LMFDB - Embedded newform 1000.2.t.b.901.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(101,1000)]

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, 6]))

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

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

chi := DirichletCharacter("1000.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (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:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			901.50
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31025 + 0.532208i) q^{2} +(0.171463 + 0.235999i) q^{3} +(1.43351 + 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} -0.234809 q^{7} +(1.13601 + 2.59027i) q^{8} +(0.900755 - 2.77224i) q^{9} +O(q^{10})$	\(q+(1.31025 + 0.532208i) q^{2} +(0.171463 + 0.235999i) q^{3} +(1.43351 + 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} -0.234809 q^{7} +(1.13601 + 2.59027i) q^{8} +(0.900755 - 2.77224i) q^{9} +(5.50105 - 1.78740i) q^{11} +(-0.0833422 + 0.577439i) q^{12} +(-1.78589 - 0.580270i) q^{13} +(-0.307658 - 0.124967i) q^{14} +(0.109896 + 3.99849i) q^{16} +(3.34149 + 2.42773i) q^{17} +(2.65562 - 3.15294i) q^{18} +(-1.59154 + 2.19056i) q^{19} +(-0.0402612 - 0.0554147i) q^{21} +(8.15902 + 0.585764i) q^{22} +(-0.754772 - 2.32295i) q^{23} +(-0.416517 + 0.712234i) q^{24} +(-2.03113 - 1.71076i) q^{26} +(1.64099 - 0.533191i) q^{27} +(-0.336601 - 0.327477i) q^{28} +(3.89100 + 5.35551i) q^{29} +(-4.28302 - 3.11180i) q^{31} +(-1.98404 + 5.29751i) q^{32} +(1.36505 + 0.991770i) q^{33} +(3.08612 + 4.95930i) q^{34} +(5.15755 - 2.71779i) q^{36} +(1.92303 + 0.624829i) q^{37} +(-3.25115 + 2.02316i) q^{38} +(-0.169271 - 0.520963i) q^{39} +(2.13805 - 6.58023i) q^{41} +(-0.0232600 - 0.0940345i) q^{42} +8.04419i q^{43} +(10.3786 + 5.10979i) q^{44} +(0.247353 - 3.44534i) q^{46} +(-8.51367 + 6.18554i) q^{47} +(-0.924798 + 0.711530i) q^{48} -6.94486 q^{49} +1.20486i q^{51} +(-1.75081 - 3.32251i) q^{52} +(-2.22765 - 3.06610i) q^{53} +(2.43388 + 0.174737i) q^{54} +(-0.266745 - 0.608218i) q^{56} -0.789862 q^{57} +(2.24794 + 9.08787i) q^{58} +(6.66931 + 2.16699i) q^{59} +(-1.54958 + 0.503489i) q^{61} +(-3.95570 - 6.35669i) q^{62} +(-0.211505 + 0.650947i) q^{63} +(-5.41896 + 5.88514i) q^{64} +(1.26073 + 2.02596i) q^{66} +(-6.54617 + 9.01003i) q^{67} +(1.40421 + 8.14038i) q^{68} +(0.418799 - 0.576427i) q^{69} +(2.21139 - 1.60667i) q^{71} +(8.20411 - 0.816095i) q^{72} +(-4.67339 - 14.3832i) q^{73} +(2.18711 + 1.84213i) q^{74} +(-5.33656 + 0.920553i) q^{76} +(-1.29170 + 0.419697i) q^{77} +(0.0554733 - 0.772679i) q^{78} +(10.3770 - 7.53932i) q^{79} +(-6.66742 - 4.84416i) q^{81} +(6.30342 - 7.48385i) q^{82} +(1.85452 - 2.55253i) q^{83} +(0.0195695 - 0.135588i) q^{84} +(-4.28118 + 10.5399i) q^{86} +(-0.596730 + 1.83655i) q^{87} +(10.8791 + 12.2187i) q^{88} +(-3.51258 - 10.8106i) q^{89} +(0.419342 + 0.136252i) q^{91} +(2.15773 - 4.38261i) q^{92} -1.54435i q^{93} +(-14.4470 + 3.57356i) q^{94} +(-1.59040 + 0.440098i) q^{96} +(5.66961 - 4.11921i) q^{97} +(-9.09951 - 3.69611i) q^{98} -16.8602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

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 $

$2$	1.31025	+	0.532208i	0.926486	+	0.376328i
$2$	1.31025	+	0.532208i	0.926486	+	0.376328i
$3$	0.171463	+	0.235999i	0.0989945	+	0.136254i	0.855641	−	0.517570i	$-0.173163\pi$
$3$	0.171463	+	0.235999i	0.0989945	+	0.136254i	−0.756646	+	0.653825i	$0.773163\pi$
$4$	1.43351	+	1.39465i	0.716754	+	0.697326i
$5$		0			0
$5$		0			0
$6$	0.0990593	+	0.400472i	0.0404408	+	0.163492i
$7$	−0.234809			−0.0887494			−0.0443747	−	0.999015i	$-0.514130\pi$
$7$	−0.234809			−0.0887494			−0.0443747	+	0.999015i	$0.514130\pi$
$8$	1.13601	+	2.59027i	0.401640	+	0.915798i
$9$	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	$0.0628276\pi$
$12$	−0.0833422	+	0.577439i	−0.0240588	+	0.166692i
$13$	−1.78589	−	0.580270i	−0.495316	−	0.160938i	0.0506981	−	0.998714i	$-0.483855\pi$
$13$	−1.78589	−	0.580270i	−0.495316	−	0.160938i	−0.546014	+	0.837776i	$0.683855\pi$
$14$	−0.307658	−	0.124967i	−0.0822252	−	0.0333989i
$15$		0			0
$16$	0.109896	+	3.99849i	0.0274739	+	0.999623i
$17$	3.34149	+	2.42773i	0.810429	+	0.588811i	0.913955	−	0.405815i	$-0.133012\pi$
$17$	3.34149	+	2.42773i	0.810429	+	0.588811i	−0.103526	+	0.994627i	$0.533012\pi$
$18$	2.65562	−	3.15294i	0.625936	−	0.743154i
$19$	−1.59154	+	2.19056i	−0.365124	+	0.502550i	−0.951567	−	0.307440i	$-0.900528\pi$
$19$	−1.59154	+	2.19056i	−0.365124	+	0.502550i	0.586443	+	0.809990i	$0.300528\pi$
$20$		0			0
$21$	−0.0402612	−	0.0554147i	−0.00878571	−	0.0120925i
$22$	8.15902	+	0.585764i	1.73951	+	0.124885i
$23$	−0.754772	−	2.32295i	−0.157381	−	0.484369i	0.841013	−	0.541014i	$-0.181959\pi$
$23$	−0.754772	−	2.32295i	−0.157381	−	0.484369i	−0.998394	+	0.0566456i	$0.981959\pi$
$24$	−0.416517	+	0.712234i	−0.0850211	+	0.145384i
$25$		0			0
$26$	−2.03113	−	1.71076i	−0.398338	−	0.335508i
$27$	1.64099	−	0.533191i	0.315809	−	0.102613i
$28$	−0.336601	−	0.327477i	−0.0636116	−	0.0618873i
$29$	3.89100	+	5.35551i	0.722541	+	0.994493i	0.999436	+	0.0335922i	$0.0106948\pi$
$29$	3.89100	+	5.35551i	0.722541	+	0.994493i	−0.276894	+	0.960900i	$0.589305\pi$
$30$		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	$0.857705\pi$
$32$	−1.98404	+	5.29751i	−0.350732	+	0.936476i
$33$	1.36505	+	0.991770i	0.237625	+	0.172645i
$34$	3.08612	+	4.95930i	0.529266	+	0.850513i
$35$		0			0
$36$	5.15755	−	2.71779i	0.859591	−	0.452965i
$37$	1.92303	+	0.624829i	0.316144	+	0.102721i	0.462791	−	0.886468i	$-0.346848\pi$
$37$	1.92303	+	0.624829i	0.316144	+	0.102721i	−0.146647	+	0.989189i	$0.546848\pi$
$38$	−3.25115	+	2.02316i	−0.527406	+	0.328199i
$39$	−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	$-0.0816787\pi$
$42$	−0.0232600	−	0.0940345i	−0.00358910	−	0.0145098i
$43$			8.04419i			1.22673i	0.789801	+	0.613364i	$0.210184\pi$
$43$			8.04419i			1.22673i	−0.789801	+	0.613364i	$0.789816\pi$
$44$	10.3786	+	5.10979i	1.56463	+	0.770330i
$45$		0			0
$46$	0.247353	−	3.44534i	0.0364702	−	0.507988i
$47$	−8.51367	+	6.18554i	−1.24185	+	0.902254i	−0.997720	−	0.0674892i	$-0.978501\pi$
$47$	−8.51367	+	6.18554i	−1.24185	+	0.902254i	−0.244126	+	0.969743i	$0.578501\pi$
$48$	−0.924798	+	0.711530i	−0.133483	+	0.102701i
$49$	−6.94486			−0.992124
$50$		0			0
$51$			1.20486i			0.168714i
$52$	−1.75081	−	3.32251i	−0.242794	−	0.460749i
$53$	−2.22765	−	3.06610i	−0.305991	−	0.421161i	0.628135	−	0.778105i	$-0.283819\pi$
$53$	−2.22765	−	3.06610i	−0.305991	−	0.421161i	−0.934126	+	0.356944i	$0.883819\pi$
$54$	2.43388	+	0.174737i	0.331209	+	0.0237787i
$55$		0			0
$56$	−0.266745	−	0.608218i	−0.0356453	−	0.0812765i
$57$	−0.789862			−0.104620
$58$	2.24794	+	9.08787i	0.295169	+	1.19330i
$59$	6.66931	+	2.16699i	0.868270	+	0.282118i	0.709078	−	0.705130i	$-0.249111\pi$
$59$	6.66931	+	2.16699i	0.868270	+	0.282118i	0.159192	+	0.987248i	$0.449111\pi$
$60$		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	$0.433262\pi$
$62$	−3.95570	−	6.35669i	−0.502375	−	0.807300i
$63$	−0.211505	+	0.650947i	−0.0266472	+	0.0820116i
$64$	−5.41896	+	5.88514i	−0.677370	+	0.735642i
$65$		0			0
$66$	1.26073	+	2.02596i	0.155186	+	0.249378i
$67$	−6.54617	+	9.01003i	−0.799742	+	1.10075i	0.193084	+	0.981182i	$0.438151\pi$
$67$	−6.54617	+	9.01003i	−0.799742	+	1.10075i	−0.992826	+	0.119569i	$0.961849\pi$
$68$	1.40421	+	8.14038i	0.170286	+	0.987166i
$69$	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	$0.248141\pi$
$72$	8.20411	−	0.816095i	0.966863	−	0.0961777i
$73$	−4.67339	−	14.3832i	−0.546979	−	1.68343i	−0.716237	−	0.697857i	$-0.754137\pi$
