LMFDB - Embedded newform 936.2.w.k.811.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(307,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			811.12
Character	$\chi$	$=$	936.811
Dual form			936.2.w.k.307.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.189453 - 1.40147i) q^{2} +(-1.92821 + 0.531025i) q^{4} +(-0.612096 - 0.612096i) q^{5} +(1.94766 - 1.94766i) q^{7} +(1.10952 + 2.60172i) q^{8} +(-0.741868 + 0.973796i) q^{10} +(0.148872 + 0.148872i) q^{11} +(0.952638 - 3.47742i) q^{13} +(-3.09856 - 2.36058i) q^{14} +(3.43602 - 2.04786i) q^{16} +3.60967i q^{17} +(1.89240 - 1.89240i) q^{19} +(1.50529 + 0.855214i) q^{20} +(0.180435 - 0.236844i) q^{22} -2.04327 q^{23} -4.25068i q^{25} +(-5.05397 - 0.676280i) q^{26} +(-2.72124 + 4.78975i) q^{28} -6.31014i q^{29} +(0.261807 + 0.261807i) q^{31} +(-3.52097 - 4.42750i) q^{32} +(5.05883 - 0.683863i) q^{34} -2.38430 q^{35} +(-1.73417 + 1.73417i) q^{37} +(-3.01066 - 2.29362i) q^{38} +(0.913371 - 2.27164i) q^{40} +(-0.454360 + 0.454360i) q^{41} -10.8239i q^{43} +(-0.366113 - 0.208003i) q^{44} +(0.387104 + 2.86357i) q^{46} +(-6.24940 + 6.24940i) q^{47} -0.586721i q^{49} +(-5.95718 + 0.805305i) q^{50} +(0.00970845 + 7.21110i) q^{52} -7.10635i q^{53} -0.182248i q^{55} +(7.22822 + 2.90630i) q^{56} +(-8.84344 + 1.19548i) q^{58} +(-7.60381 - 7.60381i) q^{59} +5.54058i q^{61} +(0.317314 - 0.416514i) q^{62} +(-5.53793 + 5.77333i) q^{64} +(-2.71162 + 1.54541i) q^{65} +(-1.25346 + 1.25346i) q^{67} +(-1.91682 - 6.96021i) q^{68} +(0.451714 + 3.34152i) q^{70} +(-7.84227 - 7.84227i) q^{71} +(-5.73583 - 5.73583i) q^{73} +(2.75892 + 2.10183i) q^{74} +(-2.64404 + 4.65387i) q^{76} +0.579904 q^{77} +6.43580i q^{79} +(-3.35666 - 0.849690i) q^{80} +(0.722851 + 0.550691i) q^{82} +(3.01711 - 3.01711i) q^{83} +(2.20946 - 2.20946i) q^{85} +(-15.1693 + 2.05063i) q^{86} +(-0.222148 + 0.552501i) q^{88} +(7.13489 + 7.13489i) q^{89} +(-4.91741 - 8.62823i) q^{91} +(3.93986 - 1.08503i) q^{92} +(9.94229 + 7.57435i) q^{94} -2.31666 q^{95} +(7.21217 - 7.21217i) q^{97} +(-0.822269 + 0.111156i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 40 q^{16} - 8 q^{19} - 32 q^{22} + 24 q^{28} + 8 q^{34} + 16 q^{40} - 8 q^{46} + 24 q^{52} - 24 q^{58} + 40 q^{67} - 24 q^{70} + 56 q^{76} + 104 q^{91} - 64 q^{94} - 32 q^{97}+O(q^{100}) $ 48 * q - 40 * q^16 - 8 * q^19 - 32 * q^22 + 24 * q^28 + 8 * q^34 + 16 * q^40 - 8 * q^46 + 24 * q^52 - 24 * q^58 + 40 * q^67 - 24 * q^70 + 56 * q^76 + 104 * q^91 - 64 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−0.189453	−	1.40147i	−0.133964	−	0.990986i
$2$	−0.189453	−	1.40147i	−0.133964	−	0.990986i
$3$		0			0
$3$		0			0
$4$	−1.92821	+	0.531025i	−0.964107	+	0.265513i
$5$	−0.612096	−	0.612096i	−0.273738	−	0.273738i	0.556865	−	0.830603i	$-0.312004\pi$
$5$	−0.612096	−	0.612096i	−0.273738	−	0.273738i	−0.830603	+	0.556865i	$0.812004\pi$
$6$		0			0
$7$	1.94766	−	1.94766i	0.736144	−	0.736144i	−0.235685	−	0.971829i	$-0.575733\pi$
$7$	1.94766	−	1.94766i	0.736144	−	0.736144i	0.971829	+	0.235685i	$0.0757334\pi$
$8$	1.10952	+	2.60172i	0.392275	+	0.919848i
$9$		0			0
$10$	−0.741868	+	0.973796i	−0.234599	+	0.307941i
$11$	0.148872	+	0.148872i	0.0448867	+	0.0448867i	0.729194	−	0.684307i	$-0.239895\pi$
$11$	0.148872	+	0.148872i	0.0448867	+	0.0448867i	−0.684307	+	0.729194i	$0.739895\pi$
$12$		0			0
$13$	0.952638	−	3.47742i	0.264214	−	0.964464i
$13$	0.952638	−	3.47742i	0.264214	−	0.964464i
$14$	−3.09856	−	2.36058i	−0.828126	−	0.630892i
$15$		0			0
$16$	3.43602	−	2.04786i	0.859006	−	0.511965i
$17$			3.60967i			0.875473i	0.899103	+	0.437736i	$0.144220\pi$
$17$			3.60967i			0.875473i	−0.899103	+	0.437736i	$0.855780\pi$
$18$		0			0
$19$	1.89240	−	1.89240i	0.434147	−	0.434147i	−0.455890	−	0.890036i	$-0.650679\pi$
$19$	1.89240	−	1.89240i	0.434147	−	0.434147i	0.890036	+	0.455890i	$0.150679\pi$
$20$	1.50529	+	0.855214i	0.336593	+	0.191232i
$21$		0			0
$22$	0.180435	−	0.236844i	0.0384689	−	0.0504953i
$23$	−2.04327			−0.426051			−0.213026	−	0.977047i	$-0.568332\pi$
$23$	−2.04327			−0.426051			−0.213026	+	0.977047i	$0.568332\pi$
$24$		0			0
$25$		−	4.25068i		−	0.850135i
$26$	−5.05397	−	0.676280i	−0.991166	−	0.132629i
$27$		0			0
$28$	−2.72124	+	4.78975i	−0.514267	+	0.905178i
$29$		−	6.31014i		−	1.17176i	−0.810397	−	0.585881i	$-0.800748\pi$
$29$		−	6.31014i		−	1.17176i	0.810397	−	0.585881i	$-0.199252\pi$
$30$		0			0
$31$	0.261807	+	0.261807i	0.0470220	+	0.0470220i	0.730227	−	0.683205i	$-0.239414\pi$
$31$	0.261807	+	0.261807i	0.0470220	+	0.0470220i	−0.683205	+	0.730227i	$0.739414\pi$
$32$	−3.52097	−	4.42750i	−0.622426	−	0.782679i
$33$		0			0
$34$	5.05883	−	0.683863i	0.867581	−	0.117282i
$35$	−2.38430			−0.403021
$36$		0			0
$37$	−1.73417	+	1.73417i	−0.285095	+	0.285095i	−0.835137	−	0.550042i	$-0.814612\pi$
$37$	−1.73417	+	1.73417i	−0.285095	+	0.285095i	0.550042	+	0.835137i	$0.314612\pi$
$38$	−3.01066	−	2.29362i	−0.488393	−	0.372074i
$39$		0			0
$40$	0.913371	−	2.27164i	0.144417	−	0.359177i
$41$	−0.454360	+	0.454360i	−0.0709592	+	0.0709592i	−0.741696	−	0.670737i	$-0.765978\pi$
$41$	−0.454360	+	0.454360i	−0.0709592	+	0.0709592i	0.670737	+	0.741696i	$0.265978\pi$
$42$		0			0
$43$		−	10.8239i		−	1.65063i	−0.564672	−	0.825315i	$-0.690997\pi$
$43$		−	10.8239i		−	1.65063i	0.564672	−	0.825315i	$-0.309003\pi$
$44$	−0.366113	−	0.208003i	−0.0551936	−	0.0313576i
$45$		0			0
$46$	0.387104	+	2.86357i	0.0570754	+	0.422211i
$47$	−6.24940	+	6.24940i	−0.911569	+	0.911569i	−0.996396	−	0.0848271i	$-0.972966\pi$
$47$	−6.24940	+	6.24940i	−0.911569	+	0.911569i	0.0848271	+	0.996396i	$0.472966\pi$
$48$		0			0
$49$		−	0.586721i		−	0.0838173i
$50$	−5.95718	+	0.805305i	−0.842472	+	0.113887i
$51$		0			0
$52$	0.00970845	+	7.21110i	0.00134632	+	0.999999i
$53$		−	7.10635i		−	0.976132i	−0.872807	−	0.488066i	$-0.837703\pi$
$53$		−	7.10635i		−	0.976132i	0.872807	−	0.488066i	$-0.162297\pi$
$54$		0			0
$55$		−	0.182248i		−	0.0245743i
$56$	7.22822	+	2.90630i	0.965912	+	0.388370i
$57$		0			0
$58$	−8.84344	+	1.19548i	−1.16120	+	0.156974i
$59$	−7.60381	−	7.60381i	−0.989932	−	0.989932i	0.0100179	−	0.999950i	$-0.496811\pi$
$59$	−7.60381	−	7.60381i	−0.989932	−	0.989932i	−0.999950	+	0.0100179i	$0.996811\pi$
$60$		0			0
$61$			5.54058i			0.709398i	0.934981	+	0.354699i	$0.115417\pi$
$61$			5.54058i			0.709398i	−0.934981	+	0.354699i	$0.884583\pi$
$62$	0.317314	−	0.416514i	0.0402989	−	0.0528974i
$63$		0			0
$64$	−5.53793	+	5.77333i	−0.692241	+	0.721666i
$65$	−2.71162	+	1.54541i	−0.336336	+	0.191685i
$66$		0			0
$67$	−1.25346	+	1.25346i	−0.153134	+	0.153134i	−0.779516	−	0.626382i	$-0.784535\pi$
$67$	−1.25346	+	1.25346i	−0.153134	+	0.153134i	0.626382	+	0.779516i	$0.284535\pi$
$68$	−1.91682	−	6.96021i	−0.232449	−	0.844050i
$69$		0			0
$70$	0.451714	+	3.34152i	0.0539902	+	0.399388i
$71$	−7.84227	−	7.84227i	−0.930706	−	0.930706i	0.0670439	−	0.997750i	$-0.478643\pi$
$71$	−7.84227	−	7.84227i	−0.930706	−	0.930706i	−0.997750	+	0.0670439i	$0.978643\pi$
$72$		0			0
$73$	−5.73583	−	5.73583i	−0.671328	−	0.671328i	0.286694	−	0.958022i	$-0.407444\pi$
$73$	−5.73583	−	5.73583i	−0.671328	−	0.671328i	−0.958022	+	0.286694i	$0.907444\pi$
$74$	2.75892	+	2.10183i	0.320718	+	0.244333i
$75$		0			0
$76$	−2.64404	+	4.65387i	−0.303293	+	0.533836i
