LMFDB - Embedded newform 1512.2.j.d.323.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.20
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.508876 + 1.31949i) q^{2} +(-1.48209 - 1.34291i) q^{4} -2.29653 q^{5} -1.00000i q^{7} +(2.52615 - 1.27222i) q^{8} +O(q^{10})$	\(q+(-0.508876 + 1.31949i) q^{2} +(-1.48209 - 1.34291i) q^{4} -2.29653 q^{5} -1.00000i q^{7} +(2.52615 - 1.27222i) q^{8} +(1.16865 - 3.03024i) q^{10} +4.02419i q^{11} -1.82461i q^{13} +(1.31949 + 0.508876i) q^{14} +(0.393186 + 3.98063i) q^{16} +0.430472i q^{17} +5.01046 q^{19} +(3.40366 + 3.08403i) q^{20} +(-5.30987 - 2.04781i) q^{22} +3.49479 q^{23} +0.274031 q^{25} +(2.40754 + 0.928498i) q^{26} +(-1.34291 + 1.48209i) q^{28} -2.16016 q^{29} -2.10635i q^{31} +(-5.45247 - 1.50684i) q^{32} +(-0.568002 - 0.219057i) q^{34} +2.29653i q^{35} -2.19775i q^{37} +(-2.54970 + 6.61124i) q^{38} +(-5.80137 + 2.92170i) q^{40} +4.35032i q^{41} -12.0354 q^{43} +(5.40413 - 5.96422i) q^{44} +(-1.77842 + 4.61133i) q^{46} -1.72531 q^{47} -1.00000 q^{49} +(-0.139448 + 0.361580i) q^{50} +(-2.45028 + 2.70423i) q^{52} -10.0938 q^{53} -9.24166i q^{55} +(-1.27222 - 2.52615i) q^{56} +(1.09925 - 2.85030i) q^{58} +10.6175i q^{59} +8.44575i q^{61} +(2.77930 + 1.07187i) q^{62} +(4.76289 - 6.42767i) q^{64} +4.19026i q^{65} -12.6358 q^{67} +(0.578085 - 0.637998i) q^{68} +(-3.03024 - 1.16865i) q^{70} -8.95532 q^{71} -7.16051 q^{73} +(2.89991 + 1.11838i) q^{74} +(-7.42596 - 6.72860i) q^{76} +4.02419 q^{77} -15.2405i q^{79} +(-0.902963 - 9.14162i) q^{80} +(-5.74018 - 2.21377i) q^{82} +13.4507i q^{83} -0.988589i q^{85} +(6.12452 - 15.8805i) q^{86} +(5.11968 + 10.1657i) q^{88} -7.44987i q^{89} -1.82461 q^{91} +(-5.17960 - 4.69319i) q^{92} +(0.877970 - 2.27653i) q^{94} -11.5067 q^{95} +1.68878 q^{97} +(0.508876 - 1.31949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * 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 $

$2$	−0.508876	+	1.31949i	−0.359830	+	0.933018i
$2$	−0.508876	+	1.31949i	−0.359830	+	0.933018i
$3$		0			0
$3$		0			0
$4$	−1.48209	−	1.34291i	−0.741045	−	0.671455i
$5$	−2.29653			−1.02704			−0.513519	−	0.858078i	$-0.671658\pi$
$5$	−2.29653			−1.02704			−0.513519	+	0.858078i	$0.671658\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.52615	−	1.27222i	0.893130	−	0.449799i
$9$		0			0
$10$	1.16865	−	3.03024i	0.369558	−	0.958245i
$11$			4.02419i			1.21334i	0.794954	+	0.606670i	$0.207495\pi$
$11$			4.02419i			1.21334i	−0.794954	+	0.606670i	$0.792505\pi$
$12$		0			0
$13$		−	1.82461i		−	0.506055i	−0.967459	−	0.253027i	$-0.918574\pi$
$13$		−	1.82461i		−	0.506055i	0.967459	−	0.253027i	$-0.0814263\pi$
$14$	1.31949	+	0.508876i	0.352648	+	0.136003i
$15$		0			0
$16$	0.393186	+	3.98063i	0.0982966	+	0.995157i
$17$			0.430472i			0.104405i	0.998637	+	0.0522024i	$0.0166241\pi$
$17$			0.430472i			0.104405i	−0.998637	+	0.0522024i	$0.983376\pi$
$18$		0			0
$19$	5.01046			1.14948			0.574739	−	0.818336i	$-0.305103\pi$
$19$	5.01046			1.14948			0.574739	+	0.818336i	$0.305103\pi$
$20$	3.40366	+	3.08403i	0.761081	+	0.689609i
$21$		0			0
$22$	−5.30987	−	2.04781i	−1.13207	−	0.436595i
$23$	3.49479			0.728715			0.364357	−	0.931259i	$-0.381289\pi$
$23$	3.49479			0.728715			0.364357	+	0.931259i	$0.381289\pi$
$24$		0			0
$25$	0.274031			0.0548062
$26$	2.40754	+	0.928498i	0.472158	+	0.182093i
$27$		0			0
$28$	−1.34291	+	1.48209i	−0.253786	+	0.280089i
$29$	−2.16016			−0.401131			−0.200565	−	0.979680i	$-0.564278\pi$
$29$	−2.16016			−0.401131			−0.200565	+	0.979680i	$0.564278\pi$
$30$		0			0
$31$		−	2.10635i		−	0.378311i	−0.981947	−	0.189156i	$-0.939425\pi$
$31$		−	2.10635i		−	0.378311i	0.981947	−	0.189156i	$-0.0605750\pi$
$32$	−5.45247	−	1.50684i	−0.963870	−	0.266374i
$33$		0			0
$34$	−0.568002	−	0.219057i	−0.0974115	−	0.0375679i
$35$			2.29653i			0.388184i
$36$		0			0
$37$		−	2.19775i		−	0.361309i	−0.983547	−	0.180654i	$-0.942178\pi$
$37$		−	2.19775i		−	0.361309i	0.983547	−	0.180654i	$-0.0578215\pi$
$38$	−2.54970	+	6.61124i	−0.413616	+	1.07248i
$39$		0			0
$40$	−5.80137	+	2.92170i	−0.917278	+	0.461961i
$41$			4.35032i			0.679405i	0.940533	+	0.339703i	$0.110326\pi$
$41$			4.35032i			0.679405i	−0.940533	+	0.339703i	$0.889674\pi$
$42$		0			0
$43$	−12.0354			−1.83538			−0.917690	−	0.397298i	$-0.869948\pi$
$43$	−12.0354			−1.83538			−0.917690	+	0.397298i	$0.869948\pi$
$44$	5.40413	−	5.96422i	0.814703	−	0.899140i
$45$		0			0
$46$	−1.77842	+	4.61133i	−0.262213	+	0.679904i
$47$	−1.72531			−0.251663			−0.125831	−	0.992052i	$-0.540160\pi$
$47$	−1.72531			−0.251663			−0.125831	+	0.992052i	$0.540160\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−0.139448	+	0.361580i	−0.0197209	+	0.0511351i
$51$		0			0
$52$	−2.45028	+	2.70423i	−0.339793	+	0.375010i
$53$	−10.0938			−1.38649			−0.693246	−	0.720701i	$-0.743820\pi$
$53$	−10.0938			−1.38649			−0.693246	+	0.720701i	$0.743820\pi$
$54$		0			0
$55$		−	9.24166i		−	1.24615i
$56$	−1.27222	−	2.52615i	−0.170008	−	0.337571i
$57$		0			0
$58$	1.09925	−	2.85030i	0.144339	−	0.374262i
$59$			10.6175i			1.38228i	0.722721	+	0.691140i	$0.242891\pi$
$59$			10.6175i			1.38228i	−0.722721	+	0.691140i	$0.757109\pi$
$60$		0			0
$61$			8.44575i			1.08137i	0.841226	+	0.540684i	$0.181834\pi$
$61$			8.44575i			1.08137i	−0.841226	+	0.540684i	$0.818166\pi$
$62$	2.77930	+	1.07187i	0.352971	+	0.136127i
$63$		0			0
$64$	4.76289	−	6.42767i	0.595361	−	0.803458i
$65$			4.19026i			0.519737i
$66$		0			0
$67$	−12.6358			−1.54370			−0.771852	−	0.635802i	$-0.780669\pi$
$67$	−12.6358			−1.54370			−0.771852	+	0.635802i	$0.780669\pi$
$68$	0.578085	−	0.637998i	0.0701031	−	0.0773686i
$69$		0			0
$70$	−3.03024	−	1.16865i	−0.362182	−	0.139680i
$71$	−8.95532			−1.06280			−0.531401	−	0.847121i	$-0.678334\pi$
$71$	−8.95532			−1.06280			−0.531401	+	0.847121i	$0.678334\pi$
$72$		0			0
$73$	−7.16051			−0.838075			−0.419037	−	0.907969i	$-0.637632\pi$
$73$	−7.16051			−0.838075			−0.419037	+	0.907969i	$0.637632\pi$
$74$	2.89991	+	1.11838i	0.337108	+	0.130010i
$75$		0			0
$76$	−7.42596	−	6.72860i	−0.851816	−	0.771823i
$77$	4.02419			0.458599
$78$		0			0
$79$		−	15.2405i		−	1.71468i	−0.514747	−	0.857342i	$-0.672114\pi$
$79$		−	15.2405i		−	1.71468i	0.514747	−	0.857342i	$-0.327886\pi$
$80$	−0.902963	−	9.14162i	−0.100954	−	1.02206i
$81$		0			0
$82$	−5.74018	−	2.21377i	−0.633897	−	0.244470i
$83$			13.4507i			1.47640i	0.674581	+	0.738201i	$0.264324\pi$
$83$			13.4507i			1.47640i	−0.674581	+	0.738201i	$0.735676\pi$
