LMFDB - Embedded newform 464.2.u.h.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(49,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("464.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.u (of order $7$, degree $6$, not 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 9 x^{9} - 5 x^{8} + 35 x^{7} + 197 x^{6} - 140 x^{5} - 80 x^{4} + \cdots + 4096 $ x^12 - 3x^11 + 13x^10 - 9x^9 - 5x^8 + 35x^7 + 197x^6 - 140x^5 - 80x^4 + 576x^3 + 3328x^2 + 3072*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			65.1
Root			$-1.56920 + 0.755686i$ of defining polynomial
Character	$\chi$	$=$	464.65
Dual form			464.2.u.h.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56920 - 0.755686i) q^{3} +(0.110081 + 0.482295i) q^{5} +(2.82760 + 1.36170i) q^{7} +(0.0208506 + 0.0261458i) q^{9} +O(q^{10})$	\(q+(-1.56920 - 0.755686i) q^{3} +(0.110081 + 0.482295i) q^{5} +(2.82760 + 1.36170i) q^{7} +(0.0208506 + 0.0261458i) q^{9} +(-0.870839 + 1.09200i) q^{11} +(-3.56353 + 4.46852i) q^{13} +(0.191725 - 0.840003i) q^{15} +5.31800 q^{17} +(4.47471 - 2.15491i) q^{19} +(-3.40804 - 4.27355i) q^{21} +(-0.181045 + 0.793210i) q^{23} +(4.28435 - 2.06324i) q^{25} +(1.14972 + 5.03725i) q^{27} +(5.38501 + 0.0414712i) q^{29} +(1.41596 + 6.20373i) q^{31} +(2.19173 - 1.05548i) q^{33} +(-0.345477 + 1.51363i) q^{35} +(5.56630 + 6.97992i) q^{37} +(8.96867 - 4.31909i) q^{39} -4.01226 q^{41} +(-0.310799 + 1.36170i) q^{43} +(-0.0103147 + 0.0129343i) q^{45} +(6.42079 - 8.05142i) q^{47} +(1.77665 + 2.22785i) q^{49} +(-8.34499 - 4.01873i) q^{51} +(-0.944288 - 4.13720i) q^{53} +(-0.622528 - 0.299794i) q^{55} -8.65014 q^{57} -11.1598 q^{59} +(-4.38454 - 2.11149i) q^{61} +(0.0233543 + 0.102322i) q^{63} +(-2.54742 - 1.22677i) q^{65} +(-4.45072 - 5.58102i) q^{67} +(0.883513 - 1.10789i) q^{69} +(-3.76423 + 4.72019i) q^{71} +(-2.73238 + 11.9713i) q^{73} -8.28215 q^{75} +(-3.94935 + 1.90191i) q^{77} +(5.86220 + 7.35096i) q^{79} +(2.02476 - 8.87107i) q^{81} +(11.4508 - 5.51441i) q^{83} +(0.585409 + 2.56484i) q^{85} +(-8.41880 - 4.13445i) q^{87} +(-0.398796 - 1.74724i) q^{89} +(-16.1610 + 7.78272i) q^{91} +(2.46615 - 10.8049i) q^{93} +(1.53188 + 1.92092i) q^{95} +(-3.42035 + 1.64715i) q^{97} -0.0467086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - q^{7} - 11 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - q^7 - 11 * q^9	$ 12 q + 3 q^{3} - q^{7} - 11 q^{9} + 2 q^{11} + q^{13} + 9 q^{15} - 12 q^{17} + 6 q^{19} - 13 q^{21} - 35 q^{23} - 6 q^{25} - 39 q^{27} - 14 q^{29} + 8 q^{31} + 33 q^{33} + 18 q^{35} + 31 q^{37} + 22 q^{39} - 30 q^{41} + 5 q^{43} - 20 q^{45} + 33 q^{47} + 37 q^{49} + 15 q^{51} + 13 q^{53} - 36 q^{55} - 38 q^{57} - 38 q^{59} - 5 q^{61} - 4 q^{63} - 20 q^{65} + 7 q^{67} + 20 q^{69} - 3 q^{71} - 22 q^{73} + 2 q^{75} + 10 q^{77} + 60 q^{79} + 88 q^{81} + 39 q^{83} + 38 q^{85} - 9 q^{87} + 39 q^{89} - 61 q^{91} - 54 q^{93} - 55 q^{95} - 19 q^{97} + 8 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - q^7 - 11 * q^9 + 2 * q^11 + q^13 + 9 * q^15 - 12 * q^17 + 6 * q^19 - 13 * q^21 - 35 * q^23 - 6 * q^25 - 39 * q^27 - 14 * q^29 + 8 * q^31 + 33 * q^33 + 18 * q^35 + 31 * q^37 + 22 * q^39 - 30 * q^41 + 5 * q^43 - 20 * q^45 + 33 * q^47 + 37 * q^49 + 15 * q^51 + 13 * q^53 - 36 * q^55 - 38 * q^57 - 38 * q^59 - 5 * q^61 - 4 * q^63 - 20 * q^65 + 7 * q^67 + 20 * q^69 - 3 * q^71 - 22 * q^73 + 2 * q^75 + 10 * q^77 + 60 * q^79 + 88 * q^81 + 39 * q^83 + 38 * q^85 - 9 * q^87 + 39 * q^89 - 61 * q^91 - 54 * q^93 - 55 * q^95 - 19 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{7}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.56920	−	0.755686i	−0.905977	−	0.436295i	−0.0779327	−	0.996959i	$-0.524832\pi$
$3$	−1.56920	−	0.755686i	−0.905977	−	0.436295i	−0.828044	+	0.560663i	$0.810546\pi$
$4$		0			0
$5$	0.110081	+	0.482295i	0.0492296	+	0.215689i	0.993560	−	0.113311i	$-0.0361456\pi$
$5$	0.110081	+	0.482295i	0.0492296	+	0.215689i	−0.944330	+	0.329000i	$0.893288\pi$
$6$		0			0
$7$	2.82760	+	1.36170i	1.06873	+	0.514674i	0.883697	−	0.468059i	$-0.155046\pi$
$7$	2.82760	+	1.36170i	1.06873	+	0.514674i	0.185033	+	0.982732i	$0.440761\pi$
$8$		0			0
$9$	0.0208506	+	0.0261458i	0.00695019	+	0.00871526i
$10$		0			0
$11$	−0.870839	+	1.09200i	−0.262568	+	0.329250i	−0.895587	−	0.444887i	$-0.853244\pi$
$11$	−0.870839	+	1.09200i	−0.262568	+	0.329250i	0.633019	+	0.774136i	$0.281815\pi$
$12$		0			0
$13$	−3.56353	+	4.46852i	−0.988344	+	1.23934i	−0.0174472	+	0.999848i	$0.505554\pi$
$13$	−3.56353	+	4.46852i	−0.988344	+	1.23934i	−0.970897	+	0.239497i	$0.923018\pi$
$14$		0			0
$15$	0.191725	−	0.840003i	0.0495032	−	0.216888i
$16$		0			0
$17$	5.31800			1.28980			0.644902	−	0.764265i	$-0.276898\pi$
$17$	5.31800			1.28980			0.644902	+	0.764265i	$0.276898\pi$
$18$		0			0
$19$	4.47471	−	2.15491i	1.02657	−	0.494370i	0.156697	−	0.987647i	$-0.449915\pi$
$19$	4.47471	−	2.15491i	1.02657	−	0.494370i	0.869872	+	0.493277i	$0.164201\pi$
$20$		0			0
$21$	−3.40804	−	4.27355i	−0.743695	−	0.932565i
$22$		0			0
$23$	−0.181045	+	0.793210i	−0.0377505	+	0.165396i	−0.990289	−	0.139021i	$-0.955604\pi$
$23$	−0.181045	+	0.793210i	−0.0377505	+	0.165396i	0.952539	+	0.304417i	$0.0984616\pi$
$24$		0			0
$25$	4.28435	−	2.06324i	0.856871	−	0.412647i
$26$		0			0
$27$	1.14972	+	5.03725i	0.221263	+	0.969419i
$28$		0			0
$29$	5.38501	+	0.0414712i	0.999970	+	0.00770101i
$29$	5.38501	+	0.0414712i	0.999970	+	0.00770101i
$30$		0			0
$31$	1.41596	+	6.20373i	0.254314	+	1.11422i	0.927226	+	0.374501i	$0.122186\pi$
$31$	1.41596	+	6.20373i	0.254314	+	1.11422i	−0.672912	+	0.739722i	$0.734957\pi$
$32$		0			0
$33$	2.19173	−	1.05548i	0.381530	−	0.183735i
$34$		0			0
$35$	−0.345477	+	1.51363i	−0.0583962	+	0.255851i
$36$		0			0
$37$	5.56630	+	6.97992i	0.915095	+	1.14749i	0.988655	+	0.150202i	$0.0479923\pi$
$37$	5.56630	+	6.97992i	0.915095	+	1.14749i	−0.0735606	+	0.997291i	$0.523436\pi$
$38$		0			0
$39$	8.96867	−	4.31909i	1.43614	−	0.691607i
$40$		0			0
$41$	−4.01226			−0.626610			−0.313305	−	0.949652i	$-0.601436\pi$
$41$	−4.01226			−0.626610			−0.313305	+	0.949652i	$0.601436\pi$
$42$		0			0
$43$	−0.310799	+	1.36170i	−0.0473964	+	0.207657i	−0.993082	−	0.117427i	$-0.962535\pi$
$43$	−0.310799	+	1.36170i	−0.0473964	+	0.207657i	0.945685	+	0.325084i	$0.105393\pi$
$44$		0			0
$45$	−0.0103147	+	0.0129343i	−0.00153763	+	0.00192813i
$46$		0			0
$47$	6.42079	−	8.05142i	0.936569	−	1.17442i	−0.0478986	−	0.998852i	$-0.515252\pi$
$47$	6.42079	−	8.05142i	0.936569	−	1.17442i	0.984467	−	0.175568i	$-0.0561761\pi$
$48$		0			0
$49$	1.77665	+	2.22785i	0.253807	+	0.318264i
$50$		0			0
$51$	−8.34499	−	4.01873i	−1.16853	−	0.562735i
$52$		0			0
$53$	−0.944288	−	4.13720i	−0.129708	−	0.568288i	−0.997456	−	0.0712835i	$-0.977291\pi$
$53$	−0.944288	−	4.13720i	−0.129708	−	0.568288i	0.867748	−	0.497004i	$-0.165567\pi$
$54$		0			0
$55$	−0.622528	−	0.299794i	−0.0839416	−	0.0404241i
$56$		0			0
$57$	−8.65014			−1.14574
$58$		0			0
$59$	−11.1598			−1.45288			−0.726438	−	0.687232i	$-0.758826\pi$
$59$	−11.1598			−1.45288			−0.726438	+	0.687232i	$0.758826\pi$
