LMFDB - Embedded newform 128.5.l.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,Mod(3,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("128.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	128.l (of order $32$, degree $16$, 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:	$13.2313552747$
Analytic rank:	$0$
Dimension:	$1008$
Relative dimension:	$63$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	128.43
Dual form			128.5.l.a.3.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.35233 - 3.23520i) q^{2} +(1.64666 + 1.35138i) q^{3} +(-4.93309 + 15.2205i) q^{4} +(31.2429 - 9.47742i) q^{5} +(0.498498 - 8.50617i) q^{6} +(-6.24158 + 31.3785i) q^{7} +(60.8458 - 19.8442i) q^{8} +(-14.9171 - 74.9931i) q^{9} +O(q^{10})$	\(q+(-2.35233 - 3.23520i) q^{2} +(1.64666 + 1.35138i) q^{3} +(-4.93309 + 15.2205i) q^{4} +(31.2429 - 9.47742i) q^{5} +(0.498498 - 8.50617i) q^{6} +(-6.24158 + 31.3785i) q^{7} +(60.8458 - 19.8442i) q^{8} +(-14.9171 - 74.9931i) q^{9} +(-104.155 - 78.7830i) q^{10} +(-22.4545 + 227.984i) q^{11} +(-28.6918 + 18.3966i) q^{12} +(-13.4564 + 44.3598i) q^{13} +(116.198 - 53.6199i) q^{14} +(64.2540 + 26.6149i) q^{15} +(-207.329 - 150.168i) q^{16} +(23.6566 + 57.1121i) q^{17} +(-207.528 + 224.668i) q^{18} +(197.207 + 368.948i) q^{19} +(-9.87233 + 522.286i) q^{20} +(-52.6821 + 43.2351i) q^{21} +(790.395 - 463.649i) q^{22} +(362.906 + 242.486i) q^{23} +(127.009 + 49.5491i) q^{24} +(366.627 - 244.972i) q^{25} +(175.167 - 60.8147i) q^{26} +(158.118 - 295.818i) q^{27} +(-446.808 - 249.793i) q^{28} +(-13.1941 - 133.962i) q^{29} +(-65.0420 - 270.482i) q^{30} +(1037.08 - 1037.08i) q^{31} +(1.88173 + 1024.00i) q^{32} +(-345.068 + 345.068i) q^{33} +(129.121 - 210.880i) q^{34} +(102.383 + 1039.51i) q^{35} +(1215.02 + 142.902i) q^{36} +(-285.081 + 533.348i) q^{37} +(729.727 - 1505.89i) q^{38} +(-82.1049 + 54.8608i) q^{39} +(1712.92 - 1196.65i) q^{40} +(1982.79 + 1324.86i) q^{41} +(263.800 + 68.7341i) q^{42} +(1282.80 - 1052.77i) q^{43} +(-3359.27 - 1466.43i) q^{44} +(-1176.79 - 2201.62i) q^{45} +(-69.1830 - 1744.48i) q^{46} +(-19.6692 - 47.4857i) q^{47} +(-138.467 - 527.457i) q^{48} +(1272.58 + 527.119i) q^{49} +(-1654.96 - 609.857i) q^{50} +(-38.2257 + 126.013i) q^{51} +(-608.798 - 423.644i) q^{52} +(-108.877 + 1105.45i) q^{53} +(-1328.98 + 184.318i) q^{54} +(1459.16 + 7335.68i) q^{55} +(242.908 + 2033.11i) q^{56} +(-173.856 + 874.034i) q^{57} +(-402.359 + 357.809i) q^{58} +(-3213.26 + 974.732i) q^{59} +(-722.063 + 846.686i) q^{60} +(2229.46 + 1829.67i) q^{61} +(-5794.70 - 915.608i) q^{62} +2446.28 q^{63} +(3308.42 - 2414.87i) q^{64} +1513.46i q^{65} +(1928.08 + 304.651i) q^{66} +(-2639.09 + 3215.74i) q^{67} +(-985.977 + 78.3273i) q^{68} +(269.892 + 889.715i) q^{69} +(3122.19 - 2776.50i) q^{70} +(-4066.62 - 808.900i) q^{71} +(-2395.82 - 4267.00i) q^{72} +(-5314.94 + 1057.21i) q^{73} +(2396.09 - 332.318i) q^{74} +(934.760 + 92.0658i) q^{75} +(-6588.43 + 1181.54i) q^{76} +(-7013.66 - 2127.57i) q^{77} +(370.624 + 136.576i) q^{78} +(2383.86 - 5755.14i) q^{79} +(-7900.77 - 2726.74i) q^{80} +(-5061.87 + 2096.69i) q^{81} +(-377.991 - 9531.22i) q^{82} +(3898.13 - 2083.59i) q^{83} +(-398.176 - 1015.13i) q^{84} +(1280.38 + 1560.14i) q^{85} +(-6423.48 - 1673.66i) q^{86} +(159.308 - 238.421i) q^{87} +(3157.90 + 14317.5i) q^{88} +(-7968.66 - 11925.9i) q^{89} +(-4354.50 + 8986.11i) q^{90} +(-1307.96 - 699.117i) q^{91} +(-5481.01 + 4327.42i) q^{92} +(3109.20 - 306.229i) q^{93} +(-107.357 + 175.336i) q^{94} +(9657.99 + 9657.99i) q^{95} +(-1380.71 + 1688.72i) q^{96} +(-4859.05 - 4859.05i) q^{97} +(-1288.19 - 5357.01i) q^{98} +(17432.2 - 1716.92i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 43072 q^{50} - 16 q^{51} - 17968 q^{52} - 16 q^{53} + 31088 q^{54} - 16 q^{55} + 49376 q^{56} - 16 q^{57} + 65504 q^{58} - 16 q^{59} + 63920 q^{60} - 16 q^{61} + 11792 q^{62} - 32 q^{63} - 24400 q^{64} - 70864 q^{66} - 16 q^{67} - 53296 q^{68} - 16 q^{69} - 122320 q^{70} - 16 q^{71} - 81664 q^{72} - 16 q^{73} - 33280 q^{74} - 16 q^{75} + 28272 q^{76} - 16 q^{77} + 99344 q^{78} - 16 q^{79} + 105248 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 43072 * q^50 - 16 * q^51 - 17968 * q^52 - 16 * q^53 + 31088 * q^54 - 16 * q^55 + 49376 * q^56 - 16 * q^57 + 65504 * q^58 - 16 * q^59 + 63920 * q^60 - 16 * q^61 + 11792 * q^62 - 32 * q^63 - 24400 * q^64 - 70864 * q^66 - 16 * q^67 - 53296 * q^68 - 16 * q^69 - 122320 * q^70 - 16 * q^71 - 81664 * q^72 - 16 * q^73 - 33280 * q^74 - 16 * q^75 + 28272 * q^76 - 16 * q^77 + 99344 * q^78 - 16 * q^79 + 105248 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{29}{32}\right)$	$-1$

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 $

$2$	−2.35233	−	3.23520i	−0.588083	−	0.808801i
$2$	−2.35233	−	3.23520i	−0.588083	−	0.808801i
$3$	1.64666	+	1.35138i	0.182962	+	0.150153i	0.721416	−	0.692502i	$-0.243491\pi$
$3$	1.64666	+	1.35138i	0.182962	+	0.150153i	−0.538454	+	0.842655i	$0.680991\pi$
$4$	−4.93309	+	15.2205i	−0.308318	+	0.951283i
$5$	31.2429	−	9.47742i	1.24971	−	0.379097i	0.405001	−	0.914316i	$-0.367271\pi$
$5$	31.2429	−	9.47742i	1.24971	−	0.379097i	0.844713	+	0.535219i	$0.179771\pi$
$6$	0.498498	−	8.50617i	0.0138472	−	0.236283i
$7$	−6.24158	+	31.3785i	−0.127379	+	0.640378i	0.863359	+	0.504591i	$0.168357\pi$
$7$	−6.24158	+	31.3785i	−0.127379	+	0.640378i	−0.990738	+	0.135788i	$0.956643\pi$
$8$	60.8458	−	19.8442i	0.950715	−	0.310065i
$9$	−14.9171	−	74.9931i	−0.184161	−	0.925841i
$10$	−104.155	−	78.7830i	−1.04155	−	0.787830i
$11$	−22.4545	+	227.984i	−0.185574	+	1.88417i	0.227951	+	0.973673i	$0.426798\pi$
$11$	−22.4545	+	227.984i	−0.185574	+	1.88417i	−0.413525	+	0.910493i	$0.635702\pi$
$12$	−28.6918	+	18.3966i	−0.199249	+	0.127754i
$13$	−13.4564	+	44.3598i	−0.0796236	+	0.262484i	−0.987710	−	0.156300i	$-0.950043\pi$
$13$	−13.4564	+	44.3598i	−0.0796236	+	0.262484i	0.908086	+	0.418784i	$0.137543\pi$
$14$	116.198	−	53.6199i	0.592848	−	0.273571i
$15$	64.2540	+	26.6149i	0.285573	+	0.118288i
$16$	−207.329	−	150.168i	−0.809880	−	0.586595i
$17$	23.6566	+	57.1121i	0.0818568	+	0.197620i	0.959509	−	0.281679i	$-0.0908912\pi$
$17$	23.6566	+	57.1121i	0.0818568	+	0.197620i	−0.877652	+	0.479298i	$0.840891\pi$
$18$	−207.528	+	224.668i	−0.640519	+	0.693420i
$19$	197.207	+	368.948i	0.546280	+	1.02202i	0.991927	+	0.126809i	$0.0404736\pi$
$19$	197.207	+	368.948i	0.546280	+	1.02202i	−0.445647	+	0.895209i	$0.647026\pi$
$20$	−9.87233	+	522.286i	−0.0246808	+	1.30572i
$21$	−52.6821	+	43.2351i	−0.119460	+	0.0980387i
$22$	790.395	−	463.649i	1.63305	−	0.957952i
$23$	362.906	+	242.486i	0.686022	+	0.458385i	0.849103	−	0.528227i	$-0.177143\pi$
$23$	362.906	+	242.486i	0.686022	+	0.458385i	−0.163081	+	0.986613i	$0.552143\pi$
$24$	127.009	+	49.5491i	0.220502	+	0.0860227i
$25$	366.627	−	244.972i	0.586603	−	0.391955i
$26$	175.167	−	60.8147i	0.259122	−	0.0899625i
$27$	158.118	−	295.818i	0.216897	−	0.405786i
$28$	−446.808	−	249.793i	−0.569908	−	0.318614i
$29$	−13.1941	−	133.962i	−0.0156886	−	0.159289i	0.984148	−	0.177347i	$-0.0567516\pi$
$29$	−13.1941	−	133.962i	−0.0156886	−	0.159289i	−0.999837	+	0.0180581i	$0.994252\pi$
$30$	−65.0420	−	270.482i	−0.0722689	−	0.300535i
$31$	1037.08	−	1037.08i	1.07916	−	1.07916i	0.0825801	−	0.996584i	$-0.473684\pi$
$31$	1037.08	−	1037.08i	1.07916	−	1.07916i	0.996584	−	0.0825801i	$-0.0263160\pi$
$32$	1.88173	+	1024.00i	0.00183763	+	0.999998i
$33$	−345.068	+	345.068i	−0.316867	+	0.316867i
$34$	129.121	−	210.880i	0.111696	−	0.182423i
$35$	102.383	+	1039.51i	0.0835778	+	0.848579i
$36$	1215.02	+	142.902i	0.937517	+	0.110264i
$37$	−285.081	+	533.348i	−0.208240	+	0.389590i	−0.964260	−	0.264959i	$-0.914641\pi$
$37$	−285.081	+	533.348i	−0.208240	+	0.389590i	0.756020	+	0.654549i	$0.227141\pi$
$38$	729.727	−	1505.89i	0.505351	−	1.04286i
$39$	−82.1049	+	54.8608i	−0.0539809	+	0.0360689i
$40$	1712.92	−	1196.65i	1.07058	−	0.747906i
$41$	1982.79	+	1324.86i	1.17953	+	0.788136i	0.981387	−	0.192038i	$-0.0615097\pi$
$41$	1982.79	+	1324.86i	1.17953	+	0.788136i	0.198141	+	0.980174i	$0.436510\pi$
$42$	263.800	+	68.7341i	0.149546	+	0.0389649i
$43$	1282.80	−	1052.77i	0.693780	−	0.569370i	−0.220040	−	0.975491i	$-0.570619\pi$
$43$	1282.80	−	1052.77i	0.693780	−	0.569370i	0.913820	+	0.406121i	$0.133119\pi$
$44$	−3359.27	−	1466.43i	−1.73516	−	0.757455i
$45$	−1176.79	−	2201.62i	−0.581132	−	1.08722i
$46$	−69.1830	−	1744.48i	−0.0326952	−	0.824424i
$47$	−19.6692	−	47.4857i	−0.00890412	−	0.0214964i	0.919365	−	0.393406i	$-0.128703\pi$
$47$	−19.6692	−	47.4857i	−0.00890412	−	0.0214964i	−0.928269	+	0.371909i	$0.878703\pi$
$48$	−138.467	−	527.457i	−0.0600983	−	0.228931i
$49$	1272.58	+	527.119i	0.530020	+	0.219542i
$50$	−1654.96	−	609.857i	−0.661985	−	0.243943i
$51$	−38.2257	+	126.013i	−0.0146965	+	0.0484480i
$52$	−608.798	−	423.644i	−0.225147	−	0.156673i
$53$	−108.877	+	1105.45i	−0.0387602	+	0.393539i	0.956158	+	0.292851i	$0.0946041\pi$
$53$	−108.877	+	1105.45i	−0.0387602	+	0.393539i	−0.994918	+	0.100687i	$0.967896\pi$
$54$	−1328.98	+	184.318i	−0.455754	+	0.0632091i
$55$	1459.16	+	7335.68i	0.482366	+	2.42502i
$56$	242.908	+	2033.11i	0.0774579	+	0.648313i
$57$	−173.856	+	874.034i	−0.0535107	+	0.269016i
$58$	−402.359	+	357.809i	−0.119607	+	0.106364i
$59$	−3213.26	+	974.732i	−0.923086	+	0.280015i	−0.715832	−	0.698272i	$-0.753952\pi$
$59$	−3213.26	+	974.732i	−0.923086	+	0.280015i	−0.207253	+	0.978287i	$0.566452\pi$
$60$	−722.063	+	846.686i	−0.200573	+	0.235191i
$61$	2229.46	+	1829.67i	0.599157	+	0.491716i	0.884394	−	0.466741i	$-0.154572\pi$
