LMFDB - Embedded newform 378.2.v.a.205.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			205.10
Character	$\chi$	$=$	378.205
Dual form			378.2.v.a.319.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.25695 - 1.19167i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.748511 + 0.628075i) q^{5} +(0.773574 - 1.54970i) q^{6} +(1.70861 + 2.02007i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.159855 - 2.99574i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.25695 - 1.19167i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.748511 + 0.628075i) q^{5} +(0.773574 - 1.54970i) q^{6} +(1.70861 + 2.02007i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.159855 - 2.99574i) q^{9} +(-0.488556 + 0.846204i) q^{10} +(-0.810909 - 0.680433i) q^{11} +(0.196891 - 1.72082i) q^{12} +(3.99834 - 3.35501i) q^{13} +(2.29647 + 1.31386i) q^{14} +(-0.192385 + 1.68144i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.95072 + 5.11079i) q^{17} +(-0.874388 - 2.86975i) q^{18} +(-2.03016 - 3.51634i) q^{19} +(-0.169674 + 0.962267i) q^{20} +(4.55488 + 0.503035i) q^{21} +(-0.994727 - 0.362051i) q^{22} +(1.97085 + 0.717332i) q^{23} +(-0.403539 - 1.68439i) q^{24} +(-0.702451 + 3.98380i) q^{25} +(2.60973 - 4.52019i) q^{26} +(-3.36899 - 3.95599i) q^{27} +(2.60734 + 0.449190i) q^{28} +(-3.91297 - 3.28337i) q^{29} +(0.394303 + 1.64583i) q^{30} +(-7.70660 + 6.46661i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.83012 + 0.111062i) q^{33} +(-1.02477 + 5.81178i) q^{34} +(-2.54766 - 0.438909i) q^{35} +(-1.80317 - 2.39762i) q^{36} +2.42788 q^{37} +(-3.11038 - 2.60992i) q^{38} +(1.02767 - 8.98178i) q^{39} +(0.169674 + 0.962267i) q^{40} +(-6.40260 + 5.37242i) q^{41} +(4.45224 - 1.08516i) q^{42} +(6.27403 - 2.28356i) q^{43} -1.05857 q^{44} +(1.76190 + 2.34274i) q^{45} +2.09734 q^{46} +(4.24578 + 3.56264i) q^{47} +(-0.955296 - 1.44479i) q^{48} +(-1.16133 + 6.90299i) q^{49} +(0.702451 + 3.98380i) q^{50} +(2.38146 + 9.94030i) q^{51} +(0.906351 - 5.14017i) q^{52} +(-1.57375 - 2.72581i) q^{53} +(-4.51885 - 2.56515i) q^{54} +1.03434 q^{55} +(2.60373 - 0.469663i) q^{56} +(-6.74212 - 2.00059i) q^{57} +(-4.79997 - 1.74705i) q^{58} +(2.16581 + 12.2829i) q^{59} +(0.933432 + 1.41172i) q^{60} +(-3.81593 - 3.20194i) q^{61} +(-5.03013 + 8.71244i) q^{62} +(6.32472 - 4.79562i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.885606 + 5.02252i) q^{65} +(-1.68177 + 0.730304i) q^{66} +(0.585437 + 0.213082i) q^{67} +(1.02477 + 5.81178i) q^{68} +(3.33209 - 1.44695i) q^{69} +(-2.54414 + 0.458913i) q^{70} +(-1.89823 - 3.28783i) q^{71} +(-2.51446 - 1.63631i) q^{72} +12.9161 q^{73} +(2.28146 - 0.830384i) q^{74} +(3.86442 + 5.84453i) q^{75} +(-3.81545 - 1.38871i) q^{76} +(-0.0110033 - 2.80068i) q^{77} +(-2.10626 - 8.79160i) q^{78} +(11.5620 - 4.20822i) q^{79} +(0.488556 + 0.846204i) q^{80} +(-8.94889 - 0.957768i) q^{81} +(-4.17900 + 7.23824i) q^{82} +(-5.08455 - 4.26644i) q^{83} +(3.81259 - 2.54248i) q^{84} +(-1.00132 - 5.67876i) q^{85} +(5.11464 - 4.29169i) q^{86} +(-8.83110 + 0.535921i) q^{87} +(-0.994727 + 0.362051i) q^{88} +(-7.53295 - 13.0475i) q^{89} +(2.45691 + 1.59886i) q^{90} +(13.6089 + 2.34453i) q^{91} +(1.97085 - 0.717332i) q^{92} +(-1.98078 + 17.3119i) q^{93} +(5.20823 + 1.89564i) q^{94} +(3.72812 + 1.35693i) q^{95} +(-1.39183 - 1.03092i) q^{96} +(-1.96702 + 0.715936i) q^{97} +(1.26967 + 6.88389i) q^{98} +(-2.16803 + 2.32050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.25695	−	1.19167i	0.725701	−	0.688010i
$3$	1.25695	−	1.19167i	0.725701	−	0.688010i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.748511	+	0.628075i	−0.334744	+	0.280884i	−0.794630	−	0.607094i	$-0.792335\pi$
$5$	−0.748511	+	0.628075i	−0.334744	+	0.280884i	0.459885	+	0.887978i	$0.347891\pi$
$6$	0.773574	−	1.54970i	0.315810	−	0.632664i
$7$	1.70861	+	2.02007i	0.645792	+	0.763513i
$7$	1.70861	+	2.02007i	0.645792	+	0.763513i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.159855	−	2.99574i	0.0532850	−	0.998579i
$10$	−0.488556	+	0.846204i	−0.154495	+	0.267593i
$11$	−0.810909	−	0.680433i	−0.244498	−	0.205158i	0.512301	−	0.858806i	$-0.328793\pi$
$11$	−0.810909	−	0.680433i	−0.244498	−	0.205158i	−0.756799	+	0.653648i	$0.773238\pi$
$12$	0.196891	−	1.72082i	0.0568377	−	0.496759i
$13$	3.99834	−	3.35501i	1.10894	−	0.930512i	0.110948	−	0.993826i	$-0.464611\pi$
$13$	3.99834	−	3.35501i	1.10894	−	0.930512i	0.997994	+	0.0633141i	$0.0201670\pi$
$14$	2.29647	+	1.31386i	0.613757	+	0.351145i
$15$	−0.192385	+	1.68144i	−0.0496736	+	0.434145i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.95072	+	5.11079i	−0.715654	+	1.23955i	0.247052	+	0.969002i	$0.420538\pi$
$17$	−2.95072	+	5.11079i	−0.715654	+	1.23955i	−0.962707	+	0.270548i	$0.912795\pi$
$18$	−0.874388	−	2.86975i	−0.206095	−	0.676406i
$19$	−2.03016	−	3.51634i	−0.465750	−	0.806703i	0.533485	−	0.845810i	$-0.320882\pi$
$19$	−2.03016	−	3.51634i	−0.465750	−	0.806703i	−0.999235	+	0.0391063i	$0.987549\pi$
$20$	−0.169674	+	0.962267i	−0.0379402	+	0.215170i
$21$	4.55488	+	0.503035i	0.993957	+	0.109771i
$22$	−0.994727	−	0.362051i	−0.212077	−	0.0771895i
$23$	1.97085	+	0.717332i	0.410951	+	0.149574i	0.539219	−	0.842166i	$-0.318719\pi$
$23$	1.97085	+	0.717332i	0.410951	+	0.149574i	−0.128268	+	0.991740i	$0.540942\pi$
$24$	−0.403539	−	1.68439i	−0.0823720	−	0.343824i
$25$	−0.702451	+	3.98380i	−0.140490	+	0.796759i
$26$	2.60973	−	4.52019i	0.511811	−	0.886483i
$27$	−3.36899	−	3.95599i	−0.648363	−	0.761331i
$28$	2.60734	+	0.449190i	0.492741	+	0.0848889i
$29$	−3.91297	−	3.28337i	−0.726620	−	0.609707i	0.202588	−	0.979264i	$-0.435065\pi$
$29$	−3.91297	−	3.28337i	−0.726620	−	0.609707i	−0.929208	+	0.369557i	$0.879509\pi$
$30$	0.394303	+	1.64583i	0.0719895	+	0.300487i
$31$	−7.70660	+	6.46661i	−1.38415	+	1.16144i	−0.416497	+	0.909137i	$0.636743\pi$
$31$	−7.70660	+	6.46661i	−1.38415	+	1.16144i	−0.967649	+	0.252300i	$0.918813\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−1.83012	+	0.111062i	−0.318584	+	0.0193335i
$34$	−1.02477	+	5.81178i	−0.175747	+	0.996712i
$35$	−2.54766	−	0.438909i	−0.430634	−	0.0741891i
$36$	−1.80317	−	2.39762i	−0.300528	−	0.399604i
$37$	2.42788			0.399141			0.199570	−	0.979883i	$-0.436045\pi$
$37$	2.42788			0.399141			0.199570	+	0.979883i	$0.436045\pi$
$38$	−3.11038	−	2.60992i	−0.504571	−	0.423385i
$39$	1.02767	−	8.98178i	0.164559	−	1.43824i
$40$	0.169674	+	0.962267i	0.0268278	+	0.152148i
$41$	−6.40260	+	5.37242i	−0.999918	+	0.839031i	−0.986973	−	0.160885i	$-0.948565\pi$
$41$	−6.40260	+	5.37242i	−0.999918	+	0.839031i	−0.0129450	+	0.999916i	$0.504121\pi$
$42$	4.45224	−	1.08516i	0.686995	−	0.167444i
$43$	6.27403	−	2.28356i	0.956781	−	0.348240i	0.184010	−	0.982924i	$-0.441092\pi$
$43$	6.27403	−	2.28356i	0.956781	−	0.348240i	0.772771	+	0.634685i	$0.218870\pi$
$44$	−1.05857			−0.159585
$45$	1.76190	+	2.34274i	0.262648	+	0.349236i
$46$	2.09734			0.309236
$47$	4.24578	+	3.56264i	0.619311	+	0.519664i	0.897587	−	0.440837i	$-0.145318\pi$
$47$	4.24578	+	3.56264i	0.619311	+	0.519664i	−0.278276	+	0.960501i	$0.589763\pi$
$48$	−0.955296	−	1.44479i	−0.137885	−	0.208537i
$49$	−1.16133	+	6.90299i	−0.165905	+	0.986142i
$50$	0.702451	+	3.98380i	0.0993415	+	0.563394i
$51$	2.38146	+	9.94030i	0.333471	+	1.39192i
$52$	0.906351	−	5.14017i	0.125688	−	0.712814i
$53$	−1.57375	−	2.72581i	−0.216171	−	0.374418i	0.737463	−	0.675387i	$-0.236023\pi$
$53$	−1.57375	−	2.72581i	−0.216171	−	0.374418i	−0.953634	+	0.300969i	$0.902690\pi$
$54$	−4.51885	−	2.56515i	−0.614937	−	0.349073i
$55$	1.03434			0.139470
$56$	2.60373	−	0.469663i	0.347938	−	0.0627614i
$57$	−6.74212	−	2.00059i	−0.893016	−	0.264985i
$58$	−4.79997	−	1.74705i	−0.630267	−	0.229398i
$59$	2.16581	+	12.2829i	0.281964	+	1.59910i	0.715933	+	0.698169i	$0.246001\pi$
$59$	2.16581	+	12.2829i	0.281964	+	1.59910i	−0.433970	+	0.900928i	$0.642887\pi$
$60$	0.933432	+	1.41172i	0.120505	+	0.182252i
$61$	−3.81593	−	3.20194i	−0.488579	−	0.409967i	0.364938	−	0.931032i	$-0.381090\pi$
$61$	−3.81593	−	3.20194i	−0.488579	−	0.409967i	−0.853517	+	0.521065i	$0.825535\pi$
$62$	−5.03013	+	8.71244i	−0.638827	+	1.10648i
$63$	6.32472	−	4.79562i	0.796840	−	0.604191i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.885606	+	5.02252i	−0.109846	+	0.622967i
$66$	−1.68177	+	0.730304i	−0.207011	+	0.0898942i
$67$	0.585437	+	0.213082i	0.0715225	+	0.0260321i	0.377534	−	0.925996i	$-0.376772\pi$
$67$	0.585437	+	0.213082i	0.0715225	+	0.0260321i	−0.306011	+	0.952028i	$0.598994\pi$
$68$	1.02477	+	5.81178i	0.124272	+	0.704782i
$69$	3.33209	−	1.44695i	0.401136	−	0.174192i
$70$	−2.54414	+	0.458913i	−0.304083	+	0.0548506i
$71$	−1.89823	−	3.28783i	−0.225278	−	0.390194i	0.731125	−	0.682244i	$-0.238996\pi$
$71$	−1.89823	−	3.28783i	−0.225278	−	0.390194i	−0.956403	+	0.292050i	$0.905662\pi$
$72$	−2.51446	−	1.63631i	−0.296332	−	0.192841i
$73$	12.9161			1.51172			0.755858	−	0.654736i	$-0.227220\pi$
$73$	12.9161			1.51172			0.755858	+	0.654736i	$0.227220\pi$
$74$	2.28146	−	0.830384i	0.265214	−	0.0965301i
$75$	3.86442	+	5.84453i	0.446224	+	0.674868i
$76$	−3.81545	−	1.38871i	−0.437662	−	0.159296i
$77$	−0.0110033	−	2.80068i	−0.00125394	−	0.319167i
$78$	−2.10626	−	8.79160i	−0.238487	−	0.995453i
$79$	11.5620	−	4.20822i	1.30082	−	0.473461i	0.403560	−	0.914953i	$-0.367773\pi$
