LMFDB - Embedded newform 896.2.u.c.337.1

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			337.1
Character	$\chi$	$=$	896.337
Dual form			896.2.u.c.561.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.91760 - 1.20851i) q^{3} +(-0.629460 - 1.51965i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(4.93055 + 4.93055i) q^{9} +O(q^{10})$	\(q+(-2.91760 - 1.20851i) q^{3} +(-0.629460 - 1.51965i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(4.93055 + 4.93055i) q^{9} +(5.75610 - 2.38425i) q^{11} +(0.0753604 - 0.181936i) q^{13} +5.19444i q^{15} +3.98721i q^{17} +(-1.18647 + 2.86440i) q^{19} +(2.91760 - 1.20851i) q^{21} +(-0.860956 - 0.860956i) q^{23} +(1.62241 - 1.62241i) q^{25} +(-4.80123 - 11.5912i) q^{27} +(5.85615 + 2.42570i) q^{29} +5.52776 q^{31} -19.6754 q^{33} +(1.51965 + 0.629460i) q^{35} +(-4.25158 - 10.2642i) q^{37} +(-0.439742 + 0.439742i) q^{39} +(-2.48800 - 2.48800i) q^{41} +(1.99108 - 0.824733i) q^{43} +(4.38913 - 10.5963i) q^{45} -7.41348i q^{47} -1.00000i q^{49} +(4.81857 - 11.6331i) q^{51} +(1.28857 - 0.533743i) q^{53} +(-7.24647 - 7.24647i) q^{55} +(6.92330 - 6.92330i) q^{57} +(-0.0193914 - 0.0468150i) q^{59} +(-11.0396 - 4.57274i) q^{61} -6.97285 q^{63} -0.323916 q^{65} +(-3.63165 - 1.50428i) q^{67} +(1.47145 + 3.55239i) q^{69} +(0.181485 - 0.181485i) q^{71} +(2.49063 + 2.49063i) q^{73} +(-6.69425 + 2.77285i) q^{75} +(-2.38425 + 5.75610i) q^{77} +4.65759i q^{79} +18.7021i q^{81} +(-2.03104 + 4.90335i) q^{83} +(6.05917 - 2.50979i) q^{85} +(-14.1544 - 14.1544i) q^{87} +(5.52373 - 5.52373i) q^{89} +(0.0753604 + 0.181936i) q^{91} +(-16.1278 - 6.68033i) q^{93} +5.09973 q^{95} +14.4758 q^{97} +(40.1364 + 16.6251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.91760	−	1.20851i	−1.68447	−	0.697732i	−0.684951	−	0.728589i	$-0.740176\pi$
$3$	−2.91760	−	1.20851i	−1.68447	−	0.697732i	−0.999524	+	0.0308571i	$0.990176\pi$
$4$		0			0
$5$	−0.629460	−	1.51965i	−0.281503	−	0.679609i	0.718368	−	0.695663i	$-0.244889\pi$
$5$	−0.629460	−	1.51965i	−0.281503	−	0.679609i	−0.999871	+	0.0160546i	$0.994889\pi$
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$		0			0
$9$	4.93055	+	4.93055i	1.64352	+	1.64352i
$10$		0			0
$11$	5.75610	−	2.38425i	1.73553	−	0.718880i	0.736426	−	0.676518i	$-0.236512\pi$
$11$	5.75610	−	2.38425i	1.73553	−	0.718880i	0.999102	−	0.0423620i	$-0.0134883\pi$
$12$		0			0
$13$	0.0753604	−	0.181936i	0.0209012	−	0.0504600i	−0.913084	−	0.407771i	$-0.866306\pi$
$13$	0.0753604	−	0.181936i	0.0209012	−	0.0504600i	0.933986	+	0.357311i	$0.116306\pi$
$14$		0			0
$15$			5.19444i			1.34120i
$16$		0			0
$17$			3.98721i			0.967041i	0.875333	+	0.483520i	$0.160642\pi$
$17$			3.98721i			0.967041i	−0.875333	+	0.483520i	$0.839358\pi$
$18$		0			0
$19$	−1.18647	+	2.86440i	−0.272196	+	0.657139i	−0.999577	−	0.0290951i	$-0.990737\pi$
$19$	−1.18647	+	2.86440i	−0.272196	+	0.657139i	0.727381	+	0.686234i	$0.240737\pi$
$20$		0			0
$21$	2.91760	−	1.20851i	0.636672	−	0.263718i
$22$		0			0
$23$	−0.860956	−	0.860956i	−0.179522	−	0.179522i	0.611626	−	0.791147i	$-0.290516\pi$
$23$	−0.860956	−	0.860956i	−0.179522	−	0.179522i	−0.791147	+	0.611626i	$0.790516\pi$
$24$		0			0
$25$	1.62241	−	1.62241i	0.324483	−	0.324483i
$26$		0			0
$27$	−4.80123	−	11.5912i	−0.923996	−	2.23072i
$28$		0			0
$29$	5.85615	+	2.42570i	1.08746	+	0.450441i	0.853120	−	0.521714i	$-0.174707\pi$
$29$	5.85615	+	2.42570i	1.08746	+	0.450441i	0.234340	+	0.972155i	$0.424707\pi$
$30$		0			0
$31$	5.52776			0.992814			0.496407	−	0.868090i	$-0.334652\pi$
$31$	5.52776			0.992814			0.496407	+	0.868090i	$0.334652\pi$
$32$		0			0
$33$	−19.6754			−3.42504
$34$		0			0
$35$	1.51965	+	0.629460i	0.256868	+	0.106398i
$36$		0			0
$37$	−4.25158	−	10.2642i	−0.698955	−	1.68743i	−0.725909	−	0.687790i	$-0.758581\pi$
$37$	−4.25158	−	10.2642i	−0.698955	−	1.68743i	0.0269541	−	0.999637i	$-0.491419\pi$
$38$		0			0
$39$	−0.439742	+	0.439742i	−0.0704152	+	0.0704152i
$40$		0			0
$41$	−2.48800	−	2.48800i	−0.388561	−	0.388561i	0.485613	−	0.874174i	$-0.338596\pi$
$41$	−2.48800	−	2.48800i	−0.388561	−	0.388561i	−0.874174	+	0.485613i	$0.838596\pi$
$42$		0			0
$43$	1.99108	−	0.824733i	0.303637	−	0.125771i	−0.225663	−	0.974206i	$-0.572455\pi$
$43$	1.99108	−	0.824733i	0.303637	−	0.125771i	0.529300	+	0.848435i	$0.322455\pi$
$44$		0			0
$45$	4.38913	−	10.5963i	0.654293	−	1.57960i
$46$		0			0
$47$		−	7.41348i		−	1.08137i	−0.841226	−	0.540684i	$-0.818166\pi$
$47$		−	7.41348i		−	1.08137i	0.841226	−	0.540684i	$-0.181834\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	4.81857	−	11.6331i	0.674735	−	1.62896i
$52$		0			0
$53$	1.28857	−	0.533743i	0.176999	−	0.0733152i	−0.292424	−	0.956289i	$-0.594462\pi$
$53$	1.28857	−	0.533743i	0.176999	−	0.0733152i	0.469423	+	0.882973i	$0.344462\pi$
$54$		0			0
$55$	−7.24647	−	7.24647i	−0.977114	−	0.977114i
$56$		0			0
$57$	6.92330	−	6.92330i	0.917014	−	0.917014i
$58$		0			0
$59$	−0.0193914	−	0.0468150i	−0.00252455	−	0.00609480i	0.922612	−	0.385729i	$-0.126050\pi$
$59$	−0.0193914	−	0.0468150i	−0.00252455	−	0.00609480i	−0.925137	+	0.379634i	$0.876050\pi$
$60$		0			0
$61$	−11.0396	−	4.57274i	−1.41347	−	0.585479i	−0.460261	−	0.887784i	$-0.652244\pi$
$61$	−11.0396	−	4.57274i	−1.41347	−	0.585479i	−0.953211	+	0.302305i	$0.902244\pi$
$62$		0			0
$63$	−6.97285			−0.878497
$64$		0			0
$65$	−0.323916			−0.0401768
$66$		0			0
$67$	−3.63165	−	1.50428i	−0.443677	−	0.183777i	0.149649	−	0.988739i	$-0.452186\pi$
$67$	−3.63165	−	1.50428i	−0.443677	−	0.183777i	−0.593326	+	0.804962i	$0.702186\pi$
$68$		0			0
$69$	1.47145	+	3.55239i	0.177142	+	0.427658i
$70$		0			0
$71$	0.181485	−	0.181485i	0.0215383	−	0.0215383i	−0.696256	−	0.717794i	$-0.745152\pi$
$71$	0.181485	−	0.181485i	0.0215383	−	0.0215383i	0.717794	+	0.696256i	$0.245152\pi$
$72$		0			0
$73$	2.49063	+	2.49063i	0.291506	+	0.291506i	0.837675	−	0.546169i	$-0.183914\pi$
$73$	2.49063	+	2.49063i	0.291506	+	0.291506i	−0.546169	+	0.837675i	$0.683914\pi$
$74$		0			0
$75$	−6.69425	+	2.77285i	−0.772985	+	0.320181i
$76$		0			0
$77$	−2.38425	+	5.75610i	−0.271711	+	0.655968i
$78$		0			0
$79$			4.65759i			0.524020i	0.965065	+	0.262010i	$0.0843854\pi$
$79$			4.65759i			0.524020i	−0.965065	+	0.262010i	$0.915615\pi$
$80$		0			0
$81$			18.7021i			2.07802i
$82$		0			0
$83$	−2.03104	+	4.90335i	−0.222935	+	0.538213i	−0.995286	−	0.0969831i	$-0.969081\pi$
$83$	−2.03104	+	4.90335i	−0.222935	+	0.538213i	0.772351	+	0.635196i	$0.219081\pi$
