LMFDB - Embedded newform 768.2.o.b.95.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, not 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			95.8
Character	$\chi$	$=$	768.95
Dual form			768.2.o.b.671.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0380372 + 1.73163i) q^{3} +(-2.18808 + 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(-2.99711 + 0.131733i) q^{9} +O(q^{10})$	\(q+(0.0380372 + 1.73163i) q^{3} +(-2.18808 + 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(-2.99711 + 0.131733i) q^{9} +(1.42447 - 0.590036i) q^{11} +(0.110405 - 0.266541i) q^{13} +(-1.65266 - 3.75448i) q^{15} +6.17031 q^{17} +(-7.34269 - 3.04144i) q^{19} +(3.27272 - 3.41972i) q^{21} +(-1.85295 - 1.85295i) q^{23} +(0.430727 - 0.430727i) q^{25} +(-0.342114 - 5.18488i) q^{27} +(2.11574 - 5.10784i) q^{29} -3.42046i q^{31} +(1.07591 + 2.44422i) q^{33} +(5.97967 + 2.47686i) q^{35} +(-2.52377 - 6.09293i) q^{37} +(0.465751 + 0.181042i) q^{39} +(0.753641 - 0.753641i) q^{41} +(-1.57129 - 3.79343i) q^{43} +(6.43852 - 3.00462i) q^{45} +1.54798i q^{47} +0.468394i q^{49} +(0.234701 + 10.6847i) q^{51} +(5.12700 + 12.3777i) q^{53} +(-2.58210 + 2.58210i) q^{55} +(4.98737 - 12.8305i) q^{57} +(-3.08775 - 7.45449i) q^{59} +(4.28571 + 1.77520i) q^{61} +(6.04619 + 5.53707i) q^{63} +0.683277i q^{65} +(0.531731 - 1.28371i) q^{67} +(3.13814 - 3.27910i) q^{69} +(-8.72539 + 8.72539i) q^{71} +(-2.73022 - 2.73022i) q^{73} +(0.762244 + 0.729477i) q^{75} +(-3.89285 - 1.61247i) q^{77} -2.76080 q^{79} +(8.96529 - 0.789635i) q^{81} +(2.53133 - 6.11116i) q^{83} +(-13.5011 + 5.59235i) q^{85} +(8.92538 + 3.46939i) q^{87} +(-4.14369 - 4.14369i) q^{89} +(-0.728413 + 0.301719i) q^{91} +(5.92298 - 0.130105i) q^{93} +18.8230 q^{95} -10.3656 q^{97} +(-4.19157 + 1.95605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

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			0
$2$		0			0
$3$	0.0380372	+	1.73163i	0.0219608	+	0.999759i
$3$	0.0380372	+	1.73163i	0.0219608	+	0.999759i
$4$		0			0
$5$	−2.18808	+	0.906333i	−0.978540	+	0.405324i	−0.813884	−	0.581027i	$-0.802651\pi$
$5$	−2.18808	+	0.906333i	−0.978540	+	0.405324i	−0.164655	+	0.986351i	$0.552651\pi$
$6$		0			0
$7$	−1.93241	−	1.93241i	−0.730381	−	0.730381i	0.240314	−	0.970695i	$-0.422750\pi$
$7$	−1.93241	−	1.93241i	−0.730381	−	0.730381i	−0.970695	+	0.240314i	$0.922750\pi$
$8$		0			0
$9$	−2.99711	+	0.131733i	−0.999035	+	0.0439110i
$10$		0			0
$11$	1.42447	−	0.590036i	0.429495	−	0.177903i	−0.157454	−	0.987526i	$-0.550329\pi$
$11$	1.42447	−	0.590036i	0.429495	−	0.177903i	0.586949	+	0.809624i	$0.300329\pi$
$12$		0			0
$13$	0.110405	−	0.266541i	0.0306208	−	0.0739252i	−0.907829	−	0.419340i	$-0.862262\pi$
$13$	0.110405	−	0.266541i	0.0306208	−	0.0739252i	0.938450	+	0.345414i	$0.112262\pi$
$14$		0			0
$15$	−1.65266	−	3.75448i	−0.426716	−	0.969402i
$16$		0			0
$17$	6.17031			1.49652			0.748260	−	0.663406i	$-0.230890\pi$
$17$	6.17031			1.49652			0.748260	+	0.663406i	$0.230890\pi$
$18$		0			0
$19$	−7.34269	−	3.04144i	−1.68453	−	0.697755i	−0.685004	−	0.728540i	$-0.740199\pi$
$19$	−7.34269	−	3.04144i	−1.68453	−	0.697755i	−0.999526	+	0.0307845i	$0.990199\pi$
$20$		0			0
$21$	3.27272	−	3.41972i	0.714165	−	0.746245i
$22$		0			0
$23$	−1.85295	−	1.85295i	−0.386366	−	0.386366i	0.487023	−	0.873389i	$-0.338083\pi$
$23$	−1.85295	−	1.85295i	−0.386366	−	0.386366i	−0.873389	+	0.487023i	$0.838083\pi$
$24$		0			0
$25$	0.430727	−	0.430727i	0.0861453	−	0.0861453i
$26$		0			0
$27$	−0.342114	−	5.18488i	−0.0658400	−	0.997830i
$28$		0			0
$29$	2.11574	−	5.10784i	0.392882	−	0.948501i	−0.596427	−	0.802667i	$-0.703413\pi$
$29$	2.11574	−	5.10784i	0.392882	−	0.948501i	0.989309	−	0.145834i	$-0.0465866\pi$
$30$		0			0
$31$		−	3.42046i		−	0.614332i	−0.951656	−	0.307166i	$-0.900619\pi$
$31$		−	3.42046i		−	0.614332i	0.951656	−	0.307166i	$-0.0993807\pi$
$32$		0			0
$33$	1.07591	+	2.44422i	0.187292	+	0.425485i
$34$		0			0
$35$	5.97967	+	2.47686i	1.01075	+	0.418666i
$36$		0			0
$37$	−2.52377	−	6.09293i	−0.414906	−	1.00167i	−0.983801	−	0.179262i	$-0.942629\pi$
$37$	−2.52377	−	6.09293i	−0.414906	−	1.00167i	0.568895	−	0.822410i	$-0.307371\pi$
$38$		0			0
$39$	0.465751	+	0.181042i	0.0745798	+	0.0289900i
$40$		0			0
$41$	0.753641	−	0.753641i	0.117699	−	0.117699i	−0.645804	−	0.763503i	$-0.723478\pi$
$41$	0.753641	−	0.753641i	0.117699	−	0.117699i	0.763503	+	0.645804i	$0.223478\pi$
$42$		0			0
$43$	−1.57129	−	3.79343i	−0.239619	−	0.578492i	0.757624	−	0.652691i	$-0.226360\pi$
$43$	−1.57129	−	3.79343i	−0.239619	−	0.578492i	−0.997243	+	0.0741989i	$0.976360\pi$
$44$		0			0
$45$	6.43852	−	3.00462i	0.959798	−	0.447902i
$46$		0			0
$47$			1.54798i			0.225796i	0.993607	+	0.112898i	$0.0360133\pi$
$47$			1.54798i			0.225796i	−0.993607	+	0.112898i	$0.963987\pi$
$48$		0			0
$49$			0.468394i			0.0669135i
$50$		0			0
$51$	0.234701	+	10.6847i	0.0328647	+	1.49616i
$52$		0			0
$53$	5.12700	+	12.3777i	0.704248	+	1.70020i	0.713897	+	0.700251i	$0.246928\pi$
$53$	5.12700	+	12.3777i	0.704248	+	1.70020i	−0.00964932	+	0.999953i	$0.503072\pi$
$54$		0			0
$55$	−2.58210	+	2.58210i	−0.348170	+	0.348170i
$56$		0			0
$57$	4.98737	−	12.8305i	0.660593	−	1.69945i
$58$		0			0
$59$	−3.08775	−	7.45449i	−0.401991	−	0.970492i	−0.987182	−	0.159597i	$-0.948981\pi$
$59$	−3.08775	−	7.45449i	−0.401991	−	0.970492i	0.585191	−	0.810895i	$-0.301019\pi$
$60$		0			0
$61$	4.28571	+	1.77520i	0.548728	+	0.227291i	0.639784	−	0.768555i	$-0.279024\pi$
$61$	4.28571	+	1.77520i	0.548728	+	0.227291i	−0.0910552	+	0.995846i	$0.529024\pi$
$62$		0			0
$63$	6.04619	+	5.53707i	0.761748	+	0.697605i
$64$		0			0
$65$			0.683277i			0.0847501i
$66$		0			0
$67$	0.531731	−	1.28371i	0.0649613	−	0.156831i	−0.888065	−	0.459718i	$-0.847951\pi$
$67$	0.531731	−	1.28371i	0.0649613	−	0.156831i	0.953026	+	0.302887i	$0.0979506\pi$
$68$		0			0
$69$	3.13814	−	3.27910i	0.377788	−	0.394758i
$70$		0			0
$71$	−8.72539	+	8.72539i	−1.03551	+	1.03551i	−0.0361678	+	0.999346i	$0.511515\pi$
$71$	−8.72539	+	8.72539i	−1.03551	+	1.03551i	−0.999346	+	0.0361678i	$0.988485\pi$
$72$		0			0
$73$	−2.73022	−	2.73022i	−0.319548	−	0.319548i	0.529046	−	0.848593i	$-0.322550\pi$
$73$	−2.73022	−	2.73022i	−0.319548	−	0.319548i	−0.848593	+	0.529046i	$0.822550\pi$
$74$		0			0
$75$	0.762244	+	0.729477i	0.0880164	+	0.0842327i
$76$		0			0
$77$	−3.89285	−	1.61247i	−0.443632	−	0.183758i
$78$		0			0
$79$	−2.76080			−0.310614			−0.155307	−	0.987866i	$-0.549637\pi$
$79$	−2.76080			−0.310614			−0.155307	+	0.987866i	$0.549637\pi$
$80$		0			0
$81$	8.96529	−	0.789635i	0.996144	−	0.0877372i
$82$		0			0
$83$	2.53133	−	6.11116i	0.277849	−	0.670787i	−0.721927	−	0.691970i	$-0.756743\pi$
$83$	2.53133	−	6.11116i	0.277849	−	0.670787i	0.999776	+	0.0211827i	$0.00674318\pi$
$84$		0			0
