LMFDB - Embedded newform 324.3.j.a.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			307.1
Character	$\chi$	$=$	324.307
Dual form			324.3.j.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99738 + 0.102316i) q^{2} +(3.97906 - 0.408727i) q^{4} +(-1.35104 + 7.66211i) q^{5} +(-0.787463 - 0.938462i) q^{7} +(-7.90589 + 1.22351i) q^{8} +O(q^{10})$	\(q+(-1.99738 + 0.102316i) q^{2} +(3.97906 - 0.408727i) q^{4} +(-1.35104 + 7.66211i) q^{5} +(-0.787463 - 0.938462i) q^{7} +(-7.90589 + 1.22351i) q^{8} +(1.91458 - 15.4424i) q^{10} +(-10.6286 + 1.87412i) q^{11} +(-14.7898 + 5.38306i) q^{13} +(1.66888 + 1.79390i) q^{14} +(15.6659 - 3.25270i) q^{16} +(5.26562 - 9.12033i) q^{17} +(11.1663 - 6.44687i) q^{19} +(-2.24415 + 31.0402i) q^{20} +(21.0377 - 4.83081i) q^{22} +(23.2142 - 27.6656i) q^{23} +(-33.3903 - 12.1531i) q^{25} +(28.9902 - 12.2653i) q^{26} +(-3.51694 - 3.41234i) q^{28} +(-33.5701 - 12.2185i) q^{29} +(-10.8917 + 12.9803i) q^{31} +(-30.9579 + 8.09976i) q^{32} +(-9.58430 + 18.7555i) q^{34} +(8.25450 - 4.76574i) q^{35} +(-8.21996 + 14.2374i) q^{37} +(-21.6438 + 14.0194i) q^{38} +(1.30651 - 62.2288i) q^{40} +(-2.31562 + 0.842818i) q^{41} +(6.21529 - 1.09592i) q^{43} +(-41.5260 + 11.8014i) q^{44} +(-43.5369 + 57.6339i) q^{46} +(-50.0238 - 59.6160i) q^{47} +(8.24815 - 46.7776i) q^{49} +(67.9367 + 20.8580i) q^{50} +(-56.6495 + 27.4645i) q^{52} -81.4993 q^{53} -83.9699i q^{55} +(7.37381 + 6.45591i) q^{56} +(68.3025 + 20.9703i) q^{58} +(1.50977 + 0.266214i) q^{59} +(-79.3366 + 66.5713i) q^{61} +(20.4269 - 27.0409i) q^{62} +(61.0061 - 19.3458i) q^{64} +(-21.2640 - 120.594i) q^{65} +(-35.9599 - 98.7991i) q^{67} +(17.2245 - 38.4426i) q^{68} +(-15.9998 + 10.3636i) q^{70} +(97.5023 + 56.2930i) q^{71} +(1.32256 + 2.29075i) q^{73} +(14.9617 - 29.2785i) q^{74} +(41.7965 - 30.2165i) q^{76} +(10.1285 + 8.49879i) q^{77} +(-23.0193 + 63.2449i) q^{79} +(3.75740 + 124.428i) q^{80} +(4.53895 - 1.92035i) q^{82} +(-35.7180 + 98.1345i) q^{83} +(62.7669 + 52.6677i) q^{85} +(-12.3022 + 2.82490i) q^{86} +(81.7359 - 27.8208i) q^{88} +(56.9070 + 98.5658i) q^{89} +(16.6982 + 9.64074i) q^{91} +(81.0630 - 119.571i) q^{92} +(106.016 + 113.958i) q^{94} +(34.3106 + 94.2675i) q^{95} +(6.72108 + 38.1171i) q^{97} +(-11.6886 + 94.2766i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−1.99738	+	0.102316i	−0.998691	+	0.0511579i
$2$	−1.99738	+	0.102316i	−0.998691	+	0.0511579i
$3$		0			0
$3$		0			0
$4$	3.97906	−	0.408727i	0.994766	−	0.102182i
$5$	−1.35104	+	7.66211i	−0.270207	+	1.53242i	0.483578	+	0.875301i	$0.339337\pi$
$5$	−1.35104	+	7.66211i	−0.270207	+	1.53242i	−0.753785	+	0.657121i	$0.771774\pi$
$6$		0			0
$7$	−0.787463	−	0.938462i	−0.112495	−	0.134066i	0.706859	−	0.707355i	$-0.250112\pi$
$7$	−0.787463	−	0.938462i	−0.112495	−	0.134066i	−0.819353	+	0.573289i	$0.805667\pi$
$8$	−7.90589	+	1.22351i	−0.988236	+	0.152938i
$9$		0			0
$10$	1.91458	−	15.4424i	0.191458	−	1.54424i
$11$	−10.6286	+	1.87412i	−0.966241	+	0.170374i	−0.634437	−	0.772974i	$-0.718768\pi$
$11$	−10.6286	+	1.87412i	−0.966241	+	0.170374i	−0.331803	+	0.943349i	$0.607657\pi$
$12$		0			0
$13$	−14.7898	+	5.38306i	−1.13768	+	0.414081i	−0.841075	−	0.540919i	$-0.818077\pi$
$13$	−14.7898	+	5.38306i	−1.13768	+	0.414081i	−0.296604	+	0.955000i	$0.595854\pi$
$14$	1.66888	+	1.79390i	0.119206	+	0.128135i
$15$		0			0
$16$	15.6659	−	3.25270i	0.979118	−	0.203294i
$17$	5.26562	−	9.12033i	0.309742	−	0.536490i	−0.668563	−	0.743655i	$-0.733090\pi$
$17$	5.26562	−	9.12033i	0.309742	−	0.536490i	0.978306	+	0.207165i	$0.0664238\pi$
$18$		0			0
$19$	11.1663	−	6.44687i	0.587701	−	0.339309i	−0.176487	−	0.984303i	$-0.556473\pi$
$19$	11.1663	−	6.44687i	0.587701	−	0.339309i	0.764188	+	0.644994i	$0.223140\pi$
$20$	−2.24415	+	31.0402i	−0.112207	+	1.55201i
$21$		0			0
$22$	21.0377	−	4.83081i	0.956259	−	0.219582i
$23$	23.2142	−	27.6656i	1.00931	−	1.20285i	0.0301965	−	0.999544i	$-0.490387\pi$
$23$	23.2142	−	27.6656i	1.00931	−	1.20285i	0.979115	−	0.203307i	$-0.0651689\pi$
$24$		0			0
$25$	−33.3903	−	12.1531i	−1.33561	−	0.486124i
$26$	28.9902	−	12.2653i	1.11501	−	0.471740i
$27$		0			0
$28$	−3.51694	−	3.41234i	−0.125605	−	0.121869i
$29$	−33.5701	−	12.2185i	−1.15759	−	0.421329i	−0.309355	−	0.950947i	$-0.600113\pi$
$29$	−33.5701	−	12.2185i	−1.15759	−	0.421329i	−0.848236	+	0.529618i	$0.822335\pi$
$30$		0			0
$31$	−10.8917	+	12.9803i	−0.351346	+	0.418718i	−0.912554	−	0.408957i	$-0.865893\pi$
$31$	−10.8917	+	12.9803i	−0.351346	+	0.418718i	0.561207	+	0.827675i	$0.310337\pi$
$32$	−30.9579	+	8.09976i	−0.967436	+	0.253117i
$33$		0			0
$34$	−9.58430	+	18.7555i	−0.281891	+	0.551633i
$35$	8.25450	−	4.76574i	0.235843	−	0.136164i
$36$		0			0
$37$	−8.21996	+	14.2374i	−0.222161	+	0.384794i	−0.955464	−	0.295108i	$-0.904644\pi$
$37$	−8.21996	+	14.2374i	−0.222161	+	0.384794i	0.733303	+	0.679902i	$0.237978\pi$
$38$	−21.6438	+	14.0194i	−0.569573	+	0.368930i
$39$		0			0
$40$	1.30651	−	62.2288i	0.0326627	−	1.55572i
$41$	−2.31562	+	0.842818i	−0.0564786	+	0.0205565i	−0.370105	−	0.928990i	$-0.620678\pi$
$41$	−2.31562	+	0.842818i	−0.0564786	+	0.0205565i	0.313626	+	0.949546i	$0.398456\pi$
$42$		0			0
$43$	6.21529	−	1.09592i	0.144542	−	0.0254866i	−0.100909	−	0.994896i	$-0.532175\pi$
$43$	6.21529	−	1.09592i	0.144542	−	0.0254866i	0.245451	+	0.969409i	$0.421064\pi$
$44$	−41.5260	+	11.8014i	−0.943774	+	0.268215i
$45$		0			0
$46$	−43.5369	+	57.6339i	−0.946455	+	1.25291i
$47$	−50.0238	−	59.6160i	−1.06434	−	1.26843i	−0.961817	−	0.273694i	$-0.911754\pi$
$47$	−50.0238	−	59.6160i	−1.06434	−	1.26843i	−0.102518	−	0.994731i	$-0.532690\pi$
$48$		0			0
$49$	8.24815	−	46.7776i	0.168330	−	0.954644i
$50$	67.9367	+	20.8580i	1.35873	+	0.417160i
$51$		0			0
$52$	−56.6495	+	27.4645i	−1.08941	+	0.528164i
$53$	−81.4993			−1.53772			−0.768861	−	0.639415i	$-0.779176\pi$
$53$	−81.4993			−1.53772			−0.768861	+	0.639415i	$0.779176\pi$
$54$		0			0
$55$		−	83.9699i		−	1.52673i
$56$	7.37381	+	6.45591i	0.131675	+	0.115284i
$57$		0			0
$58$	68.3025	+	20.9703i	1.17763	+	0.361557i
$59$	1.50977	+	0.266214i	0.0255894	+	0.00451210i	0.186428	−	0.982469i	$-0.440309\pi$
$59$	1.50977	+	0.266214i	0.0255894	+	0.00451210i	−0.160839	+	0.986981i	$0.551420\pi$
$60$		0			0
$61$	−79.3366	+	66.5713i	−1.30060	+	1.09133i	−0.310559	+	0.950554i	$0.600516\pi$
$61$	−79.3366	+	66.5713i	−1.30060	+	1.09133i	−0.990041	+	0.140779i	$0.955039\pi$
$62$	20.4269	−	27.0409i	0.329465	−	0.436144i
$63$		0			0
$64$	61.0061	−	19.3458i	0.953220	−	0.302278i
$65$	−21.2640	−	120.594i	−0.327138	−	1.85529i
$66$		0			0
$67$	−35.9599	−	98.7991i	−0.536715	−	1.47461i	−0.850939	−	0.525264i	$-0.823966\pi$
$67$	−35.9599	−	98.7991i	−0.536715	−	1.47461i	0.314224	−	0.949349i	$-0.398256\pi$
$68$	17.2245	−	38.4426i	0.253302	−	0.565332i
$69$		0			0
$70$	−15.9998	+	10.3636i	−0.228568	+	0.148051i
$71$	97.5023	+	56.2930i	1.37327	+	0.792859i	0.991339	−	0.131332i	$-0.0419252\pi$
$71$	97.5023	+	56.2930i	1.37327	+	0.792859i	0.381933	+	0.924190i	$0.375259\pi$
$72$		0			0
$73$	1.32256	+	2.29075i	0.0181173	+	0.0313801i	0.874942	−	0.484228i	$-0.160899\pi$
$73$	1.32256	+	2.29075i	0.0181173	+	0.0313801i	−0.856825	+	0.515608i	$0.827566\pi$
$74$	14.9617	−	29.2785i	0.202185	−	0.395656i
$75$		0			0
$76$	41.7965	−	30.2165i	0.549953	−	0.397586i
$77$	10.1285	+	8.49879i	0.131538	+	0.110374i
$78$		0			0
$79$	−23.0193	+	63.2449i	−0.291383	+	0.800568i	0.704482	+	0.709722i	$0.251179\pi$
$79$	−23.0193	+	63.2449i	−0.291383	+	0.800568i	−0.995865	+	0.0908462i	$0.971043\pi$
$80$	3.75740	+	124.428i	0.0469675	+	1.55535i
$81$		0			0
$82$	4.53895	−	1.92035i	0.0553530	−	0.0234189i
