LMFDB - Embedded newform 471.2.q.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32814 - 0.327356i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.114131 - 0.0599004i) q^{4} +(-1.19669 + 0.899253i) q^{5} +(0.947566 + 0.986521i) q^{6} +(-3.33061 + 1.74804i) q^{7} +(2.17972 + 1.93107i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-1.32814 - 0.327356i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.114131 - 0.0599004i) q^{4} +(-1.19669 + 0.899253i) q^{5} +(0.947566 + 0.986521i) q^{6} +(-3.33061 + 1.74804i) q^{7} +(2.17972 + 1.93107i) q^{8} +(0.428693 + 0.903450i) q^{9} +(1.88374 - 0.802587i) q^{10} +(-0.289642 - 0.301550i) q^{11} +(0.0644474 + 0.111626i) q^{12} +(0.309186 - 0.535526i) q^{13} +(4.99574 - 1.23134i) q^{14} +(1.49205 - 0.120451i) q^{15} +(-2.11638 - 3.06611i) q^{16} +(5.79661 - 4.35587i) q^{17} +(-0.273612 - 1.34024i) q^{18} +(-0.841953 + 4.12416i) q^{19} +(0.190445 - 0.0309503i) q^{20} +(3.74927 + 0.302672i) q^{21} +(0.285970 + 0.495315i) q^{22} +(-2.06767 - 2.99554i) q^{23} +(-0.810192 - 2.79711i) q^{24} +(-0.767680 + 2.65034i) q^{25} +(-0.585949 + 0.610037i) q^{26} +(0.120537 - 0.992709i) q^{27} +0.484833 q^{28} +(0.916114 - 7.54488i) q^{29} +(-2.02107 - 0.328457i) q^{30} +(-5.20963 - 6.38064i) q^{31} +(-0.258145 - 0.680671i) q^{32} +(0.0836349 + 0.409671i) q^{33} +(-9.12460 + 3.88763i) q^{34} +(2.41378 - 5.08693i) q^{35} +(0.00519007 - 0.128790i) q^{36} +(4.34059 + 3.26174i) q^{37} +(2.46830 - 5.20183i) q^{38} +(-0.547542 + 0.287372i) q^{39} +(-4.34497 - 0.350762i) q^{40} +(-0.285744 + 0.413972i) q^{41} +(-4.88046 - 1.62934i) q^{42} +(5.01615 - 3.17202i) q^{43} +(0.0149941 + 0.0517658i) q^{44} +(-1.32544 - 0.695646i) q^{45} +(1.76554 + 4.65535i) q^{46} +(8.96969 + 3.82163i) q^{47} +(0.150015 + 3.72258i) q^{48} +(4.06089 - 5.88321i) q^{49} +(1.88719 - 3.26870i) q^{50} +(-7.22730 + 0.583448i) q^{51} +(-0.0673659 + 0.0425996i) q^{52} +(5.54871 - 1.85243i) q^{53} +(-0.485058 + 1.27899i) q^{54} +(0.617782 + 0.100399i) q^{55} +(-10.6354 - 2.62139i) q^{56} +(2.91583 - 3.03570i) q^{57} +(-3.68658 + 9.72072i) q^{58} +(3.26553 - 2.89301i) q^{59} +(-0.177504 - 0.0756273i) q^{60} +(2.48483 - 12.1715i) q^{61} +(4.83035 + 10.1798i) q^{62} +(-3.00708 - 2.25967i) q^{63} +(1.01817 + 8.38539i) q^{64} +(0.111574 + 0.918895i) q^{65} +(0.0230297 - 0.571477i) q^{66} +(-1.04453 - 0.925377i) q^{67} +(-0.922489 + 0.149919i) q^{68} +(0.146562 + 3.63690i) q^{69} +(-4.87106 + 5.96596i) q^{70} +(4.47591 - 1.49428i) q^{71} +(-0.810192 + 2.79711i) q^{72} +(-2.40436 - 1.52043i) q^{73} +(-4.69714 - 5.75295i) q^{74} +(2.06535 - 1.82974i) q^{75} +(0.343132 - 0.420260i) q^{76} +(1.49181 + 0.498039i) q^{77} +(0.821282 - 0.202428i) q^{78} +(0.768478 - 0.189413i) q^{79} +(5.28985 + 1.76601i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.515023 - 0.456271i) q^{82} +(6.64937 + 8.14400i) q^{83} +(-0.409776 - 0.259127i) q^{84} +(-3.01971 + 10.4252i) q^{85} +(-7.70051 + 2.57081i) q^{86} +(-4.80677 + 5.88722i) q^{87} +(-0.0490279 - 1.21661i) q^{88} +(14.1271 - 2.29587i) q^{89} +(1.53264 + 1.35780i) q^{90} +(-0.0936581 + 2.32410i) q^{91} +(0.0565508 + 0.465738i) q^{92} +(0.992894 + 8.17722i) q^{93} +(-10.6619 - 8.01192i) q^{94} +(-2.70111 - 5.69247i) q^{95} +(-0.145614 + 0.713266i) q^{96} +(4.53193 + 1.93087i) q^{97} +(-7.31931 + 6.48434i) q^{98} +(0.148268 - 0.390950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

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 $

$2$	−1.32814	−	0.327356i	−0.939133	−	0.231476i	−0.260099	−	0.965582i	$-0.583755\pi$
$2$	−1.32814	−	0.327356i	−0.939133	−	0.231476i	−0.679035	+	0.734106i	$0.737601\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	−0.114131	−	0.0599004i	−0.0570653	−	0.0299502i
$5$	−1.19669	+	0.899253i	−0.535176	+	0.402158i	−0.833678	−	0.552250i	$-0.813769\pi$
$5$	−1.19669	+	0.899253i	−0.535176	+	0.402158i	0.298503	+	0.954409i	$0.403513\pi$
$6$	0.947566	+	0.986521i	0.386842	+	0.402745i
$7$	−3.33061	+	1.74804i	−1.25885	+	0.660697i	−0.956287	−	0.292431i	$-0.905536\pi$
$7$	−3.33061	+	1.74804i	−1.25885	+	0.660697i	−0.302567	+	0.953128i	$0.597844\pi$
$8$	2.17972	+	1.93107i	0.770649	+	0.682735i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	1.88374	−	0.802587i	0.595691	−	0.253800i
$11$	−0.289642	−	0.301550i	−0.0873305	−	0.0909207i	0.676103	−	0.736807i	$-0.263667\pi$
$11$	−0.289642	−	0.301550i	−0.0873305	−	0.0909207i	−0.763433	+	0.645886i	$0.776488\pi$
$12$	0.0644474	+	0.111626i	0.0186044	+	0.0322237i
$13$	0.309186	−	0.535526i	0.0857528	−	0.148528i	−0.819959	−	0.572422i	$-0.806004\pi$
$13$	0.309186	−	0.535526i	0.0857528	−	0.148528i	0.905712	+	0.423894i	$0.139337\pi$
$14$	4.99574	−	1.23134i	1.33517	−	0.329089i
$15$	1.49205	−	0.120451i	0.385246	−	0.0311002i
$16$	−2.11638	−	3.06611i	−0.529095	−	0.766526i
$17$	5.79661	−	4.35587i	1.40588	−	1.05645i	0.416817	−	0.908991i	$-0.363146\pi$
$17$	5.79661	−	4.35587i	1.40588	−	1.05645i	0.989068	−	0.147463i	$-0.0471107\pi$
$18$	−0.273612	−	1.34024i	−0.0644909	−	0.315897i
$19$	−0.841953	+	4.12416i	−0.193157	+	0.946147i	0.761437	+	0.648239i	$0.224494\pi$
$19$	−0.841953	+	4.12416i	−0.193157	+	0.946147i	−0.954594	+	0.297909i	$0.903711\pi$
$20$	0.190445	−	0.0309503i	0.0425847	−	0.00692069i
$21$	3.74927	+	0.302672i	0.818158	+	0.0660485i
$22$	0.285970	+	0.495315i	0.0609691	+	0.105602i
$23$	−2.06767	−	2.99554i	−0.431140	−	0.624614i	0.545854	−	0.837880i	$-0.316205\pi$
$23$	−2.06767	−	2.99554i	−0.431140	−	0.624614i	−0.976994	+	0.213266i	$0.931590\pi$
$24$	−0.810192	−	2.79711i	−0.165380	−	0.570957i
$25$	−0.767680	+	2.65034i	−0.153536	+	0.530067i
$26$	−0.585949	+	0.610037i	−0.114914	+	0.119638i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	0.484833			0.0916249
$29$	0.916114	−	7.54488i	0.170118	−	1.40105i	−0.618316	−	0.785929i	$-0.712185\pi$
$29$	0.916114	−	7.54488i	0.170118	−	1.40105i	0.788434	−	0.615119i	$-0.210892\pi$
$30$	−2.02107	−	0.328457i	−0.368996	−	0.0599677i
$31$	−5.20963	−	6.38064i	−0.935677	−	1.14600i	−0.989074	−	0.147423i	$-0.952902\pi$
$31$	−5.20963	−	6.38064i	−0.935677	−	1.14600i	0.0533964	−	0.998573i	$-0.482995\pi$
$32$	−0.258145	−	0.680671i	−0.0456339	−	0.120327i
$33$	0.0836349	+	0.409671i	0.0145590	+	0.0713145i
$34$	−9.12460	+	3.88763i	−1.56486	+	0.666723i
$35$	2.41378	−	5.08693i	0.408003	−	0.859848i
$36$	0.00519007	−	0.128790i	0.000865012	−	0.0214650i
$37$	4.34059	+	3.26174i	0.713589	+	0.536227i	0.894388	−	0.447293i	$-0.147612\pi$
$37$	4.34059	+	3.26174i	0.713589	+	0.536227i	−0.180799	+	0.983520i	$0.557868\pi$
$38$	2.46830	−	5.20183i	0.400411	−	0.843847i
$39$	−0.547542	+	0.287372i	−0.0876768	+	0.0460164i
$40$	−4.34497	−	0.350762i	−0.687000	−	0.0554604i
$41$	−0.285744	+	0.413972i	−0.0446258	+	0.0646516i	−0.844662	−	0.535301i	$-0.820198\pi$
$41$	−0.285744	+	0.413972i	−0.0446258	+	0.0646516i	0.800036	+	0.599952i	$0.204814\pi$
$42$	−4.88046	−	1.62934i	−0.753071	−	0.251412i
$43$	5.01615	−	3.17202i	0.764956	−	0.483729i	−0.0941300	−	0.995560i	$-0.530007\pi$
$43$	5.01615	−	3.17202i	0.764956	−	0.483729i	0.859086	+	0.511831i	$0.171033\pi$
$44$	0.0149941	+	0.0517658i	0.00226045	+	0.00780398i
$45$	−1.32544	−	0.695646i	−0.197585	−	0.103701i
$46$	1.76554	+	4.65535i	0.260315	+	0.686394i
$47$	8.96969	+	3.82163i	1.30836	+	0.557442i	0.929777	−	0.368124i	$-0.120000\pi$
$47$	8.96969	+	3.82163i	1.30836	+	0.557442i	0.378587	+	0.925566i	$0.376410\pi$
$48$	0.150015	+	3.72258i	0.0216527	+	0.537307i
$49$	4.06089	−	5.88321i	0.580127	−	0.840458i
$50$	1.88719	−	3.26870i	0.266888	−	0.462264i
$51$	−7.22730	+	0.583448i	−1.01202	+	0.0816991i
$52$	−0.0673659	+	0.0425996i	−0.00934197	+	0.00590750i
$53$	5.54871	−	1.85243i	0.762174	−	0.254451i	0.0911005	−	0.995842i	$-0.470962\pi$
$53$	5.54871	−	1.85243i	0.762174	−	0.254451i	0.671074	+	0.741391i	$0.265833\pi$
$54$	−0.485058	+	1.27899i	−0.0660081	+	0.174049i
$55$	0.617782	+	0.100399i	0.0833016	+	0.0135378i
$56$	−10.6354	−	2.62139i	−1.42121	−	0.350298i
$57$	2.91583	−	3.03570i	0.386212	−	0.402089i
$58$	−3.68658	+	9.72072i	−0.484072	+	1.27639i
$59$	3.26553	−	2.89301i	0.425136	−	0.376638i	−0.423252	−	0.906012i	$-0.639112\pi$
$59$	3.26553	−	2.89301i	0.425136	−	0.376638i	0.848388	+	0.529374i	$0.177573\pi$
$60$	−0.177504	−	0.0756273i	−0.0229156	−	0.00976344i
$61$	2.48483	−	12.1715i	0.318150	−	1.55840i	−0.434925	−	0.900467i	$-0.643225\pi$
$61$	2.48483	−	12.1715i	0.318150	−	1.55840i	0.753075	−	0.657935i	$-0.228570\pi$
$62$	4.83035	+	10.1798i	0.613455	+	1.29283i
$63$	−3.00708	−	2.25967i	−0.378856	−	0.284692i
$64$	1.01817	+	8.38539i	0.127271	+	1.04817i
$65$	0.111574	+	0.918895i	0.0138391	+	0.113975i
$66$	0.0230297	−	0.571477i	0.00283476	−	0.0703439i
$67$	−1.04453	−	0.925377i	−0.127610	−	0.113053i	0.596904	−	0.802313i	$-0.296397\pi$
$67$	−1.04453	−	0.925377i	−0.127610	−	0.113053i	−0.724514	+	0.689260i	$0.757936\pi$
$68$	−0.922489	+	0.149919i	−0.111868	+	0.0181804i
$69$	0.146562	+	3.63690i	0.0176440	+	0.437832i
$70$	−4.87106	+	5.96596i	−0.582203	+	0.713069i
$71$	4.47591	−	1.49428i	0.531193	−	0.177338i	−0.0384042	−	0.999262i	$-0.512227\pi$
$71$	4.47591	−	1.49428i	0.531193	−	0.177338i	0.569597	+	0.821924i	$0.307099\pi$
$72$	−0.810192	+	2.79711i	−0.0954820	+	0.329642i
$73$	−2.40436	−	1.52043i	−0.281410	−	0.177953i	0.386303	−	0.922372i	$-0.373752\pi$
$73$	−2.40436	−	1.52043i	−0.281410	−	0.177953i	−0.667712	+	0.744419i	$0.732726\pi$
$74$	−4.69714	−	5.75295i	−0.546032	−	0.668767i
$75$	2.06535	−	1.82974i	0.238486	−	0.211280i
