LMFDB - Embedded newform 1512.2.c.g.757.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.15
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.g.757.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.497658 - 1.32376i) q^{2} +(-1.50467 - 1.31756i) q^{4} +1.25392i q^{5} +1.00000 q^{7} +(-2.49294 + 1.33613i) q^{8} +O(q^{10})$	\(q+(0.497658 - 1.32376i) q^{2} +(-1.50467 - 1.31756i) q^{4} +1.25392i q^{5} +1.00000 q^{7} +(-2.49294 + 1.33613i) q^{8} +(1.65989 + 0.624024i) q^{10} +1.55766i q^{11} -1.07281i q^{13} +(0.497658 - 1.32376i) q^{14} +(0.528080 + 3.96499i) q^{16} +0.0158095 q^{17} -2.35077i q^{19} +(1.65211 - 1.88674i) q^{20} +(2.06197 + 0.775184i) q^{22} +5.95129 q^{23} +3.42768 q^{25} +(-1.42014 - 0.533891i) q^{26} +(-1.50467 - 1.31756i) q^{28} +0.469737i q^{29} +1.69031 q^{31} +(5.51149 + 1.27416i) q^{32} +(0.00786775 - 0.0209280i) q^{34} +1.25392i q^{35} -4.59800i q^{37} +(-3.11185 - 1.16988i) q^{38} +(-1.67540 - 3.12595i) q^{40} +12.2190 q^{41} +1.97482i q^{43} +(2.05231 - 2.34377i) q^{44} +(2.96171 - 7.87807i) q^{46} +7.12571 q^{47} +1.00000 q^{49} +(1.70581 - 4.53742i) q^{50} +(-1.41348 + 1.61422i) q^{52} +1.86735i q^{53} -1.95319 q^{55} +(-2.49294 + 1.33613i) q^{56} +(0.621818 + 0.233768i) q^{58} +8.54291i q^{59} -3.92502i q^{61} +(0.841198 - 2.23757i) q^{62} +(4.42952 - 6.66179i) q^{64} +1.34521 q^{65} -12.7403i q^{67} +(-0.0237882 - 0.0208300i) q^{68} +(1.65989 + 0.624024i) q^{70} -4.22205 q^{71} +6.51561 q^{73} +(-6.08664 - 2.28823i) q^{74} +(-3.09727 + 3.53713i) q^{76} +1.55766i q^{77} -6.15343 q^{79} +(-4.97178 + 0.662170i) q^{80} +(6.08088 - 16.1750i) q^{82} +8.88604i q^{83} +0.0198239i q^{85} +(2.61419 + 0.982787i) q^{86} +(-2.08124 - 3.88316i) q^{88} -0.240788 q^{89} -1.07281i q^{91} +(-8.95474 - 7.84117i) q^{92} +(3.54617 - 9.43272i) q^{94} +2.94767 q^{95} +5.86131 q^{97} +(0.497658 - 1.32376i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) $ 24 * q + 6 * q^4 + 24 * q^7	$ 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) $ 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	0.497658	−	1.32376i	0.351897	−	0.936039i
$2$	0.497658	−	1.32376i	0.351897	−	0.936039i
$3$		0			0
$3$		0			0
$4$	−1.50467	−	1.31756i	−0.752336	−	0.658779i
$5$			1.25392i			0.560770i	0.959888	+	0.280385i	$0.0904622\pi$
$5$			1.25392i			0.560770i	−0.959888	+	0.280385i	$0.909538\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.49294	+	1.33613i	−0.881388	+	0.472393i
$9$		0			0
$10$	1.65989	+	0.624024i	0.524903	+	0.197334i
$11$			1.55766i			0.469653i	0.972037	+	0.234827i	$0.0754522\pi$
$11$			1.55766i			0.469653i	−0.972037	+	0.234827i	$0.924548\pi$
$12$		0			0
$13$		−	1.07281i		−	0.297543i	−0.988872	−	0.148771i	$-0.952468\pi$
$13$		−	1.07281i		−	0.297543i	0.988872	−	0.148771i	$-0.0475319\pi$
$14$	0.497658	−	1.32376i	0.133005	−	0.353789i
$15$		0			0
$16$	0.528080	+	3.96499i	0.132020	+	0.991247i
$17$	0.0158095			0.00383438			0.00191719	−	0.999998i	$-0.499390\pi$
$17$	0.0158095			0.00383438			0.00191719	+	0.999998i	$0.499390\pi$
$18$		0			0
$19$		−	2.35077i		−	0.539303i	−0.962958	−	0.269651i	$-0.913092\pi$
$19$		−	2.35077i		−	0.539303i	0.962958	−	0.269651i	$-0.0869085\pi$
$20$	1.65211	−	1.88674i	0.369424	−	0.421888i
$21$		0			0
$22$	2.06197	+	0.775184i	0.439614	+	0.165270i
$23$	5.95129			1.24093			0.620465	−	0.784235i	$-0.286944\pi$
$23$	5.95129			1.24093			0.620465	+	0.784235i	$0.286944\pi$
$24$		0			0
$25$	3.42768			0.685537
$26$	−1.42014	−	0.533891i	−0.278512	−	0.104705i
$27$		0			0
$28$	−1.50467	−	1.31756i	−0.284356	−	0.248995i
$29$			0.469737i			0.0872279i	0.999048	+	0.0436139i	$0.0138872\pi$
$29$			0.469737i			0.0872279i	−0.999048	+	0.0436139i	$0.986113\pi$
$30$		0			0
$31$	1.69031			0.303589			0.151795	−	0.988412i	$-0.451495\pi$
$31$	1.69031			0.303589			0.151795	+	0.988412i	$0.451495\pi$
$32$	5.51149	+	1.27416i	0.974303	+	0.225242i
$33$		0			0
$34$	0.00786775	−	0.0209280i	0.00134931	−	0.00358913i
$35$			1.25392i			0.211951i
$36$		0			0
$37$		−	4.59800i		−	0.755906i	−0.925825	−	0.377953i	$-0.876628\pi$
$37$		−	4.59800i		−	0.755906i	0.925825	−	0.377953i	$-0.123372\pi$
$38$	−3.11185	−	1.16988i	−0.504808	−	0.189779i
$39$		0			0
$40$	−1.67540	−	3.12595i	−0.264904	−	0.494256i
$41$	12.2190			1.90829			0.954143	−	0.299350i	$-0.0967698\pi$
$41$	12.2190			1.90829			0.954143	+	0.299350i	$0.0967698\pi$
$42$		0			0
$43$			1.97482i			0.301158i	0.988598	+	0.150579i	$0.0481137\pi$
$43$			1.97482i			0.301158i	−0.988598	+	0.150579i	$0.951886\pi$
$44$	2.05231	−	2.34377i	0.309398	−	0.353337i
$45$		0			0
$46$	2.96171	−	7.87807i	0.436680	−	1.16156i
$47$	7.12571			1.03939			0.519696	−	0.854351i	$-0.326045\pi$
$47$	7.12571			1.03939			0.519696	+	0.854351i	$0.326045\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	1.70581	−	4.53742i	0.241239	−	0.641689i
$51$		0			0
$52$	−1.41348	+	1.61422i	−0.196015	+	0.223852i
$53$			1.86735i			0.256500i	0.991742	+	0.128250i	$0.0409360\pi$
$53$			1.86735i			0.256500i	−0.991742	+	0.128250i	$0.959064\pi$
$54$		0			0
$55$	−1.95319			−0.263368
$56$	−2.49294	+	1.33613i	−0.333133	+	0.178548i
$57$		0			0
$58$	0.621818	+	0.233768i	0.0816487	+	0.0306953i
$59$			8.54291i			1.11219i	0.831118	+	0.556096i	$0.187701\pi$
$59$			8.54291i			1.11219i	−0.831118	+	0.556096i	$0.812299\pi$
$60$		0			0
$61$		−	3.92502i		−	0.502547i	−0.967916	−	0.251274i	$-0.919151\pi$
$61$		−	3.92502i		−	0.502547i	0.967916	−	0.251274i	$-0.0808494\pi$
$62$	0.841198	−	2.23757i	0.106832	−	0.284171i
$63$		0			0
$64$	4.42952	−	6.66179i	0.553690	−	0.832723i
$65$	1.34521			0.166853
$66$		0			0
$67$		−	12.7403i		−	1.55647i	−0.627972	−	0.778236i	$-0.716115\pi$
$67$		−	12.7403i		−	1.55647i	0.627972	−	0.778236i	$-0.283885\pi$
$68$	−0.0237882	−	0.0208300i	−0.00288474	−	0.00252601i
$69$		0			0
$70$	1.65989	+	0.624024i	0.198395	+	0.0745851i
$71$	−4.22205			−0.501066			−0.250533	−	0.968108i	$-0.580606\pi$
$71$	−4.22205			−0.501066			−0.250533	+	0.968108i	$0.580606\pi$
$72$		0			0
$73$	6.51561			0.762595			0.381297	−	0.924452i	$-0.375477\pi$
$73$	6.51561			0.762595			0.381297	+	0.924452i	$0.375477\pi$
$74$	−6.08664	−	2.28823i	−0.707557	−	0.266001i
$75$		0			0
$76$	−3.09727	+	3.53713i	−0.355282	+	0.405737i
$77$			1.55766i			0.177512i
$78$		0			0
$79$	−6.15343			−0.692315			−0.346158	−	0.938176i	$-0.612514\pi$
$79$	−6.15343			−0.692315			−0.346158	+	0.938176i	$0.612514\pi$
$80$	−4.97178	+	0.662170i	−0.555862	+	0.0740328i
$81$		0			0
$82$	6.08088	−	16.1750i	0.671521	−	1.78623i
$83$			8.88604i			0.975370i	0.873020	+	0.487685i	$0.162158\pi$