$83$	−35.7180	+	98.1345i	−0.430338	+	1.18234i	0.515268	+	0.857029i	$0.327692\pi$
$83$	−35.7180	+	98.1345i	−0.430338	+	1.18234i	−0.945606	+	0.325315i	$0.894530\pi$
$84$		0			0
$85$	62.7669	+	52.6677i	0.738434	+	0.619620i
$86$	−12.3022	+	2.82490i	−0.143048	+	0.0328476i
$87$		0			0
$88$	81.7359	−	27.8208i	0.928817	−	0.316145i
$89$	56.9070	+	98.5658i	0.639404	+	1.10748i	0.985564	+	0.169305i	$0.0541524\pi$
$89$	56.9070	+	98.5658i	0.639404	+	1.10748i	−0.346159	+	0.938176i	$0.612514\pi$
$90$		0			0
$91$	16.6982	+	9.64074i	0.183497	+	0.105942i
$92$	81.0630	−	119.571i	0.881119	−	1.29969i
$93$		0			0
$94$	106.016	+	113.958i	1.12783	+	1.21232i
$95$	34.3106	+	94.2675i	0.361164	+	0.992290i
$96$		0			0
$97$	6.72108	+	38.1171i	0.0692895	+	0.392960i	0.999653	+	0.0263229i	$0.00837982\pi$
$97$	6.72108	+	38.1171i	0.0692895	+	0.392960i	−0.930364	+	0.366637i	$0.880509\pi$
$98$	−11.6886	+	94.2766i	−0.119272	+	0.962006i
$99$		0			0
$100$	−137.830	−	34.7104i	−1.37830	−	0.347104i
$101$	6.39658	−	5.36736i	0.0633324	−	0.0531422i	−0.610572	−	0.791961i	$-0.709060\pi$
$101$	6.39658	−	5.36736i	0.0633324	−	0.0531422i	0.673904	+	0.738819i	$0.264616\pi$
$102$		0			0
$103$	−26.7737	−	4.72093i	−0.259939	−	0.0458343i	0.0421598	−	0.999111i	$-0.486576\pi$
$103$	−26.7737	−	4.72093i	−0.259939	−	0.0458343i	−0.302099	+	0.953277i	$0.597687\pi$
$104$	110.340	−	60.6533i	1.06097	−	0.583205i
$105$		0			0
$106$	162.785	−	8.33867i	1.53571	−	0.0786667i
$107$		−	129.877i		−	1.21380i	−0.794778	−	0.606901i	$-0.792413\pi$
$107$		−	129.877i		−	1.21380i	0.794778	−	0.606901i	$-0.207587\pi$
$108$		0			0
$109$	−27.0858			−0.248493			−0.124247	−	0.992251i	$-0.539651\pi$
$109$	−27.0858			−0.248493			−0.124247	+	0.992251i	$0.539651\pi$
$110$	8.59145	+	167.720i	0.0781041	+	1.52473i
$111$		0			0
$112$	−15.3889	−	12.1405i	−0.137400	−	0.108397i
$113$	9.15298	−	51.9092i	0.0809999	−	0.459373i	−0.917148	−	0.398546i	$-0.869515\pi$
$113$	9.15298	−	51.9092i	0.0809999	−	0.459373i	0.998148	−	0.0608273i	$-0.0193739\pi$
$114$		0			0
$115$	180.613	+	215.247i	1.57055	+	1.87171i
$116$	−138.572	−	34.8973i	−1.19458	−	0.300838i
$117$		0			0
$118$	−3.04283	−	0.377257i	−0.0257867	−	0.00319709i
$119$	−12.7056	+	2.24033i	−0.106769	+	0.0188263i
$120$		0			0
$121$	−4.24701	+	1.54578i	−0.0350992	+	0.0127751i
$122$	151.654	−	141.086i	1.24307	−	1.15644i
$123$		0			0
$124$	−38.0335	+	56.1010i	−0.306722	+	0.452428i
$125$	40.9760	−	70.9726i	0.327808	−	0.567780i
$126$		0			0
$127$	−170.290	+	98.3172i	−1.34087	+	0.774151i	−0.986935	−	0.161119i	$-0.948490\pi$
$127$	−170.290	+	98.3172i	−1.34087	+	0.774151i	−0.353934	+	0.935270i	$0.615156\pi$
$128$	−119.873	+	44.8828i	−0.936508	+	0.350647i
$129$		0			0
$130$	54.8110	+	238.697i	0.421623	+	1.83613i
$131$	−66.8393	+	79.6560i	−0.510224	+	0.608061i	−0.958240	−	0.285964i	$-0.907686\pi$
$131$	−66.8393	+	79.6560i	−0.510224	+	0.608061i	0.448016	+	0.894025i	$0.352131\pi$
$132$		0			0
$133$	−14.8432	−	5.40249i	−0.111603	−	0.0406202i
$134$	81.9344	+	193.660i	0.611451	+	1.44523i
$135$		0			0
$136$	−30.4706	+	78.5468i	−0.224049	+	0.577550i
$137$	151.331	+	55.0801i	1.10461	+	0.402044i	0.829013	−	0.559229i	$-0.188903\pi$
$137$	151.331	+	55.0801i	1.10461	+	0.402044i	0.275595	+	0.961274i	$0.411125\pi$
$138$		0			0
$139$	−9.29954	+	11.0828i	−0.0669032	+	0.0797321i	−0.798458	−	0.602051i	$-0.794351\pi$
$139$	−9.29954	+	11.0828i	−0.0669032	+	0.0797321i	0.731555	+	0.681783i	$0.238795\pi$
$140$	30.8973	−	22.3370i	0.220695	−	0.159550i
$141$		0			0
$142$	−200.509	−	102.462i	−1.41203	−	0.721567i
$143$	147.107	−	84.9325i	1.02872	−	0.593933i
$144$		0			0
$145$	138.974	−	240.710i	0.958443	−	1.66007i
$146$	−2.87604	−	4.44017i	−0.0196989	−	0.0304122i
$147$		0			0
$148$	−26.8885	+	60.0112i	−0.181679	+	0.405481i
$149$	−8.80971	+	3.20647i	−0.0591256	+	0.0215200i	−0.371414	−	0.928468i	$-0.621127\pi$
$149$	−8.80971	+	3.20647i	−0.0591256	+	0.0215200i	0.312288	+	0.949987i	$0.398905\pi$
$150$		0			0
$151$	70.2988	−	12.3956i	0.465555	−	0.0820899i	0.0640500	−	0.997947i	$-0.479598\pi$
$151$	70.2988	−	12.3956i	0.465555	−	0.0820899i	0.401505	+	0.915857i	$0.368487\pi$
$152$	−80.3918	+	64.6303i	−0.528894	+	0.425199i
$153$		0			0
$154$	−21.1000	−	15.9390i	−0.137013	−	0.103500i
$155$	−84.7411	−	100.990i	−0.546717	−	0.651551i
$156$		0			0
$157$	−1.45325	+	8.24176i	−0.00925634	+	0.0524953i	−0.989086	−	0.147339i	$-0.952929\pi$
$157$	−1.45325	+	8.24176i	−0.00925634	+	0.0524953i	0.979830	+	0.199834i	$0.0640403\pi$
$158$	39.5073	−	128.679i	0.250046	−	0.814426i
$159$		0			0
$160$	−20.2359	−	248.146i	−0.126475	−	1.55091i
$161$	−44.2434			−0.274804
$162$		0			0
$163$		−	206.041i		−	1.26405i	−0.774947	−	0.632027i	$-0.782223\pi$
$163$		−	206.041i		−	1.26405i	0.774947	−	0.632027i	$-0.217777\pi$
$164$	−8.86953	+	4.30008i	−0.0540825	+	0.0262200i
$165$		0			0
$166$	61.3018	−	199.667i	0.369288	−	1.20281i
$167$	−14.5869	−	2.57206i	−0.0873467	−	0.0154016i	0.129804	−	0.991540i	$-0.458565\pi$
$167$	−14.5869	−	2.57206i	−0.0873467	−	0.0154016i	−0.217151	+	0.976138i	$0.569676\pi$
$168$		0			0
$169$	60.3002	−	50.5979i	0.356806	−	0.299396i
$170$	−130.758	−	98.7754i	−0.769166	−	0.581032i
$171$		0			0
$172$	24.2831	−	6.90110i	0.141181	−	0.0401227i
$173$	−4.15084	−	23.5406i	−0.0239933	−	0.136073i	0.970458	−	0.241270i	$-0.0775638\pi$
$173$	−4.15084	−	23.5406i	−0.0239933	−	0.136073i	−0.994451	+	0.105197i	$0.966453\pi$
$174$		0			0
$175$	14.8885	+	40.9057i	0.0850769	+	0.233747i
$176$	−160.411	+	63.9315i	−0.911427	+	0.363247i
$177$		0			0
$178$	−123.750	−	191.051i	−0.695224	−	1.07332i
$179$	−0.708443	−	0.409020i	−0.00395778	−	0.00228503i	0.498020	−	0.867166i	$-0.334061\pi$
$179$	−0.708443	−	0.409020i	−0.00395778	−	0.00228503i	−0.501978	+	0.864881i	$0.667394\pi$
$180$		0			0
$181$	56.9236	+	98.5946i	0.314495	+	0.544722i	0.979330	−	0.202269i	$-0.0648315\pi$
$181$	56.9236	+	98.5946i	0.314495	+	0.544722i	−0.664835	+	0.746990i	$0.731498\pi$
$182$	−34.3392	−	17.5477i	−0.188677	−	0.0964161i
$183$		0			0
$184$	−149.680	+	247.123i	−0.813476	+	1.34306i
$185$	−97.9830	−	82.2175i	−0.529638	−	0.444419i
$186$		0			0
$187$	−38.8739	+	106.805i	−0.207882	+	0.571150i
$188$	−223.414	−	216.770i	−1.18837	−	1.15303i
$189$		0			0
$190$	−78.1763	−	184.778i	−0.411454	−	0.972514i
$191$	39.9174	−	109.672i	0.208992	−	0.574200i	−0.790264	−	0.612766i	$-0.790057\pi$
$191$	39.9174	−	109.672i	0.208992	−	0.574200i	0.999256	+	0.0385663i	$0.0122791\pi$
$192$		0			0
$193$	38.4587	+	32.2707i	0.199268	+	0.167206i	0.736962	−	0.675935i	$-0.236260\pi$
$193$	38.4587	+	32.2707i	0.199268	+	0.167206i	−0.537694	+	0.843140i	$0.680704\pi$
$194$	−17.3245	−	75.4468i	−0.0893018	−	0.388901i
$195$		0			0
$196$	13.7006	−	189.502i	0.0699011	−	0.966848i
$197$	171.700	+	297.393i	0.871572	+	1.50961i	0.860370	+	0.509670i	$0.170233\pi$
$197$	171.700	+	297.393i	0.871572	+	1.50961i	0.0112024	+	0.999937i	$0.496434\pi$
$198$		0			0
$199$	118.265	+	68.2803i	0.594296	+	0.343117i	0.766794	−	0.641893i	$-0.221851\pi$
$199$	118.265	+	68.2803i	0.594296	+	0.343117i	−0.172498	+	0.985010i	$0.555184\pi$
$200$	278.850	+	55.2277i	1.39425	+	0.276138i
$201$		0			0
$202$	−12.2272	+	11.3751i	−0.0605309	+	0.0563126i
$203$	14.9686	+	41.1259i	0.0737370	+	0.202591i
$204$		0			0
$205$	−3.32927	−	18.8812i	−0.0162404	−	0.0921036i
$206$	53.9604	+	6.69012i	0.261943	+	0.0324763i
$207$		0			0
$208$	−214.186	+	132.437i	−1.02974	+	0.636718i
$209$	−106.601	+	89.4485i	−0.510051	+	0.427983i
$210$		0			0
$211$	−296.188	−	52.2260i	−1.40374	−	0.247516i	−0.580058	−	0.814575i	$-0.696970\pi$
