LMFDB - Embedded newform 104.2.s.c.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(69,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("104.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.s (of order $6$, degree $2$, 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:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.8607891481591137382656.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 20 x^{10} + 48 x^{9} - 76 x^{8} + 96 x^{7} + \cdots + 256 $ x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 20x^10 + 48x^9 - 76x^8 + 96x^7 - 80x^6 + 96x^4 - 192x^3 + 320x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Root			$1.40104 + 0.192615i$ of defining polynomial
Character	$\chi$	$=$	104.101
Dual form			104.2.s.c.69.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.867327 - 1.11702i) q^{2} +(-0.323315 + 0.186666i) q^{3} +(-0.495487 - 1.93765i) q^{4} +2.04528 q^{5} +(-0.0719095 + 0.523052i) q^{6} +(-0.768362 - 0.443614i) q^{7} +(-2.59415 - 1.12711i) q^{8} +(-1.43031 + 2.47737i) q^{9} +(1.77393 - 2.28463i) q^{10} +(-0.654547 - 1.13371i) q^{11} +(0.521893 + 0.533982i) q^{12} +(3.57202 + 0.490616i) q^{13} +(-1.16195 + 0.473521i) q^{14} +(-0.661270 + 0.381784i) q^{15} +(-3.50898 + 1.92016i) q^{16} +(-1.02189 + 1.76997i) q^{17} +(1.52674 + 3.74638i) q^{18} +(-3.29348 + 5.70447i) q^{19} +(-1.01341 - 3.96304i) q^{20} +0.331231 q^{21} +(-1.83409 - 0.252151i) q^{22} +(1.76836 + 3.06289i) q^{23} +(1.04912 - 0.119830i) q^{24} -0.816837 q^{25} +(3.64614 - 3.56450i) q^{26} -2.18796i q^{27} +(-0.478856 + 1.70862i) q^{28} +(2.84932 - 1.64506i) q^{29} +(-0.147075 + 1.06979i) q^{30} -7.97252i q^{31} +(-0.898567 + 5.58503i) q^{32} +(0.423250 + 0.244364i) q^{33} +(1.09078 + 2.67662i) q^{34} +(-1.57151 - 0.907314i) q^{35} +(5.50898 + 1.54394i) q^{36} +(-2.25567 - 3.90694i) q^{37} +(3.51551 + 8.62654i) q^{38} +(-1.24647 + 0.508151i) q^{39} +(-5.30577 - 2.30524i) q^{40} +(6.06568 - 3.50202i) q^{41} +(0.287286 - 0.369993i) q^{42} +(-5.81252 - 3.35586i) q^{43} +(-1.87241 + 1.83002i) q^{44} +(-2.92538 + 5.06692i) q^{45} +(4.95508 + 0.681226i) q^{46} +0.0334334i q^{47} +(0.776079 - 1.27583i) q^{48} +(-3.10641 - 5.38047i) q^{49} +(-0.708465 + 0.912427i) q^{50} -0.763012i q^{51} +(-0.819246 - 7.16441i) q^{52} +2.79586i q^{53} +(-2.44401 - 1.89768i) q^{54} +(-1.33873 - 2.31875i) q^{55} +(1.49325 + 2.01683i) q^{56} -2.45912i q^{57} +(0.633726 - 4.60957i) q^{58} +(3.94011 - 6.82447i) q^{59} +(1.06742 + 1.09214i) q^{60} +(-11.4816 - 6.62888i) q^{61} +(-8.90551 - 6.91479i) q^{62} +(2.19799 - 1.26901i) q^{63} +(5.45927 + 5.84777i) q^{64} +(7.30577 + 1.00345i) q^{65} +(0.640056 - 0.260838i) q^{66} +(6.31662 + 10.9407i) q^{67} +(3.93592 + 1.10307i) q^{68} +(-1.14348 - 0.660187i) q^{69} +(-2.37651 + 0.968482i) q^{70} +(10.0115 + 5.78014i) q^{71} +(6.50271 - 4.81457i) q^{72} +3.99523i q^{73} +(-6.32055 - 0.868952i) q^{74} +(0.264096 - 0.152476i) q^{75} +(12.6851 + 3.55512i) q^{76} +1.16146i q^{77} +(-0.513479 + 1.83307i) q^{78} -1.04379 q^{79} +(-7.17685 + 3.92727i) q^{80} +(-3.88252 - 6.72471i) q^{81} +(1.34908 - 9.81291i) q^{82} +11.8200 q^{83} +(-0.164121 - 0.641810i) q^{84} +(-2.09006 + 3.62008i) q^{85} +(-8.78993 + 3.58210i) q^{86} +(-0.614153 + 1.06375i) q^{87} +(0.420186 + 3.67876i) q^{88} +(-12.5257 + 7.23169i) q^{89} +(3.12260 + 7.66240i) q^{90} +(-2.52696 - 1.96157i) q^{91} +(5.05862 - 4.94409i) q^{92} +(1.48820 + 2.57764i) q^{93} +(0.0373460 + 0.0289977i) q^{94} +(-6.73608 + 11.6672i) q^{95} +(-0.752016 - 1.97346i) q^{96} +(0.592940 + 0.342334i) q^{97} +(-8.70439 - 1.19668i) q^{98} +3.74482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - q^{4} + 6 q^{6} + 18 q^{7} + 2 q^{9} - 9 q^{10} - 16 q^{12} - 24 q^{14} - 36 q^{15} - q^{16} + 8 q^{17} - 15 q^{20} + 22 q^{22} - 2 q^{23} - 12 q^{24} - 12 q^{25} + 23 q^{26} - 8 q^{30}+ \cdots - 93 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - q^4 + 6 * q^6 + 18 * q^7 + 2 * q^9 - 9 * q^10 - 16 * q^12 - 24 * q^14 - 36 * q^15 - q^16 + 8 * q^17 - 15 * q^20 + 22 * q^22 - 2 * q^23 - 12 * q^24 - 12 * q^25 + 23 * q^26 - 8 * q^30 - 27 * q^32 - 30 * q^33 + 33 * q^36 - 14 * q^39 + 26 * q^40 + 24 * q^41 + 14 * q^42 + 42 * q^46 + 6 * q^48 - 14 * q^49 + 6 * q^50 + 28 * q^52 + 6 * q^54 + 4 * q^55 - 8 * q^56 - 33 * q^58 - 4 * q^62 + 50 * q^64 + 6 * q^65 + 40 * q^66 + 5 * q^68 + 6 * q^71 + 39 * q^72 - 29 * q^74 + 24 * q^76 - 20 * q^78 + 32 * q^79 - 33 * q^80 + 12 * q^81 + 9 * q^82 - 24 * q^84 + 34 * q^87 - 8 * q^88 - 30 * q^89 - 62 * q^90 - 4 * q^92 - 24 * q^94 + 28 * q^95 - 30 * q^97 - 93 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.867327	−	1.11702i	0.613293	−	0.789856i
$2$	0.867327	−	1.11702i	0.613293	−	0.789856i
$3$	−0.323315	+	0.186666i	−0.186666	+	0.107772i	−0.590421	−	0.807095i	$-0.701038\pi$
$3$	−0.323315	+	0.186666i	−0.186666	+	0.107772i	0.403755	+	0.914867i	$0.367705\pi$
$4$	−0.495487	−	1.93765i	−0.247744	−	0.968826i
$5$	2.04528			0.914676			0.457338	−	0.889293i	$-0.348803\pi$
$5$	2.04528			0.914676			0.457338	+	0.889293i	$0.348803\pi$
$6$	−0.0719095	+	0.523052i	−0.0293569	+	0.213535i
$7$	−0.768362	−	0.443614i	−0.290414	−	0.167670i	0.347715	−	0.937600i	$-0.386958\pi$
$7$	−0.768362	−	0.443614i	−0.290414	−	0.167670i	−0.638128	+	0.769930i	$0.720291\pi$
$8$	−2.59415	−	1.12711i	−0.917172	−	0.398492i
$9$	−1.43031	+	2.47737i	−0.476770	+	0.825791i
$10$	1.77393	−	2.28463i	0.560964	−	0.722462i
$11$	−0.654547	−	1.13371i	−0.197353	−	0.341826i	0.750316	−	0.661079i	$-0.229901\pi$
$11$	−0.654547	−	1.13371i	−0.197353	−	0.341826i	−0.947669	+	0.319253i	$0.896568\pi$
$12$	0.521893	+	0.533982i	0.150657	+	0.154147i
$13$	3.57202	+	0.490616i	0.990699	+	0.136072i
$13$	3.57202	+	0.490616i	0.990699	+	0.136072i
$14$	−1.16195	+	0.473521i	−0.310544	+	0.126554i
$15$	−0.661270	+	0.381784i	−0.170739	+	0.0985763i
$16$	−3.50898	+	1.92016i	−0.877246	+	0.480041i
$17$	−1.02189	+	1.76997i	−0.247845	+	0.429281i	−0.962928	−	0.269759i	$-0.913056\pi$
$17$	−1.02189	+	1.76997i	−0.247845	+	0.429281i	0.715082	+	0.699040i	$0.246389\pi$
$18$	1.52674	+	3.74638i	0.359855	+	0.883031i
$19$	−3.29348	+	5.70447i	−0.755575	+	1.30870i	0.189512	+	0.981878i	$0.439309\pi$
$19$	−3.29348	+	5.70447i	−0.755575	+	1.30870i	−0.945088	+	0.326817i	$0.894024\pi$
$20$	−1.01341	−	3.96304i	−0.226605	−	0.886162i
$21$	0.331231			0.0722806
$22$	−1.83409	−	0.252151i	−0.391028	−	0.0537588i
$23$	1.76836	+	3.06289i	0.368729	+	0.638657i	0.989367	−	0.145440i	$-0.0464597\pi$
$23$	1.76836	+	3.06289i	0.368729	+	0.638657i	−0.620638	+	0.784097i	$0.713126\pi$
$24$	1.04912	−	0.119830i	0.214151	−	0.0244603i
$25$	−0.816837			−0.163367
$26$	3.64614	−	3.56450i	0.715066	−	0.699057i
$27$		−	2.18796i		−	0.421073i
$28$	−0.478856	+	1.70862i	−0.0904952	+	0.322899i
$29$	2.84932	−	1.64506i	0.529106	−	0.305480i	−0.211546	−	0.977368i	$-0.567850\pi$
$29$	2.84932	−	1.64506i	0.529106	−	0.305480i	0.740652	+	0.671888i	$0.234517\pi$
$30$	−0.147075	+	1.06979i	−0.0268521	+	0.195315i
$31$		−	7.97252i		−	1.43191i	−0.698148	−	0.715954i	$-0.745992\pi$
$31$		−	7.97252i		−	1.43191i	0.698148	−	0.715954i	$-0.254008\pi$
$32$	−0.898567	+	5.58503i	−0.158846	+	0.987303i
$33$	0.423250	+	0.244364i	0.0736784	+	0.0425382i
$34$	1.09078	+	2.67662i	0.187068	+	0.459037i
$35$	−1.57151	−	0.907314i	−0.265634	−	0.153364i
$36$	5.50898	+	1.54394i	0.918164	+	0.257323i
$37$	−2.25567	−	3.90694i	−0.370830	−	0.642296i	0.618863	−	0.785499i	$-0.287593\pi$
$37$	−2.25567	−	3.90694i	−0.370830	−	0.642296i	−0.989693	+	0.143202i	$0.954260\pi$
$38$	3.51551	+	8.62654i	0.570291	+	1.39941i
$39$	−1.24647	+	0.508151i	−0.199595	+	0.0813693i
$40$	−5.30577	−	2.30524i	−0.838915	−	0.364491i
$41$	6.06568	−	3.50202i	0.947300	−	0.546924i	0.0550587	−	0.998483i	$-0.482465\pi$
$41$	6.06568	−	3.50202i	0.947300	−	0.546924i	0.892241	+	0.451559i	$0.149132\pi$
$42$	0.287286	−	0.369993i	0.0443292	−	0.0570912i
$43$	−5.81252	−	3.35586i	−0.886401	−	0.511764i	−0.0136373	−	0.999907i	$-0.504341\pi$
$43$	−5.81252	−	3.35586i	−0.886401	−	0.511764i	−0.872764	+	0.488143i	$0.837674\pi$
$44$	−1.87241	+	1.83002i	−0.282277	+	0.275886i
$45$	−2.92538	+	5.06692i	−0.436091	+	0.755331i
$46$	4.95508	+	0.681226i	0.730586	+	0.100441i
$47$			0.0334334i			0.00487677i	0.999997	+	0.00243838i	$0.000776162\pi$
$47$			0.0334334i			0.00487677i	−0.999997	+	0.00243838i	$0.999224\pi$
$48$	0.776079	−	1.27583i	0.112017	−	0.184150i
$49$	−3.10641	−	5.38047i	−0.443773	−	0.768638i
$50$	−0.708465	+	0.912427i	−0.100192	+	0.129037i
$51$		−	0.763012i		−	0.106843i
$52$	−0.819246	−	7.16441i	−0.113609	−	0.993526i
$53$			2.79586i			0.384041i	0.981391	+	0.192021i	$0.0615040\pi$
$53$			2.79586i			0.384041i	−0.981391	+	0.192021i	$0.938496\pi$
$54$	−2.44401	−	1.89768i	−0.332587	−	0.258241i
$55$	−1.33873	−	2.31875i	−0.180514	−	0.312660i
$56$	1.49325	+	2.01683i	0.199544	+	0.269510i
$57$		−	2.45912i		−	0.325719i
$58$	0.633726	−	4.60957i	0.0832122	−	0.605266i
$59$	3.94011	−	6.82447i	0.512958	−	0.888470i	−0.486929	−	0.873442i	$-0.661883\pi$
$59$	3.94011	−	6.82447i	0.512958	−	0.888470i	0.999887	−	0.0150283i	$-0.00478382\pi$
$60$	1.06742	+	1.09214i	0.137803	+	0.140995i
$61$	−11.4816	−	6.62888i	−1.47006	−	0.848741i	−0.470627	−	0.882332i	$-0.655972\pi$
$61$	−11.4816	−	6.62888i	−1.47006	−	0.848741i	−0.999436	+	0.0335913i	$0.989306\pi$