$83$			8.88604i			0.975370i	−0.873020	+	0.487685i	$0.837842\pi$
$84$		0			0
$85$			0.0198239i			0.00215021i
$86$	2.61419	+	0.982787i	0.281895	+	0.105977i
$87$		0			0
$88$	−2.08124	−	3.88316i	−0.221861	−	0.413947i
$89$	−0.240788			−0.0255235			−0.0127618	−	0.999919i	$-0.504062\pi$
$89$	−0.240788			−0.0255235			−0.0127618	+	0.999919i	$0.504062\pi$
$90$		0			0
$91$		−	1.07281i		−	0.112461i
$92$	−8.95474	−	7.84117i	−0.933596	−	0.817498i
$93$		0			0
$94$	3.54617	−	9.43272i	0.365759	−	0.972911i
$95$	2.94767			0.302425
$96$		0			0
$97$	5.86131			0.595126			0.297563	−	0.954702i	$-0.403826\pi$
$97$	5.86131			0.595126			0.297563	+	0.954702i	$0.403826\pi$
$98$	0.497658	−	1.32376i	0.0502711	−	0.133720i
$99$		0			0
$100$	−5.15754	−	4.51617i	−0.515754	−	0.451617i
$101$		−	3.12870i		−	0.311317i	−0.987811	−	0.155659i	$-0.950250\pi$
$101$		−	3.12870i		−	0.311317i	0.987811	−	0.155659i	$-0.0497500\pi$
$102$		0			0
$103$	2.72832			0.268830			0.134415	−	0.990925i	$-0.457085\pi$
$103$	2.72832			0.268830			0.134415	+	0.990925i	$0.457085\pi$
$104$	1.43341	+	2.67444i	0.140557	+	0.262251i
$105$		0			0
$106$	2.47192	+	0.929302i	0.240094	+	0.0902618i
$107$		−	2.05577i		−	0.198738i	−0.995051	−	0.0993692i	$-0.968318\pi$
$107$		−	2.05577i		−	0.198738i	0.995051	−	0.0993692i	$-0.0316825\pi$
$108$		0			0
$109$		−	13.8179i		−	1.32351i	−0.749719	−	0.661756i	$-0.769811\pi$
$109$		−	13.8179i		−	1.32351i	0.749719	−	0.661756i	$-0.230189\pi$
$110$	−0.972019	+	2.58555i	−0.0926784	+	0.246522i
$111$		0			0
$112$	0.528080	+	3.96499i	0.0498988	+	0.374656i
$113$	−3.72061			−0.350005			−0.175003	−	0.984568i	$-0.555993\pi$
$113$	−3.72061			−0.350005			−0.175003	+	0.984568i	$0.555993\pi$
$114$		0			0
$115$			7.46244i			0.695876i
$116$	0.618905	−	0.706800i	0.0574639	−	0.0656247i
$117$		0			0
$118$	11.3088	+	4.25145i	1.04106	+	0.391378i
$119$	0.0158095			0.00144926
$120$		0			0
$121$	8.57368			0.779426
$122$	−5.19578	−	1.95332i	−0.470404	−	0.176845i
$123$		0			0
$124$	−2.54337	−	2.22709i	−0.228401	−	0.199998i
$125$			10.5676i			0.945199i
$126$		0			0
$127$	−19.8627			−1.76253			−0.881264	−	0.472625i	$-0.843307\pi$
$127$	−19.8627			−1.76253			−0.881264	+	0.472625i	$0.843307\pi$
$128$	−6.61421	−	9.17890i	−0.584619	−	0.811308i
$129$		0			0
$130$	0.669456	−	1.78074i	0.0587152	−	0.156181i
$131$			7.24798i			0.633259i	0.948549	+	0.316629i	$0.102551\pi$
$131$			7.24798i			0.633259i	−0.948549	+	0.316629i	$0.897449\pi$
$132$		0			0
$133$		−	2.35077i		−	0.203837i
$134$	−16.8650	−	6.34030i	−1.45692	−	0.547718i
$135$		0			0
$136$	−0.0394123	+	0.0211236i	−0.00337958	+	0.00181133i
$137$	−13.1526			−1.12371			−0.561853	−	0.827237i	$-0.689911\pi$
$137$	−13.1526			−1.12371			−0.561853	+	0.827237i	$0.689911\pi$
$138$		0			0
$139$			5.29486i			0.449104i	0.974462	+	0.224552i	$0.0720919\pi$
$139$			5.29486i			0.449104i	−0.974462	+	0.224552i	$0.927908\pi$
$140$	1.65211	−	1.88674i	0.139629	−	0.159459i
$141$		0			0
$142$	−2.10114	+	5.58898i	−0.176324	+	0.469017i
$143$	1.67107			0.139742
$144$		0			0
$145$	−0.589012			−0.0489148
$146$	3.24255	−	8.62509i	0.268355	−	0.713818i
$147$		0			0
$148$	−6.05813	+	6.91848i	−0.497975	+	0.568696i
$149$			6.59368i			0.540175i	0.962836	+	0.270088i	$0.0870526\pi$
$149$			6.59368i			0.540175i	−0.962836	+	0.270088i	$0.912947\pi$
$150$		0			0
$151$	−9.51585			−0.774389			−0.387195	−	0.921998i	$-0.626556\pi$
$151$	−9.51585			−0.774389			−0.387195	+	0.921998i	$0.626556\pi$
$152$	3.14093	+	5.86032i	0.254763	+	0.475335i
$153$		0			0
$154$	2.06197	+	0.775184i	0.166158	+	0.0624661i
$155$			2.11952i			0.170244i
$156$		0			0
$157$		−	16.0109i		−	1.27781i	−0.769285	−	0.638905i	$-0.779388\pi$
$157$		−	16.0109i		−	1.27781i	0.769285	−	0.638905i	$-0.220612\pi$
$158$	−3.06231	+	8.14566i	−0.243624	+	0.648034i
$159$		0			0
$160$	−1.59769	+	6.91097i	−0.126309	+	0.546360i
$161$	5.95129			0.469027
$162$		0			0
$163$			12.5751i			0.984959i	0.870324	+	0.492480i	$0.163909\pi$
$163$			12.5751i			0.984959i	−0.870324	+	0.492480i	$0.836091\pi$
$164$	−18.3856	−	16.0992i	−1.43567	−	1.25714i
$165$		0			0
$166$	11.7630	+	4.42221i	0.912984	+	0.343230i
$167$	17.2841			1.33748			0.668741	−	0.743495i	$-0.266834\pi$
$167$	17.2841			1.33748			0.668741	+	0.743495i	$0.266834\pi$
$168$		0			0
$169$	11.8491			0.911468
$170$	0.0262421	+	0.00986553i	0.00201268	+	0.000756652i
$171$		0			0
$172$	2.60194	−	2.97146i	0.198396	−	0.226572i
$173$		−	8.78719i		−	0.668078i	−0.942559	−	0.334039i	$-0.891588\pi$
$173$		−	8.78719i		−	0.668078i	0.942559	−	0.334039i	$-0.108412\pi$
$174$		0			0
$175$	3.42768			0.259109
$176$	−6.17612	+	0.822570i	−0.465542	+	0.0620036i
$177$		0			0
$178$	−0.119830	+	0.318745i	−0.00898166	+	0.0238910i
$179$		−	11.6964i		−	0.874233i	−0.899405	−	0.437117i	$-0.856000\pi$
$179$		−	11.6964i		−	0.874233i	0.899405	−	0.437117i	$-0.144000\pi$
$180$		0			0
$181$			24.2624i			1.80341i	0.432351	+	0.901705i	$0.357684\pi$
$181$			24.2624i			1.80341i	−0.432351	+	0.901705i	$0.642316\pi$
$182$	−1.42014	−	0.533891i	−0.105267	−	0.0395746i
$183$		0			0
$184$	−14.8362	+	7.95169i	−1.09374	+	0.586206i
$185$	5.76552			0.423890
$186$		0			0
$187$			0.0246260i			0.00180083i
$188$	−10.7219	−	9.38854i	−0.781972	−	0.684730i
$189$		0			0
$190$	1.46693	−	3.90201i	0.106423	−	0.283081i
$191$	−10.4850			−0.758665			−0.379333	−	0.925260i	$-0.623846\pi$
$191$	−10.4850			−0.758665			−0.379333	+	0.925260i	$0.623846\pi$
$192$		0			0
$193$	12.7092			0.914832			0.457416	−	0.889253i	$-0.348775\pi$
$193$	12.7092			0.914832			0.457416	+	0.889253i	$0.348775\pi$
$194$	2.91693	−	7.75896i	0.209423	−	0.557061i
$195$		0			0
$196$	−1.50467	−	1.31756i	−0.107477	−	0.0941113i
$197$			16.0117i			1.14079i	0.821372	+	0.570394i	$0.193209\pi$
$197$			16.0117i			1.14079i	−0.821372	+	0.570394i	$0.806791\pi$
$198$		0			0
$199$	−11.1888			−0.793156			−0.396578	−	0.918001i	$-0.629802\pi$
$199$	−11.1888			−0.793156			−0.396578	+	0.918001i	$0.629802\pi$
$200$	−8.54502	+	4.57983i	−0.604224	+	0.323843i
$201$		0			0
$202$	−4.14164	−	1.55702i	−0.291405	−	0.109552i
$203$			0.469737i			0.0329690i
$204$		0			0
$205$			15.3217i			1.07011i
$206$	1.35777	−	3.61164i	0.0946004	−	0.251635i
$207$		0			0
$208$	4.25366	−	0.566527i	0.294938	−	0.0392816i
$209$	3.66170			0.253285
$210$		0			0
$211$			20.1657i			1.38827i	0.719847	+	0.694133i	$0.244212\pi$
$211$			20.1657i			1.38827i	−0.719847	+	0.694133i	$0.755788\pi$
$212$	2.46034	−	2.80975i	0.168977	−	0.192974i
$213$		0			0
$214$	−2.72134	−	1.02307i	−0.186027	−	0.0699355i
$215$	−2.47627			−0.168880
$216$		0			0
$217$	1.69031			0.114746