$61$	2229.46	+	1829.67i	0.599157	+	0.491716i	−0.285236	+	0.958457i	$0.592072\pi$
$62$	−5794.70	−	915.608i	−1.50747	−	0.238191i
$63$	2446.28			0.616347
$64$	3308.42	−	2414.87i	0.807719	−	0.589568i
$65$			1513.46i			0.358215i
$66$	1928.08	+	304.651i	0.442626	+	0.0699383i
$67$	−2639.09	+	3215.74i	−0.587902	+	0.716361i	−0.978971	−	0.204001i	$-0.934606\pi$
$67$	−2639.09	+	3215.74i	−0.587902	+	0.716361i	0.391069	+	0.920362i	$0.372106\pi$
$68$	−985.977	+	78.3273i	−0.213230	+	0.0169393i
$69$	269.892	+	889.715i	0.0566881	+	0.186876i
$70$	3122.19	−	2776.50i	0.637181	−	0.566633i
$71$	−4066.62	−	808.900i	−0.806708	−	0.160464i	−0.225525	−	0.974237i	$-0.572410\pi$
$71$	−4066.62	−	808.900i	−0.806708	−	0.160464i	−0.581183	+	0.813773i	$0.697410\pi$
$72$	−2395.82	−	4267.00i	−0.462156	−	0.823109i
$73$	−5314.94	+	1057.21i	−0.997361	+	0.198388i	−0.666671	−	0.745352i	$-0.732282\pi$
$73$	−5314.94	+	1057.21i	−0.997361	+	0.198388i	−0.330690	+	0.943739i	$0.607282\pi$
$74$	2396.09	−	332.318i	0.437563	−	0.0606862i
$75$	934.760	+	92.0658i	0.166179	+	0.0163672i
$76$	−6588.43	+	1181.54i	−1.14066	+	0.204561i
$77$	−7013.66	−	2127.57i	−1.18294	−	0.358841i
$78$	370.624	+	136.576i	0.0609178	+	0.0224483i
$79$	2383.86	−	5755.14i	0.381967	−	0.922151i	−0.609618	−	0.792695i	$-0.708677\pi$
$79$	2383.86	−	5755.14i	0.381967	−	0.922151i	0.991585	−	0.129455i	$-0.0413229\pi$
$80$	−7900.77	−	2726.74i	−1.23450	−	0.426054i
$81$	−5061.87	+	2096.69i	−0.771509	+	0.319569i
$82$	−377.991	−	9531.22i	−0.0562152	−	1.41749i
$83$	3898.13	−	2083.59i	0.565848	−	0.302452i	−0.163557	−	0.986534i	$-0.552297\pi$
$83$	3898.13	−	2083.59i	0.565848	−	0.302452i	0.729405	+	0.684082i	$0.239797\pi$
$84$	−398.176	−	1015.13i	−0.0564308	−	0.143868i
$85$	1280.38	+	1560.14i	0.177215	+	0.215937i
$86$	−6423.48	−	1673.66i	−0.868507	−	0.226293i
$87$	159.308	−	238.421i	0.0210474	−	0.0314996i
$88$	3157.90	+	14317.5i	0.407786	+	1.84885i
$89$	−7968.66	−	11925.9i	−1.00602	−	1.50561i	−0.856032	−	0.516922i	$-0.827078\pi$
$89$	−7968.66	−	11925.9i	−1.00602	−	1.50561i	−0.149985	−	0.988688i	$-0.547922\pi$
$90$	−4354.50	+	8986.11i	−0.537592	+	1.10940i
$91$	−1307.96	−	699.117i	−0.157947	−	0.0844242i
$92$	−5481.01	+	4327.42i	−0.647567	+	0.511273i
$93$	3109.20	−	306.229i	0.359486	−	0.0354063i
$94$	−107.357	+	175.336i	−0.0121500	+	0.0198433i
$95$	9657.99	+	9657.99i	1.07014	+	1.07014i
$96$	−1380.71	+	1688.72i	−0.149817	+	0.183238i
$97$	−4859.05	−	4859.05i	−0.516426	−	0.516426i	0.400062	−	0.916488i	$-0.368989\pi$
$97$	−4859.05	−	4859.05i	−0.516426	−	0.516426i	−0.916488	+	0.400062i	$0.868989\pi$
$98$	−1288.19	−	5357.01i	−0.134130	−	0.557790i
$99$	17432.2	−	1716.92i	1.77861	−	0.175178i
$100$	1920.01	+	6788.72i	0.192001	+	0.678872i
$101$	7626.12	+	4076.25i	0.747585	+	0.399593i	0.800754	−	0.598993i	$-0.204432\pi$
$101$	7626.12	+	4076.25i	0.747585	+	0.399593i	−0.0531690	+	0.998586i	$0.516932\pi$
$102$	497.598	−	172.757i	0.0478276	−	0.0166048i
$103$	−439.598	−	657.905i	−0.0414363	−	0.0620139i	0.810173	−	0.586191i	$-0.199373\pi$
$103$	−439.598	−	657.905i	−0.0414363	−	0.0620139i	−0.851609	+	0.524177i	$0.824373\pi$
$104$	61.5191	+	2966.14i	0.00568779	+	0.274236i
$105$	−1236.18	+	1850.08i	−0.112125	+	0.167807i
$106$	3832.47	−	2248.14i	0.341089	−	0.200084i
$107$	1616.90	+	1970.20i	0.141226	+	0.172085i	0.838820	−	0.544409i	$-0.183246\pi$
$107$	1616.90	+	1970.20i	0.141226	+	0.172085i	−0.697594	+	0.716493i	$0.745746\pi$
$108$	3722.50	+	3865.94i	0.319144	+	0.331442i
$109$	−4554.08	+	2434.21i	−0.383308	+	0.204882i	−0.651785	−	0.758404i	$-0.725980\pi$
$109$	−4554.08	+	2434.21i	−0.383308	+	0.204882i	0.268477	+	0.963286i	$0.413480\pi$
$110$	20300.0	−	21976.6i	1.67769	−	1.81625i
$111$	−1190.19	+	492.991i	−0.0965982	+	0.0400123i
$112$	6006.13	−	5568.40i	0.478805	−	0.443910i
$113$	8667.16	−	20924.4i	0.678766	−	1.63869i	−0.0875020	−	0.996164i	$-0.527888\pi$
$113$	8667.16	−	20924.4i	0.678766	−	1.63869i	0.766268	−	0.642521i	$-0.222112\pi$
$114$	3236.65	−	1493.56i	0.249049	−	0.114924i
$115$	13636.4	+	4136.54i	1.03110	+	0.312782i
$116$	2104.07	+	460.026i	0.156366	+	0.0341874i
$117$	3527.40	+	347.419i	0.257682	+	0.0253794i
$118$	10712.1	+	8102.66i	0.769327	+	0.581921i
$119$	−1939.75	+	385.840i	−0.136978	+	0.0272467i
$120$	4437.73	+	344.334i	0.308176	+	0.0239121i
$121$	−37112.8	−	7382.20i	−2.53486	−	0.504214i
$122$	674.932	−	11516.8i	0.0453461	−	0.773768i
$123$	1474.59	+	4861.08i	0.0974680	+	0.321309i
$124$	10668.9	+	20900.9i	0.693866	+	1.35932i
$125$	−3812.31	+	4645.32i	−0.243988	+	0.297300i
$126$	−5754.46	−	7914.21i	−0.362463	−	0.498502i
$127$			25390.7i			1.57423i	0.616807	+	0.787114i	$0.288426\pi$
$127$			25390.7i			1.57423i	−0.616807	+	0.787114i	$0.711574\pi$
$128$	−15595.1	−	5022.83i	−0.951848	−	0.306569i
$129$	3535.02			0.212428
$130$	4896.34	−	3560.15i	0.289725	−	0.210660i
$131$	1187.65	+	974.678i	0.0692063	+	0.0567961i	0.668360	−	0.743838i	$-0.266996\pi$
$131$	1187.65	+	974.678i	0.0692063	+	0.0567961i	−0.599154	+	0.800634i	$0.704496\pi$
$132$	−3549.87	−	6954.36i	−0.203734	−	0.399126i
$133$	−12808.0	+	3885.25i	−0.724063	+	0.219642i
$134$	16611.6	+	973.511i	0.925128	+	0.0542165i
$135$	2136.47	−	10740.8i	0.117227	−	0.589342i
$136$	2572.75	+	3005.58i	0.139098	+	0.162499i
$137$	−1992.18	−	10015.4i	−0.106142	−	0.533613i	−0.996869	−	0.0790734i	$-0.974804\pi$
$137$	−1992.18	−	10015.4i	−0.106142	−	0.533613i	0.890727	−	0.454540i	$-0.150196\pi$
$138$	2243.53	−	2966.06i	0.117808	−	0.155748i
$139$	1500.28	−	15232.6i	0.0776502	−	0.788396i	−0.874959	−	0.484198i	$-0.839112\pi$
$139$	1500.28	−	15232.6i	0.0776502	−	0.788396i	0.952609	−	0.304198i	$-0.0983884\pi$
$140$	−16327.0	−	3569.67i	−0.833008	−	0.182126i
$141$	31.7826	−	104.773i	0.00159864	−	0.00527002i
$142$	6949.07	+	15059.1i	0.344627	+	0.746833i
$143$	−9811.16	−	4063.92i	−0.479787	−	0.198734i
$144$	−8168.85	+	17788.3i	−0.393945	+	0.857848i
$145$	−1681.84	−	4060.32i	−0.0799924	−	0.193119i
$146$	15922.8	+	14708.0i	0.746987	+	0.689999i
$147$	1383.17	+	2587.72i	0.0640088	+	0.119752i
$148$	−6711.52	−	6970.13i	−0.306406	−	0.318213i
$149$	23532.7	−	19312.8i	1.05998	−	0.869906i	0.0681791	−	0.997673i	$-0.478281\pi$
$149$	23532.7	−	19312.8i	1.05998	−	0.869906i	0.991804	+	0.127767i	$0.0407811\pi$
$150$	−1901.01	−	3240.71i	−0.0844894	−	0.144031i
$151$	8789.40	+	5872.89i	0.385483	+	0.257572i	0.733179	−	0.680036i	$-0.238036\pi$
$151$	8789.40	+	5872.89i	0.385483	+	0.257572i	−0.347696	+	0.937607i	$0.613036\pi$
$152$	19320.7	+	18535.5i	0.836249	+	0.802266i
$153$	3930.13	−	2626.03i	0.167890	−	0.112180i
$154$	9615.32	+	27695.4i	0.405436	+	1.16779i
$155$	22572.4	−	42230.1i	0.939540	−	1.75776i
$156$	−429.980	−	1520.31i	−0.0176685	−	0.0624718i
$157$	1253.22	+	12724.1i	0.0508425	+	0.516213i	0.986553	+	0.163443i	$0.0522601\pi$
$157$	1253.22	+	12724.1i	0.0508425	+	0.516213i	−0.935710	+	0.352770i	$0.885240\pi$
$158$	−24226.7	+	5825.73i	−0.970465	+	0.233365i
$159$	−1673.17	+	1673.17i	−0.0661827	+	0.0661827i
$160$	9763.65	+	31974.8i	0.381393	+	1.24902i
$161$	−9873.96	+	9873.96i	−0.380925	+	0.380925i
$162$	18690.4	+	11444.1i	0.712179	+	0.436064i
$163$	−3917.39	−	39773.9i	−0.147442	−	1.49700i	−0.729570	−	0.683906i	$-0.760280\pi$
$163$	−3917.39	−	39773.9i	−0.147442	−	1.49700i	0.582128	−	0.813097i	$-0.302220\pi$
$164$	−29946.3	+	23643.5i	−1.11341	+	0.879069i
$165$	−7510.55	+	14051.3i	−0.275870	+	0.516116i
$166$	−15910.5	−	7709.94i	−0.577389	−	0.279792i
$167$	−45989.6	+	30729.3i	−1.64902	+	1.10184i	−0.752789	+	0.658262i	$0.771292\pi$
$167$	−45989.6	+	30729.3i	−1.64902	+	1.10184i	−0.896235	+	0.443580i	$0.853708\pi$
$168$	−2347.52	+	3676.10i	−0.0831745	+	0.130247i
$169$	21960.9	+	14673.8i	0.768912	+	0.513770i
$170$	2035.51	−	7812.24i	0.0704329	−	0.270320i
$171$	24726.8	−	20292.8i	0.845622	−	0.693984i
$172$	9695.50	+	24718.3i	0.327728	+	0.835528i
$173$	−23221.3	−	43444.0i	−0.775880	−	1.45157i	−0.888961	−	0.457983i	$-0.848572\pi$
$173$	−23221.3	−	43444.0i	−0.775880	−	1.45157i	0.113081	−	0.993586i	$-0.463928\pi$
$174$	−1146.08	+	45.4516i	−0.0378545	+	0.00150124i
$175$	5398.54	+	13033.2i	0.176279	+	0.425575i
$176$	38891.5	−	43895.8i	1.25554	−	1.41709i
$177$	−6608.38	−	2737.28i	−0.210935	−	0.0873721i
$178$	−19837.9	+	53834.0i	−0.626118	+	1.69909i
$179$	−3945.15	+	13005.4i	−0.123128	+	0.405899i	−0.996736	−	0.0807316i	$-0.974274\pi$
$179$	−3945.15	+	13005.4i	−0.123128	+	0.405899i	0.873608	+	0.486631i	$0.161774\pi$
$180$	39315.1	−	7050.61i	1.21343	−	0.217611i
$181$	−701.085	+	7118.24i	−0.0214000	+	0.217278i	0.978537	+	0.206070i	$0.0660675\pi$
$181$	−701.085	+	7118.24i	−0.0214000	+	0.217278i	−0.999937	+	0.0112076i	$0.996432\pi$
$182$	814.958	+	5876.06i	0.0246033	+	0.177396i
$183$	1198.59	+	6025.70i	0.0357905	+	0.179931i
$184$	26893.2	+	7552.67i	0.794341	+	0.223082i
$185$	−3851.97	+	19365.2i	−0.112548	+	0.565819i
$186$	−8304.57	−	9338.54i	−0.240044	−	0.269931i
$187$	−13551.8	+	4110.91i	−0.387539	+	0.117559i
$188$	819.787	−	65.1250i	0.0231945	−	0.00184260i
$189$	8295.44	+	6807.89i	0.232229	+	0.190585i
$190$	8526.79	−	53964.4i	0.236199	−	1.49486i
$191$	−62598.8			−1.71593			−0.857964	−	0.513709i	$-0.828271\pi$
$191$	−62598.8			−1.71593			−0.857964	+	0.513709i	$0.828271\pi$
$192$	8711.24	+	494.455i	0.236308	+	0.0134129i
$193$		−	70749.4i		−	1.89936i	−0.313218	−	0.949681i	$-0.601407\pi$
$193$		−	70749.4i		−	1.89936i	0.313218	−	0.949681i	$-0.398593\pi$
$194$	−4289.93	+	27150.1i	−0.113985	+	0.721387i
$195$	−2045.26	+	2492.15i	−0.0537871	+	0.0655398i
$196$	−14300.8	+	16769.0i	−0.372261	+	0.436511i
$197$	−8523.61	−	28098.6i	−0.219630	−	0.724022i	−0.995638	−	0.0932996i	$-0.970259\pi$
