LMFDB - Embedded newform 980.2.x.l.67.10

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			67.10
Character	$\chi$	$=$	980.67
Dual form			980.2.x.l.863.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0657371 + 1.41268i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-1.99136 + 0.185732i) q^{4} +(1.95767 - 1.08052i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +(6.41872 - 3.70585i) q^{9} +O(q^{10})$	\(q+(0.0657371 + 1.41268i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-1.99136 + 0.185732i) q^{4} +(1.95767 - 1.08052i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +(6.41872 - 3.70585i) q^{9} +(1.65512 + 2.69455i) q^{10} +(-1.21832 - 0.703395i) q^{11} +(-6.05149 + 2.24194i) q^{12} +(0.699298 - 0.699298i) q^{13} +(5.19924 - 5.00264i) q^{15} +(3.93101 - 0.739716i) q^{16} +(-4.46506 + 1.19641i) q^{17} +(5.65715 + 8.82402i) q^{18} +(1.40337 + 2.43071i) q^{19} +(-3.69774 + 2.51529i) q^{20} +(0.913587 - 1.76734i) q^{22} +(-0.543980 + 2.03016i) q^{23} +(-3.56496 - 8.40147i) q^{24} +(2.66497 - 4.23059i) q^{25} +(1.03386 + 0.941917i) q^{26} +(10.0659 - 10.0659i) q^{27} -4.85706i q^{29} +(7.40894 + 7.01603i) q^{30} +(3.18470 + 1.83869i) q^{31} +(1.30340 + 5.50465i) q^{32} +(-4.38464 - 1.17486i) q^{33} +(-1.98367 - 6.22907i) q^{34} +(-12.0937 + 8.57184i) q^{36} +(-2.14283 + 7.99714i) q^{37} +(-3.34157 + 2.14231i) q^{38} +(1.59554 - 2.76356i) q^{39} +(-3.79640 - 5.05840i) q^{40} -3.53368 q^{41} +(-2.49869 - 2.49869i) q^{43} +(2.55675 + 1.17443i) q^{44} +(8.56153 - 14.1904i) q^{45} +(-2.90374 - 0.635016i) q^{46} +(2.55312 + 0.684106i) q^{47} +(11.6343 - 5.58845i) q^{48} +(6.15168 + 3.48666i) q^{50} +(-12.9174 + 7.45786i) q^{51} +(-1.26267 + 1.52243i) q^{52} +(-0.254952 - 0.951495i) q^{53} +(14.8816 + 13.5582i) q^{54} +(-3.14510 - 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(6.86149 - 0.319289i) q^{58} +(-3.53286 + 6.11910i) q^{59} +(-9.42439 + 10.9277i) q^{60} +(1.09916 + 1.90379i) q^{61} +(-2.38814 + 4.61985i) q^{62} +(-7.69065 + 2.20315i) q^{64} +(0.613394 - 2.12460i) q^{65} +(1.37148 - 6.27135i) q^{66} +(0.827081 + 3.08671i) q^{67} +(8.66931 - 3.21178i) q^{68} +6.78184i q^{69} +12.1891i q^{71} +(-12.9043 - 16.5211i) q^{72} +(-1.71613 - 6.40469i) q^{73} +(-11.4383 - 2.50143i) q^{74} +(4.77298 - 15.4114i) q^{75} +(-3.24607 - 4.57976i) q^{76} +(4.00892 + 2.07233i) q^{78} +(0.299644 + 0.518999i) q^{79} +(6.89635 - 5.69564i) q^{80} +(11.8491 - 20.5233i) q^{81} +(-0.232294 - 4.99198i) q^{82} +(-4.53764 - 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(3.36560 - 3.69412i) q^{86} +(-4.05630 - 15.1383i) q^{87} +(-1.49103 + 3.68908i) q^{88} +(0.401553 - 0.231837i) q^{89} +(20.6093 + 11.1619i) q^{90} +(0.706194 - 4.14381i) q^{92} +(11.4615 + 3.07111i) q^{93} +(-0.798592 + 3.65172i) q^{94} +(5.37376 + 3.24217i) q^{95} +(8.65952 + 16.0682i) q^{96} +(-8.00558 - 8.00558i) q^{97} -10.4267 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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.0657371	+	1.41268i	0.0464831	+	0.998919i
$2$	0.0657371	+	1.41268i	0.0464831	+	0.998919i
$3$	3.11677	−	0.835136i	1.79947	−	0.482166i	0.805573	−	0.592497i	$-0.201858\pi$
$3$	3.11677	−	0.835136i	1.79947	−	0.482166i	0.993895	+	0.110331i	$0.0351911\pi$
$4$	−1.99136	+	0.185732i	−0.995679	+	0.0928658i
$5$	1.95767	−	1.08052i	0.875498	−	0.483221i
$5$	1.95767	−	1.08052i	0.875498	−	0.483221i
$6$	1.38467	+	4.34811i	0.565290	+	1.77511i
$7$		0			0
$7$		0			0
$8$	−0.393286	−	2.80095i	−0.139048	−	0.990286i
$9$	6.41872	−	3.70585i	2.13957	−	1.23528i
$10$	1.65512	+	2.69455i	0.523395	+	0.852090i
$11$	−1.21832	−	0.703395i	−0.367336	−	0.212082i	0.304958	−	0.952366i	$-0.401358\pi$
$11$	−1.21832	−	0.703395i	−0.367336	−	0.212082i	−0.672294	+	0.740284i	$0.734691\pi$
$12$	−6.05149	+	2.24194i	−1.74691	+	0.647191i
$13$	0.699298	−	0.699298i	0.193950	−	0.193950i	−0.603450	−	0.797401i	$-0.706208\pi$
$13$	0.699298	−	0.699298i	0.193950	−	0.193950i	0.797401	+	0.603450i	$0.206208\pi$
$14$		0			0
$15$	5.19924	−	5.00264i	1.34244	−	1.29168i
$16$	3.93101	−	0.739716i	0.982752	−	0.184929i
$17$	−4.46506	+	1.19641i	−1.08294	+	0.290172i	−0.755798	−	0.654805i	$-0.772751\pi$
$17$	−4.46506	+	1.19641i	−1.08294	+	0.290172i	−0.327138	+	0.944977i	$0.606084\pi$
$18$	5.65715	+	8.82402i	1.33340	+	2.07984i
$19$	1.40337	+	2.43071i	0.321955	+	0.557643i	0.980891	−	0.194556i	$-0.0623266\pi$
$19$	1.40337	+	2.43071i	0.321955	+	0.557643i	−0.658936	+	0.752199i	$0.728993\pi$
$20$	−3.69774	+	2.51529i	−0.826840	+	0.562437i
$21$		0			0
$22$	0.913587	−	1.76734i	0.194777	−	0.376797i
$23$	−0.543980	+	2.03016i	−0.113428	+	0.423318i	−0.999164	−	0.0408699i	$-0.986987\pi$
$23$	−0.543980	+	2.03016i	−0.113428	+	0.423318i	0.885737	+	0.464188i	$0.153654\pi$
$24$	−3.56496	−	8.40147i	−0.727694	−	1.71494i
$25$	2.66497	−	4.23059i	0.532994	−	0.846119i
$26$	1.03386	+	0.941917i	0.202756	+	0.184725i
$27$	10.0659	−	10.0659i	1.93718	−	1.93718i
$28$		0			0
$29$		−	4.85706i		−	0.901933i	−0.892541	−	0.450967i	$-0.851079\pi$
$29$		−	4.85706i		−	0.901933i	0.892541	−	0.450967i	$-0.148921\pi$
$30$	7.40894	+	7.01603i	1.35268	+	1.28095i
$31$	3.18470	+	1.83869i	0.571990	+	0.330238i	0.757944	−	0.652320i	$-0.226204\pi$
$31$	3.18470	+	1.83869i	0.571990	+	0.330238i	−0.185954	+	0.982558i	$0.559538\pi$
$32$	1.30340	+	5.50465i	0.230410	+	0.973094i
$33$	−4.38464	−	1.17486i	−0.763268	−	0.204517i
$34$	−1.98367	−	6.22907i	−0.340196	−	1.06828i
$35$		0			0
$36$	−12.0937	+	8.57184i	−2.01561	+	1.42864i
$37$	−2.14283	+	7.99714i	−0.352279	+	1.31472i	0.531596	+	0.846998i	$0.321592\pi$
$37$	−2.14283	+	7.99714i	−0.352279	+	1.31472i	−0.883875	+	0.467724i	$0.845074\pi$
$38$	−3.34157	+	2.14231i	−0.542074	+	0.347528i
$39$	1.59554	−	2.76356i	0.255491	−	0.442523i
$40$	−3.79640	−	5.05840i	−0.600263	−	0.799803i
$41$	−3.53368			−0.551868			−0.275934	−	0.961177i	$-0.588987\pi$
$41$	−3.53368			−0.551868			−0.275934	+	0.961177i	$0.588987\pi$
$42$		0			0
$43$	−2.49869	−	2.49869i	−0.381046	−	0.381046i	0.490433	−	0.871479i	$-0.336839\pi$
$43$	−2.49869	−	2.49869i	−0.381046	−	0.381046i	−0.871479	+	0.490433i	$0.836839\pi$
$44$	2.55675	+	1.17443i	0.385444	+	0.177052i
$45$	8.56153	−	14.1904i	1.27628	−	2.11538i
$46$	−2.90374	−	0.635016i	−0.428133	−	0.0936280i
$47$	2.55312	+	0.684106i	0.372411	+	0.0997872i	0.440170	−	0.897915i	$-0.354918\pi$
$47$	2.55312	+	0.684106i	0.372411	+	0.0997872i	−0.0677590	+	0.997702i	$0.521585\pi$
$48$	11.6343	−	5.58845i	1.67926	−	0.806623i
$49$		0			0
$50$	6.15168	+	3.48666i	0.869980	+	0.493088i
$51$	−12.9174	+	7.45786i	−1.80880	+	1.04431i
$52$	−1.26267	+	1.52243i	−0.175101	+	0.211123i
$53$	−0.254952	−	0.951495i	−0.0350204	−	0.130698i	0.946203	−	0.323575i	$-0.104885\pi$
$53$	−0.254952	−	0.951495i	−0.0350204	−	0.130698i	−0.981223	+	0.192877i	$0.938218\pi$
$54$	14.8816	+	13.5582i	2.02513	+	1.84504i
$55$	−3.14510	−	0.0606082i	−0.424085	−	0.00817240i
$56$		0			0
$57$	6.40395	+	6.40395i	0.848224	+	0.848224i
$58$	6.86149	−	0.319289i	0.900958	−	0.0419247i
$59$	−3.53286	+	6.11910i	−0.459940	+	0.796639i	−0.998957	−	0.0456557i	$-0.985462\pi$
$59$	−3.53286	+	6.11910i	−0.459940	+	0.796639i	0.539018	+	0.842294i	$0.318796\pi$
$60$	−9.42439	+	10.9277i	−1.21668	+	1.41076i
$61$	1.09916	+	1.90379i	0.140732	+	0.243756i	0.927773	−	0.373146i	$-0.121721\pi$
$61$	1.09916	+	1.90379i	0.140732	+	0.243756i	−0.787040	+	0.616902i	$0.788388\pi$
$62$	−2.38814	+	4.61985i	−0.303294	+	0.586722i
$63$		0			0
$64$	−7.69065	+	2.20315i	−0.961331	+	0.275394i
$65$	0.613394	−	2.12460i	0.0760822	−	0.263524i
$66$	1.37148	−	6.27135i	0.168817	−	0.771950i
$67$	0.827081	+	3.08671i	0.101044	+	0.377101i	0.997866	−	0.0652895i	$-0.0207971\pi$
$67$	0.827081	+	3.08671i	0.101044	+	0.377101i	−0.896822	+	0.442391i	$0.854130\pi$
$68$	8.66931	−	3.21178i	1.05131	−	0.389485i
$69$			6.78184i			0.816438i
$70$		0			0
$71$			12.1891i			1.44658i	0.690546	+	0.723289i	$0.257370\pi$
$71$			12.1891i			1.44658i	−0.690546	+	0.723289i	$0.742630\pi$
$72$	−12.9043	−	16.5211i	−1.52079	−	1.94703i
$73$	−1.71613	−	6.40469i	−0.200858	−	0.749612i	−0.990672	−	0.136266i	$-0.956490\pi$
$73$	−1.71613	−	6.40469i	−0.200858	−	0.749612i	0.789814	−	0.613346i	$-0.210177\pi$
$74$	−11.4383	−	2.50143i	−1.32968	−	0.290785i
$75$	4.77298	−	15.4114i	0.551136	−	1.77956i
$76$	−3.24607	−	4.57976i	−0.372350	−	0.525334i
$77$		0			0
$78$	4.00892	+	2.07233i	0.453921	+	0.234645i
$79$	0.299644	+	0.518999i	0.0337126	+	0.0583919i	0.882389	−	0.470520i	$-0.155934\pi$
$79$	0.299644	+	0.518999i	0.0337126	+	0.0583919i	−0.848677	+	0.528912i	$0.822600\pi$
$80$	6.89635	−	5.69564i	0.771036	−	0.636792i
$81$	11.8491	−	20.5233i	1.31657	−	2.28036i
