LMFDB - Embedded newform 1000.2.o.a.149.17

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			149.17
Character	$\chi$	$=$	1000.149
Dual form			1000.2.o.a.349.17

$q$-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 $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

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

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	0.517570	−	0.855641i	$-0.326837\pi$
$3$	−0.235999	−	0.171463i	−0.136254	−	0.0989945i	−0.653825	+	0.756646i	$0.726837\pi$
$4$	−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	$-0.985870\pi$
$7$		−	0.234809i		−	0.0887494i	0.999015	−	0.0443747i	$-0.0141296\pi$
$8$	−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	0.980584	−	0.196099i	$-0.0628276\pi$
$11$	5.50105	+	1.78740i	1.65863	+	0.538921i	0.678045	+	0.735021i	$0.262828\pi$
$12$	0.577439	−	0.0833422i	0.166692	−	0.0240588i
$13$	0.580270	+	1.78589i	0.160938	+	0.495316i	0.998714	−	0.0506981i	$-0.0161446\pi$
$13$	0.580270	+	1.78589i	0.160938	+	0.495316i	−0.837776	+	0.546014i	$0.816145\pi$
$14$	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	0.994627	−	0.103526i	$-0.0330124\pi$
$17$	2.42773	+	3.34149i	0.588811	+	0.810429i	−0.405815	+	0.913955i	$0.633012\pi$
$18$	3.15294	−	2.65562i	0.743154	−	0.625936i
$19$	1.59154	+	2.19056i	0.365124	+	0.502550i	0.951567	−	0.307440i	$-0.0994724\pi$
$19$	1.59154	+	2.19056i	0.365124	+	0.502550i	−0.586443	+	0.809990i	$0.699472\pi$
$20$		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	0.541014	−	0.841013i	$-0.318041\pi$
$23$	2.32295	+	0.754772i	0.484369	+	0.157381i	−0.0566456	+	0.998394i	$0.518041\pi$
$24$	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	0.276894	+	0.960900i	$0.410695\pi$
$29$	−3.89100	+	5.35551i	−0.722541	+	0.994493i	−0.999436	+	0.0335922i	$0.989305\pi$
$30$		0			0
$31$	−4.28302	+	3.11180i	−0.769253	+	0.558895i	−0.901734	−	0.432291i	$-0.857705\pi$
$31$	−4.28302	+	3.11180i	−0.769253	+	0.558895i	0.132482	+	0.991185i	$0.457705\pi$
$32$	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	0.989189	−	0.146647i	$-0.0468481\pi$
$37$	0.624829	+	1.92303i	0.102721	+	0.316144i	−0.886468	+	0.462791i	$0.846848\pi$
$38$	−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	0.967258	+	0.253795i	$0.0816787\pi$
$41$	2.13805	+	6.58023i	0.333907	+	1.02766i	−0.633352	+	0.773864i	$0.718321\pi$
$42$	−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	−0.0674892	−	0.997720i	$-0.521499\pi$
$47$	6.18554	−	8.51367i	0.902254	−	1.24185i	0.969743	−	0.244126i	$-0.0785012\pi$
$48$	−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	0.778105	−	0.628135i	$-0.216181\pi$
$53$	3.06610	+	2.22765i	0.421161	+	0.305991i	−0.356944	+	0.934126i	$0.616181\pi$
$54$	−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	−0.709078	−	0.705130i	$-0.750889\pi$
$59$	−6.66931	+	2.16699i	−0.868270	+	0.282118i	−0.159192	+	0.987248i	$0.550889\pi$
$60$		0			0
$61$	−1.54958	−	0.503489i	−0.198403	−	0.0644651i	0.208130	−	0.978101i	$-0.433262\pi$
$61$	−1.54958	−	0.503489i	−0.198403	−	0.0644651i	−0.406533	+	0.913636i	$0.633262\pi$
$62$	−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	0.119569	−	0.992826i	$-0.461849\pi$
$67$	9.01003	−	6.54617i	1.10075	−	0.799742i	0.981182	+	0.193084i	$0.0618489\pi$
$68$	−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	0.711223	−	0.702966i	$-0.248141\pi$
$71$	2.21139	+	1.60667i	0.262443	+	0.190676i	−0.448780	+	0.893642i	$0.648141\pi$
$72$	−0.816095	+	8.20411i	−0.0961777	+	0.966863i
$73$	14.3832	+	4.67339i	1.68343	+	0.546979i	0.985572	−	0.169258i	$-0.0541371\pi$
$73$	14.3832	+	4.67339i	1.68343	+	0.546979i	0.697857	+	0.716237i	$0.254137\pi$
