	8.00343i	−1.01918	−	0.588424i
$186$		0			0
$187$	9.05648	−	5.22876i	0.662275	−	0.382365i
$188$	0.540992	+	0.611662i	0.0394559	+	0.0446101i
$189$		0			0
$190$	−11.7337	−	5.28670i	−0.851253	−	0.383537i
$191$	0.730882	−	0.421975i	0.0528848	−	0.0305330i	−0.473324	−	0.880888i	$-0.656946\pi$
$191$	0.730882	−	0.421975i	0.0528848	−	0.0305330i	0.526209	+	0.850355i	$0.323613\pi$
$192$		0			0
$193$	−8.77738	+	15.2029i	−0.631810	+	1.09433i	0.355372	+	0.934725i	$0.384354\pi$
$193$	−8.77738	+	15.2029i	−0.631810	+	1.09433i	−0.987182	+	0.159601i	$0.948979\pi$
$194$	−0.170694	−	1.69642i	−0.0122551	−	0.121796i
$195$		0			0
$196$	−6.86817	−	12.1995i	−0.490584	−	0.871394i
$197$			7.92348i			0.564524i	0.959337	+	0.282262i	$0.0910848\pi$
$197$			7.92348i			0.564524i	−0.959337	+	0.282262i	$0.908915\pi$
$198$		0			0
$199$	9.03385	−	15.6471i	0.640392	−	1.10919i	−0.344953	−	0.938620i	$-0.612105\pi$
$199$	9.03385	−	15.6471i	0.640392	−	1.10919i	0.985345	−	0.170572i	$-0.0545616\pi$
$200$	6.08200	−	26.8509i	0.430063	−	1.89864i
$201$		0			0
$202$	−7.83325	+	17.3857i	−0.551145	+	1.22326i
$203$	5.78725	+	4.21337i	0.406185	+	0.295721i
$204$		0			0
$205$	−19.8219	+	11.4442i	−1.38442	+	0.799298i
$206$	−4.34728	−	6.03969i	−0.302889	−	0.420805i
$207$		0			0
$208$	−22.0645	+	9.35812i	−1.52990	+	0.648869i
$209$			6.07519i			0.420230i
$210$		0			0
$211$	−0.699927			−0.0481849			−0.0240925	−	0.999710i	$-0.507670\pi$
$211$	−0.699927			−0.0481849			−0.0240925	+	0.999710i	$0.507670\pi$
$212$	9.66723	+	3.23620i	0.663948	+	0.222263i
$213$		0			0
$214$	−2.89021	−	4.01539i	−0.197571	−	0.274486i
$215$	15.4708	+	26.7963i	1.05510	+	1.82749i
$216$		0			0
$217$	−6.23329	−	14.0373i	−0.423143	−	0.952913i
$218$	−22.2697	−	10.0337i	−1.50829	−	0.679570i
$219$		0			0
$220$	−19.2777	+	3.91911i	−1.29970	+	0.264226i
$221$	−21.1763	−	12.2262i	−1.42447	−	0.822420i
$222$		0			0
$223$	2.52067			0.168797			0.0843983	−	0.996432i	$-0.473103\pi$
$223$	2.52067			0.168797			0.0843983	+	0.996432i	$0.473103\pi$
$224$	−1.90885	+	14.8444i	−0.127540	+	0.991833i
$225$		0			0
$226$	−16.4857	+	1.65879i	−1.09661	+	0.110341i
$227$	−7.20056	−	4.15724i	−0.477918	−	0.275926i	0.241631	−	0.970368i	$-0.422318\pi$
$227$	−7.20056	−	4.15724i	−0.477918	−	0.275926i	−0.719548	+	0.694442i	$0.755651\pi$
$228$		0			0
$229$	−2.61750	−	4.53364i	−0.172969	−	0.299592i	0.766487	−	0.642259i	$-0.222003\pi$
$229$	−2.61750	−	4.53364i	−0.172969	−	0.299592i	−0.939457	+	0.342668i	$0.888669\pi$
$230$	−37.3624	−	16.8339i	−2.46360	−	1.10999i
$231$		0			0
$232$	−2.26775	−	7.30909i	−0.148885	−	0.479865i
$233$	−10.9830	−	19.0231i	−0.719520	−	1.24624i	−0.961190	−	0.275886i	$-0.911029\pi$
$233$	−10.9830	−	19.0231i	−0.719520	−	1.24624i	0.241671	−	0.970358i	$-0.422305\pi$
$234$		0			0
$235$	0.783601	−	1.35724i	0.0511165	−	0.0885363i
$236$	−19.8331	−	6.63931i	−1.29102	−	0.432183i
$237$		0			0
$238$	−13.2651	+	7.56307i	−0.859850	+	0.490241i
$239$		−	28.5156i		−	1.84452i	−0.386572	−	0.922259i	$-0.626341\pi$
$239$		−	28.5156i		−	1.84452i	0.386572	−	0.922259i	$-0.373659\pi$
$240$		0			0
$241$	8.01239	+	4.62596i	0.516123	+	0.297984i	0.735347	−	0.677691i	$-0.237019\pi$
$241$	8.01239	+	4.62596i	0.516123	+	0.297984i	−0.219224	+	0.975675i	$0.570352\pi$
$242$	−3.66293	−	5.08893i	−0.235462	−	0.327129i
$243$		0			0
$244$	−3.56522	−	4.03095i	−0.228240	−	0.258055i
$245$	−18.0182	+	19.9323i	−1.15114	+	1.27343i
$246$		0			0
$247$	12.3022	−	7.10266i	0.782768	−	0.451931i
$248$	−3.62729	+	16.0138i	−0.230333	+	1.01688i
$249$		0			0
$250$	−25.5673	+	2.57258i	−1.61702	+	0.162704i
$251$		−	0.208623i		−	0.0131682i	−0.999978	−	0.00658409i	$-0.997904\pi$
$251$		−	0.208623i		−	0.0131682i	0.999978	−	0.00658409i	$-0.00209580\pi$
$252$		0			0
$253$			19.3446i			1.21618i
$254$	1.48460	+	14.7546i	0.0931523	+	0.925784i
$255$		0			0
$256$	11.1213	−	11.5029i	0.695084	−	0.718928i
$257$	17.1020	−	9.87383i	1.06679	−	0.615912i	0.139488	−	0.990224i	$-0.455454\pi$
$257$	17.1020	−	9.87383i	1.06679	−	0.615912i	0.927303	+	0.374311i	$0.122121\pi$
$258$		0			0
$259$	1.16405	−	10.9716i	0.0723308	−	0.681739i
$260$	30.4741	+	34.4550i	1.88993	+	2.13681i
$261$		0			0
$262$	−2.57027	+	1.85004i	−0.158792	+	0.114296i
$263$	−14.0976	−	8.13925i	−0.869295	−	0.501888i	−0.00218129	−	0.999998i	$-0.500694\pi$
$263$	−14.0976	−	8.13925i	−0.869295	−	0.501888i	−0.867114	+	0.498110i	$0.834028\pi$
$264$		0			0
$265$		−	19.5656i		−	1.20191i
$266$	0.0480755	−	8.87064i	0.00294770	−	0.543894i
$267$		0			0
$268$	3.02265	−	9.02931i	0.184638	−	0.551553i
$269$	−3.99040	+	6.91158i	−0.243299	+	0.421406i	−0.961652	−	0.274272i	$-0.911563\pi$
$269$	−3.99040	+	6.91158i	−0.243299	+	0.421406i	0.718353	+	0.695679i	$0.244896\pi$
$270$		0			0
$271$	−6.26335	−	10.8484i	−0.380471	−	0.658995i	0.610658	−	0.791894i	$-0.290905\pi$
$271$	−6.26335	−	10.8484i	−0.380471	−	0.658995i	−0.991130	+	0.132899i	$0.957572\pi$
$272$	16.2017	+	1.99419i	0.982374	+	0.120916i
$273$		0			0
$274$	−3.30007	+	7.32444i	−0.199365	+	0.442486i
$275$	12.4713	+	21.6009i	0.752046	+	1.30258i
$276$		0			0
$277$	17.4329	+	10.0649i	1.04744	+	0.604740i	0.921932	−	0.387353i	$-0.126610\pi$
$277$	17.4329	+	10.0649i	1.04744	+	0.604740i	0.125508	+	0.992093i	$0.459944\pi$
$278$	2.12586	+	21.1276i	0.127501	+	1.26715i
$279$		0			0
$280$	28.1791	−	5.56991i	1.68403	−	0.332866i
$281$	2.22654			0.132824			0.0664121	−	0.997792i	$-0.478845\pi$
$281$	2.22654			0.132824			0.0664121	+	0.997792i	$0.478845\pi$
$282$		0			0
$283$	2.89693	+	1.67254i	0.172204	+	0.0994222i	0.583625	−	0.812023i	$-0.301634\pi$
$283$	2.89693	+	1.67254i	0.172204	+	0.0994222i	−0.411420	+	0.911446i	$0.634967\pi$
$284$	−0.484038	−	2.38093i	−0.0287224	−	0.141282i
$285$		0			0
$286$	8.91963	−	19.7969i	0.527429	−	1.17062i
$287$	−12.7543	−	9.28568i	−0.752862	−	0.548117i