$82$	−0.232294	−	4.99198i	−0.0256526	−	0.551271i
$83$	−4.53764	−	4.53764i	−0.498071	−	0.498071i	0.412766	−	0.910837i	$-0.364563\pi$
$83$	−4.53764	−	4.53764i	−0.498071	−	0.498071i	−0.910837	+	0.412766i	$0.864563\pi$
$84$		0			0
$85$	−7.44839	+	7.16674i	−0.807891	+	0.777342i
$86$	3.36560	−	3.69412i	0.362922	−	0.398347i
$87$	−4.05630	−	15.1383i	−0.434882	−	1.62300i
$88$	−1.49103	+	3.68908i	−0.158944	+	0.393257i
$89$	0.401553	−	0.231837i	0.0425645	−	0.0245746i	−0.478567	−	0.878051i	$-0.658844\pi$
$89$	0.401553	−	0.231837i	0.0425645	−	0.0245746i	0.521131	+	0.853477i	$0.325510\pi$
$90$	20.6093	+	11.1619i	2.17242	+	1.17657i
$91$		0			0
$92$	0.706194	−	4.14381i	0.0736258	−	0.432022i
$93$	11.4615	+	3.07111i	1.18851	+	0.318459i
$94$	−0.798592	+	3.65172i	−0.0823685	+	0.376647i
$95$	5.37376	+	3.24217i	0.551336	+	0.332640i
$96$	8.65952	+	16.0682i	0.883809	+	1.63995i
$97$	−8.00558	−	8.00558i	−0.812843	−	0.812843i	0.172216	−	0.985059i	$-0.444907\pi$
$97$	−8.00558	−	8.00558i	−0.812843	−	0.812843i	−0.985059	+	0.172216i	$0.944907\pi$
$98$		0			0
$99$	−10.4267			−1.04792
$100$	−4.52115	+	8.91959i	−0.452115	+	0.891959i
$101$	−3.01549	+	5.22299i	−0.300053	+	0.519707i	−0.976148	−	0.217108i	$-0.930338\pi$
$101$	−3.01549	+	5.22299i	−0.300053	+	0.519707i	0.676095	+	0.736815i	$0.263671\pi$
$102$	−11.3848	−	17.7579i	−1.12726	−	1.75830i
$103$	−3.64227	+	13.5932i	−0.358884	+	1.33937i	0.516642	+	0.856202i	$0.327182\pi$
$103$	−3.64227	+	13.5932i	−0.358884	+	1.33937i	−0.875526	+	0.483171i	$0.839485\pi$
$104$	−2.23372	−	1.68367i	−0.219035	−	0.165098i
$105$		0			0
$106$	1.32740	−	0.422716i	0.128929	−	0.0410578i
$107$	19.3758	+	5.19174i	1.87313	+	0.501905i	0.999893	+	0.0146144i	$0.00465208\pi$
$107$	19.3758	+	5.19174i	1.87313	+	0.501905i	0.873240	+	0.487290i	$0.162015\pi$
$108$	−18.1752	+	21.9143i	−1.74891	+	2.10871i
$109$	0.879139	+	0.507571i	0.0842062	+	0.0486165i	0.541512	−	0.840693i	$-0.317852\pi$
$109$	0.879139	+	0.507571i	0.0842062	+	0.0486165i	−0.457306	+	0.889310i	$0.651185\pi$
$110$	−0.121129	−	4.44701i	−0.0115492	−	0.424006i
$111$			26.7148i			2.53566i
$112$		0			0
$113$	7.39345	−	7.39345i	0.695518	−	0.695518i	−0.267923	−	0.963440i	$-0.586337\pi$
$113$	7.39345	−	7.39345i	0.695518	−	0.695518i	0.963440	+	0.267923i	$0.0863372\pi$
$114$	−8.62579	+	9.46774i	−0.807879	+	0.886735i
$115$	1.12869	+	4.56217i	0.105251	+	0.425425i
$116$	0.902109	+	9.67214i	0.0837588	+	0.898036i
$117$	1.89711	−	7.08009i	0.175387	−	0.654555i
$118$	−8.87660	−	4.58857i	−0.817157	−	0.422412i
$119$		0			0
$120$	−16.0569	−	12.5953i	−1.46579	−	1.14979i
$121$	−4.51047	−	7.81236i	−0.410043	−	0.710215i
$122$	−2.61721	+	1.67791i	−0.236951	+	0.151911i
$123$	−11.0137	+	2.95110i	−0.993069	+	0.266092i
$124$	−6.68339	−	3.06999i	−0.600186	−	0.275693i
$125$	0.645919	−	11.1617i	0.0577727	−	0.998330i
$126$		0			0
$127$	−8.87092	+	8.87092i	−0.787167	+	0.787167i	−0.981029	−	0.193862i	$-0.937899\pi$
$127$	−8.87092	+	8.87092i	−0.787167	+	0.787167i	0.193862	+	0.981029i	$0.437899\pi$
$128$	−3.61792	−	10.7196i	−0.319782	−	0.947491i
$129$	−9.87458	−	5.70109i	−0.869408	−	0.501953i
$130$	3.04171	+	0.726868i	0.266776	+	0.0637505i
$131$	−11.3871	+	6.57436i	−0.994898	+	0.574404i	−0.906735	−	0.421702i	$-0.861433\pi$
$131$	−11.3871	+	6.57436i	−0.994898	+	0.574404i	−0.0881630	+	0.996106i	$0.528100\pi$
$132$	8.94960	+	1.52520i	0.778962	+	0.132752i
$133$		0			0
$134$	−4.30618	+	1.37132i	−0.371997	+	0.118464i
$135$	8.82937	−	30.5821i	0.759912	−	2.63209i
$136$	5.10713	+	12.0359i	0.437933	+	1.03207i
$137$	−6.75090	+	1.80890i	−0.576769	+	0.154545i	−0.535399	−	0.844599i	$-0.679839\pi$
$137$	−6.75090	+	1.80890i	−0.576769	+	0.154545i	−0.0413695	+	0.999144i	$0.513172\pi$
$138$	−9.58061	+	0.445819i	−0.815556	+	0.0379506i
$139$	−21.2377			−1.80136			−0.900679	−	0.434485i	$-0.856931\pi$
$139$	−21.2377			−1.80136			−0.900679	+	0.434485i	$0.856931\pi$
$140$		0			0
$141$	8.52881			0.718255
$142$	−17.2193	+	0.801275i	−1.44501	+	0.0672415i
$143$	−1.34385	+	0.360083i	−0.112378	+	0.0301117i
$144$	22.4908	−	19.3158i	1.87423	−	1.60965i
$145$	−5.24813	−	9.50854i	−0.435833	−	0.789641i
$146$	8.93499	−	2.84538i	0.739465	−	0.235485i
$147$		0			0
$148$	2.78181	−	16.3232i	0.228664	−	1.34176i
$149$	−5.75434	+	3.32227i	−0.471414	+	0.272171i	−0.716831	−	0.697247i	$-0.754408\pi$
$149$	−5.75434	+	3.32227i	−0.471414	+	0.272171i	0.245418	+	0.969417i	$0.421075\pi$
$150$	22.0852	+	5.72962i	1.80325	+	0.467821i
$151$	17.6555	+	10.1934i	1.43679	+	0.829529i	0.997625	−	0.0688796i	$-0.0219424\pi$
$151$	17.6555	+	10.1934i	1.43679	+	0.829529i	0.439161	+	0.898408i	$0.355276\pi$
$152$	6.25637	−	4.88673i	0.507458	−	0.396367i
$153$	−24.2263	+	24.2263i	−1.95858	+	1.95858i
$154$		0			0
$155$	8.22134	+	0.158431i	0.660354	+	0.0127255i
$156$	−2.66401	+	5.79957i	−0.213292	+	0.464338i
$157$	17.1639	−	4.59905i	1.36983	−	0.367044i	0.502412	−	0.864628i	$-0.332446\pi$
$157$	17.1639	−	4.59905i	1.36983	−	0.367044i	0.867416	+	0.497584i	$0.165779\pi$
$158$	−0.713484	+	0.457420i	−0.0567617	+	0.0363904i
$159$	−1.58925	−	2.75267i	−0.126036	−	0.218301i
$160$	8.49949	+	9.36796i	0.671944	+	0.740602i
$161$		0			0
$162$	29.7719	+	15.3899i	2.33910	+	1.20915i
$163$	−4.50039	+	16.7957i	−0.352498	+	1.31554i	0.531106	+	0.847305i	$0.321776\pi$
$163$	−4.50039	+	16.7957i	−0.352498	+	1.31554i	−0.883604	+	0.468235i	$0.844890\pi$
$164$	7.03682	−	0.656316i	0.549483	−	0.0512497i
$165$	−9.85315	+	2.43768i	−0.767067	+	0.189773i
$166$	6.11196	−	6.70855i	0.474380	−	0.520684i
$167$	−6.88960	+	6.88960i	−0.533133	+	0.533133i	−0.921503	−	0.388370i	$-0.873038\pi$
$167$	−6.88960	+	6.88960i	−0.533133	+	0.533133i	0.388370	+	0.921503i	$0.373038\pi$
$168$		0			0
$169$			12.0220i			0.924767i
$170$	−10.6140	−	10.0511i	−0.814056	−	0.770884i
$171$	18.0157	+	10.4014i	1.37769	+	0.795412i
$172$	5.43987	+	4.51170i	0.414786	+	0.344014i
$173$	−23.8977	−	6.40337i	−1.81691	−	0.486839i	−0.820510	−	0.571632i	$-0.806311\pi$
$173$	−23.8977	−	6.40337i	−1.81691	−	0.486839i	−0.996399	+	0.0847922i	$0.972977\pi$
$174$	21.1190	−	6.72543i	1.60103	−	0.509854i
$175$		0			0
$176$	−5.30952	−	1.86384i	−0.400220	−	0.140493i
$177$	−5.90084	+	22.0222i	−0.443534	+	1.65529i
$178$	0.353909	+	0.552027i	0.0265266	+	0.0413762i
$179$	10.2777	−	17.8015i	0.768192	−	1.33055i	−0.170350	−	0.985384i	$-0.554490\pi$
$179$	10.2777	−	17.8015i	0.768192	−	1.33055i	0.938542	−	0.345164i	$-0.112177\pi$
$180$	−14.4135	+	29.8483i	−1.07432	+	2.22476i
$181$	7.85989			0.584221			0.292110	−	0.956385i	$-0.405643\pi$
$181$	7.85989			0.584221			0.292110	+	0.956385i	$0.405643\pi$
$182$		0			0
$183$	5.01574	+	5.01574i	0.370774	+	0.370774i
$184$	5.90032	+	0.725227i	0.434978	+	0.0534645i
$185$	4.44608	+	17.9711i	0.326882	+	1.32127i
$186$	−3.58506	+	16.3934i	−0.262870	+	1.20203i
$187$	6.28140	+	1.68310i	0.459342	+	0.123080i
$188$	−5.21123	−	0.888105i	−0.380068	−	0.0647717i
$189$		0			0
$190$	−4.22691	+	7.80456i	−0.306652	+	0.566202i
$191$	7.51061	−	4.33625i	0.543449	−	0.313760i	−0.203027	−	0.979173i	$-0.565078\pi$
$191$	7.51061	−	4.33625i	0.543449	−	0.313760i	0.746475	+	0.665413i	$0.231745\pi$
$192$	−22.1301	+	13.2895i	−1.59710	+	0.959084i
$193$	−1.37318	−	5.12478i	−0.0988437	−	0.368890i	0.898730	−	0.438502i	$-0.144491\pi$
$193$	−1.37318	−	5.12478i	−0.0988437	−	0.368890i	−0.997574	+	0.0696118i	$0.977824\pi$
$194$	10.7831	−	11.8356i	0.774181	−	0.849748i
$195$	0.137480	−	7.13415i	0.00984515	−	0.510887i
$196$		0			0
$197$	−12.3437	−	12.3437i	−0.879452	−	0.879452i	0.114026	−	0.993478i	$-0.463625\pi$
$197$	−12.3437	−	12.3437i	−0.879452	−	0.879452i	−0.993478	+	0.114026i	$0.963625\pi$
$198$	−0.685422	−	14.7297i	−0.0487108	−	1.04679i
$199$	2.14941	−	3.72289i	0.152368	−	0.263909i	−0.779730	−	0.626116i	$-0.784644\pi$
$199$	2.14941	−	3.72289i	0.152368	−	0.263909i	0.932097	+	0.362208i	$0.117977\pi$
$200$	−12.8978	−	5.80062i	−0.912011	−	0.410166i
$201$	5.15564	+	8.92983i	0.363651	+	0.629862i
$202$	−7.57667	−	3.91660i	−0.533092	−	0.275571i
$203$		0			0
$204$	24.3380	−	17.2504i	1.70400	−	1.20777i
$205$	−6.91779	+	3.81820i	−0.483159	+	0.266674i
$206$	−19.4423	−	4.25181i	−1.35461	−	0.296238i
$207$	4.03182	+	15.0470i	0.280231	+	1.04584i
$208$	2.23166	−	3.26623i	0.154738	−	0.226472i
$209$		−	3.94849i		−	0.273123i
$210$		0			0
$211$		−	19.5494i		−	1.34583i	−0.739718	−	0.672917i	$-0.765041\pi$
$211$		−	19.5494i		−	1.34583i	0.739718	−	0.672917i	$-0.234959\pi$
$212$	0.684424	+	1.84741i	0.0470064	+	0.126881i
$213$	10.1795	+	37.9906i	0.697490	+	2.60307i
$214$	−6.06058	+	27.7132i	−0.414293	+	1.89444i
$215$	−7.59149	−	2.19174i	−0.517735	−	0.149476i
$216$	−32.1528	−	24.2353i	−2.18772	−	1.64900i
$217$		0			0
$218$	−0.659246	+	1.27531i	−0.0446498	+	0.0863751i
