LMFDB - Embedded newform 768.2.o.b.95.3

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			95.3
Character	$\chi$	$=$	768.95
Dual form			768.2.o.b.671.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25135 + 1.19755i) q^{3} +(2.18808 - 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(0.131733 - 2.99711i) q^{9} +O(q^{10})$	\(q+(-1.25135 + 1.19755i) q^{3} +(2.18808 - 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(0.131733 - 2.99711i) q^{9} +(-1.42447 + 0.590036i) q^{11} +(0.110405 - 0.266541i) q^{13} +(-1.65266 + 3.75448i) q^{15} -6.17031 q^{17} +(-7.34269 - 3.04144i) q^{19} +(4.73227 + 0.103949i) q^{21} +(1.85295 + 1.85295i) q^{23} +(0.430727 - 0.430727i) q^{25} +(3.42435 + 3.90817i) q^{27} +(-2.11574 + 5.10784i) q^{29} -3.42046i q^{31} +(1.07591 - 2.44422i) q^{33} +(-5.97967 - 2.47686i) q^{35} +(-2.52377 - 6.09293i) q^{37} +(0.181042 + 0.465751i) q^{39} +(-0.753641 + 0.753641i) q^{41} +(-1.57129 - 3.79343i) q^{43} +(-2.42813 - 6.67731i) q^{45} -1.54798i q^{47} +0.468394i q^{49} +(7.72119 - 7.38927i) q^{51} +(-5.12700 - 12.3777i) q^{53} +(-2.58210 + 2.58210i) q^{55} +(12.8305 - 4.98737i) q^{57} +(3.08775 + 7.45449i) q^{59} +(4.28571 + 1.77520i) q^{61} +(-6.04619 + 5.53707i) q^{63} -0.683277i q^{65} +(0.531731 - 1.28371i) q^{67} +(-4.53768 - 0.0996750i) q^{69} +(8.72539 - 8.72539i) q^{71} +(-2.73022 - 2.73022i) q^{73} +(-0.0231699 + 1.05481i) q^{75} +(3.89285 + 1.61247i) q^{77} -2.76080 q^{79} +(-8.96529 - 0.789635i) q^{81} +(-2.53133 + 6.11116i) q^{83} +(-13.5011 + 5.59235i) q^{85} +(-3.46939 - 8.92538i) q^{87} +(4.14369 + 4.14369i) q^{89} +(-0.728413 + 0.301719i) q^{91} +(4.09618 + 4.28017i) q^{93} -18.8230 q^{95} -10.3656 q^{97} +(1.58075 + 4.34703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.25135	+	1.19755i	−0.722465	+	0.691408i
$3$	−1.25135	+	1.19755i	−0.722465	+	0.691408i
$4$		0			0
$5$	2.18808	−	0.906333i	0.978540	−	0.405324i	0.164655	−	0.986351i	$-0.447349\pi$
$5$	2.18808	−	0.906333i	0.978540	−	0.405324i	0.813884	+	0.581027i	$0.197349\pi$
$6$		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
$9$	0.131733	−	2.99711i	0.0439110	−	0.999035i
$10$		0			0
$11$	−1.42447	+	0.590036i	−0.429495	+	0.177903i	−0.586949	−	0.809624i	$-0.699671\pi$
$11$	−1.42447	+	0.590036i	−0.429495	+	0.177903i	0.157454	+	0.987526i	$0.449671\pi$
$12$		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	$-0.769110\pi$
$17$	−6.17031			−1.49652			−0.748260	+	0.663406i	$0.769110\pi$
$18$		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
$21$	4.73227	+	0.103949i	1.03267	+	0.0226836i
$22$		0			0
$23$	1.85295	+	1.85295i	0.386366	+	0.386366i	0.873389	−	0.487023i	$-0.161917\pi$
$23$	1.85295	+	1.85295i	0.386366	+	0.386366i	−0.487023	+	0.873389i	$0.661917\pi$
$24$		0			0
$25$	0.430727	−	0.430727i	0.0861453	−	0.0861453i
$26$		0			0
$27$	3.42435	+	3.90817i	0.659017	+	0.752128i
$28$		0			0
$29$	−2.11574	+	5.10784i	−0.392882	+	0.948501i	0.596427	+	0.802667i	$0.296587\pi$
$29$	−2.11574	+	5.10784i	−0.392882	+	0.948501i	−0.989309	+	0.145834i	$0.953413\pi$
$30$		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
$39$	0.181042	+	0.465751i	0.0289900	+	0.0745798i
$40$		0			0
$41$	−0.753641	+	0.753641i	−0.117699	+	0.117699i	−0.763503	−	0.645804i	$-0.776522\pi$
$41$	−0.753641	+	0.753641i	−0.117699	+	0.117699i	0.645804	+	0.763503i	$0.276522\pi$
$42$		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
$45$	−2.42813	−	6.67731i	−0.361965	−	0.995394i
$46$		0			0
$47$		−	1.54798i		−	0.225796i	−0.993607	−	0.112898i	$-0.963987\pi$
$47$		−	1.54798i		−	0.225796i	0.993607	−	0.112898i	$-0.0360133\pi$
$48$		0			0
$49$			0.468394i			0.0669135i
$50$		0			0
$51$	7.72119	−	7.38927i	1.08118	−	1.03471i
$52$		0			0
$53$	−5.12700	−	12.3777i	−0.704248	−	1.70020i	−0.713897	−	0.700251i	$-0.753072\pi$
$53$	−5.12700	−	12.3777i	−0.704248	−	1.70020i	0.00964932	−	0.999953i	$-0.496928\pi$
$54$		0			0
$55$	−2.58210	+	2.58210i	−0.348170	+	0.348170i
$56$		0			0
$57$	12.8305	−	4.98737i	1.69945	−	0.660593i
$58$		0			0
$59$	3.08775	+	7.45449i	0.401991	+	0.970492i	0.987182	+	0.159597i	$0.0510195\pi$
