LMFDB - Embedded newform 980.2.x.k.263.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(67,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("980.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.6
Character	$\chi$	$=$	980.263
Dual form			980.2.x.k.667.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.788610 + 1.17392i) q^{2} +(0.767216 + 2.86329i) q^{3} +(-0.756188 - 1.85153i) q^{4} +(0.517671 + 2.17532i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(2.76990 + 0.572433i) q^{8} +(-5.01173 + 2.89352i) q^{9} +O(q^{10})$	\(q+(-0.788610 + 1.17392i) q^{2} +(0.767216 + 2.86329i) q^{3} +(-0.756188 - 1.85153i) q^{4} +(0.517671 + 2.17532i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(2.76990 + 0.572433i) q^{8} +(-5.01173 + 2.89352i) q^{9} +(-2.96190 - 1.10777i) q^{10} +(0.186127 + 0.107460i) q^{11} +(4.72132 - 3.58571i) q^{12} +(4.29923 + 4.29923i) q^{13} +(-5.83140 + 3.15118i) q^{15} +(-2.85636 + 2.80022i) q^{16} +(0.735462 + 2.74478i) q^{17} +(0.555529 - 8.16524i) q^{18} +(0.438952 + 0.760287i) q^{19} +(3.63622 - 2.60344i) q^{20} +(-0.272931 + 0.133754i) q^{22} +(-0.123270 - 0.0330301i) q^{23} +(0.486067 + 8.37019i) q^{24} +(-4.46403 + 2.25220i) q^{25} +(-8.43738 + 1.65655i) q^{26} +(-5.84185 - 5.84185i) q^{27} -4.03098i q^{29} +(0.899463 - 9.33067i) q^{30} +(-7.44914 - 4.30076i) q^{31} +(-1.03468 - 5.56142i) q^{32} +(-0.164890 + 0.615379i) q^{33} +(-3.80215 - 1.30119i) q^{34} +(9.14726 + 7.09134i) q^{36} +(1.76528 + 0.473005i) q^{37} +(-1.23868 - 0.0842746i) q^{38} +(-9.01151 + 15.6084i) q^{39} +(0.188668 + 6.32174i) q^{40} +2.91481 q^{41} +(2.06108 - 2.06108i) q^{43} +(0.0582196 - 0.425880i) q^{44} +(-8.88876 - 9.40422i) q^{45} +(0.135987 - 0.118661i) q^{46} +(1.78918 - 6.67731i) q^{47} +(-10.2093 - 6.03021i) q^{48} +(0.876477 - 7.01654i) q^{50} +(-7.29484 + 4.21168i) q^{51} +(4.70915 - 11.2112i) q^{52} +(3.78963 - 1.01543i) q^{53} +(11.4648 - 2.25094i) q^{54} +(-0.137408 + 0.460514i) q^{55} +(-1.84015 + 1.84015i) q^{57} +(4.73205 + 3.17887i) q^{58} +(5.24601 - 9.08635i) q^{59} +(10.2442 + 8.41416i) q^{60} +(4.16343 + 7.21127i) q^{61} +(10.9232 - 5.35309i) q^{62} +(7.34464 + 3.17116i) q^{64} +(-7.12662 + 11.5778i) q^{65} +(-0.592373 - 0.678863i) q^{66} +(-0.759268 + 0.203445i) q^{67} +(4.52591 - 3.43730i) q^{68} -0.378298i q^{69} -1.75036i q^{71} +(-15.5383 + 5.14588i) q^{72} +(-5.71993 + 1.53265i) q^{73} +(-1.94739 + 1.69928i) q^{74} +(-9.87357 - 11.0539i) q^{75} +(1.07577 - 1.38765i) q^{76} +(-11.2165 - 22.8877i) q^{78} +(6.20636 + 10.7497i) q^{79} +(-7.57002 - 4.76391i) q^{80} +(3.56437 - 6.17368i) q^{81} +(-2.29865 + 3.42176i) q^{82} +(-5.30716 + 5.30716i) q^{83} +(-5.59005 + 3.02076i) q^{85} +(0.794160 + 4.04494i) q^{86} +(11.5419 - 3.09263i) q^{87} +(0.454037 + 0.404198i) q^{88} +(11.0339 - 6.37043i) q^{89} +(18.0496 - 3.01845i) q^{90} +(0.0320589 + 0.253215i) q^{92} +(6.59923 - 24.6287i) q^{93} +(6.42768 + 7.36615i) q^{94} +(-1.42663 + 1.34844i) q^{95} +(15.1301 - 7.22941i) q^{96} +(-2.58579 + 2.58579i) q^{97} -1.24375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{6}+O(q^{10}) $ 72 * q - 16 * q^6	$ 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48} + 80 q^{50} - 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} + 64 q^{61} + 80 q^{62} - 4 q^{65} - 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 16 q^{76} - 152 q^{78} + 20 q^{80} + 36 q^{81} - 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} - 32 q^{90} - 112 q^{92} - 32 q^{93} - 120 q^{96} + 40 q^{97}+O(q^{100}) $ 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.788610	+	1.17392i	−0.557632	+	0.830089i
$2$	−0.788610	+	1.17392i	−0.557632	+	0.830089i
$3$	0.767216	+	2.86329i	0.442952	+	1.65312i	0.721287	+	0.692636i	$0.243551\pi$
$3$	0.767216	+	2.86329i	0.442952	+	1.65312i	−0.278335	+	0.960484i	$0.589782\pi$
$4$	−0.756188	−	1.85153i	−0.378094	−	0.925767i
$5$	0.517671	+	2.17532i	0.231509	+	0.972833i
$5$	0.517671	+	2.17532i	0.231509	+	0.972833i
$6$	−3.96631	−	1.35737i	−1.61924	−	0.554143i
$7$		0			0
$7$		0			0
$8$	2.76990	+	0.572433i	0.979306	+	0.202386i
$9$	−5.01173	+	2.89352i	−1.67058	+	0.964507i
$10$	−2.96190	−	1.10777i	−0.936634	−	0.350309i
$11$	0.186127	+	0.107460i	0.0561193	+	0.0324005i	0.527797	−	0.849370i	$-0.323018\pi$
$11$	0.186127	+	0.107460i	0.0561193	+	0.0324005i	−0.471678	+	0.881771i	$0.656351\pi$
$12$	4.72132	−	3.58571i	1.36293	−	1.03511i
$13$	4.29923	+	4.29923i	1.19239	+	1.19239i	0.976394	+	0.215999i	$0.0693008\pi$
$13$	4.29923	+	4.29923i	1.19239	+	1.19239i	0.215999	+	0.976394i	$0.430699\pi$
$14$		0			0
$15$	−5.83140	+	3.15118i	−1.50566	+	0.813631i
$16$	−2.85636	+	2.80022i	−0.714090	+	0.700054i
$17$	0.735462	+	2.74478i	0.178376	+	0.665707i	0.995952	+	0.0898868i	$0.0286505\pi$
$17$	0.735462	+	2.74478i	0.178376	+	0.665707i	−0.817576	+	0.575820i	$0.804683\pi$
$18$	0.555529	−	8.16524i	0.130939	−	1.92457i
$19$	0.438952	+	0.760287i	0.100702	+	0.174422i	0.911974	−	0.410247i	$-0.134558\pi$
$19$	0.438952	+	0.760287i	0.100702	+	0.174422i	−0.811272	+	0.584669i	$0.801224\pi$
$20$	3.63622	−	2.60344i	0.813084	−	0.582146i
$21$		0			0
$22$	−0.272931	+	0.133754i	−0.0581891	+	0.0285164i
$23$	−0.123270	−	0.0330301i	−0.0257035	−	0.00688724i	0.245944	−	0.969284i	$-0.420902\pi$
$23$	−0.123270	−	0.0330301i	−0.0257035	−	0.00688724i	−0.271648	+	0.962397i	$0.587569\pi$
$24$	0.486067	+	8.37019i	0.0992180	+	1.70856i
$25$	−4.46403	+	2.25220i	−0.892807	+	0.450440i
$26$	−8.43738	+	1.65655i	−1.65471	+	0.324876i
$27$	−5.84185	−	5.84185i	−1.12426	−	1.12426i
$28$		0			0
$29$		−	4.03098i		−	0.748534i	−0.927321	−	0.374267i	$-0.877894\pi$
$29$		−	4.03098i		−	0.748534i	0.927321	−	0.374267i	$-0.122106\pi$
$30$	0.899463	−	9.33067i	0.164219	−	1.70354i
$31$	−7.44914	−	4.30076i	−1.33790	−	0.772440i	−0.351408	−	0.936222i	$-0.614297\pi$
$31$	−7.44914	−	4.30076i	−1.33790	−	0.772440i	−0.986496	+	0.163783i	$0.947630\pi$
$32$	−1.03468	−	5.56142i	−0.182908	−	0.983130i
$33$	−0.164890	+	0.615379i	−0.0287037	+	0.107124i
$34$	−3.80215	−	1.30119i	−0.652064	−	0.223152i
$35$		0			0
$36$	9.14726	+	7.09134i	1.52454	+	1.18189i
$37$	1.76528	+	0.473005i	0.290210	+	0.0777615i	0.400987	−	0.916084i	$-0.368667\pi$
$37$	1.76528	+	0.473005i	0.290210	+	0.0777615i	−0.110777	+	0.993845i	$0.535334\pi$
$38$	−1.23868	−	0.0842746i	−0.200940	−	0.0136711i
$39$	−9.01151	+	15.6084i	−1.44300	+	2.49934i
$40$	0.188668	+	6.32174i	0.0298311	+	0.999555i
$41$	2.91481			0.455217			0.227608	−	0.973753i	$-0.426909\pi$
$41$	2.91481			0.455217			0.227608	+	0.973753i	$0.426909\pi$
$42$		0			0
$43$	2.06108	−	2.06108i	0.314312	−	0.314312i	−0.532265	−	0.846578i	$-0.678659\pi$
$43$	2.06108	−	2.06108i	0.314312	−	0.314312i	0.846578	+	0.532265i	$0.178659\pi$
$44$	0.0582196	−	0.425880i	0.00877694	−	0.0642038i
$45$	−8.88876	−	9.40422i	−1.32506	−	1.40190i
$46$	0.135987	−	0.118661i	0.0200501	−	0.0174957i
$47$	1.78918	−	6.67731i	0.260979	−	0.973986i	−0.703687	−	0.710510i	$-0.748464\pi$
$47$	1.78918	−	6.67731i	0.260979	−	0.973986i	0.964666	−	0.263476i	$-0.0848689\pi$
$48$	−10.2093	−	6.03021i	−1.47358	−	0.870386i
$49$		0			0
$50$	0.876477	−	7.01654i	0.123953	−	0.992288i
$51$	−7.29484	+	4.21168i	−1.02148	+	0.589753i
$52$	4.70915	−	11.2112i	0.653042	−	1.55471i
$53$	3.78963	−	1.01543i	0.520546	−	0.139480i	0.0110266	−	0.999939i	$-0.496490\pi$
$53$	3.78963	−	1.01543i	0.520546	−	0.139480i	0.509519	+	0.860459i	$0.329823\pi$
$54$	11.4648	−	2.25094i	1.56016	−	0.306314i
$55$	−0.137408	+	0.460514i	−0.0185281	+	0.0620957i
$56$		0			0
$57$	−1.84015	+	1.84015i	−0.243734	+	0.243734i
$58$	4.73205	+	3.17887i	0.621349	+	0.417406i
$59$	5.24601	−	9.08635i	0.682972	−	1.18294i	−0.291098	−	0.956693i	$-0.594021\pi$
$59$	5.24601	−	9.08635i	0.682972	−	1.18294i	0.974070	−	0.226249i	$-0.0726462\pi$
$60$	10.2442	+	8.41416i	1.32252	+	1.08626i
$61$	4.16343	+	7.21127i	0.533073	+	0.923309i	0.999254	+	0.0386198i	$0.0122961\pi$
$61$	4.16343	+	7.21127i	0.533073	+	0.923309i	−0.466181	+	0.884689i	$0.654371\pi$
$62$	10.9232	−	5.35309i	1.38725	−	0.679843i
$63$		0			0
$64$	7.34464	+	3.17116i	0.918080	+	0.396395i
$65$	−7.12662	+	11.5778i	−0.883948	+	1.43605i
$66$	−0.592373	−	0.678863i	−0.0729161	−	0.0835622i
$67$	−0.759268	+	0.203445i	−0.0927593	+	0.0248548i	−0.304900	−	0.952384i	$-0.598623\pi$
$67$	−0.759268	+	0.203445i	−0.0927593	+	0.0248548i	0.212141	+	0.977239i	$0.431956\pi$
$68$	4.52591	−	3.43730i	0.548847	−	0.416834i
$69$		−	0.378298i		−	0.0455418i
$70$		0			0
$71$		−	1.75036i		−	0.207729i	−0.994591	−	0.103865i	$-0.966879\pi$
$71$		−	1.75036i		−	0.207729i	0.994591	−	0.103865i	$-0.0331209\pi$
$72$	−15.5383	+	5.14588i	−1.83121	+	0.606447i
$73$	−5.71993	+	1.53265i	−0.669467	+	0.179383i	−0.577515	−	0.816380i	$-0.695977\pi$
$73$	−5.71993	+	1.53265i	−0.669467	+	0.179383i	−0.0919523	+	0.995763i	$0.529311\pi$
$74$	−1.94739	+	1.69928i	−0.226379	+	0.197538i
$75$	−9.87357	−	11.0539i	−1.14010	−	1.27639i
