LMFDB - Embedded newform 950.2.u.g.499.5

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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.5
Character	$\chi$	$=$	950.499
Dual form			950.2.u.g.99.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 + 0.939693i) q^{2} +(-0.0355948 - 0.00627632i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.00627632 - 0.0355948i) q^{6} +(1.59124 - 0.918706i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.81785 - 1.02561i) q^{9} +O(q^{10})$	\(q+(0.342020 + 0.939693i) q^{2} +(-0.0355948 - 0.00627632i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.00627632 - 0.0355948i) q^{6} +(1.59124 - 0.918706i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.81785 - 1.02561i) q^{9} +(1.23288 - 2.13541i) q^{11} +(0.0313015 - 0.0180720i) q^{12} +(2.35673 - 0.415556i) q^{13} +(1.40754 + 1.18107i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.30589 - 6.33539i) q^{17} -2.99869i q^{18} +(4.34868 - 0.298357i) q^{19} +(-0.0624061 + 0.0227140i) q^{21} +(2.42830 + 0.428174i) q^{22} +(-1.04191 - 1.24170i) q^{23} +(0.0276878 + 0.0232329i) q^{24} +(1.19655 + 2.07248i) q^{26} +(0.187768 + 0.108408i) q^{27} +(-0.628432 + 1.72660i) q^{28} +(3.10246 + 1.12920i) q^{29} +(1.75192 + 3.03441i) q^{31} +(0.984808 - 0.173648i) q^{32} +(-0.0572866 + 0.0682715i) q^{33} +(5.16466 - 4.33366i) q^{34} +(2.81785 - 1.02561i) q^{36} -6.00888i q^{37} +(1.76770 + 3.98437i) q^{38} -0.0864957 q^{39} +(-1.38582 + 7.85939i) q^{41} +(-0.0426883 - 0.0508739i) q^{42} +(3.67317 - 4.37751i) q^{43} +(0.428174 + 2.42830i) q^{44} +(0.810460 - 1.40376i) q^{46} +(4.27274 - 11.7392i) q^{47} +(-0.0123619 + 0.0339642i) q^{48} +(-1.81196 + 3.13841i) q^{49} +(0.0423149 + 0.239980i) q^{51} +(-1.53825 + 1.83321i) q^{52} +(1.23503 + 1.47185i) q^{53} +(-0.0376497 + 0.213522i) q^{54} -1.83741 q^{56} +(-0.156663 - 0.0166738i) q^{57} +3.30157i q^{58} +(-4.46726 + 1.62595i) q^{59} +(10.4674 - 8.78317i) q^{61} +(-2.25222 + 2.68410i) q^{62} +(-5.42613 + 0.956772i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.0837473 - 0.0304815i) q^{66} +(-1.27151 + 3.49344i) q^{67} +(5.83873 + 3.37099i) q^{68} +(0.0292932 + 0.0507373i) q^{69} +(4.46844 + 3.74946i) q^{71} +(1.92752 + 2.29713i) q^{72} +(0.502654 + 0.0886314i) q^{73} +(5.64650 - 2.05516i) q^{74} +(-3.13950 + 3.02383i) q^{76} -4.53061i q^{77} +(-0.0295833 - 0.0812794i) q^{78} +(-2.10729 + 11.9511i) q^{79} +(6.88539 + 5.77753i) q^{81} +(-7.85939 + 1.38582i) q^{82} +(-5.39755 + 3.11628i) q^{83} +(0.0332056 - 0.0575138i) q^{84} +(5.36981 + 1.95445i) q^{86} +(-0.103344 - 0.0596659i) q^{87} +(-2.13541 + 1.23288i) q^{88} +(-2.95236 - 16.7437i) q^{89} +(3.36837 - 2.82640i) q^{91} +(1.59629 + 0.281470i) q^{92} +(-0.0433143 - 0.119005i) q^{93} +12.4926 q^{94} -0.0361439 q^{96} +(4.67194 + 12.8360i) q^{97} +(-3.56887 - 0.629287i) q^{98} +(-5.66417 + 4.75280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{9}+O(q^{10}) $ 36 * q + 36 * q^9	$ 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) $ 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$3$	−0.0355948	−	0.00627632i	−0.0205507	−	0.00362364i	0.163363	−	0.986566i	$-0.447766\pi$
$3$	−0.0355948	−	0.00627632i	−0.0205507	−	0.00362364i	−0.183914	+	0.982942i	$0.558877\pi$
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.00627632	−	0.0355948i	−0.00256230	−	0.0145315i
$7$	1.59124	−	0.918706i	0.601434	−	0.347238i	−0.168172	−	0.985758i	$-0.553786\pi$
$7$	1.59124	−	0.918706i	0.601434	−	0.347238i	0.769605	+	0.638520i	$0.220453\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−2.81785	−	1.02561i	−0.939283	−	0.341871i
$10$		0			0
$11$	1.23288	−	2.13541i	0.371727	−	0.643850i	−0.618105	−	0.786096i	$-0.712099\pi$
$11$	1.23288	−	2.13541i	0.371727	−	0.643850i	0.989831	+	0.142246i	$0.0454325\pi$
$12$	0.0313015	−	0.0180720i	0.00903598	−	0.00521692i
$13$	2.35673	−	0.415556i	0.653641	−	0.115254i	0.163013	−	0.986624i	$-0.447879\pi$
$13$	2.35673	−	0.415556i	0.653641	−	0.115254i	0.490627	+	0.871369i	$0.336768\pi$
$14$	1.40754	+	1.18107i	0.376180	+	0.315653i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.30589	−	6.33539i	−0.559261	−	1.53656i	−0.820712	−	0.571341i	$-0.806423\pi$
$17$	−2.30589	−	6.33539i	−0.559261	−	1.53656i	0.261451	−	0.965217i	$-0.415799\pi$
$18$		−	2.99869i		−	0.706799i
$19$	4.34868	−	0.298357i	0.997655	−	0.0684477i
$19$	4.34868	−	0.298357i	0.997655	−	0.0684477i
$20$		0			0
$21$	−0.0624061	+	0.0227140i	−0.0136181	+	0.00495660i
$22$	2.42830	+	0.428174i	0.517714	+	0.0912870i
$23$	−1.04191	−	1.24170i	−0.217253	−	0.258912i	0.646400	−	0.762998i	$-0.276274\pi$
$23$	−1.04191	−	1.24170i	−0.217253	−	0.258912i	−0.863653	+	0.504087i	$0.831829\pi$
$24$	0.0276878	+	0.0232329i	0.00565176	+	0.00474239i
$25$		0			0
$26$	1.19655	+	2.07248i	0.234662	+	0.406446i
$27$	0.187768	+	0.108408i	0.0361360	+	0.0208632i
$28$	−0.628432	+	1.72660i	−0.118762	+	0.326297i
$29$	3.10246	+	1.12920i	0.576113	+	0.209688i	0.613611	−	0.789609i	$-0.289716\pi$
$29$	3.10246	+	1.12920i	0.576113	+	0.209688i	−0.0374978	+	0.999297i	$0.511939\pi$
$30$		0			0
$31$	1.75192	+	3.03441i	0.314654	+	0.544997i	0.979364	−	0.202105i	$-0.0647782\pi$
$31$	1.75192	+	3.03441i	0.314654	+	0.544997i	−0.664710	+	0.747102i	$0.731445\pi$
$32$	0.984808	−	0.173648i	0.174091	−	0.0306970i
$33$	−0.0572866	+	0.0682715i	−0.00997231	+	0.0118845i
$34$	5.16466	−	4.33366i	0.885732	−	0.743217i
$35$		0			0
$36$	2.81785	−	1.02561i	0.469642	−	0.170936i
$37$		−	6.00888i		−	0.987854i	−0.869503	−	0.493927i	$-0.835561\pi$
$37$		−	6.00888i		−	0.987854i	0.869503	−	0.493927i	$-0.164439\pi$
$38$	1.76770	+	3.98437i	0.286759	+	0.646351i
$39$	−0.0864957			−0.0138504
$40$		0			0
$41$	−1.38582	+	7.85939i	−0.216429	+	1.22743i	0.661980	+	0.749521i	$0.269716\pi$
$41$	−1.38582	+	7.85939i	−0.216429	+	1.22743i	−0.878409	+	0.477909i	$0.841395\pi$
$42$	−0.0426883	−	0.0508739i	−0.00658695	−	0.00785002i
$43$	3.67317	−	4.37751i	0.560153	−	0.667564i	−0.409426	−	0.912343i	$-0.634271\pi$
$43$	3.67317	−	4.37751i	0.560153	−	0.667564i	0.969579	+	0.244779i	$0.0787155\pi$
$44$	0.428174	+	2.42830i	0.0645497	+	0.366079i
$45$		0			0
$46$	0.810460	−	1.40376i	0.119496	−	0.206973i
$47$	4.27274	−	11.7392i	0.623243	−	1.71234i	−0.0756655	−	0.997133i	$-0.524108\pi$
$47$	4.27274	−	11.7392i	0.623243	−	1.71234i	0.698908	−	0.715212i	$-0.253670\pi$
$48$	−0.0123619	+	0.0339642i	−0.00178429	+	0.00490231i
$49$	−1.81196	+	3.13841i	−0.258851	+	0.448344i
$50$		0			0
$51$	0.0423149	+	0.239980i	0.00592527	+	0.0336039i
$52$	−1.53825	+	1.83321i	−0.213317	+	0.254221i
$53$	1.23503	+	1.47185i	0.169644	+	0.202174i	0.844167	−	0.536080i	$-0.180095\pi$
$53$	1.23503	+	1.47185i	0.169644	+	0.202174i	−0.674524	+	0.738253i	$0.735651\pi$
$54$	−0.0376497	+	0.213522i	−0.00512348	+	0.0290567i
$55$		0			0
$56$	−1.83741			−0.245534
$57$	−0.156663	−	0.0166738i	−0.0207505	−	0.00220849i
$58$			3.30157i			0.433518i
$59$	−4.46726	+	1.62595i	−0.581587	+	0.211681i	−0.616025	−	0.787726i	$-0.711258\pi$
$59$	−4.46726	+	1.62595i	−0.581587	+	0.211681i	0.0344379	+	0.999407i	$0.489036\pi$
$60$		0			0
$61$	10.4674	−	8.78317i	1.34021	−	1.12457i	0.358638	−	0.933477i	$-0.383241\pi$
$61$	10.4674	−	8.78317i	1.34021	−	1.12457i	0.981572	−	0.191093i	$-0.0612033\pi$
$62$	−2.25222	+	2.68410i	−0.286033	+	0.340881i
$63$	−5.42613	+	0.956772i	−0.683628	+	0.120542i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−0.0837473	−	0.0304815i	−0.0103086	−	0.00375202i
$67$	−1.27151	+	3.49344i	−0.155340	+	0.426792i	−0.992812	−	0.119688i	$-0.961810\pi$
$67$	−1.27151	+	3.49344i	−0.155340	+	0.426792i	0.837472	+	0.546480i	$0.184033\pi$
$68$	5.83873	+	3.37099i	0.708050	+	0.408793i
$69$	0.0292932	+	0.0507373i	0.00352648	+	0.00610805i
$70$		0			0
$71$	4.46844	+	3.74946i	0.530306	+	0.444980i	0.868207	−	0.496202i	$-0.165272\pi$
$71$	4.46844	+	3.74946i	0.530306	+	0.444980i	−0.337901	+	0.941182i	$0.609717\pi$
$72$	1.92752	+	2.29713i	0.227161	+	0.270720i
$73$	0.502654	+	0.0886314i	0.0588311	+	0.0103735i	0.202986	−	0.979182i	$-0.434935\pi$
$73$	0.502654	+	0.0886314i	0.0588311	+	0.0103735i	−0.144155	+	0.989555i	$0.546046\pi$
$74$	5.64650	−	2.05516i	0.656393	−	0.238907i
$75$		0			0
$76$	−3.13950	+	3.02383i	−0.360125	+	0.346857i
$77$		−	4.53061i		−	0.516311i
$78$	−0.0295833	−	0.0812794i	−0.00334965	−	0.00920307i
$79$	−2.10729	+	11.9511i	−0.237089	+	1.34460i	0.601080	+	0.799189i	$0.294737\pi$