$59$	3.08775	+	7.45449i	0.401991	+	0.970492i	−0.585191	+	0.810895i	$0.698981\pi$
$60$		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
$69$	−4.53768	−	0.0996750i	−0.546272	−	0.0119995i
$70$		0			0
$71$	8.72539	−	8.72539i	1.03551	−	1.03551i	0.0361678	−	0.999346i	$-0.488485\pi$
$71$	8.72539	−	8.72539i	1.03551	−	1.03551i	0.999346	−	0.0361678i	$-0.0115151\pi$
$72$		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
$75$	−0.0231699	+	1.05481i	−0.00267543	+	0.121799i
$76$		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	−0.999776	−	0.0211827i	$-0.993257\pi$
$83$	−2.53133	+	6.11116i	−0.277849	+	0.670787i	0.721927	+	0.691970i	$0.243257\pi$
$84$		0			0
$85$	−13.5011	+	5.59235i	−1.46440	+	0.606576i
$86$		0			0
$87$	−3.46939	−	8.92538i	−0.371958	−	0.956901i
$88$		0			0
$89$	4.14369	+	4.14369i	0.439230	+	0.439230i	0.891753	−	0.452523i	$-0.149476\pi$
$89$	4.14369	+	4.14369i	0.439230	+	0.439230i	−0.452523	+	0.891753i	$0.649476\pi$
$90$		0			0
$91$	−0.728413	+	0.301719i	−0.0763585	+	0.0316287i
$92$		0			0
$93$	4.09618	+	4.28017i	0.424754	+	0.443833i
$94$		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
$99$	1.58075	+	4.34703i	0.158872	+	0.436893i
$100$		0			0
$101$	10.5700	−	4.37825i	1.05176	−	0.435652i	0.211238	−	0.977435i	$-0.432250\pi$
$101$	10.5700	−	4.37825i	1.05176	−	0.435652i	0.840519	+	0.541783i	$0.182250\pi$
$102$		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
$105$	10.4488	−	4.06156i	1.01970	−	0.396368i
$106$		0			0
$107$	9.39578	−	3.89186i	0.908325	−	0.376240i	0.120910	−	0.992664i	$-0.461419\pi$
$107$	9.39578	−	3.89186i	0.908325	−	0.376240i	0.787415	+	0.616423i	$0.211419\pi$
$108$		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	$-0.278338\pi$
$113$	13.6372			1.28288			0.641438	+	0.767175i	$0.278338\pi$
$114$		0			0
$115$	5.73378	+	2.37501i	0.534678	+	0.221471i
$116$		0			0
$117$	−0.784308	−	0.366008i	−0.0725093	−	0.0338374i
$118$		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
$123$	0.0405404	−	1.84559i	0.00365540	−	0.166411i
$124$		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	0.433116	−	0.901338i	$-0.357414\pi$
$131$	1.16782	+	0.483728i	0.102033	+	0.0422635i	−0.331083	+	0.943602i	$0.607414\pi$
$132$		0			0
$133$	8.31177	+	20.0664i	0.720722	+	1.73998i
$134$		0			0
$135$	11.0349	+	5.44780i	0.949730	+	0.468872i
$136$		0			0
$137$	−7.54494	+	7.54494i	−0.644608	+	0.644608i	−0.951685	−	0.307077i	$-0.900649\pi$
$137$	−7.54494	+	7.54494i	−0.644608	+	0.644608i	0.307077	+	0.951685i	$0.400649\pi$
$138$		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
$141$	1.85379	+	1.93706i	0.156117	+	0.163130i
$142$		0			0
$143$			0.444824i			0.0371980i
$144$		0			0
$145$			13.0939i			1.08739i
$146$		0			0
$147$	−0.560927	−	0.586123i	−0.0462645	−	0.0483426i
$148$		0			0
$149$	0.458938	+	1.10798i	0.0375977	+	0.0907689i	0.941563	−	0.336837i	$-0.109357\pi$
$149$	0.458938	+	1.10798i	0.0375977	+	0.0907689i	−0.903965	+	0.427606i	$0.859357\pi$
$150$		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
$153$	−0.812833	+	18.4931i	−0.0657136	+	1.49508i
$154$		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
$165$	0.138898	−	6.32329i	0.0108132	−	0.492267i
$166$		0			0
$167$	−1.86833	+	1.86833i	−0.144576	+	0.144576i	−0.775690	−	0.631114i	$-0.782598\pi$
$167$	−1.86833	+	1.86833i	−0.144576	+	0.144576i	0.631114	+	0.775690i	$0.282598\pi$
$168$		0			0
$169$	9.13353	+	9.13353i	0.702579	+	0.702579i
$170$		0			0
$171$	−10.0828	+	21.6062i	−0.771051	+	1.65227i
$172$		0			0
$173$	9.59196	+	3.97312i	0.729263	+	0.302071i	0.716249	−	0.697845i	$-0.245857\pi$
$173$	9.59196	+	3.97312i	0.729263	+	0.302071i	0.0130138	+	0.999915i	$0.495857\pi$
$174$		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	−0.924078	−	0.382203i	$-0.875165\pi$
$179$	−0.00532113	+	0.0128464i	−0.000397720	+	0.000960181i	0.923681	+	0.383163i	$0.125165\pi$
$180$		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
$183$	−7.48879	+	2.91097i	−0.553588	+	0.215185i
$184$		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