$74$	−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	−0.176795	−	0.984248i	$-0.556573\pi$
$79$	−10.3770	−	7.53932i	−1.16750	−	0.848240i	−0.990708	+	0.136008i	$0.956573\pi$
$80$		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	−0.438818	−	0.898576i	$-0.644603\pi$
$83$	2.55253	−	1.85452i	0.280176	−	0.203560i	0.718994	+	0.695016i	$0.244603\pi$
$84$	−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	−0.572927	−	0.819606i	$-0.694192\pi$
$89$	3.51258	−	10.8106i	0.372333	−	1.14592i	0.945260	−	0.326317i	$-0.105808\pi$
$90$		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	−0.965205	−	0.261496i	$-0.915784\pi$
$97$	−4.11921	+	5.66961i	−0.418243	+	0.575661i	0.546962	+	0.837157i	$0.315784\pi$
$98$	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	$0.183358\pi$
$101$			10.9484i			1.08941i	−0.838628	+	0.544704i	$0.816642\pi$
$102$	1.57866	−	0.641234i	0.156311	−	0.0634916i
$103$	−6.88143	+	9.47147i	−0.678047	+	0.933252i	−0.999908	−	0.0135350i	$-0.995692\pi$
$103$	−6.88143	+	9.47147i	−0.678047	+	0.933252i	0.321861	+	0.946787i	$0.395692\pi$
$104$	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	0.169382	−	0.985550i	$-0.445823\pi$
$109$	9.24706	−	3.00455i	0.885708	−	0.287784i	0.716325	+	0.697767i	$0.245823\pi$
$110$		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	−0.294332	−	0.955703i	$-0.595097\pi$
$113$	0.311428	−	0.101189i	0.0292967	−	0.00951907i	0.323629	+	0.946184i	$0.395097\pi$
$114$	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	0.671687	−	0.740835i	$-0.265570\pi$
$127$	8.78610	+	2.85478i	0.779640	+	0.253320i	0.107954	+	0.994156i	$0.465570\pi$
$128$	−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	0.568430	−	0.822732i	$-0.307551\pi$
$131$	−4.46019	−	6.13893i	−0.389689	−	0.536361i	−0.958119	+	0.286371i	$0.907551\pi$
$132$	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	0.282083	−	0.959390i	$-0.408975\pi$
$137$	12.5733	−	4.08531i	1.07421	−	0.349032i	0.792125	+	0.610358i	$0.208975\pi$
$138$	0.532375	−	0.855510i	0.0453188	−	0.0728258i
$139$	−2.15160	−	0.699096i	−0.182496	−	0.0592965i	0.216343	−	0.976317i	$-0.430587\pi$
$139$	−2.15160	−	0.699096i	−0.182496	−	0.0592965i	−0.398839	+	0.917021i	$0.630587\pi$
$140$		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	$0.217243\pi$
$149$			15.3980i			1.26145i	−0.776004	+	0.630727i	$0.782757\pi$
$150$		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	−0.980479	−	0.196624i	$-0.937002\pi$
$163$	−3.86624	−	11.8991i	−0.302827	−	0.932006i	0.677652	−	0.735383i	$-0.262998\pi$
$164$	−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	−0.936694	−	0.350149i	$-0.886131\pi$
$167$	−12.6676	−	17.4355i	−0.980251	−	1.34920i	−0.0435571	−	0.999051i	$-0.513869\pi$
$168$	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	−0.930591	−	0.366061i	$-0.880706\pi$
$173$	0.492423	−	1.51552i	0.0374382	−	0.115223i	0.968029	+	0.250838i	$0.0807061\pi$
$174$	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	−0.492987	−	0.870037i	$-0.664095\pi$
$179$	6.51305	−	8.96444i	0.486808	−	0.670034i	0.979795	+	0.200003i	$0.0640951\pi$
$180$		0			0
$181$	−11.7991	−	16.2401i	−0.877020	−	1.20711i	−0.977237	−	0.212149i	$-0.931954\pi$
$181$	−11.7991	−	16.2401i	−0.877020	−	1.20711i	0.100217	−	0.994966i	$-0.468046\pi$
$182$	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	−0.904099	−	0.427324i	$-0.859456\pi$
$191$	−5.85762	−	18.0279i	−0.423842	−	1.30445i	0.480256	−	0.877128i	$-0.340544\pi$
$192$	−0.269785	−	2.31804i	−0.0194701	−	0.167290i
$193$		−	2.63353i		−	0.189566i	−0.995498	−	0.0947828i	$-0.969784\pi$
$193$		−	2.63353i		−	0.189566i	0.995498	−	0.0947828i	$-0.0302157\pi$
