LMFDB - Embedded newform 950.2.l.i.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} + \cdots + 64 $ x^18 + 24x^16 - 12x^15 + 393x^14 - 222x^13 + 3518x^12 - 2478x^11 + 22809x^10 - 12862x^9 + 77397x^8 - 24822x^7 + 178501x^6 - 39408x^5 + 132588x^4 + 45584x^3 + 50640x^2 + 1824x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.2
Root			$-0.0180720 - 0.0313015i$ of defining polynomial
Character	$\chi$	$=$	950.251
Dual form			950.2.l.i.651.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.00627632 - 0.0355948i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.00627632 + 0.0355948i) q^{6} +(0.918706 - 1.59124i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81785 - 1.02561i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.00627632 - 0.0355948i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.00627632 + 0.0355948i) q^{6} +(0.918706 - 1.59124i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81785 - 1.02561i) q^{9} +(1.23288 + 2.13541i) q^{11} +(0.0180720 - 0.0313015i) q^{12} +(-0.415556 + 2.35673i) q^{13} +(-1.40754 + 1.18107i) q^{14} +(0.173648 + 0.984808i) q^{16} +(6.33539 + 2.30589i) q^{17} -2.99869 q^{18} +(-4.34868 - 0.298357i) q^{19} +(-0.0624061 - 0.0227140i) q^{21} +(-0.428174 - 2.42830i) q^{22} +(-1.24170 - 1.04191i) q^{23} +(-0.0276878 + 0.0232329i) q^{24} +(1.19655 - 2.07248i) q^{26} +(-0.108408 - 0.187768i) q^{27} +(1.72660 - 0.628432i) q^{28} +(-3.10246 + 1.12920i) q^{29} +(1.75192 - 3.03441i) q^{31} +(0.173648 - 0.984808i) q^{32} +(0.0682715 - 0.0572866i) q^{33} +(-5.16466 - 4.33366i) q^{34} +(2.81785 + 1.02561i) q^{36} +6.00888 q^{37} +(3.98437 + 1.76770i) q^{38} +0.0864957 q^{39} +(-1.38582 - 7.85939i) q^{41} +(0.0508739 + 0.0426883i) q^{42} +(-4.37751 + 3.67317i) q^{43} +(-0.428174 + 2.42830i) q^{44} +(0.810460 + 1.40376i) q^{46} +(11.7392 - 4.27274i) q^{47} +(0.0339642 - 0.0123619i) q^{48} +(1.81196 + 3.13841i) q^{49} +(0.0423149 - 0.239980i) q^{51} +(-1.83321 + 1.53825i) q^{52} +(1.47185 + 1.23503i) q^{53} +(0.0376497 + 0.213522i) q^{54} -1.83741 q^{56} +(0.0166738 + 0.156663i) q^{57} +3.30157 q^{58} +(4.46726 + 1.62595i) q^{59} +(10.4674 + 8.78317i) q^{61} +(-2.68410 + 2.25222i) q^{62} +(0.956772 - 5.42613i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0837473 + 0.0304815i) q^{66} +(-3.49344 + 1.27151i) q^{67} +(3.37099 + 5.83873i) q^{68} +(-0.0292932 + 0.0507373i) q^{69} +(4.46844 - 3.74946i) q^{71} +(-2.29713 - 1.92752i) q^{72} +(0.0886314 + 0.502654i) q^{73} +(-5.64650 - 2.05516i) q^{74} +(-3.13950 - 3.02383i) q^{76} +4.53061 q^{77} +(-0.0812794 - 0.0295833i) q^{78} +(2.10729 + 11.9511i) q^{79} +(6.88539 - 5.77753i) q^{81} +(-1.38582 + 7.85939i) q^{82} +(3.11628 - 5.39755i) q^{83} +(-0.0332056 - 0.0575138i) q^{84} +(5.36981 - 1.95445i) q^{86} +(0.0596659 + 0.103344i) q^{87} +(1.23288 - 2.13541i) q^{88} +(2.95236 - 16.7437i) q^{89} +(3.36837 + 2.82640i) q^{91} +(-0.281470 - 1.59629i) q^{92} +(-0.119005 - 0.0433143i) q^{93} -12.4926 q^{94} -0.0361439 q^{96} +(-12.8360 - 4.67194i) q^{97} +(-0.629287 - 3.56887i) q^{98} +(5.66417 + 4.75280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 9 * q^8 - 18 * q^9	$ 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) $ 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.00627632	−	0.0355948i	−0.00362364	−	0.0205507i	0.982942	−	0.183914i	$-0.0588768\pi$
$3$	−0.00627632	−	0.0355948i	−0.00362364	−	0.0205507i	−0.986566	+	0.163363i	$0.947766\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.00627632	+	0.0355948i	−0.00256230	+	0.0145315i
$7$	0.918706	−	1.59124i	0.347238	−	0.601434i	−0.638520	−	0.769605i	$-0.720453\pi$
$7$	0.918706	−	1.59124i	0.347238	−	0.601434i	0.985758	+	0.168172i	$0.0537863\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.81785	−	1.02561i	0.939283	−	0.341871i
$10$		0			0
$11$	1.23288	+	2.13541i	0.371727	+	0.643850i	0.989831	−	0.142246i	$-0.0454325\pi$
$11$	1.23288	+	2.13541i	0.371727	+	0.643850i	−0.618105	+	0.786096i	$0.712099\pi$
$12$	0.0180720	−	0.0313015i	0.00521692	−	0.00903598i
$13$	−0.415556	+	2.35673i	−0.115254	+	0.653641i	0.871369	+	0.490627i	$0.163232\pi$
$13$	−0.415556	+	2.35673i	−0.115254	+	0.653641i	−0.986624	+	0.163013i	$0.947879\pi$
$14$	−1.40754	+	1.18107i	−0.376180	+	0.315653i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	6.33539	+	2.30589i	1.53656	+	0.559261i	0.965217	−	0.261451i	$-0.0842010\pi$
$17$	6.33539	+	2.30589i	1.53656	+	0.559261i	0.571341	+	0.820712i	$0.306423\pi$
$18$	−2.99869			−0.706799
$19$	−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
$22$	−0.428174	−	2.42830i	−0.0912870	−	0.517714i
$23$	−1.24170	−	1.04191i	−0.258912	−	0.217253i	0.504087	−	0.863653i	$-0.331829\pi$
$23$	−1.24170	−	1.04191i	−0.258912	−	0.217253i	−0.762998	+	0.646400i	$0.776274\pi$
$24$	−0.0276878	+	0.0232329i	−0.00565176	+	0.00474239i
$25$		0			0
$26$	1.19655	−	2.07248i	0.234662	−	0.406446i
$27$	−0.108408	−	0.187768i	−0.0208632	−	0.0361360i
$28$	1.72660	−	0.628432i	0.326297	−	0.118762i
$29$	−3.10246	+	1.12920i	−0.576113	+	0.209688i	−0.613611	−	0.789609i	$-0.710284\pi$
$29$	−3.10246	+	1.12920i	−0.576113	+	0.209688i	0.0374978	+	0.999297i	$0.488061\pi$
$30$		0			0
$31$	1.75192	−	3.03441i	0.314654	−	0.544997i	−0.664710	−	0.747102i	$-0.731445\pi$
$31$	1.75192	−	3.03441i	0.314654	−	0.544997i	0.979364	+	0.202105i	$0.0647782\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	0.0682715	−	0.0572866i	0.0118845	−	0.00997231i
$34$	−5.16466	−	4.33366i	−0.885732	−	0.743217i
$35$		0			0
$36$	2.81785	+	1.02561i	0.469642	+	0.170936i
$37$	6.00888			0.987854			0.493927	−	0.869503i	$-0.335561\pi$
$37$	6.00888			0.987854			0.493927	+	0.869503i	$0.335561\pi$
$38$	3.98437	+	1.76770i	0.646351	+	0.286759i
$39$	0.0864957			0.0138504
$40$		0			0
$41$	−1.38582	−	7.85939i	−0.216429	−	1.22743i	−0.878409	−	0.477909i	$-0.841395\pi$
$41$	−1.38582	−	7.85939i	−0.216429	−	1.22743i	0.661980	−	0.749521i	$-0.269716\pi$
$42$	0.0508739	+	0.0426883i	0.00785002	+	0.00658695i
$43$	−4.37751	+	3.67317i	−0.667564	+	0.560153i	−0.912343	−	0.409426i	$-0.865729\pi$
$43$	−4.37751	+	3.67317i	−0.667564	+	0.560153i	0.244779	+	0.969579i	$0.421285\pi$
$44$	−0.428174	+	2.42830i	−0.0645497	+	0.366079i
$45$		0			0
$46$	0.810460	+	1.40376i	0.119496	+	0.206973i
$47$	11.7392	−	4.27274i	1.71234	−	0.623243i	0.715212	−	0.698908i	$-0.246330\pi$
$47$	11.7392	−	4.27274i	1.71234	−	0.623243i	0.997133	+	0.0756655i	$0.0241081\pi$
$48$	0.0339642	−	0.0123619i	0.00490231	−	0.00178429i
$49$	1.81196	+	3.13841i	0.258851	+	0.448344i
$50$		0			0
$51$	0.0423149	−	0.239980i	0.00592527	−	0.0336039i
$52$	−1.83321	+	1.53825i	−0.254221	+	0.213317i
$53$	1.47185	+	1.23503i	0.202174	+	0.169644i	0.738253	−	0.674524i	$-0.235651\pi$
$53$	1.47185	+	1.23503i	0.202174	+	0.169644i	−0.536080	+	0.844167i	$0.680095\pi$
$54$	0.0376497	+	0.213522i	0.00512348	+	0.0290567i
$55$		0			0
$56$	−1.83741			−0.245534
$57$	0.0166738	+	0.156663i	0.00220849	+	0.0207505i
$58$	3.30157			0.433518
$59$	4.46726	+	1.62595i	0.581587	+	0.211681i	0.616025	−	0.787726i	$-0.288742\pi$
$59$	4.46726	+	1.62595i	0.581587	+	0.211681i	−0.0344379	+	0.999407i	$0.510964\pi$
$60$		0			0
$61$	10.4674	+	8.78317i	1.34021	+	1.12457i	0.981572	+	0.191093i	$0.0612033\pi$
$61$	10.4674	+	8.78317i	1.34021	+	1.12457i	0.358638	+	0.933477i	$0.383241\pi$
$62$	−2.68410	+	2.25222i	−0.340881	+	0.286033i
$63$	0.956772	−	5.42613i	0.120542	−	0.683628i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−0.0837473	+	0.0304815i	−0.0103086	+	0.00375202i
$67$	−3.49344	+	1.27151i	−0.426792	+	0.155340i	−0.546480	−	0.837472i	$-0.684033\pi$
$67$	−3.49344	+	1.27151i	−0.426792	+	0.155340i	0.119688	+	0.992812i	$0.461810\pi$
$68$	3.37099	+	5.83873i	0.408793	+	0.708050i
$69$	−0.0292932	+	0.0507373i	−0.00352648	+	0.00610805i
$70$		0			0
$71$	4.46844	−	3.74946i	0.530306	−	0.444980i	−0.337901	−	0.941182i	$-0.609717\pi$
$71$	4.46844	−	3.74946i	0.530306	−	0.444980i	0.868207	+	0.496202i	$0.165272\pi$
$72$	−2.29713	−	1.92752i	−0.270720	−	0.227161i
$73$	0.0886314	+	0.502654i	0.0103735	+	0.0588311i	0.989555	−	0.144155i	$-0.0460464\pi$
$73$	0.0886314	+	0.502654i	0.0103735	+	0.0588311i	−0.979182	+	0.202986i	$0.934935\pi$
$74$	−5.64650	−	2.05516i	−0.656393	−	0.238907i
$75$		0			0
$76$	−3.13950	−	3.02383i	−0.360125	−	0.346857i
$77$	4.53061			0.516311
