LMFDB - Embedded newform 576.2.bm.a.205.84

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(13,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 45, 16]))

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

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

chi := DirichletCharacter("576.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bm (of order $48$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$1504$
Relative dimension:	$94$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			205.84
Character	$\chi$	$=$	576.205
Dual form			576.2.bm.a.517.84

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31272 - 0.526080i) q^{2} +(-0.444563 - 1.67403i) q^{3} +(1.44648 - 1.38119i) q^{4} +(1.97729 + 2.25467i) q^{5} +(-1.46426 - 1.96366i) q^{6} +(2.41702 + 0.318207i) q^{7} +(1.17221 - 2.57409i) q^{8} +(-2.60473 + 1.48842i) q^{9} +O(q^{10})$	\(q+(1.31272 - 0.526080i) q^{2} +(-0.444563 - 1.67403i) q^{3} +(1.44648 - 1.38119i) q^{4} +(1.97729 + 2.25467i) q^{5} +(-1.46426 - 1.96366i) q^{6} +(2.41702 + 0.318207i) q^{7} +(1.17221 - 2.57409i) q^{8} +(-2.60473 + 1.48842i) q^{9} +(3.78177 + 1.91954i) q^{10} +(-1.72557 - 3.49911i) q^{11} +(-2.95521 - 1.80742i) q^{12} +(0.704925 + 2.07664i) q^{13} +(3.34028 - 0.853829i) q^{14} +(2.89534 - 4.31238i) q^{15} +(0.184609 - 3.99574i) q^{16} +(3.82425 + 3.82425i) q^{17} +(-2.63626 + 3.32418i) q^{18} +(-0.537285 + 2.70111i) q^{19} +(5.97424 + 0.530311i) q^{20} +(-0.541831 - 4.18762i) q^{21} +(-4.10601 - 3.68557i) q^{22} +(-0.895190 - 6.79964i) q^{23} +(-4.83021 - 0.817965i) q^{24} +(-0.521217 + 3.95904i) q^{25} +(2.01785 + 2.35521i) q^{26} +(3.64962 + 3.69869i) q^{27} +(3.93568 - 2.87810i) q^{28} +(-5.36918 + 0.351915i) q^{29} +(1.53213 - 7.18413i) q^{30} +(-7.30782 + 4.21917i) q^{31} +(-1.85974 - 5.34241i) q^{32} +(-5.09048 + 4.44423i) q^{33} +(7.03204 + 3.00832i) q^{34} +(4.06170 + 6.07877i) q^{35} +(-1.71189 + 5.75060i) q^{36} +(-1.95977 - 9.85245i) q^{37} +(0.715696 + 3.82847i) q^{38} +(3.16297 - 2.10326i) q^{39} +(8.12151 - 2.44678i) q^{40} +(0.331410 + 2.51731i) q^{41} +(-2.91430 - 5.21214i) q^{42} +(-9.01742 + 4.44690i) q^{43} +(-7.32896 - 2.67805i) q^{44} +(-8.50619 - 2.92976i) q^{45} +(-4.75229 - 8.45510i) q^{46} +(7.66285 - 2.05325i) q^{47} +(-6.77104 + 1.46732i) q^{48} +(-1.02074 - 0.273507i) q^{49} +(1.39856 + 5.47132i) q^{50} +(4.70177 - 8.10201i) q^{51} +(3.88790 + 2.03018i) q^{52} +(-0.653975 + 0.978744i) q^{53} +(6.73674 + 2.93536i) q^{54} +(4.47738 - 10.8093i) q^{55} +(3.65235 - 5.84862i) q^{56} +(4.76059 - 0.301385i) q^{57} +(-6.86311 + 3.28659i) q^{58} +(-3.24475 - 3.69993i) q^{59} +(-1.76817 - 10.2368i) q^{60} +(0.628588 + 9.59040i) q^{61} +(-7.37352 + 9.38310i) q^{62} +(-6.76931 + 2.76870i) q^{63} +(-5.25185 - 6.03473i) q^{64} +(-3.28829 + 5.69549i) q^{65} +(-4.34437 + 8.51203i) q^{66} +(12.6331 + 6.22993i) q^{67} +(10.8137 + 0.249671i) q^{68} +(-10.9848 + 4.52144i) q^{69} +(8.52981 + 5.84295i) q^{70} +(-0.603921 - 1.45800i) q^{71} +(0.778036 + 8.44954i) q^{72} +(-1.50613 + 3.63613i) q^{73} +(-7.75582 - 11.9025i) q^{74} +(6.85925 - 0.887509i) q^{75} +(2.95359 + 4.64920i) q^{76} +(-3.05730 - 9.00652i) q^{77} +(3.04562 - 4.42497i) q^{78} +(2.17386 + 8.11296i) q^{79} +(9.37408 - 7.48450i) q^{80} +(4.56922 - 7.75385i) q^{81} +(1.75935 + 3.13018i) q^{82} +(-2.50488 - 2.19672i) q^{83} +(-6.56766 - 5.30894i) q^{84} +(-1.06076 + 16.1841i) q^{85} +(-9.49795 + 10.5814i) q^{86} +(2.97605 + 8.83171i) q^{87} +(-11.0298 + 0.340082i) q^{88} +(-2.21853 + 0.918946i) q^{89} +(-12.7076 + 0.628976i) q^{90} +(1.04302 + 5.24360i) q^{91} +(-10.6865 - 8.59912i) q^{92} +(10.3118 + 10.3578i) q^{93} +(8.97901 - 6.72662i) q^{94} +(-7.15248 + 4.12949i) q^{95} +(-8.11657 + 5.48829i) q^{96} +(0.636059 + 0.367229i) q^{97} +(-1.48384 + 0.177953i) q^{98} +(9.70279 + 6.54586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	1.31272	−	0.526080i	0.928235	−	0.371995i
$2$	1.31272	−	0.526080i	0.928235	−	0.371995i
$3$	−0.444563	−	1.67403i	−0.256668	−	0.966500i
$3$	−0.444563	−	1.67403i	−0.256668	−	0.966500i
$4$	1.44648	−	1.38119i	0.723240	−	0.690597i
$5$	1.97729	+	2.25467i	0.884271	+	1.00832i	0.999887	+	0.0150239i	$0.00478242\pi$
$5$	1.97729	+	2.25467i	0.884271	+	1.00832i	−0.115616	+	0.993294i	$0.536884\pi$
$6$	−1.46426	−	1.96366i	−0.597781	−	0.801659i
$7$	2.41702	+	0.318207i	0.913548	+	0.120271i	0.572622	−	0.819819i	$-0.305926\pi$
$7$	2.41702	+	0.318207i	0.913548	+	0.120271i	0.340926	+	0.940090i	$0.389259\pi$
$8$	1.17221	−	2.57409i	0.414438	−	0.910077i
$9$	−2.60473	+	1.48842i	−0.868243	+	0.496140i
$10$	3.78177	+	1.91954i	1.19590	+	0.607012i
$11$	−1.72557	−	3.49911i	−0.520279	−	1.05502i	−0.985476	−	0.169815i	$-0.945683\pi$
$11$	−1.72557	−	3.49911i	−0.520279	−	1.05502i	0.465197	−	0.885207i	$-0.345984\pi$
$12$	−2.95521	−	1.80742i	−0.853094	−	0.521757i
$13$	0.704925	+	2.07664i	0.195511	+	0.575956i	0.999834	−	0.0182361i	$-0.00580504\pi$
$13$	0.704925	+	2.07664i	0.195511	+	0.575956i	−0.804323	+	0.594193i	$0.797472\pi$
$14$	3.34028	−	0.853829i	0.892728	−	0.228195i
$15$	2.89534	−	4.31238i	0.747574	−	1.11345i
$16$	0.184609	−	3.99574i	0.0461522	−	0.998934i
$17$	3.82425	+	3.82425i	0.927516	+	0.927516i	0.997545	−	0.0700287i	$-0.0223091\pi$
$17$	3.82425	+	3.82425i	0.927516	+	0.927516i	−0.0700287	+	0.997545i	$0.522309\pi$
$18$	−2.63626	+	3.32418i	−0.621372	+	0.783516i
$19$	−0.537285	+	2.70111i	−0.123262	+	0.619678i	0.868928	+	0.494939i	$0.164809\pi$
$19$	−0.537285	+	2.70111i	−0.123262	+	0.619678i	−0.992190	+	0.124739i	$0.960191\pi$
$20$	5.97424	+	0.530311i	1.33588	+	0.118581i
$21$	−0.541831	−	4.18762i	−0.118237	−	0.913814i
$22$	−4.10601	−	3.68557i	−0.875404	−	0.785767i
$23$	−0.895190	−	6.79964i	−0.186660	−	1.41782i	−0.786444	−	0.617662i	$-0.788080\pi$
$23$	−0.895190	−	6.79964i	−0.186660	−	1.41782i	0.599784	−	0.800162i	$-0.295253\pi$
$24$	−4.83021	−	0.817965i	−0.985963	−	0.166966i
$25$	−0.521217	+	3.95904i	−0.104243	+	0.791808i
$26$	2.01785	+	2.35521i	0.395733	+	0.461894i
$27$	3.64962	+	3.69869i	0.702369	+	0.711813i
$28$	3.93568	−	2.87810i	0.743773	−	0.543909i
$29$	−5.36918	+	0.351915i	−0.997032	+	0.0653489i	−0.555173	−	0.831735i	$-0.687348\pi$
$29$	−5.36918	+	0.351915i	−0.997032	+	0.0653489i	−0.441860	+	0.897084i	$0.645681\pi$
$30$	1.53213	−	7.18413i	0.279727	−	1.31164i
$31$	−7.30782	+	4.21917i	−1.31252	+	0.757786i	−0.982514	−	0.186191i	$-0.940386\pi$
$31$	−7.30782	+	4.21917i	−1.31252	+	0.757786i	−0.330010	+	0.943977i	$0.607052\pi$
$32$	−1.85974	−	5.34241i	−0.328758	−	0.944414i
$33$	−5.09048	+	4.44423i	−0.886139	+	0.773640i
$34$	7.03204	+	3.00832i	1.20598	+	0.515922i
$35$	4.06170	+	6.07877i	0.686553	+	1.02750i
$36$	−1.71189	+	5.75060i	−0.285315	+	0.958434i
$37$	−1.95977	−	9.85245i	−0.322185	−	1.61973i	−0.714316	−	0.699823i	$-0.753262\pi$
$37$	−1.95977	−	9.85245i	−0.322185	−	1.61973i	0.392131	−	0.919909i	$-0.371738\pi$
$38$	0.715696	+	3.82847i	0.116101	+	0.621059i
$39$	3.16297	−	2.10326i	0.506480	−	0.336791i
$40$	8.12151	−	2.44678i	1.28412	−	0.386870i
$41$	0.331410	+	2.51731i	0.0517575	+	0.393137i	0.997642	+	0.0686335i	$0.0218639\pi$
$41$	0.331410	+	2.51731i	0.0517575	+	0.393137i	−0.945884	+	0.324504i	$0.894803\pi$
$42$	−2.91430	−	5.21214i	−0.449686	−	0.804250i
$43$	−9.01742	+	4.44690i	−1.37514	+	0.678146i	−0.971559	−	0.236796i	$-0.923903\pi$
$43$	−9.01742	+	4.44690i	−1.37514	+	0.678146i	−0.403585	+	0.914942i	$0.632236\pi$
$44$	−7.32896	−	2.67805i	−1.10488	−	0.403731i
$45$	−8.50619	−	2.92976i	−1.26803	−	0.436743i
$46$	−4.75229	−	8.45510i	−0.700687	−	1.24664i
$47$	7.66285	−	2.05325i	1.11774	−	0.299498i	0.347772	−	0.937579i	$-0.386938\pi$
$47$	7.66285	−	2.05325i	1.11774	−	0.299498i	0.769969	+	0.638081i	$0.220272\pi$
$48$	−6.77104	+	1.46732i	−0.977315	+	0.211789i
$49$	−1.02074	−	0.273507i	−0.145820	−	0.0390724i
$50$	1.39856	+	5.47132i	0.197786	+	0.773761i
$51$	4.70177	−	8.10201i	0.658380	−	1.13451i
$52$	3.88790	+	2.03018i	0.539155	+	0.281536i
$53$	−0.653975	+	0.978744i	−0.0898304	+	0.134441i	−0.873663	−	0.486531i	$-0.838262\pi$
$53$	−0.653975	+	0.978744i	−0.0898304	+	0.134441i	0.783833	+	0.620972i	$0.213262\pi$
$54$	6.73674	+	2.93536i	0.916754	+	0.399452i
$55$	4.47738	−	10.8093i	0.603730	−	1.45753i
$56$	3.65235	−	5.84862i	0.488065	−	0.781555i
$57$	4.76059	−	0.301385i	0.630556	−	0.0399194i
$58$	−6.86311	+	3.28659i	−0.901171	+	0.431550i
$59$	−3.24475	−	3.69993i	−0.422431	−	0.481690i	0.501004	−	0.865445i	$-0.332964\pi$
$59$	−3.24475	−	3.69993i	−0.422431	−	0.481690i	−0.923435	+	0.383755i	$0.874631\pi$
$60$	−1.76817	−	10.2368i	−0.228270	−	1.32156i
$61$	0.628588	+	9.59040i	0.0804825	+	1.22793i	0.826862	+	0.562405i	$0.190124\pi$
$61$	0.628588	+	9.59040i	0.0804825	+	1.22793i	−0.746380	+	0.665520i	$0.768210\pi$
$62$	−7.37352	+	9.38310i	−0.936438	+	1.19166i
$63$	−6.76931	+	2.76870i	−0.852853	+	0.348823i
$64$	−5.25185	−	6.03473i	−0.656482	−	0.754342i
$65$	−3.28829	+	5.69549i	−0.407863	+	0.706439i
$66$	−4.34437	+	8.51203i	−0.534755	+	1.04776i
$67$	12.6331	+	6.22993i	1.54337	+	0.761108i	0.997071	−	0.0764804i	$-0.0243683\pi$
$67$	12.6331	+	6.22993i	1.54337	+	0.761108i	0.546302	+	0.837588i	$0.316035\pi$
$68$	10.8137	+	0.249671i	1.31136	+	0.0302771i
$69$	−10.9848	+	4.52144i	−1.32242	+	0.544317i
$70$	8.52981	+	5.84295i	1.01951	+	0.698367i
$71$	−0.603921	−	1.45800i	−0.0716723	−	0.173032i	0.883984	−	0.467518i	$-0.154852\pi$
$71$	−0.603921	−	1.45800i	−0.0716723	−	0.173032i	−0.955656	+	0.294486i	$0.904852\pi$
$72$	0.778036	+	8.44954i	0.0916924	+	0.995787i
$73$	−1.50613	+	3.63613i	−0.176280	+	0.425577i	−0.987181	−	0.159607i	$-0.948977\pi$