$211$	−296.188	−	52.2260i	−1.40374	−	0.247516i	−0.823678	+	0.567059i	$0.808081\pi$
$212$	−324.291	+	33.3110i	−1.52967	+	0.157127i
$213$		0			0
$214$	13.2884	+	259.413i	0.0620956	+	1.21221i
$215$			49.1028i			0.228385i
$216$		0			0
$217$	20.7583			0.0956605
$218$	54.1006	−	2.77130i	0.248168	−	0.0127124i
$219$		0			0
$220$	−34.3208	−	334.121i	−0.156004	−	1.51873i
$221$	−28.7824	+	163.233i	−0.130237	+	0.738612i
$222$		0			0
$223$	−117.578	−	140.123i	−0.527254	−	0.628356i	0.435026	−	0.900418i	$-0.356739\pi$
$223$	−117.578	−	140.123i	−0.527254	−	0.628356i	−0.962280	+	0.272061i	$0.912295\pi$
$224$	31.9796	+	22.6746i	0.142766	+	0.101226i
$225$		0			0
$226$	−12.9709	+	104.619i	−0.0573932	+	0.462915i
$227$	−230.139	+	40.5797i	−1.01383	+	0.178765i	−0.655791	−	0.754943i	$-0.727665\pi$
$227$	−230.139	+	40.5797i	−1.01383	+	0.178765i	−0.358036	+	0.933708i	$0.616554\pi$
$228$		0			0
$229$	−40.4694	+	14.7296i	−0.176722	+	0.0643216i	−0.428866	−	0.903368i	$-0.641087\pi$
$229$	−40.4694	+	14.7296i	−0.176722	+	0.0643216i	0.252144	+	0.967690i	$0.418864\pi$
$230$	−382.777	−	411.450i	−1.66425	−	1.78891i
$231$		0			0
$232$	280.351	+	55.5250i	1.20841	+	0.239332i
$233$	−119.884	+	207.646i	−0.514526	+	0.891184i	0.485332	+	0.874330i	$0.338699\pi$
$233$	−119.884	+	207.646i	−0.514526	+	0.891184i	−0.999858	+	0.0168547i	$0.994635\pi$
$234$		0			0
$235$	524.368	−	302.744i	2.23135	−	1.28827i
$236$	6.11629	+	0.442195i	0.0259165	+	0.00187371i
$237$		0			0
$238$	25.1486	−	5.77478i	0.105667	−	0.0242638i
$239$	−245.960	+	293.124i	−1.02912	+	1.22646i	−0.0554608	+	0.998461i	$0.517663\pi$
$239$	−245.960	+	293.124i	−1.02912	+	1.22646i	−0.973661	+	0.227999i	$0.926782\pi$
$240$		0			0
$241$	76.9657	+	28.0132i	0.319360	+	0.116237i	0.496726	−	0.867907i	$-0.334535\pi$
$241$	76.9657	+	28.0132i	0.319360	+	0.116237i	−0.177366	+	0.984145i	$0.556758\pi$
$242$	8.32473	−	3.52205i	0.0343997	−	0.0145539i
$243$		0			0
$244$	−288.476	+	297.318i	−1.18228	+	1.21852i
$245$	347.271	+	126.396i	1.41743	+	0.515904i
$246$		0			0
$247$	−130.444	+	155.457i	−0.528113	+	0.629381i
$248$	70.2274	−	115.947i	0.283175	−	0.467526i
$249$		0			0
$250$	−74.5831	+	145.952i	−0.298332	+	0.583807i
$251$	−32.4564	+	18.7387i	−0.129308	+	0.0746563i	−0.563259	−	0.826280i	$-0.690453\pi$
$251$	−32.4564	+	18.7387i	−0.129308	+	0.0746563i	0.433950	+	0.900937i	$0.357119\pi$
$252$		0			0
$253$	−194.887	+	337.554i	−0.770303	+	1.33420i
$254$	330.075	−	213.800i	1.29951	−	0.841734i
$255$		0			0
$256$	234.840	−	101.913i	0.917343	−	0.398098i
$257$	−140.021	+	50.9636i	−0.544830	+	0.198302i	−0.599748	−	0.800189i	$-0.704733\pi$
$257$	−140.021	+	50.9636i	−0.544830	+	0.198302i	0.0549179	+	0.998491i	$0.482510\pi$
$258$		0			0
$259$	19.8342	−	3.49730i	0.0765798	−	0.0135031i
$260$	−133.901	−	471.160i	−0.515003	−	1.81215i
$261$		0			0
$262$	125.354	−	165.942i	0.478449	−	0.633367i
$263$	−298.935	−	356.256i	−1.13663	−	1.35459i	−0.926224	−	0.376973i	$-0.876965\pi$
$263$	−298.935	−	356.256i	−1.13663	−	1.35459i	−0.210409	−	0.977613i	$-0.567480\pi$
$264$		0			0
$265$	110.109	−	624.457i	0.415504	−	2.35644i
$266$	30.2003	+	9.27213i	0.113535	+	0.0348576i
$267$		0			0
$268$	−183.469	−	378.430i	−0.684585	−	1.41205i
$269$	321.810			1.19632			0.598160	−	0.801377i	$-0.295899\pi$
$269$	321.810			1.19632			0.598160	+	0.801377i	$0.295899\pi$
$270$		0			0
$271$		−	73.9743i		−	0.272968i	−0.990642	−	0.136484i	$-0.956420\pi$
$271$		−	73.9743i		−	0.272968i	0.990642	−	0.136484i	$-0.0435802\pi$
$272$	52.8249	−	160.005i	0.194209	−	0.588255i
$273$		0			0
$274$	−307.902	−	94.5324i	−1.12373	−	0.345009i
$275$	377.670	+	66.5935i	1.37335	+	0.242158i
$276$		0			0
$277$	94.2270	−	79.0658i	0.340170	−	0.285436i	−0.456659	−	0.889642i	$-0.650954\pi$
$277$	94.2270	−	79.0658i	0.340170	−	0.285436i	0.796828	+	0.604206i	$0.206509\pi$
$278$	17.4408	−	23.0880i	0.0627366	−	0.0830503i
$279$		0			0
$280$	−59.4282	+	47.7768i	−0.212244	+	0.170631i
$281$	−43.0735	−	244.282i	−0.153286	−	0.869330i	−0.960336	−	0.278846i	$-0.910048\pi$
$281$	−43.0735	−	244.282i	−0.153286	−	0.869330i	0.807049	−	0.590484i	$-0.201063\pi$
$282$		0			0
$283$	−3.90946	−	10.7412i	−0.0138143	−	0.0379546i	0.932594	−	0.360928i	$-0.117540\pi$
$283$	−3.90946	−	10.7412i	−0.0138143	−	0.0379546i	−0.946408	+	0.322973i	$0.895318\pi$
$284$	410.976	+	184.141i	1.44710	+	0.648385i
$285$		0			0
$286$	−285.140	+	184.694i	−0.996991	+	0.645783i
$287$	2.61442	+	1.50944i	0.00910948	+	0.00525936i
$288$		0			0
$289$	89.0464	+	154.233i	0.308119	+	0.533678i
$290$	−252.956	+	495.010i	−0.872262	+	1.70693i
$291$		0			0
$292$	6.19885	+	8.57446i	0.0212289	+	0.0293646i
$293$	204.044	+	171.214i	0.696397	+	0.584347i	0.920746	−	0.390162i	$-0.127581\pi$
$293$	204.044	+	171.214i	0.696397	+	0.584347i	−0.224349	+	0.974509i	$0.572025\pi$
$294$		0			0
$295$	−4.07952	+	11.2084i	−0.0138289	+	0.0379945i
$296$	47.5666	−	122.616i	0.160698	−	0.414245i
$297$		0			0
$298$	17.2683	−	7.30592i	0.0579473	−	0.0245165i
$299$	−194.408	+	534.132i	−0.650195	+	1.78640i
$300$		0			0
$301$	−5.92279	−	4.96981i	−0.0196770	−	0.0165110i
$302$	−139.145	+	31.9514i	−0.460746	+	0.105799i
$303$		0			0
$304$	153.960	−	137.317i	0.506449	−	0.451700i
$305$	−402.890	−	697.826i	−1.32095	−	2.28795i
$306$		0			0
$307$	217.448	+	125.544i	0.708301	+	0.408938i	0.810431	−	0.585833i	$-0.199233\pi$
$307$	217.448	+	125.544i	0.708301	+	0.408938i	−0.102131	+	0.994771i	$0.532566\pi$
$308$	43.7755	+	29.6774i	0.142128	+	0.0963553i
$309$		0			0
$310$	179.593	+	193.046i	0.579333	+	0.622729i
$311$	55.6734	+	152.961i	0.179014	+	0.491837i	0.996450	−	0.0841819i	$-0.0268277\pi$
$311$	55.6734	+	152.961i	0.179014	+	0.491837i	−0.817436	+	0.576019i	$0.804605\pi$
$312$		0			0
$313$	−20.7516	−	117.688i	−0.0662990	−	0.376001i	−0.999846	−	0.0175456i	$-0.994415\pi$
$313$	−20.7516	−	117.688i	−0.0662990	−	0.376001i	0.933547	−	0.358455i	$-0.116696\pi$
$314$	2.05942	−	16.6106i	0.00655867	−	0.0529001i
$315$		0			0
$316$	−65.7451	+	261.064i	−0.208054	+	0.826152i
$317$	−73.7327	+	61.8691i	−0.232595	+	0.195171i	−0.751635	−	0.659580i	$-0.770734\pi$
$317$	−73.7327	+	61.8691i	−0.232595	+	0.195171i	0.519039	+	0.854750i	$0.326290\pi$
$318$		0			0
$319$	379.704	+	66.9521i	1.19029	+	0.209881i
$320$	65.8082	+	493.572i	0.205651	+	1.54241i
$321$		0			0
$322$	88.3709	−	4.52680i	0.274444	−	0.0140584i
$323$		−	135.787i		−	0.420394i
$324$		0			0
$325$	559.258			1.72079
$326$	21.0812	+	411.542i	0.0646664	+	1.26240i
$327$		0			0
$328$	17.2759	−	9.49640i	0.0526703	−	0.0289524i
$329$	−16.5555	+	93.8908i	−0.0503206	+	0.285382i
$330$		0			0
$331$	−67.5154	−	80.4617i	−0.203974	−	0.243087i	0.654354	−	0.756189i	$-0.272941\pi$
$331$	−67.5154	−	80.4617i	−0.203974	−	0.243087i	−0.858328	+	0.513102i	$0.828496\pi$
$332$	−102.014	+	405.082i	−0.307271	+	1.22013i
$333$		0			0
$334$	29.3988	+	3.64492i	0.0880202	+	0.0109129i
$335$	805.593	−	142.048i	2.40475	−	0.424023i
$336$		0			0
$337$	−535.469	+	194.895i	−1.58893	+	0.578322i	−0.977121	−	0.212685i	$-0.931779\pi$
$337$	−535.469	+	194.895i	−1.58893	+	0.578322i	−0.611807	+	0.791007i	$0.709557\pi$
$338$	−115.266	+	107.233i	−0.341022	+	0.317257i
$339$		0			0
$340$	271.280	+	183.913i	0.797883	+	0.540922i
$341$	91.4378	−	158.375i	0.268146	−	0.464443i
$342$		0			0
$343$	−102.380	+	59.1094i	−0.298485	+	0.172331i
$344$	−47.7965	+	16.2687i	−0.138943	+	0.0472927i
$345$		0			0
$346$	10.6994	+	46.5949i	0.0309231	+	0.134667i
$347$	231.680	−	276.105i	0.667665	−	0.795692i	−0.320799	−	0.947147i	$-0.603951\pi$
$347$	231.680	−	276.105i	0.667665	−	0.795692i	0.988464	+	0.151455i	$0.0483959\pi$
$348$		0			0
$349$	29.5663	+	10.7613i	0.0847173	+	0.0308346i	0.384031	−	0.923320i	$-0.374536\pi$
