LMFDB - Embedded newform 1000.2.f.d.749.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(749,1000)]

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, 1]))

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

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

chi := DirichletCharacter("1000.749");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 6 x^{18} - 5 x^{17} - 3 x^{16} + 20 x^{15} - 28 x^{14} + 24 x^{13} + 16 x^{12} + \cdots + 1024 $ x^20 - 3x^19 + 6x^18 - 5x^17 - 3x^16 + 20x^15 - 28x^14 + 24x^13 + 16x^12 - 60x^11 + 116x^10 - 120x^9 + 64x^8 + 192x^7 - 448x^6 + 640x^5 - 192x^4 - 640x^3 + 1536x^2 - 1536*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			749.11
Root			$0.368522 - 1.36535i$ of defining polynomial
Character	$\chi$	$=$	1000.749
Dual form			1000.2.f.d.749.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.368522 - 1.36535i) q^{2} +0.513027 q^{3} +(-1.72838 - 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} +1.12889i q^{7} +(-2.01094 + 1.98900i) q^{8} -2.73680 q^{9} +O(q^{10})$	\(q+(0.368522 - 1.36535i) q^{2} +0.513027 q^{3} +(-1.72838 - 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} +1.12889i q^{7} +(-2.01094 + 1.98900i) q^{8} -2.73680 q^{9} +3.99787i q^{11} +(-0.886708 - 0.516272i) q^{12} -1.12390 q^{13} +(1.54133 + 0.416020i) q^{14} +(1.97462 + 3.47863i) q^{16} +2.93982i q^{17} +(-1.00857 + 3.73671i) q^{18} -3.24181i q^{19} +0.579150i q^{21} +(5.45850 + 1.47330i) q^{22} +5.39053i q^{23} +(-1.03167 + 1.02041i) q^{24} +(-0.414183 + 1.53452i) q^{26} -2.94314 q^{27} +(1.13603 - 1.95115i) q^{28} +7.35068i q^{29} +7.19613 q^{31} +(5.47725 - 1.41410i) q^{32} +2.05101i q^{33} +(4.01389 + 1.08339i) q^{34} +(4.73025 + 2.75411i) q^{36} -10.6176 q^{37} +(-4.42622 - 1.19468i) q^{38} -0.576592 q^{39} +2.08421 q^{41} +(0.790745 + 0.213429i) q^{42} -6.26007 q^{43} +(4.02315 - 6.90984i) q^{44} +(7.35999 + 1.98653i) q^{46} +2.24328i q^{47} +(1.01303 + 1.78463i) q^{48} +5.72561 q^{49} +1.50821i q^{51} +(1.94253 + 1.13101i) q^{52} -1.64494 q^{53} +(-1.08461 + 4.01842i) q^{54} +(-2.24536 - 2.27012i) q^{56} -1.66314i q^{57} +(10.0363 + 2.70889i) q^{58} -5.55039i q^{59} +6.65010i q^{61} +(2.65193 - 9.82527i) q^{62} -3.08954i q^{63} +(0.0877382 - 7.99952i) q^{64} +(2.80036 + 0.755843i) q^{66} -6.79788 q^{67} +(2.95841 - 5.08113i) q^{68} +2.76549i q^{69} -3.27833 q^{71} +(5.50354 - 5.44351i) q^{72} -6.97819i q^{73} +(-3.91280 + 14.4967i) q^{74} +(-3.26232 + 5.60310i) q^{76} -4.51314 q^{77} +(-0.212487 + 0.787253i) q^{78} -8.60333 q^{79} +6.70050 q^{81} +(0.768075 - 2.84568i) q^{82} +13.4761 q^{83} +(0.582813 - 1.00099i) q^{84} +(-2.30697 + 8.54721i) q^{86} +3.77110i q^{87} +(-7.95176 - 8.03946i) q^{88} +10.9910 q^{89} -1.26876i q^{91} +(5.42463 - 9.31691i) q^{92} +3.69181 q^{93} +(3.06287 + 0.826697i) q^{94} +(2.80998 - 0.725472i) q^{96} +18.6691i q^{97} +(2.11001 - 7.81749i) q^{98} -10.9414i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 20 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - q^6 - 12 * q^8 + 12 * q^9	$ 20 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - q^{6} - 12 q^{8} + 12 q^{9} - 6 q^{12} - 6 q^{13} - 6 q^{14} + 9 q^{16} + 17 q^{18} + 8 q^{22} + 3 q^{24} + 10 q^{26} + 8 q^{27} + 2 q^{28} + 24 q^{31} - 7 q^{32} + 3 q^{34} - 20 q^{36} - 18 q^{37} - 24 q^{38} - 4 q^{39} + 22 q^{41} - q^{42} + 60 q^{43} - 4 q^{44} - 15 q^{46} - 57 q^{48} - 6 q^{49} - 13 q^{52} - 10 q^{53} + q^{54} + 25 q^{56} + 27 q^{58} + 34 q^{62} - 36 q^{64} + 21 q^{66} + 40 q^{67} + 29 q^{68} + 48 q^{71} + 47 q^{72} - 3 q^{74} - q^{76} - 24 q^{77} - 66 q^{78} - 48 q^{79} - 28 q^{81} - 54 q^{82} - 40 q^{83} - 58 q^{84} + 23 q^{86} - 17 q^{88} + 22 q^{89} - 75 q^{92} - 8 q^{93} + 7 q^{94} + 6 q^{96} + 55 q^{98}+O(q^{100}) $ 20 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - q^6 - 12 * q^8 + 12 * q^9 - 6 * q^12 - 6 * q^13 - 6 * q^14 + 9 * q^16 + 17 * q^18 + 8 * q^22 + 3 * q^24 + 10 * q^26 + 8 * q^27 + 2 * q^28 + 24 * q^31 - 7 * q^32 + 3 * q^34 - 20 * q^36 - 18 * q^37 - 24 * q^38 - 4 * q^39 + 22 * q^41 - q^42 + 60 * q^43 - 4 * q^44 - 15 * q^46 - 57 * q^48 - 6 * q^49 - 13 * q^52 - 10 * q^53 + q^54 + 25 * q^56 + 27 * q^58 + 34 * q^62 - 36 * q^64 + 21 * q^66 + 40 * q^67 + 29 * q^68 + 48 * q^71 + 47 * q^72 - 3 * q^74 - q^76 - 24 * q^77 - 66 * q^78 - 48 * q^79 - 28 * q^81 - 54 * q^82 - 40 * q^83 - 58 * q^84 + 23 * q^86 - 17 * q^88 + 22 * q^89 - 75 * q^92 - 8 * q^93 + 7 * q^94 + 6 * q^96 + 55 * q^98

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 $

$2$	0.368522	−	1.36535i	0.260584	−	0.965451i
$2$	0.368522	−	1.36535i	0.260584	−	0.965451i
$3$	0.513027			0.296196			0.148098	−	0.988973i	$-0.452685\pi$
$3$	0.513027			0.296196			0.148098	+	0.988973i	$0.452685\pi$
$4$	−1.72838	−	1.00633i	−0.864192	−	0.503163i
$5$		0			0
$5$		0			0
$6$	0.189062	−	0.700464i	0.0771841	−	0.285963i
$7$			1.12889i			0.426679i	0.976978	+	0.213340i	$0.0684341\pi$
$7$			1.12889i			0.426679i	−0.976978	+	0.213340i	$0.931566\pi$
$8$	−2.01094	+	1.98900i	−0.710974	+	0.703219i
$9$	−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	$0.794091\pi$
$12$	−0.886708	−	0.516272i	−0.255970	−	0.149035i
$13$	−1.12390			−0.311714			−0.155857	−	0.987780i	$-0.549814\pi$
$13$	−1.12390			−0.311714			−0.155857	+	0.987780i	$0.549814\pi$
$14$	1.54133	+	0.416020i	0.411938	+	0.111186i
$15$		0			0
$16$	1.97462	+	3.47863i	0.493655	+	0.869658i
$17$			2.93982i			0.713010i	0.934293	+	0.356505i	$0.116032\pi$
$17$			2.93982i			0.713010i	−0.934293	+	0.356505i	$0.883968\pi$
$18$	−1.00857	+	3.73671i	−0.237723	+	0.880750i
$19$		−	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
$22$	5.45850	+	1.47330i	1.16376	+	0.314109i
$23$			5.39053i			1.12400i	0.827136	+	0.562002i	$0.189969\pi$
$23$			5.39053i			1.12400i	−0.827136	+	0.562002i	$0.810031\pi$
$24$	−1.03167	+	1.02041i	−0.210588	+	0.208291i
$25$		0			0
$26$	−0.414183	+	1.53452i	−0.0812279	+	0.300945i
$27$	−2.94314			−0.566407
$28$	1.13603	−	1.95115i	0.214689	−	0.368733i
$29$			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	$0.276344\pi$
$32$	5.47725	−	1.41410i	0.968251	−	0.249980i
$33$			2.05101i			0.357036i
$34$	4.01389	+	1.08339i	0.688377	+	0.185799i
$35$		0			0
$36$	4.73025	+	2.75411i	0.788374	+	0.459019i
$37$	−10.6176			−1.74552			−0.872759	−	0.488152i	$-0.837671\pi$
$37$	−10.6176			−1.74552			−0.872759	+	0.488152i	$0.837671\pi$
$38$	−4.42622	−	1.19468i	−0.718028	−	0.193803i
$39$	−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	$0.447964\pi$
$42$	0.790745	+	0.213429i	0.122015	+	0.0329329i
$43$	−6.26007			−0.954652			−0.477326	−	0.878726i	$-0.658394\pi$
