LMFDB - Embedded newform 896.2.x.b.111.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(111,896)]

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([4, 7, 4]))

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

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

chi := DirichletCharacter("896.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.x (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.17
Character	$\chi$	$=$	896.111
Dual form			896.2.x.b.783.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.311327 - 0.751610i) q^{3} +(-1.37157 - 3.31126i) q^{5} +(2.28614 - 1.33176i) q^{7} +(1.65333 + 1.65333i) q^{9} +O(q^{10})$	\(q+(0.311327 - 0.751610i) q^{3} +(-1.37157 - 3.31126i) q^{5} +(2.28614 - 1.33176i) q^{7} +(1.65333 + 1.65333i) q^{9} +(5.28229 - 2.18800i) q^{11} +(0.105369 - 0.254384i) q^{13} -2.91578 q^{15} -5.29348 q^{17} +(3.74605 + 1.55167i) q^{19} +(-0.289226 - 2.13289i) q^{21} +(-0.968314 + 0.968314i) q^{23} +(-5.54771 + 5.54771i) q^{25} +(4.01221 - 1.66191i) q^{27} +(1.68537 - 4.06885i) q^{29} -1.43114 q^{31} -4.65140i q^{33} +(-7.54539 - 5.74340i) q^{35} +(-5.41648 + 2.24358i) q^{37} +(-0.158393 - 0.158393i) q^{39} +(0.427071 - 0.427071i) q^{41} +(-2.09991 + 0.869810i) q^{43} +(3.20695 - 7.74225i) q^{45} -5.50376i q^{47} +(3.45284 - 6.08916i) q^{49} +(-1.64800 + 3.97863i) q^{51} +(-2.37839 - 5.74193i) q^{53} +(-14.4901 - 14.4901i) q^{55} +(2.33249 - 2.33249i) q^{57} +(-9.62996 + 3.98886i) q^{59} +(7.27600 + 3.01382i) q^{61} +(5.98157 + 1.57790i) q^{63} -0.986852 q^{65} +(-2.12190 - 0.878921i) q^{67} +(0.426332 + 1.02926i) q^{69} +(2.53724 + 2.53724i) q^{71} +(-11.0124 + 11.0124i) q^{73} +(2.44256 + 5.89686i) q^{75} +(9.16216 - 12.0368i) q^{77} +7.98231 q^{79} +3.48146i q^{81} +(5.90559 + 2.44618i) q^{83} +(7.26038 + 17.5281i) q^{85} +(-2.53348 - 2.53348i) q^{87} +(10.4668 + 10.4668i) q^{89} +(-0.0978891 - 0.721882i) q^{91} +(-0.445552 + 1.07566i) q^{93} -14.5324i q^{95} -7.99833i q^{97} +(12.3508 + 5.11588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 112 * q + 4 * q^7 - 8 * q^9	$ 112 q + 4 q^{7} - 8 q^{9} + 8 q^{11} + 16 q^{15} - 4 q^{21} + 48 q^{23} - 8 q^{25} - 8 q^{29} - 20 q^{35} - 8 q^{37} + 8 q^{39} - 32 q^{43} + 32 q^{51} - 32 q^{53} - 8 q^{57} - 16 q^{65} + 64 q^{67} - 56 q^{71} + 52 q^{77} + 16 q^{79} - 48 q^{85} + 52 q^{91} - 32 q^{93} - 16 q^{99}+O(q^{100}) $ 112 * q + 4 * q^7 - 8 * q^9 + 8 * q^11 + 16 * q^15 - 4 * q^21 + 48 * q^23 - 8 * q^25 - 8 * q^29 - 20 * q^35 - 8 * q^37 + 8 * q^39 - 32 * q^43 + 32 * q^51 - 32 * q^53 - 8 * q^57 - 16 * q^65 + 64 * q^67 - 56 * q^71 + 52 * q^77 + 16 * q^79 - 48 * q^85 + 52 * q^91 - 32 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.311327	−	0.751610i	0.179745	−	0.433942i	−0.808168	−	0.588952i	$-0.799541\pi$
$3$	0.311327	−	0.751610i	0.179745	−	0.433942i	0.987913	+	0.155010i	$0.0495408\pi$
$4$		0			0
$5$	−1.37157	−	3.31126i	−0.613384	−	1.48084i	−0.859260	−	0.511539i	$-0.829076\pi$
$5$	−1.37157	−	3.31126i	−0.613384	−	1.48084i	0.245876	−	0.969301i	$-0.420924\pi$
$6$		0			0
$7$	2.28614	−	1.33176i	0.864079	−	0.503357i
$7$	2.28614	−	1.33176i	0.864079	−	0.503357i
$8$		0			0
$9$	1.65333	+	1.65333i	0.551109	+	0.551109i
$10$		0			0
$11$	5.28229	−	2.18800i	1.59267	−	0.659706i	0.602316	−	0.798258i	$-0.294245\pi$
$11$	5.28229	−	2.18800i	1.59267	−	0.659706i	0.990355	+	0.138552i	$0.0442448\pi$
$12$		0			0
$13$	0.105369	−	0.254384i	0.0292242	−	0.0705534i	−0.908594	−	0.417681i	$-0.862843\pi$
$13$	0.105369	−	0.254384i	0.0292242	−	0.0705534i	0.937818	+	0.347128i	$0.112843\pi$
$14$		0			0
$15$	−2.91578			−0.752851
$16$		0			0
$17$	−5.29348			−1.28386			−0.641929	−	0.766764i	$-0.721866\pi$
$17$	−5.29348			−1.28386			−0.641929	+	0.766764i	$0.721866\pi$
$18$		0			0
$19$	3.74605	+	1.55167i	0.859403	+	0.355977i	0.768474	−	0.639881i	$-0.221016\pi$
$19$	3.74605	+	1.55167i	0.859403	+	0.355977i	0.0909292	+	0.995857i	$0.471016\pi$
$20$		0			0
$21$	−0.289226	−	2.13289i	−0.0631143	−	0.465436i
$22$		0			0
$23$	−0.968314	+	0.968314i	−0.201907	+	0.201907i	−0.800817	−	0.598909i	$-0.795601\pi$
$23$	−0.968314	+	0.968314i	−0.201907	+	0.201907i	0.598909	+	0.800817i	$0.295601\pi$
$24$		0			0
$25$	−5.54771	+	5.54771i	−1.10954	+	1.10954i
$26$		0			0
$27$	4.01221	−	1.66191i	0.772150	−	0.319835i
$28$		0			0
$29$	1.68537	−	4.06885i	0.312966	−	0.755566i	−0.686627	−	0.727010i	$-0.740909\pi$
$29$	1.68537	−	4.06885i	0.312966	−	0.755566i	0.999592	−	0.0285554i	$-0.00909070\pi$
$30$		0			0
$31$	−1.43114			−0.257040			−0.128520	−	0.991707i	$-0.541023\pi$
$31$	−1.43114			−0.257040			−0.128520	+	0.991707i	$0.541023\pi$
$32$		0			0
$33$		−	4.65140i		−	0.809706i
$34$		0			0
$35$	−7.54539	−	5.74340i	−1.27540	−	0.970811i
$36$		0			0
$37$	−5.41648	+	2.24358i	−0.890463	+	0.368842i	−0.780546	−	0.625099i	$-0.785059\pi$
$37$	−5.41648	+	2.24358i	−0.890463	+	0.368842i	−0.109918	+	0.993941i	$0.535059\pi$
$38$		0			0
$39$	−0.158393	−	0.158393i	−0.0253632	−	0.0253632i
$40$		0			0
$41$	0.427071	−	0.427071i	0.0666973	−	0.0666973i	−0.672971	−	0.739669i	$-0.734982\pi$
$41$	0.427071	−	0.427071i	0.0666973	−	0.0666973i	0.739669	+	0.672971i	$0.234982\pi$
$42$		0			0
$43$	−2.09991	+	0.869810i	−0.320233	+	0.132645i	−0.537009	−	0.843577i	$-0.680446\pi$
$43$	−2.09991	+	0.869810i	−0.320233	+	0.132645i	0.216776	+	0.976221i	$0.430446\pi$
$44$		0			0
$45$	3.20695	−	7.74225i	0.478063	−	1.15415i
$46$		0			0
$47$		−	5.50376i		−	0.802806i	−0.915902	−	0.401403i	$-0.868523\pi$
$47$		−	5.50376i		−	0.802806i	0.915902	−	0.401403i	$-0.131477\pi$
$48$		0			0
$49$	3.45284	−	6.08916i	0.493263	−	0.869880i
$50$		0			0
$51$	−1.64800	+	3.97863i	−0.230767	+	0.557120i
$52$		0			0
$53$	−2.37839	−	5.74193i	−0.326696	−	0.788715i	−0.998833	−	0.0482882i	$-0.984623\pi$
$53$	−2.37839	−	5.74193i	−0.326696	−	0.788715i	0.672137	−	0.740427i	$-0.265377\pi$
$54$		0			0
$55$	−14.4901	−	14.4901i	−1.95384	−	1.95384i
$56$		0			0
$57$	2.33249	−	2.33249i	0.308946	−	0.308946i
$58$		0			0
$59$	−9.62996	+	3.98886i	−1.25371	+	0.519306i	−0.907975	−	0.419025i	$-0.862372\pi$
$59$	−9.62996	+	3.98886i	−1.25371	+	0.519306i	−0.345740	+	0.938330i	$0.612372\pi$
$60$		0			0
$61$	7.27600	+	3.01382i	0.931596	+	0.385880i	0.796284	−	0.604923i	$-0.206796\pi$
$61$	7.27600	+	3.01382i	0.931596	+	0.385880i	0.135312	+	0.990803i	$0.456796\pi$
$62$		0			0
$63$	5.98157	+	1.57790i	0.753606	+	0.198797i
$64$		0			0
$65$	−0.986852			−0.122404
$66$		0			0
$67$	−2.12190	−	0.878921i	−0.259232	−	0.107377i	0.249283	−	0.968431i	$-0.419805\pi$
$67$	−2.12190	−	0.878921i	−0.259232	−	0.107377i	−0.508514	+	0.861053i	$0.669805\pi$
$68$		0			0
$69$	0.426332	+	1.02926i	0.0513244	+	0.123908i
$70$		0			0
