LMFDB - Embedded newform 1000.2.d.c.501.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(501,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1000.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.d (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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			501.36
Character	$\chi$	$=$	1000.501
Dual form			1000.2.d.c.501.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36535 + 0.368522i) q^{2} -0.513027i q^{3} +(1.72838 + 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} -1.12889 q^{7} +(1.98900 + 2.01094i) q^{8} +2.73680 q^{9} +O(q^{10})$	\(q+(1.36535 + 0.368522i) q^{2} -0.513027i q^{3} +(1.72838 + 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} -1.12889 q^{7} +(1.98900 + 2.01094i) q^{8} +2.73680 q^{9} +3.99787i q^{11} +(0.516272 - 0.886708i) q^{12} +1.12390i q^{13} +(-1.54133 - 0.416020i) q^{14} +(1.97462 + 3.47863i) q^{16} -2.93982 q^{17} +(3.73671 + 1.00857i) q^{18} +3.24181i q^{19} +0.579150i q^{21} +(-1.47330 + 5.45850i) q^{22} +5.39053 q^{23} +(1.03167 - 1.02041i) q^{24} +(-0.414183 + 1.53452i) q^{26} -2.94314i q^{27} +(-1.95115 - 1.13603i) q^{28} -7.35068i q^{29} +7.19613 q^{31} +(1.41410 + 5.47725i) q^{32} +2.05101 q^{33} +(-4.01389 - 1.08339i) q^{34} +(4.73025 + 2.75411i) q^{36} -10.6176i q^{37} +(-1.19468 + 4.42622i) q^{38} +0.576592 q^{39} +2.08421 q^{41} +(-0.213429 + 0.790745i) q^{42} +6.26007i q^{43} +(-4.02315 + 6.90984i) q^{44} +(7.35999 + 1.98653i) q^{46} -2.24328 q^{47} +(1.78463 - 1.01303i) q^{48} -5.72561 q^{49} +1.50821i q^{51} +(-1.13101 + 1.94253i) q^{52} +1.64494i q^{53} +(1.08461 - 4.01842i) q^{54} +(-2.24536 - 2.27012i) q^{56} +1.66314 q^{57} +(2.70889 - 10.0363i) q^{58} +5.55039i q^{59} +6.65010i q^{61} +(9.82527 + 2.65193i) q^{62} -3.08954 q^{63} +(-0.0877382 + 7.99952i) q^{64} +(2.80036 + 0.755843i) q^{66} -6.79788i q^{67} +(-5.08113 - 2.95841i) q^{68} -2.76549i q^{69} -3.27833 q^{71} +(5.44351 + 5.50354i) q^{72} -6.97819 q^{73} +(3.91280 - 14.4967i) q^{74} +(-3.26232 + 5.60310i) q^{76} -4.51314i q^{77} +(0.787253 + 0.212487i) q^{78} +8.60333 q^{79} +6.70050 q^{81} +(2.84568 + 0.768075i) q^{82} -13.4761i q^{83} +(-0.582813 + 1.00099i) q^{84} +(-2.30697 + 8.54721i) q^{86} -3.77110 q^{87} +(-8.03946 + 7.95176i) q^{88} -10.9910 q^{89} -1.26876i q^{91} +(9.31691 + 5.42463i) q^{92} -3.69181i q^{93} +(-3.06287 - 0.826697i) q^{94} +(2.80998 - 0.725472i) q^{96} -18.6691 q^{97} +(-7.81749 - 2.11001i) q^{98} +10.9414i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.36535	+	0.368522i	0.965451	+	0.260584i
$2$	1.36535	+	0.368522i	0.965451	+	0.260584i
$3$		−	0.513027i		−	0.296196i	−0.988973	−	0.148098i	$-0.952685\pi$
$3$		−	0.513027i		−	0.296196i	0.988973	−	0.148098i	$-0.0473152\pi$
$4$	1.72838	+	1.00633i	0.864192	+	0.503163i
$5$		0			0
$5$		0			0
$6$	0.189062	−	0.700464i	0.0771841	−	0.285963i
$7$	−1.12889			−0.426679			−0.213340	−	0.976978i	$-0.568434\pi$
$7$	−1.12889			−0.426679			−0.213340	+	0.976978i	$0.568434\pi$
$8$	1.98900	+	2.01094i	0.703219	+	0.710974i
$9$	2.73680			0.912268
$10$		0			0
$11$			3.99787i			1.20540i	0.797967	+	0.602701i	$0.205909\pi$
$11$			3.99787i			1.20540i	−0.797967	+	0.602701i	$0.794091\pi$
$12$	0.516272	−	0.886708i	0.149035	−	0.255970i
$13$			1.12390i			0.311714i	0.987780	+	0.155857i	$0.0498140\pi$
$13$			1.12390i			0.311714i	−0.987780	+	0.155857i	$0.950186\pi$
$14$	−1.54133	−	0.416020i	−0.411938	−	0.111186i
$15$		0			0
$16$	1.97462	+	3.47863i	0.493655	+	0.869658i
$17$	−2.93982			−0.713010			−0.356505	−	0.934293i	$-0.616032\pi$
$17$	−2.93982			−0.713010			−0.356505	+	0.934293i	$0.616032\pi$
$18$	3.73671	+	1.00857i	0.880750	+	0.237723i
$19$			3.24181i			0.743723i	0.928288	+	0.371862i	$0.121280\pi$
$19$			3.24181i			0.743723i	−0.928288	+	0.371862i	$0.878720\pi$
$20$		0			0
$21$			0.579150i			0.126381i
$22$	−1.47330	+	5.45850i	−0.314109	+	1.16376i
$23$	5.39053			1.12400			0.562002	−	0.827136i	$-0.310031\pi$
$23$	5.39053			1.12400			0.562002	+	0.827136i	$0.310031\pi$
$24$	1.03167	−	1.02041i	0.210588	−	0.208291i
$25$		0			0
$26$	−0.414183	+	1.53452i	−0.0812279	+	0.300945i
$27$		−	2.94314i		−	0.566407i
$28$	−1.95115	−	1.13603i	−0.368733	−	0.214689i
$29$		−	7.35068i		−	1.36499i	−0.730891	−	0.682494i	$-0.760895\pi$
$29$		−	7.35068i		−	1.36499i	0.730891	−	0.682494i	$-0.239105\pi$
$30$		0			0
$31$	7.19613			1.29246			0.646232	−	0.763141i	$-0.276344\pi$
$31$	7.19613			1.29246			0.646232	+	0.763141i	$0.276344\pi$
$32$	1.41410	+	5.47725i	0.249980	+	0.968251i
$33$	2.05101			0.357036
$34$	−4.01389	−	1.08339i	−0.688377	−	0.185799i
$35$		0			0
$36$	4.73025	+	2.75411i	0.788374	+	0.459019i
$37$		−	10.6176i		−	1.74552i	−0.488152	−	0.872759i	$-0.662329\pi$
$37$		−	10.6176i		−	1.74552i	0.488152	−	0.872759i	$-0.337671\pi$
$38$	−1.19468	+	4.42622i	−0.193803	+	0.718028i
$39$	0.576592			0.0923287
$40$		0			0
$41$	2.08421			0.325498			0.162749	−	0.986667i	$-0.447964\pi$
$41$	2.08421			0.325498			0.162749	+	0.986667i	$0.447964\pi$
$42$	−0.213429	+	0.790745i	−0.0329329	+	0.122015i
$43$			6.26007i			0.954652i	0.878726	+	0.477326i	$0.158394\pi$
$43$			6.26007i			0.954652i	−0.878726	+	0.477326i	$0.841606\pi$
$44$	−4.02315	+	6.90984i	−0.606513	+	1.04170i
$45$		0			0
$46$	7.35999	+	1.98653i	1.08517	+	0.292898i
$47$	−2.24328			−0.327216			−0.163608	−	0.986525i	$-0.552313\pi$
$47$	−2.24328			−0.327216			−0.163608	+	0.986525i	$0.552313\pi$
$48$	1.78463	−	1.01303i	0.257590	−	0.146219i
$49$	−5.72561			−0.817945
$50$		0			0
$51$			1.50821i			0.211191i
$52$	−1.13101	+	1.94253i	−0.156843	+	0.269381i
$53$			1.64494i			0.225950i	0.993598	+	0.112975i	$0.0360380\pi$
$53$			1.64494i			0.225950i	−0.993598	+	0.112975i	$0.963962\pi$
$54$	1.08461	−	4.01842i	0.147597	−	0.546838i
$55$		0			0
$56$	−2.24536	−	2.27012i	−0.300049	−	0.303358i
$57$	1.66314			0.220288
$58$	2.70889	−	10.0363i	0.355694	−	1.31783i
$59$			5.55039i			0.722599i	0.932450	+	0.361299i	$0.117667\pi$
$59$			5.55039i			0.722599i	−0.932450	+	0.361299i	$0.882333\pi$
$60$		0			0
$61$			6.65010i			0.851458i	0.904851	+	0.425729i	$0.139982\pi$
$61$			6.65010i			0.851458i	−0.904851	+	0.425729i	$0.860018\pi$
$62$	9.82527	+	2.65193i	1.24781	+	0.336796i
$63$	−3.08954			−0.389246
$64$	−0.0877382	+	7.99952i	−0.0109673	+	0.999940i
$65$		0			0
$66$	2.80036	+	0.755843i	0.344700	+	0.0930379i
$67$		−	6.79788i		−	0.830493i	−0.909709	−	0.415247i	$-0.863695\pi$
$67$		−	6.79788i		−	0.830493i	0.909709	−	0.415247i	$-0.136305\pi$
$68$	−5.08113	−	2.95841i	−0.616178	−	0.358760i
$69$		−	2.76549i		−	0.332926i
$70$		0			0
$71$	−3.27833			−0.389066			−0.194533	−	0.980896i	$-0.562319\pi$
$71$	−3.27833			−0.389066			−0.194533	+	0.980896i	$0.562319\pi$
$72$	5.44351	+	5.50354i	0.641524	+	0.648598i
$73$	−6.97819			−0.816736			−0.408368	−	0.912817i	$-0.633902\pi$
$73$	−6.97819			−0.816736			−0.408368	+	0.912817i	$0.633902\pi$
$74$	3.91280	−	14.4967i	0.454854	−	1.68521i
$75$		0			0
$76$	−3.26232	+	5.60310i	−0.374214	+	0.642719i
$77$		−	4.51314i		−	0.514320i
$78$	0.787253	+	0.212487i	0.0891388	+	0.0240594i
