LMFDB - Embedded newform 950.2.u.h.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.4
Character	$\chi$	$=$	950.149
Dual form			950.2.u.h.899.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(1.01464 + 2.78771i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.78771 - 1.01464i) q^{6} +(0.787850 - 0.454865i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-4.44370 + 3.72870i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(1.01464 + 2.78771i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.78771 - 1.01464i) q^{6} +(0.787850 - 0.454865i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-4.44370 + 3.72870i) q^{9} +(-1.82620 + 3.16308i) q^{11} +(2.56917 - 1.48331i) q^{12} +(-0.969680 + 2.66417i) q^{13} +(-0.157973 + 0.895910i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.46550 - 4.13002i) q^{17} -5.80083i q^{18} +(-3.41525 + 2.70851i) q^{19} +(2.06742 + 1.73477i) q^{21} +(-1.24920 - 3.43214i) q^{22} +(-1.28391 + 0.226388i) q^{23} +(-0.515148 + 2.92155i) q^{24} +(-1.41758 - 2.45532i) q^{26} +(-7.19581 - 4.15450i) q^{27} +(-0.584764 - 0.696894i) q^{28} +(-3.16720 + 2.65759i) q^{29} +(-2.98230 - 5.16550i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-10.6707 - 1.88153i) q^{33} +(0.936199 + 5.30945i) q^{34} +(4.44370 + 3.72870i) q^{36} +9.82228i q^{37} +(0.120443 - 4.35723i) q^{38} -8.41082 q^{39} +(-0.0389690 + 0.0141836i) q^{41} +(-2.65782 + 0.468646i) q^{42} +(8.74115 + 1.54130i) q^{43} +(3.43214 + 1.24920i) q^{44} +(0.651859 - 1.12905i) q^{46} +(-1.46512 - 1.74606i) q^{47} +(-1.90691 - 2.27256i) q^{48} +(-3.08619 + 5.34545i) q^{49} +(15.0295 + 5.47031i) q^{51} +(2.79208 + 0.492319i) q^{52} +(-10.0319 + 1.76889i) q^{53} +(7.80791 - 2.84185i) q^{54} +0.909731 q^{56} +(-11.0158 - 6.77257i) q^{57} -4.13448i q^{58} +(-4.30588 - 3.61306i) q^{59} +(-0.646366 - 3.66573i) q^{61} +(5.87399 + 1.03574i) q^{62} +(-1.80491 + 4.95894i) q^{63} +(0.500000 + 0.866025i) q^{64} +(8.30033 - 6.96480i) q^{66} +(8.80793 + 10.4969i) q^{67} +(-4.66905 - 2.69568i) q^{68} +(-1.93382 - 3.34947i) q^{69} +(1.01452 - 5.75362i) q^{71} +(-5.71271 + 1.00730i) q^{72} +(-4.81464 - 13.2281i) q^{73} +(-7.52430 - 6.31364i) q^{74} +(3.26042 + 2.89304i) q^{76} +3.32271i q^{77} +(5.40637 - 6.44307i) q^{78} +(14.0814 - 5.12522i) q^{79} +(1.25846 - 7.13707i) q^{81} +(0.0141836 - 0.0389690i) q^{82} +(4.15585 - 2.39938i) q^{83} +(1.34941 - 2.33725i) q^{84} +(-6.79940 + 5.70538i) q^{86} +(-10.6222 - 6.13272i) q^{87} +(-3.16308 + 1.82620i) q^{88} +(8.41552 + 3.06300i) q^{89} +(0.447878 + 2.54004i) q^{91} +(0.445898 + 1.22509i) q^{92} +(11.3739 - 13.5549i) q^{93} +2.27932 q^{94} +2.96662 q^{96} +(10.7026 - 12.7549i) q^{97} +(-2.11108 - 5.80015i) q^{98} +(-3.67909 - 20.8651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	1.01464	+	2.78771i	0.585805	+	1.60949i	0.778094	+	0.628147i	$0.216187\pi$
$3$	1.01464	+	2.78771i	0.585805	+	1.60949i	−0.192290	+	0.981338i	$0.561591\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−2.78771	−	1.01464i	−1.13808	−	0.414227i
$7$	0.787850	−	0.454865i	0.297779	−	0.171923i	−0.343666	−	0.939092i	$-0.611669\pi$
$7$	0.787850	−	0.454865i	0.297779	−	0.171923i	0.641445	+	0.767169i	$0.278335\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−4.44370	+	3.72870i	−1.48123	+	1.24290i
$10$		0			0
$11$	−1.82620	+	3.16308i	−0.550621	+	0.953704i	0.447608	+	0.894230i	$0.352276\pi$
$11$	−1.82620	+	3.16308i	−0.550621	+	0.953704i	−0.998230	+	0.0594745i	$0.981057\pi$
$12$	2.56917	−	1.48331i	0.741655	−	0.428195i
$13$	−0.969680	+	2.66417i	−0.268941	+	0.738909i	0.729547	+	0.683931i	$0.239731\pi$
$13$	−0.969680	+	2.66417i	−0.268941	+	0.738909i	−0.998488	+	0.0549779i	$0.982491\pi$
$14$	−0.157973	+	0.895910i	−0.0422201	+	0.239442i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.46550	−	4.13002i	0.840507	−	1.00168i	−0.159389	−	0.987216i	$-0.550952\pi$
$17$	3.46550	−	4.13002i	0.840507	−	1.00168i	0.999895	−	0.0144610i	$-0.00460323\pi$
$18$		−	5.80083i		−	1.36727i
$19$	−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
$22$	−1.24920	−	3.43214i	−0.266330	−	0.731735i
$23$	−1.28391	+	0.226388i	−0.267714	+	0.0472052i	−0.305894	−	0.952066i	$-0.598955\pi$
$23$	−1.28391	+	0.226388i	−0.267714	+	0.0472052i	0.0381796	+	0.999271i	$0.487844\pi$
$24$	−0.515148	+	2.92155i	−0.105154	+	0.596359i
$25$		0			0
$26$	−1.41758	−	2.45532i	−0.278010	−	0.481527i
$27$	−7.19581	−	4.15450i	−1.38483	−	0.799535i
$28$	−0.584764	−	0.696894i	−0.110510	−	0.131701i
$29$	−3.16720	+	2.65759i	−0.588134	+	0.493503i	−0.887607	−	0.460602i	$-0.847634\pi$
$29$	−3.16720	+	2.65759i	−0.588134	+	0.493503i	0.299473	+	0.954105i	$0.403189\pi$
$30$		0			0
$31$	−2.98230	−	5.16550i	−0.535637	−	0.927751i	−0.999132	−	0.0416513i	$-0.986738\pi$
$31$	−2.98230	−	5.16550i	−0.535637	−	0.927751i	0.463495	−	0.886100i	$-0.346595\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	−10.6707	−	1.88153i	−1.85753	−	0.327533i
$34$	0.936199	+	5.30945i	0.160557	+	0.910563i
$35$		0			0
$36$	4.44370	+	3.72870i	0.740616	+	0.621451i
$37$			9.82228i			1.61477i	0.590023	+	0.807386i	$0.299119\pi$
$37$			9.82228i			1.61477i	−0.590023	+	0.807386i	$0.700881\pi$
$38$	0.120443	−	4.35723i	0.0195384	−	0.706837i
$39$	−8.41082			−1.34681
$40$		0			0
$41$	−0.0389690	+	0.0141836i	−0.00608594	+	0.00221510i	−0.345061	−	0.938580i	$-0.612142\pi$
$41$	−0.0389690	+	0.0141836i	−0.00608594	+	0.00221510i	0.338975	+	0.940795i	$0.389920\pi$
$42$	−2.65782	+	0.468646i	−0.410111	+	0.0723137i
$43$	8.74115	+	1.54130i	1.33301	+	0.235046i	0.794342	−	0.607471i	$-0.207816\pi$
$43$	8.74115	+	1.54130i	1.33301	+	0.235046i	0.538670	+	0.842517i	$0.318927\pi$
$44$	3.43214	+	1.24920i	0.517415	+	0.188324i
$45$		0			0
$46$	0.651859	−	1.12905i	0.0961114	−	0.166470i
$47$	−1.46512	−	1.74606i	−0.213709	−	0.254689i	0.648531	−	0.761188i	$-0.275384\pi$
$47$	−1.46512	−	1.74606i	−0.213709	−	0.254689i	−0.862240	+	0.506499i	$0.830939\pi$
$48$	−1.90691	−	2.27256i	−0.275238	−	0.328016i
$49$	−3.08619	+	5.34545i	−0.440885	+	0.763635i
$50$		0			0
$51$	15.0295	+	5.47031i	2.10456	+	0.765996i
$52$	2.79208	+	0.492319i	0.387192	+	0.0682724i
$53$	−10.0319	+	1.76889i	−1.37798	+	0.242975i	−0.813065	−	0.582173i	$-0.802203\pi$
$53$	−10.0319	+	1.76889i	−1.37798	+	0.242975i	−0.564917	+	0.825148i	$0.691092\pi$
$54$	7.80791	−	2.84185i	1.06252	−	0.386727i
$55$		0			0
$56$	0.909731			0.121568
$57$	−11.0158	−	6.77257i	−1.45908	−	0.897048i
$58$		−	4.13448i		−	0.542884i
$59$	−4.30588	−	3.61306i	−0.560578	−	0.470381i	0.317926	−	0.948116i	$-0.397014\pi$
$59$	−4.30588	−	3.61306i	−0.560578	−	0.470381i	−0.878504	+	0.477735i	$0.841458\pi$
$60$		0			0
$61$	−0.646366	−	3.66573i	−0.0827587	−	0.469348i	−0.997818	−	0.0660281i	$-0.978967\pi$
$61$	−0.646366	−	3.66573i	−0.0827587	−	0.469348i	0.915059	−	0.403320i	$-0.132144\pi$
$62$	5.87399	+	1.03574i	0.745997	+	0.131539i
$63$	−1.80491	+	4.95894i	−0.227397	+	0.624768i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	8.30033	−	6.96480i	1.02170	−	0.857308i
$67$	8.80793	+	10.4969i	1.07606	+	1.28240i	0.957181	+	0.289489i	$0.0934855\pi$
$67$	8.80793	+	10.4969i	1.07606	+	1.28240i	0.118879	+	0.992909i	$0.462070\pi$
$68$	−4.66905	−	2.69568i	−0.566206	−	0.326899i
$69$	−1.93382	−	3.34947i	−0.232804	−	0.403229i
$70$		0			0
$71$	1.01452	−	5.75362i	0.120401	−	0.682829i	−0.863532	−	0.504294i	$-0.831753\pi$
$71$	1.01452	−	5.75362i	0.120401	−	0.682829i	0.983933	−	0.178536i	$-0.0571360\pi$
$72$	−5.71271	+	1.00730i	−0.673249	+	0.118712i
$73$	−4.81464	−	13.2281i	−0.563511	−	1.54823i	−0.814452	−	0.580232i	$-0.802962\pi$
$73$	−4.81464	−	13.2281i	−0.563511	−	1.54823i	0.250940	−	0.968003i	$-0.419260\pi$
$74$	−7.52430	−	6.31364i	−0.874682	−	0.733946i
$75$		0			0
$76$	3.26042	+	2.89304i	0.373995	+	0.331855i
$77$			3.32271i			0.378658i
$78$	5.40637	−	6.44307i	0.612151	−	0.729534i
$79$	14.0814	−	5.12522i	1.58428	−	0.576632i	0.608153	−	0.793820i	$-0.291911\pi$
$79$	14.0814	−	5.12522i	1.58428	−	0.576632i	0.976130	+	0.217188i	$0.0696884\pi$
$80$		0			0
$81$	1.25846	−	7.13707i	0.139829	−	0.793008i
$82$	0.0141836	−	0.0389690i	0.00156631	−	0.00430341i
