LMFDB - Embedded newform 378.2.v.a.67.2

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			67.2
Character	$\chi$	$=$	378.67
Dual form			378.2.v.a.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.42403 - 0.985977i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.327106 + 1.85511i) q^{5} +(1.72464 - 0.160044i) q^{6} +(-1.01788 - 2.44211i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.05570 + 2.80811i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.42403 - 0.985977i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.327106 + 1.85511i) q^{5} +(1.72464 - 0.160044i) q^{6} +(-1.01788 - 2.44211i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.05570 + 2.80811i) q^{9} +(-0.941864 - 1.63136i) q^{10} +(-0.0590960 - 0.335150i) q^{11} +(-1.21828 + 1.23118i) q^{12} +(-0.168029 + 0.952940i) q^{13} +(2.34950 + 1.21648i) q^{14} +(2.29490 - 2.31921i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.23143 + 3.86494i) q^{17} +(-2.61373 - 1.47255i) q^{18} +(-0.592867 + 1.02688i) q^{19} +(1.77013 + 0.644273i) q^{20} +(-0.958371 + 4.48124i) q^{21} +(0.260700 + 0.218754i) q^{22} +(3.39619 + 2.84974i) q^{23} +(0.141868 - 1.72623i) q^{24} +(1.36403 + 0.496466i) q^{25} +(-0.483820 - 0.838001i) q^{26} +(1.26539 - 5.03972i) q^{27} +(-2.58176 + 0.578353i) q^{28} +(1.20762 + 6.84877i) q^{29} +(-0.267241 + 3.25175i) q^{30} +(-1.63766 + 9.28765i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.246296 + 0.535529i) q^{33} +(-4.19371 - 1.52638i) q^{34} +(4.86334 - 1.08946i) q^{35} +(2.94877 - 0.552038i) q^{36} +1.81191 q^{37} +(-0.205901 - 1.16772i) q^{38} +(1.17885 - 1.19134i) q^{39} +(-1.77013 + 0.644273i) q^{40} +(-1.05102 + 5.96062i) q^{41} +(-2.14633 - 4.04886i) q^{42} +(1.95189 - 1.63783i) q^{43} -0.340320 q^{44} +(-5.55468 + 1.03989i) q^{45} -4.43341 q^{46} +(0.00577148 + 0.0327317i) q^{47} +(1.00092 + 1.41356i) q^{48} +(-4.92782 + 4.97158i) q^{49} +(-1.36403 + 0.496466i) q^{50} +(0.633135 - 7.70391i) q^{51} +(0.909284 + 0.330952i) q^{52} +(5.22772 - 9.05468i) q^{53} +(2.27013 + 4.67403i) q^{54} +0.641071 q^{55} +(1.60599 - 2.10257i) q^{56} +(1.85673 - 0.877745i) q^{57} +(-5.32740 - 4.47022i) q^{58} +(-0.869877 + 0.316609i) q^{59} +(-1.88547 - 2.66276i) q^{60} +(-0.993133 - 5.63234i) q^{61} +(-4.71546 - 8.16742i) q^{62} +(5.78314 - 5.43647i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.71284 - 0.623424i) q^{65} +(-0.155558 - 0.568555i) q^{66} +(-1.63245 - 1.36979i) q^{67} +(4.19371 - 1.52638i) q^{68} +(-2.02648 - 7.40667i) q^{69} +(-3.02525 + 3.96067i) q^{70} +(-6.38672 + 11.0621i) q^{71} +(-1.90405 + 2.31832i) q^{72} -10.4240 q^{73} +(-1.38800 + 1.16467i) q^{74} +(-1.45291 - 2.05188i) q^{75} +(0.908325 + 0.762175i) q^{76} +(-0.758321 + 0.485463i) q^{77} +(-0.137277 + 1.67037i) q^{78} +(13.5842 - 11.3985i) q^{79} +(0.941864 - 1.63136i) q^{80} +(-6.77100 + 5.92905i) q^{81} +(-3.02629 - 5.24169i) q^{82} +(-0.527591 - 2.99212i) q^{83} +(4.24674 + 1.72197i) q^{84} +(-7.89981 + 2.87529i) q^{85} +(-0.442457 + 2.50930i) q^{86} +(5.03304 - 10.9435i) q^{87} +(0.260700 - 0.218754i) q^{88} +(-0.522204 + 0.904483i) q^{89} +(3.58671 - 4.36708i) q^{90} +(2.49822 - 0.559637i) q^{91} +(3.39619 - 2.84974i) q^{92} +(11.4895 - 11.6112i) q^{93} +(-0.0254607 - 0.0213641i) q^{94} +(-1.71104 - 1.43573i) q^{95} +(-1.67537 - 0.439470i) q^{96} +(10.1353 - 8.50450i) q^{97} +(0.579261 - 6.97599i) q^{98} +(0.878751 - 0.519766i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−1.42403	−	0.985977i	−0.822162	−	0.569254i
$3$	−1.42403	−	0.985977i	−0.822162	−	0.569254i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.327106	+	1.85511i	−0.146286	+	0.829630i	0.820039	+	0.572307i	$0.193952\pi$
$5$	−0.327106	+	1.85511i	−0.146286	+	0.829630i	−0.966325	+	0.257323i	$0.917160\pi$
$6$	1.72464	−	0.160044i	0.704082	−	0.0653378i
$7$	−1.01788	−	2.44211i	−0.384724	−	0.923032i
$7$	−1.01788	−	2.44211i	−0.384724	−	0.923032i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	1.05570	+	2.80811i	0.351900	+	0.936038i
$10$	−0.941864	−	1.63136i	−0.297844	−	0.515880i
$11$	−0.0590960	−	0.335150i	−0.0178181	−	0.101051i	0.974602	−	0.223945i	$-0.0718937\pi$
$11$	−0.0590960	−	0.335150i	−0.0178181	−	0.101051i	−0.992420	+	0.122894i	$0.960783\pi$
$12$	−1.21828	+	1.23118i	−0.351686	+	0.355411i
$13$	−0.168029	+	0.952940i	−0.0466029	+	0.264298i	−0.999203	−	0.0399287i	$-0.987287\pi$
$13$	−0.168029	+	0.952940i	−0.0466029	+	0.264298i	0.952600	+	0.304227i	$0.0983980\pi$
$14$	2.34950	+	1.21648i	0.627931	+	0.325119i
$15$	2.29490	−	2.31921i	0.592541	−	0.598816i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.23143	+	3.86494i	0.541200	+	0.937386i	0.998835	+	0.0482462i	$0.0153632\pi$
$17$	2.23143	+	3.86494i	0.541200	+	0.937386i	−0.457635	+	0.889140i	$0.651303\pi$
$18$	−2.61373	−	1.47255i	−0.616063	−	0.347083i
$19$	−0.592867	+	1.02688i	−0.136013	+	0.235582i	−0.925984	−	0.377563i	$-0.876762\pi$
$19$	−0.592867	+	1.02688i	−0.136013	+	0.235582i	0.789971	+	0.613144i	$0.210096\pi$
$20$	1.77013	+	0.644273i	0.395812	+	0.144064i
$21$	−0.958371	+	4.48124i	−0.209134	+	0.977887i
$22$	0.260700	+	0.218754i	0.0555815	+	0.0466384i
$23$	3.39619	+	2.84974i	0.708155	+	0.594213i	0.924081	−	0.382197i	$-0.124833\pi$
$23$	3.39619	+	2.84974i	0.708155	+	0.594213i	−0.215926	+	0.976410i	$0.569277\pi$
$24$	0.141868	−	1.72623i	0.0289587	−	0.352365i
$25$	1.36403	+	0.496466i	0.272806	+	0.0992931i
$26$	−0.483820	−	0.838001i	−0.0948849	−	0.164346i
$27$	1.26539	−	5.03972i	0.243524	−	0.969895i
$28$	−2.58176	+	0.578353i	−0.487908	+	0.109298i
$29$	1.20762	+	6.84877i	0.224250	+	1.27178i	0.864114	+	0.503296i	$0.167880\pi$
$29$	1.20762	+	6.84877i	0.224250	+	1.27178i	−0.639864	+	0.768488i	$0.721009\pi$
$30$	−0.267241	+	3.25175i	−0.0487912	+	0.593686i
$31$	−1.63766	+	9.28765i	−0.294133	+	1.66811i	0.376572	+	0.926387i	$0.377103\pi$
$31$	−1.63766	+	9.28765i	−0.294133	+	1.66811i	−0.670705	+	0.741724i	$0.734008\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.246296	+	0.535529i	−0.0428746	+	0.0932237i
$34$	−4.19371	−	1.52638i	−0.719215	−	0.261773i
$35$	4.86334	−	1.08946i	0.822055	−	0.184152i
$36$	2.94877	−	0.552038i	0.491462	−	0.0920063i
$37$	1.81191			0.297876			0.148938	−	0.988847i	$-0.452415\pi$
$37$	1.81191			0.297876			0.148938	+	0.988847i	$0.452415\pi$
$38$	−0.205901	−	1.16772i	−0.0334015	−	0.189429i
$39$	1.17885	−	1.19134i	0.188768	−	0.190767i
$40$	−1.77013	+	0.644273i	−0.279881	+	0.101868i
$41$	−1.05102	+	5.96062i	−0.164142	+	0.930893i	0.785804	+	0.618476i	$0.212250\pi$
$41$	−1.05102	+	5.96062i	−0.164142	+	0.930893i	−0.949945	+	0.312417i	$0.898861\pi$
$42$	−2.14633	−	4.04886i	−0.331186	−	0.624753i
$43$	1.95189	−	1.63783i	0.297660	−	0.249766i	−0.481710	−	0.876331i	$-0.659984\pi$
$43$	1.95189	−	1.63783i	0.297660	−	0.249766i	0.779370	+	0.626565i	$0.215540\pi$
$44$	−0.340320			−0.0513052
$45$	−5.55468	+	1.03989i	−0.828043	+	0.155017i
$46$	−4.43341			−0.653671
$47$	0.00577148	+	0.0327317i	0.000841857	+	0.00477441i	0.985226	−	0.171260i	$-0.0547840\pi$
$47$	0.00577148	+	0.0327317i	0.000841857	+	0.00477441i	−0.984384	+	0.176035i	$0.943673\pi$
$48$	1.00092	+	1.41356i	0.144471	+	0.204030i
$49$	−4.92782	+	4.97158i	−0.703974	+	0.710225i
$50$	−1.36403	+	0.496466i	−0.192903	+	0.0702108i
$51$	0.633135	−	7.70391i	0.0886567	−	1.07876i
$52$	0.909284	+	0.330952i	0.126095	+	0.0458949i
$53$	5.22772	−	9.05468i	0.718082	−	1.24376i	−0.243676	−	0.969857i	$-0.578353\pi$
$53$	5.22772	−	9.05468i	0.718082	−	1.24376i	0.961759	−	0.273899i	$-0.0883133\pi$
$54$	2.27013	+	4.67403i	0.308925	+	0.636055i
$55$	0.641071			0.0864419
$56$	1.60599	−	2.10257i	0.214609	−	0.280968i
$57$	1.85673	−	0.877745i	0.245930	−	0.116260i
$58$	−5.32740	−	4.47022i	−0.699522	−	0.586968i
$59$	−0.869877	+	0.316609i	−0.113248	+	0.0412190i	−0.398023	−	0.917376i	$-0.630304\pi$
$59$	−0.869877	+	0.316609i	−0.113248	+	0.0412190i	0.284774	+	0.958595i	$0.408081\pi$
$60$	−1.88547	−	2.66276i	−0.243413	−	0.343761i
$61$	−0.993133	−	5.63234i	−0.127158	−	0.721147i	−0.980003	−	0.198983i	$-0.936236\pi$
$61$	−0.993133	−	5.63234i	−0.127158	−	0.721147i	0.852845	−	0.522164i	$-0.174875\pi$
$62$	−4.71546	−	8.16742i	−0.598865	−	1.03726i
$63$	5.78314	−	5.43647i	0.728608	−	0.684931i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.71284	−	0.623424i	−0.212452	−	0.0773263i
$66$	−0.155558	−	0.568555i	−0.0191479	−	0.0699843i
$67$	−1.63245	−	1.36979i	−0.199435	−	0.167346i	0.537601	−	0.843199i	$-0.319331\pi$
$67$	−1.63245	−	1.36979i	−0.199435	−	0.167346i	−0.737036	+	0.675854i	$0.763775\pi$
$68$	4.19371	−	1.52638i	0.508562	−	0.185101i
$69$	−2.02648	−	7.40667i	−0.243960	−	0.891659i
$70$	−3.02525	+	3.96067i	−0.361586	+	0.473391i
$71$	−6.38672	+	11.0621i	−0.757964	+	1.31283i	0.185923	+	0.982564i	$0.440473\pi$
$71$	−6.38672	+	11.0621i	−0.757964	+	1.31283i	−0.943887	+	0.330268i	$0.892861\pi$
$72$	−1.90405	+	2.31832i	−0.224394	+	0.273217i
$73$	−10.4240			−1.22004			−0.610019	−	0.792387i	$-0.708838\pi$
$73$	−10.4240			−1.22004			−0.610019	+	0.792387i	$0.708838\pi$
$74$	−1.38800	+	1.16467i	−0.161352	+	0.135390i
$75$	−1.45291	−	2.05188i	−0.167767	−	0.236931i
$76$	0.908325	+	0.762175i	0.104192	+	0.0874275i
$77$	−0.758321	+	0.485463i	−0.0864187	+	0.0553236i
$78$	−0.137277	+	1.67037i	−0.0155436	+	0.189132i