$189$	0.934943	−	14.1694i	0.0680071	−	1.03067i
$190$		0			0
$191$	7.77941			0.562898			0.281449	−	0.959576i	$-0.409185\pi$
$191$	7.77941			0.562898			0.281449	+	0.959576i	$0.409185\pi$
$192$		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
$195$	0.818261	+	0.855016i	0.0585969	+	0.0612290i
$196$		0			0
$197$	−6.90773	+	2.86128i	−0.492156	+	0.203858i	−0.614937	−	0.788576i	$-0.710819\pi$
$197$	−6.90773	+	2.86128i	−0.492156	+	0.203858i	0.122781	+	0.992434i	$0.460819\pi$
$198$		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
$201$	0.871935	+	2.24315i	0.0615015	+	0.158219i
$202$		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
$213$	−0.469362	+	21.3676i	−0.0321602	+	1.46408i
$214$		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
$219$	6.68602	+	0.146866i	0.451800	+	0.00992426i
$220$		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	−0.251806	−	0.967778i	$-0.581025\pi$
$227$	−16.7869	−	6.95334i	−1.11418	−	0.461509i	−0.862376	+	0.506268i	$0.831025\pi$
$228$		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
$231$	−6.80233	+	2.64414i	−0.447560	+	0.173972i
$232$		0			0
$233$	2.54073	−	2.54073i	0.166449	−	0.166449i	−0.618968	−	0.785416i	$-0.712449\pi$
$233$	2.54073	−	2.54073i	0.166449	−	0.166449i	0.785416	+	0.618968i	$0.212449\pi$
$234$		0			0
$235$	−1.40298	−	3.38711i	−0.0915206	−	0.220950i
$236$		0			0
$237$	3.45471	−	3.30620i	0.224408	−	0.214761i
$238$		0			0
$239$		−	17.6107i		−	1.13914i	−0.821943	−	0.569570i	$-0.807110\pi$
$239$		−	17.6107i		−	1.13914i	0.821943	−	0.569570i	$-0.192890\pi$
$240$		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
$243$	12.1643	−	9.74831i	0.780341	−	0.625354i
$244$		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
$249$	−4.15088	−	10.6786i	−0.263051	−	0.676727i
$250$		0			0
$251$	−9.18840	−	22.1828i	−0.579967	−	1.40016i	−0.892842	−	0.450369i	$-0.851292\pi$
$251$	−9.18840	−	22.1828i	−0.579967	−	1.40016i	0.312876	−	0.949794i	$-0.398708\pi$
$252$		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	$0.120861\pi$
$257$			11.8836i			0.741276i	−0.928777	+	0.370638i	$0.879139\pi$
$258$		0			0
$259$	−6.89706	+	16.6510i	−0.428563	+	1.03464i
$260$		0			0
$261$	15.0300	+	7.01395i	0.930335	+	0.434153i
$262$		0			0
$263$	−11.6191	+	11.6191i	−0.716464	+	0.716464i	−0.967879	−	0.251415i	$-0.919104\pi$
$263$	−11.6191	+	11.6191i	−0.716464	+	0.716464i	0.251415	+	0.967879i	$0.419104\pi$
$264$		0			0
$265$	−22.4366	−	22.4366i	−1.37827	−	1.37827i
$266$		0			0
$267$	−10.1475	−	0.222900i	−0.621015	−	0.0136413i
$268$		0			0
$269$	−13.7480	−	5.69459i	−0.838228	−	0.347205i	−0.0780733	−	0.996948i	$-0.524877\pi$
$269$	−13.7480	−	5.69459i	−0.838228	−	0.347205i	−0.760155	+	0.649742i	$0.774877\pi$
$270$		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
$279$	−10.2515	−	0.450587i	−0.613740	−	0.0269759i
$280$		0			0
$281$	−12.0212	−	12.0212i	−0.717122	−	0.717122i	0.250893	−	0.968015i	$-0.419276\pi$
$281$	−12.0212	−	12.0212i	−0.717122	−	0.717122i	−0.968015	+	0.250893i	$0.919276\pi$
$282$		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
$285$	23.5541	−	22.5415i	1.39522	−	1.33524i
$286$		0			0
$287$	2.91268			0.171930
$288$		0			0
$289$	21.0727			1.23957
$290$		0			0
$291$	12.9709	−	12.4133i	0.760369	−	0.727682i
$292$		0			0
$293$	−24.7412	+	10.2481i	−1.44539	+	0.598702i	−0.961099	−	0.276203i	$-0.910924\pi$
$293$	−24.7412	+	10.2481i	−1.44539	+	0.598702i	−0.484295	+	0.874905i	$0.660924\pi$
$294$		0			0
$295$	13.5125	+	13.5125i	0.786729	+	0.786729i
$296$		0			0
$297$	−7.18386	−	3.54660i	−0.416850	−	0.205795i
$298$		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
$309$	25.6701	+	0.563871i	1.46032	+	0.0320775i
$310$		0			0
$311$	3.60638	+	3.60638i	0.204499	+	0.204499i	0.801924	−	0.597425i	$-0.203810\pi$
$311$	3.60638	+	3.60638i	0.204499	+	0.204499i	−0.597425	+	0.801924i	$0.703810\pi$
$312$		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
$315$	−8.21113	+	17.5954i	−0.462645	+	0.991389i
$316$		0			0
$317$	−1.42053	+	3.42947i	−0.0797850	+	0.192618i	−0.958738	−	0.284289i	$-0.908242\pi$