$219$	−10.6976	−	18.5287i	−0.722875	−	1.25206i
$220$	6.27426	−	0.463451i	0.423011	−	0.0312459i
$221$	−2.28576	+	3.95905i	−0.153757	+	0.266315i
$222$	−37.7396	+	1.75615i	−2.53292	+	0.117865i
$223$	9.54503	+	9.54503i	0.639183	+	0.639183i	0.950354	−	0.311171i	$-0.100721\pi$
$223$	9.54503	+	9.54503i	0.639183	+	0.639183i	−0.311171	+	0.950354i	$0.600721\pi$
$224$		0			0
$225$	1.42776	−	37.0310i	0.0951838	−	2.46873i
$226$	10.9306	+	9.95860i	0.727096	+	0.662436i
$227$	−4.77541	−	17.8221i	−0.316955	−	1.18289i	−0.922155	−	0.386819i	$-0.873574\pi$
$227$	−4.77541	−	17.8221i	−0.316955	−	1.18289i	0.605200	−	0.796073i	$-0.293093\pi$
$228$	−13.9420	−	11.5631i	−0.923330	−	0.765788i
$229$	13.5250	−	7.80865i	0.893755	−	0.516010i	0.0185864	−	0.999827i	$-0.494083\pi$
$229$	13.5250	−	7.80865i	0.893755	−	0.516010i	0.875169	+	0.483817i	$0.160750\pi$
$230$	−6.37072	+	1.89438i	−0.420073	+	0.124912i
$231$		0			0
$232$	−13.6044	+	1.91021i	−0.893172	+	0.125412i
$233$	−3.69263	−	0.989436i	−0.241912	−	0.0648201i	0.135826	−	0.990733i	$-0.456631\pi$
$233$	−3.69263	−	0.989436i	−0.241912	−	0.0648201i	−0.377738	+	0.925913i	$0.623298\pi$
$234$	10.1266	+	2.21459i	0.662000	+	0.144772i
$235$	5.73736	−	1.41943i	0.374264	−	0.0925934i
$236$	5.89868	−	12.8415i	0.383972	−	0.835909i
$237$	1.36736	+	1.36736i	0.0888193	+	0.0888193i
$238$		0			0
$239$	15.4752			1.00101			0.500505	−	0.865734i	$-0.333148\pi$
$239$	15.4752			1.00101			0.500505	+	0.865734i	$0.333148\pi$
$240$	16.7377	−	23.5114i	1.08041	−	1.51765i
$241$	14.3810	−	24.9086i	0.926361	−	1.60450i	0.137004	−	0.990570i	$-0.456253\pi$
$241$	14.3810	−	24.9086i	0.926361	−	1.60450i	0.789357	−	0.613934i	$-0.210414\pi$
$242$	10.7399	−	6.88544i	0.690387	−	0.442613i
$243$	8.73814	−	32.6112i	0.560552	−	2.09201i
$244$	−2.54241	−	3.58699i	−0.162761	−	0.229633i
$245$		0			0
$246$	−4.89298	−	15.3648i	−0.311965	−	0.979626i
$247$	2.68116	+	0.718415i	0.170598	+	0.0457117i
$248$	3.89758	−	9.64333i	0.247497	−	0.612352i
$249$	−17.9323	−	10.3532i	−1.13641	−	0.656109i
$250$	15.8104	+	0.178744i	0.999936	+	0.0113048i
$251$		−	26.0285i		−	1.64291i	−0.570277	−	0.821453i	$-0.693164\pi$
$251$		−	26.0285i		−	1.64291i	0.570277	−	0.821453i	$-0.306836\pi$
$252$		0			0
$253$	2.09075	−	2.09075i	0.131444	−	0.131444i
$254$	−13.1150	−	11.9487i	−0.822906	−	0.749726i
$255$	−17.2297	+	28.5575i	−1.07897	+	1.78834i
$256$	14.9056	−	5.81566i	0.931603	−	0.363479i
$257$	−5.97352	+	22.2935i	−0.372618	+	1.39063i	0.484176	+	0.874971i	$0.339119\pi$
$257$	−5.97352	+	22.2935i	−0.372618	+	1.39063i	−0.856794	+	0.515659i	$0.827547\pi$
$258$	7.40472	−	14.3244i	0.460998	−	0.891801i
$259$		0			0
$260$	−0.826882	+	4.34476i	−0.0512811	+	0.269451i
$261$	−17.9995	−	31.1761i	−1.11414	−	1.92975i
$262$	−10.0361	−	15.6542i	−0.620029	−	0.967122i
$263$	−10.9633	+	2.93759i	−0.676023	+	0.181140i	−0.580466	−	0.814284i	$-0.697130\pi$
$263$	−10.9633	+	2.93759i	−0.676023	+	0.181140i	−0.0955566	+	0.995424i	$0.530463\pi$
$264$	−1.56631	+	12.7432i	−0.0963997	+	0.784291i
$265$	−1.52722	−	1.58724i	−0.0938163	−	0.0975031i
$266$		0			0
$267$	1.05793	−	1.05793i	0.0647444	−	0.0647444i
$268$	−2.22031	−	5.99312i	−0.135627	−	0.366088i
$269$	−23.5713	−	13.6089i	−1.43717	−	0.829749i	−0.439516	−	0.898235i	$-0.644850\pi$
$269$	−23.5713	−	13.6089i	−1.43717	−	0.829749i	−0.997652	+	0.0684854i	$0.978183\pi$
$270$	43.7833	+	10.4627i	2.66456	+	0.636743i
$271$	0.134959	−	0.0779185i	0.00819817	−	0.00473321i	−0.495895	−	0.868382i	$-0.665160\pi$
$271$	0.134959	−	0.0779185i	0.00819817	−	0.00473321i	0.504093	+	0.863649i	$0.331827\pi$
$272$	−16.6672	+	8.00597i	−1.01060	+	0.485433i
$273$		0			0
$274$	−2.99919	−	9.41799i	−0.181188	−	0.568961i
$275$	−6.22256	+	3.27967i	−0.375234	+	0.197772i
$276$	−1.25960	−	13.5051i	−0.0758192	−	0.812910i
$277$	20.2196	−	5.41783i	1.21488	−	0.325526i	0.406204	−	0.913782i	$-0.366852\pi$
$277$	20.2196	−	5.41783i	1.21488	−	0.325526i	0.808674	+	0.588256i	$0.200185\pi$
$278$	−1.39610	−	30.0022i	−0.0837328	−	1.79941i
$279$	27.2556			1.63175
$280$		0			0
$281$	−2.56355			−0.152929			−0.0764644	−	0.997072i	$-0.524363\pi$
$281$	−2.56355			−0.152929			−0.0764644	+	0.997072i	$0.524363\pi$
$282$	0.560659	+	12.0485i	0.0333868	+	0.717479i
$283$	−19.8738	+	5.32518i	−1.18138	+	0.316549i	−0.795472	−	0.605990i	$-0.792777\pi$
$283$	−19.8738	+	5.32518i	−1.18138	+	0.316549i	−0.385904	+	0.922539i	$0.626111\pi$
$284$	−2.26390	−	24.2728i	−0.134338	−	1.44033i
$285$	19.4564	+	5.61728i	1.15250	+	0.332739i
$286$	−0.597025	−	1.87476i	−0.0353028	−	0.110857i
$287$		0			0
$288$	28.7656	+	30.5026i	1.69503	+	1.79738i
$289$	3.78292	−	2.18407i	0.222525	−	0.128475i
$290$	13.0876	−	8.03902i	0.768529	−	0.472067i
$291$	−31.6373	−	18.2658i	−1.85461	−	1.07076i
$292$	4.60698	+	12.4353i	0.269603	+	0.727720i
$293$	−4.71102	+	4.71102i	−0.275221	+	0.275221i	−0.831198	−	0.555977i	$-0.812344\pi$
$293$	−4.71102	+	4.71102i	−0.275221	+	0.275221i	0.555977	+	0.831198i	$0.312344\pi$
$294$		0			0
$295$	−0.304410	+	15.7965i	−0.0177234	+	0.919708i
$296$	23.2423	+	2.85679i	1.35093	+	0.166047i
$297$	−19.3437	+	5.18314i	−1.12244	+	0.300756i
$298$	−5.07159	−	7.91067i	−0.293790	−	0.458253i
$299$	1.03928	+	1.80009i	0.0601033	+	0.104102i
$300$	−6.64232	+	31.5761i	−0.383495	+	1.82305i
$301$		0			0
$302$	−13.2395	+	25.6118i	−0.761846	+	1.47379i
$303$	−5.03669	+	18.7972i	−0.289350	+	1.07987i
$304$	7.31469	+	8.51704i	0.419526	+	0.488486i
$305$	4.20887	+	2.53935i	0.240999	+	0.145403i
$306$	−35.8166	−	32.6315i	−2.04750	−	1.86542i
$307$	16.8508	−	16.8508i	0.961723	−	0.961723i	−0.0375706	−	0.999294i	$-0.511962\pi$
$307$	16.8508	−	16.8508i	0.961723	−	0.961723i	0.999294	+	0.0375706i	$0.0119619\pi$
$308$		0			0
$309$			45.4085i			2.58320i
$310$	0.316634	+	11.6246i	0.0179836	+	0.660232i
$311$	−15.7287	−	9.08099i	−0.891895	−	0.514936i	−0.0173329	−	0.999850i	$-0.505518\pi$
$311$	−15.7287	−	9.08099i	−0.891895	−	0.514936i	−0.874562	+	0.484914i	$0.838851\pi$
$312$	−8.36809	−	3.38216i	−0.473750	−	0.191477i
$313$	−1.51498	−	0.405938i	−0.0856319	−	0.0229450i	0.215749	−	0.976449i	$-0.430781\pi$
$313$	−1.51498	−	0.405938i	−0.0856319	−	0.0229450i	−0.301381	+	0.953504i	$0.597447\pi$
$314$	7.62532	+	23.9449i	0.430322	+	1.35129i
$315$		0			0
$316$	−0.693093	−	0.977859i	−0.0389895	−	0.0550088i
$317$	7.64549	−	28.5334i	0.429414	−	1.60259i	−0.324678	−	0.945825i	$-0.605256\pi$
$317$	7.64549	−	28.5334i	0.429414	−	1.60259i	0.754092	−	0.656769i	$-0.228077\pi$
$318$	3.78418	−	2.42607i	0.212206	−	0.136047i
$319$	−3.41643	+	5.91743i	−0.191283	+	0.331313i
$320$	−12.6752	+	12.6229i	−0.708568	+	0.705643i
$321$	64.7258			3.61264
$322$		0			0
$323$	−9.17425	−	9.17425i	−0.510469	−	0.510469i
$324$	−19.7840	+	43.0699i	−1.09911	+	2.39277i
$325$	−1.09484	−	4.82205i	−0.0607306	−	0.267479i
$326$	−24.0229	−	5.25353i	−1.33050	−	0.290966i
$327$	3.16396	+	0.847782i	0.174968	+	0.0468824i
$328$	1.38975	+	9.89766i	0.0767360	+	0.546507i
$329$		0			0
$330$	−4.09139	−	13.7592i	−0.225224	−	0.757416i
$331$	−10.9400	+	6.31623i	−0.601319	+	0.347172i	−0.769560	−	0.638574i	$-0.779525\pi$
$331$	−10.9400	+	6.31623i	−0.601319	+	0.347172i	0.168241	+	0.985746i	$0.446191\pi$
$332$	9.87885	+	8.19328i	0.542172	+	0.449665i
$333$	15.8820	+	59.2724i	0.870328	+	3.24811i
$334$	−10.1857	−	9.27993i	−0.557339	−	0.507775i
$335$	4.95439	+	5.14909i	0.270687	+	0.281325i
$336$		0			0
$337$	4.10542	+	4.10542i	0.223636	+	0.223636i	0.810028	−	0.586391i	$-0.199452\pi$
$337$	4.10542	+	4.10542i	0.223636	+	0.223636i	−0.586391	+	0.810028i	$0.699452\pi$
$338$	−16.9832	+	0.790289i	−0.923767	+	0.0429861i
$339$	16.8692	−	29.2182i	0.916207	−	1.58692i
$340$	13.5013	−	15.6549i	0.732211	−	0.849009i
$341$	−2.58665	−	4.48021i	−0.140075	−	0.242617i
$342$	−13.5095	+	26.1342i	−0.730513	+	1.41318i
$343$		0			0
$344$	−6.01600	+	7.98140i	−0.324361	+	0.430328i
$345$	7.32789	+	13.2766i	0.394520	+	0.714790i
$346$	7.47498	−	34.1809i	0.401857	−	1.83757i
$347$	−3.82255	−	14.2660i	−0.205205	−	0.765837i	−0.989387	−	0.145305i	$-0.953584\pi$
$347$	−3.82255	−	14.2660i	−0.205205	−	0.765837i	0.784182	−	0.620531i	$-0.213083\pi$
$348$	10.8892	+	29.3925i	0.583723	+	1.57560i
$349$			5.05181i			0.270417i	0.990817	+	0.135209i	$0.0431705\pi$
$349$			5.05181i			0.270417i	−0.990817	+	0.135209i	$0.956830\pi$
$350$		0			0
$351$		−	14.0781i		−	0.751434i
$352$	2.28399	−	7.62321i	0.121737	−	0.406318i
$353$	−2.81454	−	10.5040i	−0.149803	−	0.559072i	−0.999495	−	0.0317919i	$-0.989879\pi$
$353$	−2.81454	−	10.5040i	−0.149803	−	0.559072i	0.849692	−	0.527280i	$-0.176788\pi$
$354$	−31.4984	−	6.88835i	−1.67412	−	0.366112i
$355$	13.1705	+	23.8622i	0.699017	+	1.26648i
$356$	−0.756576	+	0.536251i	−0.0400984	+	0.0284212i
