LMFDB - Embedded newform 525.2.j.a.218.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.3
Root			$1.47240 + 0.912166i$ of defining polynomial
Character	$\chi$	$=$	525.218
Dual form			525.2.j.a.407.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.560232 - 0.560232i) q^{2} +(-1.73122 + 0.0537601i) q^{3} -1.37228i q^{4} +(1.00000 + 0.939764i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.88926 + 1.88926i) q^{8} +(2.99422 - 0.186141i) q^{9} +O(q^{10})$	\(q+(-0.560232 - 0.560232i) q^{2} +(-1.73122 + 0.0537601i) q^{3} -1.37228i q^{4} +(1.00000 + 0.939764i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.88926 + 1.88926i) q^{8} +(2.99422 - 0.186141i) q^{9} +4.10891i q^{11} +(0.0737740 + 2.37572i) q^{12} +(1.67746 + 1.67746i) q^{13} +0.792287 q^{14} -0.627719 q^{16} +(0.664513 + 0.664513i) q^{17} +(-1.78174 - 1.57317i) q^{18} -4.00000i q^{19} +(1.18614 - 1.26217i) q^{21} +(2.30194 - 2.30194i) q^{22} +(2.44949 - 2.44949i) q^{23} +(3.16915 - 3.37228i) q^{24} -1.87953i q^{26} +(-5.17364 + 0.483219i) q^{27} +(0.970349 + 0.970349i) q^{28} +5.98844 q^{29} +4.74456 q^{31} +(4.13018 + 4.13018i) q^{32} +(-0.220895 - 7.11342i) q^{33} -0.744563i q^{34} +(-0.255437 - 4.10891i) q^{36} +(3.35491 - 3.35491i) q^{37} +(-2.24093 + 2.24093i) q^{38} +(-2.99422 - 2.81386i) q^{39} +11.9769i q^{41} +(-1.37162 + 0.0425934i) q^{42} +(5.65685 + 5.65685i) q^{43} +5.63858 q^{44} -2.74456 q^{46} +(-3.11400 - 3.11400i) q^{47} +(1.08672 - 0.0337462i) q^{48} -1.00000i q^{49} +(-1.18614 - 1.11469i) q^{51} +(2.30194 - 2.30194i) q^{52} +(8.46893 - 8.46893i) q^{53} +(3.16915 + 2.62772i) q^{54} -2.67181i q^{56} +(0.215040 + 6.92487i) q^{57} +(-3.35491 - 3.35491i) q^{58} -11.9769 q^{59} +6.74456 q^{61} +(-2.65805 - 2.65805i) q^{62} +(-1.98561 + 2.24885i) q^{63} -3.37228i q^{64} +(-3.86141 + 4.10891i) q^{66} +(9.01177 - 9.01177i) q^{67} +(0.911899 - 0.911899i) q^{68} +(-4.10891 + 4.37228i) q^{69} -1.87953i q^{71} +(-5.30519 + 6.00852i) q^{72} +(9.01177 + 9.01177i) q^{73} -3.75906 q^{74} -5.48913 q^{76} +(-2.90544 - 2.90544i) q^{77} +(0.101044 + 3.25387i) q^{78} +15.1168i q^{79} +(8.93070 - 1.11469i) q^{81} +(6.70982 - 6.70982i) q^{82} +(-11.8303 + 11.8303i) q^{83} +(-1.73205 - 1.62772i) q^{84} -6.33830i q^{86} +(-10.3673 + 0.321939i) q^{87} +(-7.76280 - 7.76280i) q^{88} -3.75906 q^{89} -2.37228 q^{91} +(-3.36139 - 3.36139i) q^{92} +(-8.21386 + 0.255068i) q^{93} +3.48913i q^{94} +(-7.37228 - 6.92820i) q^{96} +(-1.67746 + 1.67746i) q^{97} +(-0.560232 + 0.560232i) q^{98} +(0.764836 + 12.3030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{6}+O(q^{10}) $ 16 * q + 16 * q^6	$ 16 q + 16 q^{6} - 56 q^{16} - 4 q^{21} - 16 q^{31} - 96 q^{36} + 48 q^{46} + 4 q^{51} + 16 q^{61} + 168 q^{66} + 96 q^{76} + 28 q^{81} + 8 q^{91} - 72 q^{96}+O(q^{100}) $ 16 * q + 16 * q^6 - 56 * q^16 - 4 * q^21 - 16 * q^31 - 96 * q^36 + 48 * q^46 + 4 * q^51 + 16 * q^61 + 168 * q^66 + 96 * q^76 + 28 * q^81 + 8 * q^91 - 72 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.560232	−	0.560232i	−0.396143	−	0.396143i	0.480727	−	0.876870i	$-0.340373\pi$
$2$	−0.560232	−	0.560232i	−0.396143	−	0.396143i	−0.876870	+	0.480727i	$0.840373\pi$
$3$	−1.73122	+	0.0537601i	−0.999518	+	0.0310384i
$3$	−1.73122	+	0.0537601i	−0.999518	+	0.0310384i
$4$		−	1.37228i		−	0.686141i
$5$		0			0
$5$		0			0
$6$	1.00000	+	0.939764i	0.408248	+	0.383657i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.88926	+	1.88926i	−0.667954	+	0.667954i
$9$	2.99422	−	0.186141i	0.998073	−	0.0620469i
$10$		0			0
$11$			4.10891i			1.23888i	0.785043	+	0.619442i	$0.212641\pi$
$11$			4.10891i			1.23888i	−0.785043	+	0.619442i	$0.787359\pi$
$12$	0.0737740	+	2.37572i	0.0212967	+	0.685810i
$13$	1.67746	+	1.67746i	0.465243	+	0.465243i	0.900369	−	0.435127i	$-0.143296\pi$
$13$	1.67746	+	1.67746i	0.465243	+	0.465243i	−0.435127	+	0.900369i	$0.643296\pi$
$14$	0.792287			0.211748
$15$		0			0
$16$	−0.627719			−0.156930
$17$	0.664513	+	0.664513i	0.161168	+	0.161168i	0.783084	−	0.621916i	$-0.213645\pi$
$17$	0.664513	+	0.664513i	0.161168	+	0.161168i	−0.621916	+	0.783084i	$0.713645\pi$
$18$	−1.78174	−	1.57317i	−0.419960	−	0.370801i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$	1.18614	−	1.26217i	0.258837	−	0.275428i
$22$	2.30194	−	2.30194i	0.490776	−	0.490776i
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	−0.404004	−	0.914757i	$-0.632382\pi$
$23$	2.44949	−	2.44949i	0.510754	−	0.510754i	0.914757	+	0.404004i	$0.132382\pi$
$24$	3.16915	−	3.37228i	0.646900	−	0.688364i
$25$		0			0
$26$		−	1.87953i		−	0.368606i
$27$	−5.17364	+	0.483219i	−0.995667	+	0.0929956i
$28$	0.970349	+	0.970349i	0.183379	+	0.183379i
$29$	5.98844			1.11203			0.556013	−	0.831174i	$-0.312331\pi$
$29$	5.98844			1.11203			0.556013	+	0.831174i	$0.312331\pi$
$30$		0			0
$31$	4.74456			0.852149			0.426074	−	0.904688i	$-0.359896\pi$
$31$	4.74456			0.852149			0.426074	+	0.904688i	$0.359896\pi$
$32$	4.13018	+	4.13018i	0.730120	+	0.730120i
$33$	−0.220895	−	7.11342i	−0.0384530	−	1.23829i
$34$		−	0.744563i		−	0.127691i
$35$		0			0
$36$	−0.255437	−	4.10891i	−0.0425729	−	0.684819i
$37$	3.35491	−	3.35491i	0.551544	−	0.551544i	−0.375342	−	0.926886i	$-0.622475\pi$
$37$	3.35491	−	3.35491i	0.551544	−	0.551544i	0.926886	+	0.375342i	$0.122475\pi$
$38$	−2.24093	+	2.24093i	−0.363526	+	0.363526i
$39$	−2.99422	−	2.81386i	−0.479459	−	0.450578i
$40$		0			0
$41$			11.9769i			1.87047i	0.354022	+	0.935237i	$0.384814\pi$
$41$			11.9769i			1.87047i	−0.354022	+	0.935237i	$0.615186\pi$
$42$	−1.37162	+	0.0425934i	−0.211646	+	0.00657231i
$43$	5.65685	+	5.65685i	0.862662	+	0.862662i	0.991647	−	0.128984i	$-0.0411717\pi$
$43$	5.65685	+	5.65685i	0.862662	+	0.862662i	−0.128984	+	0.991647i	$0.541172\pi$
$44$	5.63858			0.850048
$45$		0			0
$46$	−2.74456			−0.404664
$47$	−3.11400	−	3.11400i	−0.454224	−	0.454224i	0.442530	−	0.896754i	$-0.354081\pi$
$47$	−3.11400	−	3.11400i	−0.454224	−	0.454224i	−0.896754	+	0.442530i	$0.854081\pi$
$48$	1.08672	−	0.0337462i	0.156854	−	0.00487085i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−1.18614	−	1.11469i	−0.166093	−	0.156088i
$52$	2.30194	−	2.30194i	0.319222	−	0.319222i
$53$	8.46893	−	8.46893i	1.16330	−	1.16330i	0.179548	−	0.983749i	$-0.442536\pi$
$53$	8.46893	−	8.46893i	1.16330	−	1.16330i	0.983749	−	0.179548i	$-0.0574636\pi$
$54$	3.16915	+	2.62772i	0.431266	+	0.357587i
$55$		0			0
$56$		−	2.67181i		−	0.357036i
$57$	0.215040	+	6.92487i	0.0284828	+	0.917221i
$58$	−3.35491	−	3.35491i	−0.440522	−	0.440522i
$59$	−11.9769			−1.55926			−0.779628	−	0.626242i	$-0.784592\pi$
$59$	−11.9769			−1.55926			−0.779628	+	0.626242i	$0.784592\pi$
$60$		0			0
$61$	6.74456			0.863553			0.431776	−	0.901981i	$-0.357887\pi$
$61$	6.74456			0.863553			0.431776	+	0.901981i	$0.357887\pi$
$62$	−2.65805	−	2.65805i	−0.337573	−	0.337573i
$63$	−1.98561	+	2.24885i	−0.250164	+	0.283329i
$64$		−	3.37228i		−	0.421535i
$65$		0			0
$66$	−3.86141	+	4.10891i	−0.475306	+	0.505772i
$67$	9.01177	−	9.01177i	1.10096	−	1.10096i	0.106668	−	0.994295i	$-0.465982\pi$
$67$	9.01177	−	9.01177i	1.10096	−	1.10096i	0.994295	−	0.106668i	$-0.0340181\pi$
$68$	0.911899	−	0.911899i	0.110584	−	0.110584i
$69$	−4.10891	+	4.37228i	−0.494655	+	0.526361i
$70$		0			0
$71$		−	1.87953i		−	0.223059i	−0.993761	−	0.111529i	$-0.964425\pi$
$71$		−	1.87953i		−	0.223059i	0.993761	−	0.111529i	$-0.0355749\pi$
$72$	−5.30519	+	6.00852i	−0.625222	+	0.708111i
$73$	9.01177	+	9.01177i	1.05475	+	1.05475i	0.998412	+	0.0563356i	$0.0179417\pi$
$73$	9.01177	+	9.01177i	1.05475	+	1.05475i	0.0563356	+	0.998412i	$0.482058\pi$
$74$	−3.75906			−0.436981