$79$	8.60333			0.967950			0.483975	−	0.875082i	$-0.339193\pi$
$79$	8.60333			0.967950			0.483975	+	0.875082i	$0.339193\pi$
$80$		0			0
$81$	6.70050			0.744500
$82$	2.84568	+	0.768075i	0.314253	+	0.0848197i
$83$		−	13.4761i		−	1.47919i	−0.673052	−	0.739596i	$-0.735017\pi$
$83$		−	13.4761i		−	1.47919i	0.673052	−	0.739596i	$-0.264983\pi$
$84$	−0.582813	+	1.00099i	−0.0635901	+	0.109217i
$85$		0			0
$86$	−2.30697	+	8.54721i	−0.248767	+	0.921669i
$87$	−3.77110			−0.404304
$88$	−8.03946	+	7.95176i	−0.857009	+	0.847661i
$89$	−10.9910			−1.16504			−0.582521	−	0.812816i	$-0.697934\pi$
$89$	−10.9910			−1.16504			−0.582521	+	0.812816i	$0.697934\pi$
$90$		0			0
$91$		−	1.26876i		−	0.133002i
$92$	9.31691	+	5.42463i	0.971355	+	0.565557i
$93$		−	3.69181i		−	0.382823i
$94$	−3.06287	−	0.826697i	−0.315911	−	0.0852673i
$95$		0			0
$96$	2.80998	−	0.725472i	0.286792	−	0.0740432i
$97$	−18.6691			−1.89556			−0.947778	−	0.318931i	$-0.896676\pi$
$97$	−18.6691			−1.89556			−0.947778	+	0.318931i	$0.896676\pi$
$98$	−7.81749	−	2.11001i	−0.789686	−	0.213144i
$99$			10.9414i			1.09965i
$100$		0			0
$101$			1.76372i			0.175497i	0.996143	+	0.0877485i	$0.0279672\pi$
$101$			1.76372i			0.175497i	−0.996143	+	0.0877485i	$0.972033\pi$
$102$	−0.555807	+	2.05923i	−0.0550331	+	0.203895i
$103$	−3.89194			−0.383484			−0.191742	−	0.981445i	$-0.561414\pi$
$103$	−3.89194			−0.383484			−0.191742	+	0.981445i	$0.561414\pi$
$104$	−2.26010	+	2.23545i	−0.221621	+	0.219203i
$105$		0			0
$106$	−0.606196	+	2.24592i	−0.0588789	+	0.218143i
$107$		−	16.0146i		−	1.54819i	−0.633071	−	0.774094i	$-0.718206\pi$
$107$		−	16.0146i		−	1.54819i	0.633071	−	0.774094i	$-0.281794\pi$
$108$	2.96175	−	5.08687i	0.284995	−	0.489484i
$109$		−	15.6094i		−	1.49511i	−0.664199	−	0.747556i	$-0.731227\pi$
$109$		−	15.6094i		−	1.49511i	0.664199	−	0.747556i	$-0.268773\pi$
$110$		0			0
$111$	−5.44710			−0.517016
$112$	−2.22912	−	3.92698i	−0.210632	−	0.371065i
$113$	−2.97052			−0.279443			−0.139722	−	0.990191i	$-0.544621\pi$
$113$	−2.97052			−0.279443			−0.139722	+	0.990191i	$0.544621\pi$
$114$	2.27077	+	0.612903i	0.212677	+	0.0574036i
$115$		0			0
$116$	7.39718	−	12.7048i	0.686811	−	1.17961i
$117$			3.07590i			0.284367i
$118$	−2.04544	+	7.57824i	−0.188298	+	0.697634i
$119$	3.31872			0.304227
$120$		0			0
$121$	−4.98293			−0.452994
$122$	−2.45071	+	9.07974i	−0.221876	+	0.822041i
$123$		−	1.06925i		−	0.0964114i
$124$	12.4377	+	7.24165i	1.11694	+	0.650320i
$125$		0			0
$126$	−4.21832	−	1.13856i	−0.375798	−	0.101431i
$127$	−12.2692			−1.08871			−0.544356	−	0.838855i	$-0.683226\pi$
$127$	−12.2692			−1.08871			−0.544356	+	0.838855i	$0.683226\pi$
$128$	−3.06779	+	10.8898i	−0.271157	+	0.962535i
$129$	3.21158			0.282764
$130$		0			0
$131$		−	13.2639i		−	1.15887i	−0.815019	−	0.579434i	$-0.803274\pi$
$131$		−	13.2639i		−	1.15887i	0.815019	−	0.579434i	$-0.196726\pi$
$132$	3.54494	+	2.06399i	0.308547	+	0.179647i
$133$		−	3.65964i		−	0.317331i
$134$	2.50517	−	9.28151i	0.216413	−	0.801800i
$135$		0			0
$136$	−5.84730	−	5.91179i	−0.501402	−	0.506932i
$137$	13.3863			1.14367			0.571836	−	0.820368i	$-0.306231\pi$
$137$	13.3863			1.14367			0.571836	+	0.820368i	$0.306231\pi$
$138$	1.01914	−	3.77587i	0.0867552	−	0.321424i
$139$			20.2594i			1.71838i	0.511657	+	0.859190i	$0.329032\pi$
$139$			20.2594i			1.71838i	−0.511657	+	0.859190i	$0.670968\pi$
$140$		0			0
$141$			1.15086i			0.0969201i
$142$	−4.47608	−	1.20814i	−0.375624	−	0.101385i
$143$	−4.49321			−0.375741
$144$	5.40414	+	9.52033i	0.450345	+	0.793361i
$145$		0			0
$146$	−9.52770	−	2.57162i	−0.788518	−	0.212828i
$147$			2.93739i			0.242272i
$148$	10.6847	−	18.3512i	0.878279	−	1.50846i
$149$		−	14.8567i		−	1.21711i	−0.793512	−	0.608555i	$-0.791749\pi$
$149$		−	14.8567i		−	1.21711i	0.793512	−	0.608555i	$-0.208251\pi$
$150$		0			0
$151$	10.1436			0.825477			0.412739	−	0.910850i	$-0.364572\pi$
$151$	10.1436			0.825477			0.412739	+	0.910850i	$0.364572\pi$
$152$	−6.51909	+	6.44798i	−0.528768	+	0.523000i
$153$	−8.04570			−0.650456
$154$	1.66319	−	6.16203i	0.134024	−	0.496551i
$155$		0			0
$156$	0.996573	+	0.580240i	0.0797897	+	0.0464564i
$157$		−	7.49744i		−	0.598361i	−0.954197	−	0.299180i	$-0.903287\pi$
$157$		−	7.49744i		−	0.598361i	0.954197	−	0.299180i	$-0.0967132\pi$
$158$	11.7466	+	3.17051i	0.934508	+	0.252232i
$159$	0.843898			0.0669255
$160$		0			0
$161$	−6.08530			−0.479589
$162$	9.14856	+	2.46928i	0.718778	+	0.194005i
$163$			8.95189i			0.701166i	0.936532	+	0.350583i	$0.114017\pi$
$163$			8.95189i			0.701166i	−0.936532	+	0.350583i	$0.885983\pi$
$164$	3.60231	+	2.09739i	0.281293	+	0.163779i
$165$		0			0
$166$	4.96623	−	18.3996i	0.385454	−	1.42809i
$167$	2.49946			0.193414			0.0967070	−	0.995313i	$-0.469169\pi$
$167$	2.49946			0.193414			0.0967070	+	0.995313i	$0.469169\pi$
$168$	−1.16463	+	1.15193i	−0.0898535	+	0.0888734i
$169$	11.7368			0.902834
$170$		0			0
$171$			8.87221i			0.678475i
$172$	−6.29967	+	10.8198i	−0.480345	+	0.825002i
$173$		−	0.589561i		−	0.0448235i	−0.999749	−	0.0224118i	$-0.992866\pi$
$173$		−	0.589561i		−	0.0448235i	0.999749	−	0.0224118i	$-0.00713448\pi$
$174$	−5.14889	−	1.38973i	−0.390336	−	0.105355i
$175$		0			0
$176$	−13.9071	+	7.89426i	−1.04829	+	0.595052i
$177$	2.84750			0.214031
$178$	−15.0066	−	4.05042i	−1.12479	−	0.303592i
$179$			10.3029i			0.770077i	0.922901	+	0.385038i	$0.125812\pi$
$179$			10.3029i			0.770077i	−0.922901	+	0.385038i	$0.874188\pi$
$180$		0			0
$181$		−	17.8021i		−	1.32322i	−0.749848	−	0.661610i	$-0.769873\pi$
$181$		−	17.8021i		−	1.32322i	0.749848	−	0.661610i	$-0.230127\pi$
$182$	0.467565	−	1.73231i	0.0346583	−	0.128407i
$183$	3.41168			0.252199
$184$	10.7218	+	10.8400i	0.790420	+	0.799137i
$185$		0			0
$186$	1.36051	−	5.04063i	0.0997577	−	0.369597i
$187$		−	11.7530i		−	0.859464i
$188$	−3.87724	−	2.25747i	−0.282777	−	0.164643i
$189$			3.32247i			0.241674i
$190$		0			0
$191$	−18.9069			−1.36806			−0.684029	−	0.729455i	$-0.739774\pi$
$191$	−18.9069			−1.36806			−0.684029	+	0.729455i	$0.739774\pi$
$192$	4.10397	+	0.0450121i	0.296179	+	0.00324847i
$193$	10.2705			0.739288			0.369644	−	0.929173i	$-0.379480\pi$
$193$	10.2705			0.739288			0.369644	+	0.929173i	$0.379480\pi$
$194$	−25.4899	−	6.87995i	−1.83007	−	0.493952i
$195$		0			0
$196$	−9.89606	−	5.76183i	−0.706861	−	0.411559i
$197$			0.207142i			0.0147583i	0.999973	+	0.00737913i	$0.00234887\pi$
$197$			0.207142i			0.0147583i	−0.999973	+	0.00737913i	$0.997651\pi$
$198$	−4.03213	+	14.9388i	−0.286551	+	1.06166i
$199$	−12.2911			−0.871295			−0.435647	−	0.900117i	$-0.643481\pi$
$199$	−12.2911			−0.871295			−0.435647	+	0.900117i	$0.643481\pi$
$200$		0			0
$201$	−3.48750			−0.245989
$202$	−0.649970	+	2.40811i	−0.0457318	+	0.169434i
$203$			8.29809i			0.582412i
$204$	−1.51775	+	2.60676i	−0.106263	+	0.182510i
$205$		0			0
$206$	−5.31387	−	1.43426i	−0.370235	−	0.0999299i
$207$	14.7528			1.02539
$208$	−3.90964	+	2.21928i	−0.271085	+	0.153879i
$209$	−12.9603			−0.896485
$210$		0			0
$211$			3.91559i			0.269560i	0.990876	+	0.134780i	$0.0430328\pi$