$349$	29.5663	+	10.7613i	0.0847173	+	0.0308346i	−0.299314	+	0.954155i	$0.596758\pi$
$350$	−33.9232	−	80.1809i	−0.0969235	−	0.229088i
$351$		0			0
$352$	313.861	−	144.108i	0.891651	−	0.409399i
$353$	−309.372	−	112.602i	−0.876408	−	0.318987i	−0.135649	−	0.990757i	$-0.543312\pi$
$353$	−309.372	−	112.602i	−0.876408	−	0.318987i	−0.740759	+	0.671770i	$0.765534\pi$
$354$		0			0
$355$	−563.052	+	671.019i	−1.58606	+	1.89020i
$356$	266.723	+	368.940i	0.749222	+	1.03635i
$357$		0			0
$358$	1.45688	+	0.744483i	0.00406950	+	0.00207956i
$359$	−14.0326	+	8.10171i	−0.0390879	+	0.0225674i	−0.519417	−	0.854521i	$-0.673851\pi$
$359$	−14.0326	+	8.10171i	−0.0390879	+	0.0225674i	0.480329	+	0.877089i	$0.340517\pi$
$360$		0			0
$361$	−97.3756	+	168.660i	−0.269739	+	0.467201i
$362$	−123.786	−	191.107i	−0.341950	−	0.527919i
$363$		0			0
$364$	70.3838	+	31.5361i	0.193362	+	0.0866375i
$365$	−19.3388	+	7.03874i	−0.0529830	+	0.0192842i
$366$		0			0
$367$	−51.2504	+	9.03682i	−0.139647	+	0.0246235i	−0.243035	−	0.970018i	$-0.578143\pi$
$367$	−51.2504	+	9.03682i	−0.139647	+	0.0246235i	0.103388	+	0.994641i	$0.467032\pi$
$368$	273.683	−	508.914i	0.743702	−	1.38292i
$369$		0			0
$370$	204.122	+	154.195i	0.551680	+	0.416742i
$371$	64.1777	+	76.4840i	0.172986	+	0.206156i
$372$		0			0
$373$	51.2834	−	290.843i	0.137489	−	0.779740i	−0.835605	−	0.549331i	$-0.814883\pi$
$373$	51.2834	−	290.843i	0.137489	−	0.779740i	0.973094	−	0.230409i	$-0.0740063\pi$
$374$	66.7181	−	217.308i	0.178391	−	0.581037i
$375$		0			0
$376$	468.423	+	410.113i	1.24580	+	1.09073i
$377$	562.270			1.49143
$378$		0			0
$379$			359.299i			0.948017i	0.880520	+	0.474009i	$0.157193\pi$
$379$			359.299i			0.948017i	−0.880520	+	0.474009i	$0.842807\pi$
$380$	175.054	+	361.073i	0.460667	+	0.950191i
$381$		0			0
$382$	−68.5090	+	223.141i	−0.179343	+	0.584139i
$383$	−272.469	−	48.0437i	−0.711408	−	0.125441i	−0.193779	−	0.981045i	$-0.562074\pi$
$383$	−272.469	−	48.0437i	−0.711408	−	0.125441i	−0.517630	+	0.855605i	$0.673186\pi$
$384$		0			0
$385$	−78.8026	+	66.1232i	−0.204682	+	0.171749i
$386$	−80.1185	−	60.5220i	−0.207561	−	0.156793i
$387$		0			0
$388$	42.3231	+	148.923i	0.109080	+	0.383823i
$389$	29.5321	+	167.485i	0.0759180	+	0.430552i	0.998949	+	0.0458277i	$0.0145925\pi$
$389$	29.5321	+	167.485i	0.0759180	+	0.430552i	−0.923031	+	0.384725i	$0.874296\pi$
$390$		0			0
$391$	−130.082	−	357.397i	−0.332690	−	0.914059i
$392$	−7.97629	+	379.910i	−0.0203477	+	0.969158i
$393$		0			0
$394$	−373.378	−	576.439i	−0.947659	−	1.46304i
$395$	−453.489	−	261.822i	−1.14807	−	0.662841i
$396$		0			0
$397$	−113.268	−	196.185i	−0.285309	−	0.494169i	0.687375	−	0.726302i	$-0.258763\pi$
$397$	−113.268	−	196.185i	−0.285309	−	0.494169i	−0.972684	+	0.232133i	$0.925429\pi$
$398$	−243.206	−	124.281i	−0.611071	−	0.312265i
$399$		0			0
$400$	−562.620	−	81.7800i	−1.40655	−	0.204450i
$401$	−411.774	−	345.519i	−1.02687	−	0.861644i	−0.0363921	−	0.999338i	$-0.511587\pi$
$401$	−411.774	−	345.519i	−1.02687	−	0.861644i	−0.990475	+	0.137694i	$0.956031\pi$
$402$		0			0
$403$	91.2134	−	250.607i	0.226336	−	0.621853i
$404$	23.2586	−	23.9715i	0.0575708	−	0.0593355i
$405$		0			0
$406$	−34.1059	−	80.6127i	−0.0840046	−	0.198553i
$407$	60.6845	−	166.729i	0.149102	−	0.409655i
$408$		0			0
$409$	524.976	+	440.507i	1.28356	+	1.07703i	0.992743	+	0.120255i	$0.0383713\pi$
$409$	524.976	+	440.507i	1.28356	+	1.07703i	0.290816	+	0.956779i	$0.406073\pi$
$410$	8.58168	+	37.3724i	0.0209309	+	0.0911522i
$411$		0			0
$412$	−108.464	−	7.84172i	−0.263262	−	0.0190333i
$413$	−0.939059	−	1.62650i	−0.00227375	−	0.00393825i
$414$		0			0
$415$	−703.661	−	406.259i	−1.69557	−	0.978938i
$416$	414.261	−	286.442i	0.995820	−	0.688563i
$417$		0			0
$418$	203.770	−	189.570i	0.487488	−	0.453516i
$419$	−32.9727	−	90.5917i	−0.0786938	−	0.216209i	0.894107	−	0.447854i	$-0.147812\pi$
$419$	−32.9727	−	90.5917i	−0.0786938	−	0.216209i	−0.972800	+	0.231645i	$0.925589\pi$
$420$		0			0
$421$	66.8410	+	379.074i	0.158767	+	0.900414i	0.955260	+	0.295766i	$0.0955750\pi$
$421$	66.8410	+	379.074i	0.158767	+	0.900414i	−0.796493	+	0.604648i	$0.793314\pi$
$422$	596.944	+	74.0104i	1.41456	+	0.175380i
$423$		0			0
$424$	644.324	−	99.7149i	1.51963	−	0.235177i
$425$	−286.661	+	240.537i	−0.674497	+	0.565970i
$426$		0			0
$427$	124.949	+	22.0319i	0.292621	+	0.0515970i
$428$	−53.0842	−	516.788i	−0.124028	−	1.20745i
$429$		0			0
$430$	−5.02400	−	98.0771i	−0.0116837	−	0.228086i
$431$			113.065i			0.262333i	0.991360	+	0.131166i	$0.0418722\pi$
$431$			113.065i			0.262333i	−0.991360	+	0.131166i	$0.958128\pi$
$432$		0			0
$433$	−741.629			−1.71277			−0.856384	−	0.516339i	$-0.827294\pi$
$433$	−741.629			−1.71277			−0.856384	+	0.516339i	$0.827294\pi$
$434$	−41.4623	+	2.12391i	−0.0955352	+	0.00489379i
$435$		0			0
$436$	−107.776	+	11.0707i	−0.247193	+	0.0253915i
$437$	80.8602	−	458.581i	0.185035	−	1.04938i
$438$		0			0
$439$	155.409	+	185.209i	0.354006	+	0.421888i	0.913432	−	0.406992i	$-0.133422\pi$
$439$	155.409	+	185.209i	0.354006	+	0.421888i	−0.559425	+	0.828881i	$0.688978\pi$
$440$	102.738	+	663.856i	0.233495	+	1.50876i
$441$		0			0
$442$	40.7881	−	328.984i	0.0922808	−	0.744307i
$443$	405.157	−	71.4401i	0.914575	−	0.161264i	0.303495	−	0.952833i	$-0.401846\pi$
$443$	405.157	−	71.4401i	0.914575	−	0.161264i	0.611080	+	0.791569i	$0.290735\pi$
$444$		0			0
$445$	−832.106	+	302.862i	−1.86990	+	0.680588i
$446$	249.184	+	267.850i	0.558709	+	0.600560i
$447$		0			0
$448$	−66.1953	−	42.0178i	−0.147757	−	0.0937897i
$449$	−0.909646	+	1.57555i	−0.00202594	+	0.00350903i	−0.867037	−	0.498244i	$-0.833978\pi$
$449$	−0.909646	+	1.57555i	−0.00202594	+	0.00350903i	0.865011	+	0.501753i	$0.167312\pi$
$450$		0			0
$451$	23.0324	−	13.2978i	0.0510696	−	0.0294851i
$452$	15.2036	−	210.291i	0.0336363	−	0.465245i
$453$		0			0
$454$	455.523	−	104.600i	1.00335	−	0.230396i
$455$	−96.4283	+	114.919i	−0.211930	+	0.252569i
$456$		0			0
$457$	−363.648	−	132.357i	−0.795730	−	0.289622i	−0.0880140	−	0.996119i	$-0.528052\pi$
$457$	−363.648	−	132.357i	−0.795730	−	0.289622i	−0.707716	+	0.706497i	$0.750274\pi$
$458$	79.3257	−	33.5614i	0.173200	−	0.0732781i
$459$		0			0
$460$	806.650	+	782.659i	1.75359	+	1.70143i
$461$	311.071	+	113.220i	0.674773	+	0.245597i	0.656602	−	0.754237i	$-0.271993\pi$
$461$	311.071	+	113.220i	0.674773	+	0.245597i	0.0181716	+	0.999835i	$0.494215\pi$
$462$		0			0
$463$	501.978	−	598.234i	1.08418	−	1.29208i	0.130443	−	0.991456i	$-0.458360\pi$
$463$	501.978	−	598.234i	1.08418	−	1.29208i	0.953742	−	0.300625i	$-0.0971954\pi$
$464$	−565.649	−	82.2203i	−1.21907	−	0.177199i
$465$		0			0
$466$	218.209	−	427.014i	0.468261	−	0.916340i
$467$	578.288	−	333.875i	1.23830	−	0.714935i	0.269557	−	0.962985i	$-0.413123\pi$
$467$	578.288	−	333.875i	1.23830	−	0.714935i	0.968747	+	0.248049i	$0.0797896\pi$
$468$		0			0
$469$	−64.4021	+	111.548i	−0.137318	+	0.237842i
$470$	−1016.39	+	658.347i	−2.16253	+	1.40074i
$471$		0			0
$472$	−12.2618	−	0.257439i	−0.0259784	−	0.000545422i
$473$	−64.0062	+	23.2963i	−0.135320	+	0.0492523i
$474$		0			0
$475$	−451.196	+	79.5581i	−0.949887	+	0.167491i
$476$	−49.6406	+	14.1075i	−0.104287	+	0.0296377i
$477$		0			0
$478$	461.285	−	610.646i	0.965031	−	1.27750i
$479$	217.111	+	258.743i	0.453259	+	0.540173i	0.943482	−	0.331424i	$-0.107529\pi$
$479$	217.111	+	258.743i	0.453259	+	0.540173i	−0.490223	+	0.871597i	$0.663085\pi$
$480$		0			0
$481$	44.9311	−	254.817i	0.0934119	−	0.529765i
$482$	−156.596	−	48.0783i	−0.324888	−	0.0997475i
$483$		0			0
$484$	−16.2673	+	7.88664i	−0.0336101	+	0.0162947i
