LMFDB - Embedded newform 1000.2.d.c.501.6

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			501.6
Character	$\chi$	$=$	1000.501
Dual form			1000.2.d.c.501.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36535 + 0.368522i) q^{2} -0.513027i q^{3} +(1.72838 - 1.00633i) q^{4} +(0.189062 + 0.700464i) q^{6} +1.12889 q^{7} +(-1.98900 + 2.01094i) q^{8} +2.73680 q^{9} +O(q^{10})$	\(q+(-1.36535 + 0.368522i) q^{2} -0.513027i q^{3} +(1.72838 - 1.00633i) q^{4} +(0.189062 + 0.700464i) q^{6} +1.12889 q^{7} +(-1.98900 + 2.01094i) q^{8} +2.73680 q^{9} -3.99787i q^{11} +(-0.516272 - 0.886708i) q^{12} +1.12390i q^{13} +(-1.54133 + 0.416020i) q^{14} +(1.97462 - 3.47863i) q^{16} +2.93982 q^{17} +(-3.73671 + 1.00857i) q^{18} -3.24181i q^{19} -0.579150i q^{21} +(1.47330 + 5.45850i) q^{22} -5.39053 q^{23} +(1.03167 + 1.02041i) q^{24} +(-0.414183 - 1.53452i) q^{26} -2.94314i q^{27} +(1.95115 - 1.13603i) q^{28} +7.35068i q^{29} +7.19613 q^{31} +(-1.41410 + 5.47725i) q^{32} -2.05101 q^{33} +(-4.01389 + 1.08339i) q^{34} +(4.73025 - 2.75411i) q^{36} -10.6176i q^{37} +(1.19468 + 4.42622i) q^{38} +0.576592 q^{39} +2.08421 q^{41} +(0.213429 + 0.790745i) q^{42} +6.26007i q^{43} +(-4.02315 - 6.90984i) q^{44} +(7.35999 - 1.98653i) q^{46} +2.24328 q^{47} +(-1.78463 - 1.01303i) q^{48} -5.72561 q^{49} -1.50821i q^{51} +(1.13101 + 1.94253i) q^{52} +1.64494i q^{53} +(1.08461 + 4.01842i) q^{54} +(-2.24536 + 2.27012i) q^{56} -1.66314 q^{57} +(-2.70889 - 10.0363i) q^{58} -5.55039i q^{59} -6.65010i q^{61} +(-9.82527 + 2.65193i) q^{62} +3.08954 q^{63} +(-0.0877382 - 7.99952i) q^{64} +(2.80036 - 0.755843i) q^{66} -6.79788i q^{67} +(5.08113 - 2.95841i) q^{68} +2.76549i q^{69} -3.27833 q^{71} +(-5.44351 + 5.50354i) q^{72} +6.97819 q^{73} +(3.91280 + 14.4967i) q^{74} +(-3.26232 - 5.60310i) q^{76} -4.51314i q^{77} +(-0.787253 + 0.212487i) q^{78} +8.60333 q^{79} +6.70050 q^{81} +(-2.84568 + 0.768075i) q^{82} -13.4761i q^{83} +(-0.582813 - 1.00099i) q^{84} +(-2.30697 - 8.54721i) q^{86} +3.77110 q^{87} +(8.03946 + 7.95176i) q^{88} -10.9910 q^{89} +1.26876i q^{91} +(-9.31691 + 5.42463i) q^{92} -3.69181i q^{93} +(-3.06287 + 0.826697i) q^{94} +(2.80998 + 0.725472i) q^{96} +18.6691 q^{97} +(7.81749 - 2.11001i) q^{98} -10.9414i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.431566\pi$
$7$	1.12889			0.426679			0.213340	+	0.976978i	$0.431566\pi$
$8$	−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	$-0.794091\pi$
$11$		−	3.99787i		−	1.20540i	0.797967	−	0.602701i	$-0.205909\pi$
$12$	−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	$-0.383968\pi$
$17$	2.93982			0.713010			0.356505	+	0.934293i	$0.383968\pi$
$18$	−3.73671	+	1.00857i	−0.880750	+	0.237723i
$19$		−	3.24181i		−	0.743723i	−0.928288	−	0.371862i	$-0.878720\pi$
$19$		−	3.24181i		−	0.743723i	0.928288	−	0.371862i	$-0.121280\pi$
$20$		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	$-0.689969\pi$
$23$	−5.39053			−1.12400			−0.562002	+	0.827136i	$0.689969\pi$
$24$	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	$0.239105\pi$
$29$			7.35068i			1.36499i	−0.730891	+	0.682494i	$0.760895\pi$
$30$		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	$-0.447687\pi$
$47$	2.24328			0.327216			0.163608	+	0.986525i	$0.447687\pi$
$48$	−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	$-0.882333\pi$
$59$		−	5.55039i		−	0.722599i	0.932450	−	0.361299i	$-0.117667\pi$
$60$		0			0
$61$		−	6.65010i		−	0.851458i	−0.904851	−	0.425729i	$-0.860018\pi$
$61$		−	6.65010i		−	0.851458i	0.904851	−	0.425729i	$-0.139982\pi$
$62$	−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	$-0.366098\pi$
$73$	6.97819			0.816736			0.408368	+	0.912817i	$0.366098\pi$
$74$	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	$-0.103324\pi$