$211$			3.91559i			0.269560i	−0.990876	+	0.134780i	$0.956967\pi$
$212$	−1.65534	+	2.84309i	−0.113689	+	0.195264i
$213$			1.68187i			0.115240i
$214$	5.90172	−	21.8656i	0.403433	−	1.49470i
$215$		0			0
$216$	5.91846	−	5.85390i	0.402700	−	0.398308i
$217$	−8.12363			−0.551468
$218$	5.75241	−	21.3124i	0.389603	−	1.44346i
$219$			3.58000i			0.241914i
$220$		0			0
$221$		−	3.30407i		−	0.222256i
$222$	−7.43722	−	2.00737i	−0.499153	−	0.134726i
$223$	23.8519			1.59724			0.798621	−	0.601834i	$-0.205563\pi$
$223$	23.8519			1.59724			0.798621	+	0.601834i	$0.205563\pi$
$224$	−1.59636	−	6.18320i	−0.106661	−	0.413133i
$225$		0			0
$226$	−4.05582	−	1.09470i	−0.269789	−	0.0728185i
$227$			24.7012i			1.63948i	0.572738	+	0.819738i	$0.305881\pi$
$227$			24.7012i			1.63948i	−0.572738	+	0.819738i	$0.694119\pi$
$228$	2.87454	+	1.67366i	0.190371	+	0.110841i
$229$		−	22.0732i		−	1.45864i	−0.684175	−	0.729318i	$-0.739837\pi$
$229$		−	22.0732i		−	1.45864i	0.684175	−	0.729318i	$-0.260163\pi$
$230$		0			0
$231$	−2.31536			−0.152340
$232$	14.7818	−	14.6205i	0.970470	−	0.959884i
$233$	19.6085			1.28460			0.642299	−	0.766454i	$-0.277981\pi$
$233$	19.6085			1.28460			0.642299	+	0.766454i	$0.277981\pi$
$234$	−1.13354	+	4.19969i	−0.0741016	+	0.274543i
$235$		0			0
$236$	−5.58550	+	9.59320i	−0.363585	+	0.624464i
$237$		−	4.41374i		−	0.286703i
$238$	4.53123	+	1.22302i	0.293716	+	0.0792767i
$239$	−12.3845			−0.801088			−0.400544	−	0.916278i	$-0.631179\pi$
$239$	−12.3845			−0.801088			−0.400544	+	0.916278i	$0.631179\pi$
$240$		0			0
$241$	−20.4095			−1.31469			−0.657347	−	0.753588i	$-0.728321\pi$
$241$	−20.4095			−1.31469			−0.657347	+	0.753588i	$0.728321\pi$
$242$	−6.80346	−	1.83632i	−0.437343	−	0.118043i
$243$		−	12.2669i		−	0.786925i
$244$	−6.69216	+	11.4939i	−0.428422	+	0.735823i
$245$		0			0
$246$	0.394043	−	1.45991i	0.0251233	−	0.0930805i
$247$	−3.64348			−0.231829
$248$	14.3131	+	14.4710i	0.908885	+	0.918908i
$249$	−6.91359			−0.438131
$250$		0			0
$251$		−	22.2016i		−	1.40135i	−0.713479	−	0.700676i	$-0.752882\pi$
$251$		−	22.2016i		−	1.40135i	0.713479	−	0.700676i	$-0.247118\pi$
$252$	−5.33991	−	3.10908i	−0.336383	−	0.195854i
$253$			21.5506i			1.35488i
$254$	−16.7517	−	4.52145i	−1.05110	−	0.283701i
$255$		0			0
$256$	−8.20176	+	13.7379i	−0.512610	+	0.858621i
$257$	−13.0592			−0.814614			−0.407307	−	0.913291i	$-0.633532\pi$
$257$	−13.0592			−0.814614			−0.407307	+	0.913291i	$0.633532\pi$
$258$	4.38495	+	1.18354i	0.272995	+	0.0736839i
$259$			11.9860i			0.744776i
$260$		0			0
$261$		−	20.1174i		−	1.24523i
$262$	4.88802	−	18.1099i	0.301983	−	1.11883i
$263$	−29.2389			−1.80295			−0.901473	−	0.432835i	$-0.857513\pi$
$263$	−29.2389			−1.80295			−0.901473	+	0.432835i	$0.857513\pi$
$264$	4.07947	+	4.12446i	0.251074	+	0.253843i
$265$		0			0
$266$	1.34866	−	4.99671i	0.0826915	−	0.306368i
$267$			5.63867i			0.345081i
$268$	6.84088	−	11.7493i	0.417873	−	0.717705i
$269$		−	21.4247i		−	1.30629i	−0.757235	−	0.653143i	$-0.773450\pi$
$269$		−	21.4247i		−	1.30629i	0.757235	−	0.653143i	$-0.226550\pi$
$270$		0			0
$271$	1.15797			0.0703415			0.0351708	−	0.999381i	$-0.488802\pi$
$271$	1.15797			0.0703415			0.0351708	+	0.999381i	$0.488802\pi$
$272$	−5.80502	−	10.2265i	−0.351981	−	0.620075i
$273$	−0.650908			−0.0393947
$274$	18.2771	+	4.93316i	1.10416	+	0.298023i
$275$		0			0
$276$	2.78298	−	4.77983i	0.167516	−	0.287712i
$277$			16.8055i			1.00975i	0.863194	+	0.504873i	$0.168461\pi$
$277$			16.8055i			1.00975i	−0.863194	+	0.504873i	$0.831539\pi$
$278$	−7.46603	+	27.6612i	−0.447783	+	1.65901i
$279$	19.6944			1.17907
$280$		0			0
$281$	8.99127			0.536374			0.268187	−	0.963367i	$-0.413575\pi$
$281$	8.99127			0.536374			0.268187	+	0.963367i	$0.413575\pi$
$282$	−0.424118	+	1.57133i	−0.0252559	+	0.0935716i
$283$			15.4397i			0.917798i	0.888489	+	0.458899i	$0.151756\pi$
$283$			15.4397i			0.917798i	−0.888489	+	0.458899i	$0.848244\pi$
$284$	−5.66621	−	3.29907i	−0.336228	−	0.195764i
$285$		0			0
$286$	−6.13482	−	1.65585i	−0.362760	−	0.0979122i
$287$	−2.35283			−0.138883
$288$	3.87012	+	14.9902i	0.228049	+	0.883304i
$289$	−8.35748			−0.491616
$290$		0			0
$291$			9.57773i			0.561457i
$292$	−12.0610	−	7.02233i	−0.705816	−	0.410951i
$293$		−	1.62062i		−	0.0946777i	−0.998879	−	0.0473389i	$-0.984926\pi$
$293$		−	1.62062i		−	0.0946777i	0.998879	−	0.0473389i	$-0.0150741\pi$
$294$	−1.08249	+	4.01058i	−0.0631323	+	0.233902i
$295$		0			0
$296$	21.3513	−	21.1184i	1.24102	−	1.22748i
$297$	11.7663			0.682748
$298$	5.47503	−	20.2847i	0.317160	−	1.17506i
$299$			6.05843i			0.350368i
$300$		0			0
$301$		−	7.06691i		−	0.407330i
$302$	13.8496	+	3.73815i	0.796958	+	0.215106i
$303$	0.904838			0.0519816
$304$	−11.2771	+	6.40135i	−0.646785	+	0.367142i
$305$		0			0
$306$	−10.9852	−	2.96502i	−0.627984	−	0.169499i
$307$			13.3243i			0.760458i	0.924892	+	0.380229i	$0.124155\pi$
$307$			13.3243i			0.760458i	−0.924892	+	0.380229i	$0.875845\pi$
$308$	4.54169	−	7.80044i	0.258787	−	0.444471i
$309$			1.99667i			0.113587i
$310$		0			0
$311$	−3.20457			−0.181714			−0.0908572	−	0.995864i	$-0.528961\pi$
$311$	−3.20457			−0.181714			−0.0908572	+	0.995864i	$0.528961\pi$
$312$	1.14684	+	1.15949i	0.0649273	+	0.0656433i
$313$	24.2715			1.37190			0.685952	−	0.727647i	$-0.259386\pi$
$313$	24.2715			1.37190			0.685952	+	0.727647i	$0.259386\pi$
$314$	2.76297	−	10.2367i	0.155923	−	0.577688i
$315$		0			0
$316$	14.8698	+	8.65775i	0.836494	+	0.487036i
$317$			3.79177i			0.212967i	0.994314	+	0.106483i	$0.0339591\pi$
$317$			3.79177i			0.212967i	−0.994314	+	0.106483i	$0.966041\pi$
$318$	1.15222	+	0.310995i	0.0646133	+	0.0174397i
$319$	29.3870			1.64536
$320$		0			0
$321$	−8.21591			−0.458567
$322$	−8.30859	−	2.24257i	−0.463020	−	0.124973i
$323$		−	9.53034i		−	0.530282i
$324$	11.5810	+	6.74288i	0.643391	+	0.374605i
$325$		0			0
$326$	−3.29897	+	12.2225i	−0.182713	+	0.676941i
$327$	−8.00806			−0.442847
$328$	4.14549	+	4.19121i	0.228896	+	0.231421i
$329$	2.53241			0.139616
$330$		0			0
$331$			2.26196i			0.124328i	0.998066	+	0.0621642i	$0.0198002\pi$
$331$			2.26196i			0.124328i	−0.998066	+	0.0621642i	$0.980200\pi$
$332$	13.5613	−	23.2918i	0.744274	−	1.27830i
$333$		−	29.0582i		−	1.59238i
$334$	3.41265	+	0.921106i	0.186732	+	0.0504007i
$335$		0			0
$336$	−2.01465	+	1.14360i	−0.109908	+	0.0623885i
$337$	28.6654			1.56150			0.780751	−	0.624843i	$-0.214837\pi$
$337$	28.6654			1.56150			0.780751	+	0.624843i	$0.214837\pi$
$338$	16.0249	+	4.32528i	0.871642	+	0.235264i
$339$			1.52396i			0.0827701i
$340$		0			0
$341$			28.7692i			1.55794i
$342$	−3.26960	+	12.1137i	−0.176800	+	0.655034i
$343$	14.3658			0.775679
$344$	−12.5886	+	12.4513i	−0.678732	+	0.671329i
$345$		0			0
$346$	0.217266	−	0.804960i	0.0116803	−	0.0432749i
$347$		−	3.03845i		−	0.163112i	−0.996669	−	0.0815562i	$-0.974011\pi$
$347$		−	3.03845i		−	0.163112i	0.996669	−	0.0815562i	$-0.0259890\pi$
$348$	−6.51791	−	3.79495i	−0.349396	−	0.203431i
$349$			26.1606i			1.40035i	0.713973	+	0.700173i	$0.246894\pi$
$349$			26.1606i			1.40035i	−0.713973	+	0.700173i	$0.753106\pi$
$350$		0			0
