LMFDB - Embedded newform 1610.2.g.a.1609.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1610,2,Mod(1609,1610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("1610.1609");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1610 = 2 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1610.g (of order $2$, degree $1$, 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:	$12.8559147254$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1609.3
Character	$\chi$	$=$	1610.1609
Dual form			1610.2.g.a.1609.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +3.32094 q^{3} -1.00000 q^{4} +(-0.0164715 + 2.23601i) q^{5} -3.32094i q^{6} +(2.20809 - 1.45752i) q^{7} +1.00000i q^{8} +8.02867 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +3.32094 q^{3} -1.00000 q^{4} +(-0.0164715 + 2.23601i) q^{5} -3.32094i q^{6} +(2.20809 - 1.45752i) q^{7} +1.00000i q^{8} +8.02867 q^{9} +(2.23601 + 0.0164715i) q^{10} +3.09468i q^{11} -3.32094 q^{12} +3.13074 q^{13} +(-1.45752 - 2.20809i) q^{14} +(-0.0547010 + 7.42565i) q^{15} +1.00000 q^{16} +0.517611i q^{17} -8.02867i q^{18} -4.30476 q^{19} +(0.0164715 - 2.23601i) q^{20} +(7.33293 - 4.84033i) q^{21} +3.09468 q^{22} +(-3.05303 - 3.69851i) q^{23} +3.32094i q^{24} +(-4.99946 - 0.0736609i) q^{25} -3.13074i q^{26} +16.6999 q^{27} +(-2.20809 + 1.45752i) q^{28} -7.27310 q^{29} +(7.42565 + 0.0547010i) q^{30} +3.31132i q^{31} -1.00000i q^{32} +10.2773i q^{33} +0.517611 q^{34} +(3.22265 + 4.96130i) q^{35} -8.02867 q^{36} +6.17419 q^{37} +4.30476i q^{38} +10.3970 q^{39} +(-2.23601 - 0.0164715i) q^{40} +5.26619i q^{41} +(-4.84033 - 7.33293i) q^{42} -1.14534 q^{43} -3.09468i q^{44} +(-0.132244 + 17.9522i) q^{45} +(-3.69851 + 3.05303i) q^{46} -2.02900 q^{47} +3.32094 q^{48} +(2.75128 - 6.43665i) q^{49} +(-0.0736609 + 4.99946i) q^{50} +1.71896i q^{51} -3.13074 q^{52} -11.4339 q^{53} -16.6999i q^{54} +(-6.91972 - 0.0509741i) q^{55} +(1.45752 + 2.20809i) q^{56} -14.2959 q^{57} +7.27310i q^{58} -14.3623i q^{59} +(0.0547010 - 7.42565i) q^{60} +11.6493 q^{61} +3.31132 q^{62} +(17.7280 - 11.7019i) q^{63} -1.00000 q^{64} +(-0.0515681 + 7.00037i) q^{65} +10.2773 q^{66} +3.04370 q^{67} -0.517611i q^{68} +(-10.1389 - 12.2826i) q^{69} +(4.96130 - 3.22265i) q^{70} -3.83097 q^{71} +8.02867i q^{72} +4.21001 q^{73} -6.17419i q^{74} +(-16.6029 - 0.244624i) q^{75} +4.30476 q^{76} +(4.51055 + 6.83332i) q^{77} -10.3970i q^{78} -1.67775i q^{79} +(-0.0164715 + 2.23601i) q^{80} +31.3735 q^{81} +5.26619 q^{82} -11.1018i q^{83} +(-7.33293 + 4.84033i) q^{84} +(-1.15738 - 0.00852584i) q^{85} +1.14534i q^{86} -24.1535 q^{87} -3.09468 q^{88} +2.13097 q^{89} +(17.9522 + 0.132244i) q^{90} +(6.91295 - 4.56311i) q^{91} +(3.05303 + 3.69851i) q^{92} +10.9967i q^{93} +2.02900i q^{94} +(0.0709060 - 9.62548i) q^{95} -3.32094i q^{96} +6.62988i q^{97} +(-6.43665 - 2.75128i) q^{98} +24.8461i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 96 q^{4} + 88 q^{9}+O(q^{10}) $ 96 * q - 96 * q^4 + 88 * q^9	$ 96 q - 96 q^{4} + 88 q^{9} + 96 q^{16} + 8 q^{25} + 8 q^{35} - 88 q^{36} - 16 q^{39} - 16 q^{46} + 36 q^{49} + 24 q^{50} - 96 q^{64} - 12 q^{70} + 8 q^{71} + 128 q^{81} + 16 q^{85} - 32 q^{95}+O(q^{100}) $ 96 * q - 96 * q^4 + 88 * q^9 + 96 * q^16 + 8 * q^25 + 8 * q^35 - 88 * q^36 - 16 * q^39 - 16 * q^46 + 36 * q^49 + 24 * q^50 - 96 * q^64 - 12 * q^70 + 8 * q^71 + 128 * q^81 + 16 * q^85 - 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1610\mathbb{Z}\right)^\times$.

$n$	$281$	$967$	$1151$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	3.32094			1.91735			0.958674	−	0.284508i	$-0.0918301\pi$
$3$	3.32094			1.91735			0.958674	+	0.284508i	$0.0918301\pi$
$4$	−1.00000			−0.500000
$5$	−0.0164715	+	2.23601i	−0.00736629	+	0.999973i
$5$	−0.0164715	+	2.23601i	−0.00736629	+	0.999973i
$6$		−	3.32094i		−	1.35577i
$7$	2.20809	−	1.45752i	0.834578	−	0.550890i
$7$	2.20809	−	1.45752i	0.834578	−	0.550890i
$8$			1.00000i			0.353553i
$9$	8.02867			2.67622
$10$	2.23601	+	0.0164715i	0.707088	+	0.00520875i
$11$			3.09468i			0.933081i	0.884500	+	0.466540i	$0.154500\pi$
$11$			3.09468i			0.933081i	−0.884500	+	0.466540i	$0.845500\pi$
$12$	−3.32094			−0.958674
$13$	3.13074			0.868312			0.434156	−	0.900838i	$-0.357047\pi$
$13$	3.13074			0.868312			0.434156	+	0.900838i	$0.357047\pi$
$14$	−1.45752	−	2.20809i	−0.389538	−	0.590136i
$15$	−0.0547010	+	7.42565i	−0.0141237	+	1.91730i
$16$	1.00000			0.250000
$17$			0.517611i			0.125539i	0.998028	+	0.0627696i	$0.0199933\pi$
$17$			0.517611i			0.125539i	−0.998028	+	0.0627696i	$0.980007\pi$
$18$		−	8.02867i		−	1.89237i
$19$	−4.30476			−0.987580			−0.493790	−	0.869581i	$-0.664389\pi$
$19$	−4.30476			−0.987580			−0.493790	+	0.869581i	$0.664389\pi$
$20$	0.0164715	−	2.23601i	0.00368314	−	0.499986i
$21$	7.33293	−	4.84033i	1.60018	−	1.05625i
$22$	3.09468			0.659788
$23$	−3.05303	−	3.69851i	−0.636601	−	0.771193i
$23$	−3.05303	−	3.69851i	−0.636601	−	0.771193i
$24$			3.32094i			0.677885i
$25$	−4.99946	−	0.0736609i	−0.999891	−	0.0147322i
$26$		−	3.13074i		−	0.613989i
$27$	16.6999			3.21390
$28$	−2.20809	+	1.45752i	−0.417289	+	0.275445i
$29$	−7.27310			−1.35058			−0.675290	−	0.737552i	$-0.735982\pi$
$29$	−7.27310			−1.35058			−0.675290	+	0.737552i	$0.735982\pi$
$30$	7.42565	+	0.0547010i	1.35573	+	0.00998699i
$31$			3.31132i			0.594731i	0.954764	+	0.297365i	$0.0961079\pi$
$31$			3.31132i			0.594731i	−0.954764	+	0.297365i	$0.903892\pi$
$32$		−	1.00000i		−	0.176777i
$33$			10.2773i			1.78904i
$34$	0.517611			0.0887696
$35$	3.22265	+	4.96130i	0.544727	+	0.838613i
$36$	−8.02867			−1.33811
$37$	6.17419			1.01503			0.507515	−	0.861643i	$-0.330564\pi$
$37$	6.17419			1.01503			0.507515	+	0.861643i	$0.330564\pi$
$38$			4.30476i			0.698325i
$39$	10.3970			1.66486
$40$	−2.23601	−	0.0164715i	−0.353544	−	0.00260438i
$41$			5.26619i			0.822441i	0.911536	+	0.411221i	$0.134897\pi$
$41$			5.26619i			0.822441i	−0.911536	+	0.411221i	$0.865103\pi$
$42$	−4.84033	−	7.33293i	−0.746880	−	1.13150i
$43$	−1.14534			−0.174663			−0.0873317	−	0.996179i	$-0.527834\pi$
$43$	−1.14534			−0.174663			−0.0873317	+	0.996179i	$0.527834\pi$
$44$		−	3.09468i		−	0.466540i
$45$	−0.132244	+	17.9522i	−0.0197138	+	2.67615i
$46$	−3.69851	+	3.05303i	−0.545316	+	0.450145i
$47$	−2.02900			−0.295959			−0.147980	−	0.988990i	$-0.547277\pi$
$47$	−2.02900			−0.295959			−0.147980	+	0.988990i	$0.547277\pi$
$48$	3.32094			0.479337
$49$	2.75128	−	6.43665i	0.393041	−	0.919521i
$50$	−0.0736609	+	4.99946i	−0.0104172	+	0.707030i
$51$			1.71896i			0.240702i
$52$	−3.13074			−0.434156
$53$	−11.4339			−1.57056			−0.785281	−	0.619139i	$-0.787482\pi$
$53$	−11.4339			−1.57056			−0.785281	+	0.619139i	$0.787482\pi$
$54$		−	16.6999i		−	2.27257i
$55$	−6.91972	−	0.0509741i	−0.933056	−	0.00687334i
$56$	1.45752	+	2.20809i	0.194769	+	0.295068i
$57$	−14.2959			−1.89354
$58$			7.27310i			0.955004i
$59$		−	14.3623i		−	1.86982i	−0.354890	−	0.934908i	$-0.615482\pi$
$59$		−	14.3623i		−	1.86982i	0.354890	−	0.934908i	$-0.384518\pi$
$60$	0.0547010	−	7.42565i	0.00706187	−	0.958648i
$61$	11.6493			1.49154			0.745769	−	0.666204i	$-0.232082\pi$
$61$	11.6493			1.49154			0.745769	+	0.666204i	$0.232082\pi$
$62$	3.31132			0.420538
$63$	17.7280	−	11.7019i	2.23352	−	1.47430i
$64$	−1.00000			−0.125000
$65$	−0.0515681	+	7.00037i	−0.00639624	+	0.868288i
$66$	10.2773			1.26504
$67$	3.04370			0.371848			0.185924	−	0.982564i	$-0.440472\pi$
$67$	3.04370			0.371848			0.185924	+	0.982564i	$0.440472\pi$