$78$	−0.0812794	−	0.0295833i	−0.00920307	−	0.00334965i
$79$	2.10729	+	11.9511i	0.237089	+	1.34460i	0.838169	+	0.545411i	$0.183626\pi$
$79$	2.10729	+	11.9511i	0.237089	+	1.34460i	−0.601080	+	0.799189i	$0.705263\pi$
$80$		0			0
$81$	6.88539	−	5.77753i	0.765044	−	0.641948i
$82$	−1.38582	+	7.85939i	−0.153038	+	0.867924i
$83$	3.11628	−	5.39755i	0.342056	−	0.592459i	−0.642758	−	0.766069i	$-0.722210\pi$
$83$	3.11628	−	5.39755i	0.342056	−	0.592459i	0.984814	+	0.173610i	$0.0555434\pi$
$84$	−0.0332056	−	0.0575138i	−0.00362303	−	0.00627527i
$85$		0			0
$86$	5.36981	−	1.95445i	0.579042	−	0.210754i
$87$	0.0596659	+	0.103344i	0.00639685	+	0.0110797i
$88$	1.23288	−	2.13541i	0.131425	−	0.227635i
$89$	2.95236	−	16.7437i	0.312949	−	1.77482i	−0.270545	−	0.962707i	$-0.587204\pi$
$89$	2.95236	−	16.7437i	0.312949	−	1.77482i	0.583494	−	0.812117i	$-0.301685\pi$
$90$		0			0
$91$	3.36837	+	2.82640i	0.353101	+	0.296287i
$92$	−0.281470	−	1.59629i	−0.0293452	−	0.166425i
$93$	−0.119005	−	0.0433143i	−0.0123402	−	0.00449148i
$94$	−12.4926			−1.28852
$95$		0			0
$96$	−0.0361439			−0.00368892
$97$	−12.8360	−	4.67194i	−1.30330	−	0.474363i	−0.405232	−	0.914214i	$-0.632809\pi$
$97$	−12.8360	−	4.67194i	−1.30330	−	0.474363i	−0.898071	+	0.439851i	$0.855031\pi$
$98$	−0.629287	−	3.56887i	−0.0635676	−	0.360510i
$99$	5.66417	+	4.75280i	0.569270	+	0.477675i
$100$		0			0
$101$	−1.85079	+	10.4964i	−0.184161	+	1.04443i	0.742868	+	0.669438i	$0.233465\pi$
$101$	−1.85079	+	10.4964i	−0.184161	+	1.04443i	−0.927029	+	0.374990i	$0.877646\pi$
$102$	−0.121841	+	0.211034i	−0.0120640	+	0.0208955i
$103$	−4.87465	−	8.44314i	−0.480313	−	0.831927i	0.519431	−	0.854512i	$-0.326144\pi$
$103$	−4.87465	−	8.44314i	−0.480313	−	0.831927i	−0.999745	+	0.0225848i	$0.992810\pi$
$104$	2.24877	−	0.818485i	0.220510	−	0.0802591i
$105$		0			0
$106$	−0.960680	−	1.66395i	−0.0933095	−	0.161617i
$107$	6.64287	−	11.5058i	0.642191	−	1.11231i	−0.342752	−	0.939426i	$-0.611359\pi$
$107$	6.64287	−	11.5058i	0.642191	−	1.11231i	0.984943	−	0.172881i	$-0.0553076\pi$
$108$	0.0376497	−	0.213522i	0.00362285	−	0.0205462i
$109$	1.10611	−	0.928135i	0.105946	−	0.0888992i	−0.588276	−	0.808660i	$-0.700193\pi$
$109$	1.10611	−	0.928135i	0.105946	−	0.0888992i	0.694222	+	0.719761i	$0.255749\pi$
$110$		0			0
$111$	−0.0377137	−	0.213885i	−0.00357963	−	0.0203011i
$112$	1.72660	+	0.628432i	0.163149	+	0.0593812i
$113$	0.841529			0.0791644			0.0395822	−	0.999216i	$-0.487397\pi$
$113$	0.841529			0.0791644			0.0395822	+	0.999216i	$0.487397\pi$
$114$	0.0379136	−	0.152918i	0.00355094	−	0.0143221i
$115$		0			0
$116$	−3.10246	−	1.12920i	−0.288056	−	0.104844i
$117$	1.24612	+	7.06713i	0.115204	+	0.653356i
$118$	−3.64174	−	3.05578i	−0.335250	−	0.281308i
$119$	9.48960	−	7.96272i	0.869910	−	0.729941i
$120$		0			0
$121$	2.46002	−	4.26089i	0.223639	−	0.387353i
$122$	−6.83209	−	11.8335i	−0.618549	−	1.07136i
$123$	−0.271056	+	0.0986562i	−0.0244403	+	0.00889553i
$124$	3.29253	−	1.19838i	0.295678	−	0.107618i
$125$		0			0
$126$	−2.75492	+	4.77166i	−0.245427	+	0.425093i
$127$	−2.25496	+	12.7885i	−0.200095	+	1.13480i	0.704878	+	0.709329i	$0.251002\pi$
$127$	−2.25496	+	12.7885i	−0.200095	+	1.13480i	−0.904973	+	0.425469i	$0.860109\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	0.158220	+	0.132763i	0.0139305	+	0.0116891i
$130$		0			0
$131$	−8.39051	−	3.05389i	−0.733082	−	0.266820i	−0.0516131	−	0.998667i	$-0.516436\pi$
$131$	−8.39051	−	3.05389i	−0.733082	−	0.266820i	−0.681469	+	0.731847i	$0.738658\pi$
$132$	0.0891221			0.00775708
$133$	−4.46991	+	6.64571i	−0.387590	+	0.576256i
$134$	3.71765			0.321156
$135$		0			0
$136$	−1.17073	−	6.63956i	−0.100390	−	0.569337i
$137$	−3.41165	−	2.86271i	−0.291477	−	0.244578i	0.485309	−	0.874343i	$-0.338707\pi$
$137$	−3.41165	−	2.86271i	−0.291477	−	0.244578i	−0.776786	+	0.629764i	$0.783151\pi$
$138$	0.0448798	−	0.0376586i	0.00382042	−	0.00320571i
$139$	−0.210369	+	1.19306i	−0.0178433	+	0.101194i	−0.992429	−	0.122822i	$-0.960806\pi$
$139$	−0.210369	+	1.19306i	−0.0178433	+	0.101194i	0.974585	+	0.224016i	$0.0719168\pi$
$140$		0			0
$141$	−0.225767	−	0.391039i	−0.0190130	−	0.0329314i
$142$	−5.48135	+	1.99505i	−0.459985	+	0.167421i
$143$	−5.54492	+	2.01819i	−0.463689	+	0.168769i
$144$	1.49935	+	2.59694i	0.124946	+	0.216412i
$145$		0			0
$146$	0.0886314	−	0.502654i	0.00733519	−	0.0415999i
$147$	0.100339	−	0.0841940i	0.00827578	−	0.00694421i
$148$	4.60307	+	3.86244i	0.378370	+	0.317490i
$149$	1.61216	+	9.14300i	0.132073	+	0.749024i	0.976853	+	0.213910i	$0.0686201\pi$
$149$	1.61216	+	9.14300i	0.132073	+	0.749024i	−0.844780	+	0.535114i	$0.820269\pi$
$150$		0			0
$151$	−3.34570			−0.272269			−0.136135	−	0.990690i	$-0.543468\pi$
$151$	−3.34570			−0.272269			−0.136135	+	0.990690i	$0.543468\pi$
$152$	1.91595	+	3.91524i	0.155404	+	0.317568i
$153$	20.2171			1.63446
$154$	−4.25738	−	1.54956i	−0.343069	−	0.124867i
$155$		0			0
$156$	0.0662595	+	0.0555984i	0.00530501	+	0.00445143i
$157$	−5.40304	+	4.53369i	−0.431210	+	0.361828i	−0.832408	−	0.554163i	$-0.813038\pi$
$157$	−5.40304	+	4.53369i	−0.431210	+	0.361828i	0.401198	+	0.915991i	$0.368594\pi$
$158$	2.10729	−	11.9511i	0.167647	−	0.950775i
$159$	0.0347227	−	0.0601415i	0.00275369	−	0.00476953i
$160$		0			0
$161$	−2.79868	+	1.01864i	−0.220567	+	0.0802798i
$162$	−8.44619	+	3.07416i	−0.663595	+	0.241529i
$163$	−7.92794	−	13.7316i	−0.620964	−	1.07554i	−0.989307	−	0.145851i	$-0.953408\pi$
$163$	−7.92794	−	13.7316i	−0.620964	−	1.07554i	0.368343	−	0.929690i	$-0.379925\pi$
$164$	3.99032	−	6.91143i	0.311591	−	0.539692i
$165$		0			0
$166$	−4.77442	+	4.00621i	−0.370567	+	0.310942i
$167$	10.4379	+	8.75846i	0.807711	+	0.677750i	0.950060	−	0.312066i	$-0.101021\pi$
$167$	10.4379	+	8.75846i	0.807711	+	0.677750i	−0.142349	+	0.989817i	$0.545466\pi$
$168$	0.0115322	+	0.0654023i	0.000889728	+	0.00504590i
$169$	6.83449	+	2.48755i	0.525730	+	0.191350i
$170$		0			0
$171$	−12.5599	+	3.61934i	−0.960481	+	0.276778i
$172$	−5.71443			−0.435721
$173$	11.3134	+	4.11774i	0.860142	+	0.313066i	0.734168	−	0.678968i	$-0.237572\pi$
$173$	11.3134	+	4.11774i	0.860142	+	0.313066i	0.125973	+	0.992034i	$0.459795\pi$
$174$	−0.0207217	−	0.117519i	−0.00157091	−	0.00890908i
$175$		0			0
$176$	−1.88888	+	1.58496i	−0.142380	+	0.119471i
$177$	0.0298374	−	0.169216i	0.00224271	−	0.0127191i
$178$	−8.50098	+	14.7241i	−0.637175	+	1.10362i
$179$	−8.03649	−	13.9196i	−0.600675	−	1.04040i	−0.992719	−	0.120454i	$-0.961565\pi$
$179$	−8.03649	−	13.9196i	−0.600675	−	1.04040i	0.392044	−	0.919947i	$-0.371768\pi$
$180$		0			0
$181$	−5.40615	+	1.96768i	−0.401836	+	0.146256i	−0.535029	−	0.844834i	$-0.679699\pi$
$181$	−5.40615	+	1.96768i	−0.401836	+	0.146256i	0.133193	+	0.991090i	$0.457477\pi$
$182$	−2.19855	−	3.80799i	−0.162967	−	0.282267i
$183$	0.246939	−	0.427710i	0.0182542	−	0.0316173i
$184$	−0.281470	+	1.59629i	−0.0207502	+	0.117680i
$185$		0			0
$186$	0.0970138	+	0.0814042i	0.00711339	+	0.00596885i
$187$	2.88674	+	16.3715i	0.211099	+	1.19720i
$188$	11.7392	+	4.27274i	0.856172	+	0.311621i
$189$	−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	$0.766754\pi$
$192$	0.0339642	+	0.0123619i	0.00245115	+	0.000892147i
$193$	2.17302	+	12.3238i	0.156418	+	0.887089i	0.957478	+	0.288506i	$0.0931584\pi$
$193$	2.17302	+	12.3238i	0.156418	+	0.887089i	−0.801060	+	0.598583i	$0.795731\pi$
$194$	10.4640	+	8.78037i	0.751274	+	0.630394i
$195$		0			0
$196$	−0.629287	+	3.56887i	−0.0449491	+	0.254919i
$197$	3.01173	−	5.21647i	0.214577	−	0.371658i	−0.738565	−	0.674183i	$-0.764496\pi$
$197$	3.01173	−	5.21647i	0.214577	−	0.371658i	0.953142	+	0.302524i	$0.0978294\pi$
$198$	−3.69702	−	6.40343i	−0.262736	−	0.455072i
$199$	−10.5749	+	3.84894i	−0.749633	+	0.272844i	−0.688451	−	0.725283i	$-0.741709\pi$
$199$	−10.5749	+	3.84894i	−0.749633	+	0.272844i	−0.0611814	+	0.998127i	$0.519487\pi$
$200$		0			0
$201$	0.0671851	+	0.116368i	0.00473887	+	0.00820797i
$202$	5.32914	−	9.23035i	0.374957	−	0.649445i
$203$	−1.05341	+	5.97418i	−0.0739349	+	0.419305i
$204$	0.186671	−	0.156636i	0.0130696	−	0.0109667i
$205$		0			0
$206$	1.69295	+	9.60119i	0.117953	+	0.668946i
$207$	−4.56751	−	1.66244i	−0.317464	−	0.115547i
$208$	−2.39309			−0.165931
$209$	−4.72427	−	9.65403i	−0.326785	−	0.667783i
$210$		0			0
$211$	−13.2192	−	4.81141i	−0.910049	−	0.331231i	−0.155777	−	0.987792i	$-0.549788\pi$
