LMFDB - Embedded newform 147.4.o.a.101.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(5,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 29]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.o (of order $42$, degree $12$, 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			101.28
Character	$\chi$	$=$	147.101
Dual form			147.4.o.a.131.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.283103 + 0.111110i) q^{2} +(-4.60008 - 2.41646i) q^{3} +(-5.79661 - 5.37847i) q^{4} +(14.9795 + 10.2129i) q^{5} +(-1.03380 - 1.19522i) q^{6} +(-13.0100 + 13.1810i) q^{7} +(-2.09908 - 4.35878i) q^{8} +(15.3215 + 22.2318i) q^{9} +O(q^{10})$	\(q+(0.283103 + 0.111110i) q^{2} +(-4.60008 - 2.41646i) q^{3} +(-5.79661 - 5.37847i) q^{4} +(14.9795 + 10.2129i) q^{5} +(-1.03380 - 1.19522i) q^{6} +(-13.0100 + 13.1810i) q^{7} +(-2.09908 - 4.35878i) q^{8} +(15.3215 + 22.2318i) q^{9} +(3.10600 + 4.55566i) q^{10} +(-4.06296 - 26.9560i) q^{11} +(13.6681 + 38.7487i) q^{12} +(40.2721 - 32.1159i) q^{13} +(-5.14771 + 2.28604i) q^{14} +(-44.2281 - 83.1773i) q^{15} +(4.61748 + 61.6160i) q^{16} +(81.2257 + 25.0548i) q^{17} +(1.86739 + 7.99625i) q^{18} +(94.1016 - 54.3296i) q^{19} +(-31.9009 - 139.767i) q^{20} +(91.6985 - 29.1956i) q^{21} +(1.84483 - 8.08274i) q^{22} +(-8.40103 - 27.2355i) q^{23} +(-0.876869 + 25.1231i) q^{24} +(74.4157 + 189.608i) q^{25} +(14.9695 - 4.61749i) q^{26} +(-16.7580 - 139.292i) q^{27} +(146.308 - 6.43121i) q^{28} +(251.444 - 57.3904i) q^{29} +(-3.27929 - 28.4619i) q^{30} +(33.3614 + 19.2612i) q^{31} +(-16.9468 + 54.9403i) q^{32} +(-46.4479 + 133.818i) q^{33} +(20.2114 + 16.1180i) q^{34} +(-329.500 + 64.5757i) q^{35} +(30.7602 - 211.275i) q^{36} +(-84.6140 + 78.5103i) q^{37} +(32.6770 - 4.92526i) q^{38} +(-262.862 + 50.4201i) q^{39} +(13.0725 - 86.7301i) q^{40} +(-416.591 + 200.620i) q^{41} +(29.2040 + 1.92323i) q^{42} +(296.963 + 143.010i) q^{43} +(-121.430 + 178.106i) q^{44} +(2.45843 + 489.497i) q^{45} +(0.647769 - 8.64388i) q^{46} +(-67.7263 + 172.564i) q^{47} +(127.651 - 294.596i) q^{48} +(-4.47846 - 342.971i) q^{49} +61.9469i q^{50} +(-313.101 - 311.532i) q^{51} +(-406.176 - 30.4387i) q^{52} +(200.228 - 215.795i) q^{53} +(10.7324 - 41.2958i) q^{54} +(214.436 - 445.282i) q^{55} +(84.7623 + 29.0399i) q^{56} +(-564.160 + 22.5282i) q^{57} +(77.5610 + 11.6904i) q^{58} +(433.618 - 295.636i) q^{59} +(-190.994 + 720.026i) q^{60} +(467.341 + 503.674i) q^{61} +(7.30461 + 9.15969i) q^{62} +(-492.370 - 87.2832i) q^{63} +(297.295 - 372.796i) q^{64} +(931.252 - 69.7877i) q^{65} +(-28.0180 + 32.7233i) q^{66} +(-123.279 + 213.526i) q^{67} +(-336.077 - 582.103i) q^{68} +(-27.1679 + 145.586i) q^{69} +(-100.457 - 18.3291i) q^{70} +(-306.770 - 70.0182i) q^{71} +(64.7425 - 113.449i) q^{72} +(-263.143 + 103.276i) q^{73} +(-32.6777 + 12.8251i) q^{74} +(115.861 - 1052.03i) q^{75} +(-837.680 - 191.195i) q^{76} +(408.166 + 297.144i) q^{77} +(-80.0190 - 14.9324i) q^{78} +(52.8640 + 91.5632i) q^{79} +(-560.107 + 970.135i) q^{80} +(-259.504 + 681.248i) q^{81} +(-140.229 + 10.5087i) q^{82} +(-280.931 + 352.277i) q^{83} +(-688.568 - 323.962i) q^{84} +(960.840 + 1204.86i) q^{85} +(68.1814 + 73.4821i) q^{86} +(-1295.34 - 343.602i) q^{87} +(-108.967 + 74.2923i) q^{88} +(-1028.52 - 155.025i) q^{89} +(-53.6919 + 138.851i) q^{90} +(-100.620 + 948.656i) q^{91} +(-97.7877 + 203.058i) q^{92} +(-106.921 - 169.220i) q^{93} +(-38.3470 + 41.3283i) q^{94} +(1964.46 + 147.216i) q^{95} +(210.718 - 211.779i) q^{96} -214.821i q^{97} +(36.8395 - 97.5936i) q^{98} +(537.028 - 503.332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9}+O(q^{10}) $ 648 * q - 11 * q^3 - 234 * q^4 + 14 * q^6 + 28 * q^7 - 125 * q^9	$ 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9} - 58 q^{10} - 207 q^{12} - 28 q^{13} - 148 q^{15} + 726 q^{16} - 81 q^{18} - 342 q^{19} - 371 q^{21} - 156 q^{22} - 428 q^{24} + 1250 q^{25} - 56 q^{27} + 700 q^{28} + 389 q^{30} + 888 q^{31} + 841 q^{33} - 532 q^{34} - 38 q^{36} + 1178 q^{37} - 180 q^{39} + 194 q^{40} + 56 q^{42} + 1296 q^{43} - 617 q^{45} - 6756 q^{46} - 2380 q^{49} + 787 q^{51} - 5204 q^{52} + 4144 q^{54} - 5698 q^{55} + 863 q^{57} - 3066 q^{58} + 2820 q^{60} + 1492 q^{61} - 1085 q^{63} + 7648 q^{64} + 2568 q^{66} + 142 q^{67} - 5474 q^{69} + 5180 q^{70} + 1278 q^{72} + 2876 q^{73} - 1754 q^{75} + 7644 q^{76} + 936 q^{78} - 992 q^{79} + 911 q^{81} + 1022 q^{82} + 7868 q^{84} + 2672 q^{85} - 196 q^{87} + 370 q^{88} - 18767 q^{90} - 2254 q^{91} - 11096 q^{93} - 3628 q^{94} - 24248 q^{96} + 10982 q^{99}+O(q^{100}) $ 648 * q - 11 * q^3 - 234 * q^4 + 14 * q^6 + 28 * q^7 - 125 * q^9 - 58 * q^10 - 207 * q^12 - 28 * q^13 - 148 * q^15 + 726 * q^16 - 81 * q^18 - 342 * q^19 - 371 * q^21 - 156 * q^22 - 428 * q^24 + 1250 * q^25 - 56 * q^27 + 700 * q^28 + 389 * q^30 + 888 * q^31 + 841 * q^33 - 532 * q^34 - 38 * q^36 + 1178 * q^37 - 180 * q^39 + 194 * q^40 + 56 * q^42 + 1296 * q^43 - 617 * q^45 - 6756 * q^46 - 2380 * q^49 + 787 * q^51 - 5204 * q^52 + 4144 * q^54 - 5698 * q^55 + 863 * q^57 - 3066 * q^58 + 2820 * q^60 + 1492 * q^61 - 1085 * q^63 + 7648 * q^64 + 2568 * q^66 + 142 * q^67 - 5474 * q^69 + 5180 * q^70 + 1278 * q^72 + 2876 * q^73 - 1754 * q^75 + 7644 * q^76 + 936 * q^78 - 992 * q^79 + 911 * q^81 + 1022 * q^82 + 7868 * q^84 + 2672 * q^85 - 196 * q^87 + 370 * q^88 - 18767 * q^90 - 2254 * q^91 - 11096 * q^93 - 3628 * q^94 - 24248 * q^96 + 10982 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{42}\right)$

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 $

$2$	0.283103	+	0.111110i	0.100092	+	0.0392832i	0.414859	−	0.909886i	$-0.363831\pi$
$2$	0.283103	+	0.111110i	0.100092	+	0.0392832i	−0.314767	+	0.949169i	$0.601926\pi$
$3$	−4.60008	−	2.41646i	−0.885286	−	0.465047i
$3$	−4.60008	−	2.41646i	−0.885286	−	0.465047i
$4$	−5.79661	−	5.37847i	−0.724577	−	0.672309i
$5$	14.9795	+	10.2129i	1.33981	+	0.913466i	0.999638	−	0.0268981i	$-0.00856297\pi$
$5$	14.9795	+	10.2129i	1.33981	+	0.913466i	0.340170	+	0.940364i	$0.389515\pi$
$6$	−1.03380	−	1.19522i	−0.0703415	−	0.0813243i
$7$	−13.0100	+	13.1810i	−0.702475	+	0.711708i
$7$	−13.0100	+	13.1810i	−0.702475	+	0.711708i
$8$	−2.09908	−	4.35878i	−0.0927671	−	0.192633i
$9$	15.3215	+	22.2318i	0.567463	+	0.823399i
$10$	3.10600	+	4.55566i	0.0982202	+	0.144063i
$11$	−4.06296	−	26.9560i	−0.111366	−	0.738866i	−0.972910	−	0.231183i	$-0.925740\pi$
$11$	−4.06296	−	26.9560i	−0.111366	−	0.738866i	0.861544	−	0.507683i	$-0.169498\pi$
$12$	13.6681	+	38.7487i	0.328802	+	0.932148i
$13$	40.2721	−	32.1159i	0.859190	−	0.685181i	−0.0913380	−	0.995820i	$-0.529114\pi$
$13$	40.2721	−	32.1159i	0.859190	−	0.685181i	0.950528	+	0.310639i	$0.100543\pi$
$14$	−5.14771	+	2.28604i	−0.0982703	+	0.0436408i
$15$	−44.2281	−	83.1773i	−0.761309	−	1.43175i
$16$	4.61748	+	61.6160i	0.0721481	+	0.962749i
$17$	81.2257	+	25.0548i	1.15883	+	0.357452i	0.813803	−	0.581141i	$-0.197393\pi$
$17$	81.2257	+	25.0548i	1.15883	+	0.357452i	0.345028	+	0.938593i	$0.387870\pi$
$18$	1.86739	+	7.99625i	0.0244527	+	0.104707i
$19$	94.1016	−	54.3296i	1.13623	−	0.656003i	0.190736	−	0.981641i	$-0.438913\pi$
$19$	94.1016	−	54.3296i	1.13623	−	0.656003i	0.945494	+	0.325638i	$0.105579\pi$
$20$	−31.9009	−	139.767i	−0.356663	−	1.56264i
$21$	91.6985	−	29.1956i	0.952869	−	0.303381i
$22$	1.84483	−	8.08274i	0.0178782	−	0.0783294i
$23$	−8.40103	−	27.2355i	−0.0761624	−	0.246913i	0.909483	−	0.415741i	$-0.136478\pi$
$23$	−8.40103	−	27.2355i	−0.0761624	−	0.246913i	−0.985645	+	0.168829i	$0.946002\pi$
$24$	−0.876869	+	25.1231i	−0.00745793	+	0.213676i
$25$	74.4157	+	189.608i	0.595325	+	1.51686i
$26$	14.9695	−	4.61749i	0.112914	−	0.0348294i
$27$	−16.7580	−	139.292i	−0.119447	−	0.992841i
$28$	146.308	−	6.43121i	0.987485	−	0.0434066i
$29$	251.444	−	57.3904i	1.61007	−	0.367487i	0.679518	−	0.733658i	$-0.262189\pi$
$29$	251.444	−	57.3904i	1.61007	−	0.367487i	0.930547	+	0.366171i	$0.119332\pi$
$30$	−3.27929	−	28.4619i	−0.0199571	−	0.173214i
$31$	33.3614	+	19.2612i	0.193287	+	0.111594i	0.593520	−	0.804819i	$-0.297738\pi$
$31$	33.3614	+	19.2612i	0.193287	+	0.111594i	−0.400234	+	0.916413i	$0.631071\pi$
$32$	−16.9468	+	54.9403i	−0.0936190	+	0.303505i
$33$	−46.4479	+	133.818i	−0.245017	+	0.705898i
$34$	20.2114	+	16.1180i	0.101948	+	0.0813007i
$35$	−329.500	+	64.5757i	−1.59130	+	0.311865i
$36$	30.7602	−	211.275i	0.142408	−	0.978126i
$37$	−84.6140	+	78.5103i	−0.375958	+	0.348838i	−0.845408	−	0.534121i	$-0.820643\pi$
$37$	−84.6140	+	78.5103i	−0.375958	+	0.348838i	0.469450	+	0.882959i	$0.344452\pi$
$38$	32.6770	−	4.92526i	0.139497	−	0.0210259i
$39$	−262.862	+	50.4201i	−1.07927	+	0.207018i
$40$	13.0725	−	86.7301i	0.0516734	−	0.342831i
$41$	−416.591	+	200.620i	−1.58684	+	0.764184i	−0.998997	−	0.0447873i	$-0.985739\pi$
$41$	−416.591	+	200.620i	−1.58684	+	0.764184i	−0.587848	+	0.808971i	$0.700025\pi$
$42$	29.2040	+	1.92323i	0.107292	+	0.00706575i
$43$	296.963	+	143.010i	1.05317	+	0.507182i	0.878648	−	0.477470i	$-0.158446\pi$
$43$	296.963	+	143.010i	1.05317	+	0.507182i	0.174527	+	0.984652i	$0.444161\pi$
$44$	−121.430	+	178.106i	−0.416053	+	0.610238i
$45$	2.45843	+	489.497i	0.00814401	+	1.62155i
$46$	0.647769	−	8.64388i	0.00207627	−	0.0277059i
$47$	−67.7263	+	172.564i	−0.210189	+	0.535554i	−0.996622	−	0.0821219i	$-0.973830\pi$
$47$	−67.7263	+	172.564i	−0.210189	+	0.535554i	0.786433	+	0.617676i	$0.211926\pi$
$48$	127.651	−	294.596i	0.383852	−	0.885861i
$49$	−4.47846	−	342.971i	−0.0130567	−	0.999915i
$50$			61.9469i			0.175212i
$51$	−313.101	−	311.532i	−0.859665	−	0.855358i
$52$	−406.176	−	30.4387i	−1.08320	−	0.0811748i
$53$	200.228	−	215.795i	0.518933	−	0.559277i	−0.418152	−	0.908377i	$-0.637322\pi$
$53$	200.228	−	215.795i	0.518933	−	0.559277i	0.937085	+	0.349100i	$0.113513\pi$
$54$	10.7324	−	41.2958i	0.0270462	−	0.104068i
$55$	214.436	−	445.282i	0.525720	−	1.09167i