$62$	−8.90551	−	6.91479i	−1.13100	−	0.878179i
$63$	2.19799	−	1.26901i	0.276921	−	0.159881i
$64$	5.45927	+	5.84777i	0.682408	+	0.730971i
$65$	7.30577	+	1.00345i	0.906169	+	0.124462i
$66$	0.640056	−	0.260838i	0.0787855	−	0.0321069i
$67$	6.31662	+	10.9407i	0.771698	+	1.33662i	0.936632	+	0.350315i	$0.113925\pi$
$67$	6.31662	+	10.9407i	0.771698	+	1.33662i	−0.164934	+	0.986305i	$0.552741\pi$
$68$	3.93592	+	1.10307i	0.477300	+	0.133767i
$69$	−1.14348	−	0.660187i	−0.137659	−	0.0794772i
$70$	−2.37651	+	0.968482i	−0.284047	+	0.115756i
$71$	10.0115	+	5.78014i	1.18815	+	0.685977i	0.957885	−	0.287152i	$-0.0927085\pi$
$71$	10.0115	+	5.78014i	1.18815	+	0.685977i	0.230262	+	0.973129i	$0.426042\pi$
$72$	6.50271	−	4.81457i	0.766351	−	0.567403i
$73$			3.99523i			0.467607i	0.972284	+	0.233803i	$0.0751172\pi$
$73$			3.99523i			0.467607i	−0.972284	+	0.233803i	$0.924883\pi$
$74$	−6.32055	−	0.868952i	−0.734749	−	0.101014i
$75$	0.264096	−	0.152476i	0.0304952	−	0.0176064i
$76$	12.6851	+	3.55512i	1.45509	+	0.407800i
$77$			1.16146i			0.132361i
$78$	−0.513479	+	1.83307i	−0.0581401	+	0.207554i
$79$	−1.04379			−0.117435			−0.0587175	−	0.998275i	$-0.518701\pi$
$79$	−1.04379			−0.117435			−0.0587175	+	0.998275i	$0.518701\pi$
$80$	−7.17685	+	3.92727i	−0.802396	+	0.439082i
$81$	−3.88252	−	6.72471i	−0.431391	−	0.747190i
$82$	1.34908	−	9.81291i	0.148981	−	1.08365i
$83$	11.8200			1.29741			0.648706	−	0.761039i	$-0.275311\pi$
$83$	11.8200			1.29741			0.648706	+	0.761039i	$0.275311\pi$
$84$	−0.164121	−	0.641810i	−0.0179071	−	0.0700273i
$85$	−2.09006	+	3.62008i	−0.226698	+	0.392653i
$86$	−8.78993	+	3.58210i	−0.947843	+	0.386268i
$87$	−0.614153	+	1.06375i	−0.0658442	+	0.114045i
$88$	0.420186	+	3.67876i	0.0447920	+	0.392157i
$89$	−12.5257	+	7.23169i	−1.32772	+	0.766558i	−0.984946	−	0.172862i	$-0.944699\pi$
$89$	−12.5257	+	7.23169i	−1.32772	+	0.766558i	−0.342770	+	0.939419i	$0.611365\pi$
$90$	3.12260	+	7.66240i	0.329151	+	0.807688i
$91$	−2.52696	−	1.96157i	−0.264897	−	0.205628i
$92$	5.05862	−	4.94409i	0.527397	−	0.515457i
$93$	1.48820	+	2.57764i	0.154319	+	0.267289i
$94$	0.0373460	+	0.0289977i	0.00385194	+	0.00299089i
$95$	−6.73608	+	11.6672i	−0.691107	+	1.19703i
$96$	−0.752016	−	1.97346i	−0.0767524	−	0.201415i
$97$	0.592940	+	0.342334i	0.0602039	+	0.0347587i	0.529800	−	0.848123i	$-0.322267\pi$
$97$	0.592940	+	0.342334i	0.0602039	+	0.0347587i	−0.469596	+	0.882881i	$0.655600\pi$
$98$	−8.70439	−	1.19668i	−0.879276	−	0.120883i
$99$	3.74482			0.376369
$100$	0.404733	+	1.58275i	0.0404733	+	0.158275i
$101$	−0.362516	+	0.209299i	−0.0360717	+	0.0208260i	−0.517927	−	0.855425i	$-0.673296\pi$
$101$	−0.362516	+	0.209299i	−0.0360717	+	0.0208260i	0.481856	+	0.876251i	$0.339963\pi$
$102$	−0.852303	−	0.661781i	−0.0843905	−	0.0655261i
$103$	−15.8088			−1.55769			−0.778845	−	0.627217i	$-0.784194\pi$
$103$	−15.8088			−1.55769			−0.778845	+	0.627217i	$0.784194\pi$
$104$	−8.71338	−	5.29877i	−0.854417	−	0.519587i
$105$	0.677460			0.0661133
$106$	3.12304	+	2.42493i	0.303337	+	0.235530i
$107$	11.8891	−	6.86419i	1.14937	−	0.663587i	0.200633	−	0.979666i	$-0.435700\pi$
$107$	11.8891	−	6.86419i	1.14937	−	0.663587i	0.948733	+	0.316080i	$0.102367\pi$
$108$	−4.23951	+	1.08411i	−0.407947	+	0.104318i
$109$	11.3558			1.08769			0.543844	−	0.839186i	$-0.316968\pi$
$109$	11.3558			1.08769			0.543844	+	0.839186i	$0.316968\pi$
$110$	−3.75122	−	0.515719i	−0.357664	−	0.0491719i
$111$	1.45859	+	0.842115i	0.138443	+	0.0799300i
$112$	3.54798	+	0.0812537i	0.335253	+	0.00767775i
$113$	−5.55862	+	9.62781i	−0.522911	+	0.905708i	0.476734	+	0.879048i	$0.341821\pi$
$113$	−5.55862	+	9.62781i	−0.522911	+	0.905708i	−0.999645	+	0.0266602i	$0.991513\pi$
$114$	−2.74690	−	2.13287i	−0.257271	−	0.199761i
$115$	3.61679	+	6.26447i	0.337268	+	0.584165i
$116$	−4.59935	−	4.70589i	−0.427039	−	0.436931i
$117$	−6.32453	+	8.14748i	−0.584703	+	0.753235i
$118$	−4.20573	−	10.3202i	−0.387169	−	0.950055i
$119$	1.57037	−	0.906652i	0.143955	−	0.0831127i
$120$	2.14575	−	0.245086i	0.195879	−	0.0223732i
$121$	4.64314	−	8.04215i	0.422103	−	0.731105i
$122$	−17.3629	+	7.07577i	−1.57196	+	0.640610i
$123$	−1.30742	+	2.26452i	−0.117886	+	0.204184i
$124$	−15.4480	+	3.95029i	−1.38727	+	0.354746i
$125$	−11.8971			−1.06410
$126$	0.488862	−	3.55586i	0.0435513	−	0.316781i
$127$	10.6438	+	18.4356i	0.944486	+	1.63590i	0.756777	+	0.653673i	$0.226773\pi$
$127$	10.6438	+	18.4356i	0.944486	+	1.63590i	0.187709	+	0.982225i	$0.439894\pi$
$128$	11.2671	−	1.02620i	0.995878	−	0.0907045i
$129$	2.50570			0.220615
$130$	7.45736	−	7.29040i	0.654054	−	0.639411i
$131$			6.27001i			0.547813i	0.961756	+	0.273906i	$0.0883159\pi$
$131$			6.27001i			0.547813i	−0.961756	+	0.273906i	$0.911684\pi$
$132$	0.263776	−	0.941190i	0.0229588	−	0.0819201i
$133$	5.06117	−	2.92207i	0.438859	−	0.253375i
$134$	17.6996	+	2.43335i	1.52901	+	0.210210i
$135$		−	4.47499i		−	0.385146i
$136$	4.64589	−	3.43979i	0.398382	−	0.294960i
$137$	2.96328	+	1.71085i	0.253170	+	0.146168i	0.621215	−	0.783640i	$-0.286639\pi$
$137$	2.96328	+	1.71085i	0.253170	+	0.146168i	−0.368045	+	0.929808i	$0.619973\pi$
$138$	−1.72921	+	0.704694i	−0.147201	+	0.0599876i
$139$	−5.17548	−	2.98806i	−0.438978	−	0.253444i	0.264186	−	0.964472i	$-0.414897\pi$
$139$	−5.17548	−	2.98806i	−0.438978	−	0.253444i	−0.703164	+	0.711028i	$0.748230\pi$
$140$	−0.979393	+	3.49461i	−0.0827738	+	0.295348i
$141$	−0.00624089	−	0.0108095i	−0.000525578	−	0.000910328i
$142$	15.1398	−	6.16982i	1.27050	−	0.517760i
$143$	−1.78184	−	4.37075i	−0.149005	−	0.365501i
$144$	0.261980	−	11.4395i	0.0218317	−	0.953291i
$145$	5.82766	−	3.36460i	0.483961	−	0.279415i
$146$	4.46277	+	3.46517i	0.369342	+	0.286780i
$147$	2.00870	+	1.15973i	0.165675	+	0.0956525i
$148$	−6.45262	+	6.30654i	−0.530402	+	0.518395i
$149$	3.18055	−	5.50888i	0.260561	−	0.451305i	−0.705830	−	0.708381i	$-0.749426\pi$
$149$	3.18055	−	5.50888i	0.260561	−	0.451305i	0.966391	+	0.257076i	$0.0827591\pi$
$150$	0.0587383	−	0.427248i	0.00479596	−	0.0348847i
$151$		−	16.9225i		−	1.37713i	−0.725173	−	0.688567i	$-0.758240\pi$
$151$		−	16.9225i		−	1.37713i	0.725173	−	0.688567i	$-0.241760\pi$
$152$	14.9733	−	11.0862i	1.21450	−	0.899207i
$153$	−2.92325	−	5.06322i	−0.236331	−	0.409337i
$154$	1.29738	+	1.00737i	0.104546	+	0.0811762i
$155$		−	16.3060i		−	1.30973i
$156$	1.60223	+	2.16344i	0.128281	+	0.173214i
$157$		−	4.22081i		−	0.336857i	−0.985714	−	0.168429i	$-0.946131\pi$
$157$		−	4.22081i		−	0.336857i	0.985714	−	0.168429i	$-0.0538693\pi$
$158$	−0.905304	+	1.16593i	−0.0720221	+	0.0927567i
$159$	−0.521893	−	0.903945i	−0.0413888	−	0.0716875i
$160$	−1.83782	+	11.4229i	−0.145292	+	0.903063i
$161$		−	3.13788i		−	0.247300i
$162$	−10.8791	−	1.49566i	−0.854741	−	0.117510i
$163$	−7.46735	+	12.9338i	−0.584888	+	1.01306i	0.410002	+	0.912085i	$0.365528\pi$
$163$	−7.46735	+	12.9338i	−0.584888	+	1.01306i	−0.994889	+	0.100971i	$0.967805\pi$
$164$	−9.79116	−	10.0180i	−0.764561	−	0.782271i
$165$	0.865664	+	0.499791i	0.0673919	+	0.0389087i
$166$	10.2518	−	13.2032i	0.795693	−	1.02477i
$167$	11.1644	−	6.44574i	0.863923	−	0.498786i	−0.00140075	−	0.999999i	$-0.500446\pi$
$167$	11.1644	−	6.44574i	0.863923	−	0.498786i	0.865324	+	0.501213i	$0.167113\pi$
$168$	−0.859265	−	0.373333i	−0.0662937	−	0.0288032i
$169$	12.5186	+	3.50498i	0.962969	+	0.269614i
$170$	2.23096	+	5.47444i	0.171107	+	0.419870i
$171$	−9.42140	−	16.3183i	−0.720472	−	1.24789i
$172$	−3.62245	+	12.9254i	−0.276210	+	0.985554i
$173$	3.08337	+	1.78018i	0.234424	+	0.135345i	0.612611	−	0.790384i	$-0.290119\pi$
$173$	3.08337	+	1.78018i	0.234424	+	0.135345i	−0.378187	+	0.925729i	$0.623452\pi$
$174$	0.655557	+	1.60864i	0.0496977	+	0.121951i
$175$	0.627627	+	0.362360i	0.0474441	+	0.0273919i
$176$	4.47370	+	2.72133i	0.337218	+	0.205128i
$177$			2.94194i			0.221130i
$178$	−2.78586	+	20.2637i	−0.208809	+	1.51883i
$179$	−20.7900	+	12.0031i	−1.55392	+	0.897156i	−0.556103	+	0.831113i	$0.687704\pi$
$179$	−20.7900	+	12.0031i	−1.55392	+	0.897156i	−0.997817	+	0.0660425i	$0.978963\pi$
$180$	11.2674	+	3.15778i	0.839823	+	0.235367i
$181$		−	13.1094i		−	0.974415i	−0.873286	−	0.487208i	$-0.838015\pi$
$181$		−	13.1094i		−	0.974415i	0.873286	−	0.487208i	$-0.161985\pi$
$182$	−4.38282	+	1.12135i	−0.324876	+	0.0831202i
$183$	4.94955			0.365881
$184$	−1.13520	−	9.93875i	−0.0836880	−	0.732694i
$185$	−4.61347	−	7.99077i	−0.339189	−	0.587493i
$186$	4.17004	+	0.573300i	0.305763	+	0.0420364i
$187$	2.67551			0.195652
$188$	0.0647823	−	0.0165658i	0.00472474	−	0.00120819i
$189$	−0.970610	+	1.68115i	−0.0706015	+	0.122285i
$190$	7.19020	+	17.6437i	0.521632	+	1.28001i
$191$	6.34887	−	10.9966i	0.459388	−	0.795684i	−0.539540	−	0.841960i	$-0.681402\pi$
$191$	6.34887	−	10.9966i	0.459388	−	0.795684i	0.998929	+	0.0462759i	$0.0147353\pi$
$192$	−2.85665	−	0.871614i	−0.206161	−	0.0629033i
$193$	−16.9573	+	9.79031i	−1.22061	+	0.704722i	−0.965049	−	0.262069i	$-0.915595\pi$
$193$	−16.9573	+	9.79031i	−1.22061	+	0.704722i	−0.255566	+	0.966792i	$0.582262\pi$
$194$	0.896668	−	0.365413i	0.0643770	−	0.0262351i
$195$	−2.54938	+	1.03931i	−0.182565	+	0.0744266i
$196$	−8.88628	+	8.68510i	−0.634734	+	0.620364i
$197$	6.30145	+	10.9144i	0.448960	+	0.777621i	0.998319	−	0.0579655i	$-0.0184613\pi$