$76$	0.343132	−	0.420260i	0.0393599	−	0.0482071i
$77$	1.49181	+	0.498039i	0.170007	+	0.0567568i
$78$	0.821282	−	0.202428i	0.0929919	−	0.0229205i
$79$	0.768478	−	0.189413i	0.0864605	−	0.0213106i	−0.195848	−	0.980634i	$-0.562746\pi$
$79$	0.768478	−	0.189413i	0.0864605	−	0.0213106i	0.282309	+	0.959324i	$0.408900\pi$
$80$	5.28985	+	1.76601i	0.591424	+	0.197446i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	0.515023	−	0.456271i	0.0568748	−	0.0503867i
$83$	6.64937	+	8.14400i	0.729863	+	0.893920i	0.997576	−	0.0695783i	$-0.0221654\pi$
$83$	6.64937	+	8.14400i	0.729863	+	0.893920i	−0.267713	+	0.963499i	$0.586268\pi$
$84$	−0.409776	−	0.259127i	−0.0447103	−	0.0282731i
$85$	−3.01971	+	10.4252i	−0.327533	+	1.13078i
$86$	−7.70051	+	2.57081i	−0.830367	+	0.277217i
$87$	−4.80677	+	5.88722i	−0.515340	+	0.631177i
$88$	−0.0490279	−	1.21661i	−0.00522639	−	0.129691i
$89$	14.1271	−	2.29587i	1.49747	−	0.243362i	0.644208	−	0.764850i	$-0.277187\pi$
$89$	14.1271	−	2.29587i	1.49747	−	0.243362i	0.853258	+	0.521488i	$0.174623\pi$
$90$	1.53264	+	1.35780i	0.161555	+	0.143125i
$91$	−0.0936581	+	2.32410i	−0.00981804	+	0.243632i
$92$	0.0565508	+	0.465738i	0.00589583	+	0.0485565i
$93$	0.992894	+	8.17722i	0.102958	+	0.847938i
$94$	−10.6619	−	8.01192i	−1.09969	−	0.826367i
$95$	−2.70111	−	5.69247i	−0.277128	−	0.584035i
$96$	−0.145614	+	0.713266i	−0.0148617	+	0.0727974i
$97$	4.53193	+	1.93087i	0.460148	+	0.196051i	0.609585	−	0.792721i	$-0.291336\pi$
$97$	4.53193	+	1.93087i	0.460148	+	0.196051i	−0.149438	+	0.988771i	$0.547746\pi$
$98$	−7.31931	+	6.48434i	−0.739362	+	0.655017i
$99$	0.148268	−	0.390950i	0.0149015	−	0.0392919i
$100$	0.246372	−	0.256500i	0.0246372	−	0.0256500i
$101$	−16.6487	−	4.10354i	−1.65661	−	0.408318i	−0.703441	−	0.710754i	$-0.748354\pi$
$101$	−16.6487	−	4.10354i	−1.65661	−	0.408318i	−0.953170	+	0.302436i	$0.902200\pi$
$102$	9.78983	+	1.59100i	0.969337	+	0.157533i
$103$	−2.73782	+	7.21903i	−0.269765	+	0.711312i	0.729851	+	0.683606i	$0.239589\pi$
$103$	−2.73782	+	7.21903i	−0.269765	+	0.711312i	−0.999616	+	0.0277059i	$0.991180\pi$
$104$	1.70808	−	0.570240i	0.167491	−	0.0559166i
$105$	−4.75889	+	3.00934i	−0.464420	+	0.293681i
$106$	−7.97585	+	0.643877i	−0.774683	+	0.0625389i
$107$	−4.08109	+	7.06866i	−0.394534	+	0.683353i	−0.993042	−	0.117764i	$-0.962427\pi$
$107$	−4.08109	+	7.06866i	−0.394534	+	0.683353i	0.598507	+	0.801117i	$0.295761\pi$
$108$	−0.0732206	+	0.106078i	−0.00704565	+	0.0102074i
$109$	0.182404	+	4.52632i	0.0174712	+	0.433542i	0.984127	+	0.177464i	$0.0567894\pi$
$109$	0.182404	+	4.52632i	0.0174712	+	0.433542i	−0.966656	+	0.256078i	$0.917570\pi$
$110$	−0.787631	−	0.335578i	−0.0750977	−	0.0319961i
$111$	−1.92533	−	5.07669i	−0.182745	−	0.481858i
$112$	12.4085	+	6.51249i	1.17250	+	0.615373i
$113$	−0.100587	−	0.347266i	−0.00946241	−	0.0326680i	0.955648	−	0.294511i	$-0.0951568\pi$
$113$	−0.100587	−	0.347266i	−0.00946241	−	0.0326680i	−0.965110	+	0.261843i	$0.915670\pi$
$114$	−4.86638	+	3.07731i	−0.455778	+	0.288217i
$115$	5.16812	+	1.72537i	0.481929	+	0.160892i
$116$	−0.556498	+	0.806226i	−0.0516695	+	0.0748562i
$117$	0.616367	+	0.0497583i	0.0569832	+	0.00460016i
$118$	−5.28411	+	2.77332i	−0.486442	+	0.255304i
$119$	−11.6920	+	24.6404i	−1.07181	+	2.25878i
$120$	3.48485	+	2.61870i	0.318122	+	0.239053i
$121$	0.435886	−	10.8164i	0.0396260	−	0.983309i
$122$	−7.28460	+	15.3520i	−0.659517	+	1.38990i
$123$	0.462762	−	0.197165i	0.0417259	−	0.0177777i
$124$	0.212376	+	1.04029i	0.0190719	+	0.0934204i
$125$	−4.11870	−	10.8601i	−0.368388	−	0.971358i
$126$	3.25409	+	3.98553i	0.289897	+	0.355060i
$127$	8.49032	+	1.37981i	0.753394	+	0.122438i	0.524967	−	0.851123i	$-0.324078\pi$
$127$	8.49032	+	1.37981i	0.753394	+	0.122438i	0.228427	+	0.973561i	$0.426642\pi$
$128$	1.21724	−	10.0249i	0.107590	−	0.886084i
$129$	−5.93494			−0.522542
$130$	0.152620	−	1.25694i	0.0133857	−	0.110241i
$131$	−8.58722	+	8.94024i	−0.750268	+	0.781112i	−0.981434	−	0.191802i	$-0.938567\pi$
$131$	−8.58722	+	8.94024i	−0.750268	+	0.781112i	0.231165	+	0.972915i	$0.425746\pi$
$132$	0.0149941	−	0.0517658i	0.00130507	−	0.00450563i
$133$	−4.40498	−	15.2078i	−0.381960	−	1.31868i
$134$	1.08436	+	1.57096i	0.0936740	+	0.135710i
$135$	0.748452	+	1.29636i	0.0644165	+	0.111573i
$136$	21.0465	+	1.69905i	1.80472	+	0.145692i
$137$	9.97975	−	1.62187i	0.852627	−	0.138565i	0.281636	−	0.959521i	$-0.409123\pi$
$137$	9.97975	−	1.62187i	0.852627	−	0.138565i	0.570992	+	0.820956i	$0.306559\pi$
$138$	0.995908	−	4.87828i	0.0847773	−	0.415267i
$139$	1.73948	+	8.52052i	0.147541	+	0.722701i	0.984493	+	0.175425i	$0.0561301\pi$
$139$	1.73948	+	8.52052i	0.147541	+	0.722701i	−0.836952	+	0.547276i	$0.815665\pi$
$140$	−0.580195	+	0.435988i	−0.0490354	+	0.0368477i
$141$	−5.53856	−	8.02400i	−0.466431	−	0.675742i
$142$	−6.43378	+	0.519388i	−0.539910	+	0.0435861i
$143$	−0.251041	+	0.0618761i	−0.0209931	+	0.00517434i
$144$	1.86280	−	3.22646i	0.155233	−	0.268872i
$145$	5.68845	+	9.85269i	0.472400	+	0.818221i
$146$	2.69560	+	2.80642i	0.223089	+	0.232261i
$147$	−6.57659	+	2.80202i	−0.542428	+	0.231107i
$148$	−0.300015	−	0.632268i	−0.0246611	−	0.0519721i
$149$	1.46583	+	1.29861i	0.120085	+	0.106386i	0.721028	−	0.692906i	$-0.243670\pi$
$149$	1.46583	+	1.29861i	0.120085	+	0.106386i	−0.600943	+	0.799292i	$0.705208\pi$
$150$	−3.34204	+	1.75404i	−0.272876	+	0.143217i
$151$	−9.66766	−	10.0651i	−0.786743	−	0.819087i	0.200267	−	0.979741i	$-0.435819\pi$
$151$	−9.66766	−	10.0651i	−0.786743	−	0.819087i	−0.987011	+	0.160655i	$0.948639\pi$
$152$	−9.79925	+	7.36366i	−0.794824	+	0.597272i
$153$	6.42027	+	3.36962i	0.519048	+	0.272418i
$154$	−1.81829	−	1.14982i	−0.146522	−	0.0926547i
$155$	11.9721	+	2.95086i	0.961624	+	0.237019i
$156$	0.0797050			0.00638151
$157$	11.8930	−	3.94413i	0.949166	−	0.314776i
$157$	11.8930	−	3.94413i	0.949166	−	0.314776i
$158$	−1.08265			−0.0861308
$159$	−5.67978	−	1.39994i	−0.450436	−	0.111022i
$160$	0.921015	+	0.582414i	0.0728126	+	0.0460439i
$161$	12.1230	+	6.36262i	0.955423	+	0.501445i
$162$	1.09354	−	0.821745i	0.0859170	−	0.0645624i
$163$	−12.3910	−	12.9004i	−0.970536	−	1.01043i	−0.999941	−	0.0108670i	$-0.996541\pi$
$163$	−12.3910	−	12.9004i	−0.970536	−	1.01043i	0.0294053	−	0.999568i	$-0.490639\pi$
$164$	0.0574093	−	0.0301307i	0.00448291	−	0.00235281i
$165$	−0.468483	−	0.415040i	−0.0364713	−	0.0323108i
$166$	−6.16528	−	12.9930i	−0.478518	−	1.00846i
$167$	18.0477	−	7.68940i	1.39657	−	0.595024i	0.443091	−	0.896477i	$-0.353882\pi$
$167$	18.0477	−	7.68940i	1.39657	−	0.595024i	0.953481	+	0.301453i	$0.0974717\pi$
$168$	7.58789	+	7.89983i	0.585418	+	0.609485i
$169$	6.30881	+	10.9272i	0.485293	+	0.840552i
$170$	7.42334	−	12.8576i	0.569345	−	0.986134i
$171$	−4.08691	+	1.00733i	−0.312534	+	0.0770327i
$172$	−0.762502	+	0.0615556i	−0.0581403	+	0.00469357i
$173$	−10.0816	−	14.6057i	−0.766490	−	1.11045i	−0.990720	−	0.135916i	$-0.956602\pi$
$173$	−10.0816	−	14.6057i	−0.766490	−	1.11045i	0.224231	−	0.974536i	$-0.428013\pi$
$174$	8.31126	−	6.24550i	0.630075	−	0.473470i
$175$	−2.07605	−	10.1692i	−0.156935	−	0.768718i
$176$	−0.311590	+	1.52627i	−0.0234870	+	0.115047i
$177$	−4.30621	+	0.699827i	−0.323675	+	0.0526022i
$178$	−19.5142	−	1.57535i	−1.46265	−	0.118078i
$179$	−10.0127	−	17.3425i	−0.748385	−	1.29624i	−0.948597	−	0.316488i	$-0.897496\pi$
$179$	−10.0127	−	17.3425i	−0.748385	−	1.29624i	0.200212	−	0.979753i	$-0.435837\pi$
$180$	0.109604	+	0.158789i	0.00816941	+	0.0118354i
$181$	2.35480	+	8.12970i	0.175031	+	0.604276i	0.999276	+	0.0380431i	$0.0121124\pi$
$181$	2.35480	+	8.12970i	0.175031	+	0.604276i	−0.824246	+	0.566233i	$0.808400\pi$
$182$	0.885199	−	3.05606i	0.0656153	−	0.226530i
$183$	−8.60541	+	8.95918i	−0.636130	+	0.662281i
$184$	1.27764	−	10.5223i	0.0941885	−	0.775712i
$185$	−8.12747			−0.597544
$186$	1.35816	−	11.1855i	0.0995854	−	0.820160i
$187$	−2.99245	−	0.486321i	−0.218830	−	0.0355633i
$188$	−0.794800	−	0.973453i	−0.0579667	−	0.0709964i
$189$	1.33383	+	3.51703i	0.0970222	+	0.255826i
$190$	1.72398	+	8.44459i	0.125070	+	0.612635i
$191$	3.53086	−	1.50436i	0.255484	−	0.108851i	−0.260428	−	0.965493i	$-0.583864\pi$
$191$	3.53086	−	1.50436i	0.255484	−	0.108851i	0.515912	+	0.856642i	$0.327453\pi$
$192$	3.62116	−	7.63143i	0.261335	−	0.550751i
$193$	−0.633542	+	15.7212i	−0.0456034	+	1.13164i	0.800745	+	0.599006i	$0.204437\pi$
$193$	−0.633542	+	15.7212i	−0.0456034	+	1.13164i	−0.846348	+	0.532630i	$0.821204\pi$
$194$	−5.38693	−	4.04802i	−0.386759	−	0.290631i
$195$	0.396817	−	0.836274i	0.0284166	−	0.0598868i
$196$	−0.815878	+	0.428206i	−0.0582770	+	0.0305861i
$197$	8.47487	+	0.684162i	0.603810	+	0.0487446i	0.378592	−	0.925564i	$-0.376409\pi$
$197$	8.47487	+	0.684162i	0.603810	+	0.0487446i	0.225218	+	0.974308i	$0.427691\pi$
$198$	−0.324899	+	0.470698i	−0.0230896	+	0.0334510i
$199$	−20.0218	−	6.68427i	−1.41931	−	0.473835i	−0.499539	−	0.866292i	$-0.666497\pi$
$199$	−20.0218	−	6.68427i	−1.41931	−	0.473835i	−0.919771	+	0.392456i	$0.871625\pi$
$200$	−6.79131	+	4.29456i	−0.480218	+	0.303671i
$201$	0.388248	+	1.34039i	0.0273849	+	0.0945436i
$202$	20.7684	+	10.9001i	1.46126	+	0.766930i
$203$	10.1375	+	26.7305i	0.711515	+	1.87611i
$204$	0.859805	+	0.366329i	0.0601984	+	0.0256481i
$205$	−0.0303188	−	0.752353i	−0.00211755	−	0.0525466i
$206$	5.99938	−	8.69161i	0.417997	−	0.605573i
$207$	1.81993	−	3.15221i	0.126494	−	0.219094i
$208$	−2.29634	+	0.185379i	−0.159222	+	0.0128538i
$209$	1.48750	−	0.940641i	0.102893	−	0.0650655i
$210$	7.30557	−	2.43896i	0.504132	−	0.168304i