$194$	−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	−0.984658	−	0.174498i	$-0.944170\pi$
$197$	−20.4204	−	14.8363i	−1.45489	−	1.05704i	−0.470233	−	0.882542i	$-0.655830\pi$
$198$	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	0.746678	−	0.665186i	$-0.231648\pi$
$211$	13.9414	+	4.52984i	0.959766	+	0.311847i	0.213088	+	0.977033i	$0.431648\pi$
$212$	−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	0.796686	−	0.604393i	$-0.206584\pi$
$223$	16.2169	+	5.26920i	1.08597	+	0.352852i	0.289280	+	0.957245i	$0.406584\pi$
$224$	−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	−0.681185	−	0.732111i	$-0.738535\pi$
$227$	4.52341	−	13.9216i	0.300229	−	0.924011i	0.981414	−	0.191900i	$-0.0614649\pi$
$228$	1.10158	+	1.13227i	0.0729541	+	0.0749867i
$229$	3.58252	−	4.93092i	0.236740	−	0.325844i	−0.674072	−	0.738665i	$-0.735456\pi$
$229$	3.58252	−	4.93092i	0.236740	−	0.325844i	0.910812	+	0.412821i	$0.135456\pi$
$230$		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	0.649196	−	0.760621i	$-0.275106\pi$
$233$	−4.19480	−	5.77365i	−0.274811	−	0.378244i	−0.924006	+	0.382377i	$0.875106\pi$
$234$	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	−0.990237	−	0.139392i	$-0.955485\pi$
$239$	−1.65706	+	5.09989i	−0.107186	+	0.329885i	0.883051	+	0.469276i	$0.155485\pi$
$240$		0			0
$241$	−0.583541	−	1.79595i	−0.0375892	−	0.115688i	0.930501	−	0.366289i	$-0.119372\pi$
$241$	−0.583541	−	1.79595i	−0.0375892	−	0.115688i	−0.968090	+	0.250601i	$0.919372\pi$
$242$	−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	$-0.954129\pi$
$251$		−	4.55040i		−	0.287219i	0.989634	−	0.143609i	$-0.0458709\pi$
$252$	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	$0.0699653\pi$
$257$			6.99079i			0.436074i	−0.975941	+	0.218037i	$0.930035\pi$
$258$	−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	−0.884742	−	0.466081i	$-0.845665\pi$
$263$	−21.5131	+	6.99005i	−1.32656	+	0.431025i	−0.441816	+	0.897106i	$0.645665\pi$
$264$	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	0.681585	−	0.731739i	$-0.261291\pi$
$269$	−3.68963	−	5.07835i	−0.224961	−	0.309632i	−0.906546	+	0.422106i	$0.861291\pi$
$270$		0			0
$271$	−2.75055	−	1.99839i	−0.167084	−	0.121393i	0.501101	−	0.865389i	$-0.332928\pi$
$271$	−2.75055	−	1.99839i	−0.167084	−	0.121393i	−0.668185	+	0.743995i	$0.732928\pi$
$272$	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	0.363867	+	0.931451i	$0.381456\pi$
$277$	−7.95552	+	24.4846i	−0.478001	+	1.47114i	−0.841868	+	0.539684i	$0.818544\pi$
$278$	−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	−0.678047	−	0.735019i	$-0.737173\pi$
$281$	−3.16034	+	2.29612i	−0.188530	+	0.136975i	0.489517	+	0.871994i	$0.337173\pi$
$282$	−2.79675	−	3.32050i	−0.166544	−	0.197733i
$283$	1.03911	−	0.754960i	0.0617689	−	0.0448777i	−0.556472	−	0.830866i	$-0.687845\pi$
$283$	1.03911	−	0.754960i	0.0617689	−	0.0448777i	0.618241	+	0.785988i	$0.287845\pi$
$284$	−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	−0.234160	−	0.972198i	$-0.575234\pi$
$311$	9.28886	−	28.5882i	0.526723	−	1.62109i	0.760883	−	0.648889i	$-0.224766\pi$
$312$	−1.03028	+	1.15714i	−0.0583279	+	0.0655101i
$313$	−0.0349980	+	0.0113715i	−0.00197820	+	0.000642758i	−0.310006	−	0.950735i	$-0.600331\pi$
$313$	−0.0349980	+	0.0113715i	−0.00197820	+	0.000642758i	0.308028	+	0.951377i	$0.400331\pi$
$314$	−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	−0.153326	−	0.988176i	$-0.548998\pi$
$317$	13.1594	−	9.56085i	0.739104	−	0.536991i	0.892431	+	0.451185i	$0.148998\pi$
$318$	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	−0.998942	−	0.0459939i	$-0.985355\pi$
$331$	−13.3539	−	18.3800i	−0.733995	−	1.01026i	0.264947	−	0.964263i	$-0.414645\pi$