$288$		0			0
$289$	−0.172731	−	0.299179i	−0.0101607	−	0.0175988i
$290$	−11.9206	+	8.58026i	−0.700002	+	0.503850i
$291$		0			0
$292$	−14.5642	−	4.87550i	−0.852304	−	0.285317i
$293$	9.88541			0.577512			0.288756	−	0.957403i	$-0.406758\pi$
$293$	9.88541			0.577512			0.288756	+	0.957403i	$0.406758\pi$
$294$		0			0
$295$			40.1403i			2.33706i
$296$	−8.00832	+	8.65950i	−0.465474	+	0.503323i
$297$		0			0
$298$	3.84810	−	2.76980i	0.222914	−	0.160450i
$299$	39.1724	−	22.6162i	2.26540	−	1.30793i
$300$		0			0
$301$	−12.5528	+	17.2419i	−0.723534	+	0.993805i
$302$	−9.49524	−	4.27814i	−0.546390	−	0.246179i
$303$		0			0
$304$	−5.70941	+	7.57197i	−0.327457	+	0.434282i
$305$	−5.16405	+	8.94439i	−0.295693	+	0.512154i
$306$		0			0
$307$			3.58312i			0.204500i	0.994759	+	0.102250i	$0.0326041\pi$
$307$			3.58312i			0.204500i	−0.994759	+	0.102250i	$0.967396\pi$
$308$	−7.86152	−	11.0478i	−0.447952	−	0.629509i
$309$		0			0
$310$	31.3544	−	3.15488i	1.78081	−	0.179185i
$311$	13.1626	−	22.7982i	0.746381	−	1.29277i	−0.203166	−	0.979144i	$-0.565123\pi$
$311$	13.1626	−	22.7982i	0.746381	−	1.29277i	0.949547	−	0.313626i	$-0.101544\pi$
$312$		0			0
$313$	13.5565	−	7.82684i	0.766257	−	0.442399i	−0.0652804	−	0.997867i	$-0.520794\pi$
$313$	13.5565	−	7.82684i	0.766257	−	0.442399i	0.831538	+	0.555468i	$0.187461\pi$
$314$	5.26586	−	11.6875i	0.297169	−	0.659561i
$315$		0			0
$316$	−15.3860	+	13.6083i	−0.865530	+	0.765528i
$317$	13.8585	−	8.00123i	0.778373	−	0.449394i	−0.0574803	−	0.998347i	$-0.518307\pi$
$317$	13.8585	−	8.00123i	0.778373	−	0.449394i	0.835853	+	0.548953i	$0.184973\pi$
$318$		0			0
$319$	6.00439	+	3.46664i	0.336181	+	0.194094i
$320$	−27.7104	−	13.2323i	−1.54906	−	0.739707i
$321$		0			0
$322$	0.153082	−	28.2458i	0.00853090	−	1.57408i
$323$	−9.67528			−0.538347
$324$		0			0
$325$	29.1610	−	50.5083i	1.61756	−	2.80170i
$326$	16.0834	+	22.3447i	0.890776	+	1.23756i
$327$		0			0
$328$	4.99781	+	16.1082i	0.275958	+	0.889427i
$329$	1.07420	+	0.113970i	0.0592228	+	0.00628339i
$330$		0			0
$331$	8.13686	+	14.0935i	0.447242	+	0.774646i	0.998205	−	0.0598834i	$-0.0190729\pi$
$331$	8.13686	+	14.0935i	0.447242	+	0.774646i	−0.550963	+	0.834530i	$0.685740\pi$
$332$	−1.79081	−	8.80880i	−0.0982836	−	0.483446i
$333$		0			0
$334$	24.5652	−	2.47175i	1.34415	−	0.135248i
$335$	−18.2745			−0.998443
$336$		0			0
$337$	−5.91266			−0.322083			−0.161042	−	0.986948i	$-0.551485\pi$
$337$	−5.91266			−0.322083			−0.161042	+	0.986948i	$0.551485\pi$
$338$	−32.2243	+	3.24240i	−1.75277	+	0.176364i
$339$		0			0
$340$	−6.24154	−	30.7014i	−0.338495	−	1.66502i
$341$	−7.43784	−	12.8827i	−0.402782	−	0.697638i
$342$		0			0
$343$	−17.5969	−	5.77495i	−0.950142	−	0.311818i
$344$	21.7759	−	6.75628i	1.17408	−	0.364274i
$345$		0			0
$346$	2.92014	+	4.05696i	0.156987	+	0.218103i
$347$	−14.5658	+	25.2288i	−0.781936	+	1.35435i	0.148877	+	0.988856i	$0.452434\pi$
$347$	−14.5658	+	25.2288i	−0.781936	+	1.35435i	−0.930813	+	0.365496i	$0.880899\pi$
$348$		0			0
$349$	−11.2807			−0.603841			−0.301921	−	0.953333i	$-0.597628\pi$
$349$	−11.2807			−0.603841			−0.301921	+	0.953333i	$0.597628\pi$
$350$	−18.0389	−	31.6391i	−0.964220	−	1.69118i
$351$		0			0
$352$	−0.321584	+	14.4921i	−0.0171405	+	0.772430i
$353$	−24.0732	−	13.8987i	−1.28129	−	0.739753i	−0.304205	−	0.952606i	$-0.598391\pi$
$353$	−24.0732	−	13.8987i	−1.28129	−	0.739753i	−0.977084	+	0.212854i	$0.931724\pi$
$354$		0			0
$355$	−4.03829	+	2.33151i	−0.214330	+	0.123743i
$356$	5.80685	−	5.13593i	0.307762	−	0.272204i
$357$		0			0
$358$	−5.45633	+	12.1102i	−0.288376	+	0.640045i
$359$	2.79904	−	1.61602i	0.147727	−	0.0852905i	−0.424314	−	0.905515i	$-0.639485\pi$
$359$	2.79904	−	1.61602i	0.147727	−	0.0852905i	0.572042	+	0.820224i	$0.306152\pi$
$360$		0			0
$361$	−6.68962	+	11.5868i	−0.352085	+	0.609830i
$362$	0.130083	−	0.0130889i	0.00683701	−	0.000687939i
$363$		0			0
$364$	−13.1806	+	28.8358i	−0.690851	+	1.51140i
$365$			29.4766i			1.54287i
$366$		0			0
$367$	0.139516	−	0.241649i	0.00728269	−	0.0126140i	−0.862361	−	0.506294i	$-0.831015\pi$
$367$	0.139516	−	0.241649i	0.00728269	−	0.0126140i	0.869644	+	0.493680i	$0.164348\pi$
$368$	−18.1798	+	24.1106i	−0.947690	+	1.25685i
$369$		0			0
$370$	20.6390	+	9.29902i	1.07297	+	0.483433i
$371$	12.3255	−	5.47318i	0.639910	−	0.284154i
$372$		0			0
$373$	26.9934	−	15.5846i	1.39767	−	0.806943i	0.403518	−	0.914972i	$-0.367787\pi$
$373$	26.9934	−	15.5846i	1.39767	−	0.806943i	0.994148	+	0.108029i	$0.0344540\pi$
$374$	−12.0031	+	8.63968i	−0.620668	+	0.446747i
$375$		0			0
$376$	−0.847835	−	0.784080i	−0.0437238	−	0.0404358i
$377$		−	16.2117i		−	0.834947i
$378$		0			0
$379$	24.0156			1.23360			0.616799	−	0.787121i	$-0.288429\pi$
$379$	24.0156			1.23360			0.616799	+	0.787121i	$0.288429\pi$
$380$	17.2591	+	5.77766i	0.885374	+	0.296388i
$381$		0			0
$382$	−0.968686	+	0.697245i	−0.0495623	+	0.0356742i
$383$	7.38565	+	12.7923i	0.377389	+	0.653657i	0.990681	−	0.136199i	$-0.0434887\pi$
$383$	7.38565	+	12.7923i	0.377389	+	0.653657i	−0.613293	+	0.789856i	$0.710155\pi$
$384$		0			0
$385$	−15.3170	+	21.0385i	−0.780625	+	1.07222i
$386$	10.1983	−	22.6348i	0.519077	−	1.15208i
$387$		0			0
$388$	0.480370	+	2.36288i	0.0243871	+	0.119957i
$389$	1.63155	+	0.941976i	0.0827229	+	0.0477601i	0.540791	−	0.841157i	$-0.318125\pi$
$389$	1.63155	+	0.941976i	0.0827229	+	0.0477601i	−0.458068	+	0.888917i	$0.651458\pi$
$390$		0			0
$391$	−30.8079			−1.55802
$392$	11.3915	+	16.1936i	0.575358	+	0.817902i
$393$		0			0
$394$	−1.12183	−	11.1492i	−0.0565170	−	0.561688i
$395$	34.1405	+	19.7110i	1.71779	+	0.991768i
$396$		0			0
$397$	2.50329	+	4.33582i	0.125636	+	0.217609i	0.921982	−	0.387234i	$-0.126569\pi$
$397$	2.50329	+	4.33582i	0.125636	+	0.217609i	−0.796345	+	0.604842i	$0.793236\pi$