$79$	11.5620	−	4.20822i	1.30082	−	0.473461i	0.897265	+	0.441492i	$0.145551\pi$
$80$	0.488556	+	0.846204i	0.0546222	+	0.0946085i
$81$	−8.94889	−	0.957768i	−0.994321	−	0.106419i
$82$	−4.17900	+	7.23824i	−0.461493	+	0.799330i
$83$	−5.08455	−	4.26644i	−0.558102	−	0.468303i	0.319572	−	0.947562i	$-0.396461\pi$
$83$	−5.08455	−	4.26644i	−0.558102	−	0.468303i	−0.877674	+	0.479259i	$0.840905\pi$
$84$	3.81259	−	2.54248i	0.415987	−	0.277407i
$85$	−1.00132	−	5.67876i	−0.108608	−	0.615948i
$86$	5.11464	−	4.29169i	0.551526	−	0.462785i
$87$	−8.83110	+	0.535921i	−0.946793	+	0.0574568i
$88$	−0.994727	+	0.362051i	−0.106038	+	0.0385948i
$89$	−7.53295	−	13.0475i	−0.798491	−	1.38303i	−0.920598	−	0.390511i	$-0.872298\pi$
$89$	−7.53295	−	13.0475i	−0.798491	−	1.38303i	0.122107	−	0.992517i	$-0.461035\pi$
$90$	2.45691	+	1.59886i	0.258981	+	0.168534i
$91$	13.6089	+	2.34453i	1.42660	+	0.245774i
$92$	1.97085	−	0.717332i	0.205476	−	0.0747870i
$93$	−1.98078	+	17.3119i	−0.205397	+	1.79516i
$94$	5.20823	+	1.89564i	0.537187	+	0.195520i
$95$	3.72812	+	1.35693i	0.382497	+	0.139218i
$96$	−1.39183	−	1.03092i	−0.142053	−	0.105218i
$97$	−1.96702	+	0.715936i	−0.199720	+	0.0726922i	−0.439944	−	0.898025i	$-0.645002\pi$
$97$	−1.96702	+	0.715936i	−0.199720	+	0.0726922i	0.240223	+	0.970718i	$0.422779\pi$
$98$	1.26967	+	6.88389i	0.128256	+	0.695378i
$99$	−2.16803	+	2.32050i	−0.217895	+	0.233219i
$100$	2.02263	+	3.50329i	0.202263	+	0.350329i
$101$	−13.0273	+	4.74155i	−1.29627	+	0.471802i	−0.895779	−	0.444500i	$-0.853381\pi$
$101$	−13.0273	+	4.74155i	−1.29627	+	0.471802i	−0.400487	+	0.916302i	$0.631159\pi$
$102$	5.63762	+	8.52632i	0.558208	+	0.844231i
$103$	−9.39438	+	7.88282i	−0.925656	+	0.776718i	−0.975032	−	0.222063i	$-0.928721\pi$
$103$	−9.39438	+	7.88282i	−0.925656	+	0.776718i	0.0493763	+	0.998780i	$0.484277\pi$
$104$	−0.906351	−	5.14017i	−0.0888750	−	0.504035i
$105$	−3.72532	+	2.48428i	−0.363554	+	0.242441i
$106$	−2.41112	−	2.02317i	−0.234188	−	0.196507i
$107$	−1.17938	+	2.04275i	−0.114015	+	0.197480i	−0.917386	−	0.397999i	$-0.869705\pi$
$107$	−1.17938	+	2.04275i	−0.114015	+	0.197480i	0.803370	+	0.595480i	$0.203038\pi$
$108$	−5.12366	−	0.864918i	−0.493025	−	0.0832267i
$109$	−1.50717	−	2.61050i	−0.144361	−	0.250041i	0.784773	−	0.619783i	$-0.212779\pi$
$109$	−1.50717	−	2.61050i	−0.144361	−	0.250041i	−0.929134	+	0.369742i	$0.879446\pi$
$110$	0.971960	−	0.353764i	0.0926727	−	0.0337301i
$111$	3.05173	−	2.89323i	0.289657	−	0.274613i
$112$	2.28607	−	1.33187i	0.216014	−	0.125850i
$113$	6.39460	+	2.32744i	0.601553	+	0.218947i	0.624803	−	0.780782i	$-0.285179\pi$
$113$	6.39460	+	2.32744i	0.601553	+	0.218947i	−0.0232501	+	0.999730i	$0.507401\pi$
$114$	−7.01976	+	0.425999i	−0.657461	+	0.0398985i
$115$	−1.92574	+	0.700914i	−0.179577	+	0.0653605i
$116$	−5.10802			−0.474268
$117$	−9.41157	−	12.5143i	−0.870100	−	1.15695i
$118$	6.23619	+	10.8014i	0.574088	+	0.994349i
$119$	−15.3658	+	2.77169i	−1.40858	+	0.254080i
$120$	1.35997	+	1.00733i	0.124148	+	0.0919561i
$121$	−1.71555	−	9.72935i	−0.155959	−	0.884486i
$122$	−4.68093	−	1.70372i	−0.423791	−	0.154247i
$123$	−1.64562	+	14.3826i	−0.148380	+	1.29684i
$124$	−1.74694	+	9.90742i	−0.156880	+	0.889712i
$125$	−4.41911	−	7.65413i	−0.395257	−	0.684606i
$126$	4.30309	−	6.66959i	0.383350	−	0.594174i
$127$	2.92741	−	5.07042i	0.259765	−	0.449927i	−0.706414	−	0.707799i	$-0.749688\pi$
$127$	2.92741	−	5.07042i	0.259765	−	0.449927i	0.966179	+	0.257872i	$0.0830214\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	5.16491	−	10.3469i	0.454745	−	0.910993i
$130$	0.885606	+	5.02252i	0.0776728	+	0.440504i
$131$	5.95613	+	2.16785i	0.520389	+	0.189406i	0.588842	−	0.808248i	$-0.299584\pi$
$131$	5.95613	+	2.16785i	0.520389	+	0.189406i	−0.0684528	+	0.997654i	$0.521806\pi$
$132$	−1.33057	+	1.26146i	−0.115811	+	0.109796i
$133$	3.63449	−	10.1091i	0.315151	−	0.876569i
$134$	0.623009			0.0538198
$135$	5.00639	+	0.845121i	0.430882	+	0.0727365i
$136$	2.95072	+	5.11079i	0.253022	+	0.438247i
$137$	2.87155	−	16.2854i	0.245333	−	1.39135i	−0.574384	−	0.818586i	$-0.694759\pi$
$137$	2.87155	−	16.2854i	0.245333	−	1.39135i	0.819718	−	0.572768i	$-0.194130\pi$
$138$	2.63625	−	2.49933i	0.224413	−	0.212757i
$139$	2.34880	+	13.3207i	0.199223	+	1.12985i	0.906276	+	0.422687i	$0.138913\pi$
$139$	2.34880	+	13.3207i	0.199223	+	1.12985i	−0.707053	+	0.707161i	$0.749976\pi$
$140$	−2.23375	+	1.30138i	−0.188786	+	0.109987i
$141$	9.58223	−	0.581504i	0.806969	−	0.0489714i
$142$	−2.90826	−	2.44032i	−0.244055	−	0.204787i
$143$	−5.52515			−0.462037
$144$	−2.92247	−	0.677631i	−0.243539	−	0.0564692i
$145$	4.99111			0.414489
$146$	12.1372	−	4.41757i	1.00448	−	0.365600i
$147$	6.76634	+	10.0607i	0.558078	+	0.829789i
$148$	1.85986	−	1.56061i	0.152880	−	0.128281i
$149$	1.00172	+	5.68105i	0.0820643	+	0.465410i	0.997952	+	0.0639741i	$0.0203775\pi$
$149$	1.00172	+	5.68105i	0.0820643	+	0.465410i	−0.915887	+	0.401436i	$0.868511\pi$
$150$	5.63031	+	4.17035i	0.459713	+	0.340508i
$151$	−7.66902	−	6.43507i	−0.624096	−	0.523679i	0.274992	−	0.961446i	$-0.411325\pi$
$151$	−7.66902	−	6.43507i	−0.624096	−	0.523679i	−0.899088	+	0.437768i	$0.855769\pi$
$152$	−4.06032			−0.329335
$153$	14.8389	+	9.65657i	1.19966	+	0.780687i
$154$	−0.968229	−	2.62802i	−0.0780221	−	0.211772i
$155$	1.70696	−	9.68065i	0.137106	−	0.777569i
$156$	−4.98614	−	7.54102i	−0.399211	−	0.603765i
$157$	−2.14675	−	12.1748i	−0.171329	−	0.971657i	−0.942296	−	0.334781i	$-0.891338\pi$
$157$	−2.14675	−	12.1748i	−0.171329	−	0.971657i	0.770967	−	0.636876i	$-0.219774\pi$
$158$	9.42542	−	7.90886i	0.749846	−	0.629195i
$159$	−5.22638	−	1.55083i	−0.414479	−	0.122988i
$160$	0.748511	+	0.628075i	0.0591750	+	0.0496537i
$161$	1.91835	+	5.20689i	0.151187	+	0.410360i
$162$	−8.73678	+	2.16069i	−0.686427	+	0.169760i
$163$	−7.16497	+	12.4101i	−0.561203	+	0.972033i	0.436188	+	0.899855i	$0.356328\pi$
$163$	−7.16497	+	12.4101i	−0.561203	+	0.972033i	−0.997392	+	0.0721774i	$0.977005\pi$
$164$	−1.45135	+	8.23102i	−0.113332	+	0.642735i
$165$	1.30011	−	1.23259i	0.101214	−	0.0959568i
$166$	−6.23713	−	2.27013i	−0.484095	−	0.176196i
$167$	−2.82345	−	1.02765i	−0.218485	−	0.0795220i	0.230459	−	0.973082i	$-0.425977\pi$
$167$	−2.82345	−	1.02765i	−0.218485	−	0.0795220i	−0.448944	+	0.893560i	$0.648200\pi$
$168$	2.71308	−	3.69313i	0.209319	−	0.284931i
$169$	2.47324	−	14.0265i	0.190250	−	1.07896i
$170$	−2.88318	−	4.99382i	−0.221130	−	0.383008i
$171$	−10.8586	+	5.51972i	−0.830375	+	0.422104i
$172$	3.33834	−	5.78218i	0.254546	−	0.440887i
$173$	2.86893	−	16.2705i	0.218121	−	1.23702i	−0.657287	−	0.753640i	$-0.728296\pi$
$173$	2.86893	−	16.2705i	0.218121	−	1.23702i	0.875408	−	0.483384i	$-0.160593\pi$
$174$	−8.11522	+	3.52402i	−0.615214	+	0.267155i
$175$	−9.24774	+	5.38774i	−0.699064	+	0.407275i
$176$	−0.810909	+	0.680433i	−0.0611246	+	0.0512896i
$177$	17.3594	+	12.8581i	1.30482	+	0.966472i
$178$	−11.5412	−	9.68418i	−0.865046	−	0.725860i
$179$	0.596177	−	1.03261i	0.0445604	−	0.0771808i	−0.842885	−	0.538094i	$-0.819145\pi$
$179$	0.596177	−	1.03261i	0.0445604	−	0.0771808i	0.887445	+	0.460913i	$0.152478\pi$
$180$	2.85558	+	0.662121i	0.212842	+	0.0493516i
$181$	4.80136	−	8.31619i	0.356882	−	0.618138i	−0.630556	−	0.776144i	$-0.717173\pi$
$181$	4.80136	−	8.31619i	0.356882	−	0.618138i	0.987438	+	0.158006i	$0.0505065\pi$
$182$	13.5901	−	2.45139i	1.00736	−	0.181709i
$183$	−8.61208	+	0.522630i	−0.636624	+	0.0386339i
$184$	1.60665	−	1.34814i	0.118444	−	0.0993864i
$185$	−1.81729	+	1.52489i	−0.133610	+	0.112112i
$186$	4.05970	+	16.9454i	0.297672	+	1.24249i
$187$	5.87032	−	2.13662i	0.429280	−	0.156245i
$188$	5.54248			0.404227
$189$	2.23508	−	13.5648i	0.162578	−	0.986696i
$190$	3.96739			0.287824
$191$	21.8977	−	7.97012i	1.58446	−	0.576698i	0.608296	−	0.793711i	$-0.291854\pi$
$191$	21.8977	−	7.97012i	1.58446	−	0.576698i	0.976169	+	0.217013i	$0.0696313\pi$
$192$	−1.66049	−	0.492718i	−0.119836	−	0.0355589i
$193$	−8.14592	+	6.83523i	−0.586356	+	0.492011i	−0.887027	−	0.461717i	$-0.847234\pi$
$193$	−8.14592	+	6.83523i	−0.586356	+	0.492011i	0.300672	+	0.953728i	$0.402789\pi$
$194$	−1.60353	+	1.34552i	−0.115127	+	0.0966026i
$195$	4.87202	+	7.36842i	0.348892	+	0.527663i
$196$	3.54753	+	6.03449i	0.253395	+	0.431035i
$197$	5.73952	−	9.94114i	0.408924	−	0.708277i	−0.585846	−	0.810423i	$-0.699238\pi$
$197$	5.73952	−	9.94114i	0.408924	−	0.708277i	0.994769	+	0.102146i	$0.0325709\pi$
$198$	−1.24362	+	2.92207i	−0.0883804	+	0.207662i
$199$	7.33384	−	12.7026i	0.519882	−	0.900463i	−0.479850	−	0.877350i	$-0.659309\pi$
$199$	7.33384	−	12.7026i	0.519882	−	0.900463i	0.999733	−	0.0231125i	$-0.00735760\pi$
$200$	3.09884	+	2.60024i	0.219121	+	0.183865i
$201$	0.989788	−	0.429813i	0.0698143	−	0.0303167i
$202$	−10.6200	+	8.91120i	−0.747218	+	0.626990i
$203$	−0.0530955	−	13.5144i	−0.00372658	−	0.948528i
$204$	8.21380	+	6.08394i	0.575081	+	0.425961i
$205$	1.41813	−	8.04263i	0.0990467	−	0.561722i
$206$	−6.13175	+	10.6205i	−0.427219	+	0.739965i
$207$	2.46399	−	5.78949i	0.171259	−	0.402397i
$208$	−2.60973	−	4.52019i	−0.180952	−	0.313419i
$209$	−0.746360	+	4.23282i	−0.0516268	+	0.292790i
$210$	−2.65098	+	3.60860i	−0.182935	+	0.249017i
