LMFDB - Embedded newform 225.2.q.a.31.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.13
Character	$\chi$	$=$	225.31
Dual form			225.2.q.a.196.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.220390 + 0.244767i) q^{2} +(1.41069 + 1.00496i) q^{3} +(0.197717 + 1.88116i) q^{4} +(2.09765 + 0.774498i) q^{5} +(-0.556884 + 0.123809i) q^{6} +(-1.22023 - 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(0.980112 + 2.83538i) q^{9} +O(q^{10})$	\(q+(-0.220390 + 0.244767i) q^{2} +(1.41069 + 1.00496i) q^{3} +(0.197717 + 1.88116i) q^{4} +(2.09765 + 0.774498i) q^{5} +(-0.556884 + 0.123809i) q^{6} +(-1.22023 - 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(0.980112 + 2.83538i) q^{9} +(-0.651873 + 0.342746i) q^{10} +(1.13179 - 1.25698i) q^{11} +(-1.61157 + 2.85243i) q^{12} +(-1.44915 - 1.60944i) q^{13} +(0.786239 + 0.167120i) q^{14} +(2.18081 + 3.20064i) q^{15} +(-3.28743 + 0.698765i) q^{16} +(-3.09482 - 2.24852i) q^{17} +(-0.910015 - 0.384989i) q^{18} +(-4.15077 - 3.01571i) q^{19} +(-1.04221 + 4.09915i) q^{20} +(0.402611 - 4.20777i) q^{21} +(0.0582329 + 0.554049i) q^{22} +(8.53438 + 1.81404i) q^{23} +(-0.705692 - 2.10489i) q^{24} +(3.80031 + 3.24926i) q^{25} +0.713316 q^{26} +(-1.46680 + 4.98483i) q^{27} +(3.73455 - 2.71331i) q^{28} +(5.29950 + 2.35949i) q^{29} +(-1.26404 - 0.171596i) q^{30} +(-6.49762 + 2.89293i) q^{31} +(1.83522 - 3.17869i) q^{32} +(2.85981 - 0.635808i) q^{33} +(1.23243 - 0.261961i) q^{34} +(-0.922715 - 5.37844i) q^{35} +(-5.14001 + 2.40435i) q^{36} +(2.56039 - 7.88008i) q^{37} +(1.65293 - 0.351342i) q^{38} +(-0.426879 - 3.72676i) q^{39} +(-1.59166 - 2.38346i) q^{40} +(2.89941 + 3.22012i) q^{41} +(0.941193 + 1.02589i) q^{42} +(-3.28981 - 5.69811i) q^{43} +(2.58834 + 1.88054i) q^{44} +(-0.140060 + 6.70674i) q^{45} +(-2.32491 + 1.68914i) q^{46} +(-7.27748 - 3.24014i) q^{47} +(-5.33979 - 2.31799i) q^{48} +(0.522100 - 0.904304i) q^{49} +(-1.63286 + 0.214089i) q^{50} +(-2.10617 - 6.28214i) q^{51} +(2.74109 - 3.04429i) q^{52} +(-2.04603 + 1.48652i) q^{53} +(-0.896854 - 1.45763i) q^{54} +(3.34762 - 1.76013i) q^{55} +(-0.326967 + 3.11088i) q^{56} +(-2.82480 - 8.42560i) q^{57} +(-1.74548 + 0.777139i) q^{58} +(-0.645013 - 0.716360i) q^{59} +(-5.58971 + 4.73526i) q^{60} +(-5.83429 + 6.47963i) q^{61} +(0.723913 - 2.22798i) q^{62} +(4.79660 - 5.53126i) q^{63} +(-1.70356 - 5.24301i) q^{64} +(-1.79330 - 4.49841i) q^{65} +(-0.474648 + 0.840115i) q^{66} +(3.08866 - 1.37516i) q^{67} +(3.61791 - 6.26641i) q^{68} +(10.2164 + 11.1358i) q^{69} +(1.51982 + 0.959501i) q^{70} +(-0.529305 + 0.384563i) q^{71} +(1.11981 - 3.67854i) q^{72} +(3.37004 + 10.3719i) q^{73} +(1.36450 + 2.36339i) q^{74} +(2.09569 + 8.40286i) q^{75} +(4.85234 - 8.40450i) q^{76} +(-4.03764 - 0.858227i) q^{77} +(1.00627 + 0.716854i) q^{78} +(5.75281 + 2.56132i) q^{79} +(-7.43708 - 1.08034i) q^{80} +(-7.07876 + 5.55798i) q^{81} -1.42718 q^{82} +(1.49547 - 14.2285i) q^{83} +(7.99507 - 0.0745756i) q^{84} +(-4.75039 - 7.11355i) q^{85} +(2.11975 + 0.450567i) q^{86} +(5.10478 + 8.65431i) q^{87} +(-2.12059 + 0.450746i) q^{88} +(-2.96245 - 9.11749i) q^{89} +(-1.61072 - 1.51238i) q^{90} +(-1.63326 + 5.02664i) q^{91} +(-1.72509 + 16.4132i) q^{92} +(-12.0734 - 2.44881i) q^{93} +(2.39696 - 1.06720i) q^{94} +(-6.37122 - 9.54068i) q^{95} +(5.78339 - 2.63984i) q^{96} +(-1.40779 - 0.626788i) q^{97} +(0.106279 + 0.327092i) q^{98} +(4.67328 + 1.97707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.220390	+	0.244767i	−0.155839	+	0.173077i	−0.816008	−	0.578040i	$-0.803818\pi$
$2$	−0.220390	+	0.244767i	−0.155839	+	0.173077i	0.660169	+	0.751117i	$0.270484\pi$
$3$	1.41069	+	1.00496i	0.814464	+	0.580214i
$3$	1.41069	+	1.00496i	0.814464	+	0.580214i
$4$	0.197717	+	1.88116i	0.0988587	+	0.940578i
$5$	2.09765	+	0.774498i	0.938099	+	0.346366i
$5$	2.09765	+	0.774498i	0.938099	+	0.346366i
$6$	−0.556884	+	0.123809i	−0.227347	+	0.0505449i
$7$	−1.22023	−	2.11349i	−0.461202	−	0.798825i	0.537819	−	0.843060i	$-0.319248\pi$
$7$	−1.22023	−	2.11349i	−0.461202	−	0.798825i	−0.999021	+	0.0442351i	$0.985915\pi$
$8$	−1.03695	−	0.753387i	−0.366616	−	0.266362i
$9$	0.980112	+	2.83538i	0.326704	+	0.945127i
$10$	−0.651873	+	0.342746i	−0.206140	+	0.108386i
$11$	1.13179	−	1.25698i	0.341246	−	0.378992i	−0.547956	−	0.836507i	$-0.684594\pi$
$11$	1.13179	−	1.25698i	0.341246	−	0.378992i	0.889202	+	0.457515i	$0.151260\pi$
$12$	−1.61157	+	2.85243i	−0.465219	+	0.823426i
$13$	−1.44915	−	1.60944i	−0.401921	−	0.446379i	0.507877	−	0.861430i	$-0.330430\pi$
$13$	−1.44915	−	1.60944i	−0.401921	−	0.446379i	−0.909798	+	0.415051i	$0.863764\pi$
$14$	0.786239	+	0.167120i	0.210131	+	0.0446648i
$15$	2.18081	+	3.20064i	0.563082	+	0.826401i
$16$	−3.28743	+	0.698765i	−0.821857	+	0.174691i
$17$	−3.09482	−	2.24852i	−0.750604	−	0.545346i	0.145410	−	0.989372i	$-0.453550\pi$
$17$	−3.09482	−	2.24852i	−0.750604	−	0.545346i	−0.896014	+	0.444025i	$0.853550\pi$
$18$	−0.910015	−	0.384989i	−0.214493	−	0.0907427i
$19$	−4.15077	−	3.01571i	−0.952252	−	0.691851i	−0.000913382	−	1.00000i	$-0.500291\pi$
$19$	−4.15077	−	3.01571i	−0.952252	−	0.691851i	−0.951338	+	0.308148i	$0.900291\pi$
$20$	−1.04221	+	4.09915i	−0.233045	+	0.916597i
$21$	0.402611	−	4.20777i	0.0878568	−	0.918210i
$22$	0.0582329	+	0.554049i	0.0124153	+	0.118124i
$23$	8.53438	+	1.81404i	1.77954	+	0.378253i	0.976133	−	0.217175i	$-0.0696842\pi$
$23$	8.53438	+	1.81404i	1.77954	+	0.378253i	0.803409	+	0.595428i	$0.203018\pi$
$24$	−0.705692	−	2.10489i	−0.144049	−	0.429658i
$25$	3.80031	+	3.24926i	0.760061	+	0.649852i
$26$	0.713316			0.139893
$27$	−1.46680	+	4.98483i	−0.282287	+	0.959330i
$28$	3.73455	−	2.71331i	0.705763	−	0.512767i
$29$	5.29950	+	2.35949i	0.984093	+	0.438147i	0.834744	−	0.550638i	$-0.185616\pi$
$29$	5.29950	+	2.35949i	0.984093	+	0.438147i	0.149349	+	0.988785i	$0.452282\pi$
$30$	−1.26404	−	0.171596i	−0.230781	−	0.0313291i
$31$	−6.49762	+	2.89293i	−1.16701	+	0.519585i	−0.896461	−	0.443123i	$-0.853871\pi$
$31$	−6.49762	+	2.89293i	−1.16701	+	0.519585i	−0.270545	+	0.962707i	$0.587204\pi$
$32$	1.83522	−	3.17869i	0.324424	−	0.561918i
$33$	2.85981	−	0.635808i	0.497830	−	0.110680i
$34$	1.23243	−	0.261961i	0.211360	−	0.0449260i
$35$	−0.922715	−	5.37844i	−0.155967	−	0.909122i
$36$	−5.14001	+	2.40435i	−0.856668	+	0.400725i
$37$	2.56039	−	7.88008i	0.420926	−	1.29548i	−0.485916	−	0.874006i	$-0.661514\pi$
$37$	2.56039	−	7.88008i	0.420926	−	1.29548i	0.906842	−	0.421472i	$-0.138486\pi$
$38$	1.65293	−	0.351342i	0.268141	−	0.0569952i
$39$	−0.426879	−	3.72676i	−0.0683554	−	0.596760i
$40$	−1.59166	−	2.38346i	−0.251664	−	0.376858i
$41$	2.89941	+	3.22012i	0.452812	+	0.502898i	0.925718	−	0.378214i	$-0.123462\pi$
$41$	2.89941	+	3.22012i	0.452812	+	0.502898i	−0.472906	+	0.881113i	$0.656795\pi$
$42$	0.941193	+	1.02589i	0.145229	+	0.158299i
$43$	−3.28981	−	5.69811i	−0.501691	−	0.868954i	−0.999998	−	0.00195353i	$-0.999378\pi$
$43$	−3.28981	−	5.69811i	−0.501691	−	0.868954i	0.498307	−	0.867001i	$-0.333955\pi$
$44$	2.58834	+	1.88054i	0.390207	+	0.283502i
$45$	−0.140060	+	6.70674i	−0.0208789	+	0.999782i
$46$	−2.32491	+	1.68914i	−0.342789	+	0.249051i
$47$	−7.27748	−	3.24014i	−1.06153	−	0.472623i	−0.199719	−	0.979853i	$-0.564003\pi$
$47$	−7.27748	−	3.24014i	−1.06153	−	0.472623i	−0.861811	+	0.507230i	$0.830670\pi$
$48$	−5.33979	−	2.31799i	−0.770732	−	0.334573i
$49$	0.522100	−	0.904304i	0.0745857	−	0.129186i
$50$	−1.63286	+	0.214089i	−0.230921	+	0.0302767i
$51$	−2.10617	−	6.28214i	−0.294923	−	0.879676i
$52$	2.74109	−	3.04429i	0.380120	−	0.422166i
$53$	−2.04603	+	1.48652i	−0.281043	+	0.204190i	−0.719372	−	0.694625i	$-0.755570\pi$
$53$	−2.04603	+	1.48652i	−0.281043	+	0.204190i	0.438329	+	0.898815i	$0.355570\pi$
$54$	−0.896854	−	1.45763i	−0.122046	−	0.198358i
$55$	3.34762	−	1.76013i	0.451393	−	0.237336i
$56$	−0.326967	+	3.11088i	−0.0436928	+	0.415709i
$57$	−2.82480	−	8.42560i	−0.374153	−	1.11600i
$58$	−1.74548	+	0.777139i	−0.229193	+	0.102043i
$59$	−0.645013	−	0.716360i	−0.0839736	−	0.0932621i	0.699694	−	0.714443i	$-0.253320\pi$
$59$	−0.645013	−	0.716360i	−0.0839736	−	0.0932621i	−0.783667	+	0.621181i	$0.786653\pi$
$60$	−5.58971	+	4.73526i	−0.721629	+	0.611319i
$61$	−5.83429	+	6.47963i	−0.747004	+	0.829632i	−0.990099	−	0.140371i	$-0.955171\pi$
$61$	−5.83429	+	6.47963i	−0.747004	+	0.829632i	0.243095	+	0.970002i	$0.421837\pi$
$62$	0.723913	−	2.22798i	0.0919371	−	0.282953i
$63$	4.79660	−	5.53126i	0.604314	−	0.696874i
$64$	−1.70356	−	5.24301i	−0.212945	−	0.655376i
$65$	−1.79330	−	4.49841i	−0.222432	−	0.557959i
$66$	−0.474648	+	0.840115i	−0.0584251	+	0.103411i
$67$	3.08866	−	1.37516i	0.377339	−	0.168002i	−0.209298	−	0.977852i	$-0.567118\pi$
$67$	3.08866	−	1.37516i	0.377339	−	0.168002i	0.586638	+	0.809850i	$0.300451\pi$
$68$	3.61791	−	6.26641i	0.438737	−	0.759914i
$69$	10.2164	+	11.1358i	1.22991	+	1.34059i
$70$	1.51982	+	0.959501i	0.181654	+	0.114682i
$71$	−0.529305	+	0.384563i	−0.0628170	+	0.0456392i	−0.618751	−	0.785587i	$-0.712361\pi$
$71$	−0.529305	+	0.384563i	−0.0628170	+	0.0456392i	0.555934	+	0.831227i	$0.312361\pi$
$72$	1.11981	−	3.67854i	0.131971	−	0.433521i
$73$	3.37004	+	10.3719i	0.394434	+	1.21394i	0.929402	+	0.369070i	$0.120324\pi$
$73$	3.37004	+	10.3719i	0.394434	+	1.21394i	−0.534968	+	0.844872i	$0.679676\pi$
$74$	1.36450	+	2.36339i	0.158620	+	0.274738i
$75$	2.09569	+	8.40286i	0.241990	+	0.970279i
$76$	4.85234	−	8.40450i	0.556602	−	0.964062i