$332$	−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	−0.752701	−	0.658362i	$-0.771249\pi$
$337$	−17.8926	+	5.81367i	−0.974674	+	0.316691i	−0.221972	+	0.975053i	$0.571249\pi$
$338$	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	−0.283235	−	0.959051i	$-0.591408\pi$
$347$	−23.8972	−	17.3624i	−1.28287	−	0.932060i	−0.999636	+	0.0269903i	$0.991408\pi$
$348$	−1.80048	+	3.41676i	−0.0965157	+	0.183158i
$349$			15.7634i			0.843797i	0.906643	+	0.421898i	$0.138636\pi$
$349$			15.7634i			0.843797i	−0.906643	+	0.421898i	$0.861364\pi$
$350$		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	−0.661989	−	0.749513i	$-0.730288\pi$
$353$	4.79864	−	6.60477i	0.255406	−	0.351536i	0.917395	+	0.397977i	$0.130288\pi$
$354$	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	−0.813148	−	0.582056i	$-0.802248\pi$
$359$	−9.42480	−	29.0065i	−0.497422	−	1.53091i	0.315727	−	0.948850i	$-0.397752\pi$
$360$		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	0.908432	−	0.418033i	$-0.137280\pi$
$367$	4.40881	+	6.06821i	0.230138	+	0.316758i	−0.678294	+	0.734791i	$0.737280\pi$
$368$	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	0.795619	+	0.605797i	$0.207146\pi$
$373$	−3.94238	+	12.1334i	−0.204129	+	0.628243i	−0.999748	+	0.0224465i	$0.992854\pi$
$374$	−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	−0.952863	−	0.303402i	$-0.901878\pi$
$379$	−7.20040	+	9.91051i	−0.369860	+	0.509069i	0.583003	+	0.812470i	$0.301878\pi$
$380$		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	−0.991525	−	0.129912i	$-0.958530\pi$
$383$	−15.8262	−	21.7829i	−0.808681	−	1.11305i	0.182844	−	0.983142i	$-0.441470\pi$
$384$	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	0.0700104	−	0.997546i	$-0.477697\pi$
$389$	−9.06656	−	2.94590i	−0.459693	−	0.149363i	−0.529703	+	0.848183i	$0.677697\pi$
$390$		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	0.949575	−	0.313539i	$-0.101515\pi$
$397$	18.8253	+	13.6774i	0.944816	+	0.686449i	−0.00475885	+	0.999989i	$0.501515\pi$
$398$	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	0.835029	+	0.550206i	$0.185451\pi$
$409$	9.76563	+	30.0555i	0.482879	+	1.48615i	−0.352150	+	0.935944i	$0.614549\pi$
$410$		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	0.914771	−	0.403973i	$-0.132371\pi$
$419$	5.07417	+	6.98399i	0.247889	+	0.341190i	−0.666881	+	0.745164i	$0.732371\pi$
$420$		0			0
$421$	7.53026	−	10.3645i	0.367002	−	0.505135i	−0.585081	−	0.810975i	$-0.698937\pi$
$421$	7.53026	−	10.3645i	0.367002	−	0.505135i	0.952083	+	0.305840i	$0.0989371\pi$
$422$	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	−0.991238	−	0.132087i	$-0.957832\pi$
$431$	−24.3298	+	17.6766i	−1.17193	+	0.851454i	−0.180688	+	0.983541i	$0.557832\pi$
$432$	6.50290	+	2.31230i	0.312871	+	0.111251i
$433$	0.945079	+	1.30079i	0.0454176	+	0.0625120i	0.831122	−	0.556090i	$-0.187699\pi$
$433$	0.945079	+	1.30079i	0.0454176	+	0.0625120i	−0.785704	+	0.618602i	$0.787699\pi$
$434$	−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	0.122061	+	0.992523i	$0.461050\pi$
$439$	−11.7350	+	36.1165i	−0.560079	+	1.72374i	−0.682139	+	0.731222i	$0.738950\pi$
$440$		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	$0.118803\pi$
$457$			15.5897i			0.729254i	−0.931154	+	0.364627i	$0.881197\pi$
$458$	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	0.177820	−	0.984063i	$-0.443096\pi$
$461$	−5.51241	−	1.79109i	−0.256739	−	0.0834194i	−0.434558	+	0.900644i	$0.643096\pi$
$462$	−0.475713	−	0.296032i	−0.0221322	−	0.0137726i
$463$	11.3046	−	3.67309i	0.525370	−	0.170703i	−0.0343111	−	0.999411i	$-0.510924\pi$
$463$	11.3046	−	3.67309i	0.525370	−	0.170703i	0.559681	+	0.828708i	$0.310924\pi$
