LMFDB - Embedded newform 525.2.j.a.407.5

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			407.5
Root			$0.912166 - 1.47240i$ of defining polynomial
Character	$\chi$	$=$	525.407
Dual form			525.2.j.a.218.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.560232 - 0.560232i) q^{2} +(0.0537601 + 1.73122i) q^{3} +1.37228i q^{4} +(1.00000 + 0.939764i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.88926 + 1.88926i) q^{8} +(-2.99422 + 0.186141i) q^{9} +O(q^{10})$	\(q+(0.560232 - 0.560232i) q^{2} +(0.0537601 + 1.73122i) 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} +(-2.37572 + 0.0737740i) q^{12} +(1.67746 - 1.67746i) q^{13} -0.792287 q^{14} -0.627719 q^{16} +(-0.664513 + 0.664513i) q^{17} +(-1.57317 + 1.78174i) 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} +(-0.483219 - 5.17364i) q^{27} +(0.970349 - 0.970349i) q^{28} -5.98844 q^{29} +4.74456 q^{31} +(-4.13018 + 4.13018i) q^{32} +(-7.11342 + 0.220895i) 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} +(-0.0425934 - 1.37162i) q^{42} +(5.65685 - 5.65685i) q^{43} -5.63858 q^{44} -2.74456 q^{46} +(3.11400 - 3.11400i) q^{47} +(-0.0337462 - 1.08672i) 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} +(-6.92487 + 0.215040i) q^{57} +(-3.35491 + 3.35491i) q^{58} +11.9769 q^{59} +6.74456 q^{61} +(2.65805 - 2.65805i) q^{62} +(2.24885 + 1.98561i) 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} +(-6.00852 - 5.30519i) q^{72} +(9.01177 - 9.01177i) q^{73} +3.75906 q^{74} -5.48913 q^{76} +(2.90544 - 2.90544i) q^{77} +(3.25387 - 0.101044i) 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} +(-0.321939 - 10.3673i) q^{87} +(-7.76280 + 7.76280i) q^{88} +3.75906 q^{89} -2.37228 q^{91} +(3.36139 - 3.36139i) q^{92} +(0.255068 + 8.21386i) 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	$-0.659627\pi$
$2$	0.560232	−	0.560232i	0.396143	−	0.396143i	0.876870	+	0.480727i	$0.159627\pi$
$3$	0.0537601	+	1.73122i	0.0310384	+	0.999518i
$3$	0.0537601	+	1.73122i	0.0310384	+	0.999518i
$4$			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	$0.787359\pi$
$12$	−2.37572	+	0.0737740i	−0.685810	+	0.0212967i
$13$	1.67746	−	1.67746i	0.465243	−	0.465243i	−0.435127	−	0.900369i	$-0.643296\pi$
$13$	1.67746	−	1.67746i	0.465243	−	0.465243i	0.900369	+	0.435127i	$0.143296\pi$
$14$	−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	$-0.786355\pi$
$17$	−0.664513	+	0.664513i	−0.161168	+	0.161168i	0.621916	+	0.783084i	$0.286355\pi$
$18$	−1.57317	+	1.78174i	−0.370801	+	0.419960i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		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	$-0.367618\pi$
$23$	−2.44949	−	2.44949i	−0.510754	−	0.510754i	−0.914757	+	0.404004i	$0.867618\pi$
$24$	−3.16915	+	3.37228i	−0.646900	+	0.688364i
$25$		0			0
$26$		−	1.87953i		−	0.368606i
$27$	−0.483219	−	5.17364i	−0.0929956	−	0.995667i
$28$	0.970349	−	0.970349i	0.183379	−	0.183379i
$29$	−5.98844			−1.11203			−0.556013	−	0.831174i	$-0.687669\pi$
$29$	−5.98844			−1.11203			−0.556013	+	0.831174i	$0.687669\pi$
$30$		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
$33$	−7.11342	+	0.220895i	−1.23829	+	0.0384530i
$34$			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	0.926886	−	0.375342i	$-0.122475\pi$
$37$	3.35491	+	3.35491i	0.551544	+	0.551544i	−0.375342	+	0.926886i	$0.622475\pi$
$38$	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	$0.615186\pi$
$42$	−0.0425934	−	1.37162i	−0.00657231	−	0.211646i
$43$	5.65685	−	5.65685i	0.862662	−	0.862662i	−0.128984	−	0.991647i	$-0.541172\pi$
$43$	5.65685	−	5.65685i	0.862662	−	0.862662i	0.991647	+	0.128984i	$0.0411717\pi$
$44$	−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	$-0.645919\pi$
$47$	3.11400	−	3.11400i	0.454224	−	0.454224i	0.896754	+	0.442530i	$0.145919\pi$
$48$	−0.0337462	−	1.08672i	−0.00487085	−	0.156854i
$49$			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	−0.983749	−	0.179548i	$-0.942536\pi$
$53$	−8.46893	−	8.46893i	−1.16330	−	1.16330i	−0.179548	−	0.983749i	$-0.557464\pi$
$54$	−3.16915	−	2.62772i	−0.431266	−	0.357587i
$55$		0			0
$56$		−	2.67181i		−	0.357036i
$57$	−6.92487	+	0.215040i	−0.917221	+	0.0284828i
$58$	−3.35491	+	3.35491i	−0.440522	+	0.440522i
$59$	11.9769			1.55926			0.779628	−	0.626242i	$-0.215408\pi$
$59$	11.9769			1.55926			0.779628	+	0.626242i	$0.215408\pi$
$60$		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
$63$	2.24885	+	1.98561i	0.283329	+	0.250164i
$64$			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	0.994295	+	0.106668i	$0.0340181\pi$
$67$	9.01177	+	9.01177i	1.10096	+	1.10096i	0.106668	+	0.994295i	$0.465982\pi$
$68$	−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	$-0.0355749\pi$
$72$	−6.00852	−	5.30519i	−0.708111	−	0.625222i
$73$	9.01177	−	9.01177i	1.05475	−	1.05475i	0.0563356	−	0.998412i	$-0.482058\pi$
$73$	9.01177	−	9.01177i	1.05475	−	1.05475i	0.998412	−	0.0563356i	$-0.0179417\pi$
