LMFDB - Embedded newform 141.2.g.a.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [141,2,Mod(5,141)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(141, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([23, 1]))

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

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

chi := DirichletCharacter("141.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 141 = 3 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	141.g (of order $46$, degree $22$, 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:	$1.12589066850$
Analytic rank:	$0$
Dimension:	$308$
Relative dimension:	$14$ over $\Q(\zeta_{46})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{46}]$

Embedding invariants

Embedding label			107.8
Character	$\chi$	$=$	141.107
Dual form			141.2.g.a.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.176299 - 0.124445i) q^{2} +(-1.45742 - 0.935916i) q^{3} +(-0.654165 + 1.84064i) q^{4} +(-1.82983 + 1.95927i) q^{5} +(-0.373412 + 0.0163677i) q^{6} +(-0.487368 + 0.940578i) q^{7} +(0.230173 + 0.821499i) q^{8} +(1.24812 + 2.72804i) q^{9} +O(q^{10})$	\(q+(0.176299 - 0.124445i) q^{2} +(-1.45742 - 0.935916i) q^{3} +(-0.654165 + 1.84064i) q^{4} +(-1.82983 + 1.95927i) q^{5} +(-0.373412 + 0.0163677i) q^{6} +(-0.487368 + 0.940578i) q^{7} +(0.230173 + 0.821499i) q^{8} +(1.24812 + 2.72804i) q^{9} +(-0.0787752 + 0.573132i) q^{10} +(-1.35387 - 0.823304i) q^{11} +(2.67608 - 2.07034i) q^{12} +(-0.986116 + 2.27027i) q^{13} +(0.0311281 + 0.226474i) q^{14} +(4.50054 - 1.14290i) q^{15} +(-2.88779 - 2.34939i) q^{16} +(0.873469 + 1.43636i) q^{17} +(0.559535 + 0.325628i) q^{18} +(4.36426 - 4.07594i) q^{19} +(-2.40931 - 4.64975i) q^{20} +(1.59060 - 0.914678i) q^{21} +(-0.341142 + 0.0233347i) q^{22} +(-4.17637 + 5.91657i) q^{23} +(0.433396 - 1.41269i) q^{24} +(-0.149249 - 2.18194i) q^{25} +(0.108673 + 0.522963i) q^{26} +(0.734183 - 5.14402i) q^{27} +(-1.41245 - 1.51236i) q^{28} +(-0.0334184 + 0.0145156i) q^{29} +(0.651212 - 0.761565i) q^{30} +(2.29995 - 2.82701i) q^{31} +(-2.50378 - 0.171263i) q^{32} +(1.20260 + 2.46700i) q^{33} +(0.332740 + 0.144529i) q^{34} +(-0.951047 - 2.67599i) q^{35} +(-5.83782 + 0.512760i) q^{36} +(-6.66376 - 0.915913i) q^{37} +(0.262184 - 1.26170i) q^{38} +(3.56196 - 2.38580i) q^{39} +(-2.03072 - 1.05223i) q^{40} +(8.60650 + 2.41143i) q^{41} +(0.166594 - 0.359200i) q^{42} +(11.0801 + 3.93788i) q^{43} +(2.40106 - 1.95341i) q^{44} +(-7.62882 - 2.54644i) q^{45} +1.56282i q^{46} +(4.43330 + 5.22933i) q^{47} +(2.00988 + 6.12676i) q^{48} +(3.38960 + 4.80197i) q^{49} +(-0.297845 - 0.366100i) q^{50} +(0.0713037 - 2.91087i) q^{51} +(-3.53367 - 3.30021i) q^{52} +(-1.18007 + 4.21173i) q^{53} +(-0.510715 - 0.998252i) q^{54} +(4.09042 - 1.14608i) q^{55} +(-0.884864 - 0.183877i) q^{56} +(-10.1753 + 1.85575i) q^{57} +(-0.00408522 + 0.00671786i) q^{58} +(1.48728 - 0.528580i) q^{59} +(-0.840416 + 9.03154i) q^{60} +(-0.601327 + 0.0826505i) q^{61} +(0.0536693 - 0.784618i) q^{62} +(-3.17423 - 0.155603i) q^{63} +(5.89887 - 3.58718i) q^{64} +(-2.64364 - 6.08628i) q^{65} +(0.519024 + 0.285272i) q^{66} +(-9.42475 + 4.88351i) q^{67} +(-3.21522 + 0.668130i) q^{68} +(11.6241 - 4.71417i) q^{69} +(-0.500683 - 0.353421i) q^{70} +(-8.35790 - 5.89965i) q^{71} +(-1.95380 + 1.65325i) q^{72} +(-10.3043 + 2.14126i) q^{73} +(-1.28880 + 0.667800i) q^{74} +(-1.82459 + 3.31968i) q^{75} +(4.64740 + 10.6994i) q^{76} +(1.43421 - 0.872164i) q^{77} +(0.331068 - 0.863884i) q^{78} +(-0.583622 + 8.53225i) q^{79} +(9.88726 - 1.35897i) q^{80} +(-5.88438 + 6.80985i) q^{81} +(1.81741 - 0.645907i) q^{82} +(8.87887 - 14.6007i) q^{83} +(0.643080 + 3.52608i) q^{84} +(-4.41252 - 0.916933i) q^{85} +(2.44347 - 0.684627i) q^{86} +(0.0622899 + 0.0101215i) q^{87} +(0.364720 - 1.30170i) q^{88} +(9.19470 + 8.58725i) q^{89} +(-1.66185 + 0.500437i) q^{90} +(-1.65476 - 2.03397i) q^{91} +(-8.15825 - 11.5576i) q^{92} +(-5.99783 + 1.96758i) q^{93} +(1.43235 + 0.370222i) q^{94} +16.0091i q^{95} +(3.48876 + 2.59293i) q^{96} +(-4.49660 + 3.65825i) q^{97} +(1.19517 + 0.424763i) q^{98} +(0.556215 - 4.72098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 308 q - 19 q^{3} - 26 q^{4} - 15 q^{6} - 42 q^{7} - 19 q^{9}+O(q^{10}) $ 308 * q - 19 * q^3 - 26 * q^4 - 15 * q^6 - 42 * q^7 - 19 * q^9	$ 308 q - 19 q^{3} - 26 q^{4} - 15 q^{6} - 42 q^{7} - 19 q^{9} - 46 q^{10} - 28 q^{12} - 46 q^{13} - 23 q^{15} - 70 q^{16} - 14 q^{18} - 46 q^{19} - 27 q^{21} - 46 q^{22} - 42 q^{24} - 36 q^{25} - 43 q^{27} - 46 q^{28} - 23 q^{30} - 46 q^{31} - 23 q^{33} - 38 q^{34} + 69 q^{36} - 66 q^{37} + 46 q^{39} - 46 q^{40} + 162 q^{42} - 46 q^{43} + 92 q^{45} + 178 q^{48} - 92 q^{49} + 80 q^{51} - 46 q^{52} + 58 q^{54} + 14 q^{55} + 46 q^{57} - 46 q^{58} + 69 q^{60} - 78 q^{61} + 13 q^{63} + 66 q^{64} - 23 q^{66} - 46 q^{67} - 23 q^{69} - 46 q^{70} - 105 q^{72} - 46 q^{73} + 17 q^{75} - 23 q^{78} + 50 q^{79} + 5 q^{81} + 368 q^{82} + 62 q^{84} + 138 q^{85} - 23 q^{87} + 230 q^{88} - 23 q^{90} + 322 q^{91} + 198 q^{94} + 93 q^{96} + 26 q^{97} - 23 q^{99}+O(q^{100}) $ 308 * q - 19 * q^3 - 26 * q^4 - 15 * q^6 - 42 * q^7 - 19 * q^9 - 46 * q^10 - 28 * q^12 - 46 * q^13 - 23 * q^15 - 70 * q^16 - 14 * q^18 - 46 * q^19 - 27 * q^21 - 46 * q^22 - 42 * q^24 - 36 * q^25 - 43 * q^27 - 46 * q^28 - 23 * q^30 - 46 * q^31 - 23 * q^33 - 38 * q^34 + 69 * q^36 - 66 * q^37 + 46 * q^39 - 46 * q^40 + 162 * q^42 - 46 * q^43 + 92 * q^45 + 178 * q^48 - 92 * q^49 + 80 * q^51 - 46 * q^52 + 58 * q^54 + 14 * q^55 + 46 * q^57 - 46 * q^58 + 69 * q^60 - 78 * q^61 + 13 * q^63 + 66 * q^64 - 23 * q^66 - 46 * q^67 - 23 * q^69 - 46 * q^70 - 105 * q^72 - 46 * q^73 + 17 * q^75 - 23 * q^78 + 50 * q^79 + 5 * q^81 + 368 * q^82 + 62 * q^84 + 138 * q^85 - 23 * q^87 + 230 * q^88 - 23 * q^90 + 322 * q^91 + 198 * q^94 + 93 * q^96 + 26 * q^97 - 23 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/141\mathbb{Z}\right)^\times$.

$n$	$52$	$95$
$\chi(n)$	$e\left(\frac{11}{46}\right)$	$-1$

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 $

$2$	0.176299	−	0.124445i	0.124662	−	0.0879962i	−0.512668	−	0.858587i	$-0.671343\pi$
$2$	0.176299	−	0.124445i	0.124662	−	0.0879962i	0.637331	+	0.770591i	$0.280039\pi$
$3$	−1.45742	−	0.935916i	−0.841439	−	0.540351i
$3$	−1.45742	−	0.935916i	−0.841439	−	0.540351i
$4$	−0.654165	+	1.84064i	−0.327082	+	0.920321i
$5$	−1.82983	+	1.95927i	−0.818326	+	0.876213i	−0.994128	−	0.108212i	$-0.965487\pi$
$5$	−1.82983	+	1.95927i	−0.818326	+	0.876213i	0.175802	+	0.984426i	$0.443748\pi$
$6$	−0.373412	+	0.0163677i	−0.152445	+	0.00668207i
$7$	−0.487368	+	0.940578i	−0.184208	+	0.355505i	−0.962014	−	0.272999i	$-0.911985\pi$
$7$	−0.487368	+	0.940578i	−0.184208	+	0.355505i	0.777806	+	0.628504i	$0.216332\pi$
$8$	0.230173	+	0.821499i	0.0813786	+	0.290444i
$9$	1.24812	+	2.72804i	0.416041	+	0.909346i
$10$	−0.0787752	+	0.573132i	−0.0249109	+	0.181240i
$11$	−1.35387	−	0.823304i	−0.408206	−	0.248235i	0.300439	−	0.953801i	$-0.402867\pi$
$11$	−1.35387	−	0.823304i	−0.408206	−	0.248235i	−0.708644	+	0.705566i	$0.750693\pi$
$12$	2.67608	−	2.07034i	0.772517	−	0.597655i
$13$	−0.986116	+	2.27027i	−0.273499	+	0.629658i	−0.998236	−	0.0593672i	$-0.981092\pi$
$13$	−0.986116	+	2.27027i	−0.273499	+	0.629658i	0.724737	+	0.689026i	$0.241961\pi$
$14$	0.0311281	+	0.226474i	0.00831934	+	0.0605277i
$15$	4.50054	−	1.14290i	1.16204	−	0.295097i
$16$	−2.88779	−	2.34939i	−0.721947	−	0.587347i
$17$	0.873469	+	1.43636i	0.211847	+	0.348368i	0.942400	−	0.334488i	$-0.108563\pi$
$17$	0.873469	+	1.43636i	0.211847	+	0.348368i	−0.730552	+	0.682857i	$0.760737\pi$
$18$	0.559535	+	0.325628i	0.131884	+	0.0767511i
$19$	4.36426	−	4.07594i	1.00123	−	0.935084i	0.00333918	−	0.999994i	$-0.498937\pi$
$19$	4.36426	−	4.07594i	1.00123	−	0.935084i	0.997891	+	0.0649106i	$0.0206762\pi$
$20$	−2.40931	−	4.64975i	−0.538738	−	1.03972i
$21$	1.59060	−	0.914678i	0.347098	−	0.199599i
$22$	−0.341142	+	0.0233347i	−0.0727316	+	0.00497498i
$23$	−4.17637	+	5.91657i	−0.870833	+	1.23369i	0.100254	+	0.994962i	$0.468035\pi$
$23$	−4.17637	+	5.91657i	−0.870833	+	1.23369i	−0.971087	+	0.238727i	$0.923270\pi$
$24$	0.433396	−	1.41269i	0.0884667	−	0.288364i
$25$	−0.149249	−	2.18194i	−0.0298497	−	0.436388i
$26$	0.108673	+	0.522963i	0.0213125	+	0.102562i
$27$	0.734183	−	5.14402i	0.141293	−	0.989968i
$28$	−1.41245	−	1.51236i	−0.266928	−	0.285810i
$29$	−0.0334184	+	0.0145156i	−0.00620563	+	0.00269549i	−0.401502	−	0.915858i	$-0.631512\pi$
$29$	−0.0334184	+	0.0145156i	−0.00620563	+	0.00269549i	0.395296	+	0.918554i	$0.370642\pi$
$30$	0.651212	−	0.761565i	0.118895	−	0.139042i
$31$	2.29995	−	2.82701i	0.413083	−	0.507747i	−0.526450	−	0.850206i	$-0.676477\pi$
$31$	2.29995	−	2.82701i	0.413083	−	0.507747i	0.939533	+	0.342459i	$0.111260\pi$
$32$	−2.50378	−	0.171263i	−0.442610	−	0.0302753i
$33$	1.20260	+	2.46700i	0.209346	+	0.429450i
$34$	0.332740	+	0.144529i	0.0570645	+	0.0247866i
$35$	−0.951047	−	2.67599i	−0.160756	−	0.452325i
$36$	−5.83782	+	0.512760i	−0.972970	+	0.0854601i
$37$	−6.66376	−	0.915913i	−1.09552	−	0.150575i	−0.434298	−	0.900769i	$-0.643003\pi$
$37$	−6.66376	−	0.915913i	−1.09552	−	0.150575i	−0.661218	+	0.750194i	$0.729960\pi$
$38$	0.262184	−	1.26170i	0.0425318	−	0.204674i
$39$	3.56196	−	2.38580i	0.570370	−	0.382034i
$40$	−2.03072	−	1.05223i	−0.321085	−	0.166373i
$41$	8.60650	+	2.41143i	1.34411	+	0.376602i	0.865272	−	0.501302i	$-0.167146\pi$
$41$	8.60650	+	2.41143i	1.34411	+	0.376602i	0.478837	+	0.877904i	$0.341059\pi$
$42$	0.166594	−	0.359200i	0.0257060	−	0.0554258i
$43$	11.0801	+	3.93788i	1.68970	+	0.600521i	0.993135	−	0.116971i	$-0.0373183\pi$
$43$	11.0801	+	3.93788i	1.68970	+	0.600521i	0.696568	+	0.717491i	$0.254710\pi$
$44$	2.40106	−	1.95341i	0.361973	−	0.294487i
$45$	−7.62882	−	2.54644i	−1.13724	−	0.379601i
$46$			1.56282i			0.230425i
$47$	4.43330	+	5.22933i	0.646663	+	0.762776i
$47$	4.43330	+	5.22933i	0.646663	+	0.762776i
$48$	2.00988	+	6.12676i	0.290101	+	0.884322i
$49$	3.38960	+	4.80197i	0.484229	+	0.685996i