$211$	24.3633	+	8.86753i	1.67724	+	0.610466i	0.992927	−	0.118723i	$-0.0378800\pi$
$211$	24.3633	+	8.86753i	1.67724	+	0.610466i	0.684313	+	0.729188i	$0.260102\pi$
$212$	−2.95767	−	1.07651i	−0.203134	−	0.0739347i
$213$	−6.30398	−	1.87058i	−0.431942	−	0.128170i
$214$	−0.409595	+	2.32293i	−0.0279994	+	0.158792i
$215$	−3.26193	+	5.64984i	−0.222462	+	0.385316i
$216$	−5.11049	+	0.939639i	−0.347725	+	0.0639343i
$217$	−26.2305	−	4.51896i	−1.78064	−	0.306767i
$218$	−2.30913	−	1.93759i	−0.156394	−	0.131230i
$219$	16.2349	−	15.3917i	1.09705	−	1.04007i
$220$	0.792349	−	0.664860i	0.0534201	−	0.0448248i
$221$	5.34877	+	30.3344i	0.359798	+	2.04051i
$222$	1.87814	−	3.76250i	0.126053	−	0.252522i
$223$	0.177100	−	1.00439i	0.0118595	−	0.0672586i	−0.978304	−	0.207176i	$-0.933573\pi$
$223$	0.177100	−	1.00439i	0.0118595	−	0.0672586i	0.990163	+	0.139918i	$0.0446838\pi$
$224$	1.69268	−	2.03343i	0.113097	−	0.135864i
$225$	11.8221	+	2.74119i	0.788141	+	0.182746i
$226$	6.80499			0.452661
$227$	17.8112	+	14.9454i	1.18217	+	0.991961i	0.999962	+	0.00870114i	$0.00276969\pi$
$227$	17.8112	+	14.9454i	1.18217	+	0.991961i	0.182211	+	0.983260i	$0.441675\pi$
$228$	−6.45072	+	2.80121i	−0.427209	+	0.185515i
$229$	−0.672359	−	3.81314i	−0.0444307	−	0.251979i	0.954500	−	0.298211i	$-0.0963899\pi$
$229$	−0.672359	−	3.81314i	−0.0444307	−	0.251979i	−0.998931	+	0.0462317i	$0.985279\pi$
$230$	−1.56988	+	1.31729i	−0.103515	+	0.0868593i
$231$	−3.35131	−	3.50721i	−0.220500	−	0.230757i
$232$	−4.79997	+	1.74705i	−0.315133	+	0.114699i
$233$	12.0645			0.790369			0.395185	−	0.918602i	$-0.370681\pi$
$233$	12.0645			0.790369			0.395185	+	0.918602i	$0.370681\pi$
$234$	−13.1241	−	8.54065i	−0.857951	−	0.558320i
$235$	−5.41562			−0.353276
$236$	9.55439	+	8.01709i	0.621938	+	0.521868i
$237$	9.51806	−	19.0676i	0.618264	−	1.23857i
$238$	−13.4911	+	7.85993i	−0.874499	+	0.509484i
$239$	−2.50772	−	14.2220i	−0.162211	−	0.919944i	−0.951894	−	0.306429i	$-0.900866\pi$
$239$	−2.50772	−	14.2220i	−0.162211	−	0.919944i	0.789683	−	0.613515i	$-0.210245\pi$
$240$	1.62249	+	0.481441i	0.104731	+	0.0310769i
$241$	2.72038	−	15.4280i	0.175235	−	0.993807i	−0.762637	−	0.646826i	$-0.776096\pi$
$241$	2.72038	−	15.4280i	0.175235	−	0.993807i	0.937872	−	0.346981i	$-0.112793\pi$
$242$	−4.93972	−	8.55584i	−0.317537	−	0.549990i
$243$	−12.3897	+	9.46024i	−0.794798	+	0.606875i
$244$	−4.98134			−0.318897
$245$	−3.46633	−	5.89637i	−0.221456	−	0.376705i
$246$	3.37278	+	14.0781i	0.215040	+	0.897587i
$247$	−19.9146	−	7.24833i	−1.26714	−	0.461200i
$248$	1.74694	+	9.90742i	0.110931	+	0.629122i
$249$	−11.4752	+	0.696381i	−0.727213	+	0.0441314i
$250$	−6.77047	−	5.68110i	−0.428202	−	0.359304i
$251$	11.1712	−	19.3492i	0.705123	−	1.22131i	−0.261525	−	0.965197i	$-0.584225\pi$
$251$	11.1712	−	19.3492i	0.705123	−	1.22131i	0.966647	−	0.256111i	$-0.0824414\pi$
$252$	1.76245	−	7.73911i	0.111024	−	0.487518i
$253$	−1.11009	−	1.92272i	−0.0697905	−	0.120881i
$254$	1.01668	−	5.76587i	0.0637920	−	0.361783i
$255$	−8.02581	−	5.94469i	−0.502596	−	0.372271i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	3.26076	+	18.4927i	0.203401	+	1.15354i	0.899936	+	0.436021i	$0.143613\pi$
$257$	3.26076	+	18.4927i	0.203401	+	1.15354i	−0.696536	+	0.717522i	$0.745276\pi$
$258$	1.31458	−	11.4894i	0.0818423	−	0.715299i
$259$	4.14829	+	4.90448i	0.257762	+	0.304749i
$260$	2.55000	+	4.41673i	0.158144	+	0.273914i
$261$	−10.4616	+	11.1974i	−0.647558	+	0.693100i
$262$	6.33838			0.391586
$263$	1.47205	−	0.535783i	0.0907706	−	0.0330378i	−0.296236	−	0.955115i	$-0.595731\pi$
$263$	1.47205	−	0.535783i	0.0907706	−	0.0330378i	0.387006	+	0.922077i	$0.373509\pi$
$264$	−0.818879	+	1.64046i	−0.0503985	+	0.100964i
$265$	2.88998	+	1.05187i	0.177530	+	0.0646156i
$266$	−0.0422052	−	10.7425i	−0.00258776	−	0.658666i
$267$	−25.0168	−	7.42324i	−1.53100	−	0.454295i
$268$	0.585437	−	0.213082i	0.0357612	−	0.0130160i
$269$	−6.08541	−	10.5402i	−0.371034	−	0.642650i	0.618691	−	0.785635i	$-0.287663\pi$
$269$	−6.08541	−	10.5402i	−0.371034	−	0.642650i	−0.989725	+	0.142985i	$0.954330\pi$
$270$	4.99352	−	0.918132i	0.303896	−	0.0558758i
$271$	−10.1686	+	17.6126i	−0.617700	+	1.06989i	0.372204	+	0.928151i	$0.378602\pi$
$271$	−10.1686	+	17.6126i	−0.617700	+	1.06989i	−0.989904	+	0.141737i	$0.954731\pi$
$272$	4.52076	+	3.79337i	0.274112	+	0.230007i
$273$	19.8997	−	13.2704i	1.20438	−	0.803159i
$274$	−2.87155	−	16.2854i	−0.173477	−	0.983836i
$275$	3.28033	−	2.75252i	0.197811	−	0.165983i
$276$	1.62245	−	3.25025i	0.0976598	−	0.195642i
$277$	−11.1622	+	4.06272i	−0.670673	+	0.244105i	−0.654838	−	0.755770i	$-0.727263\pi$
$277$	−11.1622	+	4.06272i	−0.670673	+	0.244105i	−0.0158355	+	0.999875i	$0.505041\pi$
$278$	6.76310	+	11.7140i	0.405624	+	0.702561i
$279$	18.1403	+	24.1207i	1.08603	+	1.44407i
$280$	−1.65394	+	1.98689i	−0.0988417	+	0.118739i
$281$	−3.28364	+	1.19515i	−0.195886	+	0.0712966i	−0.438100	−	0.898926i	$-0.644348\pi$
$281$	−3.28364	+	1.19515i	−0.195886	+	0.0712966i	0.242214	+	0.970223i	$0.422126\pi$
$282$	8.80546	−	3.82375i	0.524358	−	0.227701i
$283$	0.0158424	+	0.00576617i	0.000941734	+	0.000342763i	0.342491	−	0.939521i	$-0.388729\pi$
$283$	0.0158424	+	0.00576617i	0.000941734	+	0.000342763i	−0.341549	+	0.939864i	$0.610952\pi$
$284$	−3.56750	−	1.29847i	−0.211692	−	0.0770497i
$285$	6.30307	−	2.73709i	0.373362	−	0.162131i
$286$	−5.19195	+	1.88971i	−0.307006	+	0.111741i
$287$	−21.7922	−	3.75433i	−1.28635	−	0.221611i
$288$	−2.97798	+	0.362778i	−0.175479	+	0.0213769i
$289$	−8.91348	−	15.4386i	−0.524323	−	0.908153i
$290$	4.69010	−	1.70706i	0.275412	−	0.100242i
$291$	−1.61929	+	3.24393i	−0.0949243	+	0.190162i
$292$	9.89431	−	8.30231i	0.579020	−	0.485856i
$293$	−0.685925	−	3.89007i	−0.0400721	−	0.227260i	0.958194	−	0.286119i	$-0.0923651\pi$
$293$	−0.685925	−	3.89007i	−0.0400721	−	0.227260i	−0.998266	+	0.0588582i	$0.981254\pi$
$294$	9.79922	+	7.13970i	0.571502	+	0.416396i
$295$	−9.33571	−	7.83359i	−0.543546	−	0.456089i
$296$	1.21394	−	2.10261i	0.0705588	−	0.122211i
$297$	0.0401589	+	5.50033i	0.00233025	+	0.319161i
$298$	2.88434	+	4.99583i	0.167086	+	0.289401i
$299$	10.2868	−	3.74409i	0.594901	−	0.216526i
$300$	6.71710	+	1.99317i	0.387812	+	0.115076i
$301$	15.3328	+	8.77225i	0.883767	+	0.505624i
$302$	−9.40744	−	3.42403i	−0.541338	−	0.197031i
$303$	−10.7243	+	21.4841i	−0.616097	+	1.23423i
$304$	−3.81545	+	1.38871i	−0.218831	+	0.0796480i
$305$	4.86732			0.278702
$306$	17.2468	+	3.99900i	0.985932	+	0.228607i
$307$	4.13593	+	7.16364i	0.236050	+	0.408850i	0.959577	−	0.281445i	$-0.0908138\pi$
$307$	4.13593	+	7.16364i	0.236050	+	0.408850i	−0.723527	+	0.690296i	$0.757480\pi$
$308$	−1.80867	−	2.13837i	−0.103059	−	0.121845i
$309$	−2.41458	+	21.1033i	−0.137361	+	1.20053i
$310$	−1.70696	−	9.68065i	−0.0969488	−	0.549824i
$311$	19.8478	+	7.22401i	1.12547	+	0.409636i	0.836644	−	0.547747i	$-0.184514\pi$
$311$	19.8478	+	7.22401i	1.12547	+	0.409636i	0.288821	+	0.957383i	$0.406737\pi$
$312$	−7.26462	−	5.38088i	−0.411278	−	0.304632i
$313$	1.30467	−	7.39913i	0.0737441	−	0.418223i	−0.925479	−	0.378800i	$-0.876337\pi$
$313$	1.30467	−	7.39913i	0.0737441	−	0.418223i	0.999223	−	0.0394233i	$-0.0125521\pi$
$314$	−6.18132	−	10.7064i	−0.348832	−	0.604195i
$315$	−1.72211	+	7.56197i	−0.0970300	+	0.426069i
$316$	6.15200	−	10.6556i	0.346077	−	0.599423i
$317$	3.61993	+	3.03748i	0.203316	+	0.170602i	0.738760	−	0.673968i	$-0.235412\pi$
$317$	3.61993	+	3.03748i	0.203316	+	0.170602i	−0.535445	+	0.844570i	$0.679856\pi$
$318$	−5.44160	+	0.330227i	−0.305150	+	0.0185182i
$319$	0.938946	+	5.32503i	0.0525709	+	0.298144i
$320$	0.918185	+	0.334192i	0.0513281	+	0.0186819i
$321$	0.951853	+	3.97307i	0.0531273	+	0.221755i
$322$	3.58352	+	4.23676i	0.199702	+	0.236105i
$323$	23.9617			1.33327
$324$	−7.47089	+	5.01854i	−0.415049	+	0.278808i
$325$	10.5570	+	18.2853i	0.585599	+	1.01429i
$326$	−2.48837	+	14.1122i	−0.137818	+	0.781604i
$327$	−5.00530	−	1.48522i	−0.276794	−	0.0821331i
$328$	1.45135	+	8.23102i	0.0801375	+	0.454482i
$329$	0.0576115	+	14.6639i	0.00317623	+	0.808447i
$330$	0.800137	−	1.60292i	0.0440461	−	0.0882377i
$331$	4.19645	+	3.52124i	0.230658	+	0.193545i	0.750790	−	0.660541i	$-0.229673\pi$
$331$	4.19645	+	3.52124i	0.230658	+	0.193545i	−0.520132	+	0.854086i	$0.674117\pi$
$332$	−6.63741			−0.364275
$333$	0.388109	−	7.27329i	0.0212682	−	0.398574i
$334$	−3.00465			−0.164407
$335$	−0.572037	+	0.208205i	−0.0312537	+	0.0113754i
$336$	1.28634	−	4.39833i	0.0701756	−	0.239949i
$337$	−25.7119	+	21.5748i	−1.40062	+	1.17526i	−0.439790	+	0.898101i	$0.644947\pi$
$337$	−25.7119	+	21.5748i	−1.40062	+	1.17526i	−0.960825	+	0.277155i	$0.910609\pi$
$338$	−2.47324	−	14.0265i	−0.134527	−	0.762939i
$339$	10.8112	−	4.69475i	0.587186	−	0.254984i
$340$	−4.41729	−	3.70655i	−0.239561	−	0.201016i
$341$	10.6494			0.576700
$342$	−8.31585	+	8.90069i	−0.449670	+	0.481294i
$343$	−15.9288	+	9.44852i	−0.860072	+	0.510172i
$344$	1.15939	−	6.57525i	0.0625103	−	0.354514i
$345$	−1.58531	+	3.17586i	−0.0853503	+	0.170983i
$346$	−2.86893	−	16.2705i	−0.154235	−	0.874708i
$347$	5.78909	−	4.85762i	0.310775	−	0.260771i	−0.474038	−	0.880505i	$-0.657204\pi$
$347$	5.78909	−	4.85762i	0.310775	−	0.260771i	0.784812	+	0.619734i	$0.212759\pi$
$348$	−6.42053	+	6.08706i	−0.344177	+	0.326301i
