LMFDB - Embedded newform 50.3.f.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, 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:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			3.2
Root			$-1.64599i$ of defining polynomial
Character	$\chi$	$=$	50.3
Dual form			50.3.f.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642040 - 1.26007i) q^{2} +(0.569657 + 3.59668i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(2.10649 + 4.53461i) q^{5} +(4.16633 - 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-4.05206 + 1.31659i) q^{9} +O(q^{10})$	\(q+(-0.642040 - 1.26007i) q^{2} +(0.569657 + 3.59668i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(2.10649 + 4.53461i) q^{5} +(4.16633 - 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-4.05206 + 1.31659i) q^{9} +(4.36149 - 5.56574i) q^{10} +(4.24327 - 13.0594i) q^{11} +(-6.48922 - 3.30642i) q^{12} +(-4.14356 + 8.13219i) q^{13} +(-1.20932 - 0.392933i) q^{14} +(-15.1095 + 10.1596i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.920559 + 5.81218i) q^{17} +(4.26058 + 4.26058i) q^{18} +(-18.5227 - 25.4943i) q^{19} +(-9.81348 - 1.92237i) q^{20} +(2.64887 + 1.92451i) q^{21} +(-19.1802 + 3.03784i) q^{22} +(27.4902 - 14.0070i) q^{23} +10.2997i q^{24} +(-16.1254 + 19.1043i) q^{25} +12.9075 q^{26} +(7.83525 + 15.3775i) q^{27} +(0.281309 + 1.77612i) q^{28} +(33.4337 - 46.0176i) q^{29} +(22.5027 + 12.5163i) q^{30} +(-1.57058 + 1.14109i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(49.3877 + 7.82225i) q^{33} +(7.91481 - 2.57168i) q^{34} +(4.22228 + 1.54374i) q^{35} +(2.63319 - 8.10411i) q^{36} +(-10.4788 - 5.33922i) q^{37} +(-20.2324 + 39.7083i) q^{38} +(-31.6093 - 10.2705i) q^{39} +(3.87831 + 13.6000i) q^{40} +(20.6793 + 63.6443i) q^{41} +(0.724353 - 4.57338i) q^{42} +(-38.8107 - 38.8107i) q^{43} +(16.1423 + 22.2180i) q^{44} +(-14.5059 - 15.6011i) q^{45} +(-35.2996 - 25.6467i) q^{46} +(-49.2685 + 7.80337i) q^{47} +(12.9784 - 6.61284i) q^{48} +48.1916i q^{49} +(34.4259 + 8.05346i) q^{50} -21.4289 q^{51} +(-8.28712 - 16.2644i) q^{52} +(-5.69932 - 35.9841i) q^{53} +(14.3463 - 19.7460i) q^{54} +(68.1578 - 8.26806i) q^{55} +(2.05742 - 1.49481i) q^{56} +(81.1431 - 81.1431i) q^{57} +(-79.4513 - 12.5838i) q^{58} +(-57.8198 + 18.7868i) q^{59} +(1.32383 - 36.3910i) q^{60} +(4.37780 - 13.4735i) q^{61} +(2.44623 + 1.24642i) q^{62} +(-1.73915 + 3.41328i) q^{63} +(7.60845 + 2.47214i) q^{64} +(-45.6047 - 1.65901i) q^{65} +(-21.8523 - 67.2544i) q^{66} +(-10.1080 + 63.8194i) q^{67} +(-8.32212 - 8.32212i) q^{68} +(66.0385 + 90.8943i) q^{69} +(-0.765635 - 6.31152i) q^{70} +(25.4392 + 18.4826i) q^{71} +(-11.9024 + 1.88515i) q^{72} +(-61.7220 + 31.4489i) q^{73} +16.6321i q^{74} +(-77.8977 - 47.1148i) q^{75} +63.0254 q^{76} +(-5.60513 - 11.0007i) q^{77} +(7.35285 + 46.4241i) q^{78} +(33.4082 - 45.9825i) q^{79} +(14.6469 - 13.6187i) q^{80} +(-81.8666 + 59.4796i) q^{81} +(66.9196 - 66.9196i) q^{82} +(40.0044 + 6.33607i) q^{83} +(-6.22786 + 2.02355i) q^{84} +(-28.2951 + 8.06895i) q^{85} +(-23.9863 + 73.8222i) q^{86} +(184.556 + 94.0360i) q^{87} +(17.6323 - 34.6054i) q^{88} +(-57.1826 - 18.5798i) q^{89} +(-10.3452 + 28.2950i) q^{90} +(2.53589 + 7.80467i) q^{91} +(-9.65295 + 60.9463i) q^{92} +(-4.99882 - 4.99882i) q^{93} +(41.4652 + 57.0719i) q^{94} +(76.5887 - 137.697i) q^{95} +(-16.6653 - 12.1081i) q^{96} +(12.3027 - 1.94856i) q^{97} +(60.7249 - 30.9409i) q^{98} +58.5042i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{7}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.642040	−	1.26007i	−0.321020	−	0.630037i
$2$	−0.642040	−	1.26007i	−0.321020	−	0.630037i
$3$	0.569657	+	3.59668i	0.189886	+	1.19889i	0.879922	+	0.475117i	$0.157594\pi$
$3$	0.569657	+	3.59668i	0.189886	+	1.19889i	−0.690037	+	0.723774i	$0.742406\pi$
$4$	−1.17557	+	1.61803i	−0.293893	+	0.404508i
$5$	2.10649	+	4.53461i	0.421299	+	0.906922i
$5$	2.10649	+	4.53461i	0.421299	+	0.906922i
$6$	4.16633	−	3.02702i	0.694389	−	0.504503i
$7$	0.635779	−	0.635779i	0.0908256	−	0.0908256i	−0.660234	−	0.751060i	$-0.729543\pi$
$7$	0.635779	−	0.635779i	0.0908256	−	0.0908256i	0.751060	+	0.660234i	$0.229543\pi$
$8$	2.79360	+	0.442463i	0.349201	+	0.0553079i
$9$	−4.05206	+	1.31659i	−0.450229	+	0.146288i
$10$	4.36149	−	5.56574i	0.436149	−	0.556574i
$11$	4.24327	−	13.0594i	0.385751	−	1.18722i	−0.550182	−	0.835045i	$-0.685442\pi$
$11$	4.24327	−	13.0594i	0.385751	−	1.18722i	0.935934	−	0.352176i	$-0.114558\pi$
$12$	−6.48922	−	3.30642i	−0.540768	−	0.275535i
$13$	−4.14356	+	8.13219i	−0.318735	+	0.625553i	−0.993672	−	0.112323i	$-0.964171\pi$
$13$	−4.14356	+	8.13219i	−0.318735	+	0.625553i	0.674936	+	0.737876i	$0.264171\pi$
$14$	−1.20932	−	0.392933i	−0.0863803	−	0.0280667i
$15$	−15.1095	+	10.1596i	−1.00730	+	0.677303i
$16$	−1.23607	−	3.80423i	−0.0772542	−	0.237764i
$17$	−0.920559	+	5.81218i	−0.0541505	+	0.341893i	0.945707	+	0.325020i	$0.105371\pi$
$17$	−0.920559	+	5.81218i	−0.0541505	+	0.341893i	−0.999858	+	0.0168729i	$0.994629\pi$
$18$	4.26058	+	4.26058i	0.236699	+	0.236699i
$19$	−18.5227	−	25.4943i	−0.974878	−	1.34180i	−0.939544	−	0.342429i	$-0.888750\pi$
$19$	−18.5227	−	25.4943i	−0.974878	−	1.34180i	−0.0353349	−	0.999376i	$-0.511250\pi$
$20$	−9.81348	−	1.92237i	−0.490674	−	0.0961187i
$21$	2.64887	+	1.92451i	0.126137	+	0.0916436i
$22$	−19.1802	+	3.03784i	−0.871827	+	0.138084i
$23$	27.4902	−	14.0070i	1.19523	−	0.608999i	0.260883	−	0.965370i	$-0.415986\pi$
$23$	27.4902	−	14.0070i	1.19523	−	0.608999i	0.934344	+	0.356372i	$0.115986\pi$
$24$			10.2997i			0.429156i
$25$	−16.1254	+	19.1043i	−0.645015	+	0.764170i
$26$	12.9075			0.496442
$27$	7.83525	+	15.3775i	0.290194	+	0.569539i
$28$	0.281309	+	1.77612i	0.0100468	+	0.0634327i
$29$	33.4337	−	46.0176i	1.15289	−	1.58681i	0.418282	−	0.908317i	$-0.362632\pi$
$29$	33.4337	−	46.0176i	1.15289	−	1.58681i	0.734604	−	0.678496i	$-0.237368\pi$
$30$	22.5027	+	12.5163i	0.750090	+	0.417210i
$31$	−1.57058	+	1.14109i	−0.0506637	+	0.0368093i	−0.612829	−	0.790216i	$-0.709969\pi$
$31$	−1.57058	+	1.14109i	−0.0506637	+	0.0368093i	0.562165	+	0.827025i	$0.309969\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	49.3877	+	7.82225i	1.49660	+	0.237038i
$34$	7.91481	−	2.57168i	0.232788	−	0.0756376i
$35$	4.22228	+	1.54374i	0.120636	+	0.0441070i
$36$	2.63319	−	8.10411i	0.0731441	−	0.225114i
$37$	−10.4788	−	5.33922i	−0.283211	−	0.144303i	0.306615	−	0.951834i	$-0.400804\pi$
$37$	−10.4788	−	5.33922i	−0.283211	−	0.144303i	−0.589826	+	0.807530i	$0.700804\pi$
$38$	−20.2324	+	39.7083i	−0.532431	+	1.04496i
$39$	−31.6093	−	10.2705i	−0.810494	−	0.263345i
$40$	3.87831	+	13.6000i	0.0969578	+	0.339999i
$41$	20.6793	+	63.6443i	0.504373	+	1.55230i	0.801822	+	0.597563i	$0.203864\pi$
$41$	20.6793	+	63.6443i	0.504373	+	1.55230i	−0.297449	+	0.954738i	$0.596136\pi$
$42$	0.724353	−	4.57338i	0.0172465	−	0.108890i
$43$	−38.8107	−	38.8107i	−0.902573	−	0.902573i	0.0930849	−	0.995658i	$-0.470327\pi$
$43$	−38.8107	−	38.8107i	−0.902573	−	0.902573i	−0.995658	+	0.0930849i	$0.970327\pi$
$44$	16.1423	+	22.2180i	0.366871	+	0.504955i
$45$	−14.5059	−	15.6011i	−0.322353	−	0.346691i
$46$	−35.2996	−	25.6467i	−0.767383	−	0.557537i
$47$	−49.2685	+	7.80337i	−1.04827	+	0.166029i	−0.656724	−	0.754131i	$-0.728058\pi$
$47$	−49.2685	+	7.80337i	−1.04827	+	0.166029i	−0.391542	+	0.920160i	$0.628058\pi$
$48$	12.9784	−	6.61284i	0.270384	−	0.137768i
$49$			48.1916i			0.983501i
$50$	34.4259	+	8.05346i	0.688518	+	0.161069i
$51$	−21.4289			−0.420175
$52$	−8.28712	−	16.2644i	−0.159368	−	0.312777i
$53$	−5.69932	−	35.9841i	−0.107534	−	0.678945i	−0.981284	−	0.192568i	$-0.938318\pi$
$53$	−5.69932	−	35.9841i	−0.107534	−	0.678945i	0.873749	−	0.486377i	$-0.161682\pi$
$54$	14.3463	−	19.7460i	0.265672	−	0.365666i
$55$	68.1578	−	8.26806i	1.23923	−	0.150328i
$56$	2.05742	−	1.49481i	0.0367397	−	0.0266930i
$57$	81.1431	−	81.1431i	1.42356	−	1.42356i
$58$	−79.4513	−	12.5838i	−1.36985	−	0.216963i
$59$	−57.8198	+	18.7868i	−0.979997	+	0.318420i	−0.754845	−	0.655904i	$-0.772288\pi$
$59$	−57.8198	+	18.7868i	−0.979997	+	0.318420i	−0.225152	+	0.974324i	$0.572288\pi$
$60$	1.32383	−	36.3910i	0.0220638	−	0.606517i
$61$	4.37780	−	13.4735i	0.0717672	−	0.220877i	−0.908739	−	0.417365i	$-0.862954\pi$
$61$	4.37780	−	13.4735i	0.0717672	−	0.220877i	0.980506	+	0.196488i	$0.0629537\pi$
$62$	2.44623	+	1.24642i	0.0394553	+	0.0201035i
$63$	−1.73915	+	3.41328i	−0.0276056	+	0.0541790i
$64$	7.60845	+	2.47214i	0.118882	+	0.0386271i
$65$	−45.6047	−	1.65901i	−0.701611	−	0.0255232i
$66$	−21.8523	−	67.2544i	−0.331095	−	1.01901i
$67$	−10.1080	+	63.8194i	−0.150866	+	0.952528i	0.789842	+	0.613310i	$0.210162\pi$
$67$	−10.1080	+	63.8194i	−0.150866	+	0.952528i	−0.940708	+	0.339218i	$0.889838\pi$
$68$	−8.32212	−	8.32212i	−0.122384	−	0.122384i
$69$	66.0385	+	90.8943i	0.957080	+	1.31731i
$70$	−0.765635	−	6.31152i	−0.0109376	−	0.0901646i
$71$	25.4392	+	18.4826i	0.358298	+	0.260319i	0.752342	−	0.658773i	$-0.228924\pi$
$71$	25.4392	+	18.4826i	0.358298	+	0.260319i	−0.394044	+	0.919092i	$0.628924\pi$
$72$	−11.9024	+	1.88515i	−0.165311	+	0.0261827i
$73$	−61.7220	+	31.4489i	−0.845506	+	0.430807i	−0.822389	−	0.568926i	$-0.807359\pi$
$73$	−61.7220	+	31.4489i	−0.845506	+	0.430807i	−0.0231175	+	0.999733i	$0.507359\pi$
$74$			16.6321i			0.224757i