$85$	−13.5011	+	5.59235i	−1.46440	+	0.606576i
$86$		0			0
$87$	8.92538	+	3.46939i	0.956901	+	0.371958i
$88$		0			0
$89$	−4.14369	−	4.14369i	−0.439230	−	0.439230i	0.452523	−	0.891753i	$-0.350524\pi$
$89$	−4.14369	−	4.14369i	−0.439230	−	0.439230i	−0.891753	+	0.452523i	$0.850524\pi$
$90$		0			0
$91$	−0.728413	+	0.301719i	−0.0763585	+	0.0316287i
$92$		0			0
$93$	5.92298	−	0.130105i	0.614184	−	0.0134912i
$94$		0			0
$95$	18.8230			1.93120
$96$		0			0
$97$	−10.3656			−1.05246			−0.526232	−	0.850341i	$-0.676396\pi$
$97$	−10.3656			−1.05246			−0.526232	+	0.850341i	$0.676396\pi$
$98$		0			0
$99$	−4.19157	+	1.95605i	−0.421269	+	0.196591i
$100$		0			0
$101$	−10.5700	+	4.37825i	−1.05176	+	0.435652i	−0.840519	−	0.541783i	$-0.817750\pi$
$101$	−10.5700	+	4.37825i	−1.05176	+	0.435652i	−0.211238	+	0.977435i	$0.567750\pi$
$102$		0			0
$103$	−10.4823	−	10.4823i	−1.03285	−	1.03285i	−0.999442	−	0.0334101i	$-0.989363\pi$
$103$	−10.4823	−	10.4823i	−1.03285	−	1.03285i	−0.0334101	−	0.999442i	$-0.510637\pi$
$104$		0			0
$105$	−4.06156	+	10.4488i	−0.396368	+	1.01970i
$106$		0			0
$107$	−9.39578	+	3.89186i	−0.908325	+	0.376240i	−0.787415	−	0.616423i	$-0.788581\pi$
$107$	−9.39578	+	3.89186i	−0.908325	+	0.376240i	−0.120910	+	0.992664i	$0.538581\pi$
$108$		0			0
$109$	−3.00588	+	7.25683i	−0.287911	+	0.695078i	−0.999975	−	0.00703600i	$-0.997760\pi$
$109$	−3.00588	+	7.25683i	−0.287911	+	0.695078i	0.712064	+	0.702114i	$0.247760\pi$
$110$		0			0
$111$	10.4547	−	4.60201i	0.992318	−	0.436803i
$112$		0			0
$113$	−13.6372			−1.28288			−0.641438	−	0.767175i	$-0.721662\pi$
$113$	−13.6372			−1.28288			−0.641438	+	0.767175i	$0.721662\pi$
$114$		0			0
$115$	5.73378	+	2.37501i	0.534678	+	0.221471i
$116$		0			0
$117$	−0.295783	+	0.813396i	−0.0273452	+	0.0751985i
$118$		0			0
$119$	−11.9235	−	11.9235i	−1.09303	−	1.09303i
$120$		0			0
$121$	−6.09719	+	6.09719i	−0.554290	+	0.554290i
$122$		0			0
$123$	1.33370	+	1.27636i	0.120255	+	0.115086i
$124$		0			0
$125$	3.97958	−	9.60756i	0.355945	−	0.859326i
$126$		0			0
$127$			7.75395i			0.688052i	0.938960	+	0.344026i	$0.111791\pi$
$127$			7.75395i			0.688052i	−0.938960	+	0.344026i	$0.888209\pi$
$128$		0			0
$129$	6.50906	−	2.86519i	0.573090	−	0.252266i
$130$		0			0
$131$	−1.16782	−	0.483728i	−0.102033	−	0.0422635i	0.331083	−	0.943602i	$-0.392586\pi$
$131$	−1.16782	−	0.483728i	−0.102033	−	0.0422635i	−0.433116	+	0.901338i	$0.642586\pi$
$132$		0			0
$133$	8.31177	+	20.0664i	0.720722	+	1.73998i
$134$		0			0
$135$	5.44780	+	11.0349i	0.468872	+	0.949730i
$136$		0			0
$137$	7.54494	−	7.54494i	0.644608	−	0.644608i	−0.307077	−	0.951685i	$-0.599351\pi$
$137$	7.54494	−	7.54494i	0.644608	−	0.644608i	0.951685	+	0.307077i	$0.0993509\pi$
$138$		0			0
$139$	−0.412435	−	0.995705i	−0.0349822	−	0.0844546i	0.905423	−	0.424511i	$-0.139554\pi$
$139$	−0.412435	−	0.995705i	−0.0349822	−	0.0844546i	−0.940405	+	0.340056i	$0.889554\pi$
$140$		0			0
$141$	−2.68053	+	0.0588808i	−0.225742	+	0.00495866i
$142$		0			0
$143$		−	0.444824i		−	0.0371980i
$144$		0			0
$145$			13.0939i			1.08739i
$146$		0			0
$147$	−0.811087	+	0.0178164i	−0.0668973	+	0.00146947i
$148$		0			0
$149$	−0.458938	−	1.10798i	−0.0375977	−	0.0907689i	0.903965	−	0.427606i	$-0.140643\pi$
$149$	−0.458938	−	1.10798i	−0.0375977	−	0.0907689i	−0.941563	+	0.336837i	$0.890643\pi$
$150$		0			0
$151$	9.80869	−	9.80869i	0.798220	−	0.798220i	−0.184595	−	0.982815i	$-0.559097\pi$
$151$	9.80869	−	9.80869i	0.798220	−	0.798220i	0.982815	+	0.184595i	$0.0590974\pi$
$152$		0			0
$153$	−18.4931	+	0.812833i	−1.49508	+	0.0657136i
$154$		0			0
$155$	3.10007	+	7.48424i	0.249004	+	0.601148i
$156$		0			0
$157$	−8.28207	−	3.43055i	−0.660981	−	0.273787i	0.0268702	−	0.999639i	$-0.491446\pi$
$157$	−8.28207	−	3.43055i	−0.660981	−	0.273787i	−0.687851	+	0.725852i	$0.741446\pi$
$158$		0			0
$159$	−21.2386	+	9.34890i	−1.68433	+	0.741416i
$160$		0			0
$161$			7.16129i			0.564389i
$162$		0			0
$163$	1.15049	−	2.77752i	0.0901131	−	0.217552i	−0.872397	−	0.488798i	$-0.837436\pi$
$163$	1.15049	−	2.77752i	0.0901131	−	0.217552i	0.962510	+	0.271246i	$0.0874355\pi$
$164$		0			0
$165$	−4.56946	−	4.37303i	−0.355732	−	0.340440i
$166$		0			0
$167$	1.86833	−	1.86833i	0.144576	−	0.144576i	−0.631114	−	0.775690i	$-0.717402\pi$
$167$	1.86833	−	1.86833i	0.144576	−	0.144576i	0.775690	+	0.631114i	$0.217402\pi$
$168$		0			0
$169$	9.13353	+	9.13353i	0.702579	+	0.702579i
$170$		0			0
$171$	22.4075	+	8.14826i	1.71354	+	0.623113i
$172$		0			0
$173$	−9.59196	−	3.97312i	−0.729263	−	0.302071i	−0.0130138	−	0.999915i	$-0.504143\pi$
$173$	−9.59196	−	3.97312i	−0.729263	−	0.302071i	−0.716249	+	0.697845i	$0.754143\pi$
$174$		0			0
$175$	−1.66468			−0.125838
$176$		0			0
$177$	12.7910	−	5.63040i	0.961430	−	0.423207i
$178$		0			0
$179$	0.00532113	−	0.0128464i	0.000397720	−	0.000960181i	−0.923681	−	0.383163i	$-0.874835\pi$
$179$	0.00532113	−	0.0128464i	0.000397720	−	0.000960181i	0.924078	+	0.382203i	$0.124835\pi$
$180$		0			0
$181$	9.45181	−	3.91507i	0.702547	−	0.291005i	−0.00266940	−	0.999996i	$-0.500850\pi$
$181$	9.45181	−	3.91507i	0.702547	−	0.291005i	0.705217	+	0.708992i	$0.250850\pi$
$182$		0			0
$183$	−2.91097	+	7.48879i	−0.215185	+	0.553588i
$184$		0			0
$185$	11.0444	+	11.0444i	0.812004	+	0.812004i
$186$		0			0
$187$	8.78944	−	3.64071i	0.642748	−	0.266235i
$188$		0			0
$189$	−9.35819	+	10.6804i	−0.680708	+	0.776885i
$190$		0			0
$191$	−7.77941			−0.562898			−0.281449	−	0.959576i	$-0.590815\pi$
$191$	−7.77941			−0.562898			−0.281449	+	0.959576i	$0.590815\pi$
$192$		0			0
$193$	−6.23528			−0.448825			−0.224413	−	0.974494i	$-0.572046\pi$
$193$	−6.23528			−0.448825			−0.224413	+	0.974494i	$0.572046\pi$
$194$		0			0
$195$	−1.18319	+	0.0259899i	−0.0847297	+	0.00186118i
$196$		0			0
$197$	6.90773	−	2.86128i	0.492156	−	0.203858i	−0.122781	−	0.992434i	$-0.539181\pi$
$197$	6.90773	−	2.86128i	0.492156	−	0.203858i	0.614937	+	0.788576i	$0.289181\pi$
$198$		0			0
$199$	12.4517	+	12.4517i	0.882681	+	0.882681i	0.993806	−	0.111125i	$-0.0354455\pi$
$199$	12.4517	+	12.4517i	0.882681	+	0.882681i	−0.111125	+	0.993806i	$0.535445\pi$
$200$		0			0
$201$	2.24315	+	0.871935i	0.158219	+	0.0615015i
$202$		0			0
$203$	−13.9589	+	5.78196i	−0.979721	+	0.405814i
$204$		0			0
$205$	−0.965978	+	2.33208i	−0.0674668	+	0.162879i
$206$		0			0
$207$	5.79757	+	5.30938i	0.402959	+	0.369028i
$208$		0			0
$209$	−12.2540			−0.847630
$210$		0			0
$211$	1.16851	+	0.484011i	0.0804432	+	0.0333207i	0.422542	−	0.906343i	$-0.361138\pi$
$211$	1.16851	+	0.484011i	0.0804432	+	0.0333207i	−0.342099	+	0.939664i	$0.611138\pi$
$212$		0			0
$213$	−15.4411	−	14.7773i	−1.05800	−	1.01252i
$214$		0			0
$215$	6.87622	+	6.87622i	0.468954	+	0.468954i
$216$		0			0
$217$	−6.60972	+	6.60972i	−0.448697	+	0.448697i
$218$		0			0
