LMFDB - Embedded newform 1000.2.o.a.149.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1000.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			149.23
Character	$\chi$	$=$	1000.149
Dual form			1000.2.o.a.349.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20071 - 0.747190i) q^{2} +(0.235999 + 0.171463i) q^{3} +(0.883414 - 1.79432i) q^{4} +(0.411483 + 0.0295418i) q^{6} -0.234809i q^{7} +(-0.279973 - 2.81454i) q^{8} +(-0.900755 - 2.77224i) q^{9} +O(q^{10})$	\(q+(1.20071 - 0.747190i) q^{2} +(0.235999 + 0.171463i) q^{3} +(0.883414 - 1.79432i) q^{4} +(0.411483 + 0.0295418i) q^{6} -0.234809i q^{7} +(-0.279973 - 2.81454i) q^{8} +(-0.900755 - 2.77224i) q^{9} +(-5.50105 - 1.78740i) q^{11} +(0.516145 - 0.271985i) q^{12} +(-0.580270 - 1.78589i) q^{13} +(-0.175447 - 0.281938i) q^{14} +(-2.43916 - 3.17025i) q^{16} +(2.42773 + 3.34149i) q^{17} +(-3.15294 - 2.65562i) q^{18} +(-1.59154 - 2.19056i) q^{19} +(0.0402612 - 0.0554147i) q^{21} +(-7.94070 + 1.96418i) q^{22} +(2.32295 + 0.754772i) q^{23} +(0.416517 - 0.712234i) q^{24} +(-2.03113 - 1.71076i) q^{26} +(0.533191 - 1.64099i) q^{27} +(-0.421322 - 0.207433i) q^{28} +(3.89100 - 5.35551i) q^{29} +(-4.28302 + 3.11180i) q^{31} +(-5.29751 - 1.98404i) q^{32} +(-0.991770 - 1.36505i) q^{33} +(5.41173 + 2.19818i) q^{34} +(-5.77002 - 0.832792i) q^{36} +(-0.624829 - 1.92303i) q^{37} +(-3.54775 - 1.44105i) q^{38} +(0.169271 - 0.520963i) q^{39} +(2.13805 + 6.58023i) q^{41} +(0.00693667 - 0.0966198i) q^{42} +8.04419 q^{43} +(-8.06687 + 8.29162i) q^{44} +(3.35315 - 0.829422i) q^{46} +(6.18554 - 8.51367i) q^{47} +(-0.0320578 - 1.16640i) q^{48} +6.94486 q^{49} +1.20486i q^{51} +(-3.71707 - 0.536487i) q^{52} +(-3.06610 - 2.22765i) q^{53} +(-0.585926 - 2.36875i) q^{54} +(-0.660878 + 0.0657402i) q^{56} -0.789862i q^{57} +(0.670388 - 9.33773i) q^{58} +(6.66931 - 2.16699i) q^{59} +(1.54958 + 0.503489i) q^{61} +(-2.81756 + 6.93660i) q^{62} +(-0.650947 + 0.211505i) q^{63} +(-7.84323 + 1.57599i) q^{64} +(-2.21078 - 0.897995i) q^{66} +(-9.01003 + 6.54617i) q^{67} +(8.14038 - 1.40421i) q^{68} +(0.418799 + 0.576427i) q^{69} +(2.21139 + 1.60667i) q^{71} +(-7.55038 + 3.31136i) q^{72} +(14.3832 + 4.67339i) q^{73} +(-2.18711 - 1.84213i) q^{74} +(-5.33656 + 0.920553i) q^{76} +(-0.419697 + 1.29170i) q^{77} +(-0.186013 - 0.752003i) q^{78} +(-10.3770 - 7.53932i) q^{79} +(-6.66742 + 4.84416i) q^{81} +(7.48385 + 6.30342i) q^{82} +(-2.55253 + 1.85452i) q^{83} +(-0.0638644 - 0.121195i) q^{84} +(9.65874 - 6.01054i) q^{86} +(1.83655 - 0.596730i) q^{87} +(-3.49055 + 15.9833i) q^{88} +(3.51258 - 10.8106i) q^{89} +(-0.419342 + 0.136252i) q^{91} +(3.40643 - 3.50134i) q^{92} -1.54435 q^{93} +(1.06572 - 14.8442i) q^{94} +(-0.910018 - 1.37656i) q^{96} +(-4.11921 + 5.66961i) q^{97} +(8.33878 - 5.18913i) q^{98} +16.8602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.20071	−	0.747190i	0.849031	−	0.528343i
$2$	1.20071	−	0.747190i	0.849031	−	0.528343i
$3$	0.235999	+	0.171463i	0.136254	+	0.0989945i	0.653825	−	0.756646i	$-0.273163\pi$
$3$	0.235999	+	0.171463i	0.136254	+	0.0989945i	−0.517570	+	0.855641i	$0.673163\pi$
$4$	0.883414	−	1.79432i	0.441707	−	0.897159i
$5$		0			0
$5$		0			0
$6$	0.411483	+	0.0295418i	0.167987	+	0.0120604i
$7$		−	0.234809i		−	0.0887494i	−0.999015	−	0.0443747i	$-0.985870\pi$
$7$		−	0.234809i		−	0.0887494i	0.999015	−	0.0443747i	$-0.0141296\pi$
$8$	−0.279973	−	2.81454i	−0.0989855	−	0.995089i
$9$	−0.900755	−	2.77224i	−0.300252	−	0.924080i
$10$		0			0
$11$	−5.50105	−	1.78740i	−1.65863	−	0.538921i	−0.678045	−	0.735021i	$-0.737172\pi$
$11$	−5.50105	−	1.78740i	−1.65863	−	0.538921i	−0.980584	+	0.196099i	$0.937172\pi$
$12$	0.516145	−	0.271985i	0.148998	−	0.0785152i
$13$	−0.580270	−	1.78589i	−0.160938	−	0.495316i	0.837776	−	0.546014i	$-0.183855\pi$
$13$	−0.580270	−	1.78589i	−0.160938	−	0.495316i	−0.998714	+	0.0506981i	$0.983855\pi$
$14$	−0.175447	−	0.281938i	−0.0468902	−	0.0753510i
$15$		0			0
$16$	−2.43916	−	3.17025i	−0.609790	−	0.792563i
$17$	2.42773	+	3.34149i	0.588811	+	0.810429i	0.994627	−	0.103526i	$-0.0330124\pi$
$17$	2.42773	+	3.34149i	0.588811	+	0.810429i	−0.405815	+	0.913955i	$0.633012\pi$
$18$	−3.15294	−	2.65562i	−0.743154	−	0.625936i
$19$	−1.59154	−	2.19056i	−0.365124	−	0.502550i	0.586443	−	0.809990i	$-0.300528\pi$
$19$	−1.59154	−	2.19056i	−0.365124	−	0.502550i	−0.951567	+	0.307440i	$0.900528\pi$
$20$		0			0
$21$	0.0402612	−	0.0554147i	0.00878571	−	0.0120925i
$22$	−7.94070	+	1.96418i	−1.69296	+	0.418765i
$23$	2.32295	+	0.754772i	0.484369	+	0.157381i	0.541014	−	0.841013i	$-0.318041\pi$
$23$	2.32295	+	0.754772i	0.484369	+	0.157381i	−0.0566456	+	0.998394i	$0.518041\pi$
$24$	0.416517	−	0.712234i	0.0850211	−	0.145384i
$25$		0			0
$26$	−2.03113	−	1.71076i	−0.398338	−	0.335508i
$27$	0.533191	−	1.64099i	0.102613	−	0.315809i
$28$	−0.421322	−	0.207433i	−0.0796224	−	0.0392012i
$29$	3.89100	−	5.35551i	0.722541	−	0.994493i	−0.276894	−	0.960900i	$-0.589305\pi$
$29$	3.89100	−	5.35551i	0.722541	−	0.994493i	0.999436	−	0.0335922i	$-0.0106948\pi$
$30$		0			0
$31$	−4.28302	+	3.11180i	−0.769253	+	0.558895i	−0.901734	−	0.432291i	$-0.857705\pi$
$31$	−4.28302	+	3.11180i	−0.769253	+	0.558895i	0.132482	+	0.991185i	$0.457705\pi$
$32$	−5.29751	−	1.98404i	−0.936476	−	0.350732i
$33$	−0.991770	−	1.36505i	−0.172645	−	0.237625i
$34$	5.41173	+	2.19818i	0.928104	+	0.376985i
$35$		0			0
$36$	−5.77002	−	0.832792i	−0.961670	−	0.138799i
$37$	−0.624829	−	1.92303i	−0.102721	−	0.316144i	0.886468	−	0.462791i	$-0.153152\pi$
$37$	−0.624829	−	1.92303i	−0.102721	−	0.316144i	−0.989189	+	0.146647i	$0.953152\pi$
$38$	−3.54775	−	1.44105i	−0.575520	−	0.233770i
$39$	0.169271	−	0.520963i	0.0271051	−	0.0834208i
$40$		0			0
$41$	2.13805	+	6.58023i	0.333907	+	1.02766i	0.967258	+	0.253795i	$0.0816787\pi$
$41$	2.13805	+	6.58023i	0.333907	+	1.02766i	−0.633352	+	0.773864i	$0.718321\pi$
$42$	0.00693667	−	0.0966198i	0.00107035	−	0.0149088i
$43$	8.04419			1.22673			0.613364	−	0.789801i	$-0.289816\pi$
$43$	8.04419			1.22673			0.613364	+	0.789801i	$0.289816\pi$
$44$	−8.06687	+	8.29162i	−1.21613	+	1.25001i
$45$		0			0
$46$	3.35315	−	0.829422i	0.494395	−	0.122292i
$47$	6.18554	−	8.51367i	0.902254	−	1.24185i	−0.0674892	−	0.997720i	$-0.521499\pi$
$47$	6.18554	−	8.51367i	0.902254	−	1.24185i	0.969743	−	0.244126i	$-0.0785012\pi$
$48$	−0.0320578	−	1.16640i	−0.00462714	−	0.168356i
$49$	6.94486			0.992124
$50$		0			0
$51$			1.20486i			0.168714i
$52$	−3.71707	−	0.536487i	−0.515464	−	0.0743974i
$53$	−3.06610	−	2.22765i	−0.421161	−	0.305991i	0.356944	−	0.934126i	$-0.383819\pi$
$53$	−3.06610	−	2.22765i	−0.421161	−	0.305991i	−0.778105	+	0.628135i	$0.783819\pi$
$54$	−0.585926	−	2.36875i	−0.0797344	−	0.322347i
$55$		0			0
$56$	−0.660878	+	0.0657402i	−0.0883136	+	0.00878491i
$57$		−	0.789862i		−	0.104620i
$58$	0.670388	−	9.33773i	0.0880263	−	1.22610i
$59$	6.66931	−	2.16699i	0.868270	−	0.282118i	0.159192	−	0.987248i	$-0.449111\pi$
$59$	6.66931	−	2.16699i	0.868270	−	0.282118i	0.709078	+	0.705130i	$0.249111\pi$
$60$		0			0
$61$	1.54958	+	0.503489i	0.198403	+	0.0644651i	0.406533	−	0.913636i	$-0.366738\pi$
$61$	1.54958	+	0.503489i	0.198403	+	0.0644651i	−0.208130	+	0.978101i	$0.566738\pi$
$62$	−2.81756	+	6.93660i	−0.357831	+	0.880949i
$63$	−0.650947	+	0.211505i	−0.0820116	+	0.0266472i
$64$	−7.84323	+	1.57599i	−0.980404	+	0.196999i
$65$		0			0
$66$	−2.21078	−	0.897995i	−0.272129	−	0.110535i
$67$	−9.01003	+	6.54617i	−1.10075	+	0.799742i	−0.981182	−	0.193084i	$-0.938151\pi$
$67$	−9.01003	+	6.54617i	−1.10075	+	0.799742i	−0.119569	+	0.992826i	$0.538151\pi$
$68$	8.14038	−	1.40421i	0.987166	−	0.170286i
$69$	0.418799	+	0.576427i	0.0504174	+	0.0693936i
$70$		0			0
$71$	2.21139	+	1.60667i	0.262443	+	0.190676i	0.711223	−	0.702966i	$-0.248141\pi$
$71$	2.21139	+	1.60667i	0.262443	+	0.190676i	−0.448780	+	0.893642i	$0.648141\pi$
$72$	−7.55038	+	3.31136i	−0.889821	+	0.390248i
$73$	14.3832	+	4.67339i	1.68343	+	0.546979i	0.985572	−	0.169258i	$-0.0541371\pi$
$73$	14.3832	+	4.67339i	1.68343	+	0.546979i	0.697857	+	0.716237i	$0.254137\pi$
$74$	−2.18711	−	1.84213i	−0.254246	−	0.214144i
$75$		0			0
