LMFDB - Embedded newform 950.2.l.j.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	950.101
Dual form			950.2.l.j.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(2.78771 + 1.01464i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.78771 + 1.01464i) q^{6} +(0.454865 - 0.787850i) q^{7} +(0.500000 + 0.866025i) q^{8} +(4.44370 + 3.72870i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(2.78771 + 1.01464i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.78771 + 1.01464i) q^{6} +(0.454865 - 0.787850i) q^{7} +(0.500000 + 0.866025i) q^{8} +(4.44370 + 3.72870i) q^{9} +(-1.82620 - 3.16308i) q^{11} +(1.48331 - 2.56917i) q^{12} +(2.66417 - 0.969680i) q^{13} +(0.157973 + 0.895910i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(4.13002 - 3.46550i) q^{17} -5.80083 q^{18} +(3.41525 + 2.70851i) q^{19} +(2.06742 - 1.73477i) q^{21} +(3.43214 + 1.24920i) q^{22} +(0.226388 - 1.28391i) q^{23} +(0.515148 + 2.92155i) q^{24} +(-1.41758 + 2.45532i) q^{26} +(4.15450 + 7.19581i) q^{27} +(-0.696894 - 0.584764i) q^{28} +(3.16720 + 2.65759i) q^{29} +(-2.98230 + 5.16550i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-1.88153 - 10.6707i) q^{33} +(-0.936199 + 5.30945i) q^{34} +(4.44370 - 3.72870i) q^{36} -9.82228 q^{37} +(-4.35723 + 0.120443i) q^{38} +8.41082 q^{39} +(-0.0389690 - 0.0141836i) q^{41} +(-0.468646 + 2.65782i) q^{42} +(1.54130 + 8.74115i) q^{43} +(-3.43214 + 1.24920i) q^{44} +(0.651859 + 1.12905i) q^{46} +(1.74606 + 1.46512i) q^{47} +(-2.27256 - 1.90691i) q^{48} +(3.08619 + 5.34545i) q^{49} +(15.0295 - 5.47031i) q^{51} +(-0.492319 - 2.79208i) q^{52} +(1.76889 - 10.0319i) q^{53} +(-7.80791 - 2.84185i) q^{54} +0.909731 q^{56} +(6.77257 + 11.0158i) q^{57} -4.13448 q^{58} +(4.30588 - 3.61306i) q^{59} +(-0.646366 + 3.66573i) q^{61} +(-1.03574 - 5.87399i) q^{62} +(4.95894 - 1.80491i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(8.30033 + 6.96480i) q^{66} +(-10.4969 - 8.80793i) q^{67} +(-2.69568 - 4.66905i) q^{68} +(1.93382 - 3.34947i) q^{69} +(1.01452 + 5.75362i) q^{71} +(-1.00730 + 5.71271i) q^{72} +(-13.2281 - 4.81464i) q^{73} +(7.52430 - 6.31364i) q^{74} +(3.26042 - 2.89304i) q^{76} -3.32271 q^{77} +(-6.44307 + 5.40637i) q^{78} +(-14.0814 - 5.12522i) q^{79} +(1.25846 + 7.13707i) q^{81} +(0.0389690 - 0.0141836i) q^{82} +(-2.39938 + 4.15585i) q^{83} +(-1.34941 - 2.33725i) q^{84} +(-6.79940 - 5.70538i) q^{86} +(6.13272 + 10.6222i) q^{87} +(1.82620 - 3.16308i) q^{88} +(-8.41552 + 3.06300i) q^{89} +(0.447878 - 2.54004i) q^{91} +(-1.22509 - 0.445898i) q^{92} +(-13.5549 + 11.3739i) q^{93} -2.27932 q^{94} +2.96662 q^{96} +(12.7549 - 10.7026i) q^{97} +(-5.80015 - 2.11108i) q^{98} +(3.67909 - 20.8651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) $ 24 * q - 3 * q^7 + 12 * q^8	$ 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	2.78771	+	1.01464i	1.60949	+	0.585805i	0.981338	−	0.192290i	$-0.0615913\pi$
$3$	2.78771	+	1.01464i	1.60949	+	0.585805i	0.628147	+	0.778094i	$0.283813\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−2.78771	+	1.01464i	−1.13808	+	0.414227i
$7$	0.454865	−	0.787850i	0.171923	−	0.297779i	−0.767169	−	0.641445i	$-0.778335\pi$
$7$	0.454865	−	0.787850i	0.171923	−	0.297779i	0.939092	+	0.343666i	$0.111669\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	4.44370	+	3.72870i	1.48123	+	1.24290i
$10$		0			0
$11$	−1.82620	−	3.16308i	−0.550621	−	0.953704i	−0.998230	−	0.0594745i	$-0.981057\pi$
$11$	−1.82620	−	3.16308i	−0.550621	−	0.953704i	0.447608	−	0.894230i	$-0.352276\pi$
$12$	1.48331	−	2.56917i	0.428195	−	0.741655i
$13$	2.66417	−	0.969680i	0.738909	−	0.268941i	0.0549779	−	0.998488i	$-0.482491\pi$
$13$	2.66417	−	0.969680i	0.738909	−	0.268941i	0.683931	+	0.729547i	$0.260269\pi$
$14$	0.157973	+	0.895910i	0.0422201	+	0.239442i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	4.13002	−	3.46550i	1.00168	−	0.840507i	0.0144610	−	0.999895i	$-0.495397\pi$
$17$	4.13002	−	3.46550i	1.00168	−	0.840507i	0.987216	+	0.159389i	$0.0509523\pi$
$18$	−5.80083			−1.36727
$19$	3.41525	+	2.70851i	0.783513	+	0.621375i
$19$	3.41525	+	2.70851i	0.783513	+	0.621375i
$20$		0			0
$21$	2.06742	−	1.73477i	0.451148	−	0.378558i
$22$	3.43214	+	1.24920i	0.731735	+	0.266330i
$23$	0.226388	−	1.28391i	0.0472052	−	0.267714i	−0.952066	−	0.305894i	$-0.901045\pi$
$23$	0.226388	−	1.28391i	0.0472052	−	0.267714i	0.999271	+	0.0381796i	$0.0121559\pi$
$24$	0.515148	+	2.92155i	0.105154	+	0.596359i
$25$		0			0
$26$	−1.41758	+	2.45532i	−0.278010	+	0.481527i
$27$	4.15450	+	7.19581i	0.799535	+	1.38483i
$28$	−0.696894	−	0.584764i	−0.131701	−	0.110510i
$29$	3.16720	+	2.65759i	0.588134	+	0.493503i	0.887607	−	0.460602i	$-0.152366\pi$
$29$	3.16720	+	2.65759i	0.588134	+	0.493503i	−0.299473	+	0.954105i	$0.596811\pi$
$30$		0			0
$31$	−2.98230	+	5.16550i	−0.535637	+	0.927751i	0.463495	+	0.886100i	$0.346595\pi$
$31$	−2.98230	+	5.16550i	−0.535637	+	0.927751i	−0.999132	+	0.0416513i	$0.986738\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−1.88153	−	10.6707i	−0.327533	−	1.85753i
$34$	−0.936199	+	5.30945i	−0.160557	+	0.910563i
$35$		0			0
$36$	4.44370	−	3.72870i	0.740616	−	0.621451i
$37$	−9.82228			−1.61477			−0.807386	−	0.590023i	$-0.799119\pi$
$37$	−9.82228			−1.61477			−0.807386	+	0.590023i	$0.799119\pi$
$38$	−4.35723	+	0.120443i	−0.706837	+	0.0195384i
$39$	8.41082			1.34681
$40$		0			0
$41$	−0.0389690	−	0.0141836i	−0.00608594	−	0.00221510i	0.338975	−	0.940795i	$-0.389920\pi$
$41$	−0.0389690	−	0.0141836i	−0.00608594	−	0.00221510i	−0.345061	+	0.938580i	$0.612142\pi$
$42$	−0.468646	+	2.65782i	−0.0723137	+	0.410111i
$43$	1.54130	+	8.74115i	0.235046	+	1.33301i	0.842517	+	0.538670i	$0.181073\pi$
$43$	1.54130	+	8.74115i	0.235046	+	1.33301i	−0.607471	+	0.794342i	$0.707816\pi$
$44$	−3.43214	+	1.24920i	−0.517415	+	0.188324i
$45$		0			0
$46$	0.651859	+	1.12905i	0.0961114	+	0.166470i
$47$	1.74606	+	1.46512i	0.254689	+	0.213709i	0.761188	−	0.648531i	$-0.224616\pi$
$47$	1.74606	+	1.46512i	0.254689	+	0.213709i	−0.506499	+	0.862240i	$0.669061\pi$
$48$	−2.27256	−	1.90691i	−0.328016	−	0.275238i
$49$	3.08619	+	5.34545i	0.440885	+	0.763635i
$50$		0			0
$51$	15.0295	−	5.47031i	2.10456	−	0.765996i
$52$	−0.492319	−	2.79208i	−0.0682724	−	0.387192i
$53$	1.76889	−	10.0319i	0.242975	−	1.37798i	−0.582173	−	0.813065i	$-0.697797\pi$
$53$	1.76889	−	10.0319i	0.242975	−	1.37798i	0.825148	−	0.564917i	$-0.191092\pi$
$54$	−7.80791	−	2.84185i	−1.06252	−	0.386727i
$55$		0			0
$56$	0.909731			0.121568
$57$	6.77257	+	11.0158i	0.897048	+	1.45908i
$58$	−4.13448			−0.542884
$59$	4.30588	−	3.61306i	0.560578	−	0.470381i	−0.317926	−	0.948116i	$-0.602986\pi$
$59$	4.30588	−	3.61306i	0.560578	−	0.470381i	0.878504	+	0.477735i	$0.158542\pi$
$60$		0			0
$61$	−0.646366	+	3.66573i	−0.0827587	+	0.469348i	0.915059	+	0.403320i	$0.132144\pi$
$61$	−0.646366	+	3.66573i	−0.0827587	+	0.469348i	−0.997818	+	0.0660281i	$0.978967\pi$
$62$	−1.03574	−	5.87399i	−0.131539	−	0.745997i
$63$	4.95894	−	1.80491i	0.624768	−	0.227397i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	8.30033	+	6.96480i	1.02170	+	0.857308i
$67$	−10.4969	−	8.80793i	−1.28240	−	1.07606i	−0.992909	−	0.118879i	$-0.962070\pi$
$67$	−10.4969	−	8.80793i	−1.28240	−	1.07606i	−0.289489	−	0.957181i	$-0.593485\pi$
$68$	−2.69568	−	4.66905i	−0.326899	−	0.566206i
$69$	1.93382	−	3.34947i	0.232804	−	0.403229i
$70$		0			0
$71$	1.01452	+	5.75362i	0.120401	+	0.682829i	0.983933	+	0.178536i	$0.0571360\pi$
$71$	1.01452	+	5.75362i	0.120401	+	0.682829i	−0.863532	+	0.504294i	$0.831753\pi$
$72$	−1.00730	+	5.71271i	−0.118712	+	0.673249i
$73$	−13.2281	−	4.81464i	−1.54823	−	0.563511i	−0.580232	−	0.814452i	$-0.697038\pi$
$73$	−13.2281	−	4.81464i	−1.54823	−	0.563511i	−0.968003	+	0.250940i	$0.919260\pi$
$74$	7.52430	−	6.31364i	0.874682	−	0.733946i
$75$		0			0
$76$	3.26042	−	2.89304i	0.373995	−	0.331855i
$77$	−3.32271			−0.378658
$78$	−6.44307	+	5.40637i	−0.729534	+	0.612151i
$79$	−14.0814	−	5.12522i	−1.58428	−	0.576632i	−0.608153	−	0.793820i	$-0.708089\pi$
$79$	−14.0814	−	5.12522i	−1.58428	−	0.576632i	−0.976130	+	0.217188i	$0.930312\pi$
$80$		0			0
$81$	1.25846	+	7.13707i	0.139829	+	0.793008i