$73$	−4.67339	−	14.3832i	−0.546979	−	1.68343i	0.169258	−	0.985572i	$-0.445863\pi$
$74$	2.18711	+	1.84213i	0.254246	+	0.214144i
$75$		0			0
$76$	−5.33656	+	0.920553i	−0.612145	+	0.105595i
$77$	−1.29170	+	0.419697i	−0.147202	+	0.0478290i
$78$	0.0554733	−	0.772679i	0.00628111	−	0.0874886i
$79$	10.3770	−	7.53932i	1.16750	−	0.848240i	0.176795	−	0.984248i	$-0.443427\pi$
$79$	10.3770	−	7.53932i	1.16750	−	0.848240i	0.990708	+	0.136008i	$0.0434272\pi$
$80$		0			0
$81$	−6.66742	−	4.84416i	−0.740824	−	0.538240i
$82$	6.30342	−	7.48385i	0.696097	−	0.826454i
$83$	1.85452	−	2.55253i	0.203560	−	0.280176i	−0.695016	−	0.718994i	$-0.744603\pi$
$83$	1.85452	−	2.55253i	0.203560	−	0.280176i	0.898576	+	0.438818i	$0.144603\pi$
$84$	0.0195695	−	0.135588i	0.00213521	−	0.0147938i
$85$		0			0
$86$	−4.28118	+	10.5399i	−0.461652	+	1.13655i
$87$	−0.596730	+	1.83655i	−0.0639762	+	0.196899i
$88$	10.8791	+	12.2187i	1.15971	+	1.30252i
$89$	−3.51258	−	10.8106i	−0.372333	−	1.14592i	−0.945260	−	0.326317i	$-0.894192\pi$
$89$	−3.51258	−	10.8106i	−0.372333	−	1.14592i	0.572927	−	0.819606i	$-0.305808\pi$
$90$		0			0
$91$	0.419342	+	0.136252i	0.0439590	+	0.0142831i
$92$	2.15773	−	4.38261i	0.224959	−	0.456919i
$93$		−	1.54435i		−	0.160141i
$94$	−14.4470	+	3.57356i	−1.49010	+	0.368585i
$95$		0			0
$96$	−1.59040	+	0.440098i	−0.162319	+	0.0449173i
$97$	5.66961	−	4.11921i	0.575661	−	0.418243i	−0.261496	−	0.965205i	$-0.584216\pi$
$97$	5.66961	−	4.11921i	0.575661	−	0.418243i	0.837157	+	0.546962i	$0.184216\pi$
$98$	−9.09951	−	3.69611i	−0.919189	−	0.373364i
$99$		−	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	$-0.183358\pi$
$102$	−0.641234	+	1.57866i	−0.0634916	+	0.156311i
$103$	−9.47147	+	6.88143i	−0.933252	+	0.678047i	−0.946787	−	0.321861i	$-0.895692\pi$
$103$	−9.47147	+	6.88143i	−0.933252	+	0.678047i	0.0135350	+	0.999908i	$0.495692\pi$
$104$	−0.525731	−	5.28511i	−0.0515522	−	0.518248i
$105$		0			0
$106$	−1.28698	−	5.20293i	−0.125002	−	0.505353i
$107$		−	0.352640i		−	0.0340910i	−0.999855	−	0.0170455i	$-0.994574\pi$
$107$		−	0.352640i		−	0.0340910i	0.999855	−	0.0170455i	$-0.00542602\pi$
$108$	3.09600	+	1.52428i	0.297912	+	0.146674i
$109$	−9.24706	−	3.00455i	−0.885708	−	0.287784i	−0.169382	−	0.985550i	$-0.554177\pi$
$109$	−9.24706	−	3.00455i	−0.885708	−	0.287784i	−0.716325	+	0.697767i	$0.754177\pi$
$110$		0			0
$111$	0.182270	+	0.560968i	0.0173003	+	0.0532448i
$112$	−0.0258045	−	0.938881i	−0.00243829	−	0.0887159i
$113$	0.101189	−	0.311428i	0.00951907	−	0.0292967i	−0.946184	−	0.323629i	$-0.895097\pi$
$113$	0.101189	−	0.311428i	0.00951907	−	0.0292967i	0.955703	+	0.294332i	$0.0950971\pi$
$114$	−1.03492	−	0.420371i	−0.0969288	−	0.0393714i
$115$		0			0
$116$	−1.89128	+	13.1038i	−0.175601	+	1.21665i
$117$	−3.21729	+	4.42822i	−0.297439	+	0.409389i
$118$	7.58517	+	6.38876i	0.698272	+	0.588133i
$119$	−0.784611	−	0.570053i	−0.0719252	−	0.0522567i
$120$		0			0
$121$	18.1676	−	13.1995i	1.65160	−	1.19995i
$122$	−2.29830	−	0.165003i	−0.208078	−	0.0149386i
$123$	1.91953	−	0.623691i	0.173078	−	0.0562364i
$124$	−1.79988	−	10.4341i	−0.161634	−	0.937010i
$125$		0			0
$126$	−0.623564	+	0.740338i	−0.0555515	+	0.0659545i
$127$	2.85478	+	8.78610i	0.253320	+	0.779640i	0.994156	+	0.107954i	$0.0344298\pi$
$127$	2.85478	+	8.78610i	0.253320	+	0.779640i	−0.740835	+	0.671687i	$0.765570\pi$
$128$	−10.2323	+	4.82698i	−0.904417	+	0.426649i
$129$	−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	$0.307551\pi$
$132$	0.573644	+	3.32548i	0.0499293	+	0.289446i
$133$	0.373707	−	0.514364i	0.0324045	−	0.0446010i
$134$	−13.3723	+	8.32147i	−1.15519	+	0.718865i
$135$		0			0
$136$	−2.49251	+	11.4133i	−0.213731	+	0.978680i
$137$	−4.08531	+	12.5733i	−0.349032	+	1.07421i	0.610358	+	0.792125i	$0.291025\pi$
$137$	−4.08531	+	12.5733i	−0.349032	+	1.07421i	−0.959390	+	0.282083i	$0.908975\pi$
$138$	0.855510	−	0.532375i	0.0728258	−	0.0453188i
$139$	2.15160	−	0.699096i	0.182496	−	0.0592965i	−0.216343	−	0.976317i	$-0.569413\pi$
$139$	2.15160	−	0.699096i	0.182496	−	0.0592965i	0.398839	+	0.917021i	$0.369413\pi$
$140$		0			0
$141$	−2.91957	−	0.948625i	−0.245872	−	0.0798886i
$142$	3.75255	−	0.928216i	0.314907	−	0.0778941i
$143$	−10.8614			−0.908278
$144$	11.1838	+	3.29700i	0.931980	+	0.274750i
$145$		0			0
$146$	1.53156	−	21.3328i	0.126753	−	1.76552i
$147$	−1.19079	−	1.63898i	−0.0982148	−	0.135181i
$148$	1.88526	+	3.57765i	0.154967	+	0.294081i
$149$			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	$0.496114\pi$
$152$	−7.48215	−	1.63401i	−0.606882	−	0.132535i
$153$	9.74011	−	7.07661i	0.787441	−	0.572110i
$154$	−1.91581	−	0.137543i	−0.154380	−	0.0110835i
$155$		0			0
$156$	0.483910	−	0.982879i	0.0387438	−	0.0786933i
$157$		−	20.8929i		−	1.66744i	−0.552189	−	0.833719i	$-0.686207\pi$
$157$		−	20.8929i		−	1.66744i	0.552189	−	0.833719i	$-0.313793\pi$
$158$	17.6089	−	4.35568i	1.40089	−	0.346519i
$159$	0.341636	−	1.05145i	0.0270935	−	0.0833852i
$160$		0			0
$161$	0.177227	+	0.545449i	0.0139675	+	0.0429874i
$162$	−6.15788	−	9.89552i	−0.483809	−	0.777465i
$163$	11.8991	+	3.86624i	0.932006	+	0.302827i	0.735383	−	0.677652i	$-0.237002\pi$
$163$	11.8991	+	3.86624i	0.932006	+	0.302827i	0.196624	+	0.980479i	$0.437002\pi$
$164$	12.2420	−	6.45099i	0.955942	−	0.503737i
$165$		0			0
$166$	3.78836	−	2.35746i	0.294034	−	0.182974i
$167$	−17.4355	−	12.6676i	−1.34920	−	0.980251i	−0.999051	−	0.0435571i	$-0.986131\pi$
$167$	−17.4355	−	12.6676i	−1.34920	−	0.980251i	−0.350149	−	0.936694i	$-0.613869\pi$
$168$	0.0978019	−	0.167239i	0.00754558	−	0.0129028i
$169$	−7.66454	−	5.56862i	−0.589580	−	0.428355i
$170$		0			0
$171$	4.63918	+	6.38529i	0.354767	+	0.488295i
$172$	−11.2188	+	11.5314i	−0.855428	+	0.879262i
$173$	1.51552	−	0.492423i	0.115223	−	0.0374382i	−0.250838	−	0.968029i	$-0.580706\pi$
$173$	1.51552	−	0.492423i	0.115223	−	0.0374382i	0.366061	+	0.930591i	$0.380706\pi$
$174$	−1.75929	+	2.08875i	−0.133372	+	0.158348i
$175$		0			0
$176$	7.75144	+	21.7995i	0.584287	+	1.64320i
$177$	0.632135	+	1.94551i	0.0475142	+	0.146234i
$178$	1.15114	−	16.0340i	0.0862815	−	1.20180i
$179$	−6.51305	−	8.96444i	−0.486808	−	0.670034i	0.492987	−	0.870037i	$-0.335905\pi$
$179$	−6.51305	−	8.96444i	−0.486808	−	0.670034i	−0.979795	+	0.200003i	$0.935905\pi$
$180$		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	$0.931954\pi$
$182$	0.476928	+	0.401702i	0.0353523	+	0.0297761i
$183$	−0.384519	−	0.279369i	−0.0284245	−	0.0206516i
$184$	5.15963	−	4.59396i	0.380373	−	0.338671i
$185$		0			0
$186$	0.821915	−	2.02348i	0.0602657	−	0.148369i
$187$	22.7210	+	7.38250i	1.66152	+	0.539862i
$188$	−20.8311	−	3.00657i	−1.51926	−	0.219277i
$189$	−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	$0.859456\pi$
$192$	−2.31804	−	0.269785i	−0.167290	−	0.0194701i
$193$	2.63353			0.189566			0.0947828	−	0.995498i	$-0.469784\pi$
$193$	2.63353			0.189566			0.0947828	+	0.995498i	$0.469784\pi$
$194$	9.62088	−	2.37978i	0.690739	−	0.170859i
$195$		0			0
$196$	−9.95553	−	9.68566i	−0.711109	−	0.691833i
$197$	−14.8363	−	20.4204i	−1.05704	−	1.45489i	−0.882542	−	0.470233i	$-0.844170\pi$
$197$	−14.8363	−	20.4204i	−1.05704	−	1.45489i	−0.174498	−	0.984658i	$-0.555830\pi$
$198$	8.97315	−	22.0911i	0.637694	−	1.56995i
$199$	−3.97231			−0.281589			−0.140795	−	0.990039i	$-0.544966\pi$
$199$	−3.97231			−0.281589			−0.140795	+	0.990039i	$0.544966\pi$
$200$		0			0
$201$	−3.24879			−0.229152
$202$	5.82683	−	14.3452i	0.409975	−	1.00932i
$203$	−0.913642	−	1.25752i	−0.0641251	−	0.0882607i
$204$	−1.68035	+	1.72717i	−0.117648	+	0.120926i
$205$		0			0
$206$	−16.0723	+	3.97559i	−1.11981	+	0.276993i
$207$	−7.11964			−0.494849
$208$	2.12394	−	7.20462i	0.147269	−	0.499550i