$84$		0			0
$85$		−	0.988589i		−	0.107228i
$86$	6.12452	−	15.8805i	0.660424	−	1.71244i
$87$		0			0
$88$	5.11968	+	10.1657i	0.545760	+	1.08367i
$89$		−	7.44987i		−	0.789684i	−0.918749	−	0.394842i	$-0.870799\pi$
$89$		−	7.44987i		−	0.789684i	0.918749	−	0.394842i	$-0.129201\pi$
$90$		0			0
$91$	−1.82461			−0.191271
$92$	−5.17960	−	4.69319i	−0.540011	−	0.489299i
$93$		0			0
$94$	0.877970	−	2.27653i	0.0905556	−	0.234806i
$95$	−11.5067			−1.18056
$96$		0			0
$97$	1.68878			0.171469			0.0857347	−	0.996318i	$-0.472676\pi$
$97$	1.68878			0.171469			0.0857347	+	0.996318i	$0.472676\pi$
$98$	0.508876	−	1.31949i	0.0514042	−	0.133288i
$99$		0			0
$100$	−0.406139	−	0.367999i	−0.0406139	−	0.0367999i
$101$	−13.3668			−1.33005			−0.665024	−	0.746822i	$-0.731579\pi$
$101$	−13.3668			−1.33005			−0.665024	+	0.746822i	$0.731579\pi$
$102$		0			0
$103$			4.59723i			0.452978i	0.974014	+	0.226489i	$0.0727248\pi$
$103$			4.59723i			0.452978i	−0.974014	+	0.226489i	$0.927275\pi$
$104$	−2.32131	−	4.60923i	−0.227623	−	0.451973i
$105$		0			0
$106$	5.13650	−	13.3186i	0.498901	−	1.29362i
$107$		−	15.7048i		−	1.51824i	−0.650951	−	0.759120i	$-0.725630\pi$
$107$		−	15.7048i		−	1.51824i	0.650951	−	0.759120i	$-0.274370\pi$
$108$		0			0
$109$			16.0140i			1.53386i	0.641728	+	0.766932i	$0.278218\pi$
$109$			16.0140i			1.53386i	−0.641728	+	0.766932i	$0.721782\pi$
$110$	12.1943	+	4.70286i	1.16268	+	0.448400i
$111$		0			0
$112$	3.98063	−	0.393186i	0.376134	−	0.0371526i
$113$			1.46858i			0.138152i	0.997611	+	0.0690760i	$0.0220051\pi$
$113$			1.46858i			0.138152i	−0.997611	+	0.0690760i	$0.977995\pi$
$114$		0			0
$115$	−8.02588			−0.748417
$116$	3.20155	+	2.90089i	0.297256	+	0.269341i
$117$		0			0
$118$	−14.0096	−	5.40298i	−1.28969	−	0.497385i
$119$	0.430472			0.0394613
$120$		0			0
$121$	−5.19413			−0.472193
$122$	−11.1441	−	4.29784i	−1.00893	−	0.389108i
$123$		0			0
$124$	−2.82863	+	3.12180i	−0.254019	+	0.280346i
$125$	10.8533			0.970750
$126$		0			0
$127$			6.35551i			0.563960i	0.959420	+	0.281980i	$0.0909913\pi$
$127$			6.35551i			0.563960i	−0.959420	+	0.281980i	$0.909009\pi$
$128$	6.05750	+	9.55545i	0.535413	+	0.844591i
$129$		0			0
$130$	−5.52899	−	2.13232i	−0.484924	−	0.187017i
$131$			7.75532i			0.677585i	0.940861	+	0.338793i	$0.110018\pi$
$131$			7.75532i			0.677585i	−0.940861	+	0.338793i	$0.889982\pi$
$132$		0			0
$133$		−	5.01046i		−	0.434462i
$134$	6.43003	−	16.6727i	0.555470	−	1.44030i
$135$		0			0
$136$	0.547657	+	1.08744i	0.0469612	+	0.0932469i
$137$		−	3.09831i		−	0.264706i	−0.991203	−	0.132353i	$-0.957747\pi$
$137$		−	3.09831i		−	0.264706i	0.991203	−	0.132353i	$-0.0422533\pi$
$138$		0			0
$139$	−3.76422			−0.319277			−0.159638	−	0.987176i	$-0.551033\pi$
$139$	−3.76422			−0.319277			−0.159638	+	0.987176i	$0.551033\pi$
$140$	3.08403	−	3.40366i	0.260648	−	0.287662i
$141$		0			0
$142$	4.55715	−	11.8164i	0.382427	−	0.991613i
$143$	7.34257			0.614016
$144$		0			0
$145$	4.96085			0.411976
$146$	3.64381	−	9.44820i	0.301564	−	0.781939i
$147$		0			0
$148$	−2.95139	+	3.25727i	−0.242602	+	0.267746i
$149$	6.57894			0.538968			0.269484	−	0.963005i	$-0.413147\pi$
$149$	6.57894			0.538968			0.269484	+	0.963005i	$0.413147\pi$
$150$		0			0
$151$		−	1.08336i		−	0.0881627i	−0.999028	−	0.0440814i	$-0.985964\pi$
$151$		−	1.08336i		−	0.0881627i	0.999028	−	0.0440814i	$-0.0140361\pi$
$152$	12.6572	−	6.37444i	1.02663	−	0.517035i
$153$		0			0
$154$	−2.04781	+	5.30987i	−0.165018	+	0.427881i
$155$			4.83728i			0.388540i
$156$		0			0
$157$			16.6130i			1.32586i	0.748680	+	0.662932i	$0.230688\pi$
$157$			16.6130i			1.32586i	−0.748680	+	0.662932i	$0.769312\pi$
$158$	20.1096	+	7.75550i	1.59983	+	0.616994i
$159$		0			0
$160$	12.5217	+	3.46050i	0.989930	+	0.273577i
$161$		−	3.49479i		−	0.275428i
$162$		0			0
$163$	11.4881			0.899818			0.449909	−	0.893074i	$-0.351456\pi$
$163$	11.4881			0.899818			0.449909	+	0.893074i	$0.351456\pi$
$164$	5.84208	−	6.44756i	0.456190	−	0.503470i
$165$		0			0
$166$	−17.7480	−	6.84472i	−1.37751	−	0.531253i
$167$	−13.4761			−1.04281			−0.521405	−	0.853309i	$-0.674592\pi$
$167$	−13.4761			−1.04281			−0.521405	+	0.853309i	$0.674592\pi$
$168$		0			0
$169$	9.67081			0.743909
$170$	1.30443	+	0.503069i	0.100045	+	0.0385836i
$171$		0			0
$172$	17.8375	+	16.1624i	1.36010	+	1.23237i
$173$	−4.98344			−0.378884			−0.189442	−	0.981892i	$-0.560668\pi$
$173$	−4.98344			−0.378884			−0.189442	+	0.981892i	$0.560668\pi$
$174$		0			0
$175$		−	0.274031i		−	0.0207148i
$176$	−16.0188	+	1.58226i	−1.20746	+	0.119267i
$177$		0			0
$178$	9.83000	+	3.79106i	0.736790	+	0.284152i
$179$		−	3.45929i		−	0.258559i	−0.991608	−	0.129280i	$-0.958733\pi$
$179$		−	3.45929i		−	0.258559i	0.991608	−	0.129280i	$-0.0412665\pi$
$180$		0			0
$181$			10.1409i			0.753768i	0.926260	+	0.376884i	$0.123004\pi$
$181$			10.1409i			0.753768i	−0.926260	+	0.376884i	$0.876996\pi$
$182$	0.928498	−	2.40754i	0.0688249	−	0.178459i
$183$		0			0
$184$	8.82838	−	4.44616i	0.650837	−	0.327775i
$185$			5.04720i			0.371078i
$186$		0			0
$187$	−1.73230			−0.126678
$188$	2.55707	+	2.31694i	0.186493	+	0.168980i
$189$		0			0
$190$	5.85546	−	15.1829i	0.424800	−	1.10148i
$191$	−10.9743			−0.794074			−0.397037	−	0.917803i	$-0.629962\pi$
$191$	−10.9743			−0.794074			−0.397037	+	0.917803i	$0.629962\pi$
$192$		0			0
$193$	2.07226			0.149165			0.0745824	−	0.997215i	$-0.476238\pi$
$193$	2.07226			0.149165			0.0745824	+	0.997215i	$0.476238\pi$
$194$	−0.859378	+	2.22832i	−0.0616998	+	0.159984i
$195$		0			0
$196$	1.48209	+	1.34291i	0.105864	+	0.0959221i
$197$	−4.69547			−0.334539			−0.167269	−	0.985911i	$-0.553495\pi$
$197$	−4.69547			−0.334539			−0.167269	+	0.985911i	$0.553495\pi$
$198$		0			0
$199$		−	16.7556i		−	1.18777i	−0.804549	−	0.593887i	$-0.797593\pi$
$199$		−	16.7556i		−	1.18777i	0.804549	−	0.593887i	$-0.202407\pi$
$200$	0.692244	−	0.348629i	0.0489490	−	0.0246518i
$201$		0			0
$202$	6.80205	−	17.6373i	0.478591	−	1.24096i
$203$			2.16016i			0.151613i
$204$		0			0
$205$		−	9.99061i		−	0.697775i
$206$	−6.06598	−	2.33942i	−0.422637	−	0.162995i
$207$		0			0
$208$	7.26308	−	0.717410i	0.503604	−	0.0497435i
$209$			20.1631i			1.39471i
$210$		0			0
$211$	15.2955			1.05299			0.526494	−	0.850179i	$-0.323506\pi$
$211$	15.2955			1.05299			0.526494	+	0.850179i	$0.323506\pi$
$212$	14.9599	+	13.5551i	1.02745	+	0.930967i
$213$		0			0
$214$	20.7223	+	7.99179i	1.41654	+	0.546307i