$60$		0			0
$61$	−4.38454	−	2.11149i	−0.561383	−	0.270348i	0.131598	−	0.991303i	$-0.457989\pi$
$61$	−4.38454	−	2.11149i	−0.561383	−	0.270348i	−0.692982	+	0.720955i	$0.743703\pi$
$62$		0			0
$63$	0.0233543	+	0.102322i	0.00294237	+	0.0128913i
$64$		0			0
$65$	−2.54742	−	1.22677i	−0.315969	−	0.152163i
$66$		0			0
$67$	−4.45072	−	5.58102i	−0.543742	−	0.681830i	0.431718	−	0.902009i	$-0.357908\pi$
$67$	−4.45072	−	5.58102i	−0.543742	−	0.681830i	−0.975460	+	0.220178i	$0.929336\pi$
$68$		0			0
$69$	0.883513	−	1.10789i	0.106362	−	0.133374i
$70$		0			0
$71$	−3.76423	+	4.72019i	−0.446732	+	0.560184i	−0.953304	−	0.302014i	$-0.902341\pi$
$71$	−3.76423	+	4.72019i	−0.446732	+	0.560184i	0.506572	+	0.862198i	$0.330913\pi$
$72$		0			0
$73$	−2.73238	+	11.9713i	−0.319801	+	1.40114i	0.518103	+	0.855319i	$0.326639\pi$
$73$	−2.73238	+	11.9713i	−0.319801	+	1.40114i	−0.837903	+	0.545819i	$0.816219\pi$
$74$		0			0
$75$	−8.28215			−0.956341
$76$		0			0
$77$	−3.94935	+	1.90191i	−0.450070	+	0.216743i
$78$		0			0
$79$	5.86220	+	7.35096i	0.659549	+	0.827048i	0.993294	−	0.115615i	$-0.0368840\pi$
$79$	5.86220	+	7.35096i	0.659549	+	0.827048i	−0.333745	+	0.942663i	$0.608313\pi$
$80$		0			0
$81$	2.02476	−	8.87107i	0.224974	−	0.985675i
$82$		0			0
$83$	11.4508	−	5.51441i	1.25689	−	0.605285i	0.317538	−	0.948246i	$-0.397144\pi$
$83$	11.4508	−	5.51441i	1.25689	−	0.605285i	0.939350	+	0.342960i	$0.111430\pi$
$84$		0			0
$85$	0.585409	+	2.56484i	0.0634965	+	0.278196i
$86$		0			0
$87$	−8.41880	−	4.13445i	−0.902590	−	0.443259i
$88$		0			0
$89$	−0.398796	−	1.74724i	−0.0422722	−	0.185207i	0.949384	−	0.314118i	$-0.101709\pi$
$89$	−0.398796	−	1.74724i	−0.0422722	−	0.185207i	−0.991656	+	0.128911i	$0.958852\pi$
$90$		0			0
$91$	−16.1610	+	7.78272i	−1.69413	+	0.815851i
$92$		0			0
$93$	2.46615	−	10.8049i	0.255728	−	1.12042i
$94$		0			0
$95$	1.53188	+	1.92092i	0.157168	+	0.197082i
$96$		0			0
$97$	−3.42035	+	1.64715i	−0.347283	+	0.167243i	−0.599391	−	0.800456i	$-0.704591\pi$
$97$	−3.42035	+	1.64715i	−0.347283	+	0.167243i	0.252108	+	0.967699i	$0.418876\pi$
$98$		0			0
$99$	−0.0467086			−0.00469439
$100$		0			0
$101$	0.271881	−	1.19119i	0.0270532	−	0.118528i	−0.959598	−	0.281373i	$-0.909210\pi$
$101$	0.271881	−	1.19119i	0.0270532	−	0.118528i	0.986652	+	0.162846i	$0.0520672\pi$
$102$		0			0
$103$	−1.12736	+	1.41366i	−0.111082	+	0.139292i	−0.834264	−	0.551365i	$-0.814107\pi$
$103$	−1.12736	+	1.41366i	−0.111082	+	0.139292i	0.723182	+	0.690657i	$0.242679\pi$
$104$		0			0
$105$	1.68595	−	2.11412i	0.164532	−	0.206317i
$106$		0			0
$107$	−2.58788	−	3.24509i	−0.250179	−	0.313715i	0.640845	−	0.767670i	$-0.278584\pi$
$107$	−2.58788	−	3.24509i	−0.250179	−	0.313715i	−0.891025	+	0.453955i	$0.850013\pi$
$108$		0			0
$109$	−13.0682	−	6.29330i	−1.25170	−	0.602789i	−0.313736	−	0.949510i	$-0.601581\pi$
$109$	−13.0682	−	6.29330i	−1.25170	−	0.602789i	−0.937968	+	0.346721i	$0.887295\pi$
$110$		0			0
$111$	−3.46000	−	15.1593i	−0.328409	−	1.43885i
$112$		0			0
$113$	−15.0312	−	7.23864i	−1.41402	−	0.680954i	−0.438065	−	0.898943i	$-0.644336\pi$
$113$	−15.0312	−	7.23864i	−1.41402	−	0.680954i	−0.975951	+	0.217989i	$0.930050\pi$
$114$		0			0
$115$	−0.402491			−0.0375325
$116$		0			0
$117$	−0.191135			−0.0176704
$118$		0			0
$119$	15.0371	+	7.24151i	1.37845	+	0.663828i
$120$		0			0
$121$	2.01363	+	8.82230i	0.183057	+	0.802027i
$122$		0			0
$123$	6.29603	+	3.03201i	0.567694	+	0.273387i
$124$		0			0
$125$	3.00891	+	3.77305i	0.269125	+	0.337472i
$126$		0			0
$127$	7.91387	−	9.92368i	0.702243	−	0.880584i	−0.294946	−	0.955514i	$-0.595302\pi$
$127$	7.91387	−	9.92368i	0.702243	−	0.880584i	0.997189	+	0.0749295i	$0.0238732\pi$
$128$		0			0
$129$	1.51672	−	1.90191i	0.133540	−	0.167454i
$130$		0			0
$131$	−3.29243	+	14.4251i	−0.287661	+	1.26033i	0.600064	+	0.799952i	$0.295142\pi$
$131$	−3.29243	+	14.4251i	−0.287661	+	1.26033i	−0.887725	+	0.460374i	$0.847715\pi$
$132$		0			0
$133$	15.5870			1.35157
$134$		0			0
$135$	−2.30288	+	1.10901i	−0.198200	+	0.0954482i
$136$		0			0
$137$	−0.941003	−	1.17998i	−0.0803953	−	0.100813i	0.740007	−	0.672599i	$-0.234822\pi$
$137$	−0.941003	−	1.17998i	−0.0803953	−	0.100813i	−0.820403	+	0.571786i	$0.806251\pi$
$138$		0			0
$139$	1.94848	−	8.53684i	0.165268	−	0.724086i	−0.822578	−	0.568652i	$-0.807465\pi$
$139$	1.94848	−	8.53684i	0.165268	−	0.724086i	0.987846	−	0.155434i	$-0.0496776\pi$
$140$		0			0
$141$	−16.1598	+	7.78216i	−1.36090	+	0.655377i
$142$		0			0
$143$	−1.77636	−	7.78272i	−0.148546	−	0.650824i
$144$		0			0
$145$	0.572784	+	2.60173i	0.0475671	+	0.216062i
$146$		0			0
$147$	−1.10436	−	4.83852i	−0.0910861	−	0.399074i
$148$		0			0
$149$	4.27124	−	2.05692i	0.349914	−	0.168510i	−0.250668	−	0.968073i	$-0.580650\pi$
$149$	4.27124	−	2.05692i	0.349914	−	0.168510i	0.600581	+	0.799564i	$0.294936\pi$
$150$		0			0
$151$	−1.44508	+	6.33133i	−0.117599	+	0.515236i	0.881475	+	0.472230i	$0.156551\pi$
$151$	−1.44508	+	6.33133i	−0.117599	+	0.515236i	−0.999075	+	0.0430064i	$0.986306\pi$
$152$		0			0
$153$	0.110883	+	0.139043i	0.00896438	+	0.0112410i
$154$		0			0
$155$	−2.83616	+	1.36582i	−0.227806	+	0.109706i
$156$		0			0
$157$	6.56139			0.523656			0.261828	−	0.965115i	$-0.415675\pi$
$157$	6.56139			0.523656			0.261828	+	0.965115i	$0.415675\pi$
$158$		0			0
$159$	−1.64465	+	7.20566i	−0.130429	+	0.571446i
$160$		0			0
$161$	−1.59204	+	1.99635i	−0.125470	+	0.157334i
$162$		0			0
$163$	−3.52776	+	4.42367i	−0.276315	+	0.346488i	−0.900553	−	0.434746i	$-0.856838\pi$
$163$	−3.52776	+	4.42367i	−0.276315	+	0.346488i	0.624238	+	0.781234i	$0.285410\pi$
$164$		0			0
$165$	0.750319	+	0.940870i	0.0584123	+	0.0732467i
$166$		0			0
$167$	−10.8919	−	5.24527i	−0.842842	−	0.405891i	−0.0379260	−	0.999281i	$-0.512075\pi$
$167$	−10.8919	−	5.24527i	−0.842842	−	0.405891i	−0.804915	+	0.593389i	$0.797789\pi$
$168$		0			0
$169$	−4.37618	−	19.1733i	−0.336630	−	1.47487i
$170$		0			0
$171$	0.149642	+	0.0720639i	0.0114434	+	0.00551086i
$172$		0			0
$173$	11.6405			0.885008			0.442504	−	0.896767i	$-0.354090\pi$
$173$	11.6405			0.885008			0.442504	+	0.896767i	$0.354090\pi$
$174$		0			0
$175$	14.9239			1.12814
$176$		0			0
$177$	17.5119	+	8.43327i	1.31627	+	0.633883i
$178$		0			0
$179$	−4.08440	−	17.8949i	−0.305282	−	1.33753i	−0.862034	−	0.506850i	$-0.830810\pi$
$179$	−4.08440	−	17.8949i	−0.305282	−	1.33753i	0.556752	−	0.830678i	$-0.312047\pi$
$180$		0			0
$181$	8.91422	+	4.29286i	0.662589	+	0.319086i	0.734781	−	0.678305i	$-0.237285\pi$
$181$	8.91422	+	4.29286i	0.662589	+	0.319086i	−0.0721917	+	0.997391i	$0.522999\pi$
$182$		0			0
$183$	5.28460	+	6.62667i	0.390649	+	0.489858i
$184$		0			0
$185$	−2.75364	+	3.45296i	−0.202452	+	0.253866i
$186$		0			0
$187$	−4.63112	+	5.80724i	−0.338661	+	0.424667i
$188$		0			0
$189$	−3.60827	+	15.8089i	−0.262463	+	1.14993i
$190$		0			0
$191$	−0.424259			−0.0306983			−0.0153492	−	0.999882i	$-0.504886\pi$
$191$	−0.424259			−0.0306983			−0.0153492	+	0.999882i	$0.504886\pi$
$192$		0			0
$193$	9.30230	−	4.47975i	0.669594	−	0.322460i	−0.0680181	−	0.997684i	$-0.521668\pi$