$197$	6.30145	+	10.9144i	0.448960	+	0.777621i	−0.549359	+	0.835587i	$0.685128\pi$
$198$	3.24799	−	4.18306i	0.230824	−	0.297277i
$199$	−2.06195	+	3.57140i	−0.146168	+	0.253170i	−0.929808	−	0.368045i	$-0.880027\pi$
$199$	−2.06195	+	3.57140i	−0.146168	+	0.253170i	0.783640	+	0.621215i	$0.213361\pi$
$200$	2.11900	+	0.920662i	0.149836	+	0.0651006i
$201$	−4.08452	−	2.35820i	−0.288100	−	0.166335i
$202$	−0.0806281	+	0.586469i	−0.00567297	+	0.0412638i
$203$	−2.91908			−0.204879
$204$	−1.47845	+	0.378063i	−0.103512	+	0.0264697i
$205$	12.4060	−	7.16261i	0.866473	−	0.500258i
$206$	−13.7114	+	17.6588i	−0.955320	+	1.23035i
$207$	−10.1172			−0.703196
$208$	−13.4762	+	5.13729i	−0.934407	+	0.356207i
$209$	8.62294			0.596461
$210$	0.587579	−	0.756739i	0.0405468	−	0.0522200i
$211$	−14.0385	+	8.10511i	−0.966448	+	0.557979i	−0.898152	−	0.439686i	$-0.855090\pi$
$211$	−14.0385	+	8.10511i	−0.966448	+	0.557979i	−0.0682966	+	0.997665i	$0.521756\pi$
$212$	5.41740	−	1.38531i	0.372069	−	0.0951438i
$213$	−4.31583			−0.295716
$214$	2.64429	−	19.2340i	0.180760	−	1.31481i
$215$	−11.8882	−	6.86367i	−0.810770	−	0.468098i
$216$	−2.46606	+	5.67591i	−0.167794	+	0.386197i
$217$	−3.53672	+	6.12579i	−0.240088	+	0.415845i
$218$	9.84920	−	12.6847i	0.667072	−	0.859117i
$219$	−0.745775	−	1.29172i	−0.0503948	−	0.0872864i
$220$	−3.82960	+	3.74290i	−0.258192	+	0.252346i
$221$	−4.51859	+	5.82100i	−0.303953	+	0.391563i
$222$	2.20573	−	0.898887i	0.148039	−	0.0603294i
$223$	−4.40068	+	2.54073i	−0.294691	+	0.170140i	−0.640056	−	0.768329i	$-0.721089\pi$
$223$	−4.40068	+	2.54073i	−0.294691	+	0.170140i	0.345364	+	0.938469i	$0.387755\pi$
$224$	3.16802	−	3.89271i	0.211672	−	0.260093i
$225$	1.16833	−	2.02361i	0.0778888	−	0.134907i
$226$	5.93336	+	14.5596i	0.394681	+	0.968488i
$227$	3.62471	−	6.27818i	0.240580	−	0.416697i	−0.720299	−	0.693663i	$-0.755996\pi$
$227$	3.62471	−	6.27818i	0.240580	−	0.416697i	0.960880	+	0.276966i	$0.0893289\pi$
$228$	−4.76493	+	1.21847i	−0.315565	+	0.0806948i
$229$	11.6284			0.768426			0.384213	−	0.923245i	$-0.374473\pi$
$229$	11.6284			0.768426			0.384213	+	0.923245i	$0.374473\pi$
$230$	10.1345	+	1.39330i	0.668250	+	0.0918713i
$231$	−0.216806	−	0.375519i	−0.0142648	−	0.0247074i
$232$	−9.24574	+	1.05604i	−0.607012	+	0.0693327i
$233$	7.01554			0.459603			0.229802	−	0.973237i	$-0.426192\pi$
$233$	7.01554			0.459603			0.229802	+	0.973237i	$0.426192\pi$
$234$	3.61549	+	14.1312i	0.236352	+	0.923785i
$235$			0.0683807i			0.00446066i
$236$	−15.1757	−	4.25312i	−0.987855	−	0.276854i
$237$	0.337472	−	0.194840i	0.0219212	−	0.0126562i
$238$	0.349270	−	2.54050i	0.0226398	−	0.164676i
$239$		−	17.8151i		−	1.15237i	−0.817321	−	0.576183i	$-0.804542\pi$
$239$		−	17.8151i		−	1.15237i	0.817321	−	0.576183i	$-0.195458\pi$
$240$	1.58730	−	2.60942i	0.102460	−	0.168437i
$241$	17.5803	+	10.1500i	1.13244	+	0.653817i	0.944548	−	0.328372i	$-0.106500\pi$
$241$	17.5803	+	10.1500i	1.13244	+	0.653817i	0.187896	+	0.982189i	$0.439833\pi$
$242$	−4.95616	−	12.1617i	−0.318594	−	0.781782i
$243$	8.19504	+	4.73141i	0.525712	+	0.303520i
$244$	−7.15549	+	25.5318i	−0.458083	+	1.63450i
$245$	−6.35348	−	11.0045i	−0.405909	−	0.703055i
$246$	1.39556	+	3.42449i	0.0889776	+	0.218338i
$247$	−14.5631	+	18.7606i	−0.926625	+	1.19371i
$248$	−8.98588	+	20.6820i	−0.570604	+	1.31331i
$249$	−3.82158	+	2.20639i	−0.242183	+	0.139824i
$250$	−10.3186	+	13.2893i	−0.652608	+	0.840489i
$251$	−13.8573	−	8.00054i	−0.874668	−	0.504990i	−0.00577105	−	0.999983i	$-0.501837\pi$
$251$	−13.8573	−	8.00054i	−0.874668	−	0.504990i	−0.868897	+	0.494994i	$0.835170\pi$
$252$	−3.54798	−	3.63017i	−0.223502	−	0.228679i
$253$	2.31495	−	4.00961i	0.145540	−	0.252082i
$254$	29.8247	+	4.10032i	1.87137	+	0.257277i
$255$		−	1.56057i		−	0.0977268i
$256$	8.62594	−	13.4756i	0.539121	−	0.842228i
$257$	−8.09534	−	14.0215i	−0.504974	−	0.874640i	−0.999983	−	0.00575250i	$-0.998169\pi$
$257$	−8.09534	−	14.0215i	−0.504974	−	0.874640i	0.495010	−	0.868887i	$-0.335164\pi$
$258$	2.17326	−	2.79893i	0.135302	−	0.174254i
$259$			4.00259i			0.248709i
$260$	−1.67559	−	14.6532i	−0.103915	−	0.908754i
$261$			9.41178i			0.582574i
$262$	7.00375	+	5.43815i	0.432693	+	0.335970i
$263$	5.76836	+	9.99110i	0.355692	+	0.616077i	0.987236	−	0.159263i	$-0.0509117\pi$
$263$	5.76836	+	9.99110i	0.355692	+	0.616077i	−0.631544	+	0.775340i	$0.717578\pi$
$264$	−0.822552	−	1.11096i	−0.0506246	−	0.0683751i
$265$			5.71831i			0.351273i
$266$	1.12567	−	8.18783i	0.0690191	−	0.502028i
$267$	2.69982	−	4.67623i	0.165227	−	0.286181i
$268$	18.0695	−	17.6604i	1.10377	−	1.07878i
$269$	21.8601	+	12.6210i	1.33284	+	0.769513i	0.985733	−	0.168314i	$-0.0538323\pi$
$269$	21.8601	+	12.6210i	1.33284	+	0.769513i	0.347102	+	0.937827i	$0.387166\pi$
$270$	−4.99867	−	3.88128i	−0.304210	−	0.236207i
$271$	6.07814	−	3.50921i	0.369221	−	0.213170i	−0.303897	−	0.952705i	$-0.598288\pi$
$271$	6.07814	−	3.50921i	0.369221	−	0.213170i	0.673118	+	0.739535i	$0.264955\pi$
$272$	0.187173	−	8.17300i	0.0113490	−	0.495561i
$273$	1.18316	+	0.162507i	0.0716083	+	0.00983539i
$274$	4.48119	−	1.82619i	0.270718	−	0.110324i
$275$	0.534658	+	0.926055i	0.0322411	+	0.0558432i
$276$	−0.712634	+	2.54278i	−0.0428955	+	0.153057i
$277$	1.54647	+	0.892855i	0.0929184	+	0.0536465i	0.545739	−	0.837955i	$-0.316249\pi$
$277$	1.54647	+	0.892855i	0.0929184	+	0.0536465i	−0.452821	+	0.891602i	$0.649582\pi$
$278$	−7.82657	+	3.18951i	−0.469407	+	0.191294i
$279$	19.7509	+	11.4032i	1.18246	+	0.682691i
$280$	3.05411	+	4.12498i	0.182518	+	0.246514i
$281$			6.48188i			0.386677i	0.981132	+	0.193338i	$0.0619315\pi$
$281$			6.48188i			0.386677i	−0.981132	+	0.193338i	$0.938069\pi$
$282$	−0.0174874	−	0.00240418i	−0.00104136	−	0.000143167i
$283$	−8.57758	+	4.95227i	−0.509884	+	0.294382i	−0.732786	−	0.680459i	$-0.761780\pi$
$283$	−8.57758	+	4.95227i	−0.509884	+	0.294382i	0.222902	+	0.974841i	$0.428447\pi$
$284$	6.23933	−	22.2628i	0.370236	−	1.32105i
$285$		−	5.02959i		−	0.297927i
$286$	−6.42767	−	1.80052i	−0.380076	−	0.106467i
$287$	−6.21418			−0.366812
$288$	−12.5510	−	10.2144i	−0.739573	−	0.601890i
$289$	6.41147	+	11.1050i	0.377145	+	0.653235i
$290$	1.29615	−	9.42785i	0.0761123	−	0.553622i
$291$	−0.255609			−0.0149841
$292$	7.74137	−	1.97959i	0.453029	−	0.115847i
$293$	2.97111	−	5.14612i	0.173574	−	0.300639i	−0.766093	−	0.642730i	$-0.777802\pi$
$293$	2.97111	−	5.14612i	0.173574	−	0.300639i	0.939667	+	0.342091i	$0.111135\pi$
$294$	3.03764	−	1.23791i	0.177159	−	0.0721963i
$295$	8.05862	−	13.9579i	0.469191	−	0.812662i
$296$	1.44803	+	12.6776i	0.0841648	+	0.736869i
$297$	−2.48051	+	1.43212i	−0.143934	+	0.0831002i
$298$	−3.39498	−	8.33076i	−0.196666	−	0.482588i
$299$	4.81391	+	11.8083i	0.278396	+	0.682891i
$300$	−0.426301	−	0.436176i	−0.0246125	−	0.0251826i
$301$	2.97741	+	5.15703i	0.171615	+	0.297246i
$302$	−18.9029	−	14.6773i	−1.08774	−	0.844586i
$303$	0.0781380	−	0.135339i	0.00448891	−	0.00777502i
$304$	0.603243	−	26.3409i	0.0345984	−	1.51075i
$305$	−23.4830	−	13.5579i	−1.34463	−	0.776323i
$306$	−8.19115	−	1.12612i	−0.468257	−	0.0643762i
$307$	24.9622			1.42467			0.712335	−	0.701840i	$-0.247638\pi$
$307$	24.9622			1.42467			0.712335	+	0.701840i	$0.247638\pi$
$308$	2.25051	−	0.575491i	0.128235	−	0.0327917i
$309$	5.11123	−	2.95097i	0.290768	−	0.167875i
$310$	−18.2142	−	14.1427i	−1.03450	−	0.803249i
$311$	−7.69300			−0.436230			−0.218115	−	0.975923i	$-0.569991\pi$
$311$	−7.69300			−0.436230			−0.218115	+	0.975923i	$0.569991\pi$
$312$	3.80627	+	0.0866807i	0.215488	+	0.00490733i
$313$	9.69158			0.547801			0.273900	−	0.961758i	$-0.411686\pi$
$313$	9.69158			0.547801			0.273900	+	0.961758i	$0.411686\pi$
$314$	−4.71475	−	3.66082i	−0.266069	−	0.206592i
$315$	4.49551	−	2.59548i	0.253293	−	0.146239i
$316$	0.517183	+	2.02249i	0.0290938	+	0.113774i
$317$	−30.4231			−1.70873			−0.854366	−	0.519671i	$-0.826054\pi$
$317$	−30.4231			−1.70873			−0.854366	+	0.519671i	$0.826054\pi$
$318$	−1.46238	−	0.201049i	−0.0820062	−	0.0112743i
$319$	−3.73003	−	2.15353i	−0.208842	−	0.120575i
$320$	11.1657	+	11.9603i	0.624183	+	0.668602i
$321$	−2.56263	+	4.43860i	−0.143032	+	0.247739i
$322$	−3.50509	−	2.72157i	−0.195331	−	0.151667i
$323$	−6.73116	−	11.6587i	−0.374532	−	0.648708i
$324$	−11.1064	+	10.8550i	−0.617023	+	0.603054i
$325$	−2.91775	−	0.400753i	−0.161848	−	0.0222298i
$326$	7.97077	+	19.5591i	0.441460	+	1.08328i
$327$	−3.67151	+	2.11975i	−0.203035	+	0.117222i
$328$	−19.6824	+	2.24812i	−1.08678	+	0.124132i
$329$	0.0148315	−	0.0256890i	0.000817690	−	0.00141628i
$330$	1.30909	−	0.533485i	0.0720632	−	0.0293674i
$331$	0.111973	−	0.193943i	0.00615459	−	0.0106601i	−0.862932	−	0.505321i	$-0.831374\pi$
$331$	0.111973	−	0.193943i	0.00615459	−	0.0106601i	0.869086	+	0.494660i	$0.164708\pi$
$332$	−5.85665	−	22.9030i	−0.321425	−	1.25697i
$333$	12.9052			0.707203
$334$	2.48309	−	18.0614i	0.135869	−	0.988277i
$335$	12.9192	+	22.3768i	0.705853	+	1.22257i
$336$	−1.16228	+	0.636018i	−0.0634078	+	0.0346976i
$337$	−7.31452			−0.398447			−0.199224	−	0.979954i	$-0.563842\pi$
$337$	−7.31452			−0.398447			−0.199224	+	0.979954i	$0.563842\pi$
$338$	14.7729	−	10.9436i	0.803538	−	0.595254i
$339$		−	4.15043i		−	0.225420i
$340$	8.05005	+	2.25609i	0.436575	+	0.122354i
$341$	−9.03851	+	5.21839i	−0.489463	+	0.282592i
$342$	−26.3994	−	3.62940i	−1.42752	−	0.196256i