$76$	1.07577	−	1.38765i	0.123399	−	0.159175i
$77$		0			0
$78$	−11.2165	−	22.8877i	−1.27002	−	2.59153i
$79$	6.20636	+	10.7497i	0.698270	+	1.20944i	0.969066	+	0.246803i	$0.0793800\pi$
$79$	6.20636	+	10.7497i	0.698270	+	1.20944i	−0.270795	+	0.962637i	$0.587287\pi$
$80$	−7.57002	−	4.76391i	−0.846354	−	0.532621i
$81$	3.56437	−	6.17368i	0.396041	−	0.685964i
$82$	−2.29865	+	3.42176i	−0.253843	+	0.377870i
$83$	−5.30716	+	5.30716i	−0.582537	+	0.582537i	−0.935600	−	0.353063i	$-0.885140\pi$
$83$	−5.30716	+	5.30716i	−0.582537	+	0.582537i	0.353063	+	0.935600i	$0.385140\pi$
$84$		0			0
$85$	−5.59005	+	3.02076i	−0.606326	+	0.327647i
$86$	0.794160	+	4.04494i	0.0856365	+	0.436177i
$87$	11.5419	−	3.09263i	1.23742	−	0.331565i
$88$	0.454037	+	0.404198i	0.0484005	+	0.0430877i
$89$	11.0339	−	6.37043i	1.16959	−	0.675264i	0.216008	−	0.976392i	$-0.430696\pi$
$89$	11.0339	−	6.37043i	1.16959	−	0.675264i	0.953584	+	0.301127i	$0.0973628\pi$
$90$	18.0496	−	3.01845i	1.90259	−	0.318173i
$91$		0			0
$92$	0.0320589	+	0.253215i	0.00334237	+	0.0263995i
$93$	6.59923	−	24.6287i	0.684308	−	2.55387i
$94$	6.42768	+	7.36615i	0.662964	+	0.759761i
$95$	−1.42663	+	1.34844i	−0.146370	+	0.138347i
$96$	15.1301	−	7.22941i	1.54421	−	0.737848i
$97$	−2.58579	+	2.58579i	−0.262547	+	0.262547i	−0.826088	−	0.563541i	$-0.809439\pi$
$97$	−2.58579	+	2.58579i	−0.262547	+	0.262547i	0.563541	+	0.826088i	$0.309439\pi$
$98$		0			0
$99$	−1.24375			−0.125002
$100$	7.54567	+	6.56223i	0.754567	+	0.656223i
$101$	7.59723	−	13.1588i	0.755952	−	1.30935i	−0.188947	−	0.981987i	$-0.560508\pi$
$101$	7.59723	−	13.1588i	0.755952	−	1.30935i	0.944900	−	0.327361i	$-0.106159\pi$
$102$	0.808602	−	11.8850i	0.0800635	−	1.17679i
$103$	−1.48770	−	0.398628i	−0.146587	−	0.0392780i	0.184779	−	0.982780i	$-0.440843\pi$
$103$	−1.48770	−	0.398628i	−0.146587	−	0.0392780i	−0.331367	+	0.943502i	$0.607510\pi$
$104$	9.44740	+	14.3694i	0.926394	+	1.40904i
$105$		0			0
$106$	−1.79651	+	5.24951i	−0.174492	+	0.509877i
$107$	3.54506	−	13.2303i	0.342714	−	1.27903i	−0.552546	−	0.833482i	$-0.686344\pi$
$107$	3.54506	−	13.2303i	0.342714	−	1.27903i	0.895260	−	0.445544i	$-0.146990\pi$
$108$	−6.39885	+	15.2339i	−0.615729	+	1.46588i
$109$	10.4283	+	6.02078i	0.998850	+	0.576686i	0.907908	−	0.419170i	$-0.137679\pi$
$109$	10.4283	+	6.02078i	0.998850	+	0.576686i	0.0909422	+	0.995856i	$0.471012\pi$
$110$	−0.432246	−	0.524472i	−0.0412130	−	0.0500065i
$111$			5.41740i			0.514197i
$112$		0			0
$113$	−3.14409	−	3.14409i	−0.295771	−	0.295771i	0.543584	−	0.839355i	$-0.317067\pi$
$113$	−3.14409	−	3.14409i	−0.295771	−	0.295771i	−0.839355	+	0.543584i	$0.817067\pi$
$114$	−0.709032	−	3.61135i	−0.0664070	−	0.338234i
$115$	0.00803777	−	0.285250i	0.000749526	−	0.0265997i
$116$	−7.46349	+	3.04818i	−0.692968	+	0.283016i
$117$	−33.9865	−	9.10666i	−3.14205	−	0.841911i
$118$	6.52961	+	13.3240i	0.601100	+	1.22657i
$119$		0			0
$120$	−17.9562	+	5.39035i	−1.63917	+	0.492070i
$121$	−5.47690	−	9.48628i	−0.497900	−	0.862389i
$122$	−11.7488	−	0.799339i	−1.06369	−	0.0723688i
$123$	2.23629	+	8.34594i	0.201639	+	0.752528i
$124$	−2.33006	+	17.0445i	−0.209246	+	1.53064i
$125$	−7.21015	−	8.54481i	−0.644896	−	0.764271i
$126$		0			0
$127$	−2.21268	−	2.21268i	−0.196344	−	0.196344i	0.602087	−	0.798431i	$-0.294336\pi$
$127$	−2.21268	−	2.21268i	−0.196344	−	0.196344i	−0.798431	+	0.602087i	$0.794336\pi$
$128$	−9.51475	+	6.12123i	−0.840993	+	0.541045i
$129$	7.48277	+	4.32018i	0.658821	+	0.380370i
$130$	−7.97131	−	17.4965i	−0.699130	−	1.53454i
$131$	−3.21980	+	1.85895i	−0.281316	+	0.162418i	−0.634019	−	0.773318i	$-0.718596\pi$
$131$	−3.21980	+	1.85895i	−0.281316	+	0.162418i	0.352703	+	0.935735i	$0.385263\pi$
$132$	1.26408	−	0.160042i	0.110024	−	0.0139299i
$133$		0			0
$134$	0.359937	−	1.05176i	0.0310939	−	0.0908582i
$135$	9.68374	−	15.7320i	0.833443	−	1.35400i
$136$	0.465949	+	8.02376i	0.0399548	+	0.688031i
$137$	0.677005	+	2.52662i	0.0578404	+	0.215863i	0.988797	−	0.149267i	$-0.0476912\pi$
$137$	0.677005	+	2.52662i	0.0578404	+	0.215863i	−0.930957	+	0.365130i	$0.881025\pi$
$138$	0.444093	+	0.298330i	0.0378037	+	0.0253955i
$139$	−10.9071			−0.925130			−0.462565	−	0.886585i	$-0.653071\pi$
$139$	−10.9071			−0.925130			−0.462565	+	0.886585i	$0.653071\pi$
$140$		0			0
$141$	20.4918			1.72572
$142$	2.05478	+	1.38035i	0.172434	+	0.115836i
$143$	0.338205	+	1.26220i	0.0282821	+	0.105550i
$144$	6.21281	−	22.2989i	0.517734	−	1.85824i
$145$	8.76866	−	2.08672i	0.728198	−	0.173293i
$146$	2.71158	−	7.92342i	0.224412	−	0.655747i
$147$		0			0
$148$	−0.459097	−	3.62615i	−0.0377376	−	0.298068i
$149$	−9.73603	+	5.62110i	−0.797606	+	0.460498i	−0.842634	−	0.538487i	$-0.818996\pi$
$149$	−9.73603	+	5.62110i	−0.797606	+	0.460498i	0.0450271	+	0.998986i	$0.485663\pi$
$150$	20.7628	−	2.87359i	1.69528	−	0.234628i
$151$	−7.86444	−	4.54054i	−0.639999	−	0.369504i	0.144615	−	0.989488i	$-0.453806\pi$
$151$	−7.86444	−	4.54054i	−0.639999	−	0.369504i	−0.784614	+	0.619984i	$0.787139\pi$
$152$	0.780637	+	2.35719i	0.0633180	+	0.191193i
$153$	−11.6280	−	11.6280i	−0.940069	−	0.940069i
$154$		0			0
$155$	5.49933	−	18.4306i	0.441717	−	1.48038i
$156$	35.7139	+	4.88224i	2.85940	+	0.390892i
$157$	5.42108	+	20.2317i	0.432649	+	1.61467i	0.746630	+	0.665240i	$0.231671\pi$
$157$	5.42108	+	20.2317i	0.432649	+	1.61467i	−0.313981	+	0.949429i	$0.601663\pi$
$158$	−17.5138	−	1.19156i	−1.39332	−	0.0947956i
$159$	5.81493	+	10.0717i	0.461154	+	0.798742i
$160$	11.5623	−	5.12975i	0.914076	−	0.405542i
$161$		0			0
$162$	4.43652	+	9.05292i	0.348566	+	0.711265i
$163$	−15.3601	−	4.11572i	−1.20309	−	0.322368i	−0.399046	−	0.916931i	$-0.630659\pi$
$163$	−15.3601	−	4.11572i	−1.20309	−	0.322368i	−0.804049	+	0.594563i	$0.797325\pi$
$164$	−2.20414	−	5.39687i	−0.172115	−	0.421425i
$165$	−1.42401	−	0.0401256i	−0.110859	−	0.00312377i
$166$	−2.04492	−	10.4155i	−0.158716	−	0.808398i
$167$	12.0570	+	12.0570i	0.932995	+	0.932995i	0.997892	−	0.0648970i	$-0.0206719\pi$
$167$	12.0570	+	12.0570i	0.932995	+	0.932995i	−0.0648970	+	0.997892i	$0.520672\pi$
$168$		0			0
$169$			23.9668i			1.84360i
$170$	0.862235	−	8.94448i	0.0661304	−	0.686011i
$171$	−4.39981	−	2.54023i	−0.336462	−	0.194256i
$172$	−5.37473	−	2.25760i	−0.409819	−	0.172140i
$173$	−0.117498	+	0.438509i	−0.00893321	+	0.0333392i	−0.970249	−	0.242111i	$-0.922160\pi$
$173$	−0.117498	+	0.438509i	−0.00893321	+	0.0333392i	0.961315	+	0.275450i	$0.0888269\pi$
$174$	−5.47151	+	15.9881i	−0.414794	+	1.21206i
$175$		0			0
$176$	−0.832556	+	0.214249i	−0.0627563	+	0.0161497i
$177$	30.0417	+	8.04964i	2.25807	+	0.605048i
$178$	−1.22306	+	17.9767i	−0.0916724	+	1.34741i
$179$	2.42760	−	4.20473i	0.181448	−	0.314276i	−0.760926	−	0.648839i	$-0.775255\pi$
$179$	2.42760	−	4.20473i	0.181448	−	0.314276i	0.942374	+	0.334562i	$0.108588\pi$
$180$	−10.6907	+	23.5692i	−0.796835	+	1.75674i
$181$	6.88269			0.511586			0.255793	−	0.966732i	$-0.417663\pi$
$181$	6.88269			0.511586			0.255793	+	0.966732i	$0.417663\pi$
$182$		0			0
$183$	−17.4537	+	17.4537i	−1.29022	+	1.29022i
$184$	−0.322537	−	0.162054i	−0.0237777	−	0.0119467i
$185$	−0.115104	+	4.08491i	−0.00846264	+	0.300328i
$186$	23.7079	+	27.1694i	1.73835	+	1.99216i
$187$	−0.158066	+	0.589909i	−0.0115589	+	0.0431384i
$188$	−13.7162	+	1.73657i	−1.00036	+	0.126653i
$189$		0			0
$190$	−0.457904	−	2.73815i	−0.0332198	−	0.198646i
$191$	−14.9328	+	8.62145i	−1.08050	+	0.623826i	−0.931031	−	0.364940i	$-0.881089\pi$
$191$	−14.9328	+	8.62145i	−1.08050	+	0.623826i	−0.149468	+	0.988767i	$0.547756\pi$
$192$	−3.44502	+	23.4628i	−0.248623	+	1.69328i
$193$	19.5798	−	5.24638i	1.40938	−	0.377643i	0.527678	−	0.849445i	$-0.323063\pi$
$193$	19.5798	−	5.24638i	1.40938	−	0.377643i	0.881705	+	0.471802i	$0.156396\pi$
$194$	−0.996337	−	5.07470i	−0.0715328	−	0.364342i
$195$	−38.6182	−	11.5229i	−2.76551	−	0.825172i
$196$		0			0
$197$	−12.9394	+	12.9394i	−0.921891	+	0.921891i	−0.997163	−	0.0752724i	$-0.976017\pi$
$197$	−12.9394	+	12.9394i	−0.921891	+	0.921891i	0.0752724	+	0.997163i	$0.476017\pi$
$198$	0.980837	−	1.46007i	0.0697050	−	0.103763i
$199$	−10.9429	+	18.9536i	−0.775720	+	1.34359i	0.158669	+	0.987332i	$0.449280\pi$
$199$	−10.9429	+	18.9536i	−0.775720	+	1.34359i	−0.934389	+	0.356255i	$0.884053\pi$
$200$	−13.6541	+	3.68299i	−0.965494	+	0.260427i
$201$	−1.16504	−	2.01792i	−0.0821759	−	0.142333i
$202$	9.45614	+	19.2957i	0.665332	+	1.35764i
$203$		0			0
$204$	13.3143	+	10.3218i	0.932190	+	0.722673i
$205$	1.50891	+	6.34064i	0.105387	+	0.442850i
$206$	1.64117	−	1.43208i	0.114346	−	0.0997778i
$207$	0.713368	−	0.191146i	0.0495825	−	0.0132856i
$208$	−24.3189	−	0.241376i	−1.68621	−	0.0167364i
$209$			0.188679i			0.0130512i
$210$		0			0
$211$			3.39701i			0.233860i	0.993140	+	0.116930i	$0.0373053\pi$
$211$			3.39701i			0.233860i	−0.993140	+	0.116930i	$0.962695\pi$
$212$	−4.74577	−	6.24877i	−0.325941	−	0.429168i
$213$	5.01178	−	1.34290i	0.343401	−	0.0920141i
$214$	12.7357	+	14.5952i	0.870597	+	0.997708i
