LMFDB - Embedded newform 403.2.k.e.287.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.8
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0877385 + 0.270031i) q^{2} +(0.851349 + 2.62018i) q^{3} +(1.55282 + 1.12819i) q^{4} +0.880734 q^{5} -0.782228 q^{6} +(-3.90316 - 2.83581i) q^{7} +(-0.900292 + 0.654101i) q^{8} +(-3.71351 + 2.69802i) q^{9} +O(q^{10})$	\(q+(-0.0877385 + 0.270031i) q^{2} +(0.851349 + 2.62018i) q^{3} +(1.55282 + 1.12819i) q^{4} +0.880734 q^{5} -0.782228 q^{6} +(-3.90316 - 2.83581i) q^{7} +(-0.900292 + 0.654101i) q^{8} +(-3.71351 + 2.69802i) q^{9} +(-0.0772743 + 0.237826i) q^{10} +(4.27300 + 3.10452i) q^{11} +(-1.63407 + 5.02914i) q^{12} +(0.309017 + 0.951057i) q^{13} +(1.10822 - 0.805167i) q^{14} +(0.749812 + 2.30768i) q^{15} +(1.08861 + 3.35039i) q^{16} +(-1.13461 + 0.824339i) q^{17} +(-0.402733 - 1.23948i) q^{18} +(0.116784 - 0.359424i) q^{19} +(1.36762 + 0.993632i) q^{20} +(4.10740 - 12.6413i) q^{21} +(-1.21322 + 0.881459i) q^{22} +(-2.83527 + 2.05994i) q^{23} +(-2.48033 - 1.80206i) q^{24} -4.22431 q^{25} -0.283928 q^{26} +(-3.54422 - 2.57503i) q^{27} +(-2.86156 - 8.80699i) q^{28} +(3.05368 - 9.39825i) q^{29} -0.688935 q^{30} +(4.83693 - 2.75756i) q^{31} -3.22587 q^{32} +(-4.49658 + 13.8391i) q^{33} +(-0.123049 - 0.378706i) q^{34} +(-3.43765 - 2.49760i) q^{35} -8.81026 q^{36} +6.37648 q^{37} +(0.0868093 + 0.0630706i) q^{38} +(-2.22886 + 1.61936i) q^{39} +(-0.792919 + 0.576089i) q^{40} +(3.40418 - 10.4770i) q^{41} +(3.05316 + 2.21825i) q^{42} +(0.0680907 - 0.209562i) q^{43} +(3.13271 + 9.64148i) q^{44} +(-3.27061 + 2.37624i) q^{45} +(-0.307487 - 0.946349i) q^{46} +(0.138409 + 0.425979i) q^{47} +(-7.85185 + 5.70470i) q^{48} +(5.02972 + 15.4799i) q^{49} +(0.370635 - 1.14070i) q^{50} +(-3.12586 - 2.27107i) q^{51} +(-0.593123 + 1.82544i) q^{52} +(3.98033 - 2.89188i) q^{53} +(1.00630 - 0.731122i) q^{54} +(3.76338 + 2.73425i) q^{55} +5.36890 q^{56} +1.04118 q^{57} +(2.26990 + 1.64918i) q^{58} +(0.422494 + 1.30030i) q^{59} +(-1.43918 + 4.42933i) q^{60} -2.51912 q^{61} +(0.320244 + 1.54807i) q^{62} +22.1455 q^{63} +(-1.89418 + 5.82969i) q^{64} +(0.272162 + 0.837628i) q^{65} +(-3.34246 - 2.42844i) q^{66} -2.74637 q^{67} -2.69184 q^{68} +(-7.81124 - 5.67519i) q^{69} +(0.976045 - 0.709138i) q^{70} +(8.10646 - 5.88969i) q^{71} +(1.57847 - 4.85802i) q^{72} +(11.4349 + 8.30791i) q^{73} +(-0.559463 + 1.72185i) q^{74} +(-3.59636 - 11.0685i) q^{75} +(0.586840 - 0.426365i) q^{76} +(-7.87438 - 24.2349i) q^{77} +(-0.241722 - 0.743943i) q^{78} +(3.27074 - 2.37633i) q^{79} +(0.958774 + 2.95080i) q^{80} +(-0.525631 + 1.61773i) q^{81} +(2.53044 + 1.83847i) q^{82} +(-0.787331 + 2.42316i) q^{83} +(20.6397 - 14.9956i) q^{84} +(-0.999286 + 0.726024i) q^{85} +(0.0506141 + 0.0367733i) q^{86} +27.2249 q^{87} -5.87761 q^{88} +(-9.38656 - 6.81974i) q^{89} +(-0.354701 - 1.09166i) q^{90} +(1.49088 - 4.58844i) q^{91} -6.72665 q^{92} +(11.3432 + 10.3260i) q^{93} -0.127172 q^{94} +(0.102856 - 0.316557i) q^{95} +(-2.74634 - 8.45236i) q^{96} +(-6.83174 - 4.96355i) q^{97} -4.62136 q^{98} -24.2439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.0877385	+	0.270031i	−0.0620405	+	0.190941i	−0.977273	−	0.211986i	$-0.932007\pi$
$2$	−0.0877385	+	0.270031i	−0.0620405	+	0.190941i	0.915232	+	0.402927i	$0.132007\pi$
$3$	0.851349	+	2.62018i	0.491526	+	1.51276i	0.822301	+	0.569053i	$0.192690\pi$
$3$	0.851349	+	2.62018i	0.491526	+	1.51276i	−0.330774	+	0.943710i	$0.607310\pi$
$4$	1.55282	+	1.12819i	0.776408	+	0.564093i
$5$	0.880734			0.393876			0.196938	−	0.980416i	$-0.436900\pi$
$5$	0.880734			0.393876			0.196938	+	0.980416i	$0.436900\pi$
$6$	−0.782228			−0.319343
$7$	−3.90316	−	2.83581i	−1.47526	−	1.07184i	−0.979047	−	0.203635i	$-0.934725\pi$
$7$	−3.90316	−	2.83581i	−1.47526	−	1.07184i	−0.496210	−	0.868202i	$-0.665275\pi$
$8$	−0.900292	+	0.654101i	−0.318301	+	0.231260i
$9$	−3.71351	+	2.69802i	−1.23784	+	0.899341i
$10$	−0.0772743	+	0.237826i	−0.0244363	+	0.0752072i
$11$	4.27300	+	3.10452i	1.28836	+	0.936047i	0.999771	−	0.0214071i	$-0.00681460\pi$
$11$	4.27300	+	3.10452i	1.28836	+	0.936047i	0.288587	+	0.957454i	$0.406815\pi$
$12$	−1.63407	+	5.02914i	−0.471714	+	1.45179i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	1.10822	−	0.805167i	0.296183	−	0.215190i
$15$	0.749812	+	2.30768i	0.193601	+	0.595842i
$16$	1.08861	+	3.35039i	0.272152	+	0.837598i
$17$	−1.13461	+	0.824339i	−0.275182	+	0.199932i	−0.716813	−	0.697265i	$-0.754400\pi$
$17$	−1.13461	+	0.824339i	−0.275182	+	0.199932i	0.441631	+	0.897197i	$0.354400\pi$
$18$	−0.402733	−	1.23948i	−0.0949251	−	0.292149i
$19$	0.116784	−	0.359424i	0.0267920	−	0.0824574i	−0.936766	−	0.349955i	$-0.886197\pi$
$19$	0.116784	−	0.359424i	0.0267920	−	0.0824574i	0.963558	+	0.267498i	$0.0861968\pi$
$20$	1.36762	+	0.993632i	0.305809	+	0.222183i
$21$	4.10740	−	12.6413i	0.896307	−	2.75855i
$22$	−1.21322	+	0.881459i	−0.258660	+	0.187928i
$23$	−2.83527	+	2.05994i	−0.591195	+	0.429528i	−0.842743	−	0.538317i	$-0.819060\pi$
$23$	−2.83527	+	2.05994i	−0.591195	+	0.429528i	0.251548	+	0.967845i	$0.419060\pi$
$24$	−2.48033	−	1.80206i	−0.506294	−	0.367844i
$25$	−4.22431			−0.844861
$26$	−0.283928			−0.0556828
$27$	−3.54422	−	2.57503i	−0.682085	−	0.495564i
$28$	−2.86156	−	8.80699i	−0.540785	−	1.66436i
$29$	3.05368	−	9.39825i	0.567053	−	1.74521i	−0.0947171	−	0.995504i	$-0.530195\pi$
$29$	3.05368	−	9.39825i	0.567053	−	1.74521i	0.661770	−	0.749707i	$-0.269805\pi$
$30$	−0.688935			−0.125782
$31$	4.83693	−	2.75756i	0.868737	−	0.495273i
$31$	4.83693	−	2.75756i	0.868737	−	0.495273i
$32$	−3.22587			−0.570258
$33$	−4.49658	+	13.8391i	−0.782755	+	2.40907i
$34$	−0.123049	−	0.378706i	−0.0211027	−	0.0649475i
$35$	−3.43765	−	2.49760i	−0.581069	−	0.422171i
$36$	−8.81026			−1.46838
$37$	6.37648			1.04829			0.524144	−	0.851630i	$-0.324386\pi$
$37$	6.37648			1.04829			0.524144	+	0.851630i	$0.324386\pi$
$38$	0.0868093	+	0.0630706i	0.0140823	+	0.0102314i
$39$	−2.22886	+	1.61936i	−0.356903	+	0.259305i
$40$	−0.792919	+	0.576089i	−0.125371	+	0.0910877i
$41$	3.40418	−	10.4770i	0.531644	−	1.63623i	−0.219147	−	0.975692i	$-0.570327\pi$
$41$	3.40418	−	10.4770i	0.531644	−	1.63623i	0.750791	−	0.660540i	$-0.229673\pi$
$42$	3.05316	+	2.21825i	0.471113	+	0.342284i
$43$	0.0680907	−	0.209562i	0.0103837	−	0.0319579i	−0.945730	−	0.324952i	$-0.894652\pi$
$43$	0.0680907	−	0.209562i	0.0103837	−	0.0319579i	0.956114	+	0.292994i	$0.0946517\pi$
$44$	3.13271	+	9.64148i	0.472273	+	1.45351i
$45$	−3.27061	+	2.37624i	−0.487554	+	0.354229i
$46$	−0.307487	−	0.946349i	−0.0453365	−	0.139532i
$47$	0.138409	+	0.425979i	0.0201890	+	0.0621355i	0.960643	−	0.277784i	$-0.0896001\pi$
$47$	0.138409	+	0.425979i	0.0201890	+	0.0621355i	−0.940454	+	0.339920i	$0.889600\pi$
$48$	−7.85185	+	5.70470i	−1.13332	+	0.823403i
$49$	5.02972	+	15.4799i	0.718532	+	2.21141i
$50$	0.370635	−	1.14070i	0.0524156	−	0.161319i
$51$	−3.12586	−	2.27107i	−0.437709	−	0.318014i
$52$	−0.593123	+	1.82544i	−0.0822513	+	0.253143i
$53$	3.98033	−	2.89188i	0.546741	−	0.397230i	−0.279842	−	0.960046i	$-0.590282\pi$
$53$	3.98033	−	2.89188i	0.546741	−	0.397230i	0.826582	+	0.562816i	$0.190282\pi$
$54$	1.00630	−	0.731122i	0.136940	−	0.0994931i
$55$	3.76338	+	2.73425i	0.507454	+	0.368687i
$56$	5.36890			0.717449
$57$	1.04118			0.137908
$58$	2.26990	+	1.64918i	0.298052	+	0.216548i
$59$	0.422494	+	1.30030i	0.0550040	+	0.169285i	0.974785	−	0.223148i	$-0.0716334\pi$
$59$	0.422494	+	1.30030i	0.0550040	+	0.169285i	−0.919780	+	0.392433i	$0.871633\pi$
$60$	−1.43918	+	4.42933i	−0.185797	+	0.571825i
$61$	−2.51912			−0.322540			−0.161270	−	0.986910i	$-0.551559\pi$
$61$	−2.51912			−0.322540			−0.161270	+	0.986910i	$0.551559\pi$
$62$	0.320244	+	1.54807i	0.0406710	+	0.196605i
$63$	22.1455			2.79007
$64$	−1.89418	+	5.82969i	−0.236773	+	0.728712i
$65$	0.272162	+	0.837628i	0.0337575	+	0.103895i
$66$	−3.34246	−	2.42844i	−0.411428	−	0.298920i
$67$	−2.74637			−0.335522			−0.167761	−	0.985828i	$-0.553654\pi$
$67$	−2.74637			−0.335522			−0.167761	+	0.985828i	$0.553654\pi$
$68$	−2.69184			−0.326434
$69$	−7.81124	−	5.67519i	−0.940362	−	0.683213i
$70$	0.976045	−	0.709138i	0.116660	−	0.0847582i
$71$	8.10646	−	5.88969i	0.962060	−	0.698977i	0.00843137	−	0.999964i	$-0.497316\pi$
$71$	8.10646	−	5.88969i	0.962060	−	0.698977i	0.953628	+	0.300987i	$0.0973162\pi$
$72$	1.57847	−	4.85802i	0.186024	−	0.572523i
$73$	11.4349	+	8.30791i	1.33835	+	0.972367i	0.999503	+	0.0315248i	$0.0100363\pi$
$73$	11.4349	+	8.30791i	1.33835	+	0.972367i	0.338845	+	0.940842i	$0.389964\pi$
$74$	−0.559463	+	1.72185i	−0.0650363	+	0.200161i
$75$	−3.59636	−	11.0685i	−0.415272	−	1.27807i
$76$	0.586840	−	0.426365i	0.0673152	−	0.0489074i
$77$	−7.87438	−	24.2349i	−0.897369	−	2.76182i
$78$	−0.241722	−	0.743943i	−0.0273696	−	0.0842349i