$50$	−0.297845	−	0.366100i	−0.0421216	−	0.0517744i
$51$	0.0713037	−	2.91087i	0.00998452	−	0.407603i
$52$	−3.53367	−	3.30021i	−0.490031	−	0.457657i
$53$	−1.18007	+	4.21173i	−0.162095	+	0.578525i	0.837395	+	0.546598i	$0.184077\pi$
$53$	−1.18007	+	4.21173i	−0.162095	+	0.578525i	−0.999490	+	0.0319270i	$0.989836\pi$
$54$	−0.510715	−	0.998252i	−0.0694995	−	0.135845i
$55$	4.09042	−	1.14608i	0.551552	−	0.154538i
$56$	−0.884864	−	0.183877i	−0.118245	−	0.0245716i
$57$	−10.1753	+	1.85575i	−1.34775	+	0.245800i
$58$	−0.00408522	+	0.00671786i	−0.000536416	+	0.000882098i
$59$	1.48728	−	0.528580i	0.193628	−	0.0688152i	−0.236294	−	0.971682i	$-0.575933\pi$
$59$	1.48728	−	0.528580i	0.193628	−	0.0688152i	0.429921	+	0.902866i	$0.358541\pi$
$60$	−0.840416	+	9.03154i	−0.108497	+	1.16597i
$61$	−0.601327	+	0.0826505i	−0.0769920	+	0.0105823i	−0.174560	−	0.984647i	$-0.555850\pi$
$61$	−0.601327	+	0.0826505i	−0.0769920	+	0.0105823i	0.0975678	+	0.995229i	$0.468894\pi$
$62$	0.0536693	−	0.784618i	0.00681601	−	0.0996466i
$63$	−3.17423	−	0.155603i	−0.399915	−	0.0196042i
$64$	5.89887	−	3.58718i	0.737359	−	0.448398i
$65$	−2.64364	−	6.08628i	−0.327904	−	0.754910i
$66$	0.519024	+	0.285272i	0.0638875	+	0.0351145i
$67$	−9.42475	+	4.88351i	−1.15142	+	0.596616i	−0.925954	−	0.377636i	$-0.876737\pi$
$67$	−9.42475	+	4.88351i	−1.15142	+	0.596616i	−0.225463	+	0.974252i	$0.572389\pi$
$68$	−3.21522	+	0.668130i	−0.389902	+	0.0810226i
$69$	11.6241	−	4.71417i	1.39938	−	0.567519i
$70$	−0.500683	−	0.353421i	−0.0598431	−	0.0422419i
$71$	−8.35790	−	5.89965i	−0.991901	−	0.700160i	−0.0376882	−	0.999290i	$-0.511999\pi$
$71$	−8.35790	−	5.89965i	−0.991901	−	0.700160i	−0.954213	+	0.299130i	$0.903304\pi$
$72$	−1.95380	+	1.65325i	−0.230257	+	0.194838i
$73$	−10.3043	+	2.14126i	−1.20603	+	0.250615i	−0.763302	−	0.646042i	$-0.776423\pi$
$73$	−10.3043	+	2.14126i	−1.20603	+	0.250615i	−0.442725	+	0.896657i	$0.645988\pi$
$74$	−1.28880	+	0.667800i	−0.149820	+	0.0776302i
$75$	−1.82459	+	3.31968i	−0.210686	+	0.383323i
$76$	4.64740	+	10.6994i	0.533093	+	1.22730i
$77$	1.43421	−	0.872164i	0.163444	−	0.0993923i
$78$	0.331068	−	0.863884i	0.0374861	−	0.0978156i
$79$	−0.583622	+	8.53225i	−0.0656626	+	0.959953i	0.841792	+	0.539802i	$0.181501\pi$
$79$	−0.583622	+	8.53225i	−0.0656626	+	0.959953i	−0.907454	+	0.420151i	$0.861977\pi$
$80$	9.88726	−	1.35897i	1.10543	−	0.151938i
$81$	−5.88438	+	6.80985i	−0.653820	+	0.756650i
$82$	1.81741	−	0.645907i	0.200699	−	0.0713285i
$83$	8.87887	−	14.6007i	0.974583	−	1.60263i	0.190772	−	0.981634i	$-0.438901\pi$
$83$	8.87887	−	14.6007i	0.974583	−	1.60263i	0.783811	−	0.620999i	$-0.213273\pi$
$84$	0.643080	+	3.52608i	0.0701658	+	0.384727i
$85$	−4.41252	−	0.916933i	−0.478605	−	0.0994553i
$86$	2.44347	−	0.684627i	0.263486	−	0.0738253i
$87$	0.0622899	+	0.0101215i	0.00667818	+	0.00108513i
$88$	0.364720	−	1.30170i	0.0388793	−	0.138762i
$89$	9.19470	+	8.58725i	0.974636	+	0.910246i	0.995985	−	0.0895258i	$-0.0285351\pi$
$89$	9.19470	+	8.58725i	0.974636	+	0.910246i	−0.0213487	+	0.999772i	$0.506796\pi$
$90$	−1.66185	+	0.500437i	−0.175174	+	0.0527507i
$91$	−1.65476	−	2.03397i	−0.173466	−	0.213219i
$92$	−8.15825	−	11.5576i	−0.850556	−	1.20496i
$93$	−5.99783	+	1.96758i	−0.621946	+	0.204028i
$94$	1.43235	+	0.370222i	0.147736	+	0.0381855i
$95$			16.0091i			1.64249i
$96$	3.48876	+	2.59293i	0.356070	+	0.264640i
$97$	−4.49660	+	3.65825i	−0.456560	+	0.371439i	−0.831422	−	0.555641i	$-0.812473\pi$
$97$	−4.49660	+	3.65825i	−0.456560	+	0.371439i	0.374862	+	0.927081i	$0.377690\pi$
$98$	1.19517	+	0.424763i	0.120730	+	0.0429075i
$99$	0.556215	−	4.72098i	0.0559017	−	0.474476i
$100$	4.11380	+	1.15263i	0.411380	+	0.115263i
$101$	−10.6479	−	5.51731i	−1.05951	−	0.548993i	−0.160550	−	0.987028i	$-0.551327\pi$
$101$	−10.6479	−	5.51731i	−1.05951	−	0.548993i	−0.898958	+	0.438035i	$0.855675\pi$
$102$	−0.349673	−	0.522057i	−0.0346228	−	0.0516913i
$103$	1.88371	−	9.06491i	0.185608	−	0.893192i	−0.778493	−	0.627654i	$-0.784015\pi$
$103$	1.88371	−	9.06491i	0.185608	−	0.893192i	0.964100	−	0.265539i	$-0.0855498\pi$
$104$	−2.09200	−	0.287539i	−0.205137	−	0.0281955i
$105$	−1.11843	+	4.79013i	−0.109148	+	0.467469i
$106$	0.316085	+	0.889378i	0.0307009	+	0.0863840i
$107$	8.42824	+	3.66090i	0.814788	+	0.353913i	0.764339	−	0.644814i	$-0.223065\pi$
$107$	8.42824	+	3.66090i	0.814788	+	0.353913i	0.0504490	+	0.998727i	$0.483935\pi$
$108$	8.98803	+	4.71641i	0.864874	+	0.453836i
$109$	3.99337	+	0.273154i	0.382495	+	0.0261634i	0.258224	−	0.966085i	$-0.416863\pi$
$109$	3.99337	+	0.273154i	0.382495	+	0.0261634i	0.124271	+	0.992248i	$0.460341\pi$
$110$	0.578513	−	0.711088i	0.0551590	−	0.0677996i
$111$	8.85465	+	7.57159i	0.840446	+	0.718663i
$112$	3.61720	−	1.57117i	0.341793	−	0.148462i
$113$	6.38653	+	6.83830i	0.600794	+	0.643293i	0.956647	−	0.291248i	$-0.0940706\pi$
$113$	6.38653	+	6.83830i	0.600794	+	0.643293i	−0.355853	+	0.934542i	$0.615810\pi$
$114$	−1.56295	+	1.59343i	−0.146384	+	0.149239i
$115$	−3.95011	−	19.0090i	−0.368350	−	1.77260i
$116$	−0.00485700	−	0.0710069i	−0.000450962	−	0.00659282i
$117$	−7.42416	+	0.143407i	−0.686364	+	0.0132580i
$118$	0.196427	−	0.278274i	0.0180826	−	0.0256172i
$119$	−1.77671	+	0.121530i	−0.162871	+	0.0111407i
$120$	1.97480	+	3.43413i	0.180274	+	0.313491i
$121$	−3.90559	−	7.53745i	−0.355054	−	0.685223i
$122$	−0.0957279	+	0.0894036i	−0.00866680	+	0.00809422i
$123$	−10.2864	−	11.5694i	−0.927489	−	1.04318i
$124$	3.69898	+	6.08271i	0.332178	+	0.546244i
$125$	−5.84977	−	4.75914i	−0.523220	−	0.425671i
$126$	−0.578978	+	0.367586i	−0.0515794	+	0.0327471i
$127$	0.286184	+	2.08214i	0.0253947	+	0.184760i	0.999067	−	0.0431931i	$-0.0137531\pi$
$127$	0.286184	+	2.08214i	0.0253947	+	0.184760i	−0.973672	+	0.227954i	$0.926797\pi$
$128$	2.59324	−	5.97023i	0.229212	−	0.527698i
$129$	−12.4628	−	16.1092i	−1.09729	−	1.41834i
$130$	−1.22348	−	0.744016i	−0.107306	−	0.0652545i
$131$	1.23362	−	8.97522i	0.107782	−	0.784169i	−0.855905	−	0.517133i	$-0.826999\pi$
$131$	1.23362	−	8.97522i	0.107782	−	0.784169i	0.963687	−	0.267036i	$-0.0860442\pi$
$132$	−5.32756	+	0.599735i	−0.463705	+	0.0522002i
$133$	1.70673	+	6.09141i	0.147993	+	0.528192i
$134$	−1.05384	+	2.03383i	−0.0910383	+	0.175696i
$135$	8.73511	+	10.8512i	0.751799	+	0.933920i
$136$	−0.978919	+	1.04817i	−0.0839416	+	0.0898795i
$137$	4.16889	−	11.7301i	0.356172	−	1.00217i	−0.619892	−	0.784687i	$-0.712823\pi$
$137$	4.16889	−	11.7301i	0.356172	−	1.00217i	0.976064	−	0.217485i	$-0.0697852\pi$
$138$	1.46266	−	2.27767i	0.124510	−	0.193888i
$139$	9.70584	−	6.85113i	0.823239	−	0.581105i	−0.0865166	−	0.996250i	$-0.527574\pi$
$139$	9.70584	−	6.85113i	0.823239	−	0.581105i	0.909755	+	0.415145i	$0.136269\pi$
$140$	5.54768			0.468865
$141$	−1.56695	−	11.7705i	−0.131961	−	0.991255i
$142$	−2.20768			−0.185264
$143$	3.20419	−	2.26176i	0.267947	−	0.189138i
$144$	2.80491	−	10.8103i	0.233743	−	0.900860i
$145$	0.0327099	−	0.0920369i	0.00271641	−	0.00764325i
$146$	−1.55017	+	1.65982i	−0.128293	+	0.137368i
$147$	−0.445816	−	10.1709i	−0.0367703	−	0.838878i
$148$	6.04506	−	11.6664i	0.496901	−	0.958976i
$149$	1.24163	+	4.43142i	0.101718	+	0.363036i	0.996513	−	0.0834416i	$-0.0265912\pi$
$149$	1.24163	+	4.43142i	0.101718	+	0.363036i	−0.894795	+	0.446478i	$0.852678\pi$
$150$	0.0914444	+	0.812318i	0.00746641	+	0.0663255i
$151$	−0.393767	+	2.86487i	−0.0320443	+	0.233140i	−0.999826	−	0.0186509i	$-0.994063\pi$
$151$	−0.393767	+	2.86487i	−0.0320443	+	0.233140i	0.967782	+	0.251791i	$0.0810194\pi$
$152$	4.35292	+	2.64707i	0.353068	+	0.214705i
$153$	−2.82825	+	4.17561i	−0.228650	+	0.337578i
$154$	0.144314	−	0.332243i	0.0116291	−	0.0267729i
$155$	1.33037	+	9.67919i	0.106858	+	0.777451i
$156$	2.06130	+	8.11700i	0.165036	+	0.649880i
$157$	−8.85522	−	7.20426i	−0.706724	−	0.574962i	0.208445	−	0.978034i	$-0.433160\pi$
$157$	−8.85522	−	7.20426i	−0.706724	−	0.574962i	−0.915168	+	0.403072i	$0.867942\pi$
$158$	0.958908	+	1.57686i	0.0762866	+	0.125448i
$159$	5.66168	−	5.03379i	0.449000	−	0.399206i
$160$	4.91705	−	4.59220i	0.388727	−	0.363046i
$161$	−3.52956	−	6.81175i	−0.278169	−	0.536841i
$162$	−0.189957	+	1.93285i	−0.0149244	+	0.151859i
$163$	−7.75633	+	0.530548i	−0.607523	+	0.0415557i	−0.368764	−	0.929523i	$-0.620219\pi$
$163$	−7.75633	+	0.530548i	−0.607523	+	0.0415557i	−0.238759	+	0.971079i	$0.576741\pi$
$164$	−10.0686	+	14.2640i	−0.786229	+	1.11383i
$165$	−7.03408	−	2.15797i	−0.547603	−	0.167998i
$166$	−0.251652	−	3.67902i	−0.0195320	−	0.285548i
$167$	1.29604	+	6.23691i	0.100291	+	0.482627i	0.999026	+	0.0441337i	$0.0140528\pi$
$167$	1.29604	+	6.23691i	0.100291	+	0.482627i	−0.898735	+	0.438493i	$0.855512\pi$
$168$	1.11752	+	1.09614i	0.0862186	+	0.0845693i
$169$	4.69151	+	5.02338i	0.360885	+	0.386414i
$170$	−0.892032	+	0.387464i	−0.0684157	+	0.0297171i
$171$	16.5664	+	6.81861i	1.26687	+	0.521432i
$172$	−14.4964	+	17.8185i	−1.10534	+	1.35865i
$173$	−1.86802	−	0.127776i	−0.142023	−	0.00971463i	−0.00294210	−	0.999996i	$-0.500937\pi$
$173$	−1.86802	−	0.127776i	−0.142023	−	0.00971463i	−0.139081	+	0.990281i	$0.544415\pi$
$174$	0.0122412	−	0.00596729i	0.000928004	−	0.000452379i
$175$	2.12502	+	0.923028i	0.160637	+	0.0697744i
$176$	1.97541	+	5.55828i	0.148902	+	0.418971i
$177$	−2.66229	−	0.621610i	−0.200110	−	0.0467231i
$178$	2.68966	+	0.369685i	0.201599	+	0.0277091i
$179$	−4.83890	+	23.2860i	−0.361676	+	1.74048i	0.267813	+	0.963471i	$0.413699\pi$
$179$	−4.83890	+	23.2860i	−0.361676	+	1.74048i	−0.629489	+	0.777010i	$0.716736\pi$
$180$	9.67760	−	12.3761i	0.721326	−	0.922464i
$181$	4.14146	+	2.14593i	0.307833	+	0.159506i	0.607016	−	0.794690i	$-0.292366\pi$
$181$	4.14146	+	2.14593i	0.307833	+	0.159506i	−0.299183	+	0.954196i	$0.596714\pi$
$182$	−0.544852	−	0.152660i	−0.0403871	−	0.0113159i
$183$	0.953737	+	0.442335i	0.0705023	+	0.0326984i
$184$	−5.82174	−	2.06905i	−0.429185	−	0.152532i
$185$	13.9881	−	11.3802i	1.02842	−	0.836686i
$186$	−0.812555	+	1.09328i	−0.0595794	+	0.0801635i
$187$		−	2.66377i		−	0.194794i
$188$	−12.5254	+	4.73928i	−0.913511	+	0.345647i