$77$	0.579904			0.0660862
$78$		0			0
$79$			6.43580i			0.724085i	0.932162	+	0.362042i	$0.117920\pi$
$79$			6.43580i			0.724085i	−0.932162	+	0.362042i	$0.882080\pi$
$80$	−3.35666	−	0.849690i	−0.375286	−	0.0949982i
$81$		0			0
$82$	0.722851	+	0.550691i	0.0798255	+	0.0608136i
$83$	3.01711	−	3.01711i	0.331171	−	0.331171i	−0.521860	−	0.853031i	$-0.674762\pi$
$83$	3.01711	−	3.01711i	0.331171	−	0.331171i	0.853031	+	0.521860i	$0.174762\pi$
$84$		0			0
$85$	2.20946	−	2.20946i	0.239650	−	0.239650i
$86$	−15.1693	+	2.05063i	−1.63575	+	0.221125i
$87$		0			0
$88$	−0.222148	+	0.552501i	−0.0236810	+	0.0588968i
$89$	7.13489	+	7.13489i	0.756297	+	0.756297i	0.975646	−	0.219350i	$-0.0703935\pi$
$89$	7.13489	+	7.13489i	0.756297	+	0.756297i	−0.219350	+	0.975646i	$0.570394\pi$
$90$		0			0
$91$	−4.91741	−	8.62823i	−0.515485	−	0.904485i
$92$	3.93986	−	1.08503i	0.410759	−	0.113122i
$93$		0			0
$94$	9.94229	+	7.57435i	1.02547	+	0.781235i
$95$	−2.31666			−0.237685
$96$		0			0
$97$	7.21217	−	7.21217i	0.732285	−	0.732285i	−0.238787	−	0.971072i	$-0.576750\pi$
$97$	7.21217	−	7.21217i	0.732285	−	0.732285i	0.971072	+	0.238787i	$0.0767497\pi$
$98$	−0.822269	+	0.111156i	−0.0830618	+	0.0112285i
$99$		0			0
$100$	2.25722	+	8.19622i	0.225722	+	0.819622i
$101$	9.96869			0.991922			0.495961	−	0.868345i	$-0.334816\pi$
$101$	9.96869			0.991922			0.495961	+	0.868345i	$0.334816\pi$
$102$		0			0
$103$	8.19929			0.807900			0.403950	−	0.914781i	$-0.367637\pi$
$103$	8.19929			0.807900			0.403950	+	0.914781i	$0.367637\pi$
$104$	10.1043	−	1.37977i	0.990805	−	0.135298i
$105$		0			0
$106$	−9.95930	+	1.34632i	−0.967333	+	0.130766i
$107$	−4.86415			−0.470235			−0.235118	−	0.971967i	$-0.575548\pi$
$107$	−4.86415			−0.470235			−0.235118	+	0.971967i	$0.575548\pi$
$108$		0			0
$109$	6.69167	+	6.69167i	0.640946	+	0.640946i	0.950788	−	0.309842i	$-0.100276\pi$
$109$	6.69167	+	6.69167i	0.640946	+	0.640946i	−0.309842	+	0.950788i	$0.600276\pi$
$110$	−0.255415	+	0.0345275i	−0.0243528	+	0.00329207i
$111$		0			0
$112$	2.70367	−	10.6807i	0.255472	−	1.00923i
$113$	18.2063			1.71271			0.856353	−	0.516391i	$-0.172725\pi$
$113$	18.2063			1.71271			0.856353	+	0.516391i	$0.172725\pi$
$114$		0			0
$115$	1.25068	+	1.25068i	0.116626	+	0.116626i
$116$	3.35084	+	12.1673i	0.311118	+	1.12971i
$117$		0			0
$118$	−9.21592	+	12.0971i	−0.848394	+	1.11362i
$119$	7.03038	+	7.03038i	0.644474	+	0.644474i
$120$		0			0
$121$		−	10.9557i		−	0.995970i
$122$	7.76493	−	1.04968i	0.703004	−	0.0950337i
$123$		0			0
$124$	−0.643847	−	0.365794i	−0.0578191	−	0.0328493i
$125$	−5.66230	+	5.66230i	−0.506452	+	0.506452i
$126$		0			0
$127$	−1.99734			−0.177235			−0.0886177	−	0.996066i	$-0.528245\pi$
$127$	−1.99734			−0.177235			−0.0886177	+	0.996066i	$0.528245\pi$
$128$	9.14031	+	6.66744i	0.807897	+	0.589324i
$129$		0			0
$130$	2.67957	+	3.50747i	0.235014	+	0.307625i
$131$	−16.0431			−1.40169			−0.700846	−	0.713312i	$-0.747194\pi$
$131$	−16.0431			−1.40169			−0.700846	+	0.713312i	$0.747194\pi$
$132$		0			0
$133$		−	7.37149i		−	0.639190i
$134$	1.99415	+	1.51921i	0.172268	+	0.131239i
$135$		0			0
$136$	−9.39135	+	4.00500i	−0.805302	+	0.343426i
$137$	12.5509	+	12.5509i	1.07229	+	1.07229i	0.997175	+	0.0751182i	$0.0239334\pi$
$137$	12.5509	+	12.5509i	1.07229	+	1.07229i	0.0751182	+	0.997175i	$0.476067\pi$
$138$		0			0
$139$	2.18436			0.185275			0.0926375	−	0.995700i	$-0.470470\pi$
$139$	2.18436			0.185275			0.0926375	+	0.995700i	$0.470470\pi$
$140$	4.59745	−	1.26612i	0.388555	−	0.107007i
$141$		0			0
$142$	−9.50493	+	12.4764i	−0.797636	+	1.04700i
$143$	0.659513	−	0.375871i	0.0551513	−	0.0314319i
$144$		0			0
$145$	−3.86241	+	3.86241i	−0.320756	+	0.320756i
$146$	−6.95190	+	9.12525i	−0.575343	+	0.755211i
$147$		0			0
$148$	2.42296	−	4.26473i	0.199166	−	0.350559i
$149$	3.22148	+	3.22148i	0.263914	+	0.263914i	0.826642	−	0.562728i	$-0.190248\pi$
$149$	3.22148	+	3.22148i	0.263914	+	0.263914i	−0.562728	+	0.826642i	$0.690248\pi$
$150$		0			0
$151$	−4.75516	+	4.75516i	−0.386969	+	0.386969i	−0.873605	−	0.486636i	$-0.838224\pi$
$151$	−4.75516	+	4.75516i	−0.386969	+	0.386969i	0.486636	+	0.873605i	$0.338224\pi$
$152$	7.02317	+	2.82385i	0.569654	+	0.229044i
$153$		0			0
$154$	−0.109865	−	0.812715i	−0.00885315	−	0.0654905i
$155$		−	0.320502i		−	0.0257434i
$156$		0			0
$157$		−	1.95742i		−	0.156219i	−0.996945	−	0.0781097i	$-0.975112\pi$
$157$		−	1.95742i		−	0.156219i	0.996945	−	0.0781097i	$-0.0248884\pi$
$158$	9.01956	−	1.21928i	0.717558	−	0.0970011i
$159$		0			0
$160$	−0.554880	+	4.86523i	−0.0438671	+	0.384630i
$161$	−3.97958	+	3.97958i	−0.313635	+	0.313635i
$162$		0			0
$163$	−1.25346	−	1.25346i	−0.0981783	−	0.0981783i	0.656312	−	0.754490i	$-0.272116\pi$
$163$	−1.25346	−	1.25346i	−0.0981783	−	0.0981783i	−0.754490	+	0.656312i	$0.772116\pi$
$164$	0.634828	−	1.11738i	0.0495717	−	0.0872528i
$165$		0			0
$166$	−4.79998	−	3.65678i	−0.372551	−	0.283821i
$167$	−1.38331	+	1.38331i	−0.107044	+	0.107044i	−0.758600	−	0.651557i	$-0.774116\pi$
$167$	−1.38331	+	1.38331i	−0.107044	+	0.107044i	0.651557	+	0.758600i	$0.274116\pi$
$168$		0			0
$169$	−11.1850	−	6.62545i	−0.860382	−	0.509650i
$170$	−3.51508	−	2.67790i	−0.269594	−	0.205385i
$171$		0			0
$172$	5.74777	+	20.8708i	0.438263	+	1.59138i
$173$	22.3012			1.69553			0.847764	−	0.530374i	$-0.177949\pi$
$173$	22.3012			1.69553			0.847764	+	0.530374i	$0.177949\pi$
$174$		0			0
$175$	−8.27885	−	8.27885i	−0.625822	−	0.625822i
$176$	0.816398	+	0.206659i	0.0615384	+	0.0155775i
$177$		0			0
$178$	8.64758	−	11.3510i	0.648163	−	0.850796i
$179$		−	22.0773i		−	1.65014i	−0.565033	−	0.825069i	$-0.691136\pi$
$179$		−	22.0773i		−	1.65014i	0.565033	−	0.825069i	$-0.308864\pi$
$180$		0			0
$181$	3.99980			0.297303			0.148651	−	0.988890i	$-0.452507\pi$
$181$	3.99980			0.297303			0.148651	+	0.988890i	$0.452507\pi$
$182$	−11.1606	+	8.52624i	−0.827276	+	0.632007i
$183$		0			0
$184$	−2.26705	−	5.31602i	−0.167129	−	0.391902i
$185$	2.12295			0.156083
$186$		0			0
$187$	−0.537379	+	0.537379i	−0.0392971	+	0.0392971i
$188$	8.73160	−	15.3688i	0.636817	−	1.12088i
$189$		0			0
$190$	0.438900	+	3.24673i	0.0318411	+	0.235542i
$191$			16.3774i			1.18503i	0.805560	+	0.592515i	$0.201865\pi$
$191$			16.3774i			1.18503i	−0.805560	+	0.592515i	$0.798135\pi$
$192$		0			0
$193$	17.2782	+	17.2782i	1.24371	+	1.24371i	0.958449	+	0.285265i	$0.0920817\pi$
$193$	17.2782	+	17.2782i	1.24371	+	1.24371i	0.285265	+	0.958449i	$0.407918\pi$
$194$	−11.4740	−	8.74125i	−0.823784	−	0.627585i
$195$		0			0
$196$	0.311563	+	1.13132i	0.0222545	+	0.0808088i
$197$	−0.612096	−	0.612096i	−0.0436100	−	0.0436100i	0.684965	−	0.728576i	$-0.259817\pi$
$197$	−0.612096	−	0.612096i	−0.0436100	−	0.0436100i	−0.728576	+	0.684965i	$0.759817\pi$
$198$		0			0
$199$	20.8691			1.47937			0.739686	−	0.672952i	$-0.234974\pi$
$199$	20.8691			1.47937			0.739686	+	0.672952i	$0.234974\pi$
$200$	11.0591	−	4.71621i	0.781995	−	0.333487i
$201$		0			0
$202$	−1.88860	−	13.9708i	−0.132882	−	0.982981i
$203$	−12.2900	−	12.2900i	−0.862587	−	0.862587i
$204$		0			0
$205$	0.556224			0.0388484
$206$	−1.55338	−	11.4910i	−0.108229	−	0.800618i
$207$		0			0
$208$	−3.84799	−	13.8994i	−0.266810	−	0.963749i
$209$	0.563452			0.0389748
$210$		0			0