$215$	27.6396			1.88500
$216$		0			0
$217$	−2.10635			−0.142988
$218$	−21.1303	−	8.14914i	−1.43112	−	0.551930i
$219$		0			0
$220$	−12.4107	+	13.6970i	−0.836731	+	0.923450i
$221$	0.785442			0.0528345
$222$		0			0
$223$		−	23.5657i		−	1.57808i	−0.614343	−	0.789039i	$-0.710579\pi$
$223$		−	23.5657i		−	1.57808i	0.614343	−	0.789039i	$-0.289421\pi$
$224$	−1.50684	+	5.45247i	−0.100680	+	0.364308i
$225$		0			0
$226$	−1.93777	−	0.747323i	−0.128898	−	0.0497112i
$227$		−	16.6514i		−	1.10519i	−0.833450	−	0.552595i	$-0.813638\pi$
$227$		−	16.6514i		−	1.10519i	0.833450	−	0.552595i	$-0.186362\pi$
$228$		0			0
$229$			24.4291i			1.61432i	0.590332	+	0.807161i	$0.298997\pi$
$229$			24.4291i			1.61432i	−0.590332	+	0.807161i	$0.701003\pi$
$230$	4.08418	−	10.5900i	0.269303	−	0.698287i
$231$		0			0
$232$	−5.45688	+	2.74820i	−0.358262	+	0.180428i
$233$			18.3470i			1.20195i	0.799268	+	0.600975i	$0.205221\pi$
$233$			18.3470i			1.20195i	−0.799268	+	0.600975i	$0.794779\pi$
$234$		0			0
$235$	3.96222			0.258467
$236$	14.2583	−	15.7361i	0.928138	−	1.02433i
$237$		0			0
$238$	−0.219057	+	0.568002i	−0.0141993	+	0.0368181i
$239$	−30.1173			−1.94812			−0.974062	−	0.226280i	$-0.927344\pi$
$239$	−30.1173			−1.94812			−0.974062	+	0.226280i	$0.927344\pi$
$240$		0			0
$241$	−5.51878			−0.355496			−0.177748	−	0.984076i	$-0.556881\pi$
$241$	−5.51878			−0.355496			−0.177748	+	0.984076i	$0.556881\pi$
$242$	2.64317	−	6.85358i	0.169909	−	0.440565i
$243$		0			0
$244$	11.3419	−	12.5174i	0.726089	−	0.801342i
$245$	2.29653			0.146720
$246$		0			0
$247$		−	9.14212i		−	0.581699i
$248$	−2.67975	−	5.32095i	−0.170164	−	0.337881i
$249$		0			0
$250$	−5.52299	+	14.3208i	−0.349304	+	0.905727i
$251$		−	18.2010i		−	1.14884i	−0.818561	−	0.574420i	$-0.805228\pi$
$251$		−	18.2010i		−	1.14884i	0.818561	−	0.574420i	$-0.194772\pi$
$252$		0			0
$253$			14.0637i			0.884178i
$254$	−8.38601	−	3.23417i	−0.526185	−	0.202930i
$255$		0			0
$256$	−15.6908	+	3.13026i	−0.980676	+	0.195641i
$257$			5.91116i			0.368728i	0.982858	+	0.184364i	$0.0590226\pi$
$257$			5.91116i			0.368728i	−0.982858	+	0.184364i	$0.940977\pi$
$258$		0			0
$259$	−2.19775			−0.136562
$260$	5.62714	−	6.21034i	0.348980	−	0.385149i
$261$		0			0
$262$	−10.2330	−	3.94649i	−0.632199	−	0.243815i
$263$	−15.7132			−0.968916			−0.484458	−	0.874815i	$-0.660983\pi$
$263$	−15.7132			−0.968916			−0.484458	+	0.874815i	$0.660983\pi$
$264$		0			0
$265$	23.1807			1.42398
$266$	6.61124	+	2.54970i	0.405361	+	0.156332i
$267$		0			0
$268$	18.7273	+	16.9687i	1.14395	+	1.03653i
$269$	−26.9473			−1.64301			−0.821504	−	0.570202i	$-0.806865\pi$
$269$	−26.9473			−1.64301			−0.821504	+	0.570202i	$0.806865\pi$
$270$		0			0
$271$			5.68443i			0.345305i	0.984983	+	0.172652i	$0.0552337\pi$
$271$			5.68443i			0.345305i	−0.984983	+	0.172652i	$0.944766\pi$
$272$	−1.71355	+	0.169256i	−0.103899	+	0.0102626i
$273$		0			0
$274$	4.08818	+	1.57665i	0.246976	+	0.0952491i
$275$			1.10275i			0.0664985i
$276$		0			0
$277$		−	7.86390i		−	0.472496i	−0.971693	−	0.236248i	$-0.924082\pi$
$277$		−	7.86390i		−	0.472496i	0.971693	−	0.236248i	$-0.0759178\pi$
$278$	1.91552	−	4.96683i	0.114885	−	0.297891i
$279$		0			0
$280$	2.92170	+	5.80137i	0.174605	+	0.346698i
$281$		−	0.186660i		−	0.0111352i	−0.999985	−	0.00556760i	$-0.998228\pi$
$281$		−	0.186660i		−	0.0111352i	0.999985	−	0.00556760i	$-0.00177223\pi$
$282$		0			0
$283$	−12.4545			−0.740343			−0.370171	−	0.928963i	$-0.620701\pi$
$283$	−12.4545			−0.740343			−0.370171	+	0.928963i	$0.620701\pi$
$284$	13.2726	+	12.0262i	0.787584	+	0.713623i
$285$		0			0
$286$	−3.73646	+	9.68842i	−0.220941	+	0.572888i
$287$	4.35032			0.256791
$288$		0			0
$289$	16.8147			0.989100
$290$	−2.52446	+	6.54578i	−0.148241	+	0.384381i
$291$		0			0
$292$	10.6125	+	9.61592i	0.621051	+	0.562729i
$293$	8.52169			0.497843			0.248921	−	0.968524i	$-0.419924\pi$
$293$	8.52169			0.497843			0.248921	+	0.968524i	$0.419924\pi$
$294$		0			0
$295$		−	24.3833i		−	1.41965i
$296$	−2.79604	−	5.55186i	−0.162516	−	0.322695i
$297$		0			0
$298$	−3.34787	+	8.68083i	−0.193937	+	0.502867i
$299$		−	6.37662i		−	0.368770i
$300$		0			0
$301$			12.0354i			0.693708i
$302$	1.42948	+	0.551296i	0.0822574	+	0.0317235i
$303$		0			0
$304$	1.97005	+	19.9448i	0.112990	+	1.14391i
$305$		−	19.3959i		−	1.11060i
$306$		0			0
$307$	23.4380			1.33768			0.668838	−	0.743408i	$-0.266792\pi$
$307$	23.4380			1.33768			0.668838	+	0.743408i	$0.266792\pi$
$308$	−5.96422	−	5.40413i	−0.339843	−	0.307929i
$309$		0			0
$310$	−6.38273	−	2.46157i	−0.362515	−	0.139808i
$311$	12.1365			0.688199			0.344099	−	0.938933i	$-0.388184\pi$
$311$	12.1365			0.688199			0.344099	+	0.938933i	$0.388184\pi$
$312$		0			0
$313$	−7.54204			−0.426301			−0.213151	−	0.977019i	$-0.568372\pi$
$313$	−7.54204			−0.426301			−0.213151	+	0.977019i	$0.568372\pi$
$314$	−21.9207	−	8.45396i	−1.23705	−	0.477085i
$315$		0			0
$316$	−20.4666	+	22.5877i	−1.15133	+	1.27066i
$317$	−29.7545			−1.67118			−0.835590	−	0.549354i	$-0.814874\pi$
$317$	−29.7545			−1.67118			−0.835590	+	0.549354i	$0.814874\pi$
$318$		0			0
$319$		−	8.69288i		−	0.486708i
$320$	−10.9381	+	14.7613i	−0.611458	+	0.825182i
$321$		0			0
$322$	4.61133	+	1.77842i	0.256980	+	0.0991072i
$323$			2.15686i			0.120011i
$324$		0			0
$325$		−	0.499998i		−	0.0277349i
$326$	−5.84602	+	15.1584i	−0.323781	+	0.839547i
$327$		0			0
$328$	5.53458	+	10.9896i	0.305596	+	0.606797i
$329$			1.72531i			0.0951195i
$330$		0			0
$331$	−16.2670			−0.894117			−0.447058	−	0.894505i	$-0.647528\pi$
$331$	−16.2670			−0.894117			−0.447058	+	0.894505i	$0.647528\pi$
$332$	18.0630	−	19.9351i	0.991337	−	1.09408i
$333$		0			0
$334$	6.85765	−	17.7815i	0.375234	−	0.972961i
$335$	29.0184			1.58544
$336$		0			0
$337$	32.0056			1.74345			0.871727	−	0.489992i	$-0.163000\pi$
$337$	32.0056			1.74345			0.871727	+	0.489992i	$0.163000\pi$
$338$	−4.92124	+	12.7605i	−0.267680	+	0.694080i
$339$		0			0
$340$	−1.32759	+	1.46518i	−0.0719985	+	0.0794605i
$341$	8.47634			0.459020
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−30.4032	+	15.3117i	−1.63923	+	0.825553i
$345$		0			0
$346$	2.53595	−	6.57559i	0.136334	−	0.353506i
$347$		−	15.3562i		−	0.824366i	−0.911101	−	0.412183i	$-0.864766\pi$
$347$		−	15.3562i		−	0.824366i	0.911101	−	0.412183i	$-0.135234\pi$
$348$		0			0
$349$			10.7044i			0.572996i	0.958081	+	0.286498i	$0.0924912\pi$
$349$			10.7044i			0.572996i	−0.958081	+	0.286498i	$0.907509\pi$
