LMFDB - Embedded newform 950.2.l.k.101.1

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			101.1
Character	$\chi$	$=$	950.101
Dual form			950.2.l.k.301.1

$q$-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	−0.628147	−	0.778094i	$-0.716187\pi$
$3$	−2.78771	−	1.01464i	−1.60949	−	0.585805i	−0.981338	+	0.192290i	$0.938409\pi$
$4$	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	−0.939092	−	0.343666i	$-0.888331\pi$
$7$	−0.454865	+	0.787850i	−0.171923	+	0.297779i	0.767169	+	0.641445i	$0.221665\pi$
$8$	−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	−0.683931	−	0.729547i	$-0.739731\pi$
$13$	−2.66417	+	0.969680i	−0.738909	+	0.268941i	−0.0549779	+	0.998488i	$0.517509\pi$
$14$	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	−0.987216	−	0.159389i	$-0.949048\pi$
$17$	−4.13002	+	3.46550i	−1.00168	+	0.840507i	−0.0144610	+	0.999895i	$0.504603\pi$
$18$	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	−0.999271	−	0.0381796i	$-0.987844\pi$
$23$	−0.226388	+	1.28391i	−0.0472052	+	0.267714i	0.952066	+	0.305894i	$0.0989552\pi$
$24$	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	$-0.200881\pi$
$37$	9.82228			1.61477			0.807386	+	0.590023i	$0.200881\pi$
$38$	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	$-0.818927\pi$
$43$	−1.54130	−	8.74115i	−0.235046	−	1.33301i	0.607471	−	0.794342i	$-0.292184\pi$
$44$	−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	0.506499	−	0.862240i	$-0.330939\pi$
$47$	−1.74606	−	1.46512i	−0.254689	−	0.213709i	−0.761188	+	0.648531i	$0.775384\pi$
$48$	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	$0.302203\pi$
$53$	−1.76889	+	10.0319i	−0.242975	+	1.37798i	−0.825148	+	0.564917i	$0.808908\pi$
$54$	−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	$0.0379299\pi$
$67$	10.4969	+	8.80793i	1.28240	+	1.07606i	0.289489	+	0.957181i	$0.406515\pi$
$68$	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	0.968003	−	0.250940i	$-0.0807398\pi$
$73$	13.2281	+	4.81464i	1.54823	+	0.563511i	0.580232	+	0.814452i	$0.302962\pi$
$74$	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	−0.703768	−	0.710430i	$-0.748500\pi$
$83$	2.39938	−	4.15585i	0.263367	−	0.456164i	0.967134	+	0.254266i	$0.0818338\pi$
$84$	−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	$0.598353\pi$
$97$	−12.7549	+	10.7026i	−1.29507	+	1.08669i	−0.990975	+	0.134046i	$0.957203\pi$
$98$	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	$-0.956699\pi$
$103$	−6.21950	−	10.7725i	−0.612826	−	1.06145i	0.377936	−	0.925832i	$-0.376634\pi$
$104$	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	$0.371611\pi$
$107$	−6.20935	+	10.7549i	−0.600280	+	1.03972i	−0.992778	+	0.119963i	$0.961722\pi$
$108$	−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	$-0.830525\pi$
$113$	−18.3175			−1.72316			−0.861581	+	0.507621i	$0.830525\pi$
$114$	−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	0.0821000	−	0.996624i	$-0.473837\pi$
$127$	8.85337	−	3.22236i	0.785610	−	0.285939i	0.703510	+	0.710685i	$0.251615\pi$
$128$	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	$-0.832268\pi$
$137$	1.40309	−	7.95729i	0.119874	−	0.679838i	0.984221	−	0.176942i	$-0.0566207\pi$
$138$	−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	$0.158802\pi$
$157$	2.71395	+	15.3916i	0.216597	+	1.22838i	−0.661516	+	0.749931i	$0.730087\pi$
$158$	−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	0.515418	−	0.856939i	$-0.327637\pi$
$163$	−6.18468	−	10.7122i	−0.484421	−	0.839042i	−0.999840	+	0.0178962i	$0.994303\pi$
$164$	−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	$0.362631\pi$
$167$	−3.68865	+	20.9194i	−0.285437	+	1.61879i	−0.703722	+	0.710476i	$0.748480\pi$
$168$	−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	−0.891300	−	0.453414i	$-0.850206\pi$
$173$	−7.88581	+	6.61698i	−0.599547	+	0.503080i	0.291753	+	0.956494i	$0.405761\pi$
$174$	−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	0.366149	−	0.930556i	$-0.380676\pi$