$71$	2.53724	+	2.53724i	0.301115	+	0.301115i	0.841450	−	0.540335i	$-0.181703\pi$
$71$	2.53724	+	2.53724i	0.301115	+	0.301115i	−0.540335	+	0.841450i	$0.681703\pi$
$72$		0			0
$73$	−11.0124	+	11.0124i	−1.28890	+	1.28890i	−0.353447	+	0.935455i	$0.614990\pi$
$73$	−11.0124	+	11.0124i	−1.28890	+	1.28890i	−0.935455	+	0.353447i	$0.885010\pi$
$74$		0			0
$75$	2.44256	+	5.89686i	0.282043	+	0.680911i
$76$		0			0
$77$	9.16216	−	12.0368i	1.04413	−	1.37172i
$78$		0			0
$79$	7.98231			0.898080			0.449040	−	0.893512i	$-0.351766\pi$
$79$	7.98231			0.898080			0.449040	+	0.893512i	$0.351766\pi$
$80$		0			0
$81$			3.48146i			0.386829i
$82$		0			0
$83$	5.90559	+	2.44618i	0.648223	+	0.268503i	0.682473	−	0.730910i	$-0.260904\pi$
$83$	5.90559	+	2.44618i	0.648223	+	0.268503i	−0.0342502	+	0.999413i	$0.510904\pi$
$84$		0			0
$85$	7.26038	+	17.5281i	0.787499	+	1.90119i
$86$		0			0
$87$	−2.53348	−	2.53348i	−0.271618	−	0.271618i
$88$		0			0
$89$	10.4668	+	10.4668i	1.10948	+	1.10948i	0.993218	+	0.116264i	$0.0370919\pi$
$89$	10.4668	+	10.4668i	1.10948	+	1.10948i	0.116264	+	0.993218i	$0.462908\pi$
$90$		0			0
$91$	−0.0978891	−	0.721882i	−0.0102616	−	0.0756738i
$92$		0			0
$93$	−0.445552	+	1.07566i	−0.0462016	+	0.111540i
$94$		0			0
$95$		−	14.5324i		−	1.49099i
$96$		0			0
$97$		−	7.99833i		−	0.812107i	−0.913849	−	0.406054i	$-0.866905\pi$
$97$		−	7.99833i		−	0.812107i	0.913849	−	0.406054i	$-0.133095\pi$
$98$		0			0
$99$	12.3508	+	5.11588i	1.24131	+	0.514166i
$100$		0			0
$101$	−2.23582	−	5.39774i	−0.222472	−	0.537095i	0.772752	−	0.634707i	$-0.218879\pi$
$101$	−2.23582	−	5.39774i	−0.222472	−	0.537095i	−0.995224	+	0.0976125i	$0.968879\pi$
$102$		0			0
$103$	−5.02917	+	5.02917i	−0.495539	+	0.495539i	−0.910046	−	0.414507i	$-0.863954\pi$
$103$	−5.02917	+	5.02917i	−0.495539	+	0.495539i	0.414507	+	0.910046i	$0.363954\pi$
$104$		0			0
$105$	−6.66588	+	3.88311i	−0.650523	+	0.378953i
$106$		0			0
$107$	0.274004	−	0.113496i	0.0264890	−	0.0109721i	−0.369400	−	0.929271i	$-0.620437\pi$
$107$	0.274004	−	0.113496i	0.0264890	−	0.0109721i	0.395889	+	0.918299i	$0.370437\pi$
$108$		0			0
$109$	−8.69436	−	3.60132i	−0.832769	−	0.344944i	−0.0747706	−	0.997201i	$-0.523822\pi$
$109$	−8.69436	−	3.60132i	−0.832769	−	0.344944i	−0.757998	+	0.652257i	$0.773822\pi$
$110$		0			0
$111$			4.76956i			0.452707i
$112$		0			0
$113$			9.76376i			0.918497i	0.888308	+	0.459249i	$0.151881\pi$
$113$			9.76376i			0.918497i	−0.888308	+	0.459249i	$0.848119\pi$
$114$		0			0
$115$	4.53445	+	1.87823i	0.422840	+	0.175146i
$116$		0			0
$117$	0.594790	−	0.246370i	0.0549883	−	0.0227769i
$118$		0			0
$119$	−12.1016	+	7.04964i	−1.10935	+	0.646239i
$120$		0			0
$121$	15.3371	−	15.3371i	1.39428	−	1.39428i
$122$		0			0
$123$	−0.188032	−	0.453950i	−0.0169543	−	0.0409313i
$124$		0			0
$125$	9.42267	+	3.90300i	0.842789	+	0.349095i
$126$		0			0
$127$			19.5490i			1.73469i	0.497705	+	0.867346i	$0.334176\pi$
$127$			19.5490i			1.73469i	−0.497705	+	0.867346i	$0.665824\pi$
$128$		0			0
$129$			1.84911i			0.162805i
$130$		0			0
$131$	6.95520	−	16.7913i	0.607679	−	1.46707i	−0.257839	−	0.966188i	$-0.583010\pi$
$131$	6.95520	−	16.7913i	0.607679	−	1.46707i	0.865517	−	0.500879i	$-0.166990\pi$
$132$		0			0
$133$	10.6304	−	1.44151i	0.921775	−	0.124995i
$134$		0			0
$135$	−11.0060	−	11.0060i	−0.947250	−	0.947250i
$136$		0			0
$137$	−9.87319	−	9.87319i	−0.843524	−	0.843524i	0.145791	−	0.989315i	$-0.453427\pi$
$137$	−9.87319	−	9.87319i	−0.843524	−	0.843524i	−0.989315	+	0.145791i	$0.953427\pi$
$138$		0			0
$139$	7.57631	+	18.2908i	0.642614	+	1.55141i	0.823141	+	0.567837i	$0.192220\pi$
$139$	7.57631	+	18.2908i	0.642614	+	1.55141i	−0.180527	+	0.983570i	$0.557780\pi$
$140$		0			0
$141$	−4.13668	−	1.71347i	−0.348371	−	0.144300i
$142$		0			0
$143$		−	1.57428i		−	0.131648i
$144$		0			0
$145$	−15.7846			−1.31084
$146$		0			0
$147$	−3.50171	−	4.49091i	−0.288816	−	0.370404i
$148$		0			0
$149$	−2.06244	−	4.97918i	−0.168962	−	0.407910i	0.816605	−	0.577197i	$-0.195854\pi$
$149$	−2.06244	−	4.97918i	−0.168962	−	0.407910i	−0.985567	+	0.169287i	$0.945854\pi$
$150$		0			0
$151$	1.82839	−	1.82839i	0.148792	−	0.148792i	−0.628786	−	0.777578i	$-0.716448\pi$
$151$	1.82839	−	1.82839i	0.148792	−	0.148792i	0.777578	+	0.628786i	$0.216448\pi$
$152$		0			0
$153$	−8.75186	−	8.75186i	−0.707546	−	0.707546i
$154$		0			0
$155$	1.96290	+	4.73887i	0.157664	+	0.380635i
$156$		0			0
$157$	9.99837	+	4.14146i	0.797957	+	0.330525i	0.744138	−	0.668026i	$-0.232861\pi$
$157$	9.99837	+	4.14146i	0.797957	+	0.330525i	0.0538192	+	0.998551i	$0.482861\pi$
$158$		0			0
$159$	−5.05615			−0.400979
$160$		0			0
$161$	−0.924139	+	3.50326i	−0.0728324	+	0.276095i
$162$		0			0
$163$	5.89470	+	2.44167i	0.461709	+	0.191246i	0.601398	−	0.798949i	$-0.294610\pi$
$163$	5.89470	+	2.44167i	0.461709	+	0.191246i	−0.139690	+	0.990195i	$0.544610\pi$
$164$		0			0
$165$	−15.4020	+	6.37972i	−1.19904	+	0.496661i
$166$		0			0
$167$	−5.00406	+	5.00406i	−0.387226	+	0.387226i	−0.873697	−	0.486471i	$-0.838284\pi$
$167$	−5.00406	+	5.00406i	−0.387226	+	0.387226i	0.486471	+	0.873697i	$0.338284\pi$
$168$		0			0
$169$	9.13878	+	9.13878i	0.702983	+	0.702983i
$170$		0			0
$171$	3.62804	+	8.75886i	0.277443	+	0.669807i
$172$		0			0
$173$	−8.89691	+	21.4790i	−0.676419	+	1.63302i	0.0940681	+	0.995566i	$0.470013\pi$
$173$	−8.89691	+	21.4790i	−0.676419	+	1.63302i	−0.770487	+	0.637455i	$0.779987\pi$
$174$		0			0
$175$	−5.29462	+	20.0710i	−0.400235	+	1.51723i
$176$		0			0
$177$			8.47981i			0.637382i
$178$		0			0
$179$	7.86244	−	18.9816i	0.587666	−	1.41875i	−0.298061	−	0.954547i	$-0.596340\pi$
$179$	7.86244	−	18.9816i	0.587666	−	1.41875i	0.885728	−	0.464205i	$-0.153660\pi$
$180$		0			0
$181$	−18.8806	+	7.82061i	−1.40339	+	0.581301i	−0.950628	−	0.310332i	$-0.899560\pi$
$181$	−18.8806	+	7.82061i	−1.40339	+	0.581301i	−0.452758	+	0.891634i	$0.649560\pi$
$182$		0			0
$183$	4.53043	−	4.53043i	0.334899	−	0.334899i
$184$		0			0
$185$	14.8581	+	14.8581i	1.09239	+	1.09239i
$186$		0			0
$187$	−27.9617	+	11.5821i	−2.04476	+	0.846969i
$188$		0			0
$189$	6.95920	−	9.14265i	0.506207	−	0.665030i
$190$		0			0
$191$		−	1.01843i		−	0.0736910i	−0.999321	−	0.0368455i	$-0.988269\pi$
$191$		−	1.01843i		−	0.0736910i	0.999321	−	0.0368455i	$-0.0117309\pi$
$192$		0			0
$193$	3.70779			0.266893			0.133446	−	0.991056i	$-0.457396\pi$
$193$	3.70779			0.266893			0.133446	+	0.991056i	$0.457396\pi$
$194$		0			0
$195$	−0.307234	+	0.741728i	−0.0220015	+	0.0531162i
$196$		0			0
$197$	15.3126	−	6.34270i	1.09098	−	0.451899i	0.236632	−	0.971599i	$-0.423956\pi$
$197$	15.3126	−	6.34270i	1.09098	−	0.451899i	0.854348	+	0.519701i	$0.173956\pi$
$198$		0			0
$199$	3.61849	−	3.61849i	0.256508	−	0.256508i	−0.567124	−	0.823632i	$-0.691944\pi$