$398$	−10.4962	+	23.2962i	−0.526129	+	1.16773i
$399$		0			0
$400$	−4.75641	+	38.6432i	−0.237820	+	1.93216i
$401$	−13.4430	−	23.2840i	−0.671313	−	1.16275i	−0.977532	−	0.210787i	$-0.932397\pi$
$401$	−13.4430	−	23.2840i	−0.671313	−	1.16275i	0.306219	−	0.951961i	$-0.400936\pi$
$402$		0			0
$403$	−17.3915	+	30.1230i	−0.866334	+	1.50054i
$404$	8.56070	−	25.5727i	0.425911	−	1.27229i
$405$		0			0
$406$	−8.73983	−	5.10930i	−0.433750	−	0.253570i
$407$		−	10.6859i		−	0.529682i
$408$		0			0
$409$	22.4884	+	12.9837i	1.11198	+	0.642002i	0.939341	−	0.342984i	$-0.111438\pi$
$409$	22.4884	+	12.9837i	1.11198	+	0.642002i	0.172638	+	0.984985i	$0.444771\pi$
$410$	26.2713	−	18.9097i	1.29745	−	0.933883i
$411$		0			0
$412$	6.97221	+	7.88300i	0.343496	+	0.388367i
$413$	−25.2868	+	11.2287i	−1.24428	+	0.552526i
$414$		0			0
$415$	−14.9406	+	8.62595i	−0.733404	+	0.423431i
$416$	29.7222	−	16.2919i	1.45725	−	0.798774i
$417$		0			0
$418$	−0.860144	−	8.54845i	−0.0420710	−	0.418118i
$419$			33.9652i			1.65931i	0.558278	+	0.829654i	$0.311462\pi$
$419$			33.9652i			1.65931i	−0.558278	+	0.829654i	$0.688538\pi$
$420$		0			0
$421$		−	2.75866i		−	0.134449i	−0.997738	−	0.0672245i	$-0.978586\pi$
$421$		−	2.75866i		−	0.134449i	0.997738	−	0.0672245i	$-0.0214144\pi$
$422$	0.984873	−	0.0990978i	0.0479429	−	0.00482401i
$423$		0			0
$424$	−14.0610	−	3.18497i	−0.682864	−	0.154676i
$425$	−34.4013	+	19.8616i	−1.66871	+	0.963430i
$426$		0			0
$427$	−7.07917	−	0.751082i	−0.342585	−	0.0363474i
$428$	4.63536	+	5.24088i	0.224058	+	0.253328i
$429$		0			0
$430$	−25.5631	−	35.5149i	−1.23276	−	1.71268i
$431$	31.3514	+	18.1007i	1.51014	+	0.871881i	0.999930	+	0.0118334i	$0.00376678\pi$
$431$	31.3514	+	18.1007i	1.51014	+	0.871881i	0.510213	+	0.860048i	$0.329567\pi$
$432$		0			0
$433$		−	20.2448i		−	0.972901i	−0.873708	−	0.486451i	$-0.838291\pi$
$433$		−	20.2448i		−	0.972901i	0.873708	−	0.486451i	$-0.161709\pi$
$434$	10.7584	+	18.8695i	0.516418	+	0.905763i
$435$		0			0
$436$	32.7564	+	10.9655i	1.56875	+	0.525154i
$437$	8.94878	−	15.4997i	0.428078	−	0.741453i
$438$		0			0
$439$	−14.6398	−	25.3569i	−0.698719	−	1.21022i	−0.968911	−	0.247410i	$-0.920421\pi$
$439$	−14.6398	−	25.3569i	−0.698719	−	1.21022i	0.270192	−	0.962806i	$-0.412913\pi$
$440$	26.5709	−	8.24401i	1.26672	−	0.393018i
$441$		0			0
$442$	31.5284	+	14.2053i	1.49965	+	0.675678i
$443$	−11.6580	−	20.1922i	−0.553886	−	0.959359i	−0.997989	−	0.0633831i	$-0.979811\pi$
$443$	−11.6580	−	20.1922i	−0.553886	−	0.959359i	0.444103	−	0.895976i	$-0.353522\pi$
$444$		0			0
$445$	−12.8850	−	7.43915i	−0.610807	−	0.352650i
$446$	−3.54686	+	0.356884i	−0.167948	+	0.0168990i
$447$		0			0
$448$	0.584240	−	21.1579i	0.0276028	−	0.999619i
$449$	−27.8410			−1.31390			−0.656949	−	0.753935i	$-0.728153\pi$
$449$	−27.8410			−1.31390			−0.656949	+	0.753935i	$0.728153\pi$
$450$		0			0
$451$	−13.2328	−	7.63998i	−0.623110	−	0.359752i
$452$	22.9623	−	4.66819i	1.08006	−	0.219573i
$453$		0			0
$454$	10.7206	+	4.83022i	0.503141	+	0.226693i
$455$	60.5101	+	6.41997i	2.83676	+	0.300973i
$456$		0			0
$457$	−9.56098	−	16.5601i	−0.447244	−	0.774649i	0.550962	−	0.834531i	$-0.314261\pi$
$457$	−9.56098	−	16.5601i	−0.447244	−	0.774649i	−0.998205	+	0.0598816i	$0.980928\pi$
$458$	4.32499	+	6.00873i	0.202094	+	0.280770i
$459$		0			0
$460$	54.9563	+	18.3972i	2.56235	+	0.857772i
$461$	20.5529			0.957242			0.478621	−	0.878022i	$-0.341137\pi$
$461$	20.5529			0.957242			0.478621	+	0.878022i	$0.341137\pi$
$462$		0			0
$463$		−	31.7517i		−	1.47563i	−0.675005	−	0.737813i	$-0.735858\pi$
$463$		−	31.7517i		−	1.47563i	0.675005	−	0.737813i	$-0.264142\pi$
$464$	4.22582	+	9.96360i	0.196179	+	0.462549i
$465$		0			0
$466$	18.1476	+	25.2126i	0.840672	+	1.16795i
$467$	−0.764809	+	0.441563i	−0.0353911	+	0.0204331i	−0.517591	−	0.855628i	$-0.673171\pi$
$467$	−0.764809	+	0.441563i	−0.0353911	+	0.0204331i	0.482200	+	0.876061i	$0.339838\pi$
$468$		0			0
$469$	−5.11202	−	11.5122i	−0.236051	−	0.531584i
$470$	−0.910449	+	2.02072i	−0.0419959	+	0.0932090i
$471$		0			0
$472$	28.8473	+	6.53421i	1.32780	+	0.300761i
$473$	−10.3281	+	17.8888i	−0.474886	+	0.822527i
$474$		0			0
$475$		−	23.0768i		−	1.05884i
$476$	17.5947	−	12.5202i	0.806450	−	0.573861i
$477$		0			0
$478$	4.03732	+	40.1245i	0.184663	+	1.83525i
$479$	−17.7492	+	30.7425i	−0.810981	+	1.40466i	0.101197	+	0.994866i	$0.467733\pi$
$479$	−17.7492	+	30.7425i	−0.810981	+	1.40466i	−0.912178	+	0.409794i	$0.865601\pi$
$480$		0			0
$481$	−21.6389	+	12.4932i	−0.986647	+	0.569641i
$482$	−11.9293	−	5.37480i	−0.543363	−	0.244816i
$483$		0			0
$484$	5.87465	+	6.64207i	0.267030	+	0.301912i
$485$	4.00768	−	2.31384i	0.181979	−	0.105066i
$486$		0			0
$487$	30.6502	+	17.6959i	1.38889	+	0.801878i	0.993191	−	0.116500i	$-0.0371675\pi$
$487$	30.6502	+	17.6959i	1.38889	+	0.801878i	0.395703	+	0.918378i	$0.370501\pi$
$488$	5.58736	+	5.16721i	0.252928	+	0.233908i
$489$		0			0
$490$	22.5314	−	30.5980i	1.01787	−	1.38228i
$491$	34.2187			1.54427			0.772134	−	0.635460i	$-0.219190\pi$
$491$	34.2187			1.54427			0.772134	+	0.635460i	$0.219190\pi$
$492$		0			0
$493$	−5.52093	+	9.56253i	−0.248650	+	0.430675i
$494$	−16.3049	+	11.7360i	−0.733590	+	0.528027i
$495$		0			0
$496$	2.83671	−	23.0467i	0.127372	−	1.03483i
$497$	−2.59840	−	1.89175i	−0.116554	−	0.0848567i
$498$		0			0
$499$	2.40315	+	4.16237i	0.107580	+	0.186333i	0.914789	−	0.403932i	$-0.132357\pi$
$499$	2.40315	+	4.16237i	0.107580	+	0.186333i	−0.807210	+	0.590265i	$0.799023\pi$
$500$	35.6118	−	7.23981i	1.59261	−	0.323774i
$501$		0			0
$502$	0.0295375	+	0.293555i	0.00131832	+	0.0131020i
$503$	−20.5529			−0.916406			−0.458203	−	0.888847i	$-0.651507\pi$
$503$	−20.5529			−0.916406			−0.458203	+	0.888847i	$0.651507\pi$
$504$		0			0
$505$	−51.7567			−2.30314
$506$	−2.73886	−	27.2199i	−0.121757	−	1.21007i
