LMFDB - Embedded newform 804.2.e.a.535.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.18
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.219472 + 1.39708i) q^{2} -1.00000 q^{3} +(-1.90366 - 0.613241i) q^{4} +3.15947i q^{5} +(0.219472 - 1.39708i) q^{6} +0.761043 q^{7} +(1.27455 - 2.52498i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.219472 + 1.39708i) q^{2} -1.00000 q^{3} +(-1.90366 - 0.613241i) q^{4} +3.15947i q^{5} +(0.219472 - 1.39708i) q^{6} +0.761043 q^{7} +(1.27455 - 2.52498i) q^{8} +1.00000 q^{9} +(-4.41403 - 0.693416i) q^{10} +5.14871 q^{11} +(1.90366 + 0.613241i) q^{12} +4.67319i q^{13} +(-0.167028 + 1.06324i) q^{14} -3.15947i q^{15} +(3.24787 + 2.33481i) q^{16} +1.78889 q^{17} +(-0.219472 + 1.39708i) q^{18} +5.49920i q^{19} +(1.93751 - 6.01456i) q^{20} -0.761043 q^{21} +(-1.13000 + 7.19316i) q^{22} -2.96158i q^{23} +(-1.27455 + 2.52498i) q^{24} -4.98223 q^{25} +(-6.52882 - 1.02564i) q^{26} -1.00000 q^{27} +(-1.44877 - 0.466703i) q^{28} -9.79158 q^{29} +(4.41403 + 0.693416i) q^{30} +3.67432 q^{31} +(-3.97473 + 4.02511i) q^{32} -5.14871 q^{33} +(-0.392611 + 2.49922i) q^{34} +2.40449i q^{35} +(-1.90366 - 0.613241i) q^{36} +8.38084 q^{37} +(-7.68282 - 1.20692i) q^{38} -4.67319i q^{39} +(7.97759 + 4.02689i) q^{40} -1.00221i q^{41} +(0.167028 - 1.06324i) q^{42} -7.22273 q^{43} +(-9.80142 - 3.15740i) q^{44} +3.15947i q^{45} +(4.13756 + 0.649985i) q^{46} -11.6884i q^{47} +(-3.24787 - 2.33481i) q^{48} -6.42081 q^{49} +(1.09346 - 6.96057i) q^{50} -1.78889 q^{51} +(2.86579 - 8.89618i) q^{52} +9.25172i q^{53} +(0.219472 - 1.39708i) q^{54} +16.2672i q^{55} +(0.969986 - 1.92162i) q^{56} -5.49920i q^{57} +(2.14898 - 13.6796i) q^{58} -0.539474i q^{59} +(-1.93751 + 6.01456i) q^{60} +2.35281i q^{61} +(-0.806411 + 5.13332i) q^{62} +0.761043 q^{63} +(-4.75105 - 6.43642i) q^{64} -14.7648 q^{65} +(1.13000 - 7.19316i) q^{66} +(-8.09955 + 1.18208i) q^{67} +(-3.40544 - 1.09702i) q^{68} +2.96158i q^{69} +(-3.35927 - 0.527719i) q^{70} +11.8375i q^{71} +(1.27455 - 2.52498i) q^{72} -7.50732 q^{73} +(-1.83936 + 11.7087i) q^{74} +4.98223 q^{75} +(3.37233 - 10.4686i) q^{76} +3.91839 q^{77} +(6.52882 + 1.02564i) q^{78} +4.41239 q^{79} +(-7.37675 + 10.2615i) q^{80} +1.00000 q^{81} +(1.40016 + 0.219956i) q^{82} -8.49721i q^{83} +(1.44877 + 0.466703i) q^{84} +5.65193i q^{85} +(1.58519 - 10.0907i) q^{86} +9.79158 q^{87} +(6.56228 - 13.0004i) q^{88} +13.5366 q^{89} +(-4.41403 - 0.693416i) q^{90} +3.55650i q^{91} +(-1.81616 + 5.63785i) q^{92} -3.67432 q^{93} +(16.3297 + 2.56529i) q^{94} -17.3745 q^{95} +(3.97473 - 4.02511i) q^{96} +8.80067i q^{97} +(1.40919 - 8.97039i) q^{98} +5.14871 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	$ 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) $ 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.219472	+	1.39708i	−0.155190	+	0.987885i
$2$	−0.219472	+	1.39708i	−0.155190	+	0.987885i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.90366	−	0.613241i	−0.951832	−	0.306620i
$5$			3.15947i			1.41296i	0.707735	+	0.706478i	$0.249717\pi$
$5$			3.15947i			1.41296i	−0.707735	+	0.706478i	$0.750283\pi$
$6$	0.219472	−	1.39708i	0.0895992	−	0.570355i
$7$	0.761043			0.287647			0.143824	−	0.989603i	$-0.454060\pi$
$7$	0.761043			0.287647			0.143824	+	0.989603i	$0.454060\pi$
$8$	1.27455	−	2.52498i	0.450621	−	0.892715i
$9$	1.00000			0.333333
$10$	−4.41403	−	0.693416i	−1.39584	−	0.219277i
$11$	5.14871			1.55239			0.776197	−	0.630490i	$-0.217146\pi$
$11$	5.14871			1.55239			0.776197	+	0.630490i	$0.217146\pi$
$12$	1.90366	+	0.613241i	0.549540	+	0.177027i
$13$			4.67319i			1.29611i	0.761594	+	0.648055i	$0.224417\pi$
$13$			4.67319i			1.29611i	−0.761594	+	0.648055i	$0.775583\pi$
$14$	−0.167028	+	1.06324i	−0.0446401	+	0.284162i
$15$		−	3.15947i		−	0.815771i
$16$	3.24787	+	2.33481i	0.811968	+	0.583702i
$17$	1.78889			0.433869			0.216934	−	0.976186i	$-0.430394\pi$
$17$	1.78889			0.433869			0.216934	+	0.976186i	$0.430394\pi$
$18$	−0.219472	+	1.39708i	−0.0517301	+	0.329295i
$19$			5.49920i			1.26160i	0.775945	+	0.630801i	$0.217274\pi$
$19$			5.49920i			1.26160i	−0.775945	+	0.630801i	$0.782726\pi$
$20$	1.93751	−	6.01456i	0.433241	−	1.34490i
$21$	−0.761043			−0.166073
$22$	−1.13000	+	7.19316i	−0.240917	+	1.53359i
$23$		−	2.96158i		−	0.617532i	−0.951138	−	0.308766i	$-0.900084\pi$
$23$		−	2.96158i		−	0.617532i	0.951138	−	0.308766i	$-0.0999160\pi$
$24$	−1.27455	+	2.52498i	−0.260166	+	0.515410i
$25$	−4.98223			−0.996445
$26$	−6.52882	−	1.02564i	−1.28041	−	0.201144i
$27$	−1.00000			−0.192450
$28$	−1.44877	−	0.466703i	−0.273792	−	0.0881985i
$29$	−9.79158			−1.81825			−0.909125	−	0.416523i	$-0.863249\pi$
$29$	−9.79158			−1.81825			−0.909125	+	0.416523i	$0.863249\pi$
$30$	4.41403	+	0.693416i	0.805887	+	0.126600i
$31$	3.67432			0.659927			0.329963	−	0.943994i	$-0.392964\pi$
$31$	3.67432			0.659927			0.329963	+	0.943994i	$0.392964\pi$
$32$	−3.97473	+	4.02511i	−0.702640	+	0.711546i
$33$	−5.14871			−0.896276
$34$	−0.392611	+	2.49922i	−0.0673323	+	0.428612i
$35$			2.40449i			0.406433i
$36$	−1.90366	−	0.613241i	−0.317277	−	0.102207i
$37$	8.38084			1.37780			0.688901	−	0.724856i	$-0.258094\pi$
$37$	8.38084			1.37780			0.688901	+	0.724856i	$0.258094\pi$
$38$	−7.68282	−	1.20692i	−1.24632	−	0.195789i
$39$		−	4.67319i		−	0.748309i
$40$	7.97759	+	4.02689i	1.26137	+	0.636707i
$41$		−	1.00221i		−	0.156518i	−0.996933	−	0.0782591i	$-0.975064\pi$
$41$		−	1.00221i		−	0.156518i	0.996933	−	0.0782591i	$-0.0249361\pi$
$42$	0.167028	−	1.06324i	0.0257730	−	0.164061i
$43$	−7.22273			−1.10146			−0.550728	−	0.834685i	$-0.685650\pi$
$43$	−7.22273			−1.10146			−0.550728	+	0.834685i	$0.685650\pi$
$44$	−9.80142	−	3.15740i	−1.47762	−	0.475996i
$45$			3.15947i			0.470985i
$46$	4.13756	+	0.649985i	0.610050	+	0.0958350i
$47$		−	11.6884i		−	1.70493i	−0.522781	−	0.852467i	$-0.675106\pi$
$47$		−	11.6884i		−	1.70493i	0.522781	−	0.852467i	$-0.324894\pi$
$48$	−3.24787	−	2.33481i	−0.468790	−	0.337001i
$49$	−6.42081			−0.917259
$50$	1.09346	−	6.96057i	0.154639	−	0.984373i
$51$	−1.78889			−0.250494
$52$	2.86579	−	8.89618i	0.397414	−	1.23368i
$53$			9.25172i			1.27082i	0.772174	+	0.635411i	$0.219169\pi$
$53$			9.25172i			1.27082i	−0.772174	+	0.635411i	$0.780831\pi$
$54$	0.219472	−	1.39708i	0.0298664	−	0.190118i
$55$			16.2672i			2.19347i
$56$	0.969986	−	1.92162i	0.129620	−	0.256787i
$57$		−	5.49920i		−	0.728386i
$58$	2.14898	−	13.6796i	0.282175	−	1.79622i
$59$		−	0.539474i		−	0.0702335i	−0.999383	−	0.0351168i	$-0.988820\pi$
$59$		−	0.539474i		−	0.0702335i	0.999383	−	0.0351168i	$-0.0111803\pi$
$60$	−1.93751	+	6.01456i	−0.250132	+	0.776477i
$61$			2.35281i			0.301247i	0.988591	+	0.150624i	$0.0481281\pi$
$61$			2.35281i			0.301247i	−0.988591	+	0.150624i	$0.951872\pi$
$62$	−0.806411	+	5.13332i	−0.102414	+	0.651932i
$63$	0.761043			0.0958824
$64$	−4.75105	−	6.43642i	−0.593882	−	0.804552i
$65$	−14.7648			−1.83135
$66$	1.13000	−	7.19316i	0.139093	−	0.885417i
$67$	−8.09955	+	1.18208i	−0.989517	+	0.144415i
$67$	−8.09955	+	1.18208i	−0.989517	+	0.144415i
$68$	−3.40544	−	1.09702i	−0.412970	−	0.133033i
$69$			2.96158i			0.356532i
$70$	−3.35927	−	0.527719i	−0.401509	−	0.0630745i
$71$			11.8375i			1.40486i	0.711754	+	0.702429i	$0.247901\pi$
$71$			11.8375i			1.40486i	−0.711754	+	0.702429i	$0.752099\pi$
$72$	1.27455	−	2.52498i	0.150207	−	0.297572i
$73$	−7.50732			−0.878665			−0.439333	−	0.898324i	$-0.644785\pi$
$73$	−7.50732			−0.878665			−0.439333	+	0.898324i	$0.644785\pi$
$74$	−1.83936	+	11.7087i	−0.213822	+	1.36111i
$75$	4.98223			0.575298
$76$	3.37233	−	10.4686i	0.386833	−	1.20083i
$77$	3.91839			0.446542
$78$	6.52882	+	1.02564i	0.739243	+	0.116130i
$79$	4.41239			0.496432			0.248216	−	0.968705i	$-0.420156\pi$
$79$	4.41239			0.496432			0.248216	+	0.968705i	$0.420156\pi$
$80$	−7.37675	+	10.2615i	−0.824746	+	1.14728i
