LMFDB - Embedded newform 287.2.u.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(8,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("287.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	287.8
Dual form			287.2.u.a.36.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21144 + 1.66740i) q^{2} +(-0.0854640 - 0.0854640i) q^{3} +(-0.694607 - 2.13778i) q^{4} +(1.91874 - 0.623438i) q^{5} +(0.246037 - 0.0389684i) q^{6} +(0.987688 + 0.156434i) q^{7} +(0.485715 + 0.157818i) q^{8} -2.98539i q^{9} +O(q^{10})$	\(q+(-1.21144 + 1.66740i) q^{2} +(-0.0854640 - 0.0854640i) q^{3} +(-0.694607 - 2.13778i) q^{4} +(1.91874 - 0.623438i) q^{5} +(0.246037 - 0.0389684i) q^{6} +(0.987688 + 0.156434i) q^{7} +(0.485715 + 0.157818i) q^{8} -2.98539i q^{9} +(-1.28492 + 3.95457i) q^{10} +(3.80903 - 1.94080i) q^{11} +(-0.123339 + 0.242067i) q^{12} +(-0.409792 - 2.58733i) q^{13} +(-1.45736 + 1.45736i) q^{14} +(-0.217265 - 0.110702i) q^{15} +(2.78545 - 2.02375i) q^{16} +(1.82854 + 3.58871i) q^{17} +(4.97784 + 3.61661i) q^{18} +(0.210863 - 1.33133i) q^{19} +(-2.66555 - 3.66881i) q^{20} +(-0.0710423 - 0.0977813i) q^{21} +(-1.37831 + 8.70233i) q^{22} +(1.53181 + 1.11293i) q^{23} +(-0.0280233 - 0.0549989i) q^{24} +(-0.752179 + 0.546490i) q^{25} +(4.81054 + 2.45109i) q^{26} +(-0.511535 + 0.511535i) q^{27} +(-0.351633 - 2.22012i) q^{28} +(-2.32782 + 4.56861i) q^{29} +(0.447787 - 0.228159i) q^{30} +(-0.579058 + 1.78216i) q^{31} +8.11752i q^{32} +(-0.491403 - 0.159667i) q^{33} +(-8.19897 - 1.29859i) q^{34} +(1.99265 - 0.315605i) q^{35} +(-6.38211 + 2.07367i) q^{36} +(-0.820624 - 2.52562i) q^{37} +(1.96442 + 1.96442i) q^{38} +(-0.186101 + 0.256146i) q^{39} +1.03035 q^{40} +(3.73036 - 5.20427i) q^{41} +0.249104 q^{42} +(-5.78424 + 7.96132i) q^{43} +(-6.79478 - 6.79478i) q^{44} +(-1.86121 - 5.72820i) q^{45} +(-3.71138 + 1.20590i) q^{46} +(6.89307 - 1.09176i) q^{47} +(-0.411013 - 0.0650981i) q^{48} +(0.951057 + 0.309017i) q^{49} -1.91622i q^{50} +(0.150431 - 0.462980i) q^{51} +(-5.24649 + 2.67322i) q^{52} +(0.311222 - 0.610807i) q^{53} +(-0.233241 - 1.47263i) q^{54} +(6.09859 - 6.09859i) q^{55} +(0.455047 + 0.231858i) q^{56} +(-0.131802 + 0.0957600i) q^{57} +(-4.79769 - 9.41599i) q^{58} +(7.09486 + 5.15472i) q^{59} +(-0.0857429 + 0.541359i) q^{60} +(-7.34152 - 10.1047i) q^{61} +(-2.27008 - 3.12449i) q^{62} +(0.467018 - 2.94864i) q^{63} +(-7.96424 - 5.78636i) q^{64} +(-2.39932 - 4.70894i) q^{65} +(0.861532 - 0.625940i) q^{66} +(-4.40610 - 2.24502i) q^{67} +(6.40176 - 6.40176i) q^{68} +(-0.0357996 - 0.226030i) q^{69} +(-1.88773 + 3.70487i) q^{70} +(10.6093 - 5.40568i) q^{71} +(0.471149 - 1.45005i) q^{72} +4.98331i q^{73} +(5.20535 + 1.69132i) q^{74} +(0.110989 + 0.0175790i) q^{75} +(-2.99257 + 0.473976i) q^{76} +(4.06574 - 1.32104i) q^{77} +(-0.201648 - 0.620608i) q^{78} +(-1.93961 - 1.93961i) q^{79} +(4.08289 - 5.61961i) q^{80} -8.86874 q^{81} +(4.15850 + 12.5246i) q^{82} +8.84052 q^{83} +(-0.159688 + 0.219792i) q^{84} +(5.74584 + 5.74584i) q^{85} +(-6.26746 - 19.2893i) q^{86} +(0.589397 - 0.191507i) q^{87} +(2.15640 - 0.341540i) q^{88} +(-11.9982 - 1.90034i) q^{89} +(11.8059 + 3.83598i) q^{90} -2.61958i q^{91} +(1.31518 - 4.04772i) q^{92} +(0.201799 - 0.102822i) q^{93} +(-6.53012 + 12.8161i) q^{94} +(-0.425413 - 2.68595i) q^{95} +(0.693756 - 0.693756i) q^{96} +(-7.70972 - 3.92830i) q^{97} +(-1.66740 + 1.21144i) q^{98} +(-5.79404 - 11.3715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6}+O(q^{10}) $ 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6	$ 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6} - 48 q^{10} + 8 q^{11} - 16 q^{12} - 16 q^{13} - 32 q^{15} - 28 q^{16} - 20 q^{17} + 12 q^{18} - 40 q^{19} - 4 q^{22} - 36 q^{23} - 108 q^{24} + 40 q^{25} + 20 q^{26} + 20 q^{27} + 12 q^{29} - 4 q^{30} + 20 q^{31} - 32 q^{34} - 4 q^{35} + 140 q^{36} - 44 q^{38} + 80 q^{39} - 64 q^{40} + 4 q^{41} - 72 q^{42} - 8 q^{44} + 8 q^{45} + 40 q^{46} - 56 q^{47} + 120 q^{48} + 24 q^{51} + 16 q^{52} + 12 q^{53} - 52 q^{54} - 72 q^{55} + 48 q^{57} + 36 q^{58} - 48 q^{59} - 52 q^{60} + 8 q^{63} - 96 q^{64} - 96 q^{65} + 24 q^{66} + 20 q^{67} - 80 q^{68} - 68 q^{69} + 8 q^{70} + 60 q^{71} + 100 q^{72} - 40 q^{74} - 120 q^{75} + 4 q^{76} - 12 q^{78} + 12 q^{79} + 200 q^{80} - 56 q^{81} - 68 q^{82} - 40 q^{83} + 132 q^{85} + 80 q^{86} - 16 q^{88} + 8 q^{89} + 140 q^{92} + 64 q^{93} + 128 q^{94} - 68 q^{96} + 4 q^{98} + 96 q^{99}+O(q^{100}) $ 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6 - 48 * q^10 + 8 * q^11 - 16 * q^12 - 16 * q^13 - 32 * q^15 - 28 * q^16 - 20 * q^17 + 12 * q^18 - 40 * q^19 - 4 * q^22 - 36 * q^23 - 108 * q^24 + 40 * q^25 + 20 * q^26 + 20 * q^27 + 12 * q^29 - 4 * q^30 + 20 * q^31 - 32 * q^34 - 4 * q^35 + 140 * q^36 - 44 * q^38 + 80 * q^39 - 64 * q^40 + 4 * q^41 - 72 * q^42 - 8 * q^44 + 8 * q^45 + 40 * q^46 - 56 * q^47 + 120 * q^48 + 24 * q^51 + 16 * q^52 + 12 * q^53 - 52 * q^54 - 72 * q^55 + 48 * q^57 + 36 * q^58 - 48 * q^59 - 52 * q^60 + 8 * q^63 - 96 * q^64 - 96 * q^65 + 24 * q^66 + 20 * q^67 - 80 * q^68 - 68 * q^69 + 8 * q^70 + 60 * q^71 + 100 * q^72 - 40 * q^74 - 120 * q^75 + 4 * q^76 - 12 * q^78 + 12 * q^79 + 200 * q^80 - 56 * q^81 - 68 * q^82 - 40 * q^83 + 132 * q^85 + 80 * q^86 - 16 * q^88 + 8 * q^89 + 140 * q^92 + 64 * q^93 + 128 * q^94 - 68 * q^96 + 4 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	−1.21144	+	1.66740i	−0.856615	+	1.17903i	0.125752	+	0.992062i	$0.459866\pi$
$2$	−1.21144	+	1.66740i	−0.856615	+	1.17903i	−0.982366	+	0.186967i	$0.940134\pi$
$3$	−0.0854640	−	0.0854640i	−0.0493427	−	0.0493427i	0.682005	−	0.731348i	$-0.261108\pi$
$3$	−0.0854640	−	0.0854640i	−0.0493427	−	0.0493427i	−0.731348	+	0.682005i	$0.761108\pi$
$4$	−0.694607	−	2.13778i	−0.347303	−	1.06889i
$5$	1.91874	−	0.623438i	0.858089	−	0.278810i	0.153259	−	0.988186i	$-0.451023\pi$
$5$	1.91874	−	0.623438i	0.858089	−	0.278810i	0.704830	+	0.709376i	$0.251023\pi$
$6$	0.246037	−	0.0389684i	0.100444	−	0.0159088i
$7$	0.987688	+	0.156434i	0.373311	+	0.0591267i
$7$	0.987688	+	0.156434i	0.373311	+	0.0591267i
$8$	0.485715	+	0.157818i	0.171726	+	0.0557972i
$9$		−	2.98539i		−	0.995131i
$10$	−1.28492	+	3.95457i	−0.406326	+	1.25054i
$11$	3.80903	−	1.94080i	1.14847	−	0.585173i	0.227101	−	0.973871i	$-0.427075\pi$
$11$	3.80903	−	1.94080i	1.14847	−	0.585173i	0.921365	+	0.388698i	$0.127075\pi$
$12$	−0.123339	+	0.242067i	−0.0356050	+	0.0698788i
$13$	−0.409792	−	2.58733i	−0.113656	−	0.717595i	−0.977041	−	0.213050i	$-0.931660\pi$
$13$	−0.409792	−	2.58733i	−0.113656	−	0.717595i	0.863385	−	0.504545i	$-0.168340\pi$
$14$	−1.45736	+	1.45736i	−0.389496	+	0.389496i
$15$	−0.217265	−	0.110702i	−0.0560976	−	0.0285832i
$16$	2.78545	−	2.02375i	0.696363	−	0.505937i
$17$	1.82854	+	3.58871i	0.443486	+	0.870390i	0.999238	+	0.0390419i	$0.0124306\pi$
$17$	1.82854	+	3.58871i	0.443486	+	0.870390i	−0.555752	+	0.831348i	$0.687569\pi$
$18$	4.97784	+	3.61661i	1.17329	+	0.852443i
$19$	0.210863	−	1.33133i	0.0483752	−	0.305429i	−0.951623	−	0.307268i	$-0.900585\pi$
$19$	0.210863	−	1.33133i	0.0483752	−	0.305429i	0.999998	+	0.00183863i	$0.000585255\pi$
$20$	−2.66555	−	3.66881i	−0.596034	−	0.820371i
$21$	−0.0710423	−	0.0977813i	−0.0155027	−	0.0213376i
$22$	−1.37831	+	8.70233i	−0.293857	+	1.85534i
$23$	1.53181	+	1.11293i	0.319404	+	0.232061i	0.735921	−	0.677067i	$-0.236749\pi$
$23$	1.53181	+	1.11293i	0.319404	+	0.232061i	−0.416517	+	0.909128i	$0.636749\pi$
$24$	−0.0280233	−	0.0549989i	−0.00572024	−	0.0112266i
$25$	−0.752179	+	0.546490i	−0.150436	+	0.109298i
$26$	4.81054	+	2.45109i	0.943425	+	0.480699i
$27$	−0.511535	+	0.511535i	−0.0984450	+	0.0984450i
$28$	−0.351633	−	2.22012i	−0.0664523	−	0.419563i
$29$	−2.32782	+	4.56861i	−0.432266	+	0.848370i	0.567423	+	0.823426i	$0.307940\pi$
$29$	−2.32782	+	4.56861i	−0.432266	+	0.848370i	−0.999689	+	0.0249431i	$0.992060\pi$
$30$	0.447787	−	0.228159i	0.0817544	−	0.0416559i
$31$	−0.579058	+	1.78216i	−0.104002	+	0.320085i	−0.989495	−	0.144568i	$-0.953821\pi$
$31$	−0.579058	+	1.78216i	−0.104002	+	0.320085i	0.885493	+	0.464653i	$0.153821\pi$
$32$			8.11752i			1.43499i
$33$	−0.491403	−	0.159667i	−0.0855424	−	0.0277944i
$34$	−8.19897	−	1.29859i	−1.40611	−	0.222706i
$35$	1.99265	−	0.315605i	0.336819	−	0.0533469i
$36$	−6.38211	+	2.07367i	−1.06369	+	0.345612i
$37$	−0.820624	−	2.52562i	−0.134910	−	0.415210i	0.860666	−	0.509170i	$-0.170047\pi$
$37$	−0.820624	−	2.52562i	−0.134910	−	0.415210i	−0.995576	+	0.0939601i	$0.970047\pi$
$38$	1.96442	+	1.96442i	0.318671	+	0.318671i
$39$	−0.186101	+	0.256146i	−0.0298000	+	0.0410162i
$40$	1.03035			0.162913
$41$	3.73036	−	5.20427i	0.582584	−	0.812770i
$41$	3.73036	−	5.20427i	0.582584	−	0.812770i
$42$	0.249104			0.0384375
$43$	−5.78424	+	7.96132i	−0.882088	+	1.21409i	0.0937507	+	0.995596i	$0.470114\pi$
$43$	−5.78424	+	7.96132i	−0.882088	+	1.21409i	−0.975838	+	0.218494i	$0.929886\pi$
$44$	−6.79478	−	6.79478i	−1.02435	−	1.02435i
$45$	−1.86121	−	5.72820i	−0.277452	−	0.853910i
$46$	−3.71138	+	1.20590i	−0.547213	+	0.177800i
$47$	6.89307	−	1.09176i	1.00546	−	0.159249i	0.368075	−	0.929796i	$-0.380017\pi$
$47$	6.89307	−	1.09176i	1.00546	−	0.159249i	0.637383	+	0.770547i	$0.280017\pi$
$48$	−0.411013	−	0.0650981i	−0.0593247	−	0.00939610i
$49$	0.951057	+	0.309017i	0.135865	+	0.0441453i
$50$		−	1.91622i		−	0.270994i
$51$	0.150431	−	0.462980i	0.0210646	−	0.0648302i
$52$	−5.24649	+	2.67322i	−0.727558	+	0.370709i
$53$	0.311222	−	0.610807i	0.0427496	−	0.0839009i	−0.868644	−	0.495437i	$-0.835008\pi$
$53$	0.311222	−	0.610807i	0.0427496	−	0.0839009i	0.911393	+	0.411537i	$0.135008\pi$
$54$	−0.233241	−	1.47263i	−0.0317401	−	0.200399i
$55$	6.09859	−	6.09859i	0.822334	−	0.822334i
