LMFDB - Embedded newform 1000.2.o.a.349.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(149,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, 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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.17
Character	$\chi$	$=$	1000.349
Dual form			1000.2.o.a.149.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.532208 - 1.31025i) q^{2} +(-0.235999 + 0.171463i) q^{3} +(-1.43351 - 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} +0.234809i q^{7} +(-2.59027 + 1.13601i) q^{8} +(-0.900755 + 2.77224i) q^{9} +O(q^{10})$	\(q+(0.532208 - 1.31025i) q^{2} +(-0.235999 + 0.171463i) q^{3} +(-1.43351 - 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} +0.234809i q^{7} +(-2.59027 + 1.13601i) q^{8} +(-0.900755 + 2.77224i) q^{9} +(5.50105 - 1.78740i) q^{11} +(0.577439 + 0.0833422i) q^{12} +(0.580270 - 1.78589i) q^{13} +(0.307658 + 0.124967i) q^{14} +(0.109896 + 3.99849i) q^{16} +(2.42773 - 3.34149i) q^{17} +(3.15294 + 2.65562i) q^{18} +(1.59154 - 2.19056i) q^{19} +(-0.0402612 - 0.0554147i) q^{21} +(0.585764 - 8.15902i) q^{22} +(2.32295 - 0.754772i) q^{23} +(0.416517 - 0.712234i) q^{24} +(-2.03113 - 1.71076i) q^{26} +(-0.533191 - 1.64099i) q^{27} +(0.327477 - 0.336601i) q^{28} +(-3.89100 - 5.35551i) q^{29} +(-4.28302 - 3.11180i) q^{31} +(5.29751 + 1.98404i) q^{32} +(-0.991770 + 1.36505i) q^{33} +(-3.08612 - 4.95930i) q^{34} +(5.15755 - 2.71779i) q^{36} +(0.624829 - 1.92303i) q^{37} +(-2.02316 - 3.25115i) q^{38} +(0.169271 + 0.520963i) q^{39} +(2.13805 - 6.58023i) q^{41} +(-0.0940345 + 0.0232600i) q^{42} -8.04419 q^{43} +(-10.3786 - 5.10979i) q^{44} +(0.247353 - 3.44534i) q^{46} +(6.18554 + 8.51367i) q^{47} +(-0.711530 - 0.924798i) q^{48} +6.94486 q^{49} +1.20486i q^{51} +(-3.32251 + 1.75081i) q^{52} +(3.06610 - 2.22765i) q^{53} +(-2.43388 - 0.174737i) q^{54} +(-0.266745 - 0.608218i) q^{56} +0.789862i q^{57} +(-9.08787 + 2.24794i) q^{58} +(-6.66931 - 2.16699i) q^{59} +(-1.54958 + 0.503489i) q^{61} +(-6.35669 + 3.95570i) q^{62} +(-0.650947 - 0.211505i) q^{63} +(5.41896 - 5.88514i) q^{64} +(1.26073 + 2.02596i) q^{66} +(9.01003 + 6.54617i) q^{67} +(-8.14038 + 1.40421i) q^{68} +(-0.418799 + 0.576427i) q^{69} +(2.21139 - 1.60667i) q^{71} +(-0.816095 - 8.20411i) q^{72} +(14.3832 - 4.67339i) q^{73} +(-2.18711 - 1.84213i) q^{74} +(-5.33656 + 0.920553i) q^{76} +(0.419697 + 1.29170i) q^{77} +(0.772679 + 0.0554733i) q^{78} +(-10.3770 + 7.53932i) q^{79} +(-6.66742 - 4.84416i) q^{81} +(-7.48385 - 6.30342i) q^{82} +(2.55253 + 1.85452i) q^{83} +(-0.0195695 + 0.135588i) q^{84} +(-4.28118 + 10.5399i) q^{86} +(1.83655 + 0.596730i) q^{87} +(-12.2187 + 10.8791i) q^{88} +(3.51258 + 10.8106i) q^{89} +(0.419342 + 0.136252i) q^{91} +(-4.38261 - 2.15773i) q^{92} +1.54435 q^{93} +(14.4470 - 3.57356i) q^{94} +(-1.59040 + 0.440098i) q^{96} +(-4.11921 - 5.66961i) q^{97} +(3.69611 - 9.09951i) q^{98} +16.8602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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 $

$2$	0.532208	−	1.31025i	0.376328	−	0.926486i
$2$	0.532208	−	1.31025i	0.376328	−	0.926486i
$3$	−0.235999	+	0.171463i	−0.136254	+	0.0989945i	−0.653825	−	0.756646i	$-0.726837\pi$
$3$	−0.235999	+	0.171463i	−0.136254	+	0.0989945i	0.517570	+	0.855641i	$0.326837\pi$
$4$	−1.43351	−	1.39465i	−0.716754	−	0.697326i
$5$		0			0
$5$		0			0
$6$	0.0990593	+	0.400472i	0.0404408	+	0.163492i
$7$			0.234809i			0.0887494i	0.999015	+	0.0443747i	$0.0141296\pi$
$7$			0.234809i			0.0887494i	−0.999015	+	0.0443747i	$0.985870\pi$
$8$	−2.59027	+	1.13601i	−0.915798	+	0.401640i
$9$	−0.900755	+	2.77224i	−0.300252	+	0.924080i
$10$		0			0
$11$	5.50105	−	1.78740i	1.65863	−	0.538921i	0.678045	−	0.735021i	$-0.262828\pi$
$11$	5.50105	−	1.78740i	1.65863	−	0.538921i	0.980584	+	0.196099i	$0.0628276\pi$
$12$	0.577439	+	0.0833422i	0.166692	+	0.0240588i
$13$	0.580270	−	1.78589i	0.160938	−	0.495316i	−0.837776	−	0.546014i	$-0.816145\pi$
$13$	0.580270	−	1.78589i	0.160938	−	0.495316i	0.998714	+	0.0506981i	$0.0161446\pi$
$14$	0.307658	+	0.124967i	0.0822252	+	0.0333989i
$15$		0			0
$16$	0.109896	+	3.99849i	0.0274739	+	0.999623i
$17$	2.42773	−	3.34149i	0.588811	−	0.810429i	−0.405815	−	0.913955i	$-0.633012\pi$
$17$	2.42773	−	3.34149i	0.588811	−	0.810429i	0.994627	+	0.103526i	$0.0330124\pi$
$18$	3.15294	+	2.65562i	0.743154	+	0.625936i
$19$	1.59154	−	2.19056i	0.365124	−	0.502550i	−0.586443	−	0.809990i	$-0.699472\pi$
$19$	1.59154	−	2.19056i	0.365124	−	0.502550i	0.951567	+	0.307440i	$0.0994724\pi$
$20$		0			0
$21$	−0.0402612	−	0.0554147i	−0.00878571	−	0.0120925i
$22$	0.585764	−	8.15902i	0.124885	−	1.73951i
$23$	2.32295	−	0.754772i	0.484369	−	0.157381i	−0.0566456	−	0.998394i	$-0.518041\pi$
$23$	2.32295	−	0.754772i	0.484369	−	0.157381i	0.541014	+	0.841013i	$0.318041\pi$
$24$	0.416517	−	0.712234i	0.0850211	−	0.145384i
$25$		0			0
$26$	−2.03113	−	1.71076i	−0.398338	−	0.335508i
$27$	−0.533191	−	1.64099i	−0.102613	−	0.315809i
$28$	0.327477	−	0.336601i	0.0618873	−	0.0636116i
$29$	−3.89100	−	5.35551i	−0.722541	−	0.994493i	−0.999436	−	0.0335922i	$-0.989305\pi$
$29$	−3.89100	−	5.35551i	−0.722541	−	0.994493i	0.276894	−	0.960900i	$-0.410695\pi$
$30$		0			0
$31$	−4.28302	−	3.11180i	−0.769253	−	0.558895i	0.132482	−	0.991185i	$-0.457705\pi$
$31$	−4.28302	−	3.11180i	−0.769253	−	0.558895i	−0.901734	+	0.432291i	$0.857705\pi$
$32$	5.29751	+	1.98404i	0.936476	+	0.350732i
$33$	−0.991770	+	1.36505i	−0.172645	+	0.237625i
$34$	−3.08612	−	4.95930i	−0.529266	−	0.850513i
$35$		0			0
$36$	5.15755	−	2.71779i	0.859591	−	0.452965i
$37$	0.624829	−	1.92303i	0.102721	−	0.316144i	−0.886468	−	0.462791i	$-0.846848\pi$
$37$	0.624829	−	1.92303i	0.102721	−	0.316144i	0.989189	+	0.146647i	$0.0468481\pi$
$38$	−2.02316	−	3.25115i	−0.328199	−	0.527406i
$39$	0.169271	+	0.520963i	0.0271051	+	0.0834208i
$40$		0			0
$41$	2.13805	−	6.58023i	0.333907	−	1.02766i	−0.633352	−	0.773864i	$-0.718321\pi$
$41$	2.13805	−	6.58023i	0.333907	−	1.02766i	0.967258	−	0.253795i	$-0.0816787\pi$
$42$	−0.0940345	+	0.0232600i	−0.0145098	+	0.00358910i
$43$	−8.04419			−1.22673			−0.613364	−	0.789801i	$-0.710184\pi$
$43$	−8.04419			−1.22673			−0.613364	+	0.789801i	$0.710184\pi$
$44$	−10.3786	−	5.10979i	−1.56463	−	0.770330i
$45$		0			0
$46$	0.247353	−	3.44534i	0.0364702	−	0.507988i
$47$	6.18554	+	8.51367i	0.902254	+	1.24185i	0.969743	+	0.244126i	$0.0785012\pi$
$47$	6.18554	+	8.51367i	0.902254	+	1.24185i	−0.0674892	+	0.997720i	$0.521499\pi$
$48$	−0.711530	−	0.924798i	−0.102701	−	0.133483i
$49$	6.94486			0.992124
$50$		0			0
$51$			1.20486i			0.168714i
$52$	−3.32251	+	1.75081i	−0.460749	+	0.242794i
$53$	3.06610	−	2.22765i	0.421161	−	0.305991i	−0.356944	−	0.934126i	$-0.616181\pi$
$53$	3.06610	−	2.22765i	0.421161	−	0.305991i	0.778105	+	0.628135i	$0.216181\pi$
$54$	−2.43388	−	0.174737i	−0.331209	−	0.0237787i
$55$		0			0
$56$	−0.266745	−	0.608218i	−0.0356453	−	0.0812765i
$57$			0.789862i			0.104620i
$58$	−9.08787	+	2.24794i	−1.19330	+	0.295169i
$59$	−6.66931	−	2.16699i	−0.868270	−	0.282118i	−0.159192	−	0.987248i	$-0.550889\pi$
$59$	−6.66931	−	2.16699i	−0.868270	−	0.282118i	−0.709078	+	0.705130i	$0.750889\pi$
$60$		0			0
$61$	−1.54958	+	0.503489i	−0.198403	+	0.0644651i	−0.406533	−	0.913636i	$-0.633262\pi$
$61$	−1.54958	+	0.503489i	−0.198403	+	0.0644651i	0.208130	+	0.978101i	$0.433262\pi$
$62$	−6.35669	+	3.95570i	−0.807300	+	0.502375i
$63$	−0.650947	−	0.211505i	−0.0820116	−	0.0266472i
$64$	5.41896	−	5.88514i	0.677370	−	0.735642i
$65$		0			0
$66$	1.26073	+	2.02596i	0.155186	+	0.249378i
$67$	9.01003	+	6.54617i	1.10075	+	0.799742i	0.981182	−	0.193084i	$-0.0618489\pi$
$67$	9.01003	+	6.54617i	1.10075	+	0.799742i	0.119569	+	0.992826i	$0.461849\pi$
$68$	−8.14038	+	1.40421i	−0.987166	+	0.170286i
$69$	−0.418799	+	0.576427i	−0.0504174	+	0.0693936i
$70$		0			0
$71$	2.21139	−	1.60667i	0.262443	−	0.190676i	−0.448780	−	0.893642i	$-0.648141\pi$
$71$	2.21139	−	1.60667i	0.262443	−	0.190676i	0.711223	+	0.702966i	$0.248141\pi$
$72$	−0.816095	−	8.20411i	−0.0961777	−	0.966863i
$73$	14.3832	−	4.67339i	1.68343	−	0.546979i	0.697857	−	0.716237i	$-0.254137\pi$
$73$	14.3832	−	4.67339i	1.68343	−	0.546979i	0.985572	+	0.169258i	$0.0541371\pi$
$74$	−2.18711	−	1.84213i	−0.254246	−	0.214144i
$75$		0			0
$76$	−5.33656	+	0.920553i	−0.612145	+	0.105595i
$77$	0.419697	+	1.29170i	0.0478290	+	0.147202i