$211$	2.97031			0.204485			0.102242	−	0.994760i	$-0.467398\pi$
$211$	2.97031			0.204485			0.102242	+	0.994760i	$0.467398\pi$
$212$	3.77365	+	13.7026i	0.259175	+	0.941096i
$213$		0			0
$214$	0.921530	+	6.81694i	0.0629945	+	0.465997i
$215$	−6.62527	+	6.62527i	−0.451840	+	0.451840i
$216$		0			0
$217$	1.01982			0.0692299
$218$	8.11039	−	10.6459i	0.549305	−	0.721032i
$219$		0			0
$220$	0.0967784	+	0.351414i	0.00652480	+	0.0236923i
$221$	12.5523	+	3.43871i	0.844362	+	0.231312i
$222$		0			0
$223$	−12.6750	−	12.6750i	−0.848782	−	0.848782i	0.141199	−	0.989981i	$-0.454904\pi$
$223$	−12.6750	−	12.6750i	−0.848782	−	0.848782i	−0.989981	+	0.141199i	$0.954904\pi$
$224$	−15.4809	−	1.76560i	−1.03436	−	0.117969i
$225$		0			0
$226$	−3.44925	−	25.5155i	−0.229441	−	1.69727i
$227$	15.3983	−	15.3983i	1.02202	−	1.02202i	0.0222717	−	0.999752i	$-0.492910\pi$
$227$	15.3983	−	15.3983i	1.02202	−	1.02202i	0.999752	−	0.0222717i	$-0.00708990\pi$
$228$		0			0
$229$	−4.47509	+	4.47509i	−0.295723	+	0.295723i	−0.839336	−	0.543613i	$-0.817056\pi$
$229$	−4.47509	+	4.47509i	−0.295723	+	0.295723i	0.543613	+	0.839336i	$0.317056\pi$
$230$	1.51584	−	1.98973i	0.0999513	−	0.131199i
$231$		0			0
$232$	16.4172	−	7.00122i	1.07784	−	0.459653i
$233$		−	12.4145i		−	0.813304i	−0.913583	−	0.406652i	$-0.866696\pi$
$233$		−	12.4145i		−	0.813304i	0.913583	−	0.406652i	$-0.133304\pi$
$234$		0			0
$235$	7.65046			0.499061
$236$	18.6996	+	10.6240i	1.21724	+	0.691561i
$237$		0			0
$238$	8.52092	−	11.1848i	0.552329	−	0.725001i
$239$	4.32760	+	4.32760i	0.279929	+	0.279929i	0.833081	−	0.553151i	$-0.186575\pi$
$239$	4.32760	+	4.32760i	0.279929	+	0.279929i	−0.553151	+	0.833081i	$0.686575\pi$
$240$		0			0
$241$	−4.44913	−	4.44913i	−0.286594	−	0.286594i	0.549138	−	0.835732i	$-0.314956\pi$
$241$	−4.44913	−	4.44913i	−0.286594	−	0.286594i	−0.835732	+	0.549138i	$0.814956\pi$
$242$	−15.3540	+	2.07559i	−0.986993	+	0.133424i
$243$		0			0
$244$	−2.94218	−	10.6834i	−0.188354	−	0.683936i
$245$	−0.359129	+	0.359129i	−0.0229439	+	0.0229439i
$246$		0			0
$247$	−4.77791	−	8.38346i	−0.304011	−	0.533427i
$248$	−0.390669	+	0.971630i	−0.0248075	+	0.0616986i
$249$		0			0
$250$	9.00827	+	6.86278i	0.569733	+	0.434041i
$251$			19.9908i			1.26181i	0.775862	+	0.630903i	$0.217315\pi$
$251$			19.9908i			1.26181i	−0.775862	+	0.630903i	$0.782685\pi$
$252$		0			0
$253$	−0.304186	−	0.304186i	−0.0191240	−	0.0191240i
$254$	0.378403	+	2.79921i	0.0237431	+	0.175638i
$255$		0			0
$256$	7.61253	−	14.0730i	0.475783	−	0.879562i
$257$			17.5555i			1.09508i	0.836778	+	0.547542i	$0.184436\pi$
$257$			17.5555i			1.09508i	−0.836778	+	0.547542i	$0.815564\pi$
$258$		0			0
$259$			6.75511i			0.419742i
$260$	4.40794	−	4.41983i	0.273369	−	0.274106i
$261$		0			0
$262$	3.03942	+	22.4839i	0.187776	+	1.38906i
$263$			27.6745i			1.70649i	0.521514	+	0.853243i	$0.325367\pi$
$263$			27.6745i			1.70649i	−0.521514	+	0.853243i	$0.674633\pi$
$264$		0			0
$265$	−4.34977	+	4.34977i	−0.267204	+	0.267204i
$266$	−10.3309	+	1.39655i	−0.633428	+	0.0856282i
$267$		0			0
$268$	1.75132	−	3.08255i	0.106979	−	0.188297i
$269$		−	21.7213i		−	1.32437i	−0.749341	−	0.662185i	$-0.769629\pi$
$269$		−	21.7213i		−	1.32437i	0.749341	−	0.662185i	$-0.230371\pi$
$270$		0			0
$271$	−12.0894	+	12.0894i	−0.734379	+	0.734379i	−0.971484	−	0.237105i	$-0.923801\pi$
$271$	−12.0894	+	12.0894i	−0.734379	+	0.734379i	0.237105	+	0.971484i	$0.423801\pi$
$272$	7.39209	+	12.4029i	0.448211	+	0.752036i
$273$		0			0
$274$	15.2118	−	19.9674i	0.918979	−	1.20628i
$275$	0.632808	−	0.632808i	0.0381598	−	0.0381598i
$276$		0			0
$277$	11.2590			0.676485			0.338242	−	0.941059i	$-0.390168\pi$
$277$	11.2590			0.676485			0.338242	+	0.941059i	$0.390168\pi$
$278$	−0.413835	−	3.06131i	−0.0248202	−	0.183605i
$279$		0			0
$280$	−2.64543	−	6.20330i	−0.158095	−	0.370718i
$281$	−8.00783	−	8.00783i	−0.477707	−	0.477707i	0.426691	−	0.904398i	$-0.359679\pi$
$281$	−8.00783	−	8.00783i	−0.477707	−	0.477707i	−0.904398	+	0.426691i	$0.859679\pi$
$282$		0			0
$283$			20.4299i			1.21443i	0.794537	+	0.607216i	$0.207714\pi$
$283$			20.4299i			1.21443i	−0.794537	+	0.607216i	$0.792286\pi$
$284$	19.2860	+	10.9571i	1.14441	+	0.650187i
$285$		0			0
$286$	−0.651717	−	0.853076i	−0.0385368	−	0.0504434i
$287$			1.76987i			0.104472i
$288$		0			0
$289$	3.97031			0.233548
$290$	6.14478	+	4.68129i	0.360834	+	0.274895i
$291$		0			0
$292$	14.1058	+	8.01405i	0.825479	+	0.468987i
$293$	10.5808	−	10.5808i	0.618136	−	0.618136i	−0.326917	−	0.945053i	$-0.606010\pi$
$293$	10.5808	−	10.5808i	0.618136	−	0.618136i	0.945053	+	0.326917i	$0.106010\pi$
$294$		0			0
$295$			9.30852i			0.541963i
$296$	−6.43591	−	2.58773i	−0.374080	−	0.150409i
$297$		0			0
$298$	3.90447	−	5.12511i	0.226180	−	0.296890i
$299$	−1.94650	+	7.10531i	−0.112569	+	0.410911i
$300$		0			0
$301$	−21.0812	−	21.0812i	−1.21510	−	1.21510i
$302$	7.56507	+	5.76331i	0.435321	+	0.331641i
$303$		0			0
$304$	2.62696	−	10.3777i	0.150667	−	0.595203i
$305$	3.39137	−	3.39137i	0.194189	−	0.194189i
$306$		0			0
$307$	−3.60647	−	3.60647i	−0.205832	−	0.205832i	0.596661	−	0.802493i	$-0.296494\pi$
$307$	−3.60647	−	3.60647i	−0.205832	−	0.205832i	−0.802493	+	0.596661i	$0.796494\pi$
$308$	−1.11818	+	0.307943i	−0.0637142	+	0.0175467i
$309$		0			0
$310$	−0.449173	+	0.0607202i	−0.0255113	+	0.00344868i
$311$	−9.13650			−0.518084			−0.259042	−	0.965866i	$-0.583407\pi$
$311$	−9.13650			−0.518084			−0.259042	+	0.965866i	$0.583407\pi$
$312$		0			0
$313$	11.1291			0.629055			0.314527	−	0.949248i	$-0.398154\pi$
$313$	11.1291			0.629055			0.314527	+	0.949248i	$0.398154\pi$
$314$	−2.74326	+	0.370841i	−0.154811	+	0.0209277i
$315$		0			0
$316$	−3.41757	−	12.4096i	−0.192254	−	0.698095i
$317$	−9.07790	−	9.07790i	−0.509866	−	0.509866i	0.404620	−	0.914485i	$-0.367404\pi$
$317$	−9.07790	−	9.07790i	−0.509866	−	0.509866i	−0.914485	+	0.404620i	$0.867404\pi$
$318$		0			0
$319$	0.939404	−	0.939404i	0.0525965	−	0.0525965i
$320$	6.92358	−	0.144088i	0.387040	−	0.00805478i
$321$		0			0
$322$	6.33120	+	4.82331i	0.352824	+	0.268792i
$323$	6.83094	+	6.83094i	0.380084	+	0.380084i
$324$		0			0
$325$	−14.7814	−	4.04936i	−0.819925	−	0.224618i
$326$	−1.51921	+	1.99415i	−0.0841410	+	0.110446i
$327$		0			0
$328$	−1.68624	−	0.677998i	−0.0931072	−	0.0374362i
$329$			24.3433i			1.34209i
$330$		0			0
$331$	4.54016	−	4.54016i	0.249550	−	0.249550i	−0.571236	−	0.820786i	$-0.693536\pi$
$331$	4.54016	−	4.54016i	0.249550	−	0.249550i	0.820786	+	0.571236i	$0.193536\pi$
$332$	−4.21548	+	7.41980i	−0.231354	+	0.407215i
$333$		0			0
$334$	2.20073	+	1.67659i	0.120419	+	0.0917387i
$335$	1.53447			0.0838372
$336$		0			0
$337$			29.5600i			1.61023i	0.593116	+	0.805117i	$0.297898\pi$
$337$			29.5600i			1.61023i	−0.593116	+	0.805117i	$0.702102\pi$
$338$	−7.16632	+	16.9306i	−0.389796	+	0.920901i
$339$		0			0
$340$	−3.08704	+	5.43360i	−0.167418	+	0.294678i
$341$			0.0779517i			0.00422132i
$342$		0			0
$343$	12.4909	+	12.4909i	0.674443	+	0.674443i
$344$	28.1608	−	12.0093i	1.51833	−	0.647500i
$345$		0			0
$346$	−4.22503	−	31.2544i	−0.227139	−	1.68024i
$347$	7.48795			0.401974			0.200987	−	0.979594i	$-0.435585\pi$
$347$	7.48795			0.401974			0.200987	+	0.979594i	$0.435585\pi$
$348$		0			0