$485$	−301.138			−0.620903
$486$		0			0
$487$			651.667i			1.33812i	0.743206	+	0.669062i	$0.233304\pi$
$487$			651.667i			1.33812i	−0.743206	+	0.669062i	$0.766696\pi$
$488$	545.776	−	623.374i	1.11839	−	1.27741i
$489$		0			0
$490$	−706.566	−	216.931i	−1.44197	−	0.442715i
$491$	−483.613	−	85.2739i	−0.984954	−	0.173674i	−0.342101	−	0.939663i	$-0.611138\pi$
$491$	−483.613	−	85.2739i	−0.984954	−	0.173674i	−0.642853	+	0.765989i	$0.722250\pi$
$492$		0			0
$493$	−288.205	+	241.832i	−0.584593	+	0.490532i
$494$	244.641	−	323.854i	0.495224	−	0.655574i
$495$		0			0
$496$	−128.408	+	238.775i	−0.258886	+	0.481401i
$497$	−23.9506	−	135.831i	−0.0481904	−	0.273301i
$498$		0			0
$499$	−206.604	−	567.640i	−0.414036	−	1.13755i	−0.955025	−	0.296525i	$-0.904172\pi$
$499$	−206.604	−	567.640i	−0.414036	−	1.13755i	0.540989	−	0.841030i	$-0.318050\pi$
$500$	134.038	−	299.152i	0.268075	−	0.598305i
$501$		0			0
$502$	62.9106	−	40.7492i	0.125320	−	0.0811737i
$503$	−275.495	−	159.057i	−0.547703	−	0.316217i	0.200492	−	0.979695i	$-0.435746\pi$
$503$	−275.495	−	159.057i	−0.547703	−	0.316217i	−0.748195	+	0.663479i	$0.769079\pi$
$504$		0			0
$505$	32.4833	+	56.2628i	0.0643234	+	0.111411i
$506$	354.726	−	694.163i	0.701039	−	1.37186i
$507$		0			0
$508$	−637.411	+	460.813i	−1.25475	+	0.907112i
$509$	−46.7110	−	39.1952i	−0.0917702	−	0.0770044i	0.595748	−	0.803171i	$-0.296856\pi$
$509$	−46.7110	−	39.1952i	−0.0917702	−	0.0770044i	−0.687519	+	0.726167i	$0.741300\pi$
$510$		0			0
$511$	1.10831	−	3.04505i	0.00216890	−	0.00595901i
$512$	−458.637	+	227.587i	−0.895776	+	0.444506i
$513$		0			0
$514$	274.462	−	116.120i	0.533972	−	0.225915i
$515$	72.3446	−	198.765i	0.140475	−	0.385952i
$516$		0			0
$517$	643.412	+	539.887i	1.24451	+	1.04427i
$518$	−39.2586	+	9.01479i	−0.0757888	+	0.0174031i
$519$		0			0
$520$	315.658	+	927.386i	0.607035	+	1.78343i
$521$	−201.877	−	349.661i	−0.387479	−	0.671134i	0.604631	−	0.796506i	$-0.293321\pi$
$521$	−201.877	−	349.661i	−0.387479	−	0.671134i	−0.992110	+	0.125372i	$0.959987\pi$
$522$		0			0
$523$	−26.1714	−	15.1101i	−0.0500409	−	0.0288911i	0.474771	−	0.880109i	$-0.342531\pi$
$523$	−26.1714	−	15.1101i	−0.0500409	−	0.0288911i	−0.524812	+	0.851218i	$0.675864\pi$
$524$	−233.400	+	344.275i	−0.445420	+	0.657014i
$525$		0			0
$526$	633.537	+	680.994i	1.20444	+	1.29467i
$527$	61.0324	+	167.685i	0.115811	+	0.318188i
$528$		0			0
$529$	−134.626	−	763.503i	−0.254492	−	1.44329i
$530$	−156.037	+	1258.54i	−0.294409	+	2.37461i
$531$		0			0
$532$	−61.2702	−	15.4300i	−0.115170	−	0.0290038i
$533$	29.7107	−	24.9303i	0.0557425	−	0.0467735i
$534$		0			0
$535$	995.130	+	175.468i	1.86006	+	0.327978i
$536$	405.176	+	737.097i	0.755926	+	1.37518i
$537$		0			0
$538$	−642.777	+	32.9263i	−1.19475	+	0.0612013i
$539$			512.640i			0.951095i
$540$		0			0
$541$	−301.597			−0.557480			−0.278740	−	0.960367i	$-0.589917\pi$
$541$	−301.597			−0.557480			−0.278740	+	0.960367i	$0.589917\pi$
$542$	7.56874	+	147.755i	0.0139645	+	0.272610i
$543$		0			0
$544$	−89.1404	+	324.997i	−0.163861	+	0.597420i
$545$	36.5939	−	207.534i	0.0671447	−	0.380797i
$546$		0			0
$547$	−306.591	−	365.381i	−0.560496	−	0.667973i	0.409156	−	0.912465i	$-0.365823\pi$
$547$	−306.591	−	365.381i	−0.560496	−	0.667973i	−0.969651	+	0.244492i	$0.921379\pi$
$548$	624.670	+	157.314i	1.13991	+	0.287069i
$549$		0			0
$550$	−761.165	−	94.3709i	−1.38394	−	0.171583i
$551$	−453.626	+	79.9865i	−0.823278	+	0.145166i
$552$		0			0
$553$	77.4797	−	28.2003i	0.140108	−	0.0509952i
$554$	−180.118	+	167.566i	−0.325122	+	0.302465i
$555$		0			0
$556$	−32.4736	+	47.9000i	−0.0584058	+	0.0861511i
$557$	−373.600	+	647.095i	−0.670737	+	1.16175i	0.306959	+	0.951723i	$0.400689\pi$
$557$	−373.600	+	647.095i	−0.670737	+	1.16175i	−0.977695	+	0.210028i	$0.932645\pi$
$558$		0			0
$559$	−86.0236	+	49.6657i	−0.153888	+	0.0888475i
$560$	113.812	−	101.509i	0.203236	−	0.181266i
$561$		0			0
$562$	111.028	+	483.517i	0.197559	+	0.860350i
$563$	387.777	−	462.135i	0.688769	−	0.820843i	−0.302437	−	0.953169i	$-0.597800\pi$
$563$	387.777	−	462.135i	0.688769	−	0.820843i	0.991206	+	0.132326i	$0.0422447\pi$
$564$		0			0
$565$	385.368	+	140.262i	0.682067	+	0.248252i
$566$	8.90767	+	21.0542i	0.0157379	+	0.0371982i
$567$		0			0
$568$	−839.717	−	325.751i	−1.47837	−	0.573505i
$569$	−427.388	−	155.557i	−0.751122	−	0.273386i	−0.0620439	−	0.998073i	$-0.519762\pi$
$569$	−427.388	−	155.557i	−0.751122	−	0.273386i	−0.689078	+	0.724688i	$0.741984\pi$
$570$		0			0
$571$	258.606	−	308.195i	0.452901	−	0.539746i	−0.490483	−	0.871451i	$-0.663179\pi$
$571$	258.606	−	308.195i	0.452901	−	0.539746i	0.943383	+	0.331705i	$0.107624\pi$
$572$	550.635	−	398.079i	0.962649	−	0.695941i
$573$		0			0
$574$	−5.37643	−	2.74742i	−0.00936661	−	0.00478645i
$575$	−1111.35	+	641.639i	−1.93278	+	1.11589i
$576$		0			0
$577$	542.933	−	940.388i	0.940959	−	1.62979i	0.177312	−	0.984155i	$-0.443260\pi$
$577$	542.933	−	940.388i	0.940959	−	1.62979i	0.763647	−	0.645634i	$-0.223407\pi$
$578$	−193.640	−	298.951i	−0.335018	−	0.517217i
$579$		0			0
$580$	454.602	−	1014.60i	0.783797	−	1.74932i
$581$	120.222	−	43.7573i	0.206923	−	0.0753138i
$582$		0			0
$583$	866.227	−	152.739i	1.48581	−	0.261988i
$584$	−13.2588	−	16.4922i	−0.0227034	−	0.0282401i
$585$		0			0
$586$	−425.072	−	321.102i	−0.725380	−	0.547955i
$587$	473.005	+	563.705i	0.805801	+	0.960316i	0.999786	−	0.0206885i	$-0.00658583\pi$
$587$	473.005	+	563.705i	0.805801	+	0.960316i	−0.193985	+	0.981004i	$0.562141\pi$
$588$		0			0
$589$	−37.9384	+	215.159i	−0.0644115	+	0.365296i
$590$	7.00156	−	22.8048i	0.0118670	−	0.0386522i
$591$		0			0
$592$	−82.4629	+	249.778i	−0.139296	+	0.421923i
$593$	−1075.48			−1.81363			−0.906817	−	0.421526i	$-0.861495\pi$
$593$	−1075.48			−1.81363			−0.906817	+	0.421526i	$0.861495\pi$
$594$		0			0
$595$		−	100.378i		−	0.168703i
$596$	−33.7438	+	16.3595i	−0.0566172	+	0.0274489i
$597$		0			0
$598$	333.657	−	1086.76i	0.557955	−	1.81732i
$599$	−131.020	−	23.1023i	−0.218731	−	0.0385682i	0.0632086	−	0.998000i	$-0.479867\pi$
$599$	−131.020	−	23.1023i	−0.218731	−	0.0385682i	−0.281940	+	0.959432i	$0.590978\pi$
$600$		0			0
$601$	594.716	−	499.026i	0.989544	−	0.830326i	0.00404198	−	0.999992i	$-0.498713\pi$
$601$	594.716	−	499.026i	0.989544	−	0.830326i	0.985502	+	0.169666i	$0.0542689\pi$
$602$	12.3386	+	9.32061i	0.0204960	+	0.0154827i
$603$		0			0
$604$	274.657	−	78.0559i	0.454730	−	0.129232i
$605$	−6.10610	−	34.6294i	−0.0100927	−	0.0572387i
$606$		0			0
$607$	170.646	+	468.846i	0.281130	+	0.772399i	0.997229	+	0.0743997i	$0.0237041\pi$
$607$	170.646	+	468.846i	0.281130	+	0.772399i	−0.716098	+	0.698000i	$0.754074\pi$
$608$	−293.468	+	290.026i	−0.482678	+	0.477017i
$609$		0			0
$610$	876.124	+	1352.60i	1.43627	+	2.21738i
$611$	1060.76	+	612.429i	1.73610	+	1.00234i
$612$		0			0
$613$	−610.527	−	1057.46i	−0.995965	−	1.72506i	−0.575699	−	0.817662i	$-0.695270\pi$
$613$	−610.527	−	1057.46i	−0.995965	−	1.72506i	−0.420267	−	0.907401i	$-0.638063\pi$
$614$	−447.172	−	228.510i	−0.728294	−	0.372167i
$615$		0			0
$616$	−90.4727	−	54.7982i	−0.146871	−	0.0889581i
$617$	394.103	+	330.692i	0.638741	+	0.535968i	0.903631	−	0.428311i	$-0.140891\pi$
$617$	394.103	+	330.692i	0.638741	+	0.535968i	−0.264890	+	0.964279i	$0.585336\pi$
$618$		0			0
$619$	308.830	−	848.502i	0.498917	−	1.37076i	−0.393406	−	0.919365i	$-0.628703\pi$
$619$	308.830	−	848.502i	0.498917	−	1.37076i	0.892323	−	0.451398i	$-0.149075\pi$
$620$	−378.468	−	367.211i	−0.610432	−	0.592277i
$621$		0			0
$622$	−126.851	−	299.826i	−0.203941	−	0.482035i
$623$	47.6881	−	131.022i	0.0765459	−	0.210308i