$350$	0.361580	+	0.139448i	0.0193273	+	0.00745379i
$351$		0			0
$352$	6.06382	−	21.9418i	0.323203	−	1.16950i
$353$			17.0572i			0.907866i	0.891036	+	0.453933i	$0.149979\pi$
$353$			17.0572i			0.907866i	−0.891036	+	0.453933i	$0.850021\pi$
$354$		0			0
$355$	20.5661			1.09154
$356$	−10.0045	+	11.0414i	−0.530237	+	0.585192i
$357$		0			0
$358$	4.56449	+	1.76035i	0.241241	+	0.0930373i
$359$	17.2174			0.908697			0.454349	−	0.890824i	$-0.349872\pi$
$359$	17.2174			0.908697			0.454349	+	0.890824i	$0.349872\pi$
$360$		0			0
$361$	6.10474			0.321302
$362$	−13.3808	−	5.16047i	−0.703279	−	0.271228i
$363$		0			0
$364$	2.70423	+	2.45028i	0.141740	+	0.128430i
$365$	16.4443			0.860734
$366$		0			0
$367$			25.6116i			1.33692i	0.743750	+	0.668458i	$0.233045\pi$
$367$			25.6116i			1.33692i	−0.743750	+	0.668458i	$0.766955\pi$
$368$	1.37410	+	13.9115i	0.0716302	+	0.725186i
$369$		0			0
$370$	−6.65972	−	2.56840i	−0.346222	−	0.133525i
$371$			10.0938i			0.524045i
$372$		0			0
$373$			3.99889i			0.207054i	0.994627	+	0.103527i	$0.0330129\pi$
$373$			3.99889i			0.207054i	−0.994627	+	0.103527i	$0.966987\pi$
$374$	0.881526	−	2.28575i	0.0455826	−	0.118193i
$375$		0			0
$376$	−4.35840	+	2.19498i	−0.224767	+	0.113198i
$377$			3.94143i			0.202994i
$378$		0			0
$379$	−21.0603			−1.08180			−0.540898	−	0.841088i	$-0.681915\pi$
$379$	−21.0603			−1.08180			−0.540898	+	0.841088i	$0.681915\pi$
$380$	17.0539	+	15.4524i	0.874847	+	0.792692i
$381$		0			0
$382$	5.58457	−	14.4805i	0.285731	−	0.740885i
$383$	−27.1156			−1.38554			−0.692771	−	0.721158i	$-0.743610\pi$
$383$	−27.1156			−1.38554			−0.692771	+	0.721158i	$0.743610\pi$
$384$		0			0
$385$	−9.24166			−0.470999
$386$	−1.05452	+	2.73432i	−0.0536739	+	0.139173i
$387$		0			0
$388$	−2.50292	−	2.26788i	−0.127067	−	0.115134i
$389$	8.59148			0.435605			0.217803	−	0.975993i	$-0.430111\pi$
$389$	8.59148			0.435605			0.217803	+	0.975993i	$0.430111\pi$
$390$		0			0
$391$			1.50441i			0.0760813i
$392$	−2.52615	+	1.27222i	−0.127590	+	0.0642571i
$393$		0			0
$394$	2.38941	−	6.19561i	0.120377	−	0.312130i
$395$			35.0001i			1.76105i
$396$		0			0
$397$			33.3145i			1.67201i	0.548725	+	0.836003i	$0.315113\pi$
$397$			33.3145i			1.67201i	−0.548725	+	0.836003i	$0.684887\pi$
$398$	22.1088	+	8.52653i	1.10821	+	0.427396i
$399$		0			0
$400$	0.107745	+	1.09082i	0.00538726	+	0.0545408i
$401$			5.42643i			0.270983i	0.990779	+	0.135491i	$0.0432613\pi$
$401$			5.42643i			0.270983i	−0.990779	+	0.135491i	$0.956739\pi$
$402$		0			0
$403$	−3.84325			−0.191446
$404$	19.8108	+	17.9504i	0.985626	+	0.893068i
$405$		0			0
$406$	−2.85030	−	1.09925i	−0.141458	−	0.0545549i
$407$	8.84419			0.438390
$408$		0			0
$409$	37.1175			1.83534			0.917672	−	0.397339i	$-0.130066\pi$
$409$	37.1175			1.83534			0.917672	+	0.397339i	$0.130066\pi$
$410$	13.1825	+	5.08398i	0.651036	+	0.251080i
$411$		0			0
$412$	6.17366	−	6.81351i	0.304155	−	0.335678i
$413$	10.6175			0.522452
$414$		0			0
$415$		−	30.8898i		−	1.51632i
$416$	−2.74939	+	9.94861i	−0.134800	+	0.487771i
$417$		0			0
$418$	−26.6049	−	10.2605i	−1.30129	−	0.501857i
$419$			19.7739i			0.966016i	0.875616	+	0.483008i	$0.160456\pi$
$419$			19.7739i			0.966016i	−0.875616	+	0.483008i	$0.839544\pi$
$420$		0			0
$421$		−	19.4861i		−	0.949692i	−0.880069	−	0.474846i	$-0.842504\pi$
$421$		−	19.4861i		−	0.949692i	0.880069	−	0.474846i	$-0.157496\pi$
$422$	−7.78353	+	20.1823i	−0.378896	+	0.982457i
$423$		0			0
$424$	−25.4985	+	12.8416i	−1.23832	+	0.623643i
$425$			0.117963i			0.00572202i
$426$		0			0
$427$	8.44575			0.408718
$428$	−21.0901	+	23.2759i	−1.01943	+	1.12508i
$429$		0			0
$430$	−14.0651	+	36.4701i	−0.678280	+	1.75874i
$431$	−33.0237			−1.59069			−0.795347	−	0.606154i	$-0.792712\pi$
$431$	−33.0237			−1.59069			−0.795347	+	0.606154i	$0.792712\pi$
$432$		0			0
$433$	−33.2428			−1.59755			−0.798773	−	0.601632i	$-0.794517\pi$
$433$	−33.2428			−1.59755			−0.798773	+	0.601632i	$0.794517\pi$
$434$	1.07187	−	2.77930i	0.0514514	−	0.133411i
$435$		0			0
$436$	21.5054	−	23.7342i	1.02992	−	1.13666i
$437$	17.5105			0.837642
$438$		0			0
$439$			9.28199i			0.443005i	0.975160	+	0.221503i	$0.0710962\pi$
$439$			9.28199i			0.443005i	−0.975160	+	0.221503i	$0.928904\pi$
$440$	−11.7575	−	23.3458i	−0.560516	−	1.11297i
$441$		0			0
$442$	−0.399692	+	1.03638i	−0.0190114	+	0.0492956i
$443$		−	2.61270i		−	0.124133i	−0.998072	−	0.0620667i	$-0.980231\pi$
$443$		−	2.61270i		−	0.124133i	0.998072	−	0.0620667i	$-0.0197691\pi$
$444$		0			0
$445$			17.1088i			0.811035i
$446$	31.0947	+	11.9920i	1.47238	+	0.567839i
$447$		0			0
$448$	−6.42767	−	4.76289i	−0.303679	−	0.225025i
$449$			30.3318i			1.43145i	0.698384	+	0.715723i	$0.253903\pi$
$449$			30.3318i			1.43145i	−0.698384	+	0.715723i	$0.746097\pi$
$450$		0			0
$451$	−17.5065			−0.824349
$452$	1.97217	−	2.17656i	0.0927629	−	0.102377i
$453$		0			0
$454$	21.9713	+	8.47348i	1.03116	+	0.397680i
$455$	4.19026			0.196442
$456$		0			0
$457$	6.64077			0.310642			0.155321	−	0.987864i	$-0.450359\pi$
$457$	6.64077			0.310642			0.155321	+	0.987864i	$0.450359\pi$
$458$	−32.2339	−	12.4314i	−1.50619	−	0.580881i
$459$		0			0
$460$	11.8951	+	10.7780i	0.554611	+	0.502528i
$461$	35.1189			1.63565			0.817826	−	0.575465i	$-0.195179\pi$
$461$	35.1189			1.63565			0.817826	+	0.575465i	$0.195179\pi$
$462$		0			0
$463$		−	2.53401i		−	0.117765i	−0.998265	−	0.0588826i	$-0.981246\pi$
$463$		−	2.53401i		−	0.117765i	0.998265	−	0.0588826i	$-0.0187538\pi$
$464$	−0.849343	−	8.59878i	−0.0394298	−	0.399188i
$465$		0			0
$466$	−24.2086	−	9.33633i	−1.12144	−	0.432497i
$467$		−	16.0379i		−	0.742145i	−0.928604	−	0.371072i	$-0.878990\pi$
$467$		−	16.0379i		−	0.742145i	0.928604	−	0.371072i	$-0.121010\pi$
$468$		0			0
$469$			12.6358i			0.583465i
$470$	−2.01628	+	5.22810i	−0.0930040	+	0.241154i
$471$		0			0
$472$	13.5078	+	26.8214i	0.621748	+	1.23455i
$473$		−	48.4327i		−	2.22694i
$474$		0			0
$475$	1.37302			0.0629985
$476$	−0.637998	−	0.578085i	−0.0292426	−	0.0264965i
$477$		0			0
$478$	15.3260	−	39.7394i	0.700993	−	1.81764i
$479$	29.2616			1.33700			0.668498	−	0.743714i	$-0.266938\pi$
$479$	29.2616			1.33700			0.668498	+	0.743714i	$0.266938\pi$
$480$		0			0
$481$	−4.01004			−0.182842
$482$	2.80837	−	7.28196i	0.127918	−	0.331684i
$483$		0			0
$484$	7.69817	+	6.97524i	0.349917	+	0.317057i
$485$	−3.87832			−0.176106
$486$		0			0
$487$			2.81399i			0.127514i	0.997965	+	0.0637570i	$0.0203083\pi$