$349$	−19.0539	−	15.9881i	−1.01993	−	0.855823i	−0.0303109	−	0.999541i	$-0.509650\pi$
$349$	−19.0539	−	15.9881i	−1.01993	−	0.855823i	−0.989619	+	0.143718i	$0.954094\pi$
$350$	−6.84732	+	8.22573i	−0.366005	+	0.439684i
$351$	−26.7428	−	4.51441i	−1.42742	−	0.240961i
$352$	−0.529283	+	0.916745i	−0.0282109	+	0.0488627i
$353$	−1.44428	+	8.19089i	−0.0768710	+	0.435957i	0.921945	+	0.387320i	$0.126599\pi$
$353$	−1.44428	+	8.19089i	−0.0768710	+	0.435957i	−0.998816	+	0.0486376i	$0.984512\pi$
$354$	20.7103	+	6.14536i	1.10074	+	0.326622i
$355$	3.48585	+	1.26875i	0.185010	+	0.0673380i
$356$	−14.1573	−	5.15284i	−0.750336	−	0.273100i
$357$	−16.0111	+	21.7948i	−0.847396	+	1.15350i
$358$	0.207050	−	1.17424i	0.0109429	−	0.0620605i
$359$	17.7714	+	30.7810i	0.937938	+	1.62456i	0.769309	+	0.638877i	$0.220601\pi$
$359$	17.7714	+	30.7810i	0.937938	+	1.62456i	0.168629	+	0.985680i	$0.446066\pi$
$360$	2.90982	−	0.354475i	0.153361	−	0.0186825i
$361$	1.25691	−	2.17703i	0.0661530	−	0.114580i
$362$	1.66749	−	9.45683i	0.0876415	−	0.497040i
$363$	−13.7505	−	10.1850i	−0.721715	−	0.534572i
$364$	11.9321	−	6.95164i	0.625411	−	0.364365i
$365$	−9.66784	+	8.11228i	−0.506038	+	0.424616i
$366$	−7.91396	+	3.43662i	−0.413669	+	0.179635i
$367$	11.7921	+	9.89472i	0.615541	+	0.516500i	0.896398	−	0.443249i	$-0.146174\pi$
$367$	11.7921	+	9.89472i	0.615541	+	0.516500i	−0.280857	+	0.959750i	$0.590619\pi$
$368$	1.04867	−	1.81635i	0.0546657	−	0.0946837i
$369$	15.0709	+	20.0393i	0.784558	+	1.04321i
$370$	−1.18615	+	2.05448i	−0.0616653	+	0.106807i
$371$	2.81740	−	7.83640i	0.146272	−	0.406846i
$372$	9.61053	+	14.5349i	0.498283	+	0.753601i
$373$	−24.8762	+	20.8736i	−1.28804	+	1.08080i	−0.295961	+	0.955200i	$0.595640\pi$
$373$	−24.8762	+	20.8736i	−1.28804	+	1.08080i	−0.992081	+	0.125596i	$0.959916\pi$
$374$	4.78553	−	4.01553i	0.247454	−	0.207638i
$375$	−14.6758	−	4.35475i	−0.757854	−	0.224878i
$376$	5.20823	−	1.89564i	0.268594	−	0.0977601i
$377$	−26.6611			−1.37312
$378$	−2.53915	−	13.5112i	−0.130600	−	0.694941i
$379$	−32.5372			−1.67132			−0.835661	−	0.549246i	$-0.814915\pi$
$379$	−32.5372			−1.67132			−0.835661	+	0.549246i	$0.814915\pi$
$380$	3.72812	−	1.35693i	0.191249	−	0.0696088i
$381$	−2.36265	−	9.86177i	−0.121042	−	0.505234i
$382$	17.8512	−	14.9789i	0.913347	−	0.766389i
$383$	20.4978	−	17.1997i	1.04739	−	0.878863i	0.0545718	−	0.998510i	$-0.482621\pi$
$383$	20.4978	−	17.1997i	1.04739	−	0.878863i	0.992817	+	0.119647i	$0.0381762\pi$
$384$	−1.72887	+	0.104918i	−0.0882260	+	0.00535406i
$385$	1.76728	+	2.08943i	0.0900687	+	0.106487i
$386$	−5.31687	+	9.20909i	−0.270621	+	0.468730i
$387$	−5.83801	−	19.1604i	−0.296763	−	0.973978i
$388$	−1.04663	+	1.81281i	−0.0531345	+	0.0920316i
$389$	−22.1722	−	18.6047i	−1.12417	−	0.943295i	−0.125367	−	0.992110i	$-0.540011\pi$
$389$	−22.1722	−	18.6047i	−1.12417	−	0.943295i	−0.998808	+	0.0488157i	$0.984455\pi$
$390$	7.09835	+	5.25772i	0.359439	+	0.266235i
$391$	−9.48157	+	7.95598i	−0.479504	+	0.402351i
$392$	5.39750	+	4.45724i	0.272615	+	0.225125i
$393$	10.0699	−	4.37284i	0.507960	−	0.220581i
$394$	1.99331	−	11.3046i	0.100422	−	0.569520i
$395$	−6.01120	+	10.4117i	−0.302456	+	0.523869i
$396$	−0.169217	+	3.17119i	−0.00850348	+	0.159358i
$397$	−1.30328	−	2.25734i	−0.0654095	−	0.113293i	0.831466	−	0.555576i	$-0.187502\pi$
$397$	−1.30328	−	2.25734i	−0.0654095	−	0.113293i	−0.896876	+	0.442283i	$0.854169\pi$
$398$	2.54702	−	14.4449i	0.127670	−	0.724055i
$399$	−7.47830	−	17.0378i	−0.374383	−	0.852954i
$400$	3.80129	+	1.38356i	0.190065	+	0.0691779i
$401$	−17.1152	−	6.22942i	−0.854692	−	0.311082i	−0.122740	−	0.992439i	$-0.539168\pi$
$401$	−17.1152	−	6.22942i	−0.854692	−	0.311082i	−0.731952	+	0.681356i	$0.761390\pi$
$402$	0.783092	−	0.742420i	0.0390571	−	0.0370285i
$403$	−9.11812	+	51.7114i	−0.454206	+	2.57593i
$404$	−6.93169	+	12.0060i	−0.344864	+	0.597322i
$405$	7.29990	−	4.90368i	0.362735	−	0.243666i
$406$	−4.67210	−	12.6813i	−0.231873	−	0.629360i
$407$	−1.96879	−	1.65201i	−0.0975892	−	0.0818871i
$408$	9.79928	+	2.90775i	0.485137	+	0.143955i
$409$	14.9335	−	12.5307i	0.738415	−	0.619603i	−0.193997	−	0.981002i	$-0.562145\pi$
$409$	14.9335	−	12.5307i	0.738415	−	0.619603i	0.932411	+	0.361399i	$0.117701\pi$
$410$	−1.41813	−	8.04263i	−0.0700366	−	0.397197i
$411$	−15.7974	−	23.8919i	−0.779226	−	1.17850i
$412$	−2.12953	+	12.0772i	−0.104915	+	0.595000i
$413$	−21.1117	+	25.3617i	−1.03884	+	1.24797i
$414$	0.335270	−	6.28308i	0.0164776	−	0.308796i
$415$	6.48549			0.318360
$416$	−3.99834	−	3.35501i	−0.196035	−	0.164493i
$417$	18.8262	+	13.9445i	0.921923	+	0.682865i
$418$	0.746360	+	4.23282i	0.0365057	+	0.207034i
$419$	−9.40025	+	7.88775i	−0.459232	+	0.385342i	−0.842848	−	0.538151i	$-0.819123\pi$
$419$	−9.40025	+	7.88775i	−0.459232	+	0.385342i	0.383616	+	0.923493i	$0.374679\pi$
$420$	−1.25690	+	4.29766i	−0.0613303	+	0.209704i
$421$	12.3299	−	4.48773i	0.600925	−	0.218719i	−0.0236029	−	0.999721i	$-0.507514\pi$
$421$	12.3299	−	4.48773i	0.600925	−	0.218719i	0.624528	+	0.781003i	$0.285292\pi$
$422$	25.9269			1.26210
$423$	11.3514	−	12.1498i	0.551926	−	0.590741i
$424$	−3.14749			−0.152856
$425$	−18.2876	−	15.3451i	−0.887080	−	0.744349i
$426$	−6.56358	+	0.398315i	−0.318007	+	0.0192984i
$427$	−0.0517787	−	13.1793i	−0.00250575	−	0.637790i
$428$	0.409595	+	2.32293i	0.0197985	+	0.112283i
$429$	−6.94485	+	6.58415i	−0.335301	+	0.317886i
$430$	−1.13286	+	6.42476i	−0.0546313	+	0.309829i
$431$	10.6837	+	18.5047i	0.514616	+	0.891341i	0.999856	+	0.0169603i	$0.00539888\pi$
$431$	10.6837	+	18.5047i	0.514616	+	0.891341i	−0.485240	+	0.874381i	$0.661268\pi$
$432$	−4.48091	+	2.63086i	−0.215588	+	0.126577i
$433$	−18.4711			−0.887667			−0.443833	−	0.896109i	$-0.646382\pi$
$433$	−18.4711			−0.887667			−0.443833	+	0.896109i	$0.646382\pi$
$434$	−26.1942	+	4.72493i	−1.25736	+	0.226804i
$435$	6.27358	−	5.94774i	0.300795	−	0.285172i
$436$	−2.83256	−	1.03097i	−0.135655	−	0.0493744i
$437$	−1.47876	−	8.38649i	−0.0707389	−	0.401180i
$438$	9.99156	−	20.0161i	0.477415	−	0.956408i
$439$	7.94595	+	6.66745i	0.379240	+	0.318220i	0.812404	−	0.583095i	$-0.198159\pi$
$439$	7.94595	+	6.66745i	0.379240	+	0.318220i	−0.433164	+	0.901315i	$0.642603\pi$
$440$	0.517169	−	0.895763i	0.0246551	−	0.0427038i
$441$	20.4939	+	4.58253i	0.975901	+	0.218216i
$442$	15.4012	+	26.6756i	0.732560	+	1.26883i
$443$	−4.08661	+	23.1763i	−0.194161	+	1.10114i	0.719448	+	0.694546i	$0.244395\pi$
$443$	−4.08661	+	23.1763i	−0.194161	+	1.10114i	−0.913609	+	0.406594i	$0.866716\pi$
$444$	0.478029	−	4.17795i	0.0226862	−	0.198277i
$445$	13.8333	+	5.03490i	0.655761	+	0.238677i
$446$	−0.177100	−	1.00439i	−0.00838594	−	0.0475590i
$447$	8.02904	+	5.94708i	0.379761	+	0.281287i
$448$	0.895126	−	2.48973i	0.0422907	−	0.117629i
$449$	12.2956	+	21.2967i	0.580267	+	1.00505i	0.995447	+	0.0953133i	$0.0303853\pi$
$449$	12.2956	+	21.2967i	0.580267	+	1.00505i	−0.415180	+	0.909739i	$0.636281\pi$
$450$	12.0467	−	1.46753i	0.567887	−	0.0691799i
$451$	8.84750			0.416612
$452$	6.39460	−	2.32744i	0.300777	−	0.109474i
$453$	−17.3081	+	1.05035i	−0.813203	+	0.0493498i
$454$	21.8487	+	7.95228i	1.02541	+	0.373219i
$455$	−11.6590	+	6.79253i	−0.546581	+	0.318439i
$456$	−5.10362	+	4.83855i	−0.238999	+	0.226586i
$457$	−9.17706	+	3.34018i	−0.429285	+	0.156247i	−0.547621	−	0.836727i	$-0.684466\pi$
$457$	−9.17706	+	3.34018i	−0.429285	+	0.156247i	0.118336	+	0.992974i	$0.462244\pi$
$458$	−1.93598	−	3.35322i	−0.0904624	−	0.156685i
$459$	30.1592	−	5.54522i	1.40771	−	0.258829i
$460$	−1.02467	+	1.77478i	−0.0477753	+	0.0827493i
$461$	18.0763	+	15.1678i	0.841896	+	0.706434i	0.957989	−	0.286804i	$-0.0925928\pi$
$461$	18.0763	+	15.1678i	0.841896	+	0.706434i	−0.116094	+	0.993238i	$0.537037\pi$
$462$	−4.34874	−	2.14948i	−0.202322	−	0.100003i
$463$	4.44046	+	25.1831i	0.206366	+	1.17036i	0.895276	+	0.445512i	$0.146978\pi$
$463$	4.44046	+	25.1831i	0.206366	+	1.17036i	−0.688910	+	0.724847i	$0.741911\pi$
$464$	−3.91297	+	3.28337i	−0.181655	+	0.152427i
$465$	−9.39056	−	14.2022i	−0.435477	−	0.658613i
$466$	11.3369	−	4.12629i	0.525171	−	0.191147i
$467$	−11.2412	−	19.4704i	−0.520182	−	0.900982i	−0.999725	−	0.0234633i	$-0.992531\pi$
$467$	−11.2412	−	19.4704i	−0.520182	−	0.900982i	0.479543	−	0.877519i	$-0.340803\pi$
$468$	−15.2537	−	3.53687i	−0.705104	−	0.163492i
$469$	0.569842	+	1.54669i	0.0263129	+	0.0714197i
$470$	−5.08902	+	1.85225i	−0.234739	+	0.0854380i
$471$	−17.2067	−	12.7450i	−0.792843	−	0.587256i
$472$	11.7202	+	4.26580i	0.539466	+	0.196350i
$473$	−6.64148	−	2.41730i	−0.305376	−	0.111148i
$474$	2.42255	−	21.1730i	0.111272	−	0.972509i
$475$	15.4345	−	5.61768i	0.708182	−	0.257757i
$476$	−9.98925	+	12.0002i	−0.457856	+	0.550026i
$477$	−8.41737	+	4.27879i	−0.385405	+	0.195913i
$478$	−7.22069	−	12.5066i	−0.330267	−	0.572039i
$479$	−11.0359	+	4.01673i	−0.504242	+	0.183529i	−0.581601	−	0.813474i	$-0.697573\pi$
$479$	−11.0359	+	4.01673i	−0.504242	+	0.183529i	0.0773591	+	0.997003i	$0.475351\pi$
$480$	1.68930	−	0.102516i	0.0771056	−	0.00467921i
$481$	9.70750	−	8.14556i	0.442624	−	0.371405i
$482$	−2.72038	−	15.4280i	−0.123910	−	0.702728i
$483$	8.61616	+	4.25877i	0.392049	+	0.193781i
$484$	−7.56809	−	6.35038i	−0.344004	−	0.288654i
$485$	1.02267	−	1.77132i	0.0464372	−	0.0804315i