$219$	4.62388	−	4.83158i	0.312453	−	0.326488i
$220$		0			0
$221$	0.681233	−	1.64464i	0.0458247	−	0.110631i
$222$		0			0
$223$		−	10.5047i		−	0.703449i	−0.936104	−	0.351724i	$-0.885595\pi$
$223$		−	10.5047i		−	0.703449i	0.936104	−	0.351724i	$-0.114405\pi$
$224$		0			0
$225$	−1.23419	+	1.34767i	−0.0822795	+	0.0898450i
$226$		0			0
$227$	16.7869	+	6.95334i	1.11418	+	0.461509i	0.862376	−	0.506268i	$-0.168975\pi$
$227$	16.7869	+	6.95334i	1.11418	+	0.461509i	0.251806	+	0.967778i	$0.418975\pi$
$228$		0			0
$229$	−5.87646	−	14.1870i	−0.388327	−	0.937505i	−0.990295	−	0.138984i	$-0.955616\pi$
$229$	−5.87646	−	14.1870i	−0.388327	−	0.937505i	0.601967	−	0.798521i	$-0.294384\pi$
$230$		0			0
$231$	2.64414	−	6.80233i	0.173972	−	0.447560i
$232$		0			0
$233$	−2.54073	+	2.54073i	−0.166449	+	0.166449i	−0.785416	−	0.618968i	$-0.787551\pi$
$233$	−2.54073	+	2.54073i	−0.166449	+	0.166449i	0.618968	+	0.785416i	$0.287551\pi$
$234$		0			0
$235$	−1.40298	−	3.38711i	−0.0915206	−	0.220950i
$236$		0			0
$237$	−0.105013	−	4.78069i	−0.00682132	−	0.310539i
$238$		0			0
$239$			17.6107i			1.13914i	0.821943	+	0.569570i	$0.192890\pi$
$239$			17.6107i			1.13914i	−0.821943	+	0.569570i	$0.807110\pi$
$240$		0			0
$241$			6.18628i			0.398493i	0.979949	+	0.199247i	$0.0638495\pi$
$241$			6.18628i			0.398493i	−0.979949	+	0.199247i	$0.936151\pi$
$242$		0			0
$243$	1.70837	+	15.4946i	0.109592	+	0.993977i
$244$		0			0
$245$	−0.424521	−	1.02489i	−0.0271217	−	0.0654775i
$246$		0			0
$247$	−1.62134	+	1.62134i	−0.103163	+	0.103163i
$248$		0			0
$249$	10.6786	+	4.15088i	0.676727	+	0.263051i
$250$		0			0
$251$	9.18840	+	22.1828i	0.579967	+	1.40016i	0.892842	+	0.450369i	$0.148708\pi$
$251$	9.18840	+	22.1828i	0.579967	+	1.40016i	−0.312876	+	0.949794i	$0.601292\pi$
$252$		0			0
$253$	−3.73278	−	1.54617i	−0.234678	−	0.0972067i
$254$		0			0
$255$	−10.1975	−	23.1663i	−0.638589	−	1.45073i
$256$		0			0
$257$		−	11.8836i		−	0.741276i	−0.928777	−	0.370638i	$-0.879139\pi$
$257$		−	11.8836i		−	0.741276i	0.928777	−	0.370638i	$-0.120861\pi$
$258$		0			0
$259$	−6.89706	+	16.6510i	−0.428563	+	1.03464i
$260$		0			0
$261$	−5.66821	+	15.5874i	−0.350854	+	0.964838i
$262$		0			0
$263$	11.6191	−	11.6191i	0.716464	−	0.716464i	−0.251415	−	0.967879i	$-0.580896\pi$
$263$	11.6191	−	11.6191i	0.716464	−	0.716464i	0.967879	+	0.251415i	$0.0808959\pi$
$264$		0			0
$265$	−22.4366	−	22.4366i	−1.37827	−	1.37827i
$266$		0			0
$267$	7.01773	−	7.33296i	0.429478	−	0.448770i
$268$		0			0
$269$	13.7480	+	5.69459i	0.838228	+	0.347205i	0.760155	−	0.649742i	$-0.225123\pi$
$269$	13.7480	+	5.69459i	0.838228	+	0.347205i	0.0780733	+	0.996948i	$0.475123\pi$
$270$		0			0
$271$	7.07297			0.429652			0.214826	−	0.976652i	$-0.431081\pi$
$271$	7.07297			0.429652			0.214826	+	0.976652i	$0.431081\pi$
$272$		0			0
$273$	−0.550173	−	1.24987i	−0.0332980	−	0.0756455i
$274$		0			0
$275$	0.359414	−	0.867703i	0.0216735	−	0.0523245i
$276$		0			0
$277$	1.13397	−	0.469705i	0.0681335	−	0.0282218i	−0.348356	−	0.937362i	$-0.613260\pi$
$277$	1.13397	−	0.469705i	0.0681335	−	0.0282218i	0.416490	+	0.909140i	$0.363260\pi$
$278$		0			0
$279$	0.450587	+	10.2515i	0.0269759	+	0.613740i
$280$		0			0
$281$	12.0212	+	12.0212i	0.717122	+	0.717122i	0.968015	−	0.250893i	$-0.0807241\pi$
$281$	12.0212	+	12.0212i	0.717122	+	0.717122i	−0.250893	+	0.968015i	$0.580724\pi$
$282$		0			0
$283$	−12.8158	+	5.30848i	−0.761821	+	0.315557i	−0.729555	−	0.683923i	$-0.760273\pi$
$283$	−12.8158	+	5.30848i	−0.761821	+	0.315557i	−0.0322666	+	0.999479i	$0.510273\pi$
$284$		0			0
$285$	0.715973	+	32.5945i	0.0424106	+	1.93073i
$286$		0			0
$287$	−2.91268			−0.171930
$288$		0			0
$289$	21.0727			1.23957
$290$		0			0
$291$	−0.394277	−	17.9494i	−0.0231129	−	1.05221i
$292$		0			0
$293$	24.7412	−	10.2481i	1.44539	−	0.598702i	0.484295	−	0.874905i	$-0.339076\pi$
$293$	24.7412	−	10.2481i	1.44539	−	0.598702i	0.961099	+	0.276203i	$0.0890763\pi$
$294$		0			0
$295$	13.5125	+	13.5125i	0.786729	+	0.786729i
$296$		0			0
$297$	−3.54660	−	7.18386i	−0.205795	−	0.416850i
$298$		0			0
$299$	−0.698461	+	0.289312i	−0.0403930	+	0.0167313i
$300$		0			0
$301$	−4.29408	+	10.3668i	−0.247506	+	0.597533i
$302$		0			0
$303$	−7.98357	−	18.1369i	−0.458644	−	1.04194i
$304$		0			0
$305$	−10.9864			−0.629079
$306$		0			0
$307$	0.664375	+	0.275193i	0.0379179	+	0.0157061i	0.401562	−	0.915832i	$-0.368468\pi$
$307$	0.664375	+	0.275193i	0.0379179	+	0.0157061i	−0.363644	+	0.931538i	$0.618468\pi$
$308$		0			0
$309$	17.7528	−	18.5502i	1.00992	−	1.05528i
$310$		0			0
$311$	−3.60638	−	3.60638i	−0.204499	−	0.204499i	0.597425	−	0.801924i	$-0.296190\pi$
$311$	−3.60638	−	3.60638i	−0.204499	−	0.204499i	−0.801924	+	0.597425i	$0.796190\pi$
$312$		0			0
$313$	23.2233	−	23.2233i	1.31266	−	1.31266i	0.393210	−	0.919449i	$-0.371365\pi$
$313$	23.2233	−	23.2233i	1.31266	−	1.31266i	0.919449	−	0.393210i	$-0.128635\pi$
$314$		0			0
$315$	−18.2480	−	6.63569i	−1.02816	−	0.373879i
$316$		0			0
$317$	1.42053	−	3.42947i	0.0797850	−	0.192618i	−0.878954	−	0.476907i	$-0.841758\pi$
$317$	1.42053	−	3.42947i	0.0797850	−	0.192618i	0.958738	+	0.284289i	$0.0917577\pi$
$318$		0			0
$319$		−	8.52434i		−	0.477271i
$320$		0			0
$321$	−7.09666	−	16.1220i	−0.396097	−	0.899843i
$322$		0			0
$323$	−45.3067	−	18.7666i	−2.52093	−	1.04420i
$324$		0			0
$325$	−0.0672520	−	0.162361i	−0.00373047	−	0.00900615i
$326$		0			0
$327$	−12.6805	−	4.92905i	−0.701233	−	0.272577i
$328$		0			0
$329$	2.99133	−	2.99133i	0.164917	−	0.164917i
$330$		0			0
$331$	3.25086	+	7.84826i	0.178683	+	0.431380i	0.987691	−	0.156419i	$-0.0499949\pi$
$331$	3.25086	+	7.84826i	0.178683	+	0.431380i	−0.809008	+	0.587798i	$0.799995\pi$
$332$		0			0
$333$	8.36666	+	17.9287i	0.458490	+	0.982487i
$334$		0			0
$335$			3.29079i			0.179795i
$336$		0			0
$337$		−	24.2771i		−	1.32246i	−0.750183	−	0.661230i	$-0.770035\pi$
$337$		−	24.2771i		−	1.32246i	0.750183	−	0.661230i	$-0.229965\pi$
$338$		0			0
$339$	−0.518719	−	23.6146i	−0.0281730	−	1.28257i
$340$		0			0
$341$	−2.01819	−	4.87235i	−0.109291	−	0.263853i
$342$		0			0
$343$	−12.6217	+	12.6217i	−0.681509	+	0.681509i
$344$		0			0
$345$	−3.89455	+	10.0191i	−0.209676	+	0.539413i
$346$		0			0
$347$	−1.37907	−	3.32937i	−0.0740325	−	0.178730i	0.882531	−	0.470254i	$-0.155838\pi$
$347$	−1.37907	−	3.32937i	−0.0740325	−	0.178730i	−0.956564	+	0.291524i	$0.905838\pi$
$348$		0			0
$349$	−10.7378	−	4.44775i	−0.574782	−	0.238083i	0.0763062	−	0.997084i	$-0.475687\pi$
$349$	−10.7378	−	4.44775i	−0.574782	−	0.238083i	−0.651089	+	0.759002i	$0.725687\pi$
$350$		0			0
$351$	−1.41975	−	0.481249i	−0.0757809	−	0.0256871i
$352$		0			0
$353$		−	5.62531i		−	0.299405i	−0.988731	−	0.149703i	$-0.952168\pi$
$353$		−	5.62531i		−	0.299405i	0.988731	−	0.149703i	$-0.0478316\pi$
