LMFDB - Embedded newform 1610.2.g.a.1609.90

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			1609.90
Character	$\chi$	$=$	1610.1609
Dual form			1610.2.g.a.1609.89

$q$-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} +(3.29539 + 4.91329i) 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} +(-4.91329 + 3.29539i) 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	$-0.908170\pi$
$3$	−3.32094			−1.91735			−0.958674	+	0.284508i	$0.908170\pi$
$4$	−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	$-0.845500\pi$
$11$		−	3.09468i		−	0.933081i	0.884500	−	0.466540i	$-0.154500\pi$
$12$	3.32094			0.958674
$13$	−3.13074			−0.868312			−0.434156	−	0.900838i	$-0.642953\pi$
$13$	−3.13074			−0.868312			−0.434156	+	0.900838i	$0.642953\pi$
$14$	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	$-0.335611\pi$
$19$	4.30476			0.987580			0.493790	+	0.869581i	$0.335611\pi$
$20$	−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
$35$	3.29539	+	4.91329i	0.557023	+	0.830497i
$36$	−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	$-0.452723\pi$
$47$	2.02900			0.295959			0.147980	+	0.988990i	$0.452723\pi$
$48$	−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	$-0.767918\pi$
$61$	−11.6493			−1.49154			−0.745769	+	0.666204i	$0.767918\pi$
$62$	−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
$70$	−4.91329	+	3.29539i	−0.587250	+	0.393875i
$71$	−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	$-0.579239\pi$
$73$	−4.21001			−0.492745			−0.246372	+	0.969175i	$0.579239\pi$
$74$			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	$0.0300872\pi$
$79$			1.67775i			0.188762i	−0.995536	+	0.0943811i	$0.969913\pi$
$80$	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	$-0.536027\pi$
$89$	−2.13097			−0.225882			−0.112941	+	0.993602i	$0.536027\pi$
$90$	−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
$105$	−10.9438	−	16.3168i	−1.06801	−	1.59235i
$106$		−	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	$0.366402\pi$
$109$			19.0683i			1.82641i	−0.407497	+	0.913206i	$0.633598\pi$
$110$	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	$-0.761643\pi$
$127$		−	15.3439i		−	1.36155i	0.732493	−	0.680775i	$-0.238357\pi$
$128$		−	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	$0.876110\pi$
$140$	−3.29539	−	4.91329i	−0.278511	−	0.415249i
$141$	−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	$0.0530372\pi$
$149$			4.04895i			0.331703i	−0.986151	+	0.165851i	$0.946963\pi$
$150$	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
$161$	−1.35070	+	12.6165i	−0.106450	+	0.994318i
$162$			31.3735i			2.46493i
$163$		−	17.1512i		−	1.34338i	−0.740830	−	0.671692i	$-0.765568\pi$
$163$		−	17.1512i		−	1.34338i	0.740830	−	0.671692i	$-0.234432\pi$
$164$		−	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	$-0.481793\pi$
$167$	1.47756			0.114337			0.0571685	+	0.998365i	$0.481793\pi$
$168$	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	$-0.619906\pi$
$173$	−9.67659			−0.735698			−0.367849	+	0.929886i	$0.619906\pi$
$174$			24.1535i			1.83108i
$175$	−10.9319	+	7.44945i	−0.826372	+	0.563125i
$176$		−	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	$-0.376318\pi$
$181$	10.1939			0.757709			0.378855	+	0.925456i	$0.376318\pi$
$182$	−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	$0.157538\pi$
$191$			13.1282i			0.949921i	−0.880007	+	0.474961i	$0.842462\pi$
$192$	3.32094			0.239668
$193$		−	12.7361i		−	0.916763i	−0.888755	−	0.458382i	$-0.848429\pi$
$193$		−	12.7361i		−	0.916763i	0.888755	−	0.458382i	$-0.151571\pi$
$194$	−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	$-0.770936\pi$
$197$		−	18.5019i		−	1.31821i	0.752052	−	0.659104i	$-0.229064\pi$
$198$	24.8461			1.76574
$199$	6.70733			0.475470			0.237735	−	0.971330i	$-0.423595\pi$
$199$	6.70733			0.475470			0.237735	+	0.971330i	$0.423595\pi$
$200$	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
$210$	16.3168	−	10.9438i	1.12596	−	0.755194i
$211$	−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	$-0.196678\pi$
$223$	24.3443			1.63022			0.815108	+	0.579310i	$0.196678\pi$
