LMFDB - Embedded newform 980.2.x.l.863.10

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			863.10
Character	$\chi$	$=$	980.863
Dual form			980.2.x.l.67.10

$q$-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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.0657371	−	1.41268i	0.0464831	−	0.998919i
$2$	0.0657371	−	1.41268i	0.0464831	−	0.998919i
$3$	3.11677	+	0.835136i	1.79947	+	0.482166i	0.993895	−	0.110331i	$-0.0351911\pi$
$3$	3.11677	+	0.835136i	1.79947	+	0.482166i	0.805573	+	0.592497i	$0.201858\pi$
$4$	−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	−0.672294	−	0.740284i	$-0.734691\pi$
$11$	−1.21832	+	0.703395i	−0.367336	+	0.212082i	0.304958	+	0.952366i	$0.401358\pi$
$12$	−6.05149	−	2.24194i	−1.74691	−	0.647191i
$13$	0.699298	+	0.699298i	0.193950	+	0.193950i	0.797401	−	0.603450i	$-0.206208\pi$
$13$	0.699298	+	0.699298i	0.193950	+	0.193950i	−0.603450	+	0.797401i	$0.706208\pi$
$14$		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	−0.327138	−	0.944977i	$-0.606084\pi$
$17$	−4.46506	−	1.19641i	−1.08294	−	0.290172i	−0.755798	+	0.654805i	$0.772751\pi$
$18$	5.65715	−	8.82402i	1.33340	−	2.07984i
$19$	1.40337	−	2.43071i	0.321955	−	0.557643i	−0.658936	−	0.752199i	$-0.728993\pi$
$19$	1.40337	−	2.43071i	0.321955	−	0.557643i	0.980891	+	0.194556i	$0.0623266\pi$
$20$	−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	0.885737	−	0.464188i	$-0.153654\pi$
$23$	−0.543980	−	2.03016i	−0.113428	−	0.423318i	−0.999164	+	0.0408699i	$0.986987\pi$
$24$	−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	$0.148921\pi$
$29$			4.85706i			0.901933i	−0.892541	+	0.450967i	$0.851079\pi$
$30$	7.40894	−	7.01603i	1.35268	−	1.28095i
$31$	3.18470	−	1.83869i	0.571990	−	0.330238i	−0.185954	−	0.982558i	$-0.559538\pi$
$31$	3.18470	−	1.83869i	0.571990	−	0.330238i	0.757944	+	0.652320i	$0.226204\pi$
$32$	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	−0.883875	−	0.467724i	$-0.845074\pi$
$37$	−2.14283	−	7.99714i	−0.352279	−	1.31472i	0.531596	−	0.846998i	$-0.321592\pi$
$38$	−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	−0.871479	−	0.490433i	$-0.836839\pi$
$43$	−2.49869	+	2.49869i	−0.381046	+	0.381046i	0.490433	+	0.871479i	$0.336839\pi$
$44$	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	−0.0677590	−	0.997702i	$-0.521585\pi$
$47$	2.55312	−	0.684106i	0.372411	−	0.0997872i	0.440170	+	0.897915i	$0.354918\pi$
$48$	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	−0.981223	−	0.192877i	$-0.938218\pi$
$53$	−0.254952	+	0.951495i	−0.0350204	+	0.130698i	0.946203	+	0.323575i	$0.104885\pi$
$54$	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	0.539018	−	0.842294i	$-0.318796\pi$
$59$	−3.53286	−	6.11910i	−0.459940	−	0.796639i	−0.998957	+	0.0456557i	$0.985462\pi$
$60$	−9.42439	−	10.9277i	−1.21668	−	1.41076i
$61$	1.09916	−	1.90379i	0.140732	−	0.243756i	−0.787040	−	0.616902i	$-0.788388\pi$
$61$	1.09916	−	1.90379i	0.140732	−	0.243756i	0.927773	+	0.373146i	$0.121721\pi$
$62$	−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	−0.896822	−	0.442391i	$-0.854130\pi$
$67$	0.827081	−	3.08671i	0.101044	−	0.377101i	0.997866	+	0.0652895i	$0.0207971\pi$
$68$	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	$-0.742630\pi$
$71$		−	12.1891i		−	1.44658i	0.690546	−	0.723289i	$-0.257370\pi$
$72$	−12.9043	+	16.5211i	−1.52079	+	1.94703i
$73$	−1.71613	+	6.40469i	−0.200858	+	0.749612i	0.789814	+	0.613346i	$0.210177\pi$
$73$	−1.71613	+	6.40469i	−0.200858	+	0.749612i	−0.990672	+	0.136266i	$0.956490\pi$
$74$	−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	−0.848677	−	0.528912i	$-0.822600\pi$
$79$	0.299644	−	0.518999i	0.0337126	−	0.0583919i	0.882389	+	0.470520i	$0.155934\pi$
$80$	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	−0.910837	−	0.412766i	$-0.864563\pi$
