LMFDB - Embedded newform 896.2.u.c.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(113,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("896.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.u (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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			337.2
Character	$\chi$	$=$	896.337
Dual form			896.2.u.c.561.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47594 - 1.02557i) q^{3} +(-1.23251 - 2.97553i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(2.95715 + 2.95715i) q^{9} +O(q^{10})$	\(q+(-2.47594 - 1.02557i) q^{3} +(-1.23251 - 2.97553i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(2.95715 + 2.95715i) q^{9} +(-5.37782 + 2.22756i) q^{11} +(-1.34780 + 3.25387i) q^{13} +8.63125i q^{15} -1.12373i q^{17} +(2.14294 - 5.17351i) q^{19} +(2.47594 - 1.02557i) q^{21} +(1.63790 + 1.63790i) q^{23} +(-3.79919 + 3.79919i) q^{25} +(-1.21227 - 2.92667i) q^{27} +(-1.95805 - 0.811051i) q^{29} +0.620923 q^{31} +15.5996 q^{33} +(2.97553 + 1.23251i) q^{35} +(1.28245 + 3.09611i) q^{37} +(6.67412 - 6.67412i) q^{39} +(-0.552778 - 0.552778i) q^{41} +(6.93125 - 2.87102i) q^{43} +(5.15440 - 12.4438i) q^{45} -12.3828i q^{47} -1.00000i q^{49} +(-1.15246 + 2.78228i) q^{51} +(-2.75692 + 1.14195i) q^{53} +(13.2564 + 13.2564i) q^{55} +(-10.6116 + 10.6116i) q^{57} +(5.00009 + 12.0713i) q^{59} +(3.80216 + 1.57491i) q^{61} -4.18205 q^{63} +11.3432 q^{65} +(9.62375 + 3.98629i) q^{67} +(-2.37556 - 5.73510i) q^{69} +(-10.0462 + 10.0462i) q^{71} +(8.53603 + 8.53603i) q^{73} +(13.3029 - 5.51023i) q^{75} +(2.22756 - 5.37782i) q^{77} +7.40965i q^{79} -4.05662i q^{81} +(3.57555 - 8.63214i) q^{83} +(-3.34369 + 1.38500i) q^{85} +(4.01622 + 4.01622i) q^{87} +(-9.02149 + 9.02149i) q^{89} +(-1.34780 - 3.25387i) q^{91} +(-1.53737 - 0.636798i) q^{93} -18.0351 q^{95} -1.17783 q^{97} +(-22.4903 - 9.31578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) $ 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.47594	−	1.02557i	−1.42948	−	0.592111i	−0.472259	−	0.881460i	$-0.656561\pi$
$3$	−2.47594	−	1.02557i	−1.42948	−	0.592111i	−0.957224	+	0.289349i	$0.906561\pi$
$4$		0			0
$5$	−1.23251	−	2.97553i	−0.551193	−	1.33070i	−0.916583	−	0.399844i	$-0.869064\pi$
$5$	−1.23251	−	2.97553i	−0.551193	−	1.33070i	0.365390	−	0.930855i	$-0.380936\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$	2.95715	+	2.95715i	0.985718	+	0.985718i
$10$		0			0
$11$	−5.37782	+	2.22756i	−1.62147	+	0.671636i	−0.994238	−	0.107195i	$-0.965813\pi$
$11$	−5.37782	+	2.22756i	−1.62147	+	0.671636i	−0.627234	+	0.778831i	$0.715813\pi$
$12$		0			0
$13$	−1.34780	+	3.25387i	−0.373812	+	0.902462i	0.619285	+	0.785166i	$0.287423\pi$
$13$	−1.34780	+	3.25387i	−0.373812	+	0.902462i	−0.993097	+	0.117296i	$0.962577\pi$
$14$		0			0
$15$			8.63125i			2.22858i
$16$		0			0
$17$		−	1.12373i		−	0.272544i	−0.990671	−	0.136272i	$-0.956488\pi$
$17$		−	1.12373i		−	0.272544i	0.990671	−	0.136272i	$-0.0435121\pi$
$18$		0			0
$19$	2.14294	−	5.17351i	0.491623	−	1.18688i	−0.462270	−	0.886739i	$-0.652965\pi$
$19$	2.14294	−	5.17351i	0.491623	−	1.18688i	0.953894	−	0.300145i	$-0.0970350\pi$
$20$		0			0
$21$	2.47594	−	1.02557i	0.540294	−	0.223797i
$22$		0			0
$23$	1.63790	+	1.63790i	0.341525	+	0.341525i	0.856940	−	0.515415i	$-0.172362\pi$
$23$	1.63790	+	1.63790i	0.341525	+	0.341525i	−0.515415	+	0.856940i	$0.672362\pi$
$24$		0			0
$25$	−3.79919	+	3.79919i	−0.759838	+	0.759838i
$26$		0			0
$27$	−1.21227	−	2.92667i	−0.233301	−	0.563239i
$28$		0			0
$29$	−1.95805	−	0.811051i	−0.363601	−	0.150608i	0.193401	−	0.981120i	$-0.438048\pi$
$29$	−1.95805	−	0.811051i	−0.363601	−	0.150608i	−0.557001	+	0.830512i	$0.688048\pi$
$30$		0			0
$31$	0.620923			0.111521			0.0557605	−	0.998444i	$-0.482242\pi$
$31$	0.620923			0.111521			0.0557605	+	0.998444i	$0.482242\pi$
$32$		0			0
$33$	15.5996			2.71555
$34$		0			0
$35$	2.97553	+	1.23251i	0.502957	+	0.208332i
$36$		0			0
$37$	1.28245	+	3.09611i	0.210834	+	0.508997i	0.993552	−	0.113379i	$-0.0361674\pi$
$37$	1.28245	+	3.09611i	0.210834	+	0.508997i	−0.782718	+	0.622376i	$0.786167\pi$
$38$		0			0
$39$	6.67412	−	6.67412i	1.06872	−	1.06872i
$40$		0			0
$41$	−0.552778	−	0.552778i	−0.0863294	−	0.0863294i	0.662623	−	0.748953i	$-0.269443\pi$
$41$	−0.552778	−	0.552778i	−0.0863294	−	0.0863294i	−0.748953	+	0.662623i	$0.769443\pi$
$42$		0			0
$43$	6.93125	−	2.87102i	1.05701	−	0.437826i	0.214619	−	0.976698i	$-0.431149\pi$
$43$	6.93125	−	2.87102i	1.05701	−	0.437826i	0.842388	+	0.538872i	$0.181149\pi$
$44$		0			0
$45$	5.15440	−	12.4438i	0.768372	−	1.85502i
$46$		0			0
$47$		−	12.3828i		−	1.80621i	−0.429417	−	0.903107i	$-0.641281\pi$
$47$		−	12.3828i		−	1.80621i	0.429417	−	0.903107i	$-0.358719\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−1.15246	+	2.78228i	−0.161376	+	0.389597i
$52$		0			0
$53$	−2.75692	+	1.14195i	−0.378692	+	0.156859i	−0.563906	−	0.825839i	$-0.690702\pi$
$53$	−2.75692	+	1.14195i	−0.378692	+	0.156859i	0.185214	+	0.982698i	$0.440702\pi$
$54$		0			0
$55$	13.2564	+	13.2564i	1.78749	+	1.78749i
$56$		0			0
$57$	−10.6116	+	10.6116i	−1.40553	+	1.40553i
$58$		0			0
$59$	5.00009	+	12.0713i	0.650957	+	1.57155i	0.811392	+	0.584502i	$0.198710\pi$
$59$	5.00009	+	12.0713i	0.650957	+	1.57155i	−0.160435	+	0.987046i	$0.551290\pi$
$60$		0			0
$61$	3.80216	+	1.57491i	0.486817	+	0.201646i	0.612571	−	0.790415i	$-0.290135\pi$
$61$	3.80216	+	1.57491i	0.486817	+	0.201646i	−0.125755	+	0.992061i	$0.540135\pi$
$62$		0			0
$63$	−4.18205			−0.526888
$64$		0			0
$65$	11.3432			1.40695
$66$		0			0
$67$	9.62375	+	3.98629i	1.17573	+	0.487002i	0.883082	−	0.469219i	$-0.155464\pi$
$67$	9.62375	+	3.98629i	1.17573	+	0.487002i	0.292646	+	0.956221i	$0.405464\pi$
$68$		0			0
$69$	−2.37556	−	5.73510i	−0.285983	−	0.690425i
$70$		0			0
$71$	−10.0462	+	10.0462i	−1.19227	+	1.19227i	−0.215840	+	0.976429i	$0.569249\pi$
$71$	−10.0462	+	10.0462i	−1.19227	+	1.19227i	−0.976429	+	0.215840i	$0.930751\pi$
$72$		0			0
$73$	8.53603	+	8.53603i	0.999067	+	0.999067i	1.00000		0.000932621i	$-0.000296862\pi$
$73$	8.53603	+	8.53603i	0.999067	+	0.999067i	−0.000932621		1.00000i	$0.500297\pi$
$74$		0			0
$75$	13.3029	−	5.51023i	1.53608	−	0.636267i
$76$		0			0
$77$	2.22756	−	5.37782i	0.253854	−	0.612859i
$78$		0			0
$79$			7.40965i			0.833651i	0.908987	+	0.416825i	$0.136857\pi$
$79$			7.40965i			0.833651i	−0.908987	+	0.416825i	$0.863143\pi$
$80$		0			0
$81$		−	4.05662i		−	0.450736i
