LMFDB - Embedded newform 504.2.bk.b.19.12

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			19.12
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.b.451.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826169 + 1.14780i) q^{2} +(-0.634890 + 1.89655i) q^{4} +(1.91923 - 3.32420i) q^{5} +(-1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +O(q^{10})$	\(q+(0.826169 + 1.14780i) q^{2} +(-0.634890 + 1.89655i) q^{4} +(1.91923 - 3.32420i) q^{5} +(-1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +(5.40112 - 0.543460i) q^{10} +(1.28125 + 2.21918i) q^{11} +5.99175 q^{13} +(1.16852 - 3.55451i) q^{14} +(-3.19383 - 2.40821i) q^{16} +(3.53425 - 2.04050i) q^{17} +(-2.05318 - 1.18541i) q^{19} +(5.08602 + 5.75041i) q^{20} +(-1.48865 + 3.30403i) q^{22} +(6.53773 + 3.77456i) q^{23} +(-4.86686 - 8.42964i) q^{25} +(4.95020 + 6.87733i) q^{26} +(5.04527 - 1.59539i) q^{28} +2.70568i q^{29} +(-2.90258 - 5.02742i) q^{31} +(0.125497 - 5.65546i) q^{32} +(5.26197 + 2.37081i) q^{34} +(-10.0989 + 1.07147i) q^{35} +(-3.61144 - 2.08507i) q^{37} +(-0.335667 - 3.33599i) q^{38} +(-2.39841 + 10.5885i) q^{40} +5.96293i q^{41} -8.06098 q^{43} +(-5.02225 + 1.02101i) q^{44} +(1.06883 + 10.6224i) q^{46} +(-0.204145 + 0.353590i) q^{47} +(-2.15004 + 6.66163i) q^{49} +(5.65470 - 12.5505i) q^{50} +(-3.80410 + 11.3637i) q^{52} +(-4.41436 + 2.54863i) q^{53} +9.83600 q^{55} +(5.99944 + 4.47289i) q^{56} +(-3.10557 + 2.23534i) q^{58} +(-9.05639 + 5.22871i) q^{59} +(1.34535 - 2.33021i) q^{61} +(3.37245 - 7.48508i) q^{62} +(6.59502 - 4.52832i) q^{64} +(11.4995 - 19.9178i) q^{65} +(2.38045 + 4.12307i) q^{67} +(1.62606 + 7.99838i) q^{68} +(-9.57323 - 10.7063i) q^{70} -1.21482i q^{71} +(-6.65046 + 3.83964i) q^{73} +(-0.590421 - 5.86783i) q^{74} +(3.55173 - 3.14137i) q^{76} +(2.75147 - 6.19628i) q^{77} +(8.89433 + 5.13514i) q^{79} +(-14.1350 + 5.99503i) q^{80} +(-6.84425 + 4.92639i) q^{82} +4.49449i q^{83} -15.6647i q^{85} +(-6.65973 - 9.25239i) q^{86} +(-5.32115 - 4.92101i) q^{88} +(3.35682 + 1.93806i) q^{89} +(-9.33056 - 12.8159i) q^{91} +(-11.3094 + 10.0027i) q^{92} +(-0.574508 + 0.0578070i) q^{94} +(-7.88105 + 4.55013i) q^{95} -1.20561i q^{97} +(-9.42252 + 3.03582i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.826169	+	1.14780i	0.584190	+	0.811617i
$2$	0.826169	+	1.14780i	0.584190	+	0.811617i
$3$		0			0
$3$		0			0
$4$	−0.634890	+	1.89655i	−0.317445	+	0.948277i
$5$	1.91923	−	3.32420i	0.858304	−	1.48663i	−0.0152419	−	0.999884i	$-0.504852\pi$
$5$	1.91923	−	3.32420i	0.858304	−	1.48663i	0.873546	−	0.486742i	$-0.161815\pi$
$6$		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
$10$	5.40112	−	0.543460i	1.70798	−	0.171857i
$11$	1.28125	+	2.21918i	0.386310	+	0.669109i	0.991950	−	0.126630i	$-0.0404161\pi$
$11$	1.28125	+	2.21918i	0.386310	+	0.669109i	−0.605640	+	0.795739i	$0.707083\pi$
$12$		0			0
$13$	5.99175			1.66181			0.830906	−	0.556413i	$-0.187823\pi$
$13$	5.99175			1.66181			0.830906	+	0.556413i	$0.187823\pi$
$14$	1.16852	−	3.55451i	0.312301	−	0.949983i
$15$		0			0
$16$	−3.19383	−	2.40821i	−0.798457	−	0.602051i
$17$	3.53425	−	2.04050i	0.857181	−	0.494894i	−0.00588636	−	0.999983i	$-0.501874\pi$
$17$	3.53425	−	2.04050i	0.857181	−	0.494894i	0.863067	+	0.505089i	$0.168540\pi$
$18$		0			0
$19$	−2.05318	−	1.18541i	−0.471033	−	0.271951i	0.245639	−	0.969361i	$-0.421002\pi$
$19$	−2.05318	−	1.18541i	−0.471033	−	0.271951i	−0.716672	+	0.697410i	$0.754335\pi$
$20$	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	$-0.0449405\pi$
$23$	6.53773	+	3.77456i	1.36321	+	0.787050i	0.373161	+	0.927767i	$0.378274\pi$
$24$		0			0
$25$	−4.86686	−	8.42964i	−0.973371	−	1.68593i
$26$	4.95020	+	6.87733i	0.970813	+	1.34876i
$27$		0			0
$28$	5.04527	−	1.59539i	0.953466	−	0.301501i
$29$			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	−0.999693	−	0.0247947i	$-0.992107\pi$
$31$	−2.90258	−	5.02742i	−0.521319	−	0.902951i	0.478373	−	0.878156i	$-0.341227\pi$
$32$	0.125497	−	5.65546i	0.0221849	−	0.999754i
$33$		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	$-0.444703\pi$
$37$	−3.61144	−	2.08507i	−0.593717	−	0.342783i	−0.766566	+	0.642166i	$0.778036\pi$
$38$	−0.335667	−	3.33599i	−0.0544524	−	0.541169i
$39$		0			0
$40$	−2.39841	+	10.5885i	−0.379223	+	1.67420i
$41$			5.96293i			0.931253i	0.884981	+	0.465627i	$0.154171\pi$
$41$			5.96293i			0.931253i	−0.884981	+	0.465627i	$0.845829\pi$
$42$		0			0
$43$	−8.06098			−1.22929			−0.614644	−	0.788805i	$-0.710700\pi$
$43$	−8.06098			−1.22929			−0.614644	+	0.788805i	$0.710700\pi$
$44$	−5.02225	+	1.02101i	−0.757132	+	0.153924i
$45$		0			0
$46$	1.06883	+	10.6224i	0.157590	+	1.56619i
$47$	−0.204145	+	0.353590i	−0.0297776	+	0.0515763i	−0.880530	−	0.473990i	$-0.842813\pi$
$47$	−0.204145	+	0.353590i	−0.0297776	+	0.0515763i	0.850753	+	0.525566i	$0.176147\pi$
$48$		0			0
$49$	−2.15004	+	6.66163i	−0.307148	+	0.951662i
$50$	5.65470	−	12.5505i	0.799695	−	1.77491i
$51$		0			0
$52$	−3.80410	+	11.3637i	−0.527534	+	1.57586i
$53$	−4.41436	+	2.54863i	−0.606359	+	0.350082i	−0.771539	−	0.636182i	$-0.780513\pi$
$53$	−4.41436	+	2.54863i	−0.606359	+	0.350082i	0.165180	+	0.986263i	$0.447179\pi$
$54$		0			0
$55$	9.83600			1.32629
$56$	5.99944	+	4.47289i	0.801708	+	0.597715i
$57$		0			0
$58$	−3.10557	+	2.23534i	−0.407782	+	0.293515i
$59$	−9.05639	+	5.22871i	−1.17904	+	0.680720i	−0.955793	−	0.294041i	$-0.905000\pi$
$59$	−9.05639	+	5.22871i	−1.17904	+	0.680720i	−0.223249	+	0.974761i	$0.571666\pi$
$60$		0			0
$61$	1.34535	−	2.33021i	0.172254	−	0.298353i	−0.766954	−	0.641703i	$-0.778228\pi$
$61$	1.34535	−	2.33021i	0.172254	−	0.298353i	0.939208	+	0.343350i	$0.111562\pi$
$62$	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	0.974004	−	0.226533i	$-0.0727390\pi$
$67$	2.38045	+	4.12307i	0.290819	+	0.503713i	−0.683185	+	0.730245i	$0.739406\pi$
$68$	1.62606	+	7.99838i	0.197188	+	0.969946i
$69$		0			0
$70$	−9.57323	−	10.7063i	−1.14422	−	1.27965i
$71$		−	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	−0.835855	−	0.548951i	$-0.815027\pi$
$73$	−6.65046	+	3.83964i	−0.778377	+	0.449396i	0.0574778	+	0.998347i	$0.481694\pi$