$79$	3.27074	−	2.37633i	0.367987	−	0.267358i	−0.388389	−	0.921496i	$-0.626968\pi$
$79$	3.27074	−	2.37633i	0.367987	−	0.267358i	0.756376	+	0.654137i	$0.226968\pi$
$80$	0.958774	+	2.95080i	0.107194	+	0.329910i
$81$	−0.525631	+	1.61773i	−0.0584034	+	0.179747i
$82$	2.53044	+	1.83847i	0.279440	+	0.203025i
$83$	−0.787331	+	2.42316i	−0.0864208	+	0.265976i	−0.984923	−	0.172993i	$-0.944656\pi$
$83$	−0.787331	+	2.42316i	−0.0864208	+	0.265976i	0.898502	+	0.438969i	$0.144656\pi$
$84$	20.6397	−	14.9956i	2.25198	−	1.63616i
$85$	−0.999286	+	0.726024i	−0.108388	+	0.0787484i
$86$	0.0506141	+	0.0367733i	0.00545786	+	0.00396537i
$87$	27.2249			2.91881
$88$	−5.87761			−0.626556
$89$	−9.38656	−	6.81974i	−0.994973	−	0.722891i	−0.0339688	−	0.999423i	$-0.510815\pi$
$89$	−9.38656	−	6.81974i	−0.994973	−	0.722891i	−0.961005	+	0.276532i	$0.910815\pi$
$90$	−0.354701	−	1.09166i	−0.0373887	−	0.115071i
$91$	1.49088	−	4.58844i	0.156286	−	0.481000i
$92$	−6.72665			−0.701302
$93$	11.3432	+	10.3260i	1.17624	+	1.07075i
$94$	−0.127172			−0.0131168
$95$	0.102856	−	0.316557i	0.0105528	−	0.0324780i
$96$	−2.74634	−	8.45236i	−0.280297	−	0.862666i
$97$	−6.83174	−	4.96355i	−0.693658	−	0.503972i	0.184202	−	0.982888i	$-0.441030\pi$
$97$	−6.83174	−	4.96355i	−0.693658	−	0.503972i	−0.877861	+	0.478916i	$0.841030\pi$
$98$	−4.62136			−0.466828
$99$	−24.2439			−2.43660
$100$	−6.55957	−	4.76580i	−0.655957	−	0.476580i
$101$	−6.35259	+	4.61543i	−0.632107	+	0.459252i	−0.857129	−	0.515101i	$-0.827754\pi$
$101$	−6.35259	+	4.61543i	−0.632107	+	0.459252i	0.225023	+	0.974354i	$0.427754\pi$
$102$	0.887520	−	0.644821i	0.0878776	−	0.0638468i
$103$	−4.95673	+	15.2552i	−0.488401	+	1.50314i	0.338593	+	0.940933i	$0.390049\pi$
$103$	−4.95673	+	15.2552i	−0.488401	+	1.50314i	−0.826994	+	0.562211i	$0.809951\pi$
$104$	−0.900292	−	0.654101i	−0.0882809	−	0.0641399i
$105$	3.61753	−	11.1336i	0.353034	−	1.08653i
$106$	0.431670	+	1.32854i	0.0419275	+	0.129040i
$107$	0.0337098	−	0.0244916i	0.00325885	−	0.00236769i	−0.586155	−	0.810199i	$-0.699359\pi$
$107$	0.0337098	−	0.0244916i	0.00325885	−	0.00236769i	0.589413	+	0.807832i	$0.299359\pi$
$108$	−2.59841	−	7.99708i	−0.250032	−	0.769519i
$109$	−0.336094	−	1.03439i	−0.0321920	−	0.0990766i	0.933669	−	0.358136i	$-0.116588\pi$
$109$	−0.336094	−	1.03439i	−0.0321920	−	0.0990766i	−0.965861	+	0.259059i	$0.916588\pi$
$110$	−1.06853	+	0.776331i	−0.101880	+	0.0740202i
$111$	5.42861	+	16.7075i	0.515261	+	1.58581i
$112$	5.25207	−	16.1642i	0.496274	−	1.52737i
$113$	−1.82274	−	1.32430i	−0.171469	−	0.124579i	0.498741	−	0.866751i	$-0.333796\pi$
$113$	−1.82274	−	1.32430i	−0.171469	−	0.124579i	−0.670210	+	0.742172i	$0.733796\pi$
$114$	−0.0913515	+	0.281151i	−0.00855586	+	0.0263322i
$115$	−2.49712	+	1.81426i	−0.232858	+	0.169181i
$116$	15.3448	−	11.1486i	1.42473	−	1.03512i
$117$	−3.71351	−	2.69802i	−0.343314	−	0.249432i
$118$	−0.388192			−0.0357359
$119$	6.76623			0.620259
$120$	−2.18451	−	1.58714i	−0.199417	−	0.144885i
$121$	5.22132	+	16.0696i	0.474665	+	1.46087i
$122$	0.221024	−	0.680242i	0.0200106	−	0.0615862i
$123$	30.3498			2.73655
$124$	10.6219	+	1.17497i	0.953874	+	0.105515i
$125$	−8.12416			−0.726647
$126$	−1.94302	+	5.97999i	−0.173098	+	0.532740i
$127$	3.70052	+	11.3890i	0.328368	+	1.01061i	0.969897	+	0.243514i	$0.0783002\pi$
$127$	3.70052	+	11.3890i	0.328368	+	1.01061i	−0.641529	+	0.767098i	$0.721700\pi$
$128$	−6.62757	−	4.81521i	−0.585800	−	0.425609i
$129$	0.607059			0.0534486
$130$	−0.250065			−0.0219322
$131$	−7.01246	−	5.09485i	−0.612681	−	0.445139i	0.237676	−	0.971344i	$-0.423614\pi$
$131$	−7.01246	−	5.09485i	−0.612681	−	0.445139i	−0.850358	+	0.526205i	$0.823614\pi$
$132$	−22.5954	+	16.4165i	−1.96668	+	1.42887i
$133$	−1.47509	+	1.07171i	−0.127906	+	0.0929292i
$134$	0.240962	−	0.741606i	0.0208160	−	0.0640650i
$135$	−3.12152	−	2.26791i	−0.268657	−	0.195191i
$136$	0.482276	−	1.48429i	0.0413548	−	0.127277i
$137$	−6.22501	−	19.1586i	−0.531839	−	1.63683i	−0.750383	−	0.661004i	$-0.770131\pi$
$137$	−6.22501	−	19.1586i	−0.531839	−	1.63683i	0.218544	−	0.975827i	$-0.429869\pi$
$138$	2.21783	−	1.61135i	0.188794	−	0.137167i
$139$	1.44339	+	4.44230i	0.122427	+	0.376791i	0.993423	−	0.114498i	$-0.0365260\pi$
$139$	1.44339	+	4.44230i	0.122427	+	0.376791i	−0.870997	+	0.491289i	$0.836526\pi$
$140$	−2.52028	−	7.75662i	−0.213002	−	0.655554i
$141$	−0.998309	+	0.725314i	−0.0840728	+	0.0610825i
$142$	0.879152	+	2.70575i	0.0737768	+	0.227062i
$143$	−1.63214	+	5.02321i	−0.136486	+	0.420062i
$144$	−13.0820	−	9.50462i	−1.09017	−	0.792051i
$145$	2.68948	−	8.27736i	0.223349	−	0.687397i
$146$	−3.24667	+	2.35885i	−0.268697	+	0.195220i
$147$	−36.2781	+	26.3576i	−2.99217	+	2.17394i
$148$	9.90150	+	7.19386i	0.813898	+	0.591331i
$149$	3.97173			0.325376			0.162688	−	0.986678i	$-0.447984\pi$
$149$	3.97173			0.325376			0.162688	+	0.986678i	$0.447984\pi$
$150$	3.30437			0.269801
$151$	−15.7997	−	11.4791i	−1.28576	−	0.934159i	−0.286049	−	0.958215i	$-0.592342\pi$
$151$	−15.7997	−	11.4791i	−1.28576	−	0.934159i	−0.999711	+	0.0240559i	$0.992342\pi$
$152$	0.129960	+	0.399975i	0.0105411	+	0.0324422i
$153$	1.98928	−	6.12238i	0.160824	−	0.494965i
$154$	7.23506			0.583018
$155$	4.26005	−	2.42868i	0.342175	−	0.195076i
$156$	−5.28795			−0.423375
$157$	5.65510	−	17.4046i	0.451326	−	1.38904i	−0.424069	−	0.905630i	$-0.639399\pi$
$157$	5.65510	−	17.4046i	0.451326	−	1.38904i	0.875395	−	0.483408i	$-0.160601\pi$
$158$	0.354714	+	1.09170i	0.0282196	+	0.0868509i
$159$	10.9659	+	7.96720i	0.869653	+	0.631840i
$160$	−2.84113			−0.224611
$161$	16.9081			1.33255
$162$	−0.390719	−	0.283874i	−0.0306978	−	0.0223032i
$163$	−4.11896	+	2.99260i	−0.322622	+	0.234399i	−0.737294	−	0.675573i	$-0.763897\pi$
$163$	−4.11896	+	2.99260i	−0.322622	+	0.234399i	0.414671	+	0.909971i	$0.363897\pi$
$164$	17.1061	−	12.4283i	1.33576	−	0.970486i
$165$	−3.96030	+	12.1885i	−0.308309	+	0.948876i
$166$	−0.585249	−	0.425208i	−0.0454241	−	0.0330026i
$167$	−0.00737432	+	0.0226958i	−0.000570642	+	0.00175625i	−0.951341	−	0.308139i	$-0.900294\pi$
$167$	−0.00737432	+	0.0226958i	−0.000570642	+	0.00175625i	0.950771	+	0.309895i	$0.100294\pi$
$168$	4.57080	+	14.0675i	0.352645	+	1.08533i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−0.108373	−	0.333539i	−0.00831186	−	0.0255813i
$171$	0.536055	+	1.64981i	0.0409932	+	0.126164i
$172$	0.342157	−	0.248592i	0.0260892	−	0.0189549i
$173$	−3.28272	−	10.1032i	−0.249581	−	0.768130i	−0.994849	−	0.101366i	$-0.967679\pi$
$173$	−3.28272	−	10.1032i	−0.249581	−	0.768130i	0.745269	−	0.666764i	$-0.232321\pi$
$174$	−2.38867	+	7.35157i	−0.181085	+	0.557321i
$175$	16.4882	+	11.9794i	1.24639	+	0.905554i
$176$	−5.74972	+	17.6958i	−0.433401	+	1.33387i
$177$	−3.04734	+	2.21402i	−0.229052	+	0.166416i
$178$	2.66511	−	1.93631i	0.199758	−	0.145133i
$179$	18.2617	+	13.2679i	1.36495	+	0.991691i	0.998113	+	0.0614037i	$0.0195577\pi$
$179$	18.2617	+	13.2679i	1.36495	+	0.991691i	0.366832	+	0.930287i	$0.380442\pi$
$180$	−7.75950			−0.578359
$181$	−16.9193			−1.25760			−0.628802	−	0.777566i	$-0.716454\pi$
$181$	−16.9193			−1.25760			−0.628802	+	0.777566i	$0.716454\pi$
$182$	1.10822	+	0.805167i	0.0821465	+	0.0596829i
$183$	−2.14465	−	6.60056i	−0.158537	−	0.487927i
$184$	1.20516	−	3.70911i	0.0888457	−	0.273439i
$185$	5.61599			0.412896
$186$	−3.78358	+	2.15704i	−0.277425	+	0.158162i
$187$	−7.40734			−0.541679
$188$	−0.265660	+	0.817618i	−0.0193753	+	0.0596309i
$189$	6.53137	+	20.1015i	0.475088	+	1.46217i
$190$	0.0764559	+	0.0555485i	0.00554669	+	0.00402991i
$191$	17.4818			1.26494			0.632470	−	0.774585i	$-0.282041\pi$
$191$	17.4818			1.26494			0.632470	+	0.774585i	$0.282041\pi$
$192$	−16.8875			−1.21875
$193$	−17.8388	−	12.9607i	−1.28407	−	0.932929i	−0.284399	−	0.958706i	$-0.591794\pi$
$193$	−17.8388	−	12.9607i	−1.28407	−	0.932929i	−0.999668	+	0.0257770i	$0.991794\pi$
$194$	1.93972	−	1.40929i	0.139264	−	0.101181i
$195$	−1.96303	+	1.42623i	−0.140576	+	0.102134i
$196$	−9.65398	+	29.7119i	−0.689570	+	2.12228i
$197$	−5.47491	−	3.97775i	−0.390071	−	0.283403i	0.375414	−	0.926857i	$-0.377501\pi$
$197$	−5.47491	−	3.97775i	−0.390071	−	0.283403i	−0.765485	+	0.643454i	$0.777501\pi$
$198$	2.12712	−	6.54661i	0.151168	−	0.465247i
$199$	−0.0636494	−	0.195893i	−0.00451199	−	0.0138865i	0.948775	−	0.315952i	$-0.102324\pi$
$199$	−0.0636494	−	0.195893i	−0.00451199	−	0.0138865i	−0.953287	+	0.302066i	$0.902324\pi$
$200$	3.80311	−	2.76312i	0.268921	−	0.195382i
$201$	−2.33812	−	7.19598i	−0.164918	−	0.507566i
$202$	−0.688944	−	2.12035i	−0.0484739	−	0.149187i
$203$	−38.5707	+	28.0232i	−2.70713	+	1.96685i
$204$	−2.29170	−	7.05312i	−0.160451	−	0.493817i
$205$	2.99818	−	9.22745i	0.209402	−	0.644473i
$206$	−3.68450	−	2.67694i	−0.256711	−	0.186512i
$207$	4.97103	−	15.2992i	0.345510	−	1.06337i
$208$	−2.85001	+	2.07065i	−0.197613	+	0.143574i
