LMFDB - Embedded newform 384.2.o.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(47,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, 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("384.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.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:	$3.06625543762$
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			47.3
Character	$\chi$	$=$	384.47
Dual form			384.2.o.a.335.3

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			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	−0.813884	−	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	0.970695	−	0.240314i	$-0.0772504\pi$
$7$	1.93241	+	1.93241i	0.730381	+	0.730381i	−0.240314	+	0.970695i	$0.577250\pi$
$8$		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	−0.938450	−	0.345414i	$-0.887738\pi$
$13$	−0.110405	+	0.266541i	−0.0306208	+	0.0739252i	0.907829	+	0.419340i	$0.137738\pi$
$14$		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	0.487023	−	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
$27$	3.42435	+	3.90817i	0.659017	+	0.752128i
$28$		0			0
$29$	2.11574	−	5.10784i	0.392882	−	0.948501i	−0.596427	−	0.802667i	$-0.703413\pi$
$29$	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	$0.0993807\pi$
$31$			3.42046i			0.614332i	−0.951656	+	0.307166i	$0.900619\pi$
$32$		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	$0.0573709\pi$
$37$	2.52377	+	6.09293i	0.414906	+	1.00167i	−0.568895	+	0.822410i	$0.692629\pi$
$38$		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	$0.0360133\pi$
$47$			1.54798i			0.225796i	−0.993607	+	0.112898i	$0.963987\pi$
$48$		0			0
$49$			0.468394i			0.0669135i
$50$		0			0
$51$	7.72119	−	7.38927i	1.08118	−	1.03471i
$52$		0			0
$53$	5.12700	+	12.3777i	0.704248	+	1.70020i	0.713897	+	0.700251i	$0.246928\pi$
$53$	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
$57$	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	0.0910552	−	0.995846i	$-0.470976\pi$
$61$	−4.28571	−	1.77520i	−0.548728	−	0.227291i	−0.639784	+	0.768555i	$0.720976\pi$
$62$		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	$0.511515\pi$
$71$	−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
$75$	−0.0231699	+	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	$-0.450363\pi$
$79$	2.76080			0.310614			0.155307	+	0.987866i	$0.450363\pi$
$80$		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	−0.840519	−	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	$0.0106367\pi$
$103$	10.4823	+	10.4823i	1.03285	+	1.03285i	0.0334101	+	0.999442i	$0.489363\pi$
$104$		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	−0.712064	−	0.702114i	$-0.752240\pi$
$109$	3.00588	−	7.25683i	0.287911	−	0.695078i	0.999975	+	0.00703600i	$0.00223965\pi$
$110$		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	$-0.888209\pi$
$127$		−	7.75395i		−	0.688052i	0.938960	−	0.344026i	$-0.111791\pi$
$128$		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	0.903965	−	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	−0.982815	−	0.184595i	$-0.940903\pi$
$151$	−9.80869	+	9.80869i	−0.798220	+	0.798220i	0.184595	+	0.982815i	$0.440903\pi$
$152$		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	0.687851	−	0.725852i	$-0.258554\pi$
$157$	8.28207	+	3.43055i	0.660981	+	0.273787i	−0.0268702	+	0.999639i	$0.508554\pi$
$158$		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	−0.631114	−	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
$171$	−10.0828	+	21.6062i	−0.771051	+	1.65227i
$172$		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	−0.924078	−	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	−0.705217	−	0.708992i	$-0.749150\pi$
$181$	−9.45181	+	3.91507i	−0.702547	+	0.291005i	0.00266940	+	0.999996i	$0.499150\pi$
$182$		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	$-0.590815\pi$
$191$	−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
$195$	0.818261	+	0.855016i	0.0585969	+	0.0612290i
$196$		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	0.111125	−	0.993806i	$-0.464555\pi$
$199$	−12.4517	−	12.4517i	−0.882681	−	0.882681i	−0.993806	+	0.111125i	$0.964555\pi$
$200$		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	$0.114405\pi$
$223$			10.5047i			0.703449i	−0.936104	+	0.351724i	$0.885595\pi$
$224$		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	$0.0443838\pi$
$229$	5.87646	+	14.1870i	0.388327	+	0.937505i	−0.601967	+	0.798521i	$0.705616\pi$
$230$		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	$0.192890\pi$
$239$			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
$243$	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	−0.251415	−	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
