LMFDB - Embedded newform 225.2.w.a.113.8

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			113.8
Character	$\chi$	$=$	225.113
Dual form			225.2.w.a.2.8

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{20}\right)$

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	−0.962258	−	0.272138i	$-0.912269\pi$
$2$	−1.26732	+	1.02626i	−0.896132	+	0.725673i	0.0661265	+	0.997811i	$0.478936\pi$
$3$	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	−0.477361	−	0.878707i	$-0.658407\pi$
$7$	−3.51917	−	0.942959i	−1.33012	−	0.356405i	−0.852761	+	0.522302i	$0.825073\pi$
$8$	−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	−0.641044	−	0.767504i	$-0.721498\pi$
$11$	−4.73499	−	0.497667i	−1.42765	−	0.150052i	−0.786608	+	0.617452i	$0.788165\pi$
$12$	1.05539	−	0.436124i	0.304666	−	0.125898i
$13$	−2.32419	+	2.87014i	−0.644616	+	0.796034i	−0.989794	−	0.142503i	$-0.954485\pi$
$13$	−2.32419	+	2.87014i	−0.644616	+	0.796034i	0.345179	+	0.938537i	$0.387818\pi$
$14$	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	−0.734987	−	0.678081i	$-0.762812\pi$
$17$	−2.54982	+	1.29920i	−0.618422	+	0.315102i	0.116565	+	0.993183i	$0.462812\pi$
$18$	−1.50399	−	4.65530i	−0.354494	−	1.09726i
$19$	6.31730	+	2.05262i	1.44929	+	0.470903i	0.924780	−	0.380502i	$-0.124249\pi$
$19$	6.31730	+	2.05262i	1.44929	+	0.470903i	0.524509	+	0.851405i	$0.324249\pi$
$20$	−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	−0.995433	−	0.0954622i	$-0.969567\pi$
$23$	−0.919867	+	2.39633i	−0.191805	+	0.499670i	0.803628	+	0.595133i	$0.202900\pi$
$24$	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	−0.421012	−	0.907055i	$-0.638325\pi$
$29$	2.82765	−	3.14043i	0.525082	−	0.583163i	0.946094	+	0.323892i	$0.104992\pi$
$30$	1.37653	+	6.16399i	0.251320	+	1.12539i
$31$	−0.908934	−	1.00947i	−0.163249	−	0.181307i	0.655970	−	0.754787i	$-0.272260\pi$
$31$	−0.908934	−	1.00947i	−0.163249	−	0.181307i	−0.819220	+	0.573480i	$0.805593\pi$
$32$	−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	−0.959690	−	0.281060i	$-0.909314\pi$
$37$	0.242591	−	1.53166i	0.0398818	−	0.251803i	0.999572	+	0.0292566i	$0.00931398\pi$
$38$	−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	−0.0394490	−	0.999222i	$-0.512560\pi$
$41$	0.830574	−	0.0872968i	0.129714	−	0.0136335i	0.169163	+	0.985588i	$0.445894\pi$
$42$	8.76970	+	5.38417i	1.35319	+	0.830796i
$43$	−1.23082	+	4.59349i	−0.187699	+	0.700501i	0.806338	+	0.591455i	$0.201446\pi$
$43$	−1.23082	+	4.59349i	−0.187699	+	0.700501i	−0.994037	+	0.109046i	$0.965220\pi$
$44$	−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	0.247771	−	0.968819i	$-0.420302\pi$
$47$	4.08223	−	0.213941i	0.595454	−	0.0312064i	0.347683	+	0.937612i	$0.386969\pi$
$48$	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	0.589427	−	0.807822i	$-0.299354\pi$
$53$	2.05548	+	1.04732i	0.282342	+	0.143861i	−0.307085	+	0.951682i	$0.599354\pi$
$54$	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	0.721062	+	0.692870i	$0.243654\pi$
$59$	1.22755	+	11.6793i	0.159813	+	1.52052i	−0.561249	+	0.827647i	$0.689679\pi$
$60$	−2.00084	−	1.58649i	−0.258307	−	0.204815i
$61$	0.806761	−	7.67582i	0.103295	−	0.982788i	−0.812994	−	0.582271i	$-0.802164\pi$
$61$	0.806761	−	7.67582i	0.103295	−	0.982788i	0.916290	−	0.400516i	$-0.131169\pi$
$62$	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	−0.596733	−	0.802440i	$-0.703535\pi$
$67$	−10.4288	−	0.546548i	−1.27408	−	0.0667715i	−0.677342	+	0.735668i	$0.736868\pi$
$68$	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	−0.875484	−	0.483247i	$-0.839457\pi$
$71$	−10.9516	+	3.55840i	−1.29972	+	0.422304i	−0.424236	+	0.905552i	$0.639457\pi$
$72$	6.52417	−	0.674682i	0.768880	−	0.0795120i
$73$	−2.51103	−	15.8540i	−0.293894	−	1.85557i	−0.485679	−	0.874137i	$-0.661428\pi$
$73$	−2.51103	−	15.8540i	−0.293894	−	1.85557i	0.191785	−	0.981437i	$-0.438572\pi$
$74$	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	0.223899	−	0.974612i	$-0.428121\pi$
$79$	−6.41701	−	5.77790i	−0.721970	−	0.650065i	−0.945869	+	0.324547i	$0.894788\pi$