$211$	−13.2192	−	4.81141i	−0.910049	−	0.331231i	−0.754273	+	0.656561i	$0.772010\pi$
$212$	0.333641	+	1.89217i	0.0229145	+	0.129955i
$213$	−0.161507	−	0.135520i	−0.0110663	−	0.00928570i
$214$	−10.1775	+	8.53991i	−0.695718	+	0.583776i
$215$		0			0
$216$	−0.108408	+	0.187768i	−0.00737624	+	0.0127760i
$217$	−3.21900	−	5.57547i	−0.218520	−	0.378487i
$218$	−1.35684	+	0.493850i	−0.0918969	+	0.0334477i
$219$	0.0173356	−	0.00630963i	0.00117143	−	0.000426366i
$220$		0			0
$221$	−8.06709	+	13.9726i	−0.542651	+	0.939899i
$222$	−0.0377137	+	0.213885i	−0.00253118	+	0.0143550i
$223$	−19.3828	+	16.2641i	−1.29797	+	1.08913i	−0.307477	+	0.951555i	$0.599485\pi$
$223$	−19.3828	+	16.2641i	−1.29797	+	1.08913i	−0.990492	+	0.137570i	$0.956071\pi$
$224$	−1.40754	−	1.18107i	−0.0940451	−	0.0789132i
$225$		0			0
$226$	−0.790779	−	0.287820i	−0.0526018	−	0.0191455i
$227$	−22.0111			−1.46093			−0.730464	−	0.682951i	$-0.760696\pi$
$227$	−22.0111			−1.46093			−0.730464	+	0.682951i	$0.760696\pi$
$228$	−0.0879281	+	0.130728i	−0.00582318	+	0.00865770i
$229$	−5.29529			−0.349923			−0.174961	−	0.984575i	$-0.555980\pi$
$229$	−5.29529			−0.349923			−0.174961	+	0.984575i	$0.555980\pi$
$230$		0			0
$231$	−0.0284356	−	0.161266i	−0.00187092	−	0.0106105i
$232$	2.52915	+	2.12221i	0.166047	+	0.139330i
$233$	−15.7436	+	13.2104i	−1.03140	+	0.865445i	−0.991016	−	0.133740i	$-0.957301\pi$
$233$	−15.7436	+	13.2104i	−1.03140	+	0.865445i	−0.0403803	+	0.999184i	$0.512857\pi$
$234$	1.24612	−	7.06713i	0.0814617	−	0.461992i
$235$		0			0
$236$	2.37698	+	4.11705i	0.154728	+	0.267997i
$237$	0.412170	−	0.150017i	0.0267733	−	0.00974468i
$238$	−11.6407	+	4.23688i	−0.754556	+	0.274636i
$239$	−0.443585	−	0.768312i	−0.0286931	−	0.0496980i	0.851322	−	0.524643i	$-0.175801\pi$
$239$	−0.443585	−	0.768312i	−0.0286931	−	0.0496980i	−0.880015	+	0.474945i	$0.842468\pi$
$240$		0			0
$241$	−0.694839	+	3.94063i	−0.0447585	+	0.253838i	−0.998974	−	0.0452809i	$-0.985582\pi$
$241$	−0.694839	+	3.94063i	−0.0447585	+	0.253838i	0.954216	+	0.299119i	$0.0966928\pi$
$242$	−3.76898	+	3.16255i	−0.242279	+	0.203296i
$243$	−0.747138	−	0.626923i	−0.0479289	−	0.0402171i
$244$	2.37276	+	13.4566i	0.151900	+	0.861471i
$245$		0			0
$246$	0.288451			0.0183910
$247$	2.51027	−	10.1247i	0.159724	−	0.644219i
$248$	−3.50384			−0.222494
$249$	−0.211684	−	0.0770466i	−0.0134149	−	0.00488263i
$250$		0			0
$251$	−9.70480	−	8.14329i	−0.612561	−	0.514000i	0.282894	−	0.959151i	$-0.408706\pi$
$251$	−9.70480	−	8.14329i	−0.612561	−	0.514000i	−0.895455	+	0.445151i	$0.853150\pi$
$252$	4.22078	−	3.54165i	0.265884	−	0.223103i
$253$	0.694035	−	3.93607i	0.0436336	−	0.247459i
$254$	6.49290	−	11.2460i	0.407401	−	0.705639i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−12.2581	+	4.46158i	−0.764639	+	0.278306i	−0.694752	−	0.719249i	$-0.744486\pi$
$257$	−12.2581	+	4.46158i	−0.764639	+	0.278306i	−0.0698866	+	0.997555i	$0.522264\pi$
$258$	−0.103271	−	0.178871i	−0.00642937	−	0.0111360i
$259$	5.52039	−	9.56160i	0.343021	−	0.594129i
$260$		0			0
$261$	−7.58415	+	6.36386i	−0.469447	+	0.393913i
$262$	6.84000	+	5.73944i	0.422577	+	0.354584i
$263$	−4.90583	−	27.8224i	−0.302507	−	1.71560i	−0.635015	−	0.772500i	$-0.719006\pi$
$263$	−4.90583	−	27.8224i	−0.302507	−	1.71560i	0.332508	−	0.943100i	$-0.392105\pi$
$264$	−0.0837473	−	0.0304815i	−0.00515429	−	0.00187601i
$265$		0			0
$266$	6.47331	−	4.71612i	0.396904	−	0.289164i
$267$	−0.614517			−0.0376079
$268$	−3.49344	−	1.27151i	−0.213396	−	0.0776698i
$269$	5.13013	+	29.0944i	0.312789	+	1.77392i	0.584356	+	0.811498i	$0.301347\pi$
$269$	5.13013	+	29.0944i	0.312789	+	1.77392i	−0.271566	+	0.962420i	$0.587542\pi$
$270$		0			0
$271$	20.6918	−	17.3624i	1.25693	−	1.05469i	0.260933	−	0.965357i	$-0.415970\pi$
$271$	20.6918	−	17.3624i	1.25693	−	1.05469i	0.996001	−	0.0893367i	$-0.0284747\pi$
$272$	−1.17073	+	6.63956i	−0.0709861	+	0.402582i
$273$	0.0794641	−	0.137636i	0.00480938	−	0.00833010i
$274$	2.22680	+	3.85692i	0.134526	+	0.233005i
$275$		0			0
$276$	−0.0550532	+	0.0200377i	−0.00331381	+	0.00120613i
$277$	−12.0889	−	20.9386i	−0.726352	−	1.25808i	−0.958415	−	0.285378i	$-0.907881\pi$
$277$	−12.0889	−	20.9386i	−0.726352	−	1.25808i	0.232063	−	0.972701i	$-0.425453\pi$
$278$	0.605735	−	1.04916i	0.0363295	−	0.0629246i
$279$	1.82451	−	10.3473i	0.109231	−	0.619478i
$280$		0			0
$281$	1.83928	+	1.54334i	0.109722	+	0.0920681i	0.695998	−	0.718043i	$-0.254962\pi$
$281$	1.83928	+	1.54334i	0.109722	+	0.0920681i	−0.586276	+	0.810111i	$0.699407\pi$
$282$	0.0784079	+	0.444673i	0.00466912	+	0.0264799i
$283$	7.65937	+	2.78778i	0.455302	+	0.165716i	0.559483	−	0.828842i	$-0.311000\pi$
$283$	7.65937	+	2.78778i	0.455302	+	0.165716i	−0.104181	+	0.994558i	$0.533222\pi$
$284$	5.83313			0.346133
$285$		0			0
$286$	5.90078			0.348920
$287$	−13.7794	−	5.01528i	−0.813371	−	0.296043i
$288$	−0.520718	−	2.95314i	−0.0306836	−	0.174015i
$289$	21.7973	+	18.2901i	1.28219	+	1.07589i
$290$		0			0
$291$	−0.0857335	+	0.486219i	−0.00502579	+	0.0285027i
$292$	−0.255204	+	0.442026i	−0.0149347	+	0.0258676i
$293$	4.59878	+	7.96532i	0.268664	+	0.465339i	0.968517	−	0.248947i	$-0.0800846\pi$
$293$	4.59878	+	7.96532i	0.268664	+	0.465339i	−0.699853	+	0.714287i	$0.746751\pi$
$294$	−0.123083	+	0.0447987i	−0.00717837	+	0.00261271i
$295$		0			0
$296$	−3.00444	−	5.20385i	−0.174630	−	0.302467i
$297$	0.267308	−	0.462991i	0.0155108	−	0.0268655i
$298$	1.61216	−	9.14300i	0.0933898	−	0.529640i
$299$	2.97149	−	2.49338i	0.171846	−	0.144196i
$300$		0			0
$301$	1.82326	+	10.3402i	0.105091	+	0.596002i
$302$	3.14393	+	1.14430i	0.180913	+	0.0658469i
$303$	0.385232			0.0221310
$304$	−0.461316	−	4.33442i	−0.0264583	−	0.248596i
$305$		0			0
$306$	−18.9979	−	6.91467i	−1.08604	−	0.395285i
$307$	4.92243	+	27.9165i	0.280938	+	1.59328i	0.719444	+	0.694550i	$0.244397\pi$
$307$	4.92243	+	27.9165i	0.280938	+	1.59328i	−0.438506	+	0.898728i	$0.644492\pi$
$308$	3.47065	+	2.91222i	0.197758	+	0.165939i
$309$	−0.269937	+	0.226504i	−0.0153562	+	0.0128854i
$310$		0			0
$311$	−8.72043	+	15.1042i	−0.494490	+	0.856482i	−0.999980	−	0.00635057i	$-0.997979\pi$
$311$	−8.72043	+	15.1042i	−0.494490	+	0.856482i	0.505490	+	0.862833i	$0.331312\pi$
$312$	−0.0432478	−	0.0749075i	−0.00244843	−	0.00424080i
$313$	−12.4024	+	4.51409i	−0.701022	+	0.255151i	−0.667847	−	0.744298i	$-0.732784\pi$
$313$	−12.4024	+	4.51409i	−0.701022	+	0.255151i	−0.0331750	+	0.999450i	$0.510562\pi$
$314$	6.62781	−	2.41233i	0.374029	−	0.136135i
$315$		0			0
$316$	−6.06771	+	10.5096i	−0.341336	+	0.591210i
$317$	2.13351	−	12.0997i	0.119830	−	0.679588i	−0.864415	−	0.502778i	$-0.832311\pi$
$317$	2.13351	−	12.0997i	0.119830	−	0.679588i	0.984245	−	0.176810i	$-0.0565777\pi$
$318$	−0.0531983	+	0.0446387i	−0.00298321	+	0.00250321i
$319$	−6.23627	−	5.23285i	−0.349164	−	0.292983i
$320$		0			0
$321$	−0.451239	−	0.164238i	−0.0251857	−	0.00916685i
$322$	2.97829			0.165974
$323$	−26.8626	−	11.9178i	−1.49467	−	0.663124i
$324$	8.98824			0.499347
$325$		0			0
$326$	2.75334	+	15.6150i	0.152494	+	0.864834i
$327$	−0.0399791	−	0.0335464i	−0.00221085	−	0.00185512i
$328$	−6.11352	+	5.12985i	−0.337563	+	0.283249i
$329$	3.98594	−	22.6054i	0.219752	−	1.24628i
$330$		0			0
$331$	−0.498297	−	0.863076i	−0.0273889	−	0.0474389i	0.852006	−	0.523532i	$-0.175386\pi$
$331$	−0.498297	−	0.863076i	−0.0273889	−	0.0474389i	−0.879395	+	0.476093i	$0.842053\pi$
$332$	5.85669	−	2.13166i	0.321428	−	0.116990i
$333$	16.9321	−	6.16279i	0.927875	−	0.337719i
$334$	−6.81287	−	11.8002i	−0.372784	−	0.645681i
$335$		0			0
$336$	0.0115322	−	0.0654023i	0.000629132	−	0.00356799i
$337$	−6.55672	+	5.50174i	−0.357167	+	0.299699i	−0.803660	−	0.595088i	$-0.797117\pi$
$337$	−6.55672	+	5.50174i	−0.357167	+	0.299699i	0.446493	+	0.894787i	$0.352673\pi$
$338$	−5.57153	−	4.67507i	−0.303051	−	0.254290i
$339$	−0.00528171	−	0.0299541i	−0.000286863	−	0.00162688i
$340$		0			0
$341$	8.63961			0.467861
$342$	13.0403	+	0.894680i	0.705141	+	0.0483788i
$343$	19.5205			1.05401
$344$	5.36981	+	1.95445i	0.289521	+	0.105377i
$345$		0			0
$346$	−9.22276	−	7.73882i	−0.495819	−	0.416041i
$347$	5.08479	−	4.26665i	0.272966	−	0.229046i	−0.496020	−	0.868311i	$-0.665206\pi$
$347$	5.08479	−	4.26665i	0.272966	−	0.229046i	0.768986	+	0.639265i	$0.220761\pi$
$348$	−0.0207217	+	0.117519i	−0.00111080	+	0.00629967i