$357$		0			0
$358$	25.8236	+	13.3489i	1.36482	+	0.705514i
$359$	2.49329	+	4.31850i	0.131591	+	0.227922i	0.924290	−	0.381691i	$-0.124658\pi$
$359$	2.49329	+	4.31850i	0.131591	+	0.227922i	−0.792699	+	0.609613i	$0.791325\pi$
$360$	−43.1137	−	18.3996i	−2.27229	−	0.969742i
$361$	5.56111	−	9.63212i	0.292690	−	0.506954i
$362$	0.516686	+	11.1035i	0.0271564	+	0.583589i
$363$	−20.5825	−	20.5825i	−1.08030	−	1.08030i
$364$		0			0
$365$	−10.2800	−	10.6840i	−0.538079	−	0.559225i
$366$	−6.75594	+	7.41538i	−0.353139	+	0.387608i
$367$	4.12420	+	15.3917i	0.215282	+	0.803442i	0.986067	+	0.166347i	$0.0531972\pi$
$367$	4.12420	+	15.3917i	0.215282	+	0.803442i	−0.770786	+	0.637094i	$0.780136\pi$
$368$	−0.636648	+	8.38297i	−0.0331875	+	0.436993i
$369$	−22.6817	+	13.0953i	−1.18076	+	0.681714i
$370$	−25.0953	+	7.46228i	−1.30464	+	0.387946i
$371$		0			0
$372$	−23.3944	−	3.98691i	−1.21294	−	0.206712i
$373$	0.569126	+	0.152497i	0.0294682	+	0.00789599i	0.273523	−	0.961865i	$-0.411811\pi$
$373$	0.569126	+	0.152497i	0.0294682	+	0.00789599i	−0.244055	+	0.969761i	$0.578478\pi$
$374$	−1.96476	+	8.98428i	−0.101596	+	0.464566i
$375$	−7.30833	−	35.3278i	−0.377400	−	1.82432i
$376$	0.912041	−	7.42021i	0.0470349	−	0.382668i
$377$	−3.39653	−	3.39653i	−0.174930	−	0.174930i
$378$		0			0
$379$	23.7583			1.22038			0.610191	−	0.792254i	$-0.291093\pi$
$379$	23.7583			1.22038			0.610191	+	0.792254i	$0.291093\pi$
$380$	−11.3032	−	5.45824i	−0.579844	−	0.280002i
$381$	−20.2402	+	35.0570i	−1.03694	+	1.79603i
$382$	6.61948	+	10.3251i	0.338682	+	0.528277i
$383$	−1.11189	+	4.14964i	−0.0568151	+	0.212037i	−0.988498	−	0.151237i	$-0.951674\pi$
$383$	−1.11189	+	4.14964i	−0.0568151	+	0.212037i	0.931682	+	0.363274i	$0.118341\pi$
$384$	−20.2286	−	30.3892i	−1.03229	−	1.55079i
$385$		0			0
$386$	7.14943	−	2.27676i	0.363896	−	0.115884i
$387$	−25.2982	−	6.77862i	−1.28598	−	0.344577i
$388$	17.4289	+	14.4551i	0.884816	+	0.733845i
$389$	21.8152	+	12.5950i	1.10608	+	0.638593i	0.937810	−	0.347148i	$-0.112850\pi$
$389$	21.8152	+	12.5950i	1.10608	+	0.638593i	0.168266	+	0.985742i	$0.446183\pi$
$390$	10.0873	−	0.274762i	0.510793	−	0.0139131i
$391$		−	9.71561i		−	0.491340i
$392$		0			0
$393$	−30.0006	+	30.0006i	−1.51333	+	1.51333i
$394$	16.6263	−	18.2492i	0.837622	−	0.919381i
$395$	1.14739	+	0.692260i	0.0577315	+	0.0348314i
$396$	20.7633	−	1.93657i	1.04340	−	0.0973163i
$397$	1.00160	−	3.73802i	0.0502689	−	0.187606i	−0.936226	−	0.351399i	$-0.885706\pi$
$397$	1.00160	−	3.73802i	0.0502689	−	0.187606i	0.986495	+	0.163793i	$0.0523728\pi$
$398$	5.40057	+	2.79171i	0.270706	+	0.139936i
$399$		0			0
$400$	7.34658	−	18.6018i	0.367329	−	0.930091i
$401$	2.74364	+	4.75213i	0.137011	+	0.237310i	0.926364	−	0.376630i	$-0.122917\pi$
$401$	2.74364	+	4.75213i	0.137011	+	0.237310i	−0.789353	+	0.613940i	$0.789584\pi$
$402$	−12.2761	+	7.87032i	−0.612277	+	0.392536i
$403$	3.51285	−	0.941265i	0.174987	−	0.0468877i
$404$	5.03485	−	10.9609i	0.250493	−	0.545325i
$405$	1.02098	−	52.9811i	0.0507330	−	2.63265i
$406$		0			0
$407$	8.23579	−	8.23579i	0.408233	−	0.408233i
$408$	25.9693	+	33.2479i	1.28567	+	1.64602i
$409$	14.7164	+	8.49650i	0.727678	+	0.420125i	0.817572	−	0.575826i	$-0.195320\pi$
$409$	14.7164	+	8.49650i	0.727678	+	0.420125i	−0.0898942	+	0.995951i	$0.528653\pi$
$410$	−5.84866	−	9.52166i	−0.288845	−	0.470241i
$411$	−19.5303	+	11.2758i	−0.963360	+	0.556196i
$412$	4.72839	−	27.7453i	0.232951	−	1.36691i
$413$		0			0
$414$	−20.9916	+	6.68484i	−1.03168	+	0.328542i
$415$	−13.7862	−	3.98023i	−0.676738	−	0.195382i
$416$	4.76085	+	2.93792i	0.233420	+	0.144044i
$417$	−66.1930	+	17.7364i	−3.24149	+	0.868554i
$418$	5.57798	−	0.259563i	0.272828	−	0.0126956i
$419$	−3.87556			−0.189334			−0.0946668	−	0.995509i	$-0.530179\pi$
$419$	−3.87556			−0.189334			−0.0946668	+	0.995509i	$0.530179\pi$
$420$		0			0
$421$	20.7160			1.00964			0.504818	−	0.863226i	$-0.331560\pi$
$421$	20.7160			1.00964			0.504818	+	0.863226i	$0.331560\pi$
$422$	27.6171	−	1.28512i	1.34438	−	0.0625586i
$423$	18.9230	−	5.07039i	0.920066	−	0.246531i
$424$	−2.56482	+	1.08832i	−0.124559	+	0.0528534i
$425$	−6.83773	+	22.0782i	−0.331679	+	1.07095i
$426$	−52.9995	+	16.8779i	−2.56783	+	0.817735i
$427$		0			0
$428$	−39.5485	−	6.73991i	−1.91165	−	0.325786i
$429$	−3.88775	+	2.24459i	−0.187702	+	0.108370i
$430$	2.59720	−	10.8685i	0.125248	−	0.524124i
$431$	8.46015	+	4.88447i	0.407511	+	0.235277i	0.689720	−	0.724076i	$-0.257734\pi$
$431$	8.46015	+	4.88447i	0.407511	+	0.235277i	−0.282209	+	0.959353i	$0.591067\pi$
$432$	32.1232	−	47.0150i	1.54553	−	2.26201i
$433$	−7.00877	+	7.00877i	−0.336820	+	0.336820i	−0.855169	−	0.518349i	$-0.826547\pi$
$433$	−7.00877	+	7.00877i	−0.336820	+	0.336820i	0.518349	+	0.855169i	$0.326547\pi$
$434$		0			0
$435$	−24.2981	−	25.2530i	−1.16501	−	1.21079i
$436$	−1.84495	−	0.847472i	−0.0883572	−	0.0405865i
$437$	−5.69814	+	1.52681i	−0.272579	+	0.0730373i
$438$	25.4720	−	16.3303i	1.21710	−	0.780293i
$439$	−2.21290	−	3.83285i	−0.105616	−	0.182932i	0.808374	−	0.588670i	$-0.200348\pi$
$439$	−2.21290	−	3.83285i	−0.105616	−	0.182932i	−0.913990	+	0.405737i	$0.867015\pi$
$440$	1.06716	+	8.83309i	0.0508750	+	0.421101i
$441$		0			0
$442$	−5.74315	−	2.96880i	−0.273174	−	0.141211i
$443$	1.13928	−	4.25183i	0.0541286	−	0.202011i	−0.933566	−	0.358405i	$-0.883321\pi$
$443$	1.13928	−	4.25183i	0.0541286	−	0.202011i	0.987695	+	0.156395i	$0.0499872\pi$
$444$	−4.96178	−	53.1987i	−0.235476	−	2.52470i
$445$	0.535606	−	0.887745i	0.0253902	−	0.0420831i
$446$	−12.8567	+	14.1116i	−0.608781	+	0.668203i
$447$	−15.1604	+	15.1604i	−0.717062	+	0.717062i
$448$		0			0
$449$		−	21.8355i		−	1.03048i	−0.857046	−	0.515240i	$-0.827703\pi$
$449$		−	21.8355i		−	1.03048i	0.857046	−	0.515240i	$-0.172297\pi$
$450$	52.4070	−	0.417340i	2.47049	−	0.0196736i
$451$	4.30514	+	2.48557i	0.202721	+	0.117041i
$452$	−13.3498	+	16.0962i	−0.627922	+	0.757102i
$453$	63.5411	+	17.0258i	2.98542	+	0.799941i
$454$	24.8631	−	7.91772i	1.16688	−	0.371597i
$455$		0			0
$456$	15.4186	−	20.4557i	0.722041	−	0.957928i
$457$	−5.70175	+	21.2792i	−0.266717	+	0.995400i	0.694475	+	0.719517i	$0.255637\pi$
$457$	−5.70175	+	21.2792i	−0.266717	+	0.995400i	−0.961191	+	0.275883i	$0.911030\pi$
$458$	11.9203	+	18.5932i	0.556997	+	0.868804i
$459$	−32.9019	+	56.9877i	−1.53573	+	2.65996i
$460$	−3.09496	−	8.87529i	−0.144303	−	0.413812i
$461$	19.7670			0.920641			0.460321	−	0.887753i	$-0.347734\pi$
$461$	19.7670			0.920641			0.460321	+	0.887753i	$0.347734\pi$
$462$		0			0
$463$	14.5239	+	14.5239i	0.674983	+	0.674983i	0.958861	−	0.283877i	$-0.0916209\pi$
$463$	14.5239	+	14.5239i	0.674983	+	0.674983i	−0.283877	+	0.958861i	$0.591621\pi$
$464$	−3.59284	−	19.0931i	−0.166794	−	0.886377i
$465$	25.7563	−	6.37215i	1.19442	−	0.295501i
$466$	1.15502	−	5.28156i	0.0535052	−	0.244663i
$467$	27.2315	+	7.29665i	1.26012	+	0.337649i	0.826239	−	0.563320i	$-0.190476\pi$
$467$	27.2315	+	7.29665i	1.26012	+	0.337649i	0.433884	+	0.900969i	$0.357143\pi$
$468$	−2.46282	+	14.4513i	−0.113844	+	0.668014i
$469$		0			0
$470$	2.38236	+	8.01178i	0.109890	+	0.369556i
$471$	49.6551	−	28.6684i	2.28799	−	1.32097i
$472$	18.5287	+	7.48882i	0.852853	+	0.344701i
$473$	1.28663	+	4.80176i	0.0591592	+	0.220785i
$474$	−1.84176	+	2.02153i	−0.0845947	+	0.0928519i
$475$	14.0233	+	0.540678i	0.643432	+	0.0248080i
$476$		0			0
$477$	−5.16257	−	5.16257i	−0.236378	−	0.236378i
$478$	1.01730	+	21.8616i	0.0465301	+	0.999928i
$479$	−0.709375	+	1.22867i	−0.0324122	+	0.0561395i	−0.881776	−	0.471668i	$-0.843652\pi$
$479$	−0.709375	+	1.22867i	−0.0324122	+	0.0561395i	0.849364	+	0.527807i	$0.176986\pi$
$480$	34.3145	+	22.0995i	1.56623	+	1.00870i
$481$	4.09391	+	7.09086i	0.186666	+	0.323315i
$482$	36.1334	+	18.6784i	1.64583	+	0.850777i
$483$		0			0
$484$	10.4330	+	14.7195i	0.474225	+	0.669067i
$485$	−24.3225	−	7.02215i	−1.10443	−	0.318860i
$486$	46.6437	+	10.2005i	2.11580	+	0.462703i
$487$	−8.71188	−	32.5132i	−0.394773	−	1.47331i	−0.822166	−	0.569247i	$-0.807235\pi$
$487$	−8.71188	−	32.5132i	−0.394773	−	1.47331i	0.427393	−	0.904066i	$-0.359432\pi$
$488$	4.90015	−	3.82742i	0.221819	−	0.173259i
$489$			56.1067i			2.53723i
$490$		0			0
$491$		−	3.16673i		−	0.142913i	−0.997444	−	0.0714563i	$-0.977235\pi$
$491$		−	3.16673i		−	0.142913i	0.997444	−	0.0714563i	$-0.0227647\pi$
$492$	21.3840	−	7.92228i	0.964066	−	0.357164i
$493$	5.81103	+	21.6871i	0.261716	+	0.976736i
$494$	−0.838642	+	3.83486i	−0.0377323	+	0.172539i
$495$	−20.4121	+	11.2662i	−0.917456	+	0.506379i
$496$	13.8792	+	4.87213i	0.623195	+	0.218765i
$497$		0			0
$498$	13.4470	−	26.0133i	0.602576	−	1.16568i
$499$	−3.72451	−	6.45105i	−0.166732	−	0.288789i	0.770537	−	0.637395i	$-0.219988\pi$