$77$	−4.03764	−	0.858227i	−0.460132	−	0.0978041i
$78$	1.00627	+	0.716854i	0.113938	+	0.0811677i
$79$	5.75281	+	2.56132i	0.647242	+	0.288171i	0.703982	−	0.710218i	$-0.251404\pi$
$79$	5.75281	+	2.56132i	0.647242	+	0.288171i	−0.0567394	+	0.998389i	$0.518070\pi$
$80$	−7.43708	−	1.08034i	−0.831491	−	0.120786i
$81$	−7.07876	+	5.55798i	−0.786529	+	0.617553i
$82$	−1.42718			−0.157606
$83$	1.49547	−	14.2285i	0.164150	−	1.56178i	−0.533786	−	0.845620i	$-0.679231\pi$
$83$	1.49547	−	14.2285i	0.164150	−	1.56178i	0.697936	−	0.716160i	$-0.254102\pi$
$84$	7.99507	−	0.0745756i	0.872333	−	0.00813687i
$85$	−4.75039	−	7.11355i	−0.515252	−	0.771573i
$86$	2.11975	+	0.450567i	0.228579	+	0.0485859i
$87$	5.10478	+	8.65431i	0.547290	+	0.927839i
$88$	−2.12059	+	0.450746i	−0.226056	+	0.0480496i
$89$	−2.96245	−	9.11749i	−0.314019	−	0.966452i	−0.976156	−	0.217069i	$-0.930350\pi$
$89$	−2.96245	−	9.11749i	−0.314019	−	0.966452i	0.662137	−	0.749383i	$-0.269650\pi$
$90$	−1.61072	−	1.51238i	−0.169785	−	0.159419i
$91$	−1.63326	+	5.02664i	−0.171212	+	0.526935i
$92$	−1.72509	+	16.4132i	−0.179853	+	1.71119i
$93$	−12.0734	−	2.44881i	−1.25196	−	0.253930i
$94$	2.39696	−	1.06720i	0.247228	−	0.110073i
$95$	−6.37122	−	9.54068i	−0.653673	−	0.978853i
$96$	5.78339	−	2.63984i	0.590264	−	0.269427i
$97$	−1.40779	−	0.626788i	−0.142939	−	0.0636407i	0.334020	−	0.942566i	$-0.391595\pi$
$97$	−1.40779	−	0.626788i	−0.142939	−	0.0636407i	−0.476960	+	0.878925i	$0.658261\pi$
$98$	0.106279	+	0.327092i	0.0107358	+	0.0330413i
$99$	4.67328	+	1.97707i	0.469682	+	0.198703i
$100$	−5.36097	+	7.79140i	−0.536097	+	0.779140i
$101$	4.44731	+	7.70297i	0.442524	+	0.766474i	0.997876	−	0.0651410i	$-0.0207497\pi$
$101$	4.44731	+	7.70297i	0.442524	+	0.766474i	−0.555352	+	0.831616i	$0.687416\pi$
$102$	2.00184	+	0.868996i	0.198212	+	0.0860434i
$103$	1.03592	+	9.85609i	0.102072	+	0.971150i	0.918959	+	0.394353i	$0.129031\pi$
$103$	1.03592	+	9.85609i	0.102072	+	0.971150i	−0.816887	+	0.576797i	$0.804302\pi$
$104$	0.290159	+	2.76067i	0.0284524	+	0.270706i
$105$	4.10345	−	8.51462i	0.400455	−	0.830942i
$106$	0.0870699	−	0.828415i	0.00845698	−	0.0804628i
$107$	0.789838			0.0763565			0.0381783	−	0.999271i	$-0.487845\pi$
$107$	0.789838			0.0763565			0.0381783	+	0.999271i	$0.487845\pi$
$108$	−9.66724	−	1.77370i	−0.930231	−	0.170674i
$109$	−5.37002	+	16.5272i	−0.514354	+	1.58302i	0.270100	+	0.962832i	$0.412943\pi$
$109$	−5.37002	+	16.5272i	−0.514354	+	1.58302i	−0.784454	+	0.620187i	$0.787057\pi$
$110$	−0.306957	+	1.20730i	−0.0292672	+	0.115112i
$111$	11.5311	−	8.54329i	1.09448	−	0.810893i
$112$	5.48824	+	6.09531i	0.518590	+	0.575952i
$113$	1.45439	+	1.61527i	0.136818	+	0.151951i	0.807660	−	0.589649i	$-0.200734\pi$
$113$	1.45439	+	1.61527i	0.136818	+	0.151951i	−0.670842	+	0.741600i	$0.734067\pi$
$114$	2.68487	+	1.16550i	0.251461	+	0.109159i
$115$	16.4972	+	10.4151i	1.53837	+	0.971212i
$116$	−3.39077	+	10.4357i	−0.314825	+	0.968931i
$117$	3.14305	−	5.68632i	0.290575	−	0.525700i
$118$	0.317496			0.0292279
$119$	−0.975849	+	9.28458i	−0.0894559	+	0.851116i
$120$	0.149934	−	4.96188i	0.0136870	−	0.452956i
$121$	0.850765	+	8.09449i	0.0773423	+	0.735862i
$122$	−0.300187	−	2.85609i	−0.0271776	−	0.258578i
$123$	0.854086	+	7.45639i	0.0770104	+	0.672320i
$124$	−6.72673	−	11.6510i	−0.604079	−	1.04629i
$125$	5.45518	+	9.75915i	0.487926	+	0.872885i
$126$	0.296753	+	2.39308i	0.0264369	+	0.213193i
$127$	−4.55776	−	14.0274i	−0.404436	−	1.24473i	−0.921365	−	0.388698i	$-0.872925\pi$
$127$	−4.55776	−	14.0274i	−0.404436	−	1.24473i	0.516929	−	0.856028i	$-0.327075\pi$
$128$	8.36498	+	3.72433i	0.739367	+	0.329187i
$129$	1.08546	−	11.3444i	0.0955698	−	0.998820i
$130$	1.49629	+	0.552462i	0.131233	+	0.0484541i
$131$	−1.92662	+	0.857787i	−0.168330	+	0.0749452i	−0.489172	−	0.872188i	$-0.662701\pi$
$131$	−1.92662	+	0.857787i	−0.168330	+	0.0749452i	0.320842	+	0.947133i	$0.396034\pi$
$132$	1.76149	+	5.25404i	0.153318	+	0.457306i
$133$	−1.30881	+	12.4525i	−0.113488	+	1.07977i
$134$	−0.344114	+	1.05907i	−0.0297269	+	0.0914900i
$135$	−6.93759	+	9.32040i	−0.597092	+	0.802172i
$136$	1.51516	+	4.66319i	0.129924	+	0.399866i
$137$	−4.51172	+	0.958996i	−0.385463	+	0.0819326i	−0.396567	−	0.918006i	$-0.629799\pi$
$137$	−4.51172	+	0.958996i	−0.385463	+	0.0819326i	0.0111045	+	0.999938i	$0.496465\pi$
$138$	−4.97725	+	0.0464263i	−0.423692	+	0.00395207i
$139$	3.91514	+	0.832189i	0.332078	+	0.0705853i	0.370933	−	0.928660i	$-0.379038\pi$
$139$	3.91514	+	0.832189i	0.332078	+	0.0705853i	−0.0388554	+	0.999245i	$0.512371\pi$
$140$	9.93524	−	2.79918i	0.839681	−	0.236574i
$141$	−7.01008	−	11.8844i	−0.590355	−	1.00085i
$142$	0.0225249	−	0.214310i	0.00189025	−	0.0179845i
$143$	−3.66315			−0.306328
$144$	−5.20331	−	8.63624i	−0.433609	−	0.719687i
$145$	9.28911	+	9.05385i	0.771418	+	0.751882i
$146$	−3.28143	−	1.46099i	−0.271573	−	0.120912i
$147$	1.64531	−	0.751006i	0.135703	−	0.0619419i
$148$	15.3299	+	3.25847i	1.26011	+	0.267844i
$149$	−6.88364	+	11.9228i	−0.563929	+	0.976755i	0.433219	+	0.901289i	$0.357378\pi$
$149$	−6.88364	+	11.9228i	−0.563929	+	0.976755i	−0.997148	+	0.0754658i	$0.975956\pi$
$150$	−2.51862	−	1.33895i	−0.205644	−	0.109324i
$151$	−10.1492	−	17.5789i	−0.825931	−	1.43055i	−0.901206	−	0.433391i	$-0.857317\pi$
$151$	−10.1492	−	17.5789i	−0.825931	−	1.43055i	0.0752750	−	0.997163i	$-0.476017\pi$
$152$	2.03213	+	6.25427i	0.164828	+	0.507288i
$153$	3.34214	−	10.9788i	0.270196	−	0.887583i
$154$	1.09992	−	0.799139i	0.0886341	−	0.0643965i
$155$	−15.8703	+	1.03597i	−1.27473	+	0.0832108i
$156$	6.92622	−	1.53987i	0.554541	−	0.123288i
$157$	−4.22601	+	7.31966i	−0.337272	+	0.584172i	−0.983919	−	0.178618i	$-0.942838\pi$
$157$	−4.22601	+	7.31966i	−0.337272	+	0.584172i	0.646647	+	0.762790i	$0.276171\pi$
$158$	−1.89479	+	0.843614i	−0.150741	+	0.0671143i
$159$	−4.38021	+	0.0408573i	−0.347373	+	0.00324020i
$160$	6.31154	−	5.24642i	0.498971	−	0.414766i
$161$	−6.57991	−	20.2509i	−0.518570	−	1.59599i
$162$	0.199672	−	2.95757i	0.0156878	−	0.232369i
$163$	2.21761	−	6.82510i	0.173696	−	0.534583i	−0.825875	−	0.563853i	$-0.809318\pi$
$163$	2.21761	−	6.82510i	0.173696	−	0.534583i	0.999572	+	0.0292704i	$0.00931840\pi$
$164$	−5.48428	+	6.09091i	−0.428250	+	0.475620i
$165$	6.49133	+	0.881214i	0.505349	+	0.0686024i
$166$	3.15308	+	3.50186i	0.244727	+	0.271797i
$167$	−5.53430	+	2.46403i	−0.428257	+	0.190672i	−0.609534	−	0.792760i	$-0.708643\pi$
$167$	−5.53430	+	2.46403i	−0.428257	+	0.190672i	0.181277	+	0.983432i	$0.441977\pi$
$168$	−3.58756	+	4.05991i	−0.276786	+	0.313229i
$169$	0.868597	−	8.26415i	0.0668152	−	0.635704i
$170$	2.78810	+	0.405011i	0.213838	+	0.0310629i
$171$	4.48247	−	14.7247i	0.342783	−	1.12603i
$172$	10.0686	−	7.31525i	0.767722	−	0.557783i
$173$	−13.0611	+	14.5058i	−0.993017	+	1.10286i	0.00167954	+	0.999999i	$0.499465\pi$
$173$	−13.0611	+	14.5058i	−0.993017	+	1.10286i	−0.994696	+	0.102858i	$0.967201\pi$
$174$	−3.24333	−	0.657835i	−0.245876	−	0.0498703i
$175$	2.23005	−	11.9967i	0.168576	−	0.906869i
$176$	−2.84234	+	4.92307i	−0.214249	+	0.371090i
$177$	−0.190003	−	1.65878i	−0.0142815	−	0.124681i
$178$	2.88456	+	1.28429i	0.216207	+	0.0962614i
$179$	−3.88878	+	2.82536i	−0.290661	+	0.211178i	−0.723554	−	0.690268i	$-0.757493\pi$
$179$	−3.88878	+	2.82536i	−0.290661	+	0.211178i	0.432893	+	0.901445i	$0.357493\pi$
$180$	−12.6441	+	1.06256i	−0.942437	+	0.0791989i
$181$	4.50290	+	3.27155i	0.334698	+	0.243172i	0.742421	−	0.669933i	$-0.233677\pi$
$181$	4.50290	+	3.27155i	0.334698	+	0.243172i	−0.407724	+	0.913105i	$0.633677\pi$
$182$	−0.870406	−	1.50759i	−0.0645188	−	0.111750i
$183$	−14.7422	+	3.27755i	−1.08977	+	0.242284i
$184$	−7.48303	−	8.31075i	−0.551656	−	0.612677i
$185$	11.4739	−	14.5467i	0.843580	−	1.06949i
$186$	3.26025	−	2.41549i	0.239053	−	0.177112i
$187$	−6.32901	+	1.34527i	−0.462823	+	0.0983761i
$188$	4.65633	−	14.3307i	0.339598	−	1.04517i
$189$	12.3252	−	2.98253i	0.896528	−	0.216947i
$190$	3.73940	+	0.543200i	0.271284	+	0.0394079i
$191$	23.1633	−	4.92352i	1.67604	−	0.356254i	0.730791	−	0.682601i	$-0.239151\pi$
$191$	23.1633	−	4.92352i	1.67604	−	0.356254i	0.945250	+	0.326347i	$0.105818\pi$
$192$	2.86582	−	9.10828i	0.206822	−	0.657334i
$193$	−0.637107	+	1.10350i	−0.0458600	+	0.0794318i	−0.888044	−	0.459758i	$-0.847936\pi$
$193$	−0.637107	+	1.10350i	−0.0458600	+	0.0794318i	0.842184	+	0.539190i	$0.181269\pi$
$194$	0.463679	−	0.206443i	0.0332902	−	0.0148218i
$195$	1.99093	−	8.14808i	0.142573	−	0.583496i
$196$	1.80436	+	0.803355i	0.128883	+	0.0573825i
$197$	−7.96236	+	5.78499i	−0.567295	+	0.412164i	−0.834122	−	0.551581i	$-0.814025\pi$
$197$	−7.96236	+	5.78499i	−0.567295	+	0.412164i	0.266827	+	0.963745i	$0.414025\pi$
$198$	−1.51386	+	0.708142i	−0.107586	+	0.0503255i
$199$	−18.5853			−1.31747			−0.658737	−	0.752373i	$-0.728909\pi$
$199$	−18.5853			−1.31747			−0.658737	+	0.752373i	$0.728909\pi$
$200$	−1.49277	−	6.23241i	−0.105555	−	0.440698i
$201$	5.73913	+	1.16405i	0.404807	+	0.0821056i
$202$	−2.86558	−	0.609098i	−0.201621	−	0.0428560i
$203$	−1.47982	−	14.0796i	−0.103863	−	0.988192i
$204$	11.4013	−	5.20413i	0.798248	−	0.364362i
$205$	3.58798	+	9.00028i	0.250595	+	0.628607i
$206$	−2.64076	−	1.91862i	−0.183990	−	0.133677i
$207$	3.22116	+	25.9762i	0.223886	+	1.80547i
$208$	5.88859	+	4.27831i	0.408300	+	0.296647i
$209$	−8.48846	+	1.80428i	−0.587159	+	0.124804i
$210$	1.17974	+	2.88092i	0.0814101	+	0.198803i