$78$	0.772679	+	0.0554733i	0.0874886	+	0.00628111i
$79$	−10.3770	+	7.53932i	−1.16750	+	0.848240i	−0.990708	−	0.136008i	$-0.956573\pi$
$79$	−10.3770	+	7.53932i	−1.16750	+	0.848240i	−0.176795	+	0.984248i	$0.556573\pi$
$80$		0			0
$81$	−6.66742	−	4.84416i	−0.740824	−	0.538240i
$82$	−7.48385	−	6.30342i	−0.826454	−	0.696097i
$83$	2.55253	+	1.85452i	0.280176	+	0.203560i	0.718994	−	0.695016i	$-0.244603\pi$
$83$	2.55253	+	1.85452i	0.280176	+	0.203560i	−0.438818	+	0.898576i	$0.644603\pi$
$84$	−0.0195695	+	0.135588i	−0.00213521	+	0.0147938i
$85$		0			0
$86$	−4.28118	+	10.5399i	−0.461652	+	1.13655i
$87$	1.83655	+	0.596730i	0.196899	+	0.0639762i
$88$	−12.2187	+	10.8791i	−1.30252	+	1.15971i
$89$	3.51258	+	10.8106i	0.372333	+	1.14592i	0.945260	+	0.326317i	$0.105808\pi$
$89$	3.51258	+	10.8106i	0.372333	+	1.14592i	−0.572927	+	0.819606i	$0.694192\pi$
$90$		0			0
$91$	0.419342	+	0.136252i	0.0439590	+	0.0142831i
$92$	−4.38261	−	2.15773i	−0.456919	−	0.224959i
$93$	1.54435			0.160141
$94$	14.4470	−	3.57356i	1.49010	−	0.368585i
$95$		0			0
$96$	−1.59040	+	0.440098i	−0.162319	+	0.0449173i
$97$	−4.11921	−	5.66961i	−0.418243	−	0.575661i	0.546962	−	0.837157i	$-0.315784\pi$
$97$	−4.11921	−	5.66961i	−0.418243	−	0.575661i	−0.965205	+	0.261496i	$0.915784\pi$
$98$	3.69611	−	9.09951i	0.373364	−	0.919189i
$99$			16.8602i			1.69452i
$100$		0			0
$101$		−	10.9484i		−	1.08941i	−0.838628	−	0.544704i	$-0.816642\pi$
$101$		−	10.9484i		−	1.08941i	0.838628	−	0.544704i	$-0.183358\pi$
$102$	1.57866	+	0.641234i	0.156311	+	0.0634916i
$103$	−6.88143	−	9.47147i	−0.678047	−	0.933252i	0.321861	−	0.946787i	$-0.395692\pi$
$103$	−6.88143	−	9.47147i	−0.678047	−	0.933252i	−0.999908	+	0.0135350i	$0.995692\pi$
$104$	0.525731	+	5.28511i	0.0515522	+	0.518248i
$105$		0			0
$106$	−1.28698	−	5.20293i	−0.125002	−	0.505353i
$107$	−0.352640			−0.0340910			−0.0170455	−	0.999855i	$-0.505426\pi$
$107$	−0.352640			−0.0340910			−0.0170455	+	0.999855i	$0.505426\pi$
$108$	−1.52428	+	3.09600i	−0.146674	+	0.297912i
$109$	9.24706	+	3.00455i	0.885708	+	0.287784i	0.716325	−	0.697767i	$-0.245823\pi$
$109$	9.24706	+	3.00455i	0.885708	+	0.287784i	0.169382	+	0.985550i	$0.445823\pi$
$110$		0			0
$111$	0.182270	+	0.560968i	0.0173003	+	0.0532448i
$112$	−0.938881	+	0.0258045i	−0.0887159	+	0.00243829i
$113$	0.311428	+	0.101189i	0.0292967	+	0.00951907i	0.323629	−	0.946184i	$-0.395097\pi$
$113$	0.311428	+	0.101189i	0.0292967	+	0.00951907i	−0.294332	+	0.955703i	$0.595097\pi$
$114$	1.03492	+	0.420371i	0.0969288	+	0.0393714i
$115$		0			0
$116$	−1.89128	+	13.1038i	−0.175601	+	1.21665i
$117$	4.42822	+	3.21729i	0.409389	+	0.297439i
$118$	−6.38876	+	7.58517i	−0.588133	+	0.698272i
$119$	0.784611	+	0.570053i	0.0719252	+	0.0522567i
$120$		0			0
$121$	18.1676	−	13.1995i	1.65160	−	1.19995i
$122$	−0.165003	+	2.29830i	−0.0149386	+	0.208078i
$123$	0.623691	+	1.91953i	0.0562364	+	0.173078i
$124$	1.79988	+	10.4341i	0.161634	+	0.937010i
$125$		0			0
$126$	−0.623564	+	0.740338i	−0.0555515	+	0.0659545i
$127$	8.78610	−	2.85478i	0.779640	−	0.253320i	0.107954	−	0.994156i	$-0.465570\pi$
$127$	8.78610	−	2.85478i	0.779640	−	0.253320i	0.671687	+	0.740835i	$0.265570\pi$
$128$	−4.82698	−	10.2323i	−0.426649	−	0.904417i
$129$	1.89842	−	1.37928i	0.167147	−	0.121439i
$130$		0			0
$131$	−4.46019	+	6.13893i	−0.389689	+	0.536361i	−0.958119	−	0.286371i	$-0.907551\pi$
$131$	−4.46019	+	6.13893i	−0.389689	+	0.536361i	0.568430	+	0.822732i	$0.307551\pi$
$132$	3.32548	−	0.573644i	0.289446	−	0.0499293i
$133$	0.514364	+	0.373707i	0.0446010	+	0.0324045i
$134$	13.3723	−	8.32147i	1.15519	−	0.718865i
$135$		0			0
$136$	−2.49251	+	11.4133i	−0.213731	+	0.978680i
$137$	12.5733	+	4.08531i	1.07421	+	0.349032i	0.792125	−	0.610358i	$-0.208975\pi$
$137$	12.5733	+	4.08531i	1.07421	+	0.349032i	0.282083	+	0.959390i	$0.408975\pi$
$138$	0.532375	+	0.855510i	0.0453188	+	0.0728258i
$139$	−2.15160	+	0.699096i	−0.182496	+	0.0592965i	−0.398839	−	0.917021i	$-0.630587\pi$
$139$	−2.15160	+	0.699096i	−0.182496	+	0.0592965i	0.216343	+	0.976317i	$0.430587\pi$
$140$		0			0
$141$	−2.91957	−	0.948625i	−0.245872	−	0.0798886i
$142$	−0.928216	−	3.75255i	−0.0778941	−	0.314907i
$143$		−	10.8614i		−	0.908278i
$144$	−11.1838	−	3.29700i	−0.931980	−	0.274750i
$145$		0			0
$146$	1.53156	−	21.3328i	0.126753	−	1.76552i
$147$	−1.63898	+	1.19079i	−0.135181	+	0.0982148i
$148$	−3.57765	+	1.88526i	−0.294081	+	0.154967i
$149$		−	15.3980i		−	1.26145i	−0.776004	−	0.630727i	$-0.782757\pi$
$149$		−	15.3980i		−	1.26145i	0.776004	−	0.630727i	$-0.217243\pi$
$150$		0			0
$151$	0.300063			0.0244187			0.0122094	−	0.999925i	$-0.496114\pi$
$151$	0.300063			0.0244187			0.0122094	+	0.999925i	$0.496114\pi$
$152$	−1.63401	+	7.48215i	−0.132535	+	0.606882i
$153$	7.07661	+	9.74011i	0.572110	+	0.787441i
$154$	1.91581	+	0.137543i	0.154380	+	0.0110835i
$155$		0			0
$156$	0.483910	−	0.982879i	0.0387438	−	0.0786933i
$157$	−20.8929			−1.66744			−0.833719	−	0.552189i	$-0.813793\pi$
$157$	−20.8929			−1.66744			−0.833719	+	0.552189i	$0.813793\pi$
$158$	4.35568	+	17.6089i	0.346519	+	1.40089i
$159$	−0.341636	+	1.05145i	−0.0270935	+	0.0833852i
$160$		0			0
$161$	0.177227	+	0.545449i	0.0139675	+	0.0429874i
$162$	−9.89552	+	6.15788i	−0.777465	+	0.483809i
$163$	−3.86624	+	11.8991i	−0.302827	+	0.932006i	0.677652	+	0.735383i	$0.262998\pi$
$163$	−3.86624	+	11.8991i	−0.302827	+	0.932006i	−0.980479	+	0.196624i	$0.937002\pi$
$164$	−12.2420	+	6.45099i	−0.955942	+	0.503737i
$165$		0			0
$166$	3.78836	−	2.35746i	0.294034	−	0.182974i
$167$	−12.6676	+	17.4355i	−0.980251	+	1.34920i	−0.0435571	+	0.999051i	$0.513869\pi$
$167$	−12.6676	+	17.4355i	−0.980251	+	1.34920i	−0.936694	+	0.350149i	$0.886131\pi$
$168$	0.167239	+	0.0978019i	0.0129028	+	0.00754558i
$169$	7.66454	+	5.56862i	0.589580	+	0.428355i
$170$		0			0
$171$	4.63918	+	6.38529i	0.354767	+	0.488295i
$172$	11.5314	+	11.2188i	0.879262	+	0.855428i
$173$	0.492423	+	1.51552i	0.0374382	+	0.115223i	0.968029	−	0.250838i	$-0.0807061\pi$
$173$	0.492423	+	1.51552i	0.0374382	+	0.115223i	−0.930591	+	0.366061i	$0.880706\pi$
$174$	1.75929	−	2.08875i	0.133372	−	0.158348i
$175$		0			0
$176$	7.75144	+	21.7995i	0.584287	+	1.64320i
$177$	1.94551	−	0.632135i	0.146234	−	0.0475142i
$178$	16.0340	+	1.15114i	1.20180	+	0.0862815i
$179$	6.51305	+	8.96444i	0.486808	+	0.670034i	0.979795	−	0.200003i	$-0.0640951\pi$
$179$	6.51305	+	8.96444i	0.486808	+	0.670034i	−0.492987	+	0.870037i	$0.664095\pi$
$180$		0			0
$181$	−11.7991	+	16.2401i	−0.877020	+	1.20711i	0.100217	+	0.994966i	$0.468046\pi$
$181$	−11.7991	+	16.2401i	−0.877020	+	1.20711i	−0.977237	+	0.212149i	$0.931954\pi$
$182$	0.401702	−	0.476928i	0.0297761	−	0.0353523i
$183$	0.279369	−	0.384519i	0.0206516	−	0.0284245i
$184$	−5.15963	+	4.59396i	−0.380373	+	0.338671i
$185$		0			0
$186$	0.821915	−	2.02348i	0.0602657	−	0.148369i
$187$	7.38250	−	22.7210i	0.539862	−	1.66152i
$188$	3.00657	−	20.8311i	0.219277	−	1.51926i
$189$	0.385320	−	0.125198i	0.0280279	−	0.00910682i
$190$		0			0
$191$	−5.85762	+	18.0279i	−0.423842	+	1.30445i	0.480256	+	0.877128i	$0.340544\pi$
$191$	−5.85762	+	18.0279i	−0.423842	+	1.30445i	−0.904099	+	0.427324i	$0.859456\pi$
$192$	−0.269785	+	2.31804i	−0.0194701	+	0.167290i
$193$			2.63353i			0.189566i	0.995498	+	0.0947828i	$0.0302157\pi$
$193$			2.63353i			0.189566i	−0.995498	+	0.0947828i	$0.969784\pi$
$194$	−9.62088	+	2.37978i	−0.690739	+	0.170859i
$195$		0			0
$196$	−9.95553	−	9.68566i	−0.711109	−	0.691833i
$197$	−20.4204	+	14.8363i	−1.45489	+	1.05704i	−0.470233	+	0.882542i	$0.655830\pi$
$197$	−20.4204	+	14.8363i	−1.45489	+	1.05704i	−0.984658	+	0.174498i	$0.944170\pi$
$198$	22.0911	+	8.97315i	1.56995	+	0.637694i
$199$	3.97231			0.281589			0.140795	−	0.990039i	$-0.455034\pi$
$199$	3.97231			0.281589			0.140795	+	0.990039i	$0.455034\pi$
$200$		0			0
$201$	−3.24879			−0.229152
$202$	−14.3452	−	5.82683i	−1.00932	−	0.409975i
$203$	1.25752	−	0.913642i	0.0882607	−	0.0641251i
$204$	1.68035	−	1.72717i	0.117648	−	0.120926i
$205$		0			0
$206$	−16.0723	+	3.97559i	−1.11981	+	0.276993i
$207$			7.11964i			0.494849i
$208$	7.20462	+	2.12394i	0.499550	+	0.147269i
$209$	4.83972	−	14.8951i	0.334770	−	1.03032i
$210$		0			0
$211$	13.9414	−	4.52984i	0.959766	−	0.311847i	0.213088	−	0.977033i	$-0.431648\pi$
$211$	13.9414	−	4.52984i	0.959766	−	0.311847i	0.746678	+	0.665186i	$0.231648\pi$
$212$	−7.50207	−	1.08278i	−0.515244	−	0.0743656i
