LMFDB - Embedded newform 950.2.u.f.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.2
Character	$\chi$	$=$	950.149
Dual form			950.2.u.f.899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(0.412760 + 1.13405i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.90202 + 1.09813i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.18244 - 0.992183i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(0.412760 + 1.13405i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.90202 + 1.09813i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.18244 - 0.992183i) q^{9} +(0.158441 - 0.274427i) q^{11} +(1.04514 - 0.603415i) q^{12} +(-0.0234748 + 0.0644966i) q^{13} +(0.381378 - 2.16290i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.30034 + 5.12494i) q^{17} +1.54356i q^{18} +(0.761855 + 4.29180i) q^{19} +(-2.03042 - 1.70372i) q^{21} +(0.108380 + 0.297771i) q^{22} +(-0.513603 + 0.0905620i) q^{23} +(-0.209564 + 1.18849i) q^{24} +(-0.0343179 - 0.0594403i) q^{26} +(4.74868 + 2.74165i) q^{27} +(1.41173 + 1.68244i) q^{28} +(-5.22668 + 4.38571i) q^{29} +(-2.96958 - 5.14347i) q^{31} +(0.342020 - 0.939693i) q^{32} +(0.376612 + 0.0664068i) q^{33} +(-1.16173 - 6.58850i) q^{34} +(-1.18244 - 0.992183i) q^{36} +10.8376i q^{37} +(-3.77742 - 2.17510i) q^{38} -0.0828317 q^{39} +(-2.78749 + 1.01456i) q^{41} +(2.61025 - 0.460258i) q^{42} +(-5.76298 - 1.01617i) q^{43} +(-0.297771 - 0.108380i) q^{44} +(0.260763 - 0.451655i) q^{46} +(-5.59278 - 6.66521i) q^{47} +(-0.775735 - 0.924485i) q^{48} +(-1.08821 + 1.88483i) q^{49} +(-7.58694 - 2.76142i) q^{51} +(0.0675931 + 0.0119185i) q^{52} +(8.96377 - 1.58055i) q^{53} +(-5.15262 + 1.87540i) q^{54} -2.19627 q^{56} +(-4.55265 + 2.63547i) q^{57} -6.82295i q^{58} +(-1.57825 - 1.32431i) q^{59} +(0.313061 + 1.77546i) q^{61} +(5.84894 + 1.03133i) q^{62} +(-1.15947 + 3.18563i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.292952 + 0.245816i) q^{66} +(-0.150932 - 0.179873i) q^{67} +(5.79383 + 3.34507i) q^{68} +(-0.314696 - 0.545070i) q^{69} +(-0.314696 + 1.78473i) q^{71} +(1.52011 - 0.268037i) q^{72} +(2.56629 + 7.05084i) q^{73} +(-8.30210 - 6.96629i) q^{74} +(4.09431 - 1.49554i) q^{76} +0.695955i q^{77} +(0.0532432 - 0.0634528i) q^{78} +(3.32526 - 1.21030i) q^{79} +(-0.344991 + 1.95654i) q^{81} +(1.01456 - 2.78749i) q^{82} +(-0.0844691 + 0.0487683i) q^{83} +(-1.32526 + 2.29542i) q^{84} +(4.48280 - 3.76152i) q^{86} +(-7.13097 - 4.11707i) q^{87} +(0.274427 - 0.158441i) q^{88} +(6.00343 + 2.18507i) q^{89} +(-0.0261762 - 0.148452i) q^{91} +(0.178372 + 0.490074i) q^{92} +(4.60722 - 5.49067i) q^{93} +8.70082 q^{94} +1.20683 q^{96} +(4.73510 - 5.64307i) q^{97} +(-0.744377 - 2.04516i) q^{98} +(-0.0849358 - 0.481695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 18 * q^9	$ 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	0.412760	+	1.13405i	0.238307	+	0.654743i	0.999977	+	0.00677814i	$0.00215756\pi$
$3$	0.412760	+	1.13405i	0.238307	+	0.654743i	−0.761670	+	0.647965i	$0.775620\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−1.13405	−	0.412760i	−0.462973	−	0.168509i
$7$	−1.90202	+	1.09813i	−0.718897	+	0.415055i	−0.814347	−	0.580379i	$-0.802904\pi$
$7$	−1.90202	+	1.09813i	−0.718897	+	0.415055i	0.0954496	+	0.995434i	$0.469571\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	1.18244	−	0.992183i	0.394146	−	0.330728i
$10$		0			0
$11$	0.158441	−	0.274427i	0.0477716	−	0.0827429i	−0.841151	−	0.540801i	$-0.818121\pi$
$11$	0.158441	−	0.274427i	0.0477716	−	0.0827429i	0.888922	+	0.458058i	$0.151455\pi$
$12$	1.04514	−	0.603415i	0.301707	−	0.174191i
$13$	−0.0234748	+	0.0644966i	−0.00651075	+	0.0178881i	−0.942905	−	0.333061i	$-0.891919\pi$
$13$	−0.0234748	+	0.0644966i	−0.00651075	+	0.0178881i	0.936395	+	0.350949i	$0.114141\pi$
$14$	0.381378	−	2.16290i	0.101927	−	0.578059i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−4.30034	+	5.12494i	−1.04298	+	1.24298i	−0.0736376	+	0.997285i	$0.523461\pi$
$17$	−4.30034	+	5.12494i	−1.04298	+	1.24298i	−0.969347	+	0.245696i	$0.920984\pi$
$18$			1.54356i			0.363821i
$19$	0.761855	+	4.29180i	0.174782	+	0.984607i
$19$	0.761855	+	4.29180i	0.174782	+	0.984607i
$20$		0			0
$21$	−2.03042	−	1.70372i	−0.443073	−	0.371782i
$22$	0.108380	+	0.297771i	0.0231066	+	0.0634850i
$23$	−0.513603	+	0.0905620i	−0.107094	+	0.0188835i	−0.226938	−	0.973909i	$-0.572872\pi$
$23$	−0.513603	+	0.0905620i	−0.107094	+	0.0188835i	0.119845	+	0.992793i	$0.461760\pi$
$24$	−0.209564	+	1.18849i	−0.0427770	+	0.242601i
$25$		0			0
$26$	−0.0343179	−	0.0594403i	−0.00673029	−	0.0116572i
$27$	4.74868	+	2.74165i	0.913884	+	0.527631i
$28$	1.41173	+	1.68244i	0.266792	+	0.317951i
$29$	−5.22668	+	4.38571i	−0.970570	+	0.814405i	−0.982640	−	0.185522i	$-0.940602\pi$
$29$	−5.22668	+	4.38571i	−0.970570	+	0.814405i	0.0120697	+	0.999927i	$0.496158\pi$
$30$		0			0
$31$	−2.96958	−	5.14347i	−0.533353	−	0.923795i	−0.999241	−	0.0389511i	$-0.987598\pi$
$31$	−2.96958	−	5.14347i	−0.533353	−	0.923795i	0.465888	−	0.884844i	$-0.345735\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	0.376612	+	0.0664068i	0.0655597	+	0.0115599i
$34$	−1.16173	−	6.58850i	−0.199235	−	1.12992i
$35$		0			0
$36$	−1.18244	−	0.992183i	−0.197073	−	0.165364i
$37$			10.8376i			1.78169i	0.454304	+	0.890847i	$0.349888\pi$
$37$			10.8376i			1.78169i	−0.454304	+	0.890847i	$0.650112\pi$
$38$	−3.77742	−	2.17510i	−0.612779	−	0.352848i
$39$	−0.0828317			−0.0132637
$40$		0			0
$41$	−2.78749	+	1.01456i	−0.435333	+	0.158448i	−0.550385	−	0.834911i	$-0.685519\pi$
$41$	−2.78749	+	1.01456i	−0.435333	+	0.158448i	0.115051	+	0.993360i	$0.463297\pi$
$42$	2.61025	−	0.460258i	0.402771	−	0.0710193i
$43$	−5.76298	−	1.01617i	−0.878846	−	0.154964i	−0.284019	−	0.958819i	$-0.591668\pi$
$43$	−5.76298	−	1.01617i	−0.878846	−	0.154964i	−0.594826	+	0.803854i	$0.702779\pi$
$44$	−0.297771	−	0.108380i	−0.0448906	−	0.0163389i
$45$		0			0
$46$	0.260763	−	0.451655i	0.0384474	−	0.0665928i
$47$	−5.59278	−	6.66521i	−0.815791	−	0.972221i	0.184152	−	0.982898i	$-0.441046\pi$
$47$	−5.59278	−	6.66521i	−0.815791	−	0.972221i	−0.999943	+	0.0106763i	$0.996602\pi$
$48$	−0.775735	−	0.924485i	−0.111968	−	0.133438i
$49$	−1.08821	+	1.88483i	−0.155458	+	0.269261i
$50$		0			0
$51$	−7.58694	−	2.76142i	−1.06238	−	0.386676i
$52$	0.0675931	+	0.0119185i	0.00937347	+	0.00165280i
$53$	8.96377	−	1.58055i	1.23127	−	0.217106i	0.480098	−	0.877215i	$-0.340601\pi$
$53$	8.96377	−	1.58055i	1.23127	−	0.217106i	0.751170	+	0.660109i	$0.229490\pi$
$54$	−5.15262	+	1.87540i	−0.701183	+	0.255210i
$55$		0			0
$56$	−2.19627			−0.293488
$57$	−4.55265	+	2.63547i	−0.603013	+	0.349076i
$58$		−	6.82295i		−	0.895897i
$59$	−1.57825	−	1.32431i	−0.205470	−	0.172410i	0.534246	−	0.845329i	$-0.320596\pi$
$59$	−1.57825	−	1.32431i	−0.205470	−	0.172410i	−0.739716	+	0.672919i	$0.765040\pi$
$60$		0			0
$61$	0.313061	+	1.77546i	0.0400833	+	0.227324i	0.998268	−	0.0588259i	$-0.0187357\pi$
$61$	0.313061	+	1.77546i	0.0400833	+	0.227324i	−0.958185	+	0.286150i	$0.907625\pi$
$62$	5.84894	+	1.03133i	0.742816	+	0.130979i
$63$	−1.15947	+	3.18563i	−0.146080	+	0.401351i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−0.292952	+	0.245816i	−0.0360599	+	0.0302578i
$67$	−0.150932	−	0.179873i	−0.0184393	−	0.0219750i	0.756746	−	0.653709i	$-0.226788\pi$
$67$	−0.150932	−	0.179873i	−0.0184393	−	0.0219750i	−0.775185	+	0.631734i	$0.782344\pi$
$68$	5.79383	+	3.34507i	0.702605	+	0.405649i
$69$	−0.314696	−	0.545070i	−0.0378850	−	0.0656187i
$70$		0			0
$71$	−0.314696	+	1.78473i	−0.0373476	+	0.211809i	−0.997771	−	0.0667369i	$-0.978741\pi$
$71$	−0.314696	+	1.78473i	−0.0373476	+	0.211809i	0.960423	+	0.278546i	$0.0898523\pi$
$72$	1.52011	−	0.268037i	0.179147	−	0.0315884i
$73$	2.56629	+	7.05084i	0.300362	+	0.825238i	0.994437	+	0.105335i	$0.0335915\pi$
$73$	2.56629	+	7.05084i	0.300362	+	0.825238i	−0.694075	+	0.719903i	$0.744186\pi$
$74$	−8.30210	−	6.96629i	−0.965099	−	0.809814i
$75$		0			0
$76$	4.09431	−	1.49554i	0.469649	−	0.171551i
$77$			0.695955i			0.0793115i
$78$	0.0532432	−	0.0634528i	0.00602860	−	0.00718461i
$79$	3.32526	−	1.21030i	0.374121	−	0.136169i	−0.148115	−	0.988970i	$-0.547320\pi$
$79$	3.32526	−	1.21030i	0.374121	−	0.136169i	0.522235	+	0.852801i	$0.325098\pi$
$80$		0			0
$81$	−0.344991	+	1.95654i	−0.0383324	+	0.217394i