$74$	−0.590421	−	5.86783i	−0.0686350	−	0.682121i
$75$		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	$-0.137265\pi$
$79$	8.89433	+	5.13514i	1.00069	+	0.577749i	0.0922379	+	0.995737i	$0.470598\pi$
$80$	−14.1350	+	5.99503i	−1.58034	+	0.670264i
$81$		0			0
$82$	−6.84425	+	4.92639i	−0.755821	+	0.544028i
$83$			4.49449i			0.493335i	0.969100	+	0.246667i	$0.0793355\pi$
$83$			4.49449i			0.493335i	−0.969100	+	0.246667i	$0.920664\pi$
$84$		0			0
$85$		−	15.6647i		−	1.69908i
$86$	−6.65973	−	9.25239i	−0.718137	−	0.997711i
$87$		0			0
$88$	−5.32115	−	4.92101i	−0.567236	−	0.524581i
$89$	3.35682	+	1.93806i	0.355822	+	0.205434i	0.667247	−	0.744837i	$-0.267473\pi$
$89$	3.35682	+	1.93806i	0.355822	+	0.205434i	−0.311424	+	0.950271i	$0.600806\pi$
$90$		0			0
$91$	−9.33056	−	12.8159i	−0.978109	−	1.34347i
$92$	−11.3094	+	10.0027i	−1.17909	+	1.04286i
$93$		0			0
$94$	−0.574508	+	0.0578070i	−0.0592560	+	0.00596234i
$95$	−7.88105	+	4.55013i	−0.808578	+	0.466833i
$96$		0			0
$97$		−	1.20561i		−	0.122411i	−0.998125	−	0.0612055i	$-0.980505\pi$
$97$		−	1.20561i		−	0.122411i	0.998125	−	0.0612055i	$-0.0194945\pi$
$98$	−9.42252	+	3.03582i	−0.951818	+	0.306664i
$99$		0			0
$100$	19.0772	−	3.87836i	1.90772	−	0.387836i
$101$	−6.74188	−	11.6773i	−0.670842	−	1.16193i	−0.977666	−	0.210166i	$-0.932600\pi$
$101$	−6.74188	−	11.6773i	−0.670842	−	1.16193i	0.306824	−	0.951766i	$-0.400734\pi$
$102$		0			0
$103$	−2.63098	+	4.55700i	−0.259239	+	0.449014i	−0.966038	−	0.258399i	$-0.916805\pi$
$103$	−2.63098	+	4.55700i	−0.259239	+	0.449014i	0.706800	+	0.707414i	$0.250138\pi$
$104$	−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	−0.769005	−	0.639243i	$-0.779248\pi$
$107$	1.74917	−	3.02965i	0.169098	−	0.292887i	0.938103	+	0.346356i	$0.112581\pi$
$108$		0			0
$109$	−14.9576	+	8.63578i	−1.43268	+	0.827158i	−0.997324	−	0.0731016i	$-0.976710\pi$
$109$	−14.9576	+	8.63578i	−1.43268	+	0.827158i	−0.435354	+	0.900259i	$0.643377\pi$
$110$	8.12620	+	11.2898i	0.774802	+	1.07644i
$111$		0			0
$112$	−0.177438	+	10.5815i	−0.0167664	+	0.999859i
$113$	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
$116$	−5.13146	−	1.71781i	−0.476444	−	0.159494i
$117$		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
$122$	3.78610	−	0.380957i	0.342777	−	0.0344902i
$123$		0			0
$124$	11.3776	−	2.31304i	1.02174	−	0.207717i
$125$	−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	$-0.154028\pi$
$128$	10.6462	+	3.82861i	0.941001	+	0.338404i
$129$		0			0
$130$	32.3621	−	3.25628i	2.83835	−	0.285594i
$131$	1.93929	+	1.11965i	0.169437	+	0.0978243i	0.582320	−	0.812960i	$-0.302145\pi$
$131$	1.93929	+	1.11965i	0.169437	+	0.0978243i	−0.412884	+	0.910784i	$0.635478\pi$
$132$		0			0
$133$	0.661790	+	6.23757i	0.0573845	+	0.540866i
$134$	−2.76580	+	6.13863i	−0.238929	+	0.530297i
$135$		0			0
$136$	−7.83715	+	8.47440i	−0.672030	+	0.726674i
$137$	2.84029	+	4.91953i	0.242662	+	0.420303i	0.961472	−	0.274904i	$-0.0886460\pi$
$137$	2.84029	+	4.91953i	0.242662	+	0.420303i	−0.718809	+	0.695207i	$0.755313\pi$
$138$		0			0
$139$			15.0149i			1.27355i	0.771050	+	0.636774i	$0.219732\pi$
$139$			15.0149i			1.27355i	−0.771050	+	0.636774i	$0.780268\pi$
$140$	4.37960	−	19.8334i	0.370144	−	1.67623i
$141$		0			0
$142$	1.39437	−	1.00364i	0.117013	−	0.0842238i
$143$	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	$-0.289482\pi$
$149$	2.90342	+	1.67629i	0.237858	+	0.137327i	−0.376334	+	0.926484i	$0.622815\pi$
$150$		0			0
$151$	−6.37756	+	3.68209i	−0.518998	+	0.299644i	−0.736525	−	0.676411i	$-0.763535\pi$
$151$	−6.37756	+	3.68209i	−0.518998	+	0.299644i	0.217526	+	0.976054i	$0.430201\pi$
$152$	6.54000	+	1.48138i	0.530464	+	0.120156i
$153$		0			0
$154$	9.38528	−	1.96103i	0.756287	−	0.158025i
$155$	−22.2828			−1.78980
$156$		0			0
$157$	4.53219	+	7.84998i	0.361708	+	0.626497i	0.988242	−	0.152897i	$-0.0488604\pi$
$157$	4.53219	+	7.84998i	0.361708	+	0.626497i	−0.626534	+	0.779394i	$0.715527\pi$
$158$	1.45410	+	14.4514i	0.115682	+	1.14969i
$159$		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	0.179206	+	0.983812i	$0.442647\pi$
$163$	−9.73371	+	16.8593i	−0.762403	+	1.32052i	−0.941609	+	0.336709i	$0.890686\pi$
$164$	−11.3090	−	3.78580i	−0.883086	−	0.295622i
$165$		0			0
$166$	−5.15878	+	3.71321i	−0.400399	+	0.288201i
$167$	17.4579			1.35094			0.675468	−	0.737390i	$-0.263942\pi$
$167$	17.4579			1.35094			0.675468	+	0.737390i	$0.263942\pi$
$168$		0			0
$169$	22.9011			1.76162
$170$	17.9800	−	12.9417i	1.37900	−	0.992583i
$171$		0			0
$172$	5.11784	−	15.2881i	0.390231	−	1.16571i
$173$	1.76728	−	3.06101i	0.134363	−	0.232724i	−0.790991	−	0.611828i	$-0.790434\pi$
$173$	1.76728	−	3.06101i	0.134363	−	0.232724i	0.925354	+	0.379104i	$0.123768\pi$
$174$		0			0
$175$	−10.4516	+	23.5368i	−0.790064	+	1.77921i
$176$	1.25217	−	10.1732i	0.0943858	−	0.766833i
$177$		0			0
$178$	0.548794	+	5.45412i	0.0411338	+	0.408804i
$179$	4.69613	+	8.13393i	0.351005	+	0.607958i	0.986426	−	0.164208i	$-0.0525067\pi$
$179$	4.69613	+	8.13393i	0.351005	+	0.607958i	−0.635421	+	0.772166i	$0.719173\pi$
$180$		0			0
$181$	0.0924470			0.00687153			0.00343577	−	0.999994i	$-0.498906\pi$
$181$	0.0924470			0.00687153			0.00343577	+	0.999994i	$0.498906\pi$
$182$	7.00150	−	21.2977i	0.518986	−	1.57869i
$183$		0			0
$184$	−20.8246	−	4.71699i	−1.53521	−	0.347741i
$185$	−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	$-0.343054\pi$
$191$	−0.730882	−	0.421975i	−0.0528848	−	0.0305330i	−0.526209	+	0.850355i	$0.676387\pi$
$192$		0			0
$193$	−8.77738	−	15.2029i	−0.631810	−	1.09433i	−0.987182	−	0.159601i	$-0.948979\pi$
$193$	−8.77738	−	15.2029i	−0.631810	−	1.09433i	0.355372	−	0.934725i	$-0.384354\pi$
$194$	1.38380	−	0.996036i	0.0993509	−	0.0715112i
$195$		0			0
$196$	−11.2691	−	8.30706i	−0.804936	−	0.593362i
$197$			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	−0.985345	−	0.170572i	$-0.945438\pi$
$199$	−9.03385	−	15.6471i	−0.640392	−	1.10919i	0.344953	−	0.938620i	$-0.387895\pi$
$200$	20.2125	+	18.6926i	1.42924	+	1.32177i
$201$		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