$79$	13.5842	−	11.3985i	1.52834	−	1.28243i	0.719245	−	0.694756i	$-0.244488\pi$
$79$	13.5842	−	11.3985i	1.52834	−	1.28243i	0.809097	−	0.587675i	$-0.199957\pi$
$80$	0.941864	−	1.63136i	0.105304	−	0.182391i
$81$	−6.77100	+	5.92905i	−0.752333	+	0.658783i
$82$	−3.02629	−	5.24169i	−0.334198	−	0.578847i
$83$	−0.527591	−	2.99212i	−0.0579107	−	0.328428i	0.942065	−	0.335431i	$-0.108882\pi$
$83$	−0.527591	−	2.99212i	−0.0579107	−	0.328428i	−0.999975	+	0.00700320i	$0.997771\pi$
$84$	4.24674	+	1.72197i	0.463358	+	0.187882i
$85$	−7.89981	+	2.87529i	−0.856854	+	0.311869i
$86$	−0.442457	+	2.50930i	−0.0477114	+	0.270585i
$87$	5.03304	−	10.9435i	0.539599	−	1.17327i
$88$	0.260700	−	0.218754i	0.0277908	−	0.0233192i
$89$	−0.522204	+	0.904483i	−0.0553535	+	0.0958750i	−0.892374	−	0.451296i	$-0.850962\pi$
$89$	−0.522204	+	0.904483i	−0.0553535	+	0.0958750i	0.837021	+	0.547171i	$0.184295\pi$
$90$	3.58671	−	4.36708i	0.378072	−	0.460331i
$91$	2.49822	−	0.559637i	0.261885	−	0.0586659i
$92$	3.39619	−	2.84974i	0.354077	−	0.297106i
$93$	11.4895	−	11.6112i	1.19140	−	1.20402i
$94$	−0.0254607	−	0.0213641i	−0.00262607	−	0.00220354i
$95$	−1.71104	−	1.43573i	−0.175549	−	0.147303i
$96$	−1.67537	−	0.439470i	−0.170992	−	0.0448532i
$97$	10.1353	−	8.50450i	1.02908	−	0.863501i	0.0383396	−	0.999265i	$-0.487793\pi$
$97$	10.1353	−	8.50450i	1.02908	−	0.863501i	0.990741	+	0.135763i	$0.0433487\pi$
$98$	0.579261	−	6.97599i	0.0585142	−	0.704682i
$99$	0.878751	−	0.519766i	0.0883178	−	0.0522384i
$100$	0.725784	−	1.25710i	0.0725784	−	0.125710i
$101$	−6.54968	+	5.49583i	−0.651717	+	0.546856i	−0.907591	−	0.419854i	$-0.862081\pi$
$101$	−6.54968	+	5.49583i	−0.651717	+	0.546856i	0.255874	+	0.966710i	$0.417637\pi$
$102$	4.46697	+	6.30851i	0.442296	+	0.624636i
$103$	−1.65739	+	9.39955i	−0.163308	+	0.926165i	0.787484	+	0.616335i	$0.211383\pi$
$103$	−1.65739	+	9.39955i	−0.163308	+	0.926165i	−0.950792	+	0.309830i	$0.899728\pi$
$104$	−0.909284	+	0.330952i	−0.0891627	+	0.0324526i
$105$	−7.99971	−	3.24372i	−0.780691	−	0.316555i
$106$	1.81557	+	10.2966i	0.176344	+	1.00009i
$107$	−4.23818	−	7.34075i	−0.409721	−	0.709657i	0.585138	−	0.810934i	$-0.301040\pi$
$107$	−4.23818	−	7.34075i	−0.409721	−	0.709657i	−0.994858	+	0.101277i	$0.967707\pi$
$108$	−4.74342	−	2.12130i	−0.456436	−	0.204123i
$109$	6.41995	−	11.1197i	0.614920	−	1.06507i	−0.375478	−	0.926831i	$-0.622522\pi$
$109$	6.41995	−	11.1197i	0.614920	−	1.06507i	0.990399	−	0.138242i	$-0.0441451\pi$
$110$	−0.491089	+	0.412072i	−0.0468235	+	0.0392895i
$111$	−2.58020	−	1.78650i	−0.244902	−	0.169567i
$112$	0.121248	+	2.64297i	0.0114568	+	0.249737i
$113$	6.87430	+	5.76822i	0.646679	+	0.542628i	0.906061	−	0.423146i	$-0.139074\pi$
$113$	6.87430	+	5.76822i	0.646679	+	0.542628i	−0.259382	+	0.965775i	$0.583519\pi$
$114$	−0.858137	+	1.86588i	−0.0803719	+	0.174755i
$115$	−6.39750	+	5.36814i	−0.596570	+	0.500582i
$116$	6.95442			0.645702
$117$	−2.85335	+	0.534174i	−0.263792	+	0.0493844i
$118$	0.462852	−	0.801683i	0.0426090	−	0.0738009i
$119$	7.16729	−	9.38346i	0.657024	−	0.860180i
$120$	3.15594	+	0.827841i	0.288097	+	0.0755712i
$121$	10.2278	−	3.72261i	0.929799	−	0.338419i
$122$	4.38118	+	3.67625i	0.396653	+	0.332832i
$123$	7.37372	−	7.45180i	0.664866	−	0.671906i
$124$	8.86217	+	3.22557i	0.795847	+	0.289665i
$125$	−6.07650	+	10.5248i	−0.543499	+	0.941367i
$126$	−0.935649	+	7.88191i	−0.0833542	+	0.702177i
$127$	1.52799	+	2.64656i	0.135587	+	0.234844i	0.925822	−	0.377961i	$-0.123375\pi$
$127$	1.52799	+	2.64656i	0.135587	+	0.234844i	−0.790234	+	0.612805i	$0.790041\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−4.39440	+	0.407794i	−0.386905	+	0.0359043i
$130$	1.71284	−	0.623424i	0.150226	−	0.0546779i
$131$	11.9579	+	10.0339i	1.04477	+	0.876665i	0.992534	−	0.121970i	$-0.0389211\pi$
$131$	11.9579	+	10.0339i	1.04477	+	0.876665i	0.0522348	+	0.998635i	$0.483366\pi$
$132$	0.484625	+	0.335548i	0.0421812	+	0.0292057i
$133$	3.11122	+	0.402606i	0.269777	+	0.0349104i
$134$	2.13101			0.184091
$135$	8.93532	+	3.99596i	0.769030	+	0.343918i
$136$	−2.23143	+	3.86494i	−0.191343	+	0.331416i
$137$	−13.8233	−	5.03127i	−1.18100	−	0.429851i	−0.324448	−	0.945904i	$-0.605179\pi$
$137$	−13.8233	−	5.03127i	−1.18100	−	0.429851i	−0.856557	+	0.516053i	$0.827401\pi$
$138$	6.31330	+	4.37124i	0.537423	+	0.372105i
$139$	−9.24908	+	3.36639i	−0.784497	+	0.285533i	−0.703046	−	0.711144i	$-0.748177\pi$
$139$	−9.24908	+	3.36639i	−0.784497	+	0.285533i	−0.0814503	+	0.996677i	$0.525955\pi$
$140$	−0.228397	−	4.97864i	−0.0193031	−	0.420772i
$141$	0.0240540	−	0.0523013i	0.00202571	−	0.00440457i
$142$	−2.21809	−	12.5794i	−0.186138	−	1.05564i
$143$	0.329307			0.0275381
$144$	−0.0316020	−	2.99983i	−0.00263350	−	0.249986i
$145$	−13.1002			−1.08792
$146$	7.98525	−	6.70042i	0.660864	−	0.554531i
$147$	11.9192	−	2.22094i	0.983079	−	0.183180i
$148$	0.314634	−	1.78438i	0.0258628	−	0.146675i
$149$	−18.7193	+	6.81327i	−1.53355	+	0.558165i	−0.964487	−	0.264132i	$-0.914915\pi$
$149$	−18.7193	+	6.81327i	−1.53355	+	0.558165i	−0.569059	+	0.822297i	$0.692692\pi$
$150$	2.43192	+	0.637920i	0.198565	+	0.0520860i
$151$	2.55887	+	14.5121i	0.208238	+	1.18098i	0.892262	+	0.451517i	$0.149117\pi$
$151$	2.55887	+	14.5121i	0.208238	+	1.18098i	−0.684025	+	0.729459i	$0.739772\pi$
$152$	−1.18573			−0.0961757
$153$	−8.49748	+	10.3463i	−0.686980	+	0.836450i
$154$	0.268858	−	0.859325i	0.0216652	−	0.0692464i
$155$	−16.6939	−	6.07609i	−1.34089	−	0.488044i
$156$	−0.968533	−	1.36782i	−0.0775447	−	0.109513i
$157$	−18.4885	+	6.72925i	−1.47554	+	0.537052i	−0.949598	−	0.313469i	$-0.898509\pi$
$157$	−18.4885	+	6.72925i	−1.47554	+	0.537052i	−0.525941	+	0.850521i	$0.676287\pi$
$158$	−3.07929	+	17.4635i	−0.244975	+	1.38932i
$159$	−16.3721	+	7.73968i	−1.29839	+	0.613797i
$160$	0.327106	+	1.85511i	0.0258600	+	0.146659i
$161$	3.50246	−	11.1946i	0.276032	−	0.882257i
$162$	1.37577	−	8.89423i	0.108090	−	0.698796i
$163$	2.27942	+	3.94807i	0.178538	+	0.309237i	0.941380	−	0.337348i	$-0.109530\pi$
$163$	2.27942	+	3.94807i	0.178538	+	0.309237i	−0.762842	+	0.646585i	$0.776197\pi$
$164$	5.68756	+	2.07010i	0.444124	+	0.161648i
$165$	−0.912901	−	0.632081i	−0.0710693	−	0.0492074i
$166$	2.32746	+	1.95297i	0.180646	+	0.151580i
$167$	−4.44377	−	3.72877i	−0.343870	−	0.288541i	0.454453	−	0.890771i	$-0.349835\pi$
$167$	−4.44377	−	3.72877i	−0.343870	−	0.288541i	−0.798323	+	0.602230i	$0.794279\pi$
$168$	−4.36005	+	1.41065i	−0.336385	+	0.108834i
$169$	11.3361	+	4.12602i	0.872011	+	0.317386i
$170$	4.20340	−	7.28050i	0.322386	−	0.558389i
$171$	−3.50947	−	0.580765i	−0.268376	−	0.0444122i
$172$	−1.27400	−	2.20664i	−0.0971419	−	0.168255i
$173$	−6.42530	−	2.33862i	−0.488506	−	0.177802i	0.0860110	−	0.996294i	$-0.472588\pi$
$173$	−6.42530	−	2.33862i	−0.488506	−	0.177802i	−0.574517	+	0.818492i	$0.694810\pi$
$174$	3.17882	+	11.6184i	0.240986	+	0.880788i
$175$	−0.175999	−	3.83645i	−0.0133043	−	0.290009i
$176$	−0.0590960	+	0.335150i	−0.00445453	+	0.0252629i
$177$	1.55090	+	0.406818i	0.116573	+	0.0305783i
$178$	−0.181359	−	1.02854i	−0.0135935	−	0.0770924i
$179$	−8.41713	−	14.5789i	−0.629126	−	1.08968i	−0.987727	−	0.156187i	$-0.950080\pi$
$179$	−8.41713	−	14.5789i	−0.629126	−	1.08968i	0.358602	−	0.933491i	$-0.383254\pi$
$180$	0.0595297	+	5.65087i	0.00443708	+	0.421191i
$181$	10.4465	+	18.0939i	0.776484	+	1.34491i	0.933957	+	0.357387i	$0.116332\pi$
$181$	10.4465	+	18.0939i	0.776484	+	1.34491i	−0.157472	+	0.987523i	$0.550335\pi$
$182$	−1.55402	+	2.03453i	−0.115192	+	0.150810i
$183$	−4.13911	+	8.99980i	−0.305972	+	0.665284i
$184$	−0.769854	+	4.36606i	−0.0567544	+	0.321870i
$185$	−0.592686	+	3.36129i	−0.0435751	+	0.247127i
$186$	−1.33795	+	16.2800i	−0.0981030	+	1.19370i
$187$	1.16347	−	0.976265i	0.0850811	−	0.0713915i
$188$	0.0332366			0.00242403
$189$	−13.5956	+	2.03963i	−0.988933	+	0.148361i
$190$	2.23360			0.162042
$191$	−9.91248	+	8.31756i	−0.717242	+	0.601837i	−0.926621	−	0.375997i	$-0.877300\pi$
$191$	−9.91248	+	8.31756i	−0.717242	+	0.601837i	0.209379	+	0.977835i	$0.432856\pi$
$192$	1.56589	−	0.740254i	0.113009	−	0.0534232i
$193$	1.21354	−	6.88233i	0.0873526	−	0.495401i	−0.909471	−	0.415766i	$-0.863513\pi$
$193$	1.21354	−	6.88233i	0.0873526	−	0.495401i	0.996824	−	0.0796350i	$-0.0253755\pi$
$194$	−2.29748	+	13.0297i	−0.164949	+	0.935475i
$195$	1.82445	+	2.57660i	0.130652	+	0.184514i
$196$	4.04034	+	5.71626i	0.288596	+	0.408304i
$197$	8.26055	+	14.3077i	0.588540	+	1.01938i	0.994424	+	0.105456i	$0.0336303\pi$
$197$	8.26055	+	14.3077i	0.588540	+	1.01938i	−0.405884	+	0.913925i	$0.633036\pi$
$198$	−0.339063	+	0.963014i	−0.0240962	+	0.0684384i
$199$	−6.70506	−	11.6135i	−0.475309	−	0.823259i	0.524291	−	0.851539i	$-0.324330\pi$
$199$	−6.70506	−	11.6135i	−0.475309	−	0.823259i	−0.999600	+	0.0282800i	$0.990997\pi$
$200$	0.252062	+	1.42952i	0.0178235	+	0.101082i
$201$	0.974070	+	3.56016i	0.0687056	+	0.251115i
$202$	1.48469	−	8.42010i	0.104463	−	0.592436i
$203$	15.4962	−	9.92041i	1.08762	−	0.696276i
$204$	−7.47693	−	1.96129i	−0.523490	−	0.137318i
$205$	−10.7138	−	3.89951i	−0.748286	−	0.272354i
$206$	−4.77228	−	8.26582i	−0.332500	−	0.575907i
$207$	−4.41704	+	12.5454i	−0.307006	+	0.871963i
$208$	0.483820	−	0.838001i	0.0335469	−	0.0581049i
$209$	0.379193	+	0.138015i	0.0262294	+	0.00954671i
$210$	8.21316	−	2.65728i	0.566762	−	0.183369i