$68$		−	0.517611i		−	0.0627696i
$69$	−10.1389	−	12.2826i	−1.22059	−	1.47865i
$70$	4.96130	−	3.22265i	0.592989	−	0.385180i
$71$	−3.83097			−0.454652			−0.227326	−	0.973819i	$-0.572998\pi$
$71$	−3.83097			−0.454652			−0.227326	+	0.973819i	$0.572998\pi$
$72$			8.02867i			0.946187i
$73$	4.21001			0.492745			0.246372	−	0.969175i	$-0.420761\pi$
$73$	4.21001			0.492745			0.246372	+	0.969175i	$0.420761\pi$
$74$		−	6.17419i		−	0.717735i
$75$	−16.6029	−	0.244624i	−1.91714	−	0.0282467i
$76$	4.30476			0.493790
$77$	4.51055	+	6.83332i	0.514025	+	0.778729i
$78$		−	10.3970i		−	1.17723i
$79$		−	1.67775i		−	0.188762i	−0.995536	−	0.0943811i	$-0.969913\pi$
$79$		−	1.67775i		−	0.188762i	0.995536	−	0.0943811i	$-0.0300872\pi$
$80$	−0.0164715	+	2.23601i	−0.00184157	+	0.249993i
$81$	31.3735			3.48594
$82$	5.26619			0.581554
$83$		−	11.1018i		−	1.21858i	−0.792947	−	0.609291i	$-0.791454\pi$
$83$		−	11.1018i		−	1.21858i	0.792947	−	0.609291i	$-0.208546\pi$
$84$	−7.33293	+	4.84033i	−0.800088	+	0.528124i
$85$	−1.15738	−	0.00852584i	−0.125536	−	0.000924757i
$86$			1.14534i			0.123506i
$87$	−24.1535			−2.58953
$88$	−3.09468			−0.329894
$89$	2.13097			0.225882			0.112941	−	0.993602i	$-0.463973\pi$
$89$	2.13097			0.225882			0.112941	+	0.993602i	$0.463973\pi$
$90$	17.9522	+	0.132244i	1.89232	+	0.0139398i
$91$	6.91295	−	4.56311i	0.724674	−	0.478344i
$92$	3.05303	+	3.69851i	0.318300	+	0.385597i
$93$			10.9967i			1.14031i
$94$			2.02900i			0.209275i
$95$	0.0709060	−	9.62548i	0.00727480	−	0.987554i
$96$		−	3.32094i		−	0.338942i
$97$			6.62988i			0.673163i	0.941654	+	0.336581i	$0.109271\pi$
$97$			6.62988i			0.673163i	−0.941654	+	0.336581i	$0.890729\pi$
$98$	−6.43665	−	2.75128i	−0.650200	−	0.277922i
$99$			24.8461i			2.49713i
$100$	4.99946	+	0.0736609i	0.499946	+	0.00736609i
$101$		−	12.5472i		−	1.24849i	−0.781229	−	0.624244i	$-0.785407\pi$
$101$		−	12.5472i		−	1.24849i	0.781229	−	0.624244i	$-0.214593\pi$
$102$	1.71896			0.170202
$103$		−	5.84073i		−	0.575504i	−0.957705	−	0.287752i	$-0.907092\pi$
$103$		−	5.84073i		−	0.575504i	0.957705	−	0.287752i	$-0.0929080\pi$
$104$			3.13074i			0.306995i
$105$	10.7022	+	16.4762i	1.04443	+	1.60791i
$106$			11.4339i			1.11056i
$107$	−11.1101			−1.07406			−0.537028	−	0.843564i	$-0.680453\pi$
$107$	−11.1101			−1.07406			−0.537028	+	0.843564i	$0.680453\pi$
$108$	−16.6999			−1.60695
$109$		−	19.0683i		−	1.82641i	−0.407497	−	0.913206i	$-0.633598\pi$
$109$		−	19.0683i		−	1.82641i	0.407497	−	0.913206i	$-0.366402\pi$
$110$	−0.0509741	+	6.91972i	−0.00486019	+	0.659770i
$111$	20.5041			1.94617
$112$	2.20809	−	1.45752i	0.208644	−	0.137722i
$113$	4.69728			0.441883			0.220941	−	0.975287i	$-0.429087\pi$
$113$	4.69728			0.441883			0.220941	+	0.975287i	$0.429087\pi$
$114$			14.2959i			1.33893i
$115$	8.32019	−	6.76568i	0.775862	−	0.630903i
$116$	7.27310			0.675290
$117$	25.1357			2.32380
$118$	−14.3623			−1.32216
$119$	0.754427	+	1.14293i	0.0691582	+	0.104772i
$120$	−7.42565	−	0.0547010i	−0.677866	−	0.00499349i
$121$	1.42296			0.129360
$122$		−	11.6493i		−	1.05468i
$123$			17.4887i			1.57691i
$124$		−	3.31132i		−	0.297365i
$125$	0.247055	−	11.1776i	0.0220973	−	0.999756i
$126$	−11.7019	−	17.7280i	−1.04249	−	1.57933i
$127$			15.3439i			1.36155i	0.732493	+	0.680775i	$0.238357\pi$
$127$			15.3439i			1.36155i	−0.732493	+	0.680775i	$0.761643\pi$
$128$			1.00000i			0.0883883i
$129$	−3.80362			−0.334890
$130$	7.00037	+	0.0515681i	0.613973	+	0.00452282i
$131$			5.28372i			0.461641i	0.972996	+	0.230821i	$0.0741410\pi$
$131$			5.28372i			0.461641i	−0.972996	+	0.230821i	$0.925859\pi$
$132$		−	10.2773i		−	0.894520i
$133$	−9.50529	+	6.27427i	−0.824213	+	0.544048i
$134$		−	3.04370i		−	0.262936i
$135$	−0.275073	+	37.3411i	−0.0236745	+	3.21381i
$136$	−0.517611			−0.0443848
$137$	−18.5186			−1.58215			−0.791076	−	0.611718i	$-0.790479\pi$
$137$	−18.5186			−1.58215			−0.791076	+	0.611718i	$0.790479\pi$
$138$	−12.2826	+	10.1389i	−1.04556	+	0.863084i
$139$			8.94753i			0.758920i	0.925208	+	0.379460i	$0.123890\pi$
$139$			8.94753i			0.758920i	−0.925208	+	0.379460i	$0.876110\pi$
$140$	−3.22265	−	4.96130i	−0.272364	−	0.419307i
$141$	−6.73818			−0.567457
$142$			3.83097i			0.321488i
$143$			9.68865i			0.810205i
$144$	8.02867			0.669055
$145$	0.119799	−	16.2627i	0.00994876	−	1.35054i
$146$		−	4.21001i		−	0.348423i
$147$	9.13686	−	21.3757i	0.753596	−	1.76304i
$148$	−6.17419			−0.507515
$149$		−	4.04895i		−	0.331703i	−0.986151	−	0.165851i	$-0.946963\pi$
$149$		−	4.04895i		−	0.331703i	0.986151	−	0.165851i	$-0.0530372\pi$
$150$	−0.244624	+	16.6029i	−0.0199734	+	1.35562i
$151$	13.7786			1.12129			0.560643	−	0.828058i	$-0.310554\pi$
$151$	13.7786			1.12129			0.560643	+	0.828058i	$0.310554\pi$
$152$		−	4.30476i		−	0.349162i
$153$			4.15573i			0.335971i
$154$	6.83332	−	4.51055i	0.550644	−	0.363470i
$155$	−7.40414	−	0.0545425i	−0.594714	−	0.00438096i
$156$	−10.3970			−0.832428
$157$		−	14.6304i		−	1.16763i	−0.811887	−	0.583815i	$-0.801559\pi$
$157$		−	14.6304i		−	1.16763i	0.811887	−	0.583815i	$-0.198441\pi$
$158$	−1.67775			−0.133475
$159$	−37.9712			−3.01132
$160$	2.23601	+	0.0164715i	0.176772	+	0.00130219i
$161$	−12.1320	−	3.71679i	−0.956136	−	0.292924i
$162$		−	31.3735i		−	2.46493i
$163$			17.1512i			1.34338i	0.740830	+	0.671692i	$0.234432\pi$
$163$			17.1512i			1.34338i	−0.740830	+	0.671692i	$0.765568\pi$
$164$		−	5.26619i		−	0.411221i
$165$	−22.9800	−	0.169282i	−1.78899	−	0.0131786i
$166$	−11.1018			−0.861667
$167$	−1.47756			−0.114337			−0.0571685	−	0.998365i	$-0.518207\pi$
$167$	−1.47756			−0.114337			−0.0571685	+	0.998365i	$0.518207\pi$
$168$	4.84033	+	7.33293i	0.373440	+	0.565748i
$169$	−3.19844			−0.246034
$170$	−0.00852584	+	1.15738i	−0.000653902	+	0.0887671i
$171$	−34.5615			−2.64298
$172$	1.14534			0.0873317
$173$	9.67659			0.735698			0.367849	−	0.929886i	$-0.380094\pi$
$173$	9.67659			0.735698			0.367849	+	0.929886i	$0.380094\pi$
$174$			24.1535i			1.83108i
$175$	−11.1466	+	7.12415i	−0.842603	+	0.538535i
$176$			3.09468i			0.233270i
$177$		−	47.6965i		−	3.58509i
$178$		−	2.13097i		−	0.159723i
$179$	−10.8576			−0.811531			−0.405766	−	0.913977i	$-0.632995\pi$
$179$	−10.8576			−0.811531			−0.405766	+	0.913977i	$0.632995\pi$
$180$	0.132244	−	17.9522i	0.00985691	−	1.33807i
$181$	−10.1939			−0.757709			−0.378855	−	0.925456i	$-0.623682\pi$
$181$	−10.1939			−0.757709			−0.378855	+	0.925456i	$0.623682\pi$
$182$	−4.56311	−	6.91295i	−0.338241	−	0.512422i
$183$	38.6866			2.85980
$184$	3.69851	−	3.05303i	0.272658	−	0.225072i
$185$	−0.101698	+	13.8055i	−0.00747701	+	1.01500i
$186$	10.9967			0.806318
$187$	−1.60184			−0.117138
$188$	2.02900			0.147980
$189$	36.8748	−	24.3404i	2.68225	−	1.77051i
$190$	−9.62548	−	0.0709060i	−0.698306	−	0.00514406i
$191$		−	13.1282i		−	0.949921i	−0.880007	−	0.474961i	$-0.842462\pi$
$191$		−	13.1282i		−	0.949921i	0.880007	−	0.474961i	$-0.157538\pi$
$192$	−3.32094			−0.239668
$193$			12.7361i			0.916763i	0.888755	+	0.458382i	$0.151571\pi$
$193$			12.7361i			0.916763i	−0.888755	+	0.458382i	$0.848429\pi$
$194$	6.62988			0.475998
$195$	−0.171255	+	23.2478i	−0.0122638	+	1.66481i
$196$	−2.75128	+	6.43665i	−0.196520	+	0.459761i
$197$			18.5019i			1.31821i	0.752052	+	0.659104i	$0.229064\pi$
$197$			18.5019i			1.31821i	−0.752052	+	0.659104i	$0.770936\pi$
$198$	24.8461			1.76574
$199$	−6.70733			−0.475470			−0.237735	−	0.971330i	$-0.576405\pi$
$199$	−6.70733			−0.475470			−0.237735	+	0.971330i	$0.576405\pi$