$75$	−77.8977	−	47.1148i	−1.03864	−	0.628198i
$76$	63.0254			0.829281
$77$	−5.60513	−	11.0007i	−0.0727939	−	0.142866i
$78$	7.35285	+	46.4241i	0.0942673	+	0.595180i
$79$	33.4082	−	45.9825i	0.422889	−	0.582057i	−0.543414	−	0.839465i	$-0.682868\pi$
$79$	33.4082	−	45.9825i	0.422889	−	0.582057i	0.966303	+	0.257408i	$0.0828685\pi$
$80$	14.6469	−	13.6187i	0.183086	−	0.170233i
$81$	−81.8666	+	59.4796i	−1.01070	+	0.734316i
$82$	66.9196	−	66.9196i	0.816093	−	0.816093i
$83$	40.0044	+	6.33607i	0.481981	+	0.0763382i	0.392697	−	0.919668i	$-0.371542\pi$
$83$	40.0044	+	6.33607i	0.481981	+	0.0763382i	0.0892838	+	0.996006i	$0.471542\pi$
$84$	−6.22786	+	2.02355i	−0.0741412	+	0.0240899i
$85$	−28.2951	+	8.06895i	−0.332884	+	0.0949288i
$86$	−23.9863	+	73.8222i	−0.278910	+	0.858398i
$87$	184.556	+	94.0360i	2.12133	+	1.08087i
$88$	17.6323	−	34.6054i	0.200367	−	0.393243i
$89$	−57.1826	−	18.5798i	−0.642501	−	0.208761i	−0.0303965	−	0.999538i	$-0.509677\pi$
$89$	−57.1826	−	18.5798i	−0.642501	−	0.208761i	−0.612105	+	0.790777i	$0.709677\pi$
$90$	−10.3452	+	28.2950i	−0.114947	+	0.314389i
$91$	2.53589	+	7.80467i	0.0278669	+	0.0857656i
$92$	−9.65295	+	60.9463i	−0.104923	+	0.662460i
$93$	−4.99882	−	4.99882i	−0.0537507	−	0.0537507i
$94$	41.4652	+	57.0719i	0.441119	+	0.607148i
$95$	76.5887	−	137.697i	0.806197	−	1.44944i
$96$	−16.6653	−	12.1081i	−0.173597	−	0.126126i
$97$	12.3027	−	1.94856i	0.126832	−	0.0200882i	−0.0926957	−	0.995694i	$-0.529548\pi$
$97$	12.3027	−	1.94856i	0.126832	−	0.0200882i	0.219528	+	0.975606i	$0.429548\pi$
$98$	60.7249	−	30.9409i	0.619642	−	0.315723i
$99$			58.5042i			0.590952i
$100$	−11.9548	−	48.5498i	−0.119548	−	0.485498i
$101$	−66.0665			−0.654124			−0.327062	−	0.945003i	$-0.606059\pi$
$101$	−66.0665			−0.654124			−0.327062	+	0.945003i	$0.606059\pi$
$102$	13.7582	+	27.0020i	0.134884	+	0.264726i
$103$	−1.59842	−	10.0920i	−0.0155186	−	0.0979807i	0.978713	−	0.205232i	$-0.0657950\pi$
$103$	−1.59842	−	10.0920i	−0.0155186	−	0.0979807i	−0.994232	+	0.107252i	$0.965795\pi$
$104$	−15.1737	+	20.8848i	−0.145901	+	0.200815i
$105$	−3.14710	+	16.0656i	−0.0299724	+	0.153005i
$106$	−41.6834	+	30.2848i	−0.393240	+	0.285705i
$107$	28.4807	−	28.4807i	0.266175	−	0.266175i	−0.561382	−	0.827557i	$-0.689730\pi$
$107$	28.4807	−	28.4807i	0.266175	−	0.266175i	0.827557	+	0.561382i	$0.189730\pi$
$108$	−34.0923	−	5.39969i	−0.315669	−	0.0499971i
$109$	50.7034	−	16.4745i	0.465169	−	0.151142i	−0.0670496	−	0.997750i	$-0.521359\pi$
$109$	50.7034	−	16.4745i	0.465169	−	0.151142i	0.532218	+	0.846607i	$0.321359\pi$
$110$	−54.1784	−	80.5755i	−0.492531	−	0.732504i
$111$	13.2341	−	40.7304i	0.119226	−	0.366940i
$112$	−3.20451	−	1.63278i	−0.0286117	−	0.0145784i
$113$	48.8940	−	95.9600i	0.432691	−	0.849203i	−0.566985	−	0.823728i	$-0.691890\pi$
$113$	48.8940	−	95.9600i	0.432691	−	0.849203i	0.999675	−	0.0254749i	$-0.00810980\pi$
$114$	−154.343	−	50.1492i	−1.35389	−	0.439905i
$115$	121.424	+	95.1518i	1.05586	+	0.827407i
$116$	35.1543	+	108.194i	0.303054	+	0.932705i
$117$	6.08315	−	38.4075i	0.0519927	−	0.328269i
$118$	60.7953	+	60.7953i	0.515215	+	0.515215i
$119$	3.10999	+	4.28053i	0.0261344	+	0.0359709i
$120$	−46.7053	+	21.6963i	−0.389211	+	0.180803i
$121$	−54.6524	−	39.7073i	−0.451672	−	0.328159i
$122$	−19.7883	+	3.13416i	−0.162199	+	0.0256898i
$123$	−217.128	+	110.632i	−1.76527	+	0.899449i
$124$		−	3.88268i		−	0.0313119i
$125$	−120.598	−	32.8792i	−0.964787	−	0.263034i
$126$	5.41758			0.0429967
$127$	−40.0979	−	78.6966i	−0.315732	−	0.619658i	0.677537	−	0.735488i	$-0.263047\pi$
$127$	−40.0979	−	78.6966i	−0.315732	−	0.619658i	−0.993269	+	0.115830i	$0.963047\pi$
$128$	−1.76985	−	11.1744i	−0.0138270	−	0.0873001i
$129$	117.481	−	161.698i	0.910702	−	1.25347i
$130$	27.1896	+	58.5304i	0.209150	+	0.450234i
$131$	77.7492	−	56.4881i	0.593505	−	0.431207i	−0.250062	−	0.968230i	$-0.580451\pi$
$131$	77.7492	−	56.4881i	0.593505	−	0.431207i	0.843568	+	0.537023i	$0.180451\pi$
$132$	−70.7154	+	70.7154i	−0.535723	+	0.535723i
$133$	−27.9851	−	4.43240i	−0.210414	−	0.0333263i
$134$	86.9069	−	28.2377i	0.648559	−	0.210729i
$135$	−53.2262	+	67.9225i	−0.394268	+	0.503130i
$136$	−5.14335	+	15.8296i	−0.0378188	+	0.116394i
$137$	−213.366	−	108.715i	−1.55741	−	0.793542i	−0.558071	−	0.829793i	$-0.688458\pi$
$137$	−213.366	−	108.715i	−1.55741	−	0.793542i	−0.999343	+	0.0362512i	$0.988458\pi$
$138$	72.1341	−	141.571i	0.522711	−	1.02588i
$139$	−132.664	−	43.1053i	−0.954420	−	0.310110i	−0.209910	−	0.977721i	$-0.567317\pi$
$139$	−132.664	−	43.1053i	−0.954420	−	0.310110i	−0.744510	+	0.667611i	$0.767317\pi$
$140$	−7.46141	+	5.01700i	−0.0532958	+	0.0358357i
$141$	−56.1324	−	172.758i	−0.398102	−	1.22523i
$142$	6.95653	−	43.9218i	0.0489896	−	0.309308i
$143$	88.6196	+	88.6196i	0.619717	+	0.619717i
$144$	10.0172	+	13.7875i	0.0695641	+	0.0957468i
$145$	279.100	+	54.6731i	1.92482	+	0.377056i
$146$	79.2559	+	57.5828i	0.542849	+	0.394403i
$147$	−173.329	+	27.4527i	−1.17911	+	0.186753i
$148$	20.9576	−	10.6784i	0.141605	−	0.0721516i
$149$			187.994i			1.26170i	0.775903	+	0.630852i	$0.217295\pi$
$149$			187.994i			1.26170i	−0.775903	+	0.630852i	$0.782705\pi$
$150$	−9.35471	+	128.406i	−0.0623647	+	0.856043i
$151$	160.259			1.06132			0.530660	−	0.847585i	$-0.321944\pi$
$151$	160.259			1.06132			0.530660	+	0.847585i	$0.321944\pi$
$152$	−40.4648	−	79.4166i	−0.266216	−	0.522478i
$153$	−3.92212	−	24.7633i	−0.0256348	−	0.161852i
$154$	−10.2630	+	14.1258i	−0.0666426	+	0.0917257i
$155$	−8.48280	−	4.71825i	−0.0547278	−	0.0304403i
$156$	53.7769	−	39.0712i	0.344724	−	0.250456i
$157$	−88.0051	+	88.0051i	−0.560542	+	0.560542i	−0.929461	−	0.368919i	$-0.879728\pi$
$157$	−88.0051	+	88.0051i	−0.560542	+	0.560542i	0.368919	+	0.929461i	$0.379728\pi$
$158$	−79.3907	−	12.5743i	−0.502473	−	0.0795839i
$159$	126.176	−	40.9972i	0.793562	−	0.257844i
$160$	−26.5644	−	9.71246i	−0.166028	−	0.0607029i
$161$	8.57237	−	26.3831i	0.0532446	−	0.163870i
$162$	127.510	+	64.9697i	0.787100	+	0.401048i
$163$	−82.6039	+	162.119i	−0.506772	+	0.994597i	0.485929	+	0.873998i	$0.338481\pi$
$163$	−82.6039	+	162.119i	−0.506772	+	0.994597i	−0.992701	+	0.120599i	$0.961519\pi$
$164$	−127.289	−	41.3586i	−0.776150	−	0.252186i
$165$	68.5641	+	240.432i	0.415540	+	1.45716i
$166$	−17.7005	−	54.4765i	−0.106629	−	0.328172i
$167$	−28.3937	+	179.271i	−0.170022	+	1.07348i	0.744109	+	0.668059i	$0.232874\pi$
$167$	−28.3937	+	179.271i	−0.170022	+	1.07348i	−0.914131	+	0.405419i	$0.867126\pi$
$168$	6.54836	+	6.54836i	0.0389783	+	0.0389783i
$169$	50.3722	+	69.3314i	0.298061	+	0.410245i
$170$	28.3340	+	30.4733i	0.166671	+	0.179255i
$171$	108.621	+	78.9175i	0.635208	+	0.461506i
$172$	108.422	−	17.1723i	0.630358	−	0.0998389i
$173$	197.637	−	100.701i	1.14241	−	0.582086i	0.222777	−	0.974869i	$-0.428488\pi$
$173$	197.637	−	100.701i	1.14241	−	0.582086i	0.919631	+	0.392783i	$0.128488\pi$
$174$		−	292.929i		−	1.68350i
$175$	1.89392	+	22.3983i	0.0108224	+	0.127990i
$176$	−54.9260			−0.312079
$177$	−100.507	−	197.257i	−0.567839	−	1.11445i
$178$	13.3016	+	83.9833i	0.0747283	+	0.471816i
$179$	−38.1969	+	52.5735i	−0.213391	+	0.293707i	−0.902272	−	0.431167i	$-0.858102\pi$
$179$	−38.1969	+	52.5735i	−0.213391	+	0.293707i	0.688882	+	0.724874i	$0.258102\pi$
$180$	42.2958	−	5.13080i	0.234977	−	0.0285044i
$181$	171.558	−	124.644i	0.947832	−	0.688641i	−0.00246082	−	0.999997i	$-0.500783\pi$
$181$	171.558	−	124.644i	0.947832	−	0.688641i	0.950293	+	0.311356i	$0.100783\pi$
$182$	8.20631	−	8.20631i	0.0450896	−	0.0450896i
$183$	50.9536	+	8.07025i	0.278435	+	0.0440997i
$184$	82.9944	−	26.9665i	0.451057	−	0.146557i
$185$	2.13773	−	58.7643i	0.0115553	−	0.317645i
$186$	−3.08944	+	9.50832i	−0.0166099	+	0.0511200i
$187$	71.9976	+	36.6846i	0.385014	+	0.196174i
$188$	45.2925	−	88.8916i	0.240918	−	0.472827i
$189$	14.7582	+	4.79523i	0.0780858	+	0.0253716i
$190$	−222.681	−	8.10068i	−1.17201	−	0.0426351i
$191$	28.5061	+	87.7327i	0.149247	+	0.459334i	0.997533	−	0.0702046i	$-0.0223652\pi$
$191$	28.5061	+	87.7327i	0.149247	+	0.459334i	−0.848286	+	0.529538i	$0.822365\pi$
$192$	−4.55726	+	28.7734i	−0.0237357	+	0.149861i
$193$	151.113	+	151.113i	0.782967	+	0.782967i	0.980330	−	0.197363i	$-0.0632378\pi$
$193$	151.113	+	151.113i	0.782967	+	0.782967i	−0.197363	+	0.980330i	$0.563238\pi$
$194$	−10.3541	−	14.2513i	−0.0533719	−	0.0734601i
$195$	−20.0122	−	164.970i	−0.102626	−	0.846002i
$196$	−77.9756	−	56.6526i	−0.397835	−	0.289044i
$197$	−66.9124	+	10.5979i	−0.339657	+	0.0537964i	−0.323933	−	0.946080i	$-0.605005\pi$
$197$	−66.9124	+	10.5979i	−0.339657	+	0.0537964i	−0.0157239	+	0.999876i	$0.505005\pi$
$198$	73.7196	−	37.5620i	0.372321	−	0.189707i
$199$		−	113.482i		−	0.570260i	−0.958489	−	0.285130i	$-0.907963\pi$
$199$		−	113.482i		−	0.570260i	0.958489	−	0.285130i	$-0.0920368\pi$
$200$	−53.5008	+	46.2349i	−0.267504	+	0.231174i
$201$	−235.296			−1.17063
$202$	42.4173	+	83.2487i	0.209987	+	0.412122i
$203$	−8.00055	−	50.5135i	−0.0394116	−	0.248835i
$204$	25.1912	−	34.6727i	0.123486	−	0.169964i
$205$	−245.041	+	227.839i	−1.19532	+	1.11141i
$206$	−11.6904	+	8.49360i	−0.0567497	+	0.0412311i
$207$	−92.9505	+	92.9505i	−0.449036	+	0.449036i
$208$	36.0584	+	5.71109i	0.173358	+	0.0274572i
$209$	−411.538	+	133.717i	−1.96908	+	0.639793i
$210$	22.2643	−	6.34915i	0.106021	−	0.0302340i