$487$			2.81399i			0.127514i	−0.997965	+	0.0637570i	$0.979692\pi$
$488$	10.7449	+	21.3352i	0.486398	+	0.965801i
$489$		0			0
$490$	−1.16865	+	3.03024i	−0.0527941	+	0.136892i
$491$			19.2668i			0.869497i	0.900552	+	0.434748i	$0.143163\pi$
$491$			19.2668i			0.869497i	−0.900552	+	0.434748i	$0.856837\pi$
$492$		0			0
$493$		−	0.929886i		−	0.0418799i
$494$	12.0629	+	4.65221i	0.542736	+	0.209313i
$495$		0			0
$496$	8.38458	−	0.828187i	0.376479	−	0.0371867i
$497$			8.95532i			0.401701i
$498$		0			0
$499$	39.4436			1.76574			0.882869	−	0.469620i	$-0.155609\pi$
$499$	39.4436			1.76574			0.882869	+	0.469620i	$0.155609\pi$
$500$	−16.0856	−	14.5750i	−0.719370	−	0.651815i
$501$		0			0
$502$	24.0160	+	9.26207i	1.07189	+	0.413387i
$503$	33.3860			1.48861			0.744304	−	0.667841i	$-0.232781\pi$
$503$	33.3860			1.48861			0.744304	+	0.667841i	$0.232781\pi$
$504$		0			0
$505$	30.6973			1.36601
$506$	−18.5569	−	7.15669i	−0.824954	−	0.318154i
$507$		0			0
$508$	8.53488	−	9.41945i	0.378674	−	0.417920i
$509$	−9.16584			−0.406269			−0.203134	−	0.979151i	$-0.565113\pi$
$509$	−9.16584			−0.406269			−0.203134	+	0.979151i	$0.565113\pi$
$510$		0			0
$511$			7.16051i			0.316762i
$512$	3.85434	−	22.2967i	0.170339	−	0.985385i
$513$		0			0
$514$	−7.79970	−	3.00805i	−0.344030	−	0.132679i
$515$		−	10.5577i		−	0.465226i
$516$		0			0
$517$		−	6.94299i		−	0.305352i
$518$	1.11838	−	2.89991i	0.0491390	−	0.127415i
$519$		0			0
$520$	5.33095	+	10.5852i	0.233778	+	0.464193i
$521$		−	1.14191i		−	0.0500280i	−0.999687	−	0.0250140i	$-0.992037\pi$
$521$		−	1.14191i		−	0.0500280i	0.999687	−	0.0250140i	$-0.00796304\pi$
$522$		0			0
$523$	−19.5606			−0.855323			−0.427662	−	0.903939i	$-0.640663\pi$
$523$	−19.5606			−0.855323			−0.427662	+	0.903939i	$0.640663\pi$
$524$	10.4147	−	11.4941i	0.454968	−	0.502121i
$525$		0			0
$526$	7.99605	−	20.7333i	0.348645	−	0.904016i
$527$	0.906723			0.0394975
$528$		0			0
$529$	−10.7864			−0.468975
$530$	−11.7961	+	30.5866i	−0.512390	+	1.32860i
$531$		0			0
$532$	−6.72860	+	7.42596i	−0.291722	+	0.321956i
$533$	7.93762			0.343816
$534$		0			0
$535$			36.0665i			1.55929i
$536$	−31.9199	+	16.0755i	−1.37873	+	0.694357i
$537$		0			0
$538$	13.7129	−	35.5567i	0.591203	−	1.53296i
$539$		−	4.02419i		−	0.173334i
$540$		0			0
$541$		−	35.9815i		−	1.54696i	−0.633818	−	0.773482i	$-0.718513\pi$
$541$		−	35.9815i		−	1.54696i	0.633818	−	0.773482i	$-0.281487\pi$
$542$	−7.50053	−	2.89267i	−0.322175	−	0.124251i
$543$		0			0
$544$	0.648653	−	2.34713i	0.0278108	−	0.100633i
$545$		−	36.7766i		−	1.57534i
$546$		0			0
$547$	−19.0634			−0.815092			−0.407546	−	0.913185i	$-0.633615\pi$
$547$	−19.0634			−0.815092			−0.407546	+	0.913185i	$0.633615\pi$
$548$	−4.16075	+	4.59197i	−0.177738	+	0.196159i
$549$		0			0
$550$	−1.45507	−	0.561164i	−0.0620443	−	0.0239281i
$551$	−10.8234			−0.461091
$552$		0			0
$553$	−15.2405			−0.648090
$554$	10.3763	+	4.00175i	0.440847	+	0.170018i
$555$		0			0
$556$	5.57891	+	5.05500i	0.236598	+	0.214380i
$557$	−18.4543			−0.781934			−0.390967	−	0.920405i	$-0.627859\pi$
$557$	−18.4543			−0.781934			−0.390967	+	0.920405i	$0.627859\pi$
$558$		0			0
$559$			21.9598i			0.928803i
$560$	−9.14162	+	0.902963i	−0.386304	+	0.0381571i
$561$		0			0
$562$	0.246295	+	0.0949867i	0.0103893	+	0.00400677i
$563$		−	31.6916i		−	1.33564i	−0.744322	−	0.667821i	$-0.767227\pi$
$563$		−	31.6916i		−	1.33564i	0.744322	−	0.667821i	$-0.232773\pi$
$564$		0			0
$565$		−	3.37262i		−	0.141887i
$566$	6.33779	−	16.4335i	0.266397	−	0.690753i
$567$		0			0
$568$	−22.6225	+	11.3932i	−0.949219	+	0.478047i
$569$		−	27.5168i		−	1.15357i	−0.816897	−	0.576783i	$-0.804308\pi$
$569$		−	27.5168i		−	1.15357i	0.816897	−	0.576783i	$-0.195692\pi$
$570$		0			0
$571$	−27.7326			−1.16057			−0.580287	−	0.814412i	$-0.697060\pi$
$571$	−27.7326			−1.16057			−0.580287	+	0.814412i	$0.697060\pi$
$572$	−10.8824	−	9.86041i	−0.455014	−	0.412284i
$573$		0			0
$574$	−2.21377	+	5.74018i	−0.0924010	+	0.239591i
$575$	0.957681			0.0399381
$576$		0			0
$577$	38.3530			1.59666			0.798328	−	0.602223i	$-0.205718\pi$
$577$	38.3530			1.59666			0.798328	+	0.602223i	$0.205718\pi$
$578$	−8.55659	+	22.1868i	−0.355907	+	0.922848i
$579$		0			0
$580$	−7.35243	−	6.66198i	−0.305293	−	0.276624i
$581$	13.4507			0.558027
$582$		0			0
$583$		−	40.6194i		−	1.68229i
$584$	−18.0885	+	9.10978i	−0.748509	+	0.376966i
$585$		0			0
$586$	−4.33648	+	11.2443i	−0.179138	+	0.464496i
$587$			13.7550i			0.567731i	0.958864	+	0.283865i	$0.0916169\pi$
$587$			13.7550i			0.567731i	−0.958864	+	0.283865i	$0.908383\pi$
$588$		0			0
$589$		−	10.5538i		−	0.434861i
$590$	32.1735	+	12.4081i	1.32456	+	0.510833i
$591$		0			0
$592$	8.74845	−	0.864127i	0.359559	−	0.0355154i
$593$		−	31.5293i		−	1.29475i	−0.762171	−	0.647376i	$-0.775866\pi$
$593$		−	31.5293i		−	1.29475i	0.762171	−	0.647376i	$-0.224134\pi$
$594$		0			0
$595$	−0.988589			−0.0405282
$596$	−9.75059	−	8.83493i	−0.399400	−	0.361893i
$597$		0			0
$598$	8.41387	+	3.24491i	0.344069	+	0.132694i
$599$	−14.6650			−0.599196			−0.299598	−	0.954066i	$-0.596853\pi$
$599$	−14.6650			−0.599196			−0.299598	+	0.954066i	$0.596853\pi$
$600$		0			0
$601$	−40.8677			−1.66703			−0.833515	−	0.552497i	$-0.813675\pi$
$601$	−40.8677			−1.66703			−0.833515	+	0.552497i	$0.813675\pi$
$602$	−15.8805	−	6.12452i	−0.647242	−	0.249617i
$603$		0			0
$604$	−1.45486	+	1.60564i	−0.0591973	+	0.0653326i
$605$	11.9284			0.484960
$606$		0			0
$607$		−	40.0141i		−	1.62412i	−0.583572	−	0.812061i	$-0.698345\pi$
$607$		−	40.0141i		−	1.62412i	0.583572	−	0.812061i	$-0.301655\pi$
$608$	−27.3194	−	7.54997i	−1.10795	−	0.306192i
$609$		0			0
$610$	25.5926	+	9.87009i	1.03621	+	0.399628i
$611$			3.14802i			0.127355i
$612$		0			0
$613$		−	3.46053i		−	0.139770i	−0.997555	−	0.0698848i	$-0.977737\pi$
$613$		−	3.46053i		−	0.139770i	0.997555	−	0.0698848i	$-0.0222632\pi$
$614$	−11.9270	+	30.9261i	−0.481335	+	1.24808i
$615$		0			0
$616$	10.1657	−	5.11968i	0.409589	−	0.206278i
$617$		−	36.6562i		−	1.47572i	−0.674952	−	0.737861i	$-0.735836\pi$
$617$		−	36.6562i		−	1.47572i	0.674952	−	0.737861i	$-0.264164\pi$
$618$		0			0
$619$	−10.0770			−0.405029			−0.202514	−	0.979279i	$-0.564911\pi$
$619$	−10.0770			−0.405029			−0.202514	+	0.979279i	$0.564911\pi$
$620$	6.49603	−	7.16929i	0.260887	−	0.287926i
$621$		0			0
$622$	−6.17598	+	16.0140i	−0.247634	+	0.642102i
$623$	−7.44987			−0.298473
$624$		0			0
$625$	−26.2951			−1.05180
$626$	3.83796	−	9.95162i	0.153396	−	0.397747i