$213$	−0.246401	+	0.758344i	−0.0168831	+	0.0519609i
$214$	−0.187678	+	0.462047i	−0.0128294	+	0.0315849i
$215$		0			0
$216$	3.24529	+	3.64490i	0.220814	+	0.248004i
$217$	0.730677	−	1.00569i	0.0496016	−	0.0682708i
$218$	8.85807	−	10.5169i	0.599944	−	0.712295i
$219$	−2.59311	+	3.56911i	−0.175226	+	0.241178i
$220$		0			0
$221$	−4.55877	−	6.27461i	−0.306656	−	0.422076i
$222$	0.832014	+	0.0597331i	0.0558411	+	0.00400903i
$223$	16.2169	−	5.26920i	1.08597	−	0.352852i	0.289280	−	0.957245i	$-0.406584\pi$
$223$	16.2169	−	5.26920i	1.08597	−	0.352852i	0.796686	+	0.604393i	$0.206584\pi$
$224$	−0.465870	+	1.24390i	−0.0311272	+	0.0831117i
$225$		0			0
$226$	0.298328	−	0.354195i	0.0198445	−	0.0235607i
$227$	4.52341	+	13.9216i	0.300229	+	0.924011i	0.981414	+	0.191900i	$0.0614649\pi$
$227$	4.52341	+	13.9216i	0.300229	+	0.924011i	−0.681185	+	0.732111i	$0.738535\pi$
$228$	1.10158	−	1.13227i	0.0729541	−	0.0749867i
$229$	3.58252	+	4.93092i	0.236740	+	0.325844i	0.910812	−	0.412821i	$-0.135456\pi$
$229$	3.58252	+	4.93092i	0.236740	+	0.325844i	−0.674072	+	0.738665i	$0.735456\pi$
$230$		0			0
$231$	−0.320527	−	0.232876i	−0.0210891	−	0.0153221i
$232$	16.1626	+	9.45197i	1.06113	+	0.620552i
$233$	−4.19480	+	5.77365i	−0.274811	+	0.378244i	−0.924006	−	0.382377i	$-0.875106\pi$
$233$	−4.19480	+	5.77365i	−0.274811	+	0.378244i	0.649196	+	0.760621i	$0.275106\pi$
$234$	6.57219	−	4.08981i	0.429638	−	0.267359i
$235$		0			0
$236$	6.53832	+	12.4078i	0.425608	+	0.807676i
$237$	1.15624	−	3.55855i	0.0751060	−	0.231153i
$238$	1.16449	−	0.724649i	0.0754826	−	0.0469720i
$239$	−1.65706	−	5.09989i	−0.107186	−	0.329885i	0.883051	−	0.469276i	$-0.155485\pi$
$239$	−1.65706	−	5.09989i	−0.107186	−	0.329885i	−0.990237	+	0.139392i	$0.955485\pi$
$240$		0			0
$241$	−0.583541	+	1.79595i	−0.0375892	+	0.115688i	−0.968090	−	0.250601i	$-0.919372\pi$
$241$	−0.583541	+	1.79595i	−0.0375892	+	0.115688i	0.930501	+	0.366289i	$0.119372\pi$
$242$	−7.62572	−	30.8289i	−0.490200	−	1.98176i
$243$	7.58043			0.486285
$244$	2.92353	+	1.43937i	0.187160	+	0.0921460i
$245$		0			0
$246$	2.84699	+	0.204395i	0.181518	+	0.0130318i
$247$	−2.98858	−	4.11342i	−0.190159	−	0.261731i
$248$	14.6292	+	3.19483i	0.928954	+	0.202872i
$249$	−0.920377			−0.0583265
$250$		0			0
$251$			4.55040i			0.287219i	0.989634	+	0.143609i	$0.0458709\pi$
$251$			4.55040i			0.287219i	−0.989634	+	0.143609i	$0.954129\pi$
$252$	0.638161	+	1.21104i	0.0402004	+	0.0762882i
$253$	11.4296	−	8.30408i	0.718572	−	0.522073i
$254$	0.935563	−	13.0313i	0.0587025	−	0.817658i
$255$		0			0
$256$	−15.9758	+	0.878833i	−0.998490	+	0.0549271i
$257$		−	6.99079i		−	0.436074i	−0.975941	−	0.218037i	$-0.930035\pi$
$257$		−	6.99079i		−	0.436074i	0.975941	−	0.218037i	$-0.0699653\pi$
$258$	−0.796851	−	3.22147i	−0.0496098	−	0.200560i
$259$	0.451544	+	0.146716i	0.0280576	+	0.00911646i
$260$		0			0
$261$	18.3516	−	5.96279i	1.13593	−	0.369088i
$262$	5.66978	+	9.11115i	0.350280	+	0.562889i
$263$	−21.5131	−	6.99005i	−1.32656	−	0.431025i	−0.441816	−	0.897106i	$-0.645665\pi$
$263$	−21.5131	−	6.99005i	−1.32656	−	0.431025i	−0.884742	+	0.466081i	$0.845665\pi$
$264$	1.01823	−	4.66251i	0.0626679	−	0.286958i
$265$		0			0
$266$	0.763399	−	0.475055i	0.0468070	−	0.0291275i
$267$	−2.68259	−	1.94902i	−0.164172	−	0.119278i
$268$	−3.78634	−	21.9499i	−0.231287	−	1.34080i
$269$	−3.68963	+	5.07835i	−0.224961	+	0.309632i	−0.906546	−	0.422106i	$-0.861291\pi$
$269$	−3.68963	+	5.07835i	−0.224961	+	0.309632i	0.681585	+	0.731739i	$0.261291\pi$
$270$		0			0
$271$	−2.75055	+	1.99839i	−0.167084	+	0.121393i	−0.668185	−	0.743995i	$-0.732928\pi$
$271$	−2.75055	+	1.99839i	−0.167084	+	0.121393i	0.501101	+	0.865389i	$0.332928\pi$
$272$	13.6277	+	9.34005i	0.826300	+	0.566323i
$273$	−0.122327	+	0.0397464i	−0.00740355	+	0.00240556i
$274$	12.0444	−	14.2999i	0.727628	−	0.863890i
$275$		0			0
$276$	1.40427	−	0.242235i	0.0845269	−	0.0145808i
$277$	−7.95552	−	24.4846i	−0.478001	−	1.47114i	−0.841868	−	0.539684i	$-0.818544\pi$
$277$	−7.95552	−	24.4846i	−0.478001	−	1.47114i	0.363867	−	0.931451i	$-0.381456\pi$
$278$	−0.229107	+	3.19119i	−0.0137409	+	0.191395i
$279$	12.4846	−	9.07059i	0.747433	−	0.543042i
$280$		0			0
$281$	−3.16034	−	2.29612i	−0.188530	−	0.136975i	0.489517	−	0.871994i	$-0.337173\pi$
$281$	−3.16034	−	2.29612i	−0.188530	−	0.136975i	−0.678047	+	0.735019i	$0.737173\pi$
$282$	−2.79675	+	3.32050i	−0.166544	+	0.197733i
$283$	1.03911	+	0.754960i	0.0617689	+	0.0448777i	0.618241	−	0.785988i	$-0.287845\pi$
$283$	1.03911	+	0.754960i	0.0617689	+	0.0448777i	−0.556472	+	0.830866i	$0.687845\pi$
$284$	−5.41078	−	0.780942i	−0.321071	−	0.0463404i
$285$		0			0
$286$	−14.2312	−	5.78054i	−0.841507	−	0.341810i
$287$	1.54510	+	0.502032i	0.0912041	+	0.0296340i
$288$	−10.2720	+	12.8988i	−0.605283	+	0.760071i
$289$	−0.0183581	−	0.0565005i	−0.00107989	−	0.00332356i
$290$		0			0
$291$	1.94426	+	0.631729i	0.113975	+	0.0370326i
$292$	−27.1362	−	13.3602i	−1.58803	−	0.781848i
$293$	8.55020			0.499508			0.249754	−	0.968309i	$-0.419650\pi$
$293$	8.55020			0.499508			0.249754	+	0.968309i	$0.419650\pi$
$294$	0.687953	+	2.78123i	0.0401222	+	0.162204i
$295$		0			0
$296$	0.566103	+	5.69096i	0.0329041	+	0.330781i
$297$	−5.86622	−	8.07416i	−0.340393	−	0.468510i
$298$	−20.1753	−	8.19495i	−1.16872	−	0.474721i
$299$		−	4.58650i		−	0.265244i
$300$		0			0
$301$		−	1.88885i		−	0.108871i
$302$	0.159696	−	0.393157i	0.00918946	−	0.0226236i
$303$	1.87725	+	2.58382i	0.107845	+	0.148436i
$304$	8.93385	+	6.12302i	0.512392	+	0.351179i
$305$		0			0
$306$	16.5282	−	4.08835i	0.944855	−	0.233716i
$307$	11.0920			0.633052			0.316526	−	0.948584i	$-0.397483\pi$
$307$	11.0920			0.633052			0.316526	+	0.948584i	$0.397483\pi$
$308$	1.19983	−	2.43699i	0.0683664	−	0.138860i
$309$	3.24802	+	1.05535i	0.184774	+	0.0600366i
$310$		0			0
$311$	9.28886	+	28.5882i	0.526723	+	1.62109i	0.760883	+	0.648889i	$0.224766\pi$
$311$	9.28886	+	28.5882i	0.526723	+	1.62109i	−0.234160	+	0.972198i	$0.575234\pi$
$312$	−1.03028	−	1.15714i	−0.0583279	−	0.0655101i
$313$	−0.0349980	−	0.0113715i	−0.00197820	−	0.000642758i	0.308028	−	0.951377i	$-0.400331\pi$
$313$	−0.0349980	−	0.0113715i	−0.00197820	−	0.000642758i	−0.310006	+	0.950735i	$0.600331\pi$
$314$	−11.1194	+	27.3750i	−0.627504	+	1.54486i
$315$		0			0
$316$	25.3902	+	3.66459i	1.42831	+	0.206149i
$317$	13.1594	+	9.56085i	0.739104	+	0.536991i	0.892431	−	0.451185i	$-0.148998\pi$
$317$	13.1594	+	9.56085i	0.739104	+	0.536991i	−0.153326	+	0.988176i	$0.548998\pi$
$318$	1.19584	+	1.00722i	0.0670592	+	0.0564819i
$319$	−30.9770	−	22.5061i	−1.73438	−	1.26010i
$320$		0			0
$321$	0.0832228	−	0.0604649i	0.00464505	−	0.00337482i
$322$	0.808997	+	0.0580807i	0.0450836	+	0.00323671i
$323$	−3.45591	−	10.6362i	−0.192292	−	0.591814i
$324$	2.80189	+	16.2429i	0.155660	+	0.902382i
$325$		0			0
$326$	13.5331	+	11.3985i	0.749529	+	0.631305i
$327$	−2.69747	+	0.876461i	−0.149170	+	0.0484684i
$328$	1.93710	+	19.4734i	0.106958	+	1.07524i
$329$	−1.99909	+	1.45242i	−0.110213	+	0.0800746i
$330$		0			0
$331$	−13.3539	+	18.3800i	−0.733995	+	1.01026i	0.264947	+	0.964263i	$0.414645\pi$
$331$	−13.3539	+	18.3800i	−0.733995	+	1.01026i	−0.998942	+	0.0459939i	$0.985355\pi$
$332$	−1.07266	−	6.21836i	−0.0588700	−	0.341277i
$333$	4.76827	+	3.46435i	0.261300	+	0.189845i
$334$	16.1030	+	25.8771i	0.881120	+	1.41593i
$335$		0			0
$336$	0.217151	−	0.167074i	0.0118465	−	0.00911462i
$337$	−17.8926	−	5.81367i	−0.974674	−	0.316691i	−0.221972	−	0.975053i	$-0.571249\pi$
$337$	−17.8926	−	5.81367i	−0.974674	−	0.316691i	−0.752701	+	0.658362i	$0.771249\pi$
$338$	11.3754	−	7.07880i	0.618741	−	0.385036i
$339$	−0.0908470	+	0.0295180i	−0.00493413	+	0.00160320i
$340$		0			0
$341$	−29.1231	−	9.46267i	−1.57711	−	0.512433i
$342$	10.8353	−	2.68019i	0.585908	−	0.144928i
$343$			3.27438i			0.176800i
$344$	20.8366	−	9.13828i	1.12343	−	0.492703i
$345$		0			0
$346$	2.24778	+	0.161376i	0.120842	+	0.00867564i
$347$	−23.8972	+	17.3624i	−1.28287	+	0.932060i	−0.999636	−	0.0269903i	$-0.991408\pi$
$347$	−23.8972	+	17.3624i	−1.28287	+	0.932060i	−0.283235	+	0.959051i	$0.591408\pi$
$348$	−1.80048	−	3.41676i	−0.0965157	−	0.183158i
$349$		−	15.7634i		−	0.843797i	−0.906643	−	0.421898i	$-0.861364\pi$
$349$		−	15.7634i		−	0.843797i	0.906643	−	0.421898i	$-0.138636\pi$
$350$		0			0
$351$	−3.24002			−0.172940
$352$	32.6881	+	1.44553i	1.74228	+	0.0770471i