$83$	−4.53764	+	4.53764i	−0.498071	+	0.498071i	0.412766	+	0.910837i	$0.364563\pi$
$84$		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	0.521131	−	0.853477i	$-0.325510\pi$
$89$	0.401553	+	0.231837i	0.0425645	+	0.0245746i	−0.478567	+	0.878051i	$0.658844\pi$
$90$	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	−0.985059	−	0.172216i	$-0.944907\pi$
$97$	−8.00558	+	8.00558i	−0.812843	+	0.812843i	0.172216	+	0.985059i	$0.444907\pi$
$98$		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	0.676095	−	0.736815i	$-0.263671\pi$
$101$	−3.01549	−	5.22299i	−0.300053	−	0.519707i	−0.976148	+	0.217108i	$0.930338\pi$
$102$	−11.3848	+	17.7579i	−1.12726	+	1.75830i
$103$	−3.64227	−	13.5932i	−0.358884	−	1.33937i	−0.875526	−	0.483171i	$-0.839485\pi$
$103$	−3.64227	−	13.5932i	−0.358884	−	1.33937i	0.516642	−	0.856202i	$-0.327182\pi$
$104$	−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	0.873240	−	0.487290i	$-0.162015\pi$
$107$	19.3758	−	5.19174i	1.87313	−	0.501905i	0.999893	−	0.0146144i	$-0.00465208\pi$
$108$	−18.1752	−	21.9143i	−1.74891	−	2.10871i
$109$	0.879139	−	0.507571i	0.0842062	−	0.0486165i	−0.457306	−	0.889310i	$-0.651185\pi$
$109$	0.879139	−	0.507571i	0.0842062	−	0.0486165i	0.541512	+	0.840693i	$0.317852\pi$
$110$	−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	0.963440	−	0.267923i	$-0.0863372\pi$
$113$	7.39345	+	7.39345i	0.695518	+	0.695518i	−0.267923	+	0.963440i	$0.586337\pi$
$114$	−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	0.193862	−	0.981029i	$-0.437899\pi$
$127$	−8.87092	−	8.87092i	−0.787167	−	0.787167i	−0.981029	+	0.193862i	$0.937899\pi$
$128$	−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	−0.0881630	−	0.996106i	$-0.528100\pi$
$131$	−11.3871	−	6.57436i	−0.994898	−	0.574404i	−0.906735	+	0.421702i	$0.861433\pi$
$132$	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	−0.0413695	−	0.999144i	$-0.513172\pi$
$137$	−6.75090	−	1.80890i	−0.576769	−	0.154545i	−0.535399	+	0.844599i	$0.679839\pi$
$138$	−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	0.245418	−	0.969417i	$-0.421075\pi$
$149$	−5.75434	−	3.32227i	−0.471414	−	0.272171i	−0.716831	+	0.697247i	$0.754408\pi$
$150$	22.0852	−	5.72962i	1.80325	−	0.467821i
$151$	17.6555	−	10.1934i	1.43679	−	0.829529i	0.439161	−	0.898408i	$-0.355276\pi$
$151$	17.6555	−	10.1934i	1.43679	−	0.829529i	0.997625	+	0.0688796i	$0.0219424\pi$
$152$	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	0.867416	−	0.497584i	$-0.165779\pi$
$157$	17.1639	+	4.59905i	1.36983	+	0.367044i	0.502412	+	0.864628i	$0.332446\pi$
$158$	−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	−0.883604	−	0.468235i	$-0.844890\pi$
$163$	−4.50039	−	16.7957i	−0.352498	−	1.31554i	0.531106	−	0.847305i	$-0.321776\pi$
$164$	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	0.388370	−	0.921503i	$-0.373038\pi$
$167$	−6.88960	−	6.88960i	−0.533133	−	0.533133i	−0.921503	+	0.388370i	$0.873038\pi$
$168$		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	−0.996399	−	0.0847922i	$-0.972977\pi$
$173$	−23.8977	+	6.40337i	−1.81691	+	0.486839i	−0.820510	+	0.571632i	$0.806311\pi$
$174$	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	0.938542	+	0.345164i	$0.112177\pi$
$179$	10.2777	+	17.8015i	0.768192	+	1.33055i	−0.170350	+	0.985384i	$0.554490\pi$
$180$	−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	0.746475	−	0.665413i	$-0.231745\pi$
$191$	7.51061	+	4.33625i	0.543449	+	0.313760i	−0.203027	+	0.979173i	$0.565078\pi$
$192$	−22.1301	−	13.2895i	−1.59710	−	0.959084i
$193$	−1.37318	+	5.12478i	−0.0988437	+	0.368890i	−0.997574	−	0.0696118i	$-0.977824\pi$
$193$	−1.37318	+	5.12478i	−0.0988437	+	0.368890i	0.898730	+	0.438502i	$0.144491\pi$
$194$	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	−0.993478	−	0.114026i	$-0.963625\pi$