$75$		0			0
$76$	−5.48913			−0.629646
$77$	−2.90544	−	2.90544i	−0.331106	−	0.331106i
$78$	0.101044	+	3.25387i	0.0114409	+	0.368428i
$79$			15.1168i			1.70078i	0.526155	+	0.850389i	$0.323633\pi$
$79$			15.1168i			1.70078i	−0.526155	+	0.850389i	$0.676367\pi$
$80$		0			0
$81$	8.93070	−	1.11469i	0.992300	−	0.123855i
$82$	6.70982	−	6.70982i	0.740976	−	0.740976i
$83$	−11.8303	+	11.8303i	−1.29855	+	1.29855i	−0.369194	+	0.929352i	$0.620366\pi$
$83$	−11.8303	+	11.8303i	−1.29855	+	1.29855i	−0.929352	+	0.369194i	$0.879634\pi$
$84$	−1.73205	−	1.62772i	−0.188982	−	0.177599i
$85$		0			0
$86$		−	6.33830i		−	0.683476i
$87$	−10.3673	+	0.321939i	−1.11149	+	0.0345155i
$88$	−7.76280	−	7.76280i	−0.827517	−	0.827517i
$89$	−3.75906			−0.398459			−0.199230	−	0.979953i	$-0.563844\pi$
$89$	−3.75906			−0.398459			−0.199230	+	0.979953i	$0.563844\pi$
$90$		0			0
$91$	−2.37228			−0.248683
$92$	−3.36139	−	3.36139i	−0.350449	−	0.350449i
$93$	−8.21386	+	0.255068i	−0.851738	+	0.0264493i
$94$			3.48913i			0.359876i
$95$		0			0
$96$	−7.37228	−	6.92820i	−0.752430	−	0.707107i
$97$	−1.67746	+	1.67746i	−0.170320	+	0.170320i	−0.787120	−	0.616800i	$-0.788429\pi$
$97$	−1.67746	+	1.67746i	−0.170320	+	0.170320i	0.616800	+	0.787120i	$0.288429\pi$
$98$	−0.560232	+	0.560232i	−0.0565919	+	0.0565919i
$99$	0.764836	+	12.3030i	0.0768689	+	1.23650i
$100$		0			0
$101$		−	3.75906i		−	0.374040i	−0.982356	−	0.187020i	$-0.940117\pi$
$101$		−	3.75906i		−	0.374040i	0.982356	−	0.187020i	$-0.0598829\pi$
$102$	0.0400277	+	1.28900i	0.00396334	+	0.127630i
$103$	−5.03237	−	5.03237i	−0.495854	−	0.495854i	0.414291	−	0.910145i	$-0.364030\pi$
$103$	−5.03237	−	5.03237i	−0.495854	−	0.495854i	−0.910145	+	0.414291i	$0.864030\pi$
$104$	−6.33830			−0.621521
$105$		0			0
$106$	−9.48913			−0.921665
$107$	3.77852	+	3.77852i	0.365283	+	0.365283i	0.865754	−	0.500471i	$-0.166840\pi$
$107$	3.77852	+	3.77852i	0.365283	+	0.365283i	−0.500471	+	0.865754i	$0.666840\pi$
$108$	0.663113	+	7.09968i	0.0638081	+	0.683167i
$109$			8.37228i			0.801919i	0.916096	+	0.400960i	$0.131323\pi$
$109$			8.37228i			0.801919i	−0.916096	+	0.400960i	$0.868677\pi$
$110$		0			0
$111$	−5.62772	+	5.98844i	−0.534159	+	0.568398i
$112$	0.443864	−	0.443864i	0.0419412	−	0.0419412i
$113$	−3.56995	+	3.56995i	−0.335833	+	0.335833i	−0.854796	−	0.518963i	$-0.826318\pi$
$113$	−3.56995	+	3.56995i	−0.335833	+	0.335833i	0.518963	+	0.854796i	$0.326318\pi$
$114$	3.75906	−	4.00000i	0.352068	−	0.374634i
$115$		0			0
$116$		−	8.21782i		−	0.763006i
$117$	5.33492	+	4.71043i	0.493213	+	0.435479i
$118$	6.70982	+	6.70982i	0.617689	+	0.617689i
$119$	−0.939764			−0.0861480
$120$		0			0
$121$	−5.88316			−0.534832
$122$	−3.77852	−	3.77852i	−0.342091	−	0.342091i
$123$	−0.643878	−	20.7346i	−0.0580565	−	1.86957i
$124$		−	6.51087i		−	0.584694i
$125$		0			0
$126$	2.37228	−	0.147477i	0.211340	−	0.0131383i
$127$	−2.30194	+	2.30194i	−0.204264	+	0.204264i	−0.801824	−	0.597560i	$-0.796137\pi$
$127$	−2.30194	+	2.30194i	−0.204264	+	0.204264i	0.597560	+	0.801824i	$0.296137\pi$
$128$	6.37111	−	6.37111i	0.563132	−	0.563132i
$129$	−10.0974	−	9.48913i	−0.889022	−	0.835471i
$130$		0			0
$131$		−	8.21782i		−	0.717995i	−0.933339	−	0.358997i	$-0.883119\pi$
$131$		−	8.21782i		−	0.717995i	0.933339	−	0.358997i	$-0.116881\pi$
$132$	−9.76161	+	0.303131i	−0.849639	+	0.0263841i
$133$	2.82843	+	2.82843i	0.245256	+	0.245256i
$134$	−10.0974			−0.872278
$135$		0			0
$136$	−2.51087			−0.215306
$137$	12.0389	+	12.0389i	1.02855	+	1.02855i	0.999580	+	0.0289711i	$0.00922308\pi$
$137$	12.0389	+	12.0389i	1.02855	+	1.02855i	0.0289711	+	0.999580i	$0.490777\pi$
$138$	4.75143	−	0.147548i	0.404469	−	0.0125601i
$139$			0.744563i			0.0631530i	0.999501	+	0.0315765i	$0.0100528\pi$
$139$			0.744563i			0.0631530i	−0.999501	+	0.0315765i	$0.989947\pi$
$140$		0			0
$141$	5.55842	+	5.22360i	0.468104	+	0.439907i
$142$	−1.05297	+	1.05297i	−0.0883633	+	0.0883633i
$143$	−6.89252	+	6.89252i	−0.576381	+	0.576381i
$144$	−1.87953	+	0.116844i	−0.156627	+	0.00973700i
$145$		0			0
$146$		−	10.0974i		−	0.835663i
$147$	0.0537601	+	1.73122i	0.00443406	+	0.142788i
$148$	−4.60388	−	4.60388i	−0.378437	−	0.378437i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$		0			0
$151$	−7.11684			−0.579161			−0.289580	−	0.957154i	$-0.593516\pi$
$151$	−7.11684			−0.579161			−0.289580	+	0.957154i	$0.593516\pi$
$152$	7.55703	+	7.55703i	0.612956	+	0.612956i
$153$	2.11339	+	1.86601i	0.170858	+	0.150858i
$154$			3.25544i			0.262331i
$155$		0			0
$156$	−3.86141	+	4.10891i	−0.309160	+	0.328976i
$157$	−9.01177	+	9.01177i	−0.719217	+	0.719217i	−0.968445	−	0.249228i	$-0.919823\pi$
$157$	−9.01177	+	9.01177i	−0.719217	+	0.719217i	0.249228	+	0.968445i	$0.419823\pi$
$158$	8.46893	−	8.46893i	0.673752	−	0.673752i
$159$	−14.2063	+	15.1168i	−1.12663	+	1.19884i
$160$		0			0
$161$			3.46410i			0.273009i
$162$	−5.62775	−	4.37878i	−0.442158	−	0.344029i
$163$	9.01177	+	9.01177i	0.705856	+	0.705856i	0.965661	−	0.259805i	$-0.0836583\pi$
$163$	9.01177	+	9.01177i	0.705856	+	0.705856i	−0.259805	+	0.965661i	$0.583658\pi$
$164$	16.4356			1.28341
$165$		0			0
$166$	13.2554			1.02882
$167$	7.59586	+	7.59586i	0.587785	+	0.587785i	0.937031	−	0.349246i	$-0.113562\pi$
$167$	7.59586	+	7.59586i	0.587785	+	0.587785i	−0.349246	+	0.937031i	$0.613562\pi$
$168$	0.143637	+	4.62549i	0.0110818	+	0.356864i
$169$		−	7.37228i		−	0.567099i
$170$		0			0
$171$	−0.744563	−	11.9769i	−0.0569381	−	0.915895i
$172$	7.76280	−	7.76280i	0.591908	−	0.591908i
$173$	11.3744	−	11.3744i	0.864777	−	0.864777i	−0.127111	−	0.991888i	$-0.540570\pi$
$173$	11.3744	−	11.3744i	0.864777	−	0.864777i	0.991888	+	0.127111i	$0.0405705\pi$
$174$	5.98844	+	5.62772i	0.453982	+	0.426636i
$175$		0			0
$176$		−	2.57924i		−	0.194418i
$177$	20.7346	−	0.643878i	1.55851	−	0.0483968i
$178$	2.10594	+	2.10594i	0.157847	+	0.157847i
$179$	1.87953			0.140482			0.0702412	−	0.997530i	$-0.477623\pi$
$179$	1.87953			0.140482			0.0702412	+	0.997530i	$0.477623\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	1.32903	+	1.32903i	0.0985140	+	0.0985140i
$183$	−11.6763	+	0.362588i	−0.863137	+	0.0268033i
$184$			9.25544i			0.682320i
$185$		0			0
$186$	4.74456	+	4.45877i	0.347888	+	0.326933i
$187$	−2.73043	+	2.73043i	−0.199669	+	0.199669i
$188$	−4.27329	+	4.27329i	−0.311662	+	0.311662i
$189$	3.31662	−	4.00000i	0.241249	−	0.290957i
$190$		0			0
$191$			16.0858i			1.16393i	0.813215	+	0.581963i	$0.197715\pi$
$191$			16.0858i			1.16393i	−0.813215	+	0.581963i	$0.802285\pi$
$192$	0.181294	+	5.83815i	0.0130838	+	0.421332i
$193$	−18.0235	−	18.0235i	−1.29736	−	1.29736i	−0.930129	−	0.367234i	$-0.880305\pi$
$193$	−18.0235	−	18.0235i	−1.29736	−	1.29736i	−0.367234	−	0.930129i	$-0.619695\pi$
$194$	1.87953			0.134942
$195$		0			0
$196$	−1.37228			−0.0980201
$197$	−15.6088	−	15.6088i	−1.11208	−	1.11208i	−0.992868	−	0.119215i	$-0.961962\pi$
$197$	−15.6088	−	15.6088i	−1.11208	−	1.11208i	−0.119215	−	0.992868i	$-0.538038\pi$
$198$	6.46403	−	7.32100i	0.459379	−	0.520281i
$199$			12.7446i			0.903438i	0.892160	+	0.451719i	$0.149189\pi$
$199$			12.7446i			0.903438i	−0.892160	+	0.451719i	$0.850811\pi$
$200$		0			0
$201$	−15.1168	+	16.0858i	−1.06626	+	1.13460i
$202$	−2.10594	+	2.10594i	−0.148174	+	0.148174i
$203$	−4.23447	+	4.23447i	−0.297201	+	0.297201i
$204$	−1.52967	+	1.62772i	−0.107098	+	0.113963i
$205$		0			0
$206$			5.63858i			0.392859i
$207$	6.87836	−	7.79026i	0.478079	−	0.541461i
$208$	−1.05297	−	1.05297i	−0.0730104	−	0.0730104i
$209$	16.4356			1.13688
$210$		0			0
$211$	9.62772			0.662799			0.331400	−	0.943490i	$-0.392479\pi$