$211$	−2.15974	−	0.459067i	−0.148683	−	0.0316035i	0.132969	−	0.991120i	$-0.457549\pi$
$211$	−2.15974	−	0.459067i	−0.148683	−	0.0316035i	−0.281652	+	0.959517i	$0.590882\pi$
$212$	−3.20092	−	3.55498i	−0.219840	−	0.244157i
$213$	−1.13316	+	0.0105698i	−0.0776426	+	0.000724228i
$214$	−0.174072	+	0.193327i	−0.0118993	+	0.0132155i
$215$	−2.48770	−	14.5006i	−0.169660	−	0.988934i
$216$	5.27650	−	4.06393i	0.359020	−	0.276516i
$217$	14.0427	+	10.2026i	0.953283	+	0.692600i
$218$	−2.86183	−	4.95683i	−0.193827	−	0.335719i
$219$	−5.66927	+	18.0184i	−0.383094	+	1.21757i
$220$	3.97297	+	5.94939i	0.267857	+	0.401107i
$221$	0.865993	+	8.23937i	0.0582530	+	0.554240i
$222$	−0.450215	+	4.70529i	−0.0302164	+	0.315798i
$223$	−17.5445	+	19.4851i	−1.17486	+	1.30482i	−0.231585	+	0.972815i	$0.574391\pi$
$223$	−17.5445	+	19.4851i	−1.17486	+	1.30482i	−0.943278	+	0.332003i	$0.892275\pi$
$224$	−8.95752			−0.598499
$225$	−5.48816	+	13.9599i	−0.365877	+	0.930663i
$226$	−0.715897			−0.0476208
$227$	−4.96062	+	5.50933i	−0.329248	+	0.365667i	−0.884927	−	0.465730i	$-0.845792\pi$
$227$	−4.96062	+	5.50933i	−0.329248	+	0.365667i	0.555679	+	0.831397i	$0.312458\pi$
$228$	15.2913	−	6.97977i	1.01269	−	0.462246i
$229$	−2.13178	−	20.2826i	−0.140872	−	1.34031i	−0.805260	−	0.592922i	$-0.797974\pi$
$229$	−2.13178	−	20.2826i	−0.140872	−	1.34031i	0.664387	−	0.747388i	$-0.268693\pi$
$230$	−6.18509	+	1.74260i	−0.407833	+	0.114904i
$231$	−4.83339	−	5.26836i	−0.318014	−	0.346633i
$232$	−3.71770	−	6.43924i	−0.244079	−	0.422757i
$233$	6.14372	+	4.46367i	0.402488	+	0.292425i	0.770554	−	0.637375i	$-0.219980\pi$
$233$	6.14372	+	4.46367i	0.402488	+	0.292425i	−0.368065	+	0.929800i	$0.619980\pi$
$234$	0.699129	+	2.02252i	0.0457035	+	0.132216i
$235$	−12.7562	−	12.4331i	−0.832120	−	0.811045i
$236$	1.22005	−	1.35501i	0.0794187	−	0.0882034i
$237$	5.54144	+	9.39458i	0.359955	+	0.610244i
$238$	−2.05750	−	2.28508i	−0.133368	−	0.148120i
$239$	−15.8639	−	3.37198i	−1.02615	−	0.218115i	−0.336062	−	0.941840i	$-0.609095\pi$
$239$	−15.8639	−	3.37198i	−1.02615	−	0.218115i	−0.690089	+	0.723725i	$0.742429\pi$
$240$	−9.40574	−	8.99800i	−0.607138	−	0.580818i
$241$	14.3594	−	3.05219i	0.924972	−	0.196609i	0.279282	−	0.960209i	$-0.409903\pi$
$241$	14.3594	−	3.05219i	0.924972	−	0.196609i	0.645689	+	0.763600i	$0.276570\pi$
$242$	−2.16877	−	1.57570i	−0.139414	−	0.101290i
$243$	−15.5715	+	0.726738i	−0.998913	+	0.0466203i
$244$	−13.3427	−	9.69406i	−0.854181	−	0.620599i
$245$	1.79557	−	1.49255i	0.114715	−	0.0953556i
$246$	−2.01331	−	1.43426i	−0.128364	−	0.0914450i
$247$	1.16147	+	11.0506i	0.0739024	+	0.703135i
$248$	8.91718	+	1.89540i	0.566241	+	0.120358i
$249$	16.4087	−	18.5691i	1.03986	−	1.17677i
$250$	−3.59099	−	0.815563i	−0.227114	−	0.0515808i
$251$	17.7351			1.11943			0.559716	−	0.828685i	$-0.310910\pi$
$251$	17.7351			1.11943			0.559716	+	0.828685i	$0.310910\pi$
$252$	11.3535	+	7.92952i	0.715205	+	0.499513i
$253$	11.9393	−	8.67440i	0.750617	−	0.545355i
$254$	4.43792	+	1.97589i	0.278460	+	0.123978i
$255$	0.447484	−	14.8090i	0.0280225	−	0.927375i
$256$	7.31728	−	3.25786i	0.457330	−	0.203616i
$257$	−3.02034	+	5.23139i	−0.188404	+	0.326325i	−0.944718	−	0.327883i	$-0.893665\pi$
$257$	−3.02034	+	5.23139i	−0.188404	+	0.326325i	0.756314	+	0.654208i	$0.226998\pi$
$258$	2.53752	+	2.76588i	0.157979	+	0.172196i
$259$	−19.7787	+	4.20410i	−1.22899	+	0.261230i
$260$	8.10765	−	4.26289i	0.502815	−	0.264373i
$261$	−1.49595	+	17.3387i	−0.0925968	+	1.07324i
$262$	0.214649	−	0.660622i	0.0132611	−	0.0408133i
$263$	9.90415	−	2.10519i	0.610716	−	0.129812i	0.107837	−	0.994169i	$-0.465608\pi$
$263$	9.90415	−	2.10519i	0.610716	−	0.129812i	0.502879	+	0.864357i	$0.332274\pi$
$264$	−3.44449	−	1.49524i	−0.211993	−	0.0920260i
$265$	−5.44317	+	1.53357i	−0.334371	+	0.0942066i
$266$	−2.75951	−	3.06475i	−0.169196	−	0.187912i
$267$	4.98360	−	15.8391i	0.304991	−	0.969338i
$268$	3.19757	+	5.53835i	0.195323	+	0.338309i
$269$	21.9237	+	15.9285i	1.33671	+	0.971177i	0.999558	+	0.0297274i	$0.00946393\pi$
$269$	21.9237	+	15.9285i	1.33671	+	0.971177i	0.337153	+	0.941450i	$0.390536\pi$
$270$	−0.752359	−	3.75222i	−0.0457871	−	0.228353i
$271$	−8.50805	+	6.18146i	−0.516827	+	0.375497i	−0.815407	−	0.578888i	$-0.803487\pi$
$271$	−8.50805	+	6.18146i	−0.516827	+	0.375497i	0.298580	+	0.954385i	$0.403487\pi$
$272$	11.7452	+	5.22930i	0.712157	+	0.317073i
$273$	−7.35560	+	5.44970i	−0.445181	+	0.329831i
$274$	0.759606	−	1.31568i	0.0458895	−	0.0794829i
$275$	8.38537	−	1.09943i	0.505657	−	0.0662980i
$276$	−18.9281	+	21.4203i	−1.13934	+	1.28935i
$277$	10.8806	−	12.0841i	0.653753	−	0.726066i	−0.321561	−	0.946889i	$-0.604208\pi$
$277$	10.8806	−	12.0841i	0.653753	−	0.726066i	0.975314	+	0.220823i	$0.0708743\pi$
$278$	−1.06655	+	0.774893i	−0.0639674	+	0.0464750i
$279$	−14.5709	−	15.5878i	−0.872339	−	0.933218i
$280$	−3.09524	+	6.27232i	−0.184976	+	0.374843i
$281$	1.58707	−	15.0999i	0.0946766	−	0.900787i	−0.839352	−	0.543589i	$-0.817065\pi$
$281$	1.58707	−	15.0999i	0.0946766	−	0.900787i	0.934028	−	0.357199i	$-0.116268\pi$
$282$	4.45387	+	0.903364i	0.265224	+	0.0537945i
$283$	−1.72853	+	0.769590i	−0.102750	+	0.0457474i	−0.457468	−	0.889226i	$-0.651244\pi$
$283$	−1.72853	+	0.769590i	−0.102750	+	0.0457474i	0.354718	+	0.934973i	$0.384577\pi$
$284$	−0.828075	−	0.919670i	−0.0491372	−	0.0545724i
$285$	0.600165	−	19.8618i	0.0355507	−	1.17651i
$286$	0.807321	−	0.896621i	0.0477379	−	0.0530183i
$287$	3.26777	−	10.0571i	0.192890	−	0.593655i
$288$	10.8115	+	2.08807i	0.637075	+	0.123041i
$289$	−0.731209	−	2.25043i	−0.0430123	−	0.132378i
$290$	−4.26331	+	0.278296i	−0.250350	+	0.0163421i
$291$	−1.35606	−	2.29898i	−0.0794938	−	0.134768i
$292$	−18.8449	+	8.39028i	−1.10281	+	0.491004i
$293$	−3.67099	+	6.35834i	−0.214462	+	0.371458i	−0.953106	−	0.302637i	$-0.902133\pi$
$293$	−3.67099	+	6.35834i	−0.214462	+	0.371458i	0.738644	+	0.674095i	$0.235466\pi$
$294$	−0.178788	+	0.568233i	−0.0104271	+	0.0331400i
$295$	−0.798195	−	2.00224i	−0.0464727	−	0.116575i
$296$	−8.59174	+	6.24227i	−0.499385	+	0.362824i
$297$	4.60569	+	7.48549i	0.267250	+	0.434352i
$298$	−1.40123	−	4.31255i	−0.0811713	−	0.249820i
$299$	−9.44799	−	16.3644i	−0.546391	−	0.946377i
$300$	−15.3927	+	5.60372i	−0.888700	+	0.323531i
$301$	−8.02861	+	13.9060i	−0.462761	+	0.801526i
$302$	6.53953	+	1.39002i	0.376308	+	0.0799867i
$303$	−1.46738	+	15.3359i	−0.0842988	+	0.881025i
$304$	15.7526	+	7.01352i	0.903475	+	0.402253i
$305$	−17.2568	+	9.07338i	−0.988120	+	0.519540i
$306$	1.95068	+	3.23766i	0.111513	+	0.185085i
$307$	4.38216			0.250103			0.125051	−	0.992150i	$-0.460090\pi$
$307$	4.38216			0.250103			0.125051	+	0.992150i	$0.460090\pi$
$308$	0.816147	−	7.76512i	0.0465043	−	0.442459i
$309$	−8.44362	+	14.9450i	−0.480341	+	0.850190i
$310$	3.24408	−	4.11285i	0.184251	−	0.233594i
$311$	17.4478	+	3.70864i	0.989373	+	0.210298i	0.674049	−	0.738686i	$-0.264553\pi$
$311$	17.4478	+	3.70864i	0.989373	+	0.210298i	0.315324	+	0.948984i	$0.397887\pi$
$312$	−2.36504	+	4.18606i	−0.133894	+	0.236989i
$313$	−15.9454	+	3.38931i	−0.901290	+	0.191575i	−0.635177	−	0.772367i	$-0.719073\pi$
$313$	−15.9454	+	3.38931i	−0.901290	+	0.191575i	−0.266113	+	0.963942i	$0.585739\pi$
$314$	−0.860246	−	2.64756i	−0.0485465	−	0.149411i
$315$	14.3456	−	7.88772i	0.808280	−	0.444423i
$316$	−3.68081	+	11.3284i	−0.207061	+	0.637270i
$317$	2.20283	−	20.9585i	0.123723	−	1.17715i	−0.739796	−	0.672832i	$-0.765078\pi$
$317$	2.20283	−	20.9585i	0.123723	−	1.17715i	0.863519	−	0.504317i	$-0.168256\pi$
$318$	0.955353	−	1.08114i	0.0535735	−	0.0606272i
$319$	8.96373	−	3.99091i	0.501872	−	0.223448i
$320$	0.487227	−	12.3174i	0.0272368	−	0.688565i
$321$	1.11422	+	0.793755i	0.0621897	+	0.0443031i
$322$	6.40690	+	2.85254i	0.357043	+	0.158966i
$323$	6.06501	+	18.6662i	0.337466	+	1.03861i
$324$	−11.8550	−	12.2173i	−0.658612	−	0.678741i
$325$	−0.277714	−	10.8250i	−0.0154048	−	0.600464i
$326$	1.18182	+	2.04698i	0.0654551	+	0.113372i
$327$	−24.1846	+	17.9182i	−1.33741	+	0.990877i
$328$	−0.580540	−	5.52347i	−0.0320550	−	0.304983i
$329$	2.03215	+	19.3346i	0.112036	+	1.06595i
$330$	−1.64631	+	1.39466i	−0.0906266	+	0.0767733i
$331$	1.89347	−	18.0152i	0.104075	−	0.990204i	−0.810487	−	0.585757i	$-0.800797\pi$
$331$	1.89347	−	18.0152i	0.104075	−	0.990204i	0.914561	−	0.404447i	$-0.132536\pi$
$332$	27.0617			1.48520
$333$	24.8525	−	0.463674i	1.36191	−	0.0254092i
$334$	0.616588	−	1.89766i	0.0337382	−	0.103835i
$335$	7.54399	−	0.492449i	0.412172	−	0.0269053i
$336$	1.61669	+	14.1141i	0.0881974	+	0.769985i
$337$	−2.47620	−	2.75010i	−0.134887	−	0.149807i	0.671917	−	0.740627i	$-0.265471\pi$
$337$	−2.47620	−	2.75010i	−0.134887	−	0.149807i	−0.806804	+	0.590819i	$0.798805\pi$
$338$	1.83137	+	2.03394i	0.0996131	+	0.110632i
$339$	0.428424	+	3.74025i	0.0232688	+	0.203143i
$340$	12.4425	−	10.3427i	0.674787	−	0.560911i
$341$	−3.71757	+	11.4415i	−0.201318	+	0.619593i
$342$	2.61625	+	4.34234i	0.141471	+	0.234807i
$343$	−19.6315			−1.06000
$344$	−0.881524	+	8.38714i	−0.0475286	+	0.452204i
$345$	12.8058	+	31.2715i	0.689439	+	1.68360i
$346$	−0.672022	−	6.39386i	−0.0361281	−	0.343736i
$347$	2.69542	+	25.6452i	0.144698	+	1.37671i	0.790154	+	0.612908i	$0.210000\pi$
$347$	2.69542	+	25.6452i	0.144698	+	1.37671i	−0.645457	+	0.763797i	$0.723333\pi$
$348$	−15.2708	+	11.3140i	−0.818600	+	0.606494i
$349$	15.6853	+	27.1678i	0.839616	+	1.45426i	0.890216	+	0.455538i	$0.150553\pi$