$76$	−5.33656	+	0.920553i	−0.612145	+	0.105595i
$77$	−0.419697	+	1.29170i	−0.0478290	+	0.147202i
$78$	−0.186013	−	0.752003i	−0.0210618	−	0.0851476i
$79$	−10.3770	−	7.53932i	−1.16750	−	0.848240i	−0.176795	−	0.984248i	$-0.556573\pi$
$79$	−10.3770	−	7.53932i	−1.16750	−	0.848240i	−0.990708	+	0.136008i	$0.956573\pi$
$80$		0			0
$81$	−6.66742	+	4.84416i	−0.740824	+	0.538240i
$82$	7.48385	+	6.30342i	0.826454	+	0.696097i
$83$	−2.55253	+	1.85452i	−0.280176	+	0.203560i	−0.718994	−	0.695016i	$-0.755397\pi$
$83$	−2.55253	+	1.85452i	−0.280176	+	0.203560i	0.438818	+	0.898576i	$0.355397\pi$
$84$	−0.0638644	−	0.121195i	−0.00696818	−	0.0132235i
$85$		0			0
$86$	9.65874	−	6.01054i	1.04153	−	0.648133i
$87$	1.83655	−	0.596730i	0.196899	−	0.0639762i
$88$	−3.49055	+	15.9833i	−0.372094	+	1.70383i
$89$	3.51258	−	10.8106i	0.372333	−	1.14592i	−0.572927	−	0.819606i	$-0.694192\pi$
$89$	3.51258	−	10.8106i	0.372333	−	1.14592i	0.945260	−	0.326317i	$-0.105808\pi$
$90$		0			0
$91$	−0.419342	+	0.136252i	−0.0439590	+	0.0142831i
$92$	3.40643	−	3.50134i	0.355145	−	0.365040i
$93$	−1.54435			−0.160141
$94$	1.06572	−	14.8442i	0.109920	−	1.53107i
$95$		0			0
$96$	−0.910018	−	1.37656i	−0.0928783	−	0.140495i
$97$	−4.11921	+	5.66961i	−0.418243	+	0.575661i	−0.965205	−	0.261496i	$-0.915784\pi$
$97$	−4.11921	+	5.66961i	−0.418243	+	0.575661i	0.546962	+	0.837157i	$0.315784\pi$
$98$	8.33878	−	5.18913i	0.842343	−	0.524182i
$99$			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	$-0.183358\pi$
$102$	0.900256	+	1.44668i	0.0891386	+	0.143243i
$103$	−6.88143	+	9.47147i	−0.678047	+	0.933252i	−0.999908	−	0.0135350i	$-0.995692\pi$
$103$	−6.88143	+	9.47147i	−0.678047	+	0.933252i	0.321861	+	0.946787i	$0.395692\pi$
$104$	−4.86398	+	2.13319i	−0.476953	+	0.209176i
$105$		0			0
$106$	−5.34597	−	0.383806i	−0.519247	−	0.0372785i
$107$	0.352640			0.0340910			0.0170455	−	0.999855i	$-0.494574\pi$
$107$	0.352640			0.0340910			0.0170455	+	0.999855i	$0.494574\pi$
$108$	−2.47344	−	2.40639i	−0.238007	−	0.231555i
$109$	−9.24706	+	3.00455i	−0.885708	+	0.287784i	−0.716325	−	0.697767i	$-0.754177\pi$
$109$	−9.24706	+	3.00455i	−0.885708	+	0.287784i	−0.169382	+	0.985550i	$0.554177\pi$
$110$		0			0
$111$	0.182270	−	0.560968i	0.0173003	−	0.0532448i
$112$	−0.744403	+	0.572737i	−0.0703395	+	0.0541185i
$113$	0.311428	−	0.101189i	0.0292967	−	0.00951907i	−0.294332	−	0.955703i	$-0.595097\pi$
$113$	0.311428	−	0.101189i	0.0292967	−	0.00951907i	0.323629	+	0.946184i	$0.395097\pi$
$114$	−0.590177	−	0.948396i	−0.0552752	−	0.0888254i
$115$		0			0
$116$	−6.17212	−	11.7128i	−0.573067	−	1.08751i
$117$	−4.42822	+	3.21729i	−0.409389	+	0.297439i
$118$	6.38876	−	7.58517i	0.588133	−	0.698272i
$119$	0.784611	−	0.570053i	0.0719252	−	0.0522567i
$120$		0			0
$121$	18.1676	+	13.1995i	1.65160	+	1.19995i
$122$	2.23680	−	0.553286i	0.202510	−	0.0500921i
$123$	−0.623691	+	1.91953i	−0.0562364	+	0.173078i
$124$	1.79988	+	10.4341i	0.161634	+	0.937010i
$125$		0			0
$126$	−0.623564	+	0.740338i	−0.0555515	+	0.0659545i
$127$	8.78610	+	2.85478i	0.779640	+	0.253320i	0.671687	−	0.740835i	$-0.265570\pi$
$127$	8.78610	+	2.85478i	0.779640	+	0.253320i	0.107954	+	0.994156i	$0.465570\pi$
$128$	−8.23989	+	7.75269i	−0.728310	+	0.685248i
$129$	1.89842	+	1.37928i	0.167147	+	0.121439i
$130$		0			0
$131$	4.46019	+	6.13893i	0.389689	+	0.536361i	0.958119	−	0.286371i	$-0.0924490\pi$
$131$	4.46019	+	6.13893i	0.389689	+	0.536361i	−0.568430	+	0.822732i	$0.692449\pi$
$132$	−3.32548	+	0.573644i	−0.289446	+	0.0499293i
$133$	−0.514364	+	0.373707i	−0.0446010	+	0.0324045i
$134$	−5.92721	+	14.5923i	−0.512033	+	1.26058i
$135$		0			0
$136$	8.72503	−	7.76847i	0.748165	−	0.666140i
$137$	12.5733	−	4.08531i	1.07421	−	0.349032i	0.282083	−	0.959390i	$-0.408975\pi$
$137$	12.5733	−	4.08531i	1.07421	−	0.349032i	0.792125	+	0.610358i	$0.208975\pi$
$138$	0.933557	+	0.379200i	0.0794696	+	0.0322796i
$139$	2.15160	+	0.699096i	0.182496	+	0.0592965i	0.398839	−	0.917021i	$-0.369413\pi$
$139$	2.15160	+	0.699096i	0.182496	+	0.0592965i	−0.216343	+	0.976317i	$0.569413\pi$
$140$		0			0
$141$	2.91957	−	0.948625i	0.245872	−	0.0798886i
$142$	3.85572	+	0.276815i	0.323565	+	0.0232298i
$143$			10.8614i			0.908278i
$144$	−6.59161	+	9.61756i	−0.549301	+	0.801463i
$145$		0			0
$146$	20.7620	−	5.13561i	1.71828	−	0.425026i
$147$	1.63898	+	1.19079i	0.135181	+	0.0982148i
$148$	−4.00251	−	0.577685i	−0.329004	−	0.0474854i
$149$		−	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	$0.496114\pi$
$152$	−5.71984	+	5.09274i	−0.463940	+	0.413076i
$153$	7.07661	−	9.74011i	0.572110	−	0.787441i
$154$	0.461207	+	1.86455i	0.0371651	+	0.150249i
$155$		0			0
$156$	−0.785237	−	0.763952i	−0.0628693	−	0.0611651i
$157$	20.8929			1.66744			0.833719	−	0.552189i	$-0.186207\pi$
$157$	20.8929			1.66744			0.833719	+	0.552189i	$0.186207\pi$
$158$	−18.0931	−	1.29896i	−1.43941	−	0.103340i
$159$	−0.341636	−	1.05145i	−0.0270935	−	0.0833852i
$160$		0			0
$161$	0.177227	−	0.545449i	0.0139675	−	0.0429874i
$162$	−4.38613	+	10.7983i	−0.344607	+	0.848392i
$163$	3.86624	+	11.8991i	0.302827	+	0.932006i	0.980479	+	0.196624i	$0.0629977\pi$
$163$	3.86624	+	11.8991i	0.302827	+	0.932006i	−0.677652	+	0.735383i	$0.737002\pi$
$164$	13.6958	+	1.97673i	1.06946	+	0.154356i
$165$		0			0
$166$	−1.67917	+	4.13397i	−0.130329	+	0.320858i
$167$	−12.6676	−	17.4355i	−0.980251	−	1.34920i	−0.936694	−	0.350149i	$-0.886131\pi$
$167$	−12.6676	−	17.4355i	−0.980251	−	1.34920i	−0.0435571	−	0.999051i	$-0.513869\pi$
$168$	−0.167239	−	0.0978019i	−0.0129028	−	0.00754558i
$169$	7.66454	−	5.56862i	0.589580	−	0.428355i
$170$		0			0
$171$	−4.63918	+	6.38529i	−0.354767	+	0.488295i
$172$	7.10634	−	14.4338i	0.541854	−	1.10057i
$173$	−0.492423	+	1.51552i	−0.0374382	+	0.115223i	−0.968029	−	0.250838i	$-0.919294\pi$
$173$	−0.492423	+	1.51552i	−0.0374382	+	0.115223i	0.930591	+	0.366061i	$0.119294\pi$
$174$	1.75929	−	2.08875i	0.133372	−	0.158348i
$175$		0			0
$176$	7.75144	+	21.7995i	0.584287	+	1.64320i
$177$	1.94551	+	0.632135i	0.146234	+	0.0475142i
$178$	−3.85999	−	15.6050i	−0.289319	−	1.16964i
$179$	−6.51305	+	8.96444i	−0.486808	+	0.670034i	−0.979795	−	0.200003i	$-0.935905\pi$
$179$	−6.51305	+	8.96444i	−0.486808	+	0.670034i	0.492987	+	0.870037i	$0.335905\pi$
$180$		0			0
$181$	11.7991	+	16.2401i	0.877020	+	1.20711i	0.977237	+	0.212149i	$0.0680461\pi$
$181$	11.7991	+	16.2401i	0.877020	+	1.20711i	−0.100217	+	0.994966i	$0.531954\pi$
$182$	−0.401702	+	0.476928i	−0.0297761	+	0.0353523i
$183$	0.279369	+	0.384519i	0.0206516	+	0.0284245i
$184$	1.47397	−	6.74934i	0.108663	−	0.497568i
$185$		0			0
$186$	−1.85432	+	1.15392i	−0.135965	+	0.0846097i
$187$	−7.38250	−	22.7210i	−0.539862	−	1.66152i
$188$	−9.81185	−	18.6199i	−0.715602	−	1.35800i
$189$	−0.385320	−	0.125198i	−0.0280279	−	0.00910682i
$190$		0			0
$191$	−5.85762	−	18.0279i	−0.423842	−	1.30445i	−0.904099	−	0.427324i	$-0.859456\pi$
$191$	−5.85762	−	18.0279i	−0.423842	−	1.30445i	0.480256	−	0.877128i	$-0.340544\pi$
$192$	−2.12122	−	0.972895i	−0.153086	−	0.0702127i
$193$		−	2.63353i		−	0.189566i	−0.995498	−	0.0947828i	$-0.969784\pi$
$193$		−	2.63353i		−	0.189566i	0.995498	−	0.0947828i	$-0.0302157\pi$
$194$	−0.709706	+	9.88539i	−0.0509540	+	0.709730i
$195$		0			0
$196$	6.13519	−	12.4613i	0.438228	−	0.890093i
$197$	20.4204	+	14.8363i	1.45489	+	1.05704i	0.984658	+	0.174498i	$0.0558303\pi$
$197$	20.4204	+	14.8363i	1.45489	+	1.05704i	0.470233	+	0.882542i	$0.344170\pi$
$198$	12.5978	+	20.2443i	0.895287	+	1.43870i
$199$	3.97231			0.281589			0.140795	−	0.990039i	$-0.455034\pi$
$199$	3.97231			0.281589			0.140795	+	0.990039i	$0.455034\pi$
$200$		0			0
$201$	−3.24879			−0.229152
$202$	−8.18055	−	13.1459i	−0.575581	−	0.924941i
$203$	−1.25752	−	0.913642i	−0.0882607	−	0.0641251i
$204$	2.16189	+	1.06439i	0.151363	+	0.0745219i
$205$		0			0
$206$	−1.18561	+	16.5142i	−0.0826056	+	1.15060i
$207$		−	7.11964i		−	0.494849i
$208$	−4.24634	+	6.19566i	−0.294430	+	0.429592i
$209$	4.83972	+	14.8951i	0.334770	+	1.03032i
$210$		0			0
$211$	−13.9414	−	4.52984i	−0.959766	−	0.311847i	−0.213088	−	0.977033i	$-0.568352\pi$