$193$	9.30230	−	4.47975i	0.669594	−	0.322460i	0.737612	+	0.675225i	$0.235953\pi$
$194$		0			0
$195$	3.07035	+	3.85010i	0.219872	+	0.275711i
$196$		0			0
$197$	5.97308	−	26.1698i	0.425564	−	1.86452i	−0.0724862	−	0.997369i	$-0.523093\pi$
$197$	5.97308	−	26.1698i	0.425564	−	1.86452i	0.498050	−	0.867148i	$-0.334050\pi$
$198$		0			0
$199$	−6.12924	+	2.95169i	−0.434490	+	0.209239i	−0.638327	−	0.769765i	$-0.720373\pi$
$199$	−6.12924	+	2.95169i	−0.434490	+	0.209239i	0.203837	+	0.979005i	$0.434659\pi$
$200$		0			0
$201$	2.76655	+	12.1211i	0.195138	+	0.854954i
$202$		0			0
$203$	15.1701	+	7.45002i	1.06474	+	0.522889i
$204$		0			0
$205$	−0.441673	−	1.93510i	−0.0308478	−	0.135153i
$206$		0			0
$207$	−0.0245140	+	0.0118053i	−0.00170384	+	0.000820526i
$208$		0			0
$209$	−1.54360	+	6.76296i	−0.106773	+	0.467803i
$210$		0			0
$211$	−3.64156	−	4.56638i	−0.250696	−	0.314362i	0.640521	−	0.767941i	$-0.278719\pi$
$211$	−3.64156	−	4.56638i	−0.250696	−	0.314362i	−0.891216	+	0.453579i	$0.850147\pi$
$212$		0			0
$213$	9.47380	−	4.56234i	0.649134	−	0.312607i
$214$		0			0
$215$	−0.690954			−0.0471226
$216$		0			0
$217$	−4.44385	+	19.4698i	−0.301668	+	1.32169i
$218$		0			0
$219$	13.3342	−	16.7206i	0.901042	−	1.12987i
$220$		0			0
$221$	−18.9508	+	23.7636i	−1.27477	+	1.59851i
$222$		0			0
$223$	13.6769	+	17.1503i	0.915874	+	1.14847i	0.988517	+	0.151111i	$0.0482852\pi$
$223$	13.6769	+	17.1503i	0.915874	+	1.14847i	−0.0726432	+	0.997358i	$0.523143\pi$
$224$		0			0
$225$	0.143276	+	0.0689982i	0.00955174	+	0.00459988i
$226$		0			0
$227$	−0.479626	−	2.10138i	−0.0318339	−	0.139474i	0.956514	−	0.291688i	$-0.0942168\pi$
$227$	−0.479626	−	2.10138i	−0.0318339	−	0.139474i	−0.988348	+	0.152214i	$0.951360\pi$
$228$		0			0
$229$	−8.37172	−	4.03161i	−0.553219	−	0.266416i	0.136320	−	0.990665i	$-0.456472\pi$
$229$	−8.37172	−	4.03161i	−0.553219	−	0.266416i	−0.689539	+	0.724249i	$0.742187\pi$
$230$		0			0
$231$	7.63456			0.502317
$232$		0			0
$233$	−11.7848			−0.772045			−0.386022	−	0.922489i	$-0.626151\pi$
$233$	−11.7848			−0.772045			−0.386022	+	0.922489i	$0.626151\pi$
$234$		0			0
$235$	4.58996	+	2.21041i	0.299416	+	0.144191i
$236$		0			0
$237$	−3.64393	−	15.9651i	−0.236699	−	1.03704i
$238$		0			0
$239$	−12.9462	−	6.23455i	−0.837419	−	0.403280i	−0.0345265	−	0.999404i	$-0.510992\pi$
$239$	−12.9462	−	6.23455i	−0.837419	−	0.403280i	−0.802892	+	0.596124i	$0.796707\pi$
$240$		0			0
$241$	−5.73880	−	7.19623i	−0.369669	−	0.463550i	0.561852	−	0.827238i	$-0.310089\pi$
$241$	−5.73880	−	7.19623i	−0.369669	−	0.463550i	−0.931521	+	0.363688i	$0.881517\pi$
$242$		0			0
$243$	−0.216675	+	0.271702i	−0.0138997	+	0.0174297i
$244$		0			0
$245$	−0.878905	+	1.10211i	−0.0561512	+	0.0704114i
$246$		0			0
$247$	−6.31651	+	27.6744i	−0.401910	+	1.76088i
$248$		0			0
$249$	−22.1357			−1.40279
$250$		0			0
$251$	5.33012	−	2.56685i	0.336434	−	0.162018i	−0.258037	−	0.966135i	$-0.583076\pi$
$251$	5.33012	−	2.56685i	0.336434	−	0.162018i	0.594471	+	0.804117i	$0.297361\pi$
$252$		0			0
$253$	−0.708523	−	0.888459i	−0.0445444	−	0.0558569i
$254$		0			0
$255$	1.01959	−	4.46713i	0.0638494	−	0.279743i
$256$		0			0
$257$	24.0750	−	11.5939i	1.50176	−	0.723209i	0.511094	−	0.859525i	$-0.329241\pi$
$257$	24.0750	−	11.5939i	1.50176	−	0.723209i	0.990665	+	0.136316i	$0.0435263\pi$
$258$		0			0
$259$	6.23471	+	27.3160i	0.387406	+	1.69734i
$260$		0			0
$261$	0.111196	+	0.141660i	0.00688287	+	0.00876853i
$262$		0			0
$263$	−5.19684	−	22.7688i	−0.320451	−	1.40399i	−0.836753	−	0.547581i	$-0.815549\pi$
$263$	−5.19684	−	22.7688i	−0.320451	−	1.40399i	0.516302	−	0.856407i	$-0.327308\pi$
$264$		0			0
$265$	1.89140	−	0.910851i	0.116188	−	0.0559531i
$266$		0			0
$267$	−0.694573	+	3.04312i	−0.0425072	+	0.186236i
$268$		0			0
$269$	9.73222	+	12.2038i	0.593384	+	0.744080i	0.984331	−	0.176333i	$-0.0564236\pi$
$269$	9.73222	+	12.2038i	0.593384	+	0.744080i	−0.390946	+	0.920413i	$0.627852\pi$
$270$		0			0
$271$	0.197924	−	0.0953153i	0.0120230	−	0.00578999i	−0.427863	−	0.903844i	$-0.640733\pi$
$271$	0.197924	−	0.0953153i	0.0120230	−	0.00578999i	0.439886	+	0.898054i	$0.355019\pi$
$272$		0			0
$273$	31.2411			1.89080
$274$		0			0
$275$	−1.47793	+	6.47525i	−0.0891227	+	0.390472i
$276$		0			0
$277$	2.33928	−	2.93336i	0.140554	−	0.176249i	−0.706572	−	0.707641i	$-0.749759\pi$
$277$	2.33928	−	2.93336i	0.140554	−	0.176249i	0.847126	+	0.531392i	$0.178331\pi$
$278$		0			0
$279$	−0.132678	+	0.166373i	−0.00794322	+	0.00996048i
$280$		0			0
$281$	−15.2450	−	19.1167i	−0.909442	−	1.14040i	−0.989632	−	0.143624i	$-0.954124\pi$
$281$	−15.2450	−	19.1167i	−0.909442	−	1.14040i	0.0801905	−	0.996780i	$-0.474447\pi$
$282$		0			0
$283$	6.84512	+	3.29644i	0.406900	+	0.195953i	0.626127	−	0.779721i	$-0.284639\pi$
$283$	6.84512	+	3.29644i	0.406900	+	0.195953i	−0.219227	+	0.975674i	$0.570353\pi$
$284$		0			0
$285$	−0.952214	−	4.17192i	−0.0564043	−	0.247123i
$286$		0			0
$287$	−11.3451	−	5.46349i	−0.669678	−	0.322500i
$288$		0			0
$289$	11.2811			0.663593
$290$		0			0
$291$	6.61193			0.387598
$292$		0			0
$293$	23.1750	+	11.1605i	1.35390	+	0.652003i	0.963267	−	0.268545i	$-0.0865427\pi$
$293$	23.1750	+	11.1605i	1.35390	+	0.652003i	0.390631	+	0.920547i	$0.372257\pi$
$294$		0			0
$295$	−1.22847	−	5.38230i	−0.0715245	−	0.313369i
$296$		0			0
$297$	−6.50188	−	3.13114i	−0.377277	−	0.181687i
$298$		0			0
$299$	−2.89932	−	3.63563i	−0.167672	−	0.210254i
$300$		0			0
$301$	−2.73304	+	3.42712i	−0.157530	+	0.197536i
$302$		0			0
$303$	−1.32680	+	1.66375i	−0.0762226	+	0.0955801i
$304$		0			0
$305$	0.535705	−	2.34708i	0.0306744	−	0.134393i
$306$		0			0
$307$	−1.81399			−0.103530			−0.0517649	−	0.998659i	$-0.516485\pi$
$307$	−1.81399			−0.103530			−0.0517649	+	0.998659i	$0.516485\pi$
$308$		0			0
$309$	2.83733	−	1.36639i	0.161410	−	0.0777310i
$310$		0			0
$311$	−12.1020	−	15.1754i	−0.686239	−	0.860517i	0.309673	−	0.950843i	$-0.399780\pi$
$311$	−12.1020	−	15.1754i	−0.686239	−	0.860517i	−0.995912	+	0.0903265i	$0.971209\pi$
$312$		0			0
$313$	−7.54006	+	33.0352i	−0.426189	+	1.86726i	0.0676576	+	0.997709i	$0.478447\pi$
$313$	−7.54006	+	33.0352i	−0.426189	+	1.86726i	−0.493847	+	0.869549i	$0.664410\pi$
$314$		0			0
$315$	−0.0467785	+	0.0225273i	−0.00263567	+	0.00126927i
$316$		0			0
$317$	−1.22333	−	5.35977i	−0.0687092	−	0.301035i	0.928884	−	0.370370i	$-0.120769\pi$
$317$	−1.22333	−	5.35977i	−0.0687092	−	0.301035i	−0.997593	+	0.0693356i	$0.977912\pi$
$318$		0			0
$319$	−4.73476	+	5.84430i	−0.265096	+	0.327218i
$320$		0			0
$321$	1.60862	+	7.04781i	0.0897843	+	0.393371i
$322$		0			0
$323$	23.7965	−	11.4598i	1.32407	−	0.637640i
$324$		0			0
$325$	−6.04779	+	26.4971i	−0.335471	+	1.46980i
$326$		0			0
$327$	15.7508	+	19.7509i	0.871021	+	1.09223i
$328$		0			0
$329$	29.1190	−	14.0230i	1.60538	−	0.773112i
$330$		0			0
$331$	13.6463			0.750067			0.375034	−	0.927011i	$-0.377631\pi$
$331$	13.6463			0.750067			0.375034	+	0.927011i	$0.377631\pi$
$332$		0			0
$333$	−0.0664350	+	0.291071i	−0.00364062	+	0.0159506i
$334$		0			0
$335$	2.20176	−	2.76092i	0.120295	−	0.150845i
$336$		0			0