$197$	−8523.61	−	28098.6i	−0.219630	−	0.724022i	0.776008	−	0.630723i	$-0.217241\pi$
$198$	−46560.8	−	52357.9i	−1.18766	−	1.33552i
$199$	14798.0	+	2943.51i	0.373678	+	0.0743291i	0.378356	−	0.925660i	$-0.376489\pi$
$199$	14798.0	+	2943.51i	0.373678	+	0.0743291i	−0.00467895	+	0.999989i	$0.501489\pi$
$200$	17446.4	−	22180.9i	0.436160	−	0.554523i
$201$	−8691.38	+	1728.82i	−0.215128	+	0.0427916i
$202$	−4751.66	−	34260.7i	−0.116451	−	0.839641i
$203$	4285.90	+	422.124i	0.104004	+	0.0102435i
$204$	−1729.42	−	1203.45i	−0.0415566	−	0.0289180i
$205$	74504.2	+	22600.6i	1.77285	+	0.537789i
$206$	−1094.38	+	2969.80i	−0.0257889	+	0.0699830i
$207$	12771.3	−	30832.6i	0.298053	−	0.719564i
$208$	9451.34	−	7176.36i	0.218457	−	0.165874i
$209$	−88542.5	+	36675.5i	−2.02703	+	0.839622i
$210$	8893.28	−	352.692i	0.201662	−	0.00799754i
$211$	−68833.0	+	36792.0i	−1.54608	+	0.826397i	−0.999936	−	0.0112943i	$-0.996405\pi$
$211$	−68833.0	+	36792.0i	−1.54608	+	0.826397i	−0.546144	+	0.837691i	$0.683905\pi$
$212$	−16288.4	−	7110.45i	−0.362416	−	0.158207i
$213$	−5603.20	−	6827.52i	−0.123503	−	0.150489i
$214$	2570.51	−	9865.55i	0.0561295	−	0.215424i
$215$	30100.8	−	45049.0i	0.651180	−	0.974560i
$216$	3750.55	−	21137.0i	0.0803873	−	0.453040i
$217$	26069.0	+	39015.0i	0.553611	+	0.828537i
$218$	18587.9	+	9007.32i	0.391126	+	0.189532i
$219$	−10180.6	−	5441.64i	−0.212268	−	0.113460i
$220$	−118851.	−	13978.4i	−2.45560	−	0.288810i
$221$	−2851.81	+	280.879i	−0.0583897	+	0.00575088i
$222$	4394.64	+	2690.82i	0.0891697	+	0.0545982i
$223$	54043.9	+	54043.9i	1.08677	+	1.08677i	0.995859	+	0.0909100i	$0.0289775\pi$
$223$	54043.9	+	54043.9i	1.08677	+	1.08677i	0.0909100	+	0.995859i	$0.471022\pi$
$224$	−32143.3	−	6332.32i	−0.640611	−	0.126202i
$225$	−23840.2	−	23840.2i	−0.470918	−	0.470918i
$226$	−88082.6	+	21181.0i	−1.72454	+	0.414696i
$227$	50378.9	−	4961.89i	0.977681	−	0.0962932i	0.403463	−	0.914996i	$-0.367806\pi$
$227$	50378.9	−	4961.89i	0.977681	−	0.0962932i	0.574218	+	0.818703i	$0.305306\pi$
$228$	−12445.6	−	6957.87i	−0.239413	−	0.133846i
$229$	62355.0	+	33329.4i	1.18905	+	0.635561i	0.942707	−	0.333622i	$-0.108271\pi$
$229$	62355.0	+	33329.4i	1.18905	+	0.635561i	0.246343	+	0.969183i	$0.420771\pi$
$230$	−18694.7	−	53846.9i	−0.353396	−	1.01790i
$231$	−8673.96	−	12981.5i	−0.162552	−	0.243277i
$232$	−3461.18	−	7889.22i	−0.0643055	−	0.146574i
$233$	44289.3	−	66283.6i	0.815806	−	1.22094i	−0.156604	−	0.987661i	$-0.550055\pi$
$233$	44289.3	−	66283.6i	0.815806	−	1.22094i	0.972410	−	0.233278i	$-0.0749452\pi$
$234$	−7173.65	−	12229.1i	−0.131011	−	0.223338i
$235$	−1064.56	−	1297.17i	−0.0192768	−	0.0234889i
$236$	1015.35	−	53716.0i	0.0182302	−	0.964450i
$237$	11702.8	−	6255.27i	0.208350	−	0.111365i
$238$	5811.20	+	5367.86i	0.102592	+	0.0947649i
$239$	−21240.5	+	8798.11i	−0.371851	+	0.154026i	−0.560780	−	0.827965i	$-0.689499\pi$
$239$	−21240.5	+	8798.11i	−0.371851	+	0.154026i	0.188929	+	0.981991i	$0.439499\pi$
$240$	−9325.02	−	15167.0i	−0.161893	−	0.263315i
$241$	−12361.9	+	29844.4i	−0.212840	+	0.513841i	−0.993857	−	0.110668i	$-0.964701\pi$
$241$	−12361.9	+	29844.4i	−0.212840	+	0.513841i	0.781018	+	0.624509i	$0.214701\pi$
$242$	63418.7	+	137433.i	1.08290	+	2.34671i
$243$	−37168.1	−	11274.8i	−0.629445	−	0.190940i
$244$	−38846.8	+	24907.7i	−0.652492	+	0.418364i
$245$	44754.7	+	4407.96i	0.745602	+	0.0734354i
$246$	12257.9	−	16205.5i	0.202556	−	0.267788i
$247$	−19020.2	+	3783.35i	−0.311760	+	0.0620129i
$248$	42521.8	−	83681.7i	0.691367	−	1.36059i
$249$	9234.62	+	1836.88i	0.148943	+	0.0296266i
$250$	23996.4	+	1406.29i	0.383942	+	0.0225006i
$251$	12750.2	+	42031.7i	0.202381	+	0.667160i	0.998107	+	0.0615031i	$0.0195894\pi$
$251$	12750.2	+	42031.7i	0.202381	+	0.667160i	−0.795726	+	0.605656i	$0.792911\pi$
$252$	−12067.7	+	37233.7i	−0.190031	+	0.586320i
$253$	−63431.8	+	77291.8i	−0.990982	+	1.20752i
$254$	82144.2	−	59727.4i	1.27324	−	0.925776i
$255$			4299.30i			0.0661176i
$256$	20434.9	+	62268.6i	0.311812	+	0.950144i
$257$	−62731.6			−0.949774			−0.474887	−	0.880047i	$-0.657511\pi$
$257$	−62731.6			−0.949774			−0.474887	+	0.880047i	$0.657511\pi$
$258$	−8315.53	−	11436.5i	−0.124925	−	0.171812i
$259$	−14956.3	−	12274.4i	−0.222959	−	0.182978i
$260$	−23035.6	−	7466.02i	−0.340764	−	0.110444i
$261$	−9849.43	+	2987.79i	−0.144587	+	0.0438601i
$262$	359.540	−	6135.05i	0.00523775	−	0.0893749i
$263$	−6325.63	+	31801.1i	−0.0914518	+	0.459759i	0.907739	+	0.419535i	$0.137807\pi$
$263$	−6325.63	+	31801.1i	−0.0914518	+	0.459759i	−0.999191	+	0.0402236i	$0.987193\pi$
$264$	−14148.3	+	27843.5i	−0.203001	+	0.399499i
$265$	7075.17	+	35569.3i	0.100750	+	0.506505i
$266$	42698.1	+	32296.9i	0.603456	+	0.456455i
$267$	2994.79	−	30406.7i	0.0420092	−	0.426527i
$268$	−35926.5	−	56032.0i	−0.500202	−	0.780129i
$269$	−37960.1	+	125138.i	−0.524593	+	1.72935i	0.147666	+	0.989037i	$0.452824\pi$
$269$	−37960.1	+	125138.i	−0.524593	+	1.72935i	−0.672260	+	0.740315i	$0.734676\pi$
$270$	−39774.2	+	18353.9i	−0.545600	+	0.251768i
$271$	43721.7	+	18110.1i	0.595331	+	0.246594i	0.659942	−	0.751316i	$-0.270581\pi$
$271$	43721.7	+	18110.1i	0.595331	+	0.246594i	−0.0646113	+	0.997911i	$0.520581\pi$
$272$	3671.72	−	15393.5i	0.0496286	−	0.208065i
$273$	−1208.99	−	2918.75i	−0.0162217	−	0.0391626i
$274$	−27715.5	+	30004.6i	−0.369166	+	0.399656i
$275$	47617.3	+	89085.7i	0.629650	+	1.17799i
$276$	−14873.3	−	281.138i	−0.195250	−	0.00369064i
$277$	80621.0	−	66164.0i	1.05072	−	0.862307i	0.0600007	−	0.998198i	$-0.480890\pi$
$277$	80621.0	−	66164.0i	1.05072	−	0.862307i	0.990724	+	0.135891i	$0.0433897\pi$
$278$	−52809.7	+	30978.4i	−0.683320	+	0.400838i
$279$	−93243.7	−	62303.5i	−1.19787	−	0.800394i
$280$	26857.8	+	61218.1i	0.342574	+	0.780843i
$281$	−36805.8	+	24592.8i	−0.466126	+	0.311455i	−0.766361	−	0.642410i	$-0.777935\pi$
$281$	−36805.8	+	24592.8i	−0.466126	+	0.311455i	0.300235	+	0.953865i	$0.402935\pi$
$282$	−413.726	+	143.638i	−0.00520253	+	0.00180622i
$283$	47626.0	−	89102.0i	0.594663	−	1.11254i	−0.387030	−	0.922067i	$-0.626499\pi$
$283$	47626.0	−	89102.0i	0.594663	−	1.11254i	0.981693	−	0.190470i	$-0.0610011\pi$
$284$	32372.9	−	57905.7i	0.401370	−	0.717934i
$285$	2851.82	+	28955.0i	0.0351102	+	0.356479i
$286$	9931.50	+	41300.8i	0.121418	+	0.504924i
$287$	−53947.8	+	53947.8i	−0.654952	+	0.654952i
$288$	76764.7	−	15416.2i	0.925501	−	0.185862i
$289$	56356.1	−	56356.1i	0.674754	−	0.674754i
$290$	−9179.72	+	14992.3i	−0.109152	+	0.178268i
$291$	−1434.79	−	14567.6i	−0.0169434	−	0.172029i
$292$	10127.8	−	86111.5i	0.118782	−	1.00994i
$293$	59394.4	−	111119.i	0.691847	−	1.29435i	−0.253198	−	0.967414i	$-0.581482\pi$
$293$	59394.4	−	111119.i	0.691847	−	1.29435i	0.945045	−	0.326940i	$-0.106018\pi$
$294$	5118.15	−	10562.0i	0.0592131	−	0.122195i
$295$	−91153.5	+	60906.9i	−1.04744	+	0.699878i
$296$	−6762.09	+	38109.2i	−0.0771787	+	0.434957i
$297$	63891.4	+	42690.9i	0.724318	+	0.483974i
$298$	−117837.	−	30703.0i	−1.32694	−	0.345739i
$299$	−15640.0	+	12835.4i	−0.174942	+	0.143571i
$300$	−6012.54	+	13773.4i	−0.0668060	+	0.153037i
$301$	25027.6	+	46823.3i	0.276239	+	0.516808i
$302$	−1675.58	−	42250.5i	−0.0183718	−	0.463252i
$303$	7049.07	+	17018.0i	0.0767798	+	0.185363i
$304$	14517.6	−	106108.i	0.157090	−	1.14816i
$305$	86995.4	+	36034.7i	0.935184	+	0.387366i
$306$	−17740.7	−	6537.48i	−0.189464	−	0.0698180i
$307$	42892.6	−	141398.i	0.455099	−	1.50026i	−0.366622	−	0.930370i	$-0.619486\pi$
$307$	42892.6	−	141398.i	0.455099	−	1.50026i	0.821721	−	0.569890i	$-0.193014\pi$
$308$	66981.7	−	96256.1i	0.706081	−	1.01467i
$309$	165.210	−	1677.41i	0.00173030	−	0.0175680i
$310$	−189721.	+	26312.6i	−1.97420	+	0.273805i
$311$	3231.54	+	16246.1i	0.0334110	+	0.167968i	0.993888	−	0.110390i	$-0.0352098\pi$
$311$	3231.54	+	16246.1i	0.0334110	+	0.167968i	−0.960477	+	0.278358i	$0.910210\pi$
$312$	−3907.07	+	4967.35i	−0.0401367	+	0.0510288i
$313$	4798.68	−	24124.6i	0.0489816	−	0.246247i	−0.948536	−	0.316671i	$-0.897435\pi$
$313$	4798.68	−	24124.6i	0.0489816	−	0.246247i	0.997517	+	0.0704233i	$0.0224350\pi$
$314$	38217.2	−	33985.8i	0.387614	−	0.344697i
$315$	76428.8	−	23184.4i	0.770257	−	0.233655i
$316$	75836.6	+	64674.2i	0.759460	+	0.647675i
$317$	5449.05	+	4471.92i	0.0542254	+	0.0445016i	0.661116	−	0.750284i	$-0.270083\pi$
$317$	5449.05	+	4471.92i	0.0542254	+	0.0445016i	−0.606890	+	0.794786i	$0.707583\pi$
$318$	9348.87	+	1477.19i	0.0924496	+	0.0146077i
$319$	30837.5			0.303039
$320$	80477.7	−	106803.i	0.785915	−	1.04300i
$321$			5429.29i			0.0526906i
$322$	55171.1	+	8717.46i	0.532108	+	0.0840772i
$323$	−16406.2	+	19991.0i	−0.157254	+	0.191615i
$324$	−6942.18	−	87387.5i	−0.0661311	−	0.832452i
$325$	5933.43	+	19559.9i	0.0561745	+	0.185183i
$326$	−119462.	+	106235.i	−1.12407	+	0.999613i
$327$	−10788.6	−	2145.98i	−0.100895	−	0.0200692i
$328$	146935.	+	41265.1i	1.36577	+	0.383562i
$329$	1612.80	−	320.805i	0.0149001	−	0.00296381i
$330$	63126.0	−	8755.03i	0.579669	−	0.0803951i
$331$	58490.3	+	5760.79i	0.533861	+	0.0525807i	0.361356	−	0.932428i	$-0.382314\pi$
$331$	58490.3	+	5760.79i	0.533861	+	0.0525807i	0.172505	+	0.985009i	$0.444814\pi$
$332$	12483.6	+	69610.2i	0.113257	+	0.631534i
$333$	44250.0	+	13423.1i	0.399048	+	0.121050i
$334$	207598.	+	76500.4i	1.86093	+	0.685758i
$335$	−51975.9	+	125481.i	−0.463140	+	1.11812i
$336$	17415.1	−	1052.71i	0.154258	−	0.00932464i
$337$	63076.8	−	26127.3i	0.555405	−	0.230056i	−0.0872840	−	0.996183i	$-0.527819\pi$
$337$	63076.8	−	26127.3i	0.555405	−	0.230056i	0.642689	+	0.766127i	$0.277819\pi$
$338$	−4186.54	−	105566.i	−0.0366456	−	0.924036i
$339$	42548.6	−	22742.7i	0.370242	−	0.197899i
$340$	−30062.4	+	11791.7i	−0.260055	+	0.102004i