$82$	1.01456	−	2.78749i	0.112040	−	0.307827i
$83$	−0.0844691	+	0.0487683i	−0.00927169	+	0.00535301i	−0.504629	−	0.863336i	$-0.668371\pi$
$83$	−0.0844691	+	0.0487683i	−0.00927169	+	0.00535301i	0.495357	+	0.868690i	$0.335037\pi$
$84$	−1.32526	+	2.29542i	−0.144598	+	0.250450i
$85$		0			0
$86$	4.48280	−	3.76152i	0.483393	−	0.405615i
$87$	−7.13097	−	4.11707i	−0.764520	−	0.441396i
$88$	0.274427	−	0.158441i	0.0292540	−	0.0168898i
$89$	6.00343	+	2.18507i	0.636362	+	0.231617i	0.639998	−	0.768377i	$-0.278935\pi$
$89$	6.00343	+	2.18507i	0.636362	+	0.231617i	−0.00363610	+	0.999993i	$0.501157\pi$
$90$		0			0
$91$	−0.0261762	−	0.148452i	−0.00274401	−	0.0155620i
$92$	0.178372	+	0.490074i	0.0185966	+	0.0510937i
$93$	4.60722	−	5.49067i	0.477747	−	0.569356i
$94$	8.70082			0.897421
$95$		0			0
$96$	1.20683			0.123172
$97$	4.73510	−	5.64307i	0.480777	−	0.572967i	−0.470070	−	0.882629i	$-0.655771\pi$
$97$	4.73510	−	5.64307i	0.480777	−	0.572967i	0.950847	+	0.309662i	$0.100216\pi$
$98$	−0.744377	−	2.04516i	−0.0751935	−	0.206592i
$99$	−0.0849358	−	0.481695i	−0.00853637	−	0.0484122i
$100$		0			0
$101$	−9.05592	−	3.29609i	−0.901098	−	0.327973i	−0.150405	−	0.988624i	$-0.548058\pi$
$101$	−9.05592	−	3.29609i	−0.901098	−	0.327973i	−0.750693	+	0.660652i	$0.770280\pi$
$102$	6.99216	−	4.03693i	0.692327	−	0.399715i
$103$	−15.9662	−	9.21811i	−1.57320	−	0.908287i	−0.995773	−	0.0918448i	$-0.970724\pi$
$103$	−15.9662	−	9.21811i	−1.57320	−	0.908287i	−0.577427	−	0.816443i	$-0.695943\pi$
$104$	−0.0525781	+	0.0441182i	−0.00515570	+	0.00432615i
$105$		0			0
$106$	−4.55102	+	7.88260i	−0.442034	+	0.765626i
$107$	−10.2563	+	5.92148i	−0.991515	+	0.572451i	−0.905727	−	0.423862i	$-0.860674\pi$
$107$	−10.2563	+	5.92148i	−0.991515	+	0.572451i	−0.0857880	+	0.996313i	$0.527341\pi$
$108$	1.87540	−	5.15262i	0.180461	−	0.495811i
$109$	0.136009	−	0.771345i	0.0130273	−	0.0738814i	−0.977601	−	0.210467i	$-0.932502\pi$
$109$	0.136009	−	0.771345i	0.0130273	−	0.0738814i	0.990628	+	0.136585i	$0.0436128\pi$
$110$		0			0
$111$	−12.2904	+	4.47333i	−1.16655	+	0.424590i
$112$	1.41173	−	1.68244i	0.133396	−	0.158975i
$113$		−	1.07256i		−	0.100898i	−0.998727	−	0.0504488i	$-0.983935\pi$
$113$		−	1.07256i		−	0.100898i	0.998727	−	0.0504488i	$-0.0160652\pi$
$114$	0.907504	−	5.18158i	0.0849955	−	0.485299i
$115$		0			0
$116$	5.22668	+	4.38571i	0.485285	+	0.407203i
$117$	0.0362349	+	0.0995545i	0.00334991	+	0.00920381i
$118$	2.02896	−	0.357760i	0.186781	−	0.0329345i
$119$	2.55147	−	14.4701i	0.233893	−	1.32647i
$120$		0			0
$121$	5.44979	+	9.43932i	0.495436	+	0.858120i
$122$	−1.56131	−	0.901422i	−0.141354	−	0.0816109i
$123$	−2.30113	−	2.74238i	−0.207486	−	0.247272i
$124$	−4.54967	+	3.81762i	−0.408572	+	0.342833i
$125$		0			0
$126$	−1.69504	−	2.93589i	−0.151006	−	0.261550i
$127$	3.02987	−	8.32450i	0.268857	−	0.738680i	−0.729637	−	0.683834i	$-0.760311\pi$
$127$	3.02987	−	8.32450i	0.268857	−	0.738680i	0.998495	−	0.0548454i	$-0.0174666\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	−1.22634	−	6.95493i	−0.107973	−	0.612347i
$130$		0			0
$131$	5.91581	+	4.96395i	0.516866	+	0.433702i	0.863538	−	0.504284i	$-0.168244\pi$
$131$	5.91581	+	4.96395i	0.516866	+	0.433702i	−0.346671	+	0.937987i	$0.612688\pi$
$132$		−	0.382421i		−	0.0332855i
$133$	−6.16204	−	7.32649i	−0.534316	−	0.635287i
$134$	0.234808			0.0202843
$135$		0			0
$136$	−6.28667	+	2.28816i	−0.539078	+	0.196208i
$137$	−16.6228	+	2.93106i	−1.42019	+	0.250417i	−0.830411	−	0.557151i	$-0.811894\pi$
$137$	−16.6228	+	2.93106i	−1.42019	+	0.250417i	−0.589774	+	0.807568i	$0.700783\pi$
$138$	0.619831	+	0.109293i	0.0527635	+	0.00930363i
$139$	18.7585	+	6.82755i	1.59108	+	0.579105i	0.977575	−	0.210586i	$-0.0675374\pi$
$139$	18.7585	+	6.82755i	1.59108	+	0.579105i	0.613504	+	0.789692i	$0.289760\pi$
$140$		0			0
$141$	5.25020	−	9.09362i	0.442147	−	0.765821i
$142$	−1.16490	−	1.38827i	−0.0977563	−	0.116501i
$143$	0.0139802	+	0.0166610i	0.00116909	+	0.00139326i
$144$	−0.771781	+	1.33676i	−0.0643151	+	0.111397i
$145$		0			0
$146$	−7.05084	−	2.56629i	−0.583531	−	0.212388i
$147$	−2.58666	−	0.456097i	−0.213344	−	0.0376183i
$148$	10.6730	−	1.88193i	0.877313	−	0.154694i
$149$	−14.7196	+	5.35751i	−1.20588	+	0.438904i	−0.865272	−	0.501302i	$-0.832855\pi$
$149$	−14.7196	+	5.35751i	−1.20588	+	0.438904i	−0.340606	+	0.940206i	$0.610632\pi$
$150$		0			0
$151$	13.6401			1.11001			0.555007	−	0.831846i	$-0.312716\pi$
$151$	13.6401			1.11001			0.555007	+	0.831846i	$0.312716\pi$
$152$	−1.48612	+	4.09774i	−0.120540	+	0.332370i
$153$			10.3266i			0.834860i
$154$	−0.533133	−	0.447351i	−0.0429611	−	0.0360486i
$155$		0			0
$156$	0.0143836	+	0.0815733i	0.00115161	+	0.00653109i
$157$	15.2002	+	2.68020i	1.21310	+	0.213903i	0.743355	−	0.668897i	$-0.233233\pi$
$157$	15.2002	+	2.68020i	1.21310	+	0.213903i	0.469749	+	0.882800i	$0.344344\pi$
$158$	−1.21030	+	3.32526i	−0.0962859	+	0.264543i
$159$	5.49231	+	9.51296i	0.435568	+	0.754427i
$160$		0			0
$161$	0.877435	−	0.736255i	0.0691515	−	0.0580250i
$162$	−1.27704	−	1.52192i	−0.100334	−	0.119573i
$163$	−0.615929	−	0.355607i	−0.0482433	−	0.0278533i	0.475684	−	0.879616i	$-0.342200\pi$
$163$	−0.615929	−	0.355607i	−0.0482433	−	0.0278533i	−0.523928	+	0.851763i	$0.675534\pi$
$164$	1.48319	+	2.56897i	0.115818	+	0.200603i
$165$		0			0
$166$	0.0169370	−	0.0960548i	0.00131457	−	0.00745529i
$167$	10.6438	−	1.87678i	0.823639	−	0.145230i	0.254083	−	0.967182i	$-0.418226\pi$
$167$	10.6438	−	1.87678i	0.823639	−	0.145230i	0.569556	+	0.821953i	$0.307115\pi$
$168$	−0.906531	−	2.49067i	−0.0699404	−	0.192160i
$169$	9.95497	+	8.35321i	0.765767	+	0.642555i
$170$		0			0
$171$	5.15910	+	4.31889i	0.394526	+	0.330274i
$172$			5.85188i			0.446202i
$173$	−13.7408	+	16.3757i	−1.04470	+	1.24502i	−0.0759108	+	0.997115i	$0.524186\pi$
$173$	−13.7408	+	16.3757i	−1.04470	+	1.24502i	−0.968784	+	0.247905i	$0.920258\pi$
$174$	7.73756	−	2.81624i	0.586583	−	0.213499i
$175$		0			0
$176$	−0.0550258	+	0.312067i	−0.00414773	+	0.0235229i
$177$	0.850392	−	2.33643i	0.0639194	−	0.175617i
$178$	−5.53279	+	3.19436i	−0.414700	+	0.239427i
$179$	−9.05582	+	15.6851i	−0.676864	+	1.17236i	0.299057	+	0.954235i	$0.403328\pi$
$179$	−9.05582	+	15.6851i	−0.676864	+	1.17236i	−0.975920	+	0.218127i	$0.930005\pi$
$180$		0			0
$181$	20.0377	−	16.8136i	1.48939	−	1.24975i	0.594001	−	0.804464i	$-0.297548\pi$
$181$	20.0377	−	16.8136i	1.48939	−	1.24975i	0.895390	−	0.445283i	$-0.146897\pi$
$182$	0.130547	+	0.0753712i	0.00967677	+	0.00558689i
$183$	−1.88423	+	1.08786i	−0.139287	+	0.0804171i
$184$	−0.490074	−	0.178372i	−0.0361287	−	0.0131498i
$185$		0			0
$186$	1.24463	+	7.05867i	0.0912610	+	0.517567i
$187$	0.725075	+	1.99213i	0.0530227	+	0.145679i
$188$	−5.59278	+	6.66521i	−0.407895	+	0.486111i
$189$	−12.0428			−0.875985
$190$		0			0
$191$	15.6106			1.12954			0.564770	−	0.825248i	$-0.308965\pi$
$191$	15.6106			1.12954			0.564770	+	0.825248i	$0.308965\pi$
$192$	−0.775735	+	0.924485i	−0.0559839	+	0.0667190i
$193$	3.65810	+	10.0505i	0.263315	+	0.723453i	0.998939	+	0.0460623i	$0.0146673\pi$
$193$	3.65810	+	10.0505i	0.263315	+	0.723453i	−0.735623	+	0.677391i	$0.763111\pi$
$194$	1.27918	+	7.25460i	0.0918399	+	0.520850i
$195$		0			0
$196$	2.04516	+	0.744377i	0.146083	+	0.0531698i
$197$	6.59006	−	3.80477i	0.469522	−	0.271079i	−0.246518	−	0.969138i	$-0.579286\pi$
$197$	6.59006	−	3.80477i	0.469522	−	0.271079i	0.716040	+	0.698060i	$0.245953\pi$
$198$	0.423595	+	0.244563i	0.0301036	+	0.0173803i
$199$	15.0459	−	12.6250i	1.06658	−	0.894963i	0.0718375	−	0.997416i	$-0.477114\pi$
$199$	15.0459	−	12.6250i	1.06658	−	0.894963i	0.994738	+	0.102453i	$0.0326692\pi$
$200$		0			0
$201$	0.141687	−	0.245409i	0.00999381	−	0.0173098i
$202$	8.34598	−	4.81855i	0.587221	−	0.339032i
$203$	5.12518	−	14.0813i	0.359717	−	0.988314i
$204$	−1.40201	+	7.95119i	−0.0981603	+	0.556695i
$205$		0			0
$206$	17.3244	−	6.30556i	1.20705	−	0.439329i
$207$	−0.517449	+	0.616672i	−0.0359652	+	0.0428616i
$208$		−	0.0686358i		−	0.00475904i
$209$	1.29850	+	0.470922i	0.0898188	+	0.0325744i
$210$		0			0
$211$	−14.5809	−	12.2348i	−1.00379	−	0.842278i	−0.0162836	−	0.999867i	$-0.505183\pi$
$211$	−14.5809	−	12.2348i	−1.00379	−	0.842278i	−0.987505	+	0.157589i	$0.949628\pi$
$212$	−3.11308	−	8.55313i	−0.213807	−	0.587431i
$213$	−2.15387	+	0.379785i	−0.147581	+	0.0260224i