$507$		0			0
$508$	−4.17800	−	20.5511i	−0.185369	−	0.911807i
$509$	−1.83211	−	3.17332i	−0.0812070	−	0.140655i	0.822562	−	0.568676i	$-0.192544\pi$
$509$	−1.83211	−	3.17332i	−0.0812070	−	0.140655i	−0.903769	+	0.428021i	$0.859211\pi$
$510$		0			0
$511$	−18.5690	+	8.24563i	−0.821446	+	0.364765i
$512$	−14.0203	+	17.7604i	−0.619617	+	0.784904i
$513$		0			0
$514$	−22.6664	+	16.3149i	−0.999770	+	0.719619i
$515$	10.0989	−	17.4918i	0.445011	−	0.770782i
$516$		0			0
$517$	1.04624			0.0460136
$518$	−0.0845622	+	15.6030i	−0.00371545	+	0.685556i
$519$		0			0
$520$	−47.7587	−	44.1673i	−2.09436	−	1.93687i
$521$	29.0599	+	16.7777i	1.27314	+	0.735045i	0.975577	−	0.219658i	$-0.0704942\pi$
$521$	29.0599	+	16.7777i	1.27314	+	0.735045i	0.297559	+	0.954703i	$0.403828\pi$
$522$		0			0
$523$	−2.12127	+	1.22471i	−0.0927565	+	0.0535530i	−0.545661	−	0.838006i	$-0.683721\pi$
$523$	−2.12127	+	1.22471i	−0.0927565	+	0.0535530i	0.452904	+	0.891559i	$0.350388\pi$
$524$	3.35471	−	2.96711i	0.146551	−	0.129619i
$525$		0			0
$526$	20.9892	+	9.45683i	0.915174	+	0.412337i
$527$	20.5169	−	11.8454i	0.893730	−	0.515995i
$528$		0			0
$529$	16.9946	−	29.4355i	0.738896	−	1.27981i
$530$	2.77016	+	27.5309i	0.120328	+	1.19587i
$531$		0			0
$532$	1.18829	+	12.4888i	0.0515187	+	0.541456i
$533$			35.7284i			1.54757i
$534$		0			0
$535$	6.71409	−	11.6292i	0.290276	−	0.502772i
$536$	−2.97480	+	13.1332i	−0.128492	+	0.567267i
$537$		0			0
$538$	4.63637	−	10.2903i	0.199888	−	0.443647i
$539$	−17.5381	−	3.76386i	−0.755420	−	0.162121i
$540$		0			0
$541$	−25.1467	+	14.5185i	−1.08114	+	0.624197i	−0.931204	−	0.364498i	$-0.881240\pi$
$541$	−25.1467	+	14.5185i	−1.08114	+	0.624197i	−0.149937	+	0.988696i	$0.547907\pi$
$542$	10.3492	+	14.3781i	0.444535	+	0.617594i
$543$		0			0
$544$	−23.0799	−	0.512152i	−0.989544	−	0.0219583i
$545$		−	66.2960i		−	2.83981i
$546$		0			0
$547$	−19.3001			−0.825212			−0.412606	−	0.910910i	$-0.635381\pi$
$547$	−19.3001			−0.825212			−0.412606	+	0.910910i	$0.635381\pi$
$548$	3.60654	−	10.7735i	0.154064	−	0.460222i
$549$		0			0
$550$	−20.6068	−	28.6291i	−0.878675	−	1.22075i
$551$	−3.20733	−	5.55525i	−0.136637	−	0.236662i
$552$		0			0
$553$	−2.86686	+	27.0210i	−0.121911	+	1.14905i
$554$	−25.9550	−	11.6942i	−1.10272	−	0.496838i
$555$		0			0
$556$	−5.98263	−	29.4279i	−0.253720	−	1.24802i
$557$	12.1940	+	7.04023i	0.516678	+	0.298304i	0.735574	−	0.677444i	$-0.236912\pi$
$557$	12.1940	+	7.04023i	0.516678	+	0.298304i	−0.218896	+	0.975748i	$0.570246\pi$
$558$		0			0
$559$	48.2994			2.04285
$560$	−38.8625	+	11.8272i	−1.64224	+	0.499789i
$561$		0			0
$562$	−3.13298	+	0.315240i	−0.132157	+	0.0132976i
$563$	31.6170	+	18.2541i	1.33250	+	0.769319i	0.985682	−	0.168614i	$-0.0539292\pi$
$563$	31.6170	+	18.2541i	1.33250	+	0.769319i	0.346817	+	0.937933i	$0.387263\pi$
$564$		0			0
$565$	−22.4857	−	38.9463i	−0.945979	−	1.63848i
$566$	−4.31309	−	1.94329i	−0.181293	−	0.0816826i
$567$		0			0
$568$	1.01819	+	3.28169i	0.0427224	+	0.137697i
$569$	7.10756	+	12.3107i	0.297964	+	0.516089i	0.975670	−	0.219244i	$-0.0703590\pi$
$569$	7.10756	+	12.3107i	0.297964	+	0.516089i	−0.677706	+	0.735333i	$0.737026\pi$
$570$		0			0
$571$	−23.5206	+	40.7389i	−0.984307	+	1.70487i	−0.339329	+	0.940668i	$0.610200\pi$
$571$	−23.5206	+	40.7389i	−0.984307	+	1.70487i	−0.644978	+	0.764202i	$0.723133\pi$
$572$	−9.74798	+	29.1193i	−0.407583	+	1.21754i
$573$		0			0
$574$	19.2614	+	11.2602i	0.803953	+	0.469990i
$575$		−	73.4810i		−	3.06437i
$576$		0			0
$577$	24.6447	+	14.2286i	1.02597	+	0.592344i	0.915828	−	0.401572i	$-0.131536\pi$
$577$	24.6447	+	14.2286i	1.02597	+	0.592344i	0.110143	+	0.993916i	$0.464869\pi$
$578$	0.285410	+	0.396521i	0.0118715	+	0.0164931i
$579$		0			0
$580$	15.5588	−	13.7611i	0.646042	−	0.571399i
$581$	−9.61341	−	6.99899i	−0.398831	−	0.290367i
$582$		0			0
$583$	11.3118	−	6.53085i	0.468485	−	0.270480i
$584$	21.1837	+	4.79832i	0.876586	+	0.198556i
$585$		0			0
$586$	−13.9098	+	1.39961i	−0.574611	+	0.0578173i
$587$			43.1297i			1.78015i	0.455809	+	0.890077i	$0.349350\pi$
$587$			43.1297i			1.78015i	−0.455809	+	0.890077i	$0.650650\pi$
$588$		0			0
$589$			13.7630i			0.567093i
$590$	−5.68319	−	56.4818i	−0.233973	−	2.32532i
$591$		0			0
$592$	10.0425	−	13.3187i	0.412746	−	0.547395i
$593$	−24.3679	+	14.0688i	−1.00067	+	0.577736i	−0.908446	−	0.418002i	$-0.862730\pi$
$593$	−24.3679	+	14.0688i	−1.00067	+	0.577736i	−0.0922223	+	0.995738i	$0.529397\pi$
$594$		0			0
$595$	−33.5057	−	24.3936i	−1.37360	−	1.00004i
$596$	−5.02253	+	4.44224i	−0.205731	+	0.181961i
$597$		0			0
$598$	−51.9178	+	37.3696i	−2.12308	+	1.52816i
$599$	−24.3740	−	14.0724i	−0.995896	−	0.574981i	−0.0888644	−	0.996044i	$-0.528324\pi$
$599$	−24.3740	−	14.0724i	−0.995896	−	0.574981i	−0.907031	+	0.421063i	$0.861657\pi$
$600$		0			0
$601$			43.5777i			1.77757i	0.458322	+	0.888786i	$0.348451\pi$
$601$			43.5777i			1.77757i	−0.458322	+	0.888786i	$0.651549\pi$
$602$	15.2221	−	26.0384i	0.620405	−	1.06125i
$603$		0			0
$604$	13.9665	+	4.67544i	0.568291	+	0.190241i
$605$	8.50915	−	14.7383i	0.345946	−	0.599196i
$606$		0			0
$607$	−6.20364	−	10.7450i	−0.251798	−	0.436127i	0.712223	−	0.701953i	$-0.247688\pi$
$607$	−6.20364	−	10.7450i	−0.251798	−	0.436127i	−0.964021	+	0.265827i	$0.914355\pi$
$608$	6.96169	−	11.4629i	0.282334	−	0.464884i
$609$		0			0
$610$	6.00000	−	13.3169i	0.242933	−	0.539184i
$611$	−1.22319	−	2.11862i	−0.0494848	−	0.0857102i
$612$		0			0
$613$	−20.8762	−	12.0529i	−0.843180	−	0.486810i	0.0151637	−	0.999885i	$-0.495173\pi$
$613$	−20.8762	−	12.0529i	−0.843180	−	0.486810i	−0.858344	+	0.513075i	$0.828506\pi$
$614$	−0.507310	−	5.04184i	−0.0204734	−	0.203472i
$615$		0			0
$616$	12.6262	+	14.4324i	0.508724	+	0.581500i
$617$	28.0014			1.12729			0.563647	−	0.826016i	$-0.309398\pi$