$218$	−18.2915	−	6.87658i	−1.23886	−	0.465741i
$219$		0			0
$220$	2.93891	+	2.57344i	0.198141	+	0.173501i
$221$		−	0.0169606i		−	0.00114089i
$222$		0			0
$223$	−11.1501			−0.746663			−0.373332	−	0.927698i	$-0.621785\pi$
$223$	−11.1501			−0.746663			−0.373332	+	0.927698i	$0.621785\pi$
$224$	5.51149	+	1.27416i	0.368252	+	0.0851333i
$225$		0			0
$226$	−1.85159	+	4.92518i	−0.123166	+	0.327618i
$227$			18.7414i			1.24391i	0.783053	+	0.621955i	$0.213662\pi$
$227$			18.7414i			1.24391i	−0.783053	+	0.621955i	$0.786338\pi$
$228$		0			0
$229$		−	13.5444i		−	0.895038i	−0.894274	−	0.447519i	$-0.852308\pi$
$229$		−	13.5444i		−	0.895038i	0.894274	−	0.447519i	$-0.147692\pi$
$230$	9.87847	+	3.71374i	0.651367	+	0.244877i
$231$		0			0
$232$	−0.627629	−	1.17103i	−0.0412058	−	0.0768816i
$233$	11.0070			0.721094			0.360547	−	0.932741i	$-0.382590\pi$
$233$	11.0070			0.721094			0.360547	+	0.932741i	$0.382590\pi$
$234$		0			0
$235$			8.93508i			0.582860i
$236$	11.2558	−	12.8543i	0.732689	−	0.836743i
$237$		0			0
$238$	0.00786775	−	0.0209280i	0.000509991	−	0.00135656i
$239$	−15.4366			−0.998509			−0.499255	−	0.866455i	$-0.666393\pi$
$239$	−15.4366			−0.998509			−0.499255	+	0.866455i	$0.666393\pi$
$240$		0			0
$241$	16.0354			1.03293			0.516466	−	0.856308i	$-0.327247\pi$
$241$	16.0354			1.03293			0.516466	+	0.856308i	$0.327247\pi$
$242$	4.26676	−	11.3495i	0.274278	−	0.729573i
$243$		0			0
$244$	−5.17144	+	5.90587i	−0.331068	+	0.378085i
$245$			1.25392i			0.0801100i
$246$		0			0
$247$	−2.52192			−0.160466
$248$	−4.21385	+	2.25848i	−0.267580	+	0.143413i
$249$		0			0
$250$	13.9890	+	5.25907i	0.884743	+	0.332613i
$251$		−	11.4441i		−	0.722343i	−0.932499	−	0.361172i	$-0.882377\pi$
$251$		−	11.4441i		−	0.722343i	0.932499	−	0.361172i	$-0.117623\pi$
$252$		0			0
$253$			9.27010i			0.582806i
$254$	−9.88482	+	26.2934i	−0.620229	+	1.64979i
$255$		0			0
$256$	−15.4423	+	4.18766i	−0.965141	+	0.261729i
$257$	10.7447			0.670236			0.335118	−	0.942176i	$-0.391224\pi$
$257$	10.7447			0.670236			0.335118	+	0.942176i	$0.391224\pi$
$258$		0			0
$259$		−	4.59800i		−	0.285706i
$260$	−2.02411	−	1.77240i	−0.125530	−	0.109919i
$261$		0			0
$262$	9.59457	+	3.60702i	0.592755	+	0.222842i
$263$	−14.6747			−0.904878			−0.452439	−	0.891795i	$-0.649446\pi$
$263$	−14.6747			−0.904878			−0.452439	+	0.891795i	$0.649446\pi$
$264$		0			0
$265$	−2.34151			−0.143838
$266$	−3.11185	−	1.16988i	−0.190800	−	0.0717298i
$267$		0			0
$268$	−16.7860	+	19.1699i	−1.02537	+	1.17099i
$269$			4.93110i			0.300655i	0.988636	+	0.150327i	$0.0480328\pi$
$269$			4.93110i			0.300655i	−0.988636	+	0.150327i	$0.951967\pi$
$270$		0			0
$271$	−22.6605			−1.37652			−0.688262	−	0.725462i	$-0.741626\pi$
$271$	−22.6605			−1.37652			−0.688262	+	0.725462i	$0.741626\pi$
$272$	0.00834870	+	0.0626847i	0.000506214	+	0.00380082i
$273$		0			0
$274$	−6.54552	+	17.4109i	−0.395429	+	1.05183i
$275$			5.33918i			0.321965i
$276$		0			0
$277$		−	5.99172i		−	0.360008i	−0.983666	−	0.180004i	$-0.942389\pi$
$277$		−	5.99172i		−	0.360008i	0.983666	−	0.180004i	$-0.0576110\pi$
$278$	7.00912	+	2.63503i	0.420379	+	0.158039i
$279$		0			0
$280$	−1.67540	−	3.12595i	−0.100124	−	0.186811i
$281$	−1.92544			−0.114862			−0.0574309	−	0.998349i	$-0.518291\pi$
$281$	−1.92544			−0.114862			−0.0574309	+	0.998349i	$0.518291\pi$
$282$		0			0
$283$		−	28.2195i		−	1.67747i	−0.544537	−	0.838737i	$-0.683295\pi$
$283$		−	28.2195i		−	1.67747i	0.544537	−	0.838737i	$-0.316705\pi$
$284$	6.35281	+	5.56280i	0.376970	+	0.330092i
$285$		0			0
$286$	0.831622	−	2.21209i	0.0491748	−	0.130804i
$287$	12.2190			0.721265
$288$		0			0
$289$	−16.9998			−0.999985
$290$	−0.293127	+	0.779710i	−0.0172130	+	0.0457861i
$291$		0			0
$292$	−9.80386	−	8.58470i	−0.573728	−	0.502381i
$293$			29.0957i			1.69979i	0.526955	+	0.849893i	$0.323334\pi$
$293$			29.0957i			1.69979i	−0.526955	+	0.849893i	$0.676666\pi$
$294$		0			0
$295$	−10.7121			−0.623685
$296$	6.14352	+	11.4625i	0.357085	+	0.666247i
$297$		0			0
$298$	8.72844	+	3.28140i	0.505625	+	0.190086i
$299$		−	6.38458i		−	0.369230i
$300$		0			0
$301$			1.97482i			0.113827i
$302$	−4.73564	+	12.5967i	−0.272506	+	0.724858i
$303$		0			0
$304$	9.32076	−	1.24139i	0.534582	−	0.0711987i
$305$	4.92166			0.281814
$306$		0			0
$307$			15.8372i			0.903879i	0.892049	+	0.451940i	$0.149268\pi$
$307$			15.8372i			0.903879i	−0.892049	+	0.451940i	$0.850732\pi$
$308$	2.05231	−	2.34377i	0.116941	−	0.133549i
$309$		0			0
$310$	2.80573	+	1.05480i	0.159355	+	0.0599084i
$311$	14.5620			0.825737			0.412869	−	0.910791i	$-0.364527\pi$
$311$	14.5620			0.825737			0.412869	+	0.910791i	$0.364527\pi$
$312$		0			0
$313$	6.47077			0.365749			0.182875	−	0.983136i	$-0.441460\pi$
$313$	6.47077			0.365749			0.182875	+	0.983136i	$0.441460\pi$
$314$	−21.1946	−	7.96796i	−1.19608	−	0.449658i
$315$		0			0
$316$	9.25890	+	8.10751i	0.520854	+	0.456083i
$317$		−	11.9823i		−	0.672994i	−0.941685	−	0.336497i	$-0.890758\pi$
$317$		−	11.9823i		−	0.672994i	0.941685	−	0.336497i	$-0.109242\pi$
$318$		0			0
$319$	−0.731691			−0.0409669
$320$	8.35335	+	5.55426i	0.466966	+	0.310493i
$321$		0			0
$322$	2.96171	−	7.87807i	0.165049	−	0.439027i
$323$		−	0.0371646i		−	0.00206789i
$324$		0			0
$325$		−	3.67724i		−	0.203977i
$326$	16.6464	+	6.25811i	0.921960	+	0.346605i
$327$		0			0
$328$	−30.4612	+	16.3262i	−1.68194	+	0.901461i
$329$	7.12571			0.392853
$330$		0			0
$331$			21.9422i			1.20605i	0.797720	+	0.603027i	$0.206039\pi$
$331$			21.9422i			1.20605i	−0.797720	+	0.603027i	$0.793961\pi$
$332$	11.7079	−	13.3706i	0.642553	−	0.733806i
$333$		0			0
$334$	8.60156	−	22.8799i	0.470657	−	1.25193i
$335$	15.9753			0.872823
$336$		0			0
$337$	22.3150			1.21558			0.607788	−	0.794100i	$-0.292057\pi$
$337$	22.3150			1.21558			0.607788	+	0.794100i	$0.292057\pi$
$338$	5.89680	−	15.6853i	0.320743	−	0.853169i
$339$		0			0
$340$	0.0261192	−	0.0298285i	0.00141651	−	0.00161768i
$341$			2.63294i			0.142582i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−2.63862	−	4.92312i	−0.142265	−	0.265437i
$345$		0			0
$346$	−11.6321	−	4.37302i	−0.625347	−	0.235095i
$347$		−	24.5806i		−	1.31956i	−0.751460	−	0.659779i	$-0.770650\pi$
$347$		−	24.5806i		−	1.31956i	0.751460	−	0.659779i	$-0.229350\pi$
$348$		0			0
$349$		−	12.5930i		−	0.674089i	−0.941489	−	0.337045i	$-0.890573\pi$
$349$		−	12.5930i		−	0.674089i	0.941489	−	0.337045i	$-0.109427\pi$
$350$	1.70581	−	4.53742i	0.0911796	−	0.242536i
$351$		0			0
$352$	−1.98471	+	8.58505i	−0.105785	+	0.457585i
$353$	−16.1946			−0.861953			−0.430977	−	0.902363i	$-0.641831\pi$