$79$	−2.10729	+	11.9511i	−0.237089	+	1.34460i	−0.838169	+	0.545411i	$0.816374\pi$
$80$		0			0
$81$	6.88539	+	5.77753i	0.765044	+	0.641948i
$82$	−7.85939	+	1.38582i	−0.867924	+	0.153038i
$83$	−5.39755	+	3.11628i	−0.592459	+	0.342056i	−0.766069	−	0.642758i	$-0.777790\pi$
$83$	−5.39755	+	3.11628i	−0.592459	+	0.342056i	0.173610	+	0.984814i	$0.444457\pi$
$84$	0.0332056	−	0.0575138i	0.00362303	−	0.00627527i
$85$		0			0
$86$	5.36981	+	1.95445i	0.579042	+	0.210754i
$87$	−0.103344	−	0.0596659i	−0.0110797	−	0.00639685i
$88$	−2.13541	+	1.23288i	−0.227635	+	0.131425i
$89$	−2.95236	−	16.7437i	−0.312949	−	1.77482i	−0.583494	−	0.812117i	$-0.698315\pi$
$89$	−2.95236	−	16.7437i	−0.312949	−	1.77482i	0.270545	−	0.962707i	$-0.412796\pi$
$90$		0			0
$91$	3.36837	−	2.82640i	0.353101	−	0.296287i
$92$	1.59629	+	0.281470i	0.166425	+	0.0293452i
$93$	−0.0433143	−	0.119005i	−0.00449148	−	0.0123402i
$94$	12.4926			1.28852
$95$		0			0
$96$	−0.0361439			−0.00368892
$97$	4.67194	+	12.8360i	0.474363	+	1.30330i	0.914214	+	0.405232i	$0.132809\pi$
$97$	4.67194	+	12.8360i	0.474363	+	1.30330i	−0.439851	+	0.898071i	$0.644969\pi$
$98$	−3.56887	−	0.629287i	−0.360510	−	0.0635676i
$99$	−5.66417	+	4.75280i	−0.569270	+	0.477675i
$100$		0			0
$101$	−1.85079	−	10.4964i	−0.184161	−	1.04443i	−0.927029	−	0.374990i	$-0.877646\pi$
$101$	−1.85079	−	10.4964i	−0.184161	−	1.04443i	0.742868	−	0.669438i	$-0.233465\pi$
$102$	−0.211034	+	0.121841i	−0.0208955	+	0.0120640i
$103$	−8.44314	−	4.87465i	−0.831927	−	0.480313i	0.0225848	−	0.999745i	$-0.492810\pi$
$103$	−8.44314	−	4.87465i	−0.831927	−	0.480313i	−0.854512	+	0.519431i	$0.826144\pi$
$104$	−2.24877	−	0.818485i	−0.220510	−	0.0802591i
$105$		0			0
$106$	−0.960680	+	1.66395i	−0.0933095	+	0.161617i
$107$	11.5058	−	6.64287i	1.11231	−	0.642191i	0.172881	−	0.984943i	$-0.444692\pi$
$107$	11.5058	−	6.64287i	1.11231	−	0.642191i	0.939426	+	0.342752i	$0.111359\pi$
$108$	−0.213522	+	0.0376497i	−0.0205462	+	0.00362285i
$109$	−1.10611	−	0.928135i	−0.105946	−	0.0888992i	0.588276	−	0.808660i	$-0.299807\pi$
$109$	−1.10611	−	0.928135i	−0.105946	−	0.0888992i	−0.694222	+	0.719761i	$0.744251\pi$
$110$		0			0
$111$	−0.0377137	+	0.213885i	−0.00357963	+	0.0203011i
$112$	−0.628432	−	1.72660i	−0.0593812	−	0.163149i
$113$			0.841529i			0.0791644i	0.999216	+	0.0395822i	$0.0126027\pi$
$113$			0.841529i			0.0791644i	−0.999216	+	0.0395822i	$0.987397\pi$
$114$	−0.0379136	−	0.152918i	−0.00355094	−	0.0143221i
$115$		0			0
$116$	−3.10246	+	1.12920i	−0.288056	+	0.104844i
$117$	−7.06713	−	1.24612i	−0.653356	−	0.115204i
$118$	−3.05578	−	3.64174i	−0.281308	−	0.335250i
$119$	−9.48960	−	7.96272i	−0.869910	−	0.729941i
$120$		0			0
$121$	2.46002	+	4.26089i	0.223639	+	0.387353i
$122$	11.8335	+	6.83209i	1.07136	+	0.618549i
$123$	0.0986562	−	0.271056i	0.00889553	−	0.0244403i
$124$	−3.29253	−	1.19838i	−0.295678	−	0.107618i
$125$		0			0
$126$	−2.75492	−	4.77166i	−0.245427	−	0.425093i
$127$	−12.7885	+	2.25496i	−1.13480	+	0.200095i	−0.709329	−	0.704878i	$-0.751002\pi$
$127$	−12.7885	+	2.25496i	−1.13480	+	0.200095i	−0.425469	+	0.904973i	$0.639891\pi$
$128$	−0.642788	+	0.766044i	−0.0568149	+	0.0677094i
$129$	−0.158220	+	0.132763i	−0.0139305	+	0.0116891i
$130$		0			0
$131$	−8.39051	+	3.05389i	−0.733082	+	0.266820i	−0.681469	−	0.731847i	$-0.738658\pi$
$131$	−8.39051	+	3.05389i	−0.733082	+	0.266820i	−0.0516131	+	0.998667i	$0.516436\pi$
$132$		−	0.0891221i		−	0.00775708i
$133$	6.64571	−	4.46991i	0.576256	−	0.387590i
$134$	−3.71765			−0.321156
$135$		0			0
$136$	−1.17073	+	6.63956i	−0.100390	+	0.569337i
$137$	2.86271	+	3.41165i	0.244578	+	0.291477i	0.874343	−	0.485309i	$-0.161293\pi$
$137$	2.86271	+	3.41165i	0.244578	+	0.291477i	−0.629764	+	0.776786i	$0.716849\pi$
$138$	−0.0376586	+	0.0448798i	−0.00320571	+	0.00382042i
$139$	0.210369	+	1.19306i	0.0178433	+	0.101194i	0.992429	−	0.122822i	$-0.0391943\pi$
$139$	0.210369	+	1.19306i	0.0178433	+	0.101194i	−0.974585	+	0.224016i	$0.928083\pi$
$140$		0			0
$141$	−0.225767	+	0.391039i	−0.0190130	+	0.0329314i
$142$	−1.99505	+	5.48135i	−0.167421	+	0.459985i
$143$	2.01819	−	5.54492i	0.168769	−	0.463689i
$144$	−1.49935	+	2.59694i	−0.124946	+	0.216412i
$145$		0			0
$146$	0.0886314	+	0.502654i	0.00733519	+	0.0415999i
$147$	0.0841940	−	0.100339i	0.00694421	−	0.00827578i
$148$	3.86244	+	4.60307i	0.317490	+	0.378370i
$149$	−1.61216	+	9.14300i	−0.132073	+	0.749024i	0.844780	+	0.535114i	$0.179731\pi$
$149$	−1.61216	+	9.14300i	−0.132073	+	0.749024i	−0.976853	+	0.213910i	$0.931380\pi$
$150$		0			0
$151$	−3.34570			−0.272269			−0.136135	−	0.990690i	$-0.543468\pi$
$151$	−3.34570			−0.272269			−0.136135	+	0.990690i	$0.543468\pi$
$152$	−3.91524	−	1.91595i	−0.317568	−	0.155404i
$153$			20.2171i			1.63446i
$154$	4.25738	−	1.54956i	0.343069	−	0.124867i
$155$		0			0
$156$	0.0662595	−	0.0555984i	0.00530501	−	0.00445143i
$157$	−4.53369	+	5.40304i	−0.361828	+	0.431210i	−0.915991	−	0.401198i	$-0.868594\pi$
$157$	−4.53369	+	5.40304i	−0.361828	+	0.431210i	0.554163	+	0.832408i	$0.313038\pi$
$158$	−11.9511	+	2.10729i	−0.950775	+	0.167647i
$159$	−0.0347227	−	0.0601415i	−0.00275369	−	0.00476953i
$160$		0			0
$161$	−2.79868	−	1.01864i	−0.220567	−	0.0802798i
$162$	−3.07416	+	8.44619i	−0.241529	+	0.663595i
$163$	−13.7316	−	7.92794i	−1.07554	−	0.620964i	−0.145851	−	0.989307i	$-0.546592\pi$
$163$	−13.7316	−	7.92794i	−1.07554	−	0.620964i	−0.929690	+	0.368343i	$0.879925\pi$
$164$	−3.99032	−	6.91143i	−0.311591	−	0.539692i
$165$		0			0
$166$	−4.77442	−	4.00621i	−0.370567	−	0.310942i
$167$	−8.75846	−	10.4379i	−0.677750	−	0.807711i	0.312066	−	0.950060i	$-0.398979\pi$
$167$	−8.75846	−	10.4379i	−0.677750	−	0.807711i	−0.989817	+	0.142349i	$0.954534\pi$
$168$	0.0654023	+	0.0115322i	0.00504590	+	0.000889728i
$169$	−6.83449	+	2.48755i	−0.525730	+	0.191350i
$170$		0			0
$171$	−12.5599	−	3.61934i	−0.960481	−	0.276778i
$172$			5.71443i			0.435721i
$173$	4.11774	+	11.3134i	0.313066	+	0.860142i	0.992034	+	0.125973i	$0.0402054\pi$
$173$	4.11774	+	11.3134i	0.313066	+	0.860142i	−0.678968	+	0.734168i	$0.737572\pi$
$174$	0.0207217	−	0.117519i	0.00157091	−	0.00890908i
$175$		0			0
$176$	−1.88888	−	1.58496i	−0.142380	−	0.119471i
$177$	0.169216	−	0.0298374i	0.0127191	−	0.00224271i
$178$	14.7241	−	8.50098i	1.10362	−	0.637175i
$179$	8.03649	−	13.9196i	0.600675	−	1.04040i	−0.392044	−	0.919947i	$-0.628232\pi$
$179$	8.03649	−	13.9196i	0.600675	−	1.04040i	0.992719	−	0.120454i	$-0.0384349\pi$
$180$		0			0
$181$	−5.40615	−	1.96768i	−0.401836	−	0.146256i	0.133193	−	0.991090i	$-0.457477\pi$
$181$	−5.40615	−	1.96768i	−0.401836	−	0.146256i	−0.535029	+	0.844834i	$0.679699\pi$
$182$	3.80799	+	2.19855i	0.282267	+	0.162967i
$183$	−0.427710	+	0.246939i	−0.0316173	+	0.0182542i
$184$	0.281470	+	1.59629i	0.0207502	+	0.117680i
$185$		0			0
$186$	0.0970138	−	0.0814042i	0.00711339	−	0.00596885i
$187$	−16.3715	−	2.88674i	−1.19720	−	0.211099i
$188$	4.27274	+	11.7392i	0.311621	+	0.856172i
$189$	0.398381			0.0289779
$190$		0			0
$191$	−20.5460			−1.48666			−0.743329	−	0.668926i	$-0.766754\pi$
$191$	−20.5460			−1.48666			−0.743329	+	0.668926i	$0.766754\pi$
$192$	−0.0123619	−	0.0339642i	−0.000892147	−	0.00245115i
$193$	12.3238	+	2.17302i	0.887089	+	0.156418i	0.598583	−	0.801060i	$-0.295731\pi$
$193$	12.3238	+	2.17302i	0.887089	+	0.156418i	0.288506	+	0.957478i	$0.406842\pi$
$194$	−10.4640	+	8.78037i	−0.751274	+	0.630394i
$195$		0			0
$196$	−0.629287	−	3.56887i	−0.0449491	−	0.254919i
$197$	5.21647	−	3.01173i	0.371658	−	0.214577i	−0.302524	−	0.953142i	$-0.597829\pi$
$197$	5.21647	−	3.01173i	0.371658	−	0.214577i	0.674183	+	0.738565i	$0.264496\pi$
$198$	−6.40343	−	3.69702i	−0.455072	−	0.262736i
$199$	10.5749	+	3.84894i	0.749633	+	0.272844i	0.688451	−	0.725283i	$-0.258291\pi$
$199$	10.5749	+	3.84894i	0.749633	+	0.272844i	0.0611814	+	0.998127i	$0.480513\pi$
$200$		0			0
$201$	0.0671851	−	0.116368i	0.00473887	−	0.00820797i
$202$	9.23035	−	5.32914i	0.649445	−	0.374957i
$203$	5.97418	−	1.05341i	0.419305	−	0.0739349i
$204$	−0.186671	−	0.156636i	−0.0130696	−	0.0109667i
$205$		0			0
$206$	1.69295	−	9.60119i	0.117953	−	0.668946i
$207$	1.66244	+	4.56751i	0.115547	+	0.317464i
$208$		−	2.39309i		−	0.165931i
$209$	4.72427	−	9.65403i	0.326785	−	0.667783i
$210$		0			0
$211$	−13.2192	+	4.81141i	−0.910049	+	0.331231i	−0.754273	−	0.656561i	$-0.772010\pi$
$211$	−13.2192	+	4.81141i	−0.910049	+	0.331231i	−0.155777	+	0.987792i	$0.549788\pi$
$212$	−1.89217	−	0.333641i	−0.129955	−	0.0229145i