$353$	4.79864	+	6.60477i	0.255406	+	0.351536i	0.917395	−	0.397977i	$-0.130288\pi$
$353$	4.79864	+	6.60477i	0.255406	+	0.351536i	−0.661989	+	0.749513i	$0.730288\pi$
$354$	0.207162	−	2.88553i	0.0110106	−	0.153364i
$355$		0			0
$356$	10.0417	−	20.3960i	0.532210	−	1.08098i
$357$	−0.282911			−0.0149732
$358$	15.2120	−	3.76277i	0.803977	−	0.198869i
$359$	−9.42480	+	29.0065i	−0.497422	+	1.53091i	0.315727	+	0.948850i	$0.397752\pi$
$359$	−9.42480	+	29.0065i	−0.497422	+	1.53091i	−0.813148	+	0.582056i	$0.802248\pi$
$360$		0			0
$361$	3.60574	+	11.0973i	0.189776	+	0.584071i
$362$	14.9990	+	24.1029i	0.788328	+	1.26682i
$363$	−2.02430	+	6.23015i	−0.106248	+	0.326998i
$364$	−0.411106	−	0.780155i	−0.0215478	−	0.0408912i
$365$		0			0
$366$	−0.355133	−	0.570688i	−0.0185631	−	0.0298303i
$367$	4.40881	−	6.06821i	0.230138	−	0.316758i	−0.678294	−	0.734791i	$-0.737280\pi$
$367$	4.40881	−	6.06821i	0.230138	−	0.316758i	0.908432	+	0.418033i	$0.137280\pi$
$368$	3.27323	+	9.20535i	0.170629	+	0.479862i
$369$	16.3161	+	11.8543i	0.849383	+	0.617113i
$370$		0			0
$371$	0.523072	+	0.719947i	0.0271565	+	0.0373778i
$372$	−2.21384	−	2.15383i	−0.114782	−	0.111671i
$373$	−3.94238	−	12.1334i	−0.204129	−	0.628243i	−0.999748	−	0.0224465i	$-0.992854\pi$
$373$	−3.94238	−	12.1334i	−0.204129	−	0.628243i	0.795619	−	0.605797i	$-0.207146\pi$
$374$	−25.8412	−	21.7652i	−1.33621	−	1.12545i
$375$		0			0
$376$	−25.6938	−	15.0258i	−1.32506	−	0.774898i
$377$	−11.8222	+	3.84125i	−0.608872	+	0.197834i
$378$	0.0410297	−	0.571497i	0.00211034	−	0.0293946i
$379$	−7.20040	−	9.91051i	−0.369860	−	0.509069i	0.583003	−	0.812470i	$-0.301878\pi$
$379$	−7.20040	−	9.91051i	−0.369860	−	0.509069i	−0.952863	+	0.303402i	$0.901878\pi$
$380$		0			0
$381$	−1.58402	+	2.18022i	−0.0811519	+	0.111696i
$382$	20.5036	+	17.2695i	1.04905	+	0.883586i
$383$	−15.8262	+	21.7829i	−0.808681	+	1.11305i	0.182844	+	0.983142i	$0.441470\pi$
$383$	−15.8262	+	21.7829i	−0.808681	+	1.11305i	−0.991525	+	0.129912i	$0.958530\pi$
$384$	2.89363	+	1.58717i	0.147665	+	0.0809948i
$385$		0			0
$386$	3.45058	+	1.40159i	0.175630	+	0.0713388i
$387$	7.24584	−	22.3004i	0.368327	−	1.13359i
$388$	−2.00220	+	13.8723i	−0.101646	+	0.704259i
$389$	−9.06656	+	2.94590i	−0.459693	+	0.149363i	−0.529703	−	0.848183i	$-0.677697\pi$
$389$	−9.06656	+	2.94590i	−0.459693	+	0.149363i	0.0700104	+	0.997546i	$0.477697\pi$
$390$		0			0
$391$	3.11744	−	9.59449i	0.157656	−	0.485214i
$392$	−17.9891	+	7.88944i	−0.908584	+	0.398477i
$393$		−	2.21354i		−	0.111658i
$394$	8.57133	+	34.6518i	0.431817	+	1.74573i
$395$		0			0
$396$	23.5141	−	24.1693i	1.18163	−	1.21455i
$397$	18.8253	−	13.6774i	0.944816	−	0.686449i	−0.00475885	−	0.999989i	$-0.501515\pi$
$397$	18.8253	−	13.6774i	0.944816	−	0.686449i	0.949575	+	0.313539i	$0.101515\pi$
$398$	2.11409	−	5.20471i	0.105970	−	0.260889i
$399$	−0.185467			−0.00928495
$400$		0			0
$401$	12.2917			0.613820			0.306910	−	0.951739i	$-0.400705\pi$
$401$	12.2917			0.613820			0.306910	+	0.951739i	$0.400705\pi$
$402$	−1.72903	+	4.25673i	−0.0862363	+	0.212306i
$403$	−8.04262	+	5.84330i	−0.400631	+	0.291076i
$404$	−15.2692	+	15.6946i	−0.759672	+	0.780838i
$405$		0			0
$406$	−0.527837	−	2.13391i	−0.0261961	−	0.105904i
$407$		−	11.6955i		−	0.579724i
$408$	−1.36873	−	3.12090i	−0.0677621	−	0.154507i
$409$	9.76563	−	30.0555i	0.482879	−	1.48615i	−0.352150	−	0.935944i	$-0.614549\pi$
$409$	9.76563	−	30.0555i	0.482879	−	1.48615i	0.835029	−	0.550206i	$-0.185451\pi$
$410$		0			0
$411$	−3.66777	+	1.19173i	−0.180918	+	0.0587837i
$412$	−3.34481	+	23.1746i	−0.164787	+	1.14173i
$413$	0.508829	−	1.56601i	0.0250378	−	0.0770585i
$414$	9.32850	+	3.78913i	0.458471	+	0.186226i
$415$		0			0
$416$	6.61725	−	8.30947i	0.324437	−	0.407405i
$417$	0.387905	−	0.533906i	0.0189958	−	0.0261455i
$418$	−16.9406	−	14.2685i	−0.828591	−	0.697897i
$419$	5.07417	−	6.98399i	0.247889	−	0.341190i	−0.666881	−	0.745164i	$-0.732371\pi$
$419$	5.07417	−	6.98399i	0.247889	−	0.341190i	0.914771	+	0.403973i	$0.132371\pi$
$420$		0			0
$421$	7.53026	+	10.3645i	0.367002	+	0.505135i	0.952083	−	0.305840i	$-0.0989371\pi$
$421$	7.53026	+	10.3645i	0.367002	+	0.505135i	−0.585081	+	0.810975i	$0.698937\pi$
$422$	1.48451	−	20.6775i	0.0722649	−	1.00657i
$423$	−29.1736	+	9.47907i	−1.41847	+	0.460888i
$424$	−5.41138	+	9.25332i	−0.262800	+	0.449381i
$425$		0			0
$426$	0.862483	+	0.726443i	0.0417874	+	0.0351963i
$427$	−0.118224	−	0.363855i	−0.00572124	−	0.0176082i
$428$	0.505513	+	0.491810i	0.0244349	+	0.0237725i
$429$	1.86234	+	2.56329i	0.0899145	+	0.123757i
$430$		0			0
$431$	−24.3298	−	17.6766i	−1.17193	−	0.851454i	−0.180688	−	0.983541i	$-0.557832\pi$
$431$	−24.3298	−	17.6766i	−1.17193	−	0.851454i	−0.991238	+	0.132087i	$0.957832\pi$
$432$	6.50290	−	2.31230i	0.312871	−	0.111251i
$433$	0.945079	−	1.30079i	0.0454176	−	0.0625120i	−0.785704	−	0.618602i	$-0.787699\pi$
$433$	0.945079	−	1.30079i	0.0454176	−	0.0625120i	0.831122	+	0.556090i	$0.187699\pi$
$434$	−0.928834	−	1.49261i	−0.0445855	−	0.0716474i
$435$		0			0
$436$	−9.06544	−	17.2035i	−0.434156	−	0.823897i
$437$	2.04369	−	6.28982i	0.0977628	−	0.300883i
$438$	3.29636	+	5.29714i	0.157506	+	0.253107i
$439$	−11.7350	−	36.1165i	−0.560079	−	1.72374i	−0.682139	−	0.731222i	$-0.738950\pi$
$439$	−11.7350	−	36.1165i	−0.560079	−	1.72374i	0.122061	−	0.992523i	$-0.461050\pi$
$440$		0			0
$441$	−6.25562	+	19.2528i	−0.297887	+	0.916801i
$442$	−10.6475	+	2.63373i	−0.506451	+	0.125274i
$443$	−19.5670			−0.929654			−0.464827	−	0.885402i	$-0.653883\pi$
$443$	−19.5670			−0.929654			−0.464827	+	0.885402i	$0.653883\pi$
$444$	0.521070	−	1.05836i	0.0247289	−	0.0502273i
$445$		0			0
$446$	1.72681	−	24.0525i	0.0817670	−	1.13892i
$447$	2.64020	+	3.63392i	0.124877	+	0.171879i
$448$	1.38188	+	1.27242i	0.0652878	+	0.0601162i
$449$	−33.2573			−1.56951			−0.784755	−	0.619806i	$-0.787211\pi$
$449$	−33.2573			−1.56951			−0.784755	+	0.619806i	$0.787211\pi$
$450$		0			0
$451$		−	40.0197i		−	1.88445i
$452$	−0.305311	−	0.579389i	−0.0143606	−	0.0272522i
$453$	−0.0708145	+	0.0514498i	−0.00332716	+	0.00241732i
$454$	20.6482	+	1.48241i	0.969069	+	0.0695728i
$455$		0			0
$456$	−0.897291	−	2.04595i	−0.0420195	−	0.0958106i
$457$		−	15.5897i		−	0.729254i	−0.931154	−	0.364627i	$-0.881197\pi$
$457$		−	15.5897i		−	0.729254i	0.931154	−	0.364627i	$-0.118803\pi$
$458$	8.36739	−	2.06972i	0.390982	−	0.0967119i
$459$	−6.77780	−	2.20224i	−0.316361	−	0.102792i
$460$		0			0
$461$	−5.51241	+	1.79109i	−0.256739	+	0.0834194i	−0.434558	−	0.900644i	$-0.643096\pi$
$461$	−5.51241	+	1.79109i	−0.256739	+	0.0834194i	0.177820	+	0.984063i	$0.443096\pi$
$462$	−0.475713	+	0.296032i	−0.0221322	+	0.0137726i
$463$	11.3046	+	3.67309i	0.525370	+	0.170703i	0.559681	−	0.828708i	$-0.310924\pi$
$463$	11.3046	+	3.67309i	0.525370	+	0.170703i	−0.0343111	+	0.999411i	$0.510924\pi$
$464$	20.9863	−	16.1467i	0.974266	−	0.749591i
$465$		0			0
$466$	5.33242	+	8.56902i	0.247019	+	0.396952i
$467$	20.1818	+	14.6630i	0.933903	+	0.678521i	0.946945	−	0.321394i	$-0.104152\pi$
$467$	20.1818	+	14.6630i	0.933903	+	0.678521i	−0.0130420	+	0.999915i	$0.504152\pi$
$468$	−1.86090	−	10.7878i	−0.0860199	−	0.498668i
$469$	−1.53710	+	2.11564i	−0.0709767	+	0.0976910i
$470$		0			0
$471$	4.93072	−	3.58238i	0.227196	−	0.165067i
$472$	19.7370	−	1.96332i	0.908470	−	0.0903691i
$473$	−44.2515	+	14.3782i	−2.03468	+	0.661109i
$474$	−4.04723	−	3.40886i	−0.185895	−	0.156574i
$475$		0			0
$476$	−0.329721	−	1.91143i	−0.0151127	−	0.0876105i
$477$	3.41377	+	10.5065i	0.156306	+	0.481060i
$478$	−7.56403	−	0.543048i	−0.345971	−	0.0248384i
$479$	12.4287	−	9.02994i	0.567880	−	0.412589i	−0.266455	−	0.963847i	$-0.585852\pi$
$479$	12.4287	−	9.02994i	0.567880	−	0.412589i	0.834334	+	0.551259i	$0.185852\pi$
$480$		0			0
$481$	−3.07174	−	2.23175i	−0.140059	−	0.101759i
$482$	2.04258	+	1.72041i	0.0930372	+	0.0783624i
$483$	−0.135350	−	0.0983377i	−0.00615865	−	0.00447452i
$484$	−44.4521	−	6.41580i	−2.02055	−	0.291627i
$485$		0			0
$486$	4.03437	−	9.93226i	0.183003	−	0.450536i
$487$	−21.4527	−	6.97042i	−0.972117	−	0.315860i	−0.220447	−	0.975399i	$-0.570751\pi$
$487$	−21.4527	−	6.97042i	−0.972117	−	0.315860i	−0.751670	+	0.659539i	$0.770751\pi$
$488$	3.44185	−	3.06451i	0.155805	−	0.138724i
$489$	−1.12782	−	3.47109i	−0.0510020	−	0.156968i
$490$		0			0
$491$	−7.25634	−	2.35773i	−0.327474	−	0.106403i	0.140666	−	0.990057i	$-0.455076\pi$
$491$	−7.25634	−	2.35773i	−0.327474	−	0.106403i	−0.468140	+	0.883654i	$0.655076\pi$