$206$	−7.40416	+	0.745006i	−0.515872	+	0.0519070i
$207$		0			0
$208$	−19.1366	−	14.4294i	−1.32689	−	1.00050i
$209$		−	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	$0.507670\pi$
$212$	−2.03098	−	9.99017i	−0.139488	−	0.686128i
$213$		0			0
$214$	4.92254	−	0.495305i	0.336498	−	0.0338584i
$215$	−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
$220$	−6.24478	+	18.6545i	−0.421023	+	1.25769i
$221$	21.1763	−	12.2262i	1.42447	−	0.822420i
$222$		0			0
$223$	−2.52067			−0.168797			−0.0843983	−	0.996432i	$-0.526897\pi$
$223$	−2.52067			−0.168797			−0.0843983	+	0.996432i	$0.526897\pi$
$224$	−12.2921	+	8.53846i	−0.821298	+	0.570500i
$225$		0			0
$226$	9.67940	+	13.4476i	0.643864	+	0.894524i
$227$	−7.20056	+	4.15724i	−0.477918	+	0.275926i	−0.719548	−	0.694442i	$-0.755651\pi$
$227$	−7.20056	+	4.15724i	−0.477918	+	0.275926i	0.241631	+	0.970368i	$0.422318\pi$
$228$		0			0
$229$	2.61750	−	4.53364i	0.172969	−	0.299592i	−0.766487	−	0.642259i	$-0.777997\pi$
$229$	2.61750	−	4.53364i	0.172969	−	0.299592i	0.939457	+	0.342668i	$0.111331\pi$
$230$	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	0.241671	+	0.970358i	$0.422305\pi$
$233$	−10.9830	+	19.0231i	−0.719520	+	1.24624i	−0.961190	+	0.275886i	$0.911029\pi$
$234$		0			0
$235$	0.783601	+	1.35724i	0.0511165	+	0.0885363i
$236$	−4.16672	−	20.4956i	−0.271230	−	1.33415i
$237$		0			0
$238$	−3.12312	−	14.9469i	−0.202442	−	0.968863i
$239$		−	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	−0.219224	−	0.975675i	$-0.570352\pi$
$241$	8.01239	−	4.62596i	0.516123	−	0.297984i	0.735347	+	0.677691i	$0.237019\pi$
$242$	6.23861	−	0.627728i	0.401033	−	0.0403519i
$243$		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
$248$	12.0547	+	11.1482i	0.765476	+	0.707914i
$249$		0			0
$250$	−15.0116	−	20.8557i	−0.949416	−	1.31903i
$251$			0.208623i			0.0131682i	0.999978	+	0.00658409i	$0.00209580\pi$
$251$			0.208623i			0.0131682i	−0.999978	+	0.00658409i	$0.997904\pi$
$252$		0			0
$253$			19.3446i			1.21618i
$254$	12.0355	−	8.66299i	0.755176	−	0.543564i
$255$		0			0
$256$	4.40109	+	15.3828i	0.275068	+	0.961425i
$257$	17.1020	+	9.87383i	1.06679	+	0.615912i	0.927303	−	0.374311i	$-0.122121\pi$
$257$	17.1020	+	9.87383i	1.06679	+	0.615912i	0.139488	+	0.990224i	$0.455454\pi$
$258$		0			0
$259$	1.16405	+	10.9716i	0.0723308	+	0.681739i
$260$	30.4741	+	34.4550i	1.88993	+	2.13681i
$261$		0			0
$262$	0.317047	+	3.15094i	0.0195872	+	0.194666i
$263$	14.0976	−	8.13925i	0.869295	−	0.501888i	0.00218129	−	0.999998i	$-0.499306\pi$
$263$	14.0976	−	8.13925i	0.869295	−	0.501888i	0.867114	+	0.498110i	$0.165972\pi$
$264$		0			0
$265$			19.5656i			1.20191i
$266$	−6.61274	+	5.91289i	−0.405453	+	0.362543i
$267$		0			0
$268$	−9.33094	+	1.89696i	−0.569978	+	0.115875i
$269$	3.99040	+	6.91158i	0.243299	+	0.421406i	0.961652	−	0.274272i	$-0.0884370\pi$
$269$	3.99040	+	6.91158i	0.243299	+	0.421406i	−0.718353	+	0.695679i	$0.755104\pi$
$270$		0			0
$271$	6.26335	−	10.8484i	0.380471	−	0.658995i	−0.610658	−	0.791894i	$-0.709095\pi$
$271$	6.26335	−	10.8484i	0.380471	−	0.658995i	0.991130	+	0.132899i	$0.0424285\pi$
$272$	−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	$-0.873390\pi$
$277$	−17.4329	+	10.0649i	−1.04744	+	0.604740i	−0.125508	+	0.992093i	$0.540056\pi$
$278$	−17.2341	+	12.4049i	−1.03363	+	0.743994i
$279$		0			0
$280$	26.3830	−	11.3588i	1.57669	−	0.678819i
$281$	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	−0.411420	−	0.911446i	$-0.634967\pi$
$283$	2.89693	−	1.67254i	0.172204	−	0.0994222i	0.583625	+	0.812023i	$0.301634\pi$
$284$	2.30396	+	0.771274i	0.136715	+	0.0457667i
$285$		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
$290$	1.47043	+	14.6137i	0.0863464	+	0.858144i
$291$		0			0
$292$	−3.05978	−	15.0507i	−0.179060	−	0.880775i
$293$	−9.88541			−0.577512			−0.288756	−	0.957403i	$-0.593242\pi$
$293$	−9.88541			−0.577512			−0.288756	+	0.957403i	$0.593242\pi$
$294$		0			0
$295$			40.1403i			2.33706i
$296$	11.5035	+	2.60566i	0.668628	+	0.151451i
$297$		0			0
$298$	0.474670	+	4.71745i	0.0274969	+	0.273275i
$299$	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
$304$	3.70282	+	8.73048i	0.212371	+	0.500727i
$305$	−5.16405	−	8.94439i	−0.295693	−	0.512154i
$306$		0			0
$307$		−	3.58312i		−	0.204500i	−0.994759	−	0.102250i	$-0.967396\pi$
$307$		−	3.58312i		−	0.204500i	0.994759	−	0.102250i	$-0.0326041\pi$
$308$	10.0047	+	9.15228i	0.570071	+	0.521499i
$309$		0			0
$310$	−18.4094	−	25.5762i	−1.04558	−	1.45263i
$311$	−13.1626	−	22.7982i	−0.746381	−	1.29277i	−0.949547	−	0.313626i	$-0.898456\pi$
$311$	−13.1626	−	22.7982i	−0.746381	−	1.29277i	0.203166	−	0.979144i	$-0.434877\pi$
$312$		0			0
$313$	13.5565	+	7.82684i	0.766257	+	0.442399i	0.831538	−	0.555468i	$-0.187461\pi$
$313$	13.5565	+	7.82684i	0.766257	+	0.442399i	−0.0652804	+	0.997867i	$0.520794\pi$
$314$	−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	$-0.481693\pi$
$317$	−13.8585	−	8.00123i	−0.778373	−	0.449394i	−0.835853	+	0.548953i	$0.815027\pi$
$318$		0			0
$319$	−6.00439	+	3.46664i	−0.336181	+	0.194094i
$320$	−2.39570	−	30.6140i	−0.133923	−	1.71138i
$321$		0			0
$322$	21.0562	−	18.8278i	1.17342	−	1.04923i
$323$	−9.67528			−0.538347
$324$		0			0
$325$	−29.1610	−	50.5083i	−1.61756	−	2.80170i
$326$	−27.3928	+	2.75626i	−1.51715	+	0.152655i
$327$		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	−0.550963	−	0.834530i	$-0.685740\pi$
$331$	8.13686	−	14.0935i	0.447242	−	0.774646i	0.998205	+	0.0598834i	$0.0190729\pi$
$332$	−8.52405	−	2.85351i	−0.467818	−	0.156607i
$333$		0			0
$334$	14.4232	+	20.0382i	0.789202	+	1.09644i
$335$	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	$0.551485\pi$
$338$	18.9201	+	26.2858i	1.02912	+	1.42976i
$339$		0			0
$340$	29.7090	+	9.94537i	1.61119	+	0.539363i
$341$	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
$346$	4.97350	−	0.500433i	0.267377	−	0.0269034i
$347$	−14.5658	−	25.2288i	−0.781936	−	1.35435i	−0.930813	−	0.365496i	$-0.880899\pi$
$347$	−14.5658	−	25.2288i	−0.781936	−	1.35435i	0.148877	−	0.988856i	$-0.452434\pi$
$348$		0			0