$211$	8.51283	+	7.14311i	0.586047	+	0.491752i	0.886927	−	0.461910i	$-0.152836\pi$
$211$	8.51283	+	7.14311i	0.586047	+	0.491752i	−0.300880	+	0.953662i	$0.597280\pi$
$212$	−8.00933	−	6.72063i	−0.550083	−	0.461575i
$213$	20.0019	−	9.45560i	1.37050	−	0.647887i
$214$	7.96518	+	2.89909i	0.544488	+	0.198178i
$215$	2.39988	+	4.15671i	0.163670	+	0.283485i
$216$	4.99722	−	1.42400i	0.340018	−	0.0968910i
$217$	24.3484	−	5.45440i	1.65288	−	0.370269i
$218$	2.22963	+	12.6448i	0.151009	+	0.856417i
$219$	14.8441	+	10.2778i	1.00307	+	0.694511i
$220$	0.111321	−	0.631331i	0.00750524	−	0.0425643i
$221$	−4.05800	+	1.47699i	−0.272971	+	0.0993532i
$222$	3.12489	−	0.289985i	0.209729	−	0.0194625i
$223$	19.3545	+	7.04446i	1.29607	+	0.471732i	0.895715	−	0.444628i	$-0.146664\pi$
$223$	19.3545	+	7.04446i	1.29607	+	0.471732i	0.400357	+	0.916359i	$0.368886\pi$
$224$	−1.79175	−	1.94670i	−0.119716	−	0.130069i
$225$	0.0458725	+	4.35446i	0.00305817	+	0.290298i
$226$	−8.97376			−0.596925
$227$	−3.81007	−	21.6080i	−0.252883	−	1.43417i	−0.801449	−	0.598063i	$-0.795937\pi$
$227$	−3.81007	−	21.6080i	−0.252883	−	1.43417i	0.548566	−	0.836107i	$-0.315174\pi$
$228$	−0.541991	−	1.98094i	−0.0358943	−	0.131191i
$229$	20.0905	−	7.31234i	1.32762	−	0.483213i	0.421725	−	0.906724i	$-0.361425\pi$
$229$	20.0905	−	7.31234i	1.32762	−	0.483213i	0.905891	+	0.423511i	$0.139202\pi$
$230$	1.45020	−	8.22447i	0.0956231	−	0.542305i
$231$	1.55852	+	0.0563746i	0.102543	+	0.00370918i
$232$	−5.32740	+	4.47022i	−0.349761	+	0.293484i
$233$	18.8557			1.23528			0.617638	−	0.786463i	$-0.288090\pi$
$233$	18.8557			1.23528			0.617638	+	0.786463i	$0.288090\pi$
$234$	1.84243	−	2.24330i	0.120444	−	0.146649i
$235$	−0.0626088			−0.00408415
$236$	0.160747	+	0.911640i	0.0104637	+	0.0593427i
$237$	−30.5829	+	2.83805i	−1.98657	+	0.184351i
$238$	0.541110	+	11.7952i	0.0350749	+	0.764569i
$239$	8.87313	−	3.22955i	0.573955	−	0.208902i	−0.0387029	−	0.999251i	$-0.512323\pi$
$239$	8.87313	−	3.22955i	0.573955	−	0.208902i	0.612658	+	0.790348i	$0.290100\pi$
$240$	−2.94972	+	1.39444i	−0.190403	+	0.0900106i
$241$	−4.03810	−	1.46975i	−0.260117	−	0.0946747i	0.208670	−	0.977986i	$-0.433087\pi$
$241$	−4.03810	−	1.46975i	−0.260117	−	0.0946747i	−0.468787	+	0.883311i	$0.655309\pi$
$242$	−5.44209	+	9.42598i	−0.349831	+	0.605925i
$243$	15.4880	−	1.76707i	0.993554	−	0.113358i
$244$	−5.71922			−0.366136
$245$	−7.61090	−	10.7679i	−0.486243	−	0.687935i
$246$	−0.858667	+	10.4481i	−0.0547466	+	0.666149i
$247$	−0.878932	−	0.737512i	−0.0559251	−	0.0469267i
$248$	−8.86217	+	3.22557i	−0.562749	+	0.204824i
$249$	−2.19886	+	4.78105i	−0.139347	+	0.302987i
$250$	−2.11035	−	11.9684i	−0.133470	−	0.756946i
$251$	−11.0022	−	19.0563i	−0.694451	−	1.20282i	−0.970365	−	0.241642i	$-0.922314\pi$
$251$	−11.0022	−	19.0563i	−0.694451	−	1.20282i	0.275914	−	0.961182i	$-0.411019\pi$
$252$	−4.34965	−	6.63932i	−0.274002	−	0.418238i
$253$	0.754390	−	1.30664i	0.0474281	−	0.0821479i
$254$	−2.87169	−	1.04521i	−0.180186	−	0.0655822i
$255$	14.0845	+	3.69453i	0.882006	+	0.231361i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	16.7008	−	6.07859i	1.04177	−	0.379172i	0.236216	−	0.971700i	$-0.424093\pi$
$257$	16.7008	−	6.07859i	1.04177	−	0.379172i	0.805549	+	0.592529i	$0.201870\pi$
$258$	3.10418	−	3.13705i	0.193258	−	0.195304i
$259$	−1.84431	−	4.42488i	−0.114600	−	0.274949i
$260$	−0.911386	+	1.57857i	−0.0565217	+	0.0978985i
$261$	−17.9572	+	10.6214i	−1.11152	+	0.657447i
$262$	−15.6100			−0.964387
$263$	−19.8850	+	16.6855i	−1.22616	+	1.02887i	−0.227681	+	0.973736i	$0.573114\pi$
$263$	−19.8850	+	16.6855i	−1.22616	+	1.02887i	−0.998479	+	0.0551350i	$0.982441\pi$
$264$	−0.586930	+	0.0544663i	−0.0361230	+	0.00335217i
$265$	15.0874	+	12.6598i	0.926812	+	0.777687i
$266$	−2.64212	+	1.69144i	−0.161999	+	0.103709i
$267$	1.63543	−	0.773127i	0.100087	−	0.0473146i
$268$	−1.63245	+	1.36979i	−0.0997175	+	0.0836729i
$269$	2.38738	−	4.13506i	0.145561	−	0.252119i	−0.784021	−	0.620734i	$-0.786835\pi$
$269$	2.38738	−	4.13506i	0.145561	−	0.252119i	0.929582	+	0.368615i	$0.120168\pi$
$270$	−9.41341	+	2.68243i	−0.572882	+	0.163247i
$271$	−8.28533	−	14.3506i	−0.503298	−	0.871738i	−0.999993	−	0.00381253i	$-0.998786\pi$
$271$	−8.28533	−	14.3506i	−0.503298	−	0.871738i	0.496695	−	0.867925i	$-0.334547\pi$
$272$	−0.774966	−	4.39505i	−0.0469892	−	0.266489i
$273$	−4.10932	−	1.66625i	−0.248707	−	0.100846i
$274$	13.8233	−	5.03127i	0.835096	−	0.303950i
$275$	0.0857818	−	0.486493i	0.00517284	−	0.0293366i
$276$	−7.64605	+	0.709542i	−0.460238	+	0.0427094i
$277$	7.42753	−	6.23243i	0.446277	−	0.374471i	−0.391775	−	0.920061i	$-0.628139\pi$
$277$	7.42753	−	6.23243i	0.446277	−	0.374471i	0.838052	+	0.545590i	$0.183694\pi$
$278$	4.92133	−	8.52400i	0.295162	−	0.511235i
$279$	−27.8097	+	5.20623i	−1.66492	+	0.311689i
$280$	3.37517	+	3.66705i	0.201705	+	0.219148i
$281$	−5.64454	+	4.73633i	−0.336725	+	0.282546i	−0.795433	−	0.606041i	$-0.792757\pi$
$281$	−5.64454	+	4.73633i	−0.336725	+	0.282546i	0.458708	+	0.888587i	$0.348312\pi$
$282$	0.0151922	+	0.0555267i	0.000904685	+	0.00330657i
$283$	7.74255	+	6.49677i	0.460247	+	0.386193i	0.843222	−	0.537566i	$-0.180656\pi$
$283$	7.74255	+	6.49677i	0.460247	+	0.386193i	−0.382975	+	0.923759i	$0.625100\pi$
$284$	9.78503	+	8.21061i	0.580634	+	0.487210i
$285$	1.02096	+	3.73156i	0.0604767	+	0.221039i
$286$	−0.252264	+	0.211675i	−0.0149167	+	0.0125166i
$287$	15.6263	−	3.50052i	0.922393	−	0.206629i
$288$	1.95246	+	2.27769i	0.115050	+	0.134214i
$289$	−1.45852	+	2.52623i	−0.0857953	+	0.148602i
$290$	10.0354	−	8.42067i	0.589297	−	0.494479i
$291$	−22.8181	+	2.11749i	−1.33762	+	0.124129i
$292$	−1.81011	+	10.2656i	−0.105929	+	0.600751i
$293$	−2.03220	+	0.739659i	−0.118722	+	0.0432113i	−0.400698	−	0.916210i	$-0.631232\pi$
$293$	−2.03220	+	0.739659i	−0.118722	+	0.0432113i	0.281976	+	0.959421i	$0.409010\pi$
$294$	−7.70305	+	9.36286i	−0.449251	+	0.546053i
$295$	−0.302803	−	1.71728i	−0.0176299	−	0.0999840i
$296$	0.905954	+	1.56916i	0.0526575	+	0.0912055i
$297$	−1.76384	−	0.126268i	−0.102348	−	0.00732683i
$298$	9.96033	−	17.2518i	0.576987	−	0.999370i
$299$	−3.28629	+	2.75753i	−0.190051	+	0.159472i
$300$	−2.27300	+	1.07453i	−0.131232	+	0.0620380i
$301$	−5.98656	−	3.09961i	−0.345059	−	0.178658i
$302$	−11.2884	−	9.47209i	−0.649574	−	0.545057i
$303$	14.7457	−	1.36838i	0.847117	−	0.0786112i
$304$	0.908325	−	0.762175i	0.0520960	−	0.0437137i
$305$	10.7735			0.616887
$306$	−0.141035	−	13.3878i	−0.00806245	−	0.765330i
$307$	2.78755	−	4.82818i	0.159094	−	0.275559i	−0.775448	−	0.631411i	$-0.782476\pi$
$307$	2.78755	−	4.82818i	0.159094	−	0.275559i	0.934542	+	0.355852i	$0.115809\pi$
$308$	0.346407	+	0.831100i	0.0197384	+	0.0473563i
$309$	11.6279	−	11.7510i	0.661489	−	0.668494i
$310$	16.6939	−	6.07609i	0.948151	−	0.345099i
$311$	13.5230	+	11.3471i	0.766817	+	0.643436i	0.939892	−	0.341473i	$-0.110926\pi$
$311$	13.5230	+	11.3471i	0.766817	+	0.643436i	−0.173075	+	0.984909i	$0.555370\pi$
$312$	1.62116	+	0.425248i	0.0917799	+	0.0240750i
$313$	−16.3632	−	5.95572i	−0.924902	−	0.336637i	−0.164715	−	0.986341i	$-0.552671\pi$
$313$	−16.3632	−	5.95572i	−0.924902	−	0.336637i	−0.760187	+	0.649704i	$0.774893\pi$
$314$	9.83750	−	17.0390i	0.555162	−	0.961569i
$315$	8.19355	+	12.5067i	0.461654	+	0.704671i
$316$	−8.86646	−	15.3572i	−0.498777	−	0.863908i
$317$	−0.0429560	−	0.243616i	−0.00241265	−	0.0136828i	0.983578	−	0.180485i	$-0.0577669\pi$
$317$	−0.0429560	−	0.243616i	−0.00241265	−	0.0136828i	−0.985990	+	0.166803i	$0.946656\pi$
$318$	7.56679	−	16.4527i	0.424324	−	0.922623i
$319$	2.22400	−	0.809469i	0.124520	−	0.0453216i
$320$	−1.44302	−	1.21084i	−0.0806672	−	0.0676879i
$321$	−1.20252	+	14.6322i	−0.0671184	+	0.816688i
$322$	4.51270	+	10.8269i	0.251483	+	0.603359i
$323$	−5.29176			−0.294441
$324$	4.66320	+	7.69770i	0.259067	+	0.427650i
$325$	−0.702298	+	1.21642i	−0.0389565	+	0.0674746i
$326$	−4.28390	−	1.55921i	−0.237264	−	0.0863569i
$327$	−20.1059	+	9.50480i	−1.11186	+	0.525616i
$328$	−5.68756	+	2.07010i	−0.314043	+	0.114302i
$329$	0.0740598	−	0.0474117i	0.00408305	−	0.00261389i
$330$	1.10562	−	0.102600i	0.0608622	−	0.00564792i
$331$	−1.43361	−	8.13039i	−0.0787982	−	0.446887i	−0.998523	−	0.0543239i	$-0.982700\pi$
$331$	−1.43361	−	8.13039i	−0.0787982	−	0.446887i	0.919725	−	0.392563i	$-0.128411\pi$
$332$	−3.03828			−0.166747
$333$	1.91283	+	5.08804i	0.104822	+	0.278823i
$334$	5.80094			0.317413
$335$	3.07508	−	2.58030i	0.168010	−	0.140977i
$336$	2.43325	−	3.88321i	0.132745	−	0.211846i
$337$	4.74727	−	26.9231i	0.258600	−	1.46660i	−0.528059	−	0.849208i	$-0.677080\pi$
$337$	4.74727	−	26.9231i	0.258600	−	1.46660i	0.786659	−	0.617388i	$-0.211809\pi$
$338$	−11.3361	+	4.12602i	−0.616605	+	0.224426i
$339$	−4.10185	−	14.9920i	−0.222782	−	0.814253i
$340$	1.45983	+	8.27908i	0.0791701	+	0.448996i
$341$	3.20954			0.173806
$342$	3.06172	−	1.81095i	0.165559	−	0.0979252i
$343$	17.1571	+	6.97379i	0.926397	+	0.376549i
$344$	2.39434	+	0.871470i	0.129094	+	0.0469865i
$345$	14.4031	−	1.33658i	0.775435	−	0.0719593i
$346$	6.42530	−	2.33862i	0.345426	−	0.125725i
$347$	1.76163	−	9.99070i	0.0945692	−	0.536329i	−0.900309	−	0.435251i	$-0.856660\pi$
$347$	1.76163	−	9.99070i	0.0945692	−	0.536329i	0.994879	−	0.101078i	$-0.0322292\pi$