$337$	14.0705	−	17.6438i	0.766469	−	0.961122i	−0.233468	−	0.972365i	$-0.575007\pi$
$337$	14.0705	−	17.6438i	0.766469	−	0.961122i	0.999937	+	0.0112429i	$0.00357882\pi$
$338$		0			0
$339$	18.1168	+	22.7177i	0.983968	+	1.23386i
$340$		0			0
$341$	−8.00754	−	3.85623i	−0.433632	−	0.208826i
$342$		0			0
$343$	−2.89852	−	12.6993i	−0.156505	−	0.685695i
$344$		0			0
$345$	0.631588	+	0.304157i	0.0340036	+	0.0163752i
$346$		0			0
$347$	2.97305			0.159602			0.0798008	−	0.996811i	$-0.474572\pi$
$347$	2.97305			0.159602			0.0798008	+	0.996811i	$0.474572\pi$
$348$		0			0
$349$	−5.73913			−0.307208			−0.153604	−	0.988132i	$-0.549088\pi$
$349$	−5.73913			−0.307208			−0.153604	+	0.988132i	$0.549088\pi$
$350$		0			0
$351$	−26.6061	−	12.8128i	−1.42013	−	0.683898i
$352$		0			0
$353$	1.44019	+	6.30988i	0.0766536	+	0.335841i	0.998685	−	0.0512748i	$-0.0163284\pi$
$353$	1.44019	+	6.30988i	0.0766536	+	0.335841i	−0.922031	+	0.387116i	$0.873471\pi$
$354$		0			0
$355$	−2.69090	−	1.29587i	−0.142818	−	0.0687775i
$356$		0			0
$357$	−18.1239	−	22.7267i	−0.959221	−	1.20283i
$358$		0			0
$359$	−6.69717	+	8.39798i	−0.353463	+	0.443229i	−0.926496	−	0.376303i	$-0.877195\pi$
$359$	−6.69717	+	8.39798i	−0.353463	+	0.443229i	0.573034	+	0.819532i	$0.305766\pi$
$360$		0			0
$361$	3.53313	−	4.43041i	0.185954	−	0.233179i
$362$		0			0
$363$	3.50710	−	15.3656i	0.184075	−	0.806485i
$364$		0			0
$365$	−6.07449			−0.317954
$366$		0			0
$367$	17.0637	−	8.21747i	0.890720	−	0.428948i	0.0681919	−	0.997672i	$-0.478277\pi$
$367$	17.0637	−	8.21747i	0.890720	−	0.428948i	0.822529	+	0.568724i	$0.192563\pi$
$368$		0			0
$369$	−0.0836580	−	0.104904i	−0.00435506	−	0.00546107i
$370$		0			0
$371$	2.96355	−	12.9842i	0.153860	−	0.674104i
$372$		0			0
$373$	−2.19298	+	1.05608i	−0.113548	+	0.0546819i	−0.489796	−	0.871837i	$-0.662929\pi$
$373$	−2.19298	+	1.05608i	−0.113548	+	0.0546819i	0.376247	+	0.926519i	$0.377214\pi$
$374$		0			0
$375$	−1.87033	−	8.19446i	−0.0965835	−	0.423160i
$376$		0			0
$377$	−19.3749	+	23.9152i	−0.997859	+	1.23170i
$378$		0			0
$379$	−3.81433	−	16.7117i	−0.195929	−	0.858422i	−0.973329	−	0.229415i	$-0.926319\pi$
$379$	−3.81433	−	16.7117i	−0.195929	−	0.858422i	0.777400	−	0.629007i	$-0.216538\pi$
$380$		0			0
$381$	−19.9176	+	9.59182i	−1.02041	+	0.491404i
$382$		0			0
$383$	−5.29096	+	23.1812i	−0.270355	+	1.18450i	0.639239	+	0.769008i	$0.279249\pi$
$383$	−5.29096	+	23.1812i	−0.270355	+	1.18450i	−0.909595	+	0.415497i	$0.863608\pi$
$384$		0			0
$385$	−1.35203	−	1.69539i	−0.0689057	−	0.0864051i
$386$		0			0
$387$	−0.0420830	+	0.0202661i	−0.00213920	+	0.00103018i
$388$		0			0
$389$	−11.5272			−0.584453			−0.292227	−	0.956349i	$-0.594396\pi$
$389$	−11.5272			−0.584453			−0.292227	+	0.956349i	$0.594396\pi$
$390$		0			0
$391$	−0.962797	+	4.21829i	−0.0486907	+	0.213328i
$392$		0			0
$393$	16.0673	−	20.1478i	0.810489	−	1.01632i
$394$		0			0
$395$	−2.90002	+	3.63651i	−0.145916	+	0.182973i
$396$		0			0
$397$	18.0708	+	22.6601i	0.906948	+	1.13728i	0.990047	+	0.140736i	$0.0449468\pi$
$397$	18.0708	+	22.6601i	0.906948	+	1.13728i	−0.0830990	+	0.996541i	$0.526482\pi$
$398$		0			0
$399$	−24.4591	−	11.7789i	−1.22449	−	0.589682i
$400$		0			0
$401$	−2.29856	−	10.0707i	−0.114785	−	0.502905i	−0.999335	−	0.0364602i	$-0.988392\pi$
$401$	−2.29856	−	10.0707i	−0.114785	−	0.502905i	0.884550	−	0.466445i	$-0.154465\pi$
$402$		0			0
$403$	−32.7673	−	15.7799i	−1.63226	−	0.786054i
$404$		0			0
$405$	4.50136			0.223674
$406$		0			0
$407$	−12.4694			−0.618086
$408$		0			0
$409$	−8.97519	−	4.32222i	−0.443794	−	0.213720i	0.198622	−	0.980076i	$-0.436354\pi$
$409$	−8.97519	−	4.32222i	−0.443794	−	0.213720i	−0.642416	+	0.766356i	$0.722068\pi$
$410$		0			0
$411$	0.584925	+	2.56273i	0.0288522	+	0.126410i
$412$		0			0
$413$	−31.5553	−	15.1962i	−1.55273	−	0.747757i
$414$		0			0
$415$	3.92009	+	4.91563i	0.192429	+	0.241299i
$416$		0			0
$417$	−9.50872	+	11.9236i	−0.465644	+	0.583899i
$418$		0			0
$419$	−17.6773	+	22.1667i	−0.863595	+	1.08291i	0.132193	+	0.991224i	$0.457798\pi$
$419$	−17.6773	+	22.1667i	−0.863595	+	1.08291i	−0.995788	+	0.0916894i	$0.970773\pi$
$420$		0			0
$421$	2.11840	−	9.28130i	0.103244	−	0.452343i	−0.896708	−	0.442622i	$-0.854048\pi$
$421$	2.11840	−	9.28130i	0.103244	−	0.452343i	0.999953	−	0.00972116i	$-0.00309439\pi$
$422$		0			0
$423$	0.344388			0.0167447
$424$		0			0
$425$	22.7842	−	10.9723i	1.10519	−	0.532234i
$426$		0			0
$427$	−9.52251	−	11.9409i	−0.460827	−	0.577859i
$428$		0			0
$429$	−3.09384	+	13.5550i	−0.149372	+	0.654441i
$430$		0			0
$431$	−17.0958	+	8.23291i	−0.823477	+	0.396566i	−0.797665	−	0.603101i	$-0.793931\pi$
$431$	−17.0958	+	8.23291i	−0.823477	+	0.396566i	−0.0258122	+	0.999667i	$0.508217\pi$
$432$		0			0
$433$	−6.30063	−	27.6049i	−0.302789	−	1.32661i	−0.865897	−	0.500222i	$-0.833252\pi$
$433$	−6.30063	−	27.6049i	−0.302789	−	1.32661i	0.563108	−	0.826383i	$-0.309605\pi$
$434$		0			0
$435$	1.06728	−	4.51547i	0.0511720	−	0.216500i
$436$		0			0
$437$	0.899171	+	3.93953i	0.0430132	+	0.188453i
$438$		0			0
$439$	−17.9255	+	8.63248i	−0.855539	+	0.412006i	−0.809631	−	0.586940i	$-0.800333\pi$
$439$	−17.9255	+	8.63248i	−0.855539	+	0.412006i	−0.0459084	+	0.998946i	$0.514618\pi$
$440$		0			0
$441$	−0.0212047	+	0.0929038i	−0.00100975	+	0.00442399i
$442$		0			0
$443$	22.1713	+	27.8019i	1.05339	+	1.32091i	0.945097	+	0.326790i	$0.105967\pi$
$443$	22.1713	+	27.8019i	1.05339	+	1.32091i	0.108292	+	0.994119i	$0.465462\pi$
$444$		0			0
$445$	0.798784	−	0.384674i	0.0378660	−	0.0182353i
$446$		0			0
$447$	−8.25681			−0.390534
$448$		0			0
$449$	−2.41460	+	10.5790i	−0.113952	+	0.499256i	0.885452	+	0.464731i	$0.153849\pi$
$449$	−2.41460	+	10.5790i	−0.113952	+	0.499256i	−0.999404	+	0.0345250i	$0.989008\pi$
$450$		0			0
$451$	3.49404	−	4.38138i	0.164528	−	0.206311i
$452$		0			0
$453$	7.05212	−	8.84307i	0.331337	−	0.415484i
$454$		0			0
$455$	−5.53258	−	6.93764i	−0.259371	−	0.325242i
$456$		0			0
$457$	−29.1336	−	14.0300i	−1.36281	−	0.656296i	−0.397550	−	0.917580i	$-0.630140\pi$
$457$	−29.1336	−	14.0300i	−1.36281	−	0.656296i	−0.965262	+	0.261285i	$0.915854\pi$
$458$		0			0
$459$	6.11420	+	26.7881i	0.285386	+	1.25036i
$460$		0			0
$461$	−22.8888	−	11.0227i	−1.06604	−	0.513377i	−0.183211	−	0.983074i	$-0.558649\pi$
$461$	−22.8888	−	11.0227i	−1.06604	−	0.513377i	−0.882828	+	0.469696i	$0.844363\pi$
$462$		0			0
$463$	−3.22072			−0.149680			−0.0748398	−	0.997196i	$-0.523845\pi$
$463$	−3.22072			−0.149680			−0.0748398	+	0.997196i	$0.523845\pi$
$464$		0			0
$465$	5.48263			0.254251
$466$		0			0
$467$	20.5930	+	9.91706i	0.952929	+	0.458907i	0.844712	−	0.535221i	$-0.179772\pi$
$467$	20.5930	+	9.91706i	0.952929	+	0.458907i	0.108217	+	0.994127i	$0.465486\pi$
$468$		0			0
$469$	−4.98516	−	21.8414i	−0.230193	−	1.00854i
$470$		0			0
$471$	−10.2961	−	4.95835i	−0.474420	−	0.228469i
$472$		0			0
$473$	−1.21632	−	1.52521i	−0.0559263	−	0.0701293i
$474$		0			0
$475$	14.7252	−	18.4648i	0.675637	−	0.847222i
$476$		0			0
$477$	0.0884813	−	0.110952i	0.00405128	−	0.00508015i
$478$		0			0