$349$	11.2807			0.603841			0.301921	−	0.953333i	$-0.402372\pi$
$349$	11.2807			0.603841			0.301921	+	0.953333i	$0.402372\pi$
$350$	−35.6503	+	7.44906i	−1.90559	+	0.398169i
$351$		0			0
$352$	12.7113	−	6.96754i	0.677514	−	0.371371i
$353$	−24.0732	+	13.8987i	−1.28129	+	0.739753i	−0.977084	−	0.212854i	$-0.931724\pi$
$353$	−24.0732	+	13.8987i	−1.28129	+	0.739753i	−0.304205	+	0.952606i	$0.598391\pi$
$354$		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	$-0.360515\pi$
$359$	−2.79904	−	1.61602i	−0.147727	−	0.0852905i	−0.572042	+	0.820224i	$0.693848\pi$
$360$		0			0
$361$	−6.68962	−	11.5868i	−0.352085	−	0.609830i
$362$	0.0763768	+	0.106111i	0.00401428	+	0.00557705i
$363$		0			0
$364$	30.2300	−	9.55921i	1.58448	−	0.501039i
$365$			29.4766i			1.54287i
$366$		0			0
$367$	−0.139516	−	0.241649i	−0.00728269	−	0.0126140i	0.862361	−	0.506294i	$-0.168985\pi$
$367$	−0.139516	−	0.241649i	−0.00728269	−	0.0126140i	−0.869644	+	0.493680i	$0.835652\pi$
$368$	−11.7905	−	27.7995i	−0.614621	−	1.44915i
$369$		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	$-0.632213\pi$
$373$	−26.9934	−	15.5846i	−1.39767	−	0.806943i	−0.994148	+	0.108029i	$0.965546\pi$
$374$	1.48061	+	14.7149i	0.0765605	+	0.760888i
$375$		0			0
$376$	0.255116	−	1.12629i	0.0131566	−	0.0580838i
$377$			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	$0.288429\pi$
$380$	−3.62596	−	17.8357i	−0.186008	−	0.914950i
$381$		0			0
$382$	−0.119489	−	1.18753i	−0.00611360	−	0.0607593i
$383$	−7.38565	+	12.7923i	−0.377389	+	0.653657i	−0.990681	−	0.136199i	$-0.956511\pi$
$383$	−7.38565	+	12.7923i	−0.377389	+	0.653657i	0.613293	+	0.789856i	$0.289845\pi$
$384$		0			0
$385$	−15.3170	−	21.0385i	−0.780625	−	1.07222i
$386$	10.1983	−	22.6348i	0.519077	−	1.15208i
$387$		0			0
$388$	2.28650	+	0.765429i	0.116079	+	0.0388588i
$389$	−1.63155	+	0.941976i	−0.0827229	+	0.0477601i	−0.540791	−	0.841157i	$-0.681875\pi$
$389$	−1.63155	+	0.941976i	−0.0827229	+	0.0477601i	0.458068	+	0.888917i	$0.348542\pi$
$390$		0			0
$391$	30.8079			1.55802
$392$	0.224666	−	19.7977i	0.0113473	−	0.999936i
$393$		0			0
$394$	−9.09457	+	6.54613i	−0.458178	+	0.329789i
$395$	34.1405	−	19.7110i	1.71779	−	0.991768i
$396$		0			0
$397$	−2.50329	+	4.33582i	−0.125636	+	0.217609i	−0.921982	−	0.387234i	$-0.873431\pi$
$397$	−2.50329	+	4.33582i	−0.125636	+	0.217609i	0.796345	+	0.604842i	$0.206764\pi$
$398$	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	0.306219	+	0.951961i	$0.400936\pi$
$401$	−13.4430	+	23.2840i	−0.671313	+	1.16275i	−0.977532	+	0.210787i	$0.932397\pi$
$402$		0			0
$403$	−17.3915	−	30.1230i	−0.866334	−	1.50054i
$404$	26.4269	−	5.37254i	1.31479	−	0.267294i
$405$		0			0
$406$	9.61735	+	3.16165i	0.477301	+	0.156910i
$407$		−	10.6859i		−	0.529682i
$408$		0			0
$409$	22.4884	−	12.9837i	1.11198	−	0.642002i	0.172638	−	0.984985i	$-0.444771\pi$
$409$	22.4884	−	12.9837i	1.11198	−	0.642002i	0.939341	+	0.342984i	$0.111438\pi$
$410$	3.24061	+	32.2065i	0.160043	+	1.59056i
$411$		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
$416$	0.751945	−	33.8861i	0.0368671	−	1.66140i
$417$		0			0
$418$	6.97310	−	5.01913i	0.341066	−	0.245494i
$419$		−	33.9652i		−	1.65931i	−0.558278	−	0.829654i	$-0.688538\pi$
$419$		−	33.9652i		−	1.65931i	0.558278	−	0.829654i	$-0.311462\pi$
$420$		0			0
$421$		−	2.75866i		−	0.134449i	−0.997738	−	0.0672245i	$-0.978586\pi$
$421$		−	2.75866i		−	0.134449i	0.997738	−	0.0672245i	$-0.0214144\pi$
$422$	−0.578258	−	0.803376i	−0.0281491	−	0.0391077i
$423$		0			0
$424$	9.78878	−	10.5847i	0.475385	−	0.514040i
$425$	−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
$430$	−43.5383	+	4.38082i	−2.09960	+	0.211262i
$431$	−31.3514	+	18.1007i	−1.51014	+	0.871881i	−0.510213	+	0.860048i	$0.670433\pi$
$431$	−31.3514	+	18.1007i	−1.51014	+	0.871881i	−0.999930	+	0.0118334i	$0.996233\pi$
$432$		0			0
$433$			20.2448i			0.972901i	0.873708	+	0.486451i	$0.161709\pi$
$433$			20.2448i			0.972901i	−0.873708	+	0.486451i	$0.838291\pi$
$434$	−21.2618	+	4.44260i	−1.02060	+	0.213252i
$435$		0			0
$436$	−6.88178	−	33.8507i	−0.329577	−	1.62115i
$437$	−8.94878	−	15.4997i	−0.428078	−	0.741453i
$438$		0			0
$439$	14.6398	−	25.3569i	0.698719	−	1.21022i	−0.270192	−	0.962806i	$-0.587087\pi$
$439$	14.6398	−	25.3569i	0.698719	−	1.21022i	0.968911	−	0.247410i	$-0.0795795\pi$
$440$	−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	0.444103	+	0.895976i	$0.353522\pi$
$443$	−11.6580	+	20.1922i	−0.553886	+	0.959359i	−0.997989	+	0.0633831i	$0.979811\pi$
$444$		0			0
$445$	12.8850	−	7.43915i	0.610807	−	0.352650i
$446$	−2.08250	−	2.89322i	−0.0986092	−	0.136998i
$447$		0			0
$448$	−19.9558	−	7.05462i	−0.942821	−	0.333300i
$449$	−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
$452$	−7.43838	+	22.2200i	−0.349872	+	1.04514i
$453$		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	−0.998205	−	0.0598816i	$-0.980928\pi$
$457$	−9.56098	+	16.5601i	−0.447244	+	0.774649i	0.550962	+	0.834531i	$0.314261\pi$
$458$	7.36621	−	0.741188i	0.344200	−	0.0346334i
$459$		0			0
$460$	11.5457	+	56.7921i	0.538323	+	2.64795i
$461$	−20.5529			−0.957242			−0.478621	−	0.878022i	$-0.658863\pi$
$461$	−20.5529			−0.957242			−0.478621	+	0.878022i	$0.658863\pi$
$462$		0			0
$463$		−	31.7517i		−	1.47563i	−0.675005	−	0.737813i	$-0.735858\pi$
$463$		−	31.7517i		−	1.47563i	0.675005	−	0.737813i	$-0.264142\pi$
$464$	6.51582	−	8.64147i	0.302490	−	0.401170i
$465$		0			0
$466$	−30.9085	+	3.11001i	−1.43181	+	0.144069i
$467$	−0.764809	−	0.441563i	−0.0353911	−	0.0204331i	0.482200	−	0.876061i	$-0.339838\pi$
$467$	−0.764809	−	0.441563i	−0.0353911	−	0.0204331i	−0.517591	+	0.855628i	$0.673171\pi$
$468$		0			0
$469$	5.11202	−	11.5122i	0.236051	−	0.531584i
$470$	−0.910449	+	2.02072i	−0.0419959	+	0.0932090i
$471$		0			0
$472$	20.0824	−	21.7154i	0.924369	−	0.999531i
$473$	−10.3281	−	17.8888i	−0.474886	−	0.822527i
$474$		0			0
$475$			23.0768i			1.05884i
$476$	14.5758	−	15.9334i	0.668082	−	0.730305i
$477$		0			0
$478$	32.7302	−	23.5587i	1.49704	−	1.07755i
$479$	17.7492	+	30.7425i	0.810981	+	1.40466i	0.912178	+	0.409794i	$0.134399\pi$
