LMFDB - Embedded newform 384.2.n.a.49.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(49,384)]

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([0, 5, 0]))

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

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

chi := DirichletCharacter("384.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.n (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.8
Character	$\chi$	$=$	384.49
Dual form			384.2.n.a.337.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 - 0.382683i) q^{3} +(1.36206 - 3.28830i) q^{5} +(2.73097 + 2.73097i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(0.923880 - 0.382683i) q^{3} +(1.36206 - 3.28830i) q^{5} +(2.73097 + 2.73097i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-3.01609 - 1.24931i) q^{11} +(0.932498 + 2.25125i) q^{13} -3.55923i q^{15} -0.517450i q^{17} +(-1.52739 - 3.68744i) q^{19} +(3.56818 + 1.47799i) q^{21} +(-2.39792 + 2.39792i) q^{23} +(-5.42220 - 5.42220i) q^{25} +(0.382683 - 0.923880i) q^{27} +(7.09056 - 2.93701i) q^{29} +1.50132 q^{31} -3.26460 q^{33} +(12.7000 - 5.26051i) q^{35} +(-3.40814 + 8.22797i) q^{37} +(1.72303 + 1.72303i) q^{39} +(-3.21656 + 3.21656i) q^{41} +(1.31346 + 0.544054i) q^{43} +(-1.36206 - 3.28830i) q^{45} +4.67448i q^{47} +7.91635i q^{49} +(-0.198019 - 0.478061i) q^{51} +(-4.19534 - 1.73777i) q^{53} +(-8.21621 + 8.21621i) q^{55} +(-2.82224 - 2.82224i) q^{57} +(0.680868 - 1.64376i) q^{59} +(6.71487 - 2.78139i) q^{61} +3.86217 q^{63} +8.67291 q^{65} +(-11.1312 + 4.61070i) q^{67} +(-1.29774 + 3.13303i) q^{69} +(-1.86620 - 1.86620i) q^{71} +(-9.06859 + 9.06859i) q^{73} +(-7.08445 - 2.93447i) q^{75} +(-4.82504 - 11.6487i) q^{77} -10.4412i q^{79} -1.00000i q^{81} +(1.89340 + 4.57106i) q^{83} +(-1.70153 - 0.704798i) q^{85} +(5.42688 - 5.42688i) q^{87} +(-2.70762 - 2.70762i) q^{89} +(-3.60147 + 8.69471i) q^{91} +(1.38704 - 0.574529i) q^{93} -14.2058 q^{95} +3.73293 q^{97} +(-3.01609 + 1.24931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

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
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$4$		0			0
$5$	1.36206	−	3.28830i	0.609132	−	1.47057i	−0.254814	−	0.966990i	$-0.582014\pi$
$5$	1.36206	−	3.28830i	0.609132	−	1.47057i	0.863946	−	0.503584i	$-0.167986\pi$
$6$		0			0
$7$	2.73097	+	2.73097i	1.03221	+	1.03221i	0.999464	+	0.0327442i	$0.0104247\pi$
$7$	2.73097	+	2.73097i	1.03221	+	1.03221i	0.0327442	+	0.999464i	$0.489575\pi$
$8$		0			0
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$		0			0
$11$	−3.01609	−	1.24931i	−0.909387	−	0.376680i	−0.121565	−	0.992583i	$-0.538791\pi$
$11$	−3.01609	−	1.24931i	−0.909387	−	0.376680i	−0.787822	+	0.615903i	$0.788791\pi$
$12$		0			0
$13$	0.932498	+	2.25125i	0.258628	+	0.624384i	0.998848	−	0.0479806i	$-0.0152786\pi$
$13$	0.932498	+	2.25125i	0.258628	+	0.624384i	−0.740220	+	0.672365i	$0.765279\pi$
$14$		0			0
$15$		−	3.55923i		−	0.918990i
$16$		0			0
$17$		−	0.517450i		−	0.125500i	−0.998029	−	0.0627500i	$-0.980013\pi$
$17$		−	0.517450i		−	0.125500i	0.998029	−	0.0627500i	$-0.0199871\pi$
$18$		0			0
$19$	−1.52739	−	3.68744i	−0.350407	−	0.845956i	−0.996570	−	0.0827570i	$-0.973627\pi$
$19$	−1.52739	−	3.68744i	−0.350407	−	0.845956i	0.646163	−	0.763199i	$-0.276373\pi$
$20$		0			0
$21$	3.56818	+	1.47799i	0.778640	+	0.322523i
$22$		0			0
$23$	−2.39792	+	2.39792i	−0.500000	+	0.500000i	−0.911438	−	0.411438i	$-0.865027\pi$
$23$	−2.39792	+	2.39792i	−0.500000	+	0.500000i	0.411438	+	0.911438i	$0.365027\pi$
$24$		0			0
$25$	−5.42220	−	5.42220i	−1.08444	−	1.08444i
$26$		0			0
$27$	0.382683	−	0.923880i	0.0736475	−	0.177801i
$28$		0			0
$29$	7.09056	−	2.93701i	1.31668	−	0.545389i	0.389857	−	0.920875i	$-0.372524\pi$
$29$	7.09056	−	2.93701i	1.31668	−	0.545389i	0.926828	+	0.375487i	$0.122524\pi$
$30$		0			0
$31$	1.50132			0.269644			0.134822	−	0.990870i	$-0.456954\pi$
$31$	1.50132			0.269644			0.134822	+	0.990870i	$0.456954\pi$
$32$		0			0
$33$	−3.26460			−0.568293
$34$		0			0
$35$	12.7000	−	5.26051i	2.14669	−	0.889188i
$36$		0			0
$37$	−3.40814	+	8.22797i	−0.560294	+	1.35267i	0.349237	+	0.937034i	$0.386441\pi$
$37$	−3.40814	+	8.22797i	−0.560294	+	1.35267i	−0.909531	+	0.415635i	$0.863559\pi$
$38$		0			0
$39$	1.72303	+	1.72303i	0.275906	+	0.275906i
$40$		0			0
$41$	−3.21656	+	3.21656i	−0.502342	+	0.502342i	−0.912165	−	0.409823i	$-0.865590\pi$
$41$	−3.21656	+	3.21656i	−0.502342	+	0.502342i	0.409823	+	0.912165i	$0.365590\pi$
$42$		0			0
$43$	1.31346	+	0.544054i	0.200301	+	0.0829675i	0.480579	−	0.876951i	$-0.340427\pi$
$43$	1.31346	+	0.544054i	0.200301	+	0.0829675i	−0.280278	+	0.959919i	$0.590427\pi$
$44$		0			0
$45$	−1.36206	−	3.28830i	−0.203044	−	0.490191i
$46$		0			0
$47$			4.67448i			0.681843i	0.940092	+	0.340921i	$0.110739\pi$
$47$			4.67448i			0.681843i	−0.940092	+	0.340921i	$0.889261\pi$
$48$		0			0
$49$			7.91635i			1.13091i
$50$		0			0
$51$	−0.198019	−	0.478061i	−0.0277283	−	0.0669419i
$52$		0			0
$53$	−4.19534	−	1.73777i	−0.576275	−	0.238701i	0.0754586	−	0.997149i	$-0.475958\pi$
$53$	−4.19534	−	1.73777i	−0.576275	−	0.238701i	−0.651733	+	0.758448i	$0.725958\pi$
$54$		0			0
$55$	−8.21621	+	8.21621i	−1.10787	+	1.10787i
$56$		0			0
$57$	−2.82224	−	2.82224i	−0.373815	−	0.373815i
$58$		0			0
$59$	0.680868	−	1.64376i	0.0886415	−	0.213999i	−0.873342	−	0.487108i	$-0.838052\pi$
$59$	0.680868	−	1.64376i	0.0886415	−	0.213999i	0.961983	+	0.273109i	$0.0880518\pi$
$60$		0			0
$61$	6.71487	−	2.78139i	0.859751	−	0.356121i	0.0911409	−	0.995838i	$-0.470949\pi$
$61$	6.71487	−	2.78139i	0.859751	−	0.356121i	0.768610	+	0.639717i	$0.220949\pi$
$62$		0			0
$63$	3.86217			0.486587
$64$		0			0
$65$	8.67291			1.07574
$66$		0			0
$67$	−11.1312	+	4.61070i	−1.35989	+	0.563286i	−0.939029	−	0.343837i	$-0.888273\pi$
$67$	−11.1312	+	4.61070i	−1.35989	+	0.563286i	−0.420864	+	0.907124i	$0.638273\pi$
$68$		0			0
$69$	−1.29774	+	3.13303i	−0.156230	+	0.377172i
$70$		0			0
$71$	−1.86620	−	1.86620i	−0.221477	−	0.221477i	0.587643	−	0.809120i	$-0.300056\pi$
$71$	−1.86620	−	1.86620i	−0.221477	−	0.221477i	−0.809120	+	0.587643i	$0.800056\pi$
$72$		0			0
$73$	−9.06859	+	9.06859i	−1.06140	+	1.06140i	−0.0634101	+	0.997988i	$0.520198\pi$
$73$	−9.06859	+	9.06859i	−1.06140	+	1.06140i	−0.997988	+	0.0634101i	$0.979802\pi$
$74$		0			0
$75$	−7.08445	−	2.93447i	−0.818042	−	0.338844i
$76$		0			0
$77$	−4.82504	−	11.6487i	−0.549864	−	1.32749i
$78$		0			0
$79$		−	10.4412i		−	1.17473i	−0.809323	−	0.587364i	$-0.800166\pi$