$343$			11.7228i			0.632971i
$344$	11.2962	+	15.2569i	0.609048	+	0.822599i
$345$	−2.33873	−	1.35027i	−0.125913	−	0.0726959i
$346$	4.66280	−	1.90020i	0.250674	−	0.102155i
$347$	27.0043	+	15.5909i	1.44966	+	0.836964i	0.998461	−	0.0554566i	$-0.0176614\pi$
$347$	27.0043	+	15.5909i	1.44966	+	0.836964i	0.451204	+	0.892421i	$0.350995\pi$
$348$	2.36547	+	0.662943i	0.126803	+	0.0355375i
$349$	−9.30195	−	16.1114i	−0.497922	−	0.862426i	0.502075	−	0.864824i	$-0.332570\pi$
$349$	−9.30195	−	16.1114i	−0.497922	−	0.862426i	−0.999997	+	0.00239805i	$0.999237\pi$
$350$	0.949123	−	0.386789i	0.0507328	−	0.0206748i
$351$	1.07345	−	7.81543i	0.0572965	−	0.417157i
$352$	6.91995	−	2.63695i	0.368835	−	0.140550i
$353$	9.11017	−	5.25976i	0.484886	−	0.279949i	−0.237565	−	0.971372i	$-0.576349\pi$
$353$	9.11017	−	5.25976i	0.484886	−	0.279949i	0.722450	+	0.691423i	$0.243016\pi$
$354$	3.28622	+	2.55163i	0.174661	+	0.135617i
$355$	20.4763	+	11.8220i	1.08677	+	0.627447i
$356$	20.2188	+	20.6871i	1.07159	+	1.09642i
$357$	−0.338483	+	0.586269i	−0.0179144	+	0.0310287i
$358$	−4.62397	+	33.6336i	−0.244384	+	1.77759i
$359$			7.17552i			0.378710i	0.981909	+	0.189355i	$0.0606396\pi$
$359$			7.17552i			0.378710i	−0.981909	+	0.189355i	$0.939360\pi$
$360$	13.2998	−	9.84714i	0.700963	−	0.518990i
$361$	−12.1940	−	21.1206i	−0.641789	−	1.11161i
$362$	−14.6435	−	11.3702i	−0.769647	−	0.597602i
$363$			3.46687i			0.181963i
$364$	−2.54876	+	5.86829i	−0.133591	+	0.307582i
$365$			8.17137i			0.427709i
$366$	4.29288	−	5.52877i	0.224392	−	0.288994i
$367$	2.20950	+	3.82696i	0.115335	+	0.199766i	0.917913	−	0.396781i	$-0.129873\pi$
$367$	2.20950	+	3.82696i	0.115335	+	0.199766i	−0.802579	+	0.596546i	$0.796539\pi$
$368$	−12.0864	−	7.35210i	−0.630048	−	0.383255i
$369$			20.0359i			1.04303i
$370$	−12.9273	−	1.77725i	−0.672057	−	0.0923948i
$371$	1.24028	−	2.14823i	0.0643923	−	0.111531i
$372$	4.25718	−	4.16080i	0.220725	−	0.215728i
$373$	−11.1441	−	6.43404i	−0.577019	−	0.333142i	0.182929	−	0.983126i	$-0.441442\pi$
$373$	−11.1441	−	6.43404i	−0.577019	−	0.333142i	−0.759948	+	0.649984i	$0.774776\pi$
$374$	2.32054	−	2.98861i	0.119992	−	0.154537i
$375$	3.84650	−	2.22078i	0.198632	−	0.114680i
$376$	0.0376830	−	0.0867315i	0.00194335	−	0.00447283i
$377$	10.9849	−	4.47825i	0.565752	−	0.230641i
$378$	1.03605	+	2.54230i	0.0532884	+	0.130762i
$379$	−9.49812	−	16.4512i	−0.487886	−	0.845043i	0.512017	−	0.858975i	$-0.328898\pi$
$379$	−9.49812	−	16.4512i	−0.487886	−	0.845043i	−0.999903	+	0.0139323i	$0.995565\pi$
$380$	25.9447	+	7.27120i	1.33093	+	0.373005i
$381$	−6.88262	−	3.97368i	−0.352607	−	0.203578i
$382$	−6.77689	−	16.6295i	−0.346736	−	0.850838i
$383$	−20.0856	−	11.5964i	−1.02633	−	0.592550i	−0.110396	−	0.993888i	$-0.535212\pi$
$383$	−20.0856	−	11.5964i	−1.02633	−	0.592550i	−0.915930	+	0.401338i	$0.868545\pi$
$384$	−3.45126	+	2.43497i	−0.176121	+	0.124259i
$385$			2.37552i			0.121068i
$386$	−3.77152	+	27.4332i	−0.191965	+	1.39631i
$387$	16.6274	−	9.59985i	0.845220	−	0.487988i
$388$	0.369530	−	1.31853i	0.0187600	−	0.0669384i
$389$			32.1000i			1.62753i	0.581192	+	0.813766i	$0.302586\pi$
$389$			32.1000i			1.62753i	−0.581192	+	0.813766i	$0.697414\pi$
$390$	−1.05021	+	3.74914i	−0.0531794	+	0.189845i
$391$	−7.22831			−0.365551
$392$	1.99416	+	17.4590i	0.100720	+	0.881813i
$393$	−1.17040	−	2.02719i	−0.0590388	−	0.102258i
$394$	17.6571	+	2.42751i	0.889552	+	0.122296i
$395$	−2.13483			−0.107415
$396$	−1.85551	−	7.25616i	−0.0932430	−	0.364636i
$397$	−4.72804	+	8.18920i	−0.237293	+	0.411004i	−0.959937	−	0.280217i	$-0.909594\pi$
$397$	−4.72804	+	8.18920i	−0.237293	+	0.411004i	0.722643	+	0.691221i	$0.242927\pi$
$398$	2.20096	+	5.40082i	0.110324	+	0.270719i
$399$	−1.09090	+	1.88950i	−0.0546134	+	0.0945932i
$400$	2.86627	−	1.56846i	0.143313	−	0.0784231i
$401$	4.39229	−	2.53589i	0.219341	−	0.126636i	−0.386304	−	0.922371i	$-0.626249\pi$
$401$	4.39229	−	2.53589i	0.219341	−	0.126636i	0.605645	+	0.795735i	$0.292915\pi$
$402$	−6.17678	+	2.51718i	−0.308070	+	0.125545i
$403$	3.91145	−	28.4780i	0.194843	−	1.41859i
$404$	0.585170	+	0.598724i	0.0291133	+	0.0297876i
$405$	−7.94082	−	13.7539i	−0.394583	−	0.683437i
$406$	−2.53180	+	3.26069i	−0.125651	+	0.161825i
$407$	−2.95288	+	5.11454i	−0.146369	+	0.253519i
$408$	−0.859995	+	1.97937i	−0.0425761	+	0.0979934i
$409$	−3.06568	−	1.76997i	−0.151588	−	0.0875194i	0.422287	−	0.906462i	$-0.361227\pi$
$409$	−3.06568	−	1.76997i	−0.151588	−	0.0875194i	−0.573875	+	0.818943i	$0.694561\pi$
$410$	2.75925	−	20.0701i	0.136270	−	0.991193i
$411$	−1.27743			−0.0630110
$412$	7.83307	+	30.6320i	0.385908	+	1.50913i
$413$	−6.05486	+	3.49578i	−0.297940	+	0.172016i
$414$	−8.77495	+	11.3012i	−0.431265	+	0.555424i
$415$	24.1751			1.18671
$416$	−5.94980	+	19.5090i	−0.291713	+	0.956506i
$417$	2.23108			0.109257
$418$	7.47891	−	9.63203i	0.365805	−	0.471118i
$419$	−16.9190	+	9.76816i	−0.826545	+	0.477206i	−0.852668	−	0.522453i	$-0.825017\pi$
$419$	−16.9190	+	9.76816i	−0.826545	+	0.477206i	0.0261232	+	0.999659i	$0.491684\pi$
$420$	−0.335673	−	1.31268i	−0.0163792	−	0.0640523i
$421$	5.95407			0.290184			0.145092	−	0.989418i	$-0.453652\pi$
$421$	5.95407			0.290184			0.145092	+	0.989418i	$0.453652\pi$
$422$	−3.12233	+	22.7111i	−0.151993	+	1.10556i
$423$	−0.0828271	−	0.0478202i	−0.00402719	−	0.00232510i
$424$	3.15123	−	7.25289i	0.153037	−	0.352232i
$425$	0.834720	−	1.44578i	0.0404899	−	0.0701305i
$426$	−3.74324	+	4.82089i	−0.181360	+	0.233573i
$427$	5.88133	+	10.1868i	0.284617	+	0.492972i
$428$	−19.1913	−	19.6359i	−0.927648	−	0.949136i
$429$	1.39197	+	1.08052i	0.0672048	+	0.0521682i
$430$	−17.9779	+	7.32639i	−0.866969	+	0.353310i
$431$	−24.1071	+	13.9182i	−1.16120	+	0.670418i	−0.951591	−	0.307368i	$-0.900552\pi$
$431$	−24.1071	+	13.9182i	−1.16120	+	0.670418i	−0.209607	+	0.977786i	$0.567218\pi$
$432$	4.20124	+	7.67752i	0.202132	+	0.369385i
$433$	11.5600	−	20.0225i	0.555537	−	0.962218i	−0.442325	−	0.896855i	$-0.645846\pi$
$433$	11.5600	−	20.0225i	0.555537	−	0.962218i	0.997862	−	0.0653632i	$-0.0208206\pi$
$434$	3.77516	+	9.26367i	0.181213	+	0.444670i
$435$	−1.25611	+	2.17565i	−0.0602261	+	0.104315i
$436$	−5.62666	−	22.0036i	−0.269468	−	1.05378i
$437$	−23.2962			−1.11441
$438$	−2.08972	−	0.287295i	−0.0998505	−	0.0137275i
$439$	−2.20404	−	3.81751i	−0.105193	−	0.182200i	0.808624	−	0.588326i	$-0.200213\pi$
$439$	−2.20404	−	3.81751i	−0.105193	−	0.182200i	−0.913817	+	0.406126i	$0.866879\pi$
$440$	0.859397	+	7.52408i	0.0409701	+	0.358696i
$441$	17.7726			0.846312
$442$	2.58311	+	10.0961i	0.122866	+	0.480222i
$443$			18.4093i			0.874651i	0.899303	+	0.437325i	$0.144074\pi$
$443$			18.4093i			0.874651i	−0.899303	+	0.437325i	$0.855926\pi$
$444$	0.909014	−	3.24349i	0.0431399	−	0.153929i
$445$	−25.6184	+	14.7908i	−1.21443	+	0.701152i
$446$	−0.978767	+	7.11931i	−0.0463459	+	0.337109i
$447$			2.37481i			0.112325i
$448$	−1.60054	−	6.91501i	−0.0756184	−	0.326704i
$449$	−11.3728	−	6.56609i	−0.536716	−	0.309873i	0.207031	−	0.978334i	$-0.433620\pi$
$449$	−11.3728	−	6.56609i	−0.536716	−	0.309873i	−0.743747	+	0.668461i	$0.766953\pi$
$450$	−1.24710	−	3.06019i	−0.0587887	−	0.144259i
$451$	−7.94054	−	4.58447i	−0.373905	−	0.215874i
$452$	21.4096	+	6.00020i	1.00702	+	0.282226i
$453$	3.15886	+	5.47131i	0.148416	+	0.257064i
$454$	−3.86907	−	9.49412i	−0.181585	−	0.445581i
$455$	−5.16833	−	4.01195i	−0.242295	−	0.188083i
$456$	−2.77169	+	6.37935i	−0.129796	+	0.298740i
$457$	−9.11955	+	5.26518i	−0.426595	+	0.246295i	−0.697895	−	0.716200i	$-0.745880\pi$
$457$	−9.11955	+	5.26518i	−0.426595	+	0.246295i	0.271300	+	0.962495i	$0.412546\pi$
$458$	10.0856	−	12.9892i	0.471270	−	0.606945i
$459$	3.87263	+	2.23586i	0.180759	+	0.104361i
$460$	10.3463	−	10.1120i	0.482398	−	0.471477i
$461$	15.6106	−	27.0383i	0.727058	−	1.25930i	−0.231064	−	0.972939i	$-0.574221\pi$
$461$	15.6106	−	27.0383i	0.727058	−	1.25930i	0.958121	−	0.286362i	$-0.0924460\pi$
$462$	−0.607506	−	0.0835203i	−0.0282638	−	0.00388572i
$463$		−	18.1246i		−	0.842323i	−0.906986	−	0.421161i	$-0.861623\pi$
$463$		−	18.1246i		−	0.842323i	0.906986	−	0.421161i	$-0.138377\pi$
$464$	−6.83945	+	11.2436i	−0.317514	+	0.521973i
$465$	3.04379	+	5.27199i	0.141152	+	0.244483i
$466$	6.08477	−	7.83653i	0.281871	−	0.363020i
$467$		−	15.0465i		−	0.696267i	−0.937445	−	0.348134i	$-0.886816\pi$
$467$		−	15.0465i		−	0.696267i	0.937445	−	0.348134i	$-0.113184\pi$
$468$	18.9207	+	8.21777i	0.874610	+	0.379866i
$469$		−	11.2086i		−	0.517563i
$470$	0.0763829	+	0.0593084i	0.00352328	+	0.00273569i
$471$	0.787883	+	1.36465i	0.0363037	+	0.0628799i
$472$	−17.9131	+	13.2628i	−0.824519	+	0.610470i
$473$			8.78627i			0.403993i
$474$	0.0750581	−	0.545954i	0.00344753	−	0.0250765i
$475$	2.69023	−	4.65962i	0.123436	−	0.213798i
$476$	−2.53487	−	2.59359i	−0.116186	−	0.118877i
$477$	−6.92639	−	3.99895i	−0.317137	−	0.183099i
$478$	−19.9000	−	15.4516i	−0.910203	−	0.706738i
$479$	13.2991	−	7.67826i	0.607653	−	0.350829i	−0.164393	−	0.986395i	$-0.552567\pi$
$479$	13.2991	−	7.67826i	0.607653	−	0.350829i	0.772046	+	0.635566i	$0.219233\pi$
$480$	−1.53808	−	4.03627i	−0.0702035	−	0.184230i
$481$	−6.14049	−	15.0623i	−0.279982	−	0.686782i
$482$	26.5856	−	10.8342i	1.21094	−	0.493486i
$483$	0.585737	+	1.01453i	0.0266519	+	0.0461625i
$484$	−17.8835	−	5.01200i	−0.812886	−	0.227818i