$73$	−1.50613	+	3.63613i	−0.176280	+	0.425577i	0.810901	+	0.585183i	$0.198977\pi$
$74$	−7.75582	−	11.9025i	−0.901595	−	1.38364i
$75$	6.85925	−	0.887509i	0.792038	−	0.102481i
$76$	2.95359	+	4.64920i	0.338800	+	0.533300i
$77$	−3.05730	−	9.00652i	−0.348412	−	1.02639i
$78$	3.04562	−	4.42497i	0.344848	−	0.501029i
$79$	2.17386	+	8.11296i	0.244579	+	0.912780i	0.973595	+	0.228283i	$0.0733112\pi$
$79$	2.17386	+	8.11296i	0.244579	+	0.912780i	−0.729016	+	0.684496i	$0.760022\pi$
$80$	9.37408	−	7.48450i	1.04805	−	0.836793i
$81$	4.56922	−	7.75385i	0.507691	−	0.861539i
$82$	1.75935	+	3.13018i	0.194288	+	0.345670i
$83$	−2.50488	−	2.19672i	−0.274947	−	0.241122i	0.510757	−	0.859725i	$-0.329365\pi$
$83$	−2.50488	−	2.19672i	−0.274947	−	0.241122i	−0.785703	+	0.618604i	$0.787699\pi$
$84$	−6.56766	−	5.30894i	−0.716591	−	0.579253i
$85$	−1.06076	+	16.1841i	−0.115055	+	1.75541i
$86$	−9.49795	+	10.5814i	−1.02419	+	1.14102i
$87$	2.97605	+	8.83171i	0.319066	+	0.946858i
$88$	−11.0298	+	0.340082i	−1.17578	+	0.0362529i
$89$	−2.21853	+	0.918946i	−0.235164	+	0.0974081i	−0.497153	−	0.867663i	$-0.665621\pi$
$89$	−2.21853	+	0.918946i	−0.235164	+	0.0974081i	0.261990	+	0.965071i	$0.415621\pi$
$90$	−12.7076	+	0.628976i	−1.33949	+	0.0662999i
$91$	1.04302	+	5.24360i	0.109338	+	0.549678i
$92$	−10.6865	−	8.59912i	−1.11414	−	0.896520i
$93$	10.3118	+	10.3578i	1.06928	+	1.07405i
$94$	8.97901	−	6.72662i	0.926115	−	0.693798i
$95$	−7.15248	+	4.12949i	−0.733829	+	0.423676i
$96$	−8.11657	+	5.48829i	−0.828394	+	0.560146i
$97$	0.636059	+	0.367229i	0.0645820	+	0.0372864i	0.531943	−	0.846780i	$-0.321462\pi$
$97$	0.636059	+	0.367229i	0.0645820	+	0.0372864i	−0.467361	+	0.884066i	$0.654795\pi$
$98$	−1.48384	+	0.177953i	−0.149890	+	0.0179760i
$99$	9.70279	+	6.54586i	0.975167	+	0.657884i
$100$	4.71427	+	6.44657i	0.471427	+	0.644657i
$101$	−5.62239	−	1.90854i	−0.559449	−	0.189907i	0.0273703	−	0.999625i	$-0.491287\pi$
$101$	−5.62239	−	1.90854i	−0.559449	−	0.189907i	−0.586819	+	0.809718i	$0.699620\pi$
$102$	1.90982	−	13.1092i	0.189100	−	1.29800i
$103$	12.3429	+	9.47104i	1.21618	+	0.933209i	0.999078	−	0.0429396i	$-0.0136723\pi$
$103$	12.3429	+	9.47104i	1.21618	+	0.933209i	0.217104	+	0.976149i	$0.430339\pi$
$104$	6.17177	+	0.619718i	0.605192	+	0.0607684i
$105$	8.37034	−	9.50179i	0.816861	−	0.927280i
$106$	−0.343591	+	1.62886i	−0.0333725	+	0.158209i
$107$	−3.90447	−	2.60889i	−0.377460	−	0.252210i	0.352339	−	0.935872i	$-0.385386\pi$
$107$	−3.90447	−	2.60889i	−0.377460	−	0.252210i	−0.729799	+	0.683662i	$0.760386\pi$
$108$	10.3877	+	0.309251i	0.999557	+	0.0297577i
$109$	−2.23530	+	11.2376i	−0.214103	+	1.07637i	0.712887	+	0.701279i	$0.247387\pi$
$109$	−2.23530	+	11.2376i	−0.214103	+	1.07637i	−0.926989	+	0.375087i	$0.877613\pi$
$110$	0.190975	−	16.5451i	0.0182087	−	1.57752i
$111$	−15.6220	+	7.66074i	−1.48278	+	0.727126i
$112$	1.71767	−	9.59904i	0.162305	−	0.907024i
$113$	12.0596	+	3.23136i	1.13447	+	0.303981i	0.776726	−	0.629839i	$-0.216879\pi$
$113$	12.0596	+	3.23136i	1.13447	+	0.303981i	0.357745	+	0.933819i	$0.383546\pi$
$114$	6.09078	−	2.90009i	0.570454	−	0.271618i
$115$	13.5609	−	15.4632i	1.26456	−	1.44195i
$116$	−7.28035	+	7.92492i	−0.675964	+	0.735810i
$117$	−4.92705	−	4.35986i	−0.455506	−	0.403069i
$118$	−6.20592	−	3.14998i	−0.571301	−	0.289980i
$119$	8.02639	+	10.4602i	0.735778	+	0.958884i
$120$	−7.70649	−	12.5079i	−0.703503	−	1.14181i
$121$	−2.56982	+	3.34905i	−0.233620	+	0.304459i
$122$	5.87048	+	12.2588i	0.531488	+	1.10986i
$123$	4.06670	−	1.67389i	0.366682	−	0.150929i
$124$	−4.74313	+	16.1965i	−0.425945	+	1.45449i
$125$	2.51042	−	1.67741i	0.224539	−	0.150032i
$126$	−7.42967	+	7.19573i	−0.661888	+	0.641047i
$127$	3.78851			0.336176			0.168088	−	0.985772i	$-0.446241\pi$
$127$	3.78851			0.336176			0.168088	+	0.985772i	$0.446241\pi$
$128$	−10.0690	−	5.15904i	−0.889980	−	0.455999i
$129$	11.4530	+	13.1185i	1.00838	+	1.15502i
$130$	−1.32033	+	9.20650i	−0.115801	+	0.807464i
$131$	−3.27929	−	1.61717i	−0.286513	−	0.141293i	0.293353	−	0.956004i	$-0.405229\pi$
$131$	−3.27929	−	1.61717i	−0.286513	−	0.141293i	−0.579867	+	0.814711i	$0.696895\pi$
$132$	−1.22494	+	13.4594i	−0.106618	+	1.17149i
$133$	−2.15814	+	6.35768i	−0.187135	+	0.551281i
$134$	19.8611	+	1.53218i	1.71574	+	0.132360i
$135$	−1.12296	+	15.5421i	−0.0966490	+	1.33765i
$136$	14.3268	−	5.36113i	1.22851	−	0.459713i
$137$	8.34188	+	10.8713i	0.712695	+	0.928802i	0.999575	−	0.0291649i	$-0.00928479\pi$
$137$	8.34188	+	10.8713i	0.712695	+	0.928802i	−0.286880	+	0.957967i	$0.592618\pi$
$138$	−12.0414	+	11.7143i	−1.02503	+	0.997186i
$139$	−16.2982	−	1.06824i	−1.38239	−	0.0906069i	−0.644026	−	0.765004i	$-0.722737\pi$
$139$	−16.2982	−	1.06824i	−1.38239	−	0.0906069i	−0.738369	+	0.674397i	$0.764404\pi$
$140$	14.2711	+	3.18282i	1.20613	+	0.268997i
$141$	−6.84382	−	11.9150i	−0.576353	−	1.00342i
$142$	−1.55980	−	1.59623i	−0.130896	−	0.133953i
$143$	6.05000	−	6.05000i	0.505927	−	0.505927i
$144$	5.46648	+	10.6826i	0.455540	+	0.890215i
$145$	−11.4099	−	11.4099i	−0.947539	−	0.947539i
$146$	−0.0642415	+	5.56558i	−0.00531667	+	0.460610i
$147$	−0.00407422	+	1.83034i	−0.000336036	+	0.150964i
$148$	−16.4429	−	11.5445i	−1.35160	−	0.948956i
$149$	1.30814	−	19.9583i	0.107167	−	1.63505i	−0.518587	−	0.855025i	$-0.673542\pi$
$149$	1.30814	−	19.9583i	0.107167	−	1.63505i	0.625753	−	0.780021i	$-0.284792\pi$
$150$	8.53739	−	4.77356i	0.697075	−	0.389760i
$151$	−8.70800	+	6.68188i	−0.708647	+	0.543764i	−0.898998	−	0.437952i	$-0.855704\pi$
$151$	−8.70800	+	6.68188i	−0.708647	+	0.543764i	0.190352	+	0.981716i	$0.439037\pi$
$152$	6.32309	+	4.54929i	0.512871	+	0.368996i
$153$	−15.6532	−	4.26904i	−1.26549	−	0.345132i
$154$	−8.75154	−	10.2147i	−0.705219	−	0.823122i
$155$	−23.9625	−	8.13418i	−1.92472	−	0.653353i
$156$	1.67016	−	7.41099i	0.133720	−	0.593354i
$157$	1.62781	−	3.30088i	0.129914	−	0.263439i	−0.822191	−	0.569212i	$-0.807248\pi$
$157$	1.62781	−	3.30088i	0.129914	−	0.263439i	0.952104	+	0.305773i	$0.0989149\pi$
$158$	7.12174	+	9.50644i	0.566575	+	0.756292i
$159$	1.92918	+	0.659659i	0.152994	+	0.0523144i
$160$	8.36812	−	14.7566i	0.661558	−	1.16661i
$161$		−	16.7197i		−	1.31770i
$162$	1.91897	−	12.5824i	0.150768	−	0.988569i
$163$	−1.49498	−	2.23739i	−0.117096	−	0.175246i	0.768292	−	0.640100i	$-0.221107\pi$
$163$	−1.49498	−	2.23739i	−0.117096	−	0.175246i	−0.885388	+	0.464853i	$0.846107\pi$
$164$	3.95626	+	3.18349i	0.308932	+	0.248589i
$165$	−20.0856	−	2.68982i	−1.56366	−	0.209402i
$166$	−4.44387	−	1.56592i	−0.344911	−	0.121539i
$167$	1.18245	+	0.907325i	0.0915006	+	0.0702109i	0.653499	−	0.756928i	$-0.273301\pi$
$167$	1.18245	+	0.907325i	0.0915006	+	0.0702109i	−0.561998	+	0.827139i	$0.689967\pi$
$168$	−11.4144	−	3.51405i	−0.880643	−	0.271115i
$169$	6.49808	−	4.98615i	0.499852	−	0.383550i
$170$	7.12162	+	21.8032i	0.546203	+	1.67223i
$171$	−2.62091	−	7.83537i	−0.200426	−	0.599186i
$172$	−6.90149	+	18.8872i	−0.526234	+	1.44013i
$173$	−17.3185	−	15.1879i	−1.31670	−	1.15472i	−0.976775	−	0.214267i	$-0.931264\pi$
$173$	−17.3185	−	15.1879i	−1.31670	−	1.15472i	−0.339928	−	0.940451i	$-0.610403\pi$
$174$	8.55291	+	10.0279i	0.648395	+	0.760216i
$175$	−2.51959	+	9.40323i	−0.190463	+	0.710817i
$176$	−14.3001	+	6.24896i	−1.07791	+	0.471033i
$177$	−4.75129	+	7.07665i	−0.357129	+	0.531914i
$178$	−2.42888	+	2.37345i	−0.182052	+	0.177897i
$179$	5.34507	+	1.06320i	0.399509	+	0.0794674i	0.390756	−	0.920494i	$-0.372214\pi$
$179$	5.34507	+	1.06320i	0.399509	+	0.0794674i	0.00875349	+	0.999962i	$0.497214\pi$
$180$	−16.3506	+	7.51086i	−1.21870	+	0.559826i
$181$	3.74438	−	5.60387i	0.278318	−	0.416532i	−0.665805	−	0.746126i	$-0.731912\pi$
$181$	3.74438	−	5.60387i	0.278318	−	0.416532i	0.944123	+	0.329594i	$0.106912\pi$
$182$	4.12774	+	6.33468i	0.305969	+	0.469558i
$183$	15.7751	−	5.31581i	1.16613	−	0.392956i
$184$	−18.5522	−	5.66630i	−1.36769	−	0.417725i
$185$	18.3390	−	23.8998i	1.34831	−	1.75715i
$186$	18.9856	+	8.17209i	1.39209	+	0.599207i
$187$	6.78246	−	19.9805i	0.495983	−	1.46112i
$188$	8.24821	−	13.5539i	0.601563	−	0.988517i
$189$	7.64426	+	10.1011i	0.556038	+	0.734750i
$190$	−7.21678	+	9.18364i	−0.523560	+	0.666252i
$191$	10.7351	−	18.5938i	0.776767	−	1.34540i	−0.157028	−	0.987594i	$-0.550191\pi$
$191$	10.7351	−	18.5938i	0.776767	−	1.34540i	0.933796	−	0.357806i	$-0.116475\pi$
$192$	−7.76753	+	11.4746i	−0.560573	+	0.828105i
$193$	2.46358	+	4.26705i	0.177332	+	0.307149i	0.940966	−	0.338501i	$-0.109920\pi$
$193$	2.46358	+	4.26705i	0.177332	+	0.307149i	−0.763634	+	0.645650i	$0.776587\pi$
$194$	1.02816	+	0.147452i	0.0738176	+	0.0105864i
$195$	10.9963	+	2.97269i	0.787458	+	0.212879i
$196$	−1.85425	+	1.01422i	−0.132446	+	0.0724442i
$197$	−16.4666	+	3.27541i	−1.17320	+	0.233363i	−0.742949	−	0.669348i	$-0.766574\pi$
$197$	−16.4666	+	3.27541i	−1.17320	+	0.233363i	−0.430247	+	0.902711i	$0.641574\pi$
$198$	16.1807	+	3.48846i	1.14991	+	0.247914i
$199$	−1.24108	−	2.99622i	−0.0879775	−	0.212397i	0.873767	−	0.486345i	$-0.161670\pi$
$199$	−1.24108	−	2.99622i	−0.0879775	−	0.212397i	−0.961744	+	0.273949i	$0.911670\pi$
$200$	9.57993	+	5.98248i	0.677404	+	0.423025i
$201$	4.81289	−	23.9177i	0.339475	−	1.68702i
$202$	−8.38468	+	0.452437i	−0.589944	+	0.0318334i
$203$	−13.0894	−	0.857926i	−0.918697	−	0.0602146i
$204$	−4.38942	−	18.2135i	−0.307321	−	1.27520i
$205$	−5.02039	+	5.72466i	−0.350640	+	0.399828i
$206$	21.1853	+	5.93949i	1.47605	+	0.413824i
$207$	12.4524	+	16.3788i	0.865505	+	1.13841i
$208$	8.42785	−	2.43333i	0.584366	−	0.168721i
$209$	10.3786	−	2.78094i	0.717904	−	0.192362i
$210$	5.98923	−	16.8767i	0.413296	−	1.16460i