$200$	0.0736609	−	4.99946i	0.00520861	−	0.353515i
$201$	10.1080			0.712961
$202$	−12.5472			−0.882815
$203$	−16.0596	+	10.6007i	−1.12716	+	0.744021i
$204$		−	1.71896i		−	0.120351i
$205$	−11.7752	−	0.0867422i	−0.822419	−	0.00605834i
$206$	−5.84073			−0.406943
$207$	−24.5118	−	29.6941i	−1.70369	−	2.06388i
$208$	3.13074			0.217078
$209$		−	13.3219i		−	0.921492i
$210$	16.4762	−	10.7022i	1.13697	−	0.738525i
$211$	−13.1972			−0.908535			−0.454267	−	0.890865i	$-0.650099\pi$
$211$	−13.1972			−0.908535			−0.454267	+	0.890865i	$0.650099\pi$
$212$	11.4339			0.785281
$213$	−12.7224			−0.871726
$214$			11.1101i			0.759473i
$215$	0.0188656	−	2.56100i	0.00128662	−	0.174659i
$216$			16.6999i			1.13629i
$217$	4.82631	+	7.31168i	0.327631	+	0.496349i
$218$	−19.0683			−1.29147
$219$	13.9812			0.944763
$220$	6.91972	+	0.0509741i	0.466528	+	0.00343667i
$221$			1.62051i			0.109007i
$222$		−	20.5041i		−	1.37615i
$223$	−24.3443			−1.63022			−0.815108	−	0.579310i	$-0.803322\pi$
$223$	−24.3443			−1.63022			−0.815108	+	0.579310i	$0.803322\pi$
$224$	−1.45752	−	2.20809i	−0.0973845	−	0.147534i
$225$	−40.1390	−	0.591399i	−2.67593	−	0.0394266i
$226$		−	4.69728i		−	0.312458i
$227$			8.50897i			0.564760i	0.959303	+	0.282380i	$0.0911239\pi$
$227$			8.50897i			0.564760i	−0.959303	+	0.282380i	$0.908876\pi$
$228$	14.2959			0.946768
$229$	12.0653			0.797297			0.398649	−	0.917104i	$-0.369479\pi$
$229$	12.0653			0.797297			0.398649	+	0.917104i	$0.369479\pi$
$230$	−6.76568	−	8.32019i	−0.446116	−	0.548617i
$231$	14.9793	+	22.6931i	0.985564	+	1.49309i
$232$		−	7.27310i		−	0.477502i
$233$			14.0824i			0.922568i	0.887252	+	0.461284i	$0.152611\pi$
$233$			14.0824i			0.922568i	−0.887252	+	0.461284i	$0.847389\pi$
$234$		−	25.1357i		−	1.64317i
$235$	0.0334206	−	4.53685i	0.00218012	−	0.295951i
$236$			14.3623i			0.934908i
$237$		−	5.57173i		−	0.361923i
$238$	1.14293	−	0.754427i	0.0740851	−	0.0489023i
$239$	−13.9174			−0.900243			−0.450121	−	0.892967i	$-0.648619\pi$
$239$	−13.9174			−0.900243			−0.450121	+	0.892967i	$0.648619\pi$
$240$	−0.0547010	+	7.42565i	−0.00353093	+	0.479324i
$241$	25.3696			1.63420			0.817100	−	0.576496i	$-0.195581\pi$
$241$	25.3696			1.63420			0.817100	+	0.576496i	$0.195581\pi$
$242$		−	1.42296i		−	0.0914714i
$243$	54.0898			3.46986
$244$	−11.6493			−0.745769
$245$	14.3471	+	6.25791i	0.916601	+	0.399803i
$246$	17.4887			1.11504
$247$	−13.4771			−0.857528
$248$	−3.31132			−0.210269
$249$		−	36.8685i		−	2.33644i
$250$	−11.1776	−	0.247055i	−0.706934	−	0.0156251i
$251$	20.9389			1.32165			0.660826	−	0.750539i	$-0.270206\pi$
$251$	20.9389			1.32165			0.660826	+	0.750539i	$0.270206\pi$
$252$	−17.7280	+	11.7019i	−1.11676	+	0.737152i
$253$	11.4457	−	9.44815i	0.719586	−	0.594000i
$254$	15.3439			0.962761
$255$	−3.84360	−	0.0283138i	−0.240696	−	0.00177308i
$256$	1.00000			0.0625000
$257$	14.0452			0.876116			0.438058	−	0.898947i	$-0.355666\pi$
$257$	14.0452			0.876116			0.438058	+	0.898947i	$0.355666\pi$
$258$			3.80362i			0.236803i
$259$	13.6331	−	8.99899i	0.847122	−	0.559170i
$260$	0.0515681	−	7.00037i	0.00319812	−	0.434144i
$261$	−58.3933			−3.61445
$262$	5.28372			0.326430
$263$	−3.32466			−0.205007			−0.102504	−	0.994733i	$-0.532685\pi$
$263$	−3.32466			−0.205007			−0.102504	+	0.994733i	$0.532685\pi$
$264$	−10.2773			−0.632521
$265$	0.188333	−	25.5662i	0.0115692	−	1.57052i
$266$	6.27427	+	9.50529i	0.384700	+	0.582807i
$267$	7.07682			0.433094
$268$	−3.04370			−0.185924
$269$			4.04093i			0.246380i	0.992383	+	0.123190i	$0.0393125\pi$
$269$			4.04093i			0.246380i	−0.992383	+	0.123190i	$0.960688\pi$
$270$	37.3411	+	0.275073i	2.27251	+	0.0167404i
$271$		−	21.1070i		−	1.28216i	−0.767474	−	0.641080i	$-0.778487\pi$
$271$		−	21.1070i		−	1.28216i	0.767474	−	0.641080i	$-0.221513\pi$
$272$			0.517611i			0.0313848i
$273$	22.9575	−	15.1538i	1.38945	−	0.917152i
$274$			18.5186i			1.11875i
$275$	0.227957	−	15.4717i	0.0137463	−	0.932980i
$276$	10.1389	+	12.2826i	0.610293	+	0.739323i
$277$		−	22.0132i		−	1.32264i	−0.750102	−	0.661322i	$-0.769996\pi$
$277$		−	22.0132i		−	1.32264i	0.750102	−	0.661322i	$-0.230004\pi$
$278$	8.94753			0.536637
$279$			26.5855i			1.59163i
$280$	−4.96130	+	3.22265i	−0.296495	+	0.192590i
$281$			12.5632i			0.749457i	0.927135	+	0.374728i	$0.122264\pi$
$281$			12.5632i			0.749457i	−0.927135	+	0.374728i	$0.877736\pi$
$282$			6.73818i			0.401253i
$283$			29.6641i			1.76335i	0.471858	+	0.881674i	$0.343583\pi$
$283$			29.6641i			1.76335i	−0.471858	+	0.881674i	$0.656417\pi$
$284$	3.83097			0.227326
$285$	0.235475	−	31.9657i	0.0139483	−	1.89348i
$286$	9.68865			0.572902
$287$	7.67557	+	11.6282i	0.453074	+	0.686391i
$288$		−	8.02867i		−	0.473094i
$289$	16.7321			0.984240
$290$	−16.2627	−	0.119799i	−0.954979	−	0.00703484i
$291$			22.0175i			1.29069i
$292$	−4.21001			−0.246372
$293$			7.65719i			0.447338i	0.974665	+	0.223669i	$0.0718034\pi$
$293$			7.65719i			0.447338i	−0.974665	+	0.223669i	$0.928197\pi$
$294$	−21.3757	−	9.13686i	−1.24666	−	0.532873i
$295$	32.1143	+	0.236569i	1.86977	+	0.0137736i
$296$			6.17419i			0.358867i
$297$			51.6809i			2.99883i
$298$	−4.04895			−0.234549
$299$	−9.55826	−	11.5791i	−0.552768	−	0.669637i
$300$	16.6029	+	0.244624i	0.958570	+	0.0141234i
$301$	−2.52902	+	1.66936i	−0.145770	+	0.0962203i
$302$		−	13.7786i		−	0.792869i
$303$		−	41.6684i		−	2.39379i
$304$	−4.30476			−0.246895
$305$	−0.191882	+	26.0479i	−0.0109871	+	1.49150i
$306$	4.15573			0.237567
$307$	−0.0711576			−0.00406118			−0.00203059	−	0.999998i	$-0.500646\pi$
$307$	−0.0711576			−0.00406118			−0.00203059	+	0.999998i	$0.500646\pi$
$308$	−4.51055	−	6.83332i	−0.257012	−	0.389364i
$309$		−	19.3967i		−	1.10344i
$310$	−0.0545425	+	7.40414i	−0.00309780	+	0.420527i
$311$			7.95267i			0.450954i	0.974248	+	0.225477i	$0.0723941\pi$
$311$			7.95267i			0.450954i	−0.974248	+	0.225477i	$0.927606\pi$
$312$			10.3970i			0.588615i
$313$		−	32.4502i		−	1.83419i	−0.398668	−	0.917095i	$-0.630527\pi$
$313$		−	32.4502i		−	1.83419i	0.398668	−	0.917095i	$-0.369473\pi$
$314$	−14.6304			−0.825639
$315$	25.8736	+	39.8326i	1.45781	+	2.24432i
$316$			1.67775i			0.0943811i
$317$		−	13.4918i		−	0.757773i	−0.925443	−	0.378886i	$-0.876307\pi$
$317$		−	13.4918i		−	0.757773i	0.925443	−	0.378886i	$-0.123693\pi$
$318$			37.9712i			2.12932i
$319$		−	22.5079i		−	1.26020i
$320$	0.0164715	−	2.23601i	0.000920786	−	0.124997i
$321$	−36.8961			−2.05934
$322$	−3.71679	+	12.1320i	−0.207129	+	0.676090i
$323$		−	2.22819i		−	0.123980i
$324$	−31.3735			−1.74297
$325$	−15.6520	−	0.230613i	−0.868218	−	0.0127921i
$326$	17.1512			0.949916
$327$		−	63.3248i		−	3.50187i
$328$	−5.26619			−0.290777
$329$	−4.48019	+	2.95730i	−0.247001	+	0.163041i
$330$	−0.169282	+	22.9800i	−0.00931867	+	1.26501i
$331$	−32.4703			−1.78473			−0.892364	−	0.451317i	$-0.850954\pi$
$331$	−32.4703			−1.78473			−0.892364	+	0.451317i	$0.850954\pi$
$332$			11.1018i			0.609291i
$333$	49.5705			2.71645
$334$			1.47756i			0.0808485i
$335$	−0.0501344	+	6.80574i	−0.00273914	+	0.371838i
$336$	7.33293	−	4.84033i	0.400044	−	0.264062i
$337$	−19.4710			−1.06066			−0.530328	−	0.847793i	$-0.677931\pi$
$337$	−19.4710			−1.06066			−0.530328	+	0.847793i	$0.677931\pi$
$338$			3.19844i			0.173972i
$339$	15.5994			0.847243
$340$	1.15738	+	0.00852584i	0.0627679	+	0.000462379i
$341$	−10.2475			−0.554932
$342$			34.5615i			1.86887i
$343$	−3.30646	−	18.2227i	−0.178532	−	0.983934i
$344$		−	1.14534i		−	0.0617528i
$345$	27.6309	−	22.4684i	1.48760	−	1.20966i
$346$		−	9.67659i		−	0.520217i
