LMFDB - Embedded newform 875.2.q.b.851.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(51,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 10]))

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

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

chi := DirichletCharacter("875.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.q (of order $15$, degree $8$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			851.35
Character	$\chi$	$=$	875.851
Dual form			875.2.q.b.401.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.53101 - 0.537983i) q^{2} +(0.0682015 - 0.0303653i) q^{3} +(4.28951 - 1.90981i) q^{4} +(0.156283 - 0.113546i) q^{6} +(2.59057 + 0.537537i) q^{7} +(5.64260 - 4.09959i) q^{8} +(-2.00366 + 2.22529i) q^{9} +O(q^{10})$	\(q+(2.53101 - 0.537983i) q^{2} +(0.0682015 - 0.0303653i) q^{3} +(4.28951 - 1.90981i) q^{4} +(0.156283 - 0.113546i) q^{6} +(2.59057 + 0.537537i) q^{7} +(5.64260 - 4.09959i) q^{8} +(-2.00366 + 2.22529i) q^{9} +(2.52729 + 2.80684i) q^{11} +(0.234559 - 0.260504i) q^{12} +(-0.866509 - 2.66684i) q^{13} +(6.84595 - 0.0331700i) q^{14} +(5.79224 - 6.43293i) q^{16} +(0.0314508 + 0.299235i) q^{17} +(-3.87412 + 6.71018i) q^{18} +(-3.68296 - 1.63976i) q^{19} +(0.193003 - 0.0420025i) q^{21} +(7.90663 + 5.74450i) q^{22} +(-6.87632 + 1.46161i) q^{23} +(0.260349 - 0.450937i) q^{24} +(-3.62786 - 6.28364i) q^{26} +(-0.138291 + 0.425616i) q^{27} +(12.1389 - 2.64173i) q^{28} +(-2.21189 - 1.60703i) q^{29} +(-0.929782 - 8.84628i) q^{31} +(4.22478 - 7.31754i) q^{32} +(0.257595 + 0.114689i) q^{33} +(0.240586 + 0.740447i) q^{34} +(-4.34484 + 13.3720i) q^{36} +(2.18285 - 2.42430i) q^{37} +(-10.2038 - 2.16888i) q^{38} +(-0.140077 - 0.155571i) q^{39} +(0.700664 + 2.15642i) q^{41} +(0.465897 - 0.210141i) q^{42} +9.05803 q^{43} +(16.2014 + 7.21331i) q^{44} +(-16.6177 + 7.39869i) q^{46} +(0.580225 - 5.52047i) q^{47} +(0.199702 - 0.614619i) q^{48} +(6.42211 + 2.78506i) q^{49} +(0.0112313 + 0.0194532i) q^{51} +(-8.81006 - 9.78456i) q^{52} +(-3.35264 + 1.49269i) q^{53} +(-0.121042 + 1.15164i) q^{54} +(16.8212 - 7.58716i) q^{56} -0.300975 q^{57} +(-6.46288 - 2.87746i) q^{58} +(-8.63331 - 1.83507i) q^{59} +(-13.3724 + 2.84238i) q^{61} +(-7.11244 - 21.8898i) q^{62} +(-6.38681 + 4.68773i) q^{63} +(1.40634 - 4.32826i) q^{64} +(0.713678 + 0.151697i) q^{66} +(0.359475 + 3.42017i) q^{67} +(0.706390 + 1.22350i) q^{68} +(-0.424593 + 0.308485i) q^{69} +(-2.69801 - 1.96022i) q^{71} +(-2.18308 + 20.7706i) q^{72} +(8.75399 + 9.72229i) q^{73} +(4.22058 - 7.31027i) q^{74} -18.9297 q^{76} +(5.03834 + 8.62982i) q^{77} +(-0.438230 - 0.318393i) q^{78} +(-0.885368 + 8.42371i) q^{79} +(-0.935516 - 8.90084i) q^{81} +(2.93351 + 5.08098i) q^{82} +(3.77939 - 2.74589i) q^{83} +(0.747672 - 0.548770i) q^{84} +(22.9260 - 4.87307i) q^{86} +(-0.199652 - 0.0424374i) q^{87} +(25.7673 + 5.47702i) q^{88} +(-7.53425 + 1.60146i) q^{89} +(-0.811226 - 7.37442i) q^{91} +(-26.7046 + 19.4021i) q^{92} +(-0.332032 - 0.575097i) q^{93} +(-1.50137 - 14.2845i) q^{94} +(0.0659376 - 0.627354i) q^{96} +(8.08430 + 5.87358i) q^{97} +(17.7527 + 3.59403i) q^{98} -11.3099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	$ 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) $ 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.53101	−	0.537983i	1.78970	−	0.380412i	0.810890	−	0.585199i	$-0.198984\pi$
$2$	2.53101	−	0.537983i	1.78970	−	0.380412i	0.978807	+	0.204787i	$0.0656502\pi$
$3$	0.0682015	−	0.0303653i	0.0393762	−	0.0175314i	−0.386954	−	0.922099i	$-0.626473\pi$
$3$	0.0682015	−	0.0303653i	0.0393762	−	0.0175314i	0.426330	+	0.904568i	$0.359806\pi$
$4$	4.28951	−	1.90981i	2.14475	−	0.954906i
$5$		0			0
$5$		0			0
$6$	0.156283	−	0.113546i	0.0638022	−	0.0463550i
$7$	2.59057	+	0.537537i	0.979143	+	0.203170i
$7$	2.59057	+	0.537537i	0.979143	+	0.203170i
$8$	5.64260	−	4.09959i	1.99496	−	1.44942i
$9$	−2.00366	+	2.22529i	−0.667887	+	0.741764i
$10$		0			0
$11$	2.52729	+	2.80684i	0.762006	+	0.846293i	0.991913	−	0.126919i	$-0.0405089\pi$
$11$	2.52729	+	2.80684i	0.762006	+	0.846293i	−0.229907	+	0.973213i	$0.573842\pi$
$12$	0.234559	−	0.260504i	0.0677114	−	0.0752011i
$13$	−0.866509	−	2.66684i	−0.240326	−	0.739648i	−0.996370	−	0.0851272i	$-0.972870\pi$
$13$	−0.866509	−	2.66684i	−0.240326	−	0.739648i	0.756044	−	0.654521i	$-0.227130\pi$
$14$	6.84595	−	0.0331700i	1.82966	−	0.00886506i
$15$		0			0
$16$	5.79224	−	6.43293i	1.44806	−	1.60823i
$17$	0.0314508	+	0.299235i	0.00762795	+	0.0725751i	0.997674	−	0.0681713i	$-0.0217165\pi$
$17$	0.0314508	+	0.299235i	0.00762795	+	0.0725751i	−0.990046	+	0.140746i	$0.955050\pi$
$18$	−3.87412	+	6.71018i	−0.913140	+	1.58160i
$19$	−3.68296	−	1.63976i	−0.844929	−	0.376187i	−0.0618323	−	0.998087i	$-0.519694\pi$
$19$	−3.68296	−	1.63976i	−0.844929	−	0.376187i	−0.783097	+	0.621900i	$0.786361\pi$
$20$		0			0
$21$	0.193003	−	0.0420025i	0.0421168	−	0.00916570i
$22$	7.90663	+	5.74450i	1.68570	+	1.22473i
$23$	−6.87632	+	1.46161i	−1.43381	+	0.304766i	−0.858351	−	0.513063i	$-0.828511\pi$
$23$	−6.87632	+	1.46161i	−1.43381	+	0.304766i	−0.575461	+	0.817829i	$0.695177\pi$
$24$	0.260349	−	0.450937i	0.0531435	−	0.0920472i
$25$		0			0
$26$	−3.62786	−	6.28364i	−0.711482	−	1.23232i
$27$	−0.138291	+	0.425616i	−0.0266141	+	0.0819098i
$28$	12.1389	−	2.64173i	2.29403	−	0.499240i
$29$	−2.21189	−	1.60703i	−0.410738	−	0.298418i	0.363163	−	0.931726i	$-0.381697\pi$
$29$	−2.21189	−	1.60703i	−0.410738	−	0.298418i	−0.773900	+	0.633307i	$0.781697\pi$
$30$		0			0
$31$	−0.929782	−	8.84628i	−0.166994	−	1.58884i	−0.681804	−	0.731535i	$-0.738804\pi$
$31$	−0.929782	−	8.84628i	−0.166994	−	1.58884i	0.514810	−	0.857304i	$-0.327862\pi$
$32$	4.22478	−	7.31754i	0.746843	−	1.29357i
$33$	0.257595	+	0.114689i	0.0448416	+	0.0199648i
$34$	0.240586	+	0.740447i	0.0412601	+	0.126986i
$35$		0			0
$36$	−4.34484	+	13.3720i	−0.724139	+	2.22867i
$37$	2.18285	−	2.42430i	0.358858	−	0.398552i	−0.536499	−	0.843901i	$-0.680254\pi$
$37$	2.18285	−	2.42430i	0.358858	−	0.398552i	0.895357	+	0.445349i	$0.146920\pi$
$38$	−10.2038	−	2.16888i	−1.65527	−	0.351839i
$39$	−0.140077	−	0.155571i	−0.0224302	−	0.0249113i
$40$		0			0
$41$	0.700664	+	2.15642i	0.109425	+	0.336776i	0.990744	−	0.135747i	$-0.0433433\pi$
$41$	0.700664	+	2.15642i	0.109425	+	0.336776i	−0.881318	+	0.472523i	$0.843343\pi$
$42$	0.465897	−	0.210141i	0.0718895	−	0.0324255i
$43$	9.05803			1.38134			0.690668	−	0.723172i	$-0.257317\pi$
$43$	9.05803			1.38134			0.690668	+	0.723172i	$0.257317\pi$
$44$	16.2014	+	7.21331i	2.44245	+	1.08745i
$45$		0			0
$46$	−16.6177	+	7.39869i	−2.45015	+	1.09088i
$47$	0.580225	−	5.52047i	0.0846345	−	0.805244i	−0.867061	−	0.498201i	$-0.833994\pi$
$47$	0.580225	−	5.52047i	0.0846345	−	0.805244i	0.951696	−	0.307042i	$-0.0993393\pi$
$48$	0.199702	−	0.614619i	0.0288245	−	0.0887126i
$49$	6.42211	+	2.78506i	0.917444	+	0.397865i
$50$		0			0
$51$	0.0112313	+	0.0194532i	0.00157270	+	0.00272400i
$52$	−8.81006	−	9.78456i	−1.22174	−	1.35687i
$53$	−3.35264	+	1.49269i	−0.460521	+	0.205037i	−0.623865	−	0.781532i	$-0.714439\pi$
$53$	−3.35264	+	1.49269i	−0.460521	+	0.205037i	0.163344	+	0.986569i	$0.447772\pi$
$54$	−0.121042	+	1.15164i	−0.0164717	+	0.156718i
$55$		0			0
$56$	16.8212	−	7.58716i	2.24783	−	1.01388i
$57$	−0.300975			−0.0398652
$58$	−6.46288	−	2.87746i	−0.848618	−	0.377829i
$59$	−8.63331	−	1.83507i	−1.12396	−	0.238905i	−0.391809	−	0.920047i	$-0.628151\pi$
$59$	−8.63331	−	1.83507i	−1.12396	−	0.238905i	−0.732152	+	0.681141i	$0.761484\pi$
$60$		0			0
$61$	−13.3724	+	2.84238i	−1.71215	+	0.363930i	−0.956656	−	0.291220i	$-0.905939\pi$
$61$	−13.3724	+	2.84238i	−1.71215	+	0.363930i	−0.755499	+	0.655150i	$0.772605\pi$
$62$	−7.11244	−	21.8898i	−0.903281	−	2.78001i
$63$	−6.38681	+	4.68773i	−0.804662	+	0.590599i
$64$	1.40634	−	4.32826i	0.175792	−	0.541033i
$65$		0			0
$66$	0.713678	+	0.151697i	0.0878477	+	0.0186726i
$67$	0.359475	+	3.42017i	0.0439168	+	0.417841i	0.994289	+	0.106724i	$0.0340362\pi$
$67$	0.359475	+	3.42017i	0.0439168	+	0.417841i	−0.950372	+	0.311116i	$0.899297\pi$
$68$	0.706390	+	1.22350i	0.0856624	+	0.148372i
$69$	−0.424593	+	0.308485i	−0.0511150	+	0.0371372i
$70$		0			0
$71$	−2.69801	−	1.96022i	−0.320195	−	0.232635i	0.416064	−	0.909335i	$-0.363409\pi$
$71$	−2.69801	−	1.96022i	−0.320195	−	0.232635i	−0.736258	+	0.676700i	$0.763409\pi$
$72$	−2.18308	+	20.7706i	−0.257278	+	2.44784i
$73$	8.75399	+	9.72229i	1.02458	+	1.13791i	0.990363	+	0.138494i	$0.0442260\pi$
$73$	8.75399	+	9.72229i	1.02458	+	1.13791i	0.0342137	+	0.999415i	$0.489107\pi$
$74$	4.22058	−	7.31027i	0.490633	−	0.849801i
$75$		0			0
$76$	−18.9297			−2.17139