$79$		−	10.4412i		−	1.17473i	0.809323	−	0.587364i	$-0.199834\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	1.89340	+	4.57106i	0.207827	+	0.501739i	0.993081	−	0.117435i	$-0.0374673\pi$
$83$	1.89340	+	4.57106i	0.207827	+	0.501739i	−0.785253	+	0.619175i	$0.787467\pi$
$84$		0			0
$85$	−1.70153	−	0.704798i	−0.184557	−	0.0764460i
$86$		0			0
$87$	5.42688	−	5.42688i	0.581823	−	0.581823i
$88$		0			0
$89$	−2.70762	−	2.70762i	−0.287007	−	0.287007i	0.548888	−	0.835896i	$-0.315051\pi$
$89$	−2.70762	−	2.70762i	−0.287007	−	0.287007i	−0.835896	+	0.548888i	$0.815051\pi$
$90$		0			0
$91$	−3.60147	+	8.69471i	−0.377536	+	0.911453i
$92$		0			0
$93$	1.38704	−	0.574529i	0.143829	−	0.0595759i
$94$		0			0
$95$	−14.2058			−1.45749
$96$		0			0
$97$	3.73293			0.379022			0.189511	−	0.981879i	$-0.439310\pi$
$97$	3.73293			0.379022			0.189511	+	0.981879i	$0.439310\pi$
$98$		0			0
$99$	−3.01609	+	1.24931i	−0.303129	+	0.125560i
$100$		0			0
$101$	−6.36949	+	15.3773i	−0.633788	+	1.53010i	0.201036	+	0.979584i	$0.435569\pi$
$101$	−6.36949	+	15.3773i	−0.633788	+	1.53010i	−0.834824	+	0.550517i	$0.814431\pi$
$102$		0			0
$103$	7.42244	+	7.42244i	0.731355	+	0.731355i	0.970888	−	0.239533i	$-0.0769944\pi$
$103$	7.42244	+	7.42244i	0.731355	+	0.731355i	−0.239533	+	0.970888i	$0.576994\pi$
$104$		0			0
$105$	9.72015	−	9.72015i	0.948589	−	0.948589i
$106$		0			0
$107$	−7.85343	−	3.25300i	−0.759220	−	0.314479i	−0.0307226	−	0.999528i	$-0.509781\pi$
$107$	−7.85343	−	3.25300i	−0.759220	−	0.314479i	−0.728497	+	0.685049i	$0.759781\pi$
$108$		0			0
$109$	3.33028	+	8.04001i	0.318983	+	0.770094i	0.999308	+	0.0371832i	$0.0118385\pi$
$109$	3.33028	+	8.04001i	0.318983	+	0.770094i	−0.680325	+	0.732910i	$0.738161\pi$
$110$		0			0
$111$			8.90589i			0.845310i
$112$		0			0
$113$			17.4463i			1.64121i	0.571494	+	0.820606i	$0.306364\pi$
$113$			17.4463i			1.64121i	−0.571494	+	0.820606i	$0.693636\pi$
$114$		0			0
$115$	4.61897	+	11.1512i	0.430721	+	1.03985i
$116$		0			0
$117$	2.25125	+	0.932498i	0.208128	+	0.0862095i
$118$		0			0
$119$	1.41314	−	1.41314i	0.129542	−	0.129542i
$120$		0			0
$121$	−0.242116	−	0.242116i	−0.0220105	−	0.0220105i
$122$		0			0
$123$	−1.74079	+	4.20263i	−0.156962	+	0.378939i
$124$		0			0
$125$	−8.77369	+	3.63418i	−0.784743	+	0.325051i
$126$		0			0
$127$	−1.84791			−0.163975			−0.0819876	−	0.996633i	$-0.526127\pi$
$127$	−1.84791			−0.163975			−0.0819876	+	0.996633i	$0.526127\pi$
$128$		0			0
$129$	1.42168			0.125172
$130$		0			0
$131$	7.59353	−	3.14534i	0.663450	−	0.274810i	−0.0254395	−	0.999676i	$-0.508099\pi$
$131$	7.59353	−	3.14534i	0.663450	−	0.274810i	0.688889	+	0.724866i	$0.258099\pi$
$132$		0			0
$133$	5.89902	−	14.2415i	0.511510	−	1.23490i
$134$		0			0
$135$	−2.51676	−	2.51676i	−0.216608	−	0.216608i
$136$		0			0
$137$	7.98582	−	7.98582i	0.682274	−	0.682274i	−0.278238	−	0.960512i	$-0.589750\pi$
$137$	7.98582	−	7.98582i	0.682274	−	0.682274i	0.960512	+	0.278238i	$0.0897503\pi$
$138$		0			0
$139$	−1.52261	−	0.630686i	−0.129146	−	0.0534941i	0.317174	−	0.948367i	$-0.397266\pi$
$139$	−1.52261	−	0.630686i	−0.129146	−	0.0534941i	−0.446321	+	0.894873i	$0.647266\pi$
$140$		0			0
$141$	1.78885	+	4.31865i	0.150648	+	0.363696i
$142$		0			0
$143$		−	7.95496i		−	0.665227i
$144$		0			0
$145$		−	27.3163i		−	2.26850i
$146$		0			0
$147$	3.02945	+	7.31375i	0.249865	+	0.603228i
$148$		0			0
$149$	−3.85004	−	1.59474i	−0.315408	−	0.130646i	0.219363	−	0.975643i	$-0.429602\pi$
$149$	−3.85004	−	1.59474i	−0.315408	−	0.130646i	−0.534771	+	0.844997i	$0.679602\pi$
$150$		0			0
$151$	0.409447	−	0.409447i	0.0333203	−	0.0333203i	−0.690250	−	0.723571i	$-0.742500\pi$
$151$	0.409447	−	0.409447i	0.0333203	−	0.0333203i	0.723571	+	0.690250i	$0.242500\pi$
$152$		0			0
$153$	−0.365892	−	0.365892i	−0.0295806	−	0.0295806i
$154$		0			0
$155$	2.04488	−	4.93678i	0.164249	−	0.396532i
$156$		0			0
$157$	−12.1456	+	5.03087i	−0.969324	+	0.401507i	−0.810461	−	0.585793i	$-0.800783\pi$
$157$	−12.1456	+	5.03087i	−0.969324	+	0.401507i	−0.158864	+	0.987301i	$0.550783\pi$
$158$		0			0
$159$	−4.54101			−0.360125
$160$		0			0
$161$	−13.0973			−1.03221
$162$		0			0
$163$	15.6056	−	6.46405i	1.22233	−	0.506304i	0.324177	−	0.945996i	$-0.394913\pi$
$163$	15.6056	−	6.46405i	1.22233	−	0.506304i	0.898148	+	0.439693i	$0.144913\pi$
$164$		0			0
$165$	−4.44658	+	10.7350i	−0.346166	+	0.835718i
$166$		0			0
$167$	3.65825	+	3.65825i	0.283084	+	0.283084i	0.834338	−	0.551254i	$-0.185850\pi$
$167$	3.65825	+	3.65825i	0.283084	+	0.283084i	−0.551254	+	0.834338i	$0.685850\pi$
$168$		0			0
$169$	4.99382	−	4.99382i	0.384140	−	0.384140i
$170$		0			0
$171$	−3.68744	−	1.52739i	−0.281985	−	0.116802i
$172$		0			0
$173$	−4.69766	−	11.3412i	−0.357156	−	0.862252i	−0.995697	−	0.0926640i	$-0.970462\pi$
$173$	−4.69766	−	11.3412i	−0.357156	−	0.862252i	0.638541	−	0.769588i	$-0.279538\pi$
$174$		0			0
$175$		−	29.6157i		−	2.23874i
$176$		0			0
$177$		−	1.77919i		−	0.133732i
$178$		0			0
$179$	−2.26551	−	5.46943i	−0.169332	−	0.408804i	0.816318	−	0.577602i	$-0.196011\pi$
$179$	−2.26551	−	5.46943i	−0.169332	−	0.408804i	−0.985651	+	0.168798i	$0.946011\pi$
$180$		0			0
$181$	−14.5765	−	6.03777i	−1.08346	−	0.448784i	−0.231738	−	0.972778i	$-0.574441\pi$
$181$	−14.5765	−	6.03777i	−1.08346	−	0.448784i	−0.851722	+	0.523994i	$0.824441\pi$
$182$		0			0
$183$	5.13934	−	5.13934i	0.379911	−	0.379911i
$184$		0			0
$185$	22.4140	+	22.4140i	1.64791	+	1.64791i
$186$		0			0
$187$	−0.646454	+	1.56068i	−0.0472734	+	0.114128i
$188$		0			0
$189$	3.56818	−	1.47799i	0.259547	−	0.107508i
$190$		0			0
$191$	12.3765			0.895535			0.447768	−	0.894150i	$-0.352219\pi$
$191$	12.3765			0.895535			0.447768	+	0.894150i	$0.352219\pi$
$192$		0			0
$193$	21.9343			1.57887			0.789434	−	0.613835i	$-0.210374\pi$
$193$	21.9343			1.57887			0.789434	+	0.613835i	$0.210374\pi$
$194$		0			0
$195$	8.01273	−	3.31898i	0.573803	−	0.237677i
$196$		0			0
$197$	6.52756	−	15.7589i	0.465070	−	1.12278i	−0.501220	−	0.865320i	$-0.667115\pi$
$197$	6.52756	−	15.7589i	0.465070	−	1.12278i	0.966290	−	0.257458i	$-0.0828847\pi$
$198$		0			0
$199$	−5.80270	−	5.80270i	−0.411343	−	0.411343i	0.470863	−	0.882206i	$-0.343942\pi$
$199$	−5.80270	−	5.80270i	−0.411343	−	0.411343i	−0.882206	+	0.470863i	$0.843942\pi$
$200$		0			0
$201$	−8.51946	+	8.51946i	−0.600916	+	0.600916i
$202$		0			0
$203$	27.3850	+	11.3432i	1.92205	+	0.796138i
$204$		0			0
$205$	6.19587	+	14.9582i	0.432738	+	1.04472i
$206$		0			0
$207$			3.39117i			0.235702i
$208$		0			0
$209$			13.0298i			0.901293i
$210$		0			0