$617$	28.0014			1.12729			0.563647	+	0.826016i	$0.309398\pi$
$618$		0			0
$619$	−13.1414	−	7.58717i	−0.528196	−	0.304954i	0.212086	−	0.977251i	$-0.431974\pi$
$619$	−13.1414	−	7.58717i	−0.528196	−	0.304954i	−0.740281	+	0.672297i	$0.765308\pi$
$620$	−43.6723	+	8.87850i	−1.75392	+	0.356569i
$621$		0			0
$622$	−15.2933	+	33.9432i	−0.613206	+	1.36100i
$623$	1.08198	−	10.1980i	0.0433488	−	0.408575i
$624$		0			0
$625$	−10.5383	−	18.2528i	−0.421531	−	0.730114i
$626$	−17.9673	+	12.9326i	−0.718117	+	0.516890i
$627$		0			0
$628$	−5.75488	+	17.1911i	−0.229645	+	0.685999i
$629$	17.0183			0.678564
$630$		0			0
$631$		−	37.1814i		−	1.48017i	−0.672515	−	0.740084i	$-0.734786\pi$
$631$		−	37.1814i		−	1.48017i	0.672515	−	0.740084i	$-0.265214\pi$
$632$	19.7231	−	21.3268i	0.784541	−	0.848334i
$633$		0			0
$634$	−18.3676	+	13.2207i	−0.729472	+	0.525062i
$635$	−34.8567	+	20.1245i	−1.38324	+	0.798616i
$636$		0			0
$637$	12.8825	+	39.9148i	0.510422	+	1.58148i
$638$	−8.93964	−	4.02781i	−0.353924	−	0.159463i
$639$		0			0
$640$	40.8650	+	14.6959i	1.61533	+	0.580907i
$641$	7.27131	−	12.5943i	0.287200	−	0.497444i	−0.685941	−	0.727658i	$-0.740609\pi$
$641$	7.27131	−	12.5943i	0.287200	−	0.497444i	0.973140	+	0.230213i	$0.0739423\pi$
$642$		0			0
$643$			22.1025i			0.871639i	0.900034	+	0.435820i	$0.143541\pi$
$643$			22.1025i			0.871639i	−0.900034	+	0.435820i	$0.856459\pi$
$644$	3.78373	+	39.7666i	0.149100	+	1.56702i
$645$		0			0
$646$	13.6142	−	1.36986i	0.535642	−	0.0538963i
$647$	3.21337	−	5.56572i	0.126331	−	0.218811i	−0.795922	−	0.605400i	$-0.793013\pi$
$647$	3.21337	−	5.56572i	0.126331	−	0.218811i	0.922252	+	0.386589i	$0.126347\pi$
$648$		0			0
$649$	−23.2069	+	13.3985i	−0.910952	+	0.525938i
$650$	−33.8815	+	75.1994i	−1.32894	+	2.94956i
$651$		0			0
$652$	−25.7947	−	29.1643i	−1.01020	−	1.14216i
$653$	−27.9561	+	16.1405i	−1.09401	+	0.631626i	−0.934641	−	0.355593i	$-0.884279\pi$
$653$	−27.9561	+	16.1405i	−1.09401	+	0.631626i	−0.159367	+	0.987219i	$0.550945\pi$
$654$		0			0
$655$	−7.44387	−	4.29772i	−0.290856	−	0.167926i
$656$	−9.31311	−	21.9584i	−0.363616	−	0.857331i
$657$		0			0
$658$	−1.52766	−	0.00827933i	−0.0595543	−	0.000322762i
$659$	15.9496			0.621310			0.310655	−	0.950523i	$-0.399452\pi$
$659$	15.9496			0.621310			0.310655	+	0.950523i	$0.399452\pi$
$660$		0			0
$661$	1.77351	−	3.07180i	0.0689814	−	0.119479i	−0.829472	−	0.558549i	$-0.811358\pi$
$661$	1.77351	−	3.07180i	0.0689814	−	0.119479i	0.898453	+	0.439069i	$0.144692\pi$
$662$	−13.4448	−	18.6790i	−0.522548	−	0.725979i
$663$		0			0
$664$	3.76704	+	12.1414i	0.146190	+	0.471177i
$665$	22.0050	−	9.77139i	0.853319	−	0.378918i
$666$		0			0
$667$	−10.2127	−	17.6890i	−0.395439	−	0.684920i
$668$	−34.2159	+	6.95604i	−1.32385	+	0.269137i
$669$		0			0
$670$	25.7142	−	2.58736i	0.993427	−	0.0999585i
$671$	−6.89488			−0.266174
$672$		0			0
$673$	9.86727			0.380355			0.190178	−	0.981750i	$-0.439094\pi$
$673$	9.86727			0.380355			0.190178	+	0.981750i	$0.439094\pi$
$674$	8.31976	−	0.837134i	0.320465	−	0.0322452i
$675$		0			0
$676$	44.8840	−	9.12483i	1.72631	−	0.350955i
$677$	−17.1703	−	29.7398i	−0.659906	−	1.14299i	−0.980639	−	0.195822i	$-0.937263\pi$
$677$	−17.1703	−	29.7398i	−0.659906	−	1.14299i	0.320733	−	0.947170i	$-0.396071\pi$
$678$		0			0
$679$	2.57871	+	1.87742i	0.0989619	+	0.0720486i
$680$	13.1293	+	42.3165i	0.503486	+	1.62276i
$681$		0			0
$682$	12.2898	+	17.0743i	0.470602	+	0.653809i
$683$	20.2559	−	35.0842i	0.775070	−	1.34246i	−0.159686	−	0.987168i	$-0.551048\pi$
$683$	20.2559	−	35.0842i	0.775070	−	1.34246i	0.934755	−	0.355292i	$-0.115619\pi$
$684$		0			0
$685$	−21.8046			−0.833112
$686$	25.5783	+	5.63456i	0.976586	+	0.215129i
$687$		0			0
$688$	−29.6844	+	12.5899i	−1.13171	+	0.479986i
$689$	−26.4497	−	15.2708i	−1.00765	−	0.581770i
$690$		0			0
$691$	35.0416	−	20.2313i	1.33304	−	0.769634i	0.347279	−	0.937762i	$-0.387106\pi$
$691$	35.0416	−	20.2313i	1.33304	−	0.769634i	0.985765	+	0.168128i	$0.0537722\pi$
$692$	−4.68334	−	5.29514i	−0.178034	−	0.201291i
$693$		0			0
$694$	16.9238	−	37.5619i	0.642417	−	1.42583i
$695$	−49.9125	+	28.8170i	−1.89329	+	1.09309i
$696$		0			0
$697$	12.1673	−	21.0745i	0.460871	−	0.798252i
$698$	15.8732	−	1.59716i	0.600808	−	0.0604532i
$699$		0			0
$700$	29.8622	+	41.9656i	1.12869	+	1.58615i
$701$			26.0983i			0.985718i	0.870109	+	0.492859i	$0.164048\pi$
$701$			26.0983i			0.985718i	−0.870109	+	0.492859i	$0.835952\pi$
$702$		0			0
$703$	−4.94330	+	8.56205i	−0.186440	+	0.322924i
$704$	−1.59933	−	20.4374i	−0.0602770	−	0.770265i
$705$		0			0
$706$	35.8415	+	16.1486i	1.34891	+	0.607761i
$707$	−14.4782	−	32.6047i	−0.544508	−	1.22622i
$708$		0			0
$709$	−3.75011	+	2.16513i	−0.140838	+	0.0813131i	−0.568764	−	0.822501i	$-0.692578\pi$
$709$	−3.75011	+	2.16513i	−0.140838	+	0.0813131i	0.427925	+	0.903814i	$0.359245\pi$
$710$	5.35220	−	3.85243i	0.200865	−	0.144579i
$711$		0			0
$712$	−7.44370	+	8.04897i	−0.278965	+	0.301648i
$713$			43.8239i			1.64122i
$714$		0			0
$715$	58.9348			2.20404
$716$	5.96305	−	17.8129i	0.222850	−	0.665700i
$717$		0			0
$718$	−3.70974	+	2.67022i	−0.138446	+	0.0996516i
$719$	−2.88615	−	4.99895i	−0.107635	−	0.186429i	0.807177	−	0.590310i	$-0.200994\pi$
$719$	−2.88615	−	4.99895i	−0.107635	−	0.186429i	−0.914812	+	0.403880i	$0.867661\pi$
$720$		0			0
$721$	13.8442	+	1.46883i	0.515583	+	0.0547021i
$722$	7.77253	−	17.2510i	0.289264	−	0.642015i
$723$		0			0
$724$	−0.181188	+	0.0368351i	−0.00673379	+	0.00136897i
$725$	−22.8079	−	13.1681i	−0.847063	−	0.489052i
$726$		0			0
$727$	−23.4056			−0.868066			−0.434033	−	0.900897i	$-0.642910\pi$
$727$	−23.4056			−0.868066			−0.434033	+	0.900897i	$0.642910\pi$
$728$	14.4639	−	42.4412i	0.536067	−	1.57298i
$729$		0			0
$730$	−4.17339	−	41.4767i	−0.154464	−	1.53512i