$351$	3.30780			0.176557
$352$	−21.8973	+	5.65339i	−1.16713	+	0.301327i
$353$	−29.4943			−1.56983			−0.784913	−	0.619606i	$-0.787292\pi$
$353$	−29.4943			−1.56983			−0.784913	+	0.619606i	$0.787292\pi$
$354$	3.88784	+	1.04937i	0.206637	+	0.0557731i
$355$		0			0
$356$	−18.9966	−	11.0605i	−1.00682	−	0.586206i
$357$		−	1.70259i		−	0.0901108i
$358$	−3.79685	+	14.0671i	−0.200670	+	0.743472i
$359$	8.91327			0.470424			0.235212	−	0.971944i	$-0.424422\pi$
$359$	8.91327			0.470424			0.235212	+	0.971944i	$0.424422\pi$
$360$		0			0
$361$	8.49064			0.446876
$362$	6.56046	−	24.3062i	0.344810	−	1.27750i
$363$			2.55638i			0.134175i
$364$	1.27678	−	2.19290i	0.0669217	−	0.114939i
$365$		0			0
$366$	4.65815	+	1.25728i	0.243485	+	0.0657190i
$367$	22.6852			1.18416			0.592079	−	0.805880i	$-0.298307\pi$
$367$	22.6852			1.18416			0.592079	+	0.805880i	$0.298307\pi$
$368$	10.6442	+	18.7517i	0.554870	+	0.977499i
$369$	5.70406			0.296942
$370$		0			0
$371$		−	1.85695i		−	0.0964081i
$372$	3.71516	−	6.38087i	0.192622	−	0.330833i
$373$			6.46312i			0.334648i	0.985902	+	0.167324i	$0.0535125\pi$
$373$			6.46312i			0.334648i	−0.985902	+	0.167324i	$0.946487\pi$
$374$	4.33123	−	16.0470i	0.223963	−	0.829770i
$375$		0			0
$376$	−4.46189	−	4.51109i	−0.230104	−	0.232642i
$377$	8.26145			0.425486
$378$	−1.22440	+	4.53635i	−0.0629764	+	0.233324i
$379$		−	4.31785i		−	0.221793i	−0.993832	−	0.110897i	$-0.964628\pi$
$379$		−	4.31785i		−	0.221793i	0.993832	−	0.110897i	$-0.0353722\pi$
$380$		0			0
$381$			6.29441i			0.322472i
$382$	−25.8147	−	6.96762i	−1.32079	−	0.356494i
$383$	−11.1049			−0.567432			−0.283716	−	0.958908i	$-0.591567\pi$
$383$	−11.1049			−0.567432			−0.283716	+	0.958908i	$0.591567\pi$
$384$	5.58678	+	1.57386i	0.285099	+	0.0803157i
$385$		0			0
$386$	14.0229	+	3.78491i	0.713746	+	0.192647i
$387$			17.1326i			0.870898i
$388$	−32.2673	−	18.7871i	−1.63812	−	0.953773i
$389$		−	15.5490i		−	0.788368i	−0.919032	−	0.394184i	$-0.871027\pi$
$389$		−	15.5490i		−	0.788368i	0.919032	−	0.394184i	$-0.128973\pi$
$390$		0			0
$391$	−15.8472			−0.801426
$392$	−11.3883	−	11.5139i	−0.575194	−	0.581537i
$393$	−6.80472			−0.343253
$394$	−0.0763364	+	0.282822i	−0.00384577	+	0.0142484i
$395$		0			0
$396$	−11.0106	+	18.9109i	−0.553302	+	0.950308i
$397$			26.9682i			1.35350i	0.736214	+	0.676748i	$0.236611\pi$
$397$			26.9682i			1.35350i	−0.736214	+	0.676748i	$0.763389\pi$
$398$	−16.7817	−	4.52955i	−0.841193	−	0.227046i
$399$	−1.87750			−0.0939924
$400$		0			0
$401$	36.1092			1.80321			0.901603	−	0.432565i	$-0.142391\pi$
$401$	36.1092			1.80321			0.901603	+	0.432565i	$0.142391\pi$
$402$	−4.76167	−	1.28522i	−0.237490	−	0.0641009i
$403$			8.08775i			0.402880i
$404$	−1.77488	+	3.04839i	−0.0883035	+	0.151663i
$405$		0			0
$406$	−3.05803	+	11.3298i	−0.151767	+	0.562290i
$407$	42.4476			2.10405
$408$	−3.03291	+	2.99982i	−0.150151	+	0.148513i
$409$	15.5149			0.767163			0.383581	−	0.923507i	$-0.374691\pi$
$409$	15.5149			0.767163			0.383581	+	0.923507i	$0.374691\pi$
$410$		0			0
$411$		−	6.86755i		−	0.338751i
$412$	−6.72676	−	3.91656i	−0.331404	−	0.192955i
$413$		−	6.26576i		−	0.308318i
$414$	20.1428	+	5.43674i	0.989966	+	0.267201i
$415$		0			0
$416$	−6.15590	+	1.58931i	−0.301818	+	0.0779225i
$417$	10.3936			0.508978
$418$	−17.6955	−	4.77617i	−0.865513	−	0.233610i
$419$		−	26.9362i		−	1.31592i	−0.753054	−	0.657959i	$-0.771420\pi$
$419$		−	26.9362i		−	1.31592i	0.753054	−	0.657959i	$-0.228580\pi$
$420$		0			0
$421$			6.14641i			0.299557i	0.988720	+	0.149779i	$0.0478561\pi$
$421$			6.14641i			0.299557i	−0.988720	+	0.149779i	$0.952144\pi$
$422$	−1.44298	+	5.34616i	−0.0702431	+	0.260247i
$423$	−6.13941			−0.298508
$424$	−3.30787	+	3.27179i	−0.160644	+	0.158892i
$425$		0			0
$426$	−0.619807	+	2.29635i	−0.0300297	+	0.111259i
$427$		−	7.50721i		−	0.363299i
$428$	16.1159	−	27.6793i	0.778990	−	1.33793i
$429$			2.30514i			0.111293i
$430$		0			0
$431$	36.8901			1.77693			0.888467	−	0.458940i	$-0.151771\pi$
$431$	36.8901			1.77693			0.888467	+	0.458940i	$0.151771\pi$
$432$	10.2381	−	5.81157i	0.492580	−	0.279609i
$433$	11.5824			0.556617			0.278308	−	0.960492i	$-0.410226\pi$
$433$	11.5824			0.556617			0.278308	+	0.960492i	$0.410226\pi$
$434$	−11.0916	−	2.99373i	−0.532415	−	0.143704i
$435$		0			0
$436$	15.7082	−	26.9791i	0.752284	−	1.29206i
$437$			17.4751i			0.835948i
$438$	−1.31931	+	4.88797i	−0.0630390	+	0.233556i
$439$	−4.15174			−0.198152			−0.0990760	−	0.995080i	$-0.531589\pi$
$439$	−4.15174			−0.198152			−0.0990760	+	0.995080i	$0.531589\pi$
$440$		0			0
$441$	−15.6699			−0.746185
$442$	1.21762	−	4.51122i	0.0579163	−	0.214577i
$443$		−	15.7327i		−	0.747482i	−0.927533	−	0.373741i	$-0.878075\pi$
$443$		−	15.7327i		−	0.747482i	0.927533	−	0.373741i	$-0.121925\pi$
$444$	−9.41468	−	5.48155i	−0.446801	−	0.260143i
$445$		0			0
$446$	32.5663	+	8.78995i	1.54206	+	0.416216i
$447$	−7.62190			−0.360504
$448$	0.0990465	−	9.03056i	0.00467951	−	0.426654i
$449$	−20.6861			−0.976239			−0.488120	−	0.872777i	$-0.662317\pi$
$449$	−20.6861			−0.976239			−0.488120	+	0.872777i	$0.662317\pi$
$450$		0			0
$451$			8.33238i			0.392356i
$452$	−5.13420	−	2.98931i	−0.241493	−	0.140605i
$453$		−	5.20396i		−	0.244503i
$454$	−9.10293	+	33.7259i	−0.427222	+	1.58283i
$455$		0			0
$456$	3.30799	+	3.34447i	0.154911	+	0.156619i
$457$	−28.7187			−1.34340			−0.671702	−	0.740821i	$-0.734436\pi$
$457$	−28.7187			−1.34340			−0.671702	+	0.740821i	$0.734436\pi$
$458$	8.13444	−	30.1377i	0.380098	−	1.40824i
$459$			8.65228i			0.403854i
$460$		0			0
$461$			27.7063i			1.29041i	0.764008	+	0.645207i	$0.223229\pi$
$461$			27.7063i			1.29041i	−0.764008	+	0.645207i	$0.776771\pi$
$462$	−3.16129	−	0.853262i	−0.147077	−	0.0396973i
$463$	−26.9572			−1.25281			−0.626404	−	0.779499i	$-0.715474\pi$
$463$	−26.9572			−1.25281			−0.626404	+	0.779499i	$0.715474\pi$
$464$	25.5703	−	14.5148i	1.18707	−	0.673832i
$465$		0			0
$466$	26.7726	+	7.22617i	1.24022	+	0.334746i
$467$			31.3052i			1.44863i	0.689468	+	0.724316i	$0.257844\pi$
$467$			31.3052i			1.44863i	−0.689468	+	0.724316i	$0.742156\pi$
$468$	−3.09536	+	5.31633i	−0.143083	+	0.245748i
$469$			7.67404i			0.354354i
$470$		0			0
$471$	−3.84639			−0.177232
$472$	−11.1615	+	11.0397i	−0.513749	+	0.508145i
$473$	−25.0269			−1.15074
$474$	1.62656	−	6.02632i	0.0747103	−	0.276798i
$475$		0			0
$476$	5.73602	+	3.33971i	0.262910	+	0.153076i
$477$			4.50187i			0.206127i
$478$	−16.9093	−	4.56397i	−0.773411	−	0.208751i
$479$	−32.6888			−1.49359			−0.746794	−	0.665056i	$-0.768408\pi$
$479$	−32.6888			−1.49359			−0.746794	+	0.665056i	$0.768408\pi$
$480$		0			0
$481$	11.9331			0.544103
$482$	−27.8662	−	7.52136i	−1.26927	−	0.342589i
$483$			3.12193i			0.142053i
$484$	−8.61241	−	5.01445i	−0.391473	−	0.227929i
$485$		0			0
$486$	4.52064	−	16.7487i	0.205060	−	0.759738i
$487$	−17.6043			−0.797726			−0.398863	−	0.917011i	$-0.630595\pi$
$487$	−17.6043			−0.797726			−0.398863	+	0.917011i	$0.630595\pi$
$488$	−13.3729	+	13.2271i	−0.605364	+	0.598761i
$489$	4.59256			0.207683
$490$		0			0