$211$	9.62772			0.662799			0.331400	+	0.943490i	$0.392479\pi$
$212$	−11.6218	−	11.6218i	−0.798186	−	0.798186i
$213$	0.101044	+	3.25387i	0.00692339	+	0.222951i
$214$		−	4.23369i		−	0.289409i
$215$		0			0
$216$	8.86141	−	10.6873i	0.602942	−	0.727176i
$217$	−3.35491	+	3.35491i	−0.227746	+	0.227746i
$218$	4.69042	−	4.69042i	0.317675	−	0.317675i
$219$	−16.0858	−	15.1168i	−1.08698	−	1.02150i
$220$		0			0
$221$			2.22938i			0.149965i
$222$	6.50774	−	0.202087i	0.436771	−	0.0135632i
$223$	16.3461	+	16.3461i	1.09461	+	1.09461i	0.995029	+	0.0995853i	$0.0317516\pi$
$223$	16.3461	+	16.3461i	1.09461	+	1.09461i	0.0995853	+	0.995029i	$0.468248\pi$
$224$	−5.84096			−0.390266
$225$		0			0
$226$	4.00000			0.266076
$227$	−9.34201	−	9.34201i	−0.620051	−	0.620051i	0.325493	−	0.945544i	$-0.394470\pi$
$227$	−9.34201	−	9.34201i	−0.620051	−	0.620051i	−0.945544	+	0.325493i	$0.894470\pi$
$228$	9.50286	−	0.295096i	0.629342	−	0.0195432i
$229$		−	28.9783i		−	1.91494i	−0.288538	−	0.957468i	$-0.593169\pi$
$229$		−	28.9783i		−	1.91494i	0.288538	−	0.957468i	$-0.406831\pi$
$230$		0			0
$231$	5.18614	+	4.87375i	0.341223	+	0.320669i
$232$	−11.3137	+	11.3137i	−0.742781	+	0.742781i
$233$	−0.417127	+	0.417127i	−0.0273269	+	0.0273269i	−0.720638	−	0.693311i	$-0.756151\pi$
$233$	−0.417127	+	0.417127i	−0.0273269	+	0.0273269i	0.693311	+	0.720638i	$0.256151\pi$
$234$	−0.349857	−	5.62772i	−0.0228708	−	0.367895i
$235$		0			0
$236$			16.4356i			1.06987i
$237$	−0.812683	−	26.1705i	−0.0527894	−	1.69996i
$238$	0.526485	+	0.526485i	0.0341270	+	0.0341270i
$239$	7.86797			0.508936			0.254468	−	0.967081i	$-0.418100\pi$
$239$	7.86797			0.508936			0.254468	+	0.967081i	$0.418100\pi$
$240$		0			0
$241$	11.4891			0.740080			0.370040	−	0.929016i	$-0.379344\pi$
$241$	11.4891			0.740080			0.370040	+	0.929016i	$0.379344\pi$
$242$	3.29593	+	3.29593i	0.211870	+	0.211870i
$243$	−15.4011	+	2.40989i	−0.987978	+	0.154594i
$244$		−	9.25544i		−	0.592519i
$245$		0			0
$246$	−11.2554	+	11.9769i	−0.717620	+	0.763618i
$247$	6.70982	−	6.70982i	0.426936	−	0.426936i
$248$	−8.96370	+	8.96370i	−0.569196	+	0.569196i
$249$	19.8448	−	21.1168i	1.25762	−	1.33823i
$250$		0			0
$251$		−	28.4125i		−	1.79338i	−0.442656	−	0.896691i	$-0.645964\pi$
$251$		−	28.4125i		−	1.79338i	0.442656	−	0.896691i	$-0.354036\pi$
$252$	3.08606	+	2.72482i	0.194404	+	0.171647i
$253$	10.0647	+	10.0647i	0.632765	+	0.632765i
$254$	2.57924			0.161836
$255$		0			0
$256$	−13.8832			−0.867697
$257$	4.89898	+	4.89898i	0.305590	+	0.305590i	0.843196	−	0.537606i	$-0.180671\pi$
$257$	4.89898	+	4.89898i	0.305590	+	0.305590i	−0.537606	+	0.843196i	$0.680671\pi$
$258$	0.340747	+	10.9730i	0.0212140	+	0.683147i
$259$			4.74456i			0.294813i
$260$		0			0
$261$	17.9307	−	1.11469i	1.10988	−	0.0689977i
$262$	−4.60388	+	4.60388i	−0.284429	+	0.284429i
$263$	3.36139	−	3.36139i	0.207272	−	0.207272i	−0.595835	−	0.803107i	$-0.703179\pi$
$263$	3.36139	−	3.36139i	0.207272	−	0.207272i	0.803107	+	0.595835i	$0.203179\pi$
$264$	13.8564	+	13.0217i	0.852803	+	0.801433i
$265$		0			0
$266$		−	3.16915i		−	0.194313i
$267$	6.50774	−	0.202087i	0.398267	−	0.0123675i
$268$	−12.3667	−	12.3667i	−0.755415	−	0.755415i
$269$	11.9769			0.730243			0.365122	−	0.930960i	$-0.381027\pi$
$269$	11.9769			0.730243			0.365122	+	0.930960i	$0.381027\pi$
$270$		0			0
$271$	1.48913			0.0904579			0.0452290	−	0.998977i	$-0.485598\pi$
$271$	1.48913			0.0904579			0.0452290	+	0.998977i	$0.485598\pi$
$272$	−0.417127	−	0.417127i	−0.0252921	−	0.0252921i
$273$	4.10693	−	0.127534i	0.248563	−	0.00771871i
$274$		−	13.4891i		−	0.814908i
$275$		0			0
$276$	6.00000	+	5.63858i	0.361158	+	0.339403i
$277$	−14.6686	+	14.6686i	−0.881352	+	0.881352i	−0.993672	−	0.112320i	$-0.964172\pi$
$277$	−14.6686	+	14.6686i	−0.881352	+	0.881352i	0.112320	+	0.993672i	$0.464172\pi$
$278$	0.417127	−	0.417127i	0.0250176	−	0.0250176i
$279$	14.2063	−	0.883156i	0.850507	−	0.0528732i
$280$		0			0
$281$			10.4472i			0.623228i	0.950209	+	0.311614i	$0.100870\pi$
$281$			10.4472i			0.623228i	−0.950209	+	0.311614i	$0.899130\pi$
$282$	−0.187576	−	6.04043i	−0.0111700	−	0.359702i
$283$	−8.38728	−	8.38728i	−0.498572	−	0.498572i	0.412421	−	0.910993i	$-0.364683\pi$
$283$	−8.38728	−	8.38728i	−0.498572	−	0.498572i	−0.910993	+	0.412421i	$0.864683\pi$
$284$	−2.57924			−0.153050
$285$		0			0
$286$	7.72281			0.456660
$287$	−8.46893	−	8.46893i	−0.499905	−	0.499905i
$288$	13.1355	+	11.5979i	0.774015	+	0.683412i
$289$		−	16.1168i		−	0.948050i
$290$		0			0
$291$	2.81386	−	2.99422i	0.164951	−	0.175524i
$292$	12.3667	−	12.3667i	0.723705	−	0.723705i
$293$	−11.3744	+	11.3744i	−0.664498	+	0.664498i	−0.956437	−	0.291939i	$-0.905700\pi$
$293$	−11.3744	+	11.3744i	−0.664498	+	0.664498i	0.291939	+	0.956437i	$0.405700\pi$
$294$	0.939764	−	1.00000i	0.0548081	−	0.0583212i
$295$		0			0
$296$			12.6766i			0.736812i
$297$	−1.98551	−	21.2580i	−0.115211	−	1.23351i
$298$		0			0
$299$	8.21782			0.475249
$300$		0			0
$301$	−8.00000			−0.461112
$302$	3.98708	+	3.98708i	0.229431	+	0.229431i
$303$	0.202087	+	6.50774i	0.0116096	+	0.373860i
$304$			2.51087i			0.144009i
$305$		0			0
$306$	−0.138593	−	2.22938i	−0.00792286	−	0.127445i
$307$	−9.63625	+	9.63625i	−0.549970	+	0.549970i	−0.926432	−	0.376462i	$-0.877141\pi$
$307$	−9.63625	+	9.63625i	−0.549970	+	0.549970i	0.376462	+	0.926432i	$0.377141\pi$
$308$	−3.98708	+	3.98708i	−0.227185	+	0.227185i
$309$	8.98266	+	8.44158i	0.511006	+	0.480225i
$310$		0			0
$311$		−	3.75906i		−	0.213156i	−0.994304	−	0.106578i	$-0.966011\pi$
$311$		−	3.75906i		−	0.213156i	0.994304	−	0.106578i	$-0.0339895\pi$
$312$	10.9730	−	0.340747i	0.621222	−	0.0192910i
$313$	−8.38728	−	8.38728i	−0.474077	−	0.474077i	0.429154	−	0.903231i	$-0.358812\pi$
$313$	−8.38728	−	8.38728i	−0.474077	−	0.474077i	−0.903231	+	0.429154i	$0.858812\pi$
$314$	10.0974			0.569826
$315$		0			0
$316$	20.7446			1.16697
$317$	4.48185	+	4.48185i	0.251726	+	0.251726i	0.821678	−	0.569952i	$-0.193038\pi$
$317$	4.48185	+	4.48185i	0.251726	+	0.251726i	−0.569952	+	0.821678i	$0.693038\pi$
$318$	16.4277	−	0.510136i	0.921221	−	0.0286070i
$319$			24.6060i			1.37767i
$320$		0			0
$321$	−6.74456	−	6.33830i	−0.376445	−	0.353769i
$322$	1.94070	−	1.94070i	0.108151	−	0.108151i
$323$	2.65805	−	2.65805i	0.147898	−	0.147898i
$324$	−1.52967	−	12.2554i	−0.0849817	−	0.680858i
$325$		0			0
$326$		−	10.0974i		−	0.559241i
$327$	−0.450095	−	14.4942i	−0.0248903	−	0.801533i
$328$	−22.6274	−	22.6274i	−1.24939	−	1.24939i
$329$	4.40387			0.242793
$330$		0			0
$331$	−14.9783			−0.823279			−0.411640	−	0.911347i	$-0.635044\pi$
$331$	−14.9783			−0.823279			−0.411640	+	0.911347i	$0.635044\pi$
$332$	16.2345	+	16.2345i	0.890986	+	0.890986i
$333$	9.42086	−	10.6698i	0.516260	−	0.584703i
$334$		−	8.51087i		−	0.465694i
$335$		0			0
$336$	−0.744563	+	0.792287i	−0.0406192	+	0.0432228i
$337$	−3.35491	+	3.35491i	−0.182754	+	0.182754i	−0.792555	−	0.609801i	$-0.791249\pi$
$337$	−3.35491	+	3.35491i	−0.182754	+	0.182754i	0.609801	+	0.792555i	$0.291249\pi$
$338$	−4.13018	+	4.13018i	−0.224652	+	0.224652i
$339$	5.98844	−	6.37228i	0.325247	−	0.346095i
$340$		0			0
$341$			19.4950i			1.05571i
$342$	−6.29270	+	7.12695i	−0.340270	+	0.385381i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−21.3745			−1.15244
$345$		0			0
$346$	−12.7446			−0.685152
$347$	−4.69042	−	4.69042i	−0.251795	−	0.251795i	0.569911	−	0.821706i	$-0.306978\pi$
$347$	−4.69042	−	4.69042i	−0.251795	−	0.251795i	−0.821706	+	0.569911i	$0.806978\pi$
$348$	0.441791	+	14.2268i	0.0236825	+	0.762638i
$349$		−	21.7228i		−	1.16280i	−0.813619	−	0.581398i	$-0.802506\pi$
$349$		−	21.7228i		−	1.16280i	0.813619	−	0.581398i	$-0.197494\pi$