$499$	−3.72451	−	6.45105i	−0.166732	−	0.288789i	−0.937269	+	0.348607i	$0.886655\pi$
$500$	0.786819	+	22.3468i	0.0351876	+	0.999381i
$501$	−15.7195	+	27.2270i	−0.702297	+	1.21641i
$502$	36.7701	−	1.71104i	1.64113	−	0.0763674i
$503$	19.3043	+	19.3043i	0.860736	+	0.860736i	0.991424	−	0.130687i	$-0.0417184\pi$
$503$	19.3043	+	19.3043i	0.860736	+	0.860736i	−0.130687	+	0.991424i	$0.541718\pi$
$504$		0			0
$505$	−0.259830	+	13.4832i	−0.0115623	+	0.599994i
$506$	3.09101	+	2.81613i	0.137412	+	0.125192i
$507$	10.0400	+	37.4697i	0.445891	+	1.66409i
$508$	16.0176	−	19.3128i	0.710664	−	0.856866i
$509$	−9.85817	+	5.69161i	−0.436956	+	0.252276i	−0.702305	−	0.711876i	$-0.747846\pi$
$509$	−9.85817	+	5.69161i	−0.436956	+	0.252276i	0.265350	+	0.964152i	$0.414513\pi$
$510$	−41.4754	−	22.4629i	−1.83656	−	0.994672i
$511$		0			0
$512$	9.19554	+	20.6747i	0.406390	+	0.913700i
$513$	38.5934	+	10.3411i	1.70394	+	0.456570i
$514$	−31.8863	−	6.97319i	−1.40645	−	0.307574i
$515$	7.55723	+	30.5465i	0.333011	+	1.34604i
$516$	20.7227	+	9.51889i	0.912266	+	0.419046i
$517$	−2.62931	−	2.62931i	−0.115637	−	0.115637i
$518$		0			0
$519$	−79.8313			−3.50421
$520$	−6.19214	−	0.882512i	−0.271543	−	0.0387007i
$521$	−0.617798	+	1.07006i	−0.0270662	+	0.0468801i	−0.879241	−	0.476377i	$-0.841950\pi$
$521$	−0.617798	+	1.07006i	−0.0270662	+	0.0468801i	0.852175	+	0.523257i	$0.175283\pi$
$522$	42.8588	−	27.4771i	1.87588	−	1.20264i
$523$	−1.63395	+	6.09797i	−0.0714474	+	0.266646i	−0.992404	−	0.123019i	$-0.960742\pi$
$523$	−1.63395	+	6.09797i	−0.0714474	+	0.266646i	0.920957	+	0.389665i	$0.127409\pi$
$524$	21.4548	−	15.2068i	0.937256	−	0.664314i
$525$		0			0
$526$	−4.87059	−	15.2945i	−0.212368	−	0.666872i
$527$	−16.4197	−	4.39965i	−0.715254	−	0.191652i
$528$	−18.1051	−	1.37500i	−0.787924	−	0.0598392i
$529$	16.0929	+	9.29126i	0.699693	+	0.403968i
$530$	2.14187	−	2.26182i	0.0930369	−	0.0982471i
$531$			52.3691i			2.27262i
$532$		0			0
$533$	−2.47109	+	2.47109i	−0.107035	+	0.107035i
$534$	1.56407	+	1.42498i	0.0676840	+	0.0616649i
$535$	43.5413	−	10.7722i	1.88246	−	0.465722i
$536$	8.32044	−	3.53057i	0.359388	−	0.152497i
$537$	17.1666	−	64.0665i	0.740792	−	2.76467i
$538$	17.6756	−	34.1934i	0.762048	−	1.47418i
$539$		0			0
$540$	−11.9024	+	62.5398i	−0.512197	+	2.69128i
$541$	16.1355	+	27.9475i	0.693719	+	1.20156i	0.970611	+	0.240656i	$0.0773624\pi$
$541$	16.1355	+	27.9475i	0.693719	+	1.20156i	−0.276891	+	0.960901i	$0.589304\pi$
$542$	0.118946	+	0.185532i	0.00510917	+	0.00796929i
$543$	24.4975	−	6.56407i	1.05129	−	0.281691i
$544$	−12.4056	−	23.0192i	−0.531884	−	0.986939i
$545$	2.26951	+	0.0437350i	0.0972150	+	0.00187340i
$546$		0			0
$547$	−17.6256	+	17.6256i	−0.753617	+	0.753617i	−0.975152	−	0.221536i	$-0.928893\pi$
$547$	−17.6256	+	17.6256i	−0.753617	+	0.753617i	0.221536	+	0.975152i	$0.428893\pi$
$548$	13.1075	−	4.85602i	0.559924	−	0.207439i
$549$	14.1104	+	8.14662i	0.602215	+	0.347689i
$550$	−5.04220	−	8.57492i	−0.215000	−	0.365636i
$551$	11.8061	−	6.81625i	0.502957	−	0.290382i
$552$	18.9956	−	2.66721i	0.808507	−	0.113524i
$553$		0			0
$554$	8.98286	+	28.2078i	0.381645	+	1.19843i
$555$	28.8658	+	52.2988i	1.22528	+	2.21996i
$556$	42.2919	−	3.94451i	1.79357	−	0.167285i
$557$	−5.98149	+	1.60273i	−0.253444	+	0.0679101i	−0.383304	−	0.923622i	$-0.625214\pi$
$557$	−5.98149	+	1.60273i	−0.253444	+	0.0679101i	0.129860	+	0.991532i	$0.458547\pi$
$558$	1.79171	+	38.5036i	0.0758490	+	1.62999i
$559$	−3.49465			−0.147808
$560$		0			0
$561$	20.9833			0.885915
$562$	−0.168521	−	3.62149i	−0.00710861	−	0.152764i
$563$	−4.96172	+	1.32949i	−0.209112	+	0.0560313i	−0.361854	−	0.932235i	$-0.617856\pi$
$563$	−4.96172	+	1.32949i	−0.209112	+	0.0560313i	0.152742	+	0.988266i	$0.451189\pi$
$564$	−16.9839	+	1.58407i	−0.715151	+	0.0667013i
$565$	6.48523	−	22.4627i	0.272835	−	0.945014i
$566$	−8.82925	−	27.7254i	−0.371121	−	1.16539i
$567$		0			0
$568$	34.1410	−	4.79380i	1.43253	−	0.201143i
$569$	30.0136	−	17.3284i	1.25824	−	0.726442i	0.285504	−	0.958378i	$-0.407839\pi$
$569$	30.0136	−	17.3284i	1.25824	−	0.726442i	0.972731	+	0.231935i	$0.0745057\pi$
$570$	−6.65643	+	27.8551i	−0.278807	+	1.16672i
$571$	28.9237	+	16.6991i	1.21042	+	0.698836i	0.962851	−	0.270034i	$-0.0870350\pi$
$571$	28.9237	+	16.6991i	1.21042	+	0.698836i	0.247569	+	0.968870i	$0.420368\pi$
$572$	2.60920	−	0.966649i	0.109096	−	0.0404176i
$573$	19.7875	−	19.7875i	0.826634	−	0.826634i
$574$		0			0
$575$	7.13910	+	7.71168i	0.297721	+	0.321599i
$576$	−41.1996	+	42.6418i	−1.71665	+	1.77674i
$577$	−33.2773	+	8.91664i	−1.38535	+	0.371204i	−0.873063	−	0.487608i	$-0.837870\pi$
$577$	−33.2773	+	8.91664i	−1.38535	+	0.371204i	−0.512291	+	0.858812i	$0.671203\pi$
$578$	3.33408	+	5.20050i	0.138679	+	0.216312i
$579$	−8.55978	−	14.8260i	−0.355732	−	0.616146i
$580$	12.2169	+	17.9602i	0.507281	+	0.745755i
$581$		0			0
$582$	23.7241	−	45.8942i	0.983394	−	1.90238i
$583$	−0.358664	+	1.33855i	−0.0148544	+	0.0554372i
$584$	−17.2643	+	7.32567i	−0.714401	+	0.303138i
$585$	−3.93624	−	15.9104i	−0.162743	−	0.657812i
$586$	−6.96487	−	6.34549i	−0.287716	−	0.262130i
$587$	−23.3690	+	23.3690i	−0.964544	+	0.964544i	−0.999393	−	0.0348489i	$-0.988905\pi$
$587$	−23.3690	+	23.3690i	−0.964544	+	0.964544i	0.0348489	+	0.999393i	$0.488905\pi$
$588$		0			0
$589$			10.3214i			0.425288i
$590$	−22.3355	+	0.608382i	−0.919538	+	0.0250467i
$591$	−48.7811	−	28.1638i	−2.00659	−	1.15850i
$592$	−2.50786	+	33.0219i	−0.103072	+	1.35719i
$593$	−6.26739	−	1.67934i	−0.257371	−	0.0689623i	0.127826	−	0.991797i	$-0.459200\pi$
$593$	−6.26739	−	1.67934i	−0.257371	−	0.0689623i	−0.385197	+	0.922834i	$0.625867\pi$
$594$	−8.59374	−	26.9859i	−0.352606	−	1.10724i
$595$		0			0
$596$	10.8419	−	7.68459i	0.444101	−	0.314773i
$597$	3.59010	−	13.3984i	0.146933	−	0.548362i
$598$	−2.47464	+	1.58651i	−0.101196	+	0.0648773i
$599$	8.75860	−	15.1703i	0.357867	−	0.619843i	−0.629737	−	0.776808i	$-0.716838\pi$
$599$	8.75860	−	15.1703i	0.357867	−	0.619843i	0.987604	+	0.156965i	$0.0501709\pi$
$600$	−45.0437	−	7.30779i	−1.83890	−	0.298339i
$601$	−2.55297			−0.104138			−0.0520689	−	0.998643i	$-0.516582\pi$
$601$	−2.55297			−0.104138			−0.0520689	+	0.998643i	$0.516582\pi$
$602$		0			0
$603$	16.7477	+	16.7477i	0.682018	+	0.682018i
$604$	−37.0517	−	17.0196i	−1.50761	−	0.692516i
$605$	−17.2714	−	10.4204i	−0.702183	−	0.423650i
$606$	−26.8856	−	5.87959i	−1.09215	−	0.238842i
$607$	−21.3783	−	5.72830i	−0.867718	−	0.232504i	−0.202617	−	0.979258i	$-0.564945\pi$
$607$	−21.3783	−	5.72830i	−0.867718	−	0.232504i	−0.665101	+	0.746754i	$0.731611\pi$
$608$	−11.5510	+	10.8932i	−0.468457	+	0.441779i
$609$		0			0
$610$	−3.31062	+	6.11273i	−0.134043	+	0.247497i
$611$	2.26378	−	1.30700i	0.0915829	−	0.0528754i
$612$	43.7436	−	52.7427i	1.76823	−	2.13200i
$613$	2.08760	+	7.79104i	0.0843175	+	0.314677i	0.995184	−	0.0980238i	$-0.0312521\pi$
$613$	2.08760	+	7.79104i	0.0843175	+	0.314677i	−0.910867	+	0.412701i	$0.864585\pi$
$614$	24.9125	+	22.6971i	1.00539	+	0.915980i
$615$	−18.3724	+	17.6777i	−0.740849	+	0.712835i
$616$		0			0
$617$	−20.7105	−	20.7105i	−0.833772	−	0.833772i	0.154258	−	0.988031i	$-0.450701\pi$
$617$	−20.7105	−	20.7105i	−0.833772	−	0.833772i	−0.988031	+	0.154258i	$0.950701\pi$
$618$	−64.1479	+	2.98502i	−2.58041	+	0.120075i
$619$	−15.2502	+	26.4141i	−0.612956	+	1.06167i	0.377784	+	0.925894i	$0.376686\pi$
$619$	−15.2502	+	26.4141i	−0.612956	+	1.06167i	−0.990739	+	0.135777i	$0.956647\pi$
$620$	−16.4011	+	1.21147i	−0.658682	+	0.0486538i
$621$	14.9597	+	25.9110i	0.600314	+	1.03977i
$622$	11.7946	−	22.8167i	0.472921	−	0.914866i
$623$		0			0
$624$	4.22784	−	12.0438i	0.169249	−	0.482138i
$625$	−10.7959	−	22.5488i	−0.431834	−	0.901953i
$626$	0.473872	−	2.16688i	0.0189398	−	0.0866059i
$627$	−3.29753	−	12.3065i	−0.131691	−	0.491476i
$628$	−33.3253	+	12.3462i	−1.32982	+	0.492668i
$629$		−	38.2714i		−	1.52598i
$630$		0			0
$631$			24.2931i			0.967092i	0.875319	+	0.483546i	$0.160651\pi$
$631$			24.2931i			0.967092i	−0.875319	+	0.483546i	$0.839349\pi$
$632$	1.33584	−	1.04340i	0.0531370	−	0.0415044i
$633$	−16.3264	−	60.9309i	−0.648915	−	2.42178i
$634$	40.8113	+	8.92497i	1.62082	+	0.354456i
$635$	−7.78120	+	26.9515i	−0.308787	+	1.06954i
$636$	3.67603	+	5.18637i	0.145764	+	0.205653i
$637$		0			0
$638$	−8.58406	−	4.43735i	−0.339846	−	0.175676i
$639$	45.1709	+	78.2383i	1.78693	+	3.09506i
$640$	−18.6654	−	17.0763i	−0.737816	−	0.675001i
$641$	−11.2086	+	19.4138i	−0.442712	+	0.766800i	−0.997890	−	0.0649320i	$-0.979317\pi$
$641$	−11.2086	+	19.4138i	−0.442712	+	0.766800i	0.555178	+	0.831732i	$0.312650\pi$
$642$	4.25489	+	91.4372i	0.167927	+	3.60874i