$213$	−0.135520	−	0.161507i	−0.00928570	−	0.0110663i
$214$	10.1775	+	8.53991i	0.695718	+	0.583776i
$215$		0			0
$216$	−0.108408	−	0.187768i	−0.00737624	−	0.0127760i
$217$	5.57547	+	3.21900i	0.378487	+	0.218520i
$218$	0.493850	−	1.35684i	0.0334477	−	0.0918969i
$219$	−0.0173356	−	0.00630963i	−0.00117143	−	0.000426366i
$220$		0			0
$221$	−8.06709	−	13.9726i	−0.542651	−	0.939899i
$222$	−0.213885	+	0.0377137i	−0.0143550	+	0.00253118i
$223$	16.2641	−	19.3828i	1.08913	−	1.29797i	0.137570	−	0.990492i	$-0.456071\pi$
$223$	16.2641	−	19.3828i	1.08913	−	1.29797i	0.951555	−	0.307477i	$-0.0994848\pi$
$224$	1.40754	−	1.18107i	0.0940451	−	0.0789132i
$225$		0			0
$226$	−0.790779	+	0.287820i	−0.0526018	+	0.0191455i
$227$			22.0111i			1.46093i	0.682951	+	0.730464i	$0.260696\pi$
$227$			22.0111i			1.46093i	−0.682951	+	0.730464i	$0.739304\pi$
$228$	0.130728	−	0.0879281i	0.00865770	−	0.00582318i
$229$	5.29529			0.349923			0.174961	−	0.984575i	$-0.444020\pi$
$229$	5.29529			0.349923			0.174961	+	0.984575i	$0.444020\pi$
$230$		0			0
$231$	−0.0284356	+	0.161266i	−0.00187092	+	0.0106105i
$232$	−2.12221	−	2.52915i	−0.139330	−	0.166047i
$233$	13.2104	−	15.7436i	0.865445	−	1.03140i	−0.133740	−	0.991016i	$-0.542699\pi$
$233$	13.2104	−	15.7436i	0.865445	−	1.03140i	0.999184	−	0.0403803i	$-0.0128569\pi$
$234$	−1.24612	−	7.06713i	−0.0814617	−	0.461992i
$235$		0			0
$236$	2.37698	−	4.11705i	0.154728	−	0.267997i
$237$	0.150017	−	0.412170i	0.00974468	−	0.0267733i
$238$	4.23688	−	11.6407i	0.274636	−	0.754556i
$239$	0.443585	−	0.768312i	0.0286931	−	0.0496980i	−0.851322	−	0.524643i	$-0.824199\pi$
$239$	0.443585	−	0.768312i	0.0286931	−	0.0496980i	0.880015	+	0.474945i	$0.157532\pi$
$240$		0			0
$241$	−0.694839	−	3.94063i	−0.0447585	−	0.253838i	0.954216	−	0.299119i	$-0.0966928\pi$
$241$	−0.694839	−	3.94063i	−0.0447585	−	0.253838i	−0.998974	+	0.0452809i	$0.985582\pi$
$242$	−3.16255	+	3.76898i	−0.203296	+	0.242279i
$243$	−0.626923	−	0.747138i	−0.0402171	−	0.0479289i
$244$	−2.37276	+	13.4566i	−0.151900	+	0.861471i
$245$		0			0
$246$	0.288451			0.0183910
$247$	10.1247	−	2.51027i	0.644219	−	0.159724i
$248$		−	3.50384i		−	0.222494i
$249$	0.211684	−	0.0770466i	0.0134149	−	0.00488263i
$250$		0			0
$251$	−9.70480	+	8.14329i	−0.612561	+	0.514000i	−0.895455	−	0.445151i	$-0.853150\pi$
$251$	−9.70480	+	8.14329i	−0.612561	+	0.514000i	0.282894	+	0.959151i	$0.408706\pi$
$252$	3.54165	−	4.22078i	0.223103	−	0.265884i
$253$	−3.93607	+	0.694035i	−0.247459	+	0.0436336i
$254$	−6.49290	−	11.2460i	−0.407401	−	0.705639i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−4.46158	+	12.2581i	−0.278306	+	0.764639i	0.719249	+	0.694752i	$0.244486\pi$
$257$	−4.46158	+	12.2581i	−0.278306	+	0.764639i	−0.997555	+	0.0698866i	$0.977736\pi$
$258$	−0.178871	−	0.103271i	−0.0111360	−	0.00642937i
$259$	−5.52039	−	9.56160i	−0.343021	−	0.594129i
$260$		0			0
$261$	−7.58415	−	6.36386i	−0.469447	−	0.393913i
$262$	−5.73944	−	6.84000i	−0.354584	−	0.422577i
$263$	−27.8224	−	4.90583i	−1.71560	−	0.302507i	−0.772500	−	0.635015i	$-0.780994\pi$
$263$	−27.8224	−	4.90583i	−1.71560	−	0.302507i	−0.943100	+	0.332508i	$0.892105\pi$
$264$	0.0837473	−	0.0304815i	0.00515429	−	0.00187601i
$265$		0			0
$266$	6.47331	+	4.71612i	0.396904	+	0.289164i
$267$			0.614517i			0.0376079i
$268$	−1.27151	−	3.49344i	−0.0776698	−	0.213396i
$269$	−5.13013	+	29.0944i	−0.312789	+	1.77392i	0.271566	+	0.962420i	$0.412458\pi$
$269$	−5.13013	+	29.0944i	−0.312789	+	1.77392i	−0.584356	+	0.811498i	$0.698653\pi$
$270$		0			0
$271$	20.6918	+	17.3624i	1.25693	+	1.05469i	0.996001	+	0.0893367i	$0.0284747\pi$
$271$	20.6918	+	17.3624i	1.25693	+	1.05469i	0.260933	+	0.965357i	$0.415970\pi$
$272$	−6.63956	+	1.17073i	−0.402582	+	0.0709861i
$273$	−0.137636	+	0.0794641i	−0.00833010	+	0.00480938i
$274$	−2.22680	+	3.85692i	−0.134526	+	0.233005i
$275$		0			0
$276$	−0.0550532	−	0.0200377i	−0.00331381	−	0.00120613i
$277$	20.9386	+	12.0889i	1.25808	+	0.726352i	0.972701	−	0.232063i	$-0.0745474\pi$
$277$	20.9386	+	12.0889i	1.25808	+	0.726352i	0.285378	+	0.958415i	$0.407881\pi$
$278$	−1.04916	+	0.605735i	−0.0629246	+	0.0363295i
$279$	−1.82451	−	10.3473i	−0.109231	−	0.619478i
$280$		0			0
$281$	1.83928	−	1.54334i	0.109722	−	0.0920681i	−0.586276	−	0.810111i	$-0.699407\pi$
$281$	1.83928	−	1.54334i	0.109722	−	0.0920681i	0.695998	+	0.718043i	$0.254962\pi$
$282$	−0.444673	−	0.0784079i	−0.0264799	−	0.00466912i
$283$	2.78778	+	7.65937i	0.165716	+	0.455302i	0.994558	−	0.104181i	$-0.0332220\pi$
$283$	2.78778	+	7.65937i	0.165716	+	0.455302i	−0.828842	+	0.559483i	$0.811000\pi$
$284$	−5.83313			−0.346133
$285$		0			0
$286$	5.90078			0.348920
$287$	5.01528	+	13.7794i	0.296043	+	0.813371i
$288$	−2.95314	−	0.520718i	−0.174015	−	0.0306836i
$289$	−21.7973	+	18.2901i	−1.28219	+	1.07589i
$290$		0			0
$291$	−0.0857335	−	0.486219i	−0.00502579	−	0.0285027i
$292$	−0.442026	+	0.255204i	−0.0258676	+	0.0149347i
$293$	7.96532	+	4.59878i	0.465339	+	0.268664i	0.714287	−	0.699853i	$-0.246751\pi$
$293$	7.96532	+	4.59878i	0.465339	+	0.268664i	−0.248947	+	0.968517i	$0.580085\pi$
$294$	0.123083	+	0.0447987i	0.00717837	+	0.00261271i
$295$		0			0
$296$	−3.00444	+	5.20385i	−0.174630	+	0.302467i
$297$	0.462991	−	0.267308i	0.0268655	−	0.0155108i
$298$	−9.14300	+	1.61216i	−0.529640	+	0.0933898i
$299$	−2.97149	−	2.49338i	−0.171846	−	0.144196i
$300$		0			0
$301$	1.82326	−	10.3402i	0.105091	−	0.596002i
$302$	−1.14430	−	3.14393i	−0.0658469	−	0.180913i
$303$			0.385232i			0.0221310i
$304$	0.461316	−	4.33442i	0.0264583	−	0.248596i
$305$		0			0
$306$	−18.9979	+	6.91467i	−1.08604	+	0.395285i
$307$	−27.9165	−	4.92243i	−1.59328	−	0.280938i	−0.694550	−	0.719444i	$-0.744397\pi$
$307$	−27.9165	−	4.92243i	−1.59328	−	0.280938i	−0.898728	+	0.438506i	$0.855508\pi$
$308$	2.91222	+	3.47065i	0.165939	+	0.197758i
$309$	0.269937	+	0.226504i	0.0153562	+	0.0128854i
$310$		0			0
$311$	−8.72043	−	15.1042i	−0.494490	−	0.856482i	0.505490	−	0.862833i	$-0.331312\pi$
$311$	−8.72043	−	15.1042i	−0.494490	−	0.856482i	−0.999980	+	0.00635057i	$0.997979\pi$
$312$	0.0749075	+	0.0432478i	0.00424080	+	0.00244843i
$313$	4.51409	−	12.4024i	0.255151	−	0.701022i	−0.744298	−	0.667847i	$-0.767216\pi$
$313$	4.51409	−	12.4024i	0.255151	−	0.701022i	0.999450	−	0.0331750i	$-0.0105619\pi$
$314$	−6.62781	−	2.41233i	−0.374029	−	0.136135i
$315$		0			0
$316$	−6.06771	−	10.5096i	−0.341336	−	0.591210i
$317$	12.0997	−	2.13351i	0.679588	−	0.119830i	0.176810	−	0.984245i	$-0.443422\pi$
$317$	12.0997	−	2.13351i	0.679588	−	0.119830i	0.502778	+	0.864415i	$0.332311\pi$
$318$	0.0446387	−	0.0531983i	0.00250321	−	0.00298321i
$319$	6.23627	−	5.23285i	0.349164	−	0.292983i
$320$		0			0
$321$	−0.451239	+	0.164238i	−0.0251857	+	0.00916685i
$322$		−	2.97829i		−	0.165974i
$323$	−11.9178	−	26.8626i	−0.663124	−	1.49467i
$324$	−8.98824			−0.499347
$325$		0			0
$326$	2.75334	−	15.6150i	0.152494	−	0.864834i
$327$	0.0335464	+	0.0399791i	0.00185512	+	0.00221085i
$328$	5.12985	−	6.11352i	0.283249	−	0.337563i
$329$	−3.98594	−	22.6054i	−0.219752	−	1.24628i
$330$		0			0
$331$	−0.498297	+	0.863076i	−0.0273889	+	0.0474389i	−0.879395	−	0.476093i	$-0.842053\pi$
$331$	−0.498297	+	0.863076i	−0.0273889	+	0.0474389i	0.852006	+	0.523532i	$0.175386\pi$
$332$	2.13166	−	5.85669i	0.116990	−	0.321428i
$333$	−6.16279	+	16.9321i	−0.337719	+	0.927875i
$334$	6.81287	−	11.8002i	0.372784	−	0.645681i
$335$		0			0
$336$	0.0115322	+	0.0654023i	0.000629132	+	0.00356799i
$337$	−5.50174	+	6.55672i	−0.299699	+	0.357167i	−0.894787	−	0.446493i	$-0.852673\pi$
$337$	−5.50174	+	6.55672i	−0.299699	+	0.357167i	0.595088	+	0.803660i	$0.297117\pi$
$338$	−4.67507	−	5.57153i	−0.254290	−	0.303051i
$339$	0.00528171	−	0.0299541i	0.000286863	−	0.00162688i
$340$		0			0
$341$	8.63961			0.467861
$342$	−0.894680	−	13.0403i	−0.0483788	−	0.705141i
$343$			19.5205i			1.05401i
$344$	−5.36981	+	1.95445i	−0.289521	+	0.105377i
$345$		0			0
$346$	−9.22276	+	7.73882i	−0.495819	+	0.416041i
$347$	4.26665	−	5.08479i	0.229046	−	0.272966i	−0.639265	−	0.768986i	$-0.720761\pi$
$347$	4.26665	−	5.08479i	0.229046	−	0.272966i	0.868311	+	0.496020i	$0.165206\pi$
$348$	0.117519	−	0.0207217i	0.00629967	−	0.00111080i
$349$	15.5221	+	26.8851i	0.830881	+	1.43913i	0.897341	+	0.441339i	$0.145496\pi$
$349$	15.5221	+	26.8851i	0.830881	+	1.43913i	−0.0664599	+	0.997789i	$0.521170\pi$
$350$		0			0
$351$	0.487570	+	0.177461i	0.0260246	+	0.00947216i