$84$		0			0
$85$	6.05917	−	2.50979i	0.657209	−	0.272225i
$86$		0			0
$87$	−14.1544	−	14.1544i	−1.51751	−	1.51751i
$88$		0			0
$89$	5.52373	−	5.52373i	0.585514	−	0.585514i	−0.350899	−	0.936413i	$-0.614124\pi$
$89$	5.52373	−	5.52373i	0.585514	−	0.585514i	0.936413	+	0.350899i	$0.114124\pi$
$90$		0			0
$91$	0.0753604	+	0.181936i	0.00789992	+	0.0190721i
$92$		0			0
$93$	−16.1278	−	6.68033i	−1.67237	−	0.692718i
$94$		0			0
$95$	5.09973			0.523221
$96$		0			0
$97$	14.4758			1.46980			0.734898	−	0.678178i	$-0.237230\pi$
$97$	14.4758			1.46980			0.734898	+	0.678178i	$0.237230\pi$
$98$		0			0
$99$	40.1364	+	16.6251i	4.03386	+	1.67088i
$100$		0			0
$101$	−0.393131	−	0.949102i	−0.0391180	−	0.0944392i	0.903113	−	0.429403i	$-0.141276\pi$
$101$	−0.393131	−	0.949102i	−0.0391180	−	0.0944392i	−0.942231	+	0.334964i	$0.891276\pi$
$102$		0			0
$103$	5.11797	−	5.11797i	0.504288	−	0.504288i	−0.408479	−	0.912768i	$-0.633941\pi$
$103$	5.11797	−	5.11797i	0.504288	−	0.504288i	0.912768	+	0.408479i	$0.133941\pi$
$104$		0			0
$105$	−3.67302	−	3.67302i	−0.358450	−	0.358450i
$106$		0			0
$107$	−2.14692	+	0.889284i	−0.207551	+	0.0859703i	−0.484037	−	0.875048i	$-0.660830\pi$
$107$	−2.14692	+	0.889284i	−0.207551	+	0.0859703i	0.276486	+	0.961018i	$0.410830\pi$
$108$		0			0
$109$	4.70861	−	11.3676i	0.451003	−	1.08882i	−0.520939	−	0.853594i	$-0.674418\pi$
$109$	4.70861	−	11.3676i	0.451003	−	1.08882i	0.971941	−	0.235223i	$-0.0755821\pi$
$110$		0			0
$111$			35.0849i			3.33011i
$112$		0			0
$113$			2.11397i			0.198865i	0.995044	+	0.0994327i	$0.0317028\pi$
$113$			2.11397i			0.198865i	−0.995044	+	0.0994327i	$0.968297\pi$
$114$		0			0
$115$	−0.766415	+	1.85029i	−0.0714686	+	0.172540i
$116$		0			0
$117$	1.26861	−	0.525477i	0.117283	−	0.0485804i
$118$		0			0
$119$	−2.81938	−	2.81938i	−0.258452	−	0.258452i
$120$		0			0
$121$	19.6698	−	19.6698i	1.78817	−	1.78817i
$122$		0			0
$123$	4.25222	+	10.2658i	0.383410	+	0.925633i
$124$		0			0
$125$	−11.0850	−	4.59156i	−0.991473	−	0.410682i
$126$		0			0
$127$	−3.19723			−0.283708			−0.141854	−	0.989888i	$-0.545306\pi$
$127$	−3.19723			−0.283708			−0.141854	+	0.989888i	$0.545306\pi$
$128$		0			0
$129$	−6.80587			−0.599223
$130$		0			0
$131$	9.81263	+	4.06453i	0.857334	+	0.355119i	0.767664	−	0.640852i	$-0.221419\pi$
$131$	9.81263	+	4.06453i	0.857334	+	0.355119i	0.0896695	+	0.995972i	$0.471419\pi$
$132$		0			0
$133$	−1.18647	−	2.86440i	−0.102880	−	0.248375i
$134$		0			0
$135$	−14.5924	+	14.5924i	−1.25591	+	1.25591i
$136$		0			0
$137$	3.70378	+	3.70378i	0.316436	+	0.316436i	0.847396	−	0.530961i	$-0.178169\pi$
$137$	3.70378	+	3.70378i	0.316436	+	0.316436i	−0.530961	+	0.847396i	$0.678169\pi$
$138$		0			0
$139$	16.6880	−	6.91241i	1.41546	−	0.586303i	0.461744	−	0.887013i	$-0.347224\pi$
$139$	16.6880	−	6.91241i	1.41546	−	0.586303i	0.953715	+	0.300711i	$0.0972238\pi$
$140$		0			0
$141$	−8.95925	+	21.6295i	−0.754505	+	1.82154i
$142$		0			0
$143$		−	1.22692i		−	0.102600i
$144$		0			0
$145$		−	10.4262i		−	0.865848i
$146$		0			0
$147$	−1.20851	+	2.91760i	−0.0996760	+	0.240639i
$148$		0			0
$149$	−17.6053	+	7.29236i	−1.44228	+	0.597413i	−0.960351	−	0.278795i	$-0.910065\pi$
$149$	−17.6053	+	7.29236i	−1.44228	+	0.597413i	−0.481933	+	0.876208i	$0.660065\pi$
$150$		0			0
$151$	−5.85547	−	5.85547i	−0.476512	−	0.476512i	0.427502	−	0.904014i	$-0.359394\pi$
$151$	−5.85547	−	5.85547i	−0.476512	−	0.476512i	−0.904014	+	0.427502i	$0.859394\pi$
$152$		0			0
$153$	−19.6592	+	19.6592i	−1.58935	+	1.58935i
$154$		0			0
$155$	−3.47950	−	8.40026i	−0.279480	−	0.674725i
$156$		0			0
$157$	10.2112	+	4.22962i	0.814943	+	0.337560i	0.750924	−	0.660388i	$-0.229608\pi$
$157$	10.2112	+	4.22962i	0.814943	+	0.337560i	0.0640187	+	0.997949i	$0.479608\pi$
$158$		0			0
$159$	−4.40455			−0.349304
$160$		0			0
$161$	1.21758			0.0959584
$162$		0			0
$163$	−18.8888	−	7.82400i	−1.47949	−	0.612823i	−0.510487	−	0.859886i	$-0.670535\pi$
$163$	−18.8888	−	7.82400i	−1.47949	−	0.612823i	−0.969000	+	0.247062i	$0.920535\pi$
$164$		0			0
$165$	12.3849	+	29.8997i	0.964159	+	2.32769i
$166$		0			0
$167$	13.8476	−	13.8476i	1.07156	−	1.07156i	0.0743233	−	0.997234i	$-0.476320\pi$
$167$	13.8476	−	13.8476i	1.07156	−	1.07156i	0.997234	−	0.0743233i	$-0.0236797\pi$
$168$		0			0
$169$	9.16497	+	9.16497i	0.704997	+	0.704997i
$170$		0			0
$171$	−19.9731	+	8.27311i	−1.52738	+	0.632661i
$172$		0			0
$173$	2.31711	−	5.59399i	0.176166	−	0.425303i	−0.810990	−	0.585060i	$-0.801071\pi$
$173$	2.31711	−	5.59399i	0.176166	−	0.425303i	0.987156	+	0.159757i	$0.0510710\pi$
$174$		0			0
$175$			2.29444i			0.173443i
$176$		0			0
$177$			0.160022i			0.0120280i
$178$		0			0
$179$	−7.14012	+	17.2378i	−0.533677	+	1.28841i	0.395394	+	0.918511i	$0.370608\pi$
$179$	−7.14012	+	17.2378i	−0.533677	+	1.28841i	−0.929072	+	0.369900i	$0.879392\pi$
$180$		0			0
$181$	1.10021	−	0.455724i	0.0817783	−	0.0338737i	−0.341419	−	0.939911i	$-0.610908\pi$
$181$	1.10021	−	0.455724i	0.0817783	−	0.0338737i	0.423198	+	0.906037i	$0.360908\pi$
$182$		0			0
$183$	26.6828	+	26.6828i	1.97245	+	1.97245i
$184$		0			0
$185$	−12.9218	+	12.9218i	−0.950032	+	0.950032i
$186$		0			0
$187$	9.50652	+	22.9508i	0.695186	+	1.67833i
$188$		0			0
$189$	11.5912	+	4.80123i	0.843135	+	0.349238i
$190$		0			0
$191$	−24.8929			−1.80119			−0.900594	−	0.434661i	$-0.856868\pi$
$191$	−24.8929			−1.80119			−0.900594	+	0.434661i	$0.856868\pi$
$192$		0			0
$193$	−0.323836			−0.0233102			−0.0116551	−	0.999932i	$-0.503710\pi$
$193$	−0.323836			−0.0233102			−0.0116551	+	0.999932i	$0.503710\pi$
$194$		0			0
$195$	0.945056	+	0.391455i	0.0676768	+	0.0280327i
$196$		0			0
$197$	−0.677417	−	1.63543i	−0.0482639	−	0.116519i	0.897909	−	0.440182i	$-0.145086\pi$
$197$	−0.677417	−	1.63543i	−0.0482639	−	0.116519i	−0.946173	+	0.323662i	$0.895086\pi$
$198$		0			0
$199$	8.39216	−	8.39216i	0.594904	−	0.594904i	−0.344048	−	0.938952i	$-0.611798\pi$
$199$	8.39216	−	8.39216i	0.594904	−	0.594904i	0.938952	+	0.344048i	$0.111798\pi$
$200$		0			0
$201$	8.77776	+	8.77776i	0.619136	+	0.619136i
$202$		0			0
$203$	−5.85615	+	2.42570i	−0.411021	+	0.170251i
$204$		0			0
$205$	−2.21480	+	5.34700i	−0.154688	+	0.373451i
$206$		0			0
$207$		−	8.48997i		−	0.590094i
$208$		0			0
$209$			19.3166i			1.33616i
$210$		0			0
$211$	5.70616	−	13.7759i	0.392828	−	0.948371i	−0.596493	−	0.802618i	$-0.703440\pi$
$211$	5.70616	−	13.7759i	0.392828	−	0.948371i	0.989321	−	0.145753i	$-0.0465603\pi$