$83$	4.15585	−	2.39938i	0.456164	−	0.263367i	−0.254266	−	0.967134i	$-0.581834\pi$
$83$	4.15585	−	2.39938i	0.456164	−	0.263367i	0.710430	+	0.703768i	$0.248500\pi$
$84$	1.34941	−	2.33725i	0.147233	−	0.255015i
$85$		0			0
$86$	−6.79940	+	5.70538i	−0.733199	+	0.615227i
$87$	−10.6222	−	6.13272i	−1.13882	−	0.657496i
$88$	−3.16308	+	1.82620i	−0.337185	+	0.194674i
$89$	8.41552	+	3.06300i	0.892043	+	0.324677i	0.747060	−	0.664757i	$-0.231465\pi$
$89$	8.41552	+	3.06300i	0.892043	+	0.324677i	0.144983	+	0.989434i	$0.453687\pi$
$90$		0			0
$91$	0.447878	+	2.54004i	0.0469504	+	0.266269i
$92$	0.445898	+	1.22509i	0.0464881	+	0.127725i
$93$	11.3739	−	13.5549i	1.17942	−	1.40558i
$94$	2.27932			0.235094
$95$		0			0
$96$	2.96662			0.302779
$97$	10.7026	−	12.7549i	1.08669	−	1.29507i	0.134046	−	0.990975i	$-0.457203\pi$
$97$	10.7026	−	12.7549i	1.08669	−	1.29507i	0.952643	−	0.304091i	$-0.0983527\pi$
$98$	−2.11108	−	5.80015i	−0.213251	−	0.585904i
$99$	−3.67909	−	20.8651i	−0.369762	−	2.09703i
$100$		0			0
$101$	−9.55205	−	3.47666i	−0.950465	−	0.345941i	−0.180175	−	0.983635i	$-0.557666\pi$
$101$	−9.55205	−	3.47666i	−0.950465	−	0.345941i	−0.770290	+	0.637694i	$0.779889\pi$
$102$	−13.8513	+	7.99705i	−1.37148	+	0.791826i
$103$	10.7725	+	6.21950i	1.06145	+	0.612826i	0.925832	−	0.377936i	$-0.123366\pi$
$103$	10.7725	+	6.21950i	1.06145	+	0.612826i	0.135613	+	0.990762i	$0.456699\pi$
$104$	−2.17185	+	1.82240i	−0.212968	+	0.178701i
$105$		0			0
$106$	5.09331	−	8.82187i	0.494706	−	0.856856i
$107$	10.7549	−	6.20935i	1.03972	−	0.600280i	0.119963	−	0.992778i	$-0.461722\pi$
$107$	10.7549	−	6.20935i	1.03972	−	0.600280i	0.919753	+	0.392498i	$0.128389\pi$
$108$	−2.84185	+	7.80791i	−0.273457	+	0.751317i
$109$	−2.29212	+	12.9993i	−0.219546	+	1.24511i	0.653296	+	0.757102i	$0.273386\pi$
$109$	−2.29212	+	12.9993i	−0.219546	+	1.24511i	−0.872842	+	0.488003i	$0.837726\pi$
$110$		0			0
$111$	−27.3817	+	9.96611i	−2.59895	+	0.945942i
$112$	−0.584764	+	0.696894i	−0.0552550	+	0.0658503i
$113$			18.3175i			1.72316i	0.507621	+	0.861581i	$0.330525\pi$
$113$			18.3175i			1.72316i	−0.507621	+	0.861581i	$0.669475\pi$
$114$	12.2689	−	4.08528i	1.14909	−	0.382622i
$115$		0			0
$116$	3.16720	+	2.65759i	0.294067	+	0.246751i
$117$	−5.62495	−	15.4544i	−0.520027	−	1.42876i
$118$	5.53554	−	0.976064i	0.509587	−	0.0898540i
$119$	0.851689	−	4.83017i	0.0780742	−	0.442781i
$120$		0			0
$121$	−1.17005	−	2.02658i	−0.106368	−	0.184234i
$122$	3.22358	+	1.86114i	0.291850	+	0.168499i
$123$	−0.0790794	−	0.0942431i	−0.00713035	−	0.00849762i
$124$	−4.56915	+	3.83397i	−0.410322	+	0.344301i
$125$		0			0
$126$	−2.63860	−	4.57019i	−0.235065	−	0.407145i
$127$	−3.22236	+	8.85337i	−0.285939	+	0.785610i	0.710685	+	0.703510i	$0.248385\pi$
$127$	−3.22236	+	8.85337i	−0.285939	+	0.785610i	−0.996624	+	0.0821000i	$0.973837\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	4.57245	+	25.9317i	0.402582	+	2.28316i
$130$		0			0
$131$	−1.26905	−	1.06486i	−0.110877	−	0.0930369i	0.585664	−	0.810554i	$-0.300834\pi$
$131$	−1.26905	−	1.06486i	−0.110877	−	0.0930369i	−0.696541	+	0.717517i	$0.745278\pi$
$132$			10.8353i			0.943093i
$133$	−1.45870	+	3.68738i	−0.126485	+	0.319737i
$134$	−13.7027			−1.18373
$135$		0			0
$136$	5.06622	−	1.84395i	0.434425	−	0.158118i
$137$	−7.95729	+	1.40309i	−0.679838	+	0.119874i	−0.502895	−	0.864347i	$-0.667732\pi$
$137$	−7.95729	+	1.40309i	−0.679838	+	0.119874i	−0.176942	+	0.984221i	$0.556621\pi$
$138$	3.80888	+	0.671608i	0.324233	+	0.0571711i
$139$	6.65357	+	2.42170i	0.564348	+	0.205406i	0.608410	−	0.793623i	$-0.291808\pi$
$139$	6.65357	+	2.42170i	0.564348	+	0.205406i	−0.0440619	+	0.999029i	$0.514030\pi$
$140$		0			0
$141$	3.38094	−	5.85595i	0.284726	−	0.493160i
$142$	3.75541	+	4.47552i	0.315147	+	0.375578i
$143$	−6.65616	−	7.93250i	−0.556616	−	0.663349i
$144$	2.90042	−	5.02367i	0.241701	−	0.418639i
$145$		0			0
$146$	13.2281	+	4.81464i	1.09477	+	0.398463i
$147$	−18.0329	−	3.17970i	−1.48733	−	0.262257i
$148$	9.67305	−	1.70562i	0.795120	−	0.140201i
$149$	−3.71415	+	1.35184i	−0.304275	+	0.110747i	−0.489645	−	0.871922i	$-0.662874\pi$
$149$	−3.71415	+	1.35184i	−0.304275	+	0.110747i	0.185370	+	0.982669i	$0.440652\pi$
$150$		0			0
$151$	−10.9225			−0.888864			−0.444432	−	0.895813i	$-0.646594\pi$
$151$	−10.9225			−0.888864			−0.444432	+	0.895813i	$0.646594\pi$
$152$	−4.31195	+	0.638013i	−0.349746	+	0.0517497i
$153$			31.2744i			2.52838i
$154$	−2.54534	−	2.13580i	−0.205110	−	0.172107i
$155$		0			0
$156$	1.46052	+	8.28305i	0.116936	+	0.663174i
$157$	15.3916	+	2.71395i	1.22838	+	0.216597i	0.749931	−	0.661516i	$-0.230087\pi$
$157$	15.3916	+	2.71395i	1.22838	+	0.216597i	0.478453	+	0.878113i	$0.341198\pi$
$158$	−5.12522	+	14.0814i	−0.407740	+	1.12026i
$159$	−15.1099	−	26.1711i	−1.19829	−	2.07551i
$160$		0			0
$161$	−0.908554	+	0.762367i	−0.0716041	+	0.0600829i
$162$	4.65839	+	5.55166i	0.365998	+	0.436179i
$163$	10.7122	+	6.18468i	0.839042	+	0.484421i	0.856939	−	0.515418i	$-0.172363\pi$
$163$	10.7122	+	6.18468i	0.839042	+	0.484421i	−0.0178962	+	0.999840i	$0.505697\pi$
$164$	0.0207350	+	0.0359141i	0.00161913	+	0.00280442i
$165$		0			0
$166$	−0.833297	+	4.72586i	−0.0646764	+	0.366798i
$167$	20.9194	−	3.68865i	1.61879	−	0.285437i	0.710476	−	0.703722i	$-0.248480\pi$
$167$	20.9194	−	3.68865i	1.61879	−	0.285437i	0.908316	+	0.418285i	$0.137369\pi$
$168$	0.923053	+	2.53607i	0.0712151	+	0.195662i
$169$	3.80104	+	3.18945i	0.292387	+	0.245342i
$170$		0			0
$171$	5.07711	−	24.7703i	0.388257	−	1.89423i
$172$		−	8.87599i		−	0.676788i
$173$	−6.61698	+	7.88581i	−0.503080	+	0.599547i	−0.956494	−	0.291753i	$-0.905761\pi$
$173$	−6.61698	+	7.88581i	−0.503080	+	0.599547i	0.453414	+	0.891300i	$0.350206\pi$
$174$	11.5257	−	4.19503i	0.873764	−	0.318024i
$175$		0			0
$176$	0.634234	−	3.59692i	0.0478072	−	0.271128i
$177$	5.70324	−	15.6695i	0.428682	−	1.17779i
$178$	−7.75578	+	4.47780i	−0.581321	+	0.335626i
$179$	−0.425281	+	0.736609i	−0.0317870	+	0.0550567i	−0.881481	−	0.472219i	$-0.843453\pi$
$179$	−0.425281	+	0.736609i	−0.0317870	+	0.0550567i	0.849694	+	0.527276i	$0.176786\pi$
$180$		0			0
$181$	−13.1433	+	11.0285i	−0.976933	+	0.819744i	−0.983624	−	0.180233i	$-0.942315\pi$
$181$	−13.1433	+	11.0285i	−0.976933	+	0.819744i	0.00669066	+	0.999978i	$0.497870\pi$
$182$	−2.23368	−	1.28961i	−0.165571	−	0.0955925i
$183$	9.56315	−	5.52129i	0.706928	−	0.408145i
$184$	−1.22509	−	0.445898i	−0.0903152	−	0.0328720i
$185$		0			0
$186$	3.07265	+	17.4259i	0.225298	+	1.27773i
$187$	6.73487	+	18.5039i	0.492502	+	1.35314i
$188$	−1.46512	+	1.74606i	−0.106855	+	0.127344i
$189$	−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	$0.549091\pi$
$192$	−1.90691	+	2.27256i	−0.137619	+	0.164008i
$193$	−0.245164	−	0.673581i	−0.0176473	−	0.0484855i	0.930556	−	0.366149i	$-0.119324\pi$
$193$	−0.245164	−	0.673581i	−0.0176473	−	0.0484855i	−0.948203	+	0.317664i	$0.897102\pi$
$194$	2.89131	+	16.3974i	0.207584	+	1.17727i
$195$		0			0
$196$	5.80015	+	2.11108i	0.414296	+	0.150792i
$197$	−23.2220	+	13.4072i	−1.65450	+	0.955224i	−0.679306	+	0.733855i	$0.737719\pi$
$197$	−23.2220	+	13.4072i	−1.65450	+	0.955224i	−0.975190	+	0.221368i	$0.928948\pi$
$198$	18.3485	+	10.5935i	1.30397	+	0.752848i
$199$	−14.1804	+	11.8988i	−1.00522	+	0.843483i	−0.987700	−	0.156363i	$-0.950023\pi$
$199$	−14.1804	+	11.8988i	−1.00522	+	0.843483i	−0.0175244	+	0.999846i	$0.505578\pi$
$200$		0			0
$201$	−20.3254	+	35.2046i	−1.43364	+	2.48314i
$202$	8.80322	−	5.08254i	0.619392	−	0.357606i
$203$	−1.28643	+	3.53443i	−0.0902896	+	0.248069i
$204$	2.77735	−	15.7511i	0.194453	−	1.10280i
$205$		0			0
$206$	−11.6888	+	4.25439i	−0.814400	+	0.296417i
$207$	4.86118	−	5.79333i	0.337875	−	0.402664i
$208$		−	2.83515i		−	0.196583i
$209$	−2.33028	−	15.7490i	−0.161189	−	1.08938i
$210$		0			0
$211$	−3.82973	−	3.21352i	−0.263649	−	0.221228i	0.501374	−	0.865231i	$-0.332828\pi$
$211$	−3.82973	−	3.21352i	−0.263649	−	0.221228i	−0.765023	+	0.644003i	$0.777273\pi$
$212$	3.48403	+	9.57229i	0.239284	+	0.657427i
$213$	17.0688	−	3.00969i	1.16954	−	0.206221i
$214$	−2.15648	+	12.2300i	−0.147414	+	0.836028i
$215$		0			0