$353$	−16.1946			−0.861953			−0.430977	+	0.902363i	$0.641831\pi$
$354$		0			0
$355$		−	5.29412i		−	0.280983i
$356$	0.362308	+	0.317253i	0.0192023	+	0.0168144i
$357$		0			0
$358$	−15.4833	−	5.82083i	−0.818316	−	0.307640i
$359$	10.1809			0.537329			0.268665	−	0.963234i	$-0.413418\pi$
$359$	10.1809			0.537329			0.268665	+	0.963234i	$0.413418\pi$
$360$		0			0
$361$	13.4739			0.709152
$362$	32.1176	+	12.0744i	1.68806	+	0.634616i
$363$		0			0
$364$	−1.41348	+	1.61422i	−0.0740867	+	0.0846082i
$365$			8.17006i			0.427640i
$366$		0			0
$367$	−12.3939			−0.646955			−0.323478	−	0.946236i	$-0.604852\pi$
$367$	−12.3939			−0.646955			−0.323478	+	0.946236i	$0.604852\pi$
$368$	3.14275	+	23.5968i	0.163827	+	1.23007i
$369$		0			0
$370$	2.86926	−	7.63216i	0.149166	−	0.396777i
$371$			1.86735i			0.0969480i
$372$		0			0
$373$			7.57921i			0.392437i	0.980560	+	0.196218i	$0.0628661\pi$
$373$			7.57921i			0.392437i	−0.980560	+	0.196218i	$0.937134\pi$
$374$	0.0325988	+	0.0122553i	0.00168564	+	0.000633707i
$375$		0			0
$376$	−17.7640	+	9.52087i	−0.916107	+	0.491001i
$377$	0.503936			0.0259540
$378$		0			0
$379$			14.1179i			0.725187i	0.931947	+	0.362594i	$0.118109\pi$
$379$			14.1179i			0.725187i	−0.931947	+	0.362594i	$0.881891\pi$
$380$	−4.43528	−	3.88373i	−0.227525	−	0.199231i
$381$		0			0
$382$	−5.21793	+	13.8796i	−0.266972	+	0.710140i
$383$	1.28678			0.0657512			0.0328756	−	0.999459i	$-0.489533\pi$
$383$	1.28678			0.0657512			0.0328756	+	0.999459i	$0.489533\pi$
$384$		0			0
$385$	−1.95319			−0.0995436
$386$	6.32486	−	16.8240i	0.321927	−	0.856318i
$387$		0			0
$388$	−8.81935	−	7.72262i	−0.447735	−	0.392057i
$389$		−	33.3310i		−	1.68995i	−0.534806	−	0.844975i	$-0.679615\pi$
$389$		−	33.3310i		−	1.68995i	0.534806	−	0.844975i	$-0.320385\pi$
$390$		0			0
$391$	0.0940872			0.00475819
$392$	−2.49294	+	1.33613i	−0.125913	+	0.0674847i
$393$		0			0
$394$	21.1956	+	7.96836i	1.06782	+	0.401440i
$395$		−	7.71591i		−	0.388230i
$396$		0			0
$397$			20.7770i			1.04277i	0.853322	+	0.521385i	$0.174584\pi$
$397$			20.7770i			1.04277i	−0.853322	+	0.521385i	$0.825416\pi$
$398$	−5.56822	+	14.8113i	−0.279110	+	0.742425i
$399$		0			0
$400$	1.81009	+	13.5907i	0.0905045	+	0.679536i
$401$	−7.38157			−0.368618			−0.184309	−	0.982868i	$-0.559005\pi$
$401$	−7.38157			−0.368618			−0.184309	+	0.982868i	$0.559005\pi$
$402$		0			0
$403$		−	1.81338i		−	0.0903308i
$404$	−4.12225	+	4.70767i	−0.205089	+	0.234215i
$405$		0			0
$406$	0.621818	+	0.233768i	0.0308603	+	0.0116017i
$407$	7.16213			0.355014
$408$		0			0
$409$	31.9846			1.58154			0.790769	−	0.612114i	$-0.209681\pi$
$409$	31.9846			1.58154			0.790769	+	0.612114i	$0.209681\pi$
$410$	20.2822	+	7.62494i	1.00166	+	0.376569i
$411$		0			0
$412$	−4.10523	−	3.59472i	−0.202250	−	0.177099i
$413$			8.54291i			0.420369i
$414$		0			0
$415$	−11.1424			−0.546958
$416$	1.36693	−	5.91276i	0.0670190	−	0.289897i
$417$		0			0
$418$	1.82228	−	4.84721i	0.0891305	−	0.237085i
$419$			14.6646i			0.716413i	0.933642	+	0.358207i	$0.116612\pi$
$419$			14.6646i			0.716413i	−0.933642	+	0.358207i	$0.883388\pi$
$420$		0			0
$421$		−	28.4958i		−	1.38880i	−0.719589	−	0.694400i	$-0.755670\pi$
$421$		−	28.4958i		−	1.38880i	0.719589	−	0.694400i	$-0.244330\pi$
$422$	26.6945	+	10.0356i	1.29947	+	0.488527i
$423$		0			0
$424$	−2.49502	−	4.65520i	−0.121169	−	0.226076i
$425$	0.0541901			0.00262861
$426$		0			0
$427$		−	3.92502i		−	0.189945i
$428$	−2.70859	+	3.09326i	−0.130925	+	0.149518i
$429$		0			0
$430$	−1.23234	+	3.27798i	−0.0594286	+	0.158078i
$431$	−35.4443			−1.70729			−0.853645	−	0.520855i	$-0.825613\pi$
$431$	−35.4443			−1.70729			−0.853645	+	0.520855i	$0.825613\pi$
$432$		0			0
$433$	−31.5907			−1.51815			−0.759077	−	0.651001i	$-0.774349\pi$
$433$	−31.5907			−1.51815			−0.759077	+	0.651001i	$0.774349\pi$
$434$	0.841198	−	2.23757i	0.0403788	−	0.107407i
$435$		0			0
$436$	−18.2059	+	20.7914i	−0.871903	+	0.995727i
$437$		−	13.9901i		−	0.669237i
$438$		0			0
$439$	23.3732			1.11554			0.557771	−	0.829995i	$-0.311657\pi$
$439$	23.3732			1.11554			0.557771	+	0.829995i	$0.311657\pi$
$440$	4.86918	−	2.60971i	0.232129	−	0.124413i
$441$		0			0
$442$	−0.0224517	−	0.00844057i	−0.00106792	−	0.000401477i
$443$			3.52932i			0.167683i	0.996479	+	0.0838416i	$0.0267190\pi$
$443$			3.52932i			0.167683i	−0.996479	+	0.0838416i	$0.973281\pi$
$444$		0			0
$445$		−	0.301929i		−	0.0143128i
$446$	−5.54892	+	14.7600i	−0.262749	+	0.698906i
$447$		0			0
$448$	4.42952	−	6.66179i	0.209275	−	0.314740i
$449$	2.94601			0.139031			0.0695154	−	0.997581i	$-0.477855\pi$
$449$	2.94601			0.139031			0.0695154	+	0.997581i	$0.477855\pi$
$450$		0			0
$451$			19.0331i			0.896233i
$452$	5.59829	+	4.90212i	0.263322	+	0.230576i
$453$		0			0
$454$	24.8091	+	9.32682i	1.16435	+	0.437729i
$455$	1.34521			0.0630646
$456$		0			0
$457$	−22.1796			−1.03752			−0.518758	−	0.854921i	$-0.673605\pi$
$457$	−22.1796			−1.03752			−0.518758	+	0.854921i	$0.673605\pi$
$458$	−17.9295	−	6.74048i	−0.837790	−	0.314962i
$459$		0			0
$460$	9.83220	−	11.2285i	0.458429	−	0.523533i
$461$		−	23.4545i		−	1.09238i	−0.837660	−	0.546192i	$-0.816077\pi$
$461$		−	23.4545i		−	1.09238i	0.837660	−	0.546192i	$-0.183923\pi$
$462$		0			0
$463$	−29.2354			−1.35868			−0.679342	−	0.733822i	$-0.737735\pi$
$463$	−29.2354			−1.35868			−0.679342	+	0.733822i	$0.737735\pi$
$464$	−1.86250	+	0.248058i	−0.0864644	+	0.0115158i
$465$		0			0
$466$	5.47773	−	14.5706i	0.253751	−	0.674972i
$467$		−	5.43057i		−	0.251297i	−0.992075	−	0.125648i	$-0.959899\pi$
$467$		−	5.43057i		−	0.251297i	0.992075	−	0.125648i	$-0.0401011\pi$
$468$		0			0
$469$		−	12.7403i		−	0.588291i
$470$	11.8279	+	4.44661i	0.545579	+	0.205107i
$471$		0			0
$472$	−11.4144	−	21.2970i	−0.525392	−	0.980273i
$473$	−3.07611			−0.141440
$474$		0			0
$475$		−	8.05768i		−	0.369712i
$476$	−0.0237882	−	0.0208300i	−0.00109033	−	0.000954742i
$477$		0			0
$478$	−7.68214	+	20.4343i	−0.351373	+	0.934643i
$479$	5.07525			0.231894			0.115947	−	0.993255i	$-0.463010\pi$
$479$	5.07525			0.231894			0.115947	+	0.993255i	$0.463010\pi$
$480$		0			0
$481$	−4.93276			−0.224914
$482$	7.98015	−	21.2270i	0.363486	−	0.966864i
$483$		0			0
$484$	−12.9006	−	11.2963i	−0.586390	−	0.513470i
$485$			7.34962i			0.333729i
$486$		0			0
$487$	−3.23366			−0.146531			−0.0732656	−	0.997312i	$-0.523342\pi$
$487$	−3.23366			−0.146531			−0.0732656	+	0.997312i	$0.523342\pi$
$488$	5.24433	+	9.78485i	0.237400	+	0.442939i
$489$		0			0
$490$	1.65989	+	0.624024i	0.0749861	+	0.0281905i
$491$		−	32.6437i		−	1.47319i	−0.676335	−	0.736594i	$-0.736433\pi$