$341$	213150.	+	259724.i	1.83306	+	2.23359i
$342$	−123817.	−	32261.0i	−1.05859	−	0.275820i
$343$	−67159.8	+	100512.i	−0.570849	+	0.854335i
$344$	57161.6	−	89512.5i	0.483045	−	0.756426i
$345$	16864.4	+	25239.4i	0.141688	+	0.212051i
$346$	−85926.0	+	177320.i	−0.717749	+	1.48117i
$347$	−57081.9	−	30510.9i	−0.474067	−	0.253394i	0.217018	−	0.976168i	$-0.430367\pi$
$347$	−57081.9	−	30510.9i	−0.474067	−	0.253394i	−0.691085	+	0.722774i	$0.742867\pi$
$348$	2843.01	+	3600.90i	0.0234758	+	0.0297339i
$349$	132197.	−	13020.3i	1.08536	−	0.106898i	0.460516	−	0.887651i	$-0.347664\pi$
$349$	132197.	−	13020.3i	1.08536	−	0.106898i	0.624840	+	0.780753i	$0.285164\pi$
$350$	29466.0	−	48123.8i	0.240539	−	0.392847i
$351$	10994.7	+	10994.7i	0.0892422	+	0.0892422i
$352$	−233498.	−	22564.3i	−1.88450	−	0.182111i
$353$	−12854.6	−	12854.6i	−0.103160	−	0.103160i	0.653643	−	0.756803i	$-0.273240\pi$
$353$	−12854.6	−	12854.6i	−0.103160	−	0.103160i	−0.756803	+	0.653643i	$0.773240\pi$
$354$	6689.43	+	27818.5i	0.0533805	+	0.221986i
$355$	−134719.	+	13268.7i	−1.06899	+	0.105286i
$356$	220829.	−	62455.6i	1.74244	−	0.492801i
$357$	−3715.52	−	1985.99i	−0.0291530	−	0.0155826i
$358$	51355.5	−	17829.7i	0.400701	−	0.139116i
$359$	−113048.	−	169188.i	−0.877149	−	1.31275i	−0.948982	−	0.315330i	$-0.897885\pi$
$359$	−113048.	−	169188.i	−0.877149	−	1.31275i	0.0718328	−	0.997417i	$-0.477115\pi$
$360$	−115292.	−	110607.i	−0.889601	−	0.853449i
$361$	−24829.9	+	37160.5i	−0.190529	+	0.285146i
$362$	24678.1	−	14476.3i	0.188319	−	0.110469i
$363$	−51136.1	−	62309.5i	−0.388074	−	0.472869i
$364$	17093.2	−	16459.0i	0.129009	−	0.124222i
$365$	−156034.	+	83402.1i	−1.17121	+	0.626024i
$366$	16674.9	−	18052.1i	0.124480	−	0.134762i
$367$	191011.	−	79119.5i	1.41817	−	0.587424i	0.463767	−	0.885957i	$-0.346497\pi$
$367$	191011.	−	79119.5i	1.41817	−	0.587424i	0.954399	+	0.298534i	$0.0964975\pi$
$368$	−38827.3	−	104771.i	−0.286709	−	0.773655i
$369$	69777.7	−	168458.i	0.512465	−	1.23720i
$370$	71711.3	−	33091.3i	0.523823	−	0.241719i
$371$	−34007.9	−	10316.2i	−0.247076	−	0.0749498i
$372$	−10677.0	+	48834.3i	−0.0771546	+	0.352890i
$373$	−23553.6	−	2319.83i	−0.169294	−	0.0166740i	0.0130152	−	0.999915i	$-0.495857\pi$
$373$	−23553.6	−	2319.83i	−0.169294	−	0.0166740i	−0.182309	+	0.983241i	$0.558357\pi$
$374$	45178.0	+	34172.8i	0.322986	+	0.244308i
$375$	−12555.2	+	2497.38i	−0.0892812	+	0.0177591i
$376$	−2139.10	−	2498.98i	−0.0151306	−	0.0176761i
$377$	6120.08	+	1217.36i	0.0430601	+	0.00856518i
$378$	2511.30	−	42851.8i	0.0175758	−	0.299907i
$379$	−21099.2	−	69554.6i	−0.146888	−	0.484226i	0.852362	−	0.522953i	$-0.175170\pi$
$379$	−21099.2	−	69554.6i	−0.146888	−	0.484226i	−0.999250	+	0.0387273i	$0.987670\pi$
$380$	−194644.	+	99356.1i	−1.34795	+	0.688062i
$381$	−34312.5	+	41809.9i	−0.236375	+	0.288024i
$382$	147253.	+	202520.i	1.00911	+	1.38784i
$383$			17012.1i			0.115974i	0.998317	+	0.0579871i	$0.0184682\pi$
$383$			17012.1i			0.115974i	−0.998317	+	0.0579871i	$0.981532\pi$
$384$	−18892.1	−	29345.8i	−0.128120	−	0.199014i
$385$	−239291.			−1.61437
$386$	−228889.	+	166426.i	−1.53621	+	1.11698i
$387$	−98085.7	−	80496.9i	−0.654913	−	0.537474i
$388$	97927.5	−	49987.2i	0.650491	−	0.332044i
$389$	96113.3	−	29155.7i	0.635162	−	0.192674i	0.0437482	−	0.999043i	$-0.486070\pi$
$389$	96113.3	−	29155.7i	0.635162	−	0.192674i	0.591414	+	0.806368i	$0.298570\pi$
$390$	12873.7	+	754.456i	0.0846399	+	0.00496026i
$391$	−5263.76	+	26462.7i	−0.0344304	+	0.173093i
$392$	87891.3	+	6819.70i	0.571971	+	0.0443806i
$393$	638.494	+	3209.93i	0.00413401	+	0.0207831i
$394$	−70854.3	+	93672.8i	−0.456429	+	0.603422i
$395$	19934.7	−	202400.i	0.127766	−	1.29723i
$396$	−59862.0	+	273797.i	−0.381734	+	1.74598i
$397$	54518.5	−	179724.i	0.345910	−	1.14031i	−0.595587	−	0.803291i	$-0.703080\pi$
$397$	54518.5	−	179724.i	0.345910	−	1.14031i	0.941497	−	0.337022i	$-0.109420\pi$
$398$	−25286.9	−	54798.7i	−0.159636	−	0.345942i
$399$	−26340.8	−	10910.7i	−0.165456	−	0.0685342i
$400$	−112800.	−	4265.83i	−0.704997	−	0.0266614i
$401$	−51701.4	−	124818.i	−0.321524	−	0.776227i	−0.999166	−	0.0408354i	$-0.986998\pi$
$401$	−51701.4	−	124818.i	−0.321524	−	0.776227i	0.677642	−	0.735392i	$-0.263002\pi$
$402$	26038.1	+	24051.6i	0.161123	+	0.148831i
$403$	32049.2	+	59959.8i	0.197336	+	0.369190i
$404$	−99662.9	+	95965.1i	−0.610620	+	0.587964i
$405$	−138276.	+	113480.i	−0.843018	+	0.691847i
$406$	−8716.19	−	14858.7i	−0.0528779	−	0.0901425i
$407$	−115194.	−	76969.9i	−0.695408	−	0.464657i
$408$	174.758	+	8425.93i	0.00104983	+	0.0506171i
$409$	−205923.	+	137593.i	−1.23100	+	0.822526i	−0.989024	−	0.147756i	$-0.952795\pi$
$409$	−205923.	+	137593.i	−1.23100	+	0.822526i	−0.241974	+	0.970283i	$0.577795\pi$
$410$	−102141.	−	294200.i	−0.607620	−	1.75015i
$411$	10254.1	−	19184.1i	0.0607037	−	0.113569i
$412$	12182.2	−	3445.42i	0.0717683	−	0.0202977i
$413$	−10529.8	−	106911.i	−0.0617337	−	0.626792i
$414$	−129792.	+	31210.8i	−0.757264	+	0.182097i
$415$	102042.	−	102042.i	0.592490	−	0.592490i
$416$	−45449.6	−	13695.8i	−0.262630	−	0.0791411i
$417$	23055.5	−	23055.5i	0.132587	−	0.132587i
$418$	326934.	+	200180.i	1.87115	+	1.14569i
$419$	25949.9	+	263474.i	0.147812	+	1.50076i	0.727607	+	0.685994i	$0.240632\pi$
$419$	25949.9	+	263474.i	0.147812	+	1.50076i	−0.579796	+	0.814762i	$0.696868\pi$
$420$	−22061.0	−	27941.9i	−0.125062	−	0.158401i
$421$	137109.	−	256513.i	0.773573	−	1.44725i	−0.117346	−	0.993091i	$-0.537439\pi$
$421$	137109.	−	256513.i	0.773573	−	1.44725i	0.890919	−	0.454162i	$-0.150061\pi$
$422$	280948.	+	136142.i	1.57761	+	0.764481i
$423$	−3267.69	+	2183.40i	−0.0182625	+	0.0122026i
$424$	15312.0	+	69422.6i	0.0851728	+	0.386161i
$425$	22664.0	+	15143.6i	0.125475	+	0.0838400i
$426$	−8907.84	+	34188.1i	−0.0490855	+	0.188389i
$427$	−71327.9	+	58537.3i	−0.391204	+	0.321053i
$428$	−37963.8	+	14890.9i	−0.207244	+	0.0812894i
$429$	−10663.8	−	19950.5i	−0.0579423	−	0.108402i
$430$	−216550.	+	8587.98i	−1.17117	+	0.0464466i
$431$	−77634.7	−	187427.i	−0.417928	−	1.00897i	−0.982947	−	0.183889i	$-0.941131\pi$
$431$	−77634.7	−	187427.i	−0.417928	−	1.00897i	0.565019	−	0.825078i	$-0.308869\pi$
$432$	−77205.1	+	37587.5i	−0.413693	+	0.201407i
$433$	−38332.1	−	15877.7i	−0.204450	−	0.0846859i	0.278109	−	0.960550i	$-0.410292\pi$
$433$	−38332.1	−	15877.7i	−0.204450	−	0.0846859i	−0.482559	+	0.875864i	$0.660292\pi$
$434$	64898.6	−	176115.i	0.344553	−	0.935009i
$435$	2717.61	−	8958.77i	0.0143618	−	0.0473446i
$436$	−14584.3	−	81323.7i	−0.0767205	−	0.427803i
$437$	−17897.2	+	181713.i	−0.0937179	+	0.951534i
$438$	6343.30	+	45736.8i	0.0330649	+	0.238406i
$439$	24504.1	+	123191.i	0.127148	+	0.639217i	0.990823	+	0.135167i	$0.0431572\pi$
$439$	24504.1	+	123191.i	0.127148	+	0.639217i	−0.863675	+	0.504050i	$0.831843\pi$
$440$	234354.	+	417390.i	1.21051	+	2.15594i
$441$	20547.2	−	103298.i	0.105651	−	0.531145i
$442$	7617.10	+	8565.47i	0.0389893	+	0.0438437i
$443$	49700.9	−	15076.6i	0.253254	−	0.0768238i	−0.161105	−	0.986937i	$-0.551506\pi$
$443$	49700.9	−	15076.6i	0.253254	−	0.0768238i	0.414359	+	0.910113i	$0.364006\pi$
$444$	−1632.30	−	20547.2i	−0.00828008	−	0.104229i
$445$	−361991.	−	297078.i	−1.82801	−	1.50021i
$446$	47714.0	−	301972.i	0.239870	−	1.51809i
$447$	64849.2			0.324556
$448$	55125.4	+	118886.i	0.274660	+	0.592344i
$449$		−	130059.i		−	0.645132i	−0.946547	−	0.322566i	$-0.895455\pi$
$449$		−	130059.i		−	0.645132i	0.946547	−	0.322566i	$-0.104545\pi$
$450$	−21047.9	+	133208.i	−0.103940	+	0.657817i
$451$	−346568.	+	422295.i	−1.70387	+	2.07617i
$452$	275724.	+	235141.i	1.34958	+	1.15093i
$453$	6536.65	+	21548.5i	0.0318536	+	0.105007i
$454$	−134561.	−	151314.i	−0.652839	−	0.734121i
$455$	−47490.1	−	9446.37i	−0.229393	−	0.0456291i
$456$	6766.08	+	56631.3i	0.0325393	+	0.272350i
$457$	−171202.	+	34054.2i	−0.819740	+	0.163056i	−0.587108	−	0.809508i	$-0.699734\pi$
$457$	−171202.	+	34054.2i	−0.819740	+	0.163056i	−0.232632	+	0.972565i	$0.574734\pi$
$458$	−38852.0	−	280133.i	−0.185218	−	1.33547i
$459$	20635.3	+	2032.40i	0.0979459	+	0.00964683i
$460$	−130230.	+	187147.i	−0.615452	+	0.884436i
$461$	−281114.	−	85275.1i	−1.32276	−	0.401255i	−0.451585	−	0.892228i	$-0.649141\pi$
$461$	−281114.	−	85275.1i	−1.32276	−	0.401255i	−0.871175	+	0.490973i	$0.836641\pi$
$462$	−21593.8	+	58598.8i	−0.101168	+	0.274539i
$463$	−45579.2	+	110038.i	−0.212620	+	0.513311i	−0.993824	−	0.110965i	$-0.964606\pi$
$463$	−45579.2	+	110038.i	−0.212620	+	0.513311i	0.781204	+	0.624276i	$0.214606\pi$
$464$	−17381.4	+	29755.7i	−0.0807325	+	0.138208i
$465$	94238.0	−	39034.7i	0.435833	−	0.180528i
$466$	−318624.	+	12636.1i	−1.46726	+	0.0581888i
$467$	68722.0	−	36732.7i	0.315110	−	0.168430i	−0.306258	−	0.951948i	$-0.599077\pi$
$467$	68722.0	−	36732.7i	0.315110	−	0.168430i	0.621368	+	0.783519i	$0.286577\pi$
$468$	−22688.9	+	51975.1i	−0.103591	+	0.237303i
$469$	−84433.3	−	102882.i	−0.383856	−	0.467729i
$470$	−1692.42	+	6495.46i	−0.00766147	+	0.0294045i
$471$	−15131.5	+	22645.9i	−0.0682088	+	0.102082i
$472$	−176171.	+	123073.i	−0.790769	+	0.552431i
$473$	211209.	+	316097.i	0.944041	+	1.41286i
$474$	−47765.9	−	23146.4i	−0.212599	−	0.103021i
$475$	162683.	+	86956.1i	0.721035	+	0.385401i
$476$	3696.26	−	31427.4i	0.0163135	−	0.138706i
$477$	84525.2	−	8325.01i	0.371492	−	0.0365888i
$478$	78428.3	+	48021.3i	0.343255	+	0.210174i
$479$	46647.3	+	46647.3i	0.203308	+	0.203308i	0.801416	−	0.598108i	$-0.204080\pi$
$479$	46647.3	+	46647.3i	0.203308	+	0.203308i	−0.598108	+	0.801416i	$0.704080\pi$
$480$	−27132.7	+	65846.0i	−0.117763	+	0.285790i
$481$	−19823.1	−	19823.1i	−0.0856802	−	0.0856802i