$731$	−28.4895	−	16.4484i	−1.05372	−	0.608367i
$732$		0			0
$733$	14.5792	+	25.2520i	0.538496	+	0.932703i	0.998985	+	0.0450374i	$0.0143407\pi$
$733$	14.5792	+	25.2520i	0.538496	+	0.932703i	−0.460489	+	0.887665i	$0.652326\pi$
$734$	−0.162101	+	0.359780i	−0.00598326	+	0.0132797i
$735$		0			0
$736$	22.1673	−	36.5002i	0.817099	−	1.34542i
$737$	−6.09989	−	10.5653i	−0.224692	−	0.389179i
$738$		0			0
$739$	1.59685	−	2.76583i	0.0587412	−	0.101743i	−0.835159	−	0.550008i	$-0.814625\pi$
$739$	1.59685	−	2.76583i	0.0587412	−	0.101743i	0.893901	+	0.448265i	$0.147958\pi$
$740$	−30.3579	−	10.1626i	−1.11598	−	0.373584i
$741$		0			0
$742$	−16.5685	+	9.44645i	−0.608247	+	0.346790i
$743$			38.2187i			1.40211i	0.713108	+	0.701054i	$0.247287\pi$
$743$			38.2187i			1.40211i	−0.713108	+	0.701054i	$0.752713\pi$
$744$		0			0
$745$	11.1447	+	6.43437i	0.408309	+	0.235737i
$746$	−35.7761	+	25.7511i	−1.30986	+	0.942815i
$747$		0			0
$748$	15.6665	−	13.8564i	0.572824	−	0.506640i
$749$	9.20406	+	0.976527i	0.336309	+	0.0356815i
$750$		0			0
$751$	−11.9634	+	6.90707i	−0.436551	+	0.252043i	−0.702133	−	0.712045i	$-0.747769\pi$
$751$	−11.9634	+	6.90707i	−0.436551	+	0.252043i	0.265583	+	0.964088i	$0.414436\pi$
$752$	1.30401	+	0.983246i	0.0475523	+	0.0358553i
$753$		0			0
$754$	2.29531	+	22.8117i	0.0835902	+	0.830752i
$755$		−	28.2670i		−	1.02874i
$756$		0			0
$757$		−	35.8711i		−	1.30376i	−0.758324	−	0.651878i	$-0.773981\pi$
$757$		−	35.8711i		−	1.30376i	0.758324	−	0.651878i	$-0.226019\pi$
$758$	−33.7925	+	3.40020i	−1.22740	+	0.123501i
$759$		0			0
$760$	−25.1035	−	5.68619i	−0.910598	−	0.206260i
$761$	−30.6897	+	17.7187i	−1.11250	+	0.642302i	−0.939476	−	0.342616i	$-0.888687\pi$
$761$	−30.6897	+	17.7187i	−1.11250	+	0.642302i	−0.173024	+	0.984918i	$0.555354\pi$
$762$		0			0
$763$	41.7638	−	18.5453i	1.51195	−	0.671386i
$764$	1.26433	−	1.11825i	0.0457418	−	0.0404568i
$765$		0			0
$766$	−12.2036	−	16.9545i	−0.440933	−	0.612591i
$767$	54.2636	+	31.3291i	1.95935	+	1.13123i
$768$		0			0
$769$		−	27.3235i		−	0.985311i	−0.870225	−	0.492655i	$-0.836026\pi$
$769$		−	27.3235i		−	0.985311i	0.870225	−	0.492655i	$-0.163974\pi$
$770$	18.5739	−	31.7721i	0.669358	−	1.14499i
$771$		0			0
$772$	−11.1453	+	33.2935i	−0.401130	+	1.19826i
$773$	−20.6653	+	35.7933i	−0.743278	+	1.28739i	0.207718	+	0.978189i	$0.433396\pi$
$773$	−20.6653	+	35.7933i	−0.743278	+	1.28739i	−0.950995	+	0.309206i	$0.899937\pi$
$774$		0			0
$775$	28.2529	+	48.9354i	1.01487	+	1.75781i
$776$	−1.01048	−	3.25682i	−0.0362740	−	0.116913i
$777$		0			0
$778$	−2.42914	−	1.09446i	−0.0870887	−	0.0392384i
$779$	7.06849	+	12.2430i	0.253255	+	0.438651i
$780$		0			0
$781$	−2.69590	−	1.55648i	−0.0964668	−	0.0556951i
$782$	43.3501	−	4.36189i	1.55020	−	0.155981i
$783$		0			0
$784$	−18.3218	−	21.1733i	−0.654351	−	0.756191i
$785$	34.7932			1.24182
$786$		0			0
$787$	−34.1512	−	19.7172i	−1.21736	−	0.702843i	−0.253008	−	0.967464i	$-0.581420\pi$
$787$	−34.1512	−	19.7172i	−1.21736	−	0.702843i	−0.964353	+	0.264621i	$0.914753\pi$
$788$	3.15708	+	15.5293i	0.112466	+	0.553208i
$789$		0			0
$790$	−50.8301	−	22.9018i	−1.80845	−	0.814810i
$791$	18.2446	−	25.0597i	0.648703	−	0.891021i
$792$		0			0
$793$	8.06098	+	13.9620i	0.286254	+	0.495806i
$794$	−4.13627	−	5.74655i	−0.146791	−	0.203937i
$795$		0			0
$796$	11.4710	−	34.2663i	0.406579	−	1.21454i
$797$	2.23985			0.0793395			0.0396697	−	0.999213i	$-0.487369\pi$
$797$	2.23985			0.0793395			0.0396697	+	0.999213i	$0.487369\pi$
$798$		0			0
$799$			1.66623i			0.0589470i
$800$	1.22155	−	55.0486i	0.0431882	−	1.94626i
$801$		0			0
$802$	22.2124	+	30.8598i	0.784348	+	1.08970i
$803$	−17.0417	+	9.83905i	−0.601390	+	0.347213i
$804$		0			0
$805$	70.0683	−	31.1140i	2.46958	−	1.09662i
$806$	20.2069	−	44.8487i	0.711757	−	1.57973i
$807$		0			0
$808$	−8.42518	+	37.1955i	−0.296397	+	1.30853i
$809$	−2.10727	+	3.64989i	−0.0740876	+	0.128323i	−0.900689	−	0.434464i	$-0.856938\pi$
$809$	−2.10727	+	3.64989i	−0.0740876	+	0.128323i	0.826602	+	0.562788i	$0.190271\pi$
$810$		0			0
$811$			19.7835i			0.694694i	0.937737	+	0.347347i	$0.112917\pi$
$811$			19.7835i			0.694694i	−0.937737	+	0.347347i	$0.887083\pi$
$812$	13.0213	+	5.95192i	0.456957	+	0.208871i
$813$		0			0
$814$	1.51295	+	15.0363i	0.0530288	+	0.527021i
$815$	−37.3624	+	64.7135i	−1.30875	+	2.26682i
$816$		0			0
$817$	16.5507	−	9.55554i	0.579035	−	0.334306i
$818$	−33.4819	−	15.0855i	−1.17067	−	0.527451i
$819$		0			0
$820$	−34.2893	+	30.3276i	−1.19743	+	1.05908i
$821$	21.2969	−	12.2958i	0.743268	−	0.429126i	−0.0799882	−	0.996796i	$-0.525488\pi$
$821$	21.2969	−	12.2958i	0.743268	−	0.429126i	0.823256	+	0.567670i	$0.192155\pi$
$822$		0			0
$823$	−5.30737	−	3.06421i	−0.185003	−	0.106812i	0.404638	−	0.914477i	$-0.367398\pi$
$823$	−5.30737	−	3.06421i	−0.185003	−	0.106812i	−0.589641	+	0.807665i	$0.700731\pi$
$824$	−10.9267	−	10.1051i	−0.380651	−	0.352027i
$825$		0			0
$826$	33.9915	−	19.3801i	1.18271	−	0.674320i
$827$	−41.0673			−1.42805			−0.714026	−	0.700119i	$-0.753130\pi$
$827$	−41.0673			−1.42805			−0.714026	+	0.700119i	$0.753130\pi$
$828$		0			0
$829$	−8.14363	+	14.1052i	−0.282840	+	0.489893i	−0.972083	−	0.234637i	$-0.924610\pi$
$829$	−8.14363	+	14.1052i	−0.282840	+	0.489893i	0.689243	+	0.724530i	$0.257943\pi$
$830$	19.8017	−	14.2530i	0.687328	−	0.494728i
$831$		0			0
$832$	−39.5157	+	27.1326i	−1.36996	+	0.940652i
$833$	5.99429	−	27.9310i	0.207690	−	0.967752i
$834$		0			0
$835$	33.5057	+	58.0336i	1.15951	+	2.00834i
$836$	2.42063	+	11.9068i	0.0837193	+	0.411806i
$837$		0			0
$838$	−4.80890	−	47.7927i	−0.166121	−	1.65097i
$839$	−40.4513			−1.39653			−0.698266	−	0.715838i	$-0.746045\pi$
$839$	−40.4513			−1.39653			−0.698266	+	0.715838i	$0.746045\pi$
$840$		0			0
$841$	21.6793			0.747563
$842$	0.390580	+	3.88174i	0.0134603	+	0.133774i