$80$	−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	−0.999953	−	0.00965169i	$-0.996928\pi$
$83$	−5.32431	+	8.19871i	−0.584418	+	0.899926i	0.415535	+	0.909577i	$0.363594\pi$
$84$	−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	0.474898	−	0.880041i	$-0.342485\pi$
$89$	−2.03131	−	1.47583i	−0.215318	−	0.156438i	−0.690217	+	0.723603i	$0.742485\pi$
$90$	−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	0.991310	+	0.131546i	$0.0419941\pi$
$97$	0.188909	+	3.60460i	0.0191808	+	0.365992i	−0.972129	+	0.234446i	$0.924673\pi$
$98$	−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	−0.677291	−	0.735715i	$-0.736846\pi$
$101$	−3.80678	+	2.19784i	−0.378789	+	0.218694i	0.298502	+	0.954409i	$0.403513\pi$
$102$	7.94890	−	1.46636i	0.787058	−	0.145192i
$103$	4.87026	+	7.49955i	0.479881	+	0.738952i	0.992839	−	0.119462i	$-0.0381168\pi$
$103$	4.87026	+	7.49955i	0.479881	+	0.738952i	−0.512958	+	0.858414i	$0.671450\pi$
$104$	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	−0.992838	−	0.119468i	$-0.961881\pi$
$107$	−11.5058	−	11.5058i	−1.11231	−	1.11231i	−0.119468	−	0.992838i	$-0.538119\pi$
$108$	0.0810826	+	3.42490i	0.00780218	+	0.329561i
$109$	−6.85156	−	9.43036i	−0.656260	−	0.903265i	0.343090	−	0.939303i	$-0.388526\pi$
$109$	−6.85156	−	9.43036i	−0.656260	−	0.903265i	−0.999350	+	0.0360376i	$0.988526\pi$
$110$	−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	0.937857	−	0.347023i	$-0.112807\pi$
$113$	8.43405	+	6.82976i	0.793408	+	0.642489i	−0.144448	+	0.989512i	$0.546141\pi$
$114$	−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	−0.280330	−	0.959904i	$-0.590444\pi$
$127$	−2.82088	+	0.446784i	−0.250313	+	0.0396456i	0.0300171	+	0.999549i	$0.490444\pi$
$128$	−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	−0.988836	−	0.149006i	$-0.952393\pi$
$131$	−10.8047	+	9.72857i	−0.944009	+	0.849989i	0.0448278	+	0.998995i	$0.485726\pi$
$132$	−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	0.928142	−	0.372227i	$-0.121406\pi$
$137$	−0.124897	−	0.325367i	−0.0106706	−	0.0277980i	−0.938812	+	0.344429i	$0.888072\pi$
$138$	4.41836	−	5.74815i	0.376116	−	0.489315i
$139$	−0.460243	−	1.03372i	−0.0390373	−	0.0876793i	0.892974	−	0.450108i	$-0.148614\pi$
$139$	−0.460243	−	1.03372i	−0.0390373	−	0.0876793i	−0.932012	+	0.362428i	$0.881948\pi$
$140$	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	−0.481482	−	0.876456i	$-0.659901\pi$
$149$	6.32656	−	10.9579i	0.518292	−	0.897708i	0.999774	−	0.0212520i	$-0.00676523\pi$
$150$	10.5403	−	9.39944i	0.860615	−	0.767461i
$151$	11.8910	+	20.5957i	0.967672	+	1.67606i	0.702258	+	0.711922i	$0.252175\pi$
$151$	11.8910	+	20.5957i	0.967672	+	1.67606i	0.265414	+	0.964135i	$0.414491\pi$
$152$	−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	0.921216	−	0.389052i	$-0.127197\pi$
$157$	−0.890963	−	3.32512i	−0.0711066	−	0.265373i	−0.992322	+	0.123679i	$0.960531\pi$
$158$	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	0.767773	−	0.640722i	$-0.221365\pi$
$163$	16.5970	+	2.62870i	1.29997	+	0.205896i	0.532202	+	0.846618i	$0.321365\pi$
$164$	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	−0.972748	−	0.231865i	$-0.925517\pi$
$167$	0.244341	−	4.66230i	0.0189077	−	0.360780i	0.991656	−	0.128915i	$-0.0411494\pi$
$168$	−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	0.782541	−	0.622599i	$-0.213923\pi$
$173$	0.142684	+	0.176200i	0.0108480	+	0.0133962i	−0.771693	+	0.635995i	$0.780590\pi$
$174$	−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	0.731725	+	0.681600i	$0.238716\pi$
$179$	7.22981	+	22.2511i	0.540382	+	1.66312i	−0.191343	+	0.981523i	$0.561284\pi$
$180$	0.305380	−	4.41221i	0.0227617	−	0.328867i
$181$	−2.50718	+	7.71631i	−0.186357	+	0.573549i	−0.999969	−	0.00785960i	$-0.997498\pi$
$181$	−2.50718	+	7.71631i	−0.186357	+	0.573549i	0.813612	+	0.581409i	$0.197498\pi$
$182$	−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	−0.747167	−	0.664637i	$-0.768586\pi$
$191$	3.40955	−	7.65798i	0.246707	−	0.554112i	0.993873	+	0.110524i	$0.0352530\pi$