$349$	−15.5221	+	26.8851i	−0.830881	+	1.43913i	0.0664599	+	0.997789i	$0.478830\pi$
$349$	−15.5221	+	26.8851i	−0.830881	+	1.43913i	−0.897341	+	0.441339i	$0.854504\pi$
$350$		0			0
$351$	0.487570	−	0.177461i	0.0260246	−	0.00947216i
$352$	2.31705	−	0.843338i	0.123499	−	0.0449501i
$353$	8.88145	+	15.3831i	0.472712	+	0.818761i	0.999512	−	0.0312277i	$-0.00994171\pi$
$353$	8.88145	+	15.3831i	0.472712	+	0.818761i	−0.526800	+	0.849989i	$0.676608\pi$
$354$	−0.0859133	+	0.148806i	−0.00456624	+	0.00790896i
$355$		0			0
$356$	13.0243	−	10.9287i	0.690284	−	0.579217i
$357$	−0.342991	−	0.287804i	−0.0181530	−	0.0152322i
$358$	2.79104	+	15.8288i	0.147511	+	0.836578i
$359$	4.82640	+	1.75667i	0.254728	+	0.0927134i	0.466228	−	0.884665i	$-0.345613\pi$
$359$	4.82640	+	1.75667i	0.254728	+	0.0927134i	−0.211500	+	0.977378i	$0.567835\pi$
$360$		0			0
$361$	18.8220	+	2.59491i	0.990630	+	0.136574i
$362$	5.75310			0.302376
$363$	−0.167105	−	0.0608214i	−0.00877076	−	0.00319229i
$364$	0.763547	+	4.33029i	0.0400207	+	0.226969i
$365$		0			0
$366$	−0.378332	+	0.317458i	−0.0197757	+	0.0165938i
$367$	0.997763	−	5.65859i	0.0520828	−	0.295376i	−0.947629	−	0.319372i	$-0.896528\pi$
$367$	0.997763	−	5.65859i	0.0520828	−	0.295376i	0.999712	+	0.0239963i	$0.00763901\pi$
$368$	0.810460	−	1.40376i	0.0422481	−	0.0731759i
$369$	−11.9657	−	20.7253i	−0.622911	−	1.07891i
$370$		0			0
$371$	3.31742	−	1.20744i	0.172232	−	0.0626873i
$372$	−0.0633212	−	0.109676i	−0.00328305	−	0.00568641i
$373$	18.8927	−	32.7231i	0.978227	−	1.69434i	0.309379	−	0.950939i	$-0.399879\pi$
$373$	18.8927	−	32.7231i	0.978227	−	1.69434i	0.668848	−	0.743399i	$-0.266788\pi$
$374$	2.88674	−	16.3715i	0.149270	−	0.846551i
$375$		0			0
$376$	−9.56992	−	8.03012i	−0.493531	−	0.414122i
$377$	−1.37199	−	7.78093i	−0.0706610	−	0.400738i
$378$	0.374355	+	0.136254i	0.0192548	+	0.00700816i
$379$	−32.2663			−1.65741			−0.828703	−	0.559689i	$-0.810921\pi$
$379$	−32.2663			−1.65741			−0.828703	+	0.559689i	$0.810921\pi$
$380$		0			0
$381$	0.469358			0.0240459
$382$	19.3069	+	7.02715i	0.987829	+	0.359540i
$383$	3.78204	+	21.4490i	0.193253	+	1.09599i	0.914885	+	0.403715i	$0.132281\pi$
$383$	3.78204	+	21.4490i	0.193253	+	1.09599i	−0.721632	+	0.692277i	$0.756608\pi$
$384$	−0.0276878	−	0.0232329i	−0.00141294	−	0.00118560i
$385$		0			0
$386$	2.17302	−	12.3238i	0.110604	−	0.627267i
$387$	−8.56792	+	14.8401i	−0.435532	+	0.754363i
$388$	−6.82991	−	11.8298i	−0.346736	−	0.600565i
$389$	−9.10078	+	3.31241i	−0.461428	+	0.167946i	−0.562265	−	0.826957i	$-0.690070\pi$
$389$	−9.10078	+	3.31241i	−0.461428	+	0.167946i	0.100837	+	0.994903i	$0.467848\pi$
$390$		0			0
$391$	−5.46410	−	9.46411i	−0.276332	−	0.478620i
$392$	1.81196	−	3.13841i	0.0915178	−	0.158514i
$393$	−0.0560412	+	0.317826i	−0.00282691	+	0.0160322i
$394$	−4.61424	+	3.87181i	−0.232462	+	0.195059i
$395$		0			0
$396$	1.28396	+	7.28171i	0.0645216	+	0.365920i
$397$	−17.2858	−	6.29151i	−0.867549	−	0.315762i	−0.130375	−	0.991465i	$-0.541618\pi$
$397$	−17.2858	−	6.29151i	−0.867549	−	0.315762i	−0.737174	+	0.675703i	$0.763840\pi$
$398$	11.2535			0.564089
$399$	0.264607	+	0.117395i	0.0132469	+	0.00587710i
$400$		0			0
$401$	34.3332	+	12.4963i	1.71452	+	0.624034i	0.997342	−	0.0728556i	$-0.0232112\pi$
$401$	34.3332	+	12.4963i	1.71452	+	0.624034i	0.717178	+	0.696890i	$0.245433\pi$
$402$	−0.0233331	−	0.132329i	−0.00116375	−	0.00659996i
$403$	6.42329	+	5.38978i	0.319967	+	0.268484i
$404$	−8.16472	+	6.85102i	−0.406210	+	0.340851i
$405$		0			0
$406$	3.03317	−	5.25361i	0.150534	−	0.260732i
$407$	7.40822	+	12.8314i	0.367212	+	0.636030i
$408$	−0.228986	+	0.0833440i	−0.0113365	+	0.00412614i
$409$	−34.1168	+	12.4175i	−1.68697	+	0.614005i	−0.994238	−	0.107194i	$-0.965813\pi$
$409$	−34.1168	+	12.4175i	−1.68697	+	0.614005i	−0.692728	+	0.721199i	$0.743591\pi$
$410$		0			0
$411$	−0.0804851	+	0.139404i	−0.00397004	+	0.00687631i
$412$	1.69295	−	9.60119i	0.0834056	−	0.473016i
$413$	6.69138	−	5.61473i	0.329261	−	0.276283i
$414$	3.72347	+	3.12436i	0.182998	+	0.153554i
$415$		0			0
$416$	2.24877	+	0.818485i	0.110255	+	0.0401295i
$417$	0.0437872			0.00214427
$418$	1.13749	+	10.6876i	0.0556366	+	0.522749i
$419$	39.5001			1.92970			0.964852	−	0.262793i	$-0.0846437\pi$
$419$	39.5001			1.92970			0.964852	+	0.262793i	$0.0846437\pi$
$420$		0			0
$421$	−2.44853	−	13.8863i	−0.119334	−	0.676777i	−0.984513	−	0.175313i	$-0.943906\pi$
$421$	−2.44853	−	13.8863i	−0.119334	−	0.676777i	0.865179	−	0.501464i	$-0.167205\pi$
$422$	10.7764	+	9.04248i	0.524588	+	0.440181i
$423$	28.6973	−	24.0799i	1.39531	−	1.17080i
$424$	0.333641	−	1.89217i	0.0162030	−	0.0918919i
$425$		0			0
$426$	0.105416	+	0.182586i	0.00510743	+	0.00884632i
$427$	23.5926	−	8.58701i	1.14173	−	0.415554i
$428$	12.4845	−	4.54399i	0.603462	−	0.219642i
$429$	0.106639	+	0.184703i	0.00514856	+	0.00891757i
$430$		0			0
$431$	3.65410	−	20.7234i	0.176012	−	0.998213i	−0.760958	−	0.648802i	$-0.775270\pi$
$431$	3.65410	−	20.7234i	0.176012	−	0.998213i	0.936969	−	0.349411i	$-0.113618\pi$
$432$	0.166091	−	0.139367i	0.00799105	−	0.00670529i
$433$	4.02763	+	3.37958i	0.193555	+	0.162412i	0.734415	−	0.678701i	$-0.237457\pi$
$433$	4.02763	+	3.37958i	0.193555	+	0.162412i	−0.540860	+	0.841113i	$0.681901\pi$
$434$	1.11795	+	6.34019i	0.0536631	+	0.304339i
$435$		0			0
$436$	1.44392			0.0691513
$437$	5.08887	+	4.90138i	0.243434	+	0.234465i
$438$	−0.0184481			−0.000881486
$439$	−34.2836	−	12.4782i	−1.63627	−	0.595552i	−0.649885	−	0.760032i	$-0.725183\pi$
$439$	−34.2836	−	12.4782i	−1.63627	−	0.595552i	−0.986380	+	0.164480i	$0.947405\pi$
$440$		0			0
$441$	8.32463	+	6.98519i	0.396411	+	0.332628i
$442$	12.3595	−	10.3709i	0.587881	−	0.493291i
$443$	1.60289	−	9.09046i	0.0761558	−	0.431901i	−0.922761	−	0.385372i	$-0.874073\pi$
$443$	1.60289	−	9.09046i	0.0761558	−	0.431901i	0.998917	−	0.0465285i	$-0.0148158\pi$
$444$	0.108592	−	0.188087i	0.00515356	−	0.00892623i
$445$		0			0
$446$	23.7765	−	8.65395i	1.12585	−	0.409777i
$447$	0.315325	−	0.114769i	0.0149144	−	0.00542838i
$448$	0.918706	+	1.59124i	0.0434048	+	0.0751792i
$449$	11.4148	−	19.7711i	0.538699	−	0.933054i	−0.460275	−	0.887776i	$-0.652249\pi$
$449$	11.4148	−	19.7711i	0.538699	−	0.933054i	0.998974	−	0.0452780i	$-0.0144174\pi$
$450$		0			0
$451$	15.0744	−	12.6490i	0.709828	−	0.595616i
$452$	0.644649	+	0.540925i	0.0303217	+	0.0254430i
$453$	0.0209987	+	0.119090i	0.000986605	+	0.00559532i
$454$	20.6837	+	7.52824i	0.970733	+	0.353318i
$455$		0			0
$456$	0.127337	−	0.0927713i	0.00596311	−	0.00434442i
$457$	7.82515			0.366045			0.183022	−	0.983109i	$-0.441412\pi$
$457$	7.82515			0.366045			0.183022	+	0.983109i	$0.441412\pi$
$458$	4.97594	+	1.81110i	0.232511	+	0.0846269i
$459$	−0.253834	−	1.43956i	−0.0118480	−	0.0671931i
$460$		0			0
$461$	−3.01184	+	2.52724i	−0.140276	+	0.117705i	−0.710225	−	0.703974i	$-0.751407\pi$
$461$	−3.01184	+	2.52724i	−0.140276	+	0.117705i	0.569950	+	0.821679i	$0.306963\pi$
$462$	−0.0284356	+	0.161266i	−0.00132294	+	0.00750278i
$463$	−8.64820	+	14.9791i	−0.401916	+	0.696139i	−0.993957	−	0.109769i	$-0.964989\pi$
$463$	−8.64820	+	14.9791i	−0.401916	+	0.696139i	0.592041	+	0.805908i	$0.298322\pi$
$464$	−1.65079	−	2.85924i	−0.0766358	−	0.132737i
$465$		0			0
$466$	19.3124	−	7.02913i	0.894628	−	0.325618i
$467$	−10.5134	−	18.2097i	−0.486501	−	0.842644i	0.513379	−	0.858162i	$-0.328394\pi$
$467$	−10.5134	−	18.2097i	−0.486501	−	0.842644i	−0.999880	+	0.0155178i	$0.995060\pi$
$468$	−3.58807	+	6.21473i	−0.165859	+	0.287276i
$469$	−1.18616	+	6.72707i	−0.0547719	+	0.310627i
$470$		0			0
$471$	0.195287	+	0.163865i	0.00899836	+	0.00755052i
$472$	−0.825516	−	4.68173i	−0.0379974	−	0.215494i
$473$	−13.2406	−	4.81920i	−0.608805	−	0.221587i
$474$	−0.438622			−0.0201466
$475$		0			0
$476$	12.3878			0.567794
$477$	5.41410	+	1.97057i	0.247895	+	0.0902263i
$478$	0.154055	+	0.873692i	0.00704633	+	0.0399617i
$479$	16.1878	+	13.5832i	0.739640	+	0.620631i	0.932741	−	0.360547i	$-0.117410\pi$
$479$	16.1878	+	13.5832i	0.739640	+	0.620631i	−0.193101	+	0.981179i	$0.561855\pi$
$480$		0			0
$481$	−2.49703	+	14.1613i	−0.113855	+	0.645702i
$482$	2.00071	−	3.46533i	0.0911298	−	0.157841i
$483$	0.0538236	+	0.0932252i	0.00244906	+	0.00424190i
$484$	4.62333	−	1.68276i	0.210151	−	0.0764889i
$485$		0			0
$486$	0.487660	+	0.844651i	0.0221207	+	0.0383142i