$352$	0.843338	−	2.31705i	0.0449501	−	0.123499i
$353$	15.3831	+	8.88145i	0.818761	+	0.472712i	0.849989	−	0.526800i	$-0.176608\pi$
$353$	15.3831	+	8.88145i	0.818761	+	0.472712i	−0.0312277	+	0.999512i	$0.509942\pi$
$354$	0.0859133	+	0.148806i	0.00456624	+	0.00790896i
$355$		0			0
$356$	13.0243	+	10.9287i	0.690284	+	0.579217i
$357$	0.287804	+	0.342991i	0.0152322	+	0.0181530i
$358$	15.8288	+	2.79104i	0.836578	+	0.147511i
$359$	−4.82640	+	1.75667i	−0.254728	+	0.0927134i	−0.466228	−	0.884665i	$-0.654387\pi$
$359$	−4.82640	+	1.75667i	−0.254728	+	0.0927134i	0.211500	+	0.977378i	$0.432165\pi$
$360$		0			0
$361$	18.8220	−	2.59491i	0.990630	−	0.136574i
$362$		−	5.75310i		−	0.302376i
$363$	−0.0608214	−	0.167105i	−0.00319229	−	0.00877076i
$364$	−0.763547	+	4.33029i	−0.0400207	+	0.226969i
$365$		0			0
$366$	−0.378332	−	0.317458i	−0.0197757	−	0.0165938i
$367$	5.65859	−	0.997763i	0.295376	−	0.0520828i	−0.0239963	−	0.999712i	$-0.507639\pi$
$367$	5.65859	−	0.997763i	0.295376	−	0.0520828i	0.319372	+	0.947629i	$0.396528\pi$
$368$	−1.40376	+	0.810460i	−0.0731759	+	0.0422481i
$369$	11.9657	−	20.7253i	0.622911	−	1.07891i
$370$		0			0
$371$	3.31742	+	1.20744i	0.172232	+	0.0626873i
$372$	0.109676	+	0.0633212i	0.00568641	+	0.00328305i
$373$	−32.7231	+	18.8927i	−1.69434	+	0.978227i	−0.743399	+	0.668848i	$0.766788\pi$
$373$	−32.7231	+	18.8927i	−1.69434	+	0.978227i	−0.950939	+	0.309379i	$0.899879\pi$
$374$	−2.88674	−	16.3715i	−0.149270	−	0.846551i
$375$		0			0
$376$	−9.56992	+	8.03012i	−0.493531	+	0.414122i
$377$	7.78093	+	1.37199i	0.400738	+	0.0706610i
$378$	0.136254	+	0.374355i	0.00700816	+	0.0192548i
$379$	32.2663			1.65741			0.828703	−	0.559689i	$-0.189079\pi$
$379$	32.2663			1.65741			0.828703	+	0.559689i	$0.189079\pi$
$380$		0			0
$381$	0.469358			0.0240459
$382$	−7.02715	−	19.3069i	−0.359540	−	0.987829i
$383$	21.4490	+	3.78204i	1.09599	+	0.193253i	0.692277	−	0.721632i	$-0.256608\pi$
$383$	21.4490	+	3.78204i	1.09599	+	0.193253i	0.403715	+	0.914885i	$0.367719\pi$
$384$	0.0276878	−	0.0232329i	0.00141294	−	0.00118560i
$385$		0			0
$386$	2.17302	+	12.3238i	0.110604	+	0.627267i
$387$	−14.8401	+	8.56792i	−0.754363	+	0.435532i
$388$	−11.8298	−	6.82991i	−0.600565	−	0.346736i
$389$	9.10078	+	3.31241i	0.461428	+	0.167946i	0.562265	−	0.826957i	$-0.309930\pi$
$389$	9.10078	+	3.31241i	0.461428	+	0.167946i	−0.100837	+	0.994903i	$0.532152\pi$
$390$		0			0
$391$	−5.46410	+	9.46411i	−0.276332	+	0.478620i
$392$	3.13841	−	1.81196i	0.158514	−	0.0915178i
$393$	0.317826	−	0.0560412i	0.0160322	−	0.00282691i
$394$	4.61424	+	3.87181i	0.232462	+	0.195059i
$395$		0			0
$396$	1.28396	−	7.28171i	0.0645216	−	0.365920i
$397$	6.29151	+	17.2858i	0.315762	+	0.867549i	0.991465	+	0.130375i	$0.0416180\pi$
$397$	6.29151	+	17.2858i	0.315762	+	0.867549i	−0.675703	+	0.737174i	$0.736160\pi$
$398$			11.2535i			0.564089i
$399$	−0.264607	+	0.117395i	−0.0132469	+	0.00587710i
$400$		0			0
$401$	34.3332	−	12.4963i	1.71452	−	0.624034i	0.717178	−	0.696890i	$-0.245433\pi$
$401$	34.3332	−	12.4963i	1.71452	−	0.624034i	0.997342	+	0.0728556i	$0.0232112\pi$
$402$	0.132329	+	0.0233331i	0.00659996	+	0.00116375i
$403$	5.38978	+	6.42329i	0.268484	+	0.319967i
$404$	8.16472	+	6.85102i	0.406210	+	0.340851i
$405$		0			0
$406$	3.03317	+	5.25361i	0.150534	+	0.260732i
$407$	−12.8314	−	7.40822i	−0.636030	−	0.367212i
$408$	0.0833440	−	0.228986i	0.00412614	−	0.0113365i
$409$	34.1168	+	12.4175i	1.68697	+	0.614005i	0.994238	−	0.107194i	$-0.0341866\pi$
$409$	34.1168	+	12.4175i	1.68697	+	0.614005i	0.692728	+	0.721199i	$0.256409\pi$
$410$		0			0
$411$	−0.0804851	−	0.139404i	−0.00397004	−	0.00687631i
$412$	9.60119	−	1.69295i	0.473016	−	0.0834056i
$413$	−5.61473	+	6.69138i	−0.276283	+	0.329261i
$414$	−3.72347	+	3.12436i	−0.182998	+	0.153554i
$415$		0			0
$416$	2.24877	−	0.818485i	0.110255	−	0.0401295i
$417$		−	0.0437872i		−	0.00214427i
$418$	10.6876	+	1.13749i	0.522749	+	0.0556366i
$419$	−39.5001			−1.92970			−0.964852	−	0.262793i	$-0.915356\pi$
$419$	−39.5001			−1.92970			−0.964852	+	0.262793i	$0.915356\pi$
$420$		0			0
$421$	−2.44853	+	13.8863i	−0.119334	+	0.676777i	0.865179	+	0.501464i	$0.167205\pi$
$421$	−2.44853	+	13.8863i	−0.119334	+	0.676777i	−0.984513	+	0.175313i	$0.943906\pi$
$422$	−9.04248	−	10.7764i	−0.440181	−	0.524588i
$423$	−24.0799	+	28.6973i	−1.17080	+	1.39531i
$424$	−0.333641	−	1.89217i	−0.0162030	−	0.0918919i
$425$		0			0
$426$	0.105416	−	0.182586i	0.00510743	−	0.00884632i
$427$	8.58701	−	23.5926i	0.415554	−	1.14173i
$428$	−4.54399	+	12.4845i	−0.219642	+	0.603462i
$429$	−0.106639	+	0.184703i	−0.00514856	+	0.00891757i
$430$		0			0
$431$	3.65410	+	20.7234i	0.176012	+	0.998213i	0.936969	+	0.349411i	$0.113618\pi$
$431$	3.65410	+	20.7234i	0.176012	+	0.998213i	−0.760958	+	0.648802i	$0.775270\pi$
$432$	0.139367	−	0.166091i	0.00670529	−	0.00799105i
$433$	3.37958	+	4.02763i	0.162412	+	0.193555i	0.841113	−	0.540860i	$-0.181901\pi$
$433$	3.37958	+	4.02763i	0.162412	+	0.193555i	−0.678701	+	0.734415i	$0.737457\pi$
$434$	−1.11795	+	6.34019i	−0.0536631	+	0.304339i
$435$		0			0
$436$	1.44392			0.0691513
$437$	−4.90138	−	5.08887i	−0.234465	−	0.243434i
$438$		−	0.0184481i		−	0.000881486i
$439$	34.2836	−	12.4782i	1.63627	−	0.595552i	0.649885	−	0.760032i	$-0.274817\pi$
$439$	34.2836	−	12.4782i	1.63627	−	0.595552i	0.986380	+	0.164480i	$0.0525947\pi$
$440$		0			0
$441$	8.32463	−	6.98519i	0.396411	−	0.332628i
$442$	10.3709	−	12.3595i	0.493291	−	0.587881i
$443$	−9.09046	+	1.60289i	−0.431901	+	0.0761558i	−0.385372	−	0.922761i	$-0.625927\pi$
$443$	−9.09046	+	1.60289i	−0.431901	+	0.0761558i	−0.0465285	+	0.998917i	$0.514816\pi$
$444$	−0.108592	−	0.188087i	−0.00515356	−	0.00892623i
$445$		0			0
$446$	23.7765	+	8.65395i	1.12585	+	0.409777i
$447$	0.114769	−	0.315325i	0.00542838	−	0.0149144i
$448$	1.59124	+	0.918706i	0.0751792	+	0.0434048i
$449$	−11.4148	−	19.7711i	−0.538699	−	0.933054i	−0.998974	−	0.0452780i	$-0.985583\pi$
$449$	−11.4148	−	19.7711i	−0.538699	−	0.933054i	0.460275	−	0.887776i	$-0.347751\pi$
$450$		0			0
$451$	15.0744	+	12.6490i	0.709828	+	0.595616i
$452$	−0.540925	−	0.644649i	−0.0254430	−	0.0303217i
$453$	0.119090	+	0.0209987i	0.00559532	+	0.000986605i
$454$	−20.6837	+	7.52824i	−0.970733	+	0.353318i
$455$		0			0
$456$	0.127337	+	0.0927713i	0.00596311	+	0.00434442i
$457$		−	7.82515i		−	0.366045i	−0.983109	−	0.183022i	$-0.941412\pi$
$457$		−	7.82515i		−	0.366045i	0.983109	−	0.183022i	$-0.0585881\pi$
$458$	1.81110	+	4.97594i	0.0846269	+	0.232511i
$459$	0.253834	−	1.43956i	0.0118480	−	0.0671931i
$460$		0			0
$461$	−3.01184	−	2.52724i	−0.140276	−	0.117705i	0.569950	−	0.821679i	$-0.306963\pi$
$461$	−3.01184	−	2.52724i	−0.140276	−	0.117705i	−0.710225	+	0.703974i	$0.751407\pi$
$462$	−0.161266	+	0.0284356i	−0.00750278	+	0.00132294i
$463$	14.9791	−	8.64820i	0.696139	−	0.401916i	−0.109769	−	0.993957i	$-0.535011\pi$
$463$	14.9791	−	8.64820i	0.696139	−	0.401916i	0.805908	+	0.592041i	$0.201678\pi$
$464$	1.65079	−	2.85924i	0.0766358	−	0.132737i
$465$		0			0
$466$	19.3124	+	7.02913i	0.894628	+	0.325618i
$467$	18.2097	+	10.5134i	0.842644	+	0.486501i	0.858162	−	0.513379i	$-0.171606\pi$
$467$	18.2097	+	10.5134i	0.842644	+	0.486501i	−0.0155178	+	0.999880i	$0.504940\pi$
$468$	6.21473	−	3.58807i	0.287276	−	0.165859i
$469$	1.18616	+	6.72707i	0.0547719	+	0.310627i
$470$		0			0
$471$	0.195287	−	0.163865i	0.00899836	−	0.00755052i
$472$	4.68173	+	0.825516i	0.215494	+	0.0379974i
$473$	−4.81920	−	13.2406i	−0.221587	−	0.608805i
$474$	0.438622			0.0201466
$475$		0			0
$476$	12.3878			0.567794
$477$	−1.97057	−	5.41410i	−0.0902263	−	0.247895i
$478$	0.873692	+	0.154055i	0.0399617	+	0.00704633i
$479$	−16.1878	+	13.5832i	−0.739640	+	0.620631i	−0.932741	−	0.360547i	$-0.882590\pi$
$479$	−16.1878	+	13.5832i	−0.739640	+	0.620631i	0.193101	+	0.981179i	$0.438145\pi$
$480$		0			0
$481$	−2.49703	−	14.1613i	−0.113855	−	0.645702i
$482$	3.46533	−	2.00071i	0.157841	−	0.0911298i
$483$	0.0932252	+	0.0538236i	0.00424190	+	0.00244906i
$484$	−4.62333	−	1.68276i	−0.210151	−	0.0764889i
$485$		0			0
$486$	0.487660	−	0.844651i	0.0221207	−	0.0383142i
$487$	−14.8959	+	8.60015i	−0.674998	+	0.389710i	−0.797968	−	0.602700i	$-0.794091\pi$
$487$	−14.8959	+	8.60015i	−0.674998	+	0.389710i	0.122970	+	0.992410i	$0.460758\pi$
$488$	−13.4566	+	2.37276i	−0.609152	+	0.107410i
$489$	0.439015	+	0.368377i	0.0198529	+	0.0166586i
$490$		0			0
$491$	−5.75424	+	32.6339i	−0.259685	+	1.47275i	0.524068	+	0.851676i	$0.324414\pi$