$56$	84.7623	+	29.0399i	0.202265	+	0.0692968i
$57$	−564.160	+	22.5282i	−1.31096	+	0.0523496i
$58$	77.5610	+	11.6904i	0.175591	+	0.0264660i
$59$	433.618	−	295.636i	0.956818	−	0.652348i	0.0191270	−	0.999817i	$-0.493911\pi$
$59$	433.618	−	295.636i	0.956818	−	0.652348i	0.937691	+	0.347469i	$0.112959\pi$
$60$	−190.994	+	720.026i	−0.410953	+	1.54925i
$61$	467.341	+	503.674i	0.980933	+	1.05719i	0.998354	+	0.0573463i	$0.0182639\pi$
$61$	467.341	+	503.674i	0.980933	+	1.05719i	−0.0174212	+	0.999848i	$0.505546\pi$
$62$	7.30461	+	9.15969i	0.0149627	+	0.0187626i
$63$	−492.370	−	87.2832i	−0.984648	−	0.174550i
$64$	297.295	−	372.796i	0.580654	−	0.728118i
$65$	931.252	−	69.7877i	1.77704	−	0.133171i
$66$	−28.0180	+	32.7233i	−0.0522541	+	0.0610297i
$67$	−123.279	+	213.526i	−0.224791	+	0.389349i	−0.956257	−	0.292529i	$-0.905503\pi$
$67$	−123.279	+	213.526i	−0.224791	+	0.389349i	0.731466	+	0.681878i	$0.238836\pi$
$68$	−336.077	−	582.103i	−0.599344	−	1.03809i
$69$	−27.1679	+	145.586i	−0.0474004	+	0.254007i
$70$	−100.457	−	18.3291i	−0.171528	−	0.0312963i
$71$	−306.770	−	70.0182i	−0.512773	−	0.117037i	−0.0416979	−	0.999130i	$-0.513277\pi$
$71$	−306.770	−	70.0182i	−0.512773	−	0.117037i	−0.471075	+	0.882093i	$0.656134\pi$
$72$	64.7425	−	113.449i	0.105972	−	0.185696i
$73$	−263.143	+	103.276i	−0.421899	+	0.165583i	−0.566786	−	0.823865i	$-0.691813\pi$
$73$	−263.143	+	103.276i	−0.421899	+	0.165583i	0.144887	+	0.989448i	$0.453718\pi$
$74$	−32.6777	+	12.8251i	−0.0513339	+	0.0201471i
$75$	115.861	−	1052.03i	0.178380	−	1.61971i
$76$	−837.680	−	191.195i	−1.26432	−	0.288573i
$77$	408.166	+	297.144i	0.604089	+	0.439775i
$78$	−80.0190	−	14.9324i	−0.116159	−	0.0216764i
$79$	52.8640	+	91.5632i	0.0752870	+	0.130401i	0.901211	−	0.433381i	$-0.142679\pi$
$79$	52.8640	+	91.5632i	0.0752870	+	0.130401i	−0.825924	+	0.563781i	$0.809346\pi$
$80$	−560.107	+	970.135i	−0.782774	+	1.35580i
$81$	−259.504	+	681.248i	−0.355972	+	0.934496i
$82$	−140.229	+	10.5087i	−0.188850	+	0.0141524i
$83$	−280.931	+	352.277i	−0.371521	+	0.465872i	−0.932085	−	0.362238i	$-0.882013\pi$
$83$	−280.931	+	352.277i	−0.371521	+	0.465872i	0.560565	+	0.828110i	$0.310584\pi$
$84$	−688.568	−	323.962i	−0.894393	−	0.420800i
$85$	960.840	+	1204.86i	1.22609	+	1.53747i
$86$	68.1814	+	73.4821i	0.0854906	+	0.0921369i
$87$	−1295.34	−	343.602i	−1.59627	−	0.423425i
$88$	−108.967	+	74.2923i	−0.131999	+	0.0899953i
$89$	−1028.52	−	155.025i	−1.22498	−	0.184636i	−0.495482	−	0.868618i	$-0.665008\pi$
$89$	−1028.52	−	155.025i	−1.22498	−	0.184636i	−0.729499	+	0.683982i	$0.760247\pi$
$90$	−53.6919	+	138.851i	−0.0628847	+	0.162625i
$91$	−100.620	+	948.656i	−0.115911	+	1.09282i
$92$	−97.7877	+	203.058i	−0.110816	+	0.230112i
$93$	−106.921	−	169.220i	−0.119218	−	0.188680i
$94$	−38.3470	+	41.3283i	−0.0420765	+	0.0453477i
$95$	1964.46	+	147.216i	2.12157	+	0.158989i
$96$	210.718	−	211.779i	0.224024	−	0.225152i
$97$		−	214.821i		−	0.224863i	−0.993659	−	0.112432i	$-0.964136\pi$
$97$		−	214.821i		−	0.224863i	0.993659	−	0.112432i	$-0.0358639\pi$
$98$	36.8395	−	97.5936i	0.0379730	−	0.100596i
$99$	537.028	−	503.332i	0.545186	−	0.510978i
$100$	588.442	−	1499.33i	0.588442	−	1.49933i
$101$	87.7814	−	1171.36i	0.0864809	−	1.15401i	−0.770075	−	0.637953i	$-0.779781\pi$
$101$	87.7814	−	1171.36i	0.0864809	−	1.15401i	0.856556	−	0.516054i	$-0.172600\pi$
$102$	−54.0255	−	122.984i	−0.0524443	−	0.119385i
$103$	−375.857	+	551.281i	−0.359556	+	0.527372i	−0.962811	−	0.270177i	$-0.912918\pi$
$103$	−375.857	+	551.281i	−0.359556	+	0.527372i	0.603255	+	0.797549i	$0.293870\pi$
$104$	−224.521	−	108.123i	−0.211693	−	0.101946i
$105$	1671.77	+	499.168i	1.55379	+	0.463941i
$106$	80.6620	−	38.8448i	0.0739112	−	0.0355938i
$107$	59.1189	−	392.228i	0.0534135	−	0.354375i	−0.946120	−	0.323818i	$-0.895034\pi$
$107$	59.1189	−	392.228i	0.0534135	−	0.354375i	0.999533	−	0.0305577i	$-0.00972833\pi$
$108$	−652.037	+	897.552i	−0.580947	+	0.799695i
$109$	1275.95	−	192.319i	1.12123	−	0.168999i	0.437842	−	0.899052i	$-0.355743\pi$
$109$	1275.95	−	192.319i	1.12123	−	0.168999i	0.683390	+	0.730053i	$0.260505\pi$
$110$	110.183	−	102.235i	0.0955045	−	0.0886153i
$111$	578.948	−	156.688i	0.495057	−	0.133983i
$112$	−872.235	−	740.762i	−0.735879	−	0.624959i
$113$	753.352	+	600.778i	0.627163	+	0.500146i	0.884723	−	0.466117i	$-0.154347\pi$
$113$	753.352	+	600.778i	0.627163	+	0.500146i	−0.257561	+	0.966262i	$0.582919\pi$
$114$	−162.218	−	56.3058i	−0.133273	−	0.0462590i
$115$	152.309	−	493.773i	0.123503	−	0.400387i
$116$	−1766.19	−	1019.71i	−1.41368	−	0.816189i
$117$	1331.02	+	403.257i	1.05174	+	0.318642i
$118$	155.607	−	35.5162i	0.121396	−	0.0277079i
$119$	−1387.00	+	744.674i	−1.06845	+	0.573648i
$120$	−269.714	+	367.376i	−0.205178	+	0.279473i
$121$	561.751	−	173.277i	0.422052	−	0.130186i
$122$	76.3426	+	194.518i	0.0566535	+	0.144351i
$123$	2401.14	+	83.8069i	1.76019	+	0.0614359i
$124$	−89.7874	−	291.083i	−0.0650253	−	0.210807i
$125$	−317.448	+	1390.83i	−0.227147	+	0.995198i
$126$	−129.693	−	79.4172i	−0.0916985	−	0.0561512i
$127$	464.885	+	2036.79i	0.324818	+	1.42312i	0.828867	+	0.559445i	$0.188986\pi$
$127$	464.885	+	2036.79i	0.324818	+	1.42312i	−0.504050	+	0.863675i	$0.668157\pi$
$128$	523.921	−	302.486i	0.361785	−	0.208877i
$129$	−1020.48	−	1375.46i	−0.696497	−	0.938777i
$130$	271.394	+	83.7140i	0.183099	+	0.0564785i
$131$	−117.404	−	1566.64i	−0.0783024	−	1.04487i	−0.888548	−	0.458783i	$-0.848286\pi$
$131$	−117.404	−	1566.64i	−0.0783024	−	1.04487i	0.810246	−	0.586090i	$-0.199333\pi$
$132$	988.975	−	525.870i	0.652115	−	0.346751i
$133$	−508.145	+	1947.18i	−0.331291	+	1.26949i
$134$	−58.6256	+	46.7523i	−0.0377946	+	0.0301402i
$135$	1171.54	−	2257.67i	0.746889	−	1.43933i
$136$	−61.2907	−	406.637i	−0.0386444	−	0.256389i
$137$	−345.472	−	506.714i	−0.215443	−	0.315996i	0.703270	−	0.710923i	$-0.251722\pi$
$137$	−345.472	−	506.714i	−0.215443	−	0.315996i	−0.918713	+	0.394926i	$0.870770\pi$
$138$	−23.8673	+	38.1972i	−0.0147226	+	0.0235621i
$139$	−1050.32	−	2181.00i	−0.640910	−	1.33086i	−0.927864	−	0.372920i	$-0.878357\pi$
$139$	−1050.32	−	2181.00i	−0.640910	−	1.33086i	0.286953	−	0.957945i	$-0.407358\pi$
$140$	2257.30	+	1397.88i	1.36269	+	0.843877i
$141$	728.539	−	630.150i	0.435135	−	0.376370i
$142$	−79.0677	−	53.9074i	−0.0467269	−	0.0318578i
$143$	−1029.34	−	955.087i	−0.601942	−	0.558520i
$144$	−1299.09	+	1046.70i	−0.751786	+	0.605731i
$145$	4352.62	+	1708.28i	2.49287	+	0.978378i
$146$	−85.9716			−0.0487333
$147$	−808.172	+	1588.52i	−0.453448	+	0.891283i
$148$	912.740			0.506938
$149$	−3025.60	−	1187.46i	−1.66353	−	0.652889i	−0.667729	−	0.744404i	$-0.732734\pi$
$149$	−3025.60	−	1187.46i	−1.66353	−	0.652889i	−0.995804	+	0.0915155i	$0.970829\pi$
$150$	149.692	−	284.961i	0.0814819	−	0.155113i
$151$	282.104	+	261.754i	0.152035	+	0.141068i	0.752523	−	0.658566i	$-0.228837\pi$
$151$	282.104	+	261.754i	0.152035	+	0.141068i	−0.600488	+	0.799634i	$0.705027\pi$
$152$	−434.337	−	296.126i	−0.231773	−	0.158020i
$153$	687.486	+	2189.67i	0.363267	+	1.15702i
$154$	82.5374	+	129.473i	0.0431887	+	0.0677485i
$155$	303.026	+	629.240i	0.157030	+	0.326076i
$156$	1794.89	+	1121.53i	0.921194	+	0.575603i
$157$	−1427.60	−	2093.91i	−0.725701	−	1.06441i	−0.994855	−	0.101311i	$-0.967696\pi$
$157$	−1427.60	−	2093.91i	−0.725701	−	1.06441i	0.269153	−	0.963097i	$-0.413256\pi$
$158$	4.79240	+	31.7955i	0.00241306	+	0.0160096i
$159$	−1442.52	+	508.830i	−0.719494	+	0.253792i
$160$	−814.953	+	649.903i	−0.402673	+	0.321121i
$161$	468.289	+	243.600i	0.229232	+	0.119245i
$162$	−149.160	+	164.030i	−0.0723400	+	0.0795519i
$163$	−28.3617	−	378.461i	−0.0136286	−	0.181861i	−0.999864	−	0.0165118i	$-0.994744\pi$
$163$	−28.3617	−	378.461i	−0.0136286	−	0.181861i	0.986235	−	0.165349i	$-0.0528752\pi$
$164$	3493.85	+	1077.71i	1.66356	+	0.513140i
$165$	−2062.43	+	1530.16i	−0.973089	+	0.721954i
$166$	−118.674	+	68.5163i	−0.0554872	+	0.0320355i
$167$	−337.252	−	1477.60i	−0.156271	−	0.684670i	−0.990984	−	0.133984i	$-0.957223\pi$
$167$	−337.252	−	1477.60i	−0.156271	−	0.684670i	0.834712	−	0.550687i	$-0.185634\pi$
$168$	−319.740	−	338.410i	−0.146836	−	0.155410i
$169$	101.531	−	444.835i	0.0462133	−	0.202474i
$170$	138.145	+	447.857i	0.0623251	+	0.202053i
$171$	2649.62	+	1259.64i	1.18492	+	0.563314i
$172$	−952.207	−	2426.18i	−0.422123	−	1.07555i
$173$	3915.54	−	1207.78i	1.72077	−	0.530787i	0.732138	−	0.681156i	$-0.238523\pi$
$173$	3915.54	−	1207.78i	1.72077	−	0.530787i	0.988630	+	0.150369i	$0.0480463\pi$
$174$	−328.538	−	241.200i	−0.143140	−	0.105088i
$175$	−3467.38	−	1485.93i	−1.49777	−	0.641862i
$176$	1642.16	−	374.812i	0.703308	−	0.160525i
$177$	−2709.07	+	312.130i	−1.15043	+	0.132549i
$178$	−273.953	−	158.167i	−0.115358	−	0.0666018i
$179$	−544.149	+	1764.09i	−0.227216	+	0.736615i	0.768134	+	0.640289i	$0.221185\pi$
$179$	−544.149	+	1764.09i	−0.227216	+	0.736615i	−0.995350	+	0.0963263i	$0.969291\pi$
$180$	2618.50	−	2850.65i	1.08428	−	1.18042i
$181$	−1066.13	−	850.213i	−0.437818	−	0.349148i	0.379642	−	0.925134i	$-0.376047\pi$
$181$	−1066.13	−	850.213i	−0.437818	−	0.349148i	−0.817460	+	0.575985i	$0.804619\pi$
$182$	−133.891	+	257.387i	−0.0545310	+	0.104829i
$183$	−932.702	−	3446.25i	−0.376761	−	1.39210i
$184$	−101.079	+	93.7877i	−0.0404981	+	0.0375767i
$185$	−2069.29	+	311.895i	−0.822364	+	0.123951i
$186$	−11.4678	−	59.7866i	−0.00452076	−	0.0235686i
$187$	345.360	−	2291.31i	0.135055	−	0.896029i
$188$	1320.71	−	636.022i	0.512356	−	0.246738i
$189$	2054.03	+	1591.30i	0.790521	+	0.612434i
$190$	539.786	+	259.947i	0.206106	+	0.0992555i
$191$	−1185.93	+	1739.45i	−0.449273	+	0.658963i	−0.982339	−	0.187111i	$-0.940087\pi$
$191$	−1185.93	+	1739.45i	−0.449273	+	0.658963i	0.533066	+	0.846074i	$0.321040\pi$
$192$	−2268.43	+	996.493i	−0.852654	+	0.374561i
$193$	−320.793	+	4280.69i	−0.119643	+	1.59653i	0.537830	+	0.843053i	$0.319244\pi$