$197$	−12.3437	+	12.3437i	−0.879452	+	0.879452i	0.114026	+	0.993478i	$0.463625\pi$
$198$	−0.685422	+	14.7297i	−0.0487108	+	1.04679i
$199$	2.14941	+	3.72289i	0.152368	+	0.263909i	0.932097	−	0.362208i	$-0.117977\pi$
$199$	2.14941	+	3.72289i	0.152368	+	0.263909i	−0.779730	+	0.626116i	$0.784644\pi$
$200$	−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	$0.234959\pi$
$211$			19.5494i			1.34583i	−0.739718	+	0.672917i	$0.765041\pi$
$212$	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	−0.311171	−	0.950354i	$-0.600721\pi$
$223$	9.54503	−	9.54503i	0.639183	−	0.639183i	0.950354	+	0.311171i	$0.100721\pi$
$224$		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	0.605200	+	0.796073i	$0.293093\pi$
$227$	−4.77541	+	17.8221i	−0.316955	+	1.18289i	−0.922155	+	0.386819i	$0.873574\pi$
$228$	−13.9420	+	11.5631i	−0.923330	+	0.765788i
$229$	13.5250	+	7.80865i	0.893755	+	0.516010i	0.875169	−	0.483817i	$-0.160750\pi$
$229$	13.5250	+	7.80865i	0.893755	+	0.516010i	0.0185864	+	0.999827i	$0.494083\pi$
$230$	−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	−0.377738	−	0.925913i	$-0.623298\pi$
$233$	−3.69263	+	0.989436i	−0.241912	+	0.0648201i	0.135826	+	0.990733i	$0.456631\pi$
$234$	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	0.789357	+	0.613934i	$0.210414\pi$
$241$	14.3810	+	24.9086i	0.926361	+	1.60450i	0.137004	+	0.990570i	$0.456253\pi$
$242$	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	$0.306836\pi$
$251$			26.0285i			1.64291i	−0.570277	+	0.821453i	$0.693164\pi$
$252$		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	−0.856794	−	0.515659i	$-0.827547\pi$
$257$	−5.97352	−	22.2935i	−0.372618	−	1.39063i	0.484176	−	0.874971i	$-0.339119\pi$
$258$	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	−0.0955566	−	0.995424i	$-0.530463\pi$
$263$	−10.9633	−	2.93759i	−0.676023	−	0.181140i	−0.580466	+	0.814284i	$0.697130\pi$
$264$	−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	−0.997652	−	0.0684854i	$-0.978183\pi$
$269$	−23.5713	+	13.6089i	−1.43717	+	0.829749i	−0.439516	+	0.898235i	$0.644850\pi$
$270$	43.7833	−	10.4627i	2.66456	−	0.636743i
$271$	0.134959	+	0.0779185i	0.00819817	+	0.00473321i	0.504093	−	0.863649i	$-0.331827\pi$
$271$	0.134959	+	0.0779185i	0.00819817	+	0.00473321i	−0.495895	+	0.868382i	$0.665160\pi$
$272$	−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	0.808674	−	0.588256i	$-0.200185\pi$
$277$	20.2196	+	5.41783i	1.21488	+	0.325526i	0.406204	+	0.913782i	$0.366852\pi$
$278$	−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	−0.385904	−	0.922539i	$-0.626111\pi$
$283$	−19.8738	−	5.32518i	−1.18138	−	0.316549i	−0.795472	+	0.605990i	$0.792777\pi$
$284$	−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	0.555977	−	0.831198i	$-0.312344\pi$
$293$	−4.71102	−	4.71102i	−0.275221	−	0.275221i	−0.831198	+	0.555977i	$0.812344\pi$
$294$		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	0.999294	−	0.0375706i	$-0.0119619\pi$
$307$	16.8508	+	16.8508i	0.961723	+	0.961723i	−0.0375706	+	0.999294i	$0.511962\pi$
$308$		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	−0.874562	−	0.484914i	$-0.838851\pi$
$311$	−15.7287	+	9.08099i	−0.891895	+	0.514936i	−0.0173329	+	0.999850i	$0.505518\pi$
$312$	−8.36809	+	3.38216i	−0.473750	+	0.191477i
$313$	−1.51498	+	0.405938i	−0.0856319	+	0.0229450i	−0.301381	−	0.953504i	$-0.597447\pi$
$313$	−1.51498	+	0.405938i	−0.0856319	+	0.0229450i	0.215749	+	0.976449i	$0.430781\pi$
$314$	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	0.754092	+	0.656769i	$0.228077\pi$
$317$	7.64549	+	28.5334i	0.429414	+	1.60259i	−0.324678	+	0.945825i	$0.605256\pi$
$318$	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	0.168241	−	0.985746i	$-0.446191\pi$
$331$	−10.9400	−	6.31623i	−0.601319	−	0.347172i	−0.769560	+	0.638574i	$0.779525\pi$