$317$	−1.42053	+	3.42947i	−0.0797850	+	0.192618i	0.878954	+	0.476907i	$0.158242\pi$
$318$		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
$327$	−4.92905	−	12.6805i	−0.272577	−	0.701233i
$328$		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
$333$	−18.5936	+	6.76138i	−1.01892	+	0.370521i
$334$		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
$339$	−17.0648	+	16.3312i	−0.926833	+	0.886990i
$340$		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
$345$	−10.0191	+	3.89455i	−0.539413	+	0.209676i
$346$		0			0
$347$	1.37907	+	3.32937i	0.0740325	+	0.178730i	0.956564	−	0.291524i	$-0.0941623\pi$
$347$	1.37907	+	3.32937i	0.0740325	+	0.178730i	−0.882531	+	0.470254i	$0.844162\pi$
$348$		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	$0.0478316\pi$
$353$			5.62531i			0.299405i	−0.988731	+	0.149703i	$0.952168\pi$
$354$		0			0
$355$	11.1838	−	27.0000i	0.593572	−	1.43301i
$356$		0			0
$357$	−29.1996	−	0.641400i	−1.54540	−	0.0339465i
$358$		0			0
$359$	−22.3781	+	22.3781i	−1.18107	+	1.18107i	−0.201603	+	0.979467i	$0.564615\pi$
$359$	−22.3781	+	22.3781i	−1.18107	+	1.18107i	−0.979467	+	0.201603i	$0.935385\pi$
$360$		0			0
$361$	31.2298	+	31.2298i	1.64367	+	1.64367i
$362$		0			0
$363$	0.327984	−	14.9314i	0.0172147	−	0.783696i
$364$		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
$375$	−6.52573	−	16.7881i	−0.336987	−	0.866936i
$376$		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
$381$	−9.28576	−	9.70287i	−0.475724	−	0.497093i
$382$		0			0
$383$	−5.25906			−0.268725			−0.134363	−	0.990932i	$-0.542899\pi$
$383$	−5.25906			−0.268725			−0.134363	+	0.990932i	$0.542899\pi$
$384$		0			0
$385$	9.97932			0.508593
$386$		0			0
$387$	−11.5763	+	4.20960i	−0.588456	+	0.213986i
$388$		0			0
$389$	25.9373	−	10.7436i	1.31507	−	0.544721i	0.388712	−	0.921359i	$-0.372920\pi$
$389$	25.9373	−	10.7436i	1.31507	−	0.544721i	0.926360	+	0.376639i	$0.122920\pi$
$390$		0			0
$391$	−11.4333	−	11.4333i	−0.578204	−	0.578204i
$392$		0			0
$393$	−2.04064	+	0.793219i	−0.102937	+	0.0400126i
$394$		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	$-0.209046\pi$
$401$	31.7191			1.58397			0.791987	+	0.610537i	$0.209046\pi$
$402$		0			0
$403$	−0.911693	−	0.377635i	−0.0454146	−	0.0188114i
$404$		0			0
$405$	−20.3325	+	6.39776i	−1.01033	+	0.317907i
$406$		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
$411$	0.405863	−	18.4768i	0.0200197	−	0.911393i
$412$		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	0.433544	−	0.901132i	$-0.357263\pi$
$419$	2.10652	+	0.872548i	0.102910	+	0.0426268i	−0.330634	+	0.943759i	$0.607263\pi$
$420$		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
$423$	−4.63946	−	0.203920i	−0.225578	−	0.00991492i
$424$		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
$429$	−0.532700	−	0.556628i	−0.0257190	−	0.0268743i
$430$		0			0
$431$		−	2.95351i		−	0.142266i	−0.997467	−	0.0711329i	$-0.977339\pi$
$431$		−	2.95351i		−	0.142266i	0.997467	−	0.0711329i	$-0.0226614\pi$
$432$		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
$435$	−15.6807	−	16.3850i	−0.751830	−	0.785602i
$436$		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
$441$	1.40383	+	0.0617029i	0.0668489	+	0.00293824i
$442$		0			0
$443$	−3.50021	−	8.45026i	−0.166300	−	0.401484i	0.818657	−	0.574283i	$-0.194719\pi$
$443$	−3.50021	−	8.45026i	−0.166300	−	0.401484i	−0.984957	+	0.172799i	$0.944719\pi$
$444$		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	$-0.807547\pi$
$449$		−	24.0900i		−	1.13688i	0.822725	−	0.568439i	$-0.192453\pi$
$450$		0			0
$451$	0.628866	−	1.51822i	0.0296121	−	0.0714901i
$452$		0			0
$453$	−0.527636	+	24.0205i	−0.0247905	+	1.12858i
$454$		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
$459$	−21.1293	−	24.1146i	−0.986231	−	1.12557i
$460$		0			0
$461$	26.4361	+	10.9502i	1.23125	+	0.510001i	0.900970	−	0.433881i	$-0.142856\pi$
$461$	26.4361	+	10.9502i	1.23125	+	0.510001i	0.330282	+	0.943882i	$0.392856\pi$
$462$		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	−0.960865	−	0.277018i	$-0.910654\pi$
$467$	−1.84875	+	4.46327i	−0.0855498	+	0.206536i	0.875315	+	0.483553i	$0.160654\pi$