$74$	3.75906			0.436981
$75$		0			0
$76$	−5.48913			−0.629646
$77$	2.90544	−	2.90544i	0.331106	−	0.331106i
$78$	3.25387	−	0.101044i	0.368428	−	0.0114409i
$79$		−	15.1168i		−	1.70078i	−0.526155	−	0.850389i	$-0.676367\pi$
$79$		−	15.1168i		−	1.70078i	0.526155	−	0.850389i	$-0.323633\pi$
$80$		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	0.929352	+	0.369194i	$0.120366\pi$
$83$	11.8303	+	11.8303i	1.29855	+	1.29855i	0.369194	+	0.929352i	$0.379634\pi$
$84$	1.73205	+	1.62772i	0.188982	+	0.177599i
$85$		0			0
$86$		−	6.33830i		−	0.683476i
$87$	−0.321939	−	10.3673i	−0.0345155	−	1.11149i
$88$	−7.76280	+	7.76280i	−0.827517	+	0.827517i
$89$	3.75906			0.398459			0.199230	−	0.979953i	$-0.436156\pi$
$89$	3.75906			0.398459			0.199230	+	0.979953i	$0.436156\pi$
$90$		0			0
$91$	−2.37228			−0.248683
$92$	3.36139	−	3.36139i	0.350449	−	0.350449i
$93$	0.255068	+	8.21386i	0.0264493	+	0.851738i
$94$		−	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	0.616800	−	0.787120i	$-0.288429\pi$
$97$	−1.67746	−	1.67746i	−0.170320	−	0.170320i	−0.787120	+	0.616800i	$0.788429\pi$
$98$	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	$-0.0598829\pi$
$102$	−1.28900	+	0.0400277i	−0.127630	+	0.00396334i
$103$	−5.03237	+	5.03237i	−0.495854	+	0.495854i	−0.910145	−	0.414291i	$-0.864030\pi$
$103$	−5.03237	+	5.03237i	−0.495854	+	0.495854i	0.414291	+	0.910145i	$0.364030\pi$
$104$	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	$-0.833160\pi$
$107$	−3.77852	+	3.77852i	−0.365283	+	0.365283i	0.500471	+	0.865754i	$0.333160\pi$
$108$	7.09968	−	0.663113i	0.683167	−	0.0638081i
$109$		−	8.37228i		−	0.801919i	−0.916096	−	0.400960i	$-0.868677\pi$
$109$		−	8.37228i		−	0.801919i	0.916096	−	0.400960i	$-0.131323\pi$
$110$		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	$-0.173682\pi$
$113$	3.56995	+	3.56995i	0.335833	+	0.335833i	−0.518963	+	0.854796i	$0.673682\pi$
$114$	−3.75906	+	4.00000i	−0.352068	+	0.374634i
$115$		0			0
$116$		−	8.21782i		−	0.763006i
$117$	−4.71043	+	5.33492i	−0.435479	+	0.493213i
$118$	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
$123$	−20.7346	+	0.643878i	−1.86957	+	0.0580565i
$124$			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	0.597560	−	0.801824i	$-0.296137\pi$
$127$	−2.30194	−	2.30194i	−0.204264	−	0.204264i	−0.801824	+	0.597560i	$0.796137\pi$
$128$	−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	$-0.116881\pi$
$132$	−0.303131	−	9.76161i	−0.0263841	−	0.849639i
$133$	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	−0.0289711	+	0.999580i	$0.509223\pi$
$137$	−12.0389	+	12.0389i	−1.02855	+	1.02855i	−0.999580	+	0.0289711i	$0.990777\pi$
$138$	−0.147548	−	4.75143i	−0.0125601	−	0.404469i
$139$		−	0.744563i		−	0.0631530i	−0.999501	−	0.0315765i	$-0.989947\pi$
$139$		−	0.744563i		−	0.0631530i	0.999501	−	0.0315765i	$-0.0100528\pi$
$140$		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
$147$	−1.73122	+	0.0537601i	−0.142788	+	0.00443406i
$148$	−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
$153$	1.86601	−	2.11339i	0.150858	−	0.170858i
$154$		−	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	0.249228	−	0.968445i	$-0.419823\pi$
$157$	−9.01177	−	9.01177i	−0.719217	−	0.719217i	−0.968445	+	0.249228i	$0.919823\pi$
$158$	−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
$162$	4.37878	−	5.62775i	0.344029	−	0.442158i
$163$	9.01177	−	9.01177i	0.705856	−	0.705856i	−0.259805	−	0.965661i	$-0.583658\pi$
$163$	9.01177	−	9.01177i	0.705856	−	0.705856i	0.965661	+	0.259805i	$0.0836583\pi$
$164$	−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	$-0.886438\pi$
$167$	−7.59586	+	7.59586i	−0.587785	+	0.587785i	0.349246	+	0.937031i	$0.386438\pi$
$168$	4.62549	−	0.143637i	0.356864	−	0.0110818i
$169$			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	$-0.459430\pi$
$173$	−11.3744	−	11.3744i	−0.864777	−	0.864777i	−0.991888	+	0.127111i	$0.959430\pi$
$174$	−5.98844	−	5.62772i	−0.453982	−	0.426636i
$175$		0			0
$176$		−	2.57924i		−	0.194418i
$177$	0.643878	+	20.7346i	0.0483968	+	1.55851i
$178$	2.10594	−	2.10594i	0.157847	−	0.157847i
$179$	−1.87953			−0.140482			−0.0702412	−	0.997530i	$-0.522377\pi$
$179$	−1.87953			−0.140482			−0.0702412	+	0.997530i	$0.522377\pi$
$180$		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
$183$	0.362588	+	11.6763i	0.0268033	+	0.863137i
$184$		−	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	$0.802285\pi$
$192$	−5.83815	+	0.181294i	−0.421332	+	0.0130838i
$193$	−18.0235	+	18.0235i	−1.29736	+	1.29736i	−0.367234	+	0.930129i	$0.619695\pi$
$193$	−18.0235	+	18.0235i	−1.29736	+	1.29736i	−0.930129	+	0.367234i	$0.880305\pi$
$194$	−1.87953			−0.134942
$195$		0			0
$196$	−1.37228			−0.0980201
$197$	15.6088	−	15.6088i	1.11208	−	1.11208i	0.119215	−	0.992868i	$-0.461962\pi$
$197$	15.6088	−	15.6088i	1.11208	−	1.11208i	0.992868	−	0.119215i	$-0.0380378\pi$
$198$	−7.32100	−	6.46403i	−0.520281	−	0.459379i