$199$	3.61849	−	3.61849i	0.256508	−	0.256508i	0.823632	+	0.567124i	$0.191944\pi$
$200$		0			0
$201$	−1.32121	+	1.32121i	−0.0931910	+	0.0931910i
$202$		0			0
$203$	−1.56573	−	11.5464i	−0.109892	−	0.810401i
$204$		0			0
$205$	−1.99990	−	0.828386i	−0.139679	−	0.0578570i
$206$		0			0
$207$	−3.20188			−0.222546
$208$		0			0
$209$	23.1828			1.60359
$210$		0			0
$211$	6.81295	−	16.4479i	0.469023	−	1.13232i	−0.495568	−	0.868569i	$-0.665040\pi$
$211$	6.81295	−	16.4479i	0.469023	−	1.13232i	0.964591	−	0.263752i	$-0.0849599\pi$
$212$		0			0
$213$	2.69692	−	1.11710i	0.184790	−	0.0765425i
$214$		0			0
$215$	5.76034	+	5.76034i	0.392852	+	0.392852i
$216$		0			0
$217$	−3.27178	+	1.90593i	−0.222103	+	0.129383i
$218$		0			0
$219$	4.84856	+	11.7055i	0.327635	+	0.790982i
$220$		0			0
$221$	−0.557770	+	1.34658i	−0.0375197	+	0.0905806i
$222$		0			0
$223$	17.3122			1.15931			0.579655	−	0.814862i	$-0.303187\pi$
$223$	17.3122			1.15931			0.579655	+	0.814862i	$0.303187\pi$
$224$		0			0
$225$	−18.3444			−1.22296
$226$		0			0
$227$	1.97300	−	4.76324i	0.130952	−	0.316147i	−0.844780	−	0.535114i	$-0.820269\pi$
$227$	1.97300	−	4.76324i	0.130952	−	0.316147i	0.975732	+	0.218967i	$0.0702686\pi$
$228$		0			0
$229$	−5.23276	−	12.6330i	−0.345790	−	0.834812i	−0.997107	−	0.0760061i	$-0.975783\pi$
$229$	−5.23276	−	12.6330i	−0.345790	−	0.834812i	0.651317	−	0.758806i	$-0.274217\pi$
$230$		0			0
$231$	−6.19454	−	10.6337i	−0.407571	−	0.699649i
$232$		0			0
$233$	18.4547	+	18.4547i	1.20901	+	1.20901i	0.971349	+	0.237658i	$0.0763798\pi$
$233$	18.4547	+	18.4547i	1.20901	+	1.20901i	0.237658	+	0.971349i	$0.423620\pi$
$234$		0			0
$235$	−18.2244	+	7.54878i	−1.18883	+	0.492428i
$236$		0			0
$237$	2.48511	−	5.99958i	0.161425	−	0.389715i
$238$		0			0
$239$	14.1947			0.918177			0.459088	−	0.888391i	$-0.348176\pi$
$239$	14.1947			0.918177			0.459088	+	0.888391i	$0.348176\pi$
$240$		0			0
$241$	−9.94215			−0.640430			−0.320215	−	0.947345i	$-0.603755\pi$
$241$	−9.94215			−0.640430			−0.320215	+	0.947345i	$0.603755\pi$
$242$		0			0
$243$	14.6533	+	6.06961i	0.940012	+	0.389366i
$244$		0			0
$245$	−24.8986	−	3.08156i	−1.59071	−	0.196874i
$246$		0			0
$247$	0.789437	−	0.789437i	0.0502307	−	0.0502307i
$248$		0			0
$249$	3.67714	−	3.67714i	0.233029	−	0.233029i
$250$		0			0
$251$	11.4857	−	4.75754i	0.724972	−	0.300293i	0.0104881	−	0.999945i	$-0.496661\pi$
$251$	11.4857	−	4.75754i	0.724972	−	0.300293i	0.714484	+	0.699652i	$0.246661\pi$
$252$		0			0
$253$	−2.99625	+	7.23359i	−0.188373	+	0.454772i
$254$		0			0
$255$	15.4346			0.966555
$256$		0			0
$257$		−	10.7998i		−	0.673671i	−0.941563	−	0.336836i	$-0.890643\pi$
$257$		−	10.7998i		−	0.673671i	0.941563	−	0.336836i	$-0.109357\pi$
$258$		0			0
$259$	−9.39490	+	12.3426i	−0.583771	+	0.766929i
$260$		0			0
$261$	9.51360	−	3.94066i	0.588877	−	0.243921i
$262$		0			0
$263$	10.9514	+	10.9514i	0.675292	+	0.675292i	0.958931	−	0.283639i	$-0.0915417\pi$
$263$	10.9514	+	10.9514i	0.675292	+	0.675292i	−0.283639	+	0.958931i	$0.591542\pi$
$264$		0			0
$265$	−15.7509	+	15.7509i	−0.967571	+	0.967571i
$266$		0			0
$267$	11.1256	−	4.60837i	0.680875	−	0.282027i
$268$		0			0
$269$	0.661310	−	1.59654i	0.0403208	−	0.0973430i	−0.902436	−	0.430824i	$-0.858223\pi$
$269$	0.661310	−	1.59654i	0.0403208	−	0.0973430i	0.942757	+	0.333481i	$0.108223\pi$
$270$		0			0
$271$			10.3316i			0.627603i	0.949489	+	0.313801i	$0.101603\pi$
$271$			10.3316i			0.627603i	−0.949489	+	0.313801i	$0.898397\pi$
$272$		0			0
$273$	−0.573049	−	0.151167i	−0.0346825	−	0.00914905i
$274$		0			0
$275$	−17.1662	+	41.4430i	−1.03516	+	2.49911i
$276$		0			0
$277$	8.07181	+	19.4871i	0.484988	+	1.17086i	0.957212	+	0.289386i	$0.0934511\pi$
$277$	8.07181	+	19.4871i	0.484988	+	1.17086i	−0.472225	+	0.881478i	$0.656549\pi$
$278$		0			0
$279$	−2.36614	−	2.36614i	−0.141657	−	0.141657i
$280$		0			0
$281$	−16.9858	+	16.9858i	−1.01329	+	1.01329i	−0.0133765	+	0.999911i	$0.504258\pi$
$281$	−16.9858	+	16.9858i	−1.01329	+	1.01329i	−0.999911	+	0.0133765i	$0.995742\pi$
$282$		0			0
$283$	0.542456	−	0.224693i	0.0322457	−	0.0133566i	−0.366502	−	0.930417i	$-0.619445\pi$
$283$	0.542456	−	0.224693i	0.0322457	−	0.0133566i	0.398748	+	0.917061i	$0.369445\pi$
$284$		0			0
$285$	−10.9227	−	4.52432i	−0.647003	−	0.267997i
$286$		0			0
$287$	0.407588	−	1.54510i	0.0240592	−	0.0912043i
$288$		0			0
$289$	11.0210			0.648293
$290$		0			0
$291$	−6.01162	−	2.49009i	−0.352407	−	0.145972i
$292$		0			0
$293$	5.67524	+	13.7012i	0.331551	+	0.800435i	0.998470	+	0.0553044i	$0.0176129\pi$
$293$	5.67524	+	13.7012i	0.331551	+	0.800435i	−0.666918	+	0.745131i	$0.732387\pi$
$294$		0			0
$295$	26.4163	+	26.4163i	1.53802	+	1.53802i
$296$		0			0
$297$	17.5574	−	17.5574i	1.01878	−	1.01878i
$298$		0			0
$299$	0.144293	+	0.348354i	0.00834468	+	0.0201458i
$300$		0			0
$301$	−3.64230	+	4.78507i	−0.209939	+	0.275807i
$302$		0			0
$303$	−4.75306			−0.273056
$304$		0			0
$305$		−	28.2264i		−	1.61624i
$306$		0			0
$307$	−21.2769	−	8.81316i	−1.21433	−	0.502994i	−0.318730	−	0.947846i	$-0.603256\pi$
$307$	−21.2769	−	8.81316i	−1.21433	−	0.502994i	−0.895604	+	0.444852i	$0.853256\pi$
$308$		0			0
$309$	2.21426	+	5.34569i	0.125965	+	0.304106i
$310$		0			0
$311$	2.17216	+	2.17216i	0.123172	+	0.123172i	0.766006	−	0.642834i	$-0.222241\pi$
$311$	2.17216	+	2.17216i	0.123172	+	0.123172i	−0.642834	+	0.766006i	$0.722241\pi$
$312$		0			0
$313$	5.31954	+	5.31954i	0.300678	+	0.300678i	0.841279	−	0.540601i	$-0.181803\pi$
$313$	5.31954	+	5.31954i	0.300678	+	0.300678i	−0.540601	+	0.841279i	$0.681803\pi$
$314$		0			0
$315$	−2.97928	−	21.9707i	−0.167864	−	1.23791i
$316$		0			0
$317$	−5.64194	+	13.6209i	−0.316883	+	0.765023i	0.682533	+	0.730855i	$0.260878\pi$
$317$	−5.64194	+	13.6209i	−0.316883	+	0.765023i	−0.999416	+	0.0341685i	$0.989122\pi$
$318$		0			0
$319$		−	25.1804i		−	1.40983i
$320$		0			0
$321$		−	0.241278i		−	0.0134669i
$322$		0			0
$323$	−19.8297	−	8.21372i	−1.10335	−	0.457024i
$324$		0			0
$325$	0.826689	+	1.99580i	0.0458565	+	0.110707i
$326$		0			0
$327$	−5.41358	+	5.41358i	−0.299372	+	0.299372i
$328$		0			0
$329$	−7.32967	−	12.5823i	−0.404098	−	0.693687i
$330$		0			0
$331$	−1.66979	+	0.691648i	−0.0917797	+	0.0380164i	−0.428101	−	0.903731i	$-0.640817\pi$
$331$	−1.66979	+	0.691648i	−0.0917797	+	0.0380164i	0.336321	+	0.941747i	$0.390817\pi$
$332$		0			0
$333$	−12.6646	−	5.24584i	−0.694015	−	0.287470i
$334$		0			0
$335$			8.23167i			0.449744i
$336$		0			0
$337$		−	6.59711i		−	0.359367i	−0.983724	−	0.179684i	$-0.942493\pi$
$337$		−	6.59711i		−	0.359367i	0.983724	−	0.179684i	$-0.0575074\pi$
$338$		0			0
$339$	7.33854	+	3.03972i	0.398575	+	0.165095i
$340$		0			0
$341$	−7.55969	+	3.13132i	−0.409380	+	0.169571i
$342$		0			0
