LMFDB - Embedded newform 225.2.w.a.2.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	225.2
Dual form			225.2.w.a.113.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26732 - 1.02626i) q^{2} +(0.979850 - 1.42825i) q^{3} +(0.137078 + 0.644900i) q^{4} +(-1.08873 + 1.95312i) q^{5} +(-2.70753 + 0.804473i) q^{6} +(-3.51917 + 0.942959i) q^{7} +(-0.992568 + 1.94802i) q^{8} +(-1.07979 - 2.79894i) q^{9} +O(q^{10})$	\(q+(-1.26732 - 1.02626i) q^{2} +(0.979850 - 1.42825i) q^{3} +(0.137078 + 0.644900i) q^{4} +(-1.08873 + 1.95312i) q^{5} +(-2.70753 + 0.804473i) q^{6} +(-3.51917 + 0.942959i) q^{7} +(-0.992568 + 1.94802i) q^{8} +(-1.07979 - 2.79894i) q^{9} +(3.38417 - 1.35792i) q^{10} +(-4.73499 + 0.497667i) q^{11} +(1.05539 + 0.436124i) q^{12} +(-2.32419 - 2.87014i) q^{13} +(5.42764 + 2.41654i) q^{14} +(1.72275 + 3.46874i) q^{15} +(4.46169 - 1.98647i) q^{16} +(-2.54982 - 1.29920i) q^{17} +(-1.50399 + 4.65530i) q^{18} +(6.31730 - 2.05262i) q^{19} +(-1.40881 - 0.434391i) q^{20} +(-2.10148 + 5.95021i) q^{21} +(6.51148 + 4.22861i) q^{22} +(-0.919867 - 2.39633i) q^{23} +(1.80970 + 3.32641i) q^{24} +(-2.62935 - 4.25283i) q^{25} +6.02261i q^{26} +(-5.05561 - 1.20033i) q^{27} +(-1.09051 - 2.14025i) q^{28} +(2.82765 + 3.14043i) q^{29} +(1.37653 - 6.16399i) q^{30} +(-0.908934 + 1.00947i) q^{31} +(-3.46938 - 0.929618i) q^{32} +(-3.92878 + 7.25038i) q^{33} +(1.89813 + 4.26327i) q^{34} +(1.98971 - 7.89999i) q^{35} +(1.65702 - 1.08003i) q^{36} +(0.242591 + 1.53166i) q^{37} +(-10.1126 - 3.88185i) q^{38} +(-6.37664 + 0.507221i) q^{39} +(-2.72409 - 4.05947i) q^{40} +(0.830574 + 0.0872968i) q^{41} +(8.76970 - 5.38417i) q^{42} +(-1.23082 - 4.59349i) q^{43} +(-0.970006 - 2.98537i) q^{44} +(6.64225 + 0.938324i) q^{45} +(-1.29349 + 3.98095i) q^{46} +(4.08223 + 0.213941i) q^{47} +(1.53461 - 8.31885i) q^{48} +(5.43322 - 3.13687i) q^{49} +(-1.03226 + 8.08808i) q^{50} +(-4.35402 + 2.36876i) q^{51} +(1.53236 - 1.89230i) q^{52} +(2.05548 - 1.04732i) q^{53} +(5.17524 + 6.70956i) q^{54} +(4.18310 - 9.78981i) q^{55} +(1.65611 - 7.79139i) q^{56} +(3.25836 - 11.0339i) q^{57} +(-0.360661 - 6.88183i) q^{58} +(1.22755 - 11.6793i) q^{59} +(-2.00084 + 1.58649i) q^{60} +(0.806761 + 7.67582i) q^{61} +(2.18789 - 0.346528i) q^{62} +(6.43925 + 8.83175i) q^{63} +(-2.29860 - 3.16376i) q^{64} +(8.13614 - 1.41463i) q^{65} +(12.4198 - 5.15662i) q^{66} +(-10.4288 + 0.546548i) q^{67} +(0.488329 - 1.82247i) q^{68} +(-4.32389 - 1.03425i) q^{69} +(-10.6290 + 7.96987i) q^{70} +(-10.9516 - 3.55840i) q^{71} +(6.52417 + 0.674682i) q^{72} +(-2.51103 + 15.8540i) q^{73} +(1.26444 - 2.19007i) q^{74} +(-8.65046 - 0.411770i) q^{75} +(2.18969 + 3.79266i) q^{76} +(16.1940 - 6.21628i) q^{77} +(8.60179 + 5.90126i) q^{78} +(-6.41701 + 5.77790i) q^{79} +(-0.977746 + 10.8769i) q^{80} +(-6.66811 + 6.04452i) q^{81} +(-0.963015 - 0.963015i) q^{82} +(-5.32431 - 8.19871i) q^{83} +(-4.12535 - 0.539602i) q^{84} +(5.31355 - 3.56563i) q^{85} +(-3.15426 + 7.08457i) q^{86} +(7.25599 - 0.961445i) q^{87} +(3.73033 - 9.71784i) q^{88} +(-2.03131 + 1.47583i) q^{89} +(-7.45491 - 8.00582i) q^{90} +(10.8857 + 7.90890i) q^{91} +(1.41930 - 0.921706i) q^{92} +(0.551161 + 2.28732i) q^{93} +(-4.95394 - 4.46055i) q^{94} +(-2.86882 + 14.5732i) q^{95} +(-4.72720 + 4.04426i) q^{96} +(0.188909 - 3.60460i) q^{97} +(-10.1049 - 1.60045i) q^{98} +(6.50572 + 12.7156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−1.26732	−	1.02626i	−0.896132	−	0.725673i	0.0661265	−	0.997811i	$-0.478936\pi$
$2$	−1.26732	−	1.02626i	−0.896132	−	0.725673i	−0.962258	+	0.272138i	$0.912269\pi$
$3$	0.979850	−	1.42825i	0.565717	−	0.824600i
$3$	0.979850	−	1.42825i	0.565717	−	0.824600i
$4$	0.137078	+	0.644900i	0.0685388	+	0.322450i
$5$	−1.08873	+	1.95312i	−0.486894	+	0.873461i
$5$	−1.08873	+	1.95312i	−0.486894	+	0.873461i
$6$	−2.70753	+	0.804473i	−1.10535	+	0.328425i
$7$	−3.51917	+	0.942959i	−1.33012	+	0.356405i	−0.852761	−	0.522302i	$-0.825073\pi$
$7$	−3.51917	+	0.942959i	−1.33012	+	0.356405i	−0.477361	+	0.878707i	$0.658407\pi$
$8$	−0.992568	+	1.94802i	−0.350926	+	0.688731i
$9$	−1.07979	−	2.79894i	−0.359930	−	0.932979i
$10$	3.38417	−	1.35792i	1.07017	−	0.429411i
$11$	−4.73499	+	0.497667i	−1.42765	+	0.150052i	−0.786608	−	0.617452i	$-0.788165\pi$
$11$	−4.73499	+	0.497667i	−1.42765	+	0.150052i	−0.641044	+	0.767504i	$0.721498\pi$
$12$	1.05539	+	0.436124i	0.304666	+	0.125898i
$13$	−2.32419	−	2.87014i	−0.644616	−	0.796034i	0.345179	−	0.938537i	$-0.387818\pi$
$13$	−2.32419	−	2.87014i	−0.644616	−	0.796034i	−0.989794	+	0.142503i	$0.954485\pi$
$14$	5.42764	+	2.41654i	1.45060	+	0.645848i
$15$	1.72275	+	3.46874i	0.444812	+	0.895624i
$16$	4.46169	−	1.98647i	1.11542	−	0.496618i
$17$	−2.54982	−	1.29920i	−0.618422	−	0.315102i	0.116565	−	0.993183i	$-0.462812\pi$
$17$	−2.54982	−	1.29920i	−0.618422	−	0.315102i	−0.734987	+	0.678081i	$0.762812\pi$
$18$	−1.50399	+	4.65530i	−0.354494	+	1.09726i
$19$	6.31730	−	2.05262i	1.44929	−	0.470903i	0.524509	−	0.851405i	$-0.324249\pi$
$19$	6.31730	−	2.05262i	1.44929	−	0.470903i	0.924780	+	0.380502i	$0.124249\pi$
$20$	−1.40881	−	0.434391i	−0.315019	−	0.0971327i
$21$	−2.10148	+	5.95021i	−0.458580	+	1.29844i
$22$	6.51148	+	4.22861i	1.38825	+	0.901542i
$23$	−0.919867	−	2.39633i	−0.191805	−	0.499670i	0.803628	−	0.595133i	$-0.202900\pi$
$23$	−0.919867	−	2.39633i	−0.191805	−	0.499670i	−0.995433	+	0.0954622i	$0.969567\pi$
$24$	1.80970	+	3.32641i	0.369403	+	0.679000i
$25$	−2.62935	−	4.25283i	−0.525869	−	0.850565i
$26$			6.02261i			1.18113i
$27$	−5.05561	−	1.20033i	−0.972953	−	0.231004i
$28$	−1.09051	−	2.14025i	−0.206088	−	0.404470i
$29$	2.82765	+	3.14043i	0.525082	+	0.583163i	0.946094	−	0.323892i	$-0.104992\pi$
$29$	2.82765	+	3.14043i	0.525082	+	0.583163i	−0.421012	+	0.907055i	$0.638325\pi$
$30$	1.37653	−	6.16399i	0.251320	−	1.12539i
$31$	−0.908934	+	1.00947i	−0.163249	+	0.181307i	−0.819220	−	0.573480i	$-0.805593\pi$
$31$	−0.908934	+	1.00947i	−0.163249	+	0.181307i	0.655970	+	0.754787i	$0.272260\pi$
$32$	−3.46938	−	0.929618i	−0.613306	−	0.164335i
$33$	−3.92878	+	7.25038i	−0.683913	+	1.26213i
$34$	1.89813	+	4.26327i	0.325527	+	0.731145i
$35$	1.98971	−	7.89999i	0.336322	−	1.33534i
$36$	1.65702	−	1.08003i	0.276170	−	0.180005i
$37$	0.242591	+	1.53166i	0.0398818	+	0.251803i	0.999572	−	0.0292566i	$-0.00931398\pi$
$37$	0.242591	+	1.53166i	0.0398818	+	0.251803i	−0.959690	+	0.281060i	$0.909314\pi$
$38$	−10.1126	−	3.88185i	−1.64048	−	0.629719i
$39$	−6.37664	+	0.507221i	−1.02108	+	0.0812203i
$40$	−2.72409	−	4.05947i	−0.430716	−	0.641859i
$41$	0.830574	+	0.0872968i	0.129714	+	0.0136335i	0.169163	−	0.985588i	$-0.445894\pi$
$41$	0.830574	+	0.0872968i	0.129714	+	0.0136335i	−0.0394490	+	0.999222i	$0.512560\pi$
$42$	8.76970	−	5.38417i	1.35319	−	0.830796i
$43$	−1.23082	−	4.59349i	−0.187699	−	0.700501i	−0.994037	−	0.109046i	$-0.965220\pi$
$43$	−1.23082	−	4.59349i	−0.187699	−	0.700501i	0.806338	−	0.591455i	$-0.201446\pi$
$44$	−0.970006	−	2.98537i	−0.146234	−	0.450062i
$45$	6.64225	+	0.938324i	0.990169	+	0.139877i
$46$	−1.29349	+	3.98095i	−0.190714	+	0.586959i
$47$	4.08223	+	0.213941i	0.595454	+	0.0312064i	0.347683	−	0.937612i	$-0.386969\pi$
$47$	4.08223	+	0.213941i	0.595454	+	0.0312064i	0.247771	+	0.968819i	$0.420302\pi$
$48$	1.53461	−	8.31885i	0.221502	−	1.20072i
$49$	5.43322	−	3.13687i	0.776174	−	0.448125i
$50$	−1.03226	+	8.08808i	−0.145984	+	1.14383i
$51$	−4.35402	+	2.36876i	−0.609685	+	0.331692i
$52$	1.53236	−	1.89230i	0.212500	−	0.262415i
$53$	2.05548	−	1.04732i	0.282342	−	0.143861i	−0.307085	−	0.951682i	$-0.599354\pi$
$53$	2.05548	−	1.04732i	0.282342	−	0.143861i	0.589427	+	0.807822i	$0.299354\pi$
$54$	5.17524	+	6.70956i	0.704260	+	0.913056i
$55$	4.18310	−	9.78981i	0.564050	−	1.32006i
$56$	1.65611	−	7.79139i	0.221307	−	1.04117i
$57$	3.25836	−	11.0339i	0.431581	−	1.46148i
$58$	−0.360661	−	6.88183i	−0.0473572	−	0.903629i
$59$	1.22755	−	11.6793i	0.159813	−	1.52052i	−0.561249	−	0.827647i	$-0.689679\pi$
$59$	1.22755	−	11.6793i	0.159813	−	1.52052i	0.721062	−	0.692870i	$-0.243654\pi$
$60$	−2.00084	+	1.58649i	−0.258307	+	0.204815i
$61$	0.806761	+	7.67582i	0.103295	+	0.982788i	0.916290	+	0.400516i	$0.131169\pi$
$61$	0.806761	+	7.67582i	0.103295	+	0.982788i	−0.812994	+	0.582271i	$0.802164\pi$
$62$	2.18789	−	0.346528i	0.277863	−	0.0440091i
$63$	6.43925	+	8.83175i	0.811269	+	1.11270i
$64$	−2.29860	−	3.16376i	−0.287326	−	0.395470i
$65$	8.13614	−	1.41463i	1.00916	−	0.175463i
$66$	12.4198	−	5.15662i	1.52877	−	0.634736i
$67$	−10.4288	+	0.546548i	−1.27408	+	0.0667715i	−0.677342	−	0.735668i	$-0.736868\pi$
$67$	−10.4288	+	0.546548i	−1.27408	+	0.0667715i	−0.596733	+	0.802440i	$0.703535\pi$
$68$	0.488329	−	1.82247i	0.0592186	−	0.221007i
$69$	−4.32389	−	1.03425i	−0.520536	−	0.124509i
$70$	−10.6290	+	7.96987i	−1.27041	+	0.952582i
$71$	−10.9516	−	3.55840i	−1.29972	−	0.422304i	−0.424236	−	0.905552i	$-0.639457\pi$
$71$	−10.9516	−	3.55840i	−1.29972	−	0.422304i	−0.875484	+	0.483247i	$0.839457\pi$
$72$	6.52417	+	0.674682i	0.768880	+	0.0795120i
$73$	−2.51103	+	15.8540i	−0.293894	+	1.85557i	0.191785	+	0.981437i	$0.438572\pi$
$73$	−2.51103	+	15.8540i	−0.293894	+	1.85557i	−0.485679	+	0.874137i	$0.661428\pi$
$74$	1.26444	−	2.19007i	0.146988	−	0.254590i
$75$	−8.65046	−	0.411770i	−0.998869	−	0.0475471i
$76$	2.18969	+	3.79266i	0.251175	+	0.435048i
$77$	16.1940	−	6.21628i	1.84547	−	0.708410i
$78$	8.60179	+	5.90126i	0.973961	+	0.668186i