$487$	−8.60015	+	14.8959i	−0.389710	+	0.674998i	−0.992410	−	0.122970i	$-0.960758\pi$
$487$	−8.60015	+	14.8959i	−0.389710	+	0.674998i	0.602700	+	0.797968i	$0.294091\pi$
$488$	2.37276	−	13.4566i	0.107410	−	0.609152i
$489$	−0.439015	+	0.368377i	−0.0198529	+	0.0166586i
$490$		0			0
$491$	−5.75424	−	32.6339i	−0.259685	−	1.47275i	−0.783753	−	0.621072i	$-0.786697\pi$
$491$	−5.75424	−	32.6339i	−0.259685	−	1.47275i	0.524068	−	0.851676i	$-0.324414\pi$
$492$	−0.271056	−	0.0986562i	−0.0122201	−	0.00444776i
$493$	−22.2591			−1.00250
$494$	−5.82173	+	8.65554i	−0.261932	+	0.389431i
$495$		0			0
$496$	3.29253	+	1.19838i	0.147839	+	0.0538090i
$497$	−1.86114	−	10.5550i	−0.0834834	−	0.473458i
$498$	0.172566	+	0.144800i	0.00773287	+	0.00648865i
$499$	−24.4903	+	20.5498i	−1.09634	+	0.919936i	−0.997173	−	0.0751346i	$-0.976061\pi$
$499$	−24.4903	+	20.5498i	−1.09634	+	0.919936i	−0.0991642	+	0.995071i	$0.531617\pi$
$500$		0			0
$501$	0.246244	−	0.426507i	0.0110014	−	0.0190549i
$502$	6.33436	+	10.9714i	0.282716	+	0.489679i
$503$	−23.7193	+	8.63311i	−1.05759	+	0.384931i	−0.811523	−	0.584321i	$-0.801361\pi$
$503$	−23.7193	+	8.63311i	−1.05759	+	0.384931i	−0.246068	+	0.969253i	$0.579139\pi$
$504$	−5.17755	+	1.88447i	−0.230626	+	0.0839411i
$505$		0			0
$506$	−1.99840	+	3.46132i	−0.0888395	+	0.153875i
$507$	0.0456484	−	0.258885i	0.00202732	−	0.0114975i
$508$	−9.94770	+	8.34711i	−0.441358	+	0.370343i
$509$	−13.0617	−	10.9600i	−0.578948	−	0.485795i	0.305654	−	0.952143i	$-0.401125\pi$
$509$	−13.0617	−	10.9600i	−0.578948	−	0.485795i	−0.884601	+	0.466348i	$0.845570\pi$
$510$		0			0
$511$	0.881271	+	0.320756i	0.0389851	+	0.0141894i
$512$	1.00000			0.0441942
$513$	0.415410	+	0.848888i	0.0183408	+	0.0374793i
$514$	13.0448			0.575381
$515$		0			0
$516$	0.0358656	+	0.203404i	0.00157890	+	0.00895437i
$517$	23.5971	+	19.8003i	1.03780	+	0.870816i
$518$	−8.45773	+	7.09688i	−0.371612	+	0.311819i
$519$	0.0755636	−	0.428542i	0.00331687	−	0.0188109i
$520$		0			0
$521$	3.40256	+	5.89342i	0.149069	+	0.258195i	0.930884	−	0.365316i	$-0.119039\pi$
$521$	3.40256	+	5.89342i	0.149069	+	0.258195i	−0.781815	+	0.623511i	$0.785706\pi$
$522$	9.30333	−	3.38614i	0.407196	−	0.148207i
$523$	4.90593	−	1.78561i	0.214521	−	0.0780794i	−0.232524	−	0.972591i	$-0.574698\pi$
$523$	4.90593	−	1.78561i	0.214521	−	0.0780794i	0.447045	+	0.894511i	$0.352476\pi$
$524$	−4.46449	−	7.73273i	−0.195032	−	0.337806i
$525$		0			0
$526$	−4.90583	+	27.8224i	−0.213904	+	1.21311i
$527$	18.0961	−	15.1845i	0.788280	−	0.661445i
$528$	0.0682715	+	0.0572866i	0.00297113	+	0.00249308i
$529$	−3.53767	−	20.0631i	−0.153812	−	0.872309i
$530$		0			0
$531$	14.2557			0.618643
$532$	−7.69593	+	2.21770i	−0.333661	+	0.0961496i
$533$	19.0984			0.827243
$534$	0.577457	+	0.210177i	0.0249890	+	0.00909526i
$535$		0			0
$536$	2.84788	+	2.38966i	0.123010	+	0.103217i
$537$	−0.445026	+	0.373421i	−0.0192043	+	0.0161143i
$538$	5.13013	−	29.0944i	0.221176	−	1.25435i
$539$	−4.46785	+	7.73855i	−0.192444	+	0.333323i
$540$		0			0
$541$	24.5890	−	8.94968i	1.05717	−	0.384777i	0.245803	−	0.969320i	$-0.420948\pi$
$541$	24.5890	−	8.94968i	1.05717	−	0.384777i	0.811363	+	0.584543i	$0.198726\pi$
$542$	−25.3822	+	9.23836i	−1.09026	+	0.396822i
$543$	0.103970	+	0.180081i	0.00446177	+	0.00772802i
$544$	3.37099	−	5.83873i	0.144530	−	0.250333i
$545$		0			0
$546$	−0.121746	+	0.102157i	−0.00521025	+	0.00437192i
$547$	−27.2225	−	22.8424i	−1.16395	−	0.976671i	−0.163999	−	0.986461i	$-0.552439\pi$
$547$	−27.2225	−	22.8424i	−1.16395	−	0.976671i	−0.999952	+	0.00978982i	$0.996884\pi$
$548$	−0.773358	−	4.38593i	−0.0330362	−	0.187358i
$549$	38.5036	+	14.0142i	1.64330	+	0.598111i
$550$		0			0
$551$	13.8285	−	3.98490i	0.589114	−	0.169763i
$552$	0.0585864			0.00249360
$553$	20.9530	+	7.62628i	0.891014	+	0.324303i
$554$	4.19844	+	23.8105i	0.178374	+	1.01161i
$555$		0			0
$556$	−0.928039	+	0.778717i	−0.0393576	+	0.0330250i
$557$	−5.32949	+	30.2250i	−0.225818	+	1.28068i	0.635298	+	0.772267i	$0.280877\pi$
$557$	−5.32949	+	30.2250i	−0.225818	+	1.28068i	−0.861116	+	0.508409i	$0.830234\pi$
$558$	−5.25347	+	9.09928i	−0.222397	+	0.385203i
$559$	−6.83758	−	11.8430i	−0.289199	−	0.500907i
$560$		0			0
$561$	0.564623	−	0.205506i	0.0238384	−	0.00867647i
$562$	−1.20051	−	2.07934i	−0.0506403	−	0.0877116i
$563$	15.6022	−	27.0238i	0.657553	−	1.13892i	−0.323694	−	0.946162i	$-0.604925\pi$
$563$	15.6022	−	27.0238i	0.657553	−	1.13892i	0.981247	−	0.192754i	$-0.0617419\pi$
$564$	0.0784079	−	0.444673i	0.00330157	−	0.0187241i
$565$		0			0
$566$	−6.24398	−	5.23932i	−0.262454	−	0.220225i
$567$	−2.86782	−	16.2642i	−0.120437	−	0.683032i
$568$	−5.48135	−	1.99505i	−0.229992	−	0.0837104i
$569$	−20.6053			−0.863820			−0.431910	−	0.901917i	$-0.642160\pi$
$569$	−20.6053			−0.863820			−0.431910	+	0.901917i	$0.642160\pi$
$570$		0			0
$571$	4.38785			0.183626			0.0918129	−	0.995776i	$-0.470734\pi$
$571$	4.38785			0.183626			0.0918129	+	0.995776i	$0.470734\pi$
$572$	−5.54492	−	2.01819i	−0.231845	−	0.0843846i
$573$	0.128953	+	0.731332i	0.00538711	+	0.0305518i
$574$	11.2330	+	9.42565i	0.468858	+	0.393419i
$575$		0			0
$576$	−0.520718	+	2.95314i	−0.0216966	+	0.123047i
$577$	14.9410	−	25.8786i	0.622004	−	1.07734i	−0.367109	−	0.930178i	$-0.619652\pi$
$577$	14.9410	−	25.8786i	0.622004	−	1.07734i	0.989112	−	0.147164i	$-0.0470144\pi$
$578$	−14.2272	−	24.6422i	−0.591772	−	1.02498i
$579$	0.425026	−	0.154697i	0.0176635	−	0.00642898i
$580$		0			0
$581$	−5.72589	−	9.91753i	−0.237550	−	0.411448i
$582$	0.246860	−	0.427574i	0.0102327	−	0.0177235i
$583$	−0.822676	+	4.66563i	−0.0340718	+	0.193231i
$584$	0.390995	−	0.328084i	0.0161795	−	0.0135762i
$585$		0			0
$586$	−1.59714	−	9.05783i	−0.0659773	−	0.374176i
$587$	37.0049	+	13.4687i	1.52736	+	0.555912i	0.962972	−	0.269601i	$-0.0868918\pi$
$587$	37.0049	+	13.4687i	1.52736	+	0.555912i	0.564383	+	0.825513i	$0.309114\pi$
$588$	0.130983			0.00540163
$589$	−8.52387	+	12.6730i	−0.351220	+	0.522181i
$590$		0			0
$591$	−0.204582	−	0.0744617i	−0.00841538	−	0.00306295i
$592$	1.04343	+	5.91759i	0.0428848	+	0.243212i
$593$	30.7274	+	25.7834i	1.26182	+	1.05880i	0.995485	+	0.0949157i	$0.0302581\pi$
$593$	30.7274	+	25.7834i	1.26182	+	1.05880i	0.266338	+	0.963880i	$0.414186\pi$
$594$	−0.409540	+	0.343645i	−0.0168036	+	0.0140999i
$595$		0			0
$596$	−4.64202	+	8.04022i	−0.190145	+	0.329340i
$597$	0.203373	+	0.352253i	0.00832352	+	0.0144168i
$598$	−3.64507	+	1.32670i	−0.149058	+	0.0542527i
$599$	−29.5623	+	10.7598i	−1.20788	+	0.439634i	−0.865970	−	0.500097i	$-0.833298\pi$
$599$	−29.5623	+	10.7598i	−1.20788	+	0.439634i	−0.341915	+	0.939731i	$0.611076\pi$
$600$		0			0
$601$	17.2445	−	29.8683i	0.703418	−	1.21836i	−0.263842	−	0.964566i	$-0.584990\pi$
$601$	17.2445	−	29.8683i	0.703418	−	1.21836i	0.967260	−	0.253789i	$-0.0816769\pi$
$602$	1.82326	−	10.3402i	0.0743107	−	0.421437i
$603$	−8.53992	+	7.16585i	−0.347773	+	0.291816i
$604$	−2.56296	−	2.15058i	−0.104285	−	0.0875057i
$605$		0			0
$606$	−0.362000	−	0.131757i	−0.0147052	−	0.00535227i
$607$	−12.9979			−0.527568			−0.263784	−	0.964582i	$-0.584971\pi$
$607$	−12.9979			−0.527568			−0.263784	+	0.964582i	$0.584971\pi$
$608$	−1.04896	+	4.23080i	−0.0425411	+	0.171582i
$609$	0.219261			0.00888492
$610$		0			0
$611$	5.19139	+	29.4418i	0.210021	+	1.19109i
$612$	15.4872	+	12.9953i	0.626034	+	0.525305i
$613$	−6.67364	+	5.59985i	−0.269546	+	0.226176i	−0.767534	−	0.641008i	$-0.778517\pi$
$613$	−6.67364	+	5.59985i	−0.269546	+	0.226176i	0.497989	+	0.867184i	$0.334072\pi$
$614$	4.92243	−	27.9165i	0.198653	−	1.12662i
$615$		0			0
$616$	−2.26530	−	3.92362i	−0.0912717	−	0.158087i
$617$	−22.8877	+	8.33044i	−0.921424	+	0.335371i	−0.758805	−	0.651318i	$-0.774216\pi$
$617$	−22.8877	+	8.33044i	−0.921424	+	0.335371i	−0.162619	+	0.986689i	$0.551994\pi$
$618$	0.331127	−	0.120520i	0.0133199	−	0.00484804i
$619$	−0.822483	−	1.42458i	−0.0330584	−	0.0572588i	0.849023	−	0.528356i	$-0.177191\pi$
$619$	−0.822483	−	1.42458i	−0.0330584	−	0.0572588i	−0.882081	+	0.471097i	$0.843858\pi$
$620$		0			0
$621$	−0.0610272	+	0.346102i	−0.00244894	+	0.0138886i
$622$	13.3605	−	11.2108i	0.535706	−	0.449511i
$623$	−23.9309	−	20.0804i	−0.958772	−	0.804505i
$624$	0.0150198	+	0.0851816i	0.000601274	+	0.00340999i
$625$		0			0
$626$	13.1983			0.527510
$627$	−0.313982	+	0.228751i	−0.0125392	+	0.00913545i
$628$	−7.05317			−0.281452