$193$	−320.793	+	4280.69i	−0.119643	+	1.59653i	−0.657474	+	0.753478i	$0.728375\pi$
$194$	23.8687	−	60.8164i	0.00883335	−	0.0225070i
$195$	−4452.47	−	1929.30i	−1.63512	−	0.708513i
$196$	−1818.70	+	2012.16i	−0.662791	+	0.733293i
$197$		−	2715.19i		−	0.981976i	−0.871166	−	0.490988i	$-0.836636\pi$
$197$		−	2715.19i		−	0.981976i	0.871166	−	0.490988i	$-0.163364\pi$
$198$	207.959	−	82.8257i	0.0746416	−	0.0297281i
$199$	−938.098	−	70.3007i	−0.334171	−	0.0250426i	−0.0934117	−	0.995628i	$-0.529777\pi$
$199$	−938.098	−	70.3007i	−0.334171	−	0.0250426i	−0.240759	+	0.970585i	$0.577396\pi$
$200$	670.256	−	722.364i	0.236971	−	0.255394i
$201$	1083.07	−	684.338i	0.380069	−	0.240147i
$202$	155.001	−	321.862i	0.0539892	−	0.112110i
$203$	−2514.82	+	4060.93i	−0.869488	+	1.40405i
$204$	139.357	+	3489.84i	0.0478282	+	1.19773i
$205$	−8289.24	−	1249.40i	−2.82412	−	0.425668i
$206$	−167.659	+	114.308i	−0.0567055	+	0.0386612i
$207$	476.777	−	604.058i	0.160088	−	0.202826i
$208$	2164.81	+	2333.11i	0.721647	+	0.777750i
$209$	−1846.84	−	2315.86i	−0.611236	−	0.766466i
$210$	417.820	+	327.066i	0.137297	+	0.107475i
$211$	842.011	−	1055.85i	0.274723	−	0.344491i	−0.625260	−	0.780416i	$-0.715007\pi$
$211$	842.011	−	1055.85i	0.274723	−	0.344491i	0.899983	+	0.435925i	$0.143579\pi$
$212$	−2321.29	+	173.957i	−0.752014	+	0.0563556i
$213$	1241.97	+	1063.38i	0.399523	+	0.342075i
$214$	60.3171	−	104.472i	0.0192673	−	0.0333719i
$215$	2987.83	+	5175.07i	0.947758	+	1.64157i
$216$	−571.966	+	365.429i	−0.180173	+	0.115112i
$217$	−687.916	+	189.149i	−0.215202	+	0.0591716i
$218$	382.595	+	87.3248i	0.118865	+	0.0271302i
$219$	1460.04	+	160.795i	0.450505	+	0.0496144i
$220$	−3637.94	+	1427.79i	−1.11486	+	0.437551i
$221$	4075.79	−	1599.63i	1.24058	−	0.486890i
$222$	181.311	+	19.9679i	0.0548145	+	0.00603675i
$223$	1606.92	+	366.769i	0.482544	+	0.110138i	0.456871	−	0.889533i	$-0.348970\pi$
$223$	1606.92	+	366.769i	0.482544	+	0.110138i	0.0256731	+	0.999670i	$0.491827\pi$
$224$	−503.690	−	938.152i	−0.150242	−	0.279834i
$225$	−3075.17	+	4559.47i	−0.911160	+	1.35095i
$226$	146.524	+	253.787i	0.0431266	+	0.0746975i
$227$	−2265.31	+	3923.63i	−0.662351	+	1.14723i	0.317645	+	0.948210i	$0.397108\pi$
$227$	−2265.31	+	3923.63i	−0.662351	+	1.14723i	−0.979996	+	0.199016i	$0.936225\pi$
$228$	3391.38	+	2903.73i	0.985087	+	0.843439i
$229$	−5615.32	+	420.810i	−1.62040	+	0.121432i	−0.853766	−	0.520656i	$-0.825687\pi$
$229$	−5615.32	+	420.810i	−1.62040	+	0.121432i	−0.766631	+	0.642088i	$0.778068\pi$
$230$	97.9819	−	122.865i	0.0280902	−	0.0352240i
$231$	−1159.56	−	2353.20i	−0.330275	−	0.670257i
$232$	−777.953	−	975.522i	−0.220151	−	0.276061i
$233$	−395.637	−	426.395i	−0.111240	−	0.119889i	0.674977	−	0.737839i	$-0.264154\pi$
$233$	−395.637	−	426.395i	−0.111240	−	0.119889i	−0.786217	+	0.617950i	$0.787963\pi$
$234$	332.011	+	262.053i	0.0927530	+	0.0732090i
$235$	−2776.88	+	1893.24i	−0.770824	+	0.525539i
$236$	−4103.59	−	618.516i	−1.13187	−	0.170602i
$237$	−21.9205	−	548.942i	−0.00600797	−	0.150454i
$238$	−475.403	+	56.7105i	−0.129478	+	0.0154454i
$239$	−72.3809	+	150.301i	−0.0195897	+	0.0406784i	−0.910534	−	0.413434i	$-0.864329\pi$
$239$	−72.3809	+	150.301i	−0.0195897	+	0.0406784i	0.890944	+	0.454112i	$0.150044\pi$
$240$	4920.83	−	3109.22i	1.32349	−	0.836248i
$241$	771.462	−	831.438i	0.206200	−	0.222231i	−0.621481	−	0.783429i	$-0.713469\pi$
$241$	771.462	−	831.438i	0.206200	−	0.222231i	0.827682	+	0.561198i	$0.189659\pi$
$242$	178.286	+	13.3607i	0.0473581	+	0.00354900i
$243$	2839.94	−	2506.72i	0.749722	−	0.661753i
$244$		−	5433.19i		−	1.42551i
$245$	3435.63	−	5183.27i	0.895894	−	1.35162i
$246$	670.458	+	290.516i	0.173768	+	0.0752952i
$247$	2044.82	−	5210.12i	0.526757	−	1.34215i
$248$	13.9272	−	185.846i	0.00356605	−	0.0475857i
$249$	2143.57	−	941.643i	0.545554	−	0.239655i
$250$	−244.405	+	358.477i	−0.0618302	+	0.0906882i
$251$	3706.03	+	1784.73i	0.931963	+	0.448810i	0.837327	−	0.546702i	$-0.184117\pi$
$251$	3706.03	+	1784.73i	0.931963	+	0.448810i	0.0946358	+	0.995512i	$0.469831\pi$
$252$	2384.63	+	3154.15i	0.596102	+	0.788463i
$253$	−700.025	+	337.114i	−0.173953	+	0.0837715i
$254$	−94.6973	+	628.275i	−0.0233930	+	0.155203i
$255$	−1508.46	−	7864.26i	−0.370446	−	1.93129i
$256$	−3590.06	+	541.114i	−0.876478	+	0.132108i
$257$	−2091.82	+	1940.92i	−0.507719	+	0.471095i	−0.891945	−	0.452145i	$-0.850659\pi$
$257$	−2091.82	+	1940.92i	−0.507719	+	0.471095i	0.384225	+	0.923239i	$0.374469\pi$
$258$	−136.074	−	502.781i	−0.0328356	−	0.121325i
$259$	65.9844	−	2136.72i	0.0158304	−	0.512623i
$260$	−5773.46	−	4604.18i	−1.37713	−	1.09823i
$261$	5128.38	+	4710.73i	1.21624	+	1.11719i
$262$	140.832	−	456.566i	0.0332085	−	0.107659i
$263$	−2849.11	−	1644.93i	−0.667999	−	0.385669i	0.127319	−	0.991862i	$-0.459363\pi$
$263$	−2849.11	−	1644.93i	−0.667999	−	0.385669i	−0.795318	+	0.606193i	$0.792696\pi$
$264$	680.780	−	78.4372i	0.158709	−	0.0182859i
$265$	5203.20	−	1187.60i	1.20615	−	0.275296i
$266$	−360.208	+	494.793i	−0.0830292	+	0.114052i
$267$	4356.68	+	3198.51i	0.998594	+	0.733129i
$268$	1863.05	−	574.674i	0.424641	−	0.130984i
$269$	156.697	+	399.259i	0.0355168	+	0.0904953i	0.947532	−	0.319662i	$-0.103569\pi$
$269$	156.697	+	399.259i	0.0355168	+	0.0904953i	−0.912015	+	0.410157i	$0.865474\pi$
$270$	582.515	−	508.983i	0.131299	−	0.114725i
$271$	153.780	+	498.541i	0.0344703	+	0.111750i	0.971173	−	0.238376i	$-0.0766150\pi$
$271$	153.780	+	498.541i	0.0344703	+	0.111750i	−0.936703	+	0.350126i	$0.886139\pi$
$272$	−1168.72	+	5120.49i	−0.260529	+	1.14145i
$273$	2755.25	−	4120.75i	0.610825	−	0.913550i
$274$	−41.5032	−	181.837i	−0.00915073	−	0.0400920i
$275$	4808.72	−	2776.32i	1.05446	−	0.608793i
$276$	940.512	−	697.785i	0.205117	−	0.152180i
$277$	2785.26	+	859.140i	0.604153	+	0.186356i	0.581716	−	0.813392i	$-0.302381\pi$
$277$	2785.26	+	859.140i	0.604153	+	0.186356i	0.0224366	+	0.999748i	$0.492858\pi$
$278$	−55.0168	−	734.148i	−0.0118694	−	0.158386i
$279$	82.9354	+	1036.79i	0.0177965	+	0.222478i
$280$	973.118	+	1300.67i	0.207696	+	0.277606i
$281$	−3876.74	+	3091.60i	−0.823014	+	0.656332i	−0.941645	−	0.336607i	$-0.890721\pi$
$281$	−3876.74	+	3091.60i	−0.823014	+	0.656332i	0.118631	+	0.992938i	$0.462149\pi$
$282$	276.267	−	97.4495i	0.0583386	−	0.0205781i
$283$	1297.76	+	8610.05i	0.272592	+	1.80853i	0.536409	+	0.843958i	$0.319780\pi$
$283$	1297.76	+	8610.05i	0.272592	+	1.80853i	−0.263817	+	0.964573i	$0.584982\pi$
$284$	1401.63	+	2055.82i	0.292858	+	0.429544i
$285$	−8680.91	−	5424.22i	−1.80426	−	1.12738i
$286$	−185.289	−	384.758i	−0.0383091	−	0.0795496i
$287$	2775.49	−	8101.17i	0.570843	−	1.66619i
$288$	−1481.07	+	465.009i	−0.303031	+	0.0951421i
$289$	1910.56	+	1302.60i	0.388878	+	0.265133i
$290$	1042.43	+	967.237i	0.211082	+	0.195856i
$291$	−519.105	+	988.193i	−0.104572	+	0.199068i
$292$	2080.81	+	816.657i	0.417021	+	0.163669i
$293$	−1019.76			−0.203327			−0.101664	−	0.994819i	$-0.532417\pi$
$293$	−1019.76			−0.203327			−0.101664	+	0.994819i	$0.532417\pi$
$294$	−405.295	+	359.917i	−0.0803990	+	0.0713973i
$295$	9514.68			1.87785
$296$	519.821	+	204.015i	0.102074	+	0.0400612i
$297$	−3686.65	+	1017.66i	−0.720274	+	0.198824i
$298$	−724.616	−	672.346i	−0.140859	−	0.130698i
$299$	−1213.02	−	827.023i	−0.234618	−	0.159960i
$300$	−6329.94	+	5475.08i	−1.21820	+	1.05368i
$301$	−5748.52	+	2053.72i	−1.10079	+	0.393270i
$302$	50.7810	+	105.448i	0.00967589	+	0.0200922i
$303$	−3234.34	+	5176.24i	−0.613228	+	0.981409i
$304$	3782.08	+	5547.29i	0.713543	+	1.04658i
$305$	1856.59	+	12317.7i	0.348551	+	2.31249i
$306$	−48.6642	+	696.288i	−0.00909134	+	0.130079i
$307$	3146.10	−	2508.93i	0.584877	−	0.466424i	−0.285793	−	0.958291i	$-0.592257\pi$
$307$	3146.10	−	2508.93i	0.584877	−	0.466424i	0.870670	+	0.491868i	$0.163686\pi$
$308$	−767.802	−	3917.74i	−0.142044	−	0.724785i
$309$	3061.12	−	1627.70i	0.563563	−	0.299665i
$310$	15.8729	+	211.809i	0.00290812	+	0.0388062i
$311$	−7989.76	−	2464.51i	−1.45678	−	0.449356i	−0.537600	−	0.843200i	$-0.680669\pi$
$311$	−7989.76	−	2464.51i	−1.45678	−	0.449356i	−0.919177	+	0.393844i	$0.871145\pi$
$312$	771.538	+	1039.92i	0.139999	+	0.188699i
$313$	−2046.55	+	1181.58i	−0.369578	+	0.213376i	−0.673274	−	0.739393i	$-0.735113\pi$
$313$	−2046.55	+	1181.58i	−0.369578	+	0.213376i	0.303696	+	0.952769i	$0.401779\pi$
$314$	−171.505	−	751.412i	−0.0308235	−	0.135047i
$315$	−6484.06	−	6335.97i	−1.15979	−	1.13331i
$316$	186.038	−	815.084i	0.0331185	−	0.145101i
$317$	−431.124	−	1397.67i	−0.0763859	−	0.247637i	0.909324	−	0.416089i	$-0.136599\pi$
$317$	−431.124	−	1397.67i	−0.0763859	−	0.247637i	−0.985710	+	0.168452i	$0.946123\pi$
$318$	−464.919	−	16.2270i	−0.0819854	−	0.00286153i
$319$	−2568.62	−	6544.73i	−0.450831	−	1.14870i
$320$	8260.65	−	2548.07i	1.44308	−	0.445130i
$321$	−1219.75	+	1661.42i	−0.212087	+	0.288884i
$322$	105.508	+	120.995i	0.0182600	+	0.0209404i
$323$	9004.68	−	2055.26i	1.55119	−	0.354049i
$324$	5168.32	−	2553.20i	0.886200	−	0.437791i
$325$	9086.31	+	5245.99i	1.55082	+	0.895369i
$326$	34.0214	−	110.295i	0.00577998	−	0.0187382i
$327$	−6334.23	−	2198.60i	−1.07120	−	0.371814i
$328$	1748.92	+	1394.71i	0.294414	+	0.234787i
$329$	−1393.45	−	3137.76i	−0.233505	−	0.525807i
$330$	−753.894	+	204.036i	−0.125759	+	0.0340358i
$331$	−1712.51	+	1588.97i	−0.284374	+	0.263861i	−0.809442	−	0.587200i	$-0.800230\pi$
$331$	−1712.51	+	1588.97i	−0.284374	+	0.263861i	0.525068	+	0.851060i	$0.324040\pi$
$332$	3523.16	−	531.031i	0.582405	−	0.0877834i
$333$	−3041.84	−	678.225i	−0.500575	−	0.111611i
$334$	68.6984	−	455.784i	0.0112545	−	0.0746688i
$335$	−4027.38	+	1939.48i	−0.656833	+	0.316314i
$336$	2222.33	+	5515.28i	0.360828	+	0.895486i
$337$	3315.98	+	1596.89i	0.536002	+	0.258125i	0.682245	−	0.731124i	$-0.261004\pi$
$337$	3315.98	+	1596.89i	0.536002	+	0.258125i	−0.146243	+	0.989249i	$0.546718\pi$
$338$	78.1691	−	114.653i	0.0125794	−	0.0184506i
$339$	−2013.73	−	4584.07i	−0.322627	−	0.734432i