$56$	0.455047	+	0.231858i	0.0608082	+	0.0309833i
$57$	−0.131802	+	0.0957600i	−0.0174577	+	0.0126837i
$58$	−4.79769	−	9.41599i	−0.629967	−	1.23638i
$59$	7.09486	+	5.15472i	0.923672	+	0.671087i	0.944435	−	0.328697i	$-0.106610\pi$
$59$	7.09486	+	5.15472i	0.923672	+	0.671087i	−0.0207633	+	0.999784i	$0.506610\pi$
$60$	−0.0857429	+	0.541359i	−0.0110694	+	0.0698892i
$61$	−7.34152	−	10.1047i	−0.939985	−	1.29378i	−0.955835	−	0.293904i	$-0.905045\pi$
$61$	−7.34152	−	10.1047i	−0.939985	−	1.29378i	0.0158501	−	0.999874i	$-0.494955\pi$
$62$	−2.27008	−	3.12449i	−0.288300	−	0.396811i
$63$	0.467018	−	2.94864i	0.0588388	−	0.371493i
$64$	−7.96424	−	5.78636i	−0.995530	−	0.723295i
$65$	−2.39932	−	4.70894i	−0.297600	−	0.584072i
$66$	0.861532	−	0.625940i	0.106047	−	0.0770478i
$67$	−4.40610	−	2.24502i	−0.538291	−	0.274273i	0.163637	−	0.986521i	$-0.447677\pi$
$67$	−4.40610	−	2.24502i	−0.538291	−	0.274273i	−0.701928	+	0.712248i	$0.747677\pi$
$68$	6.40176	−	6.40176i	0.776327	−	0.776327i
$69$	−0.0357996	−	0.226030i	−0.00430976	−	0.0272108i
$70$	−1.88773	+	3.70487i	−0.225627	+	0.442817i
$71$	10.6093	−	5.40568i	1.25909	−	0.641537i	0.308272	−	0.951298i	$-0.400249\pi$
$71$	10.6093	−	5.40568i	1.25909	−	0.641537i	0.950814	+	0.309761i	$0.100249\pi$
$72$	0.471149	−	1.45005i	0.0555255	−	0.170890i
$73$			4.98331i			0.583253i	0.956532	+	0.291626i	$0.0941964\pi$
$73$			4.98331i			0.583253i	−0.956532	+	0.291626i	$0.905804\pi$
$74$	5.20535	+	1.69132i	0.605110	+	0.196612i
$75$	0.110989	+	0.0175790i	0.0128160	+	0.00202985i
$76$	−2.99257	+	0.473976i	−0.343271	+	0.0543688i
$77$	4.06574	−	1.32104i	0.463335	−	0.150547i
$78$	−0.201648	−	0.620608i	−0.0228321	−	0.0702701i
$79$	−1.93961	−	1.93961i	−0.218223	−	0.218223i	0.589526	−	0.807749i	$-0.299314\pi$
$79$	−1.93961	−	1.93961i	−0.218223	−	0.218223i	−0.807749	+	0.589526i	$0.799314\pi$
$80$	4.08289	−	5.61961i	0.456481	−	0.628292i
$81$	−8.86874			−0.985416
$82$	4.15850	+	12.5246i	0.459229	+	1.38311i
$83$	8.84052			0.970373			0.485186	−	0.874411i	$-0.338752\pi$
$83$	8.84052			0.970373			0.485186	+	0.874411i	$0.338752\pi$
$84$	−0.159688	+	0.219792i	−0.0174234	+	0.0239813i
$85$	5.74584	+	5.74584i	0.623224	+	0.623224i
$86$	−6.26746	−	19.2893i	−0.675837	−	2.08001i
$87$	0.589397	−	0.191507i	0.0631900	−	0.0205317i
$88$	2.15640	−	0.341540i	0.229873	−	0.0364083i
$89$	−11.9982	−	1.90034i	−1.27181	−	0.201435i	−0.516207	−	0.856464i	$-0.672657\pi$
$89$	−11.9982	−	1.90034i	−1.27181	−	0.201435i	−0.755604	+	0.655029i	$0.772657\pi$
$90$	11.8059	+	3.83598i	1.24445	+	0.404348i
$91$		−	2.61958i		−	0.274606i
$92$	1.31518	−	4.04772i	0.137117	−	0.422004i
$93$	0.201799	−	0.102822i	0.0209256	−	0.0106621i
$94$	−6.53012	+	12.8161i	−0.673531	+	1.32188i
$95$	−0.425413	−	2.68595i	−0.0436464	−	0.275573i
$96$	0.693756	−	0.693756i	0.0708061	−	0.0708061i
$97$	−7.70972	−	3.92830i	−0.782803	−	0.398858i	0.0164407	−	0.999865i	$-0.494767\pi$
$97$	−7.70972	−	3.92830i	−0.782803	−	0.398858i	−0.799244	+	0.601007i	$0.794767\pi$
$98$	−1.66740	+	1.21144i	−0.168433	+	0.122374i
$99$	−5.79404	−	11.3715i	−0.582323	−	1.14287i
$100$	1.69074	+	1.22840i	0.169074	+	0.122840i
$101$	−1.61830	+	10.2175i	−0.161027	+	1.01668i	0.766314	+	0.642466i	$0.222089\pi$
$101$	−1.61830	+	10.2175i	−0.161027	+	1.01668i	−0.927341	+	0.374217i	$0.877911\pi$
$102$	0.589734	+	0.811699i	0.0583924	+	0.0803702i
$103$	−3.24105	−	4.46093i	−0.319350	−	0.439548i	0.618918	−	0.785455i	$-0.287571\pi$
$103$	−3.24105	−	4.46093i	−0.319350	−	0.439548i	−0.938269	+	0.345907i	$0.887571\pi$
$104$	0.209285	−	1.32138i	0.0205221	−	0.129572i
$105$	−0.197273	−	0.143327i	−0.0192518	−	0.0139873i
$106$	0.641434	+	1.25889i	0.0623016	+	0.122274i
$107$	−15.4842	+	11.2499i	−1.49691	+	1.08757i	−0.525319	+	0.850905i	$0.676054\pi$
$107$	−15.4842	+	11.2499i	−1.49691	+	1.08757i	−0.971591	+	0.236664i	$0.923946\pi$
$108$	1.44887	+	0.738234i	0.139417	+	0.0710366i
$109$	−8.41168	+	8.41168i	−0.805693	+	0.805693i	−0.983979	−	0.178286i	$-0.942945\pi$
$109$	−8.41168	+	8.41168i	−0.805693	+	0.805693i	0.178286	+	0.983979i	$0.442945\pi$
$110$	2.78073	+	17.5568i	0.265132	+	1.67398i
$111$	−0.145716	+	0.285983i	−0.0138307	+	0.0271443i
$112$	3.06774	−	1.56309i	0.289874	−	0.147698i
$113$	0.453420	−	1.39548i	0.0426541	−	0.131276i	−0.927462	−	0.373918i	$-0.878014\pi$
$113$	0.453420	−	1.39548i	0.0426541	−	0.131276i	0.970116	+	0.242642i	$0.0780141\pi$
$114$		−	0.335774i		−	0.0314481i
$115$	3.63299	+	1.18043i	0.338778	+	0.110076i
$116$	11.3836	+	1.80299i	1.05694	+	0.167403i
$117$	−7.72419	+	1.22339i	−0.714101	+	0.113103i
$118$	−17.1899	+	5.58535i	−1.58246	+	0.514173i
$119$	1.24463	+	3.83058i	0.114095	+	0.351148i
$120$	−0.0880580	−	0.0880580i	−0.00803856	−	0.00803856i
$121$	4.27639	−	5.88594i	0.388763	−	0.535086i
$122$	25.7424			2.33061
$123$	−0.763589	+	0.125966i	−0.0688505	+	0.0113580i
$124$	4.21208			0.378256
$125$	−7.03178	+	9.67842i	−0.628942	+	0.865664i
$126$	4.35079	+	4.35079i	0.387599	+	0.387599i
$127$	1.98026	+	6.09462i	0.175720	+	0.540810i	0.999666	−	0.0258588i	$-0.00823203\pi$
$127$	1.98026	+	6.09462i	0.175720	+	0.540810i	−0.823946	+	0.566668i	$0.808232\pi$
$128$	3.85589	−	1.25286i	0.340816	−	0.110738i
$129$	1.17475	−	0.186062i	0.103431	−	0.0163819i
$130$	10.7583	+	1.70395i	0.943566	+	0.149446i
$131$	13.1839	+	4.28370i	1.15188	+	0.374269i	0.821852	−	0.569702i	$-0.192941\pi$
$131$	13.1839	+	4.28370i	1.15188	+	0.374269i	0.330030	+	0.943971i	$0.392941\pi$
$132$			1.16142i			0.101088i
$133$	0.416533	−	1.28196i	0.0361180	−	0.111160i
$134$	9.08106	−	4.62703i	0.784484	−	0.399715i
$135$	−0.662595	+	1.30042i	−0.0570271	+	0.111922i
$136$	0.321784	+	2.03167i	0.0275928	+	0.174214i
$137$	−7.33853	+	7.33853i	−0.626973	+	0.626973i	−0.947305	−	0.320332i	$-0.896205\pi$
$137$	−7.33853	+	7.33853i	−0.626973	+	0.626973i	0.320332	+	0.947305i	$0.396205\pi$
$138$	0.420250	+	0.214128i	0.0357741	+	0.0182278i
$139$	11.9945	−	8.71453i	1.01736	−	0.739157i	0.0516219	−	0.998667i	$-0.483561\pi$
$139$	11.9945	−	8.71453i	1.01736	−	0.739157i	0.965741	+	0.259510i	$0.0835609\pi$
$140$	−2.05880	−	4.04062i	−0.174000	−	0.341495i
$141$	−0.682415	−	0.495804i	−0.0574697	−	0.0417542i
$142$	−3.83900	+	24.2385i	−0.322162	+	2.03405i
$143$	−6.58239	−	9.05989i	−0.550447	−	0.757626i
$144$	−6.04168	−	8.31566i	−0.503474	−	0.692972i
$145$	−1.61825	+	10.2172i	−0.134389	+	0.848496i
$146$	−8.30917	−	6.03696i	−0.687672	−	0.499623i
$147$	−0.0548713	−	0.107691i	−0.00452571	−	0.00888220i
$148$	−4.82921	+	3.50863i	−0.396959	+	0.288407i
$149$	−13.8512	−	7.05756i	−1.13474	−	0.578177i	−0.217319	−	0.976101i	$-0.569731\pi$
$149$	−13.8512	−	7.05756i	−1.13474	−	0.578177i	−0.917419	+	0.397923i	$0.869731\pi$
$150$	−0.163768	+	0.163768i	−0.0133716	+	0.0133716i
$151$	1.34083	+	8.46569i	0.109115	+	0.688928i	0.980232	+	0.197852i	$0.0633964\pi$
$151$	1.34083	+	8.46569i	0.109115	+	0.688928i	−0.871117	+	0.491076i	$0.836604\pi$
$152$	0.312528	−	0.613371i	0.0253494	−	0.0497510i
$153$	10.7137	−	5.45891i	0.866152	−	0.441327i
$154$	−2.72269	+	8.37957i	−0.219400	+	0.675245i
$155$			3.78051i			0.303658i
$156$	0.676850	+	0.219922i	0.0541914	+	0.0176079i
$157$	15.9667	+	2.52888i	1.27428	+	0.201827i	0.756675	−	0.653792i	$-0.226823\pi$
$157$	15.9667	+	2.52888i	1.27428	+	0.201827i	0.517608	+	0.855618i	$0.326823\pi$
$158$	5.58381	−	0.884389i	0.444224	−	0.0703582i
$159$	−0.0788003	+	0.0256038i	−0.00624927	+	0.00203051i
$160$	5.06077	+	15.5754i	0.400089	+	1.23135i
$161$	1.33885	+	1.33885i	0.105516	+	0.105516i
$162$	10.7439	−	14.7877i	0.844121	−	1.16183i
$163$	14.5675			1.14101			0.570507	−	0.821293i	$-0.306747\pi$
$163$	14.5675			1.14101			0.570507	+	0.821293i	$0.306747\pi$
$164$	−13.7167	−	4.35977i	−1.07110	−	0.340441i
$165$	−1.04242			−0.0811523
$166$	−10.7097	+	14.7407i	−0.831236	+	1.14410i
$167$	14.8068	+	14.8068i	1.14578	+	1.14578i	0.987373	+	0.158410i	$0.0506366\pi$
$167$	14.8068	+	14.8068i	1.14578	+	1.14578i	0.158410	+	0.987373i	$0.449363\pi$
$168$	−0.0190746	−	0.0587056i	−0.00147164	−	0.00452923i
$169$	5.83740	−	1.89669i	0.449031	−	0.145899i
$170$	−16.5413	+	2.61989i	−1.26866	+	0.200936i
$171$	−3.97456	−	0.629508i	−0.303942	−	0.0481397i
$172$	21.0373	+	6.83544i	1.60408	+	0.521197i
$173$			1.44765i			0.110062i	0.998485	+	0.0550312i	$0.0175258\pi$
$173$			1.44765i			0.110062i	−0.998485	+	0.0550312i	$0.982474\pi$
$174$	−0.394699	+	1.21476i	−0.0299220	+	0.0920905i
$175$	−0.828408	+	0.422095i	−0.0626218	+	0.0319074i
$176$	6.68218	−	13.1145i	0.503689	−	0.988544i
$177$	−0.165812	−	1.04690i	−0.0124632	−	0.0786896i
$178$	17.7037	−	17.7037i	1.32695	−	1.32695i
$179$	−18.7814	−	9.56962i	−1.40379	−	0.715267i	−0.422242	−	0.906483i	$-0.638757\pi$
$179$	−18.7814	−	9.56962i	−1.40379	−	0.715267i	−0.981548	+	0.191216i	$0.938757\pi$
$180$	−10.9528	+	7.95770i	−0.816376	+	0.593132i
$181$	1.24065	+	2.43491i	0.0922167	+	0.180985i	0.932508	−	0.361150i	$-0.117616\pi$
$181$	1.24065	+	2.43491i	0.0922167	+	0.180985i	−0.840291	+	0.542136i	$0.817616\pi$
$182$	4.36788	+	3.17345i	0.323769	+	0.235232i
$183$	−0.236155	+	1.49103i	−0.0174571	+	0.110220i
$184$	0.568383	+	0.782312i	0.0419017	+	0.0576728i
$185$	−3.14914	−	4.33441i	−0.231529	−	0.318672i
$186$	−0.0730217	+	0.461041i	−0.00535421	+	0.0338052i
$187$	13.9299	+	10.1207i	1.01866	+	0.740098i
$188$	−7.12191	−	13.9775i	−0.519419	−	1.01942i
$189$	−0.585259	+	0.425216i	−0.0425714	+	0.0309299i
$190$	4.99391	+	2.54453i	0.362297	+	0.184599i
$191$	2.06597	−	2.06597i	0.149488	−	0.149488i	−0.628401	−	0.777889i	$-0.716290\pi$
$191$	2.06597	−	2.06597i	0.149488	−	0.149488i	0.777889	+	0.628401i	$0.216290\pi$
$192$	0.186130	+	1.17518i	0.0134328	+	0.0848114i
$193$	−10.8289	+	21.2529i	−0.779481	+	1.52982i	0.0672148	+	0.997739i	$0.478589\pi$