$464$	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	−0.0130420	−	0.999915i	$-0.504152\pi$
$467$	20.1818	−	14.6630i	0.933903	−	0.678521i	0.946945	+	0.321394i	$0.104152\pi$
$468$	−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	0.834334	−	0.551259i	$-0.185852\pi$
$479$	12.4287	+	9.02994i	0.567880	+	0.412589i	−0.266455	+	0.963847i	$0.585852\pi$
$480$		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	−0.751670	−	0.659539i	$-0.770751\pi$
$487$	−21.4527	+	6.97042i	−0.972117	+	0.315860i	−0.220447	+	0.975399i	$0.570751\pi$
$488$	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	−0.468140	−	0.883654i	$-0.655076\pi$
$491$	−7.25634	+	2.35773i	−0.327474	+	0.106403i	0.140666	+	0.990057i	$0.455076\pi$
$492$	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	$-0.793714\pi$
$499$		−	26.9689i		−	1.20729i	0.797252	−	0.603647i	$-0.206286\pi$
$500$		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	−0.184980	−	0.982742i	$-0.559222\pi$
$503$	18.0952	−	24.9059i	0.806825	−	1.11050i	0.991805	−	0.127757i	$-0.0407778\pi$
$504$	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	−0.235041	−	0.971986i	$-0.575522\pi$
$509$	3.29675	−	1.07118i	0.146126	−	0.0474792i	0.381167	+	0.924506i	$0.375522\pi$
$510$		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	−0.992571	−	0.121663i	$-0.961177\pi$
$521$	−32.2980	−	23.4659i	−1.41500	−	1.02806i	−0.422430	−	0.906395i	$-0.638823\pi$
$522$	1.95412	+	27.2186i	0.0855294	+	1.19133i
$523$	1.93267	−	5.94816i	0.0845099	−	0.260095i	−0.899868	−	0.436162i	$-0.856338\pi$
$523$	1.93267	−	5.94816i	0.0845099	−	0.260095i	0.984378	+	0.176067i	$0.0563375\pi$
$524$	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	0.141889	−	0.989883i	$-0.454682\pi$
$541$	19.5034	−	6.33705i	0.838518	−	0.272451i	0.696629	+	0.717432i	$0.254682\pi$
$542$	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	0.133940	−	0.990989i	$-0.457237\pi$
$547$	−17.9423	−	13.0358i	−0.767157	−	0.557372i	−0.901097	+	0.433617i	$0.857237\pi$
$548$	−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	0.741854	+	0.670561i	$0.233947\pi$
$563$	12.7139	+	39.1294i	0.535828	+	1.64911i	−0.206027	+	0.978546i	$0.566053\pi$
$564$	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	−0.637751	−	0.770242i	$-0.720135\pi$
$569$	−2.43983	+	1.77264i	−0.102283	+	0.0743130i	0.535468	+	0.844555i	$0.320135\pi$
$570$		0			0
$571$	8.11104	−	11.1639i	0.339436	−	0.467194i	−0.604840	−	0.796347i	$-0.706763\pi$
$571$	8.11104	−	11.1639i	0.339436	−	0.467194i	0.944277	+	0.329153i	$0.106763\pi$
$572$	−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	0.0359612	−	0.999353i	$-0.488551\pi$
$577$	−12.5473	−	4.07686i	−0.522351	−	0.169722i	−0.558312	+	0.829631i	$0.688551\pi$
$578$	−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	0.960909	+	0.276865i	$0.0892954\pi$
$587$	8.38908	+	25.8189i	0.346254	+	1.06566i	−0.614655	+	0.788796i	$0.710705\pi$
$588$	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	$0.0693696\pi$
$593$			10.5301i			0.432420i	−0.976347	+	0.216210i	$0.930630\pi$
$594$	−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	$0.259213\pi$
$607$			35.8362i			1.45455i	−0.686347	+	0.727274i	$0.740787\pi$
$608$	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	0.839059	−	0.544041i	$-0.183106\pi$
$613$	−3.94986	−	12.1564i	−0.159533	−	0.490994i	−0.998592	+	0.0530477i	$0.983106\pi$
$614$	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	0.952842	−	0.303466i	$-0.0981437\pi$
$617$	9.18527	+	12.6424i	0.369785	+	0.508965i	−0.583057	+	0.812431i	$0.698144\pi$
$618$	3.11139	+	3.69406i	0.125159	+	0.148597i
$619$	20.9771	+	28.8724i	0.843139	+	1.16048i	0.985333	+	0.170643i	$0.0545844\pi$