$82$		0			0
$83$	3.57555	−	8.63214i	0.392467	−	0.947500i	−0.596934	−	0.802291i	$-0.703614\pi$
$83$	3.57555	−	8.63214i	0.392467	−	0.947500i	0.989401	−	0.145209i	$-0.0463856\pi$
$84$		0			0
$85$	−3.34369	+	1.38500i	−0.362674	+	0.150224i
$86$		0			0
$87$	4.01622	+	4.01622i	0.430584	+	0.430584i
$88$		0			0
$89$	−9.02149	+	9.02149i	−0.956276	+	0.956276i	−0.999083	−	0.0428074i	$-0.986370\pi$
$89$	−9.02149	+	9.02149i	−0.956276	+	0.956276i	0.0428074	+	0.999083i	$0.486370\pi$
$90$		0			0
$91$	−1.34780	−	3.25387i	−0.141288	−	0.341098i
$92$		0			0
$93$	−1.53737	−	0.636798i	−0.159417	−	0.0660329i
$94$		0			0
$95$	−18.0351			−1.85036
$96$		0			0
$97$	−1.17783			−0.119591			−0.0597955	−	0.998211i	$-0.519045\pi$
$97$	−1.17783			−0.119591			−0.0597955	+	0.998211i	$0.519045\pi$
$98$		0			0
$99$	−22.4903	−	9.31578i	−2.26036	−	0.936271i
$100$		0			0
$101$	2.12672	+	5.13436i	0.211617	+	0.510888i	0.993672	−	0.112321i	$-0.0358286\pi$
$101$	2.12672	+	5.13436i	0.211617	+	0.510888i	−0.782055	+	0.623209i	$0.785829\pi$
$102$		0			0
$103$	−0.0679587	+	0.0679587i	−0.00669617	+	0.00669617i	−0.710447	−	0.703751i	$-0.751507\pi$
$103$	−0.0679587	+	0.0679587i	−0.00669617	+	0.00669617i	0.703751	+	0.710447i	$0.251507\pi$
$104$		0			0
$105$	−6.10321	−	6.10321i	−0.595613	−	0.595613i
$106$		0			0
$107$	3.62328	−	1.50081i	0.350276	−	0.145089i	−0.200607	−	0.979672i	$-0.564291\pi$
$107$	3.62328	−	1.50081i	0.350276	−	0.145089i	0.550882	+	0.834583i	$0.314291\pi$
$108$		0			0
$109$	−3.93266	+	9.49427i	−0.376680	+	0.909386i	0.615903	+	0.787822i	$0.288791\pi$
$109$	−3.93266	+	9.49427i	−0.376680	+	0.909386i	−0.992584	+	0.121565i	$0.961209\pi$
$110$		0			0
$111$		−	8.98101i		−	0.852440i
$112$		0			0
$113$		−	9.81722i		−	0.923526i	−0.887003	−	0.461763i	$-0.847217\pi$
$113$		−	9.81722i		−	0.923526i	0.887003	−	0.461763i	$-0.152783\pi$
$114$		0			0
$115$	2.85490	−	6.89233i	0.266221	−	0.642713i
$116$		0			0
$117$	−13.6078	+	5.63656i	−1.25805	+	0.521100i
$118$		0			0
$119$	0.794595	+	0.794595i	0.0728404	+	0.0728404i
$120$		0			0
$121$	16.1807	−	16.1807i	1.47097	−	1.47097i
$122$		0			0
$123$	0.801732	+	1.93555i	0.0722897	+	0.174523i
$124$		0			0
$125$	1.10948	+	0.459561i	0.0992349	+	0.0411044i
$126$		0			0
$127$	−14.6535			−1.30029			−0.650145	−	0.759810i	$-0.725292\pi$
$127$	−14.6535			−1.30029			−0.650145	+	0.759810i	$0.725292\pi$
$128$		0			0
$129$	−20.1058			−1.77021
$130$		0			0
$131$	4.19286	+	1.73674i	0.366332	+	0.151740i	0.558253	−	0.829671i	$-0.311472\pi$
$131$	4.19286	+	1.73674i	0.366332	+	0.151740i	−0.191921	+	0.981410i	$0.561472\pi$
$132$		0			0
$133$	2.14294	+	5.17351i	0.185816	+	0.448600i
$134$		0			0
$135$	−7.21429	+	7.21429i	−0.620907	+	0.620907i
$136$		0			0
$137$	9.77584	+	9.77584i	0.835207	+	0.835207i	0.988224	−	0.153017i	$-0.0488989\pi$
$137$	9.77584	+	9.77584i	0.835207	+	0.835207i	−0.153017	+	0.988224i	$0.548899\pi$
$138$		0			0
$139$	6.44774	−	2.67074i	0.546890	−	0.226529i	−0.0920923	−	0.995750i	$-0.529355\pi$
$139$	6.44774	−	2.67074i	0.546890	−	0.226529i	0.638983	+	0.769221i	$0.279355\pi$
$140$		0			0
$141$	−12.6994	+	30.6590i	−1.06948	+	2.58195i
$142$		0			0
$143$		−	20.5010i		−	1.71438i
$144$		0			0
$145$			6.82587i			0.566857i
$146$		0			0
$147$	−1.02557	+	2.47594i	−0.0845873	+	0.204212i
$148$		0			0
$149$	−14.2771	+	5.91376i	−1.16962	+	0.484474i	−0.881069	−	0.472989i	$-0.843175\pi$
$149$	−14.2771	+	5.91376i	−1.16962	+	0.484474i	−0.288556	+	0.957463i	$0.593175\pi$
$150$		0			0
$151$	−3.96600	−	3.96600i	−0.322749	−	0.322749i	0.527072	−	0.849821i	$-0.323290\pi$
$151$	−3.96600	−	3.96600i	−0.322749	−	0.322749i	−0.849821	+	0.527072i	$0.823290\pi$
$152$		0			0
$153$	3.32303	−	3.32303i	0.268651	−	0.268651i
$154$		0			0
$155$	−0.765292	−	1.84758i	−0.0614697	−	0.148401i
$156$		0			0
$157$	−3.21542	−	1.33187i	−0.256619	−	0.106295i	0.250666	−	0.968074i	$-0.419351\pi$
$157$	−3.21542	−	1.33187i	−0.256619	−	0.106295i	−0.507284	+	0.861779i	$0.669351\pi$
$158$		0			0
$159$	7.99710			0.634212
$160$		0			0
$161$	−2.31634			−0.182553
$162$		0			0
$163$	−1.17530	−	0.486827i	−0.0920570	−	0.0381312i	0.336180	−	0.941798i	$-0.390865\pi$
$163$	−1.17530	−	0.486827i	−0.0920570	−	0.0381312i	−0.428237	+	0.903667i	$0.640865\pi$
$164$		0			0
$165$	−19.2267	−	46.4173i	−1.49679	−	3.61358i
$166$		0			0
$167$	−6.11862	+	6.11862i	−0.473473	+	0.473473i	−0.903037	−	0.429564i	$-0.858667\pi$
$167$	−6.11862	+	6.11862i	−0.473473	+	0.473473i	0.429564	+	0.903037i	$0.358667\pi$
$168$		0			0
$169$	0.421263	+	0.421263i	0.0324048	+	0.0324048i
$170$		0			0
$171$	21.6359	−	8.96186i	1.65454	−	0.685331i
$172$		0			0
$173$	6.85868	−	16.5583i	0.521456	−	1.25891i	−0.415543	−	0.909573i	$-0.636409\pi$
$173$	6.85868	−	16.5583i	0.521456	−	1.25891i	0.936999	−	0.349332i	$-0.113591\pi$
$174$		0			0
$175$		−	5.37287i		−	0.406151i
$176$		0			0
$177$		−	35.0157i		−	2.63194i
$178$		0			0
$179$	−6.54277	+	15.7956i	−0.489030	+	1.18062i	0.466180	+	0.884690i	$0.345630\pi$
$179$	−6.54277	+	15.7956i	−0.489030	+	1.18062i	−0.955209	+	0.295932i	$0.904370\pi$
$180$		0			0
$181$	−12.6175	+	5.22636i	−0.937854	+	0.388472i	−0.798653	−	0.601792i	$-0.794454\pi$
$181$	−12.6175	+	5.22636i	−0.937854	+	0.388472i	−0.139202	+	0.990264i	$0.544454\pi$
$182$		0			0
$183$	−7.79874	−	7.79874i	−0.576499	−	0.576499i
$184$		0			0
$185$	7.63195	−	7.63195i	0.561112	−	0.561112i
$186$		0			0
$187$	2.50317	+	6.04320i	0.183050	+	0.441922i
$188$		0			0
$189$	2.92667	+	1.21227i	0.212884	+	0.0881795i
$190$		0			0
$191$	20.0273			1.44912			0.724562	−	0.689210i	$-0.242042\pi$
$191$	20.0273			1.44912			0.724562	+	0.689210i	$0.242042\pi$
$192$		0			0
$193$	15.6384			1.12567			0.562837	−	0.826568i	$-0.309710\pi$
$193$	15.6384			1.12567			0.562837	+	0.826568i	$0.309710\pi$
$194$		0			0
$195$	−28.0850	−	11.6332i	−2.01121	−	0.833069i
$196$		0			0
$197$	5.50906	+	13.3000i	0.392504	+	0.947588i	0.989393	+	0.145264i	$0.0464033\pi$
$197$	5.50906	+	13.3000i	0.392504	+	0.947588i	−0.596889	+	0.802324i	$0.703597\pi$
$198$		0			0
$199$	−13.0662	+	13.0662i	−0.926238	+	0.926238i	−0.997460	−	0.0712229i	$-0.977310\pi$
$199$	−13.0662	+	13.0662i	−0.926238	+	0.926238i	0.0712229	+	0.997460i	$0.477310\pi$
$200$		0			0
$201$	−19.7396	−	19.7396i	−1.39232	−	1.39232i
$202$		0			0
$203$	1.95805	−	0.811051i	0.137428	−	0.0569246i
$204$		0			0
$205$	−0.963506	+	2.32611i	−0.0672942	+	0.162463i
$206$		0			0
$207$			9.68702i			0.673295i
$208$		0			0
$209$			32.5957i			2.25469i