$211$	2.35745	−	6.21609i	0.162294	−	0.427933i	−0.829058	−	0.559162i	$-0.811123\pi$
$211$	2.35745	−	6.21609i	0.162294	−	0.427933i	0.991352	+	0.131229i	$0.0418922\pi$
$212$	−0.744240	−	0.120951i	−0.0511146	−	0.00830693i
$213$	−4.58164	−	1.12927i	−0.313929	−	0.0773764i
$214$	7.73421	−	8.05217i	0.528700	−	0.550435i
$215$	−3.15032	+	8.30672i	−0.214850	+	0.566513i
$216$	2.17972	−	1.93107i	0.148311	−	0.131392i
$217$	28.5049	+	12.1448i	1.93504	+	0.824442i
$218$	1.23946	−	6.07127i	0.0839468	−	0.411198i
$219$	1.21953	+	2.57010i	0.0824081	+	0.173671i
$220$	−0.0644939	−	0.0484640i	−0.00434818	−	0.00326744i
$221$	−0.540451	−	4.45101i	−0.0363546	−	0.299407i
$222$	0.895220	+	7.37280i	0.0600832	+	0.494830i
$223$	1.05990	−	26.3011i	0.0709761	−	1.76125i	−0.436609	−	0.899651i	$-0.643821\pi$
$223$	1.05990	−	26.3011i	0.0709761	−	1.76125i	0.507585	−	0.861601i	$-0.330538\pi$
$224$	2.04962	+	1.81581i	0.136946	+	0.121324i
$225$	−2.72355	+	0.442619i	−0.181570	+	0.0295080i
$226$	0.0199133	+	0.494144i	0.00132461	+	0.0328699i
$227$	5.25462	−	6.43574i	0.348761	−	0.427155i	−0.570198	−	0.821507i	$-0.693134\pi$
$227$	5.25462	−	6.43574i	0.348761	−	0.427155i	0.918959	+	0.394352i	$0.129031\pi$
$228$	−0.514626	+	0.171807i	−0.0340819	+	0.0113782i
$229$	4.18684	−	14.4546i	0.276674	−	0.955189i	−0.695029	−	0.718982i	$-0.744608\pi$
$229$	4.18684	−	14.4546i	0.276674	−	0.955189i	0.971703	−	0.236207i	$-0.0759044\pi$
$230$	−6.29915	−	3.98334i	−0.415353	−	0.262654i
$231$	−0.994677	−	1.21826i	−0.0654449	−	0.0801555i
$232$	16.5665	−	14.6767i	1.08765	−	0.963570i
$233$	9.72691	−	11.9133i	0.637231	−	0.780466i	−0.350512	−	0.936558i	$-0.613992\pi$
$233$	9.72691	−	11.9133i	0.637231	−	0.780466i	0.987742	+	0.156092i	$0.0498897\pi$
$234$	−0.802331	−	0.267857i	−0.0524500	−	0.0175104i
$235$	−14.1705	+	3.49273i	−0.924384	+	0.227840i
$236$	−0.545990	+	0.134574i	−0.0355409	+	0.00876005i
$237$	−0.750745	−	0.250635i	−0.0487661	−	0.0162805i
$238$	23.5948	−	28.8984i	1.52942	−	1.87320i
$239$	−8.98442	+	7.95950i	−0.581154	+	0.514858i	−0.901692	−	0.432378i	$-0.857675\pi$
$239$	−8.98442	+	7.95950i	−0.581154	+	0.514858i	0.320538	+	0.947236i	$0.396136\pi$
$240$	−3.52706	−	4.31986i	−0.227671	−	0.278846i
$241$	−15.4732	−	9.78469i	−0.996719	−	0.630287i	−0.0666904	−	0.997774i	$-0.521244\pi$
$241$	−15.4732	−	9.78469i	−0.996719	−	0.630287i	−0.930029	+	0.367487i	$0.880218\pi$
$242$	−4.11973	+	14.2229i	−0.264826	+	0.914286i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−1.01267	+	1.24030i	−0.0648298	+	0.0794020i
$245$	0.430878	+	10.6921i	0.0275278	+	0.683096i
$246$	−0.679154	+	0.110373i	−0.0433013	+	0.00703714i
$247$	1.94828	+	1.72602i	0.123966	+	0.109824i
$248$	0.965884	−	23.9682i	0.0613337	−	1.52198i
$249$	−1.26729	−	10.4371i	−0.0803114	−	0.661424i
$250$	1.91507	+	15.7720i	0.121119	+	0.997508i
$251$	−4.64585	−	3.49113i	−0.293243	−	0.220358i	0.443931	−	0.896061i	$-0.353584\pi$
$251$	−4.64585	−	3.49113i	−0.293243	−	0.220358i	−0.737174	+	0.675703i	$0.763840\pi$
$252$	0.207845	+	0.438023i	0.0130930	+	0.0275929i
$253$	−0.304419	+	1.49114i	−0.0191387	+	0.0937474i
$254$	−10.8246	−	4.61193i	−0.679196	−	0.289378i
$255$	8.12416	−	7.19738i	0.508755	−	0.450717i
$256$	1.09231	−	2.88018i	0.0682692	−	0.180011i
$257$	2.04503	−	2.12910i	0.127565	−	0.132809i	−0.654356	−	0.756186i	$-0.727060\pi$
$257$	2.04503	−	2.12910i	0.127565	−	0.132809i	0.781921	+	0.623377i	$0.214240\pi$
$258$	7.88240	+	1.94284i	0.490737	+	0.120956i
$259$	−20.1585	−	3.27607i	−1.25259	−	0.203565i
$260$	0.0423082	−	0.111557i	0.00262384	−	0.00691850i
$261$	7.20915	−	2.40677i	0.446235	−	0.148975i
$262$	14.3316	−	9.06277i	0.885411	−	0.559900i
$263$	0.639358	−	0.0516143i	0.0394245	−	0.00318267i	−0.0607386	−	0.998154i	$-0.519346\pi$
$263$	0.639358	−	0.0516143i	0.0394245	−	0.00318267i	0.100163	+	0.994971i	$0.468064\pi$
$264$	−0.608801	+	1.05447i	−0.0374691	+	0.0648984i
$265$	−4.97428	+	7.20649i	−0.305567	+	0.442691i
$266$	0.872060	+	21.6400i	0.0534694	+	1.32683i
$267$	−13.1671	−	5.60999i	−0.805815	−	0.343326i
$268$	0.0637830	+	0.168182i	0.00389616	+	0.0102733i
$269$	−12.4236	−	6.52039i	−0.757478	−	0.397555i	0.0413266	−	0.999146i	$-0.486842\pi$
$269$	−12.4236	−	6.52039i	−0.757478	−	0.397555i	−0.798805	+	0.601591i	$0.794534\pi$
$270$	−0.569675	−	1.96675i	−0.0346693	−	0.119692i
$271$	26.7750	−	16.9315i	1.62647	−	1.02852i	0.667657	−	0.744469i	$-0.267297\pi$
$271$	26.7750	−	16.9315i	1.62647	−	1.02852i	0.958810	−	0.284047i	$-0.0916771\pi$
$272$	−25.6234	−	8.55434i	−1.55365	−	0.518683i
$273$	1.32131	−	1.91425i	0.0799694	−	0.115856i
$274$	−13.7854	−	1.11287i	−0.832806	−	0.0672310i
$275$	1.02156	−	0.536157i	0.0616024	−	0.0323315i
$276$	0.201125	−	0.423862i	0.0121063	−	0.0255135i
$277$	20.5267	+	15.4248i	1.23333	+	0.926786i	0.998970	−	0.0453648i	$-0.0144450\pi$
$277$	20.5267	+	15.4248i	1.23333	+	0.926786i	0.234357	+	0.972151i	$0.424701\pi$
$278$	0.478983	−	11.8858i	0.0287275	−	0.712865i
$279$	3.53126	−	7.44197i	0.211411	−	0.445539i
$280$	15.0846	−	6.42693i	0.901475	−	0.384082i
$281$	3.76894	+	18.4615i	0.224836	+	1.10132i	0.922828	+	0.385213i	$0.125872\pi$
$281$	3.76894	+	18.4615i	0.224836	+	1.10132i	−0.697992	+	0.716106i	$0.745923\pi$
$282$	4.72926	+	12.4700i	0.281623	+	0.742580i
$283$	17.5700	+	21.5193i	1.04443	+	1.27919i	0.959170	+	0.282831i	$0.0912737\pi$
$283$	17.5700	+	21.5193i	1.04443	+	1.27919i	0.0852570	+	0.996359i	$0.472829\pi$
$284$	−0.600347	−	0.0975658i	−0.0356240	−	0.00578947i
$285$	−0.759478	+	6.25487i	−0.0449876	+	0.370506i
$286$	0.353672			0.0209131
$287$	0.228064	−	1.87827i	0.0134622	−	0.110871i
$288$	0.504288	−	0.525020i	0.0297155	−	0.0309371i
$289$	9.89738	−	34.1697i	0.582199	−	2.00998i
$290$	−4.32970	−	14.9479i	−0.254249	−	0.877768i
$291$	−2.79836	−	4.05412i	−0.164042	−	0.237657i
$292$	0.183337	+	0.317550i	0.0107290	+	0.0185832i
$293$	−27.7717	−	2.24196i	−1.62244	−	0.130977i	−0.764464	−	0.644667i	$-0.776996\pi$
$293$	−27.7717	−	2.24196i	−1.62244	−	0.130977i	−0.857976	+	0.513690i	$0.828278\pi$
$294$	9.65187	−	1.56858i	0.562908	−	0.0914815i
$295$	−1.30628	+	6.39857i	−0.0760544	+	0.372539i
$296$	3.16265	+	15.4917i	0.183825	+	0.900435i
$297$	−0.334264	+	0.251183i	−0.0193959	+	0.0145751i
$298$	−1.52171	−	2.20458i	−0.0881503	−	0.127708i
$299$	−2.24349	+	0.181113i	−0.129744	+	0.0104740i
$300$	−0.345322	+	0.0851142i	−0.0199372	+	0.00491407i
$301$	−11.1620	+	19.3332i	−0.643369	+	1.11435i
$302$	9.54509	+	16.5326i	0.549258	+	0.951344i
$303$	11.8781	+	12.3664i	0.682381	+	0.710434i
$304$	14.4270	−	6.14677i	0.827446	−	0.352542i
$305$	7.97170	+	16.8000i	0.456458	+	0.961965i
$306$	−7.42393	−	6.57703i	−0.424398	−	0.375984i
$307$	−17.9779	+	9.43556i	−1.02606	+	0.538516i	−0.891799	−	0.452431i	$-0.850557\pi$
$307$	−17.9779	+	9.43556i	−1.02606	+	0.538516i	−0.134256	+	0.990947i	$0.542865\pi$
$308$	−0.140428	−	0.146201i	−0.00800165	−	0.00833060i
$309$	6.17230	−	4.63818i	0.351130	−	0.263857i
$310$	−14.9346	−	7.83829i	−0.848229	−	0.445185i
$311$	−6.97191	−	4.40877i	−0.395341	−	0.249998i	0.321973	−	0.946749i	$-0.395654\pi$
$311$	−6.97191	−	4.40877i	−0.395341	−	0.249998i	−0.717313	+	0.696751i	$0.754628\pi$
$312$	−1.74842	−	0.430948i	−0.0989850	−	0.0243976i
$313$	8.31606			0.470051			0.235026	−	0.971989i	$-0.424483\pi$
$313$	8.31606			0.470051			0.235026	+	0.971989i	$0.424483\pi$
$314$	−17.0867	+	1.34509i	−0.964257	+	0.0759078i
$315$	5.63055			0.317246
$316$	−0.0990528	−	0.0244143i	−0.00557216	−	0.00137341i
$317$	−15.1061	−	9.55250i	−0.848441	−	0.536522i	0.0380454	−	0.999276i	$-0.487887\pi$
$317$	−15.1061	−	9.55250i	−0.848441	−	0.536522i	−0.886487	+	0.462754i	$0.846861\pi$
$318$	7.08524	+	3.71862i	0.397320	+	0.208530i
$319$	−2.54050	+	1.90906i	−0.142241	+	0.106887i
$320$	−8.75903	−	9.11912i	−0.489645	−	0.509774i
$321$	7.22726	−	3.79316i	0.403386	−	0.211713i
$322$	−14.0181	−	12.4189i	−0.781197	−	0.692080i
$323$	13.0838	+	27.5736i	0.728004	+	1.53424i
$324$	0.118581	−	0.0505225i	0.00658781	−	0.00280680i
$325$	1.18197	+	1.23056i	0.0655639	+	0.0682592i
$326$	12.2339	+	21.1897i	0.677571	+	1.17359i
$327$	2.26500	−	3.92309i	0.125255	−	0.216947i
$328$	−1.42225	+	0.350553i	−0.0785307	+	0.0193561i
$329$	−36.5549	+	2.95102i	−2.01534	+	0.162695i
$330$	0.486343	+	0.704589i	0.0267723	+	0.0387864i
$331$	−20.1208	+	15.1198i	−1.10594	+	0.831059i	−0.986820	−	0.161821i	$-0.948263\pi$
$331$	−20.1208	+	15.1198i	−1.10594	+	0.831059i	−0.119119	+	0.992880i	$0.538007\pi$
$332$	−0.271068	−	1.32778i	−0.0148768	−	0.0728714i
$333$	−1.08604	+	5.31979i	−0.0595148	+	0.291523i
$334$	−26.4869	+	4.30455i	−1.44930	+	0.235534i
$335$	2.08213	+	0.168087i	0.113759	+	0.00918357i
$336$	−7.00685	−	12.1362i	−0.382255	−	0.662085i
$337$	10.9677	+	15.8894i	0.597448	+	0.865553i	0.998729	−	0.0504017i	$-0.0160502\pi$
$337$	10.9677	+	15.8894i	0.597448	+	0.865553i	−0.401281	+	0.915955i	$0.631435\pi$
$338$	−4.80187	−	16.5780i	−0.261188	−	0.901724i
$339$	−0.100587	+	0.347266i	−0.00546312	+	0.0188609i
$340$	0.969117	−	1.00896i	0.0525578	−	0.0547184i
$341$	−0.415150	+	3.41907i	−0.0224816	+	0.185153i
$342$	5.75773			0.311342
$343$	−0.0673889	+	0.554997i	−0.00363866	+	0.0299670i
$344$	17.0592	+	2.77239i	0.919771	+	0.149477i
$345$	−3.44589	−	4.22045i	−0.185520	−	0.227221i
$346$	8.60846	+	22.6986i	0.462794	+	1.22029i
$347$	−5.14931	−	25.2230i	−0.276429	−	1.35404i	−0.846475	−	0.532428i	$-0.821280\pi$
$347$	−5.14931	−	25.2230i	−0.276429	−	1.35404i	0.570046	−	0.821613i	$-0.306925\pi$