$189$	4.48054	+	3.19759i	0.325911	+	0.232591i
$190$	1.99226	+	2.82238i	0.144533	+	0.204757i
$191$	−17.1316	−	21.0575i	−1.23960	−	1.52367i	−0.765870	−	0.642995i	$-0.777691\pi$
$191$	−17.1316	−	21.0575i	−1.23960	−	1.52367i	−0.473726	−	0.880672i	$-0.657091\pi$
$192$	−11.9544	−	0.292832i	−0.862735	−	0.0211333i
$193$	14.6996	+	13.7284i	1.05810	+	0.988195i	0.999949	−	0.0101130i	$-0.00321914\pi$
$193$	14.6996	+	13.7284i	1.05810	+	0.988195i	0.0581495	+	0.998308i	$0.481480\pi$
$194$	−0.337493	+	1.20453i	−0.0242306	+	0.0864801i
$195$	−1.84336	+	11.3445i	−0.132006	+	0.812394i
$196$	−11.0561	+	3.09777i	−0.789720	+	0.221269i
$197$	22.5138	+	4.67842i	1.60404	+	0.333323i	0.918717	−	0.394916i	$-0.129226\pi$
$197$	22.5138	+	4.67842i	1.60404	+	0.333323i	0.685323	+	0.728239i	$0.259661\pi$
$198$	−0.489444	−	0.901523i	−0.0347833	−	0.0640684i
$199$	−0.124899	+	0.205387i	−0.00885384	+	0.0145595i	−0.858815	−	0.512285i	$-0.828799\pi$
$199$	−0.124899	+	0.205387i	−0.00885384	+	0.0145595i	0.849961	+	0.526845i	$0.176625\pi$
$200$	1.75811	−	0.624832i	0.124317	−	0.0441823i
$201$	18.3063	+	1.70347i	1.29123	+	0.120153i
$202$	−2.56382	+	0.352389i	−0.180390	+	0.0247940i
$203$	0.00263396	−	0.0385071i	0.000184867	−	0.00270267i
$204$	5.31122	+	2.03543i	0.371860	+	0.142509i
$205$	−20.4731	+	12.4500i	−1.42990	+	0.869543i
$206$	−0.795991	−	1.83256i	−0.0554593	−	0.127680i
$207$	−21.3532	−	4.00870i	−1.48415	−	0.278624i
$208$	8.18143	−	4.23928i	0.567280	−	0.293941i
$209$	−9.26435	+	1.92515i	−0.640829	+	0.133166i
$210$	0.398932	+	0.983679i	0.0275289	+	0.0678803i
$211$	0.429188	+	0.302954i	0.0295466	+	0.0208562i	0.591359	−	0.806408i	$-0.298592\pi$
$211$	0.429188	+	0.302954i	0.0295466	+	0.0208562i	−0.561813	+	0.827264i	$0.689896\pi$
$212$	−6.98032	−	4.92725i	−0.479411	−	0.338405i
$213$	6.65936	+	16.4205i	0.456292	+	1.12512i
$214$	1.94147	−	0.403443i	0.132716	−	0.0275788i
$215$	−27.9901	+	14.5033i	−1.90891	+	0.989119i
$216$	4.39480	−	0.580887i	0.299028	−	0.0395243i
$217$	1.53811	+	3.54108i	0.104414	+	0.240384i
$218$	0.738020	−	0.448800i	0.0499850	−	0.0303965i
$219$	17.0217	+	6.52326i	1.15022	+	0.440801i
$220$	−0.566281	+	8.27873i	−0.0381786	+	0.558152i
$221$	−4.12226	+	0.566591i	−0.277293	+	0.0381131i
$222$	2.50332	+	0.232942i	0.168012	+	0.0156341i
$223$	3.25940	−	1.15839i	0.218266	−	0.0775716i	−0.223493	−	0.974705i	$-0.571746\pi$
$223$	3.25940	−	1.15839i	0.218266	−	0.0775716i	0.441759	+	0.897134i	$0.354355\pi$
$224$	1.38135	−	2.27153i	0.0922953	−	0.151773i
$225$	5.76613	−	3.13048i	0.384409	−	0.208699i
$226$	1.97693	+	0.410812i	0.131504	+	0.0273268i
$227$	−9.85729	+	2.76188i	−0.654252	+	0.183313i	−0.580876	−	0.813992i	$-0.697290\pi$
$227$	−9.85729	+	2.76188i	−0.654252	+	0.183313i	−0.0733751	+	0.997304i	$0.523377\pi$
$228$	3.24053	−	19.9430i	0.214610	−	1.32076i
$229$	3.88457	−	13.8642i	0.256699	−	0.916172i	−0.718625	−	0.695397i	$-0.755228\pi$
$229$	3.88457	−	13.8642i	0.256699	−	0.916172i	0.975325	−	0.220775i	$-0.0708586\pi$
$230$	−3.06198	−	2.85969i	−0.201901	−	0.188562i
$231$	−2.90652	−	0.0711972i	−0.191235	−	0.00468443i
$232$	−0.0196166	−	0.0241121i	−0.00128789	−	0.00158303i
$233$	−11.5610	−	16.3782i	−0.757387	−	1.07297i	−0.994828	−	0.101571i	$-0.967613\pi$
$233$	−11.5610	−	16.3782i	−0.757387	−	1.07297i	0.237441	−	0.971402i	$-0.423691\pi$
$234$	−1.29103	+	0.949186i	−0.0843971	+	0.0620502i
$235$	−18.3579	−	0.882756i	−1.19754	−	0.0575846i
$236$			3.08333i			0.200708i
$237$	8.83605	−	11.8888i	0.573963	−	0.772261i
$238$	−0.298108	+	0.242529i	−0.0193235	+	0.0157208i
$239$	3.34371	+	1.18835i	0.216287	+	0.0768683i	0.440810	−	0.897600i	$-0.354691\pi$
$239$	3.34371	+	1.18835i	0.216287	+	0.0768683i	−0.224523	+	0.974469i	$0.572083\pi$
$240$	−15.6817	−	7.27306i	−1.01225	−	0.469474i
$241$	25.0401	+	7.01592i	1.61298	+	0.451935i	0.953896	−	0.300137i	$-0.0970325\pi$
$241$	25.0401	+	7.01592i	1.61298	+	0.451935i	0.659081	+	0.752072i	$0.270946\pi$
$242$	−1.62655	−	0.842813i	−0.104559	−	0.0541781i
$243$	14.9494	−	4.41749i	0.959007	−	0.283382i
$244$	0.241237	−	1.16089i	0.0154436	−	0.0743187i
$245$	−15.6108	−	2.14565i	−0.997336	−	0.137081i
$246$	−3.25324	−	0.759587i	−0.207419	−	0.0484295i
$247$	4.94979	+	13.9274i	0.314948	+	0.886178i
$248$	2.85178	+	1.23870i	0.181088	+	0.0786576i
$249$	−26.6052	+	12.9694i	−1.68604	+	0.821902i
$250$	−1.62356	−	0.111055i	−0.102683	−	0.00702372i
$251$	−9.83702	+	12.0913i	−0.620907	+	0.763197i	−0.985813	−	0.167847i	$-0.946318\pi$
$251$	−9.83702	+	12.0913i	−0.620907	+	0.763197i	0.364906	+	0.931044i	$0.381101\pi$
$252$	2.36288	−	5.74083i	0.148847	−	0.361638i
$253$	10.5254	−	4.57181i	0.661724	−	0.287427i
$254$	0.309568	+	0.331466i	0.0194240	+	0.0207980i
$255$	5.57271	+	5.46610i	0.348976	+	0.342301i
$256$	2.52352	+	12.1438i	0.157720	+	0.758990i
$257$	0.876301	+	12.8111i	0.0546621	+	0.799132i	0.941492	+	0.337036i	$0.109424\pi$
$257$	0.876301	+	12.8111i	0.0546621	+	0.799132i	−0.886830	+	0.462096i	$0.847097\pi$
$258$	−4.20190	−	1.28909i	−0.261599	−	0.0802555i
$259$	4.10919	−	5.82140i	0.255333	−	0.361724i
$260$	12.9320	−	0.884576i	0.802011	−	0.0548590i
$261$	−0.0813094	−	0.0730493i	−0.00503293	−	0.00452164i
$262$	−0.899441	−	1.73584i	−0.0555676	−	0.107241i
$263$	5.59009	−	5.22078i	0.344699	−	0.321927i	−0.490952	−	0.871186i	$-0.663351\pi$
$263$	5.59009	−	5.22078i	0.344699	−	0.321927i	0.835652	+	0.549260i	$0.185090\pi$
$264$	−1.74983	+	1.55577i	−0.107695	+	0.0957513i
$265$	−6.09259	−	10.0188i	−0.374265	−	0.615452i
$266$	1.05894	+	0.861515i	0.0649280	+	0.0528229i
$267$	−5.36355	−	21.1207i	−0.328244	−	1.29256i
$268$	−2.82346	−	20.5422i	−0.172470	−	1.25482i
$269$	−4.82376	+	11.1054i	−0.294110	+	0.677108i	−0.999497	−	0.0317138i	$-0.989903\pi$
$269$	−4.82376	+	11.1054i	−0.294110	+	0.677108i	0.705387	+	0.708822i	$0.250773\pi$
$270$	2.89037	+	0.826005i	0.175902	+	0.0502691i
$271$	21.1346	+	12.8522i	1.28383	+	0.780717i	0.984828	−	0.173534i	$-0.0555188\pi$
$271$	21.1346	+	12.8522i	1.28383	+	0.780717i	0.299006	+	0.954251i	$0.403345\pi$
$272$	0.852173	−	6.20002i	0.0516706	−	0.375931i
$273$	0.508045	+	4.51307i	0.0307483	+	0.273143i
$274$	−0.724790	−	2.58681i	−0.0437862	−	0.156275i
$275$	−1.59434	+	3.07693i	−0.0961420	+	0.185546i
$276$	1.07301	+	24.4797i	0.0645877	+	1.47350i
$277$	−2.53795	+	2.71749i	−0.152491	+	0.163278i	−0.802507	−	0.596642i	$-0.796501\pi$
$277$	−2.53795	+	2.71749i	−0.152491	+	0.163278i	0.650016	+	0.759920i	$0.274762\pi$
$278$	0.858539	−	2.41570i	0.0514917	−	0.144884i
$279$	10.5828	+	2.74588i	0.633577	+	0.164392i
$280$	1.97942	−	1.39723i	0.118293	−	0.0835002i
$281$	31.4173			1.87420			0.937099	−	0.349065i	$-0.113501\pi$
$281$	31.4173			1.87420			0.937099	+	0.349065i	$0.113501\pi$
$282$	−1.74104	−	1.88013i	−0.103677	−	0.111960i
$283$	−20.3504			−1.20971			−0.604854	−	0.796336i	$-0.706769\pi$
$283$	−20.3504			−1.20971			−0.604854	+	0.796336i	$0.706769\pi$
$284$	16.3266	−	11.5246i	0.968805	−	0.683857i
$285$	14.9831	−	23.3319i	0.887524	−	1.38206i
$286$	0.283429	−	0.797493i	0.0167595	−	0.0471567i
$287$	−6.46267	+	6.91983i	−0.381479	+	0.408465i
$288$	−2.65781	−	7.04416i	−0.156613	−	0.415081i
$289$	6.52093	−	12.5848i	0.383584	−	0.740283i
$290$	−0.00568685	−	0.0202966i	−0.000333943	−	0.00119186i
$291$	9.97723	−	1.12316i	0.584876	−	0.0658407i
$292$	2.79942	−	20.3673i	0.163823	−	1.19190i
$293$	19.0325	+	11.5739i	1.11189	+	0.676155i	0.950496	−	0.310736i	$-0.100575\pi$
$293$	19.0325	+	11.5739i	1.11189	+	0.676155i	0.161392	+	0.986890i	$0.448401\pi$
$294$	−1.34431	−	1.73763i	−0.0784020	−	0.101341i
$295$	−1.68584	+	3.88120i	−0.0981536	+	0.225972i
$296$	−0.781398	−	5.68509i	−0.0454178	−	0.330439i
$297$	−5.22908	+	6.35986i	−0.303422	+	0.369036i
$298$	0.770368	+	0.626741i	0.0446262	+	0.0363061i
$299$	−9.31379	−	15.3159i	−0.538631	−	0.885740i
$300$	−4.91675	−	5.53004i	−0.283869	−	0.319277i
$301$	−9.10398	+	8.50253i	−0.524745	+	0.490078i
$302$	0.287099	+	0.554076i	0.0165207	+	0.0318835i
$303$	10.3547	+	18.0066i	0.594862	+	1.03445i
$304$	−22.1790	+	1.51709i	−1.27205	+	0.0870109i
$305$	0.938393	−	1.32940i	0.0537322	−	0.0761212i
$306$	0.0210184	+	1.08812i	0.00120154	+	0.0622036i
$307$	−1.10095	−	16.0954i	−0.0628348	−	0.918612i	−0.917070	−	0.398726i	$-0.869452\pi$
$307$	−1.10095	−	16.0954i	−0.0628348	−	0.918612i	0.854235	−	0.519886i	$-0.174026\pi$
$308$	0.667131	+	3.21041i	0.0380133	+	0.182930i
$309$	−11.2293	+	11.4484i	−0.638815	+	0.651274i
$310$	1.43907	+	1.54087i	0.0817339	+	0.0875157i
$311$	9.60996	−	4.17419i	0.544931	−	0.236697i	−0.107952	−	0.994156i	$-0.534429\pi$
$311$	9.60996	−	4.17419i	0.544931	−	0.236697i	0.652882	+	0.757459i	$0.273560\pi$
$312$	2.77980	+	2.37700i	0.157375	+	0.134571i
$313$	−0.168149	+	0.206683i	−0.00950436	+	0.0116824i	−0.780441	−	0.625229i	$-0.785006\pi$
$313$	−0.168149	+	0.206683i	−0.00950436	+	0.0116824i	0.770937	+	0.636911i	$0.219788\pi$
$314$	−2.45770	−	0.168112i	−0.138696	−	0.00948709i
$315$	6.11318	−	5.93445i	0.344439	−	0.334368i
$316$	−15.3230	−	6.65573i	−0.861988	−	0.374414i
$317$	−2.34706	−	6.60400i	−0.131824	−	0.370918i	0.857917	−	0.513788i	$-0.171758\pi$
$317$	−2.34706	−	6.60400i	−0.131824	−	0.370918i	−0.989741	+	0.142870i	$0.954367\pi$
$318$	0.371716	−	1.59202i	0.0208448	−	0.0892762i
$319$	0.0571947	+	0.00786124i	0.00320229	+	0.000440145i
$320$	−3.76568	+	18.1214i	−0.210508	+	1.01302i
$321$	−8.85715	−	13.2236i	−0.494358	−	0.738068i
$322$	−1.46995	−	0.761667i	−0.0819171	−	0.0424460i
$323$	9.66656	+	2.70844i	0.537862	+	0.150702i
$324$	−8.68514	−	15.2858i	−0.482508	−	0.849212i
$325$	5.10076	+	1.81281i	0.282939	+	0.100557i
$326$	−1.30141	+	1.05878i	−0.0720785	+	0.0586402i
$327$	−5.56435	−	4.13555i	−0.307709	−	0.228697i
$328$			7.62528i			0.421036i
$329$	−7.07924	+	1.62126i	−0.390291	+	0.0893827i
$330$	−1.50865	+	0.494911i	−0.0830486	+	0.0272440i
$331$	−10.8566	−	15.3803i	−0.596732	−	0.845376i	0.400758	−	0.916184i	$-0.368747\pi$
$331$	−10.8566	−	15.3803i	−0.596732	−	0.845376i	−0.997490	+	0.0708078i	$0.977442\pi$
$332$	21.0664	+	25.8941i	1.15617	+	1.42112i
$333$	−5.81854	−	19.3222i	−0.318854	−	1.05885i