$77$	5.03834	+	8.62982i	0.574172	+	0.983459i
$78$	−0.438230	−	0.318393i	−0.0496198	−	0.0360509i
$79$	−0.885368	+	8.42371i	−0.0996116	+	0.947741i	0.824563	+	0.565771i	$0.191421\pi$
$79$	−0.885368	+	8.42371i	−0.0996116	+	0.947741i	−0.924174	+	0.381971i	$0.875245\pi$
$80$		0			0
$81$	−0.935516	−	8.90084i	−0.103946	−	0.988982i
$82$	2.93351	+	5.08098i	0.323952	+	0.561101i
$83$	3.77939	−	2.74589i	0.414842	−	0.301401i	−0.360717	−	0.932675i	$-0.617468\pi$
$83$	3.77939	−	2.74589i	0.414842	−	0.301401i	0.775559	+	0.631275i	$0.217468\pi$
$84$	0.747672	−	0.548770i	0.0815778	−	0.0598757i
$85$		0			0
$86$	22.9260	−	4.87307i	2.47217	−	0.525476i
$87$	−0.199652	−	0.0424374i	−0.0214050	−	0.00454977i
$88$	25.7673	+	5.47702i	2.74681	+	0.583852i
$89$	−7.53425	+	1.60146i	−0.798629	+	0.169754i	−0.589112	−	0.808051i	$-0.700522\pi$
$89$	−7.53425	+	1.60146i	−0.798629	+	0.169754i	−0.209517	+	0.977805i	$0.567189\pi$
$90$		0			0
$91$	−0.811226	−	7.37442i	−0.0850396	−	0.773049i
$92$	−26.7046	+	19.4021i	−2.78415	+	2.02280i
$93$	−0.332032	−	0.575097i	−0.0344302	−	0.0596348i
$94$	−1.50137	−	14.2845i	−0.154854	−	1.47334i
$95$		0			0
$96$	0.0659376	−	0.627354i	0.00672972	−	0.0640290i
$97$	8.08430	+	5.87358i	0.820836	+	0.596372i	0.916952	−	0.398998i	$-0.130642\pi$
$97$	8.08430	+	5.87358i	0.820836	+	0.596372i	−0.0961159	+	0.995370i	$0.530642\pi$
$98$	17.7527	+	3.59403i	1.79330	+	0.363051i
$99$	−11.3099			−1.13668
$100$		0			0
$101$	−1.10483	+	1.91362i	−0.109934	+	0.190412i	−0.915744	−	0.401763i	$-0.868397\pi$
$101$	−1.10483	+	1.91362i	−0.109934	+	0.190412i	0.805809	+	0.592175i	$0.201731\pi$
$102$	0.0388922	+	0.0431941i	0.00385090	+	0.00427686i
$103$	−0.428418	+	4.07612i	−0.0422133	+	0.401632i	0.952930	+	0.303192i	$0.0980522\pi$
$103$	−0.428418	+	4.07612i	−0.0422133	+	0.401632i	−0.995143	+	0.0984408i	$0.968614\pi$
$104$	−15.8223	−	11.4956i	−1.55150	−	1.12723i
$105$		0			0
$106$	−7.68254	+	5.58169i	−0.746194	+	0.542142i
$107$	4.80061	+	8.31490i	0.464092	+	0.803831i	0.999160	−	0.0409777i	$-0.0130473\pi$
$107$	4.80061	+	8.31490i	0.464092	+	0.803831i	−0.535068	+	0.844809i	$0.679714\pi$
$108$	0.219646	+	2.08979i	0.0211355	+	0.201090i
$109$	−5.62465	−	1.19556i	−0.538744	−	0.114514i	−0.0694996	−	0.997582i	$-0.522140\pi$
$109$	−5.62465	−	1.19556i	−0.538744	−	0.114514i	−0.469244	+	0.883068i	$0.655474\pi$
$110$		0			0
$111$	0.0752591	−	0.231624i	0.00714328	−	0.0219847i
$112$	18.4631	−	13.5514i	1.74460	−	1.28049i
$113$	−0.786587	−	2.42087i	−0.0739959	−	0.227736i	0.907217	−	0.420662i	$-0.138202\pi$
$113$	−0.786587	−	2.42087i	−0.0739959	−	0.227736i	−0.981213	+	0.192926i	$0.938202\pi$
$114$	−0.761772	+	0.161920i	−0.0713465	+	0.0151652i
$115$		0			0
$116$	−12.5571	−	2.66908i	−1.16589	−	0.247818i
$117$	7.67069	+	3.41521i	0.709155	+	0.315736i
$118$	−22.8383			−2.10243
$119$	−0.0793742	+	0.792094i	−0.00727622	+	0.0726112i
$120$		0			0
$121$	−0.341340	+	3.24763i	−0.0310309	+	0.295239i
$122$	−32.3165	+	14.3882i	−2.92579	+	1.30265i
$123$	0.113267	+	0.125795i	0.0102129	+	0.0113426i
$124$	−20.8830	−	36.1705i	−1.87535	−	3.24821i
$125$		0			0
$126$	−13.6432	+	15.3007i	−1.21543	+	1.36310i
$127$	4.14002	−	12.7417i	0.367368	−	1.13064i	−0.581118	−	0.813820i	$-0.697384\pi$
$127$	4.14002	−	12.7417i	0.367368	−	1.13064i	0.948485	−	0.316822i	$-0.102616\pi$
$128$	−0.535515	+	5.09508i	−0.0473333	+	0.450346i
$129$	0.617771	−	0.275050i	0.0543917	−	0.0242168i
$130$		0			0
$131$	15.2146	+	6.77396i	1.32930	+	0.591844i	0.943694	−	0.330819i	$-0.107325\pi$
$131$	15.2146	+	6.77396i	1.32930	+	0.591844i	0.385609	+	0.922662i	$0.373992\pi$
$132$	1.32399			0.115239
$133$	−8.65954	−	6.22764i	−0.750877	−	0.540005i
$134$	2.74983	+	8.46311i	0.237549	+	0.731101i
$135$		0			0
$136$	1.40420	+	1.55953i	0.120409	+	0.133728i
$137$	8.58584	+	1.82498i	0.733538	+	0.155918i	0.559511	−	0.828823i	$-0.310989\pi$
$137$	8.58584	+	1.82498i	0.733538	+	0.155918i	0.174026	+	0.984741i	$0.444322\pi$
$138$	−0.908691	+	1.00920i	−0.0773529	+	0.0859091i
$139$	3.27911	−	10.0921i	0.278131	−	0.855998i	−0.710243	−	0.703956i	$-0.751415\pi$
$139$	3.27911	−	10.0921i	0.278131	−	0.855998i	0.988374	−	0.152042i	$-0.0485849\pi$
$140$		0			0
$141$	−0.128058	−	0.394123i	−0.0107845	−	0.0331912i
$142$	−7.88325	−	3.50985i	−0.661548	−	0.294540i
$143$	5.29547	−	9.17202i	0.442829	−	0.767003i
$144$	2.70947	+	25.7788i	0.225789	+	2.14824i
$145$		0			0
$146$	27.3869	+	19.8977i	2.26656	+	1.64675i
$147$	0.522567	−	0.00506400i	0.0431006	−	0.000417671i
$148$	4.73339	−	14.5679i	0.389082	−	1.19747i
$149$	0.695327	+	1.20434i	0.0569634	+	0.0986635i	0.893101	−	0.449856i	$-0.148525\pi$
$149$	0.695327	+	1.20434i	0.0569634	+	0.0986635i	−0.836138	+	0.548520i	$0.815191\pi$
$150$		0			0
$151$	7.74195	−	13.4095i	0.630031	−	1.09125i	−0.357514	−	0.933908i	$-0.616375\pi$
$151$	7.74195	−	13.4095i	0.630031	−	1.09125i	0.987545	−	0.157338i	$-0.0502912\pi$
$152$	−27.5038	+	5.84611i	−2.23085	+	0.474182i
$153$	−0.728901	−	0.529578i	−0.0589282	−	0.0428138i
$154$	17.3948	+	19.1316i	1.40171	+	1.54167i
$155$		0			0
$156$	−0.897971	−	0.399802i	−0.0718952	−	0.0320098i
$157$	−0.778227	+	1.34793i	−0.0621093	+	0.107576i	−0.895408	−	0.445246i	$-0.853116\pi$
$157$	−0.778227	+	1.34793i	−0.0621093	+	0.107576i	0.833299	+	0.552823i	$0.186449\pi$
$158$	2.29094	+	21.7968i	0.182257	+	1.73406i
$159$	−0.183329	+	0.203608i	−0.0145390	+	0.0161472i
$160$		0			0
$161$	−18.5993	+	0.0901171i	−1.46583	+	0.00710222i
$162$	−7.15631	−	22.0249i	−0.562253	−	1.73044i
$163$	−6.69088	+	7.43098i	−0.524071	+	0.582039i	−0.945827	−	0.324670i	$-0.894747\pi$
$163$	−6.69088	+	7.43098i	−0.524071	+	0.582039i	0.421757	+	0.906709i	$0.361414\pi$
$164$	7.12386	+	7.91185i	0.556280	+	0.617812i
$165$		0			0
$166$	8.08845	−	8.98314i	0.627786	−	0.697227i
$167$	−12.0074	+	8.72392i	−0.929164	+	0.675077i	−0.945788	−	0.324785i	$-0.894708\pi$
$167$	−12.0074	+	8.72392i	−0.929164	+	0.675077i	0.0166240	+	0.999862i	$0.494708\pi$
$168$	0.916847	−	1.02824i	0.0707363	−	0.0793302i
$169$	4.15602	−	3.01953i	0.319694	−	0.232271i
$170$		0			0
$171$	11.0284	−	4.91014i	0.843359	−	0.375488i
$172$	38.8545	−	17.2991i	2.96263	−	1.31905i
$173$	5.17415	−	1.09980i	0.393384	−	0.0836163i	−0.00697303	−	0.999976i	$-0.502220\pi$
$173$	5.17415	−	1.09980i	0.393384	−	0.0836163i	0.400357	+	0.916359i	$0.368886\pi$
$174$	−0.528153			−0.0400392
$175$		0			0
$176$	32.6948			2.46447
$177$	−0.644527	+	0.136999i	−0.0484456	+	0.0102974i
$178$	−18.2077	+	8.10661i	−1.36473	+	0.607616i
$179$	2.11260	−	0.940590i	0.157903	−	0.0703030i	−0.326263	−	0.945279i	$-0.605790\pi$
$179$	2.11260	−	0.940590i	0.157903	−	0.0703030i	0.484166	+	0.874976i	$0.339123\pi$
$180$		0			0
$181$	−14.4034	+	10.4647i	−1.07060	+	0.777834i	−0.976019	−	0.217684i	$-0.930150\pi$
$181$	−14.4034	+	10.4647i	−1.07060	+	0.777834i	−0.0945769	+	0.995518i	$0.530150\pi$
$182$	−6.02054	−	18.2283i	−0.446272	−	1.35117i
$183$	−0.825706	+	0.599910i	−0.0610379	+	0.0443466i
$184$	−32.8083	+	36.4373i	−2.41866	+	2.68620i
$185$		0			0
$186$	−1.14977	−	1.27695i	−0.0843053	−	0.0936305i
$187$	−0.760418	+	0.844529i	−0.0556072	+	0.0617581i
$188$	−8.05419	−	24.7882i	−0.587412	−	1.80787i
$189$	−0.587037	+	1.02825i	−0.0427007	+	0.0747943i
$190$		0			0
$191$	−8.60554	+	9.55742i	−0.622675	+	0.691551i	−0.969140	−	0.246512i	$-0.920715\pi$
$191$	−8.60554	+	9.55742i	−0.622675	+	0.691551i	0.346465	+	0.938063i	$0.387382\pi$
$192$	−0.0355145	−	0.337898i	−0.00256304	−	0.0243857i
$193$	13.2916	−	23.0217i	0.956751	−	1.65714i	0.226441	−	0.974025i	$-0.427291\pi$
$193$	13.2916	−	23.0217i	0.956751	−	1.65714i	0.730310	−	0.683116i	$-0.239376\pi$
$194$	23.6213	+	10.5169i	1.69591	+	0.755069i
$195$		0			0
$196$	32.8666	−	0.318498i	2.34762	−	0.0227499i
$197$	2.67856	+	1.94609i	0.190840	+	0.138653i	0.679102	−	0.734044i	$-0.262369\pi$
$197$	2.67856	+	1.94609i	0.190840	+	0.138653i	−0.488263	+	0.872697i	$0.662369\pi$
$198$	−28.6254	+	6.08452i	−2.03432	+	0.432408i
$199$	−7.70711	+	13.3491i	−0.546342	+	0.946293i	0.452179	+	0.891927i	$0.350647\pi$
$199$	−7.70711	+	13.3491i	−0.546342	+	0.946293i	−0.998521	+	0.0543655i	$0.982686\pi$
$200$		0			0
$201$	0.128371	+	0.222345i	0.00905461	+	0.0156830i
$202$	−1.76684	+	5.43777i	−0.124314	+	0.382600i
$203$	−4.86622	−	5.35210i	−0.341541	−	0.375644i
$204$	0.0853290	+	0.0619951i	0.00597422	+	0.00434053i
$205$		0			0
$206$	1.10856	+	10.5472i	0.0772367	+	0.734858i
$207$	10.5253	−	18.2304i	0.731560	−	1.26710i
$208$	−22.1746	−	9.87278i	−1.53753	−	0.684554i
$209$	−4.70536	−	14.4816i	−0.325477	−	1.00171i
$210$		0			0
$211$	3.86469	−	11.8943i	0.266056	−	0.818836i	−0.725392	−	0.688336i	$-0.758342\pi$