$627$		0			0
$628$	22.3098	−	24.6220i	0.890257	−	0.982525i
$629$	0.946071			0.0377223
$630$		0			0
$631$			28.1634i			1.12117i	0.828098	+	0.560583i	$0.189423\pi$
$631$			28.1634i			1.12117i	−0.828098	+	0.560583i	$0.810577\pi$
$632$	−19.3893	−	38.4997i	−0.771264	−	1.53144i
$633$		0			0
$634$	15.1414	−	39.2607i	0.601340	−	1.55924i
$635$		−	14.5956i		−	0.579209i
$636$		0			0
$637$			1.82461i			0.0722935i
$638$	11.4701	+	4.42360i	0.454107	+	0.175132i
$639$		0			0
$640$	−13.9112	−	21.9443i	−0.549889	−	0.867426i
$641$		−	12.3588i		−	0.488142i	−0.969757	−	0.244071i	$-0.921517\pi$
$641$		−	12.3588i		−	0.488142i	0.969757	−	0.244071i	$-0.0784830\pi$
$642$		0			0
$643$	28.0875			1.10766			0.553831	−	0.832629i	$-0.313165\pi$
$643$	28.0875			1.10766			0.553831	+	0.832629i	$0.313165\pi$
$644$	−4.69319	+	5.17960i	−0.184938	+	0.204105i
$645$		0			0
$646$	−2.84595	−	1.09758i	−0.111972	−	0.0431835i
$647$	43.3350			1.70368			0.851838	−	0.523806i	$-0.175488\pi$
$647$	43.3350			1.70368			0.851838	+	0.523806i	$0.175488\pi$
$648$		0			0
$649$	−42.7268			−1.67717
$650$	0.659741	+	0.254437i	0.0258772	+	0.00997985i
$651$		0			0
$652$	−17.0264	−	15.4275i	−0.666806	−	0.604187i
$653$	32.0509			1.25425			0.627125	−	0.778919i	$-0.284232\pi$
$653$	32.0509			1.25425			0.627125	+	0.778919i	$0.284232\pi$
$654$		0			0
$655$		−	17.8103i		−	0.695905i
$656$	−17.3170	+	1.71048i	−0.676115	+	0.0667832i
$657$		0			0
$658$	−2.27653	−	0.877970i	−0.0887482	−	0.0342268i
$659$		−	6.88401i		−	0.268163i	−0.990970	−	0.134081i	$-0.957192\pi$
$659$		−	6.88401i		−	0.268163i	0.990970	−	0.134081i	$-0.0428084\pi$
$660$		0			0
$661$			47.2652i			1.83840i	0.393788	+	0.919201i	$0.371164\pi$
$661$			47.2652i			1.83840i	−0.393788	+	0.919201i	$0.628836\pi$
$662$	8.27790	−	21.4641i	0.321730	−	0.834227i
$663$		0			0
$664$	17.1123	+	33.9784i	0.664085	+	1.31862i
$665$			11.5067i			0.446209i
$666$		0			0
$667$	−7.54929			−0.292310
$668$	19.9728	+	18.0972i	0.772770	+	0.700200i
$669$		0			0
$670$	−14.7667	+	38.2893i	−0.570489	+	1.47925i
$671$	−33.9873			−1.31207
$672$		0			0
$673$	6.89911			0.265941			0.132971	−	0.991120i	$-0.457548\pi$
$673$	6.89911			0.265941			0.132971	+	0.991120i	$0.457548\pi$
$674$	−16.2869	+	42.2309i	−0.627346	+	1.62667i
$675$		0			0
$676$	−14.3330	−	12.9870i	−0.551270	−	0.499501i
$677$	−23.7479			−0.912707			−0.456353	−	0.889799i	$-0.650845\pi$
$677$	−23.7479			−0.912707			−0.456353	+	0.889799i	$0.650845\pi$
$678$		0			0
$679$		−	1.68878i		−	0.0648094i
$680$	−1.25771	−	2.49733i	−0.0482309	−	0.0957681i
$681$		0			0
$682$	−4.31341	+	11.1844i	−0.165169	+	0.428274i
$683$		−	41.5546i		−	1.59004i	−0.606583	−	0.795020i	$-0.707460\pi$
$683$		−	41.5546i		−	1.59004i	0.606583	−	0.795020i	$-0.292540\pi$
$684$		0			0
$685$			7.11534i			0.271863i
$686$	−1.31949	−	0.508876i	−0.0503782	−	0.0194290i
$687$		0			0
$688$	−4.73215	−	47.9084i	−0.180412	−	1.82649i
$689$			18.4172i			0.701641i
$690$		0			0
$691$	−17.5146			−0.666285			−0.333142	−	0.942876i	$-0.608109\pi$
$691$	−17.5146			−0.666285			−0.333142	+	0.942876i	$0.608109\pi$
$692$	7.38592	+	6.69232i	0.280770	+	0.254404i
$693$		0			0
$694$	20.2624	+	7.81442i	0.769149	+	0.296631i
$695$	8.64462			0.327909
$696$		0			0
$697$	−1.87269			−0.0709331
$698$	−14.1244	−	5.44724i	−0.534616	−	0.206181i
$699$		0			0
$700$	−0.367999	+	0.406139i	−0.0139090	+	0.0153506i
$701$	1.39361			0.0526361			0.0263180	−	0.999654i	$-0.491622\pi$
$701$	1.39361			0.0526361			0.0263180	+	0.999654i	$0.491622\pi$
$702$		0			0
$703$		−	11.0118i		−	0.415317i
$704$	25.8662	+	19.1668i	0.974868	+	0.722375i
$705$		0			0
$706$	−22.5068	−	8.68002i	−0.847055	−	0.326677i
$707$			13.3668i			0.502711i
$708$		0			0
$709$			42.1733i			1.58385i	0.610616	+	0.791927i	$0.290922\pi$
$709$			42.1733i			1.58385i	−0.610616	+	0.791927i	$0.709078\pi$
$710$	−10.4656	+	27.1367i	−0.392767	+	1.01842i
$711$		0			0
$712$	−9.47790	−	18.8195i	−0.355199	−	0.705290i
$713$		−	7.36125i		−	0.275681i
$714$		0			0
$715$	−16.8624			−0.630618
$716$	−4.64551	+	5.12698i	−0.173611	+	0.191604i
$717$		0			0
$718$	−8.76149	+	22.7181i	−0.326976	+	0.847831i
$719$	11.8108			0.440468			0.220234	−	0.975447i	$-0.429318\pi$
$719$	11.8108			0.440468			0.220234	+	0.975447i	$0.429318\pi$
$720$		0			0
$721$	4.59723			0.171210
$722$	−3.10655	+	8.05512i	−0.115614	+	0.299781i
$723$		0			0
$724$	13.6183	−	15.0298i	0.506121	−	0.558576i
$725$	−0.591949			−0.0219844
$726$		0			0
$727$		−	45.5504i		−	1.68937i	−0.535264	−	0.844685i	$-0.679788\pi$
$727$		−	45.5504i		−	1.68937i	0.535264	−	0.844685i	$-0.320212\pi$
$728$	−4.60923	+	2.32131i	−0.170830	+	0.0860335i
$729$		0			0
$730$	−8.36811	+	21.6980i	−0.309718	+	0.803081i
$731$		−	5.18089i		−	0.191622i
$732$		0			0
$733$		−	38.4714i		−	1.42097i	−0.703711	−	0.710487i	$-0.748475\pi$
$733$		−	38.4714i		−	1.42097i	0.703711	−	0.710487i	$-0.251525\pi$
$734$	−33.7942	−	13.0331i	−1.24737	−	0.481062i
$735$		0			0
$736$	−19.0553	−	5.26610i	−0.702386	−	0.194111i
$737$		−	50.8487i		−	1.87304i
$738$		0			0
$739$	12.1292			0.446179			0.223090	−	0.974798i	$-0.428386\pi$
$739$	12.1292			0.446179			0.223090	+	0.974798i	$0.428386\pi$
$740$	6.77794	−	7.48041i	0.249162	−	0.274985i
$741$		0			0
$742$	−13.3186	−	5.13650i	−0.488943	−	0.188567i
$743$	46.7546			1.71526			0.857630	−	0.514267i	$-0.171936\pi$
$743$	46.7546			1.71526			0.857630	+	0.514267i	$0.171936\pi$
$744$		0			0
$745$	−15.1087			−0.553540
$746$	−5.27648	−	2.03494i	−0.193186	−	0.0745043i
$747$		0			0
$748$	2.56743	+	2.32632i	0.0938744	+	0.0850588i
$749$	−15.7048			−0.573841
$750$		0			0
$751$			29.7196i			1.08448i	0.840222	+	0.542242i	$0.182424\pi$
$751$			29.7196i			1.08448i	−0.840222	+	0.542242i	$0.817576\pi$
$752$	−0.678369	−	6.86783i	−0.0247376	−	0.250444i
$753$		0			0
$754$	−5.20067	−	2.00570i	−0.189397	−	0.0730433i
$755$			2.48797i			0.0905464i
$756$		0			0
$757$		−	16.0932i		−	0.584919i	−0.956278	−	0.292459i	$-0.905526\pi$
$757$		−	16.0932i		−	0.584919i	0.956278	−	0.292459i	$-0.0944737\pi$
$758$	10.7171	−	27.7888i	0.389262	−	1.00933i
$759$		0			0
$760$	−29.0676	+	14.6391i	−1.05439	+	0.531014i
$761$		−	5.21482i		−	0.189037i	−0.995523	−	0.0945186i	$-0.969869\pi$
$761$		−	5.21482i		−	0.189037i	0.995523	−	0.0945186i	$-0.0301312\pi$
$762$		0			0
$763$	16.0140			0.579746
$764$	16.2649	+	14.7375i	0.588445	+	0.533185i
$765$		0			0
$766$	13.7985	−	35.7787i	0.498559	−	1.29274i