$334$	1.00465	+	0.938275i	0.0549718	+	0.0513401i
$335$	7.67759	−	27.4017i	0.419471	−	1.49711i
$336$	−6.74225	−	1.09555i	−0.367820	−	0.0597669i
$337$	−4.28149	+	1.19962i	−0.233228	+	0.0653473i	−0.384425	−	0.923156i	$-0.625600\pi$
$337$	−4.28149	+	1.19962i	−0.233228	+	0.0653473i	0.151197	+	0.988504i	$0.451687\pi$
$338$	1.45225	+	0.301780i	0.0789917	+	0.0164147i
$339$	−2.90775	−	15.9435i	−0.157927	−	0.865932i
$340$	4.57426	−	7.52205i	0.248074	−	0.407941i
$341$	−5.44131	+	1.93384i	−0.294663	+	0.104723i
$342$	3.76919	−	0.859504i	0.203815	−	0.0464767i
$343$	−13.5150	+	1.85759i	−0.729740	+	0.100300i
$344$	−0.684614	+	10.0087i	−0.0369119	+	0.539633i
$345$	−12.0338	+	31.4009i	−0.647881	+	1.69057i
$346$	−0.345231	+	0.209940i	−0.0185597	+	0.0112864i
$347$	−9.54825	−	21.9823i	−0.512577	−	1.18007i	−0.958524	−	0.285011i	$-0.908003\pi$
$347$	−9.54825	−	21.9823i	−0.512577	−	1.18007i	0.445947	−	0.895059i	$-0.352867\pi$
$348$	−0.0593778	+	0.108032i	−0.00318299	+	0.00579114i
$349$	5.96910	−	3.09294i	0.319519	−	0.165561i	−0.292797	−	0.956175i	$-0.594586\pi$
$349$	5.96910	−	3.09294i	0.319519	−	0.165561i	0.612316	+	0.790613i	$0.290238\pi$
$350$	0.489506	−	0.101721i	0.0261652	−	0.00543719i
$351$	10.9543	+	6.73939i	0.584698	+	0.359722i
$352$	3.24878	+	2.29324i	0.173160	+	0.122230i
$353$	−0.269529	−	0.190254i	−0.0143456	−	0.0101262i	0.569485	−	0.822002i	$-0.307143\pi$
$353$	−0.269529	−	0.190254i	−0.0143456	−	0.0101262i	−0.583831	+	0.811875i	$0.698447\pi$
$354$	−0.546716	+	0.221721i	−0.0290577	+	0.0117843i
$355$	26.8526	−	5.58003i	1.42519	−	0.296157i
$356$	−21.8209	+	11.3067i	−1.15651	+	0.599253i
$357$	2.70315	+	1.48573i	0.143066	+	0.0786332i
$358$	2.04475	+	4.70749i	0.108068	+	0.248798i
$359$	2.35654	−	1.43304i	0.124373	−	0.0756332i	−0.456019	−	0.889970i	$-0.650725\pi$
$359$	2.35654	−	1.43304i	0.124373	−	0.0756332i	0.580393	+	0.814337i	$0.302899\pi$
$360$	0.335949	−	6.85320i	0.0177061	−	0.361195i
$361$	1.13692	−	16.6212i	0.0598379	−	0.874800i
$362$	0.997188	−	0.137060i	0.0524110	−	0.00720373i
$363$	−1.36235	+	14.6405i	−0.0715049	+	0.768428i
$364$	4.82631	−	1.71527i	0.252967	−	0.0899046i
$365$	14.6598	−	24.1071i	0.767331	−	1.26182i
$366$	0.223190	−	0.0407050i	0.0116663	−	0.00212768i
$367$	13.9750	+	2.90404i	0.729490	+	0.151590i	0.553556	−	0.832812i	$-0.313271\pi$
$367$	13.9750	+	2.90404i	0.729490	+	0.151590i	0.175934	+	0.984402i	$0.443705\pi$
$368$	25.9608	−	7.27387i	1.35330	−	0.379177i
$369$	4.16349	+	26.4886i	0.216743	+	1.37894i
$370$	1.04988	−	3.74707i	0.0545806	−	0.194801i
$371$	−3.38633	−	3.16261i	−0.175810	−	0.164195i
$372$	0.301958	−	12.3270i	0.0156558	−	0.639124i
$373$	14.7051	+	18.0750i	0.761403	+	0.935890i	0.999374	−	0.0353819i	$-0.0112648\pi$
$373$	14.7051	+	18.0750i	0.761403	+	0.935890i	−0.237970	+	0.971272i	$0.576482\pi$
$374$	−0.331494	−	0.469620i	−0.0171411	−	0.0242835i
$375$	4.07139	+	12.4109i	0.210246	+	0.640899i
$376$	−3.27546	+	4.84560i	−0.168919	+	0.249893i
$377$		−	0.0901827i		−	0.00464464i
$378$	1.18784	+	0.00614940i	0.0610959	+	0.000316291i
$379$	−24.1190	+	19.6222i	−1.23891	+	1.00793i	−0.239594	+	0.970873i	$0.577014\pi$
$379$	−24.1190	+	19.6222i	−1.23891	+	1.00793i	−0.999313	+	0.0370526i	$0.988203\pi$
$380$	−29.4670	−	10.4726i	−1.51162	−	0.537231i
$381$	1.53162	−	3.30240i	0.0784675	−	0.169187i
$382$	−5.64079	−	1.58048i	−0.288608	−	0.0808641i
$383$	−14.6379	−	7.58473i	−0.747960	−	0.387562i	0.0432836	−	0.999063i	$-0.486218\pi$
$383$	−14.6379	−	7.58473i	−0.747960	−	0.387562i	−0.791243	+	0.611501i	$0.790566\pi$
$384$	−9.36705	+	6.27405i	−0.478010	+	0.320171i
$385$	−0.915562	+	4.40593i	−0.0466614	+	0.224547i
$386$	4.29996	+	0.591016i	0.218862	+	0.0300819i
$387$	3.08667	+	35.1420i	0.156904	+	1.78637i
$388$	−3.79202	−	10.6697i	−0.192511	−	0.541673i
$389$	29.0771	+	12.6300i	1.47427	+	0.640365i	0.974213	−	0.225629i	$-0.0724436\pi$
$389$	29.0771	+	12.6300i	1.47427	+	0.640365i	0.500055	+	0.865994i	$0.333313\pi$
$390$	1.08678	+	2.22942i	0.0550315	+	0.112891i
$391$	−12.1462	−	0.830826i	−0.614262	−	0.0420167i
$392$	−3.16462	+	3.88984i	−0.159838	+	0.196467i
$393$	−10.1979	+	11.9261i	−0.514418	+	0.601591i
$394$	4.55137	−	1.97694i	0.229295	−	0.0995967i
$395$	−15.6491	−	16.7561i	−0.787390	−	0.843089i
$396$	8.32578	+	4.11209i	0.418386	+	0.206640i
$397$	−1.41772	−	6.82243i	−0.0711532	−	0.342408i	0.928423	−	0.371525i	$-0.121165\pi$
$397$	−1.41772	−	6.82243i	−0.0711532	−	0.342408i	−0.999576	+	0.0291174i	$0.990730\pi$
$398$	0.00353998	+	0.0517527i	0.000177443	+	0.00259413i
$399$	3.21363	−	10.4751i	0.160883	−	0.524410i
$400$	−4.69522	+	6.65162i	−0.234761	+	0.332581i
$401$	−1.23792	+	0.0846761i	−0.0618188	+	0.00422852i	−0.0991191	−	0.995076i	$-0.531602\pi$
$401$	−1.23792	+	0.0846761i	−0.0618188	+	0.00422852i	0.0373002	+	0.999304i	$0.488124\pi$
$402$	3.43938	−	1.97782i	0.171541	−	0.0986448i
$403$	4.15006	+	8.00925i	0.206729	+	0.398969i
$404$	17.1209	−	15.9898i	0.851796	−	0.795522i
$405$	−2.57491	−	23.9900i	−0.127948	−	1.19207i
$406$	−0.00432767	−	0.00711654i	−0.000214778	−	0.000353188i
$407$	8.26776	+	6.72632i	0.409818	+	0.333411i
$408$	2.40769	−	0.611428i	0.119198	−	0.0302702i
$409$	4.64556	+	33.7990i	0.229708	+	1.67125i	0.647008	+	0.762483i	$0.276020\pi$
$409$	4.64556	+	33.7990i	0.229708	+	1.67125i	−0.417299	+	0.908769i	$0.637023\pi$
$410$	−2.06005	+	4.74270i	−0.101738	+	0.234225i
$411$	−17.0542	+	13.1939i	−0.841222	+	0.650809i
$412$	15.4530	+	9.39718i	0.761315	+	0.462966i
$413$	−0.227683	+	1.65652i	−0.0112036	+	0.0815119i
$414$	−4.26342	+	1.95058i	−0.209536	+	0.0958660i
$415$	12.3599	+	44.1130i	0.606722	+	2.16542i
$416$	2.85783	−	5.51536i	0.140117	−	0.270413i
$417$	−20.5575	+	0.901093i	−1.00671	+	0.0441267i
$418$	−1.39372	+	1.49231i	−0.0681691	+	0.0729913i
$419$	4.94375	−	13.9104i	0.241518	−	0.679566i	−0.758106	−	0.652132i	$-0.773875\pi$
$419$	4.94375	−	13.9104i	0.241518	−	0.679566i	0.999624	−	0.0274344i	$-0.00873372\pi$
$420$	−8.08528	−	5.19216i	−0.394521	−	0.253352i
$421$	21.6701	−	15.2964i	1.05614	−	0.745503i	0.0880495	−	0.996116i	$-0.471937\pi$
$421$	21.6701	−	15.2964i	1.05614	−	0.745503i	0.968087	+	0.250613i	$0.0806323\pi$
$422$	0.113367			0.00551861
$423$	−8.73251	+	18.6210i	−0.424589	+	0.905386i
$424$	−3.73155			−0.181220
$425$	3.00368	−	2.12023i	0.145700	−	0.102846i
$426$	3.21750	+	2.06620i	0.155888	+	0.100108i
$427$	0.215328	−	0.605876i	0.0104205	−	0.0293204i
$428$	−12.2519	+	13.1185i	−0.592216	+	0.634109i
$429$	−6.78665	+	0.297477i	−0.327662	+	0.0143623i
$430$	−3.12976	+	6.04017i	−0.150931	+	0.291283i
$431$	−9.54373	−	34.0620i	−0.459705	−	1.64071i	−0.734063	−	0.679081i	$-0.762378\pi$
$431$	−9.54373	−	34.0620i	−0.459705	−	1.64071i	0.274358	−	0.961628i	$-0.411535\pi$
$432$	−14.2055	+	13.1300i	−0.683461	+	0.631716i
$433$	0.908059	−	6.60662i	0.0436385	−	0.317494i	−0.956065	−	0.293154i	$-0.905295\pi$
$433$	0.908059	−	6.60662i	0.0436385	−	0.317494i	0.999704	−	0.0243398i	$-0.00774838\pi$
$434$	0.711838	+	0.432878i	0.0341693	+	0.0207788i
$435$	−0.133811	+	0.103522i	−0.00641574	+	0.00496351i
$436$	−3.11510	+	7.17167i	−0.149186	+	0.343461i
$437$	5.88878	+	42.8440i	0.281698	+	2.04951i
$438$	3.81270	−	0.968228i	0.182178	−	0.0462637i
$439$	−4.62888	−	3.76588i	−0.220924	−	0.179735i	0.514194	−	0.857674i	$-0.328091\pi$
$439$	−4.62888	−	3.76588i	−0.220924	−	0.179735i	−0.735119	+	0.677938i	$0.762874\pi$
$440$	1.88301	+	3.09648i	0.0897691	+	0.147619i
$441$	−8.86933	+	15.2404i	−0.422349	+	0.725734i
$442$	−0.656241	+	0.612886i	−0.0312142	+	0.0291520i
$443$	11.8670	+	22.9022i	0.563817	+	1.08812i	0.983578	+	0.180482i	$0.0577659\pi$
$443$	11.8670	+	22.9022i	0.563817	+	1.08812i	−0.419762	+	0.907634i	$0.637886\pi$
$444$	−19.7290	+	11.3452i	−0.936296	+	0.538419i
$445$	−33.6495	+	2.30169i	−1.59514	+	0.109111i
$446$	0.430473	−	0.609841i	0.0203835	−	0.0288768i
$447$	2.33787	−	7.62048i	0.110578	−	0.360436i
$448$	0.499103	+	7.29663i	0.0235804	+	0.344733i
$449$	−2.18253	−	10.5029i	−0.103000	−	0.495663i	−0.998699	−	0.0510016i	$-0.983759\pi$
$449$	−2.18253	−	10.5029i	−0.103000	−	0.495663i	0.895699	−	0.444662i	$-0.146676\pi$
$450$	0.626989	−	1.26947i	0.0295566	−	0.0598434i
$451$	−9.66670	−	10.3505i	−0.455187	−	0.487386i
$452$	−16.7647	+	7.28194i	−0.788546	+	0.342514i
$453$	3.25516	−	3.80677i	0.152941	−	0.178858i
$454$	−1.39413	+	1.71361i	−0.0654297	+	0.0804239i
$455$	7.01305	+	0.479706i	0.328777	+	0.0224889i
$456$	−3.86658	−	7.93184i	−0.181069	−	0.371442i
$457$	−11.8654	−	5.15387i	−0.555040	−	0.241088i	0.102207	−	0.994763i	$-0.467410\pi$
$457$	−11.8654	−	5.15387i	−0.555040	−	0.241088i	−0.657247	+	0.753675i	$0.728279\pi$
$458$	−1.04049	−	2.92766i	−0.0486190	−	0.136801i
$459$	8.02995	−	3.43860i	0.374806	−	0.160500i
$460$	37.5727	+	5.16425i	1.75184	+	0.240785i
$461$	1.47725	−	7.10892i	0.0688024	−	0.331095i	−0.930586	−	0.366074i	$-0.880702\pi$
$461$	1.47725	−	7.10892i	0.0688024	−	0.331095i	0.999388	+	0.0349790i	$0.0111364\pi$
$462$	−0.521276	+	0.349151i	−0.0242520	+	0.0162440i
$463$	2.77059	+	1.43561i	0.128760	+	0.0667182i	0.523234	−	0.852189i	$-0.324725\pi$
$463$	2.77059	+	1.43561i	0.128760	+	0.0667182i	−0.394474	+	0.918907i	$0.629073\pi$
$464$	0.130608	+	0.0365947i	0.00606333	+	0.00169886i
$465$	7.12000	−	15.3517i	0.330182	−	0.711919i
$466$	−4.07639	−	1.44875i	−0.188835	−	0.0671120i
$467$	17.7240	−	14.4196i	0.820169	−	0.667257i	−0.125605	−	0.992080i	$-0.540087\pi$
$467$	17.7240	−	14.4196i	0.820169	−	0.667257i	0.945775	+	0.324823i	$0.105305\pi$
$468$	4.59266	−	13.7590i	0.212296	−	0.636012i
$469$		−	11.2448i		−	0.519236i
$470$	−3.34633	+	2.12893i	−0.154355	+	0.0982000i
$471$	6.16316	+	18.7873i	0.283983	+	0.865675i
$472$	0.776561	+	1.10014i	0.0357441	+	0.0506378i
$473$	−11.7589	−	14.4537i	−0.540676	−	0.664580i
$474$	0.0782783	−	3.19559i	0.00359544	−	0.146778i
$475$	−9.54480	−	8.91422i	−0.437946	−	0.409013i
$476$	0.938567	−	3.34979i	0.0430191	−	0.153537i
$477$	−12.9626	+	2.03747i	−0.593518	+	0.0932894i
$478$	0.737378	−	0.206604i	0.0337269	−	0.00944984i
$479$	9.08697	+	1.88829i	0.415194	+	0.0862784i	0.406427	−	0.913683i	$-0.366774\pi$