$79$	−6.41701	+	5.77790i	−0.721970	+	0.650065i	−0.945869	−	0.324547i	$-0.894788\pi$
$79$	−6.41701	+	5.77790i	−0.721970	+	0.650065i	0.223899	+	0.974612i	$0.428121\pi$
$80$	−0.977746	+	10.8769i	−0.109315	+	1.21608i
$81$	−6.66811	+	6.04452i	−0.740901	+	0.671614i
$82$	−0.963015	−	0.963015i	−0.106347	−	0.106347i
$83$	−5.32431	−	8.19871i	−0.584418	−	0.899926i	0.415535	−	0.909577i	$-0.363594\pi$
$83$	−5.32431	−	8.19871i	−0.584418	−	0.899926i	−0.999953	+	0.00965169i	$0.996928\pi$
$84$	−4.12535	−	0.539602i	−0.450113	−	0.0588754i
$85$	5.31355	−	3.56563i	0.576335	−	0.386747i
$86$	−3.15426	+	7.08457i	−0.340132	+	0.763949i
$87$	7.25599	−	0.961445i	0.777923	−	0.103078i
$88$	3.73033	−	9.71784i	0.397654	−	1.03593i
$89$	−2.03131	+	1.47583i	−0.215318	+	0.156438i	−0.690217	−	0.723603i	$-0.742485\pi$
$89$	−2.03131	+	1.47583i	−0.215318	+	0.156438i	0.474898	+	0.880041i	$0.342485\pi$
$90$	−7.45491	−	8.00582i	−0.785817	−	0.843887i
$91$	10.8857	+	7.90890i	1.14113	+	0.829078i
$92$	1.41930	−	0.921706i	0.147972	−	0.0960945i
$93$	0.551161	+	2.28732i	0.0571527	+	0.237184i
$94$	−4.95394	−	4.46055i	−0.510960	−	0.460070i
$95$	−2.86882	+	14.5732i	−0.294334	+	1.49518i
$96$	−4.72720	+	4.04426i	−0.482468	+	0.412765i
$97$	0.188909	−	3.60460i	0.0191808	−	0.365992i	−0.972129	−	0.234446i	$-0.924673\pi$
$97$	0.188909	−	3.60460i	0.0191808	−	0.365992i	0.991310	−	0.131546i	$-0.0419941\pi$
$98$	−10.1049	−	1.60045i	−1.02075	−	0.161670i
$99$	6.50572	+	12.7156i	0.653850	+	1.27796i
$100$	2.38222	−	2.27863i	0.238222	−	0.227863i
$101$	−3.80678	−	2.19784i	−0.378789	−	0.218694i	0.298502	−	0.954409i	$-0.403513\pi$
$101$	−3.80678	−	2.19784i	−0.378789	−	0.218694i	−0.677291	+	0.735715i	$0.736846\pi$
$102$	7.94890	+	1.46636i	0.787058	+	0.145192i
$103$	4.87026	−	7.49955i	0.479881	−	0.738952i	−0.512958	−	0.858414i	$-0.671450\pi$
$103$	4.87026	−	7.49955i	0.479881	−	0.738952i	0.992839	+	0.119462i	$0.0381168\pi$
$104$	7.89803	−	1.67878i	0.774465	−	0.164618i
$105$	−9.33353	−	10.5826i	−0.910860	−	1.03276i
$106$	−3.67978	−	0.782161i	−0.357412	−	0.0759702i
$107$	−11.5058	+	11.5058i	−1.11231	+	1.11231i	−0.119468	+	0.992838i	$0.538119\pi$
$107$	−11.5058	+	11.5058i	−1.11231	+	1.11231i	−0.992838	+	0.119468i	$0.961881\pi$
$108$	0.0810826	−	3.42490i	0.00780218	−	0.329561i
$109$	−6.85156	+	9.43036i	−0.656260	+	0.903265i	−0.999350	−	0.0360376i	$-0.988526\pi$
$109$	−6.85156	+	9.43036i	−0.656260	+	0.903265i	0.343090	+	0.939303i	$0.388526\pi$
$110$	−15.3482	+	8.11390i	−1.46339	+	0.773630i
$111$	2.42530	+	1.15432i	0.230199	+	0.109563i
$112$	−13.8283	+	11.1979i	−1.30665	+	1.05811i
$113$	8.43405	−	6.82976i	0.793408	−	0.642489i	−0.144448	−	0.989512i	$-0.546141\pi$
$113$	8.43405	−	6.82976i	0.793408	−	0.642489i	0.937857	+	0.347023i	$0.112807\pi$
$114$	−15.4530	+	10.6396i	−1.44731	+	0.996493i
$115$	5.68181	+	0.812345i	0.529832	+	0.0757516i
$116$	−1.63765	+	2.25403i	−0.152052	+	0.209282i
$117$	−5.52371	+	9.60442i	−0.510667	+	0.887929i
$118$	−13.5417	+	13.5417i	−1.24661	+	1.24661i
$119$	10.1983	+	2.16773i	0.934881	+	0.198715i
$120$	−8.46713	−	0.0869963i	−0.772940	−	0.00794164i
$121$	11.4128	−	2.42587i	1.03753	−	0.220533i
$122$	6.85493	−	10.5557i	0.620617	−	0.955666i
$123$	0.938519	−	1.10073i	0.0846234	−	0.0992493i
$124$	−0.775604	−	0.447795i	−0.0696513	−	0.0402132i
$125$	11.1689	−	0.505260i	0.998978	−	0.0451918i
$126$	0.903045	−	17.8010i	0.0804496	−	1.58584i
$127$	−2.82088	−	0.446784i	−0.250313	−	0.0396456i	0.0300171	−	0.999549i	$-0.490444\pi$
$127$	−2.82088	−	0.446784i	−0.250313	−	0.0396456i	−0.280330	+	0.959904i	$0.590444\pi$
$128$	−0.709714	+	13.5422i	−0.0627305	+	1.19697i
$129$	−7.76667	−	2.74301i	−0.683817	−	0.241509i
$130$	−11.7629	−	6.55698i	−1.03167	−	0.575085i
$131$	−10.8047	−	9.72857i	−0.944009	−	0.849989i	0.0448278	−	0.998995i	$-0.485726\pi$
$131$	−10.8047	−	9.72857i	−0.944009	−	0.849989i	−0.988836	+	0.149006i	$0.952393\pi$
$132$	−5.21431	−	1.53981i	−0.453848	−	0.134023i
$133$	−20.2961	+	13.1805i	−1.75990	+	1.14289i
$134$	13.7775	+	10.0099i	1.19019	+	0.864726i
$135$	7.84857	−	8.56738i	0.675498	−	0.737362i
$136$	5.06174	−	3.67757i	0.434041	−	0.315349i
$137$	−0.124897	+	0.325367i	−0.0106706	+	0.0277980i	−0.938812	−	0.344429i	$-0.888072\pi$
$137$	−0.124897	+	0.325367i	−0.0106706	+	0.0277980i	0.928142	+	0.372227i	$0.121406\pi$
$138$	4.41836	+	5.74815i	0.376116	+	0.489315i
$139$	−0.460243	+	1.03372i	−0.0390373	+	0.0876793i	−0.932012	−	0.362428i	$-0.881948\pi$
$139$	−0.460243	+	1.03372i	−0.0390373	+	0.0876793i	0.892974	+	0.450108i	$0.148614\pi$
$140$	5.36744	+	0.200249i	0.453632	+	0.0169241i
$141$	4.30553	−	5.62081i	0.362591	−	0.473357i
$142$	10.2274	+	15.7488i	0.858265	+	1.32161i
$143$	12.4334	+	12.4334i	1.03973	+	1.03973i
$144$	−10.3777	−	10.3430i	−0.864808	−	0.861919i
$145$	−9.21217	+	2.10368i	−0.765029	+	0.174701i
$146$	19.4526	−	17.5152i	1.60991	−	1.44957i
$147$	0.843508	−	10.8337i	0.0695713	−	0.893545i
$148$	−0.954514	+	0.366403i	−0.0784605	+	0.0301182i
$149$	6.32656	+	10.9579i	0.518292	+	0.897708i	0.999774	+	0.0212520i	$0.00676523\pi$
$149$	6.32656	+	10.9579i	0.518292	+	0.897708i	−0.481482	+	0.876456i	$0.659901\pi$
$150$	10.5403	+	9.39944i	0.860615	+	0.767461i
$151$	11.8910	−	20.5957i	0.967672	−	1.67606i	0.265414	−	0.964135i	$-0.414491\pi$
$151$	11.8910	−	20.5957i	0.967672	−	1.67606i	0.702258	−	0.711922i	$-0.252175\pi$
$152$	−2.27181	+	14.3436i	−0.184268	+	1.16342i
$153$	−0.883109	+	8.53965i	−0.0713951	+	0.690390i
$154$	−26.9024	−	8.74113i	−2.16786	−	0.704381i
$155$	−0.982041	−	2.87430i	−0.0788794	−	0.230869i
$156$	−1.20120	−	4.04276i	−0.0961730	−	0.323680i
$157$	−0.890963	+	3.32512i	−0.0711066	+	0.265373i	−0.992322	−	0.123679i	$-0.960531\pi$
$157$	−0.890963	+	3.32512i	−0.0711066	+	0.265373i	0.921216	+	0.389052i	$0.127197\pi$
$158$	14.0620	−	0.736960i	1.11872	−	0.0586294i
$159$	0.518230	−	3.96196i	0.0410983	−	0.314204i
$160$	5.59287	−	5.76402i	0.442155	−	0.455686i
$161$	5.49682	+	7.56572i	0.433210	+	0.596262i
$162$	14.6539	−	0.817161i	1.15132	−	0.0642022i
$163$	16.5970	−	2.62870i	1.29997	−	0.205896i	0.532202	−	0.846618i	$-0.321365\pi$
$163$	16.5970	−	2.62870i	1.29997	−	0.205896i	0.767773	+	0.640722i	$0.221365\pi$
$164$	0.0575554	+	0.547603i	0.00449432	+	0.0427606i
$165$	−9.88348	−	15.5671i	−0.769428	−	1.21189i
$166$	−1.66638	+	15.8545i	−0.129336	+	1.23055i
$167$	0.244341	+	4.66230i	0.0189077	+	0.360780i	0.991656	+	0.128915i	$0.0411494\pi$
$167$	0.244341	+	4.66230i	0.0189077	+	0.360780i	−0.972748	+	0.231865i	$0.925517\pi$
$168$	−9.50530	−	9.99972i	−0.733350	−	0.771495i
$169$	−0.132978	+	0.625615i	−0.0102291	+	0.0481242i
$170$	−10.3932	−	0.934264i	−0.797124	−	0.0716548i
$171$	−12.5665	−	15.4654i	−0.960984	−	1.18267i
$172$	2.79362	−	1.42342i	0.213012	−	0.108535i
$173$	0.142684	−	0.176200i	0.0108480	−	0.0133962i	−0.771693	−	0.635995i	$-0.780590\pi$
$173$	0.142684	−	0.176200i	0.0108480	−	0.0133962i	0.782541	+	0.622599i	$0.213923\pi$
$174$	−10.1824	−	6.22805i	−0.771923	−	0.472147i
$175$	13.2634	+	12.4871i	1.00262	+	0.943933i
$176$	−20.1374	+	11.6264i	−1.51792	+	0.876370i
$177$	−15.4782	−	13.1972i	−1.16341	−	0.991963i
$178$	4.08890	+	0.214290i	0.306476	+	0.0160617i
$179$	7.22981	−	22.2511i	0.540382	−	1.66312i	−0.191343	−	0.981523i	$-0.561284\pi$
$179$	7.22981	−	22.2511i	0.540382	−	1.66312i	0.731725	−	0.681600i	$-0.238716\pi$
$180$	0.305380	+	4.41221i	0.0227617	+	0.328867i
$181$	−2.50718	−	7.71631i	−0.186357	−	0.573549i	0.813612	−	0.581409i	$-0.197498\pi$
$181$	−2.50718	−	7.71631i	−0.186357	−	0.573549i	−0.999969	+	0.00785960i	$0.997498\pi$
$182$	−5.67908	−	21.1946i	−0.420961	−	1.57105i
$183$	11.7535	+	6.36889i	0.868842	+	0.470802i
$184$	5.58115	+	0.586602i	0.411448	+	0.0432449i
$185$	−3.25563	−	1.19375i	−0.239359	−	0.0877663i
$186$	1.64888	−	3.46440i	0.120902	−	0.254022i
$187$	12.7199	+	4.88272i	0.930174	+	0.357060i
$188$	0.421612	+	2.66195i	0.0307492	+	0.194143i
$189$	18.9234	−	0.543059i	1.37648	−	0.0395018i
$190$	18.5915	−	15.5248i	1.34877	−	1.12629i
$191$	3.40955	+	7.65798i	0.246707	+	0.554112i	0.993873	−	0.110524i	$-0.0352530\pi$
$191$	3.40955	+	7.65798i	0.246707	+	0.554112i	−0.747167	+	0.664637i	$0.768586\pi$
$192$	−6.77092	+	0.182972i	−0.488649	+	0.0132048i
$193$	3.59845	+	0.964202i	0.259022	+	0.0694048i	0.385993	−	0.922502i	$-0.373859\pi$
$193$	3.59845	+	0.964202i	0.259022	+	0.0694048i	−0.126971	+	0.991906i	$0.540525\pi$
$194$	−3.93865	+	4.37432i	−0.282779	+	0.314058i
$195$	5.95176	−	13.0066i	0.426214	−	0.931419i
$196$	2.76774	+	3.07389i	0.197696	+	0.219563i
$197$	2.24486	+	4.40579i	0.159940	+	0.313900i	0.957044	−	0.289942i	$-0.0936360\pi$
$197$	2.24486	+	4.40579i	0.159940	+	0.313900i	−0.797104	+	0.603842i	$0.793636\pi$
$198$	4.80458	−	22.7912i	0.341447	−	1.61970i
$199$		−	24.6922i		−	1.75039i	−0.483773	−	0.875194i	$-0.660734\pi$
$199$		−	24.6922i		−	1.75039i	0.483773	−	0.875194i	$-0.339266\pi$
$200$	10.8944	−	0.900813i	0.770352	−	0.0636971i
$201$	−9.43801	+	15.4304i	−0.665706	+	1.08838i
$202$	2.56886	+	6.69211i	0.180744	+	0.470855i
$203$	−12.9123	−	8.38534i	−0.906265	−	0.588536i
$204$	−2.12445	−	2.48320i	−0.148741	−	0.173859i
$205$	−1.07477	+	1.52717i	−0.0750651	+	0.106662i
$206$	−13.8687	+	4.50620i	−0.966275	+	0.313962i
$207$	−5.71393	+	5.16219i	−0.397146	+	0.358797i
$208$	−16.0713	−	8.18873i	−1.11434	−	0.567786i
$209$	−28.8908	+	12.8630i	−1.99842	+	0.889754i
$210$	0.968127	+	22.9902i	0.0668071	+	1.58647i
$211$	3.09718	+	1.37895i	0.213218	+	0.0949310i	0.510567	−	0.859838i	$-0.329436\pi$