$192$	−6.77092	−	0.182972i	−0.488649	−	0.0132048i
$193$	3.59845	−	0.964202i	0.259022	−	0.0694048i	−0.126971	−	0.991906i	$-0.540525\pi$
$193$	3.59845	−	0.964202i	0.259022	−	0.0694048i	0.385993	+	0.922502i	$0.373859\pi$
$194$	−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	−0.797104	−	0.603842i	$-0.793636\pi$
$197$	2.24486	−	4.40579i	0.159940	−	0.313900i	0.957044	+	0.289942i	$0.0936360\pi$
$198$	4.80458	+	22.7912i	0.341447	+	1.61970i
$199$			24.6922i			1.75039i	0.483773	+	0.875194i	$0.339266\pi$
$199$			24.6922i			1.75039i	−0.483773	+	0.875194i	$0.660734\pi$
$200$	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	−0.297348	−	0.954769i	$-0.596102\pi$
$211$	3.09718	−	1.37895i	0.213218	−	0.0949310i	0.510567	+	0.859838i	$0.329436\pi$
$212$	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	−0.448407	−	0.893829i	$-0.648009\pi$
$223$	4.96769	−	4.02275i	0.332661	−	0.269383i	0.781068	+	0.624446i	$0.214675\pi$
$224$	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	−0.868459	−	0.495761i	$-0.834889\pi$
$227$	−8.49893	+	6.88230i	−0.564094	+	0.456794i	0.304365	+	0.952556i	$0.401556\pi$
$228$	7.56243	−	0.588810i	0.500834	−	0.0389949i
$229$	3.94438	−	18.5569i	0.260652	−	1.22627i	−0.631801	−	0.775131i	$-0.717684\pi$
$229$	3.94438	−	18.5569i	0.260652	−	1.22627i	0.892453	−	0.451141i	$-0.148983\pi$
$230$	−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	0.932065	+	0.362290i	$0.118005\pi$
$233$	10.3387	+	20.2908i	0.677310	+	1.32930i	−0.254755	+	0.967006i	$0.581995\pi$
$234$	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	−0.847641	−	0.530570i	$-0.821978\pi$
$239$	−15.7771	+	7.02441i	−1.02053	+	0.454371i	−0.172893	+	0.984941i	$0.555311\pi$
$240$	14.5769	−	12.0542i	0.940937	−	0.778097i
$241$	−10.0634	−	4.48050i	−0.648238	−	0.288614i	0.0561575	−	0.998422i	$-0.482115\pi$
$241$	−10.0634	−	4.48050i	−0.648238	−	0.288614i	−0.704395	+	0.709808i	$0.748782\pi$
$242$	−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	$0.0434139\pi$
$251$			4.30822i			0.271933i	−0.990713	+	0.135966i	$0.956586\pi$
$252$	−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	−0.475899	−	0.879500i	$-0.657877\pi$
$257$	−7.18663	+	1.92565i	−0.448290	+	0.120119i	0.0276093	+	0.999619i	$0.491211\pi$
$258$	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	0.0174143	−	0.999848i	$-0.494457\pi$
$263$	11.3421	−	4.35383i	0.699385	−	0.268469i	0.681971	+	0.731380i	$0.261123\pi$
$264$	−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	0.742958	+	0.669338i	$0.233422\pi$
$269$	−4.12547	+	12.6969i	−0.251534	+	0.774143i	−0.994493	+	0.104806i	$0.966578\pi$
$270$	−18.7390	−	2.80297i	−1.14042	−	0.170583i
$271$	−5.46734	−	16.8267i	−0.332117	−	1.02215i	−0.968125	−	0.250469i	$-0.919415\pi$
$271$	−5.46734	−	16.8267i	−0.332117	−	1.02215i	0.636007	−	0.771683i	$-0.280585\pi$
$272$	−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	0.635845	−	0.771817i	$-0.280652\pi$
$277$	−4.18256	−	5.16503i	−0.251306	−	0.310337i	−0.887150	+	0.461480i	$0.847319\pi$
$278$	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	−0.995618	−	0.0935187i	$-0.970189\pi$
$281$	−2.08052	−	9.78805i	−0.124113	−	0.583906i	0.871504	−	0.490388i	$-0.163145\pi$
$282$	−11.2249	−	2.70479i	−0.668432	−	0.161068i
$283$	0.692565	−	13.2149i	0.0411687	−	0.785546i	−0.897561	−	0.440891i	$-0.854663\pi$
$283$	0.692565	−	13.2149i	0.0411687	−	0.785546i	0.938729	−	0.344655i	$-0.112004\pi$
$284$	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	0.799135	+	0.601152i	$0.205291\pi$
$293$	6.97767	+	26.0410i	0.407640	+	1.52133i	−0.391495	+	0.920180i	$0.628042\pi$
$294$	−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	−0.893966	−	0.448135i	$-0.852088\pi$
$307$	−7.81159	+	7.81159i	−0.445831	+	0.445831i	0.448135	+	0.893966i	$0.352088\pi$
$308$	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	−0.992555	−	0.121799i	$-0.961134\pi$
$311$	−7.38774	−	16.5931i	−0.418920	−	0.940910i	0.573635	−	0.819111i	$-0.305533\pi$
$312$	5.34117	+	12.9253i	0.302384	+	0.731751i