$348$	−9.90328	−	6.85690i	−0.530871	−	0.367568i
$349$	−4.83658	−	27.4296i	−0.258896	−	1.46827i	−0.785870	−	0.618391i	$-0.787785\pi$
$349$	−4.83658	−	27.4296i	−0.258896	−	1.46827i	0.526974	−	0.849881i	$-0.323326\pi$
$350$	2.60085	+	2.82576i	0.139021	+	0.151043i
$351$	4.58993	+	2.05266i	0.244992	+	0.109563i
$352$	−0.170160	−	0.294726i	−0.00906956	−	0.0157089i
$353$	30.0603	+	10.9411i	1.59995	+	0.582334i	0.979417	−	0.201846i	$-0.0646940\pi$
$353$	30.0603	+	10.9411i	1.59995	+	0.582334i	0.620533	+	0.784180i	$0.286916\pi$
$354$	−1.44955	+	0.685256i	−0.0770429	+	0.0364209i
$355$	−18.4323	−	15.4666i	−0.978286	−	0.820880i
$356$	0.800062	+	0.671332i	0.0424032	+	0.0355805i
$357$	−19.4583	+	6.29551i	−1.02984	+	0.333194i
$358$	15.8190	+	5.75765i	0.836062	+	0.304302i
$359$	−9.36031	+	16.2125i	−0.494018	+	0.855665i	−0.999976	−	0.00689333i	$-0.997806\pi$
$359$	−9.36031	+	16.2125i	−0.494018	+	0.855665i	0.505958	+	0.862558i	$0.331139\pi$
$360$	−3.67791	−	4.29055i	−0.193843	−	0.226132i
$361$	8.79702	+	15.2369i	0.463001	+	0.801941i
$362$	−19.6330	−	7.14584i	−1.03189	−	0.375577i
$363$	−18.2350	−	4.78327i	−0.957091	−	0.251056i
$364$	−0.117324	−	2.55745i	−0.00614945	−	0.134047i
$365$	3.40976	−	19.3377i	0.178475	−	1.01218i
$366$	−2.61422	−	9.55481i	−0.136647	−	0.499438i
$367$	1.22868	+	6.96817i	0.0641364	+	0.363736i	0.999937	+	0.0112064i	$0.00356720\pi$
$367$	1.22868	+	6.96817i	0.0641364	+	0.363736i	−0.935801	+	0.352529i	$0.885322\pi$
$368$	−2.21671	−	3.83945i	−0.115554	−	0.200145i
$369$	−17.8477	+	3.34125i	−0.929112	+	0.173939i
$370$	−1.70657	−	2.95587i	−0.0887204	−	0.153668i
$371$	−27.4337	−	3.55006i	−1.42429	−	0.184310i
$372$	−9.43963	−	13.3312i	−0.489422	−	0.691190i
$373$	−1.95053	+	11.0620i	−0.100995	+	0.572769i	0.891750	+	0.452528i	$0.149478\pi$
$373$	−1.95053	+	11.0620i	−0.100995	+	0.572769i	−0.992745	+	0.120241i	$0.961633\pi$
$374$	−0.263737	+	1.49572i	−0.0136375	+	0.0773421i
$375$	19.0303	−	8.99631i	0.982721	−	0.464567i
$376$	−0.0254607	+	0.0213641i	−0.00131304	+	0.00110177i
$377$	−6.72938			−0.346581
$378$	9.10377	−	10.3015i	0.468247	−	0.529853i
$379$	−29.7564			−1.52848			−0.764242	−	0.644929i	$-0.776887\pi$
$379$	−29.7564			−1.52848			−0.764242	+	0.644929i	$0.776887\pi$
$380$	−1.71104	+	1.43573i	−0.0877744	+	0.0736514i
$381$	0.433546	−	5.27534i	0.0222112	−	0.270264i
$382$	2.24698	−	12.7432i	0.114965	−	0.652001i
$383$	5.09065	−	28.8705i	0.260120	−	1.47521i	−0.522460	−	0.852664i	$-0.674986\pi$
$383$	5.09065	−	28.8705i	0.260120	−	1.47521i	0.782580	−	0.622550i	$-0.213903\pi$
$384$	−0.723718	+	1.57360i	−0.0369321	+	0.0803027i
$385$	−0.652536	−	1.56557i	−0.0332563	−	0.0797886i
$386$	3.49425	+	6.05222i	0.177853	+	0.308050i
$387$	6.65981	+	3.75207i	0.338537	+	0.190728i
$388$	−6.61533	−	11.4581i	−0.335842	−	0.581696i
$389$	3.63214	+	20.5989i	0.184157	+	1.04441i	0.927034	+	0.374978i	$0.122350\pi$
$389$	3.63214	+	20.5989i	0.184157	+	1.04441i	−0.742877	+	0.669428i	$0.766539\pi$
$390$	−3.05382	−	0.801052i	−0.154636	−	0.0405629i
$391$	−3.43574	+	19.4851i	−0.173753	+	0.985403i
$392$	−6.76942	−	1.78183i	−0.341907	−	0.0899959i
$393$	−7.13521	−	26.0788i	−0.359924	−	1.31550i
$394$	−15.5248	−	5.65055i	−0.782126	−	0.284671i
$395$	16.7020	+	28.9287i	0.840369	+	1.45556i
$396$	−0.359276	−	0.955657i	−0.0180543	−	0.0480236i
$397$	17.8888	−	30.9843i	0.897812	−	1.55506i	0.0675258	−	0.997718i	$-0.478490\pi$
$397$	17.8888	−	30.9843i	0.897812	−	1.55506i	0.830286	−	0.557338i	$-0.188177\pi$
$398$	12.6014	+	4.58653i	0.631650	+	0.229902i
$399$	−4.03349	−	3.64091i	−0.201927	−	0.182273i
$400$	−1.11197	−	0.933050i	−0.0555983	−	0.0466525i
$401$	−18.6323	−	15.6344i	−0.930454	−	0.780743i	0.0454453	−	0.998967i	$-0.485529\pi$
$401$	−18.6323	−	15.6344i	−0.930454	−	0.780743i	−0.975899	+	0.218224i	$0.929974\pi$
$402$	−3.03461	−	2.10112i	−0.151353	−	0.104795i
$403$	−8.57540	−	3.12119i	−0.427171	−	0.155478i
$404$	4.27500	+	7.40451i	0.212689	+	0.368388i
$405$	−8.78420	−	14.5004i	−0.436491	−	0.720529i
$406$	−5.49409	+	17.5603i	−0.272667	+	0.871501i
$407$	−0.107076	−	0.607261i	−0.00530758	−	0.0301008i
$408$	6.98835	−	3.30364i	0.345975	−	0.163555i
$409$	−3.07007	+	17.4112i	−0.151805	+	0.860929i	0.809844	+	0.586646i	$0.199552\pi$
$409$	−3.07007	+	17.4112i	−0.151805	+	0.860929i	−0.961649	+	0.274284i	$0.911559\pi$
$410$	10.7138	−	3.89951i	0.529118	−	0.192583i
$411$	14.7240	+	20.7941i	0.726283	+	1.02570i
$412$	8.96895	+	3.26443i	0.441868	+	0.160827i
$413$	1.65863	+	1.80206i	0.0816158	+	0.0886738i
$414$	−4.68035	−	12.4495i	−0.230027	−	0.611861i
$415$	5.72329			0.280945
$416$	0.168029	+	0.952940i	0.00823830	+	0.0467217i
$417$	16.4901	+	4.32555i	0.807524	+	0.211823i
$418$	−0.379193	+	0.138015i	−0.0185470	+	0.00675054i
$419$	5.75680	−	32.6484i	0.281238	−	1.59498i	−0.437184	−	0.899372i	$-0.644024\pi$
$419$	5.75680	−	32.6484i	0.281238	−	1.59498i	0.718422	−	0.695608i	$-0.244865\pi$
$420$	−4.58358	+	7.31491i	−0.223656	+	0.356931i
$421$	9.80351	−	8.22613i	0.477794	−	0.400917i	−0.371834	−	0.928299i	$-0.621271\pi$
$421$	9.80351	−	8.22613i	0.477794	−	0.400917i	0.849628	+	0.527382i	$0.176826\pi$
$422$	−11.1127			−0.540958
$423$	−0.0858213	+	0.0507618i	−0.00417278	+	0.00246812i
$424$	10.4554			0.507761
$425$	1.12492	+	6.37972i	0.0545664	+	0.309462i
$426$	−9.24437	+	20.1004i	−0.447891	+	0.973865i
$427$	−12.7439	+	8.15841i	−0.616721	+	0.394813i
$428$	−7.96518	+	2.89909i	−0.385011	+	0.140133i
$429$	−0.468942	−	0.324690i	−0.0226408	−	0.0156762i
$430$	−4.51029	−	1.64161i	−0.217506	−	0.0791656i
$431$	7.93212	−	13.7388i	0.382077	−	0.661776i	−0.609282	−	0.792953i	$-0.708542\pi$
$431$	7.93212	−	13.7388i	0.382077	−	0.661776i	0.991359	+	0.131177i	$0.0418757\pi$
$432$	−2.91276	+	4.30300i	−0.140140	+	0.207028i
$433$	−12.8512			−0.617588			−0.308794	−	0.951129i	$-0.599925\pi$
$433$	−12.8512			−0.617588			−0.308794	+	0.951129i	$0.599925\pi$
$434$	−15.1460	+	19.8292i	−0.727029	+	0.951832i
$435$	18.6551	+	12.9165i	0.894443	+	0.619300i
$436$	−9.83594	−	8.25333i	−0.471056	−	0.395263i
$437$	−4.93982	+	1.79795i	−0.236304	+	0.0860075i
$438$	−17.9777	+	1.66830i	−0.859006	+	0.0797146i
$439$	0.861828	+	4.88767i	0.0411328	+	0.233276i	0.998443	−	0.0557880i	$-0.0177671\pi$
$439$	0.861828	+	4.88767i	0.0411328	+	0.233276i	−0.957310	+	0.289064i	$0.906656\pi$
$440$	0.320535	+	0.555183i	0.0152809	+	0.0264673i
$441$	−19.1631	−	8.58938i	−0.912526	−	0.409018i
$442$	2.15922	−	3.73987i	0.102703	−	0.177888i
$443$	−5.65634	−	2.05874i	−0.268741	−	0.0978137i	0.204135	−	0.978943i	$-0.434562\pi$
$443$	−5.65634	−	2.05874i	−0.268741	−	0.0978137i	−0.472876	+	0.881129i	$0.656784\pi$
$444$	−2.20741	+	2.23078i	−0.104759	+	0.105868i
$445$	−1.50710	−	1.26461i	−0.0714434	−	0.0599481i
$446$	−19.3545	+	7.04446i	−0.916461	+	0.333565i
$447$	33.3745	+	8.75453i	1.57856	+	0.414075i
$448$	2.62387	+	0.339542i	0.123966	+	0.0160418i
$449$	−0.599759	+	1.03881i	−0.0283044	+	0.0490246i	−0.879831	−	0.475287i	$-0.842344\pi$
$449$	−0.599759	+	1.03881i	−0.0283044	+	0.0490246i	0.851526	+	0.524312i	$0.175677\pi$
$450$	−2.83414	−	3.30623i	−0.133602	−	0.155857i
$451$	2.05981			0.0969928
$452$	6.87430	−	5.76822i	0.323340	−	0.271314i
$453$	10.6647	−	23.1886i	0.501070	−	1.08949i
$454$	16.8080	+	14.1036i	0.788839	+	0.661914i
$455$	0.221007	+	4.81753i	0.0103609	+	0.225849i
$456$	1.68852	+	1.16911i	0.0790720	+	0.0547484i
$457$	−17.5643	+	14.7382i	−0.821624	+	0.689424i	−0.953352	−	0.301862i	$-0.902392\pi$
$457$	−17.5643	+	14.7382i	−0.821624	+	0.689424i	0.131728	+	0.991286i	$0.457947\pi$
$458$	−10.6899	+	18.5155i	−0.499507	+	0.865172i
$459$	22.3019	−	6.35510i	1.04096	−	0.296631i
$460$	4.17567	+	7.23248i	0.194692	+	0.337216i
$461$	4.79983	+	27.2212i	0.223551	+	1.26782i	0.865437	+	0.501018i	$0.167041\pi$
$461$	4.79983	+	27.2212i	0.223551	+	1.26782i	−0.641886	+	0.766800i	$0.721848\pi$
$462$	−1.23014	+	0.958614i	−0.0572311	+	0.0445988i
$463$	−39.7405	+	14.4644i	−1.84690	+	0.672216i	−0.860133	+	0.510070i	$0.829619\pi$
$463$	−39.7405	+	14.4644i	−1.84690	+	0.672216i	−0.986767	+	0.162146i	$0.948158\pi$
$464$	1.20762	−	6.84877i	0.0560625	−	0.317946i
$465$	17.7817	+	25.1123i	0.824607	+	1.16456i
$466$	−14.4443	+	12.1202i	−0.669118	+	0.561457i
$467$	−14.8637	+	25.7446i	−0.687809	+	1.19132i	0.284736	+	0.958606i	$0.408094\pi$
$467$	−14.8637	+	25.7446i	−0.687809	+	1.19132i	−0.972545	+	0.232714i	$0.925239\pi$
$468$	0.0305794	+	2.90276i	0.00141353	+	0.134180i
$469$	−1.68353	+	5.38090i	−0.0777380	+	0.248467i
$470$	0.0479611	−	0.0402441i	0.00221228	−	0.00185632i
$471$	32.9629	+	8.64656i	1.51885	+	0.398413i
$472$	−0.709130	−	0.595031i	−0.0326404	−	0.0273885i
$473$	−0.664266	−	0.557386i	−0.0305430	−	0.0256286i
$474$	21.6036	−	21.8324i	0.992287	−	1.00279i
$475$	−1.31850	+	1.10635i	−0.0604968	+	0.0507628i
$476$	−7.99632	−	8.68782i	−0.366511	−	0.398206i
$477$	30.9455	+	5.12101i	1.41689	+	0.234475i
$478$	−4.72129	+	8.17752i	−0.215947	+	0.374031i
$479$	19.9736	−	16.7598i	0.912617	−	0.765776i	−0.0599984	−	0.998198i	$-0.519110\pi$
$479$	19.9736	−	16.7598i	0.912617	−	0.765776i	0.972615	+	0.232422i	$0.0746651\pi$
$480$	1.36329	−	2.96424i	0.0622253	−	0.135299i
$481$	−0.304453	+	1.72664i	−0.0138819	+	0.0787280i
$482$	4.03810	−	1.46975i	0.183930	−	0.0669452i
$483$	−16.0252	+	12.4880i	−0.729172	+	0.568226i
$484$	−1.89002	−	10.7188i	−0.0859099	−	0.487219i