$332$	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	−0.586391	−	0.810028i	$-0.699452\pi$
$337$	4.10542	−	4.10542i	0.223636	−	0.223636i	0.810028	+	0.586391i	$0.199452\pi$
$338$	−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	0.784182	+	0.620531i	$0.213083\pi$
$347$	−3.82255	+	14.2660i	−0.205205	+	0.765837i	−0.989387	+	0.145305i	$0.953584\pi$
$348$	10.8892	−	29.3925i	0.583723	−	1.57560i
$349$		−	5.05181i		−	0.270417i	−0.990817	−	0.135209i	$-0.956830\pi$
$349$		−	5.05181i		−	0.270417i	0.990817	−	0.135209i	$-0.0431705\pi$
$350$		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	0.849692	+	0.527280i	$0.176788\pi$
$353$	−2.81454	+	10.5040i	−0.149803	+	0.559072i	−0.999495	+	0.0317919i	$0.989879\pi$
$354$	−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	−0.792699	−	0.609613i	$-0.791325\pi$
$359$	2.49329	−	4.31850i	0.131591	−	0.227922i	0.924290	+	0.381691i	$0.124658\pi$
$360$	−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	−0.770786	−	0.637094i	$-0.780136\pi$
$367$	4.12420	−	15.3917i	0.215282	−	0.803442i	0.986067	−	0.166347i	$-0.0531972\pi$
$368$	−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	−0.244055	−	0.969761i	$-0.578478\pi$
$373$	0.569126	−	0.152497i	0.0294682	−	0.00789599i	0.273523	+	0.961865i	$0.411811\pi$
$374$	−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	0.931682	−	0.363274i	$-0.118341\pi$
$383$	−1.11189	−	4.14964i	−0.0568151	−	0.212037i	−0.988498	+	0.151237i	$0.951674\pi$
$384$	−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	0.168266	−	0.985742i	$-0.446183\pi$
$389$	21.8152	−	12.5950i	1.10608	−	0.638593i	0.937810	+	0.347148i	$0.112850\pi$
$390$	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	0.986495	−	0.163793i	$-0.0523728\pi$
$397$	1.00160	+	3.73802i	0.0502689	+	0.187606i	−0.936226	+	0.351399i	$0.885706\pi$
$398$	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	−0.789353	−	0.613940i	$-0.789584\pi$
$401$	2.74364	−	4.75213i	0.137011	−	0.237310i	0.926364	+	0.376630i	$0.122917\pi$
$402$	−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	−0.0898942	−	0.995951i	$-0.528653\pi$
$409$	14.7164	−	8.49650i	0.727678	−	0.420125i	0.817572	+	0.575826i	$0.195320\pi$
$410$	−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	−0.282209	−	0.959353i	$-0.591067\pi$
$431$	8.46015	−	4.88447i	0.407511	−	0.235277i	0.689720	+	0.724076i	$0.257734\pi$
$432$	32.1232	+	47.0150i	1.54553	+	2.26201i
$433$	−7.00877	−	7.00877i	−0.336820	−	0.336820i	0.518349	−	0.855169i	$-0.326547\pi$
$433$	−7.00877	−	7.00877i	−0.336820	−	0.336820i	−0.855169	+	0.518349i	$0.826547\pi$
$434$		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	−0.913990	−	0.405737i	$-0.867015\pi$
$439$	−2.21290	+	3.83285i	−0.105616	+	0.182932i	0.808374	+	0.588670i	$0.200348\pi$
$440$	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	0.987695	−	0.156395i	$-0.0499872\pi$
$443$	1.13928	+	4.25183i	0.0541286	+	0.202011i	−0.933566	+	0.358405i	$0.883321\pi$
$444$	−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	$0.172297\pi$
$449$			21.8355i			1.03048i	−0.857046	+	0.515240i	$0.827703\pi$
$450$	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	−0.961191	−	0.275883i	$-0.911030\pi$
$457$	−5.70175	−	21.2792i	−0.266717	−	0.995400i	0.694475	−	0.719517i	$-0.255637\pi$
$458$	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	−0.283877	−	0.958861i	$-0.591621\pi$
$463$	14.5239	−	14.5239i	0.674983	−	0.674983i	0.958861	+	0.283877i	$0.0916209\pi$
$464$	−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	0.433884	−	0.900969i	$-0.357143\pi$
$467$	27.2315	−	7.29665i	1.26012	−	0.337649i	0.826239	+	0.563320i	$0.190476\pi$
$468$	−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	0.849364	−	0.527807i	$-0.176986\pi$
$479$	−0.709375	−	1.22867i	−0.0324122	−	0.0561395i	−0.881776	+	0.471668i	$0.843652\pi$