$479$	0.477409	−	2.09166i	0.0218134	−	0.0955706i	−0.962849	−	0.270039i	$-0.912963\pi$
$479$	0.477409	−	2.09166i	0.0218134	−	0.0955706i	0.984663	+	0.174468i	$0.0558206\pi$
$480$		0			0
$481$	−51.0256			−2.32657
$482$		0			0
$483$	4.00683	−	1.92959i	0.182317	−	0.0877993i
$484$		0			0
$485$	−1.17093	−	1.46830i	−0.0531691	−	0.0666719i
$486$		0			0
$487$	4.84560	−	21.2300i	0.219575	−	0.962021i	−0.738218	−	0.674562i	$-0.764332\pi$
$487$	4.84560	−	21.2300i	0.219575	−	0.962021i	0.957793	−	0.287459i	$-0.0928105\pi$
$488$		0			0
$489$	8.87865	−	4.27573i	0.401507	−	0.193355i
$490$		0			0
$491$	−8.64786	−	37.8888i	−0.390273	−	1.70990i	−0.663696	−	0.748002i	$-0.731013\pi$
$491$	−8.64786	−	37.8888i	−0.390273	−	1.70990i	0.273423	−	0.961894i	$-0.411844\pi$
$492$		0			0
$493$	28.6374	+	0.220544i	1.28977	+	0.00993279i
$494$		0			0
$495$	−0.00514172	−	0.0225273i	−0.000231103	−	0.00101253i
$496$		0			0
$497$	−17.0712	+	8.22106i	−0.765748	+	0.368765i
$498$		0			0
$499$	8.74490	−	38.3139i	0.391476	−	1.71517i	−0.267981	−	0.963424i	$-0.586357\pi$
$499$	8.74490	−	38.3139i	0.391476	−	1.71517i	0.659457	−	0.751742i	$-0.270786\pi$
$500$		0			0
$501$	13.1278	+	16.4617i	0.586506	+	0.735456i
$502$		0			0
$503$	25.2735	−	12.1711i	1.12689	−	0.542680i	0.224874	−	0.974388i	$-0.427803\pi$
$503$	25.2735	−	12.1711i	1.12689	−	0.542680i	0.902014	+	0.431707i	$0.142089\pi$
$504$		0			0
$505$	0.604433			0.0268969
$506$		0			0
$507$	−7.62190	+	33.3937i	−0.338501	+	1.48307i
$508$		0			0
$509$	1.06278	−	1.33268i	0.0471069	−	0.0590701i	−0.757720	−	0.652580i	$-0.773687\pi$
$509$	1.06278	−	1.33268i	0.0471069	−	0.0590701i	0.804827	+	0.593510i	$0.202258\pi$
$510$		0			0
$511$	−24.0274	+	30.1294i	−1.06291	+	1.33285i
$512$		0			0
$513$	15.9995	+	20.0627i	0.706394	+	0.885790i
$514$		0			0
$515$	−0.805903	−	0.388102i	−0.0355123	−	0.0171018i
$516$		0			0
$517$	3.20065	+	14.0230i	0.140765	+	0.616730i
$518$		0			0
$519$	−18.2662	−	8.79653i	−0.801797	−	0.386125i
$520$		0			0
$521$	−21.0834			−0.923678			−0.461839	−	0.886964i	$-0.652810\pi$
$521$	−21.0834			−0.923678			−0.461839	+	0.886964i	$0.652810\pi$
$522$		0			0
$523$	8.93606			0.390747			0.195373	−	0.980729i	$-0.437408\pi$
$523$	8.93606			0.390747			0.195373	+	0.980729i	$0.437408\pi$
$524$		0			0
$525$	−23.4186	−	11.2778i	−1.02207	−	0.492203i
$526$		0			0
$527$	7.53008	+	32.9914i	0.328015	+	1.43713i
$528$		0			0
$529$	20.1259	+	9.69211i	0.875038	+	0.421396i
$530$		0			0
$531$	−0.232687	−	0.291781i	−0.0100978	−	0.0126622i
$532$		0			0
$533$	14.2978	−	17.9289i	0.619307	−	0.776586i
$534$		0			0
$535$	1.28022	−	1.60534i	0.0553486	−	0.0694050i
$536$		0			0
$537$	−7.11370	+	31.1672i	−0.306979	+	1.34496i
$538$		0			0
$539$	−3.97998			−0.171430
$540$		0			0
$541$	10.7827	−	5.19269i	0.463586	−	0.223251i	−0.187486	−	0.982267i	$-0.560034\pi$
$541$	10.7827	−	5.19269i	0.463586	−	0.223251i	0.651072	+	0.759016i	$0.274320\pi$
$542$		0			0
$543$	−10.7441	−	13.4727i	−0.461074	−	0.578169i
$544$		0			0
$545$	1.59668	−	6.99549i	0.0683940	−	0.299654i
$546$		0			0
$547$	−21.7331	+	10.4661i	−0.929239	+	0.447498i	−0.836361	−	0.548180i	$-0.815321\pi$
$547$	−21.7331	+	10.4661i	−0.929239	+	0.447498i	−0.0928783	+	0.995677i	$0.529607\pi$
$548$		0			0
$549$	−0.0362138	−	0.158663i	−0.00154557	−	0.00677157i
$550$		0			0
$551$	24.1857	−	11.4186i	1.03035	−	0.486450i
$552$		0			0
$553$	6.56613	+	28.7681i	0.279220	+	1.22334i
$554$		0			0
$555$	6.93036	−	3.33748i	0.294177	−	0.141668i
$556$		0			0
$557$	4.05033	−	17.7456i	0.171618	−	0.751907i	−0.813715	−	0.581264i	$-0.802558\pi$
$557$	4.05033	−	17.7456i	0.171618	−	0.751907i	0.985333	−	0.170643i	$-0.0545844\pi$
$558$		0			0
$559$	−4.97724	−	6.24126i	−0.210515	−	0.263977i
$560$		0			0
$561$	11.6556	−	5.61303i	0.492099	−	0.236982i
$562$		0			0
$563$	31.5149			1.32820			0.664098	−	0.747646i	$-0.268816\pi$
$563$	31.5149			1.32820			0.664098	+	0.747646i	$0.268816\pi$
$564$		0			0
$565$	1.83652	−	8.04631i	0.0772629	−	0.338511i
$566$		0			0
$567$	17.8049	−	22.3267i	0.747737	−	0.937633i
$568$		0			0
$569$	−17.7477	+	22.2549i	−0.744023	+	0.932975i	−0.999427	−	0.0338594i	$-0.989220\pi$
$569$	−17.7477	+	22.2549i	−0.744023	+	0.932975i	0.255404	+	0.966834i	$0.417792\pi$
$570$		0			0
$571$	2.65790	+	3.33290i	0.111230	+	0.139478i	0.834330	−	0.551266i	$-0.185855\pi$
$571$	2.65790	+	3.33290i	0.111230	+	0.139478i	−0.723100	+	0.690743i	$0.757283\pi$
$572$		0			0
$573$	0.665747	+	0.320607i	0.0278120	+	0.0133935i
$574$		0			0
$575$	0.860919	+	3.77193i	0.0359028	+	0.157300i
$576$		0			0
$577$	−20.3474	−	9.79878i	−0.847072	−	0.407929i	−0.0405823	−	0.999176i	$-0.512921\pi$
$577$	−20.3474	−	9.79878i	−0.847072	−	0.407929i	−0.806490	+	0.591248i	$0.798636\pi$
$578$		0			0
$579$	−17.9824			−0.747324
$580$		0			0
$581$	39.8872			1.65480
$582$		0			0
$583$	5.34013	+	2.57167i	0.221166	+	0.106508i
$584$		0			0
$585$	−0.0210402	−	0.0921833i	−0.000869906	−	0.00381131i
$586$		0			0
$587$	−30.1868	−	14.5372i	−1.24594	−	0.600015i	−0.309523	−	0.950892i	$-0.600169\pi$
$587$	−30.1868	−	14.5372i	−1.24594	−	0.600015i	−0.936422	+	0.350877i	$0.885884\pi$
$588$		0			0
$589$	19.7045	+	24.7087i	0.811910	+	1.01810i
$590$		0			0
$591$	−29.1490	+	36.5517i	−1.19903	+	1.50354i
$592$		0			0
$593$	8.32767	−	10.4426i	0.341977	−	0.428825i	−0.580868	−	0.813998i	$-0.697287\pi$
$593$	8.32767	−	10.4426i	0.341977	−	0.428825i	0.922844	+	0.385173i	$0.125858\pi$
$594$		0			0
$595$	−1.83724	+	8.04949i	−0.0753197	+	0.329997i
$596$		0			0
$597$	11.8485			0.484928
$598$		0			0
$599$	0.824990	−	0.397294i	0.0337082	−	0.0162330i	−0.416954	−	0.908928i	$-0.636902\pi$
$599$	0.824990	−	0.397294i	0.0337082	−	0.0162330i	0.450662	+	0.892695i	$0.351188\pi$
$600$		0			0
$601$	3.60037	+	4.51472i	0.146862	+	0.184159i	0.849821	−	0.527071i	$-0.176710\pi$
$601$	3.60037	+	4.51472i	0.146862	+	0.184159i	−0.702959	+	0.711230i	$0.748138\pi$
$602$		0			0
$603$	0.0531202	−	0.232735i	0.00216322	−	0.00947770i
$604$		0			0
$605$	−4.03329	+	1.94233i	−0.163977	+	0.0789669i
$606$		0			0
$607$	−3.33385	−	14.6065i	−0.135317	−	0.592861i	−0.996428	−	0.0844449i	$-0.973088\pi$
$607$	−3.33385	−	14.6065i	−0.135317	−	0.592861i	0.861111	−	0.508416i	$-0.169769\pi$
$608$		0			0
$609$	−18.1751	−	23.1544i	−0.736492	−	0.938264i
$610$		0			0
$611$	13.0973	+	57.3829i	0.529859	+	2.32146i
$612$		0			0
$613$	21.5458	−	10.3759i	0.870228	−	0.419080i	0.0551825	−	0.998476i	$-0.482426\pi$
$613$	21.5458	−	10.3759i	0.870228	−	0.419080i	0.815046	+	0.579396i	$0.196712\pi$
$614$		0			0
$615$	−0.769252	+	3.37031i	−0.0310192	+	0.135904i
$616$		0			0
$617$	−9.16964	−	11.4984i	−0.369156	−	0.462907i	0.562208	−	0.826996i	$-0.309952\pi$
$617$	−9.16964	−	11.4984i	−0.369156	−	0.462907i	−0.931364	+	0.364089i	$0.881380\pi$
$618$		0			0
$619$	20.6449	−	9.94208i	0.829790	−	0.399606i	0.0297537	−	0.999557i	$-0.490528\pi$
$619$	20.6449	−	9.94208i	0.829790	−	0.399606i	0.800036	+	0.599951i	$0.204813\pi$
$620$		0			0
$621$	−4.20375			−0.168691
$622$		0			0
$623$	1.25158	−	5.48352i	0.0501434	−	0.219693i
$624$		0			0
$625$	13.3358	−	16.7226i	0.533433	−	0.668904i
