LMFDB - Embedded newform 1000.2.t.b.901.39

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			901.39
Character	$\chi$	$=$	1000.901
Dual form			1000.2.t.b.101.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.747190 - 1.20071i) q^{2} +(0.171463 + 0.235999i) q^{3} +(-0.883414 - 1.79432i) q^{4} +(0.411483 - 0.0295418i) q^{6} +0.234809 q^{7} +(-2.81454 - 0.279973i) q^{8} +(0.900755 - 2.77224i) q^{9} +O(q^{10})$	\(q+(0.747190 - 1.20071i) q^{2} +(0.171463 + 0.235999i) q^{3} +(-0.883414 - 1.79432i) q^{4} +(0.411483 - 0.0295418i) q^{6} +0.234809 q^{7} +(-2.81454 - 0.279973i) q^{8} +(0.900755 - 2.77224i) q^{9} +(-5.50105 + 1.78740i) q^{11} +(0.271985 - 0.516145i) q^{12} +(-1.78589 - 0.580270i) q^{13} +(0.175447 - 0.281938i) q^{14} +(-2.43916 + 3.17025i) 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} +(-1.96418 + 7.94070i) 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} +(-0.207433 - 0.421322i) 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} +(-5.41173 + 2.19818i) q^{34} +(-5.77002 + 0.832792i) q^{36} +(1.92303 + 0.624829i) q^{37} +(-1.44105 - 3.54775i) q^{38} +(-0.169271 - 0.520963i) q^{39} +(2.13805 - 6.58023i) q^{41} +(0.0966198 - 0.00693667i) q^{42} +8.04419i q^{43} +(8.06687 + 8.29162i) q^{44} +(3.35315 + 0.829422i) q^{46} +(8.51367 - 6.18554i) q^{47} +(-1.16640 - 0.0320578i) q^{48} -6.94486 q^{49} -1.20486i q^{51} +(0.536487 + 3.71707i) q^{52} +(-2.22765 - 3.06610i) q^{53} +(0.585926 - 2.36875i) q^{54} +(-0.660878 - 0.0657402i) q^{56} +0.789862 q^{57} +(-9.33773 + 0.670388i) q^{58} +(-6.66931 - 2.16699i) q^{59} +(1.54958 - 0.503489i) q^{61} +(-6.93660 + 2.81756i) q^{62} +(0.211505 - 0.650947i) q^{63} +(7.84323 + 1.57599i) q^{64} +(-2.21078 + 0.897995i) 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} +(-3.31136 + 7.55038i) 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} +(-0.752003 - 0.186013i) 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} +(0.0638644 - 0.121195i) q^{84} +(9.65874 + 6.01054i) q^{86} +(0.596730 - 1.83655i) q^{87} +(15.9833 - 3.49055i) q^{88} +(-3.51258 - 10.8106i) q^{89} +(-0.419342 - 0.136252i) q^{91} +(3.50134 - 3.40643i) q^{92} -1.54435i q^{93} +(-1.06572 - 14.8442i) q^{94} +(-0.910018 + 1.37656i) q^{96} +(-5.66961 + 4.11921i) q^{97} +(-5.18913 + 8.33878i) 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 $

$2$	0.747190	−	1.20071i	0.528343	−	0.849031i
$2$	0.747190	−	1.20071i	0.528343	−	0.849031i
$3$	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	$0.773163\pi$
$4$	−0.883414	−	1.79432i	−0.441707	−	0.897159i
$5$		0			0
$5$		0			0
$6$	0.411483	−	0.0295418i	0.167987	−	0.0120604i
$7$	0.234809			0.0887494			0.0443747	−	0.999015i	$-0.485870\pi$
$7$	0.234809			0.0887494			0.0443747	+	0.999015i	$0.485870\pi$
$8$	−2.81454	−	0.279973i	−0.995089	−	0.0989855i
$9$	0.900755	−	2.77224i	0.300252	−	0.924080i
$10$		0			0
$11$	−5.50105	+	1.78740i	−1.65863	+	0.538921i	−0.980584	−	0.196099i	$-0.937172\pi$
$11$	−5.50105	+	1.78740i	−1.65863	+	0.538921i	−0.678045	+	0.735021i	$0.737172\pi$
$12$	0.271985	−	0.516145i	0.0785152	−	0.148998i
$13$	−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	$0.683855\pi$
$14$	0.175447	−	0.281938i	0.0468902	−	0.0753510i
$15$		0			0
$16$	−2.43916	+	3.17025i	−0.609790	+	0.792563i
$17$	−3.34149	−	2.42773i	−0.810429	−	0.588811i	0.103526	−	0.994627i	$-0.466988\pi$
$17$	−3.34149	−	2.42773i	−0.810429	−	0.588811i	−0.913955	+	0.405815i	$0.866988\pi$
$18$	−2.65562	−	3.15294i	−0.625936	−	0.743154i
$19$	1.59154	−	2.19056i	0.365124	−	0.502550i	−0.586443	−	0.809990i	$-0.699472\pi$
$19$	1.59154	−	2.19056i	0.365124	−	0.502550i	0.951567	+	0.307440i	$0.0994724\pi$
$20$		0			0
$21$	0.0402612	+	0.0554147i	0.00878571	+	0.0120925i
$22$	−1.96418	+	7.94070i	−0.418765	+	1.69296i
$23$	0.754772	+	2.32295i	0.157381	+	0.484369i	0.998394	−	0.0566456i	$-0.0180405\pi$
$23$	0.754772	+	2.32295i	0.157381	+	0.484369i	−0.841013	+	0.541014i	$0.818041\pi$
$24$	−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
$28$	−0.207433	−	0.421322i	−0.0392012	−	0.0796224i
$29$	−3.89100	−	5.35551i	−0.722541	−	0.994493i	−0.999436	−	0.0335922i	$-0.989305\pi$
$29$	−3.89100	−	5.35551i	−0.722541	−	0.994493i	0.276894	−	0.960900i	$-0.410695\pi$
$30$		0			0
$31$	−4.28302	−	3.11180i	−0.769253	−	0.558895i	0.132482	−	0.991185i	$-0.457705\pi$
$31$	−4.28302	−	3.11180i	−0.769253	−	0.558895i	−0.901734	+	0.432291i	$0.857705\pi$
$32$	1.98404	+	5.29751i	0.350732	+	0.936476i
$33$	−1.36505	−	0.991770i	−0.237625	−	0.172645i
$34$	−5.41173	+	2.19818i	−0.928104	+	0.376985i
$35$		0			0
$36$	−5.77002	+	0.832792i	−0.961670	+	0.138799i
$37$	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	$0.546848\pi$
$38$	−1.44105	−	3.54775i	−0.233770	−	0.575520i
$39$	−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	$-0.0816787\pi$
$42$	0.0966198	−	0.00693667i	0.0149088	−	0.00107035i
$43$			8.04419i			1.22673i	0.789801	+	0.613364i	$0.210184\pi$
$43$			8.04419i			1.22673i	−0.789801	+	0.613364i	$0.789816\pi$
$44$	8.06687	+	8.29162i	1.21613	+	1.25001i
$45$		0			0
$46$	3.35315	+	0.829422i	0.494395	+	0.122292i
$47$	8.51367	−	6.18554i	1.24185	−	0.902254i	0.244126	−	0.969743i	$-0.421499\pi$
$47$	8.51367	−	6.18554i	1.24185	−	0.902254i	0.997720	+	0.0674892i	$0.0214988\pi$
$48$	−1.16640	−	0.0320578i	−0.168356	−	0.00462714i
$49$	−6.94486			−0.992124
$50$		0			0
$51$		−	1.20486i		−	0.168714i
$52$	0.536487	+	3.71707i	0.0743974	+	0.515464i
$53$	−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	$0.883819\pi$
$54$	0.585926	−	2.36875i	0.0797344	−	0.322347i
$55$		0			0
$56$	−0.660878	−	0.0657402i	−0.0883136	−	0.00878491i
$57$	0.789862			0.104620
$58$	−9.33773	+	0.670388i	−1.22610	+	0.0880263i
$59$	−6.66931	−	2.16699i	−0.868270	−	0.282118i	−0.159192	−	0.987248i	$-0.550889\pi$
$59$	−6.66931	−	2.16699i	−0.868270	−	0.282118i	−0.709078	+	0.705130i	$0.750889\pi$
$60$		0			0
$61$	1.54958	−	0.503489i	0.198403	−	0.0644651i	−0.208130	−	0.978101i	$-0.566738\pi$
$61$	1.54958	−	0.503489i	0.198403	−	0.0644651i	0.406533	+	0.913636i	$0.366738\pi$
$62$	−6.93660	+	2.81756i	−0.880949	+	0.357831i
$63$	0.211505	−	0.650947i	0.0266472	−	0.0820116i
$64$	7.84323	+	1.57599i	0.980404	+	0.196999i
$65$		0			0
$66$	−2.21078	+	0.897995i	−0.272129	+	0.110535i