$491$			1.31132i			0.0591790i	0.999562	+	0.0295895i	$0.00942000\pi$
$491$			1.31132i			0.0591790i	−0.999562	+	0.0295895i	$0.990580\pi$
$492$	1.07602	−	1.84808i	0.0485106	−	0.0833179i
$493$			21.6097i			0.973250i
$494$	−4.97465	−	1.34270i	−0.223820	−	0.0604111i
$495$		0			0
$496$	14.2096	+	25.0327i	0.638031	+	1.12400i
$497$	3.70087			0.166007
$498$	−9.43950	−	2.54781i	−0.422994	−	0.114170i
$499$			21.2655i			0.951973i	0.879453	+	0.475987i	$0.157909\pi$
$499$			21.2655i			0.951973i	−0.879453	+	0.475987i	$0.842091\pi$
$500$		0			0
$501$		−	1.28229i		−	0.0572885i
$502$	8.18177	−	30.3130i	0.365170	−	1.35294i
$503$	34.4786			1.53733			0.768663	−	0.639654i	$-0.220922\pi$
$503$	34.4786			1.53733			0.768663	+	0.639654i	$0.220922\pi$
$504$	−6.14511	−	6.21288i	−0.273725	−	0.276743i
$505$		0			0
$506$	−7.94188	+	29.4242i	−0.353059	+	1.30807i
$507$		−	6.02132i		−	0.267416i
$508$	−21.2058	−	12.3468i	−0.940855	−	0.547799i
$509$		−	8.61795i		−	0.381984i	−0.981592	−	0.190992i	$-0.938830\pi$
$509$		−	8.61795i		−	0.381984i	0.981592	−	0.190992i	$-0.0611704\pi$
$510$		0			0
$511$	7.87759			0.348484
$512$	−16.2610	+	15.7346i	−0.718643	+	0.695379i
$513$	9.54110			0.421250
$514$	−17.8305	−	4.81262i	−0.786470	−	0.212275i
$515$		0			0
$516$	5.55085	+	3.23190i	0.244363	+	0.142276i
$517$		−	8.96833i		−	0.394426i
$518$	−4.41711	+	16.3652i	−0.194077	+	0.719045i
$519$	−0.302461			−0.0132766
$520$		0			0
$521$	−5.28810			−0.231676			−0.115838	−	0.993268i	$-0.536955\pi$
$521$	−5.28810			−0.231676			−0.115838	+	0.993268i	$0.536955\pi$
$522$	7.41369	−	27.4673i	0.324488	−	1.20221i
$523$		−	18.0301i		−	0.788400i	−0.919025	−	0.394200i	$-0.871022\pi$
$523$		−	18.0301i		−	0.788400i	0.919025	−	0.394200i	$-0.128978\pi$
$524$	13.3478	−	22.9250i	0.583099	−	1.00148i
$525$		0			0
$526$	−39.9214	−	10.7752i	−1.74066	−	0.469819i
$527$	−21.1553			−0.921540
$528$	4.04997	+	7.13472i	0.176252	+	0.310499i
$529$	6.05785			0.263385
$530$		0			0
$531$			15.1903i			0.659204i
$532$	3.68279	−	6.32527i	0.159669	−	0.274235i
$533$			2.34244i			0.101463i
$534$	−2.07797	+	7.69878i	−0.0899227	+	0.333159i
$535$		0			0
$536$	13.6701	−	13.5210i	0.590459	−	0.584018i
$537$	5.28568			0.228094
$538$	7.89546	−	29.2523i	0.340397	−	1.26115i
$539$		−	22.8902i		−	0.985952i
$540$		0			0
$541$			2.53085i			0.108810i	0.998519	+	0.0544050i	$0.0173262\pi$
$541$			2.53085i			0.108810i	−0.998519	+	0.0544050i	$0.982674\pi$
$542$	1.58104	+	0.426736i	0.0679113	+	0.0183299i
$543$	−9.13296			−0.391933
$544$	−4.15720	−	16.1021i	−0.178238	−	0.690373i
$545$		0			0
$546$	−0.888720	−	0.239874i	−0.0380337	−	0.0102656i
$547$			37.9439i			1.62236i	0.584794	+	0.811182i	$0.301175\pi$
$547$			37.9439i			1.62236i	−0.584794	+	0.811182i	$0.698825\pi$
$548$	23.1367	+	13.4710i	0.988352	+	0.575453i
$549$			18.2000i			0.776757i
$550$		0			0
$551$	23.8295			1.01517
$552$	5.56123	−	5.50057i	0.236702	−	0.234120i
$553$	−9.71219			−0.413004
$554$	−6.19320	+	22.9455i	−0.263124	+	0.974860i
$555$		0			0
$556$	−20.3875	+	35.0160i	−0.864624	+	1.48501i
$557$			37.0123i			1.56826i	0.620596	+	0.784130i	$0.286891\pi$
$557$			37.0123i			1.56826i	−0.620596	+	0.784130i	$0.713109\pi$
$558$	26.8898	+	7.25782i	1.13834	+	0.307248i
$559$	−7.03571			−0.297579
$560$		0			0
$561$	−6.02960			−0.254570
$562$	12.2763	+	3.31348i	0.517843	+	0.139771i
$563$			14.2506i			0.600590i	0.953846	+	0.300295i	$0.0970852\pi$
$563$			14.2506i			0.600590i	−0.953846	+	0.300295i	$0.902915\pi$
$564$	−1.15814	+	1.98913i	−0.0487666	+	0.0837576i
$565$		0			0
$566$	−5.68988	+	21.0807i	−0.239164	+	0.886089i
$567$	−7.56411			−0.317663
$568$	−6.52061	−	6.59252i	−0.273599	−	0.276616i
$569$	25.9576			1.08820			0.544101	−	0.839020i	$-0.316871\pi$
$569$	25.9576			1.08820			0.544101	+	0.839020i	$0.316871\pi$
$570$		0			0
$571$			20.3690i			0.852416i	0.904625	+	0.426208i	$0.140151\pi$
$571$			20.3690i			0.852416i	−0.904625	+	0.426208i	$0.859849\pi$
$572$	−7.76599	−	4.52163i	−0.324712	−	0.189059i
$573$			9.69977i			0.405214i
$574$	−3.21245	−	0.867070i	−0.134085	−	0.0361908i
$575$		0			0
$576$	−0.240122	+	21.8931i	−0.0100051	+	0.912213i
$577$	44.6310			1.85801			0.929007	−	0.370063i	$-0.120664\pi$
$577$	44.6310			1.85801			0.929007	+	0.370063i	$0.120664\pi$
$578$	−11.4109	−	3.07991i	−0.474632	−	0.128107i
$579$		−	5.26905i		−	0.218974i
$580$		0			0
$581$			15.2130i			0.631140i
$582$	−3.52960	+	13.0770i	−0.146307	+	0.542059i
$583$	−6.57625			−0.272360
$584$	−13.8796	−	14.0327i	−0.574344	−	0.580678i
$585$		0			0
$586$	0.597234	−	2.21272i	0.0246715	−	0.0914067i
$587$		−	18.9398i		−	0.781729i	−0.920448	−	0.390865i	$-0.872176\pi$
$587$		−	18.9398i		−	0.781729i	0.920448	−	0.390865i	$-0.127824\pi$
$588$	−2.95598	+	5.07694i	−0.121902	+	0.209370i
$589$			23.3285i			0.961236i
$590$		0			0
$591$	0.106270			0.00437134
$592$	36.9346	−	20.9656i	1.51800	−	0.861683i
$593$	−8.22399			−0.337719			−0.168859	−	0.985640i	$-0.554008\pi$
$593$	−8.22399			−0.337719			−0.168859	+	0.985640i	$0.554008\pi$
$594$	16.0651	+	4.33612i	0.659160	+	0.177913i
$595$		0			0
$596$	14.9507	−	25.6781i	0.612404	−	1.05182i
$597$			6.30568i			0.258074i
$598$	−2.23266	+	8.27191i	−0.0913005	+	0.338263i
$599$	−37.2899			−1.52362			−0.761812	−	0.647798i	$-0.775690\pi$
$599$	−37.2899			−1.52362			−0.761812	+	0.647798i	$0.775690\pi$
$600$		0			0
$601$	23.7882			0.970341			0.485170	−	0.874420i	$-0.338758\pi$
$601$	23.7882			0.970341			0.485170	+	0.874420i	$0.338758\pi$
$602$	2.60431	−	9.64884i	0.106144	−	0.393257i
$603$		−	18.6045i		−	0.757632i
$604$	17.5321	+	10.2078i	0.713370	+	0.415349i
$605$		0			0
$606$	1.23542	+	0.333452i	0.0501857	+	0.0135456i
$607$	32.6940			1.32701			0.663505	−	0.748172i	$-0.269068\pi$
$607$	32.6940			1.32701			0.663505	+	0.748172i	$0.269068\pi$
$608$	−17.7562	+	4.58425i	−0.720111	+	0.185916i
$609$	4.25715			0.172508
$610$		0			0
$611$		−	2.52123i		−	0.101998i
$612$	−13.9061	−	8.09659i	−0.562119	−	0.327285i
$613$		−	5.70642i		−	0.230480i	−0.993338	−	0.115240i	$-0.963236\pi$
$613$		−	5.70642i		−	0.230480i	0.993338	−	0.115240i	$-0.0367637\pi$
$614$	−4.91029	+	18.1924i	−0.198163	+	0.734185i
$615$		0			0
$616$	9.07564	−	8.97665i	0.365668	−	0.361679i
$617$	−18.9653			−0.763514			−0.381757	−	0.924263i	$-0.624681\pi$
$617$	−18.9653			−0.763514			−0.381757	+	0.924263i	$0.624681\pi$
$618$	−0.735816	+	2.72616i	−0.0295989	+	0.109662i
$619$		−	32.0663i		−	1.28885i	−0.764666	−	0.644427i	$-0.777096\pi$
$619$		−	32.0663i		−	1.28885i	0.764666	−	0.644427i	$-0.222904\pi$
$620$		0			0
$621$		−	15.8651i		−	0.636643i
$622$	−4.37537	−	1.18095i	−0.175436	−	0.0473519i
$623$	12.4076			0.497099
$624$	1.13855	+	2.00575i	0.0455785	+	0.0802944i
$625$		0			0
$626$	33.1391	+	8.94456i	1.32451	+	0.357497i
$627$			6.64901i			0.265536i
$628$	7.54486	−	12.9585i	0.301073	−	0.517098i
$629$			31.2137i			1.24457i
$630$		0			0
$631$	−11.4737			−0.456762			−0.228381	−	0.973572i	$-0.573343\pi$
$631$	−11.4737			−0.456762			−0.228381	+	0.973572i	$0.573343\pi$
$632$	17.1120	+	17.3008i	0.680680	+	0.688187i
$633$	2.00880			0.0798427
$634$	−1.39735	+	5.17711i	−0.0554958	+	0.205609i