$211$	3.09718	+	1.37895i	0.213218	+	0.0949310i	−0.297348	+	0.954769i	$0.596102\pi$
$212$	0.957177	+	1.18202i	0.0657392	+	0.0811812i
$213$	−15.8132	+	12.1550i	−1.08350	+	0.832844i
$214$	26.3894	−	2.77364i	1.80394	−	0.189602i
$215$	10.3117	+	2.59712i	0.703250	+	0.177122i
$216$	7.35632	−	8.65704i	0.500534	−	0.589037i
$217$	2.24680	−	4.40960i	0.152523	−	0.299343i
$218$	18.3611	−	4.91984i	1.24357	−	0.333214i
$219$	20.1831	+	19.1209i	1.36385	+	1.29207i
$220$	6.88686	+	1.35572i	0.464312	+	0.0914025i
$221$	2.19740	+	10.3379i	0.147813	+	0.695405i
$222$	−1.88900	−	3.95187i	−0.126782	−	0.265232i
$223$	4.96769	+	4.02275i	0.332661	+	0.269383i	0.781068	−	0.624446i	$-0.214675\pi$
$223$	4.96769	+	4.02275i	0.332661	+	0.269383i	−0.448407	+	0.893829i	$0.648009\pi$
$224$	13.0859			0.874342
$225$	−9.06426	+	11.9515i	−0.604284	+	0.796769i
$226$	−17.6977			−1.17724
$227$	−8.49893	−	6.88230i	−0.564094	−	0.456794i	0.304365	−	0.952556i	$-0.401556\pi$
$227$	−8.49893	−	6.88230i	−0.564094	−	0.456794i	−0.868459	+	0.495761i	$0.834889\pi$
$228$	7.56243	+	0.588810i	0.500834	+	0.0389949i
$229$	3.94438	+	18.5569i	0.260652	+	1.22627i	0.892453	+	0.451141i	$0.148983\pi$
$229$	3.94438	+	18.5569i	0.260652	+	1.22627i	−0.631801	+	0.775131i	$0.717684\pi$
$230$	−6.36701	−	6.86050i	−0.419828	−	0.452368i
$231$	6.98925	−	29.2200i	0.459859	−	1.92254i
$232$	−8.92427	+	2.39125i	−0.585907	+	0.156993i
$233$	10.3387	−	20.2908i	0.677310	−	1.32930i	−0.254755	−	0.967006i	$-0.581995\pi$
$233$	10.3387	−	20.2908i	0.677310	−	1.32930i	0.932065	−	0.362290i	$-0.118005\pi$
$234$	16.8569	−	6.50315i	1.10197	−	0.425124i
$235$	−4.86228	+	7.74016i	−0.317180	+	0.504912i
$236$	7.70025	−	0.809329i	0.501244	−	0.0526828i
$237$	1.96458	+	14.8266i	0.127613	+	0.963089i
$238$	−10.6999	−	13.2133i	−0.693574	−	0.856493i
$239$	−15.7771	−	7.02441i	−1.02053	−	0.454371i	−0.172893	−	0.984941i	$-0.555311\pi$
$239$	−15.7771	−	7.02441i	−1.02053	−	0.454371i	−0.847641	+	0.530570i	$0.821978\pi$
$240$	14.5769	+	12.0542i	0.940937	+	0.778097i
$241$	−10.0634	+	4.48050i	−0.648238	+	0.288614i	−0.704395	−	0.709808i	$-0.748782\pi$
$241$	−10.0634	+	4.48050i	−0.648238	+	0.288614i	0.0561575	+	0.998422i	$0.482115\pi$
$242$	−16.9532	−	8.63811i	−1.08980	−	0.555279i
$243$	2.09934	+	15.4464i	0.134672	+	0.990890i
$244$	−4.83954	+	1.57246i	−0.309820	+	0.100667i
$245$	0.211389	+	14.0269i	0.0135051	+	0.896147i
$246$	−2.31903	+	0.431815i	−0.147856	+	0.0275315i
$247$	−20.5739	−	13.3609i	−1.30909	−	0.850132i
$248$	−1.06430	−	2.77260i	−0.0675832	−	0.176060i
$249$	−16.9268	−	0.429073i	−1.07269	−	0.0271914i
$250$	−14.6731	−	10.8219i	−0.928011	−	0.684434i
$251$		−	4.30822i		−	0.271933i	−0.990713	−	0.135966i	$-0.956586\pi$
$251$		−	4.30822i		−	0.271933i	0.990713	−	0.135966i	$-0.0434139\pi$
$252$	−4.81291	+	5.36330i	−0.303185	+	0.337856i
$253$	5.54813	+	10.8888i	0.348808	+	0.684575i
$254$	3.11645	+	3.46117i	0.195543	+	0.217173i
$255$	0.113872	−	11.0828i	0.00713092	−	0.694035i
$256$	9.56373	−	10.6216i	0.597733	−	0.663850i
$257$	−7.18663	−	1.92565i	−0.448290	−	0.120119i	0.0276093	−	0.999619i	$-0.491211\pi$
$257$	−7.18663	−	1.92565i	−0.448290	−	0.120119i	−0.475899	+	0.879500i	$0.657877\pi$
$258$	7.02784	+	11.4469i	0.437534	+	0.712652i
$259$	−2.29801	−	5.16142i	−0.142792	−	0.320715i
$260$	2.02758	+	5.05308i	0.125745	+	0.313379i
$261$	5.73659	−	11.3054i	0.355086	−	0.699788i
$262$	3.70898	+	23.4176i	0.229142	+	1.44674i
$263$	11.3421	+	4.35383i	0.699385	+	0.268469i	0.681971	−	0.731380i	$-0.261123\pi$
$263$	11.3421	+	4.35383i	0.699385	+	0.268469i	0.0174143	+	0.999848i	$0.494457\pi$
$264$	−10.2243	−	14.8499i	−0.629264	−	0.913946i
$265$	−0.192318	+	5.15485i	−0.0118140	+	0.316660i
$266$	39.2483	+	4.12516i	2.40647	+	0.252930i
$267$	0.117478	+	4.34731i	0.00718953	+	0.266051i
$268$	−1.78202	−	6.65058i	−0.108854	−	0.406249i
$269$	−4.12547	−	12.6969i	−0.251534	−	0.774143i	−0.994493	−	0.104806i	$-0.966578\pi$
$269$	−4.12547	−	12.6969i	−0.251534	−	0.774143i	0.742958	−	0.669338i	$-0.233422\pi$
$270$	−18.7390	+	2.80297i	−1.14042	+	0.170583i
$271$	−5.46734	+	16.8267i	−0.332117	+	1.02215i	0.636007	+	0.771683i	$0.280585\pi$
$271$	−5.46734	+	16.8267i	−0.332117	+	1.02215i	−0.968125	+	0.250469i	$0.919415\pi$
$272$	−13.9573	−	0.731473i	−0.846287	−	0.0443520i
$273$	21.9622	−	7.79791i	1.32921	−	0.471951i
$274$	0.492194	−	0.284169i	0.0297345	−	0.0171672i
$275$	14.5664	+	18.8285i	0.878388	+	1.13540i
$276$	0.0742781	−	2.93025i	0.00447102	−	0.176380i
$277$	−4.18256	+	5.16503i	−0.251306	+	0.310337i	−0.887150	−	0.461480i	$-0.847319\pi$
$277$	−4.18256	+	5.16503i	−0.251306	+	0.310337i	0.635845	+	0.771817i	$0.280652\pi$
$278$	1.64414	−	0.837732i	0.0986091	−	0.0502438i
$279$	3.80691	+	1.45403i	0.227914	+	0.0870507i
$280$	13.4145	+	11.7173i	0.801667	+	0.700241i
$281$	−2.08052	+	9.78805i	−0.124113	+	0.583906i	0.871504	+	0.490388i	$0.163145\pi$
$281$	−2.08052	+	9.78805i	−0.124113	+	0.583906i	−0.995618	+	0.0935187i	$0.970189\pi$
$282$	−11.2249	+	2.70479i	−0.668432	+	0.161068i
$283$	0.692565	+	13.2149i	0.0411687	+	0.785546i	0.938729	+	0.344655i	$0.112004\pi$
$283$	0.692565	+	13.2149i	0.0411687	+	0.785546i	−0.897561	+	0.440891i	$0.854663\pi$
$284$	0.793587	−	7.55048i	0.0470907	−	0.448039i
$285$	18.0031	+	18.3769i	1.06641	+	1.08855i
$286$	−2.99726	−	28.5170i	−0.177231	−	1.68624i
$287$	−3.00525	+	0.475985i	−0.177394	+	0.0280965i
$288$	1.14426	+	10.7144i	0.0674259	+	0.631351i
$289$	−5.17868	−	7.12785i	−0.304628	−	0.419285i
$290$	13.8337	+	6.78802i	0.812342	+	0.398606i
$291$	−4.96316	−	3.80178i	−0.290946	−	0.222864i
$292$	−10.5685	+	0.553870i	−0.618473	+	0.0324128i
$293$	6.97767	−	26.0410i	0.407640	−	1.52133i	−0.391495	−	0.920180i	$-0.628042\pi$
$293$	6.97767	−	26.0410i	0.407640	−	1.52133i	0.799135	−	0.601152i	$-0.205291\pi$
$294$	−12.1871	+	12.8641i	−0.710767	+	0.750248i
$295$	21.4746	+	15.1131i	1.25030	+	0.879920i
$296$	−3.22450	−	1.04770i	−0.187420	−	0.0608966i
$297$	24.5356	+	3.16755i	1.42370	+	0.183800i
$298$	3.22786	−	20.3799i	0.186985	−	1.18057i
$299$	−4.73987	+	8.20970i	−0.274114	+	0.474779i
$300$	−0.920234	−	5.63512i	−0.0531298	−	0.325344i
$301$	8.66295	+	15.0047i	0.499324	+	0.864855i
$302$	−36.2062	+	13.8982i	−2.08343	+	0.799754i
$303$	−6.86914	+	3.28347i	−0.394622	+	0.188630i
$304$	24.1084	−	21.7073i	1.38271	−	1.24500i
$305$	−15.8701	−	6.78117i	−0.908721	−	0.388289i
$306$	9.88306	−	9.91619i	0.564977	−	0.566871i
$307$	−7.81159	−	7.81159i	−0.445831	−	0.445831i	0.448135	−	0.893966i	$-0.352088\pi$
$307$	−7.81159	−	7.81159i	−0.445831	−	0.445831i	−0.893966	+	0.448135i	$0.852088\pi$
$308$	6.22870	+	9.59136i	0.354913	+	0.546518i
$309$	−5.93909	−	14.3044i	−0.337863	−	0.813748i
$310$	−1.70521	+	4.65049i	−0.0968492	+	0.264130i
$311$	−7.38774	+	16.5931i	−0.418920	+	0.940910i	0.573635	+	0.819111i	$0.305533\pi$
$311$	−7.38774	+	16.5931i	−0.418920	+	0.940910i	−0.992555	+	0.121799i	$0.961134\pi$
$312$	5.34117	−	12.9253i	0.302384	−	0.731751i
$313$	4.11751	−	10.7265i	0.232735	−	0.606296i	−0.766624	−	0.642097i	$-0.778065\pi$
$313$	4.11751	−	10.7265i	0.232735	−	0.606296i	0.999359	+	0.0358007i	$0.0113982\pi$
$314$	4.54156	−	3.29964i	0.256295	−	0.186209i
$315$	−24.2600	+	2.96125i	−1.36690	+	0.166848i
$316$	−4.60580	−	3.34631i	−0.259096	−	0.188244i
$317$	−2.49069	+	1.61747i	−0.139891	+	0.0908463i	−0.612687	−	0.790326i	$-0.709911\pi$
$317$	−2.49069	+	1.61747i	−0.139891	+	0.0908463i	0.472796	+	0.881172i	$0.343245\pi$
$318$	−4.72275	+	4.48924i	−0.264839	+	0.251744i
$319$	−14.9518	−	13.4627i	−0.837139	−	0.753764i
$320$	8.68175	−	1.04498i	0.485325	−	0.0584161i
$321$	5.15918	+	27.7071i	0.287957	+	1.54646i
$322$	0.798136	−	15.2293i	0.0444784	−	0.848698i
$323$	−18.7747	−	2.97363i	−1.04465	−	0.165457i
$324$	−4.81216	−	3.47169i	−0.267342	−	0.192872i
$325$	−6.09510	+	17.4310i	−0.338095	+	0.966898i
$326$	−23.7314	−	13.7013i	−1.31436	−	0.758847i
$327$	6.75540	+	19.0261i	0.373575	+	1.05214i
$328$	−0.994457	+	1.53133i	−0.0549097	+	0.0845536i
$329$	−14.5678	+	3.09648i	−0.803149	+	0.170715i
$330$	−3.45026	+	29.8715i	−0.189931	+	1.64437i
$331$	−16.5790	−	3.52397i	−0.911262	−	0.193695i	−0.271653	−	0.962395i	$-0.587570\pi$
$331$	−16.5790	−	3.52397i	−0.911262	−	0.193695i	−0.639609	+	0.768700i	$0.720904\pi$
$332$	4.55750	−	4.55750i	0.250125	−	0.250125i
$333$	4.02508	−	2.33287i	0.220573	−	0.127840i
$334$	4.47506	−	6.15939i	0.244864	−	0.337027i
$335$	10.2866	−	20.9636i	0.562017	−	1.14537i
$336$	2.44378	+	30.7225i	0.133319	+	1.67605i
$337$	6.50203	−	5.26524i	0.354188	−	0.286816i	−0.435669	−	0.900107i	$-0.643488\pi$
$337$	6.50203	−	5.26524i	0.354188	−	0.286816i	0.789857	+	0.613291i	$0.210155\pi$
$338$	0.810568	−	0.656385i	0.0440891	−	0.0357026i
$339$	−1.49049	−	18.7380i	−0.0809524	−	1.01771i
$340$	3.02784	+	2.93794i	0.164208	+	0.159332i
$341$	3.80141	−	5.23219i	0.205858	−	0.283339i
$342$	0.0543748	+	32.4960i	0.00294025	+	1.75718i
$343$	1.87099	−	1.87099i	0.101024	−	0.101024i
$344$	10.1699	+	2.16168i	0.548325	+	0.116550i
$345$	6.72755	−	7.31906i	0.362199	−	0.394045i
$346$	−0.361652	+	0.0768715i	−0.0194425	+	0.00413264i
$347$	9.10601	−	14.0220i	0.488836	−	0.752742i	−0.505057	−	0.863086i	$-0.668529\pi$
$347$	9.10601	−	14.0220i	0.488836	−	0.752742i	0.993893	+	0.110344i	$0.0351952\pi$
$348$	1.61467	+	4.54759i	0.0865554	+	0.243776i
$349$	−22.8822	−	13.2110i	−1.22486	−	0.707171i	−0.258906	−	0.965902i	$-0.583362\pi$