$340$	910.661	−	12151.9i	0.145257	−	1.93833i
$341$	383.659	−	977.547i	0.0609276	−	0.155241i
$342$	610.157	+	651.005i	0.0964722	+	0.102931i
$343$	4578.97	+	4403.03i	0.720819	+	0.693123i
$344$		−	1594.59i		−	0.249926i
$345$	−1893.81	+	1903.35i	−0.295534	+	0.297022i
$346$	1242.70	+	93.1272i	0.193086	+	0.0144698i
$347$	−3000.41	+	3233.67i	−0.464180	+	0.500267i	−0.921146	−	0.389217i	$-0.872746\pi$
$347$	−3000.41	+	3233.67i	−0.464180	+	0.500267i	0.456966	+	0.889484i	$0.348936\pi$
$348$	5660.55	+	8958.69i	0.871946	+	1.37999i
$349$	−1517.20	+	3150.50i	−0.232705	+	0.483217i	−0.984322	−	0.176384i	$-0.943560\pi$
$349$	−1517.20	+	3150.50i	−0.232705	+	0.483217i	0.751617	+	0.659600i	$0.229274\pi$
$350$	−816.523	−	805.930i	−0.124700	−	0.123082i
$351$	−5148.36	−	5071.37i	−0.782904	−	0.771196i
$352$	1549.82	+	233.598i	0.234676	+	0.0353717i
$353$	4104.36	−	2798.30i	0.618846	−	0.421922i	−0.212903	−	0.977073i	$-0.568292\pi$
$353$	4104.36	−	2798.30i	0.618846	−	0.421922i	0.831750	+	0.555151i	$0.187340\pi$
$354$	−801.626	−	212.639i	−0.120356	−	0.0319255i
$355$	−3880.17	−	4181.83i	−0.580108	−	0.625208i
$356$	5128.16	+	6430.50i	0.763460	+	0.957348i
$357$	8179.76	−	73.9447i	1.21266	−	0.0109624i
$358$	−350.057	+	438.958i	−0.0516791	+	0.0648035i
$359$	3152.26	−	236.229i	0.463426	−	0.0347290i	0.159028	−	0.987274i	$-0.449164\pi$
$359$	3152.26	−	236.229i	0.463426	−	0.0347290i	0.304398	+	0.952545i	$0.401545\pi$
$360$	2128.45	−	1038.21i	0.311609	−	0.151996i
$361$	2473.90	−	4284.92i	0.360680	−	0.624715i
$362$	−207.359	−	359.156i	−0.0301064	−	0.0521459i
$363$	−3002.82	−	560.357i	−0.434179	−	0.0810224i
$364$	5685.58	−	4957.81i	0.818696	−	0.713901i
$365$	−4996.51	−	1140.42i	−0.716518	−	0.163541i
$366$	118.861	−	1079.28i	0.0169754	−	0.154138i
$367$	5926.58	−	2326.01i	0.842956	−	0.330836i	0.0957310	−	0.995407i	$-0.469481\pi$
$367$	5926.58	−	2326.01i	0.842956	−	0.330836i	0.747225	+	0.664572i	$0.231386\pi$
$368$	1639.35	−	643.397i	0.232220	−	0.0911396i
$369$	−10842.9	−	6187.77i	−1.52970	−	0.872961i
$370$	−620.477	−	141.620i	−0.0871812	−	0.0198985i
$371$	239.419	+	5446.71i	0.0335041	+	0.762207i
$372$	−290.361	+	1555.97i	−0.0404691	+	0.216864i
$373$	2671.45	+	4627.08i	0.370837	+	0.642309i	0.989695	−	0.143194i	$-0.0457374\pi$
$373$	2671.45	+	4627.08i	0.370837	+	0.642309i	−0.618857	+	0.785503i	$0.712404\pi$
$374$	352.359	−	610.304i	0.0487168	−	0.0843799i
$375$	4821.17	−	5630.84i	0.663904	−	0.775401i
$376$	894.332	−	67.0209i	0.122664	−	0.00919239i
$377$	8283.02	−	10386.6i	1.13156	−	1.41893i
$378$	404.692	+	678.724i	0.0550665	+	0.0923540i
$379$	471.925	+	591.775i	0.0639608	+	0.0802043i	0.812783	−	0.582567i	$-0.197952\pi$
$379$	471.925	+	591.775i	0.0639608	+	0.0802043i	−0.748822	+	0.662771i	$0.769380\pi$
$380$	−10595.4	−	11419.1i	−1.43035	−	1.54155i
$381$	2783.31	−	10492.8i	0.374261	−	1.41092i
$382$	−529.010	+	360.673i	−0.0708548	+	0.0483080i
$383$	−813.016	−	122.542i	−0.108468	−	0.0163489i	0.0945840	−	0.995517i	$-0.469848\pi$
$383$	−813.016	−	122.542i	−0.108468	−	0.0163489i	−0.203052	+	0.979168i	$0.565086\pi$
$384$	−3141.02	+	125.428i	−0.417421	+	0.0166686i
$385$	3079.44	+	8619.61i	0.407644	+	1.14103i
$386$	−566.443	+	1176.23i	−0.0746922	+	0.155100i
$387$	1370.55	+	8793.15i	0.180024	+	1.15499i
$388$	−1155.41	+	1245.23i	−0.151178	+	0.162931i
$389$	−2861.94	−	214.473i	−0.373024	−	0.0279542i	−0.113100	−	0.993584i	$-0.536078\pi$
$389$	−2861.94	−	214.473i	−0.373024	−	0.0279542i	−0.259923	+	0.965629i	$0.583697\pi$
$390$	−1046.14	−	1040.90i	−0.135830	−	0.135149i
$391$		−	2422.71i		−	0.313354i
$392$	−1485.53	+	739.444i	−0.191405	+	0.0952743i
$393$	−3245.66	+	7490.39i	−0.416595	+	0.961425i
$394$	301.684	−	768.678i	0.0385752	−	0.0982879i
$395$	−143.245	+	1911.47i	−0.0182466	+	0.243484i
$396$	−5820.10	+	29.2306i	−0.738564	+	0.00370932i
$397$	−7369.60	+	10809.2i	−0.931661	+	1.36650i	−0.00124201	+	0.999999i	$0.500395\pi$
$397$	−7369.60	+	10809.2i	−0.931661	+	1.36650i	−0.930419	+	0.366497i	$0.880557\pi$
$398$	−257.767	−	124.134i	−0.0324641	−	0.0156339i
$399$	7042.79	−	7729.29i	0.883660	−	0.969796i
$400$	−11339.3	+	5460.70i	−1.41741	+	0.682588i
$401$	−1239.19	+	8221.46i	−0.154319	+	1.02384i	0.768845	+	0.639435i	$0.220832\pi$
$401$	−1239.19	+	8221.46i	−0.154319	+	1.02384i	−0.923164	+	0.384406i	$0.874406\pi$
$402$	382.657	−	73.3984i	0.0474756	−	0.00910642i
$403$	1962.13	−	295.743i	0.242532	−	0.0365559i
$404$	−6808.97	+	6317.80i	−0.838512	+	0.778025i
$405$	−10844.7	+	7554.48i	−1.33057	+	0.926877i
$406$	−1163.16	+	870.240i	−0.142184	+	0.106378i
$407$	2460.10	+	1961.87i	0.299614	+	0.238934i
$408$	−700.679	+	2018.67i	−0.0850215	+	0.244949i
$409$	2354.98	−	7634.66i	0.284710	−	0.923006i	−0.694385	−	0.719603i	$-0.744324\pi$
$409$	2354.98	−	7634.66i	0.284710	−	0.923006i	0.979095	−	0.203403i	$-0.0652002\pi$
$410$	−2207.89	−	1274.72i	−0.265950	−	0.153547i
$411$	364.746	+	3165.74i	0.0437752	+	0.379938i
$412$	5143.75	−	1174.03i	0.615083	−	0.140389i
$413$	−1744.60	+	9561.76i	−0.207860	+	1.13923i
$414$	202.094	−	118.036i	0.0239912	−	0.0140124i
$415$	−7805.96	+	2407.82i	−0.923324	+	0.284808i
$416$	1081.97	+	2756.83i	0.127520	+	0.324915i
$417$	−438.758	+	12570.8i	−0.0515254	+	1.47625i
$418$	−265.530	−	860.828i	−0.0310706	−	0.100728i
$419$	1920.25	−	8413.15i	0.223891	−	0.980929i	−0.730627	−	0.682776i	$-0.760772\pi$
$419$	1920.25	−	8413.15i	0.223891	−	0.980929i	0.954518	−	0.298153i	$-0.0963706\pi$
$420$	−7005.84	−	11885.0i	−0.813929	−	1.38079i
$421$	−2929.31	−	12834.1i	−0.339111	−	1.48574i	−0.800925	−	0.598764i	$-0.795659\pi$
$421$	−2929.31	−	12834.1i	−0.339111	−	1.48574i	0.461815	−	0.886977i	$-0.347199\pi$
$422$	355.691	−	205.358i	0.0410302	−	0.0236888i
$423$	−4874.07	+	1138.26i	−0.560249	+	0.130837i
$424$	−1360.90	−	419.781i	−0.155875	−	0.0480811i
$425$	1293.87	+	17265.5i	0.147675	+	1.97059i
$426$	233.453	+	439.042i	0.0265512	+	0.0499335i
$427$	−12719.1	−	392.780i	−1.44150	−	0.0445151i
$428$	−2452.28	+	1955.63i	−0.276952	+	0.220862i
$429$	2427.12	+	6880.83i	0.273152	+	0.774382i
$430$	270.862	+	1797.05i	0.0303770	+	0.201539i
$431$	−7951.76	−	11663.1i	−0.888684	−	1.30346i	−0.952199	−	0.305479i	$-0.901183\pi$
$431$	−7951.76	−	11663.1i	−0.888684	−	1.30346i	0.0635146	−	0.997981i	$-0.479769\pi$
$432$	8505.21	−	1675.74i	0.947239	−	0.186629i
$433$	2570.16	+	5336.99i	0.285251	+	0.592331i	0.993526	−	0.113607i	$-0.0362403\pi$
$433$	2570.16	+	5336.99i	0.285251	+	0.592331i	−0.708274	+	0.705937i	$0.750526\pi$
$434$	−215.767	−	22.8856i	−0.0238644	−	0.00253121i
$435$	−15894.4	−	18376.1i	−1.75191	−	2.02544i
$436$	−8430.60	−	5747.89i	−0.926038	−	0.631362i
$437$	−2270.24	−	2106.48i	−0.248513	−	0.230587i
$438$	395.477	+	207.747i	0.0431429	+	0.0226633i
$439$	−122.752	−	48.1768i	−0.0133455	−	0.00523771i	0.358659	−	0.933469i	$-0.383234\pi$
$439$	−122.752	−	48.1768i	−0.0133455	−	0.00523771i	−0.372004	+	0.928231i	$0.621329\pi$
$440$	−2391.01			−0.259061
$441$	7556.23	−	5354.39i	0.815920	−	0.578165i
$442$	1331.60			0.143298
$443$	8415.92	+	3303.01i	0.902602	+	0.354245i	0.770834	−	0.637036i	$-0.219840\pi$
$443$	8415.92	+	3303.01i	0.902602	+	0.354245i	0.131767	+	0.991281i	$0.457935\pi$
$444$	−4198.68	−	2205.60i	−0.448785	−	0.235750i
$445$	−13823.5	−	12826.4i	−1.47258	−	1.36635i
$446$	414.172	+	282.378i	0.0439723	+	0.0299798i
$447$	11048.5	+	12773.6i	1.16908	+	1.35161i
$448$	1046.02	+	8768.74i	0.110312	+	0.924741i
$449$	4736.96	+	9836.41i	0.497887	+	1.03387i	0.986861	+	0.161574i	$0.0516571\pi$
$449$	4736.96	+	9836.41i	0.497887	+	1.03387i	−0.488974	+	0.872298i	$0.662629\pi$
$450$	−1377.19	+	949.118i	−0.144270	+	0.0994264i
$451$	7100.49	+	10414.5i	0.741351	+	1.08736i
$452$	−1135.62	−	7534.36i	−0.118175	−	0.784041i
$453$	−665.184	−	1885.78i	−0.0689913	−	0.195589i
$454$	−1077.27	+	859.093i	−0.111363	+	0.0888088i
$455$	−11195.7	+	13182.8i	−1.15355	+	1.35828i
$456$	1282.41	+	2411.76i	0.131698	+	0.247678i
$457$	295.389	+	3941.69i	0.0302357	+	0.403467i	0.991703	+	0.128548i	$0.0410318\pi$
$457$	295.389	+	3941.69i	0.0302357	+	0.403467i	−0.961468	+	0.274918i	$0.911349\pi$
$458$	−1636.47	−	504.784i	−0.166959	−	0.0515000i
$459$	2128.75	−	11733.9i	0.216474	−	1.19323i
$460$	−3538.62	+	2043.02i	−0.358671	+	0.207079i
$461$	−1744.77	−	7644.33i	−0.176273	−	0.772304i	−0.983330	−	0.181830i	$-0.941798\pi$
$461$	−1744.77	−	7644.33i	−0.176273	−	0.772304i	0.807057	−	0.590474i	$-0.201059\pi$
$462$	−66.8121	−	795.037i	−0.00672810	−	0.0800616i
$463$	1412.24	−	6187.44i	0.141755	−	0.621068i	−0.853272	−	0.521465i	$-0.825386\pi$
$463$	1412.24	−	6187.44i	0.141755	−	0.621068i	0.995027	−	0.0996030i	$-0.0317573\pi$
$464$	4697.20	+	15227.9i	0.469961	+	1.52358i
$465$	126.586	−	3626.80i	0.0126243	−	0.361697i
$466$	−64.6292	−	164.673i	−0.00642466	−	0.0163698i
$467$	1219.35	−	376.119i	0.120824	−	0.0372692i	−0.233754	−	0.972296i	$-0.575101\pi$
$467$	1219.35	−	376.119i	0.120824	−	0.0372692i	0.354577	+	0.935027i	$0.384625\pi$
$468$	−5546.52	−	9496.39i	−0.547838	−	0.937972i
$469$	−1210.62	−	4402.93i	−0.119193	−	0.433493i
$470$	−996.500	+	227.445i	−0.0977981	+	0.0223218i
$471$	1507.25	+	13081.9i	0.147453	+	1.27979i
$472$	−2198.81	−	1269.48i	−0.214425	−	0.123798i
$473$	2648.42	−	8585.98i	0.257452	−	0.834638i
$474$	54.7870	−	157.843i	0.00530897	−	0.0152952i
$475$	17304.0	+	13799.4i	1.67149	+	1.33297i
$476$	12045.1	+	3143.33i	1.15984	+	0.302677i
$477$	7865.29	+	1145.13i	0.754983	+	0.109920i
$478$	−37.1911	+	34.5083i	−0.00355875	+	0.00330203i
$479$	−1127.14	+	169.888i	−0.107516	+	0.0162054i	−0.202580	−	0.979266i	$-0.564933\pi$
$479$	−1127.14	+	169.888i	−0.107516	+	0.0162054i	0.0950639	+	0.995471i	$0.469694\pi$
$480$	5319.31	−	1020.31i	0.505817	−	0.0970221i
$481$	−886.152	+	5879.23i	−0.0840022	+	0.557318i
$482$	310.784	−	149.666i	0.0293689	−	0.0141433i
$483$	−1565.52	−	2252.18i	−0.147481	−	0.212169i
$484$	−4188.22	−	2016.94i	−0.393334	−	0.189420i