$67$	−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	$0.248141\pi$
$72$	−3.31136	+	7.55038i	−0.390248	+	0.889821i
$73$	4.67339	+	14.3832i	0.546979	+	1.68343i	0.716237	+	0.697857i	$0.245863\pi$
$73$	4.67339	+	14.3832i	0.546979	+	1.68343i	−0.169258	+	0.985572i	$0.554137\pi$
$74$	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
$78$	−0.752003	−	0.186013i	−0.0851476	−	0.0210618i
$79$	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	$0.144603\pi$
$84$	0.0638644	−	0.121195i	0.00696818	−	0.0132235i
$85$		0			0
$86$	9.65874	+	6.01054i	1.04153	+	0.648133i
$87$	0.596730	−	1.83655i	0.0639762	−	0.196899i
$88$	15.9833	−	3.49055i	1.70383	−	0.372094i
$89$	−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
$92$	3.50134	−	3.40643i	0.365040	−	0.355145i
$93$		−	1.54435i		−	0.160141i
$94$	−1.06572	−	14.8442i	−0.109920	−	1.53107i
$95$		0			0
$96$	−0.910018	+	1.37656i	−0.0928783	+	0.140495i
$97$	−5.66961	+	4.11921i	−0.575661	+	0.418243i	−0.837157	−	0.546962i	$-0.815784\pi$
$97$	−5.66961	+	4.11921i	−0.575661	+	0.418243i	0.261496	+	0.965205i	$0.415784\pi$
$98$	−5.18913	+	8.33878i	−0.524182	+	0.842343i
$99$			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	$0.816642\pi$
$102$	−1.44668	−	0.900256i	−0.143243	−	0.0891386i
$103$	9.47147	−	6.88143i	0.933252	−	0.678047i	−0.0135350	−	0.999908i	$-0.504308\pi$
$103$	9.47147	−	6.88143i	0.933252	−	0.678047i	0.946787	+	0.321861i	$0.104308\pi$
$104$	4.86398	+	2.13319i	0.476953	+	0.209176i
$105$		0			0
$106$	−5.34597	+	0.383806i	−0.519247	+	0.0372785i
$107$		−	0.352640i		−	0.0340910i	−0.999855	−	0.0170455i	$-0.994574\pi$
$107$		−	0.352640i		−	0.0340910i	0.999855	−	0.0170455i	$-0.00542602\pi$
$108$	−2.40639	−	2.47344i	−0.231555	−	0.238007i
$109$	9.24706	+	3.00455i	0.885708	+	0.287784i	0.716325	−	0.697767i	$-0.245823\pi$
$109$	9.24706	+	3.00455i	0.885708	+	0.287784i	0.169382	+	0.985550i	$0.445823\pi$
$110$		0			0
$111$	0.182270	+	0.560968i	0.0173003	+	0.0532448i
$112$	−0.572737	+	0.744403i	−0.0541185	+	0.0703395i
$113$	−0.101189	+	0.311428i	−0.00951907	+	0.0292967i	−0.955703	−	0.294332i	$-0.904903\pi$
$113$	−0.101189	+	0.311428i	−0.00951907	+	0.0292967i	0.946184	+	0.323629i	$0.104903\pi$
$114$	0.590177	−	0.948396i	0.0552752	−	0.0888254i
$115$		0			0
$116$	−6.17212	+	11.7128i	−0.573067	+	1.08751i
$117$	−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
$122$	0.553286	−	2.23680i	0.0500921	−	0.202510i
$123$	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	$-0.965570\pi$
$127$	−2.85478	−	8.78610i	−0.253320	−	0.779640i	0.740835	−	0.671687i	$-0.234430\pi$
$128$	7.75269	−	8.23989i	0.685248	−	0.728310i
$129$	−1.89842	+	1.37928i	−0.167147	+	0.121439i
$130$		0			0
$131$	4.46019	−	6.13893i	0.389689	−	0.536361i	−0.568430	−	0.822732i	$-0.692449\pi$
$131$	4.46019	−	6.13893i	0.389689	−	0.536361i	0.958119	+	0.286371i	$0.0924490\pi$
$132$	−0.573644	+	3.32548i	−0.0499293	+	0.289446i
$133$	0.373707	−	0.514364i	0.0324045	−	0.0446010i
$134$	5.92721	+	14.5923i	0.512033	+	1.26058i
$135$		0			0
$136$	8.72503	+	7.76847i	0.748165	+	0.666140i
$137$	4.08531	−	12.5733i	0.349032	−	1.07421i	−0.610358	−	0.792125i	$-0.708975\pi$
$137$	4.08531	−	12.5733i	0.349032	−	1.07421i	0.959390	−	0.282083i	$-0.0910255\pi$
$138$	0.379200	+	0.933557i	0.0322796	+	0.0794696i
$139$	−2.15160	+	0.699096i	−0.182496	+	0.0592965i	−0.398839	−	0.917021i	$-0.630587\pi$
$139$	−2.15160	+	0.699096i	−0.182496	+	0.0592965i	0.216343	+	0.976317i	$0.430587\pi$
$140$		0			0
$141$	2.91957	+	0.948625i	0.245872	+	0.0798886i
$142$	−0.276815	−	3.85572i	−0.0232298	−	0.323565i
$143$	10.8614			0.908278
$144$	6.59161	+	9.61756i	0.549301	+	0.801463i
$145$		0			0
$146$	20.7620	+	5.13561i	1.71828	+	0.425026i
$147$	−1.19079	−	1.63898i	−0.0982148	−	0.135181i
$148$	−0.577685	−	4.00251i	−0.0474854	−	0.329004i
$149$		−	15.3980i		−	1.26145i	−0.776004	−	0.630727i	$-0.782757\pi$
$149$		−	15.3980i		−	1.26145i	0.776004	−	0.630727i	$-0.217243\pi$
$150$		0			0
$151$	0.300063			0.0244187			0.0122094	−	0.999925i	$-0.496114\pi$
$151$	0.300063			0.0244187			0.0122094	+	0.999925i	$0.496114\pi$
$152$	−5.09274	+	5.71984i	−0.413076	+	0.463940i
$153$	−9.74011	+	7.07661i	−0.787441	+	0.572110i
$154$	−0.461207	+	1.86455i	−0.0371651	+	0.150249i
$155$		0			0
$156$	−0.785237	+	0.763952i	−0.0628693	+	0.0611651i
$157$		−	20.8929i		−	1.66744i	−0.552189	−	0.833719i	$-0.686207\pi$
$157$		−	20.8929i		−	1.66744i	0.552189	−	0.833719i	$-0.313793\pi$
$158$	−1.29896	−	18.0931i	−0.103340	−	1.43941i
$159$	0.341636	−	1.05145i	0.0270935	−	0.0833852i
$160$		0			0
$161$	0.177227	+	0.545449i	0.0139675	+	0.0429874i
$162$	−10.7983	+	4.38613i	−0.848392	+	0.344607i
$163$	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	$0.437002\pi$
$164$	−13.6958	+	1.97673i	−1.06946	+	0.154356i
$165$		0			0
$166$	−1.67917	−	4.13397i	−0.130329	−	0.320858i
$167$	17.4355	+	12.6676i	1.34920	+	0.980251i	0.999051	+	0.0435571i	$0.0138691\pi$
$167$	17.4355	+	12.6676i	1.34920	+	0.980251i	0.350149	+	0.936694i	$0.386131\pi$
$168$	−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
$172$	14.4338	−	7.10634i	1.10057	−	0.541854i
$173$	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
$178$	−15.6050	−	3.85999i	−1.16964	−	0.289319i
$179$	6.51305	+	8.96444i	0.486808	+	0.670034i	0.979795	−	0.200003i	$-0.0640951\pi$
$179$	6.51305	+	8.96444i	0.486808	+	0.670034i	−0.492987	+	0.870037i	$0.664095\pi$
$180$		0			0
$181$	11.7991	−	16.2401i	0.877020	−	1.20711i	−0.100217	−	0.994966i	$-0.531954\pi$
$181$	11.7991	−	16.2401i	0.877020	−	1.20711i	0.977237	−	0.212149i	$-0.0680461\pi$
$182$	−0.476928	+	0.401702i	−0.0353523	+	0.0297761i
$183$	0.384519	+	0.279369i	0.0284245	+	0.0206516i
$184$	−1.47397	−	6.74934i	−0.108663	−	0.497568i
$185$		0			0
$186$	−1.85432	−	1.15392i	−0.135965	−	0.0846097i
$187$	22.7210	+	7.38250i	1.66152	+	0.539862i
$188$	−18.6199	−	9.81185i	−1.35800	−	0.715602i
$189$	0.385320	−	0.125198i	0.0280279	−	0.00910682i
$190$		0			0
$191$	−5.85762	+	18.0279i	−0.423842	+	1.30445i	0.480256	+	0.877128i	$0.340544\pi$
$191$	−5.85762	+	18.0279i	−0.423842	+	1.30445i	−0.904099	+	0.427324i	$0.859456\pi$
$192$	0.972895	+	2.12122i	0.0702127	+	0.153086i
$193$	−2.63353			−0.189566			−0.0947828	−	0.995498i	$-0.530216\pi$