$485$	12.4615	+	21.5839i	0.565847	+	0.980075i
$486$	−10.7286	+	11.3091i	−0.486660	+	0.512993i
$487$	−3.43250	+	5.94527i	−0.155541	+	0.269406i	−0.933256	−	0.359212i	$-0.883046\pi$
$487$	−3.43250	+	5.94527i	−0.155541	+	0.269406i	0.777715	+	0.628618i	$0.216379\pi$
$488$	4.38118	−	3.67625i	0.198327	−	0.166416i
$489$	0.646753	−	7.86960i	0.0292472	−	0.355876i
$490$	12.7518	+	3.35648i	0.576065	+	0.151630i
$491$	−7.45052	−	6.25173i	−0.336237	−	0.282137i	0.458998	−	0.888437i	$-0.348208\pi$
$491$	−7.45052	−	6.25173i	−0.336237	−	0.282137i	−0.795236	+	0.606301i	$0.792653\pi$
$492$	−6.05816	−	8.55568i	−0.273123	−	0.385720i
$493$	−23.7754	+	19.9499i	−1.07079	+	0.898499i
$494$	1.14736			0.0516224
$495$	0.676778	+	1.80020i	0.0304189	+	0.0809129i
$496$	4.71546	−	8.16742i	0.211731	−	0.366728i
$497$	33.5159	+	4.33712i	1.50339	+	0.194546i
$498$	−1.38878	−	5.07589i	−0.0622326	−	0.227456i
$499$	24.0292	−	8.74593i	1.07570	−	0.391521i	0.257392	−	0.966307i	$-0.417137\pi$
$499$	24.0292	−	8.74593i	1.07570	−	0.391521i	0.818304	+	0.574785i	$0.194915\pi$
$500$	9.30974	+	7.81180i	0.416344	+	0.349354i
$501$	2.65157	+	9.69132i	0.118463	+	0.432976i
$502$	20.6773	+	7.52593i	0.922874	+	0.335899i
$503$	1.14213	−	1.97823i	0.0509252	−	0.0882051i	−0.839439	−	0.543454i	$-0.817116\pi$
$503$	1.14213	−	1.97823i	0.0509252	−	0.0882051i	0.890364	+	0.455249i	$0.150450\pi$
$504$	7.59970	+	2.29011i	0.338517	+	0.102010i
$505$	−8.05293	−	13.9481i	−0.358351	−	0.620682i
$506$	0.261997	+	1.48586i	0.0116472	+	0.0660544i
$507$	−12.0748	−	17.0527i	−0.536261	−	0.757338i
$508$	2.87169	−	1.04521i	0.127410	−	0.0463736i
$509$	−1.93279	−	1.62180i	−0.0856694	−	0.0718852i	0.598947	−	0.800789i	$-0.295586\pi$
$509$	−1.93279	−	1.62180i	−0.0856694	−	0.0718852i	−0.684617	+	0.728903i	$0.740030\pi$
$510$	−13.1642	+	6.22317i	−0.582918	+	0.275567i
$511$	10.6104	+	25.4566i	0.469378	+	1.12613i
$512$	−1.00000			−0.0441942
$513$	4.42496	+	4.28728i	0.195367	+	0.189288i
$514$	−8.88630	+	15.3915i	−0.391958	+	0.678891i
$515$	−16.8951	−	6.14930i	−0.744485	−	0.270970i
$516$	−0.361481	+	4.39845i	−0.0159133	+	0.193631i
$517$	0.0106290	−	0.00386862i	0.000467461	−	0.000170142i
$518$	4.25708	+	2.20415i	0.187046	+	0.0968450i
$519$	6.84397	+	9.66544i	0.300417	+	0.424266i
$520$	−0.316521	−	1.79508i	−0.0138804	−	0.0787194i
$521$	12.2666			0.537410			0.268705	−	0.963222i	$-0.413404\pi$
$521$	12.2666			0.537410			0.268705	+	0.963222i	$0.413404\pi$
$522$	6.92874	−	19.6791i	0.303263	−	0.861333i
$523$	−22.1108			−0.966836			−0.483418	−	0.875390i	$-0.660605\pi$
$523$	−22.1108			−0.966836			−0.483418	+	0.875390i	$0.660605\pi$
$524$	11.9579	−	10.0339i	0.522384	−	0.438332i
$525$	−3.53203	+	5.63674i	−0.154150	+	0.246008i
$526$	4.50756	−	25.5636i	0.196539	−	1.11463i
$527$	−39.5506	+	14.3952i	−1.72285	+	0.627066i
$528$	0.414604	−	0.418995i	0.0180433	−	0.0182344i
$529$	−0.580827	−	3.29403i	−0.0252533	−	0.143219i
$530$	−19.6952			−0.855505
$531$	−1.80740	−	2.10847i	−0.0784346	−	0.0914997i
$532$	0.936747	−	2.99404i	0.0406131	−	0.129808i
$533$	−5.50351	−	2.00312i	−0.238384	−	0.0867646i
$534$	−0.755856	+	1.64348i	−0.0327091	+	0.0711205i
$535$	15.0042	−	5.46109i	0.648689	−	0.236104i
$536$	0.370046	−	2.09863i	0.0159835	−	0.0906471i
$537$	−2.38824	+	29.0598i	−0.103060	+	1.25402i
$538$	0.829127	+	4.70221i	0.0357462	+	0.202727i
$539$	1.95744	+	1.35776i	0.0843128	+	0.0584828i
$540$	5.48686	−	8.10568i	0.236117	−	0.348813i
$541$	11.1968	+	19.3935i	0.481389	+	0.833791i	0.999772	−	0.0213582i	$-0.00679903\pi$
$541$	11.1968	+	19.3935i	0.481389	+	0.833791i	−0.518383	+	0.855149i	$0.673466\pi$
$542$	15.5713	+	5.66750i	0.668846	+	0.243440i
$543$	2.96405	−	36.0662i	0.127200	−	1.54775i
$544$	3.41874	+	2.86867i	0.146577	+	0.122993i
$545$	18.5282	+	15.5470i	0.793662	+	0.665962i
$546$	4.21896	−	1.36500i	0.180555	−	0.0584166i
$547$	−15.8728	−	5.77722i	−0.678671	−	0.247016i	−0.0203944	−	0.999792i	$-0.506492\pi$
$547$	−15.8728	−	5.77722i	−0.678671	−	0.247016i	−0.658277	+	0.752776i	$0.728714\pi$
$548$	−7.35523	+	12.7396i	−0.314200	+	0.544210i
$549$	14.7678	−	8.73489i	0.630274	−	0.372796i
$550$	0.246999	+	0.427815i	0.0105321	+	0.0182421i
$551$	−7.74880	−	2.82033i	−0.330110	−	0.120150i
$552$	5.40113	−	5.45832i	0.229887	−	0.232322i
$553$	−41.6636	−	21.5718i	−1.77172	−	0.917325i
$554$	−1.68368	+	9.54864i	−0.0715329	+	0.405683i
$555$	4.15815	−	4.20219i	0.176504	−	0.178373i
$556$	1.70916	+	9.69313i	0.0724846	+	0.411080i
$557$	−4.01274	−	6.95026i	−0.170025	−	0.294492i	0.768403	−	0.639966i	$-0.221052\pi$
$557$	−4.01274	−	6.95026i	−0.170025	−	0.294492i	−0.938428	+	0.345474i	$0.887718\pi$
$558$	17.9569	−	21.8639i	0.760178	−	0.925573i
$559$	1.23278	+	2.13523i	0.0521409	+	0.0903107i
$560$	−4.94266	−	0.639604i	−0.208866	−	0.0270282i
$561$	−2.61938	+	0.243075i	−0.110590	+	0.0102626i
$562$	1.27951	−	7.25649i	0.0539731	−	0.306096i
$563$	3.49907	−	19.8442i	0.147468	−	0.836335i	−0.817884	−	0.575384i	$-0.804853\pi$
$563$	3.49907	−	19.8442i	0.147468	−	0.836335i	0.965352	−	0.260951i	$-0.0840362\pi$
$564$	−0.0473298	−	0.0327705i	−0.00199295	−	0.00137989i
$565$	−12.9493	+	10.8658i	−0.544781	+	0.457126i
$566$	−10.1072			−0.424837
$567$	21.3715	+	10.5004i	0.897518	+	0.440977i
$568$	−12.7734			−0.535962
$569$	31.2393	−	26.2129i	1.30962	−	1.09890i	0.321225	−	0.947003i	$-0.395905\pi$
$569$	31.2393	−	26.2129i	1.30962	−	1.09890i	0.988396	−	0.151899i	$-0.0485390\pi$
$570$	−3.18071	−	2.20228i	−0.133225	−	0.0922433i
$571$	0.837116	−	4.74752i	0.0350322	−	0.198678i	−0.962269	−	0.272101i	$-0.912281\pi$
$571$	0.837116	−	4.74752i	0.0350322	−	0.198678i	0.997301	+	0.0734237i	$0.0233925\pi$
$572$	0.0571836	−	0.324305i	0.00239097	−	0.0135599i
$573$	22.3166	−	2.07094i	0.932287	−	0.0865149i
$574$	−9.72037	+	12.7260i	−0.405720	+	0.531172i
$575$	3.21770	+	5.57322i	0.134187	+	0.232419i
$576$	−2.95975	−	0.489794i	−0.123323	−	0.0204081i
$577$	9.87783	+	17.1089i	0.411220	+	0.712253i	0.995023	−	0.0996416i	$-0.0317696\pi$
$577$	9.87783	+	17.1089i	0.411220	+	0.712253i	−0.583804	+	0.811895i	$0.698436\pi$
$578$	−0.506538	−	2.87272i	−0.0210692	−	0.119490i
$579$	−8.51394	+	8.60410i	−0.353827	+	0.357574i
$580$	−2.27483	+	12.9012i	−0.0944573	+	0.535694i
$581$	−6.77006	+	4.33407i	−0.280869	+	0.179808i
$582$	16.1186	−	16.2893i	0.668138	−	0.675213i
$583$	−3.34361	−	1.21697i	−0.138478	−	0.0504019i
$584$	−5.21200	−	9.02746i	−0.215674	−	0.373559i
$585$	−0.0576033	−	5.46801i	−0.00238160	−	0.226074i
$586$	1.08131	−	1.87288i	0.0446685	−	0.0773680i
$587$	20.4162	+	7.43090i	0.842669	+	0.306706i	0.727048	−	0.686587i	$-0.240892\pi$
$587$	20.4162	+	7.43090i	0.842669	+	0.306706i	0.115621	+	0.993293i	$0.463114\pi$
$588$	−0.117451	−	12.1238i	−0.00484358	−	0.499977i
$589$	−8.56635	−	7.18802i	−0.352970	−	0.296177i
$590$	1.33581	+	1.12088i	0.0549943	+	0.0461457i
$591$	2.34381	−	28.5192i	0.0964116	−	1.17312i
$592$	−1.70264	−	0.619709i	−0.0699779	−	0.0254699i
$593$	−12.8927	−	22.3308i	−0.529439	−	0.917016i	−0.999410	−	0.0343341i	$-0.989069\pi$
$593$	−12.8927	−	22.3308i	−0.529439	−	0.917016i	0.469971	−	0.882682i	$-0.344264\pi$
$594$	1.43234	−	1.03705i	0.0587698	−	0.0425506i
$595$	15.0629	+	16.3655i	0.617518	+	0.670920i
$596$	3.45919	+	19.6180i	0.141694	+	0.803586i
$597$	−1.90247	+	23.1490i	−0.0778627	+	0.947424i
$598$	0.744942	−	4.22478i	0.0304629	−	0.172764i
$599$	9.28410	−	3.37914i	0.379338	−	0.138068i	−0.145312	−	0.989386i	$-0.546418\pi$
$599$	9.28410	−	3.37914i	0.379338	−	0.138068i	0.524650	+	0.851318i	$0.324196\pi$
$600$	1.05053	−	2.28420i	0.0428876	−	0.0932519i
$601$	18.6462	+	6.78666i	0.760594	+	0.276834i	0.693057	−	0.720883i	$-0.256264\pi$
$601$	18.6462	+	6.78666i	0.760594	+	0.276834i	0.0675376	+	0.997717i	$0.478486\pi$
$602$	6.57836	−	1.47365i	0.268114	−	0.0600614i
$603$	2.12314	−	6.03018i	0.0864609	−	0.245568i
$604$	14.7359			0.599597
$605$	3.56028	+	20.1914i	0.144746	+	0.820895i
$606$	−10.4163	+	10.5266i	−0.423132	+	0.427613i
$607$	31.1650	−	11.3431i	1.26495	−	0.460404i	0.379523	−	0.925182i	$-0.376088\pi$
$607$	31.1650	−	11.3431i	1.26495	−	0.460404i	0.885427	+	0.464778i	$0.153866\pi$
$608$	−0.205901	+	1.16772i	−0.00835037	+	0.0473573i
$609$	−31.8483	−	1.15201i	−1.29056	−	0.0466819i
$610$	−8.25295	+	6.92505i	−0.334152	+	0.280387i
$611$	−0.0321611			−0.00130110
$612$	8.71356	+	10.1650i	0.352225	+	0.410896i
$613$	−10.7100			−0.432571			−0.216285	−	0.976330i	$-0.569394\pi$
$613$	−10.7100			−0.432571			−0.216285	+	0.976330i	$0.569394\pi$
$614$	0.968105	+	5.49040i	0.0390696	+	0.221574i
$615$	11.4119	+	16.1166i	0.460173	+	0.649883i
$616$	−0.799584	−	0.413993i	−0.0322161	−	0.0166803i
$617$	32.8209	−	11.9458i	1.32132	−	0.480920i	0.417437	−	0.908706i	$-0.362928\pi$
$617$	32.8209	−	11.9458i	1.32132	−	0.480920i	0.903880	+	0.427785i	$0.140706\pi$
$618$	−1.35407	+	16.4761i	−0.0544685	+	0.662766i
$619$	−31.1852	−	11.3505i	−1.25344	−	0.456214i	−0.371876	−	0.928283i	$-0.621285\pi$
$619$	−31.1852	−	11.3505i	−1.25344	−	0.456214i	−0.881562	+	0.472069i	$0.843507\pi$
$620$	−8.88265	+	15.3852i	−0.356736	+	0.617885i
$621$	18.6594	−	13.5098i	0.748777	−	0.542130i
$622$	−17.6530			−0.707820
$623$	2.74039	+	0.354620i	0.109792	+	0.0142075i
$624$	−1.51522	+	0.716300i	−0.0606574	+	0.0286749i
$625$	−11.9772	−	10.0501i	−0.479087	−	0.402002i