$211$	−3.50834	+	10.7976i	−0.0166272	+	0.0511733i	−0.959026	−	0.283319i	$-0.908565\pi$
$211$	−3.50834	+	10.7976i	−0.0166272	+	0.0511733i	0.942399	+	0.334492i	$0.108565\pi$
$212$	64.9234	+	33.0801i	0.306243	+	0.156038i
$213$	−51.9844	+	102.025i	−0.244058	+	0.478991i
$214$	−54.1736	−	17.6021i	−0.253148	−	0.0822526i
$215$	94.2367	−	257.746i	0.438310	−	1.19882i
$216$	15.0846	+	46.4256i	0.0698361	+	0.214933i
$217$	−0.273058	+	1.72402i	−0.00125833	+	0.00794479i
$218$	−53.3127	−	53.3127i	−0.244554	−	0.244554i
$219$	−148.272	−	204.079i	−0.677041	−	0.931867i
$220$	−66.7463	+	120.001i	−0.303392	+	0.545461i
$221$	−43.4514	−	31.5693i	−0.196613	−	0.142847i
$222$	−59.8201	+	9.47457i	−0.269460	+	0.0426783i
$223$	−130.596	+	66.5421i	−0.585633	+	0.298395i	−0.721591	−	0.692320i	$-0.756589\pi$
$223$	−130.596	+	66.5421i	−0.585633	+	0.298395i	0.135958	+	0.990715i	$0.456589\pi$
$224$			5.08623i			0.0227064i
$225$	40.1884	−	98.6421i	0.178615	−	0.438409i
$226$	−152.309			−0.673931
$227$	−95.6214	−	187.668i	−0.421240	−	0.826729i	−0.999937	−	0.0111872i	$-0.996439\pi$
$227$	−95.6214	−	187.668i	−0.421240	−	0.826729i	0.578698	−	0.815542i	$-0.303561\pi$
$228$	35.9029	+	226.682i	0.157469	+	0.994218i
$229$	111.799	−	153.877i	0.488203	−	0.671954i	−0.491852	−	0.870679i	$-0.663680\pi$
$229$	111.799	−	153.877i	0.488203	−	0.671954i	0.980055	+	0.198725i	$0.0636800\pi$
$230$	41.9392	−	214.095i	0.182344	−	0.930846i
$231$	36.3729	−	26.4265i	0.157459	−	0.114400i
$232$	113.762	−	113.762i	0.490352	−	0.490352i
$233$	438.535	+	69.4571i	1.88212	+	0.298099i	0.988559	−	0.150836i	$-0.0481964\pi$
$233$	438.535	+	69.4571i	1.88212	+	0.298099i	0.893565	+	0.448935i	$0.148196\pi$
$234$	−52.3019	+	16.9939i	−0.223512	+	0.0726236i
$235$	−139.169	−	206.976i	−0.592209	−	0.880748i
$236$	37.5736	−	115.640i	0.159210	−	0.489998i
$237$	184.415	+	93.9643i	0.778124	+	0.396474i
$238$	3.39705	−	6.66709i	0.0142733	−	0.0280130i
$239$	245.647	+	79.8157i	1.02781	+	0.333957i	0.773925	−	0.633277i	$-0.218290\pi$
$239$	245.647	+	79.8157i	1.02781	+	0.333957i	0.253888	+	0.967234i	$0.418290\pi$
$240$	57.3256	+	44.9222i	0.238857	+	0.187176i
$241$	−50.4176	−	155.169i	−0.209202	−	0.643857i	−0.999515	−	0.0311532i	$-0.990082\pi$
$241$	−50.4176	−	155.169i	−0.209202	−	0.643857i	0.790313	−	0.612703i	$-0.209918\pi$
$242$	−14.9451	+	94.3596i	−0.0617566	+	0.389916i
$243$	−150.731	−	150.731i	−0.620294	−	0.620294i
$244$	16.6541	+	22.9224i	0.0682546	+	0.0939444i
$245$	−218.530	+	101.515i	−0.891959	+	0.414348i
$246$	278.809	+	202.567i	1.13337	+	0.823442i
$247$	284.074	−	44.9930i	1.15010	−	0.182158i
$248$	−4.89246	+	2.49283i	−0.0197276	+	0.0100517i
$249$			147.492i			0.592338i
$250$	35.9987	+	173.073i	0.143995	+	0.692290i
$251$	269.305			1.07293			0.536463	−	0.843924i	$-0.319760\pi$
$251$	269.305			1.07293			0.536463	+	0.843924i	$0.319760\pi$
$252$	−3.47830	−	6.82655i	−0.0138028	−	0.0270895i
$253$	−66.2747	−	418.442i	−0.261955	−	1.65392i
$254$	−73.4191	+	101.053i	−0.289051	+	0.397845i
$255$	−45.1399	−	97.1718i	−0.177019	−	0.381066i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	61.4130	−	61.4130i	0.238961	−	0.238961i	−0.577459	−	0.816420i	$-0.695956\pi$
$257$	61.4130	−	61.4130i	0.238961	−	0.238961i	0.816420	+	0.577459i	$0.195956\pi$
$258$	−279.179	−	44.2176i	−1.08209	−	0.171386i
$259$	−10.0568	+	3.26764i	−0.0388292	+	0.0126164i
$260$	56.2959	−	71.8397i	0.216523	−	0.276306i
$261$	−74.8889	+	230.484i	−0.286931	+	0.883082i
$262$	−121.097	−	61.7021i	−0.462203	−	0.235504i
$263$	−165.104	+	324.035i	−0.627773	+	1.23207i	0.329846	+	0.944035i	$0.393003\pi$
$263$	−165.104	+	324.035i	−0.627773	+	1.23207i	−0.957619	+	0.288039i	$0.906997\pi$
$264$	134.509	+	43.7045i	0.509503	+	0.165548i
$265$	151.168	−	101.644i	0.570446	−	0.383564i
$266$	12.3824	+	38.1090i	0.0465503	+	0.143267i
$267$	34.2509	−	216.251i	0.128280	−	0.809931i
$268$	−91.3793	−	91.3793i	−0.340967	−	0.340967i
$269$	184.825	+	254.390i	0.687082	+	0.945687i	0.999992	−	0.00409606i	$-0.00130382\pi$
$269$	184.825	+	254.390i	0.687082	+	0.945687i	−0.312910	+	0.949783i	$0.601304\pi$
$270$	119.761	+	23.4601i	0.443558	+	0.0868891i
$271$	−196.495	−	142.762i	−0.725073	−	0.526797i	0.162928	−	0.986638i	$-0.447906\pi$
$271$	−196.495	−	142.762i	−0.725073	−	0.526797i	−0.888001	+	0.459841i	$0.847906\pi$
$272$	23.2487	−	3.68224i	0.0854732	−	0.0135376i
$273$	−26.6263	+	13.5668i	−0.0975321	+	0.0496951i
$274$			338.656i			1.23597i
$275$	181.066	+	291.653i	0.658424	+	1.06055i
$276$	−224.703			−0.814141
$277$	194.750	+	382.219i	0.703070	+	1.37985i	0.915356	+	0.402646i	$0.131909\pi$
$277$	194.750	+	382.219i	0.703070	+	1.37985i	−0.212286	+	0.977208i	$0.568091\pi$
$278$	30.8600	+	194.842i	0.111007	+	0.700871i
$279$	4.86171	−	6.69157i	0.0174255	−	0.0239841i
$280$	11.1123	+	6.18082i	0.0396868	+	0.0220743i
$281$	−180.948	+	131.467i	−0.643944	+	0.467852i	−0.861203	−	0.508262i	$-0.830288\pi$
$281$	−180.948	+	131.467i	−0.643944	+	0.467852i	0.217259	+	0.976114i	$0.430288\pi$
$282$	−181.648	+	181.648i	−0.644142	+	0.644142i
$283$	−352.111	−	55.7689i	−1.24421	−	0.197063i	−0.500600	−	0.865679i	$-0.666887\pi$
$283$	−352.111	−	55.7689i	−1.24421	−	0.197063i	−0.743608	+	0.668615i	$0.766887\pi$
$284$	−59.8111	+	19.4338i	−0.210602	+	0.0684288i
$285$	538.880	+	197.025i	1.89081	+	0.691315i
$286$	54.7699	−	168.564i	0.191503	−	0.589386i
$287$	53.6112	+	27.3163i	0.186799	+	0.0951786i
$288$	10.9419	−	21.4746i	0.0379926	−	0.0745646i
$289$	241.921	+	78.6050i	0.837098	+	0.271990i
$290$	−110.301	−	386.788i	−0.380348	−	1.33375i
$291$	14.0166	+	43.1388i	0.0481672	+	0.148243i
$292$	21.6731	−	136.839i	0.0742230	−	0.468626i
$293$	−331.758	−	331.758i	−1.13228	−	1.13228i	−0.989797	−	0.142481i	$-0.954492\pi$
$293$	−331.758	−	331.758i	−1.13228	−	1.13228i	−0.142481	−	0.989797i	$-0.545508\pi$
$294$	145.877	+	200.782i	0.496179	+	0.682932i
$295$	−206.988	−	222.616i	−0.701654	−	0.754630i
$296$	−26.9112	−	19.5522i	−0.0909163	−	0.0660546i
$297$	234.069	−	37.0729i	0.788111	−	0.124825i
$298$	236.886	−	120.700i	0.794920	−	0.405032i
$299$			281.595i			0.941788i
$300$	167.808	−	70.6544i	0.559359	−	0.235515i
$301$	−49.3500			−0.163954
$302$	−102.893	−	201.938i	−0.340705	−	0.668670i
$303$	−37.6353	−	237.620i	−0.124209	−	0.784224i
$304$	−74.0908	+	101.977i	−0.243720	+	0.335451i
$305$	70.3187	−	8.53019i	0.230553	−	0.0279678i
$306$	−28.6854	+	20.8412i	−0.0937431	+	0.0681084i
$307$	5.33327	−	5.33327i	0.0173722	−	0.0173722i	−0.698367	−	0.715740i	$-0.746090\pi$
$307$	5.33327	−	5.33327i	0.0173722	−	0.0173722i	0.715740	+	0.698367i	$0.246090\pi$
$308$	24.3887	+	3.86279i	0.0791842	+	0.0125415i
$309$	35.3872	−	11.4980i	0.114522	−	0.0372103i
$310$	−0.499042	+	13.7183i	−0.00160981	+	0.0442524i
$311$	−78.3745	+	241.212i	−0.252008	+	0.775601i	0.742396	+	0.669961i	$0.233689\pi$
$311$	−78.3745	+	241.212i	−0.252008	+	0.775601i	−0.994404	+	0.105640i	$0.966311\pi$
$312$	−83.7595	−	42.6776i	−0.268460	−	0.136787i
$313$	−60.1772	+	118.104i	−0.192259	+	0.377330i	−0.966933	−	0.255031i	$-0.917914\pi$
$313$	−60.1772	+	118.104i	−0.192259	+	0.377330i	0.774673	+	0.632362i	$0.217914\pi$
$314$	167.396	+	54.3901i	0.533107	+	0.173217i
$315$	−19.1414	−	0.696324i	−0.0607663	−	0.00221055i
$316$	35.1275	+	108.111i	0.111163	+	0.342125i
$317$	35.1671	−	222.037i	0.110937	−	0.700431i	−0.868045	−	0.496486i	$-0.834624\pi$
$317$	35.1671	−	222.037i	0.110937	−	0.700431i	0.978982	−	0.203945i	$-0.0653764\pi$
$318$	−132.670	−	132.670i	−0.417200	−	0.417200i
$319$	−459.095	−	631.890i	−1.43917	−	1.98085i
$320$	4.81699	+	39.7089i	0.0150531	+	0.124090i
$321$	118.660	+	86.2117i	0.369658	+	0.268572i
$322$	−38.7484	+	6.13714i	−0.120337	+	0.0190594i
$323$	165.229	−	84.1882i	0.511544	−	0.260645i
$324$		−	202.385i		−	0.624646i
$325$	−88.5431	−	210.294i	−0.272440	−	0.647059i
$326$	257.317			0.789317
$327$	88.1371	+	172.979i	0.269532	+	0.528987i
$328$	29.6095	+	186.947i	0.0902728	+	0.569960i
$329$	−26.3627	+	36.2851i	−0.0801297	+	0.110289i
$330$	258.941	−	240.762i	0.784669	−	0.729583i
$331$	−340.878	+	247.662i	−1.02984	+	0.748225i	−0.968277	−	0.249878i	$-0.919609\pi$
$331$	−340.878	+	247.662i	−1.02984	+	0.748225i	−0.0615656	+	0.998103i	$0.519609\pi$
$332$	−57.2800	+	57.2800i	−0.172530	+	0.172530i
$333$	49.4903	+	7.83849i	0.148619	+	0.0235390i
$334$	244.124	−	79.3208i	0.730911	−	0.237487i
$335$	−310.688	+	88.5993i	−0.927428	+	0.264476i
$336$	4.04711	−	12.4557i	0.0120450	−	0.0370706i
$337$	−311.868	−	158.905i	−0.925423	−	0.471527i	−0.0747388	−	0.997203i	$-0.523812\pi$
$337$	−311.868	−	158.905i	−0.925423	−	0.471527i	−0.850685	+	0.525676i	$0.823812\pi$
$338$	55.0217	−	107.986i	0.162786	−	0.319486i
$339$	372.990	+	121.192i	1.10026	+	0.357498i
$340$	20.2071	−	55.2681i	0.0594326	−	0.162553i
$341$	8.23761	+	25.3528i	0.0241572	+	0.0743483i
$342$	29.7031	−	187.538i	0.0868512	−	0.548357i
$343$	61.7924	+	61.7924i	0.180153	+	0.180153i
$344$	−91.2493	−	125.594i	−0.265260	−	0.365099i
$345$	−273.060	+	490.927i	−0.791479	+	1.42298i
$346$	−253.781	−	184.383i	−0.733471	−	0.532898i
$347$	163.225	−	25.8523i	0.470388	−	0.0745022i	0.0832597	−	0.996528i	$-0.473467\pi$
$347$	163.225	−	25.8523i	0.470388	−	0.0745022i	0.387129	+	0.922026i	$0.373467\pi$
$348$	−369.112	+	188.072i	−1.06067	+	0.540437i