$193$	−2.63353			−0.189566			−0.0947828	+	0.995498i	$0.530216\pi$
$194$	0.709706	+	9.88539i	0.0509540	+	0.709730i
$195$		0			0
$196$	6.13519	+	12.4613i	0.438228	+	0.890093i
$197$	−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	$-0.555830\pi$
$198$	20.2443	+	12.5978i	1.43870	+	0.895287i
$199$	−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
$202$	13.1459	+	8.18055i	0.924941	+	0.575581i
$203$	−0.913642	−	1.25752i	−0.0641251	−	0.0882607i
$204$	−2.16189	+	1.06439i	−0.151363	+	0.0745219i
$205$		0			0
$206$	−1.18561	−	16.5142i	−0.0826056	−	1.15060i
$207$	7.11964			0.494849
$208$	6.19566	−	4.24634i	0.429592	−	0.294430i
$209$	−4.83972	+	14.8951i	−0.334770	+	1.03032i
$210$		0			0
$211$	−13.9414	+	4.52984i	−0.959766	+	0.311847i	−0.746678	−	0.665186i	$-0.768352\pi$
$211$	−13.9414	+	4.52984i	−0.959766	+	0.311847i	−0.213088	+	0.977033i	$0.568352\pi$
$212$	−3.53362	+	6.70574i	−0.242690	+	0.460552i
$213$	0.758344	+	0.246401i	0.0519609	+	0.0168831i
$214$	−0.423419	−	0.263489i	−0.0289443	−	0.0180118i
$215$		0			0
$216$	−4.76792	+	1.04125i	−0.324416	+	0.0708482i
$217$	−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
$222$	0.809751	+	0.200297i	0.0543469	+	0.0134430i
$223$	5.26920	+	16.2169i	0.352852	+	1.08597i	0.957245	+	0.289280i	$0.0934157\pi$
$223$	5.26920	+	16.2169i	0.352852	+	1.08597i	−0.604393	+	0.796686i	$0.706584\pi$
$224$	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	$0.561465\pi$
$228$	−0.697775	−	1.41726i	−0.0462113	−	0.0938606i
$229$	3.58252	+	4.93092i	0.236740	+	0.325844i	0.910812	−	0.412821i	$-0.135456\pi$
$229$	3.58252	+	4.93092i	0.236740	+	0.325844i	−0.674072	+	0.738665i	$0.735456\pi$
$230$		0			0
$231$	−0.320527	−	0.232876i	−0.0210891	−	0.0153221i
$232$	9.45197	+	16.1626i	0.620552	+	1.06113i
$233$	−5.77365	−	4.19480i	−0.378244	−	0.274811i	0.382377	−	0.924006i	$-0.375106\pi$
$233$	−5.77365	−	4.19480i	−0.378244	−	0.274811i	−0.760621	+	0.649196i	$0.775106\pi$
$234$	2.91309	+	7.17176i	0.190434	+	0.468833i
$235$		0			0
$236$	2.00349	+	13.8812i	0.130416	+	0.903590i
$237$	3.55855	+	1.15624i	0.231153	+	0.0751060i
$238$	−1.27072	+	0.516153i	−0.0823687	+	0.0334572i
$239$	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	$0.119372\pi$
$242$	−2.27417	−	31.6765i	−0.146189	−	2.03624i
$243$		−	7.58043i		−	0.486285i
$244$	−2.27234	−	2.33565i	−0.145472	−	0.149525i
$245$		0			0
$246$	0.685377	−	2.77081i	0.0436980	−	0.176660i
$247$	−4.11342	+	2.98858i	−0.261731	+	0.190159i
$248$	11.1835	+	9.95739i	0.710152	+	0.632295i
$249$	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	$-0.0458709\pi$
$252$	−1.35485	+	0.195547i	−0.0853477	+	0.0123183i
$253$	−8.30408	−	11.4296i	−0.522073	−	0.718572i
$254$	−12.6826	−	3.13713i	−0.795779	−	0.196841i
$255$		0			0
$256$	−4.10099	−	15.4655i	−0.256312	−	0.966594i
$257$	−6.99079			−0.436074			−0.218037	−	0.975941i	$-0.569965\pi$
$257$	−6.99079			−0.436074			−0.218037	+	0.975941i	$0.569965\pi$
$258$	0.237639	+	3.31004i	0.0147948	+	0.206074i
$259$	0.451544	+	0.146716i	0.0280576	+	0.00911646i
$260$		0			0
$261$	−18.3516	+	5.96279i	−1.13593	+	0.369088i
$262$	−4.03847	−	9.94235i	−0.249497	−	0.614240i
$263$	6.99005	−	21.5131i	0.431025	−	1.32656i	−0.466081	−	0.884742i	$-0.654335\pi$
$263$	6.99005	−	21.5131i	0.431025	−	1.32656i	0.897106	−	0.441816i	$-0.145665\pi$
$264$	3.56432	+	3.17355i	0.219369	+	0.195319i
$265$		0			0
$266$	−0.338372	−	0.833042i	−0.0207469	−	0.0510771i
$267$	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	−0.906546	−	0.422106i	$-0.861291\pi$
$269$	−3.68963	+	5.07835i	−0.224961	+	0.309632i	0.681585	+	0.731739i	$0.261291\pi$
$270$		0			0
$271$	−2.75055	+	1.99839i	−0.167084	+	0.121393i	−0.668185	−	0.743995i	$-0.732928\pi$
$271$	−2.75055	+	1.99839i	−0.167084	+	0.121393i	0.501101	+	0.865389i	$0.332928\pi$
$272$	15.8469	−	4.67172i	0.960862	−	0.283265i
$273$	−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	$0.118544\pi$
$278$	−0.768239	+	3.10580i	−0.0460759	+	0.186274i
$279$	−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	$0.187845\pi$
$284$	−4.83644	−	2.54858i	−0.286990	−	0.151230i
$285$		0			0
$286$	8.11555	−	13.0414i	0.479882	−	0.771156i
$287$	0.502032	−	1.54510i	0.0296340	−	0.0912041i
$288$	16.4731	−	0.728471i	0.970686	−	0.0429256i
$289$	0.0183581	+	0.0565005i	0.00107989	+	0.00332356i
$290$		0			0
$291$	−1.94426	−	0.631729i	−0.113975	−	0.0370326i
$292$	21.6795	−	21.0919i	1.26870	−	1.23431i
$293$		−	8.55020i		−	0.499508i	−0.968309	−	0.249754i	$-0.919650\pi$
$293$		−	8.55020i		−	0.499508i	0.968309	−	0.249754i	$-0.0803498\pi$
$294$	−2.85769	+	0.205164i	−0.166664	+	0.0119654i
$295$		0			0
$296$	−5.23749	−	2.29700i	−0.304423	−	0.133510i
$297$	−8.07416	+	5.86622i	−0.468510	+	0.340393i
$298$	−18.4886	−	11.5052i	−1.07101	−	0.666481i
$299$		−	4.58650i		−	0.265244i
$300$		0			0
$301$			1.88885i			0.108871i
$302$	0.224204	−	0.360288i	0.0129015	−	0.0207323i
$303$	−2.58382	+	1.87725i	−0.148436	+	0.107845i
$304$	3.06262	+	10.3887i	0.175653	+	0.595834i
$305$		0			0
$306$	1.21924	+	16.9826i	0.0696994	+	0.970832i
$307$			11.0920i			0.633052i	0.948584	+	0.316526i	$0.102517\pi$
$307$			11.0920i			0.633052i	−0.948584	+	0.316526i	$0.897483\pi$
$308$	1.89417	+	1.94695i	0.107930	+	0.110938i
$309$	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	$0.575234\pi$
$312$	0.330564	+	1.51366i	0.0187145	+	0.0856941i
$313$	0.0113715	−	0.0349980i	0.000642758	−	0.00197820i	−0.950735	−	0.310006i	$-0.899669\pi$
$313$	0.0113715	−	0.0349980i	0.000642758	−	0.00197820i	0.951377	+	0.308028i	$0.0996690\pi$
$314$	−25.0864	−	15.6110i	−1.41571	−	0.880980i
$315$		0			0
$316$	−22.6951	−	11.9593i	−1.27670	−	0.672762i
$317$	−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
$322$	0.787350	+	0.194756i	0.0438773	+	0.0108533i
$323$	−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
$328$	−7.85989	+	17.9217i	−0.433990	+	0.989560i
$329$	1.99909	−	1.45242i	0.110213	−	0.0800746i
$330$		0			0
$331$	13.3539	−	18.3800i	0.733995	−	1.01026i	−0.264947	−	0.964263i	$-0.585355\pi$
$331$	13.3539	−	18.3800i	0.733995	−	1.01026i	0.998942	−	0.0459939i	$-0.0146455\pi$
$332$	−6.21836	−	1.07266i	−0.341277	−	0.0588700i
$333$	3.46435	−	4.76827i	0.189845	−	0.261300i
$334$	28.2378	−	11.4699i	1.54510	−	0.627603i