$643$	−3.56268	−	3.56268i	−0.140498	−	0.140498i	0.633359	−	0.773858i	$-0.281675\pi$
$643$	−3.56268	−	3.56268i	−0.140498	−	0.140498i	−0.773858	+	0.633359i	$0.781675\pi$
$644$		0			0
$645$	−25.4913	−	0.491236i	−1.00372	−	0.0193424i
$646$	12.3572	−	13.5634i	0.486189	−	0.533645i
$647$	−4.29327	−	16.0227i	−0.168786	−	0.629918i	−0.997527	−	0.0702854i	$-0.977609\pi$
$647$	−4.29327	−	16.0227i	−0.168786	−	0.629918i	0.828741	−	0.559632i	$-0.189058\pi$
$648$	−62.1448	−	25.1173i	−2.44128	−	0.986700i
$649$	8.60829	−	4.97000i	0.337905	−	0.195089i
$650$	6.74007	−	1.86365i	0.264367	−	0.0730983i
$651$		0			0
$652$	5.84240	−	34.2821i	0.228806	−	1.34259i
$653$	12.1210	+	3.24782i	0.474332	+	0.127097i	0.488062	−	0.872809i	$-0.337704\pi$
$653$	12.1210	+	3.24782i	0.474332	+	0.127097i	−0.0137300	+	0.999906i	$0.504371\pi$
$654$	−0.989659	+	4.52542i	−0.0386987	+	0.176958i
$655$	−15.1886	+	25.1744i	−0.593467	+	0.983646i
$656$	−13.8909	+	2.61392i	−0.542349	+	0.102056i
$657$	−34.7502	−	34.7502i	−1.35573	−	1.35573i
$658$		0			0
$659$	33.3787			1.30025			0.650126	−	0.759827i	$-0.274716\pi$
$659$	33.3787			1.30025			0.650126	+	0.759827i	$0.274716\pi$
$660$	19.1684	−	6.68433i	0.746129	−	0.260187i
$661$	−3.47890	+	6.02563i	−0.135313	+	0.234370i	−0.925717	−	0.378217i	$-0.876537\pi$
$661$	−3.47890	+	6.02563i	−0.135313	+	0.234370i	0.790404	+	0.612586i	$0.209871\pi$
$662$	−9.64201	−	15.0396i	−0.374748	−	0.584531i
$663$	−3.81784	+	14.2484i	−0.148273	+	0.553361i
$664$	−10.9251	+	14.4943i	−0.423977	+	0.562488i
$665$		0			0
$666$	−82.6892	+	26.3327i	−3.20414	+	1.02037i
$667$	9.86062	+	2.64214i	0.381805	+	0.102304i
$668$	12.4400	−	14.9993i	0.481320	−	0.580339i
$669$	37.7211	+	21.7783i	1.45838	+	0.841997i
$670$	−6.94836	+	7.33748i	−0.268438	+	0.283472i
$671$		−	3.09256i		−	0.119387i
$672$		0			0
$673$	−5.34897	+	5.34897i	−0.206188	+	0.206188i	−0.802645	−	0.596457i	$-0.796575\pi$
$673$	−5.34897	+	5.34897i	−0.206188	+	0.206188i	0.596457	+	0.802645i	$0.296575\pi$
$674$	−5.52979	+	6.06954i	−0.212999	+	0.233790i
$675$	−15.7594	−	69.4100i	−0.606579	−	2.67159i
$676$	−2.23286	−	23.9400i	−0.0858792	−	0.920770i
$677$	−7.76868	+	28.9931i	−0.298575	+	1.11430i	0.639762	+	0.768573i	$0.279033\pi$
$677$	−7.76868	+	28.9931i	−0.298575	+	1.11430i	−0.938337	+	0.345723i	$0.887634\pi$
$678$	42.3851	+	21.9101i	1.62779	+	0.841451i
$679$		0			0
$680$	23.0030	+	18.0440i	0.882127	+	0.691955i
$681$	−29.7677	−	51.5592i	−1.14070	−	1.97575i
$682$	6.15909	−	3.94864i	0.235844	−	0.151201i
$683$	−18.3967	+	4.92938i	−0.703930	+	0.188618i	−0.592990	−	0.805210i	$-0.702053\pi$
$683$	−18.3967	+	4.92938i	−0.703930	+	0.188618i	−0.110940	+	0.993827i	$0.535386\pi$
$684$	−37.8075	−	17.3667i	−1.44561	−	0.664034i
$685$	−11.2615	+	10.8357i	−0.430281	+	0.414010i
$686$		0			0
$687$	35.6329	−	35.6329i	1.35948	−	1.35948i
$688$	−11.6707	−	7.97404i	−0.444941	−	0.304008i
$689$	−0.843665	−	0.487090i	−0.0321411	−	0.0185567i
$690$	−18.2740	+	11.2248i	−0.695679	+	0.427320i
$691$	24.4705	−	14.1281i	0.930903	−	0.537457i	0.0438058	−	0.999040i	$-0.486052\pi$
$691$	24.4705	−	14.1281i	0.930903	−	0.537457i	0.887097	+	0.461583i	$0.152718\pi$
$692$	48.7782	+	8.31284i	1.85427	+	0.316007i
$693$		0			0
$694$	19.9020	−	6.33786i	0.755470	−	0.240582i
$695$	−41.5765	+	22.9477i	−1.57709	+	0.870455i
$696$	−40.8064	+	17.3152i	−1.54676	+	0.656331i
$697$	15.7781	−	4.22772i	0.597638	−	0.160136i
$698$	−7.13662	+	0.332091i	−0.270125	+	0.0125698i
$699$	−12.3354			−0.466567
$700$		0			0
$701$	−26.0149			−0.982568			−0.491284	−	0.871000i	$-0.663472\pi$
$701$	−26.0149			−0.982568			−0.491284	+	0.871000i	$0.663472\pi$
$702$	19.8879	−	0.925454i	0.750622	−	0.0349290i
$703$	−22.4459	+	6.01436i	−0.846563	+	0.226836i
$704$	10.9193	+	2.72543i	0.411538	+	0.102719i
$705$	16.6966	−	9.21551i	0.628831	−	0.347076i
$706$	14.6538	−	4.66656i	0.551504	−	0.175628i
$707$		0			0
$708$	7.66046	−	44.9501i	0.287898	−	1.68933i
$709$	15.2471	−	8.80290i	0.572616	−	0.330600i	−0.185578	−	0.982630i	$-0.559416\pi$
$709$	15.2471	−	8.80290i	0.572616	−	0.330600i	0.758193	+	0.652030i	$0.226082\pi$
$710$	−32.8440	+	20.1744i	−1.23261	+	0.757131i
$711$	3.84667	+	2.22087i	0.144261	+	0.0832893i
$712$	−0.807288	−	1.03355i	−0.0302544	−	0.0387340i
$713$	−5.46525	+	5.46525i	−0.204675	+	0.204675i
$714$		0			0
$715$	−2.24174	+	2.15697i	−0.0838363	+	0.0806663i
$716$	−17.1603	+	37.3581i	−0.641310	+	1.39614i
$717$	48.2328	−	12.9239i	1.80129	−	0.482653i
$718$	−5.93678	+	3.80611i	−0.221558	+	0.142043i
$719$	−11.5866	−	20.0685i	−0.432106	−	0.748429i	0.564949	−	0.825126i	$-0.308896\pi$
$719$	−11.5866	−	20.0685i	−0.432106	−	0.748429i	−0.997054	+	0.0766969i	$0.975563\pi$
$720$	23.1586	−	62.1156i	0.863070	−	2.31491i
$721$		0			0
$722$	13.9727	+	7.22290i	0.520011	+	0.268809i
$723$	24.0202	−	89.6445i	0.893320	−	3.33391i
$724$	−15.6518	+	1.45983i	−0.581696	+	0.0542541i
$725$	−20.5482	−	12.9439i	−0.763143	−	0.480725i
$726$	27.7235	−	30.4296i	1.02892	−	1.12935i
$727$	15.3777	−	15.3777i	0.570326	−	0.570326i	−0.361893	−	0.932220i	$-0.617869\pi$
$727$	15.3777	−	15.3777i	0.570326	−	0.570326i	0.932220	+	0.361893i	$0.117869\pi$
$728$		0			0
$729$		−	37.8443i		−	1.40164i
$730$	14.4173	−	15.2247i	0.533609	−	0.563492i
$731$	14.1462	+	8.16734i	0.523218	+	0.302080i
$732$	−10.9197	−	9.05655i	−0.403604	−	0.334740i
$733$	−40.3490	−	10.8115i	−1.49032	−	0.399331i	−0.580478	−	0.814276i	$-0.697134\pi$
$733$	−40.3490	−	10.8115i	−1.49032	−	0.399331i	−0.909847	+	0.414944i	$0.863801\pi$
$734$	−21.4725	+	6.83800i	−0.792566	+	0.252395i
$735$		0			0
$736$	−11.8844	−	0.348310i	−0.438063	−	0.0128389i
$737$	1.16353	−	4.34235i	0.0428592	−	0.159953i
$738$	−19.9906	−	31.1813i	−0.735862	−	1.14780i
$739$	14.4738	−	25.0693i	0.532426	−	0.922189i	−0.466857	−	0.884333i	$-0.654614\pi$
$739$	14.4738	−	25.0693i	0.532426	−	0.922189i	0.999283	−	0.0378565i	$-0.0120530\pi$
$740$	−12.1915	−	34.9612i	−0.448170	−	1.28520i
$741$	8.95654			0.329027
$742$		0			0
$743$	−23.4115	−	23.4115i	−0.858885	−	0.858885i	0.132322	−	0.991207i	$-0.457757\pi$
$743$	−23.4115	−	23.4115i	−0.858885	−	0.858885i	−0.991207	+	0.132322i	$0.957757\pi$
$744$	4.09437	−	33.3111i	0.150107	−	1.22124i
$745$	−7.67535	+	12.7216i	−0.281203	+	0.466082i
$746$	−0.178017	+	0.814021i	−0.00651768	+	0.0298034i
$747$	−45.9417	−	12.3100i	−1.68092	−	0.450401i
$748$	−12.8211	−	2.18499i	−0.468786	−	0.0798912i
$749$		0			0
$750$	49.4266	−	12.6467i	1.80480	−	0.461793i
$751$	38.1178	−	22.0073i	1.39094	−	0.803059i	0.397520	−	0.917593i	$-0.369871\pi$
$751$	38.1178	−	22.0073i	1.39094	−	0.803059i	0.993419	+	0.114534i	$0.0365376\pi$
$752$	10.5424	+	0.800644i	0.384441	+	0.0291965i
$753$	−21.7373	−	81.1249i	−0.792153	−	2.95636i
$754$	4.57495	−	5.02151i	0.166610	−	0.182872i
$755$	45.5779	+	0.878318i	1.65875	+	0.0319653i
$756$		0			0
$757$	24.7062	+	24.7062i	0.897961	+	0.897961i	0.995256	−	0.0972943i	$-0.0310188\pi$
$757$	24.7062	+	24.7062i	0.897961	+	0.897961i	−0.0972943	+	0.995256i	$0.531019\pi$
$758$	1.56180	+	33.5630i	0.0567272	+	1.21906i
$759$	4.77032	−	8.26243i	0.173152	−	0.299907i
$760$	6.96773	−	16.3267i	0.252746	−	0.592233i
$761$	−2.24848	−	3.89448i	−0.0815073	−	0.141175i	0.822390	−	0.568924i	$-0.192640\pi$
$761$	−2.24848	−	3.89448i	−0.0815073	−	0.141175i	−0.903898	+	0.427749i	$0.859307\pi$
$762$	−50.8551	−	26.2885i	−1.84229	−	0.952331i
$763$		0			0
$764$	−14.1509	+	10.0300i	−0.511963	+	0.362872i
$765$	−21.2503	+	73.6040i	−0.768304	+	2.66116i
$766$	−5.93523	−	1.29797i	−0.214449	−	0.0468975i
$767$	1.80855	+	6.74959i	0.0653029	+	0.243714i
$768$	41.6006	−	30.5743i	1.50113	−	1.10325i
$769$			14.9079i			0.537593i	0.963197	+	0.268797i	$0.0866259\pi$
$769$			14.9079i			0.537593i	−0.963197	+	0.268797i	$0.913374\pi$
$770$		0			0
$771$			74.4723i			2.68206i
$772$	3.68633	+	9.95023i	0.132674	+	0.358116i
$773$	−7.16881	−	26.7544i	−0.257844	−	0.962287i	−0.966486	−	0.256719i	$-0.917358\pi$
$773$	−7.16881	−	26.7544i	−0.257844	−	0.962287i	0.708642	−	0.705568i	$-0.249308\pi$
$774$	7.91303	−	36.1839i	0.284428	−	1.30060i
$775$	16.2659	−	8.57314i	0.584288	−	0.307956i
$776$	−19.2747	+	25.5717i	−0.691923	+	0.917971i
$777$		0			0
$778$	−16.3587	+	31.6460i	−0.586489	+	1.13456i
$779$	−4.95906	−	8.58934i	−0.177677	−	0.307745i
$780$	1.05127	+	14.2322i	0.0376413	+	0.509594i
$781$	8.57374	−	14.8502i	0.306793	−	0.531380i
$782$	13.7251	−	0.638676i	0.490809	−	0.0228390i
$783$	−48.8906	−	48.8906i	−1.74721	−	1.74721i
$784$		0			0
$785$	28.6320	−	27.5493i	1.02192	−	0.983277i
$786$	−44.3535	−	40.4092i	−1.58204	−	1.44135i
$787$	−1.45499	−	5.43008i	−0.0518646	−	0.193561i	0.935133	−	0.354297i	$-0.115280\pi$
$787$	−1.45499	−	5.43008i	−0.0518646	−	0.193561i	−0.986997	+	0.160736i	$0.948613\pi$