$193$	−10.8289	+	21.2529i	−0.779481	+	1.52982i	−0.846695	+	0.532078i	$0.821411\pi$
$194$	15.8899	−	8.09629i	1.14083	−	0.581280i
$195$	−0.197389	+	0.607501i	−0.0141353	+	0.0435040i
$196$		−	2.24780i		−	0.160557i
$197$	−17.4731	−	5.67737i	−1.24491	−	0.404496i	−0.388815	−	0.921316i	$-0.627116\pi$
$197$	−17.4731	−	5.67737i	−1.24491	−	0.404496i	−0.856094	+	0.516820i	$0.827116\pi$
$198$	25.9799	+	4.11481i	1.84631	+	0.292427i
$199$	−18.9137	+	2.99563i	−1.34075	+	0.212354i	−0.785260	−	0.619166i	$-0.787471\pi$
$199$	−18.9137	+	2.99563i	−1.34075	+	0.212354i	−0.555494	+	0.831521i	$0.687471\pi$
$200$	−0.451591	+	0.146731i	−0.0319323	+	0.0103754i
$201$	0.184695	+	0.568432i	0.0130274	+	0.0400941i
$202$	−15.0762	−	15.0762i	−1.06076	−	1.06076i
$203$	−3.01385	+	4.14821i	−0.211531	+	0.291147i
$204$	−1.09424			−0.0766121
$205$	3.91307	−	12.3113i	0.273301	−	0.859859i
$206$	11.3645			0.791800
$207$	3.32252	−	4.57305i	0.230931	−	0.317849i
$208$	−6.37756	−	6.37756i	−0.442204	−	0.442204i
$209$	−1.78067	−	5.48034i	−0.123172	−	0.379083i
$210$	0.477966	−	0.155301i	0.0329828	−	0.0107168i
$211$	−7.55338	+	1.19634i	−0.519996	+	0.0823593i	−0.410915	−	0.911674i	$-0.634791\pi$
$211$	−7.55338	+	1.19634i	−0.519996	+	0.0823593i	−0.109081	+	0.994033i	$0.534791\pi$
$212$	−1.52195	−	0.241053i	−0.104528	−	0.0165556i
$213$	−1.36870	−	0.444718i	−0.0937818	−	0.0304716i
$214$		−	39.4468i		−	2.69653i
$215$	−6.13508	+	18.8818i	−0.418409	+	1.28773i
$216$	−0.329190	+	0.167731i	−0.0223985	+	0.0114126i
$217$	−0.850720	+	1.66963i	−0.0577506	+	0.113342i
$218$	−3.83541	−	24.2158i	−0.259767	−	1.64010i
$219$	0.425894	−	0.425894i	0.0287792	−	0.0287792i
$220$	−17.2736	−	8.80133i	−1.16458	−	0.593385i
$221$	8.53585	−	6.20166i	0.574183	−	0.417169i
$222$	−0.300323	−	0.589417i	−0.0201564	−	0.0395591i
$223$	−10.5109	−	7.63659i	−0.703860	−	0.511384i	0.177327	−	0.984152i	$-0.443255\pi$
$223$	−10.5109	−	7.63659i	−0.703860	−	0.511384i	−0.881187	+	0.472768i	$0.843255\pi$
$224$	−1.26986	+	8.01758i	−0.0848461	+	0.535697i
$225$	1.63149	+	2.24555i	0.108766	+	0.149703i
$226$	1.77754	+	2.44657i	0.118240	+	0.162743i
$227$	3.07912	−	19.4408i	0.204369	−	1.29033i	−0.645671	−	0.763615i	$-0.723422\pi$
$227$	3.07912	−	19.4408i	0.204369	−	1.29033i	0.850040	−	0.526718i	$-0.176578\pi$
$228$	0.296265	+	0.215249i	0.0196206	+	0.0142552i
$229$	−4.43029	−	8.69493i	−0.292762	−	0.574577i	0.697039	−	0.717033i	$-0.254500\pi$
$229$	−4.43029	−	8.69493i	−0.292762	−	0.574577i	−0.989801	+	0.142455i	$0.954500\pi$
$230$	−6.36939	+	4.62763i	−0.419985	+	0.305137i
$231$	−0.460376	−	0.234573i	−0.0302905	−	0.0154338i
$232$	−1.85167	+	1.85167i	−0.121568	+	0.121568i
$233$	3.07877	+	19.4386i	0.201697	+	1.27346i	0.855899	+	0.517143i	$0.173005\pi$
$233$	3.07877	+	19.4386i	0.201697	+	1.27346i	−0.654202	+	0.756320i	$0.726995\pi$
$234$	7.31748	−	14.3614i	0.478358	−	0.938831i
$235$	12.5454	−	6.39220i	0.818372	−	0.416981i
$236$	6.09151	−	18.7478i	0.396524	−	1.22037i
$237$			0.331533i			0.0215354i
$238$	−7.89488	−	2.56520i	−0.511749	−	0.166277i
$239$	−3.66584	−	0.580611i	−0.237123	−	0.0375566i	0.0367417	−	0.999325i	$-0.488302\pi$
$239$	−3.66584	−	0.580611i	−0.237123	−	0.0375566i	−0.273865	+	0.961768i	$0.588302\pi$
$240$	−0.829214	+	0.131335i	−0.0535256	+	0.00847761i
$241$	−9.91349	+	3.22109i	−0.638584	+	0.207488i	−0.610374	−	0.792114i	$-0.708981\pi$
$241$	−9.91349	+	3.22109i	−0.638584	+	0.207488i	−0.0282101	+	0.999602i	$0.508981\pi$
$242$	4.63364	+	14.2609i	0.297862	+	0.916725i
$243$	2.29256	+	2.29256i	0.147068	+	0.147068i
$244$	−16.5022	+	22.7134i	−1.05645	+	1.45407i
$245$	2.01749			0.128893
$246$	0.715004	−	1.42581i	0.0455870	−	0.0909061i
$247$	−3.53101			−0.224673
$248$	−0.562514	+	0.774234i	−0.0357197	+	0.0491639i
$249$	−0.755546	−	0.755546i	−0.0478808	−	0.0478808i
$250$	−7.61923	−	23.4496i	−0.481882	−	1.48308i
$251$	−20.1251	+	6.53905i	−1.27029	+	0.412741i	−0.865149	−	0.501515i	$-0.832776\pi$
$251$	−20.1251	+	6.53905i	−1.27029	+	0.412741i	−0.405137	+	0.914256i	$0.632776\pi$
$252$	−6.62793	+	1.04976i	−0.417520	+	0.0661287i
$253$	7.99468	+	1.26623i	0.502621	+	0.0796074i
$254$	−12.5611	−	4.08135i	−0.788154	−	0.256087i
$255$		−	0.982125i		−	0.0615030i
$256$	3.50198	−	10.7780i	0.218874	−	0.673624i
$257$	11.2533	−	5.73385i	0.701962	−	0.357668i	−0.0663027	−	0.997800i	$-0.521120\pi$
$257$	11.2533	−	5.73385i	0.701962	−	0.357668i	0.768265	+	0.640132i	$0.221120\pi$
$258$	−1.11289	+	2.18418i	−0.0692858	+	0.135981i
$259$	−0.415427	−	2.62290i	−0.0258134	−	0.162979i
$260$	−8.40009	+	8.40009i	−0.520952	+	0.520952i
$261$	13.6391	+	6.94946i	0.844239	+	0.430161i
$262$	−23.1141	+	16.7934i	−1.42799	+	1.03750i
$263$	2.02635	+	3.97693i	0.124950	+	0.245228i	0.945004	−	0.327057i	$-0.106057\pi$
$263$	2.02635	+	3.97693i	0.124950	+	0.245228i	−0.820055	+	0.572285i	$0.806057\pi$
$264$	−0.213484	−	0.155105i	−0.0131390	−	0.00954605i
$265$	0.216355	−	1.36601i	0.0132906	−	0.0839134i
$266$	1.63293	+	2.24754i	0.100121	+	0.137805i
$267$	0.863008	+	1.18783i	0.0528152	+	0.0726939i
$268$	−1.73885	+	10.9787i	−0.106217	+	0.670630i
$269$	10.6919	+	7.76813i	0.651898	+	0.473631i	0.863917	−	0.503634i	$-0.168004\pi$
$269$	10.6919	+	7.76813i	0.651898	+	0.473631i	−0.212019	+	0.977265i	$0.568004\pi$
$270$	−1.36562	−	2.68018i	−0.0831090	−	0.163111i
$271$	5.50831	−	4.00202i	0.334606	−	0.243106i	−0.407776	−	0.913082i	$-0.633696\pi$
$271$	5.50831	−	4.00202i	0.334606	−	0.243106i	0.742383	+	0.669976i	$0.233696\pi$
$272$	12.3560	+	6.29567i	0.749190	+	0.381731i
$273$	−0.223880	+	0.223880i	−0.0135498	+	0.0135498i
$274$	−3.34609	−	21.1264i	−0.202145	−	1.27629i
$275$	−1.80445	+	3.54143i	−0.108812	+	0.213556i
$276$	−0.458335	+	0.233533i	−0.0275885	+	0.0140571i
$277$	6.71419	−	20.6642i	0.403417	−	1.24159i	−0.518793	−	0.854900i	$-0.673619\pi$
$277$	6.71419	−	20.6642i	0.403417	−	1.24159i	0.922210	−	0.386689i	$-0.126381\pi$
$278$			30.5568i			1.83267i
$279$	5.32044	+	1.72872i	0.318526	+	0.103495i
$280$	1.01767	+	0.161183i	0.0608172	+	0.00963251i
$281$	−8.88241	+	1.40684i	−0.529880	+	0.0839248i	−0.415641	−	0.909529i	$-0.636443\pi$
$281$	−8.88241	+	1.40684i	−0.529880	+	0.0839248i	−0.114239	+	0.993453i	$0.536443\pi$
$282$	1.65340	−	0.537224i	0.0984588	−	0.0319912i
$283$	1.46451	+	4.50730i	0.0870562	+	0.267931i	0.985102	−	0.171970i	$-0.0550133\pi$
$283$	1.46451	+	4.50730i	0.0870562	+	0.267931i	−0.898046	+	0.439902i	$0.855013\pi$
$284$	−18.9254	−	18.9254i	−1.12302	−	1.12302i
$285$	−0.193195	+	0.265910i	−0.0114439	+	0.0157511i
$286$	23.0806			1.36478
$287$	4.49856	−	4.55664i	0.265542	−	0.268970i
$288$	24.2340			1.42800
$289$	0.457058	−	0.629086i	0.0268857	−	0.0370051i
$290$	−15.0758	−	15.0758i	−0.885282	−	0.885282i
$291$	0.323175	+	0.994631i	0.0189449	+	0.0583063i
$292$	10.6532	−	3.46144i	0.623433	−	0.202566i
$293$	8.66162	−	1.37187i	0.506017	−	0.0801452i	0.101794	−	0.994806i	$-0.467542\pi$
$293$	8.66162	−	1.37187i	0.506017	−	0.0801452i	0.404223	+	0.914660i	$0.367542\pi$
$294$	0.246037	+	0.0389684i	0.0143492	+	0.00227268i
$295$	16.8269	+	5.46738i	0.979698	+	0.318323i
$296$		−	1.35624i		−	0.0788299i
$297$	−0.955668	+	2.94124i	−0.0554535	+	0.170668i
$298$	28.5476	−	14.5457i	1.65372	−	0.842613i
$299$	2.25178	−	4.41936i	0.130224	−	0.255578i
$300$	−0.0395140	−	0.249482i	−0.00228134	−	0.0144038i
$301$	−6.95845	+	6.95845i	−0.401078	+	0.401078i
$302$	−15.7400	−	8.01994i	−0.905736	−	0.461496i
$303$	1.01154	−	0.734925i	0.0581113	−	0.0422203i
$304$	−2.10694	−	4.13510i	−0.120841	−	0.237164i
$305$	−20.3862	−	14.8114i	−1.16731	−	0.848099i
$306$	−3.87680	+	24.4771i	−0.221622	+	1.39927i
$307$	6.69528	+	9.21526i	0.382120	+	0.525943i	0.956145	−	0.292895i	$-0.0946187\pi$
$307$	6.69528	+	9.21526i	0.382120	+	0.525943i	−0.574025	+	0.818838i	$0.694619\pi$
$308$	−5.64819	−	7.77406i	−0.321835	−	0.442968i
$309$	−0.104255	+	0.658242i	−0.00593087	+	0.0374461i
$310$	−6.30362	−	4.57985i	−0.358022	−	0.260118i
$311$	13.3027	+	26.1081i	0.754329	+	1.48045i	0.873105	+	0.487533i	$0.162103\pi$
$311$	13.3027	+	26.1081i	0.754329	+	1.48045i	−0.118776	+	0.992921i	$0.537897\pi$
$312$	−0.130816	+	0.0950437i	−0.00740602	+	0.00538079i
$313$	−14.6385	−	7.45870i	−0.827419	−	0.421591i	−0.0116239	−	0.999932i	$-0.503700\pi$
$313$	−14.6385	−	7.45870i	−0.827419	−	0.421591i	−0.815795	+	0.578342i	$0.803700\pi$
$314$	−23.5593	+	23.5593i	−1.32953	+	1.32953i
$315$	−0.942203	−	5.94884i	−0.0530871	−	0.335179i
$316$	−2.79919	+	5.49372i	−0.157467	+	0.309046i
$317$	−11.3568	+	5.78657i	−0.637860	+	0.325006i	−0.742841	−	0.669468i	$-0.766522\pi$
$317$	−11.3568	+	5.78657i	−0.637860	+	0.325006i	0.104980	+	0.994474i	$0.466522\pi$
$318$	0.0527698	−	0.162409i	0.00295919	−	0.00910744i
$319$			21.9198i			1.22727i
$320$	−18.8888	−	6.13734i	−1.05591	−	0.343088i
$321$	2.28480	+	0.361877i	0.127525	+	0.0201980i
$322$	−3.85433	+	0.610466i	−0.214793	+	0.0340199i
$323$	5.16335	−	1.67767i	0.287296	−	0.0933482i
$324$	6.16029	+	18.9594i	0.342238	+	1.05330i
$325$	1.72219	+	1.72219i	0.0955297	+	0.0955297i
$326$	−17.6476	+	24.2898i	−0.977409	+	1.34529i
$327$	1.43779			0.0795100
$328$	2.63322	−	1.93907i	0.145395	−	0.107067i
$329$	6.97900			0.384764
$330$	1.26283	−	1.73813i	0.0695162	−	0.0956809i
$331$	−2.11151	−	2.11151i	−0.116059	−	0.116059i	0.646692	−	0.762751i	$-0.276152\pi$
$331$	−2.11151	−	2.11151i	−0.116059	−	0.116059i	−0.762751	+	0.646692i	$0.776152\pi$
$332$	−6.14069	−	18.8991i	−0.337014	−	1.03722i
$333$	−7.53997	+	2.44988i	−0.413188	+	0.134253i
$334$	−42.6263	+	6.75134i	−2.33241	+	0.369417i
$335$	−9.85382	−	1.56069i	−0.538372	−	0.0852697i
$336$	−0.395770	−	0.128593i	−0.0215910	−	0.00701534i
$337$			2.73537i			0.149005i	0.997221	+	0.0745024i	$0.0237369\pi$
$337$			2.73537i			0.149005i	−0.997221	+	0.0745024i	$0.976263\pi$