$224$	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	$-0.630521\pi$
$229$	−12.0653			−0.797297			−0.398649	+	0.917104i	$0.630521\pi$
$230$	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	$-0.847389\pi$
$233$		−	14.0824i		−	0.922568i	0.887252	−	0.461284i	$-0.152611\pi$
$234$		−	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	$-0.804419\pi$
$241$	−25.3696			−1.63420			−0.817100	+	0.576496i	$0.804419\pi$
$242$			1.42296i			0.0914714i
$243$	−54.0898			−3.46986
$244$	11.6493			0.745769
$245$	14.4377	+	6.04587i	0.922391	+	0.386257i
$246$	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	$-0.729794\pi$
$251$	−20.9389			−1.32165			−0.660826	+	0.750539i	$0.729794\pi$
$252$	−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	$-0.644334\pi$
$257$	−14.0452			−0.876116			−0.438058	+	0.898947i	$0.644334\pi$
$258$			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	$0.230004\pi$
$277$			22.0132i			1.32264i	−0.750102	+	0.661322i	$0.769996\pi$
$278$	−8.94753			−0.536637
$279$			26.5855i			1.59163i
$280$	4.91329	−	3.29539i	0.293625	−	0.196937i
$281$		−	12.5632i		−	0.749457i	−0.927135	−	0.374728i	$-0.877736\pi$
$281$		−	12.5632i		−	0.749457i	0.927135	−	0.374728i	$-0.122264\pi$
$282$		−	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	$-0.499354\pi$
$307$	0.0711576			0.00406118			0.00203059	+	0.999998i	$0.499354\pi$
$308$	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
$315$	26.4576	+	39.4471i	1.49072	+	2.22259i
$316$		−	1.67775i		−	0.0943811i
$317$			13.4918i			0.757773i	0.925443	+	0.378886i	$0.123693\pi$
$317$			13.4918i			0.757773i	−0.925443	+	0.378886i	$0.876307\pi$
$318$			37.9712i			2.12932i
$319$			22.5079i			1.26020i
$320$	−0.0164715	−	2.23601i	−0.000920786	−	0.124997i
$321$	36.8961			2.05934
$322$	−12.6165	−	1.35070i	−0.703089	−	0.0752718i
$323$			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	$-0.567548\pi$
$347$		−	36.4201i		−	1.95514i	0.210621	−	0.977568i	$-0.432452\pi$
$348$	−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	$-0.0149269\pi$
$350$	−7.44945	−	10.9319i	−0.398190	−	0.584333i
$351$	52.2832			2.79067
$352$	3.09468			0.164947
$353$	−17.2579			−0.918544			−0.459272	−	0.888296i	$-0.651890\pi$
$353$	−17.2579			−0.918544			−0.459272	+	0.888296i	$0.651890\pi$
$354$	−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	$-0.931495\pi$
$359$		−	8.09263i		−	0.427113i	0.976931	−	0.213556i	$-0.0685047\pi$
$360$	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	$-0.773304\pi$
$379$		−	25.4442i		−	1.30698i	0.756935	−	0.653490i	$-0.226696\pi$
$380$	−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
$385$	15.2050	−	10.1982i	0.774921	−	0.519747i
$386$	12.7361			0.648250
$387$	−9.19559			−0.467438
$388$		−	6.62988i		−	0.336581i
$389$		−	11.5292i		−	0.584554i	−0.956334	−	0.292277i	$-0.905587\pi$
$389$		−	11.5292i		−	0.584554i	0.956334	−	0.292277i	$-0.0944130\pi$
$390$	−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	$-0.229894\pi$
$397$	29.9005			1.50066			0.750332	+	0.661061i	$0.229894\pi$
$398$			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	$0.224537\pi$
$401$			25.9660i			1.29668i	−0.761350	+	0.648341i	$0.775463\pi$
$402$		−	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	$-0.371323\pi$
$419$	16.1025			0.786659			0.393329	+	0.919398i	$0.371323\pi$
$420$	10.9438	+	16.3168i	0.534003	+	0.796176i
$421$		−	32.1276i		−	1.56580i	−0.622145	−	0.782902i	$-0.713738\pi$
$421$		−	32.1276i		−	1.56580i	0.622145	−	0.782902i	$-0.286262\pi$
$422$		−	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	$-0.964096\pi$
$431$		−	4.67344i		−	0.225112i	0.993645	−	0.112556i	$-0.0359037\pi$
$432$	−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	$0.0454123\pi$
$443$			5.98523i			0.284367i	−0.989840	+	0.142183i	$0.954588\pi$
$444$	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
$455$	−10.3170	−	15.3822i	−0.483670	−	0.721131i
$456$			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	$0.0904803\pi$
$463$			12.0687i			0.560880i	−0.959872	+	0.280440i	$0.909520\pi$
$464$	−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	$-0.781422\pi$
$479$	−33.8513			−1.54671			−0.773353	+	0.633976i	$0.781422\pi$