$349$		−	541.612i		−	1.55190i	−0.630796	−	0.775949i	$-0.717272\pi$
$349$		−	541.612i		−	1.55190i	0.630796	−	0.775949i	$-0.282728\pi$
$350$	27.0075	−	16.7670i	0.0771642	−	0.0479058i
$351$	−157.519			−0.448772
$352$	35.2647	+	69.2108i	0.100184	+	0.196622i
$353$	−0.890182	−	5.62039i	−0.00252176	−	0.0159218i	0.986395	−	0.164390i	$-0.0525656\pi$
$353$	−0.890182	−	5.62039i	−0.00252176	−	0.0159218i	−0.988917	+	0.148468i	$0.952566\pi$
$354$	−184.029	+	253.294i	−0.519855	+	0.715519i
$355$	−30.2241	+	154.290i	−0.0851382	+	0.434620i
$356$	97.2849	−	70.6816i	0.273272	−	0.198544i
$357$	−13.6241	+	13.6241i	−0.0381626	+	0.0381626i
$358$	90.7704	+	14.3766i	0.253549	+	0.0401582i
$359$	−46.7523	+	15.1908i	−0.130229	+	0.0423141i	−0.373407	−	0.927668i	$-0.621810\pi$
$359$	−46.7523	+	15.1908i	−0.130229	+	0.0423141i	0.243177	+	0.969982i	$0.421810\pi$
$360$	−33.6207	−	50.0016i	−0.0933910	−	0.138893i
$361$	−195.314	+	601.114i	−0.541036	+	1.66514i
$362$	−267.207	−	136.149i	−0.738142	−	0.376102i
$363$	111.681	−	219.186i	0.307661	−	0.603819i
$364$	−15.6093	−	5.07178i	−0.0428828	−	0.0139335i
$365$	−272.626	−	213.638i	−0.746919	−	0.585310i
$366$	−22.5451	−	69.3866i	−0.0615986	−	0.189581i
$367$	−55.9723	+	353.395i	−0.152513	+	0.962929i	0.786136	+	0.618054i	$0.212079\pi$
$367$	−55.9723	+	353.395i	−0.152513	+	0.962929i	−0.938649	+	0.344875i	$0.887921\pi$
$368$	−87.2655	−	87.2655i	−0.237134	−	0.237134i
$369$	−167.587	−	230.664i	−0.454166	−	0.625106i
$370$	−75.4199	+	35.0353i	−0.203837	+	0.0946901i
$371$	−26.5014	−	19.2544i	−0.0714324	−	0.0518987i
$372$	13.9647	−	2.21180i	0.0375396	−	0.00594569i
$373$	147.336	−	75.0714i	0.395003	−	0.201264i	−0.245196	−	0.969474i	$-0.578852\pi$
$373$	147.336	−	75.0714i	0.395003	−	0.201264i	0.640198	+	0.768210i	$0.278852\pi$
$374$		−	114.275i		−	0.305549i
$375$	49.5562	−	452.483i	0.132150	−	1.20662i
$376$	−141.089			−0.375238
$377$	235.689	+	462.566i	0.625170	+	1.22697i
$378$	−3.43301	−	21.6752i	−0.00908203	−	0.0573417i
$379$	−346.461	+	476.863i	−0.914145	+	1.25821i	0.0515863	+	0.998669i	$0.483572\pi$
$379$	−346.461	+	476.863i	−0.914145	+	1.25821i	−0.965731	+	0.259544i	$0.916428\pi$
$380$	132.763	+	285.795i	0.349375	+	0.752093i
$381$	260.204	−	189.049i	0.682950	−	0.496193i
$382$	92.2477	−	92.2477i	0.241486	−	0.241486i
$383$	674.830	+	106.883i	1.76196	+	0.279067i	0.951705	−	0.307013i	$-0.0993296\pi$
$383$	674.830	+	106.883i	1.76196	+	0.279067i	0.810253	+	0.586080i	$0.199330\pi$
$384$	39.1825	−	12.7312i	0.102038	−	0.0331541i
$385$	38.0767	−	48.5900i	0.0989004	−	0.126208i
$386$	93.3928	−	287.433i	0.241950	−	0.744646i
$387$	208.361	+	106.165i	0.538400	+	0.274329i
$388$	−11.3099	+	22.1968i	−0.0291491	+	0.0572084i
$389$	149.313	+	48.5147i	0.383837	+	0.124716i	0.494579	−	0.869133i	$-0.335322\pi$
$389$	149.313	+	48.5147i	0.383837	+	0.124716i	−0.110741	+	0.993849i	$0.535322\pi$
$390$	−195.026	+	131.134i	−0.500067	+	0.336242i
$391$	56.1047	+	172.672i	0.143490	+	0.441617i
$392$	−21.3230	+	134.628i	−0.0543954	+	0.343439i
$393$	247.460	+	247.460i	0.629669	+	0.629669i
$394$	56.3145	+	77.5103i	0.142930	+	0.196727i
$395$	278.887	+	54.6315i	0.706043	+	0.138307i
$396$	−94.6618	−	68.7758i	−0.239045	−	0.173676i
$397$	171.281	−	27.1282i	0.431438	−	0.0683331i	0.0630614	−	0.998010i	$-0.479914\pi$
$397$	171.281	−	27.1282i	0.431438	−	0.0683331i	0.368377	+	0.929677i	$0.379914\pi$
$398$	−142.995	+	72.8598i	−0.359285	+	0.183065i
$399$		−	103.178i		−	0.258592i
$400$	92.6090	+	37.7304i	0.231522	+	0.0943259i
$401$	410.229			1.02302			0.511508	−	0.859278i	$-0.329087\pi$
$401$	410.229			1.02302			0.511508	+	0.859278i	$0.329087\pi$
$402$	151.069	+	296.490i	0.375794	+	0.737537i
$403$	−2.77179	−	17.5004i	−0.00687789	−	0.0434253i
$404$	77.6659	−	106.898i	0.192242	−	0.264599i
$405$	−442.168	−	245.940i	−1.09177	−	0.607258i
$406$	−58.5140	+	42.5129i	−0.144123	+	0.104712i
$407$	−114.191	+	114.191i	−0.280569	+	0.280569i
$408$	−59.8639	−	9.48152i	−0.146725	−	0.0232390i
$409$	38.3159	−	12.4496i	0.0936820	−	0.0304391i	−0.261801	−	0.965122i	$-0.584316\pi$
$409$	38.3159	−	12.4496i	0.0936820	−	0.0304391i	0.355483	+	0.934683i	$0.384316\pi$
$410$	444.420	+	162.488i	1.08395	+	0.396313i
$411$	269.468	−	829.338i	0.655640	−	2.01785i
$412$	18.2083	+	9.27758i	0.0441948	+	0.0225184i
$413$	−24.8164	+	48.7049i	−0.0600881	+	0.117929i
$414$	176.802	+	57.4466i	0.427059	+	0.138760i
$415$	55.5374	+	194.751i	0.133825	+	0.469280i
$416$	−15.9545	−	49.1030i	−0.0383522	−	0.118036i
$417$	79.4624	−	501.706i	0.190557	−	1.20313i
$418$	432.716	+	432.716i	1.03521	+	1.03521i
$419$	−256.242	−	352.687i	−0.611556	−	0.841735i	0.385148	−	0.922855i	$-0.374150\pi$
$419$	−256.242	−	352.687i	−0.611556	−	0.841735i	−0.996704	+	0.0811197i	$0.974150\pi$
$420$	−22.2950	−	23.9783i	−0.0530833	−	0.0570912i
$421$	140.600	+	102.152i	0.333967	+	0.242641i	0.742112	−	0.670276i	$-0.233824\pi$
$421$	140.600	+	102.152i	0.333967	+	0.242641i	−0.408145	+	0.912917i	$0.633824\pi$
$422$	15.8582	−	2.51169i	0.0375787	−	0.00595188i
$423$	189.365	−	96.4863i	0.447671	−	0.228100i
$424$		−	103.047i		−	0.243035i
$425$	−96.1930	−	111.310i	−0.226337	−	0.261906i
$426$	161.935			0.380130
$427$	−5.78284	−	11.3495i	−0.0135430	−	0.0265795i
$428$	12.6017	+	79.5639i	0.0294432	+	0.185897i
$429$	−268.253	+	369.219i	−0.625299	+	0.860650i
$430$	−385.282	+	46.7376i	−0.896005	+	0.108692i
$431$	−98.9485	+	71.8903i	−0.229579	+	0.166799i	−0.696628	−	0.717433i	$-0.745317\pi$
$431$	−98.9485	+	71.8903i	−0.229579	+	0.166799i	0.467049	+	0.884231i	$0.345317\pi$
$432$	48.8148	−	48.8148i	0.112997	−	0.112997i
$433$	−290.440	−	46.0011i	−0.670761	−	0.106238i	−0.188241	−	0.982123i	$-0.560279\pi$
$433$	−290.440	−	46.0011i	−0.670761	−	0.106238i	−0.482520	+	0.875885i	$0.660279\pi$
$434$	2.34771	−	0.762816i	0.00540946	−	0.00175764i
$435$	−37.6503	+	1034.98i	−0.0865524	+	2.37925i
$436$	−32.9491	+	101.407i	−0.0755712	+	0.232584i
$437$	−866.291	−	441.397i	−1.98236	−	1.01006i
$438$	−161.958	+	317.860i	−0.369767	+	0.725708i
$439$	135.892	+	44.1541i	0.309550	+	0.100579i	0.459672	−	0.888089i	$-0.347967\pi$
$439$	135.892	+	44.1541i	0.309550	+	0.100579i	−0.150123	+	0.988667i	$0.547967\pi$
$440$	194.064	+	7.05966i	0.441055	+	0.0160447i
$441$	−63.4487	−	195.275i	−0.143875	−	0.442800i
$442$	−11.8821	+	75.0206i	−0.0268826	+	0.169730i
$443$	13.7393	+	13.7393i	0.0310143	+	0.0310143i	0.722444	−	0.691430i	$-0.243019\pi$
$443$	13.7393	+	13.7393i	0.0310143	+	0.0310143i	−0.691430	+	0.722444i	$0.743019\pi$
$444$	50.3455	+	69.2947i	0.113391	+	0.156069i
$445$	−36.2029	−	298.439i	−0.0813549	−	0.670650i
$446$	167.696	+	121.838i	0.376000	+	0.273180i
$447$	−676.154	+	107.092i	−1.51265	+	0.239580i
$448$	6.40903	−	3.26556i	0.0143059	−	0.00728920i
$449$		−	313.808i		−	0.698904i	−0.936954	−	0.349452i	$-0.886368\pi$
$449$		−	313.808i		−	0.698904i	0.936954	−	0.349452i	$-0.113632\pi$
$450$	−150.099	+	12.6918i	−0.333553	+	0.0282041i
$451$	918.906			2.03749
$452$	97.7881	+	191.920i	0.216345	+	0.424602i
$453$	91.2929	+	576.401i	0.201530	+	1.27241i
$454$	−175.082	+	240.980i	−0.385644	+	0.530793i
$455$	−30.0493	+	27.9398i	−0.0660424	+	0.0614061i
$456$	262.585	−	190.779i	0.575844	−	0.418375i
$457$	−36.5102	+	36.5102i	−0.0798911	+	0.0798911i	−0.745923	−	0.666032i	$-0.767991\pi$
$457$	−36.5102	+	36.5102i	−0.0798911	+	0.0798911i	0.666032	+	0.745923i	$0.267991\pi$
$458$	−265.676	−	42.0789i	−0.580079	−	0.0918754i
$459$	−96.5899	+	31.3839i	−0.210435	+	0.0683746i
$460$	−296.702	+	84.6107i	−0.645003	+	0.183936i
$461$	252.310	−	776.530i	0.547310	−	1.68445i	−0.168124	−	0.985766i	$-0.553771\pi$
$461$	252.310	−	776.530i	0.547310	−	1.68445i	0.715434	−	0.698680i	$-0.246229\pi$
$462$	−56.6522	−	28.8657i	−0.122624	−	0.0624799i
$463$	249.688	−	490.040i	0.539283	−	1.05840i	−0.447184	−	0.894442i	$-0.647573\pi$
$463$	249.688	−	490.040i	0.539283	−	1.05840i	0.986467	−	0.163960i	$-0.0524269\pi$
$464$	−216.388	−	70.3086i	−0.466353	−	0.151527i
$465$	12.1377	−	33.1977i	0.0261026	−	0.0713929i
$466$	−194.036	−	597.180i	−0.416385	−	1.28150i
$467$	92.0733	−	581.328i	0.197159	−	1.24481i	−0.668322	−	0.743872i	$-0.732987\pi$
$467$	92.0733	−	581.328i	0.197159	−	1.24481i	0.865481	−	0.500941i	$-0.167013\pi$
$468$	54.9935	+	54.9935i	0.117507	+	0.117507i
$469$	34.1486	+	47.0015i	0.0728115	+	0.100216i
$470$	−171.453	+	308.250i	−0.364793	+	0.655851i
$471$	−366.659	−	266.393i	−0.778468	−	0.565590i
$472$	−169.838	+	26.8997i	−0.359827	+	0.0569909i
$473$	−671.529	+	342.161i	−1.41972	+	0.723385i
$474$		−	292.706i		−	0.617523i
$475$	785.735	+	57.2426i	1.65418	+	0.120511i
$476$	−10.5821			−0.0222312
$477$	70.4704	+	138.306i	0.147737	+	0.289949i
$478$	−57.1417	−	360.779i	−0.119543	−	0.754767i
$479$	−122.812	+	169.037i	−0.256393	+	0.352895i	−0.917737	−	0.397188i	$-0.869986\pi$
$479$	−122.812	+	169.037i	−0.256393	+	0.352895i	0.661344	+	0.750083i	$0.269986\pi$
$480$	19.8000	−	101.076i	0.0412499	−	0.210576i
$481$	86.8391	−	63.0923i	0.180539	−	0.131169i
$482$	−163.155	+	163.155i	−0.338495	+	0.338495i
$483$	99.7746	+	15.8027i	0.206573	+	0.0327179i
$484$	128.495	−	41.7507i	0.265486	−	0.0862617i
$485$	34.7515	+	51.6833i	0.0716526	+	0.106564i
$486$	−93.1571	+	286.708i	−0.191681	+	0.589935i
$487$	−148.346	−	75.5860i	−0.304611	−	0.155207i	0.295003	−	0.955496i	$-0.404679\pi$