$81$	1.00000			0.111111
$82$	1.40016	+	0.219956i	0.154622	+	0.0242901i
$83$		−	8.49721i		−	0.932689i	−0.884603	−	0.466345i	$-0.845571\pi$
$83$		−	8.49721i		−	0.932689i	0.884603	−	0.466345i	$-0.154429\pi$
$84$	1.44877	+	0.466703i	0.158074	+	0.0509215i
$85$			5.65193i			0.613038i
$86$	1.58519	−	10.0907i	0.170935	−	1.08811i
$87$	9.79158			1.04977
$88$	6.56228	−	13.0004i	0.699541	−	1.38585i
$89$	13.5366			1.43488			0.717439	−	0.696622i	$-0.245314\pi$
$89$	13.5366			1.43488			0.717439	+	0.696622i	$0.245314\pi$
$90$	−4.41403	−	0.693416i	−0.465279	−	0.0730924i
$91$			3.55650i			0.372823i
$92$	−1.81616	+	5.63785i	−0.189348	+	0.587786i
$93$	−3.67432			−0.381009
$94$	16.3297	+	2.56529i	1.68428	+	0.264589i
$95$	−17.3745			−1.78259
$96$	3.97473	−	4.02511i	0.405669	−	0.410811i
$97$			8.80067i			0.893572i	0.894641	+	0.446786i	$0.147431\pi$
$97$			8.80067i			0.893572i	−0.894641	+	0.446786i	$0.852569\pi$
$98$	1.40919	−	8.97039i	0.142350	−	0.906146i
$99$	5.14871			0.517465
$100$	9.48449	+	3.05531i	0.948449	+	0.305531i
$101$			2.11655i			0.210604i	0.994440	+	0.105302i	$0.0335810\pi$
$101$			2.11655i			0.210604i	−0.994440	+	0.105302i	$0.966419\pi$
$102$	0.392611	−	2.49922i	0.0388743	−	0.247459i
$103$			3.03894i			0.299436i	0.988729	+	0.149718i	$0.0478366\pi$
$103$			3.03894i			0.299436i	−0.988729	+	0.149718i	$0.952163\pi$
$104$	11.7997	+	5.95621i	1.15706	+	0.584054i
$105$		−	2.40449i		−	0.234654i
$106$	−12.9254	−	2.03050i	−1.25542	−	0.197219i
$107$		−	0.802128i		−	0.0775447i	−0.999248	−	0.0387723i	$-0.987655\pi$
$107$		−	0.802128i		−	0.0775447i	0.999248	−	0.0387723i	$-0.0123447\pi$
$108$	1.90366	+	0.613241i	0.183180	+	0.0590091i
$109$			3.94940i			0.378284i	0.981950	+	0.189142i	$0.0605707\pi$
$109$			3.94940i			0.378284i	−0.981950	+	0.189142i	$0.939429\pi$
$110$	−22.7265	−	3.57020i	−2.16689	−	0.340405i
$111$	−8.38084			−0.795474
$112$	2.47177	+	1.77689i	0.233560	+	0.167900i
$113$		−	5.98304i		−	0.562837i	−0.959585	−	0.281419i	$-0.909195\pi$
$113$		−	5.98304i		−	0.562837i	0.959585	−	0.281419i	$-0.0908050\pi$
$114$	7.68282	+	1.20692i	0.719562	+	0.113039i
$115$	9.35701			0.872545
$116$	18.6399	+	6.00460i	1.73067	+	0.557513i
$117$			4.67319i			0.432037i
$118$	0.753688	+	0.118400i	0.0693826	+	0.0108996i
$119$	1.36142			0.124801
$120$	−7.97759	−	4.02689i	−0.728251	−	0.367603i
$121$	15.5092			1.40993
$122$	−3.28707	−	0.516378i	−0.297597	−	0.0467507i
$123$			1.00221i			0.0903658i
$124$	−6.99467	−	2.25324i	−0.628140	−	0.202347i
$125$			0.0561519i			0.00502238i
$126$	−0.167028	+	1.06324i	−0.0148800	+	0.0947208i
$127$		−	3.50210i		−	0.310761i	−0.987855	−	0.155381i	$-0.950340\pi$
$127$		−	3.50210i		−	0.310761i	0.987855	−	0.155381i	$-0.0496604\pi$
$128$	10.0349	−	5.22499i	0.886970	−	0.461828i
$129$	7.22273			0.635926
$130$	3.24046	−	20.6276i	0.284207	−	1.80916i
$131$		−	16.7878i		−	1.46676i	−0.679820	−	0.733379i	$-0.737942\pi$
$131$		−	16.7878i		−	1.46676i	0.679820	−	0.733379i	$-0.262058\pi$
$132$	9.80142	+	3.15740i	0.853104	+	0.274816i
$133$			4.18513i			0.362896i
$134$	0.126160	−	11.5751i	0.0108986	−	0.999941i
$135$		−	3.15947i		−	0.271924i
$136$	2.28002	−	4.51690i	0.195510	−	0.387321i
$137$			3.76333i			0.321523i	0.986993	+	0.160762i	$0.0513950\pi$
$137$			3.76333i			0.321523i	−0.986993	+	0.160762i	$0.948605\pi$
$138$	−4.13756	−	0.649985i	−0.352213	−	0.0553304i
$139$	11.5820			0.982371			0.491186	−	0.871055i	$-0.336564\pi$
$139$	11.5820			0.982371			0.491186	+	0.871055i	$0.336564\pi$
$140$	1.47453	−	4.57734i	0.124621	−	0.386856i
$141$			11.6884i			0.984344i
$142$	−16.5380	−	2.59801i	−1.38784	−	0.218020i
$143$			24.0609i			2.01207i
$144$	3.24787	+	2.33481i	0.270656	+	0.194567i
$145$		−	30.9362i		−	2.56911i
$146$	1.64765	−	10.4883i	0.136360	−	0.868020i
$147$	6.42081			0.529580
$148$	−15.9543	−	5.13947i	−1.31144	−	0.422462i
$149$	−1.02591			−0.0840456			−0.0420228	−	0.999117i	$-0.513380\pi$
$149$	−1.02591			−0.0840456			−0.0420228	+	0.999117i	$0.513380\pi$
$150$	−1.09346	+	6.96057i	−0.0892807	+	0.568328i
$151$			5.39710i			0.439210i	0.975589	+	0.219605i	$0.0704768\pi$
$151$			5.39710i			0.439210i	−0.975589	+	0.219605i	$0.929523\pi$
$152$	13.8854	+	7.00899i	1.12625	+	0.568504i
$153$	1.78889			0.144623
$154$	−0.859979	+	5.47431i	−0.0692991	+	0.441132i
$155$			11.6089i			0.932448i
$156$	−2.86579	+	8.89618i	−0.229447	+	0.712265i
$157$	21.7154			1.73308			0.866540	−	0.499107i	$-0.166339\pi$
$157$	21.7154			1.73308			0.866540	+	0.499107i	$0.166339\pi$
$158$	−0.968397	+	6.16446i	−0.0770415	+	0.490418i
$159$		−	9.25172i		−	0.733709i
$160$	−12.7172	−	12.5580i	−1.00538	−	0.992800i
$161$		−	2.25389i		−	0.177631i
$162$	−0.219472	+	1.39708i	−0.0172434	+	0.109765i
$163$		−	12.4095i		−	0.971985i	−0.873963	−	0.485992i	$-0.838458\pi$
$163$		−	12.4095i		−	0.971985i	0.873963	−	0.485992i	$-0.161542\pi$
$164$	−0.614593	+	1.90786i	−0.0479917	+	0.148979i
$165$		−	16.2672i		−	1.26640i
$166$	11.8713	+	1.86490i	0.921390	+	0.144744i
$167$		−	23.7645i		−	1.83895i	−0.393147	−	0.919476i	$-0.628614\pi$
$167$		−	23.7645i		−	1.83895i	0.393147	−	0.919476i	$-0.371386\pi$
$168$	−0.969986	+	1.92162i	−0.0748361	+	0.148256i
$169$	−8.83872			−0.679901
$170$	−7.89619	−	1.24044i	−0.605610	−	0.0951375i
$171$			5.49920i			0.420534i
$172$	13.7497	+	4.42927i	1.04840	+	0.337729i
$173$	21.5848			1.64106			0.820529	−	0.571604i	$-0.193679\pi$
$173$	21.5848			1.64106			0.820529	+	0.571604i	$0.193679\pi$
$174$	−2.14898	+	13.6796i	−0.162914	+	1.03705i
$175$	−3.79169			−0.286625
$176$	16.7224	+	12.0213i	1.26049	+	0.906136i
$177$			0.539474i			0.0405494i
$178$	−2.97091	+	18.9117i	−0.222679	+	1.41749i
$179$	−25.0137			−1.86961			−0.934806	−	0.355159i	$-0.884427\pi$
$179$	−25.0137			−1.86961			−0.934806	+	0.355159i	$0.884427\pi$
$180$	1.93751	−	6.01456i	0.144414	−	0.448299i
$181$	7.26648			0.540113			0.270057	−	0.962844i	$-0.412958\pi$
$181$	7.26648			0.540113			0.270057	+	0.962844i	$0.412958\pi$
$182$	−4.96872	−	0.780554i	−0.368306	−	0.0578585i
$183$		−	2.35281i		−	0.173925i
$184$	−7.47793	−	3.77467i	−0.551280	−	0.278273i
$185$			26.4790i			1.94677i
$186$	0.806411	−	5.13332i	0.0591289	−	0.376393i
$187$	9.21046			0.673536
$188$	−7.16783	+	22.2509i	−0.522767	+	1.62281i
$189$	−0.761043			−0.0553578
$190$	3.81323	−	24.2736i	0.276641	−	1.76099i
$191$	−15.0240			−1.08710			−0.543548	−	0.839378i	$-0.682919\pi$
$191$	−15.0240			−1.08710			−0.543548	+	0.839378i	$0.682919\pi$
$192$	4.75105	+	6.43642i	0.342878	+	0.464508i
$193$	−7.14965			−0.514643			−0.257322	−	0.966326i	$-0.582840\pi$
$193$	−7.14965			−0.514643			−0.257322	+	0.966326i	$0.582840\pi$
$194$	−12.2952	−	1.93150i	−0.882746	−	0.138674i
$195$	14.7648			1.05733
$196$	12.2231	+	3.93750i	0.873076	+	0.281250i
$197$			0.740496i			0.0527582i	0.999652	+	0.0263791i	$0.00839770\pi$
$197$			0.740496i			0.0527582i	−0.999652	+	0.0263791i	$0.991602\pi$
$198$	−1.13000	+	7.19316i	−0.0803056	+	0.511196i
$199$			13.5738i			0.962219i	0.876660	+	0.481110i	$0.159766\pi$
$199$			13.5738i			0.962219i	−0.876660	+	0.481110i	$0.840234\pi$
$200$	−6.35009	+	12.5800i	−0.449019	+	0.889542i
$201$	8.09955	−	1.18208i	0.571298	−	0.0833778i
$202$	−2.95699	−	0.464524i	−0.208053	−	0.0326838i
$203$	−7.45181			−0.523015
$204$	3.40544	+	1.09702i	0.238428	+	0.0768066i
$205$	3.16643			0.221153
$206$	−4.24565	−	0.666964i	−0.295808	−	0.0464696i
$207$		−	2.96158i		−	0.205844i
$208$	−10.9110	+	15.1779i	−0.756542	+	1.05240i
$209$			28.3138i			1.95850i
$210$	3.35927	+	0.527719i	0.231811	+	0.0364161i
$211$			26.1007i			1.79685i	0.439131	+	0.898423i	$0.355286\pi$
$211$			26.1007i			1.79685i	−0.439131	+	0.898423i	$0.644714\pi$
$212$	5.67353	−	17.6122i	0.389660	−	1.20961i
$213$		−	11.8375i		−	0.811095i
$214$	1.12064	+	0.176045i	0.0766052	+	0.0120342i
$215$		−	22.8200i		−	1.55631i
$216$	−1.27455	+	2.52498i	−0.0867220	+	0.171803i
$217$	2.79632			0.189826