$211$	16.6833	−	5.66322i	1.14853	−	0.389872i	0.318679	−	0.947863i	$-0.396761\pi$
$211$	16.6833	−	5.66322i	1.14853	−	0.389872i	0.829847	+	0.557990i	$0.188427\pi$
$212$	0.405872	+	2.31900i	0.0278754	+	0.159270i
$213$	−2.17224	+	1.65915i	−0.148840	+	0.113683i
$214$	−6.49797	−	1.37068i	−0.444192	−	0.0936976i
$215$	−27.8563	−	11.5385i	−1.89979	−	0.786917i
$216$	13.7989	−	5.05880i	0.938894	−	0.344208i
$217$	−19.0057	+	7.87244i	−1.29019	+	0.534416i
$218$	2.97755	+	15.9278i	0.201665	+	1.07877i
$219$	6.75655	+	0.904821i	0.456565	+	0.0611422i
$220$	−8.45336	−	21.8196i	−0.569926	−	1.47108i
$221$	−5.24578	+	10.6374i	−0.352870	+	0.715549i
$222$	−16.4772	+	18.2749i	−1.10588	+	1.22653i
$223$	−21.0879	−	12.1751i	−1.41215	−	0.815307i	−0.416562	−	0.909107i	$-0.636765\pi$
$223$	−21.0879	−	12.1751i	−1.41215	−	0.815307i	−0.995591	+	0.0938001i	$0.970099\pi$
$224$	−2.79503	−	13.5045i	−0.186751	−	0.902308i
$225$	−4.53508	−	11.0880i	−0.302338	−	0.739200i
$226$	17.5309	−	2.10243i	1.16614	−	0.139852i
$227$	−2.57861	+	0.169011i	−0.171148	+	0.0112177i	−0.150736	−	0.988574i	$-0.548164\pi$
$227$	−2.57861	+	0.169011i	−0.171148	+	0.0112177i	−0.0204120	+	0.999792i	$0.506498\pi$
$228$	6.46983	−	7.01125i	0.428475	−	0.464331i
$229$	4.06521	−	3.56509i	0.268637	−	0.235588i	−0.514420	−	0.857538i	$-0.671993\pi$
$229$	4.06521	−	3.56509i	0.268637	−	0.235588i	0.783057	+	0.621950i	$0.213659\pi$
$230$	9.66678	−	27.4330i	0.637409	−	1.80888i
$231$	−13.7180	+	9.12197i	−0.902577	+	0.600181i
$232$	−5.38794	+	14.2333i	−0.353736	+	0.934460i
$233$	−5.94430	−	2.46221i	−0.389424	−	0.161305i	0.179376	−	0.983781i	$-0.442592\pi$
$233$	−5.94430	−	2.46221i	−0.389424	−	0.161305i	−0.568800	+	0.822476i	$0.692592\pi$
$234$	−8.76148	−	3.13127i	−0.572756	−	0.204697i
$235$	19.7811	+	13.2173i	1.29038	+	0.862201i
$236$	−9.80379	−	0.870245i	−0.638173	−	0.0566481i
$237$	12.6149	−	7.24582i	0.819425	−	0.470667i
$238$	16.0393	+	9.50881i	1.03967	+	0.616364i
$239$	1.43091	−	5.34021i	0.0925576	−	0.345430i	−0.904080	−	0.427363i	$-0.859443\pi$
$239$	1.43091	−	5.34021i	0.0925576	−	0.345430i	0.996638	+	0.0819331i	$0.0261094\pi$
$240$	−16.6966	−	12.3651i	−1.07776	−	0.798166i
$241$	5.62071	+	20.9768i	0.362062	+	1.35123i	0.871360	+	0.490644i	$0.163238\pi$
$241$	5.62071	+	20.9768i	0.362062	+	1.35123i	−0.509298	+	0.860590i	$0.670095\pi$
$242$	−1.61159	+	5.74830i	−0.103597	+	0.369515i
$243$	−15.0115	−	4.20192i	−0.962985	−	0.269553i
$244$	14.1554	+	13.0041i	0.906209	+	0.832504i
$245$	−1.40163	−	2.84223i	−0.0895472	−	0.181584i
$246$	4.45785	−	4.33676i	0.284222	−	0.276502i
$247$	−5.98799	+	0.788334i	−0.381007	+	0.0501605i
$248$	2.29423	+	23.7567i	0.145684	+	1.50855i
$249$	−2.56380	+	5.16982i	−0.162474	+	0.327624i
$250$	2.41304	−	3.52266i	0.152614	−	0.222792i
$251$	−26.3067	+	5.23273i	−1.66047	+	0.330287i	−0.934097	−	0.357019i	$-0.883793\pi$
$251$	−26.3067	+	5.23273i	−1.66047	+	0.330287i	−0.726368	+	0.687306i	$0.758793\pi$
$252$	−5.96756	+	13.3546i	−0.375921	+	0.841260i
$253$	−22.2480	+	14.8656i	−1.39872	+	0.934595i
$254$	4.97326	−	1.99306i	0.312050	−	0.125056i
$255$	27.5641	−	5.41909i	1.72613	−	0.339356i
$256$	−15.9318	−	1.47530i	−0.995740	−	0.0922060i
$257$	12.8729	+	22.2965i	0.802987	+	1.39081i	0.917642	+	0.397409i	$0.130091\pi$
$257$	12.8729	+	22.2965i	0.802987	+	1.39081i	−0.114655	+	0.993405i	$0.536576\pi$
$258$	21.9360	+	11.1957i	1.36568	+	0.697014i
$259$	−1.60170	−	24.4372i	−0.0995247	−	1.51845i
$260$	3.11013	+	12.7802i	0.192882	+	0.792593i
$261$	13.4615	−	8.90824i	0.833244	−	0.551406i
$262$	−5.15556	−	0.397723i	−0.318512	−	0.0245714i
$263$	12.6181	+	1.66120i	0.778064	+	0.102434i	0.509090	−	0.860713i	$-0.329982\pi$
$263$	12.6181	+	1.66120i	0.778064	+	0.102434i	0.268974	+	0.963147i	$0.413315\pi$
$264$	5.47272	+	18.3129i	0.336823	+	1.12708i
$265$	−3.49984	+	0.460763i	−0.214993	+	0.0283044i
$266$	0.511607	+	9.48123i	0.0313686	+	0.581331i
$267$	2.52462	+	3.30535i	0.154504	+	0.202284i
$268$	26.8782	−	8.43722i	1.64185	−	0.515385i
$269$	12.3598	+	2.45851i	0.753589	+	0.149898i	0.556913	−	0.830571i	$-0.311985\pi$
$269$	12.3598	+	2.45851i	0.753589	+	0.149898i	0.196675	+	0.980469i	$0.436985\pi$
$270$	6.70223	+	20.9932i	0.407884	+	1.27760i
$271$	−7.08146	+	7.08146i	−0.430168	+	0.430168i	−0.888686	−	0.458517i	$-0.848381\pi$
$271$	−7.08146	+	7.08146i	−0.430168	+	0.430168i	0.458517	+	0.888686i	$0.348381\pi$
$272$	15.9867	−	14.5747i	0.969335	−	0.883721i
$273$	8.31424	−	4.07714i	0.503200	−	0.246760i
$274$	16.6698	+	9.88256i	1.00706	+	0.597028i
$275$	14.7525	−	5.00780i	0.889610	−	0.301982i
$276$	−9.64433	+	21.7123i	−0.580521	+	1.30693i
$277$	−16.1196	+	7.94929i	−0.968531	+	0.477626i	−0.856539	−	0.516083i	$-0.827390\pi$
$277$	−16.1196	+	7.94929i	−0.968531	+	0.477626i	−0.111992	+	0.993709i	$0.535723\pi$
$278$	−21.9570	+	7.17185i	−1.31689	+	0.430139i
$279$	12.7550	−	21.8669i	0.763622	−	1.30914i
$280$	20.4084	−	3.32960i	1.21964	−	0.198981i
$281$	2.48613	−	18.8840i	0.148310	−	1.12653i	−0.741748	−	0.670678i	$-0.766003\pi$
$281$	2.48613	−	18.8840i	0.148310	−	1.12653i	0.890058	−	0.455847i	$-0.150664\pi$
$282$	−15.2523	−	12.0407i	−0.908260	−	0.717013i
$283$	21.2448	−	18.6312i	1.26287	−	1.10751i	0.273538	−	0.961861i	$-0.411806\pi$
$283$	21.2448	−	18.6312i	1.26287	−	1.10751i	0.989336	−	0.145650i	$-0.0465274\pi$
$284$	−2.88733	−	1.27483i	−0.171332	−	0.0756472i
$285$	10.0926	+	10.1376i	0.597834	+	0.600501i
$286$	4.75919	−	11.1248i	0.281417	−	0.657821i
$287$			6.18984i			0.365375i
$288$	12.7959	+	11.1475i	0.754003	+	0.656871i
$289$			12.2497i			0.720573i
$290$	−20.9805	−	8.97550i	−1.23202	−	0.527059i
$291$	0.331982	−	1.22803i	0.0194612	−	0.0719887i
$292$	2.84361	+	7.33985i	0.166409	+	0.429532i
$293$	−2.26210	+	1.98381i	−0.132153	+	0.115895i	−0.722871	−	0.690983i	$-0.757178\pi$
$293$	−2.26210	+	1.98381i	−0.132153	+	0.115895i	0.590718	+	0.806878i	$0.298845\pi$
$294$	0.957556	+	2.40487i	0.0558458	+	0.140255i
$295$	1.92630	−	14.6317i	0.112153	−	0.851889i
$296$	−27.6583	−	6.50450i	−1.60761	−	0.378066i
$297$	6.64445	−	19.1528i	0.385550	−	1.11136i
$298$	−8.78243	−	26.8879i	−0.508753	−	1.55757i
$299$	13.4894	−	6.65222i	0.780111	−	0.384708i
$300$	8.69594	−	10.7577i	0.502060	−	0.621097i
$301$	−23.2103	+	7.87885i	−1.33782	+	0.454129i
$302$	−7.91598	+	13.3526i	−0.455513	+	0.768353i
$303$	−0.695449	+	10.2605i	−0.0399525	+	0.589450i
$304$	10.6938	+	2.64550i	0.613329	+	0.151730i
$305$	−20.3803	+	20.3803i	−1.16697	+	1.16697i
$306$	−22.7942	+	2.63077i	−1.30306	+	0.150391i
$307$	−28.8802	−	5.74463i	−1.64828	−	0.327863i	−0.718372	−	0.695659i	$-0.755113\pi$
$307$	−28.8802	−	5.74463i	−1.64828	−	0.327863i	−0.929907	+	0.367796i	$0.880113\pi$
$308$	−16.8621	−	8.80503i	−0.960806	−	0.501713i
$309$	10.3676	−	24.8728i	0.589791	−	1.41496i
$310$	−35.7354	+	1.92828i	−2.02963	+	0.109519i
$311$	−5.04327	+	0.663959i	−0.285978	+	0.0376497i	−0.272150	−	0.962255i	$-0.587735\pi$
$311$	−5.04327	+	0.663959i	−0.285978	+	0.0376497i	−0.0138272	+	0.999904i	$0.504401\pi$
$312$	−1.70631	−	10.6072i	−0.0966010	−	0.600515i
$313$	−0.616998	−	0.0812293i	−0.0348748	−	0.00459135i	0.113069	−	0.993587i	$-0.463932\pi$
$313$	−0.616998	−	0.0812293i	−0.0348748	−	0.00459135i	−0.147943	+	0.988996i	$0.547265\pi$
$314$	0.400341	−	5.18950i	0.0225926	−	0.292860i
$315$	−19.6274	−	9.78802i	−1.10588	−	0.551493i
$316$	14.3500	+	8.73271i	0.807252	+	0.491254i
$317$	−0.976955	−	14.9054i	−0.0548712	−	0.837173i	−0.933254	−	0.359216i	$-0.883044\pi$
$317$	−0.976955	−	14.9054i	−0.0548712	−	0.837173i	0.878383	−	0.477957i	$-0.158623\pi$
$318$	2.87951	−	0.148951i	0.161475	−	0.00835273i
$319$	10.4963	+	18.1801i	0.587680	+	1.01789i
$320$	3.22188	−	23.7736i	0.180109	−	1.32898i
$321$	−2.63156	+	7.69600i	−0.146879	+	0.429549i
$322$	−8.79592	−	21.9484i	−0.490177	−	1.22314i
$323$	−12.3844	+	8.27502i	−0.689089	+	0.460434i
$324$	−4.10029	−	17.5268i	−0.227794	−	0.973709i
$325$	−8.58892	+	1.70844i	−0.476427	+	0.0947673i
$326$	−3.13954	−	2.15060i	−0.173883	−	0.119111i
$327$	19.8058	−	1.25387i	1.09526	−	0.0693391i
$328$	6.86825	+	2.09773i	0.379235	+	0.115828i
$329$	19.1746	−	2.52439i	1.05713	−	0.139174i
$330$	−27.7819	+	7.03565i	−1.52934	+	0.387300i
$331$	−2.16905	−	4.39841i	−0.119222	−	0.241758i	0.829078	−	0.559132i	$-0.188866\pi$
$331$	−2.16905	−	4.39841i	−0.119222	−	0.241758i	−0.948300	+	0.317374i	$0.897199\pi$
$332$	−6.65737	+	0.282212i	−0.365370	+	0.0154884i
$333$	19.7693	+	22.7460i	1.08335	+	1.24647i
$334$	2.02955	+	0.569003i	0.111052	+	0.0311345i
$335$	10.9328	+	40.8017i	0.597322	+	2.22924i
$336$	−16.8327	+	1.39194i	−0.918297	+	0.0759366i
$337$	2.98046	−	11.1232i	0.162356	−	0.605921i	−0.836007	−	0.548719i	$-0.815116\pi$
$337$	2.98046	−	11.1232i	0.162356	−	0.605921i	0.998363	−	0.0572014i	$-0.0182177\pi$
$338$	5.90706	−	9.96394i	0.321302	−	0.541967i
$339$	0.0481351	−	21.6246i	0.00261434	−	1.17449i
$340$	20.8189	+	24.8750i	1.12907	+	1.34904i
$341$	27.3735	+	18.2904i	1.48236	+	0.990481i
$342$	−7.56255	−	8.90686i	−0.408936	−	0.481628i
$343$	−18.1463	−	7.51643i	−0.979806	−	0.405849i
$344$	0.876413	+	28.4243i	0.0472530	+	1.53254i
$345$	−31.9145	−	15.8269i	−1.71822	−	0.852092i
$346$	−30.7245	−	10.8266i	−1.65176	−	0.582043i
$347$	−4.37068	+	3.83298i	−0.234630	+	0.205765i	−0.768585	−	0.639748i	$-0.779039\pi$
$347$	−4.37068	+	3.83298i	−0.234630	+	0.205765i	0.533954	+	0.845513i	$0.320705\pi$
$348$	16.5031	+	8.66438i	0.884659	+	0.464460i
$349$	18.4652	−	1.21027i	0.988417	−	0.0647843i	0.437390	−	0.899272i	$-0.355903\pi$
$349$	18.4652	−	1.21027i	0.988417	−	0.0647843i	0.551027	+	0.834488i	$0.314236\pi$