$82$	0.0389690	−	0.0141836i	0.00430341	−	0.00156631i
$83$	−2.39938	+	4.15585i	−0.263367	+	0.456164i	−0.967134	−	0.254266i	$-0.918166\pi$
$83$	−2.39938	+	4.15585i	−0.263367	+	0.456164i	0.703768	+	0.710430i	$0.251500\pi$
$84$	−1.34941	−	2.33725i	−0.147233	−	0.255015i
$85$		0			0
$86$	−6.79940	−	5.70538i	−0.733199	−	0.615227i
$87$	6.13272	+	10.6222i	0.657496	+	1.13882i
$88$	1.82620	−	3.16308i	0.194674	−	0.337185i
$89$	−8.41552	+	3.06300i	−0.892043	+	0.324677i	−0.747060	−	0.664757i	$-0.768535\pi$
$89$	−8.41552	+	3.06300i	−0.892043	+	0.324677i	−0.144983	+	0.989434i	$0.546313\pi$
$90$		0			0
$91$	0.447878	−	2.54004i	0.0469504	−	0.266269i
$92$	−1.22509	−	0.445898i	−0.127725	−	0.0464881i
$93$	−13.5549	+	11.3739i	−1.40558	+	1.17942i
$94$	−2.27932			−0.235094
$95$		0			0
$96$	2.96662			0.302779
$97$	12.7549	−	10.7026i	1.29507	−	1.08669i	0.304091	−	0.952643i	$-0.401647\pi$
$97$	12.7549	−	10.7026i	1.29507	−	1.08669i	0.990975	−	0.134046i	$-0.0427971\pi$
$98$	−5.80015	−	2.11108i	−0.585904	−	0.213251i
$99$	3.67909	−	20.8651i	0.369762	−	2.09703i
$100$		0			0
$101$	−9.55205	+	3.47666i	−0.950465	+	0.345941i	−0.770290	−	0.637694i	$-0.779889\pi$
$101$	−9.55205	+	3.47666i	−0.950465	+	0.345941i	−0.180175	+	0.983635i	$0.557666\pi$
$102$	−7.99705	+	13.8513i	−0.791826	+	1.37148i
$103$	6.21950	+	10.7725i	0.612826	+	1.06145i	0.990762	+	0.135613i	$0.0433005\pi$
$103$	6.21950	+	10.7725i	0.612826	+	1.06145i	−0.377936	+	0.925832i	$0.623366\pi$
$104$	2.17185	+	1.82240i	0.212968	+	0.178701i
$105$		0			0
$106$	5.09331	+	8.82187i	0.494706	+	0.856856i
$107$	6.20935	−	10.7549i	0.600280	−	1.03972i	−0.392498	−	0.919753i	$-0.628389\pi$
$107$	6.20935	−	10.7549i	0.600280	−	1.03972i	0.992778	−	0.119963i	$-0.0382777\pi$
$108$	7.80791	−	2.84185i	0.751317	−	0.273457i
$109$	2.29212	+	12.9993i	0.219546	+	1.24511i	0.872842	+	0.488003i	$0.162274\pi$
$109$	2.29212	+	12.9993i	0.219546	+	1.24511i	−0.653296	+	0.757102i	$0.726614\pi$
$110$		0			0
$111$	−27.3817	−	9.96611i	−2.59895	−	0.945942i
$112$	−0.696894	+	0.584764i	−0.0658503	+	0.0552550i
$113$	18.3175			1.72316			0.861581	−	0.507621i	$-0.169475\pi$
$113$	18.3175			1.72316			0.861581	+	0.507621i	$0.169475\pi$
$114$	−12.2689	−	4.08528i	−1.14909	−	0.382622i
$115$		0			0
$116$	3.16720	−	2.65759i	0.294067	−	0.246751i
$117$	15.4544	+	5.62495i	1.42876	+	0.520027i
$118$	−0.976064	+	5.53554i	−0.0898540	+	0.509587i
$119$	−0.851689	−	4.83017i	−0.0780742	−	0.442781i
$120$		0			0
$121$	−1.17005	+	2.02658i	−0.106368	+	0.184234i
$122$	−1.86114	−	3.22358i	−0.168499	−	0.291850i
$123$	−0.0942431	−	0.0790794i	−0.00849762	−	0.00713035i
$124$	4.56915	+	3.83397i	0.410322	+	0.344301i
$125$		0			0
$126$	−2.63860	+	4.57019i	−0.235065	+	0.407145i
$127$	−8.85337	+	3.22236i	−0.785610	+	0.285939i	−0.703510	−	0.710685i	$-0.748385\pi$
$127$	−8.85337	+	3.22236i	−0.785610	+	0.285939i	−0.0821000	+	0.996624i	$0.526163\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−4.57245	+	25.9317i	−0.402582	+	2.28316i
$130$		0			0
$131$	−1.26905	+	1.06486i	−0.110877	+	0.0930369i	−0.696541	−	0.717517i	$-0.745278\pi$
$131$	−1.26905	+	1.06486i	−0.110877	+	0.0930369i	0.585664	+	0.810554i	$0.300834\pi$
$132$	−10.8353			−0.943093
$133$	3.68738	−	1.45870i	0.319737	−	0.126485i
$134$	13.7027			1.18373
$135$		0			0
$136$	5.06622	+	1.84395i	0.434425	+	0.158118i
$137$	−1.40309	+	7.95729i	−0.119874	+	0.679838i	0.864347	+	0.502895i	$0.167732\pi$
$137$	−1.40309	+	7.95729i	−0.119874	+	0.679838i	−0.984221	+	0.176942i	$0.943379\pi$
$138$	0.671608	+	3.80888i	0.0571711	+	0.324233i
$139$	−6.65357	+	2.42170i	−0.564348	+	0.205406i	−0.608410	−	0.793623i	$-0.708192\pi$
$139$	−6.65357	+	2.42170i	−0.564348	+	0.205406i	0.0440619	+	0.999029i	$0.485970\pi$
$140$		0			0
$141$	3.38094	+	5.85595i	0.284726	+	0.493160i
$142$	−4.47552	−	3.75541i	−0.375578	−	0.315147i
$143$	−7.93250	−	6.65616i	−0.663349	−	0.556616i
$144$	−2.90042	−	5.02367i	−0.241701	−	0.418639i
$145$		0			0
$146$	13.2281	−	4.81464i	1.09477	−	0.398463i
$147$	3.17970	+	18.0329i	0.262257	+	1.48733i
$148$	−1.70562	+	9.67305i	−0.140201	+	0.795120i
$149$	3.71415	+	1.35184i	0.304275	+	0.110747i	0.489645	−	0.871922i	$-0.337126\pi$
$149$	3.71415	+	1.35184i	0.304275	+	0.110747i	−0.185370	+	0.982669i	$0.559348\pi$
$150$		0			0
$151$	−10.9225			−0.888864			−0.444432	−	0.895813i	$-0.646594\pi$
$151$	−10.9225			−0.888864			−0.444432	+	0.895813i	$0.646594\pi$
$152$	−0.638013	+	4.31195i	−0.0517497	+	0.349746i
$153$	31.2744			2.52838
$154$	2.54534	−	2.13580i	0.205110	−	0.172107i
$155$		0			0
$156$	1.46052	−	8.28305i	0.116936	−	0.663174i
$157$	−2.71395	−	15.3916i	−0.216597	−	1.22838i	−0.878113	−	0.478453i	$-0.841198\pi$
$157$	−2.71395	−	15.3916i	−0.216597	−	1.22838i	0.661516	−	0.749931i	$-0.269913\pi$
$158$	14.0814	−	5.12522i	1.12026	−	0.407740i
$159$	15.1099	−	26.1711i	1.19829	−	2.07551i
$160$		0			0
$161$	−0.908554	−	0.762367i	−0.0716041	−	0.0600829i
$162$	−5.55166	−	4.65839i	−0.436179	−	0.365998i
$163$	6.18468	+	10.7122i	0.484421	+	0.839042i	0.999840	−	0.0178962i	$-0.00569683\pi$
$163$	6.18468	+	10.7122i	0.484421	+	0.839042i	−0.515418	+	0.856939i	$0.672363\pi$
$164$	−0.0207350	+	0.0359141i	−0.00161913	+	0.00280442i
$165$		0			0
$166$	−0.833297	−	4.72586i	−0.0646764	−	0.366798i
$167$	3.68865	−	20.9194i	0.285437	−	1.61879i	−0.418285	−	0.908316i	$-0.637369\pi$
$167$	3.68865	−	20.9194i	0.285437	−	1.61879i	0.703722	−	0.710476i	$-0.251520\pi$
$168$	2.53607	+	0.923053i	0.195662	+	0.0712151i
$169$	−3.80104	+	3.18945i	−0.292387	+	0.245342i
$170$		0			0
$171$	5.07711	+	24.7703i	0.388257	+	1.89423i
$172$	8.87599			0.676788
$173$	7.88581	−	6.61698i	0.599547	−	0.503080i	−0.291753	−	0.956494i	$-0.594239\pi$
$173$	7.88581	−	6.61698i	0.599547	−	0.503080i	0.891300	+	0.453414i	$0.149794\pi$
$174$	−11.5257	−	4.19503i	−0.873764	−	0.318024i
$175$		0			0
$176$	0.634234	+	3.59692i	0.0478072	+	0.271128i
$177$	15.6695	−	5.70324i	1.17779	−	0.428682i
$178$	4.47780	−	7.75578i	0.335626	−	0.581321i
$179$	0.425281	+	0.736609i	0.0317870	+	0.0550567i	0.881481	−	0.472219i	$-0.156547\pi$
$179$	0.425281	+	0.736609i	0.0317870	+	0.0550567i	−0.849694	+	0.527276i	$0.823214\pi$
$180$		0			0
$181$	−13.1433	−	11.0285i	−0.976933	−	0.819744i	0.00669066	−	0.999978i	$-0.497870\pi$
$181$	−13.1433	−	11.0285i	−0.976933	−	0.819744i	−0.983624	+	0.180233i	$0.942315\pi$
$182$	1.28961	+	2.23368i	0.0955925	+	0.165571i
$183$	−5.52129	+	9.56315i	−0.408145	+	0.706928i
$184$	1.22509	−	0.445898i	0.0903152	−	0.0328720i
$185$		0			0
$186$	3.07265	−	17.4259i	0.225298	−	1.27773i
$187$	−18.5039	−	6.73487i	−1.35314	−	0.492502i
$188$	1.74606	−	1.46512i	0.127344	−	0.106855i
$189$	7.55896			0.549834
$190$		0			0
$191$	−4.24597			−0.307228			−0.153614	−	0.988131i	$-0.549091\pi$
$191$	−4.24597			−0.307228			−0.153614	+	0.988131i	$0.549091\pi$
$192$	−2.27256	+	1.90691i	−0.164008	+	0.137619i
$193$	−0.673581	−	0.245164i	−0.0484855	−	0.0176473i	0.317664	−	0.948203i	$-0.397102\pi$
$193$	−0.673581	−	0.245164i	−0.0484855	−	0.0176473i	−0.366149	+	0.930556i	$0.619324\pi$
$194$	−2.89131	+	16.3974i	−0.207584	+	1.17727i
$195$		0			0
$196$	5.80015	−	2.11108i	0.414296	−	0.150792i
$197$	−13.4072	+	23.2220i	−0.955224	+	1.65450i	−0.221368	+	0.975190i	$0.571052\pi$
$197$	−13.4072	+	23.2220i	−0.955224	+	1.65450i	−0.733855	+	0.679306i	$0.762281\pi$
$198$	10.5935	+	18.3485i	0.752848	+	1.30397i
$199$	14.1804	+	11.8988i	1.00522	+	0.843483i	0.987700	−	0.156363i	$-0.0499771\pi$
$199$	14.1804	+	11.8988i	1.00522	+	0.843483i	0.0175244	+	0.999846i	$0.494422\pi$
$200$		0			0
$201$	−20.3254	−	35.2046i	−1.43364	−	2.48314i
$202$	5.08254	−	8.80322i	0.357606	−	0.619392i
$203$	3.53443	−	1.28643i	0.248069	−	0.0902896i
$204$	−2.77735	−	15.7511i	−0.194453	−	1.10280i
$205$		0			0
$206$	−11.6888	−	4.25439i	−0.814400	−	0.296417i
$207$	5.79333	−	4.86118i	0.402664	−	0.337875i
$208$	−2.83515			−0.196583
$209$	2.33028	−	15.7490i	0.161189	−	1.08938i
$210$		0			0
$211$	−3.82973	+	3.21352i	−0.263649	+	0.221228i	−0.765023	−	0.644003i	$-0.777273\pi$
$211$	−3.82973	+	3.21352i	−0.263649	+	0.221228i	0.501374	+	0.865231i	$0.332828\pi$
$212$	−9.57229	−	3.48403i	−0.657427	−	0.239284i