$619$	20.9771	+	28.8724i	0.843139	+	1.16048i	−0.142194	+	0.989839i	$0.545416\pi$
$620$		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	0.463781	−	0.885950i	$-0.346492\pi$
$631$	36.4157	−	26.4575i	1.44969	−	1.05326i	0.985905	−	0.167308i	$-0.0535075\pi$
$632$	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	0.998556	−	0.0537145i	$-0.0171061\pi$
$641$	4.02897	+	12.3999i	0.159135	+	0.489766i	−0.839422	+	0.543481i	$0.817106\pi$
$642$	−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	−0.905386	−	0.424590i	$-0.860418\pi$
$647$	−5.64166	+	7.76508i	−0.221797	+	0.305277i	0.683589	+	0.729867i	$0.260418\pi$
$648$	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	0.129250	−	0.991612i	$-0.458743\pi$
$653$	−19.7759	−	14.3680i	−0.773889	−	0.562263i	−0.903139	+	0.429349i	$0.858743\pi$
$654$	−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	−0.967857	−	0.251502i	$-0.919076\pi$
$659$	−41.1516	+	13.3710i	−1.60304	+	0.520859i	−0.635184	+	0.772361i	$0.719076\pi$
$660$		0			0
$661$	33.1551	+	10.7728i	1.28958	+	0.419012i	0.871946	−	0.489602i	$-0.162858\pi$
$661$	33.1551	+	10.7728i	1.28958	+	0.419012i	0.417639	+	0.908613i	$0.362858\pi$
$662$	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	0.500187	−	0.865917i	$-0.333265\pi$
$673$	10.2698	+	3.33688i	0.395874	+	0.128627i	−0.104314	+	0.994544i	$0.533265\pi$
$674$	−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	0.317997	+	0.948092i	$0.396990\pi$
$677$	−12.9196	+	39.7626i	−0.496542	+	1.52820i	−0.814539	+	0.580109i	$0.803010\pi$
$678$	−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	−0.850914	−	0.525305i	$-0.823951\pi$
$683$	−16.0534	+	11.6635i	−0.614267	+	0.446291i	0.236647	+	0.971596i	$0.423951\pi$
$684$	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	−0.584632	−	0.811299i	$-0.698761\pi$
$691$	−15.2658	+	4.96017i	−0.580740	+	0.188694i	0.00389213	+	0.999992i	$0.498761\pi$
$692$	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	$-0.907164\pi$
$701$		−	15.2259i		−	0.575073i	0.957770	−	0.287537i	$-0.0928363\pi$
$702$	−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	0.434754	−	0.900549i	$-0.356835\pi$
$709$	35.0361	−	11.3839i	1.31581	−	0.427532i	0.881053	+	0.473018i	$0.156835\pi$
$710$		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	−0.203953	−	0.978981i	$-0.565379\pi$
$719$	17.8070	−	12.9375i	0.664088	−	0.482488i	0.868041	+	0.496492i	$0.165379\pi$
$720$		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	0.906069	−	0.423131i	$-0.139069\pi$
$727$	37.4888	+	12.1809i	1.39038	+	0.451763i	0.484315	+	0.874894i	$0.339069\pi$
$728$	−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	−0.137825	−	0.990457i	$-0.544011\pi$
$733$	20.6186	−	14.9803i	0.761565	−	0.553309i	0.899390	+	0.437147i	$0.144011\pi$
$734$	−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	0.148910	−	0.988851i	$-0.452424\pi$
$739$	−8.47753	−	2.75452i	−0.311851	−	0.101327i	−0.460761	+	0.887524i	$0.652424\pi$
$740$		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	$-0.870699\pi$
$743$		−	21.5410i		−	0.790261i	0.918625	−	0.395130i	$-0.129301\pi$
$744$	−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	0.771488	+	0.636243i	$0.219513\pi$
$761$	−6.25196	+	19.2415i	−0.226633	+	0.697505i	−0.998122	+	0.0612621i	$0.980487\pi$
$762$	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	−0.692347	−	0.721565i	$-0.743423\pi$
$769$	−6.10205	+	4.43340i	−0.220046	+	0.159872i	0.472302	+	0.881437i	$0.343423\pi$
$770$		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	−0.714707	−	0.699424i	$-0.753440\pi$
$773$	7.63507	−	23.4983i	0.274614	−	0.845176i	0.989321	−	0.145752i	$-0.0465601\pi$