$216$	−4.15450	−	7.19581i	−0.282678	−	0.489613i
$217$	−4.69921	−	2.71309i	−0.319003	−	0.184177i
$218$	−8.48468	−	10.1116i	−0.574655	−	0.684847i
$219$	31.9910	−	26.8437i	2.16175	−	1.81393i
$220$		0			0
$221$	7.64267	+	13.2375i	0.514101	+	0.890450i
$222$	9.96611	−	27.3817i	0.668882	−	1.83774i
$223$	−0.0253451	−	0.00446902i	−0.00169723	−	0.000299268i	0.172799	−	0.984957i	$-0.444719\pi$
$223$	−0.0253451	−	0.00446902i	−0.00169723	−	0.000299268i	−0.174497	+	0.984658i	$0.555830\pi$
$224$	−0.157973	−	0.895910i	−0.0105550	−	0.0598605i
$225$		0			0
$226$	−14.0320	−	11.7742i	−0.933394	−	0.783210i
$227$			8.25287i			0.547762i	0.961764	+	0.273881i	$0.0883075\pi$
$227$			8.25287i			0.547762i	−0.961764	+	0.273881i	$0.911693\pi$
$228$	−4.75680	+	12.0245i	−0.315027	+	0.796342i
$229$	10.7684			0.711594			0.355797	−	0.934563i	$-0.384209\pi$
$229$	10.7684			0.711594			0.355797	+	0.934563i	$0.384209\pi$
$230$		0			0
$231$	−9.26275	+	3.37137i	−0.609444	+	0.221820i
$232$	−4.07167	+	0.717945i	−0.267318	+	0.0471354i
$233$	11.1223	+	1.96116i	0.728646	+	0.128480i	0.525651	−	0.850700i	$-0.323822\pi$
$233$	11.1223	+	1.96116i	0.728646	+	0.128480i	0.202994	+	0.979180i	$0.434933\pi$
$234$	15.4544	+	5.62495i	1.01029	+	0.367715i
$235$		0			0
$236$	−2.81047	+	4.86787i	−0.182946	+	0.316871i
$237$	28.5752	+	34.0546i	1.85616	+	2.21209i
$238$	3.15267	+	3.75721i	0.204357	+	0.243543i
$239$	11.1299	−	19.2776i	0.719935	−	1.24696i	−0.241090	−	0.970503i	$-0.577505\pi$
$239$	11.1299	−	19.2776i	0.719935	−	1.24696i	0.961025	−	0.276461i	$-0.0891617\pi$
$240$		0			0
$241$	20.1153	+	7.32138i	1.29574	+	0.471612i	0.895608	−	0.444845i	$-0.146741\pi$
$241$	20.1153	+	7.32138i	1.29574	+	0.471612i	0.400135	+	0.916456i	$0.368963\pi$
$242$	2.30454	+	0.406352i	0.148141	+	0.0261213i
$243$	−3.37535	+	0.595166i	−0.216529	+	0.0381799i
$244$	−3.49779	+	1.27309i	−0.223923	+	0.0815014i
$245$		0			0
$246$	0.123026			0.00784383
$247$	−3.90424	−	11.7252i	−0.248421	−	0.746058i
$248$		−	5.96460i		−	0.378753i
$249$	10.9055	+	9.15080i	0.691108	+	0.579908i
$250$		0			0
$251$	0.878157	+	4.98028i	0.0554288	+	0.314352i	0.999899	−	0.0142461i	$-0.00453484\pi$
$251$	0.878157	+	4.98028i	0.0554288	+	0.314352i	−0.944470	+	0.328598i	$0.893424\pi$
$252$	5.19702	+	0.916376i	0.327382	+	0.0577262i
$253$	1.62860	−	4.47455i	0.102389	−	0.281312i
$254$	−4.71078	−	8.15931i	−0.295581	−	0.511961i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	10.3601	+	12.3466i	0.646243	+	0.770163i	0.985342	−	0.170588i	$-0.0545667\pi$
$257$	10.3601	+	12.3466i	0.646243	+	0.770163i	−0.339099	+	0.940751i	$0.610122\pi$
$258$	−22.8039	−	13.1658i	−1.41971	−	0.819670i
$259$	4.46781	+	7.73848i	0.277616	+	0.480846i
$260$		0			0
$261$	4.16468	−	23.6191i	0.257787	−	1.46198i
$262$	1.63145	−	0.287669i	0.100792	−	0.0177723i
$263$	−6.19808	−	17.0291i	−0.382190	−	1.05006i	−0.970432	−	0.241374i	$-0.922402\pi$
$263$	−6.19808	−	17.0291i	−0.382190	−	1.05006i	0.588242	−	0.808685i	$-0.299820\pi$
$264$	−8.30033	−	6.96480i	−0.510850	−	0.428654i
$265$		0			0
$266$	−1.88706	−	3.48763i	−0.115703	−	0.213840i
$267$			26.5679i			1.62593i
$268$	8.80793	−	10.4969i	0.538030	−	0.641199i
$269$	10.8894	−	3.96341i	0.663938	−	0.241654i	0.0120022	−	0.999928i	$-0.496179\pi$
$269$	10.8894	−	3.96341i	0.663938	−	0.241654i	0.651936	+	0.758274i	$0.273957\pi$
$270$		0			0
$271$	3.19870	−	18.1407i	0.194307	−	1.10197i	−0.719095	−	0.694912i	$-0.755443\pi$
$271$	3.19870	−	18.1407i	0.194307	−	1.10197i	0.913402	−	0.407058i	$-0.133445\pi$
$272$	−1.84395	+	5.06622i	−0.111806	+	0.307185i
$273$	−6.62647	+	3.82579i	−0.401052	+	0.231548i
$274$	4.04002	−	6.99753i	0.244067	−	0.422736i
$275$		0			0
$276$	−2.96278	+	2.48607i	−0.178338	+	0.149644i
$277$	2.44427	+	1.41120i	0.146862	+	0.0847907i	0.571630	−	0.820511i	$-0.306311\pi$
$277$	2.44427	+	1.41120i	0.146862	+	0.0847907i	−0.424769	+	0.905302i	$0.639645\pi$
$278$	−6.13196	+	3.54029i	−0.367770	+	0.212332i
$279$	32.5131	+	11.8338i	1.94651	+	0.708470i
$280$		0			0
$281$	4.31540	+	24.4738i	0.257435	+	1.45999i	0.789744	+	0.613436i	$0.210213\pi$
$281$	4.31540	+	24.4738i	0.257435	+	1.45999i	−0.532309	+	0.846550i	$0.678676\pi$
$282$	2.31270	+	6.35408i	0.137719	+	0.378380i
$283$	−5.46179	+	6.50910i	−0.324669	+	0.386926i	−0.903547	−	0.428488i	$-0.859046\pi$
$283$	−5.46179	+	6.50910i	−0.324669	+	0.386926i	0.578878	+	0.815414i	$0.303491\pi$
$284$	−5.84238			−0.346681
$285$		0			0
$286$	10.3551			0.612312
$287$	−0.0242501	+	0.0289002i	−0.00143144	+	0.00170592i
$288$	1.98400	+	5.45100i	0.116908	+	0.321203i
$289$	−2.09537	−	11.8834i	−0.123257	−	0.699024i
$290$		0			0
$291$	46.4164	+	16.8942i	2.72098	+	0.990355i
$292$	−12.1911	+	7.03853i	−0.713430	+	0.411899i
$293$	−13.5735	−	7.83667i	−0.792973	−	0.457823i	0.0480352	−	0.998846i	$-0.484704\pi$
$293$	−13.5735	−	7.83667i	−0.792973	−	0.457823i	−0.841008	+	0.541023i	$0.818037\pi$
$294$	14.0271	−	11.7702i	0.818080	−	0.686450i
$295$		0			0
$296$	−4.91114	+	8.50634i	−0.285454	+	0.494421i
$297$	26.2821	−	15.1739i	1.52504	−	0.880482i
$298$	1.35184	−	3.71415i	0.0783101	−	0.215155i
$299$	0.641846	−	3.64009i	0.0371189	−	0.210512i
$300$		0			0
$301$	7.58780	−	2.76173i	0.437353	−	0.159184i
$302$	7.02088	−	8.36715i	0.404006	−	0.481476i
$303$		−	30.1559i		−	1.73241i
$304$	2.28292	−	3.71325i	0.130935	−	0.212970i
$305$		0			0
$306$	−23.9576	−	20.1028i	−1.36956	−	1.14920i
$307$	3.44026	+	9.45204i	0.196346	+	0.539457i	0.998322	−	0.0578993i	$-0.0184402\pi$
$307$	3.44026	+	9.45204i	0.196346	+	0.539457i	−0.801976	+	0.597356i	$0.796218\pi$
$308$	3.27223	−	0.576982i	0.186453	−	0.0328766i
$309$	−6.40793	+	36.3412i	−0.364534	+	2.06738i
$310$		0			0
$311$	−1.92851	−	3.34027i	−0.109356	−	0.189409i	0.806154	−	0.591706i	$-0.201545\pi$
$311$	−1.92851	−	3.34027i	−0.109356	−	0.189409i	−0.915509	+	0.402297i	$0.868212\pi$
$312$	−7.28399	−	4.20541i	−0.412375	−	0.238085i
$313$	−1.48206	−	1.76625i	−0.0837709	−	0.0998343i	0.722531	−	0.691339i	$-0.242979\pi$
$313$	−1.48206	−	1.76625i	−0.0837709	−	0.0998343i	−0.806302	+	0.591504i	$0.798534\pi$
$314$	−11.9725	+	10.0462i	−0.675650	+	0.566937i
$315$		0			0
$316$	−7.49257	−	12.9775i	−0.421490	−	0.730042i
$317$	4.03943	−	11.0983i	0.226877	−	0.623340i	−0.773062	−	0.634330i	$-0.781276\pi$
$317$	4.03943	−	11.0983i	0.226877	−	0.623340i	0.999940	+	0.0109899i	$0.00349827\pi$
$318$	29.7607	+	5.24762i	1.66890	+	0.294272i
$319$	−2.62223	−	14.8714i	−0.146817	−	0.832639i
$320$		0			0
$321$	28.2223	+	23.6813i	1.57521	+	1.32176i
$322$		−	1.18603i		−	0.0660950i
$323$	−0.649349	+	23.4914i	−0.0361307	+	1.30710i
$324$	−7.24717			−0.402621
$325$		0			0
$326$	−11.6234	+	4.23057i	−0.643760	+	0.234310i
$327$	−38.5639	+	6.79986i	−2.13259	+	0.376033i
$328$	−0.0408400	−	0.00720119i	−0.00225501	−	0.000397619i
$329$	−1.94851	−	0.709201i	−0.107425	−	0.0390995i
$330$		0			0
$331$	7.77859	−	13.4729i	0.427550	−	0.740538i	−0.569105	−	0.822265i	$-0.692710\pi$
$331$	7.77859	−	13.4729i	0.427550	−	0.740538i	0.996655	+	0.0817270i	$0.0260436\pi$
$332$	−3.08459	−	3.67607i	−0.169289	−	0.201750i
$333$	−36.6244	−	43.6472i	−2.00700	−	2.39185i
$334$	−10.6211	+	18.3962i	−0.581158	+	1.00660i
$335$		0			0
$336$	−2.53607	−	0.923053i	−0.138354	−	0.0503567i
$337$	22.5847	+	3.98229i	1.23027	+	0.216929i	0.750740	−	0.660598i	$-0.229697\pi$
$337$	22.5847	+	3.98229i	1.23027	+	0.216929i	0.479527	+	0.877527i	$0.340808\pi$
$338$	−4.88652	+	0.861625i	−0.265792	+	0.0468662i
$339$	−51.0638	+	18.5857i	−2.77340	+	1.00944i
$340$		0			0
$341$	21.7852			1.17973
$342$	15.7116	+	19.8113i	0.849588	+	1.07127i
$343$			11.9833i			0.647039i
$344$	6.79940	+	5.70538i	0.366599	+	0.307613i
$345$		0			0
$346$	−1.78757	−	10.1378i	−0.0961003	−	0.545012i
$347$	−17.3799	−	3.06455i	−0.933003	−	0.164514i	−0.313572	−	0.949564i	$-0.601526\pi$
$347$	−17.3799	−	3.06455i	−0.933003	−	0.164514i	−0.619431	+	0.785051i	$0.712637\pi$
$348$	−4.19503	+	11.5257i	−0.224877	+	0.617844i
$349$	−8.04925	−	13.9417i	−0.430867	−	0.746283i	0.566081	−	0.824349i	$-0.308459\pi$
$349$	−8.04925	−	13.9417i	−0.430867	−	0.746283i	−0.996948	+	0.0780663i	$0.975125\pi$
$350$		0			0