$43$	−6.26007			−0.954652			−0.477326	+	0.878726i	$0.658394\pi$
$44$	4.02315	−	6.90984i	0.606513	−	1.04170i
$45$		0			0
$46$	7.35999	+	1.98653i	1.08517	+	0.292898i
$47$			2.24328i			0.327216i	0.986525	+	0.163608i	$0.0523132\pi$
$47$			2.24328i			0.327216i	−0.986525	+	0.163608i	$0.947687\pi$
$48$	1.01303	+	1.78463i	0.146219	+	0.257590i
$49$	5.72561			0.817945
$50$		0			0
$51$			1.50821i			0.211191i
$52$	1.94253	+	1.13101i	0.269381	+	0.156843i
$53$	−1.64494			−0.225950			−0.112975	−	0.993598i	$-0.536038\pi$
$53$	−1.64494			−0.225950			−0.112975	+	0.993598i	$0.536038\pi$
$54$	−1.08461	+	4.01842i	−0.147597	+	0.546838i
$55$		0			0
$56$	−2.24536	−	2.27012i	−0.300049	−	0.303358i
$57$		−	1.66314i		−	0.220288i
$58$	10.0363	+	2.70889i	1.31783	+	0.355694i
$59$		−	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	$0.139982\pi$
$61$			6.65010i			0.851458i	−0.904851	+	0.425729i	$0.860018\pi$
$62$	2.65193	−	9.82527i	0.336796	−	1.24781i
$63$		−	3.08954i		−	0.389246i
$64$	0.0877382	−	7.99952i	0.0109673	−	0.999940i
$65$		0			0
$66$	2.80036	+	0.755843i	0.344700	+	0.0930379i
$67$	−6.79788			−0.830493			−0.415247	−	0.909709i	$-0.636305\pi$
$67$	−6.79788			−0.830493			−0.415247	+	0.909709i	$0.636305\pi$
$68$	2.95841	−	5.08113i	0.358760	−	0.616178i
$69$			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	$0.562319\pi$
$72$	5.50354	−	5.44351i	0.648598	−	0.641524i
$73$		−	6.97819i		−	0.816736i	−0.912817	−	0.408368i	$-0.866098\pi$
$73$		−	6.97819i		−	0.816736i	0.912817	−	0.408368i	$-0.133902\pi$
$74$	−3.91280	+	14.4967i	−0.454854	+	1.68521i
$75$		0			0
$76$	−3.26232	+	5.60310i	−0.374214	+	0.642719i
$77$	−4.51314			−0.514320
$78$	−0.212487	+	0.787253i	−0.0240594	+	0.0891388i
$79$	−8.60333			−0.967950			−0.483975	−	0.875082i	$-0.660807\pi$
$79$	−8.60333			−0.967950			−0.483975	+	0.875082i	$0.660807\pi$
$80$		0			0
$81$	6.70050			0.744500
$82$	0.768075	−	2.84568i	0.0848197	−	0.314253i
$83$	13.4761			1.47919			0.739596	−	0.673052i	$-0.235017\pi$
$83$	13.4761			1.47919			0.739596	+	0.673052i	$0.235017\pi$
$84$	0.582813	−	1.00099i	0.0635901	−	0.109217i
$85$		0			0
$86$	−2.30697	+	8.54721i	−0.248767	+	0.921669i
$87$			3.77110i			0.404304i
$88$	−7.95176	−	8.03946i	−0.847661	−	0.857009i
$89$	10.9910			1.16504			0.582521	−	0.812816i	$-0.302066\pi$
$89$	10.9910			1.16504			0.582521	+	0.812816i	$0.302066\pi$
$90$		0			0
$91$		−	1.26876i		−	0.133002i
$92$	5.42463	−	9.31691i	0.565557	−	0.971355i
$93$	3.69181			0.382823
$94$	3.06287	+	0.826697i	0.315911	+	0.0852673i
$95$		0			0
$96$	2.80998	−	0.725472i	0.286792	−	0.0740432i
$97$			18.6691i			1.89556i	0.318931	+	0.947778i	$0.396676\pi$
$97$			18.6691i			1.89556i	−0.318931	+	0.947778i	$0.603324\pi$
$98$	2.11001	−	7.81749i	0.213144	−	0.789686i
$99$		−	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	$0.972033\pi$
$102$	2.05923	+	0.555807i	0.203895	+	0.0550331i
$103$		−	3.89194i		−	0.383484i	−0.981445	−	0.191742i	$-0.938586\pi$
$103$		−	3.89194i		−	0.383484i	0.981445	−	0.191742i	$-0.0614137\pi$
$104$	2.26010	−	2.23545i	0.221621	−	0.219203i
$105$		0			0
$106$	−0.606196	+	2.24592i	−0.0588789	+	0.218143i
$107$	−16.0146			−1.54819			−0.774094	−	0.633071i	$-0.781794\pi$
$107$	−16.0146			−1.54819			−0.774094	+	0.633071i	$0.781794\pi$
$108$	5.08687	+	2.96175i	0.489484	+	0.284995i
$109$			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
$112$	−3.92698	+	2.22912i	−0.371065	+	0.210632i
$113$		−	2.97052i		−	0.279443i	−0.990191	−	0.139722i	$-0.955379\pi$
$113$		−	2.97052i		−	0.279443i	0.990191	−	0.139722i	$-0.0446208\pi$
$114$	−2.27077	−	0.612903i	−0.212677	−	0.0574036i
$115$		0			0
$116$	7.39718	−	12.7048i	0.686811	−	1.17961i
$117$	3.07590			0.284367
$118$	−7.57824	−	2.04544i	−0.697634	−	0.188298i
$119$	−3.31872			−0.304227
$120$		0			0
$121$	−4.98293			−0.452994
$122$	9.07974	+	2.45071i	0.822041	+	0.221876i
$123$	1.06925			0.0964114
$124$	−12.4377	−	7.24165i	−1.11694	−	0.650320i
$125$		0			0
$126$	−4.21832	−	1.13856i	−0.375798	−	0.101431i
$127$			12.2692i			1.08871i	0.838855	+	0.544356i	$0.183226\pi$
$127$			12.2692i			1.08871i	−0.838855	+	0.544356i	$0.816774\pi$
$128$	−10.8898	−	3.06779i	−0.962535	−	0.271157i
$129$	−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	$-0.196726\pi$
$132$	2.06399	−	3.54494i	0.179647	−	0.308547i
$133$	3.65964			0.317331
$134$	−2.50517	+	9.28151i	−0.216413	+	0.801800i
$135$		0			0
$136$	−5.84730	−	5.91179i	−0.501402	−	0.506932i
$137$		−	13.3863i		−	1.14367i	−0.820368	−	0.571836i	$-0.806231\pi$
$137$		−	13.3863i		−	1.14367i	0.820368	−	0.571836i	$-0.193769\pi$
$138$	3.77587	+	1.01914i	0.321424	+	0.0867552i
$139$		−	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
$142$	−1.20814	+	4.47608i	−0.101385	+	0.375624i
$143$		−	4.49321i		−	0.375741i
$144$	−5.40414	−	9.52033i	−0.450345	−	0.793361i
$145$		0			0
$146$	−9.52770	−	2.57162i	−0.788518	−	0.212828i
$147$	2.93739			0.242272
$148$	18.3512	+	10.6847i	1.50846	+	0.878279i
$149$			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	$0.364572\pi$
$152$	6.44798	+	6.51909i	0.523000	+	0.528768i
$153$		−	8.04570i		−	0.650456i
$154$	−1.66319	+	6.16203i	−0.134024	+	0.496551i
$155$		0			0
$156$	0.996573	+	0.580240i	0.0797897	+	0.0464564i
$157$	−7.49744			−0.598361			−0.299180	−	0.954197i	$-0.596713\pi$
$157$	−7.49744			−0.598361			−0.299180	+	0.954197i	$0.596713\pi$
$158$	−3.17051	+	11.7466i	−0.252232	+	0.934508i
$159$	−0.843898			−0.0669255
$160$		0			0
$161$	−6.08530			−0.479589
$162$	2.46928	−	9.14856i	0.194005	−	0.718778i
$163$	−8.95189			−0.701166			−0.350583	−	0.936532i	$-0.614017\pi$
$163$	−8.95189			−0.701166			−0.350583	+	0.936532i	$0.614017\pi$
$164$	−3.60231	−	2.09739i	−0.281293	−	0.163779i
$165$		0			0
$166$	4.96623	−	18.3996i	0.385454	−	1.42809i
$167$		−	2.49946i		−	0.193414i	−0.995313	−	0.0967070i	$-0.969169\pi$
$167$		−	2.49946i		−	0.193414i	0.995313	−	0.0967070i	$-0.0308310\pi$
$168$	−1.15193	−	1.16463i	−0.0888734	−	0.0898535i
$169$	−11.7368			−0.902834
$170$		0			0
$171$			8.87221i			0.678475i
$172$	10.8198	+	6.29967i	0.825002	+	0.480345i
$173$	0.589561			0.0448235			0.0224118	−	0.999749i	$-0.492866\pi$
$173$	0.589561			0.0448235			0.0224118	+	0.999749i	$0.492866\pi$
$174$	5.14889	+	1.38973i	0.390336	+	0.105355i
$175$		0			0
$176$	−13.9071	+	7.89426i	−1.04829	+	0.595052i
$177$		−	2.84750i		−	0.214031i
$178$	4.05042	−	15.0066i	0.303592	−	1.12479i
$179$		−	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	$-0.769873\pi$
$181$		−	17.8021i		−	1.32322i	0.749848	−	0.661610i	$-0.230127\pi$
$182$	−1.73231	−	0.467565i	−0.128407	−	0.0346583i
$183$			3.41168i			0.252199i
$184$	−10.7218	−	10.8400i	−0.790420	−	0.799137i
$185$		0			0