$626$		0			0
$627$	7.53288	−	9.44594i	0.300834	−	0.377234i
$628$		0			0
$629$	29.6016	+	37.1192i	1.18029	+	1.48004i
$630$		0			0
$631$	11.8128	+	5.68872i	0.470258	+	0.226465i	0.653977	−	0.756514i	$-0.273099\pi$
$631$	11.8128	+	5.68872i	0.470258	+	0.226465i	−0.183719	+	0.982979i	$0.558814\pi$
$632$		0			0
$633$	2.26359	+	9.91742i	0.0899695	+	0.394182i
$634$		0			0
$635$	5.65731	+	2.72442i	0.224503	+	0.108115i
$636$		0			0
$637$	−16.2863			−0.645287
$638$		0			0
$639$	−0.201900			−0.00798702
$640$		0			0
$641$	38.8282	+	18.6987i	1.53362	+	0.738553i	0.994604	−	0.103742i	$-0.0330816\pi$
$641$	38.8282	+	18.6987i	1.53362	+	0.738553i	0.539017	+	0.842295i	$0.318796\pi$
$642$		0			0
$643$	−1.92324	−	8.42626i	−0.0758451	−	0.332299i	0.922743	−	0.385415i	$-0.125942\pi$
$643$	−1.92324	−	8.42626i	−0.0758451	−	0.332299i	−0.998588	+	0.0531161i	$0.983085\pi$
$644$		0			0
$645$	1.08424	+	0.522144i	0.0426920	+	0.0205594i
$646$		0			0
$647$	2.98700	+	3.74558i	0.117431	+	0.147254i	0.837073	−	0.547092i	$-0.184265\pi$
$647$	2.98700	+	3.74558i	0.117431	+	0.147254i	−0.719641	+	0.694346i	$0.755694\pi$
$648$		0			0
$649$	9.71835	−	12.1864i	0.381479	−	0.478359i
$650$		0			0
$651$	21.6863	−	27.1938i	0.849953	−	1.06581i
$652$		0			0
$653$	−1.22812	+	5.38073i	−0.0480599	+	0.210564i	−0.993257	−	0.115938i	$-0.963013\pi$
$653$	−1.22812	+	5.38073i	−0.0480599	+	0.210564i	0.945197	+	0.326502i	$0.105870\pi$
$654$		0			0
$655$	−7.31958			−0.286000
$656$		0			0
$657$	−0.369971	+	0.178169i	−0.0144340	+	0.00695103i
$658$		0			0
$659$	1.14932	+	1.44120i	0.0447712	+	0.0561413i	0.803713	−	0.595017i	$-0.202855\pi$
$659$	1.14932	+	1.44120i	0.0447712	+	0.0561413i	−0.758942	+	0.651158i	$0.774283\pi$
$660$		0			0
$661$	5.80735	−	25.4436i	0.225880	−	0.989643i	−0.727082	−	0.686551i	$-0.759124\pi$
$661$	5.80735	−	25.4436i	0.225880	−	0.989643i	0.952961	−	0.303092i	$-0.0980190\pi$
$662$		0			0
$663$	47.6954	−	22.9689i	1.85233	−	0.892037i
$664$		0			0
$665$	1.71583	+	7.51754i	0.0665371	+	0.291518i
$666$		0			0
$667$	−1.00782	+	4.26393i	−0.0390231	+	0.165100i
$668$		0			0
$669$	−8.50153	−	37.2477i	−0.328688	−	1.44008i
$670$		0			0
$671$	6.12397	−	2.94915i	0.236413	−	0.113851i
$672$		0			0
$673$	−4.88021	+	21.3816i	−0.188118	+	0.824200i	0.789489	+	0.613764i	$0.210345\pi$
$673$	−4.88021	+	21.3816i	−0.188118	+	0.824200i	−0.977608	+	0.210436i	$0.932512\pi$
$674$		0			0
$675$	15.3188	+	19.2092i	0.589622	+	0.739363i
$676$		0			0
$677$	−9.15884	+	4.41066i	−0.352003	+	0.169516i	−0.601526	−	0.798853i	$-0.705440\pi$
$677$	−9.15884	+	4.41066i	−0.352003	+	0.169516i	0.249523	+	0.968369i	$0.419726\pi$
$678$		0			0
$679$	−11.9143			−0.457228
$680$		0			0
$681$	−0.835355	+	3.65993i	−0.0320109	+	0.140249i
$682$		0			0
$683$	−12.7734	+	16.0173i	−0.488760	+	0.612886i	−0.963653	−	0.267158i	$-0.913915\pi$
$683$	−12.7734	+	16.0173i	−0.488760	+	0.612886i	0.474893	+	0.880044i	$0.342487\pi$
$684$		0			0
$685$	0.465513	−	0.583735i	0.0177863	−	0.0223033i
$686$		0			0
$687$	10.0903	+	12.6528i	0.384967	+	0.482733i
$688$		0			0
$689$	21.8521	+	10.5234i	0.832500	+	0.400911i
$690$		0			0
$691$	−6.86393	−	30.0728i	−0.261116	−	1.14402i	−0.920043	−	0.391817i	$-0.871846\pi$
$691$	−6.86393	−	30.0728i	−0.261116	−	1.14402i	0.658927	−	0.752207i	$-0.271011\pi$
$692$		0			0
$693$	−0.132073	−	0.0636031i	−0.00501704	−	0.00241608i
$694$		0			0
$695$	4.33177			0.164313
$696$		0			0
$697$	−21.3372			−0.808204
$698$		0			0
$699$	18.4926	+	8.90557i	0.699455	+	0.336840i
$700$		0			0
$701$	4.60087	+	20.1577i	0.173773	+	0.761347i	0.984423	+	0.175817i	$0.0562566\pi$
$701$	4.60087	+	20.1577i	0.173773	+	0.761347i	−0.810650	+	0.585530i	$0.800886\pi$
$702$		0			0
$703$	39.9487	+	19.2383i	1.50669	+	0.725586i
$704$		0			0
$705$	−5.53219	−	6.93714i	−0.208354	−	0.261268i
$706$		0			0
$707$	2.39081	−	2.99798i	0.0899156	−	0.112751i
$708$		0			0
$709$	−28.0695	+	35.1981i	−1.05417	+	1.32189i	−0.109461	+	0.993991i	$0.534913\pi$
$709$	−28.0695	+	35.1981i	−1.05417	+	1.32189i	−0.944712	+	0.327901i	$0.893659\pi$
$710$		0			0
$711$	−0.0699666	+	0.306544i	−0.00262395	+	0.0114963i
$712$		0			0
$713$	−5.17722			−0.193888
$714$		0			0
$715$	3.55803	−	1.71346i	0.133063	−	0.0640796i
$716$		0			0
$717$	15.6038	+	19.5665i	0.582733	+	0.730724i
$718$		0			0
$719$	−2.24249	+	9.82501i	−0.0836309	+	0.366411i	−0.999375	−	0.0353512i	$-0.988745\pi$
$719$	−2.24249	+	9.82501i	−0.0836309	+	0.366411i	0.915744	+	0.401762i	$0.131602\pi$
$720$		0			0
$721$	−5.11269	+	2.46214i	−0.190407	+	0.0916950i
$722$		0			0
$723$	3.56722	+	15.6290i	0.132666	+	0.581250i
$724$		0			0
$725$	23.1568	−	10.9329i	0.860023	−	0.406036i
$726$		0			0
$727$	4.98758	+	21.8520i	0.184979	+	0.810447i	0.979213	+	0.202835i	$0.0650153\pi$
$727$	4.98758	+	21.8520i	0.184979	+	0.810447i	−0.794234	+	0.607612i	$0.792128\pi$
$728$		0			0
$729$	−24.0490	+	11.5814i	−0.890703	+	0.428940i
$730$		0			0
$731$	−1.65283	+	7.24151i	−0.0611320	+	0.267837i
$732$		0			0
$733$	2.46035	+	3.08518i	0.0908749	+	0.113954i	0.825190	−	0.564855i	$-0.191068\pi$
$733$	2.46035	+	3.08518i	0.0908749	+	0.113954i	−0.734315	+	0.678809i	$0.762497\pi$
$734$		0			0
$735$	2.21203	−	1.06526i	0.0815918	−	0.0392925i
$736$		0			0
$737$	9.97032			0.367261
$738$		0			0
$739$	1.38003	−	6.04632i	0.0507653	−	0.222417i	−0.943182	−	0.332277i	$-0.892183\pi$
$739$	1.38003	−	6.04632i	0.0507653	−	0.222417i	0.993947	+	0.109860i	$0.0350402\pi$
$740$		0			0
$741$	30.8250	−	38.6533i	1.13239	−	1.41997i
$742$		0			0
$743$	−30.3589	+	38.0689i	−1.11376	+	1.39661i	−0.205271	+	0.978705i	$0.565808\pi$
$743$	−30.3589	+	38.0689i	−1.11376	+	1.39661i	−0.908490	+	0.417907i	$0.862764\pi$
$744$		0			0
$745$	1.46222	+	1.83357i	0.0535718	+	0.0671769i
$746$		0			0
$747$	0.382934	+	0.184411i	0.0140108	+	0.00674726i
$748$		0			0
$749$	−2.89863	−	12.6997i	−0.105914	−	0.464038i
$750$		0			0
$751$	23.7677	+	11.4459i	0.867296	+	0.417668i	0.813968	−	0.580909i	$-0.197303\pi$
$751$	23.7677	+	11.4459i	0.867296	+	0.417668i	0.0533277	+	0.998577i	$0.483017\pi$
$752$		0			0
$753$	−10.3037			−0.375489
$754$		0			0
$755$	−3.21264			−0.116920
$756$		0			0
$757$	−34.4086	−	16.5703i	−1.25060	−	0.602259i	−0.312930	−	0.949776i	$-0.601310\pi$
$757$	−34.4086	−	16.5703i	−1.25060	−	0.602259i	−0.937673	+	0.347518i	$0.887025\pi$
$758$		0			0
$759$	0.440416	+	1.92959i	0.0159861	+	0.0700396i
$760$		0			0
$761$	−5.62055	−	2.70672i	−0.203745	−	0.0981183i	0.329229	−	0.944250i	$-0.393211\pi$
$761$	−5.62055	−	2.70672i	−0.203745	−	0.0981183i	−0.532974	+	0.846132i	$0.678926\pi$
$762$		0			0
$763$	−28.3820	−	35.5898i	−1.02750	−	1.28844i
$764$		0			0
$765$	−0.0548537	+	0.0687844i	−0.00198324	+	0.00248691i
$766$		0			0
$767$	39.7681	−	49.8676i	1.43594	−	1.80061i
$768$		0			0
$769$	6.26532	−	27.4502i	0.225933	−	0.989879i	−0.726985	−	0.686653i	$-0.759079\pi$
$769$	6.26532	−	27.4502i	0.225933	−	0.989879i	0.952919	−	0.303226i	$-0.0980637\pi$
$770$		0			0
$771$	−46.5398			−1.67609
$772$		0			0
$773$	−31.5991	+	15.2173i	−1.13654	+	0.547329i	−0.904964	−	0.425488i	$-0.860103\pi$