$349$	15.6853	+	27.1678i	0.839616	+	1.45426i	−0.0506002	+	0.998719i	$0.516113\pi$
$350$	2.44493	+	3.18980i	0.130687	+	0.170502i
$351$	10.1484	−	4.86301i	0.541681	−	0.259568i
$352$	−1.91846	−	5.90442i	−0.102254	−	0.314707i
$353$	−0.0915256	−	0.0407498i	−0.00487142	−	0.00216889i	0.404299	−	0.914627i	$-0.367515\pi$
$353$	−0.0915256	−	0.0407498i	−0.00487142	−	0.00216889i	−0.409171	+	0.912458i	$0.634182\pi$
$354$	0.447889	+	0.319070i	0.0238050	+	0.0169584i
$355$	−1.40814	+	0.396734i	−0.0747364	+	0.0210564i
$356$	16.5657	−	7.37552i	0.877979	−	0.390902i
$357$	−10.7073	+	12.1170i	−0.566688	+	0.641300i
$358$	0.165490	−	1.57453i	0.00874639	−	0.0832164i
$359$	4.79343	−	14.7527i	0.252988	−	0.778616i	−0.741232	−	0.671249i	$-0.765758\pi$
$359$	4.79343	−	14.7527i	0.252988	−	0.778616i	0.994219	−	0.107367i	$-0.0342419\pi$
$360$	5.19800	−	6.84902i	0.273959	−	0.360975i
$361$	2.26305	+	6.96496i	0.119108	+	0.366577i
$362$	−1.79316	+	0.381148i	−0.0942464	+	0.0200327i
$363$	−6.93446	+	12.2738i	−0.363965	+	0.644209i
$364$	−9.77882	−	2.07855i	−0.512549	−	0.108946i
$365$	−0.963851	+	24.3668i	−0.0504503	+	1.27542i
$366$	2.44678	−	4.33074i	0.127895	−	0.226371i
$367$	1.34951	−	12.8397i	0.0704439	−	0.670229i	−0.901139	−	0.433530i	$-0.857268\pi$
$367$	1.34951	−	12.8397i	0.0704439	−	0.670229i	0.971583	−	0.236699i	$-0.0760655\pi$
$368$	−29.3238			−1.52861
$369$	−6.28852	+	11.3770i	−0.327367	+	0.592263i
$370$	1.03182	+	6.01438i	0.0536416	+	0.312673i
$371$	5.63837	+	2.51036i	0.292730	+	0.130332i
$372$	2.21947	−	23.1961i	0.115074	−	1.20266i
$373$	0.226521	+	0.0481486i	0.0117288	+	0.00249304i	0.213772	−	0.976884i	$-0.431425\pi$
$373$	0.226521	+	0.0481486i	0.0117288	+	0.00249304i	−0.202044	+	0.979377i	$0.564758\pi$
$374$	1.06557	−	1.84562i	0.0550993	−	0.0954347i
$375$	−2.11196	+	19.2494i	−0.109061	+	0.994035i
$376$	5.10529	+	8.84261i	0.263285	+	0.456023i
$377$	−3.88230	−	11.9485i	−0.199949	−	0.615379i
$378$	−1.98632	+	3.67413i	−0.102166	+	0.188977i
$379$	4.51376	−	3.27944i	0.231856	−	0.168453i	−0.465791	−	0.884895i	$-0.654230\pi$
$379$	4.51376	−	3.27944i	0.231856	−	0.168453i	0.697647	+	0.716441i	$0.254230\pi$
$380$	16.6878	−	13.8716i	0.856066	−	0.711598i
$381$	7.66732	−	24.3687i	0.392809	−	1.24844i
$382$	−3.89984	+	6.75473i	−0.199533	+	0.345602i
$383$	−12.2595	+	5.45829i	−0.626433	+	0.278906i	−0.695300	−	0.718720i	$-0.744728\pi$
$383$	−12.2595	+	5.45829i	−0.626433	+	0.278906i	0.0688668	+	0.997626i	$0.478062\pi$
$384$	8.05763	+	13.6604i	0.411189	+	0.697102i
$385$	−7.80488	−	4.92741i	−0.397774	−	0.251124i
$386$	−0.129690	−	0.399143i	−0.00660102	−	0.0203159i
$387$	12.9319	−	14.9126i	0.657367	−	0.758052i
$388$	0.900742	−	2.77220i	0.0457282	−	0.140737i
$389$	22.7699	−	25.2885i	1.15448	−	1.28218i	0.201380	−	0.979513i	$-0.435457\pi$
$389$	22.7699	−	25.2885i	1.15448	−	1.28218i	0.953097	−	0.302664i	$-0.0978759\pi$
$390$	1.55560	+	2.28307i	0.0787711	+	0.115607i
$391$	−22.3335	−	24.8038i	−1.12945	−	1.25438i
$392$	−1.22268	+	0.544373i	−0.0617547	+	0.0274950i
$393$	−3.57991	−	0.726102i	−0.180583	−	0.0366270i
$394$	0.338843	−	3.22388i	0.0170707	−	0.162417i
$395$	10.0837	+	9.82830i	0.507365	+	0.494515i
$396$	−2.79518	+	9.18207i	−0.140463	+	0.461416i
$397$	22.7816	−	16.5518i	1.14338	−	0.830711i	0.155790	−	0.987790i	$-0.450208\pi$
$397$	22.7816	−	16.5518i	1.14338	−	0.830711i	0.987586	+	0.157079i	$0.0502078\pi$
$398$	4.09600	−	4.54907i	0.205314	−	0.228024i
$399$	−14.3606	+	16.2513i	−0.718927	+	0.813583i
$400$	−14.7637	−	8.02619i	−0.738185	−	0.401309i
$401$	−6.50887	+	11.2737i	−0.325037	+	0.562981i	−0.981520	−	0.191360i	$-0.938710\pi$
$401$	−6.50887	+	11.2737i	−0.325037	+	0.562981i	0.656483	+	0.754341i	$0.272044\pi$
$402$	−1.54976	+	1.14821i	−0.0772952	+	0.0572674i
$403$	14.0720	+	6.26526i	0.700976	+	0.312095i
$404$	−13.6112	+	9.88910i	−0.677181	+	0.492001i
$405$	−19.1534	+	6.17624i	−0.951742	+	0.306900i
$406$	3.77236	+	2.74078i	0.187219	+	0.136023i
$407$	−7.00725	−	12.1369i	−0.347337	−	0.601605i
$408$	−2.54889	+	8.10101i	−0.126189	+	0.401060i
$409$	22.3589	+	24.8320i	1.10557	+	1.22786i	0.971537	+	0.236888i	$0.0761275\pi$
$409$	22.3589	+	24.8320i	1.10557	+	1.22786i	0.134037	+	0.990976i	$0.457206\pi$
$410$	−2.99373	−	1.10535i	−0.147850	−	0.0545892i
$411$	−7.32841	−	3.18125i	−0.361484	−	0.156919i
$412$	−18.3360	+	3.89744i	−0.903351	+	0.192013i
$413$	−0.726959	+	2.23735i	−0.0357713	+	0.110093i
$414$	−7.06803	−	4.93644i	−0.347375	−	0.242613i
$415$	14.1569	−	28.6882i	0.694936	−	1.40825i
$416$	−7.77542	+	1.65272i	−0.381221	+	0.0810311i
$417$	4.68675	+	5.10852i	0.229511	+	0.250165i
$418$	1.42914	−	2.47534i	0.0699015	−	0.121073i
$419$	36.0676	−	16.0583i	1.76202	−	0.784501i	0.773426	−	0.633886i	$-0.218541\pi$
$419$	36.0676	−	16.0583i	1.76202	−	0.784501i	0.988593	−	0.150615i	$-0.0481254\pi$
$420$	16.8286	+	6.03573i	0.821154	+	0.294513i
$421$	2.40676	+	1.07156i	0.117298	+	0.0522246i	0.464547	−	0.885549i	$-0.346217\pi$
$421$	2.40676	+	1.07156i	0.117298	+	0.0522246i	−0.347248	+	0.937773i	$0.612884\pi$
$422$	0.588349	−	0.427460i	0.0286404	−	0.0208084i
$423$	2.05429	−	23.8101i	0.0998830	−	1.15769i
$424$	3.24155			0.157424
$425$	−4.45525	−	18.6009i	−0.216111	−	0.902278i
$426$	0.247149	−	0.279689i	0.0119744	−	0.0135510i
$427$	20.8138	+	4.42411i	1.00725	+	0.214098i
$428$	0.156165	+	1.48581i	0.00754851	+	0.0718192i
$429$	−5.16759	−	3.68132i	−0.249493	−	0.177736i
$430$	4.09754	+	2.58688i	0.197601	+	0.124750i
$431$	27.7928	+	20.1926i	1.33873	+	0.972644i	0.999490	+	0.0319446i	$0.0101700\pi$
$431$	27.7928	+	20.1926i	1.33873	+	0.972644i	0.339240	+	0.940700i	$0.389830\pi$
$432$	1.33880	−	17.4122i	0.0644129	−	0.837745i
$433$	−22.0022	−	15.9856i	−1.05736	−	0.768217i	−0.0837621	−	0.996486i	$-0.526694\pi$
$433$	−22.0022	−	15.9856i	−1.05736	−	0.768217i	−0.973598	+	0.228269i	$0.926694\pi$
$434$	−5.59215	+	1.18865i	−0.268432	+	0.0570569i
$435$	4.00532	+	22.1074i	0.192041	+	1.05997i
$436$	−32.1520	−	6.83412i	−1.53980	−	0.327295i
$437$	−29.9536	−	33.2669i	−1.43288	−	1.59137i
$438$	−3.16086	−	5.35871i	−0.151032	−	0.256049i
$439$	−10.0470	+	11.1583i	−0.479515	+	0.532556i	−0.933559	−	0.358424i	$-0.883314\pi$
$439$	−10.0470	+	11.1583i	−0.479515	+	0.532556i	0.454044	+	0.890979i	$0.349981\pi$
$440$	−4.79737	−	0.696885i	−0.228706	−	0.0332227i
$441$	3.07576	+	0.594033i	0.146465	+	0.0282873i
$442$	−2.20759	−	1.60390i	−0.105004	−	0.0762900i
$443$	5.24719	+	9.08840i	0.249301	+	0.431803i	0.963332	−	0.268312i	$-0.0864657\pi$
$443$	5.24719	+	9.08840i	0.249301	+	0.431803i	−0.714031	+	0.700114i	$0.753132\pi$
$444$	18.3511	+	20.0026i	0.870907	+	0.949282i
$445$	0.847277	−	21.4197i	0.0401648	−	1.01539i
$446$	−0.902700	−	8.58862i	−0.0427441	−	0.406683i
$447$	−21.6926	+	9.90165i	−1.02603	+	0.468332i
$448$	−9.00233	+	9.99810i	−0.425320	+	0.472366i
$449$	19.5039			0.920444			0.460222	−	0.887804i	$-0.347770\pi$
$449$	19.5039			0.920444			0.460222	+	0.887804i	$0.347770\pi$
$450$	−2.20741	−	4.41995i	−0.104058	−	0.208358i
$451$	7.32912			0.345115
$452$	−2.75101	+	3.05530i	−0.129397	+	0.143709i
$453$	3.34871	−	34.9980i	0.157336	−	1.64435i
$454$	−0.255235	−	2.42840i	−0.0119788	−	0.113970i
$455$	−7.31913	+	9.27921i	−0.343126	+	0.435016i
$456$	−3.41857	+	10.8651i	−0.160089	+	0.508803i
$457$	−6.38012	−	11.0507i	−0.298449	−	0.516929i	0.677332	−	0.735677i	$-0.263136\pi$
$457$	−6.38012	−	11.0507i	−0.298449	−	0.516929i	−0.975781	+	0.218748i	$0.929803\pi$
$458$	5.43434	+	3.94828i	0.253930	+	0.184491i
$459$	15.7480	−	12.1290i	0.735053	−	0.566133i
$460$	−16.3306	+	33.0931i	−0.761419	+	1.54297i
$461$	−9.42808	+	10.4709i	−0.439109	+	0.487680i	−0.921556	−	0.388245i	$-0.873081\pi$
$461$	−9.42808	+	10.4709i	−0.439109	+	0.487680i	0.482447	+	0.875925i	$0.339748\pi$
$462$	2.35475	−	0.0219644i	0.109553	−	0.00102188i
$463$	20.2556	+	22.4961i	0.941356	+	1.04548i	0.998888	+	0.0471380i	$0.0150100\pi$
$463$	20.2556	+	22.4961i	0.941356	+	1.04548i	−0.0575325	+	0.998344i	$0.518323\pi$
$464$	−19.0705	−	4.05355i	−0.885325	−	0.188182i
$465$	−23.4293	−	14.4876i	−1.08651	−	0.671846i
$466$	−2.44657	+	0.520035i	−0.113335	+	0.0240902i
$467$	−0.459190	−	0.333621i	−0.0212488	−	0.0154382i	0.577110	−	0.816666i	$-0.304180\pi$
$467$	−0.459190	−	0.333621i	−0.0212488	−	0.0154382i	−0.598359	+	0.801228i	$0.704180\pi$
$468$	11.3183	+	4.78828i	0.523188	+	0.221338i
$469$	−6.67524	−	4.84985i	−0.308234	−	0.223945i
$470$	5.85454	−	0.382166i	0.270050	−	0.0176280i
$471$	−13.3176	+	6.07883i	−0.613641	+	0.280097i
$472$	0.129149	+	1.22877i	0.00594457	+	0.0565588i
$473$	−10.8857	−	2.31384i	−0.500527	−	0.106390i
$474$	−3.52076	−	0.714105i	−0.161714	−	0.0327999i
$475$	−5.97537	−	24.9475i	−0.274169	−	1.14467i
$476$	−17.6587			−0.809384
$477$	−6.22020	−	4.34430i	−0.284803	−	0.198912i
$478$	4.32159	−	3.13982i	0.197665	−	0.143612i
$479$	8.30395	+	3.69716i	0.379417	+	0.168927i	0.587579	−	0.809167i	$-0.300081\pi$
$479$	8.30395	+	3.69716i	0.379417	+	0.168927i	−0.208161	+	0.978094i	$0.566748\pi$
$480$	14.1761	−	1.05825i	0.647047	−	0.0483021i
$481$	−16.3929	+	7.29860i	−0.747453	+	0.332787i
$482$	−2.41759	+	4.18739i	−0.110118	+	0.190730i
$483$	11.0691	−	35.1803i	0.503661	−	1.60076i
$484$	−15.0588	+	3.20084i	−0.684490	+	0.145493i
$485$	−2.46761	−	2.40511i	−0.112048	−	0.109211i
$486$	3.25392	−	3.97156i	0.147601	−	0.180154i
$487$	−9.84622	+	30.3036i	−0.446175	+	1.37319i	0.435015	+	0.900423i	$0.356743\pi$
$487$	−9.84622	+	30.3036i	−0.446175	+	1.37319i	−0.881190	+	0.472762i	$0.843257\pi$