$487$	−148.346	−	75.5860i	−0.304611	−	0.155207i	−0.599614	+	0.800289i	$0.704679\pi$
$488$	18.1914	−	35.7025i	0.0372774	−	0.0731609i
$489$	−630.146	−	204.747i	−1.28864	−	0.418705i
$490$	268.222	+	210.187i	0.547391	+	0.428953i
$491$	91.4686	+	281.511i	0.186290	+	0.573343i	0.999968	−	0.00797308i	$-0.00253794\pi$
$491$	91.4686	+	281.511i	0.186290	+	0.573343i	−0.813678	+	0.581316i	$0.802538\pi$
$492$	76.2425	−	481.376i	0.154964	−	0.978407i
$493$	236.685	+	236.685i	0.480091	+	0.480091i
$494$	−239.081	−	329.067i	−0.483970	−	0.666128i
$495$	−265.294	+	123.239i	−0.535947	+	0.248967i
$496$	6.28230	+	4.56436i	0.0126659	+	0.00920234i
$497$	27.9246	−	4.42282i	0.0561862	−	0.00889903i
$498$	185.851	−	94.6958i	0.373195	−	0.190152i
$499$		−	459.459i		−	0.920759i	−0.887722	−	0.460380i	$-0.847713\pi$
$499$		−	459.459i		−	0.920759i	0.887722	−	0.460380i	$-0.152287\pi$
$500$	194.972	−	156.480i	0.389943	−	0.312961i
$501$	−660.954			−1.31927
$502$	−172.904	−	339.344i	−0.344431	−	0.675983i
$503$	36.5339	+	230.666i	0.0726319	+	0.458580i	0.997021	+	0.0771293i	$0.0245754\pi$
$503$	36.5339	+	230.666i	0.0726319	+	0.458580i	−0.924389	+	0.381451i	$0.875425\pi$
$504$	−6.36875	+	8.76583i	−0.0126364	+	0.0173925i
$505$	−139.169	−	299.586i	−0.275582	−	0.593240i
$506$	−484.717	+	352.167i	−0.957938	+	0.695983i
$507$	−220.668	+	220.668i	−0.435242	+	0.435242i
$508$	174.472	+	27.6336i	0.343448	+	0.0543969i
$509$	241.356	−	78.4213i	0.474177	−	0.154069i	−0.0621728	−	0.998065i	$-0.519803\pi$
$509$	241.356	−	78.4213i	0.474177	−	0.154069i	0.536349	+	0.843996i	$0.319803\pi$
$510$	−93.4620	+	119.268i	−0.183259	+	0.233858i
$511$	−19.2470	+	59.2361i	−0.0376653	+	0.115922i
$512$	20.1612	+	10.2726i	0.0393773	+	0.0200637i
$513$	246.910	−	484.588i	0.481306	−	0.944615i
$514$	−116.815	−	37.9553i	−0.227266	−	0.0738431i
$515$	42.3963	−	28.5070i	0.0823229	−	0.0553533i
$516$	123.526	+	380.175i	0.239392	+	0.736773i
$517$	−107.152	+	676.531i	−0.207257	+	1.30857i
$518$	10.5743	+	10.5743i	0.0204137	+	0.0204137i
$519$	474.774	+	653.470i	0.914785	+	1.25909i
$520$	−126.667	−	24.8130i	−0.243591	−	0.0477173i
$521$	260.762	+	189.454i	0.500502	+	0.363636i	0.809209	−	0.587521i	$-0.199896\pi$
$521$	260.762	+	189.454i	0.500502	+	0.363636i	−0.308707	+	0.951157i	$0.599896\pi$
$522$	338.509	−	53.6146i	0.648485	−	0.102710i
$523$	−122.646	+	62.4913i	−0.234505	+	0.119486i	−0.567295	−	0.823515i	$-0.692010\pi$
$523$	−122.646	+	62.4913i	−0.234505	+	0.119486i	0.332790	+	0.943001i	$0.392010\pi$
$524$			192.207i			0.366806i
$525$	−79.4804	+	19.5711i	−0.151391	+	0.0372784i
$526$	514.312			0.977780
$527$	−5.18641	−	10.1789i	−0.00984139	−	0.0193148i
$528$	−31.2890	−	197.551i	−0.0592595	−	0.374150i
$529$	248.579	−	342.140i	0.469904	−	0.646767i
$530$	−225.135	−	125.223i	−0.424784	−	0.236270i
$531$	209.555	−	152.250i	0.394641	−	0.286724i
$532$	40.0702	−	40.0702i	0.0753199	−	0.0753199i
$533$	−603.254	−	95.5460i	−1.13181	−	0.179261i
$534$	−294.483	+	95.6834i	−0.551467	+	0.179182i
$535$	189.144	+	69.1545i	0.353539	+	0.129261i
$536$	−56.4755	+	173.814i	−0.105365	+	0.324279i
$537$	−210.849	−	107.433i	−0.392643	−	0.200061i
$538$	201.885	−	396.221i	0.375251	−	0.736471i
$539$	629.354	+	204.490i	1.16763	+	0.379387i
$540$	−47.3297	−	165.970i	−0.0876476	−	0.307351i
$541$	195.153	+	600.618i	0.360726	+	1.11020i	0.952614	+	0.304180i	$0.0983825\pi$
$541$	195.153	+	600.618i	0.360726	+	1.11020i	−0.591889	+	0.806020i	$0.701617\pi$
$542$	−53.7330	+	339.257i	−0.0991383	+	0.625935i
$543$	546.033	+	546.033i	1.00559	+	1.00559i
$544$	−19.5665	−	26.9310i	−0.0359678	−	0.0495054i
$545$	181.512	+	195.217i	0.333049	+	0.358196i
$546$	34.1902	+	24.8407i	0.0626195	+	0.0454957i
$547$	98.4028	−	15.5855i	0.179895	−	0.0284926i	−0.0658367	−	0.997830i	$-0.520972\pi$
$547$	98.4028	−	15.5855i	0.179895	−	0.0284926i	0.245732	+	0.969338i	$0.420972\pi$
$548$	426.731	−	217.430i	0.778707	−	0.396771i
$549$			60.3591i			0.109944i
$550$	251.252	−	415.410i	0.456821	−	0.755290i
$551$	−1792.47			−3.25312
$552$	144.268	+	283.142i	0.261355	+	0.512939i
$553$	−7.99445	−	50.4750i	−0.0144565	−	0.0912748i
$554$	356.587	−	490.800i	0.643659	−	0.885920i
$555$	212.574	−	25.7868i	0.383016	−	0.0464628i
$556$	225.702	−	163.982i	0.405939	−	0.294932i
$557$	557.960	−	557.960i	1.00172	−	1.00172i	0.00172416	−	0.999999i	$-0.499451\pi$
$557$	557.960	−	557.960i	1.00172	−	1.00172i	0.999999	−	0.00172416i	$-0.000548818\pi$
$558$	−11.5533	−	1.82986i	−0.0207048	−	0.00327932i
$559$	476.430	−	154.801i	0.852290	−	0.276926i
$560$	0.653736	−	17.9707i	0.00116739	−	0.0320905i
$561$	−90.9286	+	279.850i	−0.162083	+	0.498841i
$562$	281.833	+	143.601i	0.501483	+	0.255518i
$563$	50.5821	−	99.2730i	0.0898439	−	0.176329i	−0.841712	−	0.539927i	$-0.818452\pi$
$563$	50.5821	−	99.2730i	0.0898439	−	0.176329i	0.931556	+	0.363598i	$0.118452\pi$
$564$	345.515	+	112.265i	0.612616	+	0.199051i
$565$	538.136	+	19.5763i	0.952453	+	0.0346483i
$566$	155.796	+	479.492i	0.275258	+	0.847158i
$567$	−14.2332	+	89.8649i	−0.0251027	+	0.158492i
$568$	62.8891	+	62.8891i	0.110720	+	0.110720i
$569$	1.68455	+	2.31858i	0.00296054	+	0.00407483i	0.810495	−	0.585746i	$-0.199198\pi$
$569$	1.68455	+	2.31858i	0.00296054	+	0.00407483i	−0.807534	+	0.589821i	$0.799198\pi$
$570$	−97.7164	−	805.526i	−0.171432	−	1.41320i
$571$	−144.753	−	105.169i	−0.253507	−	0.184184i	0.453773	−	0.891118i	$-0.350078\pi$
$571$	−144.753	−	105.169i	−0.253507	−	0.184184i	−0.707280	+	0.706934i	$0.750078\pi$
$572$	−247.568	+	39.2109i	−0.432811	+	0.0685506i
$573$	−299.308	+	152.505i	−0.522352	+	0.266151i
$574$		−	85.0922i		−	0.148244i
$575$	−175.697	+	751.048i	−0.305560	+	1.30617i
$576$	−34.0847			−0.0591748
$577$	217.521	+	426.909i	0.376987	+	0.739878i	0.999072	−	0.0430716i	$-0.0137144\pi$
$577$	217.521	+	426.909i	0.376987	+	0.739878i	−0.622085	+	0.782949i	$0.713714\pi$
$578$	−56.2750	−	355.306i	−0.0973615	−	0.614717i
$579$	−457.421	+	629.586i	−0.790019	+	1.08737i
$580$	−416.564	+	387.321i	−0.718214	+	0.667794i
$581$	29.4623	−	21.4056i	0.0507096	−	0.0368427i
$582$	45.3588	−	45.3588i	0.0779361	−	0.0779361i
$583$	−494.115	−	78.2602i	−0.847539	−	0.134237i
$584$	−186.342	+	60.5461i	−0.319078	+	0.103675i
$585$	186.977	−	53.3205i	0.319619	−	0.0911461i
$586$	−205.038	+	631.041i	−0.349893	+	1.07686i
$587$	766.476	+	390.539i	1.30575	+	0.665313i	0.961820	−	0.273682i	$-0.0882415\pi$
$587$	766.476	+	390.539i	1.30575	+	0.665313i	0.343931	+	0.938995i	$0.388241\pi$
$588$	159.342	−	312.725i	0.270989	−	0.531846i
$589$	58.1826	+	18.9047i	0.0987819	+	0.0320962i
$590$	−147.618	+	403.748i	−0.250200	+	0.684319i
$591$	−76.2343	−	234.625i	−0.128992	−	0.396997i
$592$	−7.35908	+	46.4634i	−0.0124309	+	0.0784854i
$593$	−735.093	−	735.093i	−1.23962	−	1.23962i	−0.960158	−	0.279459i	$-0.909845\pi$
$593$	−735.093	−	735.093i	−1.23962	−	1.23962i	−0.279459	−	0.960158i	$-0.590155\pi$
$594$	−196.996	−	271.142i	−0.331643	−	0.456468i
$595$	−12.8594	+	23.1195i	−0.0216124	+	0.0388563i
$596$	−304.181	−	221.000i	−0.510370	−	0.370806i
$597$	408.157	−	64.6457i	0.683680	−	0.108284i
$598$	354.830	−	180.795i	0.593361	−	0.302332i
$599$		−	515.872i		−	0.861222i	−0.902538	−	0.430611i	$-0.858298\pi$
$599$		−	515.872i		−	0.861222i	0.902538	−	0.430611i	$-0.141702\pi$
$600$	−196.769	−	166.087i	−0.327948	−	0.276812i
$601$	707.544			1.17728			0.588639	−	0.808396i	$-0.299664\pi$
$601$	707.544			1.17728			0.588639	+	0.808396i	$0.299664\pi$
$602$	31.6847	+	62.1846i	0.0526323	+	0.103297i
$603$	−43.0660	−	271.908i	−0.0714195	−	0.450925i
$604$	−188.396	+	259.305i	−0.311914	+	0.429313i
$605$	64.9320	−	331.470i	0.107326	−	0.547885i
$606$	−275.255	+	199.985i	−0.454217	+	0.330008i
$607$	−422.828	+	422.828i	−0.696587	+	0.696587i	−0.963673	−	0.267086i	$-0.913939\pi$
$607$	−422.828	+	422.828i	−0.696587	+	0.696587i	0.267086	+	0.963673i	$0.413939\pi$
$608$	176.068	+	27.8864i	0.289585	+	0.0458658i
$609$	177.123	−	57.5507i	0.290842	−	0.0945004i
$610$	−55.8961	−	83.1301i	−0.0916329	−	0.136279i
$611$	140.689	−	432.995i	0.230259	−	0.708666i
$612$	44.6786	+	22.7649i	0.0730042	+	0.0371975i
$613$	−447.989	+	879.227i	−0.730813	+	1.43430i	0.163353	+	0.986568i	$0.447769\pi$
$613$	−447.989	+	879.227i	−0.730813	+	1.43430i	−0.894167	+	0.447734i	$0.852231\pi$
$614$	−10.1445	−	3.29614i	−0.0165219	−	0.00536831i
$615$	−959.052	−	751.544i	−1.55943	−	1.22202i
$616$	−10.7911	−	33.2117i	−0.0175181	−	0.0539150i
$617$	−95.2002	+	601.071i	−0.154295	+	0.974182i	0.782079	+	0.623179i	$0.214159\pi$
$617$	−95.2002	+	601.071i	−0.154295	+	0.974182i	−0.936374	+	0.351003i	$0.885841\pi$
$618$	−37.2083	−	37.2083i	−0.0602075	−	0.0602075i
$619$	716.320	+	985.930i	1.15722	+	1.59278i	0.720994	+	0.692942i	$0.243686\pi$
$619$	716.320	+	985.930i	1.15722	+	1.59278i	0.436227	+	0.899836i	$0.356314\pi$
$620$	17.6064	−	8.17883i	0.0283974	−	0.0131917i
$621$	430.786	+	312.984i	0.693697	+	0.504000i
$622$	354.264	−	56.1099i	0.569557	−	0.0902089i
$623$	−48.1681	+	24.5429i	−0.0773164	+	0.0393947i
$624$			132.944i			0.213051i
$625$	−104.945	−	616.126i	−0.167912	−	0.985802i
$626$	187.456			0.299451
$627$	−715.371	−	1403.99i	−1.14094	−	2.23923i
$628$	−38.9390	−	245.851i	−0.0620048	−	0.391483i
$629$	40.6788	−	55.9896i	0.0646723	−	0.0890137i
$630$	11.4121	+	24.5666i	0.0181145	+	0.0389946i