$211$	−7.65444	−	18.4794i	−0.526953	−	1.27218i	−0.933510	−	0.358552i	$-0.883271\pi$
$211$	−7.65444	−	18.4794i	−0.526953	−	1.27218i	0.406557	−	0.913626i	$-0.366729\pi$
$212$		0			0
$213$	−2.43831	−	1.00998i	−0.167070	−	0.0692026i
$214$		0			0
$215$	3.57803	−	3.57803i	0.244020	−	0.244020i
$216$		0			0
$217$	4.10004	+	4.10004i	0.278329	+	0.278329i
$218$		0			0
$219$	−4.90788	+	11.8487i	−0.331644	+	0.800659i
$220$		0			0
$221$	1.16491	−	0.482521i	0.0783602	−	0.0324579i
$222$		0			0
$223$	29.0773			1.94716			0.973580	−	0.228346i	$-0.0733317\pi$
$223$	29.0773			1.94716			0.973580	+	0.228346i	$0.0733317\pi$
$224$		0			0
$225$	−7.66815			−0.511210
$226$		0			0
$227$	−23.2583	+	9.63391i	−1.54371	+	0.639425i	−0.982165	−	0.188022i	$-0.939792\pi$
$227$	−23.2583	+	9.63391i	−1.54371	+	0.639425i	−0.561544	+	0.827447i	$0.689792\pi$
$228$		0			0
$229$	2.92749	−	7.06760i	0.193454	−	0.467040i	−0.797153	−	0.603777i	$-0.793662\pi$
$229$	2.92749	−	7.06760i	0.193454	−	0.467040i	0.990607	+	0.136737i	$0.0436616\pi$
$230$		0			0
$231$	−8.91550	−	8.91550i	−0.586597	−	0.586597i
$232$		0			0
$233$	13.0873	−	13.0873i	0.857375	−	0.857375i	−0.133653	−	0.991028i	$-0.542671\pi$
$233$	13.0873	−	13.0873i	0.857375	−	0.857375i	0.991028	+	0.133653i	$0.0426708\pi$
$234$		0			0
$235$	15.3711	+	6.36692i	1.00270	+	0.415332i
$236$		0			0
$237$	−3.99568	−	9.64642i	−0.259547	−	0.626602i
$238$		0			0
$239$			4.10909i			0.265795i	0.991130	+	0.132897i	$0.0424281\pi$
$239$			4.10909i			0.265795i	−0.991130	+	0.132897i	$0.957572\pi$
$240$		0			0
$241$		−	14.2144i		−	0.915632i	−0.889047	−	0.457816i	$-0.848632\pi$
$241$		−	14.2144i		−	0.915632i	0.889047	−	0.457816i	$-0.151368\pi$
$242$		0			0
$243$	−0.382683	−	0.923880i	−0.0245492	−	0.0592669i
$244$		0			0
$245$	26.0314	+	10.7825i	1.66308	+	0.688871i
$246$		0			0
$247$	6.87706	−	6.87706i	0.437577	−	0.437577i
$248$		0			0
$249$	3.49854	+	3.49854i	0.221711	+	0.221711i
$250$		0			0
$251$	−2.36893	+	5.71910i	−0.149525	+	0.360986i	−0.980840	−	0.194816i	$-0.937589\pi$
$251$	−2.36893	+	5.71910i	−0.149525	+	0.360986i	0.831314	+	0.555803i	$0.187589\pi$
$252$		0			0
$253$	10.2281	−	4.23661i	0.643034	−	0.266353i
$254$		0			0
$255$	−1.84172			−0.115333
$256$		0			0
$257$	−8.28191			−0.516612			−0.258306	−	0.966063i	$-0.583164\pi$
$257$	−8.28191			−0.516612			−0.258306	+	0.966063i	$0.583164\pi$
$258$		0			0
$259$	−31.7778	+	13.1628i	−1.97458	+	0.817896i
$260$		0			0
$261$	2.93701	−	7.09056i	0.181796	−	0.438895i
$262$		0			0
$263$	−15.4068	−	15.4068i	−0.950023	−	0.950023i	0.0487861	−	0.998809i	$-0.484465\pi$
$263$	−15.4068	−	15.4068i	−0.950023	−	0.950023i	−0.998809	+	0.0487861i	$0.984465\pi$
$264$		0			0
$265$	−11.4286	+	11.4286i	−0.702055	+	0.702055i
$266$		0			0
$267$	−3.53768	−	1.46535i	−0.216502	−	0.0896782i
$268$		0			0
$269$	−3.09893	−	7.48148i	−0.188945	−	0.456154i	0.800812	−	0.598916i	$-0.204402\pi$
$269$	−3.09893	−	7.48148i	−0.188945	−	0.456154i	−0.989757	+	0.142762i	$0.954402\pi$
$270$		0			0
$271$			28.7832i			1.74846i	0.485515	+	0.874228i	$0.338632\pi$
$271$			28.7832i			1.74846i	−0.485515	+	0.874228i	$0.661368\pi$
$272$		0			0
$273$			9.41108i			0.569585i
$274$		0			0
$275$	9.57988	+	23.1279i	0.577688	+	1.39466i
$276$		0			0
$277$	−12.1515	−	5.03333i	−0.730115	−	0.302424i	−0.0135158	−	0.999909i	$-0.504302\pi$
$277$	−12.1515	−	5.03333i	−0.730115	−	0.302424i	−0.716599	+	0.697485i	$0.754302\pi$
$278$		0			0
$279$	1.06159	−	1.06159i	0.0635558	−	0.0635558i
$280$		0			0
$281$	−21.6306	−	21.6306i	−1.29037	−	1.29037i	−0.934555	−	0.355820i	$-0.884202\pi$
$281$	−21.6306	−	21.6306i	−1.29037	−	1.29037i	−0.355820	−	0.934555i	$-0.615798\pi$
$282$		0			0
$283$	11.4777	−	27.7097i	0.682281	−	1.64717i	−0.0775002	−	0.996992i	$-0.524694\pi$
$283$	11.4777	−	27.7097i	0.682281	−	1.64717i	0.759781	−	0.650179i	$-0.225306\pi$
$284$		0			0
$285$	−13.1245	+	5.43633i	−0.777426	+	0.322020i
$286$		0			0
$287$	−17.5686			−1.03704
$288$		0			0
$289$	16.7322			0.984250
$290$		0			0
$291$	3.44878	−	1.42853i	0.202171	−	0.0837420i
$292$		0			0
$293$	−1.84257	+	4.44836i	−0.107644	+	0.259876i	−0.968519	−	0.248942i	$-0.919917\pi$
$293$	−1.84257	+	4.44836i	−0.107644	+	0.259876i	0.860874	+	0.508818i	$0.169917\pi$
$294$		0			0
$295$	−4.47780	−	4.47780i	−0.260708	−	0.260708i
$296$		0			0
$297$	−2.30842	+	2.30842i	−0.133948	+	0.133948i
$298$		0			0
$299$	−7.63436	−	3.16226i	−0.441507	−	0.182878i
$300$		0			0
$301$	2.10123	+	5.07282i	0.121113	+	0.292392i
$302$		0			0
$303$			16.6443i			0.956190i
$304$		0			0
$305$		−	25.8690i		−	1.48125i
$306$		0			0
$307$	−11.7403	−	28.3435i	−0.670052	−	1.61765i	−0.781519	−	0.623881i	$-0.785555\pi$
$307$	−11.7403	−	28.3435i	−0.670052	−	1.61765i	0.111467	−	0.993768i	$-0.464445\pi$
$308$		0			0
$309$	9.69789	+	4.01700i	0.551694	+	0.228519i
$310$		0			0
$311$	−11.6121	+	11.6121i	−0.658459	+	0.658459i	−0.955015	−	0.296556i	$-0.904162\pi$
$311$	−11.6121	+	11.6121i	−0.658459	+	0.658459i	0.296556	+	0.955015i	$0.404162\pi$
$312$		0			0
$313$	−6.84409	−	6.84409i	−0.386851	−	0.386851i	0.486712	−	0.873563i	$-0.338196\pi$
$313$	−6.84409	−	6.84409i	−0.386851	−	0.386851i	−0.873563	+	0.486712i	$0.838196\pi$
$314$		0			0
$315$	5.26051	−	12.7000i	0.296396	−	0.715563i
$316$		0			0
$317$	−23.6795	+	9.80835i	−1.32997	+	0.550892i	−0.930647	−	0.365918i	$-0.880755\pi$
$317$	−23.6795	+	9.80835i	−1.32997	+	0.550892i	−0.399324	+	0.916810i	$0.630755\pi$
$318$		0			0
$319$	−25.0550			−1.40281
$320$		0			0
$321$	−8.50049			−0.474451
$322$		0			0
$323$	−1.90806	+	0.790346i	−0.106167	+	0.0439760i
$324$		0			0
$325$	7.15054	−	17.2629i	0.396640	−	0.957575i
$326$		0			0
$327$	6.15356	+	6.15356i	0.340293	+	0.340293i
$328$		0			0
$329$	−12.7658	+	12.7658i	−0.703803	+	0.703803i
$330$		0			0
$331$	21.7107	+	8.99285i	1.19333	+	0.494292i	0.888837	−	0.458224i	$-0.151514\pi$
$331$	21.7107	+	8.99285i	1.19333	+	0.494292i	0.304489	+	0.952516i	$0.401514\pi$
$332$		0			0
$333$	3.40814	+	8.22797i	0.186765	+	0.450890i
$334$		0			0
$335$			42.8828i			2.34294i
$336$		0			0
$337$			24.2394i			1.32040i	0.751088	+	0.660202i	$0.229529\pi$
$337$			24.2394i			1.32040i	−0.751088	+	0.660202i	$0.770471\pi$
$338$		0			0
$339$	6.67642	+	16.1183i	0.362613	+	0.875426i
$340$		0			0
$341$	−4.52811	−	1.87561i	−0.245211	−	0.101570i
$342$		0			0
$343$	−2.50251	+	2.50251i	−0.135123	+	0.135123i
$344$		0			0
$345$	8.53475	+	8.53475i	0.459495	+	0.459495i
$346$		0			0
$347$	1.42236	−	3.43389i	0.0763565	−	0.184341i	−0.881092	−	0.472945i	$-0.843191\pi$