$351$	18.0460	−	15.1424i	0.963222	−	0.808239i
$352$	2.34772	+	2.79791i	0.125134	+	0.149129i
$353$	3.08274	+	1.77982i	0.164077	+	0.0947302i	0.579790	−	0.814766i	$-0.303135\pi$
$353$	3.08274	+	1.77982i	0.164077	+	0.0947302i	−0.415713	+	0.909496i	$0.636468\pi$
$354$	8.33758	+	14.4411i	0.443138	+	0.767537i
$355$		0			0
$356$	1.55512	−	8.81955i	0.0824215	−	0.467435i
$357$	14.3293	−	2.52664i	0.758386	−	0.133724i
$358$	−0.290910	−	0.799267i	−0.0153750	−	0.0422426i
$359$	25.2996	+	21.2289i	1.33526	+	1.12042i	0.982817	+	0.184583i	$0.0590934\pi$
$359$	25.2996	+	21.2289i	1.33526	+	1.12042i	0.352443	+	0.935833i	$0.385351\pi$
$360$		0			0
$361$	4.32792	−	18.5005i	0.227786	−	0.973711i
$362$		−	17.1573i		−	0.901770i
$363$	4.46233	−	5.31800i	0.234212	−	0.279123i
$364$	2.42368	−	0.882148i	0.127035	−	0.0462371i
$365$		0			0
$366$	−1.91752	+	10.8748i	−0.100231	+	0.568436i
$367$	11.5567	−	31.7519i	0.603257	−	1.65744i	−0.141372	−	0.989957i	$-0.545151\pi$
$367$	11.5567	−	31.7519i	0.603257	−	1.65744i	0.744629	−	0.667479i	$-0.232627\pi$
$368$	1.12905	−	0.651859i	0.0588560	−	0.0339805i
$369$	0.120280	−	0.208331i	0.00626154	−	0.0108453i
$370$		0			0
$371$	−7.09899	+	5.95676i	−0.368561	+	0.309260i
$372$	−15.3241	−	8.84736i	−0.794516	−	0.458714i
$373$	−1.48931	+	0.859852i	−0.0771134	+	0.0445214i	−0.538061	−	0.842906i	$-0.680843\pi$
$373$	−1.48931	+	0.859852i	−0.0771134	+	0.0445214i	0.460948	+	0.887427i	$0.347510\pi$
$374$	−18.5039	−	6.73487i	−0.956814	−	0.348252i
$375$		0			0
$376$	−0.395800	−	2.24469i	−0.0204118	−	0.115761i
$377$	−4.00912	−	11.0150i	−0.206480	−	0.567300i
$378$	4.85881	−	5.79050i	0.249910	−	0.297831i
$379$	−8.89642			−0.456978			−0.228489	−	0.973546i	$-0.573379\pi$
$379$	−8.89642			−0.456978			−0.228489	+	0.973546i	$0.573379\pi$
$380$		0			0
$381$	−27.9502			−1.43193
$382$	2.72926	−	3.25260i	0.139641	−	0.166418i
$383$	−2.99074	−	8.21699i	−0.152820	−	0.419868i	0.839532	−	0.543310i	$-0.182829\pi$
$383$	−2.99074	−	8.21699i	−0.152820	−	0.419868i	−0.992352	+	0.123441i	$0.960607\pi$
$384$	−0.515148	−	2.92155i	−0.0262885	−	0.149090i
$385$		0			0
$386$	0.673581	+	0.245164i	0.0342844	+	0.0124785i
$387$	−44.5901	+	25.7441i	−2.26664	+	1.30865i
$388$	−14.4196	−	8.32518i	−0.732046	−	0.422647i
$389$	16.5424	−	13.8807i	0.838732	−	0.703779i	−0.118546	−	0.992949i	$-0.537823\pi$
$389$	16.5424	−	13.8807i	0.838732	−	0.703779i	0.957278	+	0.289169i	$0.0933790\pi$
$390$		0			0
$391$	−3.51441	+	6.08713i	−0.177731	+	0.307839i
$392$	−5.34545	+	3.08619i	−0.269986	+	0.155876i
$393$	1.68088	−	4.61818i	0.0847892	−	0.232957i
$394$	4.65627	−	26.4070i	0.234580	−	1.33037i
$395$		0			0
$396$	−19.9093	+	7.24639i	−1.00048	+	0.364145i
$397$	−16.4779	+	19.6376i	−0.827004	+	0.985585i	0.172996	+	0.984923i	$0.444655\pi$
$397$	−16.4779	+	19.6376i	−0.827004	+	0.985585i	−1.00000		0.000662490i	$0.999789\pi$
$398$		−	18.5112i		−	0.927884i
$399$	−11.7594	−	0.325053i	−0.588707	−	0.0162730i
$400$		0			0
$401$	−18.2483	−	15.3122i	−0.911278	−	0.764653i	0.0610834	−	0.998133i	$-0.480544\pi$
$401$	−18.2483	−	15.3122i	−0.911278	−	0.764653i	−0.972362	+	0.233479i	$0.924989\pi$
$402$	−13.9034	−	38.1992i	−0.693437	−	1.90520i
$403$	16.6537	−	2.93649i	0.829578	−	0.146277i
$404$	−1.76515	+	10.0107i	−0.0878194	+	0.498049i
$405$		0			0
$406$	−1.88063	−	3.25735i	−0.0933342	−	0.161660i
$407$	−31.0686	−	17.9375i	−1.54002	−	0.889128i
$408$	10.2808	+	12.2522i	0.508976	+	0.606574i
$409$	−9.10867	+	7.64308i	−0.450395	+	0.377926i	−0.839582	−	0.543232i	$-0.817200\pi$
$409$	−9.10867	+	7.64308i	−0.450395	+	0.377926i	0.389188	+	0.921159i	$0.372756\pi$
$410$		0			0
$411$	−11.9852	−	20.7590i	−0.591187	−	1.02397i
$412$	4.25439	−	11.6888i	0.209599	−	0.575868i
$413$	−5.03585	−	0.887956i	−0.247798	−	0.0436935i
$414$	1.31324	+	7.44776i	0.0645423	+	0.366037i
$415$		0			0
$416$	2.17185	+	1.82240i	0.106484	+	0.0893506i
$417$			21.0054i			1.02864i
$418$	13.5623	+	8.33817i	0.663355	+	0.407833i
$419$	−7.57187			−0.369910			−0.184955	−	0.982747i	$-0.559214\pi$
$419$	−7.57187			−0.369910			−0.184955	+	0.982747i	$0.559214\pi$
$420$		0			0
$421$	27.1515	−	9.88232i	1.32328	−	0.481635i	0.418773	−	0.908091i	$-0.362460\pi$
$421$	27.1515	−	9.88232i	1.32328	−	0.481635i	0.904508	+	0.426456i	$0.140238\pi$
$422$	4.92340	−	0.868129i	0.239667	−	0.0422598i
$423$	13.0211	+	2.29597i	0.633106	+	0.111634i
$424$	−9.57229	−	3.48403i	−0.464871	−	0.169199i
$425$		0			0
$426$	−8.66606	+	15.0101i	−0.419872	+	0.727240i
$427$	−2.17665	−	2.59403i	−0.105336	−	0.125534i
$428$	−7.98258	−	9.51327i	−0.385853	−	0.459841i
$429$	15.3599	−	26.6041i	0.741582	−	1.28446i
$430$		0			0
$431$	−24.5966	−	8.95244i	−1.18478	−	0.431224i	−0.326891	−	0.945062i	$-0.606001\pi$
$431$	−24.5966	−	8.95244i	−1.18478	−	0.431224i	−0.857887	+	0.513838i	$0.828223\pi$
$432$	8.18278	+	1.44284i	0.393694	+	0.0694189i
$433$	22.5832	−	3.98202i	1.08528	−	0.191364i	0.397729	−	0.917503i	$-0.369798\pi$
$433$	22.5832	−	3.98202i	1.08528	−	0.191364i	0.687548	+	0.726139i	$0.258687\pi$
$434$	5.09894	−	1.85586i	0.244757	−	0.0890843i
$435$		0			0
$436$	13.1998			0.632156
$437$	3.77171	−	4.25066i	0.180425	−	0.203337i
$438$			41.7613i			1.99543i
$439$	22.3653	+	18.7667i	1.06744	+	0.895688i	0.994818	−	0.101672i	$-0.0324191\pi$
$439$	22.3653	+	18.7667i	1.06744	+	0.895688i	0.0726213	+	0.997360i	$0.476864\pi$
$440$		0			0
$441$	−6.21747	−	35.2610i	−0.296070	−	1.67910i
$442$	−15.0531	−	2.65427i	−0.716004	−	0.126251i
$443$	−7.37572	+	20.2646i	−0.350431	+	0.962802i	0.631801	+	0.775131i	$0.282316\pi$
$443$	−7.37572	+	20.2646i	−0.350431	+	0.962802i	−0.982232	+	0.187671i	$0.939906\pi$
$444$	14.5695	+	25.2351i	0.691437	+	1.19760i
$445$		0			0
$446$	0.0197150	−	0.0165428i	0.000933532	−	0.000783326i
$447$	−7.53709	−	8.98235i	−0.356492	−	0.424850i
$448$	0.787850	+	0.454865i	0.0372224	+	0.0214904i
$449$	−18.9961	−	32.9021i	−0.896479	−	1.55275i	−0.831963	−	0.554831i	$-0.812783\pi$
$449$	−18.9961	−	32.9021i	−0.896479	−	1.55275i	−0.0645161	−	0.997917i	$-0.520550\pi$
$450$		0			0
$451$	0.0263017	−	0.149164i	0.00123850	−	0.00702387i
$452$	18.0392	−	3.18079i	0.848491	−	0.149612i
$453$	−11.0825	−	30.4489i	−0.520701	−	1.43061i
$454$	−6.32207	−	5.30484i	−0.296709	−	0.248969i
$455$		0			0
$456$	−6.15369	−	11.3731i	−0.288173	−	0.532595i
$457$			24.4260i			1.14260i	0.820742	+	0.571299i	$0.193560\pi$
$457$			24.4260i			1.14260i	−0.820742	+	0.571299i	$0.806440\pi$
$458$	−6.92178	+	8.24905i	−0.323433	+	0.385453i
$459$	−42.0953	+	15.3214i	−1.96484	+	0.715143i
$460$		0			0
$461$	−4.77907	+	27.1034i	−0.222583	+	1.26233i	0.644668	+	0.764463i	$0.276996\pi$
$461$	−4.77907	+	27.1034i	−0.222583	+	1.26233i	−0.867251	+	0.497871i	$0.834115\pi$
$462$	3.37137	−	9.26275i	0.156850	−	0.430942i
$463$	16.5057	−	9.52958i	0.767086	−	0.442877i	−0.0647482	−	0.997902i	$-0.520624\pi$
$463$	16.5057	−	9.52958i	0.767086	−	0.442877i	0.831834	+	0.555024i	$0.187291\pi$
$464$	2.06724	−	3.58057i	0.0959692	−	0.166224i
$465$		0			0
$466$	−8.65161	+	7.25956i	−0.400778	+	0.336293i
$467$	−29.4581	−	17.0076i	−1.36316	−	0.787019i	−0.373114	−	0.927785i	$-0.621710\pi$
$467$	−29.4581	−	17.0076i	−1.36316	−	0.787019i	−0.990043	+	0.140766i	$0.955043\pi$
$468$	−14.2429	+	8.22313i	−0.658377	+	0.380114i
$469$	11.7140	+	4.26355i	0.540902	+	0.196872i
$470$		0			0
$471$	8.05127	+	45.6610i	0.370983	+	2.10395i
$472$	−1.92247	−	5.28195i	−0.0884889	−	0.243121i
$473$	−20.8384	+	24.8342i	−0.958149	+	1.14188i
$474$	−44.4552			−2.04189
$475$		0			0
$476$	−4.90468			−0.224806
$477$	37.9829	−	45.2662i	1.73912	−	2.07260i
$478$	7.61332	+	20.9174i	0.348225	+	0.956740i
$479$	3.22838	+	18.3091i	0.147509	+	0.836562i	0.965319	+	0.261074i	$0.0840768\pi$
$479$	3.22838	+	18.3091i	0.147509	+	0.836562i	−0.817810	+	0.575488i	$0.804812\pi$
$480$		0			0
$481$	−26.1683	−	9.52446i	−1.19317	−	0.434278i
$482$	−18.5384	+	10.7031i	−0.844401	+	0.487515i
$483$	−3.04712	−	1.75925i	−0.138649	−	0.0800488i
$484$	−1.79261	+	1.50418i	−0.0814824	+	0.0683719i
$485$		0			0
$486$	1.71371	−	2.96824i	0.0777356	−	0.134642i
$487$	−6.53577	+	3.77343i	−0.296164	+	0.170990i	−0.640718	−	0.767776i	$-0.721363\pi$