$218$	−5.51763	−	0.866785i	−0.373701	−	0.0587061i
$219$	7.50732			0.507298
$220$	9.97570	−	30.9672i	0.672562	−	2.08781i
$221$			8.35981i			0.562342i
$222$	1.83936	−	11.7087i	0.123450	−	0.785836i
$223$			12.4915i			0.836490i	0.908334	+	0.418245i	$0.137355\pi$
$223$			12.4915i			0.836490i	−0.908334	+	0.418245i	$0.862645\pi$
$224$	−3.02494	+	3.06328i	−0.202113	+	0.204674i
$225$	−4.98223			−0.332148
$226$	8.35879	+	1.31311i	0.556018	+	0.0873469i
$227$		−	19.5880i		−	1.30010i	−0.759892	−	0.650050i	$-0.774748\pi$
$227$		−	19.5880i		−	1.30010i	0.759892	−	0.650050i	$-0.225252\pi$
$228$	−3.37233	+	10.4686i	−0.223338	+	0.693301i
$229$			20.1069i			1.32870i	0.747421	+	0.664351i	$0.231292\pi$
$229$			20.1069i			1.32870i	−0.747421	+	0.664351i	$0.768708\pi$
$230$	−2.05360	+	13.0725i	−0.135411	+	0.861974i
$231$	−3.91839			−0.257811
$232$	−12.4798	+	24.7235i	−0.819341	+	1.62318i
$233$		−	10.1151i		−	0.662662i	−0.943515	−	0.331331i	$-0.892502\pi$
$233$		−	10.1151i		−	0.662662i	0.943515	−	0.331331i	$-0.107498\pi$
$234$	−6.52882	−	1.02564i	−0.426802	−	0.0670479i
$235$	36.9292			2.40900
$236$	−0.330828	+	1.02698i	−0.0215350	+	0.0668505i
$237$	−4.41239			−0.286615
$238$	−0.298794	+	1.90201i	−0.0193679	+	0.123289i
$239$	10.4706			0.677286			0.338643	−	0.940915i	$-0.390032\pi$
$239$	10.4706			0.677286			0.338643	+	0.940915i	$0.390032\pi$
$240$	7.37675	−	10.2615i	0.476167	−	0.662380i
$241$	12.9470			0.833989			0.416994	−	0.908909i	$-0.363083\pi$
$241$	12.9470			0.833989			0.416994	+	0.908909i	$0.363083\pi$
$242$	−3.40385	+	21.6676i	−0.218808	+	1.39285i
$243$	−1.00000			−0.0641500
$244$	1.44284	−	4.47897i	0.0923685	−	0.286737i
$245$		−	20.2863i		−	1.29605i
$246$	−1.40016	−	0.219956i	−0.0892710	−	0.0140239i
$247$	−25.6988			−1.63518
$248$	4.68309	−	9.27758i	0.297377	−	0.589127i
$249$			8.49721i			0.538489i
$250$	−0.0784487	−	0.0123238i	−0.00496153	−	0.000779425i
$251$	16.0783			1.01485			0.507425	−	0.861696i	$-0.330597\pi$
$251$	16.0783			1.01485			0.507425	+	0.861696i	$0.330597\pi$
$252$	−1.44877	−	0.466703i	−0.0912640	−	0.0293995i
$253$		−	15.2483i		−	0.958653i
$254$	4.89272	+	0.768615i	0.306996	+	0.0482272i
$255$		−	5.65193i		−	0.353937i
$256$	5.09734	+	15.1663i	0.318584	+	0.947895i
$257$	−8.88242			−0.554070			−0.277035	−	0.960860i	$-0.589352\pi$
$257$	−8.88242			−0.554070			−0.277035	+	0.960860i	$0.589352\pi$
$258$	−1.58519	+	10.0907i	−0.0986896	+	0.628222i
$259$	6.37818			0.396321
$260$	28.1072	+	9.05437i	1.74313	+	0.561528i
$261$	−9.79158			−0.606083
$262$	23.4539	+	3.68446i	1.44899	+	0.227627i
$263$			13.4038i			0.826517i	0.910614	+	0.413258i	$0.135609\pi$
$263$			13.4038i			0.826517i	−0.910614	+	0.413258i	$0.864391\pi$
$264$	−6.56228	+	13.0004i	−0.403880	+	0.800119i
$265$	−29.2305			−1.79561
$266$	−5.84696	−	0.918520i	−0.358500	−	0.0563181i
$267$	−13.5366			−0.828427
$268$	16.1437	+	2.71668i	0.986135	+	0.165948i
$269$	2.97179			0.181193			0.0905967	−	0.995888i	$-0.471123\pi$
$269$	2.97179			0.181193			0.0905967	+	0.995888i	$0.471123\pi$
$270$	4.41403	+	0.693416i	0.268629	+	0.0421999i
$271$	3.46516			0.210494			0.105247	−	0.994446i	$-0.466437\pi$
$271$	3.46516			0.210494			0.105247	+	0.994446i	$0.466437\pi$
$272$	5.81007	+	4.17671i	0.352287	+	0.253250i
$273$		−	3.55650i		−	0.215249i
$274$	−5.25768	−	0.825948i	−0.317628	−	0.0498973i
$275$	−25.6521			−1.54688
$276$	1.81616	−	5.63785i	0.109320	−	0.339359i
$277$	16.7532			1.00660			0.503302	−	0.864111i	$-0.332118\pi$
$277$	16.7532			1.00660			0.503302	+	0.864111i	$0.332118\pi$
$278$	−2.54193	+	16.1810i	−0.152455	+	0.970469i
$279$	3.67432			0.219976
$280$	6.07129	+	3.06464i	0.362829	+	0.183147i
$281$		−	30.6334i		−	1.82743i	−0.406351	−	0.913717i	$-0.633199\pi$
$281$		−	30.6334i		−	1.82743i	0.406351	−	0.913717i	$-0.366801\pi$
$282$	−16.3297	−	2.56529i	−0.972418	−	0.152761i
$283$		−	19.2949i		−	1.14696i	−0.819218	−	0.573482i	$-0.805592\pi$
$283$		−	19.2949i		−	1.14696i	0.819218	−	0.573482i	$-0.194408\pi$
$284$	7.25926	−	22.5347i	0.430758	−	1.33719i
$285$	17.3745			1.02918
$286$	−33.6150	−	5.28071i	−1.98770	−	0.312255i
$287$		−	0.762722i		−	0.0450220i
$288$	−3.97473	+	4.02511i	−0.234213	+	0.237182i
$289$	−13.7999			−0.811758
$290$	43.2203	+	6.78963i	2.53798	+	0.398701i
$291$		−	8.80067i		−	0.515904i
$292$	14.2914	+	4.60380i	0.836342	+	0.269417i
$293$	−32.3179			−1.88803			−0.944017	−	0.329898i	$-0.892986\pi$
$293$	−32.3179			−1.88803			−0.944017	+	0.329898i	$0.892986\pi$
$294$	−1.40919	+	8.97039i	−0.0821857	+	0.523164i
$295$	1.70445			0.0992369
$296$	10.6818	−	21.1615i	0.620866	−	1.22998i
$297$	−5.14871			−0.298759
$298$	0.225158	−	1.43327i	0.0130431	−	0.0830274i
$299$	13.8400			0.800389
$300$	−9.48449	−	3.05531i	−0.547587	−	0.176398i
$301$	−5.49681			−0.316831
$302$	−7.54018	−	1.18451i	−0.433889	−	0.0681611i
$303$		−	2.11655i		−	0.121593i
$304$	−12.8396	+	17.8607i	−0.736400	+	1.02438i
$305$	−7.43364			−0.425649
$306$	−0.392611	+	2.49922i	−0.0224441	+	0.142871i
$307$		−	4.06916i		−	0.232239i	−0.993235	−	0.116120i	$-0.962954\pi$
$307$		−	4.06916i		−	0.232239i	0.993235	−	0.116120i	$-0.0370456\pi$
$308$	−7.45930	−	2.40292i	−0.425033	−	0.136919i
$309$		−	3.03894i		−	0.172880i
$310$	−16.2185	−	2.54783i	−0.921151	−	0.144707i
$311$	22.5473			1.27854			0.639270	−	0.768982i	$-0.279237\pi$
$311$	22.5473			1.27854			0.639270	+	0.768982i	$0.279237\pi$
$312$	−11.7997	−	5.95621i	−0.668027	−	0.337204i
$313$		−	20.6491i		−	1.16716i	−0.812057	−	0.583578i	$-0.801652\pi$
$313$		−	20.6491i		−	1.16716i	0.812057	−	0.583578i	$-0.198348\pi$
$314$	−4.76594	+	30.3382i	−0.268957	+	1.71208i
$315$			2.40449i			0.135478i
$316$	−8.39970	−	2.70586i	−0.472520	−	0.152216i
$317$	13.8868			0.779962			0.389981	−	0.920823i	$-0.372482\pi$
$317$	13.8868			0.779962			0.389981	+	0.920823i	$0.372482\pi$
$318$	12.9254	+	2.03050i	0.724820	+	0.113865i
$319$	−50.4140			−2.82264
$320$	20.3356	−	15.0108i	1.13680	−	0.839129i
$321$			0.802128i			0.0447704i
$322$	3.14886	+	0.494666i	0.175479	+	0.0275667i
$323$			9.83744i			0.547370i
$324$	−1.90366	−	0.613241i	−0.105759	−	0.0340689i
$325$		−	23.2829i		−	1.29150i
$326$	17.3370	+	2.72354i	0.960209	+	0.150843i
$327$		−	3.94940i		−	0.218402i
$328$	−2.53055	−	1.27736i	−0.139726	−	0.0705303i
$329$		−	8.89541i		−	0.490420i
$330$	22.7265	+	3.57020i	1.25106	+	0.196533i
$331$	−6.20476			−0.341044			−0.170522	−	0.985354i	$-0.554545\pi$
$331$	−6.20476			−0.341044			−0.170522	+	0.985354i	$0.554545\pi$
$332$	−5.21083	+	16.1758i	−0.285982	+	0.887764i
$333$	8.38084			0.459267
$334$	33.2009	+	5.21565i	1.81667	+	0.285388i
$335$	−3.73476	−	25.5902i	−0.204052	−	1.39814i
$336$	−2.47177	−	1.77689i	−0.134846	−	0.0969373i
$337$			17.2073i			0.937343i	0.883373	+	0.468672i	$0.155267\pi$
$337$			17.2073i			0.937343i	−0.883373	+	0.468672i	$0.844733\pi$
$338$	1.93985	−	12.3484i	0.105514	−	0.671664i
$339$			5.98304i			0.324954i
$340$	3.46599	−	10.7594i	0.187970	−	0.583509i
$341$	18.9180			1.02447
$342$	−7.68282	−	1.20692i	−0.415439	−	0.0652628i
$343$	−10.2138			−0.551494
$344$	−9.20572	+	18.2373i	−0.496339	+	0.983287i
$345$	−9.35701			−0.503764
$346$	−4.73726	+	30.1556i	−0.254677	+	1.62118i
$347$	1.25418			0.0673279			0.0336639	−	0.999433i	$-0.489282\pi$
$347$	1.25418			0.0673279			0.0336639	+	0.999433i	$0.489282\pi$
$348$	−18.6399	−	6.00460i	−0.999202	−	0.321880i
$349$	−20.6929			−1.10767			−0.553833	−	0.832628i	$-0.686835\pi$
$349$	−20.6929			−1.10767			−0.553833	+	0.832628i	$0.686835\pi$
$350$	0.832171	−	5.29729i	0.0444814	−	0.283152i
$351$		−	4.67319i		−	0.249436i
$352$	−20.4647	+	20.7241i	−1.09077	+	1.10460i
$353$		−	12.0262i		−	0.640089i	−0.947403	−	0.320044i	$-0.896302\pi$
$353$		−	12.0262i		−	0.640089i	0.947403	−	0.320044i	$-0.103698\pi$
$354$	−0.753688	−	0.118400i	−0.0400581	−	0.00629287i
$355$	−37.4003			−1.98500
$356$	−25.7691	−	8.30120i	−1.36576	−	0.439963i