$488$	10.9315	−	2.32357i	0.494847	−	0.105183i
$489$	9.98731	−	7.39951i	0.451642	−	0.334617i
$490$	−0.0303963	+	0.768439i	−0.00137317	+	0.0347145i
$491$	−28.2390	−	31.3625i	−1.27441	−	1.41537i	−0.864018	−	0.503461i	$-0.832060\pi$
$491$	−28.2390	−	31.3625i	−1.27441	−	1.41537i	−0.410388	−	0.911911i	$-0.634607\pi$
$492$	−13.8578	+	3.08093i	−0.624756	+	0.138899i
$493$	−11.0957	−	19.2182i	−0.499723	−	0.865546i
$494$	−2.96081	−	2.15115i	−0.133213	−	0.0967850i
$495$	8.27169	+	7.76665i	0.371785	+	0.349085i
$496$	19.3390	−	14.0506i	0.868346	−	0.630890i
$497$	1.45864	+	0.649429i	0.0654290	+	0.0291309i
$498$	0.928813	+	8.10877i	0.0416211	+	0.363363i
$499$	9.50928	−	16.4706i	0.425694	−	0.737323i	−0.570791	−	0.821095i	$-0.693363\pi$
$499$	9.50928	−	16.4706i	0.425694	−	0.737323i	0.996485	+	0.0837721i	$0.0266968\pi$
$500$	−17.2799	+	12.1916i	−0.772780	+	0.545225i
$501$	−10.2834	−	2.08576i	−0.459430	−	0.0931848i
$502$	−3.90864	+	4.34098i	−0.174451	+	0.193747i
$503$	8.48894	−	6.16758i	0.378503	−	0.274999i	−0.382225	−	0.924069i	$-0.624842\pi$
$503$	8.48894	−	6.16758i	0.378503	−	0.274999i	0.760728	+	0.649071i	$0.224842\pi$
$504$	−9.14100	+	2.12194i	−0.407172	+	0.0945186i
$505$	3.36299	+	19.6026i	0.149651	+	0.872305i
$506$	−0.508084	+	4.83410i	−0.0225871	+	0.214902i
$507$	9.53046	−	10.7853i	0.423263	−	0.478991i
$508$	25.4865	−	11.3473i	1.13078	−	0.503456i
$509$	−18.4464	−	20.4868i	−0.817624	−	0.908063i	0.179508	−	0.983757i	$-0.442550\pi$
$509$	−18.4464	−	20.4868i	−0.817624	−	0.908063i	−0.997131	+	0.0756936i	$0.975883\pi$
$510$	3.52614	+	3.37328i	0.156140	+	0.149371i
$511$	17.8088	−	19.7786i	0.787814	−	0.874956i
$512$	−6.47433	+	19.9259i	−0.286128	+	0.880611i
$513$	21.1212	−	16.2674i	0.932522	−	0.718223i
$514$	−0.614821	−	1.89222i	−0.0271186	−	0.0834624i
$515$	−5.46053	+	21.4770i	−0.240620	+	0.946389i
$516$	21.5552	−	0.201061i	0.948916	−	0.00885120i
$517$	−12.3093	+	5.48047i	−0.541364	+	0.241031i
$518$	3.33000	−	5.76773i	0.146312	−	0.253420i
$519$	−33.0030	+	7.33738i	−1.44867	+	0.322075i
$520$	−1.52948	+	6.01567i	−0.0670723	+	0.263804i
$521$	24.6933	−	17.9407i	1.08183	−	0.785998i	0.103831	−	0.994595i	$-0.466890\pi$
$521$	24.6933	−	17.9407i	1.08183	−	0.785998i	0.978002	+	0.208597i	$0.0668898\pi$
$522$	−3.91425	−	4.18742i	−0.171322	−	0.183279i
$523$	−4.73750	−	14.5805i	−0.207156	−	0.637562i	−0.999618	−	0.0276401i	$-0.991201\pi$
$523$	−4.73750	−	14.5805i	−0.207156	−	0.637562i	0.792461	−	0.609922i	$-0.208799\pi$
$524$	−1.99456	−	3.45467i	−0.0871326	−	0.150918i
$525$	15.2022	−	14.6826i	0.663477	−	0.640802i
$526$	−1.66749	+	2.88818i	−0.0727060	+	0.125930i
$527$	26.6138	+	5.65693i	1.15931	+	0.246420i
$528$	−8.95715	+	4.08851i	−0.389810	+	0.177930i
$529$	48.5334	+	21.6084i	2.11015	+	0.939498i
$530$	0.824249	−	1.67029i	0.0358031	−	0.0725529i
$531$	1.39897	−	2.53097i	0.0607100	−	0.109835i
$532$	−23.6838			−1.02682
$533$	0.980923	−	9.33285i	0.0424885	−	0.404251i
$534$	2.77857	+	4.71060i	0.120240	+	0.203848i
$535$	1.65681	+	0.611728i	0.0716300	+	0.0264473i
$536$	−4.23880	−	0.900985i	−0.183088	−	0.0389166i
$537$	−8.32525	+	0.0776555i	−0.359261	+	0.00335108i
$538$	−8.73053	+	1.85573i	−0.376400	+	0.0800063i
$539$	−0.545782	−	1.67975i	−0.0235085	−	0.0723518i
$540$	−18.9048	−	11.2079i	−0.813533	−	0.482310i
$541$	0.320574	−	0.986626i	0.0137826	−	0.0424184i	−0.943929	−	0.330149i	$-0.892901\pi$
$541$	0.320574	−	0.986626i	0.0137826	−	0.0424184i	0.957711	+	0.287731i	$0.0929009\pi$
$542$	0.362065	−	3.44482i	0.0155520	−	0.147968i
$543$	3.06444	+	9.14038i	0.131508	+	0.392251i
$544$	−12.8270	+	5.71096i	−0.549954	+	0.244855i
$545$	−24.0647	+	30.5093i	−1.03082	+	1.30687i
$546$	0.287189	−	3.00147i	0.0122905	−	0.128451i
$547$	−25.9691	−	11.5622i	−1.11036	−	0.494364i	−0.232169	−	0.972675i	$-0.574582\pi$
$547$	−25.9691	−	11.5622i	−1.11036	−	0.494364i	−0.878190	+	0.478311i	$0.841249\pi$
$548$	−2.69607	−	8.29764i	−0.115170	−	0.354458i
$549$	−24.0905	−	10.1917i	−1.02816	−	0.434969i
$550$	−1.57894	+	2.29477i	−0.0673264	+	0.0978492i
$551$	−14.8815	−	25.7755i	−0.633972	−	1.09807i
$552$	−2.20430	−	19.2441i	−0.0938211	−	0.819082i
$553$	−1.60640	−	15.2839i	−0.0683112	−	0.649938i
$554$	0.559831	+	5.32644i	0.0237850	+	0.226299i
$555$	30.8050	−	8.99005i	1.30760	−	0.381606i
$556$	−0.791385	+	7.52953i	−0.0335622	+	0.319323i
$557$	23.9335			1.01409			0.507047	−	0.861919i	$-0.330737\pi$
$557$	23.9335			1.01409			0.507047	+	0.861919i	$0.330737\pi$
$558$	7.02667	−	0.131097i	0.297463	−	0.00554977i
$559$	−4.40336	+	13.5522i	−0.186242	+	0.573195i
$560$	6.79162	+	17.0365i	0.286998	+	0.719922i
$561$	−10.2802	−	4.46263i	−0.434032	−	0.188412i
$562$	3.34620	+	3.71633i	0.141151	+	0.156764i
$563$	2.36392	+	2.62540i	0.0996272	+	0.110647i	0.790896	−	0.611950i	$-0.209615\pi$
$563$	2.36392	+	2.62540i	0.0996272	+	0.110647i	−0.691269	+	0.722597i	$0.742948\pi$
$564$	20.9704	−	15.5368i	0.883014	−	0.654218i
$565$	1.79979	+	4.51469i	0.0757178	+	0.189935i
$566$	0.192579	−	0.592697i	0.00809470	−	0.0249129i
$567$	20.3844	+	8.17892i	0.856066	+	0.343482i
$568$	0.838586			0.0351863
$569$	1.93022	−	18.3648i	0.0809189	−	0.769892i	−0.876541	−	0.481326i	$-0.840155\pi$
$569$	1.93022	−	18.3648i	0.0809189	−	0.769892i	0.957460	−	0.288565i	$-0.0931782\pi$
$570$	4.72925	+	4.52423i	0.198086	+	0.189499i
$571$	2.82412	+	26.8697i	0.118186	+	1.12446i	0.879440	+	0.476009i	$0.157917\pi$
$571$	2.82412	+	26.8697i	0.118186	+	1.12446i	−0.761255	+	0.648453i	$0.775416\pi$
$572$	−0.724269	−	6.89096i	−0.0302832	−	0.288125i
$573$	37.6243	+	16.3327i	1.57178	+	0.682306i
$574$	1.74148	+	3.01633i	0.0726880	+	0.125899i
$575$	26.5390	+	34.6243i	1.10675	+	1.44393i
$576$	13.1962	−	9.96896i	0.549843	−	0.415374i
$577$	4.52246	+	13.9187i	0.188273	+	0.579444i	0.999989	−	0.00460768i	$-0.00146668\pi$
$577$	4.52246	+	13.9187i	0.188273	+	0.579444i	−0.811717	+	0.584051i	$0.801467\pi$
$578$	0.711983	+	0.316995i	0.0296146	+	0.0131853i
$579$	−2.00774	+	0.916436i	−0.0834387	+	0.0380858i
$580$	−15.1951	+	19.2644i	−0.630942	+	0.799909i
$581$	−31.8966	+	14.2013i	−1.32329	+	0.589169i
$582$	0.861577	+	0.174751i	0.0357135	+	0.00724365i
$583$	−0.447138	+	4.25423i	−0.0185186	+	0.176192i
$584$	4.31951	−	13.2941i	0.178743	−	0.550113i
$585$	10.9971	−	9.49364i	0.454673	−	0.392514i
$586$	−0.747267	−	2.29985i	−0.0308693	−	0.0950060i
$587$	29.1470	−	6.19538i	1.20302	−	0.255711i	0.437560	−	0.899189i	$-0.355843\pi$
$587$	29.1470	−	6.19538i	1.20302	−	0.255711i	0.765464	+	0.643479i	$0.222509\pi$
$588$	1.73807	+	2.94660i	0.0716766	+	0.121516i
$589$	35.6943	+	7.58706i	1.47076	+	0.312620i
$590$	0.665996	+	0.245900i	0.0274186	+	0.0101235i
$591$	−17.0461	+	0.159001i	−0.701184	+	0.00654044i
$592$	−2.91079	+	27.6943i	−0.119633	+	1.13823i
$593$	15.3217			0.629186			0.314593	−	0.949227i	$-0.398132\pi$
$593$	15.3217			0.629186			0.314593	+	0.949227i	$0.398132\pi$
$594$	−2.84725	−	0.522401i	−0.116824	−	0.0214344i
$595$	−9.23788	+	18.7200i	−0.378716	+	0.767447i
$596$	−23.7897	−	10.5918i	−0.974463	−	0.433859i
$597$	−26.2181	−	18.6774i	−1.07304	−	0.764417i
$598$	6.08771	+	1.29398i	0.248945	+	0.0529149i
$599$	−14.5795	+	25.2524i	−0.595702	+	1.03179i	0.397745	+	0.917496i	$0.369793\pi$
$599$	−14.5795	+	25.2524i	−0.595702	+	1.03179i	−0.993447	+	0.114290i	$0.963541\pi$
$600$	4.15748	−	10.2922i	0.169728	−	0.420177i
$601$	−5.97136	−	10.3427i	−0.243577	−	0.421888i	0.718154	−	0.695885i	$-0.244987\pi$
$601$	−5.97136	−	10.3427i	−0.243577	−	0.421888i	−0.961731	+	0.273997i	$0.911654\pi$
$602$	−1.63430	−	5.02987i	−0.0666093	−	0.205002i
$603$	6.92633	+	7.40970i	0.282062	+	0.301747i
$604$	31.0621	−	22.5679i	1.26390	−	0.918275i
$605$	−4.48455	+	17.6383i	−0.182323	+	0.717101i
$606$	−3.43033	−	3.73904i	−0.139348	−	0.151888i
$607$	11.8537	−	20.5312i	0.481127	−	0.833336i	−0.518639	−	0.854993i	$-0.673561\pi$
$607$	11.8537	−	20.5312i	0.481127	−	0.833336i	0.999765	+	0.0216578i	$0.00689442\pi$
$608$	−17.2036	+	7.65953i	−0.697697	+	0.310635i
$609$	12.0618	−	21.3491i	0.488770	−	0.865110i
$610$	1.58235	−	6.22358i	0.0640673	−	0.251985i
$611$	5.33132	+	16.4081i	0.215682	+	0.663801i
$612$	21.3136	+	4.11638i	0.861552	+	0.166395i
$613$	10.4855	−	32.2710i	0.423505	−	1.30341i	−0.480914	−	0.876768i	$-0.659695\pi$
$613$	10.4855	−	32.2710i	0.423505	−	1.30341i	0.904419	−	0.426646i	$-0.140305\pi$
$614$	−0.965781	+	1.07261i	−0.0389758	+	0.0432870i
$615$	−3.98338	+	16.3024i	−0.160625	+	0.657377i
$616$	3.54025	+	3.93184i	0.142641	+	0.158418i
$617$	9.30742	−	4.14393i	0.374703	−	0.166828i	−0.210740	−	0.977542i	$-0.567587\pi$
$617$	9.30742	−	4.14393i	0.374703	−	0.166828i	0.585443	+	0.810714i	$0.300921\pi$
$618$	−1.79716	−	5.36044i	−0.0722924	−	0.215629i
$619$	0.692019	−	6.58412i	0.0278146	−	0.264638i	−0.971773	−	0.235918i	$-0.924190\pi$
$619$	0.692019	−	6.58412i	0.0278146	−	0.264638i	0.999587	−	0.0287199i	$-0.00914307\pi$
$620$	−5.08665	−	29.6497i	−0.204285	−	1.19076i
$621$	−21.5609	+	39.8816i	−0.865211	+	1.60039i
$622$	−4.75307	+	3.45330i	−0.190581	+	0.138465i
$623$	−15.6549	+	17.3865i	−0.627199	+	0.696576i
$624$	4.00747	+	11.9532i	0.160427	+	0.478510i
$625$	3.88465	+	24.6963i	0.155386	+	0.987854i
$626$	2.68462	−	4.64989i	0.107299	−	0.185847i
$627$	−13.7878	−	5.98527i	−0.550633	−	0.239029i
$628$	−14.6050	−	6.50255i	−0.582802	−	0.259480i
$629$	−25.6425	+	18.6303i	−1.02243	+	0.742841i
$630$	−1.23095	+	5.24970i	−0.0490424	+	0.209153i
$631$	18.8353	+	13.6847i	0.749823	+	0.544778i	0.895772	−	0.444514i	$-0.146623\pi$