$350$		0			0
$351$	−9.48913	−	7.86797i	−0.506492	−	0.419961i
$352$	−16.9706	+	16.9706i	−0.904534	+	0.904534i
$353$	7.80442	−	7.80442i	0.415387	−	0.415387i	−0.468223	−	0.883610i	$-0.655106\pi$
$353$	7.80442	−	7.80442i	0.415387	−	0.415387i	0.883610	+	0.468223i	$0.155106\pi$
$354$	−11.9769	−	11.2554i	−0.636564	−	0.598220i
$355$		0			0
$356$			5.15848i			0.273399i
$357$	1.62693	−	0.0505218i	0.0861065	−	0.00267390i
$358$	−1.05297	−	1.05297i	−0.0556512	−	0.0556512i
$359$	−29.5923			−1.56182			−0.780912	−	0.624641i	$-0.785245\pi$
$359$	−29.5923			−1.56182			−0.780912	+	0.624641i	$0.785245\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−3.36139	−	3.36139i	−0.176671	−	0.176671i
$363$	10.1850	−	0.316279i	0.534575	−	0.0166003i
$364$			3.25544i			0.170631i
$365$		0			0
$366$	6.74456	+	6.33830i	0.352544	+	0.331308i
$367$	−5.03237	+	5.03237i	−0.262688	+	0.262688i	−0.826145	−	0.563458i	$-0.809471\pi$
$367$	−5.03237	+	5.03237i	−0.262688	+	0.262688i	0.563458	+	0.826145i	$0.309471\pi$
$368$	−1.53759	+	1.53759i	−0.0801524	+	0.0801524i
$369$	2.22938	+	35.8614i	0.116057	+	1.86687i
$370$		0			0
$371$			11.9769i			0.621809i
$372$	0.350025	+	11.2717i	0.0181480	+	0.584412i
$373$	−11.3137	−	11.3137i	−0.585802	−	0.585802i	0.350690	−	0.936492i	$-0.385947\pi$
$373$	−11.3137	−	11.3137i	−0.585802	−	0.585802i	−0.936492	+	0.350690i	$0.885947\pi$
$374$	3.05934			0.158195
$375$		0			0
$376$	11.7663			0.606801
$377$	10.0453	+	10.0453i	0.517362	+	0.517362i
$378$	−4.09900	+	0.382848i	−0.210830	+	0.0196916i
$379$		−	12.0000i		−	0.616399i	−0.951322	−	0.308199i	$-0.900274\pi$
$379$		−	12.0000i		−	0.616399i	0.951322	−	0.308199i	$-0.0997264\pi$
$380$		0			0
$381$	3.86141	−	4.10891i	0.197826	−	0.210506i
$382$	9.01177	−	9.01177i	0.461082	−	0.461082i
$383$	18.9702	−	18.9702i	0.969333	−	0.969333i	−0.0302103	−	0.999544i	$-0.509618\pi$
$383$	18.9702	−	18.9702i	0.969333	−	0.969333i	0.999544	+	0.0302103i	$0.00961769\pi$
$384$	−10.6873	+	11.3723i	−0.545382	+	0.580339i
$385$		0			0
$386$			20.1947i			1.02788i
$387$	17.9908	+	15.8849i	0.914526	+	0.807475i
$388$	2.30194	+	2.30194i	0.116863	+	0.116863i
$389$	26.1831			1.32754			0.663769	−	0.747938i	$-0.268956\pi$
$389$	26.1831			1.32754			0.663769	+	0.747938i	$0.268956\pi$
$390$		0			0
$391$	3.25544			0.164635
$392$	1.88926	+	1.88926i	0.0954220	+	0.0954220i
$393$	0.441791	+	14.2268i	0.0222854	+	0.717649i
$394$			17.4891i			0.881089i
$395$		0			0
$396$	16.8832	−	1.04957i	0.848411	−	0.0527429i
$397$	−20.9500	+	20.9500i	−1.05145	+	1.05145i	−0.0528457	+	0.998603i	$0.516829\pi$
$397$	−20.9500	+	20.9500i	−1.05145	+	1.05145i	−0.998603	+	0.0528457i	$0.983171\pi$
$398$	7.13991	−	7.13991i	0.357891	−	0.357891i
$399$	−5.04868	−	4.74456i	−0.252750	−	0.237525i
$400$		0			0
$401$		−	26.1831i		−	1.30752i	−0.756700	−	0.653762i	$-0.773190\pi$
$401$		−	26.1831i		−	1.30752i	0.756700	−	0.653762i	$-0.226810\pi$
$402$	17.4807	−	0.542834i	0.871858	−	0.0270741i
$403$	7.95880	+	7.95880i	0.396456	+	0.396456i
$404$	−5.15848			−0.256644
$405$		0			0
$406$	4.74456			0.235469
$407$	13.7850	+	13.7850i	0.683299	+	0.683299i
$408$	4.34687	−	0.134985i	0.215202	−	0.00668274i
$409$			17.2554i			0.853226i	0.904434	+	0.426613i	$0.140293\pi$
$409$			17.2554i			0.853226i	−0.904434	+	0.426613i	$0.859707\pi$
$410$		0			0
$411$	−21.4891	−	20.1947i	−1.05998	−	0.996131i
$412$	−6.90583	+	6.90583i	−0.340226	+	0.340226i
$413$	8.46893	−	8.46893i	0.416729	−	0.416729i
$414$	−8.21782	+	0.510875i	−0.403884	+	0.0251081i
$415$		0			0
$416$			13.8564i			0.679366i
$417$	−0.0400277	−	1.28900i	−0.00196017	−	0.0631226i
$418$	−9.20777	−	9.20777i	−0.450367	−	0.450367i
$419$	−28.4125			−1.38804			−0.694021	−	0.719954i	$-0.744163\pi$
$419$	−28.4125			−1.38804			−0.694021	+	0.719954i	$0.744163\pi$
$420$		0			0
$421$	−0.372281			−0.0181439			−0.00907194	−	0.999959i	$-0.502888\pi$
$421$	−0.372281			−0.0181439			−0.00907194	+	0.999959i	$0.502888\pi$
$422$	−5.39375	−	5.39375i	−0.262564	−	0.262564i
$423$	−9.90365	−	8.74437i	−0.481532	−	0.425166i
$424$			32.0000i			1.55406i
$425$		0			0
$426$	1.76631	−	1.87953i	0.0855781	−	0.0910634i
$427$	−4.76913	+	4.76913i	−0.230794	+	0.230794i
$428$	5.18519	−	5.18519i	0.250636	−	0.250636i
$429$	11.5619	−	12.3030i	0.558214	−	0.593994i
$430$		0			0
$431$		−	0.349857i		−	0.0168520i	−0.999965	−	0.00842600i	$-0.997318\pi$
$431$		−	0.349857i		−	0.0168520i	0.999965	−	0.00842600i	$-0.00268211\pi$
$432$	3.24759	−	0.303326i	0.156250	−	0.0145938i
$433$	2.30194	+	2.30194i	0.110624	+	0.110624i	0.760252	−	0.649628i	$-0.225075\pi$
$433$	2.30194	+	2.30194i	0.110624	+	0.110624i	−0.649628	+	0.760252i	$0.725075\pi$
$434$	3.75906			0.180440
$435$		0			0
$436$	11.4891			0.550229
$437$	−9.79796	−	9.79796i	−0.468700	−	0.468700i
$438$	0.542834	+	17.4807i	0.0259376	+	0.835260i
$439$		−	19.2554i		−	0.919012i	−0.888175	−	0.459506i	$-0.848026\pi$
$439$		−	19.2554i		−	0.919012i	0.888175	−	0.459506i	$-0.151974\pi$
$440$		0			0
$441$	−0.186141	−	2.99422i	−0.00886384	−	0.142582i
$442$	1.24897	−	1.24897i	0.0594075	−	0.0594075i
$443$	−1.12046	+	1.12046i	−0.0532348	+	0.0532348i	−0.733223	−	0.679988i	$-0.761985\pi$
$443$	−1.12046	+	1.12046i	−0.0532348	+	0.0532348i	0.679988	+	0.733223i	$0.261985\pi$
$444$	8.21782	+	7.72281i	0.390001	+	0.366508i
$445$		0			0
$446$		−	18.3152i		−	0.867249i
$447$		0			0
$448$	2.38456	+	2.38456i	0.112660	+	0.112660i
$449$	1.52967			0.0721896			0.0360948	−	0.999348i	$-0.488508\pi$
$449$	1.52967			0.0721896			0.0360948	+	0.999348i	$0.488508\pi$
$450$		0			0
$451$	−49.2119			−2.31730
$452$	4.89898	+	4.89898i	0.230429	+	0.230429i
$453$	12.3208	−	0.382602i	0.578882	−	0.0179762i
$454$			10.4674i			0.491258i
$455$		0			0
$456$	−13.4891	−	12.6766i	−0.631686	−	0.593636i
$457$	−1.24897	+	1.24897i	−0.0584244	+	0.0584244i	−0.735715	−	0.677291i	$-0.763154\pi$
$457$	−1.24897	+	1.24897i	−0.0584244	+	0.0584244i	0.677291	+	0.735715i	$0.263154\pi$
$458$	−16.2345	+	16.2345i	−0.758590	+	0.758590i
$459$	−3.75906	−	3.11684i	−0.175458	−	0.145482i
$460$		0			0
$461$			20.1947i			0.940561i	0.882517	+	0.470281i	$0.155847\pi$
$461$			20.1947i			0.940561i	−0.882517	+	0.470281i	$0.844153\pi$
$462$	−0.175013	−	5.63587i	−0.00814232	−	0.262204i
$463$	−19.0765	−	19.0765i	−0.886560	−	0.886560i	0.107631	−	0.994191i	$-0.465674\pi$
$463$	−19.0765	−	19.0765i	−0.886560	−	0.886560i	−0.994191	+	0.107631i	$0.965674\pi$
$464$	−3.75906			−0.174510
$465$		0			0
$466$	0.467376			0.0216508
$467$	−15.6477	−	15.6477i	−0.724087	−	0.724087i	0.245348	−	0.969435i	$-0.421098\pi$
$467$	−15.6477	−	15.6477i	−0.724087	−	0.724087i	−0.969435	+	0.245348i	$0.921098\pi$
$468$	6.46403	−	7.32100i	0.298800	−	0.338414i
$469$			12.7446i			0.588489i
$470$		0			0
$471$	15.1168	−	16.0858i	0.696547	−	0.741194i
$472$	22.6274	−	22.6274i	1.04151	−	1.04151i
$473$	−23.2435	+	23.2435i	−1.06874	+	1.06874i
$474$	−14.2063	+	15.1168i	−0.652515	+	0.694340i
$475$		0			0
$476$			1.28962i			0.0591097i
$477$	23.7814	−	26.9343i	1.08888	−	1.23323i
$478$	−4.40788	−	4.40788i	−0.201612	−	0.201612i
$479$	−24.6535			−1.12645			−0.563223	−	0.826305i	$-0.690439\pi$
$479$	−24.6535			−1.12645			−0.563223	+	0.826305i	$0.690439\pi$
$480$		0			0
$481$	11.2554			0.513204
$482$	−6.43657	−	6.43657i	−0.293178	−	0.293178i
$483$	−0.186230	−	5.99711i	−0.00847378	−	0.272878i
$484$			8.07335i			0.366970i
$485$		0			0
$486$	9.97825	+	7.27806i	0.452623	+	0.330139i
$487$	−11.1177	+	11.1177i	−0.503791	+	0.503791i	−0.912614	−	0.408822i	$-0.865940\pi$
$487$	−11.1177	+	11.1177i	−0.503791	+	0.503791i	0.408822	+	0.912614i	$0.365940\pi$