$485$	1.21273	+	0.700168i	0.0550671	+	0.0317930i
$486$	12.3929	−	5.05038i	0.562153	−	0.229090i
$487$	2.34342	+	1.35297i	0.106190	+	0.0613091i	0.552155	−	0.833742i	$-0.313806\pi$
$487$	2.34342	+	1.35297i	0.106190	+	0.0613091i	−0.445964	+	0.895051i	$0.647139\pi$
$488$	22.3135	+	30.1373i	1.01008	+	1.36425i
$489$		−	5.57561i		−	0.252138i
$490$	−17.8029	−	2.44755i	−0.804253	−	0.110569i
$491$	12.8732	−	7.43237i	0.580961	−	0.335418i	−0.180554	−	0.983565i	$-0.557789\pi$
$491$	12.8732	−	7.43237i	0.580961	−	0.335418i	0.761515	+	0.648147i	$0.224456\pi$
$492$	5.03565	+	1.41128i	0.227025	+	0.0636255i
$493$			6.72429i			0.302847i
$494$	8.32514	+	32.5389i	0.374566	+	1.46399i
$495$	7.65920			0.344256
$496$	15.3086	+	27.9755i	0.687374	+	1.25614i
$497$	−5.12831	−	8.88249i	−0.230036	−	0.398434i
$498$	−0.849968	+	6.18246i	−0.0380880	+	0.277043i
$499$	−7.66875			−0.343300			−0.171650	−	0.985158i	$-0.554910\pi$
$499$	−7.66875			−0.343300			−0.171650	+	0.985158i	$0.554910\pi$
$500$	5.89484	+	23.0523i	0.263625	+	1.03093i
$501$	−2.40640	+	4.16802i	−0.107510	+	0.186213i
$502$	−20.9556	+	8.53990i	−0.935296	+	0.381155i
$503$	12.9967	−	22.5109i	0.579493	−	1.00371i	−0.416045	−	0.909344i	$-0.636584\pi$
$503$	12.9967	−	22.5109i	0.579493	−	1.00371i	0.995537	−	0.0943669i	$-0.0300827\pi$
$504$	−7.13225	+	0.814642i	−0.317696	+	0.0362870i
$505$	−0.741445	+	0.428074i	−0.0329939	+	0.0190490i
$506$	−2.47102	−	6.06350i	−0.109850	−	0.269556i
$507$	−4.70172	+	1.20359i	−0.208810	+	0.0534531i
$508$	30.4479	−	29.7586i	1.35091	−	1.32033i
$509$	−16.0012	−	27.7148i	−0.709239	−	1.22844i	−0.965140	−	0.261735i	$-0.915705\pi$
$509$	−16.0012	−	27.7148i	−0.709239	−	1.22844i	0.255901	−	0.966703i	$-0.417628\pi$
$510$	−1.74320	−	1.35353i	−0.0771900	−	0.0599351i
$511$	1.77234	−	3.06979i	0.0784038	−	0.135799i
$512$	−7.57112	−	21.3232i	−0.334599	−	0.942360i
$513$	12.4812	+	7.20600i	0.551057	+	0.318153i
$514$	−22.6837	−	3.11857i	−1.00054	−	0.137554i
$515$	−32.3334			−1.42478
$516$	−1.24154	−	4.85518i	−0.0546559	−	0.213737i
$517$	0.0379038	−	0.0218837i	0.00166701	−	0.000962446i
$518$	4.47099	+	3.47155i	0.196444	+	0.152531i
$519$	−1.32920			−0.0583455
$520$	−17.8213	−	10.8375i	−0.781515	−	0.475254i
$521$	−32.8191			−1.43783			−0.718914	−	0.695099i	$-0.755361\pi$
$521$	−32.8191			−1.43783			−0.718914	+	0.695099i	$0.755361\pi$
$522$	10.5132	+	8.16309i	0.460150	+	0.357289i
$523$	−2.69168	+	1.55404i	−0.117699	+	0.0679536i	−0.557694	−	0.830047i	$-0.688314\pi$
$523$	−2.69168	+	1.55404i	−0.117699	+	0.0679536i	0.439995	+	0.898000i	$0.354980\pi$
$524$	12.1491	−	3.10671i	0.530735	−	0.135717i
$525$	−0.270562			−0.0118083
$526$	16.1634	+	2.22215i	0.704756	+	0.0968902i
$527$	14.1111	+	8.14707i	0.614691	+	0.354892i
$528$	−1.95440	−	0.0447583i	−0.0850542	−	0.00194786i
$529$	5.24579	−	9.08598i	0.228078	−	0.395042i
$530$	6.38750	+	4.95965i	0.277455	+	0.215433i
$531$	11.2712	+	19.5222i	0.489127	+	0.847193i
$532$	−8.16969	−	8.35893i	−0.354201	−	0.362406i
$533$	23.3848	−	9.53336i	1.01291	−	0.412935i
$534$	−2.88184	−	7.07159i	−0.124709	−	0.306018i
$535$	24.3166	−	14.0392i	1.05130	−	0.606967i
$536$	−4.05495	−	35.5014i	−0.175147	−	1.53343i
$537$	4.48116	−	7.76159i	0.193376	−	0.334938i
$538$	33.0578	−	13.4718i	1.42522	−	0.580811i
$539$	−4.06658	+	7.04353i	−0.175160	+	0.303386i
$540$	−8.67097	+	2.21730i	−0.373139	+	0.0954175i
$541$	4.55751			0.195943			0.0979713	−	0.995189i	$-0.468765\pi$
$541$	4.55751			0.195943			0.0979713	+	0.995189i	$0.468765\pi$
$542$	1.35185	−	9.83307i	0.0580671	−	0.422366i
$543$	2.44709	+	4.23848i	0.105015	+	0.181890i
$544$	−8.96710	−	7.29774i	−0.384461	−	0.312888i
$545$	23.2258			0.994883
$546$	1.20771	−	1.18067i	0.0516854	−	0.0505282i
$547$		−	32.6477i		−	1.39592i	−0.716138	−	0.697958i	$-0.754092\pi$
$547$		−	32.6477i		−	1.39592i	0.716138	−	0.697958i	$-0.245908\pi$
$548$	1.84676	−	6.58950i	0.0788897	−	0.281489i
$549$	32.8444	−	18.9627i	1.40176	−	0.809309i
$550$	1.49815	+	0.205966i	0.0638813	+	0.00878243i
$551$			21.6718i			0.923251i
$552$	2.22226	+	3.00145i	0.0945855	+	0.127750i
$553$	0.802006	+	0.463038i	0.0341047	+	0.0196904i
$554$	2.33864	−	0.953048i	0.0993592	−	0.0404911i
$555$	2.98322	+	1.72236i	0.126630	+	0.0731101i
$556$	−3.22544	+	11.5088i	−0.136789	+	0.488083i
$557$	17.7537	+	30.7503i	0.752248	+	1.30293i	0.946731	+	0.322025i	$0.104364\pi$
$557$	17.7537	+	30.7503i	0.752248	+	1.30293i	−0.194483	+	0.980906i	$0.562303\pi$
$558$	29.8681	−	12.1720i	1.26442	−	0.515280i
$559$	−19.1160	−	14.8389i	−0.808519	−	0.627619i
$560$	7.25661	+	0.166186i	0.306648	+	0.00702265i
$561$	−0.865032	+	0.499427i	−0.0365217	+	0.0210858i
$562$	7.24042	+	5.62191i	0.305419	+	0.237146i
$563$	−20.7404	−	11.9745i	−0.874104	−	0.504664i	−0.00539390	−	0.999985i	$-0.501717\pi$
$563$	−20.7404	−	11.9745i	−0.874104	−	0.504664i	−0.868710	+	0.495321i	$0.835050\pi$
$564$	−0.0178528	+	0.0174487i	−0.000751740	+	0.000734722i
$565$	−11.3689	+	19.6915i	−0.478294	+	0.828430i
$566$	−1.90776	+	13.8766i	−0.0801892	+	0.583277i
$567$			6.88936i			0.289326i
$568$	−19.4565	−	26.2786i	−0.816378	−	1.10263i
$569$	8.34249	+	14.4496i	0.349735	+	0.605759i	0.986202	−	0.165545i	$-0.0529382\pi$
$569$	8.34249	+	14.4496i	0.349735	+	0.605759i	−0.636467	+	0.771304i	$0.719605\pi$
$570$	−5.61818	−	4.36230i	−0.235320	−	0.182717i
$571$			24.7582i			1.03610i	0.855351	+	0.518049i	$0.173342\pi$
$571$			24.7582i			1.03610i	−0.855351	+	0.518049i	$0.826658\pi$
$572$	−7.58612	+	5.61823i	−0.317192	+	0.234910i
$573$			4.74048i			0.198036i
$574$	−5.38973	+	6.94140i	−0.224963	+	0.289728i
$575$	−1.44446	−	2.50188i	−0.0602383	−	0.104336i
$576$	−22.2956	+	5.16050i	−0.928981	+	0.215021i
$577$			8.07589i			0.336204i	0.985770	+	0.168102i	$0.0537637\pi$
$577$			8.07589i			0.336204i	−0.985770	+	0.168102i	$0.946236\pi$
$578$	17.9654	+	2.46989i	0.747262	+	0.102734i
$579$	3.65504	−	6.33072i	0.151898	−	0.263096i
$580$	−9.40695	−	9.62485i	−0.390602	−	0.399650i
$581$	−9.08202	−	5.24351i	−0.376786	−	0.217537i
$582$	−0.221696	+	0.285521i	−0.00918961	+	0.0118352i
$583$	3.16969	−	1.83002i	0.131275	−	0.0757917i
$584$	4.50305	−	10.3643i	0.186338	−	0.428876i
$585$	−12.9354	+	16.6639i	−0.534814	+	0.688966i
$586$	−3.17141	−	7.78217i	−0.131010	−	0.321479i
$587$	13.3711	+	23.1594i	0.551884	+	0.955891i	0.998139	+	0.0609853i	$0.0194243\pi$
$587$	13.3711	+	23.1594i	0.551884	+	0.955891i	−0.446255	+	0.894906i	$0.647242\pi$
$588$	1.25186	−	4.46679i	0.0516257	−	0.184207i
$589$	45.4790	+	26.2573i	1.87393	+	1.08191i
$590$	−8.60190	−	21.1078i	−0.354135	−	0.868993i
$591$	−4.07471	−	2.35254i	−0.167611	−	0.0967704i
$592$	15.4171	+	9.37812i	0.633638	+	0.385438i
$593$			24.0436i			0.987352i	0.869646	+	0.493676i	$0.164347\pi$
$593$			24.0436i			0.987352i	−0.869646	+	0.493676i	$0.835653\pi$
$594$	−0.551697	+	4.01291i	−0.0226364	+	0.164652i
$595$	3.21184	−	1.85436i	0.131673	−	0.0760212i
$596$	−12.2502	−	3.43322i	−0.501788	−	0.140630i
$597$		−	1.53958i		−	0.0630110i
$598$	17.3654	+	4.86439i	0.710123	+	0.198920i
$599$	−30.9402			−1.26418			−0.632091	−	0.774894i	$-0.717803\pi$
$599$	−30.9402			−1.26418			−0.632091	+	0.774894i	$0.717803\pi$
$600$	−0.856962	+	0.0978818i	−0.0349853	+	0.00399601i
$601$	16.8166	+	29.1272i	0.685963	+	1.18812i	0.973133	+	0.230243i	$0.0739521\pi$
$601$	16.8166	+	29.1272i	0.685963	+	1.18812i	−0.287170	+	0.957880i	$0.592715\pi$
$602$	8.34292	+	1.14699i	0.340032	+	0.0467478i
$603$	−36.1389			−1.47169
$604$	−32.7899	+	8.38489i	−1.33420	+	0.341176i
$605$	9.49651	−	16.4484i	0.386088	−	0.668724i
$606$	−0.0834057	−	0.204665i	−0.00338813	−	0.00831395i
$607$	−16.7017	+	28.9282i	−0.677902	+	1.17416i	0.297709	+	0.954657i	$0.403777\pi$
$607$	−16.7017	+	28.9282i	−0.677902	+	1.17416i	−0.975612	+	0.219504i	$0.929556\pi$
$608$	−28.9002	−	23.5200i	−1.17206	−	0.953863i
$609$	0.943785	−	0.544894i	0.0382441	−	0.0220802i
$610$	−35.5119	+	14.4719i	−1.43784	+	0.585951i
$611$	−0.0164030	+	0.119425i	−0.000663594	+	0.00483141i
$612$	−8.36232	+	8.17300i	−0.338027	+	0.330374i
$613$	7.59477	+	13.1545i	0.306750	+	0.531307i	0.977649	−	0.210242i	$-0.0674251\pi$
$613$	7.59477	+	13.1545i	0.306750	+	0.531307i	−0.670899	+	0.741548i	$0.734092\pi$
$614$	21.6504	−	27.8834i	0.873740	−	1.12528i
$615$	−2.67403	+	4.63156i	−0.107827	+	0.186763i
$616$	1.30909	−	3.01302i	0.0527449	−	0.121398i
$617$	−3.45893	−	1.99701i	−0.139251	−	0.0803968i	0.428756	−	0.903420i	$-0.358952\pi$
$617$	−3.45893	−	1.99701i	−0.139251	−	0.0803968i	−0.568007	+	0.823024i	$0.692285\pi$
$618$	1.13680	−	8.26883i	0.0457289	−	0.332621i
$619$	−10.0184			−0.402673			−0.201337	−	0.979522i	$-0.564529\pi$
$619$	−10.0184			−0.402673			−0.201337	+	0.979522i	$0.564529\pi$
$620$	−31.5954	+	8.07943i	−1.26890	+	0.324478i
$621$	6.70149	−	3.86911i	0.268922	−	0.155262i
$622$	−6.67235	+	8.59327i	−0.267537	+	0.344559i
$623$	12.8323			0.514116
$624$	3.39811	−	4.17652i	0.136033	−	0.167195i
$625$	−20.2486			−0.809944
$626$	8.40577	−	10.8257i	0.335962	−	0.432683i
$627$	−2.78793	+	1.60961i	−0.111339	+	0.0642817i
$628$	−8.17846	+	2.09136i	−0.326356	+	0.0834543i
$629$	9.22022			0.367634
$630$	0.999858	−	7.27273i	0.0398353	−	0.289752i
$631$	−8.76155	−	5.05848i	−0.348792	−	0.201375i	0.315361	−	0.948972i	$-0.397874\pi$
$631$	−8.76155	−	5.05848i	−0.348792	−	0.201375i	−0.664153	+	0.747597i	$0.731208\pi$