$215$	5.55047	+	3.41655i	0.378539	+	0.233007i
$216$	−12.8372	−	19.5254i	−0.873464	−	1.32853i
$217$		0			0
$218$	−15.2918	+	7.49397i	−1.03569	+	0.507555i
$219$	−8.77684	−	15.2019i	−0.593084	−	1.02725i
$220$	0.956563	−	0.0938191i	0.0644915	−	0.00632528i
$221$	−8.63853	+	14.9624i	−0.581090	+	1.00648i
$222$	−6.35961	−	4.27222i	−0.426829	−	0.286732i
$223$	19.7618	−	19.7618i	1.32335	−	1.32335i	0.412300	−	0.911048i	$-0.364725\pi$
$223$	19.7618	−	19.7618i	1.32335	−	1.32335i	0.911048	−	0.412300i	$-0.135275\pi$
$224$		0			0
$225$	15.8557	−	24.2042i	1.05705	−	1.61361i
$226$	6.17039	−	1.21146i	0.410448	−	0.0805850i
$227$	20.1598	−	5.40179i	1.33805	−	0.358530i	0.482340	−	0.875984i	$-0.339787\pi$
$227$	20.1598	−	5.40179i	1.33805	−	0.358530i	0.855711	+	0.517454i	$0.173120\pi$
$228$	4.79860	+	2.01560i	0.317795	+	0.133486i
$229$	−2.82162	+	1.62906i	−0.186458	+	0.107652i	−0.590323	−	0.807167i	$-0.701000\pi$
$229$	−2.82162	+	1.62906i	−0.186458	+	0.107652i	0.403865	+	0.914818i	$0.367666\pi$
$230$	0.328523	+	0.234387i	0.0216622	+	0.0154550i
$231$		0			0
$232$	2.30746	−	11.1654i	0.151492	−	0.733043i
$233$	1.78808	−	6.67321i	0.117141	−	0.437176i	−0.882297	−	0.470693i	$-0.844004\pi$
$233$	1.78808	−	6.67321i	0.117141	−	0.437176i	0.999438	+	0.0335166i	$0.0106707\pi$
$234$	37.4926	−	32.7159i	2.45097	−	2.13871i
$235$	15.4515	+	0.435392i	1.00794	+	0.0284018i
$236$	−20.7907	−	2.84217i	−1.35336	−	0.185010i
$237$	−26.0180	+	26.0180i	−1.69005	+	1.69005i
$238$		0			0
$239$	−10.2770			−0.664761			−0.332380	−	0.943145i	$-0.607852\pi$
$239$	−10.2770			−0.664761			−0.332380	+	0.943145i	$0.607852\pi$
$240$	7.83260	−	25.3301i	0.505592	−	1.63505i
$241$	−2.39425	+	4.14696i	−0.154227	+	0.267129i	−0.932777	−	0.360453i	$-0.882622\pi$
$241$	−2.39425	+	4.14696i	−0.154227	+	0.267129i	0.778550	+	0.627582i	$0.215955\pi$
$242$	15.4553	+	1.05151i	0.993504	+	0.0675939i
$243$	−3.52868	−	0.945506i	−0.226365	−	0.0606542i
$244$	10.2036	−	13.1618i	0.653218	−	0.842599i
$245$		0			0
$246$	−11.5611	−	3.95647i	−0.737106	−	0.252255i
$247$	−1.38149	+	5.15581i	−0.0879023	+	0.328056i
$248$	−18.1714	−	16.1768i	−1.15389	−	1.02723i
$249$	−19.2677	−	11.1242i	−1.22104	−	0.704968i
$250$	15.7169	−	1.72564i	0.994027	−	0.109139i
$251$			26.2656i			1.65787i	0.559347	+	0.828934i	$0.311052\pi$
$251$			26.2656i			1.65787i	−0.559347	+	0.828934i	$0.688948\pi$
$252$		0			0
$253$	−0.0193944	−	0.0193944i	−0.00121931	−	0.00121931i
$254$	4.34246	−	0.852574i	0.272470	−	0.0534952i
$255$	−12.9381	−	13.6884i	−0.810214	−	0.857198i
$256$	0.317582	−	15.9968i	0.0198489	−	0.999803i
$257$	22.3889	+	5.99909i	1.39658	+	0.374213i	0.877116	−	0.480278i	$-0.159464\pi$
$257$	22.3889	+	5.99909i	1.39658	+	0.374213i	0.519466	+	0.854491i	$0.326131\pi$
$258$	−10.9725	+	5.37725i	−0.683121	+	0.334773i
$259$		0			0
$260$	26.8257	+	4.44020i	1.66366	+	0.275369i
$261$	11.6637	+	20.2022i	0.721966	+	1.25048i
$262$	0.356902	−	5.24579i	0.0220495	−	0.324086i
$263$	1.54287	+	5.75806i	0.0951373	+	0.355057i	0.997040	−	0.0768816i	$-0.0244963\pi$
$263$	1.54287	+	5.75806i	0.0951373	+	0.355057i	−0.901903	+	0.431939i	$0.857830\pi$
$264$	−0.808992	+	1.61015i	−0.0497900	+	0.0990977i
$265$	4.17066	+	7.71800i	0.256202	+	0.474113i
$266$		0			0
$267$	26.7058	+	26.7058i	1.63437	+	1.63437i
$268$	0.950835	+	1.25197i	0.0580815	+	0.0764761i
$269$	0.0578535	+	0.0334017i	0.00352739	+	0.00203654i	0.501763	−	0.865005i	$-0.332685\pi$
$269$	0.0578535	+	0.0334017i	0.00352739	+	0.00203654i	−0.498235	+	0.867042i	$0.666018\pi$
$270$	10.8315	+	23.7744i	0.659184	+	1.44686i
$271$	2.40782	−	1.39016i	0.146265	−	0.0844459i	−0.425082	−	0.905155i	$-0.639755\pi$
$271$	2.40782	−	1.39016i	0.146265	−	0.0844459i	0.571346	+	0.820709i	$0.306421\pi$
$272$	−9.78672	−	5.78063i	−0.593407	−	0.350502i
$273$		0			0
$274$	−3.49994	−	1.19776i	−0.211439	−	0.0723596i
$275$	−1.07290	−	0.0605121i	−0.0646981	−	0.00364902i
$276$	−0.700432	+	0.286065i	−0.0421611	+	0.0172191i
$277$	1.48249	+	5.53275i	0.0890745	+	0.332430i	0.996055	−	0.0887431i	$-0.0282850\pi$
$277$	1.48249	+	5.53275i	0.0890745	+	0.332430i	−0.906980	+	0.421174i	$0.861618\pi$
$278$	8.60147	−	12.8041i	0.515882	−	0.767940i
$279$	49.7774			2.98010
$280$		0			0
$281$	−22.9229			−1.36746			−0.683732	−	0.729734i	$-0.739644\pi$
$281$	−22.9229			−1.36746			−0.683732	+	0.729734i	$0.739644\pi$
$282$	−16.1600	+	24.0557i	−0.962314	+	1.43250i
$283$	−0.147161	−	0.549214i	−0.00874784	−	0.0326474i	0.961414	−	0.275106i	$-0.0887129\pi$
$283$	−0.147161	−	0.549214i	−0.00874784	−	0.0326474i	−0.970162	+	0.242458i	$0.922046\pi$
$284$	−3.24085	+	1.32360i	−0.192309	+	0.0785411i
$285$	−4.95551	−	3.05032i	−0.293539	−	0.180686i
$286$	−1.74843	−	0.598356i	−0.103387	−	0.0353815i
$287$		0			0
$288$	21.2776	+	24.8785i	1.25380	+	1.46598i
$289$	7.72952	−	4.46264i	0.454677	−	0.262508i
$290$	−4.46541	+	11.9393i	−0.262218	+	0.701102i
$291$	−9.38773	−	5.42001i	−0.550318	−	0.317726i
$292$	7.16310	+	9.43167i	0.419188	+	0.551947i
$293$	−1.43269	−	1.43269i	−0.0836989	−	0.0836989i	0.664018	−	0.747717i	$-0.268850\pi$
$293$	−1.43269	−	1.43269i	−0.0836989	−	0.0836989i	−0.747717	+	0.664018i	$0.768850\pi$
$294$		0			0
$295$	22.4814	+	6.70801i	1.30892	+	0.390555i
$296$	4.61887	+	2.32068i	0.268467	+	0.134887i
$297$	−0.459557	−	1.71509i	−0.0266662	−	0.0995196i
$298$	1.07920	−	15.8622i	0.0625162	−	0.918872i
$299$	−0.387962	−	0.671970i	−0.0224364	−	0.0388610i
$300$	−13.0004	+	26.6401i	−0.750578	+	1.53807i
$301$		0			0
$302$	11.5322	−	5.65153i	0.663604	−	0.325209i
$303$	43.5061	+	11.6574i	2.49936	+	0.669702i
$304$	−3.38277	−	0.942493i	−0.194015	−	0.0540557i
$305$	−13.5315	+	12.7899i	−0.774814	+	0.732345i
$306$	22.8204	−	4.48042i	1.30455	−	0.256128i
$307$	−1.51038	−	1.51038i	−0.0862017	−	0.0862017i	0.662691	−	0.748893i	$-0.269414\pi$
$307$	−1.51038	−	1.51038i	−0.0862017	−	0.0862017i	−0.748893	+	0.662691i	$0.769414\pi$
$308$		0			0
$309$		−	4.56555i		−	0.259725i
$310$	17.2993	+	20.9904i	0.982535	+	1.19217i
$311$	11.0383	+	6.37294i	0.625922	+	0.361376i	0.779171	−	0.626811i	$-0.215640\pi$
$311$	11.0383	+	6.37294i	0.625922	+	0.361376i	−0.153249	+	0.988188i	$0.548974\pi$
$312$	−33.8957	+	38.0751i	−1.91897	+	2.15558i
$313$	−5.26991	+	19.6676i	−0.297873	+	1.11168i	0.641036	+	0.767511i	$0.278505\pi$
$313$	−5.26991	+	19.6676i	−0.297873	+	1.11168i	−0.938909	+	0.344166i	$0.888162\pi$
$314$	−28.0256	−	9.59103i	−1.58158	−	0.541253i
$315$		0			0
$316$	15.2103	−	19.6201i	0.855648	−	1.10372i
$317$	−9.55038	−	2.55902i	−0.536403	−	0.143729i	−0.0195596	−	0.999809i	$-0.506226\pi$
$317$	−9.55038	−	2.55902i	−0.536403	−	0.143729i	−0.516843	+	0.856080i	$0.672893\pi$
$318$	−16.4092	−	1.11641i	−0.920180	−	0.0626052i
$319$	0.433170	−	0.750272i	0.0242528	−	0.0420072i
$320$	−3.09618	+	17.6186i	−0.173082	+	0.984907i
$321$	40.6021			2.26619
$322$		0			0
$323$	−1.76399	+	1.76399i	−0.0981509	+	0.0981509i
$324$	−14.1261	−	1.93110i	−0.784784	−	0.107283i
$325$	−28.8746	−	9.50920i	−1.60168	−	0.527475i
$326$	16.9447	−	14.7859i	0.938478	−	0.818912i
$327$	−9.23848	+	34.4785i	−0.510889	+	1.90666i
$328$	8.07372	+	1.66853i	0.445797	+	0.0921294i
$329$		0			0
$330$	1.17009	−	1.64003i	0.0644113	−	0.0902806i
$331$	25.4182	−	14.6752i	1.39711	−	0.806621i	0.403020	−	0.915191i	$-0.367961\pi$
$331$	25.4182	−	14.6752i	1.39711	−	0.806621i	0.994089	+	0.108570i	$0.0346273\pi$
$332$	13.8396	+	5.81318i	0.759547	+	0.319040i
$333$	−10.2157	+	2.73730i	−0.559819	+	0.150003i
$334$	−23.6622	+	4.64569i	−1.29474	+	0.254201i
$335$	−0.835609	−	1.54633i	−0.0456542	−	0.0844852i
$336$		0			0
$337$	21.9434	−	21.9434i	1.19533	−	1.19533i	0.219784	−	0.975549i	$-0.429465\pi$
$337$	21.9434	−	21.9434i	1.19533	−	1.19533i	0.975549	−	0.219784i	$-0.0705353\pi$
$338$	−28.1352	−	18.9005i	−1.53035	−	1.02805i
$339$	6.59025	−	11.4146i	0.357933	−	0.619958i
$340$	9.82016	+	8.06591i	0.532573	+	0.437435i
$341$	−0.924322	−	1.60097i	−0.0500548	−	0.0866975i
$342$	6.45177	−	3.16179i	0.348872	−	0.170970i
$343$		0			0
$344$	6.88881	−	4.52915i	0.371420	−	0.244195i
$345$	0.822920	−	0.195834i	0.0443045	−	0.0105433i
$346$	−0.422115	−	0.483746i	−0.0226930	−	0.0260063i
$347$	7.84706	−	2.10261i	0.421252	−	0.112874i	−0.0419646	−	0.999119i	$-0.513362\pi$
$347$	7.84706	−	2.10261i	0.421252	−	0.112874i	0.463217	+	0.886245i	$0.346695\pi$
$348$	−14.4539	−	19.0315i	−0.774811	−	1.02020i
$349$			8.46417i			0.453076i	0.974002	+	0.226538i	$0.0727408\pi$
$349$			8.46417i			0.453076i	−0.974002	+	0.226538i	$0.927259\pi$
$350$		0			0
$351$		−	50.2309i		−	2.68113i
$352$	0.405050	−	1.14632i	0.0215892	−	0.0610988i
$353$	−20.0892	+	5.38289i	−1.06924	+	0.286502i	−0.750181	−	0.661232i	$-0.770034\pi$
$353$	−20.0892	+	5.38289i	−1.06924	+	0.286502i	−0.319060	+	0.947735i	$0.603367\pi$
$354$	−33.1408	+	28.9186i	−1.76141	+	1.53700i
$355$	3.80759	−	0.906108i	0.202086	−	0.0480912i
$356$	−20.1388	−	15.6124i	−1.06735	−	0.827457i
$357$		0			0
$358$	3.02160	+	6.16571i	0.159696	+	0.325868i