$211$	−13.9414	−	4.52984i	−0.959766	−	0.311847i	−0.746678	+	0.665186i	$0.768352\pi$
$212$	−6.70574	+	3.53362i	−0.460552	+	0.242690i
$213$	0.246401	+	0.758344i	0.0168831	+	0.0519609i
$214$	0.423419	−	0.263489i	0.0289443	−	0.0180118i
$215$		0			0
$216$	−4.76792	−	1.04125i	−0.324416	−	0.0708482i
$217$	0.730677	+	1.00569i	0.0496016	+	0.0682708i
$218$	−8.85807	+	10.5169i	−0.599944	+	0.712295i
$219$	2.59311	+	3.56911i	0.175226	+	0.241178i
$220$		0			0
$221$	4.55877	−	6.27461i	0.306656	−	0.422076i
$222$	−0.200297	−	0.809751i	−0.0134430	−	0.0543469i
$223$	16.2169	+	5.26920i	1.08597	+	0.352852i	0.796686	−	0.604393i	$-0.206584\pi$
$223$	16.2169	+	5.26920i	1.08597	+	0.352852i	0.289280	+	0.957245i	$0.406584\pi$
$224$	−0.465870	+	1.24390i	−0.0311272	+	0.0831117i
$225$		0			0
$226$	0.298328	−	0.354195i	0.0198445	−	0.0235607i
$227$	−4.52341	+	13.9216i	−0.300229	+	0.924011i	0.681185	+	0.732111i	$0.261465\pi$
$227$	−4.52341	+	13.9216i	−0.300229	+	0.924011i	−0.981414	+	0.191900i	$0.938535\pi$
$228$	−1.41726	−	0.697775i	−0.0938606	−	0.0462113i
$229$	−3.58252	+	4.93092i	−0.236740	+	0.325844i	−0.910812	−	0.412821i	$-0.864544\pi$
$229$	−3.58252	+	4.93092i	−0.236740	+	0.325844i	0.674072	+	0.738665i	$0.264544\pi$
$230$		0			0
$231$	−0.320527	+	0.232876i	−0.0210891	+	0.0153221i
$232$	−16.1626	−	9.45197i	−1.06113	−	0.620552i
$233$	−4.19480	−	5.77365i	−0.274811	−	0.378244i	0.649196	−	0.760621i	$-0.275106\pi$
$233$	−4.19480	−	5.77365i	−0.274811	−	0.378244i	−0.924006	+	0.382377i	$0.875106\pi$
$234$	−2.91309	+	7.17176i	−0.190434	+	0.468833i
$235$		0			0
$236$	2.00349	−	13.8812i	0.130416	−	0.903590i
$237$	−1.15624	−	3.55855i	−0.0751060	−	0.231153i
$238$	0.516153	−	1.27072i	0.0334572	−	0.0823687i
$239$	−1.65706	+	5.09989i	−0.107186	+	0.329885i	−0.990237	−	0.139392i	$-0.955485\pi$
$239$	−1.65706	+	5.09989i	−0.107186	+	0.329885i	0.883051	+	0.469276i	$0.155485\pi$
$240$		0			0
$241$	−0.583541	−	1.79595i	−0.0375892	−	0.115688i	0.930501	−	0.366289i	$-0.119372\pi$
$241$	−0.583541	−	1.79595i	−0.0375892	−	0.115688i	−0.968090	+	0.250601i	$0.919372\pi$
$242$	31.6765	+	2.27417i	2.03624	+	0.146189i
$243$	−7.58043			−0.486285
$244$	2.27234	−	2.33565i	0.145472	−	0.149525i
$245$		0			0
$246$	0.685377	+	2.77081i	0.0436980	+	0.176660i
$247$	−2.98858	+	4.11342i	−0.190159	+	0.261731i
$248$	9.95739	+	11.1835i	0.632295	+	0.710152i
$249$	−0.920377			−0.0583265
$250$		0			0
$251$			4.55040i			0.287219i	0.989634	+	0.143609i	$0.0458709\pi$
$251$			4.55040i			0.287219i	−0.989634	+	0.143609i	$0.954129\pi$
$252$	−0.195547	+	1.35485i	−0.0123183	+	0.0853477i
$253$	−11.4296	−	8.30408i	−0.718572	−	0.522073i
$254$	12.6826	−	3.13713i	0.795779	−	0.196841i
$255$		0			0
$256$	−4.10099	+	15.4655i	−0.256312	+	0.966594i
$257$			6.99079i			0.436074i	0.975941	+	0.218037i	$0.0699653\pi$
$257$			6.99079i			0.436074i	−0.975941	+	0.218037i	$0.930035\pi$
$258$	3.31004	+	0.237639i	0.206074	+	0.0147948i
$259$	−0.451544	+	0.146716i	−0.0280576	+	0.00911646i
$260$		0			0
$261$	−18.3516	−	5.96279i	−1.13593	−	0.369088i
$262$	9.94235	+	4.03847i	0.614240	+	0.249497i
$263$	−21.5131	+	6.99005i	−1.32656	+	0.431025i	−0.884742	−	0.466081i	$-0.845665\pi$
$263$	−21.5131	+	6.99005i	−1.32656	+	0.431025i	−0.441816	+	0.897106i	$0.645665\pi$
$264$	−3.56432	+	3.17355i	−0.219369	+	0.195319i
$265$		0			0
$266$	−0.338372	+	0.833042i	−0.0207469	+	0.0510771i
$267$	2.68259	−	1.94902i	0.164172	−	0.119278i
$268$	3.78634	+	21.9499i	0.231287	+	1.34080i
$269$	3.68963	+	5.07835i	0.224961	+	0.309632i	0.906546	−	0.422106i	$-0.138709\pi$
$269$	3.68963	+	5.07835i	0.224961	+	0.309632i	−0.681585	+	0.731739i	$0.738709\pi$
$270$		0			0
$271$	−2.75055	−	1.99839i	−0.167084	−	0.121393i	0.501101	−	0.865389i	$-0.332928\pi$
$271$	−2.75055	−	1.99839i	−0.167084	−	0.121393i	−0.668185	+	0.743995i	$0.732928\pi$
$272$	4.67172	−	15.8469i	0.283265	−	0.960862i
$273$	−0.122327	−	0.0397464i	−0.00740355	−	0.00240556i
$274$	12.0444	−	14.2999i	0.727628	−	0.863890i
$275$		0			0
$276$	1.40427	−	0.242235i	0.0845269	−	0.0145808i
$277$	7.95552	−	24.4846i	0.478001	−	1.47114i	−0.363867	−	0.931451i	$-0.618544\pi$
$277$	7.95552	−	24.4846i	0.478001	−	1.47114i	0.841868	−	0.539684i	$-0.181456\pi$
$278$	3.10580	−	0.768239i	0.186274	−	0.0460759i
$279$	12.4846	+	9.07059i	0.747433	+	0.543042i
$280$		0			0
$281$	−3.16034	+	2.29612i	−0.188530	+	0.136975i	−0.678047	−	0.735019i	$-0.737173\pi$
$281$	−3.16034	+	2.29612i	−0.188530	+	0.136975i	0.489517	+	0.871994i	$0.337173\pi$
$282$	2.79675	−	3.32050i	0.166544	−	0.197733i
$283$	−1.03911	+	0.754960i	−0.0617689	+	0.0448777i	−0.618241	−	0.785988i	$-0.712155\pi$
$283$	−1.03911	+	0.754960i	−0.0617689	+	0.0448777i	0.556472	+	0.830866i	$0.312155\pi$
$284$	4.83644	−	2.54858i	0.286990	−	0.151230i
$285$		0			0
$286$	8.11555	+	13.0414i	0.479882	+	0.771156i
$287$	1.54510	−	0.502032i	0.0912041	−	0.0296340i
$288$	−0.728471	+	16.4731i	−0.0429256	+	0.970686i
$289$	−0.0183581	+	0.0565005i	−0.00107989	+	0.00332356i
$290$		0			0
$291$	−1.94426	+	0.631729i	−0.113975	+	0.0370326i
$292$	21.0919	−	21.6795i	1.23431	−	1.26870i
$293$	−8.55020			−0.499508			−0.249754	−	0.968309i	$-0.580350\pi$
$293$	−8.55020			−0.499508			−0.249754	+	0.968309i	$0.580350\pi$
$294$	2.85769	+	0.205164i	0.166664	+	0.0119654i
$295$		0			0
$296$	−5.23749	+	2.29700i	−0.304423	+	0.133510i
$297$	−5.86622	+	8.07416i	−0.340393	+	0.468510i
$298$	−11.5052	−	18.4886i	−0.666481	−	1.07101i
$299$		−	4.58650i		−	0.265244i
$300$		0			0
$301$		−	1.88885i		−	0.108871i
$302$	0.360288	−	0.224204i	0.0207323	−	0.0129015i
$303$	1.87725	−	2.58382i	0.107845	−	0.148436i
$304$	−3.06262	+	10.3887i	−0.175653	+	0.595834i
$305$		0			0
$306$	1.21924	−	16.9826i	0.0696994	−	0.970832i
$307$	−11.0920			−0.633052			−0.316526	−	0.948584i	$-0.602517\pi$
$307$	−11.0920			−0.633052			−0.316526	+	0.948584i	$0.602517\pi$
$308$	1.94695	+	1.89417i	0.110938	+	0.107930i
$309$	−3.24802	+	1.05535i	−0.184774	+	0.0600366i
$310$		0			0
$311$	9.28886	−	28.5882i	0.526723	−	1.62109i	−0.234160	−	0.972198i	$-0.575234\pi$
$311$	9.28886	−	28.5882i	0.526723	−	1.62109i	0.760883	−	0.648889i	$-0.224766\pi$
$312$	−1.51366	−	0.330564i	−0.0856941	−	0.0187145i
$313$	−0.0349980	+	0.0113715i	−0.00197820	+	0.000642758i	−0.310006	−	0.950735i	$-0.600331\pi$
$313$	−0.0349980	+	0.0113715i	−0.00197820	+	0.000642758i	0.308028	+	0.951377i	$0.400331\pi$
$314$	25.0864	−	15.6110i	1.41571	−	0.880980i
$315$		0			0
$316$	−22.6951	+	11.9593i	−1.27670	+	0.672762i
$317$	−13.1594	+	9.56085i	−0.739104	+	0.536991i	−0.892431	−	0.451185i	$-0.851002\pi$
$317$	−13.1594	+	9.56085i	−0.739104	+	0.536991i	0.153326	+	0.988176i	$0.451002\pi$
$318$	−1.19584	−	1.00722i	−0.0670592	−	0.0564819i
$319$	−30.9770	+	22.5061i	−1.73438	+	1.26010i
$320$		0			0
$321$	0.0832228	+	0.0604649i	0.00464505	+	0.00337482i
$322$	−0.194756	−	0.787350i	−0.0108533	−	0.0438773i
$323$	3.45591	−	10.6362i	0.192292	−	0.591814i
$324$	2.80189	+	16.2429i	0.155660	+	0.902382i
$325$		0			0
$326$	13.5331	+	11.3985i	0.749529	+	0.631305i
$327$	−2.69747	−	0.876461i	−0.149170	−	0.0484684i
$328$	17.9217	−	7.85989i	0.989560	−	0.433990i
$329$	−1.99909	−	1.45242i	−0.110213	−	0.0800746i
$330$		0			0
$331$	13.3539	+	18.3800i	0.733995	+	1.01026i	0.998942	+	0.0459939i	$0.0146455\pi$
$331$	13.3539	+	18.3800i	0.733995	+	1.01026i	−0.264947	+	0.964263i	$0.585355\pi$
$332$	1.07266	+	6.21836i	0.0588700	+	0.341277i
$333$	−4.76827	+	3.46435i	−0.261300	+	0.189845i
$334$	−28.2378	−	11.4699i	−1.54510	−	0.627603i
$335$		0			0
$336$	−0.273882	+	0.00752745i	−0.0149415	+	0.000410656i
$337$	−17.8926	+	5.81367i	−0.974674	+	0.316691i	−0.752701	−	0.658362i	$-0.771249\pi$
$337$	−17.8926	+	5.81367i	−0.974674	+	0.316691i	−0.221972	+	0.975053i	$0.571249\pi$
$338$	5.04209	−	12.4132i	0.274253	−	0.675188i
$339$	0.0908470	+	0.0295180i	0.00493413	+	0.00160320i
$340$		0			0
$341$	29.1231	−	9.46267i	1.57711	−	0.512433i
$342$	−0.799293	+	11.1332i	−0.0432208	+	0.602016i
$343$		−	3.27438i		−	0.176800i
$344$	−2.25216	−	22.6407i	−0.121428	−	1.22070i
$345$		0			0
$346$	0.541126	+	2.18764i	0.0290911	+	0.117608i
$347$	23.8972	+	17.3624i	1.28287	+	0.932060i	0.999636	−	0.0269903i	$-0.00859232\pi$