$335$		0			0
$336$	−0.273882	−	0.00752745i	−0.0149415	−	0.000410656i
$337$	−5.81367	+	17.8926i	−0.316691	+	0.974674i	0.658362	+	0.752701i	$0.271249\pi$
$337$	−5.81367	+	17.8926i	−0.316691	+	0.974674i	−0.975053	+	0.221972i	$0.928751\pi$
$338$	−12.4132	+	5.04209i	−0.675188	+	0.274253i
$339$	−0.0908470	+	0.0295180i	−0.00493413	+	0.00160320i
$340$		0			0
$341$	29.1231	+	9.46267i	1.57711	+	0.512433i
$342$	−11.1332	+	0.799293i	−0.602016	+	0.0432208i
$343$	−3.27438			−0.176800
$344$	2.25216	−	22.6407i	0.121428	−	1.22070i
$345$		0			0
$346$	0.541126	−	2.18764i	0.0290911	−	0.117608i
$347$	−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	$-0.491408\pi$
$348$	−3.82251	+	0.551706i	−0.204908	+	0.0295746i
$349$		−	15.7634i		−	0.843797i	−0.906643	−	0.421898i	$-0.861364\pi$
$349$		−	15.7634i		−	0.843797i	0.906643	−	0.421898i	$-0.138636\pi$
$350$		0			0
$351$	−3.24002			−0.172940
$352$	−20.3831	−	25.5956i	−1.08642	−	1.36425i
$353$	−6.60477	+	4.79864i	−0.351536	+	0.255406i	−0.749513	−	0.661989i	$-0.769712\pi$
$353$	−6.60477	+	4.79864i	−0.351536	+	0.255406i	0.397977	+	0.917395i	$0.369712\pi$
$354$	−2.80832	−	0.694656i	−0.149261	−	0.0369205i
$355$		0			0
$356$	−16.2946	+	15.8529i	−0.863614	+	0.840204i
$357$		−	0.282911i		−	0.0149732i
$358$	15.6302	−	1.12215i	0.826081	−	0.0593072i
$359$	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
$362$	−10.6835	−	26.3017i	−0.561510	−	1.38239i
$363$	6.23015	+	2.02430i	0.326998	+	0.106248i
$364$	0.125972	+	0.872801i	0.00660273	+	0.0457472i
$365$		0			0
$366$	0.622751	−	0.252954i	0.0325517	−	0.0132221i
$367$	−6.06821	−	4.40881i	−0.316758	−	0.230138i	0.418033	−	0.908432i	$-0.362720\pi$
$367$	−6.06821	−	4.40881i	−0.316758	−	0.230138i	−0.734791	+	0.678294i	$0.762720\pi$
$368$	−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
$372$	−2.77105	+	1.36430i	−0.143672	+	0.0707356i
$373$	−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
$378$	0.137581	−	0.556205i	0.00707639	−	0.0286081i
$379$	−7.20040	−	9.91051i	−0.369860	−	0.509069i	0.583003	−	0.812470i	$-0.301878\pi$
$379$	−7.20040	−	9.91051i	−0.369860	−	0.509069i	−0.952863	+	0.303402i	$0.901878\pi$
$380$		0			0
$381$	1.58402	−	2.18022i	0.0811519	−	0.111696i
$382$	17.2695	+	20.5036i	0.883586	+	1.04905i
$383$	−21.7829	−	15.8262i	−1.11305	−	0.808681i	−0.129912	−	0.991525i	$-0.541470\pi$
$383$	−21.7829	−	15.8262i	−1.11305	−	0.808681i	−0.983142	+	0.182844i	$0.941470\pi$
$384$	3.27391	+	0.416790i	0.167071	+	0.0212692i
$385$		0			0
$386$	−1.96775	+	3.16211i	−0.100156	+	0.160947i
$387$	22.3004	+	7.24584i	1.13359	+	0.368327i
$388$	12.3998	+	6.53412i	0.629504	+	0.331720i
$389$	−9.06656	+	2.94590i	−0.459693	+	0.149363i	−0.529703	−	0.848183i	$-0.677697\pi$
$389$	−9.06656	+	2.94590i	−0.459693	+	0.149363i	0.0700104	+	0.997546i	$0.477697\pi$
$390$		0			0
$391$	3.11744	−	9.59449i	0.157656	−	0.485214i
$392$	19.5466	+	1.94438i	0.987251	+	0.0982058i
$393$	2.21354			0.111658
$394$	−35.6045	+	2.55617i	−1.79373	+	0.128778i
$395$		0			0
$396$	30.2526	−	14.8946i	1.52025	−	0.748480i
$397$	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	$0.601515\pi$
$398$	−2.96807	+	4.76959i	−0.148776	+	0.239078i
$399$	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	$0.400705\pi$
$402$	−2.42746	+	3.90086i	−0.121071	+	0.194557i
$403$	5.84330	+	8.04262i	0.291076	+	0.400631i
$404$	19.6449	−	9.67198i	0.977372	−	0.481199i
$405$		0			0
$406$	−2.19258	+	0.157413i	−0.108816	+	0.00781228i
$407$	−11.6955			−0.579724
$408$	−0.337327	+	3.39111i	−0.0167002	+	0.167885i
$409$	−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
$412$	−20.7147	−	10.9157i	−1.02054	−	0.537778i
$413$	−1.56601	−	0.508829i	−0.0770585	−	0.0250378i
$414$	5.31972	−	8.54863i	0.261450	−	0.420142i
$415$		0			0
$416$	−0.469284	−	10.6120i	−0.0230085	−	0.520297i
$417$	−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	−0.666881	−	0.745164i	$-0.732371\pi$
$419$	5.07417	−	6.98399i	0.247889	−	0.341190i	0.914771	+	0.403973i	$0.132371\pi$
$420$		0			0
$421$	−7.53026	−	10.3645i	−0.367002	−	0.505135i	0.585081	−	0.810975i	$-0.301063\pi$
$421$	−7.53026	−	10.3645i	−0.367002	−	0.505135i	−0.952083	+	0.305840i	$0.901063\pi$
$422$	−4.97786	+	20.1242i	−0.242318	+	0.979633i
$423$	−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
$428$	−0.632749	+	0.311527i	−0.0305851	+	0.0150582i
$429$	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	0.618602	−	0.785704i	$-0.287699\pi$
$433$	1.30079	+	0.945079i	0.0625120	+	0.0454176i	−0.556090	+	0.831122i	$0.687699\pi$
$434$	−1.62877	+	0.661589i	−0.0781837	+	0.0317573i
$435$		0			0
$436$	−2.77785	−	19.2464i	−0.133035	−	0.921737i
$437$	6.28982	+	2.04369i	0.300883	+	0.0977628i
$438$	2.34793	+	5.78039i	0.112188	+	0.276198i
$439$	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
$442$	10.9403	−	0.785440i	0.520376	−	0.0373596i
$443$			19.5670i			0.929654i	0.885402	+	0.464827i	$0.153883\pi$
$443$			19.5670i			0.929654i	−0.885402	+	0.464827i	$0.846117\pi$
$444$	0.845537	−	0.822617i	0.0401274	−	0.0390397i
$445$		0			0
$446$	23.4089	+	5.79034i	1.10845	+	0.274181i
$447$	3.63392	−	2.64020i	0.171879	−	0.124877i
$448$	1.84166	+	0.370056i	0.0870103	+	0.0174835i
$449$	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
$452$	0.648193	−	0.0935543i	0.0304884	−	0.00440042i
$453$	0.0514498	+	0.0708145i	0.00241732	+	0.00332716i
$454$	−4.97080	+	20.0957i	−0.233291	+	0.943138i
$455$		0			0
$456$	−2.22310	−	0.221140i	−0.104106	−	0.0103558i
$457$	−15.5897			−0.729254			−0.364627	−	0.931154i	$-0.618803\pi$
$457$	−15.5897			−0.729254			−0.364627	+	0.931154i	$0.618803\pi$
$458$	8.59744	−	0.617240i	0.401732	−	0.0288417i
$459$	−6.77780	−	2.20224i	−0.316361	−	0.102792i
$460$		0			0
$461$	5.51241	−	1.79109i	0.256739	−	0.0834194i	−0.177820	−	0.984063i	$-0.556904\pi$
$461$	5.51241	−	1.79109i	0.256739	−	0.0834194i	0.434558	+	0.900644i	$0.356904\pi$
$462$	−0.519112	+	0.210857i	−0.0241513	+	0.00980996i
$463$	−3.67309	+	11.3046i	−0.170703	+	0.525370i	−0.999411	−	0.0343111i	$-0.989076\pi$
$463$	−3.67309	+	11.3046i	−0.170703	+	0.525370i	0.828708	+	0.559681i	$0.189076\pi$
$464$	26.4691	+	0.727484i	1.22880	+	0.0337726i
$465$		0			0
$466$	−9.35076	+	3.79817i	−0.433166	+	0.175947i
$467$	−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
