LMFDB - Embedded newform 448.2.z.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(47,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("448.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	448.47
Dual form			448.2.z.a.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0530773 + 0.198087i) q^{3} +(-1.82029 + 0.487744i) q^{5} +(-1.84933 + 1.89208i) q^{7} +(2.56165 + 1.47897i) q^{9} +O(q^{10})$	\(q+(-0.0530773 + 0.198087i) q^{3} +(-1.82029 + 0.487744i) q^{5} +(-1.84933 + 1.89208i) q^{7} +(2.56165 + 1.47897i) q^{9} +(1.09116 - 4.07225i) q^{11} +(-2.63146 + 2.63146i) q^{13} -0.386464i q^{15} +(-5.54801 + 3.20315i) q^{17} +(-4.83712 + 1.29610i) q^{19} +(-0.276640 - 0.466755i) q^{21} +(-2.51654 + 4.35877i) q^{23} +(-1.25458 + 0.724332i) q^{25} +(-0.863961 + 0.863961i) q^{27} +(0.0380909 + 0.0380909i) q^{29} +(2.32199 + 4.02180i) q^{31} +(0.748746 + 0.432288i) q^{33} +(2.44346 - 4.34613i) q^{35} +(-0.349719 - 1.30517i) q^{37} +(-0.381587 - 0.660929i) q^{39} +11.2477 q^{41} +(3.36902 + 3.36902i) q^{43} +(-5.38431 - 1.44272i) q^{45} +(1.66673 - 2.88687i) q^{47} +(-0.159948 - 6.99817i) q^{49} +(-0.340029 - 1.26900i) q^{51} +(-4.28814 - 1.14900i) q^{53} +7.94487i q^{55} -1.02696i q^{57} +(2.75886 + 0.739234i) q^{59} +(-1.44659 - 5.39876i) q^{61} +(-7.53568 + 2.11175i) q^{63} +(3.50653 - 6.07348i) q^{65} +(-7.68276 - 2.05859i) q^{67} +(-0.729846 - 0.729846i) q^{69} +10.1378 q^{71} +(-1.44429 - 2.50159i) q^{73} +(-0.0768912 - 0.286962i) q^{75} +(5.68713 + 9.59550i) q^{77} +(-5.46763 - 3.15674i) q^{79} +(4.31163 + 7.46797i) q^{81} +(5.36480 + 5.36480i) q^{83} +(8.53665 - 8.53665i) q^{85} +(-0.00956708 + 0.00552356i) q^{87} +(-0.890135 + 1.54176i) q^{89} +(-0.112496 - 9.84537i) q^{91} +(-0.919912 + 0.246490i) q^{93} +(8.17277 - 4.71855i) q^{95} +6.40791i q^{97} +(8.81792 - 8.81792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	$ 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) $ 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.0530773	+	0.198087i	−0.0306442	+	0.114366i	−0.979554	−	0.201182i	$-0.935522\pi$
$3$	−0.0530773	+	0.198087i	−0.0306442	+	0.114366i	0.948910	+	0.315548i	$0.102188\pi$
$4$		0			0
$5$	−1.82029	+	0.487744i	−0.814057	+	0.218126i	−0.641746	−	0.766917i	$-0.721790\pi$
$5$	−1.82029	+	0.487744i	−0.814057	+	0.218126i	−0.172310	+	0.985043i	$0.555123\pi$
$6$		0			0
$7$	−1.84933	+	1.89208i	−0.698982	+	0.715140i
$7$	−1.84933	+	1.89208i	−0.698982	+	0.715140i
$8$		0			0
$9$	2.56165	+	1.47897i	0.853885	+	0.492991i
$10$		0			0
$11$	1.09116	−	4.07225i	0.328996	−	1.22783i	−0.581237	−	0.813734i	$-0.697431\pi$
$11$	1.09116	−	4.07225i	0.328996	−	1.22783i	0.910233	−	0.414096i	$-0.135902\pi$
$12$		0			0
$13$	−2.63146	+	2.63146i	−0.729835	+	0.729835i	−0.970587	−	0.240752i	$-0.922606\pi$
$13$	−2.63146	+	2.63146i	−0.729835	+	0.729835i	0.240752	+	0.970587i	$0.422606\pi$
$14$		0			0
$15$		−	0.386464i		−	0.0997845i
$16$		0			0
$17$	−5.54801	+	3.20315i	−1.34559	+	0.776877i	−0.987621	−	0.156856i	$-0.949864\pi$
$17$	−5.54801	+	3.20315i	−1.34559	+	0.776877i	−0.357969	+	0.933733i	$0.616531\pi$
$18$		0			0
$19$	−4.83712	+	1.29610i	−1.10971	+	0.297346i	−0.766713	−	0.641990i	$-0.778109\pi$
$19$	−4.83712	+	1.29610i	−1.10971	+	0.297346i	−0.342998	+	0.939336i	$0.611442\pi$
$20$		0			0
$21$	−0.276640	−	0.466755i	−0.0603677	−	0.101854i
$22$		0			0
$23$	−2.51654	+	4.35877i	−0.524735	+	0.908867i	0.474850	+	0.880066i	$0.342502\pi$
$23$	−2.51654	+	4.35877i	−0.524735	+	0.908867i	−0.999585	+	0.0288006i	$0.990831\pi$
$24$		0			0
$25$	−1.25458	+	0.724332i	−0.250916	+	0.144866i
$26$		0			0
$27$	−0.863961	+	0.863961i	−0.166269	+	0.166269i
$28$		0			0
$29$	0.0380909	+	0.0380909i	0.00707330	+	0.00707330i	0.710635	−	0.703561i	$-0.248408\pi$
$29$	0.0380909	+	0.0380909i	0.00707330	+	0.00707330i	−0.703561	+	0.710635i	$0.748408\pi$
$30$		0			0
$31$	2.32199	+	4.02180i	0.417041	+	0.722337i	0.995640	−	0.0932755i	$-0.0297337\pi$
$31$	2.32199	+	4.02180i	0.417041	+	0.722337i	−0.578599	+	0.815612i	$0.696400\pi$
$32$		0			0
$33$	0.748746	+	0.432288i	0.130340	+	0.0752518i
$34$		0			0
$35$	2.44346	−	4.34613i	0.413020	−	0.734630i
$36$		0			0
$37$	−0.349719	−	1.30517i	−0.0574935	−	0.214569i	0.931203	−	0.364502i	$-0.118761\pi$
$37$	−0.349719	−	1.30517i	−0.0574935	−	0.214569i	−0.988696	+	0.149933i	$0.952094\pi$
$38$		0			0
$39$	−0.381587	−	0.660929i	−0.0611029	−	0.105833i
$40$		0			0
$41$	11.2477			1.75659			0.878295	−	0.478120i	$-0.158681\pi$
$41$	11.2477			1.75659			0.878295	+	0.478120i	$0.158681\pi$
$42$		0			0
$43$	3.36902	+	3.36902i	0.513770	+	0.513770i	0.915679	−	0.401909i	$-0.131653\pi$
$43$	3.36902	+	3.36902i	0.513770	+	0.513770i	−0.401909	+	0.915679i	$0.631653\pi$
$44$		0			0
$45$	−5.38431	−	1.44272i	−0.802645	−	0.215068i
$46$		0			0
$47$	1.66673	−	2.88687i	0.243118	−	0.421093i	−0.718483	−	0.695545i	$-0.755163\pi$
$47$	1.66673	−	2.88687i	0.243118	−	0.421093i	0.961601	+	0.274452i	$0.0884964\pi$
$48$		0			0
$49$	−0.159948	−	6.99817i	−0.0228497	−	0.999739i
$50$		0			0
$51$	−0.340029	−	1.26900i	−0.0476135	−	0.177696i
$52$		0			0
$53$	−4.28814	−	1.14900i	−0.589021	−	0.157828i	−0.0480153	−	0.998847i	$-0.515290\pi$
$53$	−4.28814	−	1.14900i	−0.589021	−	0.157828i	−0.541006	+	0.841019i	$0.681956\pi$
$54$		0			0
$55$			7.94487i			1.07129i
$56$		0			0
$57$		−	1.02696i		−	0.136025i
$58$		0			0
$59$	2.75886	+	0.739234i	0.359173	+	0.0962400i	0.433893	−	0.900965i	$-0.357140\pi$
$59$	2.75886	+	0.739234i	0.359173	+	0.0962400i	−0.0747201	+	0.997205i	$0.523806\pi$
$60$		0			0
$61$	−1.44659	−	5.39876i	−0.185217	−	0.691241i	−0.994584	−	0.103937i	$-0.966856\pi$
$61$	−1.44659	−	5.39876i	−0.185217	−	0.691241i	0.809367	−	0.587304i	$-0.199811\pi$
$62$		0			0
$63$	−7.53568	+	2.11175i	−0.949407	+	0.266056i
$64$		0			0
$65$	3.50653	−	6.07348i	0.434931	−	0.753323i
$66$		0			0
$67$	−7.68276	−	2.05859i	−0.938598	−	0.251497i	−0.243081	−	0.970006i	$-0.578158\pi$
$67$	−7.68276	−	2.05859i	−0.938598	−	0.251497i	−0.695517	+	0.718509i	$0.744825\pi$
$68$		0			0
$69$	−0.729846	−	0.729846i	−0.0878631	−	0.0878631i
$70$		0			0
$71$	10.1378			1.20313			0.601566	−	0.798823i	$-0.294544\pi$
$71$	10.1378			1.20313			0.601566	+	0.798823i	$0.294544\pi$
$72$		0			0
$73$	−1.44429	−	2.50159i	−0.169042	−	0.292789i	0.769041	−	0.639199i	$-0.220734\pi$
$73$	−1.44429	−	2.50159i	−0.169042	−	0.292789i	−0.938083	+	0.346410i	$0.887401\pi$
$74$		0			0
$75$	−0.0768912	−	0.286962i	−0.00887863	−	0.0331355i
$76$		0			0
$77$	5.68713	+	9.59550i	0.648108	+	1.09351i
$78$		0			0
$79$	−5.46763	−	3.15674i	−0.615156	−	0.355161i	0.159824	−	0.987145i	$-0.448907\pi$
$79$	−5.46763	−	3.15674i	−0.615156	−	0.355161i	−0.774981	+	0.631985i	$0.782241\pi$
$80$		0			0
$81$	4.31163	+	7.46797i	0.479070	+	0.829774i
$82$		0			0
$83$	5.36480	+	5.36480i	0.588863	+	0.588863i	0.937323	−	0.348460i	$-0.113295\pi$
$83$	5.36480	+	5.36480i	0.588863	+	0.588863i	−0.348460	+	0.937323i	$0.613295\pi$
$84$		0			0