$313$	4.11751	+	10.7265i	0.232735	+	0.606296i	0.999359	−	0.0358007i	$-0.0113982\pi$
$313$	4.11751	+	10.7265i	0.232735	+	0.606296i	−0.766624	+	0.642097i	$0.778065\pi$
$314$	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	0.472796	−	0.881172i	$-0.343245\pi$
$317$	−2.49069	−	1.61747i	−0.139891	−	0.0908463i	−0.612687	+	0.790326i	$0.709911\pi$
$318$	−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	−0.639609	−	0.768700i	$-0.720904\pi$
$331$	−16.5790	+	3.52397i	−0.911262	+	0.193695i	−0.271653	+	0.962395i	$0.587570\pi$
$332$	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	0.789857	−	0.613291i	$-0.210155\pi$
$337$	6.50203	+	5.26524i	0.354188	+	0.286816i	−0.435669	+	0.900107i	$0.643488\pi$
$338$	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	0.993893	−	0.110344i	$-0.0351952\pi$
$347$	9.10601	+	14.0220i	0.488836	+	0.752742i	−0.505057	+	0.863086i	$0.668529\pi$
$348$	1.61467	−	4.54759i	0.0865554	−	0.243776i
$349$	−22.8822	+	13.2110i	−1.22486	+	0.707171i	−0.965949	−	0.258732i	$-0.916695\pi$
$349$	−22.8822	+	13.2110i	−1.22486	+	0.707171i	−0.258906	+	0.965902i	$0.583362\pi$
$350$	−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	0.920659	+	0.390367i	$0.127652\pi$
$353$	0.861405	+	16.4366i	0.0458480	+	0.874831i	−0.874811	+	0.484464i	$0.839015\pi$
$354$	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	−0.562687	−	0.826670i	$-0.690232\pi$
$359$	0.940606	−	0.683390i	0.0496433	−	0.0360680i	0.612330	+	0.790602i	$0.290232\pi$
$360$	−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	−0.526897	−	0.849929i	$-0.676645\pi$
$367$	8.88628	−	13.6837i	0.463860	−	0.714282i	0.990757	+	0.135647i	$0.0433114\pi$
$368$	−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	−0.0407738	−	0.999168i	$-0.512982\pi$
$373$	−14.2850	−	5.48349i	−0.739649	−	0.283925i	−0.698875	+	0.715244i	$0.746316\pi$
$374$	−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	−0.652652	−	0.757658i	$-0.726344\pi$
$379$	−14.3151	+	4.65126i	−0.735318	+	0.238919i	−0.0826664	+	0.996577i	$0.526344\pi$
$380$	−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	0.631586	−	0.775306i	$-0.282404\pi$
$383$	23.0670	+	1.20889i	1.17867	+	0.0617715i	0.547085	+	0.837077i	$0.315738\pi$
$384$	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	−0.859626	−	0.510923i	$-0.829304\pi$
$389$	1.72463	−	16.4087i	0.0874420	−	0.831955i	0.947068	−	0.321032i	$-0.104030\pi$
$390$	−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	0.676615	−	0.736337i	$-0.263446\pi$
$397$	9.53622	+	4.85895i	0.478609	+	0.243864i	−0.198005	+	0.980201i	$0.563446\pi$
$398$	−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	0.598812	−	0.800889i	$-0.295640\pi$
$401$	4.09767	+	2.36579i	0.204628	+	0.118142i	−0.394184	+	0.919031i	$0.628973\pi$
$402$	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	−0.271171	−	0.962531i	$-0.587411\pi$
$409$	−6.80116	+	0.714831i	−0.336296	+	0.0353461i	−0.0651242	+	0.997877i	$0.520744\pi$
$410$	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	−0.938218	−	0.346046i	$-0.887524\pi$
$419$	−24.2420	−	26.9234i	−1.18430	−	1.31530i	−0.246080	−	0.969250i	$-0.579143\pi$
$420$	5.54529	+	7.46983i	0.270583	+	0.364490i
$421$	8.15747	−	9.05979i	0.397571	−	0.441547i	−0.510808	−	0.859695i	$-0.670654\pi$
$421$	8.15747	−	9.05979i	0.397571	−	0.441547i	0.908379	+	0.418147i	$0.137320\pi$
$422$	−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	0.537089	−	0.843525i	$-0.319524\pi$
$431$	9.87770	+	3.20946i	0.475792	+	0.154594i	−0.0612974	+	0.998120i	$0.519524\pi$
$432$	−24.9410	−	4.68732i	−1.19997	−	0.225519i
$433$	−0.410272	+	0.209044i	−0.0197164	+	0.0100460i	−0.463821	−	0.885929i	$-0.653522\pi$
$433$	−0.410272	+	0.209044i	−0.0197164	+	0.0100460i	0.444104	+	0.895975i	$0.353522\pi$
$434$	−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	0.0698324	−	0.997559i	$-0.477754\pi$
$439$	−1.45127	−	0.152535i	−0.0692654	−	0.00728008i	−0.139098	+	0.990279i	$0.544420\pi$
$440$	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	0.0327613	−	0.999463i	$-0.489570\pi$