$186$	1.36051	−	5.04063i	0.0997577	−	0.369597i
$187$	−11.7530			−0.859464
$188$	2.25747	−	3.87724i	0.164643	−	0.282777i
$189$		−	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	$0.739774\pi$
$192$	0.0450121	−	4.10397i	0.00324847	−	0.296179i
$193$			10.2705i			0.739288i	0.929173	+	0.369644i	$0.120520\pi$
$193$			10.2705i			0.739288i	−0.929173	+	0.369644i	$0.879480\pi$
$194$	25.4899	+	6.87995i	1.83007	+	0.493952i
$195$		0			0
$196$	−9.89606	−	5.76183i	−0.706861	−	0.411559i
$197$	0.207142			0.0147583			0.00737913	−	0.999973i	$-0.497651\pi$
$197$	0.207142			0.0147583			0.00737913	+	0.999973i	$0.497651\pi$
$198$	−14.9388	−	4.03213i	−1.06166	−	0.286551i
$199$	12.2911			0.871295			0.435647	−	0.900117i	$-0.356519\pi$
$199$	12.2911			0.871295			0.435647	+	0.900117i	$0.356519\pi$
$200$		0			0
$201$	−3.48750			−0.245989
$202$	2.40811	+	0.649970i	0.169434	+	0.0457318i
$203$	−8.29809			−0.582412
$204$	1.51775	−	2.60676i	0.106263	−	0.182510i
$205$		0			0
$206$	−5.31387	−	1.43426i	−0.370235	−	0.0999299i
$207$		−	14.7528i		−	1.02539i
$208$	−2.21928	−	3.90964i	−0.153879	−	0.271085i
$209$	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	$0.956967\pi$
$212$	2.84309	+	1.65534i	0.195264	+	0.113689i
$213$	−1.68187			−0.115240
$214$	−5.90172	+	21.8656i	−0.403433	+	1.49470i
$215$		0			0
$216$	5.91846	−	5.85390i	0.402700	−	0.398308i
$217$			8.12363i			0.551468i
$218$	21.3124	+	5.75241i	1.44346	+	0.389603i
$219$		−	3.58000i		−	0.241914i
$220$		0			0
$221$		−	3.30407i		−	0.222256i
$222$	−2.00737	+	7.43722i	−0.134726	+	0.499153i
$223$			23.8519i			1.59724i	0.601834	+	0.798621i	$0.294437\pi$
$223$			23.8519i			1.59724i	−0.601834	+	0.798621i	$0.705563\pi$
$224$	1.59636	+	6.18320i	0.106661	+	0.413133i
$225$		0			0
$226$	−4.05582	−	1.09470i	−0.269789	−	0.0728185i
$227$	24.7012			1.63948			0.819738	−	0.572738i	$-0.194119\pi$
$227$	24.7012			1.63948			0.819738	+	0.572738i	$0.194119\pi$
$228$	−1.67366	+	2.87454i	−0.110841	+	0.190371i
$229$			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
$232$	−14.6205	−	14.7818i	−0.959884	−	0.970470i
$233$			19.6085i			1.28460i	0.766454	+	0.642299i	$0.222019\pi$
$233$			19.6085i			1.28460i	−0.766454	+	0.642299i	$0.777981\pi$
$234$	1.13354	−	4.19969i	0.0741016	−	0.274543i
$235$		0			0
$236$	−5.58550	+	9.59320i	−0.363585	+	0.624464i
$237$	−4.41374			−0.286703
$238$	−1.22302	+	4.53123i	−0.0792767	+	0.293716i
$239$	12.3845			0.801088			0.400544	−	0.916278i	$-0.368821\pi$
$239$	12.3845			0.801088			0.400544	+	0.916278i	$0.368821\pi$
$240$		0			0
$241$	−20.4095			−1.31469			−0.657347	−	0.753588i	$-0.728321\pi$
$241$	−20.4095			−1.31469			−0.657347	+	0.753588i	$0.728321\pi$
$242$	−1.83632	+	6.80346i	−0.118043	+	0.437343i
$243$	12.2669			0.786925
$244$	6.69216	−	11.4939i	0.428422	−	0.735823i
$245$		0			0
$246$	0.394043	−	1.45991i	0.0251233	−	0.0930805i
$247$			3.64348i			0.231829i
$248$	−14.4710	+	14.3131i	−0.918908	+	0.908885i
$249$	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	$-0.247118\pi$
$252$	−3.10908	+	5.33991i	−0.195854	+	0.336383i
$253$	−21.5506			−1.35488
$254$	16.7517	+	4.52145i	1.05110	+	0.283701i
$255$		0			0
$256$	−8.20176	+	13.7379i	−0.512610	+	0.858621i
$257$			13.0592i			0.814614i	0.913291	+	0.407307i	$0.133532\pi$
$257$			13.0592i			0.814614i	−0.913291	+	0.407307i	$0.866468\pi$
$258$	−1.18354	+	4.38495i	−0.0736839	+	0.272995i
$259$		−	11.9860i		−	0.744776i
$260$		0			0
$261$		−	20.1174i		−	1.24523i
$262$	−18.1099	−	4.88802i	−1.11883	−	0.301983i
$263$		−	29.2389i		−	1.80295i	−0.432835	−	0.901473i	$-0.642487\pi$
$263$		−	29.2389i		−	1.80295i	0.432835	−	0.901473i	$-0.357513\pi$
$264$	−4.07947	−	4.12446i	−0.251074	−	0.253843i
$265$		0			0
$266$	1.34866	−	4.99671i	0.0826915	−	0.306368i
$267$	5.63867			0.345081
$268$	11.7493	+	6.84088i	0.717705	+	0.417873i
$269$			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	$0.488802\pi$
$272$	−10.2265	+	5.80502i	−0.620075	+	0.351981i
$273$		−	0.650908i		−	0.0393947i
$274$	−18.2771	−	4.93316i	−1.10416	−	0.298023i
$275$		0			0
$276$	2.78298	−	4.77983i	0.167516	−	0.287712i
$277$	16.8055			1.00975			0.504873	−	0.863194i	$-0.331539\pi$
$277$	16.8055			1.00975			0.504873	+	0.863194i	$0.331539\pi$
$278$	−27.6612	−	7.46603i	−1.65901	−	0.447783i
$279$	−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	$0.413575\pi$
$282$	1.57133	+	0.424118i	0.0935716	+	0.0252559i
$283$	−15.4397			−0.917798			−0.458899	−	0.888489i	$-0.651756\pi$
$283$	−15.4397			−0.917798			−0.458899	+	0.888489i	$0.651756\pi$
$284$	5.66621	+	3.29907i	0.336228	+	0.195764i
$285$		0			0
$286$	−6.13482	−	1.65585i	−0.362760	−	0.0979122i
$287$			2.35283i			0.138883i
$288$	−14.9902	+	3.87012i	−0.883304	+	0.228049i
$289$	8.35748			0.491616
$290$		0			0
$291$			9.57773i			0.561457i
$292$	−7.02233	+	12.0610i	−0.410951	+	0.705816i
$293$	1.62062			0.0946777			0.0473389	−	0.998879i	$-0.484926\pi$
$293$	1.62062			0.0946777			0.0473389	+	0.998879i	$0.484926\pi$
$294$	1.08249	−	4.01058i	0.0631323	−	0.233902i
$295$		0			0
$296$	21.3513	−	21.1184i	1.24102	−	1.22748i
$297$		−	11.7663i		−	0.682748i
$298$	20.2847	+	5.47503i	1.17506	+	0.317160i
$299$		−	6.05843i		−	0.350368i
$300$		0			0
$301$		−	7.06691i		−	0.407330i
$302$	3.73815	−	13.8496i	0.215106	−	0.796958i
$303$			0.904838i			0.0519816i
$304$	11.2771	−	6.40135i	0.646785	−	0.367142i
$305$		0			0
$306$	−10.9852	−	2.96502i	−0.627984	−	0.169499i
$307$	13.3243			0.760458			0.380229	−	0.924892i	$-0.375845\pi$
$307$	13.3243			0.760458			0.380229	+	0.924892i	$0.375845\pi$
$308$	7.80044	+	4.54169i	0.444471	+	0.258787i
$309$		−	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	$0.528961\pi$
$312$	1.15949	−	1.14684i	0.0656433	−	0.0649273i
$313$			24.2715i			1.37190i	0.727647	+	0.685952i	$0.240614\pi$
$313$			24.2715i			1.37190i	−0.727647	+	0.685952i	$0.759386\pi$
$314$	−2.76297	+	10.2367i	−0.155923	+	0.577688i
$315$		0			0
$316$	14.8698	+	8.65775i	0.836494	+	0.487036i
$317$	3.79177			0.212967			0.106483	−	0.994314i	$-0.466041\pi$
$317$	3.79177			0.212967			0.106483	+	0.994314i	$0.466041\pi$
$318$	−0.310995	+	1.15222i	−0.0174397	+	0.0646133i
$319$	−29.3870			−1.64536
$320$		0			0
$321$	−8.21591			−0.458567
$322$	−2.24257	+	8.30859i	−0.124973	+	0.463020i
$323$	9.53034			0.530282
$324$	−11.5810	−	6.74288i	−0.643391	−	0.374605i
$325$		0			0
$326$	−3.29897	+	12.2225i	−0.182713	+	0.676941i
$327$			8.00806i			0.442847i
$328$	−4.19121	+	4.14549i	−0.231421	+	0.228896i
$329$	−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	$0.980200\pi$
$332$	−23.2918	−	13.5613i	−1.27830	−	0.744274i
$333$	29.0582			1.59238
$334$	−3.41265	−	0.921106i	−0.186732	−	0.0504007i
$335$		0			0