$209$	1.61485	−	1.17326i	0.111702	−	0.0811561i
$210$	2.68903	+	1.95369i	0.185560	+	0.134818i
$211$	18.8226			1.29580			0.647899	−	0.761726i	$-0.275648\pi$
$211$	18.8226			1.29580			0.647899	+	0.761726i	$0.275648\pi$
$212$	9.44330			0.648569
$213$	22.3335	+	16.2262i	1.53026	+	1.11180i
$214$	0.00365586	+	0.0112516i	0.000249909	+	0.000769142i
$215$	0.0599699	−	0.184568i	0.00408991	−	0.0125875i
$216$	4.87516			0.331713
$217$	−26.6992	−	2.95341i	−1.81246	−	0.200490i
$218$	0.308806			0.0209150
$219$	−12.0332	+	37.0343i	−0.813127	+	2.50255i
$220$	2.75908	+	8.49158i	0.186017	+	0.572502i
$221$	−1.13461	−	0.824339i	−0.0763219	−	0.0554511i
$222$	−4.98786			−0.334763
$223$	−3.10347			−0.207824			−0.103912	−	0.994586i	$-0.533136\pi$
$223$	−3.10347			−0.207824			−0.103912	+	0.994586i	$0.533136\pi$
$224$	12.5911	+	9.14797i	0.841278	+	0.611224i
$225$	15.6870	−	11.3973i	1.04580	−	0.759818i
$226$	0.517526	−	0.376005i	0.0344253	−	0.0250115i
$227$	−0.602654	+	1.85478i	−0.0399996	+	0.123106i	−0.969062	−	0.246816i	$-0.920616\pi$
$227$	−0.602654	+	1.85478i	−0.0399996	+	0.123106i	0.929063	+	0.369922i	$0.120616\pi$
$228$	1.61676	+	1.17464i	0.107072	+	0.0777927i
$229$	1.73387	−	5.33632i	0.114578	−	0.352634i	−0.877281	−	0.479977i	$-0.840645\pi$
$229$	1.73387	−	5.33632i	0.114578	−	0.352634i	0.991859	+	0.127343i	$0.0406450\pi$
$230$	−0.270815	−	0.833482i	−0.0178570	−	0.0549582i
$231$	56.7959	−	41.2646i	3.73690	−	2.71501i
$232$	3.39820	+	10.4586i	0.223103	+	0.686640i
$233$	−0.579189	−	1.78256i	−0.0379439	−	0.116779i	0.930290	−	0.366824i	$-0.119555\pi$
$233$	−0.579189	−	1.78256i	−0.0379439	−	0.116779i	−0.968234	+	0.250044i	$0.919555\pi$
$234$	1.05437	−	0.766044i	0.0689262	−	0.0500778i
$235$	0.121902	+	0.375175i	0.00795199	+	0.0244737i
$236$	−0.810929	+	2.49578i	−0.0527870	+	0.162462i
$237$	9.01096	+	6.54685i	0.585325	+	0.425263i
$238$	−0.593659	+	1.82709i	−0.0384812	+	0.118433i
$239$	−12.7891	+	9.29183i	−0.827258	+	0.601038i	−0.918782	−	0.394764i	$-0.870826\pi$
$239$	−12.7891	+	9.29183i	−0.827258	+	0.601038i	0.0915240	+	0.995803i	$0.470826\pi$
$240$	−6.91539	+	5.02433i	−0.446387	+	0.324319i
$241$	−19.0564	−	13.8453i	−1.22753	−	0.891852i	−0.230827	−	0.972995i	$-0.574143\pi$
$241$	−19.0564	−	13.8453i	−1.22753	−	0.891852i	−0.996703	+	0.0811423i	$0.974143\pi$
$242$	−4.79740			−0.308388
$243$	−17.8289			−1.14373
$244$	−3.91173	−	2.84204i	−0.250423	−	0.181943i
$245$	4.42985	+	13.6337i	0.283013	+	0.871024i
$246$	−2.66285	+	8.19540i	−0.169777	+	0.522519i
$247$	0.377920			0.0240465
$248$	−2.55092	+	5.64645i	−0.161984	+	0.358550i
$249$	−7.01940			−0.444837
$250$	0.712802	−	2.19378i	0.0450816	−	0.138747i
$251$	−7.45650	−	22.9487i	−0.470650	−	1.44851i	−0.851736	−	0.523972i	$-0.824450\pi$
$251$	−7.45650	−	22.9487i	−0.470650	−	1.44851i	0.381086	−	0.924540i	$-0.375550\pi$
$252$	34.3879	+	24.9843i	2.16623	+	1.57386i
$253$	−18.5102			−1.16373
$254$	−3.40007			−0.213340
$255$	−2.75306	−	2.00021i	−0.172403	−	0.125258i
$256$	−8.03631	+	5.83872i	−0.502270	+	0.364920i
$257$	4.05491	−	2.94607i	0.252939	−	0.183771i	−0.454090	−	0.890956i	$-0.650035\pi$
$257$	4.05491	−	2.94607i	0.252939	−	0.183771i	0.707028	+	0.707185i	$0.250035\pi$
$258$	−0.0532625	+	0.163925i	−0.00331598	+	0.0102055i
$259$	−24.8884	−	18.0825i	−1.54649	−	1.12359i
$260$	−0.522383	+	1.60773i	−0.0323968	+	0.0997072i
$261$	14.0168	+	43.1394i	0.867620	+	2.67026i
$262$	1.99103	−	1.44657i	0.123006	−	0.0893694i
$263$	1.10675	+	3.40621i	0.0682449	+	0.210036i	0.979363	−	0.202109i	$-0.0647796\pi$
$263$	1.10675	+	3.40621i	0.0682449	+	0.210036i	−0.911118	+	0.412145i	$0.864780\pi$
$264$	−5.00390	−	15.4004i	−0.307969	−	0.947830i
$265$	3.50562	−	2.54698i	0.215348	−	0.156460i
$266$	−0.159974	−	0.492350i	−0.00980865	−	0.0301879i
$267$	9.87771	−	30.4005i	0.604506	−	1.86048i
$268$	−4.26460	−	3.09841i	−0.260502	−	0.189266i
$269$	4.40068	−	13.5439i	0.268314	−	0.825786i	−0.722597	−	0.691269i	$-0.757052\pi$
$269$	4.40068	−	13.5439i	0.268314	−	0.825786i	0.990911	−	0.134516i	$-0.0429481\pi$
$270$	0.886286	−	0.643924i	0.0539376	−	0.0391880i
$271$	−8.93912	+	6.49465i	−0.543013	+	0.394522i	−0.825203	−	0.564837i	$-0.808939\pi$
$271$	−8.93912	+	6.49465i	−0.543013	+	0.394522i	0.282190	+	0.959359i	$0.408939\pi$
$272$	−3.99700	−	2.90399i	−0.242354	−	0.176080i
$273$	13.2918			0.804457
$274$	5.71960			0.345534
$275$	−18.0505	−	13.1144i	−1.08848	−	0.790830i
$276$	−5.72673	−	17.6251i	−0.344709	−	1.06090i
$277$	−6.09474	+	18.7577i	−0.366197	+	1.12704i	0.583030	+	0.812450i	$0.301867\pi$
$277$	−6.09474	+	18.7577i	−0.366197	+	1.12704i	−0.949228	+	0.314589i	$0.898133\pi$
$278$	−1.32620			−0.0795402
$279$	−10.5220	+	23.2904i	−0.629936	+	1.39436i
$280$	4.72857			0.282586
$281$	−5.01500	+	15.4346i	−0.299170	+	0.920750i	0.682619	+	0.730775i	$0.260841\pi$
$281$	−5.01500	+	15.4346i	−0.299170	+	0.920750i	−0.981789	+	0.189976i	$0.939159\pi$
$282$	−0.108267	−	0.333213i	−0.00644723	−	0.0198425i
$283$	−11.5704	−	8.40636i	−0.687786	−	0.499706i	0.188145	−	0.982141i	$-0.439752\pi$
$283$	−11.5704	−	8.40636i	−0.687786	−	0.499706i	−0.875932	+	0.482435i	$0.839752\pi$
$284$	19.2325			1.14124
$285$	0.917002			0.0543185
$286$	−1.21322	−	0.881459i	−0.0717394	−	0.0521217i
$287$	−42.9979	+	31.2398i	−2.53809	+	1.84403i
$288$	11.9793	−	8.70347i	0.705887	−	0.512857i
$289$	−4.64549	+	14.2974i	−0.273264	+	0.841021i
$290$	1.99918	+	1.45249i	0.117396	+	0.0852930i
$291$	7.18921	−	22.1261i	0.421439	−	1.29706i
$292$	8.38335	+	25.8013i	0.490598	+	1.50991i
$293$	10.0212	−	7.28081i	0.585443	−	0.425350i	−0.255239	−	0.966878i	$-0.582154\pi$
$293$	10.0212	−	7.28081i	0.585443	−	0.425350i	0.840682	+	0.541528i	$0.182154\pi$
$294$	−3.93439	−	12.1088i	−0.229458	−	0.706200i
$295$	0.372105	+	1.14522i	0.0216648	+	0.0666774i
$296$	−5.74070	+	4.17086i	−0.333671	+	0.242426i
$297$	−7.15024	−	22.0062i	−0.414899	−	1.27693i
$298$	−0.348473	+	1.07249i	−0.0201865	+	0.0621277i
$299$	−2.83527	−	2.05994i	−0.163968	−	0.119130i
$300$	6.90280	−	21.2446i	0.398533	−	1.22656i
$301$	−0.860048	+	0.624861i	−0.0495723	+	0.0360164i
$302$	4.48597	−	3.25925i	0.258139	−	0.187549i
$303$	−17.5015	−	12.7156i	−1.00544	−	0.730493i
$304$	1.33134			0.0763577
$305$	−2.21868			−0.127041
$306$	1.47870	+	1.07434i	0.0845316	+	0.0614158i
$307$	0.563345	+	1.73380i	0.0321518	+	0.0989530i	0.965845	−	0.259122i	$-0.0834332\pi$
$307$	0.563345	+	1.73380i	0.0321518	+	0.0989530i	−0.933693	+	0.358075i	$0.883433\pi$
$308$	15.1140	−	46.5160i	0.861199	−	2.65050i
$309$	−44.1914			−2.51396
$310$	0.282050	+	1.36344i	0.0160193	+	0.0774379i
$311$	24.5521			1.39222			0.696110	−	0.717936i	$-0.254913\pi$
$311$	24.5521			1.39222			0.696110	+	0.717936i	$0.254913\pi$
$312$	0.947400	−	2.91580i	0.0536360	−	0.165075i
$313$	−6.25508	−	19.2512i	−0.353558	−	1.08814i	−0.956841	−	0.290612i	$-0.906141\pi$
$313$	−6.25508	−	19.2512i	−0.353558	−	1.08814i	0.603283	−	0.797527i	$-0.293859\pi$
$314$	4.20362	+	3.05411i	0.237224	+	0.172353i
$315$	19.5043			1.09894
$316$	7.75980			0.436523
$317$	−26.2737	−	19.0890i	−1.47568	−	1.07214i	−0.978917	−	0.204258i	$-0.934522\pi$
$317$	−26.2737	−	19.0890i	−1.47568	−	1.07214i	−0.496763	−	0.867886i	$-0.665478\pi$
$318$	−3.11353	+	2.26211i	−0.174598	+	0.126853i
$319$	42.2254	−	30.6785i	2.36417	−	1.71767i
$320$	−1.66827	+	5.13441i	−0.0932592	+	0.287022i
$321$	0.0928713	+	0.0674750i	0.00518357	+	0.00376609i
$322$	−1.48350	+	4.56573i	−0.0826720	+	0.254438i
$323$	0.163783	+	0.504074i	0.00911316	+	0.0280474i
$324$	−2.64130	+	1.91902i	−0.146739	+	0.106612i
$325$	−1.30538	−	4.01755i	−0.0724096	−	0.222854i
$326$	−0.446705	−	1.37482i	−0.0247407	−	0.0761440i
$327$	2.42416	−	1.76125i	0.134056	−	0.0973976i
$328$	3.78825	+	11.6590i	0.209171	+	0.643763i
$329$	0.667765	−	2.05517i	0.0368151	−	0.113305i
$330$	−2.94382	−	2.13881i	−0.162052	−	0.117738i
$331$	−6.39479	+	19.6812i	−0.351490	+	1.08177i	0.606527	+	0.795063i	$0.292562\pi$
$331$	−6.39479	+	19.6812i	−0.351490	+	1.08177i	−0.958017	+	0.286711i	$0.907438\pi$
$332$	−3.95635	+	2.87446i	−0.217133	+	0.157756i
$333$	−23.6791	+	17.2039i	−1.29761	+	0.942767i
$334$	−0.00548157	−	0.00398259i	−0.000299938	−	0.000217918i
$335$	−2.41882			−0.132154
$336$	46.8245			2.55449
$337$	24.4887	+	17.7921i	1.33398	+	0.969195i	0.999642	+	0.0267425i	$0.00851343\pi$
$337$	24.4887	+	17.7921i	1.33398	+	0.969195i	0.334340	+	0.942452i	$0.391487\pi$
$338$	−0.0877385	−	0.270031i	−0.00477235	−	0.0146878i
$339$	1.91811	−	5.90334i	0.104178	−	0.320626i
$340$	−2.37080			−0.128575
$341$	29.2291	+	3.23325i	1.58284	+	0.175090i
$342$	−0.492533			−0.0266331
$343$	13.8302	−	42.5648i	0.746758	−	2.29829i
$344$	0.0757729	+	0.233205i	0.00408540	+	0.0125736i
$345$	−6.87962	−	4.99834i	−0.370386	−	0.269102i
$346$	3.01620			0.162152
$347$	−4.77233			−0.256192			−0.128096	−	0.991762i	$-0.540887\pi$