$338$	−3.90911	+	12.0310i	−0.212627	+	0.654400i
$339$	−0.158015	+	0.0805124i	−0.00858217	+	0.00437283i
$340$	8.29224	−	16.2744i	0.449710	−	0.882606i
$341$	1.25316	+	7.91213i	0.0678623	+	0.428466i
$342$	5.86456	−	5.86456i	0.317119	−	0.317119i
$343$	0.891007	+	0.453990i	0.0481098	+	0.0245132i
$344$	−4.06593	+	2.95407i	−0.219220	+	0.159273i
$345$	−0.209606	−	0.411374i	−0.0112848	−	0.0221476i
$346$	−2.41380	−	1.75373i	−0.129767	−	0.0942811i
$347$	−1.40825	+	8.89133i	−0.0755987	+	0.477312i	0.920622	+	0.390455i	$0.127682\pi$
$347$	−1.40825	+	8.89133i	−0.0755987	+	0.477312i	−0.996221	+	0.0868568i	$0.972318\pi$
$348$	−0.818798	−	1.12698i	−0.0438922	−	0.0604124i
$349$	0.200943	+	0.276574i	0.0107562	+	0.0148046i	0.814361	−	0.580358i	$-0.197087\pi$
$349$	0.200943	+	0.276574i	0.0107562	+	0.0148046i	−0.803605	+	0.595163i	$0.797087\pi$
$350$	0.299763	−	1.89263i	0.0160230	−	0.101165i
$351$	1.53313	+	1.11389i	0.0818326	+	0.0594549i
$352$	15.7545	+	30.9199i	0.839716	+	1.64804i
$353$	−5.23603	+	3.80420i	−0.278686	+	0.202477i	−0.718344	−	0.695688i	$-0.755100\pi$
$353$	−5.23603	+	3.80420i	−0.278686	+	0.202477i	0.439658	+	0.898165i	$0.355100\pi$
$354$	1.94647	+	0.991774i	0.103454	+	0.0527122i
$355$	16.9863	−	16.9863i	0.901541	−	0.901541i
$356$	4.27156	+	26.9696i	0.226392	+	1.42939i
$357$	0.221005	−	0.433747i	0.0116968	−	0.0229563i
$358$	38.7089	−	19.7232i	2.04583	−	1.04240i
$359$	5.92342	−	18.2304i	0.312626	−	0.962164i	−0.664095	−	0.747649i	$-0.731183\pi$
$359$	5.92342	−	18.2304i	0.312626	−	0.962164i	0.976721	−	0.214515i	$-0.0688172\pi$
$360$		−	3.07601i		−	0.162120i
$361$	16.3421	+	5.30986i	0.860110	+	0.279467i
$362$	−5.56293	−	0.881082i	−0.292381	−	0.0463086i
$363$	−0.868513	+	0.137559i	−0.0455851	+	0.00721997i
$364$	−5.60008	+	1.81958i	−0.293524	+	0.0953718i
$365$	3.10679	+	9.56170i	0.162617	+	0.500482i
$366$	−2.20005	−	2.20005i	−0.114998	−	0.114998i
$367$	17.8742	−	24.6018i	0.933028	−	1.28420i	−0.0256393	−	0.999671i	$-0.508162\pi$
$367$	17.8742	−	24.6018i	0.933028	−	1.28420i	0.958667	−	0.284531i	$-0.0918379\pi$
$368$	6.51906			0.339830
$369$	−15.5368	−	11.1366i	−0.808813	−	0.579748i
$370$	11.0422			0.574055
$371$	0.402942	−	0.554602i	0.0209197	−	0.0287935i
$372$	−0.359981	−	0.359981i	−0.0186642	−	0.0186642i
$373$	−6.73940	−	20.7417i	−0.348953	−	1.07397i	−0.959433	−	0.281935i	$-0.909024\pi$
$373$	−6.73940	−	20.7417i	−0.348953	−	1.07397i	0.610481	−	0.792031i	$-0.290976\pi$
$374$	−33.7504	+	10.9662i	−1.74519	+	0.567048i
$375$	1.42812	−	0.226192i	0.0737478	−	0.0116805i
$376$	3.52037	+	0.557571i	0.181549	+	0.0287545i
$377$	12.7744	+	4.15066i	0.657916	+	0.213770i
$378$		−	1.49098i		−	0.0766879i
$379$	−10.8218	+	33.3060i	−0.555877	+	1.71081i	0.137738	+	0.990469i	$0.456017\pi$
$379$	−10.8218	+	33.3060i	−0.555877	+	1.71081i	−0.693615	+	0.720345i	$0.743983\pi$
$380$	−5.44648	+	2.77512i	−0.279399	+	0.142361i
$381$	0.351629	−	0.690111i	0.0180145	−	0.0353555i
$382$	0.942004	+	5.94758i	0.0481971	+	0.304305i
$383$	−8.05819	+	8.05819i	−0.411754	+	0.411754i	−0.882349	−	0.470595i	$-0.844039\pi$
$383$	−8.05819	+	8.05819i	−0.411754	+	0.411754i	0.470595	+	0.882349i	$0.344039\pi$
$384$	−0.436614	−	0.222466i	−0.0222809	−	0.0113527i
$385$	6.97754	−	5.06948i	0.355608	−	0.258365i
$386$	−22.3185	−	43.8026i	−1.13598	−	2.22949i
$387$	23.7677	+	17.2682i	1.20818	+	0.877792i
$388$	−3.04261	+	19.2103i	−0.154465	+	0.975256i
$389$	−12.9108	−	17.7702i	−0.654603	−	0.900984i	0.344685	−	0.938718i	$-0.387986\pi$
$389$	−12.9108	−	17.7702i	−0.654603	−	0.900984i	−0.999288	+	0.0377349i	$0.987986\pi$
$390$	−0.773822	−	1.06507i	−0.0391840	−	0.0539321i
$391$	−1.19299	+	7.53225i	−0.0603322	+	0.380922i
$392$	0.413174	+	0.300188i	0.0208684	+	0.0151618i
$393$	−0.760645	−	1.49285i	−0.0383695	−	0.0753043i
$394$	30.6340	−	22.2569i	1.54332	−	1.12129i
$395$	−4.93084	−	2.51239i	−0.248097	−	0.126412i
$396$	−20.2851	+	20.2851i	−1.01936	+	1.01936i
$397$	−3.10905	−	19.6298i	−0.156039	−	0.985191i	−0.934102	−	0.357006i	$-0.883798\pi$
$397$	−3.10905	−	19.6298i	−0.156039	−	0.985191i	0.778063	−	0.628186i	$-0.216202\pi$
$398$	17.9178	−	35.1656i	0.898137	−	1.76269i
$399$	−0.145160	+	0.0739626i	−0.00726708	+	0.00370276i
$400$	−0.989199	+	3.04444i	−0.0494600	+	0.152222i
$401$			20.9629i			1.04684i	0.852076	+	0.523419i	$0.175344\pi$
$401$			20.9629i			1.04684i	−0.852076	+	0.523419i	$0.824656\pi$
$402$	−1.17155	−	0.380659i	−0.0584315	−	0.0189855i
$403$	4.84832	+	0.767898i	0.241512	+	0.0382517i
$404$	22.9669	−	3.63760i	1.14265	−	0.180978i
$405$	−17.0168	+	5.52911i	−0.845574	+	0.274744i
$406$	−3.26563	−	10.0506i	−0.162071	−	0.498802i
$407$	−8.02750	−	8.02750i	−0.397909	−	0.397909i
$408$	0.146133	−	0.201135i	0.00723468	−	0.00995768i
$409$	34.0148			1.68192			0.840961	−	0.541095i	$-0.181990\pi$
$409$	34.0148			1.68192			0.840961	+	0.541095i	$0.181990\pi$
$410$	15.7874	+	21.4390i	0.779686	+	1.05880i
$411$	1.25436			0.0618730
$412$	−7.28522	+	10.0272i	−0.358917	+	0.494007i
$413$	6.20113	+	6.20113i	0.305138	+	0.305138i
$414$	3.60008	+	11.0799i	0.176935	+	0.544548i
$415$	16.9627	−	5.51151i	0.832666	−	0.270550i
$416$	21.0027	−	3.32650i	1.02974	−	0.163095i
$417$	−1.76988	−	0.280321i	−0.0866713	−	0.0137274i
$418$	11.2951	+	3.66999i	0.552460	+	0.179505i
$419$		−	24.1583i		−	1.18021i	−0.807326	−	0.590106i	$-0.799086\pi$
$419$		−	24.1583i		−	1.18021i	0.807326	−	0.590106i	$-0.200914\pi$
$420$	−0.169375	+	0.521281i	−0.00826463	+	0.0254359i
$421$	−18.0836	+	9.21403i	−0.881339	+	0.449064i	−0.835248	−	0.549873i	$-0.814676\pi$
$421$	−18.0836	+	9.21403i	−0.881339	+	0.449064i	−0.0460902	+	0.998937i	$0.514676\pi$
$422$	7.15567	−	14.0438i	0.348332	−	0.683641i
$423$	−3.25932	−	20.5785i	−0.158473	−	1.00056i
$424$	0.247562	−	0.247562i	0.0120227	−	0.0120227i
$425$	−3.33658	−	1.70007i	−0.161848	−	0.0824657i
$426$	2.39961	−	1.74342i	0.116262	−	0.0844691i
$427$	−5.67040	−	11.1288i	−0.274410	−	0.538560i
$428$	34.8052	+	25.2875i	1.68237	+	1.22232i
$429$	−0.211737	+	1.33685i	−0.0102227	+	0.0645438i
$430$	−24.0513	−	33.1038i	−1.15986	−	1.59641i
$431$	10.5317	+	14.4956i	0.507293	+	0.698230i	0.983460	−	0.181126i	$-0.0579741\pi$
$431$	10.5317	+	14.4956i	0.507293	+	0.698230i	−0.476167	+	0.879355i	$0.657974\pi$
$432$	−0.389638	+	2.46008i	−0.0187465	+	0.118360i
$433$	17.7840	+	12.9208i	0.854644	+	0.620935i	0.926423	−	0.376485i	$-0.122868\pi$
$433$	17.7840	+	12.9208i	0.854644	+	0.620935i	−0.0717786	+	0.997421i	$0.522868\pi$
$434$	−1.75335	−	3.44114i	−0.0841635	−	0.165180i
$435$	1.01151	−	0.734904i	0.0484982	−	0.0352360i
$436$	23.8251	+	12.1395i	1.14102	+	0.581377i
$437$	1.80468	−	1.80468i	0.0863294	−	0.0863294i
$438$	0.194192	+	1.22608i	0.00927883	+	0.0585842i
$439$	10.7374	−	21.0733i	0.512468	−	1.00577i	−0.479291	−	0.877656i	$-0.659106\pi$
$439$	10.7374	−	21.0733i	0.512468	−	1.00577i	0.991759	−	0.128119i	$-0.0408939\pi$
$440$	3.92465	−	1.99971i	0.187100	−	0.0953323i
$441$	0.922537	−	2.83928i	0.0439303	−	0.135204i
$442$			21.7456i			1.03433i
$443$	−1.04719	−	0.340252i	−0.0497535	−	0.0161659i	0.284035	−	0.958814i	$-0.408327\pi$
$443$	−1.04719	−	0.340252i	−0.0497535	−	0.0161659i	−0.333788	+	0.942648i	$0.608327\pi$
$444$	0.712585	+	0.112862i	0.0338178	+	0.00535621i
$445$	−24.2063	+	3.83390i	−1.14749	+	0.181744i
$446$	25.4665	−	8.27456i	1.20587	−	0.391812i
$447$	0.580615	+	1.78695i	0.0274621	+	0.0845198i
$448$	−6.96100	−	6.96100i	−0.328876	−	0.328876i
$449$	−16.5741	+	22.8123i	−0.782180	+	1.07658i	0.212858	+	0.977083i	$0.431723\pi$
$449$	−16.5741	+	22.8123i	−0.782180	+	1.07658i	−0.995038	+	0.0994958i	$0.968277\pi$
$450$	−5.72067			−0.269675
$451$	4.10862	−	27.0631i	0.193468	−	1.27435i
$452$	−3.29818			−0.155133
$453$	0.608919	−	0.838105i	0.0286095	−	0.0393776i
$454$	28.6854	+	28.6854i	1.34627	+	1.34627i
$455$	−1.63314	−	5.02630i	−0.0765630	−	0.235637i
$456$	−0.0791310	+	0.0257112i	−0.00370565	+	0.00120404i
$457$	−15.6421	+	2.47746i	−0.731705	+	0.115891i	−0.511159	−	0.859486i	$-0.670784\pi$
$457$	−15.6421	+	2.47746i	−0.731705	+	0.115891i	−0.220546	+	0.975377i	$0.570784\pi$
$458$	19.8649	+	3.14630i	0.928227	+	0.147017i
$459$	−2.77112	−	0.900390i	−0.129345	−	0.0420266i
$460$		−	8.58647i		−	0.400346i
$461$	12.4629	−	38.3569i	0.580455	−	1.78646i	−0.0363469	−	0.999339i	$-0.511572\pi$
$461$	12.4629	−	38.3569i	0.580455	−	1.78646i	0.616802	−	0.787118i	$-0.288428\pi$
$462$	0.948843	−	0.483460i	0.0441442	−	0.0224926i
$463$	−4.24943	+	8.33997i	−0.197488	+	0.387592i	−0.968420	−	0.249326i	$-0.919791\pi$
$463$	−4.24943	+	8.33997i	−0.197488	+	0.387592i	0.770932	+	0.636918i	$0.219791\pi$
$464$	2.76168	+	17.4366i	0.128208	+	0.809472i
$465$	0.323098	−	0.323098i	0.0149833	−	0.0149833i
$466$	−36.1416	−	18.4151i	−1.67423	−	0.853061i
$467$	9.93430	−	7.21769i	0.459705	−	0.333995i	−0.333711	−	0.942676i	$-0.608301\pi$
$467$	9.93430	−	7.21769i	0.459705	−	0.333995i	0.793415	+	0.608681i	$0.208301\pi$
$468$	7.98061	+	15.6628i	0.368904	+	0.724015i
$469$	−4.00066	−	2.90665i	−0.184733	−	0.134217i
$470$	−4.53960	+	28.6619i	−0.209396	+	1.32208i
$471$	−1.14845	−	1.58071i	−0.0529178	−	0.0728351i
$472$	2.63257	+	3.62342i	0.121174	+	0.166781i
$473$	−6.58102	+	41.5510i	−0.302596	+	1.91051i
$474$	−0.552798	−	0.401631i	−0.0253909	−	0.0184475i
$475$	0.568955	+	1.11664i	0.0261054	+	0.0512348i
$476$	7.32440	−	5.32149i	0.335713	−	0.243910i
$477$	−1.82350	−	0.929119i	−0.0834923	−	0.0425415i
$478$	5.40904	−	5.40904i	0.247404	−	0.247404i
$479$	6.40229	+	40.4225i	0.292528	+	1.84695i	0.496580	+	0.867991i	$0.334589\pi$
$479$	6.40229	+	40.4225i	0.292528	+	1.84695i	−0.204052	+	0.978960i	$0.565411\pi$
$480$	0.898626	−	1.76365i	0.0410165	−	0.0804994i
$481$	−6.19832	+	3.15820i	−0.282619	+	0.144002i