$214$	2.05651	−	11.6630i	0.140580	−	0.797269i
$215$		0			0
$216$	2.74165	+	4.74868i	0.186546	+	0.323107i
$217$	11.2964	+	6.52200i	0.766852	+	0.442742i
$218$	0.503460	+	0.600000i	0.0340986	+	0.0406371i
$219$	−6.93673	+	5.82061i	−0.468741	+	0.393320i
$220$		0			0
$221$	−0.229591	−	0.397664i	−0.0154440	−	0.0267498i
$222$	4.47333	−	12.2904i	0.300231	−	0.824877i
$223$	−1.51709	−	0.267505i	−0.101592	−	0.0179134i	0.122621	−	0.992454i	$-0.460870\pi$
$223$	−1.51709	−	0.267505i	−0.101592	−	0.0179134i	−0.224213	+	0.974540i	$0.571981\pi$
$224$	0.381378	+	2.16290i	0.0254819	+	0.144515i
$225$		0			0
$226$	0.821626	+	0.689426i	0.0546537	+	0.0458599i
$227$		−	21.9238i		−	1.45514i	−0.686036	−	0.727568i	$-0.740651\pi$
$227$		−	21.9238i		−	1.45514i	0.686036	−	0.727568i	$-0.259349\pi$
$228$	3.38599	+	4.02584i	0.224242	+	0.266618i
$229$	22.5988			1.49337			0.746687	−	0.665176i	$-0.231643\pi$
$229$	22.5988			1.49337			0.746687	+	0.665176i	$0.231643\pi$
$230$		0			0
$231$	−0.789247	+	0.287262i	−0.0519287	+	0.0189005i
$232$	−6.71929	+	1.18479i	−0.441143	+	0.0777854i
$233$	8.90312	+	1.56986i	0.583263	+	0.102845i	0.457491	−	0.889214i	$-0.348748\pi$
$233$	8.90312	+	1.56986i	0.583263	+	0.102845i	0.125772	+	0.992059i	$0.459859\pi$
$234$	−0.0995545	−	0.0362349i	−0.00650808	−	0.00236875i
$235$		0			0
$236$	−1.03013	+	1.78424i	−0.0670557	+	0.116144i
$237$	2.74507	+	3.27144i	0.178311	+	0.212503i
$238$	9.44468	+	11.2557i	0.612208	+	0.729601i
$239$	−11.7361	+	20.3275i	−0.759145	+	1.31488i	0.184142	+	0.982900i	$0.441049\pi$
$239$	−11.7361	+	20.3275i	−0.759145	+	1.31488i	−0.943287	+	0.331978i	$0.892284\pi$
$240$		0			0
$241$	25.8548	+	9.41039i	1.66546	+	0.606177i	0.991206	−	0.132326i	$-0.0422447\pi$
$241$	25.8548	+	9.41039i	1.66546	+	0.606177i	0.674250	+	0.738503i	$0.264467\pi$
$242$	−10.7340	−	1.89269i	−0.690007	−	0.121667i
$243$	13.8388	−	2.44015i	0.887759	−	0.156536i
$244$	1.69412	−	0.616609i	0.108455	−	0.0394744i
$245$		0			0
$246$	3.57993			0.228248
$247$	−0.294691	−	0.0516123i	−0.0187507	−	0.00328401i
$248$		−	5.93917i		−	0.377138i
$249$	−0.0901711	−	0.0756625i	−0.00571436	−	0.00479492i
$250$		0			0
$251$	4.58954	+	26.0286i	0.289689	+	1.64291i	0.688037	+	0.725675i	$0.258473\pi$
$251$	4.58954	+	26.0286i	0.289689	+	1.64291i	−0.398348	+	0.917234i	$0.630416\pi$
$252$	3.33857	+	0.588680i	0.210310	+	0.0370834i
$253$	−0.0565228	+	0.155295i	−0.00355356	+	0.00976332i
$254$	4.42937	+	7.67190i	0.277924	+	0.481378i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−7.13305	−	8.50084i	−0.444947	−	0.530268i	0.496225	−	0.868194i	$-0.334719\pi$
$257$	−7.13305	−	8.50084i	−0.444947	−	0.530268i	−0.941173	+	0.337926i	$0.890275\pi$
$258$	6.11606	+	3.53111i	0.380769	+	0.219837i
$259$	−11.9011	−	20.6134i	−0.739501	−	1.28085i
$260$		0			0
$261$	−1.82880	+	10.3716i	−0.113200	+	0.641989i
$262$	−7.60521	+	1.34100i	−0.469852	+	0.0828475i
$263$	9.54717	+	26.2306i	0.588704	+	1.61745i	0.772876	+	0.634557i	$0.218817\pi$
$263$	9.54717	+	26.2306i	0.588704	+	1.61745i	−0.184173	+	0.982894i	$0.558961\pi$
$264$	0.292952	+	0.245816i	0.0180299	+	0.0151289i
$265$		0			0
$266$	9.57330	−	0.0110190i	0.586976	−	0.000675616i
$267$			7.71009i			0.471850i
$268$	−0.150932	+	0.179873i	−0.00921963	+	0.0109875i
$269$	−7.91172	+	2.87963i	−0.482386	+	0.175574i	−0.571755	−	0.820424i	$-0.693737\pi$
$269$	−7.91172	+	2.87963i	−0.482386	+	0.175574i	0.0893689	+	0.995999i	$0.471515\pi$
$270$		0			0
$271$	−2.07262	+	11.7544i	−0.125903	+	0.714030i	0.854865	+	0.518851i	$0.173640\pi$
$271$	−2.07262	+	11.7544i	−0.125903	+	0.714030i	−0.980768	+	0.195179i	$0.937471\pi$
$272$	2.28816	−	6.28667i	0.138740	−	0.381185i
$273$	0.157548	−	0.0909602i	0.00953522	−	0.00550516i
$274$	8.43964	−	14.6179i	0.509857	−	0.883098i
$275$		0			0
$276$	−0.482143	+	0.404566i	−0.0290216	+	0.0243520i
$277$	2.71945	+	1.57008i	0.163396	+	0.0943367i	0.579468	−	0.814995i	$-0.303260\pi$
$277$	2.71945	+	1.57008i	0.163396	+	0.0943367i	−0.416072	+	0.909332i	$0.636594\pi$
$278$	−17.2880	+	9.98121i	−1.03686	+	0.598633i
$279$	−8.61461	−	3.13546i	−0.515743	−	0.187715i
$280$		0			0
$281$	−2.67896	−	15.1931i	−0.159813	−	0.906345i	−0.954253	−	0.299002i	$-0.903346\pi$
$281$	−2.67896	−	15.1931i	−0.159813	−	0.906345i	0.794439	−	0.607343i	$-0.207765\pi$
$282$	3.59135	+	9.86715i	0.213862	+	0.587580i
$283$	10.0831	−	12.0165i	0.599376	−	0.714309i	−0.378003	−	0.925804i	$-0.623389\pi$
$283$	10.0831	−	12.0165i	0.599376	−	0.714309i	0.977379	+	0.211496i	$0.0678335\pi$
$284$	1.81226			0.107538
$285$		0			0
$286$	−0.0217494			−0.00128607
$287$	4.18775	−	4.99077i	0.247195	−	0.294596i
$288$	−0.527930	−	1.45047i	−0.0311085	−	0.0854700i
$289$	−4.82011	−	27.3362i	−0.283536	−	1.60801i
$290$		0			0
$291$	8.35398	+	3.04060i	0.489719	+	0.178243i
$292$	6.49809	−	3.75167i	0.380272	−	0.219550i
$293$	8.97073	+	5.17925i	0.524076	+	0.302575i	0.738601	−	0.674143i	$-0.235487\pi$
$293$	8.97073	+	5.17925i	0.524076	+	0.302575i	−0.214525	+	0.976719i	$0.568820\pi$
$294$	2.01206	−	1.68832i	0.117346	−	0.0984649i
$295$		0			0
$296$	−5.41881	+	9.38565i	−0.314962	+	0.545530i
$297$	1.50477	−	0.868778i	0.0873155	−	0.0504116i
$298$	5.35751	−	14.7196i	0.310352	−	0.852685i
$299$	0.00621580	−	0.0352515i	0.000359469	−	0.00203865i
$300$		0			0
$301$	12.0772	−	4.39574i	0.696118	−	0.253366i
$302$	−8.76767	+	10.4489i	−0.504523	+	0.601267i
$303$		−	11.6303i		−	0.668146i
$304$	−2.18379	−	3.77241i	−0.125249	−	0.216362i
$305$		0			0
$306$	−7.91067	−	6.63784i	−0.452223	−	0.379460i
$307$	−2.93506	−	8.06402i	−0.167513	−	0.460238i	0.827324	−	0.561725i	$-0.189862\pi$
$307$	−2.93506	−	8.06402i	−0.167513	−	0.460238i	−0.994837	+	0.101487i	$0.967640\pi$
$308$	0.685382	−	0.120851i	0.0390533	−	0.00688615i
$309$	3.86356	−	21.9114i	0.219790	−	1.24649i
$310$		0			0
$311$	−2.12890	−	3.68737i	−0.120719	−	0.209092i	0.799332	−	0.600889i	$-0.205187\pi$
$311$	−2.12890	−	3.68737i	−0.120719	−	0.209092i	−0.920051	+	0.391798i	$0.871853\pi$
$312$	−0.0717344	−	0.0414159i	−0.00406116	−	0.00234471i
$313$	1.20925	+	1.44113i	0.0683511	+	0.0814576i	0.799136	−	0.601150i	$-0.205290\pi$
$313$	1.20925	+	1.44113i	0.0683511	+	0.0814576i	−0.730785	+	0.682607i	$0.760846\pi$
$314$	−11.8236	+	9.92120i	−0.667246	+	0.559886i
$315$		0			0
$316$	−1.76933	−	3.06458i	−0.0995328	−	0.172396i
$317$	8.24838	−	22.6622i	0.463275	−	1.27284i	−0.459733	−	0.888057i	$-0.652055\pi$
$317$	8.24838	−	22.6622i	0.463275	−	1.27284i	0.923008	−	0.384780i	$-0.125723\pi$
$318$	−10.8177	−	1.90746i	−0.606629	−	0.106965i
$319$	0.375438	+	2.12922i	0.0210205	+	0.119213i
$320$		0			0
$321$	−10.9486	−	9.18700i	−0.611094	−	0.512768i
$322$			1.14541i			0.0638312i
$323$	−25.2715	−	14.5517i	−1.40614	−	0.809680i
$324$	1.98673			0.110374
$325$		0			0
$326$	0.668322	−	0.243249i	0.0370150	−	0.0134723i
$327$	0.930882	−	0.164140i	0.0514779	−	0.00907694i
$328$	−2.92132	−	0.515108i	−0.161303	−	0.0284421i
$329$	17.9569	+	6.53577i	0.989995	+	0.360329i
$330$		0			0
$331$	−10.3508	+	17.9282i	−0.568934	+	0.985422i	0.427738	+	0.903903i	$0.359311\pi$
$331$	−10.3508	+	17.9282i	−0.568934	+	0.985422i	−0.996672	+	0.0815193i	$0.974023\pi$
$332$	0.0626953	+	0.0747173i	0.00344085	+	0.00410065i
$333$	10.7529	+	12.8148i	0.589255	+	0.702247i
$334$	−5.40398	+	9.35997i	−0.295693	+	0.512155i
$335$		0			0
$336$	2.49067	+	0.906531i	0.135877	+	0.0494553i
$337$	−4.81644	−	0.849268i	−0.262368	−	0.0462626i	0.0409166	−	0.999163i	$-0.486972\pi$
$337$	−4.81644	−	0.849268i	−0.262368	−	0.0462626i	−0.303285	+	0.952900i	$0.598083\pi$
$338$	−12.7979	+	2.25661i	−0.696112	+	0.122743i
$339$	1.21633	−	0.442708i	0.0660620	−	0.0240446i
$340$		0			0
$341$	−1.88201			−0.101917
$342$	−6.62467	+	1.17597i	−0.358221	+	0.0635892i
$343$		−	20.1538i		−	1.08821i
$344$	−4.48280	−	3.76152i	−0.241696	−	0.202807i
$345$		0			0
$346$	−3.71206	−	21.0522i	−0.199562	−	1.13177i
$347$	3.52984	+	0.622405i	0.189492	+	0.0334125i	0.267588	−	0.963533i	$-0.413773\pi$
$347$	3.52984	+	0.622405i	0.189492	+	0.0334125i	−0.0780969	+	0.996946i	$0.524884\pi$
$348$	−2.81624	+	7.73756i	−0.150966	+	0.414777i
$349$	4.16579	+	7.21535i	0.222989	+	0.386229i	0.955714	−	0.294296i	$-0.0950851\pi$
$349$	4.16579	+	7.21535i	0.222989	+	0.386229i	−0.732725	+	0.680525i	$0.761752\pi$
$350$		0			0
$351$	−0.288302	+	0.241914i	−0.0153884	+	0.0129124i