$480$	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	0.427393	+	0.904066i	$0.359432\pi$
$487$	−8.71188	+	32.5132i	−0.394773	+	1.47331i	−0.822166	+	0.569247i	$0.807235\pi$
$488$	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	$0.0227647\pi$
$491$			3.16673i			0.142913i	−0.997444	+	0.0714563i	$0.977235\pi$
$492$	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	−0.937269	−	0.348607i	$-0.886655\pi$
$499$	−3.72451	+	6.45105i	−0.166732	+	0.288789i	0.770537	+	0.637395i	$0.219988\pi$
$500$	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	−0.130687	−	0.991424i	$-0.541718\pi$
$503$	19.3043	−	19.3043i	0.860736	−	0.860736i	0.991424	+	0.130687i	$0.0417184\pi$
$504$		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	0.265350	−	0.964152i	$-0.414513\pi$
$509$	−9.85817	−	5.69161i	−0.436956	−	0.252276i	−0.702305	+	0.711876i	$0.747846\pi$
$510$	−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	0.852175	−	0.523257i	$-0.175283\pi$
$521$	−0.617798	−	1.07006i	−0.0270662	−	0.0468801i	−0.879241	+	0.476377i	$0.841950\pi$
$522$	42.8588	+	27.4771i	1.87588	+	1.20264i
$523$	−1.63395	−	6.09797i	−0.0714474	−	0.266646i	0.920957	−	0.389665i	$-0.127409\pi$
$523$	−1.63395	−	6.09797i	−0.0714474	−	0.266646i	−0.992404	+	0.123019i	$0.960742\pi$
$524$	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	−0.276891	−	0.960901i	$-0.589304\pi$
$541$	16.1355	−	27.9475i	0.693719	−	1.20156i	0.970611	−	0.240656i	$-0.0773624\pi$
$542$	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	0.221536	−	0.975152i	$-0.428893\pi$
$547$	−17.6256	−	17.6256i	−0.753617	−	0.753617i	−0.975152	+	0.221536i	$0.928893\pi$
$548$	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	0.129860	−	0.991532i	$-0.458547\pi$
$557$	−5.98149	−	1.60273i	−0.253444	−	0.0679101i	−0.383304	+	0.923622i	$0.625214\pi$
$558$	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	0.152742	−	0.988266i	$-0.451189\pi$
$563$	−4.96172	−	1.32949i	−0.209112	−	0.0560313i	−0.361854	+	0.932235i	$0.617856\pi$
$564$	−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	0.972731	−	0.231935i	$-0.0745057\pi$
$569$	30.0136	+	17.3284i	1.25824	+	0.726442i	0.285504	+	0.958378i	$0.407839\pi$
$570$	−6.65643	−	27.8551i	−0.278807	−	1.16672i
$571$	28.9237	−	16.6991i	1.21042	−	0.698836i	0.247569	−	0.968870i	$-0.420368\pi$
$571$	28.9237	−	16.6991i	1.21042	−	0.698836i	0.962851	+	0.270034i	$0.0870350\pi$
$572$	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	−0.512291	−	0.858812i	$-0.671203\pi$
$577$	−33.2773	−	8.91664i	−1.38535	−	0.371204i	−0.873063	+	0.487608i	$0.837870\pi$
$578$	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	0.0348489	−	0.999393i	$-0.488905\pi$
$587$	−23.3690	−	23.3690i	−0.964544	−	0.964544i	−0.999393	+	0.0348489i	$0.988905\pi$
$588$		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	−0.385197	−	0.922834i	$-0.625867\pi$
$593$	−6.26739	+	1.67934i	−0.257371	+	0.0689623i	0.127826	+	0.991797i	$0.459200\pi$
$594$	−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	0.987604	−	0.156965i	$-0.0501709\pi$
$599$	8.75860	+	15.1703i	0.357867	+	0.619843i	−0.629737	+	0.776808i	$0.716838\pi$
$600$	−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	−0.665101	−	0.746754i	$-0.731611\pi$
$607$	−21.3783	+	5.72830i	−0.867718	+	0.232504i	−0.202617	+	0.979258i	$0.564945\pi$
$608$	−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	−0.910867	−	0.412701i	$-0.864585\pi$
$613$	2.08760	−	7.79104i	0.0843175	−	0.314677i	0.995184	+	0.0980238i	$0.0312521\pi$
$614$	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	−0.988031	−	0.154258i	$-0.950701\pi$
$617$	−20.7105	+	20.7105i	−0.833772	+	0.833772i	0.154258	+	0.988031i	$0.450701\pi$
$618$	−64.1479	−	2.98502i	−2.58041	−	0.120075i
$619$	−15.2502	−	26.4141i	−0.612956	−	1.06167i	−0.990739	−	0.135777i	$-0.956647\pi$