$773$	−31.5991	+	15.2173i	−1.13654	+	0.547329i	−0.231576	+	0.972817i	$0.574388\pi$
$774$		0			0
$775$	18.8663	+	23.6575i	0.677696	+	0.849804i
$776$		0			0
$777$	10.8589	−	47.5757i	0.389559	−	1.70677i
$778$		0			0
$779$	−17.9537	+	8.64606i	−0.643259	+	0.309777i
$780$		0			0
$781$	−1.87640	−	8.22106i	−0.0671430	−	0.294173i
$782$		0			0
$783$	5.98234	+	27.1733i	0.213791	+	0.971094i
$784$		0			0
$785$	0.722283	+	3.16453i	0.0257794	+	0.112947i
$786$		0			0
$787$	−24.5984	+	11.8459i	−0.876837	+	0.422262i	−0.817468	−	0.575974i	$-0.804623\pi$
$787$	−24.5984	+	11.8459i	−0.876837	+	0.422262i	−0.0593688	+	0.998236i	$0.518909\pi$
$788$		0			0
$789$	−9.05122	+	39.6560i	−0.322232	+	1.41179i
$790$		0			0
$791$	−32.6453	−	40.9359i	−1.16073	−	1.45551i
$792$		0			0
$793$	25.0597	−	12.0681i	0.889894	−	0.428551i
$794$		0			0
$795$	−3.65630			−0.129676
$796$		0			0
$797$	−9.11491	+	39.9350i	−0.322867	+	1.41457i	0.509560	+	0.860435i	$0.329808\pi$
$797$	−9.11491	+	39.9350i	−0.322867	+	1.41457i	−0.832426	+	0.554136i	$0.813049\pi$
$798$		0			0
$799$	34.1457	−	42.8174i	1.20799	−	1.51477i
$800$		0			0
$801$	0.0373678	−	0.0468577i	0.00132033	−	0.00165564i
$802$		0			0
$803$	−10.6932	−	13.4088i	−0.377355	−	0.473188i
$804$		0			0
$805$	−1.13808	−	0.548071i	−0.0401121	−	0.0193170i
$806$		0			0
$807$	−6.04953	−	26.5047i	−0.212953	−	0.933010i
$808$		0			0
$809$	38.8637	+	18.7158i	1.36638	+	0.658012i	0.966049	−	0.258360i	$-0.0831821\pi$
$809$	38.8637	+	18.7158i	1.36638	+	0.658012i	0.400327	+	0.916372i	$0.368896\pi$
$810$		0			0
$811$	−38.0001			−1.33436			−0.667182	−	0.744894i	$-0.732500\pi$
$811$	−38.0001			−1.33436			−0.667182	+	0.744894i	$0.732500\pi$
$812$		0			0
$813$	−0.382611			−0.0134187
$814$		0			0
$815$	−2.52185	−	1.21446i	−0.0883366	−	0.0425407i
$816$		0			0
$817$	1.54360	+	6.76296i	0.0540037	+	0.236606i
$818$		0			0
$819$	−0.540451	−	0.260268i	−0.0188849	−	0.00909449i
$820$		0			0
$821$	−7.61753	−	9.55208i	−0.265854	−	0.333370i	0.630930	−	0.775840i	$-0.282674\pi$
$821$	−7.61753	−	9.55208i	−0.265854	−	0.333370i	−0.896783	+	0.442470i	$0.854102\pi$
$822$		0			0
$823$	−22.8365	+	28.6361i	−0.796030	+	0.998190i	0.203786	+	0.979015i	$0.434675\pi$
$823$	−22.8365	+	28.6361i	−0.796030	+	0.998190i	−0.999816	+	0.0191747i	$0.993896\pi$
$824$		0			0
$825$	7.21242	−	9.04409i	0.251104	−	0.314875i
$826$		0			0
$827$	−5.74425	+	25.1672i	−0.199747	+	0.875149i	0.771340	+	0.636423i	$0.219587\pi$
$827$	−5.74425	+	25.1672i	−0.199747	+	0.875149i	−0.971087	+	0.238726i	$0.923270\pi$
$828$		0			0
$829$	−15.7732			−0.547825			−0.273913	−	0.961755i	$-0.588318\pi$
$829$	−15.7732			−0.547825			−0.273913	+	0.961755i	$0.588318\pi$
$830$		0			0
$831$	−5.88750	+	2.83527i	−0.204235	+	0.0983544i
$832$		0			0
$833$	9.44821	+	11.8477i	0.327361	+	0.410498i
$834$		0			0
$835$	1.33078	−	5.83052i	0.0460535	−	0.201773i
$836$		0			0
$837$	−29.6218	+	14.2651i	−1.02388	+	0.493074i
$838$		0			0
$839$	0.479893	+	2.10255i	0.0165677	+	0.0725880i	0.982536	−	0.186073i	$-0.0595760\pi$
$839$	0.479893	+	2.10255i	0.0165677	+	0.0725880i	−0.965968	+	0.258661i	$0.916719\pi$
$840$		0			0
$841$	28.9966	+	0.446646i	0.999881	+	0.0154016i
$842$		0			0
$843$	9.47627	+	41.5183i	0.326380	+	1.42996i
$844$		0			0
$845$	8.76546	−	4.22123i	0.301541	−	0.145215i
$846$		0			0
$847$	−6.31957	+	27.6879i	−0.217143	+	0.951366i
$848$		0			0
$849$	−8.25027	−	10.3455i	−0.283149	−	0.355057i
$850$		0			0
$851$	−6.54430	+	3.15157i	−0.224336	+	0.108034i
$852$		0			0
$853$	−21.6578			−0.741548			−0.370774	−	0.928723i	$-0.620908\pi$
$853$	−21.6578			−0.741548			−0.370774	+	0.928723i	$0.620908\pi$
$854$		0			0
$855$	−0.0182833	+	0.0801045i	−0.000625277	+	0.00273952i
$856$		0			0
$857$	−7.86892	+	9.86732i	−0.268797	+	0.337061i	−0.897850	−	0.440302i	$-0.854872\pi$
$857$	−7.86892	+	9.86732i	−0.268797	+	0.337061i	0.629053	+	0.777363i	$0.283443\pi$
$858$		0			0
$859$	12.1127	−	15.1888i	0.413280	−	0.518236i	−0.531004	−	0.847369i	$-0.678185\pi$
$859$	12.1127	−	15.1888i	0.413280	−	0.518236i	0.944284	+	0.329133i	$0.106756\pi$
$860$		0			0
$861$	13.6740	+	17.1466i	0.466007	+	0.584355i
$862$		0			0
$863$	−41.3801	−	19.9276i	−1.40860	−	0.678344i	−0.433711	−	0.901052i	$-0.642796\pi$
$863$	−41.3801	−	19.9276i	−1.40860	−	0.678344i	−0.974885	+	0.222708i	$0.928510\pi$
$864$		0			0
$865$	1.28139	+	5.61414i	0.0435686	+	0.190886i
$866$		0			0
$867$	−17.7022	−	8.52495i	−0.601200	−	0.289523i
$868$		0			0
$869$	−13.1323			−0.445482
$870$		0			0
$871$	40.7992			1.38243
$872$		0			0
$873$	−0.114382	−	0.0550836i	−0.00387125	−	0.00186430i
$874$		0			0
$875$	3.37022	+	14.7659i	0.113934	+	0.499179i
$876$		0			0
$877$	−7.29358	−	3.51240i	−0.246287	−	0.118605i	0.306669	−	0.951816i	$-0.400786\pi$
$877$	−7.29358	−	3.51240i	−0.246287	−	0.118605i	−0.552955	+	0.833211i	$0.686500\pi$
$878$		0			0
$879$	−27.9323	−	35.0260i	−0.942134	−	1.18140i
$880$		0			0
$881$	1.87163	−	2.34695i	0.0630569	−	0.0790709i	−0.749303	−	0.662228i	$-0.769611\pi$
$881$	1.87163	−	2.34695i	0.0630569	−	0.0790709i	0.812360	+	0.583157i	$0.198183\pi$
$882$		0			0
$883$	24.0764	−	30.1908i	0.810235	−	1.01600i	−0.189184	−	0.981942i	$-0.560584\pi$
$883$	24.0764	−	30.1908i	0.810235	−	1.01600i	0.999420	−	0.0340614i	$-0.0108442\pi$
$884$		0			0
$885$	−2.13961	+	9.37422i	−0.0719221	+	0.315111i
$886$		0			0
$887$	29.4281			0.988100			0.494050	−	0.869433i	$-0.335516\pi$
$887$	29.4281			0.988100			0.494050	+	0.869433i	$0.335516\pi$
$888$		0			0
$889$	35.8903	−	17.2839i	1.20372	−	0.579682i
$890$		0			0
$891$	7.92394	+	9.93631i	0.265462	+	0.332879i
$892$		0			0
$893$	11.3811	−	49.8640i	0.380855	−	1.66864i
$894$		0			0
$895$	8.18101	−	3.93977i	0.273461	−	0.131692i
$896$		0			0
$897$	1.80221	+	7.89599i	0.0601740	+	0.263640i
$898$		0			0
$899$	7.36769	+	33.4659i	0.245726	+	1.11615i
$900$		0			0
$901$	−5.02172	−	22.0016i	−0.167298	−	0.732979i
$902$		0			0
$903$	6.87850	−	3.31251i	0.228902	−	0.110233i
$904$		0			0
$905$	−1.08914	+	4.77185i	−0.0362043	+	0.158622i
$906$		0			0
$907$	−2.90939	−	3.64825i	−0.0966046	−	0.121138i	0.731179	−	0.682185i	$-0.238970\pi$
$907$	−2.90939	−	3.64825i	−0.0966046	−	0.121138i	−0.827784	+	0.561047i	$0.810399\pi$
$908$		0			0
$909$	0.0368134	−	0.0177284i	0.00122102	−	0.000588014i
$910$		0			0
$911$	37.9571			1.25758			0.628788	−	0.777577i	$-0.283551\pi$
$911$	37.9571			1.25758			0.628788	+	0.777577i	$0.283551\pi$
$912$		0			0
$913$	−3.95007	+	17.3064i	−0.130728	+	0.572758i
$914$		0			0
$915$	−2.61428	+	3.27820i	−0.0864255	+	0.108374i
$916$		0			0
$917$	−28.9523	+	36.3050i	−0.956089	+	1.19890i
$918$		0			0
$919$	−15.8113	−	19.8268i	−0.521568	−	0.654026i	0.449373	−	0.893344i	$-0.351647\pi$
$919$	−15.8113	−	19.8268i	−0.521568	−	0.654026i	−0.970941	+	0.239318i	$0.923076\pi$
$920$		0			0
$921$	2.84651	+	1.37081i	0.0937956	+	0.0451696i
$922$		0			0
$923$	−7.67836	−	33.6411i	−0.252736	−	1.10731i
$924$		0			0
$925$	38.2492	+	18.4199i	1.25763	+	0.605641i
$926$		0			0
$927$	−0.0604674			−0.00198601
$928$		0			0
$929$	36.8642			1.20947			0.604737	−	0.796425i	$-0.293278\pi$