$359$	11.7824	+	20.4077i	0.621851	+	1.07708i	0.989141	+	0.146972i	$0.0469526\pi$
$359$	11.7824	+	20.4077i	0.621851	+	1.07708i	−0.367289	+	0.930107i	$0.619714\pi$
$360$	−19.2376	−	31.1369i	−1.01391	−	1.64106i
$361$	9.11464	−	15.7870i	0.479718	−	0.830896i
$362$	−5.42776	+	8.07974i	−0.285277	+	0.424662i
$363$	22.9600	−	22.9600i	1.20509	−	1.20509i
$364$		0			0
$365$	−6.29504	−	11.6493i	−0.329498	−	0.609751i
$366$	−6.72513	−	34.2535i	−0.351528	−	1.79046i
$367$	−5.15227	+	1.38055i	−0.268946	+	0.0720639i	−0.390772	−	0.920488i	$-0.627792\pi$
$367$	−5.15227	+	1.38055i	−0.268946	+	0.0720639i	0.121826	+	0.992552i	$0.461125\pi$
$368$	0.444594	−	0.250836i	0.0231761	−	0.0130758i
$369$	−14.6082	+	8.43407i	−0.760474	+	0.439060i
$370$	−4.70459	−	3.35652i	−0.244580	−	0.174497i
$371$		0			0
$372$	−50.5911	+	6.40519i	−2.62302	+	0.332094i
$373$	−8.34406	+	31.1404i	−0.432039	+	1.61239i	0.316016	+	0.948754i	$0.397655\pi$
$373$	−8.34406	+	31.1404i	−0.432039	+	1.61239i	−0.748055	+	0.663637i	$0.769012\pi$
$374$	−0.567856	−	0.650765i	−0.0293631	−	0.0336503i
$375$	18.9345	−	27.2005i	0.977774	−	1.40463i
$376$	8.77815	−	17.4713i	0.452699	−	0.901012i
$377$	17.3301	−	17.3301i	0.892546	−	0.892546i
$378$		0			0
$379$	−3.18566			−0.163637			−0.0818183	−	0.996647i	$-0.526073\pi$
$379$	−3.18566			−0.163637			−0.0818183	+	0.996647i	$0.526073\pi$
$380$	3.57548	+	1.62179i	0.183418	+	0.0831961i
$381$	4.63794	−	8.03316i	0.237609	−	0.411551i
$382$	1.65524	−	24.3289i	0.0846893	−	1.24478i
$383$	27.2291	+	7.29602i	1.39134	+	0.372809i	0.875228	−	0.483711i	$-0.160711\pi$
$383$	27.2291	+	7.29602i	1.39134	+	0.372809i	0.516114	+	0.856520i	$0.327378\pi$
$384$	−24.8267	−	22.5472i	−1.26693	−	1.15061i
$385$		0			0
$386$	−9.28195	+	27.1225i	−0.472439	+	1.38050i
$387$	−4.36579	+	16.2934i	−0.221926	+	0.828238i
$388$	6.74302	+	2.83234i	0.342325	+	0.143790i
$389$	−14.1562	−	8.17306i	−0.717745	−	0.414391i	0.0961769	−	0.995364i	$-0.469339\pi$
$389$	−14.1562	−	8.17306i	−0.717745	−	0.414391i	−0.813922	+	0.580974i	$0.802672\pi$
$390$	43.9817	−	36.2477i	2.22710	−	1.83547i
$391$		−	0.362641i		−	0.0183395i
$392$		0			0
$393$	−7.79301	−	7.79301i	−0.393105	−	0.393105i
$394$	−4.98569	−	25.3939i	−0.251175	−	1.27933i
$395$	−20.1713	+	19.0656i	−1.01493	+	0.959297i
$396$	0.940512	+	2.30285i	0.0472625	+	0.115723i
$397$	14.6722	+	3.93142i	0.736379	+	0.197312i	0.607468	−	0.794344i	$-0.292185\pi$
$397$	14.6722	+	3.93142i	0.736379	+	0.197312i	0.128911	+	0.991656i	$0.458852\pi$
$398$	−13.6204	−	27.7931i	−0.682730	−	1.39314i
$399$		0			0
$400$	6.44425	−	18.9333i	0.322212	−	0.946667i
$401$	−11.8802	−	20.5772i	−0.593271	−	1.02758i	−0.993788	−	0.111287i	$-0.964503\pi$
$401$	−11.8802	−	20.5772i	−0.593271	−	1.02758i	0.400517	−	0.916289i	$-0.368830\pi$
$402$	3.28764	+	0.223677i	0.163973	+	0.0111560i
$403$	−13.5356	−	50.5156i	−0.674256	−	2.51636i
$404$	−30.1089	−	4.11601i	−1.49797	−	0.204779i
$405$	15.2749	+	4.55772i	0.759015	+	0.226475i
$406$		0			0
$407$	0.277736	+	0.277736i	0.0137669	+	0.0137669i
$408$	−22.6169	+	7.49010i	−1.11970	+	0.370815i
$409$	19.5448	+	11.2842i	0.966427	+	0.557967i	0.898145	−	0.439699i	$-0.144915\pi$
$409$	19.5448	+	11.2842i	0.966427	+	0.557967i	0.0682817	+	0.997666i	$0.478248\pi$
$410$	−8.63337	−	3.22895i	−0.426372	−	0.159467i
$411$	−6.71502	+	3.87692i	−0.331228	+	0.191234i
$412$	0.386907	+	3.05596i	0.0190615	+	0.150557i
$413$		0			0
$414$	−0.338178	+	0.988179i	−0.0166206	+	0.0485663i
$415$	−14.2921	−	8.79742i	−0.701574	−	0.431848i
$416$	19.4615	−	28.3582i	0.954179	−	1.39037i
$417$	−8.36812	−	31.2302i	−0.409789	−	1.52935i
$418$	−0.221495	−	0.148794i	−0.0108337	−	0.00727778i
$419$	12.4351			0.607495			0.303748	−	0.952753i	$-0.401762\pi$
$419$	12.4351			0.607495			0.303748	+	0.952753i	$0.401762\pi$
$420$		0			0
$421$	−31.2799			−1.52449			−0.762244	−	0.647289i	$-0.775902\pi$
$421$	−31.2799			−1.52449			−0.762244	+	0.647289i	$0.775902\pi$
$422$	−3.98783	−	2.67892i	−0.194124	−	0.130408i
$423$	10.3541	+	38.6419i	0.503432	+	1.87883i
$424$	11.0781	−	0.643321i	0.538002	−	0.0312424i
$425$	−9.46492	−	10.5964i	−0.459116	−	0.514000i
$426$	−2.37588	+	6.94246i	−0.115112	+	0.336364i
$427$		0			0
$428$	−27.1772	+	3.44083i	−1.31366	+	0.166319i
$429$	−3.35456	+	1.93676i	−0.161960	+	0.0935075i
$430$	−8.38793	+	3.82150i	−0.404502	+	0.184289i
$431$	16.5660	+	9.56440i	0.797957	+	0.460701i	0.842756	−	0.538295i	$-0.180931\pi$
$431$	16.5660	+	9.56440i	0.797957	+	0.460701i	−0.0447992	+	0.998996i	$0.514265\pi$
$432$	33.0449	+	0.327984i	1.58987	+	0.0157801i
$433$	4.87478	+	4.87478i	0.234267	+	0.234267i	0.814471	−	0.580204i	$-0.197027\pi$
$433$	4.87478	+	4.87478i	0.234267	+	0.234267i	−0.580204	+	0.814471i	$0.697027\pi$
$434$		0			0
$435$	12.7023	+	23.5063i	0.609030	+	1.12704i
$436$	3.26193	−	23.8612i	0.156218	−	1.14274i
$437$	−0.0289972	−	0.108219i	−0.00138712	−	0.00517682i
$438$	24.7674	+	1.68507i	1.18343	+	0.0805158i
$439$	−16.3920	−	28.3918i	−0.782349	−	1.35507i	−0.930570	−	0.366113i	$-0.880688\pi$
$439$	−16.3920	−	28.3918i	−0.782349	−	1.35507i	0.148222	−	0.988954i	$-0.452645\pi$
$440$	−0.644219	+	1.19692i	−0.0307120	+	0.0570608i
$441$		0			0
$442$	−10.7522	−	21.9404i	−0.511431	−	1.04360i
$443$	−11.6298	−	3.11619i	−0.552547	−	0.148055i	−0.0282670	−	0.999600i	$-0.508999\pi$
$443$	−11.6298	−	3.11619i	−0.552547	−	0.148055i	−0.524280	+	0.851546i	$0.675666\pi$
$444$	10.0305	−	4.09657i	0.476027	−	0.194415i
$445$	19.5697	+	20.7045i	0.927691	+	0.981488i
$446$	7.61447	+	38.7832i	0.360555	+	1.83644i
$447$	−23.5645	−	23.5645i	−1.11456	−	1.11456i
$448$		0			0
$449$			5.52889i			0.260925i	0.991453	+	0.130462i	$0.0416462\pi$
$449$			5.52889i			0.260925i	−0.991453	+	0.130462i	$0.958354\pi$
$450$	15.9098	+	37.7011i	0.749997	+	1.77725i
$451$	0.542523	+	0.313226i	0.0255464	+	0.0147492i
$452$	−3.44387	+	8.19892i	−0.161986	+	0.385645i
$453$	6.96714	−	26.0017i	0.327345	−	1.22167i
$454$	−9.55691	+	27.9259i	−0.448528	+	1.31063i
$455$		0			0
$456$	−6.15038	+	4.04366i	−0.288018	+	0.189362i
$457$	−26.0905	−	6.99093i	−1.22046	−	0.327022i	−0.409603	−	0.912264i	$-0.634333\pi$
$457$	−26.0905	−	6.99093i	−1.22046	−	0.327022i	−0.810859	+	0.585242i	$0.801000\pi$
$458$	0.312765	−	4.59706i	0.0146145	−	0.214806i
$459$	11.7381	−	20.3310i	0.547889	−	0.948972i
$460$	−0.534228	+	0.200820i	−0.0249085	+	0.00936330i
$461$	−8.24886			−0.384188			−0.192094	−	0.981377i	$-0.561528\pi$
$461$	−8.24886			−0.384188			−0.192094	+	0.981377i	$0.561528\pi$
$462$		0			0
$463$	−15.4884	+	15.4884i	−0.719806	+	0.719806i	−0.968565	−	0.248759i	$-0.919977\pi$
$463$	−15.4884	+	15.4884i	−0.719806	+	0.719806i	0.248759	+	0.968565i	$0.419977\pi$
$464$	11.2876	+	11.5139i	0.524014	+	0.534520i
$465$	56.9914	+	1.60590i	2.64291	+	0.0744719i
$466$	6.42373	+	7.36163i	0.297573	+	0.341021i
$467$	10.1688	−	37.9505i	0.470556	−	1.75614i	−0.167223	−	0.985919i	$-0.553480\pi$
$467$	10.1688	−	37.9505i	0.470556	−	1.75614i	0.637779	−	0.770220i	$-0.279853\pi$
$468$	8.83889	+	69.8135i	0.408578	+	3.22713i
$469$		0			0
$470$	−12.6963	+	17.7955i	−0.585637	+	0.820845i
$471$	−53.7702	+	31.0442i	−2.47760	+	1.43044i
$472$	19.7322	−	22.1652i	0.908249	−	1.02024i
$473$	0.605106	−	0.162138i	0.0278228	−	0.00745510i
$474$	−10.0250	−	51.0611i	−0.460466	−	2.34532i
$475$	−3.67181	−	2.40534i	−0.168474	−	0.110365i
$476$		0			0
$477$	−16.0544	+	16.0544i	−0.735082	+	0.735082i
$478$	8.10451	−	12.0643i	0.370692	−	0.551810i
$479$	−1.93358	+	3.34906i	−0.0883475	+	0.153022i	−0.906813	−	0.421534i	$-0.861492\pi$
$479$	−1.93358	+	3.34906i	−0.0883475	+	0.153022i	0.818465	+	0.574556i	$0.194825\pi$
$480$	23.5587	+	29.1704i	1.07530	+	1.33144i
$481$	5.55578	+	9.62290i	0.253322	+	0.438767i
$482$	−2.98008	−	6.08099i	−0.135739	−	0.276982i
$483$		0			0
$484$	−13.4226	+	17.3141i	−0.610118	+	0.787004i
$485$	−6.96351	−	4.28633i	−0.316197	−	0.194632i
$486$	3.89270	−	3.39676i	0.176576	−	0.154080i
$487$	−0.429962	+	0.115208i	−0.0194834	+	0.00522057i	−0.268548	−	0.963266i	$-0.586544\pi$
$487$	−0.429962	+	0.115208i	−0.0194834	+	0.00522057i	0.249064	+	0.968487i	$0.419877\pi$
$488$	7.40430	+	22.3578i	0.335177	+	1.01209i
$489$		−	47.1380i		−	2.13165i
$490$		0			0
$491$		−	40.4240i		−	1.82431i	−0.409844	−	0.912156i	$-0.634417\pi$
$491$		−	40.4240i		−	1.82431i	0.409844	−	0.912156i	$-0.365583\pi$
$492$	13.7617	−	10.4517i	0.620427	−	0.471198i
$493$	11.0641	−	2.96463i	0.498304	−	0.133520i
$494$	−4.96306	−	5.68769i	−0.223298	−	0.255901i
$495$	−0.643855	−	2.70556i	−0.0289391	−	0.121606i
$496$	33.3205	−	8.57467i	1.49613	−	0.385014i
$497$		0			0
$498$	28.2536	−	13.8461i	1.26608	−	0.620459i
$499$	15.8937	+	27.5287i	0.711501	+	1.23236i	0.964294	+	0.264835i	$0.0853174\pi$
$499$	15.8937	+	27.5287i	0.711501	+	1.23236i	−0.252793	+	0.967520i	$0.581349\pi$
$500$	−10.3688	+	19.8113i	−0.463706	+	0.885989i
$501$	−25.2723	+	43.7728i	−1.12908	+	1.95563i
$502$	−30.8337	−	20.7133i	−1.37618	−	0.924479i
$503$	−6.28613	+	6.28613i	−0.280285	+	0.280285i	−0.833222	−	0.552938i	$-0.813507\pi$