$482$	6.63872	−	20.4319i	0.302385	−	0.930646i
$483$		−	0.228847i		−	0.0104129i
$484$	−15.5533	−	5.05356i	−0.706966	−	0.229707i
$485$	−17.2420	−	2.73087i	−0.782920	−	0.124002i
$486$	−6.59991	+	1.04532i	−0.299378	+	0.0474168i
$487$	−8.84389	+	2.87355i	−0.400755	+	0.130213i	−0.502458	−	0.864602i	$-0.667571\pi$
$487$	−8.84389	+	2.87355i	−0.400755	+	0.130213i	0.101703	+	0.994815i	$0.467571\pi$
$488$	−1.97117	−	6.06664i	−0.0892308	−	0.274624i
$489$	−1.24500	−	1.24500i	−0.0563007	−	0.0563007i
$490$	−2.44406	+	3.36396i	−0.110411	+	0.151968i
$491$	10.0643			0.454195			0.227097	−	0.973872i	$-0.427076\pi$
$491$	10.0643			0.454195			0.227097	+	0.973872i	$0.427076\pi$
$492$	0.799682	+	1.54489i	0.0360525	+	0.0696490i
$493$	−20.6519			−0.930117
$494$	4.27759	−	5.88760i	0.192458	−	0.264896i
$495$	−18.2067	−	18.2067i	−0.818330	−	0.818330i
$496$	1.99370	+	6.13598i	0.0895198	+	0.275514i
$497$	11.3243	−	3.67948i	0.507963	−	0.165047i
$498$	2.17509	−	0.344501i	0.0974682	−	0.0154374i
$499$	1.50601	+	0.238529i	0.0674185	+	0.0106780i	0.190053	−	0.981774i	$-0.439134\pi$
$499$	1.50601	+	0.238529i	0.0674185	+	0.0106780i	−0.122634	+	0.992452i	$0.539134\pi$
$500$	25.5747	+	8.30971i	1.14373	+	0.371622i
$501$		−	2.53089i		−	0.113072i
$502$	13.4771	−	41.4782i	0.601512	−	1.85126i
$503$	−16.4937	+	8.40395i	−0.735417	+	0.374714i	−0.781236	−	0.624236i	$-0.785410\pi$
$503$	−16.4937	+	8.40395i	−0.735417	+	0.374714i	0.0458189	+	0.998950i	$0.485410\pi$
$504$	0.692186	−	1.35849i	0.0308324	−	0.0605121i
$505$	3.26490	+	20.6138i	0.145286	+	0.917300i
$506$	−11.7964	+	11.7964i	−0.524412	+	0.524412i
$507$	−0.660986	−	0.336789i	−0.0293554	−	0.0149573i
$508$	11.6534	−	8.46673i	0.517038	−	0.375650i
$509$	−16.7793	−	32.9312i	−0.743730	−	1.45965i	−0.882988	−	0.469396i	$-0.844472\pi$
$509$	−16.7793	−	32.9312i	−0.743730	−	1.45965i	0.139258	−	0.990256i	$-0.455528\pi$
$510$	1.63759	+	1.18978i	0.0725139	+	0.0526844i
$511$	−0.779562	+	4.92196i	−0.0344858	+	0.217735i
$512$	18.4949	+	25.4561i	0.817368	+	1.12501i
$513$	0.573161	+	0.788889i	0.0253057	+	0.0348303i
$514$	−4.07206	+	25.7100i	−0.179611	+	1.13402i
$515$	−8.99986	−	6.53878i	−0.396581	−	0.288133i
$516$	−1.21375	−	2.38212i	−0.0534323	−	0.104867i
$517$	24.1371	−	17.5366i	1.06155	−	0.771259i
$518$	4.87668	+	2.48479i	0.214269	+	0.109176i
$519$	0.123722	−	0.123722i	0.00543078	−	0.00543078i
$520$	−0.422231	−	2.66586i	−0.0185160	−	0.116906i
$521$	16.4378	−	32.2610i	0.720152	−	1.41338i	−0.182587	−	0.983190i	$-0.558447\pi$
$521$	16.4378	−	32.2610i	0.720152	−	1.41338i	0.902739	−	0.430188i	$-0.141553\pi$
$522$	−28.1104	+	14.3230i	−1.23036	+	0.626899i
$523$	−0.194942	+	0.599971i	−0.00852424	+	0.0262349i	−0.955228	−	0.295870i	$-0.904390\pi$
$523$	−0.194942	+	0.599971i	−0.00852424	+	0.0262349i	0.946704	+	0.322105i	$0.104390\pi$
$524$		−	31.1597i		−	1.36122i
$525$	0.106873	+	0.0347251i	0.00466432	+	0.00151553i
$526$	−9.08591	−	1.43907i	−0.396164	−	0.0627463i
$527$	−7.45448	+	1.18067i	−0.324722	+	0.0514310i
$528$	−1.69191	+	0.549733i	−0.0736307	+	0.0239241i
$529$	−5.99955	−	18.4647i	−0.260850	−	0.802814i
$530$	2.01558	+	2.01558i	0.0875514	+	0.0875514i
$531$	15.3888	−	21.1809i	0.667819	−	0.919174i
$532$	−3.02987			−0.131362
$533$	−14.9938	−	7.51899i	−0.649454	−	0.325684i
$534$	−3.02606			−0.130950
$535$	−22.6965	+	31.2391i	−0.981257	+	1.35058i
$536$	−1.78580	−	1.78580i	−0.0771350	−	0.0771350i
$537$	0.787279	+	2.42299i	0.0339736	+	0.104560i
$538$	−25.9051	+	8.41709i	−1.11685	+	0.362887i
$539$	4.22234	−	0.668754i	0.181869	−	0.0288053i
$540$	3.24025	+	0.513205i	0.139438	+	0.0220848i
$541$	31.6015	+	10.2679i	1.35865	+	0.441453i	0.895593	−	0.444874i	$-0.146751\pi$
$541$	31.6015	+	10.2679i	1.35865	+	0.441453i	0.463060	+	0.886327i	$0.346751\pi$
$542$			14.0327i			0.602758i
$543$	0.102066	−	0.314128i	0.00438008	−	0.0134805i
$544$	−29.1314	+	14.8432i	−1.24900	+	0.636397i
$545$	−10.8957	+	21.3840i	−0.466721	+	0.915991i
$546$	−0.102081	−	0.644512i	−0.00436865	−	0.0275826i
$547$	−23.6886	+	23.6886i	−1.01285	+	1.01285i	−0.0129360	+	0.999916i	$0.504118\pi$
$547$	−23.6886	+	23.6886i	−1.01285	+	1.01285i	−0.999916	+	0.0129360i	$0.995882\pi$
$548$	20.7856	+	10.5908i	0.887915	+	0.452415i
$549$	−30.1666	+	21.9173i	−1.28748	+	0.935408i
$550$	−3.71900	−	7.29894i	−0.158579	−	0.311228i
$551$	5.59150	+	4.06246i	0.238206	+	0.173067i
$552$	0.0182832	−	0.115436i	0.000778186	−	0.00491327i
$553$	−1.61231	−	2.21915i	−0.0685623	−	0.0943679i
$554$	26.3216	+	36.2285i	1.11830	+	1.53920i
$555$	−0.101299	+	0.639574i	−0.00429988	+	0.0271484i
$556$	−26.9612	−	19.5885i	−1.14341	−	0.830737i
$557$	−12.3361	−	24.2109i	−0.522697	−	1.02585i	−0.989909	−	0.141705i	$-0.954742\pi$
$557$	−12.3361	−	24.2109i	−0.522697	−	1.02585i	0.467212	−	0.884145i	$-0.345258\pi$
$558$	−9.32783	+	6.77707i	−0.394879	+	0.286896i
$559$	22.9689	+	11.7032i	0.971480	+	0.494994i
$560$	4.91172	−	4.91172i	0.207558	−	0.207558i
$561$	−0.325553	−	2.05546i	−0.0137449	−	0.0867817i
$562$	8.41471	−	16.5148i	0.354953	−	0.696635i
$563$	−40.1164	+	20.4403i	−1.69070	+	0.861457i	−0.701894	+	0.712281i	$0.747662\pi$
$563$	−40.1164	+	20.4403i	−1.69070	+	0.861457i	−0.988811	+	0.149176i	$0.952338\pi$
$564$	−0.585909	+	1.80324i	−0.0246712	+	0.0759302i
$565$		−	2.96025i		−	0.124539i
$566$	−9.28964	−	3.01839i	−0.390473	−	0.126872i
$567$	−8.75955	−	1.38738i	−0.367867	−	0.0582643i
$568$	6.00619	−	0.951286i	0.252014	−	0.0399151i
$569$	36.5202	−	11.8661i	1.53101	−	0.497454i	0.582128	−	0.813097i	$-0.302220\pi$
$569$	36.5202	−	11.8661i	1.53101	−	0.497454i	0.948878	+	0.315643i	$0.102220\pi$
$570$	−0.209334	−	0.644265i	−0.00876805	−	0.0269853i
$571$	−0.359411	−	0.359411i	−0.0150409	−	0.0150409i	0.699546	−	0.714587i	$-0.253385\pi$
$571$	−0.359411	−	0.359411i	−0.0150409	−	0.0150409i	−0.714587	+	0.699546i	$0.753385\pi$
$572$	−14.7959	+	20.3648i	−0.618647	+	0.851494i
$573$	−0.353132			−0.0147523
$574$	2.14802	+	13.0210i	0.0896564	+	0.543485i
$575$	−1.76040			−0.0734137
$576$	−17.2745	+	23.7764i	−0.719773	+	0.990682i
$577$	6.59658	+	6.59658i	0.274619	+	0.274619i	0.830957	−	0.556337i	$-0.187794\pi$
$577$	6.59658	+	6.59658i	0.274619	+	0.274619i	−0.556337	+	0.830957i	$0.687794\pi$
$578$	0.495241	+	1.52419i	0.0205993	+	0.0633981i
$579$	2.74184	−	0.890877i	0.113947	−	0.0370236i
$580$	22.9663	−	3.63750i	0.953623	−	0.151039i
$581$	8.73168	+	1.38296i	0.362251	+	0.0573749i
$582$	−2.04995	−	0.666070i	−0.0849733	−	0.0276095i
$583$		−	2.93060i		−	0.121373i
$584$	−0.786458	+	2.42047i	−0.0325439	+	0.100160i
$585$	−14.0580	+	7.16292i	−0.581228	+	0.296150i
$586$	−8.20555	+	16.1043i	−0.338968	+	0.665262i
$587$	−0.875878	−	5.53007i	−0.0361513	−	0.228251i	0.962997	−	0.269512i	$-0.0868624\pi$
$587$	−0.875878	−	5.53007i	−0.0361513	−	0.228251i	−0.999148	+	0.0412613i	$0.986862\pi$
$588$	−0.192106	+	0.192106i	−0.00792230	+	0.00792230i
$589$	2.25055	+	1.14671i	0.0927322	+	0.0472494i
$590$	−29.5010	+	21.4337i	−1.21454	+	0.882412i
$591$	1.00811	+	1.97853i	0.0414682	+	0.0813860i
$592$	−7.39703	−	5.37426i	−0.304016	−	0.220881i
$593$	−4.04012	+	25.5083i	−0.165908	+	1.04750i	0.754431	+	0.656379i	$0.227913\pi$
$593$	−4.04012	+	25.5083i	−0.165908	+	1.04750i	−0.920339	+	0.391122i	$0.872087\pi$
$594$	−3.74649	−	5.15661i	−0.153720	−	0.211578i
$595$	4.77625	+	6.57395i	0.195807	+	0.269506i
$596$	−5.46634	+	34.5131i	−0.223910	+	1.41371i
$597$	1.87245	+	1.36042i	0.0766345	+	0.0556782i
$598$	4.64095	+	9.10839i	0.189783	+	0.372470i
$599$	27.7037	−	20.1279i	1.13194	−	0.822403i	0.145965	−	0.989290i	$-0.453371\pi$
$599$	27.7037	−	20.1279i	1.13194	−	0.822403i	0.985976	+	0.166886i	$0.0533713\pi$
$600$	0.0511349	+	0.0260545i	0.00208757	+	0.00106367i
$601$	1.64341	−	1.64341i	0.0670362	−	0.0670362i	−0.672794	−	0.739830i	$-0.734906\pi$
$601$	1.64341	−	1.64341i	0.0670362	−	0.0670362i	0.739830	+	0.672794i	$0.234906\pi$
$602$	−3.17279	−	20.0322i	−0.129313	−	0.816452i
$603$	−6.70227	+	13.1539i	−0.272938	+	0.535670i
$604$	17.1664	−	8.74673i	0.698492	−	0.355900i
$605$	4.53578	−	13.9597i	0.184406	−	0.567542i
$606$			2.57695i			0.104681i
$607$	−4.70107	−	1.52747i	−0.190811	−	0.0619981i	0.212053	−	0.977258i	$-0.431985\pi$
$607$	−4.70107	−	1.52747i	−0.190811	−	0.0619981i	−0.402864	+	0.915260i	$0.631985\pi$
$608$	10.8071	+	1.71168i	0.438287	+	0.0694179i
$609$	0.612098	−	0.0969469i	0.0248035	−	0.00392849i
$610$	49.3931	−	16.0488i	1.99987	−	0.649796i
$611$	−5.64946	−	17.3872i	−0.228553	−	0.703413i
$612$	−19.1118	−	19.1118i	−0.772547	−	0.772547i
$613$	3.60837	−	4.96650i	0.145741	−	0.200595i	−0.729905	−	0.683548i	$-0.760436\pi$
$613$	3.60837	−	4.96650i	0.145741	−	0.200595i	0.875646	+	0.482953i	$0.160436\pi$
$614$	−23.4764			−0.947431
$615$	−1.38660	+	0.717747i	−0.0559131	+	0.0289424i
$616$	2.18328			0.0879667
$617$	17.3549	−	23.8870i	0.698682	−	0.961653i	−0.301285	−	0.953534i	$-0.597416\pi$
$617$	17.3549	−	23.8870i	0.698682	−	0.961653i	0.999967	−	0.00811872i	$-0.00258430\pi$
$618$	−0.971253	−	0.971253i	−0.0390695	−	0.0390695i
$619$	8.91243	+	27.4297i	0.358221	+	1.10249i	0.954118	+	0.299430i	$0.0967966\pi$
$619$	8.91243	+	27.4297i	0.358221	+	1.10249i	−0.595897	+	0.803061i	$0.703203\pi$
$620$	8.08191	−	2.62597i	0.324577	−	0.105462i
$621$	−1.35288	+	0.214274i	−0.0542890	+	0.00859854i
$622$	−59.6480	−	9.44732i	−2.39167	−	0.378803i
$623$	−11.5532	−	3.75388i	−0.462871	−	0.150396i
$624$			1.09010i			0.0436390i
$625$	−6.02177	+	18.5331i	−0.240871	+	0.741324i
$626$	30.1703	−	15.3725i	1.20585	−	0.614409i
$627$	−0.316189	+	0.620555i	−0.0126274	+	0.0247826i
$628$	−5.68440	−	35.8899i	−0.226832	−	1.43216i
$629$	7.56318	−	7.56318i	0.301564	−	0.301564i
$630$	11.0605	+	5.63561i	0.440661	+	0.224528i
$631$	−2.82845	+	2.05499i	−0.112599	+	0.0818079i	−0.642660	−	0.766152i	$-0.722169\pi$