$624$		0			0
$625$	−192.062	−	161.159i	−0.307299	−	0.257854i
$626$	53.4902	+	232.945i	0.0854476	+	0.372117i
$627$		0			0
$628$	−2.41392	+	33.3885i	−0.00384382	+	0.0531664i
$629$	86.5664	+	149.937i	0.137626	+	0.238374i
$630$		0			0
$631$	−282.911	−	163.339i	−0.448353	−	0.258857i	0.258781	−	0.965936i	$-0.416679\pi$
$631$	−282.911	−	163.339i	−0.448353	−	0.258857i	−0.707134	+	0.707079i	$0.750012\pi$
$632$	104.607	−	528.171i	0.165518	−	0.835714i
$633$		0			0
$634$	140.942	−	131.120i	0.222306	−	0.206814i
$635$	−523.249	−	1437.61i	−0.824014	−	2.26396i
$636$		0			0
$637$	129.818	+	736.232i	0.203795	+	1.15578i
$638$	−765.264	−	94.8790i	−1.19947	−	0.148713i
$639$		0			0
$640$	−181.944	−	979.119i	−0.284288	−	1.52987i
$641$	393.127	−	329.873i	0.613303	−	0.514622i	−0.282387	−	0.959300i	$-0.591126\pi$
$641$	393.127	−	329.873i	0.613303	−	0.514622i	0.895690	+	0.444678i	$0.146682\pi$
$642$		0			0
$643$	78.9843	+	13.9271i	0.122837	+	0.0216595i	0.234729	−	0.972061i	$-0.424580\pi$
$643$	78.9843	+	13.9271i	0.122837	+	0.0216595i	−0.111892	+	0.993720i	$0.535691\pi$
$644$	−176.047	+	18.0835i	−0.273365	+	0.0280800i
$645$		0			0
$646$	13.8932	+	271.219i	0.0215065	+	0.419843i
$647$		−	24.6592i		−	0.0381131i	−0.999818	−	0.0190566i	$-0.993934\pi$
$647$		−	24.6592i		−	0.0381131i	0.999818	−	0.0190566i	$-0.00606626\pi$
$648$		0			0
$649$	−16.5458			−0.0254942
$650$	−1117.05	+	57.2210i	−1.71854	+	0.0880323i
$651$		0			0
$652$	−84.2145	−	819.849i	−0.129163	−	1.25744i
$653$	−110.282	+	625.438i	−0.168885	+	0.957792i	0.776084	+	0.630630i	$0.217203\pi$
$653$	−110.282	+	625.438i	−0.168885	+	0.957792i	−0.944968	+	0.327162i	$0.893908\pi$
$654$		0			0
$655$	−520.031	−	619.749i	−0.793940	−	0.946181i
$656$	−33.5348	+	20.7355i	−0.0511202	+	0.0316090i
$657$		0			0
$658$	23.4611	−	189.230i	0.0356552	−	0.287583i
$659$	−543.904	+	95.9050i	−0.825348	+	0.145531i	−0.570341	−	0.821408i	$-0.693189\pi$
$659$	−543.904	+	95.9050i	−0.825348	+	0.145531i	−0.255007	+	0.966939i	$0.582078\pi$
$660$		0			0
$661$	−783.324	+	285.106i	−1.18506	+	0.431326i	−0.857986	−	0.513673i	$-0.828284\pi$
$661$	−783.324	+	285.106i	−1.18506	+	0.431326i	−0.327073	+	0.944999i	$0.606062\pi$
$662$	143.086	+	153.805i	0.216143	+	0.232333i
$663$		0			0
$664$	162.315	−	819.542i	0.244450	−	1.23425i
$665$	61.4482	−	106.431i	0.0924033	−	0.160047i
$666$		0			0
$667$	−1117.34	+	645.094i	−1.67517	+	0.967157i
$668$	−59.0935	−	4.27234i	−0.0884633	−	0.00639571i
$669$		0			0
$670$	−1594.54	+	366.148i	−2.37991	+	0.546490i
$671$	718.478	−	856.249i	1.07076	−	1.27608i
$672$		0			0
$673$	699.279	+	254.517i	1.03905	+	0.378182i	0.804519	−	0.593927i	$-0.202423\pi$
$673$	699.279	+	254.517i	1.03905	+	0.378182i	0.234528	+	0.972109i	$0.424646\pi$
$674$	1049.59	−	444.066i	1.55726	−	0.658851i
$675$		0			0
$676$	219.258	−	225.979i	0.324346	−	0.334288i
$677$	124.065	+	45.1561i	0.183257	+	0.0667002i	0.432019	−	0.901865i	$-0.357801\pi$
$677$	124.065	+	45.1561i	0.183257	+	0.0667002i	−0.248762	+	0.968565i	$0.580024\pi$
$678$		0			0
$679$	30.4789	−	36.3233i	0.0448879	−	0.0534953i
$680$	−560.667	−	339.589i	−0.824511	−	0.499396i
$681$		0			0
$682$	−166.432	+	325.691i	−0.244035	+	0.477552i
$683$	−643.841	+	371.722i	−0.942667	+	0.544249i	−0.890795	−	0.454405i	$-0.849852\pi$
$683$	−643.841	+	371.722i	−0.942667	+	0.544249i	−0.0518714	+	0.998654i	$0.516519\pi$
$684$		0			0
$685$	−626.484	+	1085.10i	−0.914575	+	1.58409i
$686$	198.445	−	128.539i	0.289278	−	0.187375i
$687$		0			0
$688$	93.8032	−	37.3851i	0.136342	−	0.0543388i
$689$	1205.36	−	438.715i	1.74944	−	0.636742i
$690$		0			0
$691$	−656.067	+	115.682i	−0.949445	+	0.167413i	−0.626864	−	0.779129i	$-0.715662\pi$
$691$	−656.067	+	115.682i	−0.949445	+	0.167413i	−0.322582	+	0.946542i	$0.604551\pi$
$692$	−26.1382	−	91.9730i	−0.0377719	−	0.132909i
$693$		0			0
$694$	−434.503	+	575.192i	−0.626085	+	0.828807i
$695$	−72.3533	−	86.2274i	−0.104106	−	0.124068i
$696$		0			0
$697$	−4.50642	+	25.5572i	−0.00646546	+	0.0366674i
$698$	−60.1563	−	18.4692i	−0.0861838	−	0.0264602i
$699$		0			0
$700$	75.9614	+	156.681i	0.108516	+	0.223830i
$701$	−13.3329			−0.0190199			−0.00950994	−	0.999955i	$-0.503027\pi$
$701$	−13.3329			−0.0190199			−0.00950994	+	0.999955i	$0.503027\pi$
$702$		0			0
$703$			211.972i			0.301525i
$704$	−612.156	+	319.952i	−0.869539	+	0.454477i
$705$		0			0
$706$	629.455	+	193.256i	0.891579	+	0.273734i
$707$	−10.0741	−	1.77634i	−0.0142491	−	0.00251251i
$708$		0			0
$709$	−126.336	+	106.009i	−0.178190	+	0.149519i	−0.727520	−	0.686086i	$-0.759327\pi$
$709$	−126.336	+	106.009i	−0.178190	+	0.149519i	0.549331	+	0.835605i	$0.314883\pi$
$710$	1055.97	−	1397.89i	1.48729	−	1.96886i
$711$		0			0
$712$	−570.496	−	709.624i	−0.801259	−	0.996663i
$713$	106.264	+	602.652i	0.149038	+	0.845234i
$714$		0			0
$715$	452.015	+	1241.90i	0.632188	+	1.73692i
$716$	−2.98612	−	1.33795i	−0.00417055	−	0.00186865i
$717$		0			0
$718$	27.1995	−	17.6180i	0.0378823	−	0.0245375i
$719$	−470.134	−	271.432i	−0.653872	−	0.377513i	0.136066	−	0.990700i	$-0.456554\pi$
$719$	−470.134	−	271.432i	−0.653872	−	0.377513i	−0.789938	+	0.613187i	$0.789887\pi$
$720$		0			0
$721$	16.6529	+	28.8437i	0.0230970	+	0.0400051i
$722$	177.240	−	346.840i	0.245484	−	0.480388i
$723$		0			0
$724$	266.801	+	369.048i	0.368510	+	0.509735i
$725$	972.425	+	815.962i	1.34128	+	1.12546i
$726$		0			0
$727$	−346.604	+	952.288i	−0.476760	+	1.30989i	0.435468	+	0.900204i	$0.356583\pi$
$727$	−346.604	+	952.288i	−0.476760	+	1.30989i	−0.912228	+	0.409683i	$0.865639\pi$
$728$	−143.810	−	55.7882i	−0.197541	−	0.0766321i
$729$		0			0
$730$	37.9068	−	16.0377i	0.0519271	−	0.0219695i
$731$	22.7322	−	62.4561i	0.0310974	−	0.0854393i
$732$		0			0
$733$	834.015	+	699.822i	1.13781	+	0.954736i	0.999365	−	0.0356337i	$-0.0113450\pi$
$733$	834.015	+	699.822i	1.13781	+	0.954736i	0.138446	+	0.990370i	$0.455789\pi$
$734$	101.442	−	23.2937i	0.138204	−	0.0317353i
$735$		0			0
$736$	−494.578	+	1044.50i	−0.671981	+	1.41915i
$737$	567.366	+	982.707i	0.769832	+	1.33339i
$738$		0			0
$739$	400.886	+	231.452i	0.542471	+	0.313196i	0.746080	−	0.665857i	$-0.231934\pi$
$739$	400.886	+	231.452i	0.542471	+	0.313196i	−0.203609	+	0.979052i	$0.565267\pi$
$740$	−423.485	−	287.100i	−0.572277	−	0.387973i
$741$		0			0
$742$	−136.013	−	146.201i	−0.183306	−	0.197037i
$743$	−123.581	−	339.535i	−0.166327	−	0.456979i	0.828327	−	0.560245i	$-0.189293\pi$
$743$	−123.581	−	339.535i	−0.166327	−	0.456979i	−0.994654	+	0.103266i	$0.967071\pi$
$744$		0			0
$745$	−12.6661	−	71.8331i	−0.0170015	−	0.0964202i
$746$	−72.6747	+	586.171i	−0.0974192	+	0.785752i
$747$		0			0
$748$	−111.027	+	440.873i	−0.148432	+	0.589402i
$749$	−121.884	+	102.273i	−0.162730	+	0.136546i
$750$		0			0
$751$	247.281	+	43.6024i	0.329270	+	0.0580591i	0.335839	−	0.941919i	$-0.390980\pi$
$751$	247.281	+	43.6024i	0.329270	+	0.0580591i	−0.00656967	+	0.999978i	$0.502091\pi$
$752$	−977.579	−	771.225i	−1.29997	−	1.02556i
$753$		0			0
$754$	−1123.07	+	57.5291i	−1.48948	+	0.0762985i
$755$			555.384i			0.735608i
$756$		0			0
$757$	1038.96			1.37247			0.686235	−	0.727380i	$-0.259262\pi$
$757$	1038.96			1.37247			0.686235	+	0.727380i	$0.259262\pi$
$758$	−36.7619	−	717.656i	−0.0484986	−	0.946776i
$759$		0			0
$760$	−386.592	−	703.289i	−0.508674	−	0.925380i
$761$	−35.0354	+	198.696i	−0.0460386	+	0.261098i	−0.999136	−	0.0415666i	$-0.986765\pi$
$761$	−35.0354	+	198.696i	−0.0460386	+	0.261098i	0.953097	+	0.302665i	$0.0978762\pi$
$762$		0			0
$763$	21.3291	+	25.4190i	0.0279542	+	0.0333145i
$764$	114.008	−	452.708i	0.149225	−	0.592549i
$765$		0			0