$210$		0			0
$211$	−9.24765	+	22.3258i	−0.636634	+	1.53697i	0.194502	+	0.980902i	$0.437691\pi$
$211$	−9.24765	+	22.3258i	−0.636634	+	1.53697i	−0.831136	+	0.556069i	$0.812309\pi$
$212$		0			0
$213$	35.1769	−	14.5708i	2.41028	−	0.998372i
$214$		0			0
$215$	−17.0856	−	17.0856i	−1.16523	−	1.16523i
$216$		0			0
$217$	−0.439059	+	0.439059i	−0.0298053	+	0.0298053i
$218$		0			0
$219$	−12.3804	−	29.8889i	−0.836590	−	2.01971i
$220$		0			0
$221$	3.65646	+	1.51456i	0.245960	+	0.101880i
$222$		0			0
$223$	7.70633			0.516054			0.258027	−	0.966138i	$-0.416928\pi$
$223$	7.70633			0.516054			0.258027	+	0.966138i	$0.416928\pi$
$224$		0			0
$225$	−22.4696			−1.49797
$226$		0			0
$227$	−5.24849	−	2.17400i	−0.348355	−	0.144293i	0.201644	−	0.979459i	$-0.435372\pi$
$227$	−5.24849	−	2.17400i	−0.348355	−	0.144293i	−0.549998	+	0.835166i	$0.685372\pi$
$228$		0			0
$229$	4.78305	+	11.5473i	0.316073	+	0.763068i	0.999455	+	0.0330068i	$0.0105083\pi$
$229$	4.78305	+	11.5473i	0.316073	+	0.763068i	−0.683382	+	0.730061i	$0.739492\pi$
$230$		0			0
$231$	−11.0306	+	11.0306i	−0.725761	+	0.725761i
$232$		0			0
$233$	−5.82716	−	5.82716i	−0.381750	−	0.381750i	0.489983	−	0.871732i	$-0.337003\pi$
$233$	−5.82716	−	5.82716i	−0.381750	−	0.381750i	−0.871732	+	0.489983i	$0.837003\pi$
$234$		0			0
$235$	−36.8453	+	15.2618i	−2.40353	+	0.995573i
$236$		0			0
$237$	7.59909	−	18.3458i	0.493614	−	1.19169i
$238$		0			0
$239$			5.23408i			0.338565i	0.985568	+	0.169282i	$0.0541450\pi$
$239$			5.23408i			0.338565i	−0.985568	+	0.169282i	$0.945855\pi$
$240$		0			0
$241$		−	0.602343i		−	0.0388003i	−0.999812	−	0.0194002i	$-0.993824\pi$
$241$		−	0.602343i		−	0.0388003i	0.999812	−	0.0194002i	$-0.00617565\pi$
$242$		0			0
$243$	−7.79714	+	18.8240i	−0.500187	+	1.20756i
$244$		0			0
$245$	−2.97553	+	1.23251i	−0.190100	+	0.0787419i
$246$		0			0
$247$	13.9457	+	13.9457i	0.887343	+	0.887343i
$248$		0			0
$249$	−17.7057	+	17.7057i	−1.12205	+	1.12205i
$250$		0			0
$251$	−3.75114	−	9.05605i	−0.236770	−	0.571613i	0.760175	−	0.649718i	$-0.225113\pi$
$251$	−3.75114	−	9.05605i	−0.236770	−	0.571613i	−0.996945	+	0.0781052i	$0.975113\pi$
$252$		0			0
$253$	−12.4568	−	5.15978i	−0.783154	−	0.324393i
$254$		0			0
$255$	9.69917			0.607385
$256$		0			0
$257$	−2.95881			−0.184565			−0.0922827	−	0.995733i	$-0.529416\pi$
$257$	−2.95881			−0.184565			−0.0922827	+	0.995733i	$0.529416\pi$
$258$		0			0
$259$	−3.09611	−	1.28245i	−0.192383	−	0.0796876i
$260$		0			0
$261$	−3.39185	−	8.18866i	−0.209950	−	0.506865i
$262$		0			0
$263$	−4.55305	+	4.55305i	−0.280753	+	0.280753i	−0.833409	−	0.552656i	$-0.813614\pi$
$263$	−4.55305	+	4.55305i	−0.280753	+	0.280753i	0.552656	+	0.833409i	$0.313614\pi$
$264$		0			0
$265$	6.79584	+	6.79584i	0.417465	+	0.417465i
$266$		0			0
$267$	31.5888	−	13.0845i	1.93320	−	0.800758i
$268$		0			0
$269$	−3.39565	+	8.19783i	−0.207037	+	0.499831i	−0.992954	−	0.118501i	$-0.962191\pi$
$269$	−3.39565	+	8.19783i	−0.207037	+	0.499831i	0.785917	+	0.618332i	$0.212191\pi$
$270$		0			0
$271$			7.90544i			0.480221i	0.970746	+	0.240111i	$0.0771837\pi$
$271$			7.90544i			0.480221i	−0.970746	+	0.240111i	$0.922816\pi$
$272$		0			0
$273$			9.43864i			0.571252i
$274$		0			0
$275$	11.9684	−	28.8943i	0.721722	−	1.74239i
$276$		0			0
$277$	2.60561	−	1.07928i	0.156556	−	0.0648475i	−0.303030	−	0.952981i	$-0.597998\pi$
$277$	2.60561	−	1.07928i	0.156556	−	0.0648475i	0.459585	+	0.888134i	$0.347998\pi$
$278$		0			0
$279$	1.83617	+	1.83617i	0.109928	+	0.109928i
$280$		0			0
$281$	14.2063	−	14.2063i	0.847479	−	0.847479i	−0.142339	−	0.989818i	$-0.545462\pi$
$281$	14.2063	−	14.2063i	0.847479	−	0.847479i	0.989818	+	0.142339i	$0.0454623\pi$
$282$		0			0
$283$	1.51835	+	3.66562i	0.0902566	+	0.217899i	0.962561	−	0.271064i	$-0.0873755\pi$
$283$	1.51835	+	3.66562i	0.0902566	+	0.217899i	−0.872305	+	0.488963i	$0.837375\pi$
$284$		0			0
$285$	44.6538	+	18.4962i	2.64506	+	1.09562i
$286$		0			0
$287$	0.781746			0.0461450
$288$		0			0
$289$	15.7372			0.925720
$290$		0			0
$291$	2.91624	+	1.20795i	0.170953	+	0.0708111i
$292$		0			0
$293$	−4.45974	−	10.7668i	−0.260541	−	0.629001i	0.738431	−	0.674329i	$-0.235567\pi$
$293$	−4.45974	−	10.7668i	−0.260541	−	0.629001i	−0.998972	+	0.0453274i	$0.985567\pi$
$294$		0			0
$295$	29.7559	−	29.7559i	1.73245	−	1.73245i
$296$		0			0
$297$	13.0387	+	13.0387i	0.756583	+	0.756583i
$298$		0			0
$299$	−7.53706	+	3.12195i	−0.435879	+	0.180547i
$300$		0			0
$301$	−2.87102	+	6.93125i	−0.165483	+	0.399511i
$302$		0			0
$303$		−	14.8934i		−	0.855605i
$304$		0			0
$305$		−	13.2545i		−	0.758953i
$306$		0			0
$307$	−9.52021	+	22.9838i	−0.543347	+	1.31176i	0.379001	+	0.925396i	$0.376268\pi$
$307$	−9.52021	+	22.9838i	−0.543347	+	1.31176i	−0.922348	+	0.386360i	$0.873732\pi$
$308$		0			0
$309$	0.237958	−	0.0985653i	0.0135369	−	0.00560719i
$310$		0			0
$311$	11.0470	+	11.0470i	0.626420	+	0.626420i	0.947165	−	0.320745i	$-0.103933\pi$
$311$	11.0470	+	11.0470i	0.626420	+	0.626420i	−0.320745	+	0.947165i	$0.603933\pi$
$312$		0			0
$313$	−15.4459	+	15.4459i	−0.873054	+	0.873054i	−0.992804	−	0.119750i	$-0.961791\pi$
$313$	−15.4459	+	15.4459i	−0.873054	+	0.873054i	0.119750	+	0.992804i	$0.461791\pi$
$314$		0			0
$315$	5.15440	+	12.4438i	0.290417	+	0.701130i
$316$		0			0
$317$	28.2135	+	11.6864i	1.58463	+	0.656374i	0.989138	−	0.146989i	$-0.0469583\pi$
$317$	28.2135	+	11.6864i	1.58463	+	0.656374i	0.595489	+	0.803363i	$0.296958\pi$
$318$		0			0
$319$	12.3367			0.690722
$320$		0			0
$321$	−10.5102			−0.586622
$322$		0			0
$323$	−5.81361	−	2.40808i	−0.323478	−	0.133989i
$324$		0			0
$325$	−7.24154	−	17.4826i	−0.401688	−	0.969762i
$326$		0			0
$327$	19.4740	−	19.4740i	1.07692	−	1.07692i
$328$		0			0
$329$	8.75594	+	8.75594i	0.482731	+	0.482731i
$330$		0			0
$331$	−0.500209	+	0.207194i	−0.0274940	+	0.0113884i	−0.396388	−	0.918083i	$-0.629737\pi$
$331$	−0.500209	+	0.207194i	−0.0274940	+	0.0113884i	0.368894	+	0.929471i	$0.379737\pi$
$332$		0			0
$333$	−5.36327	+	12.9481i	−0.293905	+	0.709550i
$334$		0			0
$335$		−	33.5489i		−	1.83297i
$336$		0			0
$337$			2.29568i			0.125054i	0.998043	+	0.0625268i	$0.0199159\pi$
$337$			2.29568i			0.125054i	−0.998043	+	0.0625268i	$0.980084\pi$
$338$		0			0
$339$	−10.0682	+	24.3068i	−0.546830	+	1.32016i
$340$		0			0
$341$	−3.33921	+	1.38315i	−0.180828	+	0.0749016i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	−14.1371	+	14.1371i	−0.761115	+	0.761115i
$346$		0			0