$843$		0			0
$844$	−1.37179	+	0.278883i	−0.0472190	+	0.00959954i
$845$	−43.9523	−	76.1276i	−1.51201	−	2.61887i
$846$		0			0
$847$	11.6648	+	1.23761i	0.400808	+	0.0425247i
$848$	20.2363	+	2.49079i	0.694919	+	0.0855342i
$849$		0			0
$850$	45.5943	−	32.8181i	1.56387	−	1.12565i
$851$	−15.7404	+	27.2632i	−0.539575	+	0.934571i
$852$		0			0
$853$	38.0308			1.30215			0.651075	−	0.759013i	$-0.274318\pi$
$853$	38.0308			1.30215			0.651075	+	0.759013i	$0.274318\pi$
$854$	10.0675	+	0.0545620i	0.344503	+	0.00186707i
$855$		0			0
$856$	−7.26447	−	6.71820i	−0.248295	−	0.229623i
$857$	34.7732	+	20.0763i	1.18783	+	0.685794i	0.957813	−	0.287393i	$-0.0927884\pi$
$857$	34.7732	+	20.0763i	1.18783	+	0.685794i	0.230017	+	0.973187i	$0.426122\pi$
$858$		0			0
$859$	−25.6875	+	14.8307i	−0.876446	+	0.506016i	−0.869485	−	0.493960i	$-0.835549\pi$
$859$	−25.6875	+	14.8307i	−0.876446	+	0.506016i	−0.00696080	+	0.999976i	$0.502216\pi$
$860$	40.9983	+	46.3540i	1.39803	+	1.58066i
$861$		0			0
$862$	−46.6776	−	21.0309i	−1.58984	−	0.716314i
$863$	−8.93311	+	5.15753i	−0.304087	+	0.175564i	−0.644277	−	0.764792i	$-0.722842\pi$
$863$	−8.93311	+	5.15753i	−0.304087	+	0.175564i	0.340191	+	0.940356i	$0.389508\pi$
$864$		0			0
$865$	−6.78360	+	11.7495i	−0.230649	+	0.399496i
$866$	2.86632	+	28.4866i	0.0974015	+	0.968014i
$867$		0			0
$868$	−17.8098	−	25.0282i	−0.604503	−	0.849512i
$869$			26.3175i			0.892761i
$870$		0			0
$871$	−14.2631	+	24.7044i	−0.483286	+	0.837076i
$872$	−47.6444	−	10.7919i	−1.61344	−	0.365461i
$873$		0			0
$874$	−10.3974	+	23.0768i	−0.351697	+	0.780585i
$875$	28.2952	−	38.8646i	0.956551	−	1.31386i
$876$		0			0
$877$	−2.25040	+	1.29927i	−0.0759907	+	0.0438733i	−0.537514	−	0.843255i	$-0.680636\pi$
$877$	−2.25040	+	1.29927i	−0.0759907	+	0.0438733i	0.461523	+	0.887128i	$0.347303\pi$
$878$	24.1899	+	33.6071i	0.816369	+	1.13418i
$879$		0			0
$880$	−36.2209	+	15.3622i	−1.22101	+	0.517860i
$881$			16.6411i			0.560654i	0.959905	+	0.280327i	$0.0904428\pi$
$881$			16.6411i			0.560654i	−0.959905	+	0.280327i	$0.909557\pi$
$882$		0			0
$883$	−7.02636			−0.236456			−0.118228	−	0.992986i	$-0.537721\pi$
$883$	−7.02636			−0.236456			−0.118228	+	0.992986i	$0.537721\pi$
$884$	−46.3751	−	15.5245i	−1.55976	−	0.522146i
$885$		0			0
$886$	19.2629	+	26.7620i	0.647149	+	0.899087i
$887$	19.9044	+	34.4755i	0.668326	+	1.15757i	0.978372	+	0.206853i	$0.0663222\pi$
$887$	19.9044	+	34.4755i	0.668326	+	1.15757i	−0.310046	+	0.950722i	$0.600344\pi$
$888$		0			0
$889$	−22.4283	−	16.3288i	−0.752220	−	0.547649i
$890$	19.1838	+	8.64340i	0.643044	+	0.289727i
$891$		0			0
$892$	4.94028	−	1.00435i	0.165413	−	0.0336281i
$893$	−0.838295	−	0.483990i	−0.0280525	−	0.0161961i
$894$		0			0
$895$	−36.0517			−1.20508
$896$	2.17352	+	29.8542i	0.0726122	+	0.997360i
$897$		0			0
$898$	39.1753	−	3.94182i	1.30730	−	0.131540i
$899$	13.6026	+	7.85345i	0.453671	+	0.261927i
$900$		0			0
$901$	10.4010	+	18.0150i	0.346506	+	0.600166i
$902$	19.7017	+	8.87673i	0.655995	+	0.295563i
$903$		0			0
$904$	−31.6495	+	9.81973i	−1.05265	+	0.326599i
$905$	0.177427	+	0.307312i	0.00589786	+	0.0102154i
$906$		0			0
$907$	4.67603	−	8.09911i	0.155265	−	0.268927i	−0.777891	−	0.628400i	$-0.783710\pi$
$907$	4.67603	−	8.09911i	0.155265	−	0.268927i	0.933155	+	0.359473i	$0.117044\pi$
$908$	−15.7689	−	5.27879i	−0.523308	−	0.175183i
$909$		0			0
$910$	−86.0533	−	0.466376i	−2.85264	−	0.0154602i
$911$		−	23.5328i		−	0.779678i	−0.920883	−	0.389839i	$-0.872531\pi$
$911$		−	23.5328i		−	0.779678i	0.920883	−	0.389839i	$-0.127469\pi$
$912$		0			0
$913$	−9.97411	−	5.75855i	−0.330095	−	0.190580i
$914$	15.7980	+	21.9482i	0.522550	+	0.725981i
$915$		0			0
$916$	−6.93647	−	7.84259i	−0.229187	−	0.259127i
$917$	0.625080	−	5.89156i	0.0206420	−	0.194557i
$918$		0			0
$919$	−11.5743	+	6.68240i	−0.381799	+	0.220432i	−0.678601	−	0.734507i	$-0.737413\pi$
$919$	−11.5743	+	6.68240i	−0.381799	+	0.220432i	0.296801	+	0.954939i	$0.404080\pi$
$920$	−79.9342	−	18.1059i	−2.63535	−	0.596935i
$921$		0			0
$922$	−28.9201	+	2.90994i	−0.952433	+	0.0958337i
$923$			7.27887i			0.239587i
$924$		0			0
$925$			40.5909i			1.33462i
$926$	4.49551	+	44.6781i	0.147732	+	1.46821i
$927$		0			0
$928$	−7.35686	−	13.4216i	−0.241501	−	0.440584i
$929$	−31.1417	+	17.9797i	−1.02173	+	0.589895i	−0.914604	−	0.404351i	$-0.867497\pi$
$929$	−31.1417	+	17.9797i	−1.02173	+	0.589895i	−0.107123	+	0.994246i	$0.534164\pi$
$930$		0			0
$931$	12.3112	+	11.1289i	0.403482	+	0.364735i
$932$	−29.1053	−	32.9074i	−0.953377	−	1.07792i
$933$		0			0
$934$	1.01365	−	0.729610i	0.0331677	−	0.0238736i
$935$	−34.7629	−	20.0703i	−1.13687	−	0.656370i
$936$		0			0
$937$		−	52.0867i		−	1.70160i	−0.525491	−	0.850799i	$-0.676118\pi$
$937$		−	52.0867i		−	1.70160i	0.525491	−	0.850799i	$-0.323882\pi$
$938$	8.82310	+	15.4751i	0.288084	+	0.505281i
$939$		0			0
$940$	0.995001	−	2.97228i	0.0324533	−	0.0969451i
$941$	19.6811	−	34.0886i	0.641584	−	1.11126i	−0.343495	−	0.939154i	$-0.611611\pi$
$941$	19.6811	−	34.0886i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550558\pi$
$942$		0			0
$943$	22.5074	+	38.9840i	0.732943	+	1.26949i
$944$	−41.5164	−	5.11005i	−1.35124	−	0.166318i
$945$		0			0
$946$	12.0000	−	26.6337i	0.390154	−	0.865938i
$947$	−19.5007	−	33.7762i	−0.633688	−	1.09758i	−0.986792	−	0.161995i	$-0.948207\pi$
$947$	−19.5007	−	33.7762i	−0.633688	−	1.09758i	0.353104	−	0.935584i	$-0.385126\pi$
$948$		0			0
$949$	39.8479	+	23.0062i	1.29352	+	0.746812i
$950$	3.26729	+	32.4716i	0.106005	+	1.05352i
$951$		0			0
$952$	−22.9850	+	20.1084i	−0.744947	+	0.651715i
$953$	48.3027			1.56468			0.782340	−	0.622852i	$-0.214026\pi$
$953$	48.3027			1.56468			0.782340	+	0.622852i	$0.214026\pi$
$954$		0			0
$955$	−2.80546	−	1.61973i	−0.0907824	−	0.0524133i