$352$	−0.203687	−	0.242745i	−0.0108566	−	0.0129384i
$353$	12.3425	+	7.12593i	0.656924	+	0.379275i	0.791104	−	0.611682i	$-0.209507\pi$
$353$	12.3425	+	7.12593i	0.656924	+	0.379275i	−0.134180	+	0.990957i	$0.542840\pi$
$354$	1.24319	+	2.15327i	0.0660748	+	0.114445i
$355$		0			0
$356$	1.10939	−	6.29165i	0.0587975	−	0.333457i
$357$	17.4629	−	3.07919i	0.924236	−	0.162968i
$358$	−6.19454	−	17.0194i	−0.327392	−	0.899502i
$359$	−16.7438	−	14.0497i	−0.883706	−	0.741517i	0.0832317	−	0.996530i	$-0.473476\pi$
$359$	−16.7438	−	14.0497i	−0.883706	−	0.741517i	−0.966938	+	0.255013i	$0.917920\pi$
$360$		0			0
$361$	−17.8392	+	6.53947i	−0.938903	+	0.344182i
$362$			26.1574i			1.37480i
$363$	−8.45519	+	10.0765i	−0.443782	+	0.528879i
$364$	−0.141652	+	0.0515570i	−0.00742456	+	0.00270232i
$365$		0			0
$366$	0.377811	−	2.14267i	0.0197485	−	0.111999i
$367$	−6.40378	+	17.5942i	−0.334275	+	0.918412i	0.652712	+	0.757606i	$0.273631\pi$
$367$	−6.40378	+	17.5942i	−0.334275	+	0.918412i	−0.986986	+	0.160805i	$0.948591\pi$
$368$	0.451655	−	0.260763i	0.0235441	−	0.0135932i
$369$	−2.28940	+	3.96536i	−0.119182	+	0.206429i
$370$		0			0
$371$	−15.3136	+	12.8497i	−0.795044	+	0.667121i
$372$	−6.20729	−	3.58378i	−0.321833	−	0.185810i
$373$	−0.453240	+	0.261678i	−0.0234679	+	0.0135492i	−0.511688	−	0.859171i	$-0.670980\pi$
$373$	−0.453240	+	0.261678i	−0.0234679	+	0.0135492i	0.488220	+	0.872721i	$0.337646\pi$
$374$	−1.99213	−	0.725075i	−0.103010	−	0.0374927i
$375$		0			0
$376$	−1.51088	−	8.56863i	−0.0779178	−	0.441894i
$377$	−0.160168	−	0.440057i	−0.00824905	−	0.0226641i
$378$	7.74096	−	9.22532i	0.398152	−	0.474499i
$379$	17.7944			0.914037			0.457018	−	0.889457i	$-0.348917\pi$
$379$	17.7944			0.914037			0.457018	+	0.889457i	$0.348917\pi$
$380$		0			0
$381$	10.6910			0.547716
$382$	−10.0343	+	11.9584i	−0.513398	+	0.611844i
$383$	−4.64225	−	12.7545i	−0.237208	−	0.651723i	−0.999987	−	0.00506405i	$-0.998388\pi$
$383$	−4.64225	−	12.7545i	−0.237208	−	0.651723i	0.762780	−	0.646659i	$-0.223834\pi$
$384$	−0.209564	−	1.18849i	−0.0106943	−	0.0606501i
$385$		0			0
$386$	−10.0505	−	3.65810i	−0.511559	−	0.186192i
$387$	−7.82259	+	4.51637i	−0.397644	+	0.229580i
$388$	−6.37959	−	3.68326i	−0.323874	−	0.186989i
$389$	−18.7194	+	15.7075i	−0.949113	+	0.796400i	−0.979148	−	0.203149i	$-0.934882\pi$
$389$	−18.7194	+	15.7075i	−0.949113	+	0.796400i	0.0300352	+	0.999549i	$0.490438\pi$
$390$		0			0
$391$	1.74454	−	3.02163i	0.0882251	−	0.152810i
$392$	−1.88483	+	1.08821i	−0.0951983	+	0.0549628i
$393$	−3.18755	+	8.75773i	−0.160791	+	0.441769i
$394$	−1.32138	+	7.49393i	−0.0665703	+	0.377539i
$395$		0			0
$396$	−0.459628	+	0.167291i	−0.0230972	+	0.00840668i
$397$	18.2900	−	21.7972i	0.917951	−	1.09397i	−0.0773367	−	0.997005i	$-0.524642\pi$
$397$	18.2900	−	21.7972i	0.917951	−	1.09397i	0.995288	−	0.0969663i	$-0.0309139\pi$
$398$			19.6410i			0.984516i
$399$	5.76515	−	10.0121i	0.288619	−	0.501234i
$400$		0			0
$401$	−27.2549	−	22.8696i	−1.36104	−	1.14205i	−0.975658	−	0.219297i	$-0.929624\pi$
$401$	−27.2549	−	22.8696i	−1.36104	−	1.14205i	−0.385387	−	0.922755i	$-0.625932\pi$
$402$	0.0969194	+	0.266284i	0.00483390	+	0.0132810i
$403$	0.401447	−	0.0707859i	0.0199975	−	0.00352610i
$404$	−1.67347	+	9.49070i	−0.0832581	+	0.472180i
$405$		0			0
$406$	7.49251	+	12.9774i	0.371847	+	0.644058i
$407$	2.97414	+	1.71712i	0.147422	+	0.0851144i
$408$	−5.18977	−	6.18493i	−0.256932	−	0.306200i
$409$	−12.1081	+	10.1599i	−0.598708	+	0.502376i	−0.891030	−	0.453944i	$-0.850016\pi$
$409$	−12.1081	+	10.1599i	−0.598708	+	0.502376i	0.292322	+	0.956320i	$0.405572\pi$
$410$		0			0
$411$	−10.1852	−	17.6413i	−0.502399	−	0.870181i
$412$	−6.30556	+	17.3244i	−0.310653	+	0.853511i
$413$	4.45613	+	0.785736i	0.219272	+	0.0386635i
$414$	−0.139788	−	0.792778i	−0.00687021	−	0.0389629i
$415$		0			0
$416$	0.0525781	+	0.0441182i	0.00257785	+	0.00216307i
$417$			24.0912i			1.17975i
$418$	−1.19540	+	0.692003i	−0.0584691	+	0.0338470i
$419$	37.3327			1.82382			0.911910	−	0.410390i	$-0.134607\pi$
$419$	37.3327			1.82382			0.911910	+	0.410390i	$0.134607\pi$
$420$		0			0
$421$	18.6383	−	6.78380i	0.908377	−	0.330622i	0.154772	−	0.987950i	$-0.450536\pi$
$421$	18.6383	−	6.78380i	0.908377	−	0.330622i	0.753605	+	0.657328i	$0.228313\pi$
$422$	18.7448	−	3.30521i	0.912483	−	0.160895i
$423$	−13.2262	−	2.33214i	−0.643081	−	0.113393i
$424$	8.55313	+	3.11308i	0.415377	+	0.151185i
$425$		0			0
$426$	1.09355	−	1.89408i	0.0529825	−	0.0917684i
$427$	−2.54513	−	3.03317i	−0.123168	−	0.146786i
$428$	7.61251	+	9.07224i	0.367965	+	0.438523i
$429$	−0.0131239	+	0.0227313i	−0.000633628	+	0.00109748i
$430$		0			0
$431$	−18.7166	−	6.81227i	−0.901545	−	0.328135i	−0.150673	−	0.988584i	$-0.548144\pi$
$431$	−18.7166	−	6.81227i	−0.901545	−	0.328135i	−0.750872	+	0.660448i	$0.770366\pi$
$432$	−5.40000	−	0.952166i	−0.259808	−	0.0458111i
$433$	18.3058	−	3.22780i	0.879719	−	0.155118i	0.284494	−	0.958678i	$-0.408174\pi$
$433$	18.3058	−	3.22780i	0.879719	−	0.155118i	0.595224	+	0.803560i	$0.297063\pi$
$434$	−12.2573	+	4.46131i	−0.588372	+	0.214150i
$435$		0			0
$436$	−0.783244			−0.0375106
$437$	−0.779965	−	2.13529i	−0.0373108	−	0.102145i
$438$		−	9.05526i		−	0.432677i
$439$	−16.2135	−	13.6048i	−0.773830	−	0.649320i	0.167857	−	0.985811i	$-0.446315\pi$
$439$	−16.2135	−	13.6048i	−0.773830	−	0.649320i	−0.941687	+	0.336491i	$0.890760\pi$
$440$		0			0
$441$	0.583359	+	3.30839i	0.0277790	+	0.157543i
$442$	0.452207	+	0.0797362i	0.0215093	+	0.00379267i
$443$	11.1356	−	30.5947i	0.529066	−	1.45360i	−0.331106	−	0.943593i	$-0.607422\pi$
$443$	11.1356	−	30.5947i	0.529066	−	1.45360i	0.860172	−	0.510004i	$-0.170356\pi$
$444$	6.53958	+	11.3269i	0.310355	+	0.537550i
$445$		0			0
$446$	1.18009	−	0.990213i	0.0558789	−	0.0468879i
$447$	−12.1513	−	14.4814i	−0.574739	−	0.684947i
$448$	−1.90202	−	1.09813i	−0.0898621	−	0.0518819i
$449$	1.96092	+	3.39641i	0.0925413	+	0.160286i	0.908580	−	0.417711i	$-0.137168\pi$
$449$	1.96092	+	3.39641i	0.0925413	+	0.160286i	−0.816038	+	0.577998i	$0.803834\pi$
$450$		0			0
$451$	−0.163228	+	0.925712i	−0.00768611	+	0.0435901i
$452$	−1.05626	+	0.186247i	−0.0496824	+	0.00876034i
$453$	5.63008	+	15.4685i	0.264524	+	0.726774i
$454$	16.7946	+	14.0924i	0.788211	+	0.661388i
$455$		0			0
$456$	−5.26044	+	0.00605483i	−0.246343	+	0.000283543i
$457$			32.6101i			1.52543i	0.646732	+	0.762717i	$0.276135\pi$
$457$			32.6101i			1.52543i	−0.646732	+	0.762717i	$0.723865\pi$
$458$	−14.5263	+	17.3117i	−0.678767	+	0.808924i
$459$	−34.4717	+	12.5467i	−1.60900	+	0.585629i
$460$		0			0
$461$	5.45172	−	30.9182i	0.253912	−	1.44000i	−0.544939	−	0.838476i	$-0.683447\pi$
$461$	5.45172	−	30.9182i	0.253912	−	1.44000i	0.798851	−	0.601529i	$-0.205442\pi$
$462$	0.287262	−	0.789247i	0.0133647	−	0.0367191i
$463$	−7.80271	+	4.50489i	−0.362623	+	0.209360i	−0.670231	−	0.742153i	$-0.733805\pi$
$463$	−7.80271	+	4.50489i	−0.362623	+	0.209360i	0.307608	+	0.951513i	$0.400471\pi$
$464$	3.41147	−	5.90885i	0.158374	−	0.274311i
$465$		0			0
$466$	−6.92540	+	5.81110i	−0.320813	+	0.269194i
$467$	14.1079	+	8.14522i	0.652838	+	0.376916i	0.789543	−	0.613696i	$-0.210318\pi$
$467$	14.1079	+	8.14522i	0.652838	+	0.376916i	−0.136705	+	0.990612i	$0.543651\pi$
$468$	0.0917499	−	0.0529718i	0.00424114	−	0.00244862i
$469$	0.484601	+	0.176380i	0.0223768	+	0.00814448i
$470$		0			0
$471$	3.23454	+	18.3440i	0.149040	+	0.845247i
$472$	−0.704650	−	1.93601i	−0.0324341	−	0.0891120i
$473$	−1.19195	+	1.42051i	−0.0548061	+	0.0653153i
$474$	−4.27057			−0.196154
$475$		0			0
$476$	−14.6933			−0.673467
$477$	9.03090	−	10.7626i	0.413496	−	0.492786i
$478$	−8.02796	−	22.0566i	−0.367190	−	1.00885i
$479$	−4.31953	−	24.4973i	−0.197364	−	1.11931i	−0.909011	−	0.416771i	$-0.863162\pi$
$479$	−4.31953	−	24.4973i	−0.197364	−	1.11931i	0.711647	−	0.702537i	$-0.247949\pi$
$480$		0			0
$481$	−0.698989	−	0.254411i	−0.0318712	−	0.0116002i
$482$	−23.8279	+	13.7571i	−1.08533	+	0.626617i
$483$	1.19712	+	0.691157i	0.0544708	+	0.0314487i
$484$	8.34957	−	7.00612i	0.379526	−	0.318460i
$485$		0			0
$486$	−7.02614	+	12.1696i	−0.318712	+	0.552026i
$487$	−29.8258	+	17.2199i	−1.35154	+	0.780310i	−0.988465	−	0.151452i	$-0.951605\pi$
$487$	−29.8258	+	17.2199i	−1.35154	+	0.780310i	−0.363071	+	0.931761i	$0.618272\pi$
$488$	−0.616609	+	1.69412i	−0.0279126	+	0.0766892i