$468$		0			0
$469$	−3.50818	+	1.45313i	−0.161993	+	0.0670995i
$470$		0			0
$471$	14.4720	−	5.62542i	0.666834	−	0.259206i
$472$		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
$477$	−37.7726	+	13.7356i	−1.72949	+	0.628911i
$478$		0			0
$479$	15.8988			0.726433			0.363216	−	0.931705i	$-0.381679\pi$
$479$	15.8988			0.726433			0.363216	+	0.931705i	$0.381679\pi$
$480$		0			0
$481$	−1.90265			−0.0867535
$482$		0			0
$483$	8.57603	+	8.96126i	0.390223	+	0.407751i
$484$		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
$489$	1.88657	+	4.85341i	0.0853138	+	0.219479i
$490$		0			0
$491$	−0.306137	+	0.126806i	−0.0138158	+	0.00572268i	−0.389581	−	0.920992i	$-0.627380\pi$
$491$	−0.306137	+	0.126806i	−0.0138158	+	0.00572268i	0.375765	+	0.926715i	$0.377380\pi$
$492$		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
$501$	0.100502	−	4.57535i	0.00449012	−	0.204411i
$502$		0			0
$503$	−10.6198	−	10.6198i	−0.473513	−	0.473513i	0.429536	−	0.903050i	$-0.358677\pi$
$503$	−10.6198	−	10.6198i	−0.473513	−	0.473513i	−0.903050	+	0.429536i	$0.858677\pi$
$504$		0			0
$505$	19.1599	−	19.1599i	0.852605	−	0.852605i
$506$		0			0
$507$	−22.3671	−	0.491317i	−0.993358	−	0.0218202i
$508$		0			0
$509$	2.01172	−	4.85673i	0.0891681	−	0.215271i	−0.873004	−	0.487713i	$-0.837831\pi$
$509$	2.01172	−	4.85673i	0.0891681	−	0.215271i	0.962172	+	0.272442i	$0.0878313\pi$
$510$		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
$519$	−16.7609	+	6.51513i	−0.735721	+	0.285983i
$520$		0			0
$521$	−19.9974	+	19.9974i	−0.876102	+	0.876102i	−0.993129	−	0.117027i	$-0.962664\pi$
$521$	−19.9974	+	19.9974i	−0.876102	+	0.876102i	0.117027	+	0.993129i	$0.462664\pi$
$522$		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
$525$	2.08309	−	1.99354i	0.0909134	−	0.0870053i
$526$		0			0
$527$			21.1053i			0.919360i
$528$		0			0
$529$		−	16.1332i		−	0.701443i
$530$		0			0
$531$	22.7487	−	8.27232i	0.987208	−	0.358988i
$532$		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
$537$	−0.00872561	−	0.0224476i	−0.000376538	−	0.000968684i
$538$		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
$549$	5.88502	−	12.6109i	0.251167	−	0.538219i
$550$		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
$555$	27.0467	+	0.594111i	1.14807	+	0.0252186i
$556$		0			0
$557$	9.30090	+	3.85256i	0.394092	+	0.163238i	0.570924	−	0.821003i	$-0.306585\pi$
$557$	9.30090	+	3.85256i	0.394092	+	0.163238i	−0.176832	+	0.984241i	$0.556585\pi$
$558$		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	−0.895553	−	0.444955i	$-0.853220\pi$
$563$	1.24166	−	2.99763i	0.0523297	−	0.126335i	0.947882	+	0.318620i	$0.103220\pi$
$564$		0			0
$565$	29.8392	−	12.3598i	1.25535	−	0.519981i
$566$		0			0
$567$	15.7987	+	18.8505i	0.663483	+	0.791646i
$568$		0			0
$569$	−28.3250	−	28.3250i	−1.18745	−	1.18745i	−0.977771	−	0.209674i	$-0.932760\pi$
$569$	−28.3250	−	28.3250i	−1.18745	−	1.18745i	−0.209674	−	0.977771i	$-0.567240\pi$
$570$		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
$573$	−9.73473	+	9.31626i	−0.406674	+	0.389192i
$574$		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
$579$	7.80249	−	7.46708i	0.324260	−	0.310321i
$580$		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
$585$	−2.04785	−	0.0900101i	−0.0846684	−	0.00372146i
$586$		0			0
$587$	1.77252	−	0.734203i	0.0731599	−	0.0303038i	−0.345803	−	0.938307i	$-0.612394\pi$
$587$	1.77252	−	0.734203i	0.0731599	−	0.0303038i	0.418963	+	0.908003i	$0.362394\pi$
$588$		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	$-0.665271\pi$
$593$	−24.1664			−0.992394			−0.496197	+	0.868210i	$0.665271\pi$
$594$		0			0
$595$	36.8964	+	15.2830i	1.51260	+	0.626541i
$596$		0			0
$597$	−30.4931	−	0.669813i	−1.24800	−	0.0274136i
$598$		0			0
$599$	11.6692	+	11.6692i	0.476789	+	0.476789i	0.904103	−	0.427314i	$-0.140540\pi$
$599$	11.6692	+	11.6692i	0.476789	+	0.476789i	−0.427314	+	0.904103i	$0.640540\pi$
$600$		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
$603$	−3.77738	−	1.76276i	−0.153827	−	0.0717852i
$604$		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