$336$	−2.01465	+	1.14360i	−0.109908	+	0.0623885i
$337$		−	28.6654i		−	1.56150i	−0.624843	−	0.780751i	$-0.714837\pi$
$337$		−	28.6654i		−	1.56150i	0.624843	−	0.780751i	$-0.285163\pi$
$338$	−4.32528	+	16.0249i	−0.235264	+	0.871642i
$339$		−	1.52396i		−	0.0827701i
$340$		0			0
$341$			28.7692i			1.55794i
$342$	12.1137	+	3.26960i	0.655034	+	0.176800i
$343$			14.3658i			0.775679i
$344$	12.5886	−	12.4513i	0.678732	−	0.671329i
$345$		0			0
$346$	0.217266	−	0.804960i	0.0116803	−	0.0432749i
$347$	−3.03845			−0.163112			−0.0815562	−	0.996669i	$-0.525989\pi$
$347$	−3.03845			−0.163112			−0.0815562	+	0.996669i	$0.525989\pi$
$348$	3.79495	−	6.51791i	0.203431	−	0.349396i
$349$		−	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
$352$	5.65339	+	21.8973i	0.301327	+	1.16713i
$353$		−	29.4943i		−	1.56983i	−0.619606	−	0.784913i	$-0.712708\pi$
$353$		−	29.4943i		−	1.56983i	0.619606	−	0.784913i	$-0.287292\pi$
$354$	−3.88784	−	1.04937i	−0.206637	−	0.0557731i
$355$		0			0
$356$	−18.9966	−	11.0605i	−1.00682	−	0.586206i
$357$	−1.70259			−0.0901108
$358$	−14.0671	−	3.79685i	−0.743472	−	0.200670i
$359$	−8.91327			−0.470424			−0.235212	−	0.971944i	$-0.575578\pi$
$359$	−8.91327			−0.470424			−0.235212	+	0.971944i	$0.575578\pi$
$360$		0			0
$361$	8.49064			0.446876
$362$	−24.3062	−	6.56046i	−1.27750	−	0.344810i
$363$	−2.55638			−0.134175
$364$	−1.27678	+	2.19290i	−0.0669217	+	0.114939i
$365$		0			0
$366$	4.65815	+	1.25728i	0.243485	+	0.0657190i
$367$		−	22.6852i		−	1.18416i	−0.805880	−	0.592079i	$-0.798307\pi$
$367$		−	22.6852i		−	1.18416i	0.805880	−	0.592079i	$-0.201693\pi$
$368$	−18.7517	+	10.6442i	−0.977499	+	0.554870i
$369$	−5.70406			−0.296942
$370$		0			0
$371$		−	1.85695i		−	0.0964081i
$372$	−6.38087	−	3.71516i	−0.330833	−	0.192622i
$373$	−6.46312			−0.334648			−0.167324	−	0.985902i	$-0.553513\pi$
$373$	−6.46312			−0.334648			−0.167324	+	0.985902i	$0.553513\pi$
$374$	−4.33123	+	16.0470i	−0.223963	+	0.829770i
$375$		0			0
$376$	−4.46189	−	4.51109i	−0.230104	−	0.232642i
$377$		−	8.26145i		−	0.425486i
$378$	−4.53635	−	1.22440i	−0.233324	−	0.0629764i
$379$			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
$382$	−6.96762	+	25.8147i	−0.356494	+	1.32079i
$383$		−	11.1049i		−	0.567432i	−0.958908	−	0.283716i	$-0.908433\pi$
$383$		−	11.1049i		−	0.567432i	0.958908	−	0.283716i	$-0.0915673\pi$
$384$	−5.58678	−	1.57386i	−0.285099	−	0.0803157i
$385$		0			0
$386$	14.0229	+	3.78491i	0.713746	+	0.192647i
$387$	17.1326			0.870898
$388$	18.7871	−	32.2673i	0.953773	−	1.63812i
$389$			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
$392$	−11.5139	+	11.3883i	−0.581537	+	0.575194i
$393$		−	6.80472i		−	0.343253i
$394$	0.0763364	−	0.282822i	0.00384577	−	0.0142484i
$395$		0			0
$396$	−11.0106	+	18.9109i	−0.553302	+	0.950308i
$397$	26.9682			1.35350			0.676748	−	0.736214i	$-0.263389\pi$
$397$	26.9682			1.35350			0.676748	+	0.736214i	$0.263389\pi$
$398$	4.52955	−	16.7817i	0.227046	−	0.841193i
$399$	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	$0.142391\pi$
$402$	−1.28522	+	4.76167i	−0.0641009	+	0.237490i
$403$	−8.08775			−0.402880
$404$	1.77488	−	3.04839i	0.0883035	−	0.151663i
$405$		0			0
$406$	−3.05803	+	11.3298i	−0.151767	+	0.562290i
$407$		−	42.4476i		−	2.10405i
$408$	−2.99982	−	3.03291i	−0.148513	−	0.150151i
$409$	−15.5149			−0.767163			−0.383581	−	0.923507i	$-0.625309\pi$
$409$	−15.5149			−0.767163			−0.383581	+	0.923507i	$0.625309\pi$
$410$		0			0
$411$		−	6.86755i		−	0.338751i
$412$	−3.91656	+	6.72676i	−0.192955	+	0.331404i
$413$	6.26576			0.308318
$414$	−20.1428	−	5.43674i	−0.989966	−	0.267201i
$415$		0			0
$416$	−6.15590	+	1.58931i	−0.301818	+	0.0779225i
$417$		−	10.3936i		−	0.508978i
$418$	4.77617	−	17.6955i	0.233610	−	0.865513i
$419$			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	$0.0478561\pi$
$421$			6.14641i			0.299557i	−0.988720	+	0.149779i	$0.952144\pi$
$422$	5.34616	+	1.44298i	0.260247	+	0.0702431i
$423$		−	6.13941i		−	0.298508i
$424$	3.30787	−	3.27179i	0.160644	−	0.158892i
$425$		0			0
$426$	−0.619807	+	2.29635i	−0.0300297	+	0.111259i
$427$	−7.50721			−0.363299
$428$	27.6793	+	16.1159i	1.33793	+	0.778990i
$429$		−	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	$0.151771\pi$
$432$	−5.81157	−	10.2381i	−0.279609	−	0.492580i
$433$			11.5824i			0.556617i	0.960492	+	0.278308i	$0.0897737\pi$
$433$			11.5824i			0.556617i	−0.960492	+	0.278308i	$0.910226\pi$
$434$	11.0916	+	2.99373i	0.532415	+	0.143704i
$435$		0			0
$436$	15.7082	−	26.9791i	0.752284	−	1.29206i
$437$	17.4751			0.835948
$438$	−4.88797	−	1.31931i	−0.233556	−	0.0630390i
$439$	4.15174			0.198152			0.0990760	−	0.995080i	$-0.468411\pi$
$439$	4.15174			0.198152			0.0990760	+	0.995080i	$0.468411\pi$
$440$		0			0
$441$	−15.6699			−0.746185
$442$	−4.51122	−	1.21762i	−0.214577	−	0.0579163i
$443$	15.7327			0.747482			0.373741	−	0.927533i	$-0.378075\pi$
$443$	15.7327			0.747482			0.373741	+	0.927533i	$0.378075\pi$
$444$	9.41468	+	5.48155i	0.446801	+	0.260143i
$445$		0			0
$446$	32.5663	+	8.78995i	1.54206	+	0.416216i
$447$			7.62190i			0.360504i
$448$	9.03056	+	0.0990465i	0.426654	+	0.00467951i
$449$	20.6861			0.976239			0.488120	−	0.872777i	$-0.337683\pi$
$449$	20.6861			0.976239			0.488120	+	0.872777i	$0.337683\pi$
$450$		0			0
$451$			8.33238i			0.392356i
$452$	−2.98931	+	5.13420i	−0.140605	+	0.241493i
$453$	5.20396			0.244503
$454$	9.10293	−	33.7259i	0.427222	−	1.58283i
$455$		0			0
$456$	3.30799	+	3.34447i	0.154911	+	0.156619i
$457$			28.7187i			1.34340i	0.740821	+	0.671702i	$0.234436\pi$
$457$			28.7187i			1.34340i	−0.740821	+	0.671702i	$0.765564\pi$
$458$	30.1377	+	8.13444i	1.40824	+	0.380098i
$459$		−	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	$0.776771\pi$
$462$	−0.853262	+	3.16129i	−0.0396973	+	0.147077i
$463$		−	26.9572i		−	1.25281i	−0.779499	−	0.626404i	$-0.784526\pi$
$463$		−	26.9572i		−	1.25281i	0.779499	−	0.626404i	$-0.215474\pi$
$464$	−25.5703	+	14.5148i	−1.18707	+	0.673832i
$465$		0			0
$466$	26.7726	+	7.22617i	1.24022	+	0.334746i
$467$	31.3052			1.44863			0.724316	−	0.689468i	$-0.242156\pi$
$467$	31.3052			1.44863			0.724316	+	0.689468i	$0.242156\pi$
$468$	−5.31633	−	3.09536i	−0.245748	−	0.143083i
$469$		−	7.67404i		−	0.354354i
$470$		0			0
$471$	−3.84639			−0.177232
$472$	11.0397	+	11.1615i	0.508145	+	0.513749i
$473$		−	25.0269i		−	1.15074i
$474$	−1.62656	+	6.02632i	−0.0747103	+	0.276798i
$475$		0			0
$476$	5.73602	+	3.33971i	0.262910	+	0.153076i
$477$	4.50187			0.206127
$478$	4.56397	−	16.9093i	0.208751	−	0.773411i
$479$	32.6888			1.49359			0.746794	−	0.665056i	$-0.231592\pi$
$479$	32.6888			1.49359			0.746794	+	0.665056i	$0.231592\pi$