$348$	0.901247	−	0.383985i	0.0483119	−	0.0205838i
$349$	7.27337	−	15.3283i	0.389334	−	0.820505i	−0.610265	−	0.792197i	$-0.708937\pi$
$349$	7.27337	−	15.3283i	0.389334	−	0.820505i	0.999599	−	0.0283073i	$-0.00901170\pi$
$350$	−0.571663	+	14.1857i	−0.0305566	+	0.758255i
$351$	−0.494353	−	0.371483i	−0.0263866	−	0.0198283i
$352$	−0.130487	+	0.274995i	−0.00695496	+	0.0146573i
$353$	9.57862	−	5.02725i	0.509819	−	0.267573i	−0.190140	−	0.981757i	$-0.560894\pi$
$353$	9.57862	−	5.02725i	0.509819	−	0.267573i	0.699958	+	0.714184i	$0.253202\pi$
$354$	5.94832	+	0.480198i	0.316150	+	0.0255222i
$355$	−4.01254	+	5.81316i	−0.212963	+	0.308531i
$356$	−1.74986	−	0.584188i	−0.0927422	−	0.0309619i
$357$	23.0514	−	14.5769i	1.22001	−	0.771489i
$358$	7.62105	+	26.3109i	0.402785	+	1.39058i
$359$	21.5740	+	11.3229i	1.13863	+	0.597602i	0.925247	−	0.379366i	$-0.123858\pi$
$359$	21.5740	+	11.3229i	1.13863	+	0.597602i	0.213388	+	0.976968i	$0.431550\pi$
$360$	−1.54576	−	4.07583i	−0.0814687	−	0.214815i
$361$	1.17979	+	0.502662i	0.0620943	+	0.0264559i
$362$	−0.466182	−	11.5682i	−0.0245020	−	0.608011i
$363$	−6.14940	+	8.90894i	−0.322760	+	0.467598i
$364$	0.149904	−	0.259641i	0.00785710	−	0.0136089i
$365$	4.24453	−	0.342654i	0.222169	−	0.0179353i
$366$	14.3620	−	9.08197i	0.750713	−	0.474722i
$367$	−25.6619	+	8.56721i	−1.33954	+	0.447205i	−0.894004	−	0.448059i	$-0.852116\pi$
$367$	−25.6619	+	8.56721i	−1.33954	+	0.447205i	−0.445537	+	0.895263i	$0.646987\pi$
$368$	−4.80867	+	12.6794i	−0.250669	+	0.660960i
$369$	−0.496500	−	0.0806891i	−0.0258467	−	0.00420051i
$370$	10.7944	+	2.66058i	0.561173	+	0.138317i
$371$	−15.2425	+	15.8691i	−0.791351	+	0.823883i
$372$	0.376499	−	0.992747i	0.0195206	−	0.0514715i
$373$	−3.16954	+	2.80796i	−0.164112	+	0.145391i	−0.741182	−	0.671304i	$-0.765735\pi$
$373$	−3.16954	+	2.80796i	−0.164112	+	0.145391i	0.577070	+	0.816695i	$0.304196\pi$
$374$	3.81518	+	1.62550i	0.197278	+	0.0840525i
$375$	−2.32328	+	11.3802i	−0.119974	+	0.587669i
$376$	12.1716	+	25.6512i	0.627704	+	1.32286i
$377$	−3.75723	−	2.82338i	−0.193507	−	0.145411i
$378$	−0.620191	−	5.10773i	−0.0318992	−	0.262713i
$379$	1.15809	+	9.53770i	0.0594869	+	0.489919i	0.991755	+	0.128150i	$0.0409039\pi$
$379$	1.15809	+	9.53770i	0.0594869	+	0.489919i	−0.932268	+	0.361769i	$0.882173\pi$
$380$	−0.0327016	+	0.811483i	−0.00167756	+	0.0416282i
$381$	−6.43847	−	5.70399i	−0.329853	−	0.292224i
$382$	−5.18192	+	0.842143i	−0.265130	+	0.0430878i
$383$	−1.20133	−	29.8106i	−0.0613849	−	1.52325i	−0.677458	−	0.735562i	$-0.736918\pi$
$383$	−1.20133	−	29.8106i	−0.0613849	−	1.52325i	0.616073	−	0.787689i	$-0.288723\pi$
$384$	−6.38677	+	7.82237i	−0.325923	+	0.399184i
$385$	−2.23309	+	0.745516i	−0.113809	+	0.0379950i
$386$	5.98786	−	20.6725i	0.304774	−	1.05220i
$387$	5.01615	+	3.17202i	0.254985	+	0.161243i
$388$	−0.401572	−	0.491836i	−0.0203867	−	0.0249692i
$389$	−2.61636	+	2.31789i	−0.132655	+	0.117522i	−0.726841	−	0.686805i	$-0.759012\pi$
$389$	−2.61636	+	2.31789i	−0.132655	+	0.117522i	0.594187	+	0.804327i	$0.297474\pi$
$390$	−0.800786	+	0.980784i	−0.0405494	+	0.0496639i
$391$	−25.0337	−	8.35747i	−1.26601	−	0.422656i
$392$	20.2125	−	4.98193i	1.02088	−	0.251625i
$393$	12.0361	−	2.96663i	0.607140	−	0.149647i
$394$	−11.0318	−	3.68296i	−0.555775	−	0.185545i
$395$	−0.749299	+	0.917725i	−0.0377013	+	0.0461757i
$396$	−0.0403399	+	0.0357381i	−0.00202716	+	0.00179591i
$397$	−3.37503	−	4.13366i	−0.169388	−	0.207463i	0.682934	−	0.730480i	$-0.260704\pi$
$397$	−3.37503	−	4.13366i	−0.169388	−	0.207463i	−0.852322	+	0.523018i	$0.824806\pi$
$398$	24.4036	+	15.4319i	1.22324	+	0.773530i
$399$	−4.40498	+	15.2078i	−0.220525	+	0.761340i
$400$	9.75092	−	3.25533i	0.487546	−	0.162767i
$401$	−0.673877	+	0.825349i	−0.0336518	+	0.0412160i	−0.791157	−	0.611614i	$-0.790521\pi$
$401$	−0.673877	+	0.825349i	−0.0336518	+	0.0412160i	0.757505	+	0.652829i	$0.226418\pi$
$402$	−0.0768620	−	1.90731i	−0.00383353	−	0.0951280i
$403$	−5.02775	+	0.817088i	−0.250450	+	0.0407021i
$404$	1.65433	+	1.46561i	0.0823058	+	0.0729166i
$405$	0.0602742	−	1.49569i	0.00299505	−	0.0743214i
$406$	−4.71363	−	38.8203i	−0.233934	−	1.92662i
$407$	−0.273642	−	2.25364i	−0.0135639	−	0.111709i
$408$	−16.8802	−	12.6846i	−0.835694	−	0.627983i
$409$	10.0773	+	21.2375i	0.498292	+	1.05013i	0.984354	+	0.176204i	$0.0563817\pi$
$409$	10.0773	+	21.2375i	0.498292	+	1.05013i	−0.486062	+	0.873924i	$0.661567\pi$
$410$	−0.206020	+	1.00915i	−0.0101746	+	0.0498384i
$411$	−9.30162	−	3.96305i	−0.458815	−	0.195483i
$412$	0.744892	−	0.659916i	0.0366982	−	0.0325118i
$413$	−5.81913	+	15.3438i	−0.286340	+	0.755018i
$414$	−3.44901	+	3.59079i	−0.169509	+	0.176478i
$415$	−15.2808	−	3.76637i	−0.750103	−	0.184884i
$416$	−0.444332	−	0.0722110i	−0.0217852	−	0.00354044i
$417$	3.08374	−	8.13115i	0.151011	−	0.398184i
$418$	−2.28353	+	0.762355i	−0.111691	+	0.0372880i
$419$	2.73677	−	1.73063i	0.133700	−	0.0845468i	−0.465941	−	0.884816i	$-0.654284\pi$
$419$	2.73677	−	1.73063i	0.133700	−	0.0845468i	0.599641	+	0.800269i	$0.295310\pi$
$420$	0.723396	−	0.0583985i	0.0352981	−	0.00284956i
$421$	−19.8116	+	34.3148i	−0.965560	+	1.67240i	−0.257458	+	0.966289i	$0.582885\pi$
$421$	−19.8116	+	34.3148i	−0.965560	+	1.67240i	−0.708102	+	0.706110i	$0.750448\pi$
$422$	−5.16589	+	7.48408i	−0.251471	+	0.364319i
$423$	0.392588	+	9.74197i	0.0190883	+	0.473671i
$424$	15.6718	+	6.67714i	0.761091	+	0.324271i
$425$	7.09458	+	18.7069i	0.344138	+	0.907417i
$426$	5.71536	+	2.99965i	0.276910	+	0.145334i
$427$	13.0003	+	44.8822i	0.629127	+	2.17200i
$428$	0.889193	−	0.562292i	0.0429808	−	0.0271794i
$429$	0.245248	+	0.0818759i	0.0118407	+	0.00395301i
$430$	6.90331	−	10.0012i	0.332907	−	0.482299i
$431$	−5.98894	−	0.483477i	−0.288477	−	0.0232883i	−0.0646190	−	0.997910i	$-0.520583\pi$
$431$	−5.98894	−	0.483477i	−0.288477	−	0.0232883i	−0.223858	+	0.974622i	$0.571865\pi$
$432$	−3.29885	+	1.73137i	−0.158716	+	0.0833006i
$433$	−0.703700	+	1.48302i	−0.0338177	+	0.0712692i	−0.919656	−	0.392724i	$-0.871533\pi$
$433$	−0.703700	+	1.48302i	−0.0338177	+	0.0712692i	0.885839	+	0.463994i	$0.153584\pi$
$434$	−33.8827	−	25.4612i	−1.62642	−	1.22218i
$435$	0.458102	−	11.3677i	0.0219643	−	0.545038i
$436$	0.250310	−	0.527518i	0.0119877	−	0.0252635i
$437$	14.0950	−	6.00531i	0.674255	−	0.287273i
$438$	−0.778360	−	3.81266i	−0.0371915	−	0.182176i
$439$	−8.12161	−	21.4149i	−0.387623	−	1.02208i	−0.976815	−	0.214085i	$-0.931323\pi$
$439$	−8.12161	−	21.4149i	−0.387623	−	1.02208i	0.589192	−	0.807993i	$-0.299446\pi$
$440$	1.15272	+	1.41182i	0.0549535	+	0.0673059i
$441$	7.05606	+	1.14672i	0.336003	+	0.0546058i
$442$	−0.739274	+	6.08847i	−0.0351637	+	0.289599i
$443$	6.83872			0.324917			0.162459	−	0.986715i	$-0.448058\pi$
$443$	6.83872			0.324917			0.162459	+	0.986715i	$0.448058\pi$
$444$	−0.0843560	+	0.694734i	−0.00400336	+	0.0329706i
$445$	−14.8411	+	15.4513i	−0.703537	+	0.732460i
$446$	−10.0175	+	34.5845i	−0.474343	+	1.63762i
$447$	−0.544840	−	1.88101i	−0.0257701	−	0.0889686i
$448$	−18.0491	−	26.1487i	−0.852742	−	1.23541i
$449$	−0.241421	−	0.418154i	−0.0113934	−	0.0197339i	0.860273	−	0.509835i	$-0.170293\pi$
$449$	−0.241421	−	0.418154i	−0.0113934	−	0.0197339i	−0.871666	+	0.490101i	$0.836960\pi$
$450$	3.76213	+	0.303711i	0.177349	+	0.0143171i
$451$	0.207597	−	0.0337378i	0.00977536	−	0.00158865i
$452$	−0.00932132	+	0.0456589i	−0.000438438	+	0.00214761i
$453$	2.79156	+	13.6740i	0.131159	+	0.642459i
$454$	−9.08562	+	6.82740i	−0.426409	+	0.320426i
$455$	−1.97788	−	2.86545i	−0.0927243	−	0.134334i
$456$	12.2179	−	0.986327i	0.572154	−	0.0461890i
$457$	−5.91605	+	1.45817i	−0.276741	+	0.0682105i	−0.375243	−	0.926926i	$-0.622441\pi$
$457$	−5.91605	+	1.45817i	−0.276741	+	0.0682105i	0.0985025	+	0.995137i	$0.468595\pi$
$458$	−10.2925	+	17.8271i	−0.480937	+	0.833007i
$459$	−3.62541	−	6.27939i	−0.169219	−	0.293097i
$460$	−0.486490	−	0.506490i	−0.0226827	−	0.0236152i
$461$	32.2557	−	13.7429i	1.50230	−	0.640069i	0.524839	−	0.851202i	$-0.324126\pi$
$461$	32.2557	−	13.7429i	1.50230	−	0.640069i	0.977457	+	0.211133i	$0.0677153\pi$
$462$	0.922261	+	1.94362i	0.0429075	+	0.0904256i
$463$	−18.5122	−	16.4003i	−0.860333	−	0.762188i	0.112511	−	0.993650i	$-0.464111\pi$
$463$	−18.5122	−	16.4003i	−0.860333	−	0.762188i	−0.972844	+	0.231462i	$0.925649\pi$
$464$	−25.0722	+	13.1589i	−1.16395	+	0.610888i
$465$	−8.54158	−	8.89273i	−0.396106	−	0.412390i
$466$	−16.8185	+	12.6383i	−0.779104	+	0.585458i
$467$	12.6711	+	6.65031i	0.586349	+	0.307740i	0.731685	−	0.681643i	$-0.238734\pi$
$467$	12.6711	+	6.65031i	0.586349	+	0.307740i	−0.145336	+	0.989382i	$0.546426\pi$
$468$	−0.0673659	−	0.0425996i	−0.00311399	−	0.00196917i
$469$	5.09654	+	1.25618i	0.235336	+	0.0580052i
$470$	19.9638			0.920860
$471$	−12.1599	−	3.02287i	−0.560297	−	0.139286i
$472$	12.7045			0.584774
$473$	−2.40941	−	0.593867i	−0.110785	−	0.0273060i
$474$	0.915043	+	0.578638i	0.0420293	+	0.0265777i
$475$	−10.2841	−	5.39749i	−0.471865	−	0.247654i
$476$	2.81039	−	2.11187i	0.128814	−	0.0967975i
$477$	4.05227	+	4.21886i	0.185541	+	0.193168i
$478$	14.5381	−	7.63019i	0.664958	−	0.348997i
$479$	5.18568	+	4.59411i	0.236940	+	0.209910i	0.773234	−	0.634121i	$-0.218638\pi$
$479$	5.18568	+	4.59411i	0.236940	+	0.209910i	−0.536294	+	0.844031i	$0.680176\pi$
$480$	−0.467152	−	0.984502i	−0.0213225	−	0.0449362i
$481$	3.08880	−	1.31601i	0.140837	−	0.0600051i
$482$	17.3475	+	18.0606i	0.790156	+	0.822640i
$483$	−6.84560	−	11.8569i	−0.311486	−	0.539509i
$484$	−0.697654	+	1.20837i	−0.0317116	+	0.0549260i