$479$	9.08697	+	1.88829i	0.415194	+	0.0862784i	0.00876722	+	0.999962i	$0.497209\pi$
$480$	−11.4641	+	2.09080i	−0.523262	+	0.0954317i
$481$	8.65060	−	14.2253i	0.394434	−	0.648618i
$482$	5.28765	−	1.87923i	0.240846	−	0.0855967i
$483$	−1.23118	+	13.2309i	−0.0560208	+	0.602028i
$484$	16.4287	−	2.25807i	0.746757	−	0.102639i
$485$	1.06051	−	15.5040i	0.0481551	−	0.704003i
$486$	2.08584	−	2.63919i	0.0946154	−	0.119716i
$487$	9.60121	−	5.83862i	0.435072	−	0.264573i	−0.284926	−	0.958550i	$-0.591969\pi$
$487$	9.60121	−	5.83862i	0.435072	−	0.264573i	0.719998	+	0.693976i	$0.244143\pi$
$488$	−0.206307	−	0.474966i	−0.00933907	−	0.0215007i
$489$	11.8008	+	6.48605i	0.533648	+	0.293309i
$490$	−3.01918	+	1.56441i	−0.136393	+	0.0706730i
$491$	−19.3660	+	4.02430i	−0.873975	+	0.181614i	−0.619055	−	0.785348i	$-0.712484\pi$
$491$	−19.3660	+	4.02430i	−0.873975	+	0.181614i	−0.254920	+	0.966962i	$0.582049\pi$
$492$	28.0241	−	11.3652i	1.26342	−	0.512383i
$493$	−0.0500396	−	0.0353218i	−0.00225367	−	0.00159081i
$494$	2.60584	+	1.83940i	0.117242	+	0.0827587i
$495$	8.23190	+	9.72838i	0.369997	+	0.437258i
$496$	−13.2835	+	2.76035i	−0.596447	+	0.123943i
$497$	9.62246	−	4.98596i	0.431627	−	0.223651i
$498$	−3.07650	+	5.59739i	−0.137861	+	0.250825i
$499$	0.612681	+	1.41053i	0.0274274	+	0.0631441i	0.930381	−	0.366593i	$-0.119476\pi$
$499$	0.612681	+	1.41053i	0.0274274	+	0.0631441i	−0.902954	+	0.429737i	$0.858606\pi$
$500$	12.5866	−	7.65408i	0.562890	−	0.342301i
$501$	3.94835	−	10.3028i	0.176399	−	0.460293i
$502$	−0.229547	+	3.35586i	−0.0102452	+	0.149779i
$503$	−28.4674	+	3.91276i	−1.26930	+	0.174461i	−0.739207	−	0.673478i	$-0.764800\pi$
$503$	−28.4674	+	3.91276i	−1.26930	+	0.174461i	−0.530093	+	0.847939i	$0.677843\pi$
$504$	−0.602795	−	2.64344i	−0.0268506	−	0.117748i
$505$	30.2938	−	10.7664i	1.34806	−	0.479100i
$506$	1.28667	−	2.11584i	0.0571995	−	0.0940606i
$507$	−2.13602	−	11.7120i	−0.0948638	−	0.520149i
$508$	−4.01970	−	0.835302i	−0.178345	−	0.0370606i
$509$	−16.5149	+	4.62725i	−0.732008	+	0.205099i	−0.615552	−	0.788097i	$-0.711067\pi$
$509$	−16.5149	+	4.62725i	−0.732008	+	0.205099i	−0.116457	+	0.993196i	$0.537154\pi$
$510$	1.66270	+	0.270171i	0.0736254	+	0.0119634i
$511$	3.00797	−	10.7356i	0.133065	−	0.474914i
$512$	11.4703	+	10.7125i	0.506921	+	0.473431i
$513$	−17.7625	−	25.4423i	−0.784235	−	1.12331i
$514$	1.74877	+	2.14953i	0.0771349	+	0.0948116i
$515$	14.3138	+	20.2780i	0.630740	+	0.893555i
$516$	37.8040	−	12.4015i	1.66423	−	0.545948i
$517$	−1.69676	−	10.7298i	−0.0746236	−	0.471894i
$518$		−	1.53768i		−	0.0675617i
$519$	2.60289	+	1.93453i	0.114254	+	0.0849165i
$520$	4.39138	−	3.57265i	0.192575	−	0.156671i
$521$	4.83010	+	1.71662i	0.211611	+	0.0752064i	0.438567	−	0.898698i	$-0.355486\pi$
$521$	4.83010	+	1.71662i	0.211611	+	0.0752064i	−0.226956	+	0.973905i	$0.572877\pi$
$522$	−0.0234254	−	0.00275993i	−0.00102530	−	0.000120799i
$523$	−17.9215	−	5.02138i	−0.783654	−	0.219570i	−0.145377	−	0.989376i	$-0.546439\pi$
$523$	−17.9215	−	5.02138i	−0.783654	−	0.219570i	−0.638277	+	0.769807i	$0.720353\pi$
$524$	15.7132	+	8.14192i	0.686434	+	0.355681i
$525$	−2.23317	−	3.33408i	−0.0974634	−	0.145511i
$526$	0.335825	−	1.61608i	0.0146427	−	0.0704644i
$527$	6.06954	+	0.834239i	0.264393	+	0.0363400i
$528$	2.32309	−	9.94955i	0.101099	−	0.432999i
$529$	−9.86146	−	27.7475i	−0.428759	−	1.20641i
$530$	−2.32092	−	1.00812i	−0.100814	−	0.0437898i
$531$	3.29829	+	3.39763i	0.143134	+	0.147444i
$532$	−12.3286	−	0.843299i	−0.534513	−	0.0365617i
$533$	−13.9616	+	17.1611i	−0.604743	+	0.743329i
$534$	−3.57396	−	3.05608i	−0.154660	−	0.132250i
$535$	−22.5950	+	9.81438i	−0.976866	+	0.424313i
$536$	−6.18113	−	6.61837i	−0.266984	−	0.285870i
$537$	28.8461	−	29.4087i	1.24480	−	1.26908i
$538$	0.531593	+	2.55817i	0.0229186	+	0.110290i
$539$	−0.635583	−	9.29189i	−0.0273765	−	0.400230i
$540$	−25.6873	+	8.97977i	−1.10541	+	0.386428i
$541$	2.92085	−	4.13791i	0.125577	−	0.177903i	−0.749324	−	0.662203i	$-0.769622\pi$
$541$	2.92085	−	4.13791i	0.125577	−	0.177903i	0.874902	+	0.484301i	$0.160926\pi$
$542$	5.32541	−	0.364268i	0.228746	−	0.0156466i
$543$	−4.02742	−	7.00358i	−0.172833	−	0.300552i
$544$	−1.94098	−	3.74592i	−0.0832188	−	0.160605i
$545$	−7.84237	+	7.32427i	−0.335930	+	0.313737i
$546$	0.651199	+	0.732425i	0.0278687	+	0.0313449i
$547$	−5.89068	−	9.68681i	−0.251867	−	0.414178i	0.703009	−	0.711181i	$-0.251839\pi$
$547$	−5.89068	−	9.68681i	−0.251867	−	0.414178i	−0.954877	+	0.297002i	$0.904013\pi$
$548$	18.8638	+	15.3469i	0.805823	+	0.655585i
$549$	−0.976003	−	1.53728i	−0.0416548	−	0.0656097i
$550$	0.101830	+	0.740867i	0.00434204	+	0.0315907i
$551$	−0.0866817	+	0.199561i	−0.00369276	+	0.00850159i
$552$	6.54825	+	8.46413i	0.278712	+	0.360257i
$553$	−7.74081	−	4.70729i	−0.329173	−	0.200174i
$554$	−0.109260	+	0.794927i	−0.00464202	+	0.0337732i
$555$	−31.0373	+	3.49394i	−1.31746	+	0.148309i
$556$	6.26127	+	22.3467i	0.265537	+	0.947713i
$557$	0.0633142	−	0.122191i	0.00268271	−	0.00517739i	−0.886540	−	0.462652i	$-0.846898\pi$
$557$	0.0633142	−	0.122191i	0.00268271	−	0.00517739i	0.889223	+	0.457474i	$0.151246\pi$
$558$	2.20745	−	0.832887i	0.0934490	−	0.0352589i
$559$	−19.8663	+	21.2716i	−0.840255	+	0.899694i
$560$	−3.54052	+	9.96207i	−0.149614	+	0.420974i
$561$	−2.49306	+	3.88222i	−0.105257	+	0.163907i
$562$	5.53884	−	3.90974i	0.233642	−	0.164922i
$563$	−20.4541			−0.862040			−0.431020	−	0.902342i	$-0.641846\pi$
$563$	−20.4541			−0.862040			−0.431020	+	0.902342i	$0.641846\pi$
$564$	22.6903	+	4.81566i	0.955435	+	0.202776i
$565$	−25.0844			−1.05531
$566$	−3.58776	+	2.53252i	−0.150805	+	0.106450i
$567$	−3.53733	−	8.85363i	−0.148554	−	0.371817i
$568$	2.92279	−	8.22396i	0.122638	−	0.345070i
$569$	9.36640	−	10.0290i	0.392660	−	0.420436i	−0.503620	−	0.863925i	$-0.667999\pi$
$569$	9.36640	−	10.0290i	0.392660	−	0.420436i	0.896280	+	0.443489i	$0.146260\pi$
$570$	−0.262031	−	5.97797i	−0.0109753	−	0.250390i
$571$	4.99416	−	9.63829i	0.208999	−	0.403350i	−0.760178	−	0.649715i	$-0.774888\pi$
$571$	4.99416	−	9.63829i	0.208999	−	0.403350i	0.969177	+	0.246365i	$0.0792362\pi$
$572$	2.06703	+	7.37732i	0.0864268	+	0.308461i
$573$	5.25973	+	46.7232i	0.219729	+	1.95189i
$574$	−0.278221	+	2.02421i	−0.0116127	+	0.0844889i
$575$	13.5329	+	8.22954i	0.564361	+	0.343196i
$576$	17.1485	+	11.6151i	0.714520	+	0.483963i
$577$	9.46150	−	21.7826i	0.393887	−	0.906820i	−0.600362	−	0.799729i	$-0.704977\pi$
$577$	9.46150	−	21.7826i	0.393887	−	0.906820i	0.994249	−	0.107091i	$-0.0341537\pi$
$578$	−0.416490	−	3.03019i	−0.0173237	−	0.126039i
$579$	−8.57472	−	33.7656i	−0.356353	−	1.40325i
$580$	0.148009	+	0.120415i	0.00614575	+	0.00499994i
$581$	9.40581	+	15.4672i	0.390219	+	0.641687i
$582$	1.61920	−	1.43963i	0.0671182	−	0.0596747i
$583$	5.06519	−	4.73055i	0.209779	−	0.195919i
$584$	−4.13082	−	7.97211i	−0.170934	−	0.329888i
$585$	13.3040	−	14.8084i	0.550053	−	0.612251i
$586$	4.79573	−	0.328037i	0.198110	−	0.0135511i
$587$	−10.8840	+	15.4191i	−0.449229	+	0.636413i	−0.977067	−	0.212932i	$-0.931699\pi$
$587$	−10.8840	+	15.4191i	−0.449229	+	0.636413i	0.527838	+	0.849345i	$0.323003\pi$
$588$	19.0125	+	5.83282i	0.784064	+	0.240542i
$589$	−1.48516	−	21.7123i	−0.0611949	−	0.894638i
$590$	0.185785	+	0.894048i	0.00764866	+	0.0368074i
$591$	−28.4333	−	27.8894i	−1.16959	−	1.14722i
$592$	17.0917	+	18.3007i	0.702464	+	0.752155i
$593$	3.77445	−	1.63948i	0.154998	−	0.0673252i	−0.319477	−	0.947594i	$-0.603507\pi$
$593$	3.77445	−	1.63948i	0.154998	−	0.0673252i	0.474476	+	0.880269i	$0.342638\pi$
$594$	−0.130426	+	1.77197i	−0.00535144	+	0.0727049i
$595$	3.01297	−	3.70344i	0.123520	−	0.151826i
$596$	−8.96889	−	0.613489i	−0.367380	−	0.0251295i
$597$	0.374255	−	0.182440i	0.0153172	−	0.00746677i
$598$	−3.54801	−	1.54112i	−0.145089	−	0.0630209i
$599$	−6.12465	−	17.2331i	−0.250246	−	0.704126i	−0.999141	−	0.0414369i	$-0.986806\pi$
$599$	−6.12465	−	17.2331i	−0.250246	−	0.704126i	0.748895	−	0.662689i	$-0.230585\pi$
$600$	−3.14709	−	0.734802i	−0.128479	−	0.0299982i
$601$	−33.7892	−	4.64422i	−1.37829	−	0.189442i	−0.591322	−	0.806436i	$-0.701394\pi$
$601$	−33.7892	−	4.64422i	−1.37829	−	0.189442i	−0.786968	+	0.616994i	$0.788350\pi$
$602$	−0.546923	+	2.63194i	−0.0222909	+	0.107270i
$603$	−25.0857	−	19.6159i	−1.02157	−	0.798820i
$604$	−5.01561	−	2.59888i	−0.204082	−	0.105747i
$605$	21.9145	+	6.14016i	0.890952	+	0.249633i
$606$	4.06636	+	1.88595i	0.165185	+	0.0766113i
$607$	38.8208	+	13.7969i	1.57569	+	0.560000i	0.971541	−	0.236871i	$-0.0761220\pi$
$607$	38.8208	+	13.7969i	1.57569	+	0.560000i	0.604149	+	0.796872i	$0.293513\pi$
$608$	−11.6252	+	9.45781i	−0.471464	+	0.383565i
$609$	−0.0398781	+	0.0536556i	−0.00161594	+	0.00217424i
$610$		−	0.351151i		−	0.0142177i
$611$	−16.2437	+	4.90804i	−0.657150	+	0.198558i
$612$	−5.83567	−	7.93733i	−0.235893	−	0.320847i
$613$	21.6669	+	30.6950i	0.875117	+	1.23976i	0.969714	+	0.244243i	$0.0785394\pi$
$613$	21.6669	+	30.6950i	0.875117	+	1.23976i	−0.0945969	+	0.995516i	$0.530156\pi$
$614$	−2.19710	−	2.70059i	−0.0886676	−	0.108987i
$615$	41.4899	+	1.01632i	1.67304	+	0.0409822i
$616$	1.04660	+	0.977456i	0.0421687	+	0.0393828i
$617$	3.43617	−	12.2638i	0.138335	−	0.493724i	−0.861568	−	0.507642i	$-0.830517\pi$
$617$	3.43617	−	12.2638i	0.138335	−	0.493724i	0.999903	+	0.0139181i	$0.00443042\pi$
$618$	−0.555028	+	3.41578i	−0.0223265	+	0.137403i
$619$	0.156339	−	0.0438042i	0.00628380	−	0.00176064i	−0.266653	−	0.963792i	$-0.585918\pi$
$619$	0.156339	−	0.0438042i	0.00628380	−	0.00176064i	0.272937	+	0.962032i	$0.412005\pi$
$620$	−18.6862	−	3.88304i	−0.750456	−	0.155947i
$621$	27.3687	+	25.8272i	1.09827	+	1.03641i
$622$	1.17477	−	1.93182i	0.0471039	−	0.0774590i
$623$	−12.5582	+	4.46318i	−0.503133	+	0.178814i
$624$	−15.8914	−	1.47875i	−0.636163	−	0.0591972i
$625$	30.8619	−	4.24187i	1.23448	−	0.169675i
$626$	−0.00392377	+	0.0573635i	−0.000156825	+	0.00229271i
$627$	15.3038	+	5.86491i	0.611175	+	0.234222i
$628$	19.0532	−	11.5865i	0.760307	−	0.462353i
$629$	−4.50501	−	10.3716i	−0.179627	−	0.413542i