$347$	1.42236	−	3.43389i	0.0763565	−	0.184341i	0.957449	+	0.288604i	$0.0931910\pi$
$348$		0			0
$349$	3.17452	−	1.31493i	0.169928	−	0.0703866i	−0.296098	−	0.955158i	$-0.595685\pi$
$349$	3.17452	−	1.31493i	0.169928	−	0.0703866i	0.466026	+	0.884771i	$0.345685\pi$
$350$		0			0
$351$	2.43674			0.130063
$352$		0			0
$353$	−7.88845			−0.419860			−0.209930	−	0.977716i	$-0.567324\pi$
$353$	−7.88845			−0.419860			−0.209930	+	0.977716i	$0.567324\pi$
$354$		0			0
$355$	−8.67850	+	3.59475i	−0.460607	+	0.190790i
$356$		0			0
$357$	0.764784	−	1.84635i	0.0404767	−	0.0977193i
$358$		0			0
$359$	2.60336	+	2.60336i	0.137400	+	0.137400i	0.772462	−	0.635062i	$-0.219025\pi$
$359$	2.60336	+	2.60336i	0.137400	+	0.137400i	−0.635062	+	0.772462i	$0.719025\pi$
$360$		0			0
$361$	2.17074	−	2.17074i	0.114250	−	0.114250i
$362$		0			0
$363$	−0.316339	−	0.131032i	−0.0166035	−	0.00687740i
$364$		0			0
$365$	17.4683	+	42.1722i	0.914333	+	2.20740i
$366$		0			0
$367$			1.41682i			0.0739575i	0.999316	+	0.0369787i	$0.0117734\pi$
$367$			1.41682i			0.0739575i	−0.999316	+	0.0369787i	$0.988227\pi$
$368$		0			0
$369$			4.54890i			0.236806i
$370$		0			0
$371$	−6.71155	−	16.2031i	−0.348447	−	0.841224i
$372$		0			0
$373$	30.8483	+	12.7778i	1.59726	+	0.661609i	0.991025	−	0.133674i	$-0.0426774\pi$
$373$	30.8483	+	12.7778i	1.59726	+	0.661609i	0.606239	+	0.795282i	$0.292677\pi$
$374$		0			0
$375$	−6.71510	+	6.71510i	−0.346766	+	0.346766i
$376$		0			0
$377$	13.2239	+	13.2239i	0.681064	+	0.681064i
$378$		0			0
$379$	4.79982	−	11.5878i	0.246550	−	0.595224i	−0.751357	−	0.659896i	$-0.770600\pi$
$379$	4.79982	−	11.5878i	0.246550	−	0.595224i	0.997907	+	0.0646720i	$0.0206001\pi$
$380$		0			0
$381$	−1.70724	+	0.707163i	−0.0874647	+	0.0362291i
$382$		0			0
$383$	13.2502			0.677053			0.338527	−	0.940957i	$-0.390071\pi$
$383$	13.2502			0.677053			0.338527	+	0.940957i	$0.390071\pi$
$384$		0			0
$385$	−44.8763			−2.28711
$386$		0			0
$387$	1.31346	−	0.544054i	0.0667671	−	0.0276558i
$388$		0			0
$389$	−1.30717	+	3.15579i	−0.0662762	+	0.160005i	−0.953547	−	0.301243i	$-0.902598\pi$
$389$	−1.30717	+	3.15579i	−0.0662762	+	0.160005i	0.887271	+	0.461248i	$0.152598\pi$
$390$		0			0
$391$	1.24080	+	1.24080i	0.0627500	+	0.0627500i
$392$		0			0
$393$	5.81184	−	5.81184i	0.293168	−	0.293168i
$394$		0			0
$395$	−34.3339	−	14.2215i	−1.72752	−	0.715564i
$396$		0			0
$397$	−2.75561	−	6.65262i	−0.138300	−	0.333886i	0.839521	−	0.543327i	$-0.182836\pi$
$397$	−2.75561	−	6.65262i	−0.138300	−	0.333886i	−0.977821	+	0.209441i	$0.932836\pi$
$398$		0			0
$399$		−	15.4149i		−	0.771710i
$400$		0			0
$401$		−	22.5969i		−	1.12844i	−0.825626	−	0.564218i	$-0.809178\pi$
$401$		−	22.5969i		−	1.12844i	0.825626	−	0.564218i	$-0.190822\pi$
$402$		0			0
$403$	1.39997	+	3.37984i	0.0697377	+	0.168362i
$404$		0			0
$405$	−3.28830	−	1.36206i	−0.163397	−	0.0676813i
$406$		0			0
$407$	20.5585	−	20.5585i	1.01905	−	1.01905i
$408$		0			0
$409$	−3.48618	−	3.48618i	−0.172380	−	0.172380i	0.615644	−	0.788024i	$-0.288896\pi$
$409$	−3.48618	−	3.48618i	−0.172380	−	0.172380i	−0.788024	+	0.615644i	$0.788896\pi$
$410$		0			0
$411$	4.32189	−	10.4340i	0.213183	−	0.514670i
$412$		0			0
$413$	6.34848	−	2.62963i	0.312388	−	0.129395i
$414$		0			0
$415$	17.6100			0.864439
$416$		0			0
$417$	−1.64806			−0.0807059
$418$		0			0
$419$	−9.10369	+	3.77087i	−0.444744	+	0.184219i	−0.593805	−	0.804609i	$-0.702375\pi$
$419$	−9.10369	+	3.77087i	−0.444744	+	0.184219i	0.149061	+	0.988828i	$0.452375\pi$
$420$		0			0
$421$	−0.766817	+	1.85126i	−0.0373724	+	0.0902249i	−0.941464	−	0.337114i	$-0.890549\pi$
$421$	−0.766817	+	1.85126i	−0.0373724	+	0.0902249i	0.904091	+	0.427339i	$0.140549\pi$
$422$		0			0
$423$	3.30535	+	3.30535i	0.160712	+	0.160712i
$424$		0			0
$425$	−2.80572	+	2.80572i	−0.136097	+	0.136097i
$426$		0			0
$427$	25.9340	+	10.7422i	1.25503	+	0.519851i
$428$		0			0
$429$	−3.04423	−	7.34942i	−0.146977	−	0.354834i
$430$		0			0
$431$		−	11.5510i		−	0.556394i	−0.960524	−	0.278197i	$-0.910263\pi$
$431$		−	11.5510i		−	0.556394i	0.960524	−	0.278197i	$-0.0897368\pi$
$432$		0			0
$433$		−	3.12797i		−	0.150321i	−0.997171	−	0.0751603i	$-0.976053\pi$
$433$		−	3.12797i		−	0.150321i	0.997171	−	0.0751603i	$-0.0239468\pi$
$434$		0			0
$435$	−10.4535	−	25.2370i	−0.501207	−	1.21002i
$436$		0			0
$437$	12.5047	+	5.17962i	0.598182	+	0.247775i
$438$		0			0
$439$	−8.10867	+	8.10867i	−0.387006	+	0.387006i	−0.873618	−	0.486612i	$-0.838232\pi$
$439$	−8.10867	+	8.10867i	−0.387006	+	0.387006i	0.486612	+	0.873618i	$0.338232\pi$
$440$		0			0
$441$	5.59770	+	5.59770i	0.266557	+	0.266557i
$442$		0			0
$443$	−9.34973	+	22.5722i	−0.444219	+	1.07244i	0.530235	+	0.847851i	$0.322104\pi$
$443$	−9.34973	+	22.5722i	−0.444219	+	1.07244i	−0.974454	+	0.224588i	$0.927896\pi$
$444$		0			0
$445$	−12.5914	+	5.21554i	−0.596891	+	0.247240i
$446$		0			0
$447$	−4.16726			−0.197105
$448$		0			0
$449$	−28.6259			−1.35094			−0.675469	−	0.737388i	$-0.736059\pi$
$449$	−28.6259			−1.35094			−0.675469	+	0.737388i	$0.736059\pi$
$450$		0			0
$451$	13.7199	−	5.68297i	0.646045	−	0.267601i
$452$		0			0
$453$	0.221591	−	0.534968i	0.0104113	−	0.0251350i
$454$		0			0
$455$	23.6854	+	23.6854i	1.11039	+	1.11039i
$456$		0			0
$457$	−18.7182	+	18.7182i	−0.875602	+	0.875602i	−0.993076	−	0.117474i	$-0.962520\pi$
$457$	−18.7182	+	18.7182i	−0.875602	+	0.875602i	0.117474	+	0.993076i	$0.462520\pi$
$458$		0			0
$459$	−0.478061	−	0.198019i	−0.0223140	−	0.00924275i
$460$		0			0
$461$	2.60820	+	6.29674i	0.121476	+	0.293268i	0.972907	−	0.231198i	$-0.0742647\pi$
$461$	2.60820	+	6.29674i	0.121476	+	0.293268i	−0.851431	+	0.524467i	$0.824265\pi$
$462$		0			0
$463$			5.96406i			0.277174i	0.990350	+	0.138587i	$0.0442560\pi$
$463$			5.96406i			0.277174i	−0.990350	+	0.138587i	$0.955744\pi$
$464$		0			0
$465$		−	5.34354i		−	0.247801i
$466$		0			0
$467$	−8.88493	−	21.4501i	−0.411146	−	0.992593i	−0.984831	−	0.173518i	$-0.944487\pi$
$467$	−8.88493	−	21.4501i	−0.411146	−	0.992593i	0.573685	−	0.819076i	$-0.305513\pi$
$468$		0			0
$469$	−42.9906	−	17.8073i	−1.98512	−	0.822264i
$470$		0			0
$471$	−9.29584	+	9.29584i	−0.428330	+	0.428330i
$472$		0			0
$473$	−3.28184	−	3.28184i	−0.150899	−	0.150899i
$474$		0			0
$475$	−11.7122	+	28.2758i	−0.537394	+	1.29738i
$476$		0			0
$477$	−4.19534	+	1.73777i	−0.192092	+	0.0795669i
$478$		0			0
$479$	22.6413			1.03451			0.517254	−	0.855832i	$-0.326954\pi$
$479$	22.6413			1.03451			0.517254	+	0.855832i	$0.326954\pi$
$480$		0			0
$481$	−21.7013			−0.989494
$482$		0			0