$472$	18.1643	+	7.96630i	0.836080	+	0.366679i
$473$	−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
$478$	7.36163	+	1.82094i	0.336713	+	0.0832881i
$479$	−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
$484$	−39.7336	−	20.9378i	−1.80607	−	0.951717i
$485$		0			0
$486$	−9.10191	−	5.66403i	−0.412871	−	0.256925i
$487$	−6.97042	+	21.4527i	−0.315860	+	0.972117i	0.659539	+	0.751670i	$0.270751\pi$
$487$	−6.97042	+	21.4527i	−0.315860	+	0.972117i	−0.975399	+	0.220447i	$0.929249\pi$
$488$	−4.50231	+	0.983246i	−0.203810	+	0.0445095i
$489$	1.12782	+	3.47109i	0.0510020	+	0.156968i
$490$		0			0
$491$	7.25634	+	2.35773i	0.327474	+	0.106403i	0.468140	−	0.883654i	$-0.344924\pi$
$491$	7.25634	+	2.35773i	0.327474	+	0.106403i	−0.140666	+	0.990057i	$0.544924\pi$
$492$	−2.81484	−	2.89326i	−0.126903	−	0.130438i
$493$			27.3417i			1.23141i
$494$	0.514907	+	7.17207i	0.0231668	+	0.322687i
$495$		0			0
$496$	20.3121	−	5.98808i	0.912042	−	0.268873i
$497$	0.519253	−	0.377259i	0.0232917	−	0.0169224i
$498$	0.687697	−	1.10511i	0.0308164	−	0.0495210i
$499$			26.9689i			1.20729i	0.797252	+	0.603647i	$0.206286\pi$
$499$			26.9689i			1.20729i	−0.797252	+	0.603647i	$0.793714\pi$
$500$		0			0
$501$			6.28680i			0.280874i
$502$	−5.46371	−	3.40001i	−0.243857	−	0.151750i
$503$	−24.9059	+	18.0952i	−1.11050	+	0.806825i	−0.982742	−	0.184980i	$-0.940778\pi$
$503$	−24.9059	+	18.0952i	−1.11050	+	0.806825i	−0.127757	+	0.991805i	$0.540778\pi$
$504$	−0.777537	+	1.77290i	−0.0346343	+	0.0789711i
$505$		0			0
$506$	−19.9284	+	1.43073i	−0.885923	+	0.0636035i
$507$		−	2.76364i		−	0.122738i
$508$	−13.2431	+	12.8841i	−0.587568	+	0.571641i
$509$	3.29675	+	1.07118i	0.146126	+	0.0474792i	0.381167	−	0.924506i	$-0.375522\pi$
$509$	3.29675	+	1.07118i	0.146126	+	0.0474792i	−0.235041	+	0.971986i	$0.575522\pi$
$510$		0			0
$511$	1.09735	+	3.37731i	0.0485441	+	0.149403i
$512$	−21.6338	−	6.63157i	−0.956089	−	0.293077i
$513$	1.44371	−	4.44330i	0.0637416	−	0.196176i
$514$	−5.22345	+	8.39392i	−0.230397	+	0.370240i
$515$		0			0
$516$	4.15197	+	2.18790i	0.182780	+	0.0963168i
$517$	−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	$0.961177\pi$
$522$	−6.55254	+	26.4903i	−0.286797	+	1.15945i
$523$	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
$528$	6.47375	−	1.90848i	0.281734	−	0.0830558i
$529$	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
$534$	−1.76473	−	4.34462i	−0.0763674	−	0.188010i
$535$		0			0
$536$	20.9470	−	23.5263i	0.904773	−	1.01618i
$537$	−0.998852	+	3.07415i	−0.0431036	+	0.132659i
$538$	3.34077	+	8.22468i	0.144031	+	0.354591i
$539$	38.2040	−	12.4132i	1.64556	−	0.534676i
$540$		0			0
$541$	−19.5034	−	6.33705i	−0.838518	−	0.272451i	−0.141889	−	0.989883i	$-0.545318\pi$
$541$	−19.5034	−	6.33705i	−0.838518	−	0.272451i	−0.696629	+	0.717432i	$0.745318\pi$
$542$	0.344306	+	4.79579i	0.0147892	+	0.205997i
$543$	5.85576			0.251295
$544$	6.23129	−	22.5183i	0.267164	−	0.965462i
$545$		0			0
$546$	−0.176577	−	0.0436774i	−0.00755680	−	0.00186922i
$547$	−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	$0.957237\pi$
$548$	−26.1695	+	3.77707i	−1.11791	+	0.161348i
$549$		−	4.74932i		−	0.202696i
$550$		0			0
$551$	−17.9243			−0.763599
$552$	1.34011	−	1.50512i	0.0570388	−	0.0640622i
$553$	2.43661	−	1.77030i	0.103615	−	0.0752808i
$554$	8.74235	−	35.3432i	0.371427	−	1.50159i
$555$		0			0
$556$	3.15515	+	3.24306i	0.133808	+	0.137536i
$557$		−	36.8641i		−	1.56198i	−0.624543	−	0.780991i	$-0.714715\pi$
$557$		−	36.8641i		−	1.56198i	0.624543	−	0.780991i	$-0.285285\pi$
$558$	1.56279	+	21.7678i	0.0661581	+	0.921506i
$559$	4.66780	−	14.3660i	0.197427	−	0.607617i
$560$		0			0
$561$	2.15356	+	6.62797i	0.0909233	+	0.279833i
$562$	−5.11835	+	2.07901i	−0.215905	+	0.0876979i
$563$	−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	$0.933947\pi$
$564$	−0.877050	−	6.07666i	−0.0369305	−	0.255874i
$565$		0			0
$566$	−0.683576	−	1.68290i	−0.0287329	−	0.0707378i
$567$	−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	0.604840	−	0.796347i	$-0.293237\pi$
$571$	−8.11104	−	11.1639i	−0.339436	−	0.467194i	−0.944277	+	0.329153i	$0.893237\pi$
$572$	−9.59513	−	19.4889i	−0.401192	−	0.814870i
$573$	−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	0.999353	−	0.0359612i	$-0.0114493\pi$
$577$	4.07686	+	12.5473i	0.169722	+	0.522351i	−0.829631	+	0.558312i	$0.811449\pi$
$578$	0.0815578	+	0.0201738i	0.00339236	+	0.000839121i
$579$	−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
$584$	−9.12652	−	41.7905i	−0.377658	−	1.72930i
$585$		0			0
$586$	−10.2663	−	6.38863i	−0.424098	−	0.263912i
$587$	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	$0.410705\pi$
$588$	−1.88890	+	3.58456i	−0.0778968	+	0.147825i
$589$	−13.6332	+	4.42969i	−0.561745	+	0.182522i
$590$		0			0
$591$	2.27531	−	7.00269i	0.0935939	−	0.288052i
$592$	−6.67144	+	4.57242i	−0.274194	+	0.187925i
$593$	10.5301			0.432420			0.216210	−	0.976347i	$-0.430630\pi$
$593$	10.5301			0.432420			0.216210	+	0.976347i	$0.430630\pi$
$594$	1.01070	+	14.0779i	0.0414696	+	0.577624i
$595$		0			0
$596$	−27.6290	+	13.6028i	−1.13173	+	0.557193i
$597$	−0.681105	−	0.937461i	−0.0278758	−	0.0383677i
$598$	−5.50706	−	3.42698i	−0.225200	−	0.140140i
$599$	−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	$0.422907\pi$
$602$	2.26796	+	1.41133i	0.0924351	+	0.0575214i
$603$	19.0815	+	26.2634i	0.777058	+	1.06953i
$604$	−0.265079	−	0.538408i	−0.0107859	−	0.0219075i
$605$		0			0
$606$	0.323435	+	4.50508i	0.0131387	+	0.183006i
$607$	−35.8362			−1.45455			−0.727274	−	0.686347i	$-0.759213\pi$
$607$	−35.8362			−1.45455			−0.727274	+	0.686347i	$0.759213\pi$
$608$	14.7622	+	4.08502i	0.598686	+	0.165670i
$609$	0.140118	−	0.431238i	0.00567785	−	0.0174746i
$610$		0			0
$611$	−18.7937	+	6.10645i	−0.760313	+	0.247041i
$612$	21.3022	+	11.2253i	0.861092	+	0.453756i
$613$	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	$0.516894\pi$
$614$	13.3183	+	8.28782i	0.537481	+	0.334469i
$615$		0			0
$616$	3.75303	−	0.819613i	0.151214	−	0.0330232i
$617$	−12.6424	−	9.18527i	−0.508965	−	0.369785i	0.303466	−	0.952842i	$-0.401856\pi$
$617$	−12.6424	−	9.18527i	−0.508965	−	0.369785i	−0.812431	+	0.583057i	$0.801856\pi$