$488$	−12.7422	+	12.7422i	−0.576813	+	0.576813i
$489$	−16.0858	−	15.1168i	−0.727425	−	0.683607i
$490$		0			0
$491$		−	35.5808i		−	1.60574i	−0.596155	−	0.802869i	$-0.703306\pi$
$491$		−	35.5808i		−	1.60574i	0.596155	−	0.802869i	$-0.296694\pi$
$492$	−28.4537	+	0.883582i	−1.28279	+	0.0398349i
$493$	3.97940	+	3.97940i	0.179223	+	0.179223i
$494$	−7.51811			−0.338256
$495$		0			0
$496$	−2.97825			−0.133727
$497$	1.32903	+	1.32903i	0.0596150	+	0.0596150i
$498$	−22.9480	+	0.712613i	−1.02833	+	0.0319330i
$499$			1.62772i			0.0728667i	0.999336	+	0.0364333i	$0.0115997\pi$
$499$			1.62772i			0.0728667i	−0.999336	+	0.0364333i	$0.988400\pi$
$500$		0			0
$501$	−13.5584	−	12.7417i	−0.605746	−	0.569258i
$502$	−15.9176	+	15.9176i	−0.710437	+	0.710437i
$503$	3.53113	−	3.53113i	0.157445	−	0.157445i	−0.623988	−	0.781434i	$-0.714489\pi$
$503$	3.53113	−	3.53113i	0.157445	−	0.157445i	0.781434	+	0.623988i	$0.214489\pi$
$504$	−0.497333	−	8.00000i	−0.0221530	−	0.356348i
$505$		0			0
$506$		−	11.2772i		−	0.501331i
$507$	0.396334	+	12.7630i	0.0176018	+	0.566825i
$508$	3.15891	+	3.15891i	0.140154	+	0.140154i
$509$	−8.21782			−0.364249			−0.182124	−	0.983276i	$-0.558297\pi$
$509$	−8.21782			−0.364249			−0.182124	+	0.983276i	$0.558297\pi$
$510$		0			0
$511$	−12.7446			−0.563786
$512$	−4.96444	−	4.96444i	−0.219399	−	0.219399i
$513$	1.93288	+	20.6945i	0.0853386	+	0.913686i
$514$		−	5.48913i		−	0.242115i
$515$		0			0
$516$	−13.0217	+	13.8564i	−0.573251	+	0.609994i
$517$	12.7952	−	12.7952i	0.562731	−	0.562731i
$518$	2.65805	−	2.65805i	0.116788	−	0.116788i
$519$	−19.0800	+	20.3030i	−0.837519	+	0.891202i
$520$		0			0
$521$		−	20.1947i		−	0.884746i	−0.896831	−	0.442373i	$-0.854137\pi$
$521$		−	20.1947i		−	0.884746i	0.896831	−	0.442373i	$-0.145863\pi$
$522$	−10.6698	−	9.42086i	−0.467006	−	0.412340i
$523$	25.7863	+	25.7863i	1.12756	+	1.12756i	0.990573	+	0.136984i	$0.0437410\pi$
$523$	25.7863	+	25.7863i	1.12756	+	1.12756i	0.136984	+	0.990573i	$0.456259\pi$
$524$	−11.2772			−0.492645
$525$		0			0
$526$	−3.76631			−0.164219
$527$	3.15283	+	3.15283i	0.137339	+	0.137339i
$528$	0.138660	+	4.46522i	0.00603441	+	0.194324i
$529$			11.0000i			0.478261i
$530$		0			0
$531$	−35.8614	+	2.22938i	−1.55625	+	0.0967470i
$532$	3.88140	−	3.88140i	0.168280	−	0.168280i
$533$	−20.0907	+	20.0907i	−0.870224	+	0.870224i
$534$	−3.75906	−	3.53262i	−0.162670	−	0.152872i
$535$		0			0
$536$			34.0511i			1.47078i
$537$	−3.25387	+	0.101044i	−0.140415	+	0.00436035i
$538$	−6.70982	−	6.70982i	−0.289281	−	0.289281i
$539$	4.10891			0.176983
$540$		0			0
$541$	−24.3723			−1.04785			−0.523923	−	0.851766i	$-0.675532\pi$
$541$	−24.3723			−1.04785			−0.523923	+	0.851766i	$0.675532\pi$
$542$	−0.834255	−	0.834255i	−0.0358343	−	0.0358343i
$543$	−10.3873	+	0.322560i	−0.445762	+	0.0138424i
$544$			5.48913i			0.235344i
$545$		0			0
$546$	−2.37228	−	2.22938i	−0.101524	−	0.0954088i
$547$	23.6804	−	23.6804i	1.01250	−	1.01250i	0.0125794	−	0.999921i	$-0.495996\pi$
$547$	23.6804	−	23.6804i	1.01250	−	1.01250i	0.999921	−	0.0125794i	$-0.00400425\pi$
$548$	16.5207	−	16.5207i	0.705731	−	0.705731i
$549$	20.1947	−	1.25544i	0.861889	−	0.0535808i
$550$		0			0
$551$		−	23.9538i		−	1.02046i
$552$	−0.497573	−	16.0232i	−0.0211781	−	0.681991i
$553$	−10.6892	−	10.6892i	−0.454552	−	0.454552i
$554$	16.4356			0.698284
$555$		0			0
$556$	1.02175			0.0433318
$557$	−16.9379	−	16.9379i	−0.717680	−	0.717680i	0.250449	−	0.968130i	$-0.419422\pi$
$557$	−16.9379	−	16.9379i	−0.717680	−	0.717680i	−0.968130	+	0.250449i	$0.919422\pi$
$558$	−8.45357	−	7.46402i	−0.357868	−	0.315977i
$559$			18.9783i			0.802694i
$560$		0			0
$561$	4.58017	−	4.87375i	0.193375	−	0.205770i
$562$	5.85285	−	5.85285i	0.246888	−	0.246888i
$563$	26.1101	−	26.1101i	1.10041	−	1.10041i	0.106050	−	0.994361i	$-0.466180\pi$
$563$	26.1101	−	26.1101i	1.10041	−	1.10041i	0.994361	−	0.106050i	$-0.0338204\pi$
$564$	7.16825	−	7.62772i	0.301838	−	0.321185i
$565$		0			0
$566$			9.39764i			0.395012i
$567$	−5.52675	+	7.10317i	−0.232102	+	0.298305i
$568$	3.55091	+	3.55091i	0.148993	+	0.148993i
$569$	3.75906			0.157588			0.0787939	−	0.996891i	$-0.474893\pi$
$569$	3.75906			0.157588			0.0787939	+	0.996891i	$0.474893\pi$
$570$		0			0
$571$	−14.9783			−0.626820			−0.313410	−	0.949618i	$-0.601471\pi$
$571$	−14.9783			−0.626820			−0.313410	+	0.949618i	$0.601471\pi$
$572$	9.45848	+	9.45848i	0.395479	+	0.395479i
$573$	−0.864773	−	27.8480i	−0.0361264	−	1.16337i
$574$			9.48913i			0.396068i
$575$		0			0
$576$	−0.627719	−	10.0974i	−0.0261549	−	0.420723i
$577$	−21.8069	+	21.8069i	−0.907834	+	0.907834i	−0.996097	−	0.0882628i	$-0.971868\pi$
$577$	−21.8069	+	21.8069i	−0.907834	+	0.907834i	0.0882628	+	0.996097i	$0.471868\pi$
$578$	−9.02916	+	9.02916i	−0.375564	+	0.375564i
$579$	32.1716	+	30.2337i	1.33701	+	1.25647i
$580$		0			0
$581$		−	16.7306i		−	0.694102i
$582$	−3.25387	+	0.101044i	−0.134877	+	0.00418839i
$583$	34.7981	+	34.7981i	1.44119	+	1.44119i
$584$	−34.0511			−1.40904
$585$		0			0
$586$	12.7446			0.526473
$587$	10.0065	+	10.0065i	0.413013	+	0.413013i	0.882787	−	0.469774i	$-0.155664\pi$
$587$	10.0065	+	10.0065i	0.413013	+	0.413013i	−0.469774	+	0.882787i	$0.655664\pi$
$588$	2.37572	−	0.0737740i	0.0979729	−	0.00304239i
$589$		−	18.9783i		−	0.781985i
$590$		0			0
$591$	27.8614	+	26.1831i	1.14607	+	1.07703i
$592$	−2.10594	+	2.10594i	−0.0865536	+	0.0865536i
$593$	−18.9314	+	18.9314i	−0.777420	+	0.777420i	−0.979391	−	0.201972i	$-0.935265\pi$
$593$	−18.9314	+	18.9314i	−0.777420	+	0.777420i	0.201972	+	0.979391i	$0.435265\pi$
$594$	−10.7971	+	13.0217i	−0.443009	+	0.534289i
$595$		0			0
$596$		0			0
$597$	−0.685149	−	22.0636i	−0.0280413	−	0.903003i
$598$	−4.60388	−	4.60388i	−0.188267	−	0.188267i
$599$	−32.5214			−1.32879			−0.664395	−	0.747382i	$-0.731311\pi$
$599$	−32.5214			−1.32879			−0.664395	+	0.747382i	$0.731311\pi$
$600$		0			0
$601$	24.2337			0.988513			0.494256	−	0.869316i	$-0.335440\pi$
$601$	24.2337			0.988513			0.494256	+	0.869316i	$0.335440\pi$
$602$	4.48185	+	4.48185i	0.182667	+	0.182667i
$603$	25.3058	−	28.6607i	1.03053	−	1.16715i
$604$			9.76631i			0.397386i
$605$		0			0
$606$	3.53262	−	3.75906i	0.143503	−	0.152701i
$607$	6.28134	−	6.28134i	0.254952	−	0.254952i	−0.568045	−	0.822997i	$-0.692300\pi$
$607$	6.28134	−	6.28134i	0.254952	−	0.254952i	0.822997	+	0.568045i	$0.192300\pi$
$608$	16.5207	−	16.5207i	0.670004	−	0.670004i
$609$	7.10313	−	7.55842i	0.287833	−	0.306283i
$610$		0			0
$611$		−	10.4472i		−	0.422649i
$612$	2.56069	−	2.90017i	0.103510	−	0.117232i
$613$	22.6274	+	22.6274i	0.913913	+	0.913913i	0.996577	−	0.0826647i	$-0.0263430\pi$
$613$	22.6274	+	22.6274i	0.913913	+	0.913913i	−0.0826647	+	0.996577i	$0.526343\pi$
$614$	10.7971			0.435734
$615$		0			0
$616$	10.9783			0.442326
$617$	6.22801	+	6.22801i	0.250730	+	0.250730i	0.821270	−	0.570540i	$-0.193266\pi$
$617$	6.22801	+	6.22801i	0.250730	+	0.250730i	−0.570540	+	0.821270i	$0.693266\pi$
$618$	−0.303131	−	9.76161i	−0.0121937	−	0.392669i
$619$			15.2554i			0.613168i	0.951844	+	0.306584i	$0.0991860\pi$
$619$			15.2554i			0.613168i	−0.951844	+	0.306584i	$0.900814\pi$
$620$		0			0
$621$	−11.4891	+	13.8564i	−0.461043	+	0.556038i
$622$	−2.10594	+	2.10594i	−0.0844405	+	0.0844405i
$623$	2.65805	−	2.65805i	0.106493	−	0.106493i
$624$	1.87953	+	1.76631i	0.0752413	+	0.0707091i
$625$		0			0
$626$			9.39764i			0.375605i
$627$	−28.4537	+	0.883582i	−1.13633	+	0.0352869i
$628$	12.3667	+	12.3667i	0.493484	+	0.493484i
$629$	4.45877			0.177783
$630$		0			0
$631$	18.0951			0.720354			0.360177	−	0.932884i	$-0.382716\pi$
$631$	18.0951			0.720354			0.360177	+	0.932884i	$0.382716\pi$