$354$		0			0
$355$	11.1838	−	27.0000i	0.593572	−	1.43301i
$356$		0			0
$357$	20.1937	−	21.1007i	1.06876	−	1.11677i
$358$		0			0
$359$	22.3781	−	22.3781i	1.18107	−	1.18107i	0.201603	−	0.979467i	$-0.435385\pi$
$359$	22.3781	−	22.3781i	1.18107	−	1.18107i	0.979467	−	0.201603i	$-0.0646152\pi$
$360$		0			0
$361$	31.2298	+	31.2298i	1.64367	+	1.64367i
$362$		0			0
$363$	−10.7900	−	10.3262i	−0.566329	−	0.541984i
$364$		0			0
$365$	8.44842	+	3.49945i	0.442211	+	0.183170i
$366$		0			0
$367$	−26.0135			−1.35789			−0.678946	−	0.734188i	$-0.737563\pi$
$367$	−26.0135			−1.35789			−0.678946	+	0.734188i	$0.737563\pi$
$368$		0			0
$369$	−2.15946	+	2.35802i	−0.112417	+	0.122754i
$370$		0			0
$371$	14.0113	−	33.8262i	0.727428	−	1.75617i
$372$		0			0
$373$	16.7694	−	6.94611i	0.868286	−	0.359656i	0.0963434	−	0.995348i	$-0.469285\pi$
$373$	16.7694	−	6.94611i	0.868286	−	0.359656i	0.771942	+	0.635692i	$0.219285\pi$
$374$		0			0
$375$	16.7881	+	6.52573i	0.866936	+	0.336987i
$376$		0			0
$377$	−1.12786	−	1.12786i	−0.0580878	−	0.0580878i
$378$		0			0
$379$	−11.8673	+	4.91559i	−0.609582	+	0.252497i	−0.666050	−	0.745907i	$-0.732016\pi$
$379$	−11.8673	+	4.91559i	−0.609582	+	0.252497i	0.0564681	+	0.998404i	$0.482016\pi$
$380$		0			0
$381$	−13.4270	+	0.294938i	−0.687886	+	0.0151101i
$382$		0			0
$383$	5.25906			0.268725			0.134363	−	0.990932i	$-0.457101\pi$
$383$	5.25906			0.268725			0.134363	+	0.990932i	$0.457101\pi$
$384$		0			0
$385$	9.97932			0.508593
$386$		0			0
$387$	5.20904	+	11.1623i	0.264790	+	0.567412i
$388$		0			0
$389$	−25.9373	+	10.7436i	−1.31507	+	0.544721i	−0.926360	−	0.376639i	$-0.877080\pi$
$389$	−25.9373	+	10.7436i	−1.31507	+	0.544721i	−0.388712	+	0.921359i	$0.627080\pi$
$390$		0			0
$391$	−11.4333	−	11.4333i	−0.578204	−	0.578204i
$392$		0			0
$393$	0.793219	−	2.04064i	0.0400126	−	0.102937i
$394$		0			0
$395$	6.04085	−	2.50220i	0.303948	−	0.125899i
$396$		0			0
$397$	14.4580	−	34.9046i	0.725624	−	1.75181i	0.0689699	−	0.997619i	$-0.478029\pi$
$397$	14.4580	−	34.9046i	0.725624	−	1.75181i	0.656654	−	0.754192i	$-0.271971\pi$
$398$		0			0
$399$	−34.4315	+	15.1562i	−1.72373	+	0.758759i
$400$		0			0
$401$	−31.7191			−1.58397			−0.791987	−	0.610537i	$-0.790954\pi$
$401$	−31.7191			−1.58397			−0.791987	+	0.610537i	$0.790954\pi$
$402$		0			0
$403$	−0.911693	−	0.377635i	−0.0454146	−	0.0188114i
$404$		0			0
$405$	−18.9011	+	9.85333i	−0.939204	+	0.489616i
$406$		0			0
$407$	−7.19010	−	7.19010i	−0.356400	−	0.356400i
$408$		0			0
$409$	−17.8308	+	17.8308i	−0.881677	+	0.881677i	−0.993705	−	0.112028i	$-0.964265\pi$
$409$	−17.8308	+	17.8308i	−0.881677	+	0.881677i	0.112028	+	0.993705i	$0.464265\pi$
$410$		0			0
$411$	13.3521	+	12.7781i	0.658608	+	0.630296i
$412$		0			0
$413$	−8.43832	+	20.3719i	−0.415223	+	1.00244i
$414$		0			0
$415$			15.6659i			0.769011i
$416$		0			0
$417$	1.70851	−	0.752059i	0.0836660	−	0.0368285i
$418$		0			0
$419$	−2.10652	−	0.872548i	−0.102910	−	0.0426268i	0.330634	−	0.943759i	$-0.392737\pi$
$419$	−2.10652	−	0.872548i	−0.102910	−	0.0426268i	−0.433544	+	0.901132i	$0.642737\pi$
$420$		0			0
$421$	0.169965	+	0.410331i	0.00828357	+	0.0199983i	0.927967	−	0.372662i	$-0.121555\pi$
$421$	0.169965	+	0.410331i	0.00828357	+	0.0199983i	−0.919684	+	0.392660i	$0.871555\pi$
$422$		0			0
$423$	−0.203920	−	4.63946i	−0.00991492	−	0.225578i
$424$		0			0
$425$	2.65772	−	2.65772i	0.128918	−	0.128918i
$426$		0			0
$427$	−4.85132	−	11.7121i	−0.234772	−	0.566790i
$428$		0			0
$429$	0.770272	−	0.0169198i	0.0371891	−	0.000816898i
$430$		0			0
$431$			2.95351i			0.142266i	0.997467	+	0.0711329i	$0.0226614\pi$
$431$			2.95351i			0.142266i	−0.997467	+	0.0711329i	$0.977339\pi$
$432$		0			0
$433$		−	31.3472i		−	1.50645i	−0.657764	−	0.753224i	$-0.728497\pi$
$433$		−	31.3472i		−	1.50645i	0.657764	−	0.753224i	$-0.271503\pi$
$434$		0			0
$435$	−22.6739	+	0.498056i	−1.08713	+	0.0238800i
$436$		0			0
$437$	7.96999	+	19.2413i	0.381256	+	0.920434i
$438$		0			0
$439$	−7.44392	+	7.44392i	−0.355279	+	0.355279i	−0.862069	−	0.506791i	$-0.830832\pi$
$439$	−7.44392	+	7.44392i	−0.355279	+	0.355279i	0.506791	+	0.862069i	$0.330832\pi$
$440$		0			0
$441$	−0.0617029	−	1.40383i	−0.00293824	−	0.0668489i
$442$		0			0
$443$	3.50021	+	8.45026i	0.166300	+	0.401484i	0.984957	−	0.172799i	$-0.0552810\pi$
$443$	3.50021	+	8.45026i	0.166300	+	0.401484i	−0.818657	+	0.574283i	$0.805281\pi$
$444$		0			0
$445$	12.8223	+	5.31117i	0.607835	+	0.251773i
$446$		0			0
$447$	1.90115	−	0.836857i	0.0899213	−	0.0395820i
$448$		0			0
$449$			24.0900i			1.13688i	0.822725	+	0.568439i	$0.192453\pi$
$449$			24.0900i			1.13688i	−0.822725	+	0.568439i	$0.807547\pi$
$450$		0			0
$451$	0.628866	−	1.51822i	0.0296121	−	0.0714901i
$452$		0			0
$453$	17.3581	+	16.6120i	0.815557	+	0.780498i
$454$		0			0
$455$	1.32037	−	1.32037i	0.0618999	−	0.0618999i
$456$		0			0
$457$	−13.8807	−	13.8807i	−0.649311	−	0.649311i	0.303515	−	0.952827i	$-0.401840\pi$
$457$	−13.8807	−	13.8807i	−0.649311	−	0.649311i	−0.952827	+	0.303515i	$0.901840\pi$
$458$		0			0
$459$	−2.11095	−	31.9923i	−0.0985308	−	1.49327i
$460$		0			0
$461$	−26.4361	−	10.9502i	−1.23125	−	0.510001i	−0.330282	−	0.943882i	$-0.607144\pi$
$461$	−26.4361	−	10.9502i	−1.23125	−	0.510001i	−0.900970	+	0.433881i	$0.857144\pi$
$462$		0			0
$463$	35.7558			1.66171			0.830857	−	0.556485i	$-0.187850\pi$
$463$	35.7558			1.66171			0.830857	+	0.556485i	$0.187850\pi$
$464$		0			0
$465$	−12.8420	+	5.65287i	−0.595535	+	0.262145i
$466$		0			0
$467$	1.84875	−	4.46327i	0.0855498	−	0.206536i	−0.875315	−	0.483553i	$-0.839346\pi$
$467$	1.84875	−	4.46327i	0.0855498	−	0.206536i	0.960865	+	0.277018i	$0.0893460\pi$
$468$		0			0
$469$	−3.50818	+	1.45313i	−0.161993	+	0.0670995i
$470$		0			0
$471$	5.62542	−	14.4720i	0.259206	−	0.666834i
$472$		0			0
$473$	−4.47652	−	4.47652i	−0.205831	−	0.205831i
$474$		0			0
$475$	−4.47273	+	1.85266i	−0.205223	+	0.0850060i
$476$		0			0
$477$	−16.9967	−	36.4218i	−0.778226	−	1.66764i
$478$		0			0
$479$	−15.8988			−0.726433			−0.363216	−	0.931705i	$-0.618321\pi$
$479$	−15.8988			−0.726433			−0.363216	+	0.931705i	$0.618321\pi$
$480$		0			0
$481$	−1.90265			−0.0867535
$482$		0			0
$483$	−12.4007	+	0.272395i	−0.564253	+	0.0123944i
$484$		0			0
$485$	22.6807	−	9.39466i	1.02988	−	0.426590i
$486$		0			0
$487$	−10.4283	−	10.4283i	−0.472552	−	0.472552i	0.430187	−	0.902740i	$-0.358448\pi$
$487$	−10.4283	−	10.4283i	−0.472552	−	0.472552i	−0.902740	+	0.430187i	$0.858448\pi$
$488$		0			0
$489$	4.85341	+	1.88657i	0.219479	+	0.0853138i
$490$		0			0
$491$	0.306137	−	0.126806i	0.0138158	−	0.00572268i	−0.375765	−	0.926715i	$-0.622620\pi$
$491$	0.306137	−	0.126806i	0.0138158	−	0.00572268i	0.389581	+	0.920992i	$0.372620\pi$
$492$		0			0
$493$	13.0547	−	31.5169i	0.587956	−	1.41945i
$494$		0			0