$347$	−4.77233			−0.256192			−0.128096	+	0.991762i	$0.540887\pi$
$348$	42.2752	+	30.7147i	2.26619	+	1.64648i
$349$	−7.26487	+	5.27824i	−0.388880	+	0.282538i	−0.764996	−	0.644035i	$-0.777259\pi$
$349$	−7.26487	+	5.27824i	−0.388880	+	0.282538i	0.376117	+	0.926572i	$0.377259\pi$
$350$	−4.68145	+	3.40127i	−0.250234	+	0.181806i
$351$	1.35377	−	4.16648i	0.0722590	−	0.222390i
$352$	−13.7841	−	10.0148i	−0.734697	−	0.533789i
$353$	1.95008	−	6.00174i	0.103792	−	0.319440i	−0.885653	−	0.464348i	$-0.846289\pi$
$353$	1.95008	−	6.00174i	0.103792	−	0.319440i	0.989445	+	0.144908i	$0.0462886\pi$
$354$	−0.330487	−	1.01713i	−0.0175652	−	0.0540600i
$355$	7.13964	−	5.18725i	0.378933	−	0.275311i
$356$	−6.88166	−	21.1796i	−0.364727	−	1.12252i
$357$	5.76042	+	17.7287i	0.304874	+	0.938305i
$358$	−5.18501	+	3.76713i	−0.274036	+	0.199099i
$359$	−1.64168	−	5.05257i	−0.0866445	−	0.266664i	0.898342	−	0.439297i	$-0.144773\pi$
$359$	−1.64168	−	5.05257i	−0.0866445	−	0.266664i	−0.984986	+	0.172633i	$0.944773\pi$
$360$	1.39021	−	4.27862i	0.0732704	−	0.225503i
$361$	15.2558	+	11.0840i	0.802936	+	0.583367i
$362$	1.48448	−	4.56875i	0.0780224	−	0.240128i
$363$	−37.6600	+	27.3616i	−1.97664	+	1.43611i
$364$	7.49167	−	5.44302i	0.392670	−	0.285292i
$365$	10.0711	+	7.31706i	0.527144	+	0.382992i
$366$	1.97053			0.103001
$367$	18.2978			0.955137			0.477568	−	0.878595i	$-0.341518\pi$
$367$	18.2978			0.955137			0.477568	+	0.878595i	$0.341518\pi$
$368$	−9.98812	−	7.25679i	−0.520667	−	0.378286i
$369$	15.6257	+	48.0910i	0.813442	+	2.50352i
$370$	−0.492738	+	1.51649i	−0.0256163	+	0.0788387i
$371$	−23.7367			−1.23235
$372$	5.96431	+	28.8316i	0.309235	+	1.49485i
$373$	15.7459			0.815290			0.407645	−	0.913140i	$-0.366350\pi$
$373$	15.7459			0.815290			0.407645	+	0.913140i	$0.366350\pi$
$374$	0.649910	−	2.00022i	0.0336060	−	0.103429i
$375$	−6.91650	−	21.2868i	−0.357166	−	1.09925i
$376$	−0.403242	−	0.292973i	−0.0207956	−	0.0151089i
$377$	9.88190			0.508944
$378$	−6.00109			−0.308663
$379$	29.0725	+	21.1224i	1.49335	+	1.08498i	0.972937	+	0.231071i	$0.0742229\pi$
$379$	29.0725	+	21.1224i	1.49335	+	1.08498i	0.520415	+	0.853913i	$0.325777\pi$
$380$	0.516851	−	0.375514i	0.0265139	−	0.0192635i
$381$	−26.6909	+	19.3921i	−1.36742	+	0.993486i
$382$	−1.53383	+	4.72064i	−0.0784775	+	0.241529i
$383$	4.62362	+	3.35926i	0.236256	+	0.171650i	0.699614	−	0.714521i	$-0.253355\pi$
$383$	4.62362	+	3.35926i	0.236256	+	0.171650i	−0.463358	+	0.886171i	$0.653355\pi$
$384$	6.97436	−	21.4649i	0.355909	−	1.09537i
$385$	−6.93524	−	21.3445i	−0.353453	−	1.08782i
$386$	5.06494	−	3.67989i	0.257799	−	0.187302i
$387$	0.312547	+	0.961920i	0.0158876	+	0.0488971i
$388$	−5.00862	−	15.4150i	−0.254274	−	0.782576i
$389$	1.32555	−	0.963065i	0.0672078	−	0.0488294i	−0.553674	−	0.832733i	$-0.686775\pi$
$389$	1.32555	−	0.963065i	0.0672078	−	0.0488294i	0.620882	+	0.783904i	$0.286775\pi$
$390$	−0.212893	−	0.655216i	−0.0107802	−	0.0331782i
$391$	1.51882	−	4.67445i	0.0768101	−	0.236397i
$392$	−14.6536	−	10.6465i	−0.740120	−	0.537729i
$393$	7.37939	−	22.7114i	0.372241	−	1.14564i
$394$	1.55448	−	1.12940i	0.0783135	−	0.0568981i
$395$	2.88065	−	2.09292i	0.144941	−	0.105306i
$396$	−37.6462	−	27.3516i	−1.89180	−	1.37447i
$397$	14.5488			0.730185			0.365092	−	0.930971i	$-0.381037\pi$
$397$	14.5488			0.730185			0.365092	+	0.930971i	$0.381037\pi$
$398$	0.0584817			0.00293142
$399$	−4.06389	−	2.95259i	−0.203449	−	0.147814i
$400$	−4.59861	−	14.1531i	−0.229931	−	0.707654i
$401$	−10.1282	+	31.1715i	−0.505781	+	1.55663i	0.293674	+	0.955906i	$0.405122\pi$
$401$	−10.1282	+	31.1715i	−0.505781	+	1.55663i	−0.799454	+	0.600727i	$0.794878\pi$
$402$	2.14829			0.107147
$403$	4.11729	+	3.74806i	0.205097	+	0.186704i
$404$	−15.0715			−0.749834
$405$	−0.462941	+	1.42479i	−0.0230037	+	0.0707982i
$406$	−4.18302	−	12.8740i	−0.207600	−	0.638927i
$407$	27.2467	+	19.7959i	1.35057	+	0.981246i
$408$	4.29970			0.212867
$409$	−11.6423			−0.575676			−0.287838	−	0.957679i	$-0.592936\pi$
$409$	−11.6423			−0.575676			−0.287838	+	0.957679i	$0.592936\pi$
$410$	2.22865	+	1.61921i	0.110065	+	0.0799669i
$411$	44.8994	−	32.6213i	2.21472	−	1.60909i
$412$	−24.9076	+	18.0965i	−1.22711	+	0.891548i
$413$	2.03835	−	6.27341i	0.100301	−	0.308694i
$414$	3.69513	+	2.68467i	0.181606	+	0.131944i
$415$	−0.693429	+	2.13416i	−0.0340391	+	0.104762i
$416$	−0.996848	−	3.06798i	−0.0488745	−	0.150420i
$417$	−10.4108	+	7.56389i	−0.509819	+	0.370405i
$418$	0.175132	+	0.539001i	0.00856599	+	0.0263634i
$419$	4.51066	+	13.8824i	0.220360	+	0.678198i	0.998730	+	0.0503920i	$0.0160471\pi$
$419$	4.51066	+	13.8824i	0.220360	+	0.678198i	−0.778369	+	0.627806i	$0.783953\pi$
$420$	18.1781	−	13.2072i	0.887001	−	0.644444i
$421$	−5.10771	−	15.7199i	−0.248934	−	0.766141i	−0.994964	−	0.100229i	$-0.968042\pi$
$421$	−5.10771	−	15.7199i	−0.248934	−	0.766141i	0.746030	−	0.665912i	$-0.231958\pi$
$422$	−1.65146	+	5.08268i	−0.0803920	+	0.247421i
$423$	−1.66329	−	1.20845i	−0.0808717	−	0.0587567i
$424$	−1.69188	+	5.20708i	−0.0821651	+	0.252878i
$425$	4.79292	−	3.48226i	0.232491	−	0.168915i
$426$	−6.34110	+	4.60708i	−0.307227	+	0.223214i
$427$	9.83254	+	7.14376i	0.475830	+	0.345711i
$428$	0.0799762			0.00386580
$429$	−14.5513			−0.702541
$430$	0.0445776	+	0.0323875i	0.00214972	+	0.00156186i
$431$	1.09593	+	3.37294i	0.0527892	+	0.162469i	0.973975	−	0.226653i	$-0.0727785\pi$
$431$	1.09593	+	3.37294i	0.0527892	+	0.162469i	−0.921186	+	0.389122i	$0.872778\pi$
$432$	4.76908	−	14.6777i	0.229452	−	0.706182i
$433$	−27.8772			−1.33969			−0.669846	−	0.742500i	$-0.733640\pi$
$433$	−27.8772			−1.33969			−0.669846	+	0.742500i	$0.733640\pi$
$434$	3.14007	−	6.95051i	0.150728	−	0.333635i
$435$	23.9779			1.14965
$436$	0.645094	−	1.98539i	0.0308944	−	0.0950831i
$437$	0.409279	+	1.25963i	0.0195785	+	0.0602564i
$438$	−8.94466	−	6.49867i	−0.427392	−	0.310519i
$439$	−14.9430			−0.713192			−0.356596	−	0.934259i	$-0.616063\pi$
$439$	−14.9430			−0.713192			−0.356596	+	0.934259i	$0.616063\pi$
$440$	−5.17662			−0.246786
$441$	−60.4430	−	43.9144i	−2.87824	−	2.09116i
$442$	0.322146	−	0.234053i	0.0153229	−	0.0111328i
$443$	−11.5440	+	8.38720i	−0.548472	+	0.398488i	−0.827222	−	0.561876i	$-0.810080\pi$
$443$	−11.5440	+	8.38720i	−0.548472	+	0.398488i	0.278750	+	0.960364i	$0.410080\pi$
$444$	−10.4196	+	32.0682i	−0.494492	+	1.52189i
$445$	−8.26707	−	6.00638i	−0.391897	−	0.284730i
$446$	0.272294	−	0.838036i	0.0128935	−	0.0396821i
$447$	3.38132	+	10.4066i	0.159931	+	0.492217i
$448$	23.9252	−	17.3827i	1.13036	−	0.821255i
$449$	7.35193	+	22.6269i	0.346959	+	1.06783i	0.960527	+	0.278188i	$0.0897339\pi$
$449$	7.35193	+	22.6269i	0.346959	+	1.06783i	−0.613567	+	0.789642i	$0.710266\pi$
$450$	1.70127	+	5.23596i	0.0801985	+	0.246826i
$451$	47.0721	−	34.1999i	2.21654	−	1.61041i
$452$	−1.33632	−	4.11277i	−0.0628553	−	0.193449i
$453$	16.6264	−	51.1708i	0.781176	−	2.40421i
$454$	−0.447973	−	0.325471i	−0.0210244	−	0.0152751i
$455$	1.31307	−	4.04120i	0.0615575	−	0.189454i
$456$	−0.937366	+	0.681036i	−0.0438962	+	0.0318924i
$457$	8.71901	−	6.33473i	0.407858	−	0.296326i	−0.364876	−	0.931056i	$-0.618889\pi$
$457$	8.71901	−	6.33473i	0.407858	−	0.296326i	0.772734	+	0.634730i	$0.218889\pi$
$458$	1.28885	+	0.936401i	0.0602238	+	0.0437552i
$459$	6.14399			0.286777
$460$	−5.92439			−0.276226
$461$	−10.8424	−	7.87749i	−0.504982	−	0.366891i	0.305935	−	0.952053i	$-0.401031\pi$
$461$	−10.8424	−	7.87749i	−0.504982	−	0.366891i	−0.810917	+	0.585161i	$0.801031\pi$
$462$	6.15956	+	18.9572i	0.286569	+	0.881968i
$463$	−6.90507	+	21.2516i	−0.320906	+	0.987647i	0.652349	+	0.757919i	$0.273784\pi$
$463$	−6.90507	+	21.2516i	−0.320906	+	0.987647i	−0.973255	+	0.229728i	$0.926216\pi$
$464$	34.8120			1.61611
$465$	9.99037	+	9.09444i	0.463292	+	0.421745i
$466$	0.532165			0.0246521
$467$	10.6396	−	32.7453i	0.492341	−	1.51527i	−0.328719	−	0.944428i	$-0.606617\pi$
$467$	10.6396	−	32.7453i	0.492341	−	1.51527i	0.821060	−	0.570842i	$-0.193383\pi$
$468$	−2.72252	−	8.37906i	−0.125849	−	0.387322i
$469$	10.7195	+	7.78819i	0.494982	+	0.359625i
$470$	−0.112004			−0.00516638
$471$	50.4177			2.32312
$472$	−1.23090	−	0.894299i	−0.0566566	−	0.0411635i
$473$	0.941539	−	0.684068i	0.0432920	−	0.0314535i
$474$	−2.55846	+	1.85883i	−0.117514	+	0.0853790i
$475$	−0.493331	+	1.51832i	−0.0226356	+	0.0696651i
$476$	10.5067	+	7.63356i	0.481574	+	0.349884i
$477$	−6.97864	+	21.4781i	−0.319530	+	0.983412i
$478$	−1.38699	−	4.26871i	−0.0634394	−	0.195246i
$479$	−24.2871	+	17.6456i	−1.10971	+	0.806248i	−0.982617	−	0.185643i	$-0.940563\pi$
$479$	−24.2871	+	17.6456i	−1.10971	+	0.806248i	−0.127088	+	0.991891i	$0.540563\pi$
$480$	−2.41880	−	7.44429i	−0.110402	−	0.339784i
$481$	1.97044	+	6.06439i	0.0898444	+	0.276513i
$482$	5.41064	−	3.93106i	0.246448	−	0.179055i
$483$	14.3947	+	44.3024i	0.654983	+	2.01583i