$487$	−6.53577	+	3.77343i	−0.296164	+	0.170990i	0.344554	+	0.938766i	$0.388030\pi$
$488$	1.27309	−	3.49779i	0.0576302	−	0.158338i
$489$	−6.37205	+	36.1377i	−0.288154	+	1.63420i
$490$		0			0
$491$	17.3240	−	6.30541i	0.781819	−	0.284559i	0.0798883	−	0.996804i	$-0.474544\pi$
$491$	17.3240	−	6.30541i	0.781819	−	0.284559i	0.701931	+	0.712245i	$0.252321\pi$
$492$	−0.0790794	+	0.0942431i	−0.00356517	+	0.00424881i
$493$			22.2905i			1.00391i
$494$	11.4916	+	4.54600i	0.517033	+	0.204534i
$495$		0			0
$496$	4.56915	+	3.83397i	0.205161	+	0.172150i
$497$	−1.81783	−	4.99446i	−0.0815410	−	0.224032i
$498$	−14.0198	+	2.47208i	−0.628244	+	0.110776i
$499$	−2.65263	+	15.0438i	−0.118748	+	0.673454i	0.866078	+	0.499909i	$0.166633\pi$
$499$	−2.65263	+	15.0438i	−0.118748	+	0.673454i	−0.984826	+	0.173545i	$0.944478\pi$
$500$		0			0
$501$	31.5086	+	54.5746i	1.40770	+	2.43821i
$502$	−4.37958	−	2.52855i	−0.195470	−	0.112855i
$503$	4.71320	+	5.61697i	0.210151	+	0.250448i	0.860816	−	0.508917i	$-0.169954\pi$
$503$	4.71320	+	5.61697i	0.210151	+	0.250448i	−0.650664	+	0.759365i	$0.725510\pi$
$504$	−4.04257	+	3.39212i	−0.180070	+	0.151097i
$505$		0			0
$506$	2.38086	+	4.12376i	0.105842	+	0.183324i
$507$	−5.03456	+	13.8323i	−0.223593	+	0.614316i
$508$	9.27843	+	1.63604i	0.411664	+	0.0725874i
$509$	−4.48517	−	25.4367i	−0.198802	−	1.12746i	−0.906900	−	0.421346i	$-0.861558\pi$
$509$	−4.48517	−	25.4367i	−0.198802	−	1.12746i	0.708098	−	0.706114i	$-0.249553\pi$
$510$		0			0
$511$	−9.81023	−	8.23176i	−0.433979	−	0.364152i
$512$			1.00000i			0.0441942i
$513$	35.8281	−	5.30126i	1.58185	−	0.234056i
$514$	−16.1174			−0.710908
$515$		0			0
$516$	24.7437	−	9.00597i	1.08928	−	0.396466i
$517$	8.19853	−	1.44562i	0.360571	−	0.0635784i
$518$	−8.79988	−	1.55166i	−0.386644	−	0.0681758i
$519$	−28.6972	−	10.4449i	−1.25967	−	0.458482i
$520$		0			0
$521$	13.1495	−	22.7756i	0.576089	−	0.997815i	−0.419833	−	0.907601i	$-0.637911\pi$
$521$	13.1495	−	22.7756i	0.576089	−	0.997815i	0.995922	−	0.0902142i	$-0.0287552\pi$
$522$	15.4163	+	18.3724i	0.674751	+	0.804137i
$523$	6.03603	+	7.19346i	0.263937	+	0.314548i	0.881695	−	0.471821i	$-0.156403\pi$
$523$	6.03603	+	7.19346i	0.263937	+	0.314548i	−0.617757	+	0.786369i	$0.711959\pi$
$524$	−0.828311	+	1.43468i	−0.0361849	+	0.0626741i
$525$		0			0
$526$	17.0291	+	6.19808i	0.742503	+	0.270249i
$527$	−31.6688	−	5.58406i	−1.37951	−	0.243245i
$528$	10.6707	−	1.88153i	0.464382	−	0.0818832i
$529$	−20.0158	+	7.28514i	−0.870250	+	0.316745i
$530$		0			0
$531$	32.6061			1.41498
$532$	3.88466	+	0.796231i	0.168422	+	0.0345210i
$533$		−	0.117574i		−	0.00509269i
$534$	−20.3522	−	17.0775i	−0.880725	−	0.739016i
$535$		0			0
$536$	2.37945	+	13.4945i	0.102777	+	0.582875i
$537$	−2.48496	−	0.438166i	−0.107234	−	0.0189082i
$538$	−3.96341	+	10.8894i	−0.170875	+	0.469475i
$539$	−11.2720	−	19.5238i	−0.485521	−	0.840948i
$540$		0			0
$541$	8.90611	−	7.47311i	0.382903	−	0.321294i	−0.430938	−	0.902382i	$-0.641817\pi$
$541$	8.90611	−	7.47311i	0.382903	−	0.321294i	0.813841	+	0.581088i	$0.197373\pi$
$542$	11.8405	+	14.1110i	0.508594	+	0.606118i
$543$	−44.0801	−	25.4497i	−1.89166	−	1.09215i
$544$	−2.69568	−	4.66905i	−0.115576	−	0.200184i
$545$		0			0
$546$	1.32868	−	7.53534i	0.0568624	−	0.322483i
$547$	22.1054	−	3.89778i	0.945158	−	0.166657i	0.320230	−	0.947340i	$-0.396240\pi$
$547$	22.1054	−	3.89778i	0.945158	−	0.166657i	0.624927	+	0.780683i	$0.285129\pi$
$548$	2.76354	+	7.59276i	0.118053	+	0.324347i
$549$	16.5407	+	13.8793i	0.705938	+	0.592352i
$550$		0			0
$551$	3.61866	−	17.6547i	0.154160	−	0.752118i
$552$		−	3.86764i		−	0.164618i
$553$	8.76276	−	10.4431i	0.372630	−	0.444084i
$554$	−2.65218	+	0.965316i	−0.112681	+	0.0410124i
$555$		0			0
$556$	1.22953	−	6.97301i	0.0521437	−	0.295721i
$557$	−3.52326	+	9.68007i	−0.149285	+	0.410158i	−0.991684	−	0.128697i	$-0.958921\pi$
$557$	−3.52326	+	9.68007i	−0.149285	+	0.410158i	0.842399	+	0.538855i	$0.181143\pi$
$558$	−29.9642	+	17.2998i	−1.26849	+	0.732361i
$559$	−12.5824	+	21.7934i	−0.532179	+	0.921761i
$560$		0			0
$561$	−44.7500	+	37.5497i	−1.88935	+	1.58535i
$562$	−21.5219	−	12.4257i	−0.907848	−	0.524146i
$563$	22.6542	−	13.0794i	0.954760	−	0.551231i	0.0602035	−	0.998186i	$-0.480825\pi$
$563$	22.6542	−	13.0794i	0.954760	−	0.551231i	0.894556	+	0.446955i	$0.147492\pi$
$564$	−6.35408	−	2.31270i	−0.267555	−	0.0973821i
$565$		0			0
$566$	−1.47549	−	8.36794i	−0.0620196	−	0.351731i
$567$	−2.25493	−	6.19537i	−0.0946982	−	0.260181i
$568$	3.75541	−	4.47552i	0.157573	−	0.187789i
$569$	1.12217			0.0470437			0.0235219	−	0.999723i	$-0.492512\pi$
$569$	1.12217			0.0470437			0.0235219	+	0.999723i	$0.492512\pi$
$570$		0			0
$571$	16.7706			0.701829			0.350915	−	0.936407i	$-0.385871\pi$
$571$	16.7706			0.701829			0.350915	+	0.936407i	$0.385871\pi$
$572$	−6.65616	+	7.93250i	−0.278308	+	0.331674i
$573$	−4.30815	−	11.8365i	−0.179976	−	0.494479i
$574$	−0.00655114	−	0.0371534i	−0.000273439	−	0.00155075i
$575$		0			0
$576$	−5.45100	−	1.98400i	−0.227125	−	0.0826668i
$577$	19.1572	−	11.0604i	0.797527	−	0.460452i	−0.0450790	−	0.998983i	$-0.514354\pi$
$577$	19.1572	−	11.0604i	0.797527	−	0.460452i	0.842606	+	0.538531i	$0.181021\pi$
$578$	10.4501	+	6.03337i	0.434667	+	0.250955i
$579$	1.62900	−	1.36689i	0.0676988	−	0.0568060i
$580$		0			0
$581$	2.18279	−	3.78071i	0.0905575	−	0.156850i
$582$	−42.7776	+	24.6977i	−1.77319	+	1.02375i
$583$	12.7251	−	34.9619i	0.527020	−	1.44797i
$584$	2.44446	−	13.8632i	0.101152	−	0.573664i
$585$		0			0
$586$	14.7281	−	5.36060i	0.608413	−	0.221444i
$587$	−2.29294	+	2.73263i	−0.0946400	+	0.112788i	−0.811286	−	0.584650i	$-0.801232\pi$
$587$	−2.29294	+	2.73263i	−0.0946400	+	0.112788i	0.716646	+	0.697437i	$0.245676\pi$
$588$			18.3111i			0.755138i
$589$	24.1761	+	9.56389i	0.996160	+	0.394073i
$590$		0			0
$591$	−60.9374	−	51.1326i	−2.50663	−	2.10331i
$592$	−3.35942	−	9.22992i	−0.138071	−	0.379347i
$593$	−5.33309	+	0.940367i	−0.219004	+	0.0386162i	−0.282073	−	0.959393i	$-0.591022\pi$
$593$	−5.33309	+	0.940367i	−0.219004	+	0.0386162i	0.0630696	+	0.998009i	$0.479911\pi$
$594$	−5.26986	+	29.8868i	−0.216225	+	1.22627i
$595$		0			0
$596$	1.97626	+	3.42298i	0.0809508	+	0.140211i
$597$	−47.5585	−	27.4579i	−1.94644	−	1.12378i
$598$	2.37590	+	2.83149i	0.0971577	+	0.115788i
$599$	−4.12626	+	3.46234i	−0.168594	+	0.141467i	−0.723181	−	0.690658i	$-0.757321\pi$
$599$	−4.12626	+	3.46234i	−0.168594	+	0.141467i	0.554587	+	0.832126i	$0.312876\pi$
$600$		0			0
$601$	−13.3088	−	23.0515i	−0.542877	−	0.940290i	−0.998737	−	0.0502390i	$-0.984002\pi$
$601$	−13.3088	−	23.0515i	−0.542877	−	0.940290i	0.455860	−	0.890051i	$-0.349332\pi$
$602$	−2.76173	+	7.58780i	−0.112560	+	0.309255i
$603$	−78.2795	−	13.8028i	−3.18779	−	0.562093i
$604$	1.89668	+	10.7566i	0.0771748	+	0.437680i
$605$		0			0
$606$	23.1008	+	19.3839i	0.938405	+	0.787416i
$607$		−	5.24915i		−	0.213057i	−0.994310	−	0.106528i	$-0.966027\pi$
$607$		−	5.24915i		−	0.213057i	0.994310	−	0.106528i	$-0.0339735\pi$
$608$	1.37708	+	4.13566i	0.0558481	+	0.167723i
$609$	−11.1582			−0.452155
$610$		0			0
$611$	6.07250	−	2.21021i	0.245667	−	0.0894155i
$612$	30.7992	−	5.43074i	1.24499	−	0.219525i
$613$	−6.42528	−	1.13295i	−0.259515	−	0.0457595i	0.0423769	−	0.999102i	$-0.486507\pi$
$613$	−6.42528	−	1.13295i	−0.259515	−	0.0457595i	−0.301892	+	0.953342i	$0.597618\pi$
$614$	−9.45204	−	3.44026i	−0.381453	−	0.138838i
$615$		0			0
$616$	−1.66135	+	2.87755i	−0.0669379	+	0.115940i
$617$	−26.6502	−	31.7605i	−1.07290	−	1.27863i	−0.958468	−	0.285199i	$-0.907940\pi$
$617$	−26.6502	−	31.7605i	−1.07290	−	1.27863i	−0.114430	−	0.993431i	$-0.536504\pi$
$618$	−23.7200	−	28.2684i	−0.954159	−	1.13712i
$619$	5.69855	−	9.87017i	0.229044	−	0.396716i	−0.728481	−	0.685066i	$-0.759773\pi$
$619$	5.69855	−	9.87017i	0.229044	−	0.396716i	0.957525	+	0.288350i	$0.0931067\pi$
$620$		0			0
$621$	10.1793	+	3.70497i	0.408482	+	0.148675i
$622$	3.79842	+	0.669764i	0.152303	+	0.0268551i
$623$	8.02342	−	1.41474i	0.321451	−	0.0566806i
$624$	7.90359	−	2.87667i	0.316397	−	0.115159i
$625$		0			0
$626$	2.30567			0.0921533
$627$	41.5393	−	22.4758i	1.65892	−	0.897597i