$209$	−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	$0.231648\pi$
$212$	1.08278	−	7.50207i	0.0743656	−	0.515244i
$213$	0.758344	+	0.246401i	0.0519609	+	0.0168831i
$214$	0.187678	−	0.462047i	0.0128294	−	0.0315849i
$215$		0			0
$216$	3.24529	+	3.64490i	0.220814	+	0.248004i
$217$	1.00569	+	0.730677i	0.0682708	+	0.0496016i
$218$	−10.5169	−	8.85807i	−0.712295	−	0.599944i
$219$	2.59311	−	3.56911i	0.175226	−	0.241178i
$220$		0			0
$221$	−4.55877	−	6.27461i	−0.306656	−	0.422076i
$222$	−0.0597331	+	0.832014i	−0.00400903	+	0.0558411i
$223$	−5.26920	−	16.2169i	−0.352852	−	1.08597i	−0.957245	−	0.289280i	$-0.906584\pi$
$223$	−5.26920	−	16.2169i	−0.352852	−	1.08597i	0.604393	−	0.796686i	$-0.293416\pi$
$224$	0.465870	−	1.24390i	0.0311272	−	0.0831117i
$225$		0			0
$226$	0.298328	−	0.354195i	0.0198445	−	0.0235607i
$227$	−13.9216	+	4.52341i	−0.924011	+	0.300229i	−0.732111	−	0.681185i	$-0.761465\pi$
$227$	−13.9216	+	4.52341i	−0.924011	+	0.300229i	−0.191900	+	0.981414i	$0.561465\pi$
$228$	−1.13227	−	1.10158i	−0.0749867	−	0.0729541i
$229$	−3.58252	−	4.93092i	−0.236740	−	0.325844i	0.674072	−	0.738665i	$-0.264544\pi$
$229$	−3.58252	−	4.93092i	−0.236740	−	0.325844i	−0.910812	+	0.412821i	$0.864544\pi$
$230$		0			0
$231$	−0.320527	−	0.232876i	−0.0210891	−	0.0153221i
$232$	−9.45197	+	16.1626i	−0.620552	+	1.06113i
$233$	5.77365	+	4.19480i	0.378244	+	0.274811i	0.760621	−	0.649196i	$-0.224894\pi$
$233$	5.77365	+	4.19480i	0.378244	+	0.274811i	−0.382377	+	0.924006i	$0.624894\pi$
$234$	−6.57219	+	4.08981i	−0.429638	+	0.267359i
$235$		0			0
$236$	6.53832	+	12.4078i	0.425608	+	0.807676i
$237$	3.55855	+	1.15624i	0.231153	+	0.0751060i
$238$	−0.724649	−	1.16449i	−0.0469720	−	0.0754826i
$239$	1.65706	+	5.09989i	0.107186	+	0.329885i	0.990237	−	0.139392i	$-0.0445148\pi$
$239$	1.65706	+	5.09989i	0.107186	+	0.329885i	−0.883051	+	0.469276i	$0.844515\pi$
$240$		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	$0.119372\pi$
$242$	30.8289	−	7.62572i	1.98176	−	0.490200i
$243$		−	7.58043i		−	0.486285i
$244$	−2.92353	−	1.43937i	−0.187160	−	0.0921460i
$245$		0			0
$246$	2.84699	+	0.204395i	0.181518	+	0.0130318i
$247$	4.11342	−	2.98858i	0.261731	−	0.190159i
$248$	3.19483	−	14.6292i	0.202872	−	0.928954i
$249$	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	$0.954129\pi$
$252$	−1.21104	+	0.638161i	−0.0762882	+	0.0402004i
$253$	−8.30408	−	11.4296i	−0.522073	−	0.718572i
$254$	−0.935563	+	13.0313i	−0.0587025	+	0.817658i
$255$		0			0
$256$	−15.9758	+	0.878833i	−0.998490	+	0.0549271i
$257$	6.99079			0.436074			0.218037	−	0.975941i	$-0.430035\pi$
$257$	6.99079			0.436074			0.218037	+	0.975941i	$0.430035\pi$
$258$	−3.22147	+	0.796851i	−0.200560	+	0.0496098i
$259$	−0.451544	−	0.146716i	−0.0280576	−	0.00911646i
$260$		0			0
$261$	18.3516	−	5.96279i	1.13593	−	0.369088i
$262$	−9.11115	+	5.66978i	−0.562889	+	0.350280i
$263$	−6.99005	+	21.5131i	−0.431025	+	1.32656i	0.466081	+	0.884742i	$0.345665\pi$
$263$	−6.99005	+	21.5131i	−0.431025	+	1.32656i	−0.897106	+	0.441816i	$0.854335\pi$
$264$	−1.01823	+	4.66251i	−0.0626679	+	0.286958i
$265$		0			0
$266$	0.763399	−	0.475055i	0.0468070	−	0.0291275i
$267$	1.94902	−	2.68259i	0.119278	−	0.164172i
$268$	−21.9499	+	3.78634i	−1.34080	+	0.231287i
$269$	3.68963	−	5.07835i	0.224961	−	0.309632i	−0.681585	−	0.731739i	$-0.738709\pi$
$269$	3.68963	−	5.07835i	0.224961	−	0.309632i	0.906546	+	0.422106i	$0.138709\pi$
$270$		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	$0.332928\pi$
$272$	−9.34005	+	13.6277i	−0.566323	+	0.826300i
$273$	0.0397464	+	0.122327i	0.00240556	+	0.00740355i
$274$	−12.0444	+	14.2999i	−0.727628	+	0.863890i
$275$		0			0
$276$	1.40427	−	0.242235i	0.0845269	−	0.0145808i
$277$	24.4846	−	7.95552i	1.47114	−	0.478001i	0.539684	−	0.841868i	$-0.318544\pi$
$277$	24.4846	−	7.95552i	1.47114	−	0.478001i	0.931451	+	0.363867i	$0.118544\pi$
$278$	3.19119	+	0.229107i	0.191395	+	0.0137409i
$279$	−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	$0.737173\pi$
$282$	−3.32050	−	2.79675i	−0.197733	−	0.166544i
$283$	0.754960	−	1.03911i	0.0448777	−	0.0617689i	−0.785988	−	0.618241i	$-0.787845\pi$
$283$	0.754960	−	1.03911i	0.0448777	−	0.0617689i	0.830866	+	0.556472i	$0.187845\pi$
$284$	5.41078	+	0.780942i	0.321071	+	0.0463404i
$285$		0			0
$286$	−14.2312	−	5.78054i	−0.841507	−	0.341810i
$287$	−0.502032	+	1.54510i	−0.0296340	+	0.0912041i
$288$	12.8988	+	10.2720i	0.760071	+	0.605283i
$289$	0.0183581	+	0.0565005i	0.00107989	+	0.00332356i
$290$		0			0
$291$	1.94426	+	0.631729i	0.113975	+	0.0370326i
$292$	13.3602	−	27.1362i	0.781848	−	1.58803i
$293$		−	8.55020i		−	0.499508i	−0.968309	−	0.249754i	$-0.919650\pi$
$293$		−	8.55020i		−	0.499508i	0.968309	−	0.249754i	$-0.0803498\pi$
$294$	−0.687953	−	2.78123i	−0.0401222	−	0.162204i
$295$		0			0
$296$	0.566103	+	5.69096i	0.0329041	+	0.330781i
$297$	8.07416	−	5.86622i	0.468510	−	0.340393i
$298$	−8.19495	+	20.1753i	−0.474721	+	1.16872i
$299$			4.58650i			0.265244i
$300$		0			0
$301$		−	1.88885i		−	0.108871i
$302$	0.393157	+	0.159696i	0.0226236	+	0.00918946i
$303$	2.58382	−	1.87725i	0.148436	−	0.107845i
$304$	−8.93385	−	6.12302i	−0.512392	−	0.351179i
$305$		0			0
$306$	16.5282	−	4.08835i	0.944855	−	0.233716i
$307$			11.0920i			0.633052i	0.948584	+	0.316526i	$0.102517\pi$
$307$			11.0920i			0.633052i	−0.948584	+	0.316526i	$0.897483\pi$
$308$	−2.43699	−	1.19983i	−0.138860	−	0.0683664i
$309$	−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	$0.575234\pi$
$312$	1.15714	−	1.03028i	0.0655101	−	0.0583279i
$313$	−0.0113715	+	0.0349980i	−0.000642758	+	0.00197820i	−0.951377	−	0.308028i	$-0.900331\pi$
$313$	−0.0113715	+	0.0349980i	−0.000642758	+	0.00197820i	0.950735	+	0.310006i	$0.100331\pi$
$314$	11.1194	−	27.3750i	0.627504	−	1.54486i
$315$		0			0
$316$	25.3902	+	3.66459i	1.42831	+	0.206149i
$317$	−9.56085	+	13.1594i	−0.536991	+	0.739104i	−0.988176	−	0.153326i	$-0.951002\pi$
$317$	−9.56085	+	13.1594i	−0.536991	+	0.739104i	0.451185	+	0.892431i	$0.351002\pi$
$318$	1.00722	−	1.19584i	0.0564819	−	0.0670592i
$319$	30.9770	+	22.5061i	1.73438	+	1.26010i
$320$		0			0
$321$	0.0832228	−	0.0604649i	0.00464505	−	0.00337482i
$322$	−0.0580807	+	0.808997i	−0.00323671	+	0.0450836i
$323$	−10.6362	+	3.45591i	−0.591814	+	0.192292i
$324$	−2.80189	−	16.2429i	−0.155660	−	0.902382i
$325$		0			0
$326$	13.5331	+	11.3985i	0.749529	+	0.631305i
$327$	−0.876461	−	2.69747i	−0.0484684	−	0.149170i
$328$	19.4734	−	1.93710i	1.07524	−	0.106958i
$329$	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	$0.985355\pi$
$332$	6.21836	−	1.07266i	0.341277	−	0.0588700i
$333$	3.46435	−	4.76827i	0.189845	−	0.261300i
$334$	−16.1030	−	25.8771i	−0.881120	−	1.41593i
$335$		0			0
$336$	0.217151	−	0.167074i	0.0118465	−	0.00911462i
$337$	5.81367	−	17.8926i	0.316691	−	0.974674i	−0.658362	−	0.752701i	$-0.728751\pi$
$337$	5.81367	−	17.8926i	0.316691	−	0.974674i	0.975053	−	0.221972i	$-0.0712495\pi$
$338$	−7.07880	−	11.3754i	−0.385036	−	0.618741i
$339$	0.0908470	−	0.0295180i	0.00493413	−	0.00160320i
$340$		0			0
$341$	−29.1231	−	9.46267i	−1.57711	−	0.512433i
$342$	2.68019	+	10.8353i	0.144928	+	0.585908i
$343$	3.27438			0.176800
$344$	−20.8366	+	9.13828i	−1.12343	+	0.492703i
$345$		0			0
$346$	2.24778	+	0.161376i	0.120842	+	0.00867564i
$347$	−17.3624	−	23.8972i	−0.932060	−	1.28287i	−0.959051	−	0.283235i	$-0.908592\pi$
$347$	−17.3624	−	23.8972i	−0.932060	−	1.28287i	0.0269903	−	0.999636i	$-0.491408\pi$
$348$	−3.41676	+	1.80048i	−0.183158	+	0.0965157i
$349$			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
$352$	−1.44553	+	32.6881i	−0.0770471	+	1.74228i
$353$	6.60477	−	4.79864i	0.351536	−	0.255406i	−0.397977	−	0.917395i	$-0.630288\pi$