$343$	−0.215612	−	18.5190i	−0.0116419	−	0.999932i
$344$		0			0
$345$	2.82339	−	2.82339i	0.152006	−	0.152006i
$346$		0			0
$347$	2.33276	+	5.63178i	0.125229	+	0.302330i	0.974043	−	0.226361i	$-0.0726830\pi$
$347$	2.33276	+	5.63178i	0.125229	+	0.302330i	−0.848814	+	0.528691i	$0.822683\pi$
$348$		0			0
$349$	−9.19809	−	3.80997i	−0.492362	−	0.203943i	0.122666	−	0.992448i	$-0.460856\pi$
$349$	−9.19809	−	3.80997i	−0.492362	−	0.203943i	−0.615029	+	0.788505i	$0.710856\pi$
$350$		0			0
$351$		−	1.19576i		−	0.0638247i
$352$		0			0
$353$		−	22.4549i		−	1.19515i	−0.801812	−	0.597577i	$-0.796130\pi$
$353$		−	22.4549i		−	1.19515i	0.801812	−	0.597577i	$-0.203870\pi$
$354$		0			0
$355$	4.92145	−	11.8814i	0.261204	−	0.630602i
$356$		0			0
$357$	1.53101	+	11.2904i	0.0810298	+	0.597554i
$358$		0			0
$359$	−3.52551	−	3.52551i	−0.186069	−	0.186069i	0.607925	−	0.793994i	$-0.292002\pi$
$359$	−3.52551	−	3.52551i	−0.186069	−	0.186069i	−0.793994	+	0.607925i	$0.792002\pi$
$360$		0			0
$361$	−1.80979	−	1.80979i	−0.0952520	−	0.0952520i
$362$		0			0
$363$	−6.75266	−	16.3024i	−0.354423	−	0.855652i
$364$		0			0
$365$	51.5691	+	21.3606i	2.69925	+	1.11807i
$366$		0			0
$367$			10.3253i			0.538978i	0.963003	+	0.269489i	$0.0868548\pi$
$367$			10.3253i			0.538978i	−0.963003	+	0.269489i	$0.913145\pi$
$368$		0			0
$369$	1.41218			0.0735150
$370$		0			0
$371$	−13.0842	−	9.95941i	−0.679297	−	0.517067i
$372$		0			0
$373$	−9.91074	−	23.9266i	−0.513159	−	1.23887i	−0.942036	−	0.335512i	$-0.891091\pi$
$373$	−9.91074	−	23.9266i	−0.513159	−	1.23887i	0.428877	−	0.903363i	$-0.358909\pi$
$374$		0			0
$375$	5.86706	−	5.86706i	0.302974	−	0.302974i
$376$		0			0
$377$	−0.857462	−	0.857462i	−0.0441615	−	0.0441615i
$378$		0			0
$379$	1.01518	+	2.45085i	0.0521461	+	0.125892i	0.947806	−	0.318848i	$-0.103296\pi$
$379$	1.01518	+	2.45085i	0.0521461	+	0.125892i	−0.895660	+	0.444740i	$0.853296\pi$
$380$		0			0
$381$	14.6932	+	6.08613i	0.752756	+	0.311802i
$382$		0			0
$383$	11.8843			0.607260			0.303630	−	0.952790i	$-0.401801\pi$
$383$	11.8843			0.607260			0.303630	+	0.952790i	$0.401801\pi$
$384$		0			0
$385$	−52.4235	−	13.8290i	−2.67175	−	0.704791i
$386$		0			0
$387$	−4.90992	−	2.03375i	−0.249585	−	0.103382i
$388$		0			0
$389$	−13.6989	+	5.67426i	−0.694560	+	0.287696i	−0.701899	−	0.712277i	$-0.747664\pi$
$389$	−13.6989	+	5.67426i	−0.694560	+	0.287696i	0.00733858	+	0.999973i	$0.497664\pi$
$390$		0			0
$391$	5.12576	−	5.12576i	0.259221	−	0.259221i
$392$		0			0
$393$	−10.4552	−	10.4552i	−0.527395	−	0.527395i
$394$		0			0
$395$	−10.9483	−	26.4315i	−0.550868	−	1.32991i
$396$		0			0
$397$	1.97409	−	4.76586i	0.0990765	−	0.239192i	−0.866568	−	0.499059i	$-0.833679\pi$
$397$	1.97409	−	4.76586i	0.0990765	−	0.239192i	0.965644	+	0.259868i	$0.0836789\pi$
$398$		0			0
$399$	2.22608	−	8.43872i	0.111444	−	0.422464i
$400$		0			0
$401$		−	10.6645i		−	0.532558i	−0.963896	−	0.266279i	$-0.914206\pi$
$401$		−	10.6645i		−	0.532558i	0.963896	−	0.266279i	$-0.0857942\pi$
$402$		0			0
$403$	−0.150798	+	0.364058i	−0.00751178	+	0.0181350i
$404$		0			0
$405$	11.5280	−	4.77506i	0.572832	−	0.237275i
$406$		0			0
$407$	−23.7025	+	23.7025i	−1.17489	+	1.17489i
$408$		0			0
$409$	−8.02235	−	8.02235i	−0.396680	−	0.396680i	0.480380	−	0.877060i	$-0.340499\pi$
$409$	−8.02235	−	8.02235i	−0.396680	−	0.396680i	−0.877060	+	0.480380i	$0.840499\pi$
$410$		0			0
$411$	−10.4946	+	4.34700i	−0.517659	+	0.214422i
$412$		0			0
$413$	−16.7032	+	21.9439i	−0.821912	+	1.07979i
$414$		0			0
$415$		−	22.9101i		−	1.12461i
$416$		0			0
$417$	16.1063			0.788727
$418$		0			0
$419$	7.42712	−	17.9307i	0.362839	−	0.875970i	−0.632044	−	0.774933i	$-0.717784\pi$
$419$	7.42712	−	17.9307i	0.362839	−	0.875970i	0.994883	−	0.101038i	$-0.0322162\pi$
$420$		0			0
$421$	−4.68956	+	1.94248i	−0.228555	+	0.0946706i	−0.494022	−	0.869449i	$-0.664474\pi$
$421$	−4.68956	+	1.94248i	−0.228555	+	0.0946706i	0.265467	+	0.964120i	$0.414474\pi$
$422$		0			0
$423$	9.09952	−	9.09952i	0.442434	−	0.442434i
$424$		0			0
$425$	29.3667	−	29.3667i	1.42449	−	1.42449i
$426$		0			0
$427$	20.6476	−	2.79987i	0.999208	−	0.135495i
$428$		0			0
$429$	−1.18324	−	0.490115i	−0.0571275	−	0.0236630i
$430$		0			0
$431$	−18.9939			−0.914904			−0.457452	−	0.889234i	$-0.651238\pi$
$431$	−18.9939			−0.914904			−0.457452	+	0.889234i	$0.651238\pi$
$432$		0			0
$433$	13.8910			0.667560			0.333780	−	0.942651i	$-0.391676\pi$
$433$	13.8910			0.667560			0.333780	+	0.942651i	$0.391676\pi$
$434$		0			0
$435$	−4.91417	+	11.8639i	−0.235617	+	0.568829i
$436$		0			0
$437$	−5.12986	+	2.12486i	−0.245394	+	0.101646i
$438$		0			0
$439$	13.4642	+	13.4642i	0.642611	+	0.642611i	0.951197	−	0.308586i	$-0.0998556\pi$
$439$	13.4642	+	13.4642i	0.642611	+	0.642611i	−0.308586	+	0.951197i	$0.599856\pi$
$440$		0			0
$441$	15.7761	−	4.35869i	0.751241	−	0.207557i
$442$		0			0
$443$	4.89175	+	11.8097i	0.232414	+	0.561097i	0.996460	−	0.0840644i	$-0.0267901\pi$
$443$	4.89175	+	11.8097i	0.232414	+	0.561097i	−0.764046	+	0.645161i	$0.776790\pi$
$444$		0			0
$445$	20.3024	−	49.0144i	0.962427	−	2.32351i
$446$		0			0
$447$	−4.38449			−0.207379
$448$		0			0
$449$	36.0648			1.70200			0.851001	−	0.525163i	$-0.175996\pi$
$449$	36.0648			1.70200			0.851001	+	0.525163i	$0.175996\pi$
$450$		0			0
$451$	1.32148	−	3.19035i	0.0622263	−	0.150228i
$452$		0			0
$453$	−0.805008	−	1.94346i	−0.0378226	−	0.0913118i
$454$		0			0
$455$	−2.25608	+	1.31425i	−0.105767	+	0.0616129i
$456$		0			0
$457$	5.72823	+	5.72823i	0.267955	+	0.267955i	0.828276	−	0.560320i	$-0.189322\pi$
$457$	5.72823	+	5.72823i	0.267955	+	0.267955i	−0.560320	+	0.828276i	$0.689322\pi$
$458$		0			0
$459$	−21.2386	+	8.79731i	−0.991332	+	0.410623i
$460$		0			0
$461$	5.94446	−	14.3512i	0.276861	−	0.668402i	−0.722884	−	0.690969i	$-0.757184\pi$
$461$	5.94446	−	14.3512i	0.276861	−	0.668402i	0.999745	+	0.0225670i	$0.00718391\pi$
$462$		0			0
$463$	6.42418			0.298557			0.149279	−	0.988795i	$-0.452305\pi$
$463$	6.42418			0.298557			0.149279	+	0.988795i	$0.452305\pi$
$464$		0			0
$465$	4.17288			0.193513
$466$		0			0
$467$	−31.5563	−	13.0711i	−1.46025	−	0.604857i	−0.495640	−	0.868528i	$-0.665067\pi$
$467$	−31.5563	−	13.0711i	−1.46025	−	0.604857i	−0.964613	+	0.263671i	$0.915067\pi$
$468$		0			0
$469$	−6.02147	+	0.816527i	−0.278046	+	0.0377037i
$470$		0			0
$471$	6.22553	−	6.22553i	0.286857	−	0.286857i
$472$		0			0
$473$	−9.18918	+	9.18918i	−0.422519	+	0.422519i
$474$		0			0
$475$	−29.3902	+	12.1738i	−1.34851	+	0.558573i
$476$		0			0
$477$	5.56104	−	13.4255i	0.254623	−	0.614714i
$478$		0			0
$479$	−30.0577			−1.37337			−0.686686	−	0.726954i	$-0.740935\pi$
$479$	−30.0577			−1.37337			−0.686686	+	0.726954i	$0.740935\pi$
$480$		0			0
$481$			1.61427i			0.0736043i