$349$	−3.45262	+	3.45262i	−0.184815	+	0.184815i	−0.793450	−	0.608635i	$-0.791717\pi$
$349$	−3.45262	+	3.45262i	−0.184815	+	0.184815i	0.608635	+	0.793450i	$0.291717\pi$
$350$	−10.0341	+	13.1710i	−0.536344	+	0.704019i
$351$		0			0
$352$	0.134956	−	1.18331i	0.00719320	−	0.0630705i
$353$	13.1464	−	13.1464i	0.699710	−	0.699710i	−0.264638	−	0.964348i	$-0.585252\pi$
$353$	13.1464	−	13.1464i	0.699710	−	0.699710i	0.964348	+	0.264638i	$0.0852524\pi$
$354$		0			0
$355$			9.60044i			0.509539i
$356$	−17.5464	−	9.96879i	−0.929958	−	0.528345i
$357$		0			0
$358$	−30.9406	+	4.18262i	−1.63526	+	0.221059i
$359$	13.2695	−	13.2695i	0.700339	−	0.700339i	−0.264144	−	0.964483i	$-0.585089\pi$
$359$	13.2695	−	13.2695i	0.700339	−	0.700339i	0.964483	+	0.264144i	$0.0850894\pi$
$360$		0			0
$361$			11.8376i			0.623033i
$362$	−0.757775	−	5.60558i	−0.0398278	−	0.294623i
$363$		0			0
$364$	14.0636	+	14.0258i	0.737135	+	0.735153i
$365$			7.02176i			0.367536i
$366$		0			0
$367$		−	15.9191i		−	0.830973i	−0.909599	−	0.415486i	$-0.863611\pi$
$367$		−	15.9191i		−	0.830973i	0.909599	−	0.415486i	$-0.136389\pi$
$368$	−7.02072	+	4.18433i	−0.365981	+	0.218123i
$369$		0			0
$370$	−0.402200	−	2.97525i	−0.0209094	−	0.154676i
$371$	−13.8407	−	13.8407i	−0.718574	−	0.718574i
$372$		0			0
$373$			25.0250i			1.29574i	0.761749	+	0.647872i	$0.224341\pi$
$373$			25.0250i			1.29574i	−0.761749	+	0.647872i	$0.775659\pi$
$374$	0.854927	+	0.651310i	0.0442072	+	0.0336785i
$375$		0			0
$376$	−23.1930	−	9.32537i	−1.19609	−	0.480919i
$377$	−21.9430	−	6.01128i	−1.13012	−	0.309596i
$378$		0			0
$379$	−24.7631	+	24.7631i	−1.27199	+	1.27199i	−0.326953	+	0.945040i	$0.606022\pi$
$379$	−24.7631	+	24.7631i	−1.27199	+	1.27199i	−0.945040	+	0.326953i	$0.893978\pi$
$380$	4.46703	−	1.23021i	0.229154	−	0.0631083i
$381$		0			0
$382$	22.9524	−	3.10276i	1.17435	−	0.158751i
$383$	−22.3395	−	22.3395i	−1.14150	−	1.14150i	−0.988177	−	0.153318i	$-0.951004\pi$
$383$	−22.3395	−	22.3395i	−1.14150	−	1.14150i	−0.153318	−	0.988177i	$-0.548996\pi$
$384$		0			0
$385$	−0.354957	−	0.354957i	−0.0180903	−	0.0180903i
$386$	20.9414	−	27.4883i	1.06589	−	1.39912i
$387$		0			0
$388$	−10.0768	+	17.7365i	−0.511571	+	0.900433i
$389$	−8.16460			−0.413961			−0.206981	−	0.978345i	$-0.566364\pi$
$389$	−8.16460			−0.413961			−0.206981	+	0.978345i	$0.566364\pi$
$390$		0			0
$391$		−	7.37552i		−	0.372996i
$392$	1.52649	−	0.650979i	0.0770992	−	0.0328794i
$393$		0			0
$394$	−0.741868	+	0.973796i	−0.0373748	+	0.0490591i
$395$	3.93933	−	3.93933i	0.198209	−	0.198209i
$396$		0			0
$397$	3.64644	−	3.64644i	0.183010	−	0.183010i	−0.609656	−	0.792666i	$-0.708693\pi$
$397$	3.64644	−	3.64644i	0.183010	−	0.183010i	0.792666	+	0.609656i	$0.208693\pi$
$398$	−3.95372	−	29.2474i	−0.198182	−	1.46604i
$399$		0			0
$400$	−8.70479	−	14.6054i	−0.435240	−	0.730272i
$401$	15.8904	+	15.8904i	0.793526	+	0.793526i	0.982066	−	0.188539i	$-0.0603753\pi$
$401$	15.8904	+	15.8904i	0.793526	+	0.793526i	−0.188539	+	0.982066i	$0.560375\pi$
$402$		0			0
$403$	1.15982	−	0.661007i	0.0577749	−	0.0329271i
$404$	−19.2218	+	5.29362i	−0.956319	+	0.263368i
$405$		0			0
$406$	−14.8956	+	19.5523i	−0.739256	+	0.970367i
$407$	−0.516338			−0.0255939
$408$		0			0
$409$	−23.5920	+	23.5920i	−1.16655	+	1.16655i	−0.183534	+	0.983013i	$0.558754\pi$
$409$	−23.5920	+	23.5920i	−1.16655	+	1.16655i	−0.983013	+	0.183534i	$0.941246\pi$
$410$	−0.105379	−	0.779530i	−0.00520428	−	0.0384982i
$411$		0			0
$412$	−15.8100	+	4.35403i	−0.778903	+	0.214508i
$413$	−29.6192			−1.45747
$414$		0			0
$415$	−3.69352			−0.181308
$416$	−18.7505	+	8.02612i	−0.919319	+	0.393513i
$417$		0			0
$418$	−0.106748	−	0.789659i	−0.00522121	−	0.0386235i
$419$	−0.205279			−0.0100285			−0.00501426	−	0.999987i	$-0.501596\pi$
$419$	−0.205279			−0.0100285			−0.00501426	+	0.999987i	$0.501596\pi$
$420$		0			0
$421$	5.11031	+	5.11031i	0.249061	+	0.249061i	0.820585	−	0.571524i	$-0.193648\pi$
$421$	5.11031	+	5.11031i	0.249061	+	0.249061i	−0.571524	+	0.820585i	$0.693648\pi$
$422$	−0.562735	−	4.16279i	−0.0273935	−	0.202641i
$423$		0			0
$424$	18.4887	−	7.88464i	0.897893	−	0.382912i
$425$	15.3435			0.744270
$426$		0			0
$427$	10.7911	+	10.7911i	0.522220	+	0.522220i
$428$	9.37913	−	2.58299i	0.453357	−	0.124853i
$429$		0			0
$430$	10.5403	+	8.02991i	0.508297	+	0.387237i
$431$	−15.7282	−	15.7282i	−0.757599	−	0.757599i	0.218286	−	0.975885i	$-0.429954\pi$
$431$	−15.7282	−	15.7282i	−0.757599	−	0.757599i	−0.975885	+	0.218286i	$0.929954\pi$
$432$		0			0
$433$			3.59682i			0.172852i	0.996258	+	0.0864261i	$0.0275446\pi$
$433$			3.59682i			0.172852i	−0.996258	+	0.0864261i	$0.972455\pi$
$434$	−0.193208	−	1.42924i	−0.00927430	−	0.0686059i
$435$		0			0
$436$	−16.4564	−	9.34954i	−0.788120	−	0.447762i
$437$	−3.86669	+	3.86669i	−0.184969	+	0.184969i
$438$		0			0
$439$	34.9806			1.66953			0.834766	−	0.550604i	$-0.185603\pi$
$439$	34.9806			1.66953			0.834766	+	0.550604i	$0.185603\pi$
$440$	0.474160	−	0.202208i	0.0226047	−	0.00963990i
$441$		0			0
$442$	2.44115	−	18.2432i	0.116113	−	0.867738i
$443$	−19.1553			−0.910095			−0.455048	−	0.890467i	$-0.650378\pi$
$443$	−19.1553			−0.910095			−0.455048	+	0.890467i	$0.650378\pi$
$444$		0			0
$445$		−	8.73447i		−	0.414054i
$446$	−15.3623	+	20.1649i	−0.727425	+	0.954838i
$447$		0			0
$448$	0.458481	+	22.0304i	0.0216612	+	1.04084i
$449$	−4.05676	−	4.05676i	−0.191450	−	0.191450i	0.604872	−	0.796322i	$-0.293224\pi$
$449$	−4.05676	−	4.05676i	−0.191450	−	0.191450i	−0.796322	+	0.604872i	$0.793224\pi$
$450$		0			0
$451$	−0.135283			−0.00637024
$452$	−35.1057	+	9.66801i	−1.65123	+	0.454745i
$453$		0			0
$454$	−24.4975	−	18.6630i	−1.14973	−	0.875897i
$455$	−2.27138	+	8.29124i	−0.106484	+	0.388699i
$456$		0			0
$457$	1.87342	−	1.87342i	0.0876350	−	0.0876350i	−0.661930	−	0.749565i	$-0.730263\pi$
$457$	1.87342	−	1.87342i	0.0876350	−	0.0876350i	0.749565	+	0.661930i	$0.230263\pi$
$458$	7.11951	+	5.42387i	0.332673	+	0.253441i
$459$		0			0
$460$	−3.07571	−	1.74743i	−0.143406	−	0.0814745i
$461$	18.0653	+	18.0653i	0.841387	+	0.841387i	0.989039	−	0.147652i	$-0.0471717\pi$
$461$	18.0653	+	18.0653i	0.841387	+	0.841387i	−0.147652	+	0.989039i	$0.547172\pi$
$462$		0			0
$463$	−22.9474	+	22.9474i	−1.06646	+	1.06646i	−0.0688283	+	0.997629i	$0.521926\pi$
$463$	−22.9474	+	22.9474i	−1.06646	+	1.06646i	−0.997629	+	0.0688283i	$0.978074\pi$
$464$	−12.9223	−	21.6818i	−0.599902	−	1.00655i
$465$		0			0
$466$	−17.3986	+	2.35198i	−0.805973	+	0.108953i
$467$			33.2007i			1.53634i	0.640244	+	0.768172i	$0.278833\pi$
$467$			33.2007i			1.53634i	−0.640244	+	0.768172i	$0.721167\pi$
$468$		0			0
$469$			4.88260i			0.225458i
$470$	−1.44941	−	10.7219i	−0.0668561	−	0.494563i
$471$		0			0
$472$	11.3464	−	28.2196i	0.522262	−	1.29891i
$473$	1.61138	−	1.61138i	0.0740913	−	0.0740913i
$474$		0			0
$475$	−8.04399	−	8.04399i	−0.369084	−	0.369084i
$476$	−17.2894	−	9.82278i	−0.792458	−	0.450226i
$477$		0			0
$478$	5.24511	−	6.88487i	0.239906	−	0.314906i
$479$	27.4785	−	27.4785i	1.25553	−	1.25553i	0.302320	−	0.953207i	$-0.402239\pi$
$479$	27.4785	−	27.4785i	1.25553	−	1.25553i	0.953207	−	0.302320i	$-0.0977611\pi$
$480$		0			0
$481$	4.37840	+	7.68246i	0.199638	+	0.350290i
$482$	−5.39240	+	7.07821i	−0.245617	+	0.322404i
$483$		0			0