$491$		−	32.6437i		−	1.47319i	0.676335	−	0.736594i	$-0.263567\pi$
$492$		0			0
$493$			0.00742632i			0.000334465i
$494$	−1.25505	+	3.33841i	−0.0564675	+	0.150202i
$495$		0			0
$496$	0.892620	+	6.70207i	0.0400798	+	0.300932i
$497$	−4.22205			−0.189385
$498$		0			0
$499$		−	1.77339i		−	0.0793877i	−0.999212	−	0.0396939i	$-0.987362\pi$
$499$		−	1.77339i		−	0.0793877i	0.999212	−	0.0396939i	$-0.0126383\pi$
$500$	13.9235	−	15.9008i	0.622677	−	0.711107i
$501$		0			0
$502$	−15.1492	−	5.69523i	−0.676141	−	0.254191i
$503$	−25.3666			−1.13104			−0.565519	−	0.824735i	$-0.691324\pi$
$503$	−25.3666			−1.13104			−0.565519	+	0.824735i	$0.691324\pi$
$504$		0			0
$505$	3.92314			0.174578
$506$	12.2714	+	4.61334i	0.545529	+	0.205088i
$507$		0			0
$508$	29.8868	+	26.1702i	1.32601	+	1.16112i
$509$		−	14.3204i		−	0.634739i	−0.948302	−	0.317369i	$-0.897201\pi$
$509$		−	14.3204i		−	0.634739i	0.948302	−	0.317369i	$-0.102799\pi$
$510$		0			0
$511$	6.51561			0.288234
$512$	−2.14152	+	22.5258i	−0.0946427	+	0.995511i
$513$		0			0
$514$	5.34719	−	14.2234i	0.235854	−	0.627367i
$515$			3.42110i			0.150752i
$516$		0			0
$517$			11.0995i			0.488154i
$518$	−6.08664	−	2.28823i	−0.267431	−	0.100539i
$519$		0			0
$520$	−3.35354	+	1.79738i	−0.147062	+	0.0788203i
$521$	−5.72827			−0.250960			−0.125480	−	0.992096i	$-0.540047\pi$
$521$	−5.72827			−0.250960			−0.125480	+	0.992096i	$0.540047\pi$
$522$		0			0
$523$			11.3779i			0.497519i	0.968565	+	0.248759i	$0.0800229\pi$
$523$			11.3779i			0.497519i	−0.968565	+	0.248759i	$0.919977\pi$
$524$	9.54963	−	10.9058i	0.417178	−	0.476424i
$525$		0			0
$526$	−7.30296	+	19.4257i	−0.318424	+	0.847001i
$527$	0.0267231			0.00116408
$528$		0			0
$529$	12.4178			0.539905
$530$	−1.16527	+	3.09959i	−0.0506161	+	0.134638i
$531$		0			0
$532$	−3.09727	+	3.53713i	−0.134284	+	0.153354i
$533$		−	13.1086i		−	0.567797i
$534$		0			0
$535$	2.57777			0.111447
$536$	17.0226	+	31.7607i	0.735266	+	1.37186i
$537$		0			0
$538$	6.52759	+	2.45400i	0.281424	+	0.105800i
$539$			1.55766i			0.0670933i
$540$		0			0
$541$			43.3953i			1.86571i	0.360252	+	0.932855i	$0.382691\pi$
$541$			43.3953i			1.86571i	−0.360252	+	0.932855i	$0.617309\pi$
$542$	−11.2772	+	29.9970i	−0.484396	+	1.28848i
$543$		0			0
$544$	0.0871342	+	0.0201439i	0.00373585	+	0.000863662i
$545$	17.3265			0.742187
$546$		0			0
$547$		−	18.5677i		−	0.793898i	−0.917841	−	0.396949i	$-0.870069\pi$
$547$		−	18.5677i		−	0.793898i	0.917841	−	0.396949i	$-0.129931\pi$
$548$	19.7904	+	17.3294i	0.845404	+	0.740274i
$549$		0			0
$550$	7.06778	+	2.65709i	0.301371	+	0.113299i
$551$	1.10424			0.0470422
$552$		0			0
$553$	−6.15343			−0.261671
$554$	−7.93159	−	2.98183i	−0.336981	−	0.126686i
$555$		0			0
$556$	6.97629	−	7.96703i	0.295860	−	0.337877i
$557$		−	17.4689i		−	0.740182i	−0.928996	−	0.370091i	$-0.879327\pi$
$557$		−	17.4689i		−	0.740182i	0.928996	−	0.370091i	$-0.120673\pi$
$558$		0			0
$559$	2.11860			0.0896073
$560$	−4.97178	+	0.662170i	−0.210096	+	0.0279818i
$561$		0			0
$562$	−0.958209	+	2.54881i	−0.0404196	+	0.107515i
$563$			26.8370i			1.13105i	0.824733	+	0.565523i	$0.191325\pi$
$563$			26.8370i			1.13105i	−0.824733	+	0.565523i	$0.808675\pi$
$564$		0			0
$565$		−	4.66534i		−	0.196272i
$566$	−37.3558	−	14.0437i	−1.57018	−	0.590299i
$567$		0			0
$568$	10.5253	−	5.64121i	0.441633	−	0.236700i
$569$	−32.4375			−1.35985			−0.679926	−	0.733281i	$-0.737988\pi$
$569$	−32.4375			−1.35985			−0.679926	+	0.733281i	$0.737988\pi$
$570$		0			0
$571$			34.0452i			1.42475i	0.701800	+	0.712374i	$0.252380\pi$
$571$			34.0452i			1.42475i	−0.701800	+	0.712374i	$0.747620\pi$
$572$	−2.51441	−	2.20173i	−0.105133	−	0.0920591i
$573$		0			0
$574$	6.08088	−	16.1750i	0.253811	−	0.675131i
$575$	20.3991			0.850702
$576$		0			0
$577$	6.09534			0.253752			0.126876	−	0.991919i	$-0.459505\pi$
$577$	6.09534			0.253752			0.126876	+	0.991919i	$0.459505\pi$
$578$	−8.46006	+	22.5036i	−0.351892	+	0.936025i
$579$		0			0
$580$	0.886271	+	0.776058i	0.0368004	+	0.0322241i
$581$			8.88604i			0.368655i
$582$		0			0
$583$	−2.90870			−0.120466
$584$	−16.2430	+	8.70570i	−0.672142	+	0.360244i
$585$		0			0
$586$	38.5156	+	14.4797i	1.59107	+	0.598151i
$587$			10.7735i			0.444669i	0.974970	+	0.222334i	$0.0713677\pi$
$587$			10.7735i			0.444669i	−0.974970	+	0.222334i	$0.928632\pi$
$588$		0			0
$589$		−	3.97353i		−	0.163727i
$590$	−5.33098	+	14.1803i	−0.219473	+	0.583793i
$591$		0			0
$592$	18.2310	−	2.42811i	0.749290	−	0.0997946i
$593$	−13.4720			−0.553230			−0.276615	−	0.960981i	$-0.589213\pi$
$593$	−13.4720			−0.553230			−0.276615	+	0.960981i	$0.589213\pi$
$594$		0			0
$595$			0.0198239i			0.000812701i
$596$	8.68755	−	9.92133i	0.355856	−	0.406393i
$597$		0			0
$598$	−8.45164	−	3.17734i	−0.345613	−	0.129931i
$599$	−37.4766			−1.53125			−0.765626	−	0.643285i	$-0.777571\pi$
$599$	−37.4766			−1.53125			−0.765626	+	0.643285i	$0.777571\pi$
$600$		0			0
$601$	−3.99803			−0.163083			−0.0815415	−	0.996670i	$-0.525984\pi$
$601$	−3.99803			−0.163083			−0.0815415	+	0.996670i	$0.525984\pi$
$602$	2.61419	+	0.982787i	0.106546	+	0.0400554i
$603$		0			0
$604$	14.3182	+	12.5377i	0.582601	+	0.510151i
$605$			10.7507i			0.437079i
$606$		0			0
$607$	36.8295			1.49486			0.747432	−	0.664338i	$-0.231287\pi$
$607$	36.8295			1.49486			0.747432	+	0.664338i	$0.231287\pi$
$608$	2.99525	−	12.9562i	0.121473	−	0.525444i
$609$		0			0
$610$	2.44931	−	6.51509i	0.0991695	−	0.263788i
$611$		−	7.64451i		−	0.309264i
$612$		0			0
$613$			9.76469i			0.394392i	0.980364	+	0.197196i	$0.0631836\pi$
$613$			9.76469i			0.394392i	−0.980364	+	0.197196i	$0.936816\pi$
$614$	20.9647	+	7.88153i	0.846066	+	0.318073i
$615$		0			0
$616$	−2.08124	−	3.88316i	−0.0838555	−	0.156457i
$617$	−14.4832			−0.583070			−0.291535	−	0.956560i	$-0.594166\pi$
$617$	−14.4832			−0.583070			−0.291535	+	0.956560i	$0.594166\pi$
$618$		0			0
$619$		−	6.72500i		−	0.270301i	−0.990825	−	0.135150i	$-0.956848\pi$
$619$		−	6.72500i		−	0.270301i	0.990825	−	0.135150i	$-0.0431518\pi$
$620$	2.79259	−	3.18918i	0.112153	−	0.128081i
$621$		0			0
$622$	7.24691	−	19.2766i	0.290575	−	0.772922i
$623$	−0.240788			−0.00964698
$624$		0			0
$625$	3.88743			0.155497
$626$	3.22023	−	8.56573i	0.128706	−	0.342355i
$627$		0			0
$628$	−21.0953	+	24.0912i	−0.841795	+	0.961343i
$629$		−	0.0726923i		−	0.00289843i
$630$		0			0
$631$	−23.2251			−0.924577			−0.462288	−	0.886730i	$-0.652971\pi$
$631$	−23.2251			−0.924577			−0.462288	+	0.886730i	$0.652971\pi$
$632$	15.3401	−	8.22178i	0.610198	−	0.327045i
$633$		0			0