$211$	3.86469	−	11.8943i	0.266056	−	0.818836i	0.991448	−	0.130500i	$-0.0416584\pi$
$212$	−11.5304	+	12.8058i	−0.791913	+	0.879508i
$213$	−0.243531	−	0.0517641i	−0.0166865	−	0.00354681i
$214$	16.6237	+	18.4625i	1.13637	+	1.26207i
$215$		0			0
$216$	0.964529	+	2.96852i	0.0656279	+	0.201982i
$217$	2.34654	−	23.4167i	0.159294	−	1.58963i
$218$	−14.8792			−1.00775
$219$	0.892256	+	0.397258i	0.0602930	+	0.0268442i
$220$		0			0
$221$	0.770758	−	0.343164i	0.0518468	−	0.0230837i
$222$	0.0658720	−	0.626731i	0.00442104	−	0.0420634i
$223$	−2.40341	+	7.39692i	−0.160944	+	0.495334i	−0.998715	−	0.0506879i	$-0.983859\pi$
$223$	−2.40341	+	7.39692i	−0.160944	+	0.495334i	0.837771	+	0.546022i	$0.183859\pi$
$224$	14.8780	−	16.6856i	0.994081	−	1.11485i
$225$		0			0
$226$	−3.29325	−	5.70407i	−0.219064	−	0.379429i
$227$	4.61566	+	5.12621i	0.306352	+	0.340238i	0.876587	−	0.481243i	$-0.159815\pi$
$227$	4.61566	+	5.12621i	0.306352	+	0.340238i	−0.570235	+	0.821482i	$0.693148\pi$
$228$	−1.29104	+	0.574806i	−0.0855010	+	0.0380675i
$229$	1.91955	−	18.2633i	0.126848	−	1.20688i	−0.727106	−	0.686526i	$-0.759135\pi$
$229$	1.91955	−	18.2633i	0.126848	−	1.20688i	0.853953	−	0.520349i	$-0.174198\pi$
$230$		0			0
$231$	0.605669	+	0.435577i	0.0398501	+	0.0286588i
$232$	−19.0690			−1.25194
$233$	8.18247	+	3.64307i	0.536052	+	0.238666i	0.656863	−	0.754010i	$-0.271883\pi$
$233$	8.18247	+	3.64307i	0.536052	+	0.238666i	−0.120811	+	0.992675i	$0.538550\pi$
$234$	21.2519	+	4.51724i	1.38928	+	0.295301i
$235$		0			0
$236$	−40.5373	+	8.61647i	−2.63875	+	0.560884i
$237$	0.195405	+	0.601394i	0.0126929	+	0.0390648i
$238$	0.225236	+	2.04750i	0.0145999	+	0.132720i
$239$	−5.12153	+	15.7624i	−0.331284	+	1.01959i	0.637240	+	0.770666i	$0.280076\pi$
$239$	−5.12153	+	15.7624i	−0.331284	+	1.01959i	−0.968524	+	0.248922i	$0.919924\pi$
$240$		0			0
$241$	5.74126	+	1.22034i	0.369827	+	0.0786091i	0.389076	−	0.921206i	$-0.372794\pi$
$241$	5.74126	+	1.22034i	0.369827	+	0.0786091i	−0.0192493	+	0.999815i	$0.506128\pi$
$242$	0.883236	+	8.40343i	0.0567766	+	0.540193i
$243$	−1.00536	−	1.74133i	−0.0644938	−	0.111707i
$244$	−51.9324	+	37.7311i	−3.32463	+	2.41549i
$245$		0			0
$246$	0.354355	+	0.257454i	0.0225929	+	0.0164147i
$247$	−1.18166	+	11.2427i	−0.0751871	+	0.715358i
$248$	−41.5125	−	46.1043i	−2.63605	−	2.92763i
$249$	0.174381	−	0.302036i	0.0110509	−	0.0191408i
$250$		0			0
$251$	−3.59519			−0.226927			−0.113463	−	0.993542i	$-0.536194\pi$
$251$	−3.59519			−0.226927			−0.113463	+	0.993542i	$0.536194\pi$
$252$	−18.4436	+	32.3057i	−1.16184	+	2.03507i
$253$	−21.4809	−	15.6068i	−1.35049	−	0.981192i
$254$	3.62364	−	34.4766i	0.227367	−	2.16326i
$255$		0			0
$256$	2.33709	+	22.2360i	0.146068	+	1.38975i
$257$	−2.18455	−	3.78375i	−0.136268	−	0.236024i	0.789813	−	0.613348i	$-0.210178\pi$
$257$	−2.18455	−	3.78375i	−0.136268	−	0.236024i	−0.926081	+	0.377324i	$0.876844\pi$
$258$	1.41562	−	1.02850i	0.0881324	−	0.0640319i
$259$	6.95797	−	5.10695i	0.432347	−	0.317331i
$260$		0			0
$261$	8.00800	−	1.70215i	0.495683	−	0.105361i
$262$	42.1525	+	8.95980i	2.60419	+	0.553538i
$263$	7.71547	+	1.63997i	0.475756	+	0.101125i	0.439548	−	0.898219i	$-0.355139\pi$
$263$	7.71547	+	1.63997i	0.475756	+	0.101125i	0.0362085	+	0.999344i	$0.488472\pi$
$264$	1.92368	−	0.408892i	0.118395	−	0.0251655i
$265$		0			0
$266$	−25.2678	−	11.1036i	−1.54927	−	0.680802i
$267$	−0.465219	+	0.338001i	−0.0284709	+	0.0206854i
$268$	8.07386	+	13.9843i	0.493189	+	0.854229i
$269$	−1.86154	−	17.7114i	−0.113500	−	1.07988i	−0.891937	−	0.452160i	$-0.850653\pi$
$269$	−1.86154	−	17.7114i	−0.113500	−	1.07988i	0.778436	−	0.627724i	$-0.216013\pi$
$270$		0			0
$271$	1.11434	−	10.6022i	0.0676912	−	0.644039i	−0.907099	−	0.420917i	$-0.861708\pi$
$271$	1.11434	−	10.6022i	0.0676912	−	0.644039i	0.974791	−	0.223122i	$-0.0716249\pi$
$272$	2.10713	+	1.53092i	0.127763	+	0.0928255i
$273$	−0.279253	−	0.478313i	−0.0169012	−	0.0289488i
$274$	22.7127			1.37212
$275$		0			0
$276$	−1.23215	+	2.13414i	−0.0741666	+	0.128460i
$277$	−1.83175	−	2.03436i	−0.110059	−	0.122233i	0.685598	−	0.727980i	$-0.259541\pi$
$277$	−1.83175	−	2.03436i	−0.110059	−	0.122233i	−0.795657	+	0.605748i	$0.792874\pi$
$278$	2.87011	−	27.3073i	0.172138	−	1.63778i
$279$	21.5485	+	15.6559i	1.29008	+	0.937296i
$280$		0			0
$281$	11.9857	−	8.70811i	0.715006	−	0.519483i	−0.169779	−	0.985482i	$-0.554305\pi$
$281$	11.9857	−	8.70811i	0.715006	−	0.519483i	0.884785	+	0.466000i	$0.154305\pi$
$282$	−0.536150	−	0.928638i	−0.0319272	−	0.0552996i
$283$	0.685244	+	6.51967i	0.0407336	+	0.387554i	0.995828	+	0.0912519i	$0.0290868\pi$
$283$	0.685244	+	6.51967i	0.0407336	+	0.387554i	−0.955094	+	0.296302i	$0.904246\pi$
$284$	−15.3168	−	3.25568i	−0.908883	−	0.193189i
$285$		0			0
$286$	8.46850	−	26.0634i	0.500753	−	1.54116i
$287$	0.655962	+	5.96299i	0.0387202	+	0.351984i
$288$	7.81862	+	24.0633i	0.460717	+	1.41794i
$289$	16.5400	−	3.51568i	0.972939	−	0.206804i
$290$		0			0
$291$	0.729714	+	0.155106i	0.0427766	+	0.00909245i
$292$	56.1181	+	24.9854i	3.28406	+	1.46216i
$293$	31.4682			1.83839			0.919197	−	0.393798i	$-0.128839\pi$
$293$	31.4682			1.83839			0.919197	+	0.393798i	$0.128839\pi$
$294$	1.31990	−	0.293949i	0.0769780	−	0.0171435i
$295$		0			0
$296$	2.37831	−	22.6281i	0.138237	−	1.31523i
$297$	−1.54414	+	0.687494i	−0.0895999	+	0.0398924i
$298$	2.40780	+	2.67413i	0.139480	+	0.154908i
$299$	9.85626	+	17.0715i	0.570002	+	0.987273i
$300$		0			0
$301$	23.4655	+	4.86903i	1.35253	+	0.280646i
$302$	12.3809	−	38.1045i	0.712442	−	2.19267i
$303$	−0.0172434	+	0.164060i	−0.000990608	+	0.00942501i
$304$	−31.8810	+	14.1944i	−1.82850	+	0.814102i
$305$		0			0
$306$	−2.12976	−	0.948231i	−0.121750	−	0.0542068i
$307$	−19.5635			−1.11655			−0.558274	−	0.829657i	$-0.688536\pi$
$307$	−19.5635			−1.11655			−0.558274	+	0.829657i	$0.688536\pi$
$308$	38.0933	+	27.3954i	2.17057	+	1.56100i
$309$	0.0945539	+	0.291007i	0.00537898	+	0.0165548i
$310$		0			0
$311$	22.1198	+	24.5666i	1.25430	+	1.39304i	0.886231	+	0.463243i	$0.153314\pi$
$311$	22.1198	+	24.5666i	1.25430	+	1.39304i	0.368069	+	0.929798i	$0.380019\pi$
$312$	−1.42817	−	0.303567i	−0.0808543	−	0.0171861i
$313$	5.09319	−	5.65656i	0.287884	−	0.319728i	−0.581804	−	0.813329i	$-0.697653\pi$
$313$	5.09319	−	5.65656i	0.287884	−	0.319728i	0.869688	+	0.493601i	$0.164320\pi$
$314$	−1.24454	+	3.83030i	−0.0702334	+	0.216156i
$315$		0			0
$316$	12.2899	+	37.8245i	0.691362	+	2.12779i
$317$	−20.4642	−	9.11123i	−1.14938	−	0.511738i	−0.258517	−	0.966007i	$-0.583234\pi$
$317$	−20.4642	−	9.11123i	−1.14938	−	0.511738i	−0.890864	+	0.454269i	$0.849900\pi$
$318$	−0.354471	+	0.613962i	−0.0198778	+	0.0344293i
$319$	−1.07940	−	10.2698i	−0.0604351	−	0.575001i
$320$		0			0
$321$	0.579893	+	0.421317i	0.0323665	+	0.0235156i
$322$	−47.0265	+	10.2342i	−2.62068	+	0.570328i
$323$	0.374841	−	1.15364i	0.0208567	−	0.0641903i
$324$	−21.0118	−	36.3936i	−1.16732	−	2.02187i
$325$		0			0
$326$	−12.9370	+	22.4075i	−0.716513	+	1.24104i
$327$	−0.419913	+	0.0892553i	−0.0232212	+	0.00493583i
$328$	12.7940	+	9.29539i	0.706431	+	0.513252i
$329$	4.47057	−	13.9893i	0.246471	−	0.771254i
$330$		0			0
$331$	8.50853	+	3.78824i	0.467671	+	0.208221i	0.627022	−	0.779001i	$-0.284274\pi$
$331$	8.50853	+	3.78824i	0.467671	+	0.208221i	−0.159351	+	0.987222i	$0.550940\pi$
$332$	10.9676	−	18.9965i	0.601926	−	1.04257i
$333$	1.02108	+	9.71495i	0.0559550	+	0.532376i
$334$	−25.6977	+	28.5402i	−1.40611	+	1.56165i
$335$		0			0
$336$	0.847722	−	1.48487i	0.0462470	−	0.0810061i
$337$	−4.47228	−	13.7643i	−0.243621	−	0.749788i	−0.995860	−	0.0908979i	$-0.971026\pi$
$337$	−4.47228	−	13.7643i	−0.243621	−	0.749788i	0.752239	−	0.658890i	$-0.228974\pi$
$338$	8.89449	−	9.87834i	0.483797	−	0.537311i
$339$	−0.127157	−	0.141222i	−0.00690620	−	0.00767012i
$340$		0			0
$341$	22.4803	−	24.9668i	1.21737	−	1.35203i
$342$	25.2713	−	18.3607i	1.36652	−	0.992833i
$343$	15.1398	+	10.6670i	0.817475	+	0.575964i
$344$	51.1108	−	37.1342i	2.75571	−	2.00214i
$345$		0			0
$346$	12.5042	−	5.56722i	0.672228	−	0.299295i
$347$	−2.98632	+	1.32960i	−0.160314	+	0.0713765i	−0.485325	−	0.874334i	$-0.661299\pi$
$347$	−2.98632	+	1.32960i	−0.160314	+	0.0713765i	0.325011	+	0.945710i	$0.394632\pi$
$348$	−0.937458	+	0.199263i	−0.0502530	+	0.0106816i
$349$	−20.1244			−1.07724			−0.538618	−	0.842550i	$-0.681053\pi$
$349$	−20.1244			−1.07724			−0.538618	+	0.842550i	$0.681053\pi$
$350$		0			0
$351$	1.25488			0.0669805
$352$	31.2164	−	6.63525i	1.66384	−	0.353660i
$353$	28.8788	−	12.8577i	1.53707	−	0.684345i	0.548641	−	0.836058i	$-0.315146\pi$
$353$	28.8788	−	12.8577i	1.53707	−	0.684345i	0.988425	+	0.151713i	$0.0484789\pi$