$443$	−9.23142	−	2.47355i	−0.438598	−	0.117522i	−0.471359	+	0.881941i	$0.656237\pi$
$444$	−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	0.969467	−	0.245223i	$-0.0788613\pi$
$457$	36.0519	+	9.66008i	1.68644	+	0.451880i	0.716971	+	0.697103i	$0.245528\pi$
$458$	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	−0.122748	−	0.992438i	$-0.539171\pi$
$461$	−9.64371	−	1.01359i	−0.449152	−	0.0472078i	−0.326405	+	0.945230i	$0.605837\pi$
$462$	−38.8449	−	29.8584i	−1.80723	−	1.38914i
$463$	4.31609	−	5.32992i	0.200586	−	0.247703i	−0.666921	−	0.745129i	$-0.732388\pi$
$463$	4.31609	−	5.32992i	0.200586	−	0.247703i	0.867506	+	0.497426i	$0.165721\pi$
$464$	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	0.114756	−	0.993394i	$-0.463391\pi$
$467$	21.3051	−	10.8555i	0.985880	−	0.502331i	0.871124	+	0.491063i	$0.163391\pi$
$468$	−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	−0.442658	+	0.896691i	$0.645964\pi$
$479$	−28.1929	+	31.3114i	−1.28817	+	1.43065i	−0.845508	+	0.533963i	$0.820702\pi$
$480$	−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	0.681849	+	0.731493i	$0.261176\pi$
$487$	−4.25189	+	26.8454i	−0.192672	+	1.21648i	−0.874521	+	0.484988i	$0.838824\pi$
$488$	−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	−0.112201	−	0.993686i	$-0.535790\pi$
$491$	−0.340141	+	0.0357503i	−0.0153504	+	0.00161339i	0.0968502	+	0.995299i	$0.469123\pi$
$492$	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	0.0277123	−	0.999616i	$-0.491178\pi$
$499$	−18.4095	−	10.6288i	−0.824124	−	0.475808i	−0.851837	+	0.523808i	$0.824511\pi$
$500$	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	0.775867	−	0.630896i	$-0.217313\pi$
$503$	16.1817	+	8.24496i	0.721504	+	0.367625i	−0.0543628	+	0.998521i	$0.517313\pi$
$504$	−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	−0.998886	−	0.0471901i	$-0.984973\pi$
$509$	−0.713818	−	6.79153i	−0.0316394	−	0.301029i	0.967246	−	0.253839i	$-0.0816933\pi$
$510$	−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	−0.320610	−	0.947211i	$-0.603888\pi$
$521$	−0.530295	+	0.172303i	−0.0232326	+	0.00754874i	0.297378	+	0.954760i	$0.403888\pi$
$522$	−18.8724	−	8.44039i	−0.826022	−	0.369426i
$523$	−4.82033	−	30.4344i	−0.210778	−	1.33080i	−0.835300	−	0.549794i	$-0.814706\pi$
$523$	−4.82033	−	30.4344i	−0.210778	−	1.33080i	0.624522	−	0.781007i	$-0.285294\pi$
$524$	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	−0.782535	+	0.622606i	$0.786074\pi$
$541$	−37.5985	+	27.3169i	−1.61649	+	1.17445i	−0.833950	+	0.551839i	$0.813926\pi$
$542$	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	−0.982623	−	0.185614i	$-0.940573\pi$
$547$	−0.579669	−	11.0607i	−0.0247849	−	0.472923i	0.957838	−	0.287309i	$-0.0927608\pi$
$548$	−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	0.254143	−	0.967167i	$-0.418207\pi$
$557$	−16.8280	−	16.8280i	−0.713024	−	0.713024i	−0.967167	+	0.254143i	$0.918207\pi$
$558$	−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	−0.997983	−	0.0634809i	$-0.979780\pi$
$563$	−30.0764	−	24.3554i	−1.26757	−	1.02646i	−0.269586	−	0.962976i	$-0.586887\pi$
$564$	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	0.520974	−	0.853572i	$-0.325569\pi$
$569$	32.0615	−	6.81488i	1.34409	−	0.285695i	0.823113	+	0.567878i	$0.192235\pi$
$570$	−3.95632	+	41.7653i	−0.165712	+	1.74936i
$571$	41.9748	+	8.92202i	1.75659	+	0.373375i	0.969811	−	0.243859i	$-0.0784133\pi$
$571$	41.9748	+	8.92202i	1.75659	+	0.373375i	0.786780	+	0.617234i	$0.211747\pi$
$572$	−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	−0.0139768	−	0.999902i	$-0.504449\pi$
$577$	6.76708	−	1.07180i	0.281717	−	0.0446196i	0.295694	+	0.955283i	$0.404449\pi$
$578$	−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	−0.980050	−	0.198750i	$-0.936312\pi$
$587$	−9.32104	−	24.2822i	−0.384721	−	1.00223i	0.595330	−	0.803482i	$-0.297022\pi$
$588$	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	−0.155647	−	0.987813i	$-0.549746\pi$
$593$	20.2646	−	20.2646i	0.832166	−	0.832166i	0.987813	+	0.155647i	$0.0497463\pi$