$199$		−	12.7446i		−	0.903438i	−0.892160	−	0.451719i	$-0.850811\pi$
$199$		−	12.7446i		−	0.903438i	0.892160	−	0.451719i	$-0.149189\pi$
$200$		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
$207$	7.79026	+	6.87836i	0.541461	+	0.478079i
$208$	−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
$213$	3.25387	−	0.101044i	0.222951	−	0.00692339i
$214$			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
$222$	0.202087	+	6.50774i	0.0135632	+	0.436771i
$223$	16.3461	−	16.3461i	1.09461	−	1.09461i	0.0995853	−	0.995029i	$-0.468248\pi$
$223$	16.3461	−	16.3461i	1.09461	−	1.09461i	0.995029	−	0.0995853i	$-0.0317516\pi$
$224$	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	$-0.605530\pi$
$227$	9.34201	−	9.34201i	0.620051	−	0.620051i	0.945544	+	0.325493i	$0.105530\pi$
$228$	−0.295096	−	9.50286i	−0.0195432	−	0.629342i
$229$			28.9783i			1.91494i	0.288538	+	0.957468i	$0.406831\pi$
$229$			28.9783i			1.91494i	−0.288538	+	0.957468i	$0.593169\pi$
$230$		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	$-0.243849\pi$
$233$	0.417127	+	0.417127i	0.0273269	+	0.0273269i	−0.693311	+	0.720638i	$0.743849\pi$
$234$	0.349857	+	5.62772i	0.0228708	+	0.367895i
$235$		0			0
$236$			16.4356i			1.06987i
$237$	26.1705	−	0.812683i	1.69996	−	0.0527894i
$238$	0.526485	−	0.526485i	0.0341270	−	0.0341270i
$239$	−7.86797			−0.508936			−0.254468	−	0.967081i	$-0.581900\pi$
$239$	−7.86797			−0.508936			−0.254468	+	0.967081i	$0.581900\pi$
$240$		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
$243$	2.40989	+	15.4011i	0.154594	+	0.987978i
$244$			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	$-0.354036\pi$
$252$	−2.72482	+	3.08606i	−0.171647	+	0.194404i
$253$	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	$-0.819329\pi$
$257$	−4.89898	+	4.89898i	−0.305590	+	0.305590i	0.537606	+	0.843196i	$0.319329\pi$
$258$	10.9730	−	0.340747i	0.683147	−	0.0212140i
$259$		−	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	$-0.296821\pi$
$263$	−3.36139	−	3.36139i	−0.207272	−	0.207272i	−0.803107	+	0.595835i	$0.796821\pi$
$264$	−13.8564	−	13.0217i	−0.852803	−	0.801433i
$265$		0			0
$266$		−	3.16915i		−	0.194313i
$267$	0.202087	+	6.50774i	0.0123675	+	0.398267i
$268$	−12.3667	+	12.3667i	−0.755415	+	0.755415i
$269$	−11.9769			−0.730243			−0.365122	−	0.930960i	$-0.618973\pi$
$269$	−11.9769			−0.730243			−0.365122	+	0.930960i	$0.618973\pi$
$270$		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
$273$	−0.127534	−	4.10693i	−0.00771871	−	0.248563i
$274$			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	0.112320	−	0.993672i	$-0.464172\pi$
$277$	−14.6686	−	14.6686i	−0.881352	−	0.881352i	−0.993672	+	0.112320i	$0.964172\pi$
$278$	−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	$0.899130\pi$
$282$	6.04043	−	0.187576i	0.359702	−	0.0111700i
$283$	−8.38728	+	8.38728i	−0.498572	+	0.498572i	−0.910993	−	0.412421i	$-0.864683\pi$
$283$	−8.38728	+	8.38728i	−0.498572	+	0.498572i	0.412421	+	0.910993i	$0.364683\pi$
$284$	2.57924			0.153050
$285$		0			0
$286$	7.72281			0.456660
$287$	8.46893	−	8.46893i	0.499905	−	0.499905i
$288$	11.5979	−	13.1355i	0.683412	−	0.774015i
$289$			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	$-0.0943004\pi$
$293$	11.3744	+	11.3744i	0.664498	+	0.664498i	−0.291939	+	0.956437i	$0.594300\pi$
$294$	−0.939764	+	1.00000i	−0.0548081	+	0.0583212i
$295$		0			0
$296$			12.6766i			0.736812i
$297$	21.2580	−	1.98551i	1.23351	−	0.115211i
$298$		0			0
$299$	−8.21782			−0.475249
$300$		0			0
$301$	−8.00000			−0.461112
$302$	−3.98708	+	3.98708i	−0.229431	+	0.229431i
$303$	6.50774	−	0.202087i	0.373860	−	0.0116096i
$304$		−	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	0.376462	−	0.926432i	$-0.377141\pi$
$307$	−9.63625	−	9.63625i	−0.549970	−	0.549970i	−0.926432	+	0.376462i	$0.877141\pi$
$308$	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	$-0.0339895\pi$
$312$	0.340747	+	10.9730i	0.0192910	+	0.621222i
$313$	−8.38728	+	8.38728i	−0.474077	+	0.474077i	−0.903231	−	0.429154i	$-0.858812\pi$
$313$	−8.38728	+	8.38728i	−0.474077	+	0.474077i	0.429154	+	0.903231i	$0.358812\pi$
$314$	−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	$-0.806962\pi$
$317$	−4.48185	+	4.48185i	−0.251726	+	0.251726i	0.569952	+	0.821678i	$0.306962\pi$
$318$	−0.510136	−	16.4277i	−0.0286070	−	0.921221i
$319$		−	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
$327$	14.4942	−	0.450095i	0.801533	−	0.0248903i
$328$	−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
$333$	−10.6698	−	9.42086i	−0.584703	−	0.516260i
$334$			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	0.609801	−	0.792555i	$-0.291249\pi$
$337$	−3.35491	−	3.35491i	−0.182754	−	0.182754i	−0.792555	+	0.609801i	$0.791249\pi$
$338$	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
$342$	−7.12695	−	6.29270i	−0.385381	−	0.340270i
$343$	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	$-0.693022\pi$