$347$	0.117249	+	0.283063i	0.00629423	+	0.0151956i	0.926995	−	0.375073i	$-0.122382\pi$
$347$	0.117249	+	0.283063i	0.00629423	+	0.0151956i	−0.920701	+	0.390268i	$0.872382\pi$
$348$		0			0
$349$	−18.8618	−	7.81280i	−1.00965	−	0.418210i	−0.184322	−	0.982866i	$-0.559009\pi$
$349$	−18.8618	−	7.81280i	−1.00965	−	0.418210i	−0.825326	+	0.564656i	$0.809009\pi$
$350$		0			0
$351$	11.1569			0.595512
$352$		0			0
$353$	13.6526			0.726653			0.363326	−	0.931662i	$-0.381641\pi$
$353$	13.6526			0.726653			0.363326	+	0.931662i	$0.381641\pi$
$354$		0			0
$355$	42.2750	+	17.5109i	2.24372	+	0.929380i
$356$		0			0
$357$	−1.15246	−	2.78228i	−0.0609945	−	0.147254i
$358$		0			0
$359$	−10.2515	+	10.2515i	−0.541054	+	0.541054i	−0.923838	−	0.382784i	$-0.874965\pi$
$359$	−10.2515	+	10.2515i	−0.541054	+	0.541054i	0.382784	+	0.923838i	$0.374965\pi$
$360$		0			0
$361$	−8.73797	−	8.73797i	−0.459893	−	0.459893i
$362$		0			0
$363$	−56.6567	+	23.4680i	−2.97371	+	1.23175i
$364$		0			0
$365$	14.8785	−	35.9200i	0.778778	−	1.88014i
$366$		0			0
$367$			3.90421i			0.203798i	0.994795	+	0.101899i	$0.0324918\pi$
$367$			3.90421i			0.203798i	−0.994795	+	0.101899i	$0.967508\pi$
$368$		0			0
$369$		−	3.26930i		−	0.170193i
$370$		0			0
$371$	1.14195	−	2.75692i	0.0592872	−	0.143132i
$372$		0			0
$373$	3.68978	−	1.52836i	0.191050	−	0.0791354i	−0.285107	−	0.958496i	$-0.592029\pi$
$373$	3.68978	−	1.52836i	0.191050	−	0.0791354i	0.476157	+	0.879360i	$0.342029\pi$
$374$		0			0
$375$	−2.27569	−	2.27569i	−0.117516	−	0.117516i
$376$		0			0
$377$	5.27811	−	5.27811i	0.271837	−	0.271837i
$378$		0			0
$379$	4.66538	+	11.2632i	0.239644	+	0.578553i	0.997246	−	0.0741646i	$-0.0236290\pi$
$379$	4.66538	+	11.2632i	0.239644	+	0.578553i	−0.757602	+	0.652717i	$0.773629\pi$
$380$		0			0
$381$	36.2812	+	15.0282i	1.85874	+	0.769916i
$382$		0			0
$383$	−17.2598			−0.881936			−0.440968	−	0.897523i	$-0.645365\pi$
$383$	−17.2598			−0.881936			−0.440968	+	0.897523i	$0.645365\pi$
$384$		0			0
$385$	−18.7474			−0.955454
$386$		0			0
$387$	28.9868	+	12.0067i	1.47348	+	0.610337i
$388$		0			0
$389$	−3.00728	−	7.26021i	−0.152475	−	0.368107i	0.829123	−	0.559066i	$-0.188840\pi$
$389$	−3.00728	−	7.26021i	−0.152475	−	0.368107i	−0.981598	+	0.190959i	$0.938840\pi$
$390$		0			0
$391$	1.84055	−	1.84055i	0.0930805	−	0.0930805i
$392$		0			0
$393$	−8.60012	−	8.60012i	−0.433818	−	0.433818i
$394$		0			0
$395$	22.0477	−	9.13244i	1.10934	−	0.459503i
$396$		0			0
$397$	0.701698	−	1.69405i	0.0352172	−	0.0850218i	−0.905292	−	0.424789i	$-0.860348\pi$
$397$	0.701698	−	1.69405i	0.0352172	−	0.0850218i	0.940510	+	0.339767i	$0.110348\pi$
$398$		0			0
$399$		−	15.0070i		−	0.751290i
$400$		0			0
$401$			1.26709i			0.0632754i	0.999499	+	0.0316377i	$0.0100723\pi$
$401$			1.26709i			0.0632754i	−0.999499	+	0.0316377i	$0.989928\pi$
$402$		0			0
$403$	−0.836879	+	2.02040i	−0.0416879	+	0.100644i
$404$		0			0
$405$	−12.0706	+	4.99981i	−0.599793	+	0.248443i
$406$		0			0
$407$	−13.7936	−	13.7936i	−0.683722	−	0.683722i
$408$		0			0
$409$	−4.14840	+	4.14840i	−0.205125	+	0.205125i	−0.802192	−	0.597067i	$-0.796333\pi$
$409$	−4.14840	+	4.14840i	−0.205125	+	0.205125i	0.597067	+	0.802192i	$0.296333\pi$
$410$		0			0
$411$	−14.1786	−	34.2301i	−0.699378	−	1.68845i
$412$		0			0
$413$	−12.0713	−	5.00009i	−0.593989	−	0.246039i
$414$		0			0
$415$	−30.0921			−1.47716
$416$		0			0
$417$	−18.7032			−0.915901
$418$		0			0
$419$	−22.3678	−	9.26503i	−1.09274	−	0.452626i	−0.237776	−	0.971320i	$-0.576419\pi$
$419$	−22.3678	−	9.26503i	−1.09274	−	0.452626i	−0.854960	+	0.518694i	$0.826419\pi$
$420$		0			0
$421$	1.09191	+	2.63610i	0.0532163	+	0.128476i	0.948252	−	0.317519i	$-0.102850\pi$
$421$	1.09191	+	2.63610i	0.0532163	+	0.128476i	−0.895035	+	0.445995i	$0.852850\pi$
$422$		0			0
$423$	36.6178	−	36.6178i	1.78042	−	1.78042i
$424$		0			0
$425$	4.26925	+	4.26925i	0.207089	+	0.207089i
$426$		0			0
$427$	−3.80216	+	1.57491i	−0.183999	+	0.0762151i
$428$		0			0
$429$	−21.0252	+	50.7592i	−1.01510	+	2.45068i
$430$		0			0
$431$			8.63598i			0.415980i	0.978131	+	0.207990i	$0.0666922\pi$
$431$			8.63598i			0.415980i	−0.978131	+	0.207990i	$0.933308\pi$
$432$		0			0
$433$		−	4.81690i		−	0.231486i	−0.993279	−	0.115743i	$-0.963075\pi$
$433$		−	4.81690i		−	0.231486i	0.993279	−	0.115743i	$-0.0369248\pi$
$434$		0			0
$435$	7.00038	−	16.9004i	0.335642	−	0.810313i
$436$		0			0
$437$	11.9836	−	4.96376i	0.573252	−	0.237449i
$438$		0			0
$439$	−9.57691	−	9.57691i	−0.457081	−	0.457081i	0.440615	−	0.897696i	$-0.354760\pi$
$439$	−9.57691	−	9.57691i	−0.457081	−	0.457081i	−0.897696	+	0.440615i	$0.854760\pi$
$440$		0			0
$441$	2.95715	−	2.95715i	0.140817	−	0.140817i
$442$		0			0
$443$	12.9613	+	31.2912i	0.615808	+	1.48669i	0.856530	+	0.516098i	$0.172616\pi$
$443$	12.9613	+	31.2912i	0.615808	+	1.48669i	−0.240722	+	0.970594i	$0.577384\pi$
$444$		0			0
$445$	37.9628	+	15.7247i	1.79961	+	0.745422i
$446$		0			0
$447$	41.4141			1.95882
$448$		0			0
$449$	6.30540			0.297570			0.148785	−	0.988870i	$-0.452464\pi$
$449$	6.30540			0.297570			0.148785	+	0.988870i	$0.452464\pi$
$450$		0			0
$451$	4.20408	+	1.74139i	0.197963	+	0.0819988i
$452$		0			0
$453$	5.75217	+	13.8870i	0.270261	+	0.652467i
$454$		0			0
$455$	−8.02083	+	8.02083i	−0.376023	+	0.376023i
$456$		0			0
$457$	−14.5745	−	14.5745i	−0.681767	−	0.681767i	0.278631	−	0.960398i	$-0.410119\pi$
$457$	−14.5745	−	14.5745i	−0.681767	−	0.681767i	−0.960398	+	0.278631i	$0.910119\pi$
$458$		0			0
$459$	−3.28878	+	1.36226i	−0.153507	+	0.0635848i
$460$		0			0
$461$	12.6342	−	30.5016i	0.588433	−	1.42060i	−0.296567	−	0.955012i	$-0.595842\pi$
$461$	12.6342	−	30.5016i	0.588433	−	1.42060i	0.885000	−	0.465591i	$-0.154158\pi$
$462$		0			0
$463$			6.86681i			0.319128i	0.987188	+	0.159564i	$0.0510088\pi$
$463$			6.86681i			0.319128i	−0.987188	+	0.159564i	$0.948991\pi$
$464$		0			0
$465$			5.35934i			0.248533i
$466$		0			0
$467$	3.84799	−	9.28988i	0.178064	−	0.429884i	−0.809496	−	0.587125i	$-0.800260\pi$
$467$	3.84799	−	9.28988i	0.178064	−	0.429884i	0.987560	+	0.157241i	$0.0502598\pi$
$468$		0			0
$469$	−9.62375	+	3.98629i	−0.444383	+	0.184070i
$470$		0			0
$471$	6.59526	+	6.59526i	0.303893	+	0.303893i
$472$		0			0
$473$	−30.8796	+	30.8796i	−1.41985	+	1.41985i
$474$		0			0
$475$	11.5137	+	27.7966i	0.528286	+	1.27539i
$476$		0			0
$477$	−11.5296	−	4.77570i	−0.527902	−	0.218664i
$478$		0			0
$479$	6.21656			0.284042			0.142021	−	0.989864i	$-0.454640\pi$