$213$	−3.00969	+	17.0688i	−0.206221	+	1.16954i
$214$	2.15648	+	12.2300i	0.147414	+	0.836028i
$215$		0			0
$216$	−4.15450	+	7.19581i	−0.282678	+	0.489613i
$217$	2.71309	+	4.69921i	0.184177	+	0.319003i
$218$	−10.1116	−	8.48468i	−0.684847	−	0.574655i
$219$	−31.9910	−	26.8437i	−2.16175	−	1.81393i
$220$		0			0
$221$	7.64267	−	13.2375i	0.514101	−	0.890450i
$222$	27.3817	−	9.96611i	1.83774	−	0.668882i
$223$	−0.00446902	−	0.0253451i	−0.000299268	−	0.00169723i	0.984658	−	0.174497i	$-0.0558298\pi$
$223$	−0.00446902	−	0.0253451i	−0.000299268	−	0.00169723i	−0.984957	+	0.172799i	$0.944719\pi$
$224$	0.157973	−	0.895910i	0.0105550	−	0.0598605i
$225$		0			0
$226$	−14.0320	+	11.7742i	−0.933394	+	0.783210i
$227$	−8.25287			−0.547762			−0.273881	−	0.961764i	$-0.588307\pi$
$227$	−8.25287			−0.547762			−0.273881	+	0.961764i	$0.588307\pi$
$228$	12.0245	−	4.75680i	0.796342	−	0.315027i
$229$	−10.7684			−0.711594			−0.355797	−	0.934563i	$-0.615791\pi$
$229$	−10.7684			−0.711594			−0.355797	+	0.934563i	$0.615791\pi$
$230$		0			0
$231$	−9.26275	−	3.37137i	−0.609444	−	0.221820i
$232$	−0.717945	+	4.07167i	−0.0471354	+	0.267318i
$233$	1.96116	+	11.1223i	0.128480	+	0.728646i	0.979180	+	0.202994i	$0.0650673\pi$
$233$	1.96116	+	11.1223i	0.128480	+	0.728646i	−0.850700	+	0.525651i	$0.823822\pi$
$234$	−15.4544	+	5.62495i	−1.01029	+	0.367715i
$235$		0			0
$236$	−2.81047	−	4.86787i	−0.182946	−	0.316871i
$237$	−34.0546	−	28.5752i	−2.21209	−	1.85616i
$238$	3.75721	+	3.15267i	0.243543	+	0.204357i
$239$	−11.1299	−	19.2776i	−0.719935	−	1.24696i	−0.961025	−	0.276461i	$-0.910838\pi$
$239$	−11.1299	−	19.2776i	−0.719935	−	1.24696i	0.241090	−	0.970503i	$-0.422495\pi$
$240$		0			0
$241$	20.1153	−	7.32138i	1.29574	−	0.471612i	0.400135	−	0.916456i	$-0.368963\pi$
$241$	20.1153	−	7.32138i	1.29574	−	0.471612i	0.895608	+	0.444845i	$0.146741\pi$
$242$	−0.406352	−	2.30454i	−0.0261213	−	0.148141i
$243$	0.595166	−	3.37535i	0.0381799	−	0.216529i
$244$	3.49779	+	1.27309i	0.223923	+	0.0815014i
$245$		0			0
$246$	0.123026			0.00784383
$247$	11.7252	+	3.90424i	0.746058	+	0.248421i
$248$	−5.96460			−0.378753
$249$	−10.9055	+	9.15080i	−0.691108	+	0.579908i
$250$		0			0
$251$	0.878157	−	4.98028i	0.0554288	−	0.314352i	−0.944470	−	0.328598i	$-0.893424\pi$
$251$	0.878157	−	4.98028i	0.0554288	−	0.314352i	0.999899	+	0.0142461i	$0.00453484\pi$
$252$	−0.916376	−	5.19702i	−0.0577262	−	0.327382i
$253$	−4.47455	+	1.62860i	−0.281312	+	0.102389i
$254$	4.71078	−	8.15931i	0.295581	−	0.511961i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−12.3466	−	10.3601i	−0.770163	−	0.646243i	0.170588	−	0.985342i	$-0.445433\pi$
$257$	−12.3466	−	10.3601i	−0.770163	−	0.646243i	−0.940751	+	0.339099i	$0.889878\pi$
$258$	−13.1658	−	22.8039i	−0.819670	−	1.41971i
$259$	−4.46781	+	7.73848i	−0.277616	+	0.480846i
$260$		0			0
$261$	4.16468	+	23.6191i	0.257787	+	1.46198i
$262$	0.287669	−	1.63145i	0.0177723	−	0.100792i
$263$	−17.0291	−	6.19808i	−1.05006	−	0.382190i	−0.241374	−	0.970432i	$-0.577598\pi$
$263$	−17.0291	−	6.19808i	−1.05006	−	0.382190i	−0.808685	+	0.588242i	$0.799820\pi$
$264$	8.30033	−	6.96480i	0.510850	−	0.428654i
$265$		0			0
$266$	−1.88706	+	3.48763i	−0.115703	+	0.213840i
$267$	−26.5679			−1.62593
$268$	−10.4969	+	8.80793i	−0.641199	+	0.538030i
$269$	−10.8894	−	3.96341i	−0.663938	−	0.241654i	−0.0120022	−	0.999928i	$-0.503821\pi$
$269$	−10.8894	−	3.96341i	−0.663938	−	0.241654i	−0.651936	+	0.758274i	$0.726043\pi$
$270$		0			0
$271$	3.19870	+	18.1407i	0.194307	+	1.10197i	0.913402	+	0.407058i	$0.133445\pi$
$271$	3.19870	+	18.1407i	0.194307	+	1.10197i	−0.719095	+	0.694912i	$0.755443\pi$
$272$	−5.06622	+	1.84395i	−0.307185	+	0.111806i
$273$	3.82579	−	6.62647i	0.231548	−	0.401052i
$274$	−4.04002	−	6.99753i	−0.244067	−	0.422736i
$275$		0			0
$276$	−2.96278	−	2.48607i	−0.178338	−	0.149644i
$277$	−1.41120	−	2.44427i	−0.0847907	−	0.146862i	0.820511	−	0.571630i	$-0.193689\pi$
$277$	−1.41120	−	2.44427i	−0.0847907	−	0.146862i	−0.905302	+	0.424769i	$0.860355\pi$
$278$	3.54029	−	6.13196i	0.212332	−	0.367770i
$279$	−32.5131	+	11.8338i	−1.94651	+	0.708470i
$280$		0			0
$281$	4.31540	−	24.4738i	0.257435	−	1.45999i	−0.532309	−	0.846550i	$-0.678676\pi$
$281$	4.31540	−	24.4738i	0.257435	−	1.45999i	0.789744	−	0.613436i	$-0.210213\pi$
$282$	−6.35408	−	2.31270i	−0.378380	−	0.137719i
$283$	6.50910	−	5.46179i	0.386926	−	0.324669i	−0.428488	−	0.903547i	$-0.640954\pi$
$283$	6.50910	−	5.46179i	0.386926	−	0.324669i	0.815414	+	0.578878i	$0.196509\pi$
$284$	5.84238			0.346681
$285$		0			0
$286$	10.3551			0.612312
$287$	−0.0289002	+	0.0242501i	−0.00170592	+	0.00143144i
$288$	5.45100	+	1.98400i	0.321203	+	0.116908i
$289$	2.09537	−	11.8834i	0.123257	−	0.699024i
$290$		0			0
$291$	46.4164	−	16.8942i	2.72098	−	0.990355i
$292$	−7.03853	+	12.1911i	−0.411899	+	0.713430i
$293$	−7.83667	−	13.5735i	−0.457823	−	0.792973i	0.541023	−	0.841008i	$-0.318037\pi$
$293$	−7.83667	−	13.5735i	−0.457823	−	0.792973i	−0.998846	+	0.0480352i	$0.984704\pi$
$294$	−14.0271	−	11.7702i	−0.818080	−	0.686450i
$295$		0			0
$296$	−4.91114	−	8.50634i	−0.285454	−	0.494421i
$297$	15.1739	−	26.2821i	0.880482	−	1.52504i
$298$	−3.71415	+	1.35184i	−0.215155	+	0.0783101i
$299$	−0.641846	−	3.64009i	−0.0371189	−	0.210512i
$300$		0			0
$301$	7.58780	+	2.76173i	0.437353	+	0.159184i
$302$	8.36715	−	7.02088i	0.481476	−	0.404006i
$303$	−30.1559			−1.73241
$304$	−2.28292	−	3.71325i	−0.130935	−	0.212970i
$305$		0			0
$306$	−23.9576	+	20.1028i	−1.36956	+	1.14920i
$307$	−9.45204	−	3.44026i	−0.539457	−	0.196346i	0.0578993	−	0.998322i	$-0.481560\pi$
$307$	−9.45204	−	3.44026i	−0.539457	−	0.196346i	−0.597356	+	0.801976i	$0.703782\pi$
$308$	−0.576982	+	3.27223i	−0.0328766	+	0.186453i
$309$	6.40793	+	36.3412i	0.364534	+	2.06738i
$310$		0			0
$311$	−1.92851	+	3.34027i	−0.109356	+	0.189409i	−0.915509	−	0.402297i	$-0.868212\pi$
$311$	−1.92851	+	3.34027i	−0.109356	+	0.189409i	0.806154	+	0.591706i	$0.201545\pi$
$312$	4.20541	+	7.28399i	0.238085	+	0.412375i
$313$	−1.76625	−	1.48206i	−0.0998343	−	0.0837709i	0.591504	−	0.806302i	$-0.298534\pi$
$313$	−1.76625	−	1.48206i	−0.0998343	−	0.0837709i	−0.691339	+	0.722531i	$0.742979\pi$
$314$	11.9725	+	10.0462i	0.675650	+	0.566937i
$315$		0			0
$316$	−7.49257	+	12.9775i	−0.421490	+	0.730042i
$317$	11.0983	−	4.03943i	0.623340	−	0.226877i	−0.0109899	−	0.999940i	$-0.503498\pi$
$317$	11.0983	−	4.03943i	0.623340	−	0.226877i	0.634330	+	0.773062i	$0.281276\pi$
$318$	5.24762	+	29.7607i	0.294272	+	1.66890i
$319$	2.62223	−	14.8714i	0.146817	−	0.832639i
$320$		0			0
$321$	28.2223	−	23.6813i	1.57521	−	1.32176i
$322$	1.18603			0.0660950
$323$	23.4914	−	0.649349i	1.30710	−	0.0361307i
$324$	7.24717			0.402621
$325$		0			0
$326$	−11.6234	−	4.23057i	−0.643760	−	0.234310i
$327$	−6.79986	+	38.5639i	−0.376033	+	2.13259i
$328$	−0.00720119	−	0.0408400i	−0.000397619	−	0.00225501i
$329$	1.94851	−	0.709201i	0.107425	−	0.0390995i
$330$		0			0
$331$	7.77859	+	13.4729i	0.427550	+	0.740538i	0.996655	−	0.0817270i	$-0.0260436\pi$
$331$	7.77859	+	13.4729i	0.427550	+	0.740538i	−0.569105	+	0.822265i	$0.692710\pi$
$332$	3.67607	+	3.08459i	0.201750	+	0.169289i
$333$	−43.6472	−	36.6244i	−2.39185	−	2.00700i
$334$	10.6211	+	18.3962i	0.581158	+	1.00660i
$335$		0			0
$336$	−2.53607	+	0.923053i	−0.138354	+	0.0503567i
$337$	−3.98229	−	22.5847i	−0.216929	−	1.23027i	−0.877527	−	0.479527i	$-0.840808\pi$
$337$	−3.98229	−	22.5847i	−0.216929	−	1.23027i	0.660598	−	0.750740i	$-0.270303\pi$
$338$	0.861625	−	4.88652i	0.0468662	−	0.265792i
$339$	51.0638	+	18.5857i	2.77340	+	1.00944i
$340$		0			0
$341$	21.7852			1.17973
$342$	−19.8113	−	15.7116i	−1.07127	−	0.849588i
$343$	11.9833			0.647039
$344$	−6.79940	+	5.70538i	−0.366599	+	0.307613i
$345$		0			0
$346$	−1.78757	+	10.1378i	−0.0961003	+	0.545012i
$347$	3.06455	+	17.3799i	0.164514	+	0.933003i	0.949564	+	0.313572i	$0.101526\pi$
$347$	3.06455	+	17.3799i	0.164514	+	0.933003i	−0.785051	+	0.619431i	$0.787363\pi$
$348$	11.5257	−	4.19503i	0.617844	−	0.224877i
$349$	8.04925	−	13.9417i	0.430867	−	0.746283i	−0.566081	−	0.824349i	$-0.691541\pi$
$349$	8.04925	−	13.9417i	0.430867	−	0.746283i	0.996948	+	0.0780663i	$0.0248746\pi$