$85$	8.53665	−	8.53665i	0.925930	−	0.925930i
$86$		0			0
$87$	−0.00956708	+	0.00552356i	−0.00102570	+	0.000592187i
$88$		0			0
$89$	−0.890135	+	1.54176i	−0.0943542	+	0.163426i	−0.909339	−	0.416056i	$-0.863412\pi$
$89$	−0.890135	+	1.54176i	−0.0943542	+	0.163426i	0.814985	+	0.579482i	$0.196745\pi$
$90$		0			0
$91$	−0.112496	−	9.84537i	−0.0117928	−	1.03207i
$92$		0			0
$93$	−0.919912	+	0.246490i	−0.0953904	+	0.0255598i
$94$		0			0
$95$	8.17277	−	4.71855i	0.838509	−	0.484113i
$96$		0			0
$97$			6.40791i			0.650625i	0.945607	+	0.325312i	$0.105469\pi$
$97$			6.40791i			0.650625i	−0.945607	+	0.325312i	$0.894531\pi$
$98$		0			0
$99$	8.81792	−	8.81792i	0.886234	−	0.886234i
$100$		0			0
$101$	0.721748	−	2.69360i	0.0718166	−	0.268023i	−0.920676	−	0.390328i	$-0.872362\pi$
$101$	0.721748	−	2.69360i	0.0718166	−	0.268023i	0.992493	+	0.122304i	$0.0390284\pi$
$102$		0			0
$103$	−4.12660	−	2.38249i	−0.406606	−	0.234754i	0.282724	−	0.959201i	$-0.408762\pi$
$103$	−4.12660	−	2.38249i	−0.406606	−	0.234754i	−0.689330	+	0.724447i	$0.742095\pi$
$104$		0			0
$105$	0.731221	+	0.714699i	0.0713598	+	0.0697475i
$106$		0			0
$107$	8.62418	−	2.31084i	0.833731	−	0.223397i	0.183390	−	0.983040i	$-0.441293\pi$
$107$	8.62418	−	2.31084i	0.833731	−	0.223397i	0.650341	+	0.759643i	$0.274626\pi$
$108$		0			0
$109$	−2.28592	+	8.53116i	−0.218951	+	0.817137i	0.765787	+	0.643094i	$0.222350\pi$
$109$	−2.28592	+	8.53116i	−0.218951	+	0.817137i	−0.984738	+	0.174042i	$0.944317\pi$
$110$		0			0
$111$	0.277100			0.0263011
$112$		0			0
$113$	7.63900			0.718616			0.359308	−	0.933219i	$-0.383013\pi$
$113$	7.63900			0.718616			0.359308	+	0.933219i	$0.383013\pi$
$114$		0			0
$115$	2.45485	−	9.16164i	0.228916	−	0.854328i
$116$		0			0
$117$	−10.6327	+	2.84903i	−0.982997	+	0.263393i
$118$		0			0
$119$	4.19950	−	16.4210i	0.384967	−	1.50531i
$120$		0			0
$121$	−5.86634	−	3.38693i	−0.533304	−	0.307903i
$122$		0			0
$123$	−0.596996	+	2.22802i	−0.0538293	+	0.200894i
$124$		0			0
$125$	8.59312	−	8.59312i	0.768592	−	0.768592i
$126$		0			0
$127$		−	5.41769i		−	0.480742i	−0.970681	−	0.240371i	$-0.922731\pi$
$127$		−	5.41769i		−	0.480742i	0.970681	−	0.240371i	$-0.0772692\pi$
$128$		0			0
$129$	−0.846177	+	0.488541i	−0.0745018	+	0.0430136i
$130$		0			0
$131$	−9.68669	+	2.59554i	−0.846330	+	0.226773i	−0.655825	−	0.754913i	$-0.727679\pi$
$131$	−9.68669	+	2.59554i	−0.846330	+	0.226773i	−0.190505	+	0.981686i	$0.561012\pi$
$132$		0			0
$133$	6.49310	−	11.5491i	0.563023	−	1.00144i
$134$		0			0
$135$	1.15126	−	1.99405i	0.0990850	−	0.171620i
$136$		0			0
$137$	−2.01214	+	1.16171i	−0.171909	+	0.0992518i	−0.583486	−	0.812123i	$-0.698312\pi$
$137$	−2.01214	+	1.16171i	−0.171909	+	0.0992518i	0.411577	+	0.911375i	$0.364978\pi$
$138$		0			0
$139$	−12.3283	+	12.3283i	−1.04568	+	1.04568i	−0.0467705	+	0.998906i	$0.514893\pi$
$139$	−12.3283	+	12.3283i	−1.04568	+	1.04568i	−0.998906	+	0.0467705i	$0.985107\pi$
$140$		0			0
$141$	0.483386	+	0.483386i	0.0407084	+	0.0407084i
$142$		0			0
$143$	7.84463	+	13.5873i	0.656001	+	1.13623i
$144$		0			0
$145$	−0.0879149	−	0.0507577i	−0.00730094	−	0.00421520i
$146$		0			0
$147$	1.39474	+	0.339761i	0.115036	+	0.0280230i
$148$		0			0
$149$	6.05953	+	22.6145i	0.496416	+	1.85265i	0.521951	+	0.852976i	$0.325204\pi$
$149$	6.05953	+	22.6145i	0.496416	+	1.85265i	−0.0255350	+	0.999674i	$0.508129\pi$
$150$		0			0
$151$	−2.33877	−	4.05086i	−0.190326	−	0.329654i	0.755032	−	0.655688i	$-0.227621\pi$
$151$	−2.33877	−	4.05086i	−0.190326	−	0.329654i	−0.945358	+	0.326033i	$0.894288\pi$
$152$		0			0
$153$	−18.9495			−1.53197
$154$		0			0
$155$	−6.18829	−	6.18829i	−0.497056	−	0.497056i
$156$		0			0
$157$	17.2260	+	4.61570i	1.37479	+	0.368373i	0.869225	−	0.494417i	$-0.164618\pi$
$157$	17.2260	+	4.61570i	1.37479	+	0.368373i	0.505563	+	0.862790i	$0.331285\pi$
$158$		0			0
$159$	0.455206	−	0.788439i	0.0361001	−	0.0625273i
$160$		0			0
$161$	−3.59324	−	12.8223i	−0.283187	−	1.01054i
$162$		0			0
$163$	5.72843	+	21.3788i	0.448685	+	1.67451i	0.706019	+	0.708193i	$0.250489\pi$
$163$	5.72843	+	21.3788i	0.448685	+	1.67451i	−0.257334	+	0.966322i	$0.582844\pi$
$164$		0			0
$165$	−1.57378	−	0.421692i	−0.122518	−	0.0328287i
$166$		0			0
$167$		−	0.304378i		−	0.0235535i	−0.999931	−	0.0117768i	$-0.996251\pi$
$167$		−	0.304378i		−	0.0235535i	0.999931	−	0.0117768i	$-0.00374874\pi$
$168$		0			0
$169$		−	0.849130i		−	0.0653177i
$170$		0			0
$171$	−14.3079	−	3.83380i	−1.09415	−	0.293178i
$172$		0			0
$173$	−5.04898	−	18.8431i	−0.383867	−	1.43261i	−0.839945	−	0.542671i	$-0.817413\pi$
$173$	−5.04898	−	18.8431i	−0.383867	−	1.43261i	0.456078	−	0.889940i	$-0.349254\pi$
$174$		0			0
$175$	0.949638	−	3.71330i	0.0717859	−	0.280699i
$176$		0			0
$177$	−0.292865	+	0.507258i	−0.0220131	+	0.0381278i
$178$		0			0
$179$	9.35570	+	2.50685i	0.699278	+	0.187371i	0.590907	−	0.806740i	$-0.298770\pi$
$179$	9.35570	+	2.50685i	0.699278	+	0.187371i	0.108371	+	0.994111i	$0.465437\pi$
$180$		0			0
$181$	16.0802	+	16.0802i	1.19523	+	1.19523i	0.975577	+	0.219657i	$0.0704938\pi$
$181$	16.0802	+	16.0802i	1.19523	+	1.19523i	0.219657	+	0.975577i	$0.429506\pi$
$182$		0			0
$183$	1.14621			0.0847301
$184$		0			0
$185$	1.27318	+	2.20521i	0.0936059	+	0.162130i
$186$		0			0
$187$	6.99027	+	26.0880i	0.511179	+	1.90775i
$188$		0			0
$189$	−0.0369349	−	3.23243i	−0.00268662	−	0.235125i
$190$		0			0
$191$	−14.6659	−	8.46735i	−1.06119	−	0.612676i	−0.135426	−	0.990787i	$-0.543240\pi$
$191$	−14.6659	−	8.46735i	−1.06119	−	0.612676i	−0.925760	+	0.378111i	$0.876574\pi$
$192$		0			0
$193$	−8.83471	−	15.3022i	−0.635936	−	1.10147i	−0.986316	−	0.164866i	$-0.947281\pi$
$193$	−8.83471	−	15.3022i	−0.635936	−	1.10147i	0.350380	−	0.936608i	$-0.386052\pi$
$194$		0			0
$195$	1.01696	+	1.01696i	0.0728262	+	0.0728262i
$196$		0			0
$197$	2.92385	−	2.92385i	0.208315	−	0.208315i	−0.595236	−	0.803551i	$-0.702941\pi$
$197$	2.92385	−	2.92385i	0.208315	−	0.208315i	0.803551	+	0.595236i	$0.202941\pi$
$198$		0			0
$199$	−3.15128	+	1.81939i	−0.223388	+	0.128973i	−0.607518	−	0.794306i	$-0.707835\pi$
$199$	−3.15128	+	1.81939i	−0.223388	+	0.128973i	0.384130	+	0.923279i	$0.374501\pi$
$200$		0			0
$201$	0.815560	−	1.41259i	0.0575252	−	0.0996365i
$202$		0			0
$203$	−0.142514	+	0.00162841i	−0.0100025	+	0.000114292i
$204$		0			0
$205$	−20.4740	+	5.48598i	−1.42996	+	0.383158i
$206$		0			0
$207$	−12.8930	+	7.44378i	−0.896126	+	0.517379i
$208$		0			0
$209$			21.1122i			1.46036i
$210$		0			0
$211$	−5.47843	+	5.47843i	−0.377150	+	0.377150i	−0.870073	−	0.492923i	$-0.835929\pi$
$211$	−5.47843	+	5.47843i	−0.377150	+	0.377150i	0.492923	+	0.870073i	$0.335929\pi$
$212$		0			0
$213$	−0.538085	+	2.00816i	−0.0368690	+	0.137597i
$214$		0			0
$215$	−7.77579	−	4.48936i	−0.530305	−	0.306172i
$216$		0			0
$217$	−11.9037	−	3.04425i	−0.808076	−	0.206657i
$218$		0			0
$219$	0.572193	−	0.153319i	0.0386652	−	0.0103603i
$220$		0			0
$221$	6.17041	−	23.0283i	0.415067	−	1.54905i