$480$		0			0
$481$	11.9331			0.544103
$482$	−7.52136	+	27.8662i	−0.342589	+	1.26927i
$483$	−3.12193			−0.142053
$484$	8.61241	+	5.01445i	0.391473	+	0.227929i
$485$		0			0
$486$	4.52064	−	16.7487i	0.205060	−	0.759738i
$487$			17.6043i			0.797726i	0.917011	+	0.398863i	$0.130595\pi$
$487$			17.6043i			0.797726i	−0.917011	+	0.398863i	$0.869405\pi$
$488$	−13.2271	−	13.3729i	−0.598761	−	0.605364i
$489$	−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	$0.990580\pi$
$492$	−1.84808	−	1.07602i	−0.0833179	−	0.0485106i
$493$	−21.6097			−0.973250
$494$	4.97465	+	1.34270i	0.223820	+	0.0604111i
$495$		0			0
$496$	14.2096	+	25.0327i	0.638031	+	1.12400i
$497$		−	3.70087i		−	0.166007i
$498$	2.54781	−	9.43950i	0.114170	−	0.422994i
$499$		−	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
$502$	−30.3130	−	8.18177i	−1.35294	−	0.365170i
$503$			34.4786i			1.53733i	0.639654	+	0.768663i	$0.279078\pi$
$503$			34.4786i			1.53733i	−0.639654	+	0.768663i	$0.720922\pi$
$504$	6.14511	+	6.21288i	0.273725	+	0.276743i
$505$		0			0
$506$	−7.94188	+	29.4242i	−0.353059	+	1.30807i
$507$	−6.02132			−0.267416
$508$	12.3468	−	21.2058i	0.547799	−	0.940855i
$509$			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
$512$	15.7346	+	16.2610i	0.695379	+	0.718643i
$513$			9.54110i			0.421250i
$514$	17.8305	+	4.81262i	0.786470	+	0.212275i
$515$		0			0
$516$	5.55085	+	3.23190i	0.244363	+	0.142276i
$517$	−8.96833			−0.394426
$518$	−16.3652	−	4.41711i	−0.719045	−	0.194077i
$519$	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	$0.536955\pi$
$522$	−27.4673	−	7.41369i	−1.20221	−	0.324488i
$523$	18.0301			0.788400			0.394200	−	0.919025i	$-0.371022\pi$
$523$	18.0301			0.788400			0.394200	+	0.919025i	$0.371022\pi$
$524$	−13.3478	+	22.9250i	−0.583099	+	1.00148i
$525$		0			0
$526$	−39.9214	−	10.7752i	−1.74066	−	0.469819i
$527$			21.1553i			0.921540i
$528$	−7.13472	+	4.04997i	−0.310499	+	0.176252i
$529$	−6.05785			−0.263385
$530$		0			0
$531$			15.1903i			0.659204i
$532$	−6.32527	−	3.68279i	−0.274235	−	0.159669i
$533$	−2.34244			−0.101463
$534$	2.07797	−	7.69878i	0.0899227	−	0.333159i
$535$		0			0
$536$	13.6701	−	13.5210i	0.590459	−	0.584018i
$537$		−	5.28568i		−	0.228094i
$538$	29.2523	+	7.89546i	1.26115	+	0.340397i
$539$			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	$0.982674\pi$
$542$	0.426736	−	1.58104i	0.0183299	−	0.0679113i
$543$		−	9.13296i		−	0.391933i
$544$	4.15720	+	16.1021i	0.178238	+	0.690373i
$545$		0			0
$546$	−0.888720	−	0.239874i	−0.0380337	−	0.0102656i
$547$	37.9439			1.62236			0.811182	−	0.584794i	$-0.198825\pi$
$547$	37.9439			1.62236			0.811182	+	0.584794i	$0.198825\pi$
$548$	−13.4710	+	23.1367i	−0.575453	+	0.988352i
$549$		−	18.2000i		−	0.776757i
$550$		0			0
$551$	23.8295			1.01517
$552$	−5.50057	−	5.56123i	−0.234120	−	0.236702i
$553$		−	9.71219i		−	0.413004i
$554$	6.19320	−	22.9455i	0.263124	−	0.974860i
$555$		0			0
$556$	−20.3875	+	35.0160i	−0.864624	+	1.48501i
$557$	37.0123			1.56826			0.784130	−	0.620596i	$-0.213109\pi$
$557$	37.0123			1.56826			0.784130	+	0.620596i	$0.213109\pi$
$558$	−7.25782	+	26.8898i	−0.307248	+	1.13834i
$559$	7.03571			0.297579
$560$		0			0
$561$	−6.02960			−0.254570
$562$	3.31348	−	12.2763i	0.139771	−	0.517843i
$563$	−14.2506			−0.600590			−0.300295	−	0.953846i	$-0.597085\pi$
$563$	−14.2506			−0.600590			−0.300295	+	0.953846i	$0.597085\pi$
$564$	1.15814	−	1.98913i	0.0487666	−	0.0837576i
$565$		0			0
$566$	−5.68988	+	21.0807i	−0.239164	+	0.886089i
$567$			7.56411i			0.317663i
$568$	6.59252	−	6.52061i	0.276616	−	0.273599i
$569$	−25.9576			−1.08820			−0.544101	−	0.839020i	$-0.683129\pi$
$569$	−25.9576			−1.08820			−0.544101	+	0.839020i	$0.683129\pi$
$570$		0			0
$571$			20.3690i			0.852416i	0.904625	+	0.426208i	$0.140151\pi$
$571$			20.3690i			0.852416i	−0.904625	+	0.426208i	$0.859849\pi$
$572$	−4.52163	+	7.76599i	−0.189059	+	0.324712i
$573$	−9.69977			−0.405214
$574$	3.21245	+	0.867070i	0.134085	+	0.0361908i
$575$		0			0
$576$	−0.240122	+	21.8931i	−0.0100051	+	0.912213i
$577$		−	44.6310i		−	1.85801i	−0.370063	−	0.929007i	$-0.620664\pi$
$577$		−	44.6310i		−	1.85801i	0.370063	−	0.929007i	$-0.379336\pi$
$578$	3.07991	−	11.4109i	0.128107	−	0.474632i
$579$			5.26905i			0.218974i
$580$		0			0
$581$			15.2130i			0.631140i
$582$	13.0770	+	3.52960i	0.542059	+	0.146307i
$583$		−	6.57625i		−	0.272360i
$584$	13.8796	+	14.0327i	0.574344	+	0.580678i
$585$		0			0
$586$	0.597234	−	2.21272i	0.0246715	−	0.0914067i
$587$	−18.9398			−0.781729			−0.390865	−	0.920448i	$-0.627824\pi$
$587$	−18.9398			−0.781729			−0.390865	+	0.920448i	$0.627824\pi$
$588$	−5.07694	−	2.95598i	−0.209370	−	0.121902i
$589$		−	23.3285i		−	0.961236i
$590$		0			0
$591$	0.106270			0.00437134
$592$	−20.9656	−	36.9346i	−0.861683	−	1.51800i
$593$		−	8.22399i		−	0.337719i	−0.985640	−	0.168859i	$-0.945992\pi$
$593$		−	8.22399i		−	0.337719i	0.985640	−	0.168859i	$-0.0540084\pi$
$594$	−16.0651	−	4.33612i	−0.659160	−	0.177913i
$595$		0			0
$596$	14.9507	−	25.6781i	0.612404	−	1.05182i
$597$	6.30568			0.258074
$598$	−8.27191	−	2.23266i	−0.338263	−	0.0913005i
$599$	37.2899			1.52362			0.761812	−	0.647798i	$-0.224310\pi$
$599$	37.2899			1.52362			0.761812	+	0.647798i	$0.224310\pi$
$600$		0			0
$601$	23.7882			0.970341			0.485170	−	0.874420i	$-0.338758\pi$
$601$	23.7882			0.970341			0.485170	+	0.874420i	$0.338758\pi$
$602$	−9.64884	−	2.60431i	−0.393257	−	0.106144i
$603$	18.6045			0.757632
$604$	−17.5321	−	10.2078i	−0.713370	−	0.415349i
$605$		0			0
$606$	1.23542	+	0.333452i	0.0501857	+	0.0135456i
$607$		−	32.6940i		−	1.32701i	−0.748172	−	0.663505i	$-0.769068\pi$
$607$		−	32.6940i		−	1.32701i	0.748172	−	0.663505i	$-0.230932\pi$
$608$	−4.58425	−	17.7562i	−0.185916	−	0.720111i
$609$	−4.25715			−0.172508
$610$		0			0
$611$		−	2.52123i		−	0.101998i
$612$	−8.09659	+	13.9061i	−0.327285	+	0.562119i
$613$	5.70642			0.230480			0.115240	−	0.993338i	$-0.463236\pi$
$613$	5.70642			0.230480			0.115240	+	0.993338i	$0.463236\pi$
$614$	4.91029	−	18.1924i	0.198163	−	0.734185i
$615$		0			0
$616$	9.07564	−	8.97665i	0.365668	−	0.361679i
$617$			18.9653i			0.763514i	0.924263	+	0.381757i	$0.124681\pi$
$617$			18.9653i			0.763514i	−0.924263	+	0.381757i	$0.875319\pi$
$618$	−2.72616	−	0.735816i	−0.109662	−	0.0295989i
$619$			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
$622$	−1.18095	+	4.37537i	−0.0473519	+	0.175436i
$623$			12.4076i			0.497099i
$624$	−1.13855	−	2.00575i	−0.0455785	−	0.0802944i
$625$		0			0
$626$	33.1391	+	8.94456i	1.32451	+	0.357497i
$627$	6.64901			0.265536
$628$	12.9585	+	7.54486i	0.517098	+	0.301073i
$629$		−	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	$0.573343\pi$