$350$		0			0
$351$	18.0460	+	15.1424i	0.963222	+	0.808239i
$352$	−2.79791	−	2.34772i	−0.149129	−	0.125134i
$353$	1.77982	+	3.08274i	0.0947302	+	0.164077i	0.909496	−	0.415713i	$-0.136468\pi$
$353$	1.77982	+	3.08274i	0.0947302	+	0.164077i	−0.814766	+	0.579790i	$0.803135\pi$
$354$	−8.33758	+	14.4411i	−0.443138	+	0.767537i
$355$		0			0
$356$	1.55512	+	8.81955i	0.0824215	+	0.467435i
$357$	2.52664	−	14.3293i	0.133724	−	0.758386i
$358$	−0.799267	−	0.290910i	−0.0422426	−	0.0153750i
$359$	−25.2996	+	21.2289i	−1.33526	+	1.12042i	−0.352443	+	0.935833i	$0.614649\pi$
$359$	−25.2996	+	21.2289i	−1.33526	+	1.12042i	−0.982817	+	0.184583i	$0.940907\pi$
$360$		0			0
$361$	4.32792	+	18.5005i	0.227786	+	0.973711i
$362$	17.1573			0.901770
$363$	−5.31800	+	4.46233i	−0.279123	+	0.234212i
$364$	−2.42368	−	0.882148i	−0.127035	−	0.0462371i
$365$		0			0
$366$	−1.91752	−	10.8748i	−0.100231	−	0.568436i
$367$	31.7519	−	11.5567i	1.65744	−	0.603257i	0.667479	−	0.744629i	$-0.267373\pi$
$367$	31.7519	−	11.5567i	1.65744	−	0.603257i	0.989957	+	0.141372i	$0.0451513\pi$
$368$	−0.651859	+	1.12905i	−0.0339805	+	0.0588560i
$369$	−0.120280	−	0.208331i	−0.00626154	−	0.0108453i
$370$		0			0
$371$	−7.09899	−	5.95676i	−0.368561	−	0.309260i
$372$	8.84736	+	15.3241i	0.458714	+	0.794516i
$373$	0.859852	−	1.48931i	0.0445214	−	0.0771134i	−0.842906	−	0.538061i	$-0.819157\pi$
$373$	0.859852	−	1.48931i	0.0445214	−	0.0771134i	0.887427	+	0.460948i	$0.152490\pi$
$374$	18.5039	−	6.73487i	0.956814	−	0.348252i
$375$		0			0
$376$	−0.395800	+	2.24469i	−0.0204118	+	0.115761i
$377$	11.0150	+	4.00912i	0.567300	+	0.206480i
$378$	−5.79050	+	4.85881i	−0.297831	+	0.249910i
$379$	8.89642			0.456978			0.228489	−	0.973546i	$-0.426621\pi$
$379$	8.89642			0.456978			0.228489	+	0.973546i	$0.426621\pi$
$380$		0			0
$381$	−27.9502			−1.43193
$382$	3.25260	−	2.72926i	0.166418	−	0.139641i
$383$	−8.21699	−	2.99074i	−0.419868	−	0.152820i	0.123441	−	0.992352i	$-0.460607\pi$
$383$	−8.21699	−	2.99074i	−0.419868	−	0.152820i	−0.543310	+	0.839532i	$0.682829\pi$
$384$	0.515148	−	2.92155i	0.0262885	−	0.149090i
$385$		0			0
$386$	0.673581	−	0.245164i	0.0342844	−	0.0124785i
$387$	−25.7441	+	44.5901i	−1.30865	+	2.26664i
$388$	−8.32518	−	14.4196i	−0.422647	−	0.732046i
$389$	−16.5424	−	13.8807i	−0.838732	−	0.703779i	0.118546	−	0.992949i	$-0.462177\pi$
$389$	−16.5424	−	13.8807i	−0.838732	−	0.703779i	−0.957278	+	0.289169i	$0.906621\pi$
$390$		0			0
$391$	−3.51441	−	6.08713i	−0.177731	−	0.307839i
$392$	−3.08619	+	5.34545i	−0.155876	+	0.269986i
$393$	−4.61818	+	1.68088i	−0.232957	+	0.0847892i
$394$	−4.65627	−	26.4070i	−0.234580	−	1.33037i
$395$		0			0
$396$	−19.9093	−	7.24639i	−1.00048	−	0.364145i
$397$	−19.6376	+	16.4779i	−0.985585	+	0.827004i	−0.984923	−	0.172996i	$-0.944655\pi$
$397$	−19.6376	+	16.4779i	−0.985585	+	0.827004i	−0.000662490		1.00000i	$0.500211\pi$
$398$	−18.5112			−0.927884
$399$	11.7594	−	0.325053i	0.588707	−	0.0162730i
$400$		0			0
$401$	−18.2483	+	15.3122i	−0.911278	+	0.764653i	−0.972362	−	0.233479i	$-0.924989\pi$
$401$	−18.2483	+	15.3122i	−0.911278	+	0.764653i	0.0610834	+	0.998133i	$0.480544\pi$
$402$	38.1992	+	13.9034i	1.90520	+	0.693437i
$403$	−2.93649	+	16.6537i	−0.146277	+	0.829578i
$404$	1.76515	+	10.0107i	0.0878194	+	0.498049i
$405$		0			0
$406$	−1.88063	+	3.25735i	−0.0933342	+	0.161660i
$407$	17.9375	+	31.0686i	0.889128	+	1.54002i
$408$	12.2522	+	10.2808i	0.606574	+	0.508976i
$409$	9.10867	+	7.64308i	0.450395	+	0.377926i	0.839582	−	0.543232i	$-0.182800\pi$
$409$	9.10867	+	7.64308i	0.450395	+	0.377926i	−0.389188	+	0.921159i	$0.627244\pi$
$410$		0			0
$411$	−11.9852	+	20.7590i	−0.591187	+	1.02397i
$412$	11.6888	−	4.25439i	0.575868	−	0.209599i
$413$	−0.887956	−	5.03585i	−0.0436935	−	0.247798i
$414$	−1.31324	+	7.44776i	−0.0645423	+	0.366037i
$415$		0			0
$416$	2.17185	−	1.82240i	0.106484	−	0.0893506i
$417$	−21.0054			−1.02864
$418$	8.33817	+	13.5623i	0.407833	+	0.663355i
$419$	7.57187			0.369910			0.184955	−	0.982747i	$-0.440786\pi$
$419$	7.57187			0.369910			0.184955	+	0.982747i	$0.440786\pi$
$420$		0			0
$421$	27.1515	+	9.88232i	1.32328	+	0.481635i	0.904508	−	0.426456i	$-0.140238\pi$
$421$	27.1515	+	9.88232i	1.32328	+	0.481635i	0.418773	+	0.908091i	$0.362460\pi$
$422$	0.868129	−	4.92340i	0.0422598	−	0.239667i
$423$	2.29597	+	13.0211i	0.111634	+	0.633106i
$424$	9.57229	−	3.48403i	0.464871	−	0.169199i
$425$		0			0
$426$	−8.66606	−	15.0101i	−0.419872	−	0.727240i
$427$	2.59403	+	2.17665i	0.125534	+	0.105336i
$428$	−9.51327	−	7.98258i	−0.459841	−	0.385853i
$429$	−15.3599	−	26.6041i	−0.741582	−	1.28446i
$430$		0			0
$431$	−24.5966	+	8.95244i	−1.18478	+	0.431224i	−0.857887	−	0.513838i	$-0.828223\pi$
$431$	−24.5966	+	8.95244i	−1.18478	+	0.431224i	−0.326891	+	0.945062i	$0.606001\pi$
$432$	−1.44284	−	8.18278i	−0.0694189	−	0.393694i
$433$	−3.98202	+	22.5832i	−0.191364	+	1.08528i	0.726139	+	0.687548i	$0.241313\pi$
$433$	−3.98202	+	22.5832i	−0.191364	+	1.08528i	−0.917503	+	0.397729i	$0.869798\pi$
$434$	−5.09894	−	1.85586i	−0.244757	−	0.0890843i
$435$		0			0
$436$	13.1998			0.632156
$437$	4.25066	−	3.77171i	0.203337	−	0.180425i
$438$	41.7613			1.99543
$439$	−22.3653	+	18.7667i	−1.06744	+	0.895688i	−0.994818	−	0.101672i	$-0.967581\pi$
$439$	−22.3653	+	18.7667i	−1.06744	+	0.895688i	−0.0726213	+	0.997360i	$0.523136\pi$
$440$		0			0
$441$	−6.21747	+	35.2610i	−0.296070	+	1.67910i
$442$	2.65427	+	15.0531i	0.126251	+	0.716004i
$443$	20.2646	−	7.37572i	0.962802	−	0.350431i	0.187671	−	0.982232i	$-0.439906\pi$
$443$	20.2646	−	7.37572i	0.962802	−	0.350431i	0.775131	+	0.631801i	$0.217684\pi$
$444$	−14.5695	+	25.2351i	−0.691437	+	1.19760i
$445$		0			0
$446$	0.0197150	+	0.0165428i	0.000933532	+	0.000783326i
$447$	8.98235	+	7.53709i	0.424850	+	0.356492i
$448$	0.454865	+	0.787850i	0.0214904	+	0.0372224i
$449$	18.9961	−	32.9021i	0.896479	−	1.55275i	0.0645161	−	0.997917i	$-0.479450\pi$
$449$	18.9961	−	32.9021i	0.896479	−	1.55275i	0.831963	−	0.554831i	$-0.187217\pi$
$450$		0			0
$451$	0.0263017	+	0.149164i	0.00123850	+	0.00702387i
$452$	3.18079	−	18.0392i	0.149612	−	0.848491i
$453$	−30.4489	−	11.0825i	−1.43061	−	0.520701i
$454$	6.32207	−	5.30484i	0.296709	−	0.248969i
$455$		0			0
$456$	−6.15369	+	11.3731i	−0.288173	+	0.532595i
$457$	−24.4260			−1.14260			−0.571299	−	0.820742i	$-0.693560\pi$
$457$	−24.4260			−1.14260			−0.571299	+	0.820742i	$0.693560\pi$
$458$	8.24905	−	6.92178i	0.385453	−	0.323433i
$459$	42.0953	+	15.3214i	1.96484	+	0.715143i
$460$		0			0
$461$	−4.77907	−	27.1034i	−0.222583	−	1.26233i	−0.867251	−	0.497871i	$-0.834115\pi$
$461$	−4.77907	−	27.1034i	−0.222583	−	1.26233i	0.644668	−	0.764463i	$-0.276996\pi$
$462$	9.26275	−	3.37137i	0.430942	−	0.156850i
$463$	−9.52958	+	16.5057i	−0.442877	+	0.767086i	−0.997902	−	0.0647482i	$-0.979376\pi$
$463$	−9.52958	+	16.5057i	−0.442877	+	0.767086i	0.555024	+	0.831834i	$0.312709\pi$
$464$	−2.06724	−	3.58057i	−0.0959692	−	0.166224i
$465$		0			0
$466$	−8.65161	−	7.25956i	−0.400778	−	0.336293i
$467$	17.0076	+	29.4581i	0.787019	+	1.36316i	0.927785	+	0.373114i	$0.121710\pi$
$467$	17.0076	+	29.4581i	0.787019	+	1.36316i	−0.140766	+	0.990043i	$0.544957\pi$
$468$	8.22313	−	14.2429i	0.380114	−	0.658377i
$469$	−11.7140	+	4.26355i	−0.540902	+	0.196872i
$470$		0			0
$471$	8.05127	−	45.6610i	0.370983	−	2.10395i
$472$	5.28195	+	1.92247i	0.243121	+	0.0884889i
$473$	24.8342	−	20.8384i	1.14188	−	0.958149i
$474$	44.4552			2.04189
$475$		0			0
$476$	−4.90468			−0.224806
$477$	45.2662	−	37.9829i	2.07260	−	1.73912i
$478$	20.9174	+	7.61332i	0.956740	+	0.348225i
$479$	−3.22838	+	18.3091i	−0.147509	+	0.836562i	0.817810	+	0.575488i	$0.195188\pi$
$479$	−3.22838	+	18.3091i	−0.147509	+	0.836562i	−0.965319	+	0.261074i	$0.915923\pi$
$480$		0			0
$481$	−26.1683	+	9.52446i	−1.19317	+	0.434278i
$482$	−10.7031	+	18.5384i	−0.487515	+	0.844401i
$483$	−1.75925	−	3.04712i	−0.0800488	−	0.138649i
$484$	1.79261	+	1.50418i	0.0814824	+	0.0683719i
$485$		0			0
$486$	1.71371	+	2.96824i	0.0777356	+	0.134642i
$487$	−3.77343	+	6.53577i	−0.170990	+	0.296164i	−0.938766	−	0.344554i	$-0.888030\pi$
$487$	−3.77343	+	6.53577i	−0.170990	+	0.296164i	0.767776	+	0.640718i	$0.221363\pi$