$767$	19.3727			0.699509
$768$		0			0
$769$	17.7856			0.641367			0.320683	−	0.947186i	$-0.396087\pi$
$769$	17.7856			0.641367			0.320683	+	0.947186i	$0.396087\pi$
$770$	4.70286	−	12.1943i	0.169479	−	0.439450i
$771$		0			0
$772$	−3.07128	−	2.78286i	−0.110538	−	0.100157i
$773$	−19.9688			−0.718228			−0.359114	−	0.933294i	$-0.616921\pi$
$773$	−19.9688			−0.718228			−0.359114	+	0.933294i	$0.616921\pi$
$774$		0			0
$775$		−	0.577204i		−	0.0207338i
$776$	4.26611	−	2.14851i	0.153144	−	0.0771269i
$777$		0			0
$778$	−4.37200	+	11.3363i	−0.156744	+	0.406428i
$779$			21.7971i			0.780962i
$780$		0			0
$781$		−	36.0379i		−	1.28954i
$782$	−1.98505	−	0.765558i	−0.0709852	−	0.0273763i
$783$		0			0
$784$	−0.393186	−	3.98063i	−0.0140424	−	0.142165i
$785$		−	38.1522i		−	1.36171i
$786$		0			0
$787$	−32.1178			−1.14487			−0.572437	−	0.819948i	$-0.694002\pi$
$787$	−32.1178			−1.14487			−0.572437	+	0.819948i	$0.694002\pi$
$788$	6.95912	+	6.30560i	0.247908	+	0.224628i
$789$		0			0
$790$	−46.1822	−	17.8107i	−1.64309	−	0.633676i
$791$	1.46858			0.0522166
$792$		0			0
$793$	15.4102			0.547231
$794$	−43.9580	−	16.9529i	−1.56001	−	0.601637i
$795$		0			0
$796$	−22.5013	+	24.8333i	−0.797537	+	0.880194i
$797$	10.4964			0.371800			0.185900	−	0.982569i	$-0.440480\pi$
$797$	10.4964			0.371800			0.185900	+	0.982569i	$0.440480\pi$
$798$		0			0
$799$		−	0.742698i		−	0.0262748i
$800$	−1.49414	−	0.412921i	−0.0528260	−	0.0145990i
$801$		0			0
$802$	−7.16010	−	2.76138i	−0.252832	−	0.0975077i
$803$		−	28.8153i		−	1.01687i
$804$		0			0
$805$			8.02588i			0.282875i
$806$	1.95574	−	5.07112i	0.0688880	−	0.178623i
$807$		0			0
$808$	−33.7666	+	17.0056i	−1.18791	+	0.598255i
$809$			31.8333i			1.11920i	0.828763	+	0.559599i	$0.189045\pi$
$809$			31.8333i			1.11920i	−0.828763	+	0.559599i	$0.810955\pi$
$810$		0			0
$811$	−1.39041			−0.0488238			−0.0244119	−	0.999702i	$-0.507771\pi$
$811$	−1.39041			−0.0488238			−0.0244119	+	0.999702i	$0.507771\pi$
$812$	2.90089	−	3.20155i	0.101801	−	0.112352i
$813$		0			0
$814$	−4.50059	+	11.6698i	−0.157746	+	0.409026i
$815$	−26.3827			−0.924147
$816$		0			0
$817$	−60.3029			−2.10973
$818$	−18.8882	+	48.9761i	−0.660411	+	1.71241i
$819$		0			0
$820$	−13.4165	+	14.8070i	−0.468524	+	0.517083i
$821$	−18.4554			−0.644097			−0.322048	−	0.946723i	$-0.604371\pi$
$821$	−18.4554			−0.644097			−0.322048	+	0.946723i	$0.604371\pi$
$822$		0			0
$823$			41.1895i			1.43578i	0.696159	+	0.717888i	$0.254891\pi$
$823$			41.1895i			1.43578i	−0.696159	+	0.717888i	$0.745109\pi$
$824$	5.84871	+	11.6133i	0.203749	+	0.404568i
$825$		0			0
$826$	−5.40298	+	14.0096i	−0.187994	+	0.487457i
$827$			6.08227i			0.211501i	0.994393	+	0.105751i	$0.0337245\pi$
$827$			6.08227i			0.211501i	−0.994393	+	0.105751i	$0.966275\pi$
$828$		0			0
$829$		−	44.2474i		−	1.53677i	−0.639985	−	0.768387i	$-0.721060\pi$
$829$		−	44.2474i		−	1.53677i	0.639985	−	0.768387i	$-0.278940\pi$
$830$	40.7587	+	15.7191i	1.41475	+	0.545617i
$831$		0			0
$832$	−11.7280	−	8.69040i	−0.406594	−	0.301285i
$833$		−	0.430472i		−	0.0149150i
$834$		0			0
$835$	30.9482			1.07101
$836$	27.0772	−	29.8835i	0.936484	−	1.03354i
$837$		0			0
$838$	−26.0914	−	10.0624i	−0.901311	−	0.347601i
$839$	45.9488			1.58633			0.793164	−	0.609008i	$-0.208432\pi$
$839$	45.9488			1.58633			0.793164	+	0.609008i	$0.208432\pi$
$840$		0			0
$841$	−24.3337			−0.839094
$842$	25.7116	+	9.91598i	0.886080	+	0.341727i
$843$		0			0
$844$	−22.6694	−	20.5405i	−0.780312	−	0.707034i
$845$	−22.2093			−0.764022
$846$		0			0
$847$			5.19413i			0.178472i
$848$	−3.96875	−	40.1797i	−0.136287	−	1.37978i
$849$		0			0
$850$	−0.155650	−	0.0600283i	−0.00533875	−	0.00205895i
$851$		−	7.68070i		−	0.263291i
$852$		0			0
$853$		−	22.7862i		−	0.780185i	−0.920776	−	0.390093i	$-0.872443\pi$
$853$		−	22.7862i		−	0.780185i	0.920776	−	0.390093i	$-0.127557\pi$
$854$	−4.29784	+	11.1441i	−0.147069	+	0.381342i
$855$		0			0
$856$	−19.9800	−	39.6727i	−0.682903	−	1.35598i
$857$			28.8660i			0.986042i	0.870017	+	0.493021i	$0.164108\pi$
$857$			28.8660i			0.986042i	−0.870017	+	0.493021i	$0.835892\pi$
$858$		0			0
$859$	53.1350			1.81294			0.906471	−	0.422268i	$-0.138766\pi$
$859$	53.1350			1.81294			0.906471	+	0.422268i	$0.138766\pi$
$860$	−40.9644	−	37.1175i	−1.39687	−	1.26569i
$861$		0			0
$862$	16.8050	−	43.5743i	0.572379	−	1.48415i
$863$	27.2397			0.927250			0.463625	−	0.886032i	$-0.346549\pi$
$863$	27.2397			0.927250			0.463625	+	0.886032i	$0.346549\pi$
$864$		0			0
$865$	11.4446			0.389128
$866$	16.9165	−	43.8634i	0.574845	−	1.49054i
$867$		0			0
$868$	3.12180	+	2.82863i	0.105961	+	0.0960101i
$869$	61.3305			2.08050
$870$		0			0
$871$			23.0553i			0.781199i
$872$	20.3734	+	40.4538i	0.689931	+	1.36994i
$873$		0			0
$874$	−8.91068	+	23.1049i	−0.301408	+	0.781535i
$875$		−	10.8533i		−	0.366909i
$876$		0			0
$877$		−	24.5161i		−	0.827850i	−0.910311	−	0.413925i	$-0.864158\pi$
$877$		−	24.5161i		−	0.827850i	0.910311	−	0.413925i	$-0.135842\pi$
$878$	−12.2475	−	4.72338i	−0.413332	−	0.159406i
$879$		0			0
$880$	36.7876	−	3.63370i	1.24011	−	0.122492i
$881$			18.5560i			0.625167i	0.949890	+	0.312584i	$0.101194\pi$
$881$			18.5560i			0.625167i	−0.949890	+	0.312584i	$0.898806\pi$
$882$		0			0
$883$	−48.1013			−1.61874			−0.809369	−	0.587300i	$-0.800191\pi$
$883$	−48.1013			−1.61874			−0.809369	+	0.587300i	$0.800191\pi$
$884$	−1.16410	−	1.05478i	−0.0391528	−	0.0354760i
$885$		0			0
$886$	3.44743	+	1.32954i	0.115819	+	0.0446668i
$887$	−5.36841			−0.180254			−0.0901268	−	0.995930i	$-0.528727\pi$
$887$	−5.36841			−0.180254			−0.0901268	+	0.995930i	$0.528727\pi$
$888$		0			0
$889$	6.35551			0.213157
$890$	−22.5748	−	8.70626i	−0.756711	−	0.291834i
$891$		0			0
$892$	−31.6467	+	34.9266i	−1.05961	+	1.16943i
$893$	−8.64461			−0.289281
$894$		0			0
$895$			7.94435i			0.265550i
$896$	9.55545	−	6.05750i	0.319225	−	0.202367i
$897$		0			0
$898$	−40.0224	−	15.4351i	−1.33556	−	0.515076i
$899$			4.55004i			0.151752i
$900$		0			0
$901$		−	4.34510i		−	0.144756i
$902$	8.90864	−	23.0996i	0.296625	−	0.769133i
$903$		0			0
$904$	1.86836	+	3.70985i	0.0621407	+	0.123388i
$905$		−	23.2889i		−	0.774148i
$906$		0			0
$907$	4.80217			0.159453			0.0797267	−	0.996817i	$-0.474595\pi$
$907$	4.80217			0.159453			0.0797267	+	0.996817i	$0.474595\pi$
$908$	−22.3613	+	24.6788i	−0.742085	+	0.818996i
$909$		0			0
$910$	−2.13232	+	5.52899i	−0.0706857	+	0.183284i
$911$	2.79257			0.0925219			0.0462609	−	0.998929i	$-0.485269\pi$