$631$	18.8353	+	13.6847i	0.749823	+	0.544778i	−0.145949	+	0.989292i	$0.546623\pi$
$632$	−4.03570	−	6.99004i	−0.160532	−	0.278049i
$633$	−2.58539	−	2.81805i	−0.102760	−	0.112008i
$634$	4.64449	+	5.15822i	0.184456	+	0.204859i
$635$	1.30355	−	32.9545i	0.0517296	−	1.30776i
$636$	−0.942903	−	8.23178i	−0.0373885	−	0.326411i
$637$	−2.21202	+	0.470180i	−0.0876436	+	0.0186292i
$638$	−0.998668	+	3.07358i	−0.0395376	+	0.121684i
$639$	−1.60916	−	1.12387i	−0.0636574	−	0.0444595i
$640$	14.6624	+	14.2910i	0.579581	+	0.564902i
$641$	−24.4184	+	5.19029i	−0.964468	+	0.205004i	−0.663123	−	0.748511i	$-0.730769\pi$
$641$	−24.4184	+	5.19029i	−0.964468	+	0.205004i	−0.301346	+	0.953515i	$0.597436\pi$
$642$	−0.439848	+	0.0977892i	−0.0173594	+	0.00385943i
$643$	4.76373	−	8.25102i	0.187863	−	0.325388i	−0.756674	−	0.653792i	$-0.773177\pi$
$643$	4.76373	−	8.25102i	0.187863	−	0.325388i	0.944538	+	0.328403i	$0.106511\pi$
$644$	36.7941	−	16.3818i	1.44989	−	0.645533i
$645$	11.0632	−	22.9560i	0.435611	−	0.903890i
$646$	−5.90553	−	2.62931i	−0.232350	−	0.103449i
$647$	−38.6632	+	28.0905i	−1.52001	+	1.10435i	−0.558525	+	0.829487i	$0.688633\pi$
$647$	−38.6632	+	28.0905i	−1.52001	+	1.10435i	−0.961483	+	0.274863i	$0.911367\pi$
$648$	11.5276	−	0.430292i	0.452847	−	0.0169035i
$649$	−1.63046			−0.0640013
$650$	2.71082	+	2.31775i	0.106327	+	0.0909095i
$651$	9.55675	+	28.5052i	0.374558	+	1.11721i
$652$	13.2775	+	2.82222i	0.519988	+	0.110527i
$653$	1.42666	+	13.5738i	0.0558295	+	0.531182i	0.986317	+	0.164859i	$0.0527169\pi$
$653$	1.42666	+	13.5738i	0.0558295	+	0.531182i	−0.930488	+	0.366323i	$0.880616\pi$
$654$	0.944253	−	9.86859i	0.0369232	−	0.385892i
$655$	−4.70574	+	0.307176i	−0.183868	+	0.0120024i
$656$	−11.7817	−	8.55991i	−0.459998	−	0.334208i
$657$	−26.1053	+	19.7210i	−1.01847	+	0.769390i
$658$	−5.18035	−	3.76374i	−0.201951	−	0.146726i
$659$	7.11906	−	1.51320i	0.277319	−	0.0589460i	−0.0671526	−	0.997743i	$-0.521391\pi$
$659$	7.11906	−	1.51320i	0.277319	−	0.0589460i	0.344472	+	0.938797i	$0.388058\pi$
$660$	−0.374251	+	12.3854i	−0.0145677	+	0.482102i
$661$	21.3346	+	4.53482i	0.829821	+	0.176384i	0.603191	−	0.797597i	$-0.293896\pi$
$661$	21.3346	+	4.53482i	0.829821	+	0.176384i	0.226630	+	0.973981i	$0.427229\pi$
$662$	3.99223	+	4.43382i	0.155162	+	0.172325i
$663$	−7.05858	+	12.4935i	−0.274133	+	0.485208i
$664$	−12.2703	+	13.6275i	−0.476179	+	0.528851i
$665$	−12.3898	+	25.1073i	−0.480457	+	0.973619i
$666$	−5.36374	+	6.18527i	−0.207841	+	0.239674i
$667$	40.9478	+	29.7503i	1.58550	+	1.15194i
$668$	−5.72945	−	9.92369i	−0.221679	−	0.383959i
$669$	−44.3316	+	9.85602i	−1.71396	+	0.381056i
$670$	−1.54208	+	1.95505i	−0.0595758	+	0.0755303i
$671$	1.54158	+	14.6671i	0.0595119	+	0.566218i
$672$	−12.6363	−	9.00195i	−0.487456	−	0.347258i
$673$	32.4377	−	36.0257i	1.25038	−	1.38869i	0.360335	−	0.932823i	$-0.382662\pi$
$673$	32.4377	−	36.0257i	1.25038	−	1.38869i	0.890048	−	0.455868i	$-0.150671\pi$
$674$	1.21886			0.0469488
$675$	−21.7713	+	14.1778i	−0.837977	+	0.545705i
$676$	15.7179			0.604534
$677$	−6.61758	+	7.34956i	−0.254334	+	0.282467i	−0.856768	−	0.515702i	$-0.827531\pi$
$677$	−6.61758	+	7.34956i	−0.254334	+	0.282467i	0.602434	+	0.798169i	$0.294198\pi$
$678$	−1.00991	−	0.719448i	−0.0387854	−	0.0276302i
$679$	0.393108	+	3.74017i	0.0150861	+	0.143535i
$680$	−0.433345	+	10.9553i	−0.0166180	+	0.420115i
$681$	−12.5346	+	2.78675i	−0.480326	+	0.106788i
$682$	−1.98120	−	3.43153i	−0.0758639	−	0.131400i
$683$	22.0510	+	16.0210i	0.843757	+	0.613026i	0.923418	−	0.383796i	$-0.125384\pi$
$683$	22.0510	+	16.0210i	0.843757	+	0.613026i	−0.0796603	+	0.996822i	$0.525384\pi$
$684$	28.5858	+	5.52088i	1.09300	+	0.211096i
$685$	−10.2068	−	1.48268i	−0.389981	−	0.0566502i
$686$	4.32657	−	4.80515i	0.165189	−	0.183461i
$687$	17.3759	−	30.7549i	0.662931	−	1.17337i
$688$	14.7966	+	16.4333i	0.564117	+	0.626515i
$689$	5.35747	+	1.13876i	0.204103	+	0.0433835i
$690$	−10.4765	−	3.75748i	−0.398834	−	0.143045i
$691$	0.729910	−	0.155147i	0.0277671	−	0.00590208i	−0.194007	−	0.981000i	$-0.562149\pi$
$691$	0.729910	−	0.155147i	0.0277671	−	0.00590208i	0.221774	+	0.975098i	$0.428815\pi$
$692$	−29.8701	−	21.7019i	−1.13549	−	0.824982i
$693$	−1.52394	−	12.2894i	−0.0578897	−	0.466836i
$694$	−6.87115	−	4.99218i	−0.260825	−	0.189501i
$695$	7.56808	+	4.77791i	0.287074	+	0.181237i
$696$	1.22665	−	12.8199i	0.0464959	−	0.485938i
$697$	−1.73265	−	16.4851i	−0.0656288	−	0.624417i
$698$	−10.1067	−	2.14824i	−0.382543	−	0.0813120i
$699$	4.18109	+	12.4711i	0.158143	+	0.471699i
$700$	23.0087	+	1.82311i	0.869646	+	0.0689071i
$701$	−14.0062			−0.529006			−0.264503	−	0.964385i	$-0.585208\pi$
$701$	−14.0062			−0.529006			−0.264503	+	0.964385i	$0.585208\pi$
$702$	−1.04630	+	3.55575i	−0.0394899	+	0.134203i
$703$	−34.3916	+	24.9870i	−1.29711	+	0.942402i
$704$	−8.51839	−	3.79263i	−0.321049	−	0.142940i
$705$	−5.50026	−	30.3587i	−0.207152	−	1.14337i
$706$	0.0301455	−	0.0134217i	0.00113454	−	0.000505131i
$707$	10.8534	−	18.7987i	0.408186	−	0.706999i
$708$	3.08285	−	0.685395i	0.115861	−	0.0257587i
$709$	−24.2191	+	5.14793i	−0.909567	+	0.193334i	−0.638856	−	0.769326i	$-0.720592\pi$
$709$	−24.2191	+	5.14793i	−0.909567	+	0.193334i	−0.270711	+	0.962661i	$0.587259\pi$
$710$	0.213232	−	0.432103i	0.00800247	−	0.0162165i
$711$	−1.62391	+	18.8218i	−0.0609013	+	0.705872i
$712$	−3.79708	+	11.6862i	−0.142302	+	0.437960i
$713$	−60.7010	+	12.9024i	−2.27327	+	0.483199i
$714$	−0.606082	−	5.29125i	−0.0226821	−	0.198020i
$715$	−7.68403	−	2.83710i	−0.287366	−	0.106102i
$716$	−6.08383	−	6.75678i	−0.227363	−	0.252513i
$717$	−18.9904	−	20.6994i	−0.709210	−	0.773034i
$718$	2.55455	+	4.42461i	0.0953349	+	0.165125i
$719$	7.88850	+	5.73133i	0.294192	+	0.213743i	0.725084	−	0.688661i	$-0.241801\pi$
$719$	7.88850	+	5.73133i	0.294192	+	0.213743i	−0.430892	+	0.902403i	$0.641801\pi$
$720$	−4.22600	−	22.1458i	−0.157494	−	0.825326i
$721$	19.5667	−	14.2161i	0.728703	−	0.529434i
$722$	−2.20355	−	0.981083i	−0.0820076	−	0.0365121i
$723$	23.3241	+	10.1249i	0.867431	+	0.376550i
$724$	−5.26399	+	9.11749i	−0.195634	+	0.338849i
$725$	12.4731	+	26.1862i	0.463241	+	0.972533i
$726$	−1.47595	−	4.40235i	−0.0547776	−	0.163387i
$727$	−1.50130	+	1.66737i	−0.0556802	+	0.0618392i	−0.770341	−	0.637632i	$-0.779914\pi$
$727$	−1.50130	+	1.66737i	−0.0556802	+	0.0618392i	0.714661	+	0.699471i	$0.246581\pi$
$728$	5.48061	−	3.98189i	0.203125	−	0.147579i
$729$	−22.6970	−	14.6235i	−0.840628	−	0.541612i
$730$	−5.75178	−	5.60611i	−0.212883	−	0.207491i
$731$	−2.63095	+	25.0318i	−0.0973093	+	0.925836i
$732$	−9.08036	−	27.0843i	−0.335620	−	1.00106i
$733$	6.55459	−	2.91829i	0.242099	−	0.107790i	−0.282100	−	0.959385i	$-0.591031\pi$
$733$	6.55459	−	2.91829i	0.242099	−	0.107790i	0.524200	+	0.851595i	$0.324364\pi$
$734$	2.84533	+	3.16006i	0.105023	+	0.116640i
$735$	4.03295	−	0.301060i	0.148758	−	0.0111048i
$736$	21.4287	−	23.7990i	0.789873	−	0.877243i
$737$	1.76716	−	5.43875i	0.0650941	−	0.200339i
$738$	−1.39880	−	4.04660i	−0.0514904	−	0.148957i
$739$	3.95764	+	12.1804i	0.145584	+	0.448062i	0.997086	−	0.0762903i	$-0.0243076\pi$
$739$	3.95764	+	12.1804i	0.145584	+	0.448062i	−0.851502	+	0.524352i	$0.824308\pi$
$740$	29.6331	+	18.7081i	1.08934	+	0.687724i
$741$	−9.46696	+	16.7563i	−0.347777	+	0.615557i
$742$	−1.85709	+	0.826832i	−0.0681761	+	0.0303539i
$743$	−1.45630	+	2.52238i	−0.0534264	+	0.0925372i	−0.891502	−	0.453017i	$-0.850348\pi$
$743$	−1.45630	+	2.52238i	−0.0534264	+	0.0925372i	0.838075	+	0.545554i	$0.183681\pi$
$744$	10.6746	+	11.6352i	0.391350	+	0.426569i
$745$	−23.6737	+	19.6786i	−0.867337	+	0.720967i
$746$	−0.0617081	+	0.0448336i	−0.00225929	+	0.00164147i
$747$	41.8089	−	9.70528i	1.52971	−	0.355098i
$748$	−3.78202	−	11.6399i	−0.138284	−	0.425596i
$749$	−0.963780	−	1.66932i	−0.0352158	−	0.0609955i
$750$	−4.24617	−	4.75931i	−0.155048	−	0.173785i
$751$	−17.2581	+	29.8919i	−0.629757	+	1.09077i	0.357843	+	0.933782i	$0.383512\pi$
$751$	−17.2581	+	29.8919i	−0.629757	+	1.09077i	−0.987600	+	0.156989i	$0.949821\pi$
$752$	26.1883	+	5.56649i	0.954989	+	0.202989i
$753$	25.0188	+	17.8231i	0.911737	+	0.649509i
$754$	3.78022	+	1.68306i	0.137668	+	0.0612935i
$755$	−7.67467	−	44.7351i	−0.279310	−	1.62808i
$756$	8.04751	+	22.5960i	0.292685	+	0.821807i
$757$	4.55628			0.165601			0.0828005	−	0.996566i	$-0.473614\pi$
$757$	4.55628			0.165601			0.0828005	+	0.996566i	$0.473614\pi$
$758$	−0.192086	+	1.82758i	−0.00697687	+	0.0663805i
$759$	25.5601	−	0.238417i	0.927773	−	0.00865399i
$760$	−0.581202	+	14.6932i	−0.0210824	+	0.532977i
$761$	−25.2562	−	5.36838i	−0.915538	−	0.194604i	−0.274031	−	0.961721i	$-0.588357\pi$
$761$	−25.2562	−	5.36838i	−0.915538	−	0.194604i	−0.641507	+	0.767117i	$0.721690\pi$
$762$	4.27486	+	7.24731i	0.154862	+	0.262542i
$763$	41.4828	−	8.81743i	1.50178	−	0.319212i
$764$	13.8417	+	42.6004i	0.500775	+	1.54123i
$765$	15.5137	−	20.4412i	0.560899	−	0.739055i
$766$	1.36586	−	4.20369i	0.0493505	−	0.151885i
$767$	−0.218220	+	2.07622i	−0.00787946	+	0.0749680i
$768$	13.5965	+	2.75773i	0.490620	+	0.0995108i
$769$	30.0274	−	13.3690i	1.08281	−	0.482100i	0.213795	−	0.976879i	$-0.431418\pi$
$769$	30.0274	−	13.3690i	1.08281	−	0.482100i	0.869019	+	0.494779i	$0.164751\pi$
$770$	2.92618	−	0.824431i	0.105452	−	0.0297104i
$771$	−9.51811	+	4.34456i	−0.342786	+	0.156465i
$772$	−2.20182	−	0.980316i	−0.0792454	−	0.0352823i