$479$	6.21656			0.284042			0.142021	+	0.989864i	$0.454640\pi$
$480$		0			0
$481$	−11.8028			−0.538163
$482$		0			0
$483$	5.73510	+	2.37556i	0.260956	+	0.108092i
$484$		0			0
$485$	1.45169	+	3.50468i	0.0659177	+	0.159140i
$486$		0			0
$487$	26.4225	−	26.4225i	1.19732	−	1.19732i	0.222349	−	0.974967i	$-0.428627\pi$
$487$	26.4225	−	26.4225i	1.19732	−	1.19732i	0.974967	−	0.222349i	$-0.0713725\pi$
$488$		0			0
$489$	2.41071	+	2.41071i	0.109016	+	0.109016i
$490$		0			0
$491$	20.1620	−	8.35138i	0.909898	−	0.376892i	0.121881	−	0.992545i	$-0.461107\pi$
$491$	20.1620	−	8.35138i	0.909898	−	0.376892i	0.788018	+	0.615652i	$0.211107\pi$
$492$		0			0
$493$	−0.911400	+	2.20031i	−0.0410474	+	0.0990971i
$494$		0			0
$495$			78.4023i			3.52392i
$496$		0			0
$497$		−	14.2075i		−	0.637295i
$498$		0			0
$499$	5.41301	−	13.0682i	0.242319	−	0.585011i	−0.755193	−	0.655503i	$-0.772457\pi$
$499$	5.41301	−	13.0682i	0.242319	−	0.585011i	0.997512	+	0.0704918i	$0.0224568\pi$
$500$		0			0
$501$	21.4244	−	8.87426i	0.957170	−	0.396473i
$502$		0			0
$503$	7.30716	+	7.30716i	0.325810	+	0.325810i	0.850991	−	0.525181i	$-0.176002\pi$
$503$	7.30716	+	7.30716i	0.325810	+	0.325810i	−0.525181	+	0.850991i	$0.676002\pi$
$504$		0			0
$505$	12.6563	−	12.6563i	0.563196	−	0.563196i
$506$		0			0
$507$	−0.610987	−	1.47505i	−0.0271349	−	0.0655094i
$508$		0			0
$509$	−31.9079	−	13.2167i	−1.41429	−	0.585818i	−0.460871	−	0.887467i	$-0.652463\pi$
$509$	−31.9079	−	13.2167i	−1.41429	−	0.585818i	−0.953419	+	0.301649i	$0.902463\pi$
$510$		0			0
$511$	−12.0718			−0.534024
$512$		0			0
$513$	−17.7390			−0.783195
$514$		0			0
$515$	0.285973	+	0.118454i	0.0126015	+	0.00521970i
$516$		0			0
$517$	27.5834	+	66.5923i	1.21312	+	2.92872i
$518$		0			0
$519$	−33.9633	+	33.9633i	−1.49082	+	1.49082i
$520$		0			0
$521$	−18.9848	−	18.9848i	−0.831740	−	0.831740i	0.156014	−	0.987755i	$-0.450135\pi$
$521$	−18.9848	−	18.9848i	−0.831740	−	0.831740i	−0.987755	+	0.156014i	$0.950135\pi$
$522$		0			0
$523$	6.34733	−	2.62915i	0.277550	−	0.114965i	−0.239567	−	0.970880i	$-0.577005\pi$
$523$	6.34733	−	2.62915i	0.277550	−	0.114965i	0.517116	+	0.855915i	$0.327005\pi$
$524$		0			0
$525$	−5.51023	+	13.3029i	−0.240486	+	0.580585i
$526$		0			0
$527$		−	0.697748i		−	0.0303944i
$528$		0			0
$529$		−	17.6346i		−	0.766721i
$530$		0			0
$531$	−20.9106	+	50.4827i	−0.907444	+	2.19076i
$532$		0			0
$533$	2.54370	−	1.05364i	0.110180	−	0.0456380i
$534$		0			0
$535$	−8.93143	−	8.93143i	−0.386140	−	0.386140i
$536$		0			0
$537$	32.3990	−	32.3990i	1.39812	−	1.39812i
$538$		0			0
$539$	2.22756	+	5.37782i	0.0959480	+	0.231639i
$540$		0			0
$541$	3.31035	+	1.37119i	0.142323	+	0.0589521i	0.452708	−	0.891659i	$-0.350458\pi$
$541$	3.31035	+	1.37119i	0.142323	+	0.0589521i	−0.310385	+	0.950611i	$0.600458\pi$
$542$		0			0
$543$	36.6002			1.57067
$544$		0			0
$545$	33.0975			1.41774
$546$		0			0
$547$	−3.66912	−	1.51980i	−0.156880	−	0.0649819i	0.302862	−	0.953035i	$-0.402058\pi$
$547$	−3.66912	−	1.51980i	−0.156880	−	0.0649819i	−0.459742	+	0.888053i	$0.652058\pi$
$548$		0			0
$549$	6.58633	+	15.9008i	0.281098	+	0.678630i
$550$		0			0
$551$	−8.39195	+	8.39195i	−0.357509	+	0.357509i
$552$		0			0
$553$	−5.23941	−	5.23941i	−0.222802	−	0.222802i
$554$		0			0
$555$	−26.7233	+	11.0691i	−1.13434	+	0.469859i
$556$		0			0
$557$	−13.2897	+	32.0843i	−0.563105	+	1.35946i	0.344166	+	0.938909i	$0.388162\pi$
$557$	−13.2897	+	32.0843i	−0.563105	+	1.35946i	−0.907271	+	0.420546i	$0.861838\pi$
$558$		0			0
$559$			26.4230i			1.11757i
$560$		0			0
$561$		−	17.5297i		−	0.740106i
$562$		0			0
$563$	9.26787	−	22.3746i	0.390594	−	0.942978i	−0.599216	−	0.800587i	$-0.704521\pi$
$563$	9.26787	−	22.3746i	0.390594	−	0.942978i	0.989811	−	0.142391i	$-0.0454790\pi$
$564$		0			0
$565$	−29.2114	+	12.0998i	−1.22893	+	0.509041i
$566$		0			0
$567$	2.86846	+	2.86846i	0.120464	+	0.120464i
$568$		0			0
$569$	1.02544	−	1.02544i	0.0429886	−	0.0429886i	−0.685286	−	0.728274i	$-0.740323\pi$
$569$	1.02544	−	1.02544i	0.0429886	−	0.0429886i	0.728274	+	0.685286i	$0.240323\pi$
$570$		0			0
$571$	−17.2168	−	41.5649i	−0.720499	−	1.73944i	−0.671926	−	0.740618i	$-0.734533\pi$
$571$	−17.2168	−	41.5649i	−0.720499	−	1.73944i	−0.0485726	−	0.998820i	$-0.515467\pi$
$572$		0			0
$573$	−49.5863	−	20.5393i	−2.07150	−	0.858042i
$574$		0			0
$575$	−12.4454			−0.519007
$576$		0			0
$577$	35.0309			1.45836			0.729178	−	0.684324i	$-0.239903\pi$
$577$	35.0309			1.45836			0.729178	+	0.684324i	$0.239903\pi$
$578$		0			0
$579$	−38.7196	−	16.0382i	−1.60913	−	0.666524i
$580$		0			0
$581$	3.57555	+	8.63214i	0.148339	+	0.358121i
$582$		0			0
$583$	12.2824	−	12.2824i	0.508686	−	0.508686i
$584$		0			0
$585$	33.5435	+	33.5435i	1.38685	+	1.38685i
$586$		0			0
$587$	39.9549	−	16.5499i	1.64912	−	0.683086i	0.651946	−	0.758265i	$-0.273953\pi$
$587$	39.9549	−	16.5499i	1.64912	−	0.683086i	0.997170	+	0.0751787i	$0.0239527\pi$
$588$		0			0
$589$	1.33060	−	3.21235i	0.0548264	−	0.132363i
$590$		0			0
$591$		−	38.5799i		−	1.58697i
$592$		0			0
$593$			14.9623i			0.614428i	0.951640	+	0.307214i	$0.0993968\pi$
$593$			14.9623i			0.614428i	−0.951640	+	0.307214i	$0.900603\pi$
$594$		0			0
$595$	1.38500	−	3.34369i	0.0567795	−	0.137078i
$596$		0			0
$597$	45.7513	−	18.9508i	1.87248	−	0.775605i
$598$		0			0
$599$	−5.32543	−	5.32543i	−0.217591	−	0.217591i	0.589892	−	0.807483i	$-0.299170\pi$
$599$	−5.32543	−	5.32543i	−0.217591	−	0.217591i	−0.807483	+	0.589892i	$0.799170\pi$
$600$		0			0
$601$	0.961043	−	0.961043i	0.0392017	−	0.0392017i	−0.687234	−	0.726436i	$-0.741175\pi$
$601$	0.961043	−	0.961043i	0.0392017	−	0.0392017i	0.726436	+	0.687234i	$0.241175\pi$
$602$		0			0
$603$	16.6708	+	40.2470i	0.678889	+	1.63898i
$604$		0			0
$605$	−68.0889	−	28.2034i	−2.76821	−	1.14663i
$606$		0			0
$607$	−14.9244			−0.605763			−0.302882	−	0.953028i	$-0.597949\pi$
$607$	−14.9244			−0.605763			−0.302882	+	0.953028i	$0.597949\pi$
$608$		0			0
$609$	−5.67979			−0.230157
$610$		0			0
$611$	40.2920	+	16.6895i	1.63004	+	0.675184i
$612$		0			0
$613$	8.77913	+	21.1947i	0.354586	+	0.856045i	0.996042	+	0.0888857i	$0.0283306\pi$
$613$	8.77913	+	21.1947i	0.354586	+	0.856045i	−0.641456	+	0.767160i	$0.721669\pi$
$614$		0			0
$615$	4.77116	−	4.77116i	0.192392	−	0.192392i
$616$		0			0
$617$	6.04990	+	6.04990i	0.243560	+	0.243560i	0.818321	−	0.574761i	$-0.194905\pi$
$617$	6.04990	+	6.04990i	0.243560	+	0.243560i	−0.574761	+	0.818321i	$0.694905\pi$
$618$		0			0