$354$	−1.55760	+	0.693490i	−0.0827857	+	0.0368586i
$355$		0			0
$356$	−29.2598	+	21.2585i	−1.55076	+	1.12670i
$357$	0.0186387	+	0.0564323i	0.000986466	+	0.00298671i
$358$	4.84100	−	3.51719i	0.255855	−	0.185889i
$359$	−6.91359	+	7.67832i	−0.364885	+	0.405246i	−0.897431	−	0.441155i	$-0.854569\pi$
$359$	−6.91359	+	7.67832i	−0.364885	+	0.405246i	0.532546	+	0.846401i	$0.321235\pi$
$360$		0			0
$361$	−1.83810	−	2.04141i	−0.0967419	−	0.107443i
$362$	−30.8254	+	34.2350i	−1.62015	+	1.79935i
$363$	0.0753353	+	0.231858i	0.00395408	+	0.0121694i
$364$	−17.5635	−	30.0833i	−0.920578	−	1.57680i
$365$		0			0
$366$	−1.76713	+	1.96260i	−0.0923693	+	0.102587i
$367$	1.78671	+	16.9994i	0.0932656	+	0.887363i	0.936701	+	0.350132i	$0.113863\pi$
$367$	1.78671	+	16.9994i	0.0932656	+	0.887363i	−0.843435	+	0.537231i	$0.819470\pi$
$368$	−30.4269	+	52.7009i	−1.58611	+	2.74722i
$369$	−6.20256	−	2.76156i	−0.322892	−	0.143761i
$370$		0			0
$371$	−9.48763	+	2.06475i	−0.492573	+	0.107197i
$372$	−2.52258	−	1.83276i	−0.130790	−	0.0950244i
$373$	25.3643	−	5.39135i	1.31331	−	0.279154i	0.502561	−	0.864542i	$-0.332391\pi$
$373$	25.3643	−	5.39135i	1.31331	−	0.279154i	0.810753	+	0.585388i	$0.199058\pi$
$374$	−1.47028	+	2.54661i	−0.0760266	+	0.131682i
$375$		0			0
$376$	−19.3577	−	33.5285i	−0.998297	−	1.72910i
$377$	−2.36908	+	7.29126i	−0.122014	+	0.375519i
$378$	−0.932616	+	2.91833i	−0.0479686	+	0.150103i
$379$	−6.09850	−	4.43082i	−0.313259	−	0.227596i	0.420035	−	0.907508i	$-0.362018\pi$
$379$	−6.09850	−	4.43082i	−0.313259	−	0.227596i	−0.733293	+	0.679912i	$0.762018\pi$
$380$		0			0
$381$	−0.104549	−	0.994715i	−0.00535620	−	0.0509608i
$382$	−16.6390	+	28.8196i	−0.851325	+	1.47454i
$383$	−15.4170	−	6.86409i	−0.787772	−	0.350739i	−0.0268979	−	0.999638i	$-0.508563\pi$
$383$	−15.4170	−	6.86409i	−0.787772	−	0.350739i	−0.760874	+	0.648900i	$0.775230\pi$
$384$	0.118191	+	0.363754i	0.00603139	+	0.0185627i
$385$		0			0
$386$	21.2559	−	65.4190i	1.08190	−	3.32974i
$387$	−18.1492	+	20.1568i	−0.922577	+	1.02463i
$388$	45.8951	+	9.75530i	2.32997	+	0.495251i
$389$	7.08687	+	7.87077i	0.359319	+	0.399064i	0.895516	−	0.445029i	$-0.146807\pi$
$389$	7.08687	+	7.87077i	0.359319	+	0.399064i	−0.536198	+	0.844092i	$0.680140\pi$
$390$		0			0
$391$	−0.653629	−	2.01166i	−0.0330554	−	0.101734i
$392$	47.6550	−	10.6130i	2.40694	−	0.536039i
$393$	1.24335			0.0627187
$394$	7.82644	+	3.48456i	0.394290	+	0.175549i
$395$		0			0
$396$	−48.5138	+	21.5997i	−2.43791	+	1.08543i
$397$	3.72434	−	35.4347i	0.186919	−	1.77842i	−0.351943	−	0.936022i	$-0.614479\pi$
$397$	3.72434	−	35.4347i	0.186919	−	1.77842i	0.538862	−	0.842394i	$-0.318855\pi$
$398$	−12.3252	+	37.9330i	−0.617806	+	1.90141i
$399$	−0.779698	−	0.161785i	−0.0390337	−	0.00809940i
$400$		0			0
$401$	2.81098	+	4.86877i	0.140374	+	0.243135i	0.927637	−	0.373482i	$-0.121836\pi$
$401$	2.81098	+	4.86877i	0.140374	+	0.243135i	−0.787264	+	0.616617i	$0.788503\pi$
$402$	0.444527	+	0.493698i	0.0221710	+	0.0246234i
$403$	−22.7860	+	10.1450i	−1.13505	+	0.505356i
$404$	−1.08452	+	10.3185i	−0.0539568	+	0.513364i
$405$		0			0
$406$	−15.1958	−	10.9283i	−0.754155	−	0.542362i
$407$	12.3213			0.610744
$408$	0.143124	+	0.0637230i	0.00708570	+	0.00315476i
$409$	10.7297	+	2.28066i	0.530548	+	0.112772i	0.465394	−	0.885104i	$-0.345913\pi$
$409$	10.7297	+	2.28066i	0.530548	+	0.112772i	0.0651544	+	0.997875i	$0.479246\pi$
$410$		0			0
$411$	0.640983	−	0.136245i	0.0316174	−	0.00672048i
$412$	5.94693	+	18.3028i	0.292984	+	0.901712i
$413$	−21.3788	−	9.39460i	−1.05198	−	0.462278i
$414$	16.8321	−	51.8038i	0.827251	−	2.54602i
$415$		0			0
$416$	−23.1755	−	4.92611i	−1.13627	−	0.241522i
$417$	−0.0828080	−	0.787866i	−0.00405513	−	0.0385820i
$418$	−19.7002	−	34.1217i	−0.963568	−	1.66895i
$419$	10.3403	−	7.51266i	0.505156	−	0.367018i	−0.305827	−	0.952087i	$-0.598933\pi$
$419$	10.3403	−	7.51266i	0.505156	−	0.367018i	0.810983	+	0.585070i	$0.198933\pi$
$420$		0			0
$421$	−31.8380	−	23.1317i	−1.55169	−	1.12737i	−0.942432	−	0.334399i	$-0.891467\pi$
$421$	−31.8380	−	23.1317i	−1.55169	−	1.12737i	−0.609260	−	0.792971i	$-0.708533\pi$
$422$	3.38265	−	32.1837i	0.164665	−	1.56668i
$423$	11.1221	+	12.3523i	0.540775	+	0.600591i
$424$	−12.7982	+	22.1671i	−0.621535	+	1.07653i
$425$		0			0
$426$	−0.644228			−0.0312129
$427$	−36.1699	+	0.175250i	−1.75038	+	0.00848096i
$428$	36.4721	+	26.4986i	1.76295	+	1.28086i
$429$	0.0826481	−	0.786344i	0.00399029	−	0.0379651i
$430$		0			0
$431$	1.35516	+	12.8935i	0.0652760	+	0.621059i	0.977437	+	0.211227i	$0.0677460\pi$
$431$	1.35516	+	12.8935i	0.0652760	+	0.621059i	−0.912161	+	0.409832i	$0.865587\pi$
$432$	1.93694	+	3.35489i	0.0931913	+	0.161412i
$433$	−24.9136	+	18.1008i	−1.19727	+	0.869868i	−0.994013	−	0.109258i	$-0.965153\pi$
$433$	−24.9136	+	18.1008i	−1.19727	+	0.869868i	−0.203257	+	0.979126i	$0.565153\pi$
$434$	−6.65867	−	60.5304i	−0.319627	−	2.90555i
$435$		0			0
$436$	−26.4103	+	5.61368i	−1.26482	+	0.268846i
$437$	27.7219	+	5.89247i	1.32612	+	0.281875i
$438$	2.47203	+	0.525446i	0.118118	+	0.0251068i
$439$	9.57539	−	2.03531i	0.457008	−	0.0971401i	0.0263453	−	0.999653i	$-0.491613\pi$
$439$	9.57539	−	2.03531i	0.457008	−	0.0971401i	0.430663	+	0.902513i	$0.358280\pi$
$440$		0			0
$441$	−19.0653	+	8.71076i	−0.907871	+	0.414798i
$442$	1.76618	−	1.28321i	0.0840087	−	0.0610359i
$443$	−13.7534	−	23.8217i	−0.653446	−	1.13180i	−0.982281	−	0.187414i	$-0.939989\pi$
$443$	−13.7534	−	23.8217i	−0.653446	−	1.13180i	0.328835	−	0.944387i	$-0.393344\pi$
$444$	−0.119533	−	1.13728i	−0.00567280	−	0.0539730i
$445$		0			0
$446$	−2.10363	+	20.0147i	−0.0996097	+	0.947723i
$447$	0.0839925	+	0.0610241i	0.00397271	+	0.00288634i
$448$	5.96982	−	10.4567i	0.282047	−	0.494033i
$449$	−21.4940			−1.01436			−0.507182	−	0.861839i	$-0.669313\pi$
$449$	−21.4940			−1.01436			−0.507182	+	0.861839i	$0.669313\pi$
$450$		0			0
$451$	−4.28195	+	7.41655i	−0.201629	+	0.349232i
$452$	−7.99747	−	8.88209i	−0.376169	−	0.417778i
$453$	0.120831	−	1.14963i	0.00567714	−	0.0540144i
$454$	14.4401	+	10.4913i	0.677708	+	0.492383i
$455$		0			0
$456$	−1.69828	+	1.23387i	−0.0795294	+	0.0577815i
$457$	−9.89884	−	17.1453i	−0.463048	−	0.802023i	0.536063	−	0.844178i	$-0.319911\pi$
$457$	−9.89884	−	17.1453i	−0.463048	−	0.802023i	−0.999111	+	0.0421551i	$0.986578\pi$
$458$	−4.96695	−	47.2574i	−0.232091	−	2.20819i
$459$	−0.131708	−	0.0279955i	−0.00614762	−	0.00130672i
$460$		0			0
$461$	−1.92363	+	5.92031i	−0.0895922	+	0.275736i	−0.985807	−	0.167885i	$-0.946306\pi$
$461$	−1.92363	+	5.92031i	−0.0895922	+	0.275736i	0.896214	+	0.443621i	$0.146306\pi$
$462$	1.76729	+	0.776610i	0.0822217	+	0.0361312i
$463$	−3.40304	−	10.4735i	−0.158153	−	0.486744i	0.840314	−	0.542100i	$-0.182371\pi$
$463$	−3.40304	−	10.4735i	−0.158153	−	0.486744i	−0.998467	+	0.0553559i	$0.982371\pi$
$464$	−23.1497	+	4.92063i	−1.07470	+	0.228434i
$465$		0			0
$466$	22.6699	+	4.81863i	1.05016	+	0.223219i
$467$	10.2742	+	4.57435i	0.475431	+	0.211676i	0.630441	−	0.776237i	$-0.282874\pi$
$467$	10.2742	+	4.57435i	0.475431	+	0.211676i	−0.155010	+	0.987913i	$0.549541\pi$
$468$	39.4259			1.82246
$469$	−0.907226	+	9.05343i	−0.0418918	+	0.418048i
$470$		0			0
$471$	−0.0121460	+	0.115562i	−0.000559660	+	0.00532481i
$472$	−56.2373	+	25.0385i	−2.58853	+	1.15249i
$473$	22.8922	+	25.4244i	1.05259	+	1.16902i
$474$	0.818112	+	1.41701i	0.0375772	+	0.0650855i
$475$		0			0
$476$	1.17228	+	3.54928i	0.0537311	+	0.162681i
$477$	3.39589	−	10.4515i	0.155487	−	0.478540i
$478$	−4.48272	+	42.6502i	−0.205035	+	1.95078i
$479$	−27.1792	+	12.1010i	−1.24185	+	0.552908i	−0.919268	−	0.393633i	$-0.871218\pi$
$479$	−27.1792	+	12.1010i	−1.24185	+	0.552908i	−0.322584	+	0.946541i	$0.604551\pi$
$480$		0			0
$481$	−8.35667	−	3.72063i	−0.381032	−	0.169646i
$482$	15.1877			0.691782
$483$	−1.26576	+	0.570918i	−0.0575941	+	0.0259777i
$484$	4.73819	+	14.5826i	0.215372	+	0.662847i
$485$		0			0
$486$	−3.48138	−	3.86647i	−0.157919	−	0.175387i
$487$	−34.3058	−	7.29192i	−1.55454	−	0.330428i	−0.651051	−	0.759034i	$-0.725672\pi$
$487$	−34.3058	−	7.29192i	−1.55454	−	0.330428i	−0.903492	+	0.428606i	$0.859005\pi$
$488$	−63.8023	+	70.8596i	−2.88819	+	3.20766i
$489$	−0.230685	+	0.709975i	−0.0104319	+	0.0321062i
$490$		0			0
$491$	0.608859	+	1.87387i	0.0274774	+	0.0845667i	0.963855	−	0.266428i	$-0.0858435\pi$
$491$	0.608859	+	1.87387i	0.0274774	+	0.0845667i	−0.936377	+	0.350995i	$0.885843\pi$
$492$	0.726104	+	0.323282i	0.0327353	+	0.0145747i
$493$	0.411314	−	0.712417i	0.0185246	−	0.0320856i
$494$	3.05761	+	29.0912i	0.137568	+	1.30888i
$495$		0			0
$496$	−62.2930	−	45.2585i	−2.79704	−	2.03217i