$773$	−11.0693	−	34.0677i	−0.398134	−	1.22533i	−0.926494	−	0.376310i	$-0.877193\pi$
$773$	−11.0693	−	34.0677i	−0.398134	−	1.22533i	0.528360	−	0.849020i	$-0.322807\pi$
$774$	0.800065	+	6.45191i	0.0287578	+	0.231909i
$775$	−34.0928	−	10.1184i	−1.22465	−	0.363465i
$776$	0.987590	+	1.71056i	0.0354524	+	0.0614054i
$777$	−32.1267	−	13.9461i	−1.15254	−	0.500315i
$778$	1.17156	+	11.1466i	0.0420024	+	0.399626i
$779$	−2.32383	−	22.1097i	−0.0832598	−	0.792164i
$780$	15.7214	+	2.13422i	0.562918	+	0.0764175i
$781$	−0.115674	+	1.10057i	−0.00413915	+	0.0393814i
$782$	10.9932			0.393117
$783$	−19.5350	+	22.9562i	−0.698124	+	0.820387i
$784$	−1.08447	+	3.33766i	−0.0387311	+	0.119202i
$785$	−14.5338	+	12.0811i	−0.518732	+	0.431192i
$786$	0.966702	−	0.716221i	0.0344811	−	0.0255468i
$787$	−1.79034	−	1.98837i	−0.0638187	−	0.0708778i	0.710390	−	0.703808i	$-0.248519\pi$
$787$	−1.79034	−	1.98837i	−0.0638187	−	0.0708778i	−0.774209	+	0.632930i	$0.781852\pi$
$788$	−12.4568	−	13.8346i	−0.443754	−	0.492839i
$789$	16.0873	+	6.98349i	0.572725	+	0.248619i
$790$	−4.62799	+	0.302101i	−0.164656	+	0.0107483i
$791$	1.63917	−	5.04484i	0.0582820	−	0.179374i
$792$	−3.35645	−	5.57090i	−0.119266	−	0.197953i
$793$	18.8833			0.670567
$794$	−0.969486	+	9.22404i	−0.0344058	+	0.327349i
$795$	−9.21982	−	3.30676i	−0.326993	−	0.117279i
$796$	−3.67463	−	34.9618i	−0.130244	−	1.23919i
$797$	3.84156	+	36.5500i	0.136075	+	1.29467i	0.823043	+	0.567979i	$0.192274\pi$
$797$	3.84156	+	36.5500i	0.136075	+	1.29467i	−0.686968	+	0.726687i	$0.741059\pi$
$798$	−0.812876	−	7.09662i	−0.0287755	−	0.251217i
$799$	15.2370	+	26.3912i	0.539045	+	0.933654i
$800$	17.3028	−	6.11690i	0.611746	−	0.216265i
$801$	22.9480	−	17.3358i	0.810828	−	0.612532i
$802$	−1.32495	−	4.07776i	−0.0467854	−	0.143991i
$803$	16.8514	+	7.50274i	0.594674	+	0.264766i
$804$	−1.05503	+	11.0263i	−0.0372080	+	0.388869i
$805$	1.88189	−	47.5755i	0.0663279	−	1.67682i
$806$	−4.63485	+	2.06357i	−0.163256	+	0.0726861i
$807$	14.9201	+	44.5026i	0.525213	+	1.56657i
$808$	1.19169	−	11.3381i	0.0419233	−	0.398874i
$809$	15.1395	−	46.5946i	0.532276	−	1.63818i	−0.217186	−	0.976130i	$-0.569688\pi$
$809$	15.1395	−	46.5946i	0.532276	−	1.63818i	0.749462	−	0.662048i	$-0.230312\pi$
$810$	2.70948	−	6.04932i	0.0952013	−	0.212551i
$811$	8.75261	+	26.9378i	0.307346	+	0.945913i	0.978791	+	0.204859i	$0.0656736\pi$
$811$	8.75261	+	26.9378i	0.307346	+	0.945913i	−0.671446	+	0.741054i	$0.734326\pi$
$812$	26.1933	−	5.56755i	0.919204	−	0.195383i
$813$	−18.2144	+	0.169898i	−0.638806	+	0.00595859i
$814$	4.51505	+	0.959703i	0.158252	+	0.0336376i
$815$	9.93780	−	12.5992i	0.348106	−	0.441329i
$816$	11.3136	+	19.1804i	0.396056	+	0.671448i
$817$	−3.52863	+	33.5727i	−0.123451	+	1.17456i
$818$	−11.0057			−0.384806
$819$	−15.8532	+	0.295774i	−0.553956	+	0.0103352i
$820$	−16.2215	+	8.52906i	−0.566480	+	0.297848i
$821$	9.47344	+	4.21785i	0.330625	+	0.147204i	0.565335	−	0.824862i	$-0.308747\pi$
$821$	9.47344	+	4.21785i	0.330625	+	0.147204i	−0.234709	+	0.972066i	$0.575414\pi$
$822$	2.39377	−	1.09264i	0.0834924	−	0.0381103i
$823$	−22.4338	−	4.76845i	−0.781992	−	0.166218i	−0.200418	−	0.979711i	$-0.564230\pi$
$823$	−22.4338	−	4.76845i	−0.781992	−	0.166218i	−0.581575	+	0.813493i	$0.697563\pi$
$824$	6.35126	−	11.0007i	0.221257	−	0.383228i
$825$	12.9341	+	6.87600i	0.450306	+	0.239392i
$826$	−0.387416	−	0.671025i	−0.0134799	−	0.0233479i
$827$	3.87041	+	11.9119i	0.134587	+	0.414218i	0.995526	−	0.0944920i	$-0.0301227\pi$
$827$	3.87041	+	11.9119i	0.134587	+	0.414218i	−0.860938	+	0.508710i	$0.830123\pi$
$828$	−48.2283	+	11.1954i	−1.67605	+	0.389069i
$829$	8.58869	−	6.24005i	0.298297	−	0.216726i	−0.428561	−	0.903513i	$-0.640979\pi$
$829$	8.58869	−	6.24005i	0.298297	−	0.216726i	0.726859	+	0.686787i	$0.240979\pi$
$830$	3.90190	+	9.78774i	0.135437	+	0.339737i
$831$	27.4933	−	6.11245i	0.953731	−	0.212038i
$832$	−5.96961	+	10.3397i	−0.206959	+	0.358463i
$833$	−3.64915	+	1.62471i	−0.126436	+	0.0562928i
$834$	−2.28331	+	0.0212980i	−0.0790646	+	0.000737491i
$835$	−13.5174	+	0.882376i	−0.467790	+	0.0305359i
$836$	−5.07244	−	15.6114i	−0.175434	−	0.539930i
$837$	−4.88999	−	36.6328i	−0.169023	−	1.26622i
$838$	−4.01837	+	12.3673i	−0.138812	+	0.427220i
$839$	−4.12762	+	4.58418i	−0.142501	+	0.158264i	−0.810170	−	0.586195i	$-0.800625\pi$
$839$	−4.12762	+	4.58418i	−0.142501	+	0.158264i	0.667669	+	0.744458i	$0.267292\pi$
$840$	−10.6699	+	5.73773i	−0.368145	+	0.197971i
$841$	3.11276	+	3.45707i	0.107337	+	0.119209i
$842$	−0.792708	+	0.352936i	−0.0273185	+	0.0121630i
$843$	17.4137	−	19.7065i	0.599760	−	0.678727i
$844$	0.436558	−	4.15357i	0.0150269	−	0.142972i
$845$	8.22258	−	16.6626i	0.282865	−	0.573211i
$846$	5.37520	+	5.75033i	0.184803	+	0.197700i
$847$	16.0695	−	11.6752i	0.552155	−	0.401164i
$848$	5.68743	−	6.31654i	0.195307	−	0.216911i
$849$	−3.21183	−	0.651445i	−0.110230	−	0.0223575i
$850$	5.53479	+	3.00895i	0.189842	+	0.103206i
$851$	36.1461	−	62.6070i	1.23907	−	2.14614i
$852$	−0.243928	−	2.12955i	−0.00835684	−	0.0729573i
$853$	−25.0320	−	11.1450i	−0.857079	−	0.381596i	−0.0693309	−	0.997594i	$-0.522086\pi$
$853$	−25.0320	−	11.1450i	−0.857079	−	0.381596i	−0.787748	+	0.615998i	$0.788753\pi$
$854$	−5.67002	+	4.11951i	−0.194024	+	0.140967i
$855$	20.8069	−	27.4158i	0.711583	−	0.937599i
$856$	−0.819021	−	0.595053i	−0.0279935	−	0.0203385i
$857$	−16.4638	−	28.5161i	−0.562392	−	0.974092i	−0.997287	−	0.0736109i	$-0.976548\pi$
$857$	−16.4638	−	28.5161i	−0.562392	−	0.974092i	0.434895	−	0.900481i	$-0.356786\pi$
$858$	2.03995	−	0.453532i	0.0696427	−	0.0154833i
$859$	−30.8351	−	34.2459i	−1.05208	−	1.16845i	−0.985326	−	0.170684i	$-0.945402\pi$
$859$	−30.8351	−	34.2459i	−1.05208	−	1.16845i	−0.0667547	−	0.997769i	$-0.521264\pi$
$860$	26.7861	−	7.54678i	0.913397	−	0.257343i
$861$	14.7168	−	10.9036i	0.501549	−	0.371593i
$862$	−11.0677	+	2.35252i	−0.376968	+	0.0801271i
$863$	1.06714	−	3.28433i	0.0363260	−	0.111800i	−0.931249	−	0.364383i	$-0.881280\pi$
$863$	1.06714	−	3.28433i	0.0363260	−	0.111800i	0.967575	+	0.252583i	$0.0812800\pi$
$864$	13.1533	+	13.8108i	0.447485	+	0.469852i
$865$	−38.6324	+	20.3124i	−1.31354	+	0.690642i
$866$	8.76181	−	1.86238i	0.297738	−	0.0632863i
$867$	1.23008	−	3.90950i	0.0417757	−	0.132774i
$868$	−16.4163	+	28.4338i	−0.557204	+	0.965106i
$869$	9.73047	−	4.33228i	0.330083	−	0.146963i
$870$	−6.29390	−	3.89187i	−0.213383	−	0.131947i
$871$	−6.68915	−	2.97820i	−0.226653	−	0.100913i
$872$	18.0198	−	13.0922i	0.610227	−	0.443356i
$873$	0.397391	−	4.60594i	0.0134497	−	0.155887i
$874$	14.7441			0.498727
$875$	13.9693	−	23.4378i	0.472250	−	0.792344i
$876$	−35.0163	−	7.10223i	−1.18309	−	0.239962i
$877$	−55.9211	−	11.8864i	−1.88832	−	0.401375i	−0.889831	−	0.456290i	$-0.849178\pi$
$877$	−55.9211	−	11.8864i	−1.88832	−	0.401375i	−0.998491	+	0.0549146i	$0.982511\pi$
$878$	−0.516938	−	4.91834i	−0.0174458	−	0.165986i
$879$	−11.5685	+	5.28047i	−0.390196	+	0.178106i
$880$	−9.77515	+	8.12552i	−0.329520	+	0.273911i
$881$	−25.5288	−	18.5478i	−0.860089	−	0.624891i	0.0678204	−	0.997698i	$-0.478396\pi$
$881$	−25.5288	−	18.5478i	−0.860089	−	0.624891i	−0.927909	+	0.372807i	$0.878396\pi$
$882$	−0.823266	+	0.621928i	−0.0277208	+	0.0209414i
$883$	−32.6810	−	23.7441i	−1.09980	−	0.799053i	−0.118775	−	0.992921i	$-0.537897\pi$
$883$	−32.6810	−	23.7441i	−1.09980	−	0.799053i	−0.981028	+	0.193868i	$0.937897\pi$
$884$	−15.3283	+	3.25813i	−0.515547	+	0.109583i
$885$	0.886158	−	3.62670i	0.0297879	−	0.121910i
$886$	−3.38097	−	0.718647i	−0.113586	−	0.0241434i
$887$	−7.80917	−	8.67297i	−0.262206	−	0.291210i	0.597638	−	0.801766i	$-0.296106\pi$
$887$	−7.80917	−	8.67297i	−0.262206	−	0.291210i	−0.859844	+	0.510556i	$0.829439\pi$
$888$	−18.3935	+	0.171569i	−0.617247	+	0.00575749i
$889$	−24.0852	+	26.7493i	−0.807792	+	0.897144i
$890$	5.05612	+	4.92807i	0.169482	+	0.165189i
$891$	−1.02540	+	15.1883i	−0.0343520	+	0.508826i
$892$	−40.1233	−	29.1513i	−1.34343	−	0.976058i
$893$	20.4358	+	35.3959i	0.683858	+	1.18448i
$894$	2.35723	−	7.49187i	0.0788376	−	0.250566i
$895$	−10.3456	+	2.91478i	−0.345814	+	0.0974305i
$896$	−2.33582	−	22.2239i	−0.0780343	−	0.742447i
$897$	3.11734	−	32.5800i	0.104085	−	1.08781i
$898$	−4.29845	+	4.77391i	−0.143441	+	0.159307i
$899$	−41.2600			−1.37610
$900$	−27.3459	−	7.56395i	−0.911531	−	0.252132i
$901$	9.67456			0.322306
$902$	−1.61526	+	1.79393i	−0.0537823	+	0.0597313i
$903$	−25.3008	+	11.5486i	−0.841959	+	0.384314i
$904$	−0.291209	−	2.77067i	−0.00968546	−	0.0921510i
$905$	6.91171	+	10.3501i	0.229753	+	0.344048i
$906$	7.82836	+	8.53286i	0.260080	+	0.283485i
$907$	−15.1100	−	26.1713i	−0.501720	−	0.869005i	−0.999998	−	0.00198753i	$-0.999367\pi$
$907$	−15.1100	−	26.1713i	−0.501720	−	0.869005i	0.498278	−	0.867017i	$-0.333966\pi$
$908$	−11.3447	−	8.24241i	−0.376487	−	0.273534i
$909$	−17.4820	+	20.1596i	−0.579841	+	0.668652i
$910$	−0.658187	−	3.83652i	−0.0218187	−	0.127180i
$911$	−37.2219	+	41.3391i	−1.23322	+	1.36963i	−0.328000	+	0.944678i	$0.606375\pi$
$911$	−37.2219	+	41.3391i	−1.23322	+	1.36963i	−0.905217	+	0.424949i	$0.860292\pi$
$912$	15.1738	+	25.7247i	0.502456	+	0.851830i
$913$	−16.1923	−	17.9834i	−0.535887	−	0.595163i
$914$	4.11096	+	0.873811i	0.135978	+	0.0289031i
$915$	−33.4624	−	4.54260i	−1.10623	−	0.150174i
$916$	37.7332	−	8.02044i	1.24674	−	0.265003i
$917$	4.16384	+	3.02521i	0.137502	+	0.0999011i
$918$	−0.501905	+	6.52770i	−0.0165653	+	0.215446i