$353$	6.60477	−	4.79864i	0.351536	−	0.255406i	0.749513	+	0.661989i	$0.230288\pi$
$354$	−0.207162	+	2.88553i	−0.0110106	+	0.153364i
$355$		0			0
$356$	10.0417	−	20.3960i	0.532210	−	1.08098i
$357$		−	0.282911i		−	0.0149732i
$358$	−3.76277	−	15.2120i	−0.198869	−	0.803977i
$359$	9.42480	−	29.0065i	0.497422	−	1.53091i	−0.315727	−	0.948850i	$-0.602248\pi$
$359$	9.42480	−	29.0065i	0.497422	−	1.53091i	0.813148	−	0.582056i	$-0.197752\pi$
$360$		0			0
$361$	3.60574	+	11.0973i	0.189776	+	0.584071i
$362$	−24.1029	+	14.9990i	−1.26682	+	0.788328i
$363$	6.23015	+	2.02430i	0.326998	+	0.106248i
$364$	0.411106	+	0.780155i	0.0215478	+	0.0408912i
$365$		0			0
$366$	−0.355133	−	0.570688i	−0.0185631	−	0.0298303i
$367$	6.06821	+	4.40881i	0.316758	+	0.230138i	0.734791	−	0.678294i	$-0.237280\pi$
$367$	6.06821	+	4.40881i	0.316758	+	0.230138i	−0.418033	+	0.908432i	$0.637280\pi$
$368$	9.20535	−	3.27323i	0.479862	−	0.170629i
$369$	−16.3161	−	11.8543i	−0.849383	−	0.617113i
$370$		0			0
$371$	0.523072	+	0.719947i	0.0271565	+	0.0373778i
$372$	2.15383	−	2.21384i	0.111671	−	0.114782i
$373$	−12.1334	+	3.94238i	−0.628243	+	0.204129i	−0.605797	−	0.795619i	$-0.707146\pi$
$373$	−12.1334	+	3.94238i	−0.628243	+	0.204129i	−0.0224465	+	0.999748i	$0.507146\pi$
$374$	25.8412	+	21.7652i	1.33621	+	1.12545i
$375$		0			0
$376$	−25.6938	−	15.0258i	−1.32506	−	0.774898i
$377$	−3.84125	−	11.8222i	−0.197834	−	0.608872i
$378$	−0.571497	−	0.0410297i	−0.0293946	−	0.00211034i
$379$	7.20040	+	9.91051i	0.369860	+	0.509069i	0.952863	−	0.303402i	$-0.0981224\pi$
$379$	7.20040	+	9.91051i	0.369860	+	0.509069i	−0.583003	+	0.812470i	$0.698122\pi$
$380$		0			0
$381$	−1.58402	+	2.18022i	−0.0811519	+	0.111696i
$382$	−17.2695	+	20.5036i	−0.883586	+	1.04905i
$383$	21.7829	+	15.8262i	1.11305	+	0.808681i	0.983142	−	0.182844i	$-0.0585304\pi$
$383$	21.7829	+	15.8262i	1.11305	+	0.808681i	0.129912	+	0.991525i	$0.458530\pi$
$384$	−2.89363	−	1.58717i	−0.147665	−	0.0809948i
$385$		0			0
$386$	3.45058	+	1.40159i	0.175630	+	0.0713388i
$387$	22.3004	+	7.24584i	1.13359	+	0.368327i
$388$	13.8723	+	2.00220i	0.704259	+	0.101646i
$389$	9.06656	−	2.94590i	0.459693	−	0.149363i	−0.0700104	−	0.997546i	$-0.522303\pi$
$389$	9.06656	−	2.94590i	0.459693	−	0.149363i	0.529703	+	0.848183i	$0.322303\pi$
$390$		0			0
$391$	3.11744	−	9.59449i	0.157656	−	0.485214i
$392$	−7.88944	−	17.9891i	−0.398477	−	0.908584i
$393$	−2.21354			−0.111658
$394$	−8.57133	−	34.6518i	−0.431817	−	1.74573i
$395$		0			0
$396$	23.5141	−	24.1693i	1.18163	−	1.21455i
$397$	13.6774	+	18.8253i	0.686449	+	0.944816i	0.999989	−	0.00475885i	$-0.00151479\pi$
$397$	13.6774	+	18.8253i	0.686449	+	0.944816i	−0.313539	+	0.949575i	$0.601515\pi$
$398$	−5.20471	−	2.11409i	−0.260889	−	0.105970i
$399$	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	$0.400705\pi$
$402$	−4.25673	−	1.72903i	−0.212306	−	0.0862363i
$403$	5.84330	+	8.04262i	0.291076	+	0.400631i
$404$	15.2692	−	15.6946i	0.759672	−	0.780838i
$405$		0			0
$406$	−0.527837	−	2.13391i	−0.0261961	−	0.105904i
$407$	11.6955			0.579724
$408$	−3.12090	+	1.36873i	−0.154507	+	0.0677621i
$409$	−9.76563	+	30.0555i	−0.482879	+	1.48615i	0.352150	+	0.935944i	$0.385451\pi$
$409$	−9.76563	+	30.0555i	−0.482879	+	1.48615i	−0.835029	+	0.550206i	$0.814549\pi$
$410$		0			0
$411$	−3.66777	+	1.19173i	−0.180918	+	0.0587837i
$412$	−23.1746	−	3.34481i	−1.14173	−	0.164787i
$413$	−1.56601	−	0.508829i	−0.0770585	−	0.0250378i
$414$	−9.32850	−	3.78913i	−0.458471	−	0.186226i
$415$		0			0
$416$	6.61725	−	8.30947i	0.324437	−	0.407405i
$417$	0.533906	+	0.387905i	0.0261455	+	0.0189958i
$418$	−14.2685	+	16.9406i	−0.697897	+	0.828591i
$419$	−5.07417	+	6.98399i	−0.247889	+	0.341190i	−0.914771	−	0.403973i	$-0.867629\pi$
$419$	−5.07417	+	6.98399i	−0.247889	+	0.341190i	0.666881	+	0.745164i	$0.267629\pi$
$420$		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	$0.698937\pi$
$422$	20.6775	+	1.48451i	1.00657	+	0.0722649i
$423$	9.47907	+	29.1736i	0.460888	+	1.41847i
$424$	5.41138	−	9.25332i	0.262800	−	0.449381i
$425$		0			0
$426$	0.862483	+	0.726443i	0.0417874	+	0.0351963i
$427$	0.363855	−	0.118224i	0.0176082	−	0.00572124i
$428$	0.491810	−	0.505513i	0.0237725	−	0.0244349i
$429$	−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	$0.957832\pi$
$432$	2.31230	+	6.50290i	0.111251	+	0.312871i
$433$	−1.30079	−	0.945079i	−0.0625120	−	0.0454176i	0.556090	−	0.831122i	$-0.312301\pi$
$433$	−1.30079	−	0.945079i	−0.0625120	−	0.0454176i	−0.618602	+	0.785704i	$0.712301\pi$
$434$	0.928834	+	1.49261i	0.0445855	+	0.0716474i
$435$		0			0
$436$	−9.06544	−	17.2035i	−0.434156	−	0.823897i
$437$	6.28982	+	2.04369i	0.300883	+	0.0977628i
$438$	5.29714	−	3.29636i	0.253107	−	0.157506i
$439$	11.7350	+	36.1165i	0.560079	+	1.72374i	0.682139	+	0.731222i	$0.261050\pi$
$439$	11.7350	+	36.1165i	0.560079	+	1.72374i	−0.122061	+	0.992523i	$0.538950\pi$
$440$		0			0
$441$	−6.25562	+	19.2528i	−0.297887	+	0.916801i
$442$	−2.63373	−	10.6475i	−0.125274	−	0.506451i
$443$			19.5670i			0.929654i	0.885402	+	0.464827i	$0.153883\pi$
$443$			19.5670i			0.929654i	−0.885402	+	0.464827i	$0.846117\pi$
$444$	−0.521070	+	1.05836i	−0.0247289	+	0.0502273i
$445$		0			0
$446$	1.72681	−	24.0525i	0.0817670	−	1.13892i
$447$	−3.63392	+	2.64020i	−0.171879	+	0.124877i
$448$	1.27242	−	1.38188i	0.0601162	−	0.0652878i
$449$	33.2573			1.56951			0.784755	−	0.619806i	$-0.212789\pi$
$449$	33.2573			1.56951			0.784755	+	0.619806i	$0.212789\pi$
$450$		0			0
$451$		−	40.0197i		−	1.88445i
$452$	0.579389	−	0.305311i	0.0272522	−	0.0143606i
$453$	0.0514498	+	0.0708145i	0.00241732	+	0.00332716i
$454$	−20.6482	−	1.48241i	−0.969069	−	0.0695728i
$455$		0			0
$456$	−0.897291	−	2.04595i	−0.0420195	−	0.0958106i
$457$	15.5897			0.729254			0.364627	−	0.931154i	$-0.381197\pi$
$457$	15.5897			0.729254			0.364627	+	0.931154i	$0.381197\pi$
$458$	−2.06972	−	8.36739i	−0.0967119	−	0.390982i
$459$	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	$0.443096\pi$
$462$	−0.296032	−	0.475713i	−0.0137726	−	0.0221322i
$463$	3.67309	−	11.3046i	0.170703	−	0.525370i	−0.828708	−	0.559681i	$-0.810924\pi$
$463$	3.67309	−	11.3046i	0.170703	−	0.525370i	0.999411	+	0.0343111i	$0.0109237\pi$
$464$	−20.9863	+	16.1467i	−0.974266	+	0.749591i
$465$		0			0
$466$	5.33242	+	8.56902i	0.247019	+	0.396952i
$467$	−14.6630	+	20.1818i	−0.678521	+	0.933903i	−0.999915	−	0.0130420i	$-0.995848\pi$
$467$	−14.6630	+	20.1818i	−0.678521	+	0.933903i	0.321394	+	0.946945i	$0.395848\pi$
$468$	−10.7878	+	1.86090i	−0.498668	+	0.0860199i
$469$	1.53710	−	2.11564i	0.0709767	−	0.0976910i
$470$		0			0
$471$	4.93072	−	3.58238i	0.227196	−	0.165067i
$472$	1.96332	+	19.7370i	0.0903691	+	0.908470i
$473$	14.3782	+	44.2515i	0.661109	+	2.03468i
$474$	4.04723	+	3.40886i	0.185895	+	0.156574i
$475$		0			0
$476$	−0.329721	−	1.91143i	−0.0151127	−	0.0876105i
$477$	−10.5065	+	3.41377i	−0.481060	+	0.156306i
$478$	−0.543048	+	7.56403i	−0.0248384	+	0.345971i
$479$	−12.4287	+	9.02994i	−0.567880	+	0.412589i	−0.834334	−	0.551259i	$-0.814148\pi$
$479$	−12.4287	+	9.02994i	−0.567880	+	0.412589i	0.266455	+	0.963847i	$0.414148\pi$
$480$		0			0
$481$	−3.07174	−	2.23175i	−0.140059	−	0.101759i
$482$	−1.72041	+	2.04258i	−0.0783624	+	0.0930372i
$483$	−0.0983377	+	0.135350i	−0.00447452	+	0.00615865i
$484$	44.4521	+	6.41580i	2.02055	+	0.291627i
$485$		0			0
$486$	4.03437	−	9.93226i	0.183003	−	0.450536i
$487$	6.97042	−	21.4527i	0.315860	−	0.972117i	−0.659539	−	0.751670i	$-0.729249\pi$
$487$	6.97042	−	21.4527i	0.315860	−	0.972117i	0.975399	−	0.220447i	$-0.0707514\pi$
$488$	−3.06451	−	3.44185i	−0.138724	−	0.155805i