$594$	−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	−0.884737	−	0.466091i	$-0.845662\pi$
$599$	−0.947684	+	1.64144i	−0.0387213	+	0.0670673i	0.846015	+	0.533159i	$0.178995\pi$
$600$	9.38831	+	16.4426i	0.383276	+	0.671266i
$601$	−3.34255	−	5.78947i	−0.136346	−	0.236158i	0.789765	−	0.613409i	$-0.210202\pi$
$601$	−3.34255	−	5.78947i	−0.136346	−	0.236158i	−0.926111	+	0.377252i	$0.876869\pi$
$602$	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	−0.943276	−	0.332010i	$-0.892273\pi$
$607$	−7.20347	−	26.8837i	−0.292380	−	1.09118i	0.650896	−	0.759167i	$-0.274393\pi$
$608$	−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	−0.587861	−	0.808962i	$-0.700030\pi$
$613$	−34.5864	−	5.47795i	−1.39693	−	0.221252i	−0.809072	+	0.587710i	$0.800030\pi$
$614$	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	−0.998495	−	0.0548466i	$-0.982533\pi$
$617$	0.00653718	−	0.124737i	0.000263177	−	0.00502172i	0.998758	+	0.0498249i	$0.0158663\pi$
$618$	−7.15322	−	24.2233i	−0.287745	−	0.974403i
$619$	−2.12093	−	9.97819i	−0.0852473	−	0.401057i	0.914748	−	0.404024i	$-0.132389\pi$
$619$	−2.12093	−	9.97819i	−0.0852473	−	0.401057i	−0.999996	+	0.00296709i	$0.999056\pi$
$620$	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	−0.885245	−	0.465125i	$-0.846009\pi$
$631$	2.62067	−	8.06558i	0.104327	−	0.321086i	0.989572	+	0.144040i	$0.0460093\pi$
$632$	−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	−0.0935309	−	0.995616i	$-0.529815\pi$
$641$	17.9489	−	40.3140i	0.708941	−	1.59231i	0.802472	−	0.596690i	$-0.203518\pi$
$642$	21.8962	+	40.4084i	0.864175	+	1.59479i
$643$	−43.3011	+	11.6025i	−1.70763	+	0.457557i	−0.974841	−	0.222902i	$-0.928447\pi$
$643$	−43.3011	+	11.6025i	−1.70763	+	0.457557i	−0.732786	+	0.680459i	$0.761780\pi$
$644$	−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	−0.661347	−	0.750080i	$-0.730015\pi$
$647$	8.50104	−	16.6842i	0.334210	−	0.655924i	0.995558	+	0.0941554i	$0.0300151\pi$
$648$	−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	−0.944980	−	0.327128i	$-0.893919\pi$
$653$	−26.3330	+	17.1009i	−1.03049	+	0.669209i	−0.0855117	+	0.996337i	$0.527253\pi$
$654$	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	0.651477	−	0.758668i	$-0.274149\pi$
$659$	13.4414	+	5.98448i	0.523601	+	0.233122i	−0.127877	+	0.991790i	$0.540816\pi$
$660$	8.68439	+	8.50775i	0.338039	+	0.331164i
$661$	−24.5616	+	10.9355i	−0.955335	+	0.425343i	−0.824374	−	0.566045i	$-0.808473\pi$
$661$	−24.5616	+	10.9355i	−0.955335	+	0.425343i	−0.130961	+	0.991388i	$0.541806\pi$
$662$	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	−0.994908	−	0.100784i	$-0.967865\pi$
$673$	−28.6190	+	23.1752i	−1.10318	+	0.893337i	−0.108271	+	0.994121i	$0.534532\pi$
$674$	−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	−0.179253	−	0.983803i	$-0.557368\pi$
$677$	19.4047	−	15.7136i	0.745783	−	0.603923i	0.925036	+	0.379880i	$0.124035\pi$
$678$	−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	0.995435	−	0.0954379i	$-0.0304251\pi$
$683$	8.70591	+	17.0863i	0.333122	+	0.653789i	−0.662313	+	0.749227i	$0.730425\pi$
$684$	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	0.652190	−	0.758055i	$-0.273850\pi$
$691$	13.8071	+	6.14731i	0.525246	+	0.233855i	−0.126944	+	0.991910i	$0.540517\pi$
$692$	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	$0.118135\pi$
$701$			19.2045i			0.725343i	−0.931917	+	0.362671i	$0.881865\pi$
$702$	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	−0.446188	−	0.894939i	$-0.647219\pi$
$709$	13.7779	−	30.9457i	0.517440	−	1.16219i	0.963627	−	0.267249i	$-0.0861147\pi$
$710$	−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	−0.938081	−	0.346416i	$-0.887398\pi$
$719$	0.655900	−	2.01865i	0.0244609	−	0.0752830i	0.962542	+	0.271133i	$0.0873984\pi$
$720$	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	−0.996364	−	0.0852017i	$-0.972847\pi$
$727$	−23.5265	−	29.0528i	−0.872548	−	1.07751i	0.123816	−	0.992305i	$-0.460487\pi$
$728$	−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	0.986802	+	0.161931i	$0.0517723\pi$