$919$	−45.6386	−	33.1584i	−1.50548	−	1.09379i	−0.968134	−	0.250432i	$-0.919427\pi$
$919$	−45.6386	−	33.1584i	−1.50548	−	1.09379i	−0.537345	−	0.843363i	$-0.680573\pi$
$920$	−9.26016	−	23.2287i	−0.305298	−	0.765827i
$921$	6.18188	+	4.40389i	0.203700	+	0.145113i
$922$	−0.485095	−	4.61537i	−0.0159758	−	0.151999i
$923$	1.38597	+	0.294597i	0.0456198	+	0.00969679i
$924$	8.95496	−	10.1340i	0.294597	−	0.333384i
$925$	35.3347	−	21.6273i	1.16180	−	0.711102i
$926$	−9.97042			−0.327648
$927$	−26.9305	+	12.5973i	−0.884512	+	0.413750i
$928$	17.2258	−	12.5153i	0.565466	−	0.410835i
$929$	−12.4179	−	5.52882i	−0.407419	−	0.181395i	0.192786	−	0.981241i	$-0.438248\pi$
$929$	−12.4179	−	5.52882i	−0.407419	−	0.181395i	−0.600205	+	0.799846i	$0.704914\pi$
$930$	8.70966	−	2.54180i	0.285601	−	0.0833490i
$931$	−4.89424	+	2.17905i	−0.160402	+	0.0714156i
$932$	−7.18214	+	12.4398i	−0.235259	+	0.407480i
$933$	20.8864	+	22.7661i	0.683792	+	0.745328i
$934$	0.182860	−	0.0388682i	0.00598338	−	0.00127181i
$935$	−14.3180	−	2.07989i	−0.468248	−	0.0680196i
$936$	−7.54317	+	3.52848i	−0.246556	+	0.115332i
$937$	−5.39097	+	16.5917i	−0.176115	+	0.542027i	−0.999683	−	0.0251916i	$-0.991980\pi$
$937$	−5.39097	+	16.5917i	−0.176115	+	0.542027i	0.823567	+	0.567218i	$0.191980\pi$
$938$	2.65824	−	0.565026i	0.0867946	−	0.0184488i
$939$	−25.9002	−	11.2433i	−0.845223	−	0.366910i
$940$	20.8665	−	26.4545i	0.680589	−	0.862852i
$941$	32.8128	+	36.4424i	1.06967	+	1.18799i	0.981417	+	0.191888i	$0.0614612\pi$
$941$	32.8128	+	36.4424i	1.06967	+	1.18799i	0.0882513	+	0.996098i	$0.471872\pi$
$942$	1.44715	−	4.59941i	0.0471508	−	0.149857i
$943$	18.9032	+	32.7414i	0.615574	+	1.06621i
$944$	2.62100	+	1.90427i	0.0853063	+	0.0619787i
$945$	28.1640	+	3.28955i	0.916176	+	0.107009i
$946$	2.96546	−	2.15453i	0.0964153	−	0.0700498i
$947$	34.3978	+	15.3149i	1.11778	+	0.497667i	0.880629	−	0.473806i	$-0.157120\pi$
$947$	34.3978	+	15.3149i	1.11778	+	0.497667i	0.237150	+	0.971473i	$0.423787\pi$
$948$	−16.5770	+	12.2818i	−0.538397	+	0.398893i
$949$	11.8093	−	20.4543i	0.383347	−	0.663976i
$950$	7.42326	+	4.03560i	0.240842	+	0.130932i
$951$	24.1700	−	27.3523i	0.783766	−	0.886959i
$952$	8.00678	−	8.89243i	0.259501	−	0.288205i
$953$	−24.9618	+	18.1358i	−0.808594	+	0.587478i	−0.913423	−	0.407013i	$-0.866570\pi$
$953$	−24.9618	+	18.1358i	−0.808594	+	0.587478i	0.104829	+	0.994490i	$0.466570\pi$
$954$	2.43421	−	0.565063i	0.0788105	−	0.0182946i
$955$	52.4020	+	7.61212i	1.69569	+	0.246322i
$956$	3.20664	−	30.5092i	0.103710	−	0.986737i
$957$	16.6558	+	3.37824i	0.538405	+	0.109203i
$958$	−2.73505	+	1.21772i	−0.0883654	+	0.0393428i
$959$	7.53215	+	8.36530i	0.243226	+	0.270130i
$960$	13.0658	−	16.8865i	0.421698	−	0.545008i
$961$	13.1070	−	14.5567i	0.422805	−	0.469573i
$962$	1.82637	−	5.62099i	0.0588845	−	0.181228i
$963$	0.774130	+	2.23949i	0.0249460	+	0.0721666i
$964$	8.58075	+	26.4088i	0.276367	+	0.850571i
$965$	−2.19109	+	1.82133i	−0.0705337	+	0.0586306i
$966$	6.17149	+	10.4627i	0.198564	+	0.336633i
$967$	26.3223	−	11.7195i	0.846469	−	0.376872i	0.0627812	−	0.998027i	$-0.480003\pi$
$967$	26.3223	−	11.7195i	0.846469	−	0.376872i	0.783688	+	0.621155i	$0.213336\pi$
$968$	5.21608	−	9.03451i	0.167651	−	0.290380i
$969$	−10.2029	+	32.4273i	−0.327764	+	1.04172i
$970$	1.13253	−	0.0739280i	0.0363633	−	0.00237369i
$971$	0.696107	−	0.505751i	0.0223391	−	0.0162303i	−0.576560	−	0.817055i	$-0.695605\pi$
$971$	0.696107	−	0.505751i	0.0223391	−	0.0162303i	0.598899	+	0.800825i	$0.295605\pi$
$972$	−4.44586	−	29.1487i	−0.142601	−	0.934946i
$973$	−3.01853	−	9.29008i	−0.0967696	−	0.297826i
$974$	−5.24732	−	9.08862i	−0.168135	−	0.291218i
$975$	10.4869	−	15.5499i	0.335851	−	0.497995i
$976$	14.6521	−	25.3781i	0.469001	−	0.812334i
$977$	48.2956	+	10.2656i	1.54511	+	0.328424i	0.900078	−	0.435728i	$-0.143509\pi$
$977$	48.2956	+	10.2656i	1.54511	+	0.328424i	0.645036	+	0.764152i	$0.276842\pi$
$978$	−0.389940	+	4.07534i	−0.0124689	+	0.130315i
$979$	−14.8133	−	6.59531i	−0.473436	−	0.210787i
$980$	3.16274	+	3.08264i	0.101030	+	0.0984712i
$981$	−52.1241	+	0.972482i	−1.66420	+	0.0310489i
$982$	13.9001			0.443570
$983$	−5.03462	+	47.9012i	−0.160579	+	1.52781i	0.556517	+	0.830836i	$0.312137\pi$
$983$	−5.03462	+	47.9012i	−0.160579	+	1.52781i	−0.717097	+	0.696974i	$0.754529\pi$
$984$	4.73190	−	8.37534i	0.150847	−	0.266996i
$985$	−21.1827	+	5.96808i	−0.674938	+	0.190159i
$986$	7.14937	+	1.51965i	0.227682	+	0.0483954i
$987$	−16.5638	+	29.3174i	−0.527230	+	0.933184i
$988$	−20.5583	+	4.36980i	−0.654047	+	0.139022i
$989$	−17.7399	−	54.5977i	−0.564095	−	1.73611i
$990$	−3.72402	+	0.312953i	−0.118357	+	0.00994629i
$991$	6.36275	−	19.5825i	0.202120	−	0.622060i	−0.797700	−	0.603055i	$-0.793950\pi$
$991$	6.36275	−	19.5825i	0.202120	−	0.622060i	0.999819	−	0.0190053i	$-0.00604994\pi$
$992$	−2.72883	+	25.9631i	−0.0866404	+	0.824328i
$993$	20.7757	−	23.5110i	0.659295	−	0.746101i
$994$	−0.480429	+	0.213901i	−0.0152383	+	0.00678451i
$995$	−38.9855	−	14.3943i	−1.23592	−	0.456329i
$996$	38.1757	+	27.1959i	1.20964	+	0.861735i
$997$	52.1722	+	23.2285i	1.65231	+	0.735655i	0.999756	−	0.0220883i	$-0.00703148\pi$
$997$	52.1722	+	23.2285i	1.65231	+	0.735655i	0.652553	+	0.757743i	$0.273698\pi$
$998$	1.93571	+	5.95750i	0.0612738	+	0.188581i
$999$	35.5252	+	24.3217i	1.12397	+	0.769503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.31.13	✓	224
3.2	odd	2		675.2.r.a.631.16		224
9.2	odd	6		675.2.r.a.181.13		224
9.7	even	3	inner	225.2.q.a.106.16	yes	224
25.21	even	5	inner	225.2.q.a.121.16	yes	224
75.71	odd	10		675.2.r.a.496.13		224
225.146	odd	30		675.2.r.a.46.16		224
225.196	even	15	inner	225.2.q.a.196.13	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.13	✓	224	1.1	even	1	trivial
225.2.q.a.106.16	yes	224	9.7	even	3	inner
225.2.q.a.121.16	yes	224	25.21	even	5	inner
225.2.q.a.196.13	yes	224	225.196	even	15	inner
675.2.r.a.46.16		224	225.146	odd	30
675.2.r.a.181.13		224	9.2	odd	6
675.2.r.a.496.13		224	75.71	odd	10
675.2.r.a.631.16		224	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.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.220390 + 0.244767i) q^{2} +(1.41069 + 1.00496i) q^{3} +(0.197717 + 1.88116i) q^{4} +(2.09765 + 0.774498i) q^{5} +(-0.556884 + 0.123809i) q^{6} +(-1.22023 - 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(0.980112 + 2.83538i) q^{9} +O(q^{10})\)	\(q+(-0.220390 + 0.244767i) q^{2} +(1.41069 + 1.00496i) q^{3} +(0.197717 + 1.88116i) q^{4} +(2.09765 + 0.774498i) q^{5} +(-0.556884 + 0.123809i) q^{6} +(-1.22023 - 2.11349i) q^{7} +(-1.03695 - 0.753387i) q^{8} +(0.980112 + 2.83538i) q^{9} +(-0.651873 + 0.342746i) q^{10} +(1.13179 - 1.25698i) q^{11} +(-1.61157 + 2.85243i) q^{12} +(-1.44915 - 1.60944i) q^{13} +(0.786239 + 0.167120i) q^{14} +(2.18081 + 3.20064i) q^{15} +(-3.28743 + 0.698765i) q^{16} +(-3.09482 - 2.24852i) q^{17} +(-0.910015 - 0.384989i) q^{18} +(-4.15077 - 3.01571i) q^{19} +(-1.04221 + 4.09915i) q^{20} +(0.402611 - 4.20777i) q^{21} +(0.0582329 + 0.554049i) q^{22} +(8.53438 + 1.81404i) q^{23} +(-0.705692 - 2.10489i) q^{24} +(3.80031 + 3.24926i) q^{25} +0.713316 q^{26} +(-1.46680 + 4.98483i) q^{27} +(3.73455 - 2.71331i) q^{28} +(5.29950 + 2.35949i) q^{29} +(-1.26404 - 0.171596i) q^{30} +(-6.49762 + 2.89293i) q^{31} +(1.83522 - 3.17869i) q^{32} +(2.85981 - 0.635808i) q^{33} +(1.23243 - 0.261961i) q^{34} +(-0.922715 - 5.37844i) q^{35} +(-5.14001 + 2.40435i) q^{36} +(2.56039 - 7.88008i) q^{37} +(1.65293 - 0.351342i) q^{38} +(-0.426879 - 3.72676i) q^{39} +(-1.59166 - 2.38346i) q^{40} +(2.89941 + 3.22012i) q^{41} +(0.941193 + 1.02589i) q^{42} +(-3.28981 - 5.69811i) q^{43} +(2.58834 + 1.88054i) q^{44} +(-0.140060 + 6.70674i) q^{45} +(-2.32491 + 1.68914i) q^{46} +(-7.27748 - 3.24014i) q^{47} +(-5.33979 - 2.31799i) q^{48} +(0.522100 - 0.904304i) q^{49} +(-1.63286 + 0.214089i) q^{50} +(-2.10617 - 6.28214i) q^{51} +(2.74109 - 3.04429i) q^{52} +(-2.04603 + 1.48652i) q^{53} +(-0.896854 - 1.45763i) q^{54} +(3.34762 - 1.76013i) q^{55} +(-0.326967 + 3.11088i) q^{56} +(-2.82480 - 8.42560i) q^{57} +(-1.74548 + 0.777139i) q^{58} +(-0.645013 - 0.716360i) q^{59} +(-5.58971 + 4.73526i) q^{60} +(-5.83429 + 6.47963i) q^{61} +(0.723913 - 2.22798i) q^{62} +(4.79660 - 5.53126i) q^{63} +(-1.70356 - 5.24301i) q^{64} +(-1.79330 - 4.49841i) q^{65} +(-0.474648 + 0.840115i) q^{66} +(3.08866 - 1.37516i) q^{67} +(3.61791 - 6.26641i) q^{68} +(10.2164 + 11.1358i) q^{69} +(1.51982 + 0.959501i) q^{70} +(-0.529305 + 0.384563i) q^{71} +(1.11981 - 3.67854i) q^{72} +(3.37004 + 10.3719i) q^{73} +(1.36450 + 2.36339i) q^{74} +(2.09569 + 8.40286i) q^{75} +(4.85234 - 8.40450i) q^{76} +(-4.03764 - 0.858227i) q^{77} +(1.00627 + 0.716854i) q^{78} +(5.75281 + 2.56132i) q^{79} +(-7.43708 - 1.08034i) q^{80} +(-7.07876 + 5.55798i) q^{81} -1.42718 q^{82} +(1.49547 - 14.2285i) q^{83} +(7.99507 - 0.0745756i) q^{84} +(-4.75039 - 7.11355i) q^{85} +(2.11975 + 0.450567i) q^{86} +(5.10478 + 8.65431i) q^{87} +(-2.12059 + 0.450746i) q^{88} +(-2.96245 - 9.11749i) q^{89} +(-1.61072 - 1.51238i) q^{90} +(-1.63326 + 5.02664i) q^{91} +(-1.72509 + 16.4132i) q^{92} +(-12.0734 - 2.44881i) q^{93} +(2.39696 - 1.06720i) q^{94} +(-6.37122 - 9.54068i) q^{95} +(5.78339 - 2.63984i) q^{96} +(-1.40779 - 0.626788i) q^{97} +(0.106279 + 0.327092i) q^{98} +(4.67328 + 1.97707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

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