$911$	2.79257			0.0925219			0.0462609	+	0.998929i	$0.485269\pi$
$912$		0			0
$913$	−54.1280			−1.79138
$914$	−3.37933	+	8.76241i	−0.111778	+	0.289835i
$915$		0			0
$916$	32.8061	−	36.2062i	1.08394	−	1.19629i
$917$	7.75532			0.256103
$918$		0			0
$919$			7.90433i			0.260740i	0.991465	+	0.130370i	$0.0416165\pi$
$919$			7.90433i			0.260740i	−0.991465	+	0.130370i	$0.958384\pi$
$920$	−20.2746	+	10.2107i	−0.668434	+	0.336638i
$921$		0			0
$922$	−17.8712	+	46.3390i	−0.588556	+	1.52609i
$923$			16.3399i			0.537836i
$924$		0			0
$925$		−	0.602253i		−	0.0198019i
$926$	3.34359	+	1.28949i	0.109877	+	0.0423754i
$927$		0			0
$928$	11.7782	+	3.25501i	0.386638	+	0.106851i
$929$			4.24927i			0.139414i	0.997568	+	0.0697070i	$0.0222064\pi$
$929$			4.24927i			0.139414i	−0.997568	+	0.0697070i	$0.977794\pi$
$930$		0			0
$931$	−5.01046			−0.164211
$932$	24.6383	−	27.1919i	0.807055	−	0.890699i
$933$		0			0
$934$	21.1618	+	8.16129i	0.692434	+	0.267046i
$935$	3.97827			0.130103
$936$		0			0
$937$	1.70393			0.0556649			0.0278324	−	0.999613i	$-0.491140\pi$
$937$	1.70393			0.0556649			0.0278324	+	0.999613i	$0.491140\pi$
$938$	−16.6727	−	6.43003i	−0.544384	−	0.209948i
$939$		0			0
$940$	−5.87237	−	5.32091i	−0.191536	−	0.173549i
$941$	53.7297			1.75154			0.875769	−	0.482730i	$-0.160355\pi$
$941$	53.7297			1.75154			0.875769	+	0.482730i	$0.160355\pi$
$942$		0			0
$943$			15.2035i			0.495093i
$944$	−42.2643	+	4.17465i	−1.37558	+	0.135873i
$945$		0			0
$946$	63.9063	+	24.6462i	2.07777	+	0.801318i
$947$		−	48.4816i		−	1.57544i	−0.616033	−	0.787720i	$-0.711261\pi$
$947$		−	48.4816i		−	1.57544i	0.616033	−	0.787720i	$-0.288739\pi$
$948$		0			0
$949$			13.0651i			0.424112i
$950$	−0.698697	+	1.81168i	−0.0226687	+	0.0587788i
$951$		0			0
$952$	1.08744	−	0.547657i	0.0352440	−	0.0177497i
$953$			51.7471i			1.67625i	0.545476	+	0.838126i	$0.316349\pi$
$953$			51.7471i			1.67625i	−0.545476	+	0.838126i	$0.683651\pi$
$954$		0			0
$955$	25.2028			0.815544
$956$	44.6365	+	40.4448i	1.44365	+	1.30808i
$957$		0			0
$958$	−14.8905	+	38.6103i	−0.481090	+	1.24744i
$959$	−3.09831			−0.100050
$960$		0			0
$961$	26.5633			0.856881
$962$	2.04061	−	5.29119i	0.0657920	−	0.170595i
$963$		0			0
$964$	8.17933	+	7.41122i	0.263439	+	0.238699i
$965$	−4.75901			−0.153198
$966$		0			0
$967$		−	7.89472i		−	0.253877i	−0.991911	−	0.126939i	$-0.959485\pi$
$967$		−	7.89472i		−	0.253877i	0.991911	−	0.126939i	$-0.0405151\pi$
$968$	−13.1212	+	6.60810i	−0.421730	+	0.212392i
$969$		0			0
$970$	1.97358	−	5.11740i	0.0633680	−	0.164310i
$971$		−	15.1077i		−	0.484829i	−0.970173	−	0.242414i	$-0.922061\pi$
$971$		−	15.1077i		−	0.484829i	0.970173	−	0.242414i	$-0.0779393\pi$
$972$		0			0
$973$			3.76422i			0.120675i
$974$	−3.71302	−	1.43197i	−0.118973	−	0.0458833i
$975$		0			0
$976$	−33.6194	+	3.32075i	−1.07613	+	0.106295i
$977$		−	11.3398i		−	0.362792i	−0.983410	−	0.181396i	$-0.941938\pi$
$977$		−	11.3398i		−	0.362792i	0.983410	−	0.181396i	$-0.0580616\pi$
$978$		0			0
$979$	29.9797			0.958155
$980$	−3.40366	−	3.08403i	−0.108726	−	0.0985156i
$981$		0			0
$982$	−25.4222	−	9.80439i	−0.811256	−	0.312871i
$983$	34.3365			1.09517			0.547583	−	0.836751i	$-0.315548\pi$
$983$	34.3365			1.09517			0.547583	+	0.836751i	$0.315548\pi$
$984$		0			0
$985$	10.7833			0.343584
$986$	1.22697	+	0.473196i	0.0390747	+	0.0150696i
$987$		0			0
$988$	−12.2770	+	13.5495i	−0.390585	+	0.431066i
$989$	−42.0612			−1.33747
$990$		0			0
$991$			20.9504i			0.665510i	0.943013	+	0.332755i	$0.107978\pi$
$991$			20.9504i			0.665510i	−0.943013	+	0.332755i	$0.892022\pi$
$992$	−3.17393	+	11.4848i	−0.100772	+	0.364643i
$993$		0			0
$994$	−11.8164	−	4.55715i	−0.374794	−	0.144544i
$995$			38.4797i			1.21989i
$996$		0			0
$997$			8.15182i			0.258171i	0.991633	+	0.129085i	$0.0412041\pi$
$997$			8.15182i			0.258171i	−0.991633	+	0.129085i	$0.958796\pi$
$998$	−20.0719	+	52.0453i	−0.635365	+	1.64747i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.20	yes	48
3.2	odd	2	inner	1512.2.j.d.323.29	yes	48
4.3	odd	2		6048.2.j.d.5615.14		48
8.3	odd	2	inner	1512.2.j.d.323.30	yes	48
8.5	even	2		6048.2.j.d.5615.36		48
12.11	even	2		6048.2.j.d.5615.35		48
24.5	odd	2		6048.2.j.d.5615.13		48
24.11	even	2	inner	1512.2.j.d.323.19	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.19	✓	48	24.11	even	2	inner
1512.2.j.d.323.20	yes	48	1.1	even	1	trivial
1512.2.j.d.323.29	yes	48	3.2	odd	2	inner
1512.2.j.d.323.30	yes	48	8.3	odd	2	inner
6048.2.j.d.5615.13		48	24.5	odd	2
6048.2.j.d.5615.14		48	4.3	odd	2
6048.2.j.d.5615.35		48	12.11	even	2
6048.2.j.d.5615.36		48	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.508876 + 1.31949i) q^{2} +(-1.48209 - 1.34291i) q^{4} -2.29653 q^{5} -1.00000i q^{7} +(2.52615 - 1.27222i) q^{8} +O(q^{10})\)	\(q+(-0.508876 + 1.31949i) q^{2} +(-1.48209 - 1.34291i) q^{4} -2.29653 q^{5} -1.00000i q^{7} +(2.52615 - 1.27222i) q^{8} +(1.16865 - 3.03024i) q^{10} +4.02419i q^{11} -1.82461i q^{13} +(1.31949 + 0.508876i) q^{14} +(0.393186 + 3.98063i) q^{16} +0.430472i q^{17} +5.01046 q^{19} +(3.40366 + 3.08403i) q^{20} +(-5.30987 - 2.04781i) q^{22} +3.49479 q^{23} +0.274031 q^{25} +(2.40754 + 0.928498i) q^{26} +(-1.34291 + 1.48209i) q^{28} -2.16016 q^{29} -2.10635i q^{31} +(-5.45247 - 1.50684i) q^{32} +(-0.568002 - 0.219057i) q^{34} +2.29653i q^{35} -2.19775i q^{37} +(-2.54970 + 6.61124i) q^{38} +(-5.80137 + 2.92170i) q^{40} +4.35032i q^{41} -12.0354 q^{43} +(5.40413 - 5.96422i) q^{44} +(-1.77842 + 4.61133i) q^{46} -1.72531 q^{47} -1.00000 q^{49} +(-0.139448 + 0.361580i) q^{50} +(-2.45028 + 2.70423i) q^{52} -10.0938 q^{53} -9.24166i q^{55} +(-1.27222 - 2.52615i) q^{56} +(1.09925 - 2.85030i) q^{58} +10.6175i q^{59} +8.44575i q^{61} +(2.77930 + 1.07187i) q^{62} +(4.76289 - 6.42767i) q^{64} +4.19026i q^{65} -12.6358 q^{67} +(0.578085 - 0.637998i) q^{68} +(-3.03024 - 1.16865i) q^{70} -8.95532 q^{71} -7.16051 q^{73} +(2.89991 + 1.11838i) q^{74} +(-7.42596 - 6.72860i) q^{76} +4.02419 q^{77} -15.2405i q^{79} +(-0.902963 - 9.14162i) q^{80} +(-5.74018 - 2.21377i) q^{82} +13.4507i q^{83} -0.988589i q^{85} +(6.12452 - 15.8805i) q^{86} +(5.11968 + 10.1657i) q^{88} -7.44987i q^{89} -1.82461 q^{91} +(-5.17960 - 4.69319i) q^{92} +(0.877970 - 2.27653i) q^{94} -11.5067 q^{95} +1.68878 q^{97} +(0.508876 - 1.31949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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