$212$		0			0
$213$	−0.748827	+	0.310174i	−0.0513088	+	0.0212528i
$214$		0			0
$215$	−2.50661	−	2.50661i	−0.170950	−	0.170950i
$216$		0			0
$217$	−3.90871	+	3.90871i	−0.265341	+	0.265341i
$218$		0			0
$219$	−4.25670	−	10.2766i	−0.287641	−	0.694427i
$220$		0			0
$221$	0.725418	+	0.300478i	0.0487969	+	0.0202123i
$222$		0			0
$223$	0.469193			0.0314195			0.0157097	−	0.999877i	$-0.494999\pi$
$223$	0.469193			0.0314195			0.0157097	+	0.999877i	$0.494999\pi$
$224$		0			0
$225$	15.9988			1.06659
$226$		0			0
$227$	16.8893	+	6.99577i	1.12098	+	0.464326i	0.864706	−	0.502278i	$-0.167505\pi$
$227$	16.8893	+	6.99577i	1.12098	+	0.464326i	0.256275	+	0.966604i	$0.417505\pi$
$228$		0			0
$229$	4.60075	+	11.1072i	0.304026	+	0.733984i	0.999875	+	0.0157961i	$0.00502825\pi$
$229$	4.60075	+	11.1072i	0.304026	+	0.733984i	−0.695849	+	0.718188i	$0.744972\pi$
$230$		0			0
$231$	13.9126	−	13.9126i	0.915380	−	0.915380i
$232$		0			0
$233$	6.25804	+	6.25804i	0.409978	+	0.409978i	0.881731	−	0.471753i	$-0.156379\pi$
$233$	6.25804	+	6.25804i	0.409978	+	0.409978i	−0.471753	+	0.881731i	$0.656379\pi$
$234$		0			0
$235$	−11.2659	+	4.66649i	−0.734906	+	0.304408i
$236$		0			0
$237$	5.62874	−	13.5890i	0.365626	−	0.882699i
$238$		0			0
$239$		−	4.46457i		−	0.288789i	−0.989520	−	0.144395i	$-0.953877\pi$
$239$		−	4.46457i		−	0.288789i	0.989520	−	0.144395i	$-0.0461235\pi$
$240$		0			0
$241$		−	20.7152i		−	1.33438i	−0.744885	−	0.667192i	$-0.767496\pi$
$241$		−	20.7152i		−	1.33438i	0.744885	−	0.667192i	$-0.232504\pi$
$242$		0			0
$243$	8.19800	−	19.7917i	0.525902	−	1.26964i
$244$		0			0
$245$	−1.51965	+	0.629460i	−0.0970870	+	0.0402147i
$246$		0			0
$247$	0.431725	+	0.431725i	0.0274700	+	0.0274700i
$248$		0			0
$249$	11.8515	−	11.8515i	0.751057	−	0.751057i
$250$		0			0
$251$	−5.88475	−	14.2071i	−0.371442	−	0.896741i	−0.993507	−	0.113775i	$-0.963706\pi$
$251$	−5.88475	−	14.2071i	−0.371442	−	0.896741i	0.622064	−	0.782966i	$-0.286294\pi$
$252$		0			0
$253$	−7.00848	−	2.90301i	−0.440619	−	0.182511i
$254$		0			0
$255$	−20.7113			−1.29699
$256$		0			0
$257$	−16.7204			−1.04299			−0.521495	−	0.853254i	$-0.674626\pi$
$257$	−16.7204			−1.04299			−0.521495	+	0.853254i	$0.674626\pi$
$258$		0			0
$259$	10.2642	+	4.25158i	0.637788	+	0.264180i
$260$		0			0
$261$	16.9140	+	40.8341i	1.04695	+	2.52757i
$262$		0			0
$263$	−1.06306	+	1.06306i	−0.0655513	+	0.0655513i	−0.739122	−	0.673571i	$-0.764760\pi$
$263$	−1.06306	+	1.06306i	−0.0655513	+	0.0655513i	0.673571	+	0.739122i	$0.264760\pi$
$264$		0			0
$265$	−1.62221	−	1.62221i	−0.0996513	−	0.0996513i
$266$		0			0
$267$	−22.7915	+	9.44054i	−1.39482	+	0.577752i
$268$		0			0
$269$	0.585066	−	1.41247i	0.0356721	−	0.0861200i	−0.905039	−	0.425328i	$-0.860159\pi$
$269$	0.585066	−	1.41247i	0.0356721	−	0.0861200i	0.940712	+	0.339208i	$0.110159\pi$
$270$		0			0
$271$		−	16.2629i		−	0.987900i	−0.869490	−	0.493950i	$-0.835553\pi$
$271$		−	16.2629i		−	0.987900i	0.869490	−	0.493950i	$-0.164447\pi$
$272$		0			0
$273$		−	0.621890i		−	0.0376385i
$274$		0			0
$275$	5.47053	−	13.2070i	0.329885	−	0.796413i
$276$		0			0
$277$	15.9466	−	6.60532i	0.958141	−	0.396875i	0.151856	−	0.988403i	$-0.451475\pi$
$277$	15.9466	−	6.60532i	0.958141	−	0.396875i	0.806285	+	0.591527i	$0.201475\pi$
$278$		0			0
$279$	27.2549	+	27.2549i	1.63171	+	1.63171i
$280$		0			0
$281$	−3.53270	+	3.53270i	−0.210743	+	0.210743i	−0.804583	−	0.593840i	$-0.797611\pi$
$281$	−3.53270	+	3.53270i	−0.210743	+	0.210743i	0.593840	+	0.804583i	$0.297611\pi$
$282$		0			0
$283$	−8.09216	−	19.5362i	−0.481029	−	1.16131i	−0.959121	−	0.282997i	$-0.908671\pi$
$283$	−8.09216	−	19.5362i	−0.481029	−	1.16131i	0.478092	−	0.878310i	$-0.341329\pi$
$284$		0			0
$285$	−14.8790	−	6.16306i	−0.881353	−	0.365068i
$286$		0			0
$287$	3.51857			0.207695
$288$		0			0
$289$	1.10215			0.0648323
$290$		0			0
$291$	−42.2346	−	17.4941i	−2.47583	−	1.02552i
$292$		0			0
$293$	−10.6347	−	25.6745i	−0.621286	−	1.49992i	−0.850194	−	0.526470i	$-0.823515\pi$
$293$	−10.6347	−	25.6745i	−0.621286	−	1.49992i	0.228907	−	0.973448i	$-0.426485\pi$
$294$		0			0
$295$	−0.0589364	+	0.0589364i	−0.00343141	+	0.00343141i
$296$		0			0
$297$	−55.2726	−	55.2726i	−3.20724	−	3.20724i
$298$		0			0
$299$	−0.221521	+	0.0917570i	−0.0128109	+	0.00530644i
$300$		0			0
$301$	−0.824733	+	1.99108i	−0.0475368	+	0.114764i
$302$		0			0
$303$			3.24420i			0.186374i
$304$		0			0
$305$			19.6547i			1.12542i
$306$		0			0
$307$	5.57127	−	13.4502i	0.317969	−	0.767646i	−0.681392	−	0.731918i	$-0.738625\pi$
$307$	5.57127	−	13.4502i	0.317969	−	0.767646i	0.999362	−	0.0357274i	$-0.0113748\pi$
$308$		0			0
$309$	−21.1173	+	8.74706i	−1.20132	+	0.497603i
$310$		0			0
$311$	−4.27224	−	4.27224i	−0.242257	−	0.242257i	0.575527	−	0.817783i	$-0.304797\pi$
$311$	−4.27224	−	4.27224i	−0.242257	−	0.242257i	−0.817783	+	0.575527i	$0.804797\pi$
$312$		0			0
$313$	−11.3681	+	11.3681i	−0.642563	+	0.642563i	−0.951185	−	0.308622i	$-0.900132\pi$
$313$	−11.3681	+	11.3681i	−0.642563	+	0.642563i	0.308622	+	0.951185i	$0.400132\pi$
$314$		0			0
$315$	4.38913	+	10.5963i	0.247300	+	0.597034i
$316$		0			0
$317$	−8.38560	−	3.47343i	−0.470982	−	0.195087i	0.134552	−	0.990907i	$-0.457040\pi$
$317$	−8.38560	−	3.47343i	−0.470982	−	0.195087i	−0.605534	+	0.795819i	$0.707040\pi$
$318$		0			0
$319$	39.4921			2.21113
$320$		0			0
$321$	7.33856			0.409598
$322$		0			0
$323$	−11.4210	−	4.73072i	−0.635480	−	0.263224i
$324$		0			0
$325$	−0.172910	−	0.417442i	−0.00959132	−	0.0231555i
$326$		0			0
$327$	−27.4756	+	27.4756i	−1.51941	+	1.51941i
$328$		0			0
$329$	5.24212	+	5.24212i	0.289008	+	0.289008i
$330$		0			0
$331$	15.5741	−	6.45099i	0.856028	−	0.354579i	0.0888754	−	0.996043i	$-0.471673\pi$
$331$	15.5741	−	6.45099i	0.856028	−	0.354579i	0.767153	+	0.641464i	$0.221673\pi$
$332$		0			0
$333$	29.6456	−	71.5709i	1.62457	−	3.92206i
$334$		0			0
$335$			6.46573i			0.353261i
$336$		0			0
$337$			18.7902i			1.02357i	0.859114	+	0.511784i	$0.171015\pi$
$337$			18.7902i			1.02357i	−0.859114	+	0.511784i	$0.828985\pi$
$338$		0			0
$339$	2.55475	−	6.16770i	0.138755	−	0.334984i
$340$		0			0
$341$	31.8183	−	13.1796i	1.72306	−	0.713714i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		0			0
$345$	4.47218	−	4.47218i	0.240774	−	0.240774i
$346$		0			0
$347$	8.53942	+	20.6160i	0.458420	+	1.10672i	0.969037	+	0.246916i	$0.0794171\pi$
$347$	8.53942	+	20.6160i	0.458420	+	1.10672i	−0.510617	+	0.859808i	$0.670583\pi$