$97$	18.6691			1.89556			0.947778	+	0.318931i	$0.103324\pi$
$98$	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	$-0.972033\pi$
$101$		−	1.76372i		−	0.175497i	0.996143	−	0.0877485i	$-0.0279672\pi$
$102$	0.555807	+	2.05923i	0.0550331	+	0.203895i
$103$	3.89194			0.383484			0.191742	−	0.981445i	$-0.438586\pi$
$103$	3.89194			0.383484			0.191742	+	0.981445i	$0.438586\pi$
$104$	−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	$0.268773\pi$
$109$			15.6094i			1.49511i	−0.664199	+	0.747556i	$0.731227\pi$
$110$		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	$-0.455379\pi$
$113$	2.97052			0.279443			0.139722	+	0.990191i	$0.455379\pi$
$114$	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	$-0.316774\pi$
$127$	12.2692			1.08871			0.544356	+	0.838855i	$0.316774\pi$
$128$	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	$0.196726\pi$
$131$			13.2639i			1.15887i	−0.815019	+	0.579434i	$0.803274\pi$
$132$	−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	$-0.693769\pi$
$137$	−13.3863			−1.14367			−0.571836	+	0.820368i	$0.693769\pi$
$138$	−1.01914	−	3.77587i	−0.0867552	−	0.321424i
$139$		−	20.2594i		−	1.71838i	−0.511657	−	0.859190i	$-0.670968\pi$
$139$		−	20.2594i		−	1.71838i	0.511657	−	0.859190i	$-0.329032\pi$
$140$		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	$0.208251\pi$
$149$			14.8567i			1.21711i	−0.793512	+	0.608555i	$0.791749\pi$
$150$		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	$-0.530831\pi$
$167$	−2.49946			−0.193414			−0.0967070	+	0.995313i	$0.530831\pi$
$168$	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	$-0.874188\pi$
$179$		−	10.3029i		−	0.770077i	0.922901	−	0.385038i	$-0.125812\pi$
$180$		0			0
$181$			17.8021i			1.32322i	0.749848	+	0.661610i	$0.230127\pi$
$181$			17.8021i			1.32322i	−0.749848	+	0.661610i	$0.769873\pi$
$182$	−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	$-0.620520\pi$
$193$	−10.2705			−0.739288			−0.369644	+	0.929173i	$0.620520\pi$
$194$	−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	$-0.956967\pi$
$211$		−	3.91559i		−	0.269560i	0.990876	−	0.134780i	$-0.0430328\pi$
$212$	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	$-0.794437\pi$
$223$	−23.8519			−1.59724			−0.798621	+	0.601834i	$0.794437\pi$
$224$	−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	$0.260163\pi$
$229$			22.0732i			1.45864i	−0.684175	+	0.729318i	$0.739837\pi$
$230$		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	$-0.722019\pi$
$233$	−19.6085			−1.28460			−0.642299	+	0.766454i	$0.722019\pi$
$234$	−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	$0.247118\pi$
$251$			22.2016i			1.40135i	−0.713479	+	0.700676i	$0.752882\pi$
$252$	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	$-0.366468\pi$
$257$	13.0592			0.814614			0.407307	+	0.913291i	$0.366468\pi$
$258$	−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	$-0.142487\pi$
$263$	29.2389			1.80295			0.901473	+	0.432835i	$0.142487\pi$
$264$	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	$0.226550\pi$
$269$			21.4247i			1.30629i	−0.757235	+	0.653143i	$0.773450\pi$
$270$		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	$-0.740614\pi$
$313$	−24.2715			−1.37190			−0.685952	+	0.727647i	$0.740614\pi$
$314$	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	$-0.980200\pi$
$331$		−	2.26196i		−	0.124328i	0.998066	−	0.0621642i	$-0.0198002\pi$
$332$	−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	$-0.785163\pi$
$337$	−28.6654			−1.56150			−0.780751	+	0.624843i	$0.785163\pi$
$338$	−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	$-0.753106\pi$
$349$		−	26.1606i		−	1.40035i	0.713973	−	0.700173i	$-0.246894\pi$
$350$		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	$-0.212708\pi$