$489$	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	$0.655076\pi$
$492$	3.62149	+	1.78300i	0.163269	+	0.0803839i
$493$			27.3417i			1.23141i
$494$	6.98016	−	1.72658i	0.314052	−	0.0776827i
$495$		0			0
$496$	11.9718	−	17.4676i	0.537550	−	0.784317i
$497$	−0.519253	+	0.377259i	−0.0232917	+	0.0169224i
$498$	1.20592	+	0.489832i	0.0540387	+	0.0219499i
$499$		−	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
$502$	−2.42176	+	5.96216i	−0.108088	+	0.266104i
$503$	24.9059	−	18.0952i	1.11050	−	0.806825i	0.127757	−	0.991805i	$-0.459222\pi$
$503$	24.9059	−	18.0952i	1.11050	−	0.806825i	0.982742	+	0.184980i	$0.0592222\pi$
$504$	−1.92640	+	0.191626i	−0.0858086	+	0.00853572i
$505$		0			0
$506$	−4.79750	−	19.3951i	−0.213275	−	0.862218i
$507$		−	2.76364i		−	0.122738i
$508$	−8.16120	+	16.5764i	−0.362095	+	0.735458i
$509$	−3.29675	−	1.07118i	−0.146126	−	0.0474792i	0.235041	−	0.971986i	$-0.424478\pi$
$509$	−3.29675	−	1.07118i	−0.146126	−	0.0474792i	−0.381167	+	0.924506i	$0.624478\pi$
$510$		0			0
$511$	1.09735	+	3.37731i	0.0485441	+	0.149403i
$512$	−21.4001	−	7.35098i	−0.945758	−	0.324871i
$513$	−1.44371	+	4.44330i	−0.0637416	+	0.196176i
$514$	9.15968	+	3.72056i	0.404016	+	0.164107i
$515$		0			0
$516$	−4.64503	−	0.670420i	−0.204486	−	0.0295136i
$517$	−35.7781	+	49.2443i	−1.57352	+	2.16576i
$518$	−0.513552	−	0.432549i	−0.0225642	−	0.0190051i
$519$	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	$0.961177\pi$
$522$	27.2186	+	1.95412i	1.19133	+	0.0855294i
$523$	5.94816	−	1.93267i	0.260095	−	0.0845099i	−0.176067	−	0.984378i	$-0.556338\pi$
$523$	5.94816	−	1.93267i	0.260095	−	0.0845099i	0.436162	+	0.899868i	$0.356338\pi$
$524$	−14.9554	+	2.57980i	−0.653329	+	0.112699i
$525$		0			0
$526$	−20.6082	+	24.4674i	−0.898559	+	1.06683i
$527$	−6.75704	−	20.7960i	−0.294341	−	0.905890i
$528$	−3.81557	+	5.56715i	−0.166051	+	0.242279i
$529$	13.7810	−	10.0125i	0.599173	−	0.435325i
$530$		0			0
$531$	12.0148	−	16.5370i	0.521399	−	0.717644i
$532$	1.25307	−	0.216154i	0.0543275	−	0.00937147i
$533$	−7.63661	+	10.5109i	−0.330778	+	0.455277i
$534$	3.98140	−	2.47758i	0.172292	−	0.107216i
$535$		0			0
$536$	−30.7749	−	6.72085i	−1.32927	−	0.290296i
$537$	0.998852	−	3.07415i	0.0431036	−	0.132659i
$538$	7.53708	−	4.69025i	0.324947	−	0.202211i
$539$	−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	$0.454682\pi$
$542$	−4.66746	+	1.15453i	−0.200485	+	0.0495911i
$543$	−5.85576			−0.251295
$544$	−19.4906	+	12.8848i	−0.835651	+	0.552433i
$545$		0			0
$546$	−0.0130256	+	0.181432i	−0.000557445	+	0.00776457i
$547$	−13.0358	−	17.9423i	−0.557372	−	0.767157i	0.433617	−	0.901097i	$-0.357237\pi$
$547$	−13.0358	−	17.9423i	−0.557372	−	0.767157i	−0.990989	+	0.133940i	$0.957237\pi$
$548$	−23.3917	+	12.3263i	−0.999243	+	0.526555i
$549$			4.74932i			0.202696i
$550$		0			0
$551$	−17.9243			−0.763599
$552$	1.96886	+	0.429973i	0.0838002	+	0.0183009i
$553$	−2.43661	+	1.77030i	−0.103615	+	0.0752808i
$554$	36.3149	+	2.60717i	1.54287	+	0.110768i
$555$		0			0
$556$	4.05933	+	1.99857i	0.172154	+	0.0847580i
$557$		−	36.8641i		−	1.56198i	−0.624543	−	0.780991i	$-0.714715\pi$
$557$		−	36.8641i		−	1.56198i	0.624543	−	0.780991i	$-0.285285\pi$
$558$	−21.1854	+	5.24033i	−0.896848	+	0.221841i
$559$	4.66780	−	14.3660i	0.197427	−	0.607617i
$560$		0			0
$561$	2.15356	+	6.62797i	0.0909233	+	0.279833i
$562$	−2.91882	−	4.69045i	−0.123123	−	0.197855i
$563$	−39.1294	−	12.7139i	−1.64911	−	0.535828i	−0.670561	−	0.741854i	$-0.733947\pi$
$563$	−39.1294	−	12.7139i	−1.64911	−	0.535828i	−0.978546	+	0.206027i	$0.933947\pi$
$564$	−2.86222	−	5.43164i	−0.120521	−	0.228713i
$565$		0			0
$566$	1.54221	−	0.959702i	0.0648240	−	0.0403393i
$567$	1.56557	+	1.13745i	0.0657477	+	0.0477685i
$568$	6.67385	+	3.90289i	0.280028	+	0.163762i
$569$	2.43983	+	1.77264i	0.102283	+	0.0743130i	0.637751	−	0.770242i	$-0.279865\pi$
$569$	2.43983	+	1.77264i	0.102283	+	0.0743130i	−0.535468	+	0.844555i	$0.679865\pi$
$570$		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	$0.706763\pi$
$572$	−15.5699	−	15.1479i	−0.651012	−	0.633365i
$573$	−5.25893	+	1.70873i	−0.219695	+	0.0713833i
$574$	−1.48010	+	1.75728i	−0.0617782	+	0.0733473i
$575$		0			0
$576$	11.4338	+	20.3237i	0.476410	+	0.846822i
$577$	−4.07686	−	12.5473i	−0.169722	−	0.522351i	0.829631	−	0.558312i	$-0.188551\pi$
$577$	−4.07686	−	12.5473i	−0.169722	−	0.522351i	−0.999353	+	0.0359612i	$0.988551\pi$
$578$	−0.00601630	+	0.0838002i	−0.000250245	+	0.00348563i
$579$	0.451554	+	0.621511i	0.0187659	+	0.0258291i
$580$		0			0
$581$	−0.435458	+	0.599356i	−0.0180658	+	0.0248655i
$582$	2.21126	+	1.86247i	0.0916595	+	0.0772020i
$583$	−17.7347	−	12.8850i	−0.734498	−	0.533644i
$584$	31.9474	−	28.4448i	1.32199	−	1.17705i
$585$		0			0
$586$	4.55049	−	11.2029i	0.187979	−	0.462788i
$587$	25.8189	+	8.38908i	1.06566	+	0.346254i	0.788796	−	0.614655i	$-0.210705\pi$
$587$	25.8189	+	8.38908i	1.06566	+	0.346254i	0.276865	+	0.960909i	$0.410705\pi$
$588$	0.578800	−	4.01023i	0.0238693	−	0.165379i
$589$	13.6332	−	4.42969i	0.561745	−	0.182522i
$590$		0			0
$591$	2.27531	−	7.00269i	0.0935939	−	0.288052i
$592$	−2.28704	+	7.75787i	−0.0939968	+	0.318846i
$593$	−10.5301			−0.432420			−0.216210	−	0.976347i	$-0.569370\pi$
$593$	−10.5301			−0.432420			−0.216210	+	0.976347i	$0.569370\pi$
$594$	13.7012	−	3.38908i	0.562168	−	0.139056i
$595$		0			0
$596$	−21.4749	+	22.0732i	−0.879645	+	0.904153i
$597$	−0.681105	−	0.937461i	−0.0278758	−	0.0383677i
$598$	−2.44097	+	6.00945i	−0.0998187	+	0.245745i
$599$	−20.1787			−0.824481			−0.412241	−	0.911075i	$-0.635254\pi$
$599$	−20.1787			−0.824481			−0.412241	+	0.911075i	$0.635254\pi$
$600$		0			0
$601$	11.7592			0.479669			0.239834	−	0.970814i	$-0.422907\pi$
$601$	11.7592			0.479669			0.239834	+	0.970814i	$0.422907\pi$
$602$	1.00526	−	2.47486i	0.0409713	−	0.100868i
$603$	19.0815	+	26.2634i	0.777058	+	1.06953i
$604$	0.430142	+	0.418483i	0.0175022	+	0.0170278i
$605$		0			0
$606$	4.38453	−	1.08454i	0.178110	−	0.0440565i
$607$	35.8362			1.45455			0.727274	−	0.686347i	$-0.240787\pi$
$607$	35.8362			1.45455			0.727274	+	0.686347i	$0.240787\pi$
$608$	−8.44686	−	12.7774i	−0.342565	−	0.518190i
$609$	0.140118	−	0.431238i	0.00567785	−	0.0174746i
$610$		0			0
$611$	18.7937	−	6.10645i	0.760313	−	0.247041i
$612$	23.8319	+	3.43968i	0.963349	+	0.139041i
$613$	12.1564	+	3.94986i	0.490994	+	0.159533i	0.544041	−	0.839059i	$-0.316894\pi$
$613$	12.1564	+	3.94986i	0.490994	+	0.159533i	−0.0530477	+	0.998592i	$0.516894\pi$
$614$	−5.90324	+	14.5333i	−0.238235	+	0.586515i
$615$		0			0
$616$	−2.55451	−	2.86906i	−0.102924	−	0.115598i
$617$	12.6424	+	9.18527i	0.508965	+	0.369785i	0.812431	−	0.583057i	$-0.198144\pi$
$617$	12.6424	+	9.18527i	0.508965	+	0.369785i	−0.303466	+	0.952842i	$0.598144\pi$
$618$	−3.69406	−	3.11139i	−0.148597	−	0.125159i
$619$	−20.9771	+	28.8724i	−0.843139	+	1.16048i	0.142194	+	0.989839i	$0.454584\pi$
$619$	−20.9771	+	28.8724i	−0.843139	+	1.16048i	−0.985333	+	0.170643i	$0.945416\pi$
$620$		0			0
$621$	−2.47715	−	3.40951i	−0.0994048	−	0.136819i
$622$	−3.04413	+	42.4013i	−0.122059	+	1.70014i
$623$	0.824786	+	2.53843i	0.0330444	+	0.101700i
$624$	2.06446	−	0.734080i	0.0826446	−	0.0293867i
$625$		0			0
$626$	−0.0335258	+	0.0398041i	−0.00133996	+	0.00159089i
$627$	−4.34507	+	1.41180i	−0.173525	+	0.0563818i
$628$	29.1384	−	29.9502i	1.16275	−	1.19514i
$629$	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	$0.346492\pi$
$632$	31.3172	+	18.3144i	1.24573	+	0.728509i
$633$	3.45948	+	2.51346i	0.137502	+	0.0999010i
$634$	−19.5306	+	12.1537i	−0.775660	+	0.482686i
$635$		0			0
$636$	1.95614	−	1.03080i	0.0775660	−	0.0408737i
$637$	12.4027	+	4.02989i	0.491414	+	0.159670i