$349$	−22.8822	−	13.2110i	−1.22486	−	0.707171i	−0.965949	+	0.258732i	$0.916695\pi$
$350$	−3.99402	−	29.4367i	−0.213489	−	1.57346i
$351$	8.30510	+	17.3001i	0.443293	+	0.923412i
$352$	16.8901	+	2.67513i	0.900247	+	0.142585i
$353$	0.861405	−	16.4366i	0.0458480	−	0.874831i	−0.874811	−	0.484464i	$-0.839015\pi$
$353$	0.861405	−	16.4366i	0.0458480	−	0.874831i	0.920659	−	0.390367i	$-0.127652\pi$
$354$	6.07207	+	32.6097i	0.322727	+	1.73318i
$355$	18.8733	−	17.5157i	1.00169	−	0.929637i
$356$	−1.23021	−	1.10769i	−0.0652010	−	0.0587072i
$357$	13.0889	−	12.4417i	0.692738	−	0.658486i
$358$	−31.9978	+	20.7796i	−1.69114	+	1.09824i
$359$	0.940606	+	0.683390i	0.0496433	+	0.0360680i	0.612330	−	0.790602i	$-0.290232\pi$
$359$	0.940606	+	0.683390i	0.0496433	+	0.0360680i	−0.562687	+	0.826670i	$0.690232\pi$
$360$	−8.42077	+	12.0079i	−0.443813	+	0.632873i
$361$	20.3238	−	14.7661i	1.06967	−	0.777163i
$362$	−4.74151	+	12.3521i	−0.249208	+	0.649210i
$363$	7.71809	−	18.6773i	0.405095	−	0.980304i
$364$	−3.60826	+	8.10430i	−0.189124	+	0.424780i
$365$	−28.2310	−	22.1651i	−1.47768	−	1.16017i
$366$	−8.35932	−	20.1335i	−0.436949	−	1.05240i
$367$	8.88628	+	13.6837i	0.463860	+	0.714282i	0.990757	−	0.135647i	$-0.0433114\pi$
$367$	8.88628	+	13.6837i	0.463860	+	0.714282i	−0.526897	+	0.849929i	$0.676645\pi$
$368$	−8.86441	−	8.86441i	−0.462090	−	0.462090i
$369$	−0.652506	−	2.41899i	−0.0339681	−	0.125927i
$370$	2.90084	+	4.85398i	0.150807	+	0.252346i
$371$	−6.24602	+	5.62394i	−0.324277	+	0.291980i
$372$	−1.39954	+	0.668983i	−0.0725627	+	0.0346852i
$373$	−14.2850	+	5.48349i	−0.739649	+	0.283925i	−0.698875	−	0.715244i	$-0.746316\pi$
$373$	−14.2850	+	5.48349i	−0.739649	+	0.283925i	−0.0407738	+	0.999168i	$0.512982\pi$
$374$	−11.1093	−	19.2419i	−0.574449	−	0.994975i
$375$	10.2222	−	16.4471i	0.527873	−	0.849323i
$376$	−4.46865	+	7.73993i	−0.230453	+	0.399156i
$377$	2.44145	−	15.4147i	0.125741	−	0.793899i
$378$	−24.5394	−	18.7321i	−1.26217	−	0.963474i
$379$	−14.3151	−	4.65126i	−0.735318	−	0.238919i	−0.0826664	−	0.996577i	$-0.526344\pi$
$379$	−14.3151	−	4.65126i	−0.735318	−	0.238919i	−0.652652	+	0.757658i	$0.726344\pi$
$380$	−9.79149	+	0.147560i	−0.502293	+	0.00756966i
$381$	−3.40216	+	3.59114i	−0.174298	+	0.183980i
$382$	3.53806	−	13.2042i	0.181023	−	0.675586i
$383$	23.0670	−	1.20889i	1.17867	−	0.0617715i	0.547085	−	0.837077i	$-0.315738\pi$
$383$	23.0670	−	1.20889i	1.17867	−	0.0617715i	0.631586	+	0.775306i	$0.282404\pi$
$384$	18.6461	+	14.2829i	0.951532	+	0.728872i
$385$	−5.48967	+	38.3965i	−0.279779	+	1.95687i
$386$	−3.57088	−	4.91489i	−0.181753	−	0.250161i
$387$	−11.5279	+	8.40500i	−0.585995	+	0.427250i
$388$	2.35050	−	0.372283i	0.119329	−	0.0188998i
$389$	1.72463	+	16.4087i	0.0874420	+	0.831955i	0.947068	+	0.321032i	$0.104030\pi$
$389$	1.72463	+	16.4087i	0.0874420	+	0.831955i	−0.859626	+	0.510923i	$0.829304\pi$
$390$	−20.8909	+	10.3755i	−1.05785	+	0.525382i
$391$	−0.767819	+	7.30531i	−0.0388303	+	0.369446i
$392$	0.717861	+	13.6976i	0.0362575	+	0.691834i
$393$	−24.4818	+	5.89922i	−1.23494	+	0.297576i
$394$	1.67651	−	7.88736i	0.0844614	−	0.397360i
$395$	−4.29856	−	18.8237i	−0.216284	−	0.947125i
$396$	−7.30847	+	5.93856i	−0.367264	+	0.298424i
$397$	9.53622	−	4.85895i	0.478609	−	0.243864i	−0.198005	−	0.980201i	$-0.563446\pi$
$397$	9.53622	−	4.85895i	0.478609	−	0.243864i	0.676615	+	0.736337i	$0.263446\pi$
$398$	−25.3406	+	31.2930i	−1.27021	+	1.56858i
$399$	−1.06218	+	41.9028i	−0.0531757	+	2.09777i
$400$	−20.1795	−	13.7517i	−1.00897	−	0.687584i
$401$	4.09767	−	2.36579i	0.204628	−	0.118142i	−0.394184	−	0.919031i	$-0.628973\pi$
$401$	4.09767	−	2.36579i	0.204628	−	0.118142i	0.598812	+	0.800889i	$0.295640\pi$
$402$	27.7965	−	9.86945i	1.38637	−	0.492243i
$403$	5.00987	+	0.262556i	0.249560	+	0.0130789i
$404$	0.895565	−	2.75627i	0.0445560	−	0.137129i
$405$	−4.54592	−	19.6045i	−0.225889	−	0.974153i
$406$	7.75852	+	23.8783i	0.385049	+	1.18506i
$407$	−1.91092	−	7.13166i	−0.0947210	−	0.353503i
$408$	−0.292739	−	10.8329i	−0.0144927	−	0.536308i
$409$	−6.80116	−	0.714831i	−0.336296	−	0.0353461i	−0.0651242	−	0.997877i	$-0.520744\pi$
$409$	−6.80116	−	0.714831i	−0.336296	−	0.0353461i	−0.271171	+	0.962531i	$0.587411\pi$
$410$	2.92934	−	0.832422i	0.144670	−	0.0411104i
$411$	0.342325	+	0.497194i	0.0168856	+	0.0245248i
$412$	5.50406	+	2.11281i	0.271166	+	0.104091i
$413$	6.69317	+	42.2590i	0.329350	+	2.07943i
$414$	12.5391	−	0.678188i	0.616264	−	0.0333311i
$415$	21.8098	−	1.47284i	1.07060	−	0.0722990i
$416$	5.39539	+	12.1182i	0.264531	+	0.594145i
$417$	1.02544	+	1.67024i	0.0502163	+	0.0817918i
$418$	49.8147	+	13.3478i	2.43652	+	0.652863i
$419$	−24.2420	+	26.9234i	−1.18430	+	1.31530i	−0.246080	+	0.969250i	$0.579143\pi$
$419$	−24.2420	+	26.9234i	−1.18430	+	1.31530i	−0.938218	+	0.346046i	$0.887524\pi$
$420$	5.54529	−	7.46983i	0.270583	−	0.364490i
$421$	8.15747	+	9.05979i	0.397571	+	0.441547i	0.908379	−	0.418147i	$-0.137320\pi$
$421$	8.15747	+	9.05979i	0.397571	+	0.441547i	−0.510808	+	0.859695i	$0.670654\pi$
$422$	−2.50996	−	4.92607i	−0.122183	−	0.239798i
$423$	−3.80914	−	11.6569i	−0.185207	−	0.566779i
$424$			5.04367i			0.244942i
$425$	1.17910	+	14.2600i	0.0571946	+	0.691711i
$426$	32.5146	+	0.824203i	1.57534	+	0.0399328i
$427$	−10.0771	−	26.2518i	−0.487666	−	1.27041i
$428$	−8.99726	−	5.84289i	−0.434899	−	0.282427i
$429$	29.9409	−	5.57512i	1.44556	−	0.269170i
$430$	−10.4029	−	13.8738i	−0.501672	−	0.669054i
$431$	9.87770	−	3.20946i	0.475792	−	0.154594i	−0.0612974	−	0.998120i	$-0.519524\pi$
$431$	9.87770	−	3.20946i	0.475792	−	0.154594i	0.537089	+	0.843525i	$0.319524\pi$
$432$	−24.9410	+	4.68732i	−1.19997	+	0.225519i
$433$	−0.410272	−	0.209044i	−0.0197164	−	0.0100460i	0.444104	−	0.895975i	$-0.353522\pi$
$433$	−0.410272	−	0.209044i	−0.0197164	−	0.0100460i	−0.463821	+	0.885929i	$0.653522\pi$
$434$	−7.37281	+	3.28258i	−0.353906	+	0.157569i
$435$	−6.02197	+	15.2186i	−0.288731	+	0.729674i
$436$	−7.02083	−	3.12588i	−0.336237	−	0.149702i
$437$	−10.7298	−	13.2502i	−0.513278	−	0.633845i
$438$	−5.95543	−	44.9454i	−0.284562	−	2.14757i
$439$	−1.45127	+	0.152535i	−0.0692654	+	0.00728008i	−0.139098	−	0.990279i	$-0.544420\pi$
$439$	−1.45127	+	0.152535i	−0.0692654	+	0.00728008i	0.0698324	+	0.997559i	$0.477754\pi$
$440$	14.9188	+	17.8658i	0.711225	+	0.851721i
$441$	−14.6466	−	11.8201i	−0.697459	−	0.562862i
$442$	7.82457	−	15.3566i	0.372177	−	0.730438i
$443$	−9.23142	+	2.47355i	−0.438598	+	0.117522i	−0.471359	−	0.881941i	$-0.656237\pi$
$443$	−9.23142	+	2.47355i	−0.438598	+	0.117522i	0.0327613	+	0.999463i	$0.489570\pi$
$444$	−0.411965	+	1.72230i	−0.0195510	+	0.0817369i
$445$	−0.670935	−	5.57416i	−0.0318054	−	0.264241i
$446$	−2.16728	−	10.1962i	−0.102624	−	0.482806i
$447$	21.8497	+	1.70122i	1.03346	+	0.0804648i
$448$	11.0725	+	8.96632i	0.523126	+	0.423619i
$449$	8.65019			0.408227			0.204114	−	0.978947i	$-0.434569\pi$
$449$	8.65019			0.408227			0.204114	+	0.978947i	$0.434569\pi$
$450$	23.7527	−	5.84418i	1.11971	−	0.275497i
$451$	−3.97620			−0.187232
$452$	5.56063	+	4.50291i	0.261550	+	0.211799i
$453$	−17.7645	−	37.1640i	−0.834648	−	1.74612i
$454$	3.70787	+	17.4442i	0.174019	+	0.818696i
$455$	−27.2985	+	12.6504i	−1.27978	+	0.593058i
$456$	18.2602	+	17.2993i	0.855114	+	0.810114i
$457$	36.0519	−	9.66008i	1.68644	−	0.451880i	0.716971	−	0.697103i	$-0.245528\pi$
$457$	36.0519	−	9.66008i	1.68644	−	0.451880i	0.969467	+	0.245223i	$0.0788613\pi$
$458$	14.0453	−	27.5654i	0.656294	−	1.28805i
$459$	11.3314	+	9.62887i	0.528906	+	0.449437i
$460$	0.254968	+	3.77555i	0.0118879	+	0.176036i
$461$	−9.64371	+	1.01359i	−0.449152	+	0.0472078i	−0.326405	−	0.945230i	$-0.605837\pi$
$461$	−9.64371	+	1.01359i	−0.449152	+	0.0472078i	−0.122748	+	0.992438i	$0.539171\pi$
$462$	−38.8449	+	29.8584i	−1.80723	+	1.38914i
$463$	4.31609	+	5.32992i	0.200586	+	0.247703i	0.867506	−	0.497426i	$-0.165721\pi$
$463$	4.31609	+	5.32992i	0.200586	+	0.247703i	−0.666921	+	0.745129i	$0.732388\pi$
$464$	18.8545	+	8.39456i	0.875298	+	0.389708i
$465$	−5.06747	−	1.41378i	−0.234998	−	0.0655626i
$466$	−33.9260	+	15.1048i	−1.57159	+	0.699718i
$467$	21.3051	+	10.8555i	0.985880	+	0.502331i	0.871124	−	0.491063i	$-0.163391\pi$
$467$	21.3051	+	10.8555i	0.985880	+	0.502331i	0.114756	+	0.993394i	$0.463391\pi$
$468$	−6.95107	−	2.24569i	−0.321313	−	0.103807i
$469$	36.1852	−	11.7573i	1.67088	−	0.542901i
$470$	14.1055	−	4.81931i	0.650637	−	0.222298i
$471$	3.87609	+	4.53064i	0.178601	+	0.208761i
$472$	21.5332	+	13.9838i	0.991144	+	0.643657i
$473$	8.11396	+	21.1376i	0.373080	+	0.971907i
$474$	12.7261	−	20.8062i	0.584530	−	0.955660i
$475$	−25.3398	−	21.4694i	−1.16267	−	0.985082i
$476$			6.87406i			0.315072i
$477$	−5.15087	−	4.62228i	−0.235842	−	0.211640i
$478$	12.7858	+	25.0935i	0.584808	+	1.14775i
$479$	−28.1929	−	31.3114i	−1.28817	−	1.43065i	−0.845508	−	0.533963i	$-0.820702\pi$
$479$	−28.1929	−	31.3114i	−1.28817	−	1.43065i	−0.442658	−	0.896691i	$-0.645964\pi$
$480$	−2.75228	−	13.6359i	−0.125624	−	0.622390i
$481$	3.83225	−	4.25615i	0.174736	−	0.194064i
$482$	17.3516	+	4.64936i	0.790346	+	0.211773i
$483$	16.1918	−	0.437553i	0.736751	−	0.0199093i
$484$	3.12888	+	7.02758i	0.142222	+	0.319435i
$485$	6.83454	+	4.29339i	0.310341	+	0.194953i
$486$	13.1915	−	21.7301i	0.598378	−	0.985696i
$487$	−4.25189	−	26.8454i	−0.192672	−	1.21648i	−0.874521	−	0.484988i	$-0.838824\pi$
$487$	−4.25189	−	26.8454i	−0.192672	−	1.21648i	0.681849	−	0.731493i	$-0.261176\pi$
$488$	−15.7534	−	6.04718i	−0.713125	−	0.273743i