$488$	−3.49779	+	1.27309i	−0.158338	+	0.0576302i
$489$	6.37205	+	36.1377i	0.288154	+	1.63420i
$490$		0			0
$491$	17.3240	+	6.30541i	0.781819	+	0.284559i	0.701931	−	0.712245i	$-0.252321\pi$
$491$	17.3240	+	6.30541i	0.781819	+	0.284559i	0.0798883	+	0.996804i	$0.474544\pi$
$492$	−0.0942431	+	0.0790794i	−0.00424881	+	0.00356517i
$493$	22.2905			1.00391
$494$	−11.4916	+	4.54600i	−0.517033	+	0.204534i
$495$		0			0
$496$	4.56915	−	3.83397i	0.205161	−	0.172150i
$497$	4.99446	+	1.81783i	0.224032	+	0.0815410i
$498$	2.47208	−	14.0198i	0.110776	−	0.628244i
$499$	2.65263	+	15.0438i	0.118748	+	0.673454i	0.984826	+	0.173545i	$0.0555222\pi$
$499$	2.65263	+	15.0438i	0.118748	+	0.673454i	−0.866078	+	0.499909i	$0.833367\pi$
$500$		0			0
$501$	31.5086	−	54.5746i	1.40770	−	2.43821i
$502$	2.52855	+	4.37958i	0.112855	+	0.195470i
$503$	5.61697	+	4.71320i	0.250448	+	0.210151i	0.759365	−	0.650664i	$-0.225510\pi$
$503$	5.61697	+	4.71320i	0.250448	+	0.210151i	−0.508917	+	0.860816i	$0.669954\pi$
$504$	4.04257	+	3.39212i	0.180070	+	0.151097i
$505$		0			0
$506$	2.38086	−	4.12376i	0.105842	−	0.183324i
$507$	−13.8323	+	5.03456i	−0.614316	+	0.223593i
$508$	1.63604	+	9.27843i	0.0725874	+	0.411664i
$509$	4.48517	−	25.4367i	0.198802	−	1.12746i	−0.708098	−	0.706114i	$-0.750447\pi$
$509$	4.48517	−	25.4367i	0.198802	−	1.12746i	0.906900	−	0.421346i	$-0.138442\pi$
$510$		0			0
$511$	−9.81023	+	8.23176i	−0.433979	+	0.364152i
$512$	−1.00000			−0.0441942
$513$	−5.30126	+	35.8281i	−0.234056	+	1.58185i
$514$	16.1174			0.710908
$515$		0			0
$516$	24.7437	+	9.00597i	1.08928	+	0.396466i
$517$	1.44562	−	8.19853i	0.0635784	−	0.360571i
$518$	−1.55166	−	8.79988i	−0.0681758	−	0.386644i
$519$	28.6972	−	10.4449i	1.25967	−	0.458482i
$520$		0			0
$521$	13.1495	+	22.7756i	0.576089	+	0.997815i	0.995922	+	0.0902142i	$0.0287552\pi$
$521$	13.1495	+	22.7756i	0.576089	+	0.997815i	−0.419833	+	0.907601i	$0.637911\pi$
$522$	−18.3724	−	15.4163i	−0.804137	−	0.674751i
$523$	7.19346	+	6.03603i	0.314548	+	0.263937i	0.786369	−	0.617757i	$-0.211959\pi$
$523$	7.19346	+	6.03603i	0.314548	+	0.263937i	−0.471821	+	0.881695i	$0.656403\pi$
$524$	0.828311	+	1.43468i	0.0361849	+	0.0626741i
$525$		0			0
$526$	17.0291	−	6.19808i	0.742503	−	0.270249i
$527$	5.58406	+	31.6688i	0.243245	+	1.37951i
$528$	−1.88153	+	10.6707i	−0.0818832	+	0.464382i
$529$	20.0158	+	7.28514i	0.870250	+	0.316745i
$530$		0			0
$531$	32.6061			1.41498
$532$	−0.796231	−	3.88466i	−0.0345210	−	0.168422i
$533$	−0.117574			−0.00509269
$534$	20.3522	−	17.0775i	0.880725	−	0.739016i
$535$		0			0
$536$	2.37945	−	13.4945i	0.102777	−	0.582875i
$537$	0.438166	+	2.48496i	0.0189082	+	0.107234i
$538$	10.8894	−	3.96341i	0.469475	−	0.170875i
$539$	11.2720	−	19.5238i	0.485521	−	0.840948i
$540$		0			0
$541$	8.90611	+	7.47311i	0.382903	+	0.321294i	0.813841	−	0.581088i	$-0.197373\pi$
$541$	8.90611	+	7.47311i	0.382903	+	0.321294i	−0.430938	+	0.902382i	$0.641817\pi$
$542$	−14.1110	−	11.8405i	−0.606118	−	0.508594i
$543$	−25.4497	−	44.0801i	−1.09215	−	1.89166i
$544$	2.69568	−	4.66905i	0.115576	−	0.200184i
$545$		0			0
$546$	1.32868	+	7.53534i	0.0568624	+	0.322483i
$547$	3.89778	−	22.1054i	0.166657	−	0.945158i	−0.780683	−	0.624927i	$-0.785129\pi$
$547$	3.89778	−	22.1054i	0.166657	−	0.945158i	0.947340	−	0.320230i	$-0.103760\pi$
$548$	7.59276	+	2.76354i	0.324347	+	0.118053i
$549$	−16.5407	+	13.8793i	−0.705938	+	0.592352i
$550$		0			0
$551$	3.61866	+	17.6547i	0.154160	+	0.752118i
$552$	3.86764			0.164618
$553$	−10.4431	+	8.76276i	−0.444084	+	0.372630i
$554$	2.65218	+	0.965316i	0.112681	+	0.0410124i
$555$		0			0
$556$	1.22953	+	6.97301i	0.0521437	+	0.295721i
$557$	−9.68007	+	3.52326i	−0.410158	+	0.149285i	−0.538855	−	0.842399i	$-0.681143\pi$
$557$	−9.68007	+	3.52326i	−0.410158	+	0.149285i	0.128697	+	0.991684i	$0.458921\pi$
$558$	17.2998	−	29.9642i	0.732361	−	1.26849i
$559$	12.5824	+	21.7934i	0.532179	+	0.921761i
$560$		0			0
$561$	−44.7500	−	37.5497i	−1.88935	−	1.58535i
$562$	12.4257	+	21.5219i	0.524146	+	0.907848i
$563$	−13.0794	+	22.6542i	−0.551231	+	0.954760i	0.446955	+	0.894556i	$0.352508\pi$
$563$	−13.0794	+	22.6542i	−0.551231	+	0.954760i	−0.998186	+	0.0602035i	$0.980825\pi$
$564$	6.35408	−	2.31270i	0.267555	−	0.0973821i
$565$		0			0
$566$	−1.47549	+	8.36794i	−0.0620196	+	0.351731i
$567$	6.19537	+	2.25493i	0.260181	+	0.0946982i
$568$	−4.47552	+	3.75541i	−0.187789	+	0.157573i
$569$	−1.12217			−0.0470437			−0.0235219	−	0.999723i	$-0.507488\pi$
$569$	−1.12217			−0.0470437			−0.0235219	+	0.999723i	$0.507488\pi$
$570$		0			0
$571$	16.7706			0.701829			0.350915	−	0.936407i	$-0.385871\pi$
$571$	16.7706			0.701829			0.350915	+	0.936407i	$0.385871\pi$
$572$	−7.93250	+	6.65616i	−0.331674	+	0.278308i
$573$	−11.8365	−	4.30815i	−0.494479	−	0.179976i
$574$	0.00655114	−	0.0371534i	0.000273439	−	0.00155075i
$575$		0			0
$576$	−5.45100	+	1.98400i	−0.227125	+	0.0826668i
$577$	11.0604	−	19.1572i	0.460452	−	0.797527i	−0.538531	−	0.842606i	$-0.681021\pi$
$577$	11.0604	−	19.1572i	0.460452	−	0.797527i	0.998983	+	0.0450790i	$0.0143539\pi$
$578$	6.03337	+	10.4501i	0.250955	+	0.434667i
$579$	−1.62900	−	1.36689i	−0.0676988	−	0.0568060i
$580$		0			0
$581$	2.18279	+	3.78071i	0.0905575	+	0.156850i
$582$	−24.6977	+	42.7776i	−1.02375	+	1.77319i
$583$	−34.9619	+	12.7251i	−1.44797	+	0.527020i
$584$	−2.44446	−	13.8632i	−0.101152	−	0.573664i
$585$		0			0
$586$	14.7281	+	5.36060i	0.608413	+	0.221444i
$587$	−2.73263	+	2.29294i	−0.112788	+	0.0946400i	−0.697437	−	0.716646i	$-0.745676\pi$
$587$	−2.73263	+	2.29294i	−0.112788	+	0.0946400i	0.584650	+	0.811286i	$0.301232\pi$
$588$	18.3111			0.755138
$589$	−24.1761	+	9.56389i	−0.996160	+	0.394073i
$590$		0			0
$591$	−60.9374	+	51.1326i	−2.50663	+	2.10331i
$592$	9.22992	+	3.35942i	0.379347	+	0.138071i
$593$	0.940367	−	5.33309i	0.0386162	−	0.219004i	−0.959393	−	0.282073i	$-0.908978\pi$
$593$	0.940367	−	5.33309i	0.0386162	−	0.219004i	0.998009	+	0.0630696i	$0.0200890\pi$
$594$	5.26986	+	29.8868i	0.216225	+	1.22627i
$595$		0			0
$596$	1.97626	−	3.42298i	0.0809508	−	0.140211i
$597$	27.4579	+	47.5585i	1.12378	+	1.94644i
$598$	2.83149	+	2.37590i	0.115788	+	0.0971577i
$599$	4.12626	+	3.46234i	0.168594	+	0.141467i	0.723181	−	0.690658i	$-0.242679\pi$
$599$	4.12626	+	3.46234i	0.168594	+	0.141467i	−0.554587	+	0.832126i	$0.687124\pi$
$600$		0			0
$601$	−13.3088	+	23.0515i	−0.542877	+	0.940290i	0.455860	+	0.890051i	$0.349332\pi$
$601$	−13.3088	+	23.0515i	−0.542877	+	0.940290i	−0.998737	+	0.0502390i	$0.984002\pi$
$602$	−7.58780	+	2.76173i	−0.309255	+	0.112560i
$603$	−13.8028	−	78.2795i	−0.562093	−	3.18779i
$604$	−1.89668	+	10.7566i	−0.0771748	+	0.437680i
$605$		0			0
$606$	23.1008	−	19.3839i	0.938405	−	0.787416i
$607$	5.24915			0.213057			0.106528	−	0.994310i	$-0.466027\pi$
$607$	5.24915			0.213057			0.106528	+	0.994310i	$0.466027\pi$
$608$	4.13566	+	1.37708i	0.167723	+	0.0558481i
$609$	11.1582			0.452155
$610$		0			0
$611$	6.07250	+	2.21021i	0.245667	+	0.0894155i
$612$	5.43074	−	30.7992i	0.219525	−	1.24499i
$613$	−1.13295	−	6.42528i	−0.0457595	−	0.259515i	0.953342	−	0.301892i	$-0.0976181\pi$
$613$	−1.13295	−	6.42528i	−0.0457595	−	0.259515i	−0.999102	+	0.0423769i	$0.986507\pi$
$614$	9.45204	−	3.44026i	0.381453	−	0.138838i
$615$		0			0
$616$	−1.66135	−	2.87755i	−0.0669379	−	0.115940i
$617$	31.7605	+	26.6502i	1.27863	+	1.07290i	0.993431	+	0.114430i	$0.0365040\pi$
$617$	31.7605	+	26.6502i	1.27863	+	1.07290i	0.285199	+	0.958468i	$0.407940\pi$
$618$	−28.2684	−	23.7200i	−1.13712	−	0.954159i
$619$	−5.69855	−	9.87017i	−0.229044	−	0.396716i	0.728481	−	0.685066i	$-0.240227\pi$
$619$	−5.69855	−	9.87017i	−0.229044	−	0.396716i	−0.957525	+	0.288350i	$0.906893\pi$
$620$		0			0
$621$	10.1793	−	3.70497i	0.408482	−	0.148675i
$622$	−0.669764	−	3.79842i	−0.0268551	−	0.152303i
$623$	−1.41474	+	8.02342i	−0.0566806	+	0.321451i
$624$	−7.90359	−	2.87667i	−0.316397	−	0.115159i
$625$		0			0
$626$	2.30567			0.0921533
$627$	22.4758	−	41.5393i	0.897597	−	1.65892i
$628$	−15.6290			−0.623667
$629$	−40.5662	+	34.0391i	−1.61748	+	1.35723i
$630$		0			0
$631$	−4.25168	+	24.1125i	−0.169257	+	0.959903i	0.775309	+	0.631582i	$0.217594\pi$