$619$	−15.2502	−	26.4141i	−0.612956	−	1.06167i	0.377784	−	0.925894i	$-0.376686\pi$
$620$	−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	$-0.839349\pi$
$631$		−	24.2931i		−	0.967092i	0.875319	−	0.483546i	$-0.160651\pi$
$632$	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	0.555178	−	0.831732i	$-0.312650\pi$
$641$	−11.2086	−	19.4138i	−0.442712	−	0.766800i	−0.997890	+	0.0649320i	$0.979317\pi$
$642$	4.25489	−	91.4372i	0.167927	−	3.60874i
$643$	−3.56268	+	3.56268i	−0.140498	+	0.140498i	−0.773858	−	0.633359i	$-0.781675\pi$
$643$	−3.56268	+	3.56268i	−0.140498	+	0.140498i	0.633359	+	0.773858i	$0.281675\pi$
$644$		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	0.828741	+	0.559632i	$0.189058\pi$
$647$	−4.29327	+	16.0227i	−0.168786	+	0.629918i	−0.997527	+	0.0702854i	$0.977609\pi$
$648$	−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	−0.0137300	−	0.999906i	$-0.504371\pi$
$653$	12.1210	−	3.24782i	0.474332	−	0.127097i	0.488062	+	0.872809i	$0.337704\pi$
$654$	−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	0.790404	−	0.612586i	$-0.209871\pi$
$661$	−3.47890	−	6.02563i	−0.135313	−	0.234370i	−0.925717	+	0.378217i	$0.876537\pi$
$662$	−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	0.596457	−	0.802645i	$-0.296575\pi$
$673$	−5.34897	−	5.34897i	−0.206188	−	0.206188i	−0.802645	+	0.596457i	$0.796575\pi$
$674$	−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	−0.938337	−	0.345723i	$-0.887634\pi$
$677$	−7.76868	−	28.9931i	−0.298575	−	1.11430i	0.639762	−	0.768573i	$-0.279033\pi$
$678$	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	−0.110940	−	0.993827i	$-0.535386\pi$
$683$	−18.3967	−	4.92938i	−0.703930	−	0.188618i	−0.592990	+	0.805210i	$0.702053\pi$
$684$	−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	0.887097	−	0.461583i	$-0.152718\pi$
$691$	24.4705	+	14.1281i	0.930903	+	0.537457i	0.0438058	+	0.999040i	$0.486052\pi$
$692$	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	0.758193	−	0.652030i	$-0.226082\pi$
$709$	15.2471	+	8.80290i	0.572616	+	0.330600i	−0.185578	+	0.982630i	$0.559416\pi$
$710$	−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	−0.997054	−	0.0766969i	$-0.975563\pi$
$719$	−11.5866	+	20.0685i	−0.432106	+	0.748429i	0.564949	+	0.825126i	$0.308896\pi$
$720$	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	0.932220	−	0.361893i	$-0.117869\pi$
$727$	15.3777	+	15.3777i	0.570326	+	0.570326i	−0.361893	+	0.932220i	$0.617869\pi$
$728$		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	−0.909847	−	0.414944i	$-0.863801\pi$
$733$	−40.3490	+	10.8115i	−1.49032	+	0.399331i	−0.580478	+	0.814276i	$0.697134\pi$
$734$	−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	0.999283	+	0.0378565i	$0.0120530\pi$
$739$	14.4738	+	25.0693i	0.532426	+	0.922189i	−0.466857	+	0.884333i	$0.654614\pi$
$740$	−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	−0.991207	−	0.132322i	$-0.957757\pi$
$743$	−23.4115	+	23.4115i	−0.858885	+	0.858885i	0.132322	+	0.991207i	$0.457757\pi$
$744$	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	0.993419	−	0.114534i	$-0.0365376\pi$
$751$	38.1178	+	22.0073i	1.39094	+	0.803059i	0.397520	+	0.917593i	$0.369871\pi$
$752$	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	−0.0972943	−	0.995256i	$-0.531019\pi$
$757$	24.7062	−	24.7062i	0.897961	−	0.897961i	0.995256	+	0.0972943i	$0.0310188\pi$
$758$	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	−0.903898	−	0.427749i	$-0.859307\pi$
$761$	−2.24848	+	3.89448i	−0.0815073	+	0.141175i	0.822390	+	0.568924i	$0.192640\pi$
$762$	−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	$-0.913374\pi$
$769$		−	14.9079i		−	0.537593i	0.963197	−	0.268797i	$-0.0866259\pi$
$770$		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	0.708642	+	0.705568i	$0.249308\pi$