$491$	−5.75424	+	32.6339i	−0.259685	+	1.47275i	−0.783753	+	0.621072i	$0.786697\pi$
$492$	0.0986562	+	0.271056i	0.00444776	+	0.0122201i
$493$		−	22.2591i		−	1.00250i
$494$	5.82173	+	8.65554i	0.261932	+	0.389431i
$495$		0			0
$496$	3.29253	−	1.19838i	0.147839	−	0.0538090i
$497$	10.5550	+	1.86114i	0.473458	+	0.0834834i
$498$	0.144800	+	0.172566i	0.00648865	+	0.00773287i
$499$	24.4903	+	20.5498i	1.09634	+	0.919936i	0.997173	−	0.0751346i	$-0.0239386\pi$
$499$	24.4903	+	20.5498i	1.09634	+	0.919936i	0.0991642	+	0.995071i	$0.468383\pi$
$500$		0			0
$501$	0.246244	+	0.426507i	0.0110014	+	0.0190549i
$502$	−10.9714	−	6.33436i	−0.489679	−	0.282716i
$503$	8.63311	−	23.7193i	0.384931	−	1.05759i	−0.584321	−	0.811523i	$-0.698639\pi$
$503$	8.63311	−	23.7193i	0.384931	−	1.05759i	0.969253	−	0.246068i	$-0.0791387\pi$
$504$	5.17755	+	1.88447i	0.230626	+	0.0839411i
$505$		0			0
$506$	−1.99840	−	3.46132i	−0.0888395	−	0.153875i
$507$	0.258885	−	0.0456484i	0.0114975	−	0.00202732i
$508$	8.34711	−	9.94770i	0.370343	−	0.441358i
$509$	13.0617	−	10.9600i	0.578948	−	0.485795i	−0.305654	−	0.952143i	$-0.598875\pi$
$509$	13.0617	−	10.9600i	0.578948	−	0.485795i	0.884601	+	0.466348i	$0.154430\pi$
$510$		0			0
$511$	0.881271	−	0.320756i	0.0389851	−	0.0141894i
$512$		−	1.00000i		−	0.0441942i
$513$	0.848888	+	0.415410i	0.0374793	+	0.0183408i
$514$	−13.0448			−0.575381
$515$		0			0
$516$	0.0358656	−	0.203404i	0.00157890	−	0.00895437i
$517$	−19.8003	−	23.5971i	−0.870816	−	1.03780i
$518$	7.09688	−	8.45773i	0.311819	−	0.371612i
$519$	−0.0755636	−	0.428542i	−0.00331687	−	0.0188109i
$520$		0			0
$521$	3.40256	−	5.89342i	0.149069	−	0.258195i	−0.781815	−	0.623511i	$-0.785706\pi$
$521$	3.40256	−	5.89342i	0.149069	−	0.258195i	0.930884	+	0.365316i	$0.119039\pi$
$522$	3.38614	−	9.30333i	0.148207	−	0.407196i
$523$	−1.78561	+	4.90593i	−0.0780794	+	0.214521i	−0.972591	−	0.232524i	$-0.925302\pi$
$523$	−1.78561	+	4.90593i	−0.0780794	+	0.214521i	0.894511	+	0.447045i	$0.147524\pi$
$524$	4.46449	−	7.73273i	0.195032	−	0.337806i
$525$		0			0
$526$	−4.90583	−	27.8224i	−0.213904	−	1.21311i
$527$	15.1845	−	18.0961i	0.661445	−	0.788280i
$528$	0.0572866	+	0.0682715i	0.00249308	+	0.00297113i
$529$	3.53767	−	20.0631i	0.153812	−	0.872309i
$530$		0			0
$531$	14.2557			0.618643
$532$	−2.21770	+	7.69593i	−0.0961496	+	0.333661i
$533$			19.0984i			0.827243i
$534$	−0.577457	+	0.210177i	−0.0249890	+	0.00909526i
$535$		0			0
$536$	2.84788	−	2.38966i	0.123010	−	0.103217i
$537$	−0.373421	+	0.445026i	−0.0161143	+	0.0192043i
$538$	−29.0944	+	5.13013i	−1.25435	+	0.221176i
$539$	4.46785	+	7.73855i	0.192444	+	0.333323i
$540$		0			0
$541$	24.5890	+	8.94968i	1.05717	+	0.384777i	0.811363	−	0.584543i	$-0.198726\pi$
$541$	24.5890	+	8.94968i	1.05717	+	0.384777i	0.245803	+	0.969320i	$0.420948\pi$
$542$	−9.23836	+	25.3822i	−0.396822	+	1.09026i
$543$	0.180081	+	0.103970i	0.00772802	+	0.00446177i
$544$	−3.37099	−	5.83873i	−0.144530	−	0.250333i
$545$		0			0
$546$	−0.121746	−	0.102157i	−0.00521025	−	0.00437192i
$547$	22.8424	+	27.2225i	0.976671	+	1.16395i	0.986461	+	0.163999i	$0.0524393\pi$
$547$	22.8424	+	27.2225i	0.976671	+	1.16395i	−0.00978982	+	0.999952i	$0.503116\pi$
$548$	−4.38593	−	0.773358i	−0.187358	−	0.0330362i
$549$	−38.5036	+	14.0142i	−1.64330	+	0.598111i
$550$		0			0
$551$	13.8285	+	3.98490i	0.589114	+	0.169763i
$552$		−	0.0585864i		−	0.00249360i
$553$	7.62628	+	20.9530i	0.324303	+	0.891014i
$554$	−4.19844	+	23.8105i	−0.178374	+	1.01161i
$555$		0			0
$556$	−0.928039	−	0.778717i	−0.0393576	−	0.0330250i
$557$	−30.2250	+	5.32949i	−1.28068	+	0.225818i	−0.772267	−	0.635298i	$-0.780877\pi$
$557$	−30.2250	+	5.32949i	−1.28068	+	0.225818i	−0.508409	+	0.861116i	$0.669766\pi$
$558$	9.09928	−	5.25347i	0.385203	−	0.222397i
$559$	6.83758	−	11.8430i	0.289199	−	0.500907i
$560$		0			0
$561$	0.564623	+	0.205506i	0.0238384	+	0.00867647i
$562$	2.07934	+	1.20051i	0.0877116	+	0.0506403i
$563$	−27.0238	+	15.6022i	−1.13892	+	0.657553i	−0.946162	−	0.323694i	$-0.895075\pi$
$563$	−27.0238	+	15.6022i	−1.13892	+	0.657553i	−0.192754	+	0.981247i	$0.561742\pi$
$564$	−0.0784079	−	0.444673i	−0.00330157	−	0.0187241i
$565$		0			0
$566$	−6.24398	+	5.23932i	−0.262454	+	0.220225i
$567$	16.2642	+	2.86782i	0.683032	+	0.120437i
$568$	−1.99505	−	5.48135i	−0.0837104	−	0.229992i
$569$	20.6053			0.863820			0.431910	−	0.901917i	$-0.357840\pi$
$569$	20.6053			0.863820			0.431910	+	0.901917i	$0.357840\pi$
$570$		0			0
$571$	4.38785			0.183626			0.0918129	−	0.995776i	$-0.470734\pi$
$571$	4.38785			0.183626			0.0918129	+	0.995776i	$0.470734\pi$
$572$	2.01819	+	5.54492i	0.0843846	+	0.231845i
$573$	0.731332	+	0.128953i	0.0305518	+	0.00538711i
$574$	−11.2330	+	9.42565i	−0.468858	+	0.393419i
$575$		0			0
$576$	−0.520718	−	2.95314i	−0.0216966	−	0.123047i
$577$	25.8786	−	14.9410i	1.07734	−	0.622004i	0.147164	−	0.989112i	$-0.452986\pi$
$577$	25.8786	−	14.9410i	1.07734	−	0.622004i	0.930178	+	0.367109i	$0.119652\pi$
$578$	−24.6422	−	14.2272i	−1.02498	−	0.591772i
$579$	−0.425026	−	0.154697i	−0.0176635	−	0.00642898i
$580$		0			0
$581$	−5.72589	+	9.91753i	−0.237550	+	0.411448i
$582$	0.427574	−	0.246860i	0.0177235	−	0.0102327i
$583$	4.66563	−	0.822676i	0.193231	−	0.0340718i
$584$	−0.390995	−	0.328084i	−0.0161795	−	0.0135762i
$585$		0			0
$586$	−1.59714	+	9.05783i	−0.0659773	+	0.374176i
$587$	−13.4687	−	37.0049i	−0.555912	−	1.52736i	−0.825513	−	0.564383i	$-0.809114\pi$
$587$	−13.4687	−	37.0049i	−0.555912	−	1.52736i	0.269601	−	0.962972i	$-0.413108\pi$
$588$			0.130983i			0.00540163i
$589$	8.52387	+	12.6730i	0.351220	+	0.522181i
$590$		0			0
$591$	−0.204582	+	0.0744617i	−0.00841538	+	0.00306295i
$592$	−5.91759	−	1.04343i	−0.243212	−	0.0428848i
$593$	25.7834	+	30.7274i	1.05880	+	1.26182i	0.963880	+	0.266338i	$0.0858137\pi$
$593$	25.7834	+	30.7274i	1.05880	+	1.26182i	0.0949157	+	0.995485i	$0.469742\pi$
$594$	0.409540	+	0.343645i	0.0168036	+	0.0140999i
$595$		0			0
$596$	−4.64202	−	8.04022i	−0.190145	−	0.329340i
$597$	−0.352253	−	0.203373i	−0.0144168	−	0.00832352i
$598$	1.32670	−	3.64507i	0.0542527	−	0.149058i
$599$	29.5623	+	10.7598i	1.20788	+	0.439634i	0.865970	−	0.500097i	$-0.166702\pi$
$599$	29.5623	+	10.7598i	1.20788	+	0.439634i	0.341915	+	0.939731i	$0.388924\pi$
$600$		0			0
$601$	17.2445	+	29.8683i	0.703418	+	1.21836i	0.967260	+	0.253789i	$0.0816769\pi$
$601$	17.2445	+	29.8683i	0.703418	+	1.21836i	−0.263842	+	0.964566i	$0.584990\pi$
$602$	10.3402	−	1.82326i	0.421437	−	0.0743107i
$603$	7.16585	−	8.53992i	0.291816	−	0.347773i
$604$	2.56296	−	2.15058i	0.104285	−	0.0875057i
$605$		0			0
$606$	−0.362000	+	0.131757i	−0.0147052	+	0.00535227i
$607$			12.9979i			0.527568i	0.964582	+	0.263784i	$0.0849706\pi$
$607$			12.9979i			0.527568i	−0.964582	+	0.263784i	$0.915029\pi$
$608$	4.23080	−	1.04896i	0.171582	−	0.0425411i
$609$	−0.219261			−0.00888492
$610$		0			0
$611$	5.19139	−	29.4418i	0.210021	−	1.19109i
$612$	−12.9953	−	15.4872i	−0.525305	−	0.626034i
$613$	5.59985	−	6.67364i	0.226176	−	0.269546i	−0.641008	−	0.767534i	$-0.721483\pi$
$613$	5.59985	−	6.67364i	0.226176	−	0.269546i	0.867184	+	0.497989i	$0.165928\pi$
$614$	−4.92243	−	27.9165i	−0.198653	−	1.12662i
$615$		0			0
$616$	−2.26530	+	3.92362i	−0.0912717	+	0.158087i
$617$	−8.33044	+	22.8877i	−0.335371	+	0.921424i	0.651318	+	0.758805i	$0.274216\pi$
$617$	−8.33044	+	22.8877i	−0.335371	+	0.921424i	−0.986689	+	0.162619i	$0.948006\pi$
$618$	−0.120520	+	0.331127i	−0.00484804	+	0.0133199i
$619$	0.822483	−	1.42458i	0.0330584	−	0.0572588i	−0.849023	−	0.528356i	$-0.822809\pi$
$619$	0.822483	−	1.42458i	0.0330584	−	0.0572588i	0.882081	+	0.471097i	$0.156142\pi$
$620$		0			0
$621$	−0.0610272	−	0.346102i	−0.00244894	−	0.0138886i
$622$	11.2108	−	13.3605i	0.449511	−	0.535706i
$623$	−20.0804	−	23.9309i	−0.804505	−	0.958772i
$624$	−0.0150198	+	0.0851816i	−0.000601274	+	0.00340999i
$625$		0			0
$626$	13.1983			0.527510
$627$	−0.228751	+	0.313982i	−0.00913545	+	0.0125392i
$628$		−	7.05317i		−	0.281452i
$629$	−38.0686	+	13.8558i	−1.51790	+	0.552469i
$630$		0			0
$631$	−33.3220	+	27.9605i	−1.32653	+	1.11309i	−0.341651	+	0.939827i	$0.610986\pi$
$631$	−33.3220	+	27.9605i	−1.32653	+	1.11309i	−0.984876	+	0.173261i	$0.944570\pi$
$632$	7.80050	−	9.29628i	0.310287	−	0.369786i
$633$	0.500734	−	0.0882929i	0.0199024	−	0.00350933i
$634$	6.14319	+	10.6403i	0.243977	+	0.422581i
$635$		0			0
$636$	0.0652574	+	0.0237517i	0.00258762	+	0.000941818i