$628$		−	15.6290i		−	0.623667i
$629$	40.5662	+	34.0391i	1.61748	+	1.35723i
$630$		0			0
$631$	−4.25168	−	24.1125i	−0.169257	−	0.959903i	−0.944566	−	0.328321i	$-0.893517\pi$
$631$	−4.25168	−	24.1125i	−0.169257	−	0.959903i	0.775309	−	0.631582i	$-0.217594\pi$
$632$	14.7575	+	2.60214i	0.587021	+	0.103508i
$633$	5.07256	−	13.9368i	0.201616	−	0.553936i
$634$	5.90526	+	10.2282i	0.234528	+	0.406214i
$635$		0			0
$636$	−23.1497	+	19.4249i	−0.917946	+	0.770248i
$637$	−11.2486	−	13.4055i	−0.445685	−	0.531146i
$638$	13.0777	+	7.55041i	0.517751	+	0.298924i
$639$	16.9453	+	29.3502i	0.670347	+	1.16108i
$640$		0			0
$641$	−6.09749	+	34.5806i	−0.240836	+	1.36585i	0.589130	+	0.808038i	$0.299471\pi$
$641$	−6.09749	+	34.5806i	−0.240836	+	1.36585i	−0.829967	+	0.557813i	$0.811641\pi$
$642$	−36.2818	+	6.39747i	−1.43193	+	0.252488i
$643$	−6.13458	−	16.8546i	−0.241924	−	0.664681i	−0.999923	−	0.0124251i	$-0.996045\pi$
$643$	−6.13458	−	16.8546i	−0.241924	−	0.664681i	0.757999	−	0.652256i	$-0.226177\pi$
$644$	0.908554	+	0.762367i	0.0358020	+	0.0300415i
$645$		0			0
$646$	−17.5781	−	15.5974i	−0.691600	−	0.613672i
$647$			19.4546i			0.764839i	0.923989	+	0.382419i	$0.124909\pi$
$647$			19.4546i			0.764839i	−0.923989	+	0.382419i	$0.875091\pi$
$648$	4.65839	−	5.55166i	0.182999	−	0.218090i
$649$	19.2918	−	7.02165i	0.757271	−	0.275624i
$650$		0			0
$651$	2.79529	−	15.8529i	0.109556	−	0.621323i
$652$	4.23057	−	11.6234i	0.165682	−	0.455207i
$653$	19.3833	−	11.1910i	0.758528	−	0.437937i	−0.0702387	−	0.997530i	$-0.522376\pi$
$653$	19.3833	−	11.1910i	0.758528	−	0.437937i	0.828767	+	0.559594i	$0.189043\pi$
$654$	19.5794	−	33.9125i	0.765616	−	1.32609i
$655$		0			0
$656$	0.0317678	−	0.0266564i	0.00124033	−	0.00104076i
$657$	70.7185	+	40.8294i	2.75899	+	1.59291i
$658$	1.79576	−	1.03678i	0.0700061	−	0.0404180i
$659$	31.0531	+	11.3024i	1.20966	+	0.440279i	0.866584	−	0.499030i	$-0.166310\pi$
$659$	31.0531	+	11.3024i	1.20966	+	0.440279i	0.343072	+	0.939309i	$0.388533\pi$
$660$		0			0
$661$	0.579266	+	3.28518i	0.0225308	+	0.127779i	0.993999	−	0.109393i	$-0.0348907\pi$
$661$	0.579266	+	3.28518i	0.0225308	+	0.127779i	−0.971468	+	0.237172i	$0.923780\pi$
$662$	5.32087	+	14.6190i	0.206801	+	0.568182i
$663$	−29.1477	+	34.7369i	−1.13200	+	1.34907i
$664$	4.79877			0.186228
$665$		0			0
$666$	56.9774			2.20783
$667$	3.46475	−	4.12913i	0.134156	−	0.159881i
$668$	−7.26523	−	19.9611i	−0.281100	−	0.772316i
$669$	−0.0132579	−	0.0751893i	−0.000512580	−	0.00290699i
$670$		0			0
$671$	12.7754	+	4.64986i	0.493188	+	0.179506i
$672$	2.33725	−	1.34941i	0.0901614	−	0.0520547i
$673$	12.9332	+	7.46700i	0.498539	+	0.287832i	0.728110	−	0.685460i	$-0.240399\pi$
$673$	12.9332	+	7.46700i	0.498539	+	0.287832i	−0.229571	+	0.973292i	$0.573732\pi$
$674$	−17.5678	+	14.7411i	−0.676686	+	0.567807i
$675$		0			0
$676$	2.48095	−	4.29713i	0.0954212	−	0.165274i
$677$	38.6822	−	22.3332i	1.48668	−	0.858335i	0.486794	−	0.873517i	$-0.338166\pi$
$677$	38.6822	−	22.3332i	1.48668	−	0.858335i	0.999885	+	0.0151821i	$0.00483281\pi$
$678$	18.5857	−	51.0638i	0.713779	−	1.96109i
$679$	2.63031	−	14.9172i	0.100942	−	0.572471i
$680$		0			0
$681$	−23.0066	+	8.37372i	−0.881616	+	0.320882i
$682$	−14.0032	+	16.6884i	−0.536212	+	0.639032i
$683$		−	32.3880i		−	1.23929i	−0.784881	−	0.619647i	$-0.787276\pi$
$683$		−	32.3880i		−	1.23929i	0.784881	−	0.619647i	$-0.212724\pi$
$684$	−25.2756	−	0.698667i	−0.966436	−	0.0267142i
$685$		0			0
$686$	−9.17976	−	7.70273i	−0.350485	−	0.294092i
$687$	10.9261	+	30.0191i	0.416855	+	1.14530i
$688$	−8.74115	+	1.54130i	−0.333253	+	0.0587615i
$689$	5.01507	−	28.4419i	0.191059	−	1.08355i
$690$		0			0
$691$	−5.21755	−	9.03706i	−0.198485	−	0.343786i	0.749552	−	0.661945i	$-0.230269\pi$
$691$	−5.21755	−	9.03706i	−0.198485	−	0.343786i	−0.948037	+	0.318159i	$0.896935\pi$
$692$	8.91503	+	5.14710i	0.338899	+	0.195663i
$693$	−12.3894	−	14.7651i	−0.470634	−	0.560880i
$694$	13.5192	−	11.3439i	0.513181	−	0.430610i
$695$		0			0
$696$	−6.13272	−	10.6222i	−0.232460	−	0.402633i
$697$	−0.0764687	+	0.210096i	−0.00289646	+	0.00795795i
$698$	15.8539	+	2.79548i	0.600080	+	0.105810i
$699$	5.81802	+	32.9956i	0.220058	+	1.24801i
$700$		0			0
$701$	2.13342	+	1.79015i	0.0805783	+	0.0676132i	0.682187	−	0.731178i	$-0.261029\pi$
$701$	2.13342	+	1.79015i	0.0805783	+	0.0676132i	−0.601609	+	0.798791i	$0.705473\pi$
$702$			23.5573i			0.889114i
$703$	−26.6038	−	33.5456i	−1.00338	−	1.26520i
$704$	−3.65241			−0.137655
$705$		0			0
$706$	−3.34496	+	1.21747i	−0.125889	+	0.0458200i
$707$	−9.10700	+	1.60581i	−0.342504	+	0.0603927i
$708$	−16.4218	−	2.89561i	−0.617170	−	0.108824i
$709$	−48.2720	−	17.5696i	−1.81289	−	0.659839i	−0.996618	−	0.0821733i	$-0.973814\pi$
$709$	−48.2720	−	17.5696i	−1.81289	−	0.659839i	−0.816274	−	0.577665i	$-0.803964\pi$
$710$		0			0
$711$	−43.4631	+	75.2803i	−1.62999	+	2.82323i
$712$	5.75655	+	6.86039i	0.215736	+	0.257104i
$713$	4.99842	+	5.95689i	0.187192	+	0.223087i
$714$	−7.27517	+	12.6010i	−0.272266	+	0.471579i
$715$		0			0
$716$	0.799267	+	0.290910i	0.0298700	+	0.0108718i
$717$	65.0333	+	11.4671i	2.42871	+	0.428247i
$718$	−32.5245	+	5.73495i	−1.21380	+	0.214026i
$719$	42.8613	−	15.6002i	1.59846	−	0.581790i	0.619345	−	0.785119i	$-0.287398\pi$
$719$	42.8613	−	15.6002i	1.59846	−	0.581790i	0.979111	+	0.203328i	$0.0651758\pi$
$720$		0			0
$721$	11.3161			0.421435
$722$	11.3903	+	15.2073i	0.423902	+	0.565957i
$723$			63.5043i			2.36175i
$724$	13.1433	+	11.0285i	0.488467	+	0.409872i
$725$		0			0
$726$	1.20549	+	6.83669i	0.0447400	+	0.253733i
$727$	22.4799	+	3.96382i	0.833734	+	0.147010i	0.574191	−	0.818722i	$-0.305317\pi$
$727$	22.4799	+	3.96382i	0.833734	+	0.147010i	0.259544	+	0.965731i	$0.416428\pi$
$728$	−0.882148	+	2.42368i	−0.0326946	+	0.0898276i
$729$	−15.9547	−	27.6343i	−0.590914	−	1.02349i
$730$		0			0
$731$	36.6580	−	30.7597i	1.35585	−	1.13769i
$732$	−7.09803	−	8.45910i	−0.262351	−	0.312657i
$733$	5.00160	+	2.88768i	0.184738	+	0.106659i	0.589517	−	0.807756i	$-0.299318\pi$
$733$	5.00160	+	2.88768i	0.184738	+	0.106659i	−0.404779	+	0.914415i	$0.632651\pi$
$734$	16.8948	+	29.2627i	0.623600	+	1.08011i
$735$		0			0
$736$	−0.226388	+	1.28391i	−0.00834478	+	0.0473256i
$737$	−49.2875	+	8.69072i	−1.81553	+	0.320127i
$738$	0.0822765	+	0.226053i	0.00302864	+	0.00832112i
$739$	−9.57147	−	8.03142i	−0.352092	−	0.295441i	0.449537	−	0.893262i	$-0.351589\pi$
$739$	−9.57147	−	8.03142i	−0.352092	−	0.295441i	−0.801630	+	0.597821i	$0.796033\pi$
$740$		0			0
$741$	28.7251	−	22.7808i	1.05524	−	0.836874i
$742$		−	9.26708i		−	0.340205i
$743$	32.3373	−	38.5381i	1.18634	−	1.41383i	0.298048	−	0.954551i	$-0.403665\pi$
$743$	32.3373	−	38.5381i	1.18634	−	1.41383i	0.888294	−	0.459276i	$-0.151891\pi$
$744$	16.6276	−	6.05195i	0.609597	−	0.221875i
$745$		0			0
$746$	0.298623	−	1.69358i	0.0109334	−	0.0620063i
$747$	−9.52076	+	26.1581i	−0.348346	+	0.957074i
$748$	17.0533	−	9.84572i	0.623530	−	0.359995i
$749$	5.64884	−	9.78407i	0.206404	−	0.357502i
$750$		0			0
$751$	35.1254	−	29.4737i	1.28174	−	1.07551i	0.288743	−	0.957407i	$-0.406763\pi$
$751$	35.1254	−	29.4737i	1.28174	−	1.07551i	0.993001	−	0.118104i	$-0.0376817\pi$
$752$	1.97395	+	1.13966i	0.0719825	+	0.0415591i
$753$	−12.9926	+	7.50126i	−0.473475	+	0.273361i
$754$	11.0150	+	4.00912i	0.401142	+	0.146004i
$755$		0			0
$756$	1.31260	+	7.44412i	0.0477388	+	0.270740i
$757$	−3.79121	−	10.4163i	−0.137794	−	0.378586i	0.851533	−	0.524302i	$-0.175674\pi$
$757$	−3.79121	−	10.4163i	−0.137794	−	0.378586i	−0.989326	+	0.145716i	$0.953451\pi$
$758$	5.71851	−	6.81505i	0.207706	−	0.247534i
$759$	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	$0.254542\pi$
$762$	17.9660	−	21.4111i	0.650841	−	0.775642i
$763$	4.10707	+	11.2841i	0.148686	+	0.408511i
$764$	0.737306	+	4.18147i	0.0266748	+	0.151280i
$765$		0			0
$766$	8.21699	+	2.99074i	0.296892	+	0.108060i
$767$	13.8012	−	7.96810i	0.498331	−	0.287712i
$768$	2.56917	+	1.48331i	0.0927069	+	0.0535243i
$769$	−2.43664	+	2.04458i	−0.0878675	+	0.0737296i	−0.685663	−	0.727919i	$-0.740488\pi$
$769$	−2.43664	+	2.04458i	−0.0878675	+	0.0737296i	0.597796	+	0.801648i	$0.296043\pi$