$479$	17.7492	+	30.7425i	0.810981	+	1.40466i	−0.101197	+	0.994866i	$0.532267\pi$
$480$		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	$-0.962833\pi$
$487$	−30.6502	+	17.6959i	−1.38889	+	0.801878i	−0.395703	+	0.918378i	$0.629499\pi$
$488$	−1.68125	+	7.42240i	−0.0761066	+	0.335996i
$489$		0			0
$490$	−7.99227	+	37.1487i	−0.361054	+	1.67821i
$491$	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
$494$	−2.01123	−	19.9884i	−0.0904897	−	0.899322i
$495$		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	−0.807210	−	0.590265i	$-0.799023\pi$
$499$	2.40315	−	4.16237i	0.107580	−	0.186333i	0.914789	+	0.403932i	$0.132357\pi$
$500$	11.5360	−	34.4606i	0.515907	−	1.54112i
$501$		0			0
$502$	−0.239458	+	0.172358i	−0.0106875	+	0.00769271i
$503$	20.5529			0.916406			0.458203	−	0.888847i	$-0.348493\pi$
$503$	20.5529			0.916406			0.458203	+	0.888847i	$0.348493\pi$
$504$		0			0
$505$	−51.7567			−2.30314
$506$	−22.2037	+	15.9819i	−0.987074	+	0.710481i
$507$		0			0
$508$	19.8868	+	6.65729i	0.882332	+	0.295370i
$509$	1.83211	−	3.17332i	0.0812070	−	0.140655i	−0.822562	−	0.568676i	$-0.807456\pi$
$509$	1.83211	−	3.17332i	0.0812070	−	0.140655i	0.903769	+	0.428021i	$0.140789\pi$
$510$		0			0
$511$	18.5690	+	8.24563i	0.821446	+	0.364765i
$512$	−14.0203	+	17.7604i	−0.619617	+	0.784904i
$513$		0			0
$514$	2.79594	+	27.7871i	0.123323	+	1.22564i
$515$	10.0989	+	17.4918i	0.445011	+	0.770782i
$516$		0			0
$517$	−1.04624			−0.0460136
$518$	−11.6314	+	10.4005i	−0.511057	+	0.456970i
$519$		0			0
$520$	−14.3707	+	63.4439i	−0.630197	+	2.78220i
$521$	29.0599	−	16.7777i	1.27314	−	0.735045i	0.297559	−	0.954703i	$-0.403828\pi$
$521$	29.0599	−	16.7777i	1.27314	−	0.735045i	0.975577	+	0.219658i	$0.0704942\pi$
$522$		0			0
$523$	−2.12127	−	1.22471i	−0.0927565	−	0.0535530i	0.452904	−	0.891559i	$-0.350388\pi$
$523$	−2.12127	−	1.22471i	−0.0927565	−	0.0535530i	−0.545661	+	0.838006i	$0.683721\pi$
$524$	−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
$530$	−22.4574	+	16.1645i	−0.975487	+	0.702141i
$531$		0			0
$532$	−12.2501	−	2.70505i	−0.531107	−	0.117279i
$533$			35.7284i			1.54757i
$534$		0			0
$535$	−6.71409	−	11.6292i	−0.290276	−	0.502772i
$536$	−9.88627	−	9.14284i	−0.427022	−	0.394911i
$537$		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	$-0.118760\pi$
$541$	25.1467	+	14.5185i	1.08114	+	0.624197i	0.149937	+	0.988696i	$0.452093\pi$
$542$	17.6264	−	1.77357i	0.757119	−	0.0761813i
$543$		0			0
$544$	−11.0964	−	20.2439i	−0.475755	−	0.867949i
$545$			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	$0.635381\pi$
$548$	−11.1334	+	2.26340i	−0.475596	+	0.0966878i
$549$		0			0
$550$	35.0969	−	3.53145i	1.49654	−	0.150581i
$551$	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
$556$	−28.4766	−	9.53282i	−1.20768	−	0.404282i
$557$	−12.1940	+	7.04023i	−0.516678	+	0.298304i	−0.735574	−	0.677444i	$-0.763088\pi$
$557$	−12.1940	+	7.04023i	−0.516678	+	0.298304i	0.218896	+	0.975748i	$0.429754\pi$
$558$		0			0
$559$	−48.2994			−2.04285
$560$	34.8345	+	20.8982i	1.47203	+	0.883109i
$561$		0			0
$562$	1.83950	+	2.55562i	0.0775945	+	0.107802i
$563$	31.6170	−	18.2541i	1.33250	−	0.769319i	0.346817	−	0.937933i	$-0.387263\pi$
$563$	31.6170	−	18.2541i	1.33250	−	0.769319i	0.985682	+	0.168614i	$0.0539292\pi$
$564$		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	−0.677706	−	0.735333i	$-0.737026\pi$
$569$	7.10756	−	12.3107i	0.297964	−	0.516089i	0.975670	+	0.219244i	$0.0703590\pi$
$570$		0			0
$571$	−23.5206	−	40.7389i	−0.984307	−	1.70487i	−0.644978	−	0.764202i	$-0.723133\pi$
$571$	−23.5206	−	40.7389i	−0.984307	−	1.70487i	−0.339329	−	0.940668i	$-0.610200\pi$
$572$	−30.0921	+	6.11766i	−1.25821	+	0.255792i
$573$		0			0
$574$	21.1953	+	6.96783i	0.884675	+	0.290831i
$575$		−	73.4810i		−	3.06437i
$576$		0			0
$577$	24.6447	−	14.2286i	1.02597	−	0.592344i	0.110143	−	0.993916i	$-0.464869\pi$
$577$	24.6447	−	14.2286i	1.02597	−	0.592344i	0.915828	+	0.401572i	$0.131536\pi$
$578$	−0.486103	+	0.0489116i	−0.0202192	+	0.00203446i
$579$		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
$584$	14.7473	−	15.9464i	0.610247	−	0.659868i
$585$		0			0
$586$	−8.16702	−	11.3465i	−0.337377	−	0.468719i
$587$		−	43.1297i		−	1.78015i	−0.455809	−	0.890077i	$-0.650650\pi$
$587$		−	43.1297i		−	1.78015i	0.455809	−	0.890077i	$-0.349350\pi$
$588$		0			0
$589$			13.7630i			0.567093i
$590$	−46.0731	+	33.1627i	−1.89680	+	1.36529i
$591$		0			0
$592$	6.51306	+	15.3564i	0.267685	+	0.631146i
$593$	−24.3679	−	14.0688i	−1.00067	−	0.577736i	−0.0922223	−	0.995738i	$-0.529397\pi$
$593$	−24.3679	−	14.0688i	−1.00067	−	0.577736i	−0.908446	+	0.418002i	$0.862730\pi$
$594$		0			0
$595$	−33.5057	+	24.3936i	−1.37360	+	1.00004i
$596$	−5.02253	+	4.44224i	−0.205731	+	0.181961i
$597$		0			0
$598$	6.40415	+	63.6470i	0.261885	+	2.60272i
$599$	24.3740	−	14.0724i	0.995896	−	0.574981i	0.0888644	−	0.996044i	$-0.471676\pi$
$599$	24.3740	−	14.0724i	0.995896	−	0.574981i	0.907031	+	0.421063i	$0.138343\pi$
$600$		0			0
$601$		−	43.5777i		−	1.77757i	−0.458322	−	0.888786i	$-0.651549\pi$
$601$		−	43.5777i		−	1.77757i	0.458322	−	0.888786i	$-0.348451\pi$
$602$	−9.41945	+	28.6528i	−0.383908	+	1.16780i
$603$		0			0
$604$	−2.93422	−	14.4331i	−0.119392	−	0.587275i
$605$	−8.50915	−	14.7383i	−0.345946	−	0.599196i
$606$		0			0
$607$	6.20364	−	10.7450i	0.251798	−	0.436127i	−0.712223	−	0.701953i	$-0.752312\pi$
$607$	6.20364	−	10.7450i	0.251798	−	0.436127i	0.964021	+	0.265827i	$0.0856448\pi$
$608$	−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	$-0.504827\pi$
$613$	20.8762	−	12.0529i	0.843180	−	0.486810i	0.858344	+	0.513075i	$0.171494\pi$
$614$	4.11271	−	2.96026i	0.165975	−	0.119467i
$615$		0			0
$616$	−2.23941	+	19.0447i	−0.0902285	+	0.767334i
$617$	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	−0.740281	−	0.672297i	$-0.765308\pi$
$619$	−13.1414	+	7.58717i	−0.528196	+	0.304954i	0.212086	+	0.977251i	$0.431974\pi$
$620$	14.1472	−	42.2606i	0.568163	−	1.69723i
$621$		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
$626$	2.21630	+	22.0264i	0.0885810	+	0.880353i
$627$		0			0