$503$	−6.28613	+	6.28613i	−0.280285	+	0.280285i	0.552938	+	0.833222i	$0.313507\pi$
$504$		0			0
$505$	32.5574	+	9.71448i	1.44879	+	0.432289i
$506$	0.0380621	−	0.00747289i	0.00169207	−	0.000332210i
$507$	−68.6239	+	18.3877i	−3.04769	+	0.816627i
$508$	−2.42365	+	5.77006i	−0.107532	+	0.256005i
$509$	2.67962	−	1.54708i	0.118772	−	0.0685730i	−0.439437	−	0.898273i	$-0.644822\pi$
$509$	2.67962	−	1.54708i	0.118772	−	0.0685730i	0.558209	+	0.829700i	$0.311489\pi$
$510$	26.2722	−	4.39352i	1.16335	−	0.194548i
$511$		0			0
$512$	18.5286	+	12.9881i	0.818857	+	0.573998i
$513$	1.87719	−	7.00577i	0.0828800	−	0.309312i
$514$	−24.6986	+	21.5519i	−1.08941	+	0.950614i
$515$	0.0970049	−	3.44258i	0.00427455	−	0.151698i
$516$	2.34058	−	17.1215i	0.103038	−	0.753731i
$517$	1.05056	−	1.05056i	0.0462035	−	0.0462035i
$518$		0			0
$519$	−1.34572			−0.0590707
$520$	−26.3675	+	27.9898i	−1.15629	+	1.22743i
$521$	−2.55693	+	4.42873i	−0.112021	+	0.194026i	−0.916585	−	0.399840i	$-0.869066\pi$
$521$	−2.55693	+	4.42873i	−0.112021	+	0.194026i	0.804564	+	0.593866i	$0.202399\pi$
$522$	−32.9139	−	2.23932i	−1.44060	−	0.0980125i
$523$	24.4856	+	6.56089i	1.07068	+	0.286888i	0.750772	−	0.660561i	$-0.229682\pi$
$523$	24.4856	+	6.56089i	1.07068	+	0.286888i	0.319907	+	0.947449i	$0.396348\pi$
$524$	5.87669	+	4.55586i	0.256725	+	0.199024i
$525$		0			0
$526$	−7.97623	−	2.72966i	−0.347780	−	0.119019i
$527$	6.32609	−	23.6093i	0.275569	−	1.02844i
$528$	−1.25221	−	2.21947i	−0.0544954	−	0.0965902i
$529$	−19.9045	−	11.4919i	−0.865412	−	0.499646i
$530$	−12.3494	−	1.19046i	−0.536422	−	0.0517103i
$531$			60.7177i			2.63493i
$532$		0			0
$533$	12.5314	+	12.5314i	0.542797	+	0.542797i
$534$	−52.4110	+	10.2901i	−2.26804	+	0.445295i
$535$	30.6154	+	0.862680i	1.32362	+	0.0372969i
$536$	−2.21955	+	0.128892i	−0.0958700	+	0.00556728i
$537$	13.9019	+	3.72499i	0.599909	+	0.160745i
$538$	−0.0848349	+	0.0415746i	−0.00365749	+	0.00179241i
$539$		0			0
$540$	−36.4511	−	6.03339i	−1.56861	−	0.259636i
$541$	−0.501976	−	0.869449i	−0.0215817	−	0.0373805i	0.855033	−	0.518574i	$-0.173537\pi$
$541$	−0.501976	−	0.869449i	−0.0215817	−	0.0373805i	−0.876615	+	0.481193i	$0.840204\pi$
$542$	−0.266897	+	3.92288i	−0.0114642	+	0.168502i
$543$	5.28051	+	19.7071i	0.226608	+	0.845713i
$544$	14.5039	−	6.93019i	0.621850	−	0.297129i
$545$	−7.69870	+	25.8017i	−0.329776	+	1.10522i
$546$		0			0
$547$	−11.1953	−	11.1953i	−0.478676	−	0.478676i	0.426032	−	0.904708i	$-0.359911\pi$
$547$	−11.1953	−	11.1953i	−0.478676	−	0.478676i	−0.904708	+	0.426032i	$0.859911\pi$
$548$	4.16617	−	3.16409i	0.177970	−	0.135163i
$549$	−41.7320	−	24.0940i	−1.78108	−	1.02831i
$550$	0.917134	−	1.21178i	0.0391067	−	0.0516704i
$551$	3.06470	−	1.76940i	0.130561	−	0.0753792i
$552$	0.216550	−	1.04785i	0.00921700	−	0.0445993i
$553$		0			0
$554$	−7.66412	−	2.62285i	−0.325617	−	0.111434i
$555$	−11.7846	+	2.80443i	−0.500227	+	0.119041i
$556$	8.24783	+	20.1949i	0.349786	+	0.856455i
$557$	−2.73237	−	10.1973i	−0.115774	−	0.432075i	0.883570	−	0.468300i	$-0.155133\pi$
$557$	−2.73237	−	10.1973i	−0.115774	−	0.432075i	−0.999344	+	0.0362252i	$0.988467\pi$
$558$	−39.2550	+	58.4348i	−1.66180	+	2.47374i
$559$	17.7221			0.749567
$560$		0			0
$561$	−1.81035			−0.0764331
$562$	18.0772	−	26.9097i	0.762541	−	1.13512i
$563$	1.92836	+	7.19675i	0.0812708	+	0.303307i	0.994582	−	0.103956i	$-0.0331501\pi$
$563$	1.92836	+	7.19675i	0.0812708	+	0.303307i	−0.913311	+	0.407263i	$0.866483\pi$
$564$	−15.4956	−	37.9412i	−0.652483	−	1.59761i
$565$	5.21180	−	8.46701i	0.219262	−	0.356210i
$566$	0.760788	+	0.260360i	0.0319783	+	0.0109437i
$567$		0			0
$568$	1.00196	−	4.84831i	0.0420414	−	0.203430i
$569$	23.6353	−	13.6458i	0.990841	−	0.572063i	0.0853157	−	0.996354i	$-0.472810\pi$
$569$	23.6353	−	13.6458i	0.990841	−	0.572063i	0.905526	+	0.424291i	$0.139477\pi$
$570$	7.48881	−	3.41186i	0.313672	−	0.142907i
$571$	−5.57769	−	3.22028i	−0.233419	−	0.134765i	0.378729	−	0.925507i	$-0.376361\pi$
$571$	−5.57769	−	3.22028i	−0.233419	−	0.134765i	−0.612148	+	0.790743i	$0.709694\pi$
$572$	2.08126	−	1.58066i	0.0870217	−	0.0660906i
$573$	−36.1424	−	36.1424i	−1.50987	−	1.50987i
$574$		0			0
$575$	0.624671	−	0.130181i	0.0260506	−	0.00542892i
$576$	−45.9852	+	5.35889i	−1.91605	+	0.223287i
$577$	−3.83327	−	14.3060i	−0.159581	−	0.595565i	−0.998669	−	0.0515697i	$-0.983578\pi$
$577$	−3.83327	−	14.3060i	−0.159581	−	0.595565i	0.839088	−	0.543995i	$-0.183089\pi$
$578$	−0.856784	+	12.5931i	−0.0356375	+	0.523805i
$579$	30.0438	+	52.0374i	1.24858	+	2.16260i
$580$	−10.4944	−	14.6575i	−0.435756	−	0.608621i
$581$		0			0
$582$	13.7659	−	6.74619i	0.570616	−	0.279639i
$583$	0.814469	+	0.218236i	0.0337318	+	0.00903842i
$584$	−16.7209	+	0.971005i	−0.691918	+	0.0401805i
$585$	2.21608	−	78.6458i	0.0916235	−	3.25160i
$586$	2.81171	−	0.552035i	0.116151	−	0.0228043i
$587$	−15.0807	−	15.0807i	−0.622447	−	0.622447i	0.323710	−	0.946156i	$-0.395070\pi$
$587$	−15.0807	−	15.0807i	−0.622447	−	0.622447i	−0.946156	+	0.323710i	$0.895070\pi$
$588$		0			0
$589$		−	7.55131i		−	0.311146i
$590$	−25.6038	+	21.1014i	−1.05409	+	0.868733i
$591$	−46.9764	−	27.1218i	−1.93235	−	1.11564i
$592$	−6.36679	+	3.59209i	−0.261673	+	0.147634i
$593$	9.26689	−	34.5845i	0.380546	−	1.42022i	−0.464525	−	0.885560i	$-0.653775\pi$
$593$	9.26689	−	34.5845i	0.380546	−	1.42022i	0.845070	−	0.534655i	$-0.179558\pi$
$594$	2.37579	+	0.813053i	0.0974800	+	0.0333600i
$595$		0			0
$596$	17.7699	+	13.7760i	0.727884	+	0.564286i
$597$	−62.6653	−	16.7911i	−2.56472	−	0.687214i
$598$	1.09479	+	0.0744850i	0.0447693	+	0.00304592i
$599$	−11.1770	+	19.3591i	−0.456680	+	0.790992i	−0.998783	−	0.0493194i	$-0.984295\pi$
$599$	−11.1770	+	19.3591i	−0.456680	+	0.790992i	0.542103	+	0.840312i	$0.317628\pi$
$600$	−21.0211	−	36.2701i	−0.858185	−	1.48072i
$601$	−43.6119			−1.77897			−0.889483	−	0.456969i	$-0.848935\pi$
$601$	−43.6119			−1.77897			−0.889483	+	0.456969i	$0.848935\pi$
$602$		0			0
$603$	3.21657	−	3.21657i	0.130989	−	0.130989i
$604$	−2.45997	+	17.9948i	−0.100095	+	0.732197i
$605$	17.8005	−	16.8248i	0.723691	−	0.684025i
$606$	−47.9943	+	41.8796i	−1.94963	+	1.70124i
$607$	−6.17935	+	23.0617i	−0.250812	+	0.936044i	0.719560	+	0.694430i	$0.244343\pi$
$607$	−6.17935	+	23.0617i	−0.250812	+	0.936044i	−0.970373	+	0.241614i	$0.922323\pi$
$608$	3.77410	−	3.22785i	0.153060	−	0.130907i
$609$		0			0
$610$	−4.34319	−	25.9712i	−0.175851	−	1.05154i
$611$	36.3994	−	21.0152i	1.47256	−	0.850184i
$612$	−12.7367	+	30.3226i	−0.514851	+	1.22572i
$613$	28.4137	−	7.61342i	1.14762	−	0.307503i	0.365608	−	0.930769i	$-0.380861\pi$
$613$	28.4137	−	7.61342i	1.14762	−	0.307503i	0.782010	+	0.623266i	$0.214194\pi$
$614$	2.96416	−	0.581966i	0.119624	−	0.0234863i
$615$	−16.9974	+	9.18509i	−0.685403	+	0.370379i
$616$		0			0
$617$	12.8248	−	12.8248i	0.516307	−	0.516307i	−0.400145	−	0.916452i	$-0.631040\pi$
$617$	12.8248	−	12.8248i	0.516307	−	0.516307i	0.916452	+	0.400145i	$0.131040\pi$
$618$	5.35960	+	3.60044i	0.215595	+	0.144831i
$619$	7.38068	−	12.7837i	0.296655	−	0.513821i	−0.678714	−	0.734403i	$-0.737462\pi$
$619$	7.38068	−	12.7837i	0.296655	−	0.513821i	0.975368	+	0.220582i	$0.0707956\pi$
$620$	−38.2835	+	3.75482i	−1.53750	+	0.150797i
$621$	0.527167	+	0.913080i	0.0211545	+	0.0366406i
$622$	−16.1862	+	7.93229i	−0.649008	+	0.318056i
$623$		0			0
$624$	−17.9667	−	69.8173i	−0.719245	−	2.79493i
$625$	14.8552	−	20.1078i	0.594208	−	0.804311i
$626$	−18.9323	−	21.6965i	−0.756687	−	0.867167i
$627$	−0.540244	+	0.144758i	−0.0215752	+	0.00578107i
$628$	33.3604	−	25.3363i	1.33123	−	1.01103i
$629$			5.19318i			0.207066i
$630$		0			0
$631$			31.4840i			1.25336i	0.779278	+	0.626678i	$0.215586\pi$
$631$			31.4840i			1.25336i	−0.779278	+	0.626678i	$0.784414\pi$
$632$	11.0375	+	33.3284i	0.439047	+	1.32573i
$633$	−9.72662	+	2.60624i	−0.386598	+	0.103589i
$634$	10.5356	−	9.19334i	0.418423	−	0.365114i
$635$	3.66785	−	5.95873i	0.145554	−	0.236465i
$636$	14.2510	−	18.3827i	0.565089	−	0.728920i
$637$		0			0
$638$	0.539159	+	1.10018i	0.0213455	+	0.0435565i
$639$	5.06470	+	8.77231i	0.200356	+	0.347027i
$640$	−18.2411	−	17.5289i	−0.721044	−	0.692889i
$641$	11.4235	−	19.7861i	0.451201	−	0.781504i	−0.547260	−	0.836963i	$-0.684329\pi$
$641$	11.4235	−	19.7861i	0.451201	−	0.781504i	0.998461	+	0.0554593i	$0.0176623\pi$
$642$	−32.0193	+	47.6638i	−1.26370	+	1.88114i
$643$	13.3643	−	13.3643i	0.527038	−	0.527038i	−0.392650	−	0.919688i	$-0.628442\pi$
$643$	13.3643	−	13.3643i	0.527038	−	0.527038i	0.919688	+	0.392650i	$0.128442\pi$
$644$		0			0
$645$	−5.52416	+	18.5138i	−0.217514	+	0.728982i
$646$	−0.679686	−	3.46188i	−0.0267419	−	0.136206i
$647$	22.6155	−	6.05981i	0.889108	−	0.238236i	0.214775	−	0.976663i	$-0.431098\pi$
$647$	22.6155	−	6.05981i	0.889108	−	0.238236i	0.674333	+	0.738428i	$0.264431\pi$
$648$	13.4070	−	15.0601i	0.526675	−	0.591615i
$649$	1.95284	−	1.12747i	0.0766557	−	0.0442572i