$480$	7.42565	−	0.0547010i	0.338933	−	0.00249675i
$481$	−19.3298			−0.881363
$482$		−	25.3696i		−	1.15555i
$483$	4.48561	−	41.8986i	0.204102	−	1.90645i
$484$	−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	$0.185108\pi$
$487$			24.2442i			1.09861i	−0.835622	+	0.549305i	$0.814892\pi$
$488$			11.6493i			0.527339i
$489$			56.9581i			2.57573i
$490$	−6.04587	+	14.4377i	−0.273125	+	0.652229i
$491$	−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	$-0.187369\pi$
$521$	37.9677			1.66340			0.831698	+	0.555228i	$0.187369\pi$
$522$		−	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
$525$	36.3041	−	24.7392i	1.58444	−	1.07971i
$526$		−	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	$0.0291248\pi$
$547$			4.27396i			0.182741i	−0.995817	+	0.0913707i	$0.970875\pi$
$548$	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
$560$	3.29539	+	4.91329i	0.139256	+	0.207624i
$561$	−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	$0.334322\pi$
$569$			41.3898i			1.73515i	−0.497308	+	0.867574i	$0.665678\pi$
$570$	31.9657	−	0.235475i	1.33890	−	0.00986295i
$571$		−	42.7364i		−	1.78846i	−0.447604	−	0.894232i	$-0.647722\pi$
$571$		−	42.7364i		−	1.78846i	0.447604	−	0.894232i	$-0.352278\pi$
$572$		−	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	$-0.476836\pi$
$577$	3.49306			0.145418			0.0727089	+	0.997353i	$0.476836\pi$
$578$			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	$-0.290636\pi$
$587$	29.6226			1.22265			0.611327	+	0.791378i	$0.290636\pi$
$588$	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	$-0.587384\pi$
$593$	−13.2029			−0.542179			−0.271089	+	0.962554i	$0.587384\pi$
$594$	−51.6809			−2.12049
$595$	−2.54317	+	1.70573i	−0.104260	+	0.0699281i
$596$		−	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	$-0.568353\pi$
$607$	−10.5000			−0.426182			−0.213091	+	0.977032i	$0.568353\pi$
$608$			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	$-0.632981\pi$
$619$	−20.1887			−0.811451			−0.405725	+	0.913995i	$0.632981\pi$
$620$	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
$630$	−39.4471	+	26.4576i	−1.57161	+	1.05410i
$631$			11.0872i			0.441375i	0.975345	+	0.220688i	$0.0708301\pi$
$631$			11.0872i			0.441375i	−0.975345	+	0.220688i	$0.929170\pi$
$632$	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	$-0.802702\pi$
$641$		−	29.4143i		−	1.16180i	0.813977	−	0.580898i	$-0.197298\pi$
$642$			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	$-0.0234158\pi$
$644$	1.35070	−	12.6165i	0.0532252	−	0.497159i
$645$	0.0626515	+	8.50493i	0.00246690	+	0.334881i
$646$	−2.22819			−0.0876671
$647$	−20.4708			−0.804791			−0.402395	−	0.915466i	$-0.631822\pi$
$647$	−20.4708			−0.804791			−0.402395	+	0.915466i	$0.631822\pi$
$648$		−	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	$0.0492015\pi$
$653$			7.86835i			0.307912i	−0.988078	+	0.153956i	$0.950799\pi$
$654$	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	$-0.947704\pi$
$659$		−	8.39719i		−	0.327108i	0.986534	−	0.163554i	$-0.0522958\pi$
$660$	22.9800	−	0.169282i	0.894496	−	0.00658929i
$661$	−35.2423			−1.37077			−0.685384	−	0.728182i	$-0.740366\pi$
$661$	−35.2423			−1.37077			−0.685384	+	0.728182i	$0.740366\pi$
$662$		−	32.4703i		−	1.26199i
$663$			5.38161i			0.209005i
$664$	−11.1018			−0.430834
$665$	14.1859	+	21.1505i	0.550105	+	0.820183i
$666$			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	$-0.880598\pi$
$673$		−	19.0093i		−	0.732753i	0.930467	−	0.366377i	$-0.119402\pi$
$674$		−	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	$0.0604091\pi$
$683$			9.86013i			0.377288i	−0.982046	+	0.188644i	$0.939591\pi$
$684$	−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
$700$	10.9319	−	7.44945i	0.413186	−	0.281563i
$701$			19.7489i			0.745906i	0.927850	+	0.372953i	$0.121655\pi$
$701$			19.7489i			0.745906i	−0.927850	+	0.372953i	$0.878345\pi$
$702$			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	$0.270406\pi$
$709$			39.9914i			1.50191i	−0.660354	+	0.750954i	$0.729594\pi$
$710$	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
$735$	−47.9468	−	20.0780i	−1.76854	−	0.740588i