$495$	7.39867	−	8.07896i	0.332545	−	0.363122i
$496$		0			0
$497$	33.7220			1.51264
$498$		0			0
$499$	−5.62549	−	2.33015i	−0.251831	−	0.104312i	0.253197	−	0.967415i	$-0.418518\pi$
$499$	−5.62549	−	2.33015i	−0.251831	−	0.104312i	−0.505028	+	0.863103i	$0.668518\pi$
$500$		0			0
$501$	3.30633	+	3.16419i	0.147716	+	0.141366i
$502$		0			0
$503$	10.6198	+	10.6198i	0.473513	+	0.473513i	0.903050	−	0.429536i	$-0.141323\pi$
$503$	10.6198	+	10.6198i	0.473513	+	0.473513i	−0.429536	+	0.903050i	$0.641323\pi$
$504$		0			0
$505$	19.1599	−	19.1599i	0.852605	−	0.852605i
$506$		0			0
$507$	−15.4685	+	16.1633i	−0.686981	+	0.717839i
$508$		0			0
$509$	−2.01172	+	4.85673i	−0.0891681	+	0.215271i	−0.962172	−	0.272442i	$-0.912169\pi$
$509$	−2.01172	+	4.85673i	−0.0891681	+	0.215271i	0.873004	+	0.487713i	$0.162169\pi$
$510$		0			0
$511$			10.5518i			0.466783i
$512$		0			0
$513$	−13.2575	+	39.1115i	−0.585332	+	1.72681i
$514$		0			0
$515$	32.4366	+	13.4357i	1.42933	+	0.592046i
$516$		0			0
$517$	0.913364	+	2.20506i	0.0401697	+	0.0969783i
$518$		0			0
$519$	6.51513	−	16.7609i	0.285983	−	0.735721i
$520$		0			0
$521$	19.9974	−	19.9974i	0.876102	−	0.876102i	−0.117027	−	0.993129i	$-0.537336\pi$
$521$	19.9974	−	19.9974i	0.876102	−	0.876102i	0.993129	+	0.117027i	$0.0373363\pi$
$522$		0			0
$523$	15.2948	+	36.9248i	0.668793	+	1.61461i	0.783632	+	0.621225i	$0.213365\pi$
$523$	15.2948	+	36.9248i	0.668793	+	1.61461i	−0.114839	+	0.993384i	$0.536635\pi$
$524$		0			0
$525$	−0.0633197	−	2.88261i	−0.00276350	−	0.125808i
$526$		0			0
$527$		−	21.1053i		−	0.919360i
$528$		0			0
$529$		−	16.1332i		−	0.701443i
$530$		0			0
$531$	10.2363	+	21.9352i	0.444219	+	0.951905i
$532$		0			0
$533$	−0.117671	−	0.284082i	−0.00509688	−	0.0123050i
$534$		0			0
$535$	17.0314	−	17.0314i	0.736332	−	0.736332i
$536$		0			0
$537$	0.0224476	+	0.00872561i	0.000968684	+	0.000376538i
$538$		0			0
$539$	0.276370	+	0.667216i	0.0119041	+	0.0287390i
$540$		0			0
$541$	35.6786	+	14.7786i	1.53394	+	0.635380i	0.980325	−	0.197391i	$-0.0632468\pi$
$541$	35.6786	+	14.7786i	1.53394	+	0.635380i	0.553618	+	0.832771i	$0.313247\pi$
$542$		0			0
$543$	7.13898	+	16.2181i	0.306363	+	0.695987i
$544$		0			0
$545$		−	18.6029i		−	0.796859i
$546$		0			0
$547$	−12.4112	+	29.9634i	−0.530666	+	1.28114i	0.400416	+	0.916333i	$0.368865\pi$
$547$	−12.4112	+	29.9634i	−0.530666	+	1.28114i	−0.931083	+	0.364808i	$0.881135\pi$
$548$		0			0
$549$	−13.0786	−	4.75589i	−0.558180	−	0.202976i
$550$		0			0
$551$	−31.0704	+	31.0704i	−1.32364	+	1.32364i
$552$		0			0
$553$	5.33499	+	5.33499i	0.226867	+	0.226867i
$554$		0			0
$555$	−18.7048	+	19.5450i	−0.793976	+	0.829640i
$556$		0			0
$557$	−9.30090	−	3.85256i	−0.394092	−	0.163238i	0.176832	−	0.984241i	$-0.443415\pi$
$557$	−9.30090	−	3.85256i	−0.394092	−	0.163238i	−0.570924	+	0.821003i	$0.693415\pi$
$558$		0			0
$559$	−1.18458			−0.0501025
$560$		0			0
$561$	6.63869	+	15.0816i	0.280286	+	0.636746i
$562$		0			0
$563$	−1.24166	+	2.99763i	−0.0523297	+	0.126335i	−0.947882	−	0.318620i	$-0.896780\pi$
$563$	−1.24166	+	2.99763i	−0.0523297	+	0.126335i	0.895553	+	0.444955i	$0.146780\pi$
$564$		0			0
$565$	29.8392	−	12.3598i	1.25535	−	0.519981i
$566$		0			0
$567$	−18.8505	−	15.7987i	−0.791646	−	0.663483i
$568$		0			0
$569$	28.3250	+	28.3250i	1.18745	+	1.18745i	0.977771	+	0.209674i	$0.0672404\pi$
$569$	28.3250	+	28.3250i	1.18745	+	1.18745i	0.209674	+	0.977771i	$0.432760\pi$
$570$		0			0
$571$	37.5476	−	15.5527i	1.57132	−	0.650862i	0.584310	−	0.811530i	$-0.301365\pi$
$571$	37.5476	−	15.5527i	1.57132	−	0.650862i	0.987008	+	0.160669i	$0.0513651\pi$
$572$		0			0
$573$	−0.295907	−	13.4711i	−0.0123617	−	0.562763i
$574$		0			0
$575$	−1.59623			−0.0665673
$576$		0			0
$577$	5.37886			0.223925			0.111962	−	0.993712i	$-0.464286\pi$
$577$	5.37886			0.223925			0.111962	+	0.993712i	$0.464286\pi$
$578$		0			0
$579$	−0.237172	−	10.7972i	−0.00985655	−	0.448717i
$580$		0			0
$581$	−16.7008	+	6.91770i	−0.692866	+	0.286994i
$582$		0			0
$583$	14.6066	+	14.6066i	0.604942	+	0.604942i
$584$		0			0
$585$	−0.0900101	−	2.04785i	−0.00372146	−	0.0846684i
$586$		0			0
$587$	−1.77252	+	0.734203i	−0.0731599	+	0.0303038i	−0.418963	−	0.908003i	$-0.637606\pi$
$587$	−1.77252	+	0.734203i	−0.0731599	+	0.0303038i	0.345803	+	0.938307i	$0.387606\pi$
$588$		0			0
$589$	−10.4031	+	25.1154i	−0.428653	+	1.03486i
$590$		0			0
$591$	5.21743	+	11.8528i	0.214616	+	0.487560i
$592$		0			0
$593$	24.1664			0.992394			0.496197	−	0.868210i	$-0.334729\pi$
$593$	24.1664			0.992394			0.496197	+	0.868210i	$0.334729\pi$
$594$		0			0
$595$	36.8964	+	15.2830i	1.51260	+	0.626541i
$596$		0			0
$597$	−21.0882	+	22.0355i	−0.863084	+	0.901853i
$598$		0			0
$599$	−11.6692	−	11.6692i	−0.476789	−	0.476789i	0.427314	−	0.904103i	$-0.359460\pi$
$599$	−11.6692	−	11.6692i	−0.476789	−	0.476789i	−0.904103	+	0.427314i	$0.859460\pi$
$600$		0			0
$601$	−8.80143	+	8.80143i	−0.359018	+	0.359018i	−0.863451	−	0.504433i	$-0.831702\pi$
$601$	−8.80143	+	8.80143i	−0.359018	+	0.359018i	0.504433	+	0.863451i	$0.331702\pi$
$602$		0			0
$603$	−1.42455	+	3.91747i	−0.0580121	+	0.159532i
$604$		0			0
$605$	7.81507	−	18.8672i	0.317728	−	0.767062i
$606$		0			0
$607$		−	31.9215i		−	1.29565i	−0.761788	−	0.647826i	$-0.775678\pi$
$607$		−	31.9215i		−	1.29565i	0.761788	−	0.647826i	$-0.224322\pi$
$608$		0			0
$609$	−10.5432	−	23.9517i	−0.427231	−	0.970573i
$610$		0			0
$611$	0.412600	+	0.170905i	0.0166920	+	0.00691406i
$612$		0			0
$613$	−7.35458	−	17.7555i	−0.297049	−	0.717139i	−0.999983	−	0.00588391i	$-0.998127\pi$
$613$	−7.35458	−	17.7555i	−0.297049	−	0.717139i	0.702934	−	0.711255i	$-0.251873\pi$
$614$		0			0
$615$	−4.07504	−	1.58401i	−0.164322	−	0.0638736i
$616$		0			0
$617$	−13.5933	+	13.5933i	−0.547246	+	0.547246i	−0.925643	−	0.378397i	$-0.876475\pi$
$617$	−13.5933	+	13.5933i	−0.547246	+	0.547246i	0.378397	+	0.925643i	$0.376475\pi$
$618$		0			0
$619$	3.75210	+	9.05838i	0.150810	+	0.364087i	0.981172	−	0.193137i	$-0.0618663\pi$
$619$	3.75210	+	9.05838i	0.150810	+	0.364087i	−0.830362	+	0.557224i	$0.811866\pi$
$620$		0			0
$621$	−8.97338	+	10.2412i	−0.360089	+	0.410966i
$622$		0			0
$623$			16.0146i			0.641611i
$624$		0			0
$625$			27.6746i			1.10699i
$626$		0			0
$627$	−0.466109	−	21.2195i	−0.0186146	−	0.847425i
$628$		0			0
$629$	−15.5725	−	37.5953i	−0.620915	−	1.49902i
$630$		0			0
$631$	5.39207	−	5.39207i	0.214655	−	0.214655i	−0.591587	−	0.806242i	$-0.701498\pi$
$631$	5.39207	−	5.39207i	0.214655	−	0.214655i	0.806242	+	0.591587i	$0.201498\pi$
$632$		0			0
$633$	−0.793682	+	2.04183i	−0.0315460	+	0.0811556i
$634$		0			0
$635$	−7.02766	−	16.9663i	−0.278884	−	0.673286i
$636$		0			0
$637$	0.124846	+	0.0517131i	0.00494659	+	0.00204895i
$638$		0			0
$639$	25.0015	−	27.3003i	0.989044	−	1.07999i