$766$	549.141	+	68.0837i	0.716894	+	0.0888821i
$767$	−23.7623	+	4.18994i	−0.0309809	+	0.00546276i
$768$		0			0
$769$	884.546	−	321.948i	1.15026	−	0.418659i	0.304648	−	0.952465i	$-0.401461\pi$
$769$	884.546	−	321.948i	1.15026	−	0.418659i	0.845607	+	0.533806i	$0.179239\pi$
$770$	150.633	−	140.136i	0.195628	−	0.181995i
$771$		0			0
$772$	166.220	+	112.688i	0.215310	+	0.145969i
$773$	383.159	−	663.651i	0.495678	−	0.858540i	−0.504309	−	0.863523i	$-0.668253\pi$
$773$	383.159	−	663.651i	0.495678	−	0.858540i	0.999988	+	0.00498322i	$0.00158621\pi$
$774$		0			0
$775$	521.429	−	301.047i	0.672811	−	0.388448i
$776$	−99.7726	−	293.126i	−0.128573	−	0.377740i
$777$		0			0
$778$	−76.1232	−	331.510i	−0.0978448	−	0.426105i
$779$	−20.4234	+	24.3397i	−0.0262175	+	0.0312448i
$780$		0			0
$781$	−1141.82	−	415.587i	−1.46199	−	0.532122i
$782$	296.391	+	700.549i	0.379016	+	0.895843i
$783$		0			0
$784$	−22.9391	−	759.641i	−0.0292591	−	0.968930i
$785$	−61.1859	−	22.2699i	−0.0779439	−	0.0283692i
$786$		0			0
$787$	−254.607	+	303.429i	−0.323516	+	0.385551i	−0.903150	−	0.429326i	$-0.858751\pi$
$787$	−254.607	+	303.429i	−0.323516	+	0.385551i	0.579634	+	0.814877i	$0.303196\pi$
$788$	804.757	+	1113.17i	1.02126	+	1.41265i
$789$		0			0
$790$	932.580	+	476.560i	1.18048	+	0.603240i
$791$	−55.9224	+	32.2868i	−0.0706984	+	0.0408177i
$792$		0			0
$793$	815.017	−	1411.65i	1.02776	−	1.78014i
$794$	246.311	+	380.267i	0.310216	+	0.478926i
$795$		0			0
$796$	498.492	+	223.354i	0.626246	+	0.280595i
$797$	134.986	−	49.1310i	0.169368	−	0.0616449i	−0.255944	−	0.966691i	$-0.582386\pi$
$797$	134.986	−	49.1310i	0.169368	−	0.0616449i	0.425312	+	0.905047i	$0.360164\pi$
$798$		0			0
$799$	−807.123	+	142.318i	−1.01017	+	0.178120i
$800$	1132.13	+	105.781i	1.41517	+	0.132226i
$801$		0			0
$802$	857.821	+	648.002i	1.06960	+	0.807983i
$803$	−18.3502	−	21.8689i	−0.0228520	−	0.0272340i
$804$		0			0
$805$	59.7745	−	338.998i	0.0742540	−	0.421115i
$806$	−156.547	+	509.890i	−0.194227	+	0.632617i
$807$		0			0
$808$	−44.0036	+	50.2600i	−0.0544599	+	0.0622030i
$809$	−277.409			−0.342903			−0.171452	−	0.985193i	$-0.554846\pi$
$809$	−277.409			−0.342903			−0.171452	+	0.985193i	$0.554846\pi$
$810$		0			0
$811$			1173.06i			1.44644i	0.690620	+	0.723218i	$0.257338\pi$
$811$			1173.06i			1.44644i	−0.690620	+	0.723218i	$0.742662\pi$
$812$	76.3704	+	157.525i	0.0940522	+	0.193996i
$813$		0			0
$814$	−104.151	+	339.231i	−0.127950	+	0.416746i
$815$	1578.71	+	278.369i	1.93706	+	0.341557i
$816$		0			0
$817$	62.3366	−	52.3066i	0.0762993	−	0.0640227i
$818$	−1093.65	−	826.147i	−1.33698	−	1.00996i
$819$		0			0
$820$	−20.9647	−	73.7689i	−0.0255667	−	0.0899620i
$821$	7.87632	+	44.6689i	0.00959357	+	0.0544079i	0.989229	−	0.146378i	$-0.0467616\pi$
$821$	7.87632	+	44.6689i	0.00959357	+	0.0544079i	−0.979635	+	0.200786i	$0.935650\pi$
$822$		0			0
$823$	−469.366	−	1289.57i	−0.570311	−	1.56692i	−0.804015	−	0.594609i	$-0.797307\pi$
$823$	−469.366	−	1289.57i	−0.570311	−	1.56692i	0.233704	−	0.972308i	$-0.424915\pi$
$824$	217.446	+	4.56533i	0.263891	+	0.00554045i
$825$		0			0
$826$	2.04208	+	3.15266i	0.00247225	+	0.00381678i
$827$	704.769	+	406.899i	0.852200	+	0.492018i	0.861393	−	0.507940i	$-0.169593\pi$
$827$	704.769	+	406.899i	0.852200	+	0.492018i	−0.00919261	+	0.999958i	$0.502926\pi$
$828$		0			0
$829$	422.447	+	731.699i	0.509586	+	0.882629i	0.999938	+	0.0111044i	$0.00353471\pi$
$829$	422.447	+	731.699i	0.509586	+	0.882629i	−0.490352	+	0.871524i	$0.663132\pi$
$830$	1447.05	+	739.459i	1.74343	+	0.890914i
$831$		0			0
$832$	−798.130	+	614.520i	−0.959291	+	0.738606i
$833$	−383.195	−	321.539i	−0.460018	−	0.386001i
$834$		0			0
$835$	39.4149	−	108.291i	0.0472034	−	0.129690i
$836$	−387.610	+	399.492i	−0.463649	+	0.477861i
$837$		0			0
$838$	75.1280	+	177.573i	0.0896516	+	0.211901i
$839$	−119.576	+	328.531i	−0.142522	+	0.391575i	−0.990331	−	0.138727i	$-0.955699\pi$
$839$	−119.576	+	328.531i	−0.142522	+	0.391575i	0.847809	+	0.530301i	$0.177921\pi$
$840$		0			0
$841$	333.418	+	279.771i	0.396454	+	0.332664i
$842$	−172.292	−	750.317i	−0.204623	−	0.891113i
$843$		0			0
$844$	−1199.90	−	86.7502i	−1.42168	−	0.102785i
$845$	306.219	+	530.387i	0.362389	+	0.627676i
$846$		0			0
$847$	4.79502	+	2.76841i	0.00566118	+	0.00326848i
$848$	−1276.76	+	265.093i	−1.50561	+	0.312610i
$849$		0			0
$850$	547.961	−	509.774i	0.644660	−	0.599735i
$851$	203.066	+	557.919i	0.238620	+	0.655604i
$852$		0			0
$853$	−124.476	−	705.941i	−0.145928	−	0.827597i	−0.966618	−	0.256223i	$-0.917522\pi$
$853$	−124.476	−	705.941i	−0.145928	−	0.827597i	0.820690	−	0.571374i	$-0.193589\pi$
$854$	−251.826	−	31.2219i	−0.294878	−	0.0365596i
$855$		0			0
$856$	158.905	+	1026.79i	0.185637	+	1.19952i
$857$	649.567	−	545.052i	0.757955	−	0.636000i	−0.179639	−	0.983733i	$-0.557493\pi$
$857$	649.567	−	545.052i	0.757955	−	0.636000i	0.937594	+	0.347733i	$0.113048\pi$
$858$		0			0
$859$	821.645	+	144.878i	0.956514	+	0.168659i	0.630053	−	0.776552i	$-0.283033\pi$
$859$	821.645	+	144.878i	0.956514	+	0.168659i	0.326460	+	0.945211i	$0.394144\pi$
$860$	20.0697	+	195.383i	0.0233368	+	0.227190i
$861$		0			0
$862$	−11.5684	−	225.835i	−0.0134204	−	0.261989i
$863$			446.310i			0.517161i	0.965990	+	0.258580i	$0.0832547\pi$
$863$			446.310i			0.517161i	−0.965990	+	0.258580i	$0.916745\pi$
$864$		0			0
$865$	185.979			0.215004
$866$	1481.31	−	75.8804i	1.71053	−	0.0876217i
$867$		0			0
$868$	82.5987	−	8.48450i	0.0951598	−	0.00977477i
$869$	126.135	−	715.348i	0.145150	−	0.823185i
$870$		0			0
$871$	1063.68	+	1267.65i	1.22122	+	1.45539i
$872$	214.137	−	33.1396i	0.245570	−	0.0380041i
$873$		0			0
$874$	−114.589	+	924.235i	−0.131108	+	1.05748i
$875$	−98.8722	+	17.4338i	−0.112997	+	0.0199244i
$876$		0			0
$877$	1159.76	−	422.120i	1.32242	−	0.481323i	0.418189	−	0.908360i	$-0.362665\pi$
$877$	1159.76	−	422.120i	1.32242	−	0.481323i	0.904234	+	0.427038i	$0.140443\pi$
$878$	−329.361	−	354.032i	−0.375126	−	0.403226i
$879$		0			0
$880$	−273.129	−	1315.46i	−0.310374	−	1.49484i
$881$	763.200	−	1321.90i	0.866289	−	1.50046i	0.000527054	−	1.00000i	$-0.499832\pi$
$881$	763.200	−	1321.90i	0.866289	−	1.50046i	0.865762	−	0.500456i	$-0.166834\pi$
$882$		0			0
$883$	−160.492	+	92.6600i	−0.181757	+	0.104938i	−0.588118	−	0.808775i	$-0.700131\pi$
$883$	−160.492	+	92.6600i	−0.181757	+	0.104938i	0.406361	+	0.913713i	$0.366798\pi$
$884$	−47.8092	+	661.279i	−0.0540827	+	0.748054i
$885$		0			0
$886$	−801.943	+	184.147i	−0.905127	+	0.207841i
$887$	−1029.26	+	1226.63i	−1.16039	+	1.38290i	−0.250462	+	0.968126i	$0.580583\pi$
$887$	−1029.26	+	1226.63i	−1.16039	+	1.38290i	−0.909926	+	0.414771i	$0.863862\pi$
$888$		0			0
$889$	226.364	+	82.3899i	0.254628	+	0.0926771i
$890$	1631.04	−	690.068i	1.83263	−	0.775357i
$891$		0			0
$892$	−525.121	−	509.503i	−0.588701	−	0.571192i
$893$	−942.918	−	343.194i	−1.05590	−	0.384316i
$894$		0			0
$895$	4.09109	−	4.87557i	0.00457105	−	0.00544756i
$896$	136.516	+	77.1527i	0.152362	+	0.0861079i
$897$		0			0
$898$	1.65571	−	3.24005i	0.00184377	−	0.00360807i
$899$	524.237	−	302.668i	0.583133	−	0.336672i
$900$		0			0
$901$	−429.145	+	743.300i	−0.476298	+	0.824973i
$902$	−44.6439	+	28.9173i	−0.0494943	+	0.0320591i
$903$		0			0
$904$	−8.85130	+	421.587i	−0.00979126	+	0.466357i
$905$	−832.349	+	302.950i	−0.919722	+	0.334752i
$906$		0			0
$907$	1150.73	−	202.904i	1.26872	−	0.223709i	0.501534	−	0.865138i	$-0.332769\pi$
$907$	1150.73	−	202.904i	1.26872	−	0.223709i	0.767183	+	0.641429i	$0.221658\pi$
$908$	−899.150	+	255.533i	−0.990254	+	0.281424i
$909$		0			0
$910$	180.846	−	239.403i	0.198732	−	0.263080i