$632$	2.70774	+	1.17646i	0.107708	+	0.0467969i
$633$	3.02590	−	5.24102i	0.120269	−	0.208312i
$634$	−26.3868	+	33.9834i	−1.04795	+	1.34965i
$635$	21.7696	+	37.7060i	0.863899	+	1.49632i
$636$	−1.49294	+	1.45914i	−0.0591989	+	0.0578587i
$637$	−8.45641	−	20.7432i	−0.335055	−	0.821874i
$638$	−5.64071	+	2.29872i	−0.223318	+	0.0910071i
$639$	−28.6391	+	16.5348i	−1.13295	+	0.654107i
$640$	23.0443	−	2.09887i	0.910906	−	0.0829652i
$641$	−15.1546	+	26.2486i	−0.598571	+	1.03676i	0.394461	+	0.918913i	$0.370931\pi$
$641$	−15.1546	+	26.2486i	−0.598571	+	1.03676i	−0.993032	+	0.117843i	$0.962402\pi$
$642$	2.73539	+	6.71224i	0.107957	+	0.264911i
$643$	10.5063	−	18.1975i	0.414329	−	0.717638i	−0.581029	−	0.813883i	$-0.697350\pi$
$643$	10.5063	−	18.1975i	0.414329	−	0.717638i	0.995358	+	0.0962444i	$0.0306830\pi$
$644$	−6.08012	+	1.55478i	−0.239590	+	0.0612670i
$645$	5.12486			0.201791
$646$	−18.8612	−	2.59305i	−0.742084	−	0.102022i
$647$	−18.0101	−	31.1945i	−0.708052	−	1.22638i	−0.965579	−	0.260111i	$-0.916241\pi$
$647$	−18.0101	−	31.1945i	−0.708052	−	1.22638i	0.257527	−	0.966271i	$-0.417092\pi$
$648$	2.49238	+	21.8209i	0.0979099	+	0.857208i
$649$	−10.3159			−0.404936
$650$	−2.97830	+	2.91162i	−0.116819	+	0.114203i
$651$		−	2.64075i		−	0.103499i
$652$	28.7612	+	8.06057i	1.12638	+	0.315676i
$653$	20.9139	−	12.0747i	0.818425	−	0.472518i	−0.0314478	−	0.999505i	$-0.510012\pi$
$653$	20.9139	−	12.0747i	0.818425	−	0.472518i	0.849873	+	0.526987i	$0.176678\pi$
$654$	−0.816590	+	5.93968i	−0.0319312	+	0.232260i
$655$			12.8239i			0.501071i
$656$	−14.5599	+	23.9356i	−0.568469	+	0.934530i
$657$	−9.89768	−	5.71443i	−0.386145	−	0.222941i
$658$	−0.0158314	−	0.0388480i	−0.000617173	−	0.00151445i
$659$	−23.4859	−	13.5596i	−0.914879	−	0.528206i	−0.0328814	−	0.999459i	$-0.510468\pi$
$659$	−23.4859	−	13.5596i	−0.914879	−	0.528206i	−0.881998	+	0.471254i	$0.843802\pi$
$660$	0.539496	−	1.92500i	0.0209998	−	0.0749304i
$661$	11.2942	+	19.5621i	0.439293	+	0.760878i	0.997635	−	0.0687331i	$-0.0218957\pi$
$661$	11.2942	+	19.5621i	0.439293	+	0.760878i	−0.558342	+	0.829611i	$0.688562\pi$
$662$	−0.119522	−	0.293288i	−0.00464534	−	0.0113990i
$663$	0.374346	−	2.72549i	0.0145384	−	0.105849i
$664$	−30.6628	−	13.3224i	−1.18995	−	0.517008i
$665$	10.3515	−	5.97644i	0.401414	−	0.231756i
$666$	11.1931	−	14.4155i	0.433723	−	0.558588i
$667$	10.0773	+	5.81812i	0.390193	+	0.225278i
$668$	−18.0214	−	18.4388i	−0.697269	−	0.713420i
$669$	0.948538	−	1.64292i	0.0366726	−	0.0635188i
$670$	36.2006	+	4.97688i	1.39855	+	0.192274i
$671$			17.3556i			0.670007i
$672$	−0.297633	+	1.84994i	−0.0114815	+	0.0713629i
$673$	−8.58893	−	14.8765i	−0.331079	−	0.573445i	0.651645	−	0.758524i	$-0.274079\pi$
$673$	−8.58893	−	14.8765i	−0.331079	−	0.573445i	−0.982724	+	0.185079i	$0.940746\pi$
$674$	−6.34408	+	8.17050i	−0.244365	+	0.314716i
$675$			1.78721i			0.0687897i
$676$	0.588616	−	25.9933i	0.0226391	−	0.999744i
$677$		−	24.5139i		−	0.942145i	−0.882094	−	0.471073i	$-0.843867\pi$
$677$		−	24.5139i		−	0.942145i	0.882094	−	0.471073i	$-0.156133\pi$
$678$	−4.63613	−	3.59978i	−0.178049	−	0.138249i
$679$	−0.303728	−	0.526073i	−0.0116560	−	0.0201888i
$680$	9.50214	−	7.03534i	0.364390	−	0.269793i
$681$			2.70644i			0.103711i
$682$	−2.01028	+	14.6223i	−0.0769776	+	0.559917i
$683$	−2.22473	+	3.85335i	−0.0851270	+	0.147444i	−0.905445	−	0.424463i	$-0.860463\pi$
$683$	−2.22473	+	3.85335i	−0.0851270	+	0.147444i	0.820318	+	0.571907i	$0.193796\pi$
$684$	−26.9511	+	26.3409i	−1.03050	+	1.00717i
$685$	6.06072	+	3.49916i	0.231568	+	0.133696i
$686$	13.0946	+	10.1675i	0.499956	+	0.388197i
$687$	−3.75964	+	2.17063i	−0.143439	+	0.0828146i
$688$	26.8398	+	0.614669i	1.02326	+	0.0234340i
$689$	−1.37169	+	9.98686i	−0.0522574	+	0.380469i
$690$	−3.53672	+	1.44130i	−0.134641	+	0.0548692i
$691$	3.78174	+	6.55017i	0.143864	+	0.249180i	0.928949	−	0.370209i	$-0.120714\pi$
$691$	3.78174	+	6.55017i	0.143864	+	0.249180i	−0.785084	+	0.619389i	$0.787380\pi$
$692$	1.92161	−	6.85656i	0.0730485	−	0.260647i
$693$	−2.87738	−	1.66126i	−0.109303	−	0.0631059i
$694$	40.8370	−	16.6420i	1.55015	−	0.631722i
$695$	−10.5853	−	6.11142i	−0.401523	−	0.231819i
$696$	2.79216	−	2.06730i	0.105837	−	0.0783609i
$697$			14.3148i			0.542210i
$698$	−26.0647	−	3.58339i	−0.986564	−	0.135633i
$699$	−2.26823	+	1.30956i	−0.0857924	+	0.0495323i
$700$	0.391147	−	1.39567i	0.0147840	−	0.0527512i
$701$			32.5181i			1.22819i	0.789232	+	0.614095i	$0.210479\pi$
$701$			32.5181i			1.22819i	−0.789232	+	0.614095i	$0.789521\pi$
$702$	−7.79900	−	7.97760i	−0.294354	−	0.301095i
$703$	29.7160			1.12076
$704$	3.05632	−	10.0169i	0.115189	−	0.377524i
$705$	−0.0127644	−	0.0221085i	−0.000480734	−	0.000832655i
$706$	2.02622	−	14.7382i	0.0762577	−	0.554680i
$707$	0.371391			0.0139676
$708$	5.70046	−	1.45770i	0.214236	−	0.0547835i
$709$	−0.693747	+	1.20160i	−0.0260542	+	0.0451272i	−0.878759	−	0.477267i	$-0.841628\pi$
$709$	−0.693747	+	1.20160i	−0.0260542	+	0.0451272i	0.852704	+	0.522394i	$0.174961\pi$
$710$	30.9651	−	12.6190i	1.16210	−	0.473582i
$711$	1.49294	−	2.58585i	0.0559896	−	0.0969768i
$712$	40.6443	−	4.64238i	1.52321	−	0.173980i
$713$	24.4190	−	14.0983i	0.914498	−	0.527986i
$714$	0.361302	+	0.886581i	0.0135214	+	0.0331795i
$715$	−3.64435	−	8.93941i	−0.136291	−	0.334315i
$716$	33.5591	+	34.3364i	1.25416	+	1.28321i
$717$	3.32549	+	5.75991i	0.124193	+	0.215108i
$718$	8.01523	+	6.22352i	0.299126	+	0.232260i
$719$	16.6196	−	28.7860i	0.619807	−	1.07354i	−0.369714	−	0.929146i	$-0.620544\pi$
$719$	16.6196	−	28.7860i	0.619807	−	1.07354i	0.989521	−	0.144391i	$-0.0461224\pi$
$720$	0.535822	−	23.3969i	0.0199689	−	0.871953i
$721$	12.1469	+	7.01301i	0.452374	+	0.261178i
$722$	−34.1684	−	4.69749i	−1.27162	−	0.174822i
$723$	−7.57863			−0.281852
$724$	−25.4015	+	6.49555i	−0.944038	+	0.241405i
$725$	−2.32743	+	1.34374i	−0.0864387	+	0.0499054i
$726$	3.87258	+	3.00691i	0.143725	+	0.111597i
$727$	19.9275			0.739069			0.369534	−	0.929217i	$-0.379517\pi$
$727$	19.9275			0.739069			0.369534	+	0.929217i	$0.379517\pi$
$728$	4.34442	+	7.93676i	0.161015	+	0.294156i
$729$	19.7623			0.731938
$730$	9.12762	+	7.08725i	0.337828	+	0.262311i
$731$	11.8795	−	6.85866i	0.439381	−	0.253677i
$732$	−2.45244	−	9.59051i	−0.0906448	−	0.354475i
$733$	−14.9063			−0.550575			−0.275288	−	0.961362i	$-0.588773\pi$
$733$	−14.9063			−0.550575			−0.275288	+	0.961362i	$0.588773\pi$
$734$	6.19116	+	0.851164i	0.228520	+	0.0314170i
$735$	4.10836	+	2.37196i	0.151539	+	0.0874911i
$736$	−18.6953	+	7.12414i	−0.689120	+	0.262599i
$737$	8.26904	−	14.3224i	0.304594	−	0.527572i
$738$	22.3806	+	17.3777i	0.823842	+	0.639682i
$739$	−17.4886	−	30.2912i	−0.643330	−	1.11428i	−0.984685	−	0.174345i	$-0.944219\pi$
$739$	−17.4886	−	30.2912i	−0.643330	−	1.11428i	0.341355	−	0.939935i	$-0.389114\pi$
$740$	−13.1974	+	12.8986i	−0.485146	+	0.474163i
$741$	1.20649	−	8.78403i	0.0443214	−	0.322689i
$742$	−1.32390	−	3.24865i	−0.0486018	−	0.119262i
$743$	30.6027	−	17.6685i	1.12271	−	0.648195i	0.180616	−	0.983554i	$-0.442191\pi$
$743$	30.6027	−	17.6685i	1.12271	−	0.648195i	0.942090	+	0.335359i	$0.108858\pi$
$744$	−0.955350	−	8.36416i	−0.0350248	−	0.306645i
$745$	6.50512	−	11.2672i	0.238329	−	0.412798i
$746$	−16.8525	+	6.86780i	−0.617016	+	0.251448i
$747$	−16.9062	+	29.2825i	−0.618567	+	1.07139i
$748$	−1.32568	−	5.18420i	−0.0484717	−	0.189553i
$749$	−12.1802			−0.445055
$750$	0.855510	−	6.22278i	0.0312388	−	0.227224i
$751$	1.32723	+	2.29883i	0.0484313	+	0.0838854i	0.889225	−	0.457471i	$-0.151244\pi$
$751$	1.32723	+	2.29883i	0.0484313	+	0.0838854i	−0.840793	+	0.541356i	$0.817911\pi$
$752$	−0.0641977	−	0.117317i	−0.00234105	−	0.00427813i
$753$	5.97372			0.217695
$754$	4.52521	−	16.1545i	0.164798	−	0.588313i
$755$		−	34.6112i		−	1.25963i
$756$	3.73840	+	1.04772i	0.135964	+	0.0381051i
$757$	−21.4696	+	12.3955i	−0.780324	+	0.450520i	−0.836545	−	0.547898i	$-0.815428\pi$
$757$	−21.4696	+	12.3955i	−0.780324	+	0.450520i	0.0562209	+	0.998418i	$0.482095\pi$
$758$	−26.6144	−	3.65896i	−0.966679	−	0.132899i
$759$			1.72849i			0.0627403i
$760$	30.6246	−	22.6743i	1.11087	−	0.822484i
$761$	−5.51884	−	3.18630i	−0.200058	−	0.115503i	0.396625	−	0.917981i	$-0.370181\pi$
$761$	−5.51884	−	3.18630i	−0.200058	−	0.115503i	−0.596682	+	0.802477i	$0.703515\pi$
$762$	−10.4082	+	4.24157i	−0.377049	+	0.153656i
$763$	−8.72537	−	5.03760i	−0.315880	−	0.182373i
$764$	−24.4533	−	6.85324i	−0.884689	−	0.247941i
$765$	−5.97886	−	10.3557i	−0.216166	−	0.374411i
$766$	−30.3743	+	12.3782i	−1.09747	+	0.447243i
$767$	17.4223	−	22.4440i	0.629084	−	0.810407i
$768$	−0.273451	+	5.96706i	−0.00986731	+	0.215318i
$769$	−30.7843	+	17.7733i	−1.11011	+	0.640923i	−0.938858	−	0.344304i	$-0.888115\pi$
$769$	−30.7843	+	17.7733i	−1.11011	+	0.640923i	−0.171253	+	0.985227i	$0.554782\pi$
$770$	2.65351	+	2.06035i	0.0956259	+	0.0742499i
$771$	5.23470	+	3.02225i	0.188523	+	0.108844i
$772$	27.3724	+	28.0064i	0.985153	+	1.00797i
$773$	8.45835	−	14.6503i	0.304226	−	0.526935i	−0.672863	−	0.739767i	$-0.734936\pi$
$773$	8.45835	−	14.6503i	0.304226	−	0.526935i	0.977089	+	0.212833i	$0.0682689\pi$
$774$	3.69815	−	26.8994i	0.132927	−	0.966881i
$775$			6.51225i			0.233927i
$776$	−1.15233	−	1.55637i	−0.0413662	−	0.0558705i