$631$	−2.82845	+	2.05499i	−0.112599	+	0.0818079i	0.530061	+	0.847960i	$0.322169\pi$
$632$	−0.635991	−	1.24820i	−0.0252984	−	0.0496508i
$633$	0.747786	+	0.543298i	0.0297218	+	0.0215942i
$634$	4.10950	−	25.9463i	0.163209	−	1.03046i
$635$	7.59923	+	10.4594i	0.301566	+	0.415070i
$636$	0.109470	+	0.150673i	0.00434079	+	0.00597458i
$637$	0.409792	−	2.58733i	0.0162366	−	0.102514i
$638$	−36.5491	−	26.5545i	−1.44699	−	1.05130i
$639$	−16.1381	−	31.6728i	−0.638413	−	1.25296i
$640$	6.61740	−	4.80782i	0.261576	−	0.190046i
$641$	33.8878	+	17.2667i	1.33849	+	0.681994i	0.968958	−	0.247225i	$-0.0795187\pi$
$641$	33.8878	+	17.2667i	1.33849	+	0.681994i	0.369530	+	0.929219i	$0.379519\pi$
$642$	−3.37128	+	3.37128i	−0.133054	+	0.133054i
$643$	−5.11486	−	32.2939i	−0.201710	−	1.27355i	−0.855870	−	0.517192i	$-0.826977\pi$
$643$	−5.11486	−	32.2939i	−0.201710	−	1.27355i	0.654159	−	0.756357i	$-0.273023\pi$
$644$	1.93219	−	3.79214i	0.0761391	−	0.149431i
$645$	2.13805	−	1.08939i	0.0841855	−	0.0428947i
$646$	−3.45772	+	10.6418i	−0.136042	+	0.418694i
$647$		−	43.3544i		−	1.70444i	−0.523187	−	0.852218i	$-0.675257\pi$
$647$		−	43.3544i		−	1.70444i	0.523187	−	0.852218i	$-0.324743\pi$
$648$	−4.30768	−	1.39965i	−0.169222	−	0.0549834i
$649$	37.0288	+	5.86479i	1.45351	+	0.230213i
$650$	−4.95789	+	0.785252i	−0.194464	+	0.0308001i
$651$	0.215399	−	0.0699875i	0.00844216	−	0.00274303i
$652$	−10.1187	−	31.1421i	−0.396278	−	1.21962i
$653$	4.48407	+	4.48407i	0.175475	+	0.175475i	0.789380	−	0.613905i	$-0.210402\pi$
$653$	4.48407	+	4.48407i	0.175475	+	0.175475i	−0.613905	+	0.789380i	$0.710402\pi$
$654$	−1.74179	+	2.39737i	−0.0681094	+	0.0937446i
$655$	27.9671			1.09277
$656$	−0.141396	−	22.0455i	−0.00552059	−	0.860734i
$657$	14.8771			0.580412
$658$	−8.45461	+	11.6368i	−0.329595	+	0.453648i
$659$	2.42608	+	2.42608i	0.0945067	+	0.0945067i	0.752779	−	0.658273i	$-0.228713\pi$
$659$	2.42608	+	2.42608i	0.0945067	+	0.0945067i	−0.658273	+	0.752779i	$0.728713\pi$
$660$	0.724072	+	2.22847i	0.0281845	+	0.0867429i
$661$	−30.4198	+	9.88398i	−1.18319	+	0.384442i	−0.833552	−	0.552442i	$-0.813696\pi$
$661$	−30.4198	+	9.88398i	−1.18319	+	0.384442i	−0.349640	+	0.936884i	$0.613696\pi$
$662$	6.07868	−	0.962769i	0.236255	−	0.0374191i
$663$	−1.25953	−	0.199489i	−0.0489159	−	0.00774752i
$664$	4.29397	+	1.39520i	0.166638	+	0.0541441i
$665$		−	2.71943i		−	0.105455i
$666$	5.04926	−	15.5400i	0.195655	−	0.602163i
$667$	−8.65030	+	4.40755i	−0.334941	+	0.170661i
$668$	21.3688	−	41.9385i	0.826782	−	1.62265i
$669$	0.245647	+	1.55095i	0.00949726	+	0.0599634i
$670$	14.5396	−	14.5396i	0.561712	−	0.561712i
$671$	−47.5753	−	24.2408i	−1.83663	−	0.935807i
$672$	0.793742	−	0.576687i	0.0306192	−	0.0222462i
$673$	−11.0592	−	21.7050i	−0.426302	−	0.836665i	−0.999847	−	0.0174911i	$-0.994432\pi$
$673$	−11.0592	−	21.7050i	−0.426302	−	0.836665i	0.573545	−	0.819174i	$-0.305568\pi$
$674$	−4.56094	−	3.31372i	−0.175681	−	0.127640i
$675$	0.105217	−	0.664315i	0.00404981	−	0.0255695i
$676$	−8.10940	−	11.1616i	−0.311900	−	0.429294i
$677$	−8.18035	−	11.2593i	−0.314396	−	0.432730i	0.622350	−	0.782739i	$-0.286178\pi$
$677$	−8.18035	−	11.2593i	−0.314396	−	0.432730i	−0.936746	+	0.350010i	$0.886178\pi$
$678$	0.0571782	−	0.361009i	0.00219591	−	0.0138645i
$679$	−7.00028	−	5.08600i	−0.268646	−	0.195183i
$680$	1.88404	+	3.69764i	0.0722497	+	0.141798i
$681$	−1.92465	+	1.39834i	−0.0737526	+	0.0535844i
$682$	−14.7108	−	7.49553i	−0.563306	−	0.287019i
$683$	−1.69423	+	1.69423i	−0.0648279	+	0.0648279i	−0.738777	−	0.673950i	$-0.764597\pi$
$683$	−1.69423	+	1.69423i	−0.0648279	+	0.0648279i	0.673950	+	0.738777i	$0.264597\pi$
$684$	1.41500	+	8.93399i	0.0541041	+	0.341600i
$685$	−9.50565	+	18.6559i	−0.363192	+	0.712805i
$686$	−1.83638	+	0.935683i	−0.0701133	+	0.0357245i
$687$	−0.364473	+	1.12173i	−0.0139055	+	0.0427968i
$688$			33.8817i			1.29173i
$689$	−1.70790	−	0.554929i	−0.0650656	−	0.0211411i
$690$	0.939849	+	0.148857i	0.0357794	+	0.00566691i
$691$	30.8380	−	4.88427i	1.17313	−	0.185806i	0.460707	−	0.887552i	$-0.347596\pi$
$691$	30.8380	−	4.88427i	1.17313	−	0.185806i	0.712427	+	0.701746i	$0.247596\pi$
$692$	3.09475	−	1.00555i	0.117645	−	0.0382251i
$693$	−3.94382	−	12.1378i	−0.149813	−	0.461078i
$694$	−13.1194	−	13.1194i	−0.498005	−	0.498005i
$695$	17.5815	−	24.1988i	0.666903	−	0.917913i
$696$	0.316502			0.0119970
$697$	25.4977	+	3.87097i	0.965795	+	0.146624i
$698$	−0.704587			−0.0266690
$699$	1.39817	−	1.92442i	0.0528838	−	0.0727883i
$700$	1.47776	+	1.47776i	0.0558543	+	0.0558543i
$701$	0.722425	+	2.22340i	0.0272856	+	0.0839765i	0.963772	−	0.266727i	$-0.0859424\pi$
$701$	0.722425	+	2.22340i	0.0272856	+	0.0839765i	−0.936486	+	0.350704i	$0.885942\pi$
$702$	−3.71459	+	1.20694i	−0.140198	+	0.0455531i
$703$	−3.53549	+	0.559966i	−0.133343	+	0.0211195i
$704$	−41.5662	−	6.58344i	−1.56659	−	0.248123i
$705$	−1.61848	−	0.525877i	−0.0609556	−	0.0198057i
$706$		−	13.3391i		−	0.502024i
$707$	−3.19675	+	9.83858i	−0.120226	+	0.370018i
$708$	−2.12286	+	1.08165i	−0.0797821	+	0.0406510i
$709$	13.0026	−	25.5191i	0.488323	−	0.958388i	−0.507014	−	0.861938i	$-0.669251\pi$
$709$	13.0026	−	25.5191i	0.488323	−	0.958388i	0.995338	−	0.0964509i	$-0.0307491\pi$
$710$	7.74514	+	48.9009i	0.290670	+	1.83522i
$711$	−5.79049	+	5.79049i	−0.217160	+	0.217160i
$712$	−5.52782	−	2.81656i	−0.207164	−	0.105555i
$713$	−2.87042	+	2.08548i	−0.107498	+	0.0781018i
$714$	0.455496	+	0.893961i	0.0170465	+	0.0334556i
$715$	−18.2782	−	13.2799i	−0.683566	−	0.496640i
$716$	−7.41203	+	46.7977i	−0.277001	+	1.74891i
$717$	0.263676	+	0.362918i	0.00984715	+	0.0135534i
$718$	23.2215	+	31.9617i	0.866619	+	1.19280i
$719$	−3.53278	+	22.3051i	−0.131751	+	0.831840i	0.829970	+	0.557808i	$0.188357\pi$
$719$	−3.53278	+	22.3051i	−0.131751	+	0.831840i	−0.961721	+	0.274032i	$0.911643\pi$
$720$	−16.7767	−	12.1890i	−0.625232	−	0.454258i
$721$	−2.50331	−	4.91302i	−0.0932280	−	0.182970i
$722$	−28.6511	+	20.8162i	−1.06628	+	0.774699i
$723$	1.12253	+	0.571959i	0.0417475	+	0.0212714i
$724$	4.34354	−	4.34354i	0.161426	−	0.161426i
$725$	−0.745760	−	4.70854i	−0.0276968	−	0.174871i
$726$	0.822783	−	1.61480i	0.0305363	−	0.0599309i
$727$	−31.4413	+	16.0201i	−1.16609	+	0.594154i	−0.926343	−	0.376680i	$-0.877066\pi$
$727$	−31.4413	+	16.0201i	−1.16609	+	0.594154i	−0.239750	+	0.970835i	$0.577066\pi$
$728$	0.413417	−	1.27237i	0.0153223	−	0.0471571i
$729$			26.2144i			0.970902i
$730$	−19.7068	−	6.40314i	−0.729383	−	0.236991i
$731$	−39.1476	−	6.20037i	−1.44793	−	0.229329i
$732$	3.35152	−	0.530829i	0.123876	−	0.0196200i
$733$	34.9390	−	11.3524i	1.29050	−	0.419310i	0.418235	−	0.908339i	$-0.362649\pi$
$733$	34.9390	−	11.3524i	1.29050	−	0.419310i	0.872267	+	0.489029i	$0.162649\pi$
$734$	19.3675	+	59.6070i	0.714867	+	2.20013i
$735$	−0.172423	−	0.172423i	−0.00635990	−	0.00635990i
$736$	−9.03419	+	12.4345i	−0.333005	+	0.458342i
$737$	−21.1401			−0.778706
$738$	37.3909	−	12.4147i	1.37638	−	0.456993i
$739$	19.8144			0.728884			0.364442	−	0.931226i	$-0.381260\pi$
$739$	19.8144			0.728884			0.364442	+	0.931226i	$0.381260\pi$
$740$	−7.07861	+	9.74287i	−0.260215	+	0.358155i
$741$	0.301774	+	0.301774i	0.0110860	+	0.0110860i
$742$	0.436604	+	1.34373i	0.0160282	+	0.0493298i
$743$	9.08011	−	2.95031i	0.333117	−	0.108236i	−0.137683	−	0.990476i	$-0.543965\pi$
$743$	9.08011	−	2.95031i	0.333117	−	0.108236i	0.470800	+	0.882240i	$0.343965\pi$
$744$	0.114244	−	0.0180945i	0.00418838	−	0.000663375i
$745$	−30.9769	−	4.90626i	−1.13491	−	0.179752i
$746$	42.7491	+	13.8900i	1.56516	+	0.508550i
$747$		−	26.3924i		−	0.965648i
$748$	11.9600	−	36.8090i	0.437300	−	1.34587i
$749$	−17.0534	+	8.68914i	−0.623118	+	0.317494i
$750$	−1.35292	+	2.65526i	−0.0494018	+	0.0969565i
$751$	−5.10850	−	32.2538i	−0.186412	−	1.17696i	−0.886440	−	0.462843i	$-0.846829\pi$
$751$	−5.10850	−	32.2538i	−0.186412	−	1.17696i	0.700029	−	0.714115i	$-0.253171\pi$
$752$	16.9909	−	16.9909i	0.619594	−	0.619594i
$753$	2.27883	+	1.16112i	0.0830450	+	0.0423136i
$754$	−22.3962	+	16.2718i	−0.815621	+	0.592583i
$755$	7.85055	+	15.4076i	0.285711	+	0.560739i
$756$	1.31554	+	0.955798i	0.0478458	+	0.0347620i
$757$	6.18588	−	39.0561i	0.224830	−	1.41952i	−0.574441	−	0.818546i	$-0.694780\pi$
$757$	6.18588	−	39.0561i	0.224830	−	1.41952i	0.799270	−	0.600972i	$-0.205220\pi$
$758$	−42.4245	−	58.3923i	−1.54093	−	2.12090i
$759$	−0.575040	−	0.791474i	−0.0208726	−	0.0287287i
$760$	0.217263	−	1.37174i	0.00788096	−	0.0497584i
$761$	37.7882	+	27.4547i	1.36982	+	0.995233i	0.997751	+	0.0670283i	$0.0213518\pi$
$761$	37.7882	+	27.4547i	1.36982	+	0.995233i	0.372070	+	0.928205i	$0.378648\pi$
$762$	0.724714	+	1.42233i	0.0262536	+	0.0515256i
$763$	−9.62399	+	6.99224i	−0.348412	+	0.253136i
$764$	−5.85162	−	2.98155i	−0.211704	−	0.107869i
$765$	17.1536	−	17.1536i	0.620189	−	0.620189i
$766$	−3.67424	−	23.1982i	−0.132756	−	0.838185i
$767$	10.4295	−	20.4691i	0.376588	−	0.739096i
$768$	−1.22042	+	0.621836i	−0.0440382	+	0.0224386i
$769$	0.104741	−	0.322359i	0.00377705	−	0.0116246i	−0.949150	−	0.314824i	$-0.898055\pi$
$769$	0.104741	−	0.322359i	0.00377705	−	0.0116246i	0.952927	+	0.303199i	$0.0980547\pi$
$770$			17.7757i			0.640591i
$771$	−1.45179	−	0.471715i	−0.0522850	−	0.0169884i
$772$	52.9558	+	8.38738i	1.90592	+	0.301868i
$773$	31.9594	−	5.06187i	1.14950	−	0.182063i	0.447529	−	0.894270i	$-0.352304\pi$
$773$	31.9594	−	5.06187i	1.14950	−	0.182063i	0.701970	+	0.712207i	$0.252304\pi$
$774$	−57.5860	+	18.7108i	−2.06989	+	0.672546i
$775$	−0.538376	−	1.65695i	−0.0193390	−	0.0595194i
$776$	−3.12477	−	3.12477i	−0.112173	−	0.112173i
$777$	−0.188659	+	0.259668i	−0.00676812	+	0.00931552i
$778$	45.2706			1.62303