$485$	2193.93	−	3217.91i	0.205405	−	0.301274i
$486$	1082.52	−	394.113i	0.101037	−	0.0367846i
$487$	−1021.87	+	13635.9i	−0.0950831	+	1.26880i	0.721845	+	0.692055i	$0.243295\pi$
$487$	−1021.87	+	13635.9i	−0.0950831	+	1.26880i	−0.816928	+	0.576740i	$0.804325\pi$
$488$	1214.42	−	3094.29i	0.112652	−	0.287033i
$489$	−784.068	+	1809.49i	−0.0725088	+	0.167337i
$490$	1548.55	−	1085.67i	0.142768	−	0.100093i
$491$		−	11454.5i		−	1.05282i	−0.850231	−	0.526410i	$-0.823538\pi$
$491$		−	11454.5i		−	1.05282i	0.850231	−	0.526410i	$-0.176462\pi$
$492$	−13467.7	−	13400.3i	−1.23409	−	1.22791i
$493$	21861.6	+	1638.30i	1.99715	+	0.149666i
$494$	1157.79	−	1247.80i	0.105448	−	0.113646i
$495$	13184.9	−	2055.08i	1.19720	−	0.186604i
$496$	−1032.75	+	2144.54i	−0.0934920	+	0.194138i
$497$	4913.99	−	3132.60i	0.443506	−	0.282729i
$498$	711.475	−	28.4108i	0.0640200	−	0.00255647i
$499$	−17602.4	−	2653.13i	−1.57914	−	0.238017i	−0.699844	−	0.714296i	$-0.746747\pi$
$499$	−17602.4	−	2653.13i	−1.57914	−	0.238017i	−0.879294	+	0.476279i	$0.841985\pi$
$500$	9320.67	−	6354.73i	0.833666	−	0.568384i
$501$	−2019.16	+	7612.02i	−0.180059	+	0.678802i
$502$	850.887	+	917.038i	0.0756513	+	0.0815327i
$503$	−705.338	−	884.466i	−0.0625238	−	0.0784024i	0.749586	−	0.661907i	$-0.230253\pi$
$503$	−705.338	−	884.466i	−0.0625238	−	0.0784024i	−0.812110	+	0.583504i	$0.801681\pi$
$504$	653.076	+	2329.35i	0.0577189	+	0.205868i
$505$	13277.9	−	16649.9i	1.17001	−	1.46715i
$506$	−235.636	+	17.6585i	−0.0207022	+	0.00155141i
$507$	−1541.97	+	1800.93i	−0.135072	+	0.157756i
$508$	8260.08	−	14306.9i	0.721421	−	1.24954i
$509$	−10834.9	−	18766.6i	−0.943513	−	1.63421i	−0.758702	−	0.651438i	$-0.774166\pi$
$509$	−10834.9	−	18766.6i	−0.943513	−	1.63421i	−0.184810	−	0.982774i	$-0.559167\pi$
$510$	446.745	−	2394.00i	0.0387886	−	0.207859i
$511$	2062.22	−	4812.12i	0.178527	−	0.416587i
$512$	−5794.91	−	1322.65i	−0.500198	−	0.114167i
$513$	−9144.61	−	12197.1i	−0.787026	−	1.04974i
$514$	−807.854	+	317.059i	−0.0693248	+	0.0272080i
$515$	−11260.3	+	4419.34i	−0.963473	+	0.378135i
$516$	−1482.53	+	13461.6i	−0.126482	+	1.14848i
$517$	4926.79	+	1124.51i	0.419111	+	0.0956593i
$518$	256.091	−	597.580i	0.0217220	−	0.0506876i
$519$	−20930.3	−	3905.82i	−1.77021	−	0.330340i
$520$	−2258.96	−	3912.64i	−0.190504	−	0.329962i
$521$	8883.34	−	15386.4i	0.746999	−	1.29384i	−0.202256	−	0.979333i	$-0.564827\pi$
$521$	8883.34	−	15386.4i	0.746999	−	1.29384i	0.949255	−	0.314507i	$-0.101839\pi$
$522$	928.451	+	1903.43i	0.0778490	+	0.159600i
$523$	−2743.26	+	205.579i	−0.229358	+	0.0171880i	−0.188913	−	0.981994i	$-0.560496\pi$
$523$	−2743.26	+	205.579i	−0.229358	+	0.0171880i	−0.0404447	+	0.999182i	$0.512877\pi$
$524$	−7745.60	+	9712.68i	−0.645741	+	0.809734i
$525$	12359.5	+	15214.2i	1.02746	+	1.26476i
$526$	−623.823	−	782.249i	−0.0517110	−	0.0648435i
$527$	2227.22	+	2400.37i	0.184097	+	0.198410i
$528$	−8459.77	−	2244.03i	−0.697281	−	0.184960i
$529$	9381.65	−	6396.30i	0.771074	−	0.525709i
$530$	1604.99	+	241.914i	0.131541	+	0.0198266i
$531$	13216.2	+	5110.52i	1.08010	+	0.417661i
$532$	13418.4	−	8554.03i	1.09354	−	0.697113i
$533$	−10333.9	+	21458.6i	−0.839797	+	1.74386i
$534$	878.003	+	1389.58i	0.0711515	+	0.112608i
$535$	4891.35	−	5271.62i	0.395274	−	0.426004i
$536$	1189.49	+	89.1398i	0.0958546	+	0.00718331i
$537$	6765.97	−	6800.04i	0.543712	−	0.546449i
$538$			130.442i			0.0104531i
$539$	−9226.91	+	1514.20i	−0.737349	+	0.121004i
$540$	−18933.8	+	6785.74i	−1.50885	+	0.540762i
$541$	−5060.73	+	12894.5i	−0.402177	+	1.02473i	0.576091	+	0.817386i	$0.304577\pi$
$541$	−5060.73	+	12894.5i	−0.402177	+	1.02473i	−0.978268	+	0.207345i	$0.933518\pi$
$542$	−11.8573	+	158.225i	−0.000939696	+	0.0125394i
$543$	2849.80	+	6487.32i	0.225224	+	0.512702i
$544$	−2753.04	+	4037.96i	−0.216977	+	0.318247i
$545$	21077.3	+	10150.3i	1.65661	+	0.797782i
$546$	1237.87	−	860.462i	0.0970258	−	0.0674439i
$547$	−9067.68	+	4366.77i	−0.708786	+	0.341334i	−0.753302	−	0.657675i	$-0.771540\pi$
$547$	−9067.68	+	4366.77i	−0.708786	+	0.341334i	0.0445153	+	0.999009i	$0.485826\pi$
$548$	−722.780	+	4795.33i	−0.0563424	+	0.373808i
$549$	−4037.21	+	18106.9i	−0.313850	+	1.40762i
$550$	1669.84	−	251.688i	0.129458	−	0.0195127i
$551$	20543.2	−	19061.3i	1.58833	−	1.47376i
$552$	691.606	−	187.178i	0.0533274	−	0.0144326i
$553$	−1894.66	−	494.438i	−0.145695	−	0.0380210i
$554$	693.057	+	552.695i	0.0531502	+	0.0423858i
$555$	10272.6	+	3565.60i	0.785670	+	0.272705i
$556$	−5642.18	+	18291.5i	−0.430363	+	1.39520i
$557$	21167.4	+	12221.0i	1.61022	+	0.929658i	0.989319	+	0.145765i	$0.0465644\pi$
$557$	21167.4	+	12221.0i	1.61022	+	0.929658i	0.620896	+	0.783893i	$0.286769\pi$
$558$	−91.7187	+	302.735i	−0.00695836	+	0.0229673i
$559$	16552.2	−	3777.94i	1.25239	−	0.285850i
$560$	−5500.35	−	20004.3i	−0.415057	−	1.50953i
$561$	−7125.54	+	9705.68i	−0.536258	+	0.730435i
$562$	−1441.02	+	444.497i	−0.108160	+	0.0333629i
$563$	−3302.37	−	8414.30i	−0.247208	−	0.629876i	0.752375	−	0.658735i	$-0.228908\pi$
$563$	−3302.37	−	8414.30i	−0.247208	−	0.629876i	−0.999584	+	0.0288583i	$0.990813\pi$
$564$	−7612.31	−	265.692i	−0.568326	−	0.0198362i
$565$	5149.18	+	16693.2i	0.383412	+	1.24299i
$566$	−589.261	+	2581.72i	−0.0437606	+	0.191728i
$567$	−5603.39	−	12283.6i	−0.415027	−	0.909809i
$568$	338.740	+	1484.12i	0.0250233	+	0.109634i
$569$	4099.82	−	2367.03i	0.302062	−	0.174396i	−0.341307	−	0.939952i	$-0.610869\pi$
$569$	4099.82	−	2367.03i	0.302062	−	0.174396i	0.643369	+	0.765556i	$0.277536\pi$
$570$	−1854.91	−	2500.15i	−0.136304	−	0.183719i
$571$	10214.1	+	3150.65i	0.748597	+	0.230912i	0.645500	−	0.763760i	$-0.276649\pi$
$571$	10214.1	+	3150.65i	0.748597	+	0.230912i	0.103096	+	0.994671i	$0.467125\pi$
$572$	829.773	+	11072.5i	0.0606548	+	0.809382i
$573$	9658.68	−	5135.83i	0.704184	−	0.374437i
$574$	1685.87	−	1985.08i	0.122590	−	0.144348i
$575$	4538.90	−	3619.65i	0.329191	−	0.262521i
$576$	12842.9	+	897.605i	0.929031	+	0.0649309i
$577$	−396.208	−	2628.67i	−0.0285864	−	0.189659i	0.969980	−	0.243185i	$-0.0781921\pi$
$577$	−396.208	−	2628.67i	−0.0285864	−	0.189659i	−0.998566	+	0.0535261i	$0.982954\pi$
$578$	396.153	+	581.050i	0.0285083	+	0.0418140i
$579$	11819.8	−	18916.3i	0.848381	−	1.35775i
$580$	−16042.5	−	33312.7i	−1.14850	−	2.38489i
$581$	−988.442	−	8286.09i	−0.0705808	−	0.591678i
$582$	−256.758	+	222.083i	−0.0182869	+	0.0158172i
$583$	−6630.47	−	4520.58i	−0.471022	−	0.321138i
$584$	1002.52	+	930.200i	0.0710351	+	0.0659109i
$585$	15819.7	+	19634.1i	1.11806	+	1.38764i
$586$	−288.696	−	113.305i	−0.0203514	−	0.00798735i
$587$	−20847.9			−1.46590			−0.732951	−	0.680281i	$-0.761858\pi$
$587$	−20847.9			−1.46590			−0.732951	+	0.680281i	$0.761858\pi$
$588$	13228.4	−	4861.28i	0.927775	−	0.340945i
$589$	4185.82			0.292824
$590$	2693.63	+	1057.17i	0.187958	+	0.0737680i
$591$	−6561.13	+	12490.1i	−0.456665	+	0.869330i
$592$	−5228.19	−	4851.05i	−0.362968	−	0.336786i
$593$	−21722.3	−	14810.0i	−1.50426	−	1.02559i	−0.985308	−	0.170785i	$-0.945370\pi$
$593$	−21722.3	−	14810.0i	−1.50426	−	1.02559i	−0.518952	−	0.854803i	$-0.673678\pi$
$594$	−1156.77	−	121.519i	−0.0799041	−	0.00839394i
$595$	−28381.8	−	3010.35i	−1.95553	−	0.207416i
$596$	11151.5	+	23156.3i	0.766414	+	1.59148i
$597$	4145.45	+	2590.26i	0.284191	+	0.177575i
$598$	−251.519	−	368.911i	−0.0171996	−	0.0252272i
$599$	−4162.63	−	27617.2i	−0.283940	−	1.88382i	−0.442952	−	0.896545i	$-0.646069\pi$
$599$	−4162.63	−	27617.2i	−0.283940	−	1.88382i	0.159012	−	0.987277i	$-0.449169\pi$
$600$	−4828.79	+	1703.29i	−0.328558	+	0.115894i
$601$	−10898.3	+	8691.11i	−0.739686	+	0.589880i	−0.919161	−	0.393883i	$-0.871132\pi$
$601$	−10898.3	+	8691.11i	−0.739686	+	0.589880i	0.179475	+	0.983763i	$0.442560\pi$
$602$	−1855.61	−	57.3034i	−0.125630	−	0.00387959i
$603$	−6635.89	+	530.819i	−0.448150	+	0.0358484i
$604$	−227.410	−	3034.58i	−0.0153198	−	0.204429i
$605$	10184.4	+	3141.48i	0.684389	+	0.211106i
$606$	−1490.78	+	1106.04i	−0.0999321	+	0.0741416i
$607$	−6202.40	+	3580.96i	−0.414741	+	0.239451i	−0.692825	−	0.721106i	$-0.743634\pi$
$607$	−6202.40	+	3580.96i	−0.414741	+	0.239451i	0.278084	+	0.960557i	$0.410301\pi$
$608$	1390.16	+	6090.68i	0.0927276	+	0.406266i
$609$	21381.5	−	12603.7i	1.42269	−	0.838631i
$610$	−843.007	+	3693.46i	−0.0559547	+	0.245154i
$611$	2814.57	+	9124.60i	0.186359	+	0.604160i
$612$	7791.98	−	16390.3i	0.514660	−	1.08258i
$613$	−2799.55	−	7133.13i	−0.184458	−	0.469991i	0.808495	−	0.588504i	$-0.200283\pi$
$613$	−2799.55	−	7133.13i	−0.184458	−	0.469991i	−0.992953	+	0.118512i	$0.962187\pi$
$614$	1169.44	−	360.723i	0.0768641	−	0.0237094i
$615$	35112.0	+	25777.9i	2.30220	+	1.69019i
$616$	438.412	−	2402.84i	0.0286756	−	0.157164i
$617$	−255.218	+	58.2520i	−0.0166527	+	0.00380087i	−0.230839	−	0.972992i	$-0.574147\pi$
$617$	−255.218	+	58.2520i	−0.0166527	+	0.00380087i	0.214186	+	0.976793i	$0.431290\pi$
$618$	1047.46	−	120.685i	0.0681799	−	0.00785546i
$619$	−3455.35	−	1994.94i	−0.224365	−	0.129537i	0.383605	−	0.923497i	$-0.374683\pi$
$619$	−3455.35	−	1994.94i	−0.224365	−	0.129537i	−0.607970	+	0.793960i	$0.708016\pi$
$620$	1627.82	−	5277.27i	0.105443	−	0.341839i
$621$	−3652.89	+	1626.61i	−0.236047	+	0.105110i
$622$	−1988.09	−	1585.45i	−0.128160	−	0.102204i
$623$	15424.5	−	11540.1i	0.991926	−	0.742126i
$624$	−4320.44	−	15963.7i	−0.277173	−	1.02413i
$625$	−295.326	+	274.023i	−0.0189009	+	0.0175375i
$626$	−710.669	+	107.116i	−0.0453738	+	0.00683901i
$627$	2899.43	+	15115.9i	0.184676	+	0.962795i
$628$	−2986.77	+	19815.9i	−0.189785	+	1.25914i
$629$	−8839.89	+	4257.07i	−0.560365	+	0.269857i
$630$	−1131.67	−	2514.17i	−0.0715662	−	0.158995i
$631$	18903.1	+	9103.27i	1.19259	+	0.574319i	0.921554	−	0.388251i	$-0.126921\pi$
$631$	18903.1	+	9103.27i	1.19259	+	0.574319i	0.271033	+	0.962570i	$0.412635\pi$
$632$	288.138	−	422.621i	0.0181353	−	0.0265996i
$633$	−6424.73	+	2822.31i	−0.403413	+	0.177214i