$640$		0			0
$641$		−	1.82203i		−	0.0719659i	−0.999352	−	0.0359830i	$-0.988544\pi$
$641$		−	1.82203i		−	0.0719659i	0.999352	−	0.0359830i	$-0.0114562\pi$
$642$		0			0
$643$	10.4095	−	25.1308i	0.410511	−	0.991062i	−0.574489	−	0.818512i	$-0.694799\pi$
$643$	10.4095	−	25.1308i	0.410511	−	0.991062i	0.985001	−	0.172550i	$-0.0552007\pi$
$644$		0			0
$645$	−11.6455	+	12.1686i	−0.458542	+	0.479140i
$646$		0			0
$647$	−27.3258	+	27.3258i	−1.07429	+	1.07429i	−0.0772785	+	0.997010i	$0.524623\pi$
$647$	−27.3258	+	27.3258i	−1.07429	+	1.07429i	−0.997010	+	0.0772785i	$0.975377\pi$
$648$		0			0
$649$	−8.79684	−	8.79684i	−0.345306	−	0.345306i
$650$		0			0
$651$	−11.6970	−	11.1942i	−0.458442	−	0.438735i
$652$		0			0
$653$	21.5061	+	8.90811i	0.841598	+	0.348601i	0.761483	−	0.648184i	$-0.224471\pi$
$653$	21.5061	+	8.90811i	0.841598	+	0.348601i	0.0801145	+	0.996786i	$0.474471\pi$
$654$		0			0
$655$	2.99371			0.116974
$656$		0			0
$657$	8.54241	+	7.82309i	0.333271	+	0.305208i
$658$		0			0
$659$	−17.2778	+	41.7123i	−0.673048	+	1.62488i	0.103355	+	0.994644i	$0.467042\pi$
$659$	−17.2778	+	41.7123i	−0.673048	+	1.62488i	−0.776403	+	0.630237i	$0.782958\pi$
$660$		0			0
$661$	−44.7407	+	18.5322i	−1.74021	+	0.720819i	−0.741453	+	0.671005i	$0.765863\pi$
$661$	−44.7407	+	18.5322i	−1.74021	+	0.720819i	−0.998759	+	0.0498140i	$0.984137\pi$
$662$		0			0
$663$	2.87383	+	1.11709i	0.111610	+	0.0433841i
$664$		0			0
$665$	−36.3736	−	36.3736i	−1.41051	−	1.41051i
$666$		0			0
$667$	−13.3849	+	5.54420i	−0.518265	+	0.214672i
$668$		0			0
$669$	18.1903	−	0.399570i	0.703279	−	0.0154483i
$670$		0			0
$671$	7.15231			0.276112
$672$		0			0
$673$	−10.8139			−0.416844			−0.208422	−	0.978039i	$-0.566833\pi$
$673$	−10.8139			−0.416844			−0.208422	+	0.978039i	$0.566833\pi$
$674$		0			0
$675$	−2.38062	−	2.08591i	−0.0916302	−	0.0802866i
$676$		0			0
$677$	−16.7436	+	6.93541i	−0.643507	+	0.266549i	−0.680480	−	0.732767i	$-0.738229\pi$
$677$	−16.7436	+	6.93541i	−0.643507	+	0.266549i	0.0369727	+	0.999316i	$0.488229\pi$
$678$		0			0
$679$	20.0305	+	20.0305i	0.768701	+	0.768701i
$680$		0			0
$681$	−11.4021	+	29.3332i	−0.436930	+	1.12405i
$682$		0			0
$683$	43.5660	−	18.0456i	1.66701	−	0.690497i	0.668428	−	0.743777i	$-0.266968\pi$
$683$	43.5660	−	18.0456i	1.66701	−	0.690497i	0.998580	+	0.0532798i	$0.0169675\pi$
$684$		0			0
$685$	−9.67071	+	23.3472i	−0.369499	+	0.892049i
$686$		0			0
$687$	24.3432	−	10.7155i	0.928751	−	0.408822i
$688$		0			0
$689$	3.86521			0.147253
$690$		0			0
$691$	5.29763	+	2.19435i	0.201531	+	0.0834771i	0.481166	−	0.876629i	$-0.340213\pi$
$691$	5.29763	+	2.19435i	0.201531	+	0.0834771i	−0.279635	+	0.960106i	$0.590213\pi$
$692$		0			0
$693$	11.8797	+	4.31994i	0.451273	+	0.164101i
$694$		0			0
$695$	1.80488	+	1.80488i	0.0684630	+	0.0684630i
$696$		0			0
$697$	4.65020	−	4.65020i	0.176139	−	0.176139i
$698$		0			0
$699$	−4.49625	−	4.30297i	−0.170064	−	0.162753i
$700$		0			0
$701$	−13.7184	+	33.1190i	−0.518135	+	1.25089i	0.420912	+	0.907101i	$0.361710\pi$
$701$	−13.7184	+	33.1190i	−0.518135	+	1.25089i	−0.939047	+	0.343787i	$0.888290\pi$
$702$		0			0
$703$			52.4144i			1.97685i
$704$		0			0
$705$	5.81186	−	2.55829i	0.218887	−	0.0963508i
$706$		0			0
$707$	28.8861	+	11.9650i	1.08638	+	0.449991i
$708$		0			0
$709$	1.39804	+	3.37516i	0.0525044	+	0.126757i	0.947955	−	0.318403i	$-0.103147\pi$
$709$	1.39804	+	3.37516i	0.0525044	+	0.126757i	−0.895451	+	0.445160i	$0.853147\pi$
$710$		0			0
$711$	8.27440	−	0.363688i	0.310314	−	0.0136394i
$712$		0			0
$713$	−6.33792	+	6.33792i	−0.237357	+	0.237357i
$714$		0			0
$715$	0.403158	+	0.973311i	0.0150773	+	0.0363998i
$716$		0			0
$717$	−30.4952	+	0.669861i	−1.13887	+	0.0250164i
$718$		0			0
$719$		−	25.3851i		−	0.946706i	−0.880873	−	0.473353i	$-0.843044\pi$
$719$		−	25.3851i		−	0.946706i	0.880873	−	0.473353i	$-0.156956\pi$
$720$		0			0
$721$			40.5121i			1.50875i
$722$		0			0
$723$	−10.7124	+	0.235309i	−0.398397	+	0.00875122i
$724$		0			0
$725$	−1.28878	−	3.11138i	−0.0478640	−	0.115554i
$726$		0			0
$727$	−32.5294	+	32.5294i	−1.20645	+	1.20645i	−0.234280	+	0.972169i	$0.575273\pi$
$727$	−32.5294	+	32.5294i	−1.20645	+	1.20645i	−0.972169	+	0.234280i	$0.924727\pi$
$728$		0			0
$729$	−26.7659	+	3.54764i	−0.991330	+	0.131394i
$730$		0			0
$731$	−9.69534	−	23.4066i	−0.358595	−	0.865725i
$732$		0			0
$733$	−26.3419	−	10.9112i	−0.972961	−	0.403014i	−0.161147	−	0.986930i	$-0.551519\pi$
$733$	−26.3419	−	10.9112i	−0.972961	−	0.403014i	−0.811814	+	0.583917i	$0.801519\pi$
$734$		0			0
$735$	1.75858	−	0.774099i	0.0648661	−	0.0285531i
$736$		0			0
$737$		−	2.14236i		−	0.0789147i
$738$		0			0
$739$	−13.4201	+	32.3991i	−0.493668	+	1.19182i	0.459172	+	0.888347i	$0.348146\pi$
$739$	−13.4201	+	32.3991i	−0.493668	+	1.19182i	−0.952840	+	0.303473i	$0.901854\pi$
$740$		0			0
$741$	−2.86924	−	2.74589i	−0.105404	−	0.100873i
$742$		0			0
$743$	−5.42669	+	5.42669i	−0.199086	+	0.199086i	−0.799608	−	0.600522i	$-0.794959\pi$
$743$	−5.42669	+	5.42669i	−0.199086	+	0.199086i	0.600522	+	0.799608i	$0.294959\pi$
$744$		0			0
$745$	2.00839	+	2.00839i	0.0735817	+	0.0735817i
$746$		0			0
$747$	−6.78161	+	18.6493i	−0.248126	+	0.682341i
$748$		0			0
$749$	25.6771	+	10.6358i	0.938222	+	0.388624i
$750$		0			0
$751$	3.67683			0.134170			0.0670848	−	0.997747i	$-0.478630\pi$
$751$	3.67683			0.134170			0.0670848	+	0.997747i	$0.478630\pi$
$752$		0			0
$753$	−38.0629	+	16.7547i	−1.38709	+	0.610576i
$754$		0			0
$755$	−12.5723	+	30.3521i	−0.457552	+	1.10463i
$756$		0			0
$757$	13.0816	−	5.41857i	0.475458	−	0.196941i	−0.132068	−	0.991241i	$-0.542162\pi$
$757$	13.0816	−	5.41857i	0.475458	−	0.196941i	0.607526	+	0.794299i	$0.292162\pi$
$758$		0			0
$759$	2.53541	−	6.52262i	0.0920296	−	0.236756i
$760$		0			0
$761$	−25.8277	−	25.8277i	−0.936254	−	0.936254i	0.0618325	−	0.998087i	$-0.480306\pi$
$761$	−25.8277	−	25.8277i	−0.936254	−	0.936254i	−0.998087	+	0.0618325i	$0.980306\pi$
$762$		0			0
$763$	19.8317	−	8.21457i	0.717957	−	0.297387i
$764$		0			0
$765$	39.7276	−	18.5394i	1.43636	−	0.670294i
$766$		0			0
$767$	−2.32783			−0.0840532
$768$		0			0
$769$	−22.8386			−0.823580			−0.411790	−	0.911279i	$-0.635096\pi$
$769$	−22.8386			−0.823580			−0.411790	+	0.911279i	$0.635096\pi$
$770$		0			0
$771$	20.5780	−	0.452017i	0.741097	−	0.0162790i
$772$		0			0
$773$	−8.07057	+	3.34294i	−0.290278	+	0.120237i	−0.523071	−	0.852289i	$-0.675214\pi$
$773$	−8.07057	+	3.34294i	−0.290278	+	0.120237i	0.232793	+	0.972526i	$0.425214\pi$
$774$		0			0
$775$	−1.47328	−	1.47328i	−0.0529219	−	0.0529219i
$776$		0			0
$777$	−29.0957	−	11.3098i	−1.04380	−	0.405738i
$778$		0			0
$779$	−7.82591	+	3.24160i	−0.280392	+	0.116142i
$780$		0			0
$781$	−7.28079	+	17.5774i	−0.260527	+	0.628968i
$782$		0			0
$783$	−27.2073	−	9.22236i	−0.972311	−	0.329580i