$632$	17.3008	−	17.1120i	0.688187	−	0.680680i
$633$			2.00880i			0.0798427i
$634$	1.39735	−	5.17711i	0.0554958	−	0.205609i
$635$		0			0
$636$	1.45858	+	0.849236i	0.0578365	+	0.0336744i
$637$	−6.43503			−0.254965
$638$	−10.8298	+	40.1237i	−0.428754	+	1.58851i
$639$	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	$0.501624\pi$
$642$	−3.02774	+	11.2176i	−0.119495	+	0.442724i
$643$	−31.8119			−1.25454			−0.627269	−	0.778802i	$-0.715827\pi$
$643$	−31.8119			−1.25454			−0.627269	+	0.778802i	$0.715827\pi$
$644$	10.5177	+	6.12380i	0.414457	+	0.241311i
$645$		0			0
$646$	3.51214	−	13.0123i	0.138183	−	0.511962i
$647$		−	24.3294i		−	0.956486i	−0.878228	−	0.478243i	$-0.841274\pi$
$647$		−	24.3294i		−	0.956486i	0.878228	−	0.478243i	$-0.158726\pi$
$648$	−13.4743	+	13.3273i	−0.529320	+	0.523546i
$649$	22.1897			0.871022
$650$		0			0
$651$			4.16764i			0.163343i
$652$	15.4723	+	9.00851i	0.605942	+	0.352801i
$653$	39.3785			1.54100			0.770500	−	0.637440i	$-0.220007\pi$
$653$	39.3785			1.54100			0.770500	+	0.637440i	$0.220007\pi$
$654$	10.9338	+	2.95114i	0.427547	+	0.115399i
$655$		0			0
$656$	4.11551	+	7.25019i	0.160684	+	0.283072i
$657$			19.0979i			0.745082i
$658$	−0.933248	+	3.45763i	−0.0363818	+	0.134793i
$659$			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	$-0.778873\pi$
$661$		−	32.9163i		−	1.28029i	0.768252	−	0.640147i	$-0.221127\pi$
$662$	3.08837	+	0.833580i	0.120033	+	0.0323980i
$663$		−	1.69508i		−	0.0658313i
$664$	−27.0995	+	26.8039i	−1.05167	+	1.04019i
$665$		0			0
$666$	10.7086	−	39.6747i	0.414949	−	1.53736i
$667$	−39.6241			−1.53425
$668$	−2.51527	+	4.32003i	−0.0973187	+	0.167147i
$669$			12.2367i			0.473097i
$670$		0			0
$671$	−26.5862			−1.02635
$672$	0.818977	+	3.17215i	0.0315927	+	0.122368i
$673$		−	2.87683i		−	0.110894i	−0.998462	−	0.0554468i	$-0.982342\pi$
$673$		−	2.87683i		−	0.110894i	0.998462	−	0.0554468i	$-0.0176583\pi$
$674$	−39.1384	−	10.5638i	−1.50755	−	0.406903i
$675$		0			0
$676$	20.2858	+	11.8111i	0.780222	+	0.454272i
$677$	−28.6415			−1.10078			−0.550391	−	0.834907i	$-0.685521\pi$
$677$	−28.6415			−1.10078			−0.550391	+	0.834907i	$0.685521\pi$
$678$	−2.08074	−	0.561612i	−0.0799105	−	0.0215686i
$679$	−21.0753			−0.808794
$680$		0			0
$681$	12.6724			0.485607
$682$	39.2801	+	10.6021i	1.50411	+	0.405974i
$683$	18.3147			0.700792			0.350396	−	0.936602i	$-0.386047\pi$
$683$	18.3147			0.700792			0.350396	+	0.936602i	$0.386047\pi$
$684$	8.92833	−	15.3346i	0.341383	−	0.586332i
$685$		0			0
$686$	19.6144	+	5.29410i	0.748881	+	0.202130i
$687$			11.3241i			0.432043i
$688$	−12.3612	−	21.7765i	−0.471268	−	0.830220i
$689$	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	$0.911239\pi$
$692$	−1.01899	−	0.593291i	−0.0387361	−	0.0225535i
$693$	12.3516			0.469198
$694$	−1.11973	+	4.14856i	−0.0425045	+	0.157477i
$695$		0			0
$696$	−7.50073	−	7.58344i	−0.284314	−	0.287450i
$697$			6.12718i			0.232084i
$698$	−35.7185	−	9.64076i	−1.35197	−	0.364908i
$699$			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	$-0.113991\pi$
$702$	1.21900	−	4.51631i	0.0460080	−	0.170457i
$703$			34.4202i			1.29818i
$704$	31.9810	+	0.350765i	1.20533	+	0.0132200i
$705$		0			0
$706$	−40.2702	−	10.8693i	−1.51559	−	0.409072i
$707$	−1.99104			−0.0748809
$708$	−2.86551	+	4.92157i	−0.107692	+	0.184964i
$709$		−	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
$712$	−22.1022	+	21.8611i	−0.828314	+	0.819279i
$713$			38.7910i			1.45273i
$714$	−0.627443	+	2.32464i	−0.0234815	+	0.0869976i
$715$		0			0
$716$	−10.3681	+	17.8074i	−0.387474	+	0.665494i
$717$	6.35359			0.237279
$718$	−3.28473	+	12.1698i	−0.122585	+	0.454172i
$719$	−14.8496			−0.553797			−0.276899	−	0.960899i	$-0.589307\pi$
$719$	−14.8496			−0.553797			−0.276899	+	0.960899i	$0.589307\pi$
$720$		0			0
$721$	4.39356			0.163625
$722$	3.12899	−	11.5927i	0.116449	−	0.431437i
$723$	−10.4706			−0.389408
$724$	−17.9147	+	30.7689i	−0.665795	+	1.14352i
$725$		0			0
$726$	−0.942081	+	3.49036i	−0.0349639	+	0.129539i
$727$			6.22824i			0.230993i	0.993308	+	0.115496i	$0.0368459\pi$
$727$			6.22824i			0.230993i	−0.993308	+	0.115496i	$0.963154\pi$
$728$	2.52357	+	2.55140i	0.0935296	+	0.0945610i
$729$	−13.8082			−0.511416
$730$		0			0
$731$		−	18.4035i		−	0.680676i
$732$	3.43326	−	5.89669i	0.126897	−	0.217948i
$733$	−43.2406			−1.59713			−0.798564	−	0.601910i	$-0.794407\pi$
$733$	−43.2406			−1.59713			−0.798564	+	0.601910i	$0.794407\pi$
$734$	−30.9733	−	8.35999i	−1.14325	−	0.308573i
$735$		0			0
$736$	7.62276	+	29.5253i	0.280979	+	1.08832i
$737$		−	27.1770i		−	1.00108i
$738$	−2.10207	+	7.78806i	−0.0773783	+	0.286683i
$739$			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
$742$	−2.53540	−	0.684327i	−0.0930773	−	0.0251224i
$743$		−	5.85860i		−	0.214931i	−0.994209	−	0.107466i	$-0.965726\pi$
$743$		−	5.85860i		−	0.214931i	0.994209	−	0.107466i	$-0.0342736\pi$
$744$	−7.42400	+	7.34302i	−0.272177	+	0.269208i
$745$		0			0
$746$	−2.38180	+	8.82445i	−0.0872039	+	0.323086i
$747$	−36.8814			−1.34942
$748$	20.3137	+	11.8273i	0.742742	+	0.432450i
$749$		−	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	$0.594550\pi$
$752$	−7.80354	+	4.42962i	−0.284566	+	0.161532i
$753$		−	11.3900i		−	0.415075i
$754$	−11.2798	−	3.04452i	−0.410786	−	0.110875i
$755$		0			0
$756$	−3.34348	+	5.74250i	−0.121601	+	0.208853i
$757$	15.5665			0.565773			0.282886	−	0.959153i	$-0.408708\pi$
$757$	15.5665			0.565773			0.282886	+	0.959153i	$0.408708\pi$
$758$	5.89540	+	1.59122i	0.214130	+	0.0577958i
$759$	−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	$0.662178\pi$
$762$	8.59410	+	2.31963i	0.311331	+	0.0840312i
$763$	−17.6213			−0.637933
$764$	32.6784	+	19.0265i	1.18226	+	0.688356i
$765$		0			0
$766$	−15.1621	−	4.09238i	−0.547828	−	0.147864i
$767$			6.23810i			0.225245i
$768$	−4.20773	+	7.04794i	−0.151833	+	0.254321i
$769$	−17.0952			−0.616470			−0.308235	−	0.951310i	$-0.599738\pi$
$769$	−17.0952			−0.616470			−0.308235	+	0.951310i	$0.599738\pi$
$770$		0			0
$771$			6.69975i			0.241286i
$772$	10.3355	−	17.7514i	0.371982	−	0.638886i
$773$	−6.32624			−0.227539			−0.113770	−	0.993507i	$-0.536293\pi$
$773$	−6.32624			−0.227539			−0.113770	+	0.993507i	$0.536293\pi$
$774$	6.31373	−	23.3920i	0.226942	−	0.840809i
$775$		0			0
$776$	−37.1328	−	37.5423i	−1.33299	−	1.34769i
$777$		−	6.14916i		−	0.220600i
$778$	21.2300	+	5.73016i	0.761131	+	0.205436i
$779$		−	6.75661i		−	0.242081i
$780$		0			0
$781$		−	13.1063i		−	0.468981i
$782$	−5.84003	+	21.6370i	−0.208839	+	0.773738i
$783$		−	21.6341i		−	0.773138i
$784$	11.3059	+	19.9173i	0.403782	+	0.711332i
$785$		0			0
$786$	−9.29085	−	2.50769i	−0.331394	−	0.0894462i