$492$	1.78300	−	3.62149i	0.0803839	−	0.163269i
$493$	−27.3417			−1.23141
$494$	−6.98016	+	1.72658i	−0.314052	+	0.0776827i
$495$		0			0
$496$	11.9718	−	17.4676i	0.537550	−	0.784317i
$497$	0.377259	+	0.519253i	0.0169224	+	0.0232917i
$498$	−0.489832	+	1.20592i	−0.0219499	+	0.0540387i
$499$			26.9689i			1.20729i	0.797252	+	0.603647i	$0.206286\pi$
$499$			26.9689i			1.20729i	−0.797252	+	0.603647i	$0.793714\pi$
$500$		0			0
$501$		−	6.28680i		−	0.280874i
$502$	5.96216	+	2.42176i	0.266104	+	0.108088i
$503$	18.0952	+	24.9059i	0.806825	+	1.11050i	0.991805	+	0.127757i	$0.0407778\pi$
$503$	18.0952	+	24.9059i	0.806825	+	1.11050i	−0.184980	+	0.982742i	$0.559222\pi$
$504$	1.92640	−	0.191626i	0.0858086	−	0.00853572i
$505$		0			0
$506$	−4.79750	−	19.3951i	−0.213275	−	0.862218i
$507$	−2.76364			−0.122738
$508$	−16.5764	−	8.16120i	−0.735458	−	0.362095i
$509$	3.29675	+	1.07118i	0.146126	+	0.0474792i	0.381167	−	0.924506i	$-0.375522\pi$
$509$	3.29675	+	1.07118i	0.146126	+	0.0474792i	−0.235041	+	0.971986i	$0.575522\pi$
$510$		0			0
$511$	1.09735	+	3.37731i	0.0485441	+	0.149403i
$512$	−7.35098	+	21.4001i	−0.324871	+	0.945758i
$513$	−4.44330	−	1.44371i	−0.196176	−	0.0637416i
$514$	−9.15968	−	3.72056i	−0.404016	−	0.164107i
$515$		0			0
$516$	−4.64503	−	0.670420i	−0.204486	−	0.0295136i
$517$	49.2443	+	35.7781i	2.16576	+	1.57352i
$518$	0.432549	−	0.513552i	0.0190051	−	0.0225642i
$519$	−0.376068	−	0.273229i	−0.0165076	−	0.0119934i
$520$		0			0
$521$	−32.2980	+	23.4659i	−1.41500	+	1.02806i	−0.422430	+	0.906395i	$0.638823\pi$
$521$	−32.2980	+	23.4659i	−1.41500	+	1.02806i	−0.992571	+	0.121663i	$0.961177\pi$
$522$	1.95412	−	27.2186i	0.0855294	−	1.19133i
$523$	1.93267	+	5.94816i	0.0845099	+	0.260095i	0.984378	−	0.176067i	$-0.0563375\pi$
$523$	1.93267	+	5.94816i	0.0845099	+	0.260095i	−0.899868	+	0.436162i	$0.856338\pi$
$524$	14.9554	−	2.57980i	0.653329	−	0.112699i
$525$		0			0
$526$	−20.6082	+	24.4674i	−0.898559	+	1.06683i
$527$	−20.7960	+	6.75704i	−0.905890	+	0.294341i
$528$	−5.56715	−	3.81557i	−0.242279	−	0.166051i
$529$	−13.7810	+	10.0125i	−0.599173	+	0.435325i
$530$		0			0
$531$	12.0148	−	16.5370i	0.521399	−	0.717644i
$532$	−0.216154	−	1.25307i	−0.00937147	−	0.0543275i
$533$	−10.5109	−	7.63661i	−0.455277	−	0.330778i
$534$	−3.98140	+	2.47758i	−0.172292	+	0.107216i
$535$		0			0
$536$	−30.7749	−	6.72085i	−1.32927	−	0.290296i
$537$	−3.07415	−	0.998852i	−0.132659	−	0.0431036i
$538$	4.69025	+	7.53708i	0.202211	+	0.324947i
$539$	38.2040	−	12.4132i	1.64556	−	0.534676i
$540$		0			0
$541$	19.5034	+	6.33705i	0.838518	+	0.272451i	0.696629	−	0.717432i	$-0.254682\pi$
$541$	19.5034	+	6.33705i	0.838518	+	0.272451i	0.141889	+	0.989883i	$0.454682\pi$
$542$	1.15453	+	4.66746i	0.0495911	+	0.200485i
$543$		−	5.85576i		−	0.251295i
$544$	19.4906	−	12.8848i	0.835651	−	0.552433i
$545$		0			0
$546$	−0.0130256	+	0.181432i	−0.000557445	+	0.00776457i
$547$	−17.9423	+	13.0358i	−0.767157	+	0.557372i	−0.901097	−	0.433617i	$-0.857237\pi$
$547$	−17.9423	+	13.0358i	−0.767157	+	0.557372i	0.133940	+	0.990989i	$0.457237\pi$
$548$	−12.3263	−	23.3917i	−0.526555	−	0.999243i
$549$		−	4.74932i		−	0.202696i
$550$		0			0
$551$	−17.9243			−0.763599
$552$	0.429973	−	1.96886i	0.0183009	−	0.0838002i
$553$	−1.77030	−	2.43661i	−0.0752808	−	0.103615i
$554$	−36.3149	−	2.60717i	−1.54287	−	0.110768i
$555$		0			0
$556$	4.05933	+	1.99857i	0.172154	+	0.0847580i
$557$	−36.8641			−1.56198			−0.780991	−	0.624543i	$-0.785285\pi$
$557$	−36.8641			−1.56198			−0.780991	+	0.624543i	$0.785285\pi$
$558$	−5.24033	−	21.1854i	−0.221841	−	0.896848i
$559$	−4.66780	+	14.3660i	−0.197427	+	0.607617i
$560$		0			0
$561$	2.15356	+	6.62797i	0.0909233	+	0.279833i
$562$	−4.69045	+	2.91882i	−0.197855	+	0.123123i
$563$	12.7139	−	39.1294i	0.535828	−	1.64911i	−0.206027	−	0.978546i	$-0.566053\pi$
$563$	12.7139	−	39.1294i	0.535828	−	1.64911i	0.741854	−	0.670561i	$-0.233947\pi$
$564$	2.86222	+	5.43164i	0.120521	+	0.228713i
$565$		0			0
$566$	1.54221	−	0.959702i	0.0648240	−	0.0403393i
$567$	1.13745	−	1.56557i	0.0477685	−	0.0657477i
$568$	−3.90289	+	6.67385i	−0.163762	+	0.280028i
$569$	−2.43983	−	1.77264i	−0.102283	−	0.0743130i	0.535468	−	0.844555i	$-0.320135\pi$
$569$	−2.43983	−	1.77264i	−0.102283	−	0.0743130i	−0.637751	+	0.770242i	$0.720135\pi$
$570$		0			0
$571$	8.11104	+	11.1639i	0.339436	+	0.467194i	0.944277	−	0.329153i	$-0.106763\pi$
$571$	8.11104	+	11.1639i	0.339436	+	0.467194i	−0.604840	+	0.796347i	$0.706763\pi$
$572$	−15.1479	+	15.5699i	−0.633365	+	0.651012i
$573$	−1.70873	−	5.25893i	−0.0713833	−	0.219695i
$574$	1.48010	−	1.75728i	0.0617782	−	0.0733473i
$575$		0			0
$576$	11.4338	+	20.3237i	0.476410	+	0.846822i
$577$	−12.5473	+	4.07686i	−0.522351	+	0.169722i	−0.558312	−	0.829631i	$-0.688551\pi$
$577$	−12.5473	+	4.07686i	−0.522351	+	0.169722i	0.0359612	+	0.999353i	$0.488551\pi$
$578$	−0.0838002	−	0.00601630i	−0.00348563	−	0.000250245i
$579$	−0.451554	−	0.621511i	−0.0187659	−	0.0258291i
$580$		0			0
$581$	−0.435458	+	0.599356i	−0.0180658	+	0.0248655i
$582$	1.86247	−	2.21126i	0.0772020	−	0.0916595i
$583$	12.8850	−	17.7347i	0.533644	−	0.734498i
$584$	−31.9474	+	28.4448i	−1.32199	+	1.17705i
$585$		0			0
$586$	4.55049	−	11.2029i	0.187979	−	0.462788i
$587$	8.38908	−	25.8189i	0.346254	−	1.06566i	−0.614655	−	0.788796i	$-0.710705\pi$
$587$	8.38908	−	25.8189i	0.346254	−	1.06566i	0.960909	−	0.276865i	$-0.0892954\pi$
$588$	4.01023	+	0.578800i	0.165379	+	0.0238693i
$589$	−13.6332	+	4.42969i	−0.561745	+	0.182522i
$590$		0			0
$591$	2.27531	−	7.00269i	0.0935939	−	0.288052i
$592$	7.75787	+	2.28704i	0.318846	+	0.0939968i
$593$		−	10.5301i		−	0.432420i	−0.976347	−	0.216210i	$-0.930630\pi$
$593$		−	10.5301i		−	0.432420i	0.976347	−	0.216210i	$-0.0693696\pi$
$594$	−13.7012	+	3.38908i	−0.562168	+	0.139056i
$595$		0			0
$596$	−21.4749	+	22.0732i	−0.879645	+	0.904153i
$597$	−0.937461	+	0.681105i	−0.0383677	+	0.0278758i
$598$	−6.00945	−	2.44097i	−0.245745	−	0.0998187i
$599$	20.1787			0.824481			0.412241	−	0.911075i	$-0.364746\pi$
$599$	20.1787			0.824481			0.412241	+	0.911075i	$0.364746\pi$
$600$		0			0
$601$	11.7592			0.479669			0.239834	−	0.970814i	$-0.422907\pi$
$601$	11.7592			0.479669			0.239834	+	0.970814i	$0.422907\pi$
$602$	−2.47486	−	1.00526i	−0.100868	−	0.0409713i
$603$	−26.2634	+	19.0815i	−1.06953	+	0.777058i
$604$	−0.430142	−	0.418483i	−0.0175022	−	0.0170278i
$605$		0			0
$606$	4.38453	−	1.08454i	0.178110	−	0.0440565i
$607$		−	35.8362i		−	1.45455i	−0.686347	−	0.727274i	$-0.740787\pi$
$607$		−	35.8362i		−	1.45455i	0.686347	−	0.727274i	$-0.259213\pi$
$608$	12.7774	−	8.44686i	0.518190	−	0.342565i
$609$	−0.140118	+	0.431238i	−0.00567785	+	0.0174746i
$610$		0			0
$611$	18.7937	−	6.10645i	0.760313	−	0.247041i
$612$	3.43968	−	23.8319i	0.139041	−	0.963349i
$613$	−3.94986	+	12.1564i	−0.159533	+	0.490994i	−0.998592	−	0.0530477i	$-0.983106\pi$
$613$	−3.94986	+	12.1564i	−0.159533	+	0.490994i	0.839059	+	0.544041i	$0.183106\pi$
$614$	5.90324	−	14.5333i	0.238235	−	0.586515i
$615$		0			0
$616$	−2.55451	−	2.86906i	−0.102924	−	0.115598i
$617$	9.18527	−	12.6424i	0.369785	−	0.508965i	−0.583057	−	0.812431i	$-0.698144\pi$
$617$	9.18527	−	12.6424i	0.369785	−	0.508965i	0.952842	+	0.303466i	$0.0981437\pi$
$618$	3.11139	−	3.69406i	0.125159	−	0.148597i
$619$	20.9771	−	28.8724i	0.843139	−	1.16048i	−0.142194	−	0.989839i	$-0.545416\pi$
$619$	20.9771	−	28.8724i	0.843139	−	1.16048i	0.985333	−	0.170643i	$-0.0545844\pi$
$620$		0			0
$621$	−2.47715	−	3.40951i	−0.0994048	−	0.136819i
$622$	42.4013	+	3.04413i	1.70014	+	0.122059i
$623$	−2.53843	+	0.824786i	−0.101700	+	0.0330444i
$624$	−2.06446	+	0.734080i	−0.0826446	+	0.0293867i
$625$		0			0
$626$	−0.0335258	+	0.0398041i	−0.00133996	+	0.00159089i
$627$	1.41180	+	4.34507i	0.0563818	+	0.173525i
$628$	29.9502	+	29.1384i	1.19514	+	1.16275i
$629$	−4.90885	−	6.75645i	−0.195729	−	0.269397i
$630$		0			0
$631$	36.4157	+	26.4575i	1.44969	+	1.05326i	0.985905	+	0.167308i	$0.0535075\pi$
$631$	36.4157	+	26.4575i	1.44969	+	1.05326i	0.463781	+	0.885950i	$0.346492\pi$
$632$	18.3144	−	31.3172i	0.728509	−	1.24573i
$633$	−2.51346	+	3.45948i	−0.0999010	+	0.137502i
$634$	19.5306	−	12.1537i	0.775660	−	0.482686i
$635$		0			0
$636$	1.95614	−	1.03080i	0.0775660	−	0.0408737i
$637$	4.02989	−	12.4027i	0.159670	−	0.491414i
$638$	−45.9749	+	28.6097i	−1.82016	+	1.13267i