$784$		0			0
$785$	21.2311			0.757769
$786$		0			0
$787$	−23.1792	−	9.60114i	−0.826249	−	0.342244i	−0.0708325	−	0.997488i	$-0.522566\pi$
$787$	−23.1792	−	9.60114i	−0.826249	−	0.342244i	−0.755417	+	0.655245i	$0.772566\pi$
$788$		0			0
$789$	20.5620	+	19.6781i	0.732026	+	0.700557i
$790$		0			0
$791$	26.3525	+	26.3525i	0.936989	+	0.936989i
$792$		0			0
$793$	0.946326	−	0.946326i	0.0336050	−	0.0336050i
$794$		0			0
$795$	37.9985	−	39.7054i	1.34767	−	1.40820i
$796$		0			0
$797$	9.64229	−	23.2785i	0.341547	−	0.824568i	−0.656012	−	0.754750i	$-0.727758\pi$
$797$	9.64229	−	23.2785i	0.341547	−	0.824568i	0.997560	−	0.0698182i	$-0.0222419\pi$
$798$		0			0
$799$			9.55151i			0.337908i
$800$		0			0
$801$	12.9649	+	11.8732i	0.458093	+	0.419519i
$802$		0			0
$803$	−5.50005	−	2.27819i	−0.194092	−	0.0803957i
$804$		0			0
$805$	−6.49052	−	15.6695i	−0.228761	−	0.552277i
$806$		0			0
$807$	−9.33801	+	24.0230i	−0.328713	+	0.845651i
$808$		0			0
$809$	−24.9240	+	24.9240i	−0.876282	+	0.876282i	−0.993148	−	0.116866i	$-0.962715\pi$
$809$	−24.9240	+	24.9240i	−0.876282	+	0.876282i	0.116866	+	0.993148i	$0.462715\pi$
$810$		0			0
$811$	−6.09225	−	14.7080i	−0.213928	−	0.516467i	0.780092	−	0.625664i	$-0.215172\pi$
$811$	−6.09225	−	14.7080i	−0.213928	−	0.516467i	−0.994020	+	0.109197i	$0.965172\pi$
$812$		0			0
$813$	0.269036	+	12.2478i	0.00943550	+	0.429549i
$814$		0			0
$815$			7.12017i			0.249409i
$816$		0			0
$817$			32.6330i			1.14168i
$818$		0			0
$819$	2.14339	−	1.00024i	0.0748960	−	0.0349512i
$820$		0			0
$821$	9.49765	+	22.9294i	0.331470	+	0.800240i	0.998476	+	0.0551876i	$0.0175757\pi$
$821$	9.49765	+	22.9294i	0.331470	+	0.800240i	−0.667006	+	0.745053i	$0.732424\pi$
$822$		0			0
$823$	27.2557	−	27.2557i	0.950072	−	0.950072i	−0.0487391	−	0.998812i	$-0.515520\pi$
$823$	27.2557	−	27.2557i	0.950072	−	0.950072i	0.998812	+	0.0487391i	$0.0155203\pi$
$824$		0			0
$825$	1.51621	+	0.589369i	0.0527878	+	0.0205192i
$826$		0			0
$827$	−20.6867	−	49.9420i	−0.719345	−	1.73665i	−0.675207	−	0.737628i	$-0.735946\pi$
$827$	−20.6867	−	49.9420i	−0.719345	−	1.73665i	−0.0441379	−	0.999025i	$-0.514054\pi$
$828$		0			0
$829$	0.359915	+	0.149082i	0.0125004	+	0.00517782i	0.388925	−	0.921269i	$-0.372847\pi$
$829$	0.359915	+	0.149082i	0.0125004	+	0.00517782i	−0.376424	+	0.926447i	$0.622847\pi$
$830$		0			0
$831$	0.856489	+	1.94575i	0.0297113	+	0.0674973i
$832$		0			0
$833$			2.89014i			0.100137i
$834$		0			0
$835$	−2.39473	+	5.78138i	−0.0828730	+	0.200073i
$836$		0			0
$837$	−17.7347	+	1.17019i	−0.612999	+	0.0404476i
$838$		0			0
$839$	27.7697	−	27.7697i	0.958717	−	0.958717i	−0.0404644	−	0.999181i	$-0.512884\pi$
$839$	27.7697	−	27.7697i	0.958717	−	0.958717i	0.999181	+	0.0404644i	$0.0128837\pi$
$840$		0			0
$841$	−1.10756	−	1.10756i	−0.0381918	−	0.0381918i
$842$		0			0
$843$	−20.3590	+	21.2735i	−0.701201	+	0.732698i
$844$		0			0
$845$	−28.2629	−	11.7069i	−0.972275	−	0.402729i
$846$		0			0
$847$	23.5645			0.809686
$848$		0			0
$849$	−9.67982	−	21.9904i	−0.332211	−	0.754707i
$850$		0			0
$851$	−6.61346	+	15.9663i	−0.226706	+	0.547317i
$852$		0			0
$853$	−20.4516	+	8.47133i	−0.700250	+	0.290053i	−0.704263	−	0.709939i	$-0.748722\pi$
$853$	−20.4516	+	8.47133i	−0.700250	+	0.290053i	0.00401354	+	0.999992i	$0.498722\pi$
$854$		0			0
$855$	−56.4145	+	2.47960i	−1.92933	+	0.0848007i
$856$		0			0
$857$	−13.1734	−	13.1734i	−0.449996	−	0.449996i	0.445357	−	0.895353i	$-0.353077\pi$
$857$	−13.1734	−	13.1734i	−0.449996	−	0.449996i	−0.895353	+	0.445357i	$0.853077\pi$
$858$		0			0
$859$	7.55122	−	3.12782i	0.257644	−	0.106720i	−0.250123	−	0.968214i	$-0.580471\pi$
$859$	7.55122	−	3.12782i	0.257644	−	0.106720i	0.507767	+	0.861494i	$0.330471\pi$
$860$		0			0
$861$	−0.110790	−	5.04370i	−0.00377572	−	0.171889i
$862$		0			0
$863$	19.3590			0.658989			0.329494	−	0.944158i	$-0.393122\pi$
$863$	19.3590			0.658989			0.329494	+	0.944158i	$0.393122\pi$
$864$		0			0
$865$	24.5889			0.836049
$866$		0			0
$867$	0.801546	+	36.4902i	0.0272219	+	1.23927i
$868$		0			0
$869$	−3.93268	+	1.62897i	−0.133407	+	0.0552591i
$870$		0			0
$871$	−0.283457	−	0.283457i	−0.00960456	−	0.00960456i
$872$		0			0
$873$	31.0667	−	1.36549i	1.05145	−	0.0462147i
$874$		0			0
$875$	−26.2559	+	10.8755i	−0.887611	+	0.367661i
$876$		0			0
$877$	6.24223	−	15.0701i	0.210785	−	0.508880i	−0.782759	−	0.622325i	$-0.786188\pi$
$877$	6.24223	−	15.0701i	0.210785	−	0.508880i	0.993544	+	0.113444i	$0.0361884\pi$
$878$		0			0
$879$	18.6871	+	42.4528i	0.630299	+	1.43190i
$880$		0			0
$881$	36.6844			1.23593			0.617964	−	0.786207i	$-0.287958\pi$
$881$	36.6844			1.23593			0.617964	+	0.786207i	$0.287958\pi$
$882$		0			0
$883$	−11.4178	−	4.72942i	−0.384240	−	0.159158i	0.182198	−	0.983262i	$-0.441679\pi$
$883$	−11.4178	−	4.72942i	−0.384240	−	0.159158i	−0.566438	+	0.824104i	$0.691679\pi$
$884$		0			0
$885$	−22.8847	+	23.9127i	−0.769262	+	0.803816i
$886$		0			0
$887$	34.3135	+	34.3135i	1.15213	+	1.15213i	0.986124	+	0.166009i	$0.0530880\pi$
$887$	34.3135	+	34.3135i	1.15213	+	1.15213i	0.166009	+	0.986124i	$0.446912\pi$
$888$		0			0
$889$	14.9838	−	14.9838i	0.502540	−	0.502540i
$890$		0			0
$891$	12.3049	−	6.41466i	0.412230	−	0.214899i
$892$		0			0
$893$	4.70809	−	11.3663i	0.157550	−	0.380360i
$894$		0			0
$895$			0.0329316i			0.00110078i
$896$		0			0
$897$	−0.527550	−	1.19847i	−0.0176144	−	0.0400159i
$898$		0			0
$899$	−17.4711	−	7.23678i	−0.582695	−	0.241360i
$900$		0			0
$901$	31.6352	+	76.3741i	1.05392	+	2.54439i
$902$		0			0
$903$	−18.1149	−	7.04144i	−0.602825	−	0.234324i
$904$		0			0
$905$	−17.1330	+	17.1330i	−0.569519	+	0.569519i
$906$		0			0
$907$	−5.32554	−	12.8570i	−0.176832	−	0.426910i	0.810467	−	0.585784i	$-0.199213\pi$
$907$	−5.32554	−	12.8570i	−0.176832	−	0.426910i	−0.987299	+	0.158875i	$0.949213\pi$
$908$		0			0
$909$	31.1027	−	14.5145i	1.03161	−	0.481415i
$910$		0			0
$911$			10.5385i			0.349157i	0.984643	+	0.174579i	$0.0558563\pi$
$911$			10.5385i			0.349157i	−0.984643	+	0.174579i	$0.944144\pi$
$912$		0			0
$913$		−	10.1988i		−	0.337530i
$914$		0			0
$915$	−0.417891	−	19.0244i	−0.0138151	−	0.628927i
$916$		0			0
$917$	1.32195	+	3.19147i	0.0436546	+	0.105392i
$918$		0			0
$919$	11.9849	−	11.9849i	0.395346	−	0.395346i	−0.481242	−	0.876588i	$-0.659814\pi$
$919$	11.9849	−	11.9849i	0.395346	−	0.395346i	0.876588	+	0.481242i	$0.159814\pi$
$920$		0			0
$921$	−0.451262	+	1.16092i	−0.0148696	+	0.0382536i
$922$		0			0
$923$	1.36235	+	3.28900i	0.0448423	+	0.108259i
$924$		0			0
$925$	−3.71144	−	1.53733i	−0.122032	−	0.0505471i
$926$		0			0
$927$	32.7974	+	30.0357i	1.07721	+	0.986502i
$928$		0			0
$929$		−	0.514845i		−	0.0168915i	−0.999964	−	0.00844575i	$-0.997312\pi$
$929$		−	0.514845i		−	0.0168915i	0.999964	−	0.00844575i	$-0.00268840\pi$