$628$	−17.7654	+	3.61166i	−0.708915	+	0.144121i
$629$	−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	$-0.265214\pi$
$632$	−28.3311	−	6.41728i	−1.12695	−	0.255266i
$633$		0			0
$634$	−2.26568	−	22.5172i	−0.0899816	−	0.894272i
$635$	−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
$640$	33.1595	−	28.0421i	1.31075	−	1.10846i
$641$	7.27131	+	12.5943i	0.287200	+	0.497444i	0.973140	−	0.230213i	$-0.0739423\pi$
$641$	7.27131	+	12.5943i	0.287200	+	0.497444i	−0.685941	+	0.727658i	$0.740609\pi$
$642$		0			0
$643$		−	22.1025i		−	0.871639i	−0.900034	−	0.435820i	$-0.856459\pi$
$643$		−	22.1025i		−	0.871639i	0.900034	−	0.435820i	$-0.143541\pi$
$644$	39.0065	+	8.61340i	1.53707	+	0.339416i
$645$		0			0
$646$	−7.99342	−	11.1053i	−0.314497	−	0.436932i
$647$	−3.21337	−	5.56572i	−0.126331	−	0.218811i	0.795922	−	0.605400i	$-0.206987\pi$
$647$	−3.21337	−	5.56572i	−0.126331	−	0.218811i	−0.922252	+	0.386589i	$0.873653\pi$
$648$		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	$-0.115721\pi$
$653$	27.9561	+	16.1405i	1.09401	+	0.631626i	0.159367	+	0.987219i	$0.449055\pi$
$654$		0			0
$655$	7.44387	−	4.29772i	0.290856	−	0.167926i
$656$	14.3600	−	19.0446i	0.560662	−	0.743566i
$657$		0			0
$658$	1.01829	+	1.13881i	0.0396971	+	0.0443956i
$659$	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	$-0.188642\pi$
$661$	−1.77351	−	3.07180i	−0.0689814	−	0.119479i	−0.898453	+	0.439069i	$0.855308\pi$
$662$	22.8989	−	2.30408i	0.889990	−	0.0895508i
$663$		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
$668$	−11.0839	+	33.1099i	−0.428848	+	1.28106i
$669$		0			0
$670$	15.0978	+	20.9755i	0.583280	+	0.810354i
$671$	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	$0.439094\pi$
$674$	−4.88486	−	6.78656i	−0.188158	−	0.261408i
$675$		0			0
$676$	−14.5397	+	43.4331i	−0.559217	+	1.67050i
$677$	17.1703	−	29.7398i	0.659906	−	1.14299i	−0.320733	−	0.947170i	$-0.603929\pi$
$677$	17.1703	−	29.7398i	0.659906	−	1.14299i	0.980639	−	0.195822i	$-0.0627374\pi$
$678$		0			0
$679$	−2.57871	+	1.87742i	−0.0989619	+	0.0720486i
$680$	13.1293	+	42.3165i	0.503486	+	1.62276i
$681$		0			0
$682$	20.9317	−	2.10615i	0.801516	−	0.0806485i
$683$	20.2559	+	35.0842i	0.775070	+	1.34246i	0.934755	+	0.355292i	$0.115619\pi$
$683$	20.2559	+	35.0842i	0.775070	+	1.34246i	−0.159686	+	0.987168i	$0.551048\pi$
$684$		0			0
$685$	21.8046			0.833112
$686$	21.1665	+	15.4266i	0.808140	+	0.588991i
$687$		0			0
$688$	25.7454	+	19.4125i	0.981534	+	0.740095i
$689$	−26.4497	+	15.2708i	−1.00765	+	0.581770i
$690$		0			0
$691$	35.0416	+	20.2313i	1.33304	+	0.769634i	0.985765	−	0.168128i	$-0.0537722\pi$
$691$	35.0416	+	20.2313i	1.33304	+	0.769634i	0.347279	+	0.937762i	$0.387106\pi$
$692$	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
$698$	9.31975	+	12.9480i	0.352758	+	0.490088i
$699$		0			0
$700$	−38.0032	−	34.7652i	−1.43639	−	1.31400i
$701$			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
$704$	18.4990	+	8.83366i	0.697208	+	0.332931i
$705$		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	$-0.307422\pi$
$709$	3.75011	+	2.16513i	0.140838	+	0.0813131i	−0.427925	+	0.903814i	$0.640755\pi$
$710$	−0.660204	−	6.56136i	−0.0247770	−	0.246243i
$711$		0			0
$712$	−10.6925	−	2.42195i	−0.400717	−	0.0907665i
$713$		−	43.8239i		−	1.64122i
$714$		0			0
$715$	58.9348			2.20404
$716$	−18.4080	+	3.74230i	−0.687938	+	0.139856i
$717$		0			0
$718$	−0.457604	−	4.54784i	−0.0170776	−	0.169724i
$719$	2.88615	−	4.99895i	0.107635	−	0.186429i	−0.807177	−	0.590310i	$-0.799006\pi$
$719$	2.88615	−	4.99895i	0.107635	−	0.186429i	0.914812	+	0.403880i	$0.132339\pi$
$720$		0			0
$721$	13.8442	−	1.46883i	0.515583	−	0.0547021i
$722$	7.77253	−	17.2510i	0.289264	−	0.642015i
$723$		0			0
$724$	−0.0586937	+	0.175331i	−0.00218133	+	0.00651611i
$725$	22.8079	−	13.1681i	0.847063	−	0.489052i
$726$		0			0
$727$	23.4056			0.868066			0.434033	−	0.900897i	$-0.357090\pi$
$727$	23.4056			0.868066			0.434033	+	0.900897i	$0.357090\pi$
$728$	35.9471	+	26.8004i	1.33229	+	0.993291i
$729$		0			0
$730$	−33.8332	+	24.3526i	−1.25222	+	0.901331i
$731$	−28.4895	+	16.4484i	−1.05372	+	0.608367i
$732$		0			0
$733$	−14.5792	+	25.2520i	−0.538496	+	0.932703i	0.460489	+	0.887665i	$0.347674\pi$
$733$	−14.5792	+	25.2520i	−0.538496	+	0.932703i	−0.998985	+	0.0450374i	$0.985659\pi$
$734$	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	0.893901	−	0.448265i	$-0.147958\pi$
$739$	1.59685	+	2.76583i	0.0587412	+	0.101743i	−0.835159	+	0.550008i	$0.814625\pi$
$740$	−6.37786	−	31.3720i	−0.234455	−	1.15326i
$741$		0			0
$742$	3.90086	+	18.6690i	0.143205	+	0.685362i
$743$			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
$746$	−4.41305	−	43.8586i	−0.161573	−	1.60578i
$747$		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	$-0.252231\pi$
$751$	11.9634	+	6.90707i	0.436551	+	0.252043i	−0.265583	+	0.964088i	$0.585564\pi$
$752$	1.50352	−	0.637681i	0.0548278	−	0.0232538i
$753$		0			0
$754$	−18.6078	+	13.3936i	−0.677657	+	0.487767i
$755$			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	$-0.226019\pi$
$758$	19.8409	+	27.5651i	0.720655	+	1.00121i
$759$		0			0
$760$	17.4761	−	18.8971i	0.633925	−	0.685471i
$761$	−30.6897	−	17.7187i	−1.11250	−	0.642302i	−0.173024	−	0.984918i	$-0.555354\pi$
$761$	−30.6897	−	17.7187i	−1.11250	−	0.642302i	−0.939476	+	0.342616i	$0.888687\pi$
$762$		0			0
$763$	41.7638	+	18.5453i	1.51195	+	0.671386i
$764$	1.26433	−	1.11825i	0.0457418	−	0.0404568i
$765$		0			0
$766$	−20.7848	+	2.09137i	−0.750986	+	0.0755641i
$767$	−54.2636	+	31.3291i	−1.95935	+	1.13123i
$768$		0			0
$769$			27.3235i			0.985311i	0.870225	+	0.492655i	$0.163974\pi$
$769$			27.3235i			0.985311i	−0.870225	+	0.492655i	$0.836026\pi$
$770$	11.4936	−	34.9622i	0.414201	−	1.25995i
$771$		0			0
$772$	34.4057	−	6.99462i	1.23829	−	0.251742i
$773$	20.6653	+	35.7933i	0.743278	+	1.28739i	0.950995	+	0.309206i	$0.100063\pi$
$773$	20.6653	+	35.7933i	0.743278	+	1.28739i	−0.207718	+	0.978189i	$0.566604\pi$
$774$		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
$782$	25.4526	+	35.3614i	0.910182	+	1.26452i
$783$		0			0