$632$	−28.5596	−	28.5596i	−1.13604	−	1.13604i
$633$	−16.6677	+	0.517587i	−0.662480	+	0.0205722i
$634$		−	5.02175i		−	0.199439i
$635$		0			0
$636$	20.7446	+	19.4950i	0.822575	+	0.773027i
$637$	1.67746	−	1.67746i	0.0664632	−	0.0664632i
$638$	13.7850	−	13.7850i	0.545755	−	0.545755i
$639$	−0.349857	−	5.62772i	−0.0138401	−	0.222629i
$640$		0			0
$641$		−	3.75906i		−	0.148474i	−0.997241	−	0.0742369i	$-0.976348\pi$
$641$		−	3.75906i		−	0.148474i	0.997241	−	0.0742369i	$-0.0236521\pi$
$642$	0.227603	+	7.32943i	0.00898279	+	0.289270i
$643$	−12.9912	−	12.9912i	−0.512322	−	0.512322i	0.402916	−	0.915237i	$-0.367997\pi$
$643$	−12.9912	−	12.9912i	−0.512322	−	0.512322i	−0.915237	+	0.402916i	$0.867997\pi$
$644$	4.75372			0.187323
$645$		0			0
$646$	−2.97825			−0.117178
$647$	31.4262	+	31.4262i	1.23549	+	1.23549i	0.961824	+	0.273669i	$0.0882373\pi$
$647$	31.4262	+	31.4262i	1.23549	+	1.23549i	0.273669	+	0.961824i	$0.411763\pi$
$648$	−14.7665	+	18.9783i	−0.580081	+	0.745540i
$649$		−	49.2119i		−	1.93174i
$650$		0			0
$651$	5.62772	−	5.98844i	0.220568	−	0.234705i
$652$	12.3667	−	12.3667i	0.484317	−	0.484317i
$653$	−11.6218	+	11.6218i	−0.454795	+	0.454795i	−0.896942	−	0.442148i	$-0.854217\pi$
$653$	−11.6218	+	11.6218i	−0.454795	+	0.454795i	0.442148	+	0.896942i	$0.354217\pi$
$654$	−7.86797	+	8.37228i	−0.307662	+	0.327382i
$655$		0			0
$656$		−	7.51811i		−	0.293533i
$657$	28.6607	+	25.3058i	1.11816	+	0.987271i
$658$	−2.46718	−	2.46718i	−0.0961809	−	0.0961809i
$659$	28.0627			1.09317			0.546583	−	0.837405i	$-0.315928\pi$
$659$	28.0627			1.09317			0.546583	+	0.837405i	$0.315928\pi$
$660$		0			0
$661$	7.76631			0.302075			0.151037	−	0.988528i	$-0.451739\pi$
$661$	7.76631			0.302075			0.151037	+	0.988528i	$0.451739\pi$
$662$	8.39129	+	8.39129i	0.326137	+	0.326137i
$663$	−0.119852	−	3.85955i	−0.00465466	−	0.149892i
$664$		−	44.7011i		−	1.73474i
$665$		0			0
$666$	−11.2554	+	0.699713i	−0.436139	+	0.0271133i
$667$	14.6686	−	14.6686i	0.567971	−	0.567971i
$668$	10.4237	−	10.4237i	0.403303	−	0.403303i
$669$	−29.1774	−	27.4198i	−1.12806	−	1.06011i
$670$		0			0
$671$			27.7128i			1.06984i
$672$	10.1120	−	0.314011i	0.390078	−	0.0121132i
$673$	13.4196	+	13.4196i	0.517289	+	0.517289i	0.916750	−	0.399461i	$-0.130803\pi$
$673$	13.4196	+	13.4196i	0.517289	+	0.517289i	−0.399461	+	0.916750i	$0.630803\pi$
$674$	3.75906			0.144793
$675$		0			0
$676$	−10.1168			−0.389109
$677$	−19.8433	−	19.8433i	−0.762640	−	0.762640i	0.214159	−	0.976799i	$-0.431299\pi$
$677$	−19.8433	−	19.8433i	−0.762640	−	0.762640i	−0.976799	+	0.214159i	$0.931299\pi$
$678$	−6.92487	+	0.215040i	−0.265948	+	0.00825857i
$679$		−	2.37228i		−	0.0910398i
$680$		0			0
$681$	16.6753	+	15.6708i	0.638998	+	0.600507i
$682$	10.9217	−	10.9217i	0.418214	−	0.418214i
$683$	4.19564	−	4.19564i	0.160542	−	0.160542i	−0.622265	−	0.782807i	$-0.713787\pi$
$683$	4.19564	−	4.19564i	0.160542	−	0.160542i	0.782807	+	0.622265i	$0.213787\pi$
$684$	−16.4356	+	1.02175i	−0.628433	+	0.0390676i
$685$		0			0
$686$		−	0.792287i		−	0.0302497i
$687$	1.55787	+	50.1676i	0.0594366	+	1.91401i
$688$	−3.55091	−	3.55091i	−0.135377	−	0.135377i
$689$	28.4125			1.08243
$690$		0			0
$691$	−4.00000			−0.152167			−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000			−0.152167			−0.0760836	+	0.997101i	$0.524242\pi$
$692$	−15.6088	−	15.6088i	−0.593359	−	0.593359i
$693$	−9.24034	−	8.15870i	−0.351012	−	0.309924i
$694$			5.25544i			0.199494i
$695$		0			0
$696$	18.9783	−	20.1947i	0.719369	−	0.765478i
$697$	−7.95880	+	7.95880i	−0.301461	+	0.301461i
$698$	−12.1698	+	12.1698i	−0.460634	+	0.460634i
$699$	0.699713	−	0.744563i	0.0264656	−	0.0281619i
$700$		0			0
$701$		−	6.68815i		−	0.252608i	−0.991992	−	0.126304i	$-0.959689\pi$
$701$		−	6.68815i		−	0.252608i	0.991992	−	0.126304i	$-0.0403115\pi$
$702$	0.908224	+	9.72399i	0.0342787	+	0.367008i
$703$	−13.4196	−	13.4196i	−0.506132	−	0.506132i
$704$	13.8564			0.522233
$705$		0			0
$706$	−8.74456			−0.329106
$707$	2.65805	+	2.65805i	0.0999664	+	0.0999664i
$708$	−0.883582	−	28.4537i	−0.0332070	−	1.06935i
$709$			19.3505i			0.726724i	0.931648	+	0.363362i	$0.118371\pi$
$709$			19.3505i			0.726724i	−0.931648	+	0.363362i	$0.881629\pi$
$710$		0			0
$711$	2.81386	+	45.2632i	0.105528	+	1.69750i
$712$	7.10183	−	7.10183i	0.266152	−	0.266152i
$713$	11.6218	−	11.6218i	0.435238	−	0.435238i
$714$	−0.939764	−	0.883156i	−0.0351698	−	0.0330513i
$715$		0			0
$716$		−	2.57924i		−	0.0963907i
$717$	−13.6212	+	0.422983i	−0.508691	+	0.0157966i
$718$	16.5786	+	16.5786i	0.618706	+	0.618706i
$719$	11.9769			0.446662			0.223331	−	0.974743i	$-0.428307\pi$
$719$	11.9769			0.446662			0.223331	+	0.974743i	$0.428307\pi$
$720$		0			0
$721$	7.11684			0.265045
$722$	−1.68069	−	1.68069i	−0.0625490	−	0.0625490i
$723$	−19.8902	+	0.617656i	−0.739723	+	0.0229709i
$724$		−	8.23369i		−	0.306003i
$725$		0			0
$726$	−5.88316	−	5.52878i	−0.218344	−	0.205192i
$727$	34.9941	−	34.9941i	1.29786	−	1.29786i	0.368055	−	0.929804i	$-0.380024\pi$
$727$	34.9941	−	34.9941i	1.29786	−	1.29786i	0.929804	−	0.368055i	$-0.119976\pi$
$728$	4.48185	−	4.48185i	0.166108	−	0.166108i
$729$	26.5330	−	5.00000i	0.982704	−	0.185185i
$730$		0			0
$731$			7.51811i			0.278067i
$732$	0.497573	+	16.0232i	0.0183908	+	0.592233i
$733$	−15.0971	−	15.0971i	−0.557624	−	0.557624i	0.371006	−	0.928630i	$-0.379013\pi$
$733$	−15.0971	−	15.0971i	−0.557624	−	0.557624i	−0.928630	+	0.371006i	$0.879013\pi$
$734$	5.63858			0.208124
$735$		0			0
$736$	20.2337			0.745824
$737$	37.0286	+	37.0286i	1.36396	+	1.36396i
$738$	18.8417	−	21.3397i	0.693573	−	0.785524i
$739$			9.62772i			0.354161i	0.984196	+	0.177081i	$0.0566654\pi$
$739$			9.62772i			0.354161i	−0.984196	+	0.177081i	$0.943335\pi$
$740$		0			0
$741$	−11.2554	+	11.9769i	−0.413479	+	0.439982i
$742$	6.70982	−	6.70982i	0.246325	−	0.246325i
$743$	23.4521	−	23.4521i	0.860373	−	0.860373i	−0.131008	−	0.991381i	$-0.541821\pi$
$743$	23.4521	−	23.4521i	0.860373	−	0.860373i	0.991381	+	0.131008i	$0.0418214\pi$
$744$	15.0362	−	16.0000i	0.551255	−	0.586588i
$745$		0			0
$746$			12.6766i			0.464123i
$747$	−33.2205	+	37.6247i	−1.21547	+	1.37662i
$748$	3.74691	+	3.74691i	0.137001	+	0.137001i
$749$	−5.34363			−0.195252
$750$		0			0
$751$	−13.6277			−0.497283			−0.248641	−	0.968596i	$-0.579984\pi$
$751$	−13.6277			−0.497283			−0.248641	+	0.968596i	$0.579984\pi$
$752$	1.95472	+	1.95472i	0.0712812	+	0.0712812i
$753$	1.52746	+	49.1882i	0.0556637	+	1.79252i
$754$		−	11.2554i		−	0.409899i
$755$		0			0
$756$	−5.48913	−	4.55134i	−0.199638	−	0.165531i
$757$	−22.6274	+	22.6274i	−0.822407	+	0.822407i	−0.986453	−	0.164045i	$-0.947546\pi$
$757$	−22.6274	+	22.6274i	−0.822407	+	0.822407i	0.164045	+	0.986453i	$0.447546\pi$
$758$	−6.72278	+	6.72278i	−0.244182	+	0.244182i
$759$	−17.9653	−	16.8832i	−0.652100	−	0.612820i
$760$		0			0
$761$			32.1716i			1.16622i	0.812394	+	0.583109i	$0.198164\pi$
$761$			32.1716i			1.16622i	−0.812394	+	0.583109i	$0.801836\pi$
$762$	−4.46522	+	0.138660i	−0.161758	+	0.00502313i
$763$	−5.92010	−	5.92010i	−0.214322	−	0.214322i
$764$	22.0742			0.798618
$765$		0			0
$766$	−21.2554			−0.767990
$767$	−20.0907	−	20.0907i	−0.725433	−	0.725433i
$768$	24.0347	−	0.746360i	0.867279	−	0.0269319i
$769$			16.2337i			0.585402i	0.956204	+	0.292701i	$0.0945540\pi$
$769$			16.2337i			0.585402i	−0.956204	+	0.292701i	$0.905446\pi$
$770$		0			0
$771$	−8.74456	−	8.21782i	−0.314928	−	0.295958i
$772$	−24.7334	+	24.7334i	−0.890173	+	0.890173i
$773$	19.0090	−	19.0090i	0.683708	−	0.683708i	−0.277126	−	0.960834i	$-0.589382\pi$
$773$	19.0090	−	19.0090i	0.683708	−	0.683708i	0.960834	+	0.277126i	$0.0893818\pi$