$222$		0			0
$223$	19.4622			1.30328			0.651642	−	0.758526i	$-0.274080\pi$
$223$	19.4622			1.30328			0.651642	+	0.758526i	$0.274080\pi$
$224$		0			0
$225$	−4.28507			−0.285671
$226$		0			0
$227$	−3.30490	+	12.3341i	−0.219354	+	0.818640i	0.765234	+	0.643752i	$0.222623\pi$
$227$	−3.30490	+	12.3341i	−0.219354	+	0.818640i	−0.984588	+	0.174888i	$0.944044\pi$
$228$		0			0
$229$	−24.6050	+	6.59290i	−1.62595	+	0.435671i	−0.952741	−	0.303785i	$-0.901750\pi$
$229$	−24.6050	+	6.59290i	−1.62595	+	0.435671i	−0.673205	+	0.739456i	$0.735083\pi$
$230$		0			0
$231$	−2.20260	+	0.617243i	−0.144921	+	0.0406116i
$232$		0			0
$233$	1.00467	+	0.580046i	0.0658181	+	0.0380001i	0.532548	−	0.846400i	$-0.321235\pi$
$233$	1.00467	+	0.580046i	0.0658181	+	0.0380001i	−0.466730	+	0.884400i	$0.654568\pi$
$234$		0			0
$235$	−1.62588	+	6.06787i	−0.106061	+	0.395824i
$236$		0			0
$237$	0.915516	−	0.915516i	0.0594692	−	0.0594692i
$238$		0			0
$239$			16.7833i			1.08562i	0.839856	+	0.542809i	$0.182639\pi$
$239$			16.7833i			1.08562i	−0.839856	+	0.542809i	$0.817361\pi$
$240$		0			0
$241$	−24.1160	+	13.9234i	−1.55345	+	0.896885i	−0.555594	+	0.831454i	$0.687509\pi$
$241$	−24.1160	+	13.9234i	−1.55345	+	0.896885i	−0.997857	+	0.0654317i	$0.979158\pi$
$242$		0			0
$243$	−5.24874	+	1.40639i	−0.336707	+	0.0902203i
$244$		0			0
$245$	3.70447	+	12.6607i	0.236670	+	0.808860i
$246$		0			0
$247$	9.31803	−	16.1393i	0.592892	−	1.02692i
$248$		0			0
$249$	−1.34745	+	0.777949i	−0.0853910	+	0.0493005i
$250$		0			0
$251$	6.50977	−	6.50977i	0.410893	−	0.410893i	−0.471156	−	0.882050i	$-0.656163\pi$
$251$	6.50977	−	6.50977i	0.410893	−	0.410893i	0.882050	+	0.471156i	$0.156163\pi$
$252$		0			0
$253$	15.0041	+	15.0041i	0.943299	+	0.943299i
$254$		0			0
$255$	1.23790	+	2.14410i	0.0775203	+	0.134269i
$256$		0			0
$257$	7.67788	+	4.43283i	0.478933	+	0.276512i	0.719972	−	0.694003i	$-0.244155\pi$
$257$	7.67788	+	4.43283i	0.478933	+	0.276512i	−0.241039	+	0.970515i	$0.577488\pi$
$258$		0			0
$259$	3.11624	+	1.75199i	0.193633	+	0.108864i
$260$		0			0
$261$	0.0412403	+	0.153911i	0.00255271	+	0.00952686i
$262$		0			0
$263$	−2.87410	−	4.97808i	−0.177224	−	0.306962i	0.763704	−	0.645566i	$-0.223379\pi$
$263$	−2.87410	−	4.97808i	−0.177224	−	0.306962i	−0.940929	+	0.338604i	$0.890045\pi$
$264$		0			0
$265$	8.36606			0.513923
$266$		0			0
$267$	−0.258157	−	0.258157i	−0.0157989	−	0.0157989i
$268$		0			0
$269$	6.28055	+	1.68287i	0.382932	+	0.102606i	0.445149	−	0.895456i	$-0.353151\pi$
$269$	6.28055	+	1.68287i	0.382932	+	0.102606i	−0.0622174	+	0.998063i	$0.519817\pi$
$270$		0			0
$271$	12.7068	−	22.0089i	0.771884	−	1.33694i	−0.164645	−	0.986353i	$-0.552648\pi$
$271$	12.7068	−	22.0089i	0.771884	−	1.33694i	0.936529	−	0.350590i	$-0.114019\pi$
$272$		0			0
$273$	1.95621	+	0.500281i	0.118395	+	0.0302784i
$274$		0			0
$275$	1.58072	+	5.89932i	0.0953210	+	0.355743i
$276$		0			0
$277$	8.84136	+	2.36904i	0.531226	+	0.142342i	0.514454	−	0.857518i	$-0.327995\pi$
$277$	8.84136	+	2.36904i	0.531226	+	0.142342i	0.0167715	+	0.999859i	$0.494661\pi$
$278$		0			0
$279$			13.7366i			0.822390i
$280$		0			0
$281$		−	8.40334i		−	0.501301i	−0.968078	−	0.250651i	$-0.919355\pi$
$281$		−	8.40334i		−	0.501301i	0.968078	−	0.250651i	$-0.0806446\pi$
$282$		0			0
$283$	−24.1688	−	6.47601i	−1.43669	−	0.384959i	−0.545315	−	0.838231i	$-0.683590\pi$
$283$	−24.1688	−	6.47601i	−1.43669	−	0.384959i	−0.891372	+	0.453272i	$0.850256\pi$
$284$		0			0
$285$	0.500896	+	1.86937i	0.0296705	+	0.110732i
$286$		0			0
$287$	−20.8007	+	21.2815i	−1.22782	+	1.25621i
$288$		0			0
$289$	12.0203	−	20.8198i	0.707076	−	1.22469i
$290$		0			0
$291$	−1.26933	−	0.340115i	−0.0744092	−	0.0199379i
$292$		0			0
$293$	−15.2554	−	15.2554i	−0.891230	−	0.891230i	0.103409	−	0.994639i	$-0.467025\pi$
$293$	−15.2554	−	15.2554i	−0.891230	−	0.891230i	−0.994639	+	0.103409i	$0.967025\pi$
$294$		0			0
$295$	−5.38247			−0.313379
$296$		0			0
$297$	2.57555	+	4.46098i	0.149449	+	0.258853i
$298$		0			0
$299$	−4.84776	−	18.0921i	−0.280353	−	1.04629i
$300$		0			0
$301$	−12.6049	+	0.144028i	−0.726533	+	0.00830161i
$302$		0			0
$303$	0.495259	+	0.285938i	0.0284519	+	0.0164267i
$304$		0			0
$305$	5.26643	+	9.12173i	0.301555	+	0.522308i
$306$		0			0
$307$	−7.46885	−	7.46885i	−0.426270	−	0.426270i	0.461086	−	0.887355i	$-0.347460\pi$
$307$	−7.46885	−	7.46885i	−0.426270	−	0.426270i	−0.887355	+	0.461086i	$0.847460\pi$
$308$		0			0
$309$	0.690970	−	0.690970i	0.0393079	−	0.0393079i
$310$		0			0
$311$	−5.22714	+	3.01789i	−0.296404	+	0.171129i	−0.640826	−	0.767686i	$-0.721408\pi$
$311$	−5.22714	+	3.01789i	−0.296404	+	0.171129i	0.344423	+	0.938815i	$0.388075\pi$
$312$		0			0
$313$	−6.15303	+	10.6574i	−0.347790	+	0.602390i	−0.985857	−	0.167591i	$-0.946401\pi$
$313$	−6.15303	+	10.6574i	−0.347790	+	0.602390i	0.638067	+	0.769981i	$0.279734\pi$
$314$		0			0
$315$	12.6871	−	7.51948i	0.714838	−	0.423675i
$316$		0			0
$317$	−6.95253	+	1.86292i	−0.390493	+	0.104632i	−0.448723	−	0.893671i	$-0.648121\pi$
$317$	−6.95253	+	1.86292i	−0.390493	+	0.104632i	0.0582300	+	0.998303i	$0.481454\pi$
$318$		0			0
$319$	0.196679	−	0.113553i	0.0110119	−	0.00635773i
$320$		0			0
$321$			1.83099i			0.102196i
$322$		0			0
$323$	22.6848	−	22.6848i	1.26222	−	1.26222i
$324$		0			0
$325$	1.39532	−	5.20742i	0.0773986	−	0.288856i
$326$		0			0
$327$	−1.56858	−	0.905622i	−0.0867428	−	0.0500810i
$328$		0			0
$329$	2.37985	+	8.49237i	0.131205	+	0.468200i
$330$		0			0
$331$	7.49575	−	2.00848i	0.412004	−	0.110396i	−0.0468626	−	0.998901i	$-0.514922\pi$
$331$	7.49575	−	2.00848i	0.412004	−	0.110396i	0.458866	+	0.888505i	$0.348256\pi$
$332$		0			0
$333$	1.03445	−	3.86062i	0.0566875	−	0.211561i
$334$		0			0
$335$	14.9889			0.818930
$336$		0			0
$337$	−16.7324			−0.911474			−0.455737	−	0.890114i	$-0.650624\pi$
$337$	−16.7324			−0.911474			−0.455737	+	0.890114i	$0.650624\pi$
$338$		0			0
$339$	−0.405457	+	1.51319i	−0.0220214	+	0.0821850i
$340$		0			0
$341$	18.9114	−	5.06730i	1.02411	−	0.274410i
$342$		0			0
$343$	13.5369	+	12.6393i	0.730925	+	0.682458i
$344$		0			0
$345$	1.68451	+	0.972551i	0.0906908	+	0.0523604i
$346$		0			0
$347$	−3.09373	+	11.5460i	−0.166080	+	0.619820i	0.831820	+	0.555046i	$0.187299\pi$
$347$	−3.09373	+	11.5460i	−0.166080	+	0.619820i	−0.997900	+	0.0647741i	$0.979367\pi$
$348$		0			0
$349$	−6.65802	+	6.65802i	−0.356396	+	0.356396i	−0.862482	−	0.506087i	$-0.831092\pi$
$349$	−6.65802	+	6.65802i	−0.356396	+	0.356396i	0.506087	+	0.862482i	$0.331092\pi$
$350$		0			0
$351$		−	4.54695i		−	0.242698i
$352$		0			0
$353$	12.4963	−	7.21473i	0.665110	−	0.384002i	−0.129111	−	0.991630i	$-0.541212\pi$
$353$	12.4963	−	7.21473i	0.665110	−	0.384002i	0.794221	+	0.607629i	$0.207879\pi$
$354$		0			0
$355$	−18.4536	+	4.94464i	−0.979417	+	0.262434i
$356$		0			0
$357$	3.02989	+	1.70345i	0.160359	+	0.0901560i
$358$		0			0
$359$	−9.25686	+	16.0334i	−0.488559	+	0.846208i	−0.999913	−	0.0131614i	$-0.995810\pi$