$497$	−5.93569	−	6.52836i	−0.266252	−	0.292837i
$498$	0.278869	−	0.858272i	0.0124964	−	0.0384601i
$499$	8.83166	+	15.2969i	0.395359	+	0.684783i	0.993147	−	0.116872i	$-0.0372867\pi$
$499$	8.83166	+	15.2969i	0.395359	+	0.684783i	−0.597788	+	0.801655i	$0.703953\pi$
$500$		0			0
$501$	−0.554022	+	0.959594i	−0.0247519	+	0.0428715i
$502$	−9.09948	+	1.93415i	−0.406130	+	0.0863255i
$503$	−3.27003	−	2.37581i	−0.145803	−	0.105932i	0.512492	−	0.858692i	$-0.328722\pi$
$503$	−3.27003	−	2.37581i	−0.145803	−	0.105932i	−0.658296	+	0.752760i	$0.728722\pi$
$504$	−16.8204	+	52.6343i	−0.749240	+	2.34452i
$505$		0			0
$506$	−62.7647	−	27.9446i	−2.79023	−	1.24229i
$507$	0.191758	−	0.332135i	0.00851629	−	0.0147506i
$508$	−6.57555	−	62.5622i	−0.291743	−	2.77575i
$509$	9.19444	−	10.2115i	0.407536	−	0.452615i	−0.504080	−	0.863657i	$-0.668168\pi$
$509$	9.19444	−	10.2115i	0.407536	−	0.452615i	0.911616	+	0.411042i	$0.134835\pi$
$510$		0			0
$511$	17.4517	+	29.8919i	0.772019	+	1.32234i
$512$	14.7115	+	45.2774i	0.650163	+	2.00100i
$513$	1.20723	−	1.34076i	0.0533004	−	0.0591961i
$514$	−7.56472	−	8.40147i	−0.333665	−	0.370573i
$515$		0			0
$516$	2.12464	−	2.35965i	0.0935322	−	0.103878i
$517$	16.9615	−	12.3232i	0.745965	−	0.541975i
$518$	14.8633	−	16.6690i	0.653054	−	0.732396i
$519$	0.319489	−	0.232123i	0.0140240	−	0.0101891i
$520$		0			0
$521$	−13.7884	+	6.13900i	−0.604082	+	0.268955i	−0.685904	−	0.727692i	$-0.740593\pi$
$521$	−13.7884	+	6.13900i	−0.604082	+	0.268955i	0.0818217	+	0.996647i	$0.473926\pi$
$522$	19.3526	−	8.61634i	0.847041	−	0.377127i
$523$	21.0571	−	4.47583i	0.920763	−	0.195714i	0.276939	−	0.960888i	$-0.410680\pi$
$523$	21.0571	−	4.47583i	0.920763	−	0.195714i	0.643824	+	0.765173i	$0.277347\pi$
$524$	78.2000			3.41618
$525$		0			0
$526$	20.4102			0.889929
$527$	2.61787	−	0.556446i	0.114036	−	0.0242392i
$528$	2.22984	−	0.992788i	0.0970413	−	0.0432056i
$529$	24.1359	−	10.7460i	1.04939	−	0.467217i
$530$		0			0
$531$	21.3818	−	15.5348i	0.927891	−	0.674152i
$532$	−49.0388	−	10.1754i	−2.12610	−	0.441161i
$533$	5.14370	−	3.73712i	0.222798	−	0.161872i
$534$	−0.995636	+	1.10577i	−0.0430854	+	0.0478512i
$535$		0			0
$536$	16.0497	+	17.8250i	0.693240	+	0.769921i
$537$	0.115521	−	0.128299i	0.00498511	−	0.00553653i
$538$	−14.2400	−	43.8263i	−0.613932	−	1.88949i
$539$	8.41331	+	25.0645i	0.362387	+	1.07960i
$540$		0			0
$541$	−25.2587	+	28.0526i	−1.08595	+	1.20607i	−0.108684	+	0.994076i	$0.534664\pi$
$541$	−25.2587	+	28.0526i	−1.08595	+	1.20607i	−0.977270	+	0.211998i	$0.932003\pi$
$542$	−2.88341	−	27.4338i	−0.123853	−	1.17838i
$543$	−0.664571	+	1.15107i	−0.0285195	+	0.0493972i
$544$	2.32253	+	1.03406i	0.0995778	+	0.0443349i
$545$		0			0
$546$	−0.964118	−	1.06038i	−0.0412604	−	0.0453802i
$547$	2.90556	+	2.11101i	0.124233	+	0.0902603i	0.648166	−	0.761499i	$-0.275536\pi$
$547$	2.90556	+	2.11101i	0.124233	+	0.0902603i	−0.523934	+	0.851759i	$0.675536\pi$
$548$	40.3144	−	8.56909i	1.72215	−	0.366053i
$549$	20.4686	−	35.4526i	0.873577	−	1.51308i
$550$		0			0
$551$	5.51116	+	9.54560i	0.234783	+	0.406656i
$552$	−1.13115	+	3.48132i	−0.0481449	+	0.148175i
$553$	−6.82167	+	21.3463i	−0.290087	+	0.907737i
$554$	−5.73063	−	4.16354i	−0.243471	−	0.176892i
$555$		0			0
$556$	−5.20818	−	49.5525i	−0.220876	−	2.10149i
$557$	−7.08773	+	12.2763i	−0.300317	+	0.520164i	−0.976208	−	0.216838i	$-0.930426\pi$
$557$	−7.08773	+	12.2763i	−0.300317	+	0.520164i	0.675891	+	0.737002i	$0.263759\pi$
$558$	62.9622	+	28.0326i	2.66540	+	1.18671i
$559$	−7.84886	−	24.1563i	−0.331971	−	1.02170i
$560$		0			0
$561$	−0.0262173	+	0.0806885i	−0.00110689	+	0.00340667i
$562$	25.6511	−	28.4885i	1.08203	−	1.20171i
$563$	−15.5980	−	3.31546i	−0.657378	−	0.139730i	−0.132867	−	0.991134i	$-0.542418\pi$
$563$	−15.5980	−	3.31546i	−0.657378	−	0.139730i	−0.524511	+	0.851404i	$0.675752\pi$
$564$	−1.30201	−	1.44603i	−0.0548245	−	0.0608888i
$565$		0			0
$566$	5.24183	+	16.1327i	0.220331	+	0.678108i
$567$	2.36101	−	23.5611i	0.0991533	−	0.989474i
$568$	−23.2599			−0.975962
$569$	32.3178	+	14.3888i	1.35483	+	0.603210i	0.950306	−	0.311317i	$-0.100770\pi$
$569$	32.3178	+	14.3888i	1.35483	+	0.603210i	0.404526	+	0.914527i	$0.367437\pi$
$570$		0			0
$571$	18.1029	−	8.05995i	0.757585	−	0.337298i	0.00866787	−	0.999962i	$-0.497241\pi$
$571$	18.1029	−	8.05995i	0.757585	−	0.337298i	0.748917	+	0.662664i	$0.230574\pi$
$572$	5.19812	−	49.4568i	0.217344	−	2.06789i
$573$	−0.296697	+	0.913140i	−0.0123947	+	0.0381470i
$574$	4.86824	+	14.7395i	0.203196	+	0.615216i
$575$		0			0
$576$	6.81382	+	11.8019i	0.283909	+	0.491745i
$577$	13.3894	+	14.8704i	0.557407	+	0.619063i	0.954318	−	0.298794i	$-0.0965845\pi$
$577$	13.3894	+	14.8704i	0.557407	+	0.619063i	−0.396911	+	0.917857i	$0.629918\pi$
$578$	39.9715	−	17.7964i	1.66259	−	0.740234i
$579$	0.207446	−	1.97372i	0.00862118	−	0.0820250i
$580$		0			0
$581$	11.2668	−	5.08186i	0.467426	−	0.210831i
$582$	1.93036			0.0800160
$583$	−12.6628	−	5.63786i	−0.524441	−	0.233496i
$584$	89.2526	+	18.9712i	3.69330	+	0.785035i
$585$		0			0
$586$	79.6465	−	16.9294i	3.29017	−	0.699347i
$587$	4.77544	+	14.6973i	0.197104	+	0.606623i	0.999946	+	0.0104308i	$0.00332027\pi$
$587$	4.77544	+	14.6973i	0.197104	+	0.606623i	−0.802842	+	0.596192i	$0.796680\pi$
$588$	2.23188	−	1.01973i	0.0920413	−	0.0420528i
$589$	−11.0814	+	34.1051i	−0.456602	+	1.40528i
$590$		0			0
$591$	0.241776	+	0.0513910i	0.00994532	+	0.00211394i
$592$	−2.95177	−	28.0842i	−0.121317	−	1.15425i
$593$	−1.82785	−	3.16592i	−0.0750607	−	0.130009i	0.826052	−	0.563594i	$-0.190582\pi$
$593$	−1.82785	−	3.16592i	−0.0750607	−	0.130009i	−0.901113	+	0.433585i	$0.857248\pi$
$594$	−3.53837	+	2.57077i	−0.145181	+	0.105480i
$595$		0			0
$596$	5.28268	+	3.83809i	0.216387	+	0.157214i
$597$	−0.120287	+	1.14446i	−0.00492303	+	0.0468395i
$598$	34.1305	+	37.9058i	1.39570	+	1.55008i
$599$	−3.07128	+	5.31962i	−0.125489	+	0.217354i	−0.921924	−	0.387371i	$-0.873383\pi$
$599$	−3.07128	+	5.31962i	−0.125489	+	0.217354i	0.796435	+	0.604724i	$0.206717\pi$
$600$		0			0
$601$	33.2947			1.35812			0.679060	−	0.734083i	$-0.262388\pi$
$601$	33.2947			1.35812			0.679060	+	0.734083i	$0.262388\pi$
$602$	62.0108	−	0.300455i	2.52737	−	0.0122456i
$603$	−8.33115	−	6.05293i	−0.339271	−	0.246495i
$604$	7.59963	−	72.3056i	0.309225	−	2.94208i
$605$		0			0
$606$	0.0446183	+	0.424515i	0.00181250	+	0.0172447i
$607$	20.5670	+	35.6231i	0.834788	+	1.44590i	0.894203	+	0.447662i	$0.147743\pi$
$607$	20.5670	+	35.6231i	0.834788	+	1.44590i	−0.0594149	+	0.998233i	$0.518923\pi$
$608$	−27.5587	+	20.0226i	−1.11765	+	0.812023i
$609$	−0.494402	−	0.217258i	−0.0200342	−	0.00880372i
$610$		0			0
$611$	−15.2250	+	3.23617i	−0.615937	+	0.130921i
$612$	−4.13802	−	0.879564i	−0.167270	−	0.0355543i
$613$	−22.7203	−	4.82936i	−0.917666	−	0.195056i	−0.275215	−	0.961383i	$-0.588749\pi$
$613$	−22.7203	−	4.82936i	−0.917666	−	0.195056i	−0.642451	+	0.766327i	$0.722082\pi$
$614$	−49.5155	+	10.5248i	−1.99828	+	0.424748i
$615$		0			0
$616$	63.8080	+	28.0395i	2.57090	+	1.12974i
$617$	2.18514	−	1.58759i	0.0879702	−	0.0639141i	−0.542931	−	0.839777i	$-0.682685\pi$
$617$	2.18514	−	1.58759i	0.0879702	−	0.0639141i	0.630901	+	0.775863i	$0.282685\pi$
$618$	0.395874	+	0.685674i	0.0159244	+	0.0275818i
$619$	−5.01708	−	47.7343i	−0.201654	−	1.91861i	−0.363148	−	0.931731i	$-0.618298\pi$
$619$	−5.01708	−	47.7343i	−0.201654	−	1.91861i	0.161495	−	0.986874i	$-0.448369\pi$
$620$		0			0
$621$	0.328850	−	3.12880i	0.0131963	−	0.125554i
$622$	69.2020	+	50.2782i	2.77475	+	2.01597i
$623$	−20.3789	+	0.0987396i	−0.816462	+	0.00395592i
$624$	−1.81213			−0.0725434
$625$		0			0
$626$	9.84779	−	17.0569i	0.393597	−	0.681730i
$627$	−0.760651	−	0.844789i	−0.0303775	−	0.0337376i
$628$	−0.763920	+	7.26822i	−0.0304837	+	0.290033i
$629$	0.794086	+	0.576938i	0.0316623	+	0.0230040i
$630$		0			0
$631$	−18.3629	+	13.3414i	−0.731016	+	0.531114i	−0.889885	−	0.456186i	$-0.849215\pi$
$631$	−18.3629	+	13.3414i	−0.731016	+	0.531114i	0.158869	+	0.987300i	$0.449215\pi$
$632$	29.5380	+	51.1613i	1.17496	+	2.03509i
$633$	−0.0975956	−	0.928561i	−0.00387908	−	0.0369070i
$634$	−56.6967	−	12.0513i	−2.25171	−	0.478617i
$635$		0			0
$636$	−0.397540	+	1.22350i	−0.0157635	+	0.0485150i
$637$	1.86249	−	19.5400i	0.0737944	−	0.774203i
$638$	−8.25699	−	25.4124i	−0.326898	−	1.00609i
$639$	9.76795	−	2.07624i	0.386414	−	0.0821349i
$640$		0			0
$641$	32.8748	+	6.98776i	1.29848	+	0.276000i	0.804749	−	0.593615i	$-0.202300\pi$
$641$	32.8748	+	6.98776i	1.29848	+	0.276000i	0.493729	+	0.869616i	$0.335633\pi$
$642$	1.69438	+	0.754386i	0.0668718	+	0.0297732i
$643$	−2.04600			−0.0806863			−0.0403432	−	0.999186i	$-0.512845\pi$