$347$	4.69042	−	4.69042i	0.251795	−	0.251795i	0.821706	+	0.569911i	$0.193022\pi$
$348$	14.2268	−	0.441791i	0.762638	−	0.0236825i
$349$			21.7228i			1.16280i	0.813619	+	0.581398i	$0.197494\pi$
$349$			21.7228i			1.16280i	−0.813619	+	0.581398i	$0.802506\pi$
$350$		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	$-0.344894\pi$
$353$	−7.80442	−	7.80442i	−0.415387	−	0.415387i	−0.883610	+	0.468223i	$0.844894\pi$
$354$	11.9769	+	11.2554i	0.636564	+	0.598220i
$355$		0			0
$356$			5.15848i			0.273399i
$357$	0.0505218	+	1.62693i	0.00267390	+	0.0861065i
$358$	−1.05297	+	1.05297i	−0.0556512	+	0.0556512i
$359$	29.5923			1.56182			0.780912	−	0.624641i	$-0.214755\pi$
$359$	29.5923			1.56182			0.780912	+	0.624641i	$0.214755\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	3.36139	−	3.36139i	0.176671	−	0.176671i
$363$	−0.316279	−	10.1850i	−0.0166003	−	0.534575i
$364$		−	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	0.563458	−	0.826145i	$-0.309471\pi$
$367$	−5.03237	−	5.03237i	−0.262688	−	0.262688i	−0.826145	+	0.563458i	$0.809471\pi$
$368$	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
$372$	−11.2717	+	0.350025i	−0.584412	+	0.0181480i
$373$	−11.3137	+	11.3137i	−0.585802	+	0.585802i	−0.936492	−	0.350690i	$-0.885947\pi$
$373$	−11.3137	+	11.3137i	−0.585802	+	0.585802i	0.350690	+	0.936492i	$0.385947\pi$
$374$	−3.05934			−0.158195
$375$		0			0
$376$	11.7663			0.606801
$377$	−10.0453	+	10.0453i	−0.517362	+	0.517362i
$378$	0.382848	+	4.09900i	0.0196916	+	0.210830i
$379$			12.0000i			0.616399i	0.951322	+	0.308199i	$0.0997264\pi$
$379$			12.0000i			0.616399i	−0.951322	+	0.308199i	$0.900274\pi$
$380$		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	$-0.490382\pi$
$383$	−18.9702	−	18.9702i	−0.969333	−	0.969333i	−0.999544	+	0.0302103i	$0.990382\pi$
$384$	10.6873	−	11.3723i	0.545382	−	0.580339i
$385$		0			0
$386$			20.1947i			1.02788i
$387$	−15.8849	+	17.9908i	−0.807475	+	0.914526i
$388$	2.30194	−	2.30194i	0.116863	−	0.116863i
$389$	−26.1831			−1.32754			−0.663769	−	0.747938i	$-0.731044\pi$
$389$	−26.1831			−1.32754			−0.663769	+	0.747938i	$0.731044\pi$
$390$		0			0
$391$	3.25544			0.164635
$392$	−1.88926	+	1.88926i	−0.0954220	+	0.0954220i
$393$	14.2268	−	0.441791i	0.717649	−	0.0222854i
$394$		−	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	−0.998603	−	0.0528457i	$-0.983171\pi$
$397$	−20.9500	−	20.9500i	−1.05145	−	1.05145i	−0.0528457	−	0.998603i	$-0.516829\pi$
$398$	−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	$-0.226810\pi$
$402$	0.542834	+	17.4807i	0.0270741	+	0.871858i
$403$	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
$408$	−0.134985	−	4.34687i	−0.00668274	−	0.215202i
$409$		−	17.2554i		−	0.853226i	−0.904434	−	0.426613i	$-0.859707\pi$
$409$		−	17.2554i		−	0.853226i	0.904434	−	0.426613i	$-0.140293\pi$
$410$		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
$417$	1.28900	−	0.0400277i	0.0631226	−	0.00196017i
$418$	−9.20777	+	9.20777i	−0.450367	+	0.450367i
$419$	28.4125			1.38804			0.694021	−	0.719954i	$-0.255837\pi$
$419$	28.4125			1.38804			0.694021	+	0.719954i	$0.255837\pi$
$420$		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
$423$	−8.74437	+	9.90365i	−0.425166	+	0.481532i
$424$		−	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	$-0.00268211\pi$
$432$	0.303326	+	3.24759i	0.0145938	+	0.156250i
$433$	2.30194	−	2.30194i	0.110624	−	0.110624i	−0.649628	−	0.760252i	$-0.725075\pi$
$433$	2.30194	−	2.30194i	0.110624	−	0.110624i	0.760252	+	0.649628i	$0.225075\pi$
$434$	−3.75906			−0.180440
$435$		0			0
$436$	11.4891			0.550229
$437$	9.79796	−	9.79796i	0.468700	−	0.468700i
$438$	17.4807	−	0.542834i	0.835260	−	0.0259376i
$439$			19.2554i			0.919012i	0.888175	+	0.459506i	$0.151974\pi$
$439$			19.2554i			0.919012i	−0.888175	+	0.459506i	$0.848026\pi$
$440$		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	$-0.238015\pi$
$443$	1.12046	+	1.12046i	0.0532348	+	0.0532348i	−0.679988	+	0.733223i	$0.738015\pi$
$444$	−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	$-0.511492\pi$
$449$	−1.52967			−0.0721896			−0.0360948	+	0.999348i	$0.511492\pi$
$450$		0			0
$451$	−49.2119			−2.31730
$452$	−4.89898	+	4.89898i	−0.230429	+	0.230429i
$453$	−0.382602	−	12.3208i	−0.0179762	−	0.578882i
$454$		−	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	0.677291	−	0.735715i	$-0.263154\pi$
$457$	−1.24897	−	1.24897i	−0.0584244	−	0.0584244i	−0.735715	+	0.677291i	$0.763154\pi$
$458$	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	$0.844153\pi$
$462$	5.63587	−	0.175013i	0.262204	−	0.00814232i
$463$	−19.0765	+	19.0765i	−0.886560	+	0.886560i	−0.994191	−	0.107631i	$-0.965674\pi$
$463$	−19.0765	+	19.0765i	−0.886560	+	0.886560i	0.107631	+	0.994191i	$0.465674\pi$
$464$	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	$-0.578902\pi$
$467$	15.6477	−	15.6477i	0.724087	−	0.724087i	0.969435	+	0.245348i	$0.0789022\pi$