$350$	1.63933	+	13.6693i	0.0876259	+	0.730656i
$351$	−5.10814	+	10.1862i	−0.272652	+	0.543701i
$352$	−15.4846	+	15.7261i	−0.825332	+	0.838206i
$353$	6.61984	+	3.82197i	0.352339	+	0.203423i	0.665715	−	0.746206i	$-0.268127\pi$
$353$	6.61984	+	3.82197i	0.352339	+	0.203423i	−0.313376	+	0.949629i	$0.601460\pi$
$354$	−2.51424	+	11.7892i	−0.133630	+	0.626591i
$355$	2.09317	−	4.24452i	0.111094	−	0.225276i
$356$	−1.93982	+	4.39346i	−0.102810	+	0.232853i
$357$	13.9424	−	18.0866i	0.737910	−	0.957244i
$358$	7.57592	−	1.41625i	0.400400	−	0.0748510i
$359$	−5.98829	+	2.48043i	−0.316050	+	0.130912i	−0.535069	−	0.844808i	$-0.679714\pi$
$359$	−5.98829	+	2.48043i	−0.316050	+	0.130912i	0.219019	+	0.975721i	$0.429714\pi$
$360$	−17.5125	+	18.4614i	−0.922989	+	0.973001i
$361$	10.5464	+	4.36845i	0.555072	+	0.229918i
$362$	1.96725	−	9.32616i	0.103397	−	0.490172i
$363$	6.74884	+	2.81308i	0.354222	+	0.147648i
$364$	8.75113	+	6.14415i	0.458684	+	0.322041i
$365$	−11.1763	+	3.79385i	−0.584996	+	0.198579i
$366$	17.9118	−	15.2772i	0.936267	−	0.798550i
$367$	6.24004	−	1.67201i	0.325727	−	0.0872783i	−0.0922499	−	0.995736i	$-0.529406\pi$
$367$	6.24004	−	1.67201i	0.325727	−	0.0872783i	0.417977	+	0.908458i	$0.362739\pi$
$368$	−27.3349	+	2.32167i	−1.42493	+	0.121025i
$369$	−4.61004	−	6.06362i	−0.239989	−	0.315660i
$370$	11.5008	−	41.0215i	0.597896	−	2.13261i
$371$	−1.89212	+	2.15754i	−0.0982338	+	0.112014i
$372$	29.2219	+	0.739772i	1.51509	+	0.0383554i
$373$	18.2503	+	1.19619i	0.944966	+	0.0619363i	0.530090	−	0.847942i	$-0.322158\pi$
$373$	18.2503	+	1.19619i	0.944966	+	0.0619363i	0.414876	+	0.909878i	$0.363825\pi$
$374$	−1.60784	−	29.7969i	−0.0831396	−	1.54076i
$375$	−3.92407	−	3.45680i	−0.202638	−	0.178508i
$376$	3.69720	−	22.1317i	0.190669	−	1.14135i
$377$	−4.51567	−	10.9018i	−0.232569	−	0.561471i
$378$	15.3488	+	9.23851i	0.789457	+	0.475178i
$379$	23.7631	−	4.72677i	1.22063	−	0.242798i	0.457597	−	0.889160i	$-0.348710\pi$
$379$	23.7631	−	4.72677i	1.22063	−	0.242798i	0.763031	+	0.646362i	$0.223710\pi$
$380$	−4.64230	+	15.8522i	−0.238145	+	0.813200i
$381$	−1.68423	−	6.34207i	−0.0862857	−	0.324914i
$382$	4.31043	−	30.0560i	0.220541	−	1.53780i
$383$	−3.98083	−	6.89499i	−0.203411	−	0.352318i	0.746214	−	0.665706i	$-0.231869\pi$
$383$	−3.98083	−	6.89499i	−0.203411	−	0.352318i	−0.949625	+	0.313388i	$0.898536\pi$
$384$	−4.16007	+	19.1493i	−0.212293	+	0.977206i
$385$	14.2615	−	24.7017i	0.726835	−	1.25892i
$386$	5.47880	+	4.30541i	0.278864	+	0.219139i
$387$	16.8691	−	25.0047i	0.857504	−	1.27106i
$388$	1.42726	−	0.347331i	0.0724581	−	0.0176331i
$389$	8.21674	−	24.2057i	0.416605	−	1.22728i	−0.512893	−	0.858453i	$-0.671426\pi$
$389$	8.21674	−	24.2057i	0.416605	−	1.22728i	0.929498	−	0.368827i	$-0.120241\pi$
$390$	15.9989	−	1.88259i	0.810136	−	0.0953289i
$391$	22.5801	−	29.4269i	1.14192	−	1.48818i
$392$	−1.90055	+	2.30687i	−0.0959924	+	0.116515i
$393$	−1.24933	+	6.20856i	−0.0630205	+	0.313180i
$394$	−19.8929	+	12.9624i	−1.00219	+	0.653039i
$395$	−13.9937	+	20.9430i	−0.704098	+	1.05376i
$396$	23.0760	−	3.93297i	1.15961	−	0.197639i
$397$	−22.1081	−	4.39757i	−1.10957	−	0.220708i	−0.393907	−	0.919150i	$-0.628877\pi$
$397$	−22.1081	−	4.39757i	−1.10957	−	0.220708i	−0.715666	+	0.698443i	$0.753877\pi$
$398$	−3.20544	−	3.28030i	−0.160674	−	0.164427i
$399$	11.6024	+	0.786400i	0.580844	+	0.0393692i
$400$	15.7231	+	2.81352i	0.786153	+	0.140676i
$401$	0.0387339	−	0.144557i	0.00193428	−	0.00721884i	−0.964952	−	0.262427i	$-0.915477\pi$
$401$	0.0387339	−	0.144557i	0.00193428	−	0.00721884i	0.966886	+	0.255208i	$0.0821439\pi$
$402$	−6.26461	−	33.9292i	−0.312451	−	1.69224i
$403$	−13.9132	−	12.2015i	−0.693065	−	0.607801i
$404$	−10.7687	+	5.00494i	−0.535765	+	0.249005i
$405$	26.5170	−	5.02955i	1.31764	−	0.249920i
$406$	−17.6341	+	5.75986i	−0.875166	+	0.285857i
$407$	−31.0931	+	23.8586i	−1.54123	+	1.18263i
$408$	−15.3438	−	21.6000i	−0.759632	−	1.06936i
$409$	10.4307	+	8.00378i	0.515766	+	0.395761i	0.833586	−	0.552390i	$-0.186284\pi$
$409$	10.4307	+	8.00378i	0.515766	+	0.395761i	−0.317820	+	0.948151i	$0.602951\pi$
$410$	−3.57875	+	10.1560i	−0.176742	+	0.501570i
$411$	14.4904	−	18.7975i	0.714760	−	0.927213i
$412$	30.9351	−	3.34826i	1.52406	−	0.164957i
$413$	−6.66530	−	9.97532i	−0.327978	−	0.490853i
$414$	24.9632	+	14.9498i	1.22687	+	0.734745i
$415$		−	9.99124i		−	0.490451i
$416$	9.78330	−	7.62800i	0.479666	−	0.373994i
$417$	5.45730	+	27.7585i	0.267245	+	1.35934i
$418$	12.1613	−	9.11059i	0.594826	−	0.445614i
$419$	−7.58401	+	15.3789i	−0.370503	+	0.751306i	−0.999663	−	0.0259701i	$-0.991733\pi$
$419$	−7.58401	+	15.3789i	−0.370503	+	0.751306i	0.629160	+	0.777276i	$0.283399\pi$
$420$	−1.01629	−	25.3052i	−0.0495897	−	1.23477i
$421$	17.7897	+	6.03880i	0.867019	+	0.294313i	0.719286	−	0.694714i	$-0.244469\pi$
$421$	17.7897	+	6.03880i	0.867019	+	0.294313i	0.147733	+	0.989027i	$0.452802\pi$
$422$	18.9213	−	16.2110i	0.921072	−	0.789139i
$423$	−16.9035	+	16.7537i	−0.821878	+	0.814592i
$424$	1.75278	+	2.83068i	0.0851223	+	0.137470i
$425$	−17.1336	+	13.1471i	−0.831102	+	0.637727i
$426$	−1.97870	+	3.32078i	−0.0958685	+	0.160892i
$427$	−1.53242	+	23.3802i	−0.0741591	+	1.13145i
$428$	−9.25112	+	1.61913i	−0.447170	+	0.0782637i
$429$	−12.8175	−	7.43826i	−0.618833	−	0.359122i
$430$	−42.6378	−	0.492153i	−2.05618	−	0.0237337i
$431$	−6.57479	−	6.57479i	−0.316697	−	0.316697i	0.530800	−	0.847497i	$-0.321891\pi$
$431$	−6.57479	−	6.57479i	−0.316697	−	0.316697i	−0.847497	+	0.530800i	$0.821891\pi$
$432$	15.4527	−	13.9001i	0.743470	−	0.668769i
$433$	27.0686	−	27.0686i	1.30083	−	1.30083i	0.373004	−	0.927830i	$-0.378328\pi$
$433$	27.0686	−	27.0686i	1.30083	−	1.30083i	0.927830	−	0.373004i	$-0.121672\pi$
$434$	−20.8077	+	20.3329i	−0.998803	+	0.976009i
$435$	−14.0280	+	24.1729i	−0.672593	+	1.15900i
$436$	12.2880	+	19.3423i	0.588488	+	0.926330i
$437$	18.8476	+	1.23534i	0.901602	+	0.0590941i
$438$	9.34548	−	2.36670i	0.446544	−	0.113086i
$439$	−4.89208	−	6.37549i	−0.233486	−	0.304285i	0.661885	−	0.749605i	$-0.269757\pi$
$439$	−4.89208	−	6.37549i	−0.233486	−	0.304285i	−0.895372	+	0.445320i	$0.853090\pi$
$440$	−22.5758	−	24.1960i	−1.07626	−	1.15350i
$441$	3.06585	−	0.806880i	0.145993	−	0.0384228i
$442$	−1.29014	+	16.7236i	−0.0613656	+	0.795463i
$443$	6.94347	−	20.4548i	0.329894	−	0.971837i	−0.647801	−	0.761809i	$-0.724311\pi$
$443$	6.94347	−	20.4548i	0.329894	−	0.971837i	0.977695	−	0.210027i	$-0.0673553\pi$
$444$	−12.0160	+	32.6581i	−0.570253	+	1.54989i
$445$	−6.45860	−	3.18503i	−0.306167	−	0.150985i
$446$	−34.0877	−	4.88862i	−1.61410	−	0.231483i
$447$	−33.9922	+	6.68285i	−1.60778	+	0.316088i
$448$	−10.7736	−	16.2573i	−0.509003	−	0.768084i
$449$	20.5368			0.969192			0.484596	−	0.874738i	$-0.338967\pi$
$449$	20.5368			0.969192			0.484596	+	0.874738i	$0.338967\pi$
$450$	−11.7865	−	12.1697i	−0.555620	−	0.573683i
$451$	8.23646	−	5.50343i	0.387840	−	0.259146i
$452$	21.9071	−	11.9825i	1.03042	−	0.563611i
$453$	15.0569	+	11.6069i	0.707434	+	0.545340i
$454$	−3.29609	+	1.57842i	−0.154693	+	0.0740789i
$455$	−9.76022	+	12.7198i	−0.457566	+	0.596312i
$456$	4.80462	−	12.6075i	0.224997	−	0.590399i
$457$	−10.1517	−	13.2300i	−0.474877	−	0.618871i	0.493081	−	0.869983i	$-0.335870\pi$
$457$	−10.1517	−	13.2300i	−0.474877	−	0.618871i	−0.967958	+	0.251112i	$0.919204\pi$
$458$	3.46097	−	6.81860i	0.161720	−	0.318612i
$459$	−0.187661	+	28.1017i	−0.00875925	+	1.31168i
$460$	−1.74216	−	41.0974i	−0.0812286	−	1.91618i
$461$	−5.16042	+	5.88433i	−0.240344	+	0.274060i	−0.859419	−	0.511272i	$-0.829175\pi$
$461$	−5.16042	+	5.88433i	−0.240344	+	0.274060i	0.619075	+	0.785332i	$0.287508\pi$
$462$	−13.2090	+	19.1914i	−0.614540	+	0.892863i
$463$	−25.0181	−	6.70358i	−1.16269	−	0.311542i	−0.374650	−	0.927166i	$-0.622237\pi$
$463$	−25.0181	−	6.70358i	−1.16269	−	0.311542i	−0.788040	+	0.615624i	$0.788904\pi$
$464$	0.414962	+	21.5188i	0.0192641	+	0.998986i
$465$	−2.96399	+	43.7300i	−0.137452	+	2.02793i
$466$	−9.09854	−	0.105021i	−0.421482	−	0.00486502i
$467$	7.87808	−	39.6058i	0.364554	−	1.83274i	−0.167305	−	0.985905i	$-0.553507\pi$
$467$	7.87808	−	39.6058i	0.364554	−	1.83274i	0.531859	−	0.846833i	$-0.321493\pi$
$468$	−13.1487	+	0.498754i	−0.607798	+	0.0230549i
$469$	28.5520	+	19.0778i	1.31841	+	0.880932i
$470$	32.9204	+	6.94421i	1.51851	+	0.320312i
$471$	−6.24943	−	1.25756i	−0.287958	−	0.0579451i
$472$	−13.3275	+	4.01519i	−0.613447	+	0.184814i
$473$	31.1204	+	23.8795i	1.43092	+	1.09798i
$474$	12.7480	−	16.1482i	0.585534	−	0.741711i
$475$	−10.4138	−	3.53500i	−0.477816	−	0.162197i
$476$	26.0576	+	4.04446i	1.19435	+	0.185378i
$477$	0.246648	−	3.52275i	0.0112932	−	0.161296i
$478$	−0.930997	−	7.76299i	−0.0425828	−	0.355071i
$479$	16.2175	+	9.36320i	0.740998	+	0.427816i	0.822432	−	0.568863i	$-0.192617\pi$
$479$	16.2175	+	9.36320i	0.740998	+	0.427816i	−0.0814339	+	0.996679i	$0.525950\pi$
$480$	−28.4231	−	7.44823i	−1.29733	−	0.339964i
$481$	19.0785	−	11.0150i	0.869905	−	0.502240i
$482$	18.4139	+	24.5797i	0.838730	+	1.11958i
$483$	−27.9893	+	7.43297i	−1.27356	+	0.338212i
$484$	0.908498	+	8.39374i	0.0412954	+	0.381534i
$485$	0.429694	+	2.16022i	0.0195114	+	0.0980904i
$486$	−21.9164	+	2.38127i	−0.994149	+	0.108017i
$487$	−10.4092	+	4.31163i	−0.471686	+	0.195379i	−0.605848	−	0.795581i	$-0.707166\pi$
$487$	−10.4092	+	4.31163i	−0.471686	+	0.195379i	0.134162	+	0.990959i	$0.457166\pi$
$488$	25.4234	+	9.62391i	1.15086	+	0.435654i
$489$	−3.08085	+	3.49730i	−0.139321	+	0.158153i
$490$	−3.33520	−	2.99369i	−0.150669	−	0.135241i
$491$	0.328415	−	5.01064i	0.0148211	−	0.226127i	−0.984022	−	0.178045i	$-0.943023\pi$