$618$	3.69406	−	3.11139i	0.148597	−	0.125159i
$619$	20.9771	−	28.8724i	0.843139	−	1.16048i	−0.142194	−	0.989839i	$-0.545416\pi$
$619$	20.9771	−	28.8724i	0.843139	−	1.16048i	0.985333	−	0.170643i	$-0.0545844\pi$
$620$		0			0
$621$	2.47715	+	3.40951i	0.0994048	+	0.136819i
$622$	41.2667	+	10.2076i	1.65464	+	0.409286i
$623$	−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
$628$	−37.4886	+	18.4571i	−1.49596	+	0.736519i
$629$	−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
$634$	8.65684	+	21.3124i	0.343807	+	0.846423i
$635$		0			0
$636$	−2.18844	+	0.315859i	−0.0867772	+	0.0125246i
$637$	12.4027	+	4.02989i	0.491414	+	0.159670i
$638$	50.1691	−	20.3781i	1.98621	−	0.806777i
$639$	−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	$0.0171061\pi$
$642$	−0.0104176	−	0.145105i	−0.000411150	−	0.00572685i
$643$		−	34.5558i		−	1.36275i	−0.731935	−	0.681375i	$-0.761382\pi$
$643$		−	34.5558i		−	1.36275i	0.731935	−	0.681375i	$-0.238618\pi$
$644$	0.822145	−	0.799860i	0.0323971	−	0.0315189i
$645$		0			0
$646$	−3.79772	+	15.3532i	−0.149419	+	0.604065i
$647$	−7.76508	+	5.64166i	−0.305277	+	0.221797i	−0.729867	−	0.683589i	$-0.760418\pi$
$647$	−7.76508	+	5.64166i	−0.305277	+	0.221797i	0.424590	+	0.905386i	$0.360418\pi$
$648$	17.4095	+	15.5008i	0.683908	+	0.608928i
$649$	40.5615			1.59218
$650$		0			0
$651$		−	0.362627i		−	0.0142125i
$652$	−3.57453	−	24.7662i	−0.139989	−	0.969919i
$653$	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	$0.641257\pi$
$654$	3.89376	+	0.963147i	0.152258	+	0.0376620i
$655$		0			0
$656$	15.6459	+	22.8284i	0.610871	+	0.891298i
$657$	44.0833			1.71985
$658$	−0.250240	−	3.48556i	−0.00975538	−	0.135881i
$659$	−41.1516	−	13.3710i	−1.60304	−	0.520859i	−0.635184	−	0.772361i	$-0.719076\pi$
$659$	−41.1516	−	13.3710i	−1.60304	−	0.520859i	−0.967857	+	0.251502i	$0.919076\pi$
$660$		0			0
$661$	−33.1551	+	10.7728i	−1.28958	+	0.419012i	−0.871946	−	0.489602i	$-0.837142\pi$
$661$	−33.1551	+	10.7728i	−1.28958	+	0.419012i	−0.417639	+	0.908613i	$0.637142\pi$
$662$	−12.0912	−	29.7675i	−0.469938	−	1.15695i
$663$	−0.699141	+	2.15173i	−0.0271524	+	0.0835664i
$664$	−5.93425	+	6.66497i	−0.230294	+	0.258651i
$665$		0			0
$666$	−3.13679	−	7.72249i	−0.121548	−	0.299240i
$667$	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
$672$	−0.213680	+	0.323229i	−0.00824290	+	0.0124688i
$673$	3.33688	+	10.2698i	0.128627	+	0.395874i	0.994544	−	0.104314i	$-0.0332646\pi$
$673$	3.33688	+	10.2698i	0.128627	+	0.395874i	−0.865917	+	0.500187i	$0.833265\pi$
$674$	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	$0.103010\pi$
$678$	−0.0324374	+	0.131137i	−0.00124575	+	0.00503627i
$679$	−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	$0.323951\pi$
$684$	−7.35892	+	13.9650i	−0.281375	+	0.533966i
$685$		0			0
$686$	−2.44658	+	3.93158i	−0.0934110	+	0.150109i
$687$	−0.549422	+	1.69095i	−0.0209617	+	0.0645136i
$688$	−25.5021	−	19.6211i	−0.972258	−	0.748046i
$689$	2.19917	+	6.76834i	0.0837815	+	0.257853i
$690$		0			0
$691$	15.2658	+	4.96017i	0.580740	+	0.188694i	0.584632	−	0.811299i	$-0.301239\pi$
$691$	15.2658	+	4.96017i	0.580740	+	0.188694i	−0.00389213	+	0.999992i	$0.501239\pi$
$692$	−2.22240	−	2.28432i	−0.0844828	−	0.0868367i
$693$			3.95893i			0.150387i
$694$	−41.6667	+	2.99139i	−1.58164	+	0.113552i
$695$		0			0
$696$	−2.19370	+	5.00196i	−0.0831521	+	0.189599i
$697$	−23.1193	+	16.7971i	−0.875705	+	0.636237i
$698$	−18.9273	−	11.7783i	−0.716410	−	0.445814i
$699$		−	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	$-0.0928363\pi$
$702$	−2.42091	+	3.89033i	−0.0913715	+	0.146831i
$703$	4.42930	−	3.21807i	0.167054	−	0.121372i
$704$	−45.9629	+	5.34939i	−1.73229	+	0.201613i
$705$		0			0
$706$	0.826767	+	11.5159i	0.0311158	+	0.433407i
$707$			2.57079i			0.0966843i
$708$	−2.93243	+	2.85294i	−0.110208	+	0.107220i
$709$	35.0361	+	11.3839i	1.31581	+	0.427532i	0.881053	−	0.473018i	$-0.156835\pi$
$709$	35.0361	+	11.3839i	1.31581	+	0.427532i	0.434754	+	0.900549i	$0.356835\pi$
$710$		0			0
$711$	−11.5537	−	35.5586i	−0.433297	−	1.33355i
$712$	6.85961	+	31.4103i	0.257075	+	1.17715i
$713$	3.99584	−	12.2979i	0.149645	−	0.460561i
$714$	−0.339694	−	0.211388i	−0.0127127	−	0.00791100i
$715$		0			0
$716$	10.3314	−	19.6058i	0.386101	−	0.732703i
$717$	−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
$722$	16.0189	+	3.96237i	0.596161	+	0.147464i
$723$	−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	$-0.839069\pi$
$727$	−12.1809	−	37.4888i	−0.451763	−	1.39038i	0.423131	−	0.906069i	$-0.360931\pi$
$728$	1.14211	+	0.500892i	0.0423293	+	0.0185643i
$729$	−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	$0.0440112\pi$
$734$	−9.82781	+	3.99194i	−0.362751	+	0.147345i
$735$		0			0
$736$	−10.8084	+	8.60723i	−0.398401	+	0.317267i
$737$	19.9063	−	61.2653i	0.733258	−	2.25674i
$738$	−26.4249	+	10.7335i	−0.972713	+	0.395105i
$739$	−8.47753	+	2.75452i	−0.311851	+	0.101327i	−0.460761	−	0.887524i	$-0.652424\pi$
$739$	−8.47753	+	2.75452i	−0.311851	+	0.101327i	0.148910	+	0.988851i	$0.452424\pi$
$740$		0			0
$741$	−1.41060	−	0.458333i	−0.0518198	−	0.0168373i
$742$	−1.25528	+	0.0901210i	−0.0460829	+	0.00330845i
$743$	−21.5410			−0.790261			−0.395130	−	0.918625i	$-0.629301\pi$
$743$	−21.5410			−0.790261			−0.395130	+	0.918625i	$0.629301\pi$
$744$	−0.432376	+	4.34662i	−0.0158517	+	0.159355i
$745$		0			0
$746$	−4.33229	+	17.5144i	−0.158617	+	0.641248i
$747$	−5.40575	−	7.44038i	−0.197786	−	0.272229i
$748$	−6.82548	−	47.2905i	−0.249564	−	1.72911i
$749$		−	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	$0.305562\pi$
$752$	−1.15648	+	42.0780i	−0.0421726	+	1.53443i
$753$	1.07389	−	0.780227i	0.0391347	−	0.0284331i
$754$	17.0651	+	4.22117i	0.621476	+	0.153726i
$755$		0			0
$756$	−0.565042	−	0.580785i	−0.0205504	−	0.0211230i
$757$			3.46461i			0.125924i	0.998016	+	0.0629618i	$0.0200546\pi$
$757$			3.46461i			0.125924i	−0.998016	+	0.0629618i	$0.979945\pi$
$758$	−17.2797	+	1.24057i	−0.627628	+	0.0450596i
$759$	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	$-0.219513\pi$
$762$	−1.43425	−	3.53099i	−0.0519573	−	0.127914i
$763$	2.17129	+	0.705496i	0.0786061	+	0.0255407i
$764$	37.5225	−	5.41565i	1.35752	−	0.195931i
$765$		0			0
$766$	−35.2787	+	14.3298i	−1.27467	+	0.517756i