$629$	38.0686	+	13.8558i	1.51790	+	0.552469i
$630$		0			0
$631$	−33.3220	−	27.9605i	−1.32653	−	1.11309i	−0.984876	−	0.173261i	$-0.944570\pi$
$631$	−33.3220	−	27.9605i	−1.32653	−	1.11309i	−0.341651	−	0.939827i	$-0.610986\pi$
$632$	9.29628	−	7.80050i	0.369786	−	0.310287i
$633$	−0.0882929	+	0.500734i	−0.00350933	+	0.0199024i
$634$	−6.14319	+	10.6403i	−0.243977	+	0.422581i
$635$		0			0
$636$	0.0652574	−	0.0237517i	0.00258762	−	0.000941818i
$637$	−8.14936	+	2.96613i	−0.322890	+	0.117522i
$638$	4.07043	+	7.05020i	0.161150	+	0.279120i
$639$	8.74589	−	15.1483i	0.345982	−	0.599258i
$640$		0			0
$641$	−28.2069	+	23.6684i	−1.11411	+	0.934846i	−0.998292	−	0.0584253i	$-0.981392\pi$
$641$	−28.2069	+	23.6684i	−1.11411	+	0.934846i	−0.115814	+	0.993271i	$0.536948\pi$
$642$	0.367854	+	0.308666i	0.0145180	+	0.0121821i
$643$	2.55882	+	14.5118i	0.100910	+	0.572288i	0.992775	+	0.119988i	$0.0382855\pi$
$643$	2.55882	+	14.5118i	0.100910	+	0.572288i	−0.891866	+	0.452301i	$0.850603\pi$
$644$	−2.79868	−	1.01864i	−0.110284	−	0.0401399i
$645$		0			0
$646$	21.1664	+	20.3866i	0.832783	+	0.802100i
$647$	6.04813			0.237776			0.118888	−	0.992908i	$-0.462067\pi$
$647$	6.04813			0.237776			0.118888	+	0.992908i	$0.462067\pi$
$648$	−8.44619	−	3.07416i	−0.331798	−	0.120764i
$649$	2.03552	+	11.5440i	0.0799012	+	0.453142i
$650$		0			0
$651$	−0.178254	+	0.149573i	−0.00698633	+	0.00586223i
$652$	2.75334	−	15.6150i	0.107829	−	0.611530i
$653$	−1.44434	+	2.50167i	−0.0565213	+	0.0978978i	−0.892902	−	0.450252i	$-0.851334\pi$
$653$	−1.44434	+	2.50167i	−0.0565213	+	0.0978978i	0.836380	+	0.548150i	$0.184668\pi$
$654$	0.0260945	+	0.0451970i	0.00102037	+	0.00176734i
$655$		0			0
$656$	7.49934	−	2.72954i	0.292800	−	0.106571i
$657$	0.765278	+	1.32550i	0.0298563	+	0.0517127i
$658$	−11.4771	+	19.8789i	−0.447422	+	0.774958i
$659$	2.83413	−	16.0731i	0.110402	−	0.626120i	−0.878523	−	0.477701i	$-0.841470\pi$
$659$	2.83413	−	16.0731i	0.110402	−	0.626120i	0.988925	−	0.148419i	$-0.0474185\pi$
$660$		0			0
$661$	21.8640	+	18.3461i	0.850410	+	0.713579i	0.959880	−	0.280411i	$-0.0904708\pi$
$661$	21.8640	+	18.3461i	0.850410	+	0.713579i	−0.109470	+	0.993990i	$0.534915\pi$
$662$	0.173057	+	0.981453i	0.00672604	+	0.0381453i
$663$	0.547984	+	0.199450i	0.0212819	+	0.00774599i
$664$	−6.23256			−0.241870
$665$		0			0
$666$	−18.0188			−0.698214
$667$	5.02884	+	1.83035i	0.194718	+	0.0708714i
$668$	2.36609	+	13.4187i	0.0915466	+	0.519187i
$669$	0.700571	+	0.587849i	0.0270856	+	0.0227275i
$670$		0			0
$671$	−5.85065	+	33.1807i	−0.225862	+	1.28093i
$672$	−0.0332056	+	0.0575138i	−0.00128093	+	0.00221864i
$673$	3.11723	+	5.39921i	0.120161	+	0.208124i	0.919831	−	0.392315i	$-0.128326\pi$
$673$	3.11723	+	5.39921i	0.120161	+	0.208124i	−0.799670	+	0.600439i	$0.794992\pi$
$674$	8.04300	−	2.92741i	0.309805	−	0.112760i
$675$		0			0
$676$	3.63656	+	6.29870i	0.139868	+	0.242258i
$677$	−7.30750	+	12.6570i	−0.280850	+	0.486446i	−0.971594	−	0.236653i	$-0.923950\pi$
$677$	−7.30750	+	12.6570i	−0.280850	+	0.486446i	0.690744	+	0.723099i	$0.257283\pi$
$678$	−0.00528171	+	0.0299541i	−0.000202843	+	0.00115038i
$679$	−19.2267	+	16.1331i	−0.737854	+	0.619133i
$680$		0			0
$681$	0.138149	+	0.783481i	0.00529388	+	0.0300231i
$682$	−8.11858	−	2.95492i	−0.310877	−	0.113150i
$683$	−47.0671			−1.80097			−0.900486	−	0.434885i	$-0.856789\pi$
$683$	−47.0671			−1.80097			−0.900486	+	0.434885i	$0.856789\pi$
$684$	−11.9479	−	5.30079i	−0.456840	−	0.202681i
$685$		0			0
$686$	−18.3433	−	6.67641i	−0.700350	−	0.254906i
$687$	0.0332350	+	0.188485i	0.00126799	+	0.00719114i
$688$	−4.37751	−	3.67317i	−0.166891	−	0.140038i
$689$	−3.52226	+	2.95553i	−0.134188	+	0.112597i
$690$		0			0
$691$	13.6742	−	23.6844i	0.520191	−	0.900997i	−0.479534	−	0.877523i	$-0.659194\pi$
$691$	13.6742	−	23.6844i	0.520191	−	0.900997i	0.999724	−	0.0234732i	$-0.00747242\pi$
$692$	6.01973	+	10.4265i	0.228836	+	0.396355i
$693$	12.7666	−	4.64665i	0.484962	−	0.176512i
$694$	−6.23742	+	2.27024i	−0.236769	+	0.0861770i
$695$		0			0
$696$	0.0596659	−	0.103344i	0.00226163	−	0.00391726i
$697$	9.34319	−	52.9879i	0.353899	−	2.00706i
$698$	23.7813	−	19.9549i	0.900135	−	0.755303i
$699$	0.569035	+	0.477477i	0.0215229	+	0.0180598i
$700$		0			0
$701$	−18.6359	−	6.78290i	−0.703867	−	0.256187i	−0.0348060	−	0.999394i	$-0.511081\pi$
$701$	−18.6359	−	6.78290i	−0.703867	−	0.256187i	−0.669061	+	0.743207i	$0.733304\pi$
$702$	−0.518861			−0.0195831
$703$	−26.1307	−	1.79279i	−0.985538	−	0.0676164i
$704$	−2.46576			−0.0929317
$705$		0			0
$706$	−3.08450	−	17.4931i	−0.116087	−	0.658360i
$707$	15.0020	+	12.5881i	0.564206	+	0.473425i
$708$	0.131627	−	0.110448i	0.00494684	−	0.00415089i
$709$	5.68008	−	32.2133i	0.213320	−	1.20980i	−0.670479	−	0.741929i	$-0.733911\pi$
$709$	5.68008	−	32.2133i	0.213320	−	1.20980i	0.883799	−	0.467868i	$-0.154978\pi$
$710$		0			0
$711$	18.1952	+	31.5150i	0.682374	+	1.18191i
$712$	−15.9766	+	5.81501i	−0.598749	+	0.217927i
$713$	−5.33693	+	1.94248i	−0.199870	+	0.0727466i
$714$	0.223872	+	0.387757i	0.00837819	+	0.0145114i
$715$		0			0
$716$	2.79104	−	15.8288i	0.104306	−	0.591550i
$717$	−0.0245638	+	0.0206115i	−0.000917353	+	0.000769750i
$718$	−3.93452	−	3.30146i	−0.146835	−	0.123209i
$719$	−0.563968	−	3.19842i	−0.0210325	−	0.119281i	0.972484	−	0.232970i	$-0.0748444\pi$
$719$	−0.563968	−	3.19842i	−0.0210325	−	0.119281i	−0.993516	+	0.113689i	$0.963733\pi$
$720$		0			0
$721$	−17.9135			−0.667132
$722$	−16.7994	−	8.87591i	−0.625207	−	0.330327i
$723$	0.144627			0.00537873
$724$	−5.40615	−	1.96768i	−0.200918	−	0.0731282i
$725$		0			0
$726$	0.136226	+	0.114307i	0.00505580	+	0.00424232i
$727$	−14.8686	+	12.4762i	−0.551446	+	0.462718i	−0.875430	−	0.483344i	$-0.839422\pi$
$727$	−14.8686	+	12.4762i	−0.551446	+	0.462718i	0.323984	+	0.946062i	$0.394977\pi$
$728$	0.763547	−	4.33029i	0.0282989	−	0.160491i
$729$	13.4647	−	23.3216i	0.498694	−	0.863764i
$730$		0			0
$731$	−36.2032	+	13.1769i	−1.33902	+	0.487364i
$732$	0.464093	−	0.168916i	0.0171534	−	0.00624331i
$733$	6.03763	+	10.4575i	0.223005	+	0.386256i	0.955719	−	0.294281i	$-0.0950801\pi$
$733$	6.03763	+	10.4575i	0.223005	+	0.386256i	−0.732714	+	0.680537i	$0.761747\pi$
$734$	−2.87294	+	4.97608i	−0.106042	+	0.183671i
$735$		0			0
$736$	−1.24170	+	1.04191i	−0.0457695	+	0.0384052i
$737$	−7.02218	−	5.89231i	−0.258665	−	0.217046i
$738$	4.15566	+	23.5679i	0.152972	+	0.867547i
$739$	−2.86243	−	1.04184i	−0.105296	−	0.0383246i	0.288835	−	0.957379i	$-0.406732\pi$
$739$	−2.86243	−	1.04184i	−0.105296	−	0.0383246i	−0.394131	+	0.919054i	$0.628954\pi$
$740$		0			0
$741$	−0.376142	−	0.0258066i	−0.0138179	−	0.000948028i
$742$	−3.53033			−0.129602
$743$	37.3589	+	13.5975i	1.37057	+	0.498845i	0.919305	−	0.393547i	$-0.128752\pi$
$743$	37.3589	+	13.5975i	1.37057	+	0.498845i	0.451261	+	0.892392i	$0.350974\pi$
$744$	0.0219912	+	0.124718i	0.000806238	+	0.00457240i
$745$		0			0
$746$	−28.9453	+	24.2880i	−1.05976	+	0.889246i
$747$	3.24540	−	18.4056i	0.118743	−	0.673426i
$748$	−8.31204	+	14.3969i	−0.303918	+	0.526402i
$749$	−12.2057	−	21.1409i	−0.445986	−	0.772471i
$750$		0			0
$751$	−33.6285	+	12.2398i	−1.22712	+	0.446636i	−0.872611	−	0.488416i	$-0.837575\pi$
$751$	−33.6285	+	12.2398i	−1.22712	+	0.446636i	−0.354511	+	0.935052i	$0.615353\pi$
$752$	6.24632	+	10.8189i	0.227780	+	0.394526i
$753$	−0.228948	+	0.396550i	−0.00834334	+	0.0144511i
$754$	−1.37199	+	7.78093i	−0.0499648	+	0.283365i
$755$		0			0
$756$	−0.305177	−	0.256074i	−0.0110992	−	0.00931333i
$757$	8.66613	+	49.1480i	0.314976	+	1.78632i	0.572355	+	0.820006i	$0.306030\pi$
$757$	8.66613	+	49.1480i	0.314976	+	1.78632i	−0.257380	+	0.966310i	$0.582859\pi$
$758$	30.3204	+	11.0357i	1.10128	+	0.400835i
$759$	−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	$0.728236\pi$
$762$	−0.441052	−	0.160530i	−0.0159776	−	0.00581538i
$763$	−0.460702	−	2.61277i	−0.0166785	−	0.0945886i
$764$	−15.7392	−	13.2067i	−0.569423	−	0.477803i
$765$		0			0
$766$	3.78204	−	21.4490i	0.136651	−	0.774984i
$767$	−5.68833	+	9.85247i	−0.205394	+	0.355752i
$768$	0.0180720	+	0.0313015i	0.000652116	+	0.00112950i
$769$	5.18278	−	1.88638i	0.186896	−	0.0680246i	−0.246877	−	0.969047i	$-0.579404\pi$
$769$	5.18278	−	1.88638i	0.186896	−	0.0680246i	0.433773	+	0.901022i	$0.357182\pi$
$770$		0			0
$771$	0.235745	+	0.408322i	0.00849014	+	0.0147054i