$483$	−12.1003	+	5.01210i	−0.550582	+	0.228059i
$484$		0			0
$485$	5.08448	−	12.2750i	0.230874	−	0.557380i
$486$		0			0
$487$	−2.79015	−	2.79015i	−0.126434	−	0.126434i	0.641058	−	0.767492i	$-0.278496\pi$
$487$	−2.79015	−	2.79015i	−0.126434	−	0.126434i	−0.767492	+	0.641058i	$0.778496\pi$
$488$		0			0
$489$	11.9440	−	11.9440i	0.540127	−	0.540127i
$490$		0			0
$491$	−19.9243	−	8.25292i	−0.899172	−	0.372449i	−0.115270	−	0.993334i	$-0.536773\pi$
$491$	−19.9243	−	8.25292i	−0.899172	−	0.372449i	−0.783902	+	0.620885i	$0.786773\pi$
$492$		0			0
$493$	−1.51975	−	3.66901i	−0.0684463	−	0.165244i
$494$		0			0
$495$			11.6195i			0.522256i
$496$		0			0
$497$		−	10.1930i		−	0.457221i
$498$		0			0
$499$	14.7704	+	35.6588i	0.661212	+	1.59631i	0.795907	+	0.605419i	$0.206995\pi$
$499$	14.7704	+	35.6588i	0.661212	+	1.59631i	−0.134695	+	0.990887i	$0.543005\pi$
$500$		0			0
$501$	4.77973	+	1.97983i	0.213543	+	0.0884523i
$502$		0			0
$503$	26.5194	−	26.5194i	1.18244	−	1.18244i	0.203333	−	0.979110i	$-0.434823\pi$
$503$	26.5194	−	26.5194i	1.18244	−	1.18244i	0.979110	−	0.203333i	$-0.0651773\pi$
$504$		0			0
$505$	41.8897	+	41.8897i	1.86407	+	1.86407i
$506$		0			0
$507$	2.70263	−	6.52473i	0.120028	−	0.289774i
$508$		0			0
$509$	33.0361	−	13.6840i	1.46430	−	0.606534i	0.498750	−	0.866746i	$-0.333793\pi$
$509$	33.0361	−	13.6840i	1.46430	−	0.606534i	0.965551	+	0.260212i	$0.0837926\pi$
$510$		0			0
$511$	−49.5320			−2.19117
$512$		0			0
$513$	−3.99125			−0.176218
$514$		0			0
$515$	34.5171	−	14.2974i	1.52100	−	0.630020i
$516$		0			0
$517$	5.83986	−	14.0987i	0.256837	−	0.620059i
$518$		0			0
$519$	−8.68014	−	8.68014i	−0.381016	−	0.381016i
$520$		0			0
$521$	−2.51581	+	2.51581i	−0.110220	+	0.110220i	−0.760066	−	0.649846i	$-0.774833\pi$
$521$	−2.51581	+	2.51581i	−0.110220	+	0.110220i	0.649846	+	0.760066i	$0.274833\pi$
$522$		0			0
$523$	−21.6449	−	8.96561i	−0.946465	−	0.392039i	−0.144564	−	0.989495i	$-0.546178\pi$
$523$	−21.6449	−	8.96561i	−0.946465	−	0.392039i	−0.801901	+	0.597457i	$0.796178\pi$
$524$		0			0
$525$	−11.3334	−	27.3613i	−0.494632	−	1.19415i
$526$		0			0
$527$		−	0.776856i		−	0.0338404i
$528$		0			0
$529$			11.5000i			0.500000i
$530$		0			0
$531$	−0.680868	−	1.64376i	−0.0295472	−	0.0713331i
$532$		0			0
$533$	−10.2407	−	4.24184i	−0.443574	−	0.183734i
$534$		0			0
$535$	−21.3937	+	21.3937i	−0.924930	+	0.924930i
$536$		0			0
$537$	−4.18612	−	4.18612i	−0.180644	−	0.180644i
$538$		0			0
$539$	9.88995	−	23.8764i	0.425990	−	1.02843i
$540$		0			0
$541$	9.88526	−	4.09461i	0.425001	−	0.176041i	−0.159923	−	0.987130i	$-0.551125\pi$
$541$	9.88526	−	4.09461i	0.425001	−	0.176041i	0.584924	+	0.811088i	$0.301125\pi$
$542$		0			0
$543$	−15.7775			−0.677075
$544$		0			0
$545$	30.9741			1.32678
$546$		0			0
$547$	4.92501	−	2.04001i	0.210578	−	0.0872244i	−0.274901	−	0.961473i	$-0.588645\pi$
$547$	4.92501	−	2.04001i	0.210578	−	0.0872244i	0.485479	+	0.874248i	$0.338645\pi$
$548$		0			0
$549$	2.78139	−	6.71487i	0.118707	−	0.286584i
$550$		0			0
$551$	−21.6601	−	21.6601i	−0.922750	−	0.922750i
$552$		0			0
$553$	28.5146	−	28.5146i	1.21256	−	1.21256i
$554$		0			0
$555$	29.2853	+	12.1304i	1.24309	+	0.514905i
$556$		0			0
$557$	−1.88066	−	4.54032i	−0.0796862	−	0.192380i	0.879015	−	0.476793i	$-0.158201\pi$
$557$	−1.88066	−	4.54032i	−0.0796862	−	0.192380i	−0.958702	+	0.284414i	$0.908201\pi$
$558$		0			0
$559$			3.46426i			0.146523i
$560$		0			0
$561$			1.68926i			0.0713208i
$562$		0			0
$563$	4.16303	+	10.0504i	0.175451	+	0.423575i	0.987002	−	0.160705i	$-0.0513768\pi$
$563$	4.16303	+	10.0504i	0.175451	+	0.423575i	−0.811552	+	0.584281i	$0.801377\pi$
$564$		0			0
$565$	57.3688	+	23.7630i	2.41353	+	0.999715i
$566$		0			0
$567$	2.73097	−	2.73097i	0.114690	−	0.114690i
$568$		0			0
$569$	−1.48801	−	1.48801i	−0.0623805	−	0.0623805i	0.675228	−	0.737609i	$-0.264045\pi$
$569$	−1.48801	−	1.48801i	−0.0623805	−	0.0623805i	−0.737609	+	0.675228i	$0.764045\pi$
$570$		0			0
$571$	10.9476	−	26.4299i	0.458145	−	1.10606i	−0.511003	−	0.859579i	$-0.670726\pi$
$571$	10.9476	−	26.4299i	0.458145	−	1.10606i	0.969148	−	0.246480i	$-0.0792740\pi$
$572$		0			0
$573$	11.4344	−	4.73630i	0.477680	−	0.197862i
$574$		0			0
$575$	26.0040			1.08444
$576$		0			0
$577$	28.1723			1.17283			0.586413	−	0.810012i	$-0.300539\pi$
$577$	28.1723			1.17283			0.586413	+	0.810012i	$0.300539\pi$
$578$		0			0
$579$	20.2647	−	8.39391i	0.842172	−	0.348839i
$580$		0			0
$581$	−7.31261	+	17.6542i	−0.303378	+	0.732420i
$582$		0			0
$583$	10.4825	+	10.4825i	0.434143	+	0.434143i
$584$		0			0
$585$	6.13268	−	6.13268i	0.253555	−	0.253555i
$586$		0			0
$587$	26.4589	+	10.9597i	1.09208	+	0.452353i	0.854731	−	0.519072i	$-0.173722\pi$
$587$	26.4589	+	10.9597i	1.09208	+	0.452353i	0.237347	+	0.971425i	$0.423722\pi$
$588$		0			0
$589$	−2.29309	−	5.53601i	−0.0944851	−	0.228107i
$590$		0			0
$591$		−	17.0573i		−	0.701645i
$592$		0			0
$593$			1.34616i			0.0552802i	0.999618	+	0.0276401i	$0.00879924\pi$
$593$			1.34616i			0.0552802i	−0.999618	+	0.0276401i	$0.991201\pi$
$594$		0			0
$595$	−2.72205	−	6.57160i	−0.111593	−	0.269409i
$596$		0			0
$597$	−7.58160	−	3.14040i	−0.310294	−	0.128528i
$598$		0			0
$599$	8.34761	−	8.34761i	0.341074	−	0.341074i	−0.515697	−	0.856771i	$-0.672467\pi$
$599$	8.34761	−	8.34761i	0.341074	−	0.341074i	0.856771	+	0.515697i	$0.172467\pi$
$600$		0			0
$601$	−25.9145	−	25.9145i	−1.05707	−	1.05707i	−0.998270	−	0.0588044i	$-0.981271\pi$
$601$	−25.9145	−	25.9145i	−1.05707	−	1.05707i	−0.0588044	−	0.998270i	$-0.518729\pi$
$602$		0			0
$603$	−4.61070	+	11.1312i	−0.187762	+	0.453298i
$604$		0			0
$605$	−1.12593	+	0.466374i	−0.0457754	+	0.0189608i
$606$		0			0
$607$	2.09569			0.0850615			0.0425307	−	0.999095i	$-0.486458\pi$
$607$	2.09569			0.0850615			0.0425307	+	0.999095i	$0.486458\pi$
$608$		0			0
$609$	29.6413			1.20112
$610$		0			0
$611$	−10.5234	+	4.35894i	−0.425732	+	0.176344i
$612$		0			0
$613$	−8.75402	+	21.1341i	−0.353572	+	0.853597i	0.642602	+	0.766200i	$0.277855\pi$
$613$	−8.75402	+	21.1341i	−0.353572	+	0.853597i	−0.996174	+	0.0873972i	$0.972145\pi$
$614$		0			0
$615$	11.4485	+	11.4485i	0.461647	+	0.461647i
$616$		0			0
$617$	7.54724	−	7.54724i	0.303841	−	0.303841i	−0.538674	−	0.842514i	$-0.681074\pi$
$617$	7.54724	−	7.54724i	0.303841	−	0.303841i	0.842514	+	0.538674i	$0.181074\pi$
$618$		0			0
$619$	−30.8044	−	12.7596i	−1.23813	−	0.512851i	−0.335002	−	0.942217i	$-0.608737\pi$
$619$	−30.8044	−	12.7596i	−1.23813	−	0.512851i	−0.903130	+	0.429366i	$0.858737\pi$
$620$		0			0