$650$	33.9339	−	26.3975i	1.33100	−	1.03540i
$651$		0			0
$652$	3.99471	+	31.5520i	0.156445	+	1.23567i
$653$	5.71494	−	21.3285i	0.223643	−	0.834647i	−0.759301	−	0.650740i	$-0.774459\pi$
$653$	5.71494	−	21.3285i	0.223643	−	0.834647i	0.982944	−	0.183907i	$-0.0588746\pi$
$654$	−33.1895	−	38.0353i	−1.29781	−	1.48730i
$655$	−5.71062	−	6.04178i	−0.223132	−	0.236072i
$656$	−8.32575	+	8.16210i	−0.325066	+	0.318676i
$657$	24.2320	−	24.2320i	0.945379	−	0.945379i
$658$		0			0
$659$	23.8406			0.928696			0.464348	−	0.885653i	$-0.346289\pi$
$659$	23.8406			0.928696			0.464348	+	0.885653i	$0.346289\pi$
$660$	1.00252	+	2.66694i	0.0390231	+	0.103810i
$661$	−11.0124	+	19.0740i	−0.428331	+	0.741891i	−0.996725	−	0.0808656i	$-0.974232\pi$
$661$	−11.0124	+	19.0740i	−0.428331	+	0.741891i	0.568394	+	0.822756i	$0.307565\pi$
$662$	−2.81750	+	41.4120i	−0.109505	+	1.60952i
$663$	−49.4692	−	13.2552i	−1.92122	−	0.514791i
$664$	−17.7383	+	11.6623i	−0.688379	+	0.452585i
$665$		0			0
$666$	4.84286	−	14.1512i	0.187657	−	0.548346i
$667$	−0.133143	+	0.496898i	−0.00515533	+	0.0192400i
$668$	13.2065	−	31.4412i	0.510976	−	1.21650i
$669$	71.7453	+	41.4222i	2.77383	+	1.60147i
$670$	2.47424	+	0.238514i	0.0955884	+	0.00921458i
$671$			1.78961i			0.0690872i
$672$		0			0
$673$	15.2135	+	15.2135i	0.586437	+	0.586437i	0.936665	−	0.350227i	$-0.113896\pi$
$673$	15.2135	+	15.2135i	0.586437	+	0.586437i	−0.350227	+	0.936665i	$0.613896\pi$
$674$	8.45506	+	43.0646i	0.325677	+	1.65879i
$675$	39.2352	+	12.9212i	1.51016	+	0.497338i
$676$	44.3754	−	18.1234i	1.70674	−	0.697054i
$677$	11.4768	+	3.07519i	0.441088	+	0.118189i	0.472527	−	0.881316i	$-0.343342\pi$
$677$	11.4768	+	3.07519i	0.441088	+	0.118189i	−0.0314382	+	0.999506i	$0.510009\pi$
$678$	8.20277	+	16.7381i	0.315026	+	0.642825i
$679$		0			0
$680$	−17.2130	+	5.16725i	−0.660090	+	0.198155i
$681$	30.9338	+	53.5789i	1.18539	+	2.05315i
$682$	2.60835	+	0.177461i	0.0998787	+	0.00679533i
$683$	9.28473	+	34.6511i	0.355270	+	1.32589i	0.880144	+	0.474707i	$0.157446\pi$
$683$	9.28473	+	34.6511i	0.355270	+	1.32589i	−0.524873	+	0.851180i	$0.675887\pi$
$684$	−1.37624	+	10.0673i	−0.0526220	+	0.384933i
$685$	−5.14573	+	2.78066i	−0.196608	+	0.106243i
$686$		0			0
$687$	−6.82927	−	6.82927i	−0.260553	−	0.260553i
$688$	−0.115717	+	11.6587i	−0.00441168	+	0.444482i
$689$	20.6581	+	11.9269i	0.787009	+	0.454380i
$690$	−0.419069	+	1.12048i	−0.0159537	+	0.0426560i
$691$	−37.9496	+	21.9102i	−1.44367	+	0.833505i	−0.998092	−	0.0617372i	$-0.980336\pi$
$691$	−37.9496	+	21.9102i	−1.44367	+	0.833505i	−0.445580	+	0.895242i	$0.647003\pi$
$692$	0.900764	−	0.114043i	0.0342419	−	0.00433527i
$693$		0			0
$694$	−3.71997	+	10.8700i	−0.141208	+	0.412619i
$695$	−5.64630	−	23.7265i	−0.214176	−	0.899997i
$696$	33.7400	−	1.95932i	1.27891	−	0.0742680i
$697$	2.14373	+	8.00051i	0.0811996	+	0.303041i
$698$	−9.93628	−	6.67493i	−0.376094	−	0.252650i
$699$	20.4792			0.774593
$700$		0			0
$701$	38.4455			1.45207			0.726033	−	0.687660i	$-0.241362\pi$
$701$	38.4455			1.45207			0.726033	+	0.687660i	$0.241362\pi$
$702$	58.9672	+	39.6126i	2.22557	+	1.49508i
$703$	0.415253	+	1.54974i	0.0156616	+	0.0584497i
$704$	1.02626	+	1.37949i	0.0386786	+	0.0519916i
$705$	10.6080	+	44.5761i	0.399520	+	1.67883i
$706$	9.52347	−	27.8282i	0.358420	−	1.04733i
$707$		0			0
$708$	−7.81296	−	61.7102i	−0.293629	−	2.31921i
$709$	33.8118	−	19.5213i	1.26983	−	0.733137i	0.294874	−	0.955536i	$-0.404722\pi$
$709$	33.8118	−	19.5213i	1.26983	−	0.733137i	0.974956	+	0.222400i	$0.0713890\pi$
$710$	−1.93900	+	5.18438i	−0.0727694	+	0.194566i
$711$	−62.2092	−	35.9165i	−2.33303	−	1.34697i
$712$	34.2094	−	11.3293i	1.28205	−	0.424582i
$713$	0.776200	+	0.776200i	0.0290689	+	0.0290689i
$714$		0			0
$715$	−2.57061	+	1.38911i	−0.0961352	+	0.0519496i
$716$	−9.62093	−	1.31522i	−0.359551	−	0.0491522i
$717$	−7.88464	−	29.4259i	−0.294457	−	1.09893i
$718$	−33.2488	−	2.26211i	−1.24083	−	0.0844212i
$719$	−2.32924	−	4.03436i	−0.0868659	−	0.150456i	0.819319	−	0.573338i	$-0.194352\pi$
$719$	−2.32924	−	4.03436i	−0.0868659	−	0.150456i	−0.906185	+	0.422882i	$0.861018\pi$
$720$	51.7233	+	1.97139i	1.92762	+	0.0734692i
$721$		0			0
$722$	11.3448	+	23.1497i	0.422211	+	0.861542i
$723$	−13.7108	−	3.67381i	−0.509912	−	0.136630i
$724$	−5.20460	−	12.7435i	−0.193428	−	0.473610i
$725$	9.07856	+	17.9944i	0.337169	+	0.668296i
$726$	8.84676	+	45.0597i	0.328334	+	1.67232i
$727$	−8.55868	−	8.55868i	−0.317424	−	0.317424i	0.530353	−	0.847777i	$-0.322059\pi$
$727$	−8.55868	−	8.55868i	−0.317424	−	0.317424i	−0.847777	+	0.530353i	$0.822059\pi$
$728$		0			0
$729$		−	32.2153i		−	1.19316i
$730$	18.6397	+	1.79684i	0.689885	+	0.0665040i
$731$	7.17306	+	4.14137i	0.265305	+	0.153174i
$732$	45.5144	+	19.1179i	1.68226	+	0.706617i
$733$	−0.287351	+	1.07241i	−0.0106135	+	0.0396103i	−0.971030	−	0.238959i	$-0.923194\pi$
$733$	−0.287351	+	1.07241i	−0.0106135	+	0.0396103i	0.960416	+	0.278570i	$0.0898603\pi$
$734$	2.44248	−	7.13708i	0.0901535	−	0.263434i
$735$		0			0
$736$	−0.0561491	+	0.719731i	−0.00206968	+	0.0265297i
$737$	−0.163182	−	0.0437245i	−0.00601089	−	0.00161061i
$738$	1.61926	−	23.8001i	0.0596058	−	0.876095i
$739$	2.43294	−	4.21398i	0.0894972	−	0.155014i	−0.817802	−	0.575500i	$-0.804807\pi$
$739$	2.43294	−	4.21398i	0.0894972	−	0.155014i	0.907299	+	0.420487i	$0.138141\pi$
$740$	7.65039	−	2.87584i	0.281234	−	0.105718i
$741$	−15.8225			−0.581253
$742$		0			0
$743$	24.8474	−	24.8474i	0.911564	−	0.911564i	−0.0848314	−	0.996395i	$-0.527035\pi$
$743$	24.8474	−	24.8474i	0.911564	−	0.911564i	0.996395	+	0.0848314i	$0.0270352\pi$
$744$	32.3774	−	64.4412i	1.18701	−	2.36253i
$745$	−17.2677	−	18.2691i	−0.632641	−	0.669328i
$746$	−29.9763	−	34.3529i	−1.09751	−	1.25775i
$747$	11.2417	−	41.9545i	0.411311	−	1.53503i
$748$	1.21176	−	0.153418i	0.0443065	−	0.00560952i
$749$		0			0
$750$	16.9993	+	43.6782i	0.620726	+	1.59490i
$751$	−17.3437	+	10.0134i	−0.632882	+	0.365394i	−0.781867	−	0.623445i	$-0.785733\pi$
$751$	−17.3437	+	10.0134i	−0.632882	+	0.365394i	0.148986	+	0.988839i	$0.452399\pi$
$752$	13.5874	+	24.0829i	0.495480	+	0.878212i
$753$	−75.2059	+	20.1514i	−2.74065	+	0.734356i
$754$	6.67750	+	34.0109i	0.243180	+	1.23860i
$755$	5.80593	−	19.4582i	0.211299	−	0.708156i
$756$		0			0
$757$	10.7543	−	10.7543i	0.390871	−	0.390871i	−0.484127	−	0.874998i	$-0.660863\pi$
$757$	10.7543	−	10.7543i	0.390871	−	0.390871i	0.874998	+	0.484127i	$0.160863\pi$
$758$	2.51225	−	3.73972i	0.0912489	−	0.135833i
$759$	0.0406520	−	0.0704114i	0.00147557	−	0.00255577i
$760$	−4.72352	+	2.91838i	−0.171340	+	0.105861i
$761$	−10.3017	−	17.8431i	−0.373437	−	0.646812i	0.616655	−	0.787234i	$-0.288488\pi$
$761$	−10.3017	−	17.8431i	−0.373437	−	0.646812i	−0.990092	+	0.140422i	$0.955154\pi$
$762$	5.77277	+	11.7796i	0.209125	+	0.426730i
$763$		0			0
$764$	27.2549	+	21.1291i	0.986048	+	0.764426i
$765$	19.2752	−	31.3141i	0.696895	−	1.13216i
$766$	−30.0381	+	26.2111i	−1.08532	+	0.947047i
$767$	61.6181	−	16.5105i	2.22490	−	0.596161i
$768$	46.0473	−	11.3637i	1.66159	−	0.410052i
$769$		−	9.33534i		−	0.336641i	−0.985732	−	0.168320i	$-0.946166\pi$
$769$		−	9.33534i		−	0.336641i	0.985732	−	0.168320i	$-0.0538343\pi$
$770$		0			0
$771$			68.7086i			2.47448i
$772$	−24.5198	−	32.2854i	−0.882488	−	1.16198i
$773$	14.1711	−	3.79713i	0.509698	−	0.136573i	0.00520083	−	0.999986i	$-0.498345\pi$
$773$	14.1711	−	3.79713i	0.509698	−	0.136573i	0.504497	+	0.863413i	$0.331678\pi$
$774$	−15.6842	−	17.9742i	−0.563758	−	0.646070i
$775$	42.9394	+	2.42181i	1.54243	+	0.0869940i
$776$	−8.64256	+	5.68218i	−0.310250	+	0.203978i
$777$		0			0
$778$	20.7582	−	10.1729i	0.744218	−	0.364715i
$779$	1.27946	+	2.21609i	0.0458414	+	0.0793997i
$780$	7.86758	+	80.2165i	0.281704	+	2.87221i
$781$	0.188094	−	0.325788i	0.00673052	−	0.0116576i
$782$	0.425712	+	0.285982i	0.0152234	+	0.0102267i
$783$	−23.5484	+	23.5484i	−0.841550	+	0.841550i
$784$		0			0
$785$	−41.2042	+	22.2660i	−1.47064	+	0.794706i
$786$	15.2940	−	3.00274i	0.545520	−	0.107104i
$787$	27.4799	−	7.36321i	0.979551	−	0.262470i	0.266696	−	0.963781i	$-0.414068\pi$
$787$	27.4799	−	7.36321i	0.979551	−	0.262470i	0.712856	+	0.701311i	$0.247401\pi$
$788$	33.7422	+	14.1731i	1.20202	+	0.504895i
$789$	−15.3033	+	8.83535i	−0.544811	+	0.314547i
$790$	−6.47433	−	38.7149i	−0.230346	−	1.37741i
$791$		0			0
$792$	−3.44507	−	0.711966i	−0.122415	−	0.0252986i
$793$	−13.1034	+	48.9025i	−0.465315	+	1.73658i
$794$	−16.1859	+	14.1237i	−0.574415	+	0.501232i
$795$	−18.8991	+	17.8632i	−0.670281	+	0.633542i
$796$	43.3682	+	5.92862i	1.53714	+	0.210134i
$797$	−4.43257	+	4.43257i	−0.157010	+	0.157010i	−0.781240	−	0.624231i	$-0.785413\pi$
$797$	−4.43257	+	4.43257i	−0.157010	+	0.157010i	0.624231	+	0.781240i	$0.285413\pi$
$798$		0			0
$799$	19.6436			0.694941
$800$	17.1443	+	22.4961i	0.606142	+	0.795356i
$801$	−36.8660	+	63.8537i	−1.30260	+	2.25616i
$802$	33.5249	+	2.28089i	1.18381	+	0.0805412i
$803$	−1.22933	−	0.329398i	−0.0433821	−	0.0116242i