$631$	−694.007	+	504.226i	−1.09985	+	0.799090i	−0.981036	−	0.193827i	$-0.937910\pi$
$631$	−694.007	+	504.226i	−1.09985	+	0.799090i	−0.118817	+	0.992916i	$0.537910\pi$
$632$	113.675	−	113.675i	0.179865	−	0.179865i
$633$	−40.8339	−	6.46745i	−0.0645085	−	0.0102171i
$634$	−302.361	+	98.2430i	−0.476910	+	0.154957i
$635$	272.392	−	347.602i	0.428964	−	0.547405i
$636$	−81.9944	+	252.353i	−0.128922	+	0.396781i
$637$	−391.903	−	199.685i	−0.615233	−	0.313477i
$638$	−501.471	+	984.192i	−0.786004	+	1.54262i
$639$	−127.415	−	41.3997i	−0.199398	−	0.0647882i
$640$	46.9434	−	31.5644i	0.0733491	−	0.0493194i
$641$	−263.656	−	811.451i	−0.411321	−	1.26591i	−0.915501	−	0.402316i	$-0.868205\pi$
$641$	−263.656	−	811.451i	−0.411321	−	1.26591i	0.504180	−	0.863598i	$-0.331795\pi$
$642$	32.4485	−	204.872i	0.0505429	−	0.319115i
$643$	−382.594	−	382.594i	−0.595015	−	0.595015i	0.343967	−	0.938982i	$-0.388229\pi$
$643$	−382.594	−	382.594i	−0.595015	−	0.595015i	−0.938982	+	0.343967i	$0.888229\pi$
$644$	32.6112	+	44.8855i	0.0506386	+	0.0696980i
$645$	980.710	+	192.112i	1.52048	+	0.297849i
$646$	−212.167	−	154.148i	−0.328431	−	0.238619i
$647$	231.687	−	36.6956i	0.358094	−	0.0567165i	0.0252045	−	0.999682i	$-0.491976\pi$
$647$	231.687	−	36.6956i	0.358094	−	0.0567165i	0.332890	+	0.942966i	$0.391976\pi$
$648$	−255.020	+	129.939i	−0.393550	+	0.200524i
$649$			834.811i			1.28630i
$650$	−208.138	+	246.588i	−0.320212	+	0.379366i
$651$	−6.35629			−0.00976389
$652$	−165.208	−	324.239i	−0.253386	−	0.497298i
$653$	54.5654	+	344.513i	0.0835612	+	0.527584i	0.993590	+	0.113040i	$0.0360589\pi$
$653$	54.5654	+	344.513i	0.0835612	+	0.527584i	−0.910029	+	0.414544i	$0.863941\pi$
$654$	161.379	−	222.118i	0.246756	−	0.339631i
$655$	419.930	+	233.570i	0.641114	+	0.356596i
$656$	216.556	−	157.337i	0.330116	−	0.239844i
$657$	208.696	−	208.696i	0.317649	−	0.317649i
$658$	62.6478	+	9.92244i	0.0952094	+	0.0150797i
$659$	−130.784	+	42.4942i	−0.198458	+	0.0644829i	−0.406559	−	0.913624i	$-0.633272\pi$
$659$	−130.784	+	42.4942i	−0.198458	+	0.0644829i	0.208101	+	0.978107i	$0.433272\pi$
$660$	−469.629	−	171.705i	−0.711558	−	0.260159i
$661$	60.3829	−	185.840i	0.0913509	−	0.281149i	−0.894935	−	0.446197i	$-0.852778\pi$
$661$	60.3829	−	185.840i	0.0913509	−	0.281149i	0.986286	+	0.165048i	$0.0527780\pi$
$662$	530.930	+	270.522i	0.802009	+	0.408644i
$663$	88.7920	−	174.264i	0.133925	−	0.262842i
$664$	108.953	+	35.4010i	0.164086	+	0.0533147i
$665$	−38.8512	−	136.238i	−0.0584229	−	0.204870i
$666$	−21.8976	−	67.3940i	−0.0328793	−	0.101192i
$667$	274.534	−	1733.34i	0.411595	−	2.59871i
$668$	−256.687	−	256.687i	−0.384263	−	0.384263i
$669$	−313.726	−	431.806i	−0.468947	−	0.645450i
$670$	311.116	+	334.606i	0.464352	+	0.499412i
$671$	−157.380	−	114.343i	−0.234545	−	0.170407i
$672$	−18.2935	+	2.89741i	−0.0272225	+	0.00431162i
$673$	156.383	−	79.6810i	0.232367	−	0.118397i	−0.333931	−	0.942598i	$-0.608375\pi$
$673$	156.383	−	79.6810i	0.232367	−	0.118397i	0.566298	+	0.824201i	$0.308375\pi$
$674$			494.999i			0.734420i
$675$	−420.123	−	98.2819i	−0.622404	−	0.145603i
$676$	−171.397			−0.253545
$677$	219.405	+	430.607i	0.324084	+	0.636051i	0.994360	−	0.106061i	$-0.0338240\pi$
$677$	219.405	+	430.607i	0.324084	+	0.636051i	−0.670275	+	0.742112i	$0.733824\pi$
$678$	−86.7637	−	547.804i	−0.127970	−	0.807971i
$679$	6.58295	−	9.06065i	0.00969506	−	0.0133441i
$680$	−82.6156	+	10.0219i	−0.121493	+	0.0147381i
$681$	620.508	−	450.825i	0.911172	−	0.662005i
$682$	26.6575	−	26.6575i	0.0390872	−	0.0390872i
$683$	−266.484	−	42.2070i	−0.390167	−	0.0617964i	−0.0417309	−	0.999129i	$-0.513287\pi$
$683$	−266.484	−	42.2070i	−0.390167	−	0.0617964i	−0.348436	+	0.937332i	$0.613287\pi$
$684$	−255.382	+	82.9788i	−0.373366	+	0.121314i
$685$	43.5276	−	1196.54i	0.0635439	−	1.74677i
$686$	38.1898	−	117.536i	0.0556702	−	0.171335i
$687$	617.134	+	314.446i	0.898303	+	0.457708i
$688$	−99.6719	+	195.617i	−0.144872	+	0.284327i
$689$	316.245	+	102.754i	0.458991	+	0.149135i
$690$	793.920	+	28.8812i	1.15061	+	0.0418568i
$691$	−39.1934	−	120.625i	−0.0567198	−	0.174565i	0.918683	−	0.394996i	$-0.129254\pi$
$691$	−39.1934	−	120.625i	−0.0567198	−	0.174565i	−0.975403	+	0.220430i	$0.929254\pi$
$692$	−69.3983	+	438.164i	−0.100287	+	0.633185i
$693$	37.1958	+	37.1958i	0.0536735	+	0.0536735i
$694$	−137.373	−	189.077i	−0.197943	−	0.272445i
$695$	−83.9912	−	692.382i	−0.120851	−	0.996233i
$696$	473.969	+	344.359i	0.680990	+	0.494768i
$697$	−388.949	+	61.6034i	−0.558033	+	0.0883837i
$698$	−682.471	+	347.736i	−0.977752	+	0.498190i
$699$			1616.83i			2.31307i
$700$	−38.4676	−	23.2663i	−0.0549537	−	0.0332376i
$701$	−988.792			−1.41054			−0.705272	−	0.708937i	$-0.749175\pi$
$701$	−988.792			−1.41054			−0.705272	+	0.708937i	$0.749175\pi$
$702$	101.133	+	198.485i	0.144065	+	0.282743i
$703$	57.9761	+	366.046i	0.0824695	+	0.520692i
$704$	64.5694	−	88.8721i	0.0917179	−	0.126239i
$705$	665.146	−	618.451i	0.943469	−	0.877236i
$706$	−6.51057	+	4.73020i	−0.00922177	+	0.00670001i
$707$	−42.0037	+	42.0037i	−0.0594112	+	0.0594112i
$708$	437.322	+	69.2650i	0.617687	+	0.0978320i
$709$	−1071.72	+	348.224i	−1.51160	+	0.491148i	−0.943375	−	0.331728i	$-0.892369\pi$
$709$	−1071.72	+	348.224i	−1.51160	+	0.491148i	−0.568222	+	0.822875i	$0.692369\pi$
$710$	213.822	−	60.9759i	0.301158	−	0.0858815i
$711$	−74.8319	+	230.309i	−0.105249	+	0.323922i
$712$	−151.525	−	77.2057i	−0.212816	−	0.108435i
$713$	−27.1923	+	53.3678i	−0.0381378	+	0.0748497i
$714$	25.9145	+	8.42014i	0.0362948	+	0.0117929i
$715$	−215.179	+	588.532i	−0.300949	+	0.823121i
$716$	−40.1626	−	123.608i	−0.0560930	−	0.172637i
$717$	−147.136	+	928.982i	−0.205211	+	1.29565i
$718$	49.1583	+	49.1583i	0.0684656	+	0.0684656i
$719$	−52.6231	−	72.4294i	−0.0731892	−	0.100736i	0.770853	−	0.637013i	$-0.219830\pi$
$719$	−52.6231	−	72.4294i	−0.0731892	−	0.100736i	−0.844042	+	0.536277i	$0.819830\pi$
$720$	−41.4199	+	74.4676i	−0.0575276	+	0.103427i
$721$	−7.43253	−	5.40005i	−0.0103086	−	0.00748967i
$722$	882.848	−	139.829i	1.22278	−	0.193669i
$723$	529.373	−	269.729i	0.732190	−	0.373069i
$724$			424.114i			0.585793i
$725$	340.000	+	1380.78i	0.468966	+	1.90452i
$726$	−347.895			−0.479194
$727$	−303.763	−	596.168i	−0.417830	−	0.820038i	−0.999976	−	0.00695359i	$-0.997787\pi$
$727$	−303.763	−	596.168i	−0.417830	−	0.820038i	0.582145	−	0.813085i	$-0.302213\pi$
$728$	3.63099	+	22.9252i	0.00498763	+	0.0314906i
$729$	−79.0493	+	108.802i	−0.108435	+	0.149248i
$730$	−94.1633	+	480.692i	−0.128991	+	0.658483i
$731$	261.302	−	189.847i	0.357458	−	0.259709i
$732$	−72.9574	+	72.9574i	−0.0996686	+	0.0996686i
$733$	239.936	+	38.0021i	0.327334	+	0.0518446i	0.317939	−	0.948111i	$-0.397009\pi$
$733$	239.936	+	38.0021i	0.327334	+	0.0518446i	0.00939532	+	0.999956i	$0.497009\pi$
$734$	481.240	−	156.364i	0.655641	−	0.213031i
$735$	−489.605	−	728.152i	−0.666129	−	0.990684i
$736$	−53.9330	+	165.989i	−0.0732786	+	0.225528i
$737$	790.554	+	402.807i	1.07266	+	0.546550i
$738$	−183.056	+	359.268i	−0.248044	+	0.486813i
$739$	−1232.20	−	400.367i	−1.66739	−	0.541769i	−0.684993	−	0.728550i	$-0.740195\pi$
$739$	−1232.20	−	400.367i	−1.66739	−	0.541769i	−0.982402	+	0.186781i	$0.940195\pi$
$740$	92.5696	+	72.5405i	0.125094	+	0.0980277i
$741$	323.650	+	996.093i	0.436775	+	1.34425i
$742$	−7.24702	+	45.7559i	−0.00976687	+	0.0616656i
$743$	−560.204	−	560.204i	−0.753976	−	0.753976i	0.221243	−	0.975219i	$-0.428989\pi$
$743$	−560.204	−	560.204i	−0.753976	−	0.753976i	−0.975219	+	0.221243i	$0.928989\pi$
$744$	−11.7529	−	16.1765i	−0.0157969	−	0.0217426i
$745$	−852.480	+	396.008i	−1.14427	+	0.531555i
$746$	−189.191	−	137.455i	−0.253607	−	0.184257i
$747$	−170.442	+	26.9954i	−0.228169	+	0.0361384i
$748$	−143.995	+	73.3692i	−0.192507	+	0.0980872i
$749$		−	36.2149i		−	0.0483510i
$750$	−601.979	+	228.068i	−0.802638	+	0.304090i
$751$	1236.03			1.64585			0.822926	−	0.568149i	$-0.192340\pi$
$751$	1236.03			1.64585			0.822926	+	0.568149i	$0.192340\pi$
$752$	90.5850	+	177.783i	0.120459	+	0.236414i
$753$	153.411	+	968.601i	0.203734	+	1.28632i
$754$	431.545	−	593.971i	0.572341	−	0.787760i
$755$	337.585	+	726.713i	0.447133	+	0.962534i
$756$	−25.1082	+	18.2422i	−0.0332119	+	0.0241298i
$757$	−212.988	+	212.988i	−0.281358	+	0.281358i	−0.833650	−	0.552293i	$-0.813753\pi$
$757$	−212.988	+	212.988i	−0.281358	+	0.281358i	0.552293	+	0.833650i	$0.313753\pi$
$758$	823.324	+	130.402i	1.08618	+	0.172034i
$759$	1467.25	−	476.737i	1.93313	−	0.628112i
$760$	274.884	−	350.783i	0.361690	−	0.461556i
$761$	−93.0421	+	286.354i	−0.122263	+	0.376287i	−0.993392	−	0.114767i	$-0.963388\pi$
$761$	−93.0421	+	286.354i	−0.122263	+	0.376287i	0.871129	+	0.491053i	$0.163388\pi$
$762$	−405.277	−	206.499i	−0.531860	−	0.270996i
$763$	21.7620	−	42.7103i	0.0285216	−	0.0559768i
$764$	−175.465	−	57.0122i	−0.229667	−	0.0746233i
$765$	104.030	−	69.9490i	0.135987	−	0.0914366i
$766$	−298.588	−	918.958i	−0.389801	−	1.19968i
$767$	86.8019	−	548.046i	0.113171	−	0.714532i
$768$	−41.1990	−	41.1990i	−0.0536445	−	0.0536445i
$769$	191.979	+	264.237i	0.249648	+	0.343611i	0.915388	−	0.402573i	$-0.131884\pi$
$769$	191.979	+	264.237i	0.249648	+	0.343611i	−0.665740	+	0.746184i	$0.731884\pi$
$770$	−85.6737	−	16.7827i	−0.111265	−	0.0217957i
$771$	255.867	+	185.898i	0.331864	+	0.241113i
$772$	−422.149	+	66.8618i	−0.546825	+	0.0866086i