$347$			36.4201i			1.95514i	0.210621	+	0.977568i	$0.432452\pi$
$347$			36.4201i			1.95514i	−0.210621	+	0.977568i	$0.567548\pi$
$348$	24.1535			1.29477
$349$		−	1.75147i		−	0.0937540i	−0.998901	−	0.0468770i	$-0.985073\pi$
$349$		−	1.75147i		−	0.0937540i	0.998901	−	0.0468770i	$-0.0149269\pi$
$350$	7.12415	+	11.1466i	0.380802	+	0.595810i
$351$	52.2832			2.79067
$352$	3.09468			0.164947
$353$	17.2579			0.918544			0.459272	−	0.888296i	$-0.348110\pi$
$353$	17.2579			0.918544			0.459272	+	0.888296i	$0.348110\pi$
$354$	−47.6965			−2.53504
$355$	0.0631019	−	8.56607i	0.00334910	−	0.454640i
$356$	−2.13097			−0.112941
$357$	2.50541	+	3.79560i	0.132600	+	0.200885i
$358$			10.8576i			0.573839i
$359$			8.09263i			0.427113i	0.976931	+	0.213556i	$0.0685047\pi$
$359$			8.09263i			0.427113i	−0.976931	+	0.213556i	$0.931495\pi$
$360$	−17.9522	−	0.132244i	−0.946162	−	0.00696989i
$361$	−0.469012			−0.0246848
$362$			10.1939i			0.535781i
$363$	4.72558			0.248028
$364$	−6.91295	+	4.56311i	−0.362337	+	0.239172i
$365$	−0.0693453	+	9.41362i	−0.00362970	+	0.492731i
$366$		−	38.6866i		−	2.02218i
$367$		−	24.8578i		−	1.29757i	−0.760973	−	0.648783i	$-0.775278\pi$
$367$		−	24.8578i		−	1.29757i	0.760973	−	0.648783i	$-0.224722\pi$
$368$	−3.05303	−	3.69851i	−0.159150	−	0.192798i
$369$			42.2805i			2.20103i
$370$	13.8055	+	0.101698i	0.717715	+	0.00528704i
$371$	−25.2470	+	16.6651i	−1.31076	+	0.865207i
$372$		−	10.9967i		−	0.570153i
$373$	−23.8842			−1.23668			−0.618338	−	0.785912i	$-0.712194\pi$
$373$	−23.8842			−1.23668			−0.618338	+	0.785912i	$0.712194\pi$
$374$			1.60184i			0.0828292i
$375$	0.820455	−	37.1202i	0.0423681	−	1.91688i
$376$		−	2.02900i		−	0.104637i
$377$	−22.7702			−1.17273
$378$	−24.3404	−	36.8748i	−1.25194	−	1.89664i
$379$			25.4442i			1.30698i	0.756935	+	0.653490i	$0.226696\pi$
$379$			25.4442i			1.30698i	−0.756935	+	0.653490i	$0.773304\pi$
$380$	−0.0709060	+	9.62548i	−0.00363740	+	0.493777i
$381$			50.9562i			2.61056i
$382$	−13.1282			−0.671696
$383$			19.5218i			0.997520i	0.866740	+	0.498760i	$0.166211\pi$
$383$			19.5218i			0.997520i	−0.866740	+	0.498760i	$0.833789\pi$
$384$			3.32094i			0.169471i
$385$	−15.3536	+	9.97307i	−0.782494	+	0.508275i
$386$	12.7361			0.648250
$387$	−9.19559			−0.467438
$388$		−	6.62988i		−	0.336581i
$389$			11.5292i			0.584554i	0.956334	+	0.292277i	$0.0944130\pi$
$389$			11.5292i			0.584554i	−0.956334	+	0.292277i	$0.905587\pi$
$390$	23.2478	+	0.171255i	1.17720	+	0.00867182i
$391$	1.91439	−	1.58028i	0.0968149	−	0.0799183i
$392$	6.43665	+	2.75128i	0.325100	+	0.138961i
$393$			17.5470i			0.885127i
$394$	18.5019			0.932114
$395$	3.75147	+	0.0276352i	0.188757	+	0.00139048i
$396$		−	24.8461i		−	1.24857i
$397$	−29.9005			−1.50066			−0.750332	−	0.661061i	$-0.770106\pi$
$397$	−29.9005			−1.50066			−0.750332	+	0.661061i	$0.770106\pi$
$398$			6.70733i			0.336208i
$399$	−31.5665	+	20.8365i	−1.58030	+	1.04313i
$400$	−4.99946	−	0.0736609i	−0.249973	−	0.00368304i
$401$		−	25.9660i		−	1.29668i	−0.761350	−	0.648341i	$-0.775463\pi$
$401$		−	25.9660i		−	1.29668i	0.761350	−	0.648341i	$-0.224537\pi$
$402$		−	10.1080i		−	0.504140i
$403$			10.3669i			0.516412i
$404$			12.5472i			0.624244i
$405$	−0.516769	+	70.1513i	−0.0256785	+	3.48585i
$406$	10.6007	+	16.0596i	0.526102	+	0.797026i
$407$			19.1071i			0.947105i
$408$	−1.71896			−0.0851010
$409$			9.95124i			0.492057i	0.969263	+	0.246029i	$0.0791257\pi$
$409$			9.95124i			0.492057i	−0.969263	+	0.246029i	$0.920874\pi$
$410$	−0.0867422	+	11.7752i	−0.00428389	+	0.581538i
$411$	−61.4992			−3.03353
$412$			5.84073i			0.287752i
$413$	−20.9334	−	31.7133i	−1.03006	−	1.56051i
$414$	−29.6941	+	24.5118i	−1.45939	+	1.20469i
$415$	24.8237	+	0.182864i	1.21855	+	0.00897642i
$416$		−	3.13074i		−	0.153497i
$417$			29.7142i			1.45511i
$418$	−13.3219			−0.651594
$419$	−16.1025			−0.786659			−0.393329	−	0.919398i	$-0.628677\pi$
$419$	−16.1025			−0.786659			−0.393329	+	0.919398i	$0.628677\pi$
$420$	−10.7022	−	16.4762i	−0.522216	−	0.803957i
$421$			32.1276i			1.56580i	0.622145	+	0.782902i	$0.286262\pi$
$421$			32.1276i			1.56580i	−0.622145	+	0.782902i	$0.713738\pi$
$422$			13.1972i			0.642431i
$423$	−16.2901			−0.792053
$424$		−	11.4339i		−	0.555278i
$425$	0.0381277	−	2.58777i	0.00184946	−	0.125525i
$426$			12.7224i			0.616404i
$427$	25.7226	−	16.9790i	1.24481	−	0.821674i
$428$	11.1101			0.537028
$429$			32.1754i			1.55345i
$430$	−2.56100	−	0.0188656i	−0.123502	−	0.000909778i
$431$			4.67344i			0.225112i	0.993645	+	0.112556i	$0.0359037\pi$
$431$			4.67344i			0.225112i	−0.993645	+	0.112556i	$0.964096\pi$
$432$	16.6999			0.803475
$433$			15.6372i			0.751477i	0.926726	+	0.375739i	$0.122611\pi$
$433$			15.6372i			0.751477i	−0.926726	+	0.375739i	$0.877389\pi$
$434$	7.31168	−	4.82631i	0.350972	−	0.231670i
$435$	0.397846	−	54.0075i	0.0190752	−	2.58946i
$436$			19.0683i			0.913206i
$437$	13.1426	+	15.9212i	0.628695	+	0.761616i
$438$		−	13.9812i		−	0.668048i
$439$		−	24.8191i		−	1.18455i	−0.805736	−	0.592274i	$-0.798230\pi$
$439$		−	24.8191i		−	1.18455i	0.805736	−	0.592274i	$-0.201770\pi$
$440$	0.0509741	−	6.91972i	0.00243009	−	0.329885i
$441$	22.0891	−	51.6777i	1.05186	−	2.46084i
$442$	1.62051			0.0770797
$443$		−	5.98523i		−	0.284367i	−0.989840	−	0.142183i	$-0.954588\pi$
$443$		−	5.98523i		−	0.284367i	0.989840	−	0.142183i	$-0.0454123\pi$
$444$	−20.5041			−0.973083
$445$	−0.0351002	+	4.76485i	−0.00166391	+	0.225876i
$446$			24.3443i			1.15274i
$447$		−	13.4463i		−	0.635990i
$448$	−2.20809	+	1.45752i	−0.104322	+	0.0688612i
$449$	28.0576			1.32412			0.662060	−	0.749451i	$-0.269682\pi$
$449$	28.0576			1.32412			0.662060	+	0.749451i	$0.269682\pi$
$450$	−0.591399	+	40.1390i	−0.0278788	+	1.89217i
$451$	−16.2972			−0.767404
$452$	−4.69728			−0.220941
$453$	45.7579			2.14989
$454$	8.50897			0.399346
$455$	10.0893	+	15.5326i	0.472993	+	0.728178i
$456$		−	14.2959i		−	0.669466i
$457$	−17.5972			−0.823160			−0.411580	−	0.911374i	$-0.635023\pi$
$457$	−17.5972			−0.823160			−0.411580	+	0.911374i	$0.635023\pi$
$458$		−	12.0653i		−	0.563774i
$459$			8.64406i			0.403470i
$460$	−8.32019	+	6.76568i	−0.387931	+	0.315451i
$461$			11.7836i			0.548819i	0.961613	+	0.274409i	$0.0884823\pi$
$461$			11.7836i			0.548819i	−0.961613	+	0.274409i	$0.911518\pi$
$462$	22.6931	−	14.9793i	1.05578	−	0.696899i
$463$		−	12.0687i		−	0.560880i	−0.959872	−	0.280440i	$-0.909520\pi$
$463$		−	12.0687i		−	0.560880i	0.959872	−	0.280440i	$-0.0904803\pi$
$464$	−7.27310			−0.337645
$465$	−24.5887	−	0.181132i	−1.14027	−	0.00839982i
$466$	14.0824			0.652354
$467$			7.58594i			0.351035i	0.984476	+	0.175518i	$0.0561599\pi$
$467$			7.58594i			0.351035i	−0.984476	+	0.175518i	$0.943840\pi$
$468$	−25.1357			−1.16190
$469$	6.72076	−	4.43625i	0.310336	−	0.204847i
$470$	−4.53685	−	0.0334206i	−0.209269	−	0.00154158i
$471$		−	48.5866i		−	2.23875i
$472$	14.3623			0.661080
$473$		−	3.54447i		−	0.162975i
$474$	−5.57173			−0.255918
$475$	21.5215	+	0.317093i	0.987473	+	0.0145492i
$476$	−0.754427	−	1.14293i	−0.0345791	−	0.0523861i
$477$	−91.7987			−4.20318
$478$			13.9174i			0.636568i
$479$	33.8513			1.54671			0.773353	−	0.633976i	$-0.218578\pi$
$479$	33.8513			1.54671			0.773353	+	0.633976i	$0.218578\pi$
$480$	7.42565	+	0.0547010i	0.338933	+	0.00249675i
$481$	19.3298			0.881363
$482$		−	25.3696i		−	1.15555i
$483$	−40.2897	−	12.3432i	−1.83324	−	0.561637i
$484$	−1.42296			−0.0646801
$485$	−14.8245	−	0.109204i	−0.673144	−	0.00495871i