$787$	53.5766			1.90980			0.954899	−	0.296929i	$-0.0959626\pi$
$787$	53.5766			1.90980			0.954899	+	0.296929i	$0.0959626\pi$
$788$	−0.358021	−	0.208452i	−0.0127540	−	0.00742581i
$789$		−	15.0003i		−	0.534026i
$790$		0			0
$791$	3.35339			0.119233
$792$	21.7624	+	22.0024i	0.773294	+	0.781822i
$793$		−	7.47406i		−	0.265412i
$794$	9.93838	−	36.8212i	0.352700	−	1.30673i
$795$		0			0
$796$	−21.2438	−	12.3689i	−0.752966	−	0.438403i
$797$	−41.6834			−1.47650			−0.738251	−	0.674527i	$-0.764348\pi$
$797$	−41.6834			−1.47650			−0.738251	+	0.674527i	$0.764348\pi$
$798$	0.691898	−	2.56345i	0.0244929	−	0.0907450i
$799$	−6.59483			−0.233308
$800$		0			0
$801$	−30.0802			−1.06283
$802$	13.3070	−	49.3018i	0.469887	−	1.74091i
$803$	27.8979			0.984495
$804$	6.02773	+	3.50956i	0.212582	+	0.123772i
$805$		0			0
$806$	−2.98051	+	11.0426i	−0.104984	+	0.388961i
$807$			10.9914i			0.386917i
$808$	−3.50805	−	3.54674i	−0.123413	−	0.124774i
$809$	26.9010			0.945788			0.472894	−	0.881119i	$-0.343209\pi$
$809$	26.9010			0.945788			0.472894	+	0.881119i	$0.343209\pi$
$810$		0			0
$811$			5.88980i			0.206819i	0.994639	+	0.103409i	$0.0329752\pi$
$811$			5.88980i			0.206819i	−0.994639	+	0.103409i	$0.967025\pi$
$812$	14.3423	+	8.35058i	0.503315	+	0.293048i
$813$	0.594069			0.0208349
$814$	−57.9560	−	15.6429i	−2.03136	−	0.548282i
$815$		0			0
$816$	−5.24649	+	2.97813i	−0.183664	+	0.104255i
$817$			20.2940i			0.709997i
$818$	−5.71758	+	21.1833i	−0.199911	+	0.740658i
$819$			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	$0.681454\pi$
$822$	−9.37664	−	2.53084i	−0.327048	−	0.0882733i
$823$			51.9289i			1.81013i	0.425277	+	0.905063i	$0.360177\pi$
$823$			51.9289i			1.81013i	−0.425277	+	0.905063i	$0.639823\pi$
$824$	7.74107	+	7.82644i	0.269673	+	0.272647i
$825$		0			0
$826$	2.30907	−	8.55498i	0.0803428	−	0.297666i
$827$	−28.2849			−0.983562			−0.491781	−	0.870719i	$-0.663654\pi$
$827$	−28.2849			−0.983562			−0.491781	+	0.870719i	$0.663654\pi$
$828$	−14.8461	+	25.4985i	−0.515939	+	0.886136i
$829$		−	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
$832$	−0.0986092	+	8.99068i	−0.00341866	+	0.311696i
$833$			16.8323i			0.583203i
$834$	−14.1910	−	3.83027i	−0.491393	−	0.132632i
$835$		0			0
$836$	−22.4004	−	13.0423i	−0.774735	−	0.451078i
$837$	−21.1792			−0.732060
$838$	36.7774	+	9.92656i	1.27045	+	0.342907i
$839$	−5.04346			−0.174120			−0.0870598	−	0.996203i	$-0.527747\pi$
$839$	−5.04346			−0.174120			−0.0870598	+	0.996203i	$0.527747\pi$
$840$		0			0
$841$	−25.0325			−0.863191
$842$	8.39202	+	2.26508i	0.289208	+	0.0780600i
$843$	4.61277			0.158872
$844$	3.94035	−	6.76763i	0.135633	−	0.232952i
$845$		0			0
$846$	−8.38247	−	2.26251i	−0.288195	−	0.0777866i
$847$		−	5.62517i		−	0.193283i
$848$	−3.24813	−	5.72214i	−0.111541	−	0.196499i
$849$	−7.92101			−0.271848
$850$		0			0
$851$		−	57.2343i		−	1.96197i
$852$	2.90692	+	1.69251i	0.0995895	+	0.0579845i
$853$	−46.2026			−1.58195			−0.790974	−	0.611850i	$-0.790426\pi$
$853$	−46.2026			−1.58195			−0.790974	+	0.611850i	$0.790426\pi$
$854$	−2.76657	+	10.2500i	−0.0946701	+	0.350748i
$855$		0			0
$856$	32.2043	−	31.8530i	1.10072	−	1.08871i
$857$			41.5405i			1.41900i	0.704707	+	0.709499i	$0.251079\pi$
$857$			41.5405i			1.41900i	−0.704707	+	0.709499i	$0.748921\pi$
$858$	−3.14733	−	0.849494i	−0.107448	−	0.0290012i
$859$			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
$862$	13.5948	−	50.3681i	0.463041	−	1.71554i
$863$			2.89022i			0.0983843i	0.998789	+	0.0491922i	$0.0156647\pi$
$863$			2.89022i			0.0983843i	−0.998789	+	0.0491922i	$0.984335\pi$
$864$	−16.1203	+	4.16189i	−0.548424	+	0.141590i
$865$		0			0
$866$	15.8141	+	4.26838i	0.537386	+	0.145046i
$867$	4.28761			0.145615
$868$	8.17501	−	14.0407i	0.277478	−	0.476574i
$869$		−	34.3949i		−	1.16677i
$870$		0			0
$871$	7.64015			0.258877
$872$	−31.0472	−	31.3896i	−1.05139	−	1.06299i
$873$		−	51.0935i		−	1.72925i
$874$	6.43996	−	23.8597i	0.217835	−	0.807067i
$875$		0			0
$876$	−3.60265	+	6.18762i	−0.121722	+	0.209060i
$877$	−43.0916			−1.45510			−0.727550	−	0.686055i	$-0.759341\pi$
$877$	−43.0916			−1.45510			−0.727550	+	0.686055i	$0.759341\pi$
$878$	1.53001	−	5.66860i	0.0516353	−	0.191306i
$879$	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	$0.511070\pi$
$882$	−5.77469	+	21.3949i	−0.194444	+	0.720405i
$883$	−51.4835			−1.73256			−0.866278	−	0.499562i	$-0.833494\pi$
$883$	−51.4835			−1.73256			−0.866278	+	0.499562i	$0.833494\pi$
$884$	−3.32497	+	5.71070i	−0.111831	+	0.192071i
$885$		0			0
$886$	5.79783	−	21.4807i	0.194782	−	0.721657i
$887$			55.5749i			1.86602i	0.359845	+	0.933012i	$0.382829\pi$
$887$			55.5749i			1.86602i	−0.359845	+	0.933012i	$0.617171\pi$
$888$	10.9538	−	10.8343i	0.367585	−	0.363575i
$889$	−13.8505			−0.464531
$890$		0			0
$891$			26.7877i			0.897422i
$892$	24.0028	−	41.2252i	0.803672	−	1.38032i
$893$	7.27229			0.243358
$894$	10.4066	+	2.80884i	0.348049	+	0.0939415i
$895$		0			0
$896$	3.46319	−	12.2934i	0.115697	−	0.410694i
$897$		−	3.10814i		−	0.103778i
$898$	7.62329	−	28.2439i	0.254393	−	0.942511i
$899$			52.8965i			1.76420i
$900$		0			0
$901$		−	4.83582i		−	0.161105i
$902$	11.3766	+	3.07066i	0.378801	+	0.102242i
$903$		−	3.62552i		−	0.120650i
$904$	5.90838	+	5.97354i	0.196510	+	0.198677i
$905$		0			0
$906$	1.91777	−	7.10525i	0.0637137	−	0.236056i
$907$	−15.8669			−0.526852			−0.263426	−	0.964680i	$-0.584853\pi$
$907$	−15.8669			−0.526852			−0.263426	+	0.964680i	$0.584853\pi$
$908$	−42.6931	−	24.8574i	−1.41682	−	0.824923i
$909$		−	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	$0.668170\pi$
$912$	5.78545	−	3.28406i	0.191575	−	0.108746i
$913$			53.8755i			1.78302i
$914$	39.2112	+	10.5835i	1.29699	+	0.350070i
$915$		0			0
$916$	22.2128	−	38.1509i	0.733931	−	1.26054i
$917$	14.9734			0.494465
$918$	−11.8134	−	3.18855i	−0.389901	−	0.105238i
$919$	15.1819			0.500803			0.250402	−	0.968142i	$-0.419437\pi$
$919$	15.1819			0.500803			0.250402	+	0.968142i	$0.419437\pi$
$920$		0			0
$921$	6.83572			0.225245
$922$	37.8290	+	10.2104i	1.24583	+	0.336261i
$923$	3.68452			0.121278
$924$	4.00183	+	2.33001i	0.131651	+	0.0766517i
$925$		0			0
$926$	−36.8061	−	9.93432i	−1.20952	−	0.326462i
$927$			10.6515i			0.349840i
$928$	10.3946	+	40.2616i	0.341220	+	1.32165i
$929$	8.00028			0.262481			0.131240	−	0.991351i	$-0.458104\pi$
$929$	8.00028			0.262481			0.131240	+	0.991351i	$0.458104\pi$
$930$		0			0
$931$		−	18.5614i		−	0.608325i
$932$	19.7326	−	33.8911i	0.646362	−	1.11014i
$933$	−1.64403			−0.0538231
$934$	11.5367	−	42.7427i	0.377491	−	1.39858i
$935$		0			0
$936$	−6.18544	+	6.11797i	−0.202178	+	0.199972i
$937$			10.0303i			0.327676i	0.986487	+	0.163838i	$0.0523875\pi$