$634$	−15.8617	−	5.96310i	−0.629948	−	0.236825i
$635$		−	24.9062i		−	0.988373i
$636$		0			0
$637$		−	1.07281i		−	0.0425061i
$638$	−0.364132	+	0.968583i	−0.0144161	+	0.0383466i
$639$		0			0
$640$	11.5096	−	8.29369i	0.454957	−	0.327837i
$641$	−30.3809			−1.19998			−0.599988	−	0.800009i	$-0.704828\pi$
$641$	−30.3809			−1.19998			−0.599988	+	0.800009i	$0.704828\pi$
$642$		0			0
$643$			5.74408i			0.226524i	0.993565	+	0.113262i	$0.0361300\pi$
$643$			5.74408i			0.226524i	−0.993565	+	0.113262i	$0.963870\pi$
$644$	−8.95474	−	7.84117i	−0.352866	−	0.308985i
$645$		0			0
$646$	−0.0491969	−	0.0184952i	−0.00193563	−	0.000727686i
$647$	−4.19948			−0.165099			−0.0825494	−	0.996587i	$-0.526306\pi$
$647$	−4.19948			−0.165099			−0.0825494	+	0.996587i	$0.526306\pi$
$648$		0			0
$649$	−13.3070			−0.522345
$650$	−4.86778	−	1.83001i	−0.190930	−	0.0717788i
$651$		0			0
$652$	16.5685	−	18.9214i	0.648871	−	0.741021i
$653$		−	45.2069i		−	1.76908i	−0.466460	−	0.884542i	$-0.654471\pi$
$653$		−	45.2069i		−	1.76908i	0.466460	−	0.884542i	$-0.345529\pi$
$654$		0			0
$655$	−9.08839			−0.355113
$656$	6.45260	+	48.4482i	0.251932	+	1.89158i
$657$		0			0
$658$	3.54617	−	9.43272i	0.138244	−	0.367726i
$659$			47.0951i			1.83456i	0.398239	+	0.917282i	$0.369621\pi$
$659$			47.0951i			1.83456i	−0.398239	+	0.917282i	$0.630379\pi$
$660$		0			0
$661$		−	41.9805i		−	1.63285i	−0.577449	−	0.816427i	$-0.695952\pi$
$661$		−	41.9805i		−	1.63285i	0.577449	−	0.816427i	$-0.304048\pi$
$662$	29.0462	+	10.9197i	1.12891	+	0.424408i
$663$		0			0
$664$	−11.8729	−	22.1524i	−0.460758	−	0.859679i
$665$	2.94767			0.114306
$666$		0			0
$667$			2.79554i			0.108244i
$668$	−26.0069	−	22.7728i	−1.00624	−	0.881105i
$669$		0			0
$670$	7.95023	−	21.1474i	0.307144	−	0.816996i
$671$	6.11386			0.236023
$672$		0			0
$673$	30.0898			1.15987			0.579937	−	0.814661i	$-0.303077\pi$
$673$	30.0898			1.15987			0.579937	+	0.814661i	$0.303077\pi$
$674$	11.1052	−	29.5397i	0.427758	−	1.13783i
$675$		0			0
$676$	−17.8290	−	15.6119i	−0.685731	−	0.600456i
$677$		−	40.5494i		−	1.55844i	−0.626749	−	0.779221i	$-0.715615\pi$
$677$		−	40.5494i		−	1.55844i	0.626749	−	0.779221i	$-0.284385\pi$
$678$		0			0
$679$	5.86131			0.224936
$680$	−0.0264873	−	0.0494199i	−0.00101574	−	0.00189517i
$681$		0			0
$682$	3.48538	+	1.31030i	0.133462	+	0.0501741i
$683$		−	50.1042i		−	1.91718i	−0.284786	−	0.958591i	$-0.591923\pi$
$683$		−	50.1042i		−	1.91718i	0.284786	−	0.958591i	$-0.408077\pi$
$684$		0			0
$685$		−	16.4924i		−	0.630141i
$686$	0.497658	−	1.32376i	0.0190007	−	0.0505413i
$687$		0			0
$688$	−7.83015	+	1.04286i	−0.298522	+	0.0397588i
$689$	2.00330			0.0763198
$690$		0			0
$691$		−	43.2174i		−	1.64407i	−0.569438	−	0.822034i	$-0.692839\pi$
$691$		−	43.2174i		−	1.64407i	0.569438	−	0.822034i	$-0.307161\pi$
$692$	−11.5776	+	13.2218i	−0.440116	+	0.502619i
$693$		0			0
$694$	−32.5388	−	12.2328i	−1.23516	−	0.464349i
$695$	−6.63933			−0.251844
$696$		0			0
$697$	0.193177			0.00731709
$698$	−16.6701	−	6.26702i	−0.630973	−	0.237210i
$699$		0			0
$700$	−5.15754	−	4.51617i	−0.194937	−	0.170695i
$701$			19.4337i			0.734002i	0.930221	+	0.367001i	$0.119615\pi$
$701$			19.4337i			0.734002i	−0.930221	+	0.367001i	$0.880385\pi$
$702$		0			0
$703$	−10.8088			−0.407662
$704$	10.3768	+	6.89970i	0.391091	+	0.260042i
$705$		0			0
$706$	−8.05939	+	21.4378i	−0.303319	+	0.806821i
$707$		−	3.12870i		−	0.117667i
$708$		0			0
$709$			24.0279i			0.902387i	0.892426	+	0.451194i	$0.149002\pi$
$709$			24.0279i			0.902387i	−0.892426	+	0.451194i	$0.850998\pi$
$710$	−7.00814	−	2.63466i	−0.263011	−	0.0988771i
$711$		0			0
$712$	0.600271	−	0.321724i	0.0224961	−	0.0120571i
$713$	10.0595			0.376733
$714$		0			0
$715$			2.09539i			0.0783631i
$716$	−15.4107	+	17.5993i	−0.575927	+	0.657717i
$717$		0			0
$718$	5.06663	−	13.4771i	0.189085	−	0.502961i
$719$	−36.0898			−1.34592			−0.672961	−	0.739678i	$-0.734978\pi$
$719$	−36.0898			−1.34592			−0.672961	+	0.739678i	$0.734978\pi$
$720$		0			0
$721$	2.72832			0.101608
$722$	6.70539	−	17.8362i	0.249549	−	0.663794i
$723$		0			0
$724$	31.9671	−	36.5070i	1.18805	−	1.35677i
$725$			1.61011i			0.0597979i
$726$		0			0
$727$	36.3230			1.34714			0.673572	−	0.739122i	$-0.264759\pi$
$727$	36.3230			1.34714			0.673572	+	0.739122i	$0.264759\pi$
$728$	1.43341	+	2.67444i	0.0531256	+	0.0991214i
$729$		0			0
$730$	10.8152	+	4.06590i	0.400288	+	0.150486i
$731$			0.0312211i			0.00115475i
$732$		0			0
$733$		−	11.9814i		−	0.442544i	−0.975212	−	0.221272i	$-0.928979\pi$
$733$		−	11.9814i		−	0.442544i	0.975212	−	0.221272i	$-0.0710209\pi$
$734$	−6.16792	+	16.4065i	−0.227662	+	0.605575i
$735$		0			0
$736$	32.8005	+	7.58289i	1.20904	+	0.279509i
$737$	19.8451			0.731002
$738$		0			0
$739$		−	36.7377i		−	1.35142i	−0.737169	−	0.675708i	$-0.763838\pi$
$739$		−	36.7377i		−	1.35142i	0.737169	−	0.675708i	$-0.236162\pi$
$740$	−8.67522	−	7.59641i	−0.318908	−	0.279250i
$741$		0			0
$742$	2.47192	+	0.929302i	0.0907471	+	0.0341158i
$743$	−13.2966			−0.487805			−0.243903	−	0.969800i	$-0.578428\pi$
$743$	−13.2966			−0.487805			−0.243903	+	0.969800i	$0.578428\pi$
$744$		0			0
$745$	−8.26795			−0.302914
$746$	10.0330	+	3.77185i	0.367336	+	0.138097i
$747$		0			0
$748$	0.0324461	−	0.0370540i	0.00118635	−	0.00135483i
$749$		−	2.05577i		−	0.0751161i
$750$		0			0
$751$	−13.5953			−0.496101			−0.248051	−	0.968747i	$-0.579790\pi$
$751$	−13.5953			−0.496101			−0.248051	+	0.968747i	$0.579790\pi$
$752$	3.76294	+	28.2534i	0.137220	+	1.03029i
$753$		0			0
$754$	0.250788	−	0.667090i	0.00913316	−	0.0242940i
$755$		−	11.9321i		−	0.434254i
$756$		0			0
$757$		−	8.04991i		−	0.292579i	−0.989242	−	0.146290i	$-0.953267\pi$
$757$		−	8.04991i		−	0.292579i	0.989242	−	0.146290i	$-0.0467331\pi$
$758$	18.6887	+	7.02588i	0.678803	+	0.255192i
$759$		0			0
$760$	−7.34838	+	3.93847i	−0.266554	+	0.142863i
$761$	−53.5813			−1.94232			−0.971160	−	0.238429i	$-0.923368\pi$
$761$	−53.5813			−1.94232			−0.971160	+	0.238429i	$0.923368\pi$
$762$		0			0
$763$		−	13.8179i		−	0.500241i
$764$	15.7764	+	13.8146i	0.570771	+	0.499793i
$765$		0			0
$766$	0.640375	−	1.70338i	0.0231377	−	0.0615457i
$767$	9.16489			0.330925
$768$		0			0
$769$	3.40107			0.122646			0.0613229	−	0.998118i	$-0.480468\pi$
$769$	3.40107			0.122646			0.0613229	+	0.998118i	$0.480468\pi$
$770$	−0.972019	+	2.58555i	−0.0350291	+	0.0931766i
$771$		0			0
$772$	−19.1233	−	16.7452i	−0.688261	−	0.602672i
$773$			12.6537i			0.455123i	0.973764	+	0.227561i	$0.0730752\pi$
$773$			12.6537i			0.455123i	−0.973764	+	0.227561i	$0.926925\pi$
$774$		0			0
$775$	5.79386			0.208122