$626$	16.3632	−	5.95572i	0.654005	−	0.238038i
$627$	−0.403902	−	0.570413i	−0.0161303	−	0.0227801i
$628$	3.41653	+	19.3761i	0.136334	+	0.773190i
$629$	4.04314	+	7.00292i	0.161210	+	0.279225i
$630$	−14.3158	−	4.31395i	−0.570354	−	0.171872i
$631$	−19.9253	+	34.5117i	−0.793214	+	1.37389i	0.130753	+	0.991415i	$0.458261\pi$
$631$	−19.9253	+	34.5117i	−0.793214	+	1.37389i	−0.923967	+	0.382472i	$0.875073\pi$
$632$	16.6635	+	6.06502i	0.662838	+	0.241253i
$633$	−5.07955	−	18.5654i	−0.201894	−	0.737909i
$634$	0.189499	+	0.159009i	0.00752598	+	0.00631505i
$635$	−5.40948	+	1.96889i	−0.214668	+	0.0781329i
$636$	4.77911	+	17.4674i	0.189504	+	0.692626i
$637$	−3.90960	−	5.53128i	−0.154904	−	0.219157i
$638$	−1.18337	+	2.04965i	−0.0468499	+	0.0811464i
$639$	−37.8062	−	6.25635i	−1.49559	−	0.247497i
$640$	1.88373			0.0744609
$641$	28.3721	−	23.8071i	1.12063	−	0.940322i	0.121996	−	0.992531i	$-0.461071\pi$
$641$	28.3721	−	23.8071i	1.12063	−	0.940322i	0.998636	+	0.0522086i	$0.0166261\pi$
$642$	−8.48419	−	11.9819i	−0.334844	−	0.472886i
$643$	18.1285	+	15.2116i	0.714919	+	0.599888i	0.925975	−	0.377586i	$-0.123246\pi$
$643$	18.1285	+	15.2116i	0.714919	+	0.599888i	−0.211056	+	0.977474i	$0.567690\pi$
$644$	−10.4163	−	5.39317i	−0.410461	−	0.212521i
$645$	0.680931	−	8.28548i	0.0268116	−	0.326241i
$646$	4.05372	−	3.40147i	0.159491	−	0.133829i
$647$	−13.5369	+	23.4465i	−0.532189	+	0.921778i	0.467105	+	0.884202i	$0.345297\pi$
$647$	−13.5369	+	23.4465i	−0.532189	+	0.921778i	−0.999294	+	0.0375761i	$0.988036\pi$
$648$	−8.52020	−	2.89933i	−0.334705	−	0.113896i
$649$	0.157518	+	0.272829i	0.00618311	+	0.0107095i
$650$	−0.243906	−	1.38326i	−0.00956676	−	0.0542558i
$651$	−40.0507	−	16.2398i	−1.56971	−	0.636487i
$652$	4.28390	−	1.55921i	0.167771	−	0.0610635i
$653$	−6.09881	+	34.5880i	−0.238665	+	1.35353i	0.596092	+	0.802916i	$0.296719\pi$
$653$	−6.09881	+	34.5880i	−0.238665	+	1.35353i	−0.834757	+	0.550619i	$0.814392\pi$
$654$	9.29247	−	20.2049i	0.363364	−	0.790076i
$655$	−22.5255	+	18.9011i	−0.880143	+	0.738528i
$656$	3.02629	−	5.24169i	0.118157	−	0.204653i
$657$	−11.0046	−	29.2718i	−0.429331	−	1.14200i
$658$	−0.0262574	+	0.0839242i	−0.00102362	+	0.00327170i
$659$	2.10686	−	1.76786i	0.0820715	−	0.0688661i	−0.600829	−	0.799378i	$-0.705163\pi$
$659$	2.10686	−	1.76786i	0.0820715	−	0.0688661i	0.682900	+	0.730511i	$0.260718\pi$
$660$	−0.781002	+	0.789272i	−0.0304004	+	0.0307224i
$661$	30.5605	+	25.6433i	1.18867	+	0.997409i	0.999882	+	0.0153906i	$0.00489917\pi$
$661$	30.5605	+	25.6433i	1.18867	+	0.997409i	0.188784	+	0.982019i	$0.439545\pi$
$662$	6.32432	+	5.30674i	0.245802	+	0.206252i
$663$	7.23498	+	1.89782i	0.280983	+	0.0737052i
$664$	2.32746	−	1.95297i	0.0903228	−	0.0757898i
$665$	−1.76458	+	5.63995i	−0.0684273	+	0.218708i
$666$	−4.73584	−	2.66812i	−0.183510	−	0.103388i
$667$	−15.4159	+	26.7012i	−0.596907	+	1.03387i
$668$	−4.44377	+	3.72877i	−0.171935	+	0.144270i
$669$	−20.6156	−	29.1146i	−0.797046	−	1.12563i
$670$	−0.697065	+	3.95325i	−0.0269300	+	0.152727i
$671$	−1.82899	+	0.665697i	−0.0706073	+	0.0256989i
$672$	0.632101	+	4.53877i	0.0243838	+	0.175087i
$673$	−5.25751	−	29.8168i	−0.202662	−	1.14936i	−0.901076	−	0.433661i	$-0.857222\pi$
$673$	−5.25751	−	29.8168i	−0.202662	−	1.14936i	0.698414	−	0.715694i	$-0.253890\pi$
$674$	13.6692	+	23.6758i	0.526519	+	0.911957i
$675$	4.22808	−	6.24610i	0.162739	−	0.240412i
$676$	6.03184	−	10.4474i	0.231994	−	0.401825i
$677$	18.3087	−	15.3628i	0.703659	−	0.590440i	−0.219153	−	0.975691i	$-0.570329\pi$
$677$	18.3087	−	15.3628i	0.703659	−	0.590440i	0.922812	+	0.385250i	$0.125885\pi$
$678$	12.7789	+	8.84792i	0.490769	+	0.339802i
$679$	−31.0855	−	16.0949i	−1.19295	−	0.617664i
$680$	−6.43998	−	5.40379i	−0.246962	−	0.207226i
$681$	−15.8793	+	34.5269i	−0.608497	+	1.32307i
$682$	−2.45865	+	2.06305i	−0.0941464	+	0.0789982i
$683$	−37.4203			−1.43185			−0.715924	−	0.698178i	$-0.753994\pi$
$683$	−37.4203			−1.43185			−0.715924	+	0.698178i	$0.753994\pi$
$684$	−1.18136	+	3.35531i	−0.0451703	+	0.128293i
$685$	13.8552	−	23.9980i	0.529382	−	0.916916i
$686$	−17.6258	+	5.68614i	−0.672955	+	0.217098i
$687$	−35.8192	−	9.39579i	−1.36659	−	0.358472i
$688$	−2.39434	+	0.871470i	−0.0912835	+	0.0332245i
$689$	7.75015	+	6.50315i	0.295257	+	0.247750i
$690$	−10.1743	+	10.2820i	−0.387327	+	0.391429i
$691$	21.2732	+	7.74282i	0.809271	+	0.294551i	0.713323	−	0.700836i	$-0.247189\pi$
$691$	21.2732	+	7.74282i	0.809271	+	0.294551i	0.0959484	+	0.995386i	$0.469412\pi$
$692$	−3.41883	+	5.92159i	−0.129964	+	0.225105i
$693$	−2.16379	−	1.61695i	−0.0821957	−	0.0614227i
$694$	5.07241	+	8.78567i	0.192546	+	0.333500i
$695$	−3.21959	−	18.2592i	−0.122126	−	0.692612i
$696$	11.9939	−	1.11302i	0.454627	−	0.0421887i
$697$	−25.3827	+	9.23856i	−0.961440	+	0.349935i
$698$	21.3364	+	17.9034i	0.807596	+	0.677654i
$699$	−26.8509	−	18.5912i	−1.01560	−	0.703185i
$700$	−3.80873	−	0.492868i	−0.143957	−	0.0186287i
$701$	−6.12643			−0.231392			−0.115696	−	0.993285i	$-0.536910\pi$
$701$	−6.12643			−0.231392			−0.115696	+	0.993285i	$0.536910\pi$
$702$	−4.83551	+	1.37792i	−0.182505	+	0.0520062i
$703$	−1.07422	+	1.86060i	−0.0405150	+	0.0701740i
$704$	0.319796	+	0.116396i	0.0120528	+	0.00438685i
$705$	0.0891565	+	0.0617308i	0.00335783	+	0.00232492i
$706$	−30.0603	+	10.9411i	−1.13134	+	0.411773i
$707$	20.0883	+	10.4009i	0.755496	+	0.391167i
$708$	0.669948	−	1.45669i	0.0251782	−	0.0547458i
$709$	−8.83938	−	50.1306i	−0.331970	−	1.88270i	−0.455313	−	0.890331i	$-0.650473\pi$
$709$	−8.83938	−	50.1306i	−0.331970	−	1.88270i	0.123343	−	0.992364i	$-0.460638\pi$
$710$	24.0617			0.903019
$711$	46.3491	+	26.1126i	1.73823	+	0.979298i
$712$	−1.04441			−0.0391408
$713$	−32.0292	+	26.8757i	−1.19950	+	1.00650i
$714$	10.8592	−	17.3302i	0.406396	−	0.648566i
$715$	−0.107718	+	0.610902i	−0.00402844	+	0.0228464i
$716$	−15.8190	+	5.75765i	−0.591185	+	0.215174i
$717$	−15.8198	−	4.14973i	−0.590802	−	0.154974i
$718$	−3.25080	−	18.4362i	−0.121319	−	0.688033i
$719$	24.7161			0.921753			0.460877	−	0.887464i	$-0.347535\pi$
$719$	24.7161			0.921753			0.460877	+	0.887464i	$0.347535\pi$
$720$	5.57536	+	0.922638i	0.207781	+	0.0343847i
$721$	24.6418	−	5.52012i	0.917708	−	0.205580i
$722$	−16.5330	−	6.01751i	−0.615294	−	0.223949i
$723$	4.30122	+	6.07443i	0.159964	+	0.225910i
$724$	19.6330	−	7.14584i	0.729656	−	0.265573i
$725$	−1.75295	+	9.94146i	−0.0651028	+	0.369217i
$726$	17.0435	−	8.05706i	0.632543	−	0.299026i
$727$	6.12263	+	34.7231i	0.227076	+	1.28781i	0.858677	+	0.512517i	$0.171287\pi$
$727$	6.12263	+	34.7231i	0.227076	+	1.28781i	−0.631601	+	0.775293i	$0.717602\pi$
$728$	1.73377	+	1.88370i	0.0642578	+	0.0698147i
$729$	−23.7976	−	12.7544i	−0.881392	−	0.472386i
$730$	9.81800	+	17.0053i	0.363380	+	0.629393i
$731$	10.6856	+	3.88924i	0.395221	+	0.143849i
$732$	8.14432	+	5.63902i	0.301023	+	0.208424i
$733$	−13.0528	−	10.9526i	−0.482115	−	0.404542i	0.369076	−	0.929399i	$-0.379674\pi$
$733$	−13.0528	−	10.9526i	−0.482115	−	0.404542i	−0.851190	+	0.524857i	$0.824119\pi$
$734$	−5.42028	−	4.54815i	−0.200066	−	0.167875i
$735$	0.221245	+	22.8379i	0.00816074	+	0.842389i
$736$	4.16605	+	1.51632i	0.153562	+	0.0558922i
$737$	−0.362612	+	0.628063i	−0.0133570	+	0.0231350i
$738$	11.5244	−	14.0318i	0.424219	−	0.516518i
$739$	8.15673	+	14.1279i	0.300050	+	0.519702i	0.976147	−	0.217111i	$-0.0696633\pi$
$739$	8.15673	+	14.1279i	0.300050	+	0.519702i	−0.676097	+	0.736813i	$0.736330\pi$
$740$	3.20730	+	1.16736i	0.117903	+	0.0429131i
$741$	0.524453	+	1.91684i	0.0192663	+	0.0704170i
$742$	23.2974	−	14.9146i	0.855275	−	0.547531i
$743$	−1.99428	+	11.3101i	−0.0731630	+	0.414928i	0.926126	+	0.377215i	$0.123118\pi$
$743$	−1.99428	+	11.3101i	−0.0731630	+	0.414928i	−0.999289	+	0.0377126i	$0.987993\pi$
$744$	15.8003	+	4.14461i	0.579267	+	0.151949i
$745$	−6.51617	−	36.9550i	−0.238734	−	1.35393i
$746$	−5.61633	−	9.72777i	−0.205628	−	0.356159i
$747$	7.84523	−	4.64031i	0.287042	−	0.169780i
$748$	−0.759399	−	1.31532i	−0.0277664	−	0.0480928i
$749$	−13.6129	+	17.8222i	−0.497406	+	0.651207i
$750$	−8.79535	+	19.1240i	−0.321161	+	0.698311i
$751$	7.36838	−	41.7881i	0.268876	−	1.52487i	−0.488891	−	0.872345i	$-0.662598\pi$
$751$	7.36838	−	41.7881i	0.268876	−	1.52487i	0.757766	−	0.652526i	$-0.226291\pi$
$752$	0.00577148	−	0.0327317i	0.000210464	−	0.00119360i
$753$	−3.12171	+	37.9846i	−0.113762	+	1.38424i
$754$	5.15500	−	4.32556i	0.187734	−	0.157528i
$755$	−27.7585			−1.01024
$756$	−0.352203	+	13.7432i	−0.0128095	+	0.499836i
$757$	10.4060			0.378211			0.189106	−	0.981957i	$-0.439441\pi$
$757$	10.4060			0.378211			0.189106	+	0.981957i	$0.439441\pi$
$758$	22.7947	−	19.1271i	0.827942	−	0.694726i
$759$	−2.36259	+	1.11688i	−0.0857565	+	0.0405402i
$760$	0.387861	−	2.19967i	0.0140692	−	0.0797903i
$761$	0.215947	−	1.22470i	0.00782808	−	0.0443952i	−0.980644	−	0.195802i	$-0.937269\pi$
$761$	0.215947	−	1.22470i	0.00782808	−	0.0443952i	0.988472	+	0.151406i	$0.0483802\pi$
$762$	3.05880	+	4.31982i	0.110809	+	0.156491i
$763$	−33.6903	−	4.35968i	−1.21967	−	0.157831i
$764$	6.46991	+	11.2062i	0.234073	+	0.405427i
$765$	−16.4140	−	19.1481i	−0.593448	−	0.692301i
$766$	14.6579	+	25.3883i	0.529613	+	0.917317i
$767$	−0.155545	−	0.882140i	−0.00561640	−	0.0318522i
$768$	−0.457094	−	1.67065i	−0.0164939	−	0.0602843i