$485$	−7.15966	+	1.76470i	−0.325103	+	0.0801307i
$486$	−1.36345	+	0.110069i	−0.0618473	+	0.00499283i
$487$	18.0900	+	26.2079i	0.819736	+	1.18759i	0.979700	+	0.200470i	$0.0642469\pi$
$487$	18.0900	+	26.2079i	0.819736	+	1.18759i	−0.159964	+	0.987123i	$0.551138\pi$
$488$	28.9202	−	21.7321i	1.30916	−	0.983768i
$489$	3.57792	+	17.5258i	0.161799	+	0.792545i
$490$	2.92787	−	14.3417i	0.132268	−	0.647890i
$491$	−9.30477	+	1.51217i	−0.419918	+	0.0682434i	−0.366699	−	0.930340i	$-0.619512\pi$
$491$	−9.30477	+	1.51217i	−0.419918	+	0.0682434i	−0.0532189	+	0.998583i	$0.516948\pi$
$492$	−0.0646256	−	0.00521712i	−0.00291355	−	0.000235206i
$493$	−27.5541	−	47.7252i	−1.24098	−	2.14943i
$494$	−2.02255	−	2.93017i	−0.0909989	−	0.131835i
$495$	0.174133	+	0.601175i	0.00782668	+	0.0270208i
$496$	−8.53816	+	29.4771i	−0.383374	+	1.32356i
$497$	−12.2955	+	12.8009i	−0.551527	+	0.574201i
$498$	−1.73351	+	14.2767i	−0.0776804	+	0.639755i
$499$	21.4607			0.960713			0.480357	−	0.877073i	$-0.340507\pi$
$499$	21.4607			0.960713			0.480357	+	0.877073i	$0.340507\pi$
$500$	−0.180455	+	1.48618i	−0.00807021	+	0.0664642i
$501$	−19.3634	−	3.14687i	−0.865095	−	0.140592i
$502$	5.02747	+	6.15754i	0.224387	+	0.274824i
$503$	6.64843	+	17.5305i	0.296439	+	0.781645i	0.997639	+	0.0686800i	$0.0218787\pi$
$503$	6.64843	+	17.5305i	0.296439	+	0.781645i	−0.701200	+	0.712965i	$0.747352\pi$
$504$	−2.19102	−	10.7323i	−0.0975958	−	0.478056i
$505$	23.6135	−	10.0608i	1.05079	−	0.447698i
$506$	0.892444	−	1.88079i	0.0396740	−	0.0836111i
$507$	0.508060	−	12.6074i	0.0225637	−	0.559914i
$508$	−0.886355	−	0.666052i	−0.0393256	−	0.0295513i
$509$	0.977993	−	2.06108i	0.0433488	−	0.0913557i	−0.880621	−	0.473822i	$-0.842874\pi$
$509$	0.977993	−	2.06108i	0.0433488	−	0.0913557i	0.923969	+	0.382466i	$0.124925\pi$
$510$	−13.1461	+	6.89960i	−0.582119	+	0.305519i
$511$	10.6658	+	0.861031i	0.471826	+	0.0380898i
$512$	−13.8668	+	20.0895i	−0.612832	+	0.887841i
$513$	3.99260	+	1.33293i	0.176278	+	0.0588502i
$514$	−3.41304	+	2.15828i	−0.150543	+	0.0951976i
$515$	−3.21542	−	11.1009i	−0.141688	−	0.489165i
$516$	0.677359	+	0.355505i	0.0298191	+	0.0156502i
$517$	−1.44559	−	3.81171i	−0.0635771	−	0.167639i
$518$	25.7008	+	10.9501i	1.12923	+	0.481118i
$519$	0.714611	+	17.7329i	0.0313679	+	0.778387i
$520$	−1.53125	+	2.21839i	−0.0671496	+	0.0972830i
$521$	5.32424	−	9.22186i	0.233259	−	0.404017i	−0.725506	−	0.688216i	$-0.758394\pi$
$521$	5.32424	−	9.22186i	0.233259	−	0.404017i	0.958765	+	0.284199i	$0.0917276\pi$
$522$	−10.3626	+	0.836556i	−0.453559	+	0.0366150i
$523$	2.02664	−	1.28157i	0.0886187	−	0.0560390i	−0.489422	−	0.872047i	$-0.662792\pi$
$523$	2.02664	−	1.28157i	0.0886187	−	0.0560390i	0.578040	+	0.816008i	$0.303818\pi$
$524$	1.51559	−	0.505978i	0.0662088	−	0.0221037i
$525$	−3.68042	+	9.70447i	−0.160627	+	0.423538i
$526$	−0.866050	−	0.140747i	−0.0377616	−	0.00613685i
$527$	−57.9914	−	14.2936i	−2.52615	−	0.622639i
$528$	1.07909	−	1.12345i	0.0469614	−	0.0488920i
$529$	3.45791	−	9.11776i	0.150344	−	0.396424i
$530$	8.96560	−	7.94283i	0.389441	−	0.345014i
$531$	4.01360	+	1.71003i	0.174175	+	0.0742092i
$532$	−0.408207	+	1.99953i	−0.0176980	+	0.0866907i
$533$	0.133345	+	0.281018i	0.00577580	+	0.0121722i
$534$	15.6513	+	11.7612i	0.677296	+	0.508955i
$535$	−1.47272	−	12.1289i	−0.0636712	−	0.524379i
$536$	−0.489832	−	4.03413i	−0.0211575	−	0.174248i
$537$	−0.806342	+	20.0092i	−0.0347962	+	0.863459i
$538$	14.3657	+	12.7269i	0.619349	+	0.548695i
$539$	−2.95028	+	0.479468i	−0.127078	+	0.0206521i
$540$	−0.00776904	−	0.192787i	−0.000334326	−	0.00829622i
$541$	−3.85605	+	4.72281i	−0.165785	+	0.203049i	−0.850815	−	0.525465i	$-0.823891\pi$
$541$	−3.85605	+	4.72281i	−0.165785	+	0.203049i	0.685031	+	0.728514i	$0.259789\pi$
$542$	−41.1035	+	13.7224i	−1.76555	+	0.589426i
$543$	2.35480	−	8.12970i	0.101054	−	0.348879i
$544$	−4.46128	−	2.82114i	−0.191276	−	0.120955i
$545$	−4.28859	−	5.25257i	−0.183703	−	0.224995i
$546$	−2.38152	+	2.10984i	−0.101920	+	0.0902930i
$547$	−14.7321	+	18.0436i	−0.629901	+	0.771489i	−0.986675	−	0.162702i	$-0.947979\pi$
$547$	−14.7321	+	18.0436i	−0.629901	+	0.771489i	0.356774	+	0.934191i	$0.383877\pi$
$548$	−1.23615	−	0.412686i	−0.0528055	−	0.0176291i
$549$	12.0616	−	2.97291i	0.514776	−	0.126881i
$550$	−1.53229	+	0.377674i	−0.0653369	+	0.0161041i
$551$	30.3450	+	10.1306i	1.29274	+	0.431580i
$552$	−6.70364	+	8.21047i	−0.285326	+	0.349461i
$553$	−2.22840	+	1.97419i	−0.0947613	+	0.0839512i
$554$	−22.2128	−	27.2057i	−0.943731	−	1.15586i
$555$	6.86926	+	4.34386i	0.291584	+	0.184386i
$556$	0.311855	−	1.07665i	0.0132256	−	0.0456601i
$557$	28.8190	−	9.62119i	1.22110	−	0.407663i	0.368204	−	0.929745i	$-0.379973\pi$
$557$	28.8190	−	9.62119i	1.22110	−	0.407663i	0.852895	+	0.522082i	$0.174845\pi$
$558$	−7.12617	+	8.72797i	−0.301675	+	0.369484i
$559$	−0.147776	−	3.66703i	−0.00625027	−	0.155099i
$560$	−20.7055	+	3.36498i	−0.874968	+	0.142196i
$561$	2.26927	+	2.01040i	0.0958087	+	0.0848791i
$562$	1.03781	−	25.7531i	0.0437776	−	1.08633i
$563$	−2.39029	−	19.6858i	−0.100739	−	0.829658i	−0.952250	−	0.305321i	$-0.901236\pi$
$563$	−2.39029	−	19.6858i	−0.100739	−	0.829658i	0.851511	−	0.524337i	$-0.175687\pi$
$564$	0.151480	+	1.24755i	0.00637844	+	0.0525312i
$565$	0.432651	+	0.325116i	0.0182018	+	0.0136777i
$566$	−16.2908	−	34.3322i	−0.684755	−	1.44309i
$567$	0.752390	−	3.68545i	0.0315974	−	0.154774i
$568$	12.6418	+	5.38617i	0.530438	+	0.225999i
$569$	28.3676	−	25.1315i	1.18923	−	1.05357i	0.191839	−	0.981426i	$-0.438555\pi$
$569$	28.3676	−	25.1315i	1.18923	−	1.05357i	0.997394	−	0.0721421i	$-0.0229835\pi$
$570$	3.05626	−	8.05869i	0.128013	−	0.337541i
$571$	18.3965	−	19.1528i	0.769869	−	0.801518i	−0.214670	−	0.976687i	$-0.568868\pi$
$571$	18.3965	−	19.1528i	0.769869	−	0.801518i	0.984538	+	0.175168i	$0.0560470\pi$
$572$	0.0323579	+	0.00797551i	0.00135295	+	0.000333473i
$573$	−3.78827	−	0.615654i	−0.158257	−	0.0257193i
$574$	−0.917764	+	2.41994i	−0.0383067	+	0.101007i
$575$	9.52651	−	3.18042i	0.397283	−	0.132633i
$576$	−7.13931	+	4.51462i	−0.297471	+	0.188109i
$577$	4.97408	−	0.401550i	0.207074	−	0.0167167i	0.0235056	−	0.999724i	$-0.492517\pi$
$577$	4.97408	−	0.401550i	0.207074	−	0.0167167i	0.183568	+	0.983007i	$0.441235\pi$
$578$	−24.3307	+	42.1421i	−1.01202	+	1.75288i
$579$	8.93790	−	12.9488i	0.371447	−	0.538133i
$580$	−0.0590469	−	1.46523i	−0.00245179	−	0.0608406i
$581$	−36.3825	−	15.5011i	−1.50940	−	0.643096i
$582$	2.38945	+	6.30047i	0.0990461	+	0.261163i
$583$	−2.16574	−	1.13667i	−0.0896959	−	0.0470760i
$584$	−2.30480	−	7.95710i	−0.0953734	−	0.329267i
$585$	−0.782345	+	0.494725i	−0.0323460	+	0.0204544i
$586$	36.1507	+	12.0689i	1.49337	+	0.498560i
$587$	4.86080	−	7.04209i	0.200627	−	0.290658i	−0.709737	−	0.704467i	$-0.751186\pi$
$587$	4.86080	−	7.04209i	0.200627	−	0.290658i	0.910364	+	0.413808i	$0.135802\pi$
$588$	0.918434	+	0.0741436i	0.0378756	+	0.00305763i
$589$	30.7010	−	16.1132i	1.26501	−	0.663931i
$590$	3.82952	−	8.07055i	0.157659	−	0.332259i
$591$	−6.79722	−	5.10778i	−0.279600	−	0.210106i
$592$	0.814508	−	20.2118i	0.0334761	−	0.830700i
$593$	3.20261	−	6.74935i	0.131515	−	0.277163i	−0.827001	−	0.562200i	$-0.809955\pi$
$593$	3.20261	−	6.74935i	0.131515	−	0.277163i	0.958516	+	0.285038i	$0.0920062\pi$
$594$	0.526173	−	0.224182i	0.0215892	−	0.00919828i
$595$	−8.16627	−	40.0010i	−0.334784	−	1.63988i
$596$	−0.0895086	−	0.236015i	−0.00366642	−	0.00966755i
$597$	13.3497	+	16.3505i	0.546368	+	0.669180i
$598$	3.03895	+	0.493877i	0.124272	+	0.0201961i
$599$	1.94318	−	16.0035i	0.0793960	−	0.653885i	−0.897628	−	0.440755i	$-0.854711\pi$
$599$	1.94318	−	16.0035i	0.0793960	−	0.653885i	0.977024	−	0.213131i	$-0.0683660\pi$
$600$	8.03524			0.328037
$601$	4.23714	−	34.8960i	0.172836	−	1.42344i	−0.605629	−	0.795747i	$-0.707078\pi$
$601$	4.23714	−	34.8960i	0.172836	−	1.42344i	0.778465	−	0.627688i	$-0.215999\pi$
$602$	21.1535	−	22.0232i	0.862154	−	0.897598i
$603$	0.388248	−	1.34039i	0.0158107	−	0.0545848i
$604$	0.500473	+	1.72783i	0.0203640	+	0.0703046i
$605$	9.20506	+	13.3358i	0.374239	+	0.542179i
$606$	−11.7275	−	20.3127i	−0.476399	−	0.825147i
$607$	10.0864	+	0.814259i	0.409395	+	0.0330498i	0.283449	−	0.958987i	$-0.408521\pi$
$607$	10.0864	+	0.814259i	0.409395	+	0.0330498i	0.125946	+	0.992037i	$0.459803\pi$
$608$	3.02454	−	0.491536i	0.122661	−	0.0199344i
$609$	5.71838	−	28.0105i	0.231721	−	1.13504i
$610$	−5.08791	−	24.9222i	−0.206004	−	1.00907i
$611$	4.81989	−	3.62191i	0.194992	−	0.146527i
$612$	−0.530909	−	0.769154i	−0.0214607	−	0.0310912i
$613$	−24.4464	+	1.97352i	−0.987380	+	0.0797095i	−0.563593	−	0.826052i	$-0.690581\pi$
$613$	−24.4464	+	1.97352i	−0.987380	+	0.0797095i	−0.423787	+	0.905762i	$0.639299\pi$
$614$	26.9659	−	6.64651i	1.08826	−	0.268231i
$615$	−0.376482	+	0.652085i	−0.0151812	+	0.0262946i
$616$	2.28998	+	3.96637i	0.0922660	+	0.159809i
$617$	18.1098	+	18.8543i	0.729074	+	0.759046i	0.977803	−	0.209527i	$-0.0671923\pi$
$617$	18.1098	+	18.8543i	0.729074	+	0.759046i	−0.248729	+	0.968573i	$0.580013\pi$
$618$	−9.71599	+	4.13960i	−0.390834	+	0.166519i
$619$	−7.67601	−	16.1768i	−0.308525	−	0.650202i	0.688668	−	0.725077i	$-0.258196\pi$
$619$	−7.67601	−	16.1768i	−0.308525	−	0.650202i	−0.997193	+	0.0748743i	$0.976144\pi$
$620$	−1.18963	−	1.05392i	−0.0477766	−	0.0423264i
$621$	−3.22293	+	1.69153i	−0.129332	+	0.0678786i
$622$	7.81640	+	8.13774i	0.313409	+	0.326294i
$623$	−43.0385	+	32.3414i	−1.72430	+	1.29573i
$624$	2.03992	+	1.07063i	0.0816621	+	0.0428596i