$348$		0			0
$349$	2.92644	+	1.21217i	0.156649	+	0.0648861i	0.459630	−	0.888110i	$-0.347982\pi$
$349$	2.92644	+	1.21217i	0.156649	+	0.0648861i	−0.302981	+	0.952997i	$0.597982\pi$
$350$		0			0
$351$	−2.47068			−0.131875
$352$		0			0
$353$	−0.929161			−0.0494542			−0.0247271	−	0.999694i	$-0.507872\pi$
$353$	−0.929161			−0.0494542			−0.0247271	+	0.999694i	$0.507872\pi$
$354$		0			0
$355$	−0.390032	−	0.161557i	−0.0207008	−	0.00857454i
$356$		0			0
$357$	4.81857	+	11.6331i	0.255026	+	0.615687i
$358$		0			0
$359$	17.9614	−	17.9614i	0.947968	−	0.947968i	−0.0507435	−	0.998712i	$-0.516159\pi$
$359$	17.9614	−	17.9614i	0.947968	−	0.947968i	0.998712	+	0.0507435i	$0.0161591\pi$
$360$		0			0
$361$	6.63795	+	6.63795i	0.349366	+	0.349366i
$362$		0			0
$363$	−81.1597	+	33.6175i	−4.25978	+	1.76446i
$364$		0			0
$365$	2.21713	−	5.35263i	0.116050	−	0.280170i
$366$		0			0
$367$			10.8302i			0.565330i	0.959219	+	0.282665i	$0.0912184\pi$
$367$			10.8302i			0.565330i	−0.959219	+	0.282665i	$0.908782\pi$
$368$		0			0
$369$		−	24.5345i		−	1.27721i
$370$		0			0
$371$	−0.533743	+	1.28857i	−0.0277105	+	0.0668992i
$372$		0			0
$373$	−7.44891	+	3.08544i	−0.385690	+	0.159758i	−0.567099	−	0.823650i	$-0.691934\pi$
$373$	−7.44891	+	3.08544i	−0.385690	+	0.159758i	0.181409	+	0.983408i	$0.441934\pi$
$374$		0			0
$375$	26.7926	+	26.7926i	1.38357	+	1.38357i
$376$		0			0
$377$	0.882644	−	0.882644i	0.0454585	−	0.0454585i
$378$		0			0
$379$	3.80670	+	9.19018i	0.195537	+	0.472068i	0.990988	−	0.133950i	$-0.0427661\pi$
$379$	3.80670	+	9.19018i	0.195537	+	0.472068i	−0.795451	+	0.606018i	$0.792766\pi$
$380$		0			0
$381$	9.32823	+	3.86388i	0.477900	+	0.197953i
$382$		0			0
$383$	11.7333			0.599542			0.299771	−	0.954011i	$-0.403090\pi$
$383$	11.7333			0.599542			0.299771	+	0.954011i	$0.403090\pi$
$384$		0			0
$385$	10.2481			0.522289
$386$		0			0
$387$	13.8835	+	5.75074i	0.705739	+	0.292327i
$388$		0			0
$389$	13.5884	+	32.8053i	0.688960	+	1.66330i	0.746866	+	0.664974i	$0.231557\pi$
$389$	13.5884	+	32.8053i	0.688960	+	1.66330i	−0.0579065	+	0.998322i	$0.518443\pi$
$390$		0			0
$391$	3.43281	−	3.43281i	0.173605	−	0.173605i
$392$		0			0
$393$	−23.7173	−	23.7173i	−1.19638	−	1.19638i
$394$		0			0
$395$	7.07792	−	2.93177i	0.356129	−	0.147513i
$396$		0			0
$397$	−15.0713	+	36.3853i	−0.756406	+	1.82613i	−0.237244	+	0.971450i	$0.576244\pi$
$397$	−15.0713	+	36.3853i	−0.756406	+	1.82613i	−0.519162	+	0.854676i	$0.673756\pi$
$398$		0			0
$399$			9.79103i			0.490165i
$400$		0			0
$401$		−	20.5271i		−	1.02507i	−0.858665	−	0.512537i	$-0.828706\pi$
$401$		−	20.5271i		−	1.02507i	0.858665	−	0.512537i	$-0.171294\pi$
$402$		0			0
$403$	0.416574	−	1.00570i	0.0207510	−	0.0500974i
$404$		0			0
$405$	28.4207	−	11.7723i	1.41224	−	0.584968i
$406$		0			0
$407$	−48.9450	−	48.9450i	−2.42611	−	2.42611i
$408$		0			0
$409$	11.0718	−	11.0718i	0.547467	−	0.547467i	−0.378240	−	0.925707i	$-0.623471\pi$
$409$	11.0718	−	11.0718i	0.547467	−	0.547467i	0.925707	+	0.378240i	$0.123471\pi$
$410$		0			0
$411$	−6.33009	−	15.2822i	−0.312241	−	0.753815i
$412$		0			0
$413$	0.0468150	+	0.0193914i	0.00230362	+	0.000954190i
$414$		0			0
$415$	8.72984			0.428531
$416$		0			0
$417$	−57.0426			−2.79339
$418$		0			0
$419$	8.28075	+	3.43000i	0.404541	+	0.167566i	0.575670	−	0.817682i	$-0.304741\pi$
$419$	8.28075	+	3.43000i	0.404541	+	0.167566i	−0.171129	+	0.985249i	$0.554741\pi$
$420$		0			0
$421$	−2.04223	−	4.93038i	−0.0995323	−	0.240292i	0.866268	−	0.499580i	$-0.166512\pi$
$421$	−2.04223	−	4.93038i	−0.0995323	−	0.240292i	−0.965800	+	0.259288i	$0.916512\pi$
$422$		0			0
$423$	36.5526	−	36.5526i	1.77725	−	1.77725i
$424$		0			0
$425$	6.46891	+	6.46891i	0.313788	+	0.313788i
$426$		0			0
$427$	11.0396	−	4.57274i	0.534242	−	0.221290i
$428$		0			0
$429$	−1.48274	+	3.57966i	−0.0715875	+	0.172828i
$430$		0			0
$431$		−	5.26383i		−	0.253550i	−0.991932	−	0.126775i	$-0.959537\pi$
$431$		−	5.26383i		−	0.253550i	0.991932	−	0.126775i	$-0.0404625\pi$
$432$		0			0
$433$		−	27.8109i		−	1.33651i	−0.743933	−	0.668254i	$-0.767042\pi$
$433$		−	27.8109i		−	1.33651i	0.743933	−	0.668254i	$-0.232958\pi$
$434$		0			0
$435$	−12.6001	+	30.4194i	−0.604130	+	1.45850i
$436$		0			0
$437$	3.48763	−	1.44462i	0.166836	−	0.0691056i
$438$		0			0
$439$	8.37999	+	8.37999i	0.399955	+	0.399955i	0.878217	−	0.478262i	$-0.158733\pi$
$439$	8.37999	+	8.37999i	0.399955	+	0.399955i	−0.478262	+	0.878217i	$0.658733\pi$
$440$		0			0
$441$	4.93055	−	4.93055i	0.234788	−	0.234788i
$442$		0			0
$443$	9.51351	+	22.9676i	0.452000	+	1.09123i	0.971560	+	0.236792i	$0.0760958\pi$
$443$	9.51351	+	22.9676i	0.452000	+	1.09123i	−0.519560	+	0.854434i	$0.673904\pi$
$444$		0			0
$445$	−11.8711	−	4.91718i	−0.562745	−	0.233097i
$446$		0			0
$447$	60.1780			2.84632
$448$		0			0
$449$	−0.323826			−0.0152823			−0.00764115	−	0.999971i	$-0.502432\pi$
$449$	−0.323826			−0.0152823			−0.00764115	+	0.999971i	$0.502432\pi$
$450$		0			0
$451$	−20.2532	−	8.38916i	−0.953687	−	0.395030i
$452$		0			0
$453$	10.0075	+	24.1603i	0.470194	+	1.13515i
$454$		0			0
$455$	0.229043	−	0.229043i	0.0107377	−	0.0107377i
$456$		0			0
$457$	−24.7992	−	24.7992i	−1.16006	−	1.16006i	−0.984462	−	0.175595i	$-0.943815\pi$
$457$	−24.7992	−	24.7992i	−1.16006	−	1.16006i	−0.175595	−	0.984462i	$-0.556185\pi$
$458$		0			0
$459$	46.2165	−	19.1435i	2.15720	−	0.893542i
$460$		0			0
$461$	−15.3222	+	36.9910i	−0.713624	+	1.72284i	−0.0228829	+	0.999738i	$0.507284\pi$
$461$	−15.3222	+	36.9910i	−0.713624	+	1.72284i	−0.690741	+	0.723102i	$0.742716\pi$
$462$		0			0
$463$		−	5.19844i		−	0.241592i	−0.992677	−	0.120796i	$-0.961455\pi$
$463$		−	5.19844i		−	0.241592i	0.992677	−	0.120796i	$-0.0385447\pi$
$464$		0			0
$465$			28.7136i			1.33156i
$466$		0			0
$467$	−8.05999	+	19.4585i	−0.372972	+	0.900433i	0.620272	+	0.784387i	$0.287022\pi$
$467$	−8.05999	+	19.4585i	−0.372972	+	0.900433i	−0.993244	+	0.116047i	$0.962978\pi$
$468$		0			0
$469$	3.63165	−	1.50428i	0.167694	−	0.0694612i
$470$		0			0
$471$	−24.6806	−	24.6806i	−1.13722	−	1.13722i
$472$		0			0
$473$	9.49449	−	9.49449i	0.436557	−	0.436557i
$474$		0			0
$475$	2.72229	+	6.57220i	0.124907	+	0.301553i
$476$		0			0
$477$	8.98500	+	3.72171i	0.411395	+	0.170405i
$478$		0			0
$479$	−38.5055			−1.75936			−0.879681	−	0.475565i	$-0.842244\pi$
$479$	−38.5055			−1.75936			−0.879681	+	0.475565i	$0.842244\pi$
$480$		0			0
$481$	−2.18783			−0.0997566
$482$		0			0