$804$	−2.85525	+	3.68304i	−0.100697	+	0.129891i
$805$		0			0
$806$	69.9757	+	23.9473i	2.46479	+	0.843509i
$807$	−0.0512527	+	0.191278i	−0.00180418	+	0.00673329i
$808$	28.5760	−	32.0995i	1.00530	−	1.12926i
$809$	2.26376	+	1.30698i	0.0795895	+	0.0459510i	0.539267	−	0.842135i	$-0.318702\pi$
$809$	2.26376	+	1.30698i	0.0795895	+	0.0459510i	−0.459677	+	0.888086i	$0.652035\pi$
$810$	−17.3963	+	14.3373i	−0.611245	+	0.503760i
$811$		−	20.5143i		−	0.720354i	−0.932884	−	0.360177i	$-0.882716\pi$
$811$		−	20.5143i		−	0.720354i	0.932884	−	0.360177i	$-0.117284\pi$
$812$		0			0
$813$	5.82774	+	5.82774i	0.204388	+	0.204388i
$814$	−0.545066	+	0.107015i	−0.0191045	+	0.00375088i
$815$	1.00155	−	35.5437i	0.0350827	−	1.24504i
$816$	9.04308	−	32.4572i	0.316571	−	1.13623i
$817$	2.47173	+	0.662298i	0.0864748	+	0.0231709i
$818$	−28.6600	+	14.0452i	−1.00207	+	0.491080i
$819$		0			0
$820$	10.5989	−	7.58852i	0.370130	−	0.265003i
$821$	3.55951	+	6.16525i	0.124228	+	0.215169i	0.921431	−	0.388542i	$-0.127021\pi$
$821$	3.55951	+	6.16525i	0.124228	+	0.215169i	−0.797203	+	0.603711i	$0.793688\pi$
$822$	0.744332	−	10.9403i	0.0259615	−	0.381586i
$823$	5.83627	+	21.7813i	0.203440	+	0.759247i	0.989919	+	0.141631i	$0.0452347\pi$
$823$	5.83627	+	21.7813i	0.203440	+	0.759247i	−0.786480	+	0.617616i	$0.788099\pi$
$824$	−3.89258	−	1.95577i	−0.135605	−	0.0681323i
$825$	−0.649880	−	3.11844i	−0.0226259	−	0.108570i
$826$		0			0
$827$	−27.0197	−	27.0197i	−0.939566	−	0.939566i	0.0587089	−	0.998275i	$-0.481302\pi$
$827$	−27.0197	−	27.0197i	−0.939566	−	0.939566i	−0.998275	+	0.0587089i	$0.981302\pi$
$828$	−0.893354	−	1.17628i	−0.0310462	−	0.0408787i
$829$	19.0572	+	11.0027i	0.661884	+	0.382139i	0.792995	−	0.609229i	$-0.208521\pi$
$829$	19.0572	+	11.0027i	0.661884	+	0.382139i	−0.131110	+	0.991368i	$0.541854\pi$
$830$	21.5984	−	9.84014i	0.749692	−	0.341556i
$831$	−14.7045	+	8.48962i	−0.510092	+	0.294502i
$832$	17.9428	+	45.2099i	0.622054	+	1.56737i
$833$		0			0
$834$	43.2611	+	14.8050i	1.49801	+	0.512654i
$835$	−19.9862	+	32.4693i	−0.691651	+	1.12365i
$836$	0.349346	−	0.142677i	0.0120824	−	0.00493459i
$837$	18.3923	+	68.6411i	0.635732	+	2.37258i
$838$	−9.80646	+	14.5979i	−0.338758	+	0.504275i
$839$	−47.2741			−1.63208			−0.816041	−	0.577994i	$-0.803836\pi$
$839$	−47.2741			−1.63208			−0.816041	+	0.577994i	$0.803836\pi$
$840$		0			0
$841$	12.7512			0.439697
$842$	24.6676	−	36.7202i	0.850103	−	1.26546i
$843$	−17.5868	−	65.6348i	−0.605721	−	2.26058i
$844$	6.28968	−	2.56878i	0.216500	−	0.0884210i
$845$	−52.1355	+	12.4069i	−1.79351	+	0.426811i
$846$	−53.5279	−	18.3185i	−1.84033	−	0.629804i
$847$		0			0
$848$	−7.98113	+	13.5122i	−0.274073	+	0.464011i
$849$	1.45965	−	0.842732i	0.0500952	−	0.0289225i
$850$	19.9035	−	2.75466i	0.682683	−	0.0944840i
$851$	−0.201982	−	0.116614i	−0.00692386	−	0.00399749i
$852$	−6.27627	−	8.26399i	−0.215022	−	0.283120i
$853$	11.2255	+	11.2255i	0.384355	+	0.384355i	0.872668	−	0.488313i	$-0.162388\pi$
$853$	11.2255	+	11.2255i	0.384355	+	0.384355i	−0.488313	+	0.872668i	$0.662388\pi$
$854$		0			0
$855$	3.24817	−	10.8860i	0.111085	−	0.372294i
$856$	17.3929	−	34.6174i	0.594478	−	1.18320i
$857$	1.22415	+	4.56860i	0.0418162	+	0.156060i	0.983677	−	0.179943i	$-0.0575913\pi$
$857$	1.22415	+	4.56860i	0.0418162	+	0.156060i	−0.941861	+	0.336003i	$0.890925\pi$
$858$	0.371839	−	5.46534i	0.0126944	−	0.186584i
$859$	−2.80350	−	4.85581i	−0.0956543	−	0.165678i	0.814227	−	0.580546i	$-0.197161\pi$
$859$	−2.80350	−	4.85581i	−0.0956543	−	0.165678i	−0.909881	+	0.414868i	$0.863828\pi$
$860$	2.12866	−	12.8604i	0.0725867	−	0.438538i
$861$		0			0
$862$	−24.2920	+	11.9046i	−0.827389	+	0.405474i
$863$	48.2200	+	12.9205i	1.64143	+	0.439819i	0.957195	−	0.289445i	$-0.0934707\pi$
$863$	48.2200	+	12.9205i	1.64143	+	0.439819i	0.684232	+	0.729264i	$0.260137\pi$
$864$	−26.4445	+	38.5334i	−0.899661	+	1.31093i
$865$	−1.01472	−	0.0285928i	−0.0345016	−	0.000972184i
$866$	−9.56692	+	1.87831i	−0.325097	+	0.0638277i
$867$	18.7080	+	18.7080i	0.635358	+	0.635358i
$868$		0			0
$869$			2.66775i			0.0904971i
$870$	−37.6117	−	3.62572i	−1.27516	−	0.122923i
$871$	−4.13893	−	2.38961i	−0.140242	−	0.0809689i
$872$	25.4388	+	22.6464i	0.861467	+	0.766905i
$873$	5.47724	−	20.4413i	0.185376	−	0.691834i
$874$	0.149908	+	0.0513022i	0.00507072	+	0.00173532i
$875$		0			0
$876$	−21.5100	+	27.7461i	−0.726754	+	0.937455i
$877$	−26.8365	−	7.19083i	−0.906206	−	0.242817i	−0.224526	−	0.974468i	$-0.572083\pi$
$877$	−26.8365	−	7.19083i	−0.906206	−	0.242817i	−0.681679	+	0.731651i	$0.738750\pi$
$878$	46.2567	+	3.14711i	1.56109	+	0.106210i
$879$	3.00303	−	5.20140i	0.101290	−	0.175439i
$880$	−0.897051	−	1.70017i	−0.0302396	−	0.0573126i
$881$	−3.05077			−0.102783			−0.0513915	−	0.998679i	$-0.516366\pi$
$881$	−3.05077			−0.102783			−0.0513915	+	0.998679i	$0.516366\pi$
$882$		0			0
$883$	−15.9128	+	15.9128i	−0.535509	+	0.535509i	−0.922207	−	0.386697i	$-0.873616\pi$
$883$	−15.9128	+	15.9128i	−0.535509	+	0.535509i	0.386697	+	0.922207i	$0.373616\pi$
$884$	34.2357	+	4.68017i	1.15147	+	0.157411i
$885$	−1.95886	+	69.5173i	−0.0658462	+	2.33680i
$886$	12.8295	−	11.1950i	0.431016	−	0.376103i
$887$	10.1077	−	37.7226i	0.339384	−	1.26660i	−0.559653	−	0.828727i	$-0.689066\pi$
$887$	10.1077	−	37.7226i	0.339384	−	1.26660i	0.899037	−	0.437872i	$-0.144268\pi$
$888$	−3.10110	+	15.0056i	−0.104066	+	0.503556i
$889$		0			0
$890$	−39.7383	+	6.64548i	−1.33203	+	0.222757i
$891$	1.32685	−	0.766057i	0.0444511	−	0.0256639i
$892$	−51.5333	−	21.6460i	−1.72546	−	0.724763i
$893$	5.86203	−	1.57073i	0.196165	−	0.0525624i
$894$	46.2460	−	9.07968i	1.54670	−	0.303670i
$895$	10.4033	+	3.10415i	0.347745	+	0.103760i
$896$		0			0
$897$	1.62639	−	1.62639i	0.0543037	−	0.0543037i
$898$	−6.49049	−	4.36014i	−0.216591	−	0.145500i
$899$	−17.3363	+	30.0273i	−0.578197	+	1.00147i
$900$	−56.8048	−	11.0545i	−1.89349	−	0.368484i
$901$	5.57425	+	9.65489i	0.185705	+	0.321651i
$902$	−0.795543	+	0.389867i	−0.0264887	+	0.0129812i
$903$		0			0
$904$	−6.90903	−	10.5086i	−0.229791	−	0.349511i
$905$	3.56296	+	14.9720i	0.118437	+	0.497688i
$906$	25.0297	+	28.6841i	0.831555	+	0.952966i
$907$	−47.7753	+	12.8014i	−1.58635	+	0.425062i	−0.940885	−	0.338726i	$-0.890004\pi$
$907$	−47.7753	+	12.8014i	−1.58635	+	0.425062i	−0.645468	+	0.763788i	$0.723337\pi$
$908$	−25.2462	−	33.2417i	−0.837824	−	1.10317i
$909$			87.9310i			2.91649i
$910$		0			0
$911$		−	29.9032i		−	0.990736i	−0.868683	−	0.495368i	$-0.835033\pi$
$911$		−	29.9032i		−	0.990736i	0.868683	−	0.495368i	$-0.164967\pi$
$912$	0.103313	−	10.4089i	0.00342104	−	0.344675i
$913$	−1.55811	+	0.417495i	−0.0515660	+	0.0138171i
$914$	28.7820	−	25.1151i	0.952025	−	0.830734i
$915$	−47.0027	−	28.9321i	−1.55386	−	0.956467i
$916$	5.14994	+	3.99245i	0.170159	+	0.131914i
$917$		0			0
$918$	14.6103	+	29.8129i	0.482210	+	0.983973i
$919$	−23.0611	−	39.9429i	−0.760714	−	1.31760i	−0.942483	−	0.334254i	$-0.891516\pi$
$919$	−23.0611	−	39.9429i	−0.760714	−	1.31760i	0.181769	−	0.983341i	$-0.441818\pi$
$920$	0.185550	−	0.785512i	0.00611741	−	0.0258976i
$921$	3.16586	−	5.48343i	0.104319	−	0.180685i
$922$	6.50514	−	9.68352i	0.214235	−	0.318910i
$923$	7.52519	−	7.52519i	0.247695	−	0.247695i
$924$		0			0
$925$	−8.94556	+	1.86425i	−0.294128	+	0.0612961i
$926$	−5.96787	−	30.3965i	−0.196116	−	0.998890i
$927$	8.60938	−	2.30688i	0.282769	−	0.0757678i
$928$	−22.4180	+	4.17078i	−0.735906	+	0.136913i
$929$	−31.8393	+	18.3824i	−1.04461	+	0.603108i	−0.921137	−	0.389239i	$-0.872738\pi$
$929$	−31.8393	+	18.3824i	−1.04461	+	0.603108i	−0.123477	+	0.992347i	$0.539405\pi$
$930$	−46.8292	+	65.6371i	−1.53559	+	2.15232i
$931$		0			0
$932$	−13.7078	+	1.73551i	−0.449014	+	0.0568484i
$933$	−9.77884	+	36.4951i	−0.320145	+	1.19480i
$934$	36.5317	+	41.8655i	1.19535	+	1.36988i
$935$	−1.36507	−	0.0384648i	−0.0446425	−	0.00125793i
$936$	−88.9261	−	44.6795i	−2.90664	−	1.46039i
$937$	25.1593	−	25.1593i	0.821917	−	0.821917i	−0.164465	−	0.986383i	$-0.552590\pi$
$937$	25.1593	−	25.1593i	0.821917	−	0.821917i	0.986383	+	0.164465i	$0.0525899\pi$
$938$		0			0
$939$	−60.3571			−1.96968
$940$	−10.8781	−	28.9382i	−0.354804	−	0.943860i
$941$	12.8202	−	22.2052i	0.417926	−	0.723868i	−0.577805	−	0.816175i	$-0.696091\pi$
$941$	12.8202	−	22.2052i	0.417926	−	0.723868i	0.995731	+	0.0923065i	$0.0294240\pi$
$942$	5.96020	−	87.6038i	0.194194	−	2.85429i
$943$	−0.359308	−	0.0962763i	−0.0117007	−	0.00313519i
$944$	10.4593	+	40.6438i	0.340420	+	1.32284i
$945$		0			0
$946$	−0.286856	+	0.838211i	−0.00932649	+	0.0272526i
$947$	0.748909	−	2.79497i	0.0243363	−	0.0908242i	−0.952690	−	0.303945i	$-0.901696\pi$
$947$	0.748909	−	2.79497i	0.0243363	−	0.0908242i	0.977026	+	0.213121i	$0.0683628\pi$
$948$	67.8477	+	28.4987i	2.20359	+	0.925595i
$949$	−31.1805	−	18.0021i	−1.01216	−	0.584372i
$950$	5.71931	−	2.41355i	0.185559	−	0.0783058i
$951$		−	29.3088i		−	0.950404i
$952$		0			0