$619$	−42.1079	+	17.4417i	−1.69246	+	0.701040i	−0.999796	−	0.0202212i	$-0.993563\pi$
$619$	−42.1079	+	17.4417i	−1.69246	+	0.701040i	−0.692664	+	0.721261i	$0.743563\pi$
$620$		0			0
$621$	2.80802	−	6.77916i	0.112682	−	0.272038i
$622$		0			0
$623$		−	12.7583i		−	0.511151i
$624$		0			0
$625$			22.9966i			0.919865i
$626$		0			0
$627$	33.4291	−	80.7049i	1.33503	−	3.22304i
$628$		0			0
$629$	3.47918	−	1.44112i	0.138724	−	0.0574614i
$630$		0			0
$631$	28.3911	+	28.3911i	1.13023	+	1.13023i	0.990138	+	0.140095i	$0.0447409\pi$
$631$	28.3911	+	28.3911i	1.13023	+	1.13023i	0.140095	+	0.990138i	$0.455259\pi$
$632$		0			0
$633$	45.7932	−	45.7932i	1.82012	−	1.82012i
$634$		0			0
$635$	18.0606	+	43.6020i	0.716711	+	1.73029i
$636$		0			0
$637$	3.25387	+	1.34780i	0.128923	+	0.0534017i
$638$		0			0
$639$	−59.4165			−2.35048
$640$		0			0
$641$	−0.683472			−0.0269955			−0.0134978	−	0.999909i	$-0.504297\pi$
$641$	−0.683472			−0.0269955			−0.0134978	+	0.999909i	$0.504297\pi$
$642$		0			0
$643$	0.843549	+	0.349409i	0.0332663	+	0.0137794i	0.399255	−	0.916840i	$-0.369269\pi$
$643$	0.843549	+	0.349409i	0.0332663	+	0.0137794i	−0.365988	+	0.930619i	$0.619269\pi$
$644$		0			0
$645$	24.7805	+	59.8254i	0.975731	+	2.35562i
$646$		0			0
$647$	11.9251	−	11.9251i	0.468826	−	0.468826i	−0.432708	−	0.901534i	$-0.642442\pi$
$647$	11.9251	−	11.9251i	0.468826	−	0.468826i	0.901534	+	0.432708i	$0.142442\pi$
$648$		0			0
$649$	−53.7792	−	53.7792i	−2.11102	−	2.11102i
$650$		0			0
$651$	1.53737	−	0.636798i	0.0602541	−	0.0249581i
$652$		0			0
$653$	3.30886	−	7.98830i	0.129486	−	0.312606i	−0.845819	−	0.533470i	$-0.820888\pi$
$653$	3.30886	−	7.98830i	0.129486	−	0.312606i	0.975305	+	0.220864i	$0.0708877\pi$
$654$		0			0
$655$		−	14.6165i		−	0.571115i
$656$		0			0
$657$			50.4847i			1.96960i
$658$		0			0
$659$	15.6304	−	37.7350i	0.608872	−	1.46995i	−0.255356	−	0.966847i	$-0.582193\pi$
$659$	15.6304	−	37.7350i	0.608872	−	1.46995i	0.864228	−	0.503100i	$-0.167807\pi$
$660$		0			0
$661$	20.5509	−	8.51245i	0.799336	−	0.331096i	0.0546455	−	0.998506i	$-0.482597\pi$
$661$	20.5509	−	8.51245i	0.799336	−	0.331096i	0.744690	+	0.667410i	$0.232597\pi$
$662$		0			0
$663$	−7.49990	−	7.49990i	−0.291272	−	0.291272i
$664$		0			0
$665$	12.7528	−	12.7528i	0.494531	−	0.494531i
$666$		0			0
$667$	−1.87867	−	4.53550i	−0.0727422	−	0.175615i
$668$		0			0
$669$	−19.0804	−	7.90335i	−0.737690	−	0.305561i
$670$		0			0
$671$	−23.9555			−0.924793
$672$		0			0
$673$	−13.0268			−0.502147			−0.251073	−	0.967968i	$-0.580784\pi$
$673$	−13.0268			−0.502147			−0.251073	+	0.967968i	$0.580784\pi$
$674$		0			0
$675$	15.7246	+	6.51336i	0.605241	+	0.250699i
$676$		0			0
$677$	−3.47399	−	8.38695i	−0.133516	−	0.322337i	0.842955	−	0.537984i	$-0.180814\pi$
$677$	−3.47399	−	8.38695i	−0.133516	−	0.322337i	−0.976471	+	0.215647i	$0.930814\pi$
$678$		0			0
$679$	0.832854	−	0.832854i	0.0319620	−	0.0319620i
$680$		0			0
$681$	10.7654	+	10.7654i	0.412529	+	0.412529i
$682$		0			0
$683$	−20.5580	+	8.51541i	−0.786631	+	0.325833i	−0.739588	−	0.673060i	$-0.764980\pi$
$683$	−20.5580	+	8.51541i	−0.786631	+	0.325833i	−0.0470427	+	0.998893i	$0.514980\pi$
$684$		0			0
$685$	17.0396	−	41.1371i	0.651048	−	1.57177i
$686$		0			0
$687$		−	33.4957i		−	1.27794i
$688$		0			0
$689$		−	10.5098i		−	0.400391i
$690$		0			0
$691$	2.26569	−	5.46986i	0.0861909	−	0.208083i	−0.874907	−	0.484291i	$-0.839078\pi$
$691$	2.26569	−	5.46986i	0.0861909	−	0.208083i	0.961098	+	0.276208i	$0.0890777\pi$
$692$		0			0
$693$	22.4903	−	9.31578i	0.854335	−	0.353877i
$694$		0			0
$695$	−15.8938	−	15.8938i	−0.602885	−	0.602885i
$696$		0			0
$697$	−0.621171	+	0.621171i	−0.0235285	+	0.0235285i
$698$		0			0
$699$	8.45153	+	20.4038i	0.319666	+	0.771743i
$700$		0			0
$701$	40.4514	+	16.7555i	1.52783	+	0.632847i	0.979141	−	0.203180i	$-0.0651277\pi$
$701$	40.4514	+	16.7555i	1.52783	+	0.632847i	0.548687	+	0.836028i	$0.315128\pi$
$702$		0			0
$703$	18.7660			0.707772
$704$		0			0
$705$	106.879			4.02529
$706$		0			0
$707$	−5.13436	−	2.12672i	−0.193097	−	0.0799835i
$708$		0			0
$709$	12.7979	+	30.8968i	0.480634	+	1.16035i	0.959309	+	0.282360i	$0.0911172\pi$
$709$	12.7979	+	30.8968i	0.480634	+	1.16035i	−0.478675	+	0.877992i	$0.658883\pi$
$710$		0			0
$711$	−21.9115	+	21.9115i	−0.821744	+	0.821744i
$712$		0			0
$713$	1.01701	+	1.01701i	0.0380872	+	0.0380872i
$714$		0			0
$715$	−61.0015	+	25.2676i	−2.28133	+	0.944956i
$716$		0			0
$717$	5.36790	−	12.9593i	0.200468	−	0.483972i
$718$		0			0
$719$			38.6027i			1.43964i	0.694162	+	0.719818i	$0.255775\pi$
$719$			38.6027i			1.43964i	−0.694162	+	0.719818i	$0.744225\pi$
$720$		0			0
$721$		−	0.0961082i		−	0.00357926i
$722$		0			0
$723$	−0.617743	+	1.49136i	−0.0229741	+	0.0554644i
$724$		0			0
$725$	10.5203	−	4.35767i	0.390716	−	0.161840i
$726$		0			0
$727$	−15.7873	−	15.7873i	−0.585518	−	0.585518i	0.350896	−	0.936414i	$-0.385877\pi$
$727$	−15.7873	−	15.7873i	−0.585518	−	0.585518i	−0.936414	+	0.350896i	$0.885877\pi$
$728$		0			0
$729$	30.0050	−	30.0050i	1.11130	−	1.11130i
$730$		0			0
$731$	−3.22624	−	7.78884i	−0.119327	−	0.288081i
$732$		0			0
$733$	19.7726	+	8.19007i	0.730317	+	0.302507i	0.716682	−	0.697400i	$-0.245660\pi$
$733$	19.7726	+	8.19007i	0.730317	+	0.302507i	0.0136346	+	0.999907i	$0.495660\pi$
$734$		0			0
$735$	8.63125			0.318368
$736$		0			0
$737$	−60.6344			−2.23350
$738$		0			0
$739$	35.5446	+	14.7231i	1.30753	+	0.541597i	0.924163	−	0.381999i	$-0.124764\pi$
$739$	35.5446	+	14.7231i	1.30753	+	0.541597i	0.383368	+	0.923596i	$0.374764\pi$
$740$		0			0
$741$	−20.2264	−	48.8309i	−0.743036	−	1.79385i
$742$		0			0
$743$	−26.2045	+	26.2045i	−0.961351	+	0.961351i	−0.999280	−	0.0379295i	$-0.987924\pi$
$743$	−26.2045	+	26.2045i	−0.961351	+	0.961351i	0.0379295	+	0.999280i	$0.487924\pi$
$744$		0			0
$745$	35.1932	+	35.1932i	1.28938	+	1.28938i
$746$		0			0
$747$	36.1000	−	14.9531i	1.32083	−	0.547106i
$748$		0			0
$749$	−1.50081	+	3.62328i	−0.0548385	+	0.132392i
$750$		0			0
$751$		−	27.5199i		−	1.00421i	−0.864805	−	0.502107i	$-0.832558\pi$
$751$		−	27.5199i		−	1.00421i	0.864805	−	0.502107i	$-0.167442\pi$
$752$		0			0
$753$			26.2692i			0.957304i
$754$		0			0
$755$	−6.91285	+	16.6891i	−0.251584	+	0.607378i
$756$		0			0
$757$	−9.91107	+	4.10530i	−0.360224	+	0.149210i	−0.555453	−	0.831548i	$-0.687455\pi$
$757$	−9.91107	+	4.10530i	−0.360224	+	0.149210i	0.195229	+	0.980758i	$0.437455\pi$
$758$		0			0
$759$	25.5506	+	25.5506i	0.927428	+	0.927428i