$468$	−7.32100	−	6.46403i	−0.338414	−	0.298800i
$469$		−	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
$477$	26.9343	+	23.7814i	1.23323	+	1.08888i
$478$	−4.40788	+	4.40788i	−0.201612	+	0.201612i
$479$	24.6535			1.12645			0.563223	−	0.826305i	$-0.309561\pi$
$479$	24.6535			1.12645			0.563223	+	0.826305i	$0.309561\pi$
$480$		0			0
$481$	11.2554			0.513204
$482$	6.43657	−	6.43657i	0.293178	−	0.293178i
$483$	−5.99711	+	0.186230i	−0.272878	+	0.00847378i
$484$		−	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	0.408822	−	0.912614i	$-0.365940\pi$
$487$	−11.1177	−	11.1177i	−0.503791	−	0.503791i	−0.912614	+	0.408822i	$0.865940\pi$
$488$	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	$-0.296694\pi$
$492$	−0.883582	−	28.4537i	−0.0398349	−	1.28279i
$493$	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
$498$	0.712613	+	22.9480i	0.0319330	+	1.02833i
$499$		−	1.62772i		−	0.0728667i	−0.999336	−	0.0364333i	$-0.988400\pi$
$499$		−	1.62772i		−	0.0728667i	0.999336	−	0.0364333i	$-0.0115997\pi$
$500$		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	$-0.285511\pi$
$503$	−3.53113	−	3.53113i	−0.157445	−	0.157445i	−0.781434	+	0.623988i	$0.785511\pi$
$504$	0.497333	+	8.00000i	0.0221530	+	0.356348i
$505$		0			0
$506$		−	11.2772i		−	0.501331i
$507$	−12.7630	+	0.396334i	−0.566825	+	0.0176018i
$508$	3.15891	−	3.15891i	0.140154	−	0.140154i
$509$	8.21782			0.364249			0.182124	−	0.983276i	$-0.441703\pi$
$509$	8.21782			0.364249			0.182124	+	0.983276i	$0.441703\pi$
$510$		0			0
$511$	−12.7446			−0.563786
$512$	4.96444	−	4.96444i	0.219399	−	0.219399i
$513$	20.6945	−	1.93288i	0.913686	−	0.0853386i
$514$			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	$-0.145863\pi$
$522$	9.42086	−	10.6698i	0.412340	−	0.467006i
$523$	25.7863	−	25.7863i	1.12756	−	1.12756i	0.136984	−	0.990573i	$-0.456259\pi$
$523$	25.7863	−	25.7863i	1.12756	−	1.12756i	0.990573	−	0.136984i	$-0.0437410\pi$
$524$	11.2772			0.492645
$525$		0			0
$526$	−3.76631			−0.164219
$527$	−3.15283	+	3.15283i	−0.137339	+	0.137339i
$528$	4.46522	−	0.138660i	0.194324	−	0.00603441i
$529$		−	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
$537$	−0.101044	−	3.25387i	−0.00436035	−	0.140415i
$538$	−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
$543$	0.322560	+	10.3873i	0.0138424	+	0.445762i
$544$		−	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	0.999921	+	0.0125794i	$0.00400425\pi$
$547$	23.6804	+	23.6804i	1.01250	+	1.01250i	0.0125794	+	0.999921i	$0.495996\pi$
$548$	−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
$552$	16.0232	−	0.497573i	0.681991	−	0.0211781i
$553$	−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	$-0.580578\pi$
$557$	16.9379	−	16.9379i	0.717680	−	0.717680i	0.968130	+	0.250449i	$0.0805784\pi$
$558$	−7.46402	+	8.45357i	−0.315977	+	0.357868i
$559$		−	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	−0.994361	−	0.106050i	$-0.966180\pi$
$563$	−26.1101	−	26.1101i	−1.10041	−	1.10041i	−0.106050	−	0.994361i	$-0.533820\pi$
$564$	−7.16825	+	7.62772i	−0.301838	+	0.321185i
$565$		0			0
$566$			9.39764i			0.395012i
$567$	−7.10317	−	5.52675i	−0.298305	−	0.232102i
$568$	3.55091	−	3.55091i	0.148993	−	0.148993i
$569$	−3.75906			−0.157588			−0.0787939	−	0.996891i	$-0.525107\pi$
$569$	−3.75906			−0.157588			−0.0787939	+	0.996891i	$0.525107\pi$
$570$		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
$573$	−27.8480	+	0.864773i	−1.16337	+	0.0361264i
$574$		−	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	0.0882628	−	0.996097i	$-0.471868\pi$
$577$	−21.8069	−	21.8069i	−0.907834	−	0.907834i	−0.996097	+	0.0882628i	$0.971868\pi$
$578$	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
$582$	−0.101044	−	3.25387i	−0.00418839	−	0.134877i
$583$	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	$-0.844336\pi$
$587$	−10.0065	+	10.0065i	−0.413013	+	0.413013i	0.469774	+	0.882787i	$0.344336\pi$
$588$	−0.0737740	−	2.37572i	−0.00304239	−	0.0979729i
$589$			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	$-0.0647349\pi$
$593$	18.9314	+	18.9314i	0.777420	+	0.777420i	−0.201972	+	0.979391i	$0.564735\pi$
$594$	10.7971	−	13.0217i	0.443009	−	0.534289i
$595$		0			0
$596$		0			0
$597$	22.0636	−	0.685149i	0.903003	−	0.0280413i
$598$	−4.60388	+	4.60388i	−0.188267	+	0.188267i
$599$	32.5214			1.32879			0.664395	−	0.747382i	$-0.268689\pi$
$599$	32.5214			1.32879			0.664395	+	0.747382i	$0.268689\pi$
$600$		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
$603$	−28.6607	−	25.3058i	−1.16715	−	1.03053i
$604$		−	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	0.822997	−	0.568045i	$-0.192300\pi$
$607$	6.28134	+	6.28134i	0.254952	+	0.254952i	−0.568045	+	0.822997i	$0.692300\pi$
$608$	−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
$612$	2.90017	+	2.56069i	0.117232	+	0.103510i
$613$	22.6274	−	22.6274i	0.913913	−	0.913913i	−0.0826647	−	0.996577i	$-0.526343\pi$