$491$	0.328415	−	5.01064i	0.0148211	−	0.226127i	0.998843	−	0.0480815i	$-0.0153107\pi$
$492$	3.57044	−	8.03815i	0.160968	−	0.362388i
$493$	−21.8789	−	19.1873i	−0.985376	−	0.864151i
$494$	−7.44584	+	4.18502i	−0.335004	+	0.188293i
$495$	4.42648	+	34.8196i	0.198956	+	1.56503i
$496$	15.5096	+	29.9790i	0.696403	+	1.34610i
$497$	−0.995747	−	3.71618i	−0.0446654	−	0.166693i
$498$	−0.645813	+	8.13530i	−0.0289396	+	0.364552i
$499$	12.2352	+	36.0437i	0.547722	+	1.61354i	0.769644	+	0.638473i	$0.220434\pi$
$499$	12.2352	+	36.0437i	0.547722	+	1.61354i	−0.221922	+	0.975064i	$0.571233\pi$
$500$	1.31445	−	5.89372i	0.0587838	−	0.263575i
$501$	0.993213	−	2.38281i	0.0443735	−	0.106456i
$502$	−31.7806	+	20.7086i	−1.41844	+	0.924268i
$503$	−0.492954	+	1.19010i	−0.0219797	+	0.0530637i	−0.934488	−	0.355994i	$-0.884142\pi$
$503$	−0.492954	+	1.19010i	−0.0219797	+	0.0530637i	0.912509	+	0.409057i	$0.134142\pi$
$504$	−0.808171	+	20.6703i	−0.0359988	+	0.920728i
$505$	−6.81396	−	16.4504i	−0.303217	−	0.732032i
$506$	−21.3849	+	31.2187i	−0.950676	+	1.38784i
$507$	−11.2357	−	8.66129i	−0.498997	−	0.384662i
$508$	5.48001	−	5.23267i	0.243136	−	0.232162i
$509$	32.3065	+	15.9318i	1.43196	+	0.706164i	0.982348	−	0.187060i	$-0.0598959\pi$
$509$	32.3065	+	15.9318i	1.43196	+	0.706164i	0.449611	+	0.893224i	$0.351563\pi$
$510$	33.3331	−	21.6147i	1.47602	−	0.957114i
$511$	−4.79740	+	8.30934i	−0.212225	+	0.367584i
$512$	−21.6902	+	6.44477i	−0.958581	+	0.284821i
$513$	−11.9515	+	7.87078i	−0.527670	+	0.347503i
$514$	28.6282	+	22.4969i	1.26274	+	0.992296i
$515$	3.05145	+	46.5561i	0.134463	+	2.05151i
$516$	34.6857	+	3.15675i	1.52695	+	0.138968i
$517$	−20.4074	−	23.2701i	−0.897514	−	1.02342i
$518$	−14.9585	−	31.2366i	−0.657239	−	1.37246i
$519$	−17.7258	+	35.7437i	−0.778078	+	1.56897i
$520$	10.8061	+	15.1407i	0.473880	+	0.663962i
$521$	−12.8727	+	31.0774i	−0.563962	+	1.36152i	0.342612	+	0.939477i	$0.388689\pi$
$521$	−12.8727	+	31.0774i	−0.563962	+	1.36152i	−0.906574	+	0.422048i	$0.861311\pi$
$522$	12.9847	−	18.7758i	0.568326	−	0.821796i
$523$	−10.7925	+	16.1522i	−0.471925	+	0.706285i	−0.988712	−	0.149829i	$-0.952128\pi$
$523$	−10.7925	+	16.1522i	−0.471925	+	0.706285i	0.516787	+	0.856114i	$0.327128\pi$
$524$	−6.97706	+	2.19014i	−0.304794	+	0.0956766i
$525$	16.8614	+	0.0375324i	0.735890	+	0.00163805i
$526$	17.4380	−	4.45742i	0.760331	−	0.194353i
$527$	−44.0821	−	11.8118i	−1.92025	−	0.514528i
$528$	16.8182	+	21.1607i	0.731919	+	0.920900i
$529$	−23.2175	+	6.22111i	−1.00946	+	0.270483i
$530$	−4.35192	+	2.44605i	−0.189035	+	0.106250i
$531$	13.9587	+	4.80776i	0.605758	+	0.208639i
$532$	5.65948	+	12.1771i	0.245370	+	0.527943i
$533$	−4.99392	+	2.46273i	−0.216311	+	0.106673i
$534$	5.05300	+	3.01086i	0.218665	+	0.130293i
$535$	−1.83811	−	13.9618i	−0.0794683	−	0.603622i
$536$	30.8450	−	25.2158i	1.33230	−	1.08916i
$537$	−0.596393	−	9.42045i	−0.0257362	−	0.406522i
$538$	17.5183	−	3.27489i	0.755269	−	0.141190i
$539$	0.804331	+	4.04364i	0.0346450	+	0.174172i
$540$	19.8422	+	24.0323i	0.853874	+	1.03419i
$541$	−11.5449	−	17.2782i	−0.496356	−	0.742849i	0.495721	−	0.868482i	$-0.334904\pi$
$541$	−11.5449	−	17.2782i	−0.496356	−	0.742849i	−0.992077	+	0.125633i	$0.959904\pi$
$542$	−5.57058	+	13.0214i	−0.239277	+	0.559318i
$543$	−11.0456	−	3.77693i	−0.474013	−	0.162083i
$544$	13.3186	−	27.5428i	0.571031	−	1.18089i
$545$	−29.7569	+	17.1801i	−1.27464	+	0.735916i
$546$	8.76938	−	9.72611i	0.375295	−	0.416239i
$547$	43.2343	−	2.83373i	1.84857	−	0.121161i	0.899634	−	0.436644i	$-0.143833\pi$
$547$	43.2343	−	2.83373i	1.84857	−	0.121161i	0.948931	+	0.315483i	$0.102166\pi$
$548$	27.0818	+	4.20344i	1.15688	+	0.179562i
$549$	−15.9118	−	24.0448i	−0.679101	−	1.02621i
$550$	16.7315	−	14.3349i	0.713431	−	0.611240i
$551$	1.93422	−	14.6919i	0.0824005	−	0.625894i
$552$	−1.23791	+	33.5759i	−0.0526891	+	1.42909i
$553$	2.67267	+	20.3009i	0.113654	+	0.863284i
$554$	−16.9785	+	18.9154i	−0.721349	+	0.803638i
$555$	−48.1617	−	20.0749i	−2.04435	−	0.852134i
$556$	−25.0505	+	20.9658i	−1.06238	+	0.889147i
$557$	−4.61423	+	23.1973i	−0.195511	+	0.982901i	0.751018	+	0.660282i	$0.229563\pi$
$557$	−4.61423	+	23.1973i	−0.195511	+	0.982901i	−0.946529	+	0.322619i	$0.895437\pi$
$558$	5.24003	−	35.4153i	0.221828	−	1.49925i
$559$	−15.5912	−	15.5912i	−0.659438	−	0.659438i
$560$	25.0390	−	15.1073i	1.05809	−	0.638400i
$561$	−36.4631	−	2.47144i	−1.53947	−	0.104344i
$562$	−6.67090	−	26.0974i	−0.281395	−	1.10085i
$563$	11.1917	+	32.9698i	0.471675	+	1.38951i	0.879259	+	0.476343i	$0.158038\pi$
$563$	11.1917	+	32.9698i	0.471675	+	1.38951i	−0.407584	+	0.913168i	$0.633629\pi$
$564$	−26.3564	−	7.78219i	−1.10980	−	0.327689i
$565$	16.5597	+	33.5797i	0.696671	+	1.41271i
$566$	18.0871	−	35.6341i	0.760256	−	1.49781i
$567$	13.5112	−	17.2873i	0.567418	−	0.725997i
$568$	−4.46093	−	0.154528i	−0.187176	−	0.00648384i
$569$	−31.6799	−	4.17074i	−1.32809	−	0.174847i	−0.567122	−	0.823634i	$-0.691943\pi$
$569$	−31.6799	−	4.17074i	−1.32809	−	0.174847i	−0.760970	+	0.648787i	$0.775276\pi$
$570$	18.5820	+	7.99838i	0.778313	+	0.335015i
$571$	−12.1400	−	13.8431i	−0.508045	−	0.579314i	0.439780	−	0.898105i	$-0.355056\pi$
$571$	−12.1400	−	13.8431i	−0.508045	−	0.579314i	−0.947825	+	0.318791i	$0.896723\pi$
$572$	0.394983	−	17.1074i	0.0165151	−	0.715298i
$573$	−35.8990	−	9.70479i	−1.49970	−	0.405424i
$574$	3.25635	+	8.12554i	0.135917	+	0.339154i
$575$	27.3866			1.14210
$576$	22.6619	+	7.90189i	0.944244	+	0.329245i
$577$	18.5989			0.774284			0.387142	−	0.922020i	$-0.373462\pi$
$577$	18.5989			0.774284			0.387142	+	0.922020i	$0.373462\pi$
$578$	6.44434	+	16.0805i	0.268049	+	0.668861i
$579$	6.04793	−	6.02107i	0.251343	−	0.250227i
$580$	−32.2634	−	0.744910i	−1.33967	−	0.0309307i
$581$	−5.35535	−	6.10660i	−0.222177	−	0.253345i
$582$	−0.210244	−	1.78672i	−0.00871488	−	0.0740618i
$583$	4.55321	+	0.599442i	0.188575	+	0.0248264i
$584$	7.59421	+	8.13922i	0.314251	+	0.336803i
$585$	0.0878340	−	19.7296i	0.00363149	−	0.815717i
$586$	−1.92587	+	3.79424i	−0.0795569	+	0.156739i
$587$	1.85248	+	3.75645i	0.0764599	+	0.155045i	0.931746	−	0.363111i	$-0.118285\pi$
$587$	1.85248	+	3.75645i	0.0764599	+	0.155045i	−0.855286	+	0.518156i	$0.826619\pi$
$588$	2.52216	+	2.65318i	0.104012	+	0.109415i
$589$	−7.47009	−	22.0062i	−0.307799	−	0.906748i
$590$	−5.16874	−	20.2207i	−0.212794	−	0.832474i
$591$	12.8036	+	26.1094i	0.526668	+	1.07400i
$592$	−39.7296	+	6.01190i	−1.63288	+	0.247087i
$593$	18.8720	+	18.8720i	0.774979	+	0.774979i	0.978972	−	0.203993i	$-0.0653920\pi$
$593$	18.8720	+	18.8720i	0.774979	+	0.774979i	−0.203993	+	0.978972i	$0.565392\pi$
$594$	−1.35357	−	28.6378i	−0.0555375	−	1.17502i
$595$	−7.71376	+	38.7797i	−0.316233	+	1.58981i
$596$	−25.6741	−	30.6760i	−1.05165	−	1.25654i
$597$	−4.46402	+	3.40960i	−0.182700	+	0.139546i
$598$	14.2082	−	15.8290i	0.581017	−	0.647296i
$599$	−3.79718	−	28.8424i	−0.155148	−	1.17847i	−0.874923	−	0.484262i	$-0.839088\pi$
$599$	−3.79718	−	28.8424i	−0.155148	−	1.17847i	0.719775	−	0.694208i	$-0.244245\pi$
$600$	5.75594	−	18.6966i	0.234985	−	0.763287i
$601$	4.38688	−	33.3216i	0.178944	−	1.35922i	−0.632396	−	0.774645i	$-0.717929\pi$
$601$	4.38688	−	33.3216i	0.178944	−	1.35922i	0.811341	−	0.584573i	$-0.198738\pi$
$602$	−26.3238	+	22.5532i	−1.07288	+	0.919201i
$603$	−42.1784	+	2.57599i	−1.71764	+	0.104903i
$604$	−3.36697	+	21.6926i	−0.137000	+	0.882661i
$605$	−12.6323	+	0.827962i	−0.513574	+	0.0336614i
$606$	4.48491	+	13.8350i	0.182187	+	0.562010i
$607$	−25.6936	+	14.8342i	−1.04287	+	0.602102i	−0.920645	−	0.390400i	$-0.872337\pi$
$607$	−25.6936	+	14.8342i	−1.04287	+	0.602102i	−0.122226	+	0.992502i	$0.539003\pi$
$608$	15.4297	−	2.15296i	0.625756	−	0.0873142i
$609$	4.38287	+	22.2934i	0.177603	+	0.903375i
$610$	−16.0320	+	37.4753i	−0.649116	+	1.51733i
$611$	9.66560	+	14.4656i	0.391028	+	0.585215i
$612$	−28.5384	+	15.4450i	−1.15360	+	0.624328i
$613$	4.33277	+	21.7823i	0.174999	+	0.879778i	0.964105	+	0.265522i	$0.0855441\pi$
$613$	4.33277	+	21.7823i	0.174999	+	0.879778i	−0.789106	+	0.614257i	$0.789456\pi$
$614$	−40.9338	+	7.65218i	−1.65195	+	0.308817i
$615$	11.8151	+	5.85930i	0.476431	+	0.236270i
$616$	−26.7674	−	2.68776i	−1.07849	−	0.108293i
$617$	0.997835	+	7.57931i	0.0401713	+	0.305131i	0.999722	+	0.0235942i	$0.00751097\pi$
$617$	0.997835	+	7.57931i	0.0401713	+	0.305131i	−0.959550	+	0.281537i	$0.909156\pi$
$618$	0.524669	−	38.1053i	0.0211053	−	1.53282i
$619$	23.7325	−	11.7036i	0.953888	−	0.470406i	0.102379	−	0.994745i	$-0.467354\pi$
$619$	23.7325	−	11.7036i	0.953888	−	0.470406i	0.851509	+	0.524340i	$0.175688\pi$
$620$	−45.8962	+	21.3310i	−1.84324	+	0.856672i
$621$	21.8827	−	28.1271i	0.878121	−	1.12870i
$622$	−6.27112	+	3.52476i	−0.251449	+	0.141330i
$623$	−5.65466	+	1.51516i	−0.226549	+	0.0607036i
$624$	−7.82016	−	13.0267i	−0.313057	−	0.521484i
$625$	28.0315	+	7.51102i	1.12126	+	0.300441i
$626$	−0.852680	+	0.217959i	−0.0340800	+	0.00871138i
$627$	−9.26932	−	16.1378i	−0.370181	−	0.644481i
$628$	−2.20455	−	7.02299i	−0.0879713	−	0.280248i
$629$	30.1835	−	45.1729i	1.20350	−	1.80116i
$630$	−30.9146	−	2.52339i	−1.23167	−	0.100534i
$631$	11.0824	−	26.7553i	0.441184	−	1.06511i	−0.534350	−	0.845263i	$-0.679444\pi$
$631$	11.0824	−	26.7553i	0.441184	−	1.06511i	0.975534	−	0.219849i	$-0.0705565\pi$
$632$	23.4317	+	3.91437i	0.932063	+	0.155705i
$633$	−16.8972	−	25.4106i	−0.671602	−	1.00998i
$634$	−9.12393	−	19.0528i	−0.362357	−	0.756682i
$635$	7.49099	+	8.54183i	0.297271	+	0.338972i
$636$	3.70163	−	1.71038i	0.146779	−	0.0678210i
$637$	−0.151570	−	2.31251i	−0.00600543	−	0.0916252i