$625$	3.03422	+	1.91873i	0.121369	+	0.0767490i
$626$	−11.0448	−	2.72231i	−0.441441	−	0.108805i
$627$	−1.75997			−0.0702862
$628$	−1.59361	−	0.262250i	−0.0635921	−	0.0104649i
$629$	39.3684			1.56972
$630$	−7.47814	−	1.84320i	−0.297936	−	0.0734347i
$631$	30.8977	+	19.5385i	1.23002	+	0.777816i	0.981621	−	0.190843i	$-0.0611221\pi$
$631$	30.8977	+	19.5385i	1.23002	+	0.777816i	0.248396	+	0.968658i	$0.420096\pi$
$632$	2.04084	+	1.07111i	0.0811802	+	0.0426066i
$633$	−5.31478	+	3.99380i	−0.211244	+	0.158739i
$634$	16.9358	+	17.6321i	0.672608	+	0.700259i
$635$	−11.4011	+	5.98375i	−0.452438	+	0.237458i
$636$	0.564380	+	0.499997i	0.0223791	+	0.0198262i
$637$	−1.89504	−	3.99372i	−0.0750843	−	0.158237i
$638$	3.99907	−	1.70385i	0.158325	−	0.0674559i
$639$	3.26880	+	3.40318i	0.129312	+	0.134628i
$640$	7.55827	+	13.0913i	0.298767	+	0.517479i
$641$	−0.626864	+	1.08576i	−0.0247597	+	0.0428850i	−0.878140	−	0.478404i	$-0.841215\pi$
$641$	−0.626864	+	1.08576i	−0.0247597	+	0.0428850i	0.853380	+	0.521289i	$0.174549\pi$
$642$	−10.8405	+	2.67194i	−0.427840	+	0.105453i
$643$	−29.8601	+	2.41056i	−1.17757	+	0.0950632i	−0.653712	−	0.756743i	$-0.726789\pi$
$643$	−29.8601	+	2.41056i	−1.17757	+	0.0950632i	−0.523857	+	0.851806i	$0.675507\pi$
$644$	−1.00248	−	1.45234i	−0.0395032	−	0.0572302i
$645$	7.10228	−	5.33702i	0.279652	−	0.210145i
$646$	−8.35072	−	40.9045i	−0.328555	−	1.60937i
$647$	3.38879	−	16.5994i	0.133227	−	0.652590i	−0.857249	−	0.514903i	$-0.827828\pi$
$647$	3.38879	−	16.5994i	0.133227	−	0.652590i	0.990476	−	0.137687i	$-0.0439669\pi$
$648$	−2.87437	+	0.467130i	−0.112916	+	0.0183506i
$649$	−1.81822	−	0.146782i	−0.0713715	−	0.00576170i
$650$	−1.16698	−	2.02128i	−0.0457729	−	0.0792809i
$651$	−17.6011	−	25.4995i	−0.689840	−	0.999406i
$652$	0.641453	+	2.21455i	0.0251212	+	0.0867285i
$653$	4.09344	−	14.1322i	0.160189	−	0.553036i	−0.839760	−	0.542957i	$-0.817305\pi$
$653$	4.09344	−	14.1322i	0.160189	−	0.553036i	0.999949	−	0.0100788i	$-0.00320824\pi$
$654$	−4.29247	+	4.46893i	−0.167849	+	0.174749i
$655$	2.23669	−	18.4208i	0.0873946	−	0.719759i
$656$	1.87403			0.0731684
$657$	0.342898	−	2.82402i	0.0133777	−	0.110176i
$658$	49.5159	+	8.04712i	1.93033	+	0.313709i
$659$	14.7097	+	18.0161i	0.573007	+	0.701806i	0.977068	−	0.212926i	$-0.0682992\pi$
$659$	14.7097	+	18.0161i	0.573007	+	0.701806i	−0.404061	+	0.914732i	$0.632402\pi$
$660$	0.0286072	+	0.0754311i	0.00111353	+	0.00293615i
$661$	8.98650	+	44.0188i	0.349534	+	1.71213i	0.651360	+	0.758769i	$0.274199\pi$
$661$	8.98650	+	44.0188i	0.349534	+	1.71213i	−0.301826	+	0.953363i	$0.597596\pi$
$662$	31.6727	−	13.4945i	1.23099	−	0.524478i
$663$	−1.92213	+	4.05080i	−0.0746493	+	0.157320i
$664$	−1.23282	+	30.5920i	−0.0478426	+	1.18720i
$665$	18.9470	+	14.2378i	0.734734	+	0.552117i
$666$	3.18388	−	6.70988i	0.123373	−	0.260003i
$667$	−24.4952	+	12.8561i	−0.948459	+	0.497790i
$668$	−2.52039	−	0.203467i	−0.0975169	−	0.00787238i
$669$	−14.9529	+	21.6630i	−0.578111	+	0.837538i
$670$	−2.71033	−	0.904840i	−0.104709	−	0.0349570i
$671$	−4.39003	+	2.77608i	−0.169475	+	0.107170i
$672$	−0.761833	−	2.63015i	−0.0293884	−	0.101460i
$673$	5.60689	+	2.94272i	0.216130	+	0.113434i	0.569314	−	0.822120i	$-0.307209\pi$
$673$	5.60689	+	2.94272i	0.216130	+	0.113434i	−0.353184	+	0.935554i	$0.614901\pi$
$674$	−9.36508	−	24.6937i	−0.360729	−	0.951165i
$675$	2.53848	+	1.08155i	0.0977061	+	0.0416287i
$676$	−0.0654863	−	1.62503i	−0.00251870	−	0.0625010i
$677$	−10.8675	+	15.7443i	−0.417671	+	0.605101i	−0.974189	−	0.225735i	$-0.927522\pi$
$677$	−10.8675	+	15.7443i	−0.417671	+	0.605101i	0.556518	+	0.830836i	$0.312137\pi$
$678$	0.247272	−	0.428288i	0.00949644	−	0.0164483i
$679$	−18.4694	+	1.49100i	−0.708789	+	0.0572193i
$680$	−26.7140	+	16.8929i	−1.02443	+	0.647813i
$681$	−7.88084	+	2.63101i	−0.301994	+	0.100821i
$682$	1.67063	−	4.40508i	0.0639716	−	0.168679i
$683$	−15.2130	−	2.47236i	−0.582111	−	0.0946022i	−0.137777	−	0.990463i	$-0.543996\pi$
$683$	−15.2130	−	2.47236i	−0.582111	−	0.0946022i	−0.444334	+	0.895861i	$0.646560\pi$
$684$	0.526782	+	0.129840i	0.0201420	+	0.00496456i
$685$	−10.4842	+	10.9152i	−0.400580	+	0.417048i
$686$	0.271183	−	0.715051i	0.0103538	−	0.0273008i
$687$	−11.2642	+	9.97919i	−0.429755	+	0.380730i
$688$	−20.3418	−	8.66685i	−0.775526	−	0.330421i
$689$	0.723560	−	3.54423i	0.0275654	−	0.135024i
$690$	3.19502	+	6.73336i	0.121632	+	0.256335i
$691$	−11.8684	−	8.91855i	−0.451497	−	0.339278i	0.350545	−	0.936546i	$-0.385996\pi$
$691$	−11.8684	−	8.91855i	−0.451497	−	0.339278i	−0.802042	+	0.597268i	$0.796253\pi$
$692$	0.275731	+	2.27085i	0.0104817	+	0.0863249i
$693$	0.189574	+	1.56128i	0.00720131	+	0.0593081i
$694$	−1.41791	+	35.1852i	−0.0538233	+	1.33561i
$695$	−9.74372	−	8.63219i	−0.369601	−	0.327437i
$696$	−21.8460	+	3.55033i	−0.828072	+	0.134575i
$697$	0.146860	+	3.64430i	0.00556273	+	0.138038i
$698$	−14.6778	+	17.9771i	−0.555564	+	0.680442i
$699$	−14.5883	+	4.87030i	−0.551782	+	0.184212i
$700$	−0.372197	+	1.28497i	−0.0140677	+	0.0485674i
$701$	−21.0264	−	13.2963i	−0.794156	−	0.502194i	0.0747316	−	0.997204i	$-0.476190\pi$
$701$	−21.0264	−	13.2963i	−0.794156	−	0.502194i	−0.868887	+	0.495010i	$0.835164\pi$
$702$	0.534961	+	0.655209i	0.0201908	+	0.0247293i
$703$	−17.1065	+	15.1551i	−0.645185	+	0.571584i
$704$	2.23371	−	2.73580i	0.0841860	−	0.103109i
$705$	13.8435	+	4.62165i	0.521378	+	0.174062i
$706$	−14.3674	+	3.54125i	−0.540724	+	0.133277i
$707$	62.6236	−	15.4353i	2.35520	−	0.580506i
$708$	0.533390	+	0.178072i	0.0200460	+	0.00669235i
$709$	−21.1808	+	25.9417i	−0.795461	+	0.974263i	−0.999989	−	0.00459804i	$-0.998536\pi$
$709$	−21.1808	+	25.9417i	−0.795461	+	0.974263i	0.204529	+	0.978861i	$0.434434\pi$
$710$	7.23217	−	6.40714i	0.271418	−	0.240456i
$711$	0.500566	+	0.613082i	0.0187727	+	0.0229924i
$712$	35.2266	+	22.2759i	1.32017	+	0.834826i
$713$	−8.34166	+	28.7988i	−0.312398	+	1.07852i
$714$	−35.3873	+	11.8140i	−1.32433	+	0.442128i
$715$	0.244776	−	0.299796i	0.00915410	−	0.0112117i
$716$	0.103933	+	2.57908i	0.00388417	+	0.0963847i
$717$	11.8476	−	1.92543i	0.442458	−	0.0719064i
$718$	−24.9466	−	22.1008i	−0.931000	−	0.824794i
$719$	−0.630613	+	15.6485i	−0.0235179	+	0.583591i	0.943874	+	0.330306i	$0.107152\pi$
$719$	−0.630613	+	15.6485i	−0.0235179	+	0.583591i	−0.967392	+	0.253285i	$0.918489\pi$
$720$	0.672216	+	5.53620i	0.0250520	+	0.206322i
$721$	−3.50055	−	28.8296i	−0.130367	−	1.07367i
$722$	−1.40237	−	1.05381i	−0.0521909	−	0.0392189i
$723$	7.84825	+	16.5398i	0.291880	+	0.615123i
$724$	0.218218	−	1.06890i	0.00811000	−	0.0397254i
$725$	19.2932	+	8.22006i	0.716531	+	0.305285i
$726$	11.0836	−	9.81924i	0.411352	−	0.364426i
$727$	−8.69452	+	22.9256i	−0.322462	+	0.850262i	0.671547	+	0.740962i	$0.265630\pi$
$727$	−8.69452	+	22.9256i	−0.322462	+	0.850262i	−0.994009	+	0.109300i	$0.965139\pi$
$728$	−4.69214	+	4.88504i	−0.173902	+	0.181052i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−5.74947	−	0.934381i	−0.212798	−	0.0345830i
$731$	15.2598	−	40.2367i	0.564403	−	1.48821i
$732$	1.51880	−	0.507050i	0.0561364	−	0.0187411i
$733$	21.8695	−	13.8294i	0.807768	−	0.510802i	−0.0656094	−	0.997845i	$-0.520899\pi$
$733$	21.8695	−	13.8294i	0.807768	−	0.510802i	0.873378	+	0.487044i	$0.161925\pi$
$734$	36.8870	−	2.97783i	1.36153	−	0.109914i
$735$	5.35041	−	9.26718i	0.197353	−	0.341825i
$736$	−1.50522	+	2.18069i	−0.0554832	+	0.0803813i
$737$	0.0234944	+	0.583007i	0.000865427	+	0.0214753i
$738$	0.633005	+	0.269698i	0.0233012	+	0.00992773i
$739$	−6.70880	−	17.6897i	−0.246787	−	0.650724i	0.753188	−	0.657806i	$-0.228515\pi$
$739$	−6.70880	−	17.6897i	−0.246787	−	0.650724i	−0.999975	+	0.00708122i	$0.997746\pi$
$740$	0.927594	+	0.486839i	0.0340990	+	0.0178965i
$741$	−0.724164	−	2.50010i	−0.0266028	−	0.0918436i
$742$	25.4389	−	16.0866i	0.933893	−	0.590558i
$743$	28.8852	+	9.64331i	1.05970	+	0.353779i	0.792506	−	0.609865i	$-0.208776\pi$
$743$	28.8852	+	9.64331i	1.05970	+	0.353779i	0.267191	+	0.963644i	$0.413904\pi$
$744$	−13.6265	+	19.7414i	−0.499572	+	0.723756i
$745$	−2.92192	−	0.235882i	−0.107051	−	0.00864204i
$746$	5.12878	−	2.69179i	0.187778	−	0.0985534i
$747$	−4.50717	+	9.49865i	−0.164909	+	0.347537i
$748$	0.312400	+	0.234753i	0.0114225	+	0.00858343i
$749$	1.23624	−	30.6769i	0.0451711	−	1.12091i
$750$	6.81099	−	14.3539i	0.248702	−	0.524129i
$751$	31.2133	−	13.2987i	1.13899	−	0.485277i	0.261656	−	0.965161i	$-0.415731\pi$
$751$	31.2133	−	13.2987i	1.13899	−	0.485277i	0.877332	+	0.479884i	$0.159321\pi$
$752$	−7.26576	−	35.5900i	−0.264955	−	1.29784i
$753$	2.06074	+	5.43371i	0.0750974	+	0.198015i
$754$	4.06586	+	4.97978i	0.148070	+	0.181353i
$755$	20.6203	+	3.35112i	0.750448	+	0.121960i
$756$	0.0584402	−	0.481299i	0.00212545	−	0.0175047i
$757$	−29.9096			−1.08708			−0.543541	−	0.839382i	$-0.682917\pi$
$757$	−29.9096			−1.08708			−0.543541	+	0.839382i	$0.682917\pi$
$758$	1.58413	−	13.0465i	0.0575381	−	0.473869i
$759$	1.05426	−	1.09760i	0.0382671	−	0.0398403i
$760$	5.10486	−	17.6240i	0.185173	−	0.639291i
$761$	5.36279	+	18.5145i	0.194401	+	0.671150i	0.997192	+	0.0748895i	$0.0238604\pi$
$761$	5.36279	+	18.5145i	0.194401	+	0.671150i	−0.802791	+	0.596261i	$0.796652\pi$
$762$	6.68393	+	9.68334i	0.242133	+	0.350790i
$763$	−8.51970	−	14.7566i	−0.308434	−	0.534223i
$764$	−0.493091	−	0.0398064i	−0.0178394	−	0.00144014i
$765$	−10.7132	+	1.74107i	−0.387337	+	0.0629484i
$766$	−8.16316	+	39.9858i	−0.294947	+	1.44475i
$767$	−0.539625	−	2.64326i	−0.0194847	−	0.0954425i