$347$	23.8972	+	17.3624i	1.28287	+	0.932060i	0.283235	+	0.959051i	$0.408592\pi$
$348$	0.551706	−	3.82251i	0.0295746	−	0.204908i
$349$		−	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
$352$	25.5956	+	20.3831i	1.36425	+	1.08642i
$353$	4.79864	−	6.60477i	0.255406	−	0.351536i	−0.661989	−	0.749513i	$-0.730288\pi$
$353$	4.79864	−	6.60477i	0.255406	−	0.351536i	0.917395	+	0.397977i	$0.130288\pi$
$354$	2.80832	−	0.694656i	0.149261	−	0.0369205i
$355$		0			0
$356$	−16.2946	−	15.8529i	−0.863614	−	0.840204i
$357$	0.282911			0.0149732
$358$	−1.12215	+	15.6302i	−0.0593072	+	0.826081i
$359$	−9.42480	−	29.0065i	−0.497422	−	1.53091i	−0.813148	−	0.582056i	$-0.802248\pi$
$359$	−9.42480	−	29.0065i	−0.497422	−	1.53091i	0.315727	−	0.948850i	$-0.397752\pi$
$360$		0			0
$361$	3.60574	−	11.0973i	0.189776	−	0.584071i
$362$	26.3017	+	10.6835i	1.38239	+	0.561510i
$363$	2.02430	+	6.23015i	0.106248	+	0.326998i
$364$	−0.125972	+	0.872801i	−0.00660273	+	0.0457472i
$365$		0			0
$366$	0.622751	+	0.252954i	0.0325517	+	0.0132221i
$367$	4.40881	+	6.06821i	0.230138	+	0.316758i	0.908432	−	0.418033i	$-0.137280\pi$
$367$	4.40881	+	6.06821i	0.230138	+	0.316758i	−0.678294	+	0.734791i	$0.737280\pi$
$368$	−3.27323	−	9.20535i	−0.170629	−	0.479862i
$369$	16.3161	−	11.8543i	0.849383	−	0.617113i
$370$		0			0
$371$	−0.523072	+	0.719947i	−0.0271565	+	0.0373778i
$372$	−1.36430	+	2.77105i	−0.0707356	+	0.143672i
$373$	3.94238	−	12.1334i	0.204129	−	0.628243i	−0.795619	−	0.605797i	$-0.792854\pi$
$373$	3.94238	−	12.1334i	0.204129	−	0.628243i	0.999748	−	0.0224465i	$-0.00714553\pi$
$374$	−25.8412	−	21.7652i	−1.33621	−	1.12545i
$375$		0			0
$376$	−25.6938	−	15.0258i	−1.32506	−	0.774898i
$377$	−11.8222	−	3.84125i	−0.608872	−	0.197834i
$378$	−0.556205	+	0.137581i	−0.0286081	+	0.00707639i
$379$	7.20040	−	9.91051i	0.369860	−	0.509069i	−0.583003	−	0.812470i	$-0.698122\pi$
$379$	7.20040	−	9.91051i	0.369860	−	0.509069i	0.952863	+	0.303402i	$0.0981224\pi$
$380$		0			0
$381$	1.58402	+	2.18022i	0.0811519	+	0.111696i
$382$	−20.5036	−	17.2695i	−1.04905	−	0.883586i
$383$	−15.8262	−	21.7829i	−0.808681	−	1.11305i	−0.991525	−	0.129912i	$-0.958530\pi$
$383$	−15.8262	−	21.7829i	−0.808681	−	1.11305i	0.182844	−	0.983142i	$-0.441470\pi$
$384$	−3.27391	+	0.416790i	−0.167071	+	0.0212692i
$385$		0			0
$386$	−1.96775	−	3.16211i	−0.100156	−	0.160947i
$387$	−7.24584	−	22.3004i	−0.368327	−	1.13359i
$388$	6.53412	+	12.3998i	0.331720	+	0.629504i
$389$	9.06656	+	2.94590i	0.459693	+	0.149363i	0.529703	−	0.848183i	$-0.322303\pi$
$389$	9.06656	+	2.94590i	0.459693	+	0.149363i	−0.0700104	+	0.997546i	$0.522303\pi$
$390$		0			0
$391$	3.11744	+	9.59449i	0.157656	+	0.485214i
$392$	−1.94438	−	19.5466i	−0.0982058	−	0.987251i
$393$			2.21354i			0.111658i
$394$	35.6045	+	2.55617i	1.79373	+	0.128778i
$395$		0			0
$396$	30.2526	+	14.8946i	1.52025	+	0.748480i
$397$	−18.8253	−	13.6774i	−0.944816	−	0.686449i	0.00475885	−	0.999989i	$-0.498485\pi$
$397$	−18.8253	−	13.6774i	−0.944816	−	0.686449i	−0.949575	+	0.313539i	$0.898485\pi$
$398$	4.76959	−	2.96807i	0.239078	−	0.148776i
$399$	−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	$0.400705\pi$
$402$	−3.90086	+	2.42746i	−0.194557	+	0.121071i
$403$	8.04262	+	5.84330i	0.400631	+	0.291076i
$404$	−19.6449	−	9.67198i	−0.977372	−	0.481199i
$405$		0			0
$406$	−2.19258	−	0.157413i	−0.108816	−	0.00781228i
$407$			11.6955i			0.579724i
$408$	3.39111	−	0.337327i	0.167885	−	0.0167002i
$409$	9.76563	+	30.0555i	0.482879	+	1.48615i	0.835029	+	0.550206i	$0.185451\pi$
$409$	9.76563	+	30.0555i	0.482879	+	1.48615i	−0.352150	+	0.935944i	$0.614549\pi$
$410$		0			0
$411$	3.66777	+	1.19173i	0.180918	+	0.0587837i
$412$	10.9157	+	20.7147i	0.537778	+	1.02054i
$413$	−0.508829	−	1.56601i	−0.0250378	−	0.0770585i
$414$	−5.31972	−	8.54863i	−0.261450	−	0.420142i
$415$		0			0
$416$	−0.469284	+	10.6120i	−0.0230085	+	0.520297i
$417$	0.387905	+	0.533906i	0.0189958	+	0.0261455i
$418$	16.9406	+	14.2685i	0.828591	+	0.697897i
$419$	−5.07417	−	6.98399i	−0.247889	−	0.341190i	0.666881	−	0.745164i	$-0.267629\pi$
$419$	−5.07417	−	6.98399i	−0.247889	−	0.341190i	−0.914771	+	0.403973i	$0.867629\pi$
$420$		0			0
$421$	−7.53026	+	10.3645i	−0.367002	+	0.505135i	−0.952083	−	0.305840i	$-0.901063\pi$
$421$	−7.53026	+	10.3645i	−0.367002	+	0.505135i	0.585081	+	0.810975i	$0.301063\pi$
$422$	−20.1242	+	4.97786i	−0.979633	+	0.242318i
$423$	−29.1736	−	9.47907i	−1.41847	−	0.460888i
$424$	−5.41138	+	9.25332i	−0.262800	+	0.449381i
$425$		0			0
$426$	0.862483	+	0.726443i	0.0417874	+	0.0351963i
$427$	0.118224	−	0.363855i	0.00572124	−	0.0176082i
$428$	0.311527	−	0.632749i	0.0150582	−	0.0305851i
$429$	−1.86234	+	2.56329i	−0.0899145	+	0.123757i
$430$		0			0
$431$	−24.3298	+	17.6766i	−1.17193	+	0.851454i	−0.991238	−	0.132087i	$-0.957832\pi$
$431$	−24.3298	+	17.6766i	−1.17193	+	0.851454i	−0.180688	+	0.983541i	$0.557832\pi$
$432$	−6.50290	+	2.31230i	−0.312871	+	0.111251i
$433$	0.945079	+	1.30079i	0.0454176	+	0.0625120i	0.831122	−	0.556090i	$-0.187699\pi$
$433$	0.945079	+	1.30079i	0.0454176	+	0.0625120i	−0.785704	+	0.618602i	$0.787699\pi$
$434$	1.62877	+	0.661589i	0.0781837	+	0.0317573i
$435$		0			0
$436$	−2.77785	+	19.2464i	−0.133035	+	0.921737i
$437$	−2.04369	−	6.28982i	−0.0977628	−	0.300883i
$438$	5.78039	+	2.34793i	0.276198	+	0.112188i
$439$	−11.7350	+	36.1165i	−0.560079	+	1.72374i	0.122061	+	0.992523i	$0.461050\pi$
$439$	−11.7350	+	36.1165i	−0.560079	+	1.72374i	−0.682139	+	0.731222i	$0.738950\pi$
$440$		0			0
$441$	−6.25562	−	19.2528i	−0.297887	−	0.916801i
$442$	0.785440	−	10.9403i	0.0373596	−	0.520376i
$443$	19.5670			0.929654			0.464827	−	0.885402i	$-0.346117\pi$
$443$	19.5670			0.929654			0.464827	+	0.885402i	$0.346117\pi$
$444$	−0.845537	−	0.822617i	−0.0401274	−	0.0390397i
$445$		0			0
$446$	23.4089	−	5.79034i	1.10845	−	0.274181i
$447$	2.64020	−	3.63392i	0.124877	−	0.171879i
$448$	0.370056	+	1.84166i	0.0174835	+	0.0870103i
$449$	−33.2573			−1.56951			−0.784755	−	0.619806i	$-0.787211\pi$
$449$	−33.2573			−1.56951			−0.784755	+	0.619806i	$0.787211\pi$
$450$		0			0
$451$		−	40.0197i		−	1.88445i
$452$	0.0935543	−	0.648193i	0.00440042	−	0.0304884i
$453$	0.0708145	+	0.0514498i	0.00332716	+	0.00241732i
$454$	4.97080	+	20.0957i	0.233291	+	0.943138i
$455$		0			0
$456$	−2.22310	+	0.221140i	−0.104106	+	0.0103558i
$457$			15.5897i			0.729254i	0.931154	+	0.364627i	$0.118803\pi$
$457$			15.5897i			0.729254i	−0.931154	+	0.364627i	$0.881197\pi$
$458$	−0.617240	+	8.59744i	−0.0288417	+	0.401732i
$459$	6.77780	−	2.20224i	0.316361	−	0.102792i
$460$		0			0
$461$	5.51241	+	1.79109i	0.256739	+	0.0834194i	0.434558	−	0.900644i	$-0.356904\pi$
$461$	5.51241	+	1.79109i	0.256739	+	0.0834194i	−0.177820	+	0.984063i	$0.556904\pi$
$462$	−0.210857	+	0.519112i	−0.00980996	+	0.0241513i
$463$	11.3046	−	3.67309i	0.525370	−	0.170703i	−0.0343111	−	0.999411i	$-0.510924\pi$
$463$	11.3046	−	3.67309i	0.525370	−	0.170703i	0.559681	+	0.828708i	$0.310924\pi$
$464$	−26.4691	+	0.727484i	−1.22880	+	0.0337726i
$465$		0			0
$466$	−9.35076	−	3.79817i	−0.433166	−	0.175947i
$467$	−20.1818	+	14.6630i	−0.933903	+	0.678521i	−0.946945	−	0.321394i	$-0.895848\pi$
$467$	−20.1818	+	14.6630i	−0.933903	+	0.678521i	0.0130420	+	0.999915i	$0.495848\pi$
$468$	1.86090	+	10.7878i	0.0860199	+	0.498668i
$469$	1.53710	+	2.11564i	0.0709767	+	0.0976910i
$470$		0			0
$471$	4.93072	+	3.58238i	0.227196	+	0.165067i
$472$	−7.96630	−	18.1643i	−0.366679	−	0.836080i
$473$	−44.2515	−	14.3782i	−2.03468	−	0.661109i
$474$	−4.04723	−	3.40886i	−0.185895	−	0.156574i
$475$		0			0
$476$	−0.329721	−	1.91143i	−0.0151127	−	0.0876105i
$477$	−3.41377	+	10.5065i	−0.156306	+	0.481060i
$478$	1.82094	+	7.36163i	0.0832881	+	0.336713i
$479$	12.4287	+	9.02994i	0.567880	+	0.412589i	0.834334	−	0.551259i	$-0.185852\pi$
$479$	12.4287	+	9.02994i	0.567880	+	0.412589i	−0.266455	+	0.963847i	$0.585852\pi$
$480$		0			0
$481$	−3.07174	+	2.23175i	−0.140059	+	0.101759i
$482$	−2.04258	−	1.72041i	−0.0930372	−	0.0783624i
$483$	0.135350	−	0.0983377i	0.00615865	−	0.00447452i
$484$	39.7336	−	20.9378i	1.80607	−	0.951717i
$485$		0			0