$482$		0			0
$483$	2.34537	+	1.78525i	0.106718	+	0.0812317i
$484$		0			0
$485$	−26.4845	+	10.9703i	−1.20260	+	0.498134i
$486$		0			0
$487$	−18.5311	−	18.5311i	−0.839726	−	0.839726i	0.149097	−	0.988823i	$-0.452363\pi$
$487$	−18.5311	−	18.5311i	−0.839726	−	0.839726i	−0.988823	+	0.149097i	$0.952363\pi$
$488$		0			0
$489$	3.67036	−	3.67036i	0.165979	−	0.165979i
$490$		0			0
$491$	4.29893	−	1.78068i	0.194008	−	0.0803608i	−0.283564	−	0.958953i	$-0.591517\pi$
$491$	4.29893	−	1.78068i	0.194008	−	0.0803608i	0.477572	+	0.878592i	$0.341517\pi$
$492$		0			0
$493$	−8.92148	+	21.5384i	−0.401803	+	0.970039i
$494$		0			0
$495$		−	47.9136i		−	2.15356i
$496$		0			0
$497$	9.17945	+	2.42149i	0.411755	+	0.108618i
$498$		0			0
$499$	0.103405	−	0.249641i	0.00462903	−	0.0111755i	−0.921548	−	0.388264i	$-0.873075\pi$
$499$	0.103405	−	0.249641i	0.00462903	−	0.0111755i	0.926177	+	0.377089i	$0.123075\pi$
$500$		0			0
$501$	2.20320	+	5.31900i	0.0984318	+	0.237635i
$502$		0			0
$503$	30.2868	+	30.2868i	1.35042	+	1.35042i	0.885187	+	0.465235i	$0.154030\pi$
$503$	30.2868	+	30.2868i	1.35042	+	1.35042i	0.465235	+	0.885187i	$0.345970\pi$
$504$		0			0
$505$	−14.8067	+	14.8067i	−0.658891	+	0.658891i
$506$		0			0
$507$	9.71394	−	4.02365i	0.431411	−	0.178696i
$508$		0			0
$509$	3.22636	+	1.33640i	0.143006	+	0.0592350i	0.453039	−	0.891491i	$-0.350340\pi$
$509$	3.22636	+	1.33640i	0.143006	+	0.0592350i	−0.310033	+	0.950726i	$0.600340\pi$
$510$		0			0
$511$	−10.5100	+	39.8416i	−0.464934	+	1.76249i
$512$		0			0
$513$	17.6087			0.777443
$514$		0			0
$515$	23.5508	+	9.75505i	1.03777	+	0.429859i
$516$		0			0
$517$	−12.0422	−	29.0725i	−0.529616	−	1.27861i
$518$		0			0
$519$	13.3740	+	13.3740i	0.587054	+	0.587054i
$520$		0			0
$521$	14.0142	−	14.0142i	0.613975	−	0.613975i	−0.330005	−	0.943979i	$-0.607050\pi$
$521$	14.0142	−	14.0142i	0.613975	−	0.613975i	0.943979	+	0.330005i	$0.107050\pi$
$522$		0			0
$523$	−10.7118	−	25.8607i	−0.468396	−	1.13081i	−0.964863	−	0.262753i	$-0.915370\pi$
$523$	−10.7118	−	25.8607i	−0.468396	−	1.13081i	0.496467	−	0.868056i	$-0.334630\pi$
$524$		0			0
$525$	13.4372	+	10.2281i	0.586448	+	0.446392i
$526$		0			0
$527$	7.57571			0.330003
$528$		0			0
$529$			21.1247i			0.918467i
$530$		0			0
$531$	−22.5164	−	9.32659i	−0.977128	−	0.404740i
$532$		0			0
$533$	−0.0636398	−	0.153640i	−0.00275655	−	0.00665489i
$534$		0			0
$535$	−0.751631	−	0.751631i	−0.0324958	−	0.0324958i
$536$		0			0
$537$	−11.8190	−	11.8190i	−0.510026	−	0.510026i
$538$		0			0
$539$	4.91586	−	39.7195i	0.211741	−	1.71084i
$540$		0			0
$541$	−10.6310	+	25.6655i	−0.457063	+	1.10345i	0.512518	+	0.858676i	$0.328713\pi$
$541$	−10.6310	+	25.6655i	−0.457063	+	1.10345i	−0.969581	+	0.244770i	$0.921287\pi$
$542$		0			0
$543$			16.6256i			0.713474i
$544$		0			0
$545$			33.7288i			1.44478i
$546$		0			0
$547$	17.4319	+	7.22052i	0.745334	+	0.308727i	0.722836	−	0.691020i	$-0.242838\pi$
$547$	17.4319	+	7.22052i	0.745334	+	0.308727i	0.0224976	+	0.999747i	$0.492838\pi$
$548$		0			0
$549$	7.04678	+	17.0124i	0.300749	+	0.726073i
$550$		0			0
$551$	12.6270	−	12.6270i	0.537927	−	0.537927i
$552$		0			0
$553$	18.2487	−	10.6305i	0.776012	−	0.452055i
$554$		0			0
$555$	15.7933	−	6.54178i	0.670387	−	0.277683i
$556$		0			0
$557$	−34.0169	−	14.0903i	−1.44134	−	0.597023i	−0.481218	−	0.876601i	$-0.659806\pi$
$557$	−34.0169	−	14.0903i	−1.44134	−	0.597023i	−0.960123	+	0.279578i	$0.909806\pi$
$558$		0			0
$559$			0.625834i			0.0264699i
$560$		0			0
$561$			24.6221i			1.03955i
$562$		0			0
$563$	5.78346	+	2.39559i	0.243744	+	0.100962i	0.501211	−	0.865325i	$-0.332888\pi$
$563$	5.78346	+	2.39559i	0.243744	+	0.100962i	−0.257467	+	0.966287i	$0.582888\pi$
$564$		0			0
$565$	32.3303	−	13.3917i	1.36015	−	0.563392i
$566$		0			0
$567$	4.63646	+	7.95909i	0.194713	+	0.334251i
$568$		0			0
$569$	13.9970	−	13.9970i	0.586786	−	0.586786i	−0.349974	−	0.936760i	$-0.613809\pi$
$569$	13.9970	−	13.9970i	0.586786	−	0.586786i	0.936760	+	0.349974i	$0.113809\pi$
$570$		0			0
$571$	4.72056	+	11.3964i	0.197549	+	0.476926i	0.991349	−	0.131253i	$-0.0419001\pi$
$571$	4.72056	+	11.3964i	0.197549	+	0.476926i	−0.793800	+	0.608179i	$0.791900\pi$
$572$		0			0
$573$	−0.765461	−	0.317064i	−0.0319776	−	0.0132456i
$574$		0			0
$575$		−	10.7438i		−	0.448049i
$576$		0			0
$577$			3.86125i			0.160746i	0.996765	+	0.0803729i	$0.0256111\pi$
$577$			3.86125i			0.160746i	−0.996765	+	0.0803729i	$0.974389\pi$
$578$		0			0
$579$	1.15434	−	2.78681i	0.0479725	−	0.115816i
$580$		0			0
$581$	16.7587	−	2.27252i	0.695268	−	0.0942802i
$582$		0			0
$583$	−25.1267	−	25.1267i	−1.04064	−	1.04064i
$584$		0			0
$585$	−1.63159	−	1.63159i	−0.0674579	−	0.0674579i
$586$		0			0
$587$	−2.92601	−	7.06401i	−0.120769	−	0.291563i	0.851921	−	0.523671i	$-0.175438\pi$
$587$	−2.92601	−	7.06401i	−0.120769	−	0.291563i	−0.972690	+	0.232108i	$0.925438\pi$
$588$		0			0
$589$	−5.36112	−	2.22065i	−0.220901	−	0.0915002i
$590$		0			0
$591$		−	13.4838i		−	0.554649i
$592$		0			0
$593$	24.1361			0.991150			0.495575	−	0.868565i	$-0.334957\pi$
$593$	24.1361			0.991150			0.495575	+	0.868565i	$0.334957\pi$
$594$		0			0
$595$	39.9414	+	30.4026i	1.63744	+	1.24638i
$596$		0			0
$597$	−1.59316	−	3.84623i	−0.0652037	−	0.157416i
$598$		0			0
$599$	5.85464	−	5.85464i	0.239214	−	0.239214i	−0.577310	−	0.816525i	$-0.695898\pi$
$599$	5.85464	−	5.85464i	0.239214	−	0.239214i	0.816525	+	0.577310i	$0.195898\pi$
$600$		0			0
$601$	−13.4335	−	13.4335i	−0.547964	−	0.547964i	0.377887	−	0.925852i	$-0.376651\pi$
$601$	−13.4335	−	13.4335i	−0.547964	−	0.547964i	−0.925852	+	0.377887i	$0.876651\pi$
$602$		0			0
$603$	−2.05506	−	4.96135i	−0.0836884	−	0.202042i
$604$		0			0
$605$	−71.8210	−	29.7492i	−2.91994	−	1.20948i
$606$		0			0
$607$	−9.43873			−0.383106			−0.191553	−	0.981482i	$-0.561352\pi$
$607$	−9.43873			−0.383106			−0.191553	+	0.981482i	$0.561352\pi$
$608$		0			0
$609$	−9.16587	−	2.41790i	−0.371420	−	0.0979784i
$610$		0			0
$611$	−1.40007	−	0.579927i	−0.0566407	−	0.0234613i
$612$		0			0
$613$	33.9466	−	14.0611i	1.37109	−	0.567923i	0.429005	−	0.903302i	$-0.358864\pi$
$613$	33.9466	−	14.0611i	1.37109	−	0.567923i	0.942083	+	0.335379i	$0.108864\pi$
$614$		0			0
$615$	−1.24525	+	1.24525i	−0.0502132	+	0.0502132i
$616$		0			0
$617$	−23.1176	−	23.1176i	−0.930680	−	0.930680i	0.0670682	−	0.997748i	$-0.478635\pi$
$617$	−23.1176	−	23.1176i	−0.930680	−	0.930680i	−0.997748	+	0.0670682i	$0.978635\pi$
$618$		0			0
$619$	4.99740	+	12.0648i	0.200862	+	0.484924i	0.991927	−	0.126808i	$-0.0404731\pi$
$619$	4.99740	+	12.0648i	0.200862	+	0.484924i	−0.791065	+	0.611732i	$0.790473\pi$
$620$		0			0
$621$	−2.27583	+	5.49434i	−0.0913258	+	0.220480i
$622$		0			0
$623$	37.8679	+	9.98933i	1.51715	+	0.400214i