$484$	5.81774	+	21.1249i	0.264443	+	0.960222i
$485$	−8.82909			−0.400908
$486$		0			0
$487$	3.13453	+	3.13453i	0.142039	+	0.142039i	0.774551	−	0.632512i	$-0.217976\pi$
$487$	3.13453	+	3.13453i	0.142039	+	0.142039i	−0.632512	+	0.774551i	$0.717976\pi$
$488$	−14.4150	+	6.14738i	−0.652539	+	0.278279i
$489$		0			0
$490$	0.571346	+	0.435270i	0.0258108	+	0.0196635i
$491$		−	17.6844i		−	0.798085i	−0.916932	−	0.399043i	$-0.869343\pi$
$491$		−	17.6844i		−	0.798085i	0.916932	−	0.399043i	$-0.130657\pi$
$492$		0			0
$493$	22.7775			1.02585
$494$	−10.8439	+	8.28436i	−0.487892	+	0.372731i
$495$		0			0
$496$	1.43572	+	0.363431i	0.0644658	+	0.0163186i
$497$	−30.5481			−1.37027
$498$		0			0
$499$	−3.09631	+	3.09631i	−0.138610	+	0.138610i	−0.773007	−	0.634397i	$-0.781248\pi$
$499$	−3.09631	+	3.09631i	−0.138610	+	0.138610i	0.634397	+	0.773007i	$0.281248\pi$
$500$	7.91131	−	13.9250i	0.353805	−	0.622743i
$501$		0			0
$502$	28.0164	−	3.78732i	1.25043	−	0.169036i
$503$		−	25.5344i		−	1.13852i	−0.822156	−	0.569262i	$-0.807229\pi$
$503$		−	25.5344i		−	1.13852i	0.822156	−	0.569262i	$-0.192771\pi$
$504$		0			0
$505$	−6.10180	−	6.10180i	−0.271526	−	0.271526i
$506$	−0.368677	+	0.483936i	−0.0163897	+	0.0215136i
$507$		0			0
$508$	3.85130	−	1.06064i	0.170874	−	0.0470582i
$509$	−6.27440	−	6.27440i	−0.278108	−	0.278108i	0.554245	−	0.832353i	$-0.313007\pi$
$509$	−6.27440	−	6.27440i	−0.278108	−	0.278108i	−0.832353	+	0.554245i	$0.813007\pi$
$510$		0			0
$511$	−22.3428			−0.988389
$512$	−21.1651	−	8.00253i	−0.935372	−	0.353665i
$513$		0			0
$514$	24.6035	−	3.32596i	1.08521	−	0.146702i
$515$	−5.01875	−	5.01875i	−0.221153	−	0.221153i
$516$		0			0
$517$	−1.86072			−0.0818346
$518$	9.46706	−	1.27978i	0.415959	−	0.0562303i
$519$		0			0
$520$	−7.02934	−	5.34023i	−0.308257	−	0.234185i
$521$	−11.7610			−0.515258			−0.257629	−	0.966244i	$-0.582941\pi$
$521$	−11.7610			−0.515258			−0.257629	+	0.966244i	$0.582941\pi$
$522$		0			0
$523$	26.1848			1.14498			0.572491	−	0.819911i	$-0.305977\pi$
$523$	26.1848			1.14498			0.572491	+	0.819911i	$0.305977\pi$
$524$	30.9346	−	8.51929i	1.35138	−	0.372167i
$525$		0			0
$526$	38.7849	−	5.24304i	1.69110	−	0.228607i
$527$	−0.945037	+	0.945037i	−0.0411664	+	0.0411664i
$528$		0			0
$529$	−18.8251			−0.818480
$530$	6.92013	+	5.27197i	0.300591	+	0.229000i
$531$		0			0
$532$	3.91445	+	14.2138i	0.169713	+	0.616247i
$533$	1.14716	+	2.01285i	0.0496891	+	0.0871860i
$534$		0			0
$535$	2.97733	+	2.97733i	0.128721	+	0.128721i
$536$	−4.65188	−	1.87041i	−0.200931	−	0.0807895i
$537$		0			0
$538$	−30.4416	+	4.11517i	−1.31243	+	0.177418i
$539$	0.0873465	−	0.0873465i	0.00376228	−	0.00376228i
$540$		0			0
$541$	−31.8203	+	31.8203i	−1.36806	+	1.36806i	−0.504859	+	0.863202i	$0.668456\pi$
$541$	−31.8203	+	31.8203i	−1.36806	+	1.36806i	−0.863202	+	0.504859i	$0.831544\pi$
$542$	19.2333	+	14.6525i	0.826140	+	0.629379i
$543$		0			0
$544$	15.9818	−	12.7095i	0.685214	−	0.544917i
$545$		−	8.19189i		−	0.350902i
$546$		0			0
$547$	−8.93392			−0.381987			−0.190993	−	0.981591i	$-0.561171\pi$
$547$	−8.93392			−0.381987			−0.190993	+	0.981591i	$0.561171\pi$
$548$	−30.8656	−	17.5359i	−1.31851	−	0.749098i
$549$		0			0
$550$	−1.00675	−	0.766971i	−0.0429278	−	0.0327038i
$551$	−11.9413	−	11.9413i	−0.508717	−	0.508717i
$552$		0			0
$553$	12.5347	+	12.5347i	0.533031	+	0.533031i
$554$	−2.13305	−	15.7790i	−0.0906245	−	0.670387i
$555$		0			0
$556$	−4.21192	+	1.15995i	−0.178625	+	0.0491929i
$557$	−23.9560	+	23.9560i	−1.01505	+	1.01505i	−0.0151623	+	0.999885i	$0.504826\pi$
$557$	−23.9560	+	23.9560i	−1.01505	+	1.01505i	−0.999885	+	0.0151623i	$0.995174\pi$
$558$		0			0
$559$	−37.6393	−	10.3113i	−1.59197	−	0.436120i
$560$	−8.19253	+	4.88272i	−0.346197	+	0.206333i
$561$		0			0
$562$	−9.70559	+	12.7398i	−0.409406	+	0.537397i
$563$			30.6698i			1.29258i	0.763093	+	0.646289i	$0.223680\pi$
$563$			30.6698i			1.29258i	−0.763093	+	0.646289i	$0.776320\pi$
$564$		0			0
$565$	−11.1440	−	11.1440i	−0.468832	−	0.468832i
$566$	28.6318	−	3.87052i	1.20349	−	0.162690i
$567$		0			0
$568$	11.7023	−	29.1046i	0.491016	−	1.22120i
$569$		−	0.0185644i		−	0.000778260i	−1.00000		0.000389130i	$-0.999876\pi$
$569$		−	0.0185644i		−	0.000778260i	1.00000		0.000389130i	$-0.000123864\pi$
$570$		0			0
$571$			32.0060i			1.33941i	0.742627	+	0.669705i	$0.233580\pi$
$571$			32.0060i			1.33941i	−0.742627	+	0.669705i	$0.766420\pi$
$572$	−1.07209	+	1.07498i	−0.0448262	+	0.0449471i
$573$		0			0
$574$	2.48042	−	0.335309i	0.103531	−	0.0139955i
$575$			8.68528i			0.362201i
$576$		0			0
$577$	−0.107901	+	0.107901i	−0.00449198	+	0.00449198i	−0.709349	−	0.704857i	$-0.751011\pi$
$577$	−0.107901	+	0.107901i	−0.00449198	+	0.00449198i	0.704857	+	0.709349i	$0.251011\pi$
$578$	−0.752189	−	5.56425i	−0.0312869	−	0.231442i
$579$		0			0
$580$	5.39652	−	9.49859i	0.224078	−	0.394407i
$581$		−	11.7526i		−	0.487579i
$582$		0			0
$583$	1.05794	−	1.05794i	0.0438153	−	0.0438153i
$584$	8.55903	−	21.2871i	0.354175	−	0.880865i
$585$		0			0
$586$	−16.8332	−	12.8241i	−0.695372	−	0.529757i
$587$	−3.55046	+	3.55046i	−0.146543	+	0.146543i	−0.776572	−	0.630029i	$-0.783043\pi$
$587$	−3.55046	+	3.55046i	−0.146543	+	0.146543i	0.630029	+	0.776572i	$0.283043\pi$
$588$		0			0
$589$	0.990889			0.0408289
$590$	13.0456	−	1.76353i	0.537078	−	0.0726034i
$591$		0			0
$592$	−2.40731	+	9.50997i	−0.0989397	+	0.390857i
$593$	−28.6328	−	28.6328i	−1.17581	−	1.17581i	−0.980802	−	0.195008i	$-0.937527\pi$
$593$	−28.6328	−	28.6328i	−1.17581	−	1.17581i	−0.195008	−	0.980802i	$-0.562473\pi$
$594$		0			0
$595$		−	8.60654i		−	0.352834i
$596$	−7.92238	−	4.50101i	−0.324513	−	0.184369i
$597$		0			0
$598$	10.3266	+	1.38182i	0.422287	+	0.0565069i
$599$			8.64766i			0.353334i	0.984271	+	0.176667i	$0.0565316\pi$
$599$			8.64766i			0.353334i	−0.984271	+	0.176667i	$0.943468\pi$
$600$		0			0
$601$	32.8764			1.34106			0.670529	−	0.741884i	$-0.266067\pi$
$601$	32.8764			1.34106			0.670529	+	0.741884i	$0.266067\pi$
$602$	−25.5507	+	33.5386i	−1.04137	+	1.36693i
$603$		0			0
$604$	6.64385	−	11.6941i	0.270335	−	0.475825i
$605$	−6.70592	+	6.70592i	−0.272635	+	0.272635i
$606$		0			0
$607$			15.2968i			0.620877i	0.950593	+	0.310439i	$0.100476\pi$
$607$			15.2968i			0.620877i	−0.950593	+	0.310439i	$0.899524\pi$
$608$	−15.0417	−	1.71551i	−0.610022	−	0.0695731i
$609$		0			0
$610$	−5.39539	−	4.11038i	−0.218453	−	0.166424i
$611$	15.7784	+	27.6852i	0.638326	+	1.12002i
$612$		0			0
$613$	−12.2996	−	12.2996i	−0.496774	−	0.496774i	0.413658	−	0.910432i	$-0.364251\pi$
$613$	−12.2996	−	12.2996i	−0.496774	−	0.496774i	−0.910432	+	0.413658i	$0.864251\pi$
$614$	−4.37109	+	5.73761i	−0.176403	+	0.231551i
$615$		0			0
$616$	0.643415	+	1.50875i	0.0259239	+	0.0607892i
$617$	25.8120	−	25.8120i	1.03915	−	1.03915i	0.0399514	−	0.999202i	$-0.487280\pi$
$617$	25.8120	−	25.8120i	1.03915	−	1.03915i	0.999202	−	0.0399514i	$-0.0127203\pi$
$618$		0			0
$619$	−13.5295	−	13.5295i	−0.543795	−	0.543795i	0.380844	−	0.924639i	$-0.375633\pi$
$619$	−13.5295	−	13.5295i	−0.543795	−	0.543795i	−0.924639	+	0.380844i	$0.875633\pi$
$620$	0.170195	+	0.617997i	0.00683518	+	0.0248194i
$621$		0			0
$622$	1.73094	+	12.8045i	0.0694044	+	0.513414i
$623$	27.7926			1.11349
$624$		0			0
$625$	−14.3216			−0.572866