$773$	−7.16881	+	26.7544i	−0.257844	+	0.962287i	−0.966486	+	0.256719i	$0.917358\pi$
$774$	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	−0.986997	−	0.160736i	$-0.948613\pi$
$787$	−1.45499	+	5.43008i	−0.0518646	+	0.193561i	0.935133	+	0.354297i	$0.115280\pi$
$788$	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	−0.485205	−	0.874400i	$-0.661255\pi$
$797$	10.9874	−	10.9874i	0.389195	−	0.389195i	0.874400	+	0.485205i	$0.161255\pi$
$798$		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	−0.731731	−	0.681593i	$-0.761287\pi$
$809$	−14.4297	+	8.33096i	−0.507320	+	0.292901i	0.224412	+	0.974494i	$0.427954\pi$
$810$	74.9126	+	2.04049i	2.63216	+	0.0716957i
$811$		−	30.5372i		−	1.07231i	−0.844120	−	0.536154i	$-0.819877\pi$
$811$		−	30.5372i		−	1.07231i	0.844120	−	0.536154i	$-0.180123\pi$
$812$		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	−0.658458	−	0.752617i	$-0.728791\pi$
$821$	9.24225	−	16.0080i	0.322557	−	0.558685i	0.981015	+	0.193933i	$0.0621243\pi$
$822$	−17.2131	+	26.8490i	−0.600375	+	0.936465i
$823$	−41.3323	−	11.0750i	−1.44075	−	0.386049i	−0.547957	−	0.836507i	$-0.684594\pi$
$823$	−41.3323	−	11.0750i	−1.44075	−	0.386049i	−0.892798	+	0.450457i	$0.851261\pi$
$824$	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	0.981949	−	0.189148i	$-0.0605726\pi$
$827$	22.7990	+	22.7990i	0.792801	+	0.792801i	−0.189148	+	0.981949i	$0.560573\pi$
$828$	−10.8235	+	29.2150i	−0.376142	+	1.01529i
$829$	29.0025	−	16.7446i	1.00730	−	0.581563i	0.0968981	−	0.995294i	$-0.469108\pi$
$829$	29.0025	−	16.7446i	1.00730	−	0.581563i	0.910399	+	0.413731i	$0.135775\pi$
$830$	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	0.513629	−	0.858012i	$-0.328301\pi$
$853$	−10.0581	−	10.0581i	−0.344383	−	0.344383i	−0.858012	+	0.513629i	$0.828301\pi$
$854$		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	0.250215	−	0.968190i	$-0.419499\pi$
$857$	−0.503168	−	0.134823i	−0.0171879	−	0.00460548i	−0.267403	+	0.963585i	$0.586165\pi$
$858$	−3.42647	+	5.34461i	−0.116978	+	0.182462i
$859$	−2.00473	+	3.47230i	−0.0684006	+	0.118473i	−0.898197	−	0.439592i	$-0.855123\pi$
$859$	−2.00473	+	3.47230i	−0.0684006	+	0.118473i	0.829797	+	0.558066i	$0.188456\pi$
$860$	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	0.999978	−	0.00664926i	$-0.00211654\pi$
$863$	3.83800	+	14.3236i	0.130647	+	0.487581i	−0.869331	+	0.494231i	$0.835450\pi$
$864$	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	−0.958453	−	0.285252i	$-0.907923\pi$
$877$	−8.02646	−	29.9552i	−0.271034	−	1.01151i	0.687418	−	0.726262i	$-0.258744\pi$
$878$	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	−0.960537	−	0.278154i	$-0.910278\pi$
$883$	−20.2772	+	20.2772i	−0.682383	+	0.682383i	0.278154	+	0.960537i	$0.410278\pi$
$884$	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	−0.873274	−	0.487229i	$-0.838008\pi$
$887$	−41.2767	+	11.0601i	−1.38594	+	0.371361i	−0.512663	+	0.858590i	$0.671341\pi$
$888$	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	−0.970996	−	0.239097i	$-0.923148\pi$
$907$	−0.317430	+	1.18466i	−0.0105401	+	0.0393361i	0.960456	+	0.278433i	$0.0898152\pi$
$908$	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	$0.0713799\pi$
$911$			13.4236i			0.444743i	−0.974962	+	0.222372i	$0.928620\pi$
$912$	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	−0.997124	−	0.0757845i	$-0.975854\pi$
$919$	−13.1243	+	22.7320i	−0.432931	+	0.749858i	0.564193	+	0.825643i	$0.309187\pi$
$920$	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	0.189751	−	0.981832i	$-0.439232\pi$
$929$	−17.2412	−	9.95422i	−0.565666	−	0.326587i	−0.755416	+	0.655245i	$0.772565\pi$
$930$	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	−0.642884	−	0.765964i	$-0.722262\pi$
$937$	3.76752	−	3.76752i	0.123080	−	0.123080i	0.765964	+	0.642884i	$0.222262\pi$