$486$	−9.10191	+	5.66403i	−0.412871	+	0.256925i
$487$	−21.4527	+	6.97042i	−0.972117	+	0.315860i	−0.751670	−	0.659539i	$-0.770751\pi$
$487$	−21.4527	+	6.97042i	−0.972117	+	0.315860i	−0.220447	+	0.975399i	$0.570751\pi$
$488$	0.983246	−	4.50231i	0.0445095	−	0.203810i
$489$	−1.12782	+	3.47109i	−0.0510020	+	0.156968i
$490$		0			0
$491$	7.25634	−	2.35773i	0.327474	−	0.106403i	−0.140666	−	0.990057i	$-0.544924\pi$
$491$	7.25634	−	2.35773i	0.327474	−	0.106403i	0.468140	+	0.883654i	$0.344924\pi$
$492$	2.89326	+	2.81484i	0.130438	+	0.126903i
$493$	27.3417			1.23141
$494$	−0.514907	+	7.17207i	−0.0231668	+	0.322687i
$495$		0			0
$496$	20.3121	+	5.98808i	0.912042	+	0.268873i
$497$	0.377259	−	0.519253i	0.0169224	−	0.0232917i
$498$	−1.10511	+	0.687697i	−0.0495210	+	0.0308164i
$499$			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
$502$	3.40001	+	5.46371i	0.151750	+	0.243857i
$503$	18.0952	−	24.9059i	0.806825	−	1.11050i	−0.184980	−	0.982742i	$-0.559222\pi$
$503$	18.0952	−	24.9059i	0.806825	−	1.11050i	0.991805	−	0.127757i	$-0.0407778\pi$
$504$	0.777537	+	1.77290i	0.0346343	+	0.0789711i
$505$		0			0
$506$	−19.9284	−	1.43073i	−0.885923	−	0.0636035i
$507$	2.76364			0.122738
$508$	12.8841	−	13.2431i	0.571641	−	0.587568i
$509$	−3.29675	+	1.07118i	−0.146126	+	0.0474792i	−0.381167	−	0.924506i	$-0.624478\pi$
$509$	−3.29675	+	1.07118i	−0.146126	+	0.0474792i	0.235041	+	0.971986i	$0.424478\pi$
$510$		0			0
$511$	1.09735	−	3.37731i	0.0485441	−	0.149403i
$512$	6.63157	+	21.6338i	0.293077	+	0.956089i
$513$	−4.44330	+	1.44371i	−0.196176	+	0.0637416i
$514$	5.22345	+	8.39392i	0.230397	+	0.370240i
$515$		0			0
$516$	4.15197	−	2.18790i	0.182780	−	0.0963168i
$517$	−49.2443	+	35.7781i	−2.16576	+	1.57352i
$518$	−0.432549	+	0.513552i	−0.0190051	+	0.0225642i
$519$	−0.376068	+	0.273229i	−0.0165076	+	0.0119934i
$520$		0			0
$521$	−32.2980	−	23.4659i	−1.41500	−	1.02806i	−0.992571	−	0.121663i	$-0.961177\pi$
$521$	−32.2980	−	23.4659i	−1.41500	−	1.02806i	−0.422430	−	0.906395i	$-0.638823\pi$
$522$	−26.4903	+	6.55254i	−1.15945	+	0.286797i
$523$	−1.93267	+	5.94816i	−0.0845099	+	0.260095i	−0.984378	−	0.176067i	$-0.943662\pi$
$523$	−1.93267	+	5.94816i	−0.0845099	+	0.260095i	0.899868	+	0.436162i	$0.143662\pi$
$524$	14.9554	−	2.57980i	0.653329	−	0.112699i
$525$		0			0
$526$	−20.6082	+	24.4674i	−0.898559	+	1.06683i
$527$	−20.7960	−	6.75704i	−0.905890	−	0.294341i
$528$	−1.90848	+	6.47375i	−0.0830558	+	0.281734i
$529$	−13.7810	−	10.0125i	−0.599173	−	0.435325i
$530$		0			0
$531$	−12.0148	−	16.5370i	−0.521399	−	0.717644i
$532$	0.216154	+	1.25307i	0.00937147	+	0.0543275i
$533$	10.5109	−	7.63661i	0.455277	−	0.330778i
$534$	1.76473	−	4.34462i	0.0763674	−	0.188010i
$535$		0			0
$536$	20.9470	+	23.5263i	0.904773	+	1.01618i
$537$	−3.07415	+	0.998852i	−0.132659	+	0.0431036i
$538$	8.22468	+	3.34077i	0.354591	+	0.144031i
$539$	−38.2040	−	12.4132i	−1.64556	−	0.534676i
$540$		0			0
$541$	−19.5034	+	6.33705i	−0.838518	+	0.272451i	−0.696629	−	0.717432i	$-0.745318\pi$
$541$	−19.5034	+	6.33705i	−0.838518	+	0.272451i	−0.141889	+	0.989883i	$0.545318\pi$
$542$	−4.79579	−	0.344306i	−0.205997	−	0.0147892i
$543$			5.85576i			0.251295i
$544$	−6.23129	−	22.5183i	−0.267164	−	0.965462i
$545$		0			0
$546$	−0.176577	+	0.0436774i	−0.00755680	+	0.00186922i
$547$	17.9423	+	13.0358i	0.767157	+	0.557372i	0.901097	−	0.433617i	$-0.142763\pi$
$547$	17.9423	+	13.0358i	0.767157	+	0.557372i	−0.133940	+	0.990989i	$0.542763\pi$
$548$	3.77707	−	26.1695i	0.161348	−	1.11791i
$549$		−	4.74932i		−	0.202696i
$550$		0			0
$551$	−17.9243			−0.763599
$552$	1.50512	−	1.34011i	0.0640622	−	0.0570388i
$553$	−1.77030	+	2.43661i	−0.0752808	+	0.103615i
$554$	−8.74235	−	35.3432i	−0.371427	−	1.50159i
$555$		0			0
$556$	3.15515	−	3.24306i	0.133808	−	0.137536i
$557$	36.8641			1.56198			0.780991	−	0.624543i	$-0.214715\pi$
$557$	36.8641			1.56198			0.780991	+	0.624543i	$0.214715\pi$
$558$	21.7678	+	1.56279i	0.921506	+	0.0661581i
$559$	−4.66780	−	14.3660i	−0.197427	−	0.607617i
$560$		0			0
$561$	2.15356	−	6.62797i	0.0909233	−	0.279833i
$562$	−2.07901	+	5.11835i	−0.0876979	+	0.215905i
$563$	−12.7139	−	39.1294i	−0.535828	−	1.64911i	−0.741854	−	0.670561i	$-0.766053\pi$
$563$	−12.7139	−	39.1294i	−0.535828	−	1.64911i	0.206027	−	0.978546i	$-0.433947\pi$
$564$	0.877050	−	6.07666i	0.0369305	−	0.255874i
$565$		0			0
$566$	−0.683576	+	1.68290i	−0.0287329	+	0.0707378i
$567$	1.13745	+	1.56557i	0.0477685	+	0.0657477i
$568$	3.90289	−	6.67385i	0.163762	−	0.280028i
$569$	−2.43983	+	1.77264i	−0.102283	+	0.0743130i	−0.637751	−	0.770242i	$-0.720135\pi$
$569$	−2.43983	+	1.77264i	−0.102283	+	0.0743130i	0.535468	+	0.844555i	$0.320135\pi$
$570$		0			0
$571$	−8.11104	+	11.1639i	−0.339436	+	0.467194i	−0.944277	−	0.329153i	$-0.893237\pi$
$571$	−8.11104	+	11.1639i	−0.339436	+	0.467194i	0.604840	+	0.796347i	$0.293237\pi$
$572$	19.4889	+	9.59513i	0.814870	+	0.401192i
$573$	1.70873	−	5.25893i	0.0713833	−	0.219695i
$574$	1.48010	−	1.75728i	0.0617782	−	0.0733473i
$575$		0			0
$576$	11.4338	+	20.3237i	0.476410	+	0.846822i
$577$	−12.5473	−	4.07686i	−0.522351	−	0.169722i	0.0359612	−	0.999353i	$-0.488551\pi$
$577$	−12.5473	−	4.07686i	−0.522351	−	0.169722i	−0.558312	+	0.829631i	$0.688551\pi$
$578$	0.0201738	+	0.0815578i	0.000839121	+	0.00339236i
$579$	0.451554	−	0.621511i	0.0187659	−	0.0258291i
$580$		0			0
$581$	0.435458	+	0.599356i	0.0180658	+	0.0248655i
$582$	−1.86247	+	2.21126i	−0.0772020	+	0.0916595i
$583$	12.8850	+	17.7347i	0.533644	+	0.734498i
$584$	9.12652	−	41.7905i	0.377658	−	1.72930i
$585$		0			0
$586$	−10.2663	+	6.38863i	−0.424098	+	0.263912i
$587$	−8.38908	−	25.8189i	−0.346254	−	1.06566i	−0.960909	−	0.276865i	$-0.910705\pi$
$587$	−8.38908	−	25.8189i	−0.346254	−	1.06566i	0.614655	−	0.788796i	$-0.289295\pi$
$588$	3.58456	−	1.88890i	0.147825	−	0.0778968i
$589$	13.6332	+	4.42969i	0.561745	+	0.182522i
$590$		0			0
$591$	2.27531	+	7.00269i	0.0935939	+	0.288052i
$592$	−4.57242	+	6.67144i	−0.187925	+	0.274194i
$593$			10.5301i			0.432420i	0.976347	+	0.216210i	$0.0693696\pi$
$593$			10.5301i			0.432420i	−0.976347	+	0.216210i	$0.930630\pi$
$594$	−1.01070	+	14.0779i	−0.0414696	+	0.577624i
$595$		0			0
$596$	−27.6290	−	13.6028i	−1.13173	−	0.557193i
$597$	0.937461	+	0.681105i	0.0383677	+	0.0278758i
$598$	−3.42698	−	5.50706i	−0.140140	−	0.225200i
$599$	20.1787			0.824481			0.412241	−	0.911075i	$-0.364746\pi$
$599$	20.1787			0.824481			0.412241	+	0.911075i	$0.364746\pi$
$600$		0			0
$601$	11.7592			0.479669			0.239834	−	0.970814i	$-0.422907\pi$
$601$	11.7592			0.479669			0.239834	+	0.970814i	$0.422907\pi$
$602$	−1.41133	−	2.26796i	−0.0575214	−	0.0924351i
$603$	26.2634	+	19.0815i	1.06953	+	0.777058i
$604$	0.265079	−	0.538408i	0.0107859	−	0.0219075i
$605$		0			0
$606$	0.323435	−	4.50508i	0.0131387	−	0.183006i
$607$			35.8362i			1.45455i	0.686347	+	0.727274i	$0.259213\pi$
$607$			35.8362i			1.45455i	−0.686347	+	0.727274i	$0.740787\pi$
$608$	4.08502	+	14.7622i	0.165670	+	0.598686i
$609$	−0.140118	−	0.431238i	−0.00567785	−	0.0174746i
$610$		0			0
$611$	−18.7937	−	6.10645i	−0.760313	−	0.247041i
$612$	−11.2253	−	21.3022i	−0.453756	−	0.861092i
$613$	3.94986	+	12.1564i	0.159533	+	0.490994i	0.998592	−	0.0530477i	$-0.0168935\pi$
$613$	3.94986	+	12.1564i	0.159533	+	0.490994i	−0.839059	+	0.544041i	$0.816894\pi$
$614$	−13.3183	+	8.28782i	−0.537481	+	0.334469i
$615$		0			0
$616$	3.75303	+	0.819613i	0.151214	+	0.0330232i
$617$	9.18527	+	12.6424i	0.369785	+	0.508965i	0.952842	−	0.303466i	$-0.0981437\pi$
$617$	9.18527	+	12.6424i	0.369785	+	0.508965i	−0.583057	+	0.812431i	$0.698144\pi$
$618$	−3.11139	+	3.69406i	−0.125159	+	0.148597i
$619$	−20.9771	−	28.8724i	−0.843139	−	1.16048i	−0.985333	−	0.170643i	$-0.945416\pi$
$619$	−20.9771	−	28.8724i	−0.843139	−	1.16048i	0.142194	−	0.989839i	$-0.454584\pi$
$620$		0			0
$621$	2.47715	−	3.40951i	0.0994048	−	0.136819i
$622$	−10.2076	−	41.2667i	−0.409286	−	1.65464i
$623$	−2.53843	−	0.824786i	−0.101700	−	0.0330444i
$624$	−2.06446	+	0.734080i	−0.0826446	+	0.0293867i
$625$		0			0
$626$	−0.0335258	+	0.0398041i	−0.00133996	+	0.00159089i