$784$	22.9094	−	16.0984i	0.818194	−	0.574942i
$785$	34.7932			1.24182
$786$		0			0
$787$	−34.1512	+	19.7172i	−1.21736	+	0.702843i	−0.964353	−	0.264621i	$-0.914753\pi$
$787$	−34.1512	+	19.7172i	−1.21736	+	0.702843i	−0.253008	+	0.967464i	$0.581420\pi$
$788$	−15.0273	−	5.03054i	−0.535325	−	0.179205i
$789$		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
$794$	−7.04479	+	0.708846i	−0.250010	+	0.0251560i
$795$		0			0
$796$	35.4110	−	7.19900i	1.25511	−	0.255162i
$797$	−2.23985			−0.0793395			−0.0396697	−	0.999213i	$-0.512631\pi$
$797$	−2.23985			−0.0793395			−0.0396697	+	0.999213i	$0.512631\pi$
$798$		0			0
$799$			1.66623i			0.0589470i
$800$	−48.2843	+	26.4664i	−1.70711	+	0.935729i
$801$		0			0
$802$	−37.8316	+	3.80661i	−1.33588	+	0.134416i
$803$	−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
$808$	27.9997	+	25.8942i	0.985026	+	0.910954i
$809$	−2.10727	−	3.64989i	−0.0740876	−	0.128323i	0.826602	−	0.562788i	$-0.190271\pi$
$809$	−2.10727	−	3.64989i	−0.0740876	−	0.128323i	−0.900689	+	0.434464i	$0.856938\pi$
$810$		0			0
$811$		−	19.7835i		−	0.694694i	−0.937737	−	0.347347i	$-0.887083\pi$
$811$		−	19.7835i		−	0.694694i	0.937737	−	0.347347i	$-0.112917\pi$
$812$	4.31662	+	13.6509i	0.151484	+	0.479051i
$813$		0			0
$814$	12.2653	−	8.82838i	0.429899	−	0.309435i
$815$	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	$-0.474512\pi$
$821$	−21.2969	−	12.2958i	−0.743268	−	0.429126i	−0.823256	+	0.567670i	$0.807845\pi$
$822$		0			0
$823$	5.30737	−	3.06421i	0.185003	−	0.106812i	−0.404638	−	0.914477i	$-0.632602\pi$
$823$	5.30737	−	3.06421i	0.185003	−	0.106812i	0.589641	+	0.807665i	$0.299269\pi$
$824$	3.28788	−	14.5154i	0.114539	−	0.505667i
$825$		0			0
$826$	8.00290	+	38.3009i	0.278457	+	1.33266i
$827$	−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	$-0.0753901\pi$
$829$	8.14363	+	14.1052i	0.282840	+	0.489893i	−0.689243	+	0.724530i	$0.742057\pi$
$830$	2.44258	+	24.2753i	0.0847831	+	0.842608i
$831$		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
$836$	11.5219	+	3.85708i	0.398494	+	0.133400i
$837$		0			0
$838$	38.9852	−	28.0610i	1.34672	−	0.969351i
$839$	40.4513			1.39653			0.698266	−	0.715838i	$-0.253955\pi$
$839$	40.4513			1.39653			0.698266	+	0.715838i	$0.253955\pi$
$840$		0			0
$841$	21.6793			0.747563
$842$	3.16640	−	2.27912i	0.109121	−	0.0785438i
$843$		0			0
$844$	0.444376	−	1.32745i	0.0152961	−	0.0456927i
$845$	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
$850$	−5.62414	−	55.8949i	−0.192907	−	1.91718i
$851$	−15.7404	−	27.2632i	−0.539575	−	0.934571i
$852$		0			0
$853$	−38.0308			−1.30215			−0.651075	−	0.759013i	$-0.725682\pi$
$853$	−38.0308			−1.30215			−0.651075	+	0.759013i	$0.725682\pi$
$854$	−6.71068	−	7.50495i	−0.229635	−	0.256814i
$855$		0			0
$856$	−2.18590	+	9.65032i	−0.0747124	+	0.329841i
$857$	34.7732	−	20.0763i	1.18783	−	0.685794i	0.230017	−	0.973187i	$-0.426122\pi$
$857$	34.7732	−	20.0763i	1.18783	−	0.685794i	0.957813	+	0.287393i	$0.0927884\pi$
$858$		0			0
$859$	−25.6875	−	14.8307i	−0.876446	−	0.506016i	−0.00696080	−	0.999976i	$-0.502216\pi$
$859$	−25.6875	−	14.8307i	−0.876446	−	0.506016i	−0.869485	+	0.493960i	$0.835549\pi$
$860$	−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	$-0.277158\pi$
$863$	8.93311	+	5.15753i	0.304087	+	0.175564i	−0.340191	+	0.940356i	$0.610492\pi$
$864$		0			0
$865$	−6.78360	−	11.7495i	−0.230649	−	0.399496i
$866$	−23.2369	+	16.7256i	−0.789624	+	0.568359i
$867$		0			0
$868$	−22.6650	−	20.7339i	−0.769301	−	0.703755i
$869$			26.3175i			0.892761i
$870$		0			0
$871$	14.2631	+	24.7044i	0.483286	+	0.837076i
$872$	33.1683	−	35.8653i	1.12322	−	1.21455i
$873$		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	$-0.319364\pi$
$877$	2.25040	+	1.29927i	0.0759907	+	0.0438733i	−0.461523	+	0.887128i	$0.652697\pi$
$878$	41.1995	−	4.14549i	1.39042	−	0.139904i
$879$		0			0
$880$	−31.4145	−	23.6871i	−1.05898	−	0.798492i
$881$		−	16.6411i		−	0.560654i	−0.959905	−	0.280327i	$-0.909557\pi$
$881$		−	16.6411i		−	0.560654i	0.959905	−	0.280327i	$-0.0904428\pi$
$882$		0			0
$883$	−7.02636			−0.236456			−0.118228	−	0.992986i	$-0.537721\pi$
$883$	−7.02636			−0.236456			−0.118228	+	0.992986i	$0.537721\pi$
$884$	9.74292	+	47.9243i	0.327690	+	1.61187i
$885$		0			0
$886$	−32.8080	+	3.30114i	−1.10221	+	0.110904i
$887$	−19.9044	+	34.4755i	−0.668326	+	1.15757i	0.310046	+	0.950722i	$0.399656\pi$
$887$	−19.9044	+	34.4755i	−0.668326	+	1.15757i	−0.978372	+	0.206853i	$0.933678\pi$
$888$		0			0
$889$	−22.4283	+	16.3288i	−0.752220	+	0.547649i
$890$	19.1838	+	8.64340i	0.643044	+	0.289727i
$891$		0			0
$892$	1.60035	−	4.78058i	0.0535836	−	0.160066i
$893$	0.838295	−	0.483990i	0.0280525	−	0.0161961i
$894$		0			0
$895$	36.0517			1.20508
$896$	−8.38953	−	28.7335i	−0.280275	−	0.959920i
$897$		0			0
$898$	−23.0014	−	31.9559i	−0.767565	−	1.06638i
$899$	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	0.933155	−	0.359473i	$-0.117044\pi$
$907$	4.67603	+	8.09911i	0.155265	+	0.268927i	−0.777891	+	0.628400i	$0.783710\pi$
$908$	−3.31287	−	16.2956i	−0.109942	−	0.540790i
$909$		0			0
$910$	−57.3604	−	64.1495i	−1.90148	−	2.12654i
$911$		−	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
$914$	−26.9067	+	2.70735i	−0.889994	+	0.0895511i
$915$		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	$-0.262587\pi$
$919$	11.5743	+	6.68240i	0.381799	+	0.220432i	−0.296801	+	0.954939i	$0.595920\pi$
$920$	−55.6473	+	60.1721i	−1.83464	+	1.98382i
$921$		0			0
$922$	−16.9801	−	23.5906i	−0.559211	−	0.776914i
$923$		−	7.27887i		−	0.239587i
$924$		0			0
$925$			40.5909i			1.33462i
$926$	36.4446	−	26.2323i	1.19764	−	0.862046i
$927$		0			0
$928$	15.3018	+	0.339553i	0.502308	+	0.0111464i
$929$	−31.1417	−	17.9797i	−1.02173	−	0.589895i	−0.107123	−	0.994246i	$-0.534164\pi$
$929$	−31.1417	−	17.9797i	−1.02173	−	0.589895i	−0.914604	+	0.404351i	$0.867497\pi$
$930$		0			0
$931$	12.3112	−	11.1289i	0.403482	−	0.364735i
$932$	−29.1053	−	32.9074i	−0.953377	−	1.07792i
$933$		0			0
$934$	−0.125036	−	1.24265i	−0.00409129	−	0.0406608i
$935$	34.7629	−	20.0703i	1.13687	−	0.656370i
$936$		0			0