$357$	−1.36142			−0.0720540
$358$	5.48982	−	34.9461i	0.290146	−	1.84696i
$359$			11.0056i			0.580854i	0.956897	+	0.290427i	$0.0937973\pi$
$359$			11.0056i			0.580854i	−0.956897	+	0.290427i	$0.906203\pi$
$360$	7.97759	+	4.02689i	0.420456	+	0.212236i
$361$	−11.2412			−0.591640
$362$	−1.59479	+	10.1519i	−0.0838204	+	0.533570i
$363$	−15.5092			−0.814024
$364$	2.18099	−	6.77038i	0.114315	−	0.354864i
$365$		−	23.7191i		−	1.24152i
$366$	3.28707	+	0.516378i	0.171818	+	0.0269915i
$367$	−13.4477			−0.701965			−0.350982	−	0.936382i	$-0.614152\pi$
$367$	−13.4477			−0.701965			−0.350982	+	0.936382i	$0.614152\pi$
$368$	6.91472	−	9.61883i	0.360455	−	0.501416i
$369$		−	1.00221i		−	0.0521727i
$370$	−36.9932	−	5.81140i	−1.92319	−	0.302120i
$371$			7.04096i			0.365548i
$372$	6.99467	+	2.25324i	0.362657	+	0.116825i
$373$		−	35.9353i		−	1.86066i	−0.366725	−	0.930329i	$-0.619521\pi$
$373$		−	35.9353i		−	1.86066i	0.366725	−	0.930329i	$-0.380479\pi$
$374$	−2.02144	+	12.8677i	−0.104526	+	0.665375i
$375$		−	0.0561519i		−	0.00289967i
$376$	−29.5131	−	14.8975i	−1.52202	−	0.768278i
$377$		−	45.7579i		−	2.35665i
$378$	0.167028	−	1.06324i	0.00859099	−	0.0546871i
$379$	29.3622			1.50824			0.754118	−	0.656739i	$-0.228065\pi$
$379$	29.3622			1.50824			0.754118	+	0.656739i	$0.228065\pi$
$380$	33.0753	+	10.6548i	1.69672	+	0.546578i
$381$			3.50210i			0.179418i
$382$	3.29734	−	20.9897i	0.168707	−	1.07393i
$383$	22.1970			1.13421			0.567107	−	0.823644i	$-0.308063\pi$
$383$	22.1970			1.13421			0.567107	+	0.823644i	$0.308063\pi$
$384$	−10.0349	+	5.22499i	−0.512092	+	0.266636i
$385$			12.3800i			0.630945i
$386$	1.56915	−	9.98863i	0.0798677	−	0.508408i
$387$	−7.22273			−0.367152
$388$	5.39693	−	16.7535i	0.273987	−	0.850530i
$389$	−6.29515			−0.319177			−0.159588	−	0.987184i	$-0.551017\pi$
$389$	−6.29515			−0.319177			−0.159588	+	0.987184i	$0.551017\pi$
$390$	−3.24046	+	20.6276i	−0.164087	+	1.04452i
$391$		−	5.29793i		−	0.267928i
$392$	−8.18363	+	16.2124i	−0.413336	+	0.818851i
$393$			16.7878i			0.846833i
$394$	−1.03453	−	0.162518i	−0.0521190	−	0.00818756i
$395$			13.9408i			0.701437i
$396$	−9.80142	−	3.15740i	−0.492540	−	0.158665i
$397$	24.8494			1.24716			0.623579	−	0.781761i	$-0.285678\pi$
$397$	24.8494			1.24716			0.623579	+	0.781761i	$0.285678\pi$
$398$	−18.9636	−	2.97907i	−0.950562	−	0.149327i
$399$		−	4.18513i		−	0.209518i
$400$	−16.1816	−	11.6325i	−0.809082	−	0.581627i
$401$		−	22.5349i		−	1.12534i	−0.826683	−	0.562668i	$-0.809775\pi$
$401$		−	22.5349i		−	1.12534i	0.826683	−	0.562668i	$-0.190225\pi$
$402$	−0.126160	+	11.5751i	−0.00629231	+	0.577316i
$403$			17.1708i			0.855338i
$404$	1.29795	−	4.02920i	0.0645756	−	0.200460i
$405$			3.15947i			0.156995i
$406$	1.63547	−	10.4108i	0.0811669	−	0.516678i
$407$	43.1505			2.13889
$408$	−2.28002	+	4.51690i	−0.112878	+	0.223620i
$409$		−	16.8732i		−	0.834328i	−0.908831	−	0.417164i	$-0.863024\pi$
$409$		−	16.8732i		−	0.834328i	0.908831	−	0.417164i	$-0.136976\pi$
$410$	−0.694945	+	4.42376i	−0.0343209	+	0.218474i
$411$		−	3.76333i		−	0.185631i
$412$	1.86360	−	5.78513i	0.0918132	−	0.285013i
$413$		−	0.410563i		−	0.0202025i
$414$	4.13756	+	0.649985i	0.203350	+	0.0319450i
$415$	26.8466			1.31785
$416$	−18.8101	−	18.5747i	−0.922241	−	0.910699i
$417$	−11.5820			−0.567172
$418$	−39.5566	−	6.21409i	−1.93478	−	0.303941i
$419$			17.8232i			0.870720i	0.900256	+	0.435360i	$0.143379\pi$
$419$			17.8232i			0.870720i	−0.900256	+	0.435360i	$0.856621\pi$
$420$	−1.47453	+	4.57734i	−0.0719498	+	0.223351i
$421$	11.6776			0.569133			0.284567	−	0.958656i	$-0.408150\pi$
$421$	11.6776			0.569133			0.284567	+	0.958656i	$0.408150\pi$
$422$	−36.4647	−	5.72838i	−1.77508	−	0.278853i
$423$		−	11.6884i		−	0.568311i
$424$	23.3604	+	11.7918i	1.13448	+	0.572658i
$425$	−8.91264			−0.432327
$426$	16.5380	+	2.59801i	0.801268	+	0.125874i
$427$			1.79059i			0.0866529i
$428$	−0.491898	+	1.52698i	−0.0237768	+	0.0738095i
$429$		−	24.0609i		−	1.16167i
$430$	31.8813	+	5.00836i	1.53745	+	0.241524i
$431$		−	12.4402i		−	0.599222i	−0.954061	−	0.299611i	$-0.903143\pi$
$431$		−	12.4402i		−	0.599222i	0.954061	−	0.299611i	$-0.0968570\pi$
$432$	−3.24787	−	2.33481i	−0.156263	−	0.112334i
$433$		−	1.55511i		−	0.0747338i	−0.999302	−	0.0373669i	$-0.988103\pi$
$433$		−	1.55511i		−	0.0747338i	0.999302	−	0.0373669i	$-0.0118970\pi$
$434$	−0.613714	+	3.90668i	−0.0294592	+	0.187526i
$435$			30.9362i			1.48328i
$436$	2.42193	−	7.51833i	0.115990	−	0.360063i
$437$	16.2863			0.779079
$438$	−1.64765	+	10.4883i	−0.0787277	+	0.501152i
$439$			34.3737i			1.64057i	0.571958	+	0.820283i	$0.306184\pi$
$439$			34.3737i			1.64057i	−0.571958	+	0.820283i	$0.693816\pi$
$440$	41.0743	+	20.7333i	1.95814	+	0.988421i
$441$	−6.42081			−0.305753
$442$	−11.6793	−	1.83475i	−0.555529	−	0.0872700i
$443$	12.2786			0.583373			0.291687	−	0.956514i	$-0.405784\pi$
$443$	12.2786			0.583373			0.291687	+	0.956514i	$0.405784\pi$
$444$	15.9543	+	5.13947i	0.757157	+	0.243909i
$445$			42.7685i			2.02742i
$446$	−17.4516	−	2.74153i	−0.826356	−	0.129815i
$447$	1.02591			0.0485238
$448$	−3.61576	−	4.89839i	−0.170829	−	0.231427i
$449$	6.05108			0.285568			0.142784	−	0.989754i	$-0.454395\pi$
$449$	6.05108			0.285568			0.142784	+	0.989754i	$0.454395\pi$
$450$	1.09346	−	6.96057i	0.0515463	−	0.328124i
$451$		−	5.16007i		−	0.242978i
$452$	−3.66905	+	11.3897i	−0.172577	+	0.535726i
$453$		−	5.39710i		−	0.253578i
$454$	27.3660	+	4.29902i	1.28435	+	0.201763i
$455$	−11.2366			−0.526782
$456$	−13.8854	−	7.00899i	−0.650242	−	0.328226i
$457$	−10.5677			−0.494337			−0.247169	−	0.968972i	$-0.579500\pi$
$457$	−10.5677			−0.494337			−0.247169	+	0.968972i	$0.579500\pi$
$458$	−28.0910	−	4.41291i	−1.31260	−	0.206202i
$459$	−1.78889			−0.0834981
$460$	−17.8126	−	5.73810i	−0.830516	−	0.267540i
$461$	9.54057			0.444349			0.222174	−	0.975007i	$-0.428685\pi$
$461$	9.54057			0.444349			0.222174	+	0.975007i	$0.428685\pi$
$462$	0.859979	−	5.47431i	0.0400098	−	0.254688i
$463$	−19.5832			−0.910110			−0.455055	−	0.890463i	$-0.650380\pi$
$463$	−19.5832			−0.910110			−0.455055	+	0.890463i	$0.650380\pi$
$464$	−31.8018	−	22.8615i	−1.47636	−	1.06132i
$465$		−	11.6089i		−	0.538349i
$466$	14.1316	+	2.21998i	0.654633	+	0.102839i
$467$			3.05326i			0.141288i	0.997502	+	0.0706439i	$0.0225054\pi$
$467$			3.05326i			0.141288i	−0.997502	+	0.0706439i	$0.977495\pi$
$468$	2.86579	−	8.89618i	0.132471	−	0.411226i
$469$	−6.16411	+	0.899618i	−0.284632	+	0.0415405i
$470$	−8.10494	+	51.5931i	−0.373853	+	2.37981i
$471$	−21.7154			−1.00059
$472$	−1.36216	−	0.687586i	−0.0626986	−	0.0316487i
$473$	−37.1878			−1.70990
$474$	0.968397	−	6.16446i	0.0444800	−	0.283143i
$475$		−	27.3982i		−	1.25712i
$476$	−2.59169	−	0.834878i	−0.118790	−	0.0382666i
$477$			9.25172i			0.423607i
$478$	−2.29801	+	14.6283i	−0.105108	+	0.669081i
$479$			19.4898i			0.890512i	0.895403	+	0.445256i	$0.146887\pi$
$479$			19.4898i			0.890512i	−0.895403	+	0.445256i	$0.853113\pi$
$480$	12.7172	+	12.5580i	0.580458	+	0.573193i
$481$			39.1653i			1.78578i
$482$	−2.84151	+	18.0880i	−0.129427	+	0.823885i
$483$			2.25389i			0.102556i
$484$	−29.5244	−	9.51089i	−1.34202	−	0.432313i
$485$	−27.8054			−1.26258
$486$	0.219472	−	1.39708i	0.00995547	−	0.0633728i
$487$	18.0005			0.815682			0.407841	−	0.913053i	$-0.366282\pi$
$487$	18.0005			0.815682			0.407841	+	0.913053i	$0.366282\pi$
$488$	5.94081	+	2.99878i	0.268928	+	0.135748i
$489$			12.4095i			0.561176i
$490$	28.3416	+	4.45229i	1.28034	+	0.201134i
$491$			24.6443i			1.11218i	0.831121	+	0.556091i	$0.187700\pi$
$491$			24.6443i			1.11218i	−0.831121	+	0.556091i	$0.812300\pi$
$492$	0.614593	−	1.90786i	0.0277080	−	0.0860130i
$493$	−17.5160			−0.788882
$494$	5.64018	−	35.9033i	0.253763	−	1.61536i
$495$			16.2672i			0.731155i
$496$	11.9337	+	8.57883i	0.535839	+	0.385201i
$497$			9.00888i			0.404104i