$615$	−1.58401	−	4.07504i	−0.0638736	−	0.164322i
$616$		0			0
$617$	13.5933	−	13.5933i	0.547246	−	0.547246i	−0.378397	−	0.925643i	$-0.623525\pi$
$617$	13.5933	−	13.5933i	0.547246	−	0.547246i	0.925643	+	0.378397i	$0.123525\pi$
$618$		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
$621$	−0.896498	+	13.5868i	−0.0359752	+	0.545219i
$622$		0			0
$623$		−	16.0146i		−	0.641611i
$624$		0			0
$625$			27.6746i			1.10699i
$626$		0			0
$627$	−15.3340	+	14.6749i	−0.612383	+	0.586058i
$628$		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
$633$	−2.04183	+	0.793682i	−0.0811556	+	0.0315460i
$634$		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	$0.0114562\pi$
$641$			1.82203i			0.0719659i	−0.999352	+	0.0359830i	$0.988544\pi$
$642$		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
$645$	16.8392	+	0.369890i	0.663041	+	0.0145644i
$646$		0			0
$647$	27.3258	−	27.3258i	1.07429	−	1.07429i	0.0772785	−	0.997010i	$-0.475377\pi$
$647$	27.3258	−	27.3258i	1.07429	−	1.07429i	0.997010	−	0.0772785i	$-0.0246231\pi$
$648$		0			0
$649$	−8.79684	−	8.79684i	−0.345306	−	0.345306i
$650$		0			0
$651$	0.355554	−	16.1865i	0.0139353	−	0.634400i
$652$		0			0
$653$	−21.5061	−	8.90811i	−0.841598	−	0.348601i	−0.0801145	−	0.996786i	$-0.525529\pi$
$653$	−21.5061	−	8.90811i	−0.841598	−	0.348601i	−0.761483	+	0.648184i	$0.775529\pi$
$654$		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	$-0.532958\pi$
$659$	17.2778	−	41.7123i	0.673048	−	1.62488i	0.776403	−	0.630237i	$-0.217042\pi$
$660$		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
$663$	−1.11709	−	2.87383i	−0.0433841	−	0.111610i
$664$		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
$669$	12.5800	+	13.1451i	0.486370	+	0.508217i
$670$		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
$675$	3.15831	+	0.208395i	0.121564	+	0.00802114i
$676$		0			0
$677$	16.7436	−	6.93541i	0.643507	−	0.266549i	−0.0369727	−	0.999316i	$-0.511771\pi$
$677$	16.7436	−	6.93541i	0.643507	−	0.266549i	0.680480	+	0.732767i	$0.261771\pi$
$678$		0			0
$679$	20.0305	+	20.0305i	0.768701	+	0.768701i
$680$		0			0
$681$	29.3332	−	11.4021i	1.12405	−	0.436930i
$682$		0			0
$683$	−43.5660	+	18.0456i	−1.66701	+	0.690497i	−0.998580	−	0.0532798i	$-0.983032\pi$
$683$	−43.5660	+	18.0456i	−1.66701	+	0.690497i	−0.668428	+	0.743777i	$0.733032\pi$
$684$		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
$693$	5.34557	−	11.4549i	0.203061	−	0.435135i
$694$		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
$699$	−0.136673	+	6.22199i	−0.00516943	+	0.235337i
$700$		0			0
$701$	13.7184	−	33.1190i	0.518135	−	1.25089i	−0.420912	−	0.907101i	$-0.638290\pi$
$701$	13.7184	−	33.1190i	0.518135	−	1.25089i	0.939047	−	0.343787i	$-0.111710\pi$
$702$		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
$711$	−0.363688	+	8.27440i	−0.0136394	+	0.310314i
$712$		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
$717$	21.0897	+	22.0371i	0.787610	+	0.822989i
$718$		0			0
$719$			25.3851i			0.946706i	0.880873	+	0.473353i	$0.156956\pi$
$719$			25.3851i			0.946706i	−0.880873	+	0.473353i	$0.843044\pi$
$720$		0			0
$721$			40.5121i			1.50875i
$722$		0			0
$723$	−7.40840	−	7.74117i	−0.275521	−	0.287897i
$724$		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
$729$	−3.54764	+	26.7659i	−0.131394	+	0.991330i
$730$		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
$741$	0.0872162	−	3.97050i	0.00320397	−	0.145860i
$742$		0			0
$743$	5.42669	−	5.42669i	0.199086	−	0.199086i	−0.600522	−	0.799608i	$-0.705041\pi$
$743$	5.42669	−	5.42669i	0.199086	−	0.199086i	0.799608	+	0.600522i	$0.205041\pi$
$744$		0			0
$745$	2.00839	+	2.00839i	0.0735817	+	0.0735817i
$746$		0			0
$747$	17.9823	+	8.39169i	0.657939	+	0.307036i
$748$		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
$759$	6.52262	−	2.53541i	0.236756	−	0.0920296i
$760$		0			0
$761$	25.8277	+	25.8277i	0.936254	+	0.936254i	0.998087	−	0.0618325i	$-0.0196945\pi$
$761$	25.8277	+	25.8277i	0.936254	+	0.936254i	−0.0618325	+	0.998087i	$0.519694\pi$
$762$		0			0
$763$	19.8317	−	8.21457i	0.717957	−	0.297387i