$637$	−2.96613	+	8.14936i	−0.117522	+	0.322890i
$638$	7.05020	+	4.07043i	0.279120	+	0.161150i
$639$	−8.74589	−	15.1483i	−0.345982	−	0.599258i
$640$		0			0
$641$	−28.2069	−	23.6684i	−1.11411	−	0.934846i	−0.115814	−	0.993271i	$-0.536948\pi$
$641$	−28.2069	−	23.6684i	−1.11411	−	0.934846i	−0.998292	+	0.0584253i	$0.981392\pi$
$642$	−0.308666	−	0.367854i	−0.0121821	−	0.0145180i
$643$	14.5118	+	2.55882i	0.572288	+	0.100910i	0.452301	−	0.891866i	$-0.350603\pi$
$643$	14.5118	+	2.55882i	0.572288	+	0.100910i	0.119988	+	0.992775i	$0.461715\pi$
$644$	2.79868	−	1.01864i	0.110284	−	0.0401399i
$645$		0			0
$646$	21.1664	−	20.3866i	0.832783	−	0.802100i
$647$		−	6.04813i		−	0.237776i	−0.992908	−	0.118888i	$-0.962067\pi$
$647$		−	6.04813i		−	0.237776i	0.992908	−	0.118888i	$-0.0379330\pi$
$648$	−3.07416	−	8.44619i	−0.120764	−	0.331798i
$649$	−2.03552	+	11.5440i	−0.0799012	+	0.453142i
$650$		0			0
$651$	−0.178254	−	0.149573i	−0.00698633	−	0.00586223i
$652$	15.6150	−	2.75334i	0.611530	−	0.107829i
$653$	2.50167	−	1.44434i	0.0978978	−	0.0565213i	−0.450252	−	0.892902i	$-0.648666\pi$
$653$	2.50167	−	1.44434i	0.0978978	−	0.0565213i	0.548150	+	0.836380i	$0.315332\pi$
$654$	−0.0260945	+	0.0451970i	−0.00102037	+	0.00176734i
$655$		0			0
$656$	7.49934	+	2.72954i	0.292800	+	0.106571i
$657$	−1.32550	−	0.765278i	−0.0517127	−	0.0298563i
$658$	19.8789	−	11.4771i	0.774958	−	0.447422i
$659$	−2.83413	−	16.0731i	−0.110402	−	0.626120i	−0.988925	−	0.148419i	$-0.952581\pi$
$659$	−2.83413	−	16.0731i	−0.110402	−	0.626120i	0.878523	−	0.477701i	$-0.158530\pi$
$660$		0			0
$661$	21.8640	−	18.3461i	0.850410	−	0.713579i	−0.109470	−	0.993990i	$-0.534915\pi$
$661$	21.8640	−	18.3461i	0.850410	−	0.713579i	0.959880	+	0.280411i	$0.0904708\pi$
$662$	−0.981453	−	0.173057i	−0.0381453	−	0.00672604i
$663$	0.199450	+	0.547984i	0.00774599	+	0.0212819i
$664$	6.23256			0.241870
$665$		0			0
$666$	−18.0188			−0.698214
$667$	−1.83035	−	5.02884i	−0.0708714	−	0.194718i
$668$	13.4187	+	2.36609i	0.519187	+	0.0915466i
$669$	−0.700571	+	0.587849i	−0.0270856	+	0.0227275i
$670$		0			0
$671$	−5.85065	−	33.1807i	−0.225862	−	1.28093i
$672$	−0.0575138	+	0.0332056i	−0.00221864	+	0.00128093i
$673$	5.39921	+	3.11723i	0.208124	+	0.120161i	0.600439	−	0.799670i	$-0.294992\pi$
$673$	5.39921	+	3.11723i	0.208124	+	0.120161i	−0.392315	+	0.919831i	$0.628326\pi$
$674$	−8.04300	−	2.92741i	−0.309805	−	0.112760i
$675$		0			0
$676$	3.63656	−	6.29870i	0.139868	−	0.242258i
$677$	−12.6570	+	7.30750i	−0.486446	+	0.280850i	−0.723099	−	0.690744i	$-0.757283\pi$
$677$	−12.6570	+	7.30750i	−0.486446	+	0.280850i	0.236653	+	0.971594i	$0.423950\pi$
$678$	0.0299541	−	0.00528171i	0.00115038	−	0.000202843i
$679$	19.2267	+	16.1331i	0.737854	+	0.619133i
$680$		0			0
$681$	0.138149	−	0.783481i	0.00529388	−	0.0300231i
$682$	2.95492	+	8.11858i	0.113150	+	0.310877i
$683$		−	47.0671i		−	1.80097i	−0.434885	−	0.900486i	$-0.643211\pi$
$683$		−	47.0671i		−	1.80097i	0.434885	−	0.900486i	$-0.356789\pi$
$684$	11.9479	−	5.30079i	0.456840	−	0.202681i
$685$		0			0
$686$	−18.3433	+	6.67641i	−0.700350	+	0.254906i
$687$	−0.188485	−	0.0332350i	−0.00719114	−	0.00126799i
$688$	−3.67317	−	4.37751i	−0.140038	−	0.166891i
$689$	3.52226	+	2.95553i	0.134188	+	0.112597i
$690$		0			0
$691$	13.6742	+	23.6844i	0.520191	+	0.900997i	0.999724	+	0.0234732i	$0.00747242\pi$
$691$	13.6742	+	23.6844i	0.520191	+	0.900997i	−0.479534	+	0.877523i	$0.659194\pi$
$692$	−10.4265	−	6.01973i	−0.396355	−	0.228836i
$693$	−4.64665	+	12.7666i	−0.176512	+	0.484962i
$694$	6.23742	+	2.27024i	0.236769	+	0.0861770i
$695$		0			0
$696$	0.0596659	+	0.103344i	0.00226163	+	0.00391726i
$697$	52.9879	−	9.34319i	2.00706	−	0.353899i
$698$	−19.9549	+	23.7813i	−0.755303	+	0.900135i
$699$	−0.569035	+	0.477477i	−0.0215229	+	0.0180598i
$700$		0			0
$701$	−18.6359	+	6.78290i	−0.703867	+	0.256187i	−0.669061	−	0.743207i	$-0.733304\pi$
$701$	−18.6359	+	6.78290i	−0.703867	+	0.256187i	−0.0348060	+	0.999394i	$0.511081\pi$
$702$			0.518861i			0.0195831i
$703$	−1.79279	−	26.1307i	−0.0676164	−	0.985538i
$704$	2.46576			0.0929317
$705$		0			0
$706$	−3.08450	+	17.4931i	−0.116087	+	0.658360i
$707$	−12.5881	−	15.0020i	−0.473425	−	0.564206i
$708$	−0.110448	+	0.131627i	−0.00415089	+	0.00494684i
$709$	−5.68008	−	32.2133i	−0.213320	−	1.20980i	−0.883799	−	0.467868i	$-0.845022\pi$
$709$	−5.68008	−	32.2133i	−0.213320	−	1.20980i	0.670479	−	0.741929i	$-0.266089\pi$
$710$		0			0
$711$	18.1952	−	31.5150i	0.682374	−	1.18191i
$712$	−5.81501	+	15.9766i	−0.217927	+	0.598749i
$713$	1.94248	−	5.33693i	0.0727466	−	0.199870i
$714$	−0.223872	+	0.387757i	−0.00837819	+	0.0145114i
$715$		0			0
$716$	2.79104	+	15.8288i	0.104306	+	0.591550i
$717$	−0.0206115	+	0.0245638i	−0.000769750	+	0.000917353i
$718$	−3.30146	−	3.93452i	−0.123209	−	0.146835i
$719$	0.563968	−	3.19842i	0.0210325	−	0.119281i	−0.972484	−	0.232970i	$-0.925156\pi$
$719$	0.563968	−	3.19842i	0.0210325	−	0.119281i	0.993516	+	0.113689i	$0.0362667\pi$
$720$		0			0
$721$	−17.9135			−0.667132
$722$	8.87591	+	16.7994i	0.330327	+	0.625207i
$723$			0.144627i			0.00537873i
$724$	5.40615	−	1.96768i	0.200918	−	0.0731282i
$725$		0			0
$726$	0.136226	−	0.114307i	0.00505580	−	0.00424232i
$727$	−12.4762	+	14.8686i	−0.462718	+	0.551446i	−0.946062	−	0.323984i	$-0.894977\pi$
$727$	−12.4762	+	14.8686i	−0.462718	+	0.551446i	0.483344	+	0.875430i	$0.339422\pi$
$728$	−4.33029	+	0.763547i	−0.160491	+	0.0282989i
$729$	−13.4647	−	23.3216i	−0.498694	−	0.863764i
$730$		0			0
$731$	−36.2032	−	13.1769i	−1.33902	−	0.487364i
$732$	0.168916	−	0.464093i	0.00624331	−	0.0171534i
$733$	10.4575	+	6.03763i	0.386256	+	0.223005i	0.680537	−	0.732714i	$-0.261747\pi$
$733$	10.4575	+	6.03763i	0.386256	+	0.223005i	−0.294281	+	0.955719i	$0.595080\pi$
$734$	2.87294	+	4.97608i	0.106042	+	0.183671i
$735$		0			0
$736$	−1.24170	−	1.04191i	−0.0457695	−	0.0384052i
$737$	5.89231	+	7.02218i	0.217046	+	0.258665i
$738$	23.5679	+	4.15566i	0.867547	+	0.152972i
$739$	2.86243	−	1.04184i	0.105296	−	0.0383246i	−0.288835	−	0.957379i	$-0.593268\pi$
$739$	2.86243	−	1.04184i	0.105296	−	0.0383246i	0.394131	+	0.919054i	$0.371046\pi$
$740$		0			0
$741$	−0.376142	+	0.0258066i	−0.0138179	+	0.000948028i
$742$			3.53033i			0.129602i
$743$	13.5975	+	37.3589i	0.498845	+	1.37057i	0.892392	+	0.451261i	$0.149026\pi$
$743$	13.5975	+	37.3589i	0.498845	+	1.37057i	−0.393547	+	0.919305i	$0.628752\pi$
$744$	−0.0219912	+	0.124718i	−0.000806238	+	0.00457240i
$745$		0			0
$746$	−28.9453	−	24.2880i	−1.05976	−	0.889246i
$747$	18.4056	−	3.24540i	0.673426	−	0.118743i
$748$	14.3969	−	8.31204i	0.526402	−	0.303918i
$749$	12.2057	−	21.1409i	0.445986	−	0.772471i
$750$		0			0
$751$	−33.6285	−	12.2398i	−1.22712	−	0.446636i	−0.354511	−	0.935052i	$-0.615353\pi$
$751$	−33.6285	−	12.2398i	−1.22712	−	0.446636i	−0.872611	+	0.488416i	$0.837575\pi$
$752$	−10.8189	−	6.24632i	−0.394526	−	0.227780i
$753$	0.396550	−	0.228948i	0.0144511	−	0.00834334i
$754$	1.37199	+	7.78093i	0.0499648	+	0.283365i
$755$		0			0
$756$	−0.305177	+	0.256074i	−0.0110992	+	0.00931333i
$757$	−49.1480	−	8.66613i	−1.78632	−	0.314976i	−0.820006	−	0.572355i	$-0.806030\pi$
$757$	−49.1480	−	8.66613i	−1.78632	−	0.314976i	−0.966310	+	0.257380i	$0.917141\pi$
$758$	11.0357	+	30.3204i	0.400835	+	1.10128i
$759$	0.144460			0.00524355
$760$		0			0
$761$	−36.2563			−1.31429			−0.657145	−	0.753764i	$-0.728236\pi$
$761$	−36.2563			−1.31429			−0.657145	+	0.753764i	$0.728236\pi$
$762$	0.160530	+	0.441052i	0.00581538	+	0.0159776i
$763$	−2.61277	−	0.460702i	−0.0945886	−	0.0166785i
$764$	15.7392	−	13.2067i	0.569423	−	0.477803i
$765$		0			0
$766$	3.78204	+	21.4490i	0.136651	+	0.774984i
$767$	−9.85247	+	5.68833i	−0.355752	+	0.205394i
$768$	0.0313015	+	0.0180720i	0.00112950	+	0.000652116i
$769$	−5.18278	−	1.88638i	−0.186896	−	0.0680246i	0.246877	−	0.969047i	$-0.420596\pi$
$769$	−5.18278	−	1.88638i	−0.186896	−	0.0680246i	−0.433773	+	0.901022i	$0.642818\pi$
$770$		0			0
$771$	0.235745	−	0.408322i	0.00849014	−	0.0147054i
$772$	−10.8374	+	6.25697i	−0.390046	+	0.225193i
$773$	−37.8158	+	6.66795i	−1.36014	+	0.239830i	−0.805666	−	0.592371i	$-0.798192\pi$
$773$	−37.8158	+	6.66795i	−1.36014	+	0.239830i	−0.554475	+	0.832200i	$0.687081\pi$
$774$	−13.1268	−	11.0147i	−0.471833	−	0.395915i
$775$		0			0
$776$	2.37200	−	13.4523i	0.0851500	−	0.482910i
$777$	0.136486	+	0.374991i	0.00489639	+	0.0134527i
$778$			9.68485i			0.347219i