$772$	−6.25697	+	10.8374i	−0.225193	+	0.390046i
$773$	6.66795	−	37.8158i	0.239830	−	1.36014i	−0.592371	−	0.805666i	$-0.701808\pi$
$773$	6.66795	−	37.8158i	0.239830	−	1.36014i	0.832200	−	0.554475i	$-0.187081\pi$
$774$	13.1268	−	11.0147i	0.471833	−	0.395915i
$775$		0			0
$776$	2.37200	+	13.4523i	0.0851500	+	0.482910i
$777$	−0.374991	−	0.136486i	−0.0134527	−	0.00489639i
$778$	9.68485			0.347219
$779$	3.68159	+	34.5914i	0.131907	+	1.23937i
$780$		0			0
$781$	13.5157	+	4.91930i	0.483629	+	0.176026i
$782$	1.89766	+	10.7622i	0.0678603	+	0.384855i
$783$	0.548361	+	0.460129i	0.0195968	+	0.0164437i
$784$	−2.77608	+	2.32941i	−0.0991459	+	0.0831933i
$785$		0			0
$786$	0.161364	−	0.279491i	0.00575567	−	0.00996912i
$787$	1.56029	+	2.70250i	0.0556184	+	0.0963339i	0.892494	−	0.451059i	$-0.148954\pi$
$787$	1.56029	+	2.70250i	0.0556184	+	0.0963339i	−0.836876	+	0.547393i	$0.815620\pi$
$788$	5.66021	−	2.06015i	0.201636	−	0.0733897i
$789$	−0.959541	+	0.349244i	−0.0341606	+	0.0124334i
$790$		0			0
$791$	0.773118	−	1.33908i	0.0274889	−	0.0476122i
$792$	1.28396	−	7.28171i	0.0456236	−	0.258744i
$793$	−25.0494	+	21.0189i	−0.889530	+	0.746404i
$794$	14.0915	+	11.8242i	0.500089	+	0.419624i
$795$		0			0
$796$	−10.5749	−	3.84894i	−0.374816	−	0.136422i
$797$	0.491495			0.0174096			0.00870482	−	0.999962i	$-0.497229\pi$
$797$	0.491495			0.0174096			0.00870482	+	0.999962i	$0.497229\pi$
$798$	−0.208498	−	0.200816i	−0.00738075	−	0.00710882i
$799$	84.2252			2.97967
$800$		0			0
$801$	−8.85322	−	50.2091i	−0.312813	−	1.77405i
$802$	−27.9887	−	23.4853i	−0.988316	−	0.829296i
$803$	−0.964098	+	0.808975i	−0.0340223	+	0.0285481i
$804$	−0.0233331	+	0.132329i	−0.000822897	+	0.00466688i
$805$		0			0
$806$	−4.19250	−	7.26163i	−0.147675	−	0.255780i
$807$	1.00341	−	0.365212i	0.0353218	−	0.0128561i
$808$	10.0155	−	3.64535i	0.352345	−	0.128243i
$809$	−16.8276	−	29.1463i	−0.591628	−	1.02473i	−0.994013	−	0.109259i	$-0.965152\pi$
$809$	−16.8276	−	29.1463i	−0.591628	−	1.02473i	0.402386	−	0.915470i	$-0.368181\pi$
$810$		0			0
$811$	−8.35435	+	47.3798i	−0.293361	+	1.66373i	0.380430	+	0.924810i	$0.375776\pi$
$811$	−8.35435	+	47.3798i	−0.293361	+	1.66373i	−0.673791	+	0.738922i	$0.735335\pi$
$812$	−4.64709	+	3.89937i	−0.163081	+	0.136841i
$813$	−0.747881	−	0.627547i	−0.0262293	−	0.0220090i
$814$	−2.57285	−	14.5913i	−0.0901783	−	0.511426i
$815$		0			0
$816$	0.243682			0.00853056
$817$	20.1323	−	14.6674i	0.704340	−	0.513146i
$818$	36.3063			1.26942
$819$	12.3903	+	4.50972i	0.432954	+	0.157582i
$820$		0			0
$821$	−1.45115	−	1.21766i	−0.0506456	−	0.0424967i	0.617114	−	0.786874i	$-0.288302\pi$
$821$	−1.45115	−	1.21766i	−0.0506456	−	0.0424967i	−0.667759	+	0.744377i	$0.732746\pi$
$822$	0.123310	−	0.103470i	0.00430094	−	0.00360892i
$823$	4.61152	−	26.1532i	0.160747	−	0.911643i	−0.792594	−	0.609749i	$-0.791270\pi$
$823$	4.61152	−	26.1532i	0.160747	−	0.911643i	0.953342	−	0.301894i	$-0.0976188\pi$
$824$	−4.87465	+	8.44314i	−0.169816	+	0.294131i
$825$		0			0
$826$	−8.20819	+	2.98754i	−0.285599	+	0.103950i
$827$	24.2419	−	8.82334i	0.842974	−	0.306818i	0.115802	−	0.993272i	$-0.463056\pi$
$827$	24.2419	−	8.82334i	0.842974	−	0.306818i	0.727173	+	0.686455i	$0.240834\pi$
$828$	−2.43032	−	4.20944i	−0.0844595	−	0.146288i
$829$	13.9819	−	24.2173i	0.485611	−	0.841102i	−0.514253	−	0.857639i	$-0.671931\pi$
$829$	13.9819	−	24.2173i	0.485611	−	0.841102i	0.999863	+	0.0165364i	$0.00526395\pi$
$830$		0			0
$831$	−0.669432	+	0.561720i	−0.0232223	+	0.0194859i
$832$	−1.83321	−	1.53825i	−0.0635553	−	0.0533292i
$833$	4.24264	+	24.0612i	0.146999	+	0.833672i
$834$	−0.0411465	−	0.0149761i	−0.00142479	−	0.000518581i
$835$		0			0
$836$	2.58649	−	10.4321i	0.0894556	−	0.360802i
$837$	−0.759689			−0.0262587
$838$	−37.1179	−	13.5098i	−1.28222	−	0.466689i
$839$	8.66822	+	49.1599i	0.299260	+	1.69719i	0.649364	+	0.760478i	$0.275035\pi$
$839$	8.66822	+	49.1599i	0.299260	+	1.69719i	−0.350104	+	0.936711i	$0.613854\pi$
$840$		0			0
$841$	−13.8651	+	11.6342i	−0.478107	+	0.401180i
$842$	−2.44853	+	13.8863i	−0.0843819	+	0.478554i
$843$	0.0433910	−	0.0751555i	0.00149447	−	0.00258849i
$844$	−7.03380	−	12.1829i	−0.242114	−	0.419353i
$845$		0			0
$846$	−35.2024	+	12.8126i	−1.21028	+	0.440507i
$847$	−4.52008	−	7.82900i	−0.155312	−	0.269008i
$848$	−0.960680	+	1.66395i	−0.0329899	+	0.0571401i
$849$	0.0511579	−	0.290131i	0.00175573	−	0.00995726i
$850$		0			0
$851$	−7.46121	−	6.26070i	−0.255767	−	0.214614i
$852$	−0.0366106	−	0.207629i	−0.00125426	−	0.00711326i
$853$	−7.47637	−	2.72117i	−0.255986	−	0.0931712i	0.210840	−	0.977521i	$-0.432380\pi$
$853$	−7.47637	−	2.72117i	−0.255986	−	0.0931712i	−0.466826	+	0.884349i	$0.654602\pi$
$854$	−25.1067			−0.859135
$855$		0			0
$856$	−13.2857			−0.454097
$857$	−23.6379	−	8.60350i	−0.807456	−	0.293890i	−0.0948835	−	0.995488i	$-0.530248\pi$
$857$	−23.6379	−	8.60350i	−0.807456	−	0.293890i	−0.712573	+	0.701598i	$0.752470\pi$
$858$	−0.0370352	−	0.210037i	−0.00126436	−	0.00717055i
$859$	2.65725	+	2.22970i	0.0906643	+	0.0760764i	0.686993	−	0.726664i	$-0.258930\pi$
$859$	2.65725	+	2.22970i	0.0906643	+	0.0760764i	−0.596329	+	0.802740i	$0.703375\pi$
$860$		0			0
$861$	−0.0920342	+	0.521952i	−0.00313652	+	0.0177881i
$862$	−10.5216	+	18.2239i	−0.358366	+	0.620708i
$863$	−20.4854	−	35.4817i	−0.697331	−	1.20781i	−0.969389	−	0.245531i	$-0.921038\pi$
$863$	−20.4854	−	35.4817i	−0.697331	−	1.20781i	0.272058	−	0.962281i	$-0.412296\pi$
$864$	−0.203741	+	0.0741555i	−0.00693140	+	0.00252282i
$865$		0			0
$866$	−2.62885	−	4.55330i	−0.0893318	−	0.154727i
$867$	0.514225	−	0.890665i	0.0174640	−	0.0302486i
$868$	1.11795	−	6.34019i	0.0379456	−	0.215200i
$869$	−22.9223	+	19.2341i	−0.777587	+	0.652473i
$870$		0			0
$871$	−1.54489	−	8.76150i	−0.0523466	−	0.296872i
$872$	−1.35684	−	0.493850i	−0.0459485	−	0.0167239i
$873$	−40.9616			−1.38634
$874$	−3.10561	−	6.34629i	−0.105049	−	0.214667i
$875$		0			0
$876$	0.0173356	+	0.00630963i	0.000585715	+	0.000213183i
$877$	4.31693	+	24.4825i	0.145772	+	0.826716i	0.966744	+	0.255747i	$0.0823213\pi$
$877$	4.31693	+	24.4825i	0.145772	+	0.826716i	−0.820972	+	0.570969i	$0.806568\pi$
$878$	27.9482	+	23.4513i	0.943207	+	0.791445i
$879$	0.254661	−	0.213686i	0.00858949	−	0.00720744i
$880$		0			0
$881$	7.87057	−	13.6322i	0.265166	−	0.459281i	−0.702441	−	0.711742i	$-0.747907\pi$
$881$	7.87057	−	13.6322i	0.265166	−	0.459281i	0.967607	+	0.252461i	$0.0812398\pi$
$882$	−5.43351	−	9.41112i	−0.182956	−	0.316889i
$883$	−7.29174	+	2.65398i	−0.245386	+	0.0893134i	−0.461786	−	0.886992i	$-0.652791\pi$
$883$	−7.29174	+	2.65398i	−0.245386	+	0.0893134i	0.216399	+	0.976305i	$0.430569\pi$
$884$	−15.1612	+	5.51821i	−0.509925	+	0.185598i
$885$		0			0
$886$	−4.61535	+	7.99402i	−0.155056	+	0.268564i
$887$	−5.91436	+	33.5420i	−0.198585	+	1.12623i	0.708636	+	0.705574i	$0.249311\pi$
$887$	−5.91436	+	33.5420i	−0.198585	+	1.12623i	−0.907221	+	0.420655i	$0.861800\pi$
$888$	−0.166373	+	0.139604i	−0.00558311	+	0.00468479i
$889$	18.2780	+	15.3371i	0.613025	+	0.514389i
$890$		0			0
$891$	20.8262	+	7.58013i	0.697705	+	0.253944i
$892$	−25.3025			−0.847189
$893$	−52.3250	+	15.0783i	−1.75099	+	0.504575i
$894$	−0.335562			−0.0112229
$895$		0			0
$896$	−0.319063	−	1.80950i	−0.0106591	−	0.0604510i
$897$	−0.107401	−	0.0901204i	−0.00358603	−	0.00300903i
$898$	−17.4885	+	14.6746i	−0.583600	+	0.489698i
$899$	−2.00879	+	11.3924i	−0.0669970	+	0.379959i
$900$		0			0
$901$	6.47689	+	11.2183i	0.215776	+	0.373736i
$902$	−18.4915	+	6.73037i	−0.615701	+	0.224097i
$903$	0.356616	−	0.129798i	0.0118674	−	0.00431939i
$904$	−0.420765	−	0.728786i	−0.0139944	−	0.0242391i
$905$		0			0
$906$	0.0209987	−	0.119090i	0.000697635	−	0.00395649i
$907$	−3.68281	+	3.09024i	−0.122286	+	0.102610i	−0.701880	−	0.712296i	$-0.747656\pi$
$907$	−3.68281	+	3.09024i	−0.122286	+	0.102610i	0.579594	+	0.814905i	$0.303211\pi$
$908$	−16.8615	−	14.1485i	−0.559568	−	0.469533i
$909$	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	$0.451594\pi$
$912$	−0.151387	+	0.0436247i	−0.00501294	+	0.00144456i
$913$	15.3680			0.508606
$914$	−7.35323	−	2.67636i	−0.243223	−	0.0885260i
$915$		0			0
$916$	−4.05643	−	3.40375i	−0.134028	−	0.112463i
$917$	−12.5679	+	10.5457i	−0.415029	+	0.348250i
$918$	−0.253834	+	1.43956i	−0.00837777	+	0.0475127i