$788$	26.8733	+	22.2881i	0.957322	+	0.793980i
$789$	−31.7166	+	18.3116i	−1.12914	+	0.651911i
$790$	−0.902519	+	1.66641i	−0.0321102	+	0.0592882i
$791$		0			0
$792$	4.10068	+	29.2047i	0.145711	+	1.03774i
$793$	2.09996	+	0.562681i	0.0745716	+	0.0199814i
$794$	5.34649	+	1.16922i	0.189740	+	0.0414940i
$795$	−6.08554	−	3.67161i	−0.215832	−	0.130219i
$796$	−3.58879	+	7.81282i	−0.127201	+	0.276918i
$797$	10.9874	+	10.9874i	0.389195	+	0.389195i	0.874400	−	0.485205i	$-0.161255\pi$
$797$	10.9874	+	10.9874i	0.389195	+	0.389195i	−0.485205	+	0.874400i	$0.661255\pi$
$798$		0			0
$799$	−12.2183			−0.432252
$800$	26.7615	+	9.15558i	0.946160	+	0.323699i
$801$	1.71830	−	2.97619i	0.0607133	−	0.105159i
$802$	−6.53290	+	4.18829i	−0.230685	+	0.147894i
$803$	−2.41424	+	9.01005i	−0.0851965	+	0.317958i
$804$	−11.9253	−	16.8249i	−0.420572	−	0.593369i
$805$		0			0
$806$	1.56063	+	4.90067i	0.0549710	+	0.172619i
$807$	−84.8316	−	22.7306i	−2.98621	−	0.800154i
$808$	15.8153	+	6.39212i	0.556380	+	0.224874i
$809$	−14.4297	−	8.33096i	−0.507320	−	0.292901i	0.224412	−	0.974494i	$-0.427954\pi$
$809$	−14.4297	−	8.33096i	−0.507320	−	0.292901i	−0.731731	+	0.681593i	$0.761287\pi$
$810$	74.9126	−	2.04049i	2.63216	−	0.0716957i
$811$			30.5372i			1.07231i	0.844120	+	0.536154i	$0.180123\pi$
$811$			30.5372i			1.07231i	−0.844120	+	0.536154i	$0.819877\pi$
$812$		0			0
$813$	0.355563	−	0.355563i	0.0124701	−	0.0124701i
$814$	12.1760	+	11.0932i	0.426768	+	0.388816i
$815$	9.33771	+	37.7432i	0.327086	+	1.32209i
$816$	−45.2617	+	38.8721i	−1.58448	+	1.36080i
$817$	2.56700	−	9.58017i	0.0898079	−	0.335168i
$818$	−11.0355	+	21.3481i	−0.385846	+	0.746420i
$819$		0			0
$820$	13.0666	−	8.88825i	0.456307	−	0.310391i
$821$	9.24225	+	16.0080i	0.322557	+	0.558685i	0.981015	−	0.193933i	$-0.0621243\pi$
$821$	9.24225	+	16.0080i	0.322557	+	0.558685i	−0.658458	+	0.752617i	$0.728791\pi$
$822$	−17.2131	−	26.8490i	−0.600375	−	0.936465i
$823$	−41.3323	+	11.0750i	−1.44075	+	0.386049i	−0.892798	−	0.450457i	$-0.851261\pi$
$823$	−41.3323	+	11.0750i	−1.44075	+	0.386049i	−0.547957	+	0.836507i	$0.684594\pi$
$824$	39.5062	+	4.85583i	1.37626	+	0.169161i
$825$	−16.6553	+	15.4187i	−0.579863	+	0.536809i
$826$		0			0
$827$	22.7990	−	22.7990i	0.792801	−	0.792801i	−0.189148	−	0.981949i	$-0.560573\pi$
$827$	22.7990	−	22.7990i	0.792801	−	0.792801i	0.981949	+	0.189148i	$0.0605726\pi$
$828$	−10.8235	−	29.2150i	−0.376142	−	1.01529i
$829$	29.0025	+	16.7446i	1.00730	+	0.581563i	0.910399	−	0.413731i	$-0.135775\pi$
$829$	29.0025	+	16.7446i	1.00730	+	0.581563i	0.0968981	+	0.995294i	$0.469108\pi$
$830$	4.71654	−	19.7372i	0.163713	−	0.685089i
$831$	58.4953	−	33.7723i	2.02918	−	1.17155i
$832$	−3.83740	+	6.91871i	−0.133038	+	0.239863i
$833$		0			0
$834$	−29.4072	−	92.3440i	−1.01829	−	3.19761i
$835$	−6.04327	+	20.9319i	−0.209136	+	0.724379i
$836$	0.733360	+	7.86286i	0.0253638	+	0.271943i
$837$	50.5649	−	13.5488i	1.74778	−	0.468316i
$838$	−0.254768	−	5.47495i	−0.00880082	−	0.189129i
$839$	6.43773			0.222255			0.111127	−	0.993806i	$-0.464554\pi$
$839$	6.43773			0.222255			0.111127	+	0.993806i	$0.464554\pi$
$840$		0			0
$841$	5.40897			0.186516
$842$	1.36181	+	29.2652i	0.0469310	+	1.00854i
$843$	−7.99001	+	2.14092i	−0.275190	+	0.0737371i
$844$	3.63094	+	38.9298i	0.124982	+	1.34002i
$845$	12.9899	+	23.5351i	0.446867	+	0.809631i
$846$	8.40681	+	26.3989i	0.289032	+	0.907612i
$847$		0			0
$848$	−1.70605	−	3.55174i	−0.0585862	−	0.121967i
$849$	−57.4949	+	33.1947i	−1.97322	+	1.13924i
$850$	−31.6391	−	8.20820i	−1.08521	−	0.281539i
$851$	−15.0698	−	8.70057i	−0.516587	−	0.298252i
$852$	−27.3271	−	73.7621i	−0.936213	−	2.52705i
$853$	−10.0581	+	10.0581i	−0.344383	+	0.344383i	−0.858012	−	0.513629i	$-0.828301\pi$
$853$	−10.0581	+	10.0581i	−0.344383	+	0.344383i	0.513629	+	0.858012i	$0.328301\pi$
$854$		0			0
$855$	46.5077	+	0.896235i	1.59053	+	0.0306506i
$856$	6.92156	−	56.3126i	0.236574	−	1.92473i
$857$	−0.503168	+	0.134823i	−0.0171879	+	0.00460548i	−0.267403	−	0.963585i	$-0.586165\pi$
$857$	−0.503168	+	0.134823i	−0.0171879	+	0.00460548i	0.250215	+	0.968190i	$0.419499\pi$
$858$	−3.42647	−	5.34461i	−0.116978	−	0.182462i
$859$	−2.00473	−	3.47230i	−0.0684006	−	0.118473i	0.829797	−	0.558066i	$-0.188456\pi$
$859$	−2.00473	−	3.47230i	−0.0684006	−	0.118473i	−0.898197	+	0.439592i	$0.855123\pi$
$860$	15.5244	+	2.95457i	0.529379	+	0.100750i
$861$		0			0
$862$	−6.34407	+	12.2726i	−0.216080	+	0.418007i
$863$	3.83800	−	14.3236i	0.130647	−	0.487581i	−0.869331	−	0.494231i	$-0.835450\pi$
$863$	3.83800	−	14.3236i	0.130647	−	0.487581i	0.999978	+	0.00664926i	$0.00211654\pi$
$864$	68.5291	+	42.2893i	2.33141	+	1.43871i
$865$	−53.7029	+	13.2861i	−1.82595	+	0.451742i
$866$	−10.3619	−	9.44045i	−0.352113	−	0.320800i
$867$	9.96649	−	9.96649i	0.338480	−	0.338480i
$868$		0			0
$869$		−	0.843073i		−	0.0285993i
$870$	34.0773	−	35.9857i	1.15533	−	1.22003i
$871$	2.73690	+	1.58015i	0.0927364	+	0.0535414i
$872$	1.07593	−	2.66205i	0.0364355	−	0.0901483i
$873$	−81.0531	−	21.7181i	−2.74323	−	0.735046i
$874$	−2.53148	−	7.94930i	−0.0856287	−	0.268889i
$875$		0			0
$876$	24.7440	+	34.9104i	0.836024	+	1.17951i
$877$	−8.02646	+	29.9552i	−0.271034	+	1.01151i	0.687418	+	0.726262i	$0.258744\pi$
$877$	−8.02646	+	29.9552i	−0.271034	+	1.01151i	−0.958453	+	0.285252i	$0.907923\pi$
$878$	5.26914	−	3.37809i	0.177825	−	0.114005i
$879$	−10.7488	+	18.6175i	−0.362548	+	0.627952i
$880$	−12.4082	+	2.08823i	−0.418281	+	0.0703941i
$881$	−26.6186			−0.896802			−0.448401	−	0.893833i	$-0.648006\pi$
$881$	−26.6186			−0.896802			−0.448401	+	0.893833i	$0.648006\pi$
$882$		0			0
$883$	−20.2772	−	20.2772i	−0.682383	−	0.682383i	0.278154	−	0.960537i	$-0.410278\pi$
$883$	−20.2772	−	20.2772i	−0.682383	−	0.682383i	−0.960537	+	0.278154i	$0.910278\pi$
$884$	3.81644	−	8.30842i	0.128361	−	0.279442i
$885$	12.2435	+	49.4883i	0.411559	+	1.66353i
$886$	6.08139	+	1.32993i	0.204308	+	0.0446800i
$887$	−41.2767	−	11.0601i	−1.38594	−	0.371361i	−0.512663	−	0.858590i	$-0.671341\pi$
$887$	−41.2767	−	11.0601i	−1.38594	−	0.371361i	−0.873274	+	0.487229i	$0.838008\pi$
$888$	74.8268	−	10.5066i	2.51102	−	0.352577i
$889$		0			0
$890$	1.28931	+	0.698285i	0.0432179	+	0.0234066i
$891$	−28.8720	+	16.6692i	−0.967247	+	0.558440i
$892$	−20.7804	−	17.2348i	−0.695779	−	0.577062i
$893$	1.92011	+	7.16594i	0.0642540	+	0.239799i
$894$	−22.4135	−	20.4203i	−0.749619	−	0.682956i
$895$	0.885581	−	45.9548i	0.0296017	−	1.53610i
$896$		0			0
$897$	4.74253	+	4.74253i	0.158348	+	0.158348i
$898$	30.8467	−	1.43540i	1.02937	−	0.0479000i
$899$	8.93063	−	15.4683i	0.297853	−	0.515897i
$900$	4.03465	+	74.0071i	0.134488	+	2.46690i
$901$	2.27675	+	3.94345i	0.0758496	+	0.131375i
$902$	−3.22832	+	6.24520i	−0.107491	+	0.207942i
$903$		0			0
$904$	−23.6164	−	17.8010i	−0.785471	−	0.592051i
$905$	15.3871	−	8.49273i	0.511484	−	0.282308i
$906$	−19.8751	+	90.8828i	−0.660305	+	3.01938i
$907$	−0.317430	−	1.18466i	−0.0105401	−	0.0393361i	0.960456	−	0.278433i	$-0.0898152\pi$
$907$	−0.317430	−	1.18466i	−0.0105401	−	0.0393361i	−0.970996	+	0.239097i	$0.923148\pi$
$908$	12.8197	+	34.6032i	0.425436	+	1.14835i
$909$			44.6999i			1.48260i
$910$		0			0
$911$		−	13.4236i		−	0.444743i	−0.974962	−	0.222372i	$-0.928620\pi$
$911$		−	13.4236i		−	0.444743i	0.974962	−	0.222372i	$-0.0713799\pi$
$912$	29.9111	+	20.4369i	0.990455	+	0.676733i
$913$	2.33653	+	8.72004i	0.0773277	+	0.288591i
$914$	−30.4357	−	6.65594i	−1.00672	−	0.220159i
$915$	15.2388	+	4.39960i	0.503778	+	0.145446i
$916$	−25.4827	+	18.0618i	−0.841974	+	0.596779i
$917$		0			0
$918$	−82.6686	−	42.7338i	−2.72847	−	1.41042i
$919$	−13.1243	−	22.7320i	−0.432931	−	0.749858i	0.564193	−	0.825643i	$-0.309187\pi$
$919$	−13.1243	−	22.7320i	−0.432931	−	0.749858i	−0.997124	+	0.0757845i	$0.975854\pi$
$920$	12.3345	−	4.95564i	0.406657	−	0.163382i
$921$	38.4473	−	66.5926i	1.26688	−	2.19430i
$922$	1.29943	+	27.9246i	0.0427943	+	0.919646i
$923$	8.52380	+	8.52380i	0.280564	+	0.280564i
$924$		0			0
$925$	28.1221	+	30.3776i	0.924649	+	0.998809i
$926$	−19.5629	+	21.4725i	−0.642878	+	0.705629i
$927$	26.9955	+	100.748i	0.886647	+	3.30901i
$928$	26.7364	−	6.33068i	0.877666	−	0.207815i
$929$	−17.2412	+	9.95422i	−0.565666	+	0.326587i	−0.755416	−	0.655245i	$-0.772565\pi$
$929$	−17.2412	+	9.95422i	−0.565666	+	0.326587i	0.189751	+	0.981832i	$0.439232\pi$
$930$	10.6950	+	35.9667i	0.350702	+	1.17940i
$931$		0			0
$932$	7.53711	+	1.28448i	0.246886	+	0.0420747i
$933$	−56.6067	−	15.1677i	−1.85322	−	0.496569i
$934$	−8.51775	+	38.9491i	−0.278709	+	1.27446i
$935$	14.1155	−	3.49220i	0.461628	−	0.114207i
$936$	−20.5771	−	2.52920i	−0.672583	−	0.0826693i
$937$	3.76752	+	3.76752i	0.123080	+	0.123080i	0.765964	−	0.642884i	$-0.222262\pi$