$760$		0			0
$761$	−25.5121	+	25.5121i	−0.924812	+	0.924812i	−0.997365	−	0.0725526i	$-0.976885\pi$
$761$	−25.5121	+	25.5121i	−0.924812	+	0.924812i	0.0725526	+	0.997365i	$0.476885\pi$
$762$		0			0
$763$	−3.93266	−	9.49427i	−0.142372	−	0.343716i
$764$		0			0
$765$	−13.9835	−	5.79214i	−0.505573	−	0.209415i
$766$		0			0
$767$	−46.0176			−1.66160
$768$		0			0
$769$	−16.1430			−0.582130			−0.291065	−	0.956703i	$-0.594010\pi$
$769$	−16.1430			−0.582130			−0.291065	+	0.956703i	$0.594010\pi$
$770$		0			0
$771$	7.32582	+	3.03445i	0.263833	+	0.109283i
$772$		0			0
$773$	−7.53363	−	18.1878i	−0.270966	−	0.654170i	0.728559	−	0.684983i	$-0.240190\pi$
$773$	−7.53363	−	18.1878i	−0.270966	−	0.654170i	−0.999525	+	0.0308132i	$0.990190\pi$
$774$		0			0
$775$	−2.35901	+	2.35901i	−0.0847380	+	0.0847380i
$776$		0			0
$777$	6.35053	+	6.35053i	0.227824	+	0.227824i
$778$		0			0
$779$	−4.04437	+	1.67523i	−0.144904	+	0.0600214i
$780$		0			0
$781$	31.6482	−	76.4054i	1.13246	−	2.73400i
$782$		0			0
$783$			6.71378i			0.239931i
$784$		0			0
$785$			11.2091i			0.400071i
$786$		0			0
$787$	0.899001	−	2.17038i	0.0320459	−	0.0773657i	−0.907046	−	0.421031i	$-0.861668\pi$
$787$	0.899001	−	2.17038i	0.0320459	−	0.0773657i	0.939092	+	0.343665i	$0.111668\pi$
$788$		0			0
$789$	15.9425	−	6.60360i	0.567568	−	0.235094i
$790$		0			0
$791$	6.94182	+	6.94182i	0.246823	+	0.246823i
$792$		0			0
$793$	−10.2491	+	10.2491i	−0.363956	+	0.363956i
$794$		0			0
$795$	−9.85648	−	23.7956i	−0.349573	−	0.843945i
$796$		0			0
$797$	−33.6100	−	13.9217i	−1.19053	−	0.493133i	−0.302601	−	0.953117i	$-0.597855\pi$
$797$	−33.6100	−	13.9217i	−1.19053	−	0.493133i	−0.887927	+	0.459985i	$0.847855\pi$
$798$		0			0
$799$	−13.9149			−0.492272
$800$		0			0
$801$	−53.3559			−1.88524
$802$		0			0
$803$	−64.9198	−	26.8906i	−2.29097	−	0.948950i
$804$		0			0
$805$	2.85490	+	6.89233i	0.100622	+	0.242923i
$806$		0			0
$807$	16.8148	−	16.8148i	0.591910	−	0.591910i
$808$		0			0
$809$	−25.3002	−	25.3002i	−0.889507	−	0.889507i	0.104969	−	0.994476i	$-0.466526\pi$
$809$	−25.3002	−	25.3002i	−0.889507	−	0.889507i	−0.994476	+	0.104969i	$0.966526\pi$
$810$		0			0
$811$	18.0148	−	7.46198i	0.632586	−	0.262026i	−0.0432656	−	0.999064i	$-0.513776\pi$
$811$	18.0148	−	7.46198i	0.632586	−	0.262026i	0.675851	+	0.737038i	$0.263776\pi$
$812$		0			0
$813$	8.10755	−	19.5734i	0.284344	−	0.686468i
$814$		0			0
$815$			4.09718i			0.143518i
$816$		0			0
$817$		−	42.0113i		−	1.46979i
$818$		0			0
$819$	5.63656	−	13.6078i	0.196957	−	0.475497i
$820$		0			0
$821$	−20.3935	+	8.44725i	−0.711737	+	0.294811i	−0.709023	−	0.705185i	$-0.750864\pi$
$821$	−20.3935	+	8.44725i	−0.711737	+	0.294811i	−0.00271357	+	0.999996i	$0.500864\pi$
$822$		0			0
$823$	21.3439	+	21.3439i	0.744003	+	0.744003i	0.973346	−	0.229343i	$-0.0736576\pi$
$823$	21.3439	+	21.3439i	0.744003	+	0.744003i	−0.229343	+	0.973346i	$0.573658\pi$
$824$		0			0
$825$	−59.2660	+	59.2660i	−2.06338	+	2.06338i
$826$		0			0
$827$	−6.76818	−	16.3398i	−0.235353	−	0.568192i	0.761438	−	0.648237i	$-0.224493\pi$
$827$	−6.76818	−	16.3398i	−0.235353	−	0.568192i	−0.996791	+	0.0800454i	$0.974493\pi$
$828$		0			0
$829$	−46.1490	−	19.1156i	−1.60282	−	0.663911i	−0.611011	−	0.791622i	$-0.709237\pi$
$829$	−46.1490	−	19.1156i	−1.60282	−	0.663911i	−0.991811	+	0.127712i	$0.959237\pi$
$830$		0			0
$831$	−7.55819			−0.262191
$832$		0			0
$833$	−1.12373			−0.0389348
$834$		0			0
$835$	25.7474	+	10.6649i	0.891025	+	0.369075i
$836$		0			0
$837$	−0.752725	−	1.81724i	−0.0260180	−	0.0628130i
$838$		0			0
$839$	18.0679	−	18.0679i	0.623774	−	0.623774i	−0.322720	−	0.946494i	$-0.604597\pi$
$839$	18.0679	−	18.0679i	0.623774	−	0.623774i	0.946494	+	0.322720i	$0.104597\pi$
$840$		0			0
$841$	−17.3299	−	17.3299i	−0.597584	−	0.597584i
$842$		0			0
$843$	−49.7435	+	20.6044i	−1.71326	+	0.709655i
$844$		0			0
$845$	0.734273	−	1.77269i	0.0252597	−	0.0609824i
$846$		0			0
$847$			22.8829i			0.786267i
$848$		0			0
$849$		−	10.6330i		−	0.364924i
$850$		0			0
$851$	−2.97059	+	7.17163i	−0.101830	+	0.245840i
$852$		0			0
$853$	26.8170	−	11.1080i	0.918196	−	0.380329i	0.127008	−	0.991902i	$-0.459463\pi$
$853$	26.8170	−	11.1080i	0.918196	−	0.380329i	0.791189	+	0.611572i	$0.209463\pi$
$854$		0			0
$855$	−53.3326	−	53.3326i	−1.82394	−	1.82394i
$856$		0			0
$857$	−37.5099	+	37.5099i	−1.28131	+	1.28131i	−0.341392	+	0.939921i	$0.610898\pi$
$857$	−37.5099	+	37.5099i	−1.28131	+	1.28131i	−0.939921	+	0.341392i	$0.889102\pi$
$858$		0			0
$859$	−10.4024	−	25.1137i	−0.354927	−	0.856870i	−0.995997	−	0.0893871i	$-0.971509\pi$
$859$	−10.4024	−	25.1137i	−0.354927	−	0.856870i	0.641070	−	0.767482i	$-0.278491\pi$
$860$		0			0
$861$	−1.93555	−	0.801732i	−0.0659634	−	0.0273230i
$862$		0			0
$863$	35.1032			1.19493			0.597464	−	0.801896i	$-0.296175\pi$
$863$	35.1032			1.19493			0.597464	+	0.801896i	$0.296175\pi$
$864$		0			0
$865$	−57.7232			−1.96265
$866$		0			0
$867$	−38.9644	−	16.1396i	−1.32330	−	0.548129i
$868$		0			0
$869$	−16.5055	−	39.8477i	−0.559910	−	1.35174i
$870$		0			0
$871$	−25.9417	+	25.9417i	−0.879002	+	0.879002i
$872$		0			0
$873$	−3.48304	−	3.48304i	−0.117883	−	0.117883i
$874$		0			0
$875$	−1.10948	+	0.459561i	−0.0375073	+	0.0155360i
$876$		0			0
$877$	−5.69878	+	13.7581i	−0.192434	+	0.464577i	−0.990418	−	0.138102i	$-0.955900\pi$
$877$	−5.69878	+	13.7581i	−0.192434	+	0.464577i	0.797984	+	0.602679i	$0.205900\pi$
$878$		0			0
$879$			31.2316i			1.05342i
$880$		0			0
$881$			22.9174i			0.772108i	0.922476	+	0.386054i	$0.126162\pi$
$881$			22.9174i			0.772108i	−0.922476	+	0.386054i	$0.873838\pi$
$882$		0			0
$883$	−15.3437	+	37.0430i	−0.516357	+	1.24660i	0.423770	+	0.905770i	$0.360707\pi$
$883$	−15.3437	+	37.0430i	−0.516357	+	1.24660i	−0.940127	+	0.340826i	$0.889293\pi$
$884$		0			0
$885$	−104.190	+	43.1570i	−3.50232	+	1.45071i
$886$		0			0
$887$	5.52843	+	5.52843i	0.185626	+	0.185626i	0.793802	−	0.608176i	$-0.208098\pi$
$887$	5.52843	+	5.52843i	0.185626	+	0.185626i	−0.608176	+	0.793802i	$0.708098\pi$
$888$		0			0
$889$	10.3616	−	10.3616i	0.347517	−	0.347517i
$890$		0			0
$891$	9.03638	+	21.8158i	0.302730	+	0.730855i
$892$		0			0
$893$	−64.0624	−	26.5355i	−2.14377	−	0.887977i
$894$		0			0
$895$	55.0645			1.84060
$896$		0			0
$897$	21.8630			0.729986
$898$		0			0
$899$	−1.21580	−	0.503600i	−0.0405491	−	0.0167960i
$900$		0			0
$901$	1.28324	+	3.09802i	0.0427510	+	0.103210i
$902$		0			0
$903$	14.2169	−	14.2169i	0.473110	−	0.473110i