$773$	951.703	−	484.917i	1.23118	−	0.627318i	0.287375	−	0.957818i	$-0.407217\pi$
$773$	951.703	−	484.917i	1.23118	−	0.627318i	0.943806	+	0.330500i	$0.107217\pi$
$774$		−	330.712i		−	0.427277i
$775$	3.52643	−	48.4052i	0.00455023	−	0.0624583i
$776$	35.2310			0.0454008
$777$	−17.4816	−	34.3095i	−0.0224988	−	0.0441564i
$778$	−34.7327	−	219.293i	−0.0446435	−	0.281868i
$779$	1239.53	−	1706.07i	1.59118	−	2.19007i
$780$	290.453	+	161.554i	0.372376	+	0.207120i
$781$	349.318	−	253.794i	0.447270	−	0.324961i
$782$	181.558	−	181.558i	0.232172	−	0.232172i
$783$	969.599	+	153.569i	1.23831	+	0.196129i
$784$	183.332	−	59.5681i	0.233841	−	0.0759797i
$785$	−584.451	−	213.687i	−0.744524	−	0.272212i
$786$	152.939	−	470.696i	0.194578	−	0.598850i
$787$	−402.553	−	205.111i	−0.511503	−	0.260624i	0.179135	−	0.983825i	$-0.442670\pi$
$787$	−402.553	−	205.111i	−0.511503	−	0.260624i	−0.690638	+	0.723201i	$0.742670\pi$
$788$	61.5125	−	120.725i	0.0780616	−	0.153205i
$789$	−1259.50	−	409.237i	−1.59633	−	0.518679i
$790$	−110.217	−	386.494i	−0.139515	−	0.489232i
$791$	−29.9235	−	92.0952i	−0.0378300	−	0.116429i
$792$	−25.8860	+	163.438i	−0.0326843	+	0.206361i
$793$	91.4292	+	91.4292i	0.115295	+	0.115295i
$794$	−144.153	−	198.409i	−0.181553	−	0.249886i
$795$	451.696	+	485.800i	0.568171	+	0.611070i
$796$	183.617	+	133.406i	0.230675	+	0.167595i
$797$	−54.3922	+	8.61487i	−0.0682461	+	0.0108091i	−0.190464	−	0.981694i	$-0.560999\pi$
$797$	−54.3922	+	8.61487i	−0.0682461	+	0.0108091i	0.122218	+	0.992503i	$0.460999\pi$
$798$	−130.012	+	66.2445i	−0.162922	+	0.0830131i
$799$		−	293.541i		−	0.367385i
$800$	−11.9156	−	140.918i	−0.0148945	−	0.176148i
$801$	256.169			0.319812
$802$	−263.384	−	516.919i	−0.328408	−	0.644538i
$803$	148.802	+	939.500i	0.185308	+	1.16999i
$804$	276.607	−	380.716i	0.344038	−	0.473528i
$805$	137.694	−	16.7034i	0.171049	−	0.0207495i
$806$	−20.2722	+	14.7286i	−0.0251516	+	0.0182737i
$807$	−809.670	+	809.670i	−1.00331	+	1.00331i
$808$	−184.564	−	29.2320i	−0.228421	−	0.0361783i
$809$	33.7918	−	10.9796i	0.0417698	−	0.0135718i	−0.288058	−	0.957613i	$-0.593009\pi$
$809$	33.7918	−	10.9796i	0.0417698	−	0.0135718i	0.329827	+	0.944041i	$0.393009\pi$
$810$	−26.0127	+	715.067i	−0.0321144	+	0.882799i
$811$	−392.037	+	1206.57i	−0.483400	+	1.48775i	0.350885	+	0.936419i	$0.385881\pi$
$811$	−392.037	+	1206.57i	−0.483400	+	1.48775i	−0.834285	+	0.551333i	$0.814119\pi$
$812$	91.1377	+	46.4370i	0.112239	+	0.0571884i
$813$	401.533	−	788.054i	0.493891	−	0.969316i
$814$	217.205	+	70.5742i	0.266837	+	0.0867005i
$815$	−909.152	−	33.0731i	−1.11552	−	0.0405805i
$816$	26.4876	+	81.5205i	0.0324603	+	0.0999026i
$817$	−270.573	+	1708.33i	−0.331178	+	2.09098i
$818$	−40.2878	−	40.2878i	−0.0492515	−	0.0492515i
$819$	−20.5511	−	28.2862i	−0.0250930	−	0.0345375i
$820$	−80.5877	−	664.326i	−0.0982777	−	0.810153i
$821$	739.680	+	537.409i	0.900950	+	0.654578i	0.938710	−	0.344709i	$-0.112022\pi$
$821$	739.680	+	537.409i	0.900950	+	0.654578i	−0.0377601	+	0.999287i	$0.512022\pi$
$822$	−1218.04	+	192.918i	−1.48180	+	0.234693i
$823$	912.475	−	464.929i	1.10872	−	0.564920i	0.198939	−	0.980012i	$-0.436250\pi$
$823$	912.475	−	464.929i	1.10872	−	0.564920i	0.909780	+	0.415091i	$0.136250\pi$
$824$		−	28.9003i		−	0.0350732i
$825$	−945.834	+	817.379i	−1.14646	+	0.990763i
$826$	77.3048			0.0935894
$827$	−158.662	−	311.391i	−0.191852	−	0.376531i	0.774963	−	0.632006i	$-0.217768\pi$
$827$	−158.662	−	311.391i	−0.191852	−	0.376531i	−0.966816	+	0.255475i	$0.917768\pi$
$828$	−41.1272	−	259.667i	−0.0496705	−	0.313607i
$829$	46.1567	−	63.5292i	0.0556775	−	0.0766336i	−0.780270	−	0.625442i	$-0.784919\pi$
$829$	46.1567	−	63.5292i	0.0556775	−	0.0766336i	0.835948	+	0.548809i	$0.184919\pi$
$830$	209.744	−	195.019i	0.252703	−	0.234963i
$831$	−1263.78	+	918.188i	−1.52079	+	1.10492i
$832$	−51.6300	+	51.6300i	−0.0620552	+	0.0620552i
$833$	−280.098	−	44.3632i	−0.336252	−	0.0532571i
$834$	−683.204	+	221.987i	−0.819190	+	0.266171i
$835$	−872.734	+	248.879i	−1.04519	+	0.298058i
$836$	267.433	−	823.075i	0.319896	−	0.984540i
$837$	−29.8530	−	15.2109i	−0.0356667	−	0.0181731i
$838$	−279.894	+	549.323i	−0.334002	+	0.655517i
$839$	−251.975	−	81.8717i	−0.300328	−	0.0975824i	0.154977	−	0.987918i	$-0.450470\pi$
$839$	−251.975	−	81.8717i	−0.300328	−	0.0975824i	−0.455305	+	0.890336i	$0.650470\pi$
$840$	−15.9002	+	43.4883i	−0.0189288	+	0.0517718i
$841$	−739.920	−	2277.24i	−0.879809	−	2.70777i
$842$	38.4482	−	242.752i	0.0456629	−	0.288304i
$843$	−575.921	−	575.921i	−0.683180	−	0.683180i
$844$	−13.3465	−	18.3699i	−0.0158134	−	0.0217653i
$845$	−208.282	+	374.465i	−0.246488	+	0.443153i
$846$	−243.160	−	176.666i	−0.287423	−	0.208825i
$847$	−59.9919	+	9.50178i	−0.0708287	+	0.0112182i
$848$	−129.847	+	66.1603i	−0.153121	+	0.0780192i
$849$		−	1298.20i		−	1.52909i
$850$	−78.4992	+	192.676i	−0.0923520	+	0.226677i
$851$	−362.851			−0.426382
$852$	−103.969	−	204.050i	−0.122029	−	0.239496i
$853$	−119.409	−	753.921i	−0.139987	−	0.883846i	−0.953301	−	0.302021i	$-0.902339\pi$
$853$	−119.409	−	753.921i	−0.139987	−	0.883846i	0.813314	−	0.581825i	$-0.197661\pi$
$854$	−10.5883	+	14.5736i	−0.0123985	+	0.0170651i
$855$	−129.051	+	658.791i	−0.150937	+	0.770516i
$856$	92.1656	−	66.9622i	0.107670	−	0.0782269i
$857$	326.208	−	326.208i	0.380639	−	0.380639i	−0.490693	−	0.871332i	$-0.663256\pi$
$857$	326.208	−	326.208i	0.380639	−	0.380639i	0.871332	+	0.490693i	$0.163256\pi$
$858$	637.472	+	100.966i	0.742974	+	0.117676i
$859$	−1286.41	+	417.979i	−1.49756	+	0.486588i	−0.939306	−	0.343080i	$-0.888530\pi$
$859$	−1286.41	+	417.979i	−1.49756	+	0.486588i	−0.558257	+	0.829668i	$0.688530\pi$
$860$	306.259	+	455.476i	0.356115	+	0.529624i
$861$	−67.7077	+	208.383i	−0.0786385	+	0.242024i
$862$	154.116	+	78.5260i	0.178789	+	0.0910974i
$863$	−150.755	+	295.874i	−0.174687	+	0.342843i	−0.961705	−	0.274088i	$-0.911624\pi$
$863$	−150.755	+	295.874i	−0.174687	+	0.342843i	0.787017	+	0.616931i	$0.211624\pi$
$864$	−92.8512	−	30.1692i	−0.107467	−	0.0349180i
$865$	872.960	+	684.079i	1.00920	+	0.790843i
$866$	128.509	+	395.510i	0.148394	+	0.456709i
$867$	−144.904	+	914.890i	−0.167133	+	1.05524i
$868$	−2.46852	−	2.46852i	−0.00284392	−	0.00284392i
$869$	−458.745	−	631.409i	−0.527900	−	0.726592i
$870$	1328.32	−	617.053i	1.52680	−	0.709257i
$871$	−477.108	−	346.640i	−0.547771	−	0.397979i
$872$	148.935	−	23.5889i	0.170797	−	0.0270515i
$873$	−47.2858	+	24.0933i	−0.0541647	+	0.0275983i
$874$			1374.98i			1.57321i
$875$	−97.5778	+	55.7700i	−0.111518	+	0.0637371i
$876$	504.511			0.575925
$877$	−496.185	−	973.819i	−0.565776	−	1.11040i	−0.979772	−	0.200119i	$-0.935867\pi$
$877$	−496.185	−	973.819i	−0.565776	−	1.11040i	0.413996	−	0.910279i	$-0.364133\pi$
$878$	−31.6108	−	199.583i	−0.0360032	−	0.227316i
$879$	1004.24	−	1382.21i	1.14248	−	1.57248i
$880$	−115.701	−	249.068i	−0.131479	−	0.283032i
$881$	489.612	−	355.724i	0.555745	−	0.403773i	−0.274154	−	0.961686i	$-0.588398\pi$
$881$	489.612	−	355.724i	0.555745	−	0.403773i	0.829899	+	0.557913i	$0.188398\pi$
$882$	−205.324	+	205.324i	−0.232794	+	0.232794i
$883$	−1146.39	−	181.570i	−1.29829	−	0.205628i	−0.531241	−	0.847221i	$-0.678274\pi$
$883$	−1146.39	−	181.570i	−1.29829	−	0.205628i	−0.767046	+	0.641592i	$0.778274\pi$
$884$	102.160	−	33.1939i	0.115566	−	0.0375497i
$885$	682.765	−	871.283i	0.771486	−	0.984500i
$886$	8.49138	−	26.1338i	0.00958395	−	0.0294964i
$887$	606.984	+	309.274i	0.684311	+	0.348674i	0.761338	−	0.648355i	$-0.224543\pi$
$887$	606.984	+	309.274i	0.684311	+	0.348674i	−0.0770268	+	0.997029i	$0.524543\pi$
$888$	54.9926	−	107.929i	0.0619286	−	0.121542i
$889$	−75.5271	−	24.5402i	−0.0849574	−	0.0276043i
$890$	−352.811	+	237.228i	−0.396417	+	0.266548i
$891$	429.387	+	1321.52i	0.481916	+	1.48319i
$892$	45.8577	−	289.534i	0.0514100	−	0.324590i
$893$	1111.53	+	1111.53i	1.24471	+	1.24471i
$894$	569.061	+	783.246i	0.636534	+	0.876114i
$895$	−318.862	−	62.4622i	−0.356270	−	0.0697902i
$896$	−8.22970	−	5.97923i	−0.00918493	−	0.00667324i
$897$	−1012.80	+	160.412i	−1.12910	+	0.178832i
$898$	−395.421	+	201.477i	−0.440335	+	0.224362i
$899$			110.425i			0.122831i
$900$	112.362	+	180.987i	0.124847	+	0.201097i
$901$	214.393			0.237950
$902$	−589.974	−	1157.89i	−0.654073	−	1.28369i
$903$	−28.1126	−	177.496i	−0.0311324	−	0.196563i
$904$	179.049	−	246.440i	0.198063	−	0.272611i
$905$	926.597	+	515.385i	1.02386	+	0.569486i
$906$	667.693	−	485.108i	0.736968	−	0.535439i
$907$	911.088	−	911.088i	1.00451	−	1.00451i	0.00451769	−	0.999990i	$-0.498562\pi$
$907$	911.088	−	911.088i	1.00451	−	1.00451i	0.999990	−	0.00451769i	$-0.00143803\pi$
$908$	416.062	+	65.8978i	0.458218	+	0.0725746i
$909$	267.705	−	86.9828i	0.294505	−	0.0956906i
$910$	54.4990	+	19.9259i	0.0598890	+	0.0218966i
$911$	315.739	−	971.745i	0.346585	−	1.06668i	−0.614145	−	0.789193i	$-0.710499\pi$
$911$	315.739	−	971.745i	0.346585	−	1.06668i	0.960730	−	0.277486i	$-0.0895011\pi$
$912$	−408.985	−	208.388i	−0.448449	−	0.228496i
$913$	252.495	−	495.549i	0.276555	−	0.542770i
$914$	69.4466	+	22.5646i	0.0759810	+	0.0246877i
$915$	70.7379	+	248.054i	0.0773092	+	0.271098i
$916$	117.552	+	361.788i	0.128332	+	0.394965i
$917$	13.5174	−	85.3453i	0.0147409	−	0.0930701i
$918$	101.561	+	101.561i	0.110632	+	0.110632i