$482$	125632.	−	30210.4i	0.540762	−	0.130036i
$483$	−29602.5	+	2915.59i	−0.126892	+	0.0124978i
$484$	295442.	−	528460.i	1.26119	−	2.25591i
$485$	−197862.	−	105759.i	−0.841160	−	0.449610i
$486$	50955.3	+	146768.i	0.215733	+	0.621384i
$487$	−86179.6	−	128977.i	−0.363368	−	0.543819i	0.604069	−	0.796932i	$-0.293545\pi$
$487$	−86179.6	−	128977.i	−0.363368	−	0.543819i	−0.967437	+	0.253114i	$0.918545\pi$
$488$	171962.	+	67086.0i	0.722092	+	0.281704i
$489$	47299.0	−	70787.9i	0.197804	−	0.296034i
$490$	−91017.3	−	155160.i	−0.379081	−	0.646229i
$491$	−187176.	−	228074.i	−0.776402	−	0.946049i	0.223185	−	0.974776i	$-0.428354\pi$
$491$	−187176.	−	228074.i	−0.776402	−	0.946049i	−0.999587	+	0.0287275i	$0.990854\pi$
$492$	−81262.6	−	1536.04i	−0.335707	−	0.00634559i
$493$	7338.74	−	3922.64i	0.0301945	−	0.0161393i
$494$	56981.6	+	52634.4i	0.233497	+	0.215683i
$495$	528359.	−	218854.i	2.15635	−	0.893189i
$496$	−370753.	+	59280.3i	−1.50703	+	0.240961i
$497$	50764.2	−	122556.i	0.205516	−	0.496159i
$498$	−15780.2	−	34196.8i	−0.0636288	−	0.137888i
$499$	303870.	+	92177.8i	1.22035	+	0.370191i	0.833795	−	0.552074i	$-0.186163\pi$
$499$	303870.	+	92177.8i	1.22035	+	0.370191i	0.386560	+	0.922264i	$0.373663\pi$
$500$	−51897.7	−	80941.2i	−0.207591	−	0.323765i
$501$	−117256.	−	11548.7i	−0.467154	−	0.0460107i
$502$	105989.	−	140122.i	0.420583	−	0.556030i
$503$	254484.	−	50620.0i	1.00583	−	0.200072i	0.335425	−	0.942067i	$-0.391120\pi$
$503$	254484.	−	50620.0i	1.00583	−	0.200072i	0.670406	+	0.741995i	$0.266120\pi$
$504$	148846.	−	48544.4i	0.585970	−	0.191108i
$505$	276894.	+	55077.7i	1.08575	+	0.215970i
$506$	399267.	+	23398.8i	1.55942	+	0.0913886i
$507$	16332.3	+	53840.2i	0.0635375	+	0.209455i
$508$	−386460.	−	125255.i	−1.49754	−	0.485363i
$509$	−197493.	+	240646.i	−0.762282	+	0.928843i	−0.999087	−	0.0427141i	$-0.986400\pi$
$509$	−197493.	+	240646.i	−0.762282	+	0.928843i	0.236806	+	0.971557i	$0.423900\pi$
$510$	13909.1	−	10113.4i	0.0534760	−	0.0388826i
$511$		−	173374.i		−	0.663959i
$512$	153382.	−	212587.i	0.585106	−	0.810957i
$513$	140324.			0.533208
$514$	147566.	+	202950.i	0.558546	+	0.768178i
$515$	−19969.6	−	16388.6i	−0.0752929	−	0.0617913i
$516$	−17438.6	+	53804.9i	−0.0654954	+	0.202080i
$517$	11267.6	−	3418.00i	0.0421552	−	0.0127877i
$518$	−4527.78	+	77260.1i	−0.0168743	+	0.287936i
$519$	20471.7	−	102918.i	0.0760011	−	0.382083i
$520$	30033.3	+	92087.5i	0.111070	+	0.340560i
$521$	51674.9	+	259787.i	0.190372	+	0.957067i	0.951309	+	0.308240i	$0.0997400\pi$
$521$	51674.9	+	259787.i	0.190372	+	0.957067i	−0.760936	+	0.648827i	$0.775260\pi$
$522$	32835.2	+	24836.6i	0.120503	+	0.0911490i
$523$	36961.9	−	375281.i	0.135130	−	1.37200i	−0.653406	−	0.757008i	$-0.726661\pi$
$523$	36961.9	−	375281.i	0.135130	−	1.37200i	0.788536	−	0.614989i	$-0.210839\pi$
$524$	−20693.9	+	13268.5i	−0.0753667	+	0.0483235i
$525$	−8723.27	+	28756.8i	−0.0316490	+	0.104333i
$526$	117763.	−	54341.9i	0.425635	−	0.196410i
$527$	83763.4	+	34695.9i	0.301601	+	0.124927i
$528$	123361.	−	19724.4i	0.442496	−	0.0707515i
$529$	−34189.3	−	82540.3i	−0.122174	−	0.294954i
$530$	98430.8	−	106560.i	0.350412	−	0.379353i
$531$	121031.	+	226432.i	0.429246	+	0.803062i
$532$	4047.14	−	214110.i	0.0142996	−	0.756509i
$533$	−85451.4	+	70128.2i	−0.300791	+	0.246853i
$534$	−105416.	+	61837.7i	−0.369680	+	0.216856i
$535$	69188.9	+	46230.6i	0.241729	+	0.161518i
$536$	−96763.8	+	248035.i	−0.336809	+	0.863343i
$537$	−24071.6	+	16084.1i	−0.0834749	+	0.0557761i
$538$	494141.	−	171556.i	1.70721	−	0.592710i
$539$	−148750.	+	278292.i	−0.512011	+	0.957905i
$540$	152941.	+	85503.3i	0.524488	+	0.293221i
$541$	−13048.8	−	132487.i	−0.0445836	−	0.452665i	−0.991398	−	0.130884i	$-0.958218\pi$
$541$	−13048.8	−	132487.i	−0.0445836	−	0.452665i	0.946814	−	0.321781i	$-0.104282\pi$
$542$	−44257.9	−	184050.i	−0.150658	−	0.626522i
$543$	−10773.9	+	10773.9i	−0.0365404	+	0.0365404i
$544$	−58438.2	+	24331.8i	−0.197469	+	0.0822198i
$545$	−119213.	+	119213.i	−0.401355	+	0.401355i
$546$	−6598.82	+	10777.2i	−0.0221351	+	0.0361510i
$547$	51379.5	+	521665.i	0.171718	+	1.74348i	0.565923	+	0.824458i	$0.308520\pi$
$547$	51379.5	+	521665.i	0.171718	+	1.74348i	−0.394205	+	0.919023i	$0.628980\pi$
$548$	162267.	+	19084.6i	0.540343	+	0.0635511i
$549$	103956.	−	194488.i	0.344909	−	0.645279i
$550$	176199.	−	363611.i	0.582476	−	1.20202i
$551$	46823.2	−	31286.3i	0.154226	−	0.103051i
$552$	34077.5	+	48779.6i	0.111838	+	0.160089i
$553$	165709.	+	110723.i	0.541871	+	0.362067i
$554$	−403701.	−	105186.i	−1.31535	−	0.342719i
$555$	−32512.6	+	26682.4i	−0.105552	+	0.0866240i
$556$	224447.	+	97978.7i	0.726047	+	0.316944i
$557$	59899.4	+	112064.i	0.193069	+	0.361206i	0.959765	−	0.280803i	$-0.0906009\pi$
$557$	59899.4	+	112064.i	0.193069	+	0.361206i	−0.766697	+	0.642010i	$0.778101\pi$
$558$	17775.6	+	448221.i	0.0570896	+	1.43954i
$559$	29438.6	+	71071.1i	0.0942093	+	0.227441i
$560$	134875.	−	230896.i	0.430085	−	0.736274i
$561$	−27870.7	−	11544.4i	−0.0885568	−	0.0366814i
$562$	166142.	+	61223.7i	0.526026	+	0.193842i
$563$	5946.86	−	19604.2i	0.0187617	−	0.0618489i	−0.947060	−	0.321058i	$-0.895962\pi$
$563$	5946.86	−	19604.2i	0.0187617	−	0.0618489i	0.965821	+	0.259209i	$0.0834617\pi$
$564$	1437.92	+	1000.60i	0.00452039	+	0.00314560i
$565$	72477.8	−	735880.i	0.227043	−	2.30521i
$566$	−400295.	+	55517.5i	−1.24953	+	0.173299i
$567$	−34197.2	−	171921.i	−0.106371	−	0.534764i
$568$	−263488.	+	31480.5i	−0.816704	+	0.0975765i
$569$	−23634.6	+	118819.i	−0.0730003	+	0.366997i	−0.999967	−	0.00814688i	$-0.997407\pi$
$569$	−23634.6	+	118819.i	−0.0730003	+	0.366997i	0.926967	+	0.375144i	$0.122407\pi$
$570$	86967.0	−	77338.0i	0.267673	−	0.238036i
$571$	116284.	−	35274.4i	0.356655	−	0.108190i	−0.106872	−	0.994273i	$-0.534084\pi$
$571$	116284.	−	35274.4i	0.356655	−	0.108190i	0.463527	+	0.886083i	$0.346584\pi$
$572$	110254.	−	129283.i	0.336979	−	0.395140i
$573$	−103079.	−	84594.7i	−0.313950	−	0.257652i
$574$	301435.	+	47629.1i	0.914892	+	0.144560i
$575$	192453.			0.582089
$576$	−230450.	−	212086.i	−0.694596	−	0.639243i
$577$			89000.5i			0.267326i	0.991027	+	0.133663i	$0.0426739\pi$
$577$			89000.5i			0.267326i	−0.991027	+	0.133663i	$0.957326\pi$
$578$	−314892.	−	49755.3i	−0.942552	−	0.148931i
$579$	95609.2	−	116500.i	0.285195	−	0.347512i
$580$	70096.9	−	5568.59i	0.208374	−	0.0165535i
$581$	41049.6	+	135323.i	0.121607	+	0.400883i
$582$	−43754.2	+	38909.7i	−0.129173	+	0.114871i
$583$	−249580.	−	49644.6i	−0.734299	−	0.146061i
$584$	−302412.	+	169797.i	−0.886694	+	0.497857i
$585$	113499.	−	22576.3i	0.331650	−	0.0659693i
$586$	−499208.	+	69235.8i	−1.45374	+	0.201621i
$587$	−232678.	−	22916.8i	−0.675273	−	0.0665086i	−0.245433	−	0.969414i	$-0.578930\pi$
$587$	−232678.	−	22916.8i	−0.675273	−	0.0665086i	−0.429840	+	0.902905i	$0.641430\pi$
$588$	−46209.8	+	8287.08i	−0.133653	+	0.0239688i
$589$	587147.	+	178109.i	1.69245	+	0.513400i
$590$	411469.	+	151627.i	1.18204	+	0.435585i
$591$	23936.3	−	57787.4i	0.0685303	−	0.165447i
$592$	139198.	−	67768.7i	0.397181	−	0.193368i
$593$	205915.	−	85292.8i	0.585570	−	0.242551i	−0.0701735	−	0.997535i	$-0.522355\pi$
$593$	205915.	−	85292.8i	0.585570	−	0.242551i	0.655743	+	0.754984i	$0.272355\pi$
$594$	−12180.0	−	307125.i	−0.0345203	−	0.870446i
$595$	−56946.6	+	30438.6i	−0.160855	+	0.0859786i
$596$	177862.	+	453452.i	0.500715	+	1.27655i
$597$	20389.5	+	24844.7i	0.0572081	+	0.0697083i
$598$	78315.7	+	20405.5i	0.219001	+	0.0570616i
$599$	−89443.0	+	133861.i	−0.249283	+	0.373078i	−0.934916	−	0.354869i	$-0.884525\pi$
$599$	−89443.0	+	133861.i	−0.249283	+	0.373078i	0.685633	+	0.727947i	$0.259525\pi$
$600$	58703.1	−	12947.7i	0.163064	−	0.0359659i
$601$	196555.	+	294166.i	0.544171	+	0.814410i	0.997017	−	0.0771791i	$-0.0245913\pi$
$601$	196555.	+	294166.i	0.544171	+	0.814410i	−0.452846	+	0.891589i	$0.649591\pi$
$602$	92609.8	−	191113.i	0.255543	−	0.527348i
$603$	280526.	+	149944.i	0.771505	+	0.412378i
$604$	−132747.	+	104808.i	−0.363875	+	0.287290i
$605$	−1.22948e6	+	121093.i	−3.35899	+	0.330832i
$606$	38474.8	−	62837.1i	0.104769	−	0.171108i
$607$	351464.	+	351464.i	0.953903	+	0.953903i	0.998983	−	0.0450808i	$-0.0143545\pi$
$607$	351464.	+	351464.i	0.953903	+	0.953903i	−0.0450808	+	0.998983i	$0.514355\pi$
$608$	−377432.	+	202634.i	−1.02101	+	0.548157i
$609$	6486.96	+	6486.96i	0.0174907	+	0.0174907i
$610$	−88062.4	−	366213.i	−0.236663	−	0.984180i
$611$	2371.13	−	233.536i	0.00635145	−	0.000625563i
$612$	20581.9	+	72773.0i	0.0549518	+	0.194298i
$613$	8806.91	+	4707.39i	0.0234370	+	0.0125274i	0.483074	−	0.875580i	$-0.339520\pi$
$613$	8806.91	+	4707.39i	0.0234370	+	0.0125274i	−0.459637	+	0.888107i	$0.652020\pi$
$614$	−558349.	+	193848.i	−1.48105	+	0.514192i
$615$	92141.1	+	137899.i	0.243614	+	0.364595i
$616$	−468971.	+	9726.70i	−1.23590	+	0.0256333i
$617$	−111097.	+	166269.i	−0.291832	+	0.436758i	−0.948196	−	0.317687i	$-0.897094\pi$
$617$	−111097.	+	166269.i	−0.291832	+	0.436758i	0.656363	+	0.754445i	$0.272094\pi$
$618$	−5815.39	+	3411.33i	−0.0152266	+	0.00893197i
$619$	−27744.9	−	33807.2i	−0.0724105	−	0.0882324i	0.735545	−	0.677476i	$-0.236926\pi$
$619$	−27744.9	−	33807.2i	−0.0724105	−	0.0882324i	−0.807956	+	0.589243i	$0.799426\pi$
$620$	531413.	+	551889.i	1.38245	+	1.43572i
$621$	129114.	−	69012.7i	0.334803	−	0.178956i
$622$	44957.7	−	48670.8i	0.116205	−	0.125802i
$623$	423956.	−	175608.i	1.09231	−	0.452448i
$624$	25261.1	+	955.320i	0.0648759	+	0.00245346i
$625$	−180544.	+	435872.i	−0.462193	+	1.11583i
$626$	−89336.1	+	41224.3i	−0.227970	+	0.105197i
$627$	−195362.	−	59262.4i	−0.496941	−	0.150745i