$638$	23.3429	+	18.3436i	0.924155	+	0.726228i
$639$	3.74316	+	2.89879i	0.148077	+	0.114674i
$640$	−8.27738	−	32.9031i	−0.327192	−	1.30061i
$641$	16.9469	−	29.3530i	0.669364	−	1.15937i	−0.308719	−	0.951153i	$-0.599900\pi$
$641$	16.9469	−	29.3530i	0.669364	−	1.15937i	0.978082	−	0.208218i	$-0.0667665\pi$
$642$	0.594204	+	11.4871i	0.0234514	+	0.453361i
$643$	−22.9384	−	11.3119i	−0.904600	−	0.446100i	−0.0703733	−	0.997521i	$-0.522419\pi$
$643$	−22.9384	−	11.3119i	−0.904600	−	0.446100i	−0.834227	+	0.551421i	$0.814086\pi$
$644$	−23.0932	−	24.1848i	−0.910000	−	0.953014i
$645$	−6.93182	+	51.7618i	−0.272940	+	2.03812i
$646$	−11.9040	+	17.3780i	−0.468357	+	0.683728i
$647$	3.19259	+	7.70759i	0.125514	+	0.303017i	0.974129	−	0.225994i	$-0.0725631\pi$
$647$	3.19259	+	7.70759i	0.125514	+	0.303017i	−0.848615	+	0.529011i	$0.822563\pi$
$648$	−14.6030	−	20.8507i	−0.573661	−	0.819093i
$649$	−7.34742	+	17.7383i	−0.288412	+	0.696287i
$650$	−10.3761	+	6.76117i	−0.406984	+	0.265195i
$651$	21.6279	+	28.3163i	0.847664	+	1.10980i
$652$	−5.25273	−	1.17149i	−0.205713	−	0.0458791i
$653$	7.74038	+	22.8024i	0.302904	+	0.892328i	0.986685	+	0.162640i	$0.0520010\pi$
$653$	7.74038	+	22.8024i	0.302904	+	0.892328i	−0.683781	+	0.729687i	$0.739666\pi$
$654$	25.3398	−	12.0654i	0.990866	−	0.471794i
$655$	−2.83794	−	10.5913i	−0.110887	−	0.413838i
$656$	10.1197	−	0.859509i	0.395107	−	0.0335582i
$657$	−1.48901	−	11.7129i	−0.0580920	−	0.456963i
$658$	23.8429	−	13.4012i	0.929494	−	0.522433i
$659$	14.4042	+	12.6321i	0.561107	+	0.492077i	0.892274	−	0.451495i	$-0.149109\pi$
$659$	14.4042	+	12.6321i	0.561107	+	0.492077i	−0.331167	+	0.943572i	$0.607442\pi$
$660$	−32.7686	+	23.8513i	−1.27552	+	0.928412i
$661$	−0.933989	+	14.2499i	−0.0363279	+	0.554257i	0.940440	+	0.339959i	$0.110413\pi$
$661$	−0.933989	+	14.2499i	−0.0363279	+	0.554257i	−0.976768	+	0.214298i	$0.931253\pi$
$662$	−5.16128	−	4.63279i	−0.200599	−	0.180059i
$663$	20.1394	+	4.05259i	0.782148	+	0.157390i
$664$	−8.59081	+	3.87277i	−0.333388	+	0.150293i
$665$	−18.6017	+	7.70509i	−0.721344	+	0.298791i
$666$	37.9177	+	19.4590i	1.46928	+	0.754020i
$667$	7.19933	+	36.1935i	0.278759	+	1.40142i
$668$	2.96358	−	0.320763i	0.114664	−	0.0124107i
$669$	−11.0066	+	40.7144i	−0.425539	+	1.57411i
$670$	35.8167	+	47.8098i	1.38372	+	1.84705i
$671$	32.4732	−	18.7484i	1.25361	−	0.723775i
$672$	−21.3643	+	10.6826i	−0.824147	+	0.412089i
$673$	−24.3397	−	14.0525i	−0.938225	−	0.541685i	−0.0488218	−	0.998808i	$-0.515547\pi$
$673$	−24.3397	−	14.0525i	−0.938225	−	0.541685i	−0.889404	+	0.457123i	$0.848880\pi$
$674$	−1.93919	−	16.1697i	−0.0746948	−	0.622832i
$675$	−16.5455	+	12.5212i	−0.636836	+	0.481939i
$676$	2.51250	−	16.1875i	0.0966346	−	0.622595i
$677$	31.4717	+	10.6832i	1.20956	+	0.410589i	0.852119	−	0.523348i	$-0.175317\pi$
$677$	31.4717	+	10.6832i	1.20956	+	0.410589i	0.357437	+	0.933937i	$0.383651\pi$
$678$	−11.3131	−	28.4124i	−0.434477	−	1.09117i
$679$	1.42051	+	1.09000i	0.0545143	+	0.0418303i
$680$	40.4157	+	21.7016i	1.54987	+	0.832217i
$681$	1.42928	+	4.24152i	0.0547702	+	0.162536i
$682$	45.5561	+	9.60957i	1.74443	+	0.367969i
$683$	31.1768	+	20.8317i	1.19295	+	0.797102i	0.983534	−	0.180725i	$-0.0578444\pi$
$683$	31.1768	+	20.8317i	1.19295	+	0.797102i	0.209414	+	0.977827i	$0.432844\pi$
$684$	−14.6133	−	7.71373i	−0.558752	−	0.294942i
$685$	−8.01695	+	40.3040i	−0.306312	+	1.53993i
$686$	−27.7752	−	0.320600i	−1.06046	−	0.0122406i
$687$	−7.77530	−	5.22036i	−0.296646	−	0.199169i
$688$	16.1040	+	36.8522i	0.613957	+	1.40498i
$689$	−2.49350	−	0.668132i	−0.0949949	−	0.0254538i
$690$	−50.2211	−	3.98675i	−1.91188	−	0.151773i
$691$	−16.9308	+	19.3059i	−0.644078	+	0.734430i	−0.978100	−	0.208135i	$-0.933261\pi$
$691$	−16.9308	+	19.3059i	−0.644078	+	0.734430i	0.334022	+	0.942565i	$0.391594\pi$
$692$	−46.0284	+	1.95119i	−1.74974	+	0.0741730i
$693$	21.3689	+	18.9090i	0.811738	+	0.718293i
$694$	−3.72104	+	7.33097i	−0.141249	+	0.278280i
$695$	−29.8177	−	38.8592i	−1.13105	−	1.47401i
$696$	26.2221	+	2.69198i	0.993948	+	0.102039i
$697$	−8.35941	+	10.8942i	−0.316635	+	0.412647i
$698$	23.6029	−	11.3029i	0.893384	−	0.427821i
$699$	−1.47919	+	11.0455i	−0.0559482	+	0.417780i
$700$	9.34314	+	17.0816i	0.353138	+	0.645624i
$701$	−24.4610	+	16.3443i	−0.923881	+	0.617317i	−0.923880	−	0.382683i	$-0.875000\pi$
$701$	−24.4610	+	16.3443i	−0.923881	+	0.617317i	−9.30472e−7		1.00000i	$0.500000\pi$
$702$	−1.34680	+	16.0590i	−0.0508316	+	0.606108i
$703$	27.6655			1.04343
$704$	−12.0538	+	28.7902i	−0.454293	+	1.08507i
$705$	13.3322	−	38.9900i	0.502119	−	1.46845i
$706$	10.7007	+	1.53462i	0.402725	+	0.0577561i
$707$	−12.9821	−	6.40208i	−0.488243	−	0.240775i
$708$	2.90159	+	16.7987i	0.109048	+	0.631333i
$709$	−0.366986	+	1.08110i	−0.0137824	+	0.0406017i	−0.953604	−	0.301065i	$-0.902658\pi$
$709$	−0.366986	+	1.08110i	−0.0137824	+	0.0406017i	0.939821	+	0.341666i	$0.110991\pi$
$710$	0.514789	−	6.67305i	0.0193197	−	0.250435i
$711$	−17.7378	−	17.8964i	−0.665220	−	0.671169i
$712$	−0.235134	+	6.78789i	−0.00881204	+	0.254387i
$713$	35.2308	+	45.9136i	1.31940	+	1.71948i
$714$	8.78752	−	31.0775i	0.328864	−	1.16305i
$715$	25.6033	+	1.67813i	0.957511	+	0.0627586i
$716$	9.20003	−	5.84468i	0.343821	−	0.218426i
$717$	−9.57579	−	0.0213151i	−0.357614	−	0.000796028i
$718$	−6.55606	+	6.40644i	−0.244670	+	0.239086i
$719$	6.79654	−	6.79654i	0.253468	−	0.253468i	−0.568923	−	0.822391i	$-0.692640\pi$
$719$	6.79654	−	6.79654i	0.253468	−	0.253468i	0.822391	+	0.568923i	$0.192640\pi$
$720$	−13.2769	+	33.4477i	−0.494800	+	1.24652i
$721$	26.8193	+	26.8193i	0.998803	+	0.998803i
$722$	16.1426	+	0.186329i	0.600766	+	0.00693443i
$723$	32.6169	−	18.7347i	1.21304	−	0.696751i
$724$	−2.32385	−	13.2776i	−0.0863651	−	0.493458i
$725$	1.40527	−	21.4402i	0.0521903	−	0.796270i
$726$	10.3393	+	0.142361i	0.383726	+	0.00528350i
$727$	−3.04467	+	2.33626i	−0.112921	+	0.0866470i	−0.663678	−	0.748018i	$-0.731006\pi$
$727$	−3.04467	+	2.33626i	−0.112921	+	0.0866470i	0.550758	+	0.834665i	$0.314339\pi$
$728$	14.7201	+	3.46177i	0.545564	+	0.128302i
$729$	−0.360591	+	26.9976i	−0.0133552	+	0.999911i
$730$	−12.6755	+	10.8599i	−0.469143	+	0.401943i
$731$	−51.4909	−	17.4788i	−1.90446	−	0.646477i
$732$	15.4763	−	29.4777i	0.572019	−	1.08953i
$733$	−4.65934	+	9.44822i	−0.172097	+	0.348978i	−0.965784	−	0.259349i	$-0.916492\pi$
$733$	−4.65934	+	9.44822i	−0.172097	+	0.348978i	0.793687	+	0.608326i	$0.208159\pi$
$734$	7.31182	−	5.47765i	0.269884	−	0.202184i
$735$	−4.13486	+	3.60992i	−0.152517	+	0.133154i
$736$	−34.6617	+	17.4280i	−1.27765	+	0.642405i
$737$		−	54.9547i		−	2.02428i
$738$	−9.24165	−	5.53460i	−0.340190	−	0.203732i
$739$	12.0391	+	18.0178i	0.442866	+	0.662796i	0.984006	−	0.178137i	$-0.0570070\pi$
$739$	12.0391	+	18.0178i	0.442866	+	0.662796i	−0.541140	+	0.840933i	$0.682007\pi$
$740$	−6.48331	−	59.9002i	−0.238331	−	2.20198i
$741$	3.98173	+	9.67359i	0.146272	+	0.355368i
$742$	−1.34878	+	3.82766i	−0.0495154	+	0.140518i
$743$	−10.7142	−	8.22126i	−0.393064	−	0.301609i	0.393255	−	0.919430i	$-0.371349\pi$
$743$	−10.7142	−	8.22126i	−0.393064	−	0.301609i	−0.786319	+	0.617821i	$0.788016\pi$
$744$	38.7495	−	14.4020i	1.42062	−	0.528001i
$745$	47.5859	−	36.5139i	1.74341	−	1.33777i
$746$	24.5869	−	8.03086i	0.900190	−	0.294031i
$747$	9.79419	+	1.99355i	0.358351	+	0.0729403i
$748$	−17.7862	−	38.2693i	−0.650329	−	1.39926i
$749$	−8.60703	−	7.54816i	−0.314494	−	0.275804i
$750$	−6.96976	−	2.47344i	−0.254500	−	0.0903174i
$751$	1.04160	−	3.88731i	0.0380085	−	0.141850i	−0.944314	−	0.329045i	$-0.893273\pi$
$751$	1.04160	−	3.88731i	0.0380085	−	0.141850i	0.982323	+	0.187195i	$0.0599398\pi$
$752$	−6.78963	−	30.9978i	−0.247593	−	1.13037i
$753$	20.4547	+	41.7119i	0.745411	+	1.52006i
$754$	−11.6630	−	11.9354i	−0.424743	−	0.434662i
$755$	−32.2836	−	6.42162i	−1.17492	−	0.233707i
$756$	25.0089	+	4.05291i	0.909565	+	0.147403i
$757$	−9.77649	+	14.6316i	−0.355333	+	0.531793i	−0.965474	−	0.260500i	$-0.916113\pi$
$757$	−9.77649	+	14.6316i	−0.355333	+	0.531793i	0.610141	+	0.792293i	$0.291113\pi$
$758$	28.7077	−	18.7062i	1.04271	−	0.679441i
$759$	34.7761	+	30.6350i	1.26229	+	1.11198i
$760$	2.24546	+	23.2517i	0.0814515	+	0.843429i
$761$	−0.879816	+	1.14660i	−0.0318933	+	0.0415642i	−0.809028	−	0.587770i	$-0.800006\pi$
$761$	−0.879816	+	1.14660i	−0.0318933	+	0.0415642i	0.777134	+	0.629335i	$0.216672\pi$
$762$	−5.54736	−	7.43933i	−0.200960	−	0.269499i
$763$	−8.97864	+	26.4502i	−0.325049	+	0.957563i
$764$	−10.1535	−	41.7229i	−0.367340	−	1.50948i
$765$	−21.3257	−	43.7339i	−0.771031	−	1.58120i
$766$	−8.85304	−	6.95698i	−0.319873	−	0.251366i
$767$	5.39612	−	9.34636i	0.194843	−	0.337477i
$768$	4.61302	+	27.3262i	0.166458	+	0.986049i
$769$	8.13545	+	14.0910i	0.293372	+	0.508135i	0.974605	−	0.223932i	$-0.0718893\pi$
$769$	8.13545	+	14.0910i	0.293372	+	0.508135i	−0.681233	+	0.732067i	$0.738556\pi$
$770$	5.72637	−	39.9292i	0.206364	−	1.43895i
$771$	31.6021	−	31.4617i	1.13812	−	1.13306i
$772$	9.45713	+	2.76951i	0.340370	+	0.0996770i
$773$	−14.6599	+	2.91605i	−0.527282	+	0.104883i	−0.451551	−	0.892245i	$-0.649129\pi$
$773$	−14.6599	+	2.91605i	−0.527282	+	0.104883i	−0.0757309	+	0.997128i	$0.524129\pi$
$774$	8.98997	−	41.6987i	0.323138	−	1.49883i
$775$	−12.8949	−	31.1311i	−0.463199	−	1.11826i
$776$	1.69087	−	1.20680i	0.0606988	−	0.0433217i
$777$	−40.1965	+	13.5452i	−1.44204	+	0.485930i
$778$	−1.94785	−	36.0981i	−0.0698339	−	1.29418i
$779$	−6.97759	−	0.457335i	−0.249998	−	0.0163857i
$780$	20.0117	−	10.8880i	0.716534	−	0.389854i
$781$	−4.05958	+	4.62906i	−0.145263	+	0.165641i
$782$	14.1605	−	50.5083i	0.506377	−	1.80617i