$483$	−3.55239	−	1.47145i	−0.161639	−	0.0669532i
$484$		0			0
$485$	−9.11194	−	21.9982i	−0.413752	−	0.998886i
$486$		0			0
$487$	−19.8099	+	19.8099i	−0.897674	+	0.897674i	−0.995230	−	0.0975559i	$-0.968898\pi$
$487$	−19.8099	+	19.8099i	−0.897674	+	0.897674i	0.0975559	+	0.995230i	$0.468898\pi$
$488$		0			0
$489$	45.6546	+	45.6546i	2.06457	+	2.06457i
$490$		0			0
$491$	4.05018	−	1.67764i	0.182782	−	0.0757108i	−0.289416	−	0.957204i	$-0.593461\pi$
$491$	4.05018	−	1.67764i	0.182782	−	0.0757108i	0.472197	+	0.881493i	$0.343461\pi$
$492$		0			0
$493$	−9.67177	+	23.3497i	−0.435595	+	1.05162i
$494$		0			0
$495$		−	71.4582i		−	3.21181i
$496$		0			0
$497$			0.256659i			0.0115127i
$498$		0			0
$499$	−8.21812	+	19.8403i	−0.367893	+	0.888173i	0.626202	+	0.779661i	$0.284609\pi$
$499$	−8.21812	+	19.8403i	−0.367893	+	0.888173i	−0.994095	+	0.108512i	$0.965391\pi$
$500$		0			0
$501$	−57.1365	+	23.6667i	−2.55267	+	1.05735i
$502$		0			0
$503$	23.7800	+	23.7800i	1.06030	+	1.06030i	0.998062	+	0.0622340i	$0.0198225\pi$
$503$	23.7800	+	23.7800i	1.06030	+	1.06030i	0.0622340	+	0.998062i	$0.480177\pi$
$504$		0			0
$505$	−1.19484	+	1.19484i	−0.0531699	+	0.0531699i
$506$		0			0
$507$	−15.6637	−	37.8156i	−0.695651	−	1.67945i
$508$		0			0
$509$	7.80811	+	3.23423i	0.346089	+	0.143355i	0.548955	−	0.835852i	$-0.315026\pi$
$509$	7.80811	+	3.23423i	0.346089	+	0.143355i	−0.202867	+	0.979206i	$0.565026\pi$
$510$		0			0
$511$	−3.52228			−0.155816
$512$		0			0
$513$	38.8983			1.71740
$514$		0			0
$515$	−10.9991	−	4.55597i	−0.484677	−	0.200760i
$516$		0			0
$517$	−17.6756	−	42.6727i	−0.777373	−	1.87674i
$518$		0			0
$519$	−13.5208	+	13.5208i	−0.593495	+	0.593495i
$520$		0			0
$521$	14.9711	+	14.9711i	0.655895	+	0.655895i	0.954406	−	0.298511i	$-0.0964899\pi$
$521$	14.9711	+	14.9711i	0.655895	+	0.655895i	−0.298511	+	0.954406i	$0.596490\pi$
$522$		0			0
$523$	22.9292	−	9.49757i	1.00262	−	0.415300i	0.179864	−	0.983691i	$-0.442434\pi$
$523$	22.9292	−	9.49757i	1.00262	−	0.415300i	0.822758	+	0.568392i	$0.192434\pi$
$524$		0			0
$525$	2.77285	−	6.69425i	0.121017	−	0.292161i
$526$		0			0
$527$			22.0403i			0.960092i
$528$		0			0
$529$		−	21.5175i		−	0.935544i
$530$		0			0
$531$	0.135214	−	0.326434i	0.00586777	−	0.0141660i
$532$		0			0
$533$	−0.640155	+	0.265161i	−0.0277282	+	0.0114854i
$534$		0			0
$535$	2.70280	+	2.70280i	0.116852	+	0.116852i
$536$		0			0
$537$	41.6639	−	41.6639i	1.79793	−	1.79793i
$538$		0			0
$539$	−2.38425	−	5.75610i	−0.102697	−	0.247933i
$540$		0			0
$541$	12.9919	+	5.38144i	0.558567	+	0.231366i	0.644063	−	0.764973i	$-0.277247\pi$
$541$	12.9919	+	5.38144i	0.558567	+	0.231366i	−0.0854960	+	0.996339i	$0.527247\pi$
$542$		0			0
$543$	−3.76073			−0.161388
$544$		0			0
$545$	−20.2386			−0.866928
$546$		0			0
$547$	−4.33631	−	1.79616i	−0.185407	−	0.0767983i	0.288048	−	0.957616i	$-0.406994\pi$
$547$	−4.33631	−	1.79616i	−0.185407	−	0.0767983i	−0.473456	+	0.880818i	$0.656994\pi$
$548$		0			0
$549$	−31.8850	−	76.9773i	−1.36082	−	3.28531i
$550$		0			0
$551$	−13.8963	+	13.8963i	−0.592004	+	0.592004i
$552$		0			0
$553$	−3.29342	−	3.29342i	−0.140050	−	0.140050i
$554$		0			0
$555$	53.3168	−	22.0845i	2.26317	−	0.937437i
$556$		0			0
$557$	−17.1893	+	41.4987i	−0.728334	+	1.75835i	−0.0802647	+	0.996774i	$0.525577\pi$
$557$	−17.1893	+	41.4987i	−0.728334	+	1.75835i	−0.648070	+	0.761581i	$0.724423\pi$
$558$		0			0
$559$		−	0.424402i		−	0.0179503i
$560$		0			0
$561$		−	78.4498i		−	3.31215i
$562$		0			0
$563$	−16.6307	+	40.1500i	−0.700900	+	1.69212i	0.0206760	+	0.999786i	$0.493418\pi$
$563$	−16.6307	+	40.1500i	−0.700900	+	1.69212i	−0.721576	+	0.692335i	$0.756582\pi$
$564$		0			0
$565$	3.21249	−	1.33066i	0.135151	−	0.0559812i
$566$		0			0
$567$	−13.2244	−	13.2244i	−0.555373	−	0.555373i
$568$		0			0
$569$	−10.1679	+	10.1679i	−0.426259	+	0.426259i	−0.887352	−	0.461093i	$-0.847458\pi$
$569$	−10.1679	+	10.1679i	−0.426259	+	0.426259i	0.461093	+	0.887352i	$0.347458\pi$
$570$		0			0
$571$	9.05090	+	21.8508i	0.378769	+	0.914428i	0.992197	+	0.124678i	$0.0397898\pi$
$571$	9.05090	+	21.8508i	0.378769	+	0.914428i	−0.613429	+	0.789750i	$0.710210\pi$
$572$		0			0
$573$	72.6275	+	30.0833i	3.03406	+	1.25675i
$574$		0			0
$575$	−2.79365			−0.116503
$576$		0			0
$577$	23.0941			0.961418			0.480709	−	0.876880i	$-0.340379\pi$
$577$	23.0941			0.961418			0.480709	+	0.876880i	$0.340379\pi$
$578$		0			0
$579$	0.944823	+	0.391359i	0.0392655	+	0.0162643i
$580$		0			0
$581$	−2.03104	−	4.90335i	−0.0842616	−	0.203425i
$582$		0			0
$583$	6.14455	−	6.14455i	0.254481	−	0.254481i
$584$		0			0
$585$	−1.59708	−	1.59708i	−0.0660313	−	0.0660313i
$586$		0			0
$587$	19.9230	−	8.25238i	0.822310	−	0.340612i	0.0684564	−	0.997654i	$-0.478193\pi$
$587$	19.9230	−	8.25238i	0.822310	−	0.340612i	0.753854	+	0.657042i	$0.228193\pi$
$588$		0			0
$589$	−6.55854	+	15.8337i	−0.270240	+	0.652417i
$590$		0			0
$591$			5.59018i			0.229949i
$592$		0			0
$593$		−	6.86424i		−	0.281880i	−0.990018	−	0.140940i	$-0.954987\pi$
$593$		−	6.86424i		−	0.281880i	0.990018	−	0.140940i	$-0.0450125\pi$
$594$		0			0
$595$	−2.50979	+	6.05917i	−0.102891	+	0.248402i
$596$		0			0
$597$	−34.6269	+	14.3429i	−1.41719	+	0.587017i
$598$		0			0
$599$	−1.28148	−	1.28148i	−0.0523600	−	0.0523600i	0.680442	−	0.732802i	$-0.261788\pi$
$599$	−1.28148	−	1.28148i	−0.0523600	−	0.0523600i	−0.732802	+	0.680442i	$0.761788\pi$
$600$		0			0
$601$	−7.61024	+	7.61024i	−0.310428	+	0.310428i	−0.845075	−	0.534647i	$-0.820445\pi$
$601$	−7.61024	+	7.61024i	−0.310428	+	0.310428i	0.534647	+	0.845075i	$0.320445\pi$
$602$		0			0
$603$	−10.4891	−	25.3230i	−0.427150	−	1.03123i
$604$		0			0
$605$	−42.2726	−	17.5099i	−1.71863	−	0.711879i
$606$		0			0
$607$	22.7630			0.923922			0.461961	−	0.886900i	$-0.347146\pi$
$607$	22.7630			0.923922			0.461961	+	0.886900i	$0.347146\pi$
$608$		0			0
$609$	20.0174			0.811144
$610$		0			0
$611$	−1.34878	−	0.558683i	−0.0545658	−	0.0226019i
$612$		0			0
$613$	−7.16049	−	17.2869i	−0.289209	−	0.698213i	0.710777	−	0.703417i	$-0.248343\pi$
$613$	−7.16049	−	17.2869i	−0.289209	−	0.698213i	−0.999986	+	0.00520419i	$0.998343\pi$
$614$		0			0
$615$	12.9238	−	12.9238i	0.521137	−	0.521137i
$616$		0			0
$617$	23.7607	+	23.7607i	0.956570	+	0.956570i	0.999095	−	0.0425258i	$-0.0135405\pi$
$617$	23.7607	+	23.7607i	0.956570	+	0.956570i	−0.0425258	+	0.999095i	$0.513540\pi$
$618$		0			0
$619$	−23.1416	+	9.58555i	−0.930138	+	0.385276i	−0.795731	−	0.605650i	$-0.792913\pi$