$359$	−9.25686	+	16.0334i	−0.488559	+	0.846208i	0.511355	+	0.859370i	$0.329144\pi$
$360$		0			0
$361$	5.26334	−	3.03879i	0.277018	−	0.159937i
$362$		0			0
$363$	0.982278	−	0.982278i	0.0515562	−	0.0515562i
$364$		0			0
$365$	3.84917	+	3.84917i	0.201475	+	0.201475i
$366$		0			0
$367$	−13.2213	−	22.9000i	−0.690149	−	1.19537i	−0.971789	−	0.235852i	$-0.924212\pi$
$367$	−13.2213	−	22.9000i	−0.690149	−	1.19537i	0.281640	−	0.959520i	$-0.409122\pi$
$368$		0			0
$369$	28.8126	+	16.6350i	1.49993	+	0.865982i
$370$		0			0
$371$	10.1042	−	5.98862i	0.524584	−	0.310914i
$372$		0			0
$373$	1.23915	+	4.62458i	0.0641609	+	0.239452i	0.990558	−	0.137097i	$-0.0437773\pi$
$373$	1.23915	+	4.62458i	0.0641609	+	0.239452i	−0.926397	+	0.376549i	$0.877111\pi$
$374$		0			0
$375$	1.24609	+	2.15829i	0.0643476	+	0.111453i
$376$		0			0
$377$	−0.200469			−0.0103247
$378$		0			0
$379$	6.89734	+	6.89734i	0.354293	+	0.354293i	0.861704	−	0.507411i	$-0.169397\pi$
$379$	6.89734	+	6.89734i	0.354293	+	0.354293i	−0.507411	+	0.861704i	$0.669397\pi$
$380$		0			0
$381$	1.07318	+	0.287556i	0.0549804	+	0.0147320i
$382$		0			0
$383$	7.18887	−	12.4515i	0.367334	−	0.636242i	−0.621814	−	0.783165i	$-0.713604\pi$
$383$	7.18887	−	12.4515i	0.367334	−	0.636242i	0.989148	+	0.146924i	$0.0469372\pi$
$384$		0			0
$385$	−15.0323	−	14.6927i	−0.766119	−	0.748809i
$386$		0			0
$387$	3.64758	+	13.6129i	0.185417	+	0.691985i
$388$		0			0
$389$	−19.2050	−	5.14596i	−0.973731	−	0.260910i	−0.263329	−	0.964706i	$-0.584820\pi$
$389$	−19.2050	−	5.14596i	−0.973731	−	0.260910i	−0.710402	+	0.703796i	$0.751487\pi$
$390$		0			0
$391$		−	32.2434i		−	1.63062i
$392$		0			0
$393$		−	2.05657i		−	0.103740i
$394$		0			0
$395$	11.4923	+	3.07936i	0.578242	+	0.154939i
$396$		0			0
$397$	5.88669	+	21.9694i	0.295445	+	1.10261i	0.940864	+	0.338786i	$0.110016\pi$
$397$	5.88669	+	21.9694i	0.295445	+	1.10261i	−0.645419	+	0.763829i	$0.723317\pi$
$398$		0			0
$399$	1.94310	+	1.89920i	0.0972767	+	0.0950788i
$400$		0			0
$401$	8.54981	−	14.8087i	0.426957	−	0.739511i	−0.569644	−	0.821892i	$-0.692919\pi$
$401$	8.54981	−	14.8087i	0.426957	−	0.739511i	0.996601	+	0.0823803i	$0.0262522\pi$
$402$		0			0
$403$	−16.6934	−	4.47298i	−0.831558	−	0.222815i
$404$		0			0
$405$	−11.4909	−	11.4909i	−0.570986	−	0.570986i
$406$		0			0
$407$	−5.69658			−0.282369
$408$		0			0
$409$	−1.08695	−	1.88266i	−0.0537464	−	0.0930915i	0.837900	−	0.545823i	$-0.183783\pi$
$409$	−1.08695	−	1.88266i	−0.0537464	−	0.0930915i	−0.891647	+	0.452732i	$0.850450\pi$
$410$		0			0
$411$	−0.123321	−	0.460241i	−0.00608298	−	0.0227020i
$412$		0			0
$413$	−6.50073	+	3.85290i	−0.319880	+	0.189589i
$414$		0			0
$415$	−12.3821	−	7.14882i	−0.607814	−	0.350922i
$416$		0			0
$417$	−1.78773	−	3.09644i	−0.0875456	−	0.151633i
$418$		0			0
$419$	−15.8552	−	15.8552i	−0.774580	−	0.774580i	0.204324	−	0.978903i	$-0.434500\pi$
$419$	−15.8552	−	15.8552i	−0.774580	−	0.774580i	−0.978903	+	0.204324i	$0.934500\pi$
$420$		0			0
$421$	4.41508	−	4.41508i	0.215178	−	0.215178i	−0.591285	−	0.806463i	$-0.701379\pi$
$421$	4.41508	−	4.41508i	0.215178	−	0.215178i	0.806463	+	0.591285i	$0.201379\pi$
$422$		0			0
$423$	8.53920	−	4.93011i	0.415190	−	0.239710i
$424$		0			0
$425$	4.64028	−	8.03720i	0.225087	−	0.389862i
$426$		0			0
$427$	12.8901	+	7.24703i	0.623797	+	0.350708i
$428$		0			0
$429$	−3.10784	+	0.832743i	−0.150048	+	0.0402052i
$430$		0			0
$431$	10.5207	−	6.07413i	0.506764	−	0.292580i	−0.224738	−	0.974419i	$-0.572153\pi$
$431$	10.5207	−	6.07413i	0.506764	−	0.292580i	0.731503	+	0.681839i	$0.238819\pi$
$432$		0			0
$433$			2.59127i			0.124528i	0.998060	+	0.0622642i	$0.0198321\pi$
$433$			2.59127i			0.124528i	−0.998060	+	0.0622642i	$0.980168\pi$
$434$		0			0
$435$	0.0147207	−	0.0147207i	0.000705805	−	0.000705805i
$436$		0			0
$437$	6.52338	−	24.3456i	0.312056	−	1.16461i
$438$		0			0
$439$	18.7368	+	10.8177i	0.894256	+	0.516299i	0.875332	−	0.483522i	$-0.160643\pi$
$439$	18.7368	+	10.8177i	0.894256	+	0.516299i	0.0189240	+	0.999821i	$0.493976\pi$
$440$		0			0
$441$	9.94037	−	18.1635i	0.473351	−	0.864927i
$442$		0			0
$443$	23.1430	−	6.20114i	1.09956	−	0.294625i	0.336972	−	0.941515i	$-0.390597\pi$
$443$	23.1430	−	6.20114i	1.09956	−	0.294625i	0.762584	+	0.646890i	$0.223931\pi$
$444$		0			0
$445$	0.868317	−	3.24060i	0.0411622	−	0.153619i
$446$		0			0
$447$	−4.80126			−0.227092
$448$		0			0
$449$	9.41030			0.444100			0.222050	−	0.975035i	$-0.428725\pi$
$449$	9.41030			0.444100			0.222050	+	0.975035i	$0.428725\pi$
$450$		0			0
$451$	12.2730	−	45.8033i	0.577911	−	2.15679i
$452$		0			0
$453$	0.926559	−	0.248271i	0.0435336	−	0.0116648i
$454$		0			0
$455$	5.00680	+	17.8665i	0.234722	+	0.837595i
$456$		0			0
$457$	24.6248	+	14.2171i	1.15190	+	0.665049i	0.949349	−	0.314223i	$-0.101744\pi$
$457$	24.6248	+	14.2171i	1.15190	+	0.665049i	0.202549	+	0.979272i	$0.435077\pi$
$458$		0			0
$459$	2.02587	−	7.56066i	0.0945596	−	0.352901i
$460$		0			0
$461$	−3.31248	+	3.31248i	−0.154278	+	0.154278i	−0.780025	−	0.625748i	$-0.784794\pi$
$461$	−3.31248	+	3.31248i	−0.154278	+	0.154278i	0.625748	+	0.780025i	$0.284794\pi$
$462$		0			0
$463$			11.8198i			0.549312i	0.961543	+	0.274656i	$0.0885639\pi$
$463$			11.8198i			0.549312i	−0.961543	+	0.274656i	$0.911436\pi$
$464$		0			0
$465$	1.55428	−	0.897363i	0.0720780	−	0.0416142i
$466$		0			0
$467$	7.19465	−	1.92780i	0.332929	−	0.0892079i	−0.0884824	−	0.996078i	$-0.528202\pi$
$467$	7.19465	−	1.92780i	0.332929	−	0.0892079i	0.421411	+	0.906870i	$0.361535\pi$
$468$		0			0
$469$	18.1030	−	10.7294i	0.835918	−	0.495437i
$470$		0			0
$471$	−1.82862	+	3.16727i	−0.0842585	+	0.145940i
$472$		0			0
$473$	17.3956	−	10.0434i	0.799851	−	0.461794i
$474$		0			0
$475$	5.12974	−	5.12974i	0.235369	−	0.235369i
$476$		0			0
$477$	−9.28539	−	9.28539i	−0.425149	−	0.425149i
$478$		0			0
$479$	20.1127	+	34.8362i	0.918972	+	1.59171i	0.800980	+	0.598691i	$0.204312\pi$
$479$	20.1127	+	34.8362i	0.918972	+	1.59171i	0.117992	+	0.993015i	$0.462354\pi$
$480$		0			0
$481$	4.35477	+	2.51423i	0.198560	+	0.114639i
$482$		0			0
$483$	2.73066	−	0.0312014i	0.124249	−	0.00141971i
$484$		0			0
$485$	−3.12542	−	11.6642i	−0.141918	−	0.529646i
$486$		0			0
$487$	20.6147	+	35.7057i	0.934142	+	1.61798i	0.776157	+	0.630540i	$0.217166\pi$
$487$	20.6147	+	35.7057i	0.934142	+	1.61798i	0.157985	+	0.987442i	$0.449500\pi$
$488$		0			0
$489$	−4.53891			−0.205257
$490$		0			0
$491$	−4.78797	−	4.78797i	−0.216078	−	0.216078i	0.590765	−	0.806843i	$-0.298826\pi$
$491$	−4.78797	−	4.78797i	−0.216078	−	0.216078i	−0.806843	+	0.590765i	$0.798826\pi$
$492$		0			0
$493$	−0.333339	−	0.0893180i	−0.0150129	−	0.00402268i
$494$		0			0
$495$	−11.7502	+	20.3520i	−0.528134	+	0.914755i
$496$		0			0
$497$	−18.7481	+	19.1815i	−0.840966	+	0.860407i
$498$		0			0
$499$	−8.52472	−	31.8147i	−0.381619	−	1.42422i	−0.843428	−	0.537242i	$-0.819466\pi$
$499$	−8.52472	−	31.8147i	−0.381619	−	1.42422i	0.461809	−	0.886979i	$-0.347201\pi$