$783$	−20.8971	−	18.5746i	−0.746801	−	0.663801i
$784$	−1.28130	+	4.02812i	−0.0457607	+	0.143862i
$785$	10.6611	−	2.85662i	0.380509	−	0.101957i
$786$	1.62617	+	8.80736i	0.0580036	+	0.314148i
$787$	−13.3042	+	4.51618i	−0.474245	+	0.160985i	−0.548321	−	0.836268i	$-0.684733\pi$
$787$	−13.3042	+	4.51618i	−0.474245	+	0.160985i	0.0740757	+	0.997253i	$0.476399\pi$
$788$	−19.2946	+	27.4814i	−0.687342	+	0.978983i
$789$	−2.82863	−	21.8615i	−0.100702	−	0.778290i
$790$	−7.35211	+	34.8542i	−0.261576	+	1.24006i
$791$	28.1201	+	11.6477i	0.999835	+	0.414145i
$792$	28.2233	−	17.3027i	1.00287	−	0.614825i
$793$	−19.4727	+	8.06586i	−0.691496	+	0.286427i
$794$	−31.3352	+	5.85783i	−1.11205	+	0.207886i
$795$	2.32723	+	5.65399i	0.0825382	+	0.200526i
$796$	−5.93355	−	2.61981i	−0.210309	−	0.0928567i
$797$	−2.11596	+	4.29074i	−0.0749511	+	0.151986i	−0.931123	−	0.364705i	$-0.881170\pi$
$797$	−2.11596	+	4.29074i	−0.0749511	+	0.151986i	0.856172	+	0.516691i	$0.172836\pi$
$798$	15.6444	−	5.07144i	0.553805	−	0.179527i
$799$	37.1568	+	21.4525i	1.31451	+	0.758934i
$800$	22.1201	−	4.57821i	0.782065	−	0.161864i
$801$	4.41090	−	5.69571i	0.155851	−	0.201248i
$802$	−0.0252016	−	0.210140i	−0.000889901	−	0.00742032i
$803$	15.3222	−	1.00427i	0.540708	−	0.0354398i
$804$	−26.0732	−	41.2440i	−0.919530	−	1.45456i
$805$	37.6975	−	33.0598i	1.32866	−	1.16520i
$806$	−24.6831	−	8.69778i	−0.869425	−	0.306366i
$807$	−1.37908	−	21.7836i	−0.0485459	−	0.766817i
$808$	−11.5034	+	12.2353i	−0.404687	+	0.430437i
$809$	21.3440	+	8.84096i	0.750414	+	0.310831i	0.724910	−	0.688843i	$-0.241881\pi$
$809$	21.3440	+	8.84096i	0.750414	+	0.310831i	0.0255033	+	0.999675i	$0.491881\pi$
$810$	32.1636	−	20.5525i	1.13011	−	0.722140i
$811$	−32.4768	−	21.7003i	−1.14041	−	0.762000i	−0.165859	−	0.986150i	$-0.553040\pi$
$811$	−32.4768	−	21.7003i	−1.14041	−	0.762000i	−0.974555	+	0.224150i	$0.928040\pi$
$812$	−20.1185	+	16.8380i	−0.706022	+	0.590899i
$813$	15.0027	+	8.70640i	0.526168	+	0.305347i
$814$	−28.2651	+	47.6771i	−0.990691	+	1.67108i
$815$	2.08857	−	7.79466i	0.0731595	−	0.273035i
$816$	−31.5055	−	20.2828i	−1.10291	−	0.710038i
$817$	−7.16666	−	26.7463i	−0.250730	−	0.935736i
$818$	17.9033	+	5.01934i	0.625973	+	0.175497i
$819$	−10.5214	−	12.1057i	−0.367649	−	0.423007i
$820$	0.644967	+	15.2147i	0.0225232	+	0.531322i
$821$	−21.0147	−	42.6135i	−0.733417	−	1.48722i	−0.868130	−	0.496337i	$-0.834678\pi$
$821$	−21.0147	−	42.6135i	−0.733417	−	1.48722i	0.134713	−	0.990885i	$-0.456989\pi$
$822$	9.13292	−	32.2990i	0.318547	−	1.12656i
$823$	−11.9536	+	1.57372i	−0.416676	+	0.0548564i	−0.335950	−	0.941880i	$-0.609057\pi$
$823$	−11.9536	+	1.57372i	−0.416676	+	0.0548564i	−0.0807260	+	0.996736i	$0.525724\pi$
$824$	38.8477	−	20.6697i	1.35332	−	0.720062i
$825$	−14.9416	−	22.4698i	−0.520200	−	0.782299i
$826$	−13.9975	−	9.58835i	−0.487035	−	0.333621i
$827$	12.3544	−	2.45745i	0.429606	−	0.0854539i	0.0244490	−	0.999701i	$-0.492217\pi$
$827$	12.3544	−	2.45745i	0.429606	−	0.0854539i	0.405157	+	0.914247i	$0.367217\pi$
$828$	40.6345	+	6.49238i	1.41215	+	0.225626i
$829$	0.119482	−	0.0798352i	0.00414977	−	0.00277279i	−0.553494	−	0.832853i	$-0.686706\pi$
$829$	0.119482	−	0.0798352i	0.00414977	−	0.00277279i	0.557643	+	0.830081i	$0.311706\pi$
$830$	−5.25619	−	13.1157i	−0.182445	−	0.455253i
$831$	20.4735	+	23.4506i	0.710217	+	0.813493i
$832$	8.82982	−	15.1602i	0.306119	−	0.525587i
$833$	−2.85761	−	4.94953i	−0.0990103	−	0.171491i
$834$	21.7671	+	33.5682i	0.753734	+	1.16237i
$835$	0.292329	+	4.46007i	0.0101164	+	0.154347i
$836$	11.1714	−	18.3575i	0.386373	−	0.634906i
$837$	−42.2762	−	11.6310i	−1.46128	−	0.402026i
$838$	−1.86520	+	24.1780i	−0.0644321	+	0.835214i
$839$	18.0257	+	2.37313i	0.622316	+	0.0819295i	0.435089	−	0.900387i	$-0.356717\pi$
$839$	18.0257	+	2.37313i	0.622316	+	0.0819295i	0.187227	+	0.982317i	$0.440050\pi$
$840$	−14.6467	−	32.6841i	−0.505358	−	1.12771i
$841$	−0.0476213	+	0.00626946i	−0.00164211	+	0.000216188i
$842$	26.5299	−	1.43155i	0.914280	−	0.0493345i
$843$	−32.7176	+	4.23328i	−1.12685	+	0.145802i
$844$	16.3101	−	31.2346i	0.561416	−	1.07514i
$845$	24.0907	+	4.79194i	0.828745	+	0.164848i
$846$	−13.3759	+	30.8856i	−0.459872	+	1.06187i
$847$	−7.27699	+	7.27699i	−0.250040	+	0.250040i
$848$	3.79007	+	2.79380i	0.130152	+	0.0959395i
$849$	−40.6338	−	27.2817i	−1.39455	−	0.936305i
$850$	−15.5753	+	26.2721i	−0.534227	+	0.901126i
$851$	−65.2388	+	22.1456i	−2.23636	+	0.759141i
$852$	−0.850496	+	5.40021i	−0.0291375	+	0.185008i
$853$	4.01379	−	1.97938i	0.137430	−	0.0677727i	−0.372274	−	0.928123i	$-0.621422\pi$
$853$	4.01379	−	1.97938i	0.137430	−	0.0677727i	0.509703	+	0.860350i	$0.329755\pi$
$854$	10.2882	+	31.4979i	0.352056	+	1.07784i
$855$	12.4839	−	21.4021i	0.426939	−	0.731936i
$856$	−11.2924	+	6.99230i	−0.385965	+	0.238992i
$857$	4.93365	−	37.4748i	0.168530	−	1.28011i	−0.672894	−	0.739739i	$-0.734949\pi$
$857$	4.93365	−	37.4748i	0.168530	−	1.28011i	0.841424	−	0.540376i	$-0.181718\pi$
$858$	−20.7389	−	3.02136i	−0.708014	−	0.103147i
$859$	−0.410863	+	0.360317i	−0.0140185	+	0.0122939i	−0.666326	−	0.745660i	$-0.732134\pi$
$859$	−0.410863	+	0.360317i	−0.0140185	+	0.0122939i	0.652308	+	0.757954i	$0.273801\pi$
$860$	−56.2305	+	21.7848i	−1.91744	+	0.742856i
$861$	10.3620	−	2.75177i	0.353134	−	0.0937801i
$862$	−12.0897	−	5.17201i	−0.411778	−	0.176159i
$863$		−	3.01900i		−	0.102768i	−0.998679	−	0.0513839i	$-0.983637\pi$
$863$		−	3.01900i		−	0.102768i	0.998679	−	0.0513839i	$-0.0163632\pi$
$864$	12.9726	−	26.3763i	0.441337	−	0.897342i
$865$		−	69.0785i		−	2.34874i
$866$	21.2933	−	49.7738i	0.723576	−	1.69138i
$867$	20.5064	−	5.44578i	0.696433	−	0.184948i
$868$	−16.6181	+	37.6379i	−0.564054	+	1.27751i
$869$	24.6370	−	21.6061i	0.835753	−	0.732936i
$870$	−5.69807	+	39.1121i	−0.193183	+	1.32602i
$871$	−4.03198	+	30.6260i	−0.136619	+	1.03772i
$872$	26.3063	+	18.9267i	0.890845	+	0.640938i
$873$	−2.20335	−	0.00980909i	−0.0745721	−	0.000331987i
$874$	25.3915	−	8.29368i	0.858881	−	0.280538i
$875$	6.60151	−	3.25550i	0.223172	−	0.110056i
$876$	11.0229	−	8.02329i	0.372431	−	0.271082i
$877$	48.8778	−	16.5918i	1.65049	−	0.560264i	0.667606	−	0.744515i	$-0.267319\pi$
$877$	48.8778	−	16.5918i	1.65049	−	0.560264i	0.982879	+	0.184251i	$0.0589858\pi$
$878$	−9.77596	−	5.79562i	−0.329923	−	0.195593i
$879$	4.32660	+	2.90489i	0.145933	+	0.0979796i
$880$	−42.3648	−	19.8859i	−1.42812	−	0.670355i
$881$	22.0746	−	22.0746i	0.743711	−	0.743711i	−0.229579	−	0.973290i	$-0.573735\pi$
$881$	22.0746	−	22.0746i	0.743711	−	0.743711i	0.973290	+	0.229579i	$0.0737350\pi$
$882$	3.60012	−	2.67209i	0.121222	−	0.0899739i
$883$	−20.3533	−	4.04851i	−0.684942	−	0.136243i	−0.159660	−	0.987172i	$-0.551040\pi$
$883$	−20.3533	−	4.04851i	−0.684942	−	0.136243i	−0.525281	+	0.850929i	$0.676040\pi$
$884$	7.10438	+	22.6322i	0.238946	+	0.761204i
$885$	−25.3502	+	3.28002i	−0.852137	+	0.110257i
$886$	−1.64601	−	30.5043i	−0.0552988	−	1.02481i
$887$	14.8640	−	1.95688i	0.499083	−	0.0657056i	0.123218	−	0.992380i	$-0.460679\pi$
$887$	14.8640	−	1.95688i	0.499083	−	0.0657056i	0.375866	+	0.926674i	$0.377345\pi$
$888$	1.40716	+	49.1924i	0.0472213	+	1.65079i
$889$	9.15692	+	1.20553i	0.307113	+	0.0404322i
$890$	−10.1539	−	0.783319i	−0.340360	−	0.0262569i
$891$	−35.0161	−	2.60838i	−1.17308	−	0.0873841i
$892$	−47.3195	+	11.5155i	−1.58437	+	0.385566i
$893$	1.42894	+	21.8014i	0.0478176	+	0.729556i
$894$	−41.1067	+	26.6554i	−1.37481	+	0.891489i
$895$	8.17159	+	14.1536i	0.273146	+	0.473103i
$896$	−22.6953	−	15.6735i	−0.758197	−	0.523616i
$897$	−17.1329	−	19.6242i	−0.572050	−	0.655234i
$898$	26.9591	−	10.8040i	0.899638	−	0.360534i
$899$	37.7523	−	25.2252i	1.25911	−	0.841309i
$900$	−21.8746	−	9.77476i	−0.729153	−	0.325825i
$901$	−6.24392	+	1.24199i	−0.208015	+	0.0413768i
$902$	7.91695	−	11.5575i	0.263606	−	0.384823i
$903$	23.5079	+	35.3521i	0.782292	+	1.17644i
$904$	22.4542	−	27.2546i	0.746814	−	0.906476i
$905$	20.0386	−	2.63813i	0.666105	−	0.0876944i
$906$	25.8717	+	7.31551i	0.859529	+	0.243042i
$907$	2.65618	+	5.38620i	0.0881969	+	0.178846i	0.936502	−	0.350662i	$-0.114043\pi$
$907$	2.65618	+	5.38620i	0.0881969	+	0.178846i	−0.848305	+	0.529508i	$0.822377\pi$
$908$	−3.49647	+	3.80603i	−0.116034	+	0.126308i
$909$	17.4855	−	3.39723i	0.579958	−	0.112679i
$910$	−6.12085	+	21.8322i	−0.202904	+	0.723730i
$911$	−1.66589	−	6.21718i	−0.0551933	−	0.205984i	0.932823	−	0.360336i	$-0.117338\pi$
$911$	−1.66589	−	6.21718i	−0.0551933	−	0.205984i	−0.988016	+	0.154351i	$0.950671\pi$
$912$	−0.325408	−	19.0777i	−0.0107754	−	0.631726i
$913$	−3.36423	+	12.5555i	−0.111340	+	0.415526i
$914$	−20.2864	−	12.0267i	−0.671014	−	0.397806i
$915$	43.1774	+	25.0568i	1.42740	+	0.828352i
$916$	0.956160	−	10.7717i	0.0315924	−	0.355906i
$917$	−7.41153	−	4.95223i	−0.244750	−	0.163537i
$918$	14.5374	+	36.9885i	0.479806	+	1.22080i
$919$	−26.8367	−	11.1161i	−0.885262	−	0.366688i	−0.106727	−	0.994288i	$-0.534037\pi$
$919$	−26.8367	−	11.1161i	−0.885262	−	0.366688i	−0.778535	+	0.627601i	$0.784037\pi$
$920$	−23.9075	−	53.0330i	−0.788207	−	1.74845i
$921$	3.22239	+	50.9000i	0.106181	+	1.67721i
$922$	−3.67857	+	10.4393i	−0.121147	+	0.343799i
$923$	2.60201	−	2.28190i	0.0856463	−	0.0751098i
$924$	−7.24360	+	32.1419i	−0.238297	+	1.05739i
$925$	40.0277	−	2.62355i	1.31610	−	0.0862619i
$926$	−36.3684	+	4.36158i	−1.19514	+	0.143330i
$927$	−46.2468	−	6.29808i	−1.51894	−	0.206856i
$928$	11.8653	+	28.0299i	0.389499	+	0.920127i
$929$	−49.1482	−	28.3757i	−1.61250	−	0.930977i	−0.988789	−	0.149322i	$-0.952291\pi$
$929$	−49.1482	−	28.3757i	−1.61250	−	0.930977i	−0.623711	−	0.781655i	$-0.714376\pi$