$635$		0			0
$636$	1.45858	+	0.849236i	0.0578365	+	0.0336744i
$637$		−	6.43503i		−	0.254965i
$638$	40.1237	+	10.8298i	1.58851	+	0.428754i
$639$	−8.97215			−0.354933
$640$		0			0
$641$	−0.258289			−0.0102018			−0.00510089	−	0.999987i	$-0.501624\pi$
$641$	−0.258289			−0.0102018			−0.00510089	+	0.999987i	$0.501624\pi$
$642$	−11.2176	−	3.02774i	−0.442724	−	0.119495i
$643$			31.8119i			1.25454i	0.778802	+	0.627269i	$0.215827\pi$
$643$			31.8119i			1.25454i	−0.778802	+	0.627269i	$0.784173\pi$
$644$	−10.5177	−	6.12380i	−0.414457	−	0.241311i
$645$		0			0
$646$	3.51214	−	13.0123i	0.138183	−	0.511962i
$647$	24.3294			0.956486			0.478243	−	0.878228i	$-0.341274\pi$
$647$	24.3294			0.956486			0.478243	+	0.878228i	$0.341274\pi$
$648$	13.3273	+	13.4743i	0.523546	+	0.529320i
$649$	−22.1897			−0.871022
$650$		0			0
$651$			4.16764i			0.163343i
$652$	−9.00851	+	15.4723i	−0.352801	+	0.605942i
$653$		−	39.3785i		−	1.54100i	−0.637440	−	0.770500i	$-0.720007\pi$
$653$		−	39.3785i		−	1.54100i	0.637440	−	0.770500i	$-0.279993\pi$
$654$	−10.9338	−	2.95114i	−0.427547	−	0.115399i
$655$		0			0
$656$	4.11551	+	7.25019i	0.160684	+	0.283072i
$657$	−19.0979			−0.745082
$658$	3.45763	+	0.933248i	0.134793	+	0.0363818i
$659$		−	33.7063i		−	1.31301i	−0.754321	−	0.656506i	$-0.772034\pi$
$659$		−	33.7063i		−	1.31301i	0.754321	−	0.656506i	$-0.227966\pi$
$660$		0			0
$661$		−	32.9163i		−	1.28029i	−0.768252	−	0.640147i	$-0.778873\pi$
$661$		−	32.9163i		−	1.28029i	0.768252	−	0.640147i	$-0.221127\pi$
$662$	−0.833580	+	3.08837i	−0.0323980	+	0.120033i
$663$	−1.69508			−0.0658313
$664$	27.0995	−	26.8039i	1.05167	−	1.04019i
$665$		0			0
$666$	10.7086	−	39.6747i	0.414949	−	1.53736i
$667$		−	39.6241i		−	1.53425i
$668$	4.32003	+	2.51527i	0.167147	+	0.0973187i
$669$		−	12.2367i		−	0.473097i
$670$		0			0
$671$	−26.5862			−1.02635
$672$	−3.17215	+	0.818977i	−0.122368	+	0.0315927i
$673$	−2.87683			−0.110894			−0.0554468	−	0.998462i	$-0.517658\pi$
$673$	−2.87683			−0.110894			−0.0554468	+	0.998462i	$0.517658\pi$
$674$	39.1384	+	10.5638i	1.50755	+	0.406903i
$675$		0			0
$676$	20.2858	+	11.8111i	0.780222	+	0.454272i
$677$		−	28.6415i		−	1.10078i	−0.834907	−	0.550391i	$-0.814479\pi$
$677$		−	28.6415i		−	1.10078i	0.834907	−	0.550391i	$-0.185521\pi$
$678$	−0.561612	+	2.08074i	−0.0215686	+	0.0799105i
$679$	21.0753			0.808794
$680$		0			0
$681$	12.6724			0.485607
$682$	−10.6021	+	39.2801i	−0.405974	+	1.50411i
$683$		−	18.3147i		−	0.700792i	−0.936602	−	0.350396i	$-0.886047\pi$
$683$		−	18.3147i		−	0.700792i	0.936602	−	0.350396i	$-0.113953\pi$
$684$	−8.92833	+	15.3346i	−0.341383	+	0.586332i
$685$		0			0
$686$	19.6144	+	5.29410i	0.748881	+	0.202130i
$687$	−11.3241			−0.432043
$688$	−21.7765	+	12.3612i	−0.830220	+	0.471268i
$689$	−1.84875			−0.0704318
$690$		0			0
$691$			14.4710i			0.550502i	0.961372	+	0.275251i	$0.0887610\pi$
$691$			14.4710i			0.550502i	−0.961372	+	0.275251i	$0.911239\pi$
$692$	0.593291	−	1.01899i	0.0225535	−	0.0387361i
$693$		−	12.3516i		−	0.469198i
$694$	1.11973	−	4.14856i	0.0425045	−	0.157477i
$695$		0			0
$696$	−7.50073	−	7.58344i	−0.284314	−	0.287450i
$697$	−6.12718			−0.232084
$698$	−9.64076	+	35.7185i	−0.364908	+	1.35197i
$699$		−	10.0597i		−	0.380493i
$700$		0			0
$701$		−	18.5603i		−	0.701013i	−0.936560	−	0.350506i	$-0.886009\pi$
$701$		−	18.5603i		−	0.701013i	0.936560	−	0.350506i	$-0.113991\pi$
$702$	4.51631	+	1.21900i	0.170457	+	0.0460080i
$703$	34.4202			1.29818
$704$	−31.9810	−	0.350765i	−1.20533	−	0.0132200i
$705$		0			0
$706$	−40.2702	−	10.8693i	−1.51559	−	0.409072i
$707$		−	1.99104i		−	0.0748809i
$708$	4.92157	+	2.86551i	0.184964	+	0.107692i
$709$			43.3934i			1.62967i	0.579690	+	0.814837i	$0.303174\pi$
$709$			43.3934i			1.62967i	−0.579690	+	0.814837i	$0.696826\pi$
$710$		0			0
$711$	23.5456			0.883029
$712$	−21.8611	−	22.1022i	−0.819279	−	0.828314i
$713$	38.7910			1.45273
$714$	0.627443	−	2.32464i	0.0234815	−	0.0869976i
$715$		0			0
$716$	−10.3681	+	17.8074i	−0.387474	+	0.665494i
$717$			6.35359i			0.237279i
$718$	12.1698	+	3.28473i	0.454172	+	0.122585i
$719$	14.8496			0.553797			0.276899	−	0.960899i	$-0.410693\pi$
$719$	14.8496			0.553797			0.276899	+	0.960899i	$0.410693\pi$
$720$		0			0
$721$	4.39356			0.163625
$722$	11.5927	+	3.12899i	0.431437	+	0.116449i
$723$			10.4706i			0.389408i
$724$	17.9147	−	30.7689i	0.665795	−	1.14352i
$725$		0			0
$726$	−0.942081	+	3.49036i	−0.0349639	+	0.129539i
$727$	−6.22824			−0.230993			−0.115496	−	0.993308i	$-0.536846\pi$
$727$	−6.22824			−0.230993			−0.115496	+	0.993308i	$0.536846\pi$
$728$	2.55140	−	2.52357i	0.0945610	−	0.0935296i
$729$	13.8082			0.511416
$730$		0			0
$731$		−	18.4035i		−	0.680676i
$732$	5.89669	+	3.43326i	0.217948	+	0.126897i
$733$			43.2406i			1.59713i	0.601910	+	0.798564i	$0.294407\pi$
$733$			43.2406i			1.59713i	−0.601910	+	0.798564i	$0.705593\pi$
$734$	30.9733	+	8.35999i	1.14325	+	0.308573i
$735$		0			0
$736$	7.62276	+	29.5253i	0.280979	+	1.08832i
$737$	27.1770			1.00108
$738$	7.78806	+	2.10207i	0.286683	+	0.0773783i
$739$		−	10.0469i		−	0.369582i	−0.982778	−	0.184791i	$-0.940839\pi$
$739$		−	10.0469i		−	0.369582i	0.982778	−	0.184791i	$-0.0591608\pi$
$740$		0			0
$741$			1.86921i			0.0686670i
$742$	0.684327	−	2.53540i	0.0251224	−	0.0930773i
$743$	−5.85860			−0.214931			−0.107466	−	0.994209i	$-0.534274\pi$
$743$	−5.85860			−0.214931			−0.107466	+	0.994209i	$0.534274\pi$
$744$	7.42400	−	7.34302i	0.272177	−	0.269208i
$745$		0			0
$746$	−2.38180	+	8.82445i	−0.0872039	+	0.323086i
$747$		−	36.8814i		−	1.34942i
$748$	11.8273	−	20.3137i	0.432450	−	0.742742i
$749$			18.0786i			0.660579i
$750$		0			0
$751$	−16.0419			−0.585377			−0.292688	−	0.956208i	$-0.594550\pi$
$751$	−16.0419			−0.585377			−0.292688	+	0.956208i	$0.594550\pi$
$752$	−4.42962	−	7.80354i	−0.161532	−	0.284566i
$753$	−11.3900			−0.415075
$754$	11.2798	+	3.04452i	0.410786	+	0.110875i
$755$		0			0
$756$	−3.34348	+	5.74250i	−0.121601	+	0.208853i
$757$			15.5665i			0.565773i	0.959153	+	0.282886i	$0.0912919\pi$
$757$			15.5665i			0.565773i	−0.959153	+	0.282886i	$0.908708\pi$
$758$	1.59122	−	5.89540i	0.0577958	−	0.214130i
$759$	11.0561			0.401309
$760$		0			0
$761$	−26.9097			−0.975477			−0.487739	−	0.872990i	$-0.662178\pi$
$761$	−26.9097			−0.975477			−0.487739	+	0.872990i	$0.662178\pi$
$762$	−2.31963	+	8.59410i	−0.0840312	+	0.311331i
$763$			17.6213i			0.637933i
$764$	−32.6784	−	19.0265i	−1.18226	−	0.688356i
$765$		0			0
$766$	−15.1621	−	4.09238i	−0.547828	−	0.147864i
$767$	−6.23810			−0.225245
$768$	7.04794	+	4.20773i	0.254321	+	0.151833i
$769$	17.0952			0.616470			0.308235	−	0.951310i	$-0.400262\pi$
$769$	17.0952			0.616470			0.308235	+	0.951310i	$0.400262\pi$
$770$		0			0
$771$			6.69975i			0.241286i
$772$	17.7514	+	10.3355i	0.638886	+	0.371982i
$773$			6.32624i			0.227539i	0.993507	+	0.113770i	$0.0362926\pi$
$773$			6.32624i			0.227539i	−0.993507	+	0.113770i	$0.963707\pi$
$774$	−6.31373	+	23.3920i	−0.226942	+	0.840809i
$775$		0			0
$776$	−37.1328	−	37.5423i	−1.33299	−	1.34769i
$777$	6.14916			0.220600