$624$		0			0
$625$			2.67410i			0.106964i
$626$		0			0
$627$	7.21742	−	17.4244i	0.288236	−	0.695864i
$628$		0			0
$629$	28.6720	−	11.8763i	1.14323	−	0.473541i
$630$		0			0
$631$	−19.9610	+	19.9610i	−0.794634	+	0.794634i	−0.982244	−	0.187610i	$-0.939926\pi$
$631$	−19.9610	+	19.9610i	−0.794634	+	0.794634i	0.187610	+	0.982244i	$0.439926\pi$
$632$		0			0
$633$	−10.2414	−	10.2414i	−0.407057	−	0.407057i
$634$		0			0
$635$	64.7318	−	26.8128i	2.56880	−	1.06403i
$636$		0			0
$637$	−1.18516	−	1.51996i	−0.0469578	−	0.0602229i
$638$		0			0
$639$			8.38977i			0.331894i
$640$		0			0
$641$	14.6955			0.580437			0.290219	−	0.956960i	$-0.406272\pi$
$641$	14.6955			0.580437			0.290219	+	0.956960i	$0.406272\pi$
$642$		0			0
$643$	−16.0999	+	38.8686i	−0.634919	+	1.53283i	0.198450	+	0.980111i	$0.436409\pi$
$643$	−16.0999	+	38.8686i	−0.634919	+	1.53283i	−0.833368	+	0.552718i	$0.813591\pi$
$644$		0			0
$645$	6.12287	−	2.53618i	0.241088	−	0.0998619i
$646$		0			0
$647$	−20.2079	+	20.2079i	−0.794456	+	0.794456i	−0.982215	−	0.187759i	$-0.939878\pi$
$647$	−20.2079	+	20.2079i	−0.794456	+	0.794456i	0.187759	+	0.982215i	$0.439878\pi$
$648$		0			0
$649$	−42.1407	+	42.1407i	−1.65417	+	1.65417i
$650$		0			0
$651$	0.413922	+	3.05247i	0.0162229	+	0.119636i
$652$		0			0
$653$	−32.4008	−	13.4209i	−1.26794	−	0.525199i	−0.355605	−	0.934636i	$-0.615725\pi$
$653$	−32.4008	−	13.4209i	−1.26794	−	0.525199i	−0.912338	+	0.409437i	$0.865725\pi$
$654$		0			0
$655$	−65.1401			−2.54523
$656$		0			0
$657$	−36.4141			−1.42065
$658$		0			0
$659$	9.51545	−	22.9723i	0.370669	−	0.894875i	−0.622968	−	0.782247i	$-0.714073\pi$
$659$	9.51545	−	22.9723i	0.370669	−	0.894875i	0.993637	−	0.112627i	$-0.0359267\pi$
$660$		0			0
$661$	−28.1486	+	11.6596i	−1.09486	+	0.453504i	−0.855697	−	0.517477i	$-0.826871\pi$
$661$	−28.1486	+	11.6596i	−1.09486	+	0.453504i	−0.239158	+	0.970981i	$0.576871\pi$
$662$		0			0
$663$	0.838451	+	0.838451i	0.0325627	+	0.0325627i
$664$		0			0
$665$	−19.3536	−	33.2230i	−0.750500	−	1.28833i
$666$		0			0
$667$	2.30795	+	5.57189i	0.0893643	+	0.215744i
$668$		0			0
$669$	5.38975	−	13.0120i	0.208380	−	0.503074i
$670$		0			0
$671$	45.0282			1.73829
$672$		0			0
$673$	−14.2449			−0.549101			−0.274550	−	0.961573i	$-0.588529\pi$
$673$	−14.2449			−0.549101			−0.274550	+	0.961573i	$0.588529\pi$
$674$		0			0
$675$	−13.0388	+	31.4784i	−0.501863	+	1.21160i
$676$		0			0
$677$	1.35098	+	3.26156i	0.0519225	+	0.125352i	0.947712	−	0.319126i	$-0.103389\pi$
$677$	1.35098	+	3.26156i	0.0519225	+	0.125352i	−0.895790	+	0.444478i	$0.853389\pi$
$678$		0			0
$679$	−10.6518	−	18.2853i	−0.408780	−	0.701724i
$680$		0			0
$681$	−2.96585	−	2.96585i	−0.113652	−	0.113652i
$682$		0			0
$683$	−38.0612	+	15.7655i	−1.45637	+	0.603249i	−0.963705	−	0.266968i	$-0.913978\pi$
$683$	−38.0612	+	15.7655i	−1.45637	+	0.603249i	−0.492667	+	0.870218i	$0.663978\pi$
$684$		0			0
$685$	−19.1509	+	46.2345i	−0.731720	+	1.76653i
$686$		0			0
$687$	−11.1242			−0.424414
$688$		0			0
$689$	−1.71126			−0.0651939
$690$		0			0
$691$	17.9922	+	7.45260i	0.684454	+	0.283510i	0.697687	−	0.716402i	$-0.254212\pi$
$691$	17.9922	+	7.45260i	0.684454	+	0.283510i	−0.0132334	+	0.999912i	$0.504212\pi$
$692$		0			0
$693$	35.0488	−	4.75271i	1.33139	−	0.180540i
$694$		0			0
$695$	50.1742	−	50.1742i	1.90322	−	1.90322i
$696$		0			0
$697$	−2.26070	+	2.26070i	−0.0856299	+	0.0856299i
$698$		0			0
$699$	19.6162	−	8.12528i	0.741952	−	0.307326i
$700$		0			0
$701$	−7.55914	+	18.2494i	−0.285505	+	0.689270i	−0.999946	−	0.0104263i	$-0.996681\pi$
$701$	−7.55914	+	18.2494i	−0.285505	+	0.689270i	0.714441	+	0.699696i	$0.246681\pi$
$702$		0			0
$703$	−23.7717			−0.896566
$704$		0			0
$705$			16.0478i			0.604394i
$706$		0			0
$707$	−12.2999	−	9.36240i	−0.462584	−	0.352109i
$708$		0			0
$709$	−24.8971	+	10.3127i	−0.935031	+	0.387303i	−0.797585	−	0.603207i	$-0.793889\pi$
$709$	−24.8971	+	10.3127i	−0.935031	+	0.387303i	−0.137446	+	0.990509i	$0.543889\pi$
$710$		0			0
$711$	13.1974	+	13.1974i	0.494940	+	0.494940i
$712$		0			0
$713$	1.38579	−	1.38579i	0.0518983	−	0.0518983i
$714$		0			0
$715$	−5.21284	+	2.15923i	−0.194949	+	0.0807506i
$716$		0			0
$717$	4.41918	−	10.6688i	0.165037	−	0.398435i
$718$		0			0
$719$			43.9669i			1.63969i	0.572586	+	0.819845i	$0.305940\pi$
$719$			43.9669i			1.63969i	−0.572586	+	0.819845i	$0.694060\pi$
$720$		0			0
$721$	−4.79974	+	18.1950i	−0.178752	+	0.677618i
$722$		0			0
$723$	−3.09526	+	7.47261i	−0.115114	+	0.277910i
$724$		0			0
$725$	13.2228	+	31.9227i	0.491083	+	1.18558i
$726$		0			0
$727$	−11.8881	−	11.8881i	−0.440907	−	0.440907i	0.451410	−	0.892317i	$-0.350921\pi$
$727$	−11.8881	−	11.8881i	−0.440907	−	0.440907i	−0.892317	+	0.451410i	$0.850921\pi$
$728$		0			0
$729$	1.73866	−	1.73866i	0.0643949	−	0.0643949i
$730$		0			0
$731$	11.1158	−	4.60433i	0.411134	−	0.170297i
$732$		0			0
$733$	11.4956	+	4.76163i	0.424599	+	0.175875i	0.584742	−	0.811219i	$-0.301196\pi$
$733$	11.4956	+	4.76163i	0.424599	+	0.175875i	−0.160143	+	0.987094i	$0.551196\pi$
$734$		0			0
$735$	−10.0677	+	17.7547i	−0.371354	+	0.654890i
$736$		0			0
$737$	−13.1316			−0.483708
$738$		0			0
$739$	0.622209	+	0.257727i	0.0228883	+	0.00948066i	0.394098	−	0.919068i	$-0.371057\pi$
$739$	0.622209	+	0.257727i	0.0228883	+	0.00948066i	−0.371210	+	0.928549i	$0.621057\pi$
$740$		0			0
$741$	−0.347576	−	0.839122i	−0.0127685	−	0.0308259i
$742$		0			0
$743$	−24.5070	−	24.5070i	−0.899074	−	0.899074i	0.0962798	−	0.995354i	$-0.469306\pi$
$743$	−24.5070	−	24.5070i	−0.899074	−	0.899074i	−0.995354	+	0.0962798i	$0.969306\pi$
$744$		0			0
$745$	−13.6586	+	13.6586i	−0.500411	+	0.500411i
$746$		0			0
$747$	5.71955	+	13.8082i	0.209267	+	0.505216i
$748$		0			0
$749$	0.475261	−	0.624375i	0.0173657	−	0.0228142i
$750$		0			0
$751$	52.2891			1.90806			0.954028	−	0.299719i	$-0.0968928\pi$
$751$	52.2891			1.90806			0.954028	+	0.299719i	$0.0968928\pi$
$752$		0			0
$753$		−	10.1139i		−	0.368572i
$754$		0			0
$755$	−8.56203	−	3.54651i	−0.311604	−	0.129071i
$756$		0			0
$757$	−1.07264	−	2.58959i	−0.0389859	−	0.0941204i	0.903187	−	0.429247i	$-0.141221\pi$
$757$	−1.07264	−	2.58959i	−0.0389859	−	0.0941204i	−0.942173	+	0.335126i	$0.891221\pi$
$758$		0			0
$759$	4.50402	+	4.50402i	0.163486	+	0.163486i
$760$		0			0
$761$	−1.72551	−	1.72551i	−0.0625496	−	0.0625496i	0.675140	−	0.737690i	$-0.264083\pi$
$761$	−1.72551	−	1.72551i	−0.0625496	−	0.0625496i	−0.737690	+	0.675140i	$0.764083\pi$
$762$		0			0
$763$	−24.6726	+	3.34567i	−0.893208	+	0.121121i
$764$		0			0
$765$	−16.9759	+	40.9835i	−0.613765	+	1.48176i
$766$		0			0
$767$			2.87001i			0.103630i
$768$		0			0
$769$			19.9305i			0.718714i	0.933200	+	0.359357i	$0.117004\pi$