$634$	33.2422	−	443.586i	0.00208236	−	0.0277872i
$635$	−13837.7	+	35258.0i	−0.864778	+	2.20342i
$636$	11098.5	+	4809.08i	0.691955	+	0.299831i
$637$	−11195.2	−	13668.3i	−0.696341	−	0.850171i
$638$		−	2138.23i		−	0.132685i
$639$	−3143.54	−	7892.82i	−0.194611	−	0.488631i
$640$	10937.3	+	819.639i	0.675525	+	0.0506236i
$641$	−13952.8	+	15037.6i	−0.859757	+	0.926598i	−0.997962	−	0.0638058i	$-0.979676\pi$
$641$	−13952.8	+	15037.6i	−0.859757	+	0.926598i	0.138205	+	0.990404i	$0.455867\pi$
$642$	−529.916	+	334.827i	−0.0325765	+	0.0205835i
$643$	−7340.55	+	15242.8i	−0.450207	+	0.934865i	0.545125	+	0.838355i	$0.316482\pi$
$643$	−7340.55	+	15242.8i	−0.450207	+	0.934865i	−0.995332	+	0.0965099i	$0.969232\pi$
$644$	−1404.29	−	3930.73i	−0.0859269	−	0.240516i
$645$	−1238.93	−	31025.7i	−0.0756320	−	1.89401i
$646$	2777.61	+	418.657i	0.169170	+	0.0254982i
$647$	−24032.6	+	16385.2i	−1.46031	+	0.995623i	−0.466502	+	0.884520i	$0.654486\pi$
$647$	−24032.6	+	16385.2i	−1.46031	+	0.995623i	−0.993809	+	0.111102i	$0.964562\pi$
$648$	3514.13	−	298.872i	0.213037	−	0.0181185i
$649$	−9730.92	−	10487.4i	−0.588555	−	0.634311i
$650$	1989.48	+	2494.73i	0.120052	+	0.150541i
$651$	3621.54	+	792.219i	0.218033	+	0.0476951i
$652$	−1871.14	+	2346.34i	−0.112392	+	0.140935i
$653$	111.166	−	8.33075i	0.00666197	−	0.000499245i	−0.0713987	−	0.997448i	$-0.522746\pi$
$653$	111.166	−	8.33075i	0.00666197	−	0.000499245i	0.0780607	+	0.996949i	$0.475127\pi$
$654$	−1548.95	−	1326.22i	−0.0926128	−	0.0792959i
$655$	14241.3	−	24666.6i	0.849545	−	1.47146i
$656$	−14285.0	−	24742.3i	−0.850206	−	1.47260i
$657$	−6327.76	−	4267.80i	−0.375753	−	0.253429i
$658$	−45.8528	−	1043.13i	−0.00271661	−	0.0618019i
$659$	7616.93	+	1738.51i	0.450248	+	0.102766i	0.441631	−	0.897197i	$-0.354400\pi$
$659$	7616.93	+	1738.51i	0.450248	+	0.102766i	0.00861687	+	0.999963i	$0.497257\pi$
$660$	20185.0	+	2222.99i	1.19045	+	0.131105i
$661$	−20924.1	+	8212.10i	−1.23124	+	0.483228i	−0.889660	−	0.456623i	$-0.849059\pi$
$661$	−20924.1	+	8212.10i	−1.23124	+	0.483228i	−0.341585	+	0.939851i	$0.610964\pi$
$662$	−661.366	+	259.567i	−0.0388289	+	0.0152392i
$663$	−22614.4	−	2490.54i	−1.32469	−	0.145889i
$664$	2125.19	+	485.062i	0.124207	+	0.0283495i
$665$	−27498.1	+	23978.2i	−1.60350	+	1.39825i
$666$	−785.795	−	529.985i	−0.0457191	−	0.0308356i
$667$	−3675.44	−	6366.05i	−0.213364	−	0.369557i
$668$	−5992.30	+	10379.0i	−0.347079	+	0.601159i
$669$	−6505.69	−	5570.22i	−0.375971	−	0.321909i
$670$	−1355.66	+	101.592i	−0.0781696	+	0.00585800i
$671$	11678.2	−	14644.0i	0.671883	−	0.842514i
$672$	50.0155	+	5532.72i	0.00287112	+	0.317603i
$673$	13149.3	+	16488.6i	0.753145	+	0.944414i	0.999695	−	0.0247162i	$-0.00786821\pi$
$673$	13149.3	+	16488.6i	0.753145	+	0.944414i	−0.246549	+	0.969130i	$0.579297\pi$
$674$	761.332	+	820.521i	0.0435095	+	0.0468921i
$675$	25163.8	−	13542.9i	1.43489	−	0.772249i
$676$	−2981.07	+	2032.46i	−0.169610	+	0.115638i
$677$	23396.3	+	3526.43i	1.32820	+	0.200195i	0.774529	−	0.632538i	$-0.217987\pi$
$677$	23396.3	+	3526.43i	1.32820	+	0.200195i	0.553675	+	0.832733i	$0.313225\pi$
$678$	−60.7573	−	1521.51i	−0.00344155	−	0.0861846i
$679$	2831.56	+	2794.82i	0.160037	+	0.157961i
$680$	3234.82	−	6717.18i	0.182426	−	0.378812i
$681$	19901.9	−	12575.0i	1.11988	−	0.707599i
$682$	217.230	−	234.118i	0.0121967	−	0.0131449i
$683$	3940.78	+	295.320i	0.220775	+	0.0165448i	0.184658	−	0.982803i	$-0.440882\pi$
$683$	3940.78	+	295.320i	0.220775	+	0.0165448i	0.0361169	+	0.999348i	$0.488501\pi$
$684$	−8583.90	−	21552.5i	−0.479845	−	1.20480i
$685$		−	11118.6i		−	0.620174i
$686$	807.100	+	1755.28i	0.0449201	+	0.0976921i
$687$	26847.8	+	11633.4i	1.49099	+	0.646059i
$688$	−7440.48	+	18958.0i	−0.412305	+	1.05054i
$689$	1133.16	−	15121.0i	0.0626562	−	0.836088i
$690$	−747.624	+	328.422i	−0.0412486	+	0.0181200i
$691$	10913.7	−	16007.4i	0.600833	−	0.881259i	−0.398523	−	0.917158i	$-0.630477\pi$
$691$	10913.7	−	16007.4i	0.600833	−	0.881259i	0.999355	+	0.0358989i	$0.0114294\pi$
$692$	−29192.9	−	14058.6i	−1.60368	−	0.772292i
$693$	−352.322	+	13626.9i	−0.0193126	+	0.746962i
$694$	−1208.72	+	582.088i	−0.0661128	+	0.0318383i
$695$	6541.05	−	43397.1i	0.357002	−	2.36855i
$696$	1221.34	+	6367.37i	0.0665155	+	0.346774i
$697$	−38864.4	+	5857.87i	−2.11204	+	0.318339i
$698$	−779.576	+	723.341i	−0.0422742	+	0.0392247i
$699$	789.596	+	2917.49i	0.0427257	+	0.157868i
$700$	12107.0	+	27262.6i	0.653717	+	1.47204i
$701$	−13162.4	−	10496.6i	−0.709180	−	0.565552i	0.201087	−	0.979573i	$-0.435553\pi$
$701$	−13162.4	−	10496.6i	−0.709180	−	0.565552i	−0.910267	+	0.414021i	$0.864124\pi$
$702$	−894.037	−	2007.75i	−0.0480673	−	0.107945i
$703$	−3696.88	+	11985.0i	−0.198336	+	0.642990i
$704$	−11257.0	−	6499.22i	−0.602647	−	0.347938i
$705$	17348.8	−	1998.87i	0.926799	−	0.106783i
$706$	1472.87	−	336.174i	0.0785160	−	0.0179208i
$707$	14297.7	+	16396.5i	0.760566	+	0.872211i
$708$	17382.2	+	12761.4i	0.922689	+	0.677403i
$709$	−19887.8	+	6134.58i	−1.05346	+	0.324949i	−0.772662	−	0.634818i	$-0.781075\pi$
$709$	−19887.8	+	6134.58i	−1.05346	+	0.324949i	−0.280797	+	0.959767i	$0.590599\pi$
$710$	−633.846	−	1615.01i	−0.0335040	−	0.0853668i
$711$	−1225.66	+	2578.15i	−0.0646494	+	0.135989i
$712$	1483.23	+	4808.52i	0.0780709	+	0.253100i
$713$	244.318	−	1070.43i	0.0128328	−	0.0562242i
$714$	2323.93	+	887.917i	0.121808	+	0.0465399i
$715$	−5664.83	−	24819.2i	−0.296297	−	1.29816i
$716$	12642.3	−	7299.05i	0.659868	−	0.380975i
$717$	696.153	−	516.489i	0.0362598	−	0.0269019i
$718$	918.661	+	283.369i	0.0477495	+	0.0147288i
$719$	1320.43	+	17620.0i	0.0684894	+	0.913928i	0.920585	+	0.390542i	$0.127712\pi$
$719$	1320.43	+	17620.0i	0.0684894	+	0.913928i	−0.852096	+	0.523386i	$0.824669\pi$
$720$	−30149.5	+	2411.72i	−1.56056	+	0.124833i
$721$	−2376.53	−	12126.4i	−0.122756	−	0.626365i
$722$	1176.46	−	938.200i	0.0606420	−	0.0483603i
$723$	−5557.92	+	1960.48i	−0.285894	+	0.100845i
$724$	1607.12	+	10662.5i	0.0824973	+	0.547334i
$725$	29593.0	+	43405.0i	1.51594	+	2.22348i
$726$	−787.845	−	492.281i	−0.0402750	−	0.0251656i
$727$	−15202.2	−	31567.6i	−0.775540	−	1.61043i	−0.791970	−	0.610560i	$-0.790944\pi$
$727$	−15202.2	−	31567.6i	−0.775540	−	1.61043i	0.0164300	−	0.999865i	$-0.494770\pi$
$728$	4346.20	−	1552.72i	0.221265	−	0.0790491i
$729$	−19121.3	+	4668.50i	−0.971465	+	0.237184i
$730$	−1287.81	−	878.016i	−0.0652933	−	0.0445162i
$731$	20538.0	+	19056.5i	1.03916	+	0.964197i
$732$	−13129.0	+	24993.1i	−0.662928	+	1.26198i
$733$	−25225.1	−	9900.11i	−1.27109	−	0.498866i	−0.368604	−	0.929586i	$-0.620164\pi$
$733$	−25225.1	−	9900.11i	−1.27109	−	0.498866i	−0.902485	+	0.430720i	$0.858260\pi$
$734$	1936.27			0.0973694
$735$	−28329.3	+	15541.4i	−1.42169	+	0.779938i
$736$	1638.70			0.0820695
$737$	6256.68	+	2455.57i	0.312711	+	0.122730i
$738$	−2382.14	−	2956.53i	−0.118818	−	0.147468i
$739$	2313.66	+	2146.77i	0.115168	+	0.106861i	0.735655	−	0.677356i	$-0.236874\pi$
$739$	2313.66	+	2146.77i	0.115168	+	0.106861i	−0.620487	+	0.784217i	$0.713065\pi$
$740$	13672.4	+	9321.68i	0.679199	+	0.463070i
$741$	−21996.4	+	19025.8i	−1.09050	+	0.943224i
$742$	−537.401	+	1568.58i	−0.0265884	+	0.0776070i
$743$	−5049.09	−	10484.5i	−0.249304	−	0.517686i	0.738334	−	0.674435i	$-0.235613\pi$
$743$	−5049.09	−	10484.5i	−0.249304	−	0.517686i	−0.987638	+	0.156749i	$0.949899\pi$
$744$	−513.155	+	821.253i	−0.0252865	+	0.0404685i
$745$	−33194.6	−	48687.5i	−1.63242	−	2.39433i
$746$	242.181	+	1606.76i	0.0118859	+	0.0788577i
$747$	−12136.0	−	848.198i	−0.594423	−	0.0415448i
$748$	−14325.7	+	11424.3i	−0.700266	+	0.558443i
$749$	4400.83	+	5882.15i	0.214690	+	0.286955i
$750$	1990.53	−	1058.43i	0.0969117	−	0.0515311i
$751$	−114.508	−	1528.00i	−0.00556384	−	0.0742443i	0.993731	−	0.111800i	$-0.0356617\pi$
$751$	−114.508	−	1528.00i	−0.00556384	−	0.0742443i	−0.999295	+	0.0375562i	$0.988043\pi$
$752$	−10945.4	−	3376.21i	−0.530769	−	0.163721i
$753$	−12735.3	−	17165.4i	−0.616336	−	0.830731i
$754$	3499.00	−	2020.15i	0.169000	−	0.0975721i
$755$	1552.52	+	6802.04i	0.0748371	+	0.327883i
$756$	−3347.64	−	20271.7i	−0.161048	−	0.975230i
$757$	−2359.27	+	10336.6i	−0.113275	+	0.496290i	0.886182	+	0.463337i	$0.153348\pi$
$757$	−2359.27	+	10336.6i	−0.113275	+	0.496290i	−0.999457	+	0.0329527i	$0.989509\pi$
$758$	67.8513	+	219.969i	0.00325128	+	0.0105404i
$759$	4034.79	+	140.826i	0.192956	+	0.00673474i
$760$	−3481.87	−	8871.65i	−0.166185	−	0.423433i
$761$	−12590.1	+	3883.53i	−0.599724	+	0.184990i	−0.579729	−	0.814810i	$-0.696841\pi$
$761$	−12590.1	+	3883.53i	−0.599724	+	0.184990i	−0.0199956	+	0.999800i	$0.506365\pi$
$762$	1953.81	−	2661.29i	0.0928861	−	0.126520i
$763$	−14065.2	+	19320.5i	−0.667360	+	0.916707i
$764$	16230.0	−	3704.38i	0.768559	−	0.175419i
$765$	−12064.6	+	39821.4i	−0.570190	+	1.88202i
$766$	−216.551	−	125.026i	−0.0102145	−	0.00589735i
$767$	7968.09	−	25831.9i	0.375112	−	1.21608i
$768$	17822.1	+	6186.04i	0.837370	+	0.290650i
$769$	−19452.5	−	15512.9i	−0.912193	−	0.727450i	0.0503062	−	0.998734i	$-0.483980\pi$
$769$	−19452.5	−	15512.9i	−0.912193	−	0.727450i	−0.962499	+	0.271284i	$0.912552\pi$
$770$	−85.9236	+	2782.39i	−0.00402139	+	0.130221i
$771$	14312.7	−	3873.62i	0.668558	−	0.180940i
$772$	24883.1	−	23088.1i	1.16005	−	1.07637i
$773$	13743.8	−	2071.55i	0.639496	−	0.0963885i	0.178713	−	0.983901i	$-0.442807\pi$
$773$	13743.8	−	2071.55i	0.639496	−	0.0963885i	0.460783	+	0.887513i	$0.347569\pi$
$774$	−588.997	+	2641.65i	−0.0273528	+	0.122677i
$775$	−1169.47	+	7758.94i	−0.0542047	+	0.359625i
$776$	−936.358	+	450.926i	−0.0433161	+	0.0208599i
$777$	−5466.82	+	9669.63i	−0.252408	+	0.446456i
$778$	−786.394	−	378.707i	−0.0362385	−	0.0174516i
$779$	−28302.3	+	41511.9i	−1.30171	+	1.90926i
$780$	15432.6	+	35130.9i	0.708430	+	1.61268i
$781$	−641.015	+	8553.75i	−0.0293692	+	0.391904i
$782$	269.186	−	685.875i	0.0123096	−	0.0313642i