$498$	−11.8713	−	1.86490i	−0.531965	−	0.0835683i
$499$	−18.2260			−0.815907			−0.407953	−	0.913003i	$-0.633757\pi$
$499$	−18.2260			−0.815907			−0.407953	+	0.913003i	$0.633757\pi$
$500$	0.0344347	−	0.106894i	0.00153996	−	0.00478046i
$501$			23.7645i			1.06172i
$502$	−3.52873	+	22.4626i	−0.157495	+	1.00256i
$503$	18.5070			0.825187			0.412594	−	0.910915i	$-0.364623\pi$
$503$	18.5070			0.825187			0.412594	+	0.910915i	$0.364623\pi$
$504$	0.969986	−	1.92162i	0.0432066	−	0.0855957i
$505$	−6.68716			−0.297575
$506$	21.3031	+	3.34658i	0.947039	+	0.148774i
$507$	8.83872			0.392541
$508$	−2.14763	+	6.66682i	−0.0952858	+	0.295792i
$509$	38.4081			1.70241			0.851205	−	0.524833i	$-0.175872\pi$
$509$	38.4081			1.70241			0.851205	+	0.524833i	$0.175872\pi$
$510$	7.89619	+	1.24044i	0.349649	+	0.0549277i
$511$	−5.71340			−0.252746
$512$	−22.3073	+	3.79280i	−0.985852	+	0.167620i
$513$		−	5.49920i		−	0.242795i
$514$	1.94945	−	12.4094i	0.0859864	−	0.547357i
$515$	−9.60144			−0.423090
$516$	−13.7497	−	4.42927i	−0.605295	−	0.194988i
$517$		−	60.1804i		−	2.64673i
$518$	−1.39983	+	8.91083i	−0.0615052	+	0.391519i
$519$	−21.5848			−0.947466
$520$	−18.8184	+	37.2808i	−0.825243	+	1.63487i
$521$			23.3284i			1.02203i	0.859571	+	0.511017i	$0.170731\pi$
$521$			23.3284i			1.02203i	−0.859571	+	0.511017i	$0.829269\pi$
$522$	2.14898	−	13.6796i	0.0940583	−	0.598741i
$523$		−	1.12071i		−	0.0490051i	−0.999700	−	0.0245025i	$-0.992200\pi$
$523$		−	1.12071i		−	0.0490051i	0.999700	−	0.0245025i	$-0.00780018\pi$
$524$	−10.2950	+	31.9583i	−0.449738	+	1.39611i
$525$	3.79169			0.165483
$526$	−18.7262	−	2.94177i	−0.816503	−	0.128267i
$527$	6.57294			0.286322
$528$	−16.7224	−	12.0213i	−0.727747	−	0.523158i
$529$	14.2291			0.618655
$530$	6.41528	−	40.8373i	0.278662	−	1.77386i
$531$		−	0.539474i		−	0.0234112i
$532$	2.56649	−	7.96707i	0.111271	−	0.345416i
$533$	4.68350			0.202865
$534$	2.97091	−	18.9117i	0.128564	−	0.818390i
$535$	2.53430			0.109567
$536$	−7.33852	+	21.9578i	−0.316976	+	0.948434i
$537$	25.0137			1.07942
$538$	−0.652227	+	4.15183i	−0.0281195	+	0.178998i
$539$	−33.0589			−1.42395
$540$	−1.93751	+	6.01456i	−0.0833773	+	0.258826i
$541$			2.12087i			0.0911831i	0.998960	+	0.0455916i	$0.0145173\pi$
$541$			2.12087i			0.0911831i	−0.998960	+	0.0455916i	$0.985483\pi$
$542$	−0.760507	+	4.84111i	−0.0326666	+	0.207943i
$543$	−7.26648			−0.311835
$544$	−7.11034	+	7.20046i	−0.304854	+	0.308717i
$545$	−12.4780			−0.534499
$546$	4.96872	+	0.780554i	0.212641	+	0.0334046i
$547$	−18.3469			−0.784458			−0.392229	−	0.919868i	$-0.628296\pi$
$547$	−18.3469			−0.784458			−0.392229	+	0.919868i	$0.628296\pi$
$548$	2.30783	−	7.16412i	0.0985856	−	0.306036i
$549$			2.35281i			0.100416i
$550$	5.62992	−	35.8380i	0.240060	−	1.52814i
$551$		−	53.8458i		−	2.29391i
$552$	7.47793	+	3.77467i	0.318282	+	0.160661i
$553$	3.35802			0.142797
$554$	−3.67687	+	23.4056i	−0.156215	+	0.994408i
$555$		−	26.4790i		−	1.12397i
$556$	−22.0482	−	7.10255i	−0.935052	−	0.301215i
$557$	−17.1789			−0.727891			−0.363946	−	0.931420i	$-0.618571\pi$
$557$	−17.1789			−0.727891			−0.363946	+	0.931420i	$0.618571\pi$
$558$	−0.806411	+	5.13332i	−0.0341381	+	0.217311i
$559$		−	33.7532i		−	1.42761i
$560$	−5.61403	+	7.80948i	−0.237236	+	0.330011i
$561$	−9.21046			−0.388866
$562$	42.7973	+	6.72318i	1.80529	+	0.283600i
$563$	5.23605			0.220673			0.110337	−	0.993894i	$-0.464807\pi$
$563$	5.23605			0.220673			0.110337	+	0.993894i	$0.464807\pi$
$564$	7.16783	−	22.2509i	0.301820	−	0.936930i
$565$	18.9032			0.795264
$566$	26.9565	+	4.23470i	1.13307	+	0.177998i
$567$	0.761043			0.0319608
$568$	29.8896	+	15.0875i	1.25414	+	0.633058i
$569$	38.0114			1.59352			0.796761	−	0.604295i	$-0.206545\pi$
$569$	38.0114			1.59352			0.796761	+	0.604295i	$0.206545\pi$
$570$	−3.81323	+	24.2736i	−0.159719	+	1.01671i
$571$		−	17.6369i		−	0.738081i	−0.929413	−	0.369041i	$-0.879686\pi$
$571$		−	17.6369i		−	0.738081i	0.929413	−	0.369041i	$-0.120314\pi$
$572$	14.7551	−	45.8039i	0.616943	−	1.91516i
$573$	15.0240			0.627635
$574$	1.06558	+	0.167396i	0.0444766	+	0.00698699i
$575$			14.7553i			0.615337i
$576$	−4.75105	−	6.43642i	−0.197961	−	0.268184i
$577$			5.54549i			0.230862i	0.993316	+	0.115431i	$0.0368249\pi$
$577$			5.54549i			0.230862i	−0.993316	+	0.115431i	$0.963175\pi$
$578$	3.02869	−	19.2795i	0.125977	−	0.801923i
$579$	7.14965			0.297129
$580$	−18.9713	+	58.8920i	−0.787741	+	2.44536i
$581$		−	6.46674i		−	0.268286i
$582$	12.2952	+	1.93150i	0.509654	+	0.0800634i
$583$			47.6344i			1.97282i
$584$	−9.56844	+	18.9558i	−0.395945	+	0.784398i
$585$	−14.7648			−0.610449
$586$	7.09289	−	45.1507i	0.293005	−	1.86516i
$587$	−39.7801			−1.64190			−0.820950	−	0.571000i	$-0.806555\pi$
$587$	−39.7801			−1.64190			−0.820950	+	0.571000i	$0.806555\pi$
$588$	−12.2231	−	3.93750i	−0.504071	−	0.162380i
$589$			20.2058i			0.832565i
$590$	−0.374080	+	2.38125i	−0.0154006	+	0.0980346i
$591$		−	0.740496i		−	0.0304599i
$592$	27.2199	+	19.5677i	1.11873	+	0.804226i
$593$			36.6042i			1.50315i	0.659646	+	0.751576i	$0.270706\pi$
$593$			36.6042i			1.50315i	−0.659646	+	0.751576i	$0.729294\pi$
$594$	1.13000	−	7.19316i	0.0463645	−	0.295139i
$595$			4.30136i			0.176339i
$596$	1.95298	+	0.629128i	0.0799973	+	0.0257701i
$597$		−	13.5738i		−	0.555538i
$598$	−3.03750	+	19.3356i	−0.124213	+	0.790692i
$599$	41.8300			1.70913			0.854563	−	0.519348i	$-0.173825\pi$
$599$	41.8300			1.70913			0.854563	+	0.519348i	$0.173825\pi$
$600$	6.35009	−	12.5800i	0.259241	−	0.513577i
$601$	9.98958			0.407484			0.203742	−	0.979025i	$-0.434690\pi$
$601$	9.98958			0.407484			0.203742	+	0.979025i	$0.434690\pi$
$602$	1.20640	−	7.67948i	0.0491691	−	0.312992i
$603$	−8.09955	+	1.18208i	−0.329839	+	0.0481382i
$604$	3.30972	−	10.2743i	0.134671	−	0.418054i
$605$			49.0009i			1.99217i
$606$	2.95699	+	0.464524i	0.120119	+	0.0188700i
$607$			13.8115i			0.560593i	0.959914	+	0.280296i	$0.0904327\pi$
$607$			13.8115i			0.560593i	−0.959914	+	0.280296i	$0.909567\pi$
$608$	−22.1349	−	21.8578i	−0.897687	−	0.886452i
$609$	7.45181			0.301963
$610$	1.63148	−	10.3854i	0.0660566	−	0.420492i
$611$	54.6223			2.20978
$612$	−3.40544	−	1.09702i	−0.137657	−	0.0443443i
$613$	30.6329			1.23725			0.618625	−	0.785686i	$-0.287690\pi$
$613$	30.6329			1.23725			0.618625	+	0.785686i	$0.287690\pi$
$614$	5.68495	+	0.893069i	0.229426	+	0.0360413i
$615$	−3.16643			−0.127683
$616$	4.99418	−	9.89387i	0.201221	−	0.398635i
$617$	2.14651			0.0864153			0.0432076	−	0.999066i	$-0.486242\pi$
$617$	2.14651			0.0864153			0.0432076	+	0.999066i	$0.486242\pi$
$618$	4.24565	+	0.666964i	0.170785	+	0.0268292i
$619$		−	37.2149i		−	1.49579i	−0.663815	−	0.747897i	$-0.731064\pi$
$619$		−	37.2149i		−	1.49579i	0.663815	−	0.747897i	$-0.268936\pi$
$620$	7.11904	−	22.0994i	0.285908	−	0.887534i
$621$			2.96158i			0.118844i
$622$	−4.94851	+	31.5004i	−0.198417	+	1.26305i
$623$	10.3019			0.412739
$624$	10.9110	−	15.1779i	0.436790	−	0.607603i
$625$	−25.0885			−1.00354
$626$	28.8484	+	4.53191i	1.15302	+	0.181131i
$627$		−	28.3138i		−	1.13074i
$628$	−41.3389	−	13.3168i	−1.64960	−	0.531398i
$629$	14.9924			0.597785
$630$	−3.35927	−	0.527719i	−0.133836	−	0.0210248i
$631$	33.0047			1.31390			0.656948	−	0.753936i	$-0.271847\pi$
$631$	33.0047			1.31390			0.656948	+	0.753936i	$0.271847\pi$
$632$	5.62380	−	11.1412i	0.223703	−	0.443173i
$633$		−	26.1007i		−	1.03741i
$634$	−3.04778	+	19.4010i	−0.121043	+	0.770513i
$635$	11.0648			0.439092
$636$	−5.67353	+	17.6122i	−0.224970	+	0.698368i
$637$		−	30.0057i		−	1.18887i
$638$	11.0645	−	70.4324i	0.438047	−	2.78845i
$639$			11.8375i			0.468286i
$640$	16.5082	+	31.7050i	0.652543	+	1.25325i
$641$			5.64568i			0.222991i	0.993765	+	0.111495i	$0.0355640\pi$
$641$			5.64568i			0.222991i	−0.993765	+	0.111495i	$0.964436\pi$
$642$	−1.12064	−	0.176045i	−0.0442280	−	0.00694794i
$643$			18.7677i			0.740125i	0.929007	+	0.370063i	$0.120664\pi$