$769$	2.23762	−	12.6902i	0.0806907	−	0.457620i	−0.917513	−	0.397706i	$-0.869806\pi$
$769$	2.23762	−	12.6902i	0.0806907	−	0.457620i	0.998204	−	0.0599137i	$-0.0190826\pi$
$770$	1.50620	+	0.779851i	0.0542796	+	0.0281039i
$771$	−29.7757	−	7.81051i	−1.07235	−	0.281289i
$772$	−6.56705	−	2.39021i	−0.236353	−	0.0860255i
$773$	3.76119	+	6.51458i	0.135281	+	0.234313i	0.925705	−	0.378247i	$-0.123473\pi$
$773$	3.76119	+	6.51458i	0.135281	+	0.234313i	−0.790424	+	0.612560i	$0.790140\pi$
$774$	−7.51349	+	1.40660i	−0.270067	+	0.0505590i
$775$	−6.84482	+	11.8556i	−0.245873	+	0.425865i
$776$	12.4328	+	4.52515i	0.446310	+	0.162443i
$777$	−1.73648	+	8.11960i	−0.0622959	+	0.291289i
$778$	−16.0231	−	13.4450i	−0.574456	−	0.482026i
$779$	−5.49771	−	4.61312i	−0.196976	−	0.165282i
$780$	2.85427	−	1.34931i	0.102199	−	0.0483132i
$781$	4.08490	+	1.48678i	0.146169	+	0.0532012i
$782$	−9.89283	−	17.1349i	−0.353767	−	0.612742i
$783$	36.0440	+	2.58028i	1.28811	+	0.0922118i
$784$	6.33102	−	2.98634i	0.226108	−	0.106655i
$785$	−6.43581	−	36.4993i	−0.229704	−	1.30272i
$786$	22.2290	+	15.3911i	0.792882	+	0.548981i
$787$	8.24437	−	46.7561i	0.293880	−	1.66668i	−0.377840	−	0.925871i	$-0.623333\pi$
$787$	8.24437	−	46.7561i	0.293880	−	1.66668i	0.671720	−	0.740805i	$-0.265556\pi$
$788$	15.5248	−	5.65055i	0.553047	−	0.201292i
$789$	44.7682	−	4.15443i	1.59379	−	0.147902i
$790$	−31.3895	−	11.4248i	−1.11679	−	0.406478i
$791$	7.08939	−	22.6592i	0.252070	−	0.805668i
$792$	0.889506	+	0.501138i	0.0316072	+	0.0178072i
$793$	5.53415			0.196524
$794$	6.21270	+	35.2340i	0.220481	+	1.25041i
$795$	−9.00255	−	32.9038i	−0.319288	−	1.16698i
$796$	−12.6014	+	4.58653i	−0.446644	+	0.162565i
$797$	5.95165	−	33.7535i	0.210818	−	1.19561i	−0.677199	−	0.735799i	$-0.736807\pi$
$797$	5.95165	−	33.7535i	0.210818	−	1.19561i	0.888018	−	0.459810i	$-0.152082\pi$
$798$	5.43017	+	0.196419i	0.192226	+	0.00695315i
$799$	−0.113627	+	0.0953448i	−0.00401985	+	0.00337306i
$800$	1.45157			0.0513207
$801$	−3.09118	−	0.511544i	−0.109222	−	0.0180745i
$802$	24.3228			0.858867
$803$	0.616017	+	3.49361i	0.0217388	+	0.123287i
$804$	3.67522	−	0.341055i	0.129615	−	0.0120281i
$805$	19.6215	+	10.1593i	0.691568	+	0.358067i
$806$	8.57540	−	3.12119i	0.302056	−	0.109939i
$807$	−7.47675	+	3.53453i	−0.263194	+	0.124421i
$808$	−8.03437	−	2.92427i	−0.282648	−	0.102875i
$809$	19.3960	−	33.5948i	0.681927	−	1.18113i	−0.292466	−	0.956276i	$-0.594476\pi$
$809$	19.3960	−	33.5948i	0.681927	−	1.18113i	0.974392	−	0.224855i	$-0.0721910\pi$
$810$	16.0497	+	5.46155i	0.563931	+	0.191899i
$811$	−27.9334			−0.980875			−0.490437	−	0.871476i	$-0.663163\pi$
$811$	−27.9334			−0.980875			−0.490437	+	0.871476i	$0.663163\pi$
$812$	−7.07880	−	16.9835i	−0.248417	−	0.596003i
$813$	−2.35085	+	28.6048i	−0.0824478	+	1.00321i
$814$	0.472365	+	0.396361i	0.0165564	+	0.0138925i
$815$	−8.06971	+	2.93713i	−0.282670	+	0.102883i
$816$	−3.22985	+	7.02276i	−0.113067	+	0.245846i
$817$	0.524636	+	2.97536i	0.0183547	+	0.104095i
$818$	−8.83990	−	15.3112i	−0.309080	−	0.535342i
$819$	4.20889	+	6.42447i	0.147071	+	0.224489i
$820$	−5.70070	+	9.87391i	−0.199077	+	0.344812i
$821$	−15.6934	−	5.71193i	−0.547703	−	0.199348i	0.0533226	−	0.998577i	$-0.483019\pi$
$821$	−15.6934	−	5.71193i	−0.547703	−	0.199348i	−0.601026	+	0.799230i	$0.705241\pi$
$822$	−24.6455	−	6.46480i	−0.859609	−	0.225486i
$823$	−17.9111	−	15.0292i	−0.624342	−	0.523885i	0.274823	−	0.961495i	$-0.411381\pi$
$823$	−17.9111	−	15.0292i	−0.624342	−	0.523885i	−0.899165	+	0.437610i	$0.855825\pi$
$824$	−8.96895	+	3.26443i	−0.312448	+	0.113722i
$825$	−0.601826	+	0.608200i	−0.0209529	+	0.0211748i
$826$	−2.42893	−	0.314315i	−0.0845132	−	0.0109364i
$827$	−4.30436	+	7.45537i	−0.149677	+	0.259249i	−0.931108	−	0.364743i	$-0.881157\pi$
$827$	−4.30436	+	7.45537i	−0.149677	+	0.259249i	0.781431	+	0.623992i	$0.214490\pi$
$828$	11.5878	+	6.52842i	0.402702	+	0.226878i
$829$	18.6097			0.646340			0.323170	−	0.946341i	$-0.395251\pi$
$829$	18.6097			0.646340			0.323170	+	0.946341i	$0.395251\pi$
$830$	−4.38429	+	3.67886i	−0.152181	+	0.127695i
$831$	−16.7220	+	1.55178i	−0.580081	+	0.0538307i
$832$	−0.741256	−	0.621987i	−0.0256984	−	0.0215635i
$833$	−30.2109	−	7.95204i	−1.04675	−	0.275522i
$834$	−15.4126	+	7.28608i	−0.533694	+	0.252296i
$835$	8.37086	−	7.02399i	0.289686	−	0.243075i
$836$	0.201765	−	0.349467i	0.00697818	−	0.0120866i
$837$	44.7349	+	20.0059i	1.54626	+	0.691504i
$838$	16.5760	+	28.7105i	0.572610	+	0.991789i
$839$	1.13909	+	6.46010i	0.0393258	+	0.223028i	0.998137	−	0.0610176i	$-0.0194346\pi$
$839$	1.13909	+	6.46010i	0.0393258	+	0.223028i	−0.958811	+	0.284045i	$0.908323\pi$
$840$	−1.19071	−	8.54981i	−0.0410833	−	0.294997i
$841$	−18.1962	+	6.62288i	−0.627456	+	0.228375i
$842$	−2.22228	+	12.6032i	−0.0765847	+	0.434333i
$843$	12.7079	−	1.17927i	0.437683	−	0.0406164i
$844$	8.51283	−	7.14311i	0.293024	−	0.245876i
$845$	−11.3623	+	19.6801i	−0.390876	+	0.677018i
$846$	0.0331139	−	0.0940507i	0.00113848	−	0.00323353i
$847$	−19.5017	−	21.1882i	−0.670088	−	0.728035i
$848$	−8.00933	+	6.72063i	−0.275042	+	0.230787i
$849$	−4.61993	−	16.8855i	−0.158556	−	0.579511i
$850$	−4.96254	−	4.16406i	−0.170214	−	0.142826i
$851$	6.15359	+	5.16347i	0.210942	+	0.177002i
$852$	−5.83866	−	21.3399i	−0.200029	−	0.731094i
$853$	23.7456	−	19.9249i	0.813034	−	0.682216i	−0.138296	−	0.990391i	$-0.544163\pi$
$853$	23.7456	−	19.9249i	0.813034	−	0.682216i	0.951330	+	0.308175i	$0.0997181\pi$
$854$	4.51827	−	14.4413i	0.154612	−	0.494172i
$855$	2.22535	−	6.32049i	0.0761055	−	0.216156i
$856$	4.23818	−	7.34075i	0.144858	−	0.250902i
$857$	16.3673	−	13.7338i	0.559096	−	0.469137i	−0.318911	−	0.947785i	$-0.603317\pi$
$857$	16.3673	−	13.7338i	0.559096	−	0.469137i	0.878007	+	0.478647i	$0.158873\pi$
$858$	0.567937	−	0.0527038i	0.0193891	−	0.00179928i
$859$	−0.427338	+	2.42355i	−0.0145806	+	0.0826905i	−0.991230	−	0.132150i	$-0.957812\pi$
$859$	−0.427338	+	2.42355i	−0.0145806	+	0.0826905i	0.976649	+	0.214840i	$0.0689231\pi$
$860$	4.51029	−	1.64161i	0.153800	−	0.0559785i
$861$	−25.7037	−	10.4224i	−0.875981	−	0.355193i
$862$	2.75480	+	15.6232i	0.0938287	+	0.532129i
$863$	21.1354	+	36.6076i	0.719459	+	1.24614i	0.961215	+	0.275802i	$0.0889433\pi$
$863$	21.1354	+	36.6076i	0.719459	+	1.24614i	−0.241756	+	0.970337i	$0.577723\pi$
$864$	−0.534608	−	5.16858i	−0.0181877	−	0.175839i
$865$	6.44014	−	11.1547i	0.218971	−	0.379270i
$866$	9.84457	−	8.26058i	0.334532	−	0.280706i
$867$	4.56777	−	2.15935i	0.155130	−	0.0733354i
$868$	−1.14348	−	24.9257i	−0.0388121	−	0.846033i
$869$	−4.62298	−	3.87914i	−0.156824	−	0.131591i
$870$	−22.5932	+	2.09662i	−0.765982	+	0.0710820i
$871$	1.57962	−	1.32546i	0.0535234	−	0.0449115i
$872$	12.8399			0.434814
$873$	34.5814	+	19.4828i	1.17040	+	0.659392i
$874$	2.62842	−	4.55257i	0.0889078	−	0.153993i
$875$	31.8879	+	4.12645i	1.07801	+	0.139499i
$876$	12.6993	−	12.8338i	0.429071	−	0.433615i
$877$	8.19870	−	2.98408i	0.276850	−	0.100765i	−0.199864	−	0.979824i	$-0.564050\pi$
$877$	8.19870	−	2.98408i	0.276850	−	0.100765i	0.476714	+	0.879058i	$0.341828\pi$
$878$	−3.80193	−	3.19020i	−0.128309	−	0.107664i
$879$	3.62319	+	0.950405i	0.122207	+	0.0320564i
$880$	−0.602409	−	0.219259i	−0.0203072	−	0.00739122i
$881$	−13.4444	+	23.2864i	−0.452954	+	0.784539i	−0.998568	−	0.0534974i	$-0.982963\pi$
$881$	−13.4444	+	23.2864i	−0.452954	+	0.784539i	0.545614	+	0.838037i	$0.316296\pi$
$882$	20.2009	−	5.73792i	0.680200	−	0.193206i
$883$	−9.70390	−	16.8077i	−0.326562	−	0.565622i	0.655265	−	0.755399i	$-0.272557\pi$
$883$	−9.70390	−	16.8077i	−0.326562	−	0.565622i	−0.981827	+	0.189777i	$0.939224\pi$
$884$	0.749888	+	4.25283i	0.0252215	+	0.143038i
$885$	−1.26200	+	2.74401i	−0.0424217	+	0.0922389i
$886$	5.65634	−	2.05874i	0.190029	−	0.0691647i
$887$	−27.2597	−	22.8736i	−0.915293	−	0.768022i	0.0578259	−	0.998327i	$-0.481583\pi$
$887$	−27.2597	−	22.8736i	−0.915293	−	0.768022i	−0.973119	+	0.230305i	$0.926028\pi$
$888$	0.257052	−	3.12777i	0.00862609	−	0.104961i
$889$	4.90788	−	6.42542i	0.164605	−	0.215502i
$890$	1.96738			0.0659467
$891$	2.38726	+	1.91892i	0.0799762	+	0.0642861i
$892$	10.2983	−	17.8372i	0.344813	−	0.597233i
$893$	−0.0370331	−	0.0134790i	−0.00123927	−	0.000451056i
$894$	−31.1937	+	14.7464i	−1.04327	+	0.493192i
$895$	29.7987	−	10.8459i	0.996062	−	0.362537i
$896$	−2.22826	+	1.42649i	−0.0744408	+	0.0476557i
$897$	7.39862	−	0.686582i	0.247033	−	0.0229243i
$898$	−0.208294	−	1.18130i	−0.00695087	−	0.0394203i
$899$	−65.5867			−2.18744
$900$	4.29628	+	0.710969i	0.143209	+	0.0236990i
$901$	46.6611			1.55451
$902$	−1.57791	+	1.32402i	−0.0525386	+	0.0440851i
$903$	5.46887	+	10.3165i	0.181993	+	0.343312i
$904$	−1.55828	+	8.83743i	−0.0518275	+	0.293928i
$905$	−36.9833	+	13.4608i	−1.22937	+	0.447453i
$906$	6.73571	+	24.6186i	0.223779	+	0.817898i
$907$	8.62095	+	48.8918i	0.286254	+	1.62343i	0.700772	+	0.713386i	$0.252839\pi$
$907$	8.62095	+	48.8918i	0.286254	+	1.62343i	−0.414518	+	0.910041i	$0.636050\pi$
$908$	−21.9413			−0.728147
$909$	−22.3474	−	12.5903i	−0.741217	−	0.417593i
$910$	−3.26595	−	3.54838i	−0.108265	−	0.117628i
$911$	4.93752	+	1.79711i	0.163587	+	0.0595410i	0.422516	−	0.906356i	$-0.361147\pi$
$911$	4.93752	+	1.79711i	0.163587	+	0.0595410i	−0.258928	+	0.965897i	$0.583369\pi$
$912$	−2.04497	+	0.189770i	−0.0677156	+	0.00628391i