$767$	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
$772$	2.32650	+	4.72539i	0.0837324	+	0.170071i
$773$	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
$778$	−3.23727	+	13.0875i	−0.116062	+	0.469209i
$779$	−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
$784$	16.9396	−	22.0170i	0.604987	−	0.786320i
$785$		0			0
$786$	1.65394	−	2.65782i	0.0589940	−	0.0948015i
$787$	−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	$0.654747\pi$
$788$	−23.5341	+	44.6606i	−0.838367	+	1.59097i
$789$	6.27562	−	2.03907i	0.223418	−	0.0725930i
$790$		0			0
$791$	−0.0237601	+	0.0731261i	−0.000844812	+	0.00260007i
$792$	4.72041	−	47.4537i	0.167733	−	1.68620i
$793$	−3.05953			−0.108647
$794$	32.8234	−	2.35651i	1.16486	−	0.0836292i
$795$		0			0
$796$	3.50919	+	7.12758i	0.124380	+	0.252630i
$797$	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	$0.609087\pi$
$798$	0.138579	−	0.222692i	0.00490564	−	0.00788321i
$799$	−43.4651			−1.53769
$800$		0			0
$801$	−33.1336			−1.17072
$802$	9.18426	−	14.7588i	0.324307	−	0.521152i
$803$	−51.4171	−	70.7696i	−1.81447	−	2.49740i
$804$	2.87003	+	5.82937i	0.101218	+	0.205586i
$805$		0			0
$806$	14.0229	−	1.00675i	0.493936	−	0.0354614i
$807$	−1.83112			−0.0644586
$808$	3.06526	−	30.8147i	0.107836	−	1.08406i
$809$	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	0.420947	−	0.907085i	$-0.361698\pi$
$811$	36.8697	−	11.9797i	1.29467	−	0.420664i	0.873725	+	0.486421i	$0.161698\pi$
$812$	−1.44927	+	2.75028i	−0.0508594	+	0.0965158i
$813$	−0.943236	−	0.306476i	−0.0330807	−	0.0107486i
$814$	−8.73875	+	14.0429i	−0.306293	+	0.492203i
$815$		0			0
$816$	3.81969	+	2.93884i	0.133716	+	0.102880i
$817$	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	$-0.925372\pi$
$821$	−25.5877	−	35.2185i	−0.893017	−	1.22913i	0.0796254	−	0.996825i	$-0.474628\pi$
$822$	1.30960	−	5.29438i	0.0456775	−	0.184663i
$823$	1.45020	+	4.46326i	0.0505509	+	0.155580i	0.973145	−	0.230192i	$-0.0739354\pi$
$823$	1.45020	+	4.46326i	0.0505509	+	0.155580i	−0.922594	+	0.385771i	$0.873935\pi$
$824$	−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	$0.334793\pi$
$828$	−6.28958	−	12.7749i	−0.218578	−	0.443959i
$829$	−0.462729	−	0.636892i	−0.0160712	−	0.0221202i	0.800906	−	0.598790i	$-0.204352\pi$
$829$	−0.462729	−	0.636892i	−0.0160712	−	0.0221202i	−0.816977	+	0.576670i	$0.804352\pi$
$830$		0			0
$831$	6.07571	+	4.41426i	0.210764	+	0.153129i
$832$	−13.0926	−	7.36573i	−0.453905	−	0.255361i
$833$	23.2062	+	16.8603i	0.804046	+	0.584174i
$834$	−0.864692	+	0.351228i	−0.0299418	+	0.0121620i
$835$		0			0
$836$	31.0021	−	4.47455i	1.07223	−	0.154756i
$837$	−8.68759	−	2.82277i	−0.300287	−	0.0975692i
$838$	−4.59439	−	11.3110i	−0.158711	−	0.390731i
$839$	−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
$842$	−18.0713	+	1.29740i	−0.622779	+	0.0447114i
$843$		−	1.13954i		−	0.0392478i
$844$	20.4440	+	21.0136i	0.703711	+	0.723318i
$845$		0			0
$846$	−42.1117	−	10.4166i	−1.44783	−	0.358130i
$847$	4.26591	−	3.09936i	0.146578	−	0.106495i
$848$	15.1539	+	0.416494i	0.520387	+	0.0143025i
$849$	0.374678			0.0128589
$850$		0			0
$851$			4.93870i			0.169296i
$852$	−0.227809	−	1.57838i	−0.00780462	−	0.0540746i
$853$	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	$0.738971\pi$
$854$	0.129916	−	0.525220i	0.00444565	−	0.0179727i
$855$		0			0
$856$	−0.0987298	+	0.992519i	−0.00337452	+	0.0339236i
$857$	53.1600			1.81591			0.907955	−	0.419068i	$-0.137643\pi$
$857$	53.1600			1.81591			0.907955	+	0.419068i	$0.137643\pi$
$858$	4.46929	−	0.320865i	0.152579	−	0.0109542i
$859$	−32.6009	−	10.5927i	−1.11233	−	0.361417i	−0.305493	−	0.952194i	$-0.598821\pi$
$859$	−32.6009	−	10.5927i	−1.11233	−	0.361417i	−0.806835	+	0.590777i	$0.798821\pi$
$860$		0			0
$861$	0.450722	−	0.146448i	0.0153606	−	0.00499095i
$862$	−39.4035	+	16.0053i	−1.34209	+	0.545141i
$863$	−12.2926	+	37.8328i	−0.418446	+	1.28784i	0.490686	+	0.871336i	$0.336746\pi$
$863$	−12.2926	+	37.8328i	−0.418446	+	1.28784i	−0.909132	+	0.416508i	$0.863254\pi$
$864$	6.08038	+	7.63531i	0.206859	+	0.259758i
$865$		0			0
$866$	2.10670	−	0.855719i	0.0715887	−	0.0290785i
$867$	−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
$872$	−25.1850	−	11.0453i	−0.852871	−	0.374043i
$873$	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	$0.638908\pi$
$878$	52.1337	+	12.8956i	1.75943	+	0.435205i
$879$	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	$-0.0235458\pi$
$884$	7.23138	−	13.7230i	0.243218	−	0.461554i
$885$		0			0
$886$	23.4943	+	14.6202i	0.789305	+	0.491176i
$887$	4.72737	−	14.5493i	0.158729	−	0.488519i	−0.839790	−	0.542911i	$-0.817322\pi$
$887$	4.72737	−	14.5493i	0.158729	−	0.488519i	0.998520	+	0.0543921i	$0.0173221\pi$
$888$	−0.355948	−	1.62990i	−0.0119448	−	0.0546957i
$889$	−0.670327	−	2.06305i	−0.0224821	−	0.0691926i
$890$		0			0
$891$	45.3363	+	14.7306i	1.51882	+	0.493495i
$892$	24.4435	−	23.7809i	0.818428	−	0.796243i
$893$		−	28.4943i		−	0.953524i
$894$	−0.454885	−	6.33602i	−0.0152136	−	0.211908i
$895$		0			0
$896$	1.82040	−	1.93480i	0.0608153	−	0.0646371i
$897$	1.08241	−	0.786416i	0.0361406	−	0.0262577i
$898$	24.8496	−	39.9325i	0.829241	−	1.33256i
$899$			35.0457i			1.16884i
$900$		0			0
$901$			15.6535i			0.521492i
$902$	48.0521	+	29.9023i	1.59996	+	0.995638i
$903$	−0.445767	+	0.323868i	−0.0148342	+	0.0107777i
$904$	0.371992	−	0.848195i	0.0123723	−	0.0282106i
$905$		0			0
$906$	0.123471	−	0.00886438i	0.00410203	−	0.000294499i
$907$		−	31.6503i		−	1.05093i	−0.850815	−	0.525465i	$-0.823891\pi$
$907$		−	31.6503i		−	1.05093i	0.850815	−	0.525465i	$-0.176109\pi$
$908$	20.4150	+	20.9838i	0.677496	+	0.696372i
$909$	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	$0.928188\pi$
$912$	−1.92660	+	2.50406i	−0.0637961	+	0.0829178i
$913$	−5.63942	+	17.3564i	−0.186638	+	0.574411i
$914$	−11.6484	+	18.7187i	−0.385296	+	0.619159i
$915$		0			0
$916$	5.68280	−	10.7842i	0.187765	−	0.356321i
$917$	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
$922$	1.96824	−	7.95710i	0.0648204	−	0.262053i
$923$	−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
$928$	20.6509	−	31.2382i	0.677900	−	1.02544i
$929$	−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
$934$	13.2765	+	32.6856i	0.434421	+	1.06951i