$489$	12.5081	−	26.2803i	0.565636	−	1.18844i
$490$	14.1273	−	17.9936i	0.638208	−	0.812866i
$491$	−0.340141	−	0.0357503i	−0.0153504	−	0.00161339i	0.0968502	−	0.995299i	$-0.469123\pi$
$491$	−0.340141	−	0.0357503i	−0.0153504	−	0.00161339i	−0.112201	+	0.993686i	$0.535790\pi$
$492$	0.838509	+	0.454365i	0.0378029	+	0.0204844i
$493$	−3.12997	−	11.6812i	−0.140967	−	0.526095i
$494$	12.3621	+	38.0467i	0.556198	+	1.71180i
$495$	−31.9180	−	1.13732i	−1.43461	−	0.0511187i
$496$	−2.05009	+	6.30953i	−0.0920518	+	0.283306i
$497$	41.8961	+	2.19568i	1.87930	+	0.0984898i
$498$	21.0114	+	17.9150i	0.941543	+	0.802792i
$499$	−18.4095	+	10.6288i	−0.824124	+	0.475808i	−0.851837	−	0.523808i	$-0.824511\pi$
$499$	−18.4095	+	10.6288i	−0.824124	+	0.475808i	0.0277123	+	0.999616i	$0.491178\pi$
$500$	1.85685	+	7.13357i	0.0830409	+	0.319023i
$501$	6.89834	+	4.21937i	0.308195	+	0.188508i
$502$	−4.42134	+	5.45990i	−0.197334	+	0.243687i
$503$	16.1817	−	8.24496i	0.721504	−	0.367625i	−0.0543628	−	0.998521i	$-0.517313\pi$
$503$	16.1817	−	8.24496i	0.721504	−	0.367625i	0.775867	+	0.630896i	$0.217313\pi$
$504$	−23.5959	+	3.77770i	−1.05104	+	0.168272i
$505$	8.43720	−	5.04224i	0.375450	−	0.224377i
$506$	4.14346	−	19.4935i	0.184199	−	0.866590i
$507$	0.763234	+	0.802935i	0.0338964	+	0.0356596i
$508$	−0.0985491	−	1.88043i	−0.00437241	−	0.0834306i
$509$	−0.713818	+	6.79153i	−0.0316394	+	0.301029i	0.967246	+	0.253839i	$0.0816933\pi$
$509$	−0.713818	+	6.79153i	−0.0316394	+	0.301029i	−0.998886	+	0.0471901i	$0.984973\pi$
$510$	−11.5182	+	13.9287i	−0.510033	+	0.616772i
$511$	−6.11295	−	58.1609i	−0.270421	−	2.57289i
$512$	3.76675	−	0.596595i	0.166469	−	0.0263660i
$513$	−34.4017	+	2.79437i	−1.51887	+	0.123374i
$514$	7.13156	+	9.81575i	0.314560	+	0.432954i
$515$	9.34512	+	17.6772i	0.411795	+	0.778949i
$516$	0.704330	−	5.38473i	0.0310064	−	0.237049i
$517$	−19.4358	+	1.01859i	−0.854784	+	0.0447973i
$518$	−2.38462	+	8.89954i	−0.104774	+	0.391023i
$519$	−0.111848	−	0.376437i	−0.00490959	−	0.0165237i
$520$	−5.31994	+	17.2535i	−0.233295	+	0.756617i
$521$	−0.530295	−	0.172303i	−0.0232326	−	0.00754874i	0.297378	−	0.954760i	$-0.403888\pi$
$521$	−0.530295	−	0.172303i	−0.0232326	−	0.00754874i	−0.320610	+	0.947211i	$0.603888\pi$
$522$	−18.8724	+	8.44039i	−0.826022	+	0.369426i
$523$	−4.82033	+	30.4344i	−0.210778	+	1.33080i	0.624522	+	0.781007i	$0.285294\pi$
$523$	−4.82033	+	30.4344i	−0.210778	+	1.33080i	−0.835300	+	0.549794i	$0.814706\pi$
$524$	4.79287	−	8.30150i	0.209378	−	0.362653i
$525$	30.8307	−	6.70794i	1.34556	−	0.292759i
$526$	−9.90596	−	17.1576i	−0.431920	−	0.748108i
$527$	3.62913	−	1.39309i	0.158087	−	0.0606840i
$528$	−3.12634	+	40.1534i	−0.136056	+	1.74745i
$529$	12.1961	−	10.9814i	0.530264	−	0.477452i
$530$	5.53393	−	6.33548i	0.240378	−	0.275196i
$531$	−34.0152	+	9.17537i	−1.47613	+	0.398177i
$532$	−11.2822	−	11.2822i	−0.489147	−	0.489147i
$533$	−1.67986	−	2.58676i	−0.0727628	−	0.112045i
$534$	4.31257	−	5.63000i	0.186623	−	0.243634i
$535$	−9.94551	−	34.9988i	−0.429982	−	1.51313i
$536$	9.28656	−	20.8580i	0.401118	−	0.900927i
$537$	−24.6959	−	32.1287i	−1.06571	−	1.38646i
$538$	−7.80197	+	20.3248i	−0.336367	+	0.876266i
$539$	−24.1651	+	17.5570i	−1.04087	+	0.756233i
$540$	6.60096	+	3.88715i	0.284060	+	0.167276i
$541$	−37.5985	−	27.3169i	−1.61649	−	1.17445i	−0.833950	−	0.551839i	$-0.813926\pi$
$541$	−37.5985	−	27.3169i	−1.61649	−	1.17445i	−0.782535	−	0.622606i	$-0.786074\pi$
$542$	24.1974	−	15.7140i	1.03937	−	0.674974i
$543$	−13.4775	−	3.97995i	−0.578374	−	0.170796i
$544$	7.63854	+	6.87778i	0.327500	+	0.294882i
$545$	−10.9591	−	23.6490i	−0.469438	−	1.01301i
$546$	−35.8358	−	12.6564i	−1.53363	−	0.541644i
$547$	−0.579669	+	11.0607i	−0.0247849	+	0.472923i	0.957838	+	0.287309i	$0.0927608\pi$
$547$	−0.579669	+	11.0607i	−0.0247849	+	0.472923i	−0.982623	+	0.185614i	$0.940573\pi$
$548$	−0.226950	−	0.0359453i	−0.00969480	−	0.00153551i
$549$	20.6130	−	10.5463i	0.879742	−	0.450107i
$550$	0.862583	−	38.8107i	0.0367806	−	1.65489i
$551$	24.3092	+	14.0349i	1.03561	+	0.597909i
$552$	6.30650	−	7.39649i	0.268423	−	0.314815i
$553$	17.1342	−	26.3844i	0.728622	−	1.12198i
$554$	10.6013	−	2.25338i	0.450406	−	0.0957368i
$555$	−4.89500	+	3.48015i	−0.207781	+	0.147724i
$556$	−0.729737	−	0.155110i	−0.0309477	−	0.00657815i
$557$	−16.8280	+	16.8280i	−0.713024	+	0.713024i	−0.967167	−	0.254143i	$-0.918207\pi$
$557$	−16.8280	+	16.8280i	−0.713024	+	0.713024i	0.254143	+	0.967167i	$0.418207\pi$
$558$	−3.33237	−	5.74960i	−0.141071	−	0.243400i
$559$	−10.3233	+	14.2088i	−0.436629	+	0.600968i
$560$	−6.81565	−	39.1998i	−0.288014	−	1.65649i
$561$	19.4374	−	13.3829i	0.820646	−	0.565026i
$562$	12.6817	−	10.2695i	0.534947	−	0.433191i
$563$	−30.0764	+	24.3554i	−1.26757	+	1.02646i	−0.269586	+	0.962976i	$0.586887\pi$
$563$	−30.0764	+	24.3554i	−1.26757	+	1.02646i	−0.997983	+	0.0634809i	$0.979780\pi$
$564$	4.21505	+	2.00615i	0.177486	+	0.0844741i
$565$	4.15695	+	23.9084i	0.174884	+	1.00584i
$566$	12.6842	−	17.4583i	0.533157	−	0.733827i
$567$	17.7665	−	27.5595i	0.746123	−	1.15739i
$568$	17.8021	−	17.8021i	0.746959	−	0.746959i
$569$	32.0615	+	6.81488i	1.34409	+	0.285695i	0.823113	−	0.567878i	$-0.192235\pi$
$569$	32.0615	+	6.81488i	1.34409	+	0.285695i	0.520974	+	0.853572i	$0.325569\pi$
$570$	−3.95632	−	41.7653i	−0.165712	−	1.74936i
$571$	41.9748	−	8.92202i	1.75659	−	0.373375i	0.786780	−	0.617234i	$-0.211747\pi$
$571$	41.9748	−	8.92202i	1.75659	−	0.373375i	0.969811	+	0.243859i	$0.0784133\pi$
$572$	−6.31396	+	9.72264i	−0.264000	+	0.406524i
$573$	14.2784	+	2.63398i	0.596487	+	0.110036i
$574$	4.29710	+	2.48093i	0.179357	+	0.103552i
$575$	−7.77255	+	10.2128i	−0.324138	+	0.425904i
$576$	−6.37316	+	9.84984i	−0.265548	+	0.410410i
$577$	6.76708	+	1.07180i	0.281717	+	0.0446196i	0.295694	−	0.955283i	$-0.404449\pi$
$577$	6.76708	+	1.07180i	0.281717	+	0.0446196i	−0.0139768	+	0.999902i	$0.504449\pi$
$578$	−0.751943	+	14.3479i	−0.0312767	+	0.596795i
$579$	4.90306	−	4.19471i	0.203764	−	0.174326i
$580$	−2.61944	−	5.65256i	−0.108766	−	0.234710i
$581$	26.4682	+	23.8321i	1.09809	+	0.988721i
$582$	2.38833	+	9.91155i	0.0989993	+	0.410847i
$583$	−9.21147	+	5.98200i	−0.381500	+	0.247749i
$584$	−28.3917	−	20.6278i	−1.17486	−	0.853583i
$585$	−12.7448	−	21.2451i	−0.526931	−	0.878375i
$586$	−35.5677	+	25.8415i	−1.46929	+	1.06750i
$587$	−9.32104	+	24.2822i	−0.384721	+	1.00223i	0.595330	+	0.803482i	$0.297022\pi$
$587$	−9.32104	+	24.2822i	−0.384721	+	1.00223i	−0.980050	+	0.198750i	$0.936312\pi$
$588$	7.10225	−	0.941074i	0.292892	−	0.0388092i
$589$	−3.66995	+	8.24285i	−0.151218	+	0.339641i
$590$	−11.7053	−	41.1917i	−0.481900	−	1.69583i
$591$	8.49220	+	1.11079i	0.349322	+	0.0456919i
$592$	4.12497	+	6.35190i	0.169535	+	0.261061i
$593$	20.2646	+	20.2646i	0.832166	+	0.832166i	0.987813	−	0.155647i	$-0.0497463\pi$
$593$	20.2646	+	20.2646i	0.832166	+	0.832166i	−0.155647	+	0.987813i	$0.549746\pi$
$594$	−27.8438	−	29.1941i	−1.14244	−	1.19785i
$595$	−15.3370	+	17.5585i	−0.628757	+	0.719829i
$596$	−6.19953	+	5.58208i	−0.253943	+	0.228651i
$597$	−35.2667	−	24.1947i	−1.44337	−	0.990223i
$598$	14.4322	−	5.54000i	0.590176	−	0.226547i
$599$	−0.947684	−	1.64144i	−0.0387213	−	0.0670673i	0.846015	−	0.533159i	$-0.178995\pi$
$599$	−0.947684	−	1.64144i	−0.0387213	−	0.0670673i	−0.884737	+	0.466091i	$0.845662\pi$
$600$	9.38831	−	16.4426i	0.383276	−	0.671266i
$601$	−3.34255	+	5.78947i	−0.136346	+	0.236158i	−0.926111	−	0.377252i	$-0.876869\pi$
$601$	−3.34255	+	5.78947i	−0.136346	+	0.236158i	0.789765	+	0.613409i	$0.210202\pi$
$602$	4.41990	−	27.9062i	0.180142	−	1.13737i
$603$	12.7906	+	28.5993i	0.520874	+	1.16465i
$604$	14.9122	+	4.84526i	0.606767	+	0.197151i
$605$	−7.68742	+	24.9317i	−0.312538	+	1.01362i
$606$	12.0751	+	2.88829i	0.490517	+	0.117329i
$607$	−7.20347	+	26.8837i	−0.292380	+	1.09118i	0.650896	+	0.759167i	$0.274393\pi$
$607$	−7.20347	+	26.8837i	−0.292380	+	1.09118i	−0.943276	+	0.332010i	$0.892273\pi$
$608$	−23.8253	+	1.24863i	−0.966244	+	0.0506387i
$609$	−24.6285	+	10.2256i	−0.997996	+	0.414362i
$610$	13.1533	+	24.8807i	0.532563	+	1.00739i
$611$	−8.87385	−	12.2138i	−0.358998	−	0.494118i
$612$	−5.62827	+	0.601078i	−0.227509	+	0.0242972i
$613$	−34.5864	+	5.47795i	−1.39693	+	0.221252i	−0.809072	−	0.587710i	$-0.800030\pi$
$613$	−34.5864	+	5.47795i	−1.39693	+	0.221252i	−0.587861	+	0.808962i	$0.700030\pi$
$614$	1.88310	+	17.9165i	0.0759957	+	0.723051i
$615$	1.12806	+	3.03143i	0.0454878	+	0.122239i
$616$	−3.96414	+	37.7163i	−0.159720	+	1.51963i
$617$	0.00653718	+	0.124737i	0.000263177	+	0.00502172i	0.998758	−	0.0498249i	$-0.0158663\pi$
$617$	0.00653718	+	0.124737i	0.000263177	+	0.00502172i	−0.998495	+	0.0548466i	$0.982533\pi$
$618$	−7.15322	+	24.2233i	−0.287745	+	0.974403i
$619$	−2.12093	+	9.97819i	−0.0852473	+	0.401057i	−0.999996	−	0.00296709i	$-0.999056\pi$
$619$	−2.12093	+	9.97819i	−0.0852473	+	0.401057i	0.914748	+	0.404024i	$0.132389\pi$
$620$	1.71902	−	1.02732i	0.0690374	−	0.0412582i
$621$	1.77409	+	13.2191i	0.0711918	+	0.530463i
$622$	26.3914	−	13.4471i	1.05820	−	0.539180i
$623$	5.75687	−	7.10914i	0.230644	−	0.284822i
$624$	−27.4430	+	14.9301i	−1.09860	+	0.597681i
$625$	−11.1731	+	22.3643i	−0.446923	+	0.894573i
$626$	−16.2263	+	9.36827i	−0.648534	+	0.374431i
$627$	−9.93707	+	53.8671i	−0.396849	+	2.15125i
$628$	−2.26650	−	0.118782i	−0.0904432	−	0.00473993i
$629$	1.37137	−	4.22063i	0.0546800	−	0.168288i