$639$	2.46214	+	7.57770i	0.0974009	+	0.299769i
$640$		0			0
$641$	4.02897	−	12.3999i	0.159135	−	0.489766i	−0.839422	−	0.543481i	$-0.817106\pi$
$641$	4.02897	−	12.3999i	0.159135	−	0.489766i	0.998556	+	0.0537145i	$0.0171061\pi$
$642$	−0.0349323	−	0.141223i	−0.00137867	−	0.00557361i
$643$	34.5558			1.36275			0.681375	−	0.731935i	$-0.261382\pi$
$643$	34.5558			1.36275			0.681375	+	0.731935i	$0.261382\pi$
$644$	0.506655	−	1.02908i	0.0199650	−	0.0405513i
$645$		0			0
$646$	−15.7753	−	1.13257i	−0.620673	−	0.0445602i
$647$	−5.64166	−	7.76508i	−0.221797	−	0.305277i	0.683589	−	0.729867i	$-0.260418\pi$
$647$	−5.64166	−	7.76508i	−0.221797	−	0.305277i	−0.905386	+	0.424590i	$0.860418\pi$
$648$	22.7734	+	4.97342i	0.894624	+	0.195374i
$649$	−40.5615			−1.59218
$650$		0			0
$651$			0.362627i			0.0142125i
$652$	22.1373	−	11.6654i	0.866965	−	0.456851i
$653$	−19.7759	+	14.3680i	−0.773889	+	0.562263i	−0.903139	−	0.429349i	$-0.858743\pi$
$653$	−19.7759	+	14.3680i	−0.773889	+	0.562263i	0.129250	+	0.991612i	$0.458743\pi$
$654$	−0.287233	+	4.00082i	−0.0112317	+	0.156444i
$655$		0			0
$656$	26.5459	+	7.82581i	1.03644	+	0.305547i
$657$			44.0833i			1.71985i
$658$	0.839104	+	3.39229i	0.0327117	+	0.132245i
$659$	−41.1516	−	13.3710i	−1.60304	−	0.520859i	−0.635184	−	0.772361i	$-0.719076\pi$
$659$	−41.1516	−	13.3710i	−1.60304	−	0.520859i	−0.967857	+	0.251502i	$0.919076\pi$
$660$		0			0
$661$	33.1551	−	10.7728i	1.28958	−	0.419012i	0.417639	−	0.908613i	$-0.362858\pi$
$661$	33.1551	−	10.7728i	1.28958	−	0.419012i	0.871946	+	0.489602i	$0.162858\pi$
$662$	16.9754	+	27.2789i	0.659767	+	1.06022i
$663$	2.15173	+	0.699141i	0.0835664	+	0.0271524i
$664$	−8.71848	−	1.90400i	−0.338343	−	0.0738897i
$665$		0			0
$666$	7.07688	−	4.40387i	0.274224	−	0.170647i
$667$	−13.0808	−	9.50375i	−0.506490	−	0.367987i
$668$	42.4756	−	7.32702i	1.64343	−	0.283491i
$669$	−2.92371	+	4.02414i	−0.113037	+	0.155582i
$670$		0			0
$671$	−7.62437	+	5.53943i	−0.294336	+	0.213847i
$672$	−0.103339	−	0.373440i	−0.00398638	−	0.0144057i
$673$	10.2698	−	3.33688i	0.395874	−	0.128627i	−0.104314	−	0.994544i	$-0.533265\pi$
$673$	10.2698	−	3.33688i	0.395874	−	0.128627i	0.500187	+	0.865917i	$0.333265\pi$
$674$	−17.1400	+	20.3497i	−0.660207	+	0.783842i
$675$		0			0
$676$	−3.22091	−	18.6720i	−0.123881	−	0.718155i
$677$	−12.9196	−	39.7626i	−0.496542	−	1.52820i	−0.814539	−	0.580109i	$-0.803010\pi$
$677$	−12.9196	−	39.7626i	−0.496542	−	1.52820i	0.317997	−	0.948092i	$-0.396990\pi$
$678$	−0.00967359	+	0.134742i	−0.000371512	+	0.00517474i
$679$	1.33127	−	0.967228i	0.0510896	−	0.0371188i
$680$		0			0
$681$	−3.45457	−	2.50989i	−0.132380	−	0.0961794i
$682$	−27.8980	+	33.1224i	−1.06827	+	1.26832i
$683$	−16.0534	−	11.6635i	−0.614267	−	0.446291i	0.236647	−	0.971596i	$-0.423951\pi$
$683$	−16.0534	−	11.6635i	−0.614267	−	0.446291i	−0.850914	+	0.525305i	$0.823951\pi$
$684$	2.25494	−	15.6234i	0.0862197	−	0.597376i
$685$		0			0
$686$	4.29025	+	1.74265i	0.163803	+	0.0665347i
$687$	−1.69095	−	0.549422i	−0.0645136	−	0.0209617i
$688$	−0.884021	−	32.1646i	−0.0337030	−	1.22626i
$689$	−2.19917	−	6.76834i	−0.0837815	−	0.257853i
$690$		0			0
$691$	−15.2658	−	4.96017i	−0.580740	−	0.188694i	0.00389213	−	0.999992i	$-0.498761\pi$
$691$	−15.2658	−	4.96017i	−0.580740	−	0.188694i	−0.584632	+	0.811299i	$0.698761\pi$
$692$	1.40773	−	2.85927i	0.0535139	−	0.108693i
$693$	−3.95893			−0.150387
$694$	10.0307	+	40.5517i	0.380761	+	1.53932i
$695$		0			0
$696$	−5.43504	+	0.540645i	−0.206015	+	0.0204931i
$697$	−16.7971	−	23.1193i	−0.636237	−	0.875705i
$698$	−20.6540	−	8.38942i	−0.781766	−	0.317544i
$699$		−	2.08183i		−	0.0787422i
$700$		0			0
$701$			15.2259i			0.575073i	0.957770	+	0.287537i	$0.0928363\pi$
$701$			15.2259i			0.575073i	−0.957770	+	0.287537i	$0.907164\pi$
$702$	−1.72437	+	4.24524i	−0.0650820	+	0.160226i
$703$	−3.21807	−	4.42930i	−0.121372	−	0.167054i
$704$	19.2909	−	42.0603i	0.727053	−	1.58521i
$705$		0			0
$706$	11.2078	−	2.77231i	0.421810	−	0.104337i
$707$	2.57079			0.0966843
$708$	−3.67052	−	1.80714i	−0.137946	−	0.0679164i
$709$	35.0361	+	11.3839i	1.31581	+	0.427532i	0.881053	−	0.473018i	$-0.156835\pi$
$709$	35.0361	+	11.3839i	1.31581	+	0.427532i	0.434754	+	0.900549i	$0.356835\pi$
$710$		0			0
$711$	−11.5537	−	35.5586i	−0.433297	−	1.33355i
$712$	−21.3795	−	24.0121i	−0.801231	−	0.899890i
$713$	−12.2979	−	3.99584i	−0.460561	−	0.149645i
$714$	−0.150567	+	0.370684i	−0.00563485	+	0.0138725i
$715$		0			0
$716$	3.16576	−	21.9340i	0.118310	−	0.819714i
$717$	1.26551	+	0.919446i	0.0472613	+	0.0343373i
$718$	32.9899	+	27.7864i	1.23117	+	1.03698i
$719$	17.8070	+	12.9375i	0.664088	+	0.482488i	0.868041	−	0.496492i	$-0.165379\pi$
$719$	17.8070	+	12.9375i	0.664088	+	0.482488i	−0.203953	+	0.978981i	$0.565379\pi$
$720$		0			0
$721$	2.22399	−	1.61582i	0.0828256	−	0.0601763i
$722$	16.4593	+	1.18167i	0.612551	+	0.0439772i
$723$	−0.170225	−	0.523900i	−0.00633075	−	0.0194840i
$724$	39.5633	−	6.82465i	1.47036	−	0.253636i
$725$		0			0
$726$	7.08570	+	5.96807i	0.262975	+	0.221496i
$727$	37.4888	−	12.1809i	1.39038	−	0.451763i	0.484315	−	0.874894i	$-0.339069\pi$
$727$	37.4888	−	12.1809i	1.39038	−	0.451763i	0.906069	+	0.423131i	$0.139069\pi$
$728$	−1.24099	+	0.123446i	−0.0459942	+	0.00457523i
$729$	18.2133	−	13.2327i	0.674566	−	0.490101i
$730$		0			0
$731$	−19.5291	+	26.8795i	−0.722311	+	0.994176i
$732$	−0.936748	+	0.161589i	−0.0346232	+	0.00597248i
$733$	20.6186	+	14.9803i	0.761565	+	0.553309i	0.899390	−	0.437147i	$-0.144011\pi$
$733$	20.6186	+	14.9803i	0.761565	+	0.553309i	−0.137825	+	0.990457i	$0.544011\pi$
$734$	−5.60446	−	9.00619i	−0.206864	−	0.332425i
$735$		0			0
$736$	13.8033	+	0.610410i	0.508798	+	0.0225000i
$737$	61.2653	+	19.9063i	2.25674	+	0.733258i
$738$	24.2157	−	15.0692i	0.891393	−	0.554705i
$739$	−8.47753	+	2.75452i	−0.311851	+	0.101327i	−0.460761	−	0.887524i	$-0.652424\pi$
$739$	−8.47753	+	2.75452i	−0.311851	+	0.101327i	0.148910	+	0.988851i	$0.452424\pi$
$740$		0			0
$741$	1.41060	+	0.458333i	0.0518198	+	0.0168373i
$742$	1.22169	−	0.302193i	0.0448498	−	0.0110939i
$743$			21.5410i			0.790261i	0.918625	+	0.395130i	$0.129301\pi$
$743$			21.5410i			0.790261i	−0.918625	+	0.395130i	$0.870699\pi$
$744$	−4.00027	+	1.75439i	−0.146657	+	0.0643192i
$745$		0			0
$746$	−17.9959	−	1.29199i	−0.658878	−	0.0473031i
$747$	−7.44038	+	5.40575i	−0.272229	+	0.197786i
$748$	−42.2708	+	22.2747i	−1.54557	+	0.814445i
$749$		−	0.0828031i		−	0.00302556i
$750$		0			0
$751$	31.4361			1.14712			0.573561	−	0.819163i	$-0.305562\pi$
$751$	31.4361			1.14712			0.573561	+	0.819163i	$0.305562\pi$
$752$	−33.3621	+	25.6684i	−1.21659	+	0.936032i
$753$	−0.780227	−	1.07389i	−0.0284331	−	0.0391347i
$754$	−1.25885	+	17.5343i	−0.0458446	+	0.638562i
$755$		0			0
$756$	−0.726967	−	0.357915i	−0.0264396	−	0.0130172i
$757$	3.46461			0.125924			0.0629618	−	0.998016i	$-0.479945\pi$
$757$	3.46461			0.125924			0.0629618	+	0.998016i	$0.479945\pi$
$758$	−16.8174	+	4.15988i	−0.610834	+	0.151093i
$759$	−1.27353	+	3.91951i	−0.0462261	+	0.142269i
$760$		0			0
$761$	−6.25196	−	19.2415i	−0.226633	−	0.697505i	−0.998122	−	0.0612621i	$-0.980487\pi$
$761$	−6.25196	−	19.2415i	−0.226633	−	0.697505i	0.771488	−	0.636243i	$-0.219513\pi$
$762$	2.01360	+	3.23580i	0.0729452	+	0.117221i
$763$	−0.705496	+	2.17129i	−0.0255407	+	0.0786061i
$764$	33.5396	−	17.6738i	1.21342	−	0.639416i
$765$		0			0
$766$	20.1182	+	32.3293i	0.726900	+	1.16811i
$767$	−7.73999	+	10.6532i	−0.279475	+	0.384664i
$768$	3.61960	−	2.94668i	0.130611	−	0.106329i
$769$	−6.10205	−	4.43340i	−0.220046	−	0.159872i	0.472302	−	0.881437i	$-0.343423\pi$
$769$	−6.10205	−	4.43340i	−0.220046	−	0.159872i	−0.692347	+	0.721565i	$0.743423\pi$
$770$		0			0
$771$	1.19867	+	1.64982i	0.0431689	+	0.0594169i
$772$	3.67285	−	3.77519i	0.132189	−	0.135872i
$773$	7.63507	+	23.4983i	0.274614	+	0.845176i	0.989321	+	0.145752i	$0.0465601\pi$
$773$	7.63507	+	23.4983i	0.274614	+	0.845176i	−0.714707	+	0.699424i	$0.753440\pi$
$774$	−25.3628	−	21.3623i	−0.911647	−	0.767853i
$775$		0			0
$776$	17.1106	+	10.0063i	0.614234	+	0.359206i
$777$	−0.131720	+	0.0427985i	−0.00472544	+	0.00153539i
$778$	−0.965428	+	13.4473i	−0.0346123	+	0.482109i
$779$	−11.0116	−	15.1562i	−0.394533	−	0.543027i
$780$		0			0
$781$	9.29319	−	12.7910i	0.332536	−	0.457697i
$782$	−10.9121	−	9.19089i	−0.390214	−	0.328666i
$783$	−6.71371	+	9.24062i	−0.239928	+	0.330233i