$774$	−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	0.884138	−	0.467227i	$-0.154747\pi$
$787$	−2.96732	−	9.13248i	−0.105774	−	0.325538i	−0.989911	+	0.141689i	$0.954747\pi$
$788$	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	0.941849	−	0.336037i	$-0.109087\pi$
$797$	25.7837	+	18.7330i	0.913306	+	0.663556i	−0.0285428	+	0.999593i	$0.509087\pi$
$798$	−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	0.924362	−	0.381516i	$-0.124598\pi$
$809$	−1.35706	−	4.17661i	−0.0477118	−	0.146842i	−0.972074	+	0.234674i	$0.924598\pi$
$810$		0			0
$811$	−36.8697	−	11.9797i	−1.29467	−	0.420664i	−0.420947	−	0.907085i	$-0.638302\pi$
$811$	−36.8697	−	11.9797i	−1.29467	−	0.420664i	−0.873725	+	0.486421i	$0.838302\pi$
$812$	−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	−0.0796254	−	0.996825i	$-0.525372\pi$
$821$	25.5877	−	35.2185i	0.893017	−	1.22913i	0.972642	−	0.232308i	$-0.0746276\pi$
$822$	−0.390552	−	5.43994i	−0.0136221	−	0.189740i
$823$	4.46326	+	1.45020i	0.155580	+	0.0505509i	0.385771	−	0.922594i	$-0.373935\pi$
$823$	4.46326	+	1.45020i	0.155580	+	0.0505509i	−0.230192	+	0.973145i	$0.573935\pi$
$824$	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	−0.994032	−	0.109087i	$-0.965207\pi$
$827$	−3.61552	+	11.1274i	−0.125724	+	0.386938i	0.868308	+	0.496025i	$0.165207\pi$
$828$	9.92941	+	10.2061i	0.345071	+	0.354685i
$829$	−0.462729	+	0.636892i	−0.0160712	+	0.0221202i	−0.816977	−	0.576670i	$-0.804352\pi$
$829$	−0.462729	+	0.636892i	−0.0160712	+	0.0221202i	0.800906	+	0.598790i	$0.204352\pi$
$830$		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	−0.571611	−	0.820524i	$-0.693682\pi$
$839$	10.8077	−	33.2628i	0.373124	−	1.14836i	0.944736	−	0.327833i	$-0.106318\pi$
$840$		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	0.422852	−	0.906199i	$-0.361029\pi$
$853$	−9.00501	−	6.54252i	−0.308326	−	0.224012i	−0.731178	+	0.682187i	$0.761029\pi$
$854$	−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	$-0.637643\pi$
$857$		−	53.1600i		−	1.81591i	0.419068	−	0.907955i	$-0.362357\pi$
$858$	4.34970	+	1.07592i	0.148496	+	0.0367314i
$859$	−32.6009	+	10.5927i	−1.11233	+	0.361417i	−0.806835	−	0.590777i	$-0.798821\pi$
$859$	−32.6009	+	10.5927i	−1.11233	+	0.361417i	−0.305493	+	0.952194i	$0.598821\pi$
$860$		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	0.416508	−	0.909132i	$-0.363254\pi$
$863$	37.8328	−	12.2926i	1.28784	−	0.418446i	0.871336	+	0.490686i	$0.163254\pi$
$864$	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	−0.484758	−	0.874649i	$-0.661092\pi$
$877$	12.4831	−	38.4191i	0.421525	−	1.29732i	0.906283	−	0.422672i	$-0.138908\pi$
$878$	−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	−0.0491339	−	0.998792i	$-0.515646\pi$
$881$	26.2858	−	19.0977i	0.885591	−	0.643419i	0.934725	+	0.355373i	$0.115646\pi$
$882$	21.8967	−	18.4429i	0.737301	−	0.621006i
$883$	31.0584	−	22.5652i	1.04520	−	0.759380i	0.0739039	−	0.997265i	$-0.476454\pi$
$883$	31.0584	−	22.5652i	1.04520	−	0.759380i	0.971293	+	0.237885i	$0.0764542\pi$
$884$	−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	−0.0543921	−	0.998520i	$-0.517322\pi$
$887$	14.5493	−	4.72737i	0.488519	−	0.158729i	0.542911	+	0.839790i	$0.317322\pi$
$888$	−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	−0.974659	−	0.223694i	$-0.928188\pi$
$911$	−1.64977	+	5.07747i	−0.0546593	+	0.168224i	0.920000	+	0.391918i	$0.128188\pi$
$912$	−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	−0.379658	−	0.925127i	$-0.623958\pi$
$919$	11.6067	−	8.43275i	0.382869	−	0.278171i	0.762527	+	0.646956i	$0.223958\pi$
$920$		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	0.674405	−	0.738361i	$-0.264400\pi$