$630$	0.339232	−	1.80700i	0.0135153	−	0.0719924i
$631$	−18.6769	+	9.67759i	−0.743515	+	0.385259i	−0.789554	−	0.613681i	$-0.789688\pi$
$631$	−18.6769	+	9.67759i	−0.743515	+	0.385259i	0.0460387	+	0.998940i	$0.485340\pi$
$632$	−7.14357	+	1.48445i	−0.284156	+	0.0590483i
$633$	−0.341966	−	0.843215i	−0.0135919	−	0.0335148i
$634$	−1.23562	−	0.872198i	−0.0490729	−	0.0346394i
$635$	−4.60316	−	3.24926i	−0.182671	−	0.128943i
$636$	5.56174	+	13.7141i	0.220537	+	0.543797i
$637$	−14.2443	+	2.96000i	−0.564379	+	0.117279i
$638$	0.0110617	−	0.00573170i	0.000437936	−	0.000226920i
$639$	5.66280	−	30.1642i	0.224017	−	1.19328i
$640$	6.95211	+	16.0054i	0.274806	+	0.632668i
$641$	8.38262	−	5.09759i	0.331094	−	0.201343i	−0.344191	−	0.938900i	$-0.611847\pi$
$641$	8.38262	−	5.09759i	0.331094	−	0.201343i	0.675285	+	0.737557i	$0.264021\pi$
$642$	−3.20712	−	1.22907i	−0.126575	−	0.0485076i
$643$	−0.646926	+	9.45772i	−0.0255123	+	0.372976i	0.967328	+	0.253528i	$0.0815909\pi$
$643$	−0.646926	+	9.45772i	−0.0255123	+	0.372976i	−0.992840	+	0.119448i	$0.961887\pi$
$644$	14.8469	−	2.04066i	0.585050	−	0.0804133i
$645$	54.3672	+	5.05906i	2.14071	+	0.199200i
$646$	2.04126	−	0.725463i	0.0803122	−	0.0285430i
$647$	−21.3151	+	35.0511i	−0.837981	+	1.37800i	0.0862917	+	0.996270i	$0.472498\pi$
$647$	−21.3151	+	35.0511i	−0.837981	+	1.37800i	−0.924273	+	0.381732i	$0.875328\pi$
$648$	−6.94871	−	3.26657i	−0.272971	−	0.128323i
$649$	−2.44876	−	0.508858i	−0.0961222	−	0.0199744i
$650$	1.12485	−	0.315170i	0.0441204	−	0.0123620i
$651$	1.07249	−	6.60036i	0.0420342	−	0.258689i
$652$	4.09737	−	14.6237i	0.160465	−	0.572708i
$653$	−14.2722	−	13.3293i	−0.558513	−	0.521615i	0.351504	−	0.936186i	$-0.385670\pi$
$653$	−14.2722	−	13.3293i	−0.558513	−	0.521615i	−0.910017	+	0.414572i	$0.863931\pi$
$654$	−1.49564	−	0.0366367i	−0.0584842	−	0.00143261i
$655$	15.3276	+	18.8401i	0.598899	+	0.736145i
$656$	−19.1884	−	27.1837i	−0.749179	−	1.06135i
$657$	−18.7024	−	25.4380i	−0.729652	−	0.992429i
$658$	−1.04631	+	1.16681i	−0.0407893	+	0.0454868i
$659$			1.04664i			0.0407715i	0.999792	+	0.0203857i	$0.00648943\pi$
$659$			1.04664i			0.0407715i	−0.999792	+	0.0203857i	$0.993511\pi$
$660$	8.57351	−	11.5356i	0.333723	−	0.449021i
$661$	25.3871	−	20.6540i	0.987445	−	0.803346i	0.00696676	−	0.999976i	$-0.497782\pi$
$661$	25.3871	−	20.6540i	0.987445	−	0.803346i	0.980478	+	0.196630i	$0.0629998\pi$
$662$	−3.82801	−	1.36047i	−0.148780	−	0.0528764i
$663$	6.53813	+	3.03233i	0.253920	+	0.117766i
$664$	14.0381	+	3.93330i	0.544785	+	0.152642i
$665$	−15.0578	−	7.80231i	−0.583915	−	0.302561i
$666$	−3.43036	−	2.68239i	−0.132924	−	0.103940i
$667$	0.0536846	−	0.258345i	0.00207868	−	0.0100031i
$668$	−12.3277	−	1.69441i	−0.476975	−	0.0655587i
$669$	−5.83446	−	1.36227i	−0.225573	−	0.0526683i
$670$	−2.05646	−	5.78633i	−0.0794481	−	0.223545i
$671$	0.882162	+	0.383177i	0.0340555	+	0.0147924i
$672$	−4.13916	+	2.01774i	−0.159672	+	0.0778360i
$673$	−42.3492	−	2.89677i	−1.63244	−	0.111662i	−0.776980	−	0.629526i	$-0.783249\pi$
$673$	−42.3492	−	2.89677i	−1.63244	−	0.111662i	−0.855463	+	0.517863i	$0.826728\pi$
$674$	−0.605536	+	0.744303i	−0.0233244	+	0.0286695i
$675$	−11.3335	−	0.834203i	−0.436227	−	0.0321085i
$676$	−12.3153	+	5.34927i	−0.473664	+	0.205741i
$677$	9.07124	+	9.71293i	0.348636	+	0.373298i	0.880918	−	0.473269i	$-0.156926\pi$
$677$	9.07124	+	9.71293i	0.348636	+	0.373298i	−0.532282	+	0.846567i	$0.678665\pi$
$678$	−2.49673	−	2.44897i	−0.0958864	−	0.0940521i
$679$	−1.24937	−	6.01232i	−0.0479466	−	0.230732i
$680$	−0.262385	−	3.83594i	−0.0100620	−	0.147102i
$681$	16.9511	+	5.20039i	0.649566	+	0.199279i
$682$	−0.718640	+	1.01808i	−0.0275181	+	0.0389843i
$683$	−10.3493	+	0.707909i	−0.396003	+	0.0270874i	−0.264887	−	0.964280i	$-0.585335\pi$
$683$	−10.3493	+	0.707909i	−0.396003	+	0.0270874i	−0.131117	+	0.991367i	$0.541856\pi$
$684$	−23.3878	+	26.0324i	−0.894255	+	0.995374i
$685$	15.3541	+	29.6322i	0.586652	+	1.13219i
$686$	−2.15151	+	2.00937i	−0.0821450	+	0.0767181i
$687$	−18.6372	+	16.5703i	−0.711052	+	0.632196i
$688$	−22.7454	−	37.4033i	−0.867162	−	1.42599i
$689$	−8.39805	−	6.83232i	−0.319940	−	0.260291i
$690$	1.78615	+	7.03352i	0.0679975	+	0.267761i
$691$	3.19302	+	23.2309i	0.121468	+	0.883746i	0.947417	+	0.320001i	$0.103683\pi$
$691$	3.19302	+	23.2309i	0.121468	+	0.883746i	−0.825949	+	0.563745i	$0.809360\pi$
$692$	1.45718	−	3.35477i	0.0553937	−	0.127529i
$693$	4.16937	+	2.82402i	0.158381	+	0.107276i
$694$	−4.41894	−	2.68722i	−0.167741	−	0.102005i
$695$	−4.33683	+	31.5528i	−0.164505	+	1.19687i
$696$	0.00602270	+	0.0535008i	0.000228290	+	0.00202794i
$697$	4.05384	+	14.4683i	0.153550	+	0.548027i
$698$	0.667445	−	1.28811i	0.0252632	−	0.0487557i
$699$	1.52056	+	34.6900i	0.0575128	+	1.31210i
$700$	−3.08908	+	3.30760i	−0.116756	+	0.125015i
$701$	−8.64571	+	24.3267i	−0.326544	+	0.918807i	0.659409	+	0.751784i	$0.270807\pi$
$701$	−8.64571	+	24.3267i	−0.326544	+	0.918807i	−0.985953	+	0.167022i	$0.946585\pi$
$702$	2.76992	−	0.175066i	0.104544	−	0.00660744i
$703$	−32.8156	+	23.1638i	−1.23766	+	0.873638i
$704$	−10.9396			−0.412302
$705$	25.9289	+	18.4680i	0.976538	+	0.695544i
$706$	−0.0711939			−0.00267942
$707$	10.3789	−	7.32624i	0.390339	−	0.275532i
$708$	2.88574	−	4.49370i	0.108453	−	0.168883i
$709$	−14.0499	+	39.5327i	−0.527655	+	1.48468i	0.316506	+	0.948591i	$0.397490\pi$
$709$	−14.0499	+	39.5327i	−0.527655	+	1.48468i	−0.844161	+	0.536090i	$0.819901\pi$
$710$	4.03968	−	4.32544i	0.151606	−	0.162331i
$711$	−24.0047	+	9.05714i	−0.900248	+	0.339669i
$712$	−4.93804	+	9.52999i	−0.185061	+	0.357152i
$713$	7.12079	+	25.4144i	0.266676	+	0.951778i
$714$	0.661455	−	0.0744614i	0.0247543	−	0.00278665i
$715$	−1.43172	+	10.4165i	−0.0535432	+	0.389556i
$716$	−39.6959	−	24.1396i	−1.48350	−	0.902139i
$717$	−3.76098	−	4.86136i	−0.140456	−	0.181551i
$718$	0.237120	−	0.545905i	0.00884924	−	0.0203730i
$719$	1.49298	+	10.8622i	0.0556788	+	0.405093i	0.997599	+	0.0692561i	$0.0220626\pi$
$719$	1.49298	+	10.8622i	0.0556788	+	0.405093i	−0.941920	+	0.335837i	$0.890981\pi$
$720$	16.0478	+	25.2767i	0.598068	+	0.942006i
$721$	7.60820	+	6.18973i	0.283344	+	0.230518i
$722$	−1.86799	−	3.07179i	−0.0695195	−	0.114320i
$723$	−29.9276	−	33.6606i	−1.11302	−	1.25185i
$724$	−6.65910	+	6.21916i	−0.247483	+	0.231133i
$725$	0.0366599	+	0.0707504i	0.00136151	+	0.00262760i
$726$	1.58176	+	2.75065i	0.0587048	+	0.102086i
$727$	32.8972	−	2.25023i	1.22009	−	0.0834565i	0.556048	−	0.831150i	$-0.312317\pi$
$727$	32.8972	−	2.25023i	1.22009	−	0.0834565i	0.664044	+	0.747694i	$0.268839\pi$
$728$	1.29003	−	1.82755i	0.0478116	−	0.0677336i
$729$	−25.9220	−	7.55330i	−0.960072	−	0.279752i
$730$	−0.415501	−	6.07440i	−0.0153784	−	0.224824i
$731$	4.02194	+	19.3547i	0.148757	+	0.715858i
$732$	−1.43808	+	1.46613i	−0.0531530	+	0.0541897i
$733$	−16.9750	−	18.1758i	−0.626986	−	0.671338i	0.335697	−	0.941970i	$-0.391028\pi$
$733$	−16.9750	−	18.1758i	−0.626986	−	0.671338i	−0.962683	+	0.270632i	$0.912767\pi$
$734$	2.82518	−	1.22715i	0.104279	−	0.0452949i
$735$	20.7432	+	17.7375i	0.765126	+	0.654257i
$736$	11.4700	−	14.0985i	0.422790	−	0.519678i
$737$	16.7805	+	1.14781i	0.618116	+	0.0422803i
$738$	4.03041	+	4.15179i	0.148361	+	0.152829i
$739$	−22.6727	−	9.84816i	−0.834031	−	0.362271i	−0.0621724	−	0.998065i	$-0.519803\pi$
$739$	−22.6727	−	9.84816i	−0.834031	−	0.362271i	−0.771858	+	0.635795i	$0.780672\pi$
$740$	11.7963	+	33.1916i	0.433640	+	1.22015i
$741$	5.82095	−	24.9306i	0.213838	−	0.915847i
$742$	−0.990580	−	0.136152i	−0.0363653	−	0.00499830i
$743$	4.02785	−	19.3831i	0.147768	−	0.711096i	−0.838361	−	0.545115i	$-0.816486\pi$
$743$	4.02785	−	19.3831i	0.147768	−	0.711096i	0.986129	−	0.165981i	$-0.0530792\pi$
$744$	−2.99690	−	4.47433i	−0.109872	−	0.164037i
$745$	−10.9543	−	5.67608i	−0.401336	−	0.207955i
$746$	4.84186	+	1.35663i	0.177273	+	0.0496696i
$747$	50.9131	+	5.99847i	1.86281	+	0.219473i
$748$	4.90304	+	1.74254i	0.179273	+	0.0637136i
$749$	−7.55102	+	6.14321i	−0.275908	+	0.224468i
$750$	2.26227	+	1.68137i	0.0826064	+	0.0613950i
$751$			23.1861i			0.846074i	0.906112	+	0.423037i	$0.139036\pi$
$751$			23.1861i			0.846074i	−0.906112	+	0.423037i	$0.860964\pi$
$752$	−0.516696	−	25.5167i	−0.0188420	−	0.930499i
$753$	25.6531	−	8.41545i	0.934850	−	0.306676i
$754$	−0.0112228	−	0.0158991i	−0.000408711	−	0.000579012i
$755$	−4.89253	−	6.01373i	−0.178057	−	0.218862i
$756$	−8.81663	+	6.15532i	−0.320658	+	0.223867i
$757$	13.0128	+	12.1531i	0.472957	+	0.441711i	0.882312	−	0.470664i	$-0.155986\pi$
$757$	13.0128	+	12.1531i	0.472957	+	0.441711i	−0.409356	+	0.912375i	$0.634246\pi$
$758$	−1.81025	+	6.46087i	−0.0657513	+	0.234670i
$759$	−19.6187	−	3.18783i	−0.712113	−	0.115711i
$760$	−13.1514	+	3.68486i	−0.477053	+	0.133664i
$761$	−19.0986	−	3.96873i	−0.692323	−	0.143866i	−0.155846	−	0.987781i	$-0.549810\pi$
$761$	−19.0986	−	3.96873i	−0.692323	−	0.143866i	−0.536477	+	0.843915i	$0.680245\pi$
$762$	−0.140944	−	0.772813i	−0.00510587	−	0.0279961i
$763$	−2.20316	+	3.62295i	−0.0797599	+	0.131159i
$764$	49.9662	−	17.7580i	1.80771	−	0.642462i
$765$	−3.00594	−	13.1820i	−0.108680	−	0.476595i
$766$	−3.52453	+	0.484435i	−0.127346	+	0.0175034i
$767$	−0.266614	+	3.89776i	−0.00962689	+	0.140740i
$768$	7.68780	−	20.0604i	0.277410	−	0.723868i
$769$	15.8564	−	9.64249i	0.571796	−	0.347717i	−0.203735	−	0.979026i	$-0.565308\pi$
$769$	15.8564	−	9.64249i	0.571796	−	0.347717i	0.775531	+	0.631309i	$0.217482\pi$
$770$	0.386885	+	0.890699i	0.0139424	+	0.0320986i
$771$	10.7129	−	19.4912i	0.385817	−	0.701958i
$772$	−34.8851	+	18.0760i	−1.25554	+	0.650569i
$773$	38.3482	−	7.96885i	1.37929	−	0.286619i	0.545226	−	0.838289i	$-0.316444\pi$
$773$	38.3482	−	7.96885i	1.37929	−	0.286619i	0.834063	+	0.551670i	$0.186009\pi$
$774$	4.91743	+	5.81137i	0.176753	+	0.208885i
$775$	−6.51164	−	4.59641i	−0.233905	−	0.165108i
$776$	−4.04025	−	2.85192i	−0.145036	−	0.102378i
$777$	−11.4371	+	4.63834i	−0.410305	+	0.166400i
$778$	6.69801	−	1.39186i	0.240135	−	0.0499007i
$779$	47.3898	−	24.5554i	1.69792	−	0.879790i