$643$	−2.04600			−0.0806863			−0.0403432	+	0.999186i	$0.512845\pi$
$644$	−79.6095	+	35.9076i	−3.13706	+	1.41496i
$645$		0			0
$646$	0.328087	−	3.12154i	0.0129084	−	0.122815i
$647$	−14.2538	+	6.34621i	−0.560376	+	0.249495i	−0.667322	−	0.744769i	$-0.732559\pi$
$647$	−14.2538	+	6.34621i	−0.560376	+	0.249495i	0.106946	+	0.994265i	$0.465893\pi$
$648$	−41.7685	−	46.3886i	−1.64082	−	1.82232i
$649$	−16.6681	−	28.8700i	−0.654281	−	1.13325i
$650$		0			0
$651$	−0.551017	−	1.66831i	−0.0215961	−	0.0653862i
$652$	−14.5088	+	44.6536i	−0.568210	+	1.74877i
$653$	3.72548	−	35.4456i	0.145789	−	1.38709i	−0.639893	−	0.768464i	$-0.721021\pi$
$653$	3.72548	−	35.4456i	0.145789	−	1.38709i	0.785683	−	0.618630i	$-0.212312\pi$
$654$	−1.01479	+	0.451813i	−0.0396813	+	0.0176673i
$655$		0			0
$656$	17.9305	+	7.98318i	0.700069	+	0.311691i
$657$	−39.1750			−1.52836
$658$	3.78908	−	37.8121i	0.147714	−	1.47407i
$659$	4.30237	+	13.2413i	0.167596	+	0.515809i	0.999218	−	0.0395337i	$-0.0125873\pi$
$659$	4.30237	+	13.2413i	0.167596	+	0.515809i	−0.831622	+	0.555342i	$0.812587\pi$
$660$		0			0
$661$	5.10093	+	5.66516i	0.198403	+	0.220349i	0.834134	−	0.551562i	$-0.185968\pi$
$661$	5.10093	+	5.66516i	0.198403	+	0.220349i	−0.635731	+	0.771911i	$0.719301\pi$
$662$	23.5732	+	5.01064i	0.916199	+	0.194744i
$663$	0.0421466	−	0.0468086i	0.00163684	−	0.00181789i
$664$	10.0686	−	30.9879i	0.390737	−	1.20256i
$665$		0			0
$666$	7.81086	+	24.0393i	0.302665	+	0.931506i
$667$	17.5585	+	7.81755i	0.679868	+	0.302697i
$668$	−34.8450	+	60.3533i	−1.34819	+	2.33514i
$669$	0.0606936	+	0.577461i	0.00234655	+	0.0223259i
$670$		0			0
$671$	−41.7739	−	30.3505i	−1.61266	−	1.17167i
$672$	0.508042	−	1.58976i	0.0195981	−	0.0613263i
$673$	5.19416	−	15.9860i	0.200220	−	0.616214i	−0.799656	−	0.600459i	$-0.794985\pi$
$673$	5.19416	−	15.9860i	0.200220	−	0.616214i	0.999876	−	0.0157555i	$-0.00501534\pi$
$674$	−18.7244	−	32.4315i	−0.721235	−	1.24922i
$675$		0			0
$676$	12.0606	−	20.8895i	0.463868	−	0.803443i
$677$	−11.4933	+	2.44298i	−0.441725	+	0.0938915i	−0.423405	−	0.905941i	$-0.639165\pi$
$677$	−11.4933	+	2.44298i	−0.441725	+	0.0938915i	−0.0183202	+	0.999832i	$0.505832\pi$
$678$	−0.397810	−	0.289026i	−0.0152778	−	0.0111000i
$679$	17.7857	+	19.5615i	0.682551	+	0.750703i
$680$		0			0
$681$	0.470454	+	0.209459i	0.0180278	+	0.00802650i
$682$	43.4661	−	75.2854i	1.66440	−	2.88283i
$683$	−0.418735	−	3.98400i	−0.0160224	−	0.152443i	0.983585	−	0.180443i	$-0.0577530\pi$
$683$	−0.418735	−	3.98400i	−0.0160224	−	0.152443i	−0.999608	+	0.0279993i	$0.991086\pi$
$684$	37.9288	−	42.1242i	1.45024	−	1.61066i
$685$		0			0
$686$	44.0578	+	18.8533i	1.68214	+	0.719824i
$687$	−0.423655	−	1.30388i	−0.0161634	−	0.0497459i
$688$	52.4663	−	58.2697i	2.00026	−	2.22151i
$689$	6.88587	+	7.64753i	0.262331	+	0.291348i
$690$		0			0
$691$	11.3903	−	12.6502i	0.433309	−	0.481238i	−0.486458	−	0.873704i	$-0.661711\pi$
$691$	11.3903	−	12.6502i	0.433309	−	0.481238i	0.919766	+	0.392466i	$0.128378\pi$
$692$	20.0942	−	14.5993i	0.763865	−	0.554981i
$693$	−29.2990	−	6.07947i	−1.11298	−	0.230940i
$694$	−6.84312	+	4.97182i	−0.259761	+	0.188728i
$695$		0			0
$696$	−1.30053	+	0.579035i	−0.0492966	+	0.0219483i
$697$	−0.623239	+	0.277484i	−0.0236069	+	0.0105105i
$698$	−50.9351	+	10.8266i	−1.92792	+	0.409793i
$699$	0.668680			0.0252918
$700$		0			0
$701$	−42.3252			−1.59860			−0.799300	−	0.600932i	$-0.794796\pi$
$701$	−42.3252			−1.59860			−0.799300	+	0.600932i	$0.794796\pi$
$702$	3.17612	−	0.675105i	0.119875	−	0.0254802i
$703$	−12.0146	+	5.34925i	−0.453140	+	0.201751i
$704$	15.7029	−	6.99140i	0.591827	−	0.263498i
$705$		0			0
$706$	66.1755	−	48.0793i	2.49055	−	1.80949i
$707$	−3.89078	+	4.36348i	−0.146328	+	0.164105i
$708$	−2.50306	+	1.81858i	−0.0940709	+	0.0683465i
$709$	−7.25637	+	8.05902i	−0.272519	+	0.302663i	−0.863833	−	0.503779i	$-0.831943\pi$
$709$	−7.25637	+	8.05902i	−0.272519	+	0.302663i	0.591314	+	0.806441i	$0.298609\pi$
$710$		0			0
$711$	−16.9712	−	18.8485i	−0.636471	−	0.706873i
$712$	−35.9475	+	39.9237i	−1.34719	+	1.49620i
$713$	19.3233	+	59.4709i	0.723662	+	2.22720i
$714$	0.0775345	+	0.132803i	0.00290165	+	0.00497004i
$715$		0			0
$716$	7.26567	−	8.06934i	0.271531	−	0.301565i
$717$	0.129335	+	1.23054i	0.00483010	+	0.0459553i
$718$	−13.3676	+	23.1533i	−0.498873	+	0.864074i
$719$	−7.69245	−	3.42490i	−0.286880	−	0.127727i	0.258252	−	0.966078i	$-0.416854\pi$
$719$	−7.69245	−	3.42490i	−0.286880	−	0.127727i	−0.545132	+	0.838350i	$0.683520\pi$
$720$		0			0
$721$	−3.30091	+	10.3292i	−0.122932	+	0.384679i
$722$	−5.75049	−	4.17797i	−0.214011	−	0.155488i
$723$	0.428619	−	0.0911057i	0.0159405	−	0.00338826i
$724$	−41.7979	+	72.3961i	−1.55341	+	2.69058i
$725$		0			0
$726$	0.315411	+	0.546307i	0.0117060	+	0.0202754i
$727$	−3.45993	+	10.6486i	−0.128322	+	0.394934i	−0.994492	−	0.104816i	$-0.966575\pi$
$727$	−3.45993	+	10.6486i	−0.128322	+	0.394934i	0.866170	+	0.499750i	$0.166575\pi$
$728$	−34.8095	−	38.2852i	−1.29013	−	1.41894i
$729$	21.6003	+	15.6936i	0.800013	+	0.581243i
$730$		0			0
$731$	0.284882	+	2.71048i	0.0105368	+	0.100251i
$732$	−2.39616	+	4.15026i	−0.0885644	+	0.153398i
$733$	19.5026	+	8.68312i	0.720345	+	0.320718i	0.733963	−	0.679189i	$-0.237668\pi$
$733$	19.5026	+	8.68312i	0.720345	+	0.320718i	−0.0136185	+	0.999907i	$0.504335\pi$
$734$	13.6676	+	42.0646i	0.504480	+	1.55263i
$735$		0			0
$736$	−18.3556	+	56.4927i	−0.676596	+	2.08235i
$737$	−8.69137	+	9.65275i	−0.320151	+	0.355563i
$738$	−17.1844	−	3.65266i	−0.632568	−	0.134456i
$739$	3.96668	+	4.40544i	0.145917	+	0.162057i	0.811672	−	0.584113i	$-0.198557\pi$
$739$	3.96668	+	4.40544i	0.145917	+	0.162057i	−0.665756	+	0.746170i	$0.731891\pi$
$740$		0			0
$741$	0.260798	+	0.802653i	0.00958064	+	0.0294862i
$742$	−22.9025	+	10.3301i	−0.840778	+	0.379230i
$743$	31.5615			1.15788			0.578939	−	0.815371i	$-0.303467\pi$
$743$	31.5615			1.15788			0.578939	+	0.815371i	$0.303467\pi$
$744$	−4.23119	−	1.88385i	−0.155123	−	0.0690651i
$745$		0			0
$746$	61.2969	−	27.2912i	2.24424	−	0.999200i
$747$	−1.46222	+	13.9121i	−0.0534998	+	0.509017i
$748$	−1.64893	+	5.07487i	−0.0602907	+	0.185556i
$749$	7.96674	+	24.1208i	0.291099	+	0.881356i
$750$		0			0
$751$	17.6528	+	30.5755i	0.644160	+	1.11572i	0.984495	+	0.175413i	$0.0561262\pi$
$751$	17.6528	+	30.5755i	0.644160	+	1.11572i	−0.340335	+	0.940304i	$0.610540\pi$
$752$	−32.1520	−	35.7084i	−1.17246	−	1.30215i
$753$	−0.245198	+	0.109169i	−0.00893550	+	0.00397834i
$754$	−2.07358	+	19.7288i	−0.0755154	+	0.718481i
$755$		0			0
$756$	−0.554333	+	5.53182i	−0.0201609	+	0.201191i
$757$	9.26089			0.336593			0.168296	−	0.985736i	$-0.446173\pi$
$757$	9.26089			0.336593			0.168296	+	0.985736i	$0.446173\pi$
$758$	−17.8191	−	7.93356i	−0.647218	−	0.288160i
$759$	−1.93894	−	0.412134i	−0.0703790	−	0.0149595i
$760$		0			0
$761$	−49.4584	+	10.5127i	−1.79287	+	0.381086i	−0.979624	−	0.200839i	$-0.935633\pi$
$761$	−49.4584	+	10.5127i	−1.79287	+	0.381086i	−0.813243	+	0.581925i	$0.802300\pi$
$762$	−0.799754	−	2.46139i	−0.0289720	−	0.0891668i
$763$	−13.9284	−	6.12063i	−0.504242	−	0.221582i
$764$	−18.6607	+	57.4316i	−0.675119	+	2.07780i
$765$		0			0
$766$	−42.7134	−	9.07901i	−1.54330	−	0.328038i
$767$	2.58701	+	24.6138i	0.0934115	+	0.888751i
$768$	0.834595	+	1.44556i	0.0301158	+	0.0521622i
$769$	−14.4845	+	10.5236i	−0.522325	+	0.379492i	−0.817479	−	0.575958i	$-0.804629\pi$
$769$	−14.4845	+	10.5236i	−0.522325	+	0.379492i	0.295154	+	0.955450i	$0.404629\pi$
$770$		0			0
$771$	−0.263884	−	0.191723i	−0.00950356	−	0.00690474i
$772$	13.0473	−	124.136i	0.469581	−	4.46777i
$773$	6.42812	+	7.13915i	0.231204	+	0.256778i	0.847572	−	0.530680i	$-0.178063\pi$
$773$	6.42812	+	7.13915i	0.231204	+	0.256778i	−0.616369	+	0.787458i	$0.711397\pi$
$774$	−35.0919	+	60.7810i	−1.26135	+	2.18473i
$775$		0			0
$776$	69.6957			2.50193
$777$	0.319470	−	0.559583i	0.0114609	−	0.0200749i
$778$	22.1713	+	16.1084i	0.794880	+	0.577514i
$779$	0.955496	−	9.09094i	0.0342342	−	0.325717i
$780$		0			0
$781$	−1.31663	−	12.5269i	−0.0471127	−	0.448248i
$782$	−2.73659	−	4.73990i	−0.0978601	−	0.169499i
$783$	0.989863	−	0.719178i	0.0353748	−	0.0257013i
$784$	55.1144	−	25.1813i	1.96837	−	0.899331i
$785$		0			0
$786$	3.14693	−	0.668902i	0.112247	−	0.0238589i
$787$	−0.744513	−	0.158251i	−0.0265390	−	0.00564104i	0.194623	−	0.980878i	$-0.437652\pi$
$787$	−0.744513	−	0.158251i	−0.0265390	−	0.00564104i	−0.221162	+	0.975237i	$0.570985\pi$
$788$	15.2064	+	3.23222i	0.541705	+	0.115143i
$789$	0.576005	−	0.122434i	0.0205063	−	0.00435876i
$790$		0			0
$791$	−0.736403	−	6.69424i	−0.0261835	−	0.238020i