$935$		0			0
$936$	10.2950	−	11.5626i	0.336502	−	0.377937i
$937$	5.15839	−	15.8759i	0.168517	−	0.518643i	−0.830761	−	0.556629i	$-0.812094\pi$
$937$	5.15839	−	15.8759i	0.168517	−	0.518643i	0.999278	+	0.0379863i	$0.0120943\pi$
$938$	1.39176	+	3.42640i	0.0454426	+	0.111876i
$939$	0.0102093	−	0.00331721i	0.000333168	−	0.000108253i
$940$		0			0
$941$	10.5188	+	3.41775i	0.342902	+	0.111416i	0.475405	−	0.879767i	$-0.342301\pi$
$941$	10.5188	+	3.41775i	0.342902	+	0.111416i	−0.132503	+	0.991183i	$0.542301\pi$
$942$	−0.617214	−	8.59708i	−0.0201099	−	0.280108i
$943$	16.8993			0.550316
$944$	23.1374	−	15.8578i	0.753059	−	0.516126i
$945$		0			0
$946$	−63.8765	−	15.8002i	−2.07680	−	0.513710i
$947$	−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	$0.904333\pi$
$948$	−1.06900	−	7.40661i	−0.0347196	−	0.240556i
$949$		−	28.3986i		−	0.921858i
$950$		0			0
$951$	−4.74494			−0.153865
$952$	2.04872	+	1.82411i	0.0663993	+	0.0591196i
$953$	39.2091	−	28.4871i	1.27011	−	0.922787i	0.270900	−	0.962608i	$-0.412679\pi$
$953$	39.2091	−	28.4871i	1.27011	−	0.922787i	0.999207	+	0.0398210i	$0.0126788\pi$
$954$	−3.75141	+	15.1660i	−0.121456	+	0.491018i
$955$		0			0
$956$	7.68697	−	7.47860i	0.248614	−	0.241875i
$957$			11.1695i			0.361060i
$958$	1.55579	+	21.6703i	0.0502652	+	0.700136i
$959$	0.959267	−	2.95232i	0.0309764	−	0.0953354i
$960$		0			0
$961$	−0.918548	−	2.82700i	−0.0296306	−	0.0911936i
$962$	−4.97486	+	2.02073i	−0.160396	+	0.0651509i
$963$	−0.977603	−	0.317642i	−0.0315028	−	0.0102359i
$964$	3.73802	−	0.539512i	0.120394	−	0.0173765i
$965$		0			0
$966$	0.0890395	+	0.219207i	0.00286480	+	0.00705288i
$967$	15.9495	+	11.5880i	0.512901	+	0.372645i	0.813923	−	0.580973i	$-0.197328\pi$
$967$	15.9495	+	11.5880i	0.512901	+	0.372645i	−0.301022	+	0.953617i	$0.597328\pi$
$968$	−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	0.829590	−	0.558373i	$-0.188574\pi$
$971$	1.31463	+	1.80943i	0.0421885	+	0.0580675i	−0.787402	+	0.616440i	$0.788574\pi$
$972$	−13.6017	+	6.69666i	−0.436275	+	0.214795i
$973$	−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	0.992753	−	0.120175i	$-0.0383457\pi$
$977$	3.71838	+	11.4440i	0.118962	+	0.366126i	−0.873791	+	0.486301i	$0.838346\pi$
$978$	5.01047	+	1.23937i	0.160217	+	0.0396307i
$979$	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	0.993826	−	0.110952i	$-0.0353901\pi$
$983$	37.4796	+	27.2305i	1.19541	+	0.868518i	0.201587	+	0.979471i	$0.435390\pi$
$984$	−5.57719	+	1.21799i	−0.177794	+	0.0388280i
$985$		0			0
$986$	32.8294	+	20.4294i	1.04550	+	0.650605i
$987$	0.685540	+	0.222746i	0.0218210	+	0.00709007i
$988$	8.99631	+	4.74064i	0.286211	+	0.150820i
$989$	−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	$-0.320191\pi$
$992$	7.98709	−	28.8632i	0.253590	−	0.916409i
$993$	6.62737			0.210313
$994$	−0.0649987	−	0.905357i	−0.00206163	−	0.0287162i
$995$		0			0
$996$	−0.813074	−	1.65145i	−0.0257632	−	0.0523282i
$997$	−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	$0.971999\pi$
$998$	32.3819	+	20.1509i	1.02503	+	0.637866i
$999$	3.48883			0.110382

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.6	✓	112	200.197	odd	20
200.2.o.a.29.12	yes	112	25.22	odd	20
200.2.o.a.69.6	yes	112	5.3	odd	4
200.2.o.a.69.12	yes	112	40.13	odd	4
800.2.be.a.369.13		112	40.3	even	4
800.2.be.a.369.16		112	20.3	even	4
800.2.be.a.529.13		112	100.47	even	20
800.2.be.a.529.16		112	200.147	even	20
1000.2.o.a.149.17		112	25.3	odd	20
1000.2.o.a.149.23		112	200.53	odd	20
1000.2.o.a.349.17		112	40.37	odd	4
1000.2.o.a.349.23		112	5.2	odd	4
1000.2.t.b.101.7		224	25.21	even	5	inner
1000.2.t.b.101.18		224	200.29	even	10	inner
1000.2.t.b.101.39		224	200.21	even	10	inner
1000.2.t.b.101.50		224	25.4	even	10	inner
1000.2.t.b.901.7		224	8.5	even	2	inner
1000.2.t.b.901.18		224	5.4	even	2	inner
1000.2.t.b.901.39		224	1.1	even	1	trivial
1000.2.t.b.901.50		224	40.29	even	2	inner

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)

\(f(q)\)	\(=\)	\(q+(0.747190 - 1.20071i) q^{2} +(0.171463 + 0.235999i) q^{3} +(-0.883414 - 1.79432i) q^{4} +(0.411483 - 0.0295418i) q^{6} +0.234809 q^{7} +(-2.81454 - 0.279973i) q^{8} +(0.900755 - 2.77224i) q^{9} +O(q^{10})\)	\(q+(0.747190 - 1.20071i) q^{2} +(0.171463 + 0.235999i) q^{3} +(-0.883414 - 1.79432i) q^{4} +(0.411483 - 0.0295418i) q^{6} +0.234809 q^{7} +(-2.81454 - 0.279973i) q^{8} +(0.900755 - 2.77224i) q^{9} +(-5.50105 + 1.78740i) q^{11} +(0.271985 - 0.516145i) q^{12} +(-1.78589 - 0.580270i) q^{13} +(0.175447 - 0.281938i) q^{14} +(-2.43916 + 3.17025i) 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} +(-1.96418 + 7.94070i) 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} +(-0.207433 - 0.421322i) 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} +(-5.41173 + 2.19818i) q^{34} +(-5.77002 + 0.832792i) q^{36} +(1.92303 + 0.624829i) q^{37} +(-1.44105 - 3.54775i) q^{38} +(-0.169271 - 0.520963i) q^{39} +(2.13805 - 6.58023i) q^{41} +(0.0966198 - 0.00693667i) q^{42} +8.04419i q^{43} +(8.06687 + 8.29162i) q^{44} +(3.35315 + 0.829422i) q^{46} +(8.51367 - 6.18554i) q^{47} +(-1.16640 - 0.0320578i) q^{48} -6.94486 q^{49} -1.20486i q^{51} +(0.536487 + 3.71707i) q^{52} +(-2.22765 - 3.06610i) q^{53} +(0.585926 - 2.36875i) q^{54} +(-0.660878 - 0.0657402i) q^{56} +0.789862 q^{57} +(-9.33773 + 0.670388i) q^{58} +(-6.66931 - 2.16699i) q^{59} +(1.54958 - 0.503489i) q^{61} +(-6.93660 + 2.81756i) q^{62} +(0.211505 - 0.650947i) q^{63} +(7.84323 + 1.57599i) q^{64} +(-2.21078 + 0.897995i) 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} +(-3.31136 + 7.55038i) 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} +(-0.752003 - 0.186013i) 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} +(0.0638644 - 0.121195i) q^{84} +(9.65874 + 6.01054i) q^{86} +(0.596730 - 1.83655i) q^{87} +(15.9833 - 3.49055i) q^{88} +(-3.51258 - 10.8106i) q^{89} +(-0.419342 - 0.136252i) q^{91} +(3.50134 - 3.40643i) q^{92} -1.54435i q^{93} +(-1.06572 - 14.8442i) q^{94} +(-0.910018 + 1.37656i) q^{96} +(-5.66961 + 4.11921i) q^{97} +(-5.18913 + 8.33878i) 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

Varieties

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Database

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