$486$	−8.40689	+	13.1272i	−0.381344	+	0.595463i
$487$	−8.08445	−	14.0027i	−0.366341	−	0.634522i	0.622649	−	0.782501i	$-0.286056\pi$
$487$	−8.08445	−	14.0027i	−0.366341	−	0.634522i	−0.988990	+	0.147979i	$0.952723\pi$
$488$	−4.68093	+	1.70372i	−0.211896	+	0.0771237i
$489$	5.78268	+	24.1371i	0.261502	+	1.09152i
$490$	−5.27396	−	4.35522i	−0.238253	−	0.196749i
$491$	11.4796	+	4.17822i	0.518065	+	0.188560i	0.587801	−	0.809005i	$-0.299994\pi$
$491$	11.4796	+	4.17822i	0.518065	+	0.188560i	−0.0697365	+	0.997565i	$0.522216\pi$
$492$	7.98437	+	12.0755i	0.359963	+	0.544407i
$493$	28.3267	−	10.3101i	1.27577	−	0.464343i
$494$	−21.1927			−0.953505
$495$	0.165344	−	3.09861i	0.00743167	−	0.139272i
$496$	5.03013	+	8.71244i	0.225859	+	0.391200i
$497$	3.39831	−	9.45215i	0.152435	−	0.423987i
$498$	−10.5450	+	4.57914i	−0.472533	+	0.205196i
$499$	−5.54594	−	31.4526i	−0.248271	−	1.40801i	−0.812773	−	0.582581i	$-0.802043\pi$
$499$	−5.54594	−	31.4526i	−0.248271	−	1.40801i	0.564502	−	0.825431i	$-0.309068\pi$
$500$	−8.30521	−	3.02285i	−0.371420	−	0.135186i
$501$	−4.77356	+	2.07290i	−0.213267	+	0.0926106i
$502$	3.87973	−	22.0031i	0.173161	−	0.982044i
$503$	−11.1869	−	19.3763i	−0.498801	−	0.863948i	0.501198	−	0.865332i	$-0.332893\pi$
$503$	−11.1869	−	19.3763i	−0.498801	−	0.863948i	−0.999999	+	0.00138445i	$0.999559\pi$
$504$	−0.990768	−	7.87517i	−0.0441323	−	0.350788i
$505$	6.77303	−	11.7312i	0.301396	−	0.522033i
$506$	−1.70075	−	1.42710i	−0.0756076	−	0.0634423i
$507$	−13.6061	−	20.5779i	−0.604270	−	0.913895i
$508$	−1.01668	−	5.76587i	−0.0451078	−	0.255819i
$509$	19.2454	+	7.00476i	0.853039	+	0.310481i	0.731279	−	0.682079i	$-0.238924\pi$
$509$	19.2454	+	7.00476i	0.853039	+	0.310481i	0.121760	+	0.992560i	$0.461146\pi$
$510$	−9.57499	−	2.84119i	−0.423988	−	0.125810i
$511$	22.0685	+	26.0914i	0.976254	+	1.15421i
$512$	−1.00000			−0.0441942
$513$	−7.07101	+	19.8778i	−0.312193	+	0.877627i
$514$	9.38899	+	16.2622i	0.414131	+	0.717295i
$515$	2.08079	−	11.8008i	0.0916907	−	0.520004i
$516$	−2.69430	−	11.2461i	−0.118610	−	0.495083i
$517$	−1.01881	−	5.77795i	−0.0448071	−	0.254114i
$518$	5.57555	+	3.18990i	0.244975	+	0.140156i
$519$	−15.7829	−	23.8701i	−0.692794	−	1.04778i
$520$	3.90683	+	3.27822i	0.171326	+	0.143759i
$521$	40.7917			1.78712			0.893558	−	0.448949i	$-0.148201\pi$
$521$	40.7917			1.78712			0.893558	+	0.448949i	$0.148201\pi$
$522$	−6.00099	+	14.1002i	−0.262656	+	0.617148i
$523$	30.0762			1.31514			0.657571	−	0.753393i	$-0.271584\pi$
$523$	30.0762			1.31514			0.657571	+	0.753393i	$0.271584\pi$
$524$	5.95613	−	2.16785i	0.260195	−	0.0947031i
$525$	−5.20357	+	17.7924i	−0.227102	+	0.776522i
$526$	1.20003	−	1.00694i	0.0523237	−	0.0439048i
$527$	−10.3095	−	58.4680i	−0.449088	−	2.54691i
$528$	−0.208423	+	1.82161i	−0.00907043	+	0.0792752i
$529$	−14.2493	−	11.9566i	−0.619536	−	0.519852i
$530$	3.07545			0.133589
$531$	37.1425	−	4.52470i	1.61185	−	0.196355i
$532$	−3.71381	−	10.0802i	−0.161014	−	0.437033i
$533$	−7.57528	+	42.9616i	−0.328122	+	1.86087i
$534$	−26.0470	+	1.58068i	−1.12716	+	0.0684027i
$535$	−0.400220	−	2.26976i	−0.0173030	−	0.0981304i
$536$	0.477252	−	0.400462i	0.0206142	−	0.0172973i
$537$	−0.481161	−	2.00839i	−0.0207636	−	0.0866682i
$538$	−9.32339	−	7.82325i	−0.401960	−	0.337284i
$539$	5.63876	−	4.80749i	0.242879	−	0.207073i
$540$	4.37835	−	2.57065i	0.188414	−	0.110623i
$541$	−15.6434	+	27.0951i	−0.672561	+	1.16491i	0.304614	+	0.952476i	$0.401473\pi$
$541$	−15.6434	+	27.0951i	−0.672561	+	1.16491i	−0.977175	+	0.212434i	$0.931861\pi$
$542$	−3.53153	+	20.0283i	−0.151692	+	0.860289i
$543$	−3.87507	−	16.1747i	−0.166295	−	0.694122i
$544$	5.54554	+	2.01841i	0.237763	+	0.0865386i
$545$	2.76773	+	1.00737i	0.118557	+	0.0431510i
$546$	14.1608	−	19.2762i	0.606028	−	0.824943i
$547$	5.48496	−	31.1067i	0.234520	−	1.33003i	−0.609103	−	0.793091i	$-0.708470\pi$
$547$	5.48496	−	31.1067i	0.234520	−	1.33003i	0.843623	−	0.536937i	$-0.180419\pi$
$548$	−8.26830	−	14.3211i	−0.353204	−	0.611768i
$549$	−10.2022	+	10.9197i	−0.435418	+	0.466040i
$550$	2.14108	−	3.70847i	0.0912961	−	0.158130i
$551$	−3.60149	+	20.4251i	−0.153429	+	0.870138i
$552$	0.412948	−	3.60915i	0.0175762	−	0.153616i
$553$	28.2557	+	16.1658i	1.20156	+	0.687439i
$554$	−9.09953	+	7.63541i	−0.386602	+	0.324398i
$555$	−0.467088	+	4.08233i	−0.0198268	+	0.173285i
$556$	10.3617	+	8.69448i	0.439433	+	0.368728i
$557$	14.8948	−	25.7986i	0.631113	−	1.09312i	−0.356211	−	0.934406i	$-0.615932\pi$
$557$	14.8948	−	25.7986i	0.631113	−	1.09312i	0.987324	−	0.158715i	$-0.0507351\pi$
$558$	25.2961	+	16.4617i	1.07087	+	0.696878i
$559$	17.4244	−	30.1799i	0.736972	−	1.27647i
$560$	−0.874638	+	2.43274i	−0.0369602	+	0.102802i
$561$	4.83256	−	9.68110i	0.204031	−	0.408736i
$562$	−2.67685	+	2.24614i	−0.112916	+	0.0947479i
$563$	−24.5788	+	20.6240i	−1.03587	+	0.869199i	−0.991538	−	0.129817i	$-0.958561\pi$
$563$	−24.5788	+	20.6240i	−1.03587	+	0.869199i	−0.0443335	+	0.999017i	$0.514116\pi$
$564$	6.96663	−	6.60479i	0.293348	−	0.278112i
$565$	−6.24824	+	2.27417i	−0.262865	+	0.0956751i
$566$	0.0168591			0.000708643
$567$	−13.3554	−	19.7138i	−0.560873	−	0.827902i
$568$	−3.79646			−0.159296
$569$	−24.8649	+	9.05009i	−1.04239	+	0.379399i	−0.805786	−	0.592207i	$-0.798257\pi$
$569$	−24.8649	+	9.05009i	−1.04239	+	0.379399i	−0.236605	+	0.971606i	$0.576035\pi$
$570$	4.98681	−	4.72781i	0.208875	−	0.198026i
$571$	5.36777	−	4.50409i	0.224634	−	0.188490i	−0.523524	−	0.852011i	$-0.675383\pi$
$571$	5.36777	−	4.50409i	0.224634	−	0.188490i	0.748158	+	0.663521i	$0.230938\pi$
$572$	−4.23251	+	3.55150i	−0.176970	+	0.148496i
$573$	18.0267	−	36.1129i	0.753074	−	1.50864i
$574$	−21.7620	+	3.92544i	−0.908328	+	0.163845i
$575$	−4.24213	+	7.34759i	−0.176909	+	0.306416i
$576$	−2.67431	+	1.35943i	−0.111430	+	0.0566429i
$577$	−4.00101	+	6.92995i	−0.166564	+	0.288497i	−0.937210	−	0.348767i	$-0.886601\pi$
$577$	−4.00101	+	6.92995i	−0.166564	+	0.288497i	0.770646	+	0.637264i	$0.219934\pi$
$578$	−13.6562	−	11.4590i	−0.568025	−	0.476630i
$579$	−2.09369	+	18.2988i	−0.0870109	+	0.760472i
$580$	3.82341	−	3.20822i	0.158758	−	0.133214i
$581$	−0.0689929	−	17.5608i	−0.00286231	−	0.728545i
$582$	−0.412144	+	3.60212i	−0.0170839	+	0.149313i
$583$	−0.578566	+	3.28121i	−0.0239617	+	0.135894i
$584$	6.45805	−	11.1857i	0.267236	−	0.462866i
$585$	14.9046	+	3.45592i	0.616229	+	0.142885i
$586$	−1.97504	−	3.42087i	−0.0815882	−	0.141315i
$587$	0.0677429	−	0.384189i	0.00279605	−	0.0158572i	−0.983378	−	0.181571i	$-0.941882\pi$
$587$	0.0677429	−	0.384189i	0.00279605	−	0.0158572i	0.986174	+	0.165714i	$0.0529928\pi$
$588$	11.6502	+	3.35759i	0.480445	+	0.138465i
$589$	38.3844	+	13.9708i	1.58160	+	0.575656i
$590$	−11.4519	−	4.16817i	−0.471469	−	0.171601i
$591$	−4.63224	−	19.3351i	−0.190545	−	0.795341i
$592$	0.421597	−	2.39099i	0.0173275	−	0.0982693i
$593$	10.4446	−	18.0905i	0.428907	−	0.742890i	−0.567869	−	0.823119i	$-0.692232\pi$
$593$	10.4446	−	18.0905i	0.428907	−	0.742890i	0.996776	+	0.0802294i	$0.0255653\pi$
$594$	1.91896	+	5.15488i	0.0787358	+	0.211507i
$595$	9.76061	−	11.7255i	0.400146	−	0.480698i
$596$	4.41907	+	3.70804i	0.181012	+	0.151887i
$597$	−5.91898	−	24.7061i	−0.242248	−	1.01115i
$598$	8.38588	−	7.03659i	0.342924	−	0.287748i
$599$	−4.48759	−	25.4504i	−0.183358	−	1.03987i	−0.928047	−	0.372463i	$-0.878513\pi$
$599$	−4.48759	−	25.4504i	−0.183358	−	1.03987i	0.744689	−	0.667411i	$-0.232598\pi$
$600$	6.99372	−	0.424418i	0.285517	−	0.0173268i
$601$	−2.56287	+	14.5347i	−0.104542	+	0.592885i	0.886861	+	0.462037i	$0.152881\pi$
$601$	−2.56287	+	14.5347i	−0.104542	+	0.592885i	−0.991402	+	0.130848i	$0.958230\pi$
$602$	17.4084	+	2.99910i	0.709513	+	0.122234i
$603$	0.731922	−	1.71975i	0.0298062	−	0.0700338i
$604$	−10.0112			−0.407350
$605$	7.39487	+	6.20503i	0.300644	+	0.252270i
$606$	−2.72958	+	23.8564i	−0.110882	+	0.969101i
$607$	−1.17055	−	6.63852i	−0.0475112	−	0.269449i	0.951793	−	0.306740i	$-0.0992383\pi$
$607$	−1.17055	−	6.63852i	−0.0475112	−	0.269449i	−0.999304	+	0.0372910i	$0.988127\pi$
$608$	−3.11038	+	2.60992i	−0.126143	+	0.105846i
$609$	−16.1715	−	16.9237i	−0.655301	−	0.685784i
$610$	4.57379	−	1.66472i	0.185187	−	0.0674026i
$611$	28.9288			1.17033
$612$	17.5744	−	2.14091i	0.710403	−	0.0865412i
$613$	−16.7293			−0.675691			−0.337845	−	0.941202i	$-0.609698\pi$
$613$	−16.7293			−0.675691			−0.337845	+	0.941202i	$0.609698\pi$
$614$	6.33661	+	5.31705i	0.255725	+	0.214579i
$615$	−7.80162	−	11.7991i	−0.314592	−	0.475787i
$616$	−2.43096	−	1.39081i	−0.0979463	−	0.0560374i
$617$	6.58435	+	37.3417i	0.265076	+	1.50332i	0.768819	+	0.639467i	$0.220845\pi$
$617$	6.58435	+	37.3417i	0.265076	+	1.50332i	−0.503743	+	0.863854i	$0.668044\pi$
$618$	4.94880	+	20.6565i	0.199070	+	0.830925i
$619$	−2.50061	+	14.1817i	−0.100508	+	0.570010i	0.892412	+	0.451222i	$0.149012\pi$
$619$	−2.50061	+	14.1817i	−0.100508	+	0.570010i	−0.992920	+	0.118788i	$0.962099\pi$
$620$	−4.91500	−	8.51302i	−0.197391	−	0.341891i
$621$	−3.80203	−	10.2134i	−0.152570	−	0.409848i
$622$	21.1216			0.846898
$623$	13.4859	−	37.5100i	0.540300	−	1.50281i
$624$	−8.66688	−	2.57173i	−0.346953	−	0.102951i
$625$	−10.8913	−	3.96413i	−0.435654	−	0.158565i
$626$	−1.30467	−	7.39913i	−0.0521449	−	0.295729i
$627$	4.10598	+	6.20986i	0.163977	+	0.247998i