$621$	1.29774	+	3.13303i	0.0520766	+	0.125724i
$622$		0			0
$623$		−	14.7888i		−	0.592502i
$624$		0			0
$625$		−	4.54021i		−	0.181608i
$626$		0			0
$627$	4.98630	+	12.0380i	0.199134	+	0.480751i
$628$		0			0
$629$	4.25756	+	1.76354i	0.169760	+	0.0703169i
$630$		0			0
$631$	−4.03006	+	4.03006i	−0.160434	+	0.160434i	−0.782759	−	0.622325i	$-0.786188\pi$
$631$	−4.03006	+	4.03006i	−0.160434	+	0.160434i	0.622325	+	0.782759i	$0.286188\pi$
$632$		0			0
$633$	−14.1436	−	14.1436i	−0.562156	−	0.562156i
$634$		0			0
$635$	−2.51696	+	6.07648i	−0.0998825	+	0.241138i
$636$		0			0
$637$	−17.8217	+	7.38198i	−0.706120	+	0.292485i
$638$		0			0
$639$	−2.63920			−0.104405
$640$		0			0
$641$	10.3489			0.408757			0.204378	−	0.978892i	$-0.434483\pi$
$641$	10.3489			0.408757			0.204378	+	0.978892i	$0.434483\pi$
$642$		0			0
$643$	8.10100	−	3.35554i	0.319472	−	0.132330i	−0.217184	−	0.976131i	$-0.569687\pi$
$643$	8.10100	−	3.35554i	0.319472	−	0.132330i	0.536656	+	0.843801i	$0.319687\pi$
$644$		0			0
$645$	1.93642	−	4.67493i	0.0762464	−	0.184075i
$646$		0			0
$647$	−20.0358	−	20.0358i	−0.787689	−	0.787689i	0.193426	−	0.981115i	$-0.438040\pi$
$647$	−20.0358	−	20.0358i	−0.787689	−	0.787689i	−0.981115	+	0.193426i	$0.938040\pi$
$648$		0			0
$649$	−4.10712	+	4.10712i	−0.161219	+	0.161219i
$650$		0			0
$651$	5.35696	+	2.21893i	0.209956	+	0.0869666i
$652$		0			0
$653$	11.1811	+	26.9936i	0.437552	+	1.05634i	0.976792	+	0.214191i	$0.0687115\pi$
$653$	11.1811	+	26.9936i	0.437552	+	1.05634i	−0.539240	+	0.842152i	$0.681289\pi$
$654$		0			0
$655$		−	29.2540i		−	1.14305i
$656$		0			0
$657$			12.8249i			0.500348i
$658$		0			0
$659$	10.0306	+	24.2161i	0.390738	+	0.943325i	0.989779	+	0.142607i	$0.0455486\pi$
$659$	10.0306	+	24.2161i	0.390738	+	0.943325i	−0.599041	+	0.800718i	$0.704451\pi$
$660$		0			0
$661$	−13.8010	−	5.71657i	−0.536798	−	0.222349i	0.0977799	−	0.995208i	$-0.468826\pi$
$661$	−13.8010	−	5.71657i	−0.536798	−	0.222349i	−0.634578	+	0.772859i	$0.718826\pi$
$662$		0			0
$663$	0.891582	−	0.891582i	0.0346262	−	0.0346262i
$664$		0			0
$665$	−38.7956	−	38.7956i	−1.50443	−	1.50443i
$666$		0			0
$667$	−9.95988	+	24.0453i	−0.385648	+	0.931037i
$668$		0			0
$669$	26.8639	−	11.1274i	1.03862	−	0.430210i
$670$		0			0
$671$	−23.7275			−0.915990
$672$		0			0
$673$	31.4646			1.21287			0.606436	−	0.795132i	$-0.292599\pi$
$673$	31.4646			1.21287			0.606436	+	0.795132i	$0.292599\pi$
$674$		0			0
$675$	−7.08445	+	2.93447i	−0.272681	+	0.112948i
$676$		0			0
$677$	−6.25070	+	15.0905i	−0.240234	+	0.579976i	−0.997306	−	0.0733553i	$-0.976629\pi$
$677$	−6.25070	+	15.0905i	−0.240234	+	0.579976i	0.757072	+	0.653332i	$0.226629\pi$
$678$		0			0
$679$	10.1945	+	10.1945i	0.391229	+	0.391229i
$680$		0			0
$681$	−17.8011	+	17.8011i	−0.682141	+	0.682141i
$682$		0			0
$683$	13.3397	+	5.52548i	0.510429	+	0.211426i	0.623007	−	0.782216i	$-0.285911\pi$
$683$	13.3397	+	5.52548i	0.510429	+	0.211426i	−0.112578	+	0.993643i	$0.535911\pi$
$684$		0			0
$685$	−15.3826	−	37.1370i	−0.587740	−	1.41893i
$686$		0			0
$687$		−	7.64991i		−	0.291862i
$688$		0			0
$689$		−	11.0652i		−	0.421552i
$690$		0			0
$691$	9.47463	+	22.8738i	0.360432	+	0.870160i	0.995237	+	0.0974874i	$0.0310806\pi$
$691$	9.47463	+	22.8738i	0.360432	+	0.870160i	−0.634805	+	0.772673i	$0.718919\pi$
$692$		0			0
$693$	−11.6487	−	4.82504i	−0.442496	−	0.183288i
$694$		0			0
$695$	−4.14777	+	4.14777i	−0.157334	+	0.157334i
$696$		0			0
$697$	1.66441	+	1.66441i	0.0630439	+	0.0630439i
$698$		0			0
$699$	7.08278	−	17.0993i	0.267895	−	0.646756i
$700$		0			0
$701$	−5.36748	+	2.22328i	−0.202727	+	0.0839723i	−0.481737	−	0.876316i	$-0.659994\pi$
$701$	−5.36748	+	2.22328i	−0.202727	+	0.0839723i	0.279010	+	0.960288i	$0.409994\pi$
$702$		0			0
$703$	35.5457			1.34063
$704$		0			0
$705$	16.6376			0.626607
$706$		0			0
$707$	−59.3898	+	24.6001i	−2.23358	+	0.925180i
$708$		0			0
$709$	−14.4269	+	34.8295i	−0.541812	+	1.30805i	0.381631	+	0.924315i	$0.375362\pi$
$709$	−14.4269	+	34.8295i	−0.541812	+	1.30805i	−0.923443	+	0.383735i	$0.874638\pi$
$710$		0			0
$711$	−7.38305	−	7.38305i	−0.276886	−	0.276886i
$712$		0			0
$713$	−3.60003	+	3.60003i	−0.134822	+	0.134822i
$714$		0			0
$715$	−26.1583	−	10.8351i	−0.978266	−	0.405211i
$716$		0			0
$717$	1.57248	+	3.79630i	0.0587254	+	0.141776i
$718$		0			0
$719$		−	38.6849i		−	1.44270i	−0.692569	−	0.721351i	$-0.743521\pi$
$719$		−	38.6849i		−	1.44270i	0.692569	−	0.721351i	$-0.256479\pi$
$720$		0			0
$721$			40.5409i			1.50982i
$722$		0			0
$723$	−5.43963	−	13.1324i	−0.202302	−	0.488400i
$724$		0			0
$725$	−54.3715	−	22.5214i	−2.01931	−	0.836425i
$726$		0			0
$727$	31.8871	−	31.8871i	1.18263	−	1.18263i	0.203566	−	0.979061i	$-0.434747\pi$
$727$	31.8871	−	31.8871i	1.18263	−	1.18263i	0.979061	−	0.203566i	$-0.0652532\pi$
$728$		0			0
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$		0			0
$731$	0.281521	−	0.679651i	0.0104124	−	0.0251378i
$732$		0			0
$733$	−18.4333	+	7.63532i	−0.680849	+	0.282017i	−0.696182	−	0.717865i	$-0.745119\pi$
$733$	−18.4333	+	7.63532i	−0.680849	+	0.282017i	0.0153326	+	0.999882i	$0.495119\pi$
$734$		0			0
$735$	28.1761			1.03929
$736$		0			0
$737$	39.3330			1.44885
$738$		0			0
$739$	19.0069	−	7.87292i	0.699180	−	0.289610i	−0.00463865	−	0.999989i	$-0.501477\pi$
$739$	19.0069	−	7.87292i	0.699180	−	0.289610i	0.703819	+	0.710379i	$0.251477\pi$
$740$		0			0
$741$	3.72184	−	8.98531i	0.136725	−	0.330084i
$742$		0			0
$743$	17.5266	+	17.5266i	0.642987	+	0.642987i	0.951289	−	0.308302i	$-0.0997606\pi$
$743$	17.5266	+	17.5266i	0.642987	+	0.642987i	−0.308302	+	0.951289i	$0.599761\pi$
$744$		0			0
$745$	−10.4880	+	10.4880i	−0.384250	+	0.384250i
$746$		0			0
$747$	4.57106	+	1.89340i	0.167246	+	0.0692757i
$748$		0			0
$749$	−12.5636	−	30.3313i	−0.459065	−	1.10828i
$750$		0			0
$751$			40.4908i			1.47753i	0.673963	+	0.738765i	$0.264591\pi$
$751$			40.4908i			1.47753i	−0.673963	+	0.738765i	$0.735409\pi$
$752$		0			0
$753$			6.19031i			0.225587i
$754$		0			0
$755$	−0.788695	−	1.90408i	−0.0287035	−	0.0692965i
$756$		0			0
$757$	−29.7102	−	12.3064i	−1.07984	−	0.447283i	−0.229385	−	0.973336i	$-0.573671\pi$
$757$	−29.7102	−	12.3064i	−1.07984	−	0.447283i	−0.850452	+	0.526053i	$0.823671\pi$
$758$		0			0
$759$	7.82823	−	7.82823i	0.284147	−	0.284147i
$760$		0			0
$761$	−15.8052	−	15.8052i	−0.572939	−	0.572939i	0.360010	−	0.932949i	$-0.382773\pi$
$761$	−15.8052	−	15.8052i	−0.572939	−	0.572939i	−0.932949	+	0.360010i	$0.882773\pi$
$762$		0			0
$763$	−12.8621	+	31.0519i	−0.465640	+	1.12415i
$764$		0			0