$643$			18.7677i			0.740125i	−0.929007	+	0.370063i	$0.879336\pi$
$644$	−1.38218	+	4.29065i	−0.0544654	+	0.169075i
$645$			22.8200i			0.898536i
$646$	−13.7437	−	2.15905i	−0.540738	−	0.0849465i
$647$	−19.8431			−0.780112			−0.390056	−	0.920791i	$-0.627544\pi$
$647$	−19.8431			−0.780112			−0.390056	+	0.920791i	$0.627544\pi$
$648$	1.27455	−	2.52498i	0.0500690	−	0.0991906i
$649$		−	2.77760i		−	0.109030i
$650$	32.5281	+	5.10995i	1.27586	+	0.200429i
$651$	−2.79632			−0.109596
$652$	−7.61000	+	23.6235i	−0.298030	+	0.925166i
$653$			20.8367i			0.815402i	0.913116	+	0.407701i	$0.133669\pi$
$653$			20.8367i			0.815402i	−0.913116	+	0.407701i	$0.866331\pi$
$654$	5.51763	+	0.866785i	0.215756	+	0.0338940i
$655$	53.0405			2.07246
$656$	2.33996	−	3.25503i	0.0913600	−	0.127088i
$657$	−7.50732			−0.292888
$658$	12.4276	+	1.95230i	0.484478	+	0.0761084i
$659$		−	36.4813i		−	1.42111i	−0.703641	−	0.710555i	$-0.748444\pi$
$659$		−	36.4813i		−	1.42111i	0.703641	−	0.710555i	$-0.251556\pi$
$660$	−9.97570	+	30.9672i	−0.388304	+	1.20540i
$661$			26.5119i			1.03119i	0.856832	+	0.515596i	$0.172429\pi$
$661$			26.5119i			1.03119i	−0.856832	+	0.515596i	$0.827571\pi$
$662$	1.36177	−	8.66854i	0.0529268	−	0.336912i
$663$		−	8.35981i		−	0.324668i
$664$	−21.4553	−	10.8301i	−0.832626	−	0.420289i
$665$	−13.2228			−0.512757
$666$	−1.83936	+	11.7087i	−0.0712738	+	0.453703i
$667$			28.9985i			1.12283i
$668$	−14.5734	+	45.2396i	−0.563860	+	1.75037i
$669$		−	12.4915i		−	0.482948i
$670$	36.5713	+	0.398599i	1.41287	+	0.0153992i
$671$			12.1140i			0.467654i
$672$	3.02494	−	3.06328i	0.116690	−	0.118169i
$673$			22.4998i			0.867303i	0.901081	+	0.433651i	$0.142775\pi$
$673$			22.4998i			0.867303i	−0.901081	+	0.433651i	$0.857225\pi$
$674$	−24.0400	−	3.77653i	−0.925987	−	0.145467i
$675$	4.98223			0.191766
$676$	16.8259	+	5.42026i	0.647152	+	0.208472i
$677$		−	20.4581i		−	0.786269i	−0.919481	−	0.393135i	$-0.871391\pi$
$677$		−	20.4581i		−	0.786269i	0.919481	−	0.393135i	$-0.128609\pi$
$678$	−8.35879	−	1.31311i	−0.321017	−	0.0504298i
$679$			6.69769i			0.257034i
$680$	14.2710	+	7.20365i	0.547268	+	0.276247i
$681$			19.5880i			0.750613i
$682$	−4.15198	+	26.4300i	−0.158988	+	1.01206i
$683$	35.4929			1.35810			0.679049	−	0.734093i	$-0.262392\pi$
$683$	35.4929			1.35810			0.679049	+	0.734093i	$0.262392\pi$
$684$	3.37233	−	10.4686i	0.128944	−	0.400278i
$685$	−11.8901			−0.454298
$686$	2.24165	−	14.2695i	0.0855866	−	0.544813i
$687$		−	20.1069i		−	0.767127i
$688$	−23.4585	−	16.8637i	−0.894347	−	0.642922i
$689$	−43.2350			−1.64712
$690$	2.05360	−	13.0725i	0.0781794	−	0.497661i
$691$		−	30.7924i		−	1.17140i	−0.810529	−	0.585698i	$-0.800820\pi$
$691$		−	30.7924i		−	1.17140i	0.810529	−	0.585698i	$-0.199180\pi$
$692$	−41.0901	−	13.2367i	−1.56201	−	0.503182i
$693$	3.91839			0.148847
$694$	−0.275258	+	1.75219i	−0.0104486	+	0.0665122i
$695$			36.5929i			1.38805i
$696$	12.4798	−	24.7235i	0.473047	−	0.937144i
$697$		−	1.79283i		−	0.0679083i
$698$	4.54152	−	28.9096i	0.171899	−	1.09425i
$699$			10.1151i			0.382588i
$700$	7.21810	+	2.32522i	0.272819	+	0.0878850i
$701$		−	21.7224i		−	0.820442i	−0.911986	−	0.410221i	$-0.865452\pi$
$701$		−	21.7224i		−	0.820442i	0.911986	−	0.410221i	$-0.134548\pi$
$702$	6.52882	+	1.02564i	0.246414	+	0.0387102i
$703$			46.0879i			1.73824i
$704$	−24.4618	−	33.1393i	−0.921939	−	1.24898i
$705$	−36.9292			−1.39083
$706$	16.8015	+	2.63941i	0.632334	+	0.0993357i
$707$			1.61079i			0.0605798i
$708$	0.330828	−	1.02698i	0.0124333	−	0.0385962i
$709$	10.8581			0.407786			0.203893	−	0.978993i	$-0.434641\pi$
$709$	10.8581			0.407786			0.203893	+	0.978993i	$0.434641\pi$
$710$	8.20834	−	52.2512i	0.308053	−	1.96095i
$711$	4.41239			0.165477
$712$	17.2531	−	34.1797i	0.646586	−	1.28094i
$713$		−	10.8818i		−	0.407526i
$714$	0.298794	−	1.90201i	0.0111821	−	0.0711810i
$715$	−76.0196			−2.84297
$716$	47.6177	+	15.3394i	1.77956	+	0.573261i
$717$	−10.4706			−0.391031
$718$	−15.3757	−	2.41543i	−0.573817	−	0.0901430i
$719$			10.3815i			0.387163i	0.981084	+	0.193581i	$0.0620104\pi$
$719$			10.3815i			0.387163i	−0.981084	+	0.193581i	$0.937990\pi$
$720$	−7.37675	+	10.2615i	−0.274915	+	0.382425i
$721$			2.31277i			0.0861320i
$722$	2.46712	−	15.7048i	0.0918168	−	0.584472i
$723$	−12.9470			−0.481504
$724$	−13.8329	−	4.45610i	−0.514097	−	0.165610i
$725$	48.7839			1.81179
$726$	3.40385	−	21.6676i	0.126329	−	0.804161i
$727$	−52.6865			−1.95403			−0.977017	−	0.213160i	$-0.931624\pi$
$727$	−52.6865			−1.95403			−0.977017	+	0.213160i	$0.931624\pi$
$728$	8.98010	+	4.53293i	0.332824	+	0.168002i
$729$	1.00000			0.0370370
$730$	33.1375	+	5.20569i	1.22647	+	0.192671i
$731$	−12.9206			−0.477887
$732$	−1.44284	+	4.47897i	−0.0533290	+	0.165547i
$733$		−	3.17334i		−	0.117210i	−0.998281	−	0.0586050i	$-0.981335\pi$
$733$		−	3.17334i		−	0.117210i	0.998281	−	0.0586050i	$-0.0186652\pi$
$734$	2.95140	−	18.7875i	0.108938	−	0.693460i
$735$			20.2863i			0.748273i
$736$	11.9207	+	11.7715i	0.439402	+	0.433903i
$737$	−41.7022	+	6.08621i	−1.53612	+	0.224189i
$738$	1.40016	+	0.219956i	0.0515406	+	0.00809671i
$739$	−24.0808			−0.885826			−0.442913	−	0.896565i	$-0.646055\pi$
$739$	−24.0808			−0.885826			−0.442913	+	0.896565i	$0.646055\pi$
$740$	16.2380	−	50.4071i	0.596920	−	1.85300i
$741$	25.6988			0.944069
$742$	−9.83678	−	1.54530i	−0.361120	−	0.0567296i
$743$		−	49.0043i		−	1.79779i	−0.438160	−	0.898897i	$-0.644370\pi$
$743$		−	49.0043i		−	1.79779i	0.438160	−	0.898897i	$-0.355630\pi$
$744$	−4.68309	+	9.27758i	−0.171691	+	0.340133i
$745$		−	3.24132i		−	0.118753i
$746$	50.2045	+	7.88680i	1.83812	+	0.288756i
$747$		−	8.49721i		−	0.310896i
$748$	−17.5336	−	5.64823i	−0.641093	−	0.206520i
$749$		−	0.610454i		−	0.0223055i
$750$	0.0784487	+	0.0123238i	0.00286454	+	0.000450001i
$751$			7.55434i			0.275662i	0.990456	+	0.137831i	$0.0440130\pi$
$751$			7.55434i			0.275662i	−0.990456	+	0.137831i	$0.955987\pi$
$752$	27.2903	−	37.9625i	0.995173	−	1.38435i
$753$	−16.0783			−0.585924
$754$	63.9275	+	10.0426i	2.32810	+	0.365730i
$755$	−17.0520			−0.620584
$756$	1.44877	+	0.466703i	0.0526913	+	0.0169738i
$757$			15.3960i			0.559576i	0.960062	+	0.279788i	$0.0902642\pi$
$757$			15.3960i			0.559576i	−0.960062	+	0.279788i	$0.909736\pi$
$758$	−6.44420	+	41.0214i	−0.234064	+	1.48996i
$759$			15.2483i			0.553479i
$760$	−22.1447	+	43.8703i	−0.803271	+	1.59134i
$761$	−4.51530			−0.163680			−0.0818398	−	0.996646i	$-0.526080\pi$
$761$	−4.51530			−0.163680			−0.0818398	+	0.996646i	$0.526080\pi$
$762$	−4.89272	−	0.768615i	−0.177244	−	0.0278440i
$763$			3.00567i			0.108812i
$764$	28.6006	+	9.21331i	1.03473	+	0.333326i
$765$			5.65193i			0.204346i
$766$	−4.87163	+	31.0110i	−0.176019	+	1.12047i
$767$	2.52107			0.0910304
$768$	−5.09734	−	15.1663i	−0.183934	−	0.547267i
$769$		−	7.38615i		−	0.266351i	−0.991092	−	0.133176i	$-0.957483\pi$
$769$		−	7.38615i		−	0.266351i	0.991092	−	0.133176i	$-0.0425174\pi$
$770$	−17.2959	−	2.71707i	−0.623301	−	0.0979166i
$771$	8.88242			0.319893
$772$	13.6105	+	4.38446i	0.489854	+	0.157800i
$773$	−24.3889			−0.877206			−0.438603	−	0.898681i	$-0.644527\pi$
$773$	−24.3889			−0.877206			−0.438603	+	0.898681i	$0.644527\pi$
$774$	1.58519	−	10.0907i	0.0569785	−	0.362704i
$775$	−18.3063			−0.657581
$776$	22.2215	+	11.2169i	0.797706	+	0.402662i
$777$	−6.37818			−0.228816
$778$	1.38161	−	8.79483i	0.0495332	−	0.315310i
$779$	5.51132			0.197464
$780$	−28.1072	−	9.05437i	−1.00640	−	0.324199i
$781$			60.9481i			2.18089i
$782$	7.40163	+	1.16275i	0.264682	+	0.0415798i
$783$	9.79158			0.349922
$784$	−20.8540	−	14.9914i	−0.744785	−	0.535406i
$785$			68.6092i			2.44877i
$786$	−23.4539	−	3.68446i	−0.836573	−	0.131420i
$787$	35.2246			1.25562			0.627810	−	0.778366i	$-0.283951\pi$
$787$	35.2246			1.25562			0.627810	+	0.778366i	$0.283951\pi$