$193$	0.673581	+	0.245164i	0.0484855	+	0.0176473i	−0.317664	+	0.948203i	$0.602898\pi$
$194$	−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	$-0.428948\pi$
$197$	13.4072	−	23.2220i	0.955224	−	1.65450i	0.733855	−	0.679306i	$-0.237719\pi$
$198$	−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	0.984957	−	0.172799i	$-0.0552813\pi$
$223$	0.00446902	+	0.0253451i	0.000299268	+	0.00169723i	−0.984658	+	0.174497i	$0.944170\pi$
$224$	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	$-0.411693\pi$
$227$	8.25287			0.547762			0.273881	+	0.961764i	$0.411693\pi$
$228$	−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	$-0.934933\pi$
$233$	−1.96116	−	11.1223i	−0.128480	−	0.728646i	0.850700	−	0.525651i	$-0.176178\pi$
$234$	−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	0.940751	−	0.339099i	$-0.110122\pi$
$257$	12.3466	+	10.3601i	0.770163	+	0.646243i	−0.170588	+	0.985342i	$0.554567\pi$
$258$	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	0.808685	−	0.588242i	$-0.200180\pi$
$263$	17.0291	+	6.19808i	1.05006	+	0.382190i	0.241374	+	0.970432i	$0.422402\pi$
$264$	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	0.905302	−	0.424769i	$-0.139645\pi$
$277$	1.41120	+	2.44427i	0.0847907	+	0.146862i	−0.820511	+	0.571630i	$0.806311\pi$
$278$	−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	−0.815414	−	0.578878i	$-0.803491\pi$
$283$	−6.50910	+	5.46179i	−0.386926	+	0.324669i	0.428488	+	0.903547i	$0.359046\pi$
$284$	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	0.998846	−	0.0480352i	$-0.0152960\pi$
$293$	7.83667	+	13.5735i	0.457823	+	0.792973i	−0.541023	+	0.841008i	$0.681963\pi$
$294$	−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	0.597356	−	0.801976i	$-0.296218\pi$
$307$	9.45204	+	3.44026i	0.539457	+	0.196346i	−0.0578993	+	0.998322i	$0.518440\pi$
$308$	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	0.691339	−	0.722531i	$-0.257021\pi$
$313$	1.76625	+	1.48206i	0.0998343	+	0.0837709i	−0.591504	+	0.806302i	$0.701466\pi$
$314$	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	−0.634330	−	0.773062i	$-0.718724\pi$
$317$	−11.0983	+	4.03943i	−0.623340	+	0.226877i	0.0109899	+	0.999940i	$0.496502\pi$
$318$	−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	$0.159192\pi$
$337$	3.98229	+	22.5847i	0.216929	+	1.23027i	−0.660598	+	0.750740i	$0.729697\pi$
$338$	−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	$-0.898474\pi$
$347$	−3.06455	−	17.3799i	−0.164514	−	0.933003i	0.785051	−	0.619431i	$-0.212637\pi$
$348$	−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	0.814766	−	0.579790i	$-0.196865\pi$
$353$	−1.77982	−	3.08274i	−0.0947302	−	0.164077i	−0.909496	+	0.415713i	$0.863532\pi$
$354$	−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	−0.989957	−	0.141372i	$-0.954849\pi$
$367$	−31.7519	+	11.5567i	−1.65744	+	0.603257i	−0.667479	+	0.744629i	$0.732627\pi$
$368$	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	−0.887427	−	0.460948i	$-0.847510\pi$
$373$	−0.859852	+	1.48931i	−0.0445214	+	0.0771134i	0.842906	+	0.538061i	$0.180843\pi$
$374$	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	0.543310	−	0.839532i	$-0.317171\pi$
$383$	8.21699	+	2.99074i	0.419868	+	0.152820i	−0.123441	+	0.992352i	$0.539393\pi$
$384$	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	0.000662490	−	1.00000i	$-0.499789\pi$
$397$	19.6376	−	16.4779i	0.985585	−	0.827004i	0.984923	+	0.172996i	$0.0553447\pi$
$398$	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	$-0.758687\pi$
$433$	3.98202	−	22.5832i	0.191364	−	1.08528i	0.917503	−	0.397729i	$-0.130202\pi$
$434$	−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	−0.775131	−	0.631801i	$-0.782316\pi$
$443$	−20.2646	+	7.37572i	−0.962802	+	0.350431i	−0.187671	+	0.982232i	$0.560094\pi$
$444$	−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	$-0.306440\pi$
$457$	24.4260			1.14260			0.571299	+	0.820742i	$0.306440\pi$