$486$		−	54.0898i		−	2.45356i
$487$		−	24.2442i		−	1.09861i	−0.835622	−	0.549305i	$-0.814892\pi$
$487$		−	24.2442i		−	1.09861i	0.835622	−	0.549305i	$-0.185108\pi$
$488$			11.6493i			0.527339i
$489$			56.9581i			2.57573i
$490$	6.25791	−	14.3471i	0.282704	−	0.648135i
$491$	−25.0091			−1.12865			−0.564323	−	0.825554i	$-0.690863\pi$
$491$	−25.0091			−1.12865			−0.564323	+	0.825554i	$0.690863\pi$
$492$		−	17.4887i		−	0.788453i
$493$		−	3.76464i		−	0.169551i
$494$			13.4771i			0.606364i
$495$	−55.5562	−	0.409254i	−2.49706	−	0.0183946i
$496$			3.31132i			0.148683i
$497$	−8.45910	+	5.58370i	−0.379443	+	0.250463i
$498$	−36.8685			−1.65212
$499$	9.92230			0.444183			0.222092	−	0.975026i	$-0.428712\pi$
$499$	9.92230			0.444183			0.222092	+	0.975026i	$0.428712\pi$
$500$	−0.247055	+	11.1776i	−0.0110486	+	0.499878i
$501$	−4.90690			−0.219224
$502$		−	20.9389i		−	0.934549i
$503$		−	23.2308i		−	1.03581i	−0.855438	−	0.517906i	$-0.826712\pi$
$503$		−	23.2308i		−	1.03581i	0.855438	−	0.517906i	$-0.173288\pi$
$504$	11.7019	+	17.7280i	0.521245	+	0.789667i
$505$	28.0555	+	0.206671i	1.24845	+	0.00919673i
$506$	−9.44815	−	11.4457i	−0.420022	−	0.508824i
$507$	−10.6219			−0.471733
$508$		−	15.3439i		−	0.680775i
$509$			11.1380i			0.493685i	0.969056	+	0.246843i	$0.0793931\pi$
$509$			11.1380i			0.493685i	−0.969056	+	0.246843i	$0.920607\pi$
$510$	−0.0283138	+	3.84360i	−0.00125376	+	0.170197i
$511$	9.29607	−	6.13617i	0.411234	−	0.271448i
$512$		−	1.00000i		−	0.0441942i
$513$	−71.8892			−3.17398
$514$		−	14.0452i		−	0.619507i
$515$	13.0599	+	0.0962057i	0.575489	+	0.00423933i
$516$	3.80362			0.167445
$517$		−	6.27909i		−	0.276154i
$518$	−8.99899	−	13.6331i	−0.395393	−	0.599006i
$519$	32.1354			1.41059
$520$	−7.00037	−	0.0515681i	−0.306986	−	0.00226141i
$521$	−37.9677			−1.66340			−0.831698	−	0.555228i	$-0.812631\pi$
$521$	−37.9677			−1.66340			−0.831698	+	0.555228i	$0.812631\pi$
$522$			58.3933i			2.55580i
$523$			32.2583i			1.41056i	0.708931	+	0.705278i	$0.249178\pi$
$523$			32.2583i			1.41056i	−0.708931	+	0.705278i	$0.750822\pi$
$524$		−	5.28372i		−	0.230821i
$525$	−37.0172	+	23.6589i	−1.61556	+	1.03256i
$526$			3.32466i			0.144962i
$527$	−1.71398			−0.0746620
$528$			10.2773i			0.447260i
$529$	−4.35801	+	22.5834i	−0.189479	+	0.981885i
$530$	−25.5662	−	0.188333i	−1.11053	−	0.00818067i
$531$		−	115.310i		−	5.00404i
$532$	9.50529	−	6.27427i	0.412106	−	0.272024i
$533$			16.4871i			0.714135i
$534$		−	7.07682i		−	0.306244i
$535$	0.183001	−	24.8423i	0.00791181	−	1.07403i
$536$			3.04370i			0.131468i
$537$	−36.0573			−1.55599
$538$	4.04093			0.174217
$539$	19.9194	+	8.51434i	0.857988	+	0.366739i
$540$	0.275073	−	37.3411i	0.0118373	−	1.60691i
$541$	31.7608			1.36550			0.682752	−	0.730650i	$-0.260783\pi$
$541$	31.7608			1.36550			0.682752	+	0.730650i	$0.260783\pi$
$542$	−21.1070			−0.906624
$543$	−33.8535			−1.45279
$544$	0.517611			0.0221924
$545$	42.6369	+	0.314084i	1.82636	+	0.0134539i
$546$	−15.1538	−	22.9575i	−0.648525	−	0.982491i
$547$		−	4.27396i		−	0.182741i	−0.995817	−	0.0913707i	$-0.970875\pi$
$547$		−	4.27396i		−	0.182741i	0.995817	−	0.0913707i	$-0.0291248\pi$
$548$	18.5186			0.791076
$549$	93.5283			3.99169
$550$	−15.4717	−	0.227957i	−0.659716	−	0.00972011i
$551$	31.3090			1.33381
$552$	12.2826	−	10.1389i	0.522780	−	0.431542i
$553$	−2.44536	−	3.70463i	−0.103987	−	0.157537i
$554$	−22.0132			−0.935250
$555$	−0.337734	+	45.8474i	−0.0143360	+	1.94611i
$556$		−	8.94753i		−	0.379460i
$557$	35.1137			1.48782			0.743908	−	0.668282i	$-0.232970\pi$
$557$	35.1137			1.48782			0.743908	+	0.668282i	$0.232970\pi$
$558$	26.5855			1.12545
$559$	−3.58578			−0.151662
$560$	3.22265	+	4.96130i	0.136182	+	0.209653i
$561$	−5.31962			−0.224595
$562$	12.5632			0.529946
$563$			5.38700i			0.227035i	0.993536	+	0.113518i	$0.0362118\pi$
$563$			5.38700i			0.227035i	−0.993536	+	0.113518i	$0.963788\pi$
$564$	6.73818			0.283728
$565$	−0.0773713	+	10.5031i	−0.00325504	+	0.441871i
$566$	29.6641			1.24688
$567$	69.2753	−	45.7274i	2.90929	−	1.92037i
$568$		−	3.83097i		−	0.160744i
$569$		−	41.3898i		−	1.73515i	−0.497308	−	0.867574i	$-0.665678\pi$
$569$		−	41.3898i		−	1.73515i	0.497308	−	0.867574i	$-0.334322\pi$
$570$	−31.9657	−	0.235475i	−1.33890	−	0.00986295i
$571$			42.7364i			1.78846i	0.447604	+	0.894232i	$0.352278\pi$
$571$			42.7364i			1.78846i	−0.447604	+	0.894232i	$0.647722\pi$
$572$		−	9.68865i		−	0.405103i
$573$		−	43.5979i		−	1.82133i
$574$	11.6282	−	7.67557i	0.485352	−	0.320372i
$575$	14.9911	+	18.7155i	0.625170	+	0.780488i
$576$	−8.02867			−0.334528
$577$	−3.49306			−0.145418			−0.0727089	−	0.997353i	$-0.523164\pi$
$577$	−3.49306			−0.145418			−0.0727089	+	0.997353i	$0.523164\pi$
$578$		−	16.7321i		−	0.695963i
$579$			42.2958i			1.75775i
$580$	−0.119799	+	16.2627i	−0.00497438	+	0.675272i
$581$	−16.1811	−	24.5137i	−0.671304	−	1.01700i
$582$	22.0175			0.912653
$583$		−	35.3842i		−	1.46546i
$584$			4.21001i			0.174212i
$585$	−0.414023	+	56.2036i	−0.0171177	+	2.32373i
$586$	7.65719			0.316315
$587$	−29.6226			−1.22265			−0.611327	−	0.791378i	$-0.709364\pi$
$587$	−29.6226			−1.22265			−0.611327	+	0.791378i	$0.709364\pi$
$588$	−9.13686	+	21.3757i	−0.376798	+	0.881521i
$589$		−	14.2544i		−	0.587344i
$590$	0.236569	−	32.1143i	0.00973941	−	1.32212i
$591$			61.4439i			2.52746i
$592$	6.17419			0.253758
$593$	13.2029			0.542179			0.271089	−	0.962554i	$-0.412616\pi$
$593$	13.2029			0.542179			0.271089	+	0.962554i	$0.412616\pi$
$594$	51.6809			2.12049
$595$	−2.56803	+	1.66808i	−0.105279	+	0.0683846i
$596$			4.04895i			0.165851i
$597$	−22.2747			−0.911642
$598$	−11.5791	+	9.55826i	−0.473505	+	0.390866i
$599$	−23.9452			−0.978373			−0.489186	−	0.872179i	$-0.662706\pi$
$599$	−23.9452			−0.978373			−0.489186	+	0.872179i	$0.662706\pi$
$600$	0.244624	−	16.6029i	0.00998672	−	0.677811i
$601$			32.0581i			1.30768i	0.756634	+	0.653838i	$0.226842\pi$
$601$			32.0581i			1.30768i	−0.756634	+	0.653838i	$0.773158\pi$
$602$	1.66936	+	2.52902i	0.0680380	+	0.103075i
$603$	24.4369			0.995147
$604$	−13.7786			−0.560643
$605$	−0.0234383	+	3.18175i	−0.000952904	+	0.129357i
$606$	−41.6684			−1.69266
$607$	10.5000			0.426182			0.213091	−	0.977032i	$-0.431647\pi$
$607$	10.5000			0.426182			0.213091	+	0.977032i	$0.431647\pi$
$608$			4.30476i			0.174581i
$609$	−53.3331	+	35.2042i	−2.16117	+	1.42655i
$610$	26.0479	+	0.191882i	1.05465	+	0.00776906i
$611$	−6.35226			−0.256985
$612$		−	4.15573i		−	0.167985i
$613$	2.40931			0.0973112			0.0486556	−	0.998816i	$-0.484506\pi$
$613$	2.40931			0.0973112			0.0486556	+	0.998816i	$0.484506\pi$
$614$			0.0711576i			0.00287169i
$615$	−39.1049	−	0.288066i	−1.57686	−	0.0116159i
$616$	−6.83332	+	4.51055i	−0.275322	+	0.181735i
$617$	33.5571			1.35096			0.675480	−	0.737379i	$-0.263937\pi$
$617$	33.5571			1.35096			0.675480	+	0.737379i	$0.263937\pi$
$618$	−19.3967			−0.780251
$619$	20.1887			0.811451			0.405725	−	0.913995i	$-0.367019\pi$
$619$	20.1887			0.811451			0.405725	+	0.913995i	$0.367019\pi$
$620$	7.40414	+	0.0545425i	0.297357	+	0.00219048i
$621$	−50.9854	−	61.7649i	−2.04597	−	2.47854i
$622$	7.95267			0.318873
$623$	4.70535	−	3.10592i	0.188516	−	0.124436i
$624$	10.3970			0.416214
$625$	24.9891	+	0.736529i	0.999566	+	0.0294612i
$626$	−32.4502			−1.29697
$627$		−	44.2411i		−	1.76682i
$628$			14.6304i			0.583815i
$629$			3.19583i			0.127426i
$630$	39.8326	−	25.8736i	1.58697	−	1.03083i
$631$		−	11.0872i		−	0.441375i	−0.975345	−	0.220688i	$-0.929170\pi$