$792$	−63.8170	+	46.3658i	−2.26764	+	1.64754i
$793$	19.1674	+	33.1990i	0.680656	+	1.17893i
$794$	−9.63693	−	91.6893i	−0.342002	−	3.25393i
$795$		0			0
$796$	−7.56543	+	71.9802i	−0.268149	+	2.55127i
$797$	−14.7515	−	10.7176i	−0.522524	−	0.379636i	0.295030	−	0.955488i	$-0.404670\pi$
$797$	−14.7515	−	10.7176i	−0.522524	−	0.379636i	−0.817554	+	0.575852i	$0.804670\pi$
$798$	−2.06046	+	0.00998335i	−0.0729396	+	0.000353407i
$799$	1.67017			0.0590862
$800$		0			0
$801$	11.5324	−	19.9747i	0.407477	−	0.705771i
$802$	9.73396	+	10.8107i	0.343718	+	0.381737i
$803$	−5.16504	+	49.1421i	−0.182270	+	1.73419i
$804$	0.975287	+	0.708588i	0.0343957	+	0.0249900i
$805$		0			0
$806$	−52.2137	+	37.9355i	−1.83915	+	1.33622i
$807$	−0.664772	−	1.15142i	−0.0234011	−	0.0405319i
$808$	1.61095	+	15.3271i	0.0566729	+	0.539206i
$809$	−26.8468	−	5.70647i	−0.943885	−	0.200629i	−0.289832	−	0.957078i	$-0.593599\pi$
$809$	−26.8468	−	5.70647i	−0.943885	−	0.200629i	−0.654053	+	0.756449i	$0.726933\pi$
$810$		0			0
$811$	−8.93291	+	27.4927i	−0.313677	+	0.965399i	0.662619	+	0.748957i	$0.269445\pi$
$811$	−8.93291	+	27.4927i	−0.313677	+	0.965399i	−0.976296	+	0.216442i	$0.930555\pi$
$812$	−31.0952	−	13.6643i	−1.09123	−	0.479524i
$813$	−0.245940	−	0.756925i	−0.00862548	−	0.0265465i
$814$	31.1854	−	6.62865i	1.09305	−	0.232334i
$815$		0			0
$816$	0.190196	+	0.0404274i	0.00665819	+	0.00141524i
$817$	−33.3604	−	14.8530i	−1.16713	−	0.519640i
$818$	28.3839			0.992420
$819$	18.0357	+	12.9706i	0.630217	+	0.453230i
$820$		0			0
$821$	−2.40366	+	22.8693i	−0.0838884	+	0.798145i	0.868998	+	0.494816i	$0.164765\pi$
$821$	−2.40366	+	22.8693i	−0.0838884	+	0.798145i	−0.952886	+	0.303329i	$0.901902\pi$
$822$	1.54904	−	0.689677i	0.0540289	−	0.0240552i
$823$	−28.7456	−	31.9252i	−1.00201	−	1.11284i	−0.993609	−	0.112879i	$-0.963993\pi$
$823$	−28.7456	−	31.9252i	−1.00201	−	1.11284i	−0.00840016	−	0.999965i	$-0.502674\pi$
$824$	14.2930	+	24.7563i	0.497921	+	0.862425i
$825$		0			0
$826$	−59.1641	−	12.2764i	−2.05858	−	0.427151i
$827$	10.6865	−	32.8898i	0.371608	−	1.14369i	−0.574131	−	0.818763i	$-0.694660\pi$
$827$	10.6865	−	32.8898i	0.371608	−	1.14369i	0.945739	−	0.324927i	$-0.105340\pi$
$828$	10.3318	−	98.3008i	0.359056	−	3.41619i
$829$	31.5148	−	14.0313i	1.09456	−	0.487328i	0.221605	−	0.975136i	$-0.428870\pi$
$829$	31.5148	−	14.0313i	1.09456	−	0.487328i	0.872950	+	0.487809i	$0.162204\pi$
$830$		0			0
$831$	−0.186702	−	0.0831250i	−0.00647662	−	0.00288357i
$832$	−12.7614			−0.442421
$833$	−0.631405	+	2.00931i	−0.0218769	+	0.0696184i
$834$	−0.633447	−	1.94955i	−0.0219345	−	0.0675074i
$835$		0			0
$836$	−47.8409	−	53.1327i	−1.65461	−	1.83763i
$837$	3.89370	+	0.827631i	0.134586	+	0.0286071i
$838$	22.1297	−	24.5776i	0.764459	−	0.849017i
$839$	−0.970542	+	2.98702i	−0.0335068	+	0.103123i	−0.966411	−	0.257001i	$-0.917266\pi$
$839$	−0.970542	+	2.98702i	−0.0335068	+	0.103123i	0.932904	+	0.360124i	$0.117266\pi$
$840$		0			0
$841$	−6.65159	−	20.4715i	−0.229365	−	0.705913i
$842$	−93.0270	−	41.4183i	−3.20592	−	1.42737i
$843$	0.553018	−	0.957856i	0.0190470	−	0.0329903i
$844$	−6.13824	−	58.4015i	−0.211287	−	2.01026i
$845$		0			0
$846$	34.7955	+	25.2804i	1.19629	+	0.869159i
$847$	−2.62999	+	8.22974i	−0.0903675	+	0.282777i
$848$	−9.81691	+	30.2133i	−0.337114	+	1.03753i
$849$	0.244706	+	0.423844i	0.00839830	+	0.0145463i
$850$		0			0
$851$	−11.4666	+	19.8607i	−0.393070	+	0.680817i
$852$	−1.14349	+	0.243056i	−0.0391752	+	0.00832695i
$853$	−5.25381	−	3.81712i	−0.179887	−	0.130696i	0.494198	−	0.869349i	$-0.335462\pi$
$853$	−5.25381	−	3.81712i	−0.179887	−	0.130696i	−0.674085	+	0.738654i	$0.735462\pi$
$854$	−91.4522	+	19.9024i	−3.12943	+	0.681045i
$855$		0			0
$856$	61.1756	+	27.2371i	2.09094	+	0.930945i
$857$	−16.7947	+	29.0894i	−0.573698	+	0.993674i	0.422484	+	0.906370i	$0.361158\pi$
$857$	−16.7947	+	29.0894i	−0.573698	+	0.993674i	−0.996182	+	0.0873032i	$0.972175\pi$
$858$	−0.213857	−	2.03471i	−0.00730095	−	0.0694639i
$859$	−35.5783	+	39.5137i	−1.21392	+	1.34819i	−0.294133	+	0.955765i	$0.595031\pi$
$859$	−35.5783	+	39.5137i	−1.21392	+	1.34819i	−0.919784	+	0.392426i	$0.871636\pi$
$860$		0			0
$861$	0.225806	+	0.386767i	0.00769543	+	0.0131810i
$862$	10.3664	+	31.9046i	0.353082	+	1.08668i
$863$	−13.6291	+	15.1367i	−0.463941	+	0.515258i	−0.929029	−	0.370006i	$-0.879356\pi$
$863$	−13.6291	+	15.1367i	−0.463941	+	0.515258i	0.465089	+	0.885264i	$0.346022\pi$
$864$	2.53021	+	2.81008i	0.0860795	+	0.0956010i
$865$		0			0
$866$	−53.3187	+	59.2164i	−1.81184	+	2.01225i
$867$	1.02130	−	0.742015i	0.0346850	−	0.0252001i
$868$	−34.6560	−	104.928i	−1.17630	−	3.56148i
$869$	−25.8816	+	18.8041i	−0.877972	+	0.637884i
$870$		0			0
$871$	8.80956	−	3.92227i	0.298501	−	0.132901i
$872$	−36.6389	+	16.3127i	−1.24075	+	0.552418i
$873$	−29.2686	+	6.22124i	−0.990594	+	0.210557i
$874$	73.3345			2.48058
$875$		0			0
$876$	4.58603			0.154947
$877$	47.5462	−	10.1063i	1.60552	−	0.341264i	0.683967	−	0.729513i	$-0.260253\pi$
$877$	47.5462	−	10.1063i	1.60552	−	0.341264i	0.921555	+	0.388249i	$0.126920\pi$
$878$	23.1405	−	10.3028i	0.780953	−	0.347703i
$879$	2.14618	−	0.955542i	0.0723889	−	0.0322296i
$880$		0			0
$881$	−21.5813	+	15.6797i	−0.727092	+	0.528263i	−0.888642	−	0.458602i	$-0.848351\pi$
$881$	−21.5813	+	15.6797i	−0.727092	+	0.528263i	0.161550	+	0.986864i	$0.448351\pi$
$882$	−43.5683	+	32.3038i	−1.46702	+	1.08773i
$883$	−16.5931	+	12.0556i	−0.558401	+	0.405702i	−0.830873	−	0.556461i	$-0.812159\pi$
$883$	−16.5931	+	12.0556i	−0.558401	+	0.405702i	0.272472	+	0.962164i	$0.412159\pi$
$884$	2.65080	−	2.94401i	0.0891559	−	0.0990177i
$885$		0			0
$886$	−47.6258	−	52.8938i	−1.60002	−	1.77700i
$887$	7.69446	−	8.54556i	0.258355	−	0.286932i	−0.599988	−	0.800009i	$-0.704828\pi$
$887$	7.69446	−	8.54556i	0.258355	−	0.286932i	0.858342	+	0.513077i	$0.171495\pi$
$888$	−0.524905	−	1.61549i	−0.0176147	−	0.0542123i
$889$	17.5741	−	30.7828i	0.589418	−	1.03242i
$890$		0			0
$891$	22.6189	−	25.1208i	0.757762	−	0.841579i
$892$	3.81730	+	36.3192i	0.127813	+	1.21606i
$893$	−11.1892	+	19.3803i	−0.374432	+	0.648536i
$894$	0.245416	+	0.109266i	0.00820794	+	0.00365441i
$895$		0			0
$896$	−4.12609	+	12.9113i	−0.137843	+	0.431337i
$897$	1.19059	+	0.865017i	0.0397528	+	0.0288821i
$898$	−54.4015	+	11.5634i	−1.81540	+	0.385876i
$899$	−12.1597	+	21.0612i	−0.405548	+	0.702430i
$900$		0			0
$901$	−0.552109	−	0.956280i	−0.0183934	−	0.0318583i
$902$	−6.84768	+	21.0750i	−0.228003	+	0.701720i
$903$	1.74823	−	0.380460i	0.0581774	−	0.0126609i
$904$	−14.3629	−	10.4353i	−0.477705	−	0.347073i
$905$		0			0
$906$	−0.312658	−	2.97474i	−0.0103874	−	0.0988291i
$907$	12.6557	−	21.9203i	0.420225	−	0.727851i	−0.575736	−	0.817635i	$-0.695285\pi$
$907$	12.6557	−	21.9203i	0.420225	−	0.727851i	0.995961	+	0.0897847i	$0.0286179\pi$
$908$	29.5890	+	13.1739i	0.981945	+	0.437190i
$909$	−2.04466	−	6.29281i	−0.0678170	−	0.208719i
$910$		0			0
$911$	−1.82038	+	5.60255i	−0.0603118	+	0.185621i	−0.976673	−	0.214732i	$-0.931112\pi$
$911$	−1.82038	+	5.60255i	−0.0603118	+	0.185621i	0.916361	+	0.400352i	$0.131112\pi$
$912$	−1.74332	+	1.93615i	−0.0577271	+	0.0641125i
$913$	17.2589	+	3.66849i	0.571186	+	0.121409i
$914$	−34.2780	−	38.0695i	−1.13381	−	1.25923i
$915$		0			0
$916$	−26.6456	−	82.0067i	−0.880395	−	2.70958i
$917$	35.7731	+	25.7268i	1.18133	+	0.849574i
$918$	−0.348417			−0.0114995
$919$	13.1046	+	5.83456i	0.432282	+	0.192464i	0.611330	−	0.791376i	$-0.290635\pi$
$919$	13.1046	+	5.83456i	0.432282	+	0.192464i	−0.179048	+	0.983840i	$0.557302\pi$
$920$		0			0
$921$	−1.33426	+	0.594051i	−0.0439654	+	0.0195746i
$922$	−1.68369	+	16.0193i	−0.0554495	+	0.527566i
$923$	−2.88974	+	8.89370i	−0.0951169	+	0.292740i
$924$	3.42989	+	0.711695i	0.112835	+	0.0234130i
$925$		0			0
$926$	−14.2477	−	24.6777i	−0.468209	−	0.810961i
$927$	−8.21216	−	9.12053i	−0.269723	−	0.299558i
$928$	−21.1043	+	9.39623i	−0.692782	+	0.308446i
$929$	−1.90614	+	18.1357i	−0.0625384	+	0.595013i	0.917711	+	0.397248i	$0.130035\pi$
$929$	−1.90614	+	18.1357i	−0.0625384	+	0.595013i	−0.980250	+	0.197765i	$0.936632\pi$
$930$		0			0
$931$	−19.0855	−	20.7880i	−0.625503	−	0.681298i
$932$	42.0564			1.37760
$933$	2.25458	+	1.00380i	0.0738115	+	0.0328630i
$934$	28.4649	+	6.05041i	0.931401	+	0.197975i
$935$		0			0
$936$	57.2836	−	12.1760i	1.87237	−	0.397985i
$937$	−11.2266	−	34.5518i	−0.366756	−	1.12876i	−0.948874	−	0.315655i	$-0.897776\pi$
$937$	−11.2266	−	34.5518i	−0.366756	−	1.12876i	0.582118	−	0.813104i	$-0.302224\pi$
$938$	2.57439	+	23.4024i	0.0840569	+	0.764116i
$939$	0.175600	−	0.540442i	0.00573050	−	0.0176367i
$940$		0			0