$628$	−9.47033	−	7.94655i	−0.377907	−	0.317102i
$629$	−7.16399	+	12.4084i	−0.285647	+	0.494755i
$630$	0.968091	+	7.69493i	0.0385697	+	0.306573i
$631$	4.99996	+	8.66019i	0.199045	+	0.344757i	0.948219	−	0.317617i	$-0.102883\pi$
$631$	4.99996	+	8.66019i	0.199045	+	0.344757i	−0.749174	+	0.662373i	$0.769549\pi$
$632$	2.13657	−	12.1171i	0.0849881	−	0.481992i
$633$	41.1907	−	17.8869i	1.63718	−	0.710942i
$634$	4.44050	+	1.61621i	0.176355	+	0.0641879i
$635$	0.993408	+	5.63390i	0.0394222	+	0.223574i
$636$	−5.00049	+	2.17145i	−0.198282	+	0.0861036i
$637$	18.5162	+	31.4968i	0.733638	+	1.24795i
$638$	2.70359	+	4.68275i	0.107036	+	0.185392i
$639$	−10.1529	+	5.16102i	−0.401643	+	0.204167i
$640$	0.977112			0.0386237
$641$	−20.7982	+	7.56994i	−0.821481	+	0.298995i	−0.718358	−	0.695674i	$-0.755106\pi$
$641$	−20.7982	+	7.56994i	−0.821481	+	0.298995i	−0.103123	+	0.994669i	$0.532884\pi$
$642$	2.25332	+	3.40791i	0.0889314	+	0.134500i
$643$	−10.5331	−	3.83372i	−0.415384	−	0.151187i	0.125870	−	0.992047i	$-0.459828\pi$
$643$	−10.5331	−	3.83372i	−0.415384	−	0.151187i	−0.541253	+	0.840860i	$0.682050\pi$
$644$	4.81647	+	2.75562i	0.189795	+	0.108586i
$645$	2.63263	+	10.9887i	0.103660	+	0.432680i
$646$	22.5166	−	8.19539i	0.885906	−	0.322443i
$647$	−8.04544	−	13.9351i	−0.316299	−	0.547846i	0.663414	−	0.748253i	$-0.269107\pi$
$647$	−8.04544	−	13.9351i	−0.316299	−	0.547846i	−0.979713	+	0.200407i	$0.935774\pi$
$648$	−5.30390	+	7.27108i	−0.208357	+	0.285635i
$649$	6.60142	−	11.4340i	0.259128	−	0.448823i
$650$	16.1743	+	13.5719i	0.634409	+	0.532332i
$651$	−38.3556	+	25.5779i	−1.50327	+	1.00248i
$652$	2.48837	+	14.1122i	0.0974519	+	0.552677i
$653$	30.0290	−	25.1973i	1.17512	−	0.986047i	0.175126	−	0.984546i	$-0.443967\pi$
$653$	30.0290	−	25.1973i	1.17512	−	0.986047i	0.999999	−	0.00150092i	$-0.000477757\pi$
$654$	−5.21142	+	0.316258i	−0.203783	+	0.0123667i
$655$	−5.81980	+	2.11823i	−0.227398	+	0.0827663i
$656$	4.17900	+	7.23824i	0.163163	+	0.282606i
$657$	2.06470	−	38.6932i	0.0805518	−	1.50957i
$658$	5.06949	+	13.7599i	0.197629	+	0.536415i
$659$	14.4891	−	5.27360i	0.564416	−	0.205430i	−0.0440243	−	0.999030i	$-0.514018\pi$
$659$	14.4891	−	5.27360i	0.564416	−	0.205430i	0.608440	+	0.793600i	$0.291796\pi$
$660$	0.203652	−	1.77991i	0.00792715	−	0.0692830i
$661$	19.4389	+	7.07517i	0.756085	+	0.275192i	0.691164	−	0.722698i	$-0.257098\pi$
$661$	19.4389	+	7.07517i	0.756085	+	0.275192i	0.0649209	+	0.997890i	$0.479321\pi$
$662$	5.14770	+	1.87361i	0.200071	+	0.0728200i
$663$	42.8717	+	31.7549i	1.66500	+	1.23326i
$664$	−6.23713	+	2.27013i	−0.242047	+	0.0880980i
$665$	3.62881	+	9.84950i	0.140719	+	0.381947i
$666$	−2.12291	−	6.96740i	−0.0822610	−	0.269981i
$667$	−5.35662	−	9.27794i	−0.207409	−	0.359243i
$668$	−2.82345	+	1.02765i	−0.109242	+	0.0397610i
$669$	−0.974288	−	1.47351i	−0.0376681	−	0.0569692i
$670$	−0.466329	+	0.391297i	−0.0180159	+	0.0151171i
$671$	0.915660	+	5.19297i	0.0353487	+	0.200472i
$672$	−0.295555	−	4.57303i	−0.0114013	−	0.176409i
$673$	19.7409	+	16.5646i	0.760955	+	0.638517i	0.938375	−	0.345618i	$-0.112331\pi$
$673$	19.7409	+	16.5646i	0.760955	+	0.638517i	−0.177420	+	0.984135i	$0.556775\pi$
$674$	−16.7822	+	29.0677i	−0.646427	+	1.11965i
$675$	18.1264	−	10.6425i	0.697686	−	0.409630i
$676$	−7.12142	−	12.3347i	−0.273901	−	0.474410i
$677$	5.76996	−	2.10009i	0.221758	−	0.0807131i	−0.228752	−	0.973485i	$-0.573465\pi$
$677$	5.76996	−	2.10009i	0.221758	−	0.0807131i	0.450510	+	0.892772i	$0.351242\pi$
$678$	8.55354	−	8.10929i	0.328497	−	0.311435i
$679$	−4.80709	−	2.75025i	−0.184479	−	0.105545i
$680$	−5.41861	−	1.97221i	−0.207794	−	0.0756309i
$681$	40.1978	−	2.43943i	1.54038	−	0.0934792i
$682$	10.0072	−	3.64233i	0.383196	−	0.139472i
$683$	−7.92922			−0.303403			−0.151702	−	0.988426i	$-0.548475\pi$
$683$	−7.92922			−0.303403			−0.151702	+	0.988426i	$0.548475\pi$
$684$	−4.77013	+	11.2081i	−0.182391	+	0.428552i
$685$	8.07906	+	13.9933i	0.308685	+	0.534658i
$686$	−11.7366	+	14.3267i	−0.448104	+	0.546995i
$687$	−5.38911	−	3.99170i	−0.205608	−	0.152293i
$688$	−1.15939	−	6.57525i	−0.0442015	−	0.250679i
$689$	−15.4375	−	5.61878i	−0.588121	−	0.214059i
$690$	−0.403496	+	3.52654i	−0.0153608	+	0.134253i
$691$	−8.78981	+	49.8495i	−0.334380	+	1.89636i	0.0988875	+	0.995099i	$0.468472\pi$
$691$	−8.78981	+	49.8495i	−0.334380	+	1.89636i	−0.433268	+	0.901265i	$0.642640\pi$
$692$	−8.26076	−	14.3081i	−0.314027	−	0.543911i
$693$	−8.39187	−	0.414740i	−0.318781	−	0.0157547i
$694$	3.77856	−	6.54466i	0.143432	−	0.248432i
$695$	−10.1245	−	8.49548i	−0.384045	−	0.322252i
$696$	−3.95143	+	7.91592i	−0.149779	+	0.300052i
$697$	−8.56506	−	48.5749i	−0.324425	−	1.83990i
$698$	−23.3730	−	8.50708i	−0.884682	−	0.321998i
$699$	15.1645	−	14.3768i	0.573572	−	0.543782i
$700$	−3.62101	+	10.0716i	−0.136861	+	0.380670i
$701$	−7.39789			−0.279415			−0.139707	−	0.990193i	$-0.544616\pi$
$701$	−7.39789			−0.279415			−0.139707	+	0.990193i	$0.544616\pi$
$702$	−26.6740	+	4.90442i	−1.00675	+	0.185105i
$703$	−4.92898	−	8.53725i	−0.185900	−	0.321988i
$704$	−0.183818	+	1.04248i	−0.00692791	+	0.0392901i
$705$	−6.80717	+	6.45362i	−0.256373	+	0.243057i
$706$	1.44428	+	8.19089i	0.0543560	+	0.308268i
$707$	−31.8368	−	18.2146i	−1.19735	−	0.685030i
$708$	21.5631	−	1.30857i	0.810392	−	0.0491791i
$709$	16.0813	+	13.4938i	0.603946	+	0.506771i	0.892711	−	0.450629i	$-0.148800\pi$
$709$	16.0813	+	13.4938i	0.603946	+	0.506771i	−0.288765	+	0.957400i	$0.593245\pi$
$710$	3.70956			0.139217
$711$	−10.7585	−	35.3094i	−0.403474	−	1.32421i
$712$	−15.0659			−0.564619
$713$	−19.8273	+	7.21654i	−0.742538	+	0.270262i
$714$	−7.59125	+	25.9565i	−0.284095	+	0.971397i
$715$	4.13564	−	3.47021i	0.154664	−	0.129779i
$716$	−0.207050	−	1.17424i	−0.00773783	−	0.0438834i
$717$	−20.1000	−	14.8880i	−0.750647	−	0.556002i
$718$	27.2274	+	22.8465i	1.01612	+	0.852622i
$719$	−41.8400			−1.56037			−0.780184	−	0.625550i	$-0.784875\pi$
$719$	−41.8400			−1.56037			−0.780184	+	0.625550i	$0.784875\pi$
$720$	2.61310	−	1.32832i	0.0973846	−	0.0495034i
$721$	−31.9751	−	5.50864i	−1.19082	−	0.205152i
$722$	0.436520	−	2.47563i	0.0162456	−	0.0921332i
$723$	−14.9657	−	22.6341i	−0.556581	−	0.841771i
$724$	−1.66749	−	9.45683i	−0.0619719	−	0.351460i
$725$	15.8289	−	13.2821i	0.587872	−	0.493283i
$726$	−16.4047	−	4.86778i	−0.608836	−	0.180660i
$727$	−25.5452	−	21.4349i	−0.947418	−	0.794978i	0.0314428	−	0.999506i	$-0.489990\pi$
$727$	−25.5452	−	21.4349i	−0.947418	−	0.794978i	−0.978861	+	0.204527i	$0.934434\pi$
$728$	8.83489	−	10.6134i	0.327443	−	0.393359i
$729$	−4.29975	+	26.6554i	−0.159250	+	0.987238i
$730$	−6.31024	+	10.9297i	−0.233552	+	0.404525i
$731$	−6.84209	+	38.8034i	−0.253064	+	1.43520i
$732$	−6.26130	+	5.93610i	−0.231424	+	0.219405i
$733$	45.6667	+	16.6213i	1.68674	+	0.613922i	0.994208	−	0.107469i	$-0.0342746\pi$
$733$	45.6667	+	16.6213i	1.68674	+	0.613922i	0.692528	+	0.721391i	$0.256497\pi$
$734$	14.4651	+	5.26487i	0.533917	+	0.194330i
$735$	−11.3835	−	3.28074i	−0.419888	−	0.121012i
$736$	0.364199	−	2.06547i	0.0134246	−	0.0761344i
$737$	−0.329748	−	0.571140i	−0.0121464	−	0.0210382i
$738$	21.0158	+	13.6763i	0.773604	+	0.503430i
$739$	−14.9693	+	25.9276i	−0.550656	+	0.953763i	0.447572	+	0.894248i	$0.352289\pi$
$739$	−14.9693	+	25.9276i	−0.550656	+	0.953763i	−0.998227	+	0.0595154i	$0.981044\pi$
$740$	−0.411947	+	2.33627i	−0.0151435	+	0.0858830i
$741$	−33.6693	+	14.6208i	−1.23687	+	0.537109i
$742$	−0.0327167	−	8.32741i	−0.00120107	−	0.305709i
$743$	−11.5811	+	9.71769i	−0.424869	+	0.356508i	−0.830012	−	0.557746i	$-0.811666\pi$
$743$	−11.5811	+	9.71769i	−0.424869	+	0.356508i	0.405143	+	0.914254i	$0.367222\pi$
$744$	14.0022	+	10.3714i	0.513345	+	0.380233i
$745$	−4.31793	−	3.62317i	−0.158197	−	0.132743i
$746$	−16.2368	+	28.1230i	−0.594472	+	1.02966i
$747$	−13.5939	+	14.5500i	−0.497376	+	0.532356i
$748$	3.12353	−	5.41012i	0.114208	−	0.197813i
$749$	−6.14159	+	1.10782i	−0.224409	+	0.0404790i
$750$	−15.2801	+	0.927285i	−0.557952	+	0.0338597i
$751$	8.79699	−	7.38155i	0.321007	−	0.269357i	−0.468017	−	0.883720i	$-0.655031\pi$
$751$	8.79699	−	7.38155i	0.321007	−	0.269357i	0.789024	+	0.614363i	$0.210587\pi$
$752$	4.24578	−	3.56264i	0.154828	−	0.129916i
$753$	−9.01606	−	37.6334i	−0.328564	−	1.37144i
$754$	−25.0533	+	9.11865i	−0.912386	+	0.332081i
$755$	9.78206			0.356005
$756$	−7.00713	−	11.8279i	−0.254847	−	0.430178i
$757$	−13.8721			−0.504191			−0.252095	−	0.967702i	$-0.581120\pi$
$757$	−13.8721			−0.504191			−0.252095	+	0.967702i	$0.581120\pi$
$758$	−30.5749	+	11.1284i	−1.11053	+	0.404200i
$759$	−3.68657	−	1.09392i	−0.133814	−	0.0397067i
$760$	3.03919	−	2.55019i	0.110243	−	0.0925050i
$761$	−24.2613	+	20.3576i	−0.879470	+	0.737963i	−0.966070	−	0.258280i	$-0.916844\pi$
$761$	−24.2613	+	20.3576i	−0.879470	+	0.737963i	0.0865997	+	0.996243i	$0.472400\pi$
$762$	−5.59308	−	8.45896i	−0.202616	−	0.306436i
$763$	2.69822	−	7.50491i	0.0976822	−	0.271696i
$764$	11.6515	−	20.1811i	0.421538	−	0.730125i
$765$	−17.1721	+	2.09191i	−0.620860	+	0.0756332i
$766$	13.3790	−	23.1731i	0.483402	−	0.837277i
$767$	49.8688	+	41.8449i	1.80066	+	1.51093i
$768$	−1.58872	+	0.689899i	−0.0573281	+	0.0248946i
$769$	−16.4780	+	13.8267i	−0.594212	+	0.498603i	−0.889579	−	0.456781i	$-0.849002\pi$