$638$	28.6097	+	45.9749i	1.13267	+	1.82016i
$639$	−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	$0.0171061\pi$
$642$	0.141223	−	0.0349323i	0.00557361	−	0.00137867i
$643$		−	34.5558i		−	1.36275i	−0.731935	−	0.681375i	$-0.761382\pi$
$643$		−	34.5558i		−	1.36275i	0.731935	−	0.681375i	$-0.238618\pi$
$644$	−0.506655	+	1.02908i	−0.0199650	+	0.0405513i
$645$		0			0
$646$	−15.7753	−	1.13257i	−0.620673	−	0.0445602i
$647$	7.76508	−	5.64166i	0.305277	−	0.221797i	−0.424590	−	0.905386i	$-0.639582\pi$
$647$	7.76508	−	5.64166i	0.305277	−	0.221797i	0.729867	+	0.683589i	$0.239582\pi$
$648$	4.97342	−	22.7734i	0.195374	−	0.894624i
$649$	40.5615			1.59218
$650$		0			0
$651$			0.362627i			0.0142125i
$652$	11.6654	+	22.1373i	0.456851	+	0.866965i
$653$	14.3680	+	19.7759i	0.562263	+	0.773889i	0.991612	−	0.129250i	$-0.0412569\pi$
$653$	14.3680	+	19.7759i	0.562263	+	0.773889i	−0.429349	+	0.903139i	$0.641257\pi$
$654$	0.287233	−	4.00082i	0.0112317	−	0.156444i
$655$		0			0
$656$	26.5459	+	7.82581i	1.03644	+	0.305547i
$657$	−44.0833			−1.71985
$658$	3.39229	−	0.839104i	0.132245	−	0.0327117i
$659$	41.1516	+	13.3710i	1.60304	+	0.520859i	0.967857	−	0.251502i	$-0.0809245\pi$
$659$	41.1516	+	13.3710i	1.60304	+	0.520859i	0.635184	+	0.772361i	$0.280924\pi$
$660$		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	$0.162858\pi$
$662$	−27.2789	+	16.9754i	−1.06022	+	0.659767i
$663$	0.699141	−	2.15173i	0.0271524	−	0.0835664i
$664$	8.71848	+	1.90400i	0.338343	+	0.0738897i
$665$		0			0
$666$	7.07688	−	4.40387i	0.274224	−	0.170647i
$667$	9.50375	−	13.0808i	0.367987	−	0.506490i
$668$	−7.32702	−	42.4756i	−0.283491	−	1.64343i
$669$	2.92371	−	4.02414i	0.113037	−	0.155582i
$670$		0			0
$671$	−7.62437	+	5.53943i	−0.294336	+	0.213847i
$672$	0.373440	−	0.103339i	0.0144057	−	0.00398638i
$673$	−3.33688	−	10.2698i	−0.128627	−	0.395874i	0.865917	−	0.500187i	$-0.166735\pi$
$673$	−3.33688	−	10.2698i	−0.128627	−	0.395874i	−0.994544	+	0.104314i	$0.966735\pi$
$674$	17.1400	−	20.3497i	0.660207	−	0.783842i
$675$		0			0
$676$	−3.22091	−	18.6720i	−0.123881	−	0.718155i
$677$	39.7626	−	12.9196i	1.52820	−	0.496542i	0.580109	−	0.814539i	$-0.303010\pi$
$677$	39.7626	−	12.9196i	1.52820	−	0.496542i	0.948092	+	0.317997i	$0.103010\pi$
$678$	0.134742	+	0.00967359i	0.00517474	+	0.000371512i
$679$	−1.33127	+	0.967228i	−0.0510896	+	0.0371188i
$680$		0			0
$681$	−3.45457	−	2.50989i	−0.132380	−	0.0961794i
$682$	−33.1224	−	27.8980i	−1.26832	−	1.06827i
$683$	−11.6635	+	16.0534i	−0.446291	+	0.614267i	−0.971596	−	0.236647i	$-0.923951\pi$
$683$	−11.6635	+	16.0534i	−0.446291	+	0.614267i	0.525305	+	0.850914i	$0.323951\pi$
$684$	−2.25494	+	15.6234i	−0.0862197	+	0.597376i
$685$		0			0
$686$	4.29025	+	1.74265i	0.163803	+	0.0665347i
$687$	0.549422	−	1.69095i	0.0209617	−	0.0645136i
$688$	−32.1646	+	0.884021i	−1.22626	+	0.0337030i
$689$	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	$0.698761\pi$
$692$	2.85927	+	1.40773i	0.108693	+	0.0535139i
$693$			3.95893i			0.150387i
$694$	−10.0307	−	40.5517i	−0.380761	−	1.53932i
$695$		0			0
$696$	−5.43504	+	0.540645i	−0.206015	+	0.0204931i
$697$	23.1193	−	16.7971i	0.875705	−	0.636237i
$698$	−8.38942	+	20.6540i	−0.317544	+	0.781766i
$699$			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	$0.907164\pi$
$702$	−4.24524	−	1.72437i	−0.160226	−	0.0650820i
$703$	−4.42930	+	3.21807i	−0.167054	+	0.121372i
$704$	−19.2909	+	42.0603i	−0.727053	+	1.58521i
$705$		0			0
$706$	11.2078	−	2.77231i	0.421810	−	0.104337i
$707$			2.57079i			0.0966843i
$708$	−1.80714	+	3.67052i	−0.0679164	+	0.137946i
$709$	−35.0361	−	11.3839i	−1.31581	−	0.427532i	−0.434754	−	0.900549i	$-0.643165\pi$
$709$	−35.0361	−	11.3839i	−1.31581	−	0.427532i	−0.881053	+	0.473018i	$0.843165\pi$
$710$		0			0
$711$	−11.5537	−	35.5586i	−0.433297	−	1.33355i
$712$	24.0121	−	21.3795i	0.899890	−	0.801231i
$713$	−3.99584	+	12.2979i	−0.149645	+	0.460561i
$714$	0.150567	−	0.370684i	0.00563485	−	0.0138725i
$715$		0			0
$716$	3.16576	−	21.9340i	0.118310	−	0.819714i
$717$	−0.919446	+	1.26551i	−0.0343373	+	0.0472613i
$718$	27.7864	−	32.9899i	1.03698	−	1.23117i
$719$	−17.8070	−	12.9375i	−0.664088	−	0.482488i	0.203953	−	0.978981i	$-0.434621\pi$
$719$	−17.8070	−	12.9375i	−0.664088	−	0.482488i	−0.868041	+	0.496492i	$0.834621\pi$
$720$		0			0
$721$	2.22399	−	1.61582i	0.0828256	−	0.0601763i
$722$	−1.18167	+	16.4593i	−0.0439772	+	0.612551i
$723$	−0.523900	+	0.170225i	−0.0194840	+	0.00633075i
$724$	−39.5633	+	6.82465i	−1.47036	+	0.253636i
$725$		0			0
$726$	7.08570	+	5.96807i	0.262975	+	0.221496i
$727$	12.1809	+	37.4888i	0.451763	+	1.39038i	0.874894	+	0.484315i	$0.160931\pi$
$727$	12.1809	+	37.4888i	0.451763	+	1.39038i	−0.423131	+	0.906069i	$0.639069\pi$
$728$	0.123446	+	1.24099i	0.00457523	+	0.0459942i
$729$	−18.2133	+	13.2327i	−0.674566	+	0.490101i
$730$		0			0
$731$	−19.5291	+	26.8795i	−0.722311	+	0.994176i
$732$	−0.161589	−	0.936748i	−0.00597248	−	0.0346232i
$733$	14.9803	−	20.6186i	0.553309	−	0.761565i	−0.437147	−	0.899390i	$-0.644011\pi$
$733$	14.9803	−	20.6186i	0.553309	−	0.761565i	0.990457	+	0.137825i	$0.0440112\pi$
$734$	5.60446	+	9.00619i	0.206864	+	0.332425i
$735$		0			0
$736$	13.8033	+	0.610410i	0.508798	+	0.0225000i
$737$	−19.9063	+	61.2653i	−0.733258	+	2.25674i
$738$	−15.0692	−	24.2157i	−0.554705	−	0.891393i
$739$	8.47753	−	2.75452i	0.311851	−	0.101327i	−0.148910	−	0.988851i	$-0.547576\pi$
$739$	8.47753	−	2.75452i	0.311851	−	0.101327i	0.460761	+	0.887524i	$0.347576\pi$
$740$		0			0
$741$	1.41060	+	0.458333i	0.0518198	+	0.0168373i
$742$	0.302193	+	1.22169i	0.0110939	+	0.0448498i
$743$	21.5410			0.790261			0.395130	−	0.918625i	$-0.370699\pi$
$743$	21.5410			0.790261			0.395130	+	0.918625i	$0.370699\pi$
$744$	4.00027	−	1.75439i	0.146657	−	0.0643192i
$745$		0			0
$746$	−17.9959	−	1.29199i	−0.658878	−	0.0473031i
$747$	−5.40575	−	7.44038i	−0.197786	−	0.272229i
$748$	22.2747	+	42.2708i	0.814445	+	1.54557i
$749$			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	$0.305562\pi$
$752$	−25.6684	−	33.3621i	−0.936032	−	1.21659i
$753$	−1.07389	+	0.780227i	−0.0391347	+	0.0284331i
$754$	1.25885	−	17.5343i	0.0458446	−	0.638562i
$755$		0			0
$756$	−0.726967	−	0.357915i	−0.0264396	−	0.0130172i
$757$			3.46461i			0.125924i	0.998016	+	0.0629618i	$0.0200546\pi$
$757$			3.46461i			0.125924i	−0.998016	+	0.0629618i	$0.979945\pi$
$758$	4.15988	+	16.8174i	0.151093	+	0.610834i
$759$	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	$-0.219513\pi$
$762$	−3.23580	+	2.01360i	−0.117221	+	0.0729452i
$763$	2.17129	+	0.705496i	0.0786061	+	0.0255407i
$764$	−33.5396	+	17.6738i	−1.21342	+	0.639416i
$765$		0			0
$766$	20.1182	+	32.3293i	0.726900	+	1.16811i
$767$	−10.6532	−	7.73999i	−0.384664	−	0.279475i
$768$	−2.94668	−	3.61960i	−0.106329	−	0.130611i
$769$	6.10205	+	4.43340i	0.220046	+	0.159872i	0.692347	−	0.721565i	$-0.256577\pi$
$769$	6.10205	+	4.43340i	0.220046	+	0.159872i	−0.472302	+	0.881437i	$0.656577\pi$
$770$		0			0
$771$	1.19867	+	1.64982i	0.0431689	+	0.0594169i
$772$	3.77519	+	3.67285i	0.135872	+	0.132189i
$773$	23.4983	−	7.63507i	0.845176	−	0.274614i	0.145752	−	0.989321i	$-0.453440\pi$
$773$	23.4983	−	7.63507i	0.845176	−	0.274614i	0.699424	+	0.714707i	$0.253440\pi$
$774$	25.3628	+	21.3623i	0.911647	+	0.767853i
$775$		0			0
$776$	17.1106	+	10.0063i	0.614234	+	0.359206i
$777$	−0.0427985	−	0.131720i	−0.00153539	−	0.00472544i
$778$	13.4473	+	0.965428i	0.482109	+	0.0346123i
$779$	11.0116	+	15.1562i	0.394533	+	0.543027i
$780$		0			0
$781$	9.29319	−	12.7910i	0.332536	−	0.457697i
$782$	9.19089	−	10.9121i	0.328666	−	0.390214i
$783$	9.24062	+	6.71371i	0.330233	+	0.239928i