$919$	10.5408	−	18.2572i	0.347709	−	0.602251i	−0.638133	−	0.769926i	$-0.720293\pi$
$919$	10.5408	−	18.2572i	0.347709	−	0.602251i	0.985842	+	0.167676i	$0.0536262\pi$
$920$		0			0
$921$	0.962788	−	0.350426i	0.0317249	−	0.0115469i
$922$	3.69457	−	1.34471i	0.121674	−	0.0442858i
$923$	6.97961	+	12.0890i	0.229737	+	0.397915i
$924$	0.0818769	−	0.141815i	0.00269355	−	0.00466537i
$925$		0			0
$926$	13.2498	−	11.1179i	0.435416	−	0.365357i
$927$	−22.3954	−	18.7920i	−0.735563	−	0.617210i
$928$	0.573312	+	3.25141i	0.0188199	+	0.106733i
$929$	−17.6774	−	6.43406i	−0.579978	−	0.211095i	0.0353379	−	0.999375i	$-0.488749\pi$
$929$	−17.6774	−	6.43406i	−0.579978	−	0.211095i	−0.615316	+	0.788281i	$0.710971\pi$
$930$		0			0
$931$	−6.94326	−	14.1885i	−0.227556	−	0.465010i
$932$	−20.5518			−0.673196
$933$	0.592364	+	0.215603i	0.0193931	+	0.00705852i
$934$	3.65126	+	20.7073i	0.119473	+	0.677564i
$935$		0			0
$936$	5.49725	−	4.61274i	0.179683	−	0.150772i
$937$	3.33653	−	18.9224i	0.109000	−	0.618168i	−0.880548	−	0.473958i	$-0.842825\pi$
$937$	3.33653	−	18.9224i	0.109000	−	0.618168i	0.989547	−	0.144210i	$-0.0460640\pi$
$938$	3.41542	−	5.91568i	0.111517	−	0.193154i
$939$	0.238519	+	0.413127i	0.00778378	+	0.0134819i
$940$		0			0
$941$	−14.6200	+	5.32125i	−0.476598	+	0.173468i	−0.569139	−	0.822241i	$-0.692723\pi$
$941$	−14.6200	+	5.32125i	−0.476598	+	0.173468i	0.0925407	+	0.995709i	$0.470501\pi$
$942$	−0.127465	−	0.220775i	−0.00415302	−	0.00719324i
$943$	−6.46798	+	11.2029i	−0.210626	+	0.364816i
$944$	−0.825516	+	4.68173i	−0.0268683	+	0.152377i
$945$		0			0
$946$	10.7939	+	9.05713i	0.350939	+	0.294473i
$947$	3.85079	+	21.8389i	0.125134	+	0.709670i	0.981228	+	0.192850i	$0.0617732\pi$
$947$	3.85079	+	21.8389i	0.125134	+	0.709670i	−0.856094	+	0.516820i	$0.827116\pi$
$948$	0.412170	+	0.150017i	0.0133866	+	0.00487234i
$949$	−1.22145			−0.0396500
$950$		0			0
$951$	−0.444078			−0.0144002
$952$	−11.6407	−	4.23688i	−0.377278	−	0.137318i
$953$	0.860556	+	4.88046i	0.0278762	+	0.158094i	0.995568	−	0.0940411i	$-0.0299785\pi$
$953$	0.860556	+	4.88046i	0.0278762	+	0.158094i	−0.967692	+	0.252135i	$0.918867\pi$
$954$	−4.41362	−	3.70346i	−0.142896	−	0.119904i
$955$		0			0
$956$	0.154055	−	0.873692i	0.00498251	−	0.0282572i
$957$	−0.147121	+	0.254822i	−0.00475576	+	0.00823722i
$958$	−10.5658	−	18.3006i	−0.341367	−	0.591265i
$959$	−7.68958	+	2.79878i	−0.248309	+	0.0903772i
$960$		0			0
$961$	9.36155	+	16.2147i	0.301986	+	0.523054i
$962$	7.18990	−	12.4533i	0.231812	−	0.401510i
$963$	6.91812	−	39.2346i	0.222933	−	1.26432i
$964$	−3.06526	+	2.57206i	−0.0987255	+	0.0828406i
$965$		0			0
$966$	−0.0186927	−	0.106012i	−0.000601429	−	0.00341087i
$967$	−16.1902	−	5.89275i	−0.520642	−	0.189498i	0.0683131	−	0.997664i	$-0.478238\pi$
$967$	−16.1902	−	5.89275i	−0.520642	−	0.189498i	−0.588955	+	0.808166i	$0.700461\pi$
$968$	−4.92005			−0.158136
$969$	−0.255613	+	1.03097i	−0.00821148	+	0.0331195i
$970$		0			0
$971$	3.57394	+	1.30081i	0.114693	+	0.0417449i	0.398729	−	0.917069i	$-0.369451\pi$
$971$	3.57394	+	1.30081i	0.114693	+	0.0417449i	−0.284036	+	0.958814i	$0.591674\pi$
$972$	−0.169362	−	0.960502i	−0.00543230	−	0.0308081i
$973$	1.70519	+	1.43082i	0.0546659	+	0.0458701i
$974$	13.1762	−	11.0561i	0.422193	−	0.354262i
$975$		0			0
$976$	−6.83209	+	11.8335i	−0.218690	+	0.378782i
$977$	−30.8958	−	53.5131i	−0.988445	−	1.71204i	−0.625496	−	0.780227i	$-0.715103\pi$
$977$	−30.8958	−	53.5131i	−0.988445	−	1.71204i	−0.362949	−	0.931809i	$-0.618230\pi$
$978$	0.538531	−	0.196009i	0.0172203	−	0.00626769i
$979$	39.3944	−	14.3384i	1.25905	−	0.458257i
$980$		0			0
$981$	2.16494	−	3.74978i	0.0691212	−	0.119721i
$982$	−5.75424	+	32.6339i	−0.183625	+	1.04139i
$983$	9.12934	−	7.66042i	0.291181	−	0.244330i	−0.485482	−	0.874247i	$-0.661356\pi$
$983$	9.12934	−	7.66042i	0.291181	−	0.244330i	0.776662	+	0.629917i	$0.216911\pi$
$984$	0.220967	+	0.185413i	0.00704416	+	0.00591075i
$985$		0			0
$986$	20.9167	+	7.61307i	0.666125	+	0.242450i
$987$	−0.829652			−0.0264081
$988$	8.43100	−	6.14240i	0.268226	−	0.195416i
$989$	9.26263			0.294535
$990$		0			0
$991$	2.80361	+	15.9001i	0.0890596	+	0.505082i	0.996407	+	0.0846996i	$0.0269931\pi$
$991$	2.80361	+	15.9001i	0.0890596	+	0.505082i	−0.907347	+	0.420383i	$0.861896\pi$
$992$	−2.68410	−	2.25222i	−0.0852202	−	0.0715082i
$993$	−0.0275935	+	0.0231537i	−0.000875654	+	0.000734761i
$994$	−1.86114	+	10.5550i	−0.0590317	+	0.334785i
$995$		0			0
$996$	−0.112635	−	0.195089i	−0.00356896	−	0.00618162i
$997$	−39.9680	+	14.5471i	−1.26580	+	0.460713i	−0.885711	−	0.464238i	$-0.846328\pi$
$997$	−39.9680	+	14.5471i	−1.26580	+	0.460713i	−0.380088	+	0.924951i	$0.624106\pi$
$998$	30.0418	−	10.9343i	0.950958	−	0.346120i
$999$	−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.l.i.251.2		18
5.2	odd	4		950.2.u.g.99.5		36
5.3	odd	4		950.2.u.g.99.2		36
5.4	even	2		190.2.k.d.61.2	✓	18
19.5	even	9	inner	950.2.l.i.651.2		18
95.9	even	18		3610.2.a.bi.1.5		9
95.24	even	18		190.2.k.d.81.2	yes	18
95.29	odd	18		3610.2.a.bj.1.5		9
95.43	odd	36		950.2.u.g.499.5		36
95.62	odd	36		950.2.u.g.499.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.61.2	✓	18	5.4	even	2
190.2.k.d.81.2	yes	18	95.24	even	18
950.2.l.i.251.2		18	1.1	even	1	trivial
950.2.l.i.651.2		18	19.5	even	9	inner
950.2.u.g.99.2		36	5.3	odd	4
950.2.u.g.99.5		36	5.2	odd	4
950.2.u.g.499.2		36	95.62	odd	36
950.2.u.g.499.5		36	95.43	odd	36
3610.2.a.bi.1.5		9	95.9	even	18
3610.2.a.bj.1.5		9	95.29	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.00627632 - 0.0355948i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.00627632 + 0.0355948i) q^{6} +(0.918706 - 1.59124i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81785 - 1.02561i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.00627632 - 0.0355948i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.00627632 + 0.0355948i) q^{6} +(0.918706 - 1.59124i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.81785 - 1.02561i) q^{9} +(1.23288 + 2.13541i) q^{11} +(0.0180720 - 0.0313015i) q^{12} +(-0.415556 + 2.35673i) q^{13} +(-1.40754 + 1.18107i) q^{14} +(0.173648 + 0.984808i) q^{16} +(6.33539 + 2.30589i) q^{17} -2.99869 q^{18} +(-4.34868 - 0.298357i) q^{19} +(-0.0624061 - 0.0227140i) q^{21} +(-0.428174 - 2.42830i) q^{22} +(-1.24170 - 1.04191i) q^{23} +(-0.0276878 + 0.0232329i) q^{24} +(1.19655 - 2.07248i) q^{26} +(-0.108408 - 0.187768i) q^{27} +(1.72660 - 0.628432i) q^{28} +(-3.10246 + 1.12920i) q^{29} +(1.75192 - 3.03441i) q^{31} +(0.173648 - 0.984808i) q^{32} +(0.0682715 - 0.0572866i) q^{33} +(-5.16466 - 4.33366i) q^{34} +(2.81785 + 1.02561i) q^{36} +6.00888 q^{37} +(3.98437 + 1.76770i) q^{38} +0.0864957 q^{39} +(-1.38582 - 7.85939i) q^{41} +(0.0508739 + 0.0426883i) q^{42} +(-4.37751 + 3.67317i) q^{43} +(-0.428174 + 2.42830i) q^{44} +(0.810460 + 1.40376i) q^{46} +(11.7392 - 4.27274i) q^{47} +(0.0339642 - 0.0123619i) q^{48} +(1.81196 + 3.13841i) q^{49} +(0.0423149 - 0.239980i) q^{51} +(-1.83321 + 1.53825i) q^{52} +(1.47185 + 1.23503i) q^{53} +(0.0376497 + 0.213522i) q^{54} -1.83741 q^{56} +(0.0166738 + 0.156663i) q^{57} +3.30157 q^{58} +(4.46726 + 1.62595i) q^{59} +(10.4674 + 8.78317i) q^{61} +(-2.68410 + 2.25222i) q^{62} +(0.956772 - 5.42613i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0837473 + 0.0304815i) q^{66} +(-3.49344 + 1.27151i) q^{67} +(3.37099 + 5.83873i) q^{68} +(-0.0292932 + 0.0507373i) q^{69} +(4.46844 - 3.74946i) q^{71} +(-2.29713 - 1.92752i) q^{72} +(0.0886314 + 0.502654i) q^{73} +(-5.64650 - 2.05516i) q^{74} +(-3.13950 - 3.02383i) q^{76} +4.53061 q^{77} +(-0.0812794 - 0.0295833i) q^{78} +(2.10729 + 11.9511i) q^{79} +(6.88539 - 5.77753i) q^{81} +(-1.38582 + 7.85939i) q^{82} +(3.11628 - 5.39755i) q^{83} +(-0.0332056 - 0.0575138i) q^{84} +(5.36981 - 1.95445i) q^{86} +(0.0596659 + 0.103344i) q^{87} +(1.23288 - 2.13541i) q^{88} +(2.95236 - 16.7437i) q^{89} +(3.36837 + 2.82640i) q^{91} +(-0.281470 - 1.59629i) q^{92} +(-0.119005 - 0.0433143i) q^{93} -12.4926 q^{94} -0.0361439 q^{96} +(-12.8360 - 4.67194i) q^{97} +(-0.629287 - 3.56887i) q^{98} +(5.66417 + 4.75280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 9 * q^8 - 18 * q^9	\( 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) \) 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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