$626$	−2.10845	−	15.5971i	−0.0842706	−	0.623385i
$627$		0			0
$628$	1.03944	+	3.77433i	0.0414782	+	0.150612i
$629$	−6.25976	−	6.25976i	−0.249593	−	0.249593i
$630$		0			0
$631$	18.1643	−	18.1643i	0.723110	−	0.723110i	−0.246128	−	0.969237i	$-0.579158\pi$
$631$	18.1643	−	18.1643i	0.723110	−	0.723110i	0.969237	+	0.246128i	$0.0791583\pi$
$632$	−16.7442	+	7.14066i	−0.666048	+	0.284040i
$633$		0			0
$634$	−11.0025	+	14.4422i	−0.436966	+	0.573573i
$635$	1.22257	+	1.22257i	0.0485160	+	0.0485160i
$636$		0			0
$637$	−2.04028	−	0.558933i	−0.0808387	−	0.0221457i
$638$	−1.49452	−	1.13857i	−0.0591685	−	0.0450764i
$639$		0			0
$640$	−1.51363	−	9.67586i	−0.0598315	−	0.382472i
$641$			5.37880i			0.212450i	0.994342	+	0.106225i	$0.0338764\pi$
$641$			5.37880i			0.212450i	−0.994342	+	0.106225i	$0.966124\pi$
$642$		0			0
$643$	−7.21706	+	7.21706i	−0.284613	+	0.284613i	−0.834946	−	0.550332i	$-0.814501\pi$
$643$	−7.21706	+	7.21706i	−0.284613	+	0.284613i	0.550332	+	0.834946i	$0.314501\pi$
$644$	5.56023	−	9.78675i	0.219104	−	0.385652i
$645$		0			0
$646$	8.27919	−	10.8675i	0.325740	−	0.427575i
$647$	10.0155			0.393751			0.196876	−	0.980428i	$-0.436920\pi$
$647$	10.0155			0.393751			0.196876	+	0.980428i	$0.436920\pi$
$648$		0			0
$649$		−	2.26399i		−	0.0888695i
$650$	−2.87465	+	21.4828i	−0.112753	+	0.842625i
$651$		0			0
$652$	3.08255	+	1.75132i	0.120722	+	0.0685869i
$653$		−	36.0033i		−	1.40892i	−0.709745	−	0.704459i	$-0.751190\pi$
$653$		−	36.0033i		−	1.40892i	0.709745	−	0.704459i	$-0.248810\pi$
$654$		0			0
$655$	9.81992	+	9.81992i	0.383696	+	0.383696i
$656$	−0.630727	+	2.49166i	−0.0246257	+	0.0972830i
$657$		0			0
$658$	34.1164	−	4.61193i	1.32999	−	0.179792i
$659$	12.2051			0.475442			0.237721	−	0.971333i	$-0.423600\pi$
$659$	12.2051			0.475442			0.237721	+	0.971333i	$0.423600\pi$
$660$		0			0
$661$	5.59687	−	5.59687i	0.217693	−	0.217693i	−0.589833	−	0.807526i	$-0.700806\pi$
$661$	5.59687	−	5.59687i	0.217693	−	0.217693i	0.807526	+	0.589833i	$0.200806\pi$
$662$	−7.22303	−	5.50273i	−0.280731	−	0.213870i
$663$		0			0
$664$	11.1972	+	4.50214i	0.434537	+	0.174717i
$665$	−4.51206	+	4.51206i	−0.174970	+	0.174970i
$666$		0			0
$667$			12.8933i			0.499231i
$668$	1.93274	−	3.40188i	0.0747801	−	0.131623i
$669$		0			0
$670$	−0.290711	−	2.15051i	−0.0112311	−	0.0830815i
$671$	−0.824838	+	0.824838i	−0.0318425	+	0.0318425i
$672$		0			0
$673$		−	31.9994i		−	1.23349i	−0.787164	−	0.616744i	$-0.788452\pi$
$673$		−	31.9994i		−	1.23349i	0.787164	−	0.616744i	$-0.211548\pi$
$674$	41.4273	−	5.60024i	1.59572	−	0.215713i
$675$		0			0
$676$	25.0853	+	6.83580i	0.964819	+	0.262916i
$677$			44.2730i			1.70155i	0.525531	+	0.850775i	$0.323867\pi$
$677$			44.2730i			1.70155i	−0.525531	+	0.850775i	$0.676133\pi$
$678$		0			0
$679$		−	28.0937i		−	1.07814i
$680$	8.19985	+	3.29697i	0.314450	+	0.126433i
$681$		0			0
$682$	0.109247	−	0.0147682i	0.00418327	−	0.000565504i
$683$	31.4933	+	31.4933i	1.20506	+	1.20506i	0.972608	+	0.232450i	$0.0746743\pi$
$683$	31.4933	+	31.4933i	1.20506	+	1.20506i	0.232450	+	0.972608i	$0.425326\pi$
$684$		0			0
$685$		−	15.3647i		−	0.587054i
$686$	15.1391	−	19.8719i	0.578013	−	0.758714i
$687$		0			0
$688$	−22.1659	−	37.1912i	−0.845065	−	1.41790i
$689$	−24.7118	−	6.76978i	−0.941444	−	0.257908i
$690$		0			0
$691$	24.6092	−	24.6092i	0.936177	−	0.936177i	−0.0619046	−	0.998082i	$-0.519717\pi$
$691$	24.6092	−	24.6092i	0.936177	−	0.936177i	0.998082	+	0.0619046i	$0.0197175\pi$
$692$	−43.0015	+	11.8425i	−1.63467	+	0.450184i
$693$		0			0
$694$	−1.41862	−	10.4941i	−0.0538500	−	0.398351i
$695$	−1.33704	−	1.33704i	−0.0507168	−	0.0507168i
$696$		0			0
$697$	−1.64009	−	1.64009i	−0.0621228	−	0.0621228i
$698$	5.49285	+	4.18462i	0.207907	+	0.158390i
$699$		0			0
$700$	20.3597	+	11.5671i	0.769524	+	0.437196i
$701$	27.2407			1.02887			0.514434	−	0.857530i	$-0.328002\pi$
$701$	27.2407			1.02887			0.514434	+	0.857530i	$0.328002\pi$
$702$		0			0
$703$			6.56348i			0.247546i
$704$	−1.68393	+	0.0350447i	−0.0634656	+	0.00132080i
$705$		0			0
$706$	−20.9148	−	15.9336i	−0.787139	−	0.599667i
$707$	19.4156	−	19.4156i	0.730198	−	0.730198i
$708$		0			0
$709$	32.0653	−	32.0653i	1.20424	−	1.20424i	0.231374	−	0.972865i	$-0.425678\pi$
$709$	32.0653	−	32.0653i	1.20424	−	1.20424i	0.972865	−	0.231374i	$-0.0743220\pi$
$710$	13.4547	−	1.81884i	0.504946	−	0.0682597i
$711$		0			0
$712$	−10.6467	+	26.4793i	−0.399002	+	0.992354i
$713$	−0.534943	−	0.534943i	−0.0200338	−	0.0200338i
$714$		0			0
$715$	−0.633755	−	0.173617i	−0.0237011	−	0.00649289i
$716$	11.7236	+	42.5698i	0.438132	+	1.59091i
$717$		0			0
$718$	−21.1108	−	16.0828i	−0.787847	−	0.600207i
$719$	9.97340			0.371945			0.185973	−	0.982555i	$-0.440456\pi$
$719$	9.97340			0.371945			0.185973	+	0.982555i	$0.440456\pi$
$720$		0			0
$721$	15.9694	−	15.9694i	0.594731	−	0.594731i
$722$	16.5900	−	2.24268i	0.617417	−	0.0834639i
$723$		0			0
$724$	−7.71247	+	2.12399i	−0.286632	+	0.0789376i
$725$	−26.8223			−0.996157
$726$		0			0
$727$	47.6868			1.76861			0.884303	−	0.466914i	$-0.154634\pi$
$727$	47.6868			1.76861			0.884303	+	0.466914i	$0.154634\pi$
$728$	16.9923	−	22.3669i	0.629777	−	0.828974i
$729$		0			0
$730$	9.84076	−	1.33030i	0.364223	−	0.0492365i
$731$	39.0707			1.44508
$732$		0			0
$733$	33.1754	+	33.1754i	1.22536	+	1.22536i	0.965699	+	0.259662i	$0.0836113\pi$
$733$	33.1754	+	33.1754i	1.22536	+	1.22536i	0.259662	+	0.965699i	$0.416389\pi$
$734$	−22.3101	+	3.01594i	−0.823483	+	0.111320i
$735$		0			0
$736$	7.19430	+	9.04657i	0.265185	+	0.333461i
$737$	−0.373210			−0.0137474
$738$		0			0
$739$	−22.1483	−	22.1483i	−0.814739	−	0.814739i	0.170601	−	0.985340i	$-0.445429\pi$
$739$	−22.1483	−	22.1483i	−0.814739	−	0.814739i	−0.985340	+	0.170601i	$0.945429\pi$
$740$	−4.09351	+	1.12734i	−0.150480	+	0.0414419i
$741$		0			0
$742$	−16.7751	+	22.0195i	−0.615834	+	0.808360i
$743$	6.55392	+	6.55392i	0.240440	+	0.240440i	0.817032	−	0.576592i	$-0.195618\pi$
$743$	6.55392	+	6.55392i	0.240440	+	0.240440i	−0.576592	+	0.817032i	$0.695618\pi$
$744$		0			0
$745$		−	3.94371i		−	0.144486i
$746$	35.0717	−	4.74107i	1.28406	−	0.173583i
$747$		0			0
$748$	0.750821	−	1.32154i	0.0274527	−	0.0483204i
$749$	−9.47369	+	9.47369i	−0.346161	+	0.346161i
$750$		0			0
$751$	−28.8367			−1.05227			−0.526133	−	0.850402i	$-0.676358\pi$
$751$	−28.8367			−1.05227			−0.526133	+	0.850402i	$0.676358\pi$
$752$	−8.67519	+	34.2710i	−0.316352	+	1.24973i
$753$		0			0
$754$	−4.26742	+	31.8913i	−0.155410	+	1.16141i
$755$	5.82122			0.211856
$756$		0			0
$757$		−	24.2191i		−	0.880257i	−0.897935	−	0.440129i	$-0.854933\pi$
$757$		−	24.2191i		−	0.880257i	0.897935	−	0.440129i	$-0.145067\pi$
$758$	39.3961	+	30.0132i	1.43093	+	1.09013i
$759$		0			0
$760$	−2.57039	−	6.02732i	−0.0932377	−	0.218634i
$761$	−7.48899	−	7.48899i	−0.271476	−	0.271476i	0.558218	−	0.829694i	$-0.311485\pi$
$761$	−7.48899	−	7.48899i	−0.271476	−	0.271476i	−0.829694	+	0.558218i	$0.811485\pi$
$762$		0			0
$763$	26.0661			0.943658
$764$	−8.69683	−	31.5792i	−0.314640	−	1.14250i
$765$		0			0
$766$	−27.0758	+	35.5403i	−0.978287	+	1.28412i
$767$	−33.6854	+	19.1980i	−1.21631	+	0.693200i
$768$		0			0
$769$	5.21737	−	5.21737i	0.188143	−	0.188143i	−0.606750	−	0.794893i	$-0.707527\pi$