$776$	−14.6119	+	7.83147i	−0.524537	+	0.281133i
$777$		0			0
$778$	−44.1222	−	16.5875i	−1.58186	−	0.594689i
$779$		−	28.7240i		−	1.02914i
$780$		0			0
$781$		−	6.57654i		−	0.235327i
$782$	0.0468232	−	0.124549i	0.00167440	−	0.00445385i
$783$		0			0
$784$	0.528080	+	3.96499i	0.0188600	+	0.141607i
$785$	20.0764			0.716558
$786$		0			0
$787$		−	37.3539i		−	1.33152i	−0.746165	−	0.665761i	$-0.768107\pi$
$787$		−	37.3539i		−	1.33152i	0.746165	−	0.665761i	$-0.231893\pi$
$788$	21.0964	−	24.0924i	0.751527	−	0.858256i
$789$		0			0
$790$	−10.2140	−	3.83989i	−0.363398	−	0.136617i
$791$	−3.72061			−0.132290
$792$		0			0
$793$	−4.21079			−0.149529
$794$	27.5038	+	10.3399i	0.976073	+	0.366948i
$795$		0			0
$796$	16.8355	+	14.7420i	0.596720	+	0.522515i
$797$			15.3333i			0.543134i	0.962420	+	0.271567i	$0.0875418\pi$
$797$			15.3333i			0.543134i	−0.962420	+	0.271567i	$0.912458\pi$
$798$		0			0
$799$	0.112654			0.00398542
$800$	18.8916	+	4.36741i	0.667920	+	0.154411i
$801$		0			0
$802$	−3.67350	+	9.77141i	−0.129716	+	0.345041i
$803$			10.1491i			0.358155i
$804$		0			0
$805$			7.46244i			0.263016i
$806$	−2.40047	−	0.902443i	−0.0845531	−	0.0317872i
$807$		0			0
$808$	4.18035	+	7.79967i	0.147064	+	0.274391i
$809$	−48.1700			−1.69357			−0.846784	−	0.531938i	$-0.821464\pi$
$809$	−48.1700			−1.69357			−0.846784	+	0.531938i	$0.821464\pi$
$810$		0			0
$811$		−	21.4720i		−	0.753984i	−0.926216	−	0.376992i	$-0.876958\pi$
$811$		−	21.4720i		−	0.753984i	0.926216	−	0.376992i	$-0.123042\pi$
$812$	0.618905	−	0.706800i	0.0217193	−	0.0248038i
$813$		0			0
$814$	3.56429	−	9.48093i	0.124928	−	0.332307i
$815$	−15.7682			−0.552336
$816$		0			0
$817$	4.64235			0.162415
$818$	15.9174	−	42.3399i	0.556539	−	1.48038i
$819$		0			0
$820$	20.1872	−	23.0541i	0.704967	−	0.805083i
$821$		−	24.2783i		−	0.847318i	−0.905822	−	0.423659i	$-0.860746\pi$
$821$		−	24.2783i		−	0.847318i	0.905822	−	0.423659i	$-0.139254\pi$
$822$		0			0
$823$	15.7002			0.547275			0.273637	−	0.961833i	$-0.411773\pi$
$823$	15.7002			0.547275			0.273637	+	0.961833i	$0.411773\pi$
$824$	−6.80155	+	3.64539i	−0.236943	+	0.126993i
$825$		0			0
$826$	11.3088	+	4.25145i	0.393482	+	0.147927i
$827$		−	1.47290i		−	0.0512177i	−0.999672	−	0.0256089i	$-0.991848\pi$
$827$		−	1.47290i		−	0.0512177i	0.999672	−	0.0256089i	$-0.00815244\pi$
$828$		0			0
$829$		−	25.1759i		−	0.874395i	−0.899365	−	0.437198i	$-0.855971\pi$
$829$		−	25.1759i		−	0.874395i	0.899365	−	0.437198i	$-0.144029\pi$
$830$	−5.54510	+	14.7498i	−0.192473	+	0.511974i
$831$		0			0
$832$	−7.14680	−	4.75201i	−0.247771	−	0.164746i
$833$	0.0158095			0.000547768
$834$		0			0
$835$			21.6729i			0.750020i
$836$	−5.50966	−	4.82451i	−0.190556	−	0.166859i
$837$		0			0
$838$	19.4124	+	7.29797i	0.670591	+	0.252104i
$839$	14.4703			0.499570			0.249785	−	0.968301i	$-0.419640\pi$
$839$	14.4703			0.499570			0.249785	+	0.968301i	$0.419640\pi$
$840$		0			0
$841$	28.7793			0.992391
$842$	−37.7216	−	14.1812i	−1.29997	−	0.488716i
$843$		0			0
$844$	26.5695	−	30.3428i	0.914560	−	1.04444i
$845$			14.8578i			0.511124i
$846$		0			0
$847$	8.57368			0.294595
$848$	−7.40402	+	0.986109i	−0.254255	+	0.0338631i
$849$		0			0
$850$	0.0269682	−	0.0717346i	0.000925000	−	0.00246048i
$851$		−	27.3640i		−	0.938026i
$852$		0			0
$853$		−	0.552410i		−	0.0189142i	−0.999955	−	0.00945708i	$-0.996990\pi$
$853$		−	0.552410i		−	0.0189142i	0.999955	−	0.00945708i	$-0.00301033\pi$
$854$	−5.19578	−	1.95332i	−0.177796	−	0.0668412i
$855$		0			0
$856$	2.74677	+	5.12491i	0.0938826	+	0.175166i
$857$	47.3043			1.61588			0.807942	−	0.589262i	$-0.200581\pi$
$857$	47.3043			1.61588			0.807942	+	0.589262i	$0.200581\pi$
$858$		0			0
$859$		−	42.9031i		−	1.46384i	−0.681393	−	0.731918i	$-0.738625\pi$
$859$		−	42.9031i		−	1.46384i	0.681393	−	0.731918i	$-0.261375\pi$
$860$	3.72598	+	3.26263i	0.127055	+	0.111255i
$861$		0			0
$862$	−17.6391	+	46.9197i	−0.600791	+	1.59809i
$863$	−2.39600			−0.0815609			−0.0407805	−	0.999168i	$-0.512984\pi$
$863$	−2.39600			−0.0815609			−0.0407805	+	0.999168i	$0.512984\pi$
$864$		0			0
$865$	11.0184			0.374638
$866$	−15.7214	+	41.8185i	−0.534235	+	1.42105i
$867$		0			0
$868$	−2.54337	−	2.22709i	−0.0863275	−	0.0755922i
$869$		−	9.58498i		−	0.325148i
$870$		0			0
$871$	−13.6678			−0.463117
$872$	18.4625	+	34.4472i	0.625218	+	1.16653i
$873$		0			0
$874$	−18.5195	−	6.96228i	−0.626431	−	0.235503i
$875$			10.5676i			0.357252i
$876$		0			0
$877$		−	36.8060i		−	1.24285i	−0.783473	−	0.621426i	$-0.786554\pi$
$877$		−	36.8060i		−	1.24285i	0.783473	−	0.621426i	$-0.213446\pi$
$878$	11.6319	−	30.9405i	0.392556	−	1.04419i
$879$		0			0
$880$	−1.03144	−	7.74436i	−0.0347698	−	0.261062i
$881$	−45.1322			−1.52054			−0.760271	−	0.649606i	$-0.774934\pi$
$881$	−45.1322			−1.52054			−0.760271	+	0.649606i	$0.774934\pi$
$882$		0			0
$883$			38.0204i			1.27949i	0.768588	+	0.639744i	$0.220960\pi$
$883$			38.0204i			1.27949i	−0.768588	+	0.639744i	$0.779040\pi$
$884$	−0.0223466	+	0.0255201i	−0.000751596	+	0.000858334i
$885$		0			0
$886$	4.67197	+	1.75640i	0.156958	+	0.0590073i
$887$	−30.4326			−1.02183			−0.510913	−	0.859633i	$-0.670692\pi$
$887$	−30.4326			−1.02183			−0.510913	+	0.859633i	$0.670692\pi$
$888$		0			0
$889$	−19.8627			−0.666173
$890$	−0.399681	−	0.150258i	−0.0133974	−	0.00503665i
$891$		0			0
$892$	16.7772	+	14.6909i	0.561742	+	0.491886i
$893$		−	16.7509i		−	0.560547i
$894$		0			0
$895$	14.6664			0.490244
$896$	−6.61421	−	9.17890i	−0.220965	−	0.306646i
$897$		0			0
$898$	1.46611	−	3.89981i	0.0489246	−	0.130138i
$899$			0.794002i			0.0264814i
$900$		0			0
$901$			0.0295220i			0.000983519i
$902$	25.1952	+	9.47197i	0.838909	+	0.315382i
$903$		0			0
$904$	9.27525	−	4.97121i	0.308490	−	0.165340i
$905$	−30.4231			−1.01130
$906$		0			0
$907$			8.80211i			0.292269i	0.989265	+	0.146135i	$0.0466833\pi$
$907$			8.80211i			0.292269i	−0.989265	+	0.146135i	$0.953317\pi$
$908$	24.6929	−	28.1997i	0.819463	−	0.935839i
$909$		0			0
$910$	0.669456	−	1.78074i	0.0221923	−	0.0590309i
$911$	31.9516			1.05860			0.529302	−	0.848434i	$-0.322454\pi$
$911$	31.9516			1.05860			0.529302	+	0.848434i	$0.322454\pi$
$912$		0			0
$913$	−13.8415			−0.458086
$914$	−11.0378	+	29.3604i	−0.365099	+	0.971155i
$915$		0			0
$916$	−17.8455	+	20.3799i	−0.589633	+	0.673370i
$917$			7.24798i			0.239349i
$918$		0			0
$919$	55.5377			1.83202			0.916009	−	0.401157i	$-0.131392\pi$
$919$	55.5377			1.83202			0.916009	+	0.401157i	$0.131392\pi$
$920$	−9.97079	−	18.6034i	−0.328727	−	0.613337i
$921$		0			0
$922$	−31.0481	−	11.6723i	−1.02251	−	0.384407i