$631$		−	11.0872i		−	0.441375i	0.975345	−	0.220688i	$-0.0708301\pi$
$632$	1.67775			0.0667375
$633$	−43.8273			−1.74198
$634$	−13.4918			−0.535826
$635$	−34.3090	−	0.252737i	−1.36151	−	0.0100296i
$636$	37.9712			1.50566
$637$	8.61357	−	20.1515i	0.341282	−	0.798431i
$638$	−22.5079			−0.891096
$639$	−30.7576			−1.21675
$640$	−2.23601	−	0.0164715i	−0.0883859	−	0.000651094i
$641$			29.4143i			1.16180i	0.813977	+	0.580898i	$0.197298\pi$
$641$			29.4143i			1.16180i	−0.813977	+	0.580898i	$0.802702\pi$
$642$			36.8961i			1.45617i
$643$		−	3.72737i		−	0.146993i	−0.997295	−	0.0734966i	$-0.976584\pi$
$643$		−	3.72737i		−	0.146993i	0.997295	−	0.0734966i	$-0.0234158\pi$
$644$	12.1320	+	3.71679i	0.478068	+	0.146462i
$645$	0.0626515	−	8.50493i	0.00246690	−	0.334881i
$646$	−2.22819			−0.0876671
$647$	20.4708			0.804791			0.402395	−	0.915466i	$-0.368178\pi$
$647$	20.4708			0.804791			0.402395	+	0.915466i	$0.368178\pi$
$648$			31.3735i			1.23247i
$649$	44.4468			1.74469
$650$	−0.230613	+	15.6520i	−0.00904540	+	0.613923i
$651$	16.0279	+	24.2817i	0.628183	+	0.951674i
$652$		−	17.1512i		−	0.671692i
$653$		−	7.86835i		−	0.307912i	−0.988078	−	0.153956i	$-0.950799\pi$
$653$		−	7.86835i		−	0.307912i	0.988078	−	0.153956i	$-0.0492015\pi$
$654$	−63.3248			−2.47619
$655$	−11.8144	−	0.0870310i	−0.461629	−	0.00340058i
$656$			5.26619i			0.205610i
$657$	33.8008			1.31869
$658$	2.95730	+	4.48019i	0.115287	+	0.174656i
$659$			8.39719i			0.327108i	0.986534	+	0.163554i	$0.0522958\pi$
$659$			8.39719i			0.327108i	−0.986534	+	0.163554i	$0.947704\pi$
$660$	22.9800	+	0.169282i	0.894496	+	0.00658929i
$661$	35.2423			1.37077			0.685384	−	0.728182i	$-0.259634\pi$
$661$	35.2423			1.37077			0.685384	+	0.728182i	$0.259634\pi$
$662$			32.4703i			1.26199i
$663$			5.38161i			0.209005i
$664$	11.1018			0.430834
$665$	−13.8727	−	21.3572i	−0.537962	−	0.828198i
$666$		−	49.5705i		−	1.92082i
$667$	22.2050	+	26.8996i	0.859781	+	1.04156i
$668$	1.47756			0.0571685
$669$	−80.8461			−3.12569
$670$	6.80574	+	0.0501344i	0.262929	+	0.00193686i
$671$			36.0508i			1.39173i
$672$	−4.84033	−	7.33293i	−0.186720	−	0.282874i
$673$			19.0093i			0.732753i	0.930467	+	0.366377i	$0.119402\pi$
$673$			19.0093i			0.732753i	−0.930467	+	0.366377i	$0.880598\pi$
$674$			19.4710i			0.749997i
$675$	−83.4905	−	1.23013i	−3.21355	−	0.0473477i
$676$	3.19844			0.123017
$677$			42.5059i			1.63364i	0.576896	+	0.816818i	$0.304264\pi$
$677$			42.5059i			1.63364i	−0.576896	+	0.816818i	$0.695736\pi$
$678$		−	15.5994i		−	0.599091i
$679$	9.66317	+	14.6394i	0.370839	+	0.561807i
$680$	0.00852584	−	1.15738i	0.000326951	−	0.0443836i
$681$			28.2578i			1.08284i
$682$			10.2475i			0.392396i
$683$		−	9.86013i		−	0.377288i	−0.982046	−	0.188644i	$-0.939591\pi$
$683$		−	9.86013i		−	0.377288i	0.982046	−	0.188644i	$-0.0604091\pi$
$684$	34.5615			1.32149
$685$	0.305030	−	41.4077i	0.0116546	−	1.58211i
$686$	−18.2227	+	3.30646i	−0.695747	+	0.126241i
$687$	40.0682			1.52870
$688$	−1.14534			−0.0436658
$689$	−35.7965			−1.36374
$690$	−22.4684	−	27.6309i	−0.855359	−	1.05189i
$691$		−	8.79865i		−	0.334716i	−0.985896	−	0.167358i	$-0.946476\pi$
$691$		−	8.79865i		−	0.334716i	0.985896	−	0.167358i	$-0.0535236\pi$
$692$	−9.67659			−0.367849
$693$	36.2137	+	54.8624i	1.37564	+	2.08405i
$694$	36.4201			1.38249
$695$	−20.0067	−	0.147379i	−0.758899	−	0.00559042i
$696$		−	24.1535i		−	0.915538i
$697$	−2.72584			−0.103249
$698$	−1.75147			−0.0662941
$699$			46.7668i			1.76888i
$700$	11.1466	−	7.12415i	0.421302	−	0.269267i
$701$		−	19.7489i		−	0.745906i	−0.927850	−	0.372953i	$-0.878345\pi$
$701$		−	19.7489i		−	0.745906i	0.927850	−	0.372953i	$-0.121655\pi$
$702$		−	52.2832i		−	1.97330i
$703$	−26.5784			−1.00242
$704$		−	3.09468i		−	0.116635i
$705$	0.110988	−	15.0666i	0.00418005	−	0.567442i
$706$		−	17.2579i		−	0.649509i
$707$	−18.2877	−	27.7052i	−0.687780	−	1.04196i
$708$			47.6965i			1.79254i
$709$		−	39.9914i		−	1.50191i	−0.660354	−	0.750954i	$-0.729594\pi$
$709$		−	39.9914i		−	1.50191i	0.660354	−	0.750954i	$-0.270406\pi$
$710$	−8.56607	−	0.0631019i	−0.321479	−	0.00236817i
$711$		−	13.4701i		−	0.505169i
$712$			2.13097i			0.0798613i
$713$	12.2470	−	10.1096i	0.458652	−	0.378606i
$714$	3.79560	−	2.50541i	0.142047	−	0.0937626i
$715$	−21.6639	−	0.159587i	−0.810183	−	0.00596821i
$716$	10.8576			0.405766
$717$	−46.2190			−1.72608
$718$	8.09263			0.302014
$719$		−	22.0490i		−	0.822288i	−0.911570	−	0.411144i	$-0.865129\pi$
$719$		−	22.0490i		−	0.822288i	0.911570	−	0.411144i	$-0.134871\pi$
$720$	−0.132244	+	17.9522i	−0.00492846	+	0.669037i
$721$	−8.51297	−	12.8968i	−0.317040	−	0.480303i
$722$			0.469012i			0.0174548i
$723$	84.2510			3.13333
$724$	10.1939			0.378855
$725$	36.3615	+	0.535743i	1.35043	+	0.0198970i
$726$		−	4.72558i		−	0.175383i
$727$		−	17.6360i		−	0.654083i	−0.945010	−	0.327042i	$-0.893948\pi$
$727$		−	17.6360i		−	0.654083i	0.945010	−	0.327042i	$-0.106052\pi$
$728$	4.56311	+	6.91295i	0.169120	+	0.256211i
$729$	85.5087			3.16699
$730$	9.41362	+	0.0693453i	0.348414	+	0.00256659i
$731$		−	0.592843i		−	0.0219271i
$732$	−38.6866			−1.42990
$733$			39.2890i			1.45117i	0.688132	+	0.725586i	$0.258431\pi$
$733$			39.2890i			1.45117i	−0.688132	+	0.725586i	$0.741569\pi$
$734$	−24.8578			−0.917518
$735$	47.6458	+	20.7822i	1.75744	+	0.766562i
$736$	−3.69851	+	3.05303i	−0.136329	+	0.112536i
$737$			9.41929i			0.346964i
$738$	42.2805			1.55637
$739$	21.6623			0.796859			0.398430	−	0.917199i	$-0.369555\pi$
$739$	21.6623			0.796859			0.398430	+	0.917199i	$0.369555\pi$
$740$	0.101698	−	13.8055i	0.00373850	−	0.507501i
$741$	−44.7567			−1.64418
$742$	16.6651	+	25.2470i	0.611794	+	0.926845i
$743$	23.6298			0.866895			0.433447	−	0.901179i	$-0.357297\pi$
$743$	23.6298			0.866895			0.433447	+	0.901179i	$0.357297\pi$
$744$	−10.9967			−0.403159
$745$	9.05348	+	0.0666924i	0.331694	+	0.00244342i
$746$			23.8842i			0.874463i
$747$		−	89.1327i		−	3.26119i
$748$	1.60184			0.0585691
$749$	−24.5321	+	16.1932i	−0.896384	+	0.591687i
$750$	−37.1202	−	0.820455i	−1.35544	−	0.0299588i
$751$			3.24179i			0.118295i	0.998249	+	0.0591473i	$0.0188382\pi$
$751$			3.24179i			0.118295i	−0.998249	+	0.0591473i	$0.981162\pi$
$752$	−2.02900			−0.0739898
$753$	69.5369			2.53407
$754$			22.7702i			0.829242i
$755$	−0.226954	+	30.8090i	−0.00825971	+	1.12126i
$756$	−36.8748	+	24.3404i	−1.34113	+	0.885253i
$757$	−9.96804			−0.362294			−0.181147	−	0.983456i	$-0.557981\pi$
$757$	−9.96804			−0.362294			−0.181147	+	0.983456i	$0.557981\pi$
$758$	25.4442			0.924175
$759$	38.0106	−	31.3768i	1.37970	−	1.13890i
$760$	9.62548	+	0.0709060i	0.349153	+	0.00257203i
$761$			14.2192i			0.515446i	0.966219	+	0.257723i	$0.0829722\pi$
$761$			14.2192i			0.515446i	−0.966219	+	0.257723i	$0.917028\pi$
$762$	50.9562			1.84595
$763$	−27.7924	−	42.1045i	−1.00615	−	1.52428i
$764$			13.1282i			0.474961i
$765$	−9.29223	−	0.0684511i	−0.335961	−	0.00247486i
$766$	19.5218			0.705353
$767$		−	44.9648i		−	1.62358i
$768$	3.32094			0.119834
$769$	11.5907			0.417971			0.208986	−	0.977919i	$-0.432984\pi$
$769$	11.5907			0.417971			0.208986	+	0.977919i	$0.432984\pi$
$770$	9.97307	+	15.3536i	0.359404	+	0.553307i
$771$	46.6433			1.67982
$772$		−	12.7361i		−	0.458382i
$773$			18.3874i			0.661350i	0.943745	+	0.330675i	$0.107276\pi$
$773$			18.3874i			0.661350i	−0.943745	+	0.330675i	$0.892724\pi$
$774$			9.19559i			0.330529i
$775$	0.243915	−	16.5548i	0.00876168	−	0.594666i
$776$	−6.62988			−0.237999
$777$	45.2749	−	29.8851i	1.62423	−	1.07212i