$500$		0			0
$501$	0.0602935	+	0.0161556i	0.00269371	+	0.000721778i
$502$		0			0
$503$			10.1678i			0.453360i	0.973969	+	0.226680i	$0.0727872\pi$
$503$			10.1678i			0.453360i	−0.973969	+	0.226680i	$0.927213\pi$
$504$		0			0
$505$			5.25515i			0.233851i
$506$		0			0
$507$	0.168202	+	0.0450695i	0.00747010	+	0.00200161i
$508$		0			0
$509$	−6.77435	−	25.2822i	−0.300268	−	1.12061i	−0.936943	−	0.349483i	$-0.886357\pi$
$509$	−6.77435	−	25.2822i	−0.300268	−	1.12061i	0.636675	−	0.771132i	$-0.280309\pi$
$510$		0			0
$511$	7.40420	+	1.89355i	0.327542	+	0.0837656i
$512$		0			0
$513$	3.05930	−	5.29886i	0.135071	−	0.233950i
$514$		0			0
$515$	8.67364	+	2.32410i	0.382206	+	0.102412i
$516$		0			0
$517$	−9.93739	−	9.93739i	−0.437046	−	0.437046i
$518$		0			0
$519$	4.00055			0.175605
$520$		0			0
$521$	11.2818	+	19.5406i	0.494264	+	0.856090i	0.999978	−	0.00661081i	$-0.00210430\pi$
$521$	11.2818	+	19.5406i	0.494264	+	0.856090i	−0.505714	+	0.862701i	$0.668771\pi$
$522$		0			0
$523$	2.14641	+	8.01049i	0.0938558	+	0.350274i	0.996843	−	0.0793919i	$-0.0252978\pi$
$523$	2.14641	+	8.01049i	0.0938558	+	0.350274i	−0.902988	+	0.429666i	$0.858631\pi$
$524$		0			0
$525$	0.685152	+	0.385203i	0.0299025	+	0.0168116i
$526$		0			0
$527$	−25.7648	−	14.8753i	−1.12233	−	0.647980i
$528$		0			0
$529$	−1.16594	−	2.01946i	−0.0506930	−	0.0878028i
$530$		0			0
$531$	5.97393	+	5.97393i	0.259247	+	0.259247i
$532$		0			0
$533$	−29.5977	+	29.5977i	−1.28202	+	1.28202i
$534$		0			0
$535$	−14.5714	+	8.41278i	−0.629975	+	0.363716i
$536$		0			0
$537$	−0.993151	+	1.72019i	−0.0428576	+	0.0742316i
$538$		0			0
$539$	−28.6729	−	6.98476i	−1.23503	−	0.300855i
$540$		0			0
$541$	9.32094	−	2.49754i	0.400738	−	0.107378i	−0.0528201	−	0.998604i	$-0.516821\pi$
$541$	9.32094	−	2.49754i	0.400738	−	0.107378i	0.453558	+	0.891227i	$0.350154\pi$
$542$		0			0
$543$	−4.03878	+	2.33179i	−0.173321	+	0.100067i
$544$		0			0
$545$		−	16.6441i		−	0.712954i
$546$		0			0
$547$	−29.7649	+	29.7649i	−1.27265	+	1.27265i	−0.327965	+	0.944690i	$0.606363\pi$
$547$	−29.7649	+	29.7649i	−1.27265	+	1.27265i	−0.944690	+	0.327965i	$0.893637\pi$
$548$		0			0
$549$	4.27894	−	15.9692i	0.182621	−	0.681551i
$550$		0			0
$551$	−0.233620	−	0.134880i	−0.00995254	−	0.00574610i
$552$		0			0
$553$	16.0843	−	4.50735i	0.683972	−	0.191672i
$554$		0			0
$555$	−0.504401	+	0.135154i	−0.0214106	+	0.00573696i
$556$		0			0
$557$	−10.3052	+	38.4597i	−0.436647	+	1.62959i	0.300447	+	0.953798i	$0.402864\pi$
$557$	−10.3052	+	38.4597i	−0.436647	+	1.62959i	−0.737094	+	0.675790i	$0.763803\pi$
$558$		0			0
$559$	−17.7308			−0.749935
$560$		0			0
$561$	−5.53873			−0.233845
$562$		0			0
$563$	0.548530	−	2.04714i	0.0231178	−	0.0862768i	−0.953403	−	0.301699i	$-0.902446\pi$
$563$	0.548530	−	2.04714i	0.0231178	−	0.0862768i	0.976521	+	0.215422i	$0.0691128\pi$
$564$		0			0
$565$	−13.9052	+	3.72588i	−0.584994	+	0.156749i
$566$		0			0
$567$	−22.1036	−	5.65278i	−0.928266	−	0.237395i
$568$		0			0
$569$	−33.5719	−	19.3827i	−1.40741	−	0.812567i	−0.412270	−	0.911062i	$-0.635264\pi$
$569$	−33.5719	−	19.3827i	−1.40741	−	0.812567i	−0.995138	+	0.0984951i	$0.968597\pi$
$570$		0			0
$571$	−0.0502427	+	0.187508i	−0.00210259	+	0.00784698i	−0.966969	−	0.254893i	$-0.917960\pi$
$571$	−0.0502427	+	0.187508i	−0.00210259	+	0.00784698i	0.964867	+	0.262740i	$0.0846263\pi$
$572$		0			0
$573$	2.45570	−	2.45570i	0.102588	−	0.102588i
$574$		0			0
$575$		−	7.29124i		−	0.304066i
$576$		0			0
$577$	−11.9483	+	6.89836i	−0.497415	+	0.287182i	−0.727645	−	0.685954i	$-0.759385\pi$
$577$	−11.9483	+	6.89836i	−0.497415	+	0.287182i	0.230231	+	0.973136i	$0.426052\pi$
$578$		0			0
$579$	3.50008	−	0.937845i	0.145459	−	0.0389755i
$580$		0			0
$581$	−20.0719	+	0.229348i	−0.832724	+	0.00951498i
$582$		0			0
$583$	−9.35806	+	16.2086i	−0.387571	+	0.671293i
$584$		0			0
$585$	17.9650	−	10.3721i	0.742762	−	0.428834i
$586$		0			0
$587$	6.91792	−	6.91792i	0.285533	−	0.285533i	−0.549778	−	0.835311i	$-0.685288\pi$
$587$	6.91792	−	6.91792i	0.285533	−	0.285533i	0.835311	+	0.549778i	$0.185288\pi$
$588$		0			0
$589$	−16.4444	−	16.4444i	−0.677579	−	0.677579i
$590$		0			0
$591$	0.423987	+	0.734366i	0.0174405	+	0.0302078i
$592$		0			0
$593$	2.83209	+	1.63511i	0.116300	+	0.0671458i	0.557022	−	0.830498i	$-0.311944\pi$
$593$	2.83209	+	1.63511i	0.116300	+	0.0671458i	−0.440722	+	0.897644i	$0.645277\pi$
$594$		0			0
$595$	0.364947	+	31.9391i	0.0149614	+	1.30938i
$596$		0			0
$597$	−0.193137	−	0.720796i	−0.00790456	−	0.0295002i
$598$		0			0
$599$	−4.92332	−	8.52744i	−0.201161	−	0.348422i	0.747741	−	0.663990i	$-0.231138\pi$
$599$	−4.92332	−	8.52744i	−0.201161	−	0.348422i	−0.948903	+	0.315568i	$0.897805\pi$
$600$		0			0
$601$	15.8611			0.646986			0.323493	−	0.946230i	$-0.395143\pi$
$601$	15.8611			0.646986			0.323493	+	0.946230i	$0.395143\pi$
$602$		0			0
$603$	−16.6360	−	16.6360i	−0.677470	−	0.677470i
$604$		0			0
$605$	12.3304	+	3.30392i	0.501301	+	0.134323i
$606$		0			0
$607$	22.0856	−	38.2533i	0.896425	−	1.55265i	0.0643943	−	0.997925i	$-0.479488\pi$
$607$	22.0856	−	38.2533i	0.896425	−	1.55265i	0.832031	−	0.554729i	$-0.187178\pi$
$608$		0			0
$609$	0.00724168	−	0.0283166i	0.000293448	−	0.00114745i
$610$		0			0
$611$	3.21073	+	11.9826i	0.129892	+	0.484764i
$612$		0			0
$613$	25.9269	+	6.94710i	1.04718	+	0.280591i	0.741085	−	0.671411i	$-0.234311\pi$
$613$	25.9269	+	6.94710i	1.04718	+	0.280591i	0.306093	+	0.952002i	$0.400978\pi$
$614$		0			0
$615$		−	4.34681i		−	0.175280i
$616$		0			0
$617$			26.5771i			1.06995i	0.844867	+	0.534977i	$0.179680\pi$
$617$			26.5771i			1.06995i	−0.844867	+	0.534977i	$0.820320\pi$
$618$		0			0
$619$	34.5211	+	9.24990i	1.38752	+	0.371785i	0.873847	−	0.486201i	$-0.161618\pi$
$619$	34.5211	+	9.24990i	1.38752	+	0.371785i	0.513673	+	0.857986i	$0.328284\pi$
$620$		0			0
$621$	−1.59162	−	5.94000i	−0.0638694	−	0.238364i
$622$		0			0
$623$	−1.27098	−	4.53543i	−0.0509208	−	0.181708i
$624$		0			0
$625$	−7.82903	+	13.5603i	−0.313161	+	0.542411i
$626$		0			0
$627$	−4.18206	−	1.12058i	−0.167015	−	0.0447516i
$628$		0			0
$629$	6.12090	+	6.12090i	0.244056	+	0.244056i
$630$		0			0
$631$	−30.1246			−1.19924			−0.599622	−	0.800284i	$-0.704682\pi$
$631$	−30.1246			−1.19924			−0.599622	+	0.800284i	$0.704682\pi$
$632$		0			0
$633$	−0.794426	−	1.37599i	−0.0315756	−	0.0546905i
$634$		0			0
$635$	2.64245	+	9.86175i	0.104862	+	0.391352i
$636$		0			0
$637$	18.8363	+	17.9945i	0.746321	+	0.712968i
$638$		0			0
$639$	25.9694	+	14.9935i	1.02734	+	0.593132i
$640$		0			0
$641$	9.49750	+	16.4501i	0.375129	+	0.649742i	0.990346	−	0.138616i	$-0.0442652\pi$
$641$	9.49750	+	16.4501i	0.375129	+	0.649742i	−0.615218	+	0.788357i	$0.710932\pi$
$642$		0			0
$643$	−10.7261	−	10.7261i	−0.422996	−	0.422996i	0.463238	−	0.886234i	$-0.346688\pi$
$643$	−10.7261	−	10.7261i	−0.422996	−	0.422996i	−0.886234	+	0.463238i	$0.846688\pi$
$644$		0			0
$645$	1.30200	−	1.30200i	0.0512663	−	0.0512663i