$768$	−2.46256	+	1.85050i	−0.0888601	+	0.0667740i
$769$	−22.4387	−	32.5081i	−0.809161	−	1.17227i	−0.982289	−	0.187373i	$-0.940003\pi$
$769$	−22.4387	−	32.5081i	−0.809161	−	1.17227i	0.173128	−	0.984899i	$-0.444613\pi$
$770$	3.20990	−	0.259130i	0.115677	−	0.00933839i
$771$	−2.86637	+	0.706496i	−0.103230	+	0.0254438i
$772$	1.01401	−	1.75632i	0.0364951	−	0.0632114i
$773$	−25.7279	−	44.5621i	−0.925370	−	1.60279i	−0.790965	−	0.611861i	$-0.790421\pi$
$773$	−25.7279	−	44.5621i	−0.925370	−	1.60279i	−0.134405	−	0.990927i	$-0.542912\pi$
$774$	−5.62375	−	5.85494i	−0.202141	−	0.210452i
$775$	20.9102	−	8.90899i	0.751115	−	0.320020i
$776$	6.14970	+	12.9602i	0.220762	+	0.465245i
$777$	15.2868	+	13.5429i	0.548411	+	0.485850i
$778$	4.23365	−	2.22199i	0.151784	−	0.0796623i
$779$	−1.46670	−	1.52700i	−0.0525501	−	0.0547105i
$780$	−0.0953821	+	0.0716750i	−0.00341523	+	0.00256638i
$781$	−1.74701	−	0.916903i	−0.0625130	−	0.0328094i
$782$	30.5123	+	19.2948i	1.09112	+	0.689980i
$783$	−7.37944	−	1.81887i	−0.263720	−	0.0650011i
$784$	−26.6329			−0.951176
$785$	−10.6855	+	15.4147i	−0.381381	+	0.550175i
$786$	−16.9567			−0.604825
$787$	11.7154	+	2.88759i	0.417610	+	0.102932i	0.442521	−	0.896758i	$-0.354084\pi$
$787$	11.7154	+	2.88759i	0.417610	+	0.102932i	−0.0249111	+	0.999690i	$0.507930\pi$
$788$	−0.926261	−	0.585732i	−0.0329967	−	0.0208658i
$789$	−0.567965	−	0.298091i	−0.0202201	−	0.0106123i
$790$	1.29559	−	0.973575i	0.0460951	−	0.0346382i
$791$	0.942050	+	0.980778i	0.0334954	+	0.0348725i
$792$	1.07813	−	0.565847i	0.0383098	−	0.0201065i
$793$	−5.74988	−	5.09395i	−0.204184	−	0.180892i
$794$	3.12932	+	6.59490i	0.111055	+	0.234044i
$795$	8.05583	−	3.43227i	0.285711	−	0.121730i
$796$	1.88471	+	1.96219i	0.0668019	+	0.0695482i
$797$	18.0773	+	31.3108i	0.640332	+	1.10909i	0.985359	+	0.170494i	$0.0545365\pi$
$797$	18.0773	+	31.3108i	0.640332	+	1.10909i	−0.345027	+	0.938593i	$0.612130\pi$
$798$	10.8288	−	18.7560i	0.383334	−	0.663954i
$799$	68.6403	−	16.9183i	2.42832	−	0.598527i
$800$	2.00218	−	0.161633i	0.0707878	−	0.00571458i
$801$	8.13038	+	11.7789i	0.287273	+	0.416186i
$802$	1.16518	−	0.875578i	0.0411440	−	0.0309177i
$803$	0.237921	+	1.16542i	0.00839606	+	0.0411266i
$804$	0.0359787	−	0.176235i	0.00126887	−	0.00621535i
$805$	−20.2290	+	3.28753i	−0.712979	+	0.115870i
$806$	6.94501	+	0.560659i	0.244627	+	0.0197484i
$807$	7.01535	+	12.1509i	0.246952	+	0.427733i
$808$	−28.3654	−	41.0944i	−0.997891	−	1.44570i
$809$	14.7072	+	50.7750i	0.517076	+	1.78515i	0.613365	+	0.789800i	$0.289816\pi$
$809$	14.7072	+	50.7750i	0.517076	+	1.78515i	−0.0962889	+	0.995353i	$0.530697\pi$
$810$	−0.569675	+	1.96675i	−0.0200164	+	0.0691045i
$811$	−2.16543	+	2.25446i	−0.0760387	+	0.0791646i	−0.758135	−	0.652098i	$-0.773889\pi$
$811$	−2.16543	+	2.25446i	−0.0760387	+	0.0791646i	0.682096	+	0.731263i	$0.261069\pi$
$812$	0.444163	−	3.65801i	0.0155871	−	0.128371i
$813$	−31.6793			−1.11104
$814$	−0.374310	+	3.08272i	−0.0131196	+	0.108049i
$815$	26.4288	+	4.29510i	0.925762	+	0.150451i
$816$	17.0846	+	20.9249i	0.598082	+	0.732517i
$817$	8.85857	+	23.3581i	0.309922	+	0.817197i
$818$	−6.43183	−	31.5052i	−0.224884	−	1.10155i
$819$	−2.13986	+	0.911710i	−0.0747728	+	0.0318577i
$820$	−0.0416059	+	0.0876826i	−0.00145294	+	0.00306201i
$821$	0.386525	−	9.59152i	0.0134898	−	0.334746i	−0.978326	−	0.207070i	$-0.933607\pi$
$821$	0.386525	−	9.59152i	0.0134898	−	0.334746i	0.991816	−	0.127676i	$-0.0407518\pi$
$822$	11.0565	+	8.30840i	0.385639	+	0.289789i
$823$	−14.5751	+	30.7164i	−0.508057	+	1.07071i	0.473721	+	0.880675i	$0.342911\pi$
$823$	−14.5751	+	30.7164i	−0.508057	+	1.07071i	−0.981778	+	0.190032i	$0.939141\pi$
$824$	−19.9081	+	10.4486i	−0.693532	+	0.363994i
$825$	−1.14997	−	0.0928352i	−0.0400368	−	0.00323211i
$826$	12.7515	−	18.4737i	0.443680	−	0.642782i
$827$	−34.9209	−	11.6583i	−1.21432	−	0.405399i	−0.363866	−	0.931451i	$-0.618544\pi$
$827$	−34.9209	−	11.6583i	−1.21432	−	0.405399i	−0.850452	+	0.526052i	$0.823672\pi$
$828$	−0.396528	+	0.250749i	−0.0137803	+	0.00871414i
$829$	−1.00311	−	3.46314i	−0.0348395	−	0.120280i	0.941214	−	0.337812i	$-0.109687\pi$
$829$	−1.00311	−	3.46314i	−0.0348395	−	0.120280i	−0.976053	+	0.217532i	$0.930199\pi$
$830$	19.0620	+	10.0045i	0.661650	+	0.347261i
$831$	−9.10491	−	24.0077i	−0.315846	−	0.832817i
$832$	4.80540	+	2.04739i	0.166597	+	0.0709805i
$833$	−2.08712	−	51.7913i	−0.0723144	−	1.79446i
$834$	−6.75741	+	9.78979i	−0.233990	+	0.338993i
$835$	−14.6827	+	25.4313i	−0.508117	+	0.880085i
$836$	−0.226115	+	0.0182539i	−0.00782034	+	0.000631323i
$837$	−6.96207	+	4.40254i	−0.240644	+	0.152174i
$838$	−4.20134	+	1.40261i	−0.145133	+	0.0484524i
$839$	10.6733	−	28.1433i	0.368485	−	0.971614i	−0.614661	−	0.788791i	$-0.710707\pi$
$839$	10.6733	−	28.1433i	0.368485	−	0.971614i	0.983146	−	0.182823i	$-0.0585235\pi$
$840$	−16.1843	−	2.63020i	−0.558411	−	0.0907506i
$841$	−27.9286	−	6.88378i	−0.963055	−	0.237372i
$842$	37.5457	−	39.0892i	1.29391	−	1.34710i
$843$	6.68156	−	17.6178i	0.230125	−	0.606790i
$844$	−0.641404	+	0.568234i	−0.0220780	+	0.0195594i
$845$	−17.3760	−	7.40321i	−0.597752	−	0.254678i
$846$	2.66768	−	13.0672i	0.0917168	−	0.449259i
$847$	17.4557	+	36.7872i	0.599786	+	1.26402i
$848$	−17.4229	−	13.0925i	−0.598306	−	0.449598i
$849$	−3.34863	−	27.5785i	−0.114925	−	0.946490i
$850$	−3.29876	−	27.1677i	−0.113146	−	0.931845i
$851$	0.795763	−	19.7467i	0.0272784	−	0.676906i
$852$	0.455261	+	0.403326i	0.0155970	+	0.0138177i
$853$	28.0148	−	4.55286i	0.959210	−	0.155887i	0.339403	−	0.940641i	$-0.389775\pi$
$853$	28.0148	−	4.55286i	0.959210	−	0.155887i	0.619807	+	0.784754i	$0.287211\pi$
$854$	−2.57368	−	63.8653i	−0.0880696	−	2.18543i
$855$	3.98492	−	4.88064i	0.136281	−	0.166914i
$856$	−22.5457	+	7.52686i	−0.770596	+	0.257263i
$857$	2.88536	−	9.96140i	0.0985619	−	0.340275i	−0.896049	−	0.443956i	$-0.853575\pi$
$857$	2.88536	−	9.96140i	0.0985619	−	0.340275i	0.994611	+	0.103681i	$0.0330620\pi$
$858$	−0.298920	−	0.189026i	−0.0102050	−	0.00645323i
$859$	−18.3861	−	22.5189i	−0.627325	−	0.768333i	0.358966	−	0.933351i	$-0.383129\pi$
$859$	−18.3861	−	22.5189i	−0.627325	−	0.768333i	−0.986291	+	0.165017i	$0.947232\pi$
$860$	0.857124	−	0.759346i	0.0292277	−	0.0258935i
$861$	−1.19663	+	1.46561i	−0.0407811	+	0.0499477i
$862$	7.79586	+	2.60264i	0.265528	+	0.0886463i
$863$	16.0315	−	3.95140i	0.545717	−	0.134507i	0.0431871	−	0.999067i	$-0.486249\pi$
$863$	16.0315	−	3.95140i	0.545717	−	0.134507i	0.502530	+	0.864560i	$0.332403\pi$
$864$	−0.706824	+	0.174217i	−0.0240467	+	0.00592697i
$865$	25.1988	+	8.41259i	0.856784	+	0.286037i
$866$	1.42008	−	1.73929i	0.0482564	−	0.0591034i
$867$	−26.6277	+	23.5901i	−0.904325	+	0.801162i
$868$	−2.52580	−	3.09355i	−0.0857313	−	0.105002i
$869$	−0.279701	−	0.176872i	−0.00948821	−	0.00599998i
$870$	−4.32970	+	14.9479i	−0.146791	+	0.506780i
$871$	−0.818519	+	0.273262i	−0.0277345	+	0.00925912i
$872$	−8.34303	+	10.2184i	−0.282531	+	0.346037i
$873$	0.198355	+	4.92212i	0.00671329	+	0.166589i
$874$	−20.6859	+	3.36179i	−0.699712	+	0.113714i
$875$	32.7017	+	28.9712i	1.10552	+	0.979405i
$876$	0.0147645	−	0.366378i	0.000498847	−	0.0123788i
$877$	−3.36089	−	27.6794i	−0.113489	−	0.934667i	−0.932570	−	0.360989i	$-0.882439\pi$
$877$	−3.36089	−	27.6794i	−0.113489	−	0.934667i	0.819081	−	0.573678i	$-0.194484\pi$
$878$	3.77629	+	31.1006i	0.127444	+	1.04959i
$879$	22.2741	+	16.7379i	0.751287	+	0.564556i
$880$	−0.999626	−	2.10667i	−0.0336974	−	0.0710157i
$881$	−4.39509	+	21.5286i	−0.148074	+	0.725317i	0.836165	+	0.548478i	$0.184792\pi$
$881$	−4.39509	+	21.5286i	−0.148074	+	0.725317i	−0.984240	+	0.176839i	$0.943413\pi$
$882$	−8.99601	−	3.83284i	−0.302912	−	0.129059i
$883$	15.5454	−	13.7720i	0.523145	−	0.463466i	−0.359742	−	0.933052i	$-0.617135\pi$
$883$	15.5454	−	13.7720i	0.523145	−	0.463466i	0.882887	+	0.469586i	$0.155597\pi$
$884$	−0.204935	+	0.540370i	−0.00689272	+	0.0181746i
$885$	4.52387	−	4.70985i	0.152068	−	0.158320i
$886$	−9.08275	−	2.23870i	−0.305141	−	0.0752105i
$887$	58.4342	+	9.49649i	1.96203	+	0.318861i	0.998727	+	0.0504413i	$0.0160628\pi$
$887$	58.4342	+	9.49649i	1.96203	+	0.318861i	0.963302	+	0.268420i	$0.0865013\pi$
$888$	5.60673	−	14.7837i	0.188149	−	0.496109i
$889$	−30.6899	+	10.2458i	−1.02931	+	0.343633i
$890$	24.7691	−	15.6630i	0.830262	−	0.525026i
$891$	0.416765	−	0.0336447i	0.0139621	−	0.00112714i
$892$	−1.69641	+	2.93828i	−0.0568001	+	0.0983807i
$893$	−23.3131	+	33.7748i	−0.780142	+	1.13023i
$894$	0.107863	+	2.67659i	0.00360747	+	0.0895185i
$895$	27.5774	+	11.7496i	0.921811	+	0.392747i
$896$	13.4698	+	35.5169i	0.449993	+	1.18654i
$897$	1.99297	+	1.04599i	0.0665434	+	0.0349247i
$898$	0.183755	+	0.634396i	0.00613198	+	0.0211701i
$899$	−52.9137	+	33.4606i	−1.76477	+	1.11597i
$900$	0.337353	+	0.112625i	0.0112451	+	0.00375417i
$901$	24.0948	−	34.9073i	0.802713	−	1.16293i
$902$	−0.286761	−	0.0231497i	−0.00954810	−	0.000770802i
$903$	19.7670	−	10.3745i	0.657804	−	0.345242i
$904$	0.451342	−	0.951183i	0.0150114	−	0.0316359i
$905$	−10.1286	−	7.61116i	−0.336687	−	0.253004i
$906$	0.768684	−	19.0747i	0.0255378	−	0.633715i
$907$	4.90533	−	10.3378i	0.162879	−	0.343260i	−0.805559	−	0.592516i	$-0.798135\pi$
$907$	4.90533	−	10.3378i	0.162879	−	0.343260i	0.968438	+	0.249256i	$0.0801860\pi$
$908$	−0.985217	+	0.419762i	−0.0326956	+	0.0139303i
$909$	−3.42984	−	16.8005i	−0.113761	−	0.557236i
$910$	1.68887	+	4.45317i	0.0559854	+	0.147621i
$911$	−24.4202	−	29.9094i	−0.809078	−	0.990941i	−0.999956	−	0.00932744i	$-0.997031\pi$