$484$	−10.0217	+	30.8437i	−0.455533	+	1.40199i
$485$	−6.01695	−	4.37157i	−0.273216	−	0.198503i
$486$	1.56428	−	4.81437i	0.0709573	−	0.218384i
$487$	11.5972	−	8.42587i	0.525520	−	0.381813i	−0.293159	−	0.956064i	$-0.594707\pi$
$487$	11.5972	−	8.42587i	0.525520	−	0.381813i	0.818679	+	0.574251i	$0.194707\pi$
$488$	2.26795	−	1.64776i	0.102665	−	0.0745906i
$489$	−11.3478	−	8.24469i	−0.513167	−	0.372838i
$490$	−4.07019			−0.183872
$491$	−10.1078			−0.456158			−0.228079	−	0.973643i	$-0.573244\pi$
$491$	−10.1078			−0.456158			−0.228079	+	0.973643i	$0.573244\pi$
$492$	47.1276	+	34.2402i	2.12468	+	1.54367i
$493$	4.28263	+	13.1806i	0.192880	+	0.593623i
$494$	−0.0331582	+	0.102050i	−0.00149186	+	0.00459146i
$495$	−21.3524			−0.959719
$496$	14.5044	+	13.2037i	0.651268	+	0.592863i
$497$	−48.3429			−2.16847
$498$	0.615872	−	1.89546i	0.0275979	−	0.0849376i
$499$	5.37026	+	16.5280i	0.240406	+	0.739893i	0.996358	+	0.0852664i	$0.0271741\pi$
$499$	5.37026	+	16.5280i	0.240406	+	0.739893i	−0.755952	+	0.654627i	$0.772826\pi$
$500$	−12.6153	−	9.16557i	−0.564174	−	0.409897i
$501$	−0.0657453			−0.00293728
$502$	6.85110			0.305780
$503$	−14.5858	−	10.5972i	−0.650349	−	0.472506i	0.213041	−	0.977043i	$-0.431663\pi$
$503$	−14.5858	−	10.5972i	−0.650349	−	0.472506i	−0.863390	+	0.504537i	$0.831663\pi$
$504$	−19.9374	+	14.4854i	−0.888084	+	0.645231i
$505$	−5.59495	+	4.06497i	−0.248972	+	0.180889i
$506$	1.62406	−	4.99835i	0.0721983	−	0.222204i
$507$	−2.22886	−	1.61936i	−0.0989872	−	0.0719184i
$508$	−7.10272	+	21.8599i	−0.315132	+	0.969877i
$509$	−5.68544	−	17.4980i	−0.252003	−	0.775585i	−0.994405	−	0.105631i	$-0.966314\pi$
$509$	−5.68544	−	17.4980i	−0.252003	−	0.775585i	0.742403	−	0.669954i	$-0.233686\pi$
$510$	0.781670	−	0.567916i	0.0346129	−	0.0251478i
$511$	−21.0724	−	64.8542i	−0.932189	−	2.86898i
$512$	−5.93456	−	18.2647i	−0.262273	−	0.807193i
$513$	−1.33943	+	0.973155i	−0.0591374	+	0.0429658i
$514$	0.439759	+	1.35344i	0.0193969	+	0.0596976i
$515$	−4.36556	+	13.4358i	−0.192370	+	0.592053i
$516$	0.942650	+	0.684876i	0.0414979	+	0.0301500i
$517$	−0.731038	+	2.24990i	−0.0321510	+	0.0989506i
$518$	7.06652	−	5.13413i	0.310485	−	0.225581i
$519$	23.6774	−	17.2026i	1.03932	−	0.755112i
$520$	−0.792919	−	0.576089i	−0.0347718	−	0.0252632i
$521$	−25.7080			−1.12629			−0.563143	−	0.826359i	$-0.690408\pi$
$521$	−25.7080			−1.12629			−0.563143	+	0.826359i	$0.690408\pi$
$522$	−12.8788			−0.563690
$523$	−30.8957	−	22.4470i	−1.35097	−	0.981539i	−0.998962	−	0.0455431i	$-0.985498\pi$
$523$	−30.8957	−	22.4470i	−1.35097	−	0.981539i	−0.352010	−	0.935996i	$-0.614502\pi$
$524$	−5.14111	−	15.8227i	−0.224591	−	0.691219i
$525$	−17.3509	+	53.4006i	−0.757256	+	2.33059i
$526$	−1.01689			−0.0443385
$527$	−3.21484	+	7.11602i	−0.140040	+	0.309979i
$528$	−51.2613			−2.23086
$529$	−3.31200	+	10.1933i	−0.144000	+	0.443187i
$530$	0.380187	+	1.17009i	0.0165143	+	0.0508257i
$531$	−5.07718	−	3.68879i	−0.220331	−	0.160080i
$532$	−3.49963			−0.151728
$533$	11.0162			0.477163
$534$	7.34243	+	5.33459i	0.317738	+	0.230850i
$535$	0.0296894	−	0.0215706i	0.00128358	−	0.000932579i
$536$	2.47253	−	1.79640i	0.106797	−	0.0775927i
$537$	−19.2173	+	59.1447i	−0.829286	+	2.55228i
$538$	3.27117	+	2.37664i	0.141030	+	0.102464i
$539$	−26.5656	+	81.7605i	−1.14426	+	3.52167i
$540$	−2.28851	−	7.04330i	−0.0984817	−	0.303096i
$541$	1.41034	−	1.02467i	0.0606354	−	0.0440542i	−0.557055	−	0.830476i	$-0.688069\pi$
$541$	1.41034	−	1.02467i	0.0606354	−	0.0440542i	0.617690	+	0.786422i	$0.288069\pi$
$542$	−0.969455	−	2.98367i	−0.0416416	−	0.128160i
$543$	−14.4042	−	44.3317i	−0.618145	−	1.90246i
$544$	3.66009	−	2.65921i	0.156925	−	0.114013i
$545$	−0.296009	−	0.911023i	−0.0126797	−	0.0390240i
$546$	−1.16620	+	3.58921i	−0.0499089	+	0.153604i
$547$	10.3415	+	7.51354i	0.442170	+	0.321256i	0.786497	−	0.617594i	$-0.211893\pi$
$547$	10.3415	+	7.51354i	0.442170	+	0.321256i	−0.344326	+	0.938850i	$0.611893\pi$
$548$	11.9482	−	36.7728i	0.510402	−	1.57085i
$549$	9.35478	−	6.79665i	0.399252	−	0.290074i
$550$	5.12503	−	3.72355i	0.218532	−	0.158773i
$551$	−3.02133	−	2.19513i	−0.128713	−	0.0935155i
$552$	10.7445			0.457318
$553$	−19.5051			−0.829440
$554$	−4.53042	−	3.29154i	−0.192479	−	0.139844i
$555$	4.78116	+	14.7149i	0.202949	+	0.624613i
$556$	−2.77042	+	8.52648i	−0.117492	+	0.361603i
$557$	27.3232			1.15772			0.578861	−	0.815426i	$-0.303497\pi$
$557$	27.3232			1.15772			0.578861	+	0.815426i	$0.303497\pi$
$558$	−5.36595	−	4.88473i	−0.227159	−	0.206787i
$559$	0.220346			0.00931965
$560$	4.62568	−	14.2364i	0.195471	−	0.601597i
$561$	−6.30623	−	19.4086i	−0.266249	−	0.819431i
$562$	−3.72782	−	2.70842i	−0.157248	−	0.114248i
$563$	28.9348			1.21946			0.609728	−	0.792611i	$-0.291279\pi$
$563$	28.9348			1.21946			0.609728	+	0.792611i	$0.291279\pi$
$564$	−2.36848			−0.0997309
$565$	−1.60535	−	1.16635i	−0.0675375	−	0.0490688i
$566$	3.28515	−	2.38680i	0.138085	−	0.100325i
$567$	6.63919	−	4.82366i	0.278820	−	0.202575i
$568$	−3.44573	+	10.6049i	−0.144580	+	0.444971i
$569$	6.32797	+	4.59754i	0.265282	+	0.192739i	0.712472	−	0.701700i	$-0.247575\pi$
$569$	6.32797	+	4.59754i	0.265282	+	0.192739i	−0.447190	+	0.894439i	$0.647575\pi$
$570$	−0.0804564	+	0.247619i	−0.00336995	+	0.0103716i
$571$	5.43373	+	16.7233i	0.227395	+	0.699849i	0.998040	+	0.0625841i	$0.0199342\pi$
$571$	5.43373	+	16.7233i	0.227395	+	0.699849i	−0.770645	+	0.637265i	$0.780066\pi$
$572$	−8.20153	+	5.95876i	−0.342923	+	0.249148i
$573$	14.8831	+	45.8055i	0.621751	+	1.91355i
$574$	−4.66316	−	14.3517i	−0.194636	−	0.599029i
$575$	11.9771	−	8.70184i	0.499478	−	0.362892i
$576$	−8.69458	−	26.7592i	−0.362274	−	1.11497i
$577$	−9.15223	+	28.1677i	−0.381012	+	1.17264i	0.558320	+	0.829626i	$0.311446\pi$
$577$	−9.15223	+	28.1677i	−0.381012	+	1.17264i	−0.939332	+	0.343009i	$0.888554\pi$
$578$	−3.45315	−	2.50886i	−0.143632	−	0.104355i
$579$	18.7722	−	57.7750i	0.780148	−	2.40105i
$580$	13.5147	−	9.81898i	0.561166	−	0.407711i
$581$	9.94470	−	7.22525i	0.412576	−	0.299754i
$582$	5.34398	+	3.88263i	0.221515	+	0.160940i
$583$	25.9858			1.07622
$584$	−15.7289			−0.650867
$585$	−3.27061	−	2.37624i	−0.135223	−	0.0982455i
$586$	1.08680	+	3.34484i	0.0448955	+	0.138174i
$587$	−4.27542	+	13.1584i	−0.176465	+	0.543105i	−0.999697	−	0.0246004i	$-0.992169\pi$
$587$	−4.27542	+	13.1584i	−0.176465	+	0.543105i	0.823232	+	0.567705i	$0.192169\pi$
$588$	−86.0695			−3.54944
$589$	−0.426259	−	2.06054i	−0.0175637	−	0.0849032i
$590$	−0.341894			−0.0140755
$591$	5.76138	−	17.7317i	0.236992	−	0.729385i
$592$	6.94149	+	21.3637i	0.285293	+	0.878043i
$593$	24.8402	+	18.0474i	1.02006	+	0.741120i	0.966296	−	0.257434i	$-0.0828769\pi$
$593$	24.8402	+	18.0474i	1.02006	+	0.741120i	0.0537677	+	0.998553i	$0.482877\pi$
$594$	6.56971			0.269558
$595$	5.95925			0.244305
$596$	6.16736	+	4.48085i	0.252625	+	0.183543i
$597$	0.459087	−	0.333546i	0.0187892	−	0.0136511i
$598$	0.805012	−	0.584876i	0.0329194	−	0.0239174i
$599$	−0.656009	+	2.01899i	−0.0268038	+	0.0824936i	−0.963564	−	0.267479i	$-0.913809\pi$
$599$	−0.656009	+	2.01899i	−0.0268038	+	0.0824936i	0.936760	+	0.349973i	$0.113809\pi$
$600$	10.4777	+	7.61246i	0.427749	+	0.310778i
$601$	−2.87219	+	8.83969i	−0.117159	+	0.360578i	−0.992391	−	0.123125i	$-0.960709\pi$
$601$	−2.87219	+	8.83969i	−0.117159	+	0.360578i	0.875232	+	0.483703i	$0.160709\pi$
$602$	−0.0932728	−	0.287064i	−0.00380152	−	0.0116999i
$603$	10.1987	−	7.40976i	0.415322	−	0.301749i
$604$	−11.5834	−	35.6500i	−0.471321	−	1.45058i
$605$	4.59859	+	14.1530i	0.186959	+	0.575402i
$606$	4.96918	−	3.61032i	0.201859	−	0.146659i
$607$	6.21837	+	19.1382i	0.252396	+	0.776795i	0.994332	+	0.106324i	$0.0339080\pi$
$607$	6.21837	+	19.1382i	0.252396	+	0.776795i	−0.741936	+	0.670471i	$0.766092\pi$
$608$	−0.376729	+	1.15945i	−0.0152784	+	0.0470221i
$609$	−106.263	−	77.2047i	−4.30600	−	3.12849i
$610$	0.194663	−	0.599113i	0.00788169	−	0.0242574i
$611$	−0.362360	+	0.263270i	−0.0146595	+	0.0106508i
$612$	9.99618	−	7.26265i	0.404072	−	0.293575i
$613$	−20.6218	−	14.9826i	−0.832906	−	0.605141i	0.0874741	−	0.996167i	$-0.472120\pi$
$613$	−20.6218	−	14.9826i	−0.832906	−	0.605141i	−0.920380	+	0.391025i	$0.872120\pi$
$614$	−0.517607			−0.0208889
$615$	26.7301			1.07786
$616$	22.9413	+	16.6678i	0.924331	+	0.671566i
$617$	2.93842	+	9.04353i	0.118296	+	0.364079i	0.992620	−	0.121264i	$-0.0386948\pi$
$617$	2.93842	+	9.04353i	0.118296	+	0.364079i	−0.874324	+	0.485343i	$0.838695\pi$
$618$	3.87729	−	11.9331i	0.155967	−	0.480018i
$619$	−5.44522			−0.218862			−0.109431	−	0.993994i	$-0.534903\pi$
$619$	−5.44522			−0.218862			−0.109431	+	0.993994i	$0.534903\pi$
$620$	9.35507	+	1.03483i	0.375709	+	0.0415600i
$621$	15.3532			0.616104
$622$	−2.15416	+	6.62983i	−0.0863740	+	0.265832i
$623$	17.2978	+	53.2371i	0.693021	+	2.13290i