$619$	−23.1416	+	9.58555i	−0.930138	+	0.385276i	−0.134407	+	0.990926i	$0.542913\pi$
$620$		0			0
$621$	−5.84585	+	14.1131i	−0.234586	+	0.566341i
$622$		0			0
$623$			7.81174i			0.312971i
$624$		0			0
$625$			8.26334i			0.330534i
$626$		0			0
$627$	23.3443	−	56.3581i	0.932282	−	2.25073i
$628$		0			0
$629$	40.9256	−	16.9519i	1.63181	−	0.675918i
$630$		0			0
$631$	−9.75860	−	9.75860i	−0.388484	−	0.388484i	0.485663	−	0.874146i	$-0.338578\pi$
$631$	−9.75860	−	9.75860i	−0.388484	−	0.388484i	−0.874146	+	0.485663i	$0.838578\pi$
$632$		0			0
$633$	−33.2965	+	33.2965i	−1.32342	+	1.32342i
$634$		0			0
$635$	2.01253	+	4.85868i	0.0798648	+	0.192811i
$636$		0			0
$637$	−0.181936	−	0.0753604i	−0.00720857	−	0.00298589i
$638$		0			0
$639$	1.78965			0.0707973
$640$		0			0
$641$	−16.9429			−0.669206			−0.334603	−	0.942359i	$-0.608602\pi$
$641$	−16.9429			−0.669206			−0.334603	+	0.942359i	$0.608602\pi$
$642$		0			0
$643$	−1.94579	−	0.805973i	−0.0767345	−	0.0317845i	0.343986	−	0.938975i	$-0.388223\pi$
$643$	−1.94579	−	0.805973i	−0.0767345	−	0.0317845i	−0.420721	+	0.907190i	$0.638223\pi$
$644$		0			0
$645$	4.28402	+	10.3425i	0.168683	+	0.407237i
$646$		0			0
$647$	−17.8656	+	17.8656i	−0.702368	+	0.702368i	−0.964918	−	0.262550i	$-0.915436\pi$
$647$	−17.8656	+	17.8656i	−0.702368	+	0.702368i	0.262550	+	0.964918i	$0.415436\pi$
$648$		0			0
$649$	−0.223238	−	0.223238i	−0.00876285	−	0.00876285i
$650$		0			0
$651$	16.1278	−	6.68033i	0.632097	−	0.261823i
$652$		0			0
$653$	17.2420	−	41.6258i	0.674730	−	1.62894i	−0.0987430	−	0.995113i	$-0.531482\pi$
$653$	17.2420	−	41.6258i	0.674730	−	1.62894i	0.773473	−	0.633829i	$-0.218518\pi$
$654$		0			0
$655$		−	17.4702i		−	0.682619i
$656$		0			0
$657$			24.5603i			0.958189i
$658$		0			0
$659$	6.11881	−	14.7721i	0.238355	−	0.575440i	−0.758758	−	0.651373i	$-0.774193\pi$
$659$	6.11881	−	14.7721i	0.238355	−	0.575440i	0.997113	+	0.0759327i	$0.0241934\pi$
$660$		0			0
$661$	−16.1894	+	6.70585i	−0.629693	+	0.260828i	−0.674623	−	0.738163i	$-0.735694\pi$
$661$	−16.1894	+	6.70585i	−0.629693	+	0.260828i	0.0449295	+	0.998990i	$0.485694\pi$
$662$		0			0
$663$	−1.75335	−	1.75335i	−0.0680943	−	0.0680943i
$664$		0			0
$665$	−3.60605	+	3.60605i	−0.139837	+	0.139837i
$666$		0			0
$667$	−2.95347	−	7.13031i	−0.114359	−	0.276087i
$668$		0			0
$669$	−1.36892	−	0.567023i	−0.0529253	−	0.0219224i
$670$		0			0
$671$	−74.4474			−2.87401
$672$		0			0
$673$	2.01887			0.0778215			0.0389108	−	0.999243i	$-0.487611\pi$
$673$	2.01887			0.0778215			0.0389108	+	0.999243i	$0.487611\pi$
$674$		0			0
$675$	−26.5953	−	11.0161i	−1.02365	−	0.424011i
$676$		0			0
$677$	−5.13139	−	12.3883i	−0.197215	−	0.476120i	0.794074	−	0.607821i	$-0.207956\pi$
$677$	−5.13139	−	12.3883i	−0.197215	−	0.476120i	−0.991289	+	0.131701i	$0.957956\pi$
$678$		0			0
$679$	−10.2359	+	10.2359i	−0.392819	+	0.392819i
$680$		0			0
$681$	−40.8217	−	40.8217i	−1.56429	−	1.56429i
$682$		0			0
$683$	19.3002	−	7.99442i	0.738503	−	0.305898i	0.0184619	−	0.999830i	$-0.494123\pi$
$683$	19.3002	−	7.99442i	0.738503	−	0.305898i	0.720041	+	0.693932i	$0.244123\pi$
$684$		0			0
$685$	3.29708	−	7.95985i	0.125975	−	0.304130i
$686$		0			0
$687$		−	37.9663i		−	1.44851i
$688$		0			0
$689$		−	0.274660i		−	0.0104637i
$690$		0			0
$691$	−7.63037	+	18.4213i	−0.290273	+	0.700781i	−0.999993	−	0.00370270i	$-0.998821\pi$
$691$	−7.63037	+	18.4213i	−0.290273	+	0.700781i	0.709720	+	0.704484i	$0.248821\pi$
$692$		0			0
$693$	−40.1364	+	16.6251i	−1.52466	+	0.631534i
$694$		0			0
$695$	−21.0089	−	21.0089i	−0.796913	−	0.796913i
$696$		0			0
$697$	9.92020	−	9.92020i	0.375754	−	0.375754i
$698$		0			0
$699$	−10.6955	−	25.8213i	−0.404543	−	0.976652i
$700$		0			0
$701$	20.1097	+	8.32971i	0.759533	+	0.314609i	0.728625	−	0.684913i	$-0.240160\pi$
$701$	20.1097	+	8.32971i	0.759533	+	0.314609i	0.0309085	+	0.999522i	$0.490160\pi$
$702$		0			0
$703$	34.4452			1.29913
$704$		0			0
$705$	38.5088			1.45033
$706$		0			0
$707$	0.949102	+	0.393131i	0.0356947	+	0.0147852i
$708$		0			0
$709$	6.82463	+	16.4761i	0.256304	+	0.618773i	0.998688	−	0.0512014i	$-0.0163050\pi$
$709$	6.82463	+	16.4761i	0.256304	+	0.618773i	−0.742384	+	0.669974i	$0.766305\pi$
$710$		0			0
$711$	−22.9645	+	22.9645i	−0.861236	+	0.861236i
$712$		0			0
$713$	−4.75915	−	4.75915i	−0.178232	−	0.178232i
$714$		0			0
$715$	−1.86449	+	0.772298i	−0.0697280	+	0.0288823i
$716$		0			0
$717$	−5.39547	+	13.0258i	−0.201498	+	0.486458i
$718$		0			0
$719$			46.5403i			1.73566i	0.496861	+	0.867830i	$0.334486\pi$
$719$			46.5403i			1.73566i	−0.496861	+	0.867830i	$0.665514\pi$
$720$		0			0
$721$			7.23790i			0.269553i
$722$		0			0
$723$	−25.0345	+	60.4386i	−0.931043	+	2.24774i
$724$		0			0
$725$	13.4366	−	5.56562i	0.499022	−	0.206702i
$726$		0			0
$727$	−10.4198	−	10.4198i	−0.386448	−	0.386448i	0.486970	−	0.873418i	$-0.338102\pi$
$727$	−10.4198	−	10.4198i	−0.386448	−	0.386448i	−0.873418	+	0.486970i	$0.838102\pi$
$728$		0			0
$729$	−8.16368	+	8.16368i	−0.302359	+	0.302359i
$730$		0			0
$731$	3.28838	+	7.93886i	0.121625	+	0.293629i
$732$		0			0
$733$	33.3482	+	13.8133i	1.23175	+	0.510206i	0.901126	−	0.433558i	$-0.142742\pi$
$733$	33.3482	+	13.8133i	1.23175	+	0.510206i	0.330620	+	0.943764i	$0.392742\pi$
$734$		0			0
$735$	5.19444			0.191600
$736$		0			0
$737$	−24.4907			−0.902128
$738$		0			0
$739$	−31.7629	−	13.1566i	−1.16842	−	0.483974i	−0.287747	−	0.957706i	$-0.592906\pi$
$739$	−31.7629	−	13.1566i	−1.16842	−	0.483974i	−0.880669	+	0.473733i	$0.842906\pi$
$740$		0			0
$741$	−0.737856	−	1.78134i	−0.0271058	−	0.0654393i
$742$		0			0
$743$	−9.90027	+	9.90027i	−0.363206	+	0.363206i	−0.864992	−	0.501786i	$-0.832676\pi$
$743$	−9.90027	+	9.90027i	−0.363206	+	0.363206i	0.501786	+	0.864992i	$0.332676\pi$
$744$		0			0
$745$	22.1637	+	22.1637i	0.812015	+	0.812015i
$746$		0			0
$747$	−34.1904	+	14.1621i	−1.25096	+	0.518165i
$748$		0			0
$749$	0.889284	−	2.14692i	0.0324937	−	0.0784468i
$750$		0			0
$751$		−	38.4024i		−	1.40132i	−0.713493	−	0.700662i	$-0.752888\pi$
$751$		−	38.4024i		−	1.40132i	0.713493	−	0.700662i	$-0.247112\pi$
$752$		0			0
$753$			48.5622i			1.76971i
$754$		0			0
$755$	−5.21249	+	12.5841i	−0.189702	+	0.457981i
$756$		0			0
$757$	5.15489	−	2.13523i	0.187358	−	0.0776061i	−0.287032	−	0.957921i	$-0.592669\pi$
$757$	5.15489	−	2.13523i	0.187358	−	0.0776061i	0.474390	+	0.880315i	$0.342669\pi$
$758$		0			0
$759$	16.9396	+	16.9396i	0.614869	+	0.614869i