$765$	−1.70153	+	0.704798i	−0.0615190	+	0.0254820i
$766$		0			0
$767$	4.33542			0.156543
$768$		0			0
$769$	2.99003			0.107823			0.0539116	−	0.998546i	$-0.482831\pi$
$769$	2.99003			0.107823			0.0539116	+	0.998546i	$0.482831\pi$
$770$		0			0
$771$	−7.65149	+	3.16935i	−0.275562	+	0.114141i
$772$		0			0
$773$	1.59236	−	3.84429i	0.0572731	−	0.138269i	−0.892653	−	0.450745i	$-0.851158\pi$
$773$	1.59236	−	3.84429i	0.0572731	−	0.138269i	0.949926	+	0.312476i	$0.101158\pi$
$774$		0			0
$775$	−8.14044	−	8.14044i	−0.292413	−	0.292413i
$776$		0			0
$777$	−24.3217	+	24.3217i	−0.872535	+	0.872535i
$778$		0			0
$779$	16.7738	+	6.94792i	0.600983	+	0.248935i
$780$		0			0
$781$	3.29718	+	7.96009i	0.117982	+	0.284834i
$782$		0			0
$783$		−	7.67477i		−	0.274274i
$784$		0			0
$785$			46.7908i			1.67003i
$786$		0			0
$787$	−3.14740	−	7.59851i	−0.112193	−	0.270857i	0.857803	−	0.513978i	$-0.171829\pi$
$787$	−3.14740	−	7.59851i	−0.112193	−	0.270857i	−0.969996	+	0.243121i	$0.921829\pi$
$788$		0			0
$789$	−20.1299	−	8.33809i	−0.716645	−	0.296844i
$790$		0			0
$791$	−47.6453	+	47.6453i	−1.69407	+	1.69407i
$792$		0			0
$793$	12.5232	+	12.5232i	0.444712	+	0.444712i
$794$		0			0
$795$	−6.18513	+	14.9322i	−0.219364	+	0.529591i
$796$		0			0
$797$	−13.9175	+	5.76480i	−0.492982	+	0.204200i	−0.615303	−	0.788291i	$-0.710966\pi$
$797$	−13.9175	+	5.76480i	−0.492982	+	0.204200i	0.122321	+	0.992491i	$0.460966\pi$
$798$		0			0
$799$	2.41881			0.0855712
$800$		0			0
$801$	−3.82915			−0.135297
$802$		0			0
$803$	38.6812	−	16.0223i	1.36503	−	0.565413i
$804$		0			0
$805$	−17.8393	+	43.0678i	−0.628751	+	1.51794i
$806$		0			0
$807$	−5.72608	−	5.72608i	−0.201568	−	0.201568i
$808$		0			0
$809$	30.4595	−	30.4595i	1.07090	−	1.07090i	0.0736122	−	0.997287i	$-0.476547\pi$
$809$	30.4595	−	30.4595i	1.07090	−	1.07090i	0.997287	−	0.0736122i	$-0.0234527\pi$
$810$		0			0
$811$	−19.1190	−	7.91934i	−0.671358	−	0.278086i	0.0208509	−	0.999783i	$-0.493362\pi$
$811$	−19.1190	−	7.91934i	−0.671358	−	0.278086i	−0.692209	+	0.721697i	$0.743362\pi$
$812$		0			0
$813$	11.0149	+	26.5922i	0.386308	+	0.932631i
$814$		0			0
$815$		−	60.1204i		−	2.10593i
$816$		0			0
$817$		−	5.67430i		−	0.198519i
$818$		0			0
$819$	3.60147	+	8.69471i	0.125845	+	0.303818i
$820$		0			0
$821$	32.8139	+	13.5920i	1.14521	+	0.474363i	0.872926	−	0.487853i	$-0.162220\pi$
$821$	32.8139	+	13.5920i	1.14521	+	0.474363i	0.272287	+	0.962216i	$0.412220\pi$
$822$		0			0
$823$	−5.67489	+	5.67489i	−0.197814	+	0.197814i	−0.799062	−	0.601248i	$-0.794670\pi$
$823$	−5.67489	+	5.67489i	−0.197814	+	0.197814i	0.601248	+	0.799062i	$0.294670\pi$
$824$		0			0
$825$	17.7013	+	17.7013i	0.616280	+	0.616280i
$826$		0			0
$827$	−21.2654	+	51.3392i	−0.739471	+	1.78524i	−0.131443	+	0.991324i	$0.541961\pi$
$827$	−21.2654	+	51.3392i	−0.739471	+	1.78524i	−0.608027	+	0.793916i	$0.708039\pi$
$828$		0			0
$829$	−14.6369	+	6.06280i	−0.508361	+	0.210570i	−0.622096	−	0.782941i	$-0.713719\pi$
$829$	−14.6369	+	6.06280i	−0.508361	+	0.210570i	0.113735	+	0.993511i	$0.463719\pi$
$830$		0			0
$831$	−13.1527			−0.456263
$832$		0			0
$833$	4.09631			0.141929
$834$		0			0
$835$	17.0122	−	7.04668i	0.588731	−	0.243860i
$836$		0			0
$837$	0.574529	−	1.38704i	0.0198586	−	0.0479430i
$838$		0			0
$839$	39.7201	+	39.7201i	1.37129	+	1.37129i	0.858535	+	0.512756i	$0.171375\pi$
$839$	39.7201	+	39.7201i	1.37129	+	1.37129i	0.512756	+	0.858535i	$0.328625\pi$
$840$		0			0
$841$	21.1440	−	21.1440i	0.729103	−	0.729103i
$842$		0			0
$843$	−28.2618	−	11.7064i	−0.973387	−	0.403190i
$844$		0			0
$845$	−9.61931	−	23.2231i	−0.330914	−	0.798898i
$846$		0			0
$847$		−	1.32242i		−	0.0454389i
$848$		0			0
$849$		−	29.9928i		−	1.02935i
$850$		0			0
$851$	−11.5576	−	27.9024i	−0.396188	−	0.956482i
$852$		0			0
$853$	17.7015	+	7.33222i	0.606089	+	0.251050i	0.664555	−	0.747239i	$-0.268621\pi$
$853$	17.7015	+	7.33222i	0.606089	+	0.251050i	−0.0584662	+	0.998289i	$0.518621\pi$
$854$		0			0
$855$	−10.0450	+	10.0450i	−0.343533	+	0.343533i
$856$		0			0
$857$	34.8578	+	34.8578i	1.19072	+	1.19072i	0.976866	+	0.213853i	$0.0686015\pi$
$857$	34.8578	+	34.8578i	1.19072	+	1.19072i	0.213853	+	0.976866i	$0.431399\pi$
$858$		0			0
$859$	−13.9729	+	33.7335i	−0.476748	+	1.15097i	0.484378	+	0.874859i	$0.339046\pi$
$859$	−13.9729	+	33.7335i	−0.476748	+	1.15097i	−0.961125	+	0.276112i	$0.910954\pi$
$860$		0			0
$861$	−16.2313	+	6.72321i	−0.553160	+	0.229127i
$862$		0			0
$863$	−35.2947			−1.20144			−0.600722	−	0.799458i	$-0.705120\pi$
$863$	−35.2947			−1.20144			−0.600722	+	0.799458i	$0.705120\pi$
$864$		0			0
$865$	−43.6916			−1.48556
$866$		0			0
$867$	15.4586	−	6.40315i	0.525001	−	0.217462i
$868$		0			0
$869$	−13.0443	+	31.4917i	−0.442497	+	1.06828i
$870$		0			0
$871$	−20.7597	−	20.7597i	−0.703414	−	0.703414i
$872$		0			0
$873$	2.63958	−	2.63958i	0.0893363	−	0.0893363i
$874$		0			0
$875$	−33.8855	−	14.0358i	−1.14554	−	0.474498i
$876$		0			0
$877$	−3.81781	−	9.21700i	−0.128918	−	0.311236i	0.846220	−	0.532834i	$-0.178873\pi$
$877$	−3.81781	−	9.21700i	−0.128918	−	0.311236i	−0.975138	+	0.221598i	$0.928873\pi$
$878$		0			0
$879$			4.81487i			0.162402i
$880$		0			0
$881$			20.1037i			0.677312i	0.940910	+	0.338656i	$0.109972\pi$
$881$			20.1037i			0.677312i	−0.940910	+	0.338656i	$0.890028\pi$
$882$		0			0
$883$	9.85279	+	23.7867i	0.331573	+	0.800487i	0.998468	+	0.0553357i	$0.0176229\pi$
$883$	9.85279	+	23.7867i	0.331573	+	0.800487i	−0.666895	+	0.745152i	$0.732377\pi$
$884$		0			0
$885$	−5.85053	−	2.42337i	−0.196663	−	0.0814607i
$886$		0			0
$887$	−14.1672	+	14.1672i	−0.475688	+	0.475688i	−0.903749	−	0.428062i	$-0.859197\pi$
$887$	−14.1672	+	14.1672i	−0.475688	+	0.475688i	0.428062	+	0.903749i	$0.359197\pi$
$888$		0			0
$889$	−5.04657	−	5.04657i	−0.169256	−	0.169256i
$890$		0			0
$891$	−1.24931	+	3.01609i	−0.0418534	+	0.101043i
$892$		0			0
$893$	17.2368	−	7.13973i	0.576809	−	0.238922i
$894$		0			0
$895$	−21.0709			−0.704322
$896$		0			0
$897$	−8.26337			−0.275906
$898$		0			0
$899$	10.6452	−	4.40938i	0.355037	−	0.147061i
$900$		0			0
$901$	−0.899208	+	2.17088i	−0.0299569	+	0.0723225i
$902$		0			0
$903$	3.88257	+	3.88257i	0.129204	+	0.129204i
$904$		0			0
$905$	−39.7080	+	39.7080i	−1.31994	+	1.31994i
$906$		0			0
$907$	1.27402	+	0.527716i	0.0423031	+	0.0175225i	0.403735	−	0.914876i	$-0.367712\pi$
$907$	1.27402	+	0.527716i	0.0423031	+	0.0175225i	−0.361432	+	0.932399i	$0.617712\pi$
$908$		0			0
$909$	6.36949	+	15.3773i	0.211263	+	0.510033i
$910$		0			0
$911$			3.64101i			0.120632i	0.998179	+	0.0603161i	$0.0192109\pi$