$628$	−199850.	−	43694.6i	−0.506740	−	0.110792i
$629$	−37204.7	−	3664.34i	−0.0940365	−	0.00926178i
$630$	−254792.	−	192725.i	−0.641955	−	0.485576i
$631$	218705.	−	43503.2i	0.549289	−	0.109260i	0.0873590	−	0.996177i	$-0.472157\pi$
$631$	218705.	−	43503.2i	0.549289	−	0.109260i	0.461930	+	0.886917i	$0.347157\pi$
$632$	30841.6	−	397482.i	0.0772151	−	0.995138i
$633$	−163065.	−	32435.6i	−0.406960	−	0.0809495i
$634$	1649.61	−	28148.2i	0.00410395	−	0.0700282i
$635$	240639.	+	793279.i	0.596785	+	1.96734i
$636$	−17212.6	−	33720.4i	−0.0425532	−	0.0833639i
$637$	−40507.2	+	49358.2i	−0.0998282	+	0.121641i
$638$	−72540.1	−	99765.7i	−0.178212	−	0.245098i
$639$			317034.i			0.776434i
$640$	−534839.	−	9126.45i	−1.30576	−	0.0222814i
$641$	−622095.			−1.51405			−0.757025	−	0.653385i	$-0.773348\pi$
$641$	−622095.			−1.51405			−0.757025	+	0.653385i	$0.773348\pi$
$642$	17564.9	−	12771.5i	0.0426162	−	0.0309864i
$643$	−47823.3	−	39247.6i	−0.115669	−	0.0949272i	0.574781	−	0.818308i	$-0.305087\pi$
$643$	−47823.3	−	39247.6i	−0.115669	−	0.0949272i	−0.690450	+	0.723380i	$0.742587\pi$
$644$	−101578.	−	198996.i	−0.244922	−	0.479814i
$645$	110444.	−	33502.9i	0.265475	−	0.0805309i
$646$	103268.	+	6051.93i	0.247457	+	0.0145020i
$647$	39088.3	−	196510.i	0.0933767	−	0.469437i	−0.905597	−	0.424140i	$-0.860577\pi$
$647$	39088.3	−	196510.i	0.0933767	−	0.469437i	0.998974	−	0.0452970i	$-0.0144234\pi$
$648$	−266386.	+	228024.i	−0.634398	+	0.543038i
$649$	−150071.	−	754459.i	−0.356294	−	1.79121i
$650$	49322.9	−	65207.2i	0.116741	−	0.154337i
$651$	−9797.28	+	99473.5i	−0.0231176	+	0.234717i
$652$	624705.	+	136583.i	1.46953	+	0.321294i
$653$	−154773.	+	510220.i	−0.362969	+	1.19655i	0.565377	+	0.824833i	$0.308731\pi$
$653$	−154773.	+	510220.i	−0.362969	+	1.19655i	−0.928346	+	0.371717i	$0.878769\pi$
$654$	18435.6	+	39951.2i	0.0431024	+	0.0934060i
$655$	46343.0	+	19195.9i	0.108019	+	0.0447431i
$656$	−212138.	−	572433.i	−0.492960	−	1.33020i
$657$	158566.	+	382813.i	0.367350	+	0.886862i
$658$	−4831.70	−	4463.09i	−0.0111596	−	0.0103082i
$659$	16210.8	+	30328.3i	0.0373279	+	0.0698356i	0.899894	−	0.436109i	$-0.143644\pi$
$659$	16210.8	+	30328.3i	0.0373279	+	0.0698356i	−0.862566	+	0.505945i	$0.831144\pi$
$660$	−176817.	−	183631.i	−0.405917	−	0.421558i
$661$	−6007.07	+	4929.87i	−0.0137486	+	0.0112832i	−0.641243	−	0.767338i	$-0.721581\pi$
$661$	−6007.07	+	4929.87i	−0.0137486	+	0.0112832i	0.627494	+	0.778621i	$0.284081\pi$
$662$	−118951.	−	202779.i	−0.271427	−	0.462709i
$663$	−5075.54	−	3391.37i	−0.0115466	−	0.00771521i
$664$	195837.	−	204133.i	0.444181	−	0.462996i
$665$	−363335.	+	242773.i	−0.821607	+	0.548980i
$666$	−60664.2	−	174733.i	−0.136768	−	0.393937i
$667$	27695.8	−	51815.1i	0.0622532	−	0.116468i
$668$	−240845.	−	851577.i	−0.539741	−	1.90841i
$669$	15958.2	+	162026.i	0.0356558	+	0.362020i
$670$	528221.	−	127020.i	1.17670	−	0.282958i
$671$	−467198.	+	467198.i	−1.03766	+	1.03766i
$672$	−44371.8	−	53865.0i	−0.0982580	−	0.119280i
$673$	495555.	−	495555.i	1.09411	−	1.09411i	0.0990276	−	0.995085i	$-0.468427\pi$
$673$	495555.	−	495555.i	1.09411	−	1.09411i	0.995085	−	0.0990276i	$-0.0315732\pi$
$674$	−232904.	−	142606.i	−0.512694	−	0.313920i
$675$	−14496.9	−	147189.i	−0.0318176	−	0.323049i
$676$	−331678.	+	261869.i	−0.725811	+	0.573048i
$677$	201205.	−	376428.i	0.438996	−	0.821305i	−0.560982	−	0.827828i	$-0.689576\pi$
$677$	201205.	−	376428.i	0.438996	−	0.821305i	0.999979	+	0.00652328i	$0.00207644\pi$
$678$	−173666.	−	84155.1i	−0.377794	−	0.183072i
$679$	182798.	−	122142.i	0.396490	−	0.264926i
$680$	108865.	+	69520.0i	0.235435	+	0.150346i
$681$	89662.4	+	59910.5i	0.193337	+	0.129184i
$682$	338861.	−	1.30054e6i	0.728539	−	2.79612i
$683$	420754.	−	345304.i	0.901958	−	0.740218i	−0.0642627	−	0.997933i	$-0.520470\pi$
$683$	420754.	−	345304.i	0.901958	−	0.740218i	0.966221	+	0.257715i	$0.0829696\pi$
$684$	186888.	+	476462.i	0.399455	+	1.01839i
$685$	−157161.	−	294028.i	−0.334938	−	0.626626i
$686$	483158.	−	19161.2i	1.02669	−	0.0407168i
$687$	57636.8	+	139147.i	0.122120	+	0.294823i
$688$	−424054.	+	25633.4i	−0.895869	+	0.0541538i
$689$	−47572.4	−	19705.1i	−0.100211	−	0.0415089i
$690$	41983.8	−	113931.i	0.0881828	−	0.239301i
$691$	−95167.5	+	313725.i	−0.199312	+	0.657042i	0.799126	+	0.601164i	$0.205296\pi$
$691$	−95167.5	+	313725.i	−0.199312	+	0.657042i	−0.998438	+	0.0558787i	$0.982204\pi$
$692$	775794.	−	139128.i	1.62007	−	0.290537i
$693$	−54929.9	+	557713.i	−0.114378	+	1.16130i
$694$	35566.5	+	256443.i	0.0738451	+	0.532442i
$695$	−97492.6	−	490129.i	−0.201838	−	1.01471i
$696$	4961.93	−	17668.2i	0.0102431	−	0.0364733i
$697$	−28759.3	+	144583.i	−0.0591988	+	0.297612i
$698$	−353095.	−	397058.i	−0.724738	−	0.814972i
$699$	162504.	−	49294.9i	0.332590	−	0.100890i
$700$	−225004.	+	17874.6i	−0.459192	+	0.0364788i
$701$	202940.	+	166549.i	0.412983	+	0.338927i	0.817832	−	0.575457i	$-0.195176\pi$
$701$	202940.	+	166549.i	0.412983	+	0.338927i	−0.404849	+	0.914384i	$0.632676\pi$
$702$	9706.95	−	61433.4i	0.0196974	−	0.124661i
$703$	−252998.			−0.511925
$704$	476263.	+	808491.i	0.960952	+	1.63128i
$705$		−	3574.63i		−	0.00719206i
$706$	−11349.0	+	71825.8i	−0.0227693	+	0.144102i
$707$	−175506.	+	213854.i	−0.351117	+	0.427838i
$708$	74262.6	−	87079.9i	0.148151	−	0.173721i
$709$	−241573.	−	796361.i	−0.480570	−	1.58423i	−0.777213	−	0.629238i	$-0.783367\pi$
$709$	−241573.	−	796361.i	−0.480570	−	1.58423i	0.296643	−	0.954989i	$-0.404133\pi$
$710$	359830.	+	404631.i	0.713808	+	0.802680i
$711$	−467156.	−	92923.1i	−0.924108	−	0.183817i
$712$	−721520.	−	567512.i	−1.42327	−	1.11948i
$713$	627838.	−	124885.i	1.23500	−	0.245658i
$714$	2315.06	+	16692.2i	0.00454115	+	0.0327429i
$715$	−345044.	−	33983.9i	−0.674936	−	0.0664754i
$716$	−178488.	−	124204.i	−0.348163	−	0.242276i
$717$	−46865.5	−	14216.5i	−0.0911622	−	0.0276537i
$718$	−281432.	+	763719.i	−0.545915	+	1.48144i
$719$	77166.0	−	186295.i	0.149269	−	0.360366i	−0.831504	−	0.555518i	$-0.812520\pi$
$719$	77166.0	−	186295.i	0.149269	−	0.360366i	0.980773	+	0.195152i	$0.0625200\pi$
$720$	−86630.7	+	633178.i	−0.167112	+	1.22141i
$721$	23387.9	−	9687.58i	0.0449905	−	0.0186357i
$722$	178630.	−	7084.15i	0.342673	−	0.0135898i
$723$	−60687.0	+	32437.9i	−0.116096	+	0.0620548i
$724$	−104885.	−	45785.8i	−0.200095	−	0.0873481i
$725$	−37654.4	−	45882.0i	−0.0716373	−	0.0872903i
$726$	−81295.0	+	312008.i	−0.154238	+	0.591960i
$727$	87243.1	−	130569.i	0.165068	−	0.247041i	−0.739710	−	0.672926i	$-0.765037\pi$
$727$	87243.1	−	130569.i	0.165068	−	0.247041i	0.904777	+	0.425885i	$0.140037\pi$
$728$	−93457.0	−	16583.0i	−0.176339	−	0.0312896i
$729$	200592.	+	300206.i	0.377448	+	0.564891i
$730$	636867.	+	308614.i	1.19510	+	0.579121i
$731$	90472.3	+	48358.5i	0.169309	+	0.0904978i
$732$	−97627.1	−	11482.2i	−0.182200	−	0.0214290i
$733$	−678576.	+	66833.9i	−1.26296	+	0.124391i	−0.707238	−	0.706975i	$-0.750059\pi$
$733$	−678576.	+	66833.9i	−1.26296	+	0.124391i	−0.555725	+	0.831366i	$0.687559\pi$
$734$	−705290.	−	431845.i	−1.30911	−	0.801560i
$735$	67739.0	+	67739.0i	0.125390	+	0.125390i
$736$	−247622.	+	372071.i	−0.457124	+	0.686863i
$737$	−673879.	−	673879.i	−1.24064	−	1.24064i
$738$	−709137.	+	170524.i	−1.30202	+	0.313093i
$739$	−182373.	+	17962.1i	−0.333942	+	0.0328904i	−0.263599	−	0.964632i	$-0.584909\pi$
$739$	−182373.	+	17962.1i	−0.333942	+	0.0328904i	−0.0703433	+	0.997523i	$0.522409\pi$
$740$	−275746.	−	154159.i	−0.503554	−	0.281518i
$741$	−36432.5	−	19473.6i	−0.0663517	−	0.0354657i
$742$	46622.8	+	134289.i	0.0846819	+	0.243912i
$743$	53213.2	+	79639.2i	0.0963922	+	0.144261i	0.876531	−	0.481345i	$-0.159852\pi$
$743$	53213.2	+	79639.2i	0.0963922	+	0.144261i	−0.780139	+	0.625606i	$0.784852\pi$
$744$	183105.	−	80332.3i	0.330791	−	0.145126i
$745$	552193.	−	826416.i	0.994898	−	1.48897i
$746$	47900.8	+	81657.8i	0.0860727	+	0.146730i
$747$	−214404.	−	261252.i	−0.384230	−	0.468185i
$748$	4282.20	−	226546.i	0.00765357	−	0.404905i
$749$	−71913.9	+	38438.8i	−0.128189	+	0.0685182i
$750$	37613.4	+	34743.9i	0.0668683	+	0.0617669i
$751$	−776945.	+	321821.i	−1.37756	+	0.570604i	−0.943828	−	0.330438i	$-0.892803\pi$
$751$	−776945.	+	321821.i	−1.37756	+	0.570604i	−0.433732	+	0.901042i	$0.642803\pi$
$752$	−3052.84	+	12798.9i	−0.00539844	+	0.0226327i
$753$	−35805.6	+	86442.3i	−0.0631481	+	0.152453i
$754$	−10458.0	−	22663.4i	−0.0183953	−	0.0398641i
$755$	330266.	+	100185.i	0.579388	+	0.175756i
$756$	−144542.	+	92677.1i	−0.252901	+	0.162154i
$757$	904801.	+	89115.2i	1.57892	+	0.155511i	0.849141	−	0.528167i	$-0.177120\pi$
$757$	904801.	+	89115.2i	1.57892	+	0.155511i	0.729784	+	0.683677i	$0.239620\pi$
$758$	−175391.	+	231876.i	−0.305260	+	0.403568i
$759$	−208901.	+	41553.0i	−0.362625	+	0.0721305i
$760$	779303.	+	395993.i	1.34921	+	0.685584i
$761$	−180452.	−	35894.2i	−0.311597	−	0.0619805i	0.0368147	−	0.999322i	$-0.488279\pi$
$761$	−180452.	−	35894.2i	−0.311597	−	0.0619805i	−0.348412	+	0.937342i	$0.613279\pi$
$762$	215978.	+	12657.2i	0.371963	+	0.0217986i
$763$	−47957.2	−	158094.i	−0.0823768	−	0.271560i
$764$	308805.	−	952787.i	0.529051	−	1.63233i
$765$	97900.4	−	119292.i	0.167287	−	0.203840i
$766$	55037.8	−	40018.2i	0.0938001	−	0.0682024i
$767$		−	155656.i		−	0.264591i
$768$	−50499.2	+	130151.i	−0.0856173	+	0.220660i
$769$	1.08994e6			1.84310			0.921551	−	0.388258i	$-0.126923\pi$
$769$	1.08994e6			1.84310			0.921551	+	0.388258i	$0.126923\pi$
$770$	562890.	+	774154.i	0.949385	+	1.30571i
$771$	−103298.	−	84774.2i	−0.173773	−	0.142612i
$772$	1.07684e6	+	349013.i	1.80683	+	0.585607i
$773$	−508311.	+	154194.i	−0.850688	+	0.258053i	−0.685377	−	0.728188i	$-0.740363\pi$