$760$		0			0
$761$	−19.2892	+	19.2892i	−0.699232	+	0.699232i	−0.964245	−	0.265012i	$-0.914624\pi$
$761$	−19.2892	+	19.2892i	−0.699232	+	0.699232i	0.265012	+	0.964245i	$0.414624\pi$
$762$		0			0
$763$	4.70861	+	11.3676i	0.170463	+	0.411534i
$764$		0			0
$765$	42.2497	+	17.5004i	1.52754	+	0.632728i
$766$		0			0
$767$	−0.00997869			−0.000360310
$768$		0			0
$769$	−17.8703			−0.644420			−0.322210	−	0.946668i	$-0.604426\pi$
$769$	−17.8703			−0.644420			−0.322210	+	0.946668i	$0.604426\pi$
$770$		0			0
$771$	48.7834	+	20.2067i	1.75689	+	0.727728i
$772$		0			0
$773$	−7.59136	−	18.3272i	−0.273042	−	0.659182i	0.726568	−	0.687094i	$-0.241114\pi$
$773$	−7.59136	−	18.3272i	−0.273042	−	0.659182i	−0.999610	+	0.0279122i	$0.991114\pi$
$774$		0			0
$775$	8.96831	−	8.96831i	0.322151	−	0.322151i
$776$		0			0
$777$	−24.8088	−	24.8088i	−0.890010	−	0.890010i
$778$		0			0
$779$	10.0786	−	4.17469i	0.361103	−	0.149574i
$780$		0			0
$781$	0.611940	−	1.47735i	0.0218969	−	0.0528639i
$782$		0			0
$783$		−	79.5261i		−	2.84203i
$784$		0			0
$785$		−	18.1799i		−	0.648867i
$786$		0			0
$787$	7.14714	−	17.2547i	0.254768	−	0.615065i	−0.743809	−	0.668392i	$-0.766983\pi$
$787$	7.14714	−	17.2547i	0.254768	−	0.615065i	0.998577	+	0.0533275i	$0.0169827\pi$
$788$		0			0
$789$	4.38631	−	1.81687i	0.156157	−	0.0646823i
$790$		0			0
$791$	−1.49480	−	1.49480i	−0.0531490	−	0.0531490i
$792$		0			0
$793$	−1.66389	+	1.66389i	−0.0590866	+	0.0590866i
$794$		0			0
$795$	2.77249	+	6.69339i	0.0983302	+	0.237390i
$796$		0			0
$797$	−22.8308	−	9.45683i	−0.808709	−	0.334978i	−0.0602700	−	0.998182i	$-0.519196\pi$
$797$	−22.8308	−	9.45683i	−0.808709	−	0.334978i	−0.748439	+	0.663204i	$0.769196\pi$
$798$		0			0
$799$	29.5591			1.04573
$800$		0			0
$801$	54.4701			1.92461
$802$		0			0
$803$	20.2746	+	8.39800i	0.715474	+	0.296359i
$804$		0			0
$805$	−0.766415	−	1.85029i	−0.0270126	−	0.0652141i
$806$		0			0
$807$	−3.41397	+	3.41397i	−0.120177	+	0.120177i
$808$		0			0
$809$	0.965769	+	0.965769i	0.0339546	+	0.0339546i	0.723880	−	0.689926i	$-0.242357\pi$
$809$	0.965769	+	0.965769i	0.0339546	+	0.0339546i	−0.689926	+	0.723880i	$0.742357\pi$
$810$		0			0
$811$	−17.7733	+	7.36196i	−0.624106	+	0.258513i	−0.672247	−	0.740327i	$-0.734671\pi$
$811$	−17.7733	+	7.36196i	−0.624106	+	0.258513i	0.0481404	+	0.998841i	$0.484671\pi$
$812$		0			0
$813$	−19.6538	+	47.4485i	−0.689290	+	1.66409i
$814$		0			0
$815$			33.6293i			1.17798i
$816$		0			0
$817$			6.68178i			0.233766i
$818$		0			0
$819$	−0.525477	+	1.26861i	−0.0183617	+	0.0443290i
$820$		0			0
$821$	25.6746	−	10.6347i	0.896048	−	0.371155i	0.113349	−	0.993555i	$-0.463842\pi$
$821$	25.6746	−	10.6347i	0.896048	−	0.371155i	0.782699	+	0.622400i	$0.213842\pi$
$822$		0			0
$823$	3.51294	+	3.51294i	0.122454	+	0.122454i	0.765678	−	0.643224i	$-0.222404\pi$
$823$	3.51294	+	3.51294i	0.122454	+	0.122454i	−0.643224	+	0.765678i	$0.722404\pi$
$824$		0			0
$825$	−31.9216	+	31.9216i	−1.11137	+	1.11137i
$826$		0			0
$827$	13.1301	+	31.6988i	0.456578	+	1.10228i	0.969774	+	0.244005i	$0.0784614\pi$
$827$	13.1301	+	31.6988i	0.456578	+	1.10228i	−0.513196	+	0.858271i	$0.671539\pi$
$828$		0			0
$829$	33.6094	+	13.9215i	1.16730	+	0.483513i	0.880301	−	0.474416i	$-0.157341\pi$
$829$	33.6094	+	13.9215i	1.16730	+	0.483513i	0.287004	+	0.957930i	$0.407341\pi$
$830$		0			0
$831$	−54.5084			−1.89088
$832$		0			0
$833$	3.98721			0.138149
$834$		0			0
$835$	−29.7600	−	12.3270i	−1.02989	−	0.426593i
$836$		0			0
$837$	−26.5400	−	64.0732i	−0.917357	−	2.21469i
$838$		0			0
$839$	−9.42342	+	9.42342i	−0.325333	+	0.325333i	−0.850809	−	0.525476i	$-0.823887\pi$
$839$	−9.42342	+	9.42342i	−0.325333	+	0.325333i	0.525476	+	0.850809i	$0.323887\pi$
$840$		0			0
$841$	7.90441	+	7.90441i	0.272566	+	0.272566i
$842$		0			0
$843$	14.5763	−	6.03769i	0.502033	−	0.207949i
$844$		0			0
$845$	8.15857	−	19.6965i	0.280663	−	0.677581i
$846$		0			0
$847$			27.8173i			0.955815i
$848$		0			0
$849$			66.7782i			2.29182i
$850$		0			0
$851$	−5.17662	+	12.4975i	−0.177452	+	0.428407i
$852$		0			0
$853$	19.2625	−	7.97881i	0.659537	−	0.273189i	−0.0277067	−	0.999616i	$-0.508820\pi$
$853$	19.2625	−	7.97881i	0.659537	−	0.273189i	0.687244	+	0.726427i	$0.258820\pi$
$854$		0			0
$855$	25.1445	+	25.1445i	0.859924	+	0.859924i
$856$		0			0
$857$	1.54602	−	1.54602i	0.0528110	−	0.0528110i	−0.680208	−	0.733019i	$-0.738111\pi$
$857$	1.54602	−	1.54602i	0.0528110	−	0.0528110i	0.733019	+	0.680208i	$0.238111\pi$
$858$		0			0
$859$	−20.0607	−	48.4307i	−0.684461	−	1.65243i	−0.755653	−	0.654972i	$-0.772680\pi$
$859$	−20.0607	−	48.4307i	−0.684461	−	1.65243i	0.0711920	−	0.997463i	$-0.477320\pi$
$860$		0			0
$861$	−10.2658	−	4.25222i	−0.349856	−	0.144915i
$862$		0			0
$863$	34.4444			1.17250			0.586251	−	0.810130i	$-0.300603\pi$
$863$	34.4444			1.17250			0.586251	+	0.810130i	$0.300603\pi$
$864$		0			0
$865$	−9.95944			−0.338631
$866$		0			0
$867$	−3.21563	−	1.33196i	−0.109208	−	0.0452356i
$868$		0			0
$869$	11.1049	+	26.8096i	0.376707	+	0.909452i
$870$		0			0
$871$	−0.547366	+	0.547366i	−0.0185468	+	0.0185468i
$872$		0			0
$873$	71.3737	+	71.3737i	2.41564	+	2.41564i
$874$		0			0
$875$	11.0850	−	4.59156i	0.374742	−	0.155223i
$876$		0			0
$877$	−8.59005	+	20.7382i	−0.290065	+	0.700280i	−0.999992	−	0.00399584i	$-0.998728\pi$
$877$	−8.59005	+	20.7382i	−0.290065	+	0.700280i	0.709927	+	0.704276i	$0.248728\pi$
$878$		0			0
$879$			87.7598i			2.96007i
$880$		0			0
$881$			33.4900i			1.12831i	0.825670	+	0.564154i	$0.190798\pi$
$881$			33.4900i			1.12831i	−0.825670	+	0.564154i	$0.809202\pi$
$882$		0			0
$883$	−1.74506	+	4.21294i	−0.0587258	+	0.141777i	−0.950519	−	0.310667i	$-0.899448\pi$
$883$	−1.74506	+	4.21294i	−0.0587258	+	0.141777i	0.891793	+	0.452444i	$0.149448\pi$
$884$		0			0
$885$	0.243178	−	0.100727i	0.00817433	−	0.00338592i
$886$		0			0
$887$	24.8774	+	24.8774i	0.835301	+	0.835301i	0.988236	−	0.152935i	$-0.0488726\pi$
$887$	24.8774	+	24.8774i	0.835301	+	0.835301i	−0.152935	+	0.988236i	$0.548873\pi$
$888$		0			0
$889$	2.26078	−	2.26078i	0.0758243	−	0.0758243i
$890$		0			0
$891$	44.5906	+	107.651i	1.49384	+	3.60646i
$892$		0			0
$893$	21.2352	+	8.79590i	0.710608	+	0.294344i
$894$		0			0
$895$	30.6898			1.02585
$896$		0			0
$897$	0.757198			0.0252821
$898$		0			0
$899$	32.3714	+	13.4087i	1.07965	+	0.447204i
$900$		0			0
$901$	2.12814	+	5.13780i	0.0708988	+	0.171165i
$902$		0			0
$903$	4.81247	−	4.81247i	0.160149	−	0.160149i