$913$	−0.971630	+	0.353644i	−0.0321563	+	0.0117039i
$914$	3.98151	−	22.5802i	0.131697	−	0.746888i
$915$	−15.3417	−	10.6224i	−0.507181	−	0.351165i
$916$	−3.71257	−	21.0550i	−0.122667	−	0.695678i
$917$	12.3321	−	39.4159i	0.407241	−	1.30163i
$918$	−12.9992	+	19.2036i	−0.429039	+	0.633815i
$919$	9.29344	+	16.0967i	0.306562	+	0.530982i	0.977608	−	0.210434i	$-0.0674879\pi$
$919$	9.29344	+	16.0967i	0.306562	+	0.530982i	−0.671046	+	0.741416i	$0.734155\pi$
$920$	−7.84770	−	2.85633i	−0.258731	−	0.0941704i
$921$	−8.73001	+	4.12699i	−0.287664	+	0.135989i
$922$	−21.1743	−	17.7674i	−0.697340	−	0.585138i
$923$	−9.46839	−	7.94492i	−0.311656	−	0.261510i
$924$	0.326153	−	1.52506i	0.0107296	−	0.0501707i
$925$	2.47149	+	0.899550i	0.0812622	+	0.0295770i
$926$	21.1455	−	36.6251i	0.694884	−	1.20357i
$927$	−28.1447	+	5.26895i	−0.924393	+	0.173055i
$928$	3.47721	+	6.02271i	0.114145	+	0.197705i
$929$	27.7892	+	10.1144i	0.911735	+	0.331844i	0.754945	−	0.655788i	$-0.227663\pi$
$929$	27.7892	+	10.1144i	0.911735	+	0.331844i	0.156789	+	0.987632i	$0.449886\pi$
$930$	−29.7635	−	7.80731i	−0.975983	−	0.256012i
$931$	−2.18365	−	8.00775i	−0.0715663	−	0.262443i
$932$	3.27425	−	18.5692i	0.107252	−	0.608254i
$933$	−8.06906	−	29.4919i	−0.264169	−	0.965522i
$934$	−5.16210	−	29.2757i	−0.168909	−	0.957931i
$935$	1.43050	+	2.47770i	0.0467824	+	0.0810295i
$936$	−1.88928	−	2.20399i	−0.0617532	−	0.0720396i
$937$	−5.45899	−	9.45526i	−0.178338	−	0.308890i	0.762974	−	0.646430i	$-0.223739\pi$
$937$	−5.45899	−	9.45526i	−0.178338	−	0.308890i	−0.941311	+	0.337540i	$0.890405\pi$
$938$	−2.16912	−	5.20416i	−0.0708243	−	0.169922i
$939$	17.4294	+	24.6148i	0.568787	+	0.803274i
$940$	−0.0108719	+	0.0616576i	−0.000354602	+	0.00201105i
$941$	3.91594	−	22.2084i	0.127656	−	0.723974i	−0.852039	−	0.523479i	$-0.824634\pi$
$941$	3.91594	−	22.2084i	0.127656	−	0.723974i	0.979695	−	0.200495i	$-0.0642550\pi$
$942$	−30.8090	+	14.5645i	−1.00381	+	0.474537i
$943$	−20.5557	+	17.2483i	−0.669386	+	0.561682i
$944$	0.925703			0.0301291
$945$	0.663455	−	25.8885i	0.0215822	−	0.842152i
$946$	0.867138			0.0281931
$947$	10.0962	−	8.47172i	0.328083	−	0.275294i	−0.463835	−	0.885921i	$-0.653527\pi$
$947$	10.0962	−	8.47172i	0.328083	−	0.275294i	0.791918	+	0.610627i	$0.209083\pi$
$948$	−2.51573	+	30.6111i	−0.0817072	+	0.994203i
$949$	1.75154	−	9.93345i	0.0568573	−	0.322454i
$950$	0.298879	−	1.69503i	0.00969691	−	0.0549939i
$951$	−0.179029	+	0.389269i	−0.00580541	+	0.0126229i
$952$	11.7100	+	1.51532i	0.379522	+	0.0491119i
$953$	−25.3941	−	43.9839i	−0.822597	−	1.42478i	−0.903742	−	0.428077i	$-0.859191\pi$
$953$	−25.3941	−	43.9839i	−0.822597	−	1.42478i	0.0811451	−	0.996702i	$-0.474142\pi$
$954$	−26.9973	+	15.9684i	−0.874070	+	0.516997i
$955$	−12.1876	−	21.1095i	−0.394380	−	0.683086i
$956$	−1.63969	−	9.29913i	−0.0530313	−	0.300755i
$957$	−3.96515	−	1.04011i	−0.128175	−	0.0336218i
$958$	−4.52764	+	25.6776i	−0.146282	+	0.829604i
$959$	1.78361	+	38.8793i	0.0575957	+	1.25548i
$960$	0.861040	+	3.14705i	0.0277899	+	0.101571i
$961$	−54.4481	−	19.8175i	−1.75639	−	0.639273i
$962$	−0.876637	−	1.51838i	−0.0282639	−	0.0489546i
$963$	16.1394	−	19.6509i	0.520085	−	0.633242i
$964$	−2.14863	+	3.72153i	−0.0692026	+	0.119862i
$965$	12.3705	+	4.50251i	0.398222	+	0.144941i
$966$	4.24885	−	19.8672i	0.136705	−	0.639217i
$967$	20.0567	+	16.8295i	0.644979	+	0.541202i	0.905543	−	0.424255i	$-0.139464\pi$
$967$	20.0567	+	16.8295i	0.644979	+	0.541202i	−0.260564	+	0.965457i	$0.583908\pi$
$968$	8.33777	+	6.99622i	0.267986	+	0.224867i
$969$	7.53560	+	5.21755i	0.242078	+	0.167612i
$970$	−23.4199	−	8.52415i	−0.751968	−	0.273694i
$971$	5.68943	+	9.85438i	0.182583	+	0.316242i	0.942759	−	0.333474i	$-0.108221\pi$
$971$	5.68943	+	9.85438i	0.182583	+	0.316242i	−0.760177	+	0.649716i	$0.774888\pi$
$972$	0.949232	−	15.5595i	0.0304466	−	0.499072i
$973$	17.6356	+	19.1607i	0.565371	+	0.614264i
$974$	−1.19210	−	6.76071i	−0.0381972	−	0.216627i
$975$	2.19945	−	1.03976i	0.0704387	−	0.0332989i
$976$	−0.993133	+	5.63234i	−0.0317894	+	0.180287i
$977$	−10.0982	+	3.67546i	−0.323071	+	0.117588i	−0.498464	−	0.866910i	$-0.666103\pi$
$977$	−10.0982	+	3.67546i	−0.323071	+	0.117588i	0.175393	+	0.984498i	$0.443880\pi$
$978$	4.56304	+	6.44419i	0.145910	+	0.206062i
$979$	0.333998	+	0.121565i	0.0106746	+	0.00388524i
$980$	−11.9259	+	5.62545i	−0.380959	+	0.179699i
$981$	38.0029	+	6.28891i	1.21334	+	0.200789i
$982$	9.72597			0.310368
$983$	−2.86705	−	16.2598i	−0.0914446	−	0.518608i	−0.995779	−	0.0917833i	$-0.970743\pi$
$983$	−2.86705	−	16.2598i	−0.0914446	−	0.518608i	0.904334	−	0.426825i	$-0.140368\pi$
$984$	10.1403	+	2.65992i	0.323261	+	0.0847952i
$985$	−29.2444	+	10.6441i	−0.931805	+	0.339149i
$986$	5.38944	−	30.5650i	0.171635	−	0.973389i
$987$	−0.152210	−	0.00550570i	−0.00484489	−	0.000175248i
$988$	−0.878932	+	0.737512i	−0.0279626	+	0.0234634i
$989$	11.2964			0.359204
$990$	−1.67559	−	0.944008i	−0.0532537	−	0.0300025i
$991$	−2.92224			−0.0928281			−0.0464141	−	0.998922i	$-0.514779\pi$
$991$	−2.92224			−0.0928281			−0.0464141	+	0.998922i	$0.514779\pi$
$992$	1.63766	+	9.28765i	0.0519959	+	0.294883i
$993$	−5.97488	+	12.9914i	−0.189607	+	0.412269i
$994$	−28.4625	+	18.2212i	−0.902776	+	0.577941i
$995$	23.7376	−	8.63977i	0.752532	−	0.273899i
$996$	4.32659	+	2.99567i	0.137093	+	0.0949214i
$997$	29.8617	+	10.8688i	0.945730	+	0.344217i	0.768426	−	0.639939i	$-0.221040\pi$
$997$	29.8617	+	10.8688i	0.945730	+	0.344217i	0.177304	+	0.984156i	$0.443263\pi$
$998$	−12.7857	+	22.1455i	−0.404724	+	0.701002i
$999$	2.29277	−	9.13151i	0.0725400	−	0.288908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.67.2	✓	72
7.2	even	3		378.2.w.b.121.11	yes	72
27.25	even	9		378.2.w.b.25.11	yes	72
189.79	even	9	inner	378.2.v.a.79.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.2	✓	72	1.1	even	1	trivial
378.2.v.a.79.2	yes	72	189.79	even	9	inner
378.2.w.b.25.11	yes	72	27.25	even	9
378.2.w.b.121.11	yes	72	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.42403 - 0.985977i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.327106 + 1.85511i) q^{5} +(1.72464 - 0.160044i) q^{6} +(-1.01788 - 2.44211i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.05570 + 2.80811i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.42403 - 0.985977i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.327106 + 1.85511i) q^{5} +(1.72464 - 0.160044i) q^{6} +(-1.01788 - 2.44211i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.05570 + 2.80811i) q^{9} +(-0.941864 - 1.63136i) q^{10} +(-0.0590960 - 0.335150i) q^{11} +(-1.21828 + 1.23118i) q^{12} +(-0.168029 + 0.952940i) q^{13} +(2.34950 + 1.21648i) q^{14} +(2.29490 - 2.31921i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.23143 + 3.86494i) q^{17} +(-2.61373 - 1.47255i) q^{18} +(-0.592867 + 1.02688i) q^{19} +(1.77013 + 0.644273i) q^{20} +(-0.958371 + 4.48124i) q^{21} +(0.260700 + 0.218754i) q^{22} +(3.39619 + 2.84974i) q^{23} +(0.141868 - 1.72623i) q^{24} +(1.36403 + 0.496466i) q^{25} +(-0.483820 - 0.838001i) q^{26} +(1.26539 - 5.03972i) q^{27} +(-2.58176 + 0.578353i) q^{28} +(1.20762 + 6.84877i) q^{29} +(-0.267241 + 3.25175i) q^{30} +(-1.63766 + 9.28765i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.246296 + 0.535529i) q^{33} +(-4.19371 - 1.52638i) q^{34} +(4.86334 - 1.08946i) q^{35} +(2.94877 - 0.552038i) q^{36} +1.81191 q^{37} +(-0.205901 - 1.16772i) q^{38} +(1.17885 - 1.19134i) q^{39} +(-1.77013 + 0.644273i) q^{40} +(-1.05102 + 5.96062i) q^{41} +(-2.14633 - 4.04886i) q^{42} +(1.95189 - 1.63783i) q^{43} -0.340320 q^{44} +(-5.55468 + 1.03989i) q^{45} -4.43341 q^{46} +(0.00577148 + 0.0327317i) q^{47} +(1.00092 + 1.41356i) q^{48} +(-4.92782 + 4.97158i) q^{49} +(-1.36403 + 0.496466i) q^{50} +(0.633135 - 7.70391i) q^{51} +(0.909284 + 0.330952i) q^{52} +(5.22772 - 9.05468i) q^{53} +(2.27013 + 4.67403i) q^{54} +0.641071 q^{55} +(1.60599 - 2.10257i) q^{56} +(1.85673 - 0.877745i) q^{57} +(-5.32740 - 4.47022i) q^{58} +(-0.869877 + 0.316609i) q^{59} +(-1.88547 - 2.66276i) q^{60} +(-0.993133 - 5.63234i) q^{61} +(-4.71546 - 8.16742i) q^{62} +(5.78314 - 5.43647i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.71284 - 0.623424i) q^{65} +(-0.155558 - 0.568555i) q^{66} +(-1.63245 - 1.36979i) q^{67} +(4.19371 - 1.52638i) q^{68} +(-2.02648 - 7.40667i) q^{69} +(-3.02525 + 3.96067i) q^{70} +(-6.38672 + 11.0621i) q^{71} +(-1.90405 + 2.31832i) q^{72} -10.4240 q^{73} +(-1.38800 + 1.16467i) q^{74} +(-1.45291 - 2.05188i) q^{75} +(0.908325 + 0.762175i) q^{76} +(-0.758321 + 0.485463i) q^{77} +(-0.137277 + 1.67037i) q^{78} +(13.5842 - 11.3985i) q^{79} +(0.941864 - 1.63136i) q^{80} +(-6.77100 + 5.92905i) q^{81} +(-3.02629 - 5.24169i) q^{82} +(-0.527591 - 2.99212i) q^{83} +(4.24674 + 1.72197i) q^{84} +(-7.89981 + 2.87529i) q^{85} +(-0.442457 + 2.50930i) q^{86} +(5.03304 - 10.9435i) q^{87} +(0.260700 - 0.218754i) q^{88} +(-0.522204 + 0.904483i) q^{89} +(3.58671 - 4.36708i) q^{90} +(2.49822 - 0.559637i) q^{91} +(3.39619 - 2.84974i) q^{92} +(11.4895 - 11.6112i) q^{93} +(-0.0254607 - 0.0213641i) q^{94} +(-1.71104 - 1.43573i) q^{95} +(-1.67537 - 0.439470i) q^{96} +(10.1353 - 8.50450i) q^{97} +(0.579261 - 6.97599i) q^{98} +(0.878751 - 0.519766i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more