$624$	−7.85185	−	5.70470i	−0.314325	−	0.228371i
$625$	13.9663			0.558652
$626$	5.74723			0.229706
$627$	4.44896	+	3.23236i	0.177674	+	0.129088i
$628$	28.4169	−	20.6461i	1.13396	−	0.823870i
$629$	−7.23479	+	5.25639i	−0.288470	+	0.209586i
$630$	−1.71128	+	5.26678i	−0.0681791	+	0.209834i
$631$	−14.0162	−	10.1834i	−0.557978	−	0.405394i	0.272741	−	0.962088i	$-0.412070\pi$
$631$	−14.0162	−	10.1834i	−0.557978	−	0.405394i	−0.830718	+	0.556693i	$0.812070\pi$
$632$	−1.39026	+	4.27879i	−0.0553017	+	0.170201i
$633$	16.0246	+	49.3185i	0.636919	+	1.96024i
$634$	7.45985	−	5.41990i	0.296268	−	0.215252i
$635$	3.25917	+	10.0307i	0.129336	+	0.398056i
$636$	8.03954	+	24.7432i	0.318789	+	0.981130i
$637$	−13.1680	+	9.56710i	−0.521735	+	0.379062i
$638$	4.57937	+	14.0939i	0.181299	+	0.557981i
$639$	−14.2129	+	43.7428i	−0.562254	+	1.73044i
$640$	−5.83713	−	4.24092i	−0.230733	−	0.167637i
$641$	1.78096	−	5.48123i	0.0703436	−	0.216495i	−0.909704	−	0.415257i	$-0.863692\pi$
$641$	1.78096	−	5.48123i	0.0703436	−	0.216495i	0.980048	+	0.198761i	$0.0636918\pi$
$642$	−0.0263688	+	0.0191580i	−0.00104069	+	0.000756107i
$643$	9.99759	−	7.26367i	0.394266	−	0.286451i	−0.372935	−	0.927857i	$-0.621649\pi$
$643$	9.99759	−	7.26367i	0.394266	−	0.286451i	0.767202	+	0.641406i	$0.221649\pi$
$644$	26.2552	+	19.0755i	1.03460	+	0.751682i
$645$	0.534658			0.0210521
$646$	−0.150486			−0.00592079
$647$	−36.8487	−	26.7721i	−1.44867	−	1.05252i	−0.986139	−	0.165919i	$-0.946941\pi$
$647$	−36.8487	−	26.7721i	−1.44867	−	1.05252i	−0.462532	−	0.886603i	$-0.653059\pi$
$648$	−0.584934	−	1.80024i	−0.0229784	−	0.0707202i
$649$	−2.23149	+	6.86783i	−0.0875938	+	0.269586i
$650$	1.19940			0.0470443
$651$	−14.9919	−	72.4713i	−0.587579	−	2.84037i
$652$	−9.77220			−0.382709
$653$	−10.7430	+	33.0635i	−0.420406	+	1.29388i	0.486920	+	0.873447i	$0.338120\pi$
$653$	−10.7430	+	33.0635i	−0.420406	+	1.29388i	−0.907325	+	0.420429i	$0.861880\pi$
$654$	0.262902	+	0.809129i	0.0102803	+	0.0316394i
$655$	−6.17611	−	4.48721i	−0.241321	−	0.175330i
$656$	38.8078			1.51519
$657$	−64.8783			−2.53115
$658$	0.496372	+	0.360635i	0.0193506	+	0.0140590i
$659$	2.53634	−	1.84276i	0.0988018	−	0.0717837i	−0.537287	−	0.843399i	$-0.680551\pi$
$659$	2.53634	−	1.84276i	0.0988018	−	0.0717837i	0.636089	+	0.771615i	$0.280551\pi$
$660$	−19.9005	+	14.4586i	−0.774628	+	0.562800i
$661$	−1.72114	+	5.29712i	−0.0669446	+	0.206034i	−0.978933	−	0.204182i	$-0.934547\pi$
$661$	−1.72114	+	5.29712i	−0.0669446	+	0.206034i	0.911988	+	0.410216i	$0.134547\pi$
$662$	−4.75346	−	3.45359i	−0.184748	−	0.134228i
$663$	1.19397	−	3.67467i	0.0463701	−	0.142713i
$664$	−0.876160	−	2.69654i	−0.0340016	−	0.104646i
$665$	−1.29916	+	0.943894i	−0.0503792	+	0.0366026i
$666$	−2.56802	−	7.90355i	−0.0995087	−	0.306256i
$667$	10.7019	+	32.9370i	0.414378	+	1.27533i
$668$	−0.0370561	+	0.0269228i	−0.00143374	+	0.00104167i
$669$	−2.64214	−	8.13167i	−0.102151	−	0.314388i
$670$	0.212224	−	0.653158i	0.00819892	−	0.0252337i
$671$	−10.7642	−	7.82065i	−0.415548	−	0.301913i
$672$	−13.2499	+	40.7791i	−0.511127	+	1.57309i
$673$	30.9463	−	22.4838i	1.19289	−	0.866687i	0.199326	−	0.979933i	$-0.436125\pi$
$673$	30.9463	−	22.4838i	1.19289	−	0.866687i	0.993567	+	0.113246i	$0.0361248\pi$
$674$	−6.95301	+	5.05166i	−0.267820	+	0.194583i
$675$	14.9719	+	10.8777i	0.576268	+	0.418683i
$676$	−1.91938			−0.0738225
$677$	20.6091			0.792074			0.396037	−	0.918235i	$-0.370385\pi$
$677$	20.6091			0.792074			0.396037	+	0.918235i	$0.370385\pi$
$678$	1.42580	+	1.03590i	0.0547574	+	0.0397835i
$679$	12.5897	+	38.7471i	0.483148	+	1.48698i
$680$	0.424757	−	1.30727i	0.0162887	−	0.0501314i
$681$	−5.37293			−0.205891
$682$	−3.43760	+	7.60909i	−0.131632	+	0.291367i
$683$	8.21255			0.314244			0.157122	−	0.987579i	$-0.449778\pi$
$683$	8.21255			0.314244			0.157122	+	0.987579i	$0.449778\pi$
$684$	−1.02890	+	3.16662i	−0.0393408	+	0.121079i
$685$	−5.48258	−	16.8737i	−0.209479	−	0.644709i
$686$	10.2804	+	7.46915i	0.392508	+	0.285174i
$687$	15.4583			0.589769
$688$	0.776238			0.0295938
$689$	3.98033	+	2.89188i	0.151639	+	0.110172i
$690$	1.95332	−	1.41917i	0.0743615	−	0.0540268i
$691$	−0.705171	+	0.512336i	−0.0268260	+	0.0194902i	−0.601117	−	0.799161i	$-0.705278\pi$
$691$	−0.705171	+	0.512336i	−0.0268260	+	0.0194902i	0.574291	+	0.818651i	$0.305278\pi$
$692$	6.30080	−	19.3919i	0.239521	−	0.737168i
$693$	94.6278	+	68.7511i	3.59461	+	2.61164i
$694$	0.418717	−	1.28868i	0.0158943	−	0.0489176i
$695$	1.27124	+	3.91248i	0.0482210	+	0.148409i
$696$	−24.5103	+	17.8078i	−0.929062	+	0.675003i
$697$	4.77420	+	14.6935i	0.180836	+	0.556555i
$698$	−0.787881	−	2.42485i	−0.0298217	−	0.0917819i
$699$	4.17754	−	3.03516i	0.158009	−	0.114800i
$700$	12.0881	+	37.2034i	0.456888	+	1.40616i
$701$	−1.20138	+	3.69748i	−0.0453756	+	0.139652i	−0.971178	−	0.238357i	$-0.923391\pi$
$701$	−1.20138	+	3.69748i	−0.0453756	+	0.139652i	0.925802	+	0.378009i	$0.123391\pi$
$702$	1.00630	+	0.731122i	0.0379805	+	0.0275944i
$703$	0.744670	−	2.29186i	0.0280858	−	0.0864391i
$704$	−26.1922	+	19.0298i	−0.987156	+	0.717211i
$705$	−0.879245	+	0.638809i	−0.0331143	+	0.0240589i
$706$	1.44956	+	1.05317i	0.0545550	+	0.0396365i
$707$	37.8837			1.42476
$708$	−7.22979			−0.271712
$709$	2.46864	+	1.79357i	0.0927117	+	0.0673590i	0.633175	−	0.774008i	$-0.281751\pi$
$709$	2.46864	+	1.79357i	0.0927117	+	0.0673590i	−0.540464	+	0.841367i	$0.681751\pi$
$710$	0.774299	+	2.38305i	0.0290589	+	0.0894342i
$711$	−5.73453	+	17.6491i	−0.215062	+	0.661891i
$712$	12.9114			0.483877
$713$	−8.03357	+	17.7822i	−0.300859	+	0.665950i
$714$	−5.29273			−0.198075
$715$	−1.43748	+	4.42412i	−0.0537588	+	0.165453i
$716$	13.3884	+	41.2052i	0.500348	+	1.53991i
$717$	−35.2343	−	25.5992i	−1.31585	−	0.956020i
$718$	1.50839			0.0562927
$719$	−30.0828			−1.12190			−0.560950	−	0.827850i	$-0.689564\pi$
$719$	−30.0828			−1.12190			−0.560950	+	0.827850i	$0.689564\pi$
$720$	−11.5217	−	8.37104i	−0.429390	−	0.311970i
$721$	62.6079	−	45.4873i	2.33164	−	1.69404i
$722$	−4.33154	+	3.14705i	−0.161203	+	0.117121i
$723$	20.0535	−	61.7184i	0.745798	−	2.29533i
$724$	−26.2726	−	19.0881i	−0.976413	−	0.709405i
$725$	−12.8997	+	39.7011i	−0.479081	+	1.47446i
$726$	−4.08426	−	12.5701i	−0.151581	−	0.466519i
$727$	−5.68941	+	4.13360i	−0.211009	+	0.153307i	−0.688270	−	0.725455i	$-0.741630\pi$
$727$	−5.68941	+	4.13360i	−0.211009	+	0.153307i	0.477261	+	0.878761i	$0.341630\pi$
$728$	1.65908	+	5.10612i	0.0614896	+	0.189246i
$729$	−13.6017	−	41.8618i	−0.503768	−	1.55044i
$730$	−2.85946	+	2.07752i	−0.105833	+	0.0768924i
$731$	0.0954939	+	0.293900i	0.00353197	+	0.0108703i
$732$	4.11641	−	12.6690i	0.152147	−	0.468260i
$733$	−18.3717	−	13.3478i	−0.678575	−	0.493013i	0.194310	−	0.980940i	$-0.437753\pi$
$733$	−18.3717	−	13.3478i	−0.678575	−	0.493013i	−0.872884	+	0.487927i	$0.837753\pi$
$734$	−1.60542	+	4.94098i	−0.0592572	+	0.182375i
$735$	−31.9514	+	23.2140i	−1.17854	+	0.856262i
$736$	9.14621	−	6.64511i	0.337134	−	0.244942i
$737$	−11.7352	−	8.52614i	−0.432273	−	0.314064i
$738$	−14.3571			−0.528490
$739$	−9.89175			−0.363874			−0.181937	−	0.983310i	$-0.558237\pi$
$739$	−9.89175			−0.363874			−0.181937	+	0.983310i	$0.558237\pi$
$740$	8.72059	+	6.33588i	0.320575	+	0.232912i
$741$	0.321742	+	0.990220i	0.0118195	+	0.0363767i
$742$	2.08263	−	6.40966i	0.0764556	−	0.235306i
$743$	1.20819			0.0443242			0.0221621	−	0.999754i	$-0.492945\pi$
$743$	1.20819			0.0443242			0.0221621	+	0.999754i	$0.492945\pi$
$744$	−16.9665	−	1.87679i	−0.622020	−	0.0688064i
$745$	3.49804			0.128158
$746$	−1.38152	+	4.25188i	−0.0505810	+	0.155672i
$747$	−3.61397	−	11.1226i	−0.132228	−	0.406956i
$748$	−11.5022	−	8.35686i	−0.420563	−	0.305557i
$749$	−0.201029			−0.00734543
$750$	6.35495			0.232050
$751$	−9.80239	−	7.12185i	−0.357694	−	0.259880i	0.394396	−	0.918941i	$-0.370954\pi$
$751$	−9.80239	−	7.12185i	−0.357694	−	0.259880i	−0.752090	+	0.659061i	$0.770954\pi$
$752$	−1.27652	+	0.927449i	−0.0465500	+	0.0338206i
$753$	53.7818	−	39.0748i	1.95992	−	1.42396i
$754$	−0.867024	+	2.66842i	−0.0315751	+	0.0971783i
$755$	−13.9153	−	10.1101i	−0.506430	−	0.367943i
$756$	−12.5362	+	38.5825i	−0.455938	+	1.40323i
$757$	6.65493	+	20.4818i	0.241877	+	0.744422i	0.996134	+	0.0878427i	$0.0279973\pi$
$757$	6.65493	+	20.4818i	0.241877	+	0.744422i	−0.754257	+	0.656579i	$0.772003\pi$
$758$	−8.25448	+	5.99723i	−0.299816	+	0.217829i
$759$	−15.7587	−	48.5002i	−0.572004	−	1.76045i
$760$	0.114460	+	0.352272i	0.00415190	+	0.0127782i
$761$	26.1941	−	19.0312i	0.949537	−	0.689879i	−0.00116062	−	0.999999i	$-0.500369\pi$
$761$	26.1941	−	19.0312i	0.949537	−	0.689879i	0.950697	+	0.310121i	$0.100369\pi$
$762$	−2.89465	−	8.90881i	−0.104862	−	0.322732i
$763$	−1.62151	+	4.99050i	−0.0587026	+	0.180668i
$764$	27.1460	+	19.7227i	0.982108	+	0.713544i