$930$		0			0
$931$	1.42460	−	3.43928i	0.0466892	−	0.112718i
$932$		0			0
$933$	6.10775	−	6.38210i	0.199959	−	0.208941i
$934$		0			0
$935$	−15.9323	+	15.9323i	−0.521043	+	0.521043i
$936$		0			0
$937$	−15.6989	−	15.6989i	−0.512862	−	0.512862i	0.402540	−	0.915402i	$-0.368127\pi$
$937$	−15.6989	−	15.6989i	−0.512862	−	0.512862i	−0.915402	+	0.402540i	$0.868127\pi$
$938$		0			0
$939$	41.0976	+	39.3309i	1.34117	+	1.28351i
$940$		0			0
$941$	8.26022	+	3.42149i	0.269275	+	0.111538i	0.513236	−	0.858248i	$-0.328447\pi$
$941$	8.26022	+	3.42149i	0.269275	+	0.111538i	−0.243960	+	0.969785i	$0.578447\pi$
$942$		0			0
$943$	−2.79291			−0.0909497
$944$		0			0
$945$	10.7965	−	31.8512i	0.351210	−	1.03612i
$946$		0			0
$947$	−1.67384	+	4.04101i	−0.0543926	+	0.131315i	−0.948740	−	0.316058i	$-0.897641\pi$
$947$	−1.67384	+	4.04101i	−0.0543926	+	0.131315i	0.894347	+	0.447373i	$0.147641\pi$
$948$		0			0
$949$	−1.02914	+	0.426286i	−0.0334074	+	0.0138378i
$950$		0			0
$951$	5.99261	+	2.32939i	0.194324	+	0.0755357i
$952$		0			0
$953$	−32.0579	−	32.0579i	−1.03846	−	1.03846i	−0.999230	−	0.0392279i	$-0.987510\pi$
$953$	−32.0579	−	32.0579i	−1.03846	−	1.03846i	−0.0392279	−	0.999230i	$-0.512490\pi$
$954$		0			0
$955$	17.0220	−	7.05074i	0.550819	−	0.228157i
$956$		0			0
$957$	14.7610	−	0.324242i	0.477156	−	0.0104813i
$958$		0			0
$959$	−29.1598			−0.941619
$960$		0			0
$961$	19.3005			0.622596
$962$		0			0
$963$	27.6475	−	12.9021i	0.890927	−	0.415763i
$964$		0			0
$965$	13.6433	−	5.65124i	0.439193	−	0.181920i
$966$		0			0
$967$	−37.4258	−	37.4258i	−1.20353	−	1.20353i	−0.973085	−	0.230448i	$-0.925981\pi$
$967$	−37.4258	−	37.4258i	−1.20353	−	1.20353i	−0.230448	−	0.973085i	$-0.574019\pi$
$968$		0			0
$969$	30.7736	−	79.1684i	0.988591	−	2.54326i
$970$		0			0
$971$	33.0754	−	13.7003i	1.06144	−	0.439663i	0.217478	−	0.976065i	$-0.430217\pi$
$971$	33.0754	−	13.7003i	1.06144	−	0.439663i	0.843962	+	0.536402i	$0.180217\pi$
$972$		0			0
$973$	−1.12712	+	2.72110i	−0.0361337	+	0.0872344i
$974$		0			0
$975$	0.278591	−	0.122632i	0.00892206	−	0.00392735i
$976$		0			0
$977$	39.7489			1.27168			0.635839	−	0.771821i	$-0.280654\pi$
$977$	39.7489			1.27168			0.635839	+	0.771821i	$0.280654\pi$
$978$		0			0
$979$	−8.34750	−	3.45765i	−0.266787	−	0.110507i
$980$		0			0
$981$	8.05297	−	22.1455i	0.257112	−	0.707050i
$982$		0			0
$983$	−29.8565	−	29.8565i	−0.952276	−	0.952276i	0.0466360	−	0.998912i	$-0.485150\pi$
$983$	−29.8565	−	29.8565i	−0.952276	−	0.952276i	−0.998912	+	0.0466360i	$0.985150\pi$
$984$		0			0
$985$	−12.5214	+	12.5214i	−0.398965	+	0.398965i
$986$		0			0
$987$	5.29366	+	5.06610i	0.168499	+	0.161256i
$988$		0			0
$989$	−4.11750	+	9.94053i	−0.130929	+	0.316091i
$990$		0			0
$991$		−	56.2662i		−	1.78736i	−0.448710	−	0.893678i	$-0.648116\pi$
$991$		−	56.2662i		−	1.78736i	0.448710	−	0.893678i	$-0.351884\pi$
$992$		0			0
$993$	−13.4667	+	5.92782i	−0.427352	+	0.188114i
$994$		0			0
$995$	−38.5309	−	15.9600i	−1.22151	−	0.505966i
$996$		0			0
$997$	−13.8797	−	33.5085i	−0.439574	−	1.06122i	−0.976096	−	0.217339i	$-0.930262\pi$
$997$	−13.8797	−	33.5085i	−0.439574	−	1.06122i	0.536523	−	0.843886i	$-0.319738\pi$
$998$		0			0
$999$	−30.7277	+	15.1699i	−0.972181	+	0.479956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.b.95.8		56
3.2	odd	2	inner	768.2.o.b.95.3		56
4.3	odd	2		768.2.o.a.95.7		56
8.3	odd	2		384.2.o.a.47.8		56
8.5	even	2		96.2.o.a.35.2	yes	56
12.11	even	2		768.2.o.a.95.12		56
24.5	odd	2		96.2.o.a.35.13	yes	56
24.11	even	2		384.2.o.a.47.3		56
32.5	even	8		384.2.o.a.335.3		56
32.11	odd	8	inner	768.2.o.b.671.3		56
32.21	even	8		768.2.o.a.671.12		56
32.27	odd	8		96.2.o.a.11.13	yes	56
96.5	odd	8		384.2.o.a.335.8		56
96.11	even	8	inner	768.2.o.b.671.8		56
96.53	odd	8		768.2.o.a.671.7		56
96.59	even	8		96.2.o.a.11.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.11.2	✓	56	96.59	even	8
96.2.o.a.11.13	yes	56	32.27	odd	8
96.2.o.a.35.2	yes	56	8.5	even	2
96.2.o.a.35.13	yes	56	24.5	odd	2
384.2.o.a.47.3		56	24.11	even	2
384.2.o.a.47.8		56	8.3	odd	2
384.2.o.a.335.3		56	32.5	even	8
384.2.o.a.335.8		56	96.5	odd	8
768.2.o.a.95.7		56	4.3	odd	2
768.2.o.a.95.12		56	12.11	even	2
768.2.o.a.671.7		56	96.53	odd	8
768.2.o.a.671.12		56	32.21	even	8
768.2.o.b.95.3		56	3.2	odd	2	inner
768.2.o.b.95.8		56	1.1	even	1	trivial
768.2.o.b.671.3		56	32.11	odd	8	inner
768.2.o.b.671.8		56	96.11	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0380372 + 1.73163i) q^{3} +(-2.18808 + 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(-2.99711 + 0.131733i) q^{9} +O(q^{10})\)	\(q+(0.0380372 + 1.73163i) q^{3} +(-2.18808 + 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(-2.99711 + 0.131733i) q^{9} +(1.42447 - 0.590036i) q^{11} +(0.110405 - 0.266541i) q^{13} +(-1.65266 - 3.75448i) q^{15} +6.17031 q^{17} +(-7.34269 - 3.04144i) q^{19} +(3.27272 - 3.41972i) q^{21} +(-1.85295 - 1.85295i) q^{23} +(0.430727 - 0.430727i) q^{25} +(-0.342114 - 5.18488i) q^{27} +(2.11574 - 5.10784i) q^{29} -3.42046i q^{31} +(1.07591 + 2.44422i) q^{33} +(5.97967 + 2.47686i) q^{35} +(-2.52377 - 6.09293i) q^{37} +(0.465751 + 0.181042i) q^{39} +(0.753641 - 0.753641i) q^{41} +(-1.57129 - 3.79343i) q^{43} +(6.43852 - 3.00462i) q^{45} +1.54798i q^{47} +0.468394i q^{49} +(0.234701 + 10.6847i) q^{51} +(5.12700 + 12.3777i) q^{53} +(-2.58210 + 2.58210i) q^{55} +(4.98737 - 12.8305i) q^{57} +(-3.08775 - 7.45449i) q^{59} +(4.28571 + 1.77520i) q^{61} +(6.04619 + 5.53707i) q^{63} +0.683277i q^{65} +(0.531731 - 1.28371i) q^{67} +(3.13814 - 3.27910i) q^{69} +(-8.72539 + 8.72539i) q^{71} +(-2.73022 - 2.73022i) q^{73} +(0.762244 + 0.729477i) q^{75} +(-3.89285 - 1.61247i) q^{77} -2.76080 q^{79} +(8.96529 - 0.789635i) q^{81} +(2.53133 - 6.11116i) q^{83} +(-13.5011 + 5.59235i) q^{85} +(8.92538 + 3.46939i) q^{87} +(-4.14369 - 4.14369i) q^{89} +(-0.728413 + 0.301719i) q^{91} +(5.92298 - 0.130105i) q^{93} +18.8230 q^{95} -10.3656 q^{97} +(-4.19157 + 1.95605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9} + 8 q^{13} - 8 q^{15} + 8 q^{19} + 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} + 8 q^{37} - 28 q^{39} + 8 q^{43} + 4 q^{45} + 16 q^{51} + 24 q^{55} - 4 q^{57} + 40 q^{61} - 56 q^{67} + 4 q^{69} - 8 q^{73} - 16 q^{75} + 16 q^{79} + 48 q^{85} + 52 q^{87} - 40 q^{91} - 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 - 8 * q^7 - 4 * q^9 + 8 * q^13 - 8 * q^15 + 8 * q^19 + 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 + 8 * q^37 - 28 * q^39 + 8 * q^43 + 4 * q^45 + 16 * q^51 + 24 * q^55 - 4 * q^57 + 40 * q^61 - 56 * q^67 + 4 * q^69 - 8 * q^73 - 16 * q^75 + 16 * q^79 + 48 * q^85 + 52 * q^87 - 40 * q^91 - 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

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