$774$	−1.17981	−	18.9783i	−0.0424076	−	0.682159i
$775$		0			0
$776$		−	6.33830i		−	0.227532i
$777$	−0.255068	−	8.21386i	−0.00915052	−	0.294671i
$778$	−14.6686	−	14.6686i	−0.525896	−	0.525896i
$779$	47.9075			1.71646
$780$		0			0
$781$	7.72281			0.276344
$782$	−1.82380	−	1.82380i	−0.0652189	−	0.0652189i
$783$	−30.9820	+	2.89373i	−1.10721	+	0.103413i
$784$			0.627719i			0.0224185i
$785$		0			0
$786$	7.72281	−	8.21782i	0.275464	−	0.293120i
$787$	23.0559	−	23.0559i	0.821854	−	0.821854i	−0.164520	−	0.986374i	$-0.552607\pi$
$787$	23.0559	−	23.0559i	0.821854	−	0.821854i	0.986374	+	0.164520i	$0.0526074\pi$
$788$	−21.4197	+	21.4197i	−0.763046	+	0.763046i
$789$	−5.63858	+	6.00000i	−0.200739	+	0.213606i
$790$		0			0
$791$		−	5.04868i		−	0.179510i
$792$	−24.6885	−	21.7985i	−0.877267	−	0.774578i
$793$	11.3137	+	11.3137i	0.401762	+	0.401762i
$794$	23.4737			0.833049
$795$		0			0
$796$	17.4891			0.619886
$797$	15.3615	+	15.3615i	0.544131	+	0.544131i	0.924737	−	0.380607i	$-0.124285\pi$
$797$	15.3615	+	15.3615i	0.544131	+	0.544131i	−0.380607	+	0.924737i	$0.624285\pi$
$798$	0.170374	+	5.48648i	0.00603116	+	0.194219i
$799$		−	4.13859i		−	0.146413i
$800$		0			0
$801$	−11.2554	+	0.699713i	−0.397691	+	0.0247231i
$802$	−14.6686	+	14.6686i	−0.517967	+	0.517967i
$803$	−37.0286	+	37.0286i	−1.30671	+	1.30671i
$804$	22.0742	+	20.7446i	0.778498	+	0.731604i
$805$		0			0
$806$		−	8.91754i		−	0.314107i
$807$	−20.7346	+	0.643878i	−0.729891	+	0.0226656i
$808$	7.10183	+	7.10183i	0.249841	+	0.249841i
$809$	14.2063			0.499466			0.249733	−	0.968315i	$-0.419657\pi$
$809$	14.2063			0.499466			0.249733	+	0.968315i	$0.419657\pi$
$810$		0			0
$811$	32.7446			1.14982			0.574909	−	0.818218i	$-0.305038\pi$
$811$	32.7446			1.14982			0.574909	+	0.818218i	$0.305038\pi$
$812$	5.81088	+	5.81088i	0.203922	+	0.203922i
$813$	−2.57800	+	0.0800555i	−0.0904143	+	0.00280767i
$814$		−	15.4456i		−	0.541369i
$815$		0			0
$816$	0.744563	+	0.699713i	0.0260649	+	0.0244949i
$817$	22.6274	−	22.6274i	0.791633	−	0.791633i
$818$	9.66704	−	9.66704i	0.338000	−	0.338000i
$819$	−7.10313	+	0.441578i	−0.248204	+	0.0154300i
$820$		0			0
$821$		−	2.22938i		−	0.0778060i	−0.999243	−	0.0389030i	$-0.987614\pi$
$821$		−	2.22938i		−	0.0778060i	0.999243	−	0.0389030i	$-0.0123863\pi$
$822$	0.725176	+	23.3526i	0.0252934	+	0.814515i
$823$	15.7216	+	15.7216i	0.548020	+	0.548020i	0.925868	−	0.377848i	$-0.123336\pi$
$823$	15.7216	+	15.7216i	0.548020	+	0.548020i	−0.377848	+	0.925868i	$0.623336\pi$
$824$	19.0149			0.662415
$825$		0			0
$826$	−9.48913			−0.330169
$827$	−0.625691	−	0.625691i	−0.0217574	−	0.0217574i	0.696144	−	0.717902i	$-0.254897\pi$
$827$	−0.625691	−	0.625691i	−0.0217574	−	0.0217574i	−0.717902	+	0.696144i	$0.754897\pi$
$828$	−10.6904	−	9.43905i	−0.371518	−	0.328030i
$829$		−	46.0000i		−	1.59765i	−0.601566	−	0.798823i	$-0.705456\pi$
$829$		−	46.0000i		−	1.59765i	0.601566	−	0.798823i	$-0.294544\pi$
$830$		0			0
$831$	24.6060	−	26.1831i	0.853572	−	0.908283i
$832$	5.65685	−	5.65685i	0.196116	−	0.196116i
$833$	0.664513	−	0.664513i	0.0230240	−	0.0230240i
$834$	−0.699713	+	0.744563i	−0.0242291	+	0.0257821i
$835$		0			0
$836$		−	22.5543i		−	0.780058i
$837$	−24.5466	+	2.29266i	−0.848456	+	0.0792461i
$838$	15.9176	+	15.9176i	0.549864	+	0.549864i
$839$	−0.699713			−0.0241568			−0.0120784	−	0.999927i	$-0.503845\pi$
$839$	−0.699713			−0.0241568			−0.0120784	+	0.999927i	$0.503845\pi$
$840$		0			0
$841$	6.86141			0.236600
$842$	0.208564	+	0.208564i	0.00718758	+	0.00718758i
$843$	−0.561643	−	18.0864i	−0.0193440	−	0.622928i
$844$		−	13.2119i		−	0.454774i
$845$		0			0
$846$	0.649468	+	10.4472i	0.0223292	+	0.359182i
$847$	4.16002	−	4.16002i	0.142940	−	0.142940i
$848$	−5.31611	+	5.31611i	−0.182556	+	0.182556i
$849$	14.9711	+	14.0693i	0.513807	+	0.482857i
$850$		0			0
$851$		−	16.4356i		−	0.563407i
$852$	4.46522	−	0.138660i	0.152976	−	0.00475042i
$853$	−13.6157	−	13.6157i	−0.466191	−	0.466191i	0.434487	−	0.900678i	$-0.356930\pi$
$853$	−13.6157	−	13.6157i	−0.466191	−	0.466191i	−0.900678	+	0.434487i	$0.856930\pi$
$854$	5.34363			0.182855
$855$		0			0
$856$	−14.2772			−0.487984
$857$	−14.6969	−	14.6969i	−0.502038	−	0.502038i	0.410033	−	0.912071i	$-0.365517\pi$
$857$	−14.6969	−	14.6969i	−0.502038	−	0.502038i	−0.912071	+	0.410033i	$0.865517\pi$
$858$	−13.3699	+	0.415179i	−0.456439	+	0.0141740i
$859$		−	28.0000i		−	0.955348i	−0.878537	−	0.477674i	$-0.841480\pi$
$859$		−	28.0000i		−	0.955348i	0.878537	−	0.477674i	$-0.158520\pi$
$860$		0			0
$861$	15.1168	+	14.2063i	0.515181	+	0.484148i
$862$	−0.196001	+	0.196001i	−0.00667581	+	0.00667581i
$863$	−29.1853	+	29.1853i	−0.993480	+	0.993480i	−0.999979	−	0.00649926i	$-0.997931\pi$
$863$	−29.1853	+	29.1853i	−0.993480	+	0.993480i	0.00649926	+	0.999979i	$0.497931\pi$
$864$	−23.3639	−	19.3723i	−0.794854	−	0.659058i
$865$		0			0
$866$		−	2.57924i		−	0.0876462i
$867$	0.866443	+	27.9017i	0.0294259	+	0.947593i
$868$	4.60388	+	4.60388i	0.156266	+	0.156266i
$869$	−62.1138			−2.10707
$870$		0			0
$871$	30.2337			1.02443
$872$	−15.8174	−	15.8174i	−0.535645	−	0.535645i
$873$	−4.71043	+	5.33492i	−0.159424	+	0.180560i
$874$			10.9783i			0.371345i
$875$		0			0
$876$	−20.7446	+	22.0742i	−0.700894	+	0.745819i
$877$	20.1295	−	20.1295i	0.679724	−	0.679724i	−0.280214	−	0.959938i	$-0.590405\pi$
$877$	20.1295	−	20.1295i	0.679724	−	0.679724i	0.959938	+	0.280214i	$0.0904053\pi$
$878$	−10.7875	+	10.7875i	−0.364061	+	0.364061i
$879$	19.0800	−	20.3030i	0.643553	−	0.684803i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−1.57317	+	1.78174i	−0.0529715	+	0.0599942i
$883$	−7.76280	−	7.76280i	−0.261239	−	0.261239i	0.564318	−	0.825557i	$-0.309139\pi$
$883$	−7.76280	−	7.76280i	−0.261239	−	0.261239i	−0.825557	+	0.564318i	$0.809139\pi$
$884$	3.05934			0.102897
$885$		0			0
$886$	1.25544			0.0421772
$887$	−5.52467	−	5.52467i	−0.185500	−	0.185500i	0.608247	−	0.793748i	$-0.291873\pi$
$887$	−5.52467	−	5.52467i	−0.185500	−	0.185500i	−0.793748	+	0.608247i	$0.791873\pi$
$888$	−0.681495	−	21.9459i	−0.0228695	−	0.736457i
$889$		−	3.25544i		−	0.109184i
$890$		0			0
$891$	4.58017	+	36.6955i	0.153442	+	1.22934i
$892$	22.4314	−	22.4314i	0.751059	−	0.751059i
$893$	−12.4560	+	12.4560i	−0.416825	+	0.416825i
$894$		0			0
$895$		0			0
$896$			9.01011i			0.301007i
$897$	−14.2268	+	0.441791i	−0.475020	+	0.0147510i
$898$	−0.856970	−	0.856970i	−0.0285975	−	0.0285975i
$899$	28.4125			0.947611
$900$		0			0
$901$	11.2554			0.374973
$902$	27.5701	+	27.5701i	0.917983	+	0.917983i
$903$	13.8497	−	0.430081i	0.460890	−	0.0143122i
$904$		−	13.4891i		−	0.448642i
$905$		0			0
$906$	−7.11684	−	6.68815i	−0.236441	−	0.222199i
$907$	2.30194	−	2.30194i	0.0764347	−	0.0764347i	−0.667856	−	0.744291i	$-0.732788\pi$
$907$	2.30194	−	2.30194i	0.0764347	−	0.0764347i	0.744291	+	0.667856i	$0.232788\pi$
$908$	−12.8199	+	12.8199i	−0.425442	+	0.425442i
$909$	−0.699713	−	11.2554i	−0.0232080	−	0.373319i
$910$		0			0
$911$			18.3152i			0.606809i	0.952862	+	0.303404i	$0.0981233\pi$
$911$			18.3152i			0.606809i	−0.952862	+	0.303404i	$0.901877\pi$
$912$	−0.134985	−	4.34687i	−0.00446979	−	0.143939i
$913$	−48.6097	−	48.6097i	−1.60875	−	1.60875i
$914$	1.39943			0.0462889
$915$		0			0
$916$	−39.7663			−1.31392
$917$	5.81088	+	5.81088i	0.191892	+	0.191892i
$918$	0.359787	+	3.85210i	0.0118747	+	0.127138i
$919$			23.1168i			0.762554i	0.924461	+	0.381277i	$0.124516\pi$
$919$			23.1168i			0.762554i	−0.924461	+	0.381277i	$0.875484\pi$
$920$		0			0
$921$	16.1644	−	17.2005i	0.532635	−	0.566775i
$922$	11.3137	−	11.3137i	0.372597	−	0.372597i