$919$	713.919	+	982.625i	0.776843	+	1.06923i	0.995623	+	0.0934584i	$0.0297922\pi$
$919$	713.919	+	982.625i	0.776843	+	1.06923i	−0.218780	+	0.975774i	$0.570208\pi$
$920$	297.110	+	319.542i	0.322945	+	0.347329i
$921$	22.2202	+	16.1439i	0.0241261	+	0.0175287i
$922$	−1140.48	+	180.634i	−1.23696	+	0.195915i
$923$	−255.713	+	130.292i	−0.277045	+	0.141162i
$924$			89.9188i			0.0973147i
$925$	270.976	−	114.093i	0.292947	−	0.123344i
$926$	−777.796			−0.839953
$927$	19.7640	+	38.7890i	0.0213203	+	0.0418435i
$928$	50.3354	+	317.805i	0.0542407	+	0.342462i
$929$	−317.570	+	437.097i	−0.341840	+	0.470503i	−0.944978	−	0.327134i	$-0.893917\pi$
$929$	−317.570	+	437.097i	−0.341840	+	0.470503i	0.603137	+	0.797637i	$0.293917\pi$
$930$	−49.6244	+	6.01982i	−0.0533596	+	0.00647292i
$931$	1228.61	−	892.637i	1.31967	−	0.958794i
$932$	−627.912	+	627.912i	−0.673726	+	0.673726i
$933$	−912.208	−	144.479i	−0.977714	−	0.154855i
$934$	−791.630	+	257.216i	−0.847570	+	0.275392i
$935$	−14.6878	+	403.757i	−0.0157089	+	0.431825i
$936$	33.9878	−	104.604i	0.0363118	−	0.111756i
$937$	590.265	+	300.755i	0.629952	+	0.320976i	0.739653	−	0.672988i	$-0.234989\pi$
$937$	590.265	+	300.755i	0.629952	+	0.320976i	−0.109701	+	0.993965i	$0.534989\pi$
$938$	37.3006	−	73.2065i	0.0397661	−	0.0780453i
$939$	−459.064	−	149.159i	−0.488886	−	0.158849i
$940$	498.497	+	18.1343i	0.530316	+	0.0192918i
$941$	17.8066	+	54.8030i	0.0189230	+	0.0582391i	0.960072	−	0.279753i	$-0.0902524\pi$
$941$	17.8066	+	54.8030i	0.0189230	+	0.0582391i	−0.941149	+	0.337992i	$0.890252\pi$
$942$	−100.266	+	633.052i	−0.106439	+	0.672029i
$943$	1459.94	+	1459.94i	1.54819	+	1.54819i
$944$	142.938	+	196.738i	0.151418	+	0.208409i
$945$	9.34357	+	77.0238i	0.00988738	+	0.0815067i
$946$	862.296	+	626.495i	0.911518	+	0.662257i
$947$	107.310	−	16.9962i	0.113316	−	0.0179474i	−0.0995191	−	0.995036i	$-0.531730\pi$
$947$	107.310	−	16.9962i	0.113316	−	0.0179474i	0.212835	+	0.977088i	$0.431730\pi$
$948$	−368.831	+	187.929i	−0.389062	+	0.198237i
$949$		−	632.245i		−	0.666223i
$950$	−432.343	−	1026.84i	−0.455098	−	1.08088i
$951$	818.627			0.860806
$952$	6.79410	+	13.3342i	0.00713666	+	0.0140065i
$953$	10.9313	+	69.0176i	0.0114704	+	0.0724214i	0.992760	−	0.120119i	$-0.0383275\pi$
$953$	10.9313	+	69.0176i	0.0114704	+	0.0724214i	−0.981289	+	0.192540i	$0.938327\pi$
$954$	129.031	−	177.596i	0.135252	−	0.186159i
$955$	−337.786	+	314.073i	−0.353702	+	0.328872i
$956$	−417.920	+	303.637i	−0.437155	+	0.317612i
$957$	2011.18	−	2011.18i	2.10154	−	2.10154i
$958$	291.849	+	46.2244i	0.304644	+	0.0482509i
$959$	−204.772	+	66.5346i	−0.213527	+	0.0693791i
$960$	−140.076	+	39.9456i	−0.145912	+	0.0416100i
$961$	−295.801	+	910.381i	−0.307805	+	0.947327i
$962$	−135.255	−	68.9159i	−0.140598	−	0.0716381i
$963$	−77.9080	+	152.903i	−0.0809014	+	0.158778i
$964$	310.339	+	100.835i	0.321928	+	0.104601i
$965$	−366.919	+	1003.55i	−0.380227	+	1.03995i
$966$	−44.1466	−	135.869i	−0.0457004	−	0.140651i
$967$	60.5623	−	382.375i	0.0626290	−	0.395424i	−0.936383	−	0.350980i	$-0.885848\pi$
$967$	60.5623	−	382.375i	0.0626290	−	0.395424i	0.999012	−	0.0444438i	$-0.0141516\pi$
$968$	−135.108	−	135.108i	−0.139574	−	0.139574i
$969$	396.921	+	546.315i	0.409620	+	0.563793i
$970$	42.8129	−	76.9722i	0.0441370	−	0.0793527i
$971$	−801.968	−	582.664i	−0.825920	−	0.600066i	0.0924822	−	0.995714i	$-0.470520\pi$
$971$	−801.968	−	582.664i	−0.825920	−	0.600066i	−0.918402	+	0.395648i	$0.870520\pi$
$972$	421.084	−	66.6932i	0.433214	−	0.0686144i
$973$	−111.751	+	56.9398i	−0.114852	+	0.0585198i
$974$			235.456i			0.241741i
$975$	705.921	−	438.256i	0.724021	−	0.449494i
$976$	−56.6674			−0.0580608
$977$	414.305	+	813.120i	0.424059	+	0.832262i	0.999892	+	0.0146951i	$0.00467776\pi$
$977$	414.305	+	813.120i	0.424059	+	0.832262i	−0.575833	+	0.817567i	$0.695322\pi$
$978$	146.583	+	925.486i	0.149880	+	0.946305i
$979$	−485.282	+	667.934i	−0.495692	+	0.682261i
$980$	92.6422	−	472.927i	0.0945329	−	0.482579i
$981$	−183.763	+	133.511i	−0.187322	+	0.136097i
$982$	295.999	−	295.999i	0.301424	−	0.301424i
$983$	588.893	+	93.2715i	0.599078	+	0.0948846i	0.448606	−	0.893730i	$-0.351921\pi$
$983$	588.893	+	93.2715i	0.599078	+	0.0948846i	0.150472	+	0.988614i	$0.451921\pi$
$984$	−655.520	+	212.991i	−0.666179	+	0.216455i
$985$	−189.008	−	281.097i	−0.191886	−	0.285378i
$986$	146.279	−	450.201i	0.148356	−	0.456593i
$987$	−145.523	−	74.1479i	−0.147440	−	0.0751245i
$988$	−261.149	+	512.534i	−0.264321	+	0.518759i
$989$	−1610.53	−	523.294i	−1.62845	−	0.529114i
$990$	325.619	+	255.165i	0.328908	+	0.257743i
$991$	146.456	+	450.746i	0.147786	+	0.454840i	0.997359	−	0.0726323i	$-0.0231400\pi$
$991$	146.456	+	450.746i	0.147786	+	0.454840i	−0.849572	+	0.527472i	$0.823140\pi$
$992$	1.71794	−	10.8467i	0.00173180	−	0.0109341i
$993$	−1084.94	−	1084.94i	−1.09259	−	1.09259i
$994$	−23.5017	−	32.3474i	−0.0236436	−	0.0325426i
$995$	514.595	−	239.049i	0.517181	−	0.240250i
$996$	−238.647	−	173.387i	−0.239606	−	0.174084i
$997$	−1022.85	+	162.004i	−1.02593	+	0.162492i	−0.646648	−	0.762789i	$-0.723830\pi$
$997$	−1022.85	+	162.004i	−1.02593	+	0.162492i	−0.379284	+	0.925280i	$0.623830\pi$
$998$	−578.952	+	294.991i	−0.580112	+	0.295582i
$999$		−	202.972i		−	0.203176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.a.3.2	✓	16
4.3	odd	2		400.3.bg.a.353.1		16
5.2	odd	4		250.3.f.a.7.2		16
5.3	odd	4		250.3.f.c.7.1		16
5.4	even	2		250.3.f.b.243.1		16
25.6	even	5		250.3.f.a.143.2		16
25.8	odd	20		250.3.f.b.107.1		16
25.17	odd	20	inner	50.3.f.a.17.2	yes	16
25.19	even	10		250.3.f.c.143.1		16
100.67	even	20		400.3.bg.a.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.3.2	✓	16	1.1	even	1	trivial
50.3.f.a.17.2	yes	16	25.17	odd	20	inner
250.3.f.a.7.2		16	5.2	odd	4
250.3.f.a.143.2		16	25.6	even	5
250.3.f.b.107.1		16	25.8	odd	20
250.3.f.b.243.1		16	5.4	even	2
250.3.f.c.7.1		16	5.3	odd	4
250.3.f.c.143.1		16	25.19	even	10
400.3.bg.a.17.1		16	100.67	even	20
400.3.bg.a.353.1		16	4.3	odd	2

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642040 - 1.26007i) q^{2} +(0.569657 + 3.59668i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(2.10649 + 4.53461i) q^{5} +(4.16633 - 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-4.05206 + 1.31659i) q^{9} +O(q^{10})\)	\(q+(-0.642040 - 1.26007i) q^{2} +(0.569657 + 3.59668i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(2.10649 + 4.53461i) q^{5} +(4.16633 - 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(2.79360 + 0.442463i) q^{8} +(-4.05206 + 1.31659i) q^{9} +(4.36149 - 5.56574i) q^{10} +(4.24327 - 13.0594i) q^{11} +(-6.48922 - 3.30642i) q^{12} +(-4.14356 + 8.13219i) q^{13} +(-1.20932 - 0.392933i) q^{14} +(-15.1095 + 10.1596i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-0.920559 + 5.81218i) q^{17} +(4.26058 + 4.26058i) q^{18} +(-18.5227 - 25.4943i) q^{19} +(-9.81348 - 1.92237i) q^{20} +(2.64887 + 1.92451i) q^{21} +(-19.1802 + 3.03784i) q^{22} +(27.4902 - 14.0070i) q^{23} +10.2997i q^{24} +(-16.1254 + 19.1043i) q^{25} +12.9075 q^{26} +(7.83525 + 15.3775i) q^{27} +(0.281309 + 1.77612i) q^{28} +(33.4337 - 46.0176i) q^{29} +(22.5027 + 12.5163i) q^{30} +(-1.57058 + 1.14109i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(49.3877 + 7.82225i) q^{33} +(7.91481 - 2.57168i) q^{34} +(4.22228 + 1.54374i) q^{35} +(2.63319 - 8.10411i) q^{36} +(-10.4788 - 5.33922i) q^{37} +(-20.2324 + 39.7083i) q^{38} +(-31.6093 - 10.2705i) q^{39} +(3.87831 + 13.6000i) q^{40} +(20.6793 + 63.6443i) q^{41} +(0.724353 - 4.57338i) q^{42} +(-38.8107 - 38.8107i) q^{43} +(16.1423 + 22.2180i) q^{44} +(-14.5059 - 15.6011i) q^{45} +(-35.2996 - 25.6467i) q^{46} +(-49.2685 + 7.80337i) q^{47} +(12.9784 - 6.61284i) q^{48} +48.1916i q^{49} +(34.4259 + 8.05346i) q^{50} -21.4289 q^{51} +(-8.28712 - 16.2644i) q^{52} +(-5.69932 - 35.9841i) q^{53} +(14.3463 - 19.7460i) q^{54} +(68.1578 - 8.26806i) q^{55} +(2.05742 - 1.49481i) q^{56} +(81.1431 - 81.1431i) q^{57} +(-79.4513 - 12.5838i) q^{58} +(-57.8198 + 18.7868i) q^{59} +(1.32383 - 36.3910i) q^{60} +(4.37780 - 13.4735i) q^{61} +(2.44623 + 1.24642i) q^{62} +(-1.73915 + 3.41328i) q^{63} +(7.60845 + 2.47214i) q^{64} +(-45.6047 - 1.65901i) q^{65} +(-21.8523 - 67.2544i) q^{66} +(-10.1080 + 63.8194i) q^{67} +(-8.32212 - 8.32212i) q^{68} +(66.0385 + 90.8943i) q^{69} +(-0.765635 - 6.31152i) q^{70} +(25.4392 + 18.4826i) q^{71} +(-11.9024 + 1.88515i) q^{72} +(-61.7220 + 31.4489i) q^{73} +16.6321i q^{74} +(-77.8977 - 47.1148i) q^{75} +63.0254 q^{76} +(-5.60513 - 11.0007i) q^{77} +(7.35285 + 46.4241i) q^{78} +(33.4082 - 45.9825i) q^{79} +(14.6469 - 13.6187i) q^{80} +(-81.8666 + 59.4796i) q^{81} +(66.9196 - 66.9196i) q^{82} +(40.0044 + 6.33607i) q^{83} +(-6.22786 + 2.02355i) q^{84} +(-28.2951 + 8.06895i) q^{85} +(-23.9863 + 73.8222i) q^{86} +(184.556 + 94.0360i) q^{87} +(17.6323 - 34.6054i) q^{88} +(-57.1826 - 18.5798i) q^{89} +(-10.3452 + 28.2950i) q^{90} +(2.53589 + 7.80467i) q^{91} +(-9.65295 + 60.9463i) q^{92} +(-4.99882 - 4.99882i) q^{93} +(41.4652 + 57.0719i) q^{94} +(76.5887 - 137.697i) q^{95} +(-16.6653 - 12.1081i) q^{96} +(12.3027 - 1.94856i) q^{97} +(60.7249 - 30.9409i) q^{98} +58.5042i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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