$353$	29.4943			1.56983			0.784913	+	0.619606i	$0.212708\pi$
$354$	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	$-0.701693\pi$
$367$	−22.6852			−1.18416			−0.592079	+	0.805880i	$0.701693\pi$
$368$	−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	$0.0353722\pi$
$379$			4.31785i			0.221793i	−0.993832	+	0.110897i	$0.964628\pi$
$380$		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	$-0.408433\pi$
$383$	11.1049			0.567432			0.283716	+	0.958908i	$0.408433\pi$
$384$	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	$0.128973\pi$
$389$			15.5490i			0.788368i	−0.919032	+	0.394184i	$0.871027\pi$
$390$		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	$0.228580\pi$
$419$			26.9362i			1.31592i	−0.753054	+	0.657959i	$0.771420\pi$
$420$		0			0
$421$		−	6.14641i		−	0.299557i	−0.988720	−	0.149779i	$-0.952144\pi$
$421$		−	6.14641i		−	0.299557i	0.988720	−	0.149779i	$-0.0478561\pi$
$422$	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	$-0.589774\pi$
$433$	−11.5824			−0.556617			−0.278308	+	0.960492i	$0.589774\pi$
$434$	−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	$-0.265564\pi$
$457$	28.7187			1.34340			0.671702	+	0.740821i	$0.265564\pi$
$458$	−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	$-0.776771\pi$
$461$		−	27.7063i		−	1.29041i	0.764008	−	0.645207i	$-0.223229\pi$
$462$	3.16129	−	0.853262i	0.147077	−	0.0396973i
$463$	26.9572			1.25281			0.626404	−	0.779499i	$-0.284526\pi$
$463$	26.9572			1.25281			0.626404	+	0.779499i	$0.284526\pi$
$464$	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	$-0.369405\pi$
$487$	17.6043			0.797726			0.398863	+	0.917011i	$0.369405\pi$
$488$	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	$-0.990580\pi$
$491$		−	1.31132i		−	0.0591790i	0.999562	−	0.0295895i	$-0.00942000\pi$
$492$	−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	$-0.842091\pi$
$499$		−	21.2655i		−	0.951973i	0.879453	−	0.475987i	$-0.157909\pi$
$500$		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	$-0.779078\pi$
$503$	−34.4786			−1.53733			−0.768663	+	0.639654i	$0.779078\pi$
$504$	−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	$0.0611704\pi$
$509$			8.61795i			0.381984i	−0.981592	+	0.190992i	$0.938830\pi$
$510$		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	$-0.982674\pi$
$541$		−	2.53085i		−	0.108810i	0.998519	−	0.0544050i	$-0.0173262\pi$
$542$	−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	$-0.859849\pi$
$571$		−	20.3690i		−	0.852416i	0.904625	−	0.426208i	$-0.140151\pi$
$572$	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	$-0.879336\pi$
$577$	−44.6310			−1.85801			−0.929007	+	0.370063i	$0.879336\pi$
$578$	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	$-0.445992\pi$
$593$	8.22399			0.337719			0.168859	+	0.985640i	$0.445992\pi$
$594$	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	$-0.730932\pi$
$607$	−32.6940			−1.32701			−0.663505	+	0.748172i	$0.730932\pi$
$608$	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	$-0.375319\pi$
$617$	18.9653			0.763514			0.381757	+	0.924263i	$0.375319\pi$
$618$	0.735816	+	2.72616i	0.0295989	+	0.109662i
$619$			32.0663i			1.28885i	0.764666	+	0.644427i	$0.222904\pi$
$619$			32.0663i			1.28885i	−0.764666	+	0.644427i	$0.777096\pi$
$620$		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	$-0.658726\pi$
$647$	−24.3294			−0.956486			−0.478243	+	0.878228i	$0.658726\pi$
$648$	−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	$0.227966\pi$
$659$			33.7063i			1.31301i	−0.754321	+	0.656506i	$0.772034\pi$
$660$		0			0
$661$			32.9163i			1.28029i	0.768252	+	0.640147i	$0.221127\pi$
$661$			32.9163i			1.28029i	−0.768252	+	0.640147i	$0.778873\pi$
$662$	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	$-0.482342\pi$