$630$	33.7843	+	21.1442i	1.34600	+	0.842404i
$631$	2.62067	+	8.06558i	0.104327	+	0.321086i	0.989572	−	0.144040i	$-0.0460093\pi$
$631$	2.62067	+	8.06558i	0.104327	+	0.321086i	−0.885245	+	0.465125i	$0.846009\pi$
$632$	−4.88618	−	18.2355i	−0.194362	−	0.725368i
$633$	5.00425	−	3.07237i	0.198901	−	0.122116i
$634$	4.81645	+	0.506229i	0.191286	+	0.0201049i
$635$	3.94379	−	5.02309i	0.156505	−	0.199335i
$636$	2.62610	−	0.208890i	0.104132	−	0.00828301i
$637$	−21.6311	−	8.30341i	−0.857057	−	0.328993i
$638$	5.13259	+	32.4059i	0.203201	+	1.28296i
$639$	1.86570	+	34.4953i	0.0738061	+	1.36461i
$640$	−25.6768	−	16.1299i	−1.01496	−	0.637589i
$641$	17.9489	+	40.3140i	0.708941	+	1.59231i	0.802472	+	0.596690i	$0.203518\pi$
$641$	17.9489	+	40.3140i	0.708941	+	1.59231i	−0.0935309	+	0.995616i	$0.529815\pi$
$642$	21.8962	−	40.4084i	0.864175	−	1.59479i
$643$	−43.3011	−	11.6025i	−1.70763	−	0.457557i	−0.732786	−	0.680459i	$-0.761780\pi$
$643$	−43.3011	−	11.6025i	−1.70763	−	0.457557i	−0.974841	+	0.222902i	$0.928447\pi$
$644$	−4.12564	+	4.58198i	−0.162573	+	0.180555i
$645$	13.8132	−	12.1828i	0.543895	−	0.479699i
$646$	20.7419	+	23.0363i	0.816081	+	0.906349i
$647$	8.50104	+	16.6842i	0.334210	+	0.655924i	0.995558	−	0.0941554i	$-0.0300151\pi$
$647$	8.50104	+	16.6842i	0.334210	+	0.655924i	−0.661347	+	0.750080i	$0.730015\pi$
$648$	−5.15633	−	18.9893i	−0.202560	−	0.745968i
$649$			55.9123i			2.19475i
$650$	25.6131	−	15.8355i	1.00463	−	0.621121i
$651$	−4.09648	−	7.52974i	−0.160554	−	0.295114i
$652$	3.97032	+	10.3430i	0.155490	+	0.405065i
$653$	−26.3330	−	17.1009i	−1.03049	−	0.669209i	−0.0855117	−	0.996337i	$-0.527253\pi$
$653$	−26.3330	−	17.1009i	−1.03049	−	0.669209i	−0.944980	+	0.327128i	$0.893919\pi$
$654$	10.9644	−	31.0449i	0.428741	−	1.21395i
$655$	30.7644	−	10.5111i	1.20206	−	0.410701i
$656$	3.87918	−	1.26042i	0.151456	−	0.0492112i
$657$	47.0858	−	10.0908i	1.83699	−	0.393679i
$658$	21.6399	+	11.0261i	0.843610	+	0.429841i
$659$	13.4414	−	5.98448i	0.523601	−	0.233122i	−0.127877	−	0.991790i	$-0.540816\pi$
$659$	13.4414	−	5.98448i	0.523601	−	0.233122i	0.651477	+	0.758668i	$0.274149\pi$
$660$	8.68439	−	8.50775i	0.338039	−	0.331164i
$661$	−24.5616	−	10.9355i	−0.955335	−	0.425343i	−0.130961	−	0.991388i	$-0.541806\pi$
$661$	−24.5616	−	10.9355i	−0.955335	−	0.425343i	−0.824374	+	0.566045i	$0.808473\pi$
$662$	17.3944	+	21.4803i	0.676052	+	0.834855i
$663$	16.9183	+	6.99119i	0.657051	+	0.271516i
$664$	21.2560	−	2.23410i	0.824894	−	0.0866998i
$665$	−3.64607	−	53.9907i	−0.141388	−	2.09367i
$666$	−7.49519	−	1.17427i	−0.290433	−	0.0455020i
$667$	4.92445	−	9.66478i	0.190676	−	0.374222i
$668$	−2.97322	+	0.796672i	−0.115037	+	0.0308242i
$669$	10.6131	−	3.15340i	0.410325	−	0.121917i
$670$	−34.5505	+	16.0110i	−1.33480	+	0.618559i
$671$	−7.64000	−	35.9434i	−0.294939	−	1.38758i
$672$	12.8223	−	18.6900i	0.494630	−	0.720982i
$673$	−28.6190	−	23.1752i	−1.10318	−	0.893337i	−0.108271	−	0.994121i	$-0.534532\pi$
$673$	−28.6190	−	23.1752i	−1.10318	−	0.893337i	−0.994908	+	0.100784i	$0.967865\pi$
$674$	−13.6437			−0.525534
$675$	8.18815	+	24.6567i	0.315162	+	0.949038i
$676$	−0.421687			−0.0162187
$677$	19.4047	+	15.7136i	0.745783	+	0.603923i	0.925036	−	0.379880i	$-0.124035\pi$
$677$	19.4047	+	15.7136i	0.745783	+	0.603923i	−0.179253	+	0.983803i	$0.557368\pi$
$678$	−17.3411	+	25.2768i	−0.665982	+	0.970748i
$679$	2.73419	+	12.8633i	0.104928	+	0.493650i
$680$	1.67188	+	13.8901i	0.0641136	+	0.532659i
$681$	−18.1573	+	5.39497i	−0.695790	+	0.206736i
$682$	−10.1872	+	2.72965i	−0.390087	+	0.104524i
$683$	8.70591	−	17.0863i	0.333122	−	0.653789i	−0.662313	−	0.749227i	$-0.730425\pi$
$683$	8.70591	−	17.0863i	0.333122	−	0.653789i	0.995435	+	0.0954379i	$0.0304251\pi$
$684$	8.25101	−	10.2241i	0.315485	−	0.390928i
$685$	−0.499502	−	0.598174i	−0.0190850	−	0.0228550i
$686$	−4.29126	+	0.451030i	−0.163841	+	0.0172204i
$687$	30.3687	+	12.5494i	1.15864	+	0.478788i
$688$	−14.6164	−	18.0497i	−0.557245	−	0.688140i
$689$	−7.78330	−	3.46535i	−0.296520	−	0.132019i
$690$	−16.0372	+	2.37141i	−0.610526	+	0.0902780i
$691$	13.8071	−	6.14731i	0.525246	−	0.233855i	−0.126944	−	0.991910i	$-0.540517\pi$
$691$	13.8071	−	6.14731i	0.525246	−	0.233855i	0.652190	+	0.758055i	$0.273850\pi$
$692$	0.133190	+	0.0678635i	0.00506311	+	0.00257979i
$693$	−34.8850	−	38.6136i	−1.32517	−	1.46681i
$694$	−25.9305	+	8.42531i	−0.984307	+	0.319821i
$695$	−1.51791	−	2.02435i	−0.0575774	−	0.0767881i
$696$	−5.32914	+	15.0891i	−0.202001	+	0.571952i
$697$	−2.00440	−	1.30167i	−0.0759220	−	0.0493043i
$698$	15.4412	+	40.2256i	0.584457	+	1.52256i
$699$	−18.8500	−	34.6482i	−0.712972	−	1.31051i
$700$	−6.23479	+	10.2652i	−0.235653	+	0.387989i
$701$		−	19.2045i		−	0.725343i	−0.931917	−	0.362671i	$-0.881865\pi$
$701$		−	19.2045i		−	0.725343i	0.931917	−	0.362671i	$-0.118135\pi$
$702$	7.22914	−	30.4480i	0.272846	−	1.14919i
$703$	4.67644	+	9.17802i	0.176375	+	0.346156i
$704$	12.4584	+	13.8364i	0.469542	+	0.521479i
$705$	6.29056	+	14.5287i	0.236916	+	0.547184i
$706$	−17.9598	+	19.9464i	−0.675927	+	0.750693i
$707$	15.4692	+	4.14496i	0.581779	+	0.155887i
$708$	6.38917	−	11.7909i	0.240120	−	0.443129i
$709$	13.7779	+	30.9457i	0.517440	+	1.16219i	0.963627	+	0.267249i	$0.0861147\pi$
$709$	13.7779	+	30.9457i	0.517440	+	1.16219i	−0.446188	+	0.894939i	$0.647219\pi$
$710$	−41.8942	+	2.82917i	−1.57226	+	0.106177i
$711$	23.1010	+	11.7219i	0.866356	+	0.439606i
$712$	−0.858745	−	5.42190i	−0.0321828	−	0.203194i
$713$	3.25514	+	1.24953i	0.121906	+	0.0467953i
$714$	−29.3563	+	2.33510i	−1.09863	+	0.0873890i
$715$	−37.8205	+	10.7473i	−1.41441	+	0.401927i
$716$	15.3408	+	1.61238i	0.573311	+	0.0602574i
$717$	−25.4918	+	15.6507i	−0.952007	+	0.584487i
$718$	−0.490716	−	1.83138i	−0.0183134	−	0.0683464i
$719$	0.655900	+	2.01865i	0.0244609	+	0.0752830i	0.962542	−	0.271133i	$-0.0873984\pi$
$719$	0.655900	+	2.01865i	0.0244609	+	0.0752830i	−0.938081	+	0.346416i	$0.887398\pi$
$720$	31.4996	−	9.00815i	1.17392	−	0.335714i
$721$	−10.0675	+	30.9847i	−0.374934	+	1.15393i
$722$	−40.9106	−	2.14403i	−1.52253	−	0.0797926i
$723$	−3.46132	+	18.7632i	−0.128728	+	0.697811i
$724$	4.63257	−	2.67461i	0.172168	−	0.0994013i
$725$	5.92081	−	20.2828i	0.219893	−	0.753284i
$726$	−28.9490	+	15.7494i	−1.07440	+	0.584515i
$727$	−23.5265	+	29.0528i	−0.872548	+	1.07751i	0.123816	+	0.992305i	$0.460487\pi$
$727$	−23.5265	+	29.0528i	−0.872548	+	1.07751i	−0.996364	+	0.0852017i	$0.972847\pi$
$728$	−26.2115	+	13.3554i	−0.971463	+	0.494985i
$729$	24.1184	+	12.1368i	0.893274	+	0.449512i
$730$	13.0307	+	57.0625i	0.482288	+	2.11198i
$731$	−2.82948	+	13.3117i	−0.104652	+	0.492350i
$732$	−2.49616	+	8.45285i	−0.0922606	+	0.312426i
$733$	−0.311909	−	5.95158i	−0.0115206	−	0.219827i	−0.998323	−	0.0578954i	$-0.981561\pi$
$733$	−0.311909	−	5.95158i	−0.0115206	−	0.219827i	0.986802	−	0.161931i	$-0.0517723\pi$
$734$	2.78119	−	26.4612i	0.102655	−	0.976701i
$735$	20.2411	+	13.4424i	0.746603	+	0.495829i
$736$	0.963693	+	9.16893i	0.0355222	+	0.337971i
$737$	49.1080	−	7.77795i	1.80892	−	0.286504i
$738$	−1.65557	+	3.73527i	−0.0609423	+	0.137497i
$739$	−12.8910	−	17.7430i	−0.474203	−	0.652685i	0.503175	−	0.864185i	$-0.332165\pi$
$739$	−12.8910	−	17.7430i	−0.474203	−	0.652685i	−0.977378	+	0.211500i	$0.932165\pi$
$740$	0.323575	−	2.26319i	0.0118949	−	0.0831966i
$741$	−39.2420	+	16.2931i	−1.44159	+	0.598540i
$742$	13.6873	−	0.717322i	0.502477	−	0.0263337i
$743$	2.22593	−	8.30729i	0.0816615	−	0.304765i	−0.913000	−	0.407961i	$-0.866240\pi$
$743$	2.22593	−	8.30729i	0.0816615	−	0.304765i	0.994661	+	0.103196i	$0.0329067\pi$
$744$	−5.00282	−	1.19664i	−0.183412	−	0.0438711i
$745$	−28.2900	+	0.426337i	−1.03647	+	0.0156198i
$746$	23.7312	+	7.71072i	0.868859	+	0.282309i
$747$	−17.1986	+	23.7553i	−0.629263	+	0.869160i
$748$	−1.40525	+	8.87239i	−0.0513810	+	0.324407i
$749$	29.6414	−	51.3403i	1.08307	−	1.87593i
$750$	−29.8338	+	10.3531i	−1.08938	+	0.378042i
$751$	−22.5016	−	38.9739i	−0.821094	−	1.42218i	−0.904868	−	0.425692i	$-0.860031\pi$
$751$	−22.5016	−	38.9739i	−0.821094	−	1.42218i	0.0837743	−	0.996485i	$-0.473303\pi$
$752$	18.6386	−	7.15470i	0.679681	−	0.260905i
$753$	−6.15321	−	4.22141i	−0.224235	−	0.153837i
$754$	−18.9136	+	17.0299i	−0.688792	+	0.620191i
$755$	27.2799	+	45.6476i	0.992818	+	1.66129i
$756$	2.94420	+	12.1293i	0.107079	+	0.441137i
$757$	−33.4200	−	33.4200i	−1.21467	−	1.21467i	−0.969474	−	0.245196i	$-0.921148\pi$
$757$	−33.4200	−	33.4200i	−1.21467	−	1.21467i	−0.245196	−	0.969474i	$-0.578852\pi$
$758$	13.3685	+	20.5856i	0.485565	+	0.747704i
$759$	20.9883	+	2.74530i	0.761827	+	0.0996480i
$760$	−25.5414	−	20.0534i	−0.926485	−	0.727413i
$761$	−3.23617	+	7.26856i	−0.117311	+	0.263485i	−0.962652	−	0.270742i	$-0.912731\pi$
$761$	−3.23617	+	7.26856i	−0.117311	+	0.263485i	0.845341	+	0.534228i	$0.179397\pi$
$762$	7.99706	−	1.05964i	0.289703	−	0.0383867i
$763$	15.2194	−	39.6478i	0.550978	−	1.43535i
$764$	−4.47126	+	3.24856i	−0.161764	+	0.117529i
$765$	−15.7175	−	11.0222i	−0.568267	−	0.398507i
$766$	−30.4740	−	22.1407i	−1.10107	−	0.799974i
$767$	−36.3743	+	23.6218i	−1.31340	+	0.852933i
$768$	−5.79927	−	24.0670i	−0.209263	−	0.868442i
$769$	28.4942	+	25.6563i	1.02753	+	0.925189i	0.997232	−	0.0743518i	$-0.0236888\pi$
$769$	28.4942	+	25.6563i	1.02753	+	0.925189i	0.0302946	+	0.999541i	$0.490355\pi$
$770$	46.3619	−	43.0270i	1.67077	−	1.55058i
$771$	−9.79213	+	8.37745i	−0.352655	+	0.301706i
$772$	−0.128546	+	2.45281i	−0.00462648	+	0.0882786i