$489$	0.149045	−	0.845274i	0.00674003	−	0.0382246i
$490$		0			0
$491$	−32.1757	+	11.7110i	−1.45207	+	0.528510i	−0.943168	−	0.332315i	$-0.892170\pi$
$491$	−32.1757	+	11.7110i	−1.45207	+	0.528510i	−0.508901	+	0.860825i	$0.669948\pi$
$492$	−2.30113	+	2.74238i	−0.103743	+	0.123636i
$493$		−	45.6464i		−	2.05581i
$494$	0.228961	−	0.192571i	0.0103014	−	0.00866416i
$495$		0			0
$496$	4.54967	+	3.81762i	0.204286	+	0.171416i
$497$	−1.36131	−	3.74018i	−0.0610633	−	0.167770i
$498$	0.115922	−	0.0204401i	0.00519458	−	0.000915944i
$499$	3.85653	−	21.8715i	0.172642	−	0.979102i	−0.768188	−	0.640224i	$-0.778842\pi$
$499$	3.85653	−	21.8715i	0.172642	−	0.979102i	0.940830	−	0.338878i	$-0.110047\pi$
$500$		0			0
$501$	6.52168	+	11.2959i	0.291367	+	0.504663i
$502$	−22.8892	−	13.2151i	−1.02159	−	0.589817i
$503$	−21.7164	−	25.8806i	−0.968286	−	1.15396i	−0.988047	−	0.154153i	$-0.950735\pi$
$503$	−21.7164	−	25.8806i	−0.968286	−	1.15396i	0.0197614	−	0.999805i	$-0.493709\pi$
$504$	−2.59695	+	2.17910i	−0.115677	+	0.0970647i
$505$		0			0
$506$	−0.0826308	−	0.143121i	−0.00367339	−	0.00636250i
$507$	−5.36394	+	14.7373i	−0.238221	+	0.654506i
$508$	−8.72416	−	1.53830i	−0.387072	−	0.0682512i
$509$	2.04246	+	11.5834i	0.0905303	+	0.513423i	0.996026	+	0.0890668i	$0.0283884\pi$
$509$	2.04246	+	11.5834i	0.0905303	+	0.513423i	−0.905495	+	0.424356i	$0.860500\pi$
$510$		0			0
$511$	−12.6239	−	10.5927i	−0.558449	−	0.468594i
$512$			1.00000i			0.0441942i
$513$	−8.14883	+	22.4692i	−0.359779	+	0.992037i
$514$	11.0971			0.489470
$515$		0			0
$516$	−6.63632	+	2.41542i	−0.292148	+	0.106333i
$517$	−2.71524	+	0.478770i	−0.119416	+	0.0210563i
$518$	23.4407	+	4.13323i	1.02992	+	0.181603i
$519$	−24.2425	−	8.82354i	−1.06413	−	0.387310i
$520$		0			0
$521$	−10.3001	+	17.8403i	−0.451257	+	0.781600i	−0.998464	−	0.0553972i	$-0.982357\pi$
$521$	−10.3001	+	17.8403i	−0.451257	+	0.781600i	0.547208	+	0.836997i	$0.315691\pi$
$522$	−6.76961	−	8.06771i	−0.296298	−	0.353114i
$523$	1.38869	+	1.65498i	0.0607232	+	0.0723671i	0.795551	−	0.605887i	$-0.207181\pi$
$523$	1.38869	+	1.65498i	0.0607232	+	0.0723671i	−0.734828	+	0.678254i	$0.762737\pi$
$524$	3.86127	−	6.68791i	0.168680	−	0.292163i
$525$		0			0
$526$	−26.2306	−	9.54717i	−1.14371	−	0.416276i
$527$	39.1302	+	6.89971i	1.70454	+	0.300556i
$528$	−0.376612	+	0.0664068i	−0.0163899	+	0.00288998i
$529$	−21.3573	+	7.77344i	−0.928580	+	0.337976i
$530$		0			0
$531$	−3.18014			−0.138006
$532$	−6.14516	+	7.34065i	−0.266426	+	0.318258i
$533$		−	0.203601i		−	0.00881892i
$534$	−5.90627	−	4.95595i	−0.255589	−	0.214465i
$535$		0			0
$536$	−0.0407740	−	0.231241i	−0.00176117	−	0.00998809i
$537$	−21.5256	−	3.79554i	−0.928898	−	0.163790i
$538$	2.87963	−	7.91172i	0.124150	−	0.341099i
$539$	0.344832	+	0.597267i	0.0148530	+	0.0257261i
$540$		0			0
$541$	−2.61563	+	2.19477i	−0.112455	+	0.0943606i	−0.697281	−	0.716798i	$-0.745607\pi$
$541$	−2.61563	+	2.19477i	−0.112455	+	0.0943606i	0.584826	+	0.811158i	$0.301163\pi$
$542$	−7.67215	−	9.14331i	−0.329547	−	0.392739i
$543$	27.3382	+	15.7837i	1.17320	+	0.677345i
$544$	3.34507	+	5.79383i	0.143419	+	0.248408i
$545$		0			0
$546$	−0.0315902	+	0.179157i	−0.00135193	+	0.00766720i
$547$	9.90714	−	1.74690i	0.423599	−	0.0746919i	0.0422146	−	0.999109i	$-0.486559\pi$
$547$	9.90714	−	1.74690i	0.423599	−	0.0746919i	0.381384	+	0.924417i	$0.375448\pi$
$548$	5.77305	+	15.8613i	0.246613	+	0.677562i
$549$	2.13175	+	1.78875i	0.0909809	+	0.0763421i
$550$		0			0
$551$	−22.8046	−	19.0906i	−0.971507	−	0.813288i
$552$		−	0.629393i		−	0.0267887i
$553$	−4.99565	+	5.95359i	−0.212437	+	0.253172i
$554$	−2.95078	+	1.07399i	−0.125366	+	0.0456297i
$555$		0			0
$556$	3.46644	−	19.6592i	0.147010	−	0.833734i
$557$	−1.11159	+	3.05407i	−0.0470997	+	0.129405i	−0.961012	−	0.276506i	$-0.910824\pi$
$557$	−1.11159	+	3.05407i	−0.0470997	+	0.129405i	0.913913	+	0.405911i	$0.133046\pi$
$558$	7.93927	−	4.58374i	0.336096	−	0.194045i
$559$	0.200824	−	0.347838i	0.00849396	−	0.0147120i
$560$		0			0
$561$	−1.95989	+	1.64454i	−0.0827465	+	0.0694326i
$562$	13.3606	+	7.71375i	0.563583	+	0.325385i
$563$	−0.514275	+	0.296917i	−0.0216741	+	0.0125136i	−0.510798	−	0.859701i	$-0.670650\pi$
$563$	−0.514275	+	0.296917i	−0.0216741	+	0.0125136i	0.489124	+	0.872214i	$0.337317\pi$
$564$	−9.86715	−	3.59135i	−0.415482	−	0.151223i
$565$		0			0
$566$	2.72393	+	15.4482i	0.114495	+	0.649334i
$567$	−1.49236	−	4.10024i	−0.0626734	−	0.172194i
$568$	−1.16490	+	1.38827i	−0.0488782	+	0.0582507i
$569$	39.0985			1.63910			0.819548	−	0.573011i	$-0.194225\pi$
$569$	39.0985			1.63910			0.819548	+	0.573011i	$0.194225\pi$
$570$		0			0
$571$	−1.29501			−0.0541946			−0.0270973	−	0.999633i	$-0.508626\pi$
$571$	−1.29501			−0.0541946			−0.0270973	+	0.999633i	$0.508626\pi$
$572$	0.0139802	−	0.0166610i	0.000584543	−	0.000696631i
$573$	6.44342	+	17.7031i	0.269178	+	0.739559i
$574$	1.13131	+	6.41600i	0.0472202	+	0.267799i
$575$		0			0
$576$	1.45047	+	0.527930i	0.0604364	+	0.0219971i
$577$	−41.4888	+	23.9536i	−1.72720	+	0.997201i	−0.826218	+	0.563350i	$0.809512\pi$
$577$	−41.4888	+	23.9536i	−1.72720	+	0.997201i	−0.900985	+	0.433851i	$0.857155\pi$
$578$	24.0390	+	13.8790i	0.999893	+	0.577288i
$579$	−9.88788	+	8.29692i	−0.410926	+	0.344808i
$580$		0			0
$581$	0.107108	−	0.185517i	0.00444359	−	0.00769653i
$582$	−7.69907	+	4.44506i	−0.319137	+	0.184254i
$583$	0.986477	−	2.71032i	0.0408557	−	0.112250i
$584$	−1.30294	+	7.38935i	−0.0539161	+	0.305773i
$585$		0			0
$586$	−9.73381	+	3.54282i	−0.402100	+	0.146352i
$587$	−5.29449	+	6.30973i	−0.218527	+	0.260431i	−0.864160	−	0.503218i	$-0.832149\pi$
$587$	−5.29449	+	6.30973i	−0.218527	+	0.260431i	0.645632	+	0.763648i	$0.276594\pi$
$588$			2.62656i			0.108318i
$589$	19.8124	−	16.6635i	0.816355	−	0.686606i
$590$		0			0
$591$	7.03491	+	5.90299i	0.289377	+	0.242816i
$592$	−3.70668	−	10.1840i	−0.152344	−	0.418561i
$593$	−13.8856	+	2.44840i	−0.570213	+	0.100544i	−0.451318	−	0.892363i	$-0.649046\pi$
$593$	−13.8856	+	2.44840i	−0.570213	+	0.100544i	−0.118894	+	0.992907i	$0.537935\pi$
$594$	−0.301723	+	1.71116i	−0.0123799	+	0.0702097i
$595$		0			0
$596$	7.83215	+	13.5657i	0.320817	+	0.555672i
$597$	20.5277	+	11.8517i	0.840144	+	0.485057i
$598$	0.0230088	+	0.0274208i	0.000940900	+	0.00112132i
$599$	−20.4865	+	17.1902i	−0.837055	+	0.702373i	−0.956899	−	0.290420i	$-0.906205\pi$
$599$	−20.4865	+	17.1902i	−0.837055	+	0.702373i	0.119844	+	0.992793i	$0.461761\pi$
$600$		0			0
$601$	1.94626	+	3.37103i	0.0793898	+	0.137507i	0.902987	−	0.429668i	$-0.141369\pi$
$601$	1.94626	+	3.37103i	0.0793898	+	0.137507i	−0.823597	+	0.567175i	$0.808036\pi$
$602$	−4.39574	+	12.0772i	−0.179157	+	0.492230i
$603$	−0.356935	−	0.0629372i	−0.0145355	−	0.00256300i
$604$	−2.36857	−	13.4329i	−0.0963759	−	0.546575i
$605$		0			0
$606$	8.90936	+	7.47584i	0.361918	+	0.303685i
$607$		−	37.1711i		−	1.50873i	−0.656456	−	0.754364i	$-0.727945\pi$
$607$		−	37.1711i		−	1.50873i	0.656456	−	0.754364i	$-0.272055\pi$
$608$	4.29355	+	0.751973i	0.174126	+	0.0304966i
$609$	18.0844			0.732815
$610$		0			0
$611$	0.561173	−	0.204250i	0.0227026	−	0.00826308i
$612$	10.1698	−	1.79320i	0.411088	−	0.0724859i
$613$	−37.2746	−	6.57252i	−1.50551	−	0.265461i	−0.640788	−	0.767718i	$-0.721392\pi$
$613$	−37.2746	−	6.57252i	−1.50551	−	0.265461i	−0.864719	+	0.502257i	$0.832503\pi$
$614$	8.06402	+	2.93506i	0.325437	+	0.118450i
$615$		0			0
$616$	−0.347978	+	0.602715i	−0.0140204	+	0.0242841i
$617$	4.60826	+	5.49191i	0.185521	+	0.221096i	0.850787	−	0.525511i	$-0.176126\pi$
$617$	4.60826	+	5.49191i	0.185521	+	0.221096i	−0.665265	+	0.746607i	$0.731681\pi$
$618$	14.3016	+	17.0440i	0.575296	+	0.685611i
$619$	3.61107	−	6.25456i	0.145141	−	0.251392i	−0.784284	−	0.620402i	$-0.786970\pi$
$619$	3.61107	−	6.25456i	0.145141	−	0.251392i	0.929426	+	0.369009i	$0.120303\pi$
$620$		0			0
$621$	−2.68722	−	0.978070i	−0.107835	−	0.0392486i
$622$	4.19312	+	0.739361i	0.168129	+	0.0296457i
$623$	−13.8181	+	2.43651i	−0.553612	+	0.0976168i
$624$	0.0778363	−	0.0283301i	0.00311595	−	0.00113411i
$625$		0			0
$626$	−1.88127			−0.0751905
$627$	0.00191866	+	1.66694i	7.66239e−5	+	0.0665710i
$628$		−	15.4346i		−	0.615909i
$629$	−55.5421	−	46.6054i	−2.21461	−	1.85828i
$630$		0			0
$631$	−2.02752	−	11.4987i	−0.0807144	−	0.457754i	−0.998199	−	0.0599838i	$-0.980895\pi$