$778$	11.5292			0.413342
$779$		−	22.6697i		−	0.812227i
$780$	0.171255	−	23.2478i	0.00613190	−	0.832405i
$781$		−	11.8556i		−	0.424227i
$782$	−1.58028	−	1.91439i	−0.0565108	−	0.0684585i
$783$	−121.460			−4.34063
$784$	2.75128	−	6.43665i	0.0982602	−	0.229880i
$785$	32.7136	+	0.240984i	1.16760	+	0.00860110i
$786$	17.5470			0.625879
$787$		−	8.75690i		−	0.312150i	−0.987745	−	0.156075i	$-0.950116\pi$
$787$		−	8.75690i		−	0.312150i	0.987745	−	0.156075i	$-0.0498841\pi$
$788$		−	18.5019i		−	0.659104i
$789$	−11.0410			−0.393070
$790$	0.0276352	−	3.75147i	0.000983215	−	0.133471i
$791$	10.3720	−	6.84637i	0.368786	−	0.243429i
$792$	−24.8461			−0.882869
$793$	36.4709			1.29512
$794$			29.9005i			1.06113i
$795$	0.625444	−	84.9040i	0.0221822	−	3.01123i
$796$	6.70733			0.237735
$797$			25.9558i			0.919401i	0.888074	+	0.459700i	$0.152043\pi$
$797$			25.9558i			0.919401i	−0.888074	+	0.459700i	$0.847957\pi$
$798$	20.8365	+	31.5665i	0.737604	+	1.11744i
$799$		−	1.05023i		−	0.0371545i
$800$	−0.0736609	+	4.99946i	−0.00260431	+	0.176758i
$801$	17.1088			0.604510
$802$	−25.9660			−0.916892
$803$			13.0286i			0.459771i
$804$	−10.1080			−0.356481
$805$	8.51060	−	27.0660i	0.299959	−	0.953952i
$806$	10.3669			0.365158
$807$			13.4197i			0.472396i
$808$	12.5472			0.441407
$809$	30.3672			1.06765			0.533827	−	0.845594i	$-0.320753\pi$
$809$	30.3672			1.06765			0.533827	+	0.845594i	$0.320753\pi$
$810$	70.1513	+	0.516769i	2.46487	+	0.0181574i
$811$		−	18.7397i		−	0.658041i	−0.944323	−	0.329020i	$-0.893282\pi$
$811$		−	18.7397i		−	0.658041i	0.944323	−	0.329020i	$-0.106718\pi$
$812$	16.0596	−	10.6007i	0.563582	−	0.372010i
$813$		−	70.0952i		−	2.45835i
$814$	19.1071			0.669705
$815$	−38.3502	−	0.282506i	−1.34335	−	0.00989575i
$816$			1.71896i			0.0601755i
$817$	4.93044			0.172494
$818$	9.95124			0.347937
$819$	55.5018	−	36.6357i	1.93939	−	1.28016i
$820$	11.7752	+	0.0867422i	0.411209	+	0.00302917i
$821$	16.6449			0.580909			0.290455	−	0.956889i	$-0.406193\pi$
$821$	16.6449			0.580909			0.290455	+	0.956889i	$0.406193\pi$
$822$			61.4992i			2.14503i
$823$		−	29.2055i		−	1.01804i	−0.860755	−	0.509020i	$-0.830008\pi$
$823$		−	29.2055i		−	1.01804i	0.860755	−	0.509020i	$-0.169992\pi$
$824$	5.84073			0.203472
$825$	0.757032	−	51.3807i	0.0263565	−	1.78885i
$826$	−31.7133	+	20.9334i	−1.10345	+	0.728364i
$827$	19.9860			0.694980			0.347490	−	0.937684i	$-0.387034\pi$
$827$	19.9860			0.694980			0.347490	+	0.937684i	$0.387034\pi$
$828$	24.5118	+	29.6941i	0.851843	+	1.03194i
$829$			35.9505i			1.24861i	0.781179	+	0.624307i	$0.214619\pi$
$829$			35.9505i			1.24861i	−0.781179	+	0.624307i	$0.785381\pi$
$830$	0.182864	−	24.8237i	0.00634729	−	0.861644i
$831$		−	73.1045i		−	2.53597i
$832$	−3.13074			−0.108539
$833$	3.33168	+	1.42410i	0.115436	+	0.0493420i
$834$	29.7142			1.02892
$835$	0.0243377	−	3.30384i	0.000842240	−	0.114334i
$836$			13.3219i			0.460746i
$837$			55.2988i			1.91140i
$838$			16.1025i			0.556252i
$839$	−9.04444			−0.312249			−0.156124	−	0.987737i	$-0.549900\pi$
$839$	−9.04444			−0.312249			−0.156124	+	0.987737i	$0.549900\pi$
$840$	−16.4762	+	10.7022i	−0.568483	+	0.369262i
$841$	23.8979			0.824067
$842$	32.1276			1.10719
$843$			41.7216i			1.43697i
$844$	13.1972			0.454267
$845$	0.0526832	−	7.15175i	0.00181236	−	0.246028i
$846$			16.2901i			0.560066i
$847$	3.14202	−	2.07399i	0.107961	−	0.0712632i
$848$	−11.4339			−0.392641
$849$			98.5129i			3.38095i
$850$	−2.58777	−	0.0381277i	−0.0887599	−	0.00130777i
$851$	−18.8500	−	22.8353i	−0.646169	−	0.782785i
$852$	12.7224			0.435863
$853$	−14.8988			−0.510126			−0.255063	−	0.966924i	$-0.582096\pi$
$853$	−14.8988			−0.510126			−0.255063	+	0.966924i	$0.582096\pi$
$854$	−16.9790	−	25.7226i	−0.581011	−	0.880210i
$855$	0.569281	−	77.2798i	0.0194690	−	2.64291i
$856$		−	11.1101i		−	0.379736i
$857$	5.27884			0.180322			0.0901608	−	0.995927i	$-0.471262\pi$
$857$	5.27884			0.180322			0.0901608	+	0.995927i	$0.471262\pi$
$858$	32.1754			1.09845
$859$		−	37.7103i		−	1.28666i	−0.765590	−	0.643329i	$-0.777553\pi$
$859$		−	37.7103i		−	1.28666i	0.765590	−	0.643329i	$-0.222447\pi$
$860$	−0.0188656	+	2.56100i	−0.000643310	+	0.0873293i
$861$	25.4901	+	38.6166i	0.868701	+	1.31605i
$862$	4.67344			0.159178
$863$		−	8.94290i		−	0.304420i	−0.988348	−	0.152210i	$-0.951361\pi$
$863$		−	8.94290i		−	0.304420i	0.988348	−	0.152210i	$-0.0486390\pi$
$864$		−	16.6999i		−	0.568143i
$865$	−0.159388	+	21.6369i	−0.00541936	+	0.735678i
$866$	15.6372			0.531375
$867$	55.5663			1.88713
$868$	−4.82631	−	7.31168i	−0.163816	−	0.248175i
$869$	5.19211			0.176130
$870$	−54.0075	−	0.397846i	−1.83103	−	0.0134882i
$871$	9.52906			0.322880
$872$	19.0683			0.645734
$873$			53.2291i			1.80153i
$874$	15.9212	−	13.1426i	0.538544	−	0.444554i
$875$	−15.7460	−	25.0412i	−0.532313	−	0.846547i
$876$	−13.9812			−0.472381
$877$		−	31.9694i		−	1.07953i	−0.841816	−	0.539765i	$-0.818513\pi$
$877$		−	31.9694i		−	1.07953i	0.841816	−	0.539765i	$-0.181487\pi$
$878$	−24.8191			−0.837603
$879$			25.4291i			0.857702i
$880$	−6.91972	−	0.0509741i	−0.233264	−	0.00171834i
$881$	2.38236			0.0802636			0.0401318	−	0.999194i	$-0.487222\pi$
$881$	2.38236			0.0802636			0.0401318	+	0.999194i	$0.487222\pi$
$882$	−51.6777	−	22.0891i	−1.74008	−	0.743780i
$883$			30.9163i			1.04041i	0.854040	+	0.520207i	$0.174145\pi$
$883$			30.9163i			1.04041i	−0.854040	+	0.520207i	$0.825855\pi$
$884$		−	1.62051i		−	0.0545036i
$885$	106.650	+	0.785634i	3.58499	+	0.0264088i
$886$	−5.98523			−0.201078
$887$	−11.8818			−0.398953			−0.199476	−	0.979903i	$-0.563924\pi$
$887$	−11.8818			−0.398953			−0.199476	+	0.979903i	$0.563924\pi$
$888$			20.5041i			0.688074i
$889$	22.3640	+	33.8806i	0.750064	+	1.13632i
$890$	4.76485	+	0.0351002i	0.159718	+	0.00117656i
$891$			97.0908i			3.25267i
$892$	24.3443			0.815108
$893$	8.73434			0.292284
$894$	−13.4463			−0.449713
$895$	0.178840	−	24.2776i	0.00597797	−	0.811509i
$896$	1.45752	+	2.20809i	0.0486922	+	0.0737670i
$897$	−31.7424	−	38.4535i	−1.05985	−	1.28393i
$898$		−	28.0576i		−	0.936294i
$899$		−	24.0836i		−	0.803231i
$900$	40.1390	+	0.591399i	1.33797	+	0.0197133i
$901$		−	5.91830i		−	0.197167i
$902$			16.2972i			0.542637i
$903$	−8.39873	+	5.54385i	−0.279492	+	0.184488i
$904$			4.69728i			0.156229i
$905$	0.167910	−	22.7937i	0.00558150	−	0.757688i
$906$		−	45.7579i		−	1.52021i
$907$	−6.10449			−0.202696			−0.101348	−	0.994851i	$-0.532316\pi$
$907$	−6.10449			−0.202696			−0.101348	+	0.994851i	$0.532316\pi$
$908$		−	8.50897i		−	0.282380i
$909$		−	100.737i		−	3.34123i
$910$	15.5326	−	10.0893i	0.514900	−	0.334457i
$911$			5.84696i			0.193718i	0.995298	+	0.0968592i	$0.0308796\pi$
$911$			5.84696i			0.193718i	−0.995298	+	0.0968592i	$0.969120\pi$
$912$	−14.2959			−0.473384
$913$	34.3565			1.13704
$914$			17.5972i			0.582062i
$915$	−0.637228	+	86.5036i	−0.0210661	+	2.85972i
$916$	−12.0653			−0.398649
$917$	7.70112	+	11.6669i	0.254313	+	0.385276i
$918$	8.64406			0.285296
$919$		−	20.4092i		−	0.673237i	−0.941641	−	0.336619i	$-0.890717\pi$
$919$		−	20.4092i		−	0.673237i	0.941641	−	0.336619i	$-0.109283\pi$
$920$	6.76568	+	8.32019i	0.223058	+	0.274309i
$921$	−0.236310			−0.00778669
$922$	11.7836			0.388073
$923$	−11.9938			−0.394780
$924$	−14.9793	−	22.6931i	−0.492782	−	0.746547i
$925$	−30.8676	−	0.454796i	−1.01492	−	0.0149536i
$926$	−12.0687			−0.396602
$927$		−	46.8933i		−	1.54018i
$928$			7.27310i			0.238751i
$929$		−	14.0288i		−	0.460269i	−0.973159	−	0.230135i	$-0.926083\pi$