$769$	−16.4780	+	13.8267i	−0.594212	+	0.498603i	0.295367	+	0.955384i	$0.404558\pi$
$770$	2.37532	+	1.35898i	0.0856007	+	0.0489742i
$771$	26.1358	+	19.3587i	0.941257	+	0.697186i
$772$	−1.84653	+	10.4722i	−0.0664580	+	0.376902i
$773$	18.3770	−	31.8299i	0.660975	−	1.14484i	−0.319384	−	0.947625i	$-0.603476\pi$
$773$	18.3770	−	31.8299i	0.660975	−	1.14484i	0.980360	−	0.197218i	$-0.0631906\pi$
$774$	−12.0392	−	16.0082i	−0.432739	−	0.575402i
$775$	−20.3481	−	35.2440i	−0.730927	−	1.26600i
$776$	−0.363490	+	2.06145i	−0.0130485	+	0.0740019i
$777$	11.0587	+	1.22131i	0.396729	+	0.0438142i
$778$	−27.1982	−	9.89934i	−0.975104	−	0.354909i
$779$	31.8895	+	11.6068i	1.14256	+	0.415858i
$780$	8.46851	+	2.51286i	0.303221	+	0.0899750i
$781$	−0.697858	+	3.95775i	−0.0249713	+	0.141619i
$782$	−6.18866	+	10.7191i	−0.221306	+	0.383313i
$783$	0.193783	+	26.5413i	0.00692524	+	0.948510i
$784$	6.59646	+	2.34238i	0.235588	+	0.0836565i
$785$	9.25357	+	7.76467i	0.330274	+	0.277133i
$786$	7.96703	−	7.55324i	0.284175	−	0.269415i
$787$	−14.3583	+	12.0480i	−0.511817	+	0.429465i	−0.861768	−	0.507303i	$-0.830643\pi$
$787$	−14.3583	+	12.0480i	−0.511817	+	0.429465i	0.349951	+	0.936768i	$0.386198\pi$
$788$	−1.99331	−	11.3046i	−0.0710089	−	0.402711i
$789$	1.21182	−	2.42765i	0.0431420	−	0.0864266i
$790$	−2.08767	+	11.8397i	−0.0742758	+	0.421239i
$791$	6.22426	+	16.8942i	0.221309	+	0.600688i
$792$	0.925598	+	3.03782i	0.0328897	+	0.107944i
$793$	−25.9999			−0.923284
$794$	−1.99673	−	1.67546i	−0.0708615	−	0.0594598i
$795$	4.88604	−	2.12175i	0.173290	−	0.0752507i
$796$	−2.54702	−	14.4449i	−0.0902766	−	0.511984i
$797$	−26.8572	+	22.5358i	−0.951329	+	0.798260i	−0.979521	−	0.201342i	$-0.935470\pi$
$797$	−26.8572	+	22.5358i	−0.951329	+	0.798260i	0.0281916	+	0.999603i	$0.491025\pi$
$798$	−12.8546	−	13.4525i	−0.455046	−	0.476214i
$799$	−30.7360	+	11.1870i	−1.08736	+	0.395767i
$800$	4.04525			0.143021
$801$	−40.2909	+	20.4810i	−1.42361	+	0.723662i
$802$	−18.2136			−0.643145
$803$	−10.4738	−	8.78854i	−0.369612	−	0.310141i
$804$	0.481943	−	0.965480i	0.0169968	−	0.0340498i
$805$	−4.70623	−	2.69255i	−0.165873	−	0.0948997i
$806$	9.11812	+	51.7114i	0.321172	+	1.82146i
$807$	−20.2095	−	5.99678i	−0.711409	−	0.211097i
$808$	−2.40735	+	13.6528i	−0.0846902	+	0.480302i
$809$	16.1393	+	27.9542i	0.567429	+	0.982816i	0.996819	+	0.0796967i	$0.0253952\pi$
$809$	16.1393	+	27.9542i	0.567429	+	0.982816i	−0.429390	+	0.903119i	$0.641271\pi$
$810$	5.18250	−	7.10466i	0.182095	−	0.249632i
$811$	30.5368			1.07229			0.536146	−	0.844125i	$-0.319880\pi$
$811$	30.5368			1.07229			0.536146	+	0.844125i	$0.319880\pi$
$812$	−8.72759	−	10.3185i	−0.306278	−	0.362110i
$813$	8.20687	+	34.2558i	0.287828	+	1.20140i
$814$	−2.41508	−	0.879016i	−0.0846484	−	0.0308095i
$815$	−2.43141	−	13.7892i	−0.0851687	−	0.483015i
$816$	10.2028	−	0.619165i	0.357170	−	0.0216751i
$817$	−20.7671	−	17.4256i	−0.726547	−	0.609646i
$818$	9.74716	−	16.8826i	0.340801	−	0.590285i
$819$	9.19906	−	40.3940i	0.321441	−	1.41148i
$820$	−4.08335	−	7.07257i	−0.142597	−	0.246985i
$821$	−6.39686	+	36.2784i	−0.223252	+	1.26612i	0.642747	+	0.766079i	$0.277795\pi$
$821$	−6.39686	+	36.2784i	−0.223252	+	1.26612i	−0.865999	+	0.500046i	$0.833316\pi$
$822$	−23.0162	−	17.0480i	−0.802781	−	0.594617i
$823$	4.00476	+	1.45761i	0.139597	+	0.0508093i	0.410874	−	0.911692i	$-0.365224\pi$
$823$	4.00476	+	1.45761i	0.139597	+	0.0508093i	−0.271277	+	0.962501i	$0.587446\pi$
$824$	2.12953	+	12.0772i	0.0741858	+	0.420729i
$825$	0.843122	−	7.36886i	0.0293538	−	0.256551i
$826$	−11.1643	+	31.0528i	−0.388457	+	1.08047i
$827$	1.51645	+	2.62657i	0.0527321	+	0.0913347i	0.891187	−	0.453637i	$-0.149874\pi$
$827$	1.51645	+	2.62657i	0.0527321	+	0.0913347i	−0.838454	+	0.544972i	$0.816540\pi$
$828$	−1.83389	−	6.01883i	−0.0637320	−	0.209169i
$829$	−7.96915			−0.276780			−0.138390	−	0.990378i	$-0.544193\pi$
$829$	−7.96915			−0.276780			−0.138390	+	0.990378i	$0.544193\pi$
$830$	6.09437	−	2.21817i	0.211539	−	0.0769938i
$831$	−9.18897	+	18.4083i	−0.318762	+	0.638577i
$832$	−4.90470	−	1.78516i	−0.170040	−	0.0618894i
$833$	−31.8530	−	26.3041i	−1.10364	−	0.911384i
$834$	22.4601	+	6.66461i	0.777731	+	0.230776i
$835$	2.75882	−	1.00413i	0.0954731	−	0.0347494i
$836$	2.14906	+	3.72228i	0.0743267	+	0.128738i
$837$	51.5453	+	8.70129i	1.78167	+	0.300761i
$838$	−6.13558	+	10.6271i	−0.211950	+	0.367108i
$839$	1.87345	+	1.57201i	0.0646787	+	0.0542719i	0.674554	−	0.738226i	$-0.264336\pi$
$839$	1.87345	+	1.57201i	0.0646787	+	0.0542719i	−0.609875	+	0.792497i	$0.708780\pi$
$840$	0.288790	+	4.46837i	0.00996420	+	0.154173i
$841$	−0.504995	−	2.86397i	−0.0174136	−	0.0987576i
$842$	10.0515	−	8.43418i	0.346396	−	0.290661i
$843$	−2.70316	+	5.41526i	−0.0931018	+	0.186511i
$844$	24.3633	−	8.86753i	0.838620	−	0.305233i
$845$	6.95843	+	12.0523i	0.239377	+	0.414613i
$846$	6.51140	−	15.2995i	0.223867	−	0.526006i
$847$	16.7227	−	20.0891i	0.574600	−	0.690271i
$848$	−2.95767	+	1.07651i	−0.101567	+	0.0369673i
$849$	0.0267845	−	0.0116311i	0.000919242	−	0.000399178i
$850$	−22.4331	−	8.16498i	−0.769449	−	0.280057i
$851$	4.78499	+	1.74160i	0.164027	+	0.0597011i
$852$	−6.03152	+	2.61917i	−0.206636	+	0.0897313i
$853$	−21.1911	+	7.71292i	−0.725568	+	0.264085i	−0.678288	−	0.734796i	$-0.737278\pi$
$853$	−21.1911	+	7.71292i	−0.725568	+	0.264085i	−0.0472805	+	0.998882i	$0.515055\pi$
$854$	−4.55623	−	12.3668i	−0.155911	−	0.423182i
$855$	4.66095	−	10.9516i	0.159401	−	0.374536i
$856$	1.17938	+	2.04275i	0.0403105	+	0.0698198i
$857$	−30.9506	+	11.2651i	−1.05725	+	0.384809i	−0.811396	−	0.584497i	$-0.801292\pi$
$857$	−30.9506	+	11.2651i	−1.05725	+	0.384809i	−0.245858	+	0.969306i	$0.579070\pi$
$858$	−4.27411	+	8.56235i	−0.145916	+	0.292314i
$859$	−7.41257	+	6.21989i	−0.252914	+	0.212220i	−0.760426	−	0.649425i	$-0.775010\pi$
$859$	−7.41257	+	6.21989i	−0.252914	+	0.212220i	0.507512	+	0.861645i	$0.330565\pi$
$860$	1.13286	+	6.42476i	0.0386301	+	0.219082i
$861$	−31.8656	+	21.2500i	−1.08598	+	0.724198i
$862$	16.3684	+	13.7347i	0.557510	+	0.467806i
$863$	13.2943	−	23.0263i	0.452542	−	0.783826i	−0.546001	−	0.837784i	$-0.683851\pi$
$863$	13.2943	−	23.0263i	0.452542	−	0.783826i	0.998543	+	0.0539587i	$0.0171839\pi$
$864$	−3.31087	+	4.00476i	−0.112638	+	0.136245i
$865$	8.07168	+	13.9806i	0.274446	+	0.475354i
$866$	−17.3572	+	6.31750i	−0.589822	+	0.214678i
$867$	−29.6015	−	8.78367i	−1.00532	−	0.298309i
$868$	−22.9985	+	13.3989i	−0.780619	+	0.454789i
$869$	−12.2391	−	4.45468i	−0.415184	−	0.151115i
$870$	3.86099	−	7.73474i	0.130900	−	0.262232i
$871$	3.05567	−	1.11217i	0.103537	−	0.0376845i
$872$	−3.01435			−0.102079
$873$	1.83032	+	6.00711i	0.0619469	+	0.203310i
$874$	−4.25793	−	7.37495i	−0.144027	−	0.249461i
$875$	7.91132	−	22.0048i	0.267451	−	0.743897i
$876$	2.54307	−	22.2263i	0.0859224	−	0.750958i
$877$	1.02718	+	5.82544i	0.0346855	+	0.196711i	0.997227	−	0.0744245i	$-0.0237120\pi$
$877$	1.02718	+	5.82544i	0.0346855	+	0.196711i	−0.962541	+	0.271135i	$0.912601\pi$
$878$	9.74716	+	3.54767i	0.328951	+	0.119728i
$879$	−5.49785	−	4.07224i	−0.185438	−	0.137353i
$880$	0.179611	−	1.01862i	0.00605468	−	0.0343378i
$881$	−14.0626	−	24.3572i	−0.473781	−	0.820613i	0.525768	−	0.850628i	$-0.323778\pi$
$881$	−14.0626	−	24.3572i	−0.473781	−	0.820613i	−0.999549	+	0.0300146i	$0.990445\pi$
$882$	20.8253	−	2.70316i	0.701224	−	0.0910202i
$883$	−21.2803	+	36.8585i	−0.716138	+	1.24039i	0.246382	+	0.969173i	$0.420758\pi$
$883$	−21.2803	+	36.8585i	−0.716138	+	1.24039i	−0.962519	+	0.271214i	$0.912575\pi$
$884$	23.5960	+	19.7994i	0.793619	+	0.665925i
$885$	−21.0696	+	1.27862i	−0.708246	+	0.0429804i
$886$	4.08661	+	23.1763i	0.137292	+	0.778624i
$887$	−1.86377	−	0.678358i	−0.0625794	−	0.0227770i	0.310541	−	0.950560i	$-0.399490\pi$
$887$	−1.86377	−	0.678358i	−0.0625794	−	0.0227770i	−0.373120	+	0.927783i	$0.621712\pi$
$888$	−0.979744	−	4.08949i	−0.0328780	−	0.137234i
$889$	15.2444	−	2.74979i	0.511280	−	0.0922250i
$890$	14.7211			0.493452
$891$	6.60504	+	6.86579i	0.221277	+	0.230013i
$892$	−0.509940	−	0.883242i	−0.0170741	−	0.0295731i
$893$	3.90782	−	22.1623i	0.130770	−	0.741634i
$894$	9.57885	+	2.84234i	0.320365	+	0.0950620i
$895$	0.202311	+	1.14736i	0.00676252	+	0.0383521i
$896$	−0.0103945	−	2.64573i	−0.000347257	−	0.0883877i
$897$	8.46830	−	16.9646i	0.282748	−	0.566431i
$898$	18.8380	+	15.8070i	0.628633	+	0.527486i
$899$	51.3880			1.71388
$900$	10.8183	−	5.49924i	0.360609	−	0.183308i
$901$	18.5747			0.618814
$902$	8.31393	−	3.02602i	0.276824	−	0.100756i
$903$	29.7262	−	7.24530i	0.989226	−	0.241108i
$904$	5.21292	−	4.37416i	0.173379	−	0.145482i
$905$	1.62933	+	9.24038i	0.0541607	+	0.307161i
$906$	−15.9050	+	6.90671i	−0.528409	+	0.229460i
$907$	9.14196	+	7.67101i	0.303554	+	0.254712i	0.781822	−	0.623502i	$-0.214291\pi$
$907$	9.14196	+	7.67101i	0.303554	+	0.254712i	−0.478268	+	0.878214i	$0.658735\pi$
$908$	23.2509			0.771608
$909$	12.1220	+	39.7844i	0.402060	+	1.31956i
$910$	−8.63268	+	10.3705i	−0.286170	+	0.343779i
$911$	5.89004	−	33.4041i	0.195146	−	1.10673i	−0.717065	−	0.697006i	$-0.754515\pi$
$911$	5.89004	−	33.4041i	0.195146	−	1.10673i	0.912211	−	0.409721i	$-0.134374\pi$
$912$	−3.14096	+	6.29229i	−0.104007	+	0.208359i
$913$	1.22008	+	6.91940i	0.0403786	+	0.228999i