$627$	−1.41180	+	4.34507i	−0.0563818	+	0.173525i
$628$	18.4571	−	37.4886i	0.736519	−	1.49596i
$629$	4.90885	−	6.75645i	0.195729	−	0.269397i
$630$		0			0
$631$	36.4157	−	26.4575i	1.44969	−	1.05326i	0.463781	−	0.885950i	$-0.346492\pi$
$631$	36.4157	−	26.4575i	1.44969	−	1.05326i	0.985905	−	0.167308i	$-0.0535075\pi$
$632$	−18.3144	+	31.3172i	−0.728509	+	1.24573i
$633$	−2.51346	−	3.45948i	−0.0999010	−	0.137502i
$634$	−8.65684	+	21.3124i	−0.343807	+	0.846423i
$635$		0			0
$636$	−2.18844	−	0.315859i	−0.0867772	−	0.0125246i
$637$	−4.02989	−	12.4027i	−0.159670	−	0.491414i
$638$	−20.3781	+	50.1691i	−0.806777	+	1.98621i
$639$	2.46214	−	7.57770i	0.0974009	−	0.299769i
$640$		0			0
$641$	4.02897	+	12.3999i	0.159135	+	0.489766i	0.998556	−	0.0537145i	$-0.0171061\pi$
$641$	4.02897	+	12.3999i	0.159135	+	0.489766i	−0.839422	+	0.543481i	$0.817106\pi$
$642$	0.145105	+	0.0104176i	0.00572685	+	0.000411150i
$643$	−34.5558			−1.36275			−0.681375	−	0.731935i	$-0.738618\pi$
$643$	−34.5558			−1.36275			−0.681375	+	0.731935i	$0.738618\pi$
$644$	−0.822145	−	0.799860i	−0.0323971	−	0.0315189i
$645$		0			0
$646$	−3.79772	−	15.3532i	−0.149419	−	0.604065i
$647$	−5.64166	+	7.76508i	−0.221797	+	0.305277i	−0.905386	−	0.424590i	$-0.860418\pi$
$647$	−5.64166	+	7.76508i	−0.221797	+	0.305277i	0.683589	+	0.729867i	$0.260418\pi$
$648$	15.5008	+	17.4095i	0.608928	+	0.683908i
$649$	−40.5615			−1.59218
$650$		0			0
$651$			0.362627i			0.0142125i
$652$	24.7662	+	3.57453i	0.969919	+	0.139989i
$653$	19.7759	+	14.3680i	0.773889	+	0.562263i	0.903139	−	0.429349i	$-0.141257\pi$
$653$	19.7759	+	14.3680i	0.773889	+	0.562263i	−0.129250	+	0.991612i	$0.541257\pi$
$654$	−3.89376	+	0.963147i	−0.152258	+	0.0376620i
$655$		0			0
$656$	15.6459	−	22.8284i	0.610871	−	0.891298i
$657$		−	44.0833i		−	1.71985i
$658$	−3.48556	−	0.250240i	−0.135881	−	0.00975538i
$659$	41.1516	−	13.3710i	1.60304	−	0.520859i	0.635184	−	0.772361i	$-0.280924\pi$
$659$	41.1516	−	13.3710i	1.60304	−	0.520859i	0.967857	+	0.251502i	$0.0809245\pi$
$660$		0			0
$661$	−33.1551	−	10.7728i	−1.28958	−	0.419012i	−0.417639	−	0.908613i	$-0.637142\pi$
$661$	−33.1551	−	10.7728i	−1.28958	−	0.419012i	−0.871946	+	0.489602i	$0.837142\pi$
$662$	29.7675	+	12.0912i	1.15695	+	0.469938i
$663$	2.15173	−	0.699141i	0.0835664	−	0.0271524i
$664$	5.93425	+	6.66497i	0.230294	+	0.258651i
$665$		0			0
$666$	−3.13679	+	7.72249i	−0.121548	+	0.299240i
$667$	13.0808	−	9.50375i	0.506490	−	0.367987i
$668$	−42.4756	+	7.32702i	−1.64343	+	0.283491i
$669$	2.92371	+	4.02414i	0.113037	+	0.155582i
$670$		0			0
$671$	−7.62437	−	5.53943i	−0.294336	−	0.213847i
$672$	−0.323229	+	0.213680i	−0.0124688	+	0.00824290i
$673$	10.2698	+	3.33688i	0.395874	+	0.128627i	0.500187	−	0.865917i	$-0.333265\pi$
$673$	10.2698	+	3.33688i	0.395874	+	0.128627i	−0.104314	+	0.994544i	$0.533265\pi$
$674$	−17.1400	+	20.3497i	−0.660207	+	0.783842i
$675$		0			0
$676$	−3.22091	−	18.6720i	−0.123881	−	0.718155i
$677$	12.9196	−	39.7626i	0.496542	−	1.52820i	−0.317997	−	0.948092i	$-0.603010\pi$
$677$	12.9196	−	39.7626i	0.496542	−	1.52820i	0.814539	−	0.580109i	$-0.196990\pi$
$678$	0.131137	−	0.0324374i	0.00503627	−	0.00124575i
$679$	1.33127	+	0.967228i	0.0510896	+	0.0371188i
$680$		0			0
$681$	−3.45457	+	2.50989i	−0.132380	+	0.0961794i
$682$	27.8980	−	33.1224i	1.06827	−	1.26832i
$683$	16.0534	−	11.6635i	0.614267	−	0.446291i	−0.236647	−	0.971596i	$-0.576049\pi$
$683$	16.0534	−	11.6635i	0.614267	−	0.446291i	0.850914	+	0.525305i	$0.176049\pi$
$684$	7.35892	+	13.9650i	0.281375	+	0.533966i
$685$		0			0
$686$	−2.44658	−	3.93158i	−0.0934110	−	0.150109i
$687$	−1.69095	+	0.549422i	−0.0645136	+	0.0209617i
$688$	−19.6211	−	25.5021i	−0.748046	−	0.972258i
$689$	−2.19917	+	6.76834i	−0.0837815	+	0.257853i
$690$		0			0
$691$	15.2658	−	4.96017i	0.580740	−	0.188694i	−0.00389213	−	0.999992i	$-0.501239\pi$
$691$	15.2658	−	4.96017i	0.580740	−	0.188694i	0.584632	+	0.811299i	$0.301239\pi$
$692$	2.28432	+	2.22240i	0.0868367	+	0.0844828i
$693$	3.95893			0.150387
$694$	41.6667	+	2.99139i	1.58164	+	0.113552i
$695$		0			0
$696$	−2.19370	−	5.00196i	−0.0831521	−	0.189599i
$697$	−16.7971	+	23.1193i	−0.636237	+	0.875705i
$698$	−11.7783	−	18.9273i	−0.445814	−	0.716410i
$699$		−	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	$0.907164\pi$
$702$	−3.89033	+	2.42091i	−0.146831	+	0.0913715i
$703$	−3.21807	+	4.42930i	−0.121372	+	0.167054i
$704$	45.9629	+	5.34939i	1.73229	+	0.201613i
$705$		0			0
$706$	0.826767	−	11.5159i	0.0311158	−	0.433407i
$707$	−2.57079			−0.0966843
$708$	2.85294	−	2.93243i	0.107220	−	0.110208i
$709$	−35.0361	+	11.3839i	−1.31581	+	0.427532i	−0.881053	−	0.473018i	$-0.843165\pi$
$709$	−35.0361	+	11.3839i	−1.31581	+	0.427532i	−0.434754	+	0.900549i	$0.643165\pi$
$710$		0			0
$711$	−11.5537	+	35.5586i	−0.433297	+	1.33355i
$712$	−31.4103	−	6.85961i	−1.17715	−	0.257075i
$713$	−12.2979	+	3.99584i	−0.460561	+	0.149645i
$714$	0.339694	−	0.211388i	0.0127127	−	0.00791100i
$715$		0			0
$716$	10.3314	+	19.6058i	0.386101	+	0.732703i
$717$	−1.26551	+	0.919446i	−0.0472613	+	0.0343373i
$718$	−32.9899	−	27.7864i	−1.23117	−	1.03698i
$719$	17.8070	−	12.9375i	0.664088	−	0.482488i	−0.203953	−	0.978981i	$-0.565379\pi$
$719$	17.8070	−	12.9375i	0.664088	−	0.482488i	0.868041	+	0.496492i	$0.165379\pi$
$720$		0			0
$721$	2.22399	+	1.61582i	0.0828256	+	0.0601763i
$722$	−3.96237	−	16.0189i	−0.147464	−	0.596161i
$723$	0.170225	−	0.523900i	0.00633075	−	0.0194840i
$724$	39.5633	−	6.82465i	1.47036	−	0.253636i
$725$		0			0
$726$	7.08570	+	5.96807i	0.262975	+	0.221496i
$727$	37.4888	+	12.1809i	1.39038	+	0.451763i	0.906069	−	0.423131i	$-0.139069\pi$
$727$	37.4888	+	12.1809i	1.39038	+	0.451763i	0.484315	+	0.874894i	$0.339069\pi$
$728$	0.500892	+	1.14211i	0.0185643	+	0.0423293i
$729$	18.2133	+	13.2327i	0.674566	+	0.490101i
$730$		0			0
$731$	19.5291	+	26.8795i	0.722311	+	0.994176i
$732$	0.936748	−	0.161589i	0.0346232	−	0.00597248i
$733$	−20.6186	+	14.9803i	−0.761565	+	0.553309i	−0.899390	−	0.437147i	$-0.855989\pi$
$733$	−20.6186	+	14.9803i	−0.761565	+	0.553309i	0.137825	+	0.990457i	$0.455989\pi$
$734$	9.82781	+	3.99194i	0.362751	+	0.147345i
$735$		0			0
$736$	−10.8084	−	8.60723i	−0.398401	−	0.317267i
$737$	61.2653	−	19.9063i	2.25674	−	0.733258i
$738$	10.7335	−	26.4249i	0.395105	−	0.972713i
$739$	8.47753	+	2.75452i	0.311851	+	0.101327i	0.460761	−	0.887524i	$-0.347576\pi$
$739$	8.47753	+	2.75452i	0.311851	+	0.101327i	−0.148910	+	0.988851i	$0.547576\pi$
$740$		0			0
$741$	−1.41060	+	0.458333i	−0.0518198	+	0.0168373i
$742$	−0.0901210	+	1.25528i	−0.00330845	+	0.0460829i
$743$		−	21.5410i		−	0.790261i	−0.918625	−	0.395130i	$-0.870699\pi$
$743$		−	21.5410i		−	0.790261i	0.918625	−	0.395130i	$-0.129301\pi$
$744$	0.432376	+	4.34662i	0.0158517	+	0.159355i
$745$		0			0
$746$	−4.33229	−	17.5144i	−0.158617	−	0.641248i
$747$	7.44038	+	5.40575i	0.272229	+	0.197786i
$748$	−47.2905	−	6.82548i	−1.72911	−	0.249564i
$749$		−	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	$0.305562\pi$
$752$	−42.0780	+	1.15648i	−1.53443	+	0.0421726i
$753$	−0.780227	+	1.07389i	−0.0284331	+	0.0391347i
$754$	−17.0651	+	4.22117i	−0.621476	+	0.153726i
$755$		0			0
$756$	−0.565042	+	0.580785i	−0.0205504	+	0.0211230i
$757$	−3.46461			−0.125924			−0.0629618	−	0.998016i	$-0.520055\pi$
$757$	−3.46461			−0.125924			−0.0629618	+	0.998016i	$0.520055\pi$
$758$	1.24057	−	17.2797i	0.0450596	−	0.627628i
$759$	−1.27353	−	3.91951i	−0.0462261	−	0.142269i
$760$		0			0
$761$	−6.25196	+	19.2415i	−0.226633	+	0.697505i	0.771488	+	0.636243i	$0.219513\pi$
$761$	−6.25196	+	19.2415i	−0.226633	+	0.697505i	−0.998122	+	0.0612621i	$0.980487\pi$
$762$	3.53099	+	1.43425i	0.127914	+	0.0519573i
$763$	0.705496	+	2.17129i	0.0255407	+	0.0786061i
$764$	−37.5225	−	5.41565i	−1.35752	−	0.195931i
$765$		0			0
$766$	−35.2787	−	14.3298i	−1.27467	−	0.517756i
$767$	−7.73999	−	10.6532i	−0.279475	−	0.384664i
$768$	−3.61960	+	2.94668i	−0.130611	+	0.106329i
$769$	−6.10205	+	4.43340i	−0.220046	+	0.159872i	−0.692347	−	0.721565i	$-0.743423\pi$
$769$	−6.10205	+	4.43340i	−0.220046	+	0.159872i	0.472302	+	0.881437i	$0.343423\pi$
$770$		0			0