$779$	−3.68159	+	34.5914i	−0.131907	+	1.23937i
$780$		0			0
$781$	13.5157	−	4.91930i	0.483629	−	0.176026i
$782$	−10.7622	−	1.89766i	−0.384855	−	0.0678603i
$783$	0.460129	+	0.548361i	0.0164437	+	0.0195968i
$784$	2.77608	+	2.32941i	0.0991459	+	0.0831933i
$785$		0			0
$786$	0.161364	+	0.279491i	0.00575567	+	0.00996912i
$787$	−2.70250	−	1.56029i	−0.0963339	−	0.0556184i	0.451059	−	0.892494i	$-0.351046\pi$
$787$	−2.70250	−	1.56029i	−0.0963339	−	0.0556184i	−0.547393	+	0.836876i	$0.684380\pi$
$788$	−2.06015	+	5.66021i	−0.0733897	+	0.201636i
$789$	0.959541	+	0.349244i	0.0341606	+	0.0124334i
$790$		0			0
$791$	0.773118	+	1.33908i	0.0274889	+	0.0476122i
$792$	7.28171	−	1.28396i	0.258744	−	0.0456236i
$793$	21.0189	−	25.0494i	0.746404	−	0.889530i
$794$	−14.0915	+	11.8242i	−0.500089	+	0.419624i
$795$		0			0
$796$	−10.5749	+	3.84894i	−0.374816	+	0.136422i
$797$		−	0.491495i		−	0.0174096i	−0.999962	−	0.00870482i	$-0.997229\pi$
$797$		−	0.491495i		−	0.0174096i	0.999962	−	0.00870482i	$-0.00277087\pi$
$798$	−0.200816	−	0.208498i	−0.00710882	−	0.00738075i
$799$	−84.2252			−2.97967
$800$		0			0
$801$	−8.85322	+	50.2091i	−0.312813	+	1.77405i
$802$	23.4853	+	27.9887i	0.829296	+	0.988316i
$803$	0.808975	−	0.964098i	0.0285481	−	0.0340223i
$804$	0.0233331	+	0.132329i	0.000822897	+	0.00466688i
$805$		0			0
$806$	−4.19250	+	7.26163i	−0.147675	+	0.255780i
$807$	0.365212	−	1.00341i	0.0128561	−	0.0353218i
$808$	−3.64535	+	10.0155i	−0.128243	+	0.352345i
$809$	16.8276	−	29.1463i	0.591628	−	1.02473i	−0.402386	−	0.915470i	$-0.631819\pi$
$809$	16.8276	−	29.1463i	0.591628	−	1.02473i	0.994013	−	0.109259i	$-0.0348478\pi$
$810$		0			0
$811$	−8.35435	−	47.3798i	−0.293361	−	1.66373i	−0.673791	−	0.738922i	$-0.735335\pi$
$811$	−8.35435	−	47.3798i	−0.293361	−	1.66373i	0.380430	−	0.924810i	$-0.375776\pi$
$812$	−3.89937	+	4.64709i	−0.136841	+	0.163081i
$813$	−0.627547	−	0.747881i	−0.0220090	−	0.0262293i
$814$	2.57285	−	14.5913i	0.0901783	−	0.511426i
$815$		0			0
$816$	0.243682			0.00853056
$817$	14.6674	−	20.1323i	0.513146	−	0.704340i
$818$			36.3063i			1.26942i
$819$	−12.3903	+	4.50972i	−0.432954	+	0.157582i
$820$		0			0
$821$	−1.45115	+	1.21766i	−0.0506456	+	0.0424967i	−0.667759	−	0.744377i	$-0.732746\pi$
$821$	−1.45115	+	1.21766i	−0.0506456	+	0.0424967i	0.617114	+	0.786874i	$0.288302\pi$
$822$	0.103470	−	0.123310i	0.00360892	−	0.00430094i
$823$	−26.1532	+	4.61152i	−0.911643	+	0.160747i	−0.609749	−	0.792594i	$-0.708730\pi$
$823$	−26.1532	+	4.61152i	−0.911643	+	0.160747i	−0.301894	+	0.953342i	$0.597619\pi$
$824$	4.87465	+	8.44314i	0.169816	+	0.294131i
$825$		0			0
$826$	−8.20819	−	2.98754i	−0.285599	−	0.103950i
$827$	8.82334	−	24.2419i	0.306818	−	0.842974i	−0.686455	−	0.727173i	$-0.740834\pi$
$827$	8.82334	−	24.2419i	0.306818	−	0.842974i	0.993272	−	0.115802i	$-0.0369438\pi$
$828$	−4.20944	−	2.43032i	−0.146288	−	0.0844595i
$829$	−13.9819	−	24.2173i	−0.485611	−	0.841102i	0.514253	−	0.857639i	$-0.328069\pi$
$829$	−13.9819	−	24.2173i	−0.485611	−	0.841102i	−0.999863	+	0.0165364i	$0.994736\pi$
$830$		0			0
$831$	−0.669432	−	0.561720i	−0.0232223	−	0.0194859i
$832$	1.53825	+	1.83321i	0.0533292	+	0.0635553i
$833$	24.0612	+	4.24264i	0.833672	+	0.146999i
$834$	0.0411465	−	0.0149761i	0.00142479	−	0.000518581i
$835$		0			0
$836$	2.58649	+	10.4321i	0.0894556	+	0.360802i
$837$			0.759689i			0.0262587i
$838$	−13.5098	−	37.1179i	−0.466689	−	1.28222i
$839$	−8.66822	+	49.1599i	−0.299260	+	1.69719i	0.350104	+	0.936711i	$0.386146\pi$
$839$	−8.66822	+	49.1599i	−0.299260	+	1.69719i	−0.649364	+	0.760478i	$0.724965\pi$
$840$		0			0
$841$	−13.8651	−	11.6342i	−0.478107	−	0.401180i
$842$	−13.8863	+	2.44853i	−0.478554	+	0.0843819i
$843$	−0.0751555	+	0.0433910i	−0.00258849	+	0.00149447i
$844$	7.03380	−	12.1829i	0.242114	−	0.419353i
$845$		0			0
$846$	−35.2024	−	12.8126i	−1.21028	−	0.440507i
$847$	7.82900	+	4.52008i	0.269008	+	0.155312i
$848$	1.66395	−	0.960680i	0.0571401	−	0.0329899i
$849$	−0.0511579	−	0.290131i	−0.00175573	−	0.00995726i
$850$		0			0
$851$	−7.46121	+	6.26070i	−0.255767	+	0.214614i
$852$	0.207629	+	0.0366106i	0.00711326	+	0.00125426i
$853$	−2.72117	−	7.47637i	−0.0931712	−	0.255986i	0.884349	−	0.466826i	$-0.154602\pi$
$853$	−2.72117	−	7.47637i	−0.0931712	−	0.255986i	−0.977521	+	0.210840i	$0.932380\pi$
$854$	25.1067			0.859135
$855$		0			0
$856$	−13.2857			−0.454097
$857$	8.60350	+	23.6379i	0.293890	+	0.807456i	0.995488	+	0.0948835i	$0.0302479\pi$
$857$	8.60350	+	23.6379i	0.293890	+	0.807456i	−0.701598	+	0.712573i	$0.747530\pi$
$858$	−0.210037	−	0.0370352i	−0.00717055	−	0.00126436i
$859$	−2.65725	+	2.22970i	−0.0906643	+	0.0760764i	−0.686993	−	0.726664i	$-0.741070\pi$
$859$	−2.65725	+	2.22970i	−0.0906643	+	0.0760764i	0.596329	+	0.802740i	$0.296625\pi$
$860$		0			0
$861$	−0.0920342	−	0.521952i	−0.00313652	−	0.0177881i
$862$	−18.2239	+	10.5216i	−0.620708	+	0.358366i
$863$	−35.4817	−	20.4854i	−1.20781	−	0.697331i	−0.245531	−	0.969389i	$-0.578962\pi$
$863$	−35.4817	−	20.4854i	−1.20781	−	0.697331i	−0.962281	+	0.272058i	$0.912296\pi$
$864$	0.203741	+	0.0741555i	0.00693140	+	0.00252282i
$865$		0			0
$866$	−2.62885	+	4.55330i	−0.0893318	+	0.154727i
$867$	0.890665	−	0.514225i	0.0302486	−	0.0174640i
$868$	−6.34019	+	1.11795i	−0.215200	+	0.0379456i
$869$	22.9223	+	19.2341i	0.777587	+	0.652473i
$870$		0			0
$871$	−1.54489	+	8.76150i	−0.0523466	+	0.296872i
$872$	0.493850	+	1.35684i	0.0167239	+	0.0459485i
$873$		−	40.9616i		−	1.38634i
$874$	3.10561	−	6.34629i	0.105049	−	0.214667i
$875$		0			0
$876$	0.0173356	−	0.00630963i	0.000585715	−	0.000213183i
$877$	−24.4825	−	4.31693i	−0.826716	−	0.145772i	−0.255747	−	0.966744i	$-0.582321\pi$
$877$	−24.4825	−	4.31693i	−0.826716	−	0.145772i	−0.570969	+	0.820972i	$0.693432\pi$
$878$	23.4513	+	27.9482i	0.791445	+	0.943207i
$879$	−0.254661	−	0.213686i	−0.00858949	−	0.00720744i
$880$		0			0
$881$	7.87057	+	13.6322i	0.265166	+	0.459281i	0.967607	−	0.252461i	$-0.0812398\pi$
$881$	7.87057	+	13.6322i	0.265166	+	0.459281i	−0.702441	+	0.711742i	$0.747907\pi$
$882$	9.41112	+	5.43351i	0.316889	+	0.182956i
$883$	2.65398	−	7.29174i	0.0893134	−	0.245386i	−0.886992	−	0.461786i	$-0.847209\pi$
$883$	2.65398	−	7.29174i	0.0893134	−	0.245386i	0.976305	+	0.216399i	$0.0694312\pi$
$884$	15.1612	+	5.51821i	0.509925	+	0.185598i
$885$		0			0
$886$	−4.61535	−	7.99402i	−0.155056	−	0.268564i
$887$	−33.5420	+	5.91436i	−1.12623	+	0.198585i	−0.705574	−	0.708636i	$-0.749311\pi$
$887$	−33.5420	+	5.91436i	−1.12623	+	0.198585i	−0.420655	+	0.907221i	$0.638200\pi$
$888$	0.139604	−	0.166373i	0.00468479	−	0.00558311i
$889$	−18.2780	+	15.3371i	−0.613025	+	0.514389i
$890$		0			0
$891$	20.8262	−	7.58013i	0.697705	−	0.253944i
$892$			25.3025i			0.847189i
$893$	15.0783	−	52.3250i	0.504575	−	1.75099i
$894$	0.335562			0.0112229
$895$		0			0
$896$	−0.319063	+	1.80950i	−0.0106591	+	0.0604510i
$897$	0.0901204	+	0.107401i	0.00300903	+	0.00358603i
$898$	14.6746	−	17.4885i	0.489698	−	0.583600i
$899$	2.00879	+	11.3924i	0.0669970	+	0.379959i
$900$		0			0
$901$	6.47689	−	11.2183i	0.215776	−	0.373736i
$902$	−6.73037	+	18.4915i	−0.224097	+	0.615701i
$903$	−0.129798	+	0.356616i	−0.00431939	+	0.0118674i
$904$	0.420765	−	0.728786i	0.0139944	−	0.0242391i
$905$		0			0
$906$	0.0209987	+	0.119090i	0.000697635	+	0.00395649i
$907$	−3.09024	+	3.68281i	−0.102610	+	0.122286i	−0.814905	−	0.579594i	$-0.803211\pi$
$907$	−3.09024	+	3.68281i	−0.102610	+	0.122286i	0.712296	+	0.701880i	$0.247656\pi$
$908$	−14.1485	−	16.8615i	−0.469533	−	0.559568i
$909$	−5.54996	+	31.4754i	−0.184081	+	1.04397i
$910$		0			0
$911$	9.14462			0.302975			0.151487	−	0.988459i	$-0.451594\pi$
$911$	9.14462			0.302975			0.151487	+	0.988459i	$0.451594\pi$
$912$	−0.0436247	+	0.151387i	−0.00144456	+	0.00501294i
$913$			15.3680i			0.508606i
$914$	7.35323	−	2.67636i	0.243223	−	0.0885260i
$915$		0			0
$916$	−4.05643	+	3.40375i	−0.134028	+	0.112463i
$917$	−10.5457	+	12.5679i	−0.348250	+	0.415029i
$918$	1.43956	−	0.253834i	0.0475127	−	0.00837777i
$919$	−10.5408	−	18.2572i	−0.347709	−	0.602251i	0.638133	−	0.769926i	$-0.279707\pi$
$919$	−10.5408	−	18.2572i	−0.347709	−	0.602251i	−0.985842	+	0.167676i	$0.946374\pi$
$920$		0			0
$921$	0.962788	+	0.350426i	0.0317249	+	0.0115469i
$922$	1.34471	−	3.69457i	0.0442858	−	0.121674i
$923$	12.0890	+	6.97961i	0.397915	+	0.229737i
$924$	−0.0818769	−	0.141815i	−0.00269355	−	0.00466537i
$925$		0			0
$926$	13.2498	+	11.1179i	0.435416	+	0.365357i