$937$			10.0303i			0.327676i	−0.986487	+	0.163838i	$0.947613\pi$
$938$	−10.4778	−	2.82805i	−0.342112	−	0.0923391i
$939$			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	$0.978003\pi$
$942$	−1.41748	+	5.25168i	−0.0461839	+	0.171109i
$943$			11.2350i			0.365861i
$944$	19.3078	−	10.9599i	0.628414	−	0.356714i
$945$		0			0
$946$	−34.1706	−	9.22296i	−1.11098	−	0.299864i
$947$	3.33715			0.108443			0.0542213	−	0.998529i	$-0.482732\pi$
$947$	3.33715			0.108443			0.0542213	+	0.998529i	$0.482732\pi$
$948$	7.62863	+	4.44166i	0.247767	+	0.144258i
$949$			7.84281i			0.254588i
$950$		0			0
$951$	1.94528			0.0630800
$952$	6.67374	−	6.60095i	0.216297	−	0.213938i
$953$			10.9309i			0.354086i	0.984203	+	0.177043i	$0.0566531\pi$
$953$			10.9309i			0.354086i	−0.984203	+	0.177043i	$0.943347\pi$
$954$	1.65904	−	6.14665i	0.0537134	−	0.199005i
$955$		0			0
$956$	−21.4052	−	12.4629i	−0.692294	−	0.403078i
$957$	−15.0763			−0.487349
$958$	12.0465	−	44.6317i	0.389205	−	1.44199i
$959$	15.1117			0.487981
$960$		0			0
$961$	20.7844			0.670463
$962$	4.39761	−	16.2929i	0.141785	−	0.525305i
$963$	43.8287			1.41236
$964$	35.2755	+	20.5386i	1.13615	+	0.661505i
$965$		0			0
$966$	−1.15050	+	4.26253i	−0.0370167	+	0.137145i
$967$		−	40.7599i		−	1.31075i	−0.755304	−	0.655375i	$-0.772511\pi$
$967$		−	40.7599i		−	1.31075i	0.755304	−	0.655375i	$-0.227489\pi$
$968$	10.0204	−	9.91106i	0.322067	−	0.318553i
$969$	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	$-0.366654\pi$
$972$	−21.2020	−	12.3445i	−0.680054	−	0.395951i
$973$	22.8706			0.733197
$974$	24.0361	+	6.48756i	0.770165	+	0.207875i
$975$		0			0
$976$	−23.1332	+	13.1314i	−0.740477	+	0.420326i
$977$			17.1254i			0.547892i	0.961745	+	0.273946i	$0.0883289\pi$
$977$			17.1254i			0.547892i	−0.961745	+	0.273946i	$0.911671\pi$
$978$	−1.69246	+	6.27047i	−0.0541189	+	0.200508i
$979$			43.9405i			1.40434i
$980$		0			0
$981$		−	42.7199i		−	1.36394i
$982$	1.79041	+	0.483250i	0.0571344	+	0.0154211i
$983$		−	51.3738i		−	1.63857i	−0.573388	−	0.819284i	$-0.694371\pi$
$983$		−	51.3738i		−	1.63857i	0.573388	−	0.819284i	$-0.305629\pi$
$984$	−2.15020	+	2.12675i	−0.0685460	+	0.0677983i
$985$		0			0
$986$	−7.96363	+	29.5048i	−0.253614	+	0.939625i
$987$	−1.29919			−0.0413538
$988$	3.66653	−	6.29734i	0.116648	−	0.200345i
$989$		−	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	$0.624450\pi$
$992$	39.4151	−	10.1761i	1.25143	−	0.323090i
$993$			1.16045i			0.0368256i
$994$	−5.05299	−	1.36385i	−0.160271	−	0.0432587i
$995$		0			0
$996$	−11.9493	−	6.95732i	−0.378629	−	0.220451i
$997$	−7.90228			−0.250268			−0.125134	−	0.992140i	$-0.539936\pi$
$997$	−7.90228			−0.250268			−0.125134	+	0.992140i	$0.539936\pi$
$998$	−29.0349	−	7.83679i	−0.919084	−	0.248069i
$999$	31.2489			0.988673

Twists

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

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

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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.368522 - 1.36535i) q^{2} +0.513027 q^{3} +(-1.72838 - 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} +1.12889i q^{7} +(-2.01094 + 1.98900i) q^{8} -2.73680 q^{9} +O(q^{10})\)	\(q+(0.368522 - 1.36535i) q^{2} +0.513027 q^{3} +(-1.72838 - 1.00633i) q^{4} +(0.189062 - 0.700464i) q^{6} +1.12889i q^{7} +(-2.01094 + 1.98900i) q^{8} -2.73680 q^{9} +3.99787i q^{11} +(-0.886708 - 0.516272i) q^{12} -1.12390 q^{13} +(1.54133 + 0.416020i) q^{14} +(1.97462 + 3.47863i) q^{16} +2.93982i q^{17} +(-1.00857 + 3.73671i) q^{18} -3.24181i q^{19} +0.579150i q^{21} +(5.45850 + 1.47330i) q^{22} +5.39053i q^{23} +(-1.03167 + 1.02041i) q^{24} +(-0.414183 + 1.53452i) q^{26} -2.94314 q^{27} +(1.13603 - 1.95115i) q^{28} +7.35068i q^{29} +7.19613 q^{31} +(5.47725 - 1.41410i) q^{32} +2.05101i q^{33} +(4.01389 + 1.08339i) q^{34} +(4.73025 + 2.75411i) q^{36} -10.6176 q^{37} +(-4.42622 - 1.19468i) q^{38} -0.576592 q^{39} +2.08421 q^{41} +(0.790745 + 0.213429i) q^{42} -6.26007 q^{43} +(4.02315 - 6.90984i) q^{44} +(7.35999 + 1.98653i) q^{46} +2.24328i q^{47} +(1.01303 + 1.78463i) q^{48} +5.72561 q^{49} +1.50821i q^{51} +(1.94253 + 1.13101i) q^{52} -1.64494 q^{53} +(-1.08461 + 4.01842i) q^{54} +(-2.24536 - 2.27012i) q^{56} -1.66314i q^{57} +(10.0363 + 2.70889i) q^{58} -5.55039i q^{59} +6.65010i q^{61} +(2.65193 - 9.82527i) q^{62} -3.08954i q^{63} +(0.0877382 - 7.99952i) q^{64} +(2.80036 + 0.755843i) q^{66} -6.79788 q^{67} +(2.95841 - 5.08113i) q^{68} +2.76549i q^{69} -3.27833 q^{71} +(5.50354 - 5.44351i) q^{72} -6.97819i q^{73} +(-3.91280 + 14.4967i) q^{74} +(-3.26232 + 5.60310i) q^{76} -4.51314 q^{77} +(-0.212487 + 0.787253i) q^{78} -8.60333 q^{79} +6.70050 q^{81} +(0.768075 - 2.84568i) q^{82} +13.4761 q^{83} +(0.582813 - 1.00099i) q^{84} +(-2.30697 + 8.54721i) q^{86} +3.77110i q^{87} +(-7.95176 - 8.03946i) q^{88} +10.9910 q^{89} -1.26876i q^{91} +(5.42463 - 9.31691i) q^{92} +3.69181 q^{93} +(3.06287 + 0.826697i) q^{94} +(2.80998 - 0.725472i) q^{96} +18.6691i q^{97} +(2.11001 - 7.81749i) q^{98} -10.9414i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 20 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - q^6 - 12 * q^8 + 12 * q^9	\( 20 q + 3 q^{2} - 4 q^{3} - 3 q^{4} - q^{6} - 12 q^{8} + 12 q^{9} - 6 q^{12} - 6 q^{13} - 6 q^{14} + 9 q^{16} + 17 q^{18} + 8 q^{22} + 3 q^{24} + 10 q^{26} + 8 q^{27} + 2 q^{28} + 24 q^{31} - 7 q^{32} + 3 q^{34} - 20 q^{36} - 18 q^{37} - 24 q^{38} - 4 q^{39} + 22 q^{41} - q^{42} + 60 q^{43} - 4 q^{44} - 15 q^{46} - 57 q^{48} - 6 q^{49} - 13 q^{52} - 10 q^{53} + q^{54} + 25 q^{56} + 27 q^{58} + 34 q^{62} - 36 q^{64} + 21 q^{66} + 40 q^{67} + 29 q^{68} + 48 q^{71} + 47 q^{72} - 3 q^{74} - q^{76} - 24 q^{77} - 66 q^{78} - 48 q^{79} - 28 q^{81} - 54 q^{82} - 40 q^{83} - 58 q^{84} + 23 q^{86} - 17 q^{88} + 22 q^{89} - 75 q^{92} - 8 q^{93} + 7 q^{94} + 6 q^{96} + 55 q^{98}+O(q^{100}) \) 20 * q + 3 * q^2 - 4 * q^3 - 3 * q^4 - q^6 - 12 * q^8 + 12 * q^9 - 6 * q^12 - 6 * q^13 - 6 * q^14 + 9 * q^16 + 17 * q^18 + 8 * q^22 + 3 * q^24 + 10 * q^26 + 8 * q^27 + 2 * q^28 + 24 * q^31 - 7 * q^32 + 3 * q^34 - 20 * q^36 - 18 * q^37 - 24 * q^38 - 4 * q^39 + 22 * q^41 - q^42 + 60 * q^43 - 4 * q^44 - 15 * q^46 - 57 * q^48 - 6 * q^49 - 13 * q^52 - 10 * q^53 + q^54 + 25 * q^56 + 27 * q^58 + 34 * q^62 - 36 * q^64 + 21 * q^66 + 40 * q^67 + 29 * q^68 + 48 * q^71 + 47 * q^72 - 3 * q^74 - q^76 - 24 * q^77 - 66 * q^78 - 48 * q^79 - 28 * q^81 - 54 * q^82 - 40 * q^83 - 58 * q^84 + 23 * q^86 - 17 * q^88 + 22 * q^89 - 75 * q^92 - 8 * q^93 + 7 * q^94 + 6 * q^96 + 55 * q^98

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