$769$	5.21737	−	5.21737i	0.188143	−	0.188143i	0.794893	+	0.606750i	$0.207527\pi$
$770$	−0.430212	+	0.564708i	−0.0155038	+	0.0203506i
$771$		0			0
$772$	−42.4913	−	24.1410i	−1.52930	−	0.868852i
$773$	11.7692	+	11.7692i	0.423310	+	0.423310i	0.886342	−	0.463032i	$-0.153238\pi$
$773$	11.7692	+	11.7692i	0.423310	+	0.423310i	−0.463032	+	0.886342i	$0.653238\pi$
$774$		0			0
$775$	1.11286	−	1.11286i	0.0399750	−	0.0399750i
$776$	26.7661	+	10.7620i	0.960848	+	0.386334i
$777$		0			0
$778$	1.54681	+	11.4424i	0.0554558	+	0.410230i
$779$			1.71967i			0.0616134i
$780$		0			0
$781$		−	2.33499i		−	0.0835526i
$782$	−10.3365	+	1.39732i	−0.369634	+	0.0499680i
$783$		0			0
$784$	−1.20152	−	2.01599i	−0.0429115	−	0.0719995i
$785$	−1.19813	+	1.19813i	−0.0427631	+	0.0427631i
$786$		0			0
$787$	15.4380	+	15.4380i	0.550307	+	0.550307i	0.926529	−	0.376222i	$-0.122777\pi$
$787$	15.4380	+	15.4380i	0.550307	+	0.550307i	−0.376222	+	0.926529i	$0.622777\pi$
$788$	1.50529	+	0.855214i	0.0536238	+	0.0304657i
$789$		0			0
$790$	−6.26716	−	4.77452i	−0.222975	−	0.169870i
$791$	35.4596	−	35.4596i	1.26080	−	1.26080i
$792$		0			0
$793$	19.2669	+	5.27816i	0.684189	+	0.187433i
$794$	−5.80119	−	4.41953i	−0.205877	−	0.156843i
$795$		0			0
$796$	−40.2401	+	11.0820i	−1.42627	+	0.392792i
$797$	5.65413			0.200279			0.100140	−	0.994973i	$-0.468071\pi$
$797$	5.65413			0.200279			0.100140	+	0.994973i	$0.468071\pi$
$798$		0			0
$799$	−22.5582	−	22.5582i	−0.798053	−	0.798053i
$800$	−18.8199	+	14.9665i	−0.665383	+	0.529146i
$801$		0			0
$802$	19.2593	−	25.2803i	0.680070	−	0.892677i
$803$		−	1.70781i		−	0.0602674i
$804$		0			0
$805$	4.87177			0.171707
$806$	−1.14611	−	1.50022i	−0.0403701	−	0.0528431i
$807$		0			0
$808$	11.0605	+	25.9358i	0.389106	+	0.912418i
$809$	−48.6272			−1.70964			−0.854820	−	0.518925i	$-0.826332\pi$
$809$	−48.6272			−1.70964			−0.854820	+	0.518925i	$0.826332\pi$
$810$		0			0
$811$	14.5781	−	14.5781i	0.511907	−	0.511907i	−0.403203	−	0.915110i	$-0.632103\pi$
$811$	14.5781	−	14.5781i	0.511907	−	0.511907i	0.915110	+	0.403203i	$0.132103\pi$
$812$	30.2240	+	17.1714i	1.06065	+	0.602599i
$813$		0			0
$814$	0.0978221	+	0.723631i	0.00342866	+	0.0253632i
$815$			1.53447i			0.0537502i
$816$		0			0
$817$	−20.4832	−	20.4832i	−0.716616	−	0.716616i
$818$	37.5329	+	28.5938i	1.31231	+	0.999758i
$819$		0			0
$820$	−1.07252	+	0.295369i	−0.0374540	+	0.0103147i
$821$	−6.68836	−	6.68836i	−0.233425	−	0.233425i	0.580695	−	0.814121i	$-0.302781\pi$
$821$	−6.68836	−	6.68836i	−0.233425	−	0.233425i	−0.814121	+	0.580695i	$0.802781\pi$
$822$		0			0
$823$	25.4807			0.888201			0.444100	−	0.895977i	$-0.353523\pi$
$823$	25.4807			0.888201			0.444100	+	0.895977i	$0.353523\pi$
$824$	9.09728	+	21.3323i	0.316919	+	0.743146i
$825$		0			0
$826$	5.61146	+	41.5103i	0.195248	+	1.44433i
$827$	0.138614	+	0.138614i	0.00482008	+	0.00482008i	0.709513	−	0.704693i	$-0.248915\pi$
$827$	0.138614	+	0.138614i	0.00482008	+	0.00482008i	−0.704693	+	0.709513i	$0.748915\pi$
$828$		0			0
$829$	29.9167			1.03905			0.519525	−	0.854455i	$-0.326109\pi$
$829$	29.9167			1.03905			0.519525	+	0.854455i	$0.326109\pi$
$830$	0.699751	+	5.17635i	0.0242887	+	0.179674i
$831$		0			0
$832$	14.8007	+	24.7576i	0.513121	+	0.858316i
$833$	2.11787			0.0733797
$834$		0			0
$835$	1.69343			0.0586037
$836$	−1.08646	+	0.299207i	−0.0375759	+	0.0103483i
$837$		0			0
$838$	0.0388907	+	0.287691i	0.00134346	+	0.00993812i
$839$	27.4026	−	27.4026i	0.946042	−	0.946042i	−0.0525750	−	0.998617i	$-0.516743\pi$
$839$	27.4026	−	27.4026i	0.946042	−	0.946042i	0.998617	+	0.0525750i	$0.0167428\pi$
$840$		0			0
$841$	−10.8178			−0.373028
$842$	6.19376	−	8.13010i	0.213451	−	0.280182i
$843$		0			0
$844$	−5.72740	+	1.57731i	−0.197145	+	0.0542932i
$845$	2.79086	+	10.9017i	0.0960084	+	0.375029i
$846$		0			0
$847$	−21.3379	−	21.3379i	−0.733178	−	0.733178i
$848$	−14.5528	−	24.4176i	−0.499745	−	0.838503i
$849$		0			0
$850$	−2.90688	−	21.5034i	−0.0997053	−	0.737562i
$851$	3.54337	−	3.54337i	0.121465	−	0.121465i
$852$		0			0
$853$	−29.8041	+	29.8041i	−1.02047	+	1.02047i	−0.0206867	+	0.999786i	$0.506585\pi$
$853$	−29.8041	+	29.8041i	−1.02047	+	1.02047i	−0.999786	+	0.0206867i	$0.993415\pi$
$854$	13.0790	−	17.1678i	0.447554	−	0.587471i
$855$		0			0
$856$	−5.39687	−	12.6552i	−0.184461	−	0.432545i
$857$		−	11.7552i		−	0.401551i	−0.979637	−	0.200775i	$-0.935654\pi$
$857$		−	11.7552i		−	0.401551i	0.979637	−	0.200775i	$-0.0643461\pi$
$858$		0			0
$859$	−46.2378			−1.57761			−0.788806	−	0.614642i	$-0.789300\pi$
$859$	−46.2378			−1.57761			−0.788806	+	0.614642i	$0.789300\pi$
$860$	9.25676	−	16.2931i	0.315653	−	0.555591i
$861$		0			0
$862$	−19.0627	+	25.0223i	−0.649280	+	0.852261i
$863$	37.0232	+	37.0232i	1.26029	+	1.26029i	0.950954	+	0.309332i	$0.100105\pi$
$863$	37.0232	+	37.0232i	1.26029	+	1.26029i	0.309332	+	0.950954i	$0.399895\pi$
$864$		0			0
$865$	−13.6505	−	13.6505i	−0.464130	−	0.464130i
$866$	5.04082	−	0.681430i	0.171294	−	0.0231559i
$867$		0			0
$868$	−1.96643	+	0.541550i	−0.0667451	+	0.0183814i
$869$	−0.958113	+	0.958113i	−0.0325018	+	0.0325018i
$870$		0			0
$871$	3.16471	+	5.55289i	0.107232	+	0.188153i
$872$	−9.98533	+	24.8344i	−0.338146	+	0.841000i
$873$		0			0
$874$	6.15159	+	4.68647i	0.208081	+	0.158522i
$875$			22.0564i			0.745643i
$876$		0			0
$877$	−22.9678	−	22.9678i	−0.775567	−	0.775567i	0.203507	−	0.979074i	$-0.434766\pi$
$877$	−22.9678	−	22.9678i	−0.775567	−	0.775567i	−0.979074	+	0.203507i	$0.934766\pi$
$878$	−6.62719	−	49.0241i	−0.223657	−	1.65448i
$879$		0			0
$880$	−0.373219	−	0.626210i	−0.0125812	−	0.0211095i
$881$		−	30.2662i		−	1.01969i	−0.860265	−	0.509847i	$-0.829702\pi$
$881$		−	30.2662i		−	1.01969i	0.860265	−	0.509847i	$-0.170298\pi$
$882$		0			0
$883$		−	25.5531i		−	0.859932i	−0.902845	−	0.429966i	$-0.858526\pi$
$883$		−	25.5531i		−	0.859932i	0.902845	−	0.429966i	$-0.141474\pi$
$884$	−26.0296	+	0.0350443i	−0.875472	+	0.00117867i
$885$		0			0
$886$	3.62903	+	26.8455i	0.121920	+	0.901892i
$887$			32.3643i			1.08669i	0.839511	+	0.543343i	$0.182842\pi$
$887$			32.3643i			1.08669i	−0.839511	+	0.543343i	$0.817158\pi$
$888$		0			0
$889$	−3.89013	+	3.89013i	−0.130471	+	0.130471i
$890$	−12.2411	+	1.65478i	−0.410322	+	0.0554682i
$891$		0			0
$892$	31.1709	+	17.7094i	1.04368	+	0.592955i
$893$			23.6528i			0.791509i
$894$		0			0
$895$	−13.5134	+	13.5134i	−0.451705	+	0.451705i
$896$	30.7880	−	4.81629i	1.02856	−	0.160901i
$897$		0			0
$898$	−4.91684	+	6.45397i	−0.164077	+	0.215372i
$899$	1.65204	−	1.65204i	0.0550986	−	0.0550986i
$900$		0			0
$901$	25.6515			0.854577
$902$	0.0256299	+	0.189595i	0.000853382	+	0.00631282i
$903$		0			0
$904$	20.2003	+	47.3678i	0.671851	+	1.57543i
$905$	−2.44826	−	2.44826i	−0.0813829	−	0.0813829i
$906$		0			0
$907$		−	39.0804i		−	1.29764i	−0.760940	−	0.648822i	$-0.775262\pi$
$907$		−	39.0804i		−	1.29764i	0.760940	−	0.648822i	$-0.224738\pi$
$908$	−21.5144	+	37.8682i	−0.713981	+	1.25670i
$909$		0			0
$910$	12.0502	+	1.61246i	0.399460	+	0.0534524i
$911$		−	13.9748i		−	0.463005i	−0.972834	−	0.231503i	$-0.925636\pi$
$911$		−	13.9748i		−	0.463005i	0.972834	−	0.231503i	$-0.0743642\pi$
$912$		0			0
$913$	0.898329			0.0297303
$914$	−2.98047	−	2.27061i	−0.0985850	−	0.0751052i
$915$		0			0