$770$		0			0
$771$	−23.9071	+	41.4083i	−0.860993	+	1.49128i
$772$	−0.620776	+	0.358405i	−0.0223422	+	0.0128993i
$773$	−9.29414	+	25.5354i	−0.334287	+	0.918446i	0.652696	+	0.757620i	$0.273638\pi$
$773$	−9.29414	+	25.5354i	−0.334287	+	0.918446i	−0.986983	+	0.160826i	$0.948584\pi$
$774$	8.94082	−	50.7059i	0.321371	−	1.82259i
$775$		0			0
$776$	15.6462	−	5.69476i	0.561667	−	0.204430i
$777$	−17.0394	+	20.3068i	−0.611285	+	0.728501i
$778$			21.5945i			0.774202i
$779$	0.0946728	−	0.153989i	0.00339200	−	0.00551721i
$780$		0			0
$781$	16.3464	+	13.7163i	0.584922	+	0.490807i
$782$	−2.40400	−	6.60492i	−0.0859667	−	0.236192i
$783$	33.8315	−	5.96541i	1.20904	−	0.213186i
$784$	1.07182	−	6.07862i	0.0382794	−	0.217093i
$785$		0			0
$786$	2.45728	+	4.25614i	0.0876484	+	0.151812i
$787$	17.2358	+	9.95112i	0.614392	+	0.354719i	0.774682	−	0.632351i	$-0.217910\pi$
$787$	17.2358	+	9.95112i	0.614392	+	0.354719i	−0.160291	+	0.987070i	$0.551243\pi$
$788$	17.2360	+	20.5410i	0.614006	+	0.731744i
$789$	41.1833	−	34.5569i	1.46617	−	1.23026i
$790$		0			0
$791$	8.33198	+	14.4314i	0.296251	+	0.513122i
$792$	7.24639	−	19.9093i	0.257489	−	0.707446i
$793$	10.3929	+	1.83255i	0.369063	+	0.0650757i
$794$	−4.45149	−	25.2457i	−0.157978	−	0.895935i
$795$		0			0
$796$	14.1804	+	11.8988i	0.502612	+	0.421742i
$797$		−	16.3603i		−	0.579510i	−0.957101	−	0.289755i	$-0.906426\pi$
$797$		−	16.3603i		−	0.579510i	0.957101	−	0.289755i	$-0.0935739\pi$
$798$	7.80781	−	8.79929i	0.276394	−	0.311492i
$799$	−12.2886			−0.434740
$800$		0			0
$801$	−48.8170	+	17.7679i	−1.72486	+	0.627799i
$802$	23.4596	−	4.13656i	0.828388	−	0.146067i
$803$	50.6341	+	8.92816i	1.78684	+	0.315068i
$804$	38.1992	+	13.9034i	1.34718	+	0.490334i
$805$		0			0
$806$	−8.45529	+	14.6450i	−0.297825	+	0.515848i
$807$	22.0977	+	26.3350i	0.777876	+	0.927036i
$808$	−6.53399	−	7.78691i	−0.229865	−	0.273942i
$809$	−15.6739	+	27.1480i	−0.551064	+	0.954471i	0.447134	+	0.894467i	$0.352445\pi$
$809$	−15.6739	+	27.1480i	−0.551064	+	0.954471i	−0.998198	+	0.0600042i	$0.980889\pi$
$810$		0			0
$811$	−46.6994	−	16.9972i	−1.63984	−	0.596852i	−0.652826	−	0.757508i	$-0.726417\pi$
$811$	−46.6994	−	16.9972i	−1.63984	−	0.596852i	−0.987010	+	0.160657i	$0.948639\pi$
$812$	3.70412	+	0.653137i	0.129989	+	0.0229206i
$813$	53.8166	−	9.48932i	1.88743	−	0.332805i
$814$	33.7114	−	12.2700i	1.18159	−	0.430062i
$815$		0			0
$816$	−15.9941			−0.559906
$817$	−34.0279	+	18.4116i	−1.19048	+	0.644139i
$818$		−	11.8905i		−	0.415743i
$819$	−11.4613	−	9.61717i	−0.400490	−	0.336051i
$820$		0			0
$821$	−8.09066	−	45.8844i	−0.282366	−	1.60138i	−0.714545	−	0.699589i	$-0.753366\pi$
$821$	−8.09066	−	45.8844i	−0.282366	−	1.60138i	0.432179	−	0.901788i	$-0.357745\pi$
$822$	23.6063	+	4.16242i	0.823363	+	0.145181i
$823$	−10.8361	+	29.7720i	−0.377723	+	1.03779i	0.594575	+	0.804040i	$0.297320\pi$
$823$	−10.8361	+	29.7720i	−0.377723	+	1.03779i	−0.972298	+	0.233746i	$0.924902\pi$
$824$	6.21950	+	10.7725i	0.216667	+	0.375278i
$825$		0			0
$826$	3.91719	−	3.28692i	0.136297	−	0.114366i
$827$	−17.6144	−	20.9920i	−0.612512	−	0.729964i	0.367251	−	0.930122i	$-0.380299\pi$
$827$	−17.6144	−	20.9920i	−0.612512	−	0.729964i	−0.979764	+	0.200158i	$0.935854\pi$
$828$	−6.54945	−	3.78133i	−0.227609	−	0.131410i
$829$	−12.0124	−	20.8061i	−0.417208	−	0.722625i	0.578450	−	0.815718i	$-0.303658\pi$
$829$	−12.0124	−	20.8061i	−0.417208	−	0.722625i	−0.995657	+	0.0930932i	$0.970325\pi$
$830$		0			0
$831$	−1.45395	+	8.24577i	−0.0504370	+	0.286043i
$832$	−2.79208	+	0.492319i	−0.0967980	+	0.0170681i
$833$	11.3816	+	31.2707i	0.394349	+	1.08346i
$834$	−16.0911	−	13.5020i	−0.557188	−	0.467536i
$835$		0			0
$836$	−15.1051	+	5.02967i	−0.522421	+	0.173955i
$837$			49.5599i			1.71304i
$838$	4.86710	−	5.80039i	0.168131	−	0.200371i
$839$	−38.0042	+	13.8324i	−1.31205	+	0.477547i	−0.900902	−	0.434022i	$-0.857094\pi$
$839$	−38.0042	+	13.8324i	−1.31205	+	0.477547i	−0.411148	+	0.911569i	$0.634872\pi$
$840$		0			0
$841$	−2.06747	+	11.7252i	−0.0712919	+	0.404317i
$842$	−9.88232	+	27.1515i	−0.340567	+	0.935701i
$843$	−63.8474	+	36.8623i	−2.19902	+	1.26961i
$844$	−2.49968	+	4.32957i	−0.0860424	+	0.149030i
$845$		0			0
$846$	−10.1286	+	8.49890i	−0.348228	+	0.292198i
$847$	−1.84364	−	1.06443i	−0.0633482	−	0.0365741i
$848$	8.82187	−	5.09331i	0.302944	−	0.174905i
$849$	−23.6873	−	8.62146i	−0.812945	−	0.295888i
$850$		0			0
$851$	−2.22365	−	12.6109i	−0.0762257	−	0.432297i
$852$	−5.92793	−	16.2869i	−0.203088	−	0.557979i
$853$	−8.16082	+	9.72569i	−0.279421	+	0.333001i	−0.887442	−	0.460920i	$-0.847519\pi$
$853$	−8.16082	+	9.72569i	−0.279421	+	0.333001i	0.608020	+	0.793921i	$0.291964\pi$
$854$	3.38627			0.115876
$855$		0			0
$856$	12.4187			0.424462
$857$	−2.63097	+	3.13547i	−0.0898723	+	0.107106i	−0.809106	−	0.587662i	$-0.800048\pi$
$857$	−2.63097	+	3.13547i	−0.0898723	+	0.107106i	0.719234	+	0.694768i	$0.244493\pi$
$858$	10.5068	+	28.8671i	0.358696	+	0.985508i
$859$	−5.09546	−	28.8978i	−0.173855	−	0.985980i	−0.939457	−	0.342666i	$-0.888670\pi$
$859$	−5.09546	−	28.8978i	−0.173855	−	0.985980i	0.765603	−	0.643314i	$-0.222441\pi$
$860$		0			0
$861$	−0.105171	−	0.0382790i	−0.00358421	−	0.00130454i
$862$	22.6684	−	13.0876i	0.772088	−	0.445765i
$863$	−39.3669	−	22.7285i	−1.34006	−	0.773687i	−0.353248	−	0.935530i	$-0.614923\pi$
$863$	−39.3669	−	22.7285i	−1.34006	−	0.773687i	−0.986817	+	0.161843i	$0.948256\pi$
$864$	−6.36507	+	5.34093i	−0.216544	+	0.181702i
$865$		0			0
$866$	−11.4658	+	19.8593i	−0.389623	+	0.674846i
$867$	31.0015	−	17.8987i	1.05287	−	0.607872i
$868$	−1.85586	+	5.09894i	−0.0629921	+	0.173069i
$869$	−9.50408	+	53.9003i	−0.322404	+	1.82844i
$870$		0			0
$871$	−36.5064	+	13.2872i	−1.23697	+	0.450221i
$872$	−8.48468	+	10.1116i	−0.287327	+	0.342423i
$873$			96.5860i			3.26894i
$874$	0.831789	+	5.62157i	0.0281357	+	0.190153i
$875$		0			0
$876$	−31.9910	−	26.8437i	−1.08088	−	0.906963i
$877$	4.01777	+	11.0387i	0.135671	+	0.372752i	0.988860	−	0.148850i	$-0.0475571\pi$
$877$	4.01777	+	11.0387i	0.135671	+	0.372752i	−0.853189	+	0.521601i	$0.825335\pi$
$878$	−28.7523	+	5.06981i	−0.970344	+	0.171098i
$879$	8.07409	−	45.7905i	0.272332	−	1.54447i
$880$		0			0
$881$	11.2581	+	19.4996i	0.379294	+	0.656957i	0.990960	−	0.134160i	$-0.0428335\pi$
$881$	11.2581	+	19.4996i	0.379294	+	0.656957i	−0.611665	+	0.791117i	$0.709500\pi$
$882$	31.0080	+	17.9025i	1.04410	+	0.602809i
$883$	5.32186	+	6.34235i	0.179095	+	0.213437i	0.848122	−	0.529801i	$-0.177733\pi$
$883$	5.32186	+	6.34235i	0.179095	+	0.213437i	−0.669027	+	0.743238i	$0.733289\pi$
$884$	11.7092	−	9.82522i	0.393824	−	0.330458i
$885$		0			0
$886$	−10.7826	−	18.6760i	−0.362248	−	0.627432i
$887$	−2.33665	+	6.41989i	−0.0784570	+	0.215559i	−0.972720	−	0.231984i	$-0.925478\pi$
$887$	−2.33665	+	6.41989i	−0.0784570	+	0.215559i	0.894263	+	0.447542i	$0.147701\pi$
$888$	−28.6963	−	5.05993i	−0.962984	−	0.169800i
$889$	1.48835	+	8.44087i	0.0499178	+	0.283098i
$890$		0			0
$891$	20.2769	+	17.0144i	0.679302	+	0.570002i
$892$			0.0257361i			0.000861708i
$893$	9.73297	+	1.99495i	0.325702	+	0.0667584i
$894$	11.7256			0.392163
$895$		0			0
$896$	−0.854867	+	0.311146i	−0.0285591	+	0.0103947i
$897$	10.7988	−	1.90411i	0.360560	−	0.0635765i
$898$	37.4149	+	6.59726i	1.24855	+	0.220153i
$899$	23.1733	+	8.43440i	0.772874	+	0.281303i
$900$		0			0
$901$	−27.4598	+	47.5618i	−0.914820	+	1.58451i
$902$	0.0973600	+	0.116029i	0.00324173	+	0.00386335i
$903$	15.3978	+	18.3504i	0.512407	+	0.610663i
$904$	−9.15873	+	15.8634i	−0.304615	+	0.527608i
$905$		0			0
$906$	30.4489	+	11.0825i	1.01160	+	0.368191i
$907$	−47.8583	−	8.43871i	−1.58911	−	0.280203i	−0.691961	−	0.721935i	$-0.743253\pi$
$907$	−47.8583	−	8.43871i	−1.58911	−	0.280203i	−0.897147	+	0.441732i	$0.854364\pi$
$908$	8.12749	−	1.43310i	0.269720	−	0.0475590i
$909$	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	$0.501752\pi$
$912$	12.6678	+	2.59650i	0.419474	+	0.0859787i
$913$			17.5271i			0.580061i
$914$	−18.7114	−	15.7007i	−0.618917	−	0.519333i
$915$		0			0
$916$	−1.86991	−	10.6048i	−0.0617835	−	0.350392i