$733$	−0.311909	+	5.95158i	−0.0115206	+	0.219827i	−0.998323	+	0.0578954i	$0.981561\pi$
$734$	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	−0.977378	−	0.211500i	$-0.932165\pi$
$739$	−12.8910	+	17.7430i	−0.474203	+	0.652685i	0.503175	+	0.864185i	$0.332165\pi$
$740$	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	0.994661	−	0.103196i	$-0.0329067\pi$
$743$	2.22593	+	8.30729i	0.0816615	+	0.304765i	−0.913000	+	0.407961i	$0.866240\pi$
$744$	−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	0.0837743	+	0.996485i	$0.473303\pi$
$751$	−22.5016	+	38.9739i	−0.821094	+	1.42218i	−0.904868	+	0.425692i	$0.860031\pi$
$752$	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	−0.245196	+	0.969474i	$0.578852\pi$
$757$	−33.4200	+	33.4200i	−1.21467	+	1.21467i	−0.969474	+	0.245196i	$0.921148\pi$
$758$	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	0.845341	−	0.534228i	$-0.179397\pi$
$761$	−3.23617	−	7.26856i	−0.117311	−	0.263485i	−0.962652	+	0.270742i	$0.912731\pi$
$762$	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	0.0302946	−	0.999541i	$-0.490355\pi$
$769$	28.4942	−	25.6563i	1.02753	−	0.925189i	0.997232	+	0.0743518i	$0.0236888\pi$
$770$	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	−0.880125	−	0.474742i	$-0.842541\pi$
$773$	−43.6636	+	6.91563i	−1.57047	+	0.248738i	−0.690345	+	0.723480i	$0.742541\pi$
$774$	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	0.944254	−	0.329217i	$-0.106785\pi$
$787$	22.9633	+	18.5953i	0.818553	+	0.662851i	−0.125701	+	0.992068i	$0.540118\pi$
$788$	−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	0.885602	−	0.464445i	$-0.153746\pi$
$797$	2.85427	+	4.39519i	0.101103	+	0.155686i	−0.784498	+	0.620131i	$0.787080\pi$
$798$	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	−0.713962	−	0.700184i	$-0.753101\pi$
$809$	−7.64187	+	5.55214i	−0.268674	+	0.195203i	0.445288	+	0.895387i	$0.353101\pi$
$810$	−14.3581	−	29.5104i	−0.504491	−	1.03689i
$811$	−7.57098	−	5.50064i	−0.265853	−	0.193154i	0.446870	−	0.894599i	$-0.352539\pi$
$811$	−7.57098	−	5.50064i	−0.265853	−	0.193154i	−0.712723	+	0.701445i	$0.752539\pi$
$812$	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	0.917227	−	0.398365i	$-0.130422\pi$
$821$	17.6767	+	15.9162i	0.616920	+	0.555478i	−0.300307	+	0.953843i	$0.597089\pi$
$822$	0.0764132	+	0.981418i	0.00266522	+	0.0342309i
$823$	31.5118	+	12.0963i	1.09843	+	0.421649i	0.839011	−	0.544115i	$-0.183134\pi$
$823$	31.5118	+	12.0963i	1.09843	+	0.421649i	0.259423	+	0.965764i	$0.416468\pi$
$824$	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	−0.979803	−	0.199964i	$-0.935918\pi$
$827$	−3.15607	−	19.9266i	−0.109747	−	0.692917i	0.870056	−	0.492953i	$-0.164082\pi$
$828$	−4.11234	+	2.97729i	−0.142914	+	0.103468i
$829$	−10.6031	+	3.44515i	−0.368260	+	0.119655i	−0.487300	−	0.873235i	$-0.662018\pi$
$829$	−10.6031	+	3.44515i	−0.368260	+	0.119655i	0.119040	+	0.992889i	$0.462018\pi$
$830$	−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	0.886496	+	0.462736i	$0.153132\pi$
$839$	−2.22560	+	21.1751i	−0.0768361	+	0.731047i	−0.963332	+	0.268311i	$0.913535\pi$
$840$	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	−0.382760	−	0.923848i	$-0.625027\pi$
$853$	−19.4763	+	1.02071i	−0.666856	+	0.0349484i	−0.284095	+	0.958796i	$0.591693\pi$
$854$	−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	−0.550816	−	0.834627i	$-0.685683\pi$
$857$	10.0563	−	37.5308i	0.343518	−	1.28203i	0.894334	−	0.447400i	$-0.147650\pi$
$858$	−43.6662	+	23.6615i	−1.49074	+	0.807792i
$859$	1.17864	−	0.123880i	0.0402147	−	0.00422673i	−0.0843998	−	0.996432i	$-0.526897\pi$
$859$	1.17864	−	0.123880i	0.0402147	−	0.00422673i	0.124614	+	0.992205i	$0.460231\pi$
$860$	−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	0.859256	+	0.511546i	$0.170927\pi$
$863$	−3.40834	+	21.5194i	−0.116021	+	0.732529i	−0.975277	+	0.220984i	$0.929073\pi$
$864$	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	0.693292	+	0.720657i	$0.256160\pi$
$877$	−9.00680	+	23.4635i	−0.304138	+	0.792307i	−0.997430	+	0.0716496i	$0.977174\pi$