$631$	−2.02752	−	11.4987i	−0.0807144	−	0.457754i	0.917485	−	0.397771i	$-0.130216\pi$
$632$	3.48491	+	0.614483i	0.138622	+	0.0244428i
$633$	7.85646	−	21.5855i	0.312266	−	0.857945i
$634$	12.0583	+	20.8856i	0.478897	+	0.829474i
$635$		0			0
$636$	8.41471	−	7.06078i	0.333665	−	0.279978i
$637$	−0.0960196	−	0.114432i	−0.00380443	−	0.00453395i
$638$	−1.87240	−	1.08103i	−0.0741291	−	0.0427985i
$639$	1.39867	+	2.42257i	0.0553306	+	0.0958354i
$640$		0			0
$641$	2.14712	−	12.1769i	0.0848062	−	0.480960i	−0.912592	−	0.408871i	$-0.865922\pi$
$641$	2.14712	−	12.1769i	0.0848062	−	0.480960i	0.997398	−	0.0720885i	$-0.0229664\pi$
$642$	14.0753	−	2.48186i	0.555508	−	0.0979510i
$643$	4.01782	+	11.0389i	0.158447	+	0.435331i	0.993359	−	0.115053i	$-0.0367037\pi$
$643$	4.01782	+	11.0389i	0.158447	+	0.435331i	−0.834912	+	0.550384i	$0.814481\pi$
$644$	−0.877435	−	0.736255i	−0.0345758	−	0.0290125i
$645$		0			0
$646$	27.3915	−	10.0054i	1.07770	−	0.393657i
$647$			4.96567i			0.195221i	0.995225	+	0.0976103i	$0.0311199\pi$
$647$			4.96567i			0.195221i	−0.995225	+	0.0976103i	$0.968880\pi$
$648$	−1.27704	+	1.52192i	−0.0501670	+	0.0597867i
$649$	−0.613485	+	0.223290i	−0.0240814	+	0.00876490i
$650$		0			0
$651$	−2.73355	+	15.5027i	−0.107136	+	0.607600i
$652$	−0.243249	+	0.668322i	−0.00952638	+	0.0261735i
$653$	40.5780	−	23.4277i	1.58794	−	0.916797i	0.594293	−	0.804249i	$-0.297432\pi$
$653$	40.5780	−	23.4277i	1.58794	−	0.916797i	0.993646	−	0.112548i	$-0.0359013\pi$
$654$	−0.472621	+	0.818603i	−0.0184809	+	0.0320099i
$655$		0			0
$656$	2.27239	−	1.90676i	0.0887218	−	0.0744464i
$657$	10.0302	+	5.79094i	0.391315	+	0.225926i
$658$	−16.5492	+	9.55466i	−0.645153	+	0.372479i
$659$	−13.9640	−	5.08247i	−0.543959	−	0.197985i	0.0554016	−	0.998464i	$-0.482356\pi$
$659$	−13.9640	−	5.08247i	−0.543959	−	0.197985i	−0.599360	+	0.800479i	$0.704578\pi$
$660$		0			0
$661$	−3.68654	−	20.9074i	−0.143390	−	0.813203i	−0.968646	−	0.248445i	$-0.920081\pi$
$661$	−3.68654	−	20.9074i	−0.143390	−	0.813203i	0.825256	−	0.564758i	$-0.191031\pi$
$662$	−7.08039	−	19.4532i	−0.275187	−	0.756071i
$663$	0.356204	−	0.424508i	0.0138338	−	0.0164865i
$664$	−0.0975366			−0.00378515
$665$		0			0
$666$	−16.7285			−0.648218
$667$	2.28726	−	2.72585i	0.0885630	−	0.105545i
$668$	−3.69654	−	10.1562i	−0.143023	−	0.392954i
$669$	−0.322833	−	1.83087i	−0.0124814	−	0.0707857i
$670$		0			0
$671$	0.536834	+	0.195392i	0.0207243	+	0.00754302i
$672$	−2.29542	+	1.32526i	−0.0885476	+	0.0511230i
$673$	27.4058	+	15.8227i	1.05642	+	0.609922i	0.924439	−	0.381331i	$-0.124534\pi$
$673$	27.4058	+	15.8227i	1.05642	+	0.609922i	0.131977	+	0.991253i	$0.457867\pi$
$674$	3.74652	−	3.14371i	0.144311	−	0.121091i
$675$		0			0
$676$	6.49764	−	11.2543i	0.249909	−	0.432856i
$677$	4.54932	−	2.62655i	0.174844	−	0.100946i	−0.410024	−	0.912075i	$-0.634480\pi$
$677$	4.54932	−	2.62655i	0.174844	−	0.100946i	0.584868	+	0.811128i	$0.301146\pi$
$678$	−0.442708	+	1.21633i	−0.0170021	+	0.0467129i
$679$	−2.80942	+	15.9330i	−0.107816	+	0.611453i
$680$		0			0
$681$	24.8627	−	9.04928i	0.952740	−	0.346769i
$682$	1.20973	−	1.44170i	0.0463231	−	0.0552057i
$683$			3.28296i			0.125619i	0.998026	+	0.0628095i	$0.0200061\pi$
$683$			3.28296i			0.125619i	−0.998026	+	0.0628095i	$0.979994\pi$
$684$	3.35741	−	5.83069i	0.128374	−	0.222942i
$685$		0			0
$686$	15.4387	+	12.9546i	0.589454	+	0.494611i
$687$	9.32790	+	25.6282i	0.355882	+	0.977777i
$688$	5.76298	−	1.01617i	0.219711	−	0.0387411i
$689$	−0.108483	+	0.615235i	−0.00413286	+	0.0234386i
$690$		0			0
$691$	−6.31652	−	10.9405i	−0.240292	−	0.416197i	0.720506	−	0.693449i	$-0.243910\pi$
$691$	−6.31652	−	10.9405i	−0.240292	−	0.416197i	−0.960797	+	0.277252i	$0.910576\pi$
$692$	18.5130	+	10.6885i	0.703757	+	0.406314i
$693$	0.690515	+	0.822924i	0.0262305	+	0.0312603i
$694$	−2.74572	+	2.30394i	−0.104226	+	0.0874562i
$695$		0			0
$696$	−4.11707	−	7.13097i	−0.156057	−	0.270299i
$697$	6.78758	−	18.6487i	0.257098	−	0.706370i
$698$	−8.20500	−	1.44676i	−0.310564	−	0.0547608i
$699$	1.89455	+	10.7445i	0.0716586	+	0.406396i
$700$		0			0
$701$	21.6536	+	18.1696i	0.817847	+	0.686255i	0.952467	−	0.304642i	$-0.0985370\pi$
$701$	21.6536	+	18.1696i	0.817847	+	0.686255i	−0.134620	+	0.990897i	$0.542981\pi$
$702$		−	0.376351i		−	0.0142045i
$703$	−46.5129	+	8.25670i	−1.75427	+	0.311407i
$704$	0.316881			0.0119429
$705$		0			0
$706$	−13.3924	+	4.87443i	−0.504029	+	0.183451i
$707$	20.8441	−	3.67538i	0.783923	−	0.138227i
$708$	−2.44861	−	0.431755i	−0.0920242	−	0.0162264i
$709$	−32.4404	−	11.8074i	−1.21833	−	0.443435i	−0.348742	−	0.937219i	$-0.613391\pi$
$709$	−32.4404	−	11.8074i	−1.21833	−	0.443435i	−0.869585	+	0.493784i	$0.835613\pi$
$710$		0			0
$711$	2.73108	−	4.73036i	0.102423	−	0.177403i
$712$	4.10659	+	4.89404i	0.153901	+	0.183412i
$713$	1.99099	+	2.37277i	0.0745631	+	0.0888609i
$714$	−8.86616	+	15.3566i	−0.331808	+	0.574708i
$715$		0			0
$716$	17.0194	+	6.19454i	0.636044	+	0.231501i
$717$	−27.8966	−	4.91892i	−1.04182	−	0.183700i
$718$	21.5255	−	3.79552i	0.803323	−	0.141648i
$719$	23.2373	−	8.45770i	0.866606	−	0.315419i	0.129814	−	0.991538i	$-0.458562\pi$
$719$	23.2373	−	8.45770i	0.866606	−	0.315419i	0.736792	+	0.676119i	$0.236340\pi$
$720$		0			0
$721$	40.4909			1.50796
$722$	6.45726	−	17.8691i	0.240315	−	0.665018i
$723$			33.2049i			1.23490i
$724$	−20.0377	−	16.8136i	−0.744695	−	0.624874i
$725$		0			0
$726$	−2.28416	−	12.9541i	−0.0847731	−	0.480772i
$727$	30.8396	+	5.43786i	1.14378	+	0.201679i	0.713258	−	0.700901i	$-0.247219\pi$
$727$	30.8396	+	5.43786i	1.14378	+	0.201679i	0.430521	+	0.902581i	$0.358330\pi$
$728$	0.0515570	−	0.141652i	0.00191083	−	0.00524996i
$729$	11.4594	+	19.8483i	0.424424	+	0.735123i
$730$		0			0
$731$	29.9905	−	25.1650i	1.10924	−	0.930763i
$732$	1.39853	+	1.66670i	0.0516911	+	0.0616031i
$733$	24.8684	+	14.3578i	0.918536	+	0.530317i	0.883168	−	0.469057i	$-0.155406\pi$
$733$	24.8684	+	14.3578i	0.918536	+	0.530317i	0.0353683	+	0.999374i	$0.488740\pi$
$734$	−9.36170	−	16.2149i	−0.345547	−	0.598504i
$735$		0			0
$736$	−0.0905620	+	0.513603i	−0.00333816	+	0.0189316i
$737$	−0.0732759	+	0.0129205i	−0.00269915	+	0.000475933i
$738$	−1.56604	−	4.30267i	−0.0576469	−	0.158384i
$739$	34.1487	+	28.6541i	1.25618	+	1.05406i	0.996078	+	0.0884783i	$0.0282004\pi$
$739$	34.1487	+	28.6541i	1.25618	+	1.05406i	0.260101	+	0.965581i	$0.416244\pi$
$740$		0			0
$741$	−0.0631058	−	0.355497i	−0.00231825	−	0.0130595i
$742$		−	19.9905i		−	0.733875i
$743$	19.7358	−	23.5202i	0.724035	−	0.862871i	−0.270981	−	0.962585i	$-0.587348\pi$
$743$	19.7358	−	23.5202i	0.724035	−	0.862871i	0.995016	+	0.0997136i	$0.0317927\pi$
$744$	6.73531	−	2.45145i	0.246928	−	0.0898746i
$745$		0			0
$746$	0.0908799	−	0.515406i	0.00332735	−	0.0188703i
$747$	−0.0514924	+	0.141474i	−0.00188401	+	0.00517627i
$748$	1.83595	−	1.05999i	0.0671291	−	0.0387570i
$749$	13.0052	−	22.5256i	0.475198	−	0.823067i
$750$		0			0
$751$	−33.3471	+	27.9816i	−1.21685	+	1.02106i	−0.217870	+	0.975978i	$0.569911\pi$
$751$	−33.3471	+	27.9816i	−1.21685	+	1.02106i	−0.998983	+	0.0450837i	$0.985645\pi$
$752$	7.53513	+	4.35041i	0.274778	+	0.158643i
$753$	−27.6233	+	15.9483i	−1.00665	+	0.581189i
$754$	0.440057	+	0.160168i	0.0160259	+	0.00583296i
$755$		0			0
$756$	2.09121	+	11.8598i	0.0760566	+	0.431338i
$757$	1.41920	+	3.89923i	0.0515818	+	0.141720i	0.962808	−	0.270186i	$-0.0870853\pi$
$757$	1.41920	+	3.89923i	0.0515818	+	0.141720i	−0.911226	+	0.411906i	$0.864863\pi$
$758$	−11.4380	+	13.6313i	−0.415448	+	0.495111i
$759$	−0.199443			−0.00723931
$760$		0			0
$761$	19.2254			0.696920			0.348460	−	0.937324i	$-0.386705\pi$
$761$	19.2254			0.696920			0.348460	+	0.937324i	$0.386705\pi$
$762$	−6.87204	+	8.18978i	−0.248948	+	0.296684i
$763$	0.588347	+	1.61647i	0.0212996	+	0.0585202i
$764$	−2.71075	−	15.3734i	−0.0980713	−	0.556190i
$765$		0			0
$766$	12.7545	+	4.64225i	0.460838	+	0.167731i
$767$	0.122462	−	0.0707037i	0.00442186	−	0.00255296i
$768$	1.04514	+	0.603415i	0.0377134	+	0.0217739i
$769$	18.8160	−	15.7885i	0.678522	−	0.569347i	−0.237052	−	0.971497i	$-0.576181\pi$
$769$	18.8160	−	15.7885i	0.678522	−	0.569347i	0.915574	+	0.402150i	$0.131737\pi$
$770$		0			0
$771$	6.69612	−	11.5980i	0.241155	−	0.417693i
$772$	9.26262	−	5.34778i	0.333369	−	0.192471i