$765$	1.75203	−	5.39219i	0.0633448	−	0.194955i
$766$	−1.31278	+	0.953787i	−0.0474325	+	0.0344617i
$767$	−1.10610	+	0.803631i	−0.0399391	+	0.0290174i
$768$	−22.1402	−	16.0858i	−0.798917	−	0.580447i
$769$	−21.5194			−0.776010			−0.388005	−	0.921657i	$-0.626836\pi$
$769$	−21.5194			−0.776010			−0.388005	+	0.921657i	$0.626836\pi$
$770$	6.37217			0.229637
$771$	11.1714	+	8.11648i	0.402327	+	0.292308i
$772$	−13.0784	−	40.2510i	−0.470700	−	1.44867i
$773$	13.8680	−	42.6812i	0.498796	−	1.53514i	−0.312160	−	0.950030i	$-0.601052\pi$
$773$	13.8680	−	42.6812i	0.498796	−	1.53514i	0.810956	−	0.585107i	$-0.198948\pi$
$774$	−0.287171			−0.0103221
$775$	−20.4327	+	11.6488i	−0.733963	+	0.418437i
$776$	9.39723			0.337341
$777$	26.1907	−	80.6068i	0.939587	−	2.89175i
$778$	0.143756	+	0.442437i	0.00515392	+	0.0158621i
$779$	−3.36813	−	2.44709i	−0.120676	−	0.0876760i
$780$	−4.65728			−0.166757
$781$	52.9235			1.89375
$782$	1.12899	+	0.820259i	0.0403726	+	0.0293324i
$783$	−35.0236	+	25.4462i	−1.25164	+	0.909372i
$784$	−46.3883	+	33.7031i	−1.65673	+	1.20368i
$785$	4.98064	−	15.3288i	0.177767	−	0.547109i
$786$	5.48534	+	3.98533i	0.195656	+	0.142152i
$787$	−0.0737818	+	0.227077i	−0.00263004	+	0.00809442i	−0.952363	−	0.304967i	$-0.901355\pi$
$787$	−0.0737818	+	0.227077i	−0.00263004	+	0.00809442i	0.949733	+	0.313061i	$0.101355\pi$
$788$	−4.01387	−	12.3534i	−0.142988	−	0.440073i
$789$	−7.98268	+	5.79975i	−0.284191	+	0.206477i
$790$	0.312409	+	0.961497i	0.0111150	+	0.0342085i
$791$	3.35898	+	10.3379i	0.119432	+	0.367573i
$792$	21.8266	−	15.8579i	0.775574	−	0.563487i
$793$	−0.778451	−	2.39583i	−0.0276436	−	0.0850783i
$794$	−1.27649	+	3.92864i	−0.0453010	+	0.139422i
$795$	9.65805	+	7.01699i	0.342536	+	0.248867i
$796$	0.122168	−	0.375993i	0.00433012	−	0.0133267i
$797$	31.1282	−	22.6159i	1.10262	−	0.801097i	0.121131	−	0.992637i	$-0.461348\pi$
$797$	31.1282	−	22.6159i	1.10262	−	0.801097i	0.981485	+	0.191539i	$0.0613480\pi$
$798$	1.15385	−	0.838323i	0.0408459	−	0.0296763i
$799$	−0.508191	−	0.369223i	−0.0179785	−	0.0130622i
$800$	13.6271			0.481789
$801$	53.2569			1.88174
$802$	−7.52866	−	5.46989i	−0.265846	−	0.193149i
$803$	23.0691	+	70.9994i	0.814090	+	2.50551i
$804$	4.48775	−	13.8119i	0.158271	−	0.487107i
$805$	14.8916			0.524859
$806$	−1.37334	+	0.782949i	−0.0483738	+	0.0275782i
$807$	39.2340			1.38110
$808$	2.70024	−	8.31047i	0.0949940	−	0.292361i
$809$	2.67179	+	8.22293i	0.0939352	+	0.289103i	0.986975	−	0.160875i	$-0.0514317\pi$
$809$	2.67179	+	8.22293i	0.0939352	+	0.289103i	−0.893040	+	0.449978i	$0.851432\pi$
$810$	−0.344119	−	0.250017i	−0.0120911	−	0.00878472i
$811$	−38.1692			−1.34030			−0.670152	−	0.742224i	$-0.733771\pi$
$811$	−38.1692			−1.34030			−0.670152	+	0.742224i	$0.733771\pi$
$812$	−91.5086			−3.21132
$813$	−24.6275	−	17.8929i	−0.863723	−	0.627532i
$814$	−7.73610	+	5.62060i	−0.271150	+	0.197002i
$815$	−3.62771	+	2.63569i	−0.127073	+	0.0923241i
$816$	4.20614	−	12.9452i	0.147244	−	0.453172i
$817$	−0.0673696	−	0.0489468i	−0.00235696	−	0.00171243i
$818$	1.02148	−	3.14379i	0.0357152	−	0.109920i
$819$	6.84334	+	21.0616i	0.239126	+	0.735953i
$820$	15.0659	−	10.9460i	0.526124	−	0.382252i
$821$	8.53865	+	26.2792i	0.298001	+	0.917152i	0.982197	+	0.187854i	$0.0601532\pi$
$821$	8.53865	+	26.2792i	0.298001	+	0.917152i	−0.684196	+	0.729298i	$0.739847\pi$
$822$	4.86938	+	14.9864i	0.169839	+	0.522711i
$823$	−20.6465	+	15.0006i	−0.719691	+	0.522886i	−0.886286	−	0.463139i	$-0.846723\pi$
$823$	−20.6465	+	15.0006i	−0.719691	+	0.522886i	0.166594	+	0.986026i	$0.446723\pi$
$824$	−5.51596	−	16.9764i	−0.192158	−	0.591400i
$825$	18.9949	−	58.4604i	0.661319	−	2.03533i
$826$	1.51518	+	1.10084i	0.0527197	+	0.0383031i
$827$	−1.14496	+	3.52382i	−0.0398141	+	0.122535i	−0.968988	−	0.247108i	$-0.920520\pi$
$827$	−1.14496	+	3.52382i	−0.0398141	+	0.122535i	0.929174	+	0.369643i	$0.120520\pi$
$828$	24.9795	−	18.1487i	0.868097	−	0.630709i
$829$	11.6046	−	8.43126i	0.403045	−	0.292830i	−0.367735	−	0.929931i	$-0.619867\pi$
$829$	11.6046	−	8.43126i	0.403045	−	0.292830i	0.770780	+	0.637101i	$0.219867\pi$
$830$	−0.515449	−	0.374496i	−0.0178915	−	0.0129989i
$831$	−54.3373			−1.88494
$832$	−6.12970			−0.212509
$833$	−18.4674	−	13.4174i	−0.639859	−	0.464885i
$834$	−1.12906	−	3.47489i	−0.0390961	−	0.120326i
$835$	−0.00649481	+	0.0199890i	−0.000224762	+	0.000691747i
$836$	3.83122			0.132506
$837$	−24.2439	−	2.68180i	−0.837993	−	0.0926967i
$838$	−4.14444			−0.143167
$839$	12.4753	−	38.3950i	0.430695	−	1.32554i	−0.466740	−	0.884395i	$-0.654572\pi$
$839$	12.4753	−	38.3950i	0.430695	−	1.32554i	0.897435	−	0.441147i	$-0.145428\pi$
$840$	4.02566	+	12.3897i	0.138899	+	0.427486i
$841$	−55.5406	−	40.3526i	−1.91519	−	1.39147i
$842$	4.69301			0.161732
$843$	−44.7110			−1.53993
$844$	29.2279	+	21.2353i	1.00607	+	0.730951i
$845$	−0.712529	+	0.517683i	−0.0245117	+	0.0178088i
$846$	0.472253	−	0.343112i	0.0162364	−	0.0117964i
$847$	25.1906	−	77.5288i	0.865561	−	2.66392i
$848$	14.0220	+	10.1875i	0.481516	+	0.349842i
$849$	12.1758	−	37.4732i	0.417872	−	1.28608i
$850$	0.519796	+	1.59977i	0.0178289	+	0.0548716i
$851$	−18.0791	+	13.1352i	−0.619742	+	0.450269i
$852$	16.3736	+	50.3926i	0.560949	+	1.72642i
$853$	−0.0427231	−	0.131488i	−0.00146281	−	0.00450207i	0.950322	−	0.311267i	$-0.100753\pi$
$853$	−0.0427231	−	0.131488i	−0.00146281	−	0.00450207i	−0.951785	+	0.306765i	$0.900753\pi$
$854$	−2.79173	+	2.02831i	−0.0955311	+	0.0694074i
$855$	0.472122	+	1.45304i	0.0161462	+	0.0496930i
$856$	−0.0143287	+	0.0440992i	−0.000489745	+	0.00150728i
$857$	14.7060	+	10.6845i	0.502346	+	0.364976i	0.809912	−	0.586551i	$-0.199515\pi$
$857$	14.7060	+	10.6845i	0.502346	+	0.364976i	−0.307566	+	0.951527i	$0.599515\pi$
$858$	1.27671	−	3.92930i	0.0435860	−	0.134144i
$859$	3.17584	−	2.30738i	0.108358	−	0.0787268i	−0.532287	−	0.846564i	$-0.678667\pi$
$859$	3.17584	−	2.30738i	0.108358	−	0.0787268i	0.640645	+	0.767837i	$0.278667\pi$
$860$	0.301349	−	0.218943i	0.0102759	−	0.00746590i
$861$	−118.460	−	86.0663i	−4.03711	−	2.93313i
$862$	−1.00695			−0.0342970
$863$	53.6203			1.82526			0.912628	−	0.408792i	$-0.134050\pi$
$863$	53.6203			1.82526			0.912628	+	0.408792i	$0.134050\pi$
$864$	11.4332	+	8.30670i	0.388965	+	0.282600i
$865$	−2.89120	−	8.89821i	−0.0983039	−	0.302548i
$866$	2.44590	−	7.52771i	0.0831151	−	0.255802i
$867$	−41.4166			−1.40658
$868$	−38.1270	−	34.7078i	−1.29411	−	1.17806i
$869$	21.3532			0.724359
$870$	−2.10378	+	6.47478i	−0.0713249	+	0.219516i
$871$	−0.848674	−	2.61195i	−0.0287562	−	0.0885026i
$872$	0.979178	+	0.711415i	0.0331592	+	0.0240915i
$873$	38.7615			1.31188
$874$	−0.376050			−0.0127201
$875$	31.7099	+	23.0386i	1.07199	+	0.778848i
$876$	−60.4669	+	43.9318i	−2.04299	+	1.48432i
$877$	30.9370	−	22.4770i	1.04467	−	0.758996i	0.0734768	−	0.997297i	$-0.476591\pi$
$877$	30.9370	−	22.4770i	1.04467	−	0.758996i	0.971191	+	0.238301i	$0.0765905\pi$
$878$	1.31108	−	4.03509i	0.0442468	−	0.136178i
$879$	27.6086	+	20.0588i	0.931214	+	0.676567i
$880$	−5.06397	+	15.5853i	−0.170707	+	0.525381i
$881$	5.28396	+	16.2623i	0.178021	+	0.547892i	0.999759	−	0.0219738i	$-0.00699504\pi$
$881$	5.28396	+	16.2623i	0.178021	+	0.547892i	−0.821738	+	0.569866i	$0.806995\pi$
$882$	17.1615	−	12.4685i	0.577856	−	0.419837i
$883$	−12.7764	−	39.3218i	−0.429961	−	1.32328i	−0.898163	−	0.439663i	$-0.855098\pi$
$883$	−12.7764	−	39.3218i	−0.429961	−	1.32328i	0.468201	−	0.883622i	$-0.344902\pi$
$884$	−0.831825	−	2.56009i	−0.0279773	−	0.0861053i
$885$	−2.68390	+	1.94997i	−0.0902182	+	0.0655474i
$886$	−1.25196	−	3.85312i	−0.0420603	−	0.129448i
$887$	−14.0070	+	43.1092i	−0.470310	+	1.44746i	0.381871	+	0.924216i	$0.375280\pi$
$887$	−14.0070	+	43.1092i	−0.470310	+	1.44746i	−0.852180	+	0.523248i	$0.824720\pi$
$888$	−15.8158	−	11.4908i	−0.530742	−	0.385607i
$889$	17.8534	−	54.9472i	0.598785	−	1.84287i
$890$	2.34725	−	1.70538i	0.0786800	−	0.0571644i
$891$	−7.26828	+	5.28071i	−0.243496	+	0.176910i
$892$	−4.81912	−	3.50130i	−0.161356	−	0.117232i
$893$	0.169271			0.00566444
$894$	−3.10679			−0.103907
$895$	16.0837	+	11.6855i	0.537620	+	0.390604i
$896$	12.2135	+	37.5891i	0.408023	+	1.25576i
$897$	2.98363	−	9.18266i	0.0996204	−	0.306600i
$898$	−6.75503			−0.225418
$899$	−11.1459	−	53.8793i	−0.371735	−	1.79698i
$900$	37.2173			1.24058
$901$	−2.13222	+	6.56229i	−0.0710345	+	0.218622i
$902$	5.10500	+	15.7116i	0.169978	+	0.523138i
$903$	−2.36945	−	1.72151i	−0.0788504	−	0.0572882i
$904$	2.50722			0.0833889
$905$	−14.9014			−0.495340
$906$	12.3589	+	8.97930i	0.410599	+	0.298317i
$907$	−35.1297	+	25.5232i	−1.16646	+	0.847484i	−0.990581	−	0.136927i	$-0.956277\pi$
$907$	−35.1297	+	25.5232i	−1.16646	+	0.847484i	−0.175881	+	0.984411i	$0.556277\pi$
$908$	−3.02835	+	2.20022i	−0.100499	+	0.0730170i
$909$	11.1379	−	34.2789i	0.369420	−	1.13696i