$764$		0			0
$765$	14.9823	+	41.2010i	0.541688	+	1.48963i
$766$		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
$771$	−14.2312	−	14.8704i	−0.512524	−	0.535546i
$772$		0			0
$773$	8.07057	−	3.34294i	0.290278	−	0.120237i	−0.232793	−	0.972526i	$-0.574786\pi$
$773$	8.07057	−	3.34294i	0.290278	−	0.120237i	0.523071	+	0.852289i	$0.324786\pi$
$774$		0			0
$775$	−1.47328	−	1.47328i	−0.0529219	−	0.0529219i
$776$		0			0
$777$	−11.3098	−	29.0957i	−0.405738	−	1.04380i
$778$		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
$789$	0.625023	−	28.4540i	0.0222514	−	1.01299i
$790$		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
$795$	54.9449	+	1.20692i	1.94870	+	0.0428052i
$796$		0			0
$797$	−9.64229	+	23.2785i	−0.341547	+	0.824568i	0.656012	+	0.754750i	$0.272242\pi$
$797$	−9.64229	+	23.2785i	−0.341547	+	0.824568i	−0.997560	+	0.0698182i	$0.977758\pi$
$798$		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
$807$	24.0230	−	9.33801i	0.845651	−	0.328713i
$808$		0			0
$809$	24.9240	−	24.9240i	0.876282	−	0.876282i	−0.116866	−	0.993148i	$-0.537285\pi$
$809$	24.9240	−	24.9240i	0.876282	−	0.876282i	0.993148	+	0.116866i	$0.0372847\pi$
$810$		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
$813$	−8.85073	+	8.47026i	−0.310409	+	0.297065i
$814$		0			0
$815$		−	7.12017i		−	0.249409i
$816$		0			0
$817$			32.6330i			1.14168i
$818$		0			0
$819$	0.808327	+	2.22288i	0.0282452	+	0.0776737i
$820$		0			0
$821$	−9.49765	−	22.9294i	−0.331470	−	0.800240i	−0.998476	−	0.0551876i	$-0.982424\pi$
$821$	−9.49765	−	22.9294i	−0.331470	−	0.800240i	0.667006	−	0.745053i	$-0.267576\pi$
$822$		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
$825$	−0.589369	−	1.51621i	−0.0205192	−	0.0527878i
$826$		0			0
$827$	20.6867	+	49.9420i	0.719345	+	1.73665i	0.675207	+	0.737628i	$0.264054\pi$
$827$	20.6867	+	49.9420i	0.719345	+	1.73665i	0.0441379	+	0.999025i	$0.485946\pi$
$828$		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
$837$	13.3677	−	11.7128i	0.462057	−	0.404855i
$838$		0			0
$839$	−27.7697	+	27.7697i	−0.958717	+	0.958717i	−0.999181	−	0.0404644i	$-0.987116\pi$
$839$	−27.7697	+	27.7697i	−0.958717	+	0.958717i	0.0404644	+	0.999181i	$0.487116\pi$
$840$		0			0
$841$	−1.10756	−	1.10756i	−0.0381918	−	0.0381918i
$842$		0			0
$843$	29.4386	+	0.646651i	1.01392	+	0.0222718i
$844$		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
$855$	−2.47960	+	56.4145i	−0.0848007	+	1.92933i
$856$		0			0
$857$	13.1734	+	13.1734i	0.449996	+	0.449996i	0.895353	−	0.445357i	$-0.146923\pi$
$857$	13.1734	+	13.1734i	0.449996	+	0.449996i	−0.445357	+	0.895353i	$0.646923\pi$
$858$		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
$861$	−3.64477	+	3.48809i	−0.124214	+	0.118874i
$862$		0			0
$863$	−19.3590			−0.658989			−0.329494	−	0.944158i	$-0.606878\pi$
$863$	−19.3590			−0.658989			−0.329494	+	0.944158i	$0.606878\pi$
$864$		0			0
$865$	24.5889			0.836049
$866$		0			0
$867$	−26.3692	+	25.2357i	−0.895547	+	0.857049i
$868$		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
$873$	−1.36549	+	31.0667i	−0.0462147	+	1.05145i
$874$		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	$-0.712042\pi$
$881$	−36.6844			−1.23593			−0.617964	+	0.786207i	$0.712042\pi$
$882$		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
$885$	−33.0908	−	0.726874i	−1.11233	−	0.0244336i
$886$		0			0
$887$	−34.3135	−	34.3135i	−1.15213	−	1.15213i	−0.986124	−	0.166009i	$-0.946912\pi$
$887$	−34.3135	−	34.3135i	−1.15213	−	1.15213i	−0.166009	−	0.986124i	$-0.553088\pi$
$888$		0			0
$889$	14.9838	−	14.9838i	0.502540	−	0.502540i
$890$		0			0
$891$	13.2367	−	4.16503i	0.443447	−	0.139534i
$892$		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
$903$	−7.04144	−	18.1149i	−0.234324	−	0.602825i
$904$		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
$909$	−11.7297	−	32.2562i	−0.389048	−	1.06987i
$910$		0			0
$911$		−	10.5385i		−	0.349157i	−0.984643	−	0.174579i	$-0.944144\pi$
$911$		−	10.5385i		−	0.349157i	0.984643	−	0.174579i	$-0.0558563\pi$
$912$		0			0
$913$		−	10.1988i		−	0.337530i