$878$	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	0.987262	−	0.159106i	$-0.0508610\pi$
$881$	50.2348	+	16.3223i	1.69245	+	0.549911i	0.705191	+	0.709017i	$0.250861\pi$
$882$	6.43156	−	30.0111i	0.216562	−	1.01053i
$883$	−24.0991	+	12.2791i	−0.810999	+	0.413225i	−0.809750	−	0.586774i	$-0.800398\pi$
$883$	−24.0991	+	12.2791i	−0.810999	+	0.413225i	−0.00124880	+	0.999999i	$0.500398\pi$
$884$	−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	−0.810362	−	0.585929i	$-0.800730\pi$
$887$	−2.04765	+	2.52863i	−0.0687533	+	0.0849032i	0.741609	+	0.670832i	$0.234063\pi$
$888$	−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	0.943833	−	0.330424i	$-0.107192\pi$
$907$	48.0660	+	12.8792i	1.59600	+	0.427648i	0.652171	+	0.758072i	$0.273858\pi$
$908$	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	−0.239700	−	0.970847i	$-0.577049\pi$
$911$	−20.4040	−	2.14454i	−0.676013	−	0.0710518i	−0.436313	+	0.899795i	$0.643716\pi$
$912$	−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	0.994636	−	0.103439i	$-0.0329845\pi$
$919$	52.7031	+	17.1243i	1.73851	+	0.564877i	0.743878	+	0.668316i	$0.232985\pi$
$920$	−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	−0.848256	−	0.529586i	$-0.822347\pi$
$929$	−7.09880	+	7.88401i	−0.232904	+	0.258666i	0.615352	+	0.788252i	$0.289014\pi$
$930$	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	−0.976143	−	0.217131i	$-0.930330\pi$
$937$	0.591432	−	3.73415i	0.0193212	−	0.121989i	0.995464	+	0.0951412i	$0.0303302\pi$
$938$	−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	−0.0272140	−	0.999630i	$-0.508664\pi$
$941$	4.72410	−	0.496523i	0.154001	−	0.0161862i	0.181215	+	0.983443i	$0.441997\pi$
$942$	−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	−0.155509	−	0.987834i	$-0.549702\pi$
$947$	−6.36731	+	0.333697i	−0.206910	+	0.0108437i	−0.0514005	+	0.998678i	$0.516369\pi$
$948$	−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	0.252356	−	0.967635i	$-0.418795\pi$
$953$	−11.7971	−	6.01094i	−0.382146	−	0.194713i	−0.634502	+	0.772921i	$0.718795\pi$
$954$	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	0.217454	−	0.976071i	$-0.430225\pi$
$967$	10.3144	+	0.540556i	0.331689	+	0.0173831i	0.114235	+	0.993454i	$0.463558\pi$
$968$	−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	−0.497924	−	0.867221i	$-0.665904\pi$
$971$	−12.1843	+	3.95892i	−0.391013	+	0.127048i	0.106911	+	0.994269i	$0.465904\pi$
$972$	−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	0.511376	−	0.859357i	$-0.329136\pi$
$977$	9.88911	+	3.79607i	0.316381	+	0.121447i	−0.194996	+	0.980804i	$0.562469\pi$
$978$	−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	−0.526719	−	0.850040i	$-0.676578\pi$
$983$	14.5498	−	22.4047i	0.464067	−	0.714601i	0.990786	+	0.135439i	$0.0432445\pi$
$984$	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	−0.197591	−	0.980284i	$-0.563312\pi$
$991$	21.2068	−	15.4076i	0.673656	−	0.489439i	0.871247	+	0.490845i	$0.163312\pi$
$992$	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	0.999918	−	0.0127785i	$-0.00406765\pi$
$997$	0.130783	+	2.49549i	0.00414194	+	0.0790328i	−0.995776	+	0.0918114i	$0.970734\pi$
$998$	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.113.8	yes	448
3.2	odd	2		675.2.bd.a.638.21		448
9.2	odd	6	inner	225.2.w.a.38.8	yes	448
9.7	even	3		675.2.bd.a.413.21		448
25.2	odd	20	inner	225.2.w.a.77.8	yes	448
75.2	even	20		675.2.bd.a.152.21		448
225.2	even	60	inner	225.2.w.a.2.8	✓	448
225.52	odd	60		675.2.bd.a.602.21		448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.2.8	✓	448	225.2	even	60	inner
225.2.w.a.38.8	yes	448	9.2	odd	6	inner
225.2.w.a.77.8	yes	448	25.2	odd	20	inner
225.2.w.a.113.8	yes	448	1.1	even	1	trivial
675.2.bd.a.152.21		448	75.2	even	20
675.2.bd.a.413.21		448	9.7	even	3
675.2.bd.a.602.21		448	225.52	odd	60
675.2.bd.a.638.21		448	3.2	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
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

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