$938$		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	0.902766	−	0.430133i	$-0.141533\pi$
$941$	2.41962	+	4.19090i	0.0788772	+	0.136619i	−0.823889	+	0.566752i	$0.808200\pi$
$942$	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	0.263225	−	0.964735i	$-0.415214\pi$
$947$	29.9595	−	8.02761i	0.973551	−	0.260862i	0.710327	+	0.703872i	$0.248547\pi$
$948$	−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	0.969364	−	0.245630i	$-0.0789947\pi$
$953$	22.3422	+	22.3422i	0.723734	+	0.723734i	−0.245630	+	0.969364i	$0.578995\pi$
$954$	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	0.835020	−	0.550219i	$-0.185456\pi$
$967$	8.85634	+	8.85634i	0.284801	+	0.284801i	−0.550219	+	0.835020i	$0.685456\pi$
$968$	−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	0.625634	−	0.780117i	$-0.284840\pi$
$971$	8.19063	+	4.72886i	0.262850	+	0.151756i	−0.362784	+	0.931873i	$0.618174\pi$
$972$	−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	0.994240	+	0.107173i	$0.0341799\pi$
$977$	59.6654	+	15.9873i	1.90886	+	0.511479i	0.914624	+	0.404305i	$0.132487\pi$
$978$	−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	0.997676	−	0.0681315i	$-0.0217038\pi$
$983$	57.3012	+	15.3538i	1.82762	+	0.489710i	0.829947	+	0.557842i	$0.188370\pi$
$984$	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	−0.242089	−	0.970254i	$-0.577833\pi$
$991$	15.0202	−	8.67190i	0.477131	−	0.275472i	0.719220	+	0.694782i	$0.244499\pi$
$992$	−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	0.486958	−	0.873425i	$-0.338106\pi$
$997$	14.9024	+	3.99308i	0.471964	+	0.126462i	−0.0149945	+	0.999888i	$0.504773\pi$
$998$	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.863.10		72
4.3	odd	2	inner	980.2.x.l.863.7		72
5.2	odd	4	inner	980.2.x.l.667.18		72
7.2	even	3		980.2.k.l.883.3		36
7.3	odd	6		980.2.x.k.263.16		72
7.4	even	3	inner	980.2.x.l.263.16		72
7.5	odd	6		140.2.k.a.43.3	✓	36
7.6	odd	2		980.2.x.k.863.10		72
20.7	even	4	inner	980.2.x.l.667.16		72
28.3	even	6		980.2.x.k.263.18		72
28.11	odd	6	inner	980.2.x.l.263.18		72
28.19	even	6		140.2.k.a.43.6	yes	36
28.23	odd	6		980.2.k.l.883.6		36
28.27	even	2		980.2.x.k.863.7		72
35.2	odd	12		980.2.k.l.687.6		36
35.12	even	12		140.2.k.a.127.6	yes	36
35.17	even	12		980.2.x.k.67.7		72
35.19	odd	6		700.2.k.b.43.16		36
35.27	even	4		980.2.x.k.667.18		72
35.32	odd	12	inner	980.2.x.l.67.7		72
35.33	even	12		700.2.k.b.407.13		36
140.19	even	6		700.2.k.b.43.13		36
140.27	odd	4		980.2.x.k.667.16		72
140.47	odd	12		140.2.k.a.127.3	yes	36
140.67	even	12	inner	980.2.x.l.67.10		72
140.87	odd	12		980.2.x.k.67.10		72
140.103	odd	12		700.2.k.b.407.16		36
140.107	even	12		980.2.k.l.687.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.3	✓	36	7.5	odd	6
140.2.k.a.43.6	yes	36	28.19	even	6
140.2.k.a.127.3	yes	36	140.47	odd	12
140.2.k.a.127.6	yes	36	35.12	even	12
700.2.k.b.43.13		36	140.19	even	6
700.2.k.b.43.16		36	35.19	odd	6
700.2.k.b.407.13		36	35.33	even	12
700.2.k.b.407.16		36	140.103	odd	12
980.2.k.l.687.3		36	140.107	even	12
980.2.k.l.687.6		36	35.2	odd	12
980.2.k.l.883.3		36	7.2	even	3
980.2.k.l.883.6		36	28.23	odd	6
980.2.x.k.67.7		72	35.17	even	12
980.2.x.k.67.10		72	140.87	odd	12
980.2.x.k.263.16		72	7.3	odd	6
980.2.x.k.263.18		72	28.3	even	6
980.2.x.k.667.16		72	140.27	odd	4
980.2.x.k.667.18		72	35.27	even	4
980.2.x.k.863.7		72	28.27	even	2
980.2.x.k.863.10		72	7.6	odd	2
980.2.x.l.67.7		72	35.32	odd	12	inner
980.2.x.l.67.10		72	140.67	even	12	inner
980.2.x.l.263.16		72	7.4	even	3	inner
980.2.x.l.263.18		72	28.11	odd	6	inner
980.2.x.l.667.16		72	20.7	even	4	inner
980.2.x.l.667.18		72	5.2	odd	4	inner
980.2.x.l.863.7		72	4.3	odd	2	inner
980.2.x.l.863.10		72	1.1	even	1	trivial

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more