$784$	0.763210	+	27.7690i	0.0272575	+	0.991749i
$785$		0			0
$786$	−2.90029	−	1.17807i	−0.103450	−	0.0420202i
$787$	−2.96732	+	9.13248i	−0.105774	+	0.325538i	−0.989911	−	0.141689i	$-0.954747\pi$
$787$	−2.96732	+	9.13248i	−0.105774	+	0.325538i	0.884138	+	0.467227i	$0.154747\pi$
$788$	49.9642	+	7.21137i	1.77990	+	0.256895i
$789$	6.27562	−	2.03907i	0.223418	−	0.0725930i
$790$		0			0
$791$	−0.0237601	+	0.0731261i	−0.000844812	+	0.00260007i
$792$	−19.1534	−	43.6725i	−0.680586	−	1.55183i
$793$			3.05953i			0.108647i
$794$	−7.90182	−	31.9451i	−0.280425	−	1.13369i
$795$		0			0
$796$	−5.69434	−	5.53998i	−0.201830	−	0.196359i
$797$	25.7837	−	18.7330i	0.913306	−	0.663556i	−0.0285428	−	0.999593i	$-0.509087\pi$
$797$	25.7837	−	18.7330i	0.913306	−	0.663556i	0.941849	+	0.336037i	$0.109087\pi$
$798$	−0.0987069	+	0.243008i	−0.00349419	+	0.00860238i
$799$	43.4651			1.53769
$800$		0			0
$801$	−33.1336			−1.17072
$802$	6.54176	−	16.1052i	0.230998	−	0.568696i
$803$	70.7696	−	51.4171i	2.49740	−	1.81447i
$804$	4.65717	+	4.53093i	0.164246	+	0.159794i
$805$		0			0
$806$	3.37584	+	13.6477i	0.118909	+	0.480719i
$807$		−	1.83112i		−	0.0644586i
$808$	12.4375	+	28.3593i	0.437550	+	0.997677i
$809$	−1.35706	+	4.17661i	−0.0477118	+	0.146842i	−0.972074	−	0.234674i	$-0.924598\pi$
$809$	−1.35706	+	4.17661i	−0.0477118	+	0.146842i	0.924362	+	0.381516i	$0.124598\pi$
$810$		0			0
$811$	−36.8697	+	11.9797i	−1.29467	+	0.420664i	−0.873725	−	0.486421i	$-0.838302\pi$
$811$	−36.8697	+	11.9797i	−1.29467	+	0.420664i	−0.420947	+	0.907085i	$0.638302\pi$
$812$	−3.07688	−	0.444089i	−0.107977	−	0.0155845i
$813$	0.306476	−	0.943236i	0.0107486	−	0.0330807i
$814$	−15.3240	−	6.22443i	−0.537106	−	0.218166i
$815$		0			0
$816$	−4.81760	+	0.132408i	−0.168650	+	0.00463522i
$817$	−12.8026	+	17.6213i	−0.447907	+	0.616492i
$818$	−34.1829	−	28.7912i	−1.19518	−	1.00666i
$819$	−0.755449	+	1.03979i	−0.0263975	+	0.0363331i
$820$		0			0
$821$	25.5877	+	35.2185i	0.893017	+	1.22913i	0.972642	+	0.232308i	$0.0746276\pi$
$821$	25.5877	+	35.2185i	0.893017	+	1.22913i	−0.0796254	+	0.996825i	$0.525372\pi$
$822$	−0.390552	+	5.43994i	−0.0136221	+	0.189740i
$823$	4.46326	−	1.45020i	0.155580	−	0.0505509i	−0.230192	−	0.973145i	$-0.573935\pi$
$823$	4.46326	−	1.45020i	0.155580	−	0.0505509i	0.385771	+	0.922594i	$0.373935\pi$
$824$	28.5844	+	16.7163i	0.995785	+	0.582339i
$825$		0			0
$826$	−1.78107	−	1.50014i	−0.0619712	−	0.0521965i
$827$	−3.61552	−	11.1274i	−0.125724	−	0.386938i	0.868308	−	0.496025i	$-0.165207\pi$
$827$	−3.61552	−	11.1274i	−0.125724	−	0.386938i	−0.994032	+	0.109087i	$0.965207\pi$
$828$	9.92941	−	10.2061i	0.345071	−	0.354685i
$829$	−0.462729	−	0.636892i	−0.0160712	−	0.0221202i	0.800906	−	0.598790i	$-0.204352\pi$
$829$	−0.462729	−	0.636892i	−0.0160712	−	0.0221202i	−0.816977	+	0.576670i	$0.804352\pi$
$830$		0			0
$831$	6.07571	+	4.41426i	0.210764	+	0.153129i
$832$	−7.36573	−	13.0926i	−0.255361	−	0.453905i
$833$	16.8603	−	23.2062i	0.584174	−	0.804046i
$834$	−0.493104	−	0.792402i	−0.0170748	−	0.0274386i
$835$		0			0
$836$	−27.7113	+	14.6026i	−0.958414	+	0.505040i
$837$	−2.82277	+	8.68759i	−0.0975692	+	0.300287i
$838$	−6.45026	−	10.3654i	−0.222821	−	0.358066i
$839$	10.8077	+	33.2628i	0.373124	+	1.14836i	0.944736	+	0.327833i	$0.106318\pi$
$839$	10.8077	+	33.2628i	0.373124	+	1.14836i	−0.571611	+	0.820524i	$0.693682\pi$
$840$		0			0
$841$	−4.58005	+	14.0959i	−0.157933	+	0.486067i
$842$	17.5878	−	4.35044i	0.606114	−	0.149926i
$843$	1.13954			0.0392478
$844$	−26.3027	−	12.9498i	−0.905375	−	0.445752i
$845$		0			0
$846$	−3.10647	+	43.2695i	−0.106803	+	1.48764i
$847$	3.09936	+	4.26591i	0.106495	+	0.146578i
$848$	9.24418	+	12.0149i	0.317447	+	0.412595i
$849$	−0.374678			−0.0128589
$850$		0			0
$851$		−	4.93870i		−	0.169296i
$852$	1.41084	−	0.743449i	0.0483347	−	0.0254702i
$853$	−9.00501	+	6.54252i	−0.308326	+	0.224012i	−0.731178	−	0.682187i	$-0.761029\pi$
$853$	−9.00501	+	6.54252i	−0.308326	+	0.224012i	0.422852	+	0.906199i	$0.361029\pi$
$854$	−0.539660	−	0.0387441i	−0.0184668	−	0.00132579i
$855$		0			0
$856$	0.913432	−	0.400603i	0.0312205	−	0.0136923i
$857$			53.1600i			1.81591i	0.419068	+	0.907955i	$0.362357\pi$
$857$			53.1600i			1.81591i	−0.419068	+	0.907955i	$0.637643\pi$
$858$	4.34970	−	1.07592i	0.148496	−	0.0367314i
$859$	−32.6009	−	10.5927i	−1.11233	−	0.361417i	−0.305493	−	0.952194i	$-0.598821\pi$
$859$	−32.6009	−	10.5927i	−1.11233	−	0.361417i	−0.806835	+	0.590777i	$0.798821\pi$
$860$		0			0
$861$	−0.450722	+	0.146448i	−0.0153606	+	0.00499095i
$862$	−36.1093	+	22.4705i	−1.22989	+	0.765347i
$863$	37.8328	+	12.2926i	1.28784	+	0.418446i	0.871336	−	0.490686i	$-0.163254\pi$
$863$	37.8328	+	12.2926i	1.28784	+	0.418446i	0.416508	+	0.909132i	$0.363254\pi$
$864$	0.431210	−	9.75105i	0.0146701	−	0.331738i
$865$		0			0
$866$	−1.20138	−	1.93058i	−0.0408246	−	0.0656038i
$867$	0.0140203	+	0.0101863i	0.000476154	+	0.000345946i
$868$	−2.45002	+	0.422627i	−0.0831591	+	0.0143449i
$869$	−43.6085	+	60.0220i	−1.47932	+	2.03611i
$870$		0			0
$871$	16.9190	−	12.2923i	0.573277	−	0.416510i
$872$	−27.3655	+	2.72216i	−0.926714	+	0.0921840i
$873$	19.4279	−	6.31251i	0.657535	−	0.213646i
$874$	−7.15357	−	6.02523i	−0.241973	−	0.203807i
$875$		0			0
$876$	8.69492	−	1.49987i	0.293774	−	0.0506759i
$877$	12.4831	+	38.4191i	0.421525	+	1.29732i	0.906283	+	0.422672i	$0.138908\pi$
$877$	12.4831	+	38.4191i	0.421525	+	1.29732i	−0.484758	+	0.874649i	$0.661092\pi$
$878$	−53.5670	−	3.84576i	−1.80780	−	0.129788i
$879$	−2.01784	+	1.46605i	−0.0680601	+	0.0494486i
$880$		0			0
$881$	26.2858	+	19.0977i	0.885591	+	0.643419i	0.934725	−	0.355373i	$-0.115646\pi$
$881$	26.2858	+	19.0977i	0.885591	+	0.643419i	−0.0491339	+	0.998792i	$0.515646\pi$
$882$	21.8967	+	18.4429i	0.737301	+	0.621006i
$883$	31.0584	+	22.5652i	1.04520	+	0.759380i	0.971293	−	0.237885i	$-0.0764542\pi$
$883$	31.0584	+	22.5652i	1.04520	+	0.759380i	0.0739039	+	0.997265i	$0.476454\pi$
$884$	−2.21586	+	15.3526i	−0.0745273	+	0.516364i
$885$		0			0
$886$	−10.4137	+	25.6376i	−0.349855	+	0.861312i
$887$	14.5493	+	4.72737i	0.488519	+	0.158729i	0.542911	−	0.839790i	$-0.317322\pi$
$887$	14.5493	+	4.72737i	0.488519	+	0.158729i	−0.0543921	+	0.998520i	$0.517322\pi$
$888$	−1.10939	−	1.24600i	−0.0372288	−	0.0418129i
$889$	0.670327	+	2.06305i	0.0224821	+	0.0691926i
$890$		0			0
$891$	−45.3363	−	14.7306i	−1.51882	−	0.493495i
$892$	−30.5958	−	15.0635i	−1.02442	−	0.504364i
$893$	28.4943			0.953524
$894$	6.16648	−	1.52532i	0.206238	−	0.0510142i
$895$		0			0
$896$	2.40264	−	1.13342i	0.0802665	−	0.0378649i
$897$	0.786416	+	1.08241i	0.0262577	+	0.0361406i
$898$	−17.6998	+	43.5754i	−0.590651	+	1.45413i
$899$			35.0457i			1.16884i
$900$		0			0
$901$		−	15.6535i		−	0.521492i
$902$	−52.4358	−	21.2988i	−1.74592	−	0.709173i
$903$	0.323868	+	0.445767i	0.0107777	+	0.0148342i
$904$	−0.921634	+	0.0916786i	−0.0306531	+	0.00304918i
$905$		0			0
$906$	0.0297240	+	0.120167i	0.000987513	+	0.00399227i
$907$	−31.6503			−1.05093			−0.525465	−	0.850815i	$-0.676109\pi$
$907$	−31.6503			−1.05093			−0.525465	+	0.850815i	$0.676109\pi$
$908$	12.9315	−	26.2654i	0.429146	−	0.871647i
$909$	30.3516	+	9.86184i	1.00670	+	0.327096i
$910$		0			0
$911$	−1.64977	−	5.07747i	−0.0546593	−	0.168224i	0.920000	−	0.391918i	$-0.128188\pi$
$911$	−1.64977	−	5.07747i	−0.0546593	−	0.168224i	−0.974659	+	0.223694i	$0.928188\pi$
$912$	−3.15826	+	0.0868024i	−0.104580	+	0.00287431i
$913$	17.3564	+	5.63942i	0.574411	+	0.186638i
$914$	−20.4264	−	8.29695i	−0.675644	−	0.274439i
$915$		0			0
$916$	1.74134	−	12.0649i	0.0575353	−	0.398635i
$917$	−1.44148	−	1.04729i	−0.0476017	−	0.0345847i
$918$	−6.49269	+	7.70856i	−0.214291	+	0.254421i
$919$	11.6067	+	8.43275i	0.382869	+	0.278171i	0.762527	−	0.646956i	$-0.223958\pi$
$919$	11.6067	+	8.43275i	0.382869	+	0.278171i	−0.379658	+	0.925127i	$0.623958\pi$
$920$		0			0
$921$	−2.61770	+	1.90187i	−0.0862561	+	0.0626687i
$922$	−0.586974	+	8.17587i	−0.0193309	+	0.269258i
$923$	−1.58612	−	4.88158i	−0.0522078	−	0.160679i
$924$	0.134697	+	0.780854i	0.00443120	+	0.0256882i
$925$		0			0
$926$	10.8291	−	12.8570i	0.355865	−	0.422508i
$927$	32.4557	−	10.5455i	1.06598	−	0.346359i
$928$	−9.98709	−	36.0907i	−0.327842	−	1.18474i
$929$	5.50414	−	3.99899i	0.180585	−	0.131203i	−0.493820	−	0.869564i	$-0.664400\pi$
$929$	5.50414	−	3.99899i	0.180585	−	0.131203i	0.674405	+	0.738361i	$0.264400\pi$
$930$		0			0