$937$			52.0867i			1.70160i	0.525491	+	0.850799i	$0.323882\pi$
$937$			52.0867i			1.70160i	−0.525491	+	0.850799i	$0.676118\pi$
$938$	17.4371	−	3.64345i	0.569342	−	0.118963i
$939$		0			0
$940$	−3.07157	+	0.624445i	−0.100184	+	0.0203671i
$941$	−19.6811	−	34.0886i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$941$	−19.6811	−	34.0886i	−0.641584	−	1.11126i	0.343495	−	0.939154i	$-0.388389\pi$
$942$		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	0.353104	+	0.935584i	$0.385126\pi$
$947$	−19.5007	+	33.7762i	−0.633688	+	1.09758i	−0.986792	+	0.161995i	$0.948207\pi$
$948$		0			0
$949$	−39.8479	+	23.0062i	−1.29352	+	0.746812i
$950$	−26.4876	+	19.0653i	−0.859370	+	0.618561i
$951$		0			0
$952$	30.3304	+	3.56646i	0.983015	+	0.115590i
$953$	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
$956$	54.0813	+	18.1043i	1.74911	+	0.585533i
$957$		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
$962$	−3.53765	−	35.1586i	−0.114058	−	1.13356i
$963$		0			0
$964$	3.68638	+	18.1329i	0.118730	+	0.584021i
$965$	−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	$0.909052\pi$
$968$	−2.77031	+	12.2304i	−0.0890411	+	0.393100i
$969$		0			0
$970$	−0.655200	−	6.51163i	−0.0210372	−	0.209076i
$971$	−9.98701	−	5.76600i	−0.320498	−	0.185040i	0.331116	−	0.943590i	$-0.392575\pi$
$971$	−9.98701	−	5.76600i	−0.320498	−	0.185040i	−0.651615	+	0.758550i	$0.725908\pi$
$972$		0			0
$973$	32.1158	−	23.3817i	1.02959	−	0.749584i
$974$	−45.6336	−	20.5605i	−1.46220	−	0.658801i
$975$		0			0
$976$	−9.90843	+	4.20242i	−0.317161	+	0.134516i
$977$	19.8176	+	34.3250i	0.634020	+	1.09816i	0.986722	+	0.162419i	$0.0519297\pi$
$977$	19.8176	+	34.3250i	0.634020	+	1.09816i	−0.352702	+	0.935736i	$0.614737\pi$
$978$		0			0
$979$			9.93253i			0.317445i
$980$	−49.2423	+	21.5176i	−1.57299	+	0.687354i
$981$		0			0
$982$	28.2704	+	39.2762i	0.902145	+	1.25335i
$983$	−29.0730	−	50.3560i	−0.927286	−	1.60611i	−0.787843	−	0.615876i	$-0.788802\pi$
$983$	−29.0730	−	50.3560i	−0.927286	−	1.60611i	−0.139443	−	0.990230i	$-0.544531\pi$
$984$		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	$-0.610993\pi$
$991$	9.48813	−	5.47798i	0.301400	−	0.174014i	0.643072	+	0.765806i	$0.277660\pi$
$992$	−28.7966	+	15.7845i	−0.914294	+	0.501159i
$993$		0			0
$994$	−4.31808	−	1.41954i	−0.136961	−	0.0450251i
$995$	−69.3520			−2.19861
$996$		0			0
$997$	−13.5416	−	23.4547i	−0.428866	−	0.742818i	0.567907	−	0.823093i	$-0.307753\pi$
$997$	−13.5416	−	23.4547i	−0.428866	−	0.742818i	−0.996773	+	0.0802751i	$0.974420\pi$
$998$	6.76298	−	0.680490i	0.214078	−	0.0215405i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.b.19.12	yes	32
3.2	odd	2	inner	504.2.bk.b.19.5	yes	32
4.3	odd	2		2016.2.bs.b.271.16		32
7.3	odd	6	inner	504.2.bk.b.451.1	yes	32
8.3	odd	2	inner	504.2.bk.b.19.1	✓	32
8.5	even	2		2016.2.bs.b.271.2		32
12.11	even	2		2016.2.bs.b.271.1		32
21.17	even	6	inner	504.2.bk.b.451.16	yes	32
24.5	odd	2		2016.2.bs.b.271.15		32
24.11	even	2	inner	504.2.bk.b.19.16	yes	32
28.3	even	6		2016.2.bs.b.1711.2		32
56.3	even	6	inner	504.2.bk.b.451.12	yes	32
56.45	odd	6		2016.2.bs.b.1711.16		32
84.59	odd	6		2016.2.bs.b.1711.15		32
168.59	odd	6	inner	504.2.bk.b.451.5	yes	32
168.101	even	6		2016.2.bs.b.1711.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bk.b.19.1	✓	32	8.3	odd	2	inner
504.2.bk.b.19.5	yes	32	3.2	odd	2	inner
504.2.bk.b.19.12	yes	32	1.1	even	1	trivial
504.2.bk.b.19.16	yes	32	24.11	even	2	inner
504.2.bk.b.451.1	yes	32	7.3	odd	6	inner
504.2.bk.b.451.5	yes	32	168.59	odd	6	inner
504.2.bk.b.451.12	yes	32	56.3	even	6	inner
504.2.bk.b.451.16	yes	32	21.17	even	6	inner
2016.2.bs.b.271.1		32	12.11	even	2
2016.2.bs.b.271.2		32	8.5	even	2
2016.2.bs.b.271.15		32	24.5	odd	2
2016.2.bs.b.271.16		32	4.3	odd	2
2016.2.bs.b.1711.1		32	168.101	even	6
2016.2.bs.b.1711.2		32	28.3	even	6
2016.2.bs.b.1711.15		32	84.59	odd	6
2016.2.bs.b.1711.16		32	56.45	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.826169 + 1.14780i) q^{2} +(-0.634890 + 1.89655i) q^{4} +(1.91923 - 3.32420i) q^{5} +(-1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +O(q^{10})\)	\(q+(0.826169 + 1.14780i) q^{2} +(-0.634890 + 1.89655i) q^{4} +(1.91923 - 3.32420i) q^{5} +(-1.55724 - 2.13893i) q^{7} +(-2.70139 + 0.838146i) q^{8} +(5.40112 - 0.543460i) q^{10} +(1.28125 + 2.21918i) q^{11} +5.99175 q^{13} +(1.16852 - 3.55451i) q^{14} +(-3.19383 - 2.40821i) q^{16} +(3.53425 - 2.04050i) q^{17} +(-2.05318 - 1.18541i) q^{19} +(5.08602 + 5.75041i) q^{20} +(-1.48865 + 3.30403i) q^{22} +(6.53773 + 3.77456i) q^{23} +(-4.86686 - 8.42964i) q^{25} +(4.95020 + 6.87733i) q^{26} +(5.04527 - 1.59539i) q^{28} +2.70568i q^{29} +(-2.90258 - 5.02742i) q^{31} +(0.125497 - 5.65546i) q^{32} +(5.26197 + 2.37081i) q^{34} +(-10.0989 + 1.07147i) q^{35} +(-3.61144 - 2.08507i) q^{37} +(-0.335667 - 3.33599i) q^{38} +(-2.39841 + 10.5885i) q^{40} +5.96293i q^{41} -8.06098 q^{43} +(-5.02225 + 1.02101i) q^{44} +(1.06883 + 10.6224i) q^{46} +(-0.204145 + 0.353590i) q^{47} +(-2.15004 + 6.66163i) q^{49} +(5.65470 - 12.5505i) q^{50} +(-3.80410 + 11.3637i) q^{52} +(-4.41436 + 2.54863i) q^{53} +9.83600 q^{55} +(5.99944 + 4.47289i) q^{56} +(-3.10557 + 2.23534i) q^{58} +(-9.05639 + 5.22871i) q^{59} +(1.34535 - 2.33021i) q^{61} +(3.37245 - 7.48508i) q^{62} +(6.59502 - 4.52832i) q^{64} +(11.4995 - 19.9178i) q^{65} +(2.38045 + 4.12307i) q^{67} +(1.62606 + 7.99838i) q^{68} +(-9.57323 - 10.7063i) q^{70} -1.21482i q^{71} +(-6.65046 + 3.83964i) q^{73} +(-0.590421 - 5.86783i) q^{74} +(3.55173 - 3.14137i) q^{76} +(2.75147 - 6.19628i) q^{77} +(8.89433 + 5.13514i) q^{79} +(-14.1350 + 5.99503i) q^{80} +(-6.84425 + 4.92639i) q^{82} +4.49449i q^{83} -15.6647i q^{85} +(-6.65973 - 9.25239i) q^{86} +(-5.32115 - 4.92101i) q^{88} +(3.35682 + 1.93806i) q^{89} +(-9.33056 - 12.8159i) q^{91} +(-11.3094 + 10.0027i) q^{92} +(-0.574508 + 0.0578070i) q^{94} +(-7.88105 + 4.55013i) q^{95} -1.20561i q^{97} +(-9.42252 + 3.03582i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 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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