$930$	19.1146	+	58.9647i	0.626792	+	1.93353i
$931$	1.28720	−	2.61019i	0.0421863	−	0.0855454i
$932$	−11.9991	+	4.64869i	−0.393044	+	0.152273i
$933$	3.35353	+	8.14740i	0.109790	+	0.266734i
$934$	−10.4941	−	56.1359i	−0.343377	−	1.83682i
$935$	58.4602	−	24.2150i	1.91185	−	0.791916i
$936$	−16.9982	+	7.57199i	−0.555603	+	0.247498i
$937$	−15.2659	−	6.32334i	−0.498715	−	0.206575i	0.119123	−	0.992879i	$-0.461992\pi$
$937$	−15.2659	−	6.32334i	−0.498715	−	0.206575i	−0.617839	+	0.786305i	$0.711992\pi$
$938$	47.5173	+	10.0233i	1.55149	+	0.327271i
$939$	0.138314	+	1.06898i	0.00451371	+	0.0348849i
$940$	46.8686	−	8.20295i	1.52868	−	0.267551i
$941$	5.14508	−	1.74652i	0.167725	−	0.0569349i	−0.236314	−	0.971677i	$-0.575939\pi$
$941$	5.14508	−	1.74652i	0.167725	−	0.0569349i	0.404039	+	0.914742i	$0.367606\pi$
$942$	−8.86534	+	1.63688i	−0.288848	+	0.0533323i
$943$	16.8201	−	4.50693i	0.547738	−	0.146766i
$944$	−15.3830	+	12.2821i	−0.500673	+	0.399750i
$945$	−7.65981	+	37.2081i	−0.249174	+	1.21038i
$946$	53.4150	+	14.9754i	1.73667	+	0.486891i
$947$	−13.8529	+	15.7963i	−0.450160	+	0.513309i	−0.931756	−	0.363084i	$-0.881724\pi$
$947$	−13.8529	+	15.7963i	−0.450160	+	0.513309i	0.481596	+	0.876393i	$0.340057\pi$
$948$	8.23931	−	27.9045i	0.267600	−	0.906298i
$949$	−8.61265	−	0.564503i	−0.279578	−	0.0183245i
$950$	−15.5301	+	0.838003i	−0.503862	+	0.0271884i
$951$	−24.5178	+	8.26185i	−0.795044	+	0.267909i
$952$	36.3341	−	8.39910i	1.17759	−	0.272216i
$953$	5.12740	+	12.3786i	0.166093	+	0.400983i	0.984909	−	0.173072i	$-0.0553694\pi$
$953$	5.12740	+	12.3786i	0.166093	+	0.400983i	−0.818816	+	0.574055i	$0.805369\pi$
$954$	−1.52947	−	4.75415i	−0.0495183	−	0.153921i
$955$	63.1493	−	12.5612i	2.04346	−	0.406470i
$956$	−5.30609	−	9.70087i	−0.171611	−	0.313749i
$957$	25.7677	−	25.6533i	0.832953	−	0.829253i
$958$	26.2149	+	3.75956i	0.846966	+	0.121466i
$959$	16.7032	+	28.9307i	0.539373	+	0.934222i
$960$	−41.2300	+	5.17534i	−1.33069	+	0.167034i
$961$	20.1029	−	34.8192i	0.648479	−	1.12320i
$962$	19.2500	−	24.4964i	0.620646	−	0.789797i
$963$	14.0532	+	0.983946i	0.452858	+	0.0317072i
$964$	37.1032	+	22.5792i	1.19502	+	0.727227i
$965$	−4.74956	+	13.9917i	−0.152894	+	0.450410i
$966$	−32.8318	+	24.4820i	−1.05635	+	0.787696i
$967$	25.8595	−	33.7008i	0.831587	−	1.08375i	−0.163675	−	0.986514i	$-0.552335\pi$
$967$	25.8595	−	33.7008i	0.831587	−	1.08375i	0.995262	−	0.0972307i	$-0.0309985\pi$
$968$	5.60839	+	10.5407i	0.180260	+	0.338791i
$969$	19.3583	+	17.0531i	0.621877	+	0.547825i
$970$	1.70052	+	2.60971i	0.0546003	+	0.0837928i
$971$	6.62690	−	9.91785i	0.212667	−	0.318279i	−0.709765	−	0.704439i	$-0.751199\pi$
$971$	6.62690	−	9.91785i	0.212667	−	0.318279i	0.922432	+	0.386160i	$0.126199\pi$
$972$	−27.5174	+	14.6557i	−0.882622	+	0.470083i
$973$	−39.0532	−	7.76816i	−1.25199	−	0.249036i
$974$	−11.3961	+	11.1361i	−0.365156	+	0.356822i
$975$	6.67829	+	13.6186i	0.213876	+	0.436143i
$976$	38.4368	−	0.741202i	1.23033	−	0.0237253i
$977$	−7.73388	+	28.8632i	−0.247429	+	0.923416i	0.724718	+	0.689045i	$0.241970\pi$
$977$	−7.73388	+	28.8632i	−0.247429	+	0.923416i	−0.972147	+	0.234371i	$0.924697\pi$
$978$	−2.20444	+	6.21175i	−0.0704902	+	0.198630i
$979$	7.04373	+	6.17719i	0.225119	+	0.197424i
$980$	−5.95311	−	2.17531i	−0.190165	−	0.0694876i
$981$	−10.9039	−	32.5979i	−0.348135	−	1.04077i
$982$	−2.20488	−	6.75035i	−0.0703605	−	0.215412i
$983$	36.0538	−	27.6651i	1.14994	−	0.882379i	0.155514	−	0.987834i	$-0.450297\pi$
$983$	36.0538	−	27.6651i	1.14994	−	0.882379i	0.994424	+	0.105455i	$0.0336299\pi$
$984$	0.458290	−	12.4302i	0.0146097	−	0.396260i
$985$	−39.9442	−	30.6503i	−1.27273	−	0.976598i
$986$	−38.8150	−	13.6775i	−1.23612	−	0.435581i
$987$	−12.7502	−	30.9766i	−0.405844	−	0.985996i
$988$	−7.57266	+	9.41088i	−0.240919	+	0.299400i
$989$	38.3096	+	57.3344i	1.21818	+	1.82313i
$990$	24.1287	+	43.3798i	0.766859	+	1.37870i
$991$		−	24.7145i		−	0.785081i	−0.919735	−	0.392540i	$-0.871596\pi$
$991$		−	24.7145i		−	0.785081i	0.919735	−	0.392540i	$-0.128404\pi$
$992$	36.1312	+	31.1949i	1.14717	+	0.990438i
$993$	−6.39877	+	5.58642i	−0.203059	+	0.177280i
$994$	−3.26215	−	4.35447i	−0.103469	−	0.138115i
$995$	4.30152	−	8.72261i	0.136367	−	0.276525i
$996$	3.43205	+	11.0191i	0.108749	+	0.349155i
$997$	−16.8982	−	5.73617i	−0.535171	−	0.181666i	0.0407529	−	0.999169i	$-0.487024\pi$
$997$	−16.8982	−	5.73617i	−0.535171	−	0.181666i	−0.575924	+	0.817503i	$0.695358\pi$
$998$	35.0233	+	40.8787i	1.10864	+	1.29399i
$999$	29.2887	−	43.2063i	0.926654	−	1.36699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bm.a.205.84	yes	1504
9.4	even	3	inner	576.2.bm.a.13.42	✓	1504
64.5	even	16	inner	576.2.bm.a.133.42	yes	1504
576.517	even	48	inner	576.2.bm.a.517.84	yes	1504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.2.bm.a.13.42	✓	1504	9.4	even	3	inner
576.2.bm.a.133.42	yes	1504	64.5	even	16	inner
576.2.bm.a.205.84	yes	1504	1.1	even	1	trivial
576.2.bm.a.517.84	yes	1504	576.517	even	48	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bm (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31272 - 0.526080i) q^{2} +(-0.444563 - 1.67403i) q^{3} +(1.44648 - 1.38119i) q^{4} +(1.97729 + 2.25467i) q^{5} +(-1.46426 - 1.96366i) q^{6} +(2.41702 + 0.318207i) q^{7} +(1.17221 - 2.57409i) q^{8} +(-2.60473 + 1.48842i) q^{9} +O(q^{10})\)	\(q+(1.31272 - 0.526080i) q^{2} +(-0.444563 - 1.67403i) q^{3} +(1.44648 - 1.38119i) q^{4} +(1.97729 + 2.25467i) q^{5} +(-1.46426 - 1.96366i) q^{6} +(2.41702 + 0.318207i) q^{7} +(1.17221 - 2.57409i) q^{8} +(-2.60473 + 1.48842i) q^{9} +(3.78177 + 1.91954i) q^{10} +(-1.72557 - 3.49911i) q^{11} +(-2.95521 - 1.80742i) q^{12} +(0.704925 + 2.07664i) q^{13} +(3.34028 - 0.853829i) q^{14} +(2.89534 - 4.31238i) q^{15} +(0.184609 - 3.99574i) q^{16} +(3.82425 + 3.82425i) q^{17} +(-2.63626 + 3.32418i) q^{18} +(-0.537285 + 2.70111i) q^{19} +(5.97424 + 0.530311i) q^{20} +(-0.541831 - 4.18762i) q^{21} +(-4.10601 - 3.68557i) q^{22} +(-0.895190 - 6.79964i) q^{23} +(-4.83021 - 0.817965i) q^{24} +(-0.521217 + 3.95904i) q^{25} +(2.01785 + 2.35521i) q^{26} +(3.64962 + 3.69869i) q^{27} +(3.93568 - 2.87810i) q^{28} +(-5.36918 + 0.351915i) q^{29} +(1.53213 - 7.18413i) q^{30} +(-7.30782 + 4.21917i) q^{31} +(-1.85974 - 5.34241i) q^{32} +(-5.09048 + 4.44423i) q^{33} +(7.03204 + 3.00832i) q^{34} +(4.06170 + 6.07877i) q^{35} +(-1.71189 + 5.75060i) q^{36} +(-1.95977 - 9.85245i) q^{37} +(0.715696 + 3.82847i) q^{38} +(3.16297 - 2.10326i) q^{39} +(8.12151 - 2.44678i) q^{40} +(0.331410 + 2.51731i) q^{41} +(-2.91430 - 5.21214i) q^{42} +(-9.01742 + 4.44690i) q^{43} +(-7.32896 - 2.67805i) q^{44} +(-8.50619 - 2.92976i) q^{45} +(-4.75229 - 8.45510i) q^{46} +(7.66285 - 2.05325i) q^{47} +(-6.77104 + 1.46732i) q^{48} +(-1.02074 - 0.273507i) q^{49} +(1.39856 + 5.47132i) q^{50} +(4.70177 - 8.10201i) q^{51} +(3.88790 + 2.03018i) q^{52} +(-0.653975 + 0.978744i) q^{53} +(6.73674 + 2.93536i) q^{54} +(4.47738 - 10.8093i) q^{55} +(3.65235 - 5.84862i) q^{56} +(4.76059 - 0.301385i) q^{57} +(-6.86311 + 3.28659i) q^{58} +(-3.24475 - 3.69993i) q^{59} +(-1.76817 - 10.2368i) q^{60} +(0.628588 + 9.59040i) q^{61} +(-7.37352 + 9.38310i) q^{62} +(-6.76931 + 2.76870i) q^{63} +(-5.25185 - 6.03473i) q^{64} +(-3.28829 + 5.69549i) q^{65} +(-4.34437 + 8.51203i) q^{66} +(12.6331 + 6.22993i) q^{67} +(10.8137 + 0.249671i) q^{68} +(-10.9848 + 4.52144i) q^{69} +(8.52981 + 5.84295i) q^{70} +(-0.603921 - 1.45800i) q^{71} +(0.778036 + 8.44954i) q^{72} +(-1.50613 + 3.63613i) q^{73} +(-7.75582 - 11.9025i) q^{74} +(6.85925 - 0.887509i) q^{75} +(2.95359 + 4.64920i) q^{76} +(-3.05730 - 9.00652i) q^{77} +(3.04562 - 4.42497i) q^{78} +(2.17386 + 8.11296i) q^{79} +(9.37408 - 7.48450i) q^{80} +(4.56922 - 7.75385i) q^{81} +(1.75935 + 3.13018i) q^{82} +(-2.50488 - 2.19672i) q^{83} +(-6.56766 - 5.30894i) q^{84} +(-1.06076 + 16.1841i) q^{85} +(-9.49795 + 10.5814i) q^{86} +(2.97605 + 8.83171i) q^{87} +(-11.0298 + 0.340082i) q^{88} +(-2.21853 + 0.918946i) q^{89} +(-12.7076 + 0.628976i) q^{90} +(1.04302 + 5.24360i) q^{91} +(-10.6865 - 8.59912i) q^{92} +(10.3118 + 10.3578i) q^{93} +(8.97901 - 6.72662i) q^{94} +(-7.15248 + 4.12949i) q^{95} +(-8.11657 + 5.48829i) q^{96} +(0.636059 + 0.367229i) q^{97} +(-1.48384 + 0.177953i) q^{98} +(9.70279 + 6.54586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9	\( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) 1504 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 - 16 * q^12 - 8 * q^13 - 8 * q^14 - 16 * q^15 - 8 * q^16 - 32 * q^17 - 16 * q^18 - 32 * q^19 - 8 * q^20 - 16 * q^21 - 8 * q^22 - 8 * q^23 + 64 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 96 * q^30 - 8 * q^32 - 8 * q^34 - 32 * q^35 - 96 * q^36 - 32 * q^37 - 8 * q^38 - 16 * q^39 - 8 * q^40 - 8 * q^41 + 64 * q^42 - 8 * q^43 - 32 * q^44 - 16 * q^45 - 32 * q^46 - 8 * q^47 - 16 * q^48 - 8 * q^49 - 8 * q^50 - 16 * q^51 - 8 * q^52 - 32 * q^53 - 16 * q^54 - 32 * q^55 - 8 * q^56 - 16 * q^57 - 80 * q^58 - 8 * q^59 - 16 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 - 32 * q^64 - 16 * q^65 - 32 * q^66 - 8 * q^67 - 8 * q^68 - 16 * q^69 - 8 * q^70 - 32 * q^71 - 16 * q^72 - 32 * q^73 - 8 * q^74 - 16 * q^75 + 40 * q^76 - 8 * q^77 - 40 * q^78 - 8 * q^79 - 160 * q^80 - 16 * q^81 - 32 * q^82 - 8 * q^83 - 128 * q^84 - 8 * q^85 - 216 * q^86 - 16 * q^87 - 8 * q^88 - 32 * q^89 - 160 * q^90 - 32 * q^91 + 144 * q^92 - 40 * q^93 - 8 * q^94 - 152 * q^96 - 304 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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