$771$	−1.19867	+	1.64982i	−0.0431689	+	0.0594169i
$772$	−4.72539	−	2.32650i	−0.170071	−	0.0837324i
$773$	−7.63507	+	23.4983i	−0.274614	+	0.845176i	0.714707	+	0.699424i	$0.246560\pi$
$773$	−7.63507	+	23.4983i	−0.274614	+	0.845176i	−0.989321	+	0.145752i	$0.953440\pi$
$774$	−25.3628	−	21.3623i	−0.911647	−	0.767853i
$775$		0			0
$776$	17.1106	+	10.0063i	0.614234	+	0.359206i
$777$	−0.131720	−	0.0427985i	−0.00472544	−	0.00153539i
$778$	13.0875	−	3.23727i	0.469209	−	0.116062i
$779$	11.0116	−	15.1562i	0.394533	−	0.543027i
$780$		0			0
$781$	−9.29319	−	12.7910i	−0.332536	−	0.457697i
$782$	10.9121	+	9.19089i	0.390214	+	0.328666i
$783$	−6.71371	−	9.24062i	−0.239928	−	0.330233i
$784$	−16.9396	−	22.0170i	−0.604987	−	0.786320i
$785$		0			0
$786$	1.65394	+	2.65782i	0.0589940	+	0.0948015i
$787$	2.96732	+	9.13248i	0.105774	+	0.325538i	0.989911	−	0.141689i	$-0.0452532\pi$
$787$	2.96732	+	9.13248i	0.105774	+	0.325538i	−0.884138	+	0.467227i	$0.845253\pi$
$788$	44.6606	−	23.5341i	1.59097	−	0.838367i
$789$	−6.27562	−	2.03907i	−0.223418	−	0.0725930i
$790$		0			0
$791$	−0.0237601	−	0.0731261i	−0.000844812	−	0.00260007i
$792$	47.4537	−	4.72041i	1.68620	−	0.167733i
$793$		−	3.05953i		−	0.108647i
$794$	−32.8234	−	2.35651i	−1.16486	−	0.0836292i
$795$		0			0
$796$	3.50919	−	7.12758i	0.124380	−	0.252630i
$797$	−25.7837	−	18.7330i	−0.913306	−	0.663556i	0.0285428	−	0.999593i	$-0.490913\pi$
$797$	−25.7837	−	18.7330i	−0.913306	−	0.663556i	−0.941849	+	0.336037i	$0.890913\pi$
$798$	−0.222692	+	0.138579i	−0.00788321	+	0.00490564i
$799$	43.4651			1.53769
$800$		0			0
$801$	−33.1336			−1.17072
$802$	14.7588	−	9.18426i	0.521152	−	0.324307i
$803$	−70.7696	−	51.4171i	−2.49740	−	1.81447i
$804$	−2.87003	+	5.82937i	−0.101218	+	0.205586i
$805$		0			0
$806$	14.0229	+	1.00675i	0.493936	+	0.0354614i
$807$			1.83112i			0.0644586i
$808$	−30.8147	+	3.06526i	−1.08406	+	0.107836i
$809$	−1.35706	−	4.17661i	−0.0477118	−	0.146842i	0.924362	−	0.381516i	$-0.124598\pi$
$809$	−1.35706	−	4.17661i	−0.0477118	−	0.146842i	−0.972074	+	0.234674i	$0.924598\pi$
$810$		0			0
$811$	36.8697	+	11.9797i	1.29467	+	0.420664i	0.873725	−	0.486421i	$-0.161698\pi$
$811$	36.8697	+	11.9797i	1.29467	+	0.420664i	0.420947	+	0.907085i	$0.361698\pi$
$812$	−2.75028	+	1.44927i	−0.0965158	+	0.0508594i
$813$	−0.306476	−	0.943236i	−0.0107486	−	0.0330807i
$814$	8.73875	+	14.0429i	0.306293	+	0.492203i
$815$		0			0
$816$	3.81969	−	2.93884i	0.133716	−	0.102880i
$817$	−12.8026	−	17.6213i	−0.447907	−	0.616492i
$818$	34.1829	+	28.7912i	1.19518	+	1.00666i
$819$	0.755449	+	1.03979i	0.0263975	+	0.0363331i
$820$		0			0
$821$	−25.5877	+	35.2185i	−0.893017	+	1.22913i	0.0796254	+	0.996825i	$0.474628\pi$
$821$	−25.5877	+	35.2185i	−0.893017	+	1.22913i	−0.972642	+	0.232308i	$0.925372\pi$
$822$	5.29438	−	1.30960i	0.184663	−	0.0456775i
$823$	4.46326	+	1.45020i	0.155580	+	0.0505509i	0.385771	−	0.922594i	$-0.373935\pi$
$823$	4.46326	+	1.45020i	0.155580	+	0.0505509i	−0.230192	+	0.973145i	$0.573935\pi$
$824$	28.5844	+	16.7163i	0.995785	+	0.582339i
$825$		0			0
$826$	−1.78107	−	1.50014i	−0.0619712	−	0.0521965i
$827$	3.61552	−	11.1274i	0.125724	−	0.386938i	−0.868308	−	0.496025i	$-0.834793\pi$
$827$	3.61552	−	11.1274i	0.125724	−	0.386938i	0.994032	+	0.109087i	$0.0347926\pi$
$828$	−12.7749	−	6.28958i	−0.443959	−	0.218578i
$829$	0.462729	−	0.636892i	0.0160712	−	0.0221202i	−0.800906	−	0.598790i	$-0.795648\pi$
$829$	0.462729	−	0.636892i	0.0160712	−	0.0221202i	0.816977	+	0.576670i	$0.195648\pi$
$830$		0			0
$831$	6.07571	−	4.41426i	0.210764	−	0.153129i
$832$	7.36573	+	13.0926i	0.255361	+	0.453905i
$833$	16.8603	+	23.2062i	0.584174	+	0.804046i
$834$	0.864692	+	0.351228i	0.0299418	+	0.0121620i
$835$		0			0
$836$	31.0021	+	4.47455i	1.07223	+	0.154756i
$837$	2.82277	+	8.68759i	0.0975692	+	0.300287i
$838$	−11.3110	−	4.59439i	−0.390731	−	0.158711i
$839$	10.8077	−	33.2628i	0.373124	−	1.14836i	−0.571611	−	0.820524i	$-0.693682\pi$
$839$	10.8077	−	33.2628i	0.373124	−	1.14836i	0.944736	−	0.327833i	$-0.106318\pi$
$840$		0			0
$841$	−4.58005	−	14.0959i	−0.157933	−	0.486067i
$842$	−1.29740	+	18.0713i	−0.0447114	+	0.622779i
$843$	−1.13954			−0.0392478
$844$	−20.4440	+	21.0136i	−0.703711	+	0.723318i
$845$		0			0
$846$	−42.1117	+	10.4166i	−1.44783	+	0.358130i
$847$	3.09936	−	4.26591i	0.106495	−	0.146578i
$848$	0.416494	+	15.1539i	0.0143025	+	0.520387i
$849$	−0.374678			−0.0128589
$850$		0			0
$851$		−	4.93870i		−	0.169296i
$852$	1.57838	+	0.227809i	0.0540746	+	0.00780462i
$853$	9.00501	+	6.54252i	0.308326	+	0.224012i	0.731178	−	0.682187i	$-0.238971\pi$
$853$	9.00501	+	6.54252i	0.308326	+	0.224012i	−0.422852	+	0.906199i	$0.638971\pi$
$854$	−0.129916	−	0.525220i	−0.00444565	−	0.0179727i
$855$		0			0
$856$	−0.0987298	−	0.992519i	−0.00337452	−	0.0339236i
$857$		−	53.1600i		−	1.81591i	−0.419068	−	0.907955i	$-0.637643\pi$
$857$		−	53.1600i		−	1.81591i	0.419068	−	0.907955i	$-0.362357\pi$
$858$	−0.320865	+	4.46929i	−0.0109542	+	0.152579i
$859$	32.6009	−	10.5927i	1.11233	−	0.361417i	0.305493	−	0.952194i	$-0.401179\pi$
$859$	32.6009	−	10.5927i	1.11233	−	0.361417i	0.806835	+	0.590777i	$0.201179\pi$
$860$		0			0
$861$	0.450722	+	0.146448i	0.0153606	+	0.00499095i
$862$	−16.0053	+	39.4035i	−0.545141	+	1.34209i
$863$	37.8328	−	12.2926i	1.28784	−	0.418446i	0.416508	−	0.909132i	$-0.363254\pi$
$863$	37.8328	−	12.2926i	1.28784	−	0.418446i	0.871336	+	0.490686i	$0.163254\pi$
$864$	−6.08038	+	7.63531i	−0.206859	+	0.259758i
$865$		0			0
$866$	2.10670	+	0.855719i	0.0715887	+	0.0290785i
$867$	−0.0140203	+	0.0101863i	−0.000476154	+	0.000345946i
$868$	2.45002	−	0.422627i	0.0831591	−	0.0143449i
$869$	43.6085	+	60.0220i	1.47932	+	2.03611i
$870$		0			0
$871$	16.9190	+	12.2923i	0.573277	+	0.416510i
$872$	11.0453	+	25.1850i	0.374043	+	0.852871i
$873$	19.4279	+	6.31251i	0.657535	+	0.213646i
$874$	−7.15357	−	6.02523i	−0.241973	−	0.203807i
$875$		0			0
$876$	8.69492	−	1.49987i	0.293774	−	0.0506759i
$877$	−12.4831	+	38.4191i	−0.421525	+	1.29732i	0.484758	+	0.874649i	$0.338908\pi$
$877$	−12.4831	+	38.4191i	−0.421525	+	1.29732i	−0.906283	+	0.422672i	$0.861092\pi$
$878$	12.8956	+	52.1337i	0.435205	+	1.75943i
$879$	−2.01784	−	1.46605i	−0.0680601	−	0.0494486i
$880$		0			0
$881$	26.2858	−	19.0977i	0.885591	−	0.643419i	−0.0491339	−	0.998792i	$-0.515646\pi$
$881$	26.2858	−	19.0977i	0.885591	−	0.643419i	0.934725	+	0.355373i	$0.115646\pi$
$882$	−21.8967	−	18.4429i	−0.737301	−	0.621006i
$883$	−31.0584	+	22.5652i	−1.04520	+	0.759380i	−0.971293	−	0.237885i	$-0.923546\pi$
$883$	−31.0584	+	22.5652i	−1.04520	+	0.759380i	−0.0739039	+	0.997265i	$0.523546\pi$
$884$	−7.23138	−	13.7230i	−0.243218	−	0.461554i
$885$		0			0
$886$	23.4943	−	14.6202i	0.789305	−	0.491176i
$887$	14.5493	−	4.72737i	0.488519	−	0.158729i	−0.0543921	−	0.998520i	$-0.517322\pi$
$887$	14.5493	−	4.72737i	0.488519	−	0.158729i	0.542911	+	0.839790i	$0.317322\pi$
$888$	−1.62990	−	0.355948i	−0.0546957	−	0.0119448i
$889$	0.670327	−	2.06305i	0.0224821	−	0.0691926i
$890$		0			0
$891$	45.3363	−	14.7306i	1.51882	−	0.493495i
$892$	23.7809	−	24.4435i	0.796243	−	0.818428i
$893$	−28.4943			−0.953524
$894$	0.454885	−	6.33602i	0.0152136	−	0.211908i
$895$		0			0
$896$	1.82040	+	1.93480i	0.0608153	+	0.0646371i
$897$	0.786416	−	1.08241i	0.0262577	−	0.0361406i
$898$	−39.9325	+	24.8496i	−1.33256	+	0.829241i
$899$			35.0457i			1.16884i
$900$		0			0
$901$		−	15.6535i		−	0.521492i
$902$	−29.9023	−	48.0521i	−0.995638	−	1.59996i
$903$	0.323868	−	0.445767i	0.0107777	−	0.0148342i
$904$	−0.371992	−	0.848195i	−0.0123723	−	0.0282106i
$905$		0			0
$906$	0.123471	+	0.00886438i	0.00410203	+	0.000294499i
$907$	31.6503			1.05093			0.525465	−	0.850815i	$-0.323891\pi$
$907$	31.6503			1.05093			0.525465	+	0.850815i	$0.323891\pi$
$908$	20.9838	+	20.4150i	0.696372	+	0.677496i
$909$	−30.3516	+	9.86184i	−1.00670	+	0.327096i
$910$		0			0
$911$	−1.64977	+	5.07747i	−0.0546593	+	0.168224i	−0.974659	−	0.223694i	$-0.928188\pi$
$911$	−1.64977	+	5.07747i	−0.0546593	+	0.168224i	0.920000	+	0.391918i	$0.128188\pi$
$912$	−2.50406	+	1.92660i	−0.0829178	+	0.0637961i
$913$	17.3564	−	5.63942i	0.574411	−	0.186638i