$458$	−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	−0.555024	−	0.831834i	$-0.687291\pi$
$463$	9.52958	−	16.5057i	0.442877	−	0.767086i	0.997902	+	0.0647482i	$0.0206244\pi$
$464$	−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	$-0.878290\pi$
$467$	−17.0076	−	29.4581i	−0.787019	−	1.36316i	0.140766	−	0.990043i	$-0.455043\pi$
$468$	−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	−0.767776	−	0.640718i	$-0.778637\pi$
$487$	3.77343	−	6.53577i	0.170990	−	0.296164i	0.938766	+	0.344554i	$0.111970\pi$
$488$	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	0.508917	−	0.860816i	$-0.330046\pi$
$503$	−5.61697	−	4.71320i	−0.250448	−	0.210151i	−0.759365	+	0.650664i	$0.774490\pi$
$504$	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	0.471821	−	0.881695i	$-0.343597\pi$
$523$	−7.19346	−	6.03603i	−0.314548	−	0.263937i	−0.786369	+	0.617757i	$0.788041\pi$
$524$	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	$0.214871\pi$
$547$	−3.89778	+	22.1054i	−0.166657	+	0.945158i	−0.947340	+	0.320230i	$0.896240\pi$
$548$	−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	−0.128697	−	0.991684i	$-0.541079\pi$
$557$	9.68007	−	3.52326i	0.410158	−	0.149285i	0.538855	+	0.842399i	$0.318857\pi$
$558$	−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	$-0.647492\pi$
$563$	13.0794	−	22.6542i	0.551231	−	0.954760i	0.998186	−	0.0602035i	$-0.0191750\pi$
$564$	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	−0.998983	−	0.0450790i	$-0.985646\pi$
$577$	−11.0604	+	19.1572i	−0.460452	+	0.797527i	0.538531	+	0.842606i	$0.318979\pi$
$578$	−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	−0.584650	−	0.811286i	$-0.698768\pi$
$587$	2.73263	−	2.29294i	0.112788	−	0.0946400i	0.697437	+	0.716646i	$0.254324\pi$
$588$	−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	−0.998009	−	0.0630696i	$-0.979911\pi$
$593$	−0.940367	+	5.33309i	−0.0386162	+	0.219004i	0.959393	+	0.282073i	$0.0910221\pi$
$594$	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	$-0.533973\pi$
$607$	−5.24915			−0.213057			−0.106528	+	0.994310i	$0.533973\pi$
$608$	−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	0.999102	−	0.0423769i	$-0.0134930\pi$
$613$	1.13295	+	6.42528i	0.0457595	+	0.259515i	−0.953342	+	0.301892i	$0.902382\pi$
$614$	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	$-0.963496\pi$
$617$	−31.7605	−	26.6502i	−1.27863	−	1.07290i	−0.285199	−	0.958468i	$-0.592060\pi$
$618$	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	0.652256	−	0.757999i	$-0.273823\pi$
$643$	16.8546	+	6.13458i	0.664681	+	0.241924i	0.0124251	+	0.999923i	$0.496045\pi$
$644$	−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	$-0.375091\pi$
$647$	19.4546			0.764839			0.382419	+	0.923989i	$0.375091\pi$
$648$	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	−0.559594	−	0.828767i	$-0.689043\pi$
$653$	11.1910	−	19.3833i	0.437937	−	0.758528i	0.997530	+	0.0702387i	$0.0223761\pi$
$654$	−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	0.685460	−	0.728110i	$-0.259601\pi$
$673$	−7.46700	−	12.9332i	−0.287832	−	0.498539i	−0.973292	+	0.229571i	$0.926268\pi$
$674$	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	$0.495167\pi$
$677$	−22.3332	+	38.6822i	−0.858335	+	1.48668i	−0.873517	+	0.486794i	$0.838166\pi$
$678$	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	$-0.287276\pi$
$683$	32.3880			1.23929			0.619647	+	0.784881i	$0.287276\pi$
$684$	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	$0.0835721\pi$
$727$	3.96382	+	22.4799i	0.147010	+	0.833734i	−0.818722	+	0.574191i	$0.805317\pi$
$728$	−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	0.807756	−	0.589517i	$-0.200682\pi$
$733$	−2.88768	−	5.00160i	−0.106659	−	0.184738i	−0.914415	+	0.404779i	$0.867349\pi$
$734$	−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	$-0.348109\pi$
$743$	38.5381	−	32.3373i	1.41383	−	1.18634i	0.954551	−	0.298048i	$-0.0963355\pi$
$744$	−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	0.145716	−	0.989326i	$-0.453451\pi$