$929$		−	14.0288i		−	0.460269i	0.973159	−	0.230135i	$-0.0739166\pi$
$930$	−0.181132	+	24.5887i	−0.00593957	+	0.806296i
$931$	−11.8436	+	27.7082i	−0.388159	+	0.908101i
$932$		−	14.0824i		−	0.461284i
$933$			26.4104i			0.864636i
$934$	7.58594			0.248219
$935$	0.0263847	−	3.58173i	0.000862873	−	0.117135i
$936$			25.1357i			0.821586i
$937$			36.7185i			1.19954i	0.800172	+	0.599771i	$0.204742\pi$
$937$			36.7185i			1.19954i	−0.800172	+	0.599771i	$0.795258\pi$
$938$	−4.43625	−	6.72076i	−0.144849	−	0.219441i
$939$		−	107.765i		−	3.51678i
$940$	−0.0334206	+	4.53685i	−0.00109006	+	0.147976i
$941$	53.0985			1.73096			0.865480	−	0.500943i	$-0.167013\pi$
$941$	53.0985			1.73096			0.865480	+	0.500943i	$0.167013\pi$
$942$	−48.5866			−1.58304
$943$	19.4771	−	16.0778i	0.634261	−	0.523567i
$944$		−	14.3623i		−	0.467454i
$945$	53.8180	+	82.8533i	1.75070	+	2.69522i
$946$	−3.54447			−0.115241
$947$		−	3.97495i		−	0.129168i	−0.997912	−	0.0645842i	$-0.979428\pi$
$947$		−	3.97495i		−	0.129168i	0.997912	−	0.0645842i	$-0.0205721\pi$
$948$			5.57173i			0.180961i
$949$	13.1805			0.427856
$950$	0.317093	−	21.5215i	0.0102878	−	0.698249i
$951$		−	44.8054i		−	1.45291i
$952$	−1.14293	+	0.754427i	−0.0370426	+	0.0244511i
$953$	−25.3377			−0.820770			−0.410385	−	0.911912i	$-0.634606\pi$
$953$	−25.3377			−0.820770			−0.410385	+	0.911912i	$0.634606\pi$
$954$			91.7987i			2.97209i
$955$	29.3547	+	0.216241i	0.949896	+	0.00699739i
$956$	13.9174			0.450121
$957$		−	74.7475i		−	2.41624i
$958$		−	33.8513i		−	1.09369i
$959$	−40.8907	+	26.9912i	−1.32043	+	0.871591i
$960$	0.0547010	−	7.42565i	0.00176547	−	0.239662i
$961$	20.0352			0.646296
$962$		−	19.3298i		−	0.623218i
$963$	−89.1995			−2.87441
$964$	−25.3696			−0.817100
$965$	−28.4780	−	0.209783i	−0.916739	−	0.00675314i
$966$	−12.3432	+	40.2897i	−0.397137	+	1.29630i
$967$			47.3954i			1.52413i	0.647498	+	0.762067i	$0.275815\pi$
$967$			47.3954i			1.52413i	−0.647498	+	0.762067i	$0.724185\pi$
$968$			1.42296i			0.0457357i
$969$		−	7.39970i		−	0.237713i
$970$	−0.109204	+	14.8245i	−0.00350634	+	0.475985i
$971$	46.1525			1.48110			0.740552	−	0.671999i	$-0.234564\pi$
$971$	46.1525			1.48110			0.740552	+	0.671999i	$0.234564\pi$
$972$	−54.0898			−1.73493
$973$	13.0412	+	19.7569i	0.418081	+	0.633378i
$974$	−24.2442			−0.776835
$975$	−51.9795	−	0.765854i	−1.66468	−	0.0245270i
$976$	11.6493			0.372885
$977$	−33.7127			−1.07857			−0.539283	−	0.842125i	$-0.681305\pi$
$977$	−33.7127			−1.07857			−0.539283	+	0.842125i	$0.681305\pi$
$978$	56.9581			1.82132
$979$			6.59465i			0.210766i
$980$	−14.3471	−	6.25791i	−0.458300	−	0.199902i
$981$		−	153.093i		−	4.88789i
$982$			25.0091i			0.798073i
$983$		−	9.34328i		−	0.298004i	−0.988837	−	0.149002i	$-0.952394\pi$
$983$		−	9.34328i		−	0.298004i	0.988837	−	0.149002i	$-0.0476061\pi$
$984$	−17.4887			−0.557520
$985$	−41.3705	−	0.304755i	−1.31817	−	0.00971030i
$986$	−3.76464			−0.119890
$987$	−14.8785	+	9.82101i	−0.473587	+	0.312606i
$988$	13.4771			0.428764
$989$	3.49677	+	4.23607i	0.111191	+	0.134699i
$990$	−0.409254	+	55.5562i	−0.0130069	+	1.76569i
$991$	−23.0935			−0.733588			−0.366794	−	0.930302i	$-0.619545\pi$
$991$	−23.0935			−0.733588			−0.366794	+	0.930302i	$0.619545\pi$
$992$	3.31132			0.105135
$993$	−107.832			−3.42194
$994$	5.58370	+	8.45910i	0.177104	+	0.268306i
$995$	0.110480	−	14.9976i	0.00350245	−	0.475457i
$996$			36.8685i			1.16822i
$997$	−21.9195			−0.694197			−0.347098	−	0.937829i	$-0.612833\pi$
$997$	−21.9195			−0.694197			−0.347098	+	0.937829i	$0.612833\pi$
$998$		−	9.92230i		−	0.314085i
$999$	103.108			3.26221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1610.2.g.a.1609.3	✓	96
5.4	even	2	inner	1610.2.g.a.1609.52	yes	96
7.6	odd	2	inner	1610.2.g.a.1609.89	yes	96
23.22	odd	2	inner	1610.2.g.a.1609.53	yes	96
35.34	odd	2	inner	1610.2.g.a.1609.54	yes	96
115.114	odd	2	inner	1610.2.g.a.1609.90	yes	96
161.160	even	2	inner	1610.2.g.a.1609.51	yes	96
805.804	even	2	inner	1610.2.g.a.1609.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1610.2.g.a.1609.3	✓	96	1.1	even	1	trivial
1610.2.g.a.1609.4	yes	96	805.804	even	2	inner
1610.2.g.a.1609.51	yes	96	161.160	even	2	inner
1610.2.g.a.1609.52	yes	96	5.4	even	2	inner
1610.2.g.a.1609.53	yes	96	23.22	odd	2	inner
1610.2.g.a.1609.54	yes	96	35.34	odd	2	inner
1610.2.g.a.1609.89	yes	96	7.6	odd	2	inner
1610.2.g.a.1609.90	yes	96	115.114	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:	\( N \)	\(=\)	\( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1610.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +3.32094 q^{3} -1.00000 q^{4} +(-0.0164715 + 2.23601i) q^{5} -3.32094i q^{6} +(2.20809 - 1.45752i) q^{7} +1.00000i q^{8} +8.02867 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +3.32094 q^{3} -1.00000 q^{4} +(-0.0164715 + 2.23601i) q^{5} -3.32094i q^{6} +(2.20809 - 1.45752i) q^{7} +1.00000i q^{8} +8.02867 q^{9} +(2.23601 + 0.0164715i) q^{10} +3.09468i q^{11} -3.32094 q^{12} +3.13074 q^{13} +(-1.45752 - 2.20809i) q^{14} +(-0.0547010 + 7.42565i) q^{15} +1.00000 q^{16} +0.517611i q^{17} -8.02867i q^{18} -4.30476 q^{19} +(0.0164715 - 2.23601i) q^{20} +(7.33293 - 4.84033i) q^{21} +3.09468 q^{22} +(-3.05303 - 3.69851i) q^{23} +3.32094i q^{24} +(-4.99946 - 0.0736609i) q^{25} -3.13074i q^{26} +16.6999 q^{27} +(-2.20809 + 1.45752i) q^{28} -7.27310 q^{29} +(7.42565 + 0.0547010i) q^{30} +3.31132i q^{31} -1.00000i q^{32} +10.2773i q^{33} +0.517611 q^{34} +(3.22265 + 4.96130i) q^{35} -8.02867 q^{36} +6.17419 q^{37} +4.30476i q^{38} +10.3970 q^{39} +(-2.23601 - 0.0164715i) q^{40} +5.26619i q^{41} +(-4.84033 - 7.33293i) q^{42} -1.14534 q^{43} -3.09468i q^{44} +(-0.132244 + 17.9522i) q^{45} +(-3.69851 + 3.05303i) q^{46} -2.02900 q^{47} +3.32094 q^{48} +(2.75128 - 6.43665i) q^{49} +(-0.0736609 + 4.99946i) q^{50} +1.71896i q^{51} -3.13074 q^{52} -11.4339 q^{53} -16.6999i q^{54} +(-6.91972 - 0.0509741i) q^{55} +(1.45752 + 2.20809i) q^{56} -14.2959 q^{57} +7.27310i q^{58} -14.3623i q^{59} +(0.0547010 - 7.42565i) q^{60} +11.6493 q^{61} +3.31132 q^{62} +(17.7280 - 11.7019i) q^{63} -1.00000 q^{64} +(-0.0515681 + 7.00037i) q^{65} +10.2773 q^{66} +3.04370 q^{67} -0.517611i q^{68} +(-10.1389 - 12.2826i) q^{69} +(4.96130 - 3.22265i) q^{70} -3.83097 q^{71} +8.02867i q^{72} +4.21001 q^{73} -6.17419i q^{74} +(-16.6029 - 0.244624i) q^{75} +4.30476 q^{76} +(4.51055 + 6.83332i) q^{77} -10.3970i q^{78} -1.67775i q^{79} +(-0.0164715 + 2.23601i) q^{80} +31.3735 q^{81} +5.26619 q^{82} -11.1018i q^{83} +(-7.33293 + 4.84033i) q^{84} +(-1.15738 - 0.00852584i) q^{85} +1.14534i q^{86} -24.1535 q^{87} -3.09468 q^{88} +2.13097 q^{89} +(17.9522 + 0.132244i) q^{90} +(6.91295 - 4.56311i) q^{91} +(3.05303 + 3.69851i) q^{92} +10.9967i q^{93} +2.02900i q^{94} +(0.0709060 - 9.62548i) q^{95} -3.32094i q^{96} +6.62988i q^{97} +(-6.43665 - 2.75128i) q^{98} +24.8461i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 96 q^{4} + 88 q^{9}+O(q^{10}) \) 96 * q - 96 * q^4 + 88 * q^9	\( 96 q - 96 q^{4} + 88 q^{9} + 96 q^{16} + 8 q^{25} + 8 q^{35} - 88 q^{36} - 16 q^{39} - 16 q^{46} + 36 q^{49} + 24 q^{50} - 96 q^{64} - 12 q^{70} + 8 q^{71} + 128 q^{81} + 16 q^{85} - 32 q^{95}+O(q^{100}) \) 96 * q - 96 * q^4 + 88 * q^9 + 96 * q^16 + 8 * q^25 + 8 * q^35 - 88 * q^36 - 16 * q^39 - 16 * q^46 + 36 * q^49 + 24 * q^50 - 96 * q^64 - 12 * q^70 + 8 * q^71 + 128 * q^81 + 16 * q^85 - 32 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more