$769$			19.9305i			0.718714i	−0.933200	+	0.359357i	$0.882996\pi$
$770$		0			0
$771$	−8.11721	−	3.36226i	−0.292334	−	0.121089i
$772$		0			0
$773$	5.53504	+	13.3628i	0.199082	+	0.480626i	0.991619	−	0.129198i	$-0.0412403\pi$
$773$	5.53504	+	13.3628i	0.199082	+	0.480626i	−0.792537	+	0.609824i	$0.791240\pi$
$774$		0			0
$775$	7.93953	−	7.93953i	0.285196	−	0.285196i
$776$		0			0
$777$	6.35190	+	10.9039i	0.227873	+	0.391174i
$778$		0			0
$779$	2.26250	−	0.937159i	0.0810626	−	0.0335772i
$780$		0			0
$781$	18.9539	+	7.85096i	0.678223	+	0.280929i
$782$		0			0
$783$		−	19.1260i		−	0.683508i
$784$		0			0
$785$		−	38.7875i		−	1.38439i
$786$		0			0
$787$	−17.1890	−	7.11992i	−0.612722	−	0.253798i	0.0546698	−	0.998504i	$-0.482589\pi$
$787$	−17.1890	−	7.11992i	−0.612722	−	0.253798i	−0.667392	+	0.744707i	$0.732589\pi$
$788$		0			0
$789$	11.6406	−	4.82171i	0.414418	−	0.171658i
$790$		0			0
$791$	13.0030	+	22.3213i	0.462332	+	0.793654i
$792$		0			0
$793$	1.53333	−	1.53333i	0.0544502	−	0.0544502i
$794$		0			0
$795$	6.93485	+	16.7422i	0.245954	+	0.593785i
$796$		0			0
$797$	−26.8554	−	11.1239i	−0.951268	−	0.394028i	−0.147561	−	0.989053i	$-0.547142\pi$
$797$	−26.8554	−	11.1239i	−0.951268	−	0.394028i	−0.803707	+	0.595025i	$0.797142\pi$
$798$		0			0
$799$			29.1341i			1.03069i
$800$		0			0
$801$			34.6102i			1.22289i
$802$		0			0
$803$	−34.0755	+	82.2656i	−1.20250	+	2.90309i
$804$		0			0
$805$	12.8677	−	1.74490i	0.453528	−	0.0614995i
$806$		0			0
$807$	−0.994094	−	0.994094i	−0.0349938	−	0.0349938i
$808$		0			0
$809$	−29.6265	−	29.6265i	−1.04161	−	1.04161i	−0.999096	−	0.0425179i	$-0.986462\pi$
$809$	−29.6265	−	29.6265i	−1.04161	−	1.04161i	−0.0425179	−	0.999096i	$-0.513538\pi$
$810$		0			0
$811$	−0.0959660	−	0.231682i	−0.00336982	−	0.00813547i	0.922186	−	0.386747i	$-0.126401\pi$
$811$	−0.0959660	−	0.231682i	−0.00336982	−	0.00813547i	−0.925555	+	0.378612i	$0.876401\pi$
$812$		0			0
$813$	7.76536	+	3.21652i	0.272343	+	0.112808i
$814$		0			0
$815$		−	22.8678i		−	0.801024i
$816$		0			0
$817$	−9.21602			−0.322428
$818$		0			0
$819$	1.03167	−	1.35535i	0.0360493	−	0.0473598i
$820$		0			0
$821$	4.02552	+	9.71846i	0.140492	+	0.339177i	0.978427	−	0.206593i	$-0.0662375\pi$
$821$	4.02552	+	9.71846i	0.140492	+	0.339177i	−0.837936	+	0.545769i	$0.816238\pi$
$822$		0			0
$823$	−3.19440	+	3.19440i	−0.111350	+	0.111350i	−0.760586	−	0.649237i	$-0.775088\pi$
$823$	−3.19440	+	3.19440i	−0.111350	+	0.111350i	0.649237	+	0.760586i	$0.275088\pi$
$824$		0			0
$825$	25.8046	+	25.8046i	0.898402	+	0.898402i
$826$		0			0
$827$	−6.58578	−	15.8995i	−0.229010	−	0.552879i	0.767047	−	0.641591i	$-0.221725\pi$
$827$	−6.58578	−	15.8995i	−0.229010	−	0.552879i	−0.996057	+	0.0887113i	$0.971725\pi$
$828$		0			0
$829$	40.8651	+	16.9269i	1.41930	+	0.587895i	0.954686	−	0.297615i	$-0.0961913\pi$
$829$	40.8651	+	16.9269i	1.41930	+	0.587895i	0.464619	+	0.885511i	$0.346191\pi$
$830$		0			0
$831$	17.1596			0.595261
$832$		0			0
$833$	−18.2776	+	32.2329i	−0.633280	+	1.11680i
$834$		0			0
$835$	23.4332	+	9.70633i	0.810938	+	0.335901i
$836$		0			0
$837$	−5.74203	+	2.37843i	−0.198473	+	0.0822104i
$838$		0			0
$839$	−23.5108	+	23.5108i	−0.811683	+	0.811683i	−0.984886	−	0.173203i	$-0.944588\pi$
$839$	−23.5108	+	23.5108i	−0.811683	+	0.811683i	0.173203	+	0.984886i	$0.444588\pi$
$840$		0			0
$841$	6.79107	+	6.79107i	0.234175	+	0.234175i
$842$		0			0
$843$	7.47855	+	18.0548i	0.257575	+	0.621841i
$844$		0			0
$845$	17.7264	−	42.7953i	0.609807	−	1.47220i
$846$		0			0
$847$	14.6374	−	55.4880i	0.502947	−	1.90659i
$848$		0			0
$849$		−	0.477668i		−	0.0163935i
$850$		0			0
$851$	3.07236	−	7.41734i	0.105319	−	0.254263i
$852$		0			0
$853$	28.1078	−	11.6426i	0.962393	−	0.398636i	0.154518	−	0.987990i	$-0.450618\pi$
$853$	28.1078	−	11.6426i	0.962393	−	0.398636i	0.807875	+	0.589354i	$0.200618\pi$
$854$		0			0
$855$	24.0268	−	24.0268i	0.821698	−	0.821698i
$856$		0			0
$857$	−7.27401	−	7.27401i	−0.248475	−	0.248475i	0.571869	−	0.820345i	$-0.306218\pi$
$857$	−7.27401	−	7.27401i	−0.248475	−	0.248475i	−0.820345	+	0.571869i	$0.806218\pi$
$858$		0			0
$859$	9.17589	−	3.80078i	0.313077	−	0.129681i	−0.220612	−	0.975362i	$-0.570805\pi$
$859$	9.17589	−	3.80078i	0.313077	−	0.129681i	0.533689	+	0.845681i	$0.320805\pi$
$860$		0			0
$861$	−1.03442	−	0.787378i	−0.0352529	−	0.0268338i
$862$		0			0
$863$			0.910399i			0.0309904i	0.999880	+	0.0154952i	$0.00493247\pi$
$863$			0.910399i			0.0309904i	−0.999880	+	0.0154952i	$0.995068\pi$
$864$		0			0
$865$	83.3254			2.83315
$866$		0			0
$867$	3.43113	−	8.28347i	0.116527	−	0.281322i
$868$		0			0
$869$	42.1649	−	17.4653i	1.43035	−	0.592469i
$870$		0			0
$871$	−0.447167	+	0.447167i	−0.0151517	+	0.0151517i
$872$		0			0
$873$	13.2239	−	13.2239i	0.447560	−	0.447560i
$874$		0			0
$875$	26.7393	−	3.62592i	0.903955	−	0.122579i
$876$		0			0
$877$	−8.74522	−	3.62239i	−0.295305	−	0.122319i	0.230112	−	0.973164i	$-0.426091\pi$
$877$	−8.74522	−	3.62239i	−0.295305	−	0.122319i	−0.525417	+	0.850845i	$0.676091\pi$
$878$		0			0
$879$	12.0648			0.406937
$880$		0			0
$881$	−24.0665			−0.810821			−0.405411	−	0.914135i	$-0.632871\pi$
$881$	−24.0665			−0.810821			−0.405411	+	0.914135i	$0.632871\pi$
$882$		0			0
$883$	2.25125	−	5.43499i	0.0757605	−	0.182902i	−0.881462	−	0.472255i	$-0.843440\pi$
$883$	2.25125	−	5.43499i	0.0757605	−	0.182902i	0.957222	+	0.289353i	$0.0934402\pi$
$884$		0			0
$885$	28.0789	−	11.6306i	0.943861	−	0.390960i
$886$		0			0
$887$	−22.9074	−	22.9074i	−0.769155	−	0.769155i	0.208803	−	0.977958i	$-0.433043\pi$
$887$	−22.9074	−	22.9074i	−0.769155	−	0.769155i	−0.977958	+	0.208803i	$0.933043\pi$
$888$		0			0
$889$	26.0345	+	44.6917i	0.873170	+	1.49891i
$890$		0			0
$891$	7.61742	+	18.3901i	0.255193	+	0.616091i
$892$		0			0
$893$	8.53999	−	20.6174i	0.285780	−	0.689934i
$894$		0			0
$895$	−73.6369			−2.46141
$896$		0			0
$897$	0.306749			0.0102420
$898$		0			0
$899$	−2.41200	+	5.82308i	−0.0804446	+	0.194211i
$900$		0			0
$901$	12.5899	+	30.3948i	0.419432	+	1.01260i
$902$		0			0
$903$	2.46256	+	4.22731i	0.0819489	+	0.140676i
$904$		0			0
$905$	51.7921	+	51.7921i	1.72163	+	1.72163i
$906$		0			0
$907$	−21.0151	+	8.70472i	−0.697793	+	0.289035i	−0.703243	−	0.710950i	$-0.748265\pi$
$907$	−21.0151	+	8.70472i	−0.697793	+	0.289035i	0.00544953	+	0.999985i	$0.498265\pi$
$908$		0			0
$909$	5.22769	−	12.6208i	0.173392	−	0.418604i
$910$		0			0
$911$	−39.2986			−1.30202			−0.651010	−	0.759070i	$-0.725654\pi$
$911$	−39.2986			−1.30202			−0.651010	+	0.759070i	$0.725654\pi$
$912$		0			0
$913$	36.5473			1.20954
$914$		0			0
$915$	−21.2152	−	8.78763i	−0.701354	−	0.290510i
$916$		0			0
$917$	−6.46146	−	47.6500i	−0.213376	−	1.57354i
$918$		0			0
$919$	−13.8310	+	13.8310i	−0.456241	+	0.456241i	−0.897420	−	0.441178i	$-0.854561\pi$