$911$	−24.4202	−	29.9094i	−0.809078	−	0.990941i	0.190878	−	0.981614i	$-0.438866\pi$
$912$	−15.4788	−	2.51555i	−0.512554	−	0.0832982i
$913$	0.529881	−	4.36396i	0.0175365	−	0.144426i
$914$	8.33465			0.275686
$915$	2.24142	−	18.4598i	0.0740992	−	0.610262i
$916$	−1.34368	+	1.39892i	−0.0443966	+	0.0462217i
$917$	12.9728	−	44.7873i	0.428399	−	1.47901i
$918$	2.75943	+	9.52667i	0.0910749	+	0.314427i
$919$	19.9764	+	28.9408i	0.658961	+	0.954670i	0.999894	+	0.0145826i	$0.00464195\pi$
$919$	19.9764	+	28.9408i	0.658961	+	0.954670i	−0.340932	+	0.940088i	$0.610743\pi$
$920$	7.93326	+	13.7408i	0.261552	+	0.453021i
$921$	20.2378	+	1.63376i	0.666857	+	0.0538343i
$922$	−47.3387	+	7.69329i	−1.55902	+	0.253365i
$923$	0.583665	−	2.85898i	0.0192116	−	0.0941044i
$924$	0.0405490	+	0.198622i	0.00133396	+	0.00653419i
$925$	−11.9769	+	9.00006i	−0.393798	+	0.295920i
$926$	19.2179	+	27.8419i	0.631539	+	0.914942i
$927$	−7.69572	+	0.621263i	−0.252761	+	0.0204049i
$928$	−5.37207	+	1.32410i	−0.176347	+	0.0434656i
$929$	−24.0293	+	41.6200i	−0.788377	+	1.36551i	0.138584	+	0.990351i	$0.455745\pi$
$929$	−24.0293	+	41.6200i	−0.788377	+	1.36551i	−0.926961	+	0.375158i	$0.877588\pi$
$930$	8.43329	+	14.6069i	0.276538	+	0.478979i
$931$	20.8442	+	21.7011i	0.683142	+	0.711226i
$932$	−1.82375	+	0.777027i	−0.0597389	+	0.0254524i
$933$	3.53625	+	7.45250i	0.115772	+	0.243984i
$934$	−14.6519	−	12.9805i	−0.479426	−	0.424734i
$935$	4.01836	−	2.10900i	0.131415	−	0.0689717i
$936$	1.24742	+	1.29871i	0.0407733	+	0.0424495i
$937$	19.5977	−	14.7267i	0.640230	−	0.481102i	−0.230363	−	0.973105i	$-0.573991\pi$
$937$	19.5977	−	14.7267i	0.640230	−	0.481102i	0.870594	+	0.492003i	$0.163735\pi$
$938$	−6.35767	−	3.33676i	−0.207585	−	0.108949i
$939$	−7.02865	−	4.44465i	−0.229371	−	0.145046i
$940$	1.82651	+	0.450194i	0.0595742	+	0.0146837i
$941$	−59.3179			−1.93371			−0.966853	−	0.255332i	$-0.917815\pi$
$941$	−59.3179			−1.93371			−0.966853	+	0.255332i	$0.917815\pi$
$942$	15.1604	+	7.99538i	0.493952	+	0.260504i
$943$	1.83090			0.0596222
$944$	−15.7814	−	3.88976i	−0.513640	−	0.126601i
$945$	−4.75889	−	3.00934i	−0.154807	−	0.0978938i
$946$	3.00562	+	1.57747i	0.0977212	+	0.0512880i
$947$	−23.8583	+	17.9283i	−0.775291	+	0.582593i	−0.913038	−	0.407874i	$-0.866270\pi$
$947$	−23.8583	+	17.9283i	−0.775291	+	0.582593i	0.137748	+	0.990467i	$0.456014\pi$
$948$	0.0706698	+	0.0735751i	0.00229525	+	0.00238961i
$949$	−1.55763	+	0.817505i	−0.0505627	+	0.0265373i
$950$	11.8917	+	10.5352i	0.385819	+	0.341806i
$951$	7.66201	+	16.1474i	0.248458	+	0.523614i
$952$	−73.0677	+	31.1312i	−2.36814	+	1.00897i
$953$	−2.34168	−	2.43795i	−0.0758544	−	0.0789728i	0.682193	−	0.731172i	$-0.261026\pi$
$953$	−2.34168	−	2.43795i	−0.0758544	−	0.0789728i	−0.758048	+	0.652199i	$0.773847\pi$
$954$	−4.00090	−	6.92976i	−0.129534	−	0.224359i
$955$	−2.87254	+	4.97538i	−0.0929532	+	0.161000i
$956$	1.50218	−	0.370253i	0.0485838	−	0.0119748i
$957$	3.16753	−	0.255710i	0.102392	−	0.00826592i
$958$	−5.38338	−	7.79917i	−0.173929	−	0.251980i
$959$	−30.4036	+	22.8468i	−0.981783	+	0.737762i
$960$	2.52919	+	12.3888i	0.0816292	+	0.399846i
$961$	−7.37150	+	36.1080i	−0.237790	+	1.16477i
$962$	−4.53315	+	0.736709i	−0.146155	+	0.0237524i
$963$	−8.13572	−	0.656783i	−0.262170	−	0.0211645i
$964$	1.17987	+	2.04359i	0.0380009	+	0.0658195i
$965$	−13.3792	−	19.3831i	−0.430691	−	0.623964i
$966$	5.21045	+	17.9886i	0.167643	+	0.578772i
$967$	−17.0494	+	58.8612i	−0.548271	+	1.89285i	−0.110199	+	0.993910i	$0.535149\pi$
$967$	−17.0494	+	58.8612i	−0.548271	+	1.89285i	−0.438072	+	0.898940i	$0.644338\pi$
$968$	21.8373	−	22.7350i	0.701877	−	0.730731i
$969$	3.67882	−	30.2978i	0.118181	−	0.973305i
$970$	10.0867			0.323864
$971$	0.0411470	−	0.338876i	0.00132047	−	0.0108750i	−0.992034	−	0.125972i	$-0.959795\pi$
$971$	0.0411470	−	0.338876i	0.00132047	−	0.0108750i	0.993354	+	0.115097i	$0.0367180\pi$
$972$	−0.127226	−	0.0206762i	−0.00408076	−	0.000663189i
$973$	−20.6878	−	25.3379i	−0.663219	−	0.812296i
$974$	−15.4467	−	40.7295i	−0.494943	−	1.30506i
$975$	−0.341296	−	1.67178i	−0.0109302	−	0.0535398i
$976$	−42.5780	+	18.1408i	−1.36289	+	0.580672i
$977$	−5.20380	+	10.9668i	−0.166484	+	0.350858i	−0.969497	−	0.245104i	$-0.921178\pi$
$977$	−5.20380	+	10.9668i	−0.166484	+	0.350858i	0.803012	+	0.595962i	$0.203229\pi$
$978$	0.985217	−	24.4479i	0.0315038	−	0.781758i
$979$	−4.78412	−	3.59503i	−0.152901	−	0.114898i
$980$	0.591287	−	1.24611i	0.0188880	−	0.0398055i
$981$	−4.01111	+	2.10519i	−0.128065	+	0.0672136i
$982$	12.8530	+	1.03760i	0.410156	+	0.0331112i
$983$	5.75272	−	8.33425i	0.183483	−	0.265821i	−0.720439	−	0.693518i	$-0.756060\pi$
$983$	5.75272	−	8.33425i	0.183483	−	0.265821i	0.903922	+	0.427697i	$0.140675\pi$
$984$	1.38943	+	0.463860i	0.0442935	+	0.0147873i
$985$	−10.7570	+	6.80233i	−0.342747	+	0.216740i
$986$	20.9725	+	72.4055i	0.667901	+	2.30586i
$987$	32.4731	+	17.0432i	1.03363	+	0.542491i
$988$	−0.118969	−	0.313695i	−0.00378490	−	0.00997996i
$989$	−19.8737	−	8.46739i	−0.631947	−	0.269247i
$990$	−0.0344733	−	0.855446i	−0.00109563	−	0.0271878i
$991$	−11.5989	+	16.8039i	−0.368451	+	0.533794i	−0.962730	−	0.270465i	$-0.912822\pi$
$991$	−11.5989	+	16.8039i	−0.368451	+	0.533794i	0.594278	+	0.804260i	$0.297438\pi$
$992$	−2.99828	+	5.19317i	−0.0951955	+	0.164883i
$993$	25.0869	−	2.02523i	0.796109	−	0.0642686i
$994$	20.5205	−	12.9764i	0.650871	−	0.411586i
$995$	29.9707	−	10.0057i	0.950136	−	0.317202i
$996$	−0.480549	+	1.26710i	−0.0152268	+	0.0401497i
$997$	−43.0670	−	6.99907i	−1.36395	−	0.221663i	−0.566007	−	0.824401i	$-0.691512\pi$
$997$	−43.0670	−	6.99907i	−1.36395	−	0.221663i	−0.797939	+	0.602738i	$0.794076\pi$
$998$	−28.5027	−	7.02529i	−0.902238	−	0.222382i
$999$	3.76116	−	3.91578i	0.118998	−	0.123890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.5	✓	336
157.124	even	39	inner	471.2.q.b.124.5	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.5	✓	336	1.1	even	1	trivial
471.2.q.b.124.5	yes	336	157.124	even	39	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32814 - 0.327356i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.114131 - 0.0599004i) q^{4} +(-1.19669 + 0.899253i) q^{5} +(0.947566 + 0.986521i) q^{6} +(-3.33061 + 1.74804i) q^{7} +(2.17972 + 1.93107i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-1.32814 - 0.327356i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(-0.114131 - 0.0599004i) q^{4} +(-1.19669 + 0.899253i) q^{5} +(0.947566 + 0.986521i) q^{6} +(-3.33061 + 1.74804i) q^{7} +(2.17972 + 1.93107i) q^{8} +(0.428693 + 0.903450i) q^{9} +(1.88374 - 0.802587i) q^{10} +(-0.289642 - 0.301550i) q^{11} +(0.0644474 + 0.111626i) q^{12} +(0.309186 - 0.535526i) q^{13} +(4.99574 - 1.23134i) q^{14} +(1.49205 - 0.120451i) q^{15} +(-2.11638 - 3.06611i) q^{16} +(5.79661 - 4.35587i) q^{17} +(-0.273612 - 1.34024i) q^{18} +(-0.841953 + 4.12416i) q^{19} +(0.190445 - 0.0309503i) q^{20} +(3.74927 + 0.302672i) q^{21} +(0.285970 + 0.495315i) q^{22} +(-2.06767 - 2.99554i) q^{23} +(-0.810192 - 2.79711i) q^{24} +(-0.767680 + 2.65034i) q^{25} +(-0.585949 + 0.610037i) q^{26} +(0.120537 - 0.992709i) q^{27} +0.484833 q^{28} +(0.916114 - 7.54488i) q^{29} +(-2.02107 - 0.328457i) q^{30} +(-5.20963 - 6.38064i) q^{31} +(-0.258145 - 0.680671i) q^{32} +(0.0836349 + 0.409671i) q^{33} +(-9.12460 + 3.88763i) q^{34} +(2.41378 - 5.08693i) q^{35} +(0.00519007 - 0.128790i) q^{36} +(4.34059 + 3.26174i) q^{37} +(2.46830 - 5.20183i) q^{38} +(-0.547542 + 0.287372i) q^{39} +(-4.34497 - 0.350762i) q^{40} +(-0.285744 + 0.413972i) q^{41} +(-4.88046 - 1.62934i) q^{42} +(5.01615 - 3.17202i) q^{43} +(0.0149941 + 0.0517658i) q^{44} +(-1.32544 - 0.695646i) q^{45} +(1.76554 + 4.65535i) q^{46} +(8.96969 + 3.82163i) q^{47} +(0.150015 + 3.72258i) q^{48} +(4.06089 - 5.88321i) q^{49} +(1.88719 - 3.26870i) q^{50} +(-7.22730 + 0.583448i) q^{51} +(-0.0673659 + 0.0425996i) q^{52} +(5.54871 - 1.85243i) q^{53} +(-0.485058 + 1.27899i) q^{54} +(0.617782 + 0.100399i) q^{55} +(-10.6354 - 2.62139i) q^{56} +(2.91583 - 3.03570i) q^{57} +(-3.68658 + 9.72072i) q^{58} +(3.26553 - 2.89301i) q^{59} +(-0.177504 - 0.0756273i) q^{60} +(2.48483 - 12.1715i) q^{61} +(4.83035 + 10.1798i) q^{62} +(-3.00708 - 2.25967i) q^{63} +(1.01817 + 8.38539i) q^{64} +(0.111574 + 0.918895i) q^{65} +(0.0230297 - 0.571477i) q^{66} +(-1.04453 - 0.925377i) q^{67} +(-0.922489 + 0.149919i) q^{68} +(0.146562 + 3.63690i) q^{69} +(-4.87106 + 5.96596i) q^{70} +(4.47591 - 1.49428i) q^{71} +(-0.810192 + 2.79711i) q^{72} +(-2.40436 - 1.52043i) q^{73} +(-4.69714 - 5.75295i) q^{74} +(2.06535 - 1.82974i) q^{75} +(0.343132 - 0.420260i) q^{76} +(1.49181 + 0.498039i) q^{77} +(0.821282 - 0.202428i) q^{78} +(0.768478 - 0.189413i) q^{79} +(5.28985 + 1.76601i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.515023 - 0.456271i) q^{82} +(6.64937 + 8.14400i) q^{83} +(-0.409776 - 0.259127i) q^{84} +(-3.01971 + 10.4252i) q^{85} +(-7.70051 + 2.57081i) q^{86} +(-4.80677 + 5.88722i) q^{87} +(-0.0490279 - 1.21661i) q^{88} +(14.1271 - 2.29587i) q^{89} +(1.53264 + 1.35780i) q^{90} +(-0.0936581 + 2.32410i) q^{91} +(0.0565508 + 0.465738i) q^{92} +(0.992894 + 8.17722i) q^{93} +(-10.6619 - 8.01192i) q^{94} +(-2.70111 - 5.69247i) q^{95} +(-0.145614 + 0.713266i) q^{96} +(4.53193 + 1.93087i) q^{97} +(-7.31931 + 6.48434i) q^{98} +(0.148268 - 0.390950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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