$783$	−12207.7	−	34062.3i	−0.557174	−	1.55464i
$784$	21111.8	−	1859.60i	0.961725	−	0.0847123i
$785$		−	45945.6i		−	2.08901i
$786$	−1751.11	+	1759.93i	−0.0794657	+	0.0798658i
$787$	2754.61	+	206.429i	0.124766	+	0.00934994i	0.136967	−	0.990576i	$-0.456265\pi$
$787$	2754.61	+	206.429i	0.124766	+	0.00934994i	−0.0122006	+	0.999926i	$0.503884\pi$
$788$	−14603.6	+	15738.9i	−0.660191	+	0.711517i
$789$	9131.23	+	14451.6i	0.412016	+	0.652078i
$790$	−252.935	+	525.225i	−0.0113912	+	0.0236540i
$791$	−17720.0	+	2113.81i	−0.796524	+	0.0950168i
$792$	−3321.18	−	1284.26i	−0.149006	−	0.0576188i
$793$	34996.8	+	5274.92i	1.56718	+	0.236214i
$794$	−3287.36	+	2241.29i	−0.146932	+	0.100177i
$795$	−26804.9	−	7110.26i	−1.19581	−	0.317201i
$796$	5059.68	+	5453.04i	0.225296	+	0.242811i
$797$	2211.58	+	2773.23i	0.0982912	+	0.123253i	0.828544	−	0.559923i	$-0.189169\pi$
$797$	2211.58	+	2773.23i	0.0982912	+	0.123253i	−0.730253	+	0.683177i	$0.760598\pi$
$798$	2852.63	−	1405.66i	0.126544	−	0.0623558i
$799$	−9824.67	+	12319.7i	−0.435009	+	0.545484i
$800$	−11678.2	+	875.163i	−0.516110	+	0.0386771i
$801$	−12312.0	−	25241.1i	−0.543101	−	1.11342i
$802$	−1264.30	+	2189.83i	−0.0556658	+	0.0964161i
$803$	3853.05	+	6673.68i	0.169329	+	0.293286i
$804$	−9958.84	−	1858.42i	−0.436842	−	0.0815193i
$805$	4526.89	+	8431.58i	0.198201	+	0.369160i
$806$	588.344	+	134.286i	0.0257116	+	0.00586850i
$807$	243.970	−	2215.27i	0.0106421	−	0.0966312i
$808$	−5289.97	+	2076.16i	−0.230322	+	0.0903949i
$809$	−24932.4	+	9785.23i	−1.08353	+	0.425254i	−0.838857	−	0.544352i	$-0.816776\pi$
$809$	−24932.4	+	9785.23i	−1.08353	+	0.425254i	−0.244672	+	0.969606i	$0.578680\pi$
$810$	−3909.55	+	933.741i	−0.169590	+	0.0405041i
$811$	28427.4	+	6488.38i	1.23085	+	0.280934i	0.788009	−	0.615664i	$-0.211112\pi$
$811$	28427.4	+	6488.38i	1.23085	+	0.280934i	0.442845	+	0.896598i	$0.353969\pi$
$812$	36419.1	−	10013.7i	1.57396	−	0.432775i
$813$	497.304	−	2664.93i	0.0214529	−	0.114961i
$814$	478.480	+	828.752i	0.0206028	+	0.0356852i
$815$	3440.33	−	5958.82i	0.147864	−	0.256108i
$816$	17749.6	−	20730.5i	0.761472	−	0.889354i
$817$	35714.4	−	2676.42i	1.52936	−	0.114610i
$818$	1514.99	−	1899.73i	0.0647558	−	0.0812012i
$819$	−22632.0	+	12297.9i	−0.965598	+	0.524691i
$820$	41329.6	+	51825.7i	1.76011	+	2.20711i
$821$	−11451.1	−	12341.3i	−0.486779	−	0.524623i	0.441123	−	0.897446i	$-0.354580\pi$
$821$	−11451.1	−	12341.3i	−0.486779	−	0.524623i	−0.927902	+	0.372824i	$0.878390\pi$
$822$	−248.484	+	936.757i	−0.0105436	+	0.0397484i
$823$	−26884.8	+	18329.8i	−1.13869	+	0.776349i	−0.977575	−	0.210586i	$-0.932463\pi$
$823$	−26884.8	+	18329.8i	−1.13869	+	0.776349i	−0.161120	+	0.986935i	$0.551510\pi$
$824$	3191.87	+	481.097i	0.134944	+	0.0203396i
$825$	−28829.3	+	1151.22i	−1.21662	+	0.0485823i
$826$	−1556.31	+	2513.12i	−0.0655579	+	0.105863i
$827$	254.781	−	529.058i	0.0107129	−	0.0222456i	−0.895544	−	0.444973i	$-0.853213\pi$
$827$	254.781	−	529.058i	0.0107129	−	0.0222456i	0.906257	+	0.422728i	$0.138927\pi$
$828$	−6012.60	+	937.160i	−0.252358	+	0.0393340i
$829$	27760.7	−	29918.9i	1.16305	−	1.25347i	0.201302	−	0.979529i	$-0.435483\pi$
$829$	27760.7	−	29918.9i	1.16305	−	1.25347i	0.961747	−	0.273939i	$-0.0883268\pi$
$830$	−2477.42	−	185.657i	−0.103606	−	0.00776416i
$831$	−10736.4	−	10682.6i	−0.448183	−	0.445938i
$832$		−	24561.2i		−	1.02344i
$833$	8229.30	−	27970.2i	0.342291	−	1.16340i
$834$	−1520.95	+	3510.09i	−0.0631491	+	0.145737i
$835$	10038.6	−	25578.0i	0.416049	−	1.06008i
$836$	−1750.39	+	23357.3i	−0.0724144	+	0.966302i
$837$	2123.86	−	4969.75i	0.0877077	−	0.205233i
$838$	1478.41	−	2168.43i	0.0609437	−	0.0893880i
$839$	16073.6	+	7740.65i	0.661410	+	0.318518i	0.734303	−	0.678821i	$-0.237509\pi$
$839$	16073.6	+	7740.65i	0.661410	+	0.318518i	−0.0728933	+	0.997340i	$0.523223\pi$
$840$	−1333.41	−	8334.68i	−0.0547703	−	0.342350i
$841$	37956.5	−	18278.9i	1.55630	−	0.749473i
$842$	596.701	−	3958.85i	0.0244224	−	0.162032i
$843$	25304.0	−	4853.63i	1.03383	−	0.198301i
$844$	−10559.7	+	1591.61i	−0.430662	+	0.0649119i
$845$	6063.92	−	5626.49i	0.246870	−	0.229062i
$846$	−1506.33	−	219.312i	−0.0612161	−	0.00891265i
$847$	−5024.43	+	9658.80i	−0.203827	+	0.391830i
$848$	14220.9	+	11340.8i	0.575884	+	0.459252i
$849$	14836.0	−	42742.9i	0.599730	−	1.72783i
$850$	−1552.07	+	5031.68i	−0.0626300	+	0.203041i
$851$	2849.11	+	1644.93i	0.114766	+	0.0662604i
$852$	−1479.83	−	12843.9i	−0.0595051	−	0.516462i
$853$	7516.35	−	1715.56i	0.301706	−	0.0688624i	−0.0689881	−	0.997617i	$-0.521977\pi$
$853$	7516.35	−	1715.56i	0.301706	−	0.0688624i	0.370694	+	0.928755i	$0.379120\pi$
$854$	−3557.16	−	1524.41i	−0.142533	−	0.0610822i
$855$	26825.5	+	45928.9i	1.07300	+	1.83712i
$856$	−1833.73	+	565.632i	−0.0732193	+	0.0225852i
$857$	3584.43	+	9132.97i	0.142872	+	0.364033i	0.984341	−	0.176272i	$-0.0564040\pi$
$857$	3584.43	+	9132.97i	0.142872	+	0.364033i	−0.841469	+	0.540305i	$0.818309\pi$
$858$	−77.4028	+	2217.66i	−0.00307982	+	0.0882397i
$859$	1263.10	+	4094.86i	0.0501703	+	0.162648i	0.977191	−	0.212362i	$-0.0681155\pi$
$859$	1263.10	+	4094.86i	0.0501703	+	0.162648i	−0.927021	+	0.375010i	$0.877639\pi$
$860$	10514.7	−	46067.8i	0.416916	−	1.82663i
$861$	−32343.6	+	30559.2i	−1.28022	+	1.20959i
$862$	−955.284	−	4185.37i	−0.0377461	−	0.165376i
$863$	−4287.97	+	2475.66i	−0.169136	+	0.0976506i	−0.582178	−	0.813061i	$-0.697799\pi$
$863$	−4287.97	+	2475.66i	−0.169136	+	0.0976506i	0.413042	+	0.910712i	$0.364466\pi$
$864$	7936.72	+	1439.86i	0.312515	+	0.0566958i
$865$	70987.8	+	21896.8i	2.79035	+	0.860710i
$866$	134.628	+	1796.49i	0.00528273	+	0.0704931i
$867$	−5641.05	−	10608.8i	−0.220969	−	0.415565i
$868$	5004.91	+	2603.51i	0.195712	+	0.101808i
$869$	2253.39	−	1797.02i	0.0879643	−	0.0701492i
$870$	−2457.99	−	6968.36i	−0.0957860	−	0.271551i
$871$	1892.87	+	12558.4i	0.0736366	+	0.488547i
$872$	−3516.61	−	5157.92i	−0.136568	−	0.200309i
$873$	4775.85	−	3291.37i	0.185152	−	0.127602i
$874$	−408.662	−	848.595i	−0.0158160	−	0.0328423i
$875$	−14202.6	−	22279.0i	−0.548725	−	0.860765i
$876$	−7598.47	−	8784.87i	−0.293069	−	0.338828i
$877$	−6176.45	−	4211.03i	−0.237815	−	0.162140i	0.438548	−	0.898708i	$-0.355493\pi$
$877$	−6176.45	−	4211.03i	−0.237815	−	0.162140i	−0.676364	+	0.736568i	$0.736445\pi$
$878$	−29.3987	−	27.2780i	−0.00113002	−	0.00104850i
$879$	4690.97	+	2464.20i	0.180003	+	0.0945567i
$880$	28426.6	+	11156.6i	1.08893	+	0.427375i
$881$	25868.4			0.989250			0.494625	−	0.869106i	$-0.335305\pi$
$881$	25868.4			0.989250			0.494625	+	0.869106i	$0.335305\pi$
$882$	2734.12	−	676.272i	0.104379	−	0.0258177i
$883$	13142.7			0.500890			0.250445	−	0.968131i	$-0.419423\pi$
$883$	13142.7			0.500890			0.250445	+	0.968131i	$0.419423\pi$
$884$	−32229.3	−	12649.1i	−1.22623	−	0.481261i
$885$	−43768.3	−	22991.8i	−1.66243	−	0.873289i
$886$	2015.58	+	1870.18i	0.0764273	+	0.0709142i
$887$	−28999.1	−	19771.3i	−1.09774	−	0.748427i	−0.127807	−	0.991799i	$-0.540794\pi$
$887$	−28999.1	−	19771.3i	−1.09774	−	0.748427i	−0.969933	+	0.243372i	$0.921746\pi$
$888$	−1898.23	−	2194.61i	−0.0717346	−	0.0829349i
$889$	−32895.2	−	20371.1i	−1.24102	−	0.768531i
$890$	−2488.35	−	5167.11i	−0.0937187	−	0.194609i
$891$	19418.0	+	4227.30i	0.730111	+	0.158945i
$892$	−7342.04	−	10768.8i	−0.275594	−	0.404222i
$893$	3002.17	+	19918.1i	0.112501	+	0.746397i
$894$	1708.60	+	4843.85i	0.0639196	+	0.181211i
$895$	−26167.5	+	20867.9i	−0.977298	+	0.779369i
$896$	−2829.15	+	10841.2i	−0.105486	+	0.404216i
$897$	3581.52	+	6735.58i	0.133315	+	0.250718i
$898$	248.128	+	3311.04i	0.00922064	+	0.123041i
$899$	9493.93	+	2928.49i	0.352214	+	0.108644i
$900$	42348.5	−	9889.80i	1.56846	−	0.366289i
$901$	21670.4	−	12511.4i	0.801270	−	0.462614i
$902$	853.017	+	3737.31i	0.0314882	+	0.137959i
$903$	31406.4	+	4443.78i	1.15741	+	0.163765i
$904$	1037.32	−	4544.78i	0.0381644	−	0.167209i
$905$	−7287.06	−	23624.1i	−0.267657	−	0.867724i
$906$	21.2133	−	607.779i	0.000777884	−	0.0222871i
$907$	13570.0	+	34575.8i	0.496786	+	1.26579i	0.931013	+	0.364987i	$0.118926\pi$
$907$	13570.0	+	34575.8i	0.496786	+	1.26579i	−0.434227	+	0.900804i	$0.642978\pi$
$908$	34234.2	−	10559.9i	1.25121	−	0.385949i
$909$	27386.4	−	15995.5i	0.999284	−	0.583648i
$910$	−4634.28	+	2488.13i	−0.168819	+	0.0906381i
$911$	−25773.8	+	5882.71i	−0.937349	+	0.213944i	−0.663797	−	0.747913i	$-0.731056\pi$
$911$	−25773.8	+	5882.71i	−0.937349	+	0.213944i	−0.273553	+	0.961857i	$0.588199\pi$
$912$	−3993.09	−	34657.2i	−0.144983	−	1.25835i
$913$	10637.4	+	6141.48i	0.385592	+	0.222622i
$914$	−354.334	+	1148.72i	−0.0128231	+	0.0415716i
$915$	21224.7	−	61148.7i	0.766848	−	2.20930i
$916$	34813.2	+	27762.6i	1.25574	+	1.00142i
$917$	22177.4	+	18834.6i	0.798650	+	0.678269i
$918$	1906.41	−	3085.38i	0.0685412	−	0.110929i
$919$	−21663.4	+	20100.7i	−0.777593	+	0.721501i	−0.965420	−	0.260701i	$-0.916046\pi$
$919$	−21663.4	+	20100.7i	−0.777593	+	0.721501i	0.187826	+	0.982202i	$0.439856\pi$
$920$	−2471.96	+	372.587i	−0.0885848	+	0.0133520i
$921$	−20535.0	+	3938.87i	−0.734692	+	0.140923i
$922$	355.410	−	2357.99i	0.0126950	−	0.0842260i
$923$	−14603.0	+	7032.42i	−0.520761	+	0.250785i
$924$	−5935.09	+	19877.3i	−0.211310	+	0.707699i
$925$	−21182.8	−	10201.1i	−0.752958	−	0.362605i
$926$	1087.29	−	1594.77i	0.0385861	−	0.0565954i
$927$	−18014.6	+	90.4758i	−0.638272	+	0.00320563i
$928$	−1108.13	+	14787.0i	−0.0391985	+	0.523067i
$929$	5888.11	−	15002.7i	0.207947	−	0.529840i	−0.788407	−	0.615153i	$-0.789094\pi$
$929$	5888.11	−	15002.7i	0.207947	−	0.529840i	0.996354	+	0.0853138i	$0.0271893\pi$
$930$	438.810	−	1012.69i	0.0154722	−	0.0357070i
$931$	−19054.9	−	32030.8i	−0.670782	−	1.12757i
$932$			4599.57i			0.161656i
$933$	30798.1	+	30643.9i	1.08069	+	1.07528i
$934$	386.991	+	29.0010i	0.0135575	+	0.00101600i
$935$	28574.2	−	30795.6i	0.999439	−	1.07714i
$936$	−1036.21	−	6648.11i	−0.0361856	−	0.232158i