$929$	5.50414	+	3.99899i	0.180585	+	0.131203i	−0.493820	+	0.869564i	$0.664400\pi$
$930$		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	−0.0379863	−	0.999278i	$-0.512094\pi$
$937$	15.8759	−	5.15839i	0.518643	−	0.168517i	0.556629	+	0.830761i	$0.312094\pi$
$938$	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	−0.475405	−	0.879767i	$-0.657699\pi$
$941$	−10.5188	+	3.41775i	−0.342902	+	0.111416i	0.132503	+	0.991183i	$0.457699\pi$
$942$	−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	0.296042	−	0.955175i	$-0.404333\pi$
$947$	−16.0299	−	11.6464i	−0.520901	−	0.378457i	−0.816943	+	0.576718i	$0.804333\pi$
$948$	−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	0.0398210	+	0.999207i	$0.487321\pi$
$953$	−28.4871	+	39.2091i	−0.922787	+	1.27011i	−0.962608	+	0.270900i	$0.912679\pi$
$954$	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	0.580973	−	0.813923i	$-0.302672\pi$
$967$	−11.5880	−	15.9495i	−0.372645	−	0.512901i	−0.953617	+	0.301022i	$0.902672\pi$
$968$	−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	−0.829590	−	0.558373i	$-0.811426\pi$
$971$	−1.31463	+	1.80943i	−0.0421885	+	0.0580675i	0.787402	+	0.616440i	$0.211426\pi$
$972$	−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	0.120175	−	0.992753i	$-0.461654\pi$
$977$	−11.4440	−	3.71838i	−0.366126	−	0.118962i	−0.486301	+	0.873791i	$0.661654\pi$
$978$	−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	0.979471	+	0.201587i	$0.0646099\pi$
$983$	27.2305	+	37.4796i	0.868518	+	1.19541i	−0.110952	+	0.993826i	$0.535390\pi$
$984$	−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	0.535319	+	0.844650i	$0.320191\pi$
$991$	18.8475	+	58.0065i	0.598710	+	1.84264i	0.0633902	+	0.997989i	$0.479809\pi$
$992$	−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	0.0878532	−	0.996133i	$-0.471999\pi$
$997$	−26.2826	−	19.0954i	−0.832378	−	0.604758i	−0.920231	+	0.391375i	$0.871999\pi$
$998$	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.149.17		112
5.2	odd	4		1000.2.t.b.101.7		224
5.3	odd	4		1000.2.t.b.101.50		224
5.4	even	2		200.2.o.a.29.12	yes	112
8.5	even	2	inner	1000.2.o.a.149.23		112
20.19	odd	2		800.2.be.a.529.13		112
25.6	even	5		200.2.o.a.69.6	yes	112
25.8	odd	20		1000.2.t.b.901.18		224
25.17	odd	20		1000.2.t.b.901.39		224
25.19	even	10	inner	1000.2.o.a.349.23		112
40.13	odd	4		1000.2.t.b.101.18		224
40.19	odd	2		800.2.be.a.529.16		112
40.29	even	2		200.2.o.a.29.6	✓	112
40.37	odd	4		1000.2.t.b.101.39		224
100.31	odd	10		800.2.be.a.369.16		112
200.69	even	10	inner	1000.2.o.a.349.17		112
200.117	odd	20		1000.2.t.b.901.7		224
200.131	odd	10		800.2.be.a.369.13		112
200.133	odd	20		1000.2.t.b.901.50		224
200.181	even	10		200.2.o.a.69.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.6	✓	112	40.29	even	2
200.2.o.a.29.12	yes	112	5.4	even	2
200.2.o.a.69.6	yes	112	25.6	even	5
200.2.o.a.69.12	yes	112	200.181	even	10
800.2.be.a.369.13		112	200.131	odd	10
800.2.be.a.369.16		112	100.31	odd	10
800.2.be.a.529.13		112	20.19	odd	2
800.2.be.a.529.16		112	40.19	odd	2
1000.2.o.a.149.17		112	1.1	even	1	trivial
1000.2.o.a.149.23		112	8.5	even	2	inner
1000.2.o.a.349.17		112	200.69	even	10	inner
1000.2.o.a.349.23		112	25.19	even	10	inner
1000.2.t.b.101.7		224	5.2	odd	4
1000.2.t.b.101.18		224	40.13	odd	4
1000.2.t.b.101.39		224	40.37	odd	4
1000.2.t.b.101.50		224	5.3	odd	4
1000.2.t.b.901.7		224	200.117	odd	20
1000.2.t.b.901.18		224	25.8	odd	20
1000.2.t.b.901.39		224	25.17	odd	20
1000.2.t.b.901.50		224	200.133	odd	20

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

Fields

Representations

Groups

Database

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