$780$	−19.6752	−	10.8141i	−0.704487	−	0.387207i
$781$	6.45827	+	14.8684i	0.231095	+	0.532034i
$782$	−2.24476	+	1.36507i	−0.0802726	+	0.0488148i
$783$	0.0501336	+	0.182562i	0.00179163	+	0.00652423i
$784$	1.49325	−	21.8306i	0.0533304	−	0.779663i
$785$	30.3187	−	4.16721i	1.08212	−	0.148734i
$786$	−0.313743	+	3.37164i	−0.0111909	+	0.120263i
$787$	14.7269	−	5.23395i	0.524958	−	0.186570i	−0.0591451	−	0.998249i	$-0.518837\pi$
$787$	14.7269	−	5.23395i	0.524958	−	0.186570i	0.584104	+	0.811679i	$0.301446\pi$
$788$	−23.3390	+	38.3794i	−0.831418	+	1.36721i
$789$	−13.0333	+	2.37699i	−0.463997	+	0.0846231i
$790$	−4.84413	−	1.00662i	−0.172347	−	0.0358140i
$791$	−9.54455	+	2.67426i	−0.339365	+	0.0950857i
$792$	4.00631	−	0.629713i	0.142358	−	0.0223759i
$793$	0.405339	−	1.44667i	0.0143940	−	0.0513729i
$794$	−1.09896	−	1.02636i	−0.0390007	−	0.0364241i
$795$	−0.497355	+	20.3038i	−0.0176394	+	0.720100i
$796$	−0.296340	−	0.364251i	−0.0105035	−	0.0129105i
$797$	8.47640	+	12.0083i	0.300250	+	0.425357i	0.938926	−	0.344118i	$-0.111822\pi$
$797$	8.47640	+	12.0083i	0.300250	+	0.425357i	−0.638677	+	0.769475i	$0.720518\pi$
$798$	−0.737016	−	2.24667i	−0.0260901	−	0.0795312i
$799$	−3.63884	+	10.9355i	−0.128733	+	0.386869i
$800$			5.48865i			0.194053i
$801$	−11.9502	+	35.8014i	−0.422241	+	1.26498i
$802$	−0.207707	+	0.168982i	−0.00733438	+	0.00596696i
$803$	15.7135	+	5.58459i	0.554518	+	0.197076i
$804$	−15.1108	+	32.5811i	−0.532918	+	1.14905i
$805$	19.8046	+	5.54898i	0.698020	+	0.195576i
$806$	1.72837	+	0.895568i	0.0608791	+	0.0315450i
$807$	17.4239	−	11.6706i	0.613352	−	0.410823i
$808$	2.08160	−	10.0172i	0.0732303	−	0.352404i
$809$	−43.8744	−	6.03040i	−1.54254	−	0.212018i	−0.685811	−	0.727780i	$-0.740552\pi$
$809$	−43.8744	−	6.03040i	−1.54254	−	0.212018i	−0.856732	+	0.515762i	$0.827509\pi$
$810$	−3.43940	−	3.90898i	−0.120848	−	0.137348i
$811$	−9.22527	−	25.9574i	−0.323943	−	0.911489i	−0.986685	−	0.162641i	$-0.947999\pi$
$811$	−9.22527	−	25.9574i	−0.323943	−	0.911489i	0.662742	−	0.748848i	$-0.269393\pi$
$812$	0.0691547	+	0.0300381i	0.00242685	+	0.00105413i
$813$	−18.7733	−	38.5112i	−0.658407	−	1.35065i
$814$	2.29466	+	0.156959i	0.0804277	+	0.00550141i
$815$	13.1533	−	16.1676i	0.460740	−	0.566326i
$816$	−7.04467	+	8.23844i	−0.246613	+	0.288403i
$817$	64.4071	−	27.9759i	2.25332	−	0.978755i
$818$	5.02514	+	5.38061i	0.175700	+	0.188129i
$819$	3.48342	−	7.05290i	0.121720	−	0.246448i
$820$	−9.52316	−	45.8280i	−0.332563	−	1.60038i
$821$	−0.205698	−	3.00720i	−0.00717892	−	0.104952i	0.992698	−	0.120624i	$-0.0384895\pi$
$821$	−0.205698	−	3.00720i	−0.00717892	−	0.104952i	−0.999877	+	0.0156719i	$0.995011\pi$
$822$	−1.36472	+	4.44840i	−0.0475999	+	0.155156i
$823$	29.4758	−	41.7577i	1.02746	−	1.45558i	0.142569	−	0.989785i	$-0.454464\pi$
$823$	29.4758	−	41.7577i	1.02746	−	1.45558i	0.884892	−	0.465796i	$-0.154232\pi$
$824$	7.88040	−	0.539034i	0.274527	−	0.0187781i
$825$	5.20336	−	2.99220i	0.181158	−	0.104175i
$826$	0.166006	+	0.320377i	0.00577608	+	0.0111473i
$827$	−19.7487	+	18.4440i	−0.686729	+	0.641360i	−0.945895	−	0.324473i	$-0.894813\pi$
$827$	−19.7487	+	18.4440i	−0.686729	+	0.641360i	0.259166	+	0.965833i	$0.416552\pi$
$828$	21.3471	−	36.6813i	0.741863	−	1.27476i
$829$	−5.13212	−	8.43941i	−0.178246	−	0.293113i	0.752633	−	0.658440i	$-0.228783\pi$
$829$	−5.13212	−	8.43941i	−0.178246	−	0.293113i	−0.930879	+	0.365327i	$0.880957\pi$
$830$	7.66869	+	6.23894i	0.266184	+	0.216557i
$831$	6.24219	−	1.58519i	0.216539	−	0.0549898i
$832$	2.32689	+	16.9294i	0.0806704	+	0.586921i
$833$	−3.93664	+	9.06306i	−0.136397	+	0.314017i
$834$	−3.51214	+	2.71715i	−0.121615	+	0.0940873i
$835$	−14.5914	−	8.87320i	−0.504955	−	0.307070i
$836$	2.51689	−	18.3117i	0.0870484	−	0.633324i
$837$	−12.8536	−	13.9065i	−0.444287	−	0.480680i
$838$	−0.859505	−	3.06761i	−0.0296911	−	0.105969i
$839$	−10.2344	+	19.7514i	−0.353330	+	0.681895i	−0.996479	−	0.0838456i	$-0.973280\pi$
$839$	−10.2344	+	19.7514i	−0.353330	+	0.681895i	0.643149	+	0.765741i	$0.277628\pi$
$840$	−4.19252	+	0.183770i	−0.144656	+	0.00634066i
$841$	−19.7931	+	21.1933i	−0.682522	+	0.730803i
$842$	1.91685	−	5.39350i	0.0660590	−	0.185872i
$843$	−45.7880	−	29.4039i	−1.57702	−	1.01273i
$844$	−0.838390	+	0.591801i	−0.0288586	+	0.0203706i
$845$	−18.4268			−0.633903
$846$	0.777772	+	4.36959i	0.0267403	+	0.150230i
$847$	8.99303			0.309004
$848$	13.3028	−	9.39013i	0.456819	−	0.322458i
$849$	29.6591	+	19.0463i	1.01790	+	0.653668i
$850$	0.265693	−	0.747590i	0.00911321	−	0.0256421i
$851$	33.2494	−	35.6014i	1.13977	−	1.22040i
$852$	−34.5807	+	1.51577i	−1.18471	+	0.0519293i
$853$	16.4643	−	31.7747i	0.563729	−	1.08795i	−0.419872	−	0.907584i	$-0.637925\pi$
$853$	16.4643	−	31.7747i	0.563729	−	1.08795i	0.983600	−	0.180363i	$-0.0577273\pi$
$854$	−0.0374363	−	0.133612i	−0.00128105	−	0.00457211i
$855$	−43.6733	+	19.9813i	−1.49360	+	0.683345i
$856$	−1.06747	+	7.76643i	−0.0364854	+	0.265451i
$857$	−6.29374	−	3.82731i	−0.214990	−	0.130738i	0.407960	−	0.913000i	$-0.366240\pi$
$857$	−6.29374	−	3.82731i	−0.214990	−	0.130738i	−0.622951	+	0.782261i	$0.714066\pi$
$858$	−1.15946	+	0.897013i	−0.0395833	+	0.0306235i
$859$	−14.4062	+	33.1664i	−0.491533	+	1.13162i	0.476129	+	0.879375i	$0.342039\pi$
$859$	−14.4062	+	33.1664i	−0.491533	+	1.13162i	−0.967663	+	0.252248i	$0.918830\pi$
$860$	−8.38528	−	61.0074i	−0.285936	−	2.08034i
$861$	15.8952	−	4.03655i	0.541706	−	0.137565i
$862$	−5.92141	−	4.81743i	−0.201684	−	0.164082i
$863$	10.2392	+	16.8376i	0.348546	+	0.573160i	0.979198	−	0.202906i	$-0.0650386\pi$
$863$	10.2392	+	16.8376i	0.348546	+	0.573160i	−0.630652	+	0.776066i	$0.717212\pi$
$864$	−2.71921	+	12.7538i	−0.0925095	+	0.433892i
$865$	3.66851	−	3.42615i	0.124733	−	0.116493i
$866$	−0.662074	−	1.27775i	−0.0224982	−	0.0434195i
$867$	−21.2820	+	12.2383i	−0.722776	+	0.415633i
$868$	−7.52403	+	0.514658i	−0.255382	+	0.0174686i
$869$	7.81478	−	11.0710i	0.265098	−	0.375558i
$870$	−0.0107078	+	0.0349030i	−0.000363030	+	0.00118332i
$871$	−1.79298	−	26.2124i	−0.0607527	−	0.888173i
$872$	0.694771	+	3.34342i	0.0235279	+	0.113223i
$873$	−15.5922	−	7.70094i	−0.527714	−	0.260637i
$874$	6.36993	+	6.82053i	0.215466	+	0.230708i
$875$	7.32734	−	3.18271i	0.247709	−	0.107595i
$876$	−23.1420	+	27.0636i	−0.781894	+	0.914393i
$877$	−4.59384	+	5.64659i	−0.155123	+	0.190672i	−0.847392	−	0.530968i	$-0.821829\pi$
$877$	−4.59384	+	5.64659i	−0.155123	+	0.190672i	0.692269	+	0.721640i	$0.256611\pi$
$878$	−1.28471	−	0.0878768i	−0.0433570	−	0.00296570i
$879$	−16.9060	−	34.6808i	−0.570226	−	1.16975i
$880$	−14.5049	−	6.30035i	−0.488959	−	0.212385i
$881$	−13.6473	−	38.3999i	−0.459790	−	1.29373i	−0.915040	−	0.403362i	$-0.867842\pi$
$881$	−13.6473	−	38.3999i	−0.459790	−	1.29373i	0.455250	−	0.890364i	$-0.349550\pi$
$882$	0.332946	+	3.79062i	0.0112109	+	0.127637i
$883$	25.1431	+	3.45584i	0.846132	+	0.116298i	0.546192	−	0.837660i	$-0.316077\pi$
$883$	25.1431	+	3.45584i	0.846132	+	0.116298i	0.299940	+	0.953958i	$0.403033\pi$
$884$	1.65374	−	7.95825i	0.0556214	−	0.267665i
$885$	6.08946	−	4.07872i	0.204695	−	0.137105i
$886$	4.94221	+	2.56085i	0.166037	+	0.0860334i
$887$	−17.5166	−	4.90793i	−0.588151	−	0.164792i	−0.0371684	−	0.999309i	$-0.511834\pi$
$887$	−17.5166	−	4.90793i	−0.588151	−	0.164792i	−0.550982	+	0.834517i	$0.685747\pi$
$888$	−4.18195	+	9.01687i	−0.140337	+	0.302586i
$889$	−2.09790	−	0.745593i	−0.0703612	−	0.0250064i
$890$	−5.64594	+	4.59332i	−0.189252	+	0.153968i
$891$	13.5732	−	4.37498i	0.454720	−	0.146567i
$892$			6.75717i			0.226247i
$893$	40.6625	+	4.75231i	1.36072	+	0.159030i
$894$	−0.536170	−	1.63442i	−0.0179322	−	0.0546632i
$895$	−36.7693	−	52.0903i	−1.22906	−	1.74119i
$896$	4.35161	+	5.34884i	0.145377	+	0.178692i
$897$	−0.760311	+	31.0385i	−0.0253860	+	1.03635i
$898$	−1.69182	−	1.58005i	−0.0564567	−	0.0527269i
$899$	−0.0358245	+	0.127859i	−0.00119481	+	0.00426435i
$900$	1.99010	+	12.6612i	0.0663366	+	0.422041i
$901$	−7.08031	+	1.98381i	−0.235879	+	0.0660903i
$902$	−2.99230	−	0.621808i	−0.0996328	−	0.0207039i
$903$	21.2259	−	3.87115i	0.706355	−	0.128824i
$904$	−4.14765	+	6.82052i	−0.137949	+	0.226847i
$905$	−11.7827	+	4.18756i	−0.391669	+	0.139199i
$906$	0.100146	−	1.07622i	0.00332713	−	0.0357550i
$907$	35.8031	−	4.92102i	1.18882	−	0.163400i	0.485477	−	0.874249i	$-0.338646\pi$
$907$	35.8031	−	4.92102i	1.18882	−	0.163400i	0.703344	+	0.710849i	$0.251689\pi$
$908$	1.36465	−	19.9505i	0.0452875	−	0.662080i
$909$	1.76152	−	35.9342i	0.0584260	−	1.19186i
$910$	1.29609	−	0.788170i	0.0429650	−	0.0261276i
$911$	23.5404	+	54.1955i	0.779929	+	1.79558i	0.577721	+	0.816235i	$0.303942\pi$
$911$	23.5404	+	54.1955i	0.779929	+	1.79558i	0.202208	+	0.979343i	$0.435188\pi$
$912$	33.7439	+	18.5467i	1.11737	+	0.614142i
$913$	−24.0416	+	12.4574i	−0.795661	+	0.412278i
$914$	−2.73323	+	0.567973i	−0.0904074	+	0.0187869i
$915$	−2.61183	+	1.05923i	−0.0863446	+	0.0350171i
$916$	22.9779	+	16.2196i	0.759211	+	0.535910i
$917$	7.84068	+	5.53455i	0.258922	+	0.182767i
$918$	0.987755	−	1.60551i	0.0326008	−	0.0529898i
$919$	8.13650	−	1.69078i	0.268398	−	0.0557738i	−0.0673366	−	0.997730i	$-0.521450\pi$
$919$	8.13650	−	1.69078i	0.268398	−	0.0557738i	0.335735	+	0.941956i	$0.391015\pi$
$920$	14.7066	−	7.62037i	0.484864	−	0.251236i
$921$	−13.4594	+	24.4881i	−0.443502	+	0.806910i
$922$	−0.624235	−	1.43713i	−0.0205581	−	0.0473294i
$923$	21.6356	−	13.1569i	0.712146	−	0.433065i
$924$	2.03239	−	5.30328i	0.0668607	−	0.174465i
$925$	−1.00391	+	14.6766i	−0.0330083	+	0.482564i
$926$	0.667107	−	0.0916918i	0.0219225	−	0.00301318i
$927$	27.0805	−	6.17528i	0.889441	−	0.202823i
$928$	0.0861582	−	0.0306206i	0.00282828	−	0.00100517i
$929$	8.25214	−	13.5701i	0.270744	−	0.445220i	−0.689539	−	0.724249i	$-0.742187\pi$
$929$	8.25214	−	13.5701i	0.270744	−	0.445220i	0.960283	+	0.279029i	$0.0900127\pi$
$930$	−0.655202	−	3.59255i	−0.0214849	−	0.117804i
$931$	34.3656	+	7.14126i	1.12629	+	0.234045i
$932$	37.7093	−	10.5656i	1.23521	−	0.346089i
$933$	−17.9124	−	2.91058i	−0.586426	−	0.0952881i
$934$	1.33028	−	4.74783i	0.0435281	−	0.155354i