$778$	5.73016	−	21.2300i	0.205436	−	0.761131i
$779$			6.75661i			0.242081i
$780$		0			0
$781$		−	13.1063i		−	0.468981i
$782$	−21.6370	−	5.84003i	−0.773738	−	0.208839i
$783$	−21.6341			−0.773138
$784$	−11.3059	−	19.9173i	−0.403782	−	0.711332i
$785$		0			0
$786$	−9.29085	−	2.50769i	−0.331394	−	0.0894462i
$787$			53.5766i			1.90980i	0.296929	+	0.954899i	$0.404037\pi$
$787$			53.5766i			1.90980i	−0.296929	+	0.954899i	$0.595963\pi$
$788$	−0.208452	+	0.358021i	−0.00742581	+	0.0127540i
$789$			15.0003i			0.534026i
$790$		0			0
$791$	3.35339			0.119233
$792$	−22.0024	+	21.7624i	−0.781822	+	0.773294i
$793$	−7.47406			−0.265412
$794$	−9.93838	+	36.8212i	−0.352700	+	1.30673i
$795$		0			0
$796$	−21.2438	−	12.3689i	−0.752966	−	0.438403i
$797$		−	41.6834i		−	1.47650i	−0.674527	−	0.738251i	$-0.735652\pi$
$797$		−	41.6834i		−	1.47650i	0.674527	−	0.738251i	$-0.264348\pi$
$798$	−2.56345	−	0.691898i	−0.0907450	−	0.0244929i
$799$	6.59483			0.233308
$800$		0			0
$801$	−30.0802			−1.06283
$802$	49.3018	+	13.3070i	1.74091	+	0.469887i
$803$		−	27.8979i		−	0.984495i
$804$	−6.02773	−	3.50956i	−0.212582	−	0.123772i
$805$		0			0
$806$	−2.98051	+	11.0426i	−0.104984	+	0.388961i
$807$	−10.9914			−0.386917
$808$	−3.54674	+	3.50805i	−0.124774	+	0.123413i
$809$	−26.9010			−0.945788			−0.472894	−	0.881119i	$-0.656791\pi$
$809$	−26.9010			−0.945788			−0.472894	+	0.881119i	$0.656791\pi$
$810$		0			0
$811$			5.88980i			0.206819i	0.994639	+	0.103409i	$0.0329752\pi$
$811$			5.88980i			0.206819i	−0.994639	+	0.103409i	$0.967025\pi$
$812$	−8.35058	+	14.3423i	−0.293048	+	0.503315i
$813$		−	0.594069i		−	0.0208349i
$814$	57.9560	+	15.6429i	2.03136	+	0.548282i
$815$		0			0
$816$	−5.24649	+	2.97813i	−0.183664	+	0.104255i
$817$	−20.2940			−0.709997
$818$	21.1833	+	5.71758i	0.740658	+	0.199911i
$819$		−	3.47234i		−	0.121334i
$820$		0			0
$821$			48.2445i			1.68374i	0.539677	+	0.841872i	$0.318546\pi$
$821$			48.2445i			1.68374i	−0.539677	+	0.841872i	$0.681454\pi$
$822$	2.53084	−	9.37664i	0.0882733	−	0.327048i
$823$	51.9289			1.81013			0.905063	−	0.425277i	$-0.139823\pi$
$823$	51.9289			1.81013			0.905063	+	0.425277i	$0.139823\pi$
$824$	−7.74107	−	7.82644i	−0.269673	−	0.272647i
$825$		0			0
$826$	2.30907	−	8.55498i	0.0803428	−	0.297666i
$827$		−	28.2849i		−	0.983562i	−0.870719	−	0.491781i	$-0.836346\pi$
$827$		−	28.2849i		−	0.983562i	0.870719	−	0.491781i	$-0.163654\pi$
$828$	25.4985	+	14.8461i	0.886136	+	0.515939i
$829$			14.2294i			0.494209i	0.968989	+	0.247104i	$0.0794790\pi$
$829$			14.2294i			0.494209i	−0.968989	+	0.247104i	$0.920521\pi$
$830$		0			0
$831$	8.62168			0.299083
$832$	−8.99068	−	0.0986092i	−0.311696	−	0.00341866i
$833$	16.8323			0.583203
$834$	14.1910	+	3.83027i	0.491393	+	0.132632i
$835$		0			0
$836$	−22.4004	−	13.0423i	−0.774735	−	0.451078i
$837$		−	21.1792i		−	0.732060i
$838$	9.92656	−	36.7774i	0.342907	−	1.27045i
$839$	5.04346			0.174120			0.0870598	−	0.996203i	$-0.472253\pi$
$839$	5.04346			0.174120			0.0870598	+	0.996203i	$0.472253\pi$
$840$		0			0
$841$	−25.0325			−0.863191
$842$	−2.26508	+	8.39202i	−0.0780600	+	0.289208i
$843$		−	4.61277i		−	0.158872i
$844$	−3.94035	+	6.76763i	−0.135633	+	0.232952i
$845$		0			0
$846$	−8.38247	−	2.26251i	−0.288195	−	0.0777866i
$847$	5.62517			0.193283
$848$	−5.72214	+	3.24813i	−0.196499	+	0.111541i
$849$	7.92101			0.271848
$850$		0			0
$851$		−	57.2343i		−	1.96197i
$852$	−1.69251	+	2.90692i	−0.0579845	+	0.0995895i
$853$			46.2026i			1.58195i	0.611850	+	0.790974i	$0.290426\pi$
$853$			46.2026i			1.58195i	−0.611850	+	0.790974i	$0.709574\pi$
$854$	2.76657	−	10.2500i	0.0946701	−	0.350748i
$855$		0			0
$856$	32.2043	−	31.8530i	1.10072	−	1.08871i
$857$	−41.5405			−1.41900			−0.709499	−	0.704707i	$-0.751079\pi$
$857$	−41.5405			−1.41900			−0.709499	+	0.704707i	$0.751079\pi$
$858$	−0.849494	+	3.14733i	−0.0290012	+	0.107448i
$859$		−	37.9644i		−	1.29533i	−0.761925	−	0.647665i	$-0.775746\pi$
$859$		−	37.9644i		−	1.29533i	0.761925	−	0.647665i	$-0.224254\pi$
$860$		0			0
$861$			1.20707i			0.0411368i
$862$	50.3681	+	13.5948i	1.71554	+	0.463041i
$863$	2.89022			0.0983843			0.0491922	−	0.998789i	$-0.484335\pi$
$863$	2.89022			0.0983843			0.0491922	+	0.998789i	$0.484335\pi$
$864$	16.1203	−	4.16189i	0.548424	−	0.141590i
$865$		0			0
$866$	15.8141	+	4.26838i	0.537386	+	0.145046i
$867$			4.28761i			0.145615i
$868$	−14.0407	−	8.17501i	−0.476574	−	0.277478i
$869$			34.3949i			1.16677i
$870$		0			0
$871$	7.64015			0.258877
$872$	31.3896	−	31.0472i	1.06299	−	1.05139i
$873$	−51.0935			−1.72925
$874$	−6.43996	+	23.8597i	−0.217835	+	0.807067i
$875$		0			0
$876$	−3.60265	+	6.18762i	−0.121722	+	0.209060i
$877$		−	43.0916i		−	1.45510i	−0.686055	−	0.727550i	$-0.740659\pi$
$877$		−	43.0916i		−	1.45510i	0.686055	−	0.727550i	$-0.259341\pi$
$878$	−5.66860	−	1.53001i	−0.191306	−	0.0516353i
$879$	−0.831423			−0.0280432
$880$		0			0
$881$	−2.06410			−0.0695414			−0.0347707	−	0.999395i	$-0.511070\pi$
$881$	−2.06410			−0.0695414			−0.0347707	+	0.999395i	$0.511070\pi$
$882$	−21.3949	−	5.77469i	−0.720405	−	0.194444i
$883$			51.4835i			1.73256i	0.499562	+	0.866278i	$0.333494\pi$
$883$			51.4835i			1.73256i	−0.499562	+	0.866278i	$0.666506\pi$
$884$	3.32497	−	5.71070i	0.111831	−	0.192071i
$885$		0			0
$886$	5.79783	−	21.4807i	0.194782	−	0.721657i
$887$	−55.5749			−1.86602			−0.933012	−	0.359845i	$-0.882829\pi$
$887$	−55.5749			−1.86602			−0.933012	+	0.359845i	$0.882829\pi$
$888$	−10.8343	−	10.9538i	−0.363575	−	0.367585i
$889$	13.8505			0.464531
$890$		0			0
$891$			26.7877i			0.897422i
$892$	41.2252	+	24.0028i	1.38032	+	0.803672i
$893$		−	7.27229i		−	0.243358i
$894$	−10.4066	−	2.80884i	−0.348049	−	0.0939415i
$895$		0			0
$896$	3.46319	−	12.2934i	0.115697	−	0.410694i
$897$	3.10814			0.103778
$898$	−28.2439	−	7.62329i	−0.942511	−	0.254393i
$899$		−	52.8965i		−	1.76420i
$900$		0			0
$901$		−	4.83582i		−	0.161105i
$902$	−3.07066	+	11.3766i	−0.102242	+	0.378801i
$903$	−3.62552			−0.120650
$904$	−5.90838	−	5.97354i	−0.196510	−	0.198677i
$905$		0			0
$906$	1.91777	−	7.10525i	0.0637137	−	0.236056i
$907$		−	15.8669i		−	0.526852i	−0.964680	−	0.263426i	$-0.915147\pi$
$907$		−	15.8669i		−	0.526852i	0.964680	−	0.263426i	$-0.0848526\pi$
$908$	−24.8574	+	42.6931i	−0.824923	+	1.41682i
$909$			4.82696i			0.160100i
$910$		0			0
$911$	−30.4293			−1.00817			−0.504084	−	0.863655i	$-0.668170\pi$
$911$	−30.4293			−1.00817			−0.504084	+	0.863655i	$0.668170\pi$
$912$	3.28406	+	5.78545i	0.108746	+	0.191575i
$913$	53.8755			1.78302
$914$	−39.2112	−	10.5835i	−1.29699	−	0.350070i
$915$		0			0
$916$	22.2128	−	38.1509i	0.733931	−	1.26054i
$917$			14.9734i			0.494465i
$918$	−3.18855	+	11.8134i	−0.105238	+	0.389901i
$919$	−15.1819			−0.500803			−0.250402	−	0.968142i	$-0.580563\pi$
$919$	−15.1819			−0.500803			−0.250402	+	0.968142i	$0.580563\pi$
$920$		0			0
$921$	6.83572			0.225245
$922$	−10.2104	+	37.8290i	−0.336261	+	1.24583i
$923$		−	3.68452i		−	0.121278i
$924$	−4.00183	−	2.33001i	−0.131651	−	0.0766517i
$925$		0			0
$926$	−36.8061	−	9.93432i	−1.20952	−	0.326462i