$956$	−11.3619	−	55.8879i	−0.367470	−	1.80754i
$957$		0			0
$958$	20.6224	−	45.7710i	0.666280	−	1.47879i
$959$	−6.09952	−	13.7360i	−0.196964	−	0.443560i
$960$		0			0
$961$	−1.34996	−	2.33821i	−0.0435472	−	0.0754260i
$962$	28.6794	−	20.6430i	0.924660	−	0.665556i
$963$		0			0
$964$	17.5467	+	5.87395i	0.565143	+	0.189187i
$965$	67.3831			2.16914
$966$		0			0
$967$			17.5292i			0.563703i	0.959458	+	0.281851i	$0.0909485\pi$
$967$			17.5292i			0.563703i	−0.959458	+	0.281851i	$0.909052\pi$
$968$	−9.20668	−	8.51436i	−0.295914	−	0.273662i
$969$		0			0
$970$	−5.31164	+	3.82324i	−0.170546	+	0.122757i
$971$	−9.98701	+	5.76600i	−0.320498	+	0.185040i	−0.651615	−	0.758550i	$-0.725908\pi$
$971$	−9.98701	+	5.76600i	−0.320498	+	0.185040i	0.331116	+	0.943590i	$0.392575\pi$
$972$		0			0
$973$	−32.1158	−	23.3817i	−1.02959	−	0.749584i
$974$	−45.6336	−	20.5605i	−1.46220	−	0.658801i
$975$		0			0
$976$	−8.59361	−	6.47974i	−0.275075	−	0.207412i
$977$	19.8176	−	34.3250i	0.634020	−	1.09816i	−0.352702	−	0.935736i	$-0.614737\pi$
$977$	19.8176	−	34.3250i	0.634020	−	1.09816i	0.986722	−	0.162419i	$-0.0519297\pi$
$978$		0			0
$979$		−	9.93253i		−	0.317445i
$980$	−27.3720	+	46.2448i	−0.874367	+	1.47724i
$981$		0			0
$982$	−48.1494	+	4.84479i	−1.53651	+	0.154603i
$983$	29.0730	−	50.3560i	0.927286	−	1.60611i	0.139443	−	0.990230i	$-0.455469\pi$
$983$	29.0730	−	50.3560i	0.927286	−	1.60611i	0.787843	−	0.615876i	$-0.211198\pi$
$984$		0			0
$985$	26.3392	−	15.2069i	0.839237	−	0.484533i
$986$	6.41465	−	14.2372i	0.204284	−	0.453404i
$987$		0			0
$988$	21.2811	−	18.8223i	0.677042	−	0.598817i
$989$	52.7005	−	30.4267i	1.67578	−	0.967511i
$990$		0			0
$991$	−9.48813	−	5.47798i	−0.301400	−	0.174014i	0.341671	−	0.939819i	$-0.389007\pi$
$991$	−9.48813	−	5.47798i	−0.301400	−	0.174014i	−0.643072	+	0.765806i	$0.722340\pi$
$992$	−0.728529	+	32.8309i	−0.0231308	+	1.04238i
$993$		0			0
$994$	3.92408	+	2.29401i	0.124464	+	0.0727616i
$995$	−69.3520			−2.19861
$996$		0			0
$997$	13.5416	−	23.4547i	0.428866	−	0.742818i	−0.567907	−	0.823093i	$-0.692247\pi$
$997$	13.5416	−	23.4547i	0.428866	−	0.742818i	0.996773	+	0.0802751i	$0.0255799\pi$
$998$	−3.97081	−	5.51667i	−0.125694	−	0.174627i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.b.451.1	yes	32
3.2	odd	2	inner	504.2.bk.b.451.16	yes	32
4.3	odd	2		2016.2.bs.b.1711.2		32
7.5	odd	6	inner	504.2.bk.b.19.12	yes	32
8.3	odd	2	inner	504.2.bk.b.451.12	yes	32
8.5	even	2		2016.2.bs.b.1711.16		32
12.11	even	2		2016.2.bs.b.1711.15		32
21.5	even	6	inner	504.2.bk.b.19.5	yes	32
24.5	odd	2		2016.2.bs.b.1711.1		32
24.11	even	2	inner	504.2.bk.b.451.5	yes	32
28.19	even	6		2016.2.bs.b.271.16		32
56.5	odd	6		2016.2.bs.b.271.2		32
56.19	even	6	inner	504.2.bk.b.19.1	✓	32
84.47	odd	6		2016.2.bs.b.271.1		32
168.5	even	6		2016.2.bs.b.271.15		32
168.131	odd	6	inner	504.2.bk.b.19.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bk.b.19.1	✓	32	56.19	even	6	inner
504.2.bk.b.19.5	yes	32	21.5	even	6	inner
504.2.bk.b.19.12	yes	32	7.5	odd	6	inner
504.2.bk.b.19.16	yes	32	168.131	odd	6	inner
504.2.bk.b.451.1	yes	32	1.1	even	1	trivial
504.2.bk.b.451.5	yes	32	24.11	even	2	inner
504.2.bk.b.451.12	yes	32	8.3	odd	2	inner
504.2.bk.b.451.16	yes	32	3.2	odd	2	inner
2016.2.bs.b.271.1		32	84.47	odd	6
2016.2.bs.b.271.2		32	56.5	odd	6
2016.2.bs.b.271.15		32	168.5	even	6
2016.2.bs.b.271.16		32	28.19	even	6
2016.2.bs.b.1711.1		32	24.5	odd	2
2016.2.bs.b.1711.2		32	4.3	odd	2
2016.2.bs.b.1711.15		32	12.11	even	2
2016.2.bs.b.1711.16		32	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40711 + 0.141583i) q^{2} +(1.95991 - 0.398446i) q^{4} +(-1.91923 - 3.32420i) q^{5} +(1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +O(q^{10})\)	\(q+(-1.40711 + 0.141583i) q^{2} +(1.95991 - 0.398446i) q^{4} +(-1.91923 - 3.32420i) q^{5} +(1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +(3.17121 + 4.40578i) q^{10} +(1.28125 - 2.21918i) q^{11} -5.99175 q^{13} +(-1.88836 + 3.23018i) q^{14} +(3.68248 - 1.56183i) q^{16} +(3.53425 + 2.04050i) q^{17} +(-2.05318 + 1.18541i) q^{19} +(-5.08602 - 5.75041i) q^{20} +(-1.48865 + 3.30403i) q^{22} +(-6.53773 + 3.77456i) q^{23} +(-4.86686 + 8.42964i) q^{25} +(8.43104 - 0.848331i) q^{26} +(2.19979 - 4.81258i) q^{28} +2.70568i q^{29} +(2.90258 - 5.02742i) q^{31} +(-4.96052 + 2.71905i) q^{32} +(-5.26197 - 2.37081i) q^{34} +(-10.0989 - 1.07147i) q^{35} +(3.61144 - 2.08507i) q^{37} +(2.72122 - 1.95869i) q^{38} +(7.97074 + 7.37136i) q^{40} -5.96293i q^{41} -8.06098 q^{43} +(1.62690 - 4.85990i) q^{44} +(8.66488 - 6.23685i) q^{46} +(0.204145 + 0.353590i) q^{47} +(-2.15004 - 6.66163i) q^{49} +(5.65470 - 12.5505i) q^{50} +(-11.7433 + 2.38739i) q^{52} +(4.41436 + 2.54863i) q^{53} -9.83600 q^{55} +(-2.41396 + 7.08327i) q^{56} +(-0.383078 - 3.80718i) q^{58} +(-9.05639 - 5.22871i) q^{59} +(-1.34535 - 2.33021i) q^{61} +(-3.37245 + 7.48508i) q^{62} +(6.59502 - 4.52832i) q^{64} +(11.4995 + 19.9178i) q^{65} +(2.38045 - 4.12307i) q^{67} +(7.73983 + 2.59098i) q^{68} +(14.3620 + 0.0778363i) q^{70} -1.21482i q^{71} +(-6.65046 - 3.83964i) q^{73} +(-4.78648 + 3.44523i) q^{74} +(-3.55173 + 3.14137i) q^{76} +(-2.75147 - 6.19628i) q^{77} +(-8.89433 + 5.13514i) q^{79} +(-12.2594 - 9.24378i) q^{80} +(0.844250 + 8.39049i) q^{82} -4.49449i q^{83} -15.6647i q^{85} +(11.3427 - 1.14130i) q^{86} +(-1.60115 + 7.06875i) q^{88} +(3.35682 - 1.93806i) q^{89} +(-9.33056 + 12.8159i) q^{91} +(-11.3094 + 10.0027i) q^{92} +(-0.337316 - 0.468635i) q^{94} +(7.88105 + 4.55013i) q^{95} +1.20561i q^{97} +(3.96851 + 9.06923i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 32 * q + 2 * q^4	\( 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) \) 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

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