$613$	22.6274	−	22.6274i	0.913913	−	0.913913i	0.996577	+	0.0826647i	$0.0263430\pi$
$614$	−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	$-0.806734\pi$
$617$	−6.22801	+	6.22801i	−0.250730	+	0.250730i	0.570540	+	0.821270i	$0.306734\pi$
$618$	−9.76161	+	0.303131i	−0.392669	+	0.0121937i
$619$		−	15.2554i		−	0.613168i	−0.951844	−	0.306584i	$-0.900814\pi$
$619$		−	15.2554i		−	0.613168i	0.951844	−	0.306584i	$-0.0991860\pi$
$620$		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
$627$	−0.883582	−	28.4537i	−0.0352869	−	1.13633i
$628$	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
$633$	0.517587	+	16.6677i	0.0205722	+	0.662480i
$634$			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	$-0.0236521\pi$
$642$	−7.32943	+	0.227603i	−0.289270	+	0.00898279i
$643$	−12.9912	+	12.9912i	−0.512322	+	0.512322i	−0.915237	−	0.402916i	$-0.867997\pi$
$643$	−12.9912	+	12.9912i	−0.512322	+	0.512322i	0.402916	+	0.915237i	$0.367997\pi$
$644$	−4.75372			−0.187323
$645$		0			0
$646$	−2.97825			−0.117178
$647$	−31.4262	+	31.4262i	−1.23549	+	1.23549i	−0.273669	+	0.961824i	$0.588237\pi$
$647$	−31.4262	+	31.4262i	−1.23549	+	1.23549i	−0.961824	+	0.273669i	$0.911763\pi$
$648$	18.9783	+	14.7665i	0.745540	+	0.580081i
$649$			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	$-0.145783\pi$
$653$	11.6218	+	11.6218i	0.454795	+	0.454795i	−0.442148	+	0.896942i	$0.645783\pi$
$654$	7.86797	−	8.37228i	0.307662	−	0.327382i
$655$		0			0
$656$		−	7.51811i		−	0.293533i
$657$	−25.3058	+	28.6607i	−0.987271	+	1.11816i
$658$	−2.46718	+	2.46718i	−0.0961809	+	0.0961809i
$659$	−28.0627			−1.09317			−0.546583	−	0.837405i	$-0.684072\pi$
$659$	−28.0627			−1.09317			−0.546583	+	0.837405i	$0.684072\pi$
$660$		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
$663$	−3.85955	+	0.119852i	−0.149892	+	0.00465466i
$664$			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
$672$	0.314011	+	10.1120i	0.0121132	+	0.390078i
$673$	13.4196	−	13.4196i	0.517289	−	0.517289i	−0.399461	−	0.916750i	$-0.630803\pi$
$673$	13.4196	−	13.4196i	0.517289	−	0.517289i	0.916750	+	0.399461i	$0.130803\pi$
$674$	−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	$-0.568701\pi$
$677$	19.8433	−	19.8433i	0.762640	−	0.762640i	0.976799	+	0.214159i	$0.0687010\pi$
$678$	0.215040	+	6.92487i	0.00825857	+	0.265948i
$679$			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	$-0.286213\pi$
$683$	−4.19564	−	4.19564i	−0.160542	−	0.160542i	−0.782807	+	0.622265i	$0.786213\pi$
$684$	16.4356	−	1.02175i	0.628433	−	0.0390676i
$685$		0			0
$686$		−	0.792287i		−	0.0302497i
$687$	−50.1676	+	1.55787i	−1.91401	+	0.0594366i
$688$	−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
$693$	−8.15870	+	9.24034i	−0.309924	+	0.351012i
$694$		−	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	$-0.0403115\pi$
$702$	−9.72399	+	0.908224i	−0.367008	+	0.0342787i
$703$	−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
$708$	−28.4537	+	0.883582i	−1.06935	+	0.0332070i
$709$		−	19.3505i		−	0.726724i	−0.931648	−	0.363362i	$-0.881629\pi$
$709$		−	19.3505i		−	0.726724i	0.931648	−	0.363362i	$-0.118371\pi$
$710$		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
$717$	−0.422983	−	13.6212i	−0.0157966	−	0.508691i
$718$	16.5786	−	16.5786i	0.618706	−	0.618706i
$719$	−11.9769			−0.446662			−0.223331	−	0.974743i	$-0.571693\pi$
$719$	−11.9769			−0.446662			−0.223331	+	0.974743i	$0.571693\pi$
$720$		0			0
$721$	7.11684			0.265045
$722$	1.68069	−	1.68069i	0.0625490	−	0.0625490i
$723$	0.617656	+	19.8902i	0.0229709	+	0.739723i
$724$			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	0.929804	+	0.368055i	$0.119976\pi$
$727$	34.9941	+	34.9941i	1.29786	+	1.29786i	0.368055	+	0.929804i	$0.380024\pi$
$728$	−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
$732$	−16.0232	+	0.497573i	−0.592233	+	0.0183908i
$733$	−15.0971	+	15.0971i	−0.557624	+	0.557624i	−0.928630	−	0.371006i	$-0.879013\pi$
$733$	−15.0971	+	15.0971i	−0.557624	+	0.557624i	0.371006	+	0.928630i	$0.379013\pi$
$734$	−5.63858			−0.208124
$735$		0			0
$736$	20.2337			0.745824
$737$	−37.0286	+	37.0286i	−1.36396	+	1.36396i
$738$	−21.3397	−	18.8417i	−0.785524	−	0.693573i
$739$		−	9.62772i		−	0.354161i	−0.984196	−	0.177081i	$-0.943335\pi$
$739$		−	9.62772i		−	0.354161i	0.984196	−	0.177081i	$-0.0566654\pi$
$740$		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	$-0.458179\pi$
$743$	−23.4521	−	23.4521i	−0.860373	−	0.860373i	−0.991381	+	0.131008i	$0.958179\pi$
$744$	−15.0362	+	16.0000i	−0.551255	+	0.586588i
$745$		0			0
$746$			12.6766i			0.464123i
$747$	−37.6247	−	33.2205i	−1.37662	−	1.21547i
$748$	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
$753$	49.1882	−	1.52746i	1.79252	−	0.0556637i
$754$			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	0.164045	−	0.986453i	$-0.447546\pi$
$757$	−22.6274	−	22.6274i	−0.822407	−	0.822407i	−0.986453	+	0.164045i	$0.947546\pi$