$646$		0			0
$647$	14.9430	−	8.62736i	0.587471	−	0.339177i	−0.176626	−	0.984278i	$-0.556518\pi$
$647$	14.9430	−	8.62736i	0.587471	−	0.339177i	0.764097	+	0.645101i	$0.223185\pi$
$648$		0			0
$649$	6.02069	−	10.4281i	0.236333	−	0.409341i
$650$		0			0
$651$	1.23484	−	2.19639i	0.0483973	−	0.0860833i
$652$		0			0
$653$	−23.8690	+	6.39567i	−0.934065	+	0.250282i	−0.693587	−	0.720372i	$-0.743971\pi$
$653$	−23.8690	+	6.39567i	−0.934065	+	0.250282i	−0.240478	+	0.970655i	$0.577304\pi$
$654$		0			0
$655$	16.3666	−	9.44925i	0.639495	−	0.369213i
$656$		0			0
$657$		−	8.54429i		−	0.333344i
$658$		0			0
$659$	−30.2881	+	30.2881i	−1.17986	+	1.17986i	−0.200079	+	0.979780i	$0.564120\pi$
$659$	−30.2881	+	30.2881i	−1.17986	+	1.17986i	−0.979780	+	0.200079i	$0.935880\pi$
$660$		0			0
$661$	−7.57588	+	28.2736i	−0.294668	+	1.09971i	0.646813	+	0.762648i	$0.276101\pi$
$661$	−7.57588	+	28.2736i	−0.294668	+	1.09971i	−0.941481	+	0.337066i	$0.890565\pi$
$662$		0			0
$663$	4.23410	+	2.44456i	0.164439	+	0.0949388i
$664$		0			0
$665$	−6.18628	+	24.1897i	−0.239894	+	0.938037i
$666$		0			0
$667$	−0.261887	+	0.0701723i	−0.0101403	+	0.00271708i
$668$		0			0
$669$	−1.03300	+	3.85521i	−0.0399381	+	0.149051i
$670$		0			0
$671$	−23.5636			−0.909662
$672$		0			0
$673$	−15.2355			−0.587285			−0.293643	−	0.955915i	$-0.594868\pi$
$673$	−15.2355			−0.587285			−0.293643	+	0.955915i	$0.594868\pi$
$674$		0			0
$675$	0.458113	−	1.70970i	0.0176328	−	0.0658065i
$676$		0			0
$677$	14.6120	−	3.91529i	0.561587	−	0.150477i	0.0331514	−	0.999450i	$-0.489446\pi$
$677$	14.6120	−	3.91529i	0.561587	−	0.150477i	0.528435	+	0.848974i	$0.322779\pi$
$678$		0			0
$679$	−12.1243	−	11.8504i	−0.465288	−	0.454775i
$680$		0			0
$681$	−2.26780	−	1.30932i	−0.0869024	−	0.0501731i
$682$		0			0
$683$	−1.13536	+	4.23720i	−0.0434432	+	0.162132i	−0.984240	−	0.176840i	$-0.943413\pi$
$683$	−1.13536	+	4.23720i	−0.0434432	+	0.162132i	0.940796	+	0.338972i	$0.110079\pi$
$684$		0			0
$685$	3.09606	−	3.09606i	0.118294	−	0.118294i
$686$		0			0
$687$		−	5.22387i		−	0.199303i
$688$		0			0
$689$	14.3076	−	8.26050i	0.545076	−	0.314700i
$690$		0			0
$691$	43.1477	−	11.5614i	1.64142	−	0.439816i	0.684225	−	0.729271i	$-0.260141\pi$
$691$	43.1477	−	11.5614i	1.64142	−	0.439816i	0.957192	+	0.289455i	$0.0934741\pi$
$692$		0			0
$693$	0.376971	+	32.9915i	0.0143200	+	1.25324i
$694$		0			0
$695$	16.4280	−	28.4542i	0.623151	−	1.07933i
$696$		0			0
$697$	−62.4022	+	36.0279i	−2.36365	+	1.36465i
$698$		0			0
$699$	−0.168225	+	0.168225i	−0.00636285	+	0.00636285i
$700$		0			0
$701$	−14.3674	−	14.3674i	−0.542648	−	0.542648i	0.381656	−	0.924304i	$-0.375354\pi$
$701$	−14.3674	−	14.3674i	−0.542648	−	0.542648i	−0.924304	+	0.381656i	$0.875354\pi$
$702$		0			0
$703$	3.38327	+	5.85999i	0.127602	+	0.221014i
$704$		0			0
$705$	−1.11567	−	0.644132i	−0.0420185	−	0.0242594i
$706$		0			0
$707$	3.76176	+	6.34697i	0.141476	+	0.238702i
$708$		0			0
$709$	6.31364	+	23.5628i	0.237114	+	0.884921i	0.977185	+	0.212392i	$0.0681253\pi$
$709$	6.31364	+	23.5628i	0.237114	+	0.884921i	−0.740071	+	0.672529i	$0.765208\pi$
$710$		0			0
$711$	−9.33745	−	16.1729i	−0.350182	−	0.606533i
$712$		0			0
$713$	−23.3735			−0.875344
$714$		0			0
$715$	−20.9066	−	20.9066i	−0.781862	−	0.781862i
$716$		0			0
$717$	−3.32455	−	0.890810i	−0.124158	−	0.0332679i
$718$		0			0
$719$	−12.8743	+	22.2990i	−0.480131	+	0.831612i	−0.999740	−	0.0227924i	$-0.992744\pi$
$719$	−12.8743	+	22.2990i	−0.480131	+	0.831612i	0.519609	+	0.854404i	$0.326078\pi$
$720$		0			0
$721$	12.1393	−	3.40185i	0.452092	−	0.126691i
$722$		0			0
$723$	−1.47803	−	5.51610i	−0.0549687	−	0.205146i
$724$		0			0
$725$	−0.0753785	−	0.0201976i	−0.00279949	−	0.000750120i
$726$		0			0
$727$		−	22.1198i		−	0.820379i	−0.912000	−	0.410189i	$-0.865463\pi$
$727$		−	22.1198i		−	0.820379i	0.912000	−	0.410189i	$-0.134537\pi$
$728$		0			0
$729$			24.7554i			0.916868i
$730$		0			0
$731$	−29.4828	−	7.89989i	−1.09046	−	0.292188i
$732$		0			0
$733$	3.93153	+	14.6727i	0.145215	+	0.541948i	0.999746	+	0.0225480i	$0.00717786\pi$
$733$	3.93153	+	14.6727i	0.145215	+	0.541948i	−0.854531	+	0.519400i	$0.826155\pi$
$734$		0			0
$735$	−2.70454	+	0.0618140i	−0.0997584	+	0.00228004i
$736$		0			0
$737$	−16.7662	+	29.0399i	−0.617591	+	1.06970i
$738$		0			0
$739$	13.0301	+	3.49139i	0.479318	+	0.128433i	0.490385	−	0.871506i	$-0.336856\pi$
$739$	13.0301	+	3.49139i	0.479318	+	0.128433i	−0.0110668	+	0.999939i	$0.503523\pi$
$740$		0			0
$741$	2.70241	+	2.70241i	0.0992756	+	0.0992756i
$742$		0			0
$743$	−3.36537			−0.123463			−0.0617317	−	0.998093i	$-0.519662\pi$
$743$	−3.36537			−0.123463			−0.0617317	+	0.998093i	$0.519662\pi$
$744$		0			0
$745$	−22.0602	−	38.2093i	−0.808221	−	1.39988i
$746$		0			0
$747$	5.80837	+	21.6771i	0.212517	+	0.793125i
$748$		0			0
$749$	−11.5767	+	20.5912i	−0.423002	+	0.752385i
$750$		0			0
$751$	45.7638	+	26.4217i	1.66994	+	0.964143i	0.967664	+	0.252243i	$0.0811681\pi$
$751$	45.7638	+	26.4217i	1.66994	+	0.964143i	0.702281	+	0.711900i	$0.252165\pi$
$752$		0			0
$753$	0.943981	+	1.63502i	0.0344006	+	0.0595836i
$754$		0			0
$755$	6.23301	+	6.23301i	0.226842	+	0.226842i
$756$		0			0
$757$	16.0570	−	16.0570i	0.583603	−	0.583603i	−0.352289	−	0.935891i	$-0.614596\pi$
$757$	16.0570	−	16.0570i	0.583603	−	0.583603i	0.935891	+	0.352289i	$0.114596\pi$
$758$		0			0
$759$	−3.76849	+	2.17574i	−0.136788	+	0.0789744i
$760$		0			0
$761$	14.6707	−	25.4105i	0.531814	−	0.921129i	−0.467496	−	0.883995i	$-0.654844\pi$
$761$	14.6707	−	25.4105i	0.531814	−	0.921129i	0.999310	−	0.0371337i	$-0.0118227\pi$
$762$		0			0
$763$	−11.9142	−	20.1021i	−0.431324	−	0.727744i
$764$		0			0
$765$	34.4934	−	9.24249i	1.24711	−	0.334163i
$766$		0			0
$767$	−9.20508	+	5.31455i	−0.332376	+	0.191897i
$768$		0			0
$769$		−	38.0004i		−	1.37033i	−0.728388	−	0.685165i	$-0.759730\pi$
$769$		−	38.0004i		−	1.37033i	0.728388	−	0.685165i	$-0.240270\pi$
$770$		0			0
$771$	−1.28561	+	1.28561i	−0.0463000	+	0.0463000i
$772$		0			0
$773$	−0.283872	+	1.05943i	−0.0102102	+	0.0381049i	−0.970843	−	0.239716i	$-0.922946\pi$
$773$	−0.283872	+	1.05943i	−0.0102102	+	0.0381049i	0.960633	+	0.277821i	$0.0896123\pi$
$774$		0			0
$775$	−5.82623	−	3.36378i	−0.209285	−	0.120830i
$776$		0			0
$777$	−0.512449	+	0.524295i	−0.0183840	+	0.0188090i
$778$		0			0
$779$	−54.4063	+	14.5781i	−1.94931	+	0.522315i
$780$		0			0
$781$	11.0619	−	41.2835i	0.395826	−	1.47724i
$782$		0			0
$783$	−0.0658181			−0.00235215
$784$		0			0
$785$	−33.6076			−1.19951
$786$		0			0
$787$	−11.7363	+	43.8003i	−0.418352	+	1.56131i	0.359673	+	0.933078i	$0.382888\pi$
$787$	−11.7363	+	43.8003i	−0.418352	+	1.56131i	−0.778025	+	0.628233i	$0.783778\pi$
$788$		0			0
$789$	1.13864	−	0.305099i	0.0405368	−	0.0108618i
$790$		0			0
$791$	−14.1270	+	14.4536i	−0.502300	+	0.513911i
$792$		0			0
$793$	18.0133	+	10.4000i	0.639670	+	0.369313i
$794$		0			0
$795$	−0.444048	+	1.65721i	−0.0157488	+	0.0587751i