$916$	6.25256	−	11.0053i	0.206590	−	0.363626i
$917$	−31.2464	+	31.2464i	−1.03185	+	1.03185i
$918$		0			0
$919$			19.9206i			0.657121i	0.944483	+	0.328561i	$0.106564\pi$
$919$			19.9206i			0.657121i	−0.944483	+	0.328561i	$0.893436\pi$
$920$	−1.86626	+	4.64157i	−0.0615289	+	0.153028i
$921$		0			0
$922$	21.8954	−	28.7405i	0.721087	−	0.946518i
$923$	−34.7417	+	19.8001i	−1.14354	+	0.651727i
$924$		0			0
$925$	7.37138	+	7.37138i	0.242369	+	0.242369i
$926$	36.5075	+	27.8126i	1.19971	+	0.913977i
$927$		0			0
$928$	−27.9381	+	22.2178i	−0.917114	+	0.729336i
$929$	21.6587	−	21.6587i	0.710601	−	0.710601i	−0.256060	−	0.966661i	$-0.582425\pi$
$929$	21.6587	−	21.6587i	0.710601	−	0.710601i	0.966661	+	0.256060i	$0.0824246\pi$
$930$		0			0
$931$	−1.11031	−	1.11031i	−0.0363890	−	0.0363890i
$932$	6.59243	+	23.9379i	0.215942	+	0.784112i
$933$		0			0
$934$	46.5296	−	6.28998i	1.52250	−	0.205814i
$935$	0.657855			0.0215142
$936$		0			0
$937$	19.8950			0.649943			0.324971	−	0.945724i	$-0.394645\pi$
$937$	19.8950			0.649943			0.324971	+	0.945724i	$0.394645\pi$
$938$	6.84280	−	0.925026i	0.223425	−	0.0302032i
$939$		0			0
$940$	−14.7517	+	4.06259i	−0.481149	+	0.132507i
$941$	−0.342472	−	0.342472i	−0.0111643	−	0.0111643i	0.701503	−	0.712667i	$-0.252513\pi$
$941$	−0.342472	−	0.342472i	−0.0111643	−	0.0111643i	−0.712667	+	0.701503i	$0.752513\pi$
$942$		0			0
$943$	0.928381	−	0.928381i	0.0302322	−	0.0302322i
$944$	−41.6984	−	10.5553i	−1.35717	−	0.343547i
$945$		0			0
$946$	−2.56358	−	1.95301i	−0.0833490	−	0.0634979i
$947$	2.42042	+	2.42042i	0.0786530	+	0.0786530i	0.745339	−	0.666686i	$-0.232288\pi$
$947$	2.42042	+	2.42042i	0.0786530	+	0.0786530i	−0.666686	+	0.745339i	$0.732288\pi$
$948$		0			0
$949$	−25.4101	+	14.4817i	−0.824847	+	0.470097i
$950$	−9.74942	+	12.7973i	−0.316313	+	0.415201i
$951$		0			0
$952$	−10.4908	+	26.0915i	−0.340008	+	0.845629i
$953$		−	47.0484i		−	1.52405i	−0.647549	−	0.762024i	$-0.724206\pi$
$953$		−	47.0484i		−	1.52405i	0.647549	−	0.762024i	$-0.275794\pi$
$954$		0			0
$955$	10.0246	−	10.0246i	0.324387	−	0.324387i
$956$	−10.6426	−	6.04648i	−0.344207	−	0.195557i
$957$		0			0
$958$	−43.7161	−	33.3043i	−1.41240	−	1.07601i
$959$	48.8895			1.57872
$960$		0			0
$961$		−	30.8629i		−	0.995578i
$962$	9.93721	−	7.59165i	0.320389	−	0.244764i
$963$		0			0
$964$	10.9415	+	6.21628i	0.352401	+	0.200213i
$965$		−	21.1519i		−	0.680903i
$966$		0			0
$967$	40.3441	+	40.3441i	1.29738	+	1.29738i	0.930117	+	0.367262i	$0.119705\pi$
$967$	40.3441	+	40.3441i	1.29738	+	1.29738i	0.367262	+	0.930117i	$0.380295\pi$
$968$	28.5036	−	12.1555i	0.916141	−	0.390694i
$969$		0			0
$970$	1.67270	+	12.3737i	0.0537072	+	0.397294i
$971$	58.1744			1.86690			0.933452	−	0.358701i	$-0.116780\pi$
$971$	58.1744			1.86690			0.933452	+	0.358701i	$0.116780\pi$
$972$		0			0
$973$	4.25438	−	4.25438i	0.136389	−	0.136389i
$974$	3.79909	−	4.98678i	0.121731	−	0.159787i
$975$		0			0
$976$	11.3463	+	19.0376i	0.363187	+	0.609377i
$977$	−6.21549	+	6.21549i	−0.198851	+	0.198851i	−0.799507	−	0.600656i	$-0.794906\pi$
$977$	−6.21549	+	6.21549i	−0.198851	+	0.198851i	0.600656	+	0.799507i	$0.294906\pi$
$978$		0			0
$979$			2.12437i			0.0678953i
$980$	0.501772	−	0.883186i	0.0160285	−	0.0282123i
$981$		0			0
$982$	−24.7841	+	3.35037i	−0.790892	+	0.106915i
$983$	5.42583	−	5.42583i	0.173057	−	0.173057i	−0.615264	−	0.788321i	$-0.710951\pi$
$983$	5.42583	−	5.42583i	0.173057	−	0.173057i	0.788321	+	0.615264i	$0.210951\pi$
$984$		0			0
$985$			0.749323i			0.0238754i
$986$	−4.31527	−	31.9219i	−0.137426	−	1.01660i
$987$		0			0
$988$	13.6647	+	13.6279i	0.434731	+	0.433562i
$989$			22.1162i			0.703253i
$990$		0			0
$991$		−	25.8093i		−	0.819860i	−0.912117	−	0.409930i	$-0.865553\pi$
$991$		−	25.8093i		−	0.819860i	0.912117	−	0.409930i	$-0.134447\pi$
$992$	0.237335	−	2.08097i	0.00753538	−	0.0660708i
$993$		0			0
$994$	5.78744	+	42.8121i	0.183566	+	1.35792i
$995$	−12.7739	−	12.7739i	−0.404960	−	0.404960i
$996$		0			0
$997$			49.6491i			1.57240i	0.617971	+	0.786201i	$0.287955\pi$
$997$			49.6491i			1.57240i	−0.617971	+	0.786201i	$0.712045\pi$
$998$	4.92598	+	3.75277i	0.155929	+	0.118792i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.k.811.12	yes	48
3.2	odd	2	inner	936.2.w.k.811.13	yes	48
8.3	odd	2	inner	936.2.w.k.811.24	yes	48
13.8	odd	4	inner	936.2.w.k.307.24	yes	48
24.11	even	2	inner	936.2.w.k.811.1	yes	48
39.8	even	4	inner	936.2.w.k.307.1	✓	48
104.99	even	4	inner	936.2.w.k.307.12	yes	48
312.203	odd	4	inner	936.2.w.k.307.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.w.k.307.1	✓	48	39.8	even	4	inner
936.2.w.k.307.12	yes	48	104.99	even	4	inner
936.2.w.k.307.13	yes	48	312.203	odd	4	inner
936.2.w.k.307.24	yes	48	13.8	odd	4	inner
936.2.w.k.811.1	yes	48	24.11	even	2	inner
936.2.w.k.811.12	yes	48	1.1	even	1	trivial
936.2.w.k.811.13	yes	48	3.2	odd	2	inner
936.2.w.k.811.24	yes	48	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.189453 - 1.40147i) q^{2} +(-1.92821 + 0.531025i) q^{4} +(-0.612096 - 0.612096i) q^{5} +(1.94766 - 1.94766i) q^{7} +(1.10952 + 2.60172i) q^{8} +(-0.741868 + 0.973796i) q^{10} +(0.148872 + 0.148872i) q^{11} +(0.952638 - 3.47742i) q^{13} +(-3.09856 - 2.36058i) q^{14} +(3.43602 - 2.04786i) q^{16} +3.60967i q^{17} +(1.89240 - 1.89240i) q^{19} +(1.50529 + 0.855214i) q^{20} +(0.180435 - 0.236844i) q^{22} -2.04327 q^{23} -4.25068i q^{25} +(-5.05397 - 0.676280i) q^{26} +(-2.72124 + 4.78975i) q^{28} -6.31014i q^{29} +(0.261807 + 0.261807i) q^{31} +(-3.52097 - 4.42750i) q^{32} +(5.05883 - 0.683863i) q^{34} -2.38430 q^{35} +(-1.73417 + 1.73417i) q^{37} +(-3.01066 - 2.29362i) q^{38} +(0.913371 - 2.27164i) q^{40} +(-0.454360 + 0.454360i) q^{41} -10.8239i q^{43} +(-0.366113 - 0.208003i) q^{44} +(0.387104 + 2.86357i) q^{46} +(-6.24940 + 6.24940i) q^{47} -0.586721i q^{49} +(-5.95718 + 0.805305i) q^{50} +(0.00970845 + 7.21110i) q^{52} -7.10635i q^{53} -0.182248i q^{55} +(7.22822 + 2.90630i) q^{56} +(-8.84344 + 1.19548i) q^{58} +(-7.60381 - 7.60381i) q^{59} +5.54058i q^{61} +(0.317314 - 0.416514i) q^{62} +(-5.53793 + 5.77333i) q^{64} +(-2.71162 + 1.54541i) q^{65} +(-1.25346 + 1.25346i) q^{67} +(-1.91682 - 6.96021i) q^{68} +(0.451714 + 3.34152i) q^{70} +(-7.84227 - 7.84227i) q^{71} +(-5.73583 - 5.73583i) q^{73} +(2.75892 + 2.10183i) q^{74} +(-2.64404 + 4.65387i) q^{76} +0.579904 q^{77} +6.43580i q^{79} +(-3.35666 - 0.849690i) q^{80} +(0.722851 + 0.550691i) q^{82} +(3.01711 - 3.01711i) q^{83} +(2.20946 - 2.20946i) q^{85} +(-15.1693 + 2.05063i) q^{86} +(-0.222148 + 0.552501i) q^{88} +(7.13489 + 7.13489i) q^{89} +(-4.91741 - 8.62823i) q^{91} +(3.93986 - 1.08503i) q^{92} +(9.94229 + 7.57435i) q^{94} -2.31666 q^{95} +(7.21217 - 7.21217i) q^{97} +(-0.822269 + 0.111156i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 40 q^{16} - 8 q^{19} - 32 q^{22} + 24 q^{28} + 8 q^{34} + 16 q^{40} - 8 q^{46} + 24 q^{52} - 24 q^{58} + 40 q^{67} - 24 q^{70} + 56 q^{76} + 104 q^{91} - 64 q^{94} - 32 q^{97}+O(q^{100}) \) 48 * q - 40 * q^16 - 8 * q^19 - 32 * q^22 + 24 * q^28 + 8 * q^34 + 16 * q^40 - 8 * q^46 + 24 * q^52 - 24 * q^58 + 40 * q^67 - 24 * q^70 + 56 * q^76 + 104 * q^91 - 64 * q^94 - 32 * q^97

Introduction

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