$910$	0.976045	+	0.709138i	0.0323556	+	0.0235077i
$911$	7.06145	−	21.7329i	0.233956	−	0.720043i	−0.763302	−	0.646042i	$-0.776423\pi$
$911$	7.06145	−	21.7329i	0.233956	−	0.720043i	0.997258	−	0.0740013i	$-0.0235769\pi$
$912$	1.13344	+	3.48836i	0.0375318	+	0.115511i
$913$	−10.8870	+	7.90986i	−0.360307	+	0.261778i
$914$	0.945583	+	2.91021i	0.0312771	+	0.0962611i
$915$	−1.88887	−	5.81334i	−0.0624441	−	0.192183i
$916$	8.71275	−	6.33018i	0.287877	−	0.209155i
$917$	12.9227	+	39.7721i	0.426746	+	1.31339i
$918$	−0.539065	+	1.65907i	−0.0177918	+	0.0547575i
$919$	−14.9185	−	10.8389i	−0.492116	−	0.357543i	0.313881	−	0.949462i	$-0.398371\pi$
$919$	−14.9185	−	10.8389i	−0.492116	−	0.357543i	−0.805998	+	0.591919i	$0.798371\pi$
$920$	1.06143	−	3.26674i	0.0349942	−	0.107701i
$921$	−4.06326	+	2.95213i	−0.133889	+	0.0972760i
$922$	3.07847	−	2.23664i	0.101384	−	0.0736597i
$923$	8.10646	+	5.88969i	0.266827	+	0.193861i
$924$	134.748			4.43288
$925$	−26.9362			−0.885657
$926$	−5.13277	−	3.72917i	−0.168673	−	0.122548i
$927$	−22.7521	−	70.0238i	−0.747278	−	2.29988i
$928$	−9.85076	+	30.3175i	−0.323367	+	0.995221i
$929$	5.79581			0.190154			0.0950772	−	0.995470i	$-0.469690\pi$
$929$	5.79581			0.190154			0.0950772	+	0.995470i	$0.469690\pi$
$930$	−3.33233	+	1.89978i	−0.109271	+	0.0622963i
$931$	6.15123			0.201598
$932$	1.11169	−	3.42142i	0.0364145	−	0.112072i
$933$	20.9024	+	64.3308i	0.684313	+	2.10610i
$934$	7.90875	+	5.74604i	0.258782	+	0.188016i
$935$	−6.52390			−0.213354
$936$	5.10802			0.166961
$937$	17.7461	+	12.8933i	0.579741	+	0.421207i	0.838631	−	0.544700i	$-0.183357\pi$
$937$	17.7461	+	12.8933i	0.579741	+	0.421207i	−0.258890	+	0.965907i	$0.583357\pi$
$938$	−3.04357	+	2.21128i	−0.0993761	+	0.0722010i
$939$	45.1163	−	32.7789i	1.47231	−	1.06970i
$940$	−0.233976	+	0.720105i	−0.00763146	+	0.0234872i
$941$	10.9899	+	7.98460i	0.358259	+	0.260291i	0.752326	−	0.658791i	$-0.228932\pi$
$941$	10.9899	+	7.98460i	0.358259	+	0.260291i	−0.394066	+	0.919082i	$0.628932\pi$
$942$	−4.42357	+	13.6144i	−0.144128	+	0.443580i
$943$	11.9303	+	36.7175i	0.388503	+	1.19569i
$944$	−3.89659	+	2.83104i	−0.126823	+	0.0921425i
$945$	5.75241	+	17.7041i	0.187126	+	0.575914i
$946$	0.102111	+	0.314264i	0.00331991	+	0.0102176i
$947$	33.0429	−	24.0071i	1.07375	−	0.780126i	0.0971681	−	0.995268i	$-0.469022\pi$
$947$	33.0429	−	24.0071i	1.07375	−	0.780126i	0.976583	+	0.215142i	$0.0690216\pi$
$948$	6.60630	+	20.3321i	0.214563	+	0.660355i
$949$	−4.36772	+	13.4425i	−0.141782	+	0.436361i
$950$	−0.366709	−	0.266430i	−0.0118976	−	0.00864412i
$951$	27.6485	−	85.0934i	0.896564	−	2.75934i
$952$	−6.09158	+	4.42579i	−0.197429	+	0.143441i
$953$	27.8151	−	20.2089i	0.901020	−	0.654629i	−0.0377080	−	0.999289i	$-0.512006\pi$
$953$	27.8151	−	20.2089i	0.901020	−	0.654629i	0.938728	+	0.344660i	$0.112006\pi$
$954$	−5.18745	−	3.76891i	−0.167950	−	0.122023i
$955$	15.3968			0.498230
$956$	−30.3420			−0.981331
$957$	116.332	+	84.5200i	3.76047	+	2.73214i
$958$	−2.63395	−	8.10648i	−0.0850992	−	0.261908i
$959$	−30.0330	+	92.4322i	−0.969817	+	2.98479i
$960$	−14.8734			−0.480036
$961$	15.7917	−	26.6762i	0.509410	−	0.860524i
$962$	−1.81046			−0.0583716
$963$	−0.0591028	+	0.181900i	−0.00190456	+	0.00586164i
$964$	−13.9710	−	42.9983i	−0.449975	−	1.38488i
$965$	−15.7113	−	11.4149i	−0.505764	−	0.367459i
$966$	−13.2260			−0.425540
$967$	−11.6644			−0.375103			−0.187551	−	0.982255i	$-0.560055\pi$
$967$	−11.6644			−0.375103			−0.187551	+	0.982255i	$0.560055\pi$
$968$	−15.2118	−	11.0520i	−0.488927	−	0.355226i
$969$	−1.18133	+	0.858285i	−0.0379497	+	0.0275721i
$970$	1.70838	−	1.24121i	0.0548528	−	0.0398529i
$971$	2.44306	−	7.51897i	0.0784016	−	0.241295i	−0.904172	−	0.427168i	$-0.859511\pi$
$971$	2.44306	−	7.51897i	0.0784016	−	0.241295i	0.982574	+	0.185873i	$0.0595112\pi$
$972$	−27.6850	−	20.1143i	−0.887997	−	0.645168i
$973$	6.96374	−	21.4322i	0.223247	−	0.687085i
$974$	1.25773	+	3.87089i	0.0403002	+	0.124031i
$975$	9.41539	−	6.84068i	0.301534	−	0.219077i
$976$	−2.74234	−	8.44004i	−0.0877800	−	0.270159i
$977$	8.39039	+	25.8230i	0.268432	+	0.826150i	0.990883	+	0.134727i	$0.0430158\pi$
$977$	8.39039	+	25.8230i	0.268432	+	0.826150i	−0.722450	+	0.691423i	$0.756984\pi$
$978$	3.22197	−	2.34090i	0.103027	−	0.0748536i
$979$	−18.9368	−	58.2814i	−0.605222	−	1.86268i
$980$	−8.50259	+	26.1683i	−0.271605	+	0.835915i
$981$	4.03890	+	2.93443i	0.128952	+	0.0936891i
$982$	0.886841	−	2.72942i	0.0283002	−	0.0870992i
$983$	−22.8013	+	16.5661i	−0.727250	+	0.528378i	−0.888692	−	0.458504i	$-0.848385\pi$
$983$	−22.8013	+	16.5661i	−0.727250	+	0.528378i	0.161442	+	0.986882i	$0.448385\pi$
$984$	−27.3237	+	19.8518i	−0.871047	+	0.632853i
$985$	−4.82194	−	3.50334i	−0.153640	−	0.111626i
$986$	−3.93492			−0.125313
$987$	5.95342			0.189499
$988$	0.586840	+	0.426365i	0.0186699	+	0.0135645i
$989$	0.238630	+	0.734428i	0.00758799	+	0.0233534i
$990$	1.87343	−	5.76582i	0.0595415	−	0.183250i
$991$	−0.672075			−0.0213492			−0.0106746	−	0.999943i	$-0.503398\pi$
$991$	−0.672075			−0.0213492			−0.0106746	+	0.999943i	$0.503398\pi$
$992$	−15.6033	+	8.89554i	−0.495405	+	0.282434i
$993$	−57.0124			−1.80923
$994$	4.24153	−	13.0541i	0.134533	−	0.414051i
$995$	−0.0560582	−	0.172529i	−0.00177716	−	0.00546955i
$996$	−10.8998	−	7.91919i	−0.345374	−	0.250929i
$997$	53.6316			1.69853			0.849264	−	0.527968i	$-0.177046\pi$
$997$	53.6316			1.69853			0.849264	+	0.527968i	$0.177046\pi$
$998$	−4.93425			−0.156191
$999$	−22.5997	−	16.4196i	−0.715021	−	0.519493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.8	yes	68
31.4	even	5	inner	403.2.k.e.66.8	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.8	✓	68	31.4	even	5	inner
403.2.k.e.287.8	yes	68	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0877385 + 0.270031i) q^{2} +(0.851349 + 2.62018i) q^{3} +(1.55282 + 1.12819i) q^{4} +0.880734 q^{5} -0.782228 q^{6} +(-3.90316 - 2.83581i) q^{7} +(-0.900292 + 0.654101i) q^{8} +(-3.71351 + 2.69802i) q^{9} +O(q^{10})\)	\(q+(-0.0877385 + 0.270031i) q^{2} +(0.851349 + 2.62018i) q^{3} +(1.55282 + 1.12819i) q^{4} +0.880734 q^{5} -0.782228 q^{6} +(-3.90316 - 2.83581i) q^{7} +(-0.900292 + 0.654101i) q^{8} +(-3.71351 + 2.69802i) q^{9} +(-0.0772743 + 0.237826i) q^{10} +(4.27300 + 3.10452i) q^{11} +(-1.63407 + 5.02914i) q^{12} +(0.309017 + 0.951057i) q^{13} +(1.10822 - 0.805167i) q^{14} +(0.749812 + 2.30768i) q^{15} +(1.08861 + 3.35039i) q^{16} +(-1.13461 + 0.824339i) q^{17} +(-0.402733 - 1.23948i) q^{18} +(0.116784 - 0.359424i) q^{19} +(1.36762 + 0.993632i) q^{20} +(4.10740 - 12.6413i) q^{21} +(-1.21322 + 0.881459i) q^{22} +(-2.83527 + 2.05994i) q^{23} +(-2.48033 - 1.80206i) q^{24} -4.22431 q^{25} -0.283928 q^{26} +(-3.54422 - 2.57503i) q^{27} +(-2.86156 - 8.80699i) q^{28} +(3.05368 - 9.39825i) q^{29} -0.688935 q^{30} +(4.83693 - 2.75756i) q^{31} -3.22587 q^{32} +(-4.49658 + 13.8391i) q^{33} +(-0.123049 - 0.378706i) q^{34} +(-3.43765 - 2.49760i) q^{35} -8.81026 q^{36} +6.37648 q^{37} +(0.0868093 + 0.0630706i) q^{38} +(-2.22886 + 1.61936i) q^{39} +(-0.792919 + 0.576089i) q^{40} +(3.40418 - 10.4770i) q^{41} +(3.05316 + 2.21825i) q^{42} +(0.0680907 - 0.209562i) q^{43} +(3.13271 + 9.64148i) q^{44} +(-3.27061 + 2.37624i) q^{45} +(-0.307487 - 0.946349i) q^{46} +(0.138409 + 0.425979i) q^{47} +(-7.85185 + 5.70470i) q^{48} +(5.02972 + 15.4799i) q^{49} +(0.370635 - 1.14070i) q^{50} +(-3.12586 - 2.27107i) q^{51} +(-0.593123 + 1.82544i) q^{52} +(3.98033 - 2.89188i) q^{53} +(1.00630 - 0.731122i) q^{54} +(3.76338 + 2.73425i) q^{55} +5.36890 q^{56} +1.04118 q^{57} +(2.26990 + 1.64918i) q^{58} +(0.422494 + 1.30030i) q^{59} +(-1.43918 + 4.42933i) q^{60} -2.51912 q^{61} +(0.320244 + 1.54807i) q^{62} +22.1455 q^{63} +(-1.89418 + 5.82969i) q^{64} +(0.272162 + 0.837628i) q^{65} +(-3.34246 - 2.42844i) q^{66} -2.74637 q^{67} -2.69184 q^{68} +(-7.81124 - 5.67519i) q^{69} +(0.976045 - 0.709138i) q^{70} +(8.10646 - 5.88969i) q^{71} +(1.57847 - 4.85802i) q^{72} +(11.4349 + 8.30791i) q^{73} +(-0.559463 + 1.72185i) q^{74} +(-3.59636 - 11.0685i) q^{75} +(0.586840 - 0.426365i) q^{76} +(-7.87438 - 24.2349i) q^{77} +(-0.241722 - 0.743943i) q^{78} +(3.27074 - 2.37633i) q^{79} +(0.958774 + 2.95080i) q^{80} +(-0.525631 + 1.61773i) q^{81} +(2.53044 + 1.83847i) q^{82} +(-0.787331 + 2.42316i) q^{83} +(20.6397 - 14.9956i) q^{84} +(-0.999286 + 0.726024i) q^{85} +(0.0506141 + 0.0367733i) q^{86} +27.2249 q^{87} -5.87761 q^{88} +(-9.38656 - 6.81974i) q^{89} +(-0.354701 - 1.09166i) q^{90} +(1.49088 - 4.58844i) q^{91} -6.72665 q^{92} +(11.3432 + 10.3260i) q^{93} -0.127172 q^{94} +(0.102856 - 0.316557i) q^{95} +(-2.74634 - 8.45236i) q^{96} +(-6.83174 - 4.96355i) q^{97} -4.62136 q^{98} -24.2439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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