$917$	−1.48418	−	0.261702i	−0.0490121	−	0.00864215i
$918$	15.3214	−	42.0953i	0.505682	−	1.38935i
$919$	12.7310	+	22.0508i	0.419958	+	0.727389i	0.995935	−	0.0900775i	$-0.0287115\pi$
$919$	12.7310	+	22.0508i	0.419958	+	0.727389i	−0.575977	+	0.817466i	$0.695378\pi$
$920$		0			0
$921$	−22.8589	+	19.1809i	−0.753227	+	0.632032i
$922$	−17.6905	−	21.0827i	−0.582606	−	0.694323i
$923$	14.3449	+	8.28202i	0.472168	+	0.272606i
$924$	4.92861	+	8.53660i	0.162139	+	0.280833i
$925$		0			0
$926$	−3.30959	+	18.7696i	−0.108760	+	0.616808i
$927$	−71.0604	+	12.5299i	−2.33393	+	0.411535i
$928$	1.41408	+	3.88514i	0.0464193	+	0.127536i
$929$	−40.7777	−	34.2166i	−1.33787	−	1.12261i	−0.982167	−	0.188011i	$-0.939796\pi$
$929$	−40.7777	−	34.2166i	−1.33787	−	1.12261i	−0.355706	−	0.934598i	$-0.615760\pi$
$930$		0			0
$931$	−3.93807	−	26.6151i	−0.129065	−	0.872273i
$932$		−	11.2939i		−	0.369943i
$933$	7.35497	−	8.76531i	0.240791	−	0.286963i
$934$	31.9639	−	11.6339i	1.04589	−	0.380673i
$935$		0			0
$936$	2.85586	−	16.1964i	0.0933468	−	0.529396i
$937$	−7.08394	+	19.4630i	−0.231422	+	0.635827i	−0.999992	−	0.00393831i	$-0.998746\pi$
$937$	−7.08394	+	19.4630i	−0.231422	+	0.635827i	0.768570	+	0.639766i	$0.220969\pi$
$938$	−10.7957	+	6.23289i	−0.352491	+	0.203511i
$939$	3.42003	−	5.92366i	0.111608	−	0.193311i
$940$		0			0
$941$	−25.7268	+	21.5873i	−0.838669	+	0.703727i	−0.957264	−	0.289216i	$-0.906606\pi$
$941$	−25.7268	+	21.5873i	−0.838669	+	0.703727i	0.118595	+	0.992943i	$0.462161\pi$
$942$	−40.1536	−	23.1827i	−1.30828	−	0.755334i
$943$	0.0468218	−	0.0270326i	0.00152473	−	0.000880302i
$944$	5.28195	+	1.92247i	0.171913	+	0.0625711i
$945$		0			0
$946$	−5.62946	−	31.9262i	−0.183029	−	1.03801i
$947$	−5.53178	−	15.1984i	−0.179759	−	0.493883i	0.816786	−	0.576941i	$-0.195754\pi$
$947$	−5.53178	−	15.1984i	−0.179759	−	0.493883i	−0.996545	+	0.0830579i	$0.973531\pi$
$948$	28.5752	−	34.0546i	0.928081	−	1.10604i
$949$	39.9107			1.29555
$950$		0			0
$951$	35.0373			1.13616
$952$	3.15267	−	3.75721i	0.102179	−	0.121772i
$953$	−1.04998	−	2.88481i	−0.0340123	−	0.0934481i	0.921524	−	0.388321i	$-0.126945\pi$
$953$	−1.04998	−	2.88481i	−0.0340123	−	0.0934481i	−0.955536	+	0.294873i	$0.904723\pi$
$954$	10.2610	+	58.1931i	0.332213	+	1.88407i
$955$		0			0
$956$	−20.9174	−	7.61332i	−0.676517	−	0.246232i
$957$	38.7965	−	22.3992i	1.25411	−	0.724063i
$958$	−16.1007	−	9.29575i	−0.520191	−	0.300332i
$959$	−5.63094	+	4.72492i	−0.181832	+	0.152576i
$960$		0			0
$961$	−2.28825	+	3.96336i	−0.0738145	+	0.127850i
$962$	24.1168	−	13.9238i	0.777557	−	0.448922i
$963$	−24.6387	+	67.6943i	−0.793972	+	2.18142i
$964$	3.71716	−	21.0811i	0.119722	−	0.678976i
$965$		0			0
$966$	3.30632	−	1.20340i	0.106379	−	0.0387188i
$967$	16.1541	−	19.2517i	0.519480	−	0.619092i	−0.440978	−	0.897518i	$-0.645368\pi$
$967$	16.1541	−	19.2517i	0.519480	−	0.619092i	0.960458	+	0.278426i	$0.0898127\pi$
$968$		−	2.34009i		−	0.0752133i
$969$	−66.1461	+	22.0252i	−2.12492	+	0.707552i
$970$		0			0
$971$	21.8759	+	18.3561i	0.702032	+	0.589075i	0.922351	−	0.386353i	$-0.126265\pi$
$971$	21.8759	+	18.3561i	0.702032	+	0.589075i	−0.220319	+	0.975428i	$0.570710\pi$
$972$	1.17225	+	3.22073i	0.0375999	+	0.103305i
$973$	6.34356	−	1.11854i	0.203365	−	0.0358588i
$974$	1.31050	−	7.43220i	0.0419910	−	0.238143i
$975$		0			0
$976$	1.86114	+	3.22358i	0.0595736	+	0.103184i
$977$	14.8714	+	8.58599i	0.475777	+	0.274690i	0.718655	−	0.695367i	$-0.244758\pi$
$977$	14.8714	+	8.58599i	0.475777	+	0.274690i	−0.242878	+	0.970057i	$0.578091\pi$
$978$	−23.5872	−	28.1101i	−0.754236	−	0.898863i
$979$	−25.0570	+	21.0253i	−0.800824	+	0.671971i
$980$		0			0
$981$	−38.2850	−	66.3115i	−1.22234	−	2.11716i
$982$	−6.30541	+	17.3240i	−0.201214	+	0.552830i
$983$	36.9097	+	6.50817i	1.17724	+	0.207579i	0.727836	−	0.685752i	$-0.240526\pi$
$983$	36.9097	+	6.50817i	1.17724	+	0.207579i	0.449401	+	0.893330i	$0.351638\pi$
$984$	−0.0213632	−	0.121157i	−0.000681033	−	0.00386233i
$985$		0			0
$986$	−17.0755	−	14.3280i	−0.543794	−	0.456298i
$987$		−	6.15148i		−	0.195804i
$988$	−10.8691	+	5.88099i	−0.345793	+	0.187099i
$989$	−11.5718			−0.367962
$990$		0			0
$991$	−21.7623	+	7.92083i	−0.691302	+	0.251613i	−0.663693	−	0.748005i	$-0.731012\pi$
$991$	−21.7623	+	7.92083i	−0.691302	+	0.251613i	−0.0276096	+	0.999619i	$0.508790\pi$
$992$	−5.87399	+	1.03574i	−0.186499	+	0.0328849i
$993$	45.4511	+	8.01425i	1.44235	+	0.254324i
$994$	4.99446	+	1.81783i	0.158415	+	0.0576582i
$995$		0			0
$996$	7.11806	−	12.3288i	0.225544	−	0.390654i
$997$	−12.9380	−	15.4189i	−0.409750	−	0.488321i	0.521217	−	0.853424i	$-0.325478\pi$
$997$	−12.9380	−	15.4189i	−0.409750	−	0.488321i	−0.930967	+	0.365103i	$0.881034\pi$
$998$	−9.81916	−	11.7020i	−0.310820	−	0.370421i
$999$	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.u.h.149.4		48
5.2	odd	4		950.2.l.j.301.4	yes	24
5.3	odd	4		950.2.l.k.301.1	yes	24
5.4	even	2	inner	950.2.u.h.149.5		48
19.6	even	9	inner	950.2.u.h.899.5		48
95.44	even	18	inner	950.2.u.h.899.4		48
95.63	odd	36		950.2.l.k.101.1	yes	24
95.82	odd	36		950.2.l.j.101.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.101.4	✓	24	95.82	odd	36
950.2.l.j.301.4	yes	24	5.2	odd	4
950.2.l.k.101.1	yes	24	95.63	odd	36
950.2.l.k.301.1	yes	24	5.3	odd	4
950.2.u.h.149.4		48	1.1	even	1	trivial
950.2.u.h.149.5		48	5.4	even	2	inner
950.2.u.h.899.4		48	95.44	even	18	inner
950.2.u.h.899.5		48	19.6	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(1.01464 + 2.78771i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.78771 - 1.01464i) q^{6} +(0.787850 - 0.454865i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-4.44370 + 3.72870i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(1.01464 + 2.78771i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.78771 - 1.01464i) q^{6} +(0.787850 - 0.454865i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-4.44370 + 3.72870i) q^{9} +(-1.82620 + 3.16308i) q^{11} +(2.56917 - 1.48331i) q^{12} +(-0.969680 + 2.66417i) q^{13} +(-0.157973 + 0.895910i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.46550 - 4.13002i) q^{17} -5.80083i q^{18} +(-3.41525 + 2.70851i) q^{19} +(2.06742 + 1.73477i) q^{21} +(-1.24920 - 3.43214i) q^{22} +(-1.28391 + 0.226388i) q^{23} +(-0.515148 + 2.92155i) q^{24} +(-1.41758 - 2.45532i) q^{26} +(-7.19581 - 4.15450i) q^{27} +(-0.584764 - 0.696894i) q^{28} +(-3.16720 + 2.65759i) q^{29} +(-2.98230 - 5.16550i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-10.6707 - 1.88153i) q^{33} +(0.936199 + 5.30945i) q^{34} +(4.44370 + 3.72870i) q^{36} +9.82228i q^{37} +(0.120443 - 4.35723i) q^{38} -8.41082 q^{39} +(-0.0389690 + 0.0141836i) q^{41} +(-2.65782 + 0.468646i) q^{42} +(8.74115 + 1.54130i) q^{43} +(3.43214 + 1.24920i) q^{44} +(0.651859 - 1.12905i) q^{46} +(-1.46512 - 1.74606i) q^{47} +(-1.90691 - 2.27256i) q^{48} +(-3.08619 + 5.34545i) q^{49} +(15.0295 + 5.47031i) q^{51} +(2.79208 + 0.492319i) q^{52} +(-10.0319 + 1.76889i) q^{53} +(7.80791 - 2.84185i) q^{54} +0.909731 q^{56} +(-11.0158 - 6.77257i) q^{57} -4.13448i q^{58} +(-4.30588 - 3.61306i) q^{59} +(-0.646366 - 3.66573i) q^{61} +(5.87399 + 1.03574i) q^{62} +(-1.80491 + 4.95894i) q^{63} +(0.500000 + 0.866025i) q^{64} +(8.30033 - 6.96480i) q^{66} +(8.80793 + 10.4969i) q^{67} +(-4.66905 - 2.69568i) q^{68} +(-1.93382 - 3.34947i) q^{69} +(1.01452 - 5.75362i) q^{71} +(-5.71271 + 1.00730i) q^{72} +(-4.81464 - 13.2281i) q^{73} +(-7.52430 - 6.31364i) q^{74} +(3.26042 + 2.89304i) q^{76} +3.32271i q^{77} +(5.40637 - 6.44307i) q^{78} +(14.0814 - 5.12522i) q^{79} +(1.25846 - 7.13707i) q^{81} +(0.0141836 - 0.0389690i) q^{82} +(4.15585 - 2.39938i) q^{83} +(1.34941 - 2.33725i) q^{84} +(-6.79940 + 5.70538i) q^{86} +(-10.6222 - 6.13272i) q^{87} +(-3.16308 + 1.82620i) q^{88} +(8.41552 + 3.06300i) q^{89} +(0.447878 + 2.54004i) q^{91} +(0.445898 + 1.22509i) q^{92} +(11.3739 - 13.5549i) q^{93} +2.27932 q^{94} +2.96662 q^{96} +(10.7026 - 12.7549i) q^{97} +(-2.11108 - 5.80015i) q^{98} +(-3.67909 - 20.8651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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