$631$	−4.25168	+	24.1125i	−0.169257	+	0.959903i	−0.944566	+	0.328321i	$0.893517\pi$
$632$	−2.60214	−	14.7575i	−0.103508	−	0.587021i
$633$	−13.9368	+	5.07256i	−0.553936	+	0.201616i
$634$	−5.90526	+	10.2282i	−0.234528	+	0.406214i
$635$		0			0
$636$	−23.1497	−	19.4249i	−0.917946	−	0.770248i
$637$	13.4055	+	11.2486i	0.531146	+	0.445685i
$638$	7.55041	+	13.0777i	0.298924	+	0.517751i
$639$	−16.9453	+	29.3502i	−0.670347	+	1.16108i
$640$		0			0
$641$	−6.09749	−	34.5806i	−0.240836	−	1.36585i	−0.829967	−	0.557813i	$-0.811641\pi$
$641$	−6.09749	−	34.5806i	−0.240836	−	1.36585i	0.589130	−	0.808038i	$-0.299471\pi$
$642$	−6.39747	+	36.2818i	−0.252488	+	1.43193i
$643$	−16.8546	−	6.13458i	−0.664681	−	0.241924i	−0.0124251	−	0.999923i	$-0.503955\pi$
$643$	−16.8546	−	6.13458i	−0.664681	−	0.241924i	−0.652256	+	0.757999i	$0.726177\pi$
$644$	−0.908554	+	0.762367i	−0.0358020	+	0.0300415i
$645$		0			0
$646$	−17.5781	+	15.5974i	−0.691600	+	0.613672i
$647$	−19.4546			−0.764839			−0.382419	−	0.923989i	$-0.624909\pi$
$647$	−19.4546			−0.764839			−0.382419	+	0.923989i	$0.624909\pi$
$648$	−5.55166	+	4.65839i	−0.218090	+	0.182999i
$649$	−19.2918	−	7.02165i	−0.757271	−	0.275624i
$650$		0			0
$651$	2.79529	+	15.8529i	0.109556	+	0.621323i
$652$	11.6234	−	4.23057i	0.455207	−	0.165682i
$653$	−11.1910	+	19.3833i	−0.437937	+	0.758528i	−0.997530	−	0.0702387i	$-0.977624\pi$
$653$	−11.1910	+	19.3833i	−0.437937	+	0.758528i	0.559594	+	0.828767i	$0.310957\pi$
$654$	−19.5794	−	33.9125i	−0.765616	−	1.32609i
$655$		0			0
$656$	0.0317678	+	0.0266564i	0.00124033	+	0.00104076i
$657$	−40.8294	−	70.7185i	−1.59291	−	2.75899i
$658$	−1.03678	+	1.79576i	−0.0404180	+	0.0700061i
$659$	−31.0531	+	11.3024i	−1.20966	+	0.440279i	−0.866584	−	0.499030i	$-0.833690\pi$
$659$	−31.0531	+	11.3024i	−1.20966	+	0.440279i	−0.343072	+	0.939309i	$0.611467\pi$
$660$		0			0
$661$	0.579266	−	3.28518i	0.0225308	−	0.127779i	−0.971468	−	0.237172i	$-0.923780\pi$
$661$	0.579266	−	3.28518i	0.0225308	−	0.127779i	0.993999	+	0.109393i	$0.0348907\pi$
$662$	−14.6190	−	5.32087i	−0.568182	−	0.206801i
$663$	34.7369	−	29.1477i	1.34907	−	1.13200i
$664$	−4.79877			−0.186228
$665$		0			0
$666$	56.9774			2.20783
$667$	4.12913	−	3.46475i	0.159881	−	0.134156i
$668$	−19.9611	−	7.26523i	−0.772316	−	0.281100i
$669$	0.0132579	−	0.0751893i	0.000512580	−	0.00290699i
$670$		0			0
$671$	12.7754	−	4.64986i	0.493188	−	0.179506i
$672$	1.34941	−	2.33725i	0.0520547	−	0.0901614i
$673$	7.46700	+	12.9332i	0.287832	+	0.498539i	0.973292	−	0.229571i	$-0.0737323\pi$
$673$	7.46700	+	12.9332i	0.287832	+	0.498539i	−0.685460	+	0.728110i	$0.740399\pi$
$674$	17.5678	+	14.7411i	0.676686	+	0.567807i
$675$		0			0
$676$	2.48095	+	4.29713i	0.0954212	+	0.165274i
$677$	22.3332	−	38.6822i	0.858335	−	1.48668i	−0.0151821	−	0.999885i	$-0.504833\pi$
$677$	22.3332	−	38.6822i	0.858335	−	1.48668i	0.873517	−	0.486794i	$-0.161834\pi$
$678$	−51.0638	+	18.5857i	−1.96109	+	0.713779i
$679$	−2.63031	−	14.9172i	−0.100942	−	0.572471i
$680$		0			0
$681$	−23.0066	−	8.37372i	−0.881616	−	0.320882i
$682$	−16.6884	+	14.0032i	−0.639032	+	0.536212i
$683$	−32.3880			−1.23929			−0.619647	−	0.784881i	$-0.712724\pi$
$683$	−32.3880			−1.23929			−0.619647	+	0.784881i	$0.712724\pi$
$684$	25.2756	−	0.698667i	0.966436	−	0.0267142i
$685$		0			0
$686$	−9.17976	+	7.70273i	−0.350485	+	0.294092i
$687$	−30.0191	−	10.9261i	−1.14530	−	0.416855i
$688$	1.54130	−	8.74115i	0.0587615	−	0.333253i
$689$	−5.01507	−	28.4419i	−0.191059	−	1.08355i
$690$		0			0
$691$	−5.21755	+	9.03706i	−0.198485	+	0.343786i	−0.948037	−	0.318159i	$-0.896935\pi$
$691$	−5.21755	+	9.03706i	−0.198485	+	0.343786i	0.749552	+	0.661945i	$0.230269\pi$
$692$	−5.14710	−	8.91503i	−0.195663	−	0.338899i
$693$	−14.7651	−	12.3894i	−0.560880	−	0.470634i
$694$	−13.5192	−	11.3439i	−0.513181	−	0.430610i
$695$		0			0
$696$	−6.13272	+	10.6222i	−0.232460	+	0.402633i
$697$	−0.210096	+	0.0764687i	−0.00795795	+	0.00289646i
$698$	2.79548	+	15.8539i	0.105810	+	0.600080i
$699$	−5.81802	+	32.9956i	−0.220058	+	1.24801i
$700$		0			0
$701$	2.13342	−	1.79015i	0.0805783	−	0.0676132i	−0.601609	−	0.798791i	$-0.705473\pi$
$701$	2.13342	−	1.79015i	0.0805783	−	0.0676132i	0.682187	+	0.731178i	$0.261029\pi$
$702$	−23.5573			−0.889114
$703$	−33.5456	−	26.6038i	−1.26520	−	1.00338i
$704$	3.65241			0.137655
$705$		0			0
$706$	−3.34496	−	1.21747i	−0.125889	−	0.0458200i
$707$	−1.60581	+	9.10700i	−0.0603927	+	0.342504i
$708$	−2.89561	−	16.4218i	−0.108824	−	0.617170i
$709$	48.2720	−	17.5696i	1.81289	−	0.659839i	0.816274	−	0.577665i	$-0.196036\pi$
$709$	48.2720	−	17.5696i	1.81289	−	0.659839i	0.996618	−	0.0821733i	$-0.0261861\pi$
$710$		0			0
$711$	−43.4631	−	75.2803i	−1.62999	−	2.82323i
$712$	−6.86039	−	5.75655i	−0.257104	−	0.215736i
$713$	5.95689	+	4.99842i	0.223087	+	0.187192i
$714$	7.27517	+	12.6010i	0.272266	+	0.471579i
$715$		0			0
$716$	0.799267	−	0.290910i	0.0298700	−	0.0108718i
$717$	−11.4671	−	65.0333i	−0.428247	−	2.42871i
$718$	5.73495	−	32.5245i	0.214026	−	1.21380i
$719$	−42.8613	−	15.6002i	−1.59846	−	0.581790i	−0.619345	−	0.785119i	$-0.712602\pi$
$719$	−42.8613	−	15.6002i	−1.59846	−	0.581790i	−0.979111	+	0.203328i	$0.934824\pi$
$720$		0			0
$721$	11.3161			0.421435
$722$	−15.2073	−	11.3903i	−0.565957	−	0.423902i
$723$	63.5043			2.36175
$724$	−13.1433	+	11.0285i	−0.488467	+	0.409872i
$725$		0			0
$726$	1.20549	−	6.83669i	0.0447400	−	0.253733i
$727$	−3.96382	−	22.4799i	−0.147010	−	0.833734i	−0.965731	−	0.259544i	$-0.916428\pi$
$727$	−3.96382	−	22.4799i	−0.147010	−	0.833734i	0.818722	−	0.574191i	$-0.194683\pi$
$728$	2.42368	−	0.882148i	0.0898276	−	0.0326946i
$729$	15.9547	−	27.6343i	0.590914	−	1.02349i
$730$		0			0
$731$	36.6580	+	30.7597i	1.35585	+	1.13769i
$732$	8.45910	+	7.09803i	0.312657	+	0.262351i
$733$	2.88768	+	5.00160i	0.106659	+	0.184738i	0.914415	−	0.404779i	$-0.132651\pi$
$733$	2.88768	+	5.00160i	0.106659	+	0.184738i	−0.807756	+	0.589517i	$0.799318\pi$
$734$	−16.8948	+	29.2627i	−0.623600	+	1.08011i
$735$		0			0
$736$	−0.226388	−	1.28391i	−0.00834478	−	0.0473256i
$737$	−8.69072	+	49.2875i	−0.320127	+	1.81553i
$738$	0.226053	+	0.0822765i	0.00832112	+	0.00302864i
$739$	9.57147	−	8.03142i	0.352092	−	0.295441i	−0.449537	−	0.893262i	$-0.648411\pi$
$739$	9.57147	−	8.03142i	0.352092	−	0.295441i	0.801630	+	0.597821i	$0.203967\pi$
$740$		0			0
$741$	28.7251	+	22.7808i	1.05524	+	0.836874i
$742$	9.26708			0.340205
$743$	−38.5381	+	32.3373i	−1.41383	+	1.18634i	−0.459276	+	0.888294i	$0.651891\pi$
$743$	−38.5381	+	32.3373i	−1.41383	+	1.18634i	−0.954551	+	0.298048i	$0.903665\pi$
$744$	−16.6276	−	6.05195i	−0.609597	−	0.221875i
$745$		0			0
$746$	0.298623	+	1.69358i	0.0109334	+	0.0620063i
$747$	−26.1581	+	9.52076i	−0.957074	+	0.348346i
$748$	−9.84572	+	17.0533i	−0.359995	+	0.623530i
$749$	−5.64884	−	9.78407i	−0.206404	−	0.357502i
$750$		0			0
$751$	35.1254	+	29.4737i	1.28174	+	1.07551i	0.993001	+	0.118104i	$0.0376817\pi$
$751$	35.1254	+	29.4737i	1.28174	+	1.07551i	0.288743	+	0.957407i	$0.406763\pi$
$752$	−1.13966	−	1.97395i	−0.0415591	−	0.0719825i
$753$	7.50126	−	12.9926i	0.273361	−	0.473475i
$754$	−11.0150	+	4.00912i	−0.401142	+	0.146004i
$755$		0			0
$756$	1.31260	−	7.44412i	0.0477388	−	0.270740i
$757$	10.4163	+	3.79121i	0.378586	+	0.137794i	0.524302	−	0.851533i	$-0.324326\pi$
$757$	10.4163	+	3.79121i	0.378586	+	0.137794i	−0.145716	+	0.989326i	$0.546549\pi$
$758$	−6.81505	+	5.71851i	−0.247534	+	0.207706i
$759$	−14.1262			−0.512748
$760$		0			0
$761$	38.4522			1.39389			0.696945	−	0.717125i	$-0.254542\pi$
$761$	38.4522			1.39389			0.696945	+	0.717125i	$0.254542\pi$
$762$	21.4111	−	17.9660i	0.775642	−	0.650841i
$763$	11.2841	+	4.10707i	0.408511	+	0.148686i
$764$	−0.737306	+	4.18147i	−0.0266748	+	0.151280i
$765$		0			0
$766$	8.21699	−	2.99074i	0.296892	−	0.108060i
$767$	7.96810	−	13.8012i	0.287712	−	0.498331i
$768$	1.48331	+	2.56917i	0.0535243	+	0.0927069i
$769$	2.43664	+	2.04458i	0.0878675	+	0.0737296i	0.685663	−	0.727919i	$-0.259512\pi$
$769$	2.43664	+	2.04458i	0.0878675	+	0.0737296i	−0.597796	+	0.801648i	$0.703957\pi$
$770$		0			0
$771$	−23.9071	−	41.4083i	−0.860993	−	1.49128i