$773$	−43.6636	−	6.91563i	−1.57047	−	0.248738i	−0.690345	−	0.723480i	$-0.742541\pi$
$773$	−43.6636	−	6.91563i	−1.57047	−	0.248738i	−0.880125	+	0.474742i	$0.842541\pi$
$774$	23.2352	+	1.17872i	0.835173	+	0.0423683i
$775$	6.68302	+	1.21128i	0.240061	+	0.0435106i
$776$	6.83434	+	3.94581i	0.245339	+	0.141646i
$777$	−9.62351	−	1.77528i	−0.345241	−	0.0636880i
$778$	14.6539	−	22.5650i	0.525368	−	0.808996i
$779$	5.42617	−	1.15337i	0.194413	−	0.0413237i
$780$	9.20377	+	2.05538i	0.329548	+	0.0735943i
$781$	53.6267	+	11.3987i	1.91891	+	0.407878i
$782$	8.47020	−	8.47020i	0.302894	−	0.302894i
$783$	−10.5260	−	19.2709i	−0.376167	−	0.688686i
$784$	18.0100	−	24.7887i	0.643216	−	0.885311i
$785$	−5.52434	−	5.36031i	−0.197172	−	0.191318i
$786$	37.0804	+	17.6484i	1.32261	+	0.629497i
$787$	22.9633	−	18.5953i	0.818553	−	0.662851i	−0.125701	−	0.992068i	$-0.540118\pi$
$787$	22.9633	−	18.5953i	0.818553	−	0.662851i	0.944254	+	0.329217i	$0.106785\pi$
$788$	−2.53357	+	2.05165i	−0.0902548	+	0.0730869i
$789$	17.3319	−	11.9333i	0.617033	−	0.424835i
$790$	−13.8703	+	28.2672i	−0.493485	+	1.00570i
$791$	−23.2407	+	31.9880i	−0.826343	+	1.13736i
$792$	−31.2276	+	0.0522524i	−1.10962	+	0.00185671i
$793$	20.1556	−	20.1556i	0.715747	−	0.715747i
$794$	−17.0720	−	3.62876i	−0.605862	−	0.128780i
$795$	7.17396	+	5.32565i	0.254434	+	0.188882i
$796$	15.9240	−	3.38476i	0.564412	−	0.119969i
$797$	2.85427	−	4.39519i	0.101103	−	0.155686i	−0.784498	−	0.620131i	$-0.787080\pi$
$797$	2.85427	−	4.39519i	0.101103	−	0.155686i	0.885602	+	0.464445i	$0.153746\pi$
$798$	44.3492	−	52.0143i	1.56994	−	1.84129i
$799$	−10.1310	−	5.84913i	−0.358409	−	0.206927i
$800$	5.16871	+	17.1990i	0.182741	+	0.608076i
$801$	6.32414	+	4.09192i	0.223453	+	0.144581i
$802$	−7.62098	−	1.20704i	−0.269106	−	0.0426222i
$803$	3.99967	−	76.3183i	0.141145	−	2.69321i
$804$	−11.2448	−	3.97141i	−0.396573	−	0.140061i
$805$	−20.7613	+	2.49893i	−0.731739	+	0.0880758i
$806$	−6.07967	−	5.47416i	−0.214147	−	0.192819i
$807$	−22.1767	−	6.54885i	−0.780655	−	0.230530i
$808$	8.05994	−	5.23419i	0.283548	−	0.184138i
$809$	−7.64187	−	5.55214i	−0.268674	−	0.195203i	0.445288	−	0.895387i	$-0.353101\pi$
$809$	−7.64187	−	5.55214i	−0.268674	−	0.195203i	−0.713962	+	0.700184i	$0.753101\pi$
$810$	−14.3581	+	29.5104i	−0.504491	+	1.03689i
$811$	−7.57098	+	5.50064i	−0.265853	+	0.193154i	−0.712723	−	0.701445i	$-0.752539\pi$
$811$	−7.57098	+	5.50064i	−0.265853	+	0.193154i	0.446870	+	0.894599i	$0.352539\pi$
$812$	3.63772	−	9.47658i	0.127659	−	0.332563i
$813$	18.6756	+	24.2964i	0.654982	+	0.852112i
$814$	−4.89716	+	10.9992i	−0.171645	+	0.385522i
$815$	−12.9354	+	35.2778i	−0.453107	+	1.23573i
$816$	−14.7208	+	19.2178i	−0.515331	+	0.672758i
$817$	−17.2042	−	26.4921i	−0.601897	−	0.926841i
$818$	7.88566	+	7.88566i	0.275716	+	0.275716i
$819$	10.3823	−	39.0083i	0.362787	−	1.36306i
$820$	−1.13220	−	0.483778i	−0.0395380	−	0.0168942i
$821$	17.6767	−	15.9162i	0.616920	−	0.555478i	−0.300307	−	0.953843i	$-0.597089\pi$
$821$	17.6767	−	15.9162i	0.616920	−	0.555478i	0.917227	+	0.398365i	$0.130422\pi$
$822$	0.0764132	−	0.981418i	0.00266522	−	0.0342309i
$823$	31.5118	−	12.0963i	1.09843	−	0.421649i	0.259423	−	0.965764i	$-0.416468\pi$
$823$	31.5118	−	12.0963i	1.09843	−	0.421649i	0.839011	+	0.544115i	$0.183134\pi$
$824$	9.77524	+	16.9312i	0.340536	+	0.589826i
$825$	41.1647	−	2.35532i	1.43317	−	0.0820019i
$826$	34.8862	−	60.4247i	1.21385	−	2.10244i
$827$	−3.15607	+	19.9266i	−0.109747	+	0.692917i	0.870056	+	0.492953i	$0.164082\pi$
$827$	−3.15607	+	19.9266i	−0.109747	+	0.692917i	−0.979803	+	0.199964i	$0.935918\pi$
$828$	−4.11234	−	2.97729i	−0.142914	−	0.103468i
$829$	−10.6031	−	3.44515i	−0.368260	−	0.119655i	0.119040	−	0.992889i	$-0.462018\pi$
$829$	−10.6031	−	3.44515i	−0.368260	−	0.119655i	−0.487300	+	0.873235i	$0.662018\pi$
$830$	−29.1515	−	20.5159i	−1.01186	−	0.712116i
$831$	3.27867	+	11.0347i	0.113736	+	0.382789i
$832$	−3.73803	+	13.9505i	−0.129593	+	0.483647i
$833$	−17.9292	+	0.939627i	−0.621208	+	0.0325562i
$834$	0.414522	−	3.16910i	0.0143537	−	0.109737i
$835$	−9.37205	−	4.59874i	−0.324333	−	0.159146i
$836$	−12.2556	−	16.8685i	−0.423870	−	0.583408i
$837$	5.80692	−	4.01248i	0.200717	−	0.138692i
$838$	58.3527	−	9.24216i	2.01576	−	0.319265i
$839$	−2.22560	−	21.1751i	−0.0768361	−	0.731047i	−0.963332	−	0.268311i	$-0.913535\pi$
$839$	−2.22560	−	21.1751i	−0.0768361	−	0.731047i	0.886496	−	0.462736i	$-0.153132\pi$
$840$	29.8793	−	7.67801i	1.03093	−	0.264916i
$841$	1.16467	−	11.0811i	0.0401609	−	0.382105i
$842$	−1.04047	−	19.8533i	−0.0358569	−	0.684191i
$843$	11.9412	+	12.5623i	0.411276	+	0.432669i
$844$	−0.464732	+	2.18639i	−0.0159967	+	0.0752587i
$845$	−1.07712	−	0.940846i	−0.0370541	−	0.0323661i
$846$	−7.13559	+	18.6822i	−0.245327	+	0.642308i
$847$	−37.8761	+	19.2988i	−1.30144	+	0.663116i
$848$	7.09045	−	8.75598i	0.243487	−	0.300682i
$849$	19.5528	+	11.9595i	0.671051	+	0.410449i
$850$	13.1401	−	19.2820i	0.450702	−	0.661369i
$851$	3.44722	−	1.99025i	0.118169	−	0.0682250i
$852$	−10.0064	−	8.53178i	−0.342812	−	0.292294i
$853$	−19.4763	−	1.02071i	−0.666856	−	0.0349484i	−0.284095	−	0.958796i	$-0.591693\pi$
$853$	−19.4763	−	1.02071i	−0.666856	−	0.0349484i	−0.382760	+	0.923848i	$0.625027\pi$
$854$	−14.1701	+	43.6112i	−0.484892	+	1.49234i
$855$	43.8872	−	7.70632i	1.50091	−	0.263551i
$856$	−10.9933	−	33.8338i	−0.375743	−	1.15642i
$857$	10.0563	+	37.5308i	0.343518	+	1.28203i	0.894334	+	0.447400i	$0.147650\pi$
$857$	10.0563	+	37.5308i	0.343518	+	1.28203i	−0.550816	+	0.834627i	$0.685683\pi$
$858$	−43.6662	−	23.6615i	−1.49074	−	0.807792i
$859$	1.17864	+	0.123880i	0.0402147	+	0.00422673i	0.124614	−	0.992205i	$-0.460231\pi$
$859$	1.17864	+	0.123880i	0.0402147	+	0.00422673i	−0.0843998	+	0.996432i	$0.526897\pi$
$860$	−0.261380	+	7.00600i	−0.00891300	+	0.238903i
$861$	−2.26487	+	4.75864i	−0.0771865	+	0.162174i
$862$	−15.8119	−	6.06964i	−0.538557	−	0.206733i
$863$	−3.40834	−	21.5194i	−0.116021	−	0.732529i	−0.975277	−	0.220984i	$-0.929073\pi$
$863$	−3.40834	−	21.5194i	−0.116021	−	0.732529i	0.859256	−	0.511546i	$-0.170927\pi$
$864$	16.4240	+	8.86420i	0.558756	+	0.301566i
$865$	0.188795	+	0.470511i	0.00641923	+	0.0159979i
$866$	0.305414	+	0.685971i	0.0103784	+	0.0233102i
$867$	−15.2547	+	0.412229i	−0.518076	+	0.0140000i
$868$	3.15174	+	0.844505i	0.106977	+	0.0286644i
$869$	27.5090	−	30.5518i	0.933179	−	1.03640i
$870$	23.2499	−	13.1067i	0.788246	−	0.444359i
$871$	25.8071	+	28.6617i	0.874441	+	0.971165i
$872$	−11.5699	−	22.7073i	−0.391808	−	0.768966i
$873$	−10.2930	+	3.36346i	−0.348366	+	0.113836i
$874$			27.8039i			0.940480i
$875$	−38.8289	+	12.3099i	−1.31266	+	0.416152i
$876$	−9.56444	+	15.6371i	−0.323153	+	0.528329i
$877$	−9.00680	−	23.4635i	−0.304138	−	0.792307i	−0.997430	−	0.0716496i	$-0.977174\pi$
$877$	−9.00680	−	23.4635i	−0.304138	−	0.792307i	0.693292	−	0.720657i	$-0.256160\pi$
$878$	1.99577	+	1.29607i	0.0673539	+	0.0437401i
$879$	−30.3560	−	35.4821i	−1.02388	−	1.19678i
$880$	−0.783482	−	51.9887i	−0.0264112	−	1.75254i
$881$	50.2348	−	16.3223i	1.69245	−	0.549911i	0.705191	−	0.709017i	$-0.250861\pi$
$881$	50.2348	−	16.3223i	1.69245	−	0.549911i	0.987262	+	0.159106i	$0.0508610\pi$
$882$	6.43156	+	30.0111i	0.216562	+	1.01053i
$883$	−24.0991	−	12.2791i	−0.810999	−	0.413225i	−0.00124880	−	0.999999i	$-0.500398\pi$
$883$	−24.0991	−	12.2791i	−0.810999	−	0.413225i	−0.809750	+	0.586774i	$0.800398\pi$
$884$	−6.36572	+	2.83420i	−0.214102	+	0.0953244i
$885$	42.6272	−	15.8625i	1.43290	−	0.533213i
$886$	14.2377	+	6.33902i	0.478324	+	0.212964i
$887$	−2.04765	−	2.52863i	−0.0687533	−	0.0849032i	0.741609	−	0.670832i	$-0.234063\pi$
$887$	−2.04765	−	2.52863i	−0.0687533	−	0.0849032i	−0.810362	+	0.585929i	$0.800730\pi$
$888$	−4.65591	+	3.57880i	−0.156242	+	0.120097i
$889$	10.3485	−	1.08767i	0.347076	−	0.0364792i
$890$	−4.87023	+	7.75281i	−0.163251	+	0.259875i
$891$	28.5653	−	31.9392i	0.956972	−	1.07000i
$892$	−1.91331	+	3.75509i	−0.0640624	+	0.125730i
$893$	26.2278	−	7.02772i	0.877681	−	0.235174i
$894$	−25.9447	−	24.5794i	−0.867721	−	0.822058i
$895$	35.5877	+	38.3460i	1.18957	+	1.28177i
$896$	−10.2721	−	48.3264i	−0.343167	−	1.61447i
$897$	7.08113	+	14.8140i	0.236432	+	0.494624i
$898$	−10.9626	−	8.87731i	−0.365826	−	0.296240i
$899$	−5.74033			−0.191451
$900$	−8.95005	−	4.20725i	−0.298335	−	0.140242i
$901$	−6.60179			−0.219937
$902$	5.03912	+	4.08060i	0.167784	+	0.135869i
$903$	29.9188	+	2.32948i	0.995635	+	0.0775201i
$904$	4.93317	+	23.2087i	0.164075	+	0.771911i
$905$	17.8005	+	3.50413i	0.591709	+	0.116481i
$906$	−15.6265	+	65.3296i	−0.519154	+	2.17043i
$907$	48.0660	−	12.8792i	1.59600	−	0.427648i	0.652171	−	0.758072i	$-0.273858\pi$
$907$	48.0660	−	12.8792i	1.59600	−	0.427648i	0.943833	+	0.330424i	$0.107192\pi$
$908$	3.27338	−	6.42437i	0.108631	−	0.213200i
$909$	−2.04112	+	13.0281i	−0.0676995	+	0.432116i
$910$	47.5786	+	11.9832i	1.57721	+	0.397240i
$911$	−20.4040	+	2.14454i	−0.676013	+	0.0710518i	−0.436313	−	0.899795i	$-0.643716\pi$
$911$	−20.4040	+	2.14454i	−0.676013	+	0.0710518i	−0.239700	+	0.970847i	$0.577049\pi$
$912$	−7.38081	−	55.7027i	−0.244403	−	1.84450i
$913$	29.2907	+	36.1711i	0.969382	+	1.19709i
$914$	−55.6031	−	24.7561i	−1.83919	−	0.818859i
$915$	−25.2355	+	16.0220i	−0.834261	+	0.529670i
$916$	−11.4266	+	5.08746i	−0.377546	+	0.168094i
$917$	47.1971	+	24.0481i	1.55859	+	0.794140i
$918$	−4.47887	−	23.8318i	−0.147825	−	0.786568i