$777$	−0.747148	−	1.29410i	−0.0268038	−	0.0464255i
$778$	35.8564	+	27.8412i	1.28552	+	0.998154i
$779$			46.1353i			1.65297i
$780$	3.27701	+	4.42484i	0.117336	+	0.158435i
$781$		−	15.1335i		−	0.541519i
$782$	−6.26931	+	8.07420i	−0.224190	+	0.288733i
$783$	−3.59932	−	6.23421i	−0.128629	−	0.222792i
$784$	21.2317	+	12.9151i	0.758276	+	0.461255i
$785$		−	8.63273i		−	0.308115i
$786$	−3.27954	−	0.450873i	−0.116977	−	0.0160821i
$787$	7.27241	−	12.5962i	0.259233	−	0.449005i	−0.706803	−	0.707410i	$-0.749863\pi$
$787$	7.27241	−	12.5962i	0.259233	−	0.449005i	0.966037	+	0.258405i	$0.0831968\pi$
$788$	18.0261	−	17.6180i	0.642152	−	0.627614i
$789$	−3.73000	−	2.15352i	−0.132792	−	0.0766672i
$790$	−1.85160	+	2.38466i	−0.0658769	+	0.0848424i
$791$	8.54206	−	4.93176i	0.303721	−	0.175353i
$792$	−9.71464	−	4.22081i	−0.345195	−	0.149980i
$793$	−37.7601	−	29.3115i	−1.34090	−	1.04088i
$794$	5.04678	+	12.3840i	0.179104	+	0.439493i
$795$	−1.06742	−	1.84882i	−0.0378573	−	0.0655709i
$796$	7.94179	+	2.22575i	0.281489	+	0.0788897i
$797$	−44.4114	−	25.6409i	−1.57313	−	0.908248i	−0.995782	−	0.0917499i	$-0.970754\pi$
$797$	−44.4114	−	25.6409i	−1.57313	−	0.908248i	−0.577349	−	0.816498i	$-0.695913\pi$
$798$	1.16445	+	2.85738i	0.0412210	+	0.101150i
$799$	−0.0591762	−	0.0341654i	−0.00209350	−	0.00120868i
$800$	0.733983	−	4.56206i	0.0259502	−	0.161293i
$801$		−	41.3743i		−	1.46189i
$802$	0.976902	−	7.10575i	0.0344956	−	0.250913i
$803$	4.52943	−	2.61507i	0.159840	−	0.0922837i
$804$	−2.54554	+	9.08283i	−0.0897742	+	0.320327i
$805$		−	6.41784i		−	0.226199i
$806$	−28.4181	−	29.0689i	−1.00098	−	1.02391i
$807$	−9.42362			−0.331727
$808$	1.17632	−	0.134359i	0.0413829	−	0.00472673i
$809$	0.794944	+	1.37688i	0.0279487	+	0.0484087i	0.879661	−	0.475600i	$-0.157769\pi$
$809$	0.794944	+	1.37688i	0.0279487	+	0.0484087i	−0.851713	+	0.524009i	$0.824436\pi$
$810$	−22.2507	−	3.05904i	−0.781812	−	0.107484i
$811$	−6.29854			−0.221172			−0.110586	−	0.993867i	$-0.535273\pi$
$811$	−6.29854			−0.221172			−0.110586	+	0.993867i	$0.535273\pi$
$812$	1.44637	+	5.65616i	0.0507576	+	0.198492i
$813$	−1.31010	+	2.26917i	−0.0459474	+	0.0795831i
$814$	3.15196	+	7.73443i	0.110476	+	0.271091i
$815$	−15.2728	+	26.4533i	−0.534983	+	0.926618i
$816$	1.46511	+	2.67740i	0.0512890	+	0.0937276i
$817$	38.2868	−	22.1049i	1.33949	−	0.773352i
$818$	−4.63605	+	1.88929i	−0.162096	+	0.0660576i
$819$	8.47387	−	3.45456i	0.296101	−	0.120712i
$820$	−20.0257	−	20.4895i	−0.699326	−	0.715525i
$821$	−0.197850	−	0.342686i	−0.00690501	−	0.0119598i	0.862552	−	0.505968i	$-0.168865\pi$
$821$	−0.197850	−	0.342686i	−0.00690501	−	0.0119598i	−0.869457	+	0.494008i	$0.835531\pi$
$822$	−1.10795	+	1.42692i	−0.0386442	+	0.0497696i
$823$	−0.160256	+	0.277572i	−0.00558618	+	0.00967554i	−0.868805	−	0.495154i	$-0.835111\pi$
$823$	−0.160256	+	0.277572i	−0.00558618	+	0.00967554i	0.863219	+	0.504830i	$0.168445\pi$
$824$	41.0105	+	17.8182i	1.42867	+	0.620727i
$825$	−0.345726	−	0.199605i	−0.0120366	−	0.00694936i
$826$	−1.34668	+	9.79541i	−0.0468569	+	0.340826i
$827$	7.22490			0.251234			0.125617	−	0.992079i	$-0.459909\pi$
$827$	7.22490			0.251234			0.125617	+	0.992079i	$0.459909\pi$
$828$	5.01296	+	19.6037i	0.174213	+	0.681275i
$829$	−25.6814	+	14.8272i	−0.891952	+	0.514969i	−0.874580	−	0.484881i	$-0.838863\pi$
$829$	−25.6814	+	14.8272i	−0.891952	+	0.514969i	−0.0173713	+	0.999849i	$0.505530\pi$
$830$	20.9678	−	27.0042i	0.727801	−	0.937330i
$831$	−0.666664			−0.0231263
$832$	16.6316	+	23.5667i	0.576596	+	0.817029i
$833$	12.6977			0.439949
$834$	1.93508	−	2.49217i	0.0670063	−	0.0862969i
$835$	22.8342	−	13.1833i	0.790210	−	0.456228i
$836$	−4.27256	−	16.7082i	−0.147769	−	0.577867i
$837$	−17.4436			−0.602938
$838$	−3.76299	+	27.3711i	−0.129990	+	0.945518i
$839$	−25.6385	−	14.8024i	−0.885140	−	0.511036i	−0.0127901	−	0.999918i	$-0.504071\pi$
$839$	−25.6385	−	14.8024i	−0.885140	−	0.511036i	−0.872350	+	0.488883i	$0.837405\pi$
$840$	−1.75744	−	0.763569i	−0.0606373	−	0.0263456i
$841$	−9.08757	+	15.7401i	−0.313365	+	0.542763i
$842$	5.16413	−	6.65084i	0.177968	−	0.229203i
$843$	−1.20995	−	2.09569i	−0.0416728	−	0.0721795i
$844$	22.6608	+	23.1857i	0.780016	+	0.798084i
$845$	25.6040	+	7.16865i	0.880804	+	0.246609i
$846$	−0.125255	+	0.0510441i	−0.00430634	+	0.00175493i
$847$	−7.13522	+	4.11952i	−0.245169	+	0.141548i
$848$	−5.36851	−	9.81063i	−0.184355	−	0.336898i
$849$	1.84884	−	3.20229i	0.0634521	−	0.109902i
$850$	−0.890994	−	2.18636i	−0.0305608	−	0.0749917i
$851$	7.97769	−	13.8178i	0.273472	−	0.473667i
$852$	2.13844	+	8.36257i	0.0732617	+	0.286497i
$853$	−33.9598			−1.16276			−0.581381	−	0.813631i	$-0.697487\pi$
$853$	−33.9598			−1.16276			−0.581381	+	0.813631i	$0.697487\pi$
$854$	16.4799	+	2.26566i	0.563930	+	0.0775295i
$855$	−19.2694	−	33.3755i	−0.658999	−	1.14142i
$856$	−38.5789	+	4.40647i	−1.31860	+	0.150610i
$857$	2.52254			0.0861684			0.0430842	−	0.999071i	$-0.486282\pi$
$857$	2.52254			0.0861684			0.0430842	+	0.999071i	$0.486282\pi$
$858$	2.41426	−	0.617694i	0.0824216	−	0.0210877i
$859$			12.6979i			0.433247i	0.976255	+	0.216624i	$0.0695044\pi$
$859$			12.6979i			0.433247i	−0.976255	+	0.216624i	$0.930496\pi$
$860$	−7.40893	+	26.4361i	−0.252642	+	0.901463i
$861$	2.00914	−	1.15998i	0.0684714	−	0.0395320i
$862$	−5.36172	+	38.9999i	−0.182621	+	1.32834i
$863$		−	9.42568i		−	0.320854i	−0.987048	−	0.160427i	$-0.948713\pi$
$863$		−	9.42568i		−	0.320854i	0.987048	−	0.160427i	$-0.0512871\pi$
$864$	12.2198	+	1.96603i	0.415727	+	0.0668857i
$865$	6.30635	+	3.64097i	0.214422	+	0.123797i
$866$	−12.3393	−	30.2788i	−0.419307	−	1.02892i
$867$	−4.14585	−	2.39361i	−0.140801	−	0.0812913i
$868$	13.6220	+	3.81769i	0.462362	+	0.129581i
$869$	0.683206	+	1.18335i	0.0231762	+	0.0401423i
$870$	1.34080	+	3.29012i	0.0454573	+	0.111545i
$871$	17.1954	+	42.1794i	0.582643	+	1.42919i
$872$	−29.4587	−	12.7992i	−0.997598	−	0.433435i
$873$	−1.69618	+	0.979288i	−0.0574069	+	0.0331439i
$874$	−20.2055	+	26.0225i	−0.683460	+	0.880223i
$875$	9.14124	+	5.27770i	0.309030	+	0.178419i
$876$	−2.13338	+	2.08508i	−0.0720803	+	0.0704485i
$877$	−17.2558	+	29.8880i	−0.582688	+	1.00924i	0.412472	+	0.910970i	$0.364666\pi$
$877$	−17.2558	+	29.8880i	−0.582688	+	1.00924i	−0.995159	+	0.0982744i	$0.968668\pi$
$878$	−6.17588	−	0.849063i	−0.208426	−	0.0286545i
$879$			2.21843i			0.0748256i
$880$	9.14996	+	5.56587i	0.308445	+	0.187625i
$881$	19.0953	+	33.0741i	0.643338	+	1.11429i	0.984683	+	0.174356i	$0.0557845\pi$
$881$	19.0953	+	33.0741i	0.643338	+	1.11429i	−0.341344	+	0.939938i	$0.610882\pi$
$882$	15.4146	−	19.8524i	0.519037	−	0.668464i
$883$		−	7.69496i		−	0.258956i	−0.991582	−	0.129478i	$-0.958670\pi$
$883$		−	7.69496i		−	0.258956i	0.991582	−	0.129478i	$-0.0413301\pi$
$884$	13.5180	+	5.87122i	0.454659	+	0.197471i
$885$			6.01709i			0.202262i
$886$	20.5636	+	15.9669i	0.690848	+	0.536417i
$887$	24.1415	+	41.8143i	0.810592	+	1.40399i	0.912450	+	0.409188i	$0.134188\pi$
$887$	24.1415	+	41.8143i	0.810592	+	1.40399i	−0.101858	+	0.994799i	$0.532479\pi$
$888$	−2.83464	−	3.82856i	−0.0951244	−	0.128478i
$889$		−	18.8870i		−	0.633449i
$890$	−5.69787	+	41.4449i	−0.190993	+	1.38924i
$891$	−5.08258	+	8.80328i	−0.170273	+	0.294921i
$892$	7.10353	+	7.26808i	0.237844	+	0.243353i
$893$	−0.190720	−	0.110112i	−0.00638220	−	0.00368477i
$894$	2.65272	+	2.05974i	0.0887202	+	0.0688879i
$895$	−42.5214	+	24.5497i	−1.42133	+	0.820607i
$896$	−9.11243	−	4.20974i	−0.304425	−	0.140637i
$897$	−3.76062	−	2.91921i	−0.125564	−	0.0974695i
$898$	−17.1984	+	7.00875i	−0.573919	+	0.233885i
$899$	−13.1153	−	22.7163i	−0.437418	−	0.757631i
$900$	−4.49994	−	1.26115i	−0.149998	−	0.0420382i
$901$	−4.94859	−	2.85707i	−0.164861	−	0.0951828i
$902$	−12.0080	+	4.89354i	−0.399823	+	0.162937i
$903$	−1.92529	−	1.11157i	−0.0640696	−	0.0369906i
$904$	25.2715	−	18.7109i	0.840516	−	0.622314i
$905$		−	26.8124i		−	0.891274i
$906$	8.85135	+	1.21689i	0.294066	+	0.0404284i
$907$	9.21161	−	5.31832i	0.305866	−	0.176592i	−0.339209	−	0.940711i	$-0.610159\pi$
$907$	9.21161	−	5.31832i	0.305866	−	0.176592i	0.645075	+	0.764119i	$0.276826\pi$
$908$	−13.9609	−	3.91266i	−0.463309	−	0.129846i
$909$		−	1.19745i		−	0.0397169i
$910$	−8.96408	+	2.29348i	−0.297156	+	0.0760281i
$911$	9.54610			0.316276			0.158138	−	0.987417i	$-0.449451\pi$
$911$	9.54610			0.316276			0.158138	+	0.987417i	$0.449451\pi$
$912$	4.72192	+	8.62903i	0.156358	+	0.285736i
$913$	−7.73673	−	13.4004i	−0.256048	−	0.443489i
$914$	−2.02830	+	14.7534i	−0.0670903	+	0.487999i
$915$	10.1232			0.334663
$916$	−5.76172	−	22.5318i	−0.190373	−	0.744470i
$917$	2.78146	−	4.81764i	0.0918520	−	0.159092i
$918$	5.85635	−	2.38660i	0.193288	−	0.0787694i
$919$	−6.05600	+	10.4893i	−0.199769	+	0.346010i	−0.948453	−	0.316917i	$-0.897352\pi$
$919$	−6.05600	+	10.4893i	−0.199769	+	0.346010i	0.748685	+	0.662926i	$0.230686\pi$
$920$	−2.32180	−	20.3275i	−0.0765474	−	0.670178i
$921$	−8.07067	+	4.65961i	−0.265938	+	0.153539i
$922$	−16.6630	−	40.8885i	−0.548766	−	1.34659i
$923$	32.9254	+	25.5586i	1.08375	+	0.841270i
$924$	−0.620201	+	0.606160i	−0.0204031	+	0.0199412i
$925$	1.84252	+	3.19133i	0.0605815	+	0.104930i
$926$	−20.2457	−	15.7200i	−0.665313	−	0.516591i
$927$	22.6115	−	39.1643i	0.742660	−	1.28633i
$928$	6.62739	+	17.3918i	0.217555	+	0.570912i