$935$	5.21905	+	4.87425i	0.170681	+	0.159405i
$936$	−1.82665	−	6.06594i	−0.0597060	−	0.198271i
$937$	−7.20731	−	8.85898i	−0.235453	−	0.289410i	0.644368	−	0.764715i	$-0.277120\pi$
$937$	−7.20731	−	8.85898i	−0.235453	−	0.289410i	−0.879821	+	0.475305i	$0.842338\pi$
$938$	−1.39936	−	1.98245i	−0.0456908	−	0.0647292i
$939$	0.438502	−	0.143850i	0.0143100	−	0.00469436i
$940$	13.6339	−	33.2128i	0.444689	−	1.08328i
$941$			18.4805i			0.602449i	0.953553	+	0.301224i	$0.0973953\pi$
$941$			18.4805i			0.602449i	−0.953553	+	0.301224i	$0.902605\pi$
$942$	3.42456	+	2.54521i	0.111578	+	0.0829276i
$943$	−50.2113	+	40.8499i	−1.63510	+	1.33026i
$944$	−5.53679	−	1.96778i	−0.180207	−	0.0640457i
$945$	−14.4636	+	2.92754i	−0.470501	+	0.0952330i
$946$	−3.87178	−	1.08482i	−0.125882	−	0.0352706i
$947$	37.5724	+	19.4684i	1.22094	+	0.632639i	0.944538	−	0.328403i	$-0.106510\pi$
$947$	37.5724	+	19.4684i	1.22094	+	0.632639i	0.276401	+	0.961042i	$0.410858\pi$
$948$	16.1028	+	24.0412i	0.522995	+	0.780823i
$949$	5.30000	−	25.5050i	0.172045	−	0.827928i
$950$	−2.79207	−	0.383762i	−0.0905869	−	0.0124509i
$951$	−2.76015	+	11.8214i	−0.0895039	+	0.383336i
$952$	−0.508788	−	1.43159i	−0.0164899	−	0.0463982i
$953$	−14.3140	−	6.21745i	−0.463676	−	0.201403i	0.153626	−	0.988129i	$-0.450905\pi$
$953$	−14.3140	−	6.21745i	−0.463676	−	0.201403i	−0.617302	+	0.786726i	$0.711774\pi$
$954$	−2.03174	+	1.97234i	−0.0657802	+	0.0638570i
$955$	72.6053	+	4.96634i	2.34945	+	0.160707i
$956$	−4.37467	+	5.37720i	−0.141487	+	0.173911i
$957$	−0.0759991	−	0.0649866i	−0.00245670	−	0.00210072i
$958$	1.83701	−	0.797928i	0.0593513	−	0.0257799i
$959$	9.00132	+	9.63806i	0.290668	+	0.311229i
$960$	22.4483	−	22.8861i	0.724516	−	0.738646i
$961$	3.60488	+	17.3476i	0.116286	+	0.559601i
$962$	−0.245182	−	3.58444i	−0.00790499	−	0.115567i
$963$	0.532392	+	27.5618i	0.0171561	+	0.888167i
$964$	−29.2942	+	41.5004i	−0.943501	+	1.33664i
$965$	−53.7955	+	3.67971i	−1.73174	+	0.118454i
$966$	1.42947	+	2.48582i	0.0459925	+	0.0799798i
$967$	10.4732	+	20.2124i	0.336795	+	0.649986i	0.994666	−	0.103145i	$-0.0328906\pi$
$967$	10.4732	+	20.2124i	0.336795	+	0.649986i	−0.657871	+	0.753131i	$0.728543\pi$
$968$	5.29305	−	4.94336i	0.170125	−	0.158886i
$969$	−11.5533	−	12.9944i	−0.371146	−	0.417441i
$970$	−1.74244	−	2.86533i	−0.0559465	−	0.0920000i
$971$	−30.9605	−	25.1882i	−0.993569	−	0.808329i	−0.0120960	−	0.999927i	$-0.503850\pi$
$971$	−30.9605	−	25.1882i	−0.993569	−	0.808329i	−0.981473	+	0.191598i	$0.938633\pi$
$972$	−1.64837	+	30.4063i	−0.0528716	+	0.975284i
$973$	1.71370	+	12.4681i	0.0549389	+	0.399710i
$974$	0.966094	−	2.22417i	0.0309556	−	0.0712670i
$975$	−5.73729	−	7.41590i	−0.183740	−	0.237499i
$976$	1.93068	+	1.17407i	0.0617996	+	0.0375812i
$977$	−0.757941	+	5.51443i	−0.0242487	+	0.176422i	−0.998875	−	0.0474147i	$-0.984902\pi$
$977$	−0.757941	+	5.51443i	−0.0242487	+	0.176422i	0.974627	+	0.223837i	$0.0718583\pi$
$978$	2.88762	−	0.325066i	0.0923360	−	0.0103945i
$979$	−5.37847	−	19.1960i	−0.171897	−	0.613507i
$980$	14.1614	−	27.3303i	0.452369	−	0.873033i
$981$	4.23903	+	11.2350i	0.135342	+	0.358705i
$982$	−2.91340	+	3.11949i	−0.0929703	+	0.0995469i
$983$	11.9603	−	33.6529i	0.381473	−	1.07336i	−0.583750	−	0.811933i	$-0.698415\pi$
$983$	11.9603	−	33.6529i	0.381473	−	1.07336i	0.965223	−	0.261428i	$-0.0841934\pi$
$984$	7.13662	−	11.1132i	0.227507	−	0.354276i
$985$	−50.3627	+	35.5499i	−1.60469	+	1.13271i
$986$	−0.0132176			−0.000420933
$987$	11.8348	+	4.26273i	0.376705	+	0.135684i
$988$	−28.8733			−0.918582
$989$	−69.5734	+	49.1103i	−2.21230	+	1.56162i
$990$	2.66193	+	0.690681i	0.0846017	+	0.0219513i
$991$	9.73115	−	27.3808i	0.309120	−	0.869781i	−0.681338	−	0.731969i	$-0.738602\pi$
$991$	9.73115	−	27.3808i	0.309120	−	0.869781i	0.990458	−	0.137812i	$-0.0440071\pi$
$992$	−6.24272	+	6.68432i	−0.198207	+	0.212228i
$993$	1.42791	+	32.5763i	0.0453133	+	1.03378i
$994$	1.07595	−	2.07649i	0.0341271	−	0.0658623i
$995$	−0.173866	−	0.620535i	−0.00551191	−	0.0196723i
$996$	−6.46781	−	57.4548i	−0.204940	−	1.82053i
$997$	0.230749	−	1.67882i	0.00730790	−	0.0531689i	−0.986675	−	0.162702i	$-0.947979\pi$
$997$	0.230749	−	1.67882i	0.00730790	−	0.0531689i	0.993983	+	0.109533i	$0.0349356\pi$
$998$	0.283550	+	0.172430i	0.00897561	+	0.00545819i
$999$	−9.60389	+	33.6061i	−0.303854	+	1.06325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	141.2.g.a.107.8	yes	308
3.2	odd	2	inner	141.2.g.a.107.7	yes	308
47.29	odd	46	inner	141.2.g.a.29.7	✓	308
141.29	even	46	inner	141.2.g.a.29.8	yes	308

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
141.2.g.a.29.7	✓	308	47.29	odd	46	inner
141.2.g.a.29.8	yes	308	141.29	even	46	inner
141.2.g.a.107.7	yes	308	3.2	odd	2	inner
141.2.g.a.107.8	yes	308	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 141 = 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	141.g (of order \(46\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(0.176299 - 0.124445i) q^{2} +(-1.45742 - 0.935916i) q^{3} +(-0.654165 + 1.84064i) q^{4} +(-1.82983 + 1.95927i) q^{5} +(-0.373412 + 0.0163677i) q^{6} +(-0.487368 + 0.940578i) q^{7} +(0.230173 + 0.821499i) q^{8} +(1.24812 + 2.72804i) q^{9} +O(q^{10})\)	\(q+(0.176299 - 0.124445i) q^{2} +(-1.45742 - 0.935916i) q^{3} +(-0.654165 + 1.84064i) q^{4} +(-1.82983 + 1.95927i) q^{5} +(-0.373412 + 0.0163677i) q^{6} +(-0.487368 + 0.940578i) q^{7} +(0.230173 + 0.821499i) q^{8} +(1.24812 + 2.72804i) q^{9} +(-0.0787752 + 0.573132i) q^{10} +(-1.35387 - 0.823304i) q^{11} +(2.67608 - 2.07034i) q^{12} +(-0.986116 + 2.27027i) q^{13} +(0.0311281 + 0.226474i) q^{14} +(4.50054 - 1.14290i) q^{15} +(-2.88779 - 2.34939i) q^{16} +(0.873469 + 1.43636i) q^{17} +(0.559535 + 0.325628i) q^{18} +(4.36426 - 4.07594i) q^{19} +(-2.40931 - 4.64975i) q^{20} +(1.59060 - 0.914678i) q^{21} +(-0.341142 + 0.0233347i) q^{22} +(-4.17637 + 5.91657i) q^{23} +(0.433396 - 1.41269i) q^{24} +(-0.149249 - 2.18194i) q^{25} +(0.108673 + 0.522963i) q^{26} +(0.734183 - 5.14402i) q^{27} +(-1.41245 - 1.51236i) q^{28} +(-0.0334184 + 0.0145156i) q^{29} +(0.651212 - 0.761565i) q^{30} +(2.29995 - 2.82701i) q^{31} +(-2.50378 - 0.171263i) q^{32} +(1.20260 + 2.46700i) q^{33} +(0.332740 + 0.144529i) q^{34} +(-0.951047 - 2.67599i) q^{35} +(-5.83782 + 0.512760i) q^{36} +(-6.66376 - 0.915913i) q^{37} +(0.262184 - 1.26170i) q^{38} +(3.56196 - 2.38580i) q^{39} +(-2.03072 - 1.05223i) q^{40} +(8.60650 + 2.41143i) q^{41} +(0.166594 - 0.359200i) q^{42} +(11.0801 + 3.93788i) q^{43} +(2.40106 - 1.95341i) q^{44} +(-7.62882 - 2.54644i) q^{45} +1.56282i q^{46} +(4.43330 + 5.22933i) q^{47} +(2.00988 + 6.12676i) q^{48} +(3.38960 + 4.80197i) q^{49} +(-0.297845 - 0.366100i) q^{50} +(0.0713037 - 2.91087i) q^{51} +(-3.53367 - 3.30021i) q^{52} +(-1.18007 + 4.21173i) q^{53} +(-0.510715 - 0.998252i) q^{54} +(4.09042 - 1.14608i) q^{55} +(-0.884864 - 0.183877i) q^{56} +(-10.1753 + 1.85575i) q^{57} +(-0.00408522 + 0.00671786i) q^{58} +(1.48728 - 0.528580i) q^{59} +(-0.840416 + 9.03154i) q^{60} +(-0.601327 + 0.0826505i) q^{61} +(0.0536693 - 0.784618i) q^{62} +(-3.17423 - 0.155603i) q^{63} +(5.89887 - 3.58718i) q^{64} +(-2.64364 - 6.08628i) q^{65} +(0.519024 + 0.285272i) q^{66} +(-9.42475 + 4.88351i) q^{67} +(-3.21522 + 0.668130i) q^{68} +(11.6241 - 4.71417i) q^{69} +(-0.500683 - 0.353421i) q^{70} +(-8.35790 - 5.89965i) q^{71} +(-1.95380 + 1.65325i) q^{72} +(-10.3043 + 2.14126i) q^{73} +(-1.28880 + 0.667800i) q^{74} +(-1.82459 + 3.31968i) q^{75} +(4.64740 + 10.6994i) q^{76} +(1.43421 - 0.872164i) q^{77} +(0.331068 - 0.863884i) q^{78} +(-0.583622 + 8.53225i) q^{79} +(9.88726 - 1.35897i) q^{80} +(-5.88438 + 6.80985i) q^{81} +(1.81741 - 0.645907i) q^{82} +(8.87887 - 14.6007i) q^{83} +(0.643080 + 3.52608i) q^{84} +(-4.41252 - 0.916933i) q^{85} +(2.44347 - 0.684627i) q^{86} +(0.0622899 + 0.0101215i) q^{87} +(0.364720 - 1.30170i) q^{88} +(9.19470 + 8.58725i) q^{89} +(-1.66185 + 0.500437i) q^{90} +(-1.65476 - 2.03397i) q^{91} +(-8.15825 - 11.5576i) q^{92} +(-5.99783 + 1.96758i) q^{93} +(1.43235 + 0.370222i) q^{94} +16.0091i q^{95} +(3.48876 + 2.59293i) q^{96} +(-4.49660 + 3.65825i) q^{97} +(1.19517 + 0.424763i) q^{98} +(0.556215 - 4.72098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 308 q - 19 q^{3} - 26 q^{4} - 15 q^{6} - 42 q^{7} - 19 q^{9}+O(q^{10}) \) 308 * q - 19 * q^3 - 26 * q^4 - 15 * q^6 - 42 * q^7 - 19 * q^9	\( 308 q - 19 q^{3} - 26 q^{4} - 15 q^{6} - 42 q^{7} - 19 q^{9} - 46 q^{10} - 28 q^{12} - 46 q^{13} - 23 q^{15} - 70 q^{16} - 14 q^{18} - 46 q^{19} - 27 q^{21} - 46 q^{22} - 42 q^{24} - 36 q^{25} - 43 q^{27} - 46 q^{28} - 23 q^{30} - 46 q^{31} - 23 q^{33} - 38 q^{34} + 69 q^{36} - 66 q^{37} + 46 q^{39} - 46 q^{40} + 162 q^{42} - 46 q^{43} + 92 q^{45} + 178 q^{48} - 92 q^{49} + 80 q^{51} - 46 q^{52} + 58 q^{54} + 14 q^{55} + 46 q^{57} - 46 q^{58} + 69 q^{60} - 78 q^{61} + 13 q^{63} + 66 q^{64} - 23 q^{66} - 46 q^{67} - 23 q^{69} - 46 q^{70} - 105 q^{72} - 46 q^{73} + 17 q^{75} - 23 q^{78} + 50 q^{79} + 5 q^{81} + 368 q^{82} + 62 q^{84} + 138 q^{85} - 23 q^{87} + 230 q^{88} - 23 q^{90} + 322 q^{91} + 198 q^{94} + 93 q^{96} + 26 q^{97} - 23 q^{99}+O(q^{100}) \) 308 * q - 19 * q^3 - 26 * q^4 - 15 * q^6 - 42 * q^7 - 19 * q^9 - 46 * q^10 - 28 * q^12 - 46 * q^13 - 23 * q^15 - 70 * q^16 - 14 * q^18 - 46 * q^19 - 27 * q^21 - 46 * q^22 - 42 * q^24 - 36 * q^25 - 43 * q^27 - 46 * q^28 - 23 * q^30 - 46 * q^31 - 23 * q^33 - 38 * q^34 + 69 * q^36 - 66 * q^37 + 46 * q^39 - 46 * q^40 + 162 * q^42 - 46 * q^43 + 92 * q^45 + 178 * q^48 - 92 * q^49 + 80 * q^51 - 46 * q^52 + 58 * q^54 + 14 * q^55 + 46 * q^57 - 46 * q^58 + 69 * q^60 - 78 * q^61 + 13 * q^63 + 66 * q^64 - 23 * q^66 - 46 * q^67 - 23 * q^69 - 46 * q^70 - 105 * q^72 - 46 * q^73 + 17 * q^75 - 23 * q^78 + 50 * q^79 + 5 * q^81 + 368 * q^82 + 62 * q^84 + 138 * q^85 - 23 * q^87 + 230 * q^88 - 23 * q^90 + 322 * q^91 + 198 * q^94 + 93 * q^96 + 26 * q^97 - 23 * q^99

Introduction

L-functions

Modular forms

Varieties

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