$919$	52.7031	−	17.1243i	1.73851	−	0.564877i	0.743878	−	0.668316i	$-0.232985\pi$
$919$	52.7031	−	17.1243i	1.73851	−	0.564877i	0.994636	+	0.103439i	$0.0329845\pi$
$920$	−7.22205	+	10.2620i	−0.238104	+	0.338328i
$921$	−18.8111	+	3.50271i	−0.619846	+	0.115418i
$922$	13.2619	+	8.61237i	0.436757	+	0.283633i
$923$	15.2406	+	39.7031i	0.501651	+	1.30684i
$924$	19.8020	+	0.501957i	0.651439	+	0.0165132i
$925$	5.87603	−	5.05897i	0.193203	−	0.166338i
$926$		−	11.1841i		−	0.367534i
$927$	−26.2496	−	5.53364i	−0.862151	−	0.181749i
$928$	−6.89081	−	13.5240i	−0.226202	−	0.443947i
$929$	−7.09880	−	7.88401i	−0.232904	−	0.258666i	0.615352	−	0.788252i	$-0.289014\pi$
$929$	−7.09880	−	7.88401i	−0.232904	−	0.258666i	−0.848256	+	0.529586i	$0.822347\pi$
$930$	4.97121	+	6.99224i	0.163012	+	0.229285i
$931$	27.8845	−	30.9689i	0.913878	−	1.01496i
$932$	14.5027	+	3.88600i	0.475053	+	0.127290i
$933$	16.4602	+	26.8103i	0.538884	+	0.877730i
$934$	−15.8599	−	35.6218i	−0.518950	−	1.16558i
$935$	−23.3851	+	19.5276i	−0.764774	+	0.638620i
$936$	−13.2270	−	20.2934i	−0.432338	−	0.663309i
$937$	0.591432	+	3.73415i	0.0193212	+	0.121989i	0.995464	−	0.0951412i	$-0.0303302\pi$
$937$	0.591432	+	3.73415i	0.0193212	+	0.121989i	−0.976143	+	0.217131i	$0.930330\pi$
$938$	−57.9243	−	22.2351i	−1.89130	−	0.726000i
$939$	−11.2855	−	16.3911i	−0.368289	−	0.534905i
$940$	−5.65813	−	2.07468i	−0.184548	−	0.0676687i
$941$	4.72410	+	0.496523i	0.154001	+	0.0161862i	0.181215	−	0.983443i	$-0.441997\pi$
$941$	4.72410	+	0.496523i	0.154001	+	0.0161862i	−0.0272140	+	0.999630i	$0.508664\pi$
$942$	−0.262655	−	9.71963i	−0.00855777	−	0.316683i
$943$	−0.554825	−	2.07063i	−0.0180676	−	0.0674291i
$944$	−17.7237	−	54.5480i	−0.576858	−	1.77539i
$945$	−19.5418	+	37.5510i	−0.635694	+	1.22153i
$946$	11.4096	−	35.1151i	0.370958	−	1.14169i
$947$	−6.36731	−	0.333697i	−0.206910	−	0.0108437i	−0.0514005	−	0.998678i	$-0.516369\pi$
$947$	−6.36731	−	0.333697i	−0.206910	−	0.0108437i	−0.155509	+	0.987834i	$0.549702\pi$
$948$	−9.29235	+	3.29934i	−0.301801	+	0.107158i
$949$	51.3394	−	29.6408i	1.66655	−	0.962182i
$950$	10.0806	+	53.2137i	0.327058	+	1.72648i
$951$	−0.130348	+	5.14220i	−0.00422683	+	0.166747i
$952$	−14.3453	+	17.7150i	−0.464935	+	0.574147i
$953$	−11.7971	+	6.01094i	−0.382146	+	0.194713i	−0.634502	−	0.772921i	$-0.718795\pi$
$953$	−11.7971	+	6.01094i	−0.382146	+	0.194713i	0.252356	+	0.967635i	$0.418795\pi$
$954$	1.78416	+	11.1440i	0.0577644	+	0.360802i
$955$	−18.6690	−	1.67819i	−0.604116	−	0.0543049i
$956$	2.36735	−	11.1375i	0.0765657	−	0.360213i
$957$	−33.8785	+	8.16350i	−1.09514	+	0.263888i
$958$	3.59595	+	68.6147i	0.116180	+	2.21684i
$959$	0.132725	−	1.26279i	0.00428592	−	0.0407778i
$960$	7.01432	−	13.4236i	0.226386	−	0.433245i
$961$	3.04751	+	28.9951i	0.0983067	+	0.935325i
$962$	−9.22460	+	1.46103i	−0.297413	+	0.0471056i
$963$	44.6278	+	19.7802i	1.43811	+	0.637407i
$964$	−4.26893	−	5.87568i	−0.137493	−	0.189243i
$965$	−5.80093	+	5.97845i	−0.186739	+	0.192453i
$966$	−20.9692	−	16.0624i	−0.674674	−	0.516799i
$967$	10.3144	−	0.540556i	0.331689	−	0.0173831i	0.114235	−	0.993454i	$-0.463558\pi$
$967$	10.3144	−	0.540556i	0.331689	−	0.0173831i	0.217454	+	0.976071i	$0.430225\pi$
$968$	−6.60234	+	24.6402i	−0.212207	+	0.791968i
$969$	−22.6435	+	23.9013i	−0.727414	+	0.767820i
$970$	−4.25544	−	12.4551i	−0.136634	−	0.399909i
$971$	−12.1843	−	3.95892i	−0.391013	−	0.127048i	0.106911	−	0.994269i	$-0.465904\pi$
$971$	−12.1843	−	3.95892i	−0.391013	−	0.127048i	−0.497924	+	0.867221i	$0.665904\pi$
$972$	−9.67364	+	3.47122i	−0.310282	+	0.111340i
$973$	0.644916	−	4.07184i	0.0206751	−	0.130537i
$974$	−22.1618	+	38.3853i	−0.710109	+	1.22994i
$975$	18.9235	+	25.7851i	0.606037	+	0.825783i
$976$	18.8473	+	32.6445i	0.603288	+	1.04493i
$977$	9.88911	−	3.79607i	0.316381	−	0.121447i	−0.194996	−	0.980804i	$-0.562469\pi$
$977$	9.88911	−	3.79607i	0.316381	−	0.121447i	0.511376	+	0.859357i	$0.329136\pi$
$978$	−42.8221	+	20.4691i	−1.36930	+	0.654530i
$979$	8.88374	−	7.99896i	0.283926	−	0.255648i
$980$	−9.01698	+	2.05910i	−0.288037	+	0.0657756i
$981$	33.7932	+	8.99429i	1.07894	+	0.287166i
$982$	0.394379	+	0.394379i	0.0125852	+	0.0125852i
$983$	14.5498	+	22.4047i	0.464067	+	0.714601i	0.990786	−	0.135439i	$-0.0432445\pi$
$983$	14.5498	+	22.4047i	0.464067	+	0.714601i	−0.526719	+	0.850040i	$0.676578\pi$
$984$	1.21270	+	2.92081i	0.0386595	+	0.0931119i
$985$	−11.0491	−	0.412220i	−0.352053	−	0.0131344i
$986$	−8.02124	+	18.0160i	−0.255448	+	0.573746i
$987$	−9.85171	+	23.8405i	−0.313583	+	0.758852i
$988$	5.79620	−	15.0996i	0.184402	−	0.480382i
$989$	−9.87535	+	7.17486i	−0.314018	+	0.228147i
$990$	39.2831	+	34.1974i	1.24850	+	1.08686i
$991$	21.2068	+	15.4076i	0.673656	+	0.489439i	0.871247	−	0.490845i	$-0.163312\pi$
$991$	21.2068	+	15.4076i	0.673656	+	0.489439i	−0.197591	+	0.980284i	$0.563312\pi$
$992$	4.09187	−	2.65729i	0.129917	−	0.0843690i
$993$	−21.2780	+	20.2259i	−0.675237	+	0.641850i
$994$	−50.8425	−	45.7788i	−1.61263	−	1.45202i
$995$	48.2269	+	26.8831i	1.52890	+	0.852252i
$996$	−2.04358	−	10.9749i	−0.0647533	−	0.347753i
$997$	0.130783	−	2.49549i	0.00414194	−	0.0790328i	−0.995776	−	0.0918114i	$-0.970734\pi$
$997$	0.130783	−	2.49549i	0.00414194	−	0.0790328i	0.999918	+	0.0127785i	$0.00406765\pi$
$998$	34.2386	+	5.42287i	1.08381	+	0.171658i
$999$	0.612055	−	8.03467i	0.0193646	−	0.254206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.2.8	✓	448
3.2	odd	2		675.2.bd.a.602.21		448
9.4	even	3		675.2.bd.a.152.21		448
9.5	odd	6	inner	225.2.w.a.77.8	yes	448
25.13	odd	20	inner	225.2.w.a.38.8	yes	448
75.38	even	20		675.2.bd.a.413.21		448
225.13	odd	60		675.2.bd.a.638.21		448
225.113	even	60	inner	225.2.w.a.113.8	yes	448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.2.8	✓	448	1.1	even	1	trivial
225.2.w.a.38.8	yes	448	25.13	odd	20	inner
225.2.w.a.77.8	yes	448	9.5	odd	6	inner
225.2.w.a.113.8	yes	448	225.113	even	60	inner
675.2.bd.a.152.21		448	9.4	even	3
675.2.bd.a.413.21		448	75.38	even	20
675.2.bd.a.602.21		448	3.2	odd	2
675.2.bd.a.638.21		448	225.13	odd	60

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26732 - 1.02626i) q^{2} +(0.979850 - 1.42825i) q^{3} +(0.137078 + 0.644900i) q^{4} +(-1.08873 + 1.95312i) q^{5} +(-2.70753 + 0.804473i) q^{6} +(-3.51917 + 0.942959i) q^{7} +(-0.992568 + 1.94802i) q^{8} +(-1.07979 - 2.79894i) q^{9} +O(q^{10})\)	\(q+(-1.26732 - 1.02626i) q^{2} +(0.979850 - 1.42825i) q^{3} +(0.137078 + 0.644900i) q^{4} +(-1.08873 + 1.95312i) q^{5} +(-2.70753 + 0.804473i) q^{6} +(-3.51917 + 0.942959i) q^{7} +(-0.992568 + 1.94802i) q^{8} +(-1.07979 - 2.79894i) q^{9} +(3.38417 - 1.35792i) q^{10} +(-4.73499 + 0.497667i) q^{11} +(1.05539 + 0.436124i) q^{12} +(-2.32419 - 2.87014i) q^{13} +(5.42764 + 2.41654i) q^{14} +(1.72275 + 3.46874i) q^{15} +(4.46169 - 1.98647i) q^{16} +(-2.54982 - 1.29920i) q^{17} +(-1.50399 + 4.65530i) q^{18} +(6.31730 - 2.05262i) q^{19} +(-1.40881 - 0.434391i) q^{20} +(-2.10148 + 5.95021i) q^{21} +(6.51148 + 4.22861i) q^{22} +(-0.919867 - 2.39633i) q^{23} +(1.80970 + 3.32641i) q^{24} +(-2.62935 - 4.25283i) q^{25} +6.02261i q^{26} +(-5.05561 - 1.20033i) q^{27} +(-1.09051 - 2.14025i) q^{28} +(2.82765 + 3.14043i) q^{29} +(1.37653 - 6.16399i) q^{30} +(-0.908934 + 1.00947i) q^{31} +(-3.46938 - 0.929618i) q^{32} +(-3.92878 + 7.25038i) q^{33} +(1.89813 + 4.26327i) q^{34} +(1.98971 - 7.89999i) q^{35} +(1.65702 - 1.08003i) q^{36} +(0.242591 + 1.53166i) q^{37} +(-10.1126 - 3.88185i) q^{38} +(-6.37664 + 0.507221i) q^{39} +(-2.72409 - 4.05947i) q^{40} +(0.830574 + 0.0872968i) q^{41} +(8.76970 - 5.38417i) q^{42} +(-1.23082 - 4.59349i) q^{43} +(-0.970006 - 2.98537i) q^{44} +(6.64225 + 0.938324i) q^{45} +(-1.29349 + 3.98095i) q^{46} +(4.08223 + 0.213941i) q^{47} +(1.53461 - 8.31885i) q^{48} +(5.43322 - 3.13687i) q^{49} +(-1.03226 + 8.08808i) q^{50} +(-4.35402 + 2.36876i) q^{51} +(1.53236 - 1.89230i) q^{52} +(2.05548 - 1.04732i) q^{53} +(5.17524 + 6.70956i) q^{54} +(4.18310 - 9.78981i) q^{55} +(1.65611 - 7.79139i) q^{56} +(3.25836 - 11.0339i) q^{57} +(-0.360661 - 6.88183i) q^{58} +(1.22755 - 11.6793i) q^{59} +(-2.00084 + 1.58649i) q^{60} +(0.806761 + 7.67582i) q^{61} +(2.18789 - 0.346528i) q^{62} +(6.43925 + 8.83175i) q^{63} +(-2.29860 - 3.16376i) q^{64} +(8.13614 - 1.41463i) q^{65} +(12.4198 - 5.15662i) q^{66} +(-10.4288 + 0.546548i) q^{67} +(0.488329 - 1.82247i) q^{68} +(-4.32389 - 1.03425i) q^{69} +(-10.6290 + 7.96987i) q^{70} +(-10.9516 - 3.55840i) q^{71} +(6.52417 + 0.674682i) q^{72} +(-2.51103 + 15.8540i) q^{73} +(1.26444 - 2.19007i) q^{74} +(-8.65046 - 0.411770i) q^{75} +(2.18969 + 3.79266i) q^{76} +(16.1940 - 6.21628i) q^{77} +(8.60179 + 5.90126i) q^{78} +(-6.41701 + 5.77790i) q^{79} +(-0.977746 + 10.8769i) q^{80} +(-6.66811 + 6.04452i) q^{81} +(-0.963015 - 0.963015i) q^{82} +(-5.32431 - 8.19871i) q^{83} +(-4.12535 - 0.539602i) q^{84} +(5.31355 - 3.56563i) q^{85} +(-3.15426 + 7.08457i) q^{86} +(7.25599 - 0.961445i) q^{87} +(3.73033 - 9.71784i) q^{88} +(-2.03131 + 1.47583i) q^{89} +(-7.45491 - 8.00582i) q^{90} +(10.8857 + 7.90890i) q^{91} +(1.41930 - 0.921706i) q^{92} +(0.551161 + 2.28732i) q^{93} +(-4.95394 - 4.46055i) q^{94} +(-2.86882 + 14.5732i) q^{95} +(-4.72720 + 4.04426i) q^{96} +(0.188909 - 3.60460i) q^{97} +(-10.1049 - 1.60045i) q^{98} +(6.50572 + 12.7156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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