$788$	0.454102	−	1.40966i	0.0161767	−	0.0502169i
$789$		−	13.4038i		−	0.477190i
$790$	−19.4764	−	3.05962i	−0.692939	−	0.108856i
$791$		−	4.55335i		−	0.161899i
$792$	6.56228	−	13.0004i	0.233180	−	0.461949i
$793$	−10.9952			−0.390449
$794$	−5.45376	+	34.7166i	−0.193547	+	1.23205i
$795$	29.2305			1.03670
$796$	8.32399	−	25.8399i	0.295036	−	0.915871i
$797$	16.2956			0.577219			0.288610	−	0.957447i	$-0.406807\pi$
$797$	16.2956			0.577219			0.288610	+	0.957447i	$0.406807\pi$
$798$	5.84696	+	0.918520i	0.206980	+	0.0325152i
$799$		−	20.9093i		−	0.739717i
$800$	19.8030	−	20.0540i	0.700142	−	0.709016i
$801$	13.5366			0.478292
$802$	31.4830	+	4.94578i	1.11170	+	0.174642i
$803$	−38.6530			−1.36404
$804$	−16.1437	−	2.71668i	−0.569345	−	0.0958100i
$805$	7.12109			0.250985
$806$	−23.9890	−	3.76851i	−0.844975	−	0.132740i
$807$	−2.97179			−0.104612
$808$	5.34424	+	2.69764i	0.188010	+	0.0949027i
$809$			25.9833i			0.913524i	0.889589	+	0.456762i	$0.150991\pi$
$809$			25.9833i			0.913524i	−0.889589	+	0.456762i	$0.849009\pi$
$810$	−4.41403	−	0.693416i	−0.155093	−	0.0243641i
$811$	34.0304			1.19497			0.597484	−	0.801881i	$-0.296167\pi$
$811$	34.0304			1.19497			0.597484	+	0.801881i	$0.296167\pi$
$812$	14.1858	+	4.56976i	0.497822	+	0.160367i
$813$	−3.46516			−0.121529
$814$	−9.47035	+	60.2847i	−0.331935	+	2.11298i
$815$	39.2073			1.37337
$816$	−5.81007	−	4.17671i	−0.203393	−	0.146214i
$817$		−	39.7192i		−	1.38960i
$818$	23.5733	+	3.70321i	0.824220	+	0.129480i
$819$			3.55650i			0.124274i
$820$	−6.02782	−	1.94179i	−0.210501	−	0.0678101i
$821$	−10.3445			−0.361027			−0.180513	−	0.983573i	$-0.557776\pi$
$821$	−10.3445			−0.361027			−0.180513	+	0.983573i	$0.557776\pi$
$822$	5.25768	+	0.825948i	0.183382	+	0.0288082i
$823$		−	47.5724i		−	1.65827i	−0.559050	−	0.829134i	$-0.688834\pi$
$823$		−	47.5724i		−	1.65827i	0.559050	−	0.829134i	$-0.311166\pi$
$824$	7.67328	+	3.87328i	0.267311	+	0.134932i
$825$	25.6521			0.893090
$826$	0.573589	+	0.0901073i	0.0199577	+	0.00313523i
$827$			16.7232i			0.581523i	0.956796	+	0.290762i	$0.0939087\pi$
$827$			16.7232i			0.581523i	−0.956796	+	0.290762i	$0.906091\pi$
$828$	−1.81616	+	5.63785i	−0.0631159	+	0.195929i
$829$	34.6867			1.20472			0.602359	−	0.798226i	$-0.294228\pi$
$829$	34.6867			1.20472			0.602359	+	0.798226i	$0.294228\pi$
$830$	−5.89209	+	37.5069i	−0.204518	+	1.30188i
$831$	−16.7532			−0.581163
$832$	30.0786	−	22.2026i	1.04279	−	0.769736i
$833$	−11.4861			−0.397970
$834$	2.54193	−	16.1810i	0.0880197	−	0.560301i
$835$	75.0831			2.59836
$836$	17.3632	−	53.8999i	0.600518	−	1.86417i
$837$	−3.67432			−0.127003
$838$	−24.9004	−	3.91170i	−0.860171	−	0.135127i
$839$		−	8.59696i		−	0.296800i	−0.988927	−	0.148400i	$-0.952588\pi$
$839$		−	8.59696i		−	0.296800i	0.988927	−	0.148400i	$-0.0474123\pi$
$840$	−6.07129	−	3.06464i	−0.209479	−	0.105740i
$841$	66.8750			2.30603
$842$	−2.56292	+	16.3146i	−0.0883240	+	0.562238i
$843$			30.6334i			1.05507i
$844$	16.0060	−	49.6869i	0.550950	−	1.71029i
$845$		−	27.9256i		−	0.960671i
$846$	16.3297	+	2.56529i	0.561426	+	0.0881964i
$847$	11.8032			0.405563
$848$	−21.6010	+	30.0484i	−0.741781	+	1.03187i
$849$			19.2949i			0.662200i
$850$	1.95608	−	12.4517i	0.0670929	−	0.427089i
$851$		−	24.8205i		−	0.850836i
$852$	−7.25926	+	22.5347i	−0.248698	+	0.772026i
$853$	−35.6459			−1.22049			−0.610247	−	0.792211i	$-0.708930\pi$
$853$	−35.6459			−1.22049			−0.610247	+	0.792211i	$0.708930\pi$
$854$	−2.50160	−	0.392986i	−0.0856031	−	0.0134477i
$855$	−17.3745			−0.594196
$856$	−2.02536	−	1.02235i	−0.0692253	−	0.0349432i
$857$		−	33.1171i		−	1.13126i	−0.824660	−	0.565629i	$-0.808633\pi$
$857$		−	33.1171i		−	1.13126i	0.824660	−	0.565629i	$-0.191367\pi$
$858$	33.6150	+	5.28071i	1.14760	+	0.180280i
$859$			2.72132i			0.0928504i	0.998922	+	0.0464252i	$0.0147829\pi$
$859$			2.72132i			0.0928504i	−0.998922	+	0.0464252i	$0.985217\pi$
$860$	−13.9941	+	43.4416i	−0.477196	+	1.48135i
$861$			0.762722i			0.0259935i
$862$	17.3799	+	2.73028i	0.591963	+	0.0929936i
$863$			7.88270i			0.268330i	0.990959	+	0.134165i	$0.0428352\pi$
$863$			7.88270i			0.268330i	−0.990959	+	0.134165i	$0.957165\pi$
$864$	3.97473	−	4.02511i	0.135223	−	0.136937i
$865$			68.1963i			2.31874i
$866$	2.17261	+	0.341304i	0.0738284	+	0.0115980i
$867$	13.7999			0.468669
$868$	−5.32324	−	1.71481i	−0.180683	−	0.0582046i
$869$	22.7181			0.770659
$870$	−43.2203	−	6.78963i	−1.46530	−	0.230190i
$871$	−5.52411	−	37.8507i	−0.187177	−	1.28252i
$872$	9.97216	+	5.03370i	0.337700	+	0.170463i
$873$			8.80067i			0.297857i
$874$	−3.57439	+	22.7533i	−0.120906	+	0.769640i
$875$			0.0427340i			0.00144467i
$876$	−14.2914	−	4.60380i	−0.482862	−	0.155548i
$877$	−17.9775			−0.607058			−0.303529	−	0.952822i	$-0.598165\pi$
$877$	−17.9775			−0.607058			−0.303529	+	0.952822i	$0.598165\pi$
$878$	−48.0227	−	7.54407i	−1.62069	−	0.254600i
$879$	32.3179			1.09006
$880$	−37.9808	+	52.8337i	−1.28033	+	1.78102i
$881$	31.0253			1.04527			0.522634	−	0.852557i	$-0.324949\pi$
$881$	31.0253			1.04527			0.522634	+	0.852557i	$0.324949\pi$
$882$	1.40919	−	8.97039i	0.0474499	−	0.302049i
$883$	−34.7113			−1.16813			−0.584065	−	0.811707i	$-0.698539\pi$
$883$	−34.7113			−1.16813			−0.584065	+	0.811707i	$0.698539\pi$
$884$	5.12658	−	15.9143i	0.172425	−	0.535255i
$885$	−1.70445			−0.0572945
$886$	−2.69481	+	17.1542i	−0.0905339	+	0.576305i
$887$		−	14.8905i		−	0.499973i	−0.968249	−	0.249987i	$-0.919574\pi$
$887$		−	14.8905i		−	0.499973i	0.968249	−	0.249987i	$-0.0804262\pi$
$888$	−10.6818	+	21.1615i	−0.358457	+	0.710132i
$889$		−	2.66525i		−	0.0893896i
$890$	−59.7509	−	9.38649i	−2.00286	−	0.314636i
$891$	5.14871			0.172488
$892$	7.66027	−	23.7795i	0.256485	−	0.796198i
$893$	64.2770			2.15095
$894$	−0.225158	+	1.43327i	−0.00753042	+	0.0479359i
$895$		−	79.0300i		−	2.64168i
$896$	7.63700	−	3.97644i	0.255134	−	0.132844i
$897$	−13.8400			−0.462105
$898$	−1.32805	+	8.45384i	−0.0443174	+	0.282108i
$899$	−35.9774			−1.19991
$900$	9.48449	+	3.05531i	0.316150	+	0.101844i
$901$			16.5503i			0.551369i
$902$	7.20902	+	1.13249i	0.240034	+	0.0377079i
$903$	5.49681			0.182922
$904$	−15.1071	−	7.62567i	−0.502454	−	0.253626i
$905$			22.9582i			0.763157i
$906$	7.54018	+	1.18451i	0.250506	+	0.0393529i
$907$		−	10.0868i		−	0.334925i	−0.985878	−	0.167463i	$-0.946443\pi$
$907$		−	10.0868i		−	0.334925i	0.985878	−	0.167463i	$-0.0535573\pi$
$908$	−12.0121	+	37.2889i	−0.398637	+	1.23748i
$909$			2.11655i			0.0702015i
$910$	2.46613	−	15.6985i	0.0817515	−	0.520400i
$911$			50.7500i			1.68142i	0.541483	+	0.840712i	$0.317863\pi$
$911$			50.7500i			1.68142i	−0.541483	+	0.840712i	$0.682137\pi$
$912$	12.8396	−	17.8607i	0.425161	−	0.591426i
$913$		−	43.7497i		−	1.44790i
$914$	2.31932	−	14.7639i	0.0767164	−	0.488348i
$915$	7.43364			0.245749
$916$	12.3304	−	38.2768i	0.407407	−	1.26470i
$917$		−	12.7762i		−	0.421909i
$918$	0.392611	−	2.49922i	0.0129581	−	0.0824865i
$919$	43.3546			1.43014			0.715068	−	0.699055i	$-0.246396\pi$
$919$	43.3546			1.43014			0.715068	+	0.699055i	$0.246396\pi$
$920$	11.9260	−	23.6263i	0.393187	−	0.778935i
$921$			4.06916i			0.134083i
$922$	−2.09389	+	13.3289i	−0.0689587	+	0.438965i
$923$	−55.3191			−1.82085
$924$	7.45930	+	2.40292i	0.245393	+	0.0790502i
$925$	−41.7552			−1.37290
$926$	4.29798	−	27.3593i	0.141240	−	0.899084i
$927$			3.03894i			0.0998120i
$928$	38.9189	−	39.4122i	1.27758	−	1.29377i
$929$		−	30.2431i		−	0.992243i	−0.868253	−	0.496122i	$-0.834757\pi$
$929$		−	30.2431i		−	0.992243i	0.868253	−	0.496122i	$-0.165243\pi$
$930$	16.2185	+	2.54783i	0.531827	+	0.0835466i
$931$		−	35.3093i		−	1.15722i
$932$	−6.20299	+	19.2557i	−0.203186	+	0.630742i
$933$	−22.5473			−0.738166
$934$	−4.26564	−	0.670105i	−0.139576	−	0.0219265i
$935$			29.1001i			0.951676i
$936$	11.7997	+	5.95621i	0.385686	+	0.194685i
$937$			45.3233i			1.48065i	0.672251	+	0.740324i	$0.265328\pi$