$772$	−0.358405	+	0.620776i	−0.0128993	+	0.0223422i
$773$	25.5354	−	9.29414i	0.918446	−	0.334287i	0.160826	−	0.986983i	$-0.448584\pi$
$773$	25.5354	−	9.29414i	0.918446	−	0.334287i	0.757620	+	0.652696i	$0.226362\pi$
$774$	−8.94082	−	50.7059i	−0.321371	−	1.82259i
$775$		0			0
$776$	15.6462	+	5.69476i	0.561667	+	0.204430i
$777$	−20.3068	+	17.0394i	−0.728501	+	0.611285i
$778$	21.5945			0.774202
$779$	−0.0946728	−	0.153989i	−0.00339200	−	0.00551721i
$780$		0			0
$781$	16.3464	−	13.7163i	0.584922	−	0.490807i
$782$	6.60492	+	2.40400i	0.236192	+	0.0859667i
$783$	−5.96541	+	33.8315i	−0.213186	+	1.20904i
$784$	−1.07182	−	6.07862i	−0.0382794	−	0.217093i
$785$		0			0
$786$	2.45728	−	4.25614i	0.0876484	−	0.151812i
$787$	−9.95112	−	17.2358i	−0.354719	−	0.614392i	0.632351	−	0.774682i	$-0.282090\pi$
$787$	−9.95112	−	17.2358i	−0.354719	−	0.614392i	−0.987070	+	0.160291i	$0.948757\pi$
$788$	20.5410	+	17.2360i	0.731744	+	0.614006i
$789$	−41.1833	−	34.5569i	−1.46617	−	1.23026i
$790$		0			0
$791$	8.33198	−	14.4314i	0.296251	−	0.513122i
$792$	19.9093	−	7.24639i	0.707446	−	0.257489i
$793$	1.83255	+	10.3929i	0.0650757	+	0.369063i
$794$	4.45149	−	25.2457i	0.157978	−	0.895935i
$795$		0			0
$796$	14.1804	−	11.8988i	0.502612	−	0.421742i
$797$	16.3603			0.579510			0.289755	−	0.957101i	$-0.406426\pi$
$797$	16.3603			0.579510			0.289755	+	0.957101i	$0.406426\pi$
$798$	−8.79929	+	7.80781i	−0.311492	+	0.276394i
$799$	12.2886			0.434740
$800$		0			0
$801$	−48.8170	−	17.7679i	−1.72486	−	0.627799i
$802$	4.13656	−	23.4596i	0.146067	−	0.828388i
$803$	8.92816	+	50.6341i	0.315068	+	1.78684i
$804$	−38.1992	+	13.9034i	−1.34718	+	0.490334i
$805$		0			0
$806$	−8.45529	−	14.6450i	−0.297825	−	0.515848i
$807$	−26.3350	−	22.0977i	−0.927036	−	0.777876i
$808$	−7.78691	−	6.53399i	−0.273942	−	0.229865i
$809$	15.6739	+	27.1480i	0.551064	+	0.954471i	0.998198	+	0.0600042i	$0.0191114\pi$
$809$	15.6739	+	27.1480i	0.551064	+	0.954471i	−0.447134	+	0.894467i	$0.647555\pi$
$810$		0			0
$811$	−46.6994	+	16.9972i	−1.63984	+	0.596852i	−0.987010	−	0.160657i	$-0.948639\pi$
$811$	−46.6994	+	16.9972i	−1.63984	+	0.596852i	−0.652826	+	0.757508i	$0.726417\pi$
$812$	−0.653137	−	3.70412i	−0.0229206	−	0.129989i
$813$	−9.48932	+	53.8166i	−0.332805	+	1.88743i
$814$	−33.7114	−	12.2700i	−1.18159	−	0.430062i
$815$		0			0
$816$	−15.9941			−0.559906
$817$	−18.4116	+	34.0279i	−0.644139	+	1.19048i
$818$	−11.8905			−0.415743
$819$	11.4613	−	9.61717i	0.400490	−	0.336051i
$820$		0			0
$821$	−8.09066	+	45.8844i	−0.282366	+	1.60138i	0.432179	+	0.901788i	$0.357745\pi$
$821$	−8.09066	+	45.8844i	−0.282366	+	1.60138i	−0.714545	+	0.699589i	$0.753366\pi$
$822$	−4.16242	−	23.6063i	−0.145181	−	0.823363i
$823$	29.7720	−	10.8361i	1.03779	−	0.377723i	0.233746	−	0.972298i	$-0.424902\pi$
$823$	29.7720	−	10.8361i	1.03779	−	0.377723i	0.804040	+	0.594575i	$0.202680\pi$
$824$	−6.21950	+	10.7725i	−0.216667	+	0.375278i
$825$		0			0
$826$	3.91719	+	3.28692i	0.136297	+	0.114366i
$827$	20.9920	+	17.6144i	0.729964	+	0.612512i	0.930122	−	0.367251i	$-0.119701\pi$
$827$	20.9920	+	17.6144i	0.729964	+	0.612512i	−0.200158	+	0.979764i	$0.564146\pi$
$828$	−3.78133	−	6.54945i	−0.131410	−	0.227609i
$829$	12.0124	−	20.8061i	0.417208	−	0.722625i	−0.578450	−	0.815718i	$-0.696342\pi$
$829$	12.0124	−	20.8061i	0.417208	−	0.722625i	0.995657	+	0.0930932i	$0.0296754\pi$
$830$		0			0
$831$	−1.45395	−	8.24577i	−0.0504370	−	0.286043i
$832$	−0.492319	+	2.79208i	−0.0170681	+	0.0967980i
$833$	31.2707	+	11.3816i	1.08346	+	0.394349i
$834$	16.0911	−	13.5020i	0.557188	−	0.467536i
$835$		0			0
$836$	−15.1051	−	5.02967i	−0.522421	−	0.173955i
$837$	−49.5599			−1.71304
$838$	−5.80039	+	4.86710i	−0.200371	+	0.168131i
$839$	38.0042	+	13.8324i	1.31205	+	0.477547i	0.900902	−	0.434022i	$-0.142906\pi$
$839$	38.0042	+	13.8324i	1.31205	+	0.477547i	0.411148	+	0.911569i	$0.365128\pi$
$840$		0			0
$841$	−2.06747	−	11.7252i	−0.0712919	−	0.404317i
$842$	−27.1515	+	9.88232i	−0.935701	+	0.340567i
$843$	36.8623	−	63.8474i	1.26961	−	2.19902i
$844$	2.49968	+	4.32957i	0.0860424	+	0.149030i
$845$		0			0
$846$	−10.1286	−	8.49890i	−0.348228	−	0.292198i
$847$	1.06443	+	1.84364i	0.0365741	+	0.0633482i
$848$	−5.09331	+	8.82187i	−0.174905	+	0.302944i
$849$	23.6873	−	8.62146i	0.812945	−	0.295888i
$850$		0			0
$851$	−2.22365	+	12.6109i	−0.0762257	+	0.432297i
$852$	16.2869	+	5.92793i	0.557979	+	0.203088i
$853$	9.72569	−	8.16082i	0.333001	−	0.279421i	−0.460920	−	0.887442i	$-0.652481\pi$
$853$	9.72569	−	8.16082i	0.333001	−	0.279421i	0.793921	+	0.608020i	$0.208036\pi$
$854$	−3.38627			−0.115876
$855$		0			0
$856$	12.4187			0.424462
$857$	−3.13547	+	2.63097i	−0.107106	+	0.0898723i	−0.694768	−	0.719234i	$-0.744493\pi$
$857$	−3.13547	+	2.63097i	−0.107106	+	0.0898723i	0.587662	+	0.809106i	$0.300048\pi$
$858$	28.8671	+	10.5068i	0.985508	+	0.358696i
$859$	5.09546	−	28.8978i	0.173855	−	0.985980i	−0.765603	−	0.643314i	$-0.777559\pi$
$859$	5.09546	−	28.8978i	0.173855	−	0.985980i	0.939457	−	0.342666i	$-0.111330\pi$
$860$		0			0
$861$	−0.105171	+	0.0382790i	−0.00358421	+	0.00130454i
$862$	13.0876	−	22.6684i	0.445765	−	0.772088i
$863$	−22.7285	−	39.3669i	−0.773687	−	1.34006i	−0.935530	−	0.353248i	$-0.885077\pi$
$863$	−22.7285	−	39.3669i	−0.773687	−	1.34006i	0.161843	−	0.986817i	$-0.448256\pi$
$864$	6.36507	+	5.34093i	0.216544	+	0.181702i
$865$		0			0
$866$	−11.4658	−	19.8593i	−0.389623	−	0.674846i
$867$	17.8987	−	31.0015i	0.607872	−	1.05287i
$868$	5.09894	−	1.85586i	0.173069	−	0.0629921i
$869$	9.50408	+	53.9003i	0.322404	+	1.82844i
$870$		0			0
$871$	−36.5064	−	13.2872i	−1.23697	−	0.450221i
$872$	−10.1116	+	8.48468i	−0.342423	+	0.287327i
$873$	96.5860			3.26894
$874$	−0.831789	+	5.62157i	−0.0281357	+	0.190153i
$875$		0			0
$876$	−31.9910	+	26.8437i	−1.08088	+	0.906963i
$877$	−11.0387	−	4.01777i	−0.372752	−	0.135671i	0.148850	−	0.988860i	$-0.452443\pi$
$877$	−11.0387	−	4.01777i	−0.372752	−	0.135671i	−0.521601	+	0.853189i	$0.674665\pi$
$878$	5.06981	−	28.7523i	0.171098	−	0.970344i
$879$	−8.07409	−	45.7905i	−0.272332	−	1.54447i
$880$		0			0
$881$	11.2581	−	19.4996i	0.379294	−	0.656957i	−0.611665	−	0.791117i	$-0.709500\pi$
$881$	11.2581	−	19.4996i	0.379294	−	0.656957i	0.990960	+	0.134160i	$0.0428335\pi$
$882$	−17.9025	−	31.0080i	−0.602809	−	1.04410i
$883$	6.34235	+	5.32186i	0.213437	+	0.179095i	0.743238	−	0.669027i	$-0.233289\pi$
$883$	6.34235	+	5.32186i	0.213437	+	0.179095i	−0.529801	+	0.848122i	$0.677733\pi$
$884$	−11.7092	−	9.82522i	−0.393824	−	0.330458i
$885$		0			0
$886$	−10.7826	+	18.6760i	−0.362248	+	0.627432i
$887$	−6.41989	+	2.33665i	−0.215559	+	0.0784570i	−0.447542	−	0.894263i	$-0.647701\pi$
$887$	−6.41989	+	2.33665i	−0.215559	+	0.0784570i	0.231984	+	0.972720i	$0.425478\pi$
$888$	−5.05993	−	28.6963i	−0.169800	−	0.962984i
$889$	−1.48835	+	8.44087i	−0.0499178	+	0.283098i
$890$		0			0
$891$	20.2769	−	17.0144i	0.679302	−	0.570002i
$892$	−0.0257361			−0.000861708
$893$	1.99495	+	9.73297i	0.0667584	+	0.325702i
$894$	−11.7256			−0.392163
$895$		0			0
$896$	−0.854867	−	0.311146i	−0.0285591	−	0.0103947i
$897$	1.90411	−	10.7988i	0.0635765	−	0.360560i
$898$	6.59726	+	37.4149i	0.220153	+	1.24855i
$899$	−23.1733	+	8.43440i	−0.772874	+	0.281303i
$900$		0			0
$901$	−27.4598	−	47.5618i	−0.914820	−	1.58451i
$902$	−0.116029	−	0.0973600i	−0.00386335	−	0.00324173i
$903$	18.3504	+	15.3978i	0.610663	+	0.512407i
$904$	9.15873	+	15.8634i	0.304615	+	0.527608i
$905$		0			0
$906$	30.4489	−	11.0825i	1.01160	−	0.368191i
$907$	8.43871	+	47.8583i	0.280203	+	1.58911i	0.721935	+	0.691961i	$0.243253\pi$
$907$	8.43871	+	47.8583i	0.280203	+	1.58911i	−0.441732	+	0.897147i	$0.645636\pi$
$908$	−1.43310	+	8.12749i	−0.0475590	+	0.269720i
$909$	−55.4099	−	20.1675i	−1.83783	−	0.668915i
$910$		0			0
$911$	−0.332251			−0.0110080			−0.00550399	−	0.999985i	$-0.501752\pi$
$911$	−0.332251			−0.0110080			−0.00550399	+	0.999985i	$0.501752\pi$
$912$	−2.59650	−	12.6678i	−0.0859787	−	0.419474i
$913$	17.5271			0.580061
$914$	18.7114	−	15.7007i	0.618917	−	0.519333i
$915$		0			0
$916$	−1.86991	+	10.6048i	−0.0617835	+	0.350392i
$917$	0.261702	+	1.48418i	0.00864215	+	0.0490121i