$796$		0			0
$797$	30.1973	−	30.1973i	1.06964	−	1.06964i	0.0722560	−	0.997386i	$-0.476980\pi$
$797$	30.1973	−	30.1973i	1.06964	−	1.06964i	0.997386	−	0.0722560i	$-0.0230199\pi$
$798$		0			0
$799$			21.3552i			0.755492i
$800$		0			0
$801$	−4.56044	+	2.63297i	−0.161135	+	0.0930315i
$802$		0			0
$803$	−11.7631	+	3.15190i	−0.415110	+	0.111228i
$804$		0			0
$805$	12.7947	+	21.5877i	0.450955	+	0.760866i
$806$		0			0
$807$	−0.666710	+	1.15477i	−0.0234693	+	0.0406500i
$808$		0			0
$809$	3.60521	−	2.08147i	0.126753	−	0.0731806i	−0.435283	−	0.900294i	$-0.643352\pi$
$809$	3.60521	−	2.08147i	0.126753	−	0.0731806i	0.562036	+	0.827113i	$0.310018\pi$
$810$		0			0
$811$	−12.2223	+	12.2223i	−0.429182	+	0.429182i	−0.888350	−	0.459168i	$-0.848148\pi$
$811$	−12.2223	+	12.2223i	−0.429182	+	0.429182i	0.459168	+	0.888350i	$0.348148\pi$
$812$		0			0
$813$	3.68523	+	3.68523i	0.129247	+	0.129247i
$814$		0			0
$815$	−20.8547	−	36.1215i	−0.730510	−	1.26528i
$816$		0			0
$817$	−20.6629	−	11.9297i	−0.722904	−	0.417369i
$818$		0			0
$819$	14.2728	−	25.3868i	0.498734	−	0.887087i
$820$		0			0
$821$	−5.07820	−	18.9521i	−0.177230	−	0.661433i	−0.996161	−	0.0875401i	$-0.972099\pi$
$821$	−5.07820	−	18.9521i	−0.177230	−	0.661433i	0.818931	−	0.573892i	$-0.194567\pi$
$822$		0			0
$823$	2.27906	+	3.94745i	0.0794431	+	0.137599i	0.903010	−	0.429620i	$-0.141352\pi$
$823$	2.27906	+	3.94745i	0.0794431	+	0.137599i	−0.823567	+	0.567219i	$0.808019\pi$
$824$		0			0
$825$	−1.25248			−0.0436058
$826$		0			0
$827$	36.4309	+	36.4309i	1.26683	+	1.26683i	0.947718	+	0.319110i	$0.103384\pi$
$827$	36.4309	+	36.4309i	1.26683	+	1.26683i	0.319110	+	0.947718i	$0.396616\pi$
$828$		0			0
$829$	−18.3008	−	4.90369i	−0.635614	−	0.170312i	−0.0733979	−	0.997303i	$-0.523384\pi$
$829$	−18.3008	−	4.90369i	−0.635614	−	0.170312i	−0.562216	+	0.826991i	$0.690051\pi$
$830$		0			0
$831$	−0.938551	+	1.62562i	−0.0325580	+	0.0563921i
$832$		0			0
$833$	23.3036	+	38.3136i	0.807421	+	1.32749i
$834$		0			0
$835$	0.148459	+	0.554056i	0.00513763	+	0.0191739i
$836$		0			0
$837$	−5.48078	−	1.46857i	−0.189444	−	0.0507613i
$838$		0			0
$839$			2.08923i			0.0721282i	0.999349	+	0.0360641i	$0.0114820\pi$
$839$			2.08923i			0.0721282i	−0.999349	+	0.0360641i	$0.988518\pi$
$840$		0			0
$841$		−	28.9971i		−	0.999900i
$842$		0			0
$843$	1.66459	+	0.446027i	0.0573317	+	0.0153620i
$844$		0			0
$845$	0.414158	+	1.54566i	0.0142475	+	0.0531723i
$846$		0			0
$847$	17.2572	−	4.83604i	0.592963	−	0.166168i
$848$		0			0
$849$	2.56563	−	4.44380i	0.0880522	−	0.152511i
$850$		0			0
$851$	6.56902	+	1.76016i	0.225183	+	0.0603377i
$852$		0			0
$853$	−21.1594	−	21.1594i	−0.724483	−	0.724483i	0.245032	−	0.969515i	$-0.421202\pi$
$853$	−21.1594	−	21.1594i	−0.724483	−	0.724483i	−0.969515	+	0.245032i	$0.921202\pi$
$854$		0			0
$855$	27.9144			0.954653
$856$		0			0
$857$	−16.2012	−	28.0613i	−0.553422	−	0.958556i	−0.998024	−	0.0628275i	$-0.979988\pi$
$857$	−16.2012	−	28.0613i	−0.553422	−	0.958556i	0.444602	−	0.895728i	$-0.353345\pi$
$858$		0			0
$859$	4.82768	+	18.0172i	0.164718	+	0.614737i	0.998076	+	0.0620031i	$0.0197489\pi$
$859$	4.82768	+	18.0172i	0.164718	+	0.614737i	−0.833358	+	0.552734i	$0.813584\pi$
$860$		0			0
$861$	−3.11155	−	5.24991i	−0.106041	−	0.178916i
$862$		0			0
$863$	−29.8328	−	17.2240i	−1.01552	−	0.586312i	−0.102718	−	0.994711i	$-0.532754\pi$
$863$	−29.8328	−	17.2240i	−1.01552	−	0.586312i	−0.912804	+	0.408399i	$0.866087\pi$
$864$		0			0
$865$	18.3812	+	31.8371i	0.624979	+	1.08250i
$866$		0			0
$867$	3.48612	+	3.48612i	0.118395	+	0.118395i
$868$		0			0
$869$	−18.8211	+	18.8211i	−0.638461	+	0.638461i
$870$		0			0
$871$	25.6339	−	14.7998i	0.868573	−	0.501471i
$872$		0			0
$873$	−9.47712	+	16.4149i	−0.320752	+	0.555559i
$874$		0			0
$875$	0.367361	+	32.1504i	0.0124191	+	1.08688i
$876$		0			0
$877$	48.3882	−	12.9656i	1.63395	−	0.437817i	0.678896	−	0.734234i	$-0.262459\pi$
$877$	48.3882	−	12.9656i	1.63395	−	0.437817i	0.955058	+	0.296418i	$0.0957920\pi$
$878$		0			0
$879$	3.83162	−	2.21218i	0.129237	−	0.0746151i
$880$		0			0
$881$		−	41.5279i		−	1.39911i	−0.714578	−	0.699556i	$-0.753381\pi$
$881$		−	41.5279i		−	1.39911i	0.714578	−	0.699556i	$-0.246619\pi$
$882$		0			0
$883$	19.0558	−	19.0558i	0.641278	−	0.641278i	−0.309591	−	0.950870i	$-0.600192\pi$
$883$	19.0558	−	19.0558i	0.641278	−	0.641278i	0.950870	+	0.309591i	$0.100192\pi$
$884$		0			0
$885$	0.285687	−	1.06620i	0.00960326	−	0.0358398i
$886$		0			0
$887$	38.2027	+	22.0563i	1.28272	+	0.740579i	0.977345	−	0.211653i	$-0.0678847\pi$
$887$	38.2027	+	22.0563i	1.28272	+	0.740579i	0.305375	+	0.952232i	$0.401218\pi$
$888$		0			0
$889$	10.2507	+	10.0191i	0.343798	+	0.336030i
$890$		0			0
$891$	35.1161	−	9.40934i	1.17643	−	0.315225i
$892$		0			0
$893$	−4.32051	+	16.1244i	−0.144580	+	0.539582i
$894$		0			0
$895$	−18.2528			−0.610122
$896$		0			0
$897$	3.84112			0.128251
$898$		0			0
$899$	−0.0647474	+	0.241640i	−0.00215945	+	0.00805916i
$900$		0			0
$901$	27.4711	−	7.36085i	0.915194	−	0.245225i
$902$		0			0
$903$	0.640503	−	2.50451i	0.0213146	−	0.0833449i
$904$		0			0
$905$	−37.1137	−	21.4276i	−1.23370	−	0.712277i
$906$		0			0
$907$	6.90744	−	25.7789i	0.229358	−	0.855975i	−0.751254	−	0.660013i	$-0.770551\pi$
$907$	6.90744	−	25.7789i	0.229358	−	0.855975i	0.980612	−	0.195962i	$-0.0627828\pi$
$908$		0			0
$909$	5.83263	−	5.83263i	0.193456	−	0.193456i
$910$		0			0
$911$		−	12.2217i		−	0.404921i	−0.979290	−	0.202461i	$-0.935106\pi$
$911$		−	12.2217i		−	0.404921i	0.979290	−	0.202461i	$-0.0648939\pi$
$912$		0			0
$913$	27.7006	−	15.9930i	0.916758	−	0.529290i
$914$		0			0
$915$	−2.08642	+	0.559056i	−0.0689751	+	0.0184818i
$916$		0			0
$917$	13.0029	−	23.1280i	0.429394	−	0.763754i
$918$		0			0
$919$	21.4822	−	37.2082i	0.708632	−	1.22739i	−0.256733	−	0.966482i	$-0.582646\pi$
$919$	21.4822	−	37.2082i	0.708632	−	1.22739i	0.965365	−	0.260904i	$-0.0840207\pi$
$920$		0			0
$921$	1.87591	−	1.08306i	0.0618133	−	0.0356879i
$922$		0			0
$923$	−26.6771	+	26.6771i	−0.878087	+	0.878087i
$924$		0			0
$925$	1.38413	+	1.38413i	0.0455098	+	0.0455098i
$926$		0			0
$927$	−7.04728	−	12.2063i	−0.231463	−	0.400906i
$928$		0			0
$929$	−4.52009	−	2.60967i	−0.148299	−	0.0856206i	0.424014	−	0.905655i	$-0.360621\pi$
$929$	−4.52009	−	2.60967i	−0.148299	−	0.0856206i	−0.572314	+	0.820035i	$0.693954\pi$
$930$		0			0
$931$	9.84403	+	33.6437i	0.322625	+	1.10263i
$932$		0			0
$933$	−0.320363	−	1.19561i	−0.0104882	−	0.0391425i
$934$		0			0
$935$	−25.4486	−	44.0782i	−0.832258	−	1.44151i
$936$		0			0
$937$	14.3484			0.468741			0.234371	−	0.972147i	$-0.424697\pi$
$937$	14.3484			0.468741			0.234371	+	0.972147i	$0.424697\pi$
$938$		0			0
$939$	−1.78450	−	1.78450i	−0.0582350	−	0.0582350i
$940$		0			0
$941$	8.19041	+	2.19461i	0.267000	+	0.0715424i	0.389835	−	0.920885i	$-0.372532\pi$
$941$	8.19041	+	2.19461i	0.267000	+	0.0715424i	−0.122835	+	0.992427i	$0.539199\pi$
$942$		0			0