$904$		0			0
$905$	−1.38508	−	1.38508i	−0.0460417	−	0.0460417i
$906$		0			0
$907$	2.88600	−	1.19542i	0.0958282	−	0.0396933i	−0.334254	−	0.942483i	$-0.608484\pi$
$907$	2.88600	−	1.19542i	0.0958282	−	0.0396933i	0.430083	+	0.902790i	$0.358484\pi$
$908$		0			0
$909$	2.74124	−	6.61795i	0.0909214	−	0.219504i
$910$		0			0
$911$			46.1043i			1.52750i	0.645511	+	0.763751i	$0.276645\pi$
$911$			46.1043i			1.52750i	−0.645511	+	0.763751i	$0.723355\pi$
$912$		0			0
$913$			33.0667i			1.09435i
$914$		0			0
$915$	23.7528	−	57.3443i	0.785243	−	1.89574i
$916$		0			0
$917$	−9.81263	+	4.06453i	−0.324042	+	0.134222i
$918$		0			0
$919$	17.8289	+	17.8289i	0.588121	+	0.588121i	0.937122	−	0.349002i	$-0.113479\pi$
$919$	17.8289	+	17.8289i	0.588121	+	0.588121i	−0.349002	+	0.937122i	$0.613479\pi$
$920$		0			0
$921$	−32.5094	+	32.5094i	−1.07122	+	1.07122i
$922$		0			0
$923$	−0.0193419	−	0.0466956i	−0.000636647	−	0.00153700i
$924$		0			0
$925$	−23.5506	−	9.75499i	−0.774340	−	0.320742i
$926$		0			0
$927$	50.4688			1.65761
$928$		0			0
$929$	−40.3989			−1.32545			−0.662723	−	0.748865i	$-0.730599\pi$
$929$	−40.3989			−1.32545			−0.662723	+	0.748865i	$0.730599\pi$
$930$		0			0
$931$	2.86440	+	1.18647i	0.0938770	+	0.0388851i
$932$		0			0
$933$	7.30164	+	17.6277i	0.239045	+	0.577105i
$934$		0			0
$935$	28.8932	−	28.8932i	0.944909	−	0.944909i
$936$		0			0
$937$	−20.7984	−	20.7984i	−0.679455	−	0.679455i	0.280422	−	0.959877i	$-0.409526\pi$
$937$	−20.7984	−	20.7984i	−0.679455	−	0.679455i	−0.959877	+	0.280422i	$0.909526\pi$
$938$		0			0
$939$	46.9060	−	19.4291i	1.53072	−	0.634044i
$940$		0			0
$941$	20.6472	−	49.8468i	0.673080	−	1.62496i	−0.103268	−	0.994654i	$-0.532930\pi$
$941$	20.6472	−	49.8468i	0.673080	−	1.62496i	0.776348	−	0.630305i	$-0.217070\pi$
$942$		0			0
$943$			4.28412i			0.139510i
$944$		0			0
$945$		−	20.6367i		−	0.671313i
$946$		0			0
$947$	−1.72478	+	4.16398i	−0.0560477	+	0.135311i	−0.949423	−	0.314000i	$-0.898331\pi$
$947$	−1.72478	+	4.16398i	−0.0560477	+	0.135311i	0.893375	+	0.449312i	$0.148331\pi$
$948$		0			0
$949$	0.640829	−	0.265440i	0.0208022	−	0.00861656i
$950$		0			0
$951$	20.2681	+	20.2681i	0.657239	+	0.657239i
$952$		0			0
$953$	−5.97020	+	5.97020i	−0.193394	+	0.193394i	−0.797161	−	0.603767i	$-0.793666\pi$
$953$	−5.97020	+	5.97020i	−0.193394	+	0.193394i	0.603767	+	0.797161i	$0.293666\pi$
$954$		0			0
$955$	15.6691	+	37.8286i	0.507040	+	1.22410i
$956$		0			0
$957$	−115.222	−	47.7265i	−3.72459	−	1.54278i
$958$		0			0
$959$	−5.23794			−0.169142
$960$		0			0
$961$	−0.443919			−0.0143200
$962$		0			0
$963$	−14.9702	−	6.20085i	−0.482407	−	0.199820i
$964$		0			0
$965$	0.203842	+	0.492118i	0.00656191	+	0.0158418i
$966$		0			0
$967$	−20.7913	+	20.7913i	−0.668603	+	0.668603i	−0.957393	−	0.288789i	$-0.906747\pi$
$967$	−20.7913	+	20.7913i	−0.668603	+	0.668603i	0.288789	+	0.957393i	$0.406747\pi$
$968$		0			0
$969$	27.6047	+	27.6047i	0.886790	+	0.886790i
$970$		0			0
$971$	−34.3357	+	14.2223i	−1.10189	+	0.456416i	−0.858136	−	0.513422i	$-0.828377\pi$
$971$	−34.3357	+	14.2223i	−1.10189	+	0.456416i	−0.243749	+	0.969838i	$0.578377\pi$
$972$		0			0
$973$	−6.91241	+	16.6880i	−0.221602	+	0.534993i
$974$		0			0
$975$			1.42689i			0.0456970i
$976$		0			0
$977$			9.84891i			0.315095i	0.987511	+	0.157547i	$0.0503587\pi$
$977$			9.84891i			0.315095i	−0.987511	+	0.157547i	$0.949641\pi$
$978$		0			0
$979$	18.6252	−	44.9651i	0.595263	−	1.43709i
$980$		0			0
$981$	79.2645	−	32.8324i	2.53072	−	1.04826i
$982$		0			0
$983$	22.7161	+	22.7161i	0.724530	+	0.724530i	0.969524	−	0.244994i	$-0.0787861\pi$
$983$	22.7161	+	22.7161i	0.724530	+	0.724530i	−0.244994	+	0.969524i	$0.578786\pi$
$984$		0			0
$985$	−2.05887	+	2.05887i	−0.0656012	+	0.0656012i
$986$		0			0
$987$	−8.95925	−	21.6295i	−0.285176	−	0.688476i
$988$		0			0
$989$	−2.42429	−	1.00417i	−0.0770880	−	0.0319309i
$990$		0			0
$991$	−17.8682			−0.567603			−0.283801	−	0.958883i	$-0.591596\pi$
$991$	−17.8682			−0.567603			−0.283801	+	0.958883i	$0.591596\pi$
$992$		0			0
$993$	−53.2349			−1.68936
$994$		0			0
$995$	−18.0357	−	7.47063i	−0.571770	−	0.236835i
$996$		0			0
$997$	4.49617	+	10.8547i	0.142395	+	0.343772i	0.978947	−	0.204116i	$-0.0654319\pi$
$997$	4.49617	+	10.8547i	0.142395	+	0.343772i	−0.836552	+	0.547888i	$0.815432\pi$
$998$		0			0
$999$	−98.5617	+	98.5617i	−3.11835	+	3.11835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.u.c.337.1		52
4.3	odd	2		224.2.u.c.29.9	✓	52
32.11	odd	8		224.2.u.c.85.9	yes	52
32.21	even	8	inner	896.2.u.c.561.1		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.9	✓	52	4.3	odd	2
224.2.u.c.85.9	yes	52	32.11	odd	8
896.2.u.c.337.1		52	1.1	even	1	trivial
896.2.u.c.561.1		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)

\(f(q)\)	\(=\)	\(q+(-2.91760 - 1.20851i) q^{3} +(-0.629460 - 1.51965i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(4.93055 + 4.93055i) q^{9} +O(q^{10})\)	\(q+(-2.91760 - 1.20851i) q^{3} +(-0.629460 - 1.51965i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(4.93055 + 4.93055i) q^{9} +(5.75610 - 2.38425i) q^{11} +(0.0753604 - 0.181936i) q^{13} +5.19444i q^{15} +3.98721i q^{17} +(-1.18647 + 2.86440i) q^{19} +(2.91760 - 1.20851i) q^{21} +(-0.860956 - 0.860956i) q^{23} +(1.62241 - 1.62241i) q^{25} +(-4.80123 - 11.5912i) q^{27} +(5.85615 + 2.42570i) q^{29} +5.52776 q^{31} -19.6754 q^{33} +(1.51965 + 0.629460i) q^{35} +(-4.25158 - 10.2642i) q^{37} +(-0.439742 + 0.439742i) q^{39} +(-2.48800 - 2.48800i) q^{41} +(1.99108 - 0.824733i) q^{43} +(4.38913 - 10.5963i) q^{45} -7.41348i q^{47} -1.00000i q^{49} +(4.81857 - 11.6331i) q^{51} +(1.28857 - 0.533743i) q^{53} +(-7.24647 - 7.24647i) q^{55} +(6.92330 - 6.92330i) q^{57} +(-0.0193914 - 0.0468150i) q^{59} +(-11.0396 - 4.57274i) q^{61} -6.97285 q^{63} -0.323916 q^{65} +(-3.63165 - 1.50428i) q^{67} +(1.47145 + 3.55239i) q^{69} +(0.181485 - 0.181485i) q^{71} +(2.49063 + 2.49063i) q^{73} +(-6.69425 + 2.77285i) q^{75} +(-2.38425 + 5.75610i) q^{77} +4.65759i q^{79} +18.7021i q^{81} +(-2.03104 + 4.90335i) q^{83} +(6.05917 - 2.50979i) q^{85} +(-14.1544 - 14.1544i) q^{87} +(5.52373 - 5.52373i) q^{89} +(0.0753604 + 0.181936i) q^{91} +(-16.1278 - 6.68033i) q^{93} +5.09973 q^{95} +14.4758 q^{97} +(40.1364 + 16.6251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 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

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