$931$	11.0530	−	15.2132i	0.362248	−	0.498592i
$932$	14.0655	−	2.42629i	0.460731	−	0.0794759i
$933$	−7.09400	−	5.15409i	−0.232247	−	0.168737i
$934$	29.9531	−	18.6395i	0.980094	−	0.609903i
$935$		0			0
$936$	−15.1252	−	3.30314i	−0.494381	−	0.107966i
$937$	15.8759	+	5.15839i	0.518643	+	0.168517i	0.556629	−	0.830761i	$-0.312094\pi$
$937$	15.8759	+	5.15839i	0.518643	+	0.168517i	−0.0379863	+	0.999278i	$0.512094\pi$
$938$	1.95396	+	3.13994i	0.0637989	+	0.102523i
$939$	0.0102093	−	0.00331721i	0.000333168	−	0.000108253i
$940$		0			0
$941$	−10.5188	−	3.41775i	−0.342902	−	0.111416i	0.132503	−	0.991183i	$-0.457699\pi$
$941$	−10.5188	−	3.41775i	−0.342902	−	0.111416i	−0.475405	+	0.879767i	$0.657699\pi$
$942$	−2.06964	−	8.36704i	−0.0674325	−	0.272613i
$943$		−	16.8993i		−	0.550316i
$944$	7.93176	−	26.9053i	0.258157	−	0.875693i
$945$		0			0
$946$	−4.71199	+	65.6327i	−0.153200	+	2.13390i
$947$	−16.0299	+	11.6464i	−0.520901	+	0.378457i	−0.816943	−	0.576718i	$-0.804333\pi$
$947$	−16.0299	+	11.6464i	−0.520901	+	0.378457i	0.296042	+	0.955175i	$0.404333\pi$
$948$	−6.62042	+	3.48866i	−0.215021	+	0.113306i
$949$		−	28.3986i		−	0.921858i
$950$		0			0
$951$	−4.74494			−0.153865
$952$	−2.67994	−	0.585264i	−0.0868573	−	0.0189685i
$953$	−28.4871	−	39.2091i	−0.922787	−	1.27011i	−0.962608	−	0.270900i	$-0.912679\pi$
$953$	−28.4871	−	39.2091i	−0.922787	−	1.27011i	0.0398210	−	0.999207i	$-0.487321\pi$
$954$	15.5830	+	1.11876i	0.504518	+	0.0362211i
$955$		0			0
$956$	−4.73717	+	9.62175i	−0.153211	+	0.311190i
$957$	11.1695			0.361060
$958$	−5.21685	−	21.0905i	−0.168549	−	0.681402i
$959$	−0.959267	+	2.95232i	−0.0309764	+	0.0953354i
$960$		0			0
$961$	−0.918548	−	2.82700i	−0.0296306	−	0.0911936i
$962$	−4.55895	+	2.83699i	−0.146986	+	0.0914682i
$963$	0.317642	−	0.977603i	0.0102359	−	0.0315028i
$964$	3.34124	−	1.76068i	0.107614	−	0.0567077i
$965$		0			0
$966$	−0.200881	+	0.125006i	−0.00646325	+	0.00402202i
$967$	−11.5880	+	15.9495i	−0.372645	+	0.512901i	−0.953617	−	0.301022i	$-0.902672\pi$
$967$	−11.5880	+	15.9495i	−0.372645	+	0.512901i	0.580973	+	0.813923i	$0.302672\pi$
$968$	−32.0641	+	54.8288i	−1.03058	+	1.76226i
$969$	2.63931	+	1.91757i	0.0847870	+	0.0616013i
$970$		0			0
$971$	−1.31463	−	1.80943i	−0.0421885	−	0.0580675i	0.787402	−	0.616440i	$-0.211426\pi$
$971$	−1.31463	−	1.80943i	−0.0421885	−	0.0580675i	−0.829590	+	0.558373i	$0.811426\pi$
$972$	−10.8666	−	10.5721i	−0.348547	−	0.339099i
$973$	−0.164154	−	0.505214i	−0.00526253	−	0.0161964i
$974$	−20.5503	+	24.3987i	−0.658475	+	0.781786i
$975$		0			0
$976$	−2.18349	−	6.14064i	−0.0698917	−	0.196557i
$977$	−11.4440	+	3.71838i	−0.366126	+	0.118962i	−0.486301	−	0.873791i	$-0.661654\pi$
$977$	−11.4440	+	3.71838i	−0.366126	+	0.118962i	0.120175	+	0.992753i	$0.461654\pi$
$978$	−5.14823	−	0.369609i	−0.164622	−	0.0118188i
$979$	38.6458	+	53.1914i	1.23512	+	1.70000i
$980$		0			0
$981$	−16.6587	+	22.9287i	−0.531870	+	0.732057i
$982$	−6.95109	+	8.25281i	−0.221818	+	0.263358i
$983$	27.2305	−	37.4796i	0.868518	−	1.19541i	−0.110952	−	0.993826i	$-0.535390\pi$
$983$	27.2305	−	37.4796i	0.868518	−	1.19541i	0.979471	−	0.201587i	$-0.0646099\pi$
$984$	−3.79613	−	4.26356i	−0.121016	−	0.135917i
$985$		0			0
$986$	−14.5515	+	35.8244i	−0.463413	+	1.14088i
$987$	0.222746	−	0.685540i	0.00709007	−	0.0218210i
$988$	−1.45264	+	10.0647i	−0.0462146	+	0.320199i
$989$	−18.6862	+	6.07153i	−0.594188	+	0.193063i
$990$		0			0
$991$	18.8475	−	58.0065i	0.598710	−	1.84264i	0.0633902	−	0.997989i	$-0.479809\pi$
$991$	18.8475	−	58.0065i	0.598710	−	1.84264i	0.535319	−	0.844650i	$-0.320191\pi$
$992$	−16.5154	−	24.9824i	−0.524365	−	0.793193i
$993$		−	6.62737i		−	0.210313i
$994$	0.881132	−	0.217953i	0.0279478	−	0.00691306i
$995$		0			0
$996$	1.31937	+	1.28361i	0.0418058	+	0.0406726i
$997$	−26.2826	+	19.0954i	−0.832378	+	0.604758i	−0.920231	−	0.391375i	$-0.871999\pi$
$997$	−26.2826	+	19.0954i	−0.832378	+	0.604758i	0.0878532	+	0.996133i	$0.471999\pi$
$998$	35.3360	+	14.3531i	1.11854	+	0.454339i
$999$	−3.48883			−0.110382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.349.17		112
5.2	odd	4		1000.2.t.b.901.50		224
5.3	odd	4		1000.2.t.b.901.7		224
5.4	even	2		200.2.o.a.69.12	yes	112
8.5	even	2	inner	1000.2.o.a.349.23		112
20.19	odd	2		800.2.be.a.369.13		112
25.3	odd	20		1000.2.t.b.101.39		224
25.4	even	10	inner	1000.2.o.a.149.23		112
25.21	even	5		200.2.o.a.29.6	✓	112
25.22	odd	20		1000.2.t.b.101.18		224
40.13	odd	4		1000.2.t.b.901.39		224
40.19	odd	2		800.2.be.a.369.16		112
40.29	even	2		200.2.o.a.69.6	yes	112
40.37	odd	4		1000.2.t.b.901.18		224
100.71	odd	10		800.2.be.a.529.16		112
200.21	even	10		200.2.o.a.29.12	yes	112
200.29	even	10	inner	1000.2.o.a.149.17		112
200.53	odd	20		1000.2.t.b.101.7		224
200.171	odd	10		800.2.be.a.529.13		112
200.197	odd	20		1000.2.t.b.101.50		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.6	✓	112	25.21	even	5
200.2.o.a.29.12	yes	112	200.21	even	10
200.2.o.a.69.6	yes	112	40.29	even	2
200.2.o.a.69.12	yes	112	5.4	even	2
800.2.be.a.369.13		112	20.19	odd	2
800.2.be.a.369.16		112	40.19	odd	2
800.2.be.a.529.13		112	200.171	odd	10
800.2.be.a.529.16		112	100.71	odd	10
1000.2.o.a.149.17		112	200.29	even	10	inner
1000.2.o.a.149.23		112	25.4	even	10	inner
1000.2.o.a.349.17		112	1.1	even	1	trivial
1000.2.o.a.349.23		112	8.5	even	2	inner
1000.2.t.b.101.7		224	200.53	odd	20
1000.2.t.b.101.18		224	25.22	odd	20
1000.2.t.b.101.39		224	25.3	odd	20
1000.2.t.b.101.50		224	200.197	odd	20
1000.2.t.b.901.7		224	5.3	odd	4
1000.2.t.b.901.18		224	40.37	odd	4
1000.2.t.b.901.39		224	40.13	odd	4
1000.2.t.b.901.50		224	5.2	odd	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.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.532208 - 1.31025i) q^{2} +(-0.235999 + 0.171463i) q^{3} +(-1.43351 - 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} +0.234809i q^{7} +(-2.59027 + 1.13601i) q^{8} +(-0.900755 + 2.77224i) q^{9} +O(q^{10})\)	\(q+(0.532208 - 1.31025i) q^{2} +(-0.235999 + 0.171463i) q^{3} +(-1.43351 - 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} +0.234809i q^{7} +(-2.59027 + 1.13601i) q^{8} +(-0.900755 + 2.77224i) q^{9} +(5.50105 - 1.78740i) q^{11} +(0.577439 + 0.0833422i) q^{12} +(0.580270 - 1.78589i) q^{13} +(0.307658 + 0.124967i) q^{14} +(0.109896 + 3.99849i) q^{16} +(2.42773 - 3.34149i) q^{17} +(3.15294 + 2.65562i) q^{18} +(1.59154 - 2.19056i) q^{19} +(-0.0402612 - 0.0554147i) q^{21} +(0.585764 - 8.15902i) q^{22} +(2.32295 - 0.754772i) q^{23} +(0.416517 - 0.712234i) q^{24} +(-2.03113 - 1.71076i) q^{26} +(-0.533191 - 1.64099i) q^{27} +(0.327477 - 0.336601i) q^{28} +(-3.89100 - 5.35551i) q^{29} +(-4.28302 - 3.11180i) q^{31} +(5.29751 + 1.98404i) q^{32} +(-0.991770 + 1.36505i) q^{33} +(-3.08612 - 4.95930i) q^{34} +(5.15755 - 2.71779i) q^{36} +(0.624829 - 1.92303i) q^{37} +(-2.02316 - 3.25115i) q^{38} +(0.169271 + 0.520963i) q^{39} +(2.13805 - 6.58023i) q^{41} +(-0.0940345 + 0.0232600i) q^{42} -8.04419 q^{43} +(-10.3786 - 5.10979i) q^{44} +(0.247353 - 3.44534i) q^{46} +(6.18554 + 8.51367i) q^{47} +(-0.711530 - 0.924798i) q^{48} +6.94486 q^{49} +1.20486i q^{51} +(-3.32251 + 1.75081i) q^{52} +(3.06610 - 2.22765i) q^{53} +(-2.43388 - 0.174737i) q^{54} +(-0.266745 - 0.608218i) q^{56} +0.789862i q^{57} +(-9.08787 + 2.24794i) q^{58} +(-6.66931 - 2.16699i) q^{59} +(-1.54958 + 0.503489i) q^{61} +(-6.35669 + 3.95570i) q^{62} +(-0.650947 - 0.211505i) q^{63} +(5.41896 - 5.88514i) q^{64} +(1.26073 + 2.02596i) q^{66} +(9.01003 + 6.54617i) q^{67} +(-8.14038 + 1.40421i) q^{68} +(-0.418799 + 0.576427i) q^{69} +(2.21139 - 1.60667i) q^{71} +(-0.816095 - 8.20411i) q^{72} +(14.3832 - 4.67339i) q^{73} +(-2.18711 - 1.84213i) q^{74} +(-5.33656 + 0.920553i) q^{76} +(0.419697 + 1.29170i) q^{77} +(0.772679 + 0.0554733i) q^{78} +(-10.3770 + 7.53932i) q^{79} +(-6.66742 - 4.84416i) q^{81} +(-7.48385 - 6.30342i) q^{82} +(2.55253 + 1.85452i) q^{83} +(-0.0195695 + 0.135588i) q^{84} +(-4.28118 + 10.5399i) q^{86} +(1.83655 + 0.596730i) q^{87} +(-12.2187 + 10.8791i) q^{88} +(3.51258 + 10.8106i) q^{89} +(0.419342 + 0.136252i) q^{91} +(-4.38261 - 2.15773i) q^{92} +1.54435 q^{93} +(14.4470 - 3.57356i) q^{94} +(-1.59040 + 0.440098i) q^{96} +(-4.11921 - 5.66961i) q^{97} +(3.69611 - 9.09951i) q^{98} +16.8602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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