$923$			4.52944i			0.149088i
$924$		0			0
$925$		−	15.7605i		−	0.518201i
$926$	−14.5492	+	38.7006i	−0.478118	+	1.27178i
$927$		0			0
$928$	−0.598519	+	2.58895i	−0.0196474	+	0.0849864i
$929$	−22.4706			−0.737235			−0.368617	−	0.929581i	$-0.620169\pi$
$929$	−22.4706			−0.737235			−0.368617	+	0.929581i	$0.620169\pi$
$930$		0			0
$931$		−	2.35077i		−	0.0770433i
$932$	−16.5620	−	14.5024i	−0.542505	−	0.475042i
$933$		0			0
$934$	−7.18877	−	2.70257i	−0.235224	−	0.0884308i
$935$	−0.0308790			−0.00100985
$936$		0			0
$937$	−47.5975			−1.55494			−0.777471	−	0.628919i	$-0.783498\pi$
$937$	−47.5975			−1.55494			−0.777471	+	0.628919i	$0.783498\pi$
$938$	−16.8650	−	6.34030i	−0.550663	−	0.207018i
$939$		0			0
$940$	11.7725	−	13.4444i	0.383976	−	0.438507i
$941$		−	5.03276i		−	0.164063i	−0.996630	−	0.0820317i	$-0.973859\pi$
$941$		−	5.03276i		−	0.164063i	0.996630	−	0.0820317i	$-0.0261409\pi$
$942$		0			0
$943$	72.7188			2.36805
$944$	−33.8726	+	4.51134i	−1.10246	+	0.146832i
$945$		0			0
$946$	−1.53085	+	4.07203i	−0.0497723	+	0.132393i
$947$			18.9034i			0.614277i	0.951665	+	0.307138i	$0.0993714\pi$
$947$			18.9034i			0.614277i	−0.951665	+	0.307138i	$0.900629\pi$
$948$		0			0
$949$		−	6.98999i		−	0.226905i
$950$	−10.6664	−	4.00997i	−0.346065	−	0.130101i
$951$		0			0
$952$	−0.0394123	+	0.0211236i	−0.00127736	+	0.000684620i
$953$	59.5108			1.92774			0.963872	−	0.266365i	$-0.0858225\pi$
$953$	59.5108			1.92774			0.963872	+	0.266365i	$0.0858225\pi$
$954$		0			0
$955$		−	13.1473i		−	0.425437i
$956$	23.2270	+	20.3386i	0.751215	+	0.657797i
$957$		0			0
$958$	2.52574	−	6.71841i	0.0816030	−	0.217062i
$959$	−13.1526			−0.424721
$960$		0			0
$961$	−28.1428			−0.907834
$962$	−2.45483	+	6.52978i	−0.0791468	+	0.210529i
$963$		0			0
$964$	−24.1280	−	21.1276i	−0.777112	−	0.680474i
$965$			15.9364i			0.513010i
$966$		0			0
$967$	−26.3394			−0.847018			−0.423509	−	0.905892i	$-0.639202\pi$
$967$	−26.3394			−0.847018			−0.423509	+	0.905892i	$0.639202\pi$
$968$	−21.3737	+	11.4556i	−0.686977	+	0.368195i
$969$		0			0
$970$	9.72912	+	3.65760i	0.312383	+	0.117438i
$971$		−	50.9352i		−	1.63459i	−0.576222	−	0.817293i	$-0.695474\pi$
$971$		−	50.9352i		−	1.63459i	0.576222	−	0.817293i	$-0.304526\pi$
$972$		0			0
$973$			5.29486i			0.169745i
$974$	−1.60926	+	4.28059i	−0.0515640	+	0.137159i
$975$		0			0
$976$	15.5627	−	2.07272i	0.498149	−	0.0663463i
$977$	−23.5022			−0.751903			−0.375951	−	0.926639i	$-0.622684\pi$
$977$	−23.5022			−0.751903			−0.375951	+	0.926639i	$0.622684\pi$
$978$		0			0
$979$		−	0.375067i		−	0.0119872i
$980$	1.65211	−	1.88674i	0.0527748	−	0.0602697i
$981$		0			0
$982$	−43.2124	−	16.2454i	−1.37896	−	0.518411i
$983$	41.3639			1.31930			0.659651	−	0.751572i	$-0.270704\pi$
$983$	41.3639			1.31930			0.659651	+	0.751572i	$0.270704\pi$
$984$		0			0
$985$	−20.0774			−0.639720
$986$	0.00983066	+	0.00369577i	0.000313072	+	0.000117697i
$987$		0			0
$988$	3.79466	+	3.32277i	0.120724	+	0.105711i
$989$			11.7527i			0.373715i
$990$		0			0
$991$	−8.06637			−0.256237			−0.128118	−	0.991759i	$-0.540894\pi$
$991$	−8.06637			−0.256237			−0.128118	+	0.991759i	$0.540894\pi$
$992$	9.31614	+	2.15373i	0.295788	+	0.0683809i
$993$		0			0
$994$	−2.10114	+	5.58898i	−0.0666441	+	0.177272i
$995$		−	14.0299i		−	0.444778i
$996$		0			0
$997$			38.8503i			1.23040i	0.788371	+	0.615200i	$0.210925\pi$
$997$			38.8503i			1.23040i	−0.788371	+	0.615200i	$0.789075\pi$
$998$	−2.34754	−	0.882541i	−0.0743100	−	0.0279363i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.g.757.15	yes	24
3.2	odd	2	inner	1512.2.c.g.757.10	yes	24
4.3	odd	2		6048.2.c.f.3025.15		24
8.3	odd	2		6048.2.c.f.3025.10		24
8.5	even	2	inner	1512.2.c.g.757.16	yes	24
12.11	even	2		6048.2.c.f.3025.9		24
24.5	odd	2	inner	1512.2.c.g.757.9	✓	24
24.11	even	2		6048.2.c.f.3025.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.g.757.9	✓	24	24.5	odd	2	inner
1512.2.c.g.757.10	yes	24	3.2	odd	2	inner
1512.2.c.g.757.15	yes	24	1.1	even	1	trivial
1512.2.c.g.757.16	yes	24	8.5	even	2	inner
6048.2.c.f.3025.9		24	12.11	even	2
6048.2.c.f.3025.10		24	8.3	odd	2
6048.2.c.f.3025.15		24	4.3	odd	2
6048.2.c.f.3025.16		24	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.497658 - 1.32376i) q^{2} +(-1.50467 - 1.31756i) q^{4} +1.25392i q^{5} +1.00000 q^{7} +(-2.49294 + 1.33613i) q^{8} +O(q^{10})\)	\(q+(0.497658 - 1.32376i) q^{2} +(-1.50467 - 1.31756i) q^{4} +1.25392i q^{5} +1.00000 q^{7} +(-2.49294 + 1.33613i) q^{8} +(1.65989 + 0.624024i) q^{10} +1.55766i q^{11} -1.07281i q^{13} +(0.497658 - 1.32376i) q^{14} +(0.528080 + 3.96499i) q^{16} +0.0158095 q^{17} -2.35077i q^{19} +(1.65211 - 1.88674i) q^{20} +(2.06197 + 0.775184i) q^{22} +5.95129 q^{23} +3.42768 q^{25} +(-1.42014 - 0.533891i) q^{26} +(-1.50467 - 1.31756i) q^{28} +0.469737i q^{29} +1.69031 q^{31} +(5.51149 + 1.27416i) q^{32} +(0.00786775 - 0.0209280i) q^{34} +1.25392i q^{35} -4.59800i q^{37} +(-3.11185 - 1.16988i) q^{38} +(-1.67540 - 3.12595i) q^{40} +12.2190 q^{41} +1.97482i q^{43} +(2.05231 - 2.34377i) q^{44} +(2.96171 - 7.87807i) q^{46} +7.12571 q^{47} +1.00000 q^{49} +(1.70581 - 4.53742i) q^{50} +(-1.41348 + 1.61422i) q^{52} +1.86735i q^{53} -1.95319 q^{55} +(-2.49294 + 1.33613i) q^{56} +(0.621818 + 0.233768i) q^{58} +8.54291i q^{59} -3.92502i q^{61} +(0.841198 - 2.23757i) q^{62} +(4.42952 - 6.66179i) q^{64} +1.34521 q^{65} -12.7403i q^{67} +(-0.0237882 - 0.0208300i) q^{68} +(1.65989 + 0.624024i) q^{70} -4.22205 q^{71} +6.51561 q^{73} +(-6.08664 - 2.28823i) q^{74} +(-3.09727 + 3.53713i) q^{76} +1.55766i q^{77} -6.15343 q^{79} +(-4.97178 + 0.662170i) q^{80} +(6.08088 - 16.1750i) q^{82} +8.88604i q^{83} +0.0198239i q^{85} +(2.61419 + 0.982787i) q^{86} +(-2.08124 - 3.88316i) q^{88} -0.240788 q^{89} -1.07281i q^{91} +(-8.95474 - 7.84117i) q^{92} +(3.54617 - 9.43272i) q^{94} +2.94767 q^{95} +5.86131 q^{97} +(0.497658 - 1.32376i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 24 q^{7}+O(q^{10}) \) 24 * q + 6 * q^4 + 24 * q^7	\( 24 q + 6 q^{4} + 24 q^{7} - 16 q^{10} + 2 q^{16} + 16 q^{22} - 24 q^{25} + 6 q^{28} + 8 q^{31} + 22 q^{34} + 26 q^{46} + 24 q^{49} - 6 q^{52} + 16 q^{55} - 58 q^{58} + 6 q^{64} - 16 q^{70} + 60 q^{76} + 8 q^{79} - 28 q^{82} + 12 q^{88} + 36 q^{94}+O(q^{100}) \) 24 * q + 6 * q^4 + 24 * q^7 - 16 * q^10 + 2 * q^16 + 16 * q^22 - 24 * q^25 + 6 * q^28 + 8 * q^31 + 22 * q^34 + 26 * q^46 + 24 * q^49 - 6 * q^52 + 16 * q^55 - 58 * q^58 + 6 * q^64 - 16 * q^70 + 60 * q^76 + 8 * q^79 - 28 * q^82 + 12 * q^88 + 36 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more