$779$	−6.14203	−	6.06375i	−0.220061	−	0.217256i
$780$	1.43581			0.0514103
$781$	29.9196	−	41.1808i	1.07061	−	1.47357i
$782$	−11.1140	−	11.1140i	−0.397437	−	0.397437i
$783$	−1.14624	−	3.52777i	−0.0409633	−	0.126072i
$784$	3.27449	−	1.06395i	0.116946	−	0.0379981i
$785$	32.2126	−	5.10198i	1.14972	−	0.182098i
$786$	3.41065	+	0.540193i	0.121654	+	0.0192681i
$787$	−19.2398	−	6.25139i	−0.685825	−	0.222838i	−0.0546809	−	0.998504i	$-0.517414\pi$
$787$	−19.2398	−	6.25139i	−0.685825	−	0.222838i	−0.631144	+	0.775666i	$0.717414\pi$
$788$			41.2973i			1.47115i
$789$	0.166704	−	0.513063i	0.00593483	−	0.0182655i
$790$	10.1625	−	5.17808i	0.361567	−	0.184228i
$791$	0.666139	−	1.30737i	0.0236852	−	0.0464848i
$792$	−1.01963	−	6.43769i	−0.0362310	−	0.228753i
$793$	−23.1357	+	23.1357i	−0.821575	+	0.821575i
$794$	36.4971	+	18.5962i	1.29523	+	0.659955i
$795$	−0.135235	+	0.0982542i	−0.00479630	+	0.00348472i
$796$	19.5416	+	38.3525i	0.692632	+	1.35937i
$797$	−42.5652	−	30.9254i	−1.50774	−	1.09543i	−0.967169	−	0.254135i	$-0.918209\pi$
$797$	−42.5652	−	30.9254i	−1.50774	−	1.09543i	−0.540568	−	0.841300i	$-0.681791\pi$
$798$	0.0525267	−	0.331640i	0.00185942	−	0.0117399i
$799$	16.5223	+	22.7409i	0.584515	+	0.804516i
$800$	−4.43614	−	6.10583i	−0.156841	−	0.215874i
$801$	−5.67324	+	35.8195i	−0.200454	+	1.26562i
$802$	−34.9535	−	25.3952i	−1.23425	−	0.896736i
$803$	9.67161	+	18.9816i	0.341304	+	0.669846i
$804$	1.08689	−	0.789673i	0.0383317	−	0.0278496i
$805$	3.40360	+	1.73422i	0.119961	+	0.0611233i
$806$	−7.15382	+	7.15382i	−0.251983	+	0.251983i
$807$	−0.249878	−	1.57767i	−0.00879613	−	0.0555366i
$808$	−2.39855	+	4.70741i	−0.0843805	+	0.165606i
$809$	−8.20436	+	4.18033i	−0.288450	+	0.146973i	−0.592228	−	0.805770i	$-0.701752\pi$
$809$	−8.20436	+	4.18033i	−0.288450	+	0.146973i	0.303779	+	0.952743i	$0.401752\pi$
$810$	11.3956	−	35.0720i	0.400400	−	1.23231i
$811$			18.3170i			0.643196i	0.946876	+	0.321598i	$0.104220\pi$
$811$			18.3170i			0.643196i	−0.946876	+	0.321598i	$0.895780\pi$
$812$	10.9614	+	3.56158i	0.384670	+	0.124987i
$813$	−0.812791	−	0.128733i	−0.0285058	−	0.00451488i
$814$	23.1099	−	3.66024i	0.810000	−	0.128291i
$815$	27.9513	−	9.08193i	0.979091	−	0.318126i
$816$	−0.517936	−	1.59404i	−0.0181314	−	0.0558027i
$817$	9.37950	+	9.37950i	0.328147	+	0.328147i
$818$	−41.2067	+	56.7162i	−1.44076	+	1.98304i
$819$	−7.82047			−0.273269
$820$	−29.0369	+	0.186238i	−1.01401	+	0.00650370i
$821$	20.9780			0.732138			0.366069	−	0.930588i	$-0.380703\pi$
$821$	20.9780			0.732138			0.366069	+	0.930588i	$0.380703\pi$
$822$	−1.51958	+	2.09152i	−0.0530013	+	0.0729501i
$823$	32.4881	+	32.4881i	1.13246	+	1.13246i	0.989766	+	0.142697i	$0.0455774\pi$
$823$	32.4881	+	32.4881i	1.13246	+	1.13246i	0.142697	+	0.989766i	$0.454423\pi$
$824$	−0.870211	−	2.67823i	−0.0303152	−	0.0933007i
$825$	0.456880	−	0.148449i	0.0159065	−	0.00516834i
$826$	−17.8520	+	2.82749i	−0.621152	+	0.0983808i
$827$	15.6640	+	2.48094i	0.544692	+	0.0862707i	0.422716	−	0.906262i	$-0.361077\pi$
$827$	15.6640	+	2.48094i	0.544692	+	0.0862707i	0.121976	+	0.992533i	$0.461077\pi$
$828$	−12.0840	−	3.92634i	−0.419949	−	0.136450i
$829$			13.8474i			0.480941i	0.970656	+	0.240470i	$0.0773017\pi$
$829$			13.8474i			0.480941i	−0.970656	+	0.240470i	$0.922698\pi$
$830$	−11.3593	+	34.9604i	−0.394288	+	1.21349i
$831$	−2.33986	+	1.19222i	−0.0811689	+	0.0413576i
$832$	−11.7075	+	22.9773i	−0.405885	+	0.796595i
$833$	0.630072	+	3.97812i	0.0218307	+	0.137834i
$834$	2.61150	−	2.61150i	0.0904289	−	0.0904289i
$835$	37.6415	+	19.1793i	1.30264	+	0.663728i
$836$	−10.4789	+	7.61336i	−0.362420	+	0.263314i
$837$	−0.615428	−	1.20785i	−0.0212723	−	0.0417493i
$838$	40.2815	+	29.2663i	1.39150	+	1.01099i
$839$	1.73858	−	10.9770i	0.0600226	−	0.378967i	−0.939331	−	0.343012i	$-0.888553\pi$
$839$	1.73858	−	10.9770i	0.0600226	−	0.378967i	0.999353	−	0.0359550i	$-0.0114473\pi$
$840$	−0.0731986	−	0.100749i	−0.00252559	−	0.00347618i
$841$	1.59234	+	2.19166i	0.0549081	+	0.0755745i
$842$	6.54361	−	41.3147i	0.225508	−	1.42380i
$843$	0.879360	+	0.638892i	0.0302868	+	0.0220046i
$844$	7.80414	+	15.3165i	0.268630	+	0.527215i
$845$	10.0180	−	7.27852i	0.344630	−	0.250389i
$846$	38.2611	+	19.4950i	1.31544	+	0.670251i
$847$	5.14450	−	5.14450i	0.176767	−	0.176767i
$848$	−0.369227	−	2.33121i	−0.0126793	−	0.0800540i
$849$	0.260049	−	0.510375i	0.00892487	−	0.0175160i
$850$	6.87676	−	3.50388i	0.235871	−	0.120182i
$851$	1.55379	−	4.78206i	0.0532631	−	0.163927i
$852$			3.23488i			0.110825i
$853$	46.2221	+	15.0185i	1.58261	+	0.514222i	0.962728	−	0.270470i	$-0.0871791\pi$
$853$	46.2221	+	15.0185i	1.58261	+	0.514222i	0.619885	+	0.784692i	$0.287179\pi$
$854$	25.4255	+	4.02700i	0.870041	+	0.137801i
$855$	−8.01862	+	1.27002i	−0.274231	+	0.0434339i
$856$	−9.29633	+	3.02056i	−0.317742	+	0.103241i
$857$	7.73800	+	23.8151i	0.264325	+	0.813509i	0.991848	+	0.127425i	$0.0406714\pi$
$857$	7.73800	+	23.8151i	0.264325	+	0.813509i	−0.727523	+	0.686083i	$0.759329\pi$
$858$	−1.97256	−	1.97256i	−0.0673421	−	0.0673421i
$859$	−23.5006	+	32.3459i	−0.801831	+	1.10363i	0.190701	+	0.981648i	$0.438924\pi$
$859$	−23.5006	+	32.3459i	−0.801831	+	1.10363i	−0.992533	+	0.121978i	$0.961076\pi$
$860$	44.6267			1.52176
$861$	−0.773893	+	0.00496361i	−0.0263742	+	0.000169159i
$862$	−36.9284			−1.25779
$863$	−7.08647	+	9.75369i	−0.241226	+	0.332020i	−0.912414	−	0.409267i	$-0.865784\pi$
$863$	−7.08647	+	9.75369i	−0.241226	+	0.332020i	0.671188	+	0.741287i	$0.265784\pi$
$864$	−4.15240	−	4.15240i	−0.141267	−	0.141267i
$865$	0.902517	+	2.77766i	0.0306865	+	0.0944434i
$866$	−43.0883	+	14.0002i	−1.46420	+	0.475748i
$867$	−0.0928262	+	0.0147022i	−0.00315254	+	0.000499314i
$868$	4.16022	+	0.658914i	0.141207	+	0.0223650i
$869$	−11.1524	−	3.62364i	−0.378320	−	0.122924i
$870$			2.57688i			0.0873644i
$871$	−4.00302	+	12.3200i	−0.135637	+	0.417448i
$872$	−5.41319	+	2.75816i	−0.183314	+	0.0934031i
$873$	−11.7275	+	23.0165i	−0.396916	+	0.778992i
$874$	0.822866	+	5.19537i	0.0278338	+	0.175736i
$875$	−8.45925	+	8.45925i	−0.285975	+	0.285975i
$876$	−1.20630	−	0.614638i	−0.0407570	−	0.0207667i
$877$	−32.1724	+	23.3746i	−1.08638	+	0.789304i	−0.978785	−	0.204891i	$-0.934316\pi$
$877$	−32.1724	+	23.3746i	−1.08638	+	0.789304i	−0.107599	+	0.994194i	$0.534316\pi$
$878$	22.1300	+	43.4325i	0.746850	+	1.46578i
$879$	−0.857501	−	0.623011i	−0.0289228	−	0.0210136i
$880$	4.64531	−	29.3293i	0.156593	−	0.988692i
$881$	25.1566	+	34.6251i	0.847548	+	1.16655i	0.984398	+	0.175958i	$0.0563021\pi$
$881$	25.1566	+	34.6251i	0.847548	+	1.16655i	−0.136850	+	0.990592i	$0.543698\pi$
$882$	3.61661	+	4.97784i	0.121778	+	0.167613i
$883$	3.91276	−	24.7042i	0.131675	−	0.831363i	−0.830119	−	0.557587i	$-0.811727\pi$
$883$	3.91276	−	24.7042i	0.131675	−	0.831363i	0.961794	−	0.273776i	$-0.0882727\pi$
$884$	−19.1868	−	13.9401i	−0.645323	−	0.468855i
$885$	−0.970827	−	1.90536i	−0.0326340	−	0.0640478i
$886$	1.83594	−	1.33389i	0.0616796	−	0.0448128i
$887$	−16.8727	−	8.59707i	−0.566530	−	0.288661i	0.147172	−	0.989111i	$-0.452983\pi$
$887$	−16.8727	−	8.59707i	−0.566530	−	0.288661i	−0.713702	+	0.700449i	$0.752983\pi$
$888$	−0.115910	+	0.115910i	−0.00388968	+	0.00388968i
$889$	1.00247	+	6.32936i	0.0336218	+	0.212280i
$890$	22.9317	−	45.0061i	0.768674	−	1.50861i
$891$	−33.7813	+	17.2124i	−1.13172	+	0.576638i
$892$	−9.02444	+	27.7744i	−0.302160	+	0.929954i
$893$		−	9.40720i		−	0.314800i
$894$	−3.68293	−	1.19666i	−0.123176	−	0.0400222i
$895$	−42.0028	−	6.65260i	−1.40400	−	0.222372i
$896$	4.00441	−	0.634236i	0.133778	−	0.0211884i
$897$	−0.570142	+	0.185250i	−0.0190365	+	0.00618533i
$898$	−17.9587	−	55.2713i	−0.599291	−	1.84443i
$899$	−6.79404	−	6.79404i	−0.226594	−	0.226594i
$900$	3.66725	−	5.04753i	0.122242	−	0.168251i
$901$	2.76109			0.0919854
$902$	40.1477	+	39.6359i	1.33677	+	1.31973i
$903$	1.18939			0.0395805
$904$	0.440465	−	0.606248i	0.0146497	−	0.0201635i
$905$	3.89850	+	3.89850i	0.129591	+	0.129591i
$906$	0.659788	+	2.03062i	0.0219200	+	0.0674628i
$907$	41.0720	−	13.3451i	1.36377	−	0.443117i	0.466472	−	0.884536i	$-0.345525\pi$
$907$	41.0720	−	13.3451i	1.36377	−	0.443117i	0.897301	+	0.441420i	$0.145525\pi$
$908$	−43.6990	+	6.92124i	−1.45020	+	0.229690i
$909$	30.5033	+	4.83126i	1.01173	+	0.160243i
$910$	10.3593	+	3.36594i	0.343407	+	0.111580i
$911$		−	39.2118i		−	1.29915i	−0.760299	−	0.649573i	$-0.774948\pi$
$911$		−	39.2118i		−	1.29915i	0.760299	−	0.649573i	$-0.225052\pi$
$912$	−0.173335	+	0.533470i	−0.00573969	+	0.0176649i
$913$	33.6738	−	17.1577i	1.11444	−	0.567836i
$914$	14.8184	−	29.0828i	0.490151	−	0.961975i
$915$	0.476440	+	3.00813i	0.0157506	+	0.0994456i
$916$	−15.5105	+	15.5105i	−0.512483	+	0.512483i
$917$	12.3514	+	6.29338i	0.407881	+	0.207826i
$918$	4.85834	−	3.52979i	0.160349	−	0.116500i
$919$	7.98941	+	15.6801i	0.263546	+	0.517239i	0.984421	−	0.175827i	$-0.0562598\pi$
$919$	7.98941	+	15.6801i	0.263546	+	0.517239i	−0.720875	+	0.693065i	$0.756260\pi$
$920$	1.57830	+	1.14671i	0.0520351	+	0.0378057i
$921$	0.215368	−	1.35978i	0.00709661	−	0.0448062i
$922$	48.8582	+	67.2475i	1.60906	+	2.21468i
$923$	−18.3339	−	25.2344i	−0.603467	−	0.830600i
$924$	−0.181686	+	1.14712i	−0.00597703	+	0.0377375i
$925$	1.99748	+	1.45126i	0.0656768	+	0.0477170i
$926$	−8.75815	−	17.1888i	−0.287811	−	0.564860i
$927$	−13.3176	+	9.67581i	−0.437408	+	0.317795i
$928$	−37.0858	−	18.8962i	−1.21740	−	0.620297i
$929$	9.64429	−	9.64429i	0.316419	−	0.316419i	−0.530971	−	0.847390i	$-0.678173\pi$
$929$	9.64429	−	9.64429i	0.316419	−	0.316419i	0.847390	+	0.530971i	$0.178173\pi$
$930$	0.147320	+	0.930145i	0.00483083	+	0.0305006i
$931$	0.611948	−	1.20101i	0.0200558	−	0.0393617i
$932$	39.4169	−	20.0839i	1.29114	−	0.657870i