$927$	18.7920	+	22.3954i	0.617210	+	0.735563i
$928$	3.25141	+	0.573312i	0.106733	+	0.0188199i
$929$	17.6774	−	6.43406i	0.579978	−	0.211095i	−0.0353379	−	0.999375i	$-0.511251\pi$
$929$	17.6774	−	6.43406i	0.579978	−	0.211095i	0.615316	+	0.788281i	$0.289029\pi$
$930$		0			0
$931$	−6.94326	+	14.1885i	−0.227556	+	0.465010i
$932$			20.5518i			0.673196i
$933$	0.215603	+	0.592364i	0.00705852	+	0.0193931i
$934$	−3.65126	+	20.7073i	−0.119473	+	0.677564i
$935$		0			0
$936$	5.49725	+	4.61274i	0.179683	+	0.150772i
$937$	18.9224	−	3.33653i	0.618168	−	0.109000i	0.144210	−	0.989547i	$-0.453936\pi$
$937$	18.9224	−	3.33653i	0.618168	−	0.109000i	0.473958	+	0.880548i	$0.342825\pi$
$938$	−5.91568	+	3.41542i	−0.193154	+	0.111517i
$939$	−0.238519	+	0.413127i	−0.00778378	+	0.0134819i
$940$		0			0
$941$	−14.6200	−	5.32125i	−0.476598	−	0.173468i	0.0925407	−	0.995709i	$-0.470501\pi$
$941$	−14.6200	−	5.32125i	−0.476598	−	0.173468i	−0.569139	+	0.822241i	$0.692723\pi$
$942$	0.220775	+	0.127465i	0.00719324	+	0.00415302i
$943$	11.2029	−	6.46798i	0.364816	−	0.210626i
$944$	0.825516	+	4.68173i	0.0268683	+	0.152377i
$945$		0			0
$946$	10.7939	−	9.05713i	0.350939	−	0.294473i
$947$	−21.8389	−	3.85079i	−0.709670	−	0.125134i	−0.192850	−	0.981228i	$-0.561773\pi$
$947$	−21.8389	−	3.85079i	−0.709670	−	0.125134i	−0.516820	+	0.856094i	$0.672884\pi$
$948$	0.150017	+	0.412170i	0.00487234	+	0.0133866i
$949$	1.22145			0.0396500
$950$		0			0
$951$	−0.444078			−0.0144002
$952$	4.23688	+	11.6407i	0.137318	+	0.377278i
$953$	4.88046	+	0.860556i	0.158094	+	0.0278762i	0.252135	−	0.967692i	$-0.418867\pi$
$953$	4.88046	+	0.860556i	0.158094	+	0.0278762i	−0.0940411	+	0.995568i	$0.529979\pi$
$954$	4.41362	−	3.70346i	0.142896	−	0.119904i
$955$		0			0
$956$	0.154055	+	0.873692i	0.00498251	+	0.0282572i
$957$	−0.254822	+	0.147121i	−0.00823722	+	0.00475576i
$958$	−18.3006	−	10.5658i	−0.591265	−	0.341367i
$959$	7.68958	+	2.79878i	0.248309	+	0.0903772i
$960$		0			0
$961$	9.36155	−	16.2147i	0.301986	−	0.523054i
$962$	12.4533	−	7.18990i	0.401510	−	0.231812i
$963$	−39.2346	+	6.91812i	−1.26432	+	0.222933i
$964$	3.06526	+	2.57206i	0.0987255	+	0.0828406i
$965$		0			0
$966$	−0.0186927	+	0.106012i	−0.000601429	+	0.00341087i
$967$	5.89275	+	16.1902i	0.189498	+	0.520642i	0.997664	−	0.0683131i	$-0.0217617\pi$
$967$	5.89275	+	16.1902i	0.189498	+	0.520642i	−0.808166	+	0.588955i	$0.799539\pi$
$968$		−	4.92005i		−	0.158136i
$969$	0.255613	+	1.03097i	0.00821148	+	0.0331195i
$970$		0			0
$971$	3.57394	−	1.30081i	0.114693	−	0.0417449i	−0.284036	−	0.958814i	$-0.591674\pi$
$971$	3.57394	−	1.30081i	0.114693	−	0.0417449i	0.398729	+	0.917069i	$0.369451\pi$
$972$	0.960502	+	0.169362i	0.0308081	+	0.00543230i
$973$	1.43082	+	1.70519i	0.0458701	+	0.0546659i
$974$	−13.1762	−	11.0561i	−0.422193	−	0.354262i
$975$		0			0
$976$	−6.83209	−	11.8335i	−0.218690	−	0.378782i
$977$	53.5131	+	30.8958i	1.71204	+	0.988445i	0.931809	+	0.362949i	$0.118230\pi$
$977$	53.5131	+	30.8958i	1.71204	+	0.988445i	0.780227	+	0.625496i	$0.215103\pi$
$978$	−0.196009	+	0.538531i	−0.00626769	+	0.0172203i
$979$	−39.3944	−	14.3384i	−1.25905	−	0.458257i
$980$		0			0
$981$	2.16494	+	3.74978i	0.0691212	+	0.119721i
$982$	−32.6339	+	5.75424i	−1.04139	+	0.183625i
$983$	−7.66042	+	9.12934i	−0.244330	+	0.291181i	−0.874247	−	0.485482i	$-0.838644\pi$
$983$	−7.66042	+	9.12934i	−0.244330	+	0.291181i	0.629917	+	0.776662i	$0.283089\pi$
$984$	−0.220967	+	0.185413i	−0.00704416	+	0.00591075i
$985$		0			0
$986$	20.9167	−	7.61307i	0.666125	−	0.242450i
$987$			0.829652i			0.0264081i
$988$	−6.14240	+	8.43100i	−0.195416	+	0.268226i
$989$	−9.26263			−0.294535
$990$		0			0
$991$	2.80361	−	15.9001i	0.0890596	−	0.505082i	−0.907347	−	0.420383i	$-0.861896\pi$
$991$	2.80361	−	15.9001i	0.0890596	−	0.505082i	0.996407	−	0.0846996i	$-0.0269931\pi$
$992$	2.25222	+	2.68410i	0.0715082	+	0.0852202i
$993$	0.0231537	−	0.0275935i	0.000734761	−	0.000875654i
$994$	1.86114	+	10.5550i	0.0590317	+	0.334785i
$995$		0			0
$996$	−0.112635	+	0.195089i	−0.00356896	+	0.00618162i
$997$	−14.5471	+	39.9680i	−0.460713	+	1.26580i	0.464238	+	0.885711i	$0.346328\pi$
$997$	−14.5471	+	39.9680i	−0.460713	+	1.26580i	−0.924951	+	0.380088i	$0.875894\pi$
$998$	−10.9343	+	30.0418i	−0.346120	+	0.950958i
$999$	0.651412	−	1.12828i	0.0206098	−	0.0356971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.g.499.5		36
5.2	odd	4		950.2.l.i.651.2		18
5.3	odd	4		190.2.k.d.81.2	yes	18
5.4	even	2	inner	950.2.u.g.499.2		36
19.4	even	9	inner	950.2.u.g.99.2		36
95.4	even	18	inner	950.2.u.g.99.5		36
95.23	odd	36		190.2.k.d.61.2	✓	18
95.42	odd	36		950.2.l.i.251.2		18
95.78	even	36		3610.2.a.bj.1.5		9
95.93	odd	36		3610.2.a.bi.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.61.2	✓	18	95.23	odd	36
190.2.k.d.81.2	yes	18	5.3	odd	4
950.2.l.i.251.2		18	95.42	odd	36
950.2.l.i.651.2		18	5.2	odd	4
950.2.u.g.99.2		36	19.4	even	9	inner
950.2.u.g.99.5		36	95.4	even	18	inner
950.2.u.g.499.2		36	5.4	even	2	inner
950.2.u.g.499.5		36	1.1	even	1	trivial
3610.2.a.bi.1.5		9	95.93	odd	36
3610.2.a.bj.1.5		9	95.78	even	36

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)

\(f(q)\)	\(=\)	\(q+(0.342020 + 0.939693i) q^{2} +(-0.0355948 - 0.00627632i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.00627632 - 0.0355948i) q^{6} +(1.59124 - 0.918706i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.81785 - 1.02561i) q^{9} +O(q^{10})\)	\(q+(0.342020 + 0.939693i) q^{2} +(-0.0355948 - 0.00627632i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.00627632 - 0.0355948i) q^{6} +(1.59124 - 0.918706i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.81785 - 1.02561i) q^{9} +(1.23288 - 2.13541i) q^{11} +(0.0313015 - 0.0180720i) q^{12} +(2.35673 - 0.415556i) q^{13} +(1.40754 + 1.18107i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.30589 - 6.33539i) q^{17} -2.99869i q^{18} +(4.34868 - 0.298357i) q^{19} +(-0.0624061 + 0.0227140i) q^{21} +(2.42830 + 0.428174i) q^{22} +(-1.04191 - 1.24170i) q^{23} +(0.0276878 + 0.0232329i) q^{24} +(1.19655 + 2.07248i) q^{26} +(0.187768 + 0.108408i) q^{27} +(-0.628432 + 1.72660i) q^{28} +(3.10246 + 1.12920i) q^{29} +(1.75192 + 3.03441i) q^{31} +(0.984808 - 0.173648i) q^{32} +(-0.0572866 + 0.0682715i) q^{33} +(5.16466 - 4.33366i) q^{34} +(2.81785 - 1.02561i) q^{36} -6.00888i q^{37} +(1.76770 + 3.98437i) q^{38} -0.0864957 q^{39} +(-1.38582 + 7.85939i) q^{41} +(-0.0426883 - 0.0508739i) q^{42} +(3.67317 - 4.37751i) q^{43} +(0.428174 + 2.42830i) q^{44} +(0.810460 - 1.40376i) q^{46} +(4.27274 - 11.7392i) q^{47} +(-0.0123619 + 0.0339642i) q^{48} +(-1.81196 + 3.13841i) q^{49} +(0.0423149 + 0.239980i) q^{51} +(-1.53825 + 1.83321i) q^{52} +(1.23503 + 1.47185i) q^{53} +(-0.0376497 + 0.213522i) q^{54} -1.83741 q^{56} +(-0.156663 - 0.0166738i) q^{57} +3.30157i q^{58} +(-4.46726 + 1.62595i) q^{59} +(10.4674 - 8.78317i) q^{61} +(-2.25222 + 2.68410i) q^{62} +(-5.42613 + 0.956772i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.0837473 - 0.0304815i) q^{66} +(-1.27151 + 3.49344i) q^{67} +(5.83873 + 3.37099i) q^{68} +(0.0292932 + 0.0507373i) q^{69} +(4.46844 + 3.74946i) q^{71} +(1.92752 + 2.29713i) q^{72} +(0.502654 + 0.0886314i) q^{73} +(5.64650 - 2.05516i) q^{74} +(-3.13950 + 3.02383i) q^{76} -4.53061i q^{77} +(-0.0295833 - 0.0812794i) q^{78} +(-2.10729 + 11.9511i) q^{79} +(6.88539 + 5.77753i) q^{81} +(-7.85939 + 1.38582i) q^{82} +(-5.39755 + 3.11628i) q^{83} +(0.0332056 - 0.0575138i) q^{84} +(5.36981 + 1.95445i) q^{86} +(-0.103344 - 0.0596659i) q^{87} +(-2.13541 + 1.23288i) q^{88} +(-2.95236 - 16.7437i) q^{89} +(3.36837 - 2.82640i) q^{91} +(1.59629 + 0.281470i) q^{92} +(-0.0433143 - 0.119005i) q^{93} +12.4926 q^{94} -0.0361439 q^{96} +(4.67194 + 12.8360i) q^{97} +(-3.56887 - 0.629287i) q^{98} +(-5.66417 + 4.75280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{9}+O(q^{10}) \) 36 * q + 36 * q^9	\( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) 36 * q + 36 * q^9 - 24 * q^11 - 12 * q^14 + 24 * q^21 - 18 * q^26 + 12 * q^29 - 12 * q^31 - 36 * q^34 - 36 * q^36 - 96 * q^39 - 42 * q^41 - 6 * q^44 + 36 * q^46 + 78 * q^49 + 84 * q^51 + 108 * q^54 + 60 * q^59 + 96 * q^61 + 18 * q^64 + 48 * q^66 + 60 * q^69 + 60 * q^71 + 6 * q^74 - 42 * q^76 - 60 * q^79 + 36 * q^81 - 12 * q^84 + 72 * q^86 - 60 * q^89 - 120 * q^91 - 12 * q^94 - 342 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more