$673$	2.87683			0.110894			0.0554468	+	0.998462i	$0.482342\pi$
$674$	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	$-0.911239\pi$
$691$		−	14.4710i		−	0.550502i	0.961372	−	0.275251i	$-0.0887610\pi$
$692$	−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	$0.113991\pi$
$701$			18.5603i			0.701013i	−0.936560	+	0.350506i	$0.886009\pi$
$702$	−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	$-0.696826\pi$
$709$		−	43.3934i		−	1.62967i	0.579690	−	0.814837i	$-0.303174\pi$
$710$		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	$-0.463154\pi$
$727$	6.22824			0.230993			0.115496	+	0.993308i	$0.463154\pi$
$728$	−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	$0.0591608\pi$
$739$			10.0469i			0.369582i	−0.982778	+	0.184791i	$0.940839\pi$
$740$		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	$-0.465726\pi$
$743$	5.85860			0.214931			0.107466	+	0.994209i	$0.465726\pi$
$744$	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	$-0.967025\pi$
$811$		−	5.88980i		−	0.206819i	0.994639	−	0.103409i	$-0.0329752\pi$
$812$	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	$-0.681454\pi$
$821$		−	48.2445i		−	1.68374i	0.539677	−	0.841872i	$-0.318546\pi$
$822$	−2.53084	−	9.37664i	−0.0882733	−	0.327048i
$823$	−51.9289			−1.81013			−0.905063	−	0.425277i	$-0.860177\pi$
$823$	−51.9289			−1.81013			−0.905063	+	0.425277i	$0.860177\pi$
$824$	−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	$-0.920521\pi$
$829$		−	14.2294i		−	0.494209i	0.968989	−	0.247104i	$-0.0794790\pi$
$830$		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	$-0.248921\pi$
$857$	41.5405			1.41900			0.709499	+	0.704707i	$0.248921\pi$
$858$	0.849494	+	3.14733i	0.0290012	+	0.107448i
$859$			37.9644i			1.29533i	0.761925	+	0.647665i	$0.224254\pi$
$859$			37.9644i			1.29533i	−0.761925	+	0.647665i	$0.775746\pi$
$860$		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	$-0.515665\pi$
$863$	−2.89022			−0.0983843			−0.0491922	+	0.998789i	$0.515665\pi$
$864$	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	$-0.117171\pi$
$887$	55.5749			1.86602			0.933012	+	0.359845i	$0.117171\pi$
$888$	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	$-0.447613\pi$
$937$	10.0303			0.327676			0.163838	+	0.986487i	$0.447613\pi$
$938$	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	$-0.978003\pi$
$941$		−	4.23635i		−	0.138101i	0.997613	−	0.0690506i	$-0.0219970\pi$
$942$	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	$-0.556653\pi$
$953$	−10.9309			−0.354086			−0.177043	+	0.984203i	$0.556653\pi$
$954$	−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	$-0.727489\pi$
$967$	−40.7599			−1.31075			−0.655375	+	0.755304i	$0.727489\pi$
$968$	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	$0.366654\pi$
$971$			56.9328i			1.82706i	−0.406772	+	0.913530i	$0.633346\pi$
$972$	−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	$-0.411671\pi$
$977$	17.1254			0.547892			0.273946	+	0.961745i	$0.411671\pi$
$978$	−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	$-0.194371\pi$
$983$	51.3738			1.63857			0.819284	+	0.573388i	$0.194371\pi$
$984$	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.501.6	yes	40
4.3	odd	2		4000.2.d.c.2001.20		40
5.2	odd	4		1000.2.f.c.749.9		20
5.3	odd	4		1000.2.f.d.749.12		20
5.4	even	2	inner	1000.2.d.c.501.35	yes	40
8.3	odd	2		4000.2.d.c.2001.19		40
8.5	even	2	inner	1000.2.d.c.501.5	✓	40
20.3	even	4		4000.2.f.d.3249.8		20
20.7	even	4		4000.2.f.c.3249.13		20
20.19	odd	2		4000.2.d.c.2001.21		40
40.3	even	4		4000.2.f.c.3249.14		20
40.13	odd	4		1000.2.f.c.749.10		20
40.19	odd	2		4000.2.d.c.2001.22		40
40.27	even	4		4000.2.f.d.3249.7		20
40.29	even	2	inner	1000.2.d.c.501.36	yes	40
40.37	odd	4		1000.2.f.d.749.11		20

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