$918$	−42.0953	+	15.3214i	−1.38935	+	0.505682i
$919$	−12.7310	+	22.0508i	−0.419958	+	0.727389i	−0.995935	−	0.0900775i	$-0.971289\pi$
$919$	−12.7310	+	22.0508i	−0.419958	+	0.727389i	0.575977	+	0.817466i	$0.304622\pi$
$920$		0			0
$921$	−22.8589	−	19.1809i	−0.753227	−	0.632032i
$922$	21.0827	+	17.6905i	0.694323	+	0.582606i
$923$	8.28202	+	14.3449i	0.272606	+	0.472168i
$924$	−4.92861	+	8.53660i	−0.162139	+	0.280833i
$925$		0			0
$926$	−3.30959	−	18.7696i	−0.108760	−	0.616808i
$927$	−12.5299	+	71.0604i	−0.411535	+	2.33393i
$928$	3.88514	+	1.41408i	0.127536	+	0.0464193i
$929$	40.7777	−	34.2166i	1.33787	−	1.12261i	0.355706	−	0.934598i	$-0.384240\pi$
$929$	40.7777	−	34.2166i	1.33787	−	1.12261i	0.982167	−	0.188011i	$-0.0602040\pi$
$930$		0			0
$931$	−3.93807	+	26.6151i	−0.129065	+	0.872273i
$932$	11.2939			0.369943
$933$	−8.76531	+	7.35497i	−0.286963	+	0.240791i
$934$	−31.9639	−	11.6339i	−1.04589	−	0.380673i
$935$		0			0
$936$	2.85586	+	16.1964i	0.0933468	+	0.529396i
$937$	−19.4630	+	7.08394i	−0.635827	+	0.231422i	−0.639766	−	0.768570i	$-0.720969\pi$
$937$	−19.4630	+	7.08394i	−0.635827	+	0.231422i	0.00393831	+	0.999992i	$0.498746\pi$
$938$	6.23289	−	10.7957i	0.203511	−	0.352491i
$939$	−3.42003	−	5.92366i	−0.111608	−	0.193311i
$940$		0			0
$941$	−25.7268	−	21.5873i	−0.838669	−	0.703727i	0.118595	−	0.992943i	$-0.462161\pi$
$941$	−25.7268	−	21.5873i	−0.838669	−	0.703727i	−0.957264	+	0.289216i	$0.906606\pi$
$942$	23.1827	+	40.1536i	0.755334	+	1.30828i
$943$	−0.0270326	+	0.0468218i	−0.000880302	+	0.00152473i
$944$	−5.28195	+	1.92247i	−0.171913	+	0.0625711i
$945$		0			0
$946$	−5.62946	+	31.9262i	−0.183029	+	1.03801i
$947$	15.1984	+	5.53178i	0.493883	+	0.179759i	0.576941	−	0.816786i	$-0.304246\pi$
$947$	15.1984	+	5.53178i	0.493883	+	0.179759i	−0.0830579	+	0.996545i	$0.526469\pi$
$948$	−34.0546	+	28.5752i	−1.10604	+	0.928081i
$949$	−39.9107			−1.29555
$950$		0			0
$951$	35.0373			1.13616
$952$	3.75721	−	3.15267i	0.121772	−	0.102179i
$953$	−2.88481	−	1.04998i	−0.0934481	−	0.0340123i	0.294873	−	0.955536i	$-0.404723\pi$
$953$	−2.88481	−	1.04998i	−0.0934481	−	0.0340123i	−0.388321	+	0.921524i	$0.626945\pi$
$954$	−10.2610	+	58.1931i	−0.332213	+	1.88407i
$955$		0			0
$956$	−20.9174	+	7.61332i	−0.676517	+	0.246232i
$957$	22.3992	−	38.7965i	0.724063	−	1.25411i
$958$	−9.29575	−	16.1007i	−0.300332	−	0.520191i
$959$	5.63094	+	4.72492i	0.181832	+	0.152576i
$960$		0			0
$961$	−2.28825	−	3.96336i	−0.0738145	−	0.127850i
$962$	13.9238	−	24.1168i	0.448922	−	0.777557i
$963$	67.6943	−	24.6387i	2.18142	−	0.793972i
$964$	−3.71716	−	21.0811i	−0.119722	−	0.678976i
$965$		0			0
$966$	3.30632	+	1.20340i	0.106379	+	0.0387188i
$967$	19.2517	−	16.1541i	0.619092	−	0.519480i	−0.278426	−	0.960458i	$-0.589813\pi$
$967$	19.2517	−	16.1541i	0.619092	−	0.519480i	0.897518	+	0.440978i	$0.145368\pi$
$968$	−2.34009			−0.0752133
$969$	66.1461	+	22.0252i	2.12492	+	0.707552i
$970$		0			0
$971$	21.8759	−	18.3561i	0.702032	−	0.589075i	−0.220319	−	0.975428i	$-0.570710\pi$
$971$	21.8759	−	18.3561i	0.702032	−	0.589075i	0.922351	+	0.386353i	$0.126265\pi$
$972$	−3.22073	−	1.17225i	−0.103305	−	0.0375999i
$973$	−1.11854	+	6.34356i	−0.0358588	+	0.203365i
$974$	−1.31050	−	7.43220i	−0.0419910	−	0.238143i
$975$		0			0
$976$	1.86114	−	3.22358i	0.0595736	−	0.103184i
$977$	−8.58599	−	14.8714i	−0.274690	−	0.475777i	0.695367	−	0.718655i	$-0.255242\pi$
$977$	−8.58599	−	14.8714i	−0.274690	−	0.475777i	−0.970057	+	0.242878i	$0.921909\pi$
$978$	−28.1101	−	23.5872i	−0.898863	−	0.754236i
$979$	25.0570	+	21.0253i	0.800824	+	0.671971i
$980$		0			0
$981$	−38.2850	+	66.3115i	−1.22234	+	2.11716i
$982$	−17.3240	+	6.30541i	−0.552830	+	0.201214i
$983$	6.50817	+	36.9097i	0.207579	+	1.17724i	0.893330	+	0.449401i	$0.148362\pi$
$983$	6.50817	+	36.9097i	0.207579	+	1.17724i	−0.685752	+	0.727836i	$0.740526\pi$
$984$	0.0213632	−	0.121157i	0.000681033	−	0.00386233i
$985$		0			0
$986$	−17.0755	+	14.3280i	−0.543794	+	0.456298i
$987$	6.15148			0.195804
$988$	5.88099	−	10.8691i	0.187099	−	0.345793i
$989$	11.5718			0.367962
$990$		0			0
$991$	−21.7623	−	7.92083i	−0.691302	−	0.251613i	−0.0276096	−	0.999619i	$-0.508790\pi$
$991$	−21.7623	−	7.92083i	−0.691302	−	0.251613i	−0.663693	+	0.748005i	$0.731012\pi$
$992$	−1.03574	+	5.87399i	−0.0328849	+	0.186499i
$993$	8.01425	+	45.4511i	0.254324	+	1.44235i
$994$	−4.99446	+	1.81783i	−0.158415	+	0.0576582i
$995$		0			0
$996$	7.11806	+	12.3288i	0.225544	+	0.390654i
$997$	15.4189	+	12.9380i	0.488321	+	0.409750i	0.853424	−	0.521217i	$-0.174522\pi$
$997$	15.4189	+	12.9380i	0.488321	+	0.409750i	−0.365103	+	0.930967i	$0.618966\pi$
$998$	−11.7020	−	9.81916i	−0.370421	−	0.310820i
$999$	−40.8067	−	70.6793i	−1.29107	−	2.23619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.j.101.4	✓	24
5.2	odd	4		950.2.u.h.899.4		48
5.3	odd	4		950.2.u.h.899.5		48
5.4	even	2		950.2.l.k.101.1	yes	24
19.16	even	9	inner	950.2.l.j.301.4	yes	24
95.54	even	18		950.2.l.k.301.1	yes	24
95.73	odd	36		950.2.u.h.149.4		48
95.92	odd	36		950.2.u.h.149.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.101.4	✓	24	1.1	even	1	trivial
950.2.l.j.301.4	yes	24	19.16	even	9	inner
950.2.l.k.101.1	yes	24	5.4	even	2
950.2.l.k.301.1	yes	24	95.54	even	18
950.2.u.h.149.4		48	95.73	odd	36
950.2.u.h.149.5		48	95.92	odd	36
950.2.u.h.899.4		48	5.2	odd	4
950.2.u.h.899.5		48	5.3	odd	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(2.78771 + 1.01464i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.78771 + 1.01464i) q^{6} +(0.454865 - 0.787850i) q^{7} +(0.500000 + 0.866025i) q^{8} +(4.44370 + 3.72870i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(2.78771 + 1.01464i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.78771 + 1.01464i) q^{6} +(0.454865 - 0.787850i) q^{7} +(0.500000 + 0.866025i) q^{8} +(4.44370 + 3.72870i) q^{9} +(-1.82620 - 3.16308i) q^{11} +(1.48331 - 2.56917i) q^{12} +(2.66417 - 0.969680i) q^{13} +(0.157973 + 0.895910i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(4.13002 - 3.46550i) q^{17} -5.80083 q^{18} +(3.41525 + 2.70851i) q^{19} +(2.06742 - 1.73477i) q^{21} +(3.43214 + 1.24920i) q^{22} +(0.226388 - 1.28391i) q^{23} +(0.515148 + 2.92155i) q^{24} +(-1.41758 + 2.45532i) q^{26} +(4.15450 + 7.19581i) q^{27} +(-0.696894 - 0.584764i) q^{28} +(3.16720 + 2.65759i) q^{29} +(-2.98230 + 5.16550i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-1.88153 - 10.6707i) q^{33} +(-0.936199 + 5.30945i) q^{34} +(4.44370 - 3.72870i) q^{36} -9.82228 q^{37} +(-4.35723 + 0.120443i) q^{38} +8.41082 q^{39} +(-0.0389690 - 0.0141836i) q^{41} +(-0.468646 + 2.65782i) q^{42} +(1.54130 + 8.74115i) q^{43} +(-3.43214 + 1.24920i) q^{44} +(0.651859 + 1.12905i) q^{46} +(1.74606 + 1.46512i) q^{47} +(-2.27256 - 1.90691i) q^{48} +(3.08619 + 5.34545i) q^{49} +(15.0295 - 5.47031i) q^{51} +(-0.492319 - 2.79208i) q^{52} +(1.76889 - 10.0319i) q^{53} +(-7.80791 - 2.84185i) q^{54} +0.909731 q^{56} +(6.77257 + 11.0158i) q^{57} -4.13448 q^{58} +(4.30588 - 3.61306i) q^{59} +(-0.646366 + 3.66573i) q^{61} +(-1.03574 - 5.87399i) q^{62} +(4.95894 - 1.80491i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(8.30033 + 6.96480i) q^{66} +(-10.4969 - 8.80793i) q^{67} +(-2.69568 - 4.66905i) q^{68} +(1.93382 - 3.34947i) q^{69} +(1.01452 + 5.75362i) q^{71} +(-1.00730 + 5.71271i) q^{72} +(-13.2281 - 4.81464i) q^{73} +(7.52430 - 6.31364i) q^{74} +(3.26042 - 2.89304i) q^{76} -3.32271 q^{77} +(-6.44307 + 5.40637i) q^{78} +(-14.0814 - 5.12522i) q^{79} +(1.25846 + 7.13707i) q^{81} +(0.0389690 - 0.0141836i) q^{82} +(-2.39938 + 4.15585i) q^{83} +(-1.34941 - 2.33725i) q^{84} +(-6.79940 - 5.70538i) q^{86} +(6.13272 + 10.6222i) q^{87} +(1.82620 - 3.16308i) q^{88} +(-8.41552 + 3.06300i) q^{89} +(0.447878 - 2.54004i) q^{91} +(-1.22509 - 0.445898i) q^{92} +(-13.5549 + 11.3739i) q^{93} -2.27932 q^{94} +2.96662 q^{96} +(12.7549 - 10.7026i) q^{97} +(-5.80015 - 2.11108i) q^{98} +(3.67909 - 20.8651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) \) 24 * q - 3 * q^7 + 12 * q^8	\( 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Introduction

L-functions

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