$937$			45.3233i			1.48065i	−0.672251	+	0.740324i	$0.734672\pi$
$938$	0.0960135	−	8.80919i	0.00313495	−	0.287630i
$939$			20.6491i			0.673858i
$940$	−70.3008	−	22.6465i	−2.29296	−	0.738648i
$941$			23.7609i			0.774583i	0.921957	+	0.387292i	$0.126589\pi$
$941$			23.7609i			0.774583i	−0.921957	+	0.387292i	$0.873411\pi$
$942$	4.76594	−	30.3382i	0.155283	−	0.988472i
$943$	−2.96811			−0.0966549
$944$	1.25957	−	1.75214i	0.0409955	−	0.0570274i
$945$		−	2.40449i		−	0.0782181i
$946$	8.16169	−	51.9543i	0.265359	−	1.68918i
$947$			10.2912i			0.334419i	0.985921	+	0.167209i	$0.0534756\pi$
$947$			10.2912i			0.334419i	−0.985921	+	0.167209i	$0.946524\pi$
$948$	8.39970	+	2.70586i	0.272810	+	0.0878821i
$949$		−	35.0831i		−	1.13885i
$950$	38.2775	+	6.01316i	1.24189	+	0.195093i
$951$	−13.8868			−0.450311
$952$	1.73520	−	3.43756i	0.0562380	−	0.111412i
$953$	55.6027			1.80115			0.900575	−	0.434702i	$-0.143146\pi$
$953$	55.6027			1.80115			0.900575	+	0.434702i	$0.143146\pi$
$954$	−12.9254	−	2.03050i	−0.418475	−	0.0657397i
$955$		−	47.4677i		−	1.53602i
$956$	−19.9325	−	6.42100i	−0.644663	−	0.207670i
$957$	50.4140			1.62965
$958$	−27.2288	−	4.27747i	−0.879723	−	0.138199i
$959$			2.86406i			0.0924853i
$960$	−20.3356	+	15.0108i	−0.656330	+	0.484471i
$961$	−17.4994			−0.564496
$962$	−54.7170	−	8.59569i	−1.76415	−	0.277136i
$963$		−	0.802128i		−	0.0258482i
$964$	−24.6467	−	7.93962i	−0.793817	−	0.255718i
$965$		−	22.5891i		−	0.727168i
$966$	−3.14886	−	0.494666i	−0.101313	−	0.0159156i
$967$		−	17.7360i		−	0.570351i	−0.958475	−	0.285176i	$-0.907948\pi$
$967$		−	17.7360i		−	0.570351i	0.958475	−	0.285176i	$-0.0920519\pi$
$968$	19.7673	−	39.1605i	0.635344	−	1.25867i
$969$		−	9.83744i		−	0.316024i
$970$	6.10252	−	38.8464i	0.195940	−	1.24728i
$971$			22.1875i			0.712032i	0.934480	+	0.356016i	$0.115865\pi$
$971$			22.1875i			0.712032i	−0.934480	+	0.356016i	$0.884135\pi$
$972$	1.90366	+	0.613241i	0.0610600	+	0.0196697i
$973$	8.81439			0.282576
$974$	−3.95062	+	25.1482i	−0.126586	+	0.805800i
$975$			23.2829i			0.745650i
$976$	−5.49337	+	7.64164i	−0.175839	+	0.244603i
$977$	−21.9267			−0.701496			−0.350748	−	0.936470i	$-0.614073\pi$
$977$	−21.9267			−0.701496			−0.350748	+	0.936470i	$0.614073\pi$
$978$	−17.3370	−	2.72354i	−0.554377	−	0.0870891i
$979$	69.6961			2.22750
$980$	−12.4404	+	38.6184i	−0.397394	+	1.23362i
$981$			3.94940i			0.126095i
$982$	−34.4301	−	5.40875i	−1.09871	−	0.172600i
$983$	41.1149			1.31136			0.655681	−	0.755038i	$-0.272382\pi$
$983$	41.1149			1.31136			0.655681	+	0.755038i	$0.272382\pi$
$984$	2.53055	+	1.27736i	0.0806709	+	0.0407207i
$985$	−2.33957			−0.0745450
$986$	3.84428	−	24.4713i	0.122427	−	0.779324i
$987$			8.89541i			0.283144i
$988$	48.9219	+	15.7595i	1.55641	+	0.501378i
$989$			21.3907i			0.680184i
$990$	−22.7265	−	3.57020i	−0.722297	−	0.113468i
$991$	−38.7393			−1.23060			−0.615298	−	0.788295i	$-0.710964\pi$
$991$	−38.7393			−1.23060			−0.615298	+	0.788295i	$0.710964\pi$
$992$	−14.6044	+	14.7895i	−0.463691	+	0.469568i
$993$	6.20476			0.196902
$994$	−12.5861	−	1.97720i	−0.399208	−	0.0627130i
$995$	−42.8859			−1.35957
$996$	5.21083	−	16.1758i	0.165112	−	0.512551i
$997$	22.3693			0.708443			0.354221	−	0.935162i	$-0.384746\pi$
$997$	22.3693			0.708443			0.354221	+	0.935162i	$0.384746\pi$
$998$	4.00010	−	25.4631i	0.126621	−	0.806022i
$999$	−8.38084			−0.265158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.18	yes	34
4.3	odd	2		804.2.e.b.535.18	yes	34
67.66	odd	2		804.2.e.b.535.17	yes	34
268.267	even	2	inner	804.2.e.a.535.17	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.17	✓	34	268.267	even	2	inner
804.2.e.a.535.18	yes	34	1.1	even	1	trivial
804.2.e.b.535.17	yes	34	67.66	odd	2
804.2.e.b.535.18	yes	34	4.3	odd	2

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.219472 + 1.39708i) q^{2} -1.00000 q^{3} +(-1.90366 - 0.613241i) q^{4} +3.15947i q^{5} +(0.219472 - 1.39708i) q^{6} +0.761043 q^{7} +(1.27455 - 2.52498i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.219472 + 1.39708i) q^{2} -1.00000 q^{3} +(-1.90366 - 0.613241i) q^{4} +3.15947i q^{5} +(0.219472 - 1.39708i) q^{6} +0.761043 q^{7} +(1.27455 - 2.52498i) q^{8} +1.00000 q^{9} +(-4.41403 - 0.693416i) q^{10} +5.14871 q^{11} +(1.90366 + 0.613241i) q^{12} +4.67319i q^{13} +(-0.167028 + 1.06324i) q^{14} -3.15947i q^{15} +(3.24787 + 2.33481i) q^{16} +1.78889 q^{17} +(-0.219472 + 1.39708i) q^{18} +5.49920i q^{19} +(1.93751 - 6.01456i) q^{20} -0.761043 q^{21} +(-1.13000 + 7.19316i) q^{22} -2.96158i q^{23} +(-1.27455 + 2.52498i) q^{24} -4.98223 q^{25} +(-6.52882 - 1.02564i) q^{26} -1.00000 q^{27} +(-1.44877 - 0.466703i) q^{28} -9.79158 q^{29} +(4.41403 + 0.693416i) q^{30} +3.67432 q^{31} +(-3.97473 + 4.02511i) q^{32} -5.14871 q^{33} +(-0.392611 + 2.49922i) q^{34} +2.40449i q^{35} +(-1.90366 - 0.613241i) q^{36} +8.38084 q^{37} +(-7.68282 - 1.20692i) q^{38} -4.67319i q^{39} +(7.97759 + 4.02689i) q^{40} -1.00221i q^{41} +(0.167028 - 1.06324i) q^{42} -7.22273 q^{43} +(-9.80142 - 3.15740i) q^{44} +3.15947i q^{45} +(4.13756 + 0.649985i) q^{46} -11.6884i q^{47} +(-3.24787 - 2.33481i) q^{48} -6.42081 q^{49} +(1.09346 - 6.96057i) q^{50} -1.78889 q^{51} +(2.86579 - 8.89618i) q^{52} +9.25172i q^{53} +(0.219472 - 1.39708i) q^{54} +16.2672i q^{55} +(0.969986 - 1.92162i) q^{56} -5.49920i q^{57} +(2.14898 - 13.6796i) q^{58} -0.539474i q^{59} +(-1.93751 + 6.01456i) q^{60} +2.35281i q^{61} +(-0.806411 + 5.13332i) q^{62} +0.761043 q^{63} +(-4.75105 - 6.43642i) q^{64} -14.7648 q^{65} +(1.13000 - 7.19316i) q^{66} +(-8.09955 + 1.18208i) q^{67} +(-3.40544 - 1.09702i) q^{68} +2.96158i q^{69} +(-3.35927 - 0.527719i) q^{70} +11.8375i q^{71} +(1.27455 - 2.52498i) q^{72} -7.50732 q^{73} +(-1.83936 + 11.7087i) q^{74} +4.98223 q^{75} +(3.37233 - 10.4686i) q^{76} +3.91839 q^{77} +(6.52882 + 1.02564i) q^{78} +4.41239 q^{79} +(-7.37675 + 10.2615i) q^{80} +1.00000 q^{81} +(1.40016 + 0.219956i) q^{82} -8.49721i q^{83} +(1.44877 + 0.466703i) q^{84} +5.65193i q^{85} +(1.58519 - 10.0907i) q^{86} +9.79158 q^{87} +(6.56228 - 13.0004i) q^{88} +13.5366 q^{89} +(-4.41403 - 0.693416i) q^{90} +3.55650i q^{91} +(-1.81616 + 5.63785i) q^{92} -3.67432 q^{93} +(16.3297 + 2.56529i) q^{94} -17.3745 q^{95} +(3.97473 - 4.02511i) q^{96} +8.80067i q^{97} +(1.40919 - 8.97039i) q^{98} +5.14871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9	\( 34 q - 34 q^{3} + 2 q^{4} - 4 q^{7} + 6 q^{8} + 34 q^{9} - 6 q^{10} - 2 q^{12} - 4 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} - 34 q^{27} + 8 q^{28} - 16 q^{29} + 6 q^{30} + 4 q^{31} + 2 q^{36} + 12 q^{37} - 26 q^{38} - 18 q^{40} + 4 q^{42} + 4 q^{43} - 26 q^{44} + 4 q^{46} - 2 q^{48} + 46 q^{49} + 18 q^{50} - 32 q^{52} + 14 q^{56} - 4 q^{58} - 12 q^{60} - 2 q^{62} - 4 q^{63} + 26 q^{64} + 8 q^{66} + 18 q^{67} - 34 q^{68} - 56 q^{70} + 6 q^{72} + 12 q^{73} - 22 q^{74} + 34 q^{75} - 32 q^{76} - 8 q^{77} - 10 q^{78} + 12 q^{79} + 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} + 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} - 32 q^{94} + 40 q^{95} + 40 q^{98}+O(q^{100}) \) 34 * q - 34 * q^3 + 2 * q^4 - 4 * q^7 + 6 * q^8 + 34 * q^9 - 6 * q^10 - 2 * q^12 - 4 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 - 34 * q^27 + 8 * q^28 - 16 * q^29 + 6 * q^30 + 4 * q^31 + 2 * q^36 + 12 * q^37 - 26 * q^38 - 18 * q^40 + 4 * q^42 + 4 * q^43 - 26 * q^44 + 4 * q^46 - 2 * q^48 + 46 * q^49 + 18 * q^50 - 32 * q^52 + 14 * q^56 - 4 * q^58 - 12 * q^60 - 2 * q^62 - 4 * q^63 + 26 * q^64 + 8 * q^66 + 18 * q^67 - 34 * q^68 - 56 * q^70 + 6 * q^72 + 12 * q^73 - 22 * q^74 + 34 * q^75 - 32 * q^76 - 8 * q^77 - 10 * q^78 + 12 * q^79 + 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 + 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 - 32 * q^94 + 40 * q^95 + 40 * q^98

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