$904$		0			0
$905$	31.1024	+	31.1024i	1.03388	+	1.03388i
$906$		0			0
$907$	−36.5039	+	15.1204i	−1.21209	+	0.502065i	−0.894887	−	0.446293i	$-0.852744\pi$
$907$	−36.5039	+	15.1204i	−1.21209	+	0.502065i	−0.317204	+	0.948357i	$0.602744\pi$
$908$		0			0
$909$	−8.89405	+	21.4721i	−0.294997	+	0.712185i
$910$		0			0
$911$			47.8533i			1.58545i	0.609580	+	0.792725i	$0.291338\pi$
$911$			47.8533i			1.58545i	−0.609580	+	0.792725i	$0.708662\pi$
$912$		0			0
$913$			54.3868i			1.79994i
$914$		0			0
$915$	−13.5934	+	32.8174i	−0.449384	+	1.08491i
$916$		0			0
$917$	−4.19286	+	1.73674i	−0.138460	+	0.0573522i
$918$		0			0
$919$	−17.7323	−	17.7323i	−0.584935	−	0.584935i	0.351320	−	0.936255i	$-0.385733\pi$
$919$	−17.7323	−	17.7323i	−0.584935	−	0.584935i	−0.936255	+	0.351320i	$0.885733\pi$
$920$		0			0
$921$	47.1429	−	47.1429i	1.55341	−	1.55341i
$922$		0			0
$923$	−19.1489	−	46.2295i	−0.630293	−	1.52166i
$924$		0			0
$925$	−16.6350	−	6.89044i	−0.546955	−	0.226556i
$926$		0			0
$927$	−0.401929			−0.0132011
$928$		0			0
$929$	−4.53459			−0.148775			−0.0743876	−	0.997229i	$-0.523700\pi$
$929$	−4.53459			−0.148775			−0.0743876	+	0.997229i	$0.523700\pi$
$930$		0			0
$931$	−5.17351	−	2.14294i	−0.169555	−	0.0702319i
$932$		0			0
$933$	−16.0223	−	38.6812i	−0.524546	−	1.26637i
$934$		0			0
$935$	14.8966	−	14.8966i	0.487169	−	0.487169i
$936$		0			0
$937$	24.5140	+	24.5140i	0.800838	+	0.800838i	0.983227	−	0.182388i	$-0.0583828\pi$
$937$	24.5140	+	24.5140i	0.800838	+	0.800838i	−0.182388	+	0.983227i	$0.558383\pi$
$938$		0			0
$939$	54.0839	−	22.4023i	1.76496	−	0.731070i
$940$		0			0
$941$	−12.9562	+	31.2791i	−0.422361	+	1.01967i	0.559288	+	0.828974i	$0.311075\pi$
$941$	−12.9562	+	31.2791i	−0.422361	+	1.01967i	−0.981649	+	0.190697i	$0.938925\pi$
$942$		0			0
$943$		−	1.81078i		−	0.0589673i
$944$		0			0
$945$		−	10.2025i		−	0.331889i
$946$		0			0
$947$	0.0241472	−	0.0582964i	0.000784678	−	0.00189438i	−0.923487	−	0.383630i	$-0.874674\pi$
$947$	0.0241472	−	0.0582964i	0.000784678	−	0.00189438i	0.924271	+	0.381736i	$0.124674\pi$
$948$		0			0
$949$	−39.2800	+	16.2703i	−1.27508	+	0.528157i
$950$		0			0
$951$	−57.8696	−	57.8696i	−1.87655	−	1.87655i
$952$		0			0
$953$	−33.0335	+	33.0335i	−1.07006	+	1.07006i	−0.0727074	+	0.997353i	$0.523164\pi$
$953$	−33.0335	+	33.0335i	−1.07006	+	1.07006i	−0.997353	+	0.0727074i	$0.976836\pi$
$954$		0			0
$955$	−24.6838	−	59.5919i	−0.798748	−	1.92835i
$956$		0			0
$957$	−30.5449	−	12.6521i	−0.987375	−	0.408984i
$958$		0			0
$959$	−13.8251			−0.446437
$960$		0			0
$961$	−30.6145			−0.987563
$962$		0			0
$963$	15.1527	+	6.27647i	0.488290	+	0.202256i
$964$		0			0
$965$	−19.2744	−	46.5325i	−0.620464	−	1.49793i
$966$		0			0
$967$	19.7533	−	19.7533i	0.635223	−	0.635223i	−0.314150	−	0.949373i	$-0.601720\pi$
$967$	19.7533	−	19.7533i	0.635223	−	0.635223i	0.949373	+	0.314150i	$0.101720\pi$
$968$		0			0
$969$	11.9245	+	11.9245i	0.383070	+	0.383070i
$970$		0			0
$971$	16.6494	−	6.89642i	0.534306	−	0.221317i	−0.0991821	−	0.995069i	$-0.531623\pi$
$971$	16.6494	−	6.89642i	0.534306	−	0.221317i	0.633488	+	0.773753i	$0.281623\pi$
$972$		0			0
$973$	−2.67074	+	6.44774i	−0.0856201	+	0.206705i
$974$		0			0
$975$			50.7125i			1.62410i
$976$		0			0
$977$		−	0.630363i		−	0.0201671i	−0.999949	−	0.0100835i	$-0.996790\pi$
$977$		−	0.630363i		−	0.0201671i	0.999949	−	0.0100835i	$-0.00320975\pi$
$978$		0			0
$979$	28.4200	−	68.6118i	0.908306	−	2.19284i
$980$		0			0
$981$	−39.7055	+	16.4466i	−1.26770	+	0.525098i
$982$		0			0
$983$	−1.42764	−	1.42764i	−0.0455347	−	0.0455347i	0.683973	−	0.729508i	$-0.260251\pi$
$983$	−1.42764	−	1.42764i	−0.0455347	−	0.0455347i	−0.729508	+	0.683973i	$0.760251\pi$
$984$		0			0
$985$	32.7848	−	32.7848i	1.04461	−	1.04461i
$986$		0			0
$987$	−12.6994	−	30.6590i	−0.404225	−	0.975885i
$988$		0			0
$989$	16.0551	+	6.65024i	0.510523	+	0.211465i
$990$		0			0
$991$	16.1233			0.512175			0.256087	−	0.966654i	$-0.417567\pi$
$991$	16.1233			0.512175			0.256087	+	0.966654i	$0.417567\pi$
$992$		0			0
$993$	1.45098			0.0460454
$994$		0			0
$995$	54.9830	+	22.7747i	1.74308	+	0.722007i
$996$		0			0
$997$	8.65741	+	20.9008i	0.274183	+	0.661936i	0.999654	−	0.0263169i	$-0.00837790\pi$
$997$	8.65741	+	20.9008i	0.274183	+	0.661936i	−0.725471	+	0.688253i	$0.758378\pi$
$998$		0			0
$999$	7.50663	−	7.50663i	0.237499	−	0.237499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.u.c.337.2		52
4.3	odd	2		224.2.u.c.29.3	✓	52
32.11	odd	8		224.2.u.c.85.3	yes	52
32.21	even	8	inner	896.2.u.c.561.2		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.3	✓	52	4.3	odd	2
224.2.u.c.85.3	yes	52	32.11	odd	8
896.2.u.c.337.2		52	1.1	even	1	trivial
896.2.u.c.561.2		52	32.21	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.u (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.47594 - 1.02557i) q^{3} +(-1.23251 - 2.97553i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(2.95715 + 2.95715i) q^{9} +O(q^{10})\)	\(q+(-2.47594 - 1.02557i) q^{3} +(-1.23251 - 2.97553i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(2.95715 + 2.95715i) q^{9} +(-5.37782 + 2.22756i) q^{11} +(-1.34780 + 3.25387i) q^{13} +8.63125i q^{15} -1.12373i q^{17} +(2.14294 - 5.17351i) q^{19} +(2.47594 - 1.02557i) q^{21} +(1.63790 + 1.63790i) q^{23} +(-3.79919 + 3.79919i) q^{25} +(-1.21227 - 2.92667i) q^{27} +(-1.95805 - 0.811051i) q^{29} +0.620923 q^{31} +15.5996 q^{33} +(2.97553 + 1.23251i) q^{35} +(1.28245 + 3.09611i) q^{37} +(6.67412 - 6.67412i) q^{39} +(-0.552778 - 0.552778i) q^{41} +(6.93125 - 2.87102i) q^{43} +(5.15440 - 12.4438i) q^{45} -12.3828i q^{47} -1.00000i q^{49} +(-1.15246 + 2.78228i) q^{51} +(-2.75692 + 1.14195i) q^{53} +(13.2564 + 13.2564i) q^{55} +(-10.6116 + 10.6116i) q^{57} +(5.00009 + 12.0713i) q^{59} +(3.80216 + 1.57491i) q^{61} -4.18205 q^{63} +11.3432 q^{65} +(9.62375 + 3.98629i) q^{67} +(-2.37556 - 5.73510i) q^{69} +(-10.0462 + 10.0462i) q^{71} +(8.53603 + 8.53603i) q^{73} +(13.3029 - 5.51023i) q^{75} +(2.22756 - 5.37782i) q^{77} +7.40965i q^{79} -4.05662i q^{81} +(3.57555 - 8.63214i) q^{83} +(-3.34369 + 1.38500i) q^{85} +(4.01622 + 4.01622i) q^{87} +(-9.02149 + 9.02149i) q^{89} +(-1.34780 - 3.25387i) q^{91} +(-1.53737 - 0.636798i) q^{93} -18.0351 q^{95} -1.17783 q^{97} +(-22.4903 - 9.31578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) \) 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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