$914$		0			0
$915$	−13.7478	+	13.1568i	−0.454488	+	0.434950i
$916$		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
$921$	−1.16092	+	0.451262i	−0.0382536	+	0.0148696i
$922$		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	$0.00268840\pi$
$929$			0.514845i			0.0168915i	−0.999964	+	0.00844575i	$0.997312\pi$
$930$		0			0
$931$	1.42460	−	3.43928i	0.0466892	−	0.112718i
$932$		0			0
$933$	−8.83166	−	0.193997i	−0.289136	−	0.00635117i
$934$		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
$939$	−1.24924	+	56.8715i	−0.0407675	+	1.85593i
$940$		0			0
$941$	−8.26022	−	3.42149i	−0.269275	−	0.111538i	0.243960	−	0.969785i	$-0.421553\pi$
$941$	−8.26022	−	3.42149i	−0.269275	−	0.111538i	−0.513236	+	0.858248i	$0.671553\pi$
$942$		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	−0.894347	−	0.447373i	$-0.852359\pi$
$947$	1.67384	−	4.04101i	0.0543926	−	0.131315i	0.948740	+	0.316058i	$0.102359\pi$
$948$		0			0
$949$	−1.02914	+	0.426286i	−0.0334074	+	0.0138378i
$950$		0			0
$951$	−2.32939	−	5.99261i	−0.0755357	−	0.194324i
$952$		0			0
$953$	32.0579	+	32.0579i	1.03846	+	1.03846i	0.999230	+	0.0392279i	$0.0124898\pi$
$953$	32.0579	+	32.0579i	1.03846	+	1.03846i	0.0392279	+	0.999230i	$0.487510\pi$
$954$		0			0
$955$	17.0220	−	7.05074i	0.550819	−	0.228157i
$956$		0			0
$957$	10.2083	+	10.6669i	0.329989	+	0.344812i
$958$		0			0
$959$	29.1598			0.941619
$960$		0			0
$961$	19.3005			0.622596
$962$		0			0
$963$	−10.4266	−	28.6728i	−0.335992	−	0.923970i
$964$		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
$969$	−79.1684	+	30.7736i	−2.54326	+	0.988591i
$970$		0			0
$971$	−33.0754	+	13.7003i	−1.06144	+	0.439663i	−0.843962	−	0.536402i	$-0.819783\pi$
$971$	−33.0754	+	13.7003i	−1.06144	+	0.439663i	−0.217478	+	0.976065i	$0.569783\pi$
$972$		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	$-0.719346\pi$
$977$	−39.7489			−1.27168			−0.635839	+	0.771821i	$0.719346\pi$
$978$		0			0
$979$	−8.34750	−	3.45765i	−0.266787	−	0.110507i
$980$		0			0
$981$	21.3535	+	9.96489i	0.681765	+	0.318155i
$982$		0			0
$983$	29.8565	+	29.8565i	0.952276	+	0.952276i	0.998912	−	0.0466360i	$-0.0148501\pi$
$983$	29.8565	+	29.8565i	0.952276	+	0.952276i	−0.0466360	+	0.998912i	$0.514850\pi$
$984$		0			0
$985$	−12.5214	+	12.5214i	−0.398965	+	0.398965i
$986$		0			0
$987$	0.160912	−	7.32546i	0.00512187	−	0.233172i
$988$		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
$999$	15.1699	−	30.7277i	0.479956	−	0.972181i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.25135 + 1.19755i) q^{3} +(2.18808 - 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(0.131733 - 2.99711i) q^{9} +O(q^{10})\)	\(q+(-1.25135 + 1.19755i) q^{3} +(2.18808 - 0.906333i) q^{5} +(-1.93241 - 1.93241i) q^{7} +(0.131733 - 2.99711i) q^{9} +(-1.42447 + 0.590036i) q^{11} +(0.110405 - 0.266541i) q^{13} +(-1.65266 + 3.75448i) q^{15} -6.17031 q^{17} +(-7.34269 - 3.04144i) q^{19} +(4.73227 + 0.103949i) q^{21} +(1.85295 + 1.85295i) q^{23} +(0.430727 - 0.430727i) q^{25} +(3.42435 + 3.90817i) q^{27} +(-2.11574 + 5.10784i) q^{29} -3.42046i q^{31} +(1.07591 - 2.44422i) q^{33} +(-5.97967 - 2.47686i) q^{35} +(-2.52377 - 6.09293i) q^{37} +(0.181042 + 0.465751i) q^{39} +(-0.753641 + 0.753641i) q^{41} +(-1.57129 - 3.79343i) q^{43} +(-2.42813 - 6.67731i) q^{45} -1.54798i q^{47} +0.468394i q^{49} +(7.72119 - 7.38927i) q^{51} +(-5.12700 - 12.3777i) q^{53} +(-2.58210 + 2.58210i) q^{55} +(12.8305 - 4.98737i) q^{57} +(3.08775 + 7.45449i) q^{59} +(4.28571 + 1.77520i) q^{61} +(-6.04619 + 5.53707i) q^{63} -0.683277i q^{65} +(0.531731 - 1.28371i) q^{67} +(-4.53768 - 0.0996750i) q^{69} +(8.72539 - 8.72539i) q^{71} +(-2.73022 - 2.73022i) q^{73} +(-0.0231699 + 1.05481i) q^{75} +(3.89285 + 1.61247i) q^{77} -2.76080 q^{79} +(-8.96529 - 0.789635i) q^{81} +(-2.53133 + 6.11116i) q^{83} +(-13.5011 + 5.59235i) q^{85} +(-3.46939 - 8.92538i) q^{87} +(4.14369 + 4.14369i) q^{89} +(-0.728413 + 0.301719i) q^{91} +(4.09618 + 4.28017i) q^{93} -18.8230 q^{95} -10.3656 q^{97} +(1.58075 + 4.34703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more