$927$	−10.6515			−0.349840
$928$	40.2616	−	10.3946i	1.32165	−	0.341220i
$929$	−8.00028			−0.262481			−0.131240	−	0.991351i	$-0.541896\pi$
$929$	−8.00028			−0.262481			−0.131240	+	0.991351i	$0.541896\pi$
$930$		0			0
$931$		−	18.5614i		−	0.608325i
$932$	33.8911	+	19.7326i	1.11014	+	0.646362i
$933$			1.64403i			0.0538231i
$934$	−11.5367	+	42.7427i	−0.377491	+	1.39858i
$935$		0			0
$936$	−6.18544	+	6.11797i	−0.202178	+	0.199972i
$937$	−10.0303			−0.327676			−0.163838	−	0.986487i	$-0.552387\pi$
$937$	−10.0303			−0.327676			−0.163838	+	0.986487i	$0.552387\pi$
$938$	−2.82805	+	10.4778i	−0.0923391	+	0.342112i
$939$		−	12.4519i		−	0.406353i
$940$		0			0
$941$			4.23635i			0.138101i	0.997613	+	0.0690506i	$0.0219970\pi$
$941$			4.23635i			0.138101i	−0.997613	+	0.0690506i	$0.978003\pi$
$942$	−5.25168	−	1.41748i	−0.171109	−	0.0461839i
$943$	11.2350			0.365861
$944$	−19.3078	+	10.9599i	−0.628414	+	0.356714i
$945$		0			0
$946$	−34.1706	−	9.22296i	−1.11098	−	0.299864i
$947$			3.33715i			0.108443i	0.998529	+	0.0542213i	$0.0172677\pi$
$947$			3.33715i			0.108443i	−0.998529	+	0.0542213i	$0.982732\pi$
$948$	4.44166	−	7.62863i	0.144258	−	0.247767i
$949$		−	7.84281i		−	0.254588i
$950$		0			0
$951$	1.94528			0.0630800
$952$	6.60095	+	6.67374i	0.213938	+	0.216297i
$953$	10.9309			0.354086			0.177043	−	0.984203i	$-0.443347\pi$
$953$	10.9309			0.354086			0.177043	+	0.984203i	$0.443347\pi$
$954$	−1.65904	+	6.14665i	−0.0537134	+	0.199005i
$955$		0			0
$956$	−21.4052	−	12.4629i	−0.692294	−	0.403078i
$957$		−	15.0763i		−	0.487349i
$958$	−44.6317	−	12.0465i	−1.44199	−	0.389205i
$959$	−15.1117			−0.487981
$960$		0			0
$961$	20.7844			0.670463
$962$	16.2929	+	4.39761i	0.525305	+	0.141785i
$963$		−	43.8287i		−	1.41236i
$964$	−35.2755	−	20.5386i	−1.13615	−	0.661505i
$965$		0			0
$966$	−1.15050	+	4.26253i	−0.0370167	+	0.137145i
$967$	40.7599			1.31075			0.655375	−	0.755304i	$-0.272511\pi$
$967$	40.7599			1.31075			0.655375	+	0.755304i	$0.272511\pi$
$968$	−9.91106	−	10.0204i	−0.318553	−	0.322067i
$969$	−4.88932			−0.157068
$970$		0			0
$971$		−	56.9328i		−	1.82706i	−0.406772	−	0.913530i	$-0.633346\pi$
$971$		−	56.9328i		−	1.82706i	0.406772	−	0.913530i	$-0.366654\pi$
$972$	12.3445	−	21.2020i	0.395951	−	0.680054i
$973$		−	22.8706i		−	0.733197i
$974$	−24.0361	−	6.48756i	−0.770165	−	0.207875i
$975$		0			0
$976$	−23.1332	+	13.1314i	−0.740477	+	0.420326i
$977$	−17.1254			−0.547892			−0.273946	−	0.961745i	$-0.588329\pi$
$977$	−17.1254			−0.547892			−0.273946	+	0.961745i	$0.588329\pi$
$978$	6.27047	+	1.69246i	0.200508	+	0.0541189i
$979$		−	43.9405i		−	1.40434i
$980$		0			0
$981$		−	42.7199i		−	1.36394i
$982$	−0.483250	+	1.79041i	−0.0154211	+	0.0571344i
$983$	−51.3738			−1.63857			−0.819284	−	0.573388i	$-0.805629\pi$
$983$	−51.3738			−1.63857			−0.819284	+	0.573388i	$0.805629\pi$
$984$	2.15020	−	2.12675i	0.0685460	−	0.0677983i
$985$		0			0
$986$	−7.96363	+	29.5048i	−0.253614	+	0.939625i
$987$		−	1.29919i		−	0.0413538i
$988$	−6.29734	−	3.66653i	−0.200345	−	0.116648i
$989$			33.7451i			1.07303i
$990$		0			0
$991$	−23.9933			−0.762171			−0.381085	−	0.924540i	$-0.624450\pi$
$991$	−23.9933			−0.762171			−0.381085	+	0.924540i	$0.624450\pi$
$992$	10.1761	+	39.4151i	0.323090	+	1.25143i
$993$	1.16045			0.0368256
$994$	5.05299	+	1.36385i	0.160271	+	0.0432587i
$995$		0			0
$996$	−11.9493	−	6.95732i	−0.378629	−	0.220451i
$997$		−	7.90228i		−	0.250268i	−0.992140	−	0.125134i	$-0.960064\pi$
$997$		−	7.90228i		−	0.250268i	0.992140	−	0.125134i	$-0.0399361\pi$
$998$	−7.83679	+	29.0349i	−0.248069	+	0.919084i
$999$	−31.2489			−0.988673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.d.c.501.36	yes	40
4.3	odd	2		4000.2.d.c.2001.22		40
5.2	odd	4		1000.2.f.c.749.10		20
5.3	odd	4		1000.2.f.d.749.11		20
5.4	even	2	inner	1000.2.d.c.501.5	✓	40
8.3	odd	2		4000.2.d.c.2001.21		40
8.5	even	2	inner	1000.2.d.c.501.35	yes	40
20.3	even	4		4000.2.f.d.3249.7		20
20.7	even	4		4000.2.f.c.3249.14		20
20.19	odd	2		4000.2.d.c.2001.19		40
40.3	even	4		4000.2.f.c.3249.13		20
40.13	odd	4		1000.2.f.c.749.9		20
40.19	odd	2		4000.2.d.c.2001.20		40
40.27	even	4		4000.2.f.d.3249.8		20
40.29	even	2	inner	1000.2.d.c.501.6	yes	40
40.37	odd	4		1000.2.f.d.749.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.d.c.501.5	✓	40	5.4	even	2	inner
1000.2.d.c.501.6	yes	40	40.29	even	2	inner
1000.2.d.c.501.35	yes	40	8.5	even	2	inner
1000.2.d.c.501.36	yes	40	1.1	even	1	trivial
1000.2.f.c.749.9		20	40.13	odd	4
1000.2.f.c.749.10		20	5.2	odd	4
1000.2.f.d.749.11		20	5.3	odd	4
1000.2.f.d.749.12		20	40.37	odd	4
4000.2.d.c.2001.19		40	20.19	odd	2
4000.2.d.c.2001.20		40	40.19	odd	2
4000.2.d.c.2001.21		40	8.3	odd	2
4000.2.d.c.2001.22		40	4.3	odd	2
4000.2.f.c.3249.13		20	40.3	even	4
4000.2.f.c.3249.14		20	20.7	even	4
4000.2.f.d.3249.7		20	20.3	even	4
4000.2.f.d.3249.8		20	40.27	even	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36535 + 0.368522i) q^{2} -0.513027i q^{3} +(1.72838 + 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} -1.12889 q^{7} +(1.98900 + 2.01094i) q^{8} +2.73680 q^{9} +O(q^{10})\)	\(q+(1.36535 + 0.368522i) q^{2} -0.513027i q^{3} +(1.72838 + 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} -1.12889 q^{7} +(1.98900 + 2.01094i) q^{8} +2.73680 q^{9} +3.99787i q^{11} +(0.516272 - 0.886708i) q^{12} +1.12390i q^{13} +(-1.54133 - 0.416020i) q^{14} +(1.97462 + 3.47863i) q^{16} -2.93982 q^{17} +(3.73671 + 1.00857i) q^{18} +3.24181i q^{19} +0.579150i q^{21} +(-1.47330 + 5.45850i) q^{22} +5.39053 q^{23} +(1.03167 - 1.02041i) q^{24} +(-0.414183 + 1.53452i) q^{26} -2.94314i q^{27} +(-1.95115 - 1.13603i) q^{28} -7.35068i q^{29} +7.19613 q^{31} +(1.41410 + 5.47725i) q^{32} +2.05101 q^{33} +(-4.01389 - 1.08339i) q^{34} +(4.73025 + 2.75411i) q^{36} -10.6176i q^{37} +(-1.19468 + 4.42622i) q^{38} +0.576592 q^{39} +2.08421 q^{41} +(-0.213429 + 0.790745i) q^{42} +6.26007i q^{43} +(-4.02315 + 6.90984i) q^{44} +(7.35999 + 1.98653i) q^{46} -2.24328 q^{47} +(1.78463 - 1.01303i) q^{48} -5.72561 q^{49} +1.50821i q^{51} +(-1.13101 + 1.94253i) q^{52} +1.64494i q^{53} +(1.08461 - 4.01842i) q^{54} +(-2.24536 - 2.27012i) q^{56} +1.66314 q^{57} +(2.70889 - 10.0363i) q^{58} +5.55039i q^{59} +6.65010i q^{61} +(9.82527 + 2.65193i) q^{62} -3.08954 q^{63} +(-0.0877382 + 7.99952i) q^{64} +(2.80036 + 0.755843i) q^{66} -6.79788i q^{67} +(-5.08113 - 2.95841i) q^{68} -2.76549i q^{69} -3.27833 q^{71} +(5.44351 + 5.50354i) q^{72} -6.97819 q^{73} +(3.91280 - 14.4967i) q^{74} +(-3.26232 + 5.60310i) q^{76} -4.51314i q^{77} +(0.787253 + 0.212487i) q^{78} +8.60333 q^{79} +6.70050 q^{81} +(2.84568 + 0.768075i) q^{82} -13.4761i q^{83} +(-0.582813 + 1.00099i) q^{84} +(-2.30697 + 8.54721i) q^{86} -3.77110 q^{87} +(-8.03946 + 7.95176i) q^{88} -10.9910 q^{89} -1.26876i q^{91} +(9.31691 + 5.42463i) q^{92} -3.69181i q^{93} +(-3.06287 - 0.826697i) q^{94} +(2.80998 - 0.725472i) q^{96} -18.6691 q^{97} +(-7.81749 - 2.11001i) q^{98} +10.9414i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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