$911$	958.819	+	1142.68i	1.05249	+	1.25431i	0.966133	+	0.258045i	$0.0830784\pi$
$911$	958.819	+	1142.68i	1.05249	+	1.25431i	0.0863578	+	0.996264i	$0.472477\pi$
$912$		0			0
$913$	195.719	−	1109.98i	0.214369	−	1.21575i
$914$	739.887	+	227.161i	0.809504	+	0.248535i
$915$		0			0
$916$	−155.010	+	75.1511i	−0.169225	+	0.0820427i
$917$	127.388			0.138918
$918$		0			0
$919$		−	1342.79i		−	1.46114i	−0.682839	−	0.730569i	$-0.739255\pi$
$919$		−	1342.79i		−	1.46114i	0.682839	−	0.730569i	$-0.260745\pi$
$920$	−1691.27	−	1480.73i	−1.83833	−	1.60949i
$921$		0			0
$922$	−632.911	−	194.317i	−0.686454	−	0.210756i
$923$	−1745.07	−	307.703i	−1.89065	−	0.333373i
$924$		0			0
$925$	447.496	−	375.493i	0.483779	−	0.405939i
$926$	−941.432	+	1246.26i	−1.01667	+	1.34585i
$927$		0			0
$928$	1138.23	+	106.350i	1.22654	+	0.114602i
$929$	141.299	+	801.344i	0.152097	+	0.862587i	0.961392	+	0.275184i	$0.0887387\pi$
$929$	141.299	+	801.344i	0.152097	+	0.862587i	−0.809294	+	0.587404i	$0.800150\pi$
$930$		0			0
$931$	−209.468	−	575.508i	−0.224992	−	0.618161i
$932$	−392.157	+	875.236i	−0.420770	+	0.939095i
$933$		0			0
$934$	−1120.90	+	726.043i	−1.20011	+	0.777348i
$935$	−765.833	−	442.154i	−0.819072	−	0.472892i
$936$		0			0
$937$	363.844	+	630.197i	0.388308	+	0.672569i	0.992222	−	0.124481i	$-0.0397264\pi$
$937$	363.844	+	630.197i	0.388308	+	0.672569i	−0.603914	+	0.797049i	$0.706393\pi$
$938$	117.222	−	229.393i	0.124971	−	0.244555i
$939$		0			0
$940$	1962.75	−	1418.96i	2.08804	−	1.50953i
$941$	20.7564	+	17.4167i	0.0220578	+	0.0185087i	0.653750	−	0.756711i	$-0.273195\pi$
$941$	20.7564	+	17.4167i	0.0220578	+	0.0185087i	−0.631692	+	0.775219i	$0.717639\pi$
$942$		0			0
$943$	−30.4382	+	83.6283i	−0.0322781	+	0.0886833i
$944$	24.5178	−	0.740373i	0.0259723	−	0.000784293i
$945$		0			0
$946$	125.461	−	53.0805i	0.132623	−	0.0561105i
$947$	−33.6923	+	92.5689i	−0.0355779	+	0.0977496i	−0.956210	−	0.292682i	$-0.905452\pi$
$947$	−33.6923	+	92.5689i	−0.0355779	+	0.0977496i	0.920632	+	0.390432i	$0.127674\pi$
$948$		0			0
$949$	−31.8917	−	26.7603i	−0.0336056	−	0.0281984i
$950$	893.071	−	205.072i	0.940075	−	0.215866i
$951$		0			0
$952$	97.7077	−	33.2572i	0.102634	−	0.0349340i
$953$	−2.38736	−	4.13503i	−0.00250510	−	0.00433896i	0.864770	−	0.502168i	$-0.167464\pi$
$953$	−2.38736	−	4.13503i	−0.00250510	−	0.00433896i	−0.867275	+	0.497829i	$0.834131\pi$
$954$		0			0
$955$	786.390	+	454.023i	0.823445	+	0.475416i
$956$	−858.883	+	1266.89i	−0.898413	+	1.32520i
$957$		0			0
$958$	−460.127	−	494.594i	−0.480299	−	0.516278i
$959$	−67.4773	−	185.392i	−0.0703621	−	0.193318i
$960$		0			0
$961$	117.019	+	663.645i	0.121767	+	0.690578i
$962$	−63.6728	+	513.564i	−0.0661879	+	0.533850i
$963$		0			0
$964$	317.701	+	80.0084i	0.329566	+	0.0829963i
$965$	−299.221	+	251.076i	−0.310073	+	0.260183i
$966$		0			0
$967$	−935.379	−	164.933i	−0.967300	−	0.170561i	−0.332386	−	0.943144i	$-0.607854\pi$
$967$	−935.379	−	164.933i	−0.967300	−	0.170561i	−0.634915	+	0.772582i	$0.718965\pi$
$968$	31.6851	−	17.4170i	0.0327325	−	0.0179928i
$969$		0			0
$970$	601.488	−	30.8112i	0.620090	−	0.0317641i
$971$		−	1531.25i		−	1.57699i	−0.615044	−	0.788493i	$-0.710862\pi$
$971$		−	1531.25i		−	1.57699i	0.615044	−	0.788493i	$-0.289138\pi$
$972$		0			0
$973$	17.7238			0.0182156
$974$	−66.6758	−	1301.63i	−0.0684557	−	1.33637i
$975$		0			0
$976$	−1026.34	+	1300.96i	−1.05158	+	1.33295i
$977$	−88.2189	+	500.314i	−0.0902957	+	0.512092i	0.905792	+	0.423722i	$0.139277\pi$
$977$	−88.2189	+	500.314i	−0.0902957	+	0.512092i	−0.996088	+	0.0883697i	$0.971834\pi$
$978$		0			0
$979$	−789.568	−	940.971i	−0.806505	−	0.961155i
$980$	1433.48	+	361.000i	1.46273	+	0.368367i
$981$		0			0
$982$	974.683	+	120.843i	0.992549	+	0.123058i
$983$	288.925	−	50.9453i	0.293922	−	0.0518264i	−0.0247428	−	0.999694i	$-0.507877\pi$
$983$	288.925	−	50.9453i	0.293922	−	0.0518264i	0.318665	+	0.947867i	$0.396766\pi$
$984$		0			0
$985$	−2510.63	+	913.794i	−2.54886	+	0.927710i
$986$	550.911	−	512.519i	0.558733	−	0.519796i
$987$		0			0
$988$	−455.505	+	671.890i	−0.461038	+	0.680050i
$989$	113.963	−	197.390i	0.115231	−	0.199586i
$990$		0			0
$991$	−1037.64	+	599.081i	−1.04706	+	0.604522i	−0.921825	−	0.387605i	$-0.873302\pi$
$991$	−1037.64	+	599.081i	−1.04706	+	0.604522i	−0.125237	+	0.992127i	$0.539969\pi$
$992$	232.049	−	490.062i	0.233920	−	0.494015i
$993$		0			0
$994$	61.7362	+	268.855i	0.0621089	+	0.270478i
$995$	−682.952	+	813.910i	−0.686384	+	0.818000i
$996$		0			0
$997$	1033.20	+	376.054i	1.03631	+	0.377186i	0.803480	−	0.595332i	$-0.202980\pi$
$997$	1033.20	+	376.054i	1.03631	+	0.377186i	0.232829	+	0.972518i	$0.425202\pi$
$998$	470.746	+	1112.65i	0.471689	+	1.11488i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.307.1		204
3.2	odd	2		108.3.j.a.31.34	yes	204
4.3	odd	2	inner	324.3.j.a.307.8		204
12.11	even	2		108.3.j.a.31.27	yes	204
27.7	even	9	inner	324.3.j.a.19.8		204
27.20	odd	18		108.3.j.a.7.27	✓	204
108.7	odd	18	inner	324.3.j.a.19.1		204
108.47	even	18		108.3.j.a.7.34	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.27	✓	204	27.20	odd	18
108.3.j.a.7.34	yes	204	108.47	even	18
108.3.j.a.31.27	yes	204	12.11	even	2
108.3.j.a.31.34	yes	204	3.2	odd	2
324.3.j.a.19.1		204	108.7	odd	18	inner
324.3.j.a.19.8		204	27.7	even	9	inner
324.3.j.a.307.1		204	1.1	even	1	trivial
324.3.j.a.307.8		204	4.3	odd	2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.99738 + 0.102316i) q^{2} +(3.97906 - 0.408727i) q^{4} +(-1.35104 + 7.66211i) q^{5} +(-0.787463 - 0.938462i) q^{7} +(-7.90589 + 1.22351i) q^{8} +O(q^{10})\)	\(q+(-1.99738 + 0.102316i) q^{2} +(3.97906 - 0.408727i) q^{4} +(-1.35104 + 7.66211i) q^{5} +(-0.787463 - 0.938462i) q^{7} +(-7.90589 + 1.22351i) q^{8} +(1.91458 - 15.4424i) q^{10} +(-10.6286 + 1.87412i) q^{11} +(-14.7898 + 5.38306i) q^{13} +(1.66888 + 1.79390i) q^{14} +(15.6659 - 3.25270i) q^{16} +(5.26562 - 9.12033i) q^{17} +(11.1663 - 6.44687i) q^{19} +(-2.24415 + 31.0402i) q^{20} +(21.0377 - 4.83081i) q^{22} +(23.2142 - 27.6656i) q^{23} +(-33.3903 - 12.1531i) q^{25} +(28.9902 - 12.2653i) q^{26} +(-3.51694 - 3.41234i) q^{28} +(-33.5701 - 12.2185i) q^{29} +(-10.8917 + 12.9803i) q^{31} +(-30.9579 + 8.09976i) q^{32} +(-9.58430 + 18.7555i) q^{34} +(8.25450 - 4.76574i) q^{35} +(-8.21996 + 14.2374i) q^{37} +(-21.6438 + 14.0194i) q^{38} +(1.30651 - 62.2288i) q^{40} +(-2.31562 + 0.842818i) q^{41} +(6.21529 - 1.09592i) q^{43} +(-41.5260 + 11.8014i) q^{44} +(-43.5369 + 57.6339i) q^{46} +(-50.0238 - 59.6160i) q^{47} +(8.24815 - 46.7776i) q^{49} +(67.9367 + 20.8580i) q^{50} +(-56.6495 + 27.4645i) q^{52} -81.4993 q^{53} -83.9699i q^{55} +(7.37381 + 6.45591i) q^{56} +(68.3025 + 20.9703i) q^{58} +(1.50977 + 0.266214i) q^{59} +(-79.3366 + 66.5713i) q^{61} +(20.4269 - 27.0409i) q^{62} +(61.0061 - 19.3458i) q^{64} +(-21.2640 - 120.594i) q^{65} +(-35.9599 - 98.7991i) q^{67} +(17.2245 - 38.4426i) q^{68} +(-15.9998 + 10.3636i) q^{70} +(97.5023 + 56.2930i) q^{71} +(1.32256 + 2.29075i) q^{73} +(14.9617 - 29.2785i) q^{74} +(41.7965 - 30.2165i) q^{76} +(10.1285 + 8.49879i) q^{77} +(-23.0193 + 63.2449i) q^{79} +(3.75740 + 124.428i) q^{80} +(4.53895 - 1.92035i) q^{82} +(-35.7180 + 98.1345i) q^{83} +(62.7669 + 52.6677i) q^{85} +(-12.3022 + 2.82490i) q^{86} +(81.7359 - 27.8208i) q^{88} +(56.9070 + 98.5658i) q^{89} +(16.6982 + 9.64074i) q^{91} +(81.0630 - 119.571i) q^{92} +(106.016 + 113.958i) q^{94} +(34.3106 + 94.2675i) q^{95} +(6.72108 + 38.1171i) q^{97} +(-11.6886 + 94.2766i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

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