$773$	−508311.	+	154194.i	−0.850688	+	0.258053i	−0.165311	+	0.986242i	$0.552863\pi$
$774$	−29693.8	+	506683.i	−0.0495660	+	0.845773i
$775$	126165.	−	634275.i	0.210056	−	1.05602i
$776$	−392077.	−	199229.i	−0.651100	−	0.330848i
$777$	−8040.71	−	40423.4i	−0.0133184	−	0.0669562i
$778$	−320415.	−	242362.i	−0.529363	−	0.400411i
$779$	−97784.0	+	992817.i	−0.161136	+	1.63604i
$780$	−27842.4	−	43423.9i	−0.0457634	−	0.0713739i
$781$	275730.	−	908960.i	0.452045	−	1.49019i
$782$	97994.3	−	45219.7i	0.160246	−	0.0739459i
$783$	−41714.7	−	17278.8i	−0.0680403	−	0.0281832i
$784$	−184686.	−	300388.i	−0.300471	−	0.488710i
$785$	159746.	+	385661.i	0.259233	+	0.625844i
$786$	8882.82	−	9616.47i	0.0143782	−	0.0155658i
$787$	−476126.	−	890768.i	−0.768727	−	1.43819i	−0.894941	−	0.446184i	$-0.852783\pi$
$787$	−476126.	−	890768.i	−0.768727	−	1.43819i	0.126215	−	0.992003i	$-0.459717\pi$
$788$	469723.	+	8878.78i	0.756466	+	0.0142988i
$789$	−53391.5	+	43817.2i	−0.0857665	+	0.0703868i
$790$	−701698.	+	411619.i	−1.12434	+	0.659540i
$791$	602480.	+	402564.i	0.962918	+	0.643401i
$792$	1.02660e6	−	450395.i	1.63664	−	0.718031i
$793$	−111164.	+	74277.7i	−0.176774	+	0.118117i
$794$	−709688.	+	246391.i	−1.12571	+	0.390826i
$795$	−36417.2	+	68131.8i	−0.0576199	+	0.107799i
$796$	−117802.	+	210713.i	−0.185919	+	0.332556i
$797$	−15973.5	−	162181.i	−0.0251468	−	0.255320i	−0.999536	−	0.0304524i	$-0.990305\pi$
$797$	−15973.5	−	162181.i	−0.0251468	−	0.255320i	0.974389	−	0.224867i	$-0.0721948\pi$
$798$	26663.9	+	110883.i	0.0418714	+	0.174125i
$799$	2246.70	−	2246.70i	0.00351926	−	0.00351926i
$800$	251541.	+	374964.i	0.393033	+	0.585881i
$801$	−775494.	+	775494.i	−1.20869	+	1.20869i
$802$	−282193.	+	460878.i	−0.438731	+	0.716535i
$803$	−121682.	−	1.23546e6i	−0.188710	−	1.91601i
$804$	16561.7	−	140816.i	0.0256208	−	0.217841i
$805$	−214911.	+	402070.i	−0.331640	+	0.620455i
$806$	118592.	−	244731.i	0.182551	−	0.376720i
$807$	−231616.	+	154761.i	−0.355649	+	0.237637i
$808$	544907.	+	96688.2i	0.834641	+	0.148098i
$809$	707895.	+	473000.i	1.08161	+	0.722711i	0.962802	−	0.270206i	$-0.0870919\pi$
$809$	707895.	+	473000.i	1.08161	+	0.722711i	0.118810	+	0.992917i	$0.462092\pi$
$810$	692402.	+	180408.i	1.05533	+	0.274971i
$811$	694658.	−	570091.i	1.05616	−	0.866768i	0.0647945	−	0.997899i	$-0.479361\pi$
$811$	694658.	−	570091.i	1.05616	−	0.866768i	0.991365	+	0.131131i	$0.0418608\pi$
$812$	−27567.6	+	63151.3i	−0.0418107	+	0.0957789i
$813$	47521.1	+	88905.8i	0.0718962	+	0.134508i
$814$	21960.1	+	553733.i	0.0331425	+	0.835703i
$815$	−499344.	−	1.20552e6i	−0.751770	−	1.81493i
$816$	26848.5	−	20386.0i	0.0403218	−	0.0306162i
$817$	641393.	+	265674.i	0.960905	+	0.398020i
$818$	929539.	+	342537.i	1.38919	+	0.511919i
$819$	−32918.1	+	108516.i	−0.0490757	+	0.161781i
$820$	−711528.	+	1.02250e6i	−1.05819	+	1.52068i
$821$	−89988.1	+	913664.i	−0.133505	+	1.35550i	0.661976	+	0.749525i	$0.269718\pi$
$821$	−89988.1	+	913664.i	−0.133505	+	1.35550i	−0.795482	+	0.605978i	$0.792782\pi$
$822$	−86185.6	+	11953.2i	−0.127553	+	0.0176905i
$823$	117184.	+	589125.i	0.173009	+	0.869776i	0.965602	+	0.260025i	$0.0837308\pi$
$823$	117184.	+	589125.i	0.173009	+	0.869776i	−0.792593	+	0.609751i	$0.791269\pi$
$824$	−39803.3	−	31307.3i	−0.0586225	−	0.0461096i
$825$	−41979.1	+	211043.i	−0.0616772	+	0.310072i
$826$	−321110.	+	285557.i	−0.470646	+	0.418536i
$827$	−607919.	+	184410.i	−0.888862	+	0.269633i	−0.701510	−	0.712659i	$-0.747491\pi$
$827$	−607919.	+	184410.i	−0.888862	+	0.269633i	−0.187352	+	0.982293i	$0.559991\pi$
$828$	406287.	+	346486.i	0.592614	+	0.505387i
$829$	441096.	+	361999.i	0.641837	+	0.526742i	0.898058	−	0.439876i	$-0.144978\pi$
$829$	441096.	+	361999.i	0.641837	+	0.526742i	−0.256222	+	0.966618i	$0.582478\pi$
$830$	−570161.	−	90089.9i	−0.827640	−	0.130773i
$831$	222168.			0.321721
$832$	62603.7	+	179256.i	0.0904385	+	0.258957i
$833$			85149.5i			0.122713i
$834$	−128823.	−	20355.0i	−0.185209	−	0.0292644i
$835$	−1.14561e6	+	1.39593e6i	−1.64310	+	2.00213i
$836$	−121433.	−	1.52859e6i	−0.173750	−	2.18715i
$837$	−142806.	−	470767.i	−0.203842	−	0.671978i
$838$	791350.	−	703732.i	1.12689	−	1.00212i
$839$	−940256.	−	187029.i	−1.33574	−	0.265695i	−0.525001	−	0.851102i	$-0.675935\pi$
$839$	−940256.	−	187029.i	−1.33574	−	0.265695i	−0.810740	+	0.585407i	$0.800935\pi$
$840$	−38503.2	+	137100.i	−0.0545680	+	0.194303i
$841$	675919.	−	134449.i	0.955658	−	0.190092i
$842$	−1.15240e6	+	159827.i	−1.62546	+	0.225438i
$843$	−93840.8	−	9242.51i	−0.132049	−	0.0130057i
$844$	−220435.	−	1.22917e6i	−0.309454	−	1.72555i
$845$	825191.	+	250319.i	1.15569	+	0.350574i
$846$	14750.4	+	5435.56i	0.0206093	+	0.00759458i
$847$	463286.	−	1.11847e6i	0.645776	−	1.55904i
$848$	188577.	−	212842.i	0.262239	−	0.295983i
$849$	198834.	−	82359.9i	0.275852	−	0.114262i
$850$	−4320.58	−	108945.i	−0.00598004	−	0.150790i
$851$	−232787.	+	124427.i	−0.321440	+	0.171813i
$852$	131560.	−	51603.0i	0.181236	−	0.0710879i
$853$	46471.6	+	56625.8i	0.0638689	+	0.0778245i	0.803965	−	0.594677i	$-0.202720\pi$
$853$	46471.6	+	56625.8i	0.0638689	+	0.0778245i	−0.740096	+	0.672501i	$0.765220\pi$
$854$	357167.	+	93061.2i	0.489728	+	0.127601i
$855$	580214.	−	868351.i	0.793699	−	1.18785i
$856$	137478.	+	87792.1i	0.187623	+	0.119814i
$857$	−136171.	−	203794.i	−0.185405	−	0.277478i	0.727110	−	0.686521i	$-0.240863\pi$
$857$	−136171.	−	203794.i	−0.185405	−	0.277478i	−0.912515	+	0.409042i	$0.865863\pi$
$858$	−39459.2	+	81429.6i	−0.0536011	+	0.110613i
$859$	13806.2	+	7379.54i	0.0187105	+	0.0100010i	0.480725	−	0.876871i	$-0.340373\pi$
$859$	13806.2	+	7379.54i	0.0187105	+	0.0100010i	−0.462015	+	0.886872i	$0.652873\pi$
$860$	537181.	+	680381.i	0.726312	+	0.919931i
$861$	−161738.	+	15929.8i	−0.218175	+	0.0214883i
$862$	−423741.	+	692054.i	−0.570277	+	0.931376i
$863$	−256646.	−	256646.i	−0.344598	−	0.344598i	0.513495	−	0.858093i	$-0.328350\pi$
$863$	−256646.	−	256646.i	−0.344598	−	0.344598i	−0.858093	+	0.513495i	$0.828350\pi$
$864$	303215.	+	161356.i	0.406184	+	0.216151i
$865$	−1.13724e6	−	1.13724e6i	−1.51991	−	1.51991i
$866$	38802.2	+	161362.i	0.0517394	+	0.215162i
$867$	168958.	−	16640.9i	0.224771	−	0.0221380i
$868$	−722429.	+	204319.i	−0.958861	+	0.271188i
$869$	1.25855e6	+	672710.i	1.66660	+	0.890817i
$870$	−35376.2	+	12282.0i	−0.0467382	+	0.0162267i
$871$	−107137.	−	160342.i	−0.141222	−	0.211354i
$872$	−228792.	+	238483.i	−0.300890	+	0.313635i
$873$	−291913.	+	436878.i	−0.383023	+	0.573234i
$874$	629980.	−	369549.i	0.824715	−	0.483781i
$875$	−121968.	−	148619.i	−0.159306	−	0.194115i
$876$	133046.	−	128110.i	0.173378	−	0.166945i
$877$	373382.	−	199577.i	0.485461	−	0.259484i	−0.210460	−	0.977602i	$-0.567496\pi$
$877$	373382.	−	199577.i	0.485461	−	0.259484i	0.695921	+	0.718118i	$0.254996\pi$
$878$	340905.	−	369061.i	0.442226	−	0.478750i
$879$	247966.	−	102711.i	0.320933	−	0.132935i
$880$	799062.	−	1.74002e6i	1.03185	−	2.24693i
$881$	−161502.	+	389899.i	−0.208077	+	0.502343i	−0.993120	−	0.117098i	$-0.962641\pi$
$881$	−161502.	+	389899.i	−0.208077	+	0.502343i	0.785043	+	0.619441i	$0.212641\pi$
$882$	−382523.	+	176516.i	−0.491723	+	0.226906i
$883$	−45513.7	−	13806.4i	−0.0583742	−	0.0177076i	0.260963	−	0.965349i	$-0.415960\pi$
$883$	−45513.7	−	13806.4i	−0.0583742	−	0.0177076i	−0.319337	+	0.947641i	$0.603460\pi$
$884$	9793.10	−	44791.7i	0.0125319	−	0.0573183i
$885$	−232407.	−	22890.1i	−0.296731	−	0.0292255i
$886$	−165689.	−	125327.i	−0.211070	−	0.159654i
$887$	983012.	−	195533.i	1.24943	−	0.248527i	0.474319	−	0.880353i	$-0.342694\pi$
$887$	983012.	−	195533.i	1.24943	−	0.248527i	0.775110	+	0.631826i	$0.217694\pi$
$888$	−62634.8	+	53614.7i	−0.0794310	+	0.0679921i
$889$	−796724.	−	158478.i	−1.00810	−	0.200524i
$890$	−109587.	+	1.86994e6i	−0.138349	+	2.36074i
$891$	−364351.	−	1.20111e6i	−0.458950	−	1.51295i
$892$	−1.08918e6	+	555974.i	−1.36890	+	0.698755i
$893$	13640.9	−	16621.4i	0.0171056	−	0.0208433i
$894$	−152547.	−	209800.i	−0.190866	−	0.262501i
$895$			443716.i			0.553936i
$896$	254947.	−	458001.i	0.317566	−	0.570493i
$897$	−43099.3			−0.0535656
$898$	−420768.	+	305942.i	−0.521784	+	0.379391i
$899$	−152613.	−	125246.i	−0.188830	−	0.154969i
$900$	480466.	−	245255.i	0.593168	−	0.302784i
$901$	−65710.2	+	19933.0i	−0.0809438	+	0.0245540i
$902$	2.18145e6	+	127843.i	2.68122	+	0.157131i
$903$	−22064.1	+	110924.i	−0.0270589	+	0.136035i
$904$	112133.	−	1.44515e6i	0.137213	−	1.76839i
$905$	45558.6	+	229039.i	0.0556254	+	0.279648i
$906$	54337.3	−	71836.5i	0.0661975	−	0.0875163i
$907$	−39286.6	+	398883.i	−0.0477562	+	0.484876i	0.941325	+	0.337502i	$0.109582\pi$
$907$	−39286.6	+	398883.i	−0.0477562	+	0.484876i	−0.989081	+	0.147374i	$0.952918\pi$
$908$	−173001.	+	791272.i	−0.209834	+	0.959741i
$909$	191931.	−	632712.i	0.232283	−	0.765734i
$910$	81151.5	+	175861.i	0.0979972	+	0.212367i
$911$	−802914.	−	332578.i	−0.967458	−	0.400734i	−0.157693	−	0.987488i	$-0.550406\pi$
$911$	−802914.	−	332578.i	−0.967458	−	0.400734i	−0.809765	+	0.586754i	$0.800406\pi$
$912$	167298.	−	155105.i	0.201141	−	0.186482i
$913$	387496.	+	935497.i	0.464863	+	1.12228i
$914$	512895.	+	473766.i	0.613955	+	0.567116i
$915$	94555.4	+	176901.i	0.112939	+	0.211294i
$916$	−814894.	+	784659.i	−0.971204	+	0.935169i
$917$	−37996.8	+	31183.2i	−0.0451865	+	0.0370836i
$918$	−41965.9	−	71540.4i	−0.0497979	−	0.0848919i
$919$	1.05823e6	+	707086.i	1.25299	+	0.837223i	0.991767	−	0.128055i	$-0.0408735\pi$
$919$	1.05823e6	+	707086.i	1.25299	+	0.837223i	0.261225	+	0.965278i	$0.415874\pi$
$920$	911801.	−	18911.2i	1.07727	−	0.0223431i