$773$	−4.50041	+	12.3648i	−0.161869	+	0.444730i	−0.993938	−	0.109941i	$-0.964934\pi$
$773$	−4.50041	+	12.3648i	−0.161869	+	0.444730i	0.832070	+	0.554671i	$0.187156\pi$
$774$	1.56852	−	8.89552i	0.0563793	−	0.319743i
$775$		0			0
$776$	6.92226	−	2.51950i	0.248495	−	0.0904446i
$777$	18.4643	−	22.0049i	0.662402	−	0.789420i
$778$		−	24.4365i		−	0.876090i
$779$	−6.47798	−	11.1904i	−0.232098	−	0.400939i
$780$		0			0
$781$	0.439918	+	0.369135i	0.0157415	+	0.0132087i
$782$	1.19333	+	3.27866i	0.0426736	+	0.117245i
$783$	−36.8439	+	6.49658i	−1.31669	+	0.232169i
$784$	0.377930	−	2.14335i	0.0134975	−	0.0765482i
$785$		0			0
$786$	−4.65989	−	8.07117i	−0.166213	−	0.287889i
$787$	−26.8659	−	15.5110i	−0.957667	−	0.552909i	−0.0622126	−	0.998063i	$-0.519816\pi$
$787$	−26.8659	−	15.5110i	−0.957667	−	0.552909i	−0.895454	+	0.445154i	$0.853149\pi$
$788$	−4.89132	−	5.82925i	−0.174246	−	0.207658i
$789$	−25.8061	+	21.6539i	−0.918723	+	0.770900i
$790$		0			0
$791$	1.17781	+	2.04003i	0.0418781	+	0.0725350i
$792$	0.167291	−	0.459628i	0.00594442	−	0.0163322i
$793$	−0.121860	−	0.0214872i	−0.00432737	−	0.000763032i
$794$	4.94103	+	28.0220i	0.175351	+	0.994463i
$795$		0			0
$796$	−15.0459	−	12.6250i	−0.533288	−	0.447481i
$797$		−	3.22825i		−	0.114350i	−0.998364	−	0.0571752i	$-0.981791\pi$
$797$		−	3.22825i		−	0.114350i	0.998364	−	0.0571752i	$-0.0182094\pi$
$798$	3.96397	+	10.8520i	0.140323	+	0.384158i
$799$	58.2097			2.05931
$800$		0			0
$801$	9.26666	−	3.37279i	0.327421	−	0.119172i
$802$	35.0382	−	6.17819i	1.23724	−	0.218159i
$803$	2.34155	+	0.412878i	0.0826313	+	0.0145701i
$804$	−0.266284	−	0.0969194i	−0.00939111	−	0.00341808i
$805$		0			0
$806$	−0.203820	+	0.353026i	−0.00717925	+	0.0124348i
$807$	−6.53128	−	7.78368i	−0.229912	−	0.273999i
$808$	−6.19461	−	7.38245i	−0.217926	−	0.259714i
$809$	−17.3364	+	30.0275i	−0.609515	+	1.05571i	0.381806	+	0.924243i	$0.375302\pi$
$809$	−17.3364	+	30.0275i	−0.609515	+	1.05571i	−0.991320	+	0.131468i	$0.958031\pi$
$810$		0			0
$811$	53.2716	+	19.3893i	1.87062	+	0.680850i	0.968304	+	0.249773i	$0.0803562\pi$
$811$	53.2716	+	19.3893i	1.87062	+	0.680850i	0.902315	+	0.431076i	$0.141866\pi$
$812$	−14.7574	−	2.60212i	−0.517882	−	0.0913165i
$813$	−14.1856	+	2.50130i	−0.497510	+	0.0877244i
$814$	−3.22713	+	1.17458i	−0.113111	+	0.0411689i
$815$		0			0
$816$	8.07385			0.282641
$817$	−0.0293597	−	25.5077i	−0.00102716	−	0.892403i
$818$		−	15.8060i		−	0.552645i
$819$	−0.178244	−	0.149564i	−0.00622834	−	0.00522619i
$820$		0			0
$821$	4.12052	+	23.3686i	0.143807	+	0.815571i	0.968317	+	0.249723i	$0.0803397\pi$
$821$	4.12052	+	23.3686i	0.143807	+	0.815571i	−0.824510	+	0.565847i	$0.808549\pi$
$822$	20.0609	+	3.53728i	0.699705	+	0.123377i
$823$	−12.6227	+	34.6806i	−0.439999	+	1.20889i	0.499493	+	0.866318i	$0.333520\pi$
$823$	−12.6227	+	34.6806i	−0.439999	+	1.20889i	−0.939492	+	0.342570i	$0.888702\pi$
$824$	−9.21811	−	15.9662i	−0.321128	−	0.556210i
$825$		0			0
$826$	−3.46625	+	2.90853i	−0.120606	+	0.101201i
$827$	−8.79156	−	10.4774i	−0.305713	−	0.364334i	0.591213	−	0.806515i	$-0.298649\pi$
$827$	−8.79156	−	10.4774i	−0.305713	−	0.364334i	−0.896926	+	0.442181i	$0.854205\pi$
$828$	0.697157	+	0.402504i	0.0242279	+	0.0139880i
$829$	−5.92228	−	10.2577i	−0.205689	−	0.356265i	0.744663	−	0.667441i	$-0.232610\pi$
$829$	−5.92228	−	10.2577i	−0.205689	−	0.356265i	−0.950352	+	0.311176i	$0.899277\pi$
$830$		0			0
$831$	−0.658062	+	3.73205i	−0.0228279	+	0.129463i
$832$	−0.0675931	+	0.0119185i	−0.00234337	+	0.000413199i
$833$	−4.97999	−	13.6824i	−0.172546	−	0.474067i
$834$	−18.4550	−	15.4856i	−0.639043	−	0.536221i
$835$		0			0
$836$	0.238286	−	1.36054i	0.00824130	−	0.0470554i
$837$		−	32.5663i		−	1.12566i
$838$	−23.9970	+	28.5985i	−0.828962	+	0.987918i
$839$	9.87612	−	3.59461i	0.340962	−	0.124100i	−0.165864	−	0.986149i	$-0.553041\pi$
$839$	9.87612	−	3.59461i	0.340962	−	0.124100i	0.506825	+	0.862049i	$0.330819\pi$
$840$		0			0
$841$	3.04798	−	17.2860i	0.105103	−	0.596068i
$842$	−6.78380	+	18.6383i	−0.233785	+	0.642320i
$843$	16.1240	−	9.30918i	0.555339	−	0.320625i
$844$	−9.51699	+	16.4839i	−0.327588	+	0.567399i
$845$		0			0
$846$	10.2882	−	8.63280i	0.353715	−	0.296802i
$847$	−20.7313	−	11.9692i	−0.712334	−	0.411266i
$848$	−7.88260	+	4.55102i	−0.270690	+	0.156283i
$849$	17.7892	+	6.47475i	0.610524	+	0.222213i
$850$		0			0
$851$	−0.981476	−	5.56623i	−0.0336446	−	0.190808i
$852$	0.748030	+	2.05520i	0.0256271	+	0.0704098i
$853$	19.8250	−	23.6265i	0.678795	−	0.808957i	−0.311157	−	0.950359i	$-0.600717\pi$
$853$	19.8250	−	23.6265i	0.678795	−	0.808957i	0.989952	+	0.141402i	$0.0451609\pi$
$854$	3.95953			0.135492
$855$		0			0
$856$	−11.8430			−0.404784
$857$	−19.6449	+	23.4119i	−0.671056	+	0.799734i	−0.988927	−	0.148400i	$-0.952588\pi$
$857$	−19.6449	+	23.4119i	−0.671056	+	0.799734i	0.317871	+	0.948134i	$0.397032\pi$
$858$	−0.00897728	−	0.0246649i	−0.000306479	−	0.000842045i
$859$	7.71242	+	43.7393i	0.263144	+	1.49237i	0.774268	+	0.632858i	$0.218118\pi$
$859$	7.71242	+	43.7393i	0.263144	+	1.49237i	−0.511123	+	0.859507i	$0.670770\pi$
$860$		0			0
$861$	7.38831	+	2.68912i	0.251793	+	0.0916451i
$862$	17.2493	−	9.95887i	0.587512	−	0.339200i
$863$	16.7269	+	9.65731i	0.569392	+	0.328739i	0.756906	−	0.653523i	$-0.226710\pi$
$863$	16.7269	+	9.65731i	0.569392	+	0.328739i	−0.187514	+	0.982262i	$0.560043\pi$
$864$	4.20046	−	3.52460i	0.142902	−	0.119909i
$865$		0			0
$866$	−9.29408	+	16.0978i	−0.315826	+	0.547026i
$867$	29.0110	−	16.7495i	0.985266	−	0.568844i
$868$	4.46131	−	12.2573i	0.151427	−	0.416042i
$869$	0.194718	−	1.10430i	0.00660536	−	0.0374608i
$870$		0			0
$871$	0.0151443	−	0.00551208i	0.000513146	−	0.000186770i
$872$	0.503460	−	0.600000i	0.0170493	−	0.0203186i
$873$		−	11.3707i		−	0.384839i
$874$	2.13708	+	0.775048i	0.0722877	+	0.0262164i
$875$		0			0
$876$	6.93673	+	5.82061i	0.234370	+	0.196660i
$877$	−4.63497	−	12.7345i	−0.156512	−	0.430013i	0.836509	−	0.547953i	$-0.184593\pi$
$877$	−4.63497	−	12.7345i	−0.156512	−	0.430013i	−0.993021	+	0.117941i	$0.962371\pi$
$878$	20.8437	−	3.67531i	0.703441	−	0.124036i
$879$	−2.17077	+	12.3110i	−0.0732182	+	0.415241i
$880$		0			0
$881$	10.2941	+	17.8298i	0.346816	+	0.600703i	0.985682	−	0.168615i	$-0.0539295\pi$
$881$	10.2941	+	17.8298i	0.346816	+	0.600703i	−0.638866	+	0.769318i	$0.720596\pi$
$882$	−2.90935	−	1.67972i	−0.0979630	−	0.0565590i
$883$	−2.56215	−	3.05346i	−0.0862233	−	0.102757i	0.721208	−	0.692719i	$-0.243587\pi$
$883$	−2.56215	−	3.05346i	−0.0862233	−	0.102757i	−0.807431	+	0.589962i	$0.799143\pi$
$884$	−0.351754	+	0.295157i	−0.0118308	+	0.00992720i
$885$		0			0
$886$	16.2791	+	28.1962i	0.546907	+	0.947270i
$887$	−5.30684	+	14.5804i	−0.178186	+	0.489563i	−0.996344	−	0.0854309i	$-0.972773\pi$
$887$	−5.30684	+	14.5804i	−0.178186	+	0.489563i	0.818158	+	0.574994i	$0.194996\pi$
$888$	−12.8805	−	2.27117i	−0.432240	−	0.0762155i
$889$	3.37853	+	19.1606i	0.113312	+	0.642625i
$890$		0			0
$891$	0.482268	+	0.404671i	0.0161566	+	0.0135570i
$892$			1.54050i			0.0515797i
$893$	24.3449	−	29.0810i	0.814671	−	0.973160i
$894$	18.9041			0.632249
$895$		0			0
$896$	2.06382	−	0.751167i	0.0689472	−	0.0250947i
$897$	0.0425426	−	0.00750140i	0.00142046	−	0.000250465i
$898$	−3.86225	−	0.681019i	−0.128885	−	0.0227259i
$899$	38.0788	+	13.8596i	1.27000	+	0.462242i
$900$		0			0
$901$	−30.4470	+	52.7357i	−1.01434	+	1.75688i
$902$	−0.604216	−	0.720076i	−0.0201182	−	0.0239759i
$903$	9.96997	+	11.8817i	0.331780	+	0.395400i
$904$	0.536278	−	0.928861i	0.0178363	−	0.0308935i
$905$		0			0
$906$	−15.4685	−	5.63008i	−0.513907	−	0.187047i
$907$	−30.3910	−	5.35875i	−1.00912	−	0.177934i	−0.355432	−	0.934702i	$-0.615666\pi$
$907$	−30.3910	−	5.35875i	−1.00912	−	0.177934i	−0.653684	+	0.756768i	$0.726777\pi$
$908$	−21.5908	+	3.80703i	−0.716515	+	0.126341i
$909$	−13.9784	+	5.08771i	−0.463634	+	0.168749i
$910$		0			0
$911$	−34.4064			−1.13994			−0.569968	−	0.821667i	$-0.693044\pi$
$911$	−34.4064			−1.13994			−0.569968	+	0.821667i	$0.693044\pi$
$912$	3.37671	−	4.03363i	0.111814	−	0.133567i
$913$			0.0309075i			0.00102289i
$914$	−24.9808	−	20.9613i	−0.826290	−	0.693340i
$915$		0			0
$916$	−3.92425	−	22.2555i	−0.129661	−	0.735343i
$917$	−16.7031	−	2.94520i	−0.551584	−	0.0972592i
$918$	12.5467	−	34.4717i	0.414102	−	1.13774i