$923$	3.15283	−	3.15283i	0.103777	−	0.103777i
$924$	6.68815	−	7.11684i	0.220024	−	0.234127i
$925$		0			0
$926$			21.3745i			0.702410i
$927$	−16.0047	−	14.1313i	−0.525665	−	0.464132i
$928$	24.7334	+	24.7334i	0.811912	+	0.811912i
$929$	−44.8482			−1.47142			−0.735710	−	0.677296i	$-0.763152\pi$
$929$	−44.8482			−1.47142			−0.735710	+	0.677296i	$0.763152\pi$
$930$		0			0
$931$	−4.00000			−0.131095
$932$	0.572416	+	0.572416i	0.0187501	+	0.0187501i
$933$	0.202087	+	6.50774i	0.00661604	+	0.213054i
$934$			17.5326i			0.573685i
$935$		0			0
$936$	−18.9783	+	1.17981i	−0.620324	+	0.0385634i
$937$	5.03237	−	5.03237i	0.164400	−	0.164400i	−0.620113	−	0.784513i	$-0.712913\pi$
$937$	5.03237	−	5.03237i	0.164400	−	0.164400i	0.784513	+	0.620113i	$0.212913\pi$
$938$	7.13991	−	7.13991i	0.233126	−	0.233126i
$939$	14.9711	+	14.0693i	0.488563	+	0.459134i
$940$		0			0
$941$			36.6303i			1.19412i	0.802198	+	0.597058i	$0.203664\pi$
$941$			36.6303i			1.19412i	−0.802198	+	0.597058i	$0.796336\pi$
$942$	−17.4807	+	0.542834i	−0.569552	+	0.0176865i
$943$	29.3372	+	29.3372i	0.955352	+	0.955352i
$944$	7.51811			0.244694
$945$		0			0
$946$	26.0435			0.846747
$947$	11.4132	+	11.4132i	0.370879	+	0.370879i	0.867797	−	0.496918i	$-0.165535\pi$
$947$	11.4132	+	11.4132i	0.370879	+	0.370879i	−0.496918	+	0.867797i	$0.665535\pi$
$948$	−35.9133	+	1.11523i	−1.16641	+	0.0362210i
$949$			30.2337i			0.981427i
$950$		0			0
$951$	−8.00000	−	7.51811i	−0.259418	−	0.243791i
$952$	1.77546	−	1.77546i	0.0575429	−	0.0575429i
$953$	−12.5337	+	12.5337i	−0.406005	+	0.406005i	−0.880343	−	0.474338i	$-0.842688\pi$
$953$	−12.5337	+	12.5337i	−0.406005	+	0.406005i	0.474338	+	0.880343i	$0.342688\pi$
$954$	−28.4125	+	1.76631i	−0.919889	+	0.0571865i
$955$		0			0
$956$		−	10.7971i		−	0.349202i
$957$	−1.32282	−	42.5983i	−0.0427607	−	1.37701i
$958$	13.8117	+	13.8117i	0.446234	+	0.446234i
$959$	−17.0256			−0.549784
$960$		0			0
$961$	−8.48913			−0.273843
$962$	−6.30565	−	6.30565i	−0.203302	−	0.203302i
$963$	12.0170	+	10.6104i	0.387244	+	0.341914i
$964$		−	15.7663i		−	0.507799i
$965$		0			0
$966$	−3.25544	+	3.46410i	−0.104742	+	0.111456i
$967$	25.7863	−	25.7863i	0.829232	−	0.829232i	−0.158178	−	0.987411i	$-0.550562\pi$
$967$	25.7863	−	25.7863i	0.829232	−	0.829232i	0.987411	+	0.158178i	$0.0505620\pi$
$968$	11.1148	−	11.1148i	0.357243	−	0.357243i
$969$	−4.45877	+	4.74456i	−0.143236	+	0.152417i
$970$		0			0
$971$		−	23.2540i		−	0.746258i	−0.927780	−	0.373129i	$-0.878285\pi$
$971$		−	23.2540i		−	0.746258i	0.927780	−	0.373129i	$-0.121715\pi$
$972$	3.30704	+	21.1346i	0.106074	+	0.677892i
$973$	−0.526485	−	0.526485i	−0.0168783	−	0.0168783i
$974$	12.4570			0.399147
$975$		0			0
$976$	−4.23369			−0.135517
$977$	−40.5985	−	40.5985i	−1.29886	−	1.29886i	−0.929144	−	0.369717i	$-0.879455\pi$
$977$	−40.5985	−	40.5985i	−1.29886	−	1.29886i	−0.369717	−	0.929144i	$-0.620545\pi$
$978$	0.542834	+	17.4807i	0.0173579	+	0.558971i
$979$		−	15.4456i		−	0.493644i
$980$		0			0
$981$	1.55842	+	25.0684i	0.0497566	+	0.800374i
$982$	−19.9335	+	19.9335i	−0.636103	+	0.636103i
$983$	38.3964	−	38.3964i	1.22466	−	1.22466i	0.258696	−	0.965959i	$-0.416707\pi$
$983$	38.3964	−	38.3964i	1.22466	−	1.22466i	0.965959	−	0.258696i	$-0.0832929\pi$
$984$	40.3894	+	37.9565i	1.28757	+	1.21001i
$985$		0			0
$986$		−	4.45877i		−	0.141996i
$987$	−7.62404	+	0.236752i	−0.242676	+	0.00753590i
$988$	−9.20777	−	9.20777i	−0.292938	−	0.292938i
$989$	27.7128			0.881216
$990$		0			0
$991$	50.9783			1.61938			0.809689	−	0.586860i	$-0.199636\pi$
$991$	50.9783			1.61938			0.809689	+	0.586860i	$0.199636\pi$
$992$	19.5959	+	19.5959i	0.622171	+	0.622171i
$993$	25.9306	−	0.805232i	0.822882	−	0.0255533i
$994$		−	1.48913i		−	0.0472322i
$995$		0			0
$996$	−28.9783	−	27.2327i	−0.918211	−	0.862901i
$997$	5.03237	−	5.03237i	0.159377	−	0.159377i	−0.622914	−	0.782290i	$-0.714051\pi$
$997$	5.03237	−	5.03237i	0.159377	−	0.159377i	0.782290	+	0.622914i	$0.214051\pi$
$998$	0.911899	−	0.911899i	0.0288657	−	0.0288657i
$999$	−15.7359	+	18.9783i	−0.497863	+	0.600445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.a.218.3	✓	16
3.2	odd	2	inner	525.2.j.a.218.5	yes	16
5.2	odd	4	inner	525.2.j.a.407.5	yes	16
5.3	odd	4	inner	525.2.j.a.407.4	yes	16
5.4	even	2	inner	525.2.j.a.218.6	yes	16
15.2	even	4	inner	525.2.j.a.407.3	yes	16
15.8	even	4	inner	525.2.j.a.407.6	yes	16
15.14	odd	2	inner	525.2.j.a.218.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.j.a.218.3	✓	16	1.1	even	1	trivial
525.2.j.a.218.4	yes	16	15.14	odd	2	inner
525.2.j.a.218.5	yes	16	3.2	odd	2	inner
525.2.j.a.218.6	yes	16	5.4	even	2	inner
525.2.j.a.407.3	yes	16	15.2	even	4	inner
525.2.j.a.407.4	yes	16	5.3	odd	4	inner
525.2.j.a.407.5	yes	16	5.2	odd	4	inner
525.2.j.a.407.6	yes	16	15.8	even	4	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.560232 - 0.560232i) q^{2} +(-1.73122 + 0.0537601i) q^{3} -1.37228i q^{4} +(1.00000 + 0.939764i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.88926 + 1.88926i) q^{8} +(2.99422 - 0.186141i) q^{9} +O(q^{10})\)	\(q+(-0.560232 - 0.560232i) q^{2} +(-1.73122 + 0.0537601i) q^{3} -1.37228i q^{4} +(1.00000 + 0.939764i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.88926 + 1.88926i) q^{8} +(2.99422 - 0.186141i) q^{9} +4.10891i q^{11} +(0.0737740 + 2.37572i) q^{12} +(1.67746 + 1.67746i) q^{13} +0.792287 q^{14} -0.627719 q^{16} +(0.664513 + 0.664513i) q^{17} +(-1.78174 - 1.57317i) q^{18} -4.00000i q^{19} +(1.18614 - 1.26217i) q^{21} +(2.30194 - 2.30194i) q^{22} +(2.44949 - 2.44949i) q^{23} +(3.16915 - 3.37228i) q^{24} -1.87953i q^{26} +(-5.17364 + 0.483219i) q^{27} +(0.970349 + 0.970349i) q^{28} +5.98844 q^{29} +4.74456 q^{31} +(4.13018 + 4.13018i) q^{32} +(-0.220895 - 7.11342i) q^{33} -0.744563i q^{34} +(-0.255437 - 4.10891i) q^{36} +(3.35491 - 3.35491i) q^{37} +(-2.24093 + 2.24093i) q^{38} +(-2.99422 - 2.81386i) q^{39} +11.9769i q^{41} +(-1.37162 + 0.0425934i) q^{42} +(5.65685 + 5.65685i) q^{43} +5.63858 q^{44} -2.74456 q^{46} +(-3.11400 - 3.11400i) q^{47} +(1.08672 - 0.0337462i) q^{48} -1.00000i q^{49} +(-1.18614 - 1.11469i) q^{51} +(2.30194 - 2.30194i) q^{52} +(8.46893 - 8.46893i) q^{53} +(3.16915 + 2.62772i) q^{54} -2.67181i q^{56} +(0.215040 + 6.92487i) q^{57} +(-3.35491 - 3.35491i) q^{58} -11.9769 q^{59} +6.74456 q^{61} +(-2.65805 - 2.65805i) q^{62} +(-1.98561 + 2.24885i) q^{63} -3.37228i q^{64} +(-3.86141 + 4.10891i) q^{66} +(9.01177 - 9.01177i) q^{67} +(0.911899 - 0.911899i) q^{68} +(-4.10891 + 4.37228i) q^{69} -1.87953i q^{71} +(-5.30519 + 6.00852i) q^{72} +(9.01177 + 9.01177i) q^{73} -3.75906 q^{74} -5.48913 q^{76} +(-2.90544 - 2.90544i) q^{77} +(0.101044 + 3.25387i) q^{78} +15.1168i q^{79} +(8.93070 - 1.11469i) q^{81} +(6.70982 - 6.70982i) q^{82} +(-11.8303 + 11.8303i) q^{83} +(-1.73205 - 1.62772i) q^{84} -6.33830i q^{86} +(-10.3673 + 0.321939i) q^{87} +(-7.76280 - 7.76280i) q^{88} -3.75906 q^{89} -2.37228 q^{91} +(-3.36139 - 3.36139i) q^{92} +(-8.21386 + 0.255068i) q^{93} +3.48913i q^{94} +(-7.37228 - 6.92820i) q^{96} +(-1.67746 + 1.67746i) q^{97} +(-0.560232 + 0.560232i) q^{98} +(0.764836 + 12.3030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{6}+O(q^{10}) \) 16 * q + 16 * q^6	\( 16 q + 16 q^{6} - 56 q^{16} - 4 q^{21} - 16 q^{31} - 96 q^{36} + 48 q^{46} + 4 q^{51} + 16 q^{61} + 168 q^{66} + 96 q^{76} + 28 q^{81} + 8 q^{91} - 72 q^{96}+O(q^{100}) \) 16 * q + 16 * q^6 - 56 * q^16 - 4 * q^21 - 16 * q^31 - 96 * q^36 + 48 * q^46 + 4 * q^51 + 16 * q^61 + 168 * q^66 + 96 * q^76 + 28 * q^81 + 8 * q^91 - 72 * q^96

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