$937$	14289.4	−	29672.3i	0.498202	−	1.03453i	−0.488587	−	0.872515i	$-0.662488\pi$
$937$	14289.4	−	29672.3i	0.498202	−	1.03453i	0.986789	−	0.162011i	$-0.0517981\pi$
$938$	146.477	−	1380.99i	0.00509876	−	0.0480715i
$939$	12269.5	−	489.950i	0.426412	−	0.0170276i
$940$	26279.2	+	3960.96i	0.911845	+	0.137439i
$941$	−36118.9	+	24625.4i	−1.25127	+	0.853099i	−0.993580	−	0.113130i	$-0.963912\pi$
$941$	−36118.9	+	24625.4i	−1.25127	+	0.853099i	−0.257686	+	0.966229i	$0.582960\pi$
$942$	−1026.82	+	3870.99i	−0.0355154	+	0.133889i
$943$	8963.77	+	9660.65i	0.309545	+	0.333610i
$944$	20218.1	+	25352.7i	0.697080	+	0.874111i
$945$	14516.6	+	44814.4i	0.499709	+	1.54266i
$946$	1703.76	−	2136.45i	0.0585561	−	0.0734270i
$947$	−25659.7	+	1922.93i	−0.880495	+	0.0659839i	−0.507300	−	0.861769i	$-0.669357\pi$
$947$	−25659.7	+	1922.93i	−0.880495	+	0.0659839i	−0.373194	+	0.927753i	$0.621737\pi$
$948$	−2825.40	+	3299.90i	−0.0967983	+	0.113055i
$949$	−7280.53	+	12610.2i	−0.249037	+	0.431344i
$950$	3365.55	+	5829.30i	0.114940	+	0.199081i
$951$	−1394.20	+	7471.19i	−0.0475395	+	0.254753i
$952$	6157.29	+	4482.49i	0.209621	+	0.152603i
$953$	−11507.0	−	2626.39i	−0.391131	−	0.0892731i	0.0224325	−	0.999748i	$-0.492859\pi$
$953$	−11507.0	−	2626.39i	−0.391131	−	0.0892731i	−0.413564	+	0.910475i	$0.635716\pi$
$954$	2099.45	+	1198.10i	0.0712497	+	0.0406603i
$955$	−35529.4	+	13944.3i	−1.20388	+	0.472488i
$956$	1227.95	−	481.935i	0.0415427	−	0.0163043i
$957$	−3999.20	+	36313.2i	−0.135084	+	1.22658i
$958$	−337.971	−	77.1398i	−0.0113981	−	0.00260154i
$959$	11173.6	+	2038.69i	0.376240	+	0.0686474i
$960$	−44157.0	−	8240.15i	−1.48454	−	0.277031i
$961$	−14153.5	−	24514.6i	−0.475093	−	0.822886i
$962$	−904.112	+	1565.97i	−0.0303012	+	0.0524832i
$963$	9625.73	−	4695.21i	0.322102	−	0.157114i
$964$	−8943.73	+	670.240i	−0.298816	+	0.0223931i
$965$	−48523.4	+	60846.4i	−1.61868	+	2.02976i
$966$	−192.964	−	811.543i	−0.00642703	−	0.0270300i
$967$	6368.16	+	7985.42i	0.211775	+	0.265557i	0.876362	−	0.481654i	$-0.159964\pi$
$967$	6368.16	+	7985.42i	0.211775	+	0.265557i	−0.664587	+	0.747211i	$0.731392\pi$
$968$	−1934.44	−	2084.83i	−0.0642306	−	0.0692241i
$969$	−46388.7	−	12305.0i	−1.53789	−	0.407941i
$970$	978.650	−	667.232i	0.0323944	−	0.0220861i
$971$	−5736.94	−	864.704i	−0.189606	−	0.0285784i	0.0535529	−	0.998565i	$-0.482945\pi$
$971$	−5736.94	−	864.704i	−0.189606	−	0.0285784i	−0.243159	+	0.969987i	$0.578184\pi$
$972$	−29944.4	−	744.095i	−0.988133	−	0.0245544i
$973$	42412.4	+	14530.7i	1.39741	+	0.478758i
$974$	−1804.38	+	3746.83i	−0.0593594	+	0.123261i
$975$	−29121.1	−	46088.6i	−0.956535	−	1.51386i
$976$	−28876.4	+	31121.4i	−0.947041	+	1.02067i
$977$	37874.7	+	2838.32i	1.24025	+	0.0929435i	0.678646	−	0.734466i	$-0.262567\pi$
$977$	37874.7	+	2838.32i	1.24025	+	0.0929435i	0.561599	+	0.827409i	$0.310186\pi$
$978$	−423.024	+	425.153i	−0.0138311	+	0.0139007i
$979$			28354.7i			0.925659i
$980$	−47793.1	+	11567.0i	−1.55785	+	0.377035i
$981$	23825.1	+	25420.1i	0.775411	+	0.827321i
$982$	1272.71	−	3242.80i	0.0413581	−	0.105379i
$983$	−3328.99	+	44422.3i	−0.108015	+	1.44136i	0.635223	+	0.772328i	$0.280908\pi$
$983$	−3328.99	+	44422.3i	−0.108015	+	1.44136i	−0.743238	+	0.669027i	$0.766711\pi$
$984$	−4674.89	−	10642.0i	−0.151453	−	0.344770i
$985$	27729.9	−	40672.2i	0.897002	−	1.31566i
$986$	6007.05	+	2892.84i	0.194020	+	0.0934349i
$987$	−1172.30	+	17801.2i	−0.0378061	+	0.574080i
$988$	−39875.5	+	19203.1i	−1.28402	+	0.618351i
$989$	1400.15	−	9289.37i	0.0450173	−	0.298670i
$990$	3961.02	+	883.170i	0.127161	+	0.0283525i
$991$	29520.6	−	4449.52i	0.946270	−	0.142627i	0.342261	−	0.939605i	$-0.388807\pi$
$991$	29520.6	−	4449.52i	0.946270	−	0.142627i	0.604009	+	0.796978i	$0.293569\pi$
$992$	−1623.59	+	1506.47i	−0.0519647	+	0.0482162i
$993$	11717.4	−	3171.21i	0.374460	−	0.101345i
$994$	1739.23	−	340.855i	0.0554979	−	0.0108765i
$995$	−13334.3	−	10633.7i	−0.424849	−	0.338806i
$996$	−17490.0	−	6070.77i	−0.556418	−	0.193132i
$997$	12388.1	−	40161.1i	0.393515	−	1.27574i	−0.514748	−	0.857342i	$-0.672114\pi$
$997$	12388.1	−	40161.1i	0.393515	−	1.27574i	0.908262	−	0.418401i	$-0.137409\pi$
$998$	−4688.49	−	2706.90i	−0.148709	−	0.0858572i
$999$	12353.8	+	10470.3i	0.391248	+	0.331599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.o.a.101.28	yes	648
3.2	odd	2	inner	147.4.o.a.101.27	✓	648
49.33	odd	42	inner	147.4.o.a.131.27	yes	648
147.131	even	42	inner	147.4.o.a.131.28	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.o.a.101.27	✓	648	3.2	odd	2	inner
147.4.o.a.101.28	yes	648	1.1	even	1	trivial
147.4.o.a.131.27	yes	648	49.33	odd	42	inner
147.4.o.a.131.28	yes	648	147.131	even	42	inner

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.o (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.283103 + 0.111110i) q^{2} +(-4.60008 - 2.41646i) q^{3} +(-5.79661 - 5.37847i) q^{4} +(14.9795 + 10.2129i) q^{5} +(-1.03380 - 1.19522i) q^{6} +(-13.0100 + 13.1810i) q^{7} +(-2.09908 - 4.35878i) q^{8} +(15.3215 + 22.2318i) q^{9} +O(q^{10})\)	\(q+(0.283103 + 0.111110i) q^{2} +(-4.60008 - 2.41646i) q^{3} +(-5.79661 - 5.37847i) q^{4} +(14.9795 + 10.2129i) q^{5} +(-1.03380 - 1.19522i) q^{6} +(-13.0100 + 13.1810i) q^{7} +(-2.09908 - 4.35878i) q^{8} +(15.3215 + 22.2318i) q^{9} +(3.10600 + 4.55566i) q^{10} +(-4.06296 - 26.9560i) q^{11} +(13.6681 + 38.7487i) q^{12} +(40.2721 - 32.1159i) q^{13} +(-5.14771 + 2.28604i) q^{14} +(-44.2281 - 83.1773i) q^{15} +(4.61748 + 61.6160i) q^{16} +(81.2257 + 25.0548i) q^{17} +(1.86739 + 7.99625i) q^{18} +(94.1016 - 54.3296i) q^{19} +(-31.9009 - 139.767i) q^{20} +(91.6985 - 29.1956i) q^{21} +(1.84483 - 8.08274i) q^{22} +(-8.40103 - 27.2355i) q^{23} +(-0.876869 + 25.1231i) q^{24} +(74.4157 + 189.608i) q^{25} +(14.9695 - 4.61749i) q^{26} +(-16.7580 - 139.292i) q^{27} +(146.308 - 6.43121i) q^{28} +(251.444 - 57.3904i) q^{29} +(-3.27929 - 28.4619i) q^{30} +(33.3614 + 19.2612i) q^{31} +(-16.9468 + 54.9403i) q^{32} +(-46.4479 + 133.818i) q^{33} +(20.2114 + 16.1180i) q^{34} +(-329.500 + 64.5757i) q^{35} +(30.7602 - 211.275i) q^{36} +(-84.6140 + 78.5103i) q^{37} +(32.6770 - 4.92526i) q^{38} +(-262.862 + 50.4201i) q^{39} +(13.0725 - 86.7301i) q^{40} +(-416.591 + 200.620i) q^{41} +(29.2040 + 1.92323i) q^{42} +(296.963 + 143.010i) q^{43} +(-121.430 + 178.106i) q^{44} +(2.45843 + 489.497i) q^{45} +(0.647769 - 8.64388i) q^{46} +(-67.7263 + 172.564i) q^{47} +(127.651 - 294.596i) q^{48} +(-4.47846 - 342.971i) q^{49} +61.9469i q^{50} +(-313.101 - 311.532i) q^{51} +(-406.176 - 30.4387i) q^{52} +(200.228 - 215.795i) q^{53} +(10.7324 - 41.2958i) q^{54} +(214.436 - 445.282i) q^{55} +(84.7623 + 29.0399i) q^{56} +(-564.160 + 22.5282i) q^{57} +(77.5610 + 11.6904i) q^{58} +(433.618 - 295.636i) q^{59} +(-190.994 + 720.026i) q^{60} +(467.341 + 503.674i) q^{61} +(7.30461 + 9.15969i) q^{62} +(-492.370 - 87.2832i) q^{63} +(297.295 - 372.796i) q^{64} +(931.252 - 69.7877i) q^{65} +(-28.0180 + 32.7233i) q^{66} +(-123.279 + 213.526i) q^{67} +(-336.077 - 582.103i) q^{68} +(-27.1679 + 145.586i) q^{69} +(-100.457 - 18.3291i) q^{70} +(-306.770 - 70.0182i) q^{71} +(64.7425 - 113.449i) q^{72} +(-263.143 + 103.276i) q^{73} +(-32.6777 + 12.8251i) q^{74} +(115.861 - 1052.03i) q^{75} +(-837.680 - 191.195i) q^{76} +(408.166 + 297.144i) q^{77} +(-80.0190 - 14.9324i) q^{78} +(52.8640 + 91.5632i) q^{79} +(-560.107 + 970.135i) q^{80} +(-259.504 + 681.248i) q^{81} +(-140.229 + 10.5087i) q^{82} +(-280.931 + 352.277i) q^{83} +(-688.568 - 323.962i) q^{84} +(960.840 + 1204.86i) q^{85} +(68.1814 + 73.4821i) q^{86} +(-1295.34 - 343.602i) q^{87} +(-108.967 + 74.2923i) q^{88} +(-1028.52 - 155.025i) q^{89} +(-53.6919 + 138.851i) q^{90} +(-100.620 + 948.656i) q^{91} +(-97.7877 + 203.058i) q^{92} +(-106.921 - 169.220i) q^{93} +(-38.3470 + 41.3283i) q^{94} +(1964.46 + 147.216i) q^{95} +(210.718 - 211.779i) q^{96} -214.821i q^{97} +(36.8395 - 97.5936i) q^{98} +(537.028 - 503.332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9}+O(q^{10}) \) 648 * q - 11 * q^3 - 234 * q^4 + 14 * q^6 + 28 * q^7 - 125 * q^9	\( 648 q - 11 q^{3} - 234 q^{4} + 14 q^{6} + 28 q^{7} - 125 q^{9} - 58 q^{10} - 207 q^{12} - 28 q^{13} - 148 q^{15} + 726 q^{16} - 81 q^{18} - 342 q^{19} - 371 q^{21} - 156 q^{22} - 428 q^{24} + 1250 q^{25} - 56 q^{27} + 700 q^{28} + 389 q^{30} + 888 q^{31} + 841 q^{33} - 532 q^{34} - 38 q^{36} + 1178 q^{37} - 180 q^{39} + 194 q^{40} + 56 q^{42} + 1296 q^{43} - 617 q^{45} - 6756 q^{46} - 2380 q^{49} + 787 q^{51} - 5204 q^{52} + 4144 q^{54} - 5698 q^{55} + 863 q^{57} - 3066 q^{58} + 2820 q^{60} + 1492 q^{61} - 1085 q^{63} + 7648 q^{64} + 2568 q^{66} + 142 q^{67} - 5474 q^{69} + 5180 q^{70} + 1278 q^{72} + 2876 q^{73} - 1754 q^{75} + 7644 q^{76} + 936 q^{78} - 992 q^{79} + 911 q^{81} + 1022 q^{82} + 7868 q^{84} + 2672 q^{85} - 196 q^{87} + 370 q^{88} - 18767 q^{90} - 2254 q^{91} - 11096 q^{93} - 3628 q^{94} - 24248 q^{96} + 10982 q^{99}+O(q^{100}) \) 648 * q - 11 * q^3 - 234 * q^4 + 14 * q^6 + 28 * q^7 - 125 * q^9 - 58 * q^10 - 207 * q^12 - 28 * q^13 - 148 * q^15 + 726 * q^16 - 81 * q^18 - 342 * q^19 - 371 * q^21 - 156 * q^22 - 428 * q^24 + 1250 * q^25 - 56 * q^27 + 700 * q^28 + 389 * q^30 + 888 * q^31 + 841 * q^33 - 532 * q^34 - 38 * q^36 + 1178 * q^37 - 180 * q^39 + 194 * q^40 + 56 * q^42 + 1296 * q^43 - 617 * q^45 - 6756 * q^46 - 2380 * q^49 + 787 * q^51 - 5204 * q^52 + 4144 * q^54 - 5698 * q^55 + 863 * q^57 - 3066 * q^58 + 2820 * q^60 + 1492 * q^61 - 1085 * q^63 + 7648 * q^64 + 2568 * q^66 + 142 * q^67 - 5474 * q^69 + 5180 * q^70 + 1278 * q^72 + 2876 * q^73 - 1754 * q^75 + 7644 * q^76 + 936 * q^78 - 992 * q^79 + 911 * q^81 + 1022 * q^82 + 7868 * q^84 + 2672 * q^85 - 196 * q^87 + 370 * q^88 - 18767 * q^90 - 2254 * q^91 - 11096 * q^93 - 3628 * q^94 - 24248 * q^96 + 10982 * q^99

Introduction

L-functions

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