$941$	−42.4175	−	9.01612i	−1.38277	−	0.293917i	−0.544312	−	0.838883i	$-0.683209\pi$
$941$	−42.4175	−	9.01612i	−1.38277	−	0.293917i	−0.838458	+	0.544966i	$0.816543\pi$
$942$	0.0314286	+	0.299023i	0.00102400	+	0.00974269i
$943$	−7.96983	−	13.8041i	−0.259533	−	0.449525i
$944$	−61.8110	+	44.9084i	−2.01178	+	1.46164i
$945$		0			0
$946$	71.6185	+	52.0339i	2.32852	+	1.69177i
$947$	−2.87704	+	27.3732i	−0.0934911	+	0.889509i	0.842787	+	0.538248i	$0.180914\pi$
$947$	−2.87704	+	27.3732i	−0.0934911	+	0.889509i	−0.936278	+	0.351261i	$0.885753\pi$
$948$	1.98674	+	2.20650i	0.0645264	+	0.0716638i
$949$	18.3424	−	31.7699i	0.595419	−	1.03130i
$950$		0			0
$951$	−1.67235			−0.0542297
$952$	2.79938	+	4.79487i	0.0907285	+	0.155403i
$953$	−26.9305	−	19.5661i	−0.872363	−	0.633809i	0.0588568	−	0.998266i	$-0.481254\pi$
$953$	−26.9305	−	19.5661i	−0.872363	−	0.633809i	−0.931220	+	0.364457i	$0.881254\pi$
$954$	2.97232	−	28.2797i	0.0962323	−	0.915590i
$955$		0			0
$956$	8.13446	+	77.3943i	0.263087	+	2.50311i
$957$	−0.385464	−	0.667643i	−0.0124603	−	0.0215818i
$958$	−62.2809	+	45.2497i	−2.01220	+	1.46195i
$959$	21.2612	+	9.34294i	0.686561	+	0.301699i
$960$		0			0
$961$	−47.0696	+	10.0050i	−1.51838	+	0.322741i
$962$	−23.1525	−	4.92121i	−0.746466	−	0.158666i
$963$	−28.1219	−	5.97749i	−0.906215	−	0.192622i
$964$	26.9578	−	5.73006i	0.868252	−	0.184553i
$965$		0			0
$966$	−2.89651	+	2.12596i	−0.0931938	+	0.0684016i
$967$	−14.0062	+	10.1761i	−0.450410	+	0.327242i	−0.789758	−	0.613419i	$-0.789794\pi$
$967$	−14.0062	+	10.1761i	−0.450410	+	0.327242i	0.339348	+	0.940661i	$0.389794\pi$
$968$	11.3879	+	19.7244i	0.366021	+	0.633967i
$969$	−0.00946592	−	0.0900622i	−0.000304089	−	0.00289322i
$970$		0			0
$971$	2.30411	−	21.9221i	0.0739424	−	0.703515i	−0.893266	−	0.449529i	$-0.851592\pi$
$971$	2.30411	−	21.9221i	0.0739424	−	0.703515i	0.967208	−	0.253986i	$-0.0817416\pi$
$972$	−7.63811	−	5.54941i	−0.244993	−	0.177998i
$973$	13.9196	−	24.3816i	0.446243	−	0.781637i
$974$	−90.7513			−2.90786
$975$		0			0
$976$	−59.1710	+	102.487i	−1.89402	+	3.28054i
$977$	13.5249	+	15.0209i	0.432698	+	0.480560i	0.919577	−	0.392909i	$-0.128531\pi$
$977$	13.5249	+	15.0209i	0.432698	+	0.480560i	−0.486879	+	0.873469i	$0.661865\pi$
$978$	−0.201912	+	1.92106i	−0.00645642	+	0.0614287i
$979$	−23.5363	−	17.1001i	−0.752222	−	0.546521i
$980$		0			0
$981$	13.9304	−	10.1210i	0.444762	−	0.323139i
$982$	2.54914	+	4.41524i	0.0813464	+	0.140896i
$983$	6.11894	+	58.2178i	0.195164	+	1.85686i	0.454080	+	0.890961i	$0.349968\pi$
$983$	6.11894	+	58.2178i	0.195164	+	1.85686i	−0.258916	+	0.965900i	$0.583365\pi$
$984$	1.15483	+	0.245466i	0.0368146	+	0.00782518i
$985$		0			0
$986$	0.657772	−	2.02442i	0.0209477	−	0.0644705i
$987$	−0.119888	−	1.08984i	−0.00381609	−	0.0346900i
$988$	16.4028	+	50.4825i	0.521842	+	1.60606i
$989$	−62.2859	+	13.2393i	−1.98058	+	0.420984i
$990$		0			0
$991$	−12.4042	−	2.63659i	−0.394032	−	0.0837541i	0.00663458	−	0.999978i	$-0.497888\pi$
$991$	−12.4042	−	2.63659i	−0.394032	−	0.0837541i	−0.400667	+	0.916224i	$0.631221\pi$
$992$	−68.6611	−	30.5699i	−2.17999	−	0.970595i
$993$	0.695326			0.0220655
$994$	−18.5354	−	13.3301i	−0.587909	−	0.422804i
$995$		0			0
$996$	0.171175	−	1.62862i	0.00542389	−	0.0516049i
$997$	−0.675192	+	0.300615i	−0.0213835	+	0.00952056i	−0.417401	−	0.908723i	$-0.637059\pi$
$997$	−0.675192	+	0.300615i	−0.0213835	+	0.00952056i	0.396017	+	0.918243i	$0.370392\pi$
$998$	30.5825	+	33.9653i	0.968073	+	1.07515i
$999$	0.729952	+	1.26431i	0.0230947	+	0.0400011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.q.b.851.35		288
5.2	odd	4		175.2.t.a.4.18	✓	144
5.3	odd	4		875.2.u.a.774.1		144
5.4	even	2	inner	875.2.q.b.851.2		288
7.2	even	3	inner	875.2.q.b.226.2		288
25.6	even	5	inner	875.2.q.b.151.2		288
25.8	odd	20		175.2.t.a.144.18	yes	144
25.17	odd	20		875.2.u.a.599.1		144
25.19	even	10	inner	875.2.q.b.151.35		288
35.2	odd	12		175.2.t.a.79.18	yes	144
35.9	even	6	inner	875.2.q.b.226.35		288
35.23	odd	12		875.2.u.a.149.1		144
175.44	even	30	inner	875.2.q.b.401.2		288
175.58	odd	60		175.2.t.a.44.18	yes	144
175.142	odd	60		875.2.u.a.849.1		144
175.156	even	15	inner	875.2.q.b.401.35		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.4.18	✓	144	5.2	odd	4
175.2.t.a.44.18	yes	144	175.58	odd	60
175.2.t.a.79.18	yes	144	35.2	odd	12
175.2.t.a.144.18	yes	144	25.8	odd	20
875.2.q.b.151.2		288	25.6	even	5	inner
875.2.q.b.151.35		288	25.19	even	10	inner
875.2.q.b.226.2		288	7.2	even	3	inner
875.2.q.b.226.35		288	35.9	even	6	inner
875.2.q.b.401.2		288	175.44	even	30	inner
875.2.q.b.401.35		288	175.156	even	15	inner
875.2.q.b.851.2		288	5.4	even	2	inner
875.2.q.b.851.35		288	1.1	even	1	trivial
875.2.u.a.149.1		144	35.23	odd	12
875.2.u.a.599.1		144	25.17	odd	20
875.2.u.a.774.1		144	5.3	odd	4
875.2.u.a.849.1		144	175.142	odd	60

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.53101 - 0.537983i) q^{2} +(0.0682015 - 0.0303653i) q^{3} +(4.28951 - 1.90981i) q^{4} +(0.156283 - 0.113546i) q^{6} +(2.59057 + 0.537537i) q^{7} +(5.64260 - 4.09959i) q^{8} +(-2.00366 + 2.22529i) q^{9} +O(q^{10})\)	\(q+(2.53101 - 0.537983i) q^{2} +(0.0682015 - 0.0303653i) q^{3} +(4.28951 - 1.90981i) q^{4} +(0.156283 - 0.113546i) q^{6} +(2.59057 + 0.537537i) q^{7} +(5.64260 - 4.09959i) q^{8} +(-2.00366 + 2.22529i) q^{9} +(2.52729 + 2.80684i) q^{11} +(0.234559 - 0.260504i) q^{12} +(-0.866509 - 2.66684i) q^{13} +(6.84595 - 0.0331700i) q^{14} +(5.79224 - 6.43293i) q^{16} +(0.0314508 + 0.299235i) q^{17} +(-3.87412 + 6.71018i) q^{18} +(-3.68296 - 1.63976i) q^{19} +(0.193003 - 0.0420025i) q^{21} +(7.90663 + 5.74450i) q^{22} +(-6.87632 + 1.46161i) q^{23} +(0.260349 - 0.450937i) q^{24} +(-3.62786 - 6.28364i) q^{26} +(-0.138291 + 0.425616i) q^{27} +(12.1389 - 2.64173i) q^{28} +(-2.21189 - 1.60703i) q^{29} +(-0.929782 - 8.84628i) q^{31} +(4.22478 - 7.31754i) q^{32} +(0.257595 + 0.114689i) q^{33} +(0.240586 + 0.740447i) q^{34} +(-4.34484 + 13.3720i) q^{36} +(2.18285 - 2.42430i) q^{37} +(-10.2038 - 2.16888i) q^{38} +(-0.140077 - 0.155571i) q^{39} +(0.700664 + 2.15642i) q^{41} +(0.465897 - 0.210141i) q^{42} +9.05803 q^{43} +(16.2014 + 7.21331i) q^{44} +(-16.6177 + 7.39869i) q^{46} +(0.580225 - 5.52047i) q^{47} +(0.199702 - 0.614619i) q^{48} +(6.42211 + 2.78506i) q^{49} +(0.0112313 + 0.0194532i) q^{51} +(-8.81006 - 9.78456i) q^{52} +(-3.35264 + 1.49269i) q^{53} +(-0.121042 + 1.15164i) q^{54} +(16.8212 - 7.58716i) q^{56} -0.300975 q^{57} +(-6.46288 - 2.87746i) q^{58} +(-8.63331 - 1.83507i) q^{59} +(-13.3724 + 2.84238i) q^{61} +(-7.11244 - 21.8898i) q^{62} +(-6.38681 + 4.68773i) q^{63} +(1.40634 - 4.32826i) q^{64} +(0.713678 + 0.151697i) q^{66} +(0.359475 + 3.42017i) q^{67} +(0.706390 + 1.22350i) q^{68} +(-0.424593 + 0.308485i) q^{69} +(-2.69801 - 1.96022i) q^{71} +(-2.18308 + 20.7706i) q^{72} +(8.75399 + 9.72229i) q^{73} +(4.22058 - 7.31027i) q^{74} -18.9297 q^{76} +(5.03834 + 8.62982i) q^{77} +(-0.438230 - 0.318393i) q^{78} +(-0.885368 + 8.42371i) q^{79} +(-0.935516 - 8.90084i) q^{81} +(2.93351 + 5.08098i) q^{82} +(3.77939 - 2.74589i) q^{83} +(0.747672 - 0.548770i) q^{84} +(22.9260 - 4.87307i) q^{86} +(-0.199652 - 0.0424374i) q^{87} +(25.7673 + 5.47702i) q^{88} +(-7.53425 + 1.60146i) q^{89} +(-0.811226 - 7.37442i) q^{91} +(-26.7046 + 19.4021i) q^{92} +(-0.332032 - 0.575097i) q^{93} +(-1.50137 - 14.2845i) q^{94} +(0.0659376 - 0.627354i) q^{96} +(8.08430 + 5.87358i) q^{97} +(17.7527 + 3.59403i) q^{98} -11.3099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9}+O(q^{10}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9	\( 288 q + 38 q^{4} - 24 q^{6} + 34 q^{9} + 36 q^{14} + 10 q^{16} + 22 q^{19} - 18 q^{21} - 100 q^{24} - 120 q^{26} + 48 q^{29} + 30 q^{31} + 40 q^{34} + 32 q^{36} - 26 q^{39} - 124 q^{41} + 30 q^{44} - 54 q^{46} + 76 q^{49} - 16 q^{51} + 58 q^{54} + 64 q^{56} + 78 q^{59} + 14 q^{61} - 68 q^{64} + 22 q^{66} - 148 q^{69} - 92 q^{71} - 12 q^{74} + 360 q^{76} - 18 q^{79} - 118 q^{81} + 102 q^{84} + 22 q^{86} + 84 q^{89} + 44 q^{91} - 10 q^{94} + 106 q^{96} + 88 q^{99}+O(q^{100}) \) 288 * q + 38 * q^4 - 24 * q^6 + 34 * q^9 + 36 * q^14 + 10 * q^16 + 22 * q^19 - 18 * q^21 - 100 * q^24 - 120 * q^26 + 48 * q^29 + 30 * q^31 + 40 * q^34 + 32 * q^36 - 26 * q^39 - 124 * q^41 + 30 * q^44 - 54 * q^46 + 76 * q^49 - 16 * q^51 + 58 * q^54 + 64 * q^56 + 78 * q^59 + 14 * q^61 - 68 * q^64 + 22 * q^66 - 148 * q^69 - 92 * q^71 - 12 * q^74 + 360 * q^76 - 18 * q^79 - 118 * q^81 + 102 * q^84 + 22 * q^86 + 84 * q^89 + 44 * q^91 - 10 * q^94 + 106 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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