$784$	−0.763210	−	27.7690i	−0.0272575	−	0.991749i
$785$		0			0
$786$	−2.90029	−	1.17807i	−0.103450	−	0.0420202i
$787$	−9.13248	−	2.96732i	−0.325538	−	0.105774i	0.141689	−	0.989911i	$-0.454747\pi$
$787$	−9.13248	−	2.96732i	−0.325538	−	0.105774i	−0.467227	+	0.884138i	$0.654747\pi$
$788$	7.21137	−	49.9642i	0.256895	−	1.77990i
$789$	−6.27562	+	2.03907i	−0.223418	+	0.0725930i
$790$		0			0
$791$	−0.0237601	+	0.0731261i	−0.000844812	+	0.00260007i
$792$	43.6725	−	19.1534i	1.55183	−	0.680586i
$793$	3.05953			0.108647
$794$	7.90182	+	31.9451i	0.280425	+	1.13369i
$795$		0			0
$796$	−5.69434	−	5.53998i	−0.201830	−	0.196359i
$797$	18.7330	+	25.7837i	0.663556	+	0.913306i	0.999593	−	0.0285428i	$-0.00908668\pi$
$797$	18.7330	+	25.7837i	0.663556	+	0.913306i	−0.336037	+	0.941849i	$0.609087\pi$
$798$	0.243008	+	0.0987069i	0.00860238	+	0.00349419i
$799$	−43.4651			−1.53769
$800$		0			0
$801$	−33.1336			−1.17072
$802$	16.1052	+	6.54176i	0.568696	+	0.230998i
$803$	−51.4171	−	70.7696i	−1.81447	−	2.49740i
$804$	−4.65717	−	4.53093i	−0.164246	−	0.159794i
$805$		0			0
$806$	3.37584	+	13.6477i	0.118909	+	0.480719i
$807$	1.83112			0.0644586
$808$	28.3593	−	12.4375i	0.997677	−	0.437550i
$809$	1.35706	−	4.17661i	0.0477118	−	0.146842i	−0.924362	−	0.381516i	$-0.875402\pi$
$809$	1.35706	−	4.17661i	0.0477118	−	0.146842i	0.972074	+	0.234674i	$0.0754022\pi$
$810$		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	$0.638302\pi$
$812$	0.444089	−	3.07688i	0.0155845	−	0.107977i
$813$	−0.943236	−	0.306476i	−0.0330807	−	0.0107486i
$814$	15.3240	+	6.22443i	0.537106	+	0.218166i
$815$		0			0
$816$	−4.81760	+	0.132408i	−0.168650	+	0.00463522i
$817$	−17.6213	−	12.8026i	−0.616492	−	0.447907i
$818$	−28.7912	+	34.1829i	−1.00666	+	1.19518i
$819$	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	$0.525372\pi$
$822$	−5.43994	−	0.390552i	−0.189740	−	0.0136221i
$823$	−1.45020	−	4.46326i	−0.0505509	−	0.155580i	0.922594	−	0.385771i	$-0.126065\pi$
$823$	−1.45020	−	4.46326i	−0.0505509	−	0.155580i	−0.973145	+	0.230192i	$0.926065\pi$
$824$	−28.5844	−	16.7163i	−0.995785	−	0.582339i
$825$		0			0
$826$	−1.78107	−	1.50014i	−0.0619712	−	0.0521965i
$827$	11.1274	−	3.61552i	0.386938	−	0.125724i	−0.109087	−	0.994032i	$-0.534793\pi$
$827$	11.1274	−	3.61552i	0.386938	−	0.125724i	0.496025	+	0.868308i	$0.334793\pi$
$828$	−10.2061	−	9.92941i	−0.354685	−	0.345071i
$829$	0.462729	+	0.636892i	0.0160712	+	0.0221202i	0.816977	−	0.576670i	$-0.195648\pi$
$829$	0.462729	+	0.636892i	0.0160712	+	0.0221202i	−0.800906	+	0.598790i	$0.795648\pi$
$830$		0			0
$831$	6.07571	+	4.41426i	0.210764	+	0.153129i
$832$	13.0926	−	7.36573i	0.453905	−	0.255361i
$833$	−23.2062	−	16.8603i	−0.804046	−	0.584174i
$834$	0.493104	+	0.792402i	0.0170748	+	0.0274386i
$835$		0			0
$836$	−27.7113	+	14.6026i	−0.958414	+	0.505040i
$837$	−8.68759	−	2.82277i	−0.300287	−	0.0975692i
$838$	−10.3654	+	6.45026i	−0.358066	+	0.222821i
$839$	−10.8077	−	33.2628i	−0.373124	−	1.14836i	−0.944736	−	0.327833i	$-0.893682\pi$
$839$	−10.8077	−	33.2628i	−0.373124	−	1.14836i	0.571611	−	0.820524i	$-0.306318\pi$
$840$		0			0
$841$	−4.58005	+	14.0959i	−0.157933	+	0.486067i
$842$	4.35044	+	17.5878i	0.149926	+	0.606114i
$843$		−	1.13954i		−	0.0392478i
$844$	26.3027	+	12.9498i	0.905375	+	0.445752i
$845$		0			0
$846$	−3.10647	+	43.2695i	−0.106803	+	1.48764i
$847$	−4.26591	+	3.09936i	−0.146578	+	0.106495i
$848$	12.0149	−	9.24418i	0.412595	−	0.317447i
$849$	0.374678			0.0128589
$850$		0			0
$851$		−	4.93870i		−	0.169296i
$852$	0.743449	+	1.41084i	0.0254702	+	0.0483347i
$853$	6.54252	+	9.00501i	0.224012	+	0.308326i	0.906199	−	0.422852i	$-0.138971\pi$
$853$	6.54252	+	9.00501i	0.224012	+	0.308326i	−0.682187	+	0.731178i	$0.738971\pi$
$854$	0.539660	+	0.0387441i	0.0184668	+	0.00132579i
$855$		0			0
$856$	0.913432	−	0.400603i	0.0312205	−	0.0136923i
$857$	−53.1600			−1.81591			−0.907955	−	0.419068i	$-0.862357\pi$
$857$	−53.1600			−1.81591			−0.907955	+	0.419068i	$0.862357\pi$
$858$	−1.07592	−	4.34970i	−0.0367314	−	0.148496i
$859$	32.6009	+	10.5927i	1.11233	+	0.361417i	0.806835	−	0.590777i	$-0.201179\pi$
$859$	32.6009	+	10.5927i	1.11233	+	0.361417i	0.305493	+	0.952194i	$0.401179\pi$
$860$		0			0
$861$	−0.450722	+	0.146448i	−0.0153606	+	0.00499095i
$862$	−22.4705	−	36.1093i	−0.765347	−	1.22989i
$863$	12.2926	−	37.8328i	0.418446	−	1.28784i	−0.490686	−	0.871336i	$-0.663254\pi$
$863$	12.2926	−	37.8328i	0.418446	−	1.28784i	0.909132	−	0.416508i	$-0.136746\pi$
$864$	−0.431210	+	9.75105i	−0.0146701	+	0.331738i
$865$		0			0
$866$	−1.20138	−	1.93058i	−0.0408246	−	0.0656038i
$867$	−0.0101863	+	0.0140203i	−0.000345946	+	0.000476154i
$868$	0.422627	+	2.45002i	0.0143449	+	0.0831591i
$869$	43.6085	−	60.0220i	1.47932	−	2.03611i
$870$		0			0
$871$	16.9190	−	12.2923i	0.573277	−	0.416510i
$872$	−2.72216	−	27.3655i	−0.0921840	−	0.926714i
$873$	−6.31251	−	19.4279i	−0.213646	−	0.657535i
$874$	7.15357	+	6.02523i	0.241973	+	0.203807i
$875$		0			0
$876$	8.69492	−	1.49987i	0.293774	−	0.0506759i
$877$	−38.4191	+	12.4831i	−1.29732	+	0.421525i	−0.874649	−	0.484758i	$-0.838908\pi$
$877$	−38.4191	+	12.4831i	−1.29732	+	0.421525i	−0.422672	+	0.906283i	$0.638908\pi$
$878$	−3.84576	+	53.5670i	−0.129788	+	1.80780i
$879$	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	$0.515646\pi$
$882$	−18.4429	+	21.8967i	−0.621006	+	0.737301i
$883$	22.5652	−	31.0584i	0.759380	−	1.04520i	−0.237885	−	0.971293i	$-0.576454\pi$
$883$	22.5652	−	31.0584i	0.759380	−	1.04520i	0.997265	−	0.0739039i	$-0.0235458\pi$
$884$	2.21586	−	15.3526i	0.0745273	−	0.516364i
$885$		0			0
$886$	−10.4137	+	25.6376i	−0.349855	+	0.861312i
$887$	−4.72737	+	14.5493i	−0.158729	+	0.488519i	−0.998520	−	0.0543921i	$-0.982678\pi$
$887$	−4.72737	+	14.5493i	−0.158729	+	0.488519i	0.839790	+	0.542911i	$0.182678\pi$
$888$	−1.24600	+	1.10939i	−0.0418129	+	0.0372288i
$889$	−0.670327	−	2.06305i	−0.0224821	−	0.0691926i
$890$		0			0
$891$	−45.3363	−	14.7306i	−1.51882	−	0.493495i
$892$	15.0635	−	30.5958i	0.504364	−	1.02442i
$893$		−	28.4943i		−	0.953524i
$894$	−6.16648	+	1.52532i	−0.206238	+	0.0510142i
$895$		0			0
$896$	2.40264	−	1.13342i	0.0802665	−	0.0378649i
$897$	−1.08241	+	0.786416i	−0.0361406	+	0.0262577i
$898$	43.5754	+	17.6998i	1.45413	+	0.590651i
$899$		−	35.0457i		−	1.16884i
$900$		0			0
$901$		−	15.6535i		−	0.521492i
$902$	21.2988	−	52.4358i	0.709173	−	1.74592i
$903$	0.445767	−	0.323868i	0.0148342	−	0.0107777i
$904$	0.921634	−	0.0916786i	0.0306531	−	0.00304918i
$905$		0			0
$906$	0.0297240	+	0.120167i	0.000987513	+	0.00399227i
$907$		−	31.6503i		−	1.05093i	−0.850815	−	0.525465i	$-0.823891\pi$
$907$		−	31.6503i		−	1.05093i	0.850815	−	0.525465i	$-0.176109\pi$
$908$	−26.2654	−	12.9315i	−0.871647	−	0.429146i
$909$	−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	$0.928188\pi$
$912$	−0.0868024	−	3.15826i	−0.00287431	−	0.104580i
$913$	5.63942	−	17.3564i	0.186638	−	0.574411i
$914$	20.4264	+	8.29695i	0.675644	+	0.274439i
$915$		0			0
$916$	1.74134	−	12.0649i	0.0575353	−	0.398635i
$917$	1.04729	−	1.44148i	0.0345847	−	0.0476017i
$918$	7.70856	+	6.49269i	0.254421	+	0.214291i
$919$	−11.6067	−	8.43275i	−0.382869	−	0.278171i	0.379658	−	0.925127i	$-0.376042\pi$
$919$	−11.6067	−	8.43275i	−0.382869	−	0.278171i	−0.762527	+	0.646956i	$0.776042\pi$
$920$		0			0
$921$	−2.61770	+	1.90187i	−0.0862561	+	0.0626687i
$922$	−8.17587	−	0.586974i	−0.269258	−	0.0193309i
$923$	−4.88158	+	1.58612i	−0.160679	+	0.0522078i
$924$	−0.134697	−	0.780854i	−0.00443120	−	0.0256882i
$925$		0			0
$926$	10.8291	−	12.8570i	0.355865	−	0.422508i
$927$	10.5455	+	32.4557i	0.346359	+	1.06598i
$928$	−36.0907	+	9.98709i	−1.18474	+	0.327842i