$267$	−10.1475	−	0.222900i	−0.621015	−	0.0136413i
$268$		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	$-0.568919\pi$
$271$	−7.07297			−0.429652			−0.214826	+	0.976652i	$0.568919\pi$
$272$		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	−0.416490	−	0.909140i	$-0.636740\pi$
$277$	−1.13397	+	0.469705i	−0.0681335	+	0.0282218i	0.348356	+	0.937362i	$0.386740\pi$
$278$		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	0.484295	−	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
$297$	−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	0.597425	−	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
$315$	−8.21113	+	17.5954i	−0.462645	+	0.991389i
$316$		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
$327$	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	0.651089	−	0.759002i	$-0.274313\pi$
$349$	10.7378	+	4.44775i	0.574782	+	0.238083i	−0.0763062	+	0.997084i	$0.524313\pi$
$350$		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	$-0.435385\pi$
$359$	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
$363$	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	$-0.262437\pi$
$367$	26.0135			1.35789			0.678946	+	0.734188i	$0.262437\pi$
$368$		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	−0.771942	−	0.635692i	$-0.780715\pi$
$373$	−16.7694	+	6.94611i	−0.868286	+	0.359656i	−0.0963434	+	0.995348i	$0.530715\pi$
$374$		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	$-0.457101\pi$
$383$	5.25906			0.268725			0.134363	+	0.990932i	$0.457101\pi$
$384$		0			0
$385$	9.97932			0.508593
$386$		0			0
$387$	−11.5763	+	4.20960i	−0.588456	+	0.213986i
$388$		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
$393$	−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	$0.521971\pi$
$397$	−14.4580	+	34.9046i	−0.725624	+	1.75181i	−0.656654	+	0.754192i	$0.728029\pi$
$398$		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	0.919684	−	0.392660i	$-0.128445\pi$
$421$	−0.169965	−	0.410331i	−0.00828357	−	0.0199983i	−0.927967	+	0.372662i	$0.878445\pi$
$422$		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	$0.0226614\pi$
$431$			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
$435$	−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	−0.506791	−	0.862069i	$-0.669168\pi$
$439$	7.44392	−	7.44392i	0.355279	−	0.355279i	0.862069	+	0.506791i	$0.169168\pi$
$440$		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	−0.330282	−	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	$-0.812150\pi$
$463$	−35.7558			−1.66171			−0.830857	+	0.556485i	$0.812150\pi$
$464$		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	$-0.618321\pi$
$479$	−15.8988			−0.726433			−0.363216	+	0.931705i	$0.618321\pi$
$480$		0			0
$481$	−1.90265			−0.0867535
$482$		0			0
$483$	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	0.902740	−	0.430187i	$-0.141552\pi$
$487$	10.4283	+	10.4283i	0.472552	+	0.472552i	−0.430187	+	0.902740i	$0.641552\pi$
$488$		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	0.903050	−	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
$507$	−22.3671	−	0.491317i	−0.993358	−	0.0218202i
$508$		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
$519$	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	−0.553618	−	0.832771i	$-0.686753\pi$
$541$	−35.6786	−	14.7786i	−1.53394	−	0.635380i	−0.980325	+	0.197391i	$0.936753\pi$
$542$		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	0.176832	−	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	−0.895553	−	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	0.427314	−	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
$603$	−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	$0.224322\pi$
$607$			31.9215i			1.29565i	−0.761788	+	0.647826i	$0.775678\pi$
$608$		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	$0.00187292\pi$
$613$	7.35458	+	17.7555i	0.297049	+	0.717139i	−0.702934	+	0.711255i	$0.748127\pi$
$614$		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	−0.806242	−	0.591587i	$-0.798502\pi$
$631$	−5.39207	+	5.39207i	−0.214655	+	0.214655i	0.591587	+	0.806242i	$0.298502\pi$
$632$		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	$0.524623\pi$
$647$	−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
$651$	0.355554	−	16.1865i	0.0139353	−	0.634400i
$652$		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	$-0.532958\pi$
$659$	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	$-0.234137\pi$
$661$	44.7407	−	18.5322i	1.74021	−	0.720819i	0.998759	−	0.0498140i	$-0.0158629\pi$
$662$		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	−0.680480	−	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