$929$	36.8642			1.20947			0.604737	+	0.796425i	$0.293278\pi$
$930$		0			0
$931$	12.7508	+	6.14046i	0.417891	+	0.201246i
$932$		0			0
$933$	7.52255	+	32.9584i	0.246277	+	1.07901i
$934$		0			0
$935$	−3.31060	−	1.59430i	−0.108268	−	0.0521392i
$936$		0			0
$937$	−1.45551	−	1.82515i	−0.0475493	−	0.0596249i	0.757488	−	0.652849i	$-0.226426\pi$
$937$	−1.45551	−	1.82515i	−0.0475493	−	0.0596249i	−0.805038	+	0.593224i	$0.797855\pi$
$938$		0			0
$939$	36.7960	−	46.1408i	1.20079	−	1.50575i
$940$		0			0
$941$	5.47972	−	6.87136i	0.178634	−	0.224000i	−0.684451	−	0.729059i	$-0.739958\pi$
$941$	5.47972	−	6.87136i	0.178634	−	0.224000i	0.863085	+	0.505059i	$0.168529\pi$
$942$		0			0
$943$	0.726401	−	3.18257i	0.0236549	−	0.103639i
$944$		0			0
$945$	−8.02174			−0.260947
$946$		0			0
$947$	−11.4402	+	5.50930i	−0.371756	+	0.179028i	−0.610428	−	0.792072i	$-0.709002\pi$
$947$	−11.4402	+	5.50930i	−0.371756	+	0.179028i	0.238672	+	0.971100i	$0.423288\pi$
$948$		0			0
$949$	−43.7572	−	54.8698i	−1.42042	−	1.78115i
$950$		0			0
$951$	−2.13065	+	9.33500i	−0.0690911	+	0.302708i
$952$		0			0
$953$	−49.0633	+	23.6277i	−1.58932	+	0.765375i	−0.999122	−	0.0418854i	$-0.986664\pi$
$953$	−49.0633	+	23.6277i	−1.58932	+	0.765375i	−0.590195	+	0.807261i	$0.700949\pi$
$954$		0			0
$955$	−0.0467028	−	0.204618i	−0.00151127	−	0.00662129i
$956$		0			0
$957$	11.8462	−	5.59287i	0.382934	−	0.180792i
$958$		0			0
$959$	−1.05400	−	4.61787i	−0.0340354	−	0.149119i
$960$		0			0
$961$	−8.55134	+	4.11811i	−0.275850	+	0.132842i
$962$		0			0
$963$	0.0308868	−	0.135324i	0.000995314	−	0.00436076i
$964$		0			0
$965$	3.18457	+	3.99332i	0.102515	+	0.128549i
$966$		0			0
$967$	44.6567	−	21.5055i	1.43606	−	0.691572i	0.455949	−	0.890006i	$-0.349300\pi$
$967$	44.6567	−	21.5055i	1.43606	−	0.691572i	0.980114	+	0.198434i	$0.0635855\pi$
$968$		0			0
$969$	−46.0014			−1.47778
$970$		0			0
$971$	−6.13766	+	26.8909i	−0.196967	+	0.862969i	0.775762	+	0.631025i	$0.217366\pi$
$971$	−6.13766	+	26.8909i	−0.196967	+	0.862969i	−0.972729	+	0.231944i	$0.925492\pi$
$972$		0			0
$973$	17.1341	−	21.4855i	0.549295	−	0.688794i
$974$		0			0
$975$	29.5137	−	37.0090i	0.945194	−	1.18524i
$976$		0			0
$977$	−27.7654	−	34.8167i	−0.888294	−	1.11389i	−0.992850	−	0.119367i	$-0.961914\pi$
$977$	−27.7654	−	34.8167i	−0.888294	−	1.11389i	0.104556	−	0.994519i	$-0.466658\pi$
$978$		0			0
$979$	2.25527	+	1.08608i	0.0720786	+	0.0347112i
$980$		0			0
$981$	−0.107936	−	0.472897i	−0.00344612	−	0.0150984i
$982$		0			0
$983$	−1.07817	−	0.519217i	−0.0343882	−	0.0165605i	0.416611	−	0.909085i	$-0.363218\pi$
$983$	−1.07817	−	0.519217i	−0.0343882	−	0.0165605i	−0.450999	+	0.892525i	$0.648932\pi$
$984$		0			0
$985$	13.2791			0.423106
$986$		0			0
$987$	−56.2904			−1.79174
$988$		0			0
$989$	−1.02384	−	0.493058i	−0.0325564	−	0.0156783i
$990$		0			0
$991$	7.79435	+	34.1493i	0.247596	+	1.08479i	0.933917	+	0.357490i	$0.116367\pi$
$991$	7.79435	+	34.1493i	0.247596	+	1.08479i	−0.686321	+	0.727298i	$0.740776\pi$
$992$		0			0
$993$	−21.4137	−	10.3123i	−0.679544	−	0.327251i
$994$		0			0
$995$	−2.09829	−	2.63118i	−0.0665204	−	0.0834139i
$996$		0			0
$997$	19.4359	−	24.3719i	0.615543	−	0.771866i	−0.372167	−	0.928166i	$-0.621385\pi$
$997$	19.4359	−	24.3719i	0.615543	−	0.771866i	0.987710	+	0.156300i	$0.0499566\pi$
$998$		0			0
$999$	−28.7599	+	36.0638i	−0.909924	+	1.14101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.u.h.65.1		12
4.3	odd	2		58.2.d.b.7.2	✓	12
12.11	even	2		522.2.k.h.181.1		12
29.25	even	7	inner	464.2.u.h.257.1		12
116.27	even	28		1682.2.b.i.1681.8		12
116.31	even	28		1682.2.b.i.1681.5		12
116.63	odd	14		1682.2.a.q.1.5		6
116.83	odd	14		58.2.d.b.25.2	yes	12
116.111	odd	14		1682.2.a.t.1.2		6
348.83	even	14		522.2.k.h.199.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.7.2	✓	12	4.3	odd	2
58.2.d.b.25.2	yes	12	116.83	odd	14
464.2.u.h.65.1		12	1.1	even	1	trivial
464.2.u.h.257.1		12	29.25	even	7	inner
522.2.k.h.181.1		12	12.11	even	2
522.2.k.h.199.1		12	348.83	even	14
1682.2.a.q.1.5		6	116.63	odd	14
1682.2.a.t.1.2		6	116.111	odd	14
1682.2.b.i.1681.5		12	116.31	even	28
1682.2.b.i.1681.8		12	116.27	even	28

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.56920 - 0.755686i) q^{3} +(0.110081 + 0.482295i) q^{5} +(2.82760 + 1.36170i) q^{7} +(0.0208506 + 0.0261458i) q^{9} +O(q^{10})\)	\(q+(-1.56920 - 0.755686i) q^{3} +(0.110081 + 0.482295i) q^{5} +(2.82760 + 1.36170i) q^{7} +(0.0208506 + 0.0261458i) q^{9} +(-0.870839 + 1.09200i) q^{11} +(-3.56353 + 4.46852i) q^{13} +(0.191725 - 0.840003i) q^{15} +5.31800 q^{17} +(4.47471 - 2.15491i) q^{19} +(-3.40804 - 4.27355i) q^{21} +(-0.181045 + 0.793210i) q^{23} +(4.28435 - 2.06324i) q^{25} +(1.14972 + 5.03725i) q^{27} +(5.38501 + 0.0414712i) q^{29} +(1.41596 + 6.20373i) q^{31} +(2.19173 - 1.05548i) q^{33} +(-0.345477 + 1.51363i) q^{35} +(5.56630 + 6.97992i) q^{37} +(8.96867 - 4.31909i) q^{39} -4.01226 q^{41} +(-0.310799 + 1.36170i) q^{43} +(-0.0103147 + 0.0129343i) q^{45} +(6.42079 - 8.05142i) q^{47} +(1.77665 + 2.22785i) q^{49} +(-8.34499 - 4.01873i) q^{51} +(-0.944288 - 4.13720i) q^{53} +(-0.622528 - 0.299794i) q^{55} -8.65014 q^{57} -11.1598 q^{59} +(-4.38454 - 2.11149i) q^{61} +(0.0233543 + 0.102322i) q^{63} +(-2.54742 - 1.22677i) q^{65} +(-4.45072 - 5.58102i) q^{67} +(0.883513 - 1.10789i) q^{69} +(-3.76423 + 4.72019i) q^{71} +(-2.73238 + 11.9713i) q^{73} -8.28215 q^{75} +(-3.94935 + 1.90191i) q^{77} +(5.86220 + 7.35096i) q^{79} +(2.02476 - 8.87107i) q^{81} +(11.4508 - 5.51441i) q^{83} +(0.585409 + 2.56484i) q^{85} +(-8.41880 - 4.13445i) q^{87} +(-0.398796 - 1.74724i) q^{89} +(-16.1610 + 7.78272i) q^{91} +(2.46615 - 10.8049i) q^{93} +(1.53188 + 1.92092i) q^{95} +(-3.42035 + 1.64715i) q^{97} -0.0467086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - q^{7} - 11 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - q^7 - 11 * q^9	\( 12 q + 3 q^{3} - q^{7} - 11 q^{9} + 2 q^{11} + q^{13} + 9 q^{15} - 12 q^{17} + 6 q^{19} - 13 q^{21} - 35 q^{23} - 6 q^{25} - 39 q^{27} - 14 q^{29} + 8 q^{31} + 33 q^{33} + 18 q^{35} + 31 q^{37} + 22 q^{39} - 30 q^{41} + 5 q^{43} - 20 q^{45} + 33 q^{47} + 37 q^{49} + 15 q^{51} + 13 q^{53} - 36 q^{55} - 38 q^{57} - 38 q^{59} - 5 q^{61} - 4 q^{63} - 20 q^{65} + 7 q^{67} + 20 q^{69} - 3 q^{71} - 22 q^{73} + 2 q^{75} + 10 q^{77} + 60 q^{79} + 88 q^{81} + 39 q^{83} + 38 q^{85} - 9 q^{87} + 39 q^{89} - 61 q^{91} - 54 q^{93} - 55 q^{95} - 19 q^{97} + 8 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - q^7 - 11 * q^9 + 2 * q^11 + q^13 + 9 * q^15 - 12 * q^17 + 6 * q^19 - 13 * q^21 - 35 * q^23 - 6 * q^25 - 39 * q^27 - 14 * q^29 + 8 * q^31 + 33 * q^33 + 18 * q^35 + 31 * q^37 + 22 * q^39 - 30 * q^41 + 5 * q^43 - 20 * q^45 + 33 * q^47 + 37 * q^49 + 15 * q^51 + 13 * q^53 - 36 * q^55 - 38 * q^57 - 38 * q^59 - 5 * q^61 - 4 * q^63 - 20 * q^65 + 7 * q^67 + 20 * q^69 - 3 * q^71 - 22 * q^73 + 2 * q^75 + 10 * q^77 + 60 * q^79 + 88 * q^81 + 39 * q^83 + 38 * q^85 - 9 * q^87 + 39 * q^89 - 61 * q^91 - 54 * q^93 - 55 * q^95 - 19 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more