$911$			3.64101i			0.120632i	−0.998179	+	0.0603161i	$0.980789\pi$
$912$		0			0
$913$		−	16.1522i		−	0.534560i
$914$		0			0
$915$	−9.89962	−	23.8998i	−0.327271	−	0.790103i
$916$		0			0
$917$	29.3275	+	12.1478i	0.968479	+	0.401157i
$918$		0			0
$919$	−16.8542	+	16.8542i	−0.555970	+	0.555970i	−0.928158	−	0.372187i	$-0.878608\pi$
$919$	−16.8542	+	16.8542i	−0.555970	+	0.555970i	0.372187	+	0.928158i	$0.378608\pi$
$920$		0			0
$921$	−21.6932	−	21.6932i	−0.714815	−	0.714815i
$922$		0			0
$923$	2.46105	−	5.94151i	0.0810065	−	0.195567i
$924$		0			0
$925$	63.0933	−	26.1341i	2.07450	−	0.859284i
$926$		0			0
$927$	10.4969			0.344764
$928$		0			0
$929$	−29.1718			−0.957096			−0.478548	−	0.878061i	$-0.658837\pi$
$929$	−29.1718			−0.957096			−0.478548	+	0.878061i	$0.658837\pi$
$930$		0			0
$931$	29.1910	−	12.0913i	0.956697	−	0.396277i
$932$		0			0
$933$	−6.28440	+	15.1719i	−0.205742	+	0.496705i
$934$		0			0
$935$	4.25147	+	4.25147i	0.139038	+	0.139038i
$936$		0			0
$937$	16.6591	−	16.6591i	0.544230	−	0.544230i	−0.380536	−	0.924766i	$-0.624261\pi$
$937$	16.6591	−	16.6591i	0.544230	−	0.544230i	0.924766	+	0.380536i	$0.124261\pi$
$938$		0			0
$939$	−8.94223	−	3.70399i	−0.291819	−	0.120875i
$940$		0			0
$941$	2.44955	+	5.91373i	0.0798529	+	0.192782i	0.958764	−	0.284204i	$-0.0917293\pi$
$941$	2.44955	+	5.91373i	0.0798529	+	0.192782i	−0.878911	+	0.476986i	$0.841729\pi$
$942$		0			0
$943$		−	15.4261i		−	0.502342i
$944$		0			0
$945$		−	13.7464i		−	0.447169i
$946$		0			0
$947$	4.96711	+	11.9917i	0.161409	+	0.389676i	0.983806	−	0.179238i	$-0.0573634\pi$
$947$	4.96711	+	11.9917i	0.161409	+	0.389676i	−0.822396	+	0.568915i	$0.807363\pi$
$948$		0			0
$949$	−28.8721	−	11.9592i	−0.937228	−	0.388212i
$950$		0			0
$951$	−18.1235	+	18.1235i	−0.587694	+	0.587694i
$952$		0			0
$953$	−6.25983	−	6.25983i	−0.202776	−	0.202776i	0.598412	−	0.801188i	$-0.295798\pi$
$953$	−6.25983	−	6.25983i	−0.202776	−	0.202776i	−0.801188	+	0.598412i	$0.795798\pi$
$954$		0			0
$955$	16.8576	−	40.6978i	0.545499	−	1.31695i
$956$		0			0
$957$	−23.1478	+	9.58815i	−0.748263	+	0.309941i
$958$		0			0
$959$	43.6180			1.40850
$960$		0			0
$961$	−28.7460			−0.927292
$962$		0			0
$963$	−7.85343	+	3.25300i	−0.253073	+	0.104826i
$964$		0			0
$965$	29.8759	−	72.1268i	0.961739	−	2.32184i
$966$		0			0
$967$	−4.21628	−	4.21628i	−0.135586	−	0.135586i	0.636056	−	0.771643i	$-0.280565\pi$
$967$	−4.21628	−	4.21628i	−0.135586	−	0.135586i	−0.771643	+	0.636056i	$0.780565\pi$
$968$		0			0
$969$	−1.46037	+	1.46037i	−0.0469138	+	0.0469138i
$970$		0			0
$971$	35.3365	+	14.6369i	1.13400	+	0.469720i	0.869140	−	0.494566i	$-0.164673\pi$
$971$	35.3365	+	14.6369i	1.13400	+	0.469720i	0.264864	+	0.964286i	$0.414673\pi$
$972$		0			0
$973$	−2.43582	−	5.88058i	−0.0780887	−	0.188523i
$974$		0			0
$975$		−	18.6853i		−	0.598407i
$976$		0			0
$977$		−	60.3138i		−	1.92961i	−0.262970	−	0.964804i	$-0.584702\pi$
$977$		−	60.3138i		−	1.92961i	0.262970	−	0.964804i	$-0.415298\pi$
$978$		0			0
$979$	4.78379	+	11.5491i	0.152891	+	0.369111i
$980$		0			0
$981$	8.04001	+	3.33028i	0.256698	+	0.106328i
$982$		0			0
$983$	−38.0148	+	38.0148i	−1.21248	+	1.21248i	−0.242277	+	0.970207i	$0.577894\pi$
$983$	−38.0148	+	38.0148i	−1.21248	+	1.21248i	−0.970207	+	0.242277i	$0.922106\pi$
$984$		0			0
$985$	−42.9292	−	42.9292i	−1.36784	−	1.36784i
$986$		0			0
$987$	−6.90882	+	16.6794i	−0.219910	+	0.530910i
$988$		0			0
$989$	−4.45417	+	1.84498i	−0.141634	+	0.0586669i
$990$		0			0
$991$	−51.7734			−1.64464			−0.822319	−	0.569027i	$-0.807320\pi$
$991$	−51.7734			−1.64464			−0.822319	+	0.569027i	$0.807320\pi$
$992$		0			0
$993$	23.4995			0.745733
$994$		0			0
$995$	−26.9847	+	11.1774i	−0.855472	+	0.354348i
$996$		0			0
$997$	13.2018	−	31.8719i	0.418105	−	1.00939i	−0.564791	−	0.825234i	$-0.691043\pi$
$997$	13.2018	−	31.8719i	0.418105	−	1.00939i	0.982896	−	0.184161i	$-0.0589567\pi$
$998$		0			0
$999$	6.29742	+	6.29742i	0.199241	+	0.199241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.n.a.49.8		32
3.2	odd	2		1152.2.v.c.433.1		32
4.3	odd	2		96.2.n.a.85.5	yes	32
8.3	odd	2		768.2.n.a.97.5		32
8.5	even	2		768.2.n.b.97.1		32
12.11	even	2		288.2.v.d.181.4		32
32.3	odd	8		96.2.n.a.61.5	✓	32
32.13	even	8		768.2.n.b.673.1		32
32.19	odd	8		768.2.n.a.673.5		32
32.29	even	8	inner	384.2.n.a.337.8		32
96.29	odd	8		1152.2.v.c.721.1		32
96.35	even	8		288.2.v.d.253.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.5	✓	32	32.3	odd	8
96.2.n.a.85.5	yes	32	4.3	odd	2
288.2.v.d.181.4		32	12.11	even	2
288.2.v.d.253.4		32	96.35	even	8
384.2.n.a.49.8		32	1.1	even	1	trivial
384.2.n.a.337.8		32	32.29	even	8	inner
768.2.n.a.97.5		32	8.3	odd	2
768.2.n.a.673.5		32	32.19	odd	8
768.2.n.b.97.1		32	8.5	even	2
768.2.n.b.673.1		32	32.13	even	8
1152.2.v.c.433.1		32	3.2	odd	2
1152.2.v.c.721.1		32	96.29	odd	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.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 - 0.382683i) q^{3} +(1.36206 - 3.28830i) q^{5} +(2.73097 + 2.73097i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.923880 - 0.382683i) q^{3} +(1.36206 - 3.28830i) q^{5} +(2.73097 + 2.73097i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-3.01609 - 1.24931i) q^{11} +(0.932498 + 2.25125i) q^{13} -3.55923i q^{15} -0.517450i q^{17} +(-1.52739 - 3.68744i) q^{19} +(3.56818 + 1.47799i) q^{21} +(-2.39792 + 2.39792i) q^{23} +(-5.42220 - 5.42220i) q^{25} +(0.382683 - 0.923880i) q^{27} +(7.09056 - 2.93701i) q^{29} +1.50132 q^{31} -3.26460 q^{33} +(12.7000 - 5.26051i) q^{35} +(-3.40814 + 8.22797i) q^{37} +(1.72303 + 1.72303i) q^{39} +(-3.21656 + 3.21656i) q^{41} +(1.31346 + 0.544054i) q^{43} +(-1.36206 - 3.28830i) q^{45} +4.67448i q^{47} +7.91635i q^{49} +(-0.198019 - 0.478061i) q^{51} +(-4.19534 - 1.73777i) q^{53} +(-8.21621 + 8.21621i) q^{55} +(-2.82224 - 2.82224i) q^{57} +(0.680868 - 1.64376i) q^{59} +(6.71487 - 2.78139i) q^{61} +3.86217 q^{63} +8.67291 q^{65} +(-11.1312 + 4.61070i) q^{67} +(-1.29774 + 3.13303i) q^{69} +(-1.86620 - 1.86620i) q^{71} +(-9.06859 + 9.06859i) q^{73} +(-7.08445 - 2.93447i) q^{75} +(-4.82504 - 11.6487i) q^{77} -10.4412i q^{79} -1.00000i q^{81} +(1.89340 + 4.57106i) q^{83} +(-1.70153 - 0.704798i) q^{85} +(5.42688 - 5.42688i) q^{87} +(-2.70762 - 2.70762i) q^{89} +(-3.60147 + 8.69471i) q^{91} +(1.38704 - 0.574529i) q^{93} -14.2058 q^{95} +3.73293 q^{97} +(-3.01609 + 1.24931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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