$681$	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	$0.361710\pi$
$701$	−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	0.895451	−	0.445160i	$-0.146853\pi$
$709$	−1.39804	−	3.37516i	−0.0525044	−	0.126757i	−0.947955	+	0.318403i	$0.896853\pi$
$710$		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	$-0.843044\pi$
$719$		−	25.3851i		−	0.946706i	0.880873	−	0.473353i	$-0.156956\pi$
$720$		0			0
$721$			40.5121i			1.50875i
$722$		0			0
$723$	−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	$-0.424727\pi$
$727$	32.5294	−	32.5294i	1.20645	−	1.20645i	0.972169	−	0.234280i	$-0.0752734\pi$
$728$		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	0.811814	−	0.583917i	$-0.198481\pi$
$733$	26.3419	+	10.9112i	0.972961	+	0.403014i	0.161147	+	0.986930i	$0.448481\pi$
$734$		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	−0.799608	−	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
$747$	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	$-0.521370\pi$
$751$	−3.67683			−0.134170			−0.0670848	+	0.997747i	$0.521370\pi$
$752$		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	−0.607526	−	0.794299i	$-0.707838\pi$
$757$	−13.0816	+	5.41857i	−0.475458	+	0.196941i	0.132068	+	0.991241i	$0.457838\pi$
$758$		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	−0.523071	−	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
$777$	−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	$-0.727758\pi$
$797$	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
$807$	−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	$0.0175757\pi$
$821$	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	−0.998812	−	0.0487391i	$-0.984480\pi$
$823$	−27.2557	+	27.2557i	−0.950072	+	0.950072i	0.0487391	+	0.998812i	$0.484480\pi$
$824$		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	0.376424	−	0.926447i	$-0.377153\pi$
$829$	−0.359915	−	0.149082i	−0.0125004	−	0.00517782i	−0.388925	+	0.921269i	$0.627153\pi$
$830$		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	−0.0404644	−	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
$843$	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	−0.00401354	−	0.999992i	$-0.501278\pi$
$853$	20.4516	−	8.47133i	0.700250	−	0.290053i	0.704263	+	0.709939i	$0.251278\pi$
$854$		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	$-0.393122\pi$
$863$	19.3590			0.658989			0.329494	+	0.944158i	$0.393122\pi$
$864$		0			0
$865$	24.5889			0.836049
$866$		0			0
$867$	−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	−0.993544	−	0.113444i	$-0.963812\pi$
$877$	−6.24223	+	15.0701i	−0.210785	+	0.508880i	0.782759	+	0.622325i	$0.213812\pi$
$878$		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	$0.0530880\pi$
$887$	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
$891$	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	$0.0558563\pi$
$911$			10.5385i			0.349157i	−0.984643	+	0.174579i	$0.944144\pi$
$912$		0			0
$913$		−	10.1988i		−	0.337530i
$914$		0			0
$915$	−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	−0.876588	−	0.481242i	$-0.840186\pi$
$919$	−11.9849	+	11.9849i	−0.395346	+	0.395346i	0.481242	+	0.876588i	$0.340186\pi$
$920$		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	0.513236	−	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	−0.894347	−	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	$0.0740190\pi$
$967$	37.4258	+	37.4258i	1.20353	+	1.20353i	0.230448	+	0.973085i	$0.425981\pi$
$968$		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	0.0466360	−	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
$987$	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	$0.351884\pi$
$991$			56.2662i			1.78736i	−0.448710	+	0.893678i	$0.648116\pi$
$992$		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	$0.0697376\pi$
$997$	13.8797	+	33.5085i	0.439574	+	1.06122i	−0.536523	+	0.843886i	$0.680262\pi$
$998$		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	384.2.o.a.47.3		56
3.2	odd	2	inner	384.2.o.a.47.8		56
4.3	odd	2		96.2.o.a.35.13	yes	56
8.3	odd	2		768.2.o.b.95.3		56
8.5	even	2		768.2.o.a.95.12		56
12.11	even	2		96.2.o.a.35.2	yes	56
24.5	odd	2		768.2.o.a.95.7		56
24.11	even	2		768.2.o.b.95.8		56
32.5	even	8		768.2.o.b.671.8		56
32.11	odd	8	inner	384.2.o.a.335.8		56
32.21	even	8		96.2.o.a.11.2	✓	56
32.27	odd	8		768.2.o.a.671.7		56
96.5	odd	8		768.2.o.b.671.3		56
96.11	even	8	inner	384.2.o.a.335.3		56
96.53	odd	8		96.2.o.a.11.13	yes	56
96.59	even	8		768.2.o.a.671.12		56

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

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.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