$933$	1.09440	−	3.36821i	0.0358289	−	0.110270i
$934$			25.3082i			0.828110i
$935$	33.0376	+	10.7346i	1.08045	+	0.351058i
$936$	−3.94482	−	0.624799i	−0.128941	−	0.0204222i
$937$	−39.4433	+	6.24720i	−1.28856	+	0.204087i	−0.762848	−	0.646578i	$-0.776199\pi$
$937$	−39.4433	+	6.24720i	−1.28856	+	0.204087i	−0.525708	+	0.850665i	$0.676199\pi$
$938$	9.69308	−	3.14947i	0.316490	−	0.102834i
$939$	0.613617	+	1.88852i	0.0200246	+	0.0616294i
$940$	−22.3793	−	22.3793i	−0.729931	−	0.729931i
$941$	24.3752	−	33.5496i	0.794609	−	1.09368i	−0.198910	−	0.980018i	$-0.563740\pi$
$941$	24.3752	−	33.5496i	0.794609	−	1.09368i	0.993519	−	0.113667i	$-0.0362598\pi$
$942$	4.02694			0.131205
$943$	11.5062	−	3.82034i	0.374692	−	0.124407i
$944$	30.1942			0.982739
$945$	−0.857868	+	1.18075i	−0.0279064	+	0.0384099i
$946$	−61.3095	−	61.3095i	−1.99334	−	1.99334i
$947$	10.8252	+	33.3167i	0.351773	+	1.08265i	0.957857	+	0.287245i	$0.0927395\pi$
$947$	10.8252	+	33.3167i	0.351773	+	1.08265i	−0.606084	+	0.795401i	$0.707261\pi$
$948$	0.708745	−	0.230285i	0.0230190	−	0.00747932i
$949$	12.8935	−	2.04212i	0.418539	−	0.0662901i
$950$	−2.55113	−	0.404059i	−0.0827696	−	0.0131094i
$951$	1.46514	+	0.476052i	0.0475104	+	0.0154371i
$952$			2.05699i			0.0666675i
$953$	−7.52297	+	23.1533i	−0.243693	+	0.750010i	0.752156	+	0.658986i	$0.229014\pi$
$953$	−7.52297	+	23.1533i	−0.243693	+	0.750010i	−0.995849	+	0.0910245i	$0.970986\pi$
$954$	3.75827	−	1.91493i	0.121678	−	0.0619982i
$955$	2.67606	−	5.25207i	0.0865953	−	0.169953i
$956$	1.30510	+	8.24005i	0.0422098	+	0.266502i
$957$	1.87336	−	1.87336i	0.0605570	−	0.0605570i
$958$	−75.1564	−	38.2941i	−2.42819	−	1.23723i
$959$	−8.39618	+	6.10018i	−0.271127	+	0.196985i
$960$	1.08979	+	2.13883i	0.0351728	+	0.0690305i
$961$	22.2387	+	16.1574i	0.717379	+	0.521206i
$962$	2.24289	−	14.1610i	0.0723136	−	0.456570i
$963$	33.5854	+	46.2263i	1.08227	+	1.48962i
$964$	13.7720	+	18.9555i	0.443565	+	0.610515i
$965$	−7.52801	+	47.5300i	−0.242335	+	1.53005i
$966$	0.381579	+	0.277234i	0.0122771	+	0.00891985i
$967$	−12.6665	−	24.8595i	−0.407328	−	0.799426i	0.592654	−	0.805457i	$-0.298080\pi$
$967$	−12.6665	−	24.8595i	−0.407328	−	0.799426i	−0.999982	+	0.00603115i	$0.998080\pi$
$968$	3.00601	−	2.18400i	0.0966170	−	0.0701963i
$969$	−0.584661	−	0.297900i	−0.0187820	−	0.00956992i
$970$	25.4411	−	25.4411i	0.816863	−	0.816863i
$971$	1.35475	+	8.55356i	0.0434760	+	0.274497i	0.999844	−	0.0176683i	$-0.00562429\pi$
$971$	1.35475	+	8.55356i	0.0434760	+	0.274497i	−0.956368	+	0.292165i	$0.905624\pi$
$972$	3.30857	−	6.49343i	0.106122	−	0.208277i
$973$	13.2101	−	6.73089i	0.423497	−	0.215782i
$974$	5.92245	−	18.2274i	0.189767	−	0.584044i
$975$		−	0.294370i		−	0.00942738i
$976$	−40.8989	−	13.2888i	−1.30914	−	0.425366i
$977$	−10.0965	−	1.59913i	−0.323017	−	0.0511608i	−0.00717946	−	0.999974i	$-0.502285\pi$
$977$	−10.0965	−	1.59913i	−0.323017	−	0.0511608i	−0.315837	+	0.948813i	$0.602285\pi$
$978$	3.58414	−	0.567672i	0.114608	−	0.0181521i
$979$	−49.3899	+	16.0477i	−1.57851	+	0.512888i
$980$	−1.40136	−	4.31295i	−0.0447648	−	0.137772i
$981$	25.1122	+	25.1122i	0.801769	+	0.801769i
$982$	−12.1922	+	16.7812i	−0.389070	+	0.535509i
$983$	−56.9959			−1.81789			−0.908943	−	0.416921i	$-0.863109\pi$
$983$	−56.9959			−1.81789			−0.908943	+	0.416921i	$0.863109\pi$
$984$	−0.390766	−	0.0593247i	−0.0124572	−	0.00189120i
$985$	−37.0660			−1.18102
$986$	25.0185	−	34.4350i	0.796751	−	1.09663i
$987$	−0.596453	−	0.596453i	−0.0189853	−	0.0189853i
$988$	2.45266	+	7.54852i	0.0780296	+	0.240151i
$989$	−17.7207	+	5.75780i	−0.563485	+	0.183088i
$990$	52.4140	−	8.30157i	1.66583	−	0.263841i
$991$	−11.1190	−	1.76108i	−0.353206	−	0.0559424i	−0.0226898	−	0.999743i	$-0.507223\pi$
$991$	−11.1190	−	1.76108i	−0.353206	−	0.0559424i	−0.330517	+	0.943800i	$0.607223\pi$
$992$	−14.4667	−	4.70052i	−0.459318	−	0.149242i
$993$			0.360916i			0.0114533i
$994$	−7.58347	+	23.3395i	−0.240533	+	0.740285i
$995$	−34.4229	+	17.5393i	−1.09128	+	0.556034i
$996$	−1.09038	+	2.14000i	−0.0345501	+	0.0678085i
$997$	−8.91480	−	56.2858i	−0.282334	−	1.78259i	−0.566751	−	0.823889i	$-0.691800\pi$
$997$	−8.91480	−	56.2858i	−0.282334	−	1.78259i	0.284417	−	0.958701i	$-0.408200\pi$
$998$	−2.22216	+	2.22216i	−0.0703414	+	0.0703414i
$999$	1.71172	+	0.872166i	0.0541565	+	0.0275941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.u.a.8.3	✓	160
41.36	even	20	inner	287.2.u.a.36.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.u.a.8.3	✓	160	1.1	even	1	trivial
287.2.u.a.36.3	yes	160	41.36	even	20	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21144 + 1.66740i) q^{2} +(-0.0854640 - 0.0854640i) q^{3} +(-0.694607 - 2.13778i) q^{4} +(1.91874 - 0.623438i) q^{5} +(0.246037 - 0.0389684i) q^{6} +(0.987688 + 0.156434i) q^{7} +(0.485715 + 0.157818i) q^{8} -2.98539i q^{9} +O(q^{10})\)	\(q+(-1.21144 + 1.66740i) q^{2} +(-0.0854640 - 0.0854640i) q^{3} +(-0.694607 - 2.13778i) q^{4} +(1.91874 - 0.623438i) q^{5} +(0.246037 - 0.0389684i) q^{6} +(0.987688 + 0.156434i) q^{7} +(0.485715 + 0.157818i) q^{8} -2.98539i q^{9} +(-1.28492 + 3.95457i) q^{10} +(3.80903 - 1.94080i) q^{11} +(-0.123339 + 0.242067i) q^{12} +(-0.409792 - 2.58733i) q^{13} +(-1.45736 + 1.45736i) q^{14} +(-0.217265 - 0.110702i) q^{15} +(2.78545 - 2.02375i) q^{16} +(1.82854 + 3.58871i) q^{17} +(4.97784 + 3.61661i) q^{18} +(0.210863 - 1.33133i) q^{19} +(-2.66555 - 3.66881i) q^{20} +(-0.0710423 - 0.0977813i) q^{21} +(-1.37831 + 8.70233i) q^{22} +(1.53181 + 1.11293i) q^{23} +(-0.0280233 - 0.0549989i) q^{24} +(-0.752179 + 0.546490i) q^{25} +(4.81054 + 2.45109i) q^{26} +(-0.511535 + 0.511535i) q^{27} +(-0.351633 - 2.22012i) q^{28} +(-2.32782 + 4.56861i) q^{29} +(0.447787 - 0.228159i) q^{30} +(-0.579058 + 1.78216i) q^{31} +8.11752i q^{32} +(-0.491403 - 0.159667i) q^{33} +(-8.19897 - 1.29859i) q^{34} +(1.99265 - 0.315605i) q^{35} +(-6.38211 + 2.07367i) q^{36} +(-0.820624 - 2.52562i) q^{37} +(1.96442 + 1.96442i) q^{38} +(-0.186101 + 0.256146i) q^{39} +1.03035 q^{40} +(3.73036 - 5.20427i) q^{41} +0.249104 q^{42} +(-5.78424 + 7.96132i) q^{43} +(-6.79478 - 6.79478i) q^{44} +(-1.86121 - 5.72820i) q^{45} +(-3.71138 + 1.20590i) q^{46} +(6.89307 - 1.09176i) q^{47} +(-0.411013 - 0.0650981i) q^{48} +(0.951057 + 0.309017i) q^{49} -1.91622i q^{50} +(0.150431 - 0.462980i) q^{51} +(-5.24649 + 2.67322i) q^{52} +(0.311222 - 0.610807i) q^{53} +(-0.233241 - 1.47263i) q^{54} +(6.09859 - 6.09859i) q^{55} +(0.455047 + 0.231858i) q^{56} +(-0.131802 + 0.0957600i) q^{57} +(-4.79769 - 9.41599i) q^{58} +(7.09486 + 5.15472i) q^{59} +(-0.0857429 + 0.541359i) q^{60} +(-7.34152 - 10.1047i) q^{61} +(-2.27008 - 3.12449i) q^{62} +(0.467018 - 2.94864i) q^{63} +(-7.96424 - 5.78636i) q^{64} +(-2.39932 - 4.70894i) q^{65} +(0.861532 - 0.625940i) q^{66} +(-4.40610 - 2.24502i) q^{67} +(6.40176 - 6.40176i) q^{68} +(-0.0357996 - 0.226030i) q^{69} +(-1.88773 + 3.70487i) q^{70} +(10.6093 - 5.40568i) q^{71} +(0.471149 - 1.45005i) q^{72} +4.98331i q^{73} +(5.20535 + 1.69132i) q^{74} +(0.110989 + 0.0175790i) q^{75} +(-2.99257 + 0.473976i) q^{76} +(4.06574 - 1.32104i) q^{77} +(-0.201648 - 0.620608i) q^{78} +(-1.93961 - 1.93961i) q^{79} +(4.08289 - 5.61961i) q^{80} -8.86874 q^{81} +(4.15850 + 12.5246i) q^{82} +8.84052 q^{83} +(-0.159688 + 0.219792i) q^{84} +(5.74584 + 5.74584i) q^{85} +(-6.26746 - 19.2893i) q^{86} +(0.589397 - 0.191507i) q^{87} +(2.15640 - 0.341540i) q^{88} +(-11.9982 - 1.90034i) q^{89} +(11.8059 + 3.83598i) q^{90} -2.61958i q^{91} +(1.31518 - 4.04772i) q^{92} +(0.201799 - 0.102822i) q^{93} +(-6.53012 + 12.8161i) q^{94} +(-0.425413 - 2.68595i) q^{95} +(0.693756 - 0.693756i) q^{96} +(-7.70972 - 3.92830i) q^{97} +(-1.66740 + 1.21144i) q^{98} +(-5.79404 - 11.3715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6}+O(q^{10}) \) 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6	\( 160 q - 4 q^{3} + 36 q^{4} - 28 q^{6} - 48 q^{10} + 8 q^{11} - 16 q^{12} - 16 q^{13} - 32 q^{15} - 28 q^{16} - 20 q^{17} + 12 q^{18} - 40 q^{19} - 4 q^{22} - 36 q^{23} - 108 q^{24} + 40 q^{25} + 20 q^{26} + 20 q^{27} + 12 q^{29} - 4 q^{30} + 20 q^{31} - 32 q^{34} - 4 q^{35} + 140 q^{36} - 44 q^{38} + 80 q^{39} - 64 q^{40} + 4 q^{41} - 72 q^{42} - 8 q^{44} + 8 q^{45} + 40 q^{46} - 56 q^{47} + 120 q^{48} + 24 q^{51} + 16 q^{52} + 12 q^{53} - 52 q^{54} - 72 q^{55} + 48 q^{57} + 36 q^{58} - 48 q^{59} - 52 q^{60} + 8 q^{63} - 96 q^{64} - 96 q^{65} + 24 q^{66} + 20 q^{67} - 80 q^{68} - 68 q^{69} + 8 q^{70} + 60 q^{71} + 100 q^{72} - 40 q^{74} - 120 q^{75} + 4 q^{76} - 12 q^{78} + 12 q^{79} + 200 q^{80} - 56 q^{81} - 68 q^{82} - 40 q^{83} + 132 q^{85} + 80 q^{86} - 16 q^{88} + 8 q^{89} + 140 q^{92} + 64 q^{93} + 128 q^{94} - 68 q^{96} + 4 q^{98} + 96 q^{99}+O(q^{100}) \) 160 * q - 4 * q^3 + 36 * q^4 - 28 * q^6 - 48 * q^10 + 8 * q^11 - 16 * q^12 - 16 * q^13 - 32 * q^15 - 28 * q^16 - 20 * q^17 + 12 * q^18 - 40 * q^19 - 4 * q^22 - 36 * q^23 - 108 * q^24 + 40 * q^25 + 20 * q^26 + 20 * q^27 + 12 * q^29 - 4 * q^30 + 20 * q^31 - 32 * q^34 - 4 * q^35 + 140 * q^36 - 44 * q^38 + 80 * q^39 - 64 * q^40 + 4 * q^41 - 72 * q^42 - 8 * q^44 + 8 * q^45 + 40 * q^46 - 56 * q^47 + 120 * q^48 + 24 * q^51 + 16 * q^52 + 12 * q^53 - 52 * q^54 - 72 * q^55 + 48 * q^57 + 36 * q^58 - 48 * q^59 - 52 * q^60 + 8 * q^63 - 96 * q^64 - 96 * q^65 + 24 * q^66 + 20 * q^67 - 80 * q^68 - 68 * q^69 + 8 * q^70 + 60 * q^71 + 100 * q^72 - 40 * q^74 - 120 * q^75 + 4 * q^76 - 12 * q^78 + 12 * q^79 + 200 * q^80 - 56 * q^81 - 68 * q^82 - 40 * q^83 + 132 * q^85 + 80 * q^86 - 16 * q^88 + 8 * q^89 + 140 * q^92 + 64 * q^93 + 128 * q^94 - 68 * q^96 + 4 * q^98 + 96 * q^99

Introduction

L-functions

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