$943$	−28.3052	+	49.0260i	−0.921743	+	1.59651i
$944$		0			0
$945$	1.64383	+	5.86594i	0.0534739	+	0.190819i
$946$		0			0
$947$	−9.79481	−	36.5547i	−0.318289	−	1.18787i	−0.920889	−	0.389826i	$-0.872535\pi$
$947$	−9.79481	−	36.5547i	−0.318289	−	1.18787i	0.602600	−	0.798043i	$-0.294131\pi$
$948$		0			0
$949$	10.3834	+	2.78223i	0.337060	+	0.0903151i
$950$		0			0
$951$		−	1.47609i		−	0.0478654i
$952$		0			0
$953$		−	11.7422i		−	0.380366i	−0.981749	−	0.190183i	$-0.939092\pi$
$953$		−	11.7422i		−	0.380366i	0.981749	−	0.190183i	$-0.0609081\pi$
$954$		0			0
$955$	30.8260	+	8.25980i	0.997506	+	0.267281i
$956$		0			0
$957$	0.0120541	+	0.0449866i	0.000389655	+	0.00145421i
$958$		0			0
$959$	1.52307	−	5.95553i	0.0491824	−	0.192314i
$960$		0			0
$961$	4.71675	−	8.16965i	0.152153	−	0.263537i
$962$		0			0
$963$	25.5098	+	6.83534i	0.822043	+	0.220266i
$964$		0			0
$965$	23.5452	+	23.5452i	0.757948	+	0.757948i
$966$		0			0
$967$	−1.75678			−0.0564941			−0.0282471	−	0.999601i	$-0.508993\pi$
$967$	−1.75678			−0.0564941			−0.0282471	+	0.999601i	$0.508993\pi$
$968$		0			0
$969$	3.28952	+	5.69761i	0.105675	+	0.183034i
$970$		0			0
$971$	−13.9288	−	51.9831i	−0.446997	−	1.66822i	−0.710608	−	0.703588i	$-0.751580\pi$
$971$	−13.9288	−	51.9831i	−0.446997	−	1.66822i	0.263611	−	0.964629i	$-0.415087\pi$
$972$		0			0
$973$	−0.527044	−	46.1254i	−0.0168963	−	1.47871i
$974$		0			0
$975$	0.957463	+	0.552792i	0.0306634	+	0.0177035i
$976$		0			0
$977$	−10.4704	−	18.1353i	−0.334979	−	0.580200i	0.648502	−	0.761213i	$-0.275396\pi$
$977$	−10.4704	−	18.1353i	−0.334979	−	0.580200i	−0.983481	+	0.181013i	$0.942062\pi$
$978$		0			0
$979$	5.30716	+	5.30716i	0.169618	+	0.169618i
$980$		0			0
$981$	−18.4731	+	18.4731i	−0.589800	+	0.589800i
$982$		0			0
$983$	32.9818	−	19.0420i	1.05195	−	0.607346i	0.128759	−	0.991676i	$-0.458901\pi$
$983$	32.9818	−	19.0420i	1.05195	−	0.607346i	0.923196	+	0.384330i	$0.125567\pi$
$984$		0			0
$985$	−3.89615	+	6.74833i	−0.124142	+	0.215020i
$986$		0			0
$987$	−1.80855	+	0.0206650i	−0.0575667	+	0.000657776i
$988$		0			0
$989$	−23.1630	+	6.20652i	−0.736542	+	0.197356i
$990$		0			0
$991$	15.0146	−	8.66867i	0.476954	−	0.275369i	−0.242192	−	0.970228i	$-0.577867\pi$
$991$	15.0146	−	8.66867i	0.476954	−	0.275369i	0.719146	+	0.694859i	$0.244533\pi$
$992$		0			0
$993$			1.59142i			0.0505021i
$994$		0			0
$995$	4.84883	−	4.84883i	0.153718	−	0.153718i
$996$		0			0
$997$	1.58580	−	5.91830i	0.0502229	−	0.187434i	−0.936257	−	0.351315i	$-0.885735\pi$
$997$	1.58580	−	5.91830i	0.0502229	−	0.187434i	0.986480	+	0.163881i	$0.0524012\pi$
$998$		0			0
$999$	1.42976	+	0.825472i	0.0452356	+	0.0261168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.z.a.47.6		56
4.3	odd	2		112.2.v.a.19.11	yes	56
7.3	odd	6	inner	448.2.z.a.367.6		56
8.3	odd	2		896.2.z.b.607.6		56
8.5	even	2		896.2.z.a.607.9		56
16.3	odd	4		896.2.z.a.159.9		56
16.5	even	4		112.2.v.a.75.9	yes	56
16.11	odd	4	inner	448.2.z.a.271.6		56
16.13	even	4		896.2.z.b.159.6		56
28.3	even	6		112.2.v.a.3.9	✓	56
28.11	odd	6		784.2.w.f.227.9		56
28.19	even	6		784.2.j.a.195.3		56
28.23	odd	6		784.2.j.a.195.4		56
28.27	even	2		784.2.w.f.19.11		56
56.3	even	6		896.2.z.b.479.6		56
56.45	odd	6		896.2.z.a.479.9		56
112.3	even	12		896.2.z.a.31.9		56
112.5	odd	12		784.2.j.a.587.4		56
112.37	even	12		784.2.j.a.587.3		56
112.45	odd	12		896.2.z.b.31.6		56
112.53	even	12		784.2.w.f.619.11		56
112.59	even	12	inner	448.2.z.a.143.6		56
112.69	odd	4		784.2.w.f.411.9		56
112.101	odd	12		112.2.v.a.59.11	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.9	✓	56	28.3	even	6
112.2.v.a.19.11	yes	56	4.3	odd	2
112.2.v.a.59.11	yes	56	112.101	odd	12
112.2.v.a.75.9	yes	56	16.5	even	4
448.2.z.a.47.6		56	1.1	even	1	trivial
448.2.z.a.143.6		56	112.59	even	12	inner
448.2.z.a.271.6		56	16.11	odd	4	inner
448.2.z.a.367.6		56	7.3	odd	6	inner
784.2.j.a.195.3		56	28.19	even	6
784.2.j.a.195.4		56	28.23	odd	6
784.2.j.a.587.3		56	112.37	even	12
784.2.j.a.587.4		56	112.5	odd	12
784.2.w.f.19.11		56	28.27	even	2
784.2.w.f.227.9		56	28.11	odd	6
784.2.w.f.411.9		56	112.69	odd	4
784.2.w.f.619.11		56	112.53	even	12
896.2.z.a.31.9		56	112.3	even	12
896.2.z.a.159.9		56	16.3	odd	4
896.2.z.a.479.9		56	56.45	odd	6
896.2.z.a.607.9		56	8.5	even	2
896.2.z.b.31.6		56	112.45	odd	12
896.2.z.b.159.6		56	16.13	even	4
896.2.z.b.479.6		56	56.3	even	6
896.2.z.b.607.6		56	8.3	odd	2

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0530773 + 0.198087i) q^{3} +(-1.82029 + 0.487744i) q^{5} +(-1.84933 + 1.89208i) q^{7} +(2.56165 + 1.47897i) q^{9} +O(q^{10})\)	\(q+(-0.0530773 + 0.198087i) q^{3} +(-1.82029 + 0.487744i) q^{5} +(-1.84933 + 1.89208i) q^{7} +(2.56165 + 1.47897i) q^{9} +(1.09116 - 4.07225i) q^{11} +(-2.63146 + 2.63146i) q^{13} -0.386464i q^{15} +(-5.54801 + 3.20315i) q^{17} +(-4.83712 + 1.29610i) q^{19} +(-0.276640 - 0.466755i) q^{21} +(-2.51654 + 4.35877i) q^{23} +(-1.25458 + 0.724332i) q^{25} +(-0.863961 + 0.863961i) q^{27} +(0.0380909 + 0.0380909i) q^{29} +(2.32199 + 4.02180i) q^{31} +(0.748746 + 0.432288i) q^{33} +(2.44346 - 4.34613i) q^{35} +(-0.349719 - 1.30517i) q^{37} +(-0.381587 - 0.660929i) q^{39} +11.2477 q^{41} +(3.36902 + 3.36902i) q^{43} +(-5.38431 - 1.44272i) q^{45} +(1.66673 - 2.88687i) q^{47} +(-0.159948 - 6.99817i) q^{49} +(-0.340029 - 1.26900i) q^{51} +(-4.28814 - 1.14900i) q^{53} +7.94487i q^{55} -1.02696i q^{57} +(2.75886 + 0.739234i) q^{59} +(-1.44659 - 5.39876i) q^{61} +(-7.53568 + 2.11175i) q^{63} +(3.50653 - 6.07348i) q^{65} +(-7.68276 - 2.05859i) q^{67} +(-0.729846 - 0.729846i) q^{69} +10.1378 q^{71} +(-1.44429 - 2.50159i) q^{73} +(-0.0768912 - 0.286962i) q^{75} +(5.68713 + 9.59550i) q^{77} +(-5.46763 - 3.15674i) q^{79} +(4.31163 + 7.46797i) q^{81} +(5.36480 + 5.36480i) q^{83} +(8.53665 - 8.53665i) q^{85} +(-0.00956708 + 0.00552356i) q^{87} +(-0.890135 + 1.54176i) q^{89} +(-0.112496 - 9.84537i) q^{91} +(-0.919912 + 0.246490i) q^{93} +(8.17277 - 4.71855i) q^{95} +6.40791i q^{97} +(8.81792 - 8.81792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7}+O(q^{10}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7	\( 56 q + 6 q^{3} - 6 q^{5} + 8 q^{7} - 2 q^{11} - 12 q^{17} + 6 q^{19} - 10 q^{21} + 12 q^{23} - 24 q^{29} - 12 q^{33} + 2 q^{35} + 6 q^{37} + 4 q^{39} + 12 q^{45} - 8 q^{49} + 34 q^{51} + 6 q^{53} - 42 q^{59} - 6 q^{61} - 4 q^{65} - 6 q^{67} + 80 q^{71} - 24 q^{75} + 10 q^{77} - 8 q^{81} - 28 q^{85} + 12 q^{87} - 16 q^{91} + 10 q^{93} + 16 q^{99}+O(q^{100}) \) 56 * q + 6 * q^3 - 6 * q^5 + 8 * q^7 - 2 * q^11 - 12 * q^17 + 6 * q^19 - 10 * q^21 + 12 * q^23 - 24 * q^29 - 12 * q^33 + 2 * q^35 + 6 * q^37 + 4 * q^39 + 12 * q^45 - 8 * q^49 + 34 * q^51 + 6 * q^53 - 42 * q^59 - 6 * q^61 - 4 * q^65 - 6 * q^67 + 80 * q^71 - 24 * q^75 + 10 * q^77 - 8 * q^81 - 28 * q^85 + 12 * q^87 - 16 * q^91 + 10 * q^93 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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