$919$	−13.8310	+	13.8310i	−0.456241	+	0.456241i	0.441178	+	0.897420i	$0.354561\pi$
$920$		0			0
$921$	−13.2481	+	13.2481i	−0.436540	+	0.436540i
$922$		0			0
$923$	0.912778	−	0.378085i	0.0300445	−	0.0124448i
$924$		0			0
$925$	17.6023	−	42.4957i	0.578760	−	1.39725i
$926$		0			0
$927$	−16.6297			−0.546193
$928$		0			0
$929$			49.3151i			1.61798i	0.587825	+	0.808988i	$0.299984\pi$
$929$			49.3151i			1.61798i	−0.587825	+	0.808988i	$0.700016\pi$
$930$		0			0
$931$	22.3829	−	17.4527i	0.733569	−	0.571988i
$932$		0			0
$933$	2.30886	−	0.956363i	0.0755888	−	0.0313099i
$934$		0			0
$935$	76.7029	+	76.7029i	2.50845	+	2.50845i
$936$		0			0
$937$	21.0513	−	21.0513i	0.687716	−	0.687716i	−0.274011	−	0.961727i	$-0.588350\pi$
$937$	21.0513	−	21.0513i	0.687716	−	0.687716i	0.961727	+	0.274011i	$0.0883504\pi$
$938$		0			0
$939$	5.65434	−	2.34210i	0.184522	−	0.0764316i
$940$		0			0
$941$	−13.9886	+	33.7715i	−0.456016	+	1.10092i	0.513981	+	0.857801i	$0.328170\pi$
$941$	−13.9886	+	33.7715i	−0.456016	+	1.10092i	−0.969997	+	0.243118i	$0.921830\pi$
$942$		0			0
$943$			0.827078i			0.0269334i
$944$		0			0
$945$	−39.8187	−	10.5039i	−1.29530	−	0.341693i
$946$		0			0
$947$	−14.9909	+	36.1912i	−0.487139	+	1.17606i	0.469015	+	0.883190i	$0.344609\pi$
$947$	−14.9909	+	36.1912i	−0.487139	+	1.17606i	−0.956153	+	0.292866i	$0.905391\pi$
$948$		0			0
$949$	1.64100	+	3.96174i	0.0532693	+	0.128603i
$950$		0			0
$951$	8.48107	+	8.48107i	0.275018	+	0.275018i
$952$		0			0
$953$	14.8400	−	14.8400i	0.480715	−	0.480715i	−0.424645	−	0.905360i	$-0.639601\pi$
$953$	14.8400	−	14.8400i	0.480715	−	0.480715i	0.905360	+	0.424645i	$0.139601\pi$
$954$		0			0
$955$	−3.37228	+	1.39685i	−0.109125	+	0.0452009i
$956$		0			0
$957$	−18.9258	−	7.83934i	−0.611786	−	0.253410i
$958$		0			0
$959$	−35.7202	−	9.42277i	−1.15346	−	0.304277i
$960$		0			0
$961$	−28.9518			−0.933930
$962$		0			0
$963$	0.640665	+	0.265372i	0.0206451	+	0.00855149i
$964$		0			0
$965$	−5.08549	−	12.2775i	−0.163708	−	0.395225i
$966$		0			0
$967$	9.66348	+	9.66348i	0.310757	+	0.310757i	0.845203	−	0.534446i	$-0.179480\pi$
$967$	9.66348	+	9.66348i	0.310757	+	0.310757i	−0.534446	+	0.845203i	$0.679480\pi$
$968$		0			0
$969$	−12.3470	+	12.3470i	−0.396643	+	0.396643i
$970$		0			0
$971$	17.7776	+	42.9190i	0.570511	+	1.37734i	0.901121	+	0.433568i	$0.142746\pi$
$971$	17.7776	+	42.9190i	0.570511	+	1.37734i	−0.330610	+	0.943768i	$0.607254\pi$
$972$		0			0
$973$	41.6794	+	31.7255i	1.33618	+	1.01707i
$974$		0			0
$975$	1.75744			0.0562830
$976$		0			0
$977$			19.6064i			0.627265i	0.949544	+	0.313633i	$0.101546\pi$
$977$			19.6064i			0.627265i	−0.949544	+	0.313633i	$0.898454\pi$
$978$		0			0
$979$	78.1903	+	32.3875i	2.49897	+	1.03511i
$980$		0			0
$981$	−8.42046	−	20.3288i	−0.268845	−	0.649048i
$982$		0			0
$983$	24.9997	+	24.9997i	0.797365	+	0.797365i	0.982679	−	0.185314i	$-0.0593302\pi$
$983$	24.9997	+	24.9997i	0.797365	+	0.797365i	−0.185314	+	0.982679i	$0.559330\pi$
$984$		0			0
$985$	−42.0047	−	42.0047i	−1.33838	−	1.33838i
$986$		0			0
$987$	−11.7389	+	1.59183i	−0.373655	+	0.0506685i
$988$		0			0
$989$	1.19112	−	2.87562i	0.0378754	−	0.0914394i
$990$		0			0
$991$		−	45.8636i		−	1.45690i	−0.685096	−	0.728452i	$-0.740240\pi$
$991$		−	45.8636i		−	1.45690i	0.685096	−	0.728452i	$-0.259760\pi$
$992$		0			0
$993$			1.47036i			0.0466603i
$994$		0			0
$995$	−16.9448	−	7.01876i	−0.537186	−	0.222510i
$996$		0			0
$997$	−9.49428	−	22.9212i	−0.300687	−	0.725922i	−0.999939	−	0.0110472i	$-0.996484\pi$
$997$	−9.49428	−	22.9212i	−0.300687	−	0.725922i	0.699252	−	0.714875i	$-0.253516\pi$
$998$		0			0
$999$	−18.0034	+	18.0034i	−0.569603	+	0.569603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.x.b.111.17		112
4.3	odd	2		224.2.x.b.83.1	yes	112
7.6	odd	2	inner	896.2.x.b.111.12		112
28.27	even	2		224.2.x.b.83.2	yes	112
32.5	even	8		224.2.x.b.27.2	yes	112
32.27	odd	8	inner	896.2.x.b.783.12		112
224.27	even	8	inner	896.2.x.b.783.17		112
224.69	odd	8		224.2.x.b.27.1	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.x.b.27.1	✓	112	224.69	odd	8
224.2.x.b.27.2	yes	112	32.5	even	8
224.2.x.b.83.1	yes	112	4.3	odd	2
224.2.x.b.83.2	yes	112	28.27	even	2
896.2.x.b.111.12		112	7.6	odd	2	inner
896.2.x.b.111.17		112	1.1	even	1	trivial
896.2.x.b.783.12		112	32.27	odd	8	inner
896.2.x.b.783.17		112	224.27	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.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.311327 - 0.751610i) q^{3} +(-1.37157 - 3.31126i) q^{5} +(2.28614 - 1.33176i) q^{7} +(1.65333 + 1.65333i) q^{9} +O(q^{10})\)	\(q+(0.311327 - 0.751610i) q^{3} +(-1.37157 - 3.31126i) q^{5} +(2.28614 - 1.33176i) q^{7} +(1.65333 + 1.65333i) q^{9} +(5.28229 - 2.18800i) q^{11} +(0.105369 - 0.254384i) q^{13} -2.91578 q^{15} -5.29348 q^{17} +(3.74605 + 1.55167i) q^{19} +(-0.289226 - 2.13289i) q^{21} +(-0.968314 + 0.968314i) q^{23} +(-5.54771 + 5.54771i) q^{25} +(4.01221 - 1.66191i) q^{27} +(1.68537 - 4.06885i) q^{29} -1.43114 q^{31} -4.65140i q^{33} +(-7.54539 - 5.74340i) q^{35} +(-5.41648 + 2.24358i) q^{37} +(-0.158393 - 0.158393i) q^{39} +(0.427071 - 0.427071i) q^{41} +(-2.09991 + 0.869810i) q^{43} +(3.20695 - 7.74225i) q^{45} -5.50376i q^{47} +(3.45284 - 6.08916i) q^{49} +(-1.64800 + 3.97863i) q^{51} +(-2.37839 - 5.74193i) q^{53} +(-14.4901 - 14.4901i) q^{55} +(2.33249 - 2.33249i) q^{57} +(-9.62996 + 3.98886i) q^{59} +(7.27600 + 3.01382i) q^{61} +(5.98157 + 1.57790i) q^{63} -0.986852 q^{65} +(-2.12190 - 0.878921i) q^{67} +(0.426332 + 1.02926i) q^{69} +(2.53724 + 2.53724i) q^{71} +(-11.0124 + 11.0124i) q^{73} +(2.44256 + 5.89686i) q^{75} +(9.16216 - 12.0368i) q^{77} +7.98231 q^{79} +3.48146i q^{81} +(5.90559 + 2.44618i) q^{83} +(7.26038 + 17.5281i) q^{85} +(-2.53348 - 2.53348i) q^{87} +(10.4668 + 10.4668i) q^{89} +(-0.0978891 - 0.721882i) q^{91} +(-0.445552 + 1.07566i) q^{93} -14.5324i q^{95} -7.99833i q^{97} +(12.3508 + 5.11588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 112 * q + 4 * q^7 - 8 * q^9	\( 112 q + 4 q^{7} - 8 q^{9} + 8 q^{11} + 16 q^{15} - 4 q^{21} + 48 q^{23} - 8 q^{25} - 8 q^{29} - 20 q^{35} - 8 q^{37} + 8 q^{39} - 32 q^{43} + 32 q^{51} - 32 q^{53} - 8 q^{57} - 16 q^{65} + 64 q^{67} - 56 q^{71} + 52 q^{77} + 16 q^{79} - 48 q^{85} + 52 q^{91} - 32 q^{93} - 16 q^{99}+O(q^{100}) \) 112 * q + 4 * q^7 - 8 * q^9 + 8 * q^11 + 16 * q^15 - 4 * q^21 + 48 * q^23 - 8 * q^25 - 8 * q^29 - 20 * q^35 - 8 * q^37 + 8 * q^39 - 32 * q^43 + 32 * q^51 - 32 * q^53 - 8 * q^57 - 16 * q^65 + 64 * q^67 - 56 * q^71 + 52 * q^77 + 16 * q^79 - 48 * q^85 + 52 * q^91 - 32 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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