$758$	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	$0.801836\pi$
$762$	−0.138660	−	4.46522i	−0.00502313	−	0.161758i
$763$	−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
$768$	−0.746360	−	24.0347i	−0.0269319	−	0.867279i
$769$		−	16.2337i		−	0.585402i	−0.956204	−	0.292701i	$-0.905446\pi$
$769$		−	16.2337i		−	0.585402i	0.956204	−	0.292701i	$-0.0945540\pi$
$770$		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	$-0.410618\pi$
$773$	−19.0090	−	19.0090i	−0.683708	−	0.683708i	−0.960834	+	0.277126i	$0.910618\pi$
$774$	1.17981	+	18.9783i	0.0424076	+	0.682159i
$775$		0			0
$776$		−	6.33830i		−	0.227532i
$777$	8.21386	−	0.255068i	0.294671	−	0.00915052i
$778$	−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
$783$	2.89373	+	30.9820i	0.103413	+	1.10721i
$784$		−	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	0.986374	−	0.164520i	$-0.0526074\pi$
$787$	23.0559	+	23.0559i	0.821854	+	0.821854i	−0.164520	+	0.986374i	$0.552607\pi$
$788$	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
$792$	21.7985	−	24.6885i	0.774578	−	0.877267i
$793$	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	$-0.875715\pi$
$797$	−15.3615	+	15.3615i	−0.544131	+	0.544131i	0.380607	+	0.924737i	$0.375715\pi$
$798$	5.48648	−	0.170374i	0.194219	−	0.00603116i
$799$			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
$807$	−0.643878	−	20.7346i	−0.0226656	−	0.729891i
$808$	7.10183	−	7.10183i	0.249841	−	0.249841i
$809$	−14.2063			−0.499466			−0.249733	−	0.968315i	$-0.580343\pi$
$809$	−14.2063			−0.499466			−0.249733	+	0.968315i	$0.580343\pi$
$810$		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
$813$	0.0800555	+	2.57800i	0.00280767	+	0.0904143i
$814$			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	$-0.0123863\pi$
$822$	−23.3526	+	0.725176i	−0.814515	+	0.0252934i
$823$	15.7216	−	15.7216i	0.548020	−	0.548020i	−0.377848	−	0.925868i	$-0.623336\pi$
$823$	15.7216	−	15.7216i	0.548020	−	0.548020i	0.925868	+	0.377848i	$0.123336\pi$
$824$	−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	$-0.745103\pi$
$827$	0.625691	−	0.625691i	0.0217574	−	0.0217574i	0.717902	+	0.696144i	$0.245103\pi$
$828$	−9.43905	+	10.6904i	−0.328030	+	0.371518i
$829$			46.0000i			1.59765i	0.601566	+	0.798823i	$0.294544\pi$
$829$			46.0000i			1.59765i	−0.601566	+	0.798823i	$0.705456\pi$
$830$		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
$837$	−2.29266	−	24.5466i	−0.0792461	−	0.848456i
$838$	15.9176	−	15.9176i	0.549864	−	0.549864i
$839$	0.699713			0.0241568			0.0120784	−	0.999927i	$-0.496155\pi$
$839$	0.699713			0.0241568			0.0120784	+	0.999927i	$0.496155\pi$
$840$		0			0
$841$	6.86141			0.236600
$842$	−0.208564	+	0.208564i	−0.00718758	+	0.00718758i
$843$	−18.0864	+	0.561643i	−0.622928	+	0.0193440i
$844$			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
$852$	0.138660	+	4.46522i	0.00475042	+	0.152976i
$853$	−13.6157	+	13.6157i	−0.466191	+	0.466191i	−0.900678	−	0.434487i	$-0.856930\pi$
$853$	−13.6157	+	13.6157i	−0.466191	+	0.466191i	0.434487	+	0.900678i	$0.356930\pi$
$854$	−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	$-0.634483\pi$
$857$	14.6969	−	14.6969i	0.502038	−	0.502038i	0.912071	+	0.410033i	$0.134483\pi$
$858$	0.415179	+	13.3699i	0.0141740	+	0.456439i
$859$			28.0000i			0.955348i	0.878537	+	0.477674i	$0.158520\pi$
$859$			28.0000i			0.955348i	−0.878537	+	0.477674i	$0.841480\pi$
$860$		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	$-0.00206879\pi$
$863$	29.1853	+	29.1853i	0.993480	+	0.993480i	−0.00649926	+	0.999979i	$0.502069\pi$
$864$	23.3639	+	19.3723i	0.794854	+	0.659058i
$865$		0			0
$866$		−	2.57924i		−	0.0876462i
$867$	−27.9017	+	0.866443i	−0.947593	+	0.0294259i
$868$	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
$873$	5.33492	+	4.71043i	0.180560	+	0.159424i
$874$		−	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	0.959938	−	0.280214i	$-0.0904053\pi$
$877$	20.1295	+	20.1295i	0.679724	+	0.679724i	−0.280214	+	0.959938i	$0.590405\pi$
$878$	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			$\pi$
$882$	−1.78174	−	1.57317i	−0.0599942	−	0.0529715i
$883$	−7.76280	+	7.76280i	−0.261239	+	0.261239i	−0.825557	−	0.564318i	$-0.809139\pi$
$883$	−7.76280	+	7.76280i	−0.261239	+	0.261239i	0.564318	+	0.825557i	$0.309139\pi$
$884$	−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	$-0.708127\pi$
$887$	5.52467	−	5.52467i	0.185500	−	0.185500i	0.793748	+	0.608247i	$0.208127\pi$
$888$	−21.9459	+	0.681495i	−0.736457	+	0.0228695i
$889$			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
$897$	−0.441791	−	14.2268i	−0.0147510	−	0.475020i
$898$	−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
$903$	−0.430081	−	13.8497i	−0.0143122	−	0.460890i
$904$			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	0.744291	−	0.667856i	$-0.232788\pi$
$907$	2.30194	+	2.30194i	0.0764347	+	0.0764347i	−0.667856	+	0.744291i	$0.732788\pi$