$937$	3.76752	+	3.76752i	0.123080	+	0.123080i	−0.642884	+	0.765964i	$0.722262\pi$
$938$		0			0
$939$	−5.06087			−0.165155
$940$	−11.1615	+	3.89220i	−0.364048	+	0.126950i
$941$	2.41962	−	4.19090i	0.0788772	−	0.136619i	−0.823889	−	0.566752i	$-0.808200\pi$
$941$	2.41962	−	4.19090i	0.0788772	−	0.136619i	0.902766	+	0.430133i	$0.141533\pi$
$942$	43.7636	+	68.2624i	1.42589	+	2.22411i
$943$	1.92225	−	7.17394i	0.0625971	−	0.233616i
$944$	−9.36132	+	26.6675i	−0.304685	+	0.867954i
$945$		0			0
$946$	−6.69879	+	2.13325i	−0.217797	+	0.0693580i
$947$	29.9595	+	8.02761i	0.973551	+	0.260862i	0.710327	−	0.703872i	$-0.248547\pi$
$947$	29.9595	+	8.02761i	0.973551	+	0.260862i	0.263225	+	0.964735i	$0.415214\pi$
$948$	−2.97686	−	2.46893i	−0.0966838	−	0.0801872i
$949$	−5.67887	−	3.27870i	−0.184344	−	0.106431i
$950$	0.158043	+	19.8460i	0.00512758	+	0.643890i
$951$		−	95.3170i		−	3.09086i
$952$		0			0
$953$	22.3422	−	22.3422i	0.723734	−	0.723734i	−0.245630	−	0.969364i	$-0.578995\pi$
$953$	22.3422	−	22.3422i	0.723734	−	0.723734i	0.969364	+	0.245630i	$0.0789947\pi$
$954$	6.95371	−	7.63245i	0.225135	−	0.247110i
$955$	10.0179	−	16.6043i	0.324173	−	0.537303i
$956$	−30.8167	+	2.87424i	−0.996684	+	0.0929596i
$957$	−5.70637	+	21.2965i	−0.184461	+	0.688417i
$958$	−1.78236	−	0.921354i	−0.0575855	−	0.0297676i
$959$		0			0
$960$	−28.9640	+	49.9283i	−0.934808	+	1.61143i
$961$	−8.73844	−	15.1354i	−0.281885	−	0.488239i
$962$	−9.74802	+	6.24953i	−0.314289	+	0.201493i
$963$	143.608	−	38.4796i	4.62770	−	1.23999i
$964$	−24.0114	+	52.2729i	−0.773354	+	1.68360i
$965$	−8.22565	−	8.54890i	−0.264793	−	0.275199i
$966$		0			0
$967$	8.85634	−	8.85634i	0.284801	−	0.284801i	−0.550219	−	0.835020i	$-0.685456\pi$
$967$	8.85634	−	8.85634i	0.284801	−	0.284801i	0.835020	+	0.550219i	$0.185456\pi$
$968$	−20.1081	+	15.7061i	−0.646300	+	0.504813i
$969$	−36.2558	−	20.9323i	−1.16470	−	0.672442i
$970$	8.32120	−	34.8216i	0.267178	−	1.11805i
$971$	8.19063	−	4.72886i	0.262850	−	0.151756i	−0.362784	−	0.931873i	$-0.618174\pi$
$971$	8.19063	−	4.72886i	0.262850	−	0.151756i	0.625634	+	0.780117i	$0.284840\pi$
$972$	−11.3438	+	66.5634i	−0.363854	+	2.13502i
$973$		0			0
$974$	45.3582	−	14.4445i	1.45337	−	0.462831i
$975$	−7.43942	−	14.1149i	−0.238252	−	0.452038i
$976$	5.72906	+	6.67076i	0.183383	+	0.213526i
$977$	59.6654	−	15.9873i	1.90886	−	0.511479i	0.914624	−	0.404305i	$-0.132487\pi$
$977$	59.6654	−	15.9873i	1.90886	−	0.511479i	0.994240	−	0.107173i	$-0.0341799\pi$
$978$	−79.2611	+	3.68829i	−2.53449	+	0.117939i
$979$	−0.652291			−0.0208473
$980$		0			0
$981$	7.52393			0.240221
$982$	4.47359	−	0.208172i	0.142758	−	0.00664303i
$983$	57.3012	−	15.3538i	1.82762	−	0.489710i	0.829947	−	0.557842i	$-0.188370\pi$
$983$	57.3012	−	15.3538i	1.82762	−	0.489710i	0.997676	+	0.0681315i	$0.0217038\pi$
$984$	12.5974	+	29.6881i	0.401591	+	0.946422i
$985$	−37.5025	−	10.8274i	−1.19493	−	0.344989i
$986$	−30.2550	+	9.63480i	−0.963515	+	0.306834i
$987$		0			0
$988$	−5.47258	−	0.932645i	−0.174106	−	0.0296714i
$989$	6.43198	−	3.71351i	0.204525	−	0.118083i
$990$	−17.2575	−	28.0953i	−0.548478	−	0.892926i
$991$	15.0202	+	8.67190i	0.477131	+	0.275472i	0.719220	−	0.694782i	$-0.244499\pi$
$991$	15.0202	+	8.67190i	0.477131	+	0.275472i	−0.242089	+	0.970254i	$0.577833\pi$
$992$	−5.97040	+	19.9272i	−0.189560	+	0.632690i
$993$	−28.8227	+	28.8227i	−0.914660	+	0.914660i
$994$		0			0
$995$	0.185204	−	9.61068i	0.00587137	−	0.304679i
$996$	37.6326	+	17.2864i	1.19243	+	0.547740i
$997$	14.9024	−	3.99308i	0.471964	−	0.126462i	−0.0149945	−	0.999888i	$-0.504773\pi$
$997$	14.9024	−	3.99308i	0.471964	−	0.126462i	0.486958	+	0.873425i	$0.338106\pi$
$998$	8.86846	−	5.68564i	0.280726	−	0.179976i
$999$	58.9289	+	102.068i	1.86443	+	3.22928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.l.67.10		72
4.3	odd	2	inner	980.2.x.l.67.7		72
5.3	odd	4	inner	980.2.x.l.263.18		72
7.2	even	3	inner	980.2.x.l.667.16		72
7.3	odd	6		140.2.k.a.127.3	yes	36
7.4	even	3		980.2.k.l.687.3		36
7.5	odd	6		980.2.x.k.667.16		72
7.6	odd	2		980.2.x.k.67.10		72
20.3	even	4	inner	980.2.x.l.263.16		72
28.3	even	6		140.2.k.a.127.6	yes	36
28.11	odd	6		980.2.k.l.687.6		36
28.19	even	6		980.2.x.k.667.18		72
28.23	odd	6	inner	980.2.x.l.667.18		72
28.27	even	2		980.2.x.k.67.7		72
35.3	even	12		140.2.k.a.43.6	yes	36
35.13	even	4		980.2.x.k.263.18		72
35.17	even	12		700.2.k.b.43.13		36
35.18	odd	12		980.2.k.l.883.6		36
35.23	odd	12	inner	980.2.x.l.863.7		72
35.24	odd	6		700.2.k.b.407.16		36
35.33	even	12		980.2.x.k.863.7		72
140.3	odd	12		140.2.k.a.43.3	✓	36
140.23	even	12	inner	980.2.x.l.863.10		72
140.59	even	6		700.2.k.b.407.13		36
140.83	odd	4		980.2.x.k.263.16		72
140.87	odd	12		700.2.k.b.43.16		36
140.103	odd	12		980.2.x.k.863.10		72
140.123	even	12		980.2.k.l.883.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.3	✓	36	140.3	odd	12
140.2.k.a.43.6	yes	36	35.3	even	12
140.2.k.a.127.3	yes	36	7.3	odd	6
140.2.k.a.127.6	yes	36	28.3	even	6
700.2.k.b.43.13		36	35.17	even	12
700.2.k.b.43.16		36	140.87	odd	12
700.2.k.b.407.13		36	140.59	even	6
700.2.k.b.407.16		36	35.24	odd	6
980.2.k.l.687.3		36	7.4	even	3
980.2.k.l.687.6		36	28.11	odd	6
980.2.k.l.883.3		36	140.123	even	12
980.2.k.l.883.6		36	35.18	odd	12
980.2.x.k.67.7		72	28.27	even	2
980.2.x.k.67.10		72	7.6	odd	2
980.2.x.k.263.16		72	140.83	odd	4
980.2.x.k.263.18		72	35.13	even	4
980.2.x.k.667.16		72	7.5	odd	6
980.2.x.k.667.18		72	28.19	even	6
980.2.x.k.863.7		72	35.33	even	12
980.2.x.k.863.10		72	140.103	odd	12
980.2.x.l.67.7		72	4.3	odd	2	inner
980.2.x.l.67.10		72	1.1	even	1	trivial
980.2.x.l.263.16		72	20.3	even	4	inner
980.2.x.l.263.18		72	5.3	odd	4	inner
980.2.x.l.667.16		72	7.2	even	3	inner
980.2.x.l.667.18		72	28.23	odd	6	inner
980.2.x.l.863.7		72	35.23	odd	12	inner
980.2.x.l.863.10		72	140.23	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0657371 + 1.41268i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-1.99136 + 0.185732i) q^{4} +(1.95767 - 1.08052i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +(6.41872 - 3.70585i) q^{9} +O(q^{10})\)	\(q+(0.0657371 + 1.41268i) q^{2} +(3.11677 - 0.835136i) q^{3} +(-1.99136 + 0.185732i) q^{4} +(1.95767 - 1.08052i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +(6.41872 - 3.70585i) q^{9} +(1.65512 + 2.69455i) q^{10} +(-1.21832 - 0.703395i) q^{11} +(-6.05149 + 2.24194i) q^{12} +(0.699298 - 0.699298i) q^{13} +(5.19924 - 5.00264i) q^{15} +(3.93101 - 0.739716i) q^{16} +(-4.46506 + 1.19641i) q^{17} +(5.65715 + 8.82402i) q^{18} +(1.40337 + 2.43071i) q^{19} +(-3.69774 + 2.51529i) q^{20} +(0.913587 - 1.76734i) q^{22} +(-0.543980 + 2.03016i) q^{23} +(-3.56496 - 8.40147i) q^{24} +(2.66497 - 4.23059i) q^{25} +(1.03386 + 0.941917i) q^{26} +(10.0659 - 10.0659i) q^{27} -4.85706i q^{29} +(7.40894 + 7.01603i) q^{30} +(3.18470 + 1.83869i) q^{31} +(1.30340 + 5.50465i) q^{32} +(-4.38464 - 1.17486i) q^{33} +(-1.98367 - 6.22907i) q^{34} +(-12.0937 + 8.57184i) q^{36} +(-2.14283 + 7.99714i) q^{37} +(-3.34157 + 2.14231i) q^{38} +(1.59554 - 2.76356i) q^{39} +(-3.79640 - 5.05840i) q^{40} -3.53368 q^{41} +(-2.49869 - 2.49869i) q^{43} +(2.55675 + 1.17443i) q^{44} +(8.56153 - 14.1904i) q^{45} +(-2.90374 - 0.635016i) q^{46} +(2.55312 + 0.684106i) q^{47} +(11.6343 - 5.58845i) q^{48} +(6.15168 + 3.48666i) q^{50} +(-12.9174 + 7.45786i) q^{51} +(-1.26267 + 1.52243i) q^{52} +(-0.254952 - 0.951495i) q^{53} +(14.8816 + 13.5582i) q^{54} +(-3.14510 - 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(6.86149 - 0.319289i) q^{58} +(-3.53286 + 6.11910i) q^{59} +(-9.42439 + 10.9277i) q^{60} +(1.09916 + 1.90379i) q^{61} +(-2.38814 + 4.61985i) q^{62} +(-7.69065 + 2.20315i) q^{64} +(0.613394 - 2.12460i) q^{65} +(1.37148 - 6.27135i) q^{66} +(0.827081 + 3.08671i) q^{67} +(8.66931 - 3.21178i) q^{68} +6.78184i q^{69} +12.1891i q^{71} +(-12.9043 - 16.5211i) q^{72} +(-1.71613 - 6.40469i) q^{73} +(-11.4383 - 2.50143i) q^{74} +(4.77298 - 15.4114i) q^{75} +(-3.24607 - 4.57976i) q^{76} +(4.00892 + 2.07233i) q^{78} +(0.299644 + 0.518999i) q^{79} +(6.89635 - 5.69564i) q^{80} +(11.8491 - 20.5233i) q^{81} +(-0.232294 - 4.99198i) q^{82} +(-4.53764 - 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(3.36560 - 3.69412i) q^{86} +(-4.05630 - 15.1383i) q^{87} +(-1.49103 + 3.68908i) q^{88} +(0.401553 - 0.231837i) q^{89} +(20.6093 + 11.1619i) q^{90} +(0.706194 - 4.14381i) q^{92} +(11.4615 + 3.07111i) q^{93} +(-0.798592 + 3.65172i) q^{94} +(5.37376 + 3.24217i) q^{95} +(8.65952 + 16.0682i) q^{96} +(-8.00558 - 8.00558i) q^{97} -10.4267 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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