$757$	−10.4163	−	3.79121i	−0.378586	−	0.137794i	−0.524302	+	0.851533i	$0.675674\pi$
$758$	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	−0.757620	−	0.652696i	$-0.773638\pi$
$773$	−25.5354	+	9.29414i	−0.918446	+	0.334287i	−0.160826	+	0.986983i	$0.551416\pi$
$774$	−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	0.987070	−	0.160291i	$-0.0512431\pi$
$787$	9.95112	+	17.2358i	0.354719	+	0.614392i	−0.632351	+	0.774682i	$0.717910\pi$
$788$	−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	$-0.593574\pi$
$797$	−16.3603			−0.579510			−0.289755	+	0.957101i	$0.593574\pi$
$798$	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	−0.804040	−	0.594575i	$-0.797320\pi$
$823$	−29.7720	+	10.8361i	−1.03779	+	0.377723i	−0.233746	+	0.972298i	$0.575098\pi$
$824$	−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	0.200158	−	0.979764i	$-0.435854\pi$
$827$	−20.9920	−	17.6144i	−0.729964	−	0.612512i	−0.930122	+	0.367251i	$0.880299\pi$
$828$	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	−0.793921	−	0.608020i	$-0.791964\pi$
$853$	−9.72569	+	8.16082i	−0.333001	+	0.279421i	0.460920	+	0.887442i	$0.347519\pi$
$854$	−3.38627			−0.115876
$855$		0			0
$856$	12.4187			0.424462
$857$	3.13547	−	2.63097i	0.107106	−	0.0898723i	−0.587662	−	0.809106i	$-0.699952\pi$
$857$	3.13547	−	2.63097i	0.107106	−	0.0898723i	0.694768	+	0.719234i	$0.255507\pi$
$858$	−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	$0.114923\pi$
$863$	22.7285	+	39.3669i	0.773687	+	1.34006i	−0.161843	+	0.986817i	$0.551744\pi$
$864$	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	0.521601	−	0.853189i	$-0.325335\pi$
$877$	11.0387	+	4.01777i	0.372752	+	0.135671i	−0.148850	+	0.988860i	$0.547557\pi$
$878$	−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	0.529801	−	0.848122i	$-0.322267\pi$
$883$	−6.34235	−	5.32186i	−0.213437	−	0.179095i	−0.743238	+	0.669027i	$0.766711\pi$
$884$	−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	−0.231984	−	0.972720i	$-0.574522\pi$
$887$	6.41989	−	2.33665i	0.215559	−	0.0784570i	0.447542	+	0.894263i	$0.352299\pi$
$888$	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	$-0.756747\pi$
$907$	−8.43871	−	47.8583i	−0.280203	−	1.58911i	0.441732	−	0.897147i	$-0.354364\pi$
$908$	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	−0.00393831	−	0.999992i	$-0.501254\pi$
$937$	19.4630	−	7.08394i	0.635827	−	0.231422i	0.639766	+	0.768570i	$0.279031\pi$
$938$	−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	0.0830579	−	0.996545i	$-0.473531\pi$
$947$	−15.1984	−	5.53178i	−0.493883	−	0.179759i	−0.576941	+	0.816786i	$0.695754\pi$
$948$	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	0.388321	−	0.921524i	$-0.373055\pi$
$953$	2.88481	+	1.04998i	0.0934481	+	0.0340123i	−0.294873	+	0.955536i	$0.595277\pi$
$954$	−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	−0.897518	−	0.440978i	$-0.854632\pi$
$967$	−19.2517	+	16.1541i	−0.619092	+	0.519480i	0.278426	+	0.960458i	$0.410187\pi$
$968$	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	0.970057	−	0.242878i	$-0.0780914\pi$
$977$	8.58599	+	14.8714i	0.274690	+	0.475777i	−0.695367	+	0.718655i	$0.744758\pi$
$978$	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	$-0.851638\pi$
$983$	−6.50817	−	36.9097i	−0.207579	−	1.17724i	0.685752	−	0.727836i	$-0.259474\pi$
$984$	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	0.365103	−	0.930967i	$-0.381034\pi$
$997$	−15.4189	−	12.9380i	−0.488321	−	0.409750i	−0.853424	+	0.521217i	$0.825478\pi$
$998$	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.k.101.1	yes	24
5.2	odd	4		950.2.u.h.899.5		48
5.3	odd	4		950.2.u.h.899.4		48
5.4	even	2		950.2.l.j.101.4	✓	24
19.16	even	9	inner	950.2.l.k.301.1	yes	24
95.54	even	18		950.2.l.j.301.4	yes	24
95.73	odd	36		950.2.u.h.149.5		48
95.92	odd	36		950.2.u.h.149.4		48

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

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