$914$	−7.48121	+	6.27748i	−0.247456	+	0.207641i
$915$	6.11799	−	5.80023i	0.202255	−	0.191750i
$916$	−2.96609	−	2.48885i	−0.0980025	−	0.0822339i
$917$	5.79747	+	15.7358i	0.191449	+	0.519641i
$918$	26.4438	−	15.5259i	0.872776	−	0.512430i
$919$	6.97760	−	12.0856i	0.230170	−	0.398666i	−0.727688	−	0.685908i	$-0.759405\pi$
$919$	6.97760	−	12.0856i	0.230170	−	0.398666i	0.957858	+	0.287242i	$0.0927385\pi$
$920$	−0.355863	+	2.01820i	−0.0117325	+	0.0665381i
$921$	13.7353	+	4.07569i	0.452595	+	0.134299i
$922$	22.1738	+	8.07061i	0.730256	+	0.265791i
$923$	−18.6205	−	6.77730i	−0.612900	−	0.223077i
$924$	−4.82165	−	0.532496i	−0.158620	−	0.0175178i
$925$	−1.70547	+	9.67218i	−0.0560754	+	0.318019i
$926$	12.7858	+	22.1457i	0.420168	+	0.727752i
$927$	22.1131	+	29.4032i	0.726291	+	0.965729i
$928$	−2.55401	+	4.42367i	−0.0838395	+	0.145214i
$929$	−5.41613	+	30.7164i	−0.177698	+	1.00777i	0.757287	+	0.653083i	$0.226525\pi$
$929$	−5.41613	+	30.7164i	−0.177698	+	1.00777i	−0.934984	+	0.354690i	$0.884586\pi$
$930$	−13.6817	−	10.1340i	−0.448640	−	0.332306i
$931$	26.6310	−	9.93053i	0.872794	−	0.325460i
$932$	9.24192	−	7.75489i	0.302729	−	0.254020i
$933$	33.5563	−	14.5718i	1.09859	−	0.477058i
$934$	−17.2226	−	14.4514i	−0.563540	−	0.472866i
$935$	−3.05204	+	5.28629i	−0.0998124	+	0.172880i
$936$	−15.5435	+	1.89351i	−0.508055	+	0.0618912i
$937$	20.2431	−	35.0621i	0.661313	−	1.14543i	−0.318957	−	0.947769i	$-0.603333\pi$
$937$	20.2431	−	35.0621i	0.661313	−	1.14543i	0.980271	−	0.197659i	$-0.0633340\pi$
$938$	1.06448	+	1.25852i	0.0347564	+	0.0410921i
$939$	−7.17740	−	10.8551i	−0.234226	−	0.354242i
$940$	−4.14861	+	3.48109i	−0.135313	+	0.113541i
$941$	31.5630	−	26.4845i	1.02892	−	0.863369i	0.0382007	−	0.999270i	$-0.487837\pi$
$941$	31.5630	−	26.4845i	1.02892	−	0.863369i	0.990722	+	0.135901i	$0.0433929\pi$
$942$	−20.5280	−	6.09130i	−0.668840	−	0.198465i
$943$	−16.4724	+	5.99546i	−0.536415	+	0.195239i
$944$	12.4724			0.405941
$945$	6.84675	+	11.5572i	0.222725	+	0.375956i
$946$	−7.06771			−0.229791
$947$	−54.6866	+	19.9043i	−1.77707	+	0.646802i	−0.777230	+	0.629217i	$0.783376\pi$
$947$	−54.6866	+	19.9043i	−1.77707	+	0.646802i	−0.999845	+	0.0175853i	$0.994402\pi$
$948$	−4.96514	−	20.7247i	−0.161260	−	0.673107i
$949$	51.6430	−	43.3336i	1.67640	−	1.40667i
$950$	12.5823	−	10.5578i	0.408223	−	0.342540i
$951$	8.16975	−	0.495787i	0.264922	−	0.0160770i
$952$	−5.28253	+	14.6930i	−0.171208	+	0.476202i
$953$	21.2426	−	36.7932i	0.688114	−	1.19185i	−0.284333	−	0.958726i	$-0.591772\pi$
$953$	21.2426	−	36.7932i	0.688114	−	1.19185i	0.972447	−	0.233123i	$-0.0748945\pi$
$954$	−6.44631	+	6.89966i	−0.208707	+	0.223385i
$955$	−11.3849	+	19.7192i	−0.368405	+	0.638097i
$956$	−11.0627	−	9.28275i	−0.357795	−	0.300225i
$957$	7.52588	+	5.57439i	0.243277	+	0.180194i
$958$	−8.99652	+	7.54898i	−0.290665	+	0.243896i
$959$	37.8039	−	22.0246i	1.22075	−	0.711210i
$960$	1.55236	−	0.674108i	0.0501022	−	0.0217568i
$961$	12.1916	−	69.1421i	0.393278	−	2.23039i
$962$	6.33612	−	10.9745i	0.204285	−	0.353831i
$963$	5.93102	+	3.85967i	0.191124	+	0.124376i
$964$	−7.83302	−	13.5672i	−0.252285	−	0.436970i
$965$	1.80427	−	10.2325i	0.0580814	−	0.329396i
$966$	9.55313	+	1.05503i	0.307367	+	0.0339452i
$967$	−37.2113	−	13.5438i	−1.19664	−	0.435540i	−0.334587	−	0.942365i	$-0.608597\pi$
$967$	−37.2113	−	13.5438i	−1.19664	−	0.435540i	−0.862049	+	0.506825i	$0.830819\pi$
$968$	−9.28363	−	3.37897i	−0.298387	−	0.108604i
$969$	30.1187	−	28.5544i	0.967553	−	0.917300i
$970$	0.355170	−	2.01427i	0.0114038	−	0.0646744i
$971$	11.0557	−	19.1490i	0.354794	−	0.614521i	−0.632289	−	0.774733i	$-0.717884\pi$
$971$	11.0557	−	19.1490i	0.354794	−	0.614521i	0.987083	+	0.160212i	$0.0512177\pi$
$972$	−3.41011	+	15.2109i	−0.109379	+	0.487889i
$973$	−22.8955	+	27.5046i	−0.733997	+	0.881756i
$974$	−12.3861	−	10.3932i	−0.396876	−	0.333019i
$975$	35.0597	+	10.4033i	1.12281	+	0.333172i
$976$	−3.81593	+	3.20194i	−0.122145	+	0.102492i
$977$	10.0620	+	57.0643i	0.321911	+	1.82565i	0.530549	+	0.847654i	$0.321986\pi$
$977$	10.0620	+	57.0643i	0.321911	+	1.82565i	−0.208638	+	0.977993i	$0.566903\pi$
$978$	13.6893	+	20.7037i	0.437737	+	0.662031i
$979$	−2.76939	+	15.7060i	−0.0885100	+	0.501965i
$980$	−6.44548	−	2.28877i	−0.205893	−	0.0731120i
$981$	−8.06131	+	4.09780i	−0.257378	+	0.130833i
$982$	12.2163			0.389837
$983$	7.41204	+	6.21944i	0.236407	+	0.198369i	0.753293	−	0.657685i	$-0.228464\pi$
$983$	7.41204	+	6.21944i	0.236407	+	0.198369i	−0.516886	+	0.856055i	$0.672909\pi$
$984$	11.6329	+	8.61647i	0.370844	+	0.274683i
$985$	1.94769	+	11.0459i	0.0620586	+	0.351952i
$986$	23.0921	−	19.3766i	0.735404	−	0.617077i
$987$	17.5469	+	18.3632i	0.558525	+	0.584506i
$988$	−19.9146	+	7.24833i	−0.633569	+	0.230600i
$989$	14.0033			0.445278
$990$	−0.904413	−	2.96829i	−0.0287441	−	0.0943384i
$991$	−6.83921			−0.217255			−0.108627	−	0.994083i	$-0.534646\pi$
$991$	−6.83921			−0.217255			−0.108627	+	0.994083i	$0.534646\pi$
$992$	7.70660	+	6.46661i	0.244685	+	0.205315i
$993$	9.47088	−	0.574746i	0.300549	−	0.0182390i
$994$	−0.0394625	−	10.0444i	−0.00125167	−	0.318589i
$995$	2.48872	+	14.1142i	0.0788978	+	0.447451i
$996$	−8.34290	+	7.90959i	−0.264355	+	0.250625i
$997$	2.00655	−	11.3797i	0.0635481	−	0.360399i	−0.936407	−	0.350916i	$-0.885870\pi$
$997$	2.00655	−	11.3797i	0.0635481	−	0.360399i	0.999955	−	0.00948325i	$-0.00301866\pi$
$998$	−15.9689	−	27.6590i	−0.505487	−	0.875529i
$999$	−8.17951	−	9.60467i	−0.258788	−	0.303878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.205.10	✓	72
7.4	even	3		378.2.w.b.151.2	yes	72
27.22	even	9		378.2.w.b.373.2	yes	72
189.130	even	9	inner	378.2.v.a.319.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.205.10	✓	72	1.1	even	1	trivial
378.2.v.a.319.10	yes	72	189.130	even	9	inner
378.2.w.b.151.2	yes	72	7.4	even	3
378.2.w.b.373.2	yes	72	27.22	even	9

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.25695 - 1.19167i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.748511 + 0.628075i) q^{5} +(0.773574 - 1.54970i) q^{6} +(1.70861 + 2.02007i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.159855 - 2.99574i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.25695 - 1.19167i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.748511 + 0.628075i) q^{5} +(0.773574 - 1.54970i) q^{6} +(1.70861 + 2.02007i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.159855 - 2.99574i) q^{9} +(-0.488556 + 0.846204i) q^{10} +(-0.810909 - 0.680433i) q^{11} +(0.196891 - 1.72082i) q^{12} +(3.99834 - 3.35501i) q^{13} +(2.29647 + 1.31386i) q^{14} +(-0.192385 + 1.68144i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.95072 + 5.11079i) q^{17} +(-0.874388 - 2.86975i) q^{18} +(-2.03016 - 3.51634i) q^{19} +(-0.169674 + 0.962267i) q^{20} +(4.55488 + 0.503035i) q^{21} +(-0.994727 - 0.362051i) q^{22} +(1.97085 + 0.717332i) q^{23} +(-0.403539 - 1.68439i) q^{24} +(-0.702451 + 3.98380i) q^{25} +(2.60973 - 4.52019i) q^{26} +(-3.36899 - 3.95599i) q^{27} +(2.60734 + 0.449190i) q^{28} +(-3.91297 - 3.28337i) q^{29} +(0.394303 + 1.64583i) q^{30} +(-7.70660 + 6.46661i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.83012 + 0.111062i) q^{33} +(-1.02477 + 5.81178i) q^{34} +(-2.54766 - 0.438909i) q^{35} +(-1.80317 - 2.39762i) q^{36} +2.42788 q^{37} +(-3.11038 - 2.60992i) q^{38} +(1.02767 - 8.98178i) q^{39} +(0.169674 + 0.962267i) q^{40} +(-6.40260 + 5.37242i) q^{41} +(4.45224 - 1.08516i) q^{42} +(6.27403 - 2.28356i) q^{43} -1.05857 q^{44} +(1.76190 + 2.34274i) q^{45} +2.09734 q^{46} +(4.24578 + 3.56264i) q^{47} +(-0.955296 - 1.44479i) q^{48} +(-1.16133 + 6.90299i) q^{49} +(0.702451 + 3.98380i) q^{50} +(2.38146 + 9.94030i) q^{51} +(0.906351 - 5.14017i) q^{52} +(-1.57375 - 2.72581i) q^{53} +(-4.51885 - 2.56515i) q^{54} +1.03434 q^{55} +(2.60373 - 0.469663i) q^{56} +(-6.74212 - 2.00059i) q^{57} +(-4.79997 - 1.74705i) q^{58} +(2.16581 + 12.2829i) q^{59} +(0.933432 + 1.41172i) q^{60} +(-3.81593 - 3.20194i) q^{61} +(-5.03013 + 8.71244i) q^{62} +(6.32472 - 4.79562i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.885606 + 5.02252i) q^{65} +(-1.68177 + 0.730304i) q^{66} +(0.585437 + 0.213082i) q^{67} +(1.02477 + 5.81178i) q^{68} +(3.33209 - 1.44695i) q^{69} +(-2.54414 + 0.458913i) q^{70} +(-1.89823 - 3.28783i) q^{71} +(-2.51446 - 1.63631i) q^{72} +12.9161 q^{73} +(2.28146 - 0.830384i) q^{74} +(3.86442 + 5.84453i) q^{75} +(-3.81545 - 1.38871i) q^{76} +(-0.0110033 - 2.80068i) q^{77} +(-2.10626 - 8.79160i) q^{78} +(11.5620 - 4.20822i) q^{79} +(0.488556 + 0.846204i) q^{80} +(-8.94889 - 0.957768i) q^{81} +(-4.17900 + 7.23824i) q^{82} +(-5.08455 - 4.26644i) q^{83} +(3.81259 - 2.54248i) q^{84} +(-1.00132 - 5.67876i) q^{85} +(5.11464 - 4.29169i) q^{86} +(-8.83110 + 0.535921i) q^{87} +(-0.994727 + 0.362051i) q^{88} +(-7.53295 - 13.0475i) q^{89} +(2.45691 + 1.59886i) q^{90} +(13.6089 + 2.34453i) q^{91} +(1.97085 - 0.717332i) q^{92} +(-1.98078 + 17.3119i) q^{93} +(5.20823 + 1.89564i) q^{94} +(3.72812 + 1.35693i) q^{95} +(-1.39183 - 1.03092i) q^{96} +(-1.96702 + 0.715936i) q^{97} +(1.26967 + 6.88389i) q^{98} +(-2.16803 + 2.32050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

L-functions

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