$929$	−1.45551	−	0.840336i	−0.0477536	−	0.0275705i	0.475933	−	0.879481i	$-0.342110\pi$
$929$	−1.45551	−	0.840336i	−0.0477536	−	0.0275705i	−0.523687	+	0.851911i	$0.675444\pi$
$930$	8.52890	+	1.17256i	0.279674	+	0.0384497i
$931$	40.9236			1.34122
$932$	−3.47611	−	13.5937i	−0.113864	−	0.445275i
$933$	2.48727	−	1.43602i	0.0814294	−	0.0470133i
$934$	−16.8073	−	13.0502i	−0.549951	−	0.427016i
$935$	5.47215			0.178959
$936$	25.5899	−	14.0074i	0.836431	−	0.457846i
$937$	−4.99248			−0.163097			−0.0815486	−	0.996669i	$-0.525987\pi$
$937$	−4.99248			−0.163097			−0.0815486	+	0.996669i	$0.525987\pi$
$938$	−12.5202	−	9.72149i	−0.408800	−	0.317418i
$939$	−3.13344	+	1.80909i	−0.102256	+	0.0590375i
$940$	0.132498	−	0.0338818i	0.00432161	−	0.00110510i
$941$	13.9258			0.453968			0.226984	−	0.973898i	$-0.427113\pi$
$941$	13.9258			0.453968			0.226984	+	0.973898i	$0.427113\pi$
$942$	2.20770	+	0.303516i	0.0719309	+	0.00988909i
$943$	21.4526	+	12.3857i	0.698594	+	0.403333i
$944$	−0.721682	+	31.5126i	−0.0234887	+	1.02565i
$945$	−1.98517	+	3.43841i	−0.0645775	+	0.111852i
$946$	9.81447	+	7.62057i	0.319096	+	0.247766i
$947$	−13.1660	−	22.8042i	−0.427837	−	0.741036i	0.568843	−	0.822446i	$-0.307391\pi$
$947$	−13.1660	−	22.8042i	−0.427837	−	0.741036i	−0.996681	+	0.0814099i	$0.974058\pi$
$948$	−0.544744	−	0.557363i	−0.0176925	−	0.0181023i
$949$	−1.96013	+	14.2710i	−0.0636284	+	0.463258i
$950$	−2.87160	−	7.04647i	−0.0931670	−	0.228618i
$951$	9.83626	−	5.67897i	0.318963	−	0.184153i
$952$	−5.09567	+	0.582025i	−0.165152	+	0.0188635i
$953$	−22.4079	+	38.8117i	−0.725864	+	1.25723i	0.232754	+	0.972536i	$0.425226\pi$
$953$	−22.4079	+	38.8117i	−0.725864	+	1.25723i	−0.958618	+	0.284697i	$0.908107\pi$
$954$	−10.4744	+	4.26855i	−0.339120	+	0.138199i
$955$	12.9852	−	22.4910i	0.420192	−	0.727793i
$956$	−34.5195	+	8.82718i	−1.11644	+	0.285491i
$957$	1.60797			0.0519782
$958$	2.95790	−	21.5150i	0.0955653	−	0.695119i
$959$	−1.51791	−	2.62910i	−0.0490160	−	0.0848981i
$960$	−5.84264	−	1.78269i	−0.188570	−	0.0575362i
$961$	−32.5611			−1.05036
$962$	−22.1508	−	6.20487i	−0.714170	−	0.200053i
$963$			39.2717i			1.26551i
$964$	10.9563	−	39.0936i	0.352879	−	1.25912i
$965$	−34.6824	+	20.0239i	−1.11647	+	0.644593i
$966$	1.64128	+	0.225643i	0.0528072	+	0.00725996i
$967$			18.9504i			0.609404i	0.952448	+	0.304702i	$0.0985568\pi$
$967$			18.9504i			0.609404i	−0.952448	+	0.304702i	$0.901443\pi$
$968$	−21.1094	+	15.6293i	−0.678481	+	0.502344i
$969$	4.35258	+	2.51296i	0.139825	+	0.0807280i
$970$	1.83394	−	0.747371i	0.0588841	−	0.0239966i
$971$	7.20851	+	4.16184i	0.231332	+	0.133560i	0.611186	−	0.791487i	$-0.290693\pi$
$971$	7.20851	+	4.16184i	0.231332	+	0.133560i	−0.379854	+	0.925046i	$0.624026\pi$
$972$	5.10728	−	18.2235i	0.163816	−	0.584519i
$973$	2.65109	+	4.59183i	0.0849902	+	0.147207i
$974$	3.54382	−	1.44419i	0.113551	−	0.0462747i
$975$	1.01816	−	0.415077i	0.0326073	−	0.0132931i
$976$	53.0171	+	1.21416i	1.69704	+	0.0388645i
$977$	−2.69735	+	1.55731i	−0.0862957	+	0.0498229i	−0.542527	−	0.840038i	$-0.682532\pi$
$977$	−2.69735	+	1.55731i	−0.0862957	+	0.0498229i	0.456231	+	0.889861i	$0.349199\pi$
$978$	−6.22809	−	4.83587i	−0.199152	−	0.154634i
$979$	16.3972	+	9.46696i	0.524058	+	0.302565i
$980$	−18.1749	+	17.7634i	−0.580576	+	0.567432i
$981$	−16.2423	+	28.1326i	−0.518578	+	0.898203i
$982$	2.86317	−	20.8260i	0.0913675	−	0.664585i
$983$			60.9054i			1.94258i	0.237899	+	0.971290i	$0.423541\pi$
$983$			60.9054i			1.94258i	−0.237899	+	0.971290i	$0.576459\pi$
$984$	5.94399	−	4.40090i	0.189488	−	0.140296i
$985$	12.8882	+	22.3230i	0.410653	+	0.711272i
$986$	7.51120	+	5.83216i	0.239205	+	0.185734i
$987$			0.0110742i			0.000352496i
$988$	43.5674	+	18.9225i	1.38606	+	0.602004i
$989$		−	23.7375i		−	0.754809i
$990$	6.64303	−	8.55552i	0.211129	−	0.271912i
$991$	−27.9611	−	48.4301i	−0.888214	−	1.53843i	−0.841985	−	0.539501i	$-0.818613\pi$
$991$	−27.9611	−	48.4301i	−0.888214	−	1.53843i	−0.0462290	−	0.998931i	$-0.514720\pi$
$992$	44.5268	+	7.16385i	1.41373	+	0.227452i
$993$			0.0836063i			0.00265317i
$994$	−14.3699	−	1.97558i	−0.455785	−	0.0626615i
$995$	−4.21726	+	7.30450i	−0.133696	+	0.231568i
$996$	6.16876	+	6.31165i	0.195465	+	0.199992i
$997$	27.9026	+	16.1095i	0.883683	+	0.510194i	0.871871	−	0.489736i	$-0.162907\pi$
$997$	27.9026	+	16.1095i	0.883683	+	0.510194i	0.0118118	+	0.999930i	$0.496240\pi$
$998$	−6.65132	+	8.56618i	−0.210544	+	0.271158i
$999$	−8.54823	+	4.93532i	−0.270454	+	0.156147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.s.c.101.6	yes	16
3.2	odd	2		936.2.dg.d.829.3		16
4.3	odd	2		416.2.ba.c.49.5		16
8.3	odd	2		416.2.ba.c.49.4		16
8.5	even	2	inner	104.2.s.c.101.8	yes	16
13.4	even	6	inner	104.2.s.c.69.8	yes	16
24.5	odd	2		936.2.dg.d.829.1		16
39.17	odd	6		936.2.dg.d.901.1		16
52.43	odd	6		416.2.ba.c.17.4		16
104.43	odd	6		416.2.ba.c.17.5		16
104.69	even	6	inner	104.2.s.c.69.6	✓	16
312.173	odd	6		936.2.dg.d.901.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.c.69.6	✓	16	104.69	even	6	inner
104.2.s.c.69.8	yes	16	13.4	even	6	inner
104.2.s.c.101.6	yes	16	1.1	even	1	trivial
104.2.s.c.101.8	yes	16	8.5	even	2	inner
416.2.ba.c.17.4		16	52.43	odd	6
416.2.ba.c.17.5		16	104.43	odd	6
416.2.ba.c.49.4		16	8.3	odd	2
416.2.ba.c.49.5		16	4.3	odd	2
936.2.dg.d.829.1		16	24.5	odd	2
936.2.dg.d.829.3		16	3.2	odd	2
936.2.dg.d.901.1		16	39.17	odd	6
936.2.dg.d.901.3		16	312.173	odd	6

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.867327 - 1.11702i) q^{2} +(-0.323315 + 0.186666i) q^{3} +(-0.495487 - 1.93765i) q^{4} +2.04528 q^{5} +(-0.0719095 + 0.523052i) q^{6} +(-0.768362 - 0.443614i) q^{7} +(-2.59415 - 1.12711i) q^{8} +(-1.43031 + 2.47737i) q^{9} +(1.77393 - 2.28463i) q^{10} +(-0.654547 - 1.13371i) q^{11} +(0.521893 + 0.533982i) q^{12} +(3.57202 + 0.490616i) q^{13} +(-1.16195 + 0.473521i) q^{14} +(-0.661270 + 0.381784i) q^{15} +(-3.50898 + 1.92016i) q^{16} +(-1.02189 + 1.76997i) q^{17} +(1.52674 + 3.74638i) q^{18} +(-3.29348 + 5.70447i) q^{19} +(-1.01341 - 3.96304i) q^{20} +0.331231 q^{21} +(-1.83409 - 0.252151i) q^{22} +(1.76836 + 3.06289i) q^{23} +(1.04912 - 0.119830i) q^{24} -0.816837 q^{25} +(3.64614 - 3.56450i) q^{26} -2.18796i q^{27} +(-0.478856 + 1.70862i) q^{28} +(2.84932 - 1.64506i) q^{29} +(-0.147075 + 1.06979i) q^{30} -7.97252i q^{31} +(-0.898567 + 5.58503i) q^{32} +(0.423250 + 0.244364i) q^{33} +(1.09078 + 2.67662i) q^{34} +(-1.57151 - 0.907314i) q^{35} +(5.50898 + 1.54394i) q^{36} +(-2.25567 - 3.90694i) q^{37} +(3.51551 + 8.62654i) q^{38} +(-1.24647 + 0.508151i) q^{39} +(-5.30577 - 2.30524i) q^{40} +(6.06568 - 3.50202i) q^{41} +(0.287286 - 0.369993i) q^{42} +(-5.81252 - 3.35586i) q^{43} +(-1.87241 + 1.83002i) q^{44} +(-2.92538 + 5.06692i) q^{45} +(4.95508 + 0.681226i) q^{46} +0.0334334i q^{47} +(0.776079 - 1.27583i) q^{48} +(-3.10641 - 5.38047i) q^{49} +(-0.708465 + 0.912427i) q^{50} -0.763012i q^{51} +(-0.819246 - 7.16441i) q^{52} +2.79586i q^{53} +(-2.44401 - 1.89768i) q^{54} +(-1.33873 - 2.31875i) q^{55} +(1.49325 + 2.01683i) q^{56} -2.45912i q^{57} +(0.633726 - 4.60957i) q^{58} +(3.94011 - 6.82447i) q^{59} +(1.06742 + 1.09214i) q^{60} +(-11.4816 - 6.62888i) q^{61} +(-8.90551 - 6.91479i) q^{62} +(2.19799 - 1.26901i) q^{63} +(5.45927 + 5.84777i) q^{64} +(7.30577 + 1.00345i) q^{65} +(0.640056 - 0.260838i) q^{66} +(6.31662 + 10.9407i) q^{67} +(3.93592 + 1.10307i) q^{68} +(-1.14348 - 0.660187i) q^{69} +(-2.37651 + 0.968482i) q^{70} +(10.0115 + 5.78014i) q^{71} +(6.50271 - 4.81457i) q^{72} +3.99523i q^{73} +(-6.32055 - 0.868952i) q^{74} +(0.264096 - 0.152476i) q^{75} +(12.6851 + 3.55512i) q^{76} +1.16146i q^{77} +(-0.513479 + 1.83307i) q^{78} -1.04379 q^{79} +(-7.17685 + 3.92727i) q^{80} +(-3.88252 - 6.72471i) q^{81} +(1.34908 - 9.81291i) q^{82} +11.8200 q^{83} +(-0.164121 - 0.641810i) q^{84} +(-2.09006 + 3.62008i) q^{85} +(-8.78993 + 3.58210i) q^{86} +(-0.614153 + 1.06375i) q^{87} +(0.420186 + 3.67876i) q^{88} +(-12.5257 + 7.23169i) q^{89} +(3.12260 + 7.66240i) q^{90} +(-2.52696 - 1.96157i) q^{91} +(5.05862 - 4.94409i) q^{92} +(1.48820 + 2.57764i) q^{93} +(0.0373460 + 0.0289977i) q^{94} +(-6.73608 + 11.6672i) q^{95} +(-0.752016 - 1.97346i) q^{96} +(0.592940 + 0.342334i) q^{97} +(-8.70439 - 1.19668i) q^{98} +3.74482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - q^{4} + 6 q^{6} + 18 q^{7} + 2 q^{9} - 9 q^{10} - 16 q^{12} - 24 q^{14} - 36 q^{15} - q^{16} + 8 q^{17} - 15 q^{20} + 22 q^{22} - 2 q^{23} - 12 q^{24} - 12 q^{25} + 23 q^{26} - 8 q^{30}+ \cdots - 93 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - q^4 + 6 * q^6 + 18 * q^7 + 2 * q^9 - 9 * q^10 - 16 * q^12 - 24 * q^14 - 36 * q^15 - q^16 + 8 * q^17 - 15 * q^20 + 22 * q^22 - 2 * q^23 - 12 * q^24 - 12 * q^25 + 23 * q^26 - 8 * q^30 - 27 * q^32 - 30 * q^33 + 33 * q^36 - 14 * q^39 + 26 * q^40 + 24 * q^41 + 14 * q^42 + 42 * q^46 + 6 * q^48 - 14 * q^49 + 6 * q^50 + 28 * q^52 + 6 * q^54 + 4 * q^55 - 8 * q^56 - 33 * q^58 - 4 * q^62 + 50 * q^64 + 6 * q^65 + 40 * q^66 + 5 * q^68 + 6 * q^71 + 39 * q^72 - 29 * q^74 + 24 * q^76 - 20 * q^78 + 32 * q^79 - 33 * q^80 + 12 * q^81 + 9 * q^82 - 24 * q^84 + 34 * q^87 - 8 * q^88 - 30 * q^89 - 62 * q^90 - 4 * q^92 - 24 * q^94 + 28 * q^95 - 30 * q^97 - 93 * q^98

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