$919$	9.26696	+	16.0508i	0.305689	+	0.529468i	0.977414	−	0.211332i	$-0.0677800\pi$
$919$	9.26696	+	16.0508i	0.305689	+	0.529468i	−0.671726	+	0.740800i	$0.734447\pi$
$920$		0			0
$921$	7.93352	−	6.65701i	0.261418	−	0.219356i
$922$	20.1804	+	24.0501i	0.664607	+	0.792048i
$923$	−0.107722	−	0.0621931i	−0.00354570	−	0.00204711i
$924$	0.419950	+	0.727374i	0.0138153	+	0.0239289i
$925$		0			0
$926$	1.56453	−	8.87291i	0.0514138	−	0.291582i
$927$	−28.0251	+	4.94159i	−0.920466	+	0.162303i
$928$	2.33359	+	6.41147i	0.0766037	+	0.210467i
$929$	18.2652	+	15.3263i	0.599262	+	0.502840i	0.891208	−	0.453594i	$-0.149858\pi$
$929$	18.2652	+	15.3263i	0.599262	+	0.502840i	−0.291946	+	0.956435i	$0.594303\pi$
$930$		0			0
$931$	−8.91838	−	3.23440i	−0.292288	−	0.106003i
$932$		−	9.04046i		−	0.296130i
$933$	3.30293	−	3.93628i	0.108133	−	0.128868i
$934$	−15.3080	+	5.57166i	−0.500894	+	0.182310i
$935$		0			0
$936$	−0.0183969	+	0.104334i	−0.000601322	+	0.00341027i
$937$	−20.5431	+	56.4418i	−0.671115	+	1.84387i	−0.153744	+	0.988111i	$0.549133\pi$
$937$	−20.5431	+	56.4418i	−0.671115	+	1.84387i	−0.517370	+	0.855762i	$0.673089\pi$
$938$	−0.446610	+	0.257851i	−0.0145823	+	0.00841912i
$939$	−1.13518	+	1.96619i	−0.0370453	+	0.0641643i
$940$		0			0
$941$	−30.6397	+	25.7097i	−0.998825	+	0.838113i	−0.986821	−	0.161814i	$-0.948265\pi$
$941$	−30.6397	+	25.7097i	−0.998825	+	0.838113i	−0.0120035	+	0.999928i	$0.503821\pi$
$942$	−16.1314	−	9.31349i	−0.525591	−	0.303450i
$943$	1.33978	−	0.773524i	0.0436293	−	0.0251894i
$944$	1.93601	+	0.704650i	0.0630117	+	0.0229344i
$945$		0			0
$946$	−0.322005	−	1.82618i	−0.0104693	−	0.0593742i
$947$	−10.1287	−	27.8284i	−0.329139	−	0.904301i	−0.988330	−	0.152326i	$-0.951324\pi$
$947$	−10.1287	−	27.8284i	−0.329139	−	0.904301i	0.659192	−	0.751975i	$-0.270899\pi$
$948$	2.74507	−	3.27144i	0.0891557	−	0.106252i
$949$	−0.514998			−0.0167175
$950$		0			0
$951$	29.1047			0.943784
$952$	9.44468	−	11.2557i	0.306104	−	0.364800i
$953$	12.0998	+	33.2440i	0.391952	+	1.07688i	0.966109	+	0.258134i	$0.0831074\pi$
$953$	12.0998	+	33.2440i	0.391952	+	1.07688i	−0.574158	+	0.818745i	$0.694670\pi$
$954$	2.43968	+	13.8361i	0.0789877	+	0.447961i
$955$		0			0
$956$	22.0566	+	8.02796i	0.713363	+	0.259643i
$957$	−2.25967	+	1.30462i	−0.0730447	+	0.0421724i
$958$	21.5425	+	12.4376i	0.696007	+	0.401840i
$959$	28.3983	−	23.8290i	0.917030	−	0.769479i
$960$		0			0
$961$	−2.13687	+	3.70116i	−0.0689312	+	0.119392i
$962$	0.644192	−	0.371924i	0.0207696	−	0.0119913i
$963$	−6.25225	+	17.1779i	−0.201476	+	0.553551i
$964$	4.77778	−	27.0961i	0.153882	−	0.872708i
$965$		0			0
$966$	−1.29895	+	0.472779i	−0.0417930	+	0.0152114i
$967$	11.4118	−	13.6001i	0.366979	−	0.437349i	−0.550680	−	0.834716i	$-0.685632\pi$
$967$	11.4118	−	13.6001i	0.366979	−	0.437349i	0.917660	+	0.397367i	$0.130076\pi$
$968$			10.8996i			0.350326i
$969$	6.07132	−	34.6655i	0.195039	−	1.11361i
$970$		0			0
$971$	17.7532	+	14.8967i	0.569729	+	0.478059i	0.881556	−	0.472080i	$-0.156497\pi$
$971$	17.7532	+	14.8967i	0.569729	+	0.478059i	−0.311827	+	0.950139i	$0.600941\pi$
$972$	−4.80616	−	13.2048i	−0.154158	−	0.423545i
$973$	−43.1767	+	7.61322i	−1.38418	+	0.244069i
$974$	5.98042	−	33.9166i	0.191625	−	1.08676i
$975$		0			0
$976$	−0.901422	−	1.56131i	−0.0288538	−	0.0499763i
$977$	−13.9154	−	8.03404i	−0.445192	−	0.257032i	0.260605	−	0.965445i	$-0.416078\pi$
$977$	−13.9154	−	8.03404i	−0.445192	−	0.257032i	−0.705797	+	0.708414i	$0.749411\pi$
$978$	0.551713	+	0.657506i	0.0176419	+	0.0210247i
$979$	1.55083	−	1.30130i	0.0495647	−	0.0415897i
$980$		0			0
$981$	−0.604493	−	1.04701i	−0.0193000	−	0.0334285i
$982$	11.7110	−	32.1757i	0.373713	−	1.02677i
$983$	43.8078	+	7.72449i	1.39725	+	0.246373i	0.821013	−	0.570910i	$-0.193409\pi$
$983$	43.8078	+	7.72449i	1.39725	+	0.246373i	0.576237	+	0.817282i	$0.304520\pi$
$984$	−0.621648	−	3.52554i	−0.0198174	−	0.112390i
$985$		0			0
$986$	34.9672	+	29.3410i	1.11358	+	0.934407i
$987$			23.0617i			0.734062i
$988$	0.000344355		0.299176i	1.09554e−5		0.00951807i
$989$	3.05191			0.0970450
$990$		0			0
$991$	8.83050	−	3.21404i	0.280510	−	0.102097i	−0.197934	−	0.980215i	$-0.563423\pi$
$991$	8.83050	−	3.21404i	0.280510	−	0.102097i	0.478444	+	0.878118i	$0.341201\pi$
$992$	−5.84894	+	1.03133i	−0.185704	+	0.0327446i
$993$	−24.6038	−	4.33832i	−0.780779	−	0.137672i
$994$	3.74018	+	1.36131i	0.118631	+	0.0431782i
$995$		0			0
$996$	−0.0588550	+	0.101940i	−0.00186489	+	0.00323009i
$997$	10.5936	+	12.6250i	0.335503	+	0.399837i	0.907249	−	0.420593i	$-0.138178\pi$
$997$	10.5936	+	12.6250i	0.335503	+	0.399837i	−0.571746	+	0.820431i	$0.693734\pi$
$998$	14.2756	+	17.0130i	0.451886	+	0.538537i
$999$	−29.7130	+	51.4644i	−0.940077	+	1.62826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.f.149.2		24
5.2	odd	4		950.2.l.g.301.2		12
5.3	odd	4		190.2.k.c.111.1	yes	12
5.4	even	2	inner	950.2.u.f.149.3		24
19.6	even	9	inner	950.2.u.f.899.3		24
95.33	even	36		3610.2.a.bd.1.3		6
95.43	odd	36		3610.2.a.bf.1.4		6
95.44	even	18	inner	950.2.u.f.899.2		24
95.63	odd	36		190.2.k.c.101.1	✓	12
95.82	odd	36		950.2.l.g.101.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.101.1	✓	12	95.63	odd	36
190.2.k.c.111.1	yes	12	5.3	odd	4
950.2.l.g.101.2		12	95.82	odd	36
950.2.l.g.301.2		12	5.2	odd	4
950.2.u.f.149.2		24	1.1	even	1	trivial
950.2.u.f.149.3		24	5.4	even	2	inner
950.2.u.f.899.2		24	95.44	even	18	inner
950.2.u.f.899.3		24	19.6	even	9	inner
3610.2.a.bd.1.3		6	95.33	even	36
3610.2.a.bf.1.4		6	95.43	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(0.412760 + 1.13405i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.90202 + 1.09813i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.18244 - 0.992183i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(0.412760 + 1.13405i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.13405 - 0.412760i) q^{6} +(-1.90202 + 1.09813i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.18244 - 0.992183i) q^{9} +(0.158441 - 0.274427i) q^{11} +(1.04514 - 0.603415i) q^{12} +(-0.0234748 + 0.0644966i) q^{13} +(0.381378 - 2.16290i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.30034 + 5.12494i) q^{17} +1.54356i q^{18} +(0.761855 + 4.29180i) q^{19} +(-2.03042 - 1.70372i) q^{21} +(0.108380 + 0.297771i) q^{22} +(-0.513603 + 0.0905620i) q^{23} +(-0.209564 + 1.18849i) q^{24} +(-0.0343179 - 0.0594403i) q^{26} +(4.74868 + 2.74165i) q^{27} +(1.41173 + 1.68244i) q^{28} +(-5.22668 + 4.38571i) q^{29} +(-2.96958 - 5.14347i) q^{31} +(0.342020 - 0.939693i) q^{32} +(0.376612 + 0.0664068i) q^{33} +(-1.16173 - 6.58850i) q^{34} +(-1.18244 - 0.992183i) q^{36} +10.8376i q^{37} +(-3.77742 - 2.17510i) q^{38} -0.0828317 q^{39} +(-2.78749 + 1.01456i) q^{41} +(2.61025 - 0.460258i) q^{42} +(-5.76298 - 1.01617i) q^{43} +(-0.297771 - 0.108380i) q^{44} +(0.260763 - 0.451655i) q^{46} +(-5.59278 - 6.66521i) q^{47} +(-0.775735 - 0.924485i) q^{48} +(-1.08821 + 1.88483i) q^{49} +(-7.58694 - 2.76142i) q^{51} +(0.0675931 + 0.0119185i) q^{52} +(8.96377 - 1.58055i) q^{53} +(-5.15262 + 1.87540i) q^{54} -2.19627 q^{56} +(-4.55265 + 2.63547i) q^{57} -6.82295i q^{58} +(-1.57825 - 1.32431i) q^{59} +(0.313061 + 1.77546i) q^{61} +(5.84894 + 1.03133i) q^{62} +(-1.15947 + 3.18563i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.292952 + 0.245816i) q^{66} +(-0.150932 - 0.179873i) q^{67} +(5.79383 + 3.34507i) q^{68} +(-0.314696 - 0.545070i) q^{69} +(-0.314696 + 1.78473i) q^{71} +(1.52011 - 0.268037i) q^{72} +(2.56629 + 7.05084i) q^{73} +(-8.30210 - 6.96629i) q^{74} +(4.09431 - 1.49554i) q^{76} +0.695955i q^{77} +(0.0532432 - 0.0634528i) q^{78} +(3.32526 - 1.21030i) q^{79} +(-0.344991 + 1.95654i) q^{81} +(1.01456 - 2.78749i) q^{82} +(-0.0844691 + 0.0487683i) q^{83} +(-1.32526 + 2.29542i) q^{84} +(4.48280 - 3.76152i) q^{86} +(-7.13097 - 4.11707i) q^{87} +(0.274427 - 0.158441i) q^{88} +(6.00343 + 2.18507i) q^{89} +(-0.0261762 - 0.148452i) q^{91} +(0.178372 + 0.490074i) q^{92} +(4.60722 - 5.49067i) q^{93} +8.70082 q^{94} +1.20683 q^{96} +(4.73510 - 5.64307i) q^{97} +(-0.744377 - 2.04516i) q^{98} +(-0.0849358 - 0.481695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 18 * q^9	\( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Introduction

L-functions

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