$914$	11.6484	+	18.7187i	0.385296	+	0.619159i
$915$		0			0
$916$	5.68280	+	10.7842i	0.187765	+	0.356321i
$917$	1.44148	−	1.04729i	0.0476017	−	0.0345847i
$918$	6.49269	−	7.70856i	0.214291	−	0.254421i
$919$	11.6067	−	8.43275i	0.382869	−	0.278171i	−0.379658	−	0.925127i	$-0.623958\pi$
$919$	11.6067	−	8.43275i	0.382869	−	0.278171i	0.762527	+	0.646956i	$0.223958\pi$
$920$		0			0
$921$	−2.61770	−	1.90187i	−0.0862561	−	0.0626687i
$922$	7.95710	−	1.96824i	0.262053	−	0.0648204i
$923$	1.58612	−	4.88158i	0.0522078	−	0.160679i
$924$	0.134697	+	0.780854i	0.00443120	+	0.0256882i
$925$		0			0
$926$	10.8291	−	12.8570i	0.355865	−	0.422508i
$927$	32.4557	+	10.5455i	1.06598	+	0.346359i
$928$	−31.2382	+	20.6509i	−1.02544	+	0.677900i
$929$	5.50414	+	3.99899i	0.180585	+	0.131203i	0.674405	−	0.738361i	$-0.264400\pi$
$929$	5.50414	+	3.99899i	0.180585	+	0.131203i	−0.493820	+	0.869564i	$0.664400\pi$
$930$		0			0
$931$	−11.0530	−	15.2132i	−0.362248	−	0.498592i
$932$	−14.0655	+	2.42629i	−0.460731	+	0.0794759i
$933$	7.09400	−	5.15409i	0.232247	−	0.168737i
$934$	−13.2765	+	32.6856i	−0.434421	+	1.06951i
$935$		0			0
$936$	10.2950	+	11.5626i	0.336502	+	0.377937i
$937$	15.8759	−	5.15839i	0.518643	−	0.168517i	−0.0379863	−	0.999278i	$-0.512094\pi$
$937$	15.8759	−	5.15839i	0.518643	−	0.168517i	0.556629	+	0.830761i	$0.312094\pi$
$938$	3.42640	+	1.39176i	0.111876	+	0.0454426i
$939$	−0.0102093	−	0.00331721i	−0.000333168	−	0.000108253i
$940$		0			0
$941$	10.5188	−	3.41775i	0.342902	−	0.111416i	−0.132503	−	0.991183i	$-0.542301\pi$
$941$	10.5188	−	3.41775i	0.342902	−	0.111416i	0.475405	+	0.879767i	$0.342301\pi$
$942$	8.59708	+	0.617214i	0.280108	+	0.0201099i
$943$			16.8993i			0.550316i
$944$	−23.1374	−	15.8578i	−0.753059	−	0.516126i
$945$		0			0
$946$	−63.8765	+	15.8002i	−2.07680	+	0.513710i
$947$	16.0299	+	11.6464i	0.520901	+	0.378457i	0.816943	−	0.576718i	$-0.195667\pi$
$947$	16.0299	+	11.6464i	0.520901	+	0.378457i	−0.296042	+	0.955175i	$0.595667\pi$
$948$	−7.40661	−	1.06900i	−0.240556	−	0.0347196i
$949$		−	28.3986i		−	0.921858i
$950$		0			0
$951$	−4.74494			−0.153865
$952$	−1.82411	−	2.04872i	−0.0591196	−	0.0663993i
$953$	−28.4871	+	39.2091i	−0.922787	+	1.27011i	0.0398210	+	0.999207i	$0.487321\pi$
$953$	−28.4871	+	39.2091i	−0.922787	+	1.27011i	−0.962608	+	0.270900i	$0.912679\pi$
$954$	3.75141	+	15.1660i	0.121456	+	0.491018i
$955$		0			0
$956$	7.68697	+	7.47860i	0.248614	+	0.241875i
$957$	−11.1695			−0.361060
$958$	21.6703	+	1.55579i	0.700136	+	0.0502652i
$959$	−0.959267	−	2.95232i	−0.0309764	−	0.0953354i
$960$		0			0
$961$	−0.918548	+	2.82700i	−0.0296306	+	0.0911936i
$962$	−2.02073	+	4.97486i	−0.0651509	+	0.160396i
$963$	−0.317642	−	0.977603i	−0.0102359	−	0.0315028i
$964$	−3.73802	−	0.539512i	−0.120394	−	0.0173765i
$965$		0			0
$966$	0.0890395	−	0.219207i	0.00286480	−	0.00705288i
$967$	−11.5880	−	15.9495i	−0.372645	−	0.512901i	0.580973	−	0.813923i	$-0.302672\pi$
$967$	−11.5880	−	15.9495i	−0.372645	−	0.512901i	−0.953617	+	0.301022i	$0.902672\pi$
$968$	32.0641	−	54.8288i	1.03058	−	1.76226i
$969$	2.63931	−	1.91757i	0.0847870	−	0.0616013i
$970$		0			0
$971$	1.31463	−	1.80943i	0.0421885	−	0.0580675i	−0.787402	−	0.616440i	$-0.788574\pi$
$971$	1.31463	−	1.80943i	0.0421885	−	0.0580675i	0.829590	+	0.558373i	$0.188574\pi$
$972$	−6.69666	+	13.6017i	−0.214795	+	0.436275i
$973$	0.164154	−	0.505214i	0.00526253	−	0.0161964i
$974$	−20.5503	+	24.3987i	−0.658475	+	0.781786i
$975$		0			0
$976$	−2.18349	−	6.14064i	−0.0698917	−	0.196557i
$977$	−11.4440	−	3.71838i	−0.366126	−	0.118962i	0.120175	−	0.992753i	$-0.461654\pi$
$977$	−11.4440	−	3.71838i	−0.366126	−	0.118962i	−0.486301	+	0.873791i	$0.661654\pi$
$978$	1.23937	+	5.01047i	0.0396307	+	0.160217i
$979$	−38.6458	+	53.1914i	−1.23512	+	1.70000i
$980$		0			0
$981$	16.6587	+	22.9287i	0.531870	+	0.732057i
$982$	6.95109	−	8.25281i	0.221818	−	0.263358i
$983$	27.2305	+	37.4796i	0.868518	+	1.19541i	0.979471	+	0.201587i	$0.0646099\pi$
$983$	27.2305	+	37.4796i	0.868518	+	1.19541i	−0.110952	+	0.993826i	$0.535390\pi$
$984$	5.57719	+	1.21799i	0.177794	+	0.0388280i
$985$		0			0
$986$	32.8294	−	20.4294i	1.04550	−	0.650605i
$987$	−0.222746	−	0.685540i	−0.00709007	−	0.0218210i
$988$	4.74064	+	8.99631i	0.150820	+	0.286211i
$989$	18.6862	+	6.07153i	0.594188	+	0.193063i
$990$		0			0
$991$	18.8475	+	58.0065i	0.598710	+	1.84264i	0.535319	+	0.844650i	$0.320191\pi$
$991$	18.8475	+	58.0065i	0.598710	+	1.84264i	0.0633902	+	0.997989i	$0.479809\pi$
$992$	28.8632	−	7.98709i	0.916409	−	0.253590i
$993$			6.62737i			0.210313i
$994$	0.0649987	−	0.905357i	0.00206163	−	0.0287162i
$995$		0			0
$996$	−0.813074	+	1.65145i	−0.0257632	+	0.0523282i
$997$	26.2826	+	19.0954i	0.832378	+	0.604758i	0.920231	−	0.391375i	$-0.128001\pi$
$997$	26.2826	+	19.0954i	0.832378	+	0.604758i	−0.0878532	+	0.996133i	$0.528001\pi$
$998$	20.1509	+	32.3819i	0.637866	+	1.02503i
$999$	−3.48883			−0.110382

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20071 - 0.747190i) q^{2} +(0.235999 + 0.171463i) q^{3} +(0.883414 - 1.79432i) q^{4} +(0.411483 + 0.0295418i) q^{6} -0.234809i q^{7} +(-0.279973 - 2.81454i) q^{8} +(-0.900755 - 2.77224i) q^{9} +O(q^{10})\)	\(q+(1.20071 - 0.747190i) q^{2} +(0.235999 + 0.171463i) q^{3} +(0.883414 - 1.79432i) q^{4} +(0.411483 + 0.0295418i) q^{6} -0.234809i q^{7} +(-0.279973 - 2.81454i) q^{8} +(-0.900755 - 2.77224i) q^{9} +(-5.50105 - 1.78740i) q^{11} +(0.516145 - 0.271985i) q^{12} +(-0.580270 - 1.78589i) q^{13} +(-0.175447 - 0.281938i) q^{14} +(-2.43916 - 3.17025i) q^{16} +(2.42773 + 3.34149i) q^{17} +(-3.15294 - 2.65562i) q^{18} +(-1.59154 - 2.19056i) q^{19} +(0.0402612 - 0.0554147i) q^{21} +(-7.94070 + 1.96418i) q^{22} +(2.32295 + 0.754772i) q^{23} +(0.416517 - 0.712234i) q^{24} +(-2.03113 - 1.71076i) q^{26} +(0.533191 - 1.64099i) q^{27} +(-0.421322 - 0.207433i) q^{28} +(3.89100 - 5.35551i) q^{29} +(-4.28302 + 3.11180i) q^{31} +(-5.29751 - 1.98404i) q^{32} +(-0.991770 - 1.36505i) q^{33} +(5.41173 + 2.19818i) q^{34} +(-5.77002 - 0.832792i) q^{36} +(-0.624829 - 1.92303i) q^{37} +(-3.54775 - 1.44105i) q^{38} +(0.169271 - 0.520963i) q^{39} +(2.13805 + 6.58023i) q^{41} +(0.00693667 - 0.0966198i) q^{42} +8.04419 q^{43} +(-8.06687 + 8.29162i) q^{44} +(3.35315 - 0.829422i) q^{46} +(6.18554 - 8.51367i) q^{47} +(-0.0320578 - 1.16640i) q^{48} +6.94486 q^{49} +1.20486i q^{51} +(-3.71707 - 0.536487i) q^{52} +(-3.06610 - 2.22765i) q^{53} +(-0.585926 - 2.36875i) q^{54} +(-0.660878 + 0.0657402i) q^{56} -0.789862i q^{57} +(0.670388 - 9.33773i) q^{58} +(6.66931 - 2.16699i) q^{59} +(1.54958 + 0.503489i) q^{61} +(-2.81756 + 6.93660i) q^{62} +(-0.650947 + 0.211505i) q^{63} +(-7.84323 + 1.57599i) q^{64} +(-2.21078 - 0.897995i) q^{66} +(-9.01003 + 6.54617i) q^{67} +(8.14038 - 1.40421i) q^{68} +(0.418799 + 0.576427i) q^{69} +(2.21139 + 1.60667i) q^{71} +(-7.55038 + 3.31136i) q^{72} +(14.3832 + 4.67339i) q^{73} +(-2.18711 - 1.84213i) q^{74} +(-5.33656 + 0.920553i) q^{76} +(-0.419697 + 1.29170i) q^{77} +(-0.186013 - 0.752003i) q^{78} +(-10.3770 - 7.53932i) q^{79} +(-6.66742 + 4.84416i) q^{81} +(7.48385 + 6.30342i) q^{82} +(-2.55253 + 1.85452i) q^{83} +(-0.0638644 - 0.121195i) q^{84} +(9.65874 - 6.01054i) q^{86} +(1.83655 - 0.596730i) q^{87} +(-3.49055 + 15.9833i) q^{88} +(3.51258 - 10.8106i) q^{89} +(-0.419342 + 0.136252i) q^{91} +(3.40643 - 3.50134i) q^{92} -1.54435 q^{93} +(1.06572 - 14.8442i) q^{94} +(-0.910018 - 1.37656i) q^{96} +(-4.11921 + 5.66961i) q^{97} +(8.33878 - 5.18913i) q^{98} +16.8602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36} - 45 q^{38} - 10 q^{39} - 10 q^{41} - 75 q^{42} - 32 q^{44} + 13 q^{46} + 10 q^{47} + 70 q^{48} - 80 q^{49} + 100 q^{52} + 43 q^{54} + 36 q^{56} + 30 q^{58} - 20 q^{62} - 60 q^{63} - 36 q^{64} + 40 q^{66} + 22 q^{71} + 65 q^{72} + 10 q^{73} + 4 q^{74} - 36 q^{76} + 55 q^{78} + 14 q^{79} - 6 q^{81} + 78 q^{84} - 59 q^{86} + 10 q^{87} - 110 q^{88} + 24 q^{89} - 90 q^{92} + 45 q^{94} + 46 q^{96} + 50 q^{97} - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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