$921$	261712.	−	174870.i	0.308535	−	0.206156i
$922$	385391.	+	1.11006e6i	0.453357	+	1.30582i
$923$	90604.6	−	169509.i	0.106352	−	0.198971i
$924$	240375.	−	67983.4i	0.281543	−	0.0796268i
$925$	26137.3	+	265377.i	0.0305476	+	0.310155i
$926$	463213.	−	111388.i	0.540205	−	0.129902i
$927$	−42780.8	+	42780.8i	−0.0497840	+	0.0497840i
$928$	137152.	−	13762.9i	0.159260	−	0.0159813i
$929$	467557.	−	467557.i	0.541755	−	0.541755i	−0.382288	−	0.924043i	$-0.624864\pi$
$929$	467557.	−	467557.i	0.541755	−	0.541755i	0.924043	+	0.382288i	$0.124864\pi$
$930$	−347964.	−	213057.i	−0.402317	−	0.246337i
$931$	56481.6	+	573468.i	0.0651640	+	0.661622i
$932$	790389.	+	1.00109e6i	0.909932	+	1.15250i
$933$	−16633.3	+	31118.8i	−0.0191080	+	0.0357486i
$934$	−280495.	−	135922.i	−0.321537	−	0.155811i
$935$	−384438.	+	256873.i	−0.439747	+	0.293829i
$936$	221522.	−	48859.5i	0.252851	−	0.0557696i
$937$	−636370.	−	425209.i	−0.724820	−	0.484309i	0.137609	−	0.990487i	$-0.456058\pi$
$937$	−636370.	−	425209.i	−0.724820	−	0.484309i	−0.862430	+	0.506177i	$0.831058\pi$
$938$	−134230.	+	515172.i	−0.152561	+	0.585526i
$939$	40503.3	−	33240.2i	0.0459366	−	0.0376992i
$940$	24995.3	−	9804.16i	0.0282880	−	0.0110957i
$941$	−248883.	−	465628.i	−0.281071	−	0.525848i	0.701282	−	0.712884i	$-0.252612\pi$
$941$	−248883.	−	465628.i	−0.281071	−	0.525848i	−0.982353	+	0.187037i	$0.940112\pi$
$942$	108858.	−	4317.13i	0.122676	−	0.00486511i
$943$	398306.	+	961596.i	0.447913	+	1.08136i
$944$	812577.	+	280440.i	0.911844	+	0.314699i
$945$	323695.	+	134079.i	0.362470	+	0.150140i
$946$	525804.	−	1.42687e6i	0.587546	−	1.59442i
$947$	270386.	−	891343.i	0.301498	−	0.993905i	−0.667037	−	0.745025i	$-0.732438\pi$
$947$	270386.	−	891343.i	0.301498	−	0.993905i	0.968534	−	0.248880i	$-0.0800625\pi$
$948$	37477.7	+	208980.i	0.0417019	+	0.232535i
$949$	24622.4	−	249996.i	0.0273400	−	0.277588i
$950$	−101364.	−	730864.i	−0.112315	−	0.809821i
$951$	2929.48	+	14727.5i	0.00323913	+	0.0162842i
$952$	−110369.	+	61969.5i	−0.121779	+	0.0683760i
$953$	−75119.4	+	377651.i	−0.0827116	+	0.415819i	0.917140	+	0.398566i	$0.130492\pi$
$953$	−75119.4	+	377651.i	−0.0827116	+	0.415819i	−0.999851	+	0.0172529i	$0.994508\pi$
$954$	−225764.	−	253873.i	−0.248061	−	0.278946i
$955$	−1.95577e6	+	593275.i	−2.14442	+	0.650503i
$956$	−29130.6	−	366694.i	−0.0318738	−	0.401225i
$957$	50779.0	+	41673.2i	0.0554447	+	0.0455023i
$958$	41183.6	−	260643.i	0.0448739	−	0.283998i
$959$	326702.			0.355235
$960$	276850.	−	67111.9i	0.300402	−	0.0728211i
$961$		−	1.22754e6i		−	1.32919i
$962$	−17501.2	+	110762.i	−0.0189112	+	0.119685i
$963$	123632.	−	150646.i	0.133315	−	0.162444i
$964$	−393265.	−	335380.i	−0.423186	−	0.360897i
$965$	−670521.	−	2.21041e6i	−0.720042	−	2.37366i
$966$	79067.4	+	88911.7i	0.0847312	+	0.0952807i
$967$	−1.71513e6	−	341160.i	−1.83419	−	0.364842i	−0.847935	−	0.530101i	$-0.822154\pi$
$967$	−1.71513e6	−	341160.i	−1.83419	−	0.364842i	−0.986250	+	0.165258i	$0.947154\pi$
$968$	−2.40465e6	+	287298.i	−2.56627	+	0.306607i
$969$	−54030.8	+	10747.4i	−0.0575432	+	0.0114460i
$970$	123283.	+	888905.i	0.131027	+	0.944739i
$971$	−653954.	−	64408.9i	−0.693600	−	0.0683136i	−0.254927	−	0.966960i	$-0.582051\pi$
$971$	−653954.	−	64408.9i	−0.693600	−	0.0683136i	−0.438673	+	0.898647i	$0.644551\pi$
$972$	354962.	−	510099.i	0.375707	−	0.539910i
$973$	468612.	+	142152.i	0.494981	+	0.150151i
$974$	−214544.	+	582205.i	−0.226151	+	0.613703i
$975$	−16662.5	+	40226.8i	−0.0175279	+	0.0423162i
$976$	−187474.	−	714140.i	−0.196808	−	0.749694i
$977$	1.53833e6	−	637198.i	1.61161	−	0.667552i	0.618617	−	0.785693i	$-0.287693\pi$
$977$	1.53833e6	−	637198.i	1.61161	−	0.667552i	0.992997	+	0.118141i	$0.0376935\pi$
$978$	−340276.	+	13494.7i	−0.355757	+	0.0141087i
$979$	2.89786e6	−	1.54894e6i	3.02351	−	1.61610i
$980$	−287870.	+	659446.i	−0.299740	+	0.686637i
$981$	250482.	+	305213.i	0.260279	+	0.317151i
$982$	−297568.	+	1.14206e6i	−0.308576	+	1.18431i
$983$	−797464.	+	1.19349e6i	−0.825285	+	1.23513i	0.144096	+	0.989564i	$0.453973\pi$
$983$	−797464.	+	1.19349e6i	−0.825285	+	1.23513i	−0.969381	+	0.245562i	$0.921027\pi$
$984$	186187.	+	266514.i	0.192291	+	0.275252i
$985$	−532604.	−	797098.i	−0.548949	−	0.821560i
$986$	−29953.7	−	14515.0i	−0.0308103	−	0.0149301i
$987$	3089.26	+	1651.24i	0.00317117	+	0.00169503i
$988$	36243.5	−	308161.i	0.0371293	−	0.315692i
$989$	720816.	−	70994.2i	0.736940	−	0.0725822i
$990$	−1.95091e6	−	1.19453e6i	−1.99052	−	1.21879i
$991$	130046.	+	130046.i	0.132419	+	0.132419i	0.770210	−	0.637791i	$-0.220152\pi$
$991$	130046.	+	130046.i	0.132419	+	0.132419i	−0.637791	+	0.770210i	$0.720152\pi$
$992$	1.06392e6	+	1.06001e6i	1.08115	+	1.07718i
$993$	88528.6	+	88528.6i	0.0897812	+	0.0897812i
$994$	−515907.	+	124059.i	−0.522154	+	0.125561i
$995$	490229.	−	48283.3i	0.495168	−	0.0487698i
$996$	−73513.5	+	131494.i	−0.0741051	+	0.132553i
$997$	−813155.	−	434640.i	−0.818056	−	0.437260i	0.00860319	−	0.999963i	$-0.497261\pi$
$997$	−813155.	−	434640.i	−0.818056	−	0.437260i	−0.826659	+	0.562703i	$0.809761\pi$
$998$	−416588.	−	1.19991e6i	−0.418259	−	1.20473i
$999$	112698.	+	168664.i	0.112923	+	0.169002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.l.a.43.19	yes	1008
128.3	odd	32	inner	128.5.l.a.3.19	✓	1008

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.5.l.a.3.19	✓	1008	128.3	odd	32	inner
128.5.l.a.43.19	yes	1008	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.35233 - 3.23520i) q^{2} +(1.64666 + 1.35138i) q^{3} +(-4.93309 + 15.2205i) q^{4} +(31.2429 - 9.47742i) q^{5} +(0.498498 - 8.50617i) q^{6} +(-6.24158 + 31.3785i) q^{7} +(60.8458 - 19.8442i) q^{8} +(-14.9171 - 74.9931i) q^{9} +O(q^{10})\)	\(q+(-2.35233 - 3.23520i) q^{2} +(1.64666 + 1.35138i) q^{3} +(-4.93309 + 15.2205i) q^{4} +(31.2429 - 9.47742i) q^{5} +(0.498498 - 8.50617i) q^{6} +(-6.24158 + 31.3785i) q^{7} +(60.8458 - 19.8442i) q^{8} +(-14.9171 - 74.9931i) q^{9} +(-104.155 - 78.7830i) q^{10} +(-22.4545 + 227.984i) q^{11} +(-28.6918 + 18.3966i) q^{12} +(-13.4564 + 44.3598i) q^{13} +(116.198 - 53.6199i) q^{14} +(64.2540 + 26.6149i) q^{15} +(-207.329 - 150.168i) q^{16} +(23.6566 + 57.1121i) q^{17} +(-207.528 + 224.668i) q^{18} +(197.207 + 368.948i) q^{19} +(-9.87233 + 522.286i) q^{20} +(-52.6821 + 43.2351i) q^{21} +(790.395 - 463.649i) q^{22} +(362.906 + 242.486i) q^{23} +(127.009 + 49.5491i) q^{24} +(366.627 - 244.972i) q^{25} +(175.167 - 60.8147i) q^{26} +(158.118 - 295.818i) q^{27} +(-446.808 - 249.793i) q^{28} +(-13.1941 - 133.962i) q^{29} +(-65.0420 - 270.482i) q^{30} +(1037.08 - 1037.08i) q^{31} +(1.88173 + 1024.00i) q^{32} +(-345.068 + 345.068i) q^{33} +(129.121 - 210.880i) q^{34} +(102.383 + 1039.51i) q^{35} +(1215.02 + 142.902i) q^{36} +(-285.081 + 533.348i) q^{37} +(729.727 - 1505.89i) q^{38} +(-82.1049 + 54.8608i) q^{39} +(1712.92 - 1196.65i) q^{40} +(1982.79 + 1324.86i) q^{41} +(263.800 + 68.7341i) q^{42} +(1282.80 - 1052.77i) q^{43} +(-3359.27 - 1466.43i) q^{44} +(-1176.79 - 2201.62i) q^{45} +(-69.1830 - 1744.48i) q^{46} +(-19.6692 - 47.4857i) q^{47} +(-138.467 - 527.457i) q^{48} +(1272.58 + 527.119i) q^{49} +(-1654.96 - 609.857i) q^{50} +(-38.2257 + 126.013i) q^{51} +(-608.798 - 423.644i) q^{52} +(-108.877 + 1105.45i) q^{53} +(-1328.98 + 184.318i) q^{54} +(1459.16 + 7335.68i) q^{55} +(242.908 + 2033.11i) q^{56} +(-173.856 + 874.034i) q^{57} +(-402.359 + 357.809i) q^{58} +(-3213.26 + 974.732i) q^{59} +(-722.063 + 846.686i) q^{60} +(2229.46 + 1829.67i) q^{61} +(-5794.70 - 915.608i) q^{62} +2446.28 q^{63} +(3308.42 - 2414.87i) q^{64} +1513.46i q^{65} +(1928.08 + 304.651i) q^{66} +(-2639.09 + 3215.74i) q^{67} +(-985.977 + 78.3273i) q^{68} +(269.892 + 889.715i) q^{69} +(3122.19 - 2776.50i) q^{70} +(-4066.62 - 808.900i) q^{71} +(-2395.82 - 4267.00i) q^{72} +(-5314.94 + 1057.21i) q^{73} +(2396.09 - 332.318i) q^{74} +(934.760 + 92.0658i) q^{75} +(-6588.43 + 1181.54i) q^{76} +(-7013.66 - 2127.57i) q^{77} +(370.624 + 136.576i) q^{78} +(2383.86 - 5755.14i) q^{79} +(-7900.77 - 2726.74i) q^{80} +(-5061.87 + 2096.69i) q^{81} +(-377.991 - 9531.22i) q^{82} +(3898.13 - 2083.59i) q^{83} +(-398.176 - 1015.13i) q^{84} +(1280.38 + 1560.14i) q^{85} +(-6423.48 - 1673.66i) q^{86} +(159.308 - 238.421i) q^{87} +(3157.90 + 14317.5i) q^{88} +(-7968.66 - 11925.9i) q^{89} +(-4354.50 + 8986.11i) q^{90} +(-1307.96 - 699.117i) q^{91} +(-5481.01 + 4327.42i) q^{92} +(3109.20 - 306.229i) q^{93} +(-107.357 + 175.336i) q^{94} +(9657.99 + 9657.99i) q^{95} +(-1380.71 + 1688.72i) q^{96} +(-4859.05 - 4859.05i) q^{97} +(-1288.19 - 5357.01i) q^{98} +(17432.2 - 1716.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 43072 q^{50} - 16 q^{51} - 17968 q^{52} - 16 q^{53} + 31088 q^{54} - 16 q^{55} + 49376 q^{56} - 16 q^{57} + 65504 q^{58} - 16 q^{59} + 63920 q^{60} - 16 q^{61} + 11792 q^{62} - 32 q^{63} - 24400 q^{64} - 70864 q^{66} - 16 q^{67} - 53296 q^{68} - 16 q^{69} - 122320 q^{70} - 16 q^{71} - 81664 q^{72} - 16 q^{73} - 33280 q^{74} - 16 q^{75} + 28272 q^{76} - 16 q^{77} + 99344 q^{78} - 16 q^{79} + 105248 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 43072 * q^50 - 16 * q^51 - 17968 * q^52 - 16 * q^53 + 31088 * q^54 - 16 * q^55 + 49376 * q^56 - 16 * q^57 + 65504 * q^58 - 16 * q^59 + 63920 * q^60 - 16 * q^61 + 11792 * q^62 - 32 * q^63 - 24400 * q^64 - 70864 * q^66 - 16 * q^67 - 53296 * q^68 - 16 * q^69 - 122320 * q^70 - 16 * q^71 - 81664 * q^72 - 16 * q^73 - 33280 * q^74 - 16 * q^75 + 28272 * q^76 - 16 * q^77 + 99344 * q^78 - 16 * q^79 + 105248 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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