$736$	−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	$-0.981162\pi$
$751$		−	3.24179i		−	0.118295i	0.998249	−	0.0591473i	$-0.0188382\pi$
$752$	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	$-0.567016\pi$
$769$	−11.5907			−0.417971			−0.208986	+	0.977919i	$0.567016\pi$
$770$	10.1982	+	15.2050i	0.367517	+	0.547952i
$771$	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
$805$	−28.2328	−	2.81237i	−0.995075	−	0.0991231i
$806$	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	$0.169992\pi$
$823$			29.2055i			1.01804i	−0.860755	+	0.509020i	$0.830008\pi$
$824$	−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	$-0.450100\pi$
$839$	9.04444			0.312249			0.156124	+	0.987737i	$0.450100\pi$
$840$	−16.3168	+	10.9438i	−0.562981	+	0.377597i
$841$	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	$-0.417904\pi$
$853$	14.8988			0.510126			0.255063	+	0.966924i	$0.417904\pi$
$854$	−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	$-0.528738\pi$
$857$	−5.27884			−0.180322			−0.0901608	+	0.995927i	$0.528738\pi$
$858$	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	$0.0486390\pi$
$863$			8.94290i			0.304420i	−0.988348	+	0.152210i	$0.951361\pi$
$864$		−	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
$875$	−16.8371	−	24.3210i	−0.569197	−	0.822201i
$876$	−13.9812			−0.472381
$877$			31.9694i			1.07953i	0.841816	+	0.539765i	$0.181487\pi$
$877$			31.9694i			1.07953i	−0.841816	+	0.539765i	$0.818513\pi$
$878$	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	$-0.512778\pi$
$881$	−2.38236			−0.0802636			−0.0401318	+	0.999194i	$0.512778\pi$
$882$	51.6777	+	22.0891i	1.74008	+	0.743780i
$883$		−	30.9163i		−	1.04041i	−0.854040	−	0.520207i	$-0.825855\pi$
$883$		−	30.9163i		−	1.04041i	0.854040	−	0.520207i	$-0.174145\pi$
$884$			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	$-0.436076\pi$
$887$	11.8818			0.398953			0.199476	+	0.979903i	$0.436076\pi$
$888$			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
$910$	15.3822	−	10.3170i	0.509916	−	0.342006i
$911$		−	5.84696i		−	0.193718i	−0.995298	−	0.0968592i	$-0.969120\pi$
$911$		−	5.84696i		−	0.193718i	0.995298	−	0.0968592i	$-0.0308796\pi$
$912$	−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	$0.109283\pi$
$919$			20.4092i			0.673237i	−0.941641	+	0.336619i	$0.890717\pi$
$920$	−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	$-0.832987\pi$
$941$	−53.0985			−1.73096			−0.865480	+	0.500943i	$0.832987\pi$
$942$	−48.5866			−1.58304
$943$	−19.4771	−	16.0778i	−0.634261	−	0.523567i
$944$		−	14.3623i		−	0.467454i
$945$	−55.0327	−	82.0515i	−1.79022	−	2.66914i
$946$	−3.54447			−0.115241
$947$			3.97495i			0.129168i	0.997912	+	0.0645842i	$0.0205721\pi$
$947$			3.97495i			0.129168i	−0.997912	+	0.0645842i	$0.979428\pi$
$948$			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
$966$	41.8986	+	4.48561i	1.34807	+	0.144322i
$967$		−	47.3954i		−	1.52413i	−0.647498	−	0.762067i	$-0.724185\pi$
$967$		−	47.3954i		−	1.52413i	0.647498	−	0.762067i	$-0.275815\pi$
$968$		−	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	$-0.765436\pi$
$971$	−46.1525			−1.48110			−0.740552	+	0.671999i	$0.765436\pi$
$972$	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
$980$	−14.4377	−	6.04587i	−0.461196	−	0.193128i
$981$			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	$-0.387167\pi$
$997$	21.9195			0.694197			0.347098	+	0.937829i	$0.387167\pi$
$998$			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.1609.90	yes	96
5.4	even	2	inner	1610.2.g.a.1609.53	yes	96
7.6	odd	2	inner	1610.2.g.a.1609.4	yes	96
23.22	odd	2	inner	1610.2.g.a.1609.52	yes	96
35.34	odd	2	inner	1610.2.g.a.1609.51	yes	96
115.114	odd	2	inner	1610.2.g.a.1609.3	✓	96
161.160	even	2	inner	1610.2.g.a.1609.54	yes	96
805.804	even	2	inner	1610.2.g.a.1609.89	yes	96

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

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} +(3.29539 + 4.91329i) 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} +(-4.91329 + 3.29539i) 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

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