$929$	−5.50414	+	3.99899i	−0.180585	+	0.131203i	−0.674405	−	0.738361i	$-0.735600\pi$
$929$	−5.50414	+	3.99899i	−0.180585	+	0.131203i	0.493820	+	0.869564i	$0.335600\pi$
$930$		0			0
$931$	11.0530	−	15.2132i	0.362248	−	0.498592i
$932$	2.42629	+	14.0655i	0.0794759	+	0.460731i
$933$	−5.15409	+	7.09400i	−0.168737	+	0.232247i
$934$	−29.9531	+	18.6395i	−0.980094	+	0.609903i
$935$		0			0
$936$	−15.1252	−	3.30314i	−0.494381	−	0.107966i
$937$	−5.15839	+	15.8759i	−0.168517	+	0.518643i	−0.999278	−	0.0379863i	$-0.987906\pi$
$937$	−5.15839	+	15.8759i	−0.168517	+	0.518643i	0.830761	+	0.556629i	$0.187906\pi$
$938$	3.13994	−	1.95396i	0.102523	−	0.0637989i
$939$	−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	$0.657699\pi$
$942$	8.36704	−	2.06964i	0.272613	−	0.0674325i
$943$	−16.8993			−0.550316
$944$	−7.93176	+	26.9053i	−0.258157	+	0.875693i
$945$		0			0
$946$	−4.71199	+	65.6327i	−0.153200	+	2.13390i
$947$	−11.6464	−	16.0299i	−0.378457	−	0.520901i	0.576718	−	0.816943i	$-0.304333\pi$
$947$	−11.6464	−	16.0299i	−0.378457	−	0.520901i	−0.955175	+	0.296042i	$0.904333\pi$
$948$	3.48866	+	6.62042i	0.113306	+	0.215021i
$949$			28.3986i			0.921858i
$950$		0			0
$951$	−4.74494			−0.153865
$952$	0.585264	−	2.67994i	0.0189685	−	0.0868573i
$953$	−39.2091	+	28.4871i	−1.27011	+	0.922787i	−0.999207	−	0.0398210i	$-0.987321\pi$
$953$	−39.2091	+	28.4871i	−1.27011	+	0.922787i	−0.270900	+	0.962608i	$0.587321\pi$
$954$	−15.5830	−	1.11876i	−0.504518	−	0.0362211i
$955$		0			0
$956$	−4.73717	+	9.62175i	−0.153211	+	0.311190i
$957$			11.1695i			0.361060i
$958$	−21.0905	+	5.21685i	−0.681402	+	0.168549i
$959$	0.959267	−	2.95232i	0.0309764	−	0.0953354i
$960$		0			0
$961$	−0.918548	−	2.82700i	−0.0296306	−	0.0911936i
$962$	−2.83699	−	4.55895i	−0.0914682	−	0.146986i
$963$	−0.977603	−	0.317642i	−0.0315028	−	0.0102359i
$964$	−3.34124	+	1.76068i	−0.107614	+	0.0567077i
$965$		0			0
$966$	−0.200881	+	0.125006i	−0.00646325	+	0.00402202i
$967$	−15.9495	−	11.5880i	−0.512901	−	0.372645i	0.301022	−	0.953617i	$-0.402672\pi$
$967$	−15.9495	−	11.5880i	−0.512901	−	0.372645i	−0.813923	+	0.580973i	$0.802672\pi$
$968$	54.8288	+	32.0641i	1.76226	+	1.03058i
$969$	−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	$0.811426\pi$
$972$	10.5721	−	10.8666i	0.339099	−	0.348547i
$973$	−0.505214	+	0.164154i	−0.0161964	+	0.00526253i
$974$	20.5503	−	24.3987i	0.658475	−	0.781786i
$975$		0			0
$976$	−2.18349	−	6.14064i	−0.0698917	−	0.196557i
$977$	−3.71838	−	11.4440i	−0.118962	−	0.366126i	0.873791	−	0.486301i	$-0.161654\pi$
$977$	−3.71838	−	11.4440i	−0.118962	−	0.366126i	−0.992753	+	0.120175i	$0.961654\pi$
$978$	−0.369609	+	5.14823i	−0.0118188	+	0.164622i
$979$	−38.6458	−	53.1914i	−1.23512	−	1.70000i
$980$		0			0
$981$	−16.6587	+	22.9287i	−0.531870	+	0.732057i
$982$	−8.25281	−	6.95109i	−0.263358	−	0.221818i
$983$	−37.4796	−	27.2305i	−1.19541	−	0.868518i	−0.201587	−	0.979471i	$-0.564610\pi$
$983$	−37.4796	−	27.2305i	−1.19541	−	0.868518i	−0.993826	+	0.110952i	$0.964610\pi$
$984$	3.79613	+	4.26356i	0.121016	+	0.135917i
$985$		0			0
$986$	−14.5515	+	35.8244i	−0.463413	+	1.14088i
$987$	0.685540	+	0.222746i	0.0218210	+	0.00709007i
$988$	10.0647	+	1.45264i	0.320199	+	0.0462146i
$989$	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	$-0.320191\pi$
$992$	24.9824	−	16.5154i	0.793193	−	0.524365i
$993$	−6.62737			−0.210313
$994$	−0.881132	+	0.217953i	−0.0279478	+	0.00691306i
$995$		0			0
$996$	1.31937	+	1.28361i	0.0418058	+	0.0406726i
$997$	−19.0954	−	26.2826i	−0.604758	−	0.832378i	0.391375	−	0.920231i	$-0.371999\pi$
$997$	−19.0954	−	26.2826i	−0.604758	−	0.832378i	−0.996133	+	0.0878532i	$0.971999\pi$
$998$	14.3531	−	35.3360i	0.454339	−	1.11854i
$999$	3.48883			0.110382

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.6	✓	112	25.3	odd	20
200.2.o.a.29.12	yes	112	200.53	odd	20
200.2.o.a.69.6	yes	112	40.37	odd	4
200.2.o.a.69.12	yes	112	5.2	odd	4
800.2.be.a.369.13		112	20.7	even	4
800.2.be.a.369.16		112	40.27	even	4
800.2.be.a.529.13		112	200.3	even	20
800.2.be.a.529.16		112	100.3	even	20
1000.2.o.a.149.17		112	200.197	odd	20
1000.2.o.a.149.23		112	25.22	odd	20
1000.2.o.a.349.17		112	5.3	odd	4
1000.2.o.a.349.23		112	40.13	odd	4
1000.2.t.b.101.7		224	200.29	even	10	inner
1000.2.t.b.101.18		224	25.21	even	5	inner
1000.2.t.b.101.39		224	25.4	even	10	inner
1000.2.t.b.101.50		224	200.21	even	10	inner
1000.2.t.b.901.7		224	5.4	even	2	inner
1000.2.t.b.901.18		224	8.5	even	2	inner
1000.2.t.b.901.39		224	40.29	even	2	inner
1000.2.t.b.901.50		224	1.1	even	1	trivial

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.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.31025 + 0.532208i) q^{2} +(0.171463 + 0.235999i) q^{3} +(1.43351 + 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} -0.234809 q^{7} +(1.13601 + 2.59027i) q^{8} +(0.900755 - 2.77224i) q^{9} +O(q^{10})\)	\(q+(1.31025 + 0.532208i) q^{2} +(0.171463 + 0.235999i) q^{3} +(1.43351 + 1.39465i) q^{4} +(0.0990593 + 0.400472i) q^{6} -0.234809 q^{7} +(1.13601 + 2.59027i) q^{8} +(0.900755 - 2.77224i) q^{9} +(5.50105 - 1.78740i) q^{11} +(-0.0833422 + 0.577439i) q^{12} +(-1.78589 - 0.580270i) q^{13} +(-0.307658 - 0.124967i) q^{14} +(0.109896 + 3.99849i) q^{16} +(3.34149 + 2.42773i) q^{17} +(2.65562 - 3.15294i) q^{18} +(-1.59154 + 2.19056i) q^{19} +(-0.0402612 - 0.0554147i) q^{21} +(8.15902 + 0.585764i) q^{22} +(-0.754772 - 2.32295i) q^{23} +(-0.416517 + 0.712234i) q^{24} +(-2.03113 - 1.71076i) q^{26} +(1.64099 - 0.533191i) q^{27} +(-0.336601 - 0.327477i) q^{28} +(3.89100 + 5.35551i) q^{29} +(-4.28302 - 3.11180i) q^{31} +(-1.98404 + 5.29751i) q^{32} +(1.36505 + 0.991770i) q^{33} +(3.08612 + 4.95930i) q^{34} +(5.15755 - 2.71779i) q^{36} +(1.92303 + 0.624829i) q^{37} +(-3.25115 + 2.02316i) q^{38} +(-0.169271 - 0.520963i) q^{39} +(2.13805 - 6.58023i) q^{41} +(-0.0232600 - 0.0940345i) q^{42} +8.04419i q^{43} +(10.3786 + 5.10979i) q^{44} +(0.247353 - 3.44534i) q^{46} +(-8.51367 + 6.18554i) q^{47} +(-0.924798 + 0.711530i) q^{48} -6.94486 q^{49} +1.20486i q^{51} +(-1.75081 - 3.32251i) q^{52} +(-2.22765 - 3.06610i) q^{53} +(2.43388 + 0.174737i) q^{54} +(-0.266745 - 0.608218i) q^{56} -0.789862 q^{57} +(2.24794 + 9.08787i) q^{58} +(6.66931 + 2.16699i) q^{59} +(-1.54958 + 0.503489i) q^{61} +(-3.95570 - 6.35669i) q^{62} +(-0.211505 + 0.650947i) q^{63} +(-5.41896 + 5.88514i) q^{64} +(1.26073 + 2.02596i) q^{66} +(-6.54617 + 9.01003i) q^{67} +(1.40421 + 8.14038i) q^{68} +(0.418799 - 0.576427i) q^{69} +(2.21139 - 1.60667i) q^{71} +(8.20411 - 0.816095i) q^{72} +(-4.67339 - 14.3832i) q^{73} +(2.18711 + 1.84213i) q^{74} +(-5.33656 + 0.920553i) q^{76} +(-1.29170 + 0.419697i) q^{77} +(0.0554733 - 0.772679i) q^{78} +(10.3770 - 7.53932i) q^{79} +(-6.66742 - 4.84416i) q^{81} +(6.30342 - 7.48385i) q^{82} +(1.85452 - 2.55253i) q^{83} +(0.0195695 - 0.135588i) q^{84} +(-4.28118 + 10.5399i) q^{86} +(-0.596730 + 1.83655i) q^{87} +(10.8791 + 12.2187i) q^{88} +(-3.51258 - 10.8106i) q^{89} +(0.419342 + 0.136252i) q^{91} +(2.15773 - 4.38261i) q^{92} -1.54435i q^{93} +(-14.4470 + 3.57356i) q^{94} +(-1.59040 + 0.440098i) q^{96} +(5.66961 - 4.11921i) q^{97} +(-9.09951 - 3.69611i) q^{98} -16.8602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9}+O(q^{10}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56} + 72 q^{64} + 80 q^{66} + 44 q^{71} - 8 q^{74} - 72 q^{76} - 28 q^{79} - 12 q^{81} - 156 q^{84} - 118 q^{86} - 48 q^{89} - 90 q^{94} + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

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Database

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