$953$	−29.4048	−	29.4048i	−0.952513	−	0.952513i	0.0464091	−	0.998923i	$-0.485222\pi$
$953$	−29.4048	−	29.4048i	−0.952513	−	0.952513i	−0.998923	+	0.0464091i	$0.985222\pi$
$954$	−6.18597	−	31.5073i	−0.200278	−	1.02009i
$955$	−26.4847	−	28.0205i	−0.857024	−	0.906723i
$956$	7.77131	+	19.0281i	0.251342	+	0.615414i
$957$	2.48058	+	0.664669i	0.0801857	+	0.0214857i
$958$	−2.40669	−	4.91097i	−0.0777567	−	0.158666i
$959$		0			0
$960$	−52.8225	+	4.65198i	−1.70484	+	0.150142i
$961$	21.4931	+	37.2272i	0.693326	+	1.20088i
$962$	−15.6779	−	1.06666i	−0.505475	−	0.0343904i
$963$	20.5154	+	76.5646i	0.661100	+	2.46726i
$964$	9.48874	+	1.29715i	0.305612	+	0.0417785i
$965$	21.5484	+	39.8763i	0.693668	+	1.28367i
$966$		0			0
$967$	33.9934	+	33.9934i	1.09315	+	1.09315i	0.995190	+	0.0979625i	$0.0312325\pi$
$967$	33.9934	+	33.9934i	1.09315	+	1.09315i	0.0979625	+	0.995190i	$0.468767\pi$
$968$	−9.74019	−	29.4112i	−0.313062	−	0.945310i
$969$	−6.40417	−	3.69745i	−0.205731	−	0.118779i
$970$	10.5233	−	4.79437i	0.337883	−	0.153938i
$971$	−11.7604	+	6.78989i	−0.377410	+	0.217898i	−0.676691	−	0.736267i	$-0.736587\pi$
$971$	−11.7604	+	6.78989i	−0.377410	+	0.217898i	0.299281	+	0.954165i	$0.403253\pi$
$972$	0.917705	+	7.24844i	0.0294354	+	0.232494i
$973$		0			0
$974$	0.203827	−	0.595596i	0.00653104	−	0.0190841i
$975$	5.07449	−	89.9721i	0.162514	−	2.88141i
$976$	−32.0854	−	8.93949i	−1.02703	−	0.286146i
$977$	−10.7403	−	40.0832i	−0.343611	−	1.28238i	−0.894226	−	0.447616i	$-0.852273\pi$
$977$	−10.7403	−	40.0832i	−0.343611	−	1.28238i	0.550615	−	0.834759i	$-0.314393\pi$
$978$	55.3364	+	37.1735i	1.76946	+	1.18868i
$979$	2.73827			0.0875155
$980$		0			0
$981$	−69.6851			−2.22487
$982$	47.4547	+	31.8788i	1.51434	+	1.01729i
$983$	0.533889	+	1.99250i	0.0170284	+	0.0635509i	0.973917	−	0.226904i	$-0.0728602\pi$
$983$	0.533889	+	1.99250i	0.0170284	+	0.0635509i	−0.956889	+	0.290454i	$0.906194\pi$
$984$	1.41679	+	24.3975i	0.0451657	+	0.777764i
$985$	−34.8455	−	21.4489i	−1.11027	−	0.683419i
$986$	−5.24505	+	15.3264i	−0.167037	+	0.488092i
$987$		0			0
$988$	10.5908	−	1.34087i	0.336939	−	0.0426589i
$989$	−0.322147	+	0.185992i	−0.0102437	+	0.00591419i
$990$	3.68387	+	1.37780i	0.117081	+	0.0437893i
$991$	25.9485	+	14.9814i	0.824282	+	0.475899i	0.851891	−	0.523720i	$-0.175456\pi$
$991$	25.9485	+	14.9814i	0.824282	+	0.475899i	−0.0276091	+	0.999619i	$0.508789\pi$
$992$	−16.2109	+	45.8777i	−0.514696	+	1.45662i
$993$	61.5205	+	61.5205i	1.95229	+	1.95229i
$994$		0			0
$995$	−46.8950	−	13.9925i	−1.48667	−	0.443593i
$996$	−6.02686	+	44.0868i	−0.190968	+	1.39694i
$997$	−15.1623	−	56.5865i	−0.480196	−	1.79211i	−0.600784	−	0.799411i	$-0.705145\pi$
$997$	−15.1623	−	56.5865i	−0.480196	−	1.79211i	0.120588	−	0.992703i	$-0.461522\pi$
$998$	−44.8505	−	3.05144i	−1.41972	−	0.0965917i
$999$	−7.54927	−	13.0757i	−0.238848	−	0.413697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.k.263.6		72
4.3	odd	2	inner	980.2.x.k.263.10		72
5.2	odd	4	inner	980.2.x.k.67.4		72
7.2	even	3	inner	980.2.x.k.863.18		72
7.3	odd	6		980.2.k.l.883.7		36
7.4	even	3		140.2.k.a.43.7	✓	36
7.5	odd	6		980.2.x.l.863.18		72
7.6	odd	2		980.2.x.l.263.6		72
20.7	even	4	inner	980.2.x.k.67.18		72
28.3	even	6		980.2.k.l.883.15		36
28.11	odd	6		140.2.k.a.43.15	yes	36
28.19	even	6		980.2.x.l.863.4		72
28.23	odd	6	inner	980.2.x.k.863.4		72
28.27	even	2		980.2.x.l.263.10		72
35.2	odd	12	inner	980.2.x.k.667.10		72
35.4	even	6		700.2.k.b.43.12		36
35.12	even	12		980.2.x.l.667.10		72
35.17	even	12		980.2.k.l.687.15		36
35.18	odd	12		700.2.k.b.407.4		36
35.27	even	4		980.2.x.l.67.4		72
35.32	odd	12		140.2.k.a.127.15	yes	36
140.27	odd	4		980.2.x.l.67.18		72
140.39	odd	6		700.2.k.b.43.4		36
140.47	odd	12		980.2.x.l.667.6		72
140.67	even	12		140.2.k.a.127.7	yes	36
140.87	odd	12		980.2.k.l.687.7		36
140.107	even	12	inner	980.2.x.k.667.6		72
140.123	even	12		700.2.k.b.407.12		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.7	✓	36	7.4	even	3
140.2.k.a.43.15	yes	36	28.11	odd	6
140.2.k.a.127.7	yes	36	140.67	even	12
140.2.k.a.127.15	yes	36	35.32	odd	12
700.2.k.b.43.4		36	140.39	odd	6
700.2.k.b.43.12		36	35.4	even	6
700.2.k.b.407.4		36	35.18	odd	12
700.2.k.b.407.12		36	140.123	even	12
980.2.k.l.687.7		36	140.87	odd	12
980.2.k.l.687.15		36	35.17	even	12
980.2.k.l.883.7		36	7.3	odd	6
980.2.k.l.883.15		36	28.3	even	6
980.2.x.k.67.4		72	5.2	odd	4	inner
980.2.x.k.67.18		72	20.7	even	4	inner
980.2.x.k.263.6		72	1.1	even	1	trivial
980.2.x.k.263.10		72	4.3	odd	2	inner
980.2.x.k.667.6		72	140.107	even	12	inner
980.2.x.k.667.10		72	35.2	odd	12	inner
980.2.x.k.863.4		72	28.23	odd	6	inner
980.2.x.k.863.18		72	7.2	even	3	inner
980.2.x.l.67.4		72	35.27	even	4
980.2.x.l.67.18		72	140.27	odd	4
980.2.x.l.263.6		72	7.6	odd	2
980.2.x.l.263.10		72	28.27	even	2
980.2.x.l.667.6		72	140.47	odd	12
980.2.x.l.667.10		72	35.12	even	12
980.2.x.l.863.4		72	28.19	even	6
980.2.x.l.863.18		72	7.5	odd	6

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.788610 + 1.17392i) q^{2} +(0.767216 + 2.86329i) q^{3} +(-0.756188 - 1.85153i) q^{4} +(0.517671 + 2.17532i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(2.76990 + 0.572433i) q^{8} +(-5.01173 + 2.89352i) q^{9} +O(q^{10})\)	\(q+(-0.788610 + 1.17392i) q^{2} +(0.767216 + 2.86329i) q^{3} +(-0.756188 - 1.85153i) q^{4} +(0.517671 + 2.17532i) q^{5} +(-3.96631 - 1.35737i) q^{6} +(2.76990 + 0.572433i) q^{8} +(-5.01173 + 2.89352i) q^{9} +(-2.96190 - 1.10777i) q^{10} +(0.186127 + 0.107460i) q^{11} +(4.72132 - 3.58571i) q^{12} +(4.29923 + 4.29923i) q^{13} +(-5.83140 + 3.15118i) q^{15} +(-2.85636 + 2.80022i) q^{16} +(0.735462 + 2.74478i) q^{17} +(0.555529 - 8.16524i) q^{18} +(0.438952 + 0.760287i) q^{19} +(3.63622 - 2.60344i) q^{20} +(-0.272931 + 0.133754i) q^{22} +(-0.123270 - 0.0330301i) q^{23} +(0.486067 + 8.37019i) q^{24} +(-4.46403 + 2.25220i) q^{25} +(-8.43738 + 1.65655i) q^{26} +(-5.84185 - 5.84185i) q^{27} -4.03098i q^{29} +(0.899463 - 9.33067i) q^{30} +(-7.44914 - 4.30076i) q^{31} +(-1.03468 - 5.56142i) q^{32} +(-0.164890 + 0.615379i) q^{33} +(-3.80215 - 1.30119i) q^{34} +(9.14726 + 7.09134i) q^{36} +(1.76528 + 0.473005i) q^{37} +(-1.23868 - 0.0842746i) q^{38} +(-9.01151 + 15.6084i) q^{39} +(0.188668 + 6.32174i) q^{40} +2.91481 q^{41} +(2.06108 - 2.06108i) q^{43} +(0.0582196 - 0.425880i) q^{44} +(-8.88876 - 9.40422i) q^{45} +(0.135987 - 0.118661i) q^{46} +(1.78918 - 6.67731i) q^{47} +(-10.2093 - 6.03021i) q^{48} +(0.876477 - 7.01654i) q^{50} +(-7.29484 + 4.21168i) q^{51} +(4.70915 - 11.2112i) q^{52} +(3.78963 - 1.01543i) q^{53} +(11.4648 - 2.25094i) q^{54} +(-0.137408 + 0.460514i) q^{55} +(-1.84015 + 1.84015i) q^{57} +(4.73205 + 3.17887i) q^{58} +(5.24601 - 9.08635i) q^{59} +(10.2442 + 8.41416i) q^{60} +(4.16343 + 7.21127i) q^{61} +(10.9232 - 5.35309i) q^{62} +(7.34464 + 3.17116i) q^{64} +(-7.12662 + 11.5778i) q^{65} +(-0.592373 - 0.678863i) q^{66} +(-0.759268 + 0.203445i) q^{67} +(4.52591 - 3.43730i) q^{68} -0.378298i q^{69} -1.75036i q^{71} +(-15.5383 + 5.14588i) q^{72} +(-5.71993 + 1.53265i) q^{73} +(-1.94739 + 1.69928i) q^{74} +(-9.87357 - 11.0539i) q^{75} +(1.07577 - 1.38765i) q^{76} +(-11.2165 - 22.8877i) q^{78} +(6.20636 + 10.7497i) q^{79} +(-7.57002 - 4.76391i) q^{80} +(3.56437 - 6.17368i) q^{81} +(-2.29865 + 3.42176i) q^{82} +(-5.30716 + 5.30716i) q^{83} +(-5.59005 + 3.02076i) q^{85} +(0.794160 + 4.04494i) q^{86} +(11.5419 - 3.09263i) q^{87} +(0.454037 + 0.404198i) q^{88} +(11.0339 - 6.37043i) q^{89} +(18.0496 - 3.01845i) q^{90} +(0.0320589 + 0.253215i) q^{92} +(6.59923 - 24.6287i) q^{93} +(6.42768 + 7.36615i) q^{94} +(-1.42663 + 1.34844i) q^{95} +(15.1301 - 7.22941i) q^{96} +(-2.58579 + 2.58579i) q^{97} -1.24375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{6}+O(q^{10}) \) 72 * q - 16 * q^6	\( 72 q - 16 q^{6} + 16 q^{10} + 16 q^{12} - 8 q^{13} + 8 q^{16} + 20 q^{17} - 28 q^{18} + 40 q^{20} + 8 q^{22} + 20 q^{25} + 32 q^{26} + 4 q^{30} - 20 q^{37} + 36 q^{40} - 20 q^{45} - 16 q^{46} - 48 q^{48} + 80 q^{50} - 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} + 64 q^{61} + 80 q^{62} - 4 q^{65} - 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 16 q^{76} - 152 q^{78} + 20 q^{80} + 36 q^{81} - 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} - 32 q^{90} - 112 q^{92} - 32 q^{93} - 120 q^{96} + 40 q^{97}+O(q^{100}) \) 72 * q - 16 * q^6 + 16 * q^10 + 16 * q^12 - 8 * q^13 + 8 * q^16 + 20 * q^17 - 28 * q^18 + 40 * q^20 + 8 * q^22 + 20 * q^25 + 32 * q^26 + 4 * q^30 - 20 * q^37 + 36 * q^40 - 20 * q^45 - 16 * q^46 - 48 * q^48 + 80 * q^50 - 16 * q^52 + 44 * q^53 - 32 * q^57 + 4 * q^58 - 40 * q^60 + 64 * q^61 + 80 * q^62 - 4 * q^65 - 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 16 * q^76 - 152 * q^78 + 20 * q^80 + 36 * q^81 - 56 * q^82 - 40 * q^85 - 56 * q^86 + 40 * q^88 - 32 * q^90 - 112 * q^92 - 32 * q^93 - 120 * q^96 + 40 * q^97

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