$908$	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	$0.901877\pi$
$912$	4.34687	−	0.134985i	0.143939	−	0.00446979i
$913$	−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
$918$	3.85210	−	0.359787i	0.127138	−	0.0118747i
$919$		−	23.1168i		−	0.762554i	−0.924461	−	0.381277i	$-0.875484\pi$
$919$		−	23.1168i		−	0.762554i	0.924461	−	0.381277i	$-0.124516\pi$
$920$		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
$927$	14.1313	−	16.0047i	0.464132	−	0.525665i
$928$	24.7334	−	24.7334i	0.811912	−	0.811912i
$929$	44.8482			1.47142			0.735710	−	0.677296i	$-0.236848\pi$
$929$	44.8482			1.47142			0.735710	+	0.677296i	$0.236848\pi$
$930$		0			0
$931$	−4.00000			−0.131095
$932$	−0.572416	+	0.572416i	−0.0187501	+	0.0187501i
$933$	6.50774	−	0.202087i	0.213054	−	0.00661604i
$934$		−	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	0.784513	−	0.620113i	$-0.212913\pi$
$937$	5.03237	+	5.03237i	0.164400	+	0.164400i	−0.620113	+	0.784513i	$0.712913\pi$
$938$	−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	$0.796336\pi$
$942$	−0.542834	−	17.4807i	−0.0176865	−	0.569552i
$943$	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	$-0.834465\pi$
$947$	−11.4132	+	11.4132i	−0.370879	+	0.370879i	0.496918	+	0.867797i	$0.334465\pi$
$948$	1.11523	+	35.9133i	0.0362210	+	1.16641i
$949$		−	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	$-0.157312\pi$
$953$	12.5337	+	12.5337i	0.406005	+	0.406005i	−0.474338	+	0.880343i	$0.657312\pi$
$954$	28.4125	−	1.76631i	0.919889	−	0.0571865i
$955$		0			0
$956$		−	10.7971i		−	0.349202i
$957$	42.5983	−	1.32282i	1.37701	−	0.0427607i
$958$	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
$963$	10.6104	−	12.0170i	0.341914	−	0.387244i
$964$			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	0.987411	−	0.158178i	$-0.0505620\pi$
$967$	25.7863	+	25.7863i	0.829232	+	0.829232i	−0.158178	+	0.987411i	$0.550562\pi$
$968$	−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	$-0.121715\pi$
$972$	−21.1346	+	3.30704i	−0.677892	+	0.106074i
$973$	−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	0.369717	−	0.929144i	$-0.379455\pi$
$977$	40.5985	−	40.5985i	1.29886	−	1.29886i	0.929144	−	0.369717i	$-0.120545\pi$
$978$	17.4807	−	0.542834i	0.558971	−	0.0173579i
$979$			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	−0.965959	−	0.258696i	$-0.916707\pi$
$983$	−38.3964	−	38.3964i	−1.22466	−	1.22466i	−0.258696	−	0.965959i	$-0.583293\pi$
$984$	−40.3894	−	37.9565i	−1.28757	−	1.21001i
$985$		0			0
$986$		−	4.45877i		−	0.141996i
$987$	−0.236752	−	7.62404i	−0.00753590	−	0.242676i
$988$	−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
$993$	−0.805232	−	25.9306i	−0.0255533	−	0.822882i
$994$			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	0.782290	−	0.622914i	$-0.214051\pi$
$997$	5.03237	+	5.03237i	0.159377	+	0.159377i	−0.622914	+	0.782290i	$0.714051\pi$
$998$	−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.407.5	yes	16
3.2	odd	2	inner	525.2.j.a.407.3	yes	16
5.2	odd	4	inner	525.2.j.a.218.6	yes	16
5.3	odd	4	inner	525.2.j.a.218.3	✓	16
5.4	even	2	inner	525.2.j.a.407.4	yes	16
15.2	even	4	inner	525.2.j.a.218.4	yes	16
15.8	even	4	inner	525.2.j.a.218.5	yes	16
15.14	odd	2	inner	525.2.j.a.407.6	yes	16

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

\(f(q)\)	\(=\)	\(q+(0.560232 - 0.560232i) q^{2} +(0.0537601 + 1.73122i) q^{3} +1.37228i q^{4} +(1.00000 + 0.939764i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.88926 + 1.88926i) q^{8} +(-2.99422 + 0.186141i) q^{9} +O(q^{10})\)	\(q+(0.560232 - 0.560232i) q^{2} +(0.0537601 + 1.73122i) 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} +(-2.37572 + 0.0737740i) q^{12} +(1.67746 - 1.67746i) q^{13} -0.792287 q^{14} -0.627719 q^{16} +(-0.664513 + 0.664513i) q^{17} +(-1.57317 + 1.78174i) 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} +(-0.483219 - 5.17364i) q^{27} +(0.970349 - 0.970349i) q^{28} -5.98844 q^{29} +4.74456 q^{31} +(-4.13018 + 4.13018i) q^{32} +(-7.11342 + 0.220895i) 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} +(-0.0425934 - 1.37162i) q^{42} +(5.65685 - 5.65685i) q^{43} -5.63858 q^{44} -2.74456 q^{46} +(3.11400 - 3.11400i) q^{47} +(-0.0337462 - 1.08672i) 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} +(-6.92487 + 0.215040i) q^{57} +(-3.35491 + 3.35491i) q^{58} +11.9769 q^{59} +6.74456 q^{61} +(2.65805 - 2.65805i) q^{62} +(2.24885 + 1.98561i) 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} +(-6.00852 - 5.30519i) q^{72} +(9.01177 - 9.01177i) q^{73} +3.75906 q^{74} -5.48913 q^{76} +(2.90544 - 2.90544i) q^{77} +(3.25387 - 0.101044i) 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} +(-0.321939 - 10.3673i) q^{87} +(-7.76280 + 7.76280i) q^{88} +3.75906 q